%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ALG132+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 16:36:40 EDT 2023

% Result   : Unsatisfiable 24.68s 4.10s
% Output   : Proof 179.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG132+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.34  % Computer : n020.cluster.edu
% 0.18/0.34  % Model    : x86_64 x86_64
% 0.18/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34  % Memory   : 8042.1875MB
% 0.18/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34  % CPULimit : 300
% 0.18/0.34  % WCLimit  : 300
% 0.18/0.34  % DateTime : Mon Aug 28 05:48:14 EDT 2023
% 0.18/0.34  % CPUTime  : 
% 0.21/0.60  ________       _____
% 0.21/0.60  ___  __ \_________(_)________________________________
% 0.21/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.21/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.21/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60  
% 0.21/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60  (2023-06-19)
% 0.21/0.60  
% 0.21/0.60  (c) Philipp Rümmer, 2009-2023
% 0.21/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60                Amanda Stjerna.
% 0.21/0.60  Free software under BSD-3-Clause.
% 0.21/0.60  
% 0.21/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60  
% 0.21/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.61  Running up to 7 provers in parallel.
% 0.21/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.63  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.20/1.32  Prover 4: Preprocessing ...
% 4.20/1.32  Prover 1: Preprocessing ...
% 4.73/1.35  Prover 2: Preprocessing ...
% 4.73/1.35  Prover 6: Preprocessing ...
% 4.73/1.35  Prover 5: Preprocessing ...
% 4.73/1.35  Prover 0: Preprocessing ...
% 4.73/1.36  Prover 3: Preprocessing ...
% 7.54/1.74  Prover 2: Constructing countermodel ...
% 7.54/1.75  Prover 3: Constructing countermodel ...
% 8.15/1.83  Prover 4: Constructing countermodel ...
% 8.15/1.84  Prover 1: Constructing countermodel ...
% 8.15/1.85  Prover 0: Constructing countermodel ...
% 8.15/1.88  Prover 6: Constructing countermodel ...
% 9.70/2.05  Prover 5: Constructing countermodel ...
% 24.68/4.09  Prover 3: proved (3472ms)
% 24.68/4.09  
% 24.68/4.10  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.68/4.10  
% 24.68/4.10  Prover 0: stopped
% 24.68/4.10  Prover 6: stopped
% 24.68/4.10  Prover 2: stopped
% 24.68/4.10  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 24.68/4.10  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 24.68/4.10  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.68/4.10  Prover 5: stopped
% 24.68/4.11  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.68/4.12  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.29/4.30  Prover 11: Preprocessing ...
% 26.29/4.34  Prover 8: Preprocessing ...
% 26.29/4.35  Prover 13: Preprocessing ...
% 26.29/4.36  Prover 10: Preprocessing ...
% 26.29/4.37  Prover 7: Preprocessing ...
% 27.37/4.43  Prover 8: Constructing countermodel ...
% 27.87/4.49  Prover 11: Constructing countermodel ...
% 28.11/4.51  Prover 7: Constructing countermodel ...
% 28.11/4.52  Prover 10: Constructing countermodel ...
% 28.27/4.53  Prover 13: Constructing countermodel ...
% 66.17/9.51  Prover 13: stopped
% 66.17/9.51  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 66.56/9.56  Prover 16: Preprocessing ...
% 67.60/9.71  Prover 16: Constructing countermodel ...
% 110.50/15.35  Prover 16: stopped
% 110.50/15.36  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 111.48/15.48  Prover 19: Preprocessing ...
% 112.21/15.54  Prover 19: Constructing countermodel ...
% 115.34/15.97  Prover 1: stopped
% 139.32/19.12  Prover 19: stopped
% 164.04/23.42  Prover 8: Found proof (size 1027179)
% 164.04/23.42  Prover 8: proved (19125ms)
% 164.04/23.42  Prover 10: stopped
% 164.04/23.42  Prover 11: stopped
% 164.04/23.42  Prover 7: stopped
% 164.04/23.42  Prover 4: stopped
% 164.04/23.42  
% 164.04/23.42  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 164.04/23.42  
% 166.99/24.64  % SZS output start Proof for theBenchmark
% 167.49/24.82  Assumptions after simplification:
% 167.49/24.82  ---------------------------------
% 167.49/24.82  
% 167.49/24.82    (ax1)
% 167.49/24.88    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 167.49/24.88    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 167.49/24.88      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 167.49/24.88      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 167.49/24.88      op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 167.49/24.88      op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 167.49/24.88      op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 167.49/24.88      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 167.49/24.88      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 167.49/24.88      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 167.49/24.88        e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 167.49/24.88        v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 167.49/24.88        = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 167.49/24.88        v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 167.49/24.88        v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 167.49/24.88        v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 167.49/24.88      (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 167.49/24.88        = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 167.49/24.88        = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 167.49/24.88  
% 167.49/24.88    (ax10)
% 167.49/24.88    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.88    (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 167.49/24.88      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 167.49/24.88  
% 167.49/24.88    (ax11)
% 167.49/24.88    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.88    (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 167.49/24.88      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 167.49/24.88  
% 167.49/24.88    (ax12)
% 167.49/24.89    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.89    (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 167.49/24.89      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 167.49/24.89  
% 167.49/24.89    (ax13)
% 167.49/24.89    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.89    (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 167.49/24.89      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 167.49/24.89  
% 167.49/24.89    (ax14)
% 167.49/24.89    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.89    (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 167.49/24.89      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 167.49/24.89  
% 167.49/24.89    (ax15)
% 167.49/24.89    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.89    (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 167.49/24.89      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 167.49/24.89  
% 167.49/24.89    (ax16)
% 167.49/24.89    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.89    (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 167.49/24.89      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 167.49/24.89  
% 167.49/24.89    (ax17)
% 167.49/24.90    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.90    (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 167.49/24.90      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 167.49/24.90  
% 167.49/24.90    (ax18)
% 167.49/24.90    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.90    (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 167.49/24.90      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 167.49/24.90  
% 167.49/24.90    (ax19)
% 167.49/24.90    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.90    (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 167.49/24.90      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 167.49/24.90  
% 167.49/24.90    (ax2)
% 167.49/24.91    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 167.49/24.91    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 167.49/24.91      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 167.49/24.91      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 167.49/24.91      op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 &
% 167.49/24.91      op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 &
% 167.49/24.91      op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 167.49/24.91      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 167.49/24.91      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 167.49/24.91      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 =
% 167.49/24.91        e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 |
% 167.49/24.91        v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 =
% 167.49/24.91        e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3
% 167.49/24.91        = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0
% 167.49/24.91        | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 =
% 167.49/24.91        e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 =
% 167.49/24.91        e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 167.49/24.91        v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 =
% 167.49/24.91        e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5
% 167.49/24.91        = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 |
% 167.49/24.91        v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0
% 167.49/24.91        | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3)
% 167.49/24.91      & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 |
% 167.49/24.91        v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 |
% 167.49/24.91        v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 |
% 167.49/24.91        v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) &
% 167.49/24.91      (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 167.49/24.91        = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 |
% 167.49/24.91            v1 = e0))))
% 167.49/24.91  
% 167.49/24.91    (ax20)
% 167.49/24.91    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.91    (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 167.49/24.91      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 167.49/24.91  
% 167.49/24.91    (ax21)
% 167.49/24.91    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.91    (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 167.49/24.91      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 167.49/24.91  
% 167.49/24.91    (ax22)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 167.49/24.92  
% 167.49/24.92    (ax23)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 167.49/24.92  
% 167.49/24.92    (ax24)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 167.49/24.92  
% 167.49/24.92    (ax25)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 167.49/24.92  
% 167.49/24.92    (ax26)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 167.49/24.92  
% 167.49/24.92    (ax27)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 167.49/24.92  
% 167.49/24.92    (ax28)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e0, v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 167.49/24.92  
% 167.49/24.92    (ax29)
% 167.49/24.92    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.92    (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 167.49/24.92      $i(v0) & ( ~ (v2 = e0) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 167.49/24.93  
% 167.49/24.93    (ax3)
% 167.49/24.93    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 167.49/24.93    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 167.49/24.93      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 167.49/24.93      $i] :  ? [v14: $i] :  ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~
% 167.49/24.93      (v15 = v12) &  ~ (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 =
% 167.49/24.93        v13) &  ~ (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) & 
% 167.49/24.93      ~ (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12 =
% 167.49/24.93        v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 = v9) &  ~
% 167.49/24.93      (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9) &  ~ (v10 = v8) &
% 167.49/24.93       ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~ (v9 = v5) &  ~ (v9 = v1) &
% 167.49/24.93       ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6) &  ~ (v7 = v5) &  ~ (v7 = v4) & 
% 167.49/24.93      ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6 = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~
% 167.49/24.93      (v5 = v1) &  ~ (v4 = v0) &  ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~
% 167.49/24.93      (v2 = v1) &  ~ (v2 = v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 167.49/24.93      v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 167.49/24.93      v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 167.49/24.93      & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 167.49/24.93      op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 167.49/24.93      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 167.49/24.93      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 167.49/24.93  
% 167.49/24.93    (ax4)
% 167.49/24.93     ~ (e3 = e2) &  ~ (e3 = e1) &  ~ (e3 = e0) &  ~ (e2 = e1) &  ~ (e2 = e0) &  ~
% 167.49/24.93    (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 167.49/24.93  
% 167.49/24.93    (ax5)
% 167.49/24.94    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 167.49/24.94    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 167.49/24.94      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 167.49/24.94      $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18:
% 167.49/24.94      $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23:
% 167.49/24.94      $i] :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 167.49/24.94      $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : (op(e3, v30) = v31 &
% 167.49/24.94      op(e3, v22) = v23 & op(e3, v14) = v15 & op(e3, v6) = v7 & op(e3, e3) = v30 &
% 167.49/24.94      op(e3, e2) = v28 & op(e3, e1) = v26 & op(e3, e0) = v24 & op(e2, v28) = v29 &
% 167.49/24.94      op(e2, v20) = v21 & op(e2, v12) = v13 & op(e2, v4) = v5 & op(e2, e3) = v22 &
% 167.49/24.94      op(e2, e2) = v20 & op(e2, e1) = v18 & op(e2, e0) = v16 & op(e1, v26) = v27 &
% 167.49/24.94      op(e1, v18) = v19 & op(e1, v10) = v11 & op(e1, v2) = v3 & op(e1, e3) = v14 &
% 167.49/24.94      op(e1, e2) = v12 & op(e1, e1) = v10 & op(e1, e0) = v8 & op(e0, v24) = v25 &
% 167.49/24.94      op(e0, v16) = v17 & op(e0, v8) = v9 & op(e0, v0) = v1 & op(e0, e3) = v6 &
% 167.49/24.94      op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0 & $i(v31) & $i(v30) &
% 167.49/24.94      $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24) & $i(v23) &
% 167.49/24.94      $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) &
% 167.49/24.94      $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8)
% 167.49/24.94      & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 167.49/24.94      ((v31 = e3 & v29 = e2 & v27 = e1 & v25 = e0) | (v23 = e3 & v21 = e2 & v19 =
% 167.49/24.94          e1 & v17 = e0) | (v15 = e3 & v13 = e2 & v11 = e1 & v9 = e0) | (v7 = e3 &
% 167.49/24.94          v5 = e2 & v3 = e1 & v1 = e0)))
% 167.49/24.94  
% 167.49/24.94    (ax6)
% 167.49/24.94    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.94    (op(v1, v0) = v2 & op(e2, v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) &
% 167.49/24.94      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 167.49/24.94  
% 167.49/24.94    (ax7)
% 167.49/24.94    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.94    (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 167.49/24.94      $i(v0) & ( ~ (v2 = e2) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 167.49/24.94  
% 167.49/24.94    (ax8)
% 167.49/24.94    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.94    (op(v1, v0) = v2 & op(e1, v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) &
% 167.49/24.94      $i(v0) & ( ~ (v2 = e3) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 167.49/24.94  
% 167.49/24.94    (ax9)
% 167.49/24.94    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 167.49/24.94    (op(v1, v0) = v2 & op(e3, v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) &
% 167.49/24.94      $i(v0) & ( ~ (v2 = e1) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 167.49/24.94  
% 167.49/24.94    (function-axioms)
% 167.49/24.95     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (op(v3,
% 167.49/24.95          v2) = v1) |  ~ (op(v3, v2) = v0))
% 167.49/24.95  
% 167.49/24.95  Those formulas are unsatisfiable:
% 167.49/24.95  ---------------------------------
% 167.49/24.95  
% 167.49/24.95  Begin of proof
% 167.49/24.95  | 
% 167.49/24.95  | ALPHA: (ax1) implies:
% 167.49/24.96  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 167.49/24.96  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 167.49/24.96  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 167.49/24.96  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 167.49/24.96  |          & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 167.49/24.96  |          = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 167.49/24.96  |            e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 167.49/24.96  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 167.49/24.96  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 167.49/24.96  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 167.49/24.96  |            = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 167.49/24.96  |            = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 167.49/24.96  |            v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 167.49/24.96  |            v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 167.49/24.96  |            | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 167.49/24.96  |            = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 167.49/24.96  |            e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 167.49/24.96  |          (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 167.49/24.96  |            e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 167.49/24.96  |            | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 167.49/24.96  |            = e0))
% 167.49/24.96  | 
% 167.49/24.96  | ALPHA: (ax2) implies:
% 167.49/24.97  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 167.49/24.97  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 167.49/24.97  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 167.49/24.97  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11
% 167.49/24.97  |          & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1)
% 167.49/24.97  |          = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1,
% 167.49/24.97  |            e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 167.49/24.97  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 167.49/24.97  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 167.49/24.97  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14
% 167.49/24.97  |            = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 =
% 167.49/24.97  |            e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13
% 167.49/24.97  |            = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 =
% 167.49/24.97  |            e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 =
% 167.49/24.97  |            e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 =
% 167.49/24.97  |            e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 =
% 167.49/24.97  |            e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1)
% 167.49/24.97  |          & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 |
% 167.49/24.97  |            v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) &
% 167.49/24.97  |          (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 |
% 167.49/24.97  |            v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) &
% 167.49/24.97  |          (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7
% 167.49/24.97  |            = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 =
% 167.49/24.97  |            e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 |
% 167.49/24.97  |            v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8
% 167.49/24.97  |            = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3)
% 167.49/24.97  |          & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 =
% 167.49/24.97  |            e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2
% 167.49/24.97  |            | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0
% 167.49/24.97  |            = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 =
% 167.49/24.97  |                e0 | v1 = e0))))
% 167.49/24.97  | 
% 167.49/24.97  | ALPHA: (ax3) implies:
% 167.49/24.97  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 167.49/24.97  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 167.49/24.97  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 167.49/24.97  |         ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~ (v15 = v12) &  ~
% 167.49/24.97  |          (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 = v13) &  ~
% 167.49/24.97  |          (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) &  ~
% 167.49/24.97  |          (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12
% 167.49/24.97  |            = v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 =
% 167.49/24.97  |            v9) &  ~ (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9)
% 167.49/24.97  |          &  ~ (v10 = v8) &  ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~
% 167.49/24.97  |          (v9 = v5) &  ~ (v9 = v1) &  ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6)
% 167.49/24.97  |          &  ~ (v7 = v5) &  ~ (v7 = v4) &  ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6
% 167.49/24.97  |            = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~ (v5 = v1) &  ~ (v4 = v0) &
% 167.49/24.97  |           ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 =
% 167.49/24.97  |            v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 167.49/24.98  |            e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 167.49/24.98  |          op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 167.49/24.98  |          v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 167.49/24.98  |            e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 167.49/24.98  |          $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 167.49/24.98  |          $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 167.49/24.98  | 
% 167.49/24.98  | ALPHA: (ax4) implies:
% 167.49/24.98  |   (4)   ~ (e1 = e0)
% 167.49/24.98  |   (5)   ~ (e2 = e0)
% 167.49/24.98  |   (6)   ~ (e2 = e1)
% 167.49/24.98  |   (7)   ~ (e3 = e0)
% 167.49/24.98  |   (8)   ~ (e3 = e1)
% 167.49/24.98  |   (9)   ~ (e3 = e2)
% 167.49/24.98  | 
% 167.49/24.98  | ALPHA: (ax5) implies:
% 167.49/24.98  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 167.49/24.98  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 167.49/24.98  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 167.49/24.98  |           $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ?
% 167.49/24.98  |         [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i]
% 167.49/24.98  |         :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 167.49/24.98  |           $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : (op(e3, v30) =
% 167.49/24.98  |           v31 & op(e3, v22) = v23 & op(e3, v14) = v15 & op(e3, v6) = v7 &
% 167.49/24.98  |           op(e3, e3) = v30 & op(e3, e2) = v28 & op(e3, e1) = v26 & op(e3, e0)
% 167.49/24.98  |           = v24 & op(e2, v28) = v29 & op(e2, v20) = v21 & op(e2, v12) = v13 &
% 167.49/24.98  |           op(e2, v4) = v5 & op(e2, e3) = v22 & op(e2, e2) = v20 & op(e2, e1) =
% 167.49/24.98  |           v18 & op(e2, e0) = v16 & op(e1, v26) = v27 & op(e1, v18) = v19 &
% 167.49/24.98  |           op(e1, v10) = v11 & op(e1, v2) = v3 & op(e1, e3) = v14 & op(e1, e2)
% 167.49/24.98  |           = v12 & op(e1, e1) = v10 & op(e1, e0) = v8 & op(e0, v24) = v25 &
% 167.49/24.98  |           op(e0, v16) = v17 & op(e0, v8) = v9 & op(e0, v0) = v1 & op(e0, e3) =
% 167.49/24.98  |           v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0 & $i(v31) &
% 167.49/24.98  |           $i(v30) & $i(v29) & $i(v28) & $i(v27) & $i(v26) & $i(v25) & $i(v24)
% 167.49/24.98  |           & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) &
% 167.49/24.98  |           $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11)
% 167.49/24.98  |           & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 167.49/24.98  |           $i(v3) & $i(v2) & $i(v1) & $i(v0) & ((v31 = e3 & v29 = e2 & v27 = e1
% 167.49/24.98  |               & v25 = e0) | (v23 = e3 & v21 = e2 & v19 = e1 & v17 = e0) | (v15
% 167.49/24.98  |               = e3 & v13 = e2 & v11 = e1 & v9 = e0) | (v7 = e3 & v5 = e2 & v3
% 167.49/24.98  |               = e1 & v1 = e0)))
% 167.49/24.98  | 
% 167.49/24.98  | ALPHA: (ax6) implies:
% 167.49/24.98  |   (11)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 167.49/24.98  |             v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.98  |               e3) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax7) implies:
% 167.49/24.99  |   (12)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 167.49/24.99  |             v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e2) |  ~ (v1 = e1) |  ~ (v0 = e0)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax8) implies:
% 167.49/24.99  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 167.49/24.99  |             v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e3) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax9) implies:
% 167.49/24.99  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 167.49/24.99  |             v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e1) |  ~ (v1 = e2) |  ~ (v0 = e0)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax10) implies:
% 167.49/24.99  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 167.49/24.99  |             v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e2) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax11) implies:
% 167.49/24.99  |   (16)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 167.49/24.99  |             v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e1) |  ~ (v1 = e3) |  ~ (v0 = e0)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax12) implies:
% 167.49/24.99  |   (17)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 167.49/24.99  |             v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e3) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax13) implies:
% 167.49/24.99  |   (18)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 167.49/24.99  |             v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e2) |  ~ (v1 = e0) |  ~ (v0 = e1)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax14) implies:
% 167.49/24.99  |   (19)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 167.49/24.99  |             v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e3) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax15) implies:
% 167.49/24.99  |   (20)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 167.49/24.99  |             v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/24.99  |               e0) |  ~ (v1 = e2) |  ~ (v0 = e1)))
% 167.49/24.99  | 
% 167.49/24.99  | ALPHA: (ax16) implies:
% 167.49/25.00  |   (21)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 167.49/25.00  |             v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e2) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax17) implies:
% 167.49/25.00  |   (22)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 167.49/25.00  |             v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e0) |  ~ (v1 = e3) |  ~ (v0 = e1)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax18) implies:
% 167.49/25.00  |   (23)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 167.49/25.00  |             v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e3) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax19) implies:
% 167.49/25.00  |   (24)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 167.49/25.00  |             v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e1) |  ~ (v1 = e0) |  ~ (v0 = e2)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax20) implies:
% 167.49/25.00  |   (25)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 167.49/25.00  |             v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e3) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax21) implies:
% 167.49/25.00  |   (26)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e3,
% 167.49/25.00  |             v0) = v1 & op(e3, e3) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e0) |  ~ (v1 = e1) |  ~ (v0 = e2)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax22) implies:
% 167.49/25.00  |   (27)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 167.49/25.00  |             v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e1) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax23) implies:
% 167.49/25.00  |   (28)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 167.49/25.00  |             v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.00  |               e0) |  ~ (v1 = e3) |  ~ (v0 = e2)))
% 167.49/25.00  | 
% 167.49/25.00  | ALPHA: (ax24) implies:
% 167.49/25.00  |   (29)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 167.49/25.00  |             v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.01  |               e2) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (ax25) implies:
% 167.49/25.01  |   (30)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 167.49/25.01  |             v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.01  |               e1) |  ~ (v1 = e0) |  ~ (v0 = e3)))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (ax26) implies:
% 167.49/25.01  |   (31)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 167.49/25.01  |             v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.01  |               e2) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (ax27) implies:
% 167.49/25.01  |   (32)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e2,
% 167.49/25.01  |             v0) = v1 & op(e2, e2) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.01  |               e0) |  ~ (v1 = e1) |  ~ (v0 = e3)))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (ax28) implies:
% 167.49/25.01  |   (33)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e0,
% 167.49/25.01  |             v0) = v1 & op(e0, e0) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.01  |               e1) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (ax29) implies:
% 167.49/25.01  |   (34)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(v1, v0) = v2 & op(e1,
% 167.49/25.01  |             v0) = v1 & op(e1, e1) = v0 & $i(v2) & $i(v1) & $i(v0) & ( ~ (v2 =
% 167.49/25.01  |               e0) |  ~ (v1 = e2) |  ~ (v0 = e3)))
% 167.49/25.01  | 
% 167.49/25.01  | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 167.49/25.01  |   (35)  op(all_4_1, all_4_2) = all_4_0 & op(e3, all_4_2) = all_4_1 & op(e3,
% 167.49/25.01  |           e3) = all_4_2 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & ( ~
% 167.49/25.01  |           (all_4_0 = e0) |  ~ (all_4_1 = e2) |  ~ (all_4_2 = e1))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (35) implies:
% 167.49/25.01  |   (36)  op(e3, e3) = all_4_2
% 167.49/25.01  |   (37)  op(e3, all_4_2) = all_4_1
% 167.49/25.01  |   (38)  op(all_4_1, all_4_2) = all_4_0
% 167.49/25.01  |   (39)   ~ (all_4_0 = e0) |  ~ (all_4_1 = e2) |  ~ (all_4_2 = e1)
% 167.49/25.01  | 
% 167.49/25.01  | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 167.49/25.01  |   (40)  op(all_6_1, all_6_2) = all_6_0 & op(e0, all_6_2) = all_6_1 & op(e0,
% 167.49/25.01  |           e0) = all_6_2 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & ( ~
% 167.49/25.01  |           (all_6_0 = e1) |  ~ (all_6_1 = e3) |  ~ (all_6_2 = e2))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (40) implies:
% 167.49/25.01  |   (41)  op(e0, e0) = all_6_2
% 167.49/25.01  |   (42)  op(e0, all_6_2) = all_6_1
% 167.49/25.01  |   (43)  op(all_6_1, all_6_2) = all_6_0
% 167.49/25.01  |   (44)   ~ (all_6_0 = e1) |  ~ (all_6_1 = e3) |  ~ (all_6_2 = e2)
% 167.49/25.01  | 
% 167.49/25.01  | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 167.49/25.01  |   (45)  op(all_8_1, all_8_2) = all_8_0 & op(e0, all_8_2) = all_8_1 & op(e0,
% 167.49/25.01  |           e0) = all_8_2 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & ( ~
% 167.49/25.01  |           (all_8_0 = e2) |  ~ (all_8_1 = e3) |  ~ (all_8_2 = e1))
% 167.49/25.01  | 
% 167.49/25.01  | ALPHA: (45) implies:
% 167.49/25.01  |   (46)  op(e0, e0) = all_8_2
% 167.49/25.02  |   (47)  op(e0, all_8_2) = all_8_1
% 167.49/25.02  |   (48)  op(all_8_1, all_8_2) = all_8_0
% 167.49/25.02  |   (49)   ~ (all_8_0 = e2) |  ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 167.49/25.02  | 
% 167.49/25.02  | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 167.49/25.02  |        gives:
% 167.49/25.02  |   (50)  op(all_10_1, all_10_2) = all_10_0 & op(e2, all_10_2) = all_10_1 &
% 167.49/25.02  |         op(e2, e2) = all_10_2 & $i(all_10_0) & $i(all_10_1) & $i(all_10_2) & (
% 167.49/25.02  |           ~ (all_10_0 = e3) |  ~ (all_10_1 = e1) |  ~ (all_10_2 = e0))
% 167.49/25.02  | 
% 167.49/25.02  | ALPHA: (50) implies:
% 167.49/25.02  |   (51)  op(e2, e2) = all_10_2
% 167.49/25.02  |   (52)  op(e2, all_10_2) = all_10_1
% 167.49/25.02  |   (53)  op(all_10_1, all_10_2) = all_10_0
% 167.49/25.02  |   (54)   ~ (all_10_0 = e3) |  ~ (all_10_1 = e1) |  ~ (all_10_2 = e0)
% 167.49/25.02  | 
% 167.49/25.02  | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 167.49/25.02  |        gives:
% 167.49/25.02  |   (55)  op(all_12_1, all_12_2) = all_12_0 & op(e2, all_12_2) = all_12_1 &
% 167.49/25.02  |         op(e2, e2) = all_12_2 & $i(all_12_0) & $i(all_12_1) & $i(all_12_2) & (
% 167.49/25.02  |           ~ (all_12_0 = e0) |  ~ (all_12_1 = e3) |  ~ (all_12_2 = e1))
% 167.49/25.02  | 
% 167.49/25.02  | ALPHA: (55) implies:
% 167.49/25.02  |   (56)  op(e2, e2) = all_12_2
% 167.49/25.02  |   (57)  op(e2, all_12_2) = all_12_1
% 167.49/25.02  |   (58)  op(all_12_1, all_12_2) = all_12_0
% 167.49/25.02  |   (59)   ~ (all_12_0 = e0) |  ~ (all_12_1 = e3) |  ~ (all_12_2 = e1)
% 167.49/25.02  | 
% 167.49/25.02  | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 167.49/25.02  |        gives:
% 167.49/25.02  |   (60)  op(all_14_1, all_14_2) = all_14_0 & op(e1, all_14_2) = all_14_1 &
% 167.49/25.02  |         op(e1, e1) = all_14_2 & $i(all_14_0) & $i(all_14_1) & $i(all_14_2) & (
% 167.49/25.02  |           ~ (all_14_0 = e2) |  ~ (all_14_1 = e0) |  ~ (all_14_2 = e3))
% 167.49/25.02  | 
% 167.49/25.02  | ALPHA: (60) implies:
% 167.49/25.02  |   (61)  op(e1, e1) = all_14_2
% 167.49/25.02  |   (62)  op(e1, all_14_2) = all_14_1
% 167.49/25.02  |   (63)  op(all_14_1, all_14_2) = all_14_0
% 167.49/25.02  |   (64)   ~ (all_14_0 = e2) |  ~ (all_14_1 = e0) |  ~ (all_14_2 = e3)
% 167.49/25.02  | 
% 167.49/25.02  | DELTA: instantiating (31) with fresh symbols all_16_0, all_16_1, all_16_2
% 167.49/25.02  |        gives:
% 167.49/25.02  |   (65)  op(all_16_1, all_16_2) = all_16_0 & op(e0, all_16_2) = all_16_1 &
% 167.49/25.02  |         op(e0, e0) = all_16_2 & $i(all_16_0) & $i(all_16_1) & $i(all_16_2) & (
% 167.49/25.02  |           ~ (all_16_0 = e2) |  ~ (all_16_1 = e1) |  ~ (all_16_2 = e3))
% 167.49/25.02  | 
% 167.49/25.02  | ALPHA: (65) implies:
% 167.49/25.02  |   (66)  op(e0, e0) = all_16_2
% 167.49/25.02  |   (67)  op(e0, all_16_2) = all_16_1
% 167.49/25.02  |   (68)  op(all_16_1, all_16_2) = all_16_0
% 167.49/25.02  |   (69)   ~ (all_16_0 = e2) |  ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 167.49/25.02  | 
% 167.49/25.02  | DELTA: instantiating (23) with fresh symbols all_18_0, all_18_1, all_18_2
% 167.49/25.02  |        gives:
% 167.49/25.02  |   (70)  op(all_18_1, all_18_2) = all_18_0 & op(e1, all_18_2) = all_18_1 &
% 167.49/25.02  |         op(e1, e1) = all_18_2 & $i(all_18_0) & $i(all_18_1) & $i(all_18_2) & (
% 167.49/25.02  |           ~ (all_18_0 = e3) |  ~ (all_18_1 = e0) |  ~ (all_18_2 = e2))
% 167.49/25.02  | 
% 167.49/25.02  | ALPHA: (70) implies:
% 167.49/25.02  |   (71)  op(e1, e1) = all_18_2
% 167.49/25.02  |   (72)  op(e1, all_18_2) = all_18_1
% 167.49/25.02  |   (73)  op(all_18_1, all_18_2) = all_18_0
% 167.49/25.02  |   (74)   ~ (all_18_0 = e3) |  ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 167.49/25.02  | 
% 167.49/25.02  | DELTA: instantiating (13) with fresh symbols all_20_0, all_20_1, all_20_2
% 167.49/25.02  |        gives:
% 167.49/25.02  |   (75)  op(all_20_1, all_20_2) = all_20_0 & op(e1, all_20_2) = all_20_1 &
% 167.49/25.02  |         op(e1, e1) = all_20_2 & $i(all_20_0) & $i(all_20_1) & $i(all_20_2) & (
% 167.49/25.02  |           ~ (all_20_0 = e3) |  ~ (all_20_1 = e2) |  ~ (all_20_2 = e0))
% 167.49/25.02  | 
% 167.49/25.02  | ALPHA: (75) implies:
% 167.49/25.02  |   (76)  op(e1, e1) = all_20_2
% 167.49/25.02  |   (77)  op(e1, all_20_2) = all_20_1
% 167.49/25.02  |   (78)  op(all_20_1, all_20_2) = all_20_0
% 167.49/25.02  | 
% 167.49/25.02  | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1, all_22_2
% 167.49/25.02  |        gives:
% 167.49/25.02  |   (79)  op(all_22_1, all_22_2) = all_22_0 & op(e1, all_22_2) = all_22_1 &
% 167.49/25.02  |         op(e1, e1) = all_22_2 & $i(all_22_0) & $i(all_22_1) & $i(all_22_2) & (
% 167.49/25.02  |           ~ (all_22_0 = e0) |  ~ (all_22_1 = e3) |  ~ (all_22_2 = e2))
% 167.49/25.02  | 
% 167.49/25.02  | ALPHA: (79) implies:
% 167.49/25.02  |   (80)  op(e1, e1) = all_22_2
% 167.49/25.02  |   (81)  op(e1, all_22_2) = all_22_1
% 167.49/25.03  |   (82)  op(all_22_1, all_22_2) = all_22_0
% 167.49/25.03  |   (83)   ~ (all_22_0 = e0) |  ~ (all_22_1 = e3) |  ~ (all_22_2 = e2)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (30) with fresh symbols all_24_0, all_24_1, all_24_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (84)  op(all_24_1, all_24_2) = all_24_0 & op(e2, all_24_2) = all_24_1 &
% 167.49/25.03  |         op(e2, e2) = all_24_2 & $i(all_24_0) & $i(all_24_1) & $i(all_24_2) & (
% 167.49/25.03  |           ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3))
% 167.49/25.03  | 
% 167.49/25.03  | ALPHA: (84) implies:
% 167.49/25.03  |   (85)  op(e2, e2) = all_24_2
% 167.49/25.03  |   (86)  op(e2, all_24_2) = all_24_1
% 167.49/25.03  |   (87)  op(all_24_1, all_24_2) = all_24_0
% 167.49/25.03  |   (88)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1, all_26_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (89)  op(all_26_1, all_26_2) = all_26_0 & op(e3, all_26_2) = all_26_1 &
% 167.49/25.03  |         op(e3, e3) = all_26_2 & $i(all_26_0) & $i(all_26_1) & $i(all_26_2) & (
% 167.49/25.03  |           ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0))
% 167.49/25.03  | 
% 167.49/25.03  | ALPHA: (89) implies:
% 167.49/25.03  |   (90)  op(e3, e3) = all_26_2
% 167.49/25.03  |   (91)  op(e3, all_26_2) = all_26_1
% 167.49/25.03  |   (92)  op(all_26_1, all_26_2) = all_26_0
% 167.49/25.03  |   (93)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1, all_28_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (94)  op(all_28_1, all_28_2) = all_28_0 & op(e0, all_28_2) = all_28_1 &
% 167.49/25.03  |         op(e0, e0) = all_28_2 & $i(all_28_0) & $i(all_28_1) & $i(all_28_2) & (
% 167.49/25.03  |           ~ (all_28_0 = e3) |  ~ (all_28_1 = e2) |  ~ (all_28_2 = e1))
% 167.49/25.03  | 
% 167.49/25.03  | ALPHA: (94) implies:
% 167.49/25.03  |   (95)  op(e0, e0) = all_28_2
% 167.49/25.03  |   (96)  op(e0, all_28_2) = all_28_1
% 167.49/25.03  |   (97)  op(all_28_1, all_28_2) = all_28_0
% 167.49/25.03  |   (98)   ~ (all_28_0 = e3) |  ~ (all_28_1 = e2) |  ~ (all_28_2 = e1)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (32) with fresh symbols all_30_0, all_30_1, all_30_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (99)  op(all_30_1, all_30_2) = all_30_0 & op(e2, all_30_2) = all_30_1 &
% 167.49/25.03  |         op(e2, e2) = all_30_2 & $i(all_30_0) & $i(all_30_1) & $i(all_30_2) & (
% 167.49/25.03  |           ~ (all_30_0 = e0) |  ~ (all_30_1 = e1) |  ~ (all_30_2 = e3))
% 167.49/25.03  | 
% 167.49/25.03  | ALPHA: (99) implies:
% 167.49/25.03  |   (100)  op(e2, e2) = all_30_2
% 167.49/25.03  |   (101)  op(e2, all_30_2) = all_30_1
% 167.49/25.03  |   (102)  op(all_30_1, all_30_2) = all_30_0
% 167.49/25.03  |   (103)   ~ (all_30_0 = e0) |  ~ (all_30_1 = e1) |  ~ (all_30_2 = e3)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1, all_32_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (104)  op(all_32_1, all_32_2) = all_32_0 & op(e1, all_32_2) = all_32_1 &
% 167.49/25.03  |          op(e1, e1) = all_32_2 & $i(all_32_0) & $i(all_32_1) & $i(all_32_2) &
% 167.49/25.03  |          ( ~ (all_32_0 = e0) |  ~ (all_32_1 = e2) |  ~ (all_32_2 = e3))
% 167.49/25.03  | 
% 167.49/25.03  | ALPHA: (104) implies:
% 167.49/25.03  |   (105)  op(e1, e1) = all_32_2
% 167.49/25.03  |   (106)  op(e1, all_32_2) = all_32_1
% 167.49/25.03  |   (107)  op(all_32_1, all_32_2) = all_32_0
% 167.49/25.03  |   (108)   ~ (all_32_0 = e0) |  ~ (all_32_1 = e2) |  ~ (all_32_2 = e3)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (24) with fresh symbols all_34_0, all_34_1, all_34_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (109)  op(all_34_1, all_34_2) = all_34_0 & op(e3, all_34_2) = all_34_1 &
% 167.49/25.03  |          op(e3, e3) = all_34_2 & $i(all_34_0) & $i(all_34_1) & $i(all_34_2) &
% 167.49/25.03  |          ( ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2))
% 167.49/25.03  | 
% 167.49/25.03  | ALPHA: (109) implies:
% 167.49/25.03  |   (110)  op(e3, e3) = all_34_2
% 167.49/25.03  |   (111)  op(e3, all_34_2) = all_34_1
% 167.49/25.03  |   (112)  op(all_34_1, all_34_2) = all_34_0
% 167.49/25.03  |   (113)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1, all_36_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (114)  op(all_36_1, all_36_2) = all_36_0 & op(e0, all_36_2) = all_36_1 &
% 167.49/25.03  |          op(e0, e0) = all_36_2 & $i(all_36_0) & $i(all_36_1) & $i(all_36_2) &
% 167.49/25.03  |          ( ~ (all_36_0 = e3) |  ~ (all_36_1 = e1) |  ~ (all_36_2 = e2))
% 167.49/25.03  | 
% 167.49/25.03  | ALPHA: (114) implies:
% 167.49/25.03  |   (115)  op(e0, e0) = all_36_2
% 167.49/25.03  |   (116)  op(e0, all_36_2) = all_36_1
% 167.49/25.03  |   (117)  op(all_36_1, all_36_2) = all_36_0
% 167.49/25.03  |   (118)   ~ (all_36_0 = e3) |  ~ (all_36_1 = e1) |  ~ (all_36_2 = e2)
% 167.49/25.03  | 
% 167.49/25.03  | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1, all_38_2
% 167.49/25.03  |        gives:
% 167.49/25.03  |   (119)  op(all_38_1, all_38_2) = all_38_0 & op(e0, all_38_2) = all_38_1 &
% 167.49/25.03  |          op(e0, e0) = all_38_2 & $i(all_38_0) & $i(all_38_1) & $i(all_38_2) &
% 167.49/25.03  |          ( ~ (all_38_0 = e1) |  ~ (all_38_1 = e2) |  ~ (all_38_2 = e3))
% 167.49/25.04  | 
% 167.49/25.04  | ALPHA: (119) implies:
% 167.49/25.04  |   (120)  op(e0, e0) = all_38_2
% 167.49/25.04  |   (121)  op(e0, all_38_2) = all_38_1
% 167.49/25.04  |   (122)  op(all_38_1, all_38_2) = all_38_0
% 167.49/25.04  |   (123)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 167.49/25.04  | 
% 167.49/25.04  | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2
% 167.49/25.04  |        gives:
% 167.49/25.04  |   (124)  op(all_40_1, all_40_2) = all_40_0 & op(e3, all_40_2) = all_40_1 &
% 167.49/25.04  |          op(e3, e3) = all_40_2 & $i(all_40_0) & $i(all_40_1) & $i(all_40_2) &
% 167.49/25.04  |          ( ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2))
% 167.49/25.04  | 
% 167.49/25.04  | ALPHA: (124) implies:
% 167.49/25.04  |   (125)  op(e3, e3) = all_40_2
% 167.49/25.04  |   (126)  op(e3, all_40_2) = all_40_1
% 167.49/25.04  |   (127)  op(all_40_1, all_40_2) = all_40_0
% 167.49/25.04  |   (128)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2)
% 167.49/25.04  | 
% 167.49/25.04  | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1, all_42_2
% 167.49/25.04  |        gives:
% 167.49/25.04  |   (129)  op(all_42_1, all_42_2) = all_42_0 & op(e3, all_42_2) = all_42_1 &
% 167.49/25.04  |          op(e3, e3) = all_42_2 & $i(all_42_0) & $i(all_42_1) & $i(all_42_2) &
% 167.49/25.04  |          ( ~ (all_42_0 = e1) |  ~ (all_42_1 = e2) |  ~ (all_42_2 = e0))
% 167.49/25.04  | 
% 167.49/25.04  | ALPHA: (129) implies:
% 167.49/25.04  |   (130)  op(e3, e3) = all_42_2
% 167.49/25.04  |   (131)  op(e3, all_42_2) = all_42_1
% 167.49/25.04  |   (132)  op(all_42_1, all_42_2) = all_42_0
% 167.49/25.04  |   (133)   ~ (all_42_0 = e1) |  ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 167.49/25.04  | 
% 167.49/25.04  | DELTA: instantiating (15) with fresh symbols all_44_0, all_44_1, all_44_2
% 167.49/25.04  |        gives:
% 167.49/25.04  |   (134)  op(all_44_1, all_44_2) = all_44_0 & op(e1, all_44_2) = all_44_1 &
% 167.49/25.04  |          op(e1, e1) = all_44_2 & $i(all_44_0) & $i(all_44_1) & $i(all_44_2) &
% 167.49/25.04  |          ( ~ (all_44_0 = e2) |  ~ (all_44_1 = e3) |  ~ (all_44_2 = e0))
% 167.49/25.04  | 
% 167.49/25.04  | ALPHA: (134) implies:
% 168.46/25.04  |   (135)  op(e1, e1) = all_44_2
% 168.46/25.04  |   (136)  op(e1, all_44_2) = all_44_1
% 168.46/25.04  |   (137)  op(all_44_1, all_44_2) = all_44_0
% 168.46/25.04  | 
% 168.46/25.04  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 168.46/25.04  |        gives:
% 168.46/25.04  |   (138)  op(all_46_1, all_46_2) = all_46_0 & op(e2, all_46_2) = all_46_1 &
% 168.46/25.04  |          op(e2, e2) = all_46_2 & $i(all_46_0) & $i(all_46_1) & $i(all_46_2) &
% 168.46/25.04  |          ( ~ (all_46_0 = e1) |  ~ (all_46_1 = e3) |  ~ (all_46_2 = e0))
% 168.46/25.04  | 
% 168.46/25.04  | ALPHA: (138) implies:
% 168.46/25.04  |   (139)  op(e2, e2) = all_46_2
% 168.46/25.04  |   (140)  op(e2, all_46_2) = all_46_1
% 168.46/25.04  |   (141)  op(all_46_1, all_46_2) = all_46_0
% 168.46/25.04  |   (142)   ~ (all_46_0 = e1) |  ~ (all_46_1 = e3) |  ~ (all_46_2 = e0)
% 168.46/25.04  | 
% 168.46/25.04  | DELTA: instantiating (17) with fresh symbols all_48_0, all_48_1, all_48_2
% 168.46/25.04  |        gives:
% 168.46/25.04  |   (143)  op(all_48_1, all_48_2) = all_48_0 & op(e2, all_48_2) = all_48_1 &
% 168.46/25.04  |          op(e2, e2) = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) &
% 168.46/25.04  |          ( ~ (all_48_0 = e3) |  ~ (all_48_1 = e0) |  ~ (all_48_2 = e1))
% 168.46/25.04  | 
% 168.46/25.04  | ALPHA: (143) implies:
% 168.46/25.04  |   (144)  op(e2, e2) = all_48_2
% 168.46/25.04  |   (145)  op(e2, all_48_2) = all_48_1
% 168.46/25.04  |   (146)  op(all_48_1, all_48_2) = all_48_0
% 168.46/25.04  | 
% 168.46/25.04  | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1, all_50_2
% 168.46/25.04  |        gives:
% 168.46/25.04  |   (147)  op(all_50_1, all_50_2) = all_50_0 & op(e3, all_50_2) = all_50_1 &
% 168.46/25.04  |          op(e3, e3) = all_50_2 & $i(all_50_0) & $i(all_50_1) & $i(all_50_2) &
% 168.46/25.04  |          ( ~ (all_50_0 = e2) |  ~ (all_50_1 = e0) |  ~ (all_50_2 = e1))
% 168.46/25.04  | 
% 168.46/25.04  | ALPHA: (147) implies:
% 168.46/25.04  |   (148)  op(e3, e3) = all_50_2
% 168.46/25.04  |   (149)  op(e3, all_50_2) = all_50_1
% 168.46/25.04  |   (150)  op(all_50_1, all_50_2) = all_50_0
% 168.46/25.04  |   (151)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 168.46/25.04  | 
% 168.46/25.04  | DELTA: instantiating (10) with fresh symbols all_52_0, all_52_1, all_52_2,
% 168.46/25.04  |        all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 168.46/25.04  |        all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15,
% 168.46/25.04  |        all_52_16, all_52_17, all_52_18, all_52_19, all_52_20, all_52_21,
% 168.46/25.04  |        all_52_22, all_52_23, all_52_24, all_52_25, all_52_26, all_52_27,
% 168.46/25.04  |        all_52_28, all_52_29, all_52_30, all_52_31 gives:
% 168.46/25.05  |   (152)  op(e3, all_52_1) = all_52_0 & op(e3, all_52_9) = all_52_8 & op(e3,
% 168.46/25.05  |            all_52_17) = all_52_16 & op(e3, all_52_25) = all_52_24 & op(e3, e3)
% 168.46/25.05  |          = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 168.46/25.05  |            e0) = all_52_7 & op(e2, all_52_3) = all_52_2 & op(e2, all_52_11) =
% 168.46/25.05  |          all_52_10 & op(e2, all_52_19) = all_52_18 & op(e2, all_52_27) =
% 168.46/25.05  |          all_52_26 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2,
% 168.46/25.05  |            e1) = all_52_13 & op(e2, e0) = all_52_15 & op(e1, all_52_5) =
% 168.46/25.05  |          all_52_4 & op(e1, all_52_13) = all_52_12 & op(e1, all_52_21) =
% 168.46/25.05  |          all_52_20 & op(e1, all_52_29) = all_52_28 & op(e1, e3) = all_52_17 &
% 168.46/25.05  |          op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) =
% 168.46/25.05  |          all_52_23 & op(e0, all_52_7) = all_52_6 & op(e0, all_52_15) =
% 168.46/25.05  |          all_52_14 & op(e0, all_52_23) = all_52_22 & op(e0, all_52_31) =
% 168.46/25.05  |          all_52_30 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0,
% 168.46/25.05  |            e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_0) &
% 168.46/25.05  |          $i(all_52_1) & $i(all_52_2) & $i(all_52_3) & $i(all_52_4) &
% 168.46/25.05  |          $i(all_52_5) & $i(all_52_6) & $i(all_52_7) & $i(all_52_8) &
% 168.46/25.05  |          $i(all_52_9) & $i(all_52_10) & $i(all_52_11) & $i(all_52_12) &
% 168.46/25.05  |          $i(all_52_13) & $i(all_52_14) & $i(all_52_15) & $i(all_52_16) &
% 168.46/25.05  |          $i(all_52_17) & $i(all_52_18) & $i(all_52_19) & $i(all_52_20) &
% 168.46/25.05  |          $i(all_52_21) & $i(all_52_22) & $i(all_52_23) & $i(all_52_24) &
% 168.46/25.05  |          $i(all_52_25) & $i(all_52_26) & $i(all_52_27) & $i(all_52_28) &
% 168.46/25.05  |          $i(all_52_29) & $i(all_52_30) & $i(all_52_31) & ((all_52_0 = e3 &
% 168.46/25.05  |              all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) | (all_52_8 = e3 &
% 168.46/25.05  |              all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) | (all_52_16 =
% 168.46/25.05  |              e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 168.46/25.05  |            (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 168.46/25.05  |              e0))
% 168.46/25.05  | 
% 168.46/25.05  | ALPHA: (152) implies:
% 168.46/25.05  |   (153)  op(e0, e0) = all_52_31
% 168.46/25.05  |   (154)  op(e0, e1) = all_52_29
% 168.46/25.05  |   (155)  op(e0, e2) = all_52_27
% 168.46/25.05  |   (156)  op(e0, e3) = all_52_25
% 168.46/25.05  |   (157)  op(e0, all_52_31) = all_52_30
% 168.46/25.05  |   (158)  op(e0, all_52_23) = all_52_22
% 168.46/25.05  |   (159)  op(e0, all_52_15) = all_52_14
% 168.46/25.05  |   (160)  op(e0, all_52_7) = all_52_6
% 168.46/25.05  |   (161)  op(e1, e0) = all_52_23
% 168.46/25.05  |   (162)  op(e1, e1) = all_52_21
% 168.46/25.05  |   (163)  op(e1, e2) = all_52_19
% 168.46/25.05  |   (164)  op(e1, e3) = all_52_17
% 168.46/25.05  |   (165)  op(e1, all_52_29) = all_52_28
% 168.46/25.05  |   (166)  op(e1, all_52_21) = all_52_20
% 168.46/25.05  |   (167)  op(e1, all_52_13) = all_52_12
% 168.46/25.05  |   (168)  op(e1, all_52_5) = all_52_4
% 168.46/25.05  |   (169)  op(e2, e0) = all_52_15
% 168.46/25.05  |   (170)  op(e2, e1) = all_52_13
% 168.46/25.05  |   (171)  op(e2, e2) = all_52_11
% 168.46/25.05  |   (172)  op(e2, e3) = all_52_9
% 168.46/25.05  |   (173)  op(e2, all_52_27) = all_52_26
% 168.46/25.05  |   (174)  op(e2, all_52_19) = all_52_18
% 168.46/25.05  |   (175)  op(e2, all_52_11) = all_52_10
% 168.46/25.05  |   (176)  op(e2, all_52_3) = all_52_2
% 168.46/25.05  |   (177)  op(e3, e0) = all_52_7
% 168.46/25.05  |   (178)  op(e3, e1) = all_52_5
% 168.46/25.05  |   (179)  op(e3, e2) = all_52_3
% 168.46/25.05  |   (180)  op(e3, e3) = all_52_1
% 168.46/25.05  |   (181)  op(e3, all_52_25) = all_52_24
% 168.46/25.05  |   (182)  op(e3, all_52_17) = all_52_16
% 168.46/25.05  |   (183)  op(e3, all_52_9) = all_52_8
% 168.46/25.05  |   (184)  op(e3, all_52_1) = all_52_0
% 168.46/25.05  |   (185)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 168.46/25.05  |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 168.46/25.05  |          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 168.46/25.05  |          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 168.46/25.05  | 
% 168.46/25.05  | DELTA: instantiating (3) with fresh symbols all_54_0, all_54_1, all_54_2,
% 168.46/25.05  |        all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 168.46/25.05  |        all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 168.46/25.05  |   (186)   ~ (all_54_0 = all_54_1) &  ~ (all_54_0 = all_54_2) &  ~ (all_54_0 =
% 168.46/25.05  |            all_54_3) &  ~ (all_54_0 = all_54_4) &  ~ (all_54_0 = all_54_8) & 
% 168.46/25.05  |          ~ (all_54_0 = all_54_12) &  ~ (all_54_1 = all_54_2) &  ~ (all_54_1 =
% 168.46/25.05  |            all_54_3) &  ~ (all_54_1 = all_54_5) &  ~ (all_54_1 = all_54_9) & 
% 168.46/25.05  |          ~ (all_54_1 = all_54_13) &  ~ (all_54_2 = all_54_3) &  ~ (all_54_2 =
% 168.46/25.05  |            all_54_6) &  ~ (all_54_2 = all_54_10) &  ~ (all_54_2 = all_54_14) &
% 168.46/25.05  |           ~ (all_54_3 = all_54_7) &  ~ (all_54_3 = all_54_11) &  ~ (all_54_3 =
% 168.46/25.05  |            all_54_15) &  ~ (all_54_4 = all_54_5) &  ~ (all_54_4 = all_54_6) & 
% 168.46/25.05  |          ~ (all_54_4 = all_54_7) &  ~ (all_54_4 = all_54_8) &  ~ (all_54_4 =
% 168.46/25.05  |            all_54_12) &  ~ (all_54_5 = all_54_6) &  ~ (all_54_5 = all_54_7) & 
% 168.46/25.05  |          ~ (all_54_5 = all_54_9) &  ~ (all_54_5 = all_54_13) &  ~ (all_54_6 =
% 168.46/25.05  |            all_54_7) &  ~ (all_54_6 = all_54_10) &  ~ (all_54_6 = all_54_14) &
% 168.46/25.05  |           ~ (all_54_7 = all_54_11) &  ~ (all_54_7 = all_54_15) &  ~ (all_54_8
% 168.46/25.05  |            = all_54_9) &  ~ (all_54_8 = all_54_10) &  ~ (all_54_8 = all_54_11)
% 168.46/25.05  |          &  ~ (all_54_8 = all_54_12) &  ~ (all_54_9 = all_54_10) &  ~
% 168.46/25.05  |          (all_54_9 = all_54_11) &  ~ (all_54_9 = all_54_13) &  ~ (all_54_10 =
% 168.46/25.05  |            all_54_11) &  ~ (all_54_10 = all_54_14) &  ~ (all_54_11 =
% 168.46/25.05  |            all_54_15) &  ~ (all_54_12 = all_54_13) &  ~ (all_54_12 =
% 168.46/25.05  |            all_54_14) &  ~ (all_54_12 = all_54_15) &  ~ (all_54_13 =
% 168.46/25.05  |            all_54_14) &  ~ (all_54_13 = all_54_15) &  ~ (all_54_14 =
% 168.46/25.05  |            all_54_15) & op(e3, e3) = all_54_0 & op(e3, e2) = all_54_4 & op(e3,
% 168.46/25.05  |            e1) = all_54_8 & op(e3, e0) = all_54_12 & op(e2, e3) = all_54_1 &
% 168.46/25.05  |          op(e2, e2) = all_54_5 & op(e2, e1) = all_54_9 & op(e2, e0) =
% 168.46/25.05  |          all_54_13 & op(e1, e3) = all_54_2 & op(e1, e2) = all_54_6 & op(e1,
% 168.46/25.05  |            e1) = all_54_10 & op(e1, e0) = all_54_14 & op(e0, e3) = all_54_3 &
% 168.46/25.05  |          op(e0, e2) = all_54_7 & op(e0, e1) = all_54_11 & op(e0, e0) =
% 168.46/25.05  |          all_54_15 & $i(all_54_0) & $i(all_54_1) & $i(all_54_2) & $i(all_54_3)
% 168.46/25.05  |          & $i(all_54_4) & $i(all_54_5) & $i(all_54_6) & $i(all_54_7) &
% 168.46/25.05  |          $i(all_54_8) & $i(all_54_9) & $i(all_54_10) & $i(all_54_11) &
% 168.46/25.05  |          $i(all_54_12) & $i(all_54_13) & $i(all_54_14) & $i(all_54_15)
% 168.46/25.05  | 
% 168.46/25.05  | ALPHA: (186) implies:
% 168.46/25.05  |   (187)   ~ (all_54_14 = all_54_15)
% 168.46/25.05  |   (188)   ~ (all_54_13 = all_54_15)
% 168.46/25.05  |   (189)   ~ (all_54_13 = all_54_14)
% 168.46/25.05  |   (190)   ~ (all_54_12 = all_54_15)
% 168.46/25.05  |   (191)   ~ (all_54_12 = all_54_14)
% 168.46/25.05  |   (192)   ~ (all_54_12 = all_54_13)
% 168.46/25.05  |   (193)   ~ (all_54_11 = all_54_15)
% 168.46/25.05  |   (194)   ~ (all_54_10 = all_54_14)
% 168.46/25.06  |   (195)   ~ (all_54_10 = all_54_11)
% 168.46/25.06  |   (196)   ~ (all_54_9 = all_54_13)
% 168.46/25.06  |   (197)   ~ (all_54_9 = all_54_11)
% 168.46/25.06  |   (198)   ~ (all_54_9 = all_54_10)
% 168.46/25.06  |   (199)   ~ (all_54_8 = all_54_12)
% 168.46/25.06  |   (200)   ~ (all_54_8 = all_54_11)
% 168.46/25.06  |   (201)   ~ (all_54_8 = all_54_10)
% 168.46/25.06  |   (202)   ~ (all_54_8 = all_54_9)
% 168.46/25.06  |   (203)   ~ (all_54_7 = all_54_15)
% 168.46/25.06  |   (204)   ~ (all_54_7 = all_54_11)
% 168.46/25.06  |   (205)   ~ (all_54_6 = all_54_14)
% 168.46/25.06  |   (206)   ~ (all_54_6 = all_54_10)
% 168.46/25.06  |   (207)   ~ (all_54_6 = all_54_7)
% 168.46/25.06  |   (208)   ~ (all_54_5 = all_54_13)
% 168.46/25.06  |   (209)   ~ (all_54_5 = all_54_9)
% 168.46/25.06  |   (210)   ~ (all_54_5 = all_54_7)
% 168.46/25.06  |   (211)   ~ (all_54_5 = all_54_6)
% 168.46/25.06  |   (212)   ~ (all_54_4 = all_54_12)
% 168.46/25.06  |   (213)   ~ (all_54_4 = all_54_8)
% 168.46/25.06  |   (214)   ~ (all_54_4 = all_54_7)
% 168.46/25.06  |   (215)   ~ (all_54_4 = all_54_6)
% 168.46/25.06  |   (216)   ~ (all_54_4 = all_54_5)
% 168.46/25.06  |   (217)   ~ (all_54_3 = all_54_15)
% 168.46/25.06  |   (218)   ~ (all_54_3 = all_54_11)
% 168.46/25.06  |   (219)   ~ (all_54_3 = all_54_7)
% 168.46/25.06  |   (220)   ~ (all_54_2 = all_54_14)
% 168.46/25.06  |   (221)   ~ (all_54_2 = all_54_10)
% 168.46/25.06  |   (222)   ~ (all_54_2 = all_54_6)
% 168.46/25.06  |   (223)   ~ (all_54_2 = all_54_3)
% 168.46/25.06  |   (224)   ~ (all_54_1 = all_54_13)
% 168.46/25.06  |   (225)   ~ (all_54_1 = all_54_9)
% 168.46/25.06  |   (226)   ~ (all_54_1 = all_54_5)
% 168.46/25.06  |   (227)   ~ (all_54_1 = all_54_3)
% 168.46/25.06  |   (228)   ~ (all_54_1 = all_54_2)
% 168.46/25.06  |   (229)   ~ (all_54_0 = all_54_12)
% 168.46/25.06  |   (230)   ~ (all_54_0 = all_54_8)
% 168.46/25.06  |   (231)   ~ (all_54_0 = all_54_4)
% 168.46/25.06  |   (232)   ~ (all_54_0 = all_54_3)
% 168.46/25.06  |   (233)   ~ (all_54_0 = all_54_2)
% 168.46/25.06  |   (234)   ~ (all_54_0 = all_54_1)
% 168.46/25.06  |   (235)  op(e0, e0) = all_54_15
% 168.46/25.06  |   (236)  op(e0, e1) = all_54_11
% 168.46/25.06  |   (237)  op(e0, e2) = all_54_7
% 168.46/25.06  |   (238)  op(e0, e3) = all_54_3
% 168.46/25.06  |   (239)  op(e1, e0) = all_54_14
% 168.46/25.06  |   (240)  op(e1, e1) = all_54_10
% 168.46/25.06  |   (241)  op(e1, e2) = all_54_6
% 168.46/25.06  |   (242)  op(e1, e3) = all_54_2
% 168.46/25.06  |   (243)  op(e2, e0) = all_54_13
% 168.46/25.06  |   (244)  op(e2, e1) = all_54_9
% 168.46/25.06  |   (245)  op(e2, e2) = all_54_5
% 168.46/25.06  |   (246)  op(e2, e3) = all_54_1
% 168.46/25.06  |   (247)  op(e3, e0) = all_54_12
% 168.46/25.06  |   (248)  op(e3, e1) = all_54_8
% 168.46/25.06  |   (249)  op(e3, e2) = all_54_4
% 168.46/25.06  |   (250)  op(e3, e3) = all_54_0
% 168.46/25.06  | 
% 168.46/25.06  | DELTA: instantiating (1) with fresh symbols all_56_0, all_56_1, all_56_2,
% 168.46/25.06  |        all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 168.46/25.06  |        all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 168.46/25.06  |   (251)  op(e3, e3) = all_56_0 & op(e3, e2) = all_56_1 & op(e3, e1) = all_56_2
% 168.46/25.06  |          & op(e3, e0) = all_56_3 & op(e2, e3) = all_56_4 & op(e2, e2) =
% 168.46/25.06  |          all_56_5 & op(e2, e1) = all_56_6 & op(e2, e0) = all_56_7 & op(e1, e3)
% 168.46/25.06  |          = all_56_8 & op(e1, e2) = all_56_9 & op(e1, e1) = all_56_10 & op(e1,
% 168.46/25.06  |            e0) = all_56_11 & op(e0, e3) = all_56_12 & op(e0, e2) = all_56_13 &
% 168.46/25.06  |          op(e0, e1) = all_56_14 & op(e0, e0) = all_56_15 & $i(all_56_0) &
% 168.46/25.06  |          $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) &
% 168.46/25.06  |          $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & $i(all_56_8) &
% 168.46/25.06  |          $i(all_56_9) & $i(all_56_10) & $i(all_56_11) & $i(all_56_12) &
% 168.46/25.06  |          $i(all_56_13) & $i(all_56_14) & $i(all_56_15) & (all_56_0 = e3 |
% 168.46/25.06  |            all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0) & (all_56_1 = e3 |
% 168.46/25.06  |            all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0) & (all_56_2 = e3 |
% 168.46/25.06  |            all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0) & (all_56_3 = e3 |
% 168.46/25.06  |            all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0) & (all_56_4 = e3 |
% 168.46/25.06  |            all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0) & (all_56_5 = e3 |
% 168.46/25.06  |            all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0) & (all_56_6 = e3 |
% 168.46/25.06  |            all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0) & (all_56_7 = e3 |
% 168.46/25.06  |            all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0) & (all_56_8 = e3 |
% 168.46/25.06  |            all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0) & (all_56_9 = e3 |
% 168.46/25.06  |            all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0) & (all_56_10 = e3 |
% 168.46/25.06  |            all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0) & (all_56_11 = e3
% 168.46/25.06  |            | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0) & (all_56_12 =
% 168.46/25.06  |            e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0) & (all_56_13
% 168.46/25.06  |            = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0) &
% 168.46/25.06  |          (all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0) &
% 168.46/25.06  |          (all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0)
% 168.46/25.06  | 
% 168.46/25.06  | ALPHA: (251) implies:
% 168.46/25.06  |   (252)  op(e0, e0) = all_56_15
% 168.46/25.06  |   (253)  op(e0, e1) = all_56_14
% 168.46/25.06  |   (254)  op(e0, e2) = all_56_13
% 168.46/25.06  |   (255)  op(e0, e3) = all_56_12
% 168.46/25.06  |   (256)  op(e1, e0) = all_56_11
% 168.46/25.06  |   (257)  op(e1, e1) = all_56_10
% 168.46/25.06  |   (258)  op(e1, e2) = all_56_9
% 168.46/25.06  |   (259)  op(e1, e3) = all_56_8
% 168.46/25.06  |   (260)  op(e2, e0) = all_56_7
% 168.46/25.06  |   (261)  op(e2, e1) = all_56_6
% 168.46/25.06  |   (262)  op(e2, e2) = all_56_5
% 168.46/25.06  |   (263)  op(e2, e3) = all_56_4
% 168.46/25.06  |   (264)  op(e3, e0) = all_56_3
% 168.46/25.06  |   (265)  op(e3, e1) = all_56_2
% 168.46/25.06  |   (266)  op(e3, e2) = all_56_1
% 168.46/25.06  |   (267)  op(e3, e3) = all_56_0
% 168.46/25.06  |   (268)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 168.46/25.06  |   (269)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 168.46/25.07  |   (270)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 168.46/25.07  |   (271)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 168.46/25.07  |   (272)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 168.46/25.07  |   (273)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 168.46/25.07  |   (274)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 168.46/25.07  |   (275)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 168.46/25.07  |   (276)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 168.46/25.07  |   (277)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 168.46/25.07  |   (278)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 168.46/25.07  |   (279)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 168.46/25.07  |   (280)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 168.46/25.07  |   (281)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 168.46/25.07  |   (282)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 168.46/25.07  |   (283)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 168.46/25.07  | 
% 168.46/25.07  | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2,
% 168.46/25.07  |        all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 168.46/25.07  |        all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives:
% 168.46/25.07  |   (284)  op(e3, e3) = all_58_0 & op(e3, e2) = all_58_1 & op(e3, e1) = all_58_4
% 168.46/25.07  |          & op(e3, e0) = all_58_9 & op(e2, e3) = all_58_2 & op(e2, e2) =
% 168.46/25.07  |          all_58_3 & op(e2, e1) = all_58_5 & op(e2, e0) = all_58_10 & op(e1,
% 168.46/25.07  |            e3) = all_58_6 & op(e1, e2) = all_58_7 & op(e1, e1) = all_58_8 &
% 168.46/25.07  |          op(e1, e0) = all_58_11 & op(e0, e3) = all_58_12 & op(e0, e2) =
% 168.46/25.07  |          all_58_13 & op(e0, e1) = all_58_14 & op(e0, e0) = all_58_15 &
% 168.46/25.07  |          $i(all_58_0) & $i(all_58_1) & $i(all_58_2) & $i(all_58_3) &
% 168.46/25.07  |          $i(all_58_4) & $i(all_58_5) & $i(all_58_6) & $i(all_58_7) &
% 168.46/25.07  |          $i(all_58_8) & $i(all_58_9) & $i(all_58_10) & $i(all_58_11) &
% 168.46/25.07  |          $i(all_58_12) & $i(all_58_13) & $i(all_58_14) & $i(all_58_15) &
% 168.46/25.07  |          (all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3) &
% 168.46/25.07  |          (all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3) &
% 168.46/25.07  |          (all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2) &
% 168.46/25.07  |          (all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2) &
% 168.46/25.07  |          (all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1) &
% 168.46/25.07  |          (all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1) &
% 168.46/25.07  |          (all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0) &
% 168.46/25.07  |          (all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0) &
% 168.46/25.07  |          (all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3) &
% 168.46/25.07  |          (all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2) &
% 168.46/25.07  |          (all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1) &
% 168.46/25.07  |          (all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0) &
% 168.46/25.07  |          (all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3) &
% 168.46/25.07  |          (all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2) &
% 168.46/25.07  |          (all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1) &
% 168.46/25.07  |          (all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0) &
% 168.46/25.07  |          (all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3) &
% 168.46/25.07  |          (all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2) &
% 168.46/25.07  |          (all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1) &
% 168.46/25.07  |          (all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0) &
% 168.46/25.07  |          (all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3) &
% 168.46/25.07  |          (all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2) &
% 168.46/25.07  |          (all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1) &
% 168.46/25.07  |          (all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0) &
% 168.46/25.07  |          (all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3) &
% 168.46/25.07  |          (all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2) &
% 168.46/25.07  |          (all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1) &
% 168.46/25.07  |          (all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3) &
% 168.46/25.07  |          (all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2) &
% 168.46/25.07  |          (all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1) &
% 168.46/25.07  |          (all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 168.46/25.07  |              & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)))
% 168.46/25.07  | 
% 168.46/25.07  | ALPHA: (284) implies:
% 168.46/25.07  |   (285)  op(e0, e0) = all_58_15
% 168.46/25.07  |   (286)  op(e0, e1) = all_58_14
% 168.46/25.07  |   (287)  op(e0, e2) = all_58_13
% 168.46/25.07  |   (288)  op(e0, e3) = all_58_12
% 168.46/25.07  |   (289)  op(e1, e0) = all_58_11
% 168.46/25.07  |   (290)  op(e1, e1) = all_58_8
% 168.46/25.07  |   (291)  op(e1, e2) = all_58_7
% 168.46/25.07  |   (292)  op(e1, e3) = all_58_6
% 168.46/25.07  |   (293)  op(e2, e0) = all_58_10
% 168.46/25.07  |   (294)  op(e2, e1) = all_58_5
% 168.46/25.07  |   (295)  op(e2, e2) = all_58_3
% 168.46/25.07  |   (296)  op(e2, e3) = all_58_2
% 168.46/25.07  |   (297)  op(e3, e0) = all_58_9
% 168.46/25.07  |   (298)  op(e3, e1) = all_58_4
% 168.46/25.07  |   (299)  op(e3, e2) = all_58_1
% 168.46/25.07  |   (300)  op(e3, e3) = all_58_0
% 168.46/25.07  |   (301)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 168.46/25.07  |            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 168.46/25.08  |   (302)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 168.46/25.08  |   (303)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 168.46/25.08  |   (304)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 168.46/25.08  |   (305)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 168.46/25.08  |   (306)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 168.46/25.08  |   (307)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 168.46/25.08  |   (308)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 168.46/25.08  |   (309)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 168.46/25.08  |   (310)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 168.46/25.08  |   (311)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 168.46/25.08  |   (312)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 168.46/25.08  |   (313)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 168.46/25.08  |   (314)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 168.46/25.08  |   (315)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 168.46/25.08  |   (316)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 168.46/25.08  |   (317)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 168.46/25.08  |   (318)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 168.46/25.08  |   (319)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 168.46/25.08  |   (320)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 168.46/25.08  |   (321)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 168.46/25.08  |   (322)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 168.46/25.08  |   (323)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 168.46/25.08  |   (324)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 168.46/25.08  |   (325)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 168.46/25.08  |   (326)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 168.46/25.08  |   (327)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 168.46/25.08  |   (328)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 168.46/25.08  |   (329)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 168.46/25.08  |   (330)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 168.46/25.08  |   (331)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_28_2, all_36_2, e0, e0,
% 168.46/25.08  |              simplifying with (95), (115) gives:
% 168.46/25.08  |   (332)  all_36_2 = all_28_2
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_6_2, all_36_2, e0, e0,
% 168.46/25.08  |              simplifying with (41), (115) gives:
% 168.46/25.08  |   (333)  all_36_2 = all_6_2
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_28_2, all_38_2, e0, e0,
% 168.46/25.08  |              simplifying with (95), (120) gives:
% 168.46/25.08  |   (334)  all_38_2 = all_28_2
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_52_31, all_54_15, e0,
% 168.46/25.08  |              e0, simplifying with (153), (235) gives:
% 168.46/25.08  |   (335)  all_54_15 = all_52_31
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_38_2, all_54_15, e0, e0,
% 168.46/25.08  |              simplifying with (120), (235) gives:
% 168.46/25.08  |   (336)  all_54_15 = all_38_2
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_36_2, all_56_15, e0, e0,
% 168.46/25.08  |              simplifying with (115), (252) gives:
% 168.46/25.08  |   (337)  all_56_15 = all_36_2
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_16_2, all_56_15, e0, e0,
% 168.46/25.08  |              simplifying with (66), (252) gives:
% 168.46/25.08  |   (338)  all_56_15 = all_16_2
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_54_15, all_58_15, e0,
% 168.46/25.08  |              e0, simplifying with (235), (285) gives:
% 168.46/25.08  |   (339)  all_58_15 = all_54_15
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_8_2, all_58_15, e0, e0,
% 168.46/25.08  |              simplifying with (46), (285) gives:
% 168.46/25.08  |   (340)  all_58_15 = all_8_2
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_52_29, all_56_14, e1,
% 168.46/25.08  |              e0, simplifying with (154), (253) gives:
% 168.46/25.08  |   (341)  all_56_14 = all_52_29
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_56_14, all_58_14, e1,
% 168.46/25.08  |              e0, simplifying with (253), (286) gives:
% 168.46/25.08  |   (342)  all_58_14 = all_56_14
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_54_11, all_58_14, e1,
% 168.46/25.08  |              e0, simplifying with (236), (286) gives:
% 168.46/25.08  |   (343)  all_58_14 = all_54_11
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_52_27, all_56_13, e2,
% 168.46/25.08  |              e0, simplifying with (155), (254) gives:
% 168.46/25.08  |   (344)  all_56_13 = all_52_27
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_56_13, all_58_13, e2,
% 168.46/25.08  |              e0, simplifying with (254), (287) gives:
% 168.46/25.08  |   (345)  all_58_13 = all_56_13
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_54_7, all_58_13, e2, e0,
% 168.46/25.08  |              simplifying with (237), (287) gives:
% 168.46/25.08  |   (346)  all_58_13 = all_54_7
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_54_3, all_56_12, e3, e0,
% 168.46/25.08  |              simplifying with (238), (255) gives:
% 168.46/25.08  |   (347)  all_56_12 = all_54_3
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_56_12, all_58_12, e3,
% 168.46/25.08  |              e0, simplifying with (255), (288) gives:
% 168.46/25.08  |   (348)  all_58_12 = all_56_12
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_52_25, all_58_12, e3,
% 168.46/25.08  |              e0, simplifying with (156), (288) gives:
% 168.46/25.08  |   (349)  all_58_12 = all_52_25
% 168.46/25.08  | 
% 168.46/25.08  | GROUND_INST: instantiating (function-axioms) with all_52_23, all_56_11, e0,
% 168.46/25.08  |              e1, simplifying with (161), (256) gives:
% 168.46/25.09  |   (350)  all_56_11 = all_52_23
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_11, all_58_11, e0,
% 168.46/25.09  |              e1, simplifying with (256), (289) gives:
% 168.46/25.09  |   (351)  all_58_11 = all_56_11
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_14, all_58_11, e0,
% 168.46/25.09  |              e1, simplifying with (239), (289) gives:
% 168.46/25.09  |   (352)  all_58_11 = all_54_14
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_32_2, e1, e1,
% 168.46/25.09  |              simplifying with (80), (105) gives:
% 168.46/25.09  |   (353)  all_32_2 = all_22_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_32_2, all_44_2, e1, e1,
% 168.46/25.09  |              simplifying with (105), (135) gives:
% 168.46/25.09  |   (354)  all_44_2 = all_32_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_52_21, e1, e1,
% 168.46/25.09  |              simplifying with (80), (162) gives:
% 168.46/25.09  |   (355)  all_52_21 = all_22_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_54_10, e1, e1,
% 168.46/25.09  |              simplifying with (80), (240) gives:
% 168.46/25.09  |   (356)  all_54_10 = all_22_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_18_2, all_54_10, e1, e1,
% 168.46/25.09  |              simplifying with (71), (240) gives:
% 168.46/25.09  |   (357)  all_54_10 = all_18_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_44_2, all_56_10, e1, e1,
% 168.46/25.09  |              simplifying with (135), (257) gives:
% 168.46/25.09  |   (358)  all_56_10 = all_44_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_14_2, all_56_10, e1, e1,
% 168.46/25.09  |              simplifying with (61), (257) gives:
% 168.46/25.09  |   (359)  all_56_10 = all_14_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_21, all_58_8, e1, e1,
% 168.46/25.09  |              simplifying with (162), (290) gives:
% 168.46/25.09  |   (360)  all_58_8 = all_52_21
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_58_8, e1, e1,
% 168.46/25.09  |              simplifying with (76), (290) gives:
% 168.46/25.09  |   (361)  all_58_8 = all_20_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_6, all_56_9, e2, e1,
% 168.46/25.09  |              simplifying with (241), (258) gives:
% 168.46/25.09  |   (362)  all_56_9 = all_54_6
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_9, all_58_7, e2, e1,
% 168.46/25.09  |              simplifying with (258), (291) gives:
% 168.46/25.09  |   (363)  all_58_7 = all_56_9
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_19, all_58_7, e2, e1,
% 168.46/25.09  |              simplifying with (163), (291) gives:
% 168.46/25.09  |   (364)  all_58_7 = all_52_19
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_17, all_56_8, e3, e1,
% 168.46/25.09  |              simplifying with (164), (259) gives:
% 168.46/25.09  |   (365)  all_56_8 = all_52_17
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_8, all_58_6, e3, e1,
% 168.46/25.09  |              simplifying with (259), (292) gives:
% 168.46/25.09  |   (366)  all_58_6 = all_56_8
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_2, all_58_6, e3, e1,
% 168.46/25.09  |              simplifying with (242), (292) gives:
% 168.46/25.09  |   (367)  all_58_6 = all_54_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_13, all_56_7, e0, e2,
% 168.46/25.09  |              simplifying with (243), (260) gives:
% 168.46/25.09  |   (368)  all_56_7 = all_54_13
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_7, all_58_10, e0, e2,
% 168.46/25.09  |              simplifying with (260), (293) gives:
% 168.46/25.09  |   (369)  all_58_10 = all_56_7
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_15, all_58_10, e0,
% 168.46/25.09  |              e2, simplifying with (169), (293) gives:
% 168.46/25.09  |   (370)  all_58_10 = all_52_15
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_9, all_56_6, e1, e2,
% 168.46/25.09  |              simplifying with (244), (261) gives:
% 168.46/25.09  |   (371)  all_56_6 = all_54_9
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_6, all_58_5, e1, e2,
% 168.46/25.09  |              simplifying with (261), (294) gives:
% 168.46/25.09  |   (372)  all_58_5 = all_56_6
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_13, all_58_5, e1, e2,
% 168.46/25.09  |              simplifying with (170), (294) gives:
% 168.46/25.09  |   (373)  all_58_5 = all_52_13
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_30_2, e2, e2,
% 168.46/25.09  |              simplifying with (56), (100) gives:
% 168.46/25.09  |   (374)  all_30_2 = all_12_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_10_2, all_30_2, e2, e2,
% 168.46/25.09  |              simplifying with (51), (100) gives:
% 168.46/25.09  |   (375)  all_30_2 = all_10_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_30_2, all_52_11, e2, e2,
% 168.46/25.09  |              simplifying with (100), (171) gives:
% 168.46/25.09  |   (376)  all_52_11 = all_30_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_5, e2, e2,
% 168.46/25.09  |              simplifying with (171), (245) gives:
% 168.46/25.09  |   (377)  all_54_5 = all_52_11
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_24_2, all_54_5, e2, e2,
% 168.46/25.09  |              simplifying with (85), (245) gives:
% 168.46/25.09  |   (378)  all_54_5 = all_24_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_11, all_56_5, e2, e2,
% 168.46/25.09  |              simplifying with (171), (262) gives:
% 168.46/25.09  |   (379)  all_56_5 = all_52_11
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_46_2, all_56_5, e2, e2,
% 168.46/25.09  |              simplifying with (139), (262) gives:
% 168.46/25.09  |   (380)  all_56_5 = all_46_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_5, all_58_3, e2, e2,
% 168.46/25.09  |              simplifying with (245), (295) gives:
% 168.46/25.09  |   (381)  all_58_3 = all_54_5
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_48_2, all_58_3, e2, e2,
% 168.46/25.09  |              simplifying with (144), (295) gives:
% 168.46/25.09  |   (382)  all_58_3 = all_48_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_1, all_56_4, e3, e2,
% 168.46/25.09  |              simplifying with (246), (263) gives:
% 168.46/25.09  |   (383)  all_56_4 = all_54_1
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_4, all_58_2, e3, e2,
% 168.46/25.09  |              simplifying with (263), (296) gives:
% 168.46/25.09  |   (384)  all_58_2 = all_56_4
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_9, all_58_2, e3, e2,
% 168.46/25.09  |              simplifying with (172), (296) gives:
% 168.46/25.09  |   (385)  all_58_2 = all_52_9
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_7, all_56_3, e0, e3,
% 168.46/25.09  |              simplifying with (177), (264) gives:
% 168.46/25.09  |   (386)  all_56_3 = all_52_7
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_3, all_58_9, e0, e3,
% 168.46/25.09  |              simplifying with (264), (297) gives:
% 168.46/25.09  |   (387)  all_58_9 = all_56_3
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_12, all_58_9, e0, e3,
% 168.46/25.09  |              simplifying with (247), (297) gives:
% 168.46/25.09  |   (388)  all_58_9 = all_54_12
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_8, all_56_2, e1, e3,
% 168.46/25.09  |              simplifying with (248), (265) gives:
% 168.46/25.09  |   (389)  all_56_2 = all_54_8
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_2, all_58_4, e1, e3,
% 168.46/25.09  |              simplifying with (265), (298) gives:
% 168.46/25.09  |   (390)  all_58_4 = all_56_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_5, all_58_4, e1, e3,
% 168.46/25.09  |              simplifying with (178), (298) gives:
% 168.46/25.09  |   (391)  all_58_4 = all_52_5
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_52_3, all_56_1, e2, e3,
% 168.46/25.09  |              simplifying with (179), (266) gives:
% 168.46/25.09  |   (392)  all_56_1 = all_52_3
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_56_1, all_58_1, e2, e3,
% 168.46/25.09  |              simplifying with (266), (299) gives:
% 168.46/25.09  |   (393)  all_58_1 = all_56_1
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_54_4, all_58_1, e2, e3,
% 168.46/25.09  |              simplifying with (249), (299) gives:
% 168.46/25.09  |   (394)  all_58_1 = all_54_4
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_40_2, e3, e3,
% 168.46/25.09  |              simplifying with (110), (125) gives:
% 168.46/25.09  |   (395)  all_40_2 = all_34_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_42_2, e3, e3,
% 168.46/25.09  |              simplifying with (110), (130) gives:
% 168.46/25.09  |   (396)  all_42_2 = all_34_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_40_2, all_50_2, e3, e3,
% 168.46/25.09  |              simplifying with (125), (148) gives:
% 168.46/25.09  |   (397)  all_50_2 = all_40_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_42_2, all_52_1, e3, e3,
% 168.46/25.09  |              simplifying with (130), (180) gives:
% 168.46/25.09  |   (398)  all_52_1 = all_42_2
% 168.46/25.09  | 
% 168.46/25.09  | GROUND_INST: instantiating (function-axioms) with all_50_2, all_54_0, e3, e3,
% 168.46/25.09  |              simplifying with (148), (250) gives:
% 168.46/25.10  |   (399)  all_54_0 = all_50_2
% 168.46/25.10  | 
% 168.46/25.10  | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_0, e3, e3,
% 168.46/25.10  |              simplifying with (250), (267) gives:
% 168.46/25.10  |   (400)  all_56_0 = all_54_0
% 168.46/25.10  | 
% 168.46/25.10  | GROUND_INST: instantiating (function-axioms) with all_26_2, all_56_0, e3, e3,
% 168.46/25.10  |              simplifying with (90), (267) gives:
% 168.46/25.10  |   (401)  all_56_0 = all_26_2
% 168.46/25.10  | 
% 168.46/25.10  | GROUND_INST: instantiating (function-axioms) with all_52_1, all_58_0, e3, e3,
% 168.46/25.10  |              simplifying with (180), (300) gives:
% 168.46/25.10  |   (402)  all_58_0 = all_52_1
% 168.46/25.10  | 
% 168.46/25.10  | GROUND_INST: instantiating (function-axioms) with all_4_2, all_58_0, e3, e3,
% 168.46/25.10  |              simplifying with (36), (300) gives:
% 168.46/25.10  |   (403)  all_58_0 = all_4_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (402), (403) imply:
% 168.46/25.10  |   (404)  all_52_1 = all_4_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (404) implies:
% 168.46/25.10  |   (405)  all_52_1 = all_4_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (393), (394) imply:
% 168.46/25.10  |   (406)  all_56_1 = all_54_4
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (406) implies:
% 168.46/25.10  |   (407)  all_56_1 = all_54_4
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (384), (385) imply:
% 168.46/25.10  |   (408)  all_56_4 = all_52_9
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (408) implies:
% 168.46/25.10  |   (409)  all_56_4 = all_52_9
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (381), (382) imply:
% 168.46/25.10  |   (410)  all_54_5 = all_48_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (410) implies:
% 168.46/25.10  |   (411)  all_54_5 = all_48_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (390), (391) imply:
% 168.46/25.10  |   (412)  all_56_2 = all_52_5
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (412) implies:
% 168.46/25.10  |   (413)  all_56_2 = all_52_5
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (372), (373) imply:
% 168.46/25.10  |   (414)  all_56_6 = all_52_13
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (414) implies:
% 168.46/25.10  |   (415)  all_56_6 = all_52_13
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (366), (367) imply:
% 168.46/25.10  |   (416)  all_56_8 = all_54_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (416) implies:
% 168.46/25.10  |   (417)  all_56_8 = all_54_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (363), (364) imply:
% 168.46/25.10  |   (418)  all_56_9 = all_52_19
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (418) implies:
% 168.46/25.10  |   (419)  all_56_9 = all_52_19
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (360), (361) imply:
% 168.46/25.10  |   (420)  all_52_21 = all_20_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (420) implies:
% 168.46/25.10  |   (421)  all_52_21 = all_20_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (387), (388) imply:
% 168.46/25.10  |   (422)  all_56_3 = all_54_12
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (422) implies:
% 168.46/25.10  |   (423)  all_56_3 = all_54_12
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (369), (370) imply:
% 168.46/25.10  |   (424)  all_56_7 = all_52_15
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (424) implies:
% 168.46/25.10  |   (425)  all_56_7 = all_52_15
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (351), (352) imply:
% 168.46/25.10  |   (426)  all_56_11 = all_54_14
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (426) implies:
% 168.46/25.10  |   (427)  all_56_11 = all_54_14
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (348), (349) imply:
% 168.46/25.10  |   (428)  all_56_12 = all_52_25
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (428) implies:
% 168.46/25.10  |   (429)  all_56_12 = all_52_25
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (345), (346) imply:
% 168.46/25.10  |   (430)  all_56_13 = all_54_7
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (430) implies:
% 168.46/25.10  |   (431)  all_56_13 = all_54_7
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (342), (343) imply:
% 168.46/25.10  |   (432)  all_56_14 = all_54_11
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (432) implies:
% 168.46/25.10  |   (433)  all_56_14 = all_54_11
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (339), (340) imply:
% 168.46/25.10  |   (434)  all_54_15 = all_8_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (434) implies:
% 168.46/25.10  |   (435)  all_54_15 = all_8_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (400), (401) imply:
% 168.46/25.10  |   (436)  all_54_0 = all_26_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (436) implies:
% 168.46/25.10  |   (437)  all_54_0 = all_26_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (392), (407) imply:
% 168.46/25.10  |   (438)  all_54_4 = all_52_3
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (438) implies:
% 168.46/25.10  |   (439)  all_54_4 = all_52_3
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (389), (413) imply:
% 168.46/25.10  |   (440)  all_54_8 = all_52_5
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (440) implies:
% 168.46/25.10  |   (441)  all_54_8 = all_52_5
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (386), (423) imply:
% 168.46/25.10  |   (442)  all_54_12 = all_52_7
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (442) implies:
% 168.46/25.10  |   (443)  all_54_12 = all_52_7
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (383), (409) imply:
% 168.46/25.10  |   (444)  all_54_1 = all_52_9
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (444) implies:
% 168.46/25.10  |   (445)  all_54_1 = all_52_9
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (379), (380) imply:
% 168.46/25.10  |   (446)  all_52_11 = all_46_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (446) implies:
% 168.46/25.10  |   (447)  all_52_11 = all_46_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (371), (415) imply:
% 168.46/25.10  |   (448)  all_54_9 = all_52_13
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (448) implies:
% 168.46/25.10  |   (449)  all_54_9 = all_52_13
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (368), (425) imply:
% 168.46/25.10  |   (450)  all_54_13 = all_52_15
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (450) implies:
% 168.46/25.10  |   (451)  all_54_13 = all_52_15
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (365), (417) imply:
% 168.46/25.10  |   (452)  all_54_2 = all_52_17
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (452) implies:
% 168.46/25.10  |   (453)  all_54_2 = all_52_17
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (362), (419) imply:
% 168.46/25.10  |   (454)  all_54_6 = all_52_19
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (454) implies:
% 168.46/25.10  |   (455)  all_54_6 = all_52_19
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (358), (359) imply:
% 168.46/25.10  |   (456)  all_44_2 = all_14_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (456) implies:
% 168.46/25.10  |   (457)  all_44_2 = all_14_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (350), (427) imply:
% 168.46/25.10  |   (458)  all_54_14 = all_52_23
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (347), (429) imply:
% 168.46/25.10  |   (459)  all_54_3 = all_52_25
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (459) implies:
% 168.46/25.10  |   (460)  all_54_3 = all_52_25
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (344), (431) imply:
% 168.46/25.10  |   (461)  all_54_7 = all_52_27
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (461) implies:
% 168.46/25.10  |   (462)  all_54_7 = all_52_27
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (341), (433) imply:
% 168.46/25.10  |   (463)  all_54_11 = all_52_29
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (463) implies:
% 168.46/25.10  |   (464)  all_54_11 = all_52_29
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (337), (338) imply:
% 168.46/25.10  |   (465)  all_36_2 = all_16_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (465) implies:
% 168.46/25.10  |   (466)  all_36_2 = all_16_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (399), (437) imply:
% 168.46/25.10  |   (467)  all_50_2 = all_26_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (467) implies:
% 168.46/25.10  |   (468)  all_50_2 = all_26_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (378), (411) imply:
% 168.46/25.10  |   (469)  all_48_2 = all_24_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (377), (411) imply:
% 168.46/25.10  |   (470)  all_52_11 = all_48_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (470) implies:
% 168.46/25.10  |   (471)  all_52_11 = all_48_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (356), (357) imply:
% 168.46/25.10  |   (472)  all_22_2 = all_18_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (472) implies:
% 168.46/25.10  |   (473)  all_22_2 = all_18_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (335), (435) imply:
% 168.46/25.10  |   (474)  all_52_31 = all_8_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (335), (336) imply:
% 168.46/25.10  |   (475)  all_52_31 = all_38_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (398), (405) imply:
% 168.46/25.10  |   (476)  all_42_2 = all_4_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (476) implies:
% 168.46/25.10  |   (477)  all_42_2 = all_4_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (447), (471) imply:
% 168.46/25.10  |   (478)  all_48_2 = all_46_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (478) implies:
% 168.46/25.10  |   (479)  all_48_2 = all_46_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (376), (447) imply:
% 168.46/25.10  |   (480)  all_46_2 = all_30_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (355), (421) imply:
% 168.46/25.10  |   (481)  all_22_2 = all_20_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (481) implies:
% 168.46/25.10  |   (482)  all_22_2 = all_20_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (474), (475) imply:
% 168.46/25.10  |   (483)  all_38_2 = all_8_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (483) implies:
% 168.46/25.10  |   (484)  all_38_2 = all_8_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (397), (468) imply:
% 168.46/25.10  |   (485)  all_40_2 = all_26_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (485) implies:
% 168.46/25.10  |   (486)  all_40_2 = all_26_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (469), (479) imply:
% 168.46/25.10  |   (487)  all_46_2 = all_24_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (487) implies:
% 168.46/25.10  |   (488)  all_46_2 = all_24_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (480), (488) imply:
% 168.46/25.10  |   (489)  all_30_2 = all_24_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (489) implies:
% 168.46/25.10  |   (490)  all_30_2 = all_24_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (354), (457) imply:
% 168.46/25.10  |   (491)  all_32_2 = all_14_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (491) implies:
% 168.46/25.10  |   (492)  all_32_2 = all_14_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (396), (477) imply:
% 168.46/25.10  |   (493)  all_34_2 = all_4_2
% 168.46/25.10  | 
% 168.46/25.10  | SIMP: (493) implies:
% 168.46/25.10  |   (494)  all_34_2 = all_4_2
% 168.46/25.10  | 
% 168.46/25.10  | COMBINE_EQS: (395), (486) imply:
% 168.46/25.11  |   (495)  all_34_2 = all_26_2
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (495) implies:
% 168.46/25.11  |   (496)  all_34_2 = all_26_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (334), (484) imply:
% 168.46/25.11  |   (497)  all_28_2 = all_8_2
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (497) implies:
% 168.46/25.11  |   (498)  all_28_2 = all_8_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (332), (466) imply:
% 168.46/25.11  |   (499)  all_28_2 = all_16_2
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (499) implies:
% 168.46/25.11  |   (500)  all_28_2 = all_16_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (333), (466) imply:
% 168.46/25.11  |   (501)  all_16_2 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (494), (496) imply:
% 168.46/25.11  |   (502)  all_26_2 = all_4_2
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (502) implies:
% 168.46/25.11  |   (503)  all_26_2 = all_4_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (353), (492) imply:
% 168.46/25.11  |   (504)  all_22_2 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (504) implies:
% 168.46/25.11  |   (505)  all_22_2 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (374), (490) imply:
% 168.46/25.11  |   (506)  all_24_2 = all_12_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (375), (490) imply:
% 168.46/25.11  |   (507)  all_24_2 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (498), (500) imply:
% 168.46/25.11  |   (508)  all_16_2 = all_8_2
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (508) implies:
% 168.46/25.11  |   (509)  all_16_2 = all_8_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (506), (507) imply:
% 168.46/25.11  |   (510)  all_12_2 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (473), (482) imply:
% 168.46/25.11  |   (511)  all_20_2 = all_18_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (482), (505) imply:
% 168.46/25.11  |   (512)  all_20_2 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (511), (512) imply:
% 168.46/25.11  |   (513)  all_18_2 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (513) implies:
% 168.46/25.11  |   (514)  all_18_2 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (501), (509) imply:
% 168.46/25.11  |   (515)  all_8_2 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (498), (515) imply:
% 168.46/25.11  |   (516)  all_28_2 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (484), (515) imply:
% 168.46/25.11  |   (517)  all_38_2 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (486), (503) imply:
% 168.46/25.11  |   (518)  all_40_2 = all_4_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (488), (507) imply:
% 168.46/25.11  |   (519)  all_46_2 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (469), (507) imply:
% 168.46/25.11  |   (520)  all_48_2 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (468), (503) imply:
% 168.46/25.11  |   (521)  all_50_2 = all_4_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (474), (515) imply:
% 168.46/25.11  |   (522)  all_52_31 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (421), (512) imply:
% 168.46/25.11  |   (523)  all_52_21 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (447), (519) imply:
% 168.46/25.11  |   (524)  all_52_11 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (335), (522) imply:
% 168.46/25.11  |   (525)  all_54_15 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (357), (514) imply:
% 168.46/25.11  |   (526)  all_54_10 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (411), (520) imply:
% 168.46/25.11  |   (527)  all_54_5 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (437), (503) imply:
% 168.46/25.11  |   (528)  all_54_0 = all_4_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (338), (501) imply:
% 168.46/25.11  |   (529)  all_56_15 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (380), (519) imply:
% 168.46/25.11  |   (530)  all_56_5 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (401), (503) imply:
% 168.46/25.11  |   (531)  all_56_0 = all_4_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (340), (515) imply:
% 168.46/25.11  |   (532)  all_58_15 = all_6_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (343), (464) imply:
% 168.46/25.11  |   (533)  all_58_14 = all_52_29
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (346), (462) imply:
% 168.46/25.11  |   (534)  all_58_13 = all_52_27
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (352), (458) imply:
% 168.46/25.11  |   (535)  all_58_11 = all_52_23
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (388), (443) imply:
% 168.46/25.11  |   (536)  all_58_9 = all_52_7
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (361), (512) imply:
% 168.46/25.11  |   (537)  all_58_8 = all_14_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (367), (453) imply:
% 168.46/25.11  |   (538)  all_58_6 = all_52_17
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (382), (520) imply:
% 168.46/25.11  |   (539)  all_58_3 = all_10_2
% 168.46/25.11  | 
% 168.46/25.11  | COMBINE_EQS: (394), (439) imply:
% 168.46/25.11  |   (540)  all_58_1 = all_52_3
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (234), (445), (528) imply:
% 168.46/25.11  |   (541)   ~ (all_52_9 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (541) implies:
% 168.46/25.11  |   (542)   ~ (all_52_9 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (233), (453), (528) imply:
% 168.46/25.11  |   (543)   ~ (all_52_17 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (543) implies:
% 168.46/25.11  |   (544)   ~ (all_52_17 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (232), (460), (528) imply:
% 168.46/25.11  |   (545)   ~ (all_52_25 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (545) implies:
% 168.46/25.11  |   (546)   ~ (all_52_25 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (231), (439), (528) imply:
% 168.46/25.11  |   (547)   ~ (all_52_3 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (547) implies:
% 168.46/25.11  |   (548)   ~ (all_52_3 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (230), (441), (528) imply:
% 168.46/25.11  |   (549)   ~ (all_52_5 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (549) implies:
% 168.46/25.11  |   (550)   ~ (all_52_5 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (229), (443), (528) imply:
% 168.46/25.11  |   (551)   ~ (all_52_7 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (551) implies:
% 168.46/25.11  |   (552)   ~ (all_52_7 = all_4_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (228), (445), (453) imply:
% 168.46/25.11  |   (553)   ~ (all_52_9 = all_52_17)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (227), (445), (460) imply:
% 168.46/25.11  |   (554)   ~ (all_52_9 = all_52_25)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (226), (445), (527) imply:
% 168.46/25.11  |   (555)   ~ (all_52_9 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (225), (445), (449) imply:
% 168.46/25.11  |   (556)   ~ (all_52_9 = all_52_13)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (224), (445), (451) imply:
% 168.46/25.11  |   (557)   ~ (all_52_9 = all_52_15)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (223), (453), (460) imply:
% 168.46/25.11  |   (558)   ~ (all_52_17 = all_52_25)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (222), (453), (455) imply:
% 168.46/25.11  |   (559)   ~ (all_52_17 = all_52_19)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (221), (453), (526) imply:
% 168.46/25.11  |   (560)   ~ (all_52_17 = all_14_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (220), (453), (458) imply:
% 168.46/25.11  |   (561)   ~ (all_52_17 = all_52_23)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (219), (460), (462) imply:
% 168.46/25.11  |   (562)   ~ (all_52_25 = all_52_27)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (218), (460), (464) imply:
% 168.46/25.11  |   (563)   ~ (all_52_25 = all_52_29)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (217), (460), (525) imply:
% 168.46/25.11  |   (564)   ~ (all_52_25 = all_6_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (216), (439), (527) imply:
% 168.46/25.11  |   (565)   ~ (all_52_3 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (215), (439), (455) imply:
% 168.46/25.11  |   (566)   ~ (all_52_3 = all_52_19)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (214), (439), (462) imply:
% 168.46/25.11  |   (567)   ~ (all_52_3 = all_52_27)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (213), (439), (441) imply:
% 168.46/25.11  |   (568)   ~ (all_52_3 = all_52_5)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (212), (439), (443) imply:
% 168.46/25.11  |   (569)   ~ (all_52_3 = all_52_7)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (211), (455), (527) imply:
% 168.46/25.11  |   (570)   ~ (all_52_19 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (570) implies:
% 168.46/25.11  |   (571)   ~ (all_52_19 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (210), (462), (527) imply:
% 168.46/25.11  |   (572)   ~ (all_52_27 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (572) implies:
% 168.46/25.11  |   (573)   ~ (all_52_27 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (209), (449), (527) imply:
% 168.46/25.11  |   (574)   ~ (all_52_13 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (574) implies:
% 168.46/25.11  |   (575)   ~ (all_52_13 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (208), (451), (527) imply:
% 168.46/25.11  |   (576)   ~ (all_52_15 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | SIMP: (576) implies:
% 168.46/25.11  |   (577)   ~ (all_52_15 = all_10_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (207), (455), (462) imply:
% 168.46/25.11  |   (578)   ~ (all_52_19 = all_52_27)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (206), (455), (526) imply:
% 168.46/25.11  |   (579)   ~ (all_52_19 = all_14_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (205), (455), (458) imply:
% 168.46/25.11  |   (580)   ~ (all_52_19 = all_52_23)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (204), (462), (464) imply:
% 168.46/25.11  |   (581)   ~ (all_52_27 = all_52_29)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (203), (462), (525) imply:
% 168.46/25.11  |   (582)   ~ (all_52_27 = all_6_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (202), (441), (449) imply:
% 168.46/25.11  |   (583)   ~ (all_52_5 = all_52_13)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (201), (441), (526) imply:
% 168.46/25.11  |   (584)   ~ (all_52_5 = all_14_2)
% 168.46/25.11  | 
% 168.46/25.11  | REDUCE: (200), (441), (464) imply:
% 168.46/25.12  |   (585)   ~ (all_52_5 = all_52_29)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (199), (441), (443) imply:
% 168.46/25.12  |   (586)   ~ (all_52_5 = all_52_7)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (198), (449), (526) imply:
% 168.46/25.12  |   (587)   ~ (all_52_13 = all_14_2)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (197), (449), (464) imply:
% 168.46/25.12  |   (588)   ~ (all_52_13 = all_52_29)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (196), (449), (451) imply:
% 168.46/25.12  |   (589)   ~ (all_52_13 = all_52_15)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (195), (464), (526) imply:
% 168.46/25.12  |   (590)   ~ (all_52_29 = all_14_2)
% 168.46/25.12  | 
% 168.46/25.12  | SIMP: (590) implies:
% 168.46/25.12  |   (591)   ~ (all_52_29 = all_14_2)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (194), (458), (526) imply:
% 168.46/25.12  |   (592)   ~ (all_52_23 = all_14_2)
% 168.46/25.12  | 
% 168.46/25.12  | SIMP: (592) implies:
% 168.46/25.12  |   (593)   ~ (all_52_23 = all_14_2)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (193), (464), (525) imply:
% 168.46/25.12  |   (594)   ~ (all_52_29 = all_6_2)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (192), (443), (451) imply:
% 168.46/25.12  |   (595)   ~ (all_52_7 = all_52_15)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (191), (443), (458) imply:
% 168.46/25.12  |   (596)   ~ (all_52_7 = all_52_23)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (190), (443), (525) imply:
% 168.46/25.12  |   (597)   ~ (all_52_7 = all_6_2)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (189), (451), (458) imply:
% 168.46/25.12  |   (598)   ~ (all_52_15 = all_52_23)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (188), (451), (525) imply:
% 168.46/25.12  |   (599)   ~ (all_52_15 = all_6_2)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (187), (458), (525) imply:
% 168.46/25.12  |   (600)   ~ (all_52_23 = all_6_2)
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (150), (521) imply:
% 168.46/25.12  |   (601)  op(all_50_1, all_4_2) = all_50_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (146), (520) imply:
% 168.46/25.12  |   (602)  op(all_48_1, all_10_2) = all_48_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (141), (519) imply:
% 168.46/25.12  |   (603)  op(all_46_1, all_10_2) = all_46_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (137), (457) imply:
% 168.46/25.12  |   (604)  op(all_44_1, all_14_2) = all_44_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (132), (477) imply:
% 168.46/25.12  |   (605)  op(all_42_1, all_4_2) = all_42_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (127), (518) imply:
% 168.46/25.12  |   (606)  op(all_40_1, all_4_2) = all_40_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (122), (517) imply:
% 168.46/25.12  |   (607)  op(all_38_1, all_6_2) = all_38_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (117), (333) imply:
% 168.46/25.12  |   (608)  op(all_36_1, all_6_2) = all_36_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (112), (494) imply:
% 168.46/25.12  |   (609)  op(all_34_1, all_4_2) = all_34_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (107), (492) imply:
% 168.46/25.12  |   (610)  op(all_32_1, all_14_2) = all_32_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (102), (375) imply:
% 168.46/25.12  |   (611)  op(all_30_1, all_10_2) = all_30_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (97), (516) imply:
% 168.46/25.12  |   (612)  op(all_28_1, all_6_2) = all_28_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (92), (503) imply:
% 168.46/25.12  |   (613)  op(all_26_1, all_4_2) = all_26_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (87), (507) imply:
% 168.46/25.12  |   (614)  op(all_24_1, all_10_2) = all_24_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (82), (505) imply:
% 168.46/25.12  |   (615)  op(all_22_1, all_14_2) = all_22_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (78), (512) imply:
% 168.46/25.12  |   (616)  op(all_20_1, all_14_2) = all_20_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (73), (514) imply:
% 168.46/25.12  |   (617)  op(all_18_1, all_14_2) = all_18_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (68), (501) imply:
% 168.46/25.12  |   (618)  op(all_16_1, all_6_2) = all_16_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (58), (510) imply:
% 168.46/25.12  |   (619)  op(all_12_1, all_10_2) = all_12_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (48), (515) imply:
% 168.46/25.12  |   (620)  op(all_8_1, all_6_2) = all_8_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (184), (405) imply:
% 168.46/25.12  |   (621)  op(e3, all_4_2) = all_52_0
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (149), (521) imply:
% 168.46/25.12  |   (622)  op(e3, all_4_2) = all_50_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (131), (477) imply:
% 168.46/25.12  |   (623)  op(e3, all_4_2) = all_42_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (126), (518) imply:
% 168.46/25.12  |   (624)  op(e3, all_4_2) = all_40_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (111), (494) imply:
% 168.46/25.12  |   (625)  op(e3, all_4_2) = all_34_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (91), (503) imply:
% 168.46/25.12  |   (626)  op(e3, all_4_2) = all_26_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (175), (524) imply:
% 168.46/25.12  |   (627)  op(e2, all_10_2) = all_52_10
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (145), (520) imply:
% 168.46/25.12  |   (628)  op(e2, all_10_2) = all_48_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (140), (519) imply:
% 168.46/25.12  |   (629)  op(e2, all_10_2) = all_46_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (101), (375) imply:
% 168.46/25.12  |   (630)  op(e2, all_10_2) = all_30_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (86), (507) imply:
% 168.46/25.12  |   (631)  op(e2, all_10_2) = all_24_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (57), (510) imply:
% 168.46/25.12  |   (632)  op(e2, all_10_2) = all_12_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (166), (523) imply:
% 168.46/25.12  |   (633)  op(e1, all_14_2) = all_52_20
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (136), (457) imply:
% 168.46/25.12  |   (634)  op(e1, all_14_2) = all_44_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (106), (492) imply:
% 168.46/25.12  |   (635)  op(e1, all_14_2) = all_32_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (81), (505) imply:
% 168.46/25.12  |   (636)  op(e1, all_14_2) = all_22_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (77), (512) imply:
% 168.46/25.12  |   (637)  op(e1, all_14_2) = all_20_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (72), (514) imply:
% 168.46/25.12  |   (638)  op(e1, all_14_2) = all_18_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (157), (522) imply:
% 168.46/25.12  |   (639)  op(e0, all_6_2) = all_52_30
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (121), (517) imply:
% 168.46/25.12  |   (640)  op(e0, all_6_2) = all_38_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (116), (333) imply:
% 168.46/25.12  |   (641)  op(e0, all_6_2) = all_36_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (96), (516) imply:
% 168.46/25.12  |   (642)  op(e0, all_6_2) = all_28_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (67), (501) imply:
% 168.46/25.12  |   (643)  op(e0, all_6_2) = all_16_1
% 168.46/25.12  | 
% 168.46/25.12  | REDUCE: (47), (515) imply:
% 168.46/25.12  |   (644)  op(e0, all_6_2) = all_8_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_28_1, all_36_1, all_6_2,
% 168.46/25.12  |              e0, simplifying with (641), (642) gives:
% 168.46/25.12  |   (645)  all_36_1 = all_28_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_28_1, all_38_1, all_6_2,
% 168.46/25.12  |              e0, simplifying with (640), (642) gives:
% 168.46/25.12  |   (646)  all_38_1 = all_28_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_16_1, all_38_1, all_6_2,
% 168.46/25.12  |              e0, simplifying with (640), (643) gives:
% 168.46/25.12  |   (647)  all_38_1 = all_16_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_8_1, all_38_1, all_6_2,
% 168.46/25.12  |              e0, simplifying with (640), (644) gives:
% 168.46/25.12  |   (648)  all_38_1 = all_8_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_6_1, all_52_30, all_6_2,
% 168.46/25.12  |              e0, simplifying with (42), (639) gives:
% 168.46/25.12  |   (649)  all_52_30 = all_6_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_36_1, all_52_30,
% 168.46/25.12  |              all_6_2, e0, simplifying with (639), (641) gives:
% 168.46/25.12  |   (650)  all_52_30 = all_36_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_18_1, all_32_1,
% 168.46/25.12  |              all_14_2, e1, simplifying with (635), (638) gives:
% 168.46/25.12  |   (651)  all_32_1 = all_18_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_14_1, all_44_1,
% 168.46/25.12  |              all_14_2, e1, simplifying with (62), (634) gives:
% 168.46/25.12  |   (652)  all_44_1 = all_14_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_20_1, all_44_1,
% 168.46/25.12  |              all_14_2, e1, simplifying with (634), (637) gives:
% 168.46/25.12  |   (653)  all_44_1 = all_20_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_44_1, all_52_20,
% 168.46/25.12  |              all_14_2, e1, simplifying with (633), (634) gives:
% 168.46/25.12  |   (654)  all_52_20 = all_44_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_32_1, all_52_20,
% 168.46/25.12  |              all_14_2, e1, simplifying with (633), (635) gives:
% 168.46/25.12  |   (655)  all_52_20 = all_32_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_22_1, all_52_20,
% 168.46/25.12  |              all_14_2, e1, simplifying with (633), (636) gives:
% 168.46/25.12  |   (656)  all_52_20 = all_22_1
% 168.46/25.12  | 
% 168.46/25.12  | GROUND_INST: instantiating (function-axioms) with all_24_1, all_30_1,
% 168.46/25.12  |              all_10_2, e2, simplifying with (630), (631) gives:
% 168.46/25.12  |   (657)  all_30_1 = all_24_1
% 168.46/25.12  | 
% 168.92/25.12  | GROUND_INST: instantiating (function-axioms) with all_24_1, all_46_1,
% 168.92/25.12  |              all_10_2, e2, simplifying with (629), (631) gives:
% 168.92/25.12  |   (658)  all_46_1 = all_24_1
% 168.92/25.12  | 
% 168.92/25.12  | GROUND_INST: instantiating (function-axioms) with all_30_1, all_48_1,
% 168.92/25.12  |              all_10_2, e2, simplifying with (628), (630) gives:
% 168.92/25.12  |   (659)  all_48_1 = all_30_1
% 168.92/25.12  | 
% 168.92/25.12  | GROUND_INST: instantiating (function-axioms) with all_12_1, all_48_1,
% 168.92/25.12  |              all_10_2, e2, simplifying with (628), (632) gives:
% 168.92/25.12  |   (660)  all_48_1 = all_12_1
% 168.92/25.12  | 
% 168.92/25.12  | GROUND_INST: instantiating (function-axioms) with all_10_1, all_52_10,
% 168.92/25.12  |              all_10_2, e2, simplifying with (52), (627) gives:
% 168.92/25.12  |   (661)  all_52_10 = all_10_1
% 168.92/25.12  | 
% 168.92/25.12  | GROUND_INST: instantiating (function-axioms) with all_46_1, all_52_10,
% 168.92/25.12  |              all_10_2, e2, simplifying with (627), (629) gives:
% 168.92/25.13  |   (662)  all_52_10 = all_46_1
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_4_1, all_34_1, all_4_2,
% 168.92/25.13  |              e3, simplifying with (37), (625) gives:
% 168.92/25.13  |   (663)  all_34_1 = all_4_1
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_42_1, all_50_1, all_4_2,
% 168.92/25.13  |              e3, simplifying with (622), (623) gives:
% 168.92/25.13  |   (664)  all_50_1 = all_42_1
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_40_1, all_50_1, all_4_2,
% 168.92/25.13  |              e3, simplifying with (622), (624) gives:
% 168.92/25.13  |   (665)  all_50_1 = all_40_1
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_34_1, all_50_1, all_4_2,
% 168.92/25.13  |              e3, simplifying with (622), (625) gives:
% 168.92/25.13  |   (666)  all_50_1 = all_34_1
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_42_1, all_52_0, all_4_2,
% 168.92/25.13  |              e3, simplifying with (621), (623) gives:
% 168.92/25.13  |   (667)  all_52_0 = all_42_1
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_26_1, all_52_0, all_4_2,
% 168.92/25.13  |              e3, simplifying with (621), (626) gives:
% 168.92/25.13  |   (668)  all_52_0 = all_26_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (667), (668) imply:
% 168.92/25.13  |   (669)  all_42_1 = all_26_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (669) implies:
% 168.92/25.13  |   (670)  all_42_1 = all_26_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (661), (662) imply:
% 168.92/25.13  |   (671)  all_46_1 = all_10_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (671) implies:
% 168.92/25.13  |   (672)  all_46_1 = all_10_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (655), (656) imply:
% 168.92/25.13  |   (673)  all_32_1 = all_22_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (673) implies:
% 168.92/25.13  |   (674)  all_32_1 = all_22_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (654), (656) imply:
% 168.92/25.13  |   (675)  all_44_1 = all_22_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (675) implies:
% 168.92/25.13  |   (676)  all_44_1 = all_22_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (649), (650) imply:
% 168.92/25.13  |   (677)  all_36_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (677) implies:
% 168.92/25.13  |   (678)  all_36_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (664), (665) imply:
% 168.92/25.13  |   (679)  all_42_1 = all_40_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (679) implies:
% 168.92/25.13  |   (680)  all_42_1 = all_40_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (665), (666) imply:
% 168.92/25.13  |   (681)  all_40_1 = all_34_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (659), (660) imply:
% 168.92/25.13  |   (682)  all_30_1 = all_12_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (682) implies:
% 168.92/25.13  |   (683)  all_30_1 = all_12_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (658), (672) imply:
% 168.92/25.13  |   (684)  all_24_1 = all_10_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (684) implies:
% 168.92/25.13  |   (685)  all_24_1 = all_10_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (652), (653) imply:
% 168.92/25.13  |   (686)  all_20_1 = all_14_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (653), (676) imply:
% 168.92/25.13  |   (687)  all_22_1 = all_20_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (687) implies:
% 168.92/25.13  |   (688)  all_22_1 = all_20_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (670), (680) imply:
% 168.92/25.13  |   (689)  all_40_1 = all_26_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (689) implies:
% 168.92/25.13  |   (690)  all_40_1 = all_26_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (681), (690) imply:
% 168.92/25.13  |   (691)  all_34_1 = all_26_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (691) implies:
% 168.92/25.13  |   (692)  all_34_1 = all_26_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (646), (647) imply:
% 168.92/25.13  |   (693)  all_28_1 = all_16_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (693) implies:
% 168.92/25.13  |   (694)  all_28_1 = all_16_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (647), (648) imply:
% 168.92/25.13  |   (695)  all_16_1 = all_8_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (645), (678) imply:
% 168.92/25.13  |   (696)  all_28_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (696) implies:
% 168.92/25.13  |   (697)  all_28_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (663), (692) imply:
% 168.92/25.13  |   (698)  all_26_1 = all_4_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (651), (674) imply:
% 168.92/25.13  |   (699)  all_22_1 = all_18_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (699) implies:
% 168.92/25.13  |   (700)  all_22_1 = all_18_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (657), (683) imply:
% 168.92/25.13  |   (701)  all_24_1 = all_12_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (701) implies:
% 168.92/25.13  |   (702)  all_24_1 = all_12_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (694), (697) imply:
% 168.92/25.13  |   (703)  all_16_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (703) implies:
% 168.92/25.13  |   (704)  all_16_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (685), (702) imply:
% 168.92/25.13  |   (705)  all_12_1 = all_10_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (688), (700) imply:
% 168.92/25.13  |   (706)  all_20_1 = all_18_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (706) implies:
% 168.92/25.13  |   (707)  all_20_1 = all_18_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (686), (707) imply:
% 168.92/25.13  |   (708)  all_18_1 = all_14_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (695), (704) imply:
% 168.92/25.13  |   (709)  all_8_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | SIMP: (709) implies:
% 168.92/25.13  |   (710)  all_8_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (700), (708) imply:
% 168.92/25.13  |   (711)  all_22_1 = all_14_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (683), (705) imply:
% 168.92/25.13  |   (712)  all_30_1 = all_10_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (651), (708) imply:
% 168.92/25.13  |   (713)  all_32_1 = all_14_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (647), (704) imply:
% 168.92/25.13  |   (714)  all_38_1 = all_6_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (690), (698) imply:
% 168.92/25.13  |   (715)  all_40_1 = all_4_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (670), (698) imply:
% 168.92/25.13  |   (716)  all_42_1 = all_4_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (660), (705) imply:
% 168.92/25.13  |   (717)  all_48_1 = all_10_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (665), (715) imply:
% 168.92/25.13  |   (718)  all_50_1 = all_4_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (656), (711) imply:
% 168.92/25.13  |   (719)  all_52_20 = all_14_1
% 168.92/25.13  | 
% 168.92/25.13  | COMBINE_EQS: (668), (698) imply:
% 168.92/25.13  |   (720)  all_52_0 = all_4_1
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (601), (718) imply:
% 168.92/25.13  |   (721)  op(all_4_1, all_4_2) = all_50_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (602), (717) imply:
% 168.92/25.13  |   (722)  op(all_10_1, all_10_2) = all_48_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (603), (672) imply:
% 168.92/25.13  |   (723)  op(all_10_1, all_10_2) = all_46_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (604), (652) imply:
% 168.92/25.13  |   (724)  op(all_14_1, all_14_2) = all_44_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (605), (716) imply:
% 168.92/25.13  |   (725)  op(all_4_1, all_4_2) = all_42_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (606), (715) imply:
% 168.92/25.13  |   (726)  op(all_4_1, all_4_2) = all_40_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (607), (714) imply:
% 168.92/25.13  |   (727)  op(all_6_1, all_6_2) = all_38_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (608), (678) imply:
% 168.92/25.13  |   (728)  op(all_6_1, all_6_2) = all_36_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (609), (663) imply:
% 168.92/25.13  |   (729)  op(all_4_1, all_4_2) = all_34_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (610), (713) imply:
% 168.92/25.13  |   (730)  op(all_14_1, all_14_2) = all_32_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (611), (712) imply:
% 168.92/25.13  |   (731)  op(all_10_1, all_10_2) = all_30_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (612), (697) imply:
% 168.92/25.13  |   (732)  op(all_6_1, all_6_2) = all_28_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (613), (698) imply:
% 168.92/25.13  |   (733)  op(all_4_1, all_4_2) = all_26_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (614), (685) imply:
% 168.92/25.13  |   (734)  op(all_10_1, all_10_2) = all_24_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (615), (711) imply:
% 168.92/25.13  |   (735)  op(all_14_1, all_14_2) = all_22_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (616), (686) imply:
% 168.92/25.13  |   (736)  op(all_14_1, all_14_2) = all_20_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (617), (708) imply:
% 168.92/25.13  |   (737)  op(all_14_1, all_14_2) = all_18_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (618), (704) imply:
% 168.92/25.13  |   (738)  op(all_6_1, all_6_2) = all_16_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (619), (705) imply:
% 168.92/25.13  |   (739)  op(all_10_1, all_10_2) = all_12_0
% 168.92/25.13  | 
% 168.92/25.13  | REDUCE: (620), (710) imply:
% 168.92/25.13  |   (740)  op(all_6_1, all_6_2) = all_8_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_26_0, all_34_0, all_4_2,
% 168.92/25.13  |              all_4_1, simplifying with (729), (733) gives:
% 168.92/25.13  |   (741)  all_34_0 = all_26_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_4_0, all_50_0, all_4_2,
% 168.92/25.13  |              all_4_1, simplifying with (38), (721) gives:
% 168.92/25.13  |   (742)  all_50_0 = all_4_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_42_0, all_50_0, all_4_2,
% 168.92/25.13  |              all_4_1, simplifying with (721), (725) gives:
% 168.92/25.13  |   (743)  all_50_0 = all_42_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_40_0, all_50_0, all_4_2,
% 168.92/25.13  |              all_4_1, simplifying with (721), (726) gives:
% 168.92/25.13  |   (744)  all_50_0 = all_40_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_34_0, all_50_0, all_4_2,
% 168.92/25.13  |              all_4_1, simplifying with (721), (729) gives:
% 168.92/25.13  |   (745)  all_50_0 = all_34_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_8_0, all_16_0, all_6_2,
% 168.92/25.13  |              all_6_1, simplifying with (738), (740) gives:
% 168.92/25.13  |   (746)  all_16_0 = all_8_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_6_0, all_36_0, all_6_2,
% 168.92/25.13  |              all_6_1, simplifying with (43), (728) gives:
% 168.92/25.13  |   (747)  all_36_0 = all_6_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_16_0, all_36_0, all_6_2,
% 168.92/25.13  |              all_6_1, simplifying with (728), (738) gives:
% 168.92/25.13  |   (748)  all_36_0 = all_16_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_36_0, all_38_0, all_6_2,
% 168.92/25.13  |              all_6_1, simplifying with (727), (728) gives:
% 168.92/25.13  |   (749)  all_38_0 = all_36_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_28_0, all_38_0, all_6_2,
% 168.92/25.13  |              all_6_1, simplifying with (727), (732) gives:
% 168.92/25.13  |   (750)  all_38_0 = all_28_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_10_0, all_24_0,
% 168.92/25.13  |              all_10_2, all_10_1, simplifying with (53), (734) gives:
% 168.92/25.13  |   (751)  all_24_0 = all_10_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_24_0, all_30_0,
% 168.92/25.13  |              all_10_2, all_10_1, simplifying with (731), (734) gives:
% 168.92/25.13  |   (752)  all_30_0 = all_24_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_46_0, all_48_0,
% 168.92/25.13  |              all_10_2, all_10_1, simplifying with (722), (723) gives:
% 168.92/25.13  |   (753)  all_48_0 = all_46_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_30_0, all_48_0,
% 168.92/25.13  |              all_10_2, all_10_1, simplifying with (722), (731) gives:
% 168.92/25.13  |   (754)  all_48_0 = all_30_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_12_0, all_48_0,
% 168.92/25.13  |              all_10_2, all_10_1, simplifying with (722), (739) gives:
% 168.92/25.13  |   (755)  all_48_0 = all_12_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_14_0, all_22_0,
% 168.92/25.13  |              all_14_2, all_14_1, simplifying with (63), (735) gives:
% 168.92/25.13  |   (756)  all_22_0 = all_14_0
% 168.92/25.13  | 
% 168.92/25.13  | GROUND_INST: instantiating (function-axioms) with all_20_0, all_22_0,
% 168.92/25.13  |              all_14_2, all_14_1, simplifying with (735), (736) gives:
% 168.92/25.13  |   (757)  all_22_0 = all_20_0
% 168.92/25.13  | 
% 168.92/25.14  | GROUND_INST: instantiating (function-axioms) with all_32_0, all_44_0,
% 168.92/25.14  |              all_14_2, all_14_1, simplifying with (724), (730) gives:
% 168.92/25.14  |   (758)  all_44_0 = all_32_0
% 168.92/25.14  | 
% 168.92/25.14  | GROUND_INST: instantiating (function-axioms) with all_20_0, all_44_0,
% 168.92/25.14  |              all_14_2, all_14_1, simplifying with (724), (736) gives:
% 168.92/25.14  |   (759)  all_44_0 = all_20_0
% 168.92/25.14  | 
% 168.92/25.14  | GROUND_INST: instantiating (function-axioms) with all_18_0, all_44_0,
% 168.92/25.14  |              all_14_2, all_14_1, simplifying with (724), (737) gives:
% 168.92/25.14  |   (760)  all_44_0 = all_18_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (742), (743) imply:
% 168.92/25.14  |   (761)  all_42_0 = all_4_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (743), (745) imply:
% 168.92/25.14  |   (762)  all_42_0 = all_34_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (743), (744) imply:
% 168.92/25.14  |   (763)  all_42_0 = all_40_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (753), (754) imply:
% 168.92/25.14  |   (764)  all_46_0 = all_30_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (753), (755) imply:
% 168.92/25.14  |   (765)  all_46_0 = all_12_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (764), (765) imply:
% 168.92/25.14  |   (766)  all_30_0 = all_12_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (766) implies:
% 168.92/25.14  |   (767)  all_30_0 = all_12_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (758), (760) imply:
% 168.92/25.14  |   (768)  all_32_0 = all_18_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (758), (759) imply:
% 168.92/25.14  |   (769)  all_32_0 = all_20_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (761), (763) imply:
% 168.92/25.14  |   (770)  all_40_0 = all_4_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (762), (763) imply:
% 168.92/25.14  |   (771)  all_40_0 = all_34_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (770), (771) imply:
% 168.92/25.14  |   (772)  all_34_0 = all_4_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (772) implies:
% 168.92/25.14  |   (773)  all_34_0 = all_4_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (749), (750) imply:
% 168.92/25.14  |   (774)  all_36_0 = all_28_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (774) implies:
% 168.92/25.14  |   (775)  all_36_0 = all_28_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (747), (775) imply:
% 168.92/25.14  |   (776)  all_28_0 = all_6_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (748), (775) imply:
% 168.92/25.14  |   (777)  all_28_0 = all_16_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (741), (773) imply:
% 168.92/25.14  |   (778)  all_26_0 = all_4_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (778) implies:
% 168.92/25.14  |   (779)  all_26_0 = all_4_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (768), (769) imply:
% 168.92/25.14  |   (780)  all_20_0 = all_18_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (780) implies:
% 168.92/25.14  |   (781)  all_20_0 = all_18_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (752), (767) imply:
% 168.92/25.14  |   (782)  all_24_0 = all_12_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (782) implies:
% 168.92/25.14  |   (783)  all_24_0 = all_12_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (776), (777) imply:
% 168.92/25.14  |   (784)  all_16_0 = all_6_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (784) implies:
% 168.92/25.14  |   (785)  all_16_0 = all_6_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (751), (783) imply:
% 168.92/25.14  |   (786)  all_12_0 = all_10_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (756), (757) imply:
% 168.92/25.14  |   (787)  all_20_0 = all_14_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (787) implies:
% 168.92/25.14  |   (788)  all_20_0 = all_14_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (781), (788) imply:
% 168.92/25.14  |   (789)  all_18_0 = all_14_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (746), (785) imply:
% 168.92/25.14  |   (790)  all_8_0 = all_6_0
% 168.92/25.14  | 
% 168.92/25.14  | SIMP: (790) implies:
% 168.92/25.14  |   (791)  all_8_0 = all_6_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (767), (786) imply:
% 168.92/25.14  |   (792)  all_30_0 = all_10_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (768), (789) imply:
% 168.92/25.14  |   (793)  all_32_0 = all_14_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (750), (776) imply:
% 168.92/25.14  |   (794)  all_38_0 = all_6_0
% 168.92/25.14  | 
% 168.92/25.14  | COMBINE_EQS: (765), (786) imply:
% 168.92/25.14  |   (795)  all_46_0 = all_10_0
% 168.92/25.14  | 
% 168.92/25.14  | BETA: splitting (39) gives:
% 168.92/25.14  | 
% 168.92/25.14  | Case 1:
% 168.92/25.14  | | 
% 168.92/25.14  | |   (796)   ~ (all_4_1 = e2)
% 168.92/25.14  | | 
% 168.92/25.14  | | BETA: splitting (44) gives:
% 168.92/25.14  | | 
% 168.92/25.14  | | Case 1:
% 168.92/25.14  | | | 
% 168.92/25.14  | | |   (797)   ~ (all_6_0 = e1)
% 168.92/25.14  | | | 
% 168.92/25.14  | | | BETA: splitting (49) gives:
% 168.92/25.14  | | | 
% 168.92/25.14  | | | Case 1:
% 168.92/25.14  | | | | 
% 168.92/25.14  | | | |   (798)   ~ (all_8_0 = e2)
% 168.92/25.14  | | | | 
% 168.92/25.14  | | | | REDUCE: (791), (798) imply:
% 168.92/25.14  | | | |   (799)   ~ (all_6_0 = e2)
% 168.92/25.14  | | | | 
% 168.92/25.14  | | | | BETA: splitting (54) gives:
% 168.92/25.14  | | | | 
% 168.92/25.14  | | | | Case 1:
% 168.92/25.14  | | | | | 
% 168.92/25.14  | | | | |   (800)   ~ (all_10_0 = e3)
% 168.92/25.14  | | | | | 
% 168.92/25.14  | | | | | BETA: splitting (59) gives:
% 168.92/25.14  | | | | | 
% 168.92/25.14  | | | | | Case 1:
% 168.92/25.14  | | | | | | 
% 168.92/25.14  | | | | | |   (801)   ~ (all_12_1 = e3)
% 168.92/25.14  | | | | | | 
% 168.92/25.14  | | | | | | REDUCE: (705), (801) imply:
% 168.92/25.14  | | | | | |   (802)   ~ (all_10_1 = e3)
% 168.92/25.14  | | | | | | 
% 168.92/25.14  | | | | | | BETA: splitting (64) gives:
% 168.92/25.14  | | | | | | 
% 168.92/25.14  | | | | | | Case 1:
% 168.92/25.14  | | | | | | | 
% 168.92/25.14  | | | | | | |   (803)   ~ (all_14_0 = e2)
% 168.92/25.14  | | | | | | | 
% 168.92/25.14  | | | | | | | BETA: splitting (74) gives:
% 168.92/25.14  | | | | | | | 
% 168.92/25.14  | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | 
% 168.92/25.14  | | | | | | | |   (804)   ~ (all_18_0 = e3)
% 168.92/25.14  | | | | | | | | 
% 168.92/25.14  | | | | | | | | REDUCE: (789), (804) imply:
% 168.92/25.14  | | | | | | | |   (805)   ~ (all_14_0 = e3)
% 168.92/25.14  | | | | | | | | 
% 168.92/25.14  | | | | | | | | BETA: splitting (83) gives:
% 168.92/25.14  | | | | | | | | 
% 168.92/25.14  | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | 
% 168.92/25.14  | | | | | | | | |   (806)   ~ (all_22_1 = e3)
% 168.92/25.14  | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | REDUCE: (711), (806) imply:
% 168.92/25.14  | | | | | | | | |   (807)   ~ (all_14_1 = e3)
% 168.92/25.14  | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | BETA: splitting (88) gives:
% 168.92/25.14  | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | |   (808)   ~ (all_24_0 = e1)
% 168.92/25.14  | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | REDUCE: (751), (808) imply:
% 168.92/25.14  | | | | | | | | | |   (809)   ~ (all_10_0 = e1)
% 168.92/25.14  | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | BETA: splitting (93) gives:
% 168.92/25.14  | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | |   (810)   ~ (all_26_0 = e2)
% 168.92/25.14  | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | REDUCE: (779), (810) imply:
% 168.92/25.14  | | | | | | | | | | |   (811)   ~ (all_4_0 = e2)
% 168.92/25.14  | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | BETA: splitting (98) gives:
% 168.92/25.14  | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | |   (812)   ~ (all_28_0 = e3)
% 168.92/25.14  | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | REDUCE: (776), (812) imply:
% 168.92/25.14  | | | | | | | | | | | |   (813)   ~ (all_6_0 = e3)
% 168.92/25.14  | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | BETA: splitting (103) gives:
% 168.92/25.14  | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | |   (814)   ~ (all_30_1 = e1)
% 168.92/25.14  | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | REDUCE: (712), (814) imply:
% 168.92/25.14  | | | | | | | | | | | | |   (815)   ~ (all_10_1 = e1)
% 168.92/25.14  | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | BETA: splitting (108) gives:
% 168.92/25.14  | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | |   (816)   ~ (all_32_1 = e2)
% 168.92/25.14  | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | REDUCE: (713), (816) imply:
% 168.92/25.14  | | | | | | | | | | | | | |   (817)   ~ (all_14_1 = e2)
% 168.92/25.14  | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 168.92/25.14  | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | |   (818)   ~ (all_34_0 = e1)
% 168.92/25.14  | | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | | REDUCE: (773), (818) imply:
% 168.92/25.14  | | | | | | | | | | | | | | |   (819)   ~ (all_4_0 = e1)
% 168.92/25.14  | | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 168.92/25.14  | | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | | Case 1:
% 168.92/25.14  | | | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | | |   (820)   ~ (all_40_1 = e1)
% 168.92/25.14  | | | | | | | | | | | | | | | | 
% 168.92/25.14  | | | | | | | | | | | | | | | | REDUCE: (715), (820) imply:
% 168.92/25.14  | | | | | | | | | | | | | | | |   (821)   ~ (all_4_1 = e1)
% 168.92/25.14  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (41), (42), (43), (51), (52), (53), (61), (62),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (63), (154), (155), (156), (158), (159), (160),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (167), (168), (169),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (170), (172), (173), (174), (176), (177), (178),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (276),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (308), (310), (311), (312), (313), (314), (315),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (322), (323),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (597), (598), (599), (600), (649), (661), (719),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (720), (796), (797), (799), (800), (802), (803),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (805), (807), (809), (811), (813), (817), (819),
% 168.92/25.15  | | | | | | | | | | | | | | | |            (821), (function-axioms) are inconsistent by
% 168.92/25.15  | | | | | | | | | | | | | | | |            sub-proof #633.
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | Case 2:
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | |   (822)  all_40_1 = e1
% 168.92/25.15  | | | | | | | | | | | | | | | |   (823)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | COMBINE_EQS: (715), (822) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | |   (824)  all_4_1 = e1
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (824) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | |   (825)  all_52_0 = e1
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | REDUCE: (796), (824) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | |   (826)   ~ (e2 = e1)
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | REDUCE: (38), (824) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | |   (827)  op(e1, all_4_2) = all_4_0
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | REDUCE: (37), (824) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | |   (828)  op(e3, all_4_2) = e1
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 168.92/25.15  | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (829)  all_58_15 = e0
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (829) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (830)  all_6_2 = e0
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (597), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (831)   ~ (all_52_7 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (599), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (832)   ~ (all_52_15 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (600), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (833)   ~ (all_52_23 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (564), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (834)   ~ (all_52_25 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (582), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (835)   ~ (all_52_27 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (594), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (836)   ~ (all_52_29 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (43), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (837)  op(all_6_1, e0) = all_6_0
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (42), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (838)  op(e0, e0) = all_6_1
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (41), (830) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (839)  op(e0, e0) = e0
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 168.92/25.15  | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (838), (839) gives:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (840)  all_6_1 = e0
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (837), (840) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (841)  op(e0, e0) = all_6_0
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 168.92/25.15  | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (839), (841) gives:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (842)  all_6_0 = e0
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (813), (842) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (843)   ~ (e3 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (799), (842) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (844)   ~ (e2 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | REDUCE: (797), (842) imply:
% 168.92/25.15  | | | | | | | | | | | | | | | | |   (845)   ~ (e1 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 168.92/25.15  | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.15  | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | |   (846)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.15  | | | | | | | | | | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 168.92/25.15  | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | BETA: splitting (846) gives:
% 168.92/25.15  | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |   (847)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |          all_52_6 = e0
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (825), (847) are inconsistent by sub-proof
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            #632.
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |   (848)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |          all_52_14 = e0
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (38), (52), (53),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (154), (155), (156), (159), (164), (165), (167),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (172), (173), (178), (179), (181), (183), (270),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (271), (273), (276), (280), (282), (302), (303),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (304), (305), (306), (307), (311), (315), (319),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (323), (330), (331), (344), (349), (359), (364),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (425), (429), (533), (534), (535), (536), (537),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (548), (552), (553),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (554), (556), (558), (559), (560), (561), (562),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (563), (565), (566), (569), (571), (573), (578),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (579), (581), (586), (587), (588), (591), (595),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (596), (598), (661), (800), (809), (811), (819),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (829), (832), (834), (835), (836), (848),
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.15  | | | | | | | | | | | | | | | | | | |            #631.
% 168.92/25.15  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | | End of split
% 168.92/25.15  | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.15  | | | | | | | | | | | | | | | | | | 
% 168.92/25.15  | | | | | | | | | | | | | | | | | |   (849)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 168.92/25.15  | | | | | | | | | | | | | | | | | |            & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 168.92/25.15  | | | | | | | | | | | | | | | | | |            = e2 & all_52_28 = e1 & all_52_30 = e0)
% 168.92/25.15  | | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (62), (63), (154),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (155), (156), (158), (161), (163), (164), (165),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (181), (182), (269), (270), (271), (272), (274),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (277), (280), (283), (302), (303), (304), (305),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (313), (319), (325),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (326), (330), (331), (341), (344), (349), (350),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (403),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (415), (419), (429), (518), (531), (533), (534),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (558), (560), (562), (563), (566), (567), (569),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (571), (581), (583), (584), (585), (586), (587),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (591), (595), (596), (719), (770), (803), (805),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (811), (823), (827), (828), (829), (831), (833),
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            (834), (835), (836), (849), (function-axioms) are
% 168.92/25.16  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #614.
% 168.92/25.16  | | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.16  | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.16  | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | |   (850)   ~ (all_58_15 = e0)
% 168.92/25.16  | | | | | | | | | | | | | | | | |   (851)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 168.92/25.16  | | | | | | | | | | | | | | | | |          & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 168.92/25.16  | | | | | | | | | | | | | | | | |            e0)
% 168.92/25.16  | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | | ALPHA: (851) implies:
% 168.92/25.16  | | | | | | | | | | | | | | | | |   (852)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 168.92/25.16  | | | | | | | | | | | | | | | | |   (853)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 168.92/25.16  | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | | REDUCE: (532), (850) imply:
% 168.92/25.16  | | | | | | | | | | | | | | | | |   (854)   ~ (all_6_2 = e0)
% 168.92/25.16  | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (42), (52), (61), (62), (63), (154), (155), (156),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (270),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (278), (279), (280), (281), (283), (303), (304),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (305), (307), (310), (311), (313), (314), (315),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (322), (323),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (359), (364), (365),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (403), (409),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (413), (415), (419), (425), (429), (518), (529),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (770),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (796), (802), (803), (805), (807), (811), (815),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (819), (823), (825), (827), (828), (852), (853),
% 168.92/25.16  | | | | | | | | | | | | | | | | |            (854), (function-axioms) are inconsistent by
% 168.92/25.16  | | | | | | | | | | | | | | | | |            sub-proof #601.
% 168.92/25.16  | | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | | End of split
% 168.92/25.16  | | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | End of split
% 168.92/25.16  | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | Case 2:
% 168.92/25.16  | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | |   (855)  all_34_0 = e1
% 168.92/25.16  | | | | | | | | | | | | | | |   (856)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 168.92/25.16  | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (855) imply:
% 168.92/25.16  | | | | | | | | | | | | | | |   (857)  all_4_0 = e1
% 168.92/25.16  | | | | | | | | | | | | | | | 
% 168.92/25.16  | | | | | | | | | | | | | | | REDUCE: (38), (857) imply:
% 168.92/25.16  | | | | | | | | | | | | | | |   (858)  op(all_4_1, all_4_2) = e1
% 168.92/25.16  | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (41), (42),
% 168.92/25.17  | | | | | | | | | | | | | | |            (43), (52), (53), (61), (62), (63), (154), (155),
% 168.92/25.17  | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 168.92/25.17  | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 168.92/25.17  | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 168.92/25.17  | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 168.92/25.17  | | | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 168.92/25.17  | | | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 168.92/25.17  | | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (317),
% 168.92/25.17  | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 168.92/25.17  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (341), (344),
% 168.92/25.17  | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 168.92/25.17  | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 168.92/25.17  | | | | | | | | | | | | | | |            (415), (419), (425), (429), (494), (529), (530),
% 168.92/25.17  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 168.92/25.17  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 168.92/25.17  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 168.92/25.17  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 168.92/25.17  | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 168.92/25.17  | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 168.92/25.17  | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 168.92/25.17  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 168.92/25.17  | | | | | | | | | | | | | | |            (600), (649), (661), (663), (719), (720), (796),
% 168.92/25.17  | | | | | | | | | | | | | | |            (797), (799), (800), (802), (803), (805), (807),
% 168.92/25.17  | | | | | | | | | | | | | | |            (809), (813), (856), (858), (function-axioms) are
% 168.92/25.17  | | | | | | | | | | | | | | |            inconsistent by sub-proof #554.
% 168.92/25.17  | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | End of split
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | Case 2:
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | |   (859)  all_32_1 = e2
% 168.92/25.17  | | | | | | | | | | | | | |   (860)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e3)
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | COMBINE_EQS: (713), (859) imply:
% 168.92/25.17  | | | | | | | | | | | | | |   (861)  all_14_1 = e2
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | COMBINE_EQS: (719), (861) imply:
% 168.92/25.17  | | | | | | | | | | | | | |   (862)  all_52_20 = e2
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | REDUCE: (807), (861) imply:
% 168.92/25.17  | | | | | | | | | | | | | |   (863)   ~ (e3 = e2)
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | REDUCE: (63), (861) imply:
% 168.92/25.17  | | | | | | | | | | | | | |   (864)  op(e2, all_14_2) = all_14_0
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | REDUCE: (62), (861) imply:
% 168.92/25.17  | | | | | | | | | | | | | |   (865)  op(e1, all_14_2) = e2
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 168.92/25.17  | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | Case 1:
% 168.92/25.17  | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | |   (866)   ~ (all_34_0 = e1)
% 168.92/25.17  | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | REDUCE: (773), (866) imply:
% 168.92/25.17  | | | | | | | | | | | | | | |   (867)   ~ (all_4_0 = e1)
% 168.92/25.17  | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 168.92/25.17  | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | Case 1:
% 168.92/25.17  | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | |   (868)   ~ (all_40_1 = e1)
% 168.92/25.17  | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | REDUCE: (715), (868) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | |   (869)   ~ (all_4_1 = e1)
% 168.92/25.17  | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 168.92/25.17  | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (870)  all_58_15 = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (870) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (871)  all_6_2 = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (597), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (872)   ~ (all_52_7 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (599), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (873)   ~ (all_52_15 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (600), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (874)   ~ (all_52_23 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (564), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (875)   ~ (all_52_25 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (582), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (876)   ~ (all_52_27 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (594), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (877)   ~ (all_52_29 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (43), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (878)  op(all_6_1, e0) = all_6_0
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (42), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (879)  op(e0, e0) = all_6_1
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (41), (871) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (880)  op(e0, e0) = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (52), (53), (154),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (155), (156), (159), (160), (161), (163), (164),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (165), (167), (170), (172), (173), (177), (178),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (269), (270),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (271), (272), (273), (275), (276), (278), (280),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (282), (283), (302), (303), (304), (305), (306),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (322),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (323), (324), (326), (330), (331), (341), (344),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (425), (429),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (546), (548),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (558),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (565), (566),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (567), (569), (571), (573), (578), (579), (580),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (581), (584), (585), (586), (587), (588), (591),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (593), (595), (596), (597), (598), (661), (720),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (797), (799), (800), (809), (811), (813), (862),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (865), (867), (869), (870), (872), (873), (874),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (875), (876), (877), (878), (879), (880),
% 168.92/25.17  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.17  | | | | | | | | | | | | | | | | |            #547.
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (881)   ~ (all_58_15 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (882)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | |          & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 168.92/25.17  | | | | | | | | | | | | | | | | |            e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | ALPHA: (882) implies:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (883)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (884)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | REDUCE: (532), (881) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | |   (885)   ~ (all_6_2 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 168.92/25.17  | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | |   (886)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.17  | | | | | | | | | | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 168.92/25.17  | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0)
% 168.92/25.17  | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | BETA: splitting (886) gives:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (887)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |          all_52_6 = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | ALPHA: (887) implies:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (888)  all_52_6 = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (889)  all_52_4 = e1
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (890)  all_52_2 = e2
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (891)  all_52_0 = e3
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (891) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (892)  all_4_1 = e3
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | REDUCE: (38), (892) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (893)  op(e3, all_4_2) = all_4_0
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | REDUCE: (37), (892) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (894)  op(e3, all_4_2) = e3
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | REDUCE: (176), (890) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (895)  op(e2, all_52_3) = e2
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | REDUCE: (168), (889) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (896)  op(e1, all_52_5) = e1
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | REDUCE: (160), (888) imply:
% 168.92/25.17  | | | | | | | | | | | | | | | | | | |   (897)  op(e0, all_52_7) = e0
% 168.92/25.17  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (41), (52), (61), (154), (155), (156),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (169),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (268),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (276), (277),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (304), (305),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (312), (313), (314),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (315), (317), (319), (323), (324), (326), (327),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (328), (330), (331), (341), (344), (349), (350),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (386), (391),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (392), (403), (409), (413), (415), (425), (429),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (492), (529), (531), (532), (533), (534), (535),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (575),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (793), (803), (811), (815), (860), (864), (867),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (884), (885), (893), (894), (895), (896), (897),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            #540.
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (898)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |          all_52_14 = e0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | ALPHA: (898) implies:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (899)  all_52_14 = e0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (900)  all_52_12 = e1
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (901)  all_52_10 = e2
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (902)  all_52_8 = e3
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (901) imply:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (903)  all_10_1 = e2
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REDUCE: (53), (903) imply:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (904)  op(e2, all_10_2) = all_10_0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (902) imply:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (905)  op(e3, all_52_9) = e3
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REDUCE: (52), (903) imply:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (906)  op(e2, all_10_2) = e2
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REDUCE: (167), (900) imply:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (907)  op(e1, all_52_13) = e1
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REDUCE: (159), (899) imply:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (908)  op(e0, all_52_15) = e0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (38), (42), (61), (62),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (154), (156), (158), (161), (163), (164), (165),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (179), (181), (182), (268), (270), (272), (273),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (274), (277), (279), (280), (281), (282), (283),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (303), (304), (307), (311), (313), (315), (316),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (317), (319), (320), (321), (323), (326), (328),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (359),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (529), (531),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (578),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (585), (586),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (796), (800),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (807), (809), (811), (867), (869), (884), (885),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (904), (905), (906), (907), (908),
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            #716.
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | End of split
% 168.92/25.18  | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | |   (909)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 168.92/25.18  | | | | | | | | | | | | | | | | | |            & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 168.92/25.18  | | | | | | | | | | | | | | | | | |            = e2 & all_52_28 = e1 & all_52_30 = e0)
% 168.92/25.18  | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | BETA: splitting (909) gives:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (910)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |          all_52_22 = e0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (862), (910) are inconsistent by sub-proof
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |            #539.
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (911)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |          all_52_30 = e0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | ALPHA: (911) implies:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (912)  all_52_30 = e0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (913)  all_52_28 = e1
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (914)  all_52_26 = e2
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (915)  all_52_24 = e3
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (912) imply:
% 168.92/25.18  | | | | | | | | | | | | | | | | | | |   (916)  all_6_1 = e0
% 168.92/25.18  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (797), (799), (811), (813), (867), (883), (884),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (885), (913), (914), (915), (916),
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.19  | | | | | | | | | | | | | | | | | | |            #635.
% 168.92/25.19  | | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | End of split
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.19  | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | End of split
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | Case 2:
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | |   (917)  all_40_1 = e1
% 168.92/25.19  | | | | | | | | | | | | | | | |   (918)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | COMBINE_EQS: (715), (917) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (919)  all_4_1 = e1
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | SIMP: (919) implies:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (920)  all_4_1 = e1
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (920) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (921)  all_52_0 = e1
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (796), (920) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (922)   ~ (e2 = e1)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (38), (920) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (923)  op(e1, all_4_2) = all_4_0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (37), (920) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (924)  op(e3, all_4_2) = e1
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (42), (43), (52), (53), (61), (62), (154), (155),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (276),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (277), (279), (280), (281), (282), (283), (301),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (310),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (311), (313), (315), (316), (319), (320), (321),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (518), (529), (531), (532), (533), (534), (535),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (598), (599), (600), (649), (661), (770), (796),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (797), (800), (807), (809), (811), (813), (862),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (865), (867), (918), (921), (923), (924),
% 168.92/25.19  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.19  | | | | | | | | | | | | | | | |            #535.
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | End of split
% 168.92/25.19  | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | Case 2:
% 168.92/25.19  | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | |   (925)  all_34_0 = e1
% 168.92/25.19  | | | | | | | | | | | | | | |   (926)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 168.92/25.19  | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (925) imply:
% 168.92/25.19  | | | | | | | | | | | | | | |   (927)  all_4_0 = e1
% 168.92/25.19  | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | REDUCE: (811), (927) imply:
% 168.92/25.19  | | | | | | | | | | | | | | |   (928)   ~ (e2 = e1)
% 168.92/25.19  | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | REDUCE: (38), (927) imply:
% 168.92/25.19  | | | | | | | | | | | | | | |   (929)  op(all_4_1, all_4_2) = e1
% 168.92/25.19  | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 168.92/25.19  | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | Case 1:
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | |   (930)  all_58_15 = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (930) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (931)  all_6_2 = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (599), (931) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (932)   ~ (all_52_15 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (564), (931) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (933)   ~ (all_52_25 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (582), (931) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (934)   ~ (all_52_27 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (594), (931) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (935)   ~ (all_52_29 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (43), (931) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (936)  op(all_6_1, e0) = all_6_0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (42), (931) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (937)  op(e0, e0) = all_6_1
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (41), (931) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (938)  op(e0, e0) = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 168.92/25.19  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (937), (938) gives:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (939)  all_6_1 = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (936), (939) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (940)  op(e0, e0) = all_6_0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 168.92/25.19  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (938), (940) gives:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (941)  all_6_0 = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (813), (941) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (942)   ~ (e3 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (799), (941) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (943)   ~ (e2 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | REDUCE: (797), (941) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | |   (944)   ~ (e1 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 168.92/25.19  | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.19  | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | |   (945)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.19  | | | | | | | | | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 168.92/25.19  | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0)
% 168.92/25.19  | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | BETA: splitting (945) gives:
% 168.92/25.19  | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (946)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.19  | | | | | | | | | | | | | | | | | |          all_52_6 = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (929), (946), (function-axioms)
% 168.92/25.19  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #600.
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (947)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 168.92/25.19  | | | | | | | | | | | | | | | | | |          all_52_14 = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | ALPHA: (947) implies:
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (948)  all_52_14 = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (949)  all_52_12 = e1
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (950)  all_52_10 = e2
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (951)  all_52_8 = e3
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (950) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (952)  all_10_1 = e2
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | REDUCE: (53), (952) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (953)  op(e2, all_10_2) = all_10_0
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | REDUCE: (183), (951) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (954)  op(e3, all_52_9) = e3
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | REDUCE: (52), (952) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (955)  op(e2, all_10_2) = e2
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | REDUCE: (167), (949) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (956)  op(e1, all_52_13) = e1
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.19  | | | | | | | | | | | | | | | | | | REDUCE: (159), (948) imply:
% 168.92/25.19  | | | | | | | | | | | | | | | | | |   (957)  op(e0, all_52_15) = e0
% 168.92/25.19  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (154), (155),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (172), (173), (177),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (179), (270), (271), (273), (276), (277), (279),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (280), (282), (283), (302), (304), (305), (306),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (307), (311), (319), (323), (328), (330), (331),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (344), (349), (359), (364), (370), (373), (385),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (386), (392), (403), (409), (415), (425), (429),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (494), (531), (533), (534), (535), (536), (537),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (552), (554), (556), (557), (558), (561), (562),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (563), (565), (566), (567), (569), (571), (573),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (579), (588), (595), (596), (663), (796), (800),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (809), (926), (929), (930), (932), (933), (934),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (935), (953), (954), (955), (956), (957),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            #582.
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | |   (958)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 168.92/25.20  | | | | | | | | | | | | | | | | |            & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 168.92/25.20  | | | | | | | | | | | | | | | | |            = e2 & all_52_28 = e1 & all_52_30 = e0)
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | BETA: splitting (958) gives:
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (959)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 168.92/25.20  | | | | | | | | | | | | | | | | | |          all_52_22 = e0
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (862), (959) are inconsistent by sub-proof
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            #553.
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (960)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 168.92/25.20  | | | | | | | | | | | | | | | | | |          all_52_30 = e0
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (37), (161), (163), (164), (165),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (172), (173), (177), (179), (181), (270), (271),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (280), (282), (283), (304), (328), (330), (344),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (349), (386), (392), (403), (429), (494), (531),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (533), (534), (544), (546), (548), (552), (554),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (562), (566), (596), (663), (796), (926), (929),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (930), (933), (960), (function-axioms) are
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | End of split
% 168.92/25.20  | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | Case 2:
% 168.92/25.20  | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | |   (961)   ~ (all_58_15 = e0)
% 168.92/25.20  | | | | | | | | | | | | | | | |   (962)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 168.92/25.20  | | | | | | | | | | | | | | | |          & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 168.92/25.20  | | | | | | | | | | | | | | | |            e0)
% 168.92/25.20  | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | ALPHA: (962) implies:
% 168.92/25.20  | | | | | | | | | | | | | | | |   (963)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 168.92/25.20  | | | | | | | | | | | | | | | |   (964)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 168.92/25.20  | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | REDUCE: (532), (961) imply:
% 168.92/25.20  | | | | | | | | | | | | | | | |   (965)   ~ (all_6_2 = e0)
% 168.92/25.20  | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 168.92/25.20  | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | |   (966)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.20  | | | | | | | | | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 168.92/25.20  | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0)
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | BETA: splitting (966) gives:
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (967)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.20  | | | | | | | | | | | | | | | | | |          all_52_6 = e0
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (929), (967), (function-axioms)
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #600.
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (968)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 168.92/25.20  | | | | | | | | | | | | | | | | | |          all_52_14 = e0
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | ALPHA: (968) implies:
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (969)  all_52_14 = e0
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (970)  all_52_12 = e1
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (971)  all_52_10 = e2
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (972)  all_52_8 = e3
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (971) imply:
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (973)  all_10_1 = e2
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REDUCE: (53), (973) imply:
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (974)  op(e2, all_10_2) = all_10_0
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REDUCE: (183), (972) imply:
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (975)  op(e3, all_52_9) = e3
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REDUCE: (52), (973) imply:
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (976)  op(e2, all_10_2) = e2
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REDUCE: (167), (970) imply:
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (977)  op(e1, all_52_13) = e1
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REDUCE: (159), (969) imply:
% 168.92/25.20  | | | | | | | | | | | | | | | | | |   (978)  op(e0, all_52_15) = e0
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (42), (61), (62),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (170), (172),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (182), (268),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (270), (272), (273), (274), (277), (279), (280),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (304), (307), (311), (313),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (315), (319), (321), (323), (326), (328), (329),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (330), (331), (344), (349), (350), (359), (364),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (409), (413), (415), (419), (494), (529), (531),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (552), (553), (554), (556), (557), (558), (559),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (579), (580),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (599), (600), (663), (796), (800), (807), (809),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (926), (929), (964), (965), (974), (975), (976),
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            (977), (978), (function-axioms) are inconsistent
% 168.92/25.20  | | | | | | | | | | | | | | | | | |            by sub-proof #571.
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | |   (979)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 168.92/25.20  | | | | | | | | | | | | | | | | |            & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 168.92/25.20  | | | | | | | | | | | | | | | | |            = e2 & all_52_28 = e1 & all_52_30 = e0)
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | BETA: splitting (979) gives:
% 168.92/25.20  | | | | | | | | | | | | | | | | | 
% 168.92/25.20  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.20  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | |   (980)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 168.92/25.21  | | | | | | | | | | | | | | | | | |          all_52_22 = e0
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (862), (980) are inconsistent by sub-proof
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            #553.
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | |   (981)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 168.92/25.21  | | | | | | | | | | | | | | | | | |          all_52_30 = e0
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (61), (154),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (165), (172),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (183), (268),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (270), (280), (281), (282), (283), (303), (304),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (306), (307), (322), (324), (325), (326), (328),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (330), (344), (349), (364), (370), (385), (386),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (391), (392), (403), (413), (494), (529), (531),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (538), (539),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (540), (544), (546), (548), (552), (554), (555),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (557), (558), (559), (562), (565), (566), (567),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (568), (569), (578), (580), (581), (586), (591),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (595), (596), (597), (649), (663), (796), (797),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (799), (813), (926), (929), (963), (981),
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            #534.
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | End of split
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | End of split
% 168.92/25.21  | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | End of split
% 168.92/25.21  | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | End of split
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | Case 2:
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | |   (982)  all_30_1 = e1
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | COMBINE_EQS: (712), (982) imply:
% 168.92/25.21  | | | | | | | | | | | | |   (983)  all_10_1 = e1
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | SIMP: (983) implies:
% 168.92/25.21  | | | | | | | | | | | | |   (984)  all_10_1 = e1
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | COMBINE_EQS: (661), (984) imply:
% 168.92/25.21  | | | | | | | | | | | | |   (985)  all_52_10 = e1
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | REDUCE: (802), (984) imply:
% 168.92/25.21  | | | | | | | | | | | | |   (986)   ~ (e3 = e1)
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | REDUCE: (53), (984) imply:
% 168.92/25.21  | | | | | | | | | | | | |   (987)  op(e1, all_10_2) = all_10_0
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | REDUCE: (52), (984) imply:
% 168.92/25.21  | | | | | | | | | | | | |   (988)  op(e2, all_10_2) = e1
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | BETA: splitting (108) gives:
% 168.92/25.21  | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | Case 1:
% 168.92/25.21  | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | |   (989)   ~ (all_32_1 = e2)
% 168.92/25.21  | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | REDUCE: (713), (989) imply:
% 168.92/25.21  | | | | | | | | | | | | | |   (990)   ~ (all_14_1 = e2)
% 168.92/25.21  | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 168.92/25.21  | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | Case 1:
% 168.92/25.21  | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | |   (991)   ~ (all_34_0 = e1)
% 168.92/25.21  | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | REDUCE: (773), (991) imply:
% 168.92/25.21  | | | | | | | | | | | | | | |   (992)   ~ (all_4_0 = e1)
% 168.92/25.21  | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 168.92/25.21  | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | Case 1:
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | |   (993)   ~ (all_40_1 = e1)
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | REDUCE: (715), (993) imply:
% 168.92/25.21  | | | | | | | | | | | | | | | |   (994)   ~ (all_4_1 = e1)
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (41), (42), (43), (51), (52), (53), (61), (62),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (63), (154), (155), (156), (158), (159), (160),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (167), (168), (169),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (170), (172), (173), (174), (176), (177), (178),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (275), (276),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (277), (278), (279), (280), (281), (282), (283),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (308), (310), (311), (312), (313), (314), (315),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (322), (323),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (597), (598), (599), (600), (649), (661), (719),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (720), (796), (797), (799), (800), (802), (803),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (805), (807), (809), (811), (813), (990), (992),
% 168.92/25.21  | | | | | | | | | | | | | | | |            (994), (function-axioms) are inconsistent by
% 168.92/25.21  | | | | | | | | | | | | | | | |            sub-proof #633.
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | Case 2:
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | |   (995)  all_40_1 = e1
% 168.92/25.21  | | | | | | | | | | | | | | | |   (996)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (715), (995) imply:
% 168.92/25.21  | | | | | | | | | | | | | | | |   (997)  all_4_1 = e1
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | SIMP: (997) implies:
% 168.92/25.21  | | | | | | | | | | | | | | | |   (998)  all_4_1 = e1
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (998) imply:
% 168.92/25.21  | | | | | | | | | | | | | | | |   (999)  all_52_0 = e1
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | REDUCE: (796), (998) imply:
% 168.92/25.21  | | | | | | | | | | | | | | | |   (1000)   ~ (e2 = e1)
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | REDUCE: (38), (998) imply:
% 168.92/25.21  | | | | | | | | | | | | | | | |   (1001)  op(e1, all_4_2) = all_4_0
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | REDUCE: (37), (998) imply:
% 168.92/25.21  | | | | | | | | | | | | | | | |   (1002)  op(e3, all_4_2) = e1
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 168.92/25.21  | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | |   (1003)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.21  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 168.92/25.21  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | BETA: splitting (1003) gives:
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | |   (1004)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 168.92/25.21  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (999), (1004) are inconsistent by sub-proof
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            #632.
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | |   (1005)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 168.92/25.21  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (985), (1005) are inconsistent by sub-proof
% 168.92/25.21  | | | | | | | | | | | | | | | | | |            #533.
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | |   (1006)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 168.92/25.21  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 168.92/25.21  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | BETA: splitting (1006) gives:
% 168.92/25.21  | | | | | | | | | | | | | | | | | 
% 168.92/25.21  | | | | | | | | | | | | | | | | | Case 1:
% 168.92/25.21  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1007)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 168.92/25.22  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | ALPHA: (1007) implies:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1008)  all_52_22 = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1009)  all_52_20 = e1
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1010)  all_52_18 = e2
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1011)  all_52_16 = e3
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1009) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1012)  all_14_1 = e1
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | SIMP: (1012) implies:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1013)  all_14_1 = e1
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (63), (1013) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1014)  op(e1, all_14_2) = all_14_0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (182), (1011) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1015)  op(e3, all_52_17) = e3
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (174), (1010) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1016)  op(e2, all_52_19) = e2
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (62), (1013) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1017)  op(e1, all_14_2) = e1
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (158), (1008) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1018)  op(e0, all_52_23) = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (154),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (155), (156), (163), (164), (165), (169), (170),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (181), (183), (268),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (270), (271), (272), (274), (275), (276), (277),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (278), (283), (301), (302), (303), (304), (305),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (313), (314), (315),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (317), (319), (320), (321), (322), (323), (324),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (350), (364), (365), (370), (373), (385), (391),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (403), (415), (419), (425), (429), (518), (529),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (571), (575),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (591), (593),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (770),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (796), (802), (803), (805), (811), (992), (996),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (1001), (1002), (1014), (1015), (1016), (1017),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (1018), (function-axioms) are inconsistent by
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            sub-proof #531.
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | Case 2:
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1019)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 168.92/25.22  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | ALPHA: (1019) implies:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1020)  all_52_30 = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1021)  all_52_28 = e1
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1022)  all_52_26 = e2
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1023)  all_52_24 = e3
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1020) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1024)  all_6_1 = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | SIMP: (1024) implies:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1025)  all_6_1 = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (43), (1025) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1026)  op(e0, all_6_2) = all_6_0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (181), (1023) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1027)  op(e3, all_52_25) = e3
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (173), (1022) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1028)  op(e2, all_52_27) = e2
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (165), (1021) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1029)  op(e1, all_52_29) = e1
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REDUCE: (42), (1025) imply:
% 168.92/25.22  | | | | | | | | | | | | | | | | | |   (1030)  op(e0, all_6_2) = e0
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (154), (155),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (170), (172), (177),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (178), (179), (182), (183), (268), (269), (270),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (271), (272), (274), (276), (280), (281), (283),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (310), (311), (313), (315), (319), (321), (322),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (330),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (331), (341), (344), (349), (350), (364), (370),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (413), (419),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (425), (429), (518), (529), (531), (532), (533),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (569), (571), (573), (577), (578), (580), (581),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (582), (585), (586), (587), (588), (589), (591),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (600), (770), (797),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (799), (811), (813), (992), (996), (1001), (1002),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (1026), (1027), (1028), (1029), (1030),
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 168.92/25.22  | | | | | | | | | | | | | | | | | |            #529.
% 168.92/25.22  | | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | | End of split
% 168.92/25.22  | | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | | End of split
% 168.92/25.22  | | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | End of split
% 168.92/25.22  | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | Case 2:
% 168.92/25.22  | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | |   (1031)  all_34_0 = e1
% 168.92/25.22  | | | | | | | | | | | | | | |   (1032)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 168.92/25.22  | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (1031) imply:
% 168.92/25.22  | | | | | | | | | | | | | | |   (1033)  all_4_0 = e1
% 168.92/25.22  | | | | | | | | | | | | | | | 
% 168.92/25.22  | | | | | | | | | | | | | | | REDUCE: (38), (1033) imply:
% 168.92/25.22  | | | | | | | | | | | | | | |   (1034)  op(all_4_1, all_4_2) = e1
% 168.92/25.22  | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (41), (42),
% 169.35/25.23  | | | | | | | | | | | | | | |            (43), (52), (53), (61), (62), (63), (154), (155),
% 169.35/25.23  | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 169.35/25.23  | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 169.35/25.23  | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 169.35/25.23  | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 169.35/25.23  | | | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 169.35/25.23  | | | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 169.35/25.23  | | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (317),
% 169.35/25.23  | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 169.35/25.23  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (341), (344),
% 169.35/25.23  | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 169.35/25.23  | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 169.35/25.23  | | | | | | | | | | | | | | |            (415), (419), (425), (429), (494), (529), (530),
% 169.35/25.23  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 169.35/25.23  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 169.35/25.23  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 169.35/25.23  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 169.35/25.23  | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 169.35/25.23  | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 169.35/25.23  | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 169.35/25.23  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 169.35/25.23  | | | | | | | | | | | | | | |            (600), (649), (661), (663), (719), (720), (796),
% 169.35/25.23  | | | | | | | | | | | | | | |            (797), (799), (800), (802), (803), (805), (807),
% 169.35/25.23  | | | | | | | | | | | | | | |            (809), (813), (1032), (1034), (function-axioms)
% 169.35/25.23  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #554.
% 169.35/25.23  | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | End of split
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | Case 2:
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | |   (1035)  all_32_1 = e2
% 169.35/25.23  | | | | | | | | | | | | | |   (1036)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e3)
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | COMBINE_EQS: (713), (1035) imply:
% 169.35/25.23  | | | | | | | | | | | | | |   (1037)  all_14_1 = e2
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | SIMP: (1037) implies:
% 169.35/25.23  | | | | | | | | | | | | | |   (1038)  all_14_1 = e2
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | COMBINE_EQS: (719), (1038) imply:
% 169.35/25.23  | | | | | | | | | | | | | |   (1039)  all_52_20 = e2
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | REDUCE: (807), (1038) imply:
% 169.35/25.23  | | | | | | | | | | | | | |   (1040)   ~ (e3 = e2)
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | REDUCE: (63), (1038) imply:
% 169.35/25.23  | | | | | | | | | | | | | |   (1041)  op(e2, all_14_2) = all_14_0
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | REDUCE: (62), (1038) imply:
% 169.35/25.23  | | | | | | | | | | | | | |   (1042)  op(e1, all_14_2) = e2
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.35/25.23  | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | Case 1:
% 169.35/25.23  | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | |   (1043)   ~ (all_34_0 = e1)
% 169.35/25.23  | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | REDUCE: (773), (1043) imply:
% 169.35/25.23  | | | | | | | | | | | | | | |   (1044)   ~ (all_4_0 = e1)
% 169.35/25.23  | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.35/25.23  | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | Case 1:
% 169.35/25.23  | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | |   (1045)   ~ (all_40_1 = e1)
% 169.35/25.23  | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | REDUCE: (715), (1045) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | |   (1046)   ~ (all_4_1 = e1)
% 169.35/25.23  | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.35/25.23  | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.23  | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | |   (1047)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.35/25.23  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.35/25.23  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.35/25.23  | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | BETA: splitting (1047) gives:
% 169.35/25.23  | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1048)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.35/25.23  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | ALPHA: (1048) implies:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1049)  all_52_6 = e0
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1050)  all_52_4 = e1
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1051)  all_52_2 = e2
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1052)  all_52_0 = e3
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1052) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1053)  all_4_1 = e3
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | REDUCE: (38), (1053) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1054)  op(e3, all_4_2) = all_4_0
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | REDUCE: (37), (1053) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1055)  op(e3, all_4_2) = e3
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | REDUCE: (176), (1051) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1056)  op(e2, all_52_3) = e2
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | REDUCE: (168), (1050) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1057)  op(e1, all_52_5) = e1
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | REDUCE: (160), (1049) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1058)  op(e0, all_52_7) = e0
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 169.35/25.23  | | | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (1054), (1055)
% 169.35/25.23  | | | | | | | | | | | | | | | | | |              gives:
% 169.35/25.23  | | | | | | | | | | | | | | | | | |   (1059)  all_4_0 = e3
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1060)  all_58_15 = e0
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (1060) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1061)  all_6_2 = e0
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (597), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1062)   ~ (all_52_7 = e0)
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (599), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1063)   ~ (all_52_15 = e0)
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (600), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1064)   ~ (all_52_23 = e0)
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (564), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1065)   ~ (all_52_25 = e0)
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (582), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1066)   ~ (all_52_27 = e0)
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (594), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1067)   ~ (all_52_29 = e0)
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1068)  op(all_6_1, e0) = all_6_0
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1069)  op(e0, e0) = all_6_1
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1061) imply:
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |   (1070)  op(e0, e0) = e0
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (52), (53), (154),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (155), (156), (159), (160), (161), (163), (164),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (165), (167), (170), (172), (173), (177), (178),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (269), (270),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (271), (272), (273), (275), (276), (278), (280),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (282), (283), (302), (303), (304), (305), (306),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (322),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (323), (324), (326), (330), (331), (341), (344),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (425), (429),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (546), (548),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (558),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (565), (566),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (567), (569), (571), (573), (578), (579), (580),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (581), (584), (585), (586), (587), (588), (591),
% 169.35/25.23  | | | | | | | | | | | | | | | | | | |            (593), (595), (596), (597), (598), (661), (720),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |            (797), (799), (800), (809), (811), (813), (1039),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |            (1042), (1044), (1046), (1060), (1062), (1063),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |            (1064), (1065), (1066), (1067), (1068), (1069),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |            (1070), (function-axioms) are inconsistent by
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |            sub-proof #547.
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |   (1071)   ~ (all_58_15 = e0)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |   (1072)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |             e0)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | ALPHA: (1072) implies:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |   (1073)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | REDUCE: (532), (1071) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | |   (1074)   ~ (all_6_2 = e0)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1075)  all_56_15 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (1075) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1076)  all_6_2 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | SIMP: (1076) implies:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1077)  all_6_2 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1078)  all_58_15 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1079)   ~ (all_52_7 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (599), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1080)   ~ (all_52_15 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (600), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1081)   ~ (all_52_23 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1082)   ~ (all_52_29 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1083)  op(all_6_1, e3) = all_6_0
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1084)  op(e0, e3) = all_6_1
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1077) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1085)  op(e0, e0) = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |              all_6_1, e3, e0, simplifying with (156), (1084)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |              gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1086)  all_52_25 = all_6_1
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (1086) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1087)  all_58_12 = all_6_1
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (1086) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1088)   ~ (all_52_9 = all_6_1)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (1086) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1089)   ~ (all_52_17 = all_6_1)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (1086) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1090)   ~ (all_52_27 = all_6_1)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | SIMP: (1090) implies:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1091)   ~ (all_52_27 = all_6_1)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (1086) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1092)   ~ (all_52_29 = all_6_1)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | SIMP: (1092) implies:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1093)   ~ (all_52_29 = all_6_1)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (1086) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | |   (1094)  op(e3, all_6_1) = all_52_24
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | |   (1095)  all_56_3 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (1079), (1095) are inconsistent by
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | |   (1096)   ~ (all_56_3 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | |   (1097)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |   (1098)  all_58_9 = e2
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (1098) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |   (1099)  all_52_7 = e2
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1099) implies:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |   (1100)  all_52_7 = e2
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (1100) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |   (1101)   ~ (all_52_3 = e2)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1058), (1100) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |   (1102)  op(e0, e2) = e0
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (155), (156), (164), (170), (172),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (177), (178), (179), (273), (278), (282), (283),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (303), (307), (311), (315), (324), (326), (331),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (392), (403),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (537), (538), (540), (542), (544), (546), (548),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (550), (552), (560), (565), (566), (567), (568),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (569), (573), (575), (583), (584), (585), (586),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (587), (588), (591), (593), (595), (596), (597),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (797), (988), (1055), (1056), (1057), (1058),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (1078), (1082), (1083), (1087), (1101), (1102),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |            #523.
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | |   (1103)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |   (1104)  all_56_9 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (154), (155), (156), (163), (164), (170),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (273), (281), (282),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (283), (305), (306), (307), (311), (315), (324),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (326), (331), (359), (364), (370), (373), (386),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (391), (392), (403), (413), (419), (531), (532),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (533), (535), (536), (537), (538), (540), (542),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (544), (546), (550), (552), (560), (566), (567),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (579), (583), (584), (585), (586),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (587), (591), (593), (595), (596), (597), (1055),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (1056), (1057), (1058), (1079), (1082), (1085),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            (1097), (1104), (function-axioms) are inconsistent
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #521.
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |   (1105)   ~ (all_56_9 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (1105) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | |   (1106)   ~ (all_52_19 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |   (1107)  all_58_6 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (164), (172), (177), (178), (179), (273),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (311), (315), (324), (326), (331),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (403), (531),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            (532), (533), (535), (536), (537), (538), (540),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (550), (552), (560), (566),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (583), (584), (585), (586), (587),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (1055), (1056),
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            (1057), (1058), (1082), (1107), (function-axioms)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #850.
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | |   (1108)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1108) gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (1109)  all_58_7 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (1109) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (1110)  all_52_19 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1106), (1110) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (1111)  $false
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1111) is inconsistent.
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (1112)  all_58_8 = e3 | all_58_11 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1112) gives:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1113)  all_58_8 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (1113) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1114)  all_14_2 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (1114) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1115)  all_32_2 = e3
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (1114) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1116)   ~ (all_52_5 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (1114) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1117)   ~ (all_52_13 = e3)
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1041), (1114) imply:
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1118)  op(e2, e3) = all_14_0
% 169.35/25.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1042), (1114) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1119)  op(e1, e3) = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1036) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1120)   ~ (all_32_2 = e3)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1115), (1120) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1121)  $false
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1121) is inconsistent.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1122)   ~ (all_32_0 = e0)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (793), (1122) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1123)   ~ (all_14_0 = e0)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, e1, simplifying with (164), (1119) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1124)  all_52_17 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e3, e2, simplifying with (172), (1118)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1125)  all_52_9 = all_14_0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (1125) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1126)  all_56_4 = all_14_0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (1124) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1127)  all_58_6 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (1125) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1128)  all_58_2 = all_14_0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (1125) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1129)   ~ (all_52_13 = all_14_0)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1129) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1130)   ~ (all_52_13 = all_14_0)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (1125) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1131)   ~ (all_52_15 = all_14_0)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1131) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1132)   ~ (all_52_15 = all_14_0)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1088), (1125) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1133)   ~ (all_14_0 = all_6_1)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (1125) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1134)   ~ (all_14_0 = all_4_2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (1124) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1135)   ~ (all_52_19 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1135) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1136)   ~ (all_52_19 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (1124) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1137)   ~ (all_52_23 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1137) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1138)   ~ (all_52_23 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1089), (1124) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1139)   ~ (all_6_1 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1139) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1140)   ~ (all_6_1 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (1124) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1141)   ~ (all_4_2 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1141) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1142)   ~ (all_4_2 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (1124) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1143)  op(e3, e2) = all_52_16
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1144)  all_58_2 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1128), (1144) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1145)  all_14_0 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1145) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1146)  all_14_0 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (805), (1146) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1147)  $false
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1147) is inconsistent.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1148)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1148) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1149)  all_58_3 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (1149) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1150)  all_10_2 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (1150) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1151)   ~ (all_52_3 = e3)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (1150) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1152)  op(e2, e2) = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (987), (1150) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1153)  op(e1, e3) = all_10_0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1154)  all_58_0 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (1154) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1155)  all_4_2 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1156)  all_58_0 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1154), (1156) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1157)  e3 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1157) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1158)  $false
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1158) is inconsistent.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1159)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1103) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1160)  all_58_10 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1160) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1161)  all_52_15 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1161) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1162)  all_52_15 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (1162) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1163)   ~ (all_52_7 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (1162) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1164)   ~ (all_52_13 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1132), (1162) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1165)   ~ (all_14_0 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1159) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1166)  all_58_2 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1123), (1128), (1166) are inconsistent by
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #520.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1167)  all_58_6 = e0 | all_58_12 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1168)  all_56_4 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (805), (1126), (1168) are inconsistent by
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #519.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1169)   ~ (all_56_4 = e3)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1170)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1170) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1171)  all_56_4 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (803), (1126), (1171) are inconsistent by
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #518.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1172)  all_56_4 = e1 | all_56_4 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1167) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1173)  all_58_6 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1127), (1173) are inconsistent by sub-proof
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #517.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1174)  all_58_12 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1087), (1174) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1175)  all_6_1 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1175) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1176)  all_6_1 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1083), (1176) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1177)  op(e0, e3) = all_6_0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1094), (1176) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1178)  op(e3, e0) = all_52_24
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1084), (1176) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1179)  op(e0, e3) = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1172) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1180)  all_56_4 = e1
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1126), (1180) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1181)  all_14_0 = e1
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1181) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1182)  all_14_0 = e1
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1130), (1182) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1183)   ~ (all_52_13 = e1)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1184)  all_56_6 = e3
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (415), (1117), (1184) are inconsistent by
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #573.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1185)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (154), (177), (179), (302), (305), (322),
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (386), (415), (533), (536), (540), (588),
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (797), (800), (809), (1056), (1058), (1078),
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1079), (1085), (1097), (1119), (1136), (1143),
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1149), (1151), (1152), (1153), (1163), (1164),
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1174), (1177), (1178), (1179), (1183), (1185),
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #513.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1186)  all_56_4 = e0
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1123), (1126), (1186) are inconsistent by
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #512.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1187)   ~ (all_58_10 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1188)  all_58_11 = e2 | all_58_15 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (1187) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1189)   ~ (all_52_15 = e2)
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1190)  all_58_2 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1128), (1190) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1191)  all_14_0 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1191) implies:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1192)  all_14_0 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (803), (1192) imply:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1193)  $false
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1193) is inconsistent.
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1194)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 169.35/25.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1159) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1195)  all_58_2 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1123), (1128), (1195) are inconsistent by
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #520.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1196)  all_58_6 = e0 | all_58_12 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1196) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1197)  all_58_6 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1127), (1197) are inconsistent by sub-proof
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #517.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1198)  all_58_12 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1087), (1198) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1199)  all_6_1 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1199) implies:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1200)  all_6_1 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1091), (1200) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1201)   ~ (all_52_27 = e0)
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1093), (1200) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1202)   ~ (all_52_29 = e0)
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1140), (1200) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1203)   ~ (e2 = e0)
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1194) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1204)  all_58_3 = e2
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1149), (1204) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1205)  e3 = e2
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (1205) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1206)  $false
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1206) is inconsistent.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1207)  all_58_5 = e2 | all_58_10 = e2
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1207) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1208)  all_58_5 = e2
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1209)  all_58_2 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1123), (1128), (1209) are inconsistent by
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #520.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1210)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1210) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1211)  all_58_3 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1149), (1211) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1212)  e3 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1078), (1212) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1213)  all_58_15 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1188) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1214)  all_58_11 = e2
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (1138), (1214) are inconsistent by
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #935.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1215)  all_58_15 = e2
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1213), (1215) are inconsistent by sub-proof
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #991.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1216)  all_58_5 = e0 | all_58_10 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1216) gives:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1217)  all_58_5 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1208), (1217) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1218)  e2 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1218) implies:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1219)  e2 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1219) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1220)  $false
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1220) is inconsistent.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1221)  all_58_10 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (1221) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1222)  all_52_15 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1222) implies:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1223)  all_52_15 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (1223) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1224)   ~ (all_52_7 = e0)
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (155), (156), (178), (179), (280), (283),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (305), (306), (307), (326), (330), (331), (370),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (386), (391), (403), (531), (532), (535), (536),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (540), (546), (552), (569), (586), (595), (596),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (597), (1055), (1058), (1116), (1151), (1201),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1202), (1224), (function-axioms) are inconsistent
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1011.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1225)  all_58_10 = e2
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (1189), (1225) are inconsistent by
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #711.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1226)   ~ (all_58_0 = e3)
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (1226) imply:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1227)   ~ (all_4_2 = e3)
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (178), (179), (283), (307), (326), (331),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (370), (391), (403), (531), (532), (535), (536),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (540), (546), (552), (569), (586), (595), (596),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (597), (1055), (1058), (1116), (1151), (1227),
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1012.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1228)  all_58_5 = e3 | all_58_10 = e3
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (373), (1080), (1117), (1228) are
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1229)  all_58_11 = e3
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (1081), (1229) are inconsistent by
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1017.
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | |   (1230)   ~ (all_56_15 = e3)
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | |   (1231)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 169.35/25.26  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (158),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (169), (170),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (269), (270),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (283), (304), (305), (307), (310), (311), (312),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (1055), (1056),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (1057), (1058), (1073), (1074), (1230), (1231),
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | |            #785.
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.27  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1232)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.35/25.27  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (985), (1232) are inconsistent by sub-proof
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            #533.
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | End of split
% 169.35/25.27  | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.27  | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | |   (1233)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.35/25.27  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.35/25.27  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.35/25.27  | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | BETA: splitting (1233) gives:
% 169.35/25.27  | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1234)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.35/25.27  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1039), (1234) are inconsistent by sub-proof
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            #553.
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1235)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.35/25.27  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | ALPHA: (1235) implies:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1236)  all_52_30 = e0
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1237)  all_52_28 = e1
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1238)  all_52_26 = e2
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1239)  all_52_24 = e3
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1236) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1240)  all_6_1 = e0
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | SIMP: (1240) implies:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1241)  all_6_1 = e0
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REDUCE: (43), (1241) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1242)  op(e0, all_6_2) = all_6_0
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REDUCE: (181), (1239) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1243)  op(e3, all_52_25) = e3
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REDUCE: (173), (1238) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1244)  op(e2, all_52_27) = e2
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REDUCE: (165), (1237) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1245)  op(e1, all_52_29) = e1
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REDUCE: (42), (1241) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | | | |   (1246)  op(e0, all_6_2) = e0
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (154), (155),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (170), (172), (177),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (178), (179), (182), (183), (268), (269), (270),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (271), (272), (275), (276), (278), (280), (281),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (403), (413), (425), (429), (529), (530), (531),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (566),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (577), (578),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (585), (586), (587),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (597), (600), (796), (797), (799), (811), (813),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (1044), (1046), (1242), (1243), (1244), (1245),
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            (1246), (function-axioms) are inconsistent by
% 169.35/25.27  | | | | | | | | | | | | | | | | | |            sub-proof #511.
% 169.35/25.27  | | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | | End of split
% 169.35/25.27  | | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | End of split
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | Case 2:
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | |   (1247)  all_40_1 = e1
% 169.35/25.27  | | | | | | | | | | | | | | | |   (1248)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | COMBINE_EQS: (715), (1247) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | |   (1249)  all_4_1 = e1
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1249) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | |   (1250)  all_52_0 = e1
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | REDUCE: (796), (1249) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | |   (1251)   ~ (e2 = e1)
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | REDUCE: (38), (1249) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | |   (1252)  op(e1, all_4_2) = all_4_0
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.27  | | | | | | | | | | | | | | | | REDUCE: (37), (1249) imply:
% 169.35/25.27  | | | | | | | | | | | | | | | |   (1253)  op(e3, all_4_2) = e1
% 169.35/25.27  | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (42), (43), (52), (53), (61), (62), (154), (155),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (276),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (277), (279), (280), (281), (282), (283), (301),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (310),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (311), (313), (315), (316), (319), (320), (321),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (518), (529), (531), (532), (533), (534), (535),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (598), (599), (600), (649), (661), (770), (796),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (797), (800), (807), (809), (811), (813), (1039),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (1042), (1044), (1248), (1250), (1252), (1253),
% 169.35/25.28  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.28  | | | | | | | | | | | | | | | |            #535.
% 169.35/25.28  | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | End of split
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | Case 2:
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | |   (1254)  all_34_0 = e1
% 169.35/25.28  | | | | | | | | | | | | | | |   (1255)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (1254) imply:
% 169.35/25.28  | | | | | | | | | | | | | | |   (1256)  all_4_0 = e1
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | SIMP: (1256) implies:
% 169.35/25.28  | | | | | | | | | | | | | | |   (1257)  all_4_0 = e1
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | REDUCE: (38), (1257) imply:
% 169.35/25.28  | | | | | | | | | | | | | | |   (1258)  op(all_4_1, all_4_2) = e1
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (41), (42),
% 169.35/25.28  | | | | | | | | | | | | | | |            (43), (52), (53), (61), (62), (63), (154), (155),
% 169.35/25.28  | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 169.35/25.28  | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 169.35/25.28  | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 169.35/25.28  | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 169.35/25.28  | | | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 169.35/25.28  | | | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 169.35/25.28  | | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (317),
% 169.35/25.28  | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 169.35/25.28  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (341), (344),
% 169.35/25.28  | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 169.35/25.28  | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 169.35/25.28  | | | | | | | | | | | | | | |            (415), (419), (425), (429), (494), (529), (530),
% 169.35/25.28  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 169.35/25.28  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 169.35/25.28  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 169.35/25.28  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 169.35/25.28  | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 169.35/25.28  | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 169.35/25.28  | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 169.35/25.28  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 169.35/25.28  | | | | | | | | | | | | | | |            (600), (649), (661), (663), (719), (720), (796),
% 169.35/25.28  | | | | | | | | | | | | | | |            (797), (799), (800), (802), (803), (805), (807),
% 169.35/25.28  | | | | | | | | | | | | | | |            (809), (813), (1255), (1258), (function-axioms)
% 169.35/25.28  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #554.
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | End of split
% 169.35/25.28  | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | End of split
% 169.35/25.28  | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | End of split
% 169.35/25.28  | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | Case 2:
% 169.35/25.28  | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | |   (1259)  all_28_0 = e3
% 169.35/25.28  | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | COMBINE_EQS: (776), (1259) imply:
% 169.35/25.28  | | | | | | | | | | | |   (1260)  all_6_0 = e3
% 169.35/25.28  | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | REDUCE: (43), (1260) imply:
% 169.35/25.28  | | | | | | | | | | | |   (1261)  op(all_6_1, all_6_2) = e3
% 169.35/25.28  | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | BETA: splitting (103) gives:
% 169.35/25.28  | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | Case 1:
% 169.35/25.28  | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | |   (1262)   ~ (all_30_1 = e1)
% 169.35/25.28  | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | REDUCE: (712), (1262) imply:
% 169.35/25.28  | | | | | | | | | | | | |   (1263)   ~ (all_10_1 = e1)
% 169.35/25.28  | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | BETA: splitting (108) gives:
% 169.35/25.28  | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | Case 1:
% 169.35/25.28  | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | |   (1264)   ~ (all_32_1 = e2)
% 169.35/25.28  | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | REDUCE: (713), (1264) imply:
% 169.35/25.28  | | | | | | | | | | | | | |   (1265)   ~ (all_14_1 = e2)
% 169.35/25.28  | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.35/25.28  | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | Case 1:
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | |   (1266)   ~ (all_34_0 = e1)
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | REDUCE: (773), (1266) imply:
% 169.35/25.28  | | | | | | | | | | | | | | |   (1267)   ~ (all_4_0 = e1)
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.35/25.28  | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | Case 1:
% 169.35/25.28  | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | |   (1268)   ~ (all_40_1 = e1)
% 169.35/25.28  | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | REDUCE: (715), (1268) imply:
% 169.35/25.28  | | | | | | | | | | | | | | | |   (1269)   ~ (all_4_1 = e1)
% 169.35/25.28  | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.35/25.28  | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | |   (1270)  all_58_15 = e0
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1261), (1270),
% 169.35/25.28  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.28  | | | | | | | | | | | | | | | | |            #510.
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | |   (1271)   ~ (all_58_15 = e0)
% 169.35/25.28  | | | | | | | | | | | | | | | | |   (1272)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.35/25.28  | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.35/25.28  | | | | | | | | | | | | | | | | |             e0)
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | ALPHA: (1272) implies:
% 169.35/25.28  | | | | | | | | | | | | | | | | |   (1273)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 169.35/25.28  | | | | | | | | | | | | | | | | |   (1274)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | REDUCE: (532), (1271) imply:
% 169.35/25.28  | | | | | | | | | | | | | | | | |   (1275)   ~ (all_6_2 = e0)
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.35/25.28  | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.28  | | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | |   (1276)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.35/25.28  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.35/25.28  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.35/25.28  | | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | | BETA: splitting (1276) gives:
% 169.35/25.28  | | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.28  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | | |   (1277)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.35/25.28  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.35/25.28  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | | | ALPHA: (1277) implies:
% 169.35/25.28  | | | | | | | | | | | | | | | | | | |   (1278)  all_52_6 = e0
% 169.35/25.28  | | | | | | | | | | | | | | | | | | |   (1279)  all_52_4 = e1
% 169.35/25.28  | | | | | | | | | | | | | | | | | | |   (1280)  all_52_2 = e2
% 169.35/25.28  | | | | | | | | | | | | | | | | | | |   (1281)  all_52_0 = e3
% 169.35/25.28  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.28  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1281) imply:
% 169.35/25.28  | | | | | | | | | | | | | | | | | | |   (1282)  all_4_1 = e3
% 169.35/25.28  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (37), (38), (41), (42), (43), (51),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (52), (61), (62), (154), (155), (156), (158),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (159), (160), (161), (163), (164), (165), (168),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (176), (177), (178),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (179), (268), (269), (270), (271), (272), (273),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (274), (275), (276), (279), (280), (281), (282),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (306), (307),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (319), (321), (322), (323), (324), (325), (326),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (419), (425), (429), (529), (531), (532), (533),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (554), (556), (557), (558), (559), (560), (561),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (569), (573), (575), (578), (579), (580), (581),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (598), (599), (600), (797), (811), (1265), (1267),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (1274), (1275), (1278), (1279), (1280), (1282),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            #783.
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1283)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | ALPHA: (1283) implies:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1284)  all_52_14 = e0
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1285)  all_52_12 = e1
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1286)  all_52_10 = e2
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1287)  all_52_8 = e3
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (1286) imply:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1288)  all_10_1 = e2
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (38), (42), (52), (53),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (61), (62), (154), (156), (158), (159), (161),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (169), (170), (172),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (183), (268), (270), (272), (273), (274), (277),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (303), (304),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (307), (311), (313), (315), (316), (317), (319),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (320), (321), (323), (326), (328), (329), (330),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (359), (364), (370),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (413), (415), (419), (529), (531), (532), (533),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (568), (569), (571), (573), (578), (579), (580),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (598), (599), (600), (796), (800), (807), (809),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (811), (1267), (1269), (1274), (1275), (1284),
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            (1285), (1287), (1288), (function-axioms) are
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #715.
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.29  | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | |   (1289)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.35/25.29  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.35/25.29  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.35/25.29  | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | BETA: splitting (1289) gives:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1290)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | ALPHA: (1290) implies:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1291)  all_52_22 = e0
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1292)  all_52_20 = e1
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1293)  all_52_18 = e2
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1294)  all_52_16 = e3
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1292) imply:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1295)  all_14_1 = e1
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | SIMP: (1295) implies:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1296)  all_14_1 = e1
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | REDUCE: (63), (1296) imply:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1297)  op(e1, all_14_2) = all_14_0
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | REDUCE: (182), (1294) imply:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1298)  op(e3, all_52_17) = e3
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | REDUCE: (174), (1293) imply:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1299)  op(e2, all_52_19) = e2
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | REDUCE: (62), (1296) imply:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1300)  op(e1, all_14_2) = e1
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | REDUCE: (158), (1291) imply:
% 169.35/25.29  | | | | | | | | | | | | | | | | | | |   (1301)  op(e0, all_52_23) = e0
% 169.35/25.29  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (52),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (165), (169), (170),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (268), (270), (271), (273), (274), (275), (276),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (277), (278), (282), (283), (302), (303), (304),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (307), (308), (310), (311), (312), (313), (314),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (315), (317), (319), (320), (321), (322), (323),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (324), (326), (328), (329), (330), (331), (344),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (349), (359), (364), (365), (370), (373), (385),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (391), (392), (403), (415), (419), (425), (429),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (571),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (593), (595), (596), (597), (598), (600), (796),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (802), (803), (805), (811), (1261), (1267),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (1269), (1273), (1274), (1275), (1297), (1298),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (1299), (1300), (1301), (function-axioms) are
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #503.
% 169.35/25.30  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.30  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |   (1302)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.35/25.30  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1261), (1302),
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.30  | | | | | | | | | | | | | | | | | | |            #501.
% 169.35/25.30  | | | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | | | End of split
% 169.35/25.30  | | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | | End of split
% 169.35/25.30  | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | End of split
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | Case 2:
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | |   (1303)  all_40_1 = e1
% 169.35/25.30  | | | | | | | | | | | | | | | |   (1304)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | COMBINE_EQS: (715), (1303) imply:
% 169.35/25.30  | | | | | | | | | | | | | | | |   (1305)  all_4_1 = e1
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1305) imply:
% 169.35/25.30  | | | | | | | | | | | | | | | |   (1306)  all_52_0 = e1
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | REDUCE: (796), (1305) imply:
% 169.35/25.30  | | | | | | | | | | | | | | | |   (1307)   ~ (e2 = e1)
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | REDUCE: (38), (1305) imply:
% 169.35/25.30  | | | | | | | | | | | | | | | |   (1308)  op(e1, all_4_2) = all_4_0
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | REDUCE: (37), (1305) imply:
% 169.35/25.30  | | | | | | | | | | | | | | | |   (1309)  op(e3, all_4_2) = e1
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.35/25.30  | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | Case 1:
% 169.35/25.30  | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | |   (1310)  all_58_15 = e0
% 169.35/25.30  | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1261), (1310),
% 169.35/25.30  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.35/25.30  | | | | | | | | | | | | | | | | |            #510.
% 169.35/25.30  | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | Case 2:
% 169.35/25.30  | | | | | | | | | | | | | | | | | 
% 169.35/25.30  | | | | | | | | | | | | | | | | |   (1311)   ~ (all_58_15 = e0)
% 169.35/25.30  | | | | | | | | | | | | | | | | |   (1312)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.35/25.30  | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.35/25.30  | | | | | | | | | | | | | | | | |             e0)
% 169.35/25.30  | | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (42), (52), (61), (62), (63), (154), (155), (156),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (270),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (278), (279), (280), (281), (283), (303), (304),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (305), (307), (310), (311), (313), (314), (315),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (322), (323),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (359), (364), (365),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (403), (409),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (413), (415), (419), (425), (429), (518), (529),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (770),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (796), (802), (803), (805), (807), (811), (1263),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (1267), (1304), (1306), (1308), (1309), (1311),
% 169.66/25.30  | | | | | | | | | | | | | | | | |            (1312), (function-axioms) are inconsistent by
% 169.66/25.30  | | | | | | | | | | | | | | | | |            sub-proof #500.
% 169.66/25.30  | | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | End of split
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | End of split
% 169.66/25.30  | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | Case 2:
% 169.66/25.30  | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | |   (1313)  all_34_0 = e1
% 169.66/25.30  | | | | | | | | | | | | | | |   (1314)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 169.66/25.30  | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (1313) imply:
% 169.66/25.30  | | | | | | | | | | | | | | |   (1315)  all_4_0 = e1
% 169.66/25.30  | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | SIMP: (1315) implies:
% 169.66/25.30  | | | | | | | | | | | | | | |   (1316)  all_4_0 = e1
% 169.66/25.30  | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | REDUCE: (38), (1316) imply:
% 169.66/25.30  | | | | | | | | | | | | | | |   (1317)  op(all_4_1, all_4_2) = e1
% 169.66/25.30  | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.66/25.30  | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | |   (1318)  all_58_15 = e0
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1261), (1318),
% 169.66/25.30  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.30  | | | | | | | | | | | | | | | |            #510.
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | |   (1319)   ~ (all_58_15 = e0)
% 169.66/25.30  | | | | | | | | | | | | | | | |   (1320)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.66/25.30  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.66/25.30  | | | | | | | | | | | | | | | |             e0)
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | ALPHA: (1320) implies:
% 169.66/25.30  | | | | | | | | | | | | | | | |   (1321)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | REDUCE: (532), (1319) imply:
% 169.66/25.30  | | | | | | | | | | | | | | | |   (1322)   ~ (all_6_2 = e0)
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.30  | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.30  | | | | | | | | | | | | | | | | | 
% 169.66/25.30  | | | | | | | | | | | | | | | | |   (1323)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.30  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.30  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.30  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (42), (52), (53), (61),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (62), (156), (158), (159), (163), (164), (165),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (167), (170), (172), (173), (174), (177), (178),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (179), (182), (183), (268), (270), (272), (273),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (274), (277), (279), (280), (281), (282), (283),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (304), (307), (311), (313), (315), (319), (321),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (323), (326), (328), (329), (330), (331), (344),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (419), (494), (529), (531), (532), (533), (534),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (571), (573), (579), (580), (581), (582), (583),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (661),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (663), (720), (796), (800), (807), (809), (1314),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (1317), (1321), (1322), (1323), (function-axioms)
% 169.66/25.31  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #570.
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | |   (1324)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.31  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.31  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | BETA: splitting (1324) gives:
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1325)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.31  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | ALPHA: (1325) implies:
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1326)  all_52_22 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1327)  all_52_20 = e1
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1328)  all_52_18 = e2
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1329)  all_52_16 = e3
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1327) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1330)  all_14_1 = e1
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (62), (63),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (169), (170),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (182), (268), (270), (274), (275), (276), (277),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (278), (282), (283), (304), (307), (310), (311),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (320), (321),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (385), (391), (392), (403), (415), (419), (425),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (494), (529), (530), (531), (532), (533), (534),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (566), (568), (571), (575),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (591), (593), (595),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (663), (796), (802),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (803), (805), (1314), (1317), (1321), (1326),
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            (1328), (1329), (1330), (function-axioms) are
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #560.
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1331)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.31  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | ALPHA: (1331) implies:
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1332)  all_52_30 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1332) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1333)  all_6_1 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (1261), (1333), (function-axioms) are
% 169.66/25.31  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | End of split
% 169.66/25.31  | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | End of split
% 169.66/25.31  | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | End of split
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | Case 2:
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | |   (1334)  all_32_1 = e2
% 169.66/25.31  | | | | | | | | | | | | | |   (1335)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e3)
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | COMBINE_EQS: (713), (1334) imply:
% 169.66/25.31  | | | | | | | | | | | | | |   (1336)  all_14_1 = e2
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | SIMP: (1336) implies:
% 169.66/25.31  | | | | | | | | | | | | | |   (1337)  all_14_1 = e2
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | COMBINE_EQS: (719), (1337) imply:
% 169.66/25.31  | | | | | | | | | | | | | |   (1338)  all_52_20 = e2
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | REDUCE: (63), (1337) imply:
% 169.66/25.31  | | | | | | | | | | | | | |   (1339)  op(e2, all_14_2) = all_14_0
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.66/25.31  | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | Case 1:
% 169.66/25.31  | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | |   (1340)   ~ (all_34_0 = e1)
% 169.66/25.31  | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | REDUCE: (773), (1340) imply:
% 169.66/25.31  | | | | | | | | | | | | | | |   (1341)   ~ (all_4_0 = e1)
% 169.66/25.31  | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.66/25.31  | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.31  | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | |   (1342)   ~ (all_40_1 = e1)
% 169.66/25.31  | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | REDUCE: (715), (1342) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | |   (1343)   ~ (all_4_1 = e1)
% 169.66/25.31  | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.66/25.31  | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | |   (1344)  all_58_15 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1261), (1344),
% 169.66/25.31  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.31  | | | | | | | | | | | | | | | | |            #510.
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | |   (1345)   ~ (all_58_15 = e0)
% 169.66/25.31  | | | | | | | | | | | | | | | | |   (1346)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.66/25.31  | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.66/25.31  | | | | | | | | | | | | | | | | |             e0)
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | ALPHA: (1346) implies:
% 169.66/25.31  | | | | | | | | | | | | | | | | |   (1347)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | REDUCE: (532), (1345) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | |   (1348)   ~ (all_6_2 = e0)
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.31  | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | |   (1349)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.31  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.31  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | BETA: splitting (1349) gives:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1350)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | ALPHA: (1350) implies:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1351)  all_52_6 = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1352)  all_52_4 = e1
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1353)  all_52_2 = e2
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1354)  all_52_0 = e3
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1354) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1355)  all_4_1 = e3
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | REDUCE: (38), (1355) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1356)  op(e3, all_4_2) = all_4_0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | REDUCE: (37), (1355) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1357)  op(e3, all_4_2) = e3
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | REDUCE: (176), (1353) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1358)  op(e2, all_52_3) = e2
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | REDUCE: (168), (1352) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1359)  op(e1, all_52_5) = e1
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | REDUCE: (160), (1351) imply:
% 169.66/25.31  | | | | | | | | | | | | | | | | | | |   (1360)  op(e0, all_52_7) = e0
% 169.66/25.31  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (41), (52), (61), (154), (155), (156),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (169),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (268),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (276), (277),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (304), (305),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (312), (313), (314),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (315), (317), (319), (323), (324), (326), (327),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (328), (330), (331), (341), (344), (349), (350),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (386), (391),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (392), (403), (409), (413), (415), (425), (429),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (492), (529), (531), (532), (533), (534), (535),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (575),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (793), (803), (811), (1263), (1335), (1339),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (1341), (1347), (1348), (1356), (1357), (1358),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (1359), (1360), (function-axioms) are inconsistent
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            by sub-proof #540.
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1361)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | ALPHA: (1361) implies:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1362)  all_52_14 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1363)  all_52_12 = e1
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1364)  all_52_10 = e2
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1365)  all_52_8 = e3
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (1364) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1366)  all_10_1 = e2
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (38), (42), (52), (53),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (61), (62), (154), (156), (158), (159), (161),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (169), (170), (172),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (183), (268), (270), (272), (273), (274), (277),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (303), (304),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (307), (311), (313), (315), (316), (317), (319),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (320), (321), (323), (326), (328), (329), (330),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (359), (364), (370),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (413), (415), (419), (529), (531), (532), (533),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (568), (569), (571), (573), (578), (579), (580),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (598), (599), (600), (796), (800), (807), (809),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (811), (1341), (1343), (1347), (1348), (1362),
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            (1363), (1365), (1366), (function-axioms) are
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #715.
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | End of split
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1367)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.32  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.32  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | BETA: splitting (1367) gives:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1368)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1338), (1368) are inconsistent by sub-proof
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            #539.
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1369)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | ALPHA: (1369) implies:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1370)  all_52_30 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1370) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |   (1371)  all_6_1 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (1261), (1371), (function-axioms) are
% 169.66/25.32  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 169.66/25.32  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | End of split
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.32  | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | End of split
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | |   (1372)  all_40_1 = e1
% 169.66/25.32  | | | | | | | | | | | | | | | |   (1373)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | COMBINE_EQS: (715), (1372) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | |   (1374)  all_4_1 = e1
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1374) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | |   (1375)  all_52_0 = e1
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | REDUCE: (796), (1374) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | |   (1376)   ~ (e2 = e1)
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | REDUCE: (38), (1374) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | |   (1377)  op(e1, all_4_2) = all_4_0
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | REDUCE: (37), (1374) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | |   (1378)  op(e3, all_4_2) = e1
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.32  | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.32  | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | |   (1379)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.32  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.32  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.32  | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | BETA: splitting (1379) gives:
% 169.66/25.32  | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1380)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.32  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1375), (1380) are inconsistent by sub-proof
% 169.66/25.32  | | | | | | | | | | | | | | | | | |            #632.
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1381)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.32  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | ALPHA: (1381) implies:
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1382)  all_52_14 = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1383)  all_52_12 = e1
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1384)  all_52_10 = e2
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1385)  all_52_8 = e3
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (1384) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1386)  all_10_1 = e2
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | REDUCE: (53), (1386) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1387)  op(e2, all_10_2) = all_10_0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | REDUCE: (183), (1385) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1388)  op(e3, all_52_9) = e3
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | REDUCE: (52), (1386) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1389)  op(e2, all_10_2) = e2
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | REDUCE: (167), (1383) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1390)  op(e1, all_52_13) = e1
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.32  | | | | | | | | | | | | | | | | | | REDUCE: (159), (1382) imply:
% 169.66/25.32  | | | | | | | | | | | | | | | | | |   (1391)  op(e0, all_52_15) = e0
% 169.66/25.32  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (38), (42), (61),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (62), (154), (155), (156), (158), (161), (163),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (174),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (268), (270),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (271), (272), (273), (274), (276), (277), (279),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (280), (281), (282), (283), (301), (302), (303),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (304), (305), (306), (307), (311), (313), (315),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (316), (319), (320), (321), (323), (326), (328),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (359),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (518), (529), (531), (532), (533), (534), (535),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (573), (578), (579), (580), (581), (582), (583),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (591), (593),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (770), (796), (800), (807), (809), (811), (1341),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (1373), (1377), (1378), (1387), (1388), (1389),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (1390), (1391), (function-axioms) are inconsistent
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            by sub-proof #538.
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | |   (1392)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.33  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.33  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | BETA: splitting (1392) gives:
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | |   (1393)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.33  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1338), (1393) are inconsistent by sub-proof
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            #539.
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | |   (1394)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.33  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1261), (1394),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            #501.
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | Case 2:
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | |   (1395)  all_34_0 = e1
% 169.66/25.33  | | | | | | | | | | | | | | |   (1396)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (1395) imply:
% 169.66/25.33  | | | | | | | | | | | | | | |   (1397)  all_4_0 = e1
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | REDUCE: (811), (1397) imply:
% 169.66/25.33  | | | | | | | | | | | | | | |   (1398)   ~ (e2 = e1)
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | REDUCE: (38), (1397) imply:
% 169.66/25.33  | | | | | | | | | | | | | | |   (1399)  op(all_4_1, all_4_2) = e1
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | |   (1400)  all_58_15 = e0
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1261), (1400),
% 169.66/25.33  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.33  | | | | | | | | | | | | | | | |            #510.
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | |   (1401)   ~ (all_58_15 = e0)
% 169.66/25.33  | | | | | | | | | | | | | | | |   (1402)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.66/25.33  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.66/25.33  | | | | | | | | | | | | | | | |             e0)
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | ALPHA: (1402) implies:
% 169.66/25.33  | | | | | | | | | | | | | | | |   (1403)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | REDUCE: (532), (1401) imply:
% 169.66/25.33  | | | | | | | | | | | | | | | |   (1404)   ~ (all_6_2 = e0)
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | |   (1405)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.33  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.33  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (42), (52), (53), (61),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (62), (156), (158), (159), (163), (164), (165),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (167), (170), (172), (173), (174), (177), (178),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (179), (182), (183), (268), (270), (272), (273),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (274), (277), (279), (280), (281), (282), (283),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (304), (307), (311), (313), (315), (319), (321),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (323), (326), (328), (329), (330), (331), (344),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (419), (494), (529), (531), (532), (533), (534),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (571), (573), (579), (580), (581), (582), (583),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (661),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (663), (720), (796), (800), (807), (809), (1396),
% 169.66/25.33  | | | | | | | | | | | | | | | | |            (1399), (1403), (1404), (1405), (function-axioms)
% 169.66/25.33  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #570.
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | |   (1406)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.33  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.33  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | BETA: splitting (1406) gives:
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | |   (1407)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.33  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1338), (1407) are inconsistent by sub-proof
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            #539.
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | |   (1408)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.33  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1261), (1408),
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.33  | | | | | | | | | | | | | | | | | |            #501.
% 169.66/25.33  | | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | | 
% 169.66/25.33  | | | | | | | | | | | | | | End of split
% 169.66/25.33  | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | End of split
% 169.66/25.34  | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | Case 2:
% 169.66/25.34  | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | |   (1409)  all_30_1 = e1
% 169.66/25.34  | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | COMBINE_EQS: (712), (1409) imply:
% 169.66/25.34  | | | | | | | | | | | | |   (1410)  all_10_1 = e1
% 169.66/25.34  | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | COMBINE_EQS: (661), (1410) imply:
% 169.66/25.34  | | | | | | | | | | | | |   (1411)  all_52_10 = e1
% 169.66/25.34  | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | REDUCE: (802), (1410) imply:
% 169.66/25.34  | | | | | | | | | | | | |   (1412)   ~ (e3 = e1)
% 169.66/25.34  | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | BETA: splitting (108) gives:
% 169.66/25.34  | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | Case 1:
% 169.66/25.34  | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | |   (1413)   ~ (all_32_1 = e2)
% 169.66/25.34  | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | REDUCE: (713), (1413) imply:
% 169.66/25.34  | | | | | | | | | | | | | |   (1414)   ~ (all_14_1 = e2)
% 169.66/25.34  | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.66/25.34  | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | Case 1:
% 169.66/25.34  | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | |   (1415)   ~ (all_34_0 = e1)
% 169.66/25.34  | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | REDUCE: (773), (1415) imply:
% 169.66/25.34  | | | | | | | | | | | | | | |   (1416)   ~ (all_4_0 = e1)
% 169.66/25.34  | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.66/25.34  | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.34  | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | |   (1417)   ~ (all_40_1 = e1)
% 169.66/25.34  | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | REDUCE: (715), (1417) imply:
% 169.66/25.34  | | | | | | | | | | | | | | | |   (1418)   ~ (all_4_1 = e1)
% 169.66/25.34  | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.66/25.34  | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | |   (1419)  all_58_15 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1261), (1419),
% 169.66/25.34  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.34  | | | | | | | | | | | | | | | | |            #510.
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | |   (1420)   ~ (all_58_15 = e0)
% 169.66/25.34  | | | | | | | | | | | | | | | | |   (1421)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.66/25.34  | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.66/25.34  | | | | | | | | | | | | | | | | |             e0)
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | ALPHA: (1421) implies:
% 169.66/25.34  | | | | | | | | | | | | | | | | |   (1422)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | |   (1423)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | REDUCE: (532), (1420) imply:
% 169.66/25.34  | | | | | | | | | | | | | | | | |   (1424)   ~ (all_6_2 = e0)
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.34  | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | |   (1425)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.34  | | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.34  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.34  | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | BETA: splitting (1425) gives:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1426)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | ALPHA: (1426) implies:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1427)  all_52_6 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1428)  all_52_4 = e1
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1429)  all_52_2 = e2
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1430)  all_52_0 = e3
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1430) imply:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1431)  all_4_1 = e3
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (37), (38), (41), (42), (43), (51),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (52), (61), (62), (154), (155), (156), (158),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (159), (160), (161), (163), (164), (165), (168),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (176), (177), (178),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (179), (268), (269), (270), (271), (272), (273),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (274), (275), (276), (279), (280), (281), (282),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (306), (307),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (319), (321), (322), (323), (324), (325), (326),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (419), (425), (429), (529), (531), (532), (533),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (554), (556), (557), (558), (559), (560), (561),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (569), (573), (575), (578), (579), (580), (581),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (598), (599), (600), (797), (811), (1414), (1416),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (1423), (1424), (1427), (1428), (1429), (1431),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            #783.
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1432)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1411), (1432) are inconsistent by sub-proof
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            #533.
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | End of split
% 169.66/25.34  | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | |   (1433)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.34  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.34  | | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.34  | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | BETA: splitting (1433) gives:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1434)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | ALPHA: (1434) implies:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1435)  all_52_22 = e0
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1436)  all_52_20 = e1
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1437)  all_52_18 = e2
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1438)  all_52_16 = e3
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1436) imply:
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |   (1439)  all_14_1 = e1
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.34  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (62),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (63), (155), (156), (158), (161), (163), (164),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (165), (169), (170), (172), (173), (174), (177),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (278),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (282), (283), (304), (306), (307), (308), (310),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (317), (319),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (326), (328),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (359), (364),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (392), (403),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (415), (419), (425), (429), (529), (530), (531),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (566), (567), (568), (571), (573), (575), (577),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (796), (802),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (803), (805), (811), (1416), (1418), (1422),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (1423), (1424), (1435), (1437), (1438), (1439),
% 169.66/25.34  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.35  | | | | | | | | | | | | | | | | | | |            #666.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | |   (1440)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | ALPHA: (1440) implies:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | |   (1441)  all_52_30 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1441) imply:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | |   (1442)  all_6_1 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (1261), (1442), (function-axioms) are
% 169.66/25.35  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1443)  all_40_1 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1444)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | COMBINE_EQS: (715), (1443) imply:
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1445)  all_4_1 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1445) imply:
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1446)  all_52_0 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | REDUCE: (796), (1445) imply:
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1447)   ~ (e2 = e1)
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | REDUCE: (38), (1445) imply:
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1448)  op(e1, all_4_2) = all_4_0
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | REDUCE: (37), (1445) imply:
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1449)  op(e3, all_4_2) = e1
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | |   (1450)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.35  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | BETA: splitting (1450) gives:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1451)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1446), (1451) are inconsistent by sub-proof
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            #632.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1452)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1411), (1452) are inconsistent by sub-proof
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            #533.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | |   (1453)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.35  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | BETA: splitting (1453) gives:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1454)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (62),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (63), (154), (155), (156), (158), (163), (164),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (165), (169), (170), (172), (174), (177), (178),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (268), (270), (271),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (272), (274), (275), (276), (277), (278), (283),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (310), (311), (313), (314), (315), (317), (319),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (326), (328),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (364),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (403), (415),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (419), (425), (429), (518), (529), (530), (531),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (566), (567), (568), (571), (575), (577), (578),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (586), (587), (588), (591), (593), (594), (595),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (719), (770), (796),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (802), (803), (805), (811), (1416), (1444),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (1448), (1449), (1454), (function-axioms) are
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #499.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1455)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1261), (1455),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            #501.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | |   (1456)  all_34_0 = e1
% 169.66/25.35  | | | | | | | | | | | | | | |   (1457)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 169.66/25.35  | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (1456) imply:
% 169.66/25.35  | | | | | | | | | | | | | | |   (1458)  all_4_0 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | REDUCE: (811), (1458) imply:
% 169.66/25.35  | | | | | | | | | | | | | | |   (1459)   ~ (e2 = e1)
% 169.66/25.35  | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | REDUCE: (38), (1458) imply:
% 169.66/25.35  | | | | | | | | | | | | | | |   (1460)  op(all_4_1, all_4_2) = e1
% 169.66/25.35  | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.66/25.35  | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1461)  all_58_15 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1261), (1461),
% 169.66/25.35  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.35  | | | | | | | | | | | | | | | |            #510.
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1462)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.66/25.35  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.66/25.35  | | | | | | | | | | | | | | | |             e0)
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | ALPHA: (1462) implies:
% 169.66/25.35  | | | | | | | | | | | | | | | |   (1463)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.35  | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | |   (1464)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.35  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | BETA: splitting (1464) gives:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1465)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (1460), (1465),
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            #600.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1466)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1411), (1466) are inconsistent by sub-proof
% 169.66/25.35  | | | | | | | | | | | | | | | | | |            #533.
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | |   (1467)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.35  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | BETA: splitting (1467) gives:
% 169.66/25.35  | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1468)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.35  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | ALPHA: (1468) implies:
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1469)  all_52_22 = e0
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1470)  all_52_20 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1471)  all_52_18 = e2
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1472)  all_52_16 = e3
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.35  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1470) imply:
% 169.66/25.35  | | | | | | | | | | | | | | | | | |   (1473)  all_14_1 = e1
% 169.66/25.35  | | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (62), (63),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (169), (170),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (182), (268), (270), (274), (275), (276), (277),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (278), (282), (283), (304), (307), (310), (311),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (320), (321),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (385), (391), (392), (403), (415), (419), (425),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (494), (529), (530), (531), (532), (533), (534),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (566), (568), (571), (575),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (591), (593), (595),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (663), (796), (802),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (803), (805), (1457), (1460), (1463), (1469),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (1471), (1472), (1473), (function-axioms) are
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #560.
% 169.66/25.36  | | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.36  | | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | |   (1474)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1261), (1474),
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.36  | | | | | | | | | | | | | | | | | |            #501.
% 169.66/25.36  | | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | End of split
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | End of split
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | End of split
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | End of split
% 169.66/25.36  | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | Case 2:
% 169.66/25.36  | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | |   (1475)  all_32_1 = e2
% 169.66/25.36  | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | COMBINE_EQS: (713), (1475) imply:
% 169.66/25.36  | | | | | | | | | | | | | |   (1476)  all_14_1 = e2
% 169.66/25.36  | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | SIMP: (1476) implies:
% 169.66/25.36  | | | | | | | | | | | | | |   (1477)  all_14_1 = e2
% 169.66/25.36  | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | COMBINE_EQS: (719), (1477) imply:
% 169.66/25.36  | | | | | | | | | | | | | |   (1478)  all_52_20 = e2
% 169.66/25.36  | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.66/25.36  | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | Case 1:
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | |   (1479)   ~ (all_34_0 = e1)
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | REDUCE: (773), (1479) imply:
% 169.66/25.36  | | | | | | | | | | | | | | |   (1480)   ~ (all_4_0 = e1)
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | |   (1481)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.36  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | BETA: splitting (1481) gives:
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1482)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | ALPHA: (1482) implies:
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1483)  all_52_6 = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1484)  all_52_4 = e1
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1485)  all_52_2 = e2
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1486)  all_52_0 = e3
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1486) imply:
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1487)  all_4_1 = e3
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REDUCE: (38), (1487) imply:
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1488)  op(e3, all_4_2) = all_4_0
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REDUCE: (37), (1487) imply:
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1489)  op(e3, all_4_2) = e3
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REDUCE: (176), (1485) imply:
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1490)  op(e2, all_52_3) = e2
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REDUCE: (168), (1484) imply:
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1491)  op(e1, all_52_5) = e1
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REDUCE: (160), (1483) imply:
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1492)  op(e0, all_52_7) = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (41), (42), (61), (154), (156), (158),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (169), (170),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (268), (269),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (270), (271), (272), (273), (276), (279), (281),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (282), (283), (301), (302), (303), (304), (305),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (307), (310), (311), (312), (313), (314), (315),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (317), (319), (323), (324), (326), (327), (328),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (392), (403),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (409), (413), (425), (429), (529), (531), (532),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (553), (554), (556), (557), (558), (559), (560),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (568), (569), (575), (578), (579), (580), (581),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (598), (599), (600), (811), (1261), (1480),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (1488), (1489), (1490), (1491), (1492),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.36  | | | | | | | | | | | | | | | | |            #495.
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1493)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1411), (1493) are inconsistent by sub-proof
% 169.66/25.36  | | | | | | | | | | | | | | | | |            #533.
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | End of split
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | |   (1494)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.36  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.36  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | BETA: splitting (1494) gives:
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1495)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1478), (1495) are inconsistent by sub-proof
% 169.66/25.36  | | | | | | | | | | | | | | | | |            #539.
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1496)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1261), (1496),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.36  | | | | | | | | | | | | | | | | |            #501.
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | End of split
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | End of split
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | Case 2:
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | |   (1497)  all_34_0 = e1
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | COMBINE_EQS: (773), (1497) imply:
% 169.66/25.36  | | | | | | | | | | | | | | |   (1498)  all_4_0 = e1
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | SIMP: (1498) implies:
% 169.66/25.36  | | | | | | | | | | | | | | |   (1499)  all_4_0 = e1
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | REDUCE: (811), (1499) imply:
% 169.66/25.36  | | | | | | | | | | | | | | |   (1500)   ~ (e2 = e1)
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | REDUCE: (38), (1499) imply:
% 169.66/25.36  | | | | | | | | | | | | | | |   (1501)  op(all_4_1, all_4_2) = e1
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.36  | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | |   (1502)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.36  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | BETA: splitting (1502) gives:
% 169.66/25.36  | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | |   (1503)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.36  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (1501), (1503),
% 169.66/25.36  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.36  | | | | | | | | | | | | | | | | |            #600.
% 169.66/25.36  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | |   (1504)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.37  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1411), (1504) are inconsistent by sub-proof
% 169.66/25.37  | | | | | | | | | | | | | | | | |            #533.
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | End of split
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1505)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.66/25.37  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.66/25.37  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | BETA: splitting (1505) gives:
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | Case 1:
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | |   (1506)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.66/25.37  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1478), (1506) are inconsistent by sub-proof
% 169.66/25.37  | | | | | | | | | | | | | | | | |            #539.
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | Case 2:
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | |   (1507)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.66/25.37  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1261), (1507),
% 169.66/25.37  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.37  | | | | | | | | | | | | | | | | |            #501.
% 169.66/25.37  | | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | End of split
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | End of split
% 169.66/25.37  | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | End of split
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | End of split
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | End of split
% 169.66/25.37  | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | End of split
% 169.66/25.37  | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | Case 2:
% 169.66/25.37  | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | |   (1508)  all_26_0 = e2
% 169.66/25.37  | | | | | | | | | | |   (1509)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 169.66/25.37  | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | COMBINE_EQS: (779), (1508) imply:
% 169.66/25.37  | | | | | | | | | | |   (1510)  all_4_0 = e2
% 169.66/25.37  | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | COMBINE_EQS: (742), (1510) imply:
% 169.66/25.37  | | | | | | | | | | |   (1511)  all_50_0 = e2
% 169.66/25.37  | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | REDUCE: (38), (1510) imply:
% 169.66/25.37  | | | | | | | | | | |   (1512)  op(all_4_1, all_4_2) = e2
% 169.66/25.37  | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | BETA: splitting (98) gives:
% 169.66/25.37  | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | Case 1:
% 169.66/25.37  | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | |   (1513)   ~ (all_28_0 = e3)
% 169.66/25.37  | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | REDUCE: (776), (1513) imply:
% 169.66/25.37  | | | | | | | | | | | |   (1514)   ~ (all_6_0 = e3)
% 169.66/25.37  | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | BETA: splitting (151) gives:
% 169.66/25.37  | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | Case 1:
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | |   (1515)   ~ (all_50_0 = e2)
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | REDUCE: (1511), (1515) imply:
% 169.66/25.37  | | | | | | | | | | | | |   (1516)  $false
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | CLOSE: (1516) is inconsistent.
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | Case 2:
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | |   (1517)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.66/25.37  | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | Case 1:
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | |   (1518)  all_58_15 = e0
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | COMBINE_EQS: (532), (1518) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1519)  all_6_2 = e0
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (597), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1520)   ~ (all_52_7 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (599), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1521)   ~ (all_52_15 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (600), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1522)   ~ (all_52_23 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (564), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1523)   ~ (all_52_25 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (582), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1524)   ~ (all_52_27 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (594), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1525)   ~ (all_52_29 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (43), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1526)  op(all_6_1, e0) = all_6_0
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (42), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1527)  op(e0, e0) = all_6_1
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (41), (1519) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1528)  op(e0, e0) = e0
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 169.66/25.37  | | | | | | | | | | | | | |              e0, e0, simplifying with (1527), (1528) gives:
% 169.66/25.37  | | | | | | | | | | | | | |   (1529)  all_6_1 = e0
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (1526), (1529) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1530)  op(e0, e0) = all_6_0
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 169.66/25.37  | | | | | | | | | | | | | |              e0, e0, simplifying with (1528), (1530) gives:
% 169.66/25.37  | | | | | | | | | | | | | |   (1531)  all_6_0 = e0
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (1514), (1531) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1532)   ~ (e3 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (799), (1531) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1533)   ~ (e2 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | REDUCE: (797), (1531) imply:
% 169.66/25.37  | | | | | | | | | | | | | |   (1534)   ~ (e1 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.66/25.37  | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | Case 1:
% 169.66/25.37  | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | |   (1535)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.37  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.66/25.37  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.66/25.37  | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | BETA: splitting (1535) gives:
% 169.66/25.37  | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | Case 1:
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1536)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.66/25.37  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (1512), (1536),
% 169.66/25.37  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.66/25.37  | | | | | | | | | | | | | | | |            #494.
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | Case 2:
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1537)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.66/25.37  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | ALPHA: (1537) implies:
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1538)  all_52_14 = e0
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1539)  all_52_12 = e1
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1540)  all_52_10 = e2
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1541)  all_52_8 = e3
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (1540) imply:
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1542)  all_10_1 = e2
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | REDUCE: (53), (1542) imply:
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1543)  op(e2, all_10_2) = all_10_0
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | REDUCE: (183), (1541) imply:
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1544)  op(e3, all_52_9) = e3
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | REDUCE: (52), (1542) imply:
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1545)  op(e2, all_10_2) = e2
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | REDUCE: (167), (1539) imply:
% 169.66/25.37  | | | | | | | | | | | | | | | |   (1546)  op(e1, all_52_13) = e1
% 169.66/25.37  | | | | | | | | | | | | | | | | 
% 169.66/25.37  | | | | | | | | | | | | | | | | REDUCE: (159), (1538) imply:
% 169.94/25.37  | | | | | | | | | | | | | | | |   (1547)  op(e0, all_52_15) = e0
% 169.94/25.37  | | | | | | | | | | | | | | | | 
% 169.94/25.37  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (154), (155),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (156), (164), (165), (172), (173), (178), (179),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (181), (269), (270), (271), (273), (276), (280),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (311),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (315), (319), (323), (330), (331), (341), (344),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (349), (359), (364), (370), (373), (385), (386),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (391), (403), (425), (429), (533), (534), (535),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (548), (552), (553), (554), (556), (558), (559),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (560), (561), (562), (563), (565), (566), (569),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (571), (573), (575), (578), (579), (581), (583),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (595), (596),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (598), (796), (800), (809), (1512), (1518),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (1521), (1523), (1524), (1525), (1543), (1544),
% 169.94/25.37  | | | | | | | | | | | | | | | |            (1545), (1546), (1547), (function-axioms) are
% 169.94/25.37  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #485.
% 169.94/25.37  | | | | | | | | | | | | | | | | 
% 169.94/25.37  | | | | | | | | | | | | | | | End of split
% 169.94/25.37  | | | | | | | | | | | | | | | 
% 169.94/25.37  | | | | | | | | | | | | | | Case 2:
% 169.94/25.37  | | | | | | | | | | | | | | | 
% 169.94/25.37  | | | | | | | | | | | | | | |   (1548)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.37  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.37  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.37  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (62), (63), (156),
% 169.94/25.38  | | | | | | | | | | | | | | |            (158), (164), (165), (172), (173), (174), (177),
% 169.94/25.38  | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (270), (271),
% 169.94/25.38  | | | | | | | | | | | | | | |            (273), (274), (275), (276), (280), (281), (283),
% 169.94/25.38  | | | | | | | | | | | | | | |            (302), (303), (304), (307), (311), (315), (319),
% 169.94/25.38  | | | | | | | | | | | | | | |            (324), (325), (326), (328), (329), (330), (331),
% 169.94/25.38  | | | | | | | | | | | | | | |            (344), (349), (359), (364), (365), (370), (373),
% 169.94/25.38  | | | | | | | | | | | | | | |            (385), (386), (391), (403), (413), (419), (425),
% 169.94/25.38  | | | | | | | | | | | | | | |            (429), (503), (521), (531), (533), (534), (535),
% 169.94/25.38  | | | | | | | | | | | | | | |            (536), (537), (538), (540), (542), (544), (546),
% 169.94/25.38  | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 169.94/25.38  | | | | | | | | | | | | | | |            (558), (560), (561), (562), (563), (566), (567),
% 169.94/25.38  | | | | | | | | | | | | | | |            (568), (578), (579), (581), (584), (585), (586),
% 169.94/25.38  | | | | | | | | | | | | | | |            (589), (591), (593), (596), (598), (698), (718),
% 169.94/25.38  | | | | | | | | | | | | | | |            (719), (796), (803), (805), (1509), (1512),
% 169.94/25.38  | | | | | | | | | | | | | | |            (1517), (1518), (1520), (1521), (1522), (1523),
% 169.94/25.38  | | | | | | | | | | | | | | |            (1524), (1548), (function-axioms) are inconsistent
% 169.94/25.38  | | | | | | | | | | | | | | |            by sub-proof #469.
% 169.94/25.38  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | End of split
% 169.94/25.38  | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | Case 2:
% 169.94/25.38  | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | |   (1549)   ~ (all_58_15 = e0)
% 169.94/25.38  | | | | | | | | | | | | | |   (1550)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.94/25.38  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.94/25.38  | | | | | | | | | | | | | |             e0)
% 169.94/25.38  | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | ALPHA: (1550) implies:
% 169.94/25.38  | | | | | | | | | | | | | |   (1551)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 169.94/25.38  | | | | | | | | | | | | | |   (1552)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.94/25.38  | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | REDUCE: (532), (1549) imply:
% 169.94/25.38  | | | | | | | | | | | | | |   (1553)   ~ (all_6_2 = e0)
% 169.94/25.38  | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.38  | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | Case 1:
% 169.94/25.38  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | |   (1554)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.38  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.38  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.38  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (52), (53), (62),
% 169.94/25.38  | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 169.94/25.38  | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 169.94/25.38  | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 169.94/25.38  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 169.94/25.38  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (311),
% 169.94/25.38  | | | | | | | | | | | | | | |            (313), (315), (316), (319), (321), (323), (325),
% 169.94/25.38  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (344), (349), (350),
% 169.94/25.38  | | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 169.94/25.38  | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (415), (419),
% 169.94/25.38  | | | | | | | | | | | | | | |            (503), (521), (529), (530), (531), (532), (533),
% 169.94/25.38  | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 169.94/25.38  | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 169.94/25.38  | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 169.94/25.38  | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 169.94/25.38  | | | | | | | | | | | | | | |            (568), (569), (571), (573), (575), (579), (580),
% 169.94/25.38  | | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 169.94/25.38  | | | | | | | | | | | | | | |            (589), (593), (594), (595), (596), (597), (598),
% 169.94/25.38  | | | | | | | | | | | | | | |            (599), (600), (661), (698), (718), (720), (796),
% 169.94/25.38  | | | | | | | | | | | | | | |            (800), (807), (809), (1509), (1512), (1517),
% 169.94/25.38  | | | | | | | | | | | | | | |            (1552), (1553), (1554), (function-axioms) are
% 169.94/25.38  | | | | | | | | | | | | | | |            inconsistent by sub-proof #462.
% 169.94/25.38  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | Case 2:
% 169.94/25.38  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | |   (1555)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.38  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.38  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.38  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (42), (43),
% 169.94/25.38  | | | | | | | | | | | | | | |            (51), (62), (63), (154), (155), (156), (158),
% 169.94/25.38  | | | | | | | | | | | | | | |            (161), (163), (164), (165), (172), (173), (174),
% 169.94/25.38  | | | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 169.94/25.38  | | | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (280),
% 169.94/25.38  | | | | | | | | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 169.94/25.38  | | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 169.94/25.38  | | | | | | | | | | | | | | |            (322), (323), (324), (325), (326), (328), (329),
% 169.94/25.38  | | | | | | | | | | | | | | |            (330), (331), (344), (349), (359), (364), (365),
% 169.94/25.38  | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 169.94/25.38  | | | | | | | | | | | | | | |            (413), (419), (425), (429), (503), (521), (529),
% 169.94/25.38  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 169.94/25.38  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 169.94/25.38  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 169.94/25.38  | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (566),
% 169.94/25.38  | | | | | | | | | | | | | | |            (567), (568), (569), (573), (577), (579), (580),
% 169.94/25.38  | | | | | | | | | | | | | | |            (581), (582), (584), (585), (586), (588), (589),
% 169.94/25.38  | | | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 169.94/25.38  | | | | | | | | | | | | | | |            (600), (649), (698), (718), (719), (796), (797),
% 169.94/25.38  | | | | | | | | | | | | | | |            (799), (803), (805), (1509), (1512), (1514),
% 169.94/25.38  | | | | | | | | | | | | | | |            (1517), (1551), (1552), (1553), (1555),
% 169.94/25.38  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.38  | | | | | | | | | | | | | | |            #448.
% 169.94/25.38  | | | | | | | | | | | | | | | 
% 169.94/25.38  | | | | | | | | | | | | | | End of split
% 169.94/25.38  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | End of split
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | End of split
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | Case 2:
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | |   (1556)  all_28_0 = e3
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | COMBINE_EQS: (776), (1556) imply:
% 169.94/25.39  | | | | | | | | | | | |   (1557)  all_6_0 = e3
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | SIMP: (1557) implies:
% 169.94/25.39  | | | | | | | | | | | |   (1558)  all_6_0 = e3
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | REDUCE: (43), (1558) imply:
% 169.94/25.39  | | | | | | | | | | | |   (1559)  op(all_6_1, all_6_2) = e3
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | BETA: splitting (151) gives:
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | |   (1560)   ~ (all_50_0 = e2)
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | REDUCE: (1511), (1560) imply:
% 169.94/25.39  | | | | | | | | | | | | |   (1561)  $false
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | CLOSE: (1561) is inconsistent.
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | Case 2:
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | |   (1562)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | |   (1563)  all_58_15 = e0
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1559), (1563),
% 169.94/25.39  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.39  | | | | | | | | | | | | | |            #510.
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | Case 2:
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | |   (1564)   ~ (all_58_15 = e0)
% 169.94/25.39  | | | | | | | | | | | | | |   (1565)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.94/25.39  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.94/25.39  | | | | | | | | | | | | | |             e0)
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | ALPHA: (1565) implies:
% 169.94/25.39  | | | | | | | | | | | | | |   (1566)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | REDUCE: (532), (1564) imply:
% 169.94/25.39  | | | | | | | | | | | | | |   (1567)   ~ (all_6_2 = e0)
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | |   (1568)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.39  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.39  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (52), (53), (62),
% 169.94/25.39  | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 169.94/25.39  | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 169.94/25.39  | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 169.94/25.39  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 169.94/25.39  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (311),
% 169.94/25.39  | | | | | | | | | | | | | | |            (313), (315), (316), (319), (321), (323), (325),
% 169.94/25.39  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (344), (349), (350),
% 169.94/25.39  | | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 169.94/25.39  | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (415), (419),
% 169.94/25.39  | | | | | | | | | | | | | | |            (503), (521), (529), (530), (531), (532), (533),
% 169.94/25.39  | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 169.94/25.39  | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 169.94/25.39  | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 169.94/25.39  | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 169.94/25.39  | | | | | | | | | | | | | | |            (568), (569), (571), (573), (575), (579), (580),
% 169.94/25.39  | | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 169.94/25.39  | | | | | | | | | | | | | | |            (589), (593), (594), (595), (596), (597), (598),
% 169.94/25.39  | | | | | | | | | | | | | | |            (599), (600), (661), (698), (718), (720), (796),
% 169.94/25.39  | | | | | | | | | | | | | | |            (800), (807), (809), (1509), (1512), (1562),
% 169.94/25.39  | | | | | | | | | | | | | | |            (1566), (1567), (1568), (function-axioms) are
% 169.94/25.39  | | | | | | | | | | | | | | |            inconsistent by sub-proof #462.
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | Case 2:
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | |   (1569)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.39  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.39  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 169.94/25.39  | | | | | | | | | | | | | | |            (156), (158), (161), (163), (164), (165), (172),
% 169.94/25.39  | | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 169.94/25.39  | | | | | | | | | | | | | | |            (183), (268), (270), (273), (274), (275), (276),
% 169.94/25.39  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (310),
% 169.94/25.39  | | | | | | | | | | | | | | |            (311), (315), (319), (321), (323), (324), (325),
% 169.94/25.39  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 169.94/25.39  | | | | | | | | | | | | | | |            (359), (364), (365), (370), (385), (386), (391),
% 169.94/25.39  | | | | | | | | | | | | | | |            (392), (403), (413), (419), (425), (521), (529),
% 169.94/25.39  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 169.94/25.39  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 169.94/25.39  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (557), (558), (559),
% 169.94/25.39  | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 169.94/25.39  | | | | | | | | | | | | | | |            (568), (569), (577), (579), (580), (582), (584),
% 169.94/25.39  | | | | | | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (598),
% 169.94/25.39  | | | | | | | | | | | | | | |            (600), (649), (718), (719), (796), (803), (805),
% 169.94/25.39  | | | | | | | | | | | | | | |            (1512), (1559), (1562), (1566), (1569),
% 169.94/25.39  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.39  | | | | | | | | | | | | | | |            #447.
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | End of split
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | End of split
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | End of split
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | End of split
% 169.94/25.39  | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | End of split
% 169.94/25.39  | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | Case 2:
% 169.94/25.39  | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | |   (1570)  all_24_0 = e1
% 169.94/25.39  | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | COMBINE_EQS: (751), (1570) imply:
% 169.94/25.39  | | | | | | | | | |   (1571)  all_10_0 = e1
% 169.94/25.39  | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | REDUCE: (800), (1571) imply:
% 169.94/25.39  | | | | | | | | | |   (1572)   ~ (e3 = e1)
% 169.94/25.39  | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | REDUCE: (53), (1571) imply:
% 169.94/25.39  | | | | | | | | | |   (1573)  op(all_10_1, all_10_2) = e1
% 169.94/25.39  | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | BETA: splitting (93) gives:
% 169.94/25.39  | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | |   (1574)   ~ (all_26_0 = e2)
% 169.94/25.39  | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | REDUCE: (779), (1574) imply:
% 169.94/25.39  | | | | | | | | | | |   (1575)   ~ (all_4_0 = e2)
% 169.94/25.39  | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | BETA: splitting (98) gives:
% 169.94/25.39  | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | |   (1576)   ~ (all_28_0 = e3)
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | REDUCE: (776), (1576) imply:
% 169.94/25.39  | | | | | | | | | | | |   (1577)   ~ (all_6_0 = e3)
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | BETA: splitting (108) gives:
% 169.94/25.39  | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | |   (1578)   ~ (all_32_1 = e2)
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | REDUCE: (713), (1578) imply:
% 169.94/25.39  | | | | | | | | | | | | |   (1579)   ~ (all_14_1 = e2)
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.94/25.39  | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | |   (1580)   ~ (all_34_0 = e1)
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | REDUCE: (773), (1580) imply:
% 169.94/25.39  | | | | | | | | | | | | | |   (1581)   ~ (all_4_0 = e1)
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.94/25.39  | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | |   (1582)   ~ (all_40_1 = e1)
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | | REDUCE: (715), (1582) imply:
% 169.94/25.39  | | | | | | | | | | | | | | |   (1583)   ~ (all_4_1 = e1)
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.94/25.39  | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | | Case 1:
% 169.94/25.39  | | | | | | | | | | | | | | | | 
% 169.94/25.39  | | | | | | | | | | | | | | | |   (1584)  all_58_15 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (1584) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1585)  all_6_2 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (597), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1586)   ~ (all_52_7 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (600), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1587)   ~ (all_52_23 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (564), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1588)   ~ (all_52_25 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (582), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1589)   ~ (all_52_27 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (594), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1590)   ~ (all_52_29 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (43), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1591)  op(all_6_1, e0) = all_6_0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (42), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1592)  op(e0, e0) = all_6_1
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (41), (1585) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1593)  op(e0, e0) = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 169.94/25.40  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (1592), (1593) gives:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1594)  all_6_1 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (1591), (1594) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1595)  op(e0, e0) = all_6_0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 169.94/25.40  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (1593), (1595) gives:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1596)  all_6_0 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (1577), (1596) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1597)   ~ (e3 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (799), (1596) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1598)   ~ (e2 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (797), (1596) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1599)   ~ (e1 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | |   (1600)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.40  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.40  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | BETA: splitting (1600) gives:
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1601)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.40  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (38), (154), (155), (156), (160),
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            (178), (179), (270), (271), (280), (283), (302),
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            (303), (304), (305), (306), (307), (323), (326),
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            (330), (331), (344), (349), (370), (386), (391),
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            (403), (429), (531), (532), (533), (534), (535),
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            (536), (540), (546), (552), (562), (569), (585),
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            (586), (595), (596), (597), (720), (1584), (1586),
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            (1588), (1589), (1590), (1601), (function-axioms)
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1008.
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1602)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.94/25.40  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | ALPHA: (1602) implies:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1603)  all_52_10 = e2
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (1603) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1604)  all_10_1 = e2
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | SIMP: (1604) implies:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1605)  all_10_1 = e2
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (1573), (1605), (function-axioms) are
% 169.94/25.40  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #446.
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | End of split
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | |   (1606)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.40  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.40  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (38), (62),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (63), (154), (155), (156), (158), (163), (164),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (165), (170), (172), (173), (174), (177), (178),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (269), (270), (271),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (281), (283), (302), (303), (304), (305), (306),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (307), (310), (311), (319), (322), (323), (324),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (325), (326), (329), (330), (331), (341), (344),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (385), (386), (391), (403), (413), (419), (425),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (429), (530), (531), (533), (534), (535), (536),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (557),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (558), (561), (562), (563), (565), (568), (569),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (571), (573), (578), (579), (580), (581), (583),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (584), (585), (586), (588), (591), (593), (596),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (598), (719), (796), (803), (805), (1575), (1581),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (1583), (1584), (1586), (1587), (1588), (1589),
% 169.94/25.40  | | | | | | | | | | | | | | | | |            (1590), (1606), (function-axioms) are inconsistent
% 169.94/25.40  | | | | | | | | | | | | | | | | |            by sub-proof #877.
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | End of split
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | Case 2:
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1607)   ~ (all_58_15 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1608)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.94/25.40  | | | | | | | | | | | | | | | |             e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | ALPHA: (1608) implies:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1609)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1610)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | REDUCE: (532), (1607) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | |   (1611)   ~ (all_6_2 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.40  | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | |   (1612)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.40  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.40  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | BETA: splitting (1612) gives:
% 169.94/25.40  | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1613)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.40  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | ALPHA: (1613) implies:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1614)  all_52_6 = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1615)  all_52_4 = e1
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1616)  all_52_2 = e2
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1617)  all_52_0 = e3
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1617) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1618)  all_4_1 = e3
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | REDUCE: (38), (1618) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1619)  op(e3, all_4_2) = all_4_0
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | REDUCE: (37), (1618) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1620)  op(e3, all_4_2) = e3
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | REDUCE: (176), (1616) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1621)  op(e2, all_52_3) = e2
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | REDUCE: (168), (1615) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1622)  op(e1, all_52_5) = e1
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.40  | | | | | | | | | | | | | | | | | | REDUCE: (160), (1614) imply:
% 169.94/25.40  | | | | | | | | | | | | | | | | | |   (1623)  op(e0, all_52_7) = e0
% 169.94/25.40  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (41), (42), (43), (51), (52), (61),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (62), (154), (155), (156), (158), (159), (161),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (163), (164), (165), (169), (170), (172), (173),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (279), (280),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (281), (282), (283), (302), (303), (304), (305),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (312), (313), (314),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (315), (317), (319), (321), (322), (323), (324),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (409), (413), (419), (425), (429), (529), (531),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (552), (553), (554), (556), (557), (558), (559),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (567), (568), (569), (573), (575), (578), (579),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (797), (1575),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (1579), (1581), (1610), (1611), (1619), (1620),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (1621), (1622), (1623), (function-axioms) are
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #784.
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1624)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.94/25.41  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | ALPHA: (1624) implies:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1625)  all_52_10 = e2
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (1625) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1626)  all_10_1 = e2
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (1573), (1626), (function-axioms) are
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #446.
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | End of split
% 169.94/25.41  | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.41  | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | |   (1627)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.41  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.41  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.41  | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | BETA: splitting (1627) gives:
% 169.94/25.41  | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1628)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.94/25.41  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | ALPHA: (1628) implies:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1629)  all_52_22 = e0
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1630)  all_52_20 = e1
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1631)  all_52_18 = e2
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1632)  all_52_16 = e3
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1630) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1633)  all_14_1 = e1
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REDUCE: (63), (1633) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1634)  op(e1, all_14_2) = all_14_0
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REDUCE: (182), (1632) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1635)  op(e3, all_52_17) = e3
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REDUCE: (174), (1631) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1636)  op(e2, all_52_19) = e2
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REDUCE: (62), (1633) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1637)  op(e1, all_14_2) = e1
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REDUCE: (158), (1629) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1638)  op(e0, all_52_23) = e0
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (155),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (165), (169), (170),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (268), (270), (271), (273), (274), (275), (276),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (277), (278), (282), (283), (304), (306), (307),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (308), (310), (311), (312), (313), (314), (315),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (317), (319), (320), (321), (322), (323), (324),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (391),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (392), (403), (415), (419), (425), (429), (529),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (571), (573),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (796), (802), (803), (805), (1575), (1581),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (1583), (1609), (1610), (1611), (1634), (1635),
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            (1636), (1637), (1638), (function-axioms) are
% 169.94/25.41  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #667.
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1639)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.94/25.41  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | ALPHA: (1639) implies:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1640)  all_52_30 = e0
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1641)  all_52_28 = e1
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1642)  all_52_26 = e2
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1643)  all_52_24 = e3
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.41  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1640) imply:
% 169.94/25.41  | | | | | | | | | | | | | | | | | |   (1644)  all_6_1 = e0
% 169.94/25.41  | | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (797), (799), (1575), (1577), (1581), (1609),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (1610), (1611), (1641), (1642), (1643), (1644),
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.42  | | | | | | | | | | | | | | | | | |            #635.
% 169.94/25.42  | | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | | End of split
% 169.94/25.42  | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | End of split
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | End of split
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | Case 2:
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | |   (1645)  all_40_1 = e1
% 169.94/25.42  | | | | | | | | | | | | | | |   (1646)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | COMBINE_EQS: (715), (1645) imply:
% 169.94/25.42  | | | | | | | | | | | | | | |   (1647)  all_4_1 = e1
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | SIMP: (1647) implies:
% 169.94/25.42  | | | | | | | | | | | | | | |   (1648)  all_4_1 = e1
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1648) imply:
% 169.94/25.42  | | | | | | | | | | | | | | |   (1649)  all_52_0 = e1
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | REDUCE: (796), (1648) imply:
% 169.94/25.42  | | | | | | | | | | | | | | |   (1650)   ~ (e2 = e1)
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | REDUCE: (38), (1648) imply:
% 169.94/25.42  | | | | | | | | | | | | | | |   (1651)  op(e1, all_4_2) = all_4_0
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | REDUCE: (37), (1648) imply:
% 169.94/25.42  | | | | | | | | | | | | | | |   (1652)  op(e3, all_4_2) = e1
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.94/25.42  | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | Case 1:
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1653)  all_58_15 = e0
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (1653) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1654)  all_6_2 = e0
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (597), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1655)   ~ (all_52_7 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (600), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1656)   ~ (all_52_23 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (564), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1657)   ~ (all_52_25 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (582), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1658)   ~ (all_52_27 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (594), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1659)   ~ (all_52_29 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (43), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1660)  op(all_6_1, e0) = all_6_0
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (42), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1661)  op(e0, e0) = all_6_1
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (41), (1654) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1662)  op(e0, e0) = e0
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 169.94/25.42  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (1661), (1662) gives:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1663)  all_6_1 = e0
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (1660), (1663) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1664)  op(e0, e0) = all_6_0
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 169.94/25.42  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (1662), (1664) gives:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1665)  all_6_0 = e0
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (1577), (1665) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1666)   ~ (e3 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (799), (1665) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1667)   ~ (e2 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | REDUCE: (797), (1665) imply:
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1668)   ~ (e1 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.42  | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | |   (1669)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.42  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.42  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (52), (661), (1573), (1649), (1669),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.42  | | | | | | | | | | | | | | | | |            #445.
% 169.94/25.42  | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.42  | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | |   (1670)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.42  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.42  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (62), (63), (154),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (155), (156), (158), (161), (163), (164), (165),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (181), (182), (269), (270), (271), (272), (274),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (277), (280), (283), (302), (303), (304), (305),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (313), (319), (325),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (326), (330), (331), (341), (344), (349), (350),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (403),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (415), (419), (429), (518), (531), (533), (534),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (558), (560), (562), (563), (566), (567), (569),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (571), (581), (583), (584), (585), (586), (587),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (591), (595), (596), (719), (770), (803), (805),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (1575), (1646), (1651), (1652), (1653), (1655),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (1656), (1657), (1658), (1659), (1670),
% 169.94/25.42  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.42  | | | | | | | | | | | | | | | | |            #614.
% 169.94/25.42  | | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | | End of split
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | Case 2:
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1671)   ~ (all_58_15 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | |   (1672)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.94/25.42  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.94/25.42  | | | | | | | | | | | | | | | |             e0)
% 169.94/25.42  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (170),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (182), (183), (185), (268), (270), (271), (274),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (275), (276), (277), (278), (283), (304), (305),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (317),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (344),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (349), (364), (365), (370), (373), (385), (391),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (403), (415), (419), (425), (429), (518), (529),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (598), (600), (649), (661), (719), (770), (796),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (802), (803), (805), (1573), (1575), (1581),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (1646), (1649), (1651), (1652), (1671), (1672),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.43  | | | | | | | | | | | | | | | |            #442.
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | End of split
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | End of split
% 169.94/25.43  | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | Case 2:
% 169.94/25.43  | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | |   (1673)  all_34_0 = e1
% 169.94/25.43  | | | | | | | | | | | | | |   (1674)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 169.94/25.43  | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | COMBINE_EQS: (773), (1673) imply:
% 169.94/25.43  | | | | | | | | | | | | | |   (1675)  all_4_0 = e1
% 169.94/25.43  | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | REDUCE: (1575), (1675) imply:
% 169.94/25.43  | | | | | | | | | | | | | |   (1676)   ~ (e2 = e1)
% 169.94/25.43  | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | REDUCE: (38), (1675) imply:
% 169.94/25.43  | | | | | | | | | | | | | |   (1677)  op(all_4_1, all_4_2) = e1
% 169.94/25.43  | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.94/25.43  | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | Case 1:
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | |   (1678)  all_58_15 = e0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | COMBINE_EQS: (532), (1678) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1679)  all_6_2 = e0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (597), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1680)   ~ (all_52_7 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (600), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1681)   ~ (all_52_23 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (564), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1682)   ~ (all_52_25 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (582), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1683)   ~ (all_52_27 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (594), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1684)   ~ (all_52_29 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (43), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1685)  op(all_6_1, e0) = all_6_0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (42), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1686)  op(e0, e0) = all_6_1
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (41), (1679) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1687)  op(e0, e0) = e0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 169.94/25.43  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1686), (1687) gives:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1688)  all_6_1 = e0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (1685), (1688) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1689)  op(e0, e0) = all_6_0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 169.94/25.43  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1687), (1689) gives:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1690)  all_6_0 = e0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (1577), (1690) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1691)   ~ (e3 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (799), (1690) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1692)   ~ (e2 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | REDUCE: (797), (1690) imply:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1693)   ~ (e1 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | Case 1:
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | |   (1694)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.43  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.43  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (1573),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (1677), (1694), (function-axioms) are inconsistent
% 169.94/25.43  | | | | | | | | | | | | | | | |            by sub-proof #441.
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | Case 2:
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | |   (1695)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.43  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.43  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (62), (63),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (154), (155), (156), (158), (161), (163), (164),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (165), (172), (173), (174), (177), (178), (179),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (181), (182), (269), (270), (271), (272), (273),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (274), (275), (276), (278), (280), (282), (283),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (311),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (319), (323), (324), (325), (326), (328), (329),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (392), (403), (419), (425), (429), (494), (530),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (531), (533), (534), (535), (536), (537), (538),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (552),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (553), (554), (555), (557), (558), (561), (562),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (563), (565), (566), (567), (569), (571), (578),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (579), (580), (581), (584), (585), (586), (588),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (591), (593), (596), (598), (663), (719), (796),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (803), (805), (1674), (1677), (1678), (1680),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (1681), (1682), (1683), (1684), (1695),
% 169.94/25.43  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.43  | | | | | | | | | | | | | | | |            #575.
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | End of split
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | Case 2:
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | |   (1696)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.94/25.43  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.94/25.43  | | | | | | | | | | | | | | |             e0)
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | ALPHA: (1696) implies:
% 169.94/25.43  | | | | | | | | | | | | | | |   (1697)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 169.94/25.43  | | | | | | | | | | | | | | |   (1698)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.43  | | | | | | | | | | | | | | | 
% 169.94/25.43  | | | | | | | | | | | | | | | Case 1:
% 169.94/25.43  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1699)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.44  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.44  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (1573),
% 169.94/25.44  | | | | | | | | | | | | | | | |            (1677), (1699), (function-axioms) are inconsistent
% 169.94/25.44  | | | | | | | | | | | | | | | |            by sub-proof #441.
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | Case 2:
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1700)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.44  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.44  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | BETA: splitting (1700) gives:
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | |   (1701)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.94/25.44  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (62), (63),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (169), (170),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (182), (268), (270), (274), (275), (276), (277),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (278), (282), (283), (304), (307), (310), (311),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (320), (321),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (385), (391), (392), (403), (415), (419), (425),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (494), (529), (530), (531), (532), (533), (534),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (562), (563), (564), (566), (568), (571), (575),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (591), (593), (595),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (663), (719), (796),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (802), (803), (805), (1674), (1677), (1698),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (1701), (function-axioms) are inconsistent by
% 169.94/25.44  | | | | | | | | | | | | | | | | |            sub-proof #440.
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | |   (1702)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.94/25.44  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (61), (154),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (165), (172),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (183), (268),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (270), (280), (281), (282), (283), (303), (304),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (306), (307), (322), (324), (325), (326), (328),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (330), (344), (349), (364), (370), (385), (386),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (391), (392), (403), (413), (494), (529), (531),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (538), (539),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (540), (544), (546), (548), (552), (554), (555),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (557), (558), (559), (562), (565), (566), (567),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (568), (569), (578), (580), (581), (586), (591),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (595), (596), (597), (649), (663), (796), (797),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (799), (1577), (1674), (1677), (1697), (1702),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.44  | | | | | | | | | | | | | | | | |            #534.
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | End of split
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | End of split
% 169.94/25.44  | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | End of split
% 169.94/25.44  | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | End of split
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | Case 2:
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | |   (1703)  all_32_1 = e2
% 169.94/25.44  | | | | | | | | | | | | |   (1704)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e3)
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | COMBINE_EQS: (713), (1703) imply:
% 169.94/25.44  | | | | | | | | | | | | |   (1705)  all_14_1 = e2
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | SIMP: (1705) implies:
% 169.94/25.44  | | | | | | | | | | | | |   (1706)  all_14_1 = e2
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | COMBINE_EQS: (719), (1706) imply:
% 169.94/25.44  | | | | | | | | | | | | |   (1707)  all_52_20 = e2
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | REDUCE: (807), (1706) imply:
% 169.94/25.44  | | | | | | | | | | | | |   (1708)   ~ (e3 = e2)
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | REDUCE: (63), (1706) imply:
% 169.94/25.44  | | | | | | | | | | | | |   (1709)  op(e2, all_14_2) = all_14_0
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | REDUCE: (62), (1706) imply:
% 169.94/25.44  | | | | | | | | | | | | |   (1710)  op(e1, all_14_2) = e2
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.94/25.44  | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | Case 1:
% 169.94/25.44  | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | |   (1711)   ~ (all_34_0 = e1)
% 169.94/25.44  | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | REDUCE: (773), (1711) imply:
% 169.94/25.44  | | | | | | | | | | | | | |   (1712)   ~ (all_4_0 = e1)
% 169.94/25.44  | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.94/25.44  | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | Case 1:
% 169.94/25.44  | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | |   (1713)   ~ (all_40_1 = e1)
% 169.94/25.44  | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | REDUCE: (715), (1713) imply:
% 169.94/25.44  | | | | | | | | | | | | | | |   (1714)   ~ (all_4_1 = e1)
% 169.94/25.44  | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 169.94/25.44  | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | Case 1:
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1715)  all_58_15 = e0
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (1715) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1716)  all_6_2 = e0
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (597), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1717)   ~ (all_52_7 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (600), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1718)   ~ (all_52_23 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (564), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1719)   ~ (all_52_25 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (582), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1720)   ~ (all_52_27 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (594), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1721)   ~ (all_52_29 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (43), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1722)  op(all_6_1, e0) = all_6_0
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (42), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1723)  op(e0, e0) = all_6_1
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (41), (1716) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1724)  op(e0, e0) = e0
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 169.94/25.44  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (1723), (1724) gives:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1725)  all_6_1 = e0
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (1722), (1725) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1726)  op(e0, e0) = all_6_0
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 169.94/25.44  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (1724), (1726) gives:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1727)  all_6_0 = e0
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (1577), (1727) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1728)   ~ (e3 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | REDUCE: (797), (1727) imply:
% 169.94/25.44  | | | | | | | | | | | | | | | |   (1729)   ~ (e1 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.44  | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | |   (1730)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.44  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.44  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (37), (38), (52), (154), (155), (156),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (160), (178), (179), (270), (271), (280), (283),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (323),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (326), (330), (331), (344), (349), (370), (386),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (391), (403), (429), (531), (532), (533), (534),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (535), (536), (540), (546), (552), (562), (569),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (585), (586), (595), (596), (597), (661), (720),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (1573), (1715), (1717), (1719), (1720), (1721),
% 169.94/25.44  | | | | | | | | | | | | | | | | |            (1730), (function-axioms) are inconsistent by
% 169.94/25.44  | | | | | | | | | | | | | | | | |            sub-proof #439.
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.44  | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.44  | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | |   (1731)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.45  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.45  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.45  | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (37), (161), (163),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (269), (270), (271),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (272), (273), (275), (278), (280), (283), (302),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (304), (305), (310), (311), (313), (322), (324),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (330), (341), (344), (349), (350), (359), (364),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (365), (373), (385), (386), (391), (403), (429),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (546), (550), (552),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (553), (554), (555), (558), (560), (561), (562),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (563), (566), (567), (569), (571), (573), (580),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (581), (584), (585), (586), (587), (591), (593),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (596), (1707), (1710), (1714), (1715), (1717),
% 169.94/25.45  | | | | | | | | | | | | | | | | |            (1718), (1719), (1721), (1731), (function-axioms)
% 169.94/25.45  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #548.
% 169.94/25.45  | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | End of split
% 169.94/25.45  | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | |   (1732)   ~ (all_58_15 = e0)
% 169.94/25.45  | | | | | | | | | | | | | | | |   (1733)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 169.94/25.45  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 169.94/25.45  | | | | | | | | | | | | | | | |             e0)
% 169.94/25.45  | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | ALPHA: (1733) implies:
% 169.94/25.45  | | | | | | | | | | | | | | | |   (1734)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | |   (1735)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | REDUCE: (532), (1732) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | |   (1736)   ~ (all_6_2 = e0)
% 169.94/25.45  | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | |   (1737)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.45  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.45  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.45  | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | BETA: splitting (1737) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1738)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.45  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | ALPHA: (1738) implies:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1739)  all_52_6 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1740)  all_52_4 = e1
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1741)  all_52_2 = e2
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1742)  all_52_0 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1742) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1743)  all_4_1 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | REDUCE: (38), (1743) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1744)  op(e3, all_4_2) = all_4_0
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | REDUCE: (37), (1743) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1745)  op(e3, all_4_2) = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | REDUCE: (176), (1741) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1746)  op(e2, all_52_3) = e2
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | REDUCE: (168), (1740) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1747)  op(e1, all_52_5) = e1
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | REDUCE: (160), (1739) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1748)  op(e0, all_52_7) = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 169.94/25.45  | | | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (1744), (1745)
% 169.94/25.45  | | | | | | | | | | | | | | | | | |              gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | |   (1749)  all_4_0 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1750)  all_56_15 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (1750) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1751)  all_6_2 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | SIMP: (1751) implies:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1752)  all_6_2 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | REDUCE: (597), (1752) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1753)   ~ (all_52_7 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | REDUCE: (599), (1752) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1754)   ~ (all_52_15 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | REDUCE: (600), (1752) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1755)   ~ (all_52_23 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | REDUCE: (594), (1752) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1756)   ~ (all_52_29 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | REDUCE: (41), (1752) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | |   (1757)  op(e0, e0) = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | |   (1758)  all_56_3 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (1753), (1758) are inconsistent by
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | |   (1759)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | |   (1760)  all_58_0 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (1760) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | |   (1761)  all_4_2 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (1761) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | |   (1762)   ~ (all_52_3 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (1761) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | |   (1763)   ~ (all_52_5 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (1761) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | |   (1764)   ~ (all_52_9 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (1761) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | |   (1765)   ~ (all_52_17 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | |   (1766)  all_58_6 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (1765), (1766) are inconsistent by
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | |   (1767)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | |   (1768)  all_58_2 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (385), (1764), (1768) are inconsistent by
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #980.
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | |   (1769)   ~ (all_58_2 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | |   (1770)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | |   (1771)  all_56_1 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (1762), (1771) are inconsistent by
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | |   (1772)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (1773)  all_56_4 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (409), (1764), (1773) are inconsistent by
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #782.
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (1774)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1775)  all_56_2 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (1763), (1775) are inconsistent by
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1776)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1777)  all_56_6 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (1777) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1778)  all_52_13 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1778) implies:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1779)  all_52_13 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (1779) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1780)   ~ (all_14_2 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1780) implies:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1781)   ~ (all_14_2 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (1779) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1782)  op(e2, e1) = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (154), (155), (163), (305), (306), (364),
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (386), (392), (413), (535), (536), (537), (567),
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (569), (584), (585), (1746), (1747), (1748),
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1753), (1755), (1757), (1759), (1767), (1772),
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1776), (1781), (1782), (function-axioms) are
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #546.
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1783)   ~ (all_56_6 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (1783) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1784)   ~ (all_52_13 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1770) gives:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1785)  all_58_3 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (1785) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1786)  all_10_2 = e3
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (1786) imply:
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1787)   ~ (all_52_19 = e3)
% 169.94/25.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1573), (1786) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1788)  op(all_10_1, e3) = e1
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (1786) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1789)  op(e2, e3) = all_10_1
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1767) gives:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1790)  all_58_7 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (1790) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1791)  all_52_19 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1787), (1791) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1792)  $false
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1792) is inconsistent.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1793)  all_58_8 = e3 | all_58_11 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1793) gives:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1794)  all_58_8 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (1794) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1795)  all_14_2 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (1795) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1796)  all_32_2 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1709), (1795) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1797)  op(e2, e3) = all_14_0
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1710), (1795) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1798)  op(e1, e3) = e2
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1704) gives:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1799)   ~ (all_32_2 = e3)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1796), (1799) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1800)  $false
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1800) is inconsistent.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1801)   ~ (all_32_0 = e0)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (793), (1801) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1802)   ~ (all_14_0 = e0)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, e1, simplifying with (164), (1798) gives:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1803)  all_52_17 = e2
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_1, e3, e2, simplifying with (172), (1789)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1804)  all_52_9 = all_10_1
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e3, e2, simplifying with (172), (1797)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1805)  all_52_9 = all_14_0
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1804), (1805) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1806)  all_14_0 = all_10_1
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1806) implies:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1807)  all_14_0 = all_10_1
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (1804) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1808)  all_56_4 = all_10_1
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (803), (1807) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1809)   ~ (all_10_1 = e2)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1802), (1807) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1810)   ~ (all_10_1 = e0)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1774), (1788), (1798), (1808), (1809), (1810),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #437.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1811)  all_58_11 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (1755), (1811) are inconsistent by
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1017.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1812)  all_58_5 = e3 | all_58_10 = e3
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (373), (1754), (1784), (1812) are
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |   (1813)   ~ (all_58_0 = e3)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (1813) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |   (1814)   ~ (all_4_2 = e3)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (164), (172), (177), (178), (179), (273),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            (283), (307), (311), (315), (324), (326), (331),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (403), (531),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            (532), (533), (535), (536), (537), (538), (540),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (550), (552), (560), (566),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            (568), (569), (583), (584), (585), (586), (587),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (1745), (1746),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            (1747), (1748), (1756), (1814), (function-axioms)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #864.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |   (1815)   ~ (all_56_15 = e3)
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |   (1816)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (158),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (169), (170),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (269), (270),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (283), (304), (305), (307), (310), (311), (312),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (1735), (1736),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (1745), (1746), (1747), (1748), (1815), (1816),
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.46  | | | | | | | | | | | | | | | | | | |            #785.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | |   (1817)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 169.94/25.46  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | ALPHA: (1817) implies:
% 169.94/25.46  | | | | | | | | | | | | | | | | | |   (1818)  all_52_10 = e2
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (1818) imply:
% 169.94/25.46  | | | | | | | | | | | | | | | | | |   (1819)  all_10_1 = e2
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (1573), (1819), (function-axioms) are
% 169.94/25.46  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #446.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | End of split
% 169.94/25.46  | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | |   (1820)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.46  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.46  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.46  | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | BETA: splitting (1820) gives:
% 169.94/25.46  | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | |   (1821)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.94/25.46  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1707), (1821) are inconsistent by sub-proof
% 169.94/25.46  | | | | | | | | | | | | | | | | | |            #553.
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.46  | | | | | | | | | | | | | | | | | |   (1822)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.94/25.46  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.94/25.46  | | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (649), (797), (799), (1575), (1577), (1712),
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            (1734), (1735), (1736), (1822), (function-axioms)
% 169.94/25.47  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #634.
% 169.94/25.47  | | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | | End of split
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | End of split
% 169.94/25.47  | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | End of split
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | Case 2:
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | |   (1823)  all_40_1 = e1
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | COMBINE_EQS: (715), (1823) imply:
% 169.94/25.47  | | | | | | | | | | | | | | |   (1824)  all_4_1 = e1
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (1824) imply:
% 169.94/25.47  | | | | | | | | | | | | | | |   (1825)  all_52_0 = e1
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | REDUCE: (796), (1824) imply:
% 169.94/25.47  | | | | | | | | | | | | | | |   (1826)   ~ (e2 = e1)
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | REDUCE: (38), (1824) imply:
% 169.94/25.47  | | | | | | | | | | | | | | |   (1827)  op(e1, all_4_2) = all_4_0
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | REDUCE: (37), (1824) imply:
% 169.94/25.47  | | | | | | | | | | | | | | |   (1828)  op(e3, all_4_2) = e1
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.94/25.47  | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | Case 1:
% 169.94/25.47  | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | |   (1829)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 169.94/25.47  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 169.94/25.47  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 169.94/25.47  | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (52), (661), (1573), (1825), (1829),
% 169.94/25.47  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 169.94/25.47  | | | | | | | | | | | | | | | |            #445.
% 169.94/25.47  | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | Case 2:
% 169.94/25.47  | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | |   (1830)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 169.94/25.47  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 169.94/25.47  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 169.94/25.47  | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | BETA: splitting (1830) gives:
% 169.94/25.47  | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | Case 1:
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | |   (1831)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 169.94/25.47  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1707), (1831) are inconsistent by sub-proof
% 169.94/25.47  | | | | | | | | | | | | | | | | |            #539.
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | Case 2:
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | |   (1832)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 169.94/25.47  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | | ALPHA: (1832) implies:
% 169.94/25.47  | | | | | | | | | | | | | | | | |   (1833)  all_52_30 = e0
% 169.94/25.47  | | | | | | | | | | | | | | | | |   (1834)  all_52_28 = e1
% 169.94/25.47  | | | | | | | | | | | | | | | | |   (1835)  all_52_26 = e2
% 169.94/25.47  | | | | | | | | | | | | | | | | |   (1836)  all_52_24 = e3
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 169.94/25.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1833) imply:
% 169.94/25.47  | | | | | | | | | | | | | | | | |   (1837)  all_6_1 = e0
% 169.94/25.47  | | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (182), (183), (268), (269), (270), (271), (272),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (273), (280), (283), (301), (302), (304), (305),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (319), (321), (323),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (429), (529),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (550),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (557), (558), (559),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (568), (569), (571), (573), (577), (580), (581),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (589), (591), (594), (596), (597), (797), (1575),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (1577), (1710), (1712), (1827), (1828), (1834),
% 170.37/25.47  | | | | | | | | | | | | | | | | |            (1835), (1836), (1837), (function-axioms) are
% 170.37/25.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #536.
% 170.37/25.47  | | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | End of split
% 170.37/25.47  | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | End of split
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | End of split
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | Case 2:
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | |   (1838)  all_34_0 = e1
% 170.37/25.47  | | | | | | | | | | | | | |   (1839)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | COMBINE_EQS: (773), (1838) imply:
% 170.37/25.47  | | | | | | | | | | | | | |   (1840)  all_4_0 = e1
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | SIMP: (1840) implies:
% 170.37/25.47  | | | | | | | | | | | | | |   (1841)  all_4_0 = e1
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | REDUCE: (1575), (1841) imply:
% 170.37/25.47  | | | | | | | | | | | | | |   (1842)   ~ (e2 = e1)
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | REDUCE: (38), (1841) imply:
% 170.37/25.47  | | | | | | | | | | | | | |   (1843)  op(all_4_1, all_4_2) = e1
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.37/25.47  | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | Case 1:
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | |   (1844)  all_58_15 = e0
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | COMBINE_EQS: (532), (1844) imply:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1845)  all_6_2 = e0
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | REDUCE: (564), (1845) imply:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1846)   ~ (all_52_25 = e0)
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | REDUCE: (43), (1845) imply:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1847)  op(all_6_1, e0) = all_6_0
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | REDUCE: (42), (1845) imply:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1848)  op(e0, e0) = all_6_1
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | REDUCE: (41), (1845) imply:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1849)  op(e0, e0) = e0
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 170.37/25.47  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1848), (1849) gives:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1850)  all_6_1 = e0
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | REDUCE: (1847), (1850) imply:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1851)  op(e0, e0) = all_6_0
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.37/25.47  | | | | | | | | | | | | | | |              e0, e0, simplifying with (1849), (1851) gives:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1852)  all_6_0 = e0
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | REDUCE: (1577), (1852) imply:
% 170.37/25.47  | | | | | | | | | | | | | | |   (1853)   ~ (e3 = e0)
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.37/25.47  | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | Case 1:
% 170.37/25.47  | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | |   (1854)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.37/25.47  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.37/25.47  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.37/25.47  | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (1573),
% 170.37/25.47  | | | | | | | | | | | | | | | |            (1843), (1854), (function-axioms) are inconsistent
% 170.37/25.47  | | | | | | | | | | | | | | | |            by sub-proof #441.
% 170.37/25.47  | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | Case 2:
% 170.37/25.47  | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | |   (1855)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.37/25.47  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.37/25.47  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.37/25.47  | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | BETA: splitting (1855) gives:
% 170.37/25.47  | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | Case 1:
% 170.37/25.47  | | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | |   (1856)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.37/25.47  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.37/25.47  | | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1707), (1856) are inconsistent by sub-proof
% 170.37/25.47  | | | | | | | | | | | | | | | | |            #539.
% 170.37/25.47  | | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | Case 2:
% 170.37/25.47  | | | | | | | | | | | | | | | | | 
% 170.37/25.47  | | | | | | | | | | | | | | | | |   (1857)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.37/25.47  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.37/25.47  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (37), (161), (163), (164), (165),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (172), (173), (177), (179), (181), (270), (271),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (280), (282), (283), (304), (328), (330), (344),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (349), (386), (392), (403), (429), (494), (531),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (533), (534), (544), (546), (548), (552), (554),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (562), (566), (596), (663), (796), (1839), (1843),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (1844), (1846), (1857), (function-axioms) are
% 170.37/25.48  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | End of split
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | End of split
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | Case 2:
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | |   (1858)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.37/25.48  | | | | | | | | | | | | | | |             e0)
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | ALPHA: (1858) implies:
% 170.37/25.48  | | | | | | | | | | | | | | |   (1859)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | Case 1:
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | |   (1860)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.37/25.48  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.37/25.48  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (1573),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (1843), (1860), (function-axioms) are inconsistent
% 170.37/25.48  | | | | | | | | | | | | | | | |            by sub-proof #441.
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | Case 2:
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | |   (1861)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.37/25.48  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.37/25.48  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | BETA: splitting (1861) gives:
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | Case 1:
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1862)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.37/25.48  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1707), (1862) are inconsistent by sub-proof
% 170.37/25.48  | | | | | | | | | | | | | | | | |            #539.
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | Case 2:
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1863)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.37/25.48  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | ALPHA: (1863) implies:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1864)  all_52_30 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1865)  all_52_28 = e1
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1866)  all_52_26 = e2
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1867)  all_52_24 = e3
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1864) imply:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1868)  all_6_1 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (61), (154),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (165), (172),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (183), (268),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (270), (280), (281), (282), (283), (303), (304),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (306), (307), (322), (324), (325), (326), (328),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (330), (344), (349), (364), (370), (385), (386),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (391), (392), (403), (413), (494), (529), (531),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (538), (539),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (540), (544), (546), (548), (552), (554), (555),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (557), (558), (559), (562), (565), (566), (567),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (568), (569), (578), (580), (581), (586), (591),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (595), (596), (597), (663), (796), (797), (799),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (1577), (1839), (1843), (1859), (1865), (1866),
% 170.37/25.48  | | | | | | | | | | | | | | | | |            (1867), (1868), (function-axioms) are inconsistent
% 170.37/25.48  | | | | | | | | | | | | | | | | |            by sub-proof #555.
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | End of split
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | End of split
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | End of split
% 170.37/25.48  | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | End of split
% 170.37/25.48  | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | End of split
% 170.37/25.48  | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | Case 2:
% 170.37/25.48  | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | |   (1869)  all_28_0 = e3
% 170.37/25.48  | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | COMBINE_EQS: (776), (1869) imply:
% 170.37/25.48  | | | | | | | | | | | |   (1870)  all_6_0 = e3
% 170.37/25.48  | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | SIMP: (1870) implies:
% 170.37/25.48  | | | | | | | | | | | |   (1871)  all_6_0 = e3
% 170.37/25.48  | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | REDUCE: (43), (1871) imply:
% 170.37/25.48  | | | | | | | | | | | |   (1872)  op(all_6_1, all_6_2) = e3
% 170.37/25.48  | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | BETA: splitting (113) gives:
% 170.37/25.48  | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | Case 1:
% 170.37/25.48  | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | |   (1873)   ~ (all_34_0 = e1)
% 170.37/25.48  | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | REDUCE: (773), (1873) imply:
% 170.37/25.48  | | | | | | | | | | | | |   (1874)   ~ (all_4_0 = e1)
% 170.37/25.48  | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.37/25.48  | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | Case 1:
% 170.37/25.48  | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | |   (1875)   ~ (all_40_1 = e1)
% 170.37/25.48  | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | REDUCE: (715), (1875) imply:
% 170.37/25.48  | | | | | | | | | | | | | |   (1876)   ~ (all_4_1 = e1)
% 170.37/25.48  | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.37/25.48  | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | Case 1:
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | |   (1877)  all_58_15 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1872), (1877),
% 170.37/25.48  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.37/25.48  | | | | | | | | | | | | | | |            #510.
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | Case 2:
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | |   (1878)   ~ (all_58_15 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | |   (1879)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.37/25.48  | | | | | | | | | | | | | | |             e0)
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | ALPHA: (1879) implies:
% 170.37/25.48  | | | | | | | | | | | | | | |   (1880)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.37/25.48  | | | | | | | | | | | | | | |   (1881)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | REDUCE: (532), (1878) imply:
% 170.37/25.48  | | | | | | | | | | | | | | |   (1882)   ~ (all_6_2 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.37/25.48  | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | Case 1:
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | |   (1883)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.37/25.48  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.37/25.48  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (37), (38), (42), (52), (61),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (154), (156), (158), (159), (160), (161), (163),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (164), (165), (168), (169), (170), (172), (173),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (307), (310),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (317), (319),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (323), (324), (326), (327), (328), (330), (331),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (413),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (425), (429), (529), (531), (532), (533), (534),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (575), (578), (579), (580), (581), (582), (583),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (589), (591),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (600), (661), (720), (1573), (1575), (1872),
% 170.37/25.48  | | | | | | | | | | | | | | | |            (1874), (1881), (1882), (1883), (function-axioms)
% 170.37/25.48  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #435.
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | Case 2:
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | |   (1884)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.37/25.48  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.37/25.48  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | BETA: splitting (1884) gives:
% 170.37/25.48  | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | Case 1:
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1885)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.37/25.48  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | ALPHA: (1885) implies:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1886)  all_52_22 = e0
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1887)  all_52_20 = e1
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1888)  all_52_18 = e2
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1889)  all_52_16 = e3
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1887) imply:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1890)  all_14_1 = e1
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REDUCE: (63), (1890) imply:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1891)  op(e1, all_14_2) = all_14_0
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REDUCE: (182), (1889) imply:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1892)  op(e3, all_52_17) = e3
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REDUCE: (174), (1888) imply:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1893)  op(e2, all_52_19) = e2
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REDUCE: (62), (1890) imply:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1894)  op(e1, all_14_2) = e1
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.48  | | | | | | | | | | | | | | | | | REDUCE: (158), (1886) imply:
% 170.37/25.48  | | | | | | | | | | | | | | | | |   (1895)  op(e0, all_52_23) = e0
% 170.37/25.48  | | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (52),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (165), (169), (170),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (268), (270), (271), (273), (274), (275), (276),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (277), (278), (282), (283), (302), (303), (304),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (307), (308), (310), (311), (312), (313), (314),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (315), (317), (319), (320), (321), (322), (323),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (324), (326), (328), (329), (330), (331), (344),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (349), (359), (364), (365), (370), (373), (385),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (391), (392), (403), (415), (419), (425), (429),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (571),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (593), (595), (596), (597), (598), (600), (796),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (802), (803), (805), (1575), (1872), (1874),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (1876), (1880), (1881), (1882), (1891), (1892),
% 170.37/25.49  | | | | | | | | | | | | | | | | |            (1893), (1894), (1895), (function-axioms) are
% 170.37/25.49  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #503.
% 170.37/25.49  | | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | Case 2:
% 170.37/25.49  | | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | |   (1896)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.37/25.49  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.37/25.49  | | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | | ALPHA: (1896) implies:
% 170.37/25.49  | | | | | | | | | | | | | | | | |   (1897)  all_52_30 = e0
% 170.37/25.49  | | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (1897) imply:
% 170.37/25.49  | | | | | | | | | | | | | | | | |   (1898)  all_6_1 = e0
% 170.37/25.49  | | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (1872), (1898), (function-axioms) are
% 170.37/25.49  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 170.37/25.49  | | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | End of split
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | End of split
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | End of split
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | Case 2:
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | |   (1899)  all_40_1 = e1
% 170.37/25.49  | | | | | | | | | | | | | |   (1900)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | COMBINE_EQS: (715), (1899) imply:
% 170.37/25.49  | | | | | | | | | | | | | |   (1901)  all_4_1 = e1
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | COMBINE_EQS: (720), (1901) imply:
% 170.37/25.49  | | | | | | | | | | | | | |   (1902)  all_52_0 = e1
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | REDUCE: (796), (1901) imply:
% 170.37/25.49  | | | | | | | | | | | | | |   (1903)   ~ (e2 = e1)
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | REDUCE: (38), (1901) imply:
% 170.37/25.49  | | | | | | | | | | | | | |   (1904)  op(e1, all_4_2) = all_4_0
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | REDUCE: (37), (1901) imply:
% 170.37/25.49  | | | | | | | | | | | | | |   (1905)  op(e3, all_4_2) = e1
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | Case 1:
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | |   (1906)  all_58_15 = e0
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1872), (1906),
% 170.37/25.49  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.37/25.49  | | | | | | | | | | | | | | |            #510.
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | Case 2:
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | |   (1907)   ~ (all_58_15 = e0)
% 170.37/25.49  | | | | | | | | | | | | | | |   (1908)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.37/25.49  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.37/25.49  | | | | | | | | | | | | | | |             e0)
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | ALPHA: (1908) implies:
% 170.37/25.49  | | | | | | | | | | | | | | |   (1909)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.37/25.49  | | | | | | | | | | | | | | |   (1910)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | REDUCE: (532), (1907) imply:
% 170.37/25.49  | | | | | | | | | | | | | | |   (1911)   ~ (all_6_2 = e0)
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 170.37/25.49  | | | | | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 170.37/25.49  | | | | | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (170),
% 170.37/25.49  | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 170.37/25.49  | | | | | | | | | | | | | | |            (182), (183), (185), (268), (270), (271), (274),
% 170.37/25.49  | | | | | | | | | | | | | | |            (275), (276), (277), (278), (283), (304), (305),
% 170.37/25.49  | | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (317),
% 170.37/25.49  | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 170.37/25.49  | | | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (344),
% 170.37/25.49  | | | | | | | | | | | | | | |            (349), (364), (365), (370), (373), (385), (391),
% 170.37/25.49  | | | | | | | | | | | | | | |            (403), (415), (419), (425), (429), (518), (529),
% 170.37/25.49  | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 170.37/25.49  | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 170.37/25.49  | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 170.37/25.49  | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 170.37/25.49  | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 170.37/25.49  | | | | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 170.37/25.49  | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 170.37/25.49  | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 170.37/25.49  | | | | | | | | | | | | | | |            (598), (600), (649), (661), (719), (770), (796),
% 170.37/25.49  | | | | | | | | | | | | | | |            (802), (803), (805), (1573), (1575), (1874),
% 170.37/25.49  | | | | | | | | | | | | | | |            (1900), (1902), (1904), (1905), (1909), (1910),
% 170.37/25.49  | | | | | | | | | | | | | | |            (1911), (function-axioms) are inconsistent by
% 170.37/25.49  | | | | | | | | | | | | | | |            sub-proof #443.
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | End of split
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | End of split
% 170.37/25.49  | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | Case 2:
% 170.37/25.49  | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | |   (1912)  all_34_0 = e1
% 170.37/25.49  | | | | | | | | | | | | |   (1913)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.37/25.49  | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | COMBINE_EQS: (773), (1912) imply:
% 170.37/25.49  | | | | | | | | | | | | |   (1914)  all_4_0 = e1
% 170.37/25.49  | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | REDUCE: (1575), (1914) imply:
% 170.37/25.49  | | | | | | | | | | | | |   (1915)   ~ (e2 = e1)
% 170.37/25.49  | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | REDUCE: (38), (1914) imply:
% 170.37/25.49  | | | | | | | | | | | | |   (1916)  op(all_4_1, all_4_2) = e1
% 170.37/25.49  | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.37/25.49  | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | Case 1:
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | |   (1917)  all_58_15 = e0
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1872), (1917),
% 170.37/25.49  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.37/25.49  | | | | | | | | | | | | | |            #510.
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | Case 2:
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | |   (1918)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.37/25.49  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.37/25.49  | | | | | | | | | | | | | |             e0)
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | ALPHA: (1918) implies:
% 170.37/25.49  | | | | | | | | | | | | | |   (1919)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.37/25.49  | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | Case 1:
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | |   (1920)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.37/25.49  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.37/25.49  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (1573),
% 170.37/25.49  | | | | | | | | | | | | | | |            (1916), (1920), (function-axioms) are inconsistent
% 170.37/25.49  | | | | | | | | | | | | | | |            by sub-proof #441.
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | Case 2:
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | |   (1921)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.37/25.49  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.37/25.49  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | BETA: splitting (1921) gives:
% 170.37/25.49  | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | Case 1:
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1922)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.37/25.49  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | ALPHA: (1922) implies:
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1923)  all_52_22 = e0
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1924)  all_52_20 = e1
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1925)  all_52_18 = e2
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1926)  all_52_16 = e3
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1924) imply:
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1927)  all_14_1 = e1
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | REDUCE: (63), (1927) imply:
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1928)  op(e1, all_14_2) = all_14_0
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | REDUCE: (182), (1926) imply:
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1929)  op(e3, all_52_17) = e3
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | REDUCE: (174), (1925) imply:
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1930)  op(e2, all_52_19) = e2
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | REDUCE: (62), (1927) imply:
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1931)  op(e1, all_14_2) = e1
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | REDUCE: (158), (1923) imply:
% 170.37/25.49  | | | | | | | | | | | | | | | |   (1932)  op(e0, all_52_23) = e0
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.49  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (156),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (163), (164), (165), (169), (170), (172), (173),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (177), (178), (179), (181), (268), (270), (274),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (275), (276), (277), (278), (282), (283), (304),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (317),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (326),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (364),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (392), (403),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (415), (419), (425), (494), (529), (530), (531),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (566),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (568), (571), (575), (577), (578), (579), (580),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (598), (600),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (663), (796), (802), (803), (805), (1913), (1916),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (1919), (1928), (1929), (1930), (1931), (1932),
% 170.37/25.49  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.37/25.49  | | | | | | | | | | | | | | | |            #561.
% 170.37/25.49  | | | | | | | | | | | | | | | | 
% 170.37/25.50  | | | | | | | | | | | | | | | Case 2:
% 170.37/25.50  | | | | | | | | | | | | | | | | 
% 170.37/25.50  | | | | | | | | | | | | | | | |   (1933)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.47/25.50  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (1872), (1933),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.47/25.50  | | | | | | | | | | | | | | | |            #501.
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | Case 2:
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | |   (1934)  all_26_0 = e2
% 170.47/25.50  | | | | | | | | | | |   (1935)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | COMBINE_EQS: (779), (1934) imply:
% 170.47/25.50  | | | | | | | | | | |   (1936)  all_4_0 = e2
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | SIMP: (1936) implies:
% 170.47/25.50  | | | | | | | | | | |   (1937)  all_4_0 = e2
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | COMBINE_EQS: (742), (1937) imply:
% 170.47/25.50  | | | | | | | | | | |   (1938)  all_50_0 = e2
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | REDUCE: (38), (1937) imply:
% 170.47/25.50  | | | | | | | | | | |   (1939)  op(all_4_1, all_4_2) = e2
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | BETA: splitting (98) gives:
% 170.47/25.50  | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | Case 1:
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | |   (1940)   ~ (all_28_0 = e3)
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | REDUCE: (776), (1940) imply:
% 170.47/25.50  | | | | | | | | | | | |   (1941)   ~ (all_6_0 = e3)
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | BETA: splitting (151) gives:
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | Case 1:
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | |   (1942)   ~ (all_50_0 = e2)
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | REDUCE: (1938), (1942) imply:
% 170.47/25.50  | | | | | | | | | | | | |   (1943)  $false
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | CLOSE: (1943) is inconsistent.
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | Case 2:
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | |   (1944)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | Case 1:
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | |   (1945)  all_58_15 = e0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | COMBINE_EQS: (532), (1945) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1946)  all_6_2 = e0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (597), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1947)   ~ (all_52_7 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (599), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1948)   ~ (all_52_15 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (600), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1949)   ~ (all_52_23 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (564), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1950)   ~ (all_52_25 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (582), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1951)   ~ (all_52_27 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (43), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1952)  op(all_6_1, e0) = all_6_0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (42), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1953)  op(e0, e0) = all_6_1
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (41), (1946) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1954)  op(e0, e0) = e0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 170.47/25.50  | | | | | | | | | | | | | |              e0, e0, simplifying with (1953), (1954) gives:
% 170.47/25.50  | | | | | | | | | | | | | |   (1955)  all_6_1 = e0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (1952), (1955) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1956)  op(e0, e0) = all_6_0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.47/25.50  | | | | | | | | | | | | | |              e0, e0, simplifying with (1954), (1956) gives:
% 170.47/25.50  | | | | | | | | | | | | | |   (1957)  all_6_0 = e0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (1941), (1957) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1958)   ~ (e3 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (799), (1957) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1959)   ~ (e2 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (797), (1957) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1960)   ~ (e1 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | Case 1:
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | |   (1961)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.47/25.50  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.47/25.50  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (1573),
% 170.47/25.50  | | | | | | | | | | | | | | |            (1939), (1961), (function-axioms) are inconsistent
% 170.47/25.50  | | | | | | | | | | | | | | |            by sub-proof #434.
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | Case 2:
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | |   (1962)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.47/25.50  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.47/25.50  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | BETA: splitting (1962) gives:
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | Case 1:
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | |   (1963)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.47/25.50  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | | ALPHA: (1963) implies:
% 170.47/25.50  | | | | | | | | | | | | | | | |   (1964)  all_52_22 = e0
% 170.47/25.50  | | | | | | | | | | | | | | | |   (1965)  all_52_20 = e1
% 170.47/25.50  | | | | | | | | | | | | | | | |   (1966)  all_52_18 = e2
% 170.47/25.50  | | | | | | | | | | | | | | | |   (1967)  all_52_16 = e3
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (1965) imply:
% 170.47/25.50  | | | | | | | | | | | | | | | |   (1968)  all_14_1 = e1
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (62), (63), (156),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (158), (164), (165), (172), (173), (174), (177),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (178), (181), (182), (183), (270), (271), (273),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (274), (275), (276), (280), (281), (283), (302),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (304), (307), (311), (315), (319), (324), (325),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (391), (403), (413), (419), (425), (429), (503),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (521), (531), (533), (534), (535), (536), (537),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (538), (540), (542), (544), (546), (548), (550),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (552), (553), (554), (556), (557), (558), (560),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (561), (562), (563), (566), (567), (568), (578),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (579), (581), (584), (585), (586), (589), (591),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (593), (596), (598), (698), (718), (796), (803),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (805), (1935), (1939), (1944), (1945), (1947),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (1948), (1949), (1950), (1951), (1964), (1966),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (1967), (1968), (function-axioms) are inconsistent
% 170.47/25.50  | | | | | | | | | | | | | | | |            by sub-proof #473.
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | Case 2:
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | |   (1969)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.47/25.50  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (37), (164), (165), (172),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (270), (271),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (280), (283), (303), (304), (326), (344), (349),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (386), (403), (429), (503), (531), (533), (534),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (554),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (558), (562), (563), (586), (698), (796), (1935),
% 170.47/25.50  | | | | | | | | | | | | | | | |            (1939), (1945), (1950), (1969), (function-axioms)
% 170.47/25.50  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #470.
% 170.47/25.50  | | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | Case 2:
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | |   (1970)   ~ (all_58_15 = e0)
% 170.47/25.50  | | | | | | | | | | | | | |   (1971)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.47/25.50  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.47/25.50  | | | | | | | | | | | | | |             e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | ALPHA: (1971) implies:
% 170.47/25.50  | | | | | | | | | | | | | |   (1972)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.47/25.50  | | | | | | | | | | | | | |   (1973)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | REDUCE: (532), (1970) imply:
% 170.47/25.50  | | | | | | | | | | | | | |   (1974)   ~ (all_6_2 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | Case 1:
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | |   (1975)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.47/25.50  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.47/25.50  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (1573),
% 170.47/25.50  | | | | | | | | | | | | | | |            (1939), (1975), (function-axioms) are inconsistent
% 170.47/25.50  | | | | | | | | | | | | | | |            by sub-proof #434.
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | Case 2:
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | |   (1976)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.47/25.50  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.47/25.50  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (42), (43),
% 170.47/25.50  | | | | | | | | | | | | | | |            (51), (62), (63), (154), (155), (156), (158),
% 170.47/25.50  | | | | | | | | | | | | | | |            (161), (163), (164), (165), (172), (173), (174),
% 170.47/25.50  | | | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 170.47/25.50  | | | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (280),
% 170.47/25.50  | | | | | | | | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 170.47/25.50  | | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 170.47/25.50  | | | | | | | | | | | | | | |            (322), (323), (324), (325), (326), (328), (329),
% 170.47/25.50  | | | | | | | | | | | | | | |            (330), (331), (344), (349), (359), (364), (365),
% 170.47/25.50  | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 170.47/25.50  | | | | | | | | | | | | | | |            (413), (419), (425), (429), (503), (521), (529),
% 170.47/25.50  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.47/25.50  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.47/25.50  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 170.47/25.50  | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (566),
% 170.47/25.50  | | | | | | | | | | | | | | |            (567), (568), (569), (573), (577), (579), (580),
% 170.47/25.50  | | | | | | | | | | | | | | |            (581), (582), (584), (585), (586), (588), (589),
% 170.47/25.50  | | | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 170.47/25.50  | | | | | | | | | | | | | | |            (600), (649), (698), (718), (719), (796), (797),
% 170.47/25.50  | | | | | | | | | | | | | | |            (799), (803), (805), (1935), (1939), (1941),
% 170.47/25.50  | | | | | | | | | | | | | | |            (1944), (1972), (1973), (1974), (1976),
% 170.47/25.50  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.47/25.50  | | | | | | | | | | | | | | |            #433.
% 170.47/25.50  | | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | End of split
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | Case 2:
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | |   (1977)  all_28_0 = e3
% 170.47/25.50  | | | | | | | | | | | | 
% 170.47/25.50  | | | | | | | | | | | | COMBINE_EQS: (776), (1977) imply:
% 170.47/25.51  | | | | | | | | | | | |   (1978)  all_6_0 = e3
% 170.47/25.51  | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | SIMP: (1978) implies:
% 170.47/25.51  | | | | | | | | | | | |   (1979)  all_6_0 = e3
% 170.47/25.51  | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | REDUCE: (43), (1979) imply:
% 170.47/25.51  | | | | | | | | | | | |   (1980)  op(all_6_1, all_6_2) = e3
% 170.47/25.51  | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | BETA: splitting (151) gives:
% 170.47/25.51  | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | Case 1:
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | |   (1981)   ~ (all_50_0 = e2)
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | REDUCE: (1938), (1981) imply:
% 170.47/25.51  | | | | | | | | | | | | |   (1982)  $false
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | CLOSE: (1982) is inconsistent.
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | Case 2:
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | |   (1983)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | Case 1:
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | |   (1984)  all_58_15 = e0
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (1980), (1984),
% 170.47/25.51  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.47/25.51  | | | | | | | | | | | | | |            #510.
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | Case 2:
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | |   (1985)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.47/25.51  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.47/25.51  | | | | | | | | | | | | | |             e0)
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | ALPHA: (1985) implies:
% 170.47/25.51  | | | | | | | | | | | | | |   (1986)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | Case 1:
% 170.47/25.51  | | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | |   (1987)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.47/25.51  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.47/25.51  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.47/25.51  | | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (1573),
% 170.47/25.51  | | | | | | | | | | | | | | |            (1939), (1987), (function-axioms) are inconsistent
% 170.47/25.51  | | | | | | | | | | | | | | |            by sub-proof #434.
% 170.47/25.51  | | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | Case 2:
% 170.47/25.51  | | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | |   (1988)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.47/25.51  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.47/25.51  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.47/25.51  | | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 170.47/25.51  | | | | | | | | | | | | | | |            (156), (158), (161), (163), (164), (165), (172),
% 170.47/25.51  | | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 170.47/25.51  | | | | | | | | | | | | | | |            (183), (268), (270), (273), (274), (275), (276),
% 170.47/25.51  | | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (310),
% 170.47/25.51  | | | | | | | | | | | | | | |            (311), (315), (319), (321), (323), (324), (325),
% 170.47/25.51  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 170.47/25.51  | | | | | | | | | | | | | | |            (359), (364), (365), (370), (385), (386), (391),
% 170.47/25.51  | | | | | | | | | | | | | | |            (392), (403), (413), (419), (425), (521), (529),
% 170.47/25.51  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.47/25.51  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.47/25.51  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (557), (558), (559),
% 170.47/25.51  | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 170.47/25.51  | | | | | | | | | | | | | | |            (568), (569), (577), (579), (580), (582), (584),
% 170.47/25.51  | | | | | | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (598),
% 170.47/25.51  | | | | | | | | | | | | | | |            (600), (649), (718), (719), (796), (803), (805),
% 170.47/25.51  | | | | | | | | | | | | | | |            (1939), (1980), (1983), (1986), (1988),
% 170.47/25.51  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.47/25.51  | | | | | | | | | | | | | | |            #447.
% 170.47/25.51  | | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | | End of split
% 170.47/25.51  | | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | | End of split
% 170.47/25.51  | | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | | End of split
% 170.47/25.51  | | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | | End of split
% 170.47/25.51  | | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | | End of split
% 170.47/25.51  | | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | End of split
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | Case 2:
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | |   (1989)  all_22_1 = e3
% 170.47/25.51  | | | | | | | | |   (1990)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | COMBINE_EQS: (711), (1989) imply:
% 170.47/25.51  | | | | | | | | |   (1991)  all_14_1 = e3
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | SIMP: (1991) implies:
% 170.47/25.51  | | | | | | | | |   (1992)  all_14_1 = e3
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | COMBINE_EQS: (719), (1992) imply:
% 170.47/25.51  | | | | | | | | |   (1993)  all_52_20 = e3
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | REDUCE: (63), (1992) imply:
% 170.47/25.51  | | | | | | | | |   (1994)  op(e3, all_14_2) = all_14_0
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | REDUCE: (62), (1992) imply:
% 170.47/25.51  | | | | | | | | |   (1995)  op(e1, all_14_2) = e3
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 170.47/25.51  | | | | | | | | |            (41), (42), (43), (51), (52), (53), (61), (62),
% 170.47/25.51  | | | | | | | | |            (88), (93), (98), (113), (118), (128), (151),
% 170.47/25.51  | | | | | | | | |            (154), (155), (156), (158), (159), (160), (161),
% 170.47/25.51  | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 170.47/25.51  | | | | | | | | |            (172), (173), (174), (176), (177), (178), (179),
% 170.47/25.51  | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 170.47/25.51  | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 170.47/25.51  | | | | | | | | |            (278), (279), (280), (281), (282), (283), (301),
% 170.47/25.51  | | | | | | | | |            (302), (303), (304), (305), (306), (307), (308),
% 170.47/25.51  | | | | | | | | |            (310), (311), (312), (313), (314), (315), (316),
% 170.47/25.51  | | | | | | | | |            (317), (319), (320), (321), (322), (323), (324),
% 170.47/25.51  | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 170.47/25.51  | | | | | | | | |            (333), (341), (344), (349), (350), (359), (364),
% 170.47/25.51  | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 170.47/25.51  | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 170.47/25.51  | | | | | | | | |            (494), (503), (505), (518), (521), (529), (530),
% 170.47/25.51  | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.47/25.51  | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.47/25.51  | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.47/25.51  | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.47/25.51  | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 170.47/25.51  | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 170.47/25.51  | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 170.47/25.51  | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 170.47/25.51  | | | | | | | | |            (599), (600), (649), (661), (663), (698), (715),
% 170.47/25.51  | | | | | | | | |            (718), (720), (742), (747), (751), (756), (770),
% 170.47/25.51  | | | | | | | | |            (773), (776), (779), (796), (797), (799), (800),
% 170.47/25.51  | | | | | | | | |            (803), (1990), (1993), (1994), (1995),
% 170.47/25.51  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.47/25.51  | | | | | | | | |            #345.
% 170.47/25.51  | | | | | | | | | 
% 170.47/25.51  | | | | | | | | End of split
% 170.47/25.51  | | | | | | | | 
% 170.47/25.51  | | | | | | | Case 2:
% 170.47/25.51  | | | | | | | | 
% 170.47/25.51  | | | | | | | |   (1996)  all_18_0 = e3
% 170.47/25.51  | | | | | | | |   (1997)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 170.47/25.51  | | | | | | | | 
% 170.47/25.51  | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (37), (38), (41), (42),
% 170.47/25.51  | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (88), (93),
% 170.47/25.51  | | | | | | | |            (98), (113), (128), (151), (154), (155), (156),
% 170.47/25.51  | | | | | | | |            (158), (159), (160), (161), (163), (164), (165),
% 170.47/25.51  | | | | | | | |            (167), (168), (169), (170), (172), (173), (174),
% 170.47/25.51  | | | | | | | |            (176), (177), (178), (179), (181), (182), (183),
% 170.47/25.51  | | | | | | | |            (185), (268), (269), (270), (271), (272), (273),
% 170.47/25.51  | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 170.47/25.51  | | | | | | | |            (281), (282), (283), (301), (302), (303), (304),
% 170.47/25.51  | | | | | | | |            (305), (306), (307), (310), (311), (312), (313),
% 170.47/25.51  | | | | | | | |            (314), (315), (316), (317), (319), (320), (321),
% 170.47/25.51  | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 170.47/25.51  | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 170.47/25.51  | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 170.47/25.51  | | | | | | | |            (391), (392), (403), (409), (413), (415), (419),
% 170.47/25.51  | | | | | | | |            (425), (429), (494), (503), (514), (518), (521),
% 170.47/25.51  | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 170.47/25.51  | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.47/25.51  | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.47/25.51  | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 170.47/25.51  | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 170.47/25.51  | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 170.47/25.51  | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 170.47/25.51  | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 170.47/25.51  | | | | | | | |            (597), (598), (599), (600), (649), (661), (663),
% 170.47/25.51  | | | | | | | |            (698), (715), (718), (719), (720), (742), (751),
% 170.47/25.51  | | | | | | | |            (770), (773), (776), (779), (789), (796), (797),
% 170.47/25.51  | | | | | | | |            (799), (800), (803), (1996), (1997),
% 170.47/25.51  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #316.
% 170.47/25.51  | | | | | | | | 
% 170.47/25.51  | | | | | | | End of split
% 170.47/25.51  | | | | | | | 
% 170.47/25.51  | | | | | | Case 2:
% 170.47/25.51  | | | | | | | 
% 170.47/25.51  | | | | | | |   (1998)  all_14_0 = e2
% 170.47/25.52  | | | | | | |   (1999)   ~ (all_14_1 = e0) |  ~ (all_14_2 = e3)
% 170.47/25.52  | | | | | | | 
% 170.47/25.52  | | | | | | | REDUCE: (63), (1998) imply:
% 170.47/25.52  | | | | | | |   (2000)  op(all_14_1, all_14_2) = e2
% 170.47/25.52  | | | | | | | 
% 170.47/25.52  | | | | | | | BETA: splitting (88) gives:
% 170.47/25.52  | | | | | | | 
% 170.47/25.52  | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | 
% 170.47/25.52  | | | | | | | |   (2001)   ~ (all_24_0 = e1)
% 170.47/25.52  | | | | | | | | 
% 170.47/25.52  | | | | | | | | REDUCE: (751), (2001) imply:
% 170.47/25.52  | | | | | | | |   (2002)   ~ (all_10_0 = e1)
% 170.47/25.52  | | | | | | | | 
% 170.47/25.52  | | | | | | | | BETA: splitting (93) gives:
% 170.47/25.52  | | | | | | | | 
% 170.47/25.52  | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | 
% 170.47/25.52  | | | | | | | | |   (2003)   ~ (all_26_0 = e2)
% 170.47/25.52  | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | REDUCE: (779), (2003) imply:
% 170.47/25.52  | | | | | | | | |   (2004)   ~ (all_4_0 = e2)
% 170.47/25.52  | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | BETA: splitting (98) gives:
% 170.47/25.52  | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | |   (2005)   ~ (all_28_0 = e3)
% 170.47/25.52  | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | REDUCE: (776), (2005) imply:
% 170.47/25.52  | | | | | | | | | |   (2006)   ~ (all_6_0 = e3)
% 170.47/25.52  | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | BETA: splitting (103) gives:
% 170.47/25.52  | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | |   (2007)   ~ (all_30_1 = e1)
% 170.47/25.52  | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | REDUCE: (712), (2007) imply:
% 170.47/25.52  | | | | | | | | | | |   (2008)   ~ (all_10_1 = e1)
% 170.47/25.52  | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | BETA: splitting (113) gives:
% 170.47/25.52  | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | |   (2009)   ~ (all_34_0 = e1)
% 170.47/25.52  | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | REDUCE: (773), (2009) imply:
% 170.47/25.52  | | | | | | | | | | | |   (2010)   ~ (all_4_0 = e1)
% 170.47/25.52  | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.47/25.52  | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | |   (2011)   ~ (all_40_1 = e1)
% 170.47/25.52  | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | REDUCE: (715), (2011) imply:
% 170.47/25.52  | | | | | | | | | | | | |   (2012)   ~ (all_4_1 = e1)
% 170.47/25.52  | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.47/25.52  | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | |   (2013)  all_58_15 = e0
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | COMBINE_EQS: (532), (2013) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2014)  all_6_2 = e0
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (597), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2015)   ~ (all_52_7 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (599), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2016)   ~ (all_52_15 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (600), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2017)   ~ (all_52_23 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (564), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2018)   ~ (all_52_25 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (582), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2019)   ~ (all_52_27 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (594), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2020)   ~ (all_52_29 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (43), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2021)  op(all_6_1, e0) = all_6_0
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (42), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2022)  op(e0, e0) = all_6_1
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (41), (2014) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2023)  op(e0, e0) = e0
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (52), (53), (62),
% 170.47/25.52  | | | | | | | | | | | | | |            (154), (155), (156), (159), (160), (163), (164),
% 170.47/25.52  | | | | | | | | | | | | | |            (165), (167), (170), (172), (173), (177), (178),
% 170.47/25.52  | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (269), (270),
% 170.47/25.52  | | | | | | | | | | | | | |            (271), (273), (275), (276), (278), (280), (282),
% 170.47/25.52  | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (306), (307),
% 170.47/25.52  | | | | | | | | | | | | | |            (310), (311), (315), (319), (322), (323), (324),
% 170.47/25.52  | | | | | | | | | | | | | |            (326), (329), (330), (331), (341), (344), (349),
% 170.47/25.52  | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 170.47/25.52  | | | | | | | | | | | | | |            (391), (392), (403), (425), (429), (530), (531),
% 170.47/25.52  | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 170.47/25.52  | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 170.47/25.52  | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (558), (559),
% 170.47/25.52  | | | | | | | | | | | | | |            (560), (561), (562), (563), (565), (566), (569),
% 170.47/25.52  | | | | | | | | | | | | | |            (571), (573), (578), (579), (580), (581), (583),
% 170.47/25.52  | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (595),
% 170.47/25.52  | | | | | | | | | | | | | |            (596), (597), (598), (661), (719), (720), (796),
% 170.47/25.52  | | | | | | | | | | | | | |            (797), (799), (800), (2000), (2002), (2004),
% 170.47/25.52  | | | | | | | | | | | | | |            (2006), (2010), (2012), (2013), (2015), (2016),
% 170.47/25.52  | | | | | | | | | | | | | |            (2017), (2018), (2019), (2020), (2021), (2022),
% 170.47/25.52  | | | | | | | | | | | | | |            (2023), (function-axioms) are inconsistent by
% 170.47/25.52  | | | | | | | | | | | | | |            sub-proof #313.
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | Case 2:
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | |   (2024)   ~ (all_58_15 = e0)
% 170.47/25.52  | | | | | | | | | | | | | |   (2025)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.47/25.52  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.47/25.52  | | | | | | | | | | | | | |             e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | ALPHA: (2025) implies:
% 170.47/25.52  | | | | | | | | | | | | | |   (2026)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.47/25.52  | | | | | | | | | | | | | |   (2027)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | REDUCE: (532), (2024) imply:
% 170.47/25.52  | | | | | | | | | | | | | |   (2028)   ~ (all_6_2 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.47/25.52  | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | |   (2029)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.47/25.52  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.47/25.52  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.47/25.52  | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | BETA: splitting (2029) gives:
% 170.47/25.52  | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | Case 1:
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2030)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.47/25.52  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | ALPHA: (2030) implies:
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2031)  all_52_6 = e0
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2032)  all_52_4 = e1
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2033)  all_52_2 = e2
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2034)  all_52_0 = e3
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (2034) imply:
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2035)  all_4_1 = e3
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | REDUCE: (38), (2035) imply:
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2036)  op(e3, all_4_2) = all_4_0
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | REDUCE: (37), (2035) imply:
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2037)  op(e3, all_4_2) = e3
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | REDUCE: (176), (2033) imply:
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2038)  op(e2, all_52_3) = e2
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | REDUCE: (168), (2032) imply:
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2039)  op(e1, all_52_5) = e1
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | REDUCE: (160), (2031) imply:
% 170.47/25.52  | | | | | | | | | | | | | | | |   (2040)  op(e0, all_52_7) = e0
% 170.47/25.52  | | | | | | | | | | | | | | | | 
% 170.47/25.52  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (41), (42), (43), (51), (52), (61),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (62), (154), (155), (156), (158), (159), (161),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (163), (164), (165), (169), (170), (172), (173),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (279), (280),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (281), (282), (283), (302), (303), (304), (305),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (312), (313), (314),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (315), (317), (319), (321), (322), (323), (324),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 170.47/25.52  | | | | | | | | | | | | | | | |            (409), (413), (419), (425), (429), (529), (531),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (552), (553), (554), (556), (557), (558), (559),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (578),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (797),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (2000), (2004), (2008), (2010), (2027), (2028),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (2036), (2037), (2038), (2039), (2040),
% 170.58/25.52  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.58/25.52  | | | | | | | | | | | | | | | |            #310.
% 170.58/25.52  | | | | | | | | | | | | | | | | 
% 170.58/25.52  | | | | | | | | | | | | | | | Case 2:
% 170.58/25.52  | | | | | | | | | | | | | | | | 
% 170.58/25.52  | | | | | | | | | | | | | | | |   (2041)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.58/25.52  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 170.58/25.52  | | | | | | | | | | | | | | | | 
% 170.59/25.52  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (38), (42), (52), (53),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (61), (62), (154), (155), (156), (158), (159),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (167), (169), (170),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (182), (183), (268), (270), (272), (273), (274),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (303), (304), (307), (311), (313), (315), (316),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (317), (319), (320), (321), (323), (326), (328),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (359),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (529),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (585),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (661),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (796), (800), (2002), (2004), (2010), (2012),
% 170.59/25.52  | | | | | | | | | | | | | | | |            (2026), (2027), (2028), (2041), (function-axioms)
% 170.59/25.52  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #338.
% 170.59/25.52  | | | | | | | | | | | | | | | | 
% 170.59/25.52  | | | | | | | | | | | | | | | End of split
% 170.59/25.52  | | | | | | | | | | | | | | | 
% 170.59/25.52  | | | | | | | | | | | | | | Case 2:
% 170.59/25.52  | | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | |   (2042)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.59/25.53  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.59/25.53  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.59/25.53  | | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43), (62),
% 170.59/25.53  | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 170.59/25.53  | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 170.59/25.53  | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 170.59/25.53  | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 170.59/25.53  | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 170.59/25.53  | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 170.59/25.53  | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 170.59/25.53  | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 170.59/25.53  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.59/25.53  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.59/25.53  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.59/25.53  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.59/25.53  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 170.59/25.53  | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 170.59/25.53  | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 170.59/25.53  | | | | | | | | | | | | | | |            (649), (719), (797), (799), (2000), (2004),
% 170.59/25.53  | | | | | | | | | | | | | | |            (2006), (2010), (2026), (2027), (2028), (2042),
% 170.59/25.53  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.53  | | | | | | | | | | | | | | |            #309.
% 170.59/25.53  | | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | End of split
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | End of split
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | Case 2:
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | |   (2043)  all_40_1 = e1
% 170.59/25.53  | | | | | | | | | | | | |   (2044)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | COMBINE_EQS: (715), (2043) imply:
% 170.59/25.53  | | | | | | | | | | | | |   (2045)  all_4_1 = e1
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | SIMP: (2045) implies:
% 170.59/25.53  | | | | | | | | | | | | |   (2046)  all_4_1 = e1
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (38), (41),
% 170.59/25.53  | | | | | | | | | | | | |            (42), (43), (52), (53), (61), (62), (154), (155),
% 170.59/25.53  | | | | | | | | | | | | |            (156), (158), (159), (160), (161), (163), (164),
% 170.59/25.53  | | | | | | | | | | | | |            (165), (167), (169), (170), (172), (173), (174),
% 170.59/25.53  | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 170.59/25.53  | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (274),
% 170.59/25.53  | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 170.59/25.53  | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 170.59/25.53  | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (316), (317),
% 170.59/25.53  | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 170.59/25.53  | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (341),
% 170.59/25.53  | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 170.59/25.53  | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 170.59/25.53  | | | | | | | | | | | | |            (415), (419), (425), (429), (518), (529), (530),
% 170.59/25.53  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.59/25.53  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.59/25.53  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.59/25.53  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.59/25.53  | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 170.59/25.53  | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 170.59/25.53  | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 170.59/25.53  | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 170.59/25.53  | | | | | | | | | | | | |            (599), (600), (649), (661), (719), (720), (770),
% 170.59/25.53  | | | | | | | | | | | | |            (796), (797), (799), (800), (2000), (2002),
% 170.59/25.53  | | | | | | | | | | | | |            (2004), (2006), (2010), (2044), (2046),
% 170.59/25.53  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.53  | | | | | | | | | | | | |            #306.
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | End of split
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | Case 2:
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | |   (2047)  all_34_0 = e1
% 170.59/25.53  | | | | | | | | | | | |   (2048)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | COMBINE_EQS: (773), (2047) imply:
% 170.59/25.53  | | | | | | | | | | | |   (2049)  all_4_0 = e1
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (37), (38), (41), (42),
% 170.59/25.53  | | | | | | | | | | | |            (43), (52), (53), (61), (62), (154), (155), (156),
% 170.59/25.53  | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 170.59/25.53  | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 170.59/25.53  | | | | | | | | | | | |            (181), (182), (183), (185), (268), (270), (271),
% 170.59/25.53  | | | | | | | | | | | |            (272), (273), (274), (276), (277), (279), (280),
% 170.59/25.53  | | | | | | | | | | | |            (281), (282), (283), (301), (302), (303), (304),
% 170.59/25.53  | | | | | | | | | | | |            (305), (306), (307), (311), (313), (315), (319),
% 170.59/25.53  | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 170.59/25.53  | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (359),
% 170.59/25.53  | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 170.59/25.53  | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 170.59/25.53  | | | | | | | | | | | |            (494), (529), (531), (532), (533), (534), (535),
% 170.59/25.53  | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.59/25.53  | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.59/25.53  | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 170.59/25.53  | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 170.59/25.53  | | | | | | | | | | | |            (571), (573), (578), (579), (580), (581), (582),
% 170.59/25.53  | | | | | | | | | | | |            (583), (585), (586), (587), (588), (591), (593),
% 170.59/25.53  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 170.59/25.53  | | | | | | | | | | | |            (649), (661), (663), (719), (720), (796), (797),
% 170.59/25.53  | | | | | | | | | | | |            (799), (800), (2000), (2002), (2004), (2006),
% 170.59/25.53  | | | | | | | | | | | |            (2048), (2049), (function-axioms) are inconsistent
% 170.59/25.53  | | | | | | | | | | | |            by sub-proof #305.
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | End of split
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | Case 2:
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | |   (2050)  all_30_1 = e1
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | COMBINE_EQS: (712), (2050) imply:
% 170.59/25.53  | | | | | | | | | | |   (2051)  all_10_1 = e1
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | SIMP: (2051) implies:
% 170.59/25.53  | | | | | | | | | | |   (2052)  all_10_1 = e1
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | COMBINE_EQS: (661), (2052) imply:
% 170.59/25.53  | | | | | | | | | | |   (2053)  all_52_10 = e1
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | REDUCE: (802), (2052) imply:
% 170.59/25.53  | | | | | | | | | | |   (2054)   ~ (e3 = e1)
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | REDUCE: (53), (2052) imply:
% 170.59/25.53  | | | | | | | | | | |   (2055)  op(e1, all_10_2) = all_10_0
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | REDUCE: (52), (2052) imply:
% 170.59/25.53  | | | | | | | | | | |   (2056)  op(e2, all_10_2) = e1
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | BETA: splitting (113) gives:
% 170.59/25.53  | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | Case 1:
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | |   (2057)   ~ (all_34_0 = e1)
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | REDUCE: (773), (2057) imply:
% 170.59/25.53  | | | | | | | | | | | |   (2058)   ~ (all_4_0 = e1)
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.59/25.53  | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | Case 1:
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | |   (2059)   ~ (all_40_1 = e1)
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | REDUCE: (715), (2059) imply:
% 170.59/25.53  | | | | | | | | | | | | |   (2060)   ~ (all_4_1 = e1)
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.59/25.53  | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | Case 1:
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | |   (2061)  all_58_15 = e0
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | COMBINE_EQS: (532), (2061) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2062)  all_6_2 = e0
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (597), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2063)   ~ (all_52_7 = e0)
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (599), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2064)   ~ (all_52_15 = e0)
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (600), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2065)   ~ (all_52_23 = e0)
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (564), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2066)   ~ (all_52_25 = e0)
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (582), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2067)   ~ (all_52_27 = e0)
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (594), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2068)   ~ (all_52_29 = e0)
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (43), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2069)  op(all_6_1, e0) = all_6_0
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (42), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2070)  op(e0, e0) = all_6_1
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REDUCE: (41), (2062) imply:
% 170.59/25.53  | | | | | | | | | | | | | |   (2071)  op(e0, e0) = e0
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.53  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (37), (38), (52), (53), (62),
% 170.59/25.53  | | | | | | | | | | | | | |            (154), (155), (156), (159), (160), (163), (164),
% 170.59/25.53  | | | | | | | | | | | | | |            (165), (167), (170), (172), (173), (177), (178),
% 170.59/25.53  | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (269), (270),
% 170.59/25.53  | | | | | | | | | | | | | |            (271), (273), (275), (276), (278), (280), (282),
% 170.59/25.53  | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (306), (307),
% 170.59/25.53  | | | | | | | | | | | | | |            (310), (311), (315), (319), (322), (323), (324),
% 170.59/25.53  | | | | | | | | | | | | | |            (326), (329), (330), (331), (341), (344), (349),
% 170.59/25.53  | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 170.59/25.53  | | | | | | | | | | | | | |            (391), (392), (403), (425), (429), (530), (531),
% 170.59/25.53  | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 170.59/25.53  | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 170.59/25.53  | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (558), (559),
% 170.59/25.53  | | | | | | | | | | | | | |            (560), (561), (562), (563), (565), (566), (569),
% 170.59/25.53  | | | | | | | | | | | | | |            (571), (573), (578), (579), (580), (581), (583),
% 170.59/25.53  | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (595),
% 170.59/25.53  | | | | | | | | | | | | | |            (596), (597), (598), (661), (719), (720), (796),
% 170.59/25.53  | | | | | | | | | | | | | |            (797), (799), (800), (2000), (2002), (2004),
% 170.59/25.53  | | | | | | | | | | | | | |            (2006), (2058), (2060), (2061), (2063), (2064),
% 170.59/25.53  | | | | | | | | | | | | | |            (2065), (2066), (2067), (2068), (2069), (2070),
% 170.59/25.53  | | | | | | | | | | | | | |            (2071), (function-axioms) are inconsistent by
% 170.59/25.53  | | | | | | | | | | | | | |            sub-proof #313.
% 170.59/25.53  | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | |   (2072)   ~ (all_58_15 = e0)
% 170.59/25.54  | | | | | | | | | | | | | |   (2073)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.59/25.54  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.59/25.54  | | | | | | | | | | | | | |             e0)
% 170.59/25.54  | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | ALPHA: (2073) implies:
% 170.59/25.54  | | | | | | | | | | | | | |   (2074)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.59/25.54  | | | | | | | | | | | | | |   (2075)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.59/25.54  | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | REDUCE: (532), (2072) imply:
% 170.59/25.54  | | | | | | | | | | | | | |   (2076)   ~ (all_6_2 = e0)
% 170.59/25.54  | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.59/25.54  | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | |   (2077)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.54  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.59/25.54  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.59/25.54  | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | BETA: splitting (2077) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2078)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.54  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | ALPHA: (2078) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2079)  all_52_6 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2080)  all_52_4 = e1
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2081)  all_52_2 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2082)  all_52_0 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (2082) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2083)  all_4_1 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | REDUCE: (38), (2083) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2084)  op(e3, all_4_2) = all_4_0
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | REDUCE: (37), (2083) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2085)  op(e3, all_4_2) = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | REDUCE: (176), (2081) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2086)  op(e2, all_52_3) = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | REDUCE: (168), (2080) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2087)  op(e1, all_52_5) = e1
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | REDUCE: (160), (2079) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2088)  op(e0, all_52_7) = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 170.59/25.54  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (2084), (2085)
% 170.59/25.54  | | | | | | | | | | | | | | | |              gives:
% 170.59/25.54  | | | | | | | | | | | | | | | |   (2089)  all_4_0 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2090)  all_56_15 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (2090) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2091)  all_6_2 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | SIMP: (2091) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2092)  all_6_2 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2093)  all_58_15 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (597), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2094)   ~ (all_52_7 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (599), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2095)   ~ (all_52_15 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (600), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2096)   ~ (all_52_23 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (564), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2097)   ~ (all_52_25 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (594), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2098)   ~ (all_52_29 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (43), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2099)  op(all_6_1, e3) = all_6_0
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (42), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2100)  op(e0, e3) = all_6_1
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (41), (2092) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2101)  op(e0, e0) = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 170.59/25.54  | | | | | | | | | | | | | | | | |              all_6_1, e3, e0, simplifying with (156), (2100)
% 170.59/25.54  | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2102)  all_52_25 = all_6_1
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2103)  all_56_12 = all_6_1
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2104)  all_58_12 = all_6_1
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (554), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2105)   ~ (all_52_9 = all_6_1)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (558), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2106)   ~ (all_52_17 = all_6_1)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (563), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2107)   ~ (all_52_29 = all_6_1)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | SIMP: (2107) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2108)   ~ (all_52_29 = all_6_1)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (546), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2109)   ~ (all_6_1 = all_4_2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (2097), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2110)   ~ (all_6_1 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | REDUCE: (181), (2102) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | |   (2111)  op(e3, all_6_1) = all_52_24
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | |   (2112)  all_56_14 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (341), (2098), (2112) are inconsistent by
% 170.59/25.54  | | | | | | | | | | | | | | | | | |            sub-proof #896.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | |   (2113)   ~ (all_56_14 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | |   (2114)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | |   (2115)  all_56_3 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (2094), (2115) are inconsistent by
% 170.59/25.54  | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | |   (2116)   ~ (all_56_3 = e3)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | |   (2117)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | |   (2118)  all_56_12 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2103), (2110), (2118) are inconsistent by
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | |            sub-proof #509.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | |   (2119)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2120)  all_58_9 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (2120) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2121)  all_52_7 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | SIMP: (2121) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2122)  all_52_7 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (2122) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2123)   ~ (all_52_3 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2094), (2122) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2124)   ~ (e3 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2088), (2122) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2125)  op(e0, e2) = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (155), (156), (164), (170), (172),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (177), (178), (179), (273), (278), (282), (283),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (303), (307), (311), (315), (324), (326), (331),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (392), (403),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (537), (538), (540), (542), (544), (546), (548),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (550), (552), (560), (565), (566), (567), (568),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (569), (573), (575), (583), (584), (585), (586),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (587), (588), (591), (593), (595), (596), (597),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (797), (2056), (2085), (2086), (2087), (2088),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (2093), (2098), (2099), (2104), (2123), (2125),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |            #523.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2126)   ~ (all_58_9 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2127)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (536), (2126) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | |   (2128)   ~ (all_52_7 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2129)  all_58_12 = e1
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2104), (2129) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2130)  all_6_1 = e1
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2130) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2131)  all_6_1 = e1
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2106), (2131) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2132)   ~ (all_52_17 = e1)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2109), (2131) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2133)   ~ (all_4_2 = e1)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2133) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2134)   ~ (all_4_2 = e1)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2099), (2131) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2135)  op(e1, e3) = all_6_0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |              all_6_0, e3, e1, simplifying with (164), (2135)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2136)  all_52_17 = all_6_0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2136) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2137)  all_56_8 = all_6_0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2136) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2138)  all_58_6 = all_6_0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (2136) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | |   (2139)   ~ (all_6_0 = all_4_2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | |   (2140)  all_56_8 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2006), (2137), (2140) are inconsistent by
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #416.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | |   (2141)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2141) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | |   (2142)  all_56_8 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (799), (2137), (2142) are inconsistent by
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #415.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | |   (2143)   ~ (all_56_8 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | |   (2144)  all_56_8 = e1 | all_56_8 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2144) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2145)  all_56_8 = e1
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (797), (2137), (2145) are inconsistent by
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #414.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2146)  all_56_8 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2137), (2146) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2147)  all_6_0 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2147) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2148)  all_6_0 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2138), (2148) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2149)  all_58_6 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2139), (2148) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2150)   ~ (all_4_2 = e0)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2150) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2151)   ~ (all_4_2 = e0)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (799), (2148) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2152)   ~ (e2 = e0)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2135), (2148) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (2153)  op(e1, e3) = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2154)  all_56_4 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (2154) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2155)  all_52_9 = e3
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (164), (172), (177), (178), (179), (273),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (311), (315), (324), (326), (331),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (403), (531),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (532), (533), (535), (536), (537), (538), (540),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (550), (552), (560), (566),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (583), (584), (585), (586), (587),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (2085), (2086),
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2087), (2088), (2098), (2155), (function-axioms)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #413.
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2156)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2156) gives:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2157)  all_56_4 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (2157) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2158)  all_52_9 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2158) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2159)  all_52_9 = e2
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2159) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2160)   ~ (all_52_15 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2160) implies:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2161)   ~ (all_52_15 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (2159) imply:
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2162)   ~ (all_4_2 = e2)
% 170.59/25.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2162) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2163)   ~ (all_4_2 = e2)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2164)  all_56_0 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (2164) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2165)  all_4_2 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2165) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2166)  all_4_2 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (2166) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2167)   ~ (all_52_3 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2127) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2168)  all_58_10 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (2161), (2168) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #711.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2169)  all_58_11 = e2 | all_58_15 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2169) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2170)  all_58_11 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (2170) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2171)  all_52_23 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2171) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2172)  all_52_23 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (2172) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2173)  op(e0, e2) = all_52_22
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_27,
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_22, e2, e0, simplifying with (155), (2173)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2174)  all_52_22 = all_52_27
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2175)  all_56_9 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (2175) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2176)  all_52_19 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2176) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2177)  all_52_19 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (154), (155), (156), (163), (164), (170),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (273), (281), (282),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (305), (306), (307), (311), (315), (324),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (326), (331), (359), (364), (370), (373), (386),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (392), (403), (413), (531), (532), (533),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (540), (542), (544),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (546), (550), (552), (560), (566), (567), (568),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (569), (579), (583), (584), (585), (586), (587),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (2085), (2086),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2087), (2088), (2094), (2098), (2101), (2117),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2167), (2177), (function-axioms) are inconsistent
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #522.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2178)   ~ (all_56_9 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (2178) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2179)   ~ (all_52_19 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2180)  all_58_6 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2149), (2180) are inconsistent by sub-proof
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #559.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2181)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (273), (359), (364), (535), (537), (1999),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2096), (2153), (2179), (2181), (function-axioms)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #304.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2182)  all_58_15 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2093), (2182) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2183)  e3 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2183) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2184)  $false
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2184) is inconsistent.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2185)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (531), (2134), (2151), (2163), (2185) are
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #882.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2186)   ~ (all_56_4 = e2)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (409), (2186) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2187)   ~ (all_52_9 = e2)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (156), (164), (172), (177), (178),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (179), (273), (283), (307), (311), (315), (324),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (326), (328), (330), (331), (359), (364), (370),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (531), (532), (533),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (540), (542), (544),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (546), (550), (552), (560), (566), (568), (569),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (591), (593),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (2085), (2086), (2087),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2088), (2098), (2129), (2149), (2187),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #410.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | |   (2188)   ~ (all_58_12 = e1)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | |   (2189)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2104), (2188) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | |   (2190)   ~ (all_6_1 = e1)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |   (2191)  all_58_4 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (2191) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |   (2192)  all_52_5 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2192) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |   (2193)  all_52_5 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (164), (172), (177), (178), (179), (273),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (311), (315), (324), (326), (331),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (403), (531),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            (532), (533), (535), (536), (537), (538), (540),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (550), (552), (560), (566),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (583), (584), (585), (586), (587),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (2085), (2086),
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            (2087), (2088), (2193), (function-axioms) are
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |   (2194)   ~ (all_58_4 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |   (2195)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (2194) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | |   (2196)   ~ (all_52_5 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | |   (2197)  all_58_0 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (2197) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | |   (2198)  all_4_2 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (2198) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | |   (2199)   ~ (all_52_3 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (2198) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | |   (2200)   ~ (all_52_9 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (2198) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | |   (2201)   ~ (all_52_17 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (2202)  all_58_2 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (385), (2200), (2202) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #980.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (2203)   ~ (all_58_2 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (2204)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2205)  all_58_6 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (2201), (2205) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2206)   ~ (all_58_6 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2207)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2208)  all_56_8 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (365), (2201), (2208) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #461.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2209)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2210)  all_56_2 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (2196), (2210) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2211)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2212)  all_56_1 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (2199), (2212) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2213)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2214)  all_56_4 = e3
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (409), (2200), (2214) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #782.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2215)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2216)  all_58_12 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2104), (2216) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2217)  all_6_1 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2217) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2218)  all_6_1 = e2
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2105), (2218) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2219)   ~ (all_52_9 = e2)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2110), (2218) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2220)   ~ (e3 = e2)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2099), (2218) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2221)  op(e2, e3) = all_6_0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_6_0, e3, e2, simplifying with (172), (2221)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2222)  all_52_9 = all_6_0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (2222) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2223)  all_56_4 = all_6_0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (2222) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2224)  all_58_2 = all_6_0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2222) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2225)   ~ (all_52_15 = all_6_0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2225) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2226)   ~ (all_52_15 = all_6_0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (2222) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2227)   ~ (all_10_2 = all_6_0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2227) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2228)   ~ (all_10_2 = all_6_0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (2222) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2229)  op(e3, all_6_0) = all_52_8
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2230)  all_58_0 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2197), (2230) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2231)  e3 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2231) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2232)  $false
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2232) is inconsistent.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2233)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2233) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2234)  all_58_2 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2224), (2234) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2235)  all_6_0 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2235) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2236)  all_6_0 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2226), (2236) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2237)   ~ (all_52_15 = e0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2228), (2236) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2238)   ~ (all_10_2 = e0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (799), (2236) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2239)   ~ (e2 = e0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (797), (2236) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2240)   ~ (e1 = e0)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2229), (2236) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2241)  op(e3, e0) = all_52_8
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_8, e0, e3, simplifying with (177), (2241)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2242)  all_52_7 = all_52_8
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (2242) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2243)  all_56_3 = all_52_8
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (2242) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2244)  all_58_9 = all_52_8
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (2242) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2245)   ~ (all_52_8 = all_52_23)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2094), (2242) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2246)   ~ (all_52_8 = e3)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2128), (2242) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2247)   ~ (all_52_8 = e2)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2088), (2242) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2248)  op(e0, all_52_8) = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2249)  all_58_9 = e1
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2244), (2249) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2250)  all_52_8 = e1
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2250) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2251)  all_52_8 = e1
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2245), (2251) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2252)   ~ (all_52_23 = e1)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2252) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2253)   ~ (all_52_23 = e1)
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2248), (2251) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2254)  op(e0, e1) = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2075) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2255)  all_58_9 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2249), (2255) are inconsistent by sub-proof
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #809.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2256)  all_58_10 = e0 | all_58_11 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2256) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2257)  all_58_10 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (2237), (2257) are inconsistent by
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #741.
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2258)  all_58_11 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (2258) imply:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2259)  all_52_23 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2259) implies:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2260)  all_52_23 = e0
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2127) gives:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2261)  all_58_10 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (2261) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2262)  all_52_15 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2262) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2263)  all_52_15 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (2263) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2264)   ~ (all_10_2 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2264) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2265)   ~ (all_10_2 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_29,
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (154), (2254) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2266)  all_52_29 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (2266) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2267)  all_58_14 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2189) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2268)  all_58_13 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (2268) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2269)  all_52_27 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2269) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2270)  all_52_27 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (2270) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2271)   ~ (all_10_2 = e1)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2271) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2272)   ~ (all_10_2 = e1)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (530), (797), (2056), (2221), (2238),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2265), (2272), (function-axioms) are inconsistent
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #525.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2273)  all_58_14 = e1 | all_58_15 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (2093), (2267), (2273) are inconsistent
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #835.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2274)  all_58_11 = e2 | all_58_15 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (2093), (2258), (2274) are inconsistent
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #303.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2275)   ~ (all_58_9 = e1)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2101), (2117), (2243), (2244), (2246), (2247),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2248), (2275), (function-axioms) are inconsistent
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #409.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2276)   ~ (all_58_2 = e0)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2224), (2276) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2277)   ~ (all_6_0 = e0)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (797), (799), (2215), (2223), (2277) are
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #408.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2278)   ~ (all_58_12 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2104), (2278) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2279)   ~ (all_6_1 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2119) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2280)  all_56_12 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2103), (2279), (2280) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #507.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2281)  all_56_12 = e1 | all_56_12 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2281) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2282)  all_56_12 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2103), (2190), (2282) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #506.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2283)  all_56_12 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2103), (2283) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2284)  all_6_1 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2284) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2285)  all_6_1 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2104), (2285) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2286)  all_58_12 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2108), (2285) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2287)   ~ (all_52_29 = e0)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2099), (2285) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2288)  op(e0, e3) = all_6_0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2111), (2285) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2289)  op(e3, e0) = all_52_24
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2100), (2285) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2290)  op(e0, e3) = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (2288), (2290) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2291)  all_6_0 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e0, e3, simplifying with (177), (2289)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2292)  all_52_7 = all_52_24
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (2292) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2293)  all_56_3 = all_52_24
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (2292) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2294)  all_58_9 = all_52_24
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2094), (2292) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2295)   ~ (all_52_24 = e3)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2128), (2292) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2296)   ~ (all_52_24 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2088), (2292) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2297)  op(e0, all_52_24) = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2298)  all_56_6 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (154), (155), (163), (170), (305), (306),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (386), (392), (413), (415), (535), (536),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (537), (567), (569), (584), (585), (587), (2086),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2087), (2088), (2094), (2096), (2101), (2117),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2207), (2211), (2213), (2298), (function-axioms)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #545.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2299)   ~ (all_56_6 = e3)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2300)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (2299) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2301)   ~ (all_52_13 = e3)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2195) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2302)  all_58_5 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (373), (2301), (2302) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #969.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2303)  all_58_8 = e3 | all_58_14 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2303) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2304)  all_58_8 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (2304) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2305)  all_14_2 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2305) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2306)  all_14_2 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (2306) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2307)  op(e1, e3) = all_14_1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2204) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2308)  all_58_3 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (2308) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2309)  all_10_2 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2056), (2309) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2310)  op(e2, e3) = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2309) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2311)  op(e2, e2) = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2055), (2309) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2312)  op(e1, e3) = all_10_0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1999) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2313)   ~ (all_14_2 = e3)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (537), (2098), (2303), (2313) are
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2314)   ~ (all_14_1 = e0)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e1, simplifying with (164), (2312)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2315)  all_52_17 = all_10_0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_1, e3, e1, simplifying with (164), (2307)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2316)  all_52_17 = all_14_1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (172), (2310) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2317)  all_52_9 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2315), (2316) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2318)  all_14_1 = all_10_0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2318) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2319)  all_14_1 = all_10_0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2315) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2320)  all_56_8 = all_10_0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (2317) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2321)  all_58_2 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (2317) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2322)   ~ (all_52_13 = e1)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2322) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2323)   ~ (all_52_13 = e1)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (2315), (2317) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2324)   ~ (all_10_0 = e1)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (2315) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2325)   ~ (all_52_19 = all_10_0)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2325) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2326)   ~ (all_52_19 = all_10_0)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2314), (2319) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2327)   ~ (all_10_0 = e0)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (2315) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2328)  op(e3, all_10_0) = all_52_16
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2209) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2329)  all_56_8 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2320), (2329) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2330)  all_10_0 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2330) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2331)  all_10_0 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2326), (2331) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2332)   ~ (all_52_19 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (800), (2331) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2333)   ~ (e3 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2328), (2331) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2334)  op(e3, e2) = all_52_16
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2312), (2331) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2335)  op(e1, e3) = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2127) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2336)  all_58_10 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (2336) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2337)  all_52_15 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2337) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2338)  all_52_15 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (2338) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2339)   ~ (all_52_13 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (154), (177), (179), (302), (305), (322),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (386), (415), (533), (536), (540), (588),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (797), (800), (2002), (2086), (2088), (2093),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2094), (2101), (2117), (2128), (2199), (2286),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2288), (2289), (2290), (2300), (2308), (2311),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2312), (2323), (2332), (2334), (2335), (2339),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #513.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2340)   ~ (all_58_10 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (2340) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2341)   ~ (all_52_15 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2342)  all_58_2 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2321), (2342) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2343)  e2 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2343) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2344)  $false
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2344) is inconsistent.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2345)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2345) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2346)  all_58_3 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2308), (2346) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2347)  e3 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2347) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2348)  $false
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2348) is inconsistent.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2349)  all_58_5 = e2 | all_58_10 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2349) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2350)  all_58_5 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (2350) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2351)  all_52_13 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2351) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2352)  all_52_13 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (2352) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2353)   ~ (all_52_29 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2353) implies:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2354)   ~ (all_52_29 = e2)
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2114) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2355)  all_56_14 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (341), (2354), (2355) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #837.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2356)  all_56_14 = e1 | all_56_14 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2356) gives:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2357)  all_56_14 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (341), (2357) imply:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2358)  all_52_29 = e1
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (305), (2101), (2117), (2287), (2293),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2294), (2295), (2296), (2297), (2358),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #514.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2359)  all_56_14 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (341), (2287), (2359) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #887.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2360)  all_58_10 = e2
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (2341), (2360) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #711.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2361)  all_56_8 = e1 | all_56_8 = e0
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2002), (2320), (2327), (2361) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #302.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2362)  all_58_5 = e3 | all_58_10 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (373), (2095), (2301), (2362) are
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2363)  all_58_14 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (2098), (2363) are inconsistent by
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1000.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | |   (2364)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (172), (177), (178), (179), (283), (307),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | |            (326), (370), (391), (403), (531), (532), (535),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | |            (536), (540), (542), (546), (548), (552), (568),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | |            (569), (586), (595), (596), (597), (2085), (2086),
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | |            (2088), (2196), (2364), (function-axioms) are
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #787.
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.56  | | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | |   (2365)   ~ (all_56_15 = e3)
% 170.59/25.57  | | | | | | | | | | | | | | | | |   (2366)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 170.59/25.57  | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (158),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (169), (170),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (269), (270),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (283), (304), (305), (307), (310), (311), (312),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (2075), (2076),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (2085), (2086), (2087), (2088), (2365), (2366),
% 170.59/25.57  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.57  | | | | | | | | | | | | | | | | |            #785.
% 170.59/25.57  | | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2367)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.59/25.57  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2053), (2367) are inconsistent by sub-proof
% 170.59/25.57  | | | | | | | | | | | | | | | |            #533.
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | |   (2368)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.59/25.57  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.59/25.57  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | BETA: splitting (2368) gives:
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | Case 1:
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2369)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.59/25.57  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (2000), (2369),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.57  | | | | | | | | | | | | | | | |            #314.
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2370)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.59/25.57  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (649), (797), (799), (2004), (2006), (2058),
% 170.59/25.57  | | | | | | | | | | | | | | | |            (2074), (2075), (2076), (2370), (function-axioms)
% 170.59/25.57  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #634.
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | |   (2371)  all_40_1 = e1
% 170.59/25.57  | | | | | | | | | | | | |   (2372)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | COMBINE_EQS: (715), (2371) imply:
% 170.59/25.57  | | | | | | | | | | | | |   (2373)  all_4_1 = e1
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (38), (41),
% 170.59/25.57  | | | | | | | | | | | | |            (42), (43), (52), (53), (61), (62), (154), (155),
% 170.59/25.57  | | | | | | | | | | | | |            (156), (158), (159), (160), (161), (163), (164),
% 170.59/25.57  | | | | | | | | | | | | |            (165), (167), (169), (170), (172), (173), (174),
% 170.59/25.57  | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 170.59/25.57  | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (274),
% 170.59/25.57  | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 170.59/25.57  | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 170.59/25.57  | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (316), (317),
% 170.59/25.57  | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 170.59/25.57  | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (341),
% 170.59/25.57  | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 170.59/25.57  | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 170.59/25.57  | | | | | | | | | | | | |            (415), (419), (425), (429), (518), (529), (530),
% 170.59/25.57  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.59/25.57  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.59/25.57  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.59/25.57  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.59/25.57  | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 170.59/25.57  | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 170.59/25.57  | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 170.59/25.57  | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 170.59/25.57  | | | | | | | | | | | | |            (599), (600), (649), (661), (719), (720), (770),
% 170.59/25.57  | | | | | | | | | | | | |            (796), (797), (799), (800), (2000), (2002),
% 170.59/25.57  | | | | | | | | | | | | |            (2004), (2006), (2058), (2372), (2373),
% 170.59/25.57  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.57  | | | | | | | | | | | | |            #306.
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | |   (2374)  all_34_0 = e1
% 170.59/25.57  | | | | | | | | | | | |   (2375)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | COMBINE_EQS: (773), (2374) imply:
% 170.59/25.57  | | | | | | | | | | | |   (2376)  all_4_0 = e1
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | SIMP: (2376) implies:
% 170.59/25.57  | | | | | | | | | | | |   (2377)  all_4_0 = e1
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (36), (37), (38), (41), (42),
% 170.59/25.57  | | | | | | | | | | | |            (43), (52), (53), (61), (62), (154), (155), (156),
% 170.59/25.57  | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 170.59/25.57  | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 170.59/25.57  | | | | | | | | | | | |            (181), (182), (183), (185), (268), (270), (271),
% 170.59/25.57  | | | | | | | | | | | |            (272), (273), (274), (276), (277), (279), (280),
% 170.59/25.57  | | | | | | | | | | | |            (281), (282), (283), (301), (302), (303), (304),
% 170.59/25.57  | | | | | | | | | | | |            (305), (306), (307), (311), (313), (315), (319),
% 170.59/25.57  | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 170.59/25.57  | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (359),
% 170.59/25.57  | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 170.59/25.57  | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 170.59/25.57  | | | | | | | | | | | |            (494), (529), (531), (532), (533), (534), (535),
% 170.59/25.57  | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.59/25.57  | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.59/25.57  | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 170.59/25.57  | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 170.59/25.57  | | | | | | | | | | | |            (571), (573), (578), (579), (580), (581), (582),
% 170.59/25.57  | | | | | | | | | | | |            (583), (585), (586), (587), (588), (591), (593),
% 170.59/25.57  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 170.59/25.57  | | | | | | | | | | | |            (649), (661), (663), (719), (720), (796), (797),
% 170.59/25.57  | | | | | | | | | | | |            (799), (800), (2000), (2002), (2004), (2006),
% 170.59/25.57  | | | | | | | | | | | |            (2375), (2377), (function-axioms) are inconsistent
% 170.59/25.57  | | | | | | | | | | | |            by sub-proof #305.
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | End of split
% 170.59/25.57  | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | |   (2378)  all_28_0 = e3
% 170.59/25.57  | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | COMBINE_EQS: (776), (2378) imply:
% 170.59/25.57  | | | | | | | | | |   (2379)  all_6_0 = e3
% 170.59/25.57  | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | REDUCE: (43), (2379) imply:
% 170.59/25.57  | | | | | | | | | |   (2380)  op(all_6_1, all_6_2) = e3
% 170.59/25.57  | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | BETA: splitting (103) gives:
% 170.59/25.57  | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | Case 1:
% 170.59/25.57  | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | |   (2381)   ~ (all_30_1 = e1)
% 170.59/25.57  | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | REDUCE: (712), (2381) imply:
% 170.59/25.57  | | | | | | | | | | |   (2382)   ~ (all_10_1 = e1)
% 170.59/25.57  | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | BETA: splitting (113) gives:
% 170.59/25.57  | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | Case 1:
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | |   (2383)   ~ (all_34_0 = e1)
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | REDUCE: (773), (2383) imply:
% 170.59/25.57  | | | | | | | | | | | |   (2384)   ~ (all_4_0 = e1)
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.59/25.57  | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | Case 1:
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | |   (2385)   ~ (all_40_1 = e1)
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | REDUCE: (715), (2385) imply:
% 170.59/25.57  | | | | | | | | | | | | |   (2386)   ~ (all_4_1 = e1)
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.59/25.57  | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | Case 1:
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | |   (2387)  all_58_15 = e0
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (2380), (2387),
% 170.59/25.57  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.57  | | | | | | | | | | | | | |            #510.
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | Case 2:
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | |   (2388)   ~ (all_58_15 = e0)
% 170.59/25.57  | | | | | | | | | | | | | |   (2389)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.59/25.57  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.59/25.57  | | | | | | | | | | | | | |             e0)
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | ALPHA: (2389) implies:
% 170.59/25.57  | | | | | | | | | | | | | |   (2390)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.59/25.57  | | | | | | | | | | | | | |   (2391)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | REDUCE: (532), (2388) imply:
% 170.59/25.57  | | | | | | | | | | | | | |   (2392)   ~ (all_6_2 = e0)
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.59/25.57  | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | Case 1:
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | |   (2393)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.57  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.59/25.57  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | BETA: splitting (2393) gives:
% 170.59/25.57  | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | Case 1:
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2394)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.57  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | ALPHA: (2394) implies:
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2395)  all_52_6 = e0
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2396)  all_52_4 = e1
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2397)  all_52_2 = e2
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2398)  all_52_0 = e3
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (2398) imply:
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2399)  all_4_1 = e3
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | REDUCE: (38), (2399) imply:
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2400)  op(e3, all_4_2) = all_4_0
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.57  | | | | | | | | | | | | | | | | REDUCE: (37), (2399) imply:
% 170.59/25.57  | | | | | | | | | | | | | | | |   (2401)  op(e3, all_4_2) = e3
% 170.59/25.57  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | REDUCE: (176), (2397) imply:
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2402)  op(e2, all_52_3) = e2
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | REDUCE: (168), (2396) imply:
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2403)  op(e1, all_52_5) = e1
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | REDUCE: (160), (2395) imply:
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2404)  op(e0, all_52_7) = e0
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (41), (42), (43), (51), (52), (61),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (62), (154), (155), (156), (158), (159), (161),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (163), (164), (165), (169), (170), (172), (173),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (279), (280),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (281), (282), (283), (302), (303), (304), (305),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (306), (307), (310), (311), (312), (313), (314),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (315), (317), (319), (321), (322), (323), (324),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (409), (413), (419), (425), (429), (529), (531),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (552), (553), (554), (556), (557), (558), (559),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (578),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (797),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (2000), (2004), (2382), (2384), (2391), (2392),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (2400), (2401), (2402), (2403), (2404),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.58  | | | | | | | | | | | | | | | |            #310.
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2405)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.59/25.58  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (38), (42), (52), (53),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (61), (62), (154), (155), (156), (158), (159),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (167), (169), (170),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (182), (183), (268), (270), (272), (273), (274),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (303), (304), (307), (311), (313), (315), (316),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (317), (319), (320), (321), (323), (326), (328),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (359),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (403), (409), (413), (415), (419), (425), (529),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (585),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (661),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (796), (800), (2002), (2004), (2384), (2386),
% 170.59/25.58  | | | | | | | | | | | | | | | |            (2390), (2391), (2392), (2405), (function-axioms)
% 170.59/25.58  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #338.
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | |   (2406)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.59/25.58  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.59/25.58  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.59/25.58  | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | BETA: splitting (2406) gives:
% 170.59/25.58  | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | Case 1:
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2407)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.59/25.58  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | ALPHA: (2407) implies:
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2408)  all_52_20 = e1
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (2408) imply:
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2409)  all_14_1 = e1
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (2000), (2409), (function-axioms) are
% 170.59/25.58  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2410)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.59/25.58  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | ALPHA: (2410) implies:
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2411)  all_52_30 = e0
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (2411) imply:
% 170.59/25.58  | | | | | | | | | | | | | | | |   (2412)  all_6_1 = e0
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (2380), (2412), (function-axioms) are
% 170.59/25.58  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 170.59/25.58  | | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | |   (2413)  all_40_1 = e1
% 170.59/25.58  | | | | | | | | | | | | |   (2414)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | COMBINE_EQS: (715), (2413) imply:
% 170.59/25.58  | | | | | | | | | | | | |   (2415)  all_4_1 = e1
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | SIMP: (2415) implies:
% 170.59/25.58  | | | | | | | | | | | | |   (2416)  all_4_1 = e1
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | COMBINE_EQS: (720), (2416) imply:
% 170.59/25.58  | | | | | | | | | | | | |   (2417)  all_52_0 = e1
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | REDUCE: (796), (2416) imply:
% 170.59/25.58  | | | | | | | | | | | | |   (2418)   ~ (e2 = e1)
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | REDUCE: (38), (2416) imply:
% 170.59/25.58  | | | | | | | | | | | | |   (2419)  op(e1, all_4_2) = all_4_0
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | REDUCE: (37), (2416) imply:
% 170.59/25.58  | | | | | | | | | | | | |   (2420)  op(e3, all_4_2) = e1
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | Case 1:
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | |   (2421)  all_58_15 = e0
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (2380), (2421),
% 170.59/25.58  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.58  | | | | | | | | | | | | | |            #510.
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | |   (2422)   ~ (all_58_15 = e0)
% 170.59/25.58  | | | | | | | | | | | | | |   (2423)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.59/25.58  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.59/25.58  | | | | | | | | | | | | | |             e0)
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 170.59/25.58  | | | | | | | | | | | | | |            (42), (52), (53), (61), (62), (154), (155), (156),
% 170.59/25.58  | | | | | | | | | | | | | |            (158), (159), (160), (161), (163), (164), (165),
% 170.59/25.58  | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 170.59/25.58  | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 170.59/25.58  | | | | | | | | | | | | | |            (270), (271), (272), (273), (274), (276), (277),
% 170.59/25.58  | | | | | | | | | | | | | |            (278), (279), (280), (281), (283), (303), (304),
% 170.59/25.58  | | | | | | | | | | | | | |            (305), (307), (311), (313), (315), (316), (317),
% 170.59/25.58  | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 170.59/25.58  | | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (344),
% 170.59/25.58  | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 170.59/25.58  | | | | | | | | | | | | | |            (386), (391), (403), (409), (413), (415), (419),
% 170.59/25.58  | | | | | | | | | | | | | |            (425), (429), (518), (529), (530), (531), (532),
% 170.59/25.58  | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 170.59/25.58  | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 170.59/25.58  | | | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 170.59/25.58  | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 170.59/25.58  | | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (577),
% 170.59/25.58  | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 170.59/25.58  | | | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 170.59/25.58  | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 170.59/25.58  | | | | | | | | | | | | | |            (649), (661), (719), (770), (796), (800), (2000),
% 170.59/25.58  | | | | | | | | | | | | | |            (2002), (2004), (2384), (2414), (2417), (2419),
% 170.59/25.58  | | | | | | | | | | | | | |            (2420), (2422), (2423), (function-axioms) are
% 170.59/25.58  | | | | | | | | | | | | | |            inconsistent by sub-proof #301.
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | |   (2424)  all_34_0 = e1
% 170.59/25.58  | | | | | | | | | | | |   (2425)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | COMBINE_EQS: (773), (2424) imply:
% 170.59/25.58  | | | | | | | | | | | |   (2426)  all_4_0 = e1
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | REDUCE: (2004), (2426) imply:
% 170.59/25.58  | | | | | | | | | | | |   (2427)   ~ (e2 = e1)
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | REDUCE: (38), (2426) imply:
% 170.59/25.58  | | | | | | | | | | | |   (2428)  op(all_4_1, all_4_2) = e1
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | Case 1:
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | |   (2429)  all_58_15 = e0
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (2380), (2429),
% 170.59/25.58  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.58  | | | | | | | | | | | | |            #510.
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | |   (2430)   ~ (all_58_15 = e0)
% 170.59/25.58  | | | | | | | | | | | | |   (2431)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.59/25.58  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.59/25.58  | | | | | | | | | | | | |             e0)
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | ALPHA: (2431) implies:
% 170.59/25.58  | | | | | | | | | | | | |   (2432)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | REDUCE: (532), (2430) imply:
% 170.59/25.58  | | | | | | | | | | | | |   (2433)   ~ (all_6_2 = e0)
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | Case 1:
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | |   (2434)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.58  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.59/25.58  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (42), (52), (53), (61),
% 170.59/25.58  | | | | | | | | | | | | | |            (62), (156), (158), (159), (161), (163), (164),
% 170.59/25.58  | | | | | | | | | | | | | |            (165), (167), (170), (172), (173), (174), (177),
% 170.59/25.58  | | | | | | | | | | | | | |            (178), (179), (182), (183), (268), (270), (272),
% 170.59/25.58  | | | | | | | | | | | | | |            (273), (274), (277), (279), (280), (281), (282),
% 170.59/25.58  | | | | | | | | | | | | | |            (283), (304), (307), (311), (313), (315), (319),
% 170.59/25.58  | | | | | | | | | | | | | |            (321), (323), (326), (328), (329), (330), (331),
% 170.59/25.58  | | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 170.59/25.58  | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 170.59/25.58  | | | | | | | | | | | | | |            (415), (419), (494), (529), (531), (532), (533),
% 170.59/25.58  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 170.59/25.58  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 170.59/25.58  | | | | | | | | | | | | | |            (554), (556), (557), (558), (559), (560), (561),
% 170.59/25.58  | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 170.59/25.58  | | | | | | | | | | | | | |            (569), (571), (573), (579), (580), (581), (582),
% 170.59/25.58  | | | | | | | | | | | | | |            (583), (585), (586), (587), (588), (591), (593),
% 170.59/25.58  | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 170.59/25.58  | | | | | | | | | | | | | |            (661), (663), (720), (796), (800), (2002), (2425),
% 170.59/25.58  | | | | | | | | | | | | | |            (2428), (2432), (2433), (2434), (function-axioms)
% 170.59/25.58  | | | | | | | | | | | | | |            are inconsistent by sub-proof #327.
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | |   (2435)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.59/25.58  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.59/25.58  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (2000),
% 170.59/25.58  | | | | | | | | | | | | | |            (2380), (2435), (function-axioms) are inconsistent
% 170.59/25.58  | | | | | | | | | | | | | |            by sub-proof #300.
% 170.59/25.58  | | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | End of split
% 170.59/25.58  | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | Case 2:
% 170.59/25.58  | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | |   (2436)  all_30_1 = e1
% 170.59/25.58  | | | | | | | | | | | 
% 170.59/25.58  | | | | | | | | | | | COMBINE_EQS: (712), (2436) imply:
% 170.59/25.59  | | | | | | | | | | |   (2437)  all_10_1 = e1
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | COMBINE_EQS: (661), (2437) imply:
% 170.59/25.59  | | | | | | | | | | |   (2438)  all_52_10 = e1
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | REDUCE: (802), (2437) imply:
% 170.59/25.59  | | | | | | | | | | |   (2439)   ~ (e3 = e1)
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (37), (38), (41), (42), (61),
% 170.59/25.59  | | | | | | | | | | |            (62), (113), (154), (156), (158), (159), (160),
% 170.59/25.59  | | | | | | | | | | |            (161), (163), (164), (165), (168), (169), (170),
% 170.59/25.59  | | | | | | | | | | |            (172), (173), (176), (177), (178), (179), (185),
% 170.59/25.59  | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (276),
% 170.59/25.59  | | | | | | | | | | |            (279), (281), (282), (283), (301), (302), (303),
% 170.59/25.59  | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 170.59/25.59  | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 170.59/25.59  | | | | | | | | | | |            (327), (328), (330), (331), (341), (344), (349),
% 170.59/25.59  | | | | | | | | | | |            (350), (359), (364), (370), (373), (385), (391),
% 170.59/25.59  | | | | | | | | | | |            (392), (403), (409), (413), (425), (429), (529),
% 170.59/25.59  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.59/25.59  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.59/25.59  | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 170.59/25.59  | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 170.59/25.59  | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 170.59/25.59  | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 170.59/25.59  | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 170.59/25.59  | | | | | | | | | | |            (596), (597), (598), (599), (600), (649), (719),
% 170.59/25.59  | | | | | | | | | | |            (720), (773), (2000), (2004), (2380), (2438),
% 170.59/25.59  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.59  | | | | | | | | | | |            #299.
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | End of split
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | End of split
% 170.59/25.59  | | | | | | | | | 
% 170.59/25.59  | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | 
% 170.59/25.59  | | | | | | | | |   (2440)  all_26_0 = e2
% 170.59/25.59  | | | | | | | | |   (2441)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 170.59/25.59  | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | COMBINE_EQS: (779), (2440) imply:
% 170.59/25.59  | | | | | | | | |   (2442)  all_4_0 = e2
% 170.59/25.59  | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | COMBINE_EQS: (742), (2442) imply:
% 170.59/25.59  | | | | | | | | |   (2443)  all_50_0 = e2
% 170.59/25.59  | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | REDUCE: (38), (2442) imply:
% 170.59/25.59  | | | | | | | | |   (2444)  op(all_4_1, all_4_2) = e2
% 170.59/25.59  | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | BETA: splitting (98) gives:
% 170.59/25.59  | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | |   (2445)   ~ (all_28_0 = e3)
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | REDUCE: (776), (2445) imply:
% 170.59/25.59  | | | | | | | | | |   (2446)   ~ (all_6_0 = e3)
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | BETA: splitting (151) gives:
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | |   (2447)   ~ (all_50_0 = e2)
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | REDUCE: (2443), (2447) imply:
% 170.59/25.59  | | | | | | | | | | |   (2448)  $false
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | CLOSE: (2448) is inconsistent.
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | |   (2449)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | BETA: splitting (301) gives:
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | |   (2450)  all_58_15 = e0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | COMBINE_EQS: (532), (2450) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2451)  all_6_2 = e0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (599), (2451) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2452)   ~ (all_52_15 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (564), (2451) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2453)   ~ (all_52_25 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (582), (2451) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2454)   ~ (all_52_27 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (594), (2451) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2455)   ~ (all_52_29 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (43), (2451) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2456)  op(all_6_1, e0) = all_6_0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (42), (2451) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2457)  op(e0, e0) = all_6_1
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (41), (2451) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2458)  op(e0, e0) = e0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 170.59/25.59  | | | | | | | | | | | |              e0, e0, simplifying with (2457), (2458) gives:
% 170.59/25.59  | | | | | | | | | | | |   (2459)  all_6_1 = e0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (2456), (2459) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2460)  op(e0, e0) = all_6_0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.59/25.59  | | | | | | | | | | | |              e0, e0, simplifying with (2458), (2460) gives:
% 170.59/25.59  | | | | | | | | | | | |   (2461)  all_6_0 = e0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (2446), (2461) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2462)   ~ (e3 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (799), (2461) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2463)   ~ (e2 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (797), (2461) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2464)   ~ (e1 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | |   (2465)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.59  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.59/25.59  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (52), (53), (154),
% 170.59/25.59  | | | | | | | | | | | | |            (155), (156), (159), (164), (165), (167), (172),
% 170.59/25.59  | | | | | | | | | | | | |            (173), (178), (179), (181), (183), (269), (270),
% 170.59/25.59  | | | | | | | | | | | | |            (271), (273), (276), (280), (302), (303), (304),
% 170.59/25.59  | | | | | | | | | | | | |            (305), (306), (307), (311), (315), (319), (323),
% 170.59/25.59  | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (359), (364),
% 170.59/25.59  | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (403), (425),
% 170.59/25.59  | | | | | | | | | | | | |            (429), (533), (534), (535), (536), (537), (538),
% 170.59/25.59  | | | | | | | | | | | | |            (539), (540), (542), (544), (548), (552), (553),
% 170.59/25.59  | | | | | | | | | | | | |            (554), (556), (558), (559), (560), (561), (562),
% 170.59/25.59  | | | | | | | | | | | | |            (563), (565), (566), (569), (571), (573), (575),
% 170.59/25.59  | | | | | | | | | | | | |            (578), (579), (581), (583), (586), (587), (588),
% 170.59/25.59  | | | | | | | | | | | | |            (589), (591), (595), (596), (598), (661), (720),
% 170.59/25.59  | | | | | | | | | | | | |            (796), (800), (2002), (2444), (2450), (2452),
% 170.59/25.59  | | | | | | | | | | | | |            (2453), (2454), (2455), (2465), (function-axioms)
% 170.59/25.59  | | | | | | | | | | | | |            are inconsistent by sub-proof #325.
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | |   (2466)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.59/25.59  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.59/25.59  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (37), (62), (164),
% 170.59/25.59  | | | | | | | | | | | | |            (165), (172), (173), (177), (178), (179), (181),
% 170.59/25.59  | | | | | | | | | | | | |            (270), (271), (280), (283), (303), (304), (326),
% 170.59/25.59  | | | | | | | | | | | | |            (344), (349), (386), (403), (429), (503), (531),
% 170.59/25.59  | | | | | | | | | | | | |            (533), (534), (542), (544), (546), (548), (550),
% 170.59/25.59  | | | | | | | | | | | | |            (552), (554), (558), (562), (563), (586), (698),
% 170.59/25.59  | | | | | | | | | | | | |            (719), (796), (2000), (2441), (2444), (2450),
% 170.59/25.59  | | | | | | | | | | | | |            (2453), (2466), (function-axioms) are inconsistent
% 170.59/25.59  | | | | | | | | | | | | |            by sub-proof #298.
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | End of split
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | |   (2467)   ~ (all_58_15 = e0)
% 170.59/25.59  | | | | | | | | | | | |   (2468)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.59/25.59  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.59/25.59  | | | | | | | | | | | |             e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | ALPHA: (2468) implies:
% 170.59/25.59  | | | | | | | | | | | |   (2469)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REDUCE: (532), (2467) imply:
% 170.59/25.59  | | | | | | | | | | | |   (2470)   ~ (all_6_2 = e0)
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | |   (2471)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.59  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.59/25.59  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (52), (53), (62),
% 170.59/25.59  | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 170.59/25.59  | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 170.59/25.59  | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 170.59/25.59  | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 170.59/25.59  | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (304), (307),
% 170.59/25.59  | | | | | | | | | | | | |            (311), (313), (315), (316), (319), (321), (323),
% 170.59/25.59  | | | | | | | | | | | | |            (324), (325), (326), (328), (329), (330), (331),
% 170.59/25.59  | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 170.59/25.59  | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 170.59/25.59  | | | | | | | | | | | | |            (413), (415), (419), (425), (503), (521), (529),
% 170.59/25.59  | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 170.59/25.59  | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 170.59/25.59  | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 170.59/25.59  | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 170.59/25.59  | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 170.59/25.59  | | | | | | | | | | | | |            (573), (575), (579), (580), (581), (582), (583),
% 170.59/25.59  | | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 170.59/25.59  | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 170.59/25.59  | | | | | | | | | | | | |            (661), (698), (718), (720), (796), (2000), (2002),
% 170.59/25.59  | | | | | | | | | | | | |            (2441), (2444), (2449), (2469), (2470), (2471),
% 170.59/25.59  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.59  | | | | | | | | | | | | |            #294.
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | |   (2472)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.59/25.59  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.59/25.59  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | BETA: splitting (2472) gives:
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | |   (2473)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.59/25.59  | | | | | | | | | | | | | |           all_52_22 = e0
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | | ALPHA: (2473) implies:
% 170.59/25.59  | | | | | | | | | | | | | |   (2474)  all_52_20 = e1
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | | COMBINE_EQS: (719), (2474) imply:
% 170.59/25.59  | | | | | | | | | | | | | |   (2475)  all_14_1 = e1
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (2000), (2475), (function-axioms) are
% 170.59/25.59  | | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | |   (2476)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.59/25.59  | | | | | | | | | | | | | |           all_52_30 = e0
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | | ALPHA: (2476) implies:
% 170.59/25.59  | | | | | | | | | | | | | |   (2477)  all_52_30 = e0
% 170.59/25.59  | | | | | | | | | | | | | |   (2478)  all_52_28 = e1
% 170.59/25.59  | | | | | | | | | | | | | |   (2479)  all_52_26 = e2
% 170.59/25.59  | | | | | | | | | | | | | |   (2480)  all_52_24 = e3
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | | COMBINE_EQS: (649), (2477) imply:
% 170.59/25.59  | | | | | | | | | | | | | |   (2481)  all_6_1 = e0
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (51), (154),
% 170.59/25.59  | | | | | | | | | | | | | |            (155), (156), (164), (165), (172), (173), (177),
% 170.59/25.59  | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 170.59/25.59  | | | | | | | | | | | | | |            (271), (280), (283), (301), (303), (304), (305),
% 170.59/25.59  | | | | | | | | | | | | | |            (306), (307), (313), (322), (323), (324), (325),
% 170.59/25.59  | | | | | | | | | | | | | |            (326), (328), (330), (344), (349), (364), (370),
% 170.59/25.59  | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (429), (503),
% 170.59/25.59  | | | | | | | | | | | | | |            (521), (529), (531), (532), (533), (534), (535),
% 170.59/25.59  | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.59/25.59  | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.59/25.59  | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 170.59/25.59  | | | | | | | | | | | | | |            (564), (569), (573), (580), (581), (586), (588),
% 170.59/25.59  | | | | | | | | | | | | | |            (589), (594), (597), (698), (718), (796), (797),
% 170.59/25.59  | | | | | | | | | | | | | |            (799), (2441), (2444), (2446), (2449), (2478),
% 170.59/25.59  | | | | | | | | | | | | | |            (2479), (2480), (2481), (function-axioms) are
% 170.59/25.59  | | | | | | | | | | | | | |            inconsistent by sub-proof #293.
% 170.59/25.59  | | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | | End of split
% 170.59/25.59  | | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | End of split
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | End of split
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | End of split
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | |   (2482)  all_28_0 = e3
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | COMBINE_EQS: (776), (2482) imply:
% 170.59/25.59  | | | | | | | | | |   (2483)  all_6_0 = e3
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | SIMP: (2483) implies:
% 170.59/25.59  | | | | | | | | | |   (2484)  all_6_0 = e3
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | REDUCE: (43), (2484) imply:
% 170.59/25.59  | | | | | | | | | |   (2485)  op(all_6_1, all_6_2) = e3
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | BETA: splitting (151) gives:
% 170.59/25.59  | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | |   (2486)   ~ (all_50_0 = e2)
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | REDUCE: (2443), (2486) imply:
% 170.59/25.59  | | | | | | | | | | |   (2487)  $false
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | CLOSE: (2487) is inconsistent.
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | |   (2488)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | BETA: splitting (301) gives:
% 170.59/25.59  | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | Case 1:
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | |   (2489)  all_58_15 = e0
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (2485), (2489),
% 170.59/25.59  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.59  | | | | | | | | | | | |            #510.
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | Case 2:
% 170.59/25.59  | | | | | | | | | | | | 
% 170.59/25.59  | | | | | | | | | | | |   (2490)   ~ (all_58_15 = e0)
% 170.59/25.60  | | | | | | | | | | | |   (2491)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.59/25.60  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.59/25.60  | | | | | | | | | | | |             e0)
% 170.59/25.60  | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | ALPHA: (2491) implies:
% 170.59/25.60  | | | | | | | | | | | |   (2492)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.59/25.60  | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | REDUCE: (532), (2490) imply:
% 170.59/25.60  | | | | | | | | | | | |   (2493)   ~ (all_6_2 = e0)
% 170.59/25.60  | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.59/25.60  | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | Case 1:
% 170.59/25.60  | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | |   (2494)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.60  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.59/25.60  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.59/25.60  | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | BETA: splitting (2494) gives:
% 170.59/25.60  | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | Case 1:
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | |   (2495)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.59/25.60  | | | | | | | | | | | | | |           all_52_6 = e0
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (2444), (2495),
% 170.59/25.60  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.60  | | | | | | | | | | | | | |            #494.
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | Case 2:
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | |   (2496)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.59/25.60  | | | | | | | | | | | | | |           all_52_14 = e0
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | ALPHA: (2496) implies:
% 170.59/25.60  | | | | | | | | | | | | | |   (2497)  all_52_14 = e0
% 170.59/25.60  | | | | | | | | | | | | | |   (2498)  all_52_12 = e1
% 170.59/25.60  | | | | | | | | | | | | | |   (2499)  all_52_10 = e2
% 170.59/25.60  | | | | | | | | | | | | | |   (2500)  all_52_8 = e3
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | COMBINE_EQS: (661), (2499) imply:
% 170.59/25.60  | | | | | | | | | | | | | |   (2501)  all_10_1 = e2
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | REDUCE: (53), (2501) imply:
% 170.59/25.60  | | | | | | | | | | | | | |   (2502)  op(e2, all_10_2) = all_10_0
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | REDUCE: (183), (2500) imply:
% 170.59/25.60  | | | | | | | | | | | | | |   (2503)  op(e3, all_52_9) = e3
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | REDUCE: (52), (2501) imply:
% 170.59/25.60  | | | | | | | | | | | | | |   (2504)  op(e2, all_10_2) = e2
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | REDUCE: (167), (2498) imply:
% 170.59/25.60  | | | | | | | | | | | | | |   (2505)  op(e1, all_52_13) = e1
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | REDUCE: (159), (2497) imply:
% 170.59/25.60  | | | | | | | | | | | | | |   (2506)  op(e0, all_52_15) = e0
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (62), (156),
% 170.59/25.60  | | | | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (170),
% 170.59/25.60  | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 170.59/25.60  | | | | | | | | | | | | | |            (182), (268), (270), (272), (273), (274), (275),
% 170.59/25.60  | | | | | | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 170.59/25.60  | | | | | | | | | | | | | |            (283), (304), (307), (311), (313), (315), (316),
% 170.59/25.60  | | | | | | | | | | | | | |            (319), (321), (323), (324), (325), (326), (328),
% 170.59/25.60  | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (359),
% 170.59/25.60  | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 170.59/25.60  | | | | | | | | | | | | | |            (392), (403), (409), (413), (415), (419), (425),
% 170.59/25.60  | | | | | | | | | | | | | |            (503), (521), (529), (530), (531), (532), (533),
% 170.59/25.60  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 170.59/25.60  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 170.59/25.60  | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 170.59/25.60  | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 170.59/25.60  | | | | | | | | | | | | | |            (568), (569), (571), (573), (575), (579), (580),
% 170.59/25.60  | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 170.59/25.60  | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 170.59/25.60  | | | | | | | | | | | | | |            (598), (599), (600), (698), (718), (796), (2000),
% 170.59/25.60  | | | | | | | | | | | | | |            (2002), (2441), (2444), (2488), (2492), (2493),
% 170.59/25.60  | | | | | | | | | | | | | |            (2502), (2503), (2504), (2505), (2506),
% 170.59/25.60  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.59/25.60  | | | | | | | | | | | | | |            #295.
% 170.59/25.60  | | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | End of split
% 170.59/25.60  | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | Case 2:
% 170.59/25.60  | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | |   (2507)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.59/25.60  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.59/25.60  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.59/25.60  | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (2000),
% 170.59/25.60  | | | | | | | | | | | | |            (2485), (2507), (function-axioms) are inconsistent
% 170.59/25.60  | | | | | | | | | | | | |            by sub-proof #300.
% 170.59/25.60  | | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | | End of split
% 170.59/25.60  | | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | | End of split
% 170.59/25.60  | | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | | End of split
% 170.59/25.60  | | | | | | | | | | 
% 170.59/25.60  | | | | | | | | | End of split
% 170.59/25.60  | | | | | | | | | 
% 170.88/25.60  | | | | | | | | End of split
% 170.88/25.60  | | | | | | | | 
% 170.88/25.60  | | | | | | | Case 2:
% 170.88/25.60  | | | | | | | | 
% 170.88/25.60  | | | | | | | |   (2508)  all_24_0 = e1
% 170.88/25.60  | | | | | | | |   (2509)   ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 170.88/25.60  | | | | | | | | 
% 170.88/25.60  | | | | | | | | COMBINE_EQS: (751), (2508) imply:
% 170.88/25.60  | | | | | | | |   (2510)  all_10_0 = e1
% 170.88/25.60  | | | | | | | | 
% 170.88/25.60  | | | | | | | | REDUCE: (800), (2510) imply:
% 170.88/25.60  | | | | | | | |   (2511)   ~ (e3 = e1)
% 170.88/25.60  | | | | | | | | 
% 170.88/25.60  | | | | | | | | REDUCE: (53), (2510) imply:
% 170.88/25.60  | | | | | | | |   (2512)  op(all_10_1, all_10_2) = e1
% 170.88/25.60  | | | | | | | | 
% 170.88/25.60  | | | | | | | | BETA: splitting (93) gives:
% 170.88/25.60  | | | | | | | | 
% 170.88/25.60  | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | 
% 170.88/25.60  | | | | | | | | |   (2513)   ~ (all_26_0 = e2)
% 170.88/25.60  | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | REDUCE: (779), (2513) imply:
% 170.88/25.60  | | | | | | | | |   (2514)   ~ (all_4_0 = e2)
% 170.88/25.60  | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | BETA: splitting (98) gives:
% 170.88/25.60  | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | |   (2515)   ~ (all_28_0 = e3)
% 170.88/25.60  | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | REDUCE: (776), (2515) imply:
% 170.88/25.60  | | | | | | | | | |   (2516)   ~ (all_6_0 = e3)
% 170.88/25.60  | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | BETA: splitting (113) gives:
% 170.88/25.60  | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | |   (2517)   ~ (all_34_0 = e1)
% 170.88/25.60  | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | REDUCE: (773), (2517) imply:
% 170.88/25.60  | | | | | | | | | | |   (2518)   ~ (all_4_0 = e1)
% 170.88/25.60  | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | BETA: splitting (128) gives:
% 170.88/25.60  | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | |   (2519)   ~ (all_40_1 = e1)
% 170.88/25.60  | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | REDUCE: (715), (2519) imply:
% 170.88/25.60  | | | | | | | | | | | |   (2520)   ~ (all_4_1 = e1)
% 170.88/25.60  | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.88/25.60  | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | |   (2521)  all_58_15 = e0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | COMBINE_EQS: (532), (2521) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2522)  all_6_2 = e0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (597), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2523)   ~ (all_52_7 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (600), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2524)   ~ (all_52_23 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (564), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2525)   ~ (all_52_25 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (582), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2526)   ~ (all_52_27 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (594), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2527)   ~ (all_52_29 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (43), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2528)  op(all_6_1, e0) = all_6_0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (42), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2529)  op(e0, e0) = all_6_1
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (41), (2522) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2530)  op(e0, e0) = e0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 170.88/25.60  | | | | | | | | | | | | |              e0, e0, simplifying with (2529), (2530) gives:
% 170.88/25.60  | | | | | | | | | | | | |   (2531)  all_6_1 = e0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (2528), (2531) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2532)  op(e0, e0) = all_6_0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.88/25.60  | | | | | | | | | | | | |              e0, e0, simplifying with (2530), (2532) gives:
% 170.88/25.60  | | | | | | | | | | | | |   (2533)  all_6_0 = e0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (2516), (2533) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2534)   ~ (e3 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (797), (2533) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2535)   ~ (e1 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | |   (2536)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.60  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.60  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (37), (38), (52), (154), (155), (156),
% 170.88/25.60  | | | | | | | | | | | | | |            (160), (178), (179), (270), (271), (280), (283),
% 170.88/25.60  | | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (323),
% 170.88/25.60  | | | | | | | | | | | | | |            (326), (330), (331), (344), (349), (370), (386),
% 170.88/25.60  | | | | | | | | | | | | | |            (391), (403), (429), (531), (532), (533), (534),
% 170.88/25.60  | | | | | | | | | | | | | |            (535), (536), (540), (546), (552), (562), (569),
% 170.88/25.60  | | | | | | | | | | | | | |            (585), (586), (595), (596), (597), (661), (720),
% 170.88/25.60  | | | | | | | | | | | | | |            (2512), (2521), (2523), (2525), (2526), (2527),
% 170.88/25.60  | | | | | | | | | | | | | |            (2536), (function-axioms) are inconsistent by
% 170.88/25.60  | | | | | | | | | | | | | |            sub-proof #439.
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | Case 2:
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | |   (2537)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.60  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.60  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | BETA: splitting (2537) gives:
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | |   (2538)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.60  | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (2000), (2538),
% 170.88/25.60  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.60  | | | | | | | | | | | | | | |            #314.
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | Case 2:
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | |   (2539)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.60  | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (163), (164), (165),
% 170.88/25.60  | | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 170.88/25.60  | | | | | | | | | | | | | | |            (182), (183), (269), (270), (271), (275), (278),
% 170.88/25.60  | | | | | | | | | | | | | | |            (280), (283), (302), (304), (305), (306), (310),
% 170.88/25.60  | | | | | | | | | | | | | | |            (322), (324), (329), (330), (341), (344), (349),
% 170.88/25.60  | | | | | | | | | | | | | | |            (364), (365), (385), (386), (391), (403), (429),
% 170.88/25.60  | | | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 170.88/25.60  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.88/25.60  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (558), (561),
% 170.88/25.60  | | | | | | | | | | | | | | |            (562), (563), (569), (571), (573), (580), (581),
% 170.88/25.60  | | | | | | | | | | | | | | |            (583), (585), (586), (588), (591), (593), (796),
% 170.88/25.60  | | | | | | | | | | | | | | |            (2520), (2521), (2524), (2525), (2527), (2539),
% 170.88/25.60  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.60  | | | | | | | | | | | | | | |            #878.
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | End of split
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | End of split
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | Case 2:
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | |   (2540)   ~ (all_58_15 = e0)
% 170.88/25.60  | | | | | | | | | | | | |   (2541)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.88/25.60  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.88/25.60  | | | | | | | | | | | | |             e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | ALPHA: (2541) implies:
% 170.88/25.60  | | | | | | | | | | | | |   (2542)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.88/25.60  | | | | | | | | | | | | |   (2543)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | REDUCE: (532), (2540) imply:
% 170.88/25.60  | | | | | | | | | | | | |   (2544)   ~ (all_6_2 = e0)
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.60  | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | |   (2545)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.60  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.60  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | BETA: splitting (2545) gives:
% 170.88/25.60  | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | |   (2546)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.60  | | | | | | | | | | | | | | |           all_52_6 = e0
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | ALPHA: (2546) implies:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2547)  all_52_6 = e0
% 170.88/25.60  | | | | | | | | | | | | | | |   (2548)  all_52_4 = e1
% 170.88/25.60  | | | | | | | | | | | | | | |   (2549)  all_52_2 = e2
% 170.88/25.60  | | | | | | | | | | | | | | |   (2550)  all_52_0 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (2550) imply:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2551)  all_4_1 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | REDUCE: (38), (2551) imply:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2552)  op(e3, all_4_2) = all_4_0
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | REDUCE: (37), (2551) imply:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2553)  op(e3, all_4_2) = e3
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | REDUCE: (176), (2549) imply:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2554)  op(e2, all_52_3) = e2
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | REDUCE: (168), (2548) imply:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2555)  op(e1, all_52_5) = e1
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | REDUCE: (160), (2547) imply:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2556)  op(e0, all_52_7) = e0
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 170.88/25.60  | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (2552), (2553)
% 170.88/25.60  | | | | | | | | | | | | | | |              gives:
% 170.88/25.60  | | | | | | | | | | | | | | |   (2557)  all_4_0 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 170.88/25.60  | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2558)  all_56_15 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (2558) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2559)  all_6_2 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | SIMP: (2559) implies:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2560)  all_6_2 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2561)  all_58_15 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (597), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2562)   ~ (all_52_7 = e3)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (599), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2563)   ~ (all_52_15 = e3)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (600), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2564)   ~ (all_52_23 = e3)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (582), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2565)   ~ (all_52_27 = e3)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (594), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2566)   ~ (all_52_29 = e3)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (43), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2567)  op(all_6_1, e3) = all_6_0
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (42), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2568)  op(e0, e3) = all_6_1
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (41), (2560) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2569)  op(e0, e0) = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 170.88/25.60  | | | | | | | | | | | | | | | |              all_6_1, e3, e0, simplifying with (156), (2568)
% 170.88/25.60  | | | | | | | | | | | | | | | |              gives:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2570)  all_52_25 = all_6_1
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (2570) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2571)  all_58_12 = all_6_1
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (554), (2570) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2572)   ~ (all_52_9 = all_6_1)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (558), (2570) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2573)   ~ (all_52_17 = all_6_1)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (562), (2570) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2574)   ~ (all_52_27 = all_6_1)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | SIMP: (2574) implies:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2575)   ~ (all_52_27 = all_6_1)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | REDUCE: (563), (2570) imply:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2576)   ~ (all_52_29 = all_6_1)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | SIMP: (2576) implies:
% 170.88/25.60  | | | | | | | | | | | | | | | |   (2577)   ~ (all_52_29 = all_6_1)
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 170.88/25.60  | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | |   (2578)  all_56_13 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (2565), (2578) are inconsistent by
% 170.88/25.60  | | | | | | | | | | | | | | | | |            sub-proof #876.
% 170.88/25.60  | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.60  | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | |   (2579)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 170.88/25.60  | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 170.88/25.60  | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | |   (2580)  all_56_3 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (2562), (2580) are inconsistent by
% 170.88/25.60  | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 170.88/25.60  | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.60  | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | |   (2581)   ~ (all_56_3 = e3)
% 170.88/25.60  | | | | | | | | | | | | | | | | | |   (2582)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 170.88/25.60  | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 170.88/25.60  | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.60  | | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | | |   (2583)  all_56_14 = e3
% 170.88/25.60  | | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (341), (2566), (2583) are inconsistent by
% 170.88/25.60  | | | | | | | | | | | | | | | | | | |            sub-proof #896.
% 170.88/25.60  | | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.60  | | | | | | | | | | | | | | | | | | | 
% 170.88/25.60  | | | | | | | | | | | | | | | | | | |   (2584)   ~ (all_56_14 = e3)
% 170.88/25.60  | | | | | | | | | | | | | | | | | | |   (2585)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 170.88/25.60  | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |   (2586)  all_56_9 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (154), (155), (156), (163), (164), (170),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (273), (281), (282),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (283), (305), (306), (307), (311), (315), (324),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (326), (331), (359), (364), (370), (373), (386),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (391), (392), (403), (413), (419), (531), (532),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (533), (535), (536), (537), (538), (540), (542),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (544), (546), (550), (552), (560), (566), (567),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (568), (569), (579), (583), (584), (585), (586),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (587), (591), (593), (595), (596), (597), (2553),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (2554), (2555), (2556), (2562), (2566), (2569),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            (2582), (2586), (function-axioms) are inconsistent
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |            by sub-proof #521.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |   (2587)   ~ (all_56_9 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (2587) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | |   (2588)   ~ (all_52_19 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |   (2589)  all_58_6 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (164), (172), (177), (178), (179), (273),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            (283), (307), (311), (315), (324), (326), (331),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (403), (531),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            (532), (533), (535), (536), (537), (538), (540),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (550), (552), (560), (566),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            (568), (569), (583), (584), (585), (586), (587),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (2553), (2554),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            (2555), (2556), (2566), (2589), (function-axioms)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #850.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | |   (2590)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2590) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | |   (2591)  all_58_7 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (2591) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | |   (2592)  all_52_19 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2588), (2592) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | |   (2593)  $false
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2593) is inconsistent.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | |   (2594)  all_58_8 = e3 | all_58_11 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2594) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | |   (2595)  all_58_8 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (2595) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | |   (2596)  all_14_2 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (2596) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | |   (2597)   ~ (all_52_5 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (2596) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | |   (2598)   ~ (all_52_13 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (560), (2596) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | |   (2599)   ~ (all_52_17 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (2596) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | |   (2600)  op(e1, e3) = all_14_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1999) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2601)   ~ (all_14_2 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (537), (2564), (2594), (2601) are
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #997.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2602)   ~ (all_14_1 = e0)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |              all_14_1, e3, e1, simplifying with (164), (2600)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2603)  all_52_17 = all_14_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (2603) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2604)  all_56_8 = all_14_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (2603) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2605)  all_58_6 = all_14_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (2603) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2606)   ~ (all_52_9 = all_14_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (2603) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2607)   ~ (all_52_19 = all_14_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2607) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2608)   ~ (all_52_19 = all_14_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (2603) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2609)   ~ (all_52_23 = all_14_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2609) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2610)   ~ (all_52_23 = all_14_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2573), (2603) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2611)   ~ (all_14_1 = all_6_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2599), (2603) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | |   (2612)   ~ (all_14_1 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (2613)  all_56_8 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2604), (2612), (2613) are inconsistent by
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #849.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (2614)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2615)  all_58_2 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (2615) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2616)  all_52_9 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2616) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2617)  all_52_9 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (172), (178), (179), (283), (307),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            (323), (326), (331), (370), (391), (403), (531),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            (532), (535), (536), (540), (542), (546), (552),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            (569), (586), (595), (596), (597), (2553), (2554),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2556), (2597), (2617), (function-axioms) are
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #312.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2618)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2618) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2619)  all_58_3 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (2619) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2620)  all_10_2 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (507), (2620) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2621)  all_24_2 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (2620) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2622)   ~ (all_52_3 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2512), (2620) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2623)  op(all_10_1, e3) = e1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (2620) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2624)  op(e2, e3) = all_10_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2620) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2625)  op(e2, e2) = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2626)  all_58_0 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (2626) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2627)  all_4_2 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (2627) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2628)   ~ (all_52_9 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2509) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2629)   ~ (all_24_2 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2621), (2629) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2630)  $false
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2630) is inconsistent.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2631)   ~ (all_24_1 = e0)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (685), (2631) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2632)   ~ (all_10_1 = e0)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_1, e3, e2, simplifying with (172), (2624)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2633)  all_52_9 = all_10_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (2633) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2634)  all_56_4 = all_10_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (2633) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2635)  all_58_2 = all_10_1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (2633) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2636)   ~ (all_52_13 = all_10_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2636) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2637)   ~ (all_52_13 = all_10_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (2633) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2638)   ~ (all_52_15 = all_10_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2638) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2639)   ~ (all_52_15 = all_10_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2606), (2633) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2640)   ~ (all_14_1 = all_10_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2640) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2641)   ~ (all_14_1 = all_10_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2572), (2633) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2642)   ~ (all_10_1 = all_6_1)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2643)  all_58_0 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2626), (2643) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2644)  e3 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2644) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2645)  $false
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2645) is inconsistent.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2646)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2646) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2647)  all_58_2 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2635), (2647) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2648)  all_10_1 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2648) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2649)  all_10_1 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2632), (2649) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2650)  $false
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2650) is inconsistent.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2651)  all_58_6 = e0 | all_58_12 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2651) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2652)  all_58_6 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2605), (2652) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2653)  all_14_1 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2653) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2654)  all_14_1 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2602), (2654) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2655)  $false
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2655) is inconsistent.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2656)  all_58_12 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2571), (2656) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2657)  all_6_1 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2657) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2658)  all_6_1 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2577), (2658) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2659)   ~ (all_52_29 = e0)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2567), (2658) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2660)  op(e0, e3) = all_6_0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2568), (2658) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2661)  op(e0, e3) = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (2660), (2661) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2662)  all_6_0 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2516), (2662) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2663)   ~ (e3 = e0)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2664)  all_56_4 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2634), (2664) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2665)  all_10_1 = e3
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (802), (2665) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2666)  $false
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2666) is inconsistent.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2667)   ~ (all_56_4 = e3)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2668)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2669)  all_58_0 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2626), (2669) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2670)  e3 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2670) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2671)  $false
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2671) is inconsistent.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2672)   ~ (all_58_0 = e2)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2673)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2674)  all_58_4 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (2674) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2675)  all_52_5 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2555), (2675) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2676)  op(e1, e0) = e1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_23,
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (161), (2676) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2677)  all_52_23 = e1
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2678)  all_58_6 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2605), (2678) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2679)  all_14_1 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2679) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2680)  all_14_1 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2641), (2680) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2681)   ~ (all_10_1 = e2)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2681) implies:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2682)   ~ (all_10_1 = e2)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2600), (2680) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2683)  op(e1, e3) = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2623), (2632), (2634), (2668), (2682), (2683),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #437.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2684)   ~ (all_58_6 = e2)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2685)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2605), (2684) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2686)   ~ (all_14_1 = e2)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (154), (155), (161), (163),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (282), (302), (303), (305), (314),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (317), (321), (322), (325), (326), (327), (329),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (341), (344), (364), (386), (391), (392), (533),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (540), (566), (567), (568),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (569), (578), (580), (581), (585), (586), (596),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (797), (2554), (2555), (2556), (2561), (2562),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2564), (2565), (2566), (2567), (2571), (2575),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2577), (2579), (2582), (2585), (2595), (2604),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2605), (2608), (2610), (2611), (2614), (2622),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2624), (2625), (2626), (2635), (2637), (2639),
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2673), (2685), (2686), (function-axioms) are
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #832.
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2687)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2687) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2688)  all_58_5 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (2688) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2689)  all_52_13 = e0
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2637), (2689) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2690)   ~ (all_10_1 = e0)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (2689) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2691)  op(e1, e0) = all_52_12
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_23,
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_12, e0, e1, simplifying with (161), (2691)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2692)  all_52_12 = all_52_23
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2693)  all_58_2 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2635), (2693) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2694)  all_10_1 = e2
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2641), (2694) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2695)   ~ (all_14_1 = e2)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (802), (2694) imply:
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2696)   ~ (e3 = e2)
% 170.88/25.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (51), (52), (154), (155),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (169), (170), (172), (282), (302),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (303), (305), (310), (314), (317), (321), (322),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (323), (325), (326), (327), (328), (329), (341),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (344), (364), (385), (386), (391), (392), (533),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (539), (540), (556), (557),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (573), (578),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (580), (581), (585), (586), (596), (797), (2554),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2555), (2556), (2561), (2562), (2564), (2565),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2566), (2567), (2571), (2575), (2577), (2579),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2582), (2585), (2588), (2595), (2604), (2605),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2608), (2610), (2611), (2614), (2622), (2626),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2695), (function-axioms) are inconsistent by
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #830.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2697)   ~ (all_58_2 = e2)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2635), (2697) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2698)   ~ (all_10_1 = e2)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2699)  all_58_2 = e1
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2635), (2699) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2700)  all_10_1 = e1
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2641), (2700) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2701)   ~ (all_14_1 = e1)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2698), (2700) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2702)   ~ (e2 = e1)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2623), (2700) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2703)  op(e1, e3) = e1
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2614) gives:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2704)  all_56_8 = e2
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2604), (2704) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2705)  all_14_1 = e2
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2705) implies:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2706)  all_14_1 = e2
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2600), (2706) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2707)  op(e1, e3) = e2
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2703), (2707), (function-axioms) are
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #438.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2708)   ~ (all_56_8 = e2)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2604), (2708) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2709)   ~ (all_14_1 = e2)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (51), (52), (154), (155),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (169), (170), (172), (282), (302),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (303), (305), (310), (314), (317), (321), (322),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (323), (325), (326), (327), (328), (329), (341),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (344), (364), (385), (386), (391), (392), (533),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (539), (540), (556), (557),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (573), (578),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (580), (581), (585), (586), (596), (797), (2554),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2555), (2556), (2561), (2562), (2564), (2565),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2566), (2567), (2571), (2575), (2577), (2579),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2582), (2585), (2588), (2595), (2604), (2605),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2608), (2610), (2611), (2614), (2622), (2626),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2709), (function-axioms) are inconsistent by
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #830.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2710)   ~ (all_58_2 = e1)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2635), (2710) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2711)   ~ (all_10_1 = e1)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2632), (2634), (2668), (2698), (2711) are
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #541.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2712)  all_58_8 = e0 | all_58_14 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2713)  all_58_8 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2595), (2713) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2714)  e3 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2714) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2715)  $false
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2715) is inconsistent.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2716)  all_58_14 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (2659), (2716) are inconsistent by
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #696.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2717)   ~ (all_58_0 = e3)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (2717) imply:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2718)   ~ (all_4_2 = e3)
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (178), (179), (283), (307), (326), (331),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (370), (391), (403), (531), (532), (535), (536),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (540), (546), (552), (569), (586), (595), (596),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (597), (2553), (2556), (2597), (2622), (2718),
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1012.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2719)  all_58_5 = e3 | all_58_10 = e3
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (373), (2563), (2598), (2719) are
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | |   (2720)  all_58_11 = e3
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (2564), (2720) are inconsistent by
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1017.
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | |   (2721)   ~ (all_56_15 = e3)
% 170.88/25.62  | | | | | | | | | | | | | | | |   (2722)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (158),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (169), (170),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (269), (270),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (283), (304), (305), (307), (310), (311), (312),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (2543), (2544),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (2553), (2554), (2555), (2556), (2721), (2722),
% 170.88/25.62  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.62  | | | | | | | | | | | | | | | |            #785.
% 170.88/25.62  | | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | |   (2723)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.88/25.62  | | | | | | | | | | | | | | |           all_52_14 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | ALPHA: (2723) implies:
% 170.88/25.62  | | | | | | | | | | | | | | |   (2724)  all_52_10 = e2
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | COMBINE_EQS: (661), (2724) imply:
% 170.88/25.62  | | | | | | | | | | | | | | |   (2725)  all_10_1 = e2
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (2512), (2725), (function-axioms) are
% 170.88/25.62  | | | | | | | | | | | | | | |            inconsistent by sub-proof #446.
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | |   (2726)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.62  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.62  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | BETA: splitting (2726) gives:
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | Case 1:
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | |   (2727)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.62  | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (2000), (2727),
% 170.88/25.62  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.62  | | | | | | | | | | | | | | |            #314.
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | |   (2728)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.62  | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 170.88/25.62  | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 170.88/25.62  | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 170.88/25.62  | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 170.88/25.62  | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 170.88/25.62  | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 170.88/25.62  | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 170.88/25.62  | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 170.88/25.62  | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 170.88/25.62  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.88/25.62  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.88/25.62  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.88/25.62  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.88/25.62  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 170.88/25.62  | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 170.88/25.62  | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 170.88/25.62  | | | | | | | | | | | | | | |            (649), (797), (799), (2514), (2516), (2518),
% 170.88/25.62  | | | | | | | | | | | | | | |            (2542), (2543), (2544), (2728), (function-axioms)
% 170.88/25.62  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #634.
% 170.88/25.62  | | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | |   (2729)  all_40_1 = e1
% 170.88/25.62  | | | | | | | | | | | |   (2730)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | COMBINE_EQS: (715), (2729) imply:
% 170.88/25.62  | | | | | | | | | | | |   (2731)  all_4_1 = e1
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | COMBINE_EQS: (720), (2731) imply:
% 170.88/25.62  | | | | | | | | | | | |   (2732)  all_52_0 = e1
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | REDUCE: (796), (2731) imply:
% 170.88/25.62  | | | | | | | | | | | |   (2733)   ~ (e2 = e1)
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | REDUCE: (38), (2731) imply:
% 170.88/25.62  | | | | | | | | | | | |   (2734)  op(e1, all_4_2) = all_4_0
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | REDUCE: (37), (2731) imply:
% 170.88/25.62  | | | | | | | | | | | |   (2735)  op(e3, all_4_2) = e1
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.88/25.62  | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | Case 1:
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | |   (2736)  all_58_15 = e0
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | COMBINE_EQS: (532), (2736) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2737)  all_6_2 = e0
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (597), (2737) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2738)   ~ (all_52_7 = e0)
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (564), (2737) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2739)   ~ (all_52_25 = e0)
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (594), (2737) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2740)   ~ (all_52_29 = e0)
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (43), (2737) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2741)  op(all_6_1, e0) = all_6_0
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (42), (2737) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2742)  op(e0, e0) = all_6_1
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (41), (2737) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2743)  op(e0, e0) = e0
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 170.88/25.62  | | | | | | | | | | | | |              e0, e0, simplifying with (2742), (2743) gives:
% 170.88/25.62  | | | | | | | | | | | | |   (2744)  all_6_1 = e0
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (2741), (2744) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2745)  op(e0, e0) = all_6_0
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.88/25.62  | | | | | | | | | | | | |              e0, e0, simplifying with (2743), (2745) gives:
% 170.88/25.62  | | | | | | | | | | | | |   (2746)  all_6_0 = e0
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (2516), (2746) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2747)   ~ (e3 = e0)
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | REDUCE: (797), (2746) imply:
% 170.88/25.62  | | | | | | | | | | | | |   (2748)   ~ (e1 = e0)
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | Case 1:
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | |   (2749)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.62  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.62  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (52), (661), (2512), (2732), (2749),
% 170.88/25.62  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.62  | | | | | | | | | | | | | |            #445.
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | |   (2750)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.62  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.62  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (62), (161), (163),
% 170.88/25.62  | | | | | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 170.88/25.62  | | | | | | | | | | | | | |            (179), (181), (182), (269), (270), (271), (274),
% 170.88/25.62  | | | | | | | | | | | | | |            (280), (283), (302), (303), (304), (306), (310),
% 170.88/25.62  | | | | | | | | | | | | | |            (313), (325), (341), (344), (349), (364), (373),
% 170.88/25.62  | | | | | | | | | | | | | |            (386), (391), (403), (419), (429), (518), (531),
% 170.88/25.62  | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (542),
% 170.88/25.62  | | | | | | | | | | | | | |            (546), (548), (550), (553), (554), (558), (560),
% 170.88/25.62  | | | | | | | | | | | | | |            (562), (563), (566), (567), (569), (581), (586),
% 170.88/25.62  | | | | | | | | | | | | | |            (591), (719), (770), (2000), (2514), (2730),
% 170.88/25.62  | | | | | | | | | | | | | |            (2734), (2735), (2736), (2738), (2739), (2740),
% 170.88/25.62  | | | | | | | | | | | | | |            (2750), (function-axioms) are inconsistent by
% 170.88/25.62  | | | | | | | | | | | | | |            sub-proof #292.
% 170.88/25.62  | | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | End of split
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | Case 2:
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | |   (2751)   ~ (all_58_15 = e0)
% 170.88/25.62  | | | | | | | | | | | | |   (2752)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.88/25.62  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.88/25.62  | | | | | | | | | | | | |             e0)
% 170.88/25.62  | | | | | | | | | | | | | 
% 170.88/25.62  | | | | | | | | | | | | | ALPHA: (2752) implies:
% 170.88/25.62  | | | | | | | | | | | | |   (2753)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.88/25.63  | | | | | | | | | | | | |   (2754)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | REDUCE: (532), (2751) imply:
% 170.88/25.63  | | | | | | | | | | | | |   (2755)   ~ (all_6_2 = e0)
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | |   (2756)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.63  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.63  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.63  | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (52), (661), (2512), (2732), (2756),
% 170.88/25.63  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.63  | | | | | | | | | | | | | |            #445.
% 170.88/25.63  | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | |   (2757)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.63  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.63  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.63  | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | BETA: splitting (2757) gives:
% 170.88/25.63  | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | |   (2758)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.63  | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | | ALPHA: (2758) implies:
% 170.88/25.63  | | | | | | | | | | | | | | |   (2759)  all_52_20 = e1
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (2759) imply:
% 170.88/25.63  | | | | | | | | | | | | | | |   (2760)  all_14_1 = e1
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (2000), (2760), (function-axioms) are
% 170.88/25.63  | | | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | |   (2761)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.63  | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (38), (42),
% 170.88/25.63  | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 170.88/25.63  | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 170.88/25.63  | | | | | | | | | | | | | | |            (268), (270), (271), (283), (304), (305), (307),
% 170.88/25.63  | | | | | | | | | | | | | | |            (311), (313), (319), (321), (323), (324), (325),
% 170.88/25.63  | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (344), (349),
% 170.88/25.63  | | | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (429),
% 170.88/25.63  | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 170.88/25.63  | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 170.88/25.63  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 170.88/25.63  | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (567),
% 170.88/25.63  | | | | | | | | | | | | | | |            (568), (569), (571), (573), (577), (580), (581),
% 170.88/25.63  | | | | | | | | | | | | | | |            (582), (583), (585), (586), (588), (589), (594),
% 170.88/25.63  | | | | | | | | | | | | | | |            (597), (649), (2514), (2518), (2735), (2753),
% 170.88/25.63  | | | | | | | | | | | | | | |            (2754), (2755), (2761), (function-axioms) are
% 170.88/25.63  | | | | | | | | | | | | | | |            inconsistent by sub-proof #444.
% 170.88/25.63  | | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | |   (2762)  all_34_0 = e1
% 170.88/25.63  | | | | | | | | | | |   (2763)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | COMBINE_EQS: (773), (2762) imply:
% 170.88/25.63  | | | | | | | | | | |   (2764)  all_4_0 = e1
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | SIMP: (2764) implies:
% 170.88/25.63  | | | | | | | | | | |   (2765)  all_4_0 = e1
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | REDUCE: (2514), (2765) imply:
% 170.88/25.63  | | | | | | | | | | |   (2766)   ~ (e2 = e1)
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | REDUCE: (38), (2765) imply:
% 170.88/25.63  | | | | | | | | | | |   (2767)  op(all_4_1, all_4_2) = e1
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | BETA: splitting (301) gives:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2768)  all_58_15 = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | COMBINE_EQS: (532), (2768) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2769)  all_6_2 = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REDUCE: (564), (2769) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2770)   ~ (all_52_25 = e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REDUCE: (43), (2769) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2771)  op(all_6_1, e0) = all_6_0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REDUCE: (42), (2769) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2772)  op(e0, e0) = all_6_1
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REDUCE: (41), (2769) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2773)  op(e0, e0) = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 170.88/25.63  | | | | | | | | | | | |              e0, e0, simplifying with (2772), (2773) gives:
% 170.88/25.63  | | | | | | | | | | | |   (2774)  all_6_1 = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REDUCE: (2771), (2774) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2775)  op(e0, e0) = all_6_0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 170.88/25.63  | | | | | | | | | | | |              e0, e0, simplifying with (2773), (2775) gives:
% 170.88/25.63  | | | | | | | | | | | |   (2776)  all_6_0 = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REDUCE: (2516), (2776) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2777)   ~ (e3 = e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | |   (2778)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.63  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.63  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (2512),
% 170.88/25.63  | | | | | | | | | | | | |            (2767), (2778), (function-axioms) are inconsistent
% 170.88/25.63  | | | | | | | | | | | | |            by sub-proof #441.
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | |   (2779)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.63  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.63  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (37), (62), (161), (163),
% 170.88/25.63  | | | | | | | | | | | | |            (164), (165), (172), (173), (177), (179), (181),
% 170.88/25.63  | | | | | | | | | | | | |            (270), (271), (280), (282), (283), (304), (328),
% 170.88/25.63  | | | | | | | | | | | | |            (330), (344), (349), (386), (392), (403), (429),
% 170.88/25.63  | | | | | | | | | | | | |            (494), (531), (533), (534), (544), (546), (548),
% 170.88/25.63  | | | | | | | | | | | | |            (552), (554), (562), (566), (596), (663), (719),
% 170.88/25.63  | | | | | | | | | | | | |            (796), (2000), (2763), (2767), (2768), (2770),
% 170.88/25.63  | | | | | | | | | | | | |            (2779), (function-axioms) are inconsistent by
% 170.88/25.63  | | | | | | | | | | | | |            sub-proof #291.
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2780)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.88/25.63  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.88/25.63  | | | | | | | | | | | |             e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | ALPHA: (2780) implies:
% 170.88/25.63  | | | | | | | | | | | |   (2781)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | |   (2782)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.63  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.63  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (2512),
% 170.88/25.63  | | | | | | | | | | | | |            (2767), (2782), (function-axioms) are inconsistent
% 170.88/25.63  | | | | | | | | | | | | |            by sub-proof #441.
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | |   (2783)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.63  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.63  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (42), (43), (61), (62),
% 170.88/25.63  | | | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 170.88/25.63  | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 170.88/25.63  | | | | | | | | | | | | |            (268), (270), (280), (281), (282), (283), (303),
% 170.88/25.63  | | | | | | | | | | | | |            (304), (306), (307), (322), (324), (325), (326),
% 170.88/25.63  | | | | | | | | | | | | |            (328), (330), (344), (349), (364), (370), (385),
% 170.88/25.63  | | | | | | | | | | | | |            (386), (391), (392), (403), (413), (494), (529),
% 170.88/25.63  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (538),
% 170.88/25.63  | | | | | | | | | | | | |            (539), (540), (544), (546), (548), (552), (554),
% 170.88/25.63  | | | | | | | | | | | | |            (555), (557), (558), (559), (562), (565), (566),
% 170.88/25.63  | | | | | | | | | | | | |            (567), (568), (569), (578), (580), (581), (586),
% 170.88/25.63  | | | | | | | | | | | | |            (591), (595), (596), (597), (649), (663), (719),
% 170.88/25.63  | | | | | | | | | | | | |            (796), (797), (799), (2000), (2516), (2763),
% 170.88/25.63  | | | | | | | | | | | | |            (2767), (2781), (2783), (function-axioms) are
% 170.88/25.63  | | | | | | | | | | | | |            inconsistent by sub-proof #290.
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | |   (2784)  all_28_0 = e3
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | COMBINE_EQS: (776), (2784) imply:
% 170.88/25.63  | | | | | | | | | |   (2785)  all_6_0 = e3
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | SIMP: (2785) implies:
% 170.88/25.63  | | | | | | | | | |   (2786)  all_6_0 = e3
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | REDUCE: (43), (2786) imply:
% 170.88/25.63  | | | | | | | | | |   (2787)  op(all_6_1, all_6_2) = e3
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | BETA: splitting (113) gives:
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | |   (2788)   ~ (all_34_0 = e1)
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | REDUCE: (773), (2788) imply:
% 170.88/25.63  | | | | | | | | | | |   (2789)   ~ (all_4_0 = e1)
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | BETA: splitting (301) gives:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2790)  all_58_15 = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (2787), (2790),
% 170.88/25.63  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.63  | | | | | | | | | | | |            #510.
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2791)   ~ (all_58_15 = e0)
% 170.88/25.63  | | | | | | | | | | | |   (2792)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.88/25.63  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.88/25.63  | | | | | | | | | | | |             e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | ALPHA: (2792) implies:
% 170.88/25.63  | | | | | | | | | | | |   (2793)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REDUCE: (532), (2791) imply:
% 170.88/25.63  | | | | | | | | | | | |   (2794)   ~ (all_6_2 = e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | |   (2795)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.63  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.63  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (37), (38), (42), (52), (61),
% 170.88/25.63  | | | | | | | | | | | | |            (154), (156), (158), (159), (160), (161), (163),
% 170.88/25.63  | | | | | | | | | | | | |            (164), (165), (168), (169), (170), (172), (173),
% 170.88/25.63  | | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 170.88/25.63  | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 170.88/25.63  | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (307), (310),
% 170.88/25.63  | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (317), (319),
% 170.88/25.63  | | | | | | | | | | | | |            (323), (324), (326), (327), (328), (330), (331),
% 170.88/25.63  | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 170.88/25.63  | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (413),
% 170.88/25.63  | | | | | | | | | | | | |            (425), (429), (529), (531), (532), (533), (534),
% 170.88/25.63  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 170.88/25.63  | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 170.88/25.63  | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 170.88/25.63  | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 170.88/25.63  | | | | | | | | | | | | |            (575), (578), (579), (580), (581), (582), (583),
% 170.88/25.63  | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (589), (591),
% 170.88/25.63  | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 170.88/25.63  | | | | | | | | | | | | |            (600), (661), (720), (2512), (2514), (2787),
% 170.88/25.63  | | | | | | | | | | | | |            (2789), (2793), (2794), (2795), (function-axioms)
% 170.88/25.63  | | | | | | | | | | | | |            are inconsistent by sub-proof #435.
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | |   (2796)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.63  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.63  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (2000),
% 170.88/25.63  | | | | | | | | | | | | |            (2787), (2796), (function-axioms) are inconsistent
% 170.88/25.63  | | | | | | | | | | | | |            by sub-proof #300.
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | |   (2797)  all_34_0 = e1
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | COMBINE_EQS: (773), (2797) imply:
% 170.88/25.63  | | | | | | | | | | |   (2798)  all_4_0 = e1
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | SIMP: (2798) implies:
% 170.88/25.63  | | | | | | | | | | |   (2799)  all_4_0 = e1
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | REDUCE: (2514), (2799) imply:
% 170.88/25.63  | | | | | | | | | | |   (2800)   ~ (e2 = e1)
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | REDUCE: (38), (2799) imply:
% 170.88/25.63  | | | | | | | | | | |   (2801)  op(all_4_1, all_4_2) = e1
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2802)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.63  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.63  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (2512),
% 170.88/25.63  | | | | | | | | | | | |            (2801), (2802), (function-axioms) are inconsistent
% 170.88/25.63  | | | | | | | | | | | |            by sub-proof #441.
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2803)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.63  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.63  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (2000),
% 170.88/25.63  | | | | | | | | | | | |            (2787), (2803), (function-axioms) are inconsistent
% 170.88/25.63  | | | | | | | | | | | |            by sub-proof #300.
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | End of split
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | |   (2804)  all_26_0 = e2
% 170.88/25.63  | | | | | | | | |   (2805)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | COMBINE_EQS: (779), (2804) imply:
% 170.88/25.63  | | | | | | | | |   (2806)  all_4_0 = e2
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | SIMP: (2806) implies:
% 170.88/25.63  | | | | | | | | |   (2807)  all_4_0 = e2
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | COMBINE_EQS: (742), (2807) imply:
% 170.88/25.63  | | | | | | | | |   (2808)  all_50_0 = e2
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | REDUCE: (38), (2807) imply:
% 170.88/25.63  | | | | | | | | |   (2809)  op(all_4_1, all_4_2) = e2
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | BETA: splitting (98) gives:
% 170.88/25.63  | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | |   (2810)   ~ (all_28_0 = e3)
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | REDUCE: (776), (2810) imply:
% 170.88/25.63  | | | | | | | | | |   (2811)   ~ (all_6_0 = e3)
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | BETA: splitting (151) gives:
% 170.88/25.63  | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | |   (2812)   ~ (all_50_0 = e2)
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | REDUCE: (2808), (2812) imply:
% 170.88/25.63  | | | | | | | | | | |   (2813)  $false
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | CLOSE: (2813) is inconsistent.
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | |   (2814)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.63  | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2815)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.63  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.63  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (2512),
% 170.88/25.63  | | | | | | | | | | | |            (2809), (2815), (function-axioms) are inconsistent
% 170.88/25.63  | | | | | | | | | | | |            by sub-proof #434.
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | Case 2:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | |   (2816)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.63  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.63  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | BETA: splitting (2816) gives:
% 170.88/25.63  | | | | | | | | | | | | 
% 170.88/25.63  | | | | | | | | | | | | Case 1:
% 170.88/25.63  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | |   (2817)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.64  | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | ALPHA: (2817) implies:
% 170.88/25.64  | | | | | | | | | | | | |   (2818)  all_52_20 = e1
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | COMBINE_EQS: (719), (2818) imply:
% 170.88/25.64  | | | | | | | | | | | | |   (2819)  all_14_1 = e1
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (2000), (2819), (function-axioms) are
% 170.88/25.64  | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | Case 2:
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | |   (2820)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.64  | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | ALPHA: (2820) implies:
% 170.88/25.64  | | | | | | | | | | | | |   (2821)  all_52_30 = e0
% 170.88/25.64  | | | | | | | | | | | | |   (2822)  all_52_28 = e1
% 170.88/25.64  | | | | | | | | | | | | |   (2823)  all_52_26 = e2
% 170.88/25.64  | | | | | | | | | | | | |   (2824)  all_52_24 = e3
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | COMBINE_EQS: (649), (2821) imply:
% 170.88/25.64  | | | | | | | | | | | | |   (2825)  all_6_1 = e0
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | SIMP: (2825) implies:
% 170.88/25.64  | | | | | | | | | | | | |   (2826)  all_6_1 = e0
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (51), (154),
% 170.88/25.64  | | | | | | | | | | | | |            (155), (156), (164), (165), (172), (173), (177),
% 170.88/25.64  | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 170.88/25.64  | | | | | | | | | | | | |            (271), (280), (283), (301), (303), (304), (305),
% 170.88/25.64  | | | | | | | | | | | | |            (306), (307), (313), (322), (323), (324), (325),
% 170.88/25.64  | | | | | | | | | | | | |            (326), (328), (330), (344), (349), (364), (370),
% 170.88/25.64  | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (429), (503),
% 170.88/25.64  | | | | | | | | | | | | |            (521), (529), (531), (532), (533), (534), (535),
% 170.88/25.64  | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.88/25.64  | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.88/25.64  | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 170.88/25.64  | | | | | | | | | | | | |            (564), (569), (573), (580), (581), (586), (588),
% 170.88/25.64  | | | | | | | | | | | | |            (589), (594), (597), (698), (718), (796), (797),
% 170.88/25.64  | | | | | | | | | | | | |            (799), (2805), (2809), (2811), (2814), (2822),
% 170.88/25.64  | | | | | | | | | | | | |            (2823), (2824), (2826), (function-axioms) are
% 170.88/25.64  | | | | | | | | | | | | |            inconsistent by sub-proof #293.
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | Case 2:
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | |   (2827)  all_28_0 = e3
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | COMBINE_EQS: (776), (2827) imply:
% 170.88/25.64  | | | | | | | | | |   (2828)  all_6_0 = e3
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | SIMP: (2828) implies:
% 170.88/25.64  | | | | | | | | | |   (2829)  all_6_0 = e3
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | REDUCE: (43), (2829) imply:
% 170.88/25.64  | | | | | | | | | |   (2830)  op(all_6_1, all_6_2) = e3
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | |   (2831)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.64  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.64  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (2512),
% 170.88/25.64  | | | | | | | | | | |            (2809), (2831), (function-axioms) are inconsistent
% 170.88/25.64  | | | | | | | | | | |            by sub-proof #434.
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | Case 2:
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | |   (2832)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.64  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.64  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | BETA: splitting (2832) gives:
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | |   (2833)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.64  | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (2000), (2833),
% 170.88/25.64  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.64  | | | | | | | | | | | |            #314.
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | Case 2:
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | |   (2834)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.64  | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (2830), (2834),
% 170.88/25.64  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.64  | | | | | | | | | | | |            #501.
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | | 
% 170.88/25.64  | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | 
% 170.88/25.64  | | | | | | | End of split
% 170.88/25.64  | | | | | | | 
% 170.88/25.64  | | | | | | End of split
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | Case 2:
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | |   (2835)  all_12_1 = e3
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | | COMBINE_EQS: (705), (2835) imply:
% 170.88/25.64  | | | | | |   (2836)  all_10_1 = e3
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | | SIMP: (2836) implies:
% 170.88/25.64  | | | | | |   (2837)  all_10_1 = e3
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | | COMBINE_EQS: (661), (2837) imply:
% 170.88/25.64  | | | | | |   (2838)  all_52_10 = e3
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | | REDUCE: (52), (2837) imply:
% 170.88/25.64  | | | | | |   (2839)  op(e2, all_10_2) = e3
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | | BETA: splitting (64) gives:
% 170.88/25.64  | | | | | | 
% 170.88/25.64  | | | | | | Case 1:
% 170.88/25.64  | | | | | | | 
% 170.88/25.64  | | | | | | |   (2840)   ~ (all_14_0 = e2)
% 170.88/25.64  | | | | | | | 
% 170.88/25.64  | | | | | | | BETA: splitting (74) gives:
% 170.88/25.64  | | | | | | | 
% 170.88/25.64  | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | 
% 170.88/25.64  | | | | | | | |   (2841)   ~ (all_18_0 = e3)
% 170.88/25.64  | | | | | | | | 
% 170.88/25.64  | | | | | | | | REDUCE: (789), (2841) imply:
% 170.88/25.64  | | | | | | | |   (2842)   ~ (all_14_0 = e3)
% 170.88/25.64  | | | | | | | | 
% 170.88/25.64  | | | | | | | | BETA: splitting (83) gives:
% 170.88/25.64  | | | | | | | | 
% 170.88/25.64  | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | 
% 170.88/25.64  | | | | | | | | |   (2843)   ~ (all_22_1 = e3)
% 170.88/25.64  | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | REDUCE: (711), (2843) imply:
% 170.88/25.64  | | | | | | | | |   (2844)   ~ (all_14_1 = e3)
% 170.88/25.64  | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | BETA: splitting (93) gives:
% 170.88/25.64  | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | |   (2845)   ~ (all_26_0 = e2)
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | REDUCE: (779), (2845) imply:
% 170.88/25.64  | | | | | | | | | |   (2846)   ~ (all_4_0 = e2)
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | BETA: splitting (98) gives:
% 170.88/25.64  | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | |   (2847)   ~ (all_28_0 = e3)
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | REDUCE: (776), (2847) imply:
% 170.88/25.64  | | | | | | | | | | |   (2848)   ~ (all_6_0 = e3)
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | BETA: splitting (108) gives:
% 170.88/25.64  | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | |   (2849)   ~ (all_32_1 = e2)
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | REDUCE: (713), (2849) imply:
% 170.88/25.64  | | | | | | | | | | | |   (2850)   ~ (all_14_1 = e2)
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | BETA: splitting (113) gives:
% 170.88/25.64  | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | |   (2851)   ~ (all_34_0 = e1)
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | REDUCE: (773), (2851) imply:
% 170.88/25.64  | | | | | | | | | | | | |   (2852)   ~ (all_4_0 = e1)
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.88/25.64  | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | |   (2853)   ~ (all_40_1 = e1)
% 170.88/25.64  | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | REDUCE: (715), (2853) imply:
% 170.88/25.64  | | | | | | | | | | | | | |   (2854)   ~ (all_4_1 = e1)
% 170.88/25.64  | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.88/25.64  | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | |   (2855)  all_58_15 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | COMBINE_EQS: (532), (2855) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2856)  all_6_2 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (597), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2857)   ~ (all_52_7 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (600), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2858)   ~ (all_52_23 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (564), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2859)   ~ (all_52_25 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (582), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2860)   ~ (all_52_27 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (594), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2861)   ~ (all_52_29 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (43), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2862)  op(all_6_1, e0) = all_6_0
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (42), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2863)  op(e0, e0) = all_6_1
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (41), (2856) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2864)  op(e0, e0) = e0
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (62), (63), (154),
% 170.88/25.64  | | | | | | | | | | | | | | |            (155), (156), (158), (160), (163), (164), (165),
% 170.88/25.64  | | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 170.88/25.64  | | | | | | | | | | | | | | |            (181), (182), (183), (185), (269), (270), (271),
% 170.88/25.64  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 170.88/25.64  | | | | | | | | | | | | | | |            (281), (283), (302), (303), (304), (305), (306),
% 170.88/25.64  | | | | | | | | | | | | | | |            (307), (310), (311), (319), (322), (323), (324),
% 170.88/25.64  | | | | | | | | | | | | | | |            (325), (326), (329), (330), (331), (341), (344),
% 170.88/25.64  | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 170.88/25.64  | | | | | | | | | | | | | | |            (385), (386), (391), (403), (413), (419), (425),
% 170.88/25.64  | | | | | | | | | | | | | | |            (429), (530), (531), (532), (533), (534), (535),
% 170.88/25.64  | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.88/25.64  | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.88/25.64  | | | | | | | | | | | | | | |            (557), (558), (561), (562), (563), (565), (568),
% 170.88/25.64  | | | | | | | | | | | | | | |            (569), (571), (573), (578), (579), (580), (581),
% 170.88/25.64  | | | | | | | | | | | | | | |            (583), (584), (585), (586), (588), (591), (593),
% 170.88/25.64  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (719), (720), (796),
% 170.88/25.64  | | | | | | | | | | | | | | |            (797), (799), (2838), (2840), (2842), (2846),
% 170.88/25.64  | | | | | | | | | | | | | | |            (2848), (2852), (2854), (2855), (2857), (2858),
% 170.88/25.64  | | | | | | | | | | | | | | |            (2859), (2860), (2861), (2862), (2863), (2864),
% 170.88/25.64  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.64  | | | | | | | | | | | | | | |            #288.
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | Case 2:
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | |   (2865)   ~ (all_58_15 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | |   (2866)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.88/25.64  | | | | | | | | | | | | | | |             e0)
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | ALPHA: (2866) implies:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2867)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.88/25.64  | | | | | | | | | | | | | | |   (2868)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | REDUCE: (532), (2865) imply:
% 170.88/25.64  | | | | | | | | | | | | | | |   (2869)   ~ (all_6_2 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.64  | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | |   (2870)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.64  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.64  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | BETA: splitting (2870) gives:
% 170.88/25.64  | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2871)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.64  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | ALPHA: (2871) implies:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2872)  all_52_6 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2873)  all_52_4 = e1
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2874)  all_52_2 = e2
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2875)  all_52_0 = e3
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (2875) imply:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2876)  all_4_1 = e3
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (37), (38), (41), (42), (43), (51),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (52), (61), (62), (154), (155), (156), (158),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (159), (160), (161), (163), (164), (165), (168),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (176), (177), (178),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (179), (268), (269), (270), (271), (272), (273),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (274), (275), (276), (279), (280), (281), (282),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (306), (307),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (319), (321), (322), (323), (324), (325), (326),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (419), (425), (429), (529), (531), (532), (533),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (554), (556), (557), (558), (559), (560), (561),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (569), (573), (575), (578), (579), (580), (581),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (598), (599), (600), (797), (2846), (2850),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (2852), (2868), (2869), (2872), (2873), (2874),
% 170.88/25.64  | | | | | | | | | | | | | | | | |            (2876), (function-axioms) are inconsistent by
% 170.88/25.64  | | | | | | | | | | | | | | | | |            sub-proof #783.
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2877)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.88/25.64  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (2877) are inconsistent by sub-proof
% 170.88/25.64  | | | | | | | | | | | | | | | | |            #289.
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | End of split
% 170.88/25.64  | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | Case 2:
% 170.88/25.64  | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | |   (2878)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.64  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.64  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.64  | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | BETA: splitting (2878) gives:
% 170.88/25.64  | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2879)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.64  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | ALPHA: (2879) implies:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2880)  all_52_22 = e0
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2881)  all_52_20 = e1
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2882)  all_52_18 = e2
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2883)  all_52_16 = e3
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (2881) imply:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2884)  all_14_1 = e1
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | REDUCE: (63), (2884) imply:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2885)  op(e1, all_14_2) = all_14_0
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | REDUCE: (182), (2883) imply:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2886)  op(e3, all_52_17) = e3
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | REDUCE: (174), (2882) imply:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2887)  op(e2, all_52_19) = e2
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | REDUCE: (62), (2884) imply:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2888)  op(e1, all_14_2) = e1
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.64  | | | | | | | | | | | | | | | | | REDUCE: (158), (2880) imply:
% 170.88/25.64  | | | | | | | | | | | | | | | | |   (2889)  op(e0, all_52_23) = e0
% 170.88/25.64  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (154),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (165), (169),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (268), (269), (270), (271), (273), (274), (275),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (276), (277), (281), (282), (283), (304), (306),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (307), (308), (310), (311), (312), (313), (314),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (315), (319), (320), (321), (322), (323), (324),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (325), (326), (328), (329), (330), (331), (341),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (344), (349), (359), (364), (365), (370), (373),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (385), (391), (392), (403), (413), (415), (419),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (425), (429), (529), (531), (532), (533), (534),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (569), (571), (575), (577), (578), (579), (580),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (588), (591), (593), (595), (596), (597), (598),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (599), (600), (796), (2839), (2840), (2842),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (2846), (2852), (2854), (2867), (2868), (2869),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (2885), (2886), (2887), (2888), (2889),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.65  | | | | | | | | | | | | | | | | |            #278.
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2890)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.65  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | ALPHA: (2890) implies:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2891)  all_52_30 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2892)  all_52_28 = e1
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2893)  all_52_26 = e2
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2894)  all_52_24 = e3
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (2891) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2895)  all_6_1 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (797), (799), (2846), (2848), (2852), (2867),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (2868), (2869), (2892), (2893), (2894), (2895),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.65  | | | | | | | | | | | | | | | | |            #635.
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | End of split
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | End of split
% 170.88/25.65  | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | End of split
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | Case 2:
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | |   (2896)  all_40_1 = e1
% 170.88/25.65  | | | | | | | | | | | | | |   (2897)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | COMBINE_EQS: (715), (2896) imply:
% 170.88/25.65  | | | | | | | | | | | | | |   (2898)  all_4_1 = e1
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (38), (42),
% 170.88/25.65  | | | | | | | | | | | | | |            (43), (62), (63), (154), (155), (156), (158),
% 170.88/25.65  | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (170), (172),
% 170.88/25.65  | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 170.88/25.65  | | | | | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (272),
% 170.88/25.65  | | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (280), (281),
% 170.88/25.65  | | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 170.88/25.65  | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (319),
% 170.88/25.65  | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (325), (326),
% 170.88/25.65  | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 170.88/25.65  | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 170.88/25.65  | | | | | | | | | | | | | |            (385), (386), (391), (403), (413), (415), (419),
% 170.88/25.65  | | | | | | | | | | | | | |            (425), (429), (518), (529), (531), (532), (533),
% 170.88/25.65  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 170.88/25.65  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 170.88/25.65  | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 170.88/25.65  | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 170.88/25.65  | | | | | | | | | | | | | |            (568), (569), (571), (573), (575), (577), (578),
% 170.88/25.65  | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 170.88/25.65  | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 170.88/25.65  | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (649), (719),
% 170.88/25.65  | | | | | | | | | | | | | |            (720), (770), (796), (797), (799), (2838), (2839),
% 170.88/25.65  | | | | | | | | | | | | | |            (2840), (2842), (2846), (2848), (2852), (2897),
% 170.88/25.65  | | | | | | | | | | | | | |            (2898), (function-axioms) are inconsistent by
% 170.88/25.65  | | | | | | | | | | | | | |            sub-proof #275.
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | End of split
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | Case 2:
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | |   (2899)  all_34_0 = e1
% 170.88/25.65  | | | | | | | | | | | | |   (2900)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | COMBINE_EQS: (773), (2899) imply:
% 170.88/25.65  | | | | | | | | | | | | |   (2901)  all_4_0 = e1
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | SIMP: (2901) implies:
% 170.88/25.65  | | | | | | | | | | | | |   (2902)  all_4_0 = e1
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (36), (37), (38), (41), (42), (43),
% 170.88/25.65  | | | | | | | | | | | | |            (61), (62), (63), (154), (155), (156), (158),
% 170.88/25.65  | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (173),
% 170.88/25.65  | | | | | | | | | | | | |            (174), (177), (178), (179), (181), (182), (183),
% 170.88/25.65  | | | | | | | | | | | | |            (185), (268), (269), (270), (271), (272), (273),
% 170.88/25.65  | | | | | | | | | | | | |            (274), (275), (276), (278), (280), (281), (282),
% 170.88/25.65  | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 170.88/25.65  | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (319), (320),
% 170.88/25.65  | | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 170.88/25.65  | | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 170.88/25.65  | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 170.88/25.65  | | | | | | | | | | | | |            (391), (392), (403), (413), (419), (425), (429),
% 170.88/25.65  | | | | | | | | | | | | |            (494), (529), (530), (531), (532), (533), (534),
% 170.88/25.65  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 170.88/25.65  | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 170.88/25.65  | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 170.88/25.65  | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 170.88/25.65  | | | | | | | | | | | | |            (569), (571), (575), (578), (579), (580), (581),
% 170.88/25.65  | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (588), (591),
% 170.88/25.65  | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 170.88/25.65  | | | | | | | | | | | | |            (649), (663), (719), (720), (796), (797), (799),
% 170.88/25.65  | | | | | | | | | | | | |            (2838), (2840), (2842), (2848), (2900), (2902),
% 170.88/25.65  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.65  | | | | | | | | | | | | |            #272.
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | End of split
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | Case 2:
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | |   (2903)  all_32_1 = e2
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | COMBINE_EQS: (713), (2903) imply:
% 170.88/25.65  | | | | | | | | | | | |   (2904)  all_14_1 = e2
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | SIMP: (2904) implies:
% 170.88/25.65  | | | | | | | | | | | |   (2905)  all_14_1 = e2
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | COMBINE_EQS: (719), (2905) imply:
% 170.88/25.65  | | | | | | | | | | | |   (2906)  all_52_20 = e2
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | REDUCE: (2844), (2905) imply:
% 170.88/25.65  | | | | | | | | | | | |   (2907)   ~ (e3 = e2)
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | BETA: splitting (113) gives:
% 170.88/25.65  | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | Case 1:
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | |   (2908)   ~ (all_34_0 = e1)
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | REDUCE: (773), (2908) imply:
% 170.88/25.65  | | | | | | | | | | | | |   (2909)   ~ (all_4_0 = e1)
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.88/25.65  | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | Case 1:
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | |   (2910)   ~ (all_40_1 = e1)
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | REDUCE: (715), (2910) imply:
% 170.88/25.65  | | | | | | | | | | | | | |   (2911)   ~ (all_4_1 = e1)
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.65  | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | Case 1:
% 170.88/25.65  | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | |   (2912)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.65  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.65  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | BETA: splitting (2912) gives:
% 170.88/25.65  | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | Case 1:
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2913)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.65  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | ALPHA: (2913) implies:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2914)  all_52_6 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2915)  all_52_4 = e1
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2916)  all_52_2 = e2
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2917)  all_52_0 = e3
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (2917) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2918)  all_4_1 = e3
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | REDUCE: (38), (2918) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2919)  op(e3, all_4_2) = all_4_0
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | REDUCE: (37), (2918) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2920)  op(e3, all_4_2) = e3
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | REDUCE: (176), (2916) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2921)  op(e2, all_52_3) = e2
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | REDUCE: (168), (2915) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2922)  op(e1, all_52_5) = e1
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | REDUCE: (160), (2914) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2923)  op(e0, all_52_7) = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 170.88/25.65  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (2919), (2920)
% 170.88/25.65  | | | | | | | | | | | | | | | |              gives:
% 170.88/25.65  | | | | | | | | | | | | | | | |   (2924)  all_4_0 = e3
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.88/25.65  | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | Case 1:
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2925)  all_58_15 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (2925) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2926)  all_6_2 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (597), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2927)   ~ (all_52_7 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (600), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2928)   ~ (all_52_23 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (564), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2929)   ~ (all_52_25 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (582), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2930)   ~ (all_52_27 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (594), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2931)   ~ (all_52_29 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (43), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2932)  op(all_6_1, e0) = all_6_0
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (42), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2933)  op(e0, e0) = all_6_1
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (41), (2926) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2934)  op(e0, e0) = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (62), (63), (154),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (155), (156), (158), (160), (163), (164), (165),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (181), (182), (183), (185), (269), (270), (271),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (281), (283), (302), (303), (304), (305), (306),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (307), (310), (311), (319), (322), (323), (324),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (325), (326), (329), (330), (331), (341), (344),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (385), (386), (391), (403), (413), (419), (425),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (429), (530), (531), (532), (533), (534), (535),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (557), (558), (561), (562), (563), (565), (568),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (569), (571), (573), (578), (579), (580), (581),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (588), (591), (593),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (719), (720), (796),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (797), (799), (2838), (2840), (2842), (2846),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (2848), (2909), (2911), (2925), (2927), (2928),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (2929), (2930), (2931), (2932), (2933), (2934),
% 170.88/25.65  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.65  | | | | | | | | | | | | | | | | |            #288.
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | Case 2:
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2935)   ~ (all_58_15 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2936)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.88/25.65  | | | | | | | | | | | | | | | | |             e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | ALPHA: (2936) implies:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2937)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.65  | | | | | | | | | | | | | | | | | REDUCE: (532), (2935) imply:
% 170.88/25.65  | | | | | | | | | | | | | | | | |   (2938)   ~ (all_6_2 = e0)
% 170.88/25.65  | | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (41), (61), (154), (155),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (177), (178),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (179), (268), (269), (270), (271), (272), (273),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (276), (278), (279), (280), (281), (282), (283),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (304), (305), (306), (307), (310), (311), (312),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (425),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (429), (529), (530), (531), (532), (533), (534),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (569), (575), (578), (579), (580), (581), (582),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (599), (600), (2839), (2920), (2921), (2922),
% 170.88/25.66  | | | | | | | | | | | | | | | | |            (2923), (2937), (2938), (function-axioms) are
% 170.88/25.66  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 170.88/25.66  | | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | End of split
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | Case 2:
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2939)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.88/25.66  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (2939) are inconsistent by sub-proof
% 170.88/25.66  | | | | | | | | | | | | | | | |            #289.
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | End of split
% 170.88/25.66  | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | Case 2:
% 170.88/25.66  | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | |   (2940)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.66  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.66  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.66  | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | BETA: splitting (2940) gives:
% 170.88/25.66  | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | Case 1:
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2941)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.66  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2906), (2941) are inconsistent by sub-proof
% 170.88/25.66  | | | | | | | | | | | | | | | |            #539.
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | Case 2:
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2942)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.66  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | ALPHA: (2942) implies:
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2943)  all_52_30 = e0
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2944)  all_52_28 = e1
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2945)  all_52_26 = e2
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2946)  all_52_24 = e3
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (2943) imply:
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2947)  all_6_1 = e0
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REDUCE: (43), (2947) imply:
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2948)  op(e0, all_6_2) = all_6_0
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REDUCE: (181), (2946) imply:
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2949)  op(e3, all_52_25) = e3
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REDUCE: (173), (2945) imply:
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2950)  op(e2, all_52_27) = e2
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REDUCE: (165), (2944) imply:
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2951)  op(e1, all_52_29) = e1
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REDUCE: (42), (2947) imply:
% 170.88/25.66  | | | | | | | | | | | | | | | |   (2952)  op(e0, all_6_2) = e0
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (154), (155),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (170), (172), (177),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (178), (179), (182), (183), (268), (269), (270),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (271), (272), (275), (276), (278), (280), (281),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (403), (413), (425), (429), (529), (530), (531),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (566),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (577), (578),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (585), (586), (587),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (597), (600), (796), (797), (799), (2846), (2848),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (2909), (2911), (2948), (2949), (2950), (2951),
% 170.88/25.66  | | | | | | | | | | | | | | | |            (2952), (function-axioms) are inconsistent by
% 170.88/25.66  | | | | | | | | | | | | | | | |            sub-proof #511.
% 170.88/25.66  | | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | | End of split
% 170.88/25.66  | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | End of split
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | Case 2:
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | |   (2953)  all_40_1 = e1
% 170.88/25.66  | | | | | | | | | | | | | |   (2954)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | COMBINE_EQS: (715), (2953) imply:
% 170.88/25.66  | | | | | | | | | | | | | |   (2955)  all_4_1 = e1
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | SIMP: (2955) implies:
% 170.88/25.66  | | | | | | | | | | | | | |   (2956)  all_4_1 = e1
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (38), (42),
% 170.88/25.66  | | | | | | | | | | | | | |            (43), (62), (63), (154), (155), (156), (158),
% 170.88/25.66  | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (170), (172),
% 170.88/25.66  | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 170.88/25.66  | | | | | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (272),
% 170.88/25.66  | | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (280), (281),
% 170.88/25.66  | | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 170.88/25.66  | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (319),
% 170.88/25.66  | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (325), (326),
% 170.88/25.66  | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 170.88/25.66  | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 170.88/25.66  | | | | | | | | | | | | | |            (385), (386), (391), (403), (413), (415), (419),
% 170.88/25.66  | | | | | | | | | | | | | |            (425), (429), (518), (529), (531), (532), (533),
% 170.88/25.66  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 170.88/25.66  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 170.88/25.66  | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 170.88/25.66  | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 170.88/25.66  | | | | | | | | | | | | | |            (568), (569), (571), (573), (575), (577), (578),
% 170.88/25.66  | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 170.88/25.66  | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 170.88/25.66  | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (649), (719),
% 170.88/25.66  | | | | | | | | | | | | | |            (720), (770), (796), (797), (799), (2838), (2839),
% 170.88/25.66  | | | | | | | | | | | | | |            (2840), (2842), (2846), (2848), (2909), (2954),
% 170.88/25.66  | | | | | | | | | | | | | |            (2956), (function-axioms) are inconsistent by
% 170.88/25.66  | | | | | | | | | | | | | |            sub-proof #275.
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | End of split
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | Case 2:
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | |   (2957)  all_34_0 = e1
% 170.88/25.66  | | | | | | | | | | | | |   (2958)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | COMBINE_EQS: (773), (2957) imply:
% 170.88/25.66  | | | | | | | | | | | | |   (2959)  all_4_0 = e1
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (36), (37), (38), (41), (42), (43),
% 170.88/25.66  | | | | | | | | | | | | |            (61), (62), (63), (154), (155), (156), (158),
% 170.88/25.66  | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (173),
% 170.88/25.66  | | | | | | | | | | | | |            (174), (177), (178), (179), (181), (182), (183),
% 170.88/25.66  | | | | | | | | | | | | |            (185), (268), (269), (270), (271), (272), (273),
% 170.88/25.66  | | | | | | | | | | | | |            (274), (275), (276), (278), (280), (281), (282),
% 170.88/25.66  | | | | | | | | | | | | |            (283), (301), (302), (303), (304), (305), (306),
% 170.88/25.66  | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (319), (320),
% 170.88/25.66  | | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 170.88/25.66  | | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 170.88/25.66  | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 170.88/25.66  | | | | | | | | | | | | |            (391), (392), (403), (413), (419), (425), (429),
% 170.88/25.66  | | | | | | | | | | | | |            (494), (529), (530), (531), (532), (533), (534),
% 170.88/25.66  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 170.88/25.66  | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 170.88/25.66  | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 170.88/25.66  | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 170.88/25.66  | | | | | | | | | | | | |            (569), (571), (575), (578), (579), (580), (581),
% 170.88/25.66  | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (588), (591),
% 170.88/25.66  | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 170.88/25.66  | | | | | | | | | | | | |            (649), (663), (719), (720), (796), (797), (799),
% 170.88/25.66  | | | | | | | | | | | | |            (2838), (2840), (2842), (2848), (2958), (2959),
% 170.88/25.66  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.66  | | | | | | | | | | | | |            #272.
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | End of split
% 170.88/25.66  | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | End of split
% 170.88/25.66  | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | Case 2:
% 170.88/25.66  | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | |   (2960)  all_28_0 = e3
% 170.88/25.66  | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | COMBINE_EQS: (776), (2960) imply:
% 170.88/25.66  | | | | | | | | | | |   (2961)  all_6_0 = e3
% 170.88/25.66  | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | REDUCE: (43), (2961) imply:
% 170.88/25.66  | | | | | | | | | | |   (2962)  op(all_6_1, all_6_2) = e3
% 170.88/25.66  | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | BETA: splitting (113) gives:
% 170.88/25.66  | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | Case 1:
% 170.88/25.66  | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | |   (2963)   ~ (all_34_0 = e1)
% 170.88/25.66  | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | REDUCE: (773), (2963) imply:
% 170.88/25.66  | | | | | | | | | | | |   (2964)   ~ (all_4_0 = e1)
% 170.88/25.66  | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.88/25.66  | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | Case 1:
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | |   (2965)   ~ (all_40_1 = e1)
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | REDUCE: (715), (2965) imply:
% 170.88/25.66  | | | | | | | | | | | | |   (2966)   ~ (all_4_1 = e1)
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 170.88/25.66  | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | Case 1:
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | |   (2967)  all_58_15 = e0
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (2962), (2967),
% 170.88/25.66  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.66  | | | | | | | | | | | | | |            #510.
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | Case 2:
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | |   (2968)   ~ (all_58_15 = e0)
% 170.88/25.66  | | | | | | | | | | | | | |   (2969)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 170.88/25.66  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 170.88/25.66  | | | | | | | | | | | | | |             e0)
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | ALPHA: (2969) implies:
% 170.88/25.66  | | | | | | | | | | | | | |   (2970)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 170.88/25.66  | | | | | | | | | | | | | |   (2971)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | REDUCE: (532), (2968) imply:
% 170.88/25.66  | | | | | | | | | | | | | |   (2972)   ~ (all_6_2 = e0)
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.66  | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | Case 1:
% 170.88/25.66  | | | | | | | | | | | | | | | 
% 170.88/25.66  | | | | | | | | | | | | | | |   (2973)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.66  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.66  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.66  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (41), (61), (154), (155),
% 170.88/25.67  | | | | | | | | | | | | | | |            (156), (158), (159), (160), (161), (163), (164),
% 170.88/25.67  | | | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (172), (173),
% 170.88/25.67  | | | | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 170.88/25.67  | | | | | | | | | | | | | | |            (271), (272), (273), (276), (278), (279), (280),
% 170.88/25.67  | | | | | | | | | | | | | | |            (281), (282), (283), (304), (305), (306), (307),
% 170.88/25.67  | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 170.88/25.67  | | | | | | | | | | | | | | |            (319), (323), (324), (326), (327), (328), (330),
% 170.88/25.67  | | | | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 170.88/25.67  | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 170.88/25.67  | | | | | | | | | | | | | | |            (409), (413), (425), (429), (529), (530), (531),
% 170.88/25.67  | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 170.88/25.67  | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 170.88/25.67  | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 170.88/25.67  | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 170.88/25.67  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 170.88/25.67  | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 170.88/25.67  | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 170.88/25.67  | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (720), (796),
% 170.88/25.67  | | | | | | | | | | | | | | |            (2838), (2839), (2966), (2971), (2972), (2973),
% 170.88/25.67  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.67  | | | | | | | | | | | | | | |            #268.
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | Case 2:
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | |   (2974)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.67  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.67  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | BETA: splitting (2974) gives:
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | Case 1:
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2975)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.67  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | | ALPHA: (2975) implies:
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2976)  all_52_22 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2977)  all_52_20 = e1
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2978)  all_52_18 = e2
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2979)  all_52_16 = e3
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (2977) imply:
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2980)  all_14_1 = e1
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (62),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (63), (154), (155), (156), (158), (161), (163),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (164), (165), (169), (172), (173), (174), (177),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (269),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (277),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (281), (282), (283), (304), (306), (307), (308),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (319),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (325), (326),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (391),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (392), (403), (413), (415), (419), (425), (429),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (593), (595), (596), (597), (598), (599), (600),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (796), (2839), (2840), (2842), (2846), (2964),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (2966), (2970), (2971), (2972), (2976), (2978),
% 170.88/25.67  | | | | | | | | | | | | | | | |            (2979), (2980), (function-axioms) are inconsistent
% 170.88/25.67  | | | | | | | | | | | | | | | |            by sub-proof #267.
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | Case 2:
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2981)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.67  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | | ALPHA: (2981) implies:
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2982)  all_52_30 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (2982) imply:
% 170.88/25.67  | | | | | | | | | | | | | | | |   (2983)  all_6_1 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (2962), (2983), (function-axioms) are
% 170.88/25.67  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 170.88/25.67  | | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | End of split
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | End of split
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | End of split
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | Case 2:
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | |   (2984)  all_40_1 = e1
% 170.88/25.67  | | | | | | | | | | | | |   (2985)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | COMBINE_EQS: (715), (2984) imply:
% 170.88/25.67  | | | | | | | | | | | | |   (2986)  all_4_1 = e1
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | SIMP: (2986) implies:
% 170.88/25.67  | | | | | | | | | | | | |   (2987)  all_4_1 = e1
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | COMBINE_EQS: (720), (2987) imply:
% 170.88/25.67  | | | | | | | | | | | | |   (2988)  all_52_0 = e1
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | REDUCE: (38), (2987) imply:
% 170.88/25.67  | | | | | | | | | | | | |   (2989)  op(e1, all_4_2) = all_4_0
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | REDUCE: (37), (2987) imply:
% 170.88/25.67  | | | | | | | | | | | | |   (2990)  op(e3, all_4_2) = e1
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 170.88/25.67  | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | Case 1:
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | |   (2991)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.67  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 170.88/25.67  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | BETA: splitting (2991) gives:
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | Case 1:
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | |   (2992)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 170.88/25.67  | | | | | | | | | | | | | | |           all_52_6 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | REF_CLOSE: (8), (2988), (2992) are inconsistent by sub-proof
% 170.88/25.67  | | | | | | | | | | | | | | |            #632.
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | Case 2:
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | |   (2993)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 170.88/25.67  | | | | | | | | | | | | | | |           all_52_14 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (2993) are inconsistent by sub-proof
% 170.88/25.67  | | | | | | | | | | | | | | |            #289.
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | End of split
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | Case 2:
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | |   (2994)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 170.88/25.67  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 170.88/25.67  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | BETA: splitting (2994) gives:
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | Case 1:
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | |   (2995)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 170.88/25.67  | | | | | | | | | | | | | | |           all_52_22 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (62), (63),
% 170.88/25.67  | | | | | | | | | | | | | | |            (154), (155), (156), (158), (163), (164), (165),
% 170.88/25.67  | | | | | | | | | | | | | | |            (169), (172), (174), (177), (178), (179), (181),
% 170.88/25.67  | | | | | | | | | | | | | | |            (182), (183), (268), (269), (270), (271), (272),
% 170.88/25.67  | | | | | | | | | | | | | | |            (273), (274), (275), (276), (277), (281), (283),
% 170.88/25.67  | | | | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 170.88/25.67  | | | | | | | | | | | | | | |            (310), (311), (313), (314), (315), (319), (320),
% 170.88/25.67  | | | | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 170.88/25.67  | | | | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 170.88/25.67  | | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (391),
% 170.88/25.67  | | | | | | | | | | | | | | |            (403), (413), (415), (419), (425), (429), (518),
% 170.88/25.67  | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 170.88/25.67  | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 170.88/25.67  | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 170.88/25.67  | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 170.88/25.67  | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 170.88/25.67  | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 170.88/25.67  | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 170.88/25.67  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 170.88/25.67  | | | | | | | | | | | | | | |            (719), (770), (796), (2839), (2840), (2842),
% 170.88/25.67  | | | | | | | | | | | | | | |            (2846), (2964), (2985), (2989), (2990), (2995),
% 170.88/25.67  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 170.88/25.67  | | | | | | | | | | | | | | |            #266.
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | Case 2:
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | |   (2996)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 170.88/25.67  | | | | | | | | | | | | | | |           all_52_30 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | ALPHA: (2996) implies:
% 170.88/25.67  | | | | | | | | | | | | | | |   (2997)  all_52_30 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | COMBINE_EQS: (649), (2997) imply:
% 170.88/25.67  | | | | | | | | | | | | | | |   (2998)  all_6_1 = e0
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (2962), (2998), (function-axioms) are
% 170.88/25.67  | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 170.88/25.67  | | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | | End of split
% 170.88/25.67  | | | | | | | | | | | | | | 
% 170.88/25.67  | | | | | | | | | | | | | End of split
% 170.88/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | End of split
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | Case 2:
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | |   (2999)  all_34_0 = e1
% 171.17/25.67  | | | | | | | | | | | |   (3000)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | COMBINE_EQS: (773), (2999) imply:
% 171.17/25.67  | | | | | | | | | | | |   (3001)  all_4_0 = e1
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | SIMP: (3001) implies:
% 171.17/25.67  | | | | | | | | | | | |   (3002)  all_4_0 = e1
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | REDUCE: (38), (3002) imply:
% 171.17/25.67  | | | | | | | | | | | |   (3003)  op(all_4_1, all_4_2) = e1
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | Case 1:
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | |   (3004)  all_58_15 = e0
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (2962), (3004),
% 171.17/25.67  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.67  | | | | | | | | | | | | |            #510.
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | Case 2:
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | |   (3005)   ~ (all_58_15 = e0)
% 171.17/25.67  | | | | | | | | | | | | |   (3006)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.67  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.67  | | | | | | | | | | | | |             e0)
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | ALPHA: (3006) implies:
% 171.17/25.67  | | | | | | | | | | | | |   (3007)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | REDUCE: (532), (3005) imply:
% 171.17/25.67  | | | | | | | | | | | | |   (3008)   ~ (all_6_2 = e0)
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | Case 1:
% 171.17/25.67  | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | |   (3009)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.67  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.67  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.67  | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (37), (41), (61), (154),
% 171.17/25.67  | | | | | | | | | | | | | |            (155), (156), (158), (159), (160), (161), (163),
% 171.17/25.67  | | | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (172),
% 171.17/25.67  | | | | | | | | | | | | | |            (173), (176), (177), (178), (179), (268), (269),
% 171.17/25.67  | | | | | | | | | | | | | |            (270), (271), (272), (273), (276), (278), (279),
% 171.17/25.67  | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (305), (306),
% 171.17/25.67  | | | | | | | | | | | | | |            (307), (310), (311), (312), (313), (314), (315),
% 171.17/25.67  | | | | | | | | | | | | | |            (317), (319), (323), (324), (326), (327), (328),
% 171.17/25.67  | | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 171.17/25.67  | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 171.17/25.67  | | | | | | | | | | | | | |            (403), (409), (413), (425), (429), (529), (530),
% 171.17/25.67  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.67  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.67  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.67  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.67  | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (575), (578),
% 171.17/25.67  | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 171.17/25.67  | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 171.17/25.67  | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (720),
% 171.17/25.67  | | | | | | | | | | | | | |            (796), (2838), (2839), (3007), (3008), (3009),
% 171.17/25.67  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.67  | | | | | | | | | | | | | |            #265.
% 171.17/25.67  | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | Case 2:
% 171.17/25.67  | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | |   (3010)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.67  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.67  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.67  | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | BETA: splitting (3010) gives:
% 171.17/25.67  | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | Case 1:
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | |   (3011)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.67  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | | ALPHA: (3011) implies:
% 171.17/25.67  | | | | | | | | | | | | | | |   (3012)  all_52_22 = e0
% 171.17/25.67  | | | | | | | | | | | | | | |   (3013)  all_52_20 = e1
% 171.17/25.67  | | | | | | | | | | | | | | |   (3014)  all_52_18 = e2
% 171.17/25.67  | | | | | | | | | | | | | | |   (3015)  all_52_16 = e3
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3013) imply:
% 171.17/25.67  | | | | | | | | | | | | | | |   (3016)  all_14_1 = e1
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (37), (62), (63), (154), (156),
% 171.17/25.67  | | | | | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (172),
% 171.17/25.67  | | | | | | | | | | | | | | |            (174), (177), (178), (179), (181), (182), (183),
% 171.17/25.67  | | | | | | | | | | | | | | |            (268), (274), (275), (280), (281), (282), (283),
% 171.17/25.67  | | | | | | | | | | | | | | |            (304), (307), (310), (311), (313), (314), (319),
% 171.17/25.67  | | | | | | | | | | | | | | |            (320), (321), (322), (323), (326), (328), (329),
% 171.17/25.67  | | | | | | | | | | | | | | |            (330), (331), (349), (364), (365), (370), (373),
% 171.17/25.67  | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (413), (419),
% 171.17/25.67  | | | | | | | | | | | | | | |            (494), (529), (531), (532), (533), (534), (535),
% 171.17/25.67  | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 171.17/25.67  | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 171.17/25.67  | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 171.17/25.67  | | | | | | | | | | | | | | |            (564), (566), (567), (568), (575), (578), (579),
% 171.17/25.67  | | | | | | | | | | | | | | |            (580), (582), (583), (584), (585), (586), (591),
% 171.17/25.67  | | | | | | | | | | | | | | |            (593), (594), (596), (597), (600), (663), (796),
% 171.17/25.67  | | | | | | | | | | | | | | |            (2842), (3000), (3003), (3007), (3008), (3012),
% 171.17/25.67  | | | | | | | | | | | | | | |            (3014), (3015), (3016), (function-axioms) are
% 171.17/25.67  | | | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | Case 2:
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | |   (3017)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.67  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (2962), (3017),
% 171.17/25.67  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.67  | | | | | | | | | | | | | | |            #501.
% 171.17/25.67  | | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | | End of split
% 171.17/25.67  | | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | | End of split
% 171.17/25.67  | | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | | End of split
% 171.17/25.67  | | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | | End of split
% 171.17/25.67  | | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | End of split
% 171.17/25.67  | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | Case 2:
% 171.17/25.67  | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | |   (3018)  all_26_0 = e2
% 171.17/25.67  | | | | | | | | | |   (3019)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 171.17/25.67  | | | | | | | | | | 
% 171.17/25.67  | | | | | | | | | | COMBINE_EQS: (779), (3018) imply:
% 171.17/25.68  | | | | | | | | | |   (3020)  all_4_0 = e2
% 171.17/25.68  | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | COMBINE_EQS: (742), (3020) imply:
% 171.17/25.68  | | | | | | | | | |   (3021)  all_50_0 = e2
% 171.17/25.68  | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | REDUCE: (38), (3020) imply:
% 171.17/25.68  | | | | | | | | | |   (3022)  op(all_4_1, all_4_2) = e2
% 171.17/25.68  | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.68  | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | |   (3023)   ~ (all_28_0 = e3)
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | REDUCE: (776), (3023) imply:
% 171.17/25.68  | | | | | | | | | | |   (3024)   ~ (all_6_0 = e3)
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | |   (3025)   ~ (all_50_0 = e2)
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | REDUCE: (3021), (3025) imply:
% 171.17/25.68  | | | | | | | | | | | |   (3026)  $false
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | CLOSE: (3026) is inconsistent.
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | |   (3027)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | |   (3028)  all_58_15 = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | COMBINE_EQS: (532), (3028) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3029)  all_6_2 = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (597), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3030)   ~ (all_52_7 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (599), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3031)   ~ (all_52_15 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (600), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3032)   ~ (all_52_23 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (564), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3033)   ~ (all_52_25 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (582), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3034)   ~ (all_52_27 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (43), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3035)  op(all_6_1, e0) = all_6_0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (42), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3036)  op(e0, e0) = all_6_1
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (41), (3029) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3037)  op(e0, e0) = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.68  | | | | | | | | | | | | |              e0, e0, simplifying with (3036), (3037) gives:
% 171.17/25.68  | | | | | | | | | | | | |   (3038)  all_6_1 = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (3035), (3038) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3039)  op(e0, e0) = all_6_0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.68  | | | | | | | | | | | | |              e0, e0, simplifying with (3037), (3039) gives:
% 171.17/25.68  | | | | | | | | | | | | |   (3040)  all_6_0 = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (3024), (3040) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3041)   ~ (e3 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (799), (3040) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3042)   ~ (e2 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (797), (3040) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3043)   ~ (e1 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | |   (3044)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.68  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | BETA: splitting (3044) gives:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | |   (3045)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (3022), (3045),
% 171.17/25.68  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | | |            #494.
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | |   (3046)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3046) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | | |            #289.
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | |   (3047)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.68  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.68  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (62), (63), (156),
% 171.17/25.68  | | | | | | | | | | | | | |            (158), (164), (165), (172), (173), (174), (177),
% 171.17/25.68  | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (270), (271),
% 171.17/25.68  | | | | | | | | | | | | | |            (273), (274), (275), (276), (280), (281), (283),
% 171.17/25.68  | | | | | | | | | | | | | |            (302), (303), (304), (307), (311), (315), (319),
% 171.17/25.68  | | | | | | | | | | | | | |            (324), (325), (326), (328), (329), (330), (331),
% 171.17/25.68  | | | | | | | | | | | | | |            (344), (349), (359), (364), (365), (370), (373),
% 171.17/25.68  | | | | | | | | | | | | | |            (385), (386), (391), (403), (413), (419), (425),
% 171.17/25.68  | | | | | | | | | | | | | |            (429), (503), (521), (531), (533), (534), (535),
% 171.17/25.68  | | | | | | | | | | | | | |            (536), (537), (538), (540), (542), (544), (546),
% 171.17/25.68  | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 171.17/25.68  | | | | | | | | | | | | | |            (558), (560), (561), (562), (563), (566), (567),
% 171.17/25.68  | | | | | | | | | | | | | |            (568), (578), (579), (581), (584), (585), (586),
% 171.17/25.68  | | | | | | | | | | | | | |            (589), (591), (593), (596), (598), (698), (718),
% 171.17/25.68  | | | | | | | | | | | | | |            (719), (796), (2840), (2842), (3019), (3022),
% 171.17/25.68  | | | | | | | | | | | | | |            (3027), (3028), (3030), (3031), (3032), (3033),
% 171.17/25.68  | | | | | | | | | | | | | |            (3034), (3047), (function-axioms) are inconsistent
% 171.17/25.68  | | | | | | | | | | | | | |            by sub-proof #469.
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | |   (3048)   ~ (all_58_15 = e0)
% 171.17/25.68  | | | | | | | | | | | | |   (3049)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.68  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.68  | | | | | | | | | | | | |             e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | ALPHA: (3049) implies:
% 171.17/25.68  | | | | | | | | | | | | |   (3050)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.68  | | | | | | | | | | | | |   (3051)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REDUCE: (532), (3048) imply:
% 171.17/25.68  | | | | | | | | | | | | |   (3052)   ~ (all_6_2 = e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | |   (3053)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.68  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | BETA: splitting (3053) gives:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | |   (3054)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (3022), (3054),
% 171.17/25.68  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | | |            #494.
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | |   (3055)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3055) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | | |            #289.
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | |   (3056)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.68  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.68  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (42), (43),
% 171.17/25.68  | | | | | | | | | | | | | |            (51), (62), (63), (154), (155), (156), (158),
% 171.17/25.68  | | | | | | | | | | | | | |            (161), (163), (164), (165), (172), (173), (174),
% 171.17/25.68  | | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 171.17/25.68  | | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (280),
% 171.17/25.68  | | | | | | | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 171.17/25.68  | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 171.17/25.68  | | | | | | | | | | | | | |            (322), (323), (324), (325), (326), (328), (329),
% 171.17/25.68  | | | | | | | | | | | | | |            (330), (331), (344), (349), (359), (364), (365),
% 171.17/25.68  | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 171.17/25.68  | | | | | | | | | | | | | |            (413), (419), (425), (429), (503), (521), (529),
% 171.17/25.68  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.68  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.68  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 171.17/25.68  | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (566),
% 171.17/25.68  | | | | | | | | | | | | | |            (567), (568), (569), (573), (577), (579), (580),
% 171.17/25.68  | | | | | | | | | | | | | |            (581), (582), (584), (585), (586), (588), (589),
% 171.17/25.68  | | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 171.17/25.68  | | | | | | | | | | | | | |            (600), (649), (698), (718), (719), (796), (797),
% 171.17/25.68  | | | | | | | | | | | | | |            (799), (2840), (2842), (3019), (3022), (3024),
% 171.17/25.68  | | | | | | | | | | | | | |            (3027), (3050), (3051), (3052), (3056),
% 171.17/25.68  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | |            #448.
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | |   (3057)  all_28_0 = e3
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | COMBINE_EQS: (776), (3057) imply:
% 171.17/25.68  | | | | | | | | | | |   (3058)  all_6_0 = e3
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | SIMP: (3058) implies:
% 171.17/25.68  | | | | | | | | | | |   (3059)  all_6_0 = e3
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | REDUCE: (43), (3059) imply:
% 171.17/25.68  | | | | | | | | | | |   (3060)  op(all_6_1, all_6_2) = e3
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | |   (3061)   ~ (all_50_0 = e2)
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | REDUCE: (3021), (3061) imply:
% 171.17/25.68  | | | | | | | | | | | |   (3062)  $false
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | CLOSE: (3062) is inconsistent.
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | |   (3063)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | |   (3064)  all_58_15 = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (3060), (3064),
% 171.17/25.68  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | |            #510.
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | |   (3065)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.68  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.68  | | | | | | | | | | | | |             e0)
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | ALPHA: (3065) implies:
% 171.17/25.68  | | | | | | | | | | | | |   (3066)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | |   (3067)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.68  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | BETA: splitting (3067) gives:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | Case 1:
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | |   (3068)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (3022), (3068),
% 171.17/25.68  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | | |            #494.
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | |   (3069)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.68  | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3069) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | | |            #289.
% 171.17/25.68  | | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | |   (3070)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.68  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.68  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 171.17/25.68  | | | | | | | | | | | | | |            (156), (158), (161), (163), (164), (165), (172),
% 171.17/25.68  | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 171.17/25.68  | | | | | | | | | | | | | |            (183), (268), (270), (273), (274), (275), (276),
% 171.17/25.68  | | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (310),
% 171.17/25.68  | | | | | | | | | | | | | |            (311), (315), (319), (321), (323), (324), (325),
% 171.17/25.68  | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 171.17/25.68  | | | | | | | | | | | | | |            (359), (364), (365), (370), (385), (386), (391),
% 171.17/25.68  | | | | | | | | | | | | | |            (392), (403), (413), (419), (425), (521), (529),
% 171.17/25.68  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.68  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.68  | | | | | | | | | | | | | |            (550), (552), (553), (554), (557), (558), (559),
% 171.17/25.68  | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 171.17/25.68  | | | | | | | | | | | | | |            (568), (569), (577), (579), (580), (582), (584),
% 171.17/25.68  | | | | | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (598),
% 171.17/25.68  | | | | | | | | | | | | | |            (600), (649), (718), (719), (796), (2840), (2842),
% 171.17/25.68  | | | | | | | | | | | | | |            (3022), (3060), (3063), (3066), (3070),
% 171.17/25.68  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.68  | | | | | | | | | | | | | |            #447.
% 171.17/25.68  | | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | End of split
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.68  | | | | | | | | Case 2:
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.68  | | | | | | | | |   (3071)  all_22_1 = e3
% 171.17/25.68  | | | | | | | | |   (3072)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | COMBINE_EQS: (711), (3071) imply:
% 171.17/25.68  | | | | | | | | |   (3073)  all_14_1 = e3
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | SIMP: (3073) implies:
% 171.17/25.68  | | | | | | | | |   (3074)  all_14_1 = e3
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | COMBINE_EQS: (719), (3074) imply:
% 171.17/25.68  | | | | | | | | |   (3075)  all_52_20 = e3
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | REDUCE: (63), (3074) imply:
% 171.17/25.68  | | | | | | | | |   (3076)  op(e3, all_14_2) = all_14_0
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.68  | | | | | | | | | REDUCE: (62), (3074) imply:
% 171.17/25.68  | | | | | | | | |   (3077)  op(e1, all_14_2) = e3
% 171.17/25.68  | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 171.17/25.69  | | | | | | | | |            (41), (42), (43), (51), (52), (53), (61), (62),
% 171.17/25.69  | | | | | | | | |            (88), (93), (98), (113), (118), (128), (151),
% 171.17/25.69  | | | | | | | | |            (154), (155), (156), (158), (159), (160), (161),
% 171.17/25.69  | | | | | | | | |            (163), (164), (165), (167), (168), (169), (170),
% 171.17/25.69  | | | | | | | | |            (172), (173), (174), (176), (177), (178), (179),
% 171.17/25.69  | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 171.17/25.69  | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 171.17/25.69  | | | | | | | | |            (278), (279), (280), (281), (282), (283), (301),
% 171.17/25.69  | | | | | | | | |            (302), (303), (304), (305), (306), (307), (308),
% 171.17/25.69  | | | | | | | | |            (310), (311), (312), (313), (314), (315), (316),
% 171.17/25.69  | | | | | | | | |            (317), (319), (320), (321), (322), (323), (324),
% 171.17/25.69  | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 171.17/25.69  | | | | | | | | |            (333), (341), (344), (349), (350), (359), (364),
% 171.17/25.69  | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 171.17/25.69  | | | | | | | | |            (403), (409), (413), (415), (419), (425), (429),
% 171.17/25.69  | | | | | | | | |            (494), (503), (505), (518), (521), (529), (530),
% 171.17/25.69  | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.69  | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.69  | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.69  | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.69  | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 171.17/25.69  | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 171.17/25.69  | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 171.17/25.69  | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 171.17/25.69  | | | | | | | | |            (599), (600), (649), (661), (663), (698), (715),
% 171.17/25.69  | | | | | | | | |            (718), (720), (742), (747), (751), (756), (770),
% 171.17/25.69  | | | | | | | | |            (773), (776), (779), (796), (797), (799), (800),
% 171.17/25.69  | | | | | | | | |            (2840), (3072), (3075), (3076), (3077),
% 171.17/25.69  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.69  | | | | | | | | |            #345.
% 171.17/25.69  | | | | | | | | | 
% 171.17/25.69  | | | | | | | | End of split
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | Case 2:
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | |   (3078)  all_18_0 = e3
% 171.17/25.69  | | | | | | | |   (3079)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (37), (38), (41), (42),
% 171.17/25.69  | | | | | | | |            (43), (51), (52), (53), (61), (62), (63), (88), (93),
% 171.17/25.69  | | | | | | | |            (98), (113), (128), (151), (154), (155), (156),
% 171.17/25.69  | | | | | | | |            (158), (159), (160), (161), (163), (164), (165),
% 171.17/25.69  | | | | | | | |            (167), (168), (169), (170), (172), (173), (174),
% 171.17/25.69  | | | | | | | |            (176), (177), (178), (179), (181), (182), (183),
% 171.17/25.69  | | | | | | | |            (185), (268), (269), (270), (271), (272), (273),
% 171.17/25.69  | | | | | | | |            (274), (275), (276), (277), (278), (279), (280),
% 171.17/25.69  | | | | | | | |            (281), (282), (283), (301), (302), (303), (304),
% 171.17/25.69  | | | | | | | |            (305), (306), (307), (310), (311), (312), (313),
% 171.17/25.69  | | | | | | | |            (314), (315), (316), (317), (319), (320), (321),
% 171.17/25.69  | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 171.17/25.69  | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 171.17/25.69  | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 171.17/25.69  | | | | | | | |            (391), (392), (403), (409), (413), (415), (419),
% 171.17/25.69  | | | | | | | |            (425), (429), (494), (503), (514), (518), (521),
% 171.17/25.69  | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 171.17/25.69  | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 171.17/25.69  | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 171.17/25.69  | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 171.17/25.69  | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 171.17/25.69  | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 171.17/25.69  | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 171.17/25.69  | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 171.17/25.69  | | | | | | | |            (597), (598), (599), (600), (649), (661), (663),
% 171.17/25.69  | | | | | | | |            (698), (715), (718), (719), (720), (742), (751),
% 171.17/25.69  | | | | | | | |            (770), (773), (776), (779), (789), (796), (797),
% 171.17/25.69  | | | | | | | |            (799), (800), (2840), (3078), (3079),
% 171.17/25.69  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #316.
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | End of split
% 171.17/25.69  | | | | | | | 
% 171.17/25.69  | | | | | | Case 2:
% 171.17/25.69  | | | | | | | 
% 171.17/25.69  | | | | | | |   (3080)  all_14_0 = e2
% 171.17/25.69  | | | | | | | 
% 171.17/25.69  | | | | | | | REDUCE: (63), (3080) imply:
% 171.17/25.69  | | | | | | |   (3081)  op(all_14_1, all_14_2) = e2
% 171.17/25.69  | | | | | | | 
% 171.17/25.69  | | | | | | | BETA: splitting (93) gives:
% 171.17/25.69  | | | | | | | 
% 171.17/25.69  | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | |   (3082)   ~ (all_26_0 = e2)
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | | REDUCE: (779), (3082) imply:
% 171.17/25.69  | | | | | | | |   (3083)   ~ (all_4_0 = e2)
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.69  | | | | | | | | 
% 171.17/25.69  | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | 
% 171.17/25.69  | | | | | | | | |   (3084)   ~ (all_28_0 = e3)
% 171.17/25.69  | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | REDUCE: (776), (3084) imply:
% 171.17/25.69  | | | | | | | | |   (3085)   ~ (all_6_0 = e3)
% 171.17/25.69  | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.69  | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | |   (3086)   ~ (all_34_0 = e1)
% 171.17/25.69  | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | REDUCE: (773), (3086) imply:
% 171.17/25.69  | | | | | | | | | |   (3087)   ~ (all_4_0 = e1)
% 171.17/25.69  | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.69  | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | |   (3088)   ~ (all_40_1 = e1)
% 171.17/25.69  | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | REDUCE: (715), (3088) imply:
% 171.17/25.69  | | | | | | | | | | |   (3089)   ~ (all_4_1 = e1)
% 171.17/25.69  | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.69  | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | |   (3090)  all_58_15 = e0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | COMBINE_EQS: (532), (3090) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3091)  all_6_2 = e0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (597), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3092)   ~ (all_52_7 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (600), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3093)   ~ (all_52_23 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (564), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3094)   ~ (all_52_25 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (582), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3095)   ~ (all_52_27 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (594), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3096)   ~ (all_52_29 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (43), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3097)  op(all_6_1, e0) = all_6_0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (42), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3098)  op(e0, e0) = all_6_1
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (41), (3091) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3099)  op(e0, e0) = e0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.69  | | | | | | | | | | | |              e0, e0, simplifying with (3098), (3099) gives:
% 171.17/25.69  | | | | | | | | | | | |   (3100)  all_6_1 = e0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (3097), (3100) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3101)  op(e0, e0) = all_6_0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.69  | | | | | | | | | | | |              e0, e0, simplifying with (3099), (3101) gives:
% 171.17/25.69  | | | | | | | | | | | |   (3102)  all_6_0 = e0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (3085), (3102) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3103)   ~ (e3 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (797), (3102) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3104)   ~ (e1 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | |   (3105)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.69  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.69  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | BETA: splitting (3105) gives:
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | |   (3106)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.69  | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (38), (154), (155), (156), (160),
% 171.17/25.69  | | | | | | | | | | | | | |            (178), (179), (270), (271), (280), (283), (302),
% 171.17/25.69  | | | | | | | | | | | | | |            (303), (304), (305), (306), (307), (323), (326),
% 171.17/25.69  | | | | | | | | | | | | | |            (330), (331), (344), (349), (370), (386), (391),
% 171.17/25.69  | | | | | | | | | | | | | |            (403), (429), (531), (532), (533), (534), (535),
% 171.17/25.69  | | | | | | | | | | | | | |            (536), (540), (546), (552), (562), (569), (585),
% 171.17/25.69  | | | | | | | | | | | | | |            (586), (595), (596), (597), (720), (3090), (3092),
% 171.17/25.69  | | | | | | | | | | | | | |            (3094), (3095), (3096), (3106), (function-axioms)
% 171.17/25.69  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1008.
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | Case 2:
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | |   (3107)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.69  | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3107) are inconsistent by sub-proof
% 171.17/25.69  | | | | | | | | | | | | | |            #274.
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | End of split
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | Case 2:
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | |   (3108)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.69  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.69  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | BETA: splitting (3108) gives:
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | |   (3109)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.69  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (3081), (3109),
% 171.17/25.69  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.69  | | | | | | | | | | | | | |            #314.
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | Case 2:
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | |   (3110)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.69  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (163), (164), (165),
% 171.17/25.69  | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 171.17/25.69  | | | | | | | | | | | | | |            (182), (183), (269), (270), (271), (275), (278),
% 171.17/25.69  | | | | | | | | | | | | | |            (280), (283), (302), (304), (305), (306), (310),
% 171.17/25.69  | | | | | | | | | | | | | |            (322), (324), (329), (330), (341), (344), (349),
% 171.17/25.69  | | | | | | | | | | | | | |            (364), (365), (385), (386), (391), (403), (429),
% 171.17/25.69  | | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 171.17/25.69  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.69  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (558), (561),
% 171.17/25.69  | | | | | | | | | | | | | |            (562), (563), (569), (571), (573), (580), (581),
% 171.17/25.69  | | | | | | | | | | | | | |            (583), (585), (586), (588), (591), (593), (796),
% 171.17/25.69  | | | | | | | | | | | | | |            (3089), (3090), (3093), (3094), (3096), (3110),
% 171.17/25.69  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.69  | | | | | | | | | | | | | |            #878.
% 171.17/25.69  | | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | End of split
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | End of split
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | Case 2:
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | |   (3111)   ~ (all_58_15 = e0)
% 171.17/25.69  | | | | | | | | | | | |   (3112)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.69  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.69  | | | | | | | | | | | |             e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | ALPHA: (3112) implies:
% 171.17/25.69  | | | | | | | | | | | |   (3113)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.69  | | | | | | | | | | | |   (3114)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | REDUCE: (532), (3111) imply:
% 171.17/25.69  | | | | | | | | | | | |   (3115)   ~ (all_6_2 = e0)
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.69  | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | Case 1:
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | |   (3116)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.69  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.69  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (41), (61), (154), (155),
% 171.17/25.69  | | | | | | | | | | | | |            (156), (158), (159), (160), (161), (163), (164),
% 171.17/25.69  | | | | | | | | | | | | |            (165), (167), (168), (169), (170), (172), (173),
% 171.17/25.69  | | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 171.17/25.69  | | | | | | | | | | | | |            (271), (272), (273), (276), (278), (279), (280),
% 171.17/25.69  | | | | | | | | | | | | |            (281), (282), (283), (304), (305), (306), (307),
% 171.17/25.69  | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 171.17/25.69  | | | | | | | | | | | | |            (319), (323), (324), (326), (327), (328), (330),
% 171.17/25.69  | | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 171.17/25.69  | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 171.17/25.69  | | | | | | | | | | | | |            (409), (413), (425), (429), (529), (530), (531),
% 171.17/25.69  | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 171.17/25.69  | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 171.17/25.69  | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.69  | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 171.17/25.69  | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 171.17/25.69  | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 171.17/25.69  | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 171.17/25.69  | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (720), (796),
% 171.17/25.69  | | | | | | | | | | | | |            (2838), (2839), (3089), (3114), (3115), (3116),
% 171.17/25.69  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.69  | | | | | | | | | | | | |            #268.
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.69  | | | | | | | | | | | | Case 2:
% 171.17/25.69  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3117)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.70  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.70  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43), (62),
% 171.17/25.70  | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 171.17/25.70  | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 171.17/25.70  | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 171.17/25.70  | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 171.17/25.70  | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 171.17/25.70  | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 171.17/25.70  | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 171.17/25.70  | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 171.17/25.70  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.70  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.70  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.70  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.70  | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 171.17/25.70  | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 171.17/25.70  | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 171.17/25.70  | | | | | | | | | | | | |            (649), (719), (797), (799), (3081), (3083),
% 171.17/25.70  | | | | | | | | | | | | |            (3085), (3087), (3113), (3114), (3115), (3117),
% 171.17/25.70  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #309.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | |   (3118)  all_40_1 = e1
% 171.17/25.70  | | | | | | | | | | |   (3119)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | COMBINE_EQS: (715), (3118) imply:
% 171.17/25.70  | | | | | | | | | | |   (3120)  all_4_1 = e1
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | SIMP: (3120) implies:
% 171.17/25.70  | | | | | | | | | | |   (3121)  all_4_1 = e1
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | COMBINE_EQS: (720), (3121) imply:
% 171.17/25.70  | | | | | | | | | | |   (3122)  all_52_0 = e1
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (796), (3121) imply:
% 171.17/25.70  | | | | | | | | | | |   (3123)   ~ (e2 = e1)
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (38), (3121) imply:
% 171.17/25.70  | | | | | | | | | | |   (3124)  op(e1, all_4_2) = all_4_0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (37), (3121) imply:
% 171.17/25.70  | | | | | | | | | | |   (3125)  op(e3, all_4_2) = e1
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | |   (3126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.70  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.70  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | BETA: splitting (3126) gives:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3127)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (8), (3122), (3127) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #632.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3128)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3128) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #289.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | |   (3129)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.70  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.70  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | BETA: splitting (3129) gives:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3130)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (3081), (3130),
% 171.17/25.70  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #314.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3131)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 171.17/25.70  | | | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 171.17/25.70  | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 171.17/25.70  | | | | | | | | | | | | |            (182), (183), (268), (269), (270), (271), (272),
% 171.17/25.70  | | | | | | | | | | | | |            (274), (276), (280), (281), (283), (301), (302),
% 171.17/25.70  | | | | | | | | | | | | |            (303), (304), (305), (306), (307), (310), (311),
% 171.17/25.70  | | | | | | | | | | | | |            (313), (315), (319), (321), (322), (323), (324),
% 171.17/25.70  | | | | | | | | | | | | |            (325), (326), (327), (328), (330), (331), (341),
% 171.17/25.70  | | | | | | | | | | | | |            (344), (349), (350), (364), (370), (373), (385),
% 171.17/25.70  | | | | | | | | | | | | |            (386), (391), (403), (413), (419), (425), (429),
% 171.17/25.70  | | | | | | | | | | | | |            (518), (529), (531), (532), (533), (534), (535),
% 171.17/25.70  | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 171.17/25.70  | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 171.17/25.70  | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 171.17/25.70  | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (571),
% 171.17/25.70  | | | | | | | | | | | | |            (573), (577), (578), (580), (581), (582), (585),
% 171.17/25.70  | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (594), (595),
% 171.17/25.70  | | | | | | | | | | | | |            (596), (597), (600), (649), (770), (797), (799),
% 171.17/25.70  | | | | | | | | | | | | |            (3083), (3085), (3087), (3119), (3124), (3125),
% 171.17/25.70  | | | | | | | | | | | | |            (3131), (function-axioms) are inconsistent by
% 171.17/25.70  | | | | | | | | | | | | |            sub-proof #276.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | |   (3132)  all_34_0 = e1
% 171.17/25.70  | | | | | | | | | |   (3133)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.70  | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | COMBINE_EQS: (773), (3132) imply:
% 171.17/25.70  | | | | | | | | | |   (3134)  all_4_0 = e1
% 171.17/25.70  | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | REDUCE: (3083), (3134) imply:
% 171.17/25.70  | | | | | | | | | |   (3135)   ~ (e2 = e1)
% 171.17/25.70  | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | REDUCE: (38), (3134) imply:
% 171.17/25.70  | | | | | | | | | |   (3136)  op(all_4_1, all_4_2) = e1
% 171.17/25.70  | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.70  | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | |   (3137)  all_58_15 = e0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | COMBINE_EQS: (532), (3137) imply:
% 171.17/25.70  | | | | | | | | | | |   (3138)  all_6_2 = e0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (564), (3138) imply:
% 171.17/25.70  | | | | | | | | | | |   (3139)   ~ (all_52_25 = e0)
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (43), (3138) imply:
% 171.17/25.70  | | | | | | | | | | |   (3140)  op(all_6_1, e0) = all_6_0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (42), (3138) imply:
% 171.17/25.70  | | | | | | | | | | |   (3141)  op(e0, e0) = all_6_1
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (41), (3138) imply:
% 171.17/25.70  | | | | | | | | | | |   (3142)  op(e0, e0) = e0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.70  | | | | | | | | | | |              e0, e0, simplifying with (3141), (3142) gives:
% 171.17/25.70  | | | | | | | | | | |   (3143)  all_6_1 = e0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (3140), (3143) imply:
% 171.17/25.70  | | | | | | | | | | |   (3144)  op(e0, e0) = all_6_0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.70  | | | | | | | | | | |              e0, e0, simplifying with (3142), (3144) gives:
% 171.17/25.70  | | | | | | | | | | |   (3145)  all_6_0 = e0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (3085), (3145) imply:
% 171.17/25.70  | | | | | | | | | | |   (3146)   ~ (e3 = e0)
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | |   (3147)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.70  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.70  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | BETA: splitting (3147) gives:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3148)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (3136), (3148),
% 171.17/25.70  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #600.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3149)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3149) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #289.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | |   (3150)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.70  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.70  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | BETA: splitting (3150) gives:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3151)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (3081), (3151),
% 171.17/25.70  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #314.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3152)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (37), (161), (163), (164), (165),
% 171.17/25.70  | | | | | | | | | | | | |            (172), (173), (177), (179), (181), (270), (271),
% 171.17/25.70  | | | | | | | | | | | | |            (280), (282), (283), (304), (328), (330), (344),
% 171.17/25.70  | | | | | | | | | | | | |            (349), (386), (392), (403), (429), (494), (531),
% 171.17/25.70  | | | | | | | | | | | | |            (533), (534), (544), (546), (548), (552), (554),
% 171.17/25.70  | | | | | | | | | | | | |            (562), (566), (596), (663), (796), (3133), (3136),
% 171.17/25.70  | | | | | | | | | | | | |            (3137), (3139), (3152), (function-axioms) are
% 171.17/25.70  | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | End of split
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | |   (3153)   ~ (all_58_15 = e0)
% 171.17/25.70  | | | | | | | | | | |   (3154)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.70  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.70  | | | | | | | | | | |             e0)
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | ALPHA: (3154) implies:
% 171.17/25.70  | | | | | | | | | | |   (3155)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.70  | | | | | | | | | | |   (3156)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | REDUCE: (532), (3153) imply:
% 171.17/25.70  | | | | | | | | | | |   (3157)   ~ (all_6_2 = e0)
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.70  | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | |   (3158)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.70  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.70  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (37), (41), (61), (154),
% 171.17/25.70  | | | | | | | | | | | |            (155), (156), (158), (159), (160), (161), (163),
% 171.17/25.70  | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (172),
% 171.17/25.70  | | | | | | | | | | | |            (173), (176), (177), (178), (179), (268), (269),
% 171.17/25.70  | | | | | | | | | | | |            (270), (271), (272), (273), (276), (278), (279),
% 171.17/25.70  | | | | | | | | | | | |            (280), (281), (282), (283), (304), (305), (306),
% 171.17/25.70  | | | | | | | | | | | |            (307), (310), (311), (312), (313), (314), (315),
% 171.17/25.70  | | | | | | | | | | | |            (317), (319), (323), (324), (326), (327), (328),
% 171.17/25.70  | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 171.17/25.70  | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 171.17/25.70  | | | | | | | | | | | |            (403), (409), (413), (425), (429), (529), (530),
% 171.17/25.70  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.70  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.70  | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.70  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.70  | | | | | | | | | | | |            (565), (566), (567), (568), (569), (575), (578),
% 171.17/25.70  | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 171.17/25.70  | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 171.17/25.70  | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (720),
% 171.17/25.70  | | | | | | | | | | | |            (796), (2838), (2839), (3156), (3157), (3158),
% 171.17/25.70  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | |            #265.
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | |   (3159)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.70  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.70  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | BETA: splitting (3159) gives:
% 171.17/25.70  | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 1:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3160)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (3081), (3160),
% 171.17/25.70  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.70  | | | | | | | | | | | | |            #314.
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | Case 2:
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.70  | | | | | | | | | | | | |   (3161)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.70  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.70  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (61), (154),
% 171.17/25.71  | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (165), (172),
% 171.17/25.71  | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (183), (268),
% 171.17/25.71  | | | | | | | | | | | | |            (270), (280), (281), (282), (283), (303), (304),
% 171.17/25.71  | | | | | | | | | | | | |            (306), (307), (322), (324), (325), (326), (328),
% 171.17/25.71  | | | | | | | | | | | | |            (330), (344), (349), (364), (370), (385), (386),
% 171.17/25.71  | | | | | | | | | | | | |            (391), (392), (403), (413), (494), (529), (531),
% 171.17/25.71  | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (538), (539),
% 171.17/25.71  | | | | | | | | | | | | |            (540), (544), (546), (548), (552), (554), (555),
% 171.17/25.71  | | | | | | | | | | | | |            (557), (558), (559), (562), (565), (566), (567),
% 171.17/25.71  | | | | | | | | | | | | |            (568), (569), (578), (580), (581), (586), (591),
% 171.17/25.71  | | | | | | | | | | | | |            (595), (596), (597), (649), (663), (796), (797),
% 171.17/25.71  | | | | | | | | | | | | |            (799), (3085), (3133), (3136), (3155), (3161),
% 171.17/25.71  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.71  | | | | | | | | | | | | |            #534.
% 171.17/25.71  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | |   (3162)  all_28_0 = e3
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | COMBINE_EQS: (776), (3162) imply:
% 171.17/25.71  | | | | | | | | |   (3163)  all_6_0 = e3
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | REDUCE: (43), (3163) imply:
% 171.17/25.71  | | | | | | | | |   (3164)  op(all_6_1, all_6_2) = e3
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | |   (3165)   ~ (all_40_1 = e1)
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | REDUCE: (715), (3165) imply:
% 171.17/25.71  | | | | | | | | | |   (3166)   ~ (all_4_1 = e1)
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | |   (3167)  all_58_15 = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (3164), (3167),
% 171.17/25.71  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.71  | | | | | | | | | | |            #510.
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | |   (3168)   ~ (all_58_15 = e0)
% 171.17/25.71  | | | | | | | | | | |   (3169)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.71  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.71  | | | | | | | | | | |             e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | ALPHA: (3169) implies:
% 171.17/25.71  | | | | | | | | | | |   (3170)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (532), (3168) imply:
% 171.17/25.71  | | | | | | | | | | |   (3171)   ~ (all_6_2 = e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | |   (3172)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.71  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.71  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (41), (61), (154), (155),
% 171.17/25.71  | | | | | | | | | | | |            (156), (158), (159), (160), (161), (163), (164),
% 171.17/25.71  | | | | | | | | | | | |            (165), (167), (168), (169), (170), (172), (173),
% 171.17/25.71  | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 171.17/25.71  | | | | | | | | | | | |            (271), (272), (273), (276), (278), (279), (280),
% 171.17/25.71  | | | | | | | | | | | |            (281), (282), (283), (304), (305), (306), (307),
% 171.17/25.71  | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 171.17/25.71  | | | | | | | | | | | |            (319), (323), (324), (326), (327), (328), (330),
% 171.17/25.71  | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 171.17/25.71  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 171.17/25.71  | | | | | | | | | | | |            (409), (413), (425), (429), (529), (530), (531),
% 171.17/25.71  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 171.17/25.71  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 171.17/25.71  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.71  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 171.17/25.71  | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 171.17/25.71  | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 171.17/25.71  | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 171.17/25.71  | | | | | | | | | | | |            (596), (597), (598), (599), (600), (720), (796),
% 171.17/25.71  | | | | | | | | | | | |            (2838), (2839), (3166), (3170), (3171), (3172),
% 171.17/25.71  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.71  | | | | | | | | | | | |            #268.
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | |   (3173)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.71  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.71  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (3081),
% 171.17/25.71  | | | | | | | | | | | |            (3164), (3173), (function-axioms) are inconsistent
% 171.17/25.71  | | | | | | | | | | | |            by sub-proof #300.
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | |   (3174)  all_40_1 = e1
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | COMBINE_EQS: (715), (3174) imply:
% 171.17/25.71  | | | | | | | | | |   (3175)  all_4_1 = e1
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | COMBINE_EQS: (720), (3175) imply:
% 171.17/25.71  | | | | | | | | | |   (3176)  all_52_0 = e1
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | REDUCE: (796), (3175) imply:
% 171.17/25.71  | | | | | | | | | |   (3177)   ~ (e2 = e1)
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | |   (3178)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.71  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.71  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | BETA: splitting (3178) gives:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | |   (3179)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.71  | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | ALPHA: (3179) implies:
% 171.17/25.71  | | | | | | | | | | | |   (3180)  all_52_0 = e3
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | COMBINE_EQS: (3176), (3180) imply:
% 171.17/25.71  | | | | | | | | | | | |   (3181)  e3 = e1
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | SIMP: (3181) implies:
% 171.17/25.71  | | | | | | | | | | | |   (3182)  e3 = e1
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | COMBINE_EQS: (2838), (3182) imply:
% 171.17/25.71  | | | | | | | | | | | |   (3183)  all_52_10 = e1
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (37), (38), (41), (42), (61),
% 171.17/25.71  | | | | | | | | | | | |            (62), (113), (154), (156), (158), (159), (160),
% 171.17/25.71  | | | | | | | | | | | |            (161), (163), (164), (165), (168), (169), (170),
% 171.17/25.71  | | | | | | | | | | | |            (172), (173), (176), (177), (178), (179), (185),
% 171.17/25.71  | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (276),
% 171.17/25.71  | | | | | | | | | | | |            (279), (281), (282), (283), (301), (302), (303),
% 171.17/25.71  | | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 171.17/25.71  | | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 171.17/25.71  | | | | | | | | | | | |            (327), (328), (330), (331), (341), (344), (349),
% 171.17/25.71  | | | | | | | | | | | |            (350), (359), (364), (370), (373), (385), (391),
% 171.17/25.71  | | | | | | | | | | | |            (392), (403), (409), (413), (425), (429), (529),
% 171.17/25.71  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.71  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.71  | | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 171.17/25.71  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 171.17/25.71  | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 171.17/25.71  | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 171.17/25.71  | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 171.17/25.71  | | | | | | | | | | | |            (596), (597), (598), (599), (600), (649), (719),
% 171.17/25.71  | | | | | | | | | | | |            (720), (773), (3081), (3083), (3164), (3183),
% 171.17/25.71  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.71  | | | | | | | | | | | |            #299.
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | |   (3184)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.71  | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3184) are inconsistent by sub-proof
% 171.17/25.71  | | | | | | | | | | | |            #289.
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | |   (3185)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.71  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.71  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (3081),
% 171.17/25.71  | | | | | | | | | | |            (3164), (3185), (function-axioms) are inconsistent
% 171.17/25.71  | | | | | | | | | | |            by sub-proof #300.
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | 
% 171.17/25.71  | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | 
% 171.17/25.71  | | | | | | | |   (3186)  all_26_0 = e2
% 171.17/25.71  | | | | | | | |   (3187)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 171.17/25.71  | | | | | | | | 
% 171.17/25.71  | | | | | | | | COMBINE_EQS: (779), (3186) imply:
% 171.17/25.71  | | | | | | | |   (3188)  all_4_0 = e2
% 171.17/25.71  | | | | | | | | 
% 171.17/25.71  | | | | | | | | COMBINE_EQS: (742), (3188) imply:
% 171.17/25.71  | | | | | | | |   (3189)  all_50_0 = e2
% 171.17/25.71  | | | | | | | | 
% 171.17/25.71  | | | | | | | | REDUCE: (38), (3188) imply:
% 171.17/25.71  | | | | | | | |   (3190)  op(all_4_1, all_4_2) = e2
% 171.17/25.71  | | | | | | | | 
% 171.17/25.71  | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.71  | | | | | | | | 
% 171.17/25.71  | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | |   (3191)   ~ (all_28_0 = e3)
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | REDUCE: (776), (3191) imply:
% 171.17/25.71  | | | | | | | | |   (3192)   ~ (all_6_0 = e3)
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.71  | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | |   (3193)   ~ (all_50_0 = e2)
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | REDUCE: (3189), (3193) imply:
% 171.17/25.71  | | | | | | | | | |   (3194)  $false
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | CLOSE: (3194) is inconsistent.
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | |   (3195)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.71  | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | |   (3196)  all_58_15 = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | COMBINE_EQS: (532), (3196) imply:
% 171.17/25.71  | | | | | | | | | | |   (3197)  all_6_2 = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (564), (3197) imply:
% 171.17/25.71  | | | | | | | | | | |   (3198)   ~ (all_52_25 = e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (43), (3197) imply:
% 171.17/25.71  | | | | | | | | | | |   (3199)  op(all_6_1, e0) = all_6_0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (42), (3197) imply:
% 171.17/25.71  | | | | | | | | | | |   (3200)  op(e0, e0) = all_6_1
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (41), (3197) imply:
% 171.17/25.71  | | | | | | | | | | |   (3201)  op(e0, e0) = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.71  | | | | | | | | | | |              e0, e0, simplifying with (3200), (3201) gives:
% 171.17/25.71  | | | | | | | | | | |   (3202)  all_6_1 = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (3199), (3202) imply:
% 171.17/25.71  | | | | | | | | | | |   (3203)  op(e0, e0) = all_6_0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.71  | | | | | | | | | | |              e0, e0, simplifying with (3201), (3203) gives:
% 171.17/25.71  | | | | | | | | | | |   (3204)  all_6_0 = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (3192), (3204) imply:
% 171.17/25.71  | | | | | | | | | | |   (3205)   ~ (e3 = e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (799), (3204) imply:
% 171.17/25.71  | | | | | | | | | | |   (3206)   ~ (e2 = e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | |   (3207)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.71  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.71  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | BETA: splitting (3207) gives:
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | Case 1:
% 171.17/25.71  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | |   (3208)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.71  | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.71  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (3190), (3208),
% 171.17/25.71  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.71  | | | | | | | | | | | | |            #494.
% 171.17/25.71  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | |   (3209)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.71  | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.71  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | | REF_CLOSE: (9), (2838), (3209) are inconsistent by sub-proof
% 171.17/25.71  | | | | | | | | | | | | |            #289.
% 171.17/25.71  | | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | |   (3210)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.71  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.71  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (37), (62), (164),
% 171.17/25.71  | | | | | | | | | | | |            (165), (172), (173), (177), (178), (179), (181),
% 171.17/25.71  | | | | | | | | | | | |            (270), (271), (280), (283), (303), (304), (326),
% 171.17/25.71  | | | | | | | | | | | |            (344), (349), (386), (403), (429), (503), (531),
% 171.17/25.71  | | | | | | | | | | | |            (533), (534), (542), (544), (546), (548), (550),
% 171.17/25.71  | | | | | | | | | | | |            (552), (554), (558), (562), (563), (586), (698),
% 171.17/25.71  | | | | | | | | | | | |            (719), (796), (3081), (3187), (3190), (3196),
% 171.17/25.71  | | | | | | | | | | | |            (3198), (3210), (function-axioms) are inconsistent
% 171.17/25.71  | | | | | | | | | | | |            by sub-proof #298.
% 171.17/25.71  | | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | End of split
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | Case 2:
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | |   (3211)   ~ (all_58_15 = e0)
% 171.17/25.71  | | | | | | | | | | |   (3212)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.71  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.71  | | | | | | | | | | |             e0)
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | ALPHA: (3212) implies:
% 171.17/25.71  | | | | | | | | | | |   (3213)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.71  | | | | | | | | | | |   (3214)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.71  | | | | | | | | | | | 
% 171.17/25.71  | | | | | | | | | | | REDUCE: (532), (3211) imply:
% 171.17/25.72  | | | | | | | | | | |   (3215)   ~ (all_6_2 = e0)
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | |   (3216)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.72  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.72  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (37), (41), (61), (154),
% 171.17/25.72  | | | | | | | | | | | |            (155), (156), (158), (159), (160), (161), (163),
% 171.17/25.72  | | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (172),
% 171.17/25.72  | | | | | | | | | | | |            (173), (176), (177), (178), (179), (268), (269),
% 171.17/25.72  | | | | | | | | | | | |            (270), (271), (272), (273), (276), (278), (279),
% 171.17/25.72  | | | | | | | | | | | |            (280), (281), (282), (283), (304), (305), (306),
% 171.17/25.72  | | | | | | | | | | | |            (307), (310), (311), (312), (313), (314), (315),
% 171.17/25.72  | | | | | | | | | | | |            (317), (319), (323), (324), (326), (327), (328),
% 171.17/25.72  | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 171.17/25.72  | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 171.17/25.72  | | | | | | | | | | | |            (403), (409), (413), (425), (429), (529), (530),
% 171.17/25.72  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.72  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.72  | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.72  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.72  | | | | | | | | | | | |            (565), (566), (567), (568), (569), (575), (578),
% 171.17/25.72  | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 171.17/25.72  | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 171.17/25.72  | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (720),
% 171.17/25.72  | | | | | | | | | | | |            (796), (2838), (2839), (3214), (3215), (3216),
% 171.17/25.72  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.72  | | | | | | | | | | | |            #265.
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | Case 2:
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | |   (3217)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.72  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.72  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | BETA: splitting (3217) gives:
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | |   (3218)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.72  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | ALPHA: (3218) implies:
% 171.17/25.72  | | | | | | | | | | | | |   (3219)  all_52_20 = e1
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | COMBINE_EQS: (719), (3219) imply:
% 171.17/25.72  | | | | | | | | | | | | |   (3220)  all_14_1 = e1
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (3081), (3220), (function-axioms) are
% 171.17/25.72  | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | Case 2:
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | |   (3221)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.72  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | ALPHA: (3221) implies:
% 171.17/25.72  | | | | | | | | | | | | |   (3222)  all_52_30 = e0
% 171.17/25.72  | | | | | | | | | | | | |   (3223)  all_52_28 = e1
% 171.17/25.72  | | | | | | | | | | | | |   (3224)  all_52_26 = e2
% 171.17/25.72  | | | | | | | | | | | | |   (3225)  all_52_24 = e3
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | COMBINE_EQS: (649), (3222) imply:
% 171.17/25.72  | | | | | | | | | | | | |   (3226)  all_6_1 = e0
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (51), (154),
% 171.17/25.72  | | | | | | | | | | | | |            (155), (156), (164), (165), (172), (173), (177),
% 171.17/25.72  | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 171.17/25.72  | | | | | | | | | | | | |            (271), (280), (283), (303), (304), (305), (306),
% 171.17/25.72  | | | | | | | | | | | | |            (307), (313), (322), (323), (324), (325), (326),
% 171.17/25.72  | | | | | | | | | | | | |            (328), (330), (344), (349), (364), (370), (373),
% 171.17/25.72  | | | | | | | | | | | | |            (385), (386), (391), (403), (429), (503), (521),
% 171.17/25.72  | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 171.17/25.72  | | | | | | | | | | | | |            (537), (538), (539), (540), (544), (546), (548),
% 171.17/25.72  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 171.17/25.72  | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (569),
% 171.17/25.72  | | | | | | | | | | | | |            (573), (580), (581), (588), (589), (594), (597),
% 171.17/25.72  | | | | | | | | | | | | |            (698), (718), (796), (797), (799), (3187), (3190),
% 171.17/25.72  | | | | | | | | | | | | |            (3192), (3195), (3213), (3215), (3223), (3224),
% 171.17/25.72  | | | | | | | | | | | | |            (3225), (3226), (function-axioms) are inconsistent
% 171.17/25.72  | | | | | | | | | | | | |            by sub-proof #450.
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | End of split
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | End of split
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | End of split
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | End of split
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | Case 2:
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | |   (3227)  all_28_0 = e3
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | COMBINE_EQS: (776), (3227) imply:
% 171.17/25.72  | | | | | | | | |   (3228)  all_6_0 = e3
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | SIMP: (3228) implies:
% 171.17/25.72  | | | | | | | | |   (3229)  all_6_0 = e3
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | REDUCE: (43), (3229) imply:
% 171.17/25.72  | | | | | | | | |   (3230)  op(all_6_1, all_6_2) = e3
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | |   (3231)  all_58_15 = e0
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (3230), (3231),
% 171.17/25.72  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.72  | | | | | | | | | |            #510.
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | Case 2:
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | |   (3232)   ~ (all_58_15 = e0)
% 171.17/25.72  | | | | | | | | | |   (3233)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.72  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.72  | | | | | | | | | |             e0)
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | ALPHA: (3233) implies:
% 171.17/25.72  | | | | | | | | | |   (3234)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | REDUCE: (532), (3232) imply:
% 171.17/25.72  | | | | | | | | | |   (3235)   ~ (all_6_2 = e0)
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | |   (3236)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.72  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.72  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (37), (41), (61), (154),
% 171.17/25.72  | | | | | | | | | | |            (155), (156), (158), (159), (160), (161), (163),
% 171.17/25.72  | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (172),
% 171.17/25.72  | | | | | | | | | | |            (173), (176), (177), (178), (179), (268), (269),
% 171.17/25.72  | | | | | | | | | | |            (270), (271), (272), (273), (276), (278), (279),
% 171.17/25.72  | | | | | | | | | | |            (280), (281), (282), (283), (304), (305), (306),
% 171.17/25.72  | | | | | | | | | | |            (307), (310), (311), (312), (313), (314), (315),
% 171.17/25.72  | | | | | | | | | | |            (317), (319), (323), (324), (326), (327), (328),
% 171.17/25.72  | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 171.17/25.72  | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 171.17/25.72  | | | | | | | | | | |            (403), (409), (413), (425), (429), (529), (530),
% 171.17/25.72  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.72  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.72  | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.72  | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.72  | | | | | | | | | | |            (565), (566), (567), (568), (569), (575), (578),
% 171.17/25.72  | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 171.17/25.72  | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 171.17/25.72  | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (720),
% 171.17/25.72  | | | | | | | | | | |            (796), (2838), (2839), (3234), (3235), (3236),
% 171.17/25.72  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.72  | | | | | | | | | | |            #265.
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | Case 2:
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | |   (3237)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.72  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.72  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (3081),
% 171.17/25.72  | | | | | | | | | | |            (3230), (3237), (function-axioms) are inconsistent
% 171.17/25.72  | | | | | | | | | | |            by sub-proof #300.
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | End of split
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | End of split
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | End of split
% 171.17/25.72  | | | | | | | | 
% 171.17/25.72  | | | | | | | End of split
% 171.17/25.72  | | | | | | | 
% 171.17/25.72  | | | | | | End of split
% 171.17/25.72  | | | | | | 
% 171.17/25.72  | | | | | End of split
% 171.17/25.72  | | | | | 
% 171.17/25.72  | | | | Case 2:
% 171.17/25.72  | | | | | 
% 171.17/25.72  | | | | |   (3238)  all_10_0 = e3
% 171.17/25.72  | | | | | 
% 171.17/25.72  | | | | | REDUCE: (53), (3238) imply:
% 171.17/25.72  | | | | |   (3239)  op(all_10_1, all_10_2) = e3
% 171.17/25.72  | | | | | 
% 171.17/25.72  | | | | | BETA: splitting (64) gives:
% 171.17/25.72  | | | | | 
% 171.17/25.72  | | | | | Case 1:
% 171.17/25.72  | | | | | | 
% 171.17/25.72  | | | | | |   (3240)   ~ (all_14_0 = e2)
% 171.17/25.72  | | | | | | 
% 171.17/25.72  | | | | | | BETA: splitting (74) gives:
% 171.17/25.72  | | | | | | 
% 171.17/25.72  | | | | | | Case 1:
% 171.17/25.72  | | | | | | | 
% 171.17/25.72  | | | | | | |   (3241)   ~ (all_18_0 = e3)
% 171.17/25.72  | | | | | | | 
% 171.17/25.72  | | | | | | | REDUCE: (789), (3241) imply:
% 171.17/25.72  | | | | | | |   (3242)   ~ (all_14_0 = e3)
% 171.17/25.72  | | | | | | | 
% 171.17/25.72  | | | | | | | BETA: splitting (83) gives:
% 171.17/25.72  | | | | | | | 
% 171.17/25.72  | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | 
% 171.17/25.72  | | | | | | | |   (3243)   ~ (all_22_1 = e3)
% 171.17/25.72  | | | | | | | | 
% 171.17/25.72  | | | | | | | | REDUCE: (711), (3243) imply:
% 171.17/25.72  | | | | | | | |   (3244)   ~ (all_14_1 = e3)
% 171.17/25.72  | | | | | | | | 
% 171.17/25.72  | | | | | | | | BETA: splitting (93) gives:
% 171.17/25.72  | | | | | | | | 
% 171.17/25.72  | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | |   (3245)   ~ (all_26_0 = e2)
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | REDUCE: (779), (3245) imply:
% 171.17/25.72  | | | | | | | | |   (3246)   ~ (all_4_0 = e2)
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.72  | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | |   (3247)   ~ (all_28_0 = e3)
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | REDUCE: (776), (3247) imply:
% 171.17/25.72  | | | | | | | | | |   (3248)   ~ (all_6_0 = e3)
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | BETA: splitting (108) gives:
% 171.17/25.72  | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | |   (3249)   ~ (all_32_1 = e2)
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | REDUCE: (713), (3249) imply:
% 171.17/25.72  | | | | | | | | | | |   (3250)   ~ (all_14_1 = e2)
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.72  | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | |   (3251)   ~ (all_34_0 = e1)
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | REDUCE: (773), (3251) imply:
% 171.17/25.72  | | | | | | | | | | | |   (3252)   ~ (all_4_0 = e1)
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.72  | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | |   (3253)   ~ (all_40_1 = e1)
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | REDUCE: (715), (3253) imply:
% 171.17/25.72  | | | | | | | | | | | | |   (3254)   ~ (all_4_1 = e1)
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.72  | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | |   (3255)  all_58_15 = e0
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | COMBINE_EQS: (532), (3255) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3256)  all_6_2 = e0
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (597), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3257)   ~ (all_52_7 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (600), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3258)   ~ (all_52_23 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (564), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3259)   ~ (all_52_25 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (582), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3260)   ~ (all_52_27 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (594), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3261)   ~ (all_52_29 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (43), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3262)  op(all_6_1, e0) = all_6_0
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (42), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3263)  op(e0, e0) = all_6_1
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (41), (3256) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3264)  op(e0, e0) = e0
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.72  | | | | | | | | | | | | | |              e0, e0, simplifying with (3263), (3264) gives:
% 171.17/25.72  | | | | | | | | | | | | | |   (3265)  all_6_1 = e0
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (3262), (3265) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3266)  op(e0, e0) = all_6_0
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.72  | | | | | | | | | | | | | |              e0, e0, simplifying with (3264), (3266) gives:
% 171.17/25.72  | | | | | | | | | | | | | |   (3267)  all_6_0 = e0
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (3248), (3267) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3268)   ~ (e3 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (799), (3267) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3269)   ~ (e2 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | REDUCE: (797), (3267) imply:
% 171.17/25.72  | | | | | | | | | | | | | |   (3270)   ~ (e1 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.72  | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | |   (3271)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.72  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.72  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.72  | | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | | BETA: splitting (3271) gives:
% 171.17/25.72  | | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.72  | | | | | | | | | | | | | | | | 
% 171.17/25.72  | | | | | | | | | | | | | | | |   (3272)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.72  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.72  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (37), (38), (154), (155), (156), (160),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (178), (179), (270), (271), (280), (283), (302),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (303), (304), (305), (306), (307), (323), (326),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (330), (331), (344), (349), (370), (386), (391),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (403), (429), (531), (532), (533), (534), (535),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (536), (540), (546), (552), (562), (569), (585),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (586), (595), (596), (597), (720), (3255), (3257),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (3259), (3260), (3261), (3272), (function-axioms)
% 171.17/25.73  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1008.
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3273)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.73  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | ALPHA: (3273) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3274)  all_52_10 = e2
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (3274) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3275)  all_10_1 = e2
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | SIMP: (3275) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3276)  all_10_1 = e2
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (3276), (function-axioms) are
% 171.17/25.73  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | End of split
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | |   (3277)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.73  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.73  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | BETA: splitting (3277) gives:
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3278)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.73  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | ALPHA: (3278) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3279)  all_52_22 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3280)  all_52_20 = e1
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3281)  all_52_18 = e2
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3282)  all_52_16 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3280) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3283)  all_14_1 = e1
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | SIMP: (3283) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3284)  all_14_1 = e1
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (63), (3284) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3285)  op(e1, all_14_2) = all_14_0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (182), (3282) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3286)  op(e3, all_52_17) = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (174), (3281) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3287)  op(e2, all_52_19) = e2
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (62), (3284) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3288)  op(e1, all_14_2) = e1
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (158), (3279) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3289)  op(e0, all_52_23) = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (154),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (155), (156), (164), (165), (172), (177), (178),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (179), (269), (270), (271), (272), (273), (274),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (275), (276), (278), (280), (281), (283), (302),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (303), (304), (305), (306), (307), (311), (319),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (323), (324), (325), (326), (329), (330), (331),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (403), (413),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (419), (425), (429), (530), (531), (533), (534),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (544), (546), (548), (552), (553), (554), (555),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (557), (558), (561), (562), (563), (565), (568),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (569), (571), (578), (579), (580), (581), (584),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (585), (586), (588), (591), (593), (596), (598),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (796), (3240), (3242), (3246), (3252), (3255),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (3257), (3258), (3259), (3260), (3261), (3285),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (3286), (3287), (3288), (3289), (function-axioms)
% 171.17/25.73  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #897.
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3290)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.73  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | ALPHA: (3290) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3291)  all_52_28 = e1
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3292)  all_52_26 = e2
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3293)  all_52_24 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (181), (3293) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3294)  op(e3, all_52_25) = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (173), (3292) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3295)  op(e2, all_52_27) = e2
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (165), (3291) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3296)  op(e1, all_52_29) = e1
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (163), (164), (170),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (182), (183), (269),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (270), (271), (275), (278), (280), (283), (302),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (304), (305), (306), (310), (322), (324), (329),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (330), (341), (344), (349), (364), (365), (385),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (386), (391), (403), (429), (530), (531), (533),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (554), (555), (558), (561), (562), (563), (569),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (571), (573), (580), (581), (583), (585), (586),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (588), (591), (593), (796), (3254), (3255),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (3258), (3259), (3261), (3294), (3295), (3296),
% 171.17/25.73  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.73  | | | | | | | | | | | | | | | |            #879.
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | End of split
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | End of split
% 171.17/25.73  | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | |   (3297)   ~ (all_58_15 = e0)
% 171.17/25.73  | | | | | | | | | | | | | |   (3298)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.73  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.73  | | | | | | | | | | | | | |             e0)
% 171.17/25.73  | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | ALPHA: (3298) implies:
% 171.17/25.73  | | | | | | | | | | | | | |   (3299)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.73  | | | | | | | | | | | | | |   (3300)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.73  | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | REDUCE: (532), (3297) imply:
% 171.17/25.73  | | | | | | | | | | | | | |   (3301)   ~ (all_6_2 = e0)
% 171.17/25.73  | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.73  | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | |   (3302)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.73  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.73  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | BETA: splitting (3302) gives:
% 171.17/25.73  | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3303)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.73  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | ALPHA: (3303) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3304)  all_52_6 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3305)  all_52_4 = e1
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3306)  all_52_2 = e2
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3307)  all_52_0 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (3307) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3308)  all_4_1 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (38), (3308) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3309)  op(e3, all_4_2) = all_4_0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (37), (3308) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3310)  op(e3, all_4_2) = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (176), (3306) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3311)  op(e2, all_52_3) = e2
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (168), (3305) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3312)  op(e1, all_52_5) = e1
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | REDUCE: (160), (3304) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3313)  op(e0, all_52_7) = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 171.17/25.73  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (3309), (3310)
% 171.17/25.73  | | | | | | | | | | | | | | | |              gives:
% 171.17/25.73  | | | | | | | | | | | | | | | |   (3314)  all_4_0 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 171.17/25.73  | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3315)  all_56_15 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (3315) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3316)  all_6_2 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | SIMP: (3316) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3317)  all_6_2 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3318)  all_58_15 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (597), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3319)   ~ (all_52_7 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (600), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3320)   ~ (all_52_23 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (564), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3321)   ~ (all_52_25 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (582), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3322)   ~ (all_52_27 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (594), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3323)   ~ (all_52_29 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (43), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3324)  op(all_6_1, e3) = all_6_0
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (42), (3317) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3325)  op(e0, e3) = all_6_1
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 171.17/25.73  | | | | | | | | | | | | | | | | |              all_6_1, e3, e0, simplifying with (156), (3325)
% 171.17/25.73  | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3326)  all_52_25 = all_6_1
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (3326) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3327)  all_58_12 = all_6_1
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (554), (3326) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3328)   ~ (all_52_9 = all_6_1)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (558), (3326) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3329)   ~ (all_52_17 = all_6_1)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (562), (3326) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3330)   ~ (all_52_27 = all_6_1)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | SIMP: (3330) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3331)   ~ (all_52_27 = all_6_1)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (563), (3326) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3332)   ~ (all_52_29 = all_6_1)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | SIMP: (3332) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3333)   ~ (all_52_29 = all_6_1)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (3321), (3326) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3334)   ~ (all_6_1 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | REDUCE: (181), (3326) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | |   (3335)  op(e3, all_6_1) = all_52_24
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 171.17/25.73  | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | |   (3336)  all_56_13 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (3322), (3336) are inconsistent by
% 171.17/25.73  | | | | | | | | | | | | | | | | | |            sub-proof #876.
% 171.17/25.73  | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | |   (3337)   ~ (all_56_13 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | |   (3338)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | |   (3339)  all_56_3 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (3319), (3339) are inconsistent by
% 171.17/25.73  | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | |   (3340)   ~ (all_56_3 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | |   (3341)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | |   (3342)  all_56_14 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (341), (3323), (3342) are inconsistent by
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | |            sub-proof #896.
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | |   (3343)   ~ (all_56_14 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | |   (3344)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3345)  all_56_9 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (3345) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3346)  all_52_19 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | SIMP: (3346) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3347)  all_52_19 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3348)  all_58_7 = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3349)   ~ (all_52_3 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3350)   ~ (all_52_17 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3351)   ~ (all_52_23 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3352)   ~ (all_52_27 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3353)   ~ (all_14_2 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | SIMP: (3353) implies:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3354)   ~ (all_14_2 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3355)  op(e2, e3) = all_52_18
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (3347) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3356)  op(e1, e2) = e3
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (51), (52), (61), (154),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (156), (161), (164), (170), (172), (177), (178),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (179), (182), (273), (275), (279), (281), (282),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (283), (302), (303), (305), (306), (307), (309),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (318),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (319), (321), (322), (324), (326), (327), (328),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (329), (331), (344), (359), (364), (365), (370),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (413), (531), (532), (533), (534), (535), (536),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (555), (556), (560),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (561), (565), (566), (567), (568), (569), (573),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (575), (581), (583), (584), (585), (586), (587),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (595), (596), (597),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (797), (3239), (3299), (3310), (3311), (3312),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (3313), (3318), (3319), (3320), (3322), (3323),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (3324), (3327), (3328), (3329), (3334), (3335),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (3338), (3341), (3348), (3349), (3350), (3354),
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            (3355), (3356), (function-axioms) are inconsistent
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #255.
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3357)   ~ (all_56_9 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (3357) imply:
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | |   (3358)   ~ (all_52_19 = e3)
% 171.17/25.73  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (51), (52), (62), (154),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (169), (170),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (273), (275), (282),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (283), (302), (303), (305), (307), (310), (311),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (314), (315), (317), (321), (322), (323), (324),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (341), (344), (359), (364), (365), (370), (373),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (531), (532),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (556), (557), (559), (560), (561), (565), (566),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (567), (568), (569), (573), (578), (579), (580),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (581), (583), (584), (585), (586), (587), (591),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (593), (595), (596), (597), (797), (3250), (3310),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (3311), (3312), (3313), (3318), (3320), (3322),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (3323), (3324), (3327), (3329), (3331), (3333),
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            (3338), (3341), (3344), (3358), (function-axioms)
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #829.
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.74  | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | |   (3359)   ~ (all_56_15 = e3)
% 171.17/25.74  | | | | | | | | | | | | | | | | |   (3360)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 171.17/25.74  | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (158),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (169), (170),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (269), (270),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (283), (304), (305), (307), (310), (311), (312),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (3300), (3301),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (3310), (3311), (3312), (3313), (3359), (3360),
% 171.17/25.74  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.74  | | | | | | | | | | | | | | | | |            #785.
% 171.17/25.74  | | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3361)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.74  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | ALPHA: (3361) implies:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3362)  all_52_10 = e2
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (3362) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3363)  all_10_1 = e2
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (3363), (function-axioms) are
% 171.17/25.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | Case 2:
% 171.17/25.74  | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | |   (3364)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.74  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.74  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.74  | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | BETA: splitting (3364) gives:
% 171.17/25.74  | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3365)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.74  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | ALPHA: (3365) implies:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3366)  all_52_22 = e0
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3367)  all_52_20 = e1
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3368)  all_52_18 = e2
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3369)  all_52_16 = e3
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3367) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3370)  all_14_1 = e1
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REDUCE: (63), (3370) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3371)  op(e1, all_14_2) = all_14_0
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REDUCE: (182), (3369) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3372)  op(e3, all_52_17) = e3
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REDUCE: (174), (3368) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3373)  op(e2, all_52_19) = e2
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REDUCE: (62), (3370) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3374)  op(e1, all_14_2) = e1
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REDUCE: (158), (3366) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3375)  op(e0, all_52_23) = e0
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (155),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (165), (169), (170),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (268), (270), (271), (273), (274), (275), (276),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (278), (281), (282), (283), (304), (306), (307),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (308), (310), (311), (312), (313), (314), (315),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (326),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (359),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (392),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (403), (413), (419), (425), (429), (529), (530),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (588), (591), (593),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (796),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (3239), (3240), (3242), (3246), (3252), (3254),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (3299), (3300), (3301), (3371), (3372), (3373),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (3374), (3375), (function-axioms) are inconsistent
% 171.17/25.74  | | | | | | | | | | | | | | | |            by sub-proof #248.
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3376)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.74  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | ALPHA: (3376) implies:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3377)  all_52_30 = e0
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3378)  all_52_28 = e1
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3379)  all_52_26 = e2
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3380)  all_52_24 = e3
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (3377) imply:
% 171.17/25.74  | | | | | | | | | | | | | | | |   (3381)  all_6_1 = e0
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (797), (799), (3246), (3248), (3252), (3299),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (3300), (3301), (3378), (3379), (3380), (3381),
% 171.17/25.74  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.74  | | | | | | | | | | | | | | | |            #635.
% 171.17/25.74  | | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | End of split
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | Case 2:
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | |   (3382)  all_40_1 = e1
% 171.17/25.74  | | | | | | | | | | | | |   (3383)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | COMBINE_EQS: (715), (3382) imply:
% 171.17/25.74  | | | | | | | | | | | | |   (3384)  all_4_1 = e1
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | SIMP: (3384) implies:
% 171.17/25.74  | | | | | | | | | | | | |   (3385)  all_4_1 = e1
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | COMBINE_EQS: (720), (3385) imply:
% 171.17/25.74  | | | | | | | | | | | | |   (3386)  all_52_0 = e1
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | REDUCE: (796), (3385) imply:
% 171.17/25.74  | | | | | | | | | | | | |   (3387)   ~ (e2 = e1)
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | REDUCE: (38), (3385) imply:
% 171.17/25.74  | | | | | | | | | | | | |   (3388)  op(e1, all_4_2) = all_4_0
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | REDUCE: (37), (3385) imply:
% 171.17/25.74  | | | | | | | | | | | | |   (3389)  op(e3, all_4_2) = e1
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.74  | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | Case 1:
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | |   (3390)  all_58_15 = e0
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | COMBINE_EQS: (532), (3390) imply:
% 171.17/25.74  | | | | | | | | | | | | | |   (3391)  all_6_2 = e0
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | REDUCE: (597), (3391) imply:
% 171.17/25.74  | | | | | | | | | | | | | |   (3392)   ~ (all_52_7 = e0)
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | REDUCE: (600), (3391) imply:
% 171.17/25.74  | | | | | | | | | | | | | |   (3393)   ~ (all_52_23 = e0)
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | REDUCE: (564), (3391) imply:
% 171.17/25.74  | | | | | | | | | | | | | |   (3394)   ~ (all_52_25 = e0)
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | REDUCE: (582), (3391) imply:
% 171.17/25.74  | | | | | | | | | | | | | |   (3395)   ~ (all_52_27 = e0)
% 171.17/25.74  | | | | | | | | | | | | | | 
% 171.17/25.74  | | | | | | | | | | | | | | REDUCE: (594), (3391) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3396)   ~ (all_52_29 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (43), (3391) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3397)  op(all_6_1, e0) = all_6_0
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (42), (3391) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3398)  op(e0, e0) = all_6_1
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (41), (3391) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3399)  op(e0, e0) = e0
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.75  | | | | | | | | | | | | | |              e0, e0, simplifying with (3398), (3399) gives:
% 171.17/25.75  | | | | | | | | | | | | | |   (3400)  all_6_1 = e0
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (3397), (3400) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3401)  op(e0, e0) = all_6_0
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.75  | | | | | | | | | | | | | |              e0, e0, simplifying with (3399), (3401) gives:
% 171.17/25.75  | | | | | | | | | | | | | |   (3402)  all_6_0 = e0
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (3248), (3402) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3403)   ~ (e3 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (799), (3402) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3404)   ~ (e2 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (797), (3402) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3405)   ~ (e1 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | Case 1:
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | |   (3406)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.75  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.75  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (661), (3239), (3386), (3406),
% 171.17/25.75  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.75  | | | | | | | | | | | | | | |            #247.
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | Case 2:
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | |   (3407)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.75  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.75  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | BETA: splitting (3407) gives:
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3408)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.75  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | ALPHA: (3408) implies:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3409)  all_52_22 = e0
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3410)  all_52_20 = e1
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3411)  all_52_18 = e2
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3412)  all_52_16 = e3
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3410) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3413)  all_14_1 = e1
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | SIMP: (3413) implies:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3414)  all_14_1 = e1
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (63), (3414) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3415)  op(e1, all_14_2) = all_14_0
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (182), (3412) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3416)  op(e3, all_52_17) = e3
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (174), (3411) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3417)  op(e2, all_52_19) = e2
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (62), (3414) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3418)  op(e1, all_14_2) = e1
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (158), (3409) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3419)  op(e0, all_52_23) = e0
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (154), (155), (156),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (164), (165), (172), (178), (179), (181), (270),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (271), (272), (274), (277), (302), (303), (304),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (305), (306), (307), (311), (319), (326), (330),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (364), (370), (373),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (385), (391), (403), (415), (419), (429), (533),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (544), (550), (552), (553), (554), (558), (562),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (563), (566), (571), (581), (583), (584), (585),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (587), (591), (595), (596), (3240), (3242),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (3389), (3390), (3393), (3394), (3395), (3396),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (3415), (3416), (3417), (3418), (3419),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.75  | | | | | | | | | | | | | | | |            #622.
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3420)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.75  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | ALPHA: (3420) implies:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3421)  all_52_28 = e1
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3422)  all_52_26 = e2
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3423)  all_52_24 = e3
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (181), (3423) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3424)  op(e3, all_52_25) = e3
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (173), (3422) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3425)  op(e2, all_52_27) = e2
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REDUCE: (165), (3421) imply:
% 171.17/25.75  | | | | | | | | | | | | | | | |   (3426)  op(e1, all_52_29) = e1
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (161), (163), (164), (170),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (182), (269), (270),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (271), (274), (280), (283), (302), (303), (304),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (306), (310), (313), (325), (341), (344), (349),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (364), (373), (386), (391), (403), (419), (429),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (518), (531), (533), (534), (535), (536), (537),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (538), (542), (546), (548), (550), (553), (554),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (558), (560), (562), (563), (566), (567), (569),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (581), (586), (591), (770), (3246), (3383),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (3388), (3389), (3390), (3392), (3394), (3396),
% 171.17/25.75  | | | | | | | | | | | | | | | |            (3424), (3425), (3426), (function-axioms) are
% 171.17/25.75  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #616.
% 171.17/25.75  | | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | End of split
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | End of split
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | Case 2:
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | |   (3427)   ~ (all_58_15 = e0)
% 171.17/25.75  | | | | | | | | | | | | | |   (3428)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.75  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.75  | | | | | | | | | | | | | |             e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | ALPHA: (3428) implies:
% 171.17/25.75  | | | | | | | | | | | | | |   (3429)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.75  | | | | | | | | | | | | | |   (3430)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REDUCE: (532), (3427) imply:
% 171.17/25.75  | | | | | | | | | | | | | |   (3431)   ~ (all_6_2 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 171.17/25.75  | | | | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 171.17/25.75  | | | | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (170),
% 171.17/25.75  | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 171.17/25.75  | | | | | | | | | | | | | |            (182), (183), (185), (268), (270), (271), (274),
% 171.17/25.75  | | | | | | | | | | | | | |            (275), (276), (278), (281), (283), (304), (305),
% 171.17/25.75  | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (319),
% 171.17/25.75  | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (325), (326),
% 171.17/25.75  | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (344), (349),
% 171.17/25.75  | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (403),
% 171.17/25.75  | | | | | | | | | | | | | |            (413), (419), (425), (429), (518), (529), (530),
% 171.17/25.75  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.75  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.75  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.75  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.75  | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 171.17/25.75  | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 171.17/25.75  | | | | | | | | | | | | | |            (583), (584), (585), (586), (588), (589), (591),
% 171.17/25.75  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 171.17/25.75  | | | | | | | | | | | | | |            (649), (661), (719), (770), (796), (3239), (3240),
% 171.17/25.75  | | | | | | | | | | | | | |            (3242), (3246), (3252), (3383), (3386), (3388),
% 171.17/25.75  | | | | | | | | | | | | | |            (3389), (3429), (3430), (3431), (function-axioms)
% 171.17/25.75  | | | | | | | | | | | | | |            are inconsistent by sub-proof #244.
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | End of split
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | End of split
% 171.17/25.75  | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | Case 2:
% 171.17/25.75  | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | |   (3432)  all_34_0 = e1
% 171.17/25.75  | | | | | | | | | | | |   (3433)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.75  | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | COMBINE_EQS: (773), (3432) imply:
% 171.17/25.75  | | | | | | | | | | | |   (3434)  all_4_0 = e1
% 171.17/25.75  | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | REDUCE: (38), (3434) imply:
% 171.17/25.75  | | | | | | | | | | | |   (3435)  op(all_4_1, all_4_2) = e1
% 171.17/25.75  | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.75  | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | Case 1:
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | |   (3436)  all_58_15 = e0
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | COMBINE_EQS: (532), (3436) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3437)  all_6_2 = e0
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (597), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3438)   ~ (all_52_7 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (600), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3439)   ~ (all_52_23 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (564), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3440)   ~ (all_52_25 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (582), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3441)   ~ (all_52_27 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (594), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3442)   ~ (all_52_29 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (43), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3443)  op(all_6_1, e0) = all_6_0
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (42), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3444)  op(e0, e0) = all_6_1
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (41), (3437) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3445)  op(e0, e0) = e0
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.75  | | | | | | | | | | | | |              e0, e0, simplifying with (3444), (3445) gives:
% 171.17/25.75  | | | | | | | | | | | | |   (3446)  all_6_1 = e0
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (3443), (3446) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3447)  op(e0, e0) = all_6_0
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.75  | | | | | | | | | | | | |              e0, e0, simplifying with (3445), (3447) gives:
% 171.17/25.75  | | | | | | | | | | | | |   (3448)  all_6_0 = e0
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (3248), (3448) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3449)   ~ (e3 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (799), (3448) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3450)   ~ (e2 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | REDUCE: (797), (3448) imply:
% 171.17/25.75  | | | | | | | | | | | | |   (3451)   ~ (e1 = e0)
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.75  | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | Case 1:
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | |   (3452)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.75  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.75  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.75  | | | | | | | | | | | | | |            (3435), (3452), (function-axioms) are inconsistent
% 171.17/25.75  | | | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | Case 2:
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | |   (3453)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.75  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.75  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | BETA: splitting (3453) gives:
% 171.17/25.75  | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | Case 1:
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | |   (3454)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.75  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | ALPHA: (3454) implies:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3455)  all_52_22 = e0
% 171.17/25.75  | | | | | | | | | | | | | | |   (3456)  all_52_20 = e1
% 171.17/25.75  | | | | | | | | | | | | | | |   (3457)  all_52_18 = e2
% 171.17/25.75  | | | | | | | | | | | | | | |   (3458)  all_52_16 = e3
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3456) imply:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3459)  all_14_1 = e1
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | SIMP: (3459) implies:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3460)  all_14_1 = e1
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | REDUCE: (63), (3460) imply:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3461)  op(e1, all_14_2) = all_14_0
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | REDUCE: (182), (3458) imply:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3462)  op(e3, all_52_17) = e3
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | REDUCE: (174), (3457) imply:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3463)  op(e2, all_52_19) = e2
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | REDUCE: (62), (3460) imply:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3464)  op(e1, all_14_2) = e1
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.75  | | | | | | | | | | | | | | | REDUCE: (158), (3455) imply:
% 171.17/25.75  | | | | | | | | | | | | | | |   (3465)  op(e0, all_52_23) = e0
% 171.17/25.75  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (154), (155),
% 171.17/25.76  | | | | | | | | | | | | | | |            (156), (164), (165), (172), (177), (178), (179),
% 171.17/25.76  | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 171.17/25.76  | | | | | | | | | | | | | | |            (276), (278), (280), (283), (302), (303), (304),
% 171.17/25.76  | | | | | | | | | | | | | | |            (305), (306), (307), (311), (319), (323), (324),
% 171.17/25.76  | | | | | | | | | | | | | | |            (325), (326), (329), (330), (331), (341), (344),
% 171.17/25.76  | | | | | | | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 171.17/25.76  | | | | | | | | | | | | | | |            (385), (386), (391), (403), (419), (425), (429),
% 171.17/25.76  | | | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 171.17/25.76  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.76  | | | | | | | | | | | | | | |            (552), (553), (554), (555), (557), (558), (561),
% 171.17/25.76  | | | | | | | | | | | | | | |            (562), (563), (565), (567), (569), (571), (578),
% 171.17/25.76  | | | | | | | | | | | | | | |            (579), (580), (581), (584), (585), (586), (588),
% 171.17/25.76  | | | | | | | | | | | | | | |            (591), (593), (596), (598), (796), (3240), (3242),
% 171.17/25.76  | | | | | | | | | | | | | | |            (3435), (3436), (3438), (3439), (3440), (3441),
% 171.17/25.76  | | | | | | | | | | | | | | |            (3442), (3461), (3462), (3463), (3464), (3465),
% 171.17/25.76  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.76  | | | | | | | | | | | | | | |            #579.
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | |   (3466)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (37), (161), (163), (164), (165),
% 171.17/25.76  | | | | | | | | | | | | | | |            (172), (173), (177), (179), (181), (270), (271),
% 171.17/25.76  | | | | | | | | | | | | | | |            (280), (282), (283), (304), (328), (330), (344),
% 171.17/25.76  | | | | | | | | | | | | | | |            (349), (386), (392), (403), (429), (494), (531),
% 171.17/25.76  | | | | | | | | | | | | | | |            (533), (534), (544), (546), (548), (552), (554),
% 171.17/25.76  | | | | | | | | | | | | | | |            (562), (566), (596), (663), (796), (3433), (3435),
% 171.17/25.76  | | | | | | | | | | | | | | |            (3436), (3440), (3466), (function-axioms) are
% 171.17/25.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | |   (3467)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.76  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.76  | | | | | | | | | | | | |             e0)
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | ALPHA: (3467) implies:
% 171.17/25.76  | | | | | | | | | | | | |   (3468)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.76  | | | | | | | | | | | | |   (3469)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | |   (3470)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.76  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.76  | | | | | | | | | | | | | |            (3435), (3470), (function-axioms) are inconsistent
% 171.17/25.76  | | | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | |   (3471)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.76  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.76  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | BETA: splitting (3471) gives:
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | |   (3472)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | ALPHA: (3472) implies:
% 171.17/25.76  | | | | | | | | | | | | | | |   (3473)  all_52_22 = e0
% 171.17/25.76  | | | | | | | | | | | | | | |   (3474)  all_52_20 = e1
% 171.17/25.76  | | | | | | | | | | | | | | |   (3475)  all_52_18 = e2
% 171.17/25.76  | | | | | | | | | | | | | | |   (3476)  all_52_16 = e3
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3474) imply:
% 171.17/25.76  | | | | | | | | | | | | | | |   (3477)  all_14_1 = e1
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | SIMP: (3477) implies:
% 171.17/25.76  | | | | | | | | | | | | | | |   (3478)  all_14_1 = e1
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (62), (63),
% 171.17/25.76  | | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (169), (170),
% 171.17/25.76  | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 171.17/25.76  | | | | | | | | | | | | | | |            (182), (268), (270), (274), (275), (276), (277),
% 171.17/25.76  | | | | | | | | | | | | | | |            (278), (281), (282), (283), (304), (307), (310),
% 171.17/25.76  | | | | | | | | | | | | | | |            (311), (313), (314), (315), (319), (320), (321),
% 171.17/25.76  | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 171.17/25.76  | | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 171.17/25.76  | | | | | | | | | | | | | | |            (385), (391), (392), (403), (413), (415), (419),
% 171.17/25.76  | | | | | | | | | | | | | | |            (425), (494), (529), (530), (531), (532), (533),
% 171.17/25.76  | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 171.17/25.76  | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 171.17/25.76  | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 171.17/25.76  | | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 171.17/25.76  | | | | | | | | | | | | | | |            (569), (571), (575), (577), (578), (579), (580),
% 171.17/25.76  | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (591),
% 171.17/25.76  | | | | | | | | | | | | | | |            (593), (595), (596), (597), (598), (600), (663),
% 171.17/25.76  | | | | | | | | | | | | | | |            (796), (3239), (3240), (3242), (3433), (3435),
% 171.17/25.76  | | | | | | | | | | | | | | |            (3469), (3473), (3475), (3476), (3478),
% 171.17/25.76  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.76  | | | | | | | | | | | | | | |            #241.
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | |   (3479)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (61), (154),
% 171.17/25.76  | | | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (165), (172),
% 171.17/25.76  | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (183), (268),
% 171.17/25.76  | | | | | | | | | | | | | | |            (270), (280), (281), (282), (283), (303), (304),
% 171.17/25.76  | | | | | | | | | | | | | | |            (306), (307), (322), (324), (325), (326), (328),
% 171.17/25.76  | | | | | | | | | | | | | | |            (330), (344), (349), (364), (370), (385), (386),
% 171.17/25.76  | | | | | | | | | | | | | | |            (391), (392), (403), (413), (494), (529), (531),
% 171.17/25.76  | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (538), (539),
% 171.17/25.76  | | | | | | | | | | | | | | |            (540), (544), (546), (548), (552), (554), (555),
% 171.17/25.76  | | | | | | | | | | | | | | |            (557), (558), (559), (562), (565), (566), (567),
% 171.17/25.76  | | | | | | | | | | | | | | |            (568), (569), (578), (580), (581), (586), (591),
% 171.17/25.76  | | | | | | | | | | | | | | |            (595), (596), (597), (649), (663), (796), (797),
% 171.17/25.76  | | | | | | | | | | | | | | |            (799), (3248), (3433), (3435), (3468), (3479),
% 171.17/25.76  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.76  | | | | | | | | | | | | | | |            #534.
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | |   (3480)  all_32_1 = e2
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | COMBINE_EQS: (713), (3480) imply:
% 171.17/25.76  | | | | | | | | | | |   (3481)  all_14_1 = e2
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | SIMP: (3481) implies:
% 171.17/25.76  | | | | | | | | | | |   (3482)  all_14_1 = e2
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | COMBINE_EQS: (719), (3482) imply:
% 171.17/25.76  | | | | | | | | | | |   (3483)  all_52_20 = e2
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | REDUCE: (3244), (3482) imply:
% 171.17/25.76  | | | | | | | | | | |   (3484)   ~ (e3 = e2)
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | REDUCE: (62), (3482) imply:
% 171.17/25.76  | | | | | | | | | | |   (3485)  op(e1, all_14_2) = e2
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.76  | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | |   (3486)   ~ (all_34_0 = e1)
% 171.17/25.76  | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | REDUCE: (773), (3486) imply:
% 171.17/25.76  | | | | | | | | | | | |   (3487)   ~ (all_4_0 = e1)
% 171.17/25.76  | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.76  | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | |   (3488)   ~ (all_40_1 = e1)
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | REDUCE: (715), (3488) imply:
% 171.17/25.76  | | | | | | | | | | | | |   (3489)   ~ (all_4_1 = e1)
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.76  | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | |   (3490)  all_58_15 = e0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | COMBINE_EQS: (532), (3490) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3491)  all_6_2 = e0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (597), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3492)   ~ (all_52_7 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (600), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3493)   ~ (all_52_23 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (564), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3494)   ~ (all_52_25 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (582), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3495)   ~ (all_52_27 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (594), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3496)   ~ (all_52_29 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (43), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3497)  op(all_6_1, e0) = all_6_0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (42), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3498)  op(e0, e0) = all_6_1
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (41), (3491) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3499)  op(e0, e0) = e0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.76  | | | | | | | | | | | | | |              e0, e0, simplifying with (3498), (3499) gives:
% 171.17/25.76  | | | | | | | | | | | | | |   (3500)  all_6_1 = e0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (3497), (3500) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3501)  op(e0, e0) = all_6_0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.76  | | | | | | | | | | | | | |              e0, e0, simplifying with (3499), (3501) gives:
% 171.17/25.76  | | | | | | | | | | | | | |   (3502)  all_6_0 = e0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (3248), (3502) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3503)   ~ (e3 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (797), (3502) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3504)   ~ (e1 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | |   (3505)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.76  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (37), (38), (52), (154), (155), (156),
% 171.17/25.76  | | | | | | | | | | | | | | |            (160), (178), (179), (270), (271), (280), (283),
% 171.17/25.76  | | | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (323),
% 171.17/25.76  | | | | | | | | | | | | | | |            (326), (330), (331), (344), (349), (370), (386),
% 171.17/25.76  | | | | | | | | | | | | | | |            (391), (403), (429), (531), (532), (533), (534),
% 171.17/25.76  | | | | | | | | | | | | | | |            (535), (536), (540), (546), (552), (562), (569),
% 171.17/25.76  | | | | | | | | | | | | | | |            (585), (586), (595), (596), (597), (661), (720),
% 171.17/25.76  | | | | | | | | | | | | | | |            (3239), (3490), (3492), (3494), (3495), (3496),
% 171.17/25.76  | | | | | | | | | | | | | | |            (3505), (function-axioms) are inconsistent by
% 171.17/25.76  | | | | | | | | | | | | | | |            sub-proof #240.
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | |   (3506)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.76  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.76  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | BETA: splitting (3506) gives:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3507)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3483), (3507) are inconsistent by sub-proof
% 171.17/25.76  | | | | | | | | | | | | | | | |            #553.
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3508)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | | ALPHA: (3508) implies:
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3509)  all_52_28 = e1
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3510)  all_52_26 = e2
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3511)  all_52_24 = e3
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | | REDUCE: (181), (3511) imply:
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3512)  op(e3, all_52_25) = e3
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | | REDUCE: (173), (3510) imply:
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3513)  op(e2, all_52_27) = e2
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | | REDUCE: (165), (3509) imply:
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3514)  op(e1, all_52_29) = e1
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (161), (163), (164),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (170), (172), (177), (178), (179), (182), (183),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (275), (278),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (280), (283), (302), (304), (305), (310), (311),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (313), (322), (324), (330), (341), (344), (349),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (350), (359), (364), (365), (373), (385), (386),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (391), (403), (429), (530), (531), (533), (534),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (546), (550), (552), (553), (554), (555), (558),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (560), (561), (562), (563), (566), (567), (569),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (571), (573), (580), (581), (584), (585), (586),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (587), (591), (593), (596), (3485), (3489),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (3490), (3492), (3493), (3494), (3496), (3512),
% 171.17/25.76  | | | | | | | | | | | | | | | |            (3513), (3514), (function-axioms) are inconsistent
% 171.17/25.76  | | | | | | | | | | | | | | | |            by sub-proof #549.
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | End of split
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | Case 2:
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | |   (3515)   ~ (all_58_15 = e0)
% 171.17/25.76  | | | | | | | | | | | | | |   (3516)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.76  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.76  | | | | | | | | | | | | | |             e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | ALPHA: (3516) implies:
% 171.17/25.76  | | | | | | | | | | | | | |   (3517)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.76  | | | | | | | | | | | | | |   (3518)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | REDUCE: (532), (3515) imply:
% 171.17/25.76  | | | | | | | | | | | | | |   (3519)   ~ (all_6_2 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.76  | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | |   (3520)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.76  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | BETA: splitting (3520) gives:
% 171.17/25.76  | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | |   (3521)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.76  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.76  | | | | | | | | | | | | | | | | 
% 171.17/25.76  | | | | | | | | | | | | | | | | ALPHA: (3521) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3522)  all_52_6 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3523)  all_52_4 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3524)  all_52_2 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3525)  all_52_0 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (3525) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3526)  all_4_1 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | REDUCE: (38), (3526) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3527)  op(e3, all_4_2) = all_4_0
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | REDUCE: (37), (3526) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3528)  op(e3, all_4_2) = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | REDUCE: (176), (3524) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3529)  op(e2, all_52_3) = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | REDUCE: (168), (3523) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3530)  op(e1, all_52_5) = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | REDUCE: (160), (3522) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3531)  op(e0, all_52_7) = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 171.17/25.77  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (3527), (3528)
% 171.17/25.77  | | | | | | | | | | | | | | | |              gives:
% 171.17/25.77  | | | | | | | | | | | | | | | |   (3532)  all_4_0 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3533)  all_56_15 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (3533) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3534)  all_6_2 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | SIMP: (3534) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3535)  all_6_2 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3536)  all_58_15 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (597), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3537)   ~ (all_52_7 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (599), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3538)   ~ (all_52_15 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (600), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3539)   ~ (all_52_23 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (564), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3540)   ~ (all_52_25 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (582), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3541)   ~ (all_52_27 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (594), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3542)   ~ (all_52_29 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (43), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3543)  op(all_6_1, e3) = all_6_0
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (42), (3535) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3544)  op(e0, e3) = all_6_1
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 171.17/25.77  | | | | | | | | | | | | | | | | |              all_6_1, e3, e0, simplifying with (156), (3544)
% 171.17/25.77  | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3545)  all_52_25 = all_6_1
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (3545) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3546)  all_56_12 = all_6_1
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (3545) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3547)  all_58_12 = all_6_1
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (554), (3545) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3548)   ~ (all_52_9 = all_6_1)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (558), (3545) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3549)   ~ (all_52_17 = all_6_1)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (546), (3545) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3550)   ~ (all_6_1 = all_4_2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (3540), (3545) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3551)   ~ (all_6_1 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | REDUCE: (181), (3545) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | |   (3552)  op(e3, all_6_1) = all_52_24
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | |   (3553)  all_56_13 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (344), (3541), (3553) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | |            sub-proof #876.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | |   (3554)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | |   (3555)  all_56_3 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (3537), (3555) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | |   (3556)   ~ (all_56_3 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | |   (3557)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | |   (3558)  all_56_12 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3546), (3551), (3558) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | |            sub-proof #509.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | |   (3559)   ~ (all_56_12 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | |   (3560)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3561)  all_58_12 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3547), (3561) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3562)  all_6_1 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | SIMP: (3562) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3563)  all_6_1 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3548), (3563) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3564)   ~ (all_52_9 = e1)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3549), (3563) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3565)   ~ (all_52_17 = e1)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3551), (3563) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3566)   ~ (e3 = e1)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3543), (3563) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3567)  op(e1, e3) = all_6_0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |              all_6_0, e3, e1, simplifying with (164), (3567)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3568)  all_52_17 = all_6_0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (3568) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3569)  all_56_8 = all_6_0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (3568) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3570)  all_58_6 = all_6_0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (3568) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3571)   ~ (all_52_9 = all_6_0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (3568) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3572)   ~ (all_52_23 = all_6_0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | SIMP: (3572) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3573)   ~ (all_52_23 = all_6_0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (3568) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | |   (3574)  op(e3, all_6_0) = all_52_16
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | |   (3575)  all_56_8 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3248), (3569), (3575) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #416.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | |   (3576)   ~ (all_56_8 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | |   (3577)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3577) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | |   (3578)  all_56_8 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (799), (3569), (3578) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #415.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | |   (3579)   ~ (all_56_8 = e2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | |   (3580)  all_56_8 = e1 | all_56_8 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3580) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3581)  all_56_8 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (797), (3569), (3581) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #414.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3582)  all_56_8 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3569), (3582) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3583)  all_6_0 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3583) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3584)  all_6_0 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3570), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3585)  all_58_6 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3571), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3586)   ~ (all_52_9 = e0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3573), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3587)   ~ (all_52_23 = e0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3248), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3588)   ~ (e3 = e0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (799), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3589)   ~ (e2 = e0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (797), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3590)   ~ (e1 = e0)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3574), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3591)  op(e3, e0) = all_52_16
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3567), (3584) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3592)  op(e1, e3) = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_16, e0, e3, simplifying with (177), (3591)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3593)  all_52_7 = all_52_16
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (3593) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3594)  all_58_9 = all_52_16
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (3593) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3595)   ~ (all_52_16 = all_52_23)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3537), (3593) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | |   (3596)   ~ (all_52_16 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (3597)  all_56_4 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (3597) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (3598)  all_52_9 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (164), (172), (177), (178), (179), (273),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (311), (315), (324), (326), (331),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (403), (531),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (532), (533), (535), (536), (537), (538), (540),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (550), (552), (560), (566),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (583), (584), (585), (586), (587),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (3528), (3529),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            (3530), (3531), (3542), (3598), (function-axioms)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #413.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (3599)   ~ (all_56_4 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (3600)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (409), (3599) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (3601)   ~ (all_52_9 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3600) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3602)  all_56_4 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (3602) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3603)  all_52_9 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3603) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3604)  all_52_9 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (3604) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3605)   ~ (all_52_15 = e2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3605) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3606)   ~ (all_52_15 = e2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3607)  all_58_6 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3585), (3607) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3608)  e3 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3608) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3609)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3609) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3610)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3611)  all_58_9 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3594), (3611) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3612)  all_52_16 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3612) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3613)  all_52_16 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3595), (3613) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3614)   ~ (all_52_23 = e2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3614) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3615)   ~ (all_52_23 = e2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3616)  all_56_10 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (359), (3485), (3592), (3616),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #239.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3617)   ~ (all_56_10 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (3617) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3618)   ~ (all_14_2 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3619)  all_58_6 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3585), (3619) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3620)  e2 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3620) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3621)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3621) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3622)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3610) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3623)  all_58_7 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (3623) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3624)  all_52_19 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (3624) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3625)   ~ (all_14_2 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (3624) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3626)  op(e1, e2) = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3622) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3627)  all_58_7 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3623), (3627) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3628)  e3 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3628) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3629)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3629) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3630)  all_58_8 = e2 | all_58_11 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3630) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3631)  all_58_8 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (3631) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3632)  all_14_2 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3632) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3633)  all_14_2 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3485), (3633) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3634)  op(e1, e2) = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e2,
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (3626), (3634) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3635)  e3 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3635) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3636)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3636) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3637)  all_58_11 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (3615), (3637) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #935.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3638)  all_58_8 = e3 | all_58_11 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (537), (3539), (3618), (3638) are
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #997.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3639)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3639) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3640)  all_58_10 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (3606), (3640) are inconsistent by
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #711.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3641)  all_58_11 = e2 | all_58_15 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3641) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3642)  all_58_11 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (3642) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3643)  all_52_23 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3643) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3644)  all_52_23 = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (3644) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3645)   ~ (all_14_2 = e2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3645) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3646)   ~ (all_14_2 = e2)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3647)  all_56_10 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (359), (3485), (3592), (3647),
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #239.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3648)   ~ (all_56_10 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (3648) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3649)   ~ (all_14_2 = e3)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3610) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3650)  all_58_7 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (3650) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3651)  all_52_19 = e3
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3652)  all_58_6 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3585), (3652) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3653)  e1 = e0
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (3653) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3654)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3654) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3655)  all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3655) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3656)  all_58_7 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3650), (3656) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3657)  e3 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (3657) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3658)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3658) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3659)  all_58_8 = e1 | all_58_11 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3659) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3660)  all_58_8 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (3660) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3661)  all_14_2 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3661) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3662)  all_14_2 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3646), (3662) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3663)   ~ (e2 = e1)
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3485), (3662) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3664)  op(e1, e1) = e2
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (3662) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3665)  op(e1, e1) = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e1,
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (3664), (3665) gives:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3666)  e2 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3666) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3667)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3667) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3668)  all_58_11 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3668) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3669)  e2 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3669) implies:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3670)  e2 = e1
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3670) imply:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3671)  $false
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3671) is inconsistent.
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3672)  all_58_8 = e3 | all_58_11 = e3
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (537), (3539), (3649), (3672) are
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #997.
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3673)  all_58_15 = e2
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3536), (3673) are inconsistent by sub-proof
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #286.
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3674)   ~ (all_56_4 = e2)
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (409), (3674) imply:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3675)   ~ (all_52_9 = e2)
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (156), (164), (172), (177), (178),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (179), (273), (283), (307), (311), (315), (324),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (326), (328), (330), (331), (359), (364), (370),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (531), (532), (533),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (540), (542), (544),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (546), (550), (552), (560), (566), (568), (569),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (591), (593),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (3528), (3529), (3530),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3531), (3542), (3561), (3585), (3675),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            #410.
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | |   (3676)   ~ (all_58_12 = e1)
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3547), (3676) imply:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | |   (3677)   ~ (all_6_1 = e1)
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |   (3678)  all_58_4 = e3
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (3678) imply:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |   (3679)  all_52_5 = e3
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3679) implies:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |   (3680)  all_52_5 = e3
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (164), (172), (177), (178), (179), (273),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (311), (315), (324), (326), (331),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (391), (403), (531),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            (532), (533), (535), (536), (537), (538), (540),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (550), (552), (560), (566),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (583), (584), (585), (586), (587),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (595), (596), (597), (3528), (3529),
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            (3530), (3531), (3680), (function-axioms) are
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |   (3681)   ~ (all_58_4 = e3)
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |   (3682)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (3681) imply:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | |   (3683)   ~ (all_52_5 = e3)
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.80  | | | | | | | | | | | | | | | | | | | | | | |   (3684)  all_58_0 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (3684) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |   (3685)  all_4_2 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (3685) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |   (3686)   ~ (all_52_9 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (3685) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |   (3687)   ~ (all_52_17 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | |   (3688)  all_58_2 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (385), (3686), (3688) are inconsistent by
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #980.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | |   (3689)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (3690)  all_58_0 = e1
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3684), (3690) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (3691)  e3 = e1
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (3691) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (3692)  $false
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3692) is inconsistent.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (3693)   ~ (all_58_0 = e1)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (3694)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3695)  all_58_6 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (3687), (3695) are inconsistent by
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3696)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3697)  all_56_2 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (3683), (3697) are inconsistent by
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3698)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3699)  all_56_6 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (3699) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3700)  all_52_13 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3700) implies:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3701)  all_52_13 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (3701) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3702)  all_58_5 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (3701) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3703)   ~ (all_52_29 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (3701) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3704)   ~ (all_14_2 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3704) implies:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3705)   ~ (all_14_2 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (3701) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3706)  op(e2, e1) = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3696) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3707)  all_58_7 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (3707) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3708)  all_52_19 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (3708) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3709)   ~ (all_52_3 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (3708) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3710)   ~ (all_52_23 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (3708) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3711)   ~ (all_52_27 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (3708) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3712)   ~ (all_10_2 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3712) implies:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3713)   ~ (all_10_2 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (3708) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3714)  op(e2, e3) = all_52_18
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (3708) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3715)  op(e1, e2) = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_18, e3, e2, simplifying with (172), (3714)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3716)  all_52_9 = all_52_18
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (3716) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3717)  all_56_4 = all_52_18
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (3716) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3718)  all_58_2 = all_52_18
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (3716) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3719)   ~ (all_52_17 = all_52_18)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3719) implies:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3720)   ~ (all_52_17 = all_52_18)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (3716) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3721)   ~ (all_52_18 = all_10_2)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3548), (3716) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3722)   ~ (all_52_18 = all_6_1)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3686), (3716) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3723)   ~ (all_52_18 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (51), (52), (61), (154),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (177), (178), (179), (182), (275), (279),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (302), (303), (305), (306), (309), (310),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (312), (313), (314), (318), (321), (322), (326),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (327), (328), (329), (344), (365), (370), (386),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (392), (413), (533), (534), (536), (537),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (560), (561), (565), (567),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (573), (581), (584), (585), (595),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (596), (797), (3239), (3517), (3529), (3530),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3531), (3536), (3537), (3539), (3541), (3542),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3543), (3547), (3549), (3551), (3552), (3554),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3557), (3684), (3687), (3698), (3702), (3706),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3707), (3709), (3713), (3714), (3715), (3717),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3718), (3720), (3721), (3722), (3723),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #257.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3724)  all_58_8 = e3 | all_58_11 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (537), (3539), (3705), (3724) are
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #997.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3725)   ~ (all_56_6 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (3725) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3726)   ~ (all_52_13 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3689) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3727)  all_58_3 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (3727) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3728)  all_10_2 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3239), (3728) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3729)  op(all_10_1, e3) = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (3728) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3730)  op(e2, e3) = all_10_1
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3682) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3731)  all_58_5 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (373), (3726), (3731) are inconsistent by
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #969.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3732)  all_58_8 = e3 | all_58_14 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3732) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3733)  all_58_8 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (3733) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3734)  all_14_2 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3485), (3734) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3735)  op(e1, e3) = e2
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (172), (385), (538), (3546), (3547),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3549), (3560), (3677), (3687), (3694), (3729),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3730), (3735), (function-axioms) are inconsistent
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #238.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3736)  all_58_14 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (3542), (3736) are inconsistent by
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1000.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3737)  all_58_5 = e3 | all_58_10 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (373), (3538), (3726), (3737) are
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |   (3738)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (172), (177), (178), (179), (283), (307),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |            (326), (370), (391), (403), (531), (532), (535),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |            (536), (540), (542), (546), (548), (552), (568),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |            (569), (586), (595), (596), (597), (3528), (3529),
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |            (3531), (3683), (3738), (function-axioms) are
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #787.
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | |   (3739)   ~ (all_56_15 = e3)
% 171.17/25.81  | | | | | | | | | | | | | | | | |   (3740)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (158),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (169), (170),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (269), (270),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (283), (304), (305), (307), (310), (311), (312),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (3518), (3519),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (3528), (3529), (3530), (3531), (3739), (3740),
% 171.17/25.81  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.81  | | | | | | | | | | | | | | | | |            #785.
% 171.17/25.81  | | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3741)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.81  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | ALPHA: (3741) implies:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3742)  all_52_10 = e2
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (3742) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3743)  all_10_1 = e2
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (3743), (function-axioms) are
% 171.17/25.81  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | |   (3744)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.81  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.81  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.81  | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | BETA: splitting (3744) gives:
% 171.17/25.81  | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3745)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.81  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3483), (3745) are inconsistent by sub-proof
% 171.17/25.81  | | | | | | | | | | | | | | | |            #553.
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3746)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.81  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | ALPHA: (3746) implies:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3747)  all_52_30 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3748)  all_52_28 = e1
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3749)  all_52_26 = e2
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3750)  all_52_24 = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (3747) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3751)  all_6_1 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | SIMP: (3751) implies:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3752)  all_6_1 = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REDUCE: (43), (3752) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3753)  op(e0, all_6_2) = all_6_0
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REDUCE: (181), (3750) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3754)  op(e3, all_52_25) = e3
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REDUCE: (173), (3749) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3755)  op(e2, all_52_27) = e2
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REDUCE: (165), (3748) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3756)  op(e1, all_52_29) = e1
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REDUCE: (42), (3752) imply:
% 171.17/25.81  | | | | | | | | | | | | | | | |   (3757)  op(e0, all_6_2) = e0
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (154), (155),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (156), (161), (164), (172), (177), (178), (179),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (182), (183), (268), (269), (270), (271), (272),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (276), (281), (283), (303), (304), (305), (306),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (364),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (370), (373), (385), (391), (403), (413), (425),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (429), (529), (531), (532), (533), (534), (535),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (563), (564), (566), (567), (568), (569), (571),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (573), (577), (578), (580), (581), (582), (585),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (594), (595), (596),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (597), (600), (797), (799), (3246), (3248),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (3487), (3517), (3518), (3519), (3753), (3754),
% 171.17/25.81  | | | | | | | | | | | | | | | |            (3755), (3756), (3757), (function-axioms) are
% 171.17/25.81  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #636.
% 171.17/25.81  | | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | | 
% 171.17/25.81  | | | | | | | | | | | | | | End of split
% 171.17/25.81  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | |   (3758)  all_40_1 = e1
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | COMBINE_EQS: (715), (3758) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3759)  all_4_1 = e1
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | COMBINE_EQS: (720), (3759) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3760)  all_52_0 = e1
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (796), (3759) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3761)   ~ (e2 = e1)
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (38), (3759) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3762)  op(e1, all_4_2) = all_4_0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (37), (3759) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3763)  op(e3, all_4_2) = e1
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | |   (3764)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.82  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (661), (3239), (3760), (3764),
% 171.17/25.82  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.82  | | | | | | | | | | | | | |            #247.
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | |   (3765)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.82  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.82  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | BETA: splitting (3765) gives:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | |   (3766)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REF_CLOSE: (6), (3483), (3766) are inconsistent by sub-proof
% 171.17/25.82  | | | | | | | | | | | | | | |            #539.
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | |   (3767)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | ALPHA: (3767) implies:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3768)  all_52_30 = e0
% 171.17/25.82  | | | | | | | | | | | | | | |   (3769)  all_52_28 = e1
% 171.17/25.82  | | | | | | | | | | | | | | |   (3770)  all_52_26 = e2
% 171.17/25.82  | | | | | | | | | | | | | | |   (3771)  all_52_24 = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | COMBINE_EQS: (649), (3768) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3772)  all_6_1 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (43), (3772) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3773)  op(e0, all_6_2) = all_6_0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (181), (3771) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3774)  op(e3, all_52_25) = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (173), (3770) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3775)  op(e2, all_52_27) = e2
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (165), (3769) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3776)  op(e1, all_52_29) = e1
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (42), (3772) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3777)  op(e0, all_6_2) = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (154), (155),
% 171.17/25.82  | | | | | | | | | | | | | | |            (156), (161), (163), (164), (170), (172), (177),
% 171.17/25.82  | | | | | | | | | | | | | | |            (178), (179), (182), (183), (268), (269), (270),
% 171.17/25.82  | | | | | | | | | | | | | | |            (271), (272), (273), (280), (283), (301), (302),
% 171.17/25.82  | | | | | | | | | | | | | | |            (304), (305), (307), (310), (311), (313), (319),
% 171.17/25.82  | | | | | | | | | | | | | | |            (321), (323), (324), (325), (326), (327), (328),
% 171.17/25.82  | | | | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 171.17/25.82  | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (403),
% 171.17/25.82  | | | | | | | | | | | | | | |            (429), (529), (531), (532), (533), (534), (535),
% 171.17/25.82  | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 171.17/25.82  | | | | | | | | | | | | | | |            (546), (550), (552), (553), (554), (555), (557),
% 171.17/25.82  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.82  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 171.17/25.82  | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 171.17/25.82  | | | | | | | | | | | | | | |            (587), (588), (589), (591), (594), (596), (597),
% 171.17/25.82  | | | | | | | | | | | | | | |            (797), (3246), (3248), (3485), (3487), (3762),
% 171.17/25.82  | | | | | | | | | | | | | | |            (3763), (3773), (3774), (3775), (3776), (3777),
% 171.17/25.82  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.82  | | | | | | | | | | | | | | |            #537.
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | |   (3778)  all_34_0 = e1
% 171.17/25.82  | | | | | | | | | | | |   (3779)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | COMBINE_EQS: (773), (3778) imply:
% 171.17/25.82  | | | | | | | | | | | |   (3780)  all_4_0 = e1
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | SIMP: (3780) implies:
% 171.17/25.82  | | | | | | | | | | | |   (3781)  all_4_0 = e1
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | REDUCE: (3246), (3781) imply:
% 171.17/25.82  | | | | | | | | | | | |   (3782)   ~ (e2 = e1)
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | REDUCE: (38), (3781) imply:
% 171.17/25.82  | | | | | | | | | | | |   (3783)  op(all_4_1, all_4_2) = e1
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | |   (3784)  all_58_15 = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | COMBINE_EQS: (532), (3784) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3785)  all_6_2 = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (564), (3785) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3786)   ~ (all_52_25 = e0)
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (43), (3785) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3787)  op(all_6_1, e0) = all_6_0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (42), (3785) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3788)  op(e0, e0) = all_6_1
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (41), (3785) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3789)  op(e0, e0) = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.82  | | | | | | | | | | | | |              e0, e0, simplifying with (3788), (3789) gives:
% 171.17/25.82  | | | | | | | | | | | | |   (3790)  all_6_1 = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (3787), (3790) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3791)  op(e0, e0) = all_6_0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.82  | | | | | | | | | | | | |              e0, e0, simplifying with (3789), (3791) gives:
% 171.17/25.82  | | | | | | | | | | | | |   (3792)  all_6_0 = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (3248), (3792) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3793)   ~ (e3 = e0)
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | |   (3794)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.82  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.82  | | | | | | | | | | | | | |            (3783), (3794), (function-axioms) are inconsistent
% 171.17/25.82  | | | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | |   (3795)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.82  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.82  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | BETA: splitting (3795) gives:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | |   (3796)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REF_CLOSE: (6), (3483), (3796) are inconsistent by sub-proof
% 171.17/25.82  | | | | | | | | | | | | | | |            #539.
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | |   (3797)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | ALPHA: (3797) implies:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3798)  all_52_28 = e1
% 171.17/25.82  | | | | | | | | | | | | | | |   (3799)  all_52_26 = e2
% 171.17/25.82  | | | | | | | | | | | | | | |   (3800)  all_52_24 = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (181), (3800) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3801)  op(e3, all_52_25) = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (173), (3799) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3802)  op(e2, all_52_27) = e2
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (165), (3798) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3803)  op(e1, all_52_29) = e1
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (37), (161), (163), (164), (172),
% 171.17/25.82  | | | | | | | | | | | | | | |            (177), (179), (270), (271), (280), (282), (283),
% 171.17/25.82  | | | | | | | | | | | | | | |            (304), (328), (330), (344), (349), (386), (392),
% 171.17/25.82  | | | | | | | | | | | | | | |            (403), (429), (494), (531), (533), (534), (544),
% 171.17/25.82  | | | | | | | | | | | | | | |            (546), (548), (552), (554), (562), (566), (596),
% 171.17/25.82  | | | | | | | | | | | | | | |            (663), (796), (3779), (3783), (3784), (3786),
% 171.17/25.82  | | | | | | | | | | | | | | |            (3801), (3802), (3803), (function-axioms) are
% 171.17/25.82  | | | | | | | | | | | | | | |            inconsistent by sub-proof #577.
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | |   (3804)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.82  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.82  | | | | | | | | | | | | |             e0)
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | ALPHA: (3804) implies:
% 171.17/25.82  | | | | | | | | | | | | |   (3805)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | |   (3806)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.82  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.82  | | | | | | | | | | | | | |            (3783), (3806), (function-axioms) are inconsistent
% 171.17/25.82  | | | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | |   (3807)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.82  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.82  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | BETA: splitting (3807) gives:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | |   (3808)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REF_CLOSE: (6), (3483), (3808) are inconsistent by sub-proof
% 171.17/25.82  | | | | | | | | | | | | | | |            #539.
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | |   (3809)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | ALPHA: (3809) implies:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3810)  all_52_30 = e0
% 171.17/25.82  | | | | | | | | | | | | | | |   (3811)  all_52_28 = e1
% 171.17/25.82  | | | | | | | | | | | | | | |   (3812)  all_52_26 = e2
% 171.17/25.82  | | | | | | | | | | | | | | |   (3813)  all_52_24 = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | COMBINE_EQS: (649), (3810) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3814)  all_6_1 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (43), (3814) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3815)  op(e0, all_6_2) = all_6_0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (181), (3813) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3816)  op(e3, all_52_25) = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (173), (3812) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3817)  op(e2, all_52_27) = e2
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (165), (3811) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3818)  op(e1, all_52_29) = e1
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (42), (3814) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3819)  op(e0, all_6_2) = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (61), (154), (155), (156),
% 171.17/25.82  | | | | | | | | | | | | | | |            (161), (163), (164), (172), (177), (178), (179),
% 171.17/25.82  | | | | | | | | | | | | | | |            (183), (268), (270), (280), (281), (282), (283),
% 171.17/25.82  | | | | | | | | | | | | | | |            (303), (304), (306), (307), (322), (324), (325),
% 171.17/25.82  | | | | | | | | | | | | | | |            (326), (328), (330), (344), (349), (364), (370),
% 171.17/25.82  | | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (413), (494),
% 171.17/25.82  | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 171.17/25.82  | | | | | | | | | | | | | | |            (538), (539), (540), (544), (546), (548), (552),
% 171.17/25.82  | | | | | | | | | | | | | | |            (554), (555), (557), (558), (559), (562), (565),
% 171.17/25.82  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (578), (580), (581),
% 171.17/25.82  | | | | | | | | | | | | | | |            (586), (591), (595), (596), (597), (663), (796),
% 171.17/25.82  | | | | | | | | | | | | | | |            (797), (799), (3248), (3779), (3783), (3805),
% 171.17/25.82  | | | | | | | | | | | | | | |            (3815), (3816), (3817), (3818), (3819),
% 171.17/25.82  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.82  | | | | | | | | | | | | | | |            #556.
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | End of split
% 171.17/25.82  | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | |   (3820)  all_28_0 = e3
% 171.17/25.82  | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | COMBINE_EQS: (776), (3820) imply:
% 171.17/25.82  | | | | | | | | | |   (3821)  all_6_0 = e3
% 171.17/25.82  | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | REDUCE: (43), (3821) imply:
% 171.17/25.82  | | | | | | | | | |   (3822)  op(all_6_1, all_6_2) = e3
% 171.17/25.82  | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.82  | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | |   (3823)   ~ (all_34_0 = e1)
% 171.17/25.82  | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | REDUCE: (773), (3823) imply:
% 171.17/25.82  | | | | | | | | | | |   (3824)   ~ (all_4_0 = e1)
% 171.17/25.82  | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.82  | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | |   (3825)   ~ (all_40_1 = e1)
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | REDUCE: (715), (3825) imply:
% 171.17/25.82  | | | | | | | | | | | |   (3826)   ~ (all_4_1 = e1)
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.82  | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | |   (3827)  all_58_15 = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (3822), (3827),
% 171.17/25.82  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.82  | | | | | | | | | | | | |            #510.
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | Case 2:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | |   (3828)   ~ (all_58_15 = e0)
% 171.17/25.82  | | | | | | | | | | | | |   (3829)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.82  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.82  | | | | | | | | | | | | |             e0)
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | ALPHA: (3829) implies:
% 171.17/25.82  | | | | | | | | | | | | |   (3830)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.82  | | | | | | | | | | | | |   (3831)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | REDUCE: (532), (3828) imply:
% 171.17/25.82  | | | | | | | | | | | | |   (3832)   ~ (all_6_2 = e0)
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.82  | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | |   (3833)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.82  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | BETA: splitting (3833) gives:
% 171.17/25.82  | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | Case 1:
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | |   (3834)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.82  | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | ALPHA: (3834) implies:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3835)  all_52_6 = e0
% 171.17/25.82  | | | | | | | | | | | | | | |   (3836)  all_52_4 = e1
% 171.17/25.82  | | | | | | | | | | | | | | |   (3837)  all_52_2 = e2
% 171.17/25.82  | | | | | | | | | | | | | | |   (3838)  all_52_0 = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (3838) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3839)  all_4_1 = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (38), (3839) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3840)  op(e3, all_4_2) = all_4_0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (37), (3839) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3841)  op(e3, all_4_2) = e3
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (176), (3837) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3842)  op(e2, all_52_3) = e2
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (168), (3836) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3843)  op(e1, all_52_5) = e1
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.82  | | | | | | | | | | | | | | | REDUCE: (160), (3835) imply:
% 171.17/25.82  | | | | | | | | | | | | | | |   (3844)  op(e0, all_52_7) = e0
% 171.17/25.82  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (61), (154), (156), (158), (159),
% 171.17/25.83  | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (170), (172),
% 171.17/25.83  | | | | | | | | | | | | | | |            (173), (177), (178), (179), (268), (269), (270),
% 171.17/25.83  | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 171.17/25.83  | | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (307), (310),
% 171.17/25.83  | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (317), (319),
% 171.17/25.83  | | | | | | | | | | | | | | |            (323), (324), (326), (327), (328), (330), (331),
% 171.17/25.83  | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 171.17/25.83  | | | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (413),
% 171.17/25.83  | | | | | | | | | | | | | | |            (425), (429), (529), (531), (532), (533), (534),
% 171.17/25.83  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 171.17/25.83  | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 171.17/25.83  | | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 171.17/25.83  | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 171.17/25.83  | | | | | | | | | | | | | | |            (575), (578), (579), (580), (581), (582), (583),
% 171.17/25.83  | | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (589), (591),
% 171.17/25.83  | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 171.17/25.83  | | | | | | | | | | | | | | |            (600), (3246), (3822), (3824), (3831), (3832),
% 171.17/25.83  | | | | | | | | | | | | | | |            (3840), (3841), (3842), (3843), (3844),
% 171.17/25.83  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.83  | | | | | | | | | | | | | | |            #496.
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | |   (3845)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.83  | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | ALPHA: (3845) implies:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3846)  all_52_10 = e2
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | COMBINE_EQS: (661), (3846) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3847)  all_10_1 = e2
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (3847), (function-axioms) are
% 171.17/25.83  | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | |   (3848)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.83  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.83  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | BETA: splitting (3848) gives:
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | Case 1:
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | |   (3849)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.83  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | ALPHA: (3849) implies:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3850)  all_52_22 = e0
% 171.17/25.83  | | | | | | | | | | | | | | |   (3851)  all_52_20 = e1
% 171.17/25.83  | | | | | | | | | | | | | | |   (3852)  all_52_18 = e2
% 171.17/25.83  | | | | | | | | | | | | | | |   (3853)  all_52_16 = e3
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3851) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3854)  all_14_1 = e1
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (63), (3854) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3855)  op(e1, all_14_2) = all_14_0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (182), (3853) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3856)  op(e3, all_52_17) = e3
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (174), (3852) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3857)  op(e2, all_52_19) = e2
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (62), (3854) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3858)  op(e1, all_14_2) = e1
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (158), (3850) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3859)  op(e0, all_52_23) = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 171.17/25.83  | | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (3855), (3858)
% 171.17/25.83  | | | | | | | | | | | | | | |              gives:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3860)  all_14_0 = e1
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (3242), (3860) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3861)   ~ (e3 = e1)
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (3240), (3860) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3862)   ~ (e2 = e1)
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.83  | | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | |   (3863)  all_56_15 = e3
% 171.17/25.83  | | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (42), (156), (164), (172), (178),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (271), (274), (302), (303), (311), (319), (330),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (349), (364), (385), (403), (419), (429), (529),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (535), (537), (538), (544), (546), (553), (564),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (584), (600), (3822), (3856), (3857), (3858),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (3863), (function-axioms) are inconsistent by
% 171.17/25.83  | | | | | | | | | | | | | | | |            sub-proof #504.
% 171.17/25.83  | | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | |   (3864)   ~ (all_56_15 = e3)
% 171.17/25.83  | | | | | | | | | | | | | | | |   (3865)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | | REDUCE: (529), (3864) imply:
% 171.17/25.83  | | | | | | | | | | | | | | | |   (3866)   ~ (all_6_2 = e3)
% 171.17/25.83  | | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (52), (156), (161), (163), (164), (165), (169),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (183), (270), (271), (273), (274), (275), (276),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (278), (281), (282), (283), (304), (307), (308),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (319),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (326), (328),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (359), (364),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (392), (403),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (413), (419), (425), (429), (529), (530), (531),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (575), (577),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (585), (586), (588), (591), (593), (595), (597),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (598), (600), (796), (3239), (3246), (3824),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (3826), (3830), (3831), (3832), (3856), (3857),
% 171.17/25.83  | | | | | | | | | | | | | | | |            (3858), (3859), (3865), (3866), (function-axioms)
% 171.17/25.83  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #249.
% 171.17/25.83  | | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | |   (3867)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.83  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | ALPHA: (3867) implies:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3868)  all_52_30 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | COMBINE_EQS: (649), (3868) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3869)  all_6_1 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (3822), (3869), (function-axioms) are
% 171.17/25.83  | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | |   (3870)  all_40_1 = e1
% 171.17/25.83  | | | | | | | | | | | |   (3871)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | COMBINE_EQS: (715), (3870) imply:
% 171.17/25.83  | | | | | | | | | | | |   (3872)  all_4_1 = e1
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | SIMP: (3872) implies:
% 171.17/25.83  | | | | | | | | | | | |   (3873)  all_4_1 = e1
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | COMBINE_EQS: (720), (3873) imply:
% 171.17/25.83  | | | | | | | | | | | |   (3874)  all_52_0 = e1
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | REDUCE: (38), (3873) imply:
% 171.17/25.83  | | | | | | | | | | | |   (3875)  op(e1, all_4_2) = all_4_0
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | REDUCE: (37), (3873) imply:
% 171.17/25.83  | | | | | | | | | | | |   (3876)  op(e3, all_4_2) = e1
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | Case 1:
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | |   (3877)  all_58_15 = e0
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (3822), (3877),
% 171.17/25.83  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.83  | | | | | | | | | | | | |            #510.
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | |   (3878)   ~ (all_58_15 = e0)
% 171.17/25.83  | | | | | | | | | | | | |   (3879)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.83  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.83  | | | | | | | | | | | | |             e0)
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | ALPHA: (3879) implies:
% 171.17/25.83  | | | | | | | | | | | | |   (3880)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.83  | | | | | | | | | | | | |   (3881)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | REDUCE: (532), (3878) imply:
% 171.17/25.83  | | | | | | | | | | | | |   (3882)   ~ (all_6_2 = e0)
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | Case 1:
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | |   (3883)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.83  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.83  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (661), (3239), (3874), (3883),
% 171.17/25.83  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.83  | | | | | | | | | | | | | |            #247.
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | |   (3884)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.83  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.83  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | BETA: splitting (3884) gives:
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | Case 1:
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | |   (3885)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.83  | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | ALPHA: (3885) implies:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3886)  all_52_22 = e0
% 171.17/25.83  | | | | | | | | | | | | | | |   (3887)  all_52_20 = e1
% 171.17/25.83  | | | | | | | | | | | | | | |   (3888)  all_52_18 = e2
% 171.17/25.83  | | | | | | | | | | | | | | |   (3889)  all_52_16 = e3
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (3887) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3890)  all_14_1 = e1
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (63), (3890) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3891)  op(e1, all_14_2) = all_14_0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (182), (3889) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3892)  op(e3, all_52_17) = e3
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (174), (3888) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3893)  op(e2, all_52_19) = e2
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (62), (3890) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3894)  op(e1, all_14_2) = e1
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REDUCE: (158), (3886) imply:
% 171.17/25.83  | | | | | | | | | | | | | | |   (3895)  op(e0, all_52_23) = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (156),
% 171.17/25.83  | | | | | | | | | | | | | | |            (163), (164), (165), (169), (170), (172), (177),
% 171.17/25.83  | | | | | | | | | | | | | | |            (178), (179), (181), (183), (268), (270), (271),
% 171.17/25.83  | | | | | | | | | | | | | | |            (274), (275), (276), (278), (281), (283), (304),
% 171.17/25.83  | | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (319),
% 171.17/25.83  | | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (326), (328),
% 171.17/25.83  | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (364), (365),
% 171.17/25.83  | | | | | | | | | | | | | | |            (370), (373), (385), (391), (403), (413), (419),
% 171.17/25.83  | | | | | | | | | | | | | | |            (425), (429), (518), (529), (530), (531), (532),
% 171.17/25.83  | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 171.17/25.83  | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 171.17/25.83  | | | | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 171.17/25.83  | | | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 171.17/25.83  | | | | | | | | | | | | | | |            (567), (568), (569), (571), (575), (577), (578),
% 171.17/25.83  | | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 171.17/25.83  | | | | | | | | | | | | | | |            (586), (588), (591), (593), (595), (596), (597),
% 171.17/25.83  | | | | | | | | | | | | | | |            (598), (600), (770), (796), (3239), (3240),
% 171.17/25.83  | | | | | | | | | | | | | | |            (3242), (3246), (3824), (3871), (3875), (3876),
% 171.17/25.83  | | | | | | | | | | | | | | |            (3880), (3881), (3882), (3891), (3892), (3893),
% 171.17/25.83  | | | | | | | | | | | | | | |            (3894), (3895), (function-axioms) are inconsistent
% 171.17/25.83  | | | | | | | | | | | | | | |            by sub-proof #245.
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | |   (3896)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.83  | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (3822), (3896),
% 171.17/25.83  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.83  | | | | | | | | | | | | | | |            #501.
% 171.17/25.83  | | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | | End of split
% 171.17/25.83  | | | | | | | | | | | 
% 171.17/25.83  | | | | | | | | | | Case 2:
% 171.17/25.83  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | |   (3897)  all_34_0 = e1
% 171.17/25.84  | | | | | | | | | | |   (3898)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | COMBINE_EQS: (773), (3897) imply:
% 171.17/25.84  | | | | | | | | | | |   (3899)  all_4_0 = e1
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | REDUCE: (38), (3899) imply:
% 171.17/25.84  | | | | | | | | | | |   (3900)  op(all_4_1, all_4_2) = e1
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | |   (3901)  all_58_15 = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (3822), (3901),
% 171.17/25.84  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.84  | | | | | | | | | | | |            #510.
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | |   (3902)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.84  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.84  | | | | | | | | | | | |             e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | ALPHA: (3902) implies:
% 171.17/25.84  | | | | | | | | | | | |   (3903)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | |   (3904)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.84  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.84  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.84  | | | | | | | | | | | | |            (3900), (3904), (function-axioms) are inconsistent
% 171.17/25.84  | | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | |   (3905)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.84  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.84  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | BETA: splitting (3905) gives:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | |   (3906)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.84  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | ALPHA: (3906) implies:
% 171.17/25.84  | | | | | | | | | | | | | |   (3907)  all_52_22 = e0
% 171.17/25.84  | | | | | | | | | | | | | |   (3908)  all_52_20 = e1
% 171.17/25.84  | | | | | | | | | | | | | |   (3909)  all_52_18 = e2
% 171.17/25.84  | | | | | | | | | | | | | |   (3910)  all_52_16 = e3
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | COMBINE_EQS: (719), (3908) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3911)  all_14_1 = e1
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (63), (3911) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3912)  op(e1, all_14_2) = all_14_0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (182), (3910) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3913)  op(e3, all_52_17) = e3
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (174), (3909) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3914)  op(e2, all_52_19) = e2
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (62), (3911) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3915)  op(e1, all_14_2) = e1
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (158), (3907) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3916)  op(e0, all_52_23) = e0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (156),
% 171.17/25.84  | | | | | | | | | | | | | |            (163), (164), (165), (169), (170), (172), (173),
% 171.17/25.84  | | | | | | | | | | | | | |            (177), (178), (179), (181), (268), (270), (274),
% 171.17/25.84  | | | | | | | | | | | | | |            (275), (276), (277), (278), (281), (282), (283),
% 171.17/25.84  | | | | | | | | | | | | | |            (304), (307), (310), (311), (313), (314), (315),
% 171.17/25.84  | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (326),
% 171.17/25.84  | | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (364),
% 171.17/25.84  | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (392), (403),
% 171.17/25.84  | | | | | | | | | | | | | |            (413), (415), (419), (425), (494), (529), (530),
% 171.17/25.84  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.84  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.84  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.84  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.84  | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (575), (577),
% 171.17/25.84  | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 171.17/25.84  | | | | | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (597),
% 171.17/25.84  | | | | | | | | | | | | | |            (598), (600), (663), (796), (3239), (3240),
% 171.17/25.84  | | | | | | | | | | | | | |            (3242), (3898), (3900), (3903), (3912), (3913),
% 171.17/25.84  | | | | | | | | | | | | | |            (3914), (3915), (3916), (function-axioms) are
% 171.17/25.84  | | | | | | | | | | | | | |            inconsistent by sub-proof #242.
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | |   (3917)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.84  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (3822), (3917),
% 171.17/25.84  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.84  | | | | | | | | | | | | | |            #501.
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | 
% 171.17/25.84  | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | 
% 171.17/25.84  | | | | | | | | |   (3918)  all_26_0 = e2
% 171.17/25.84  | | | | | | | | |   (3919)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 171.17/25.84  | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | COMBINE_EQS: (779), (3918) imply:
% 171.17/25.84  | | | | | | | | |   (3920)  all_4_0 = e2
% 171.17/25.84  | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | COMBINE_EQS: (742), (3920) imply:
% 171.17/25.84  | | | | | | | | |   (3921)  all_50_0 = e2
% 171.17/25.84  | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | REDUCE: (38), (3920) imply:
% 171.17/25.84  | | | | | | | | |   (3922)  op(all_4_1, all_4_2) = e2
% 171.17/25.84  | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.84  | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | |   (3923)   ~ (all_28_0 = e3)
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | REDUCE: (776), (3923) imply:
% 171.17/25.84  | | | | | | | | | |   (3924)   ~ (all_6_0 = e3)
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | |   (3925)   ~ (all_50_0 = e2)
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | REDUCE: (3921), (3925) imply:
% 171.17/25.84  | | | | | | | | | | |   (3926)  $false
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | CLOSE: (3926) is inconsistent.
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | |   (3927)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | |   (3928)  all_58_15 = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | COMBINE_EQS: (532), (3928) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3929)  all_6_2 = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (597), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3930)   ~ (all_52_7 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (599), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3931)   ~ (all_52_15 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (600), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3932)   ~ (all_52_23 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (564), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3933)   ~ (all_52_25 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (582), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3934)   ~ (all_52_27 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (43), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3935)  op(all_6_1, e0) = all_6_0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (42), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3936)  op(e0, e0) = all_6_1
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (41), (3929) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3937)  op(e0, e0) = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.84  | | | | | | | | | | | |              e0, e0, simplifying with (3936), (3937) gives:
% 171.17/25.84  | | | | | | | | | | | |   (3938)  all_6_1 = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (3935), (3938) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3939)  op(e0, e0) = all_6_0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.84  | | | | | | | | | | | |              e0, e0, simplifying with (3937), (3939) gives:
% 171.17/25.84  | | | | | | | | | | | |   (3940)  all_6_0 = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (3924), (3940) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3941)   ~ (e3 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (799), (3940) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3942)   ~ (e2 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (797), (3940) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3943)   ~ (e1 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | |   (3944)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.84  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.84  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.84  | | | | | | | | | | | | |            (3922), (3944), (function-axioms) are inconsistent
% 171.17/25.84  | | | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | |   (3945)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.84  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.84  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | BETA: splitting (3945) gives:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | |   (3946)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.84  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | ALPHA: (3946) implies:
% 171.17/25.84  | | | | | | | | | | | | | |   (3947)  all_52_22 = e0
% 171.17/25.84  | | | | | | | | | | | | | |   (3948)  all_52_20 = e1
% 171.17/25.84  | | | | | | | | | | | | | |   (3949)  all_52_18 = e2
% 171.17/25.84  | | | | | | | | | | | | | |   (3950)  all_52_16 = e3
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | COMBINE_EQS: (719), (3948) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3951)  all_14_1 = e1
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (63), (3951) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3952)  op(e1, all_14_2) = all_14_0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (182), (3950) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3953)  op(e3, all_52_17) = e3
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (174), (3949) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3954)  op(e2, all_52_19) = e2
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (62), (3951) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3955)  op(e1, all_14_2) = e1
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REDUCE: (158), (3947) imply:
% 171.17/25.84  | | | | | | | | | | | | | |   (3956)  op(e0, all_52_23) = e0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (156), (164),
% 171.17/25.84  | | | | | | | | | | | | | |            (165), (172), (173), (177), (178), (181), (183),
% 171.17/25.84  | | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (280),
% 171.17/25.84  | | | | | | | | | | | | | |            (281), (283), (302), (304), (307), (311), (315),
% 171.17/25.84  | | | | | | | | | | | | | |            (319), (324), (325), (326), (328), (329), (330),
% 171.17/25.84  | | | | | | | | | | | | | |            (331), (344), (349), (359), (364), (365), (370),
% 171.17/25.84  | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (413), (419),
% 171.17/25.84  | | | | | | | | | | | | | |            (425), (429), (503), (521), (531), (533), (534),
% 171.17/25.84  | | | | | | | | | | | | | |            (535), (536), (537), (538), (540), (542), (544),
% 171.17/25.84  | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 171.17/25.84  | | | | | | | | | | | | | |            (557), (558), (560), (561), (562), (563), (566),
% 171.17/25.84  | | | | | | | | | | | | | |            (567), (568), (578), (579), (581), (584), (585),
% 171.17/25.84  | | | | | | | | | | | | | |            (586), (589), (591), (593), (596), (598), (698),
% 171.17/25.84  | | | | | | | | | | | | | |            (718), (796), (3240), (3242), (3919), (3922),
% 171.17/25.84  | | | | | | | | | | | | | |            (3927), (3928), (3930), (3931), (3932), (3933),
% 171.17/25.84  | | | | | | | | | | | | | |            (3934), (3952), (3953), (3954), (3955), (3956),
% 171.17/25.84  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.84  | | | | | | | | | | | | | |            #474.
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | |   (3957)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.84  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (37), (164), (165), (172),
% 171.17/25.84  | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (270), (271),
% 171.17/25.84  | | | | | | | | | | | | | |            (280), (283), (303), (304), (326), (344), (349),
% 171.17/25.84  | | | | | | | | | | | | | |            (386), (403), (429), (503), (531), (533), (534),
% 171.17/25.84  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (554),
% 171.17/25.84  | | | | | | | | | | | | | |            (558), (562), (563), (586), (698), (796), (3919),
% 171.17/25.84  | | | | | | | | | | | | | |            (3922), (3928), (3933), (3957), (function-axioms)
% 171.17/25.84  | | | | | | | | | | | | | |            are inconsistent by sub-proof #470.
% 171.17/25.84  | | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | |   (3958)   ~ (all_58_15 = e0)
% 171.17/25.84  | | | | | | | | | | | |   (3959)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.84  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.84  | | | | | | | | | | | |             e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | ALPHA: (3959) implies:
% 171.17/25.84  | | | | | | | | | | | |   (3960)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.84  | | | | | | | | | | | |   (3961)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | REDUCE: (532), (3958) imply:
% 171.17/25.84  | | | | | | | | | | | |   (3962)   ~ (all_6_2 = e0)
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | |   (3963)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.84  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.84  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.84  | | | | | | | | | | | | |            (3922), (3963), (function-axioms) are inconsistent
% 171.17/25.84  | | | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | |   (3964)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.84  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.84  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (42), (43),
% 171.17/25.84  | | | | | | | | | | | | |            (51), (62), (63), (154), (155), (156), (158),
% 171.17/25.84  | | | | | | | | | | | | |            (161), (163), (164), (165), (172), (173), (174),
% 171.17/25.84  | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 171.17/25.84  | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (280),
% 171.17/25.84  | | | | | | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 171.17/25.84  | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 171.17/25.84  | | | | | | | | | | | | |            (322), (323), (324), (325), (326), (328), (329),
% 171.17/25.84  | | | | | | | | | | | | |            (330), (331), (344), (349), (359), (364), (365),
% 171.17/25.84  | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 171.17/25.84  | | | | | | | | | | | | |            (413), (419), (425), (429), (503), (521), (529),
% 171.17/25.84  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.84  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.84  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 171.17/25.84  | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (566),
% 171.17/25.84  | | | | | | | | | | | | |            (567), (568), (569), (573), (577), (579), (580),
% 171.17/25.84  | | | | | | | | | | | | |            (581), (582), (584), (585), (586), (588), (589),
% 171.17/25.84  | | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 171.17/25.84  | | | | | | | | | | | | |            (600), (649), (698), (718), (719), (796), (797),
% 171.17/25.84  | | | | | | | | | | | | |            (799), (3240), (3242), (3919), (3922), (3924),
% 171.17/25.84  | | | | | | | | | | | | |            (3927), (3960), (3961), (3962), (3964),
% 171.17/25.84  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.84  | | | | | | | | | | | | |            #433.
% 171.17/25.84  | | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | End of split
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | Case 2:
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | |   (3965)  all_28_0 = e3
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | COMBINE_EQS: (776), (3965) imply:
% 171.17/25.84  | | | | | | | | | |   (3966)  all_6_0 = e3
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | SIMP: (3966) implies:
% 171.17/25.84  | | | | | | | | | |   (3967)  all_6_0 = e3
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | REDUCE: (43), (3967) imply:
% 171.17/25.84  | | | | | | | | | |   (3968)  op(all_6_1, all_6_2) = e3
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.84  | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | Case 1:
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | |   (3969)   ~ (all_50_0 = e2)
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | REDUCE: (3921), (3969) imply:
% 171.17/25.84  | | | | | | | | | | |   (3970)  $false
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.84  | | | | | | | | | | | CLOSE: (3970) is inconsistent.
% 171.17/25.84  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | |   (3971)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | |   (3972)  all_58_15 = e0
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (3968), (3972),
% 171.17/25.85  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.85  | | | | | | | | | | | |            #510.
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | |   (3973)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.85  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.85  | | | | | | | | | | | |             e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | ALPHA: (3973) implies:
% 171.17/25.85  | | | | | | | | | | | |   (3974)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | |   (3975)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.85  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.85  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.85  | | | | | | | | | | | | |            (3922), (3975), (function-axioms) are inconsistent
% 171.17/25.85  | | | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | |   (3976)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.85  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.85  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | BETA: splitting (3976) gives:
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | |   (3977)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.85  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | ALPHA: (3977) implies:
% 171.17/25.85  | | | | | | | | | | | | | |   (3978)  all_52_22 = e0
% 171.17/25.85  | | | | | | | | | | | | | |   (3979)  all_52_20 = e1
% 171.17/25.85  | | | | | | | | | | | | | |   (3980)  all_52_18 = e2
% 171.17/25.85  | | | | | | | | | | | | | |   (3981)  all_52_16 = e3
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | COMBINE_EQS: (719), (3979) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (3982)  all_14_1 = e1
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (63), (3982) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (3983)  op(e1, all_14_2) = all_14_0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (182), (3981) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (3984)  op(e3, all_52_17) = e3
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (174), (3980) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (3985)  op(e2, all_52_19) = e2
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (62), (3982) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (3986)  op(e1, all_14_2) = e1
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (158), (3978) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (3987)  op(e0, all_52_23) = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (156), (161),
% 171.17/25.85  | | | | | | | | | | | | | |            (163), (164), (165), (172), (173), (177), (178),
% 171.17/25.85  | | | | | | | | | | | | | |            (179), (181), (183), (268), (270), (273), (274),
% 171.17/25.85  | | | | | | | | | | | | | |            (275), (276), (280), (281), (282), (283), (304),
% 171.17/25.85  | | | | | | | | | | | | | |            (307), (310), (311), (315), (319), (321), (323),
% 171.17/25.85  | | | | | | | | | | | | | |            (324), (325), (326), (328), (329), (330), (331),
% 171.17/25.85  | | | | | | | | | | | | | |            (344), (349), (359), (364), (365), (370), (385),
% 171.17/25.85  | | | | | | | | | | | | | |            (386), (391), (392), (403), (413), (419), (425),
% 171.17/25.85  | | | | | | | | | | | | | |            (521), (529), (531), (532), (533), (534), (535),
% 171.17/25.85  | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 171.17/25.85  | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (557),
% 171.17/25.85  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.85  | | | | | | | | | | | | | |            (566), (567), (568), (569), (577), (579), (580),
% 171.17/25.85  | | | | | | | | | | | | | |            (582), (584), (585), (586), (591), (593), (595),
% 171.17/25.85  | | | | | | | | | | | | | |            (596), (598), (600), (718), (796), (3240), (3242),
% 171.17/25.85  | | | | | | | | | | | | | |            (3922), (3971), (3974), (3983), (3984), (3985),
% 171.17/25.85  | | | | | | | | | | | | | |            (3986), (3987), (function-axioms) are inconsistent
% 171.17/25.85  | | | | | | | | | | | | | |            by sub-proof #455.
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | |   (3988)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.85  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (3968), (3988),
% 171.17/25.85  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.85  | | | | | | | | | | | | | |            #501.
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | 
% 171.17/25.85  | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | |   (3989)  all_22_1 = e3
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | | COMBINE_EQS: (711), (3989) imply:
% 171.17/25.85  | | | | | | | |   (3990)  all_14_1 = e3
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | | COMBINE_EQS: (719), (3990) imply:
% 171.17/25.85  | | | | | | | |   (3991)  all_52_20 = e3
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | | REDUCE: (63), (3990) imply:
% 171.17/25.85  | | | | | | | |   (3992)  op(e3, all_14_2) = all_14_0
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | | REDUCE: (62), (3990) imply:
% 171.17/25.85  | | | | | | | |   (3993)  op(e1, all_14_2) = e3
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | | BETA: splitting (93) gives:
% 171.17/25.85  | | | | | | | | 
% 171.17/25.85  | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | 
% 171.17/25.85  | | | | | | | | |   (3994)   ~ (all_26_0 = e2)
% 171.17/25.85  | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | REDUCE: (779), (3994) imply:
% 171.17/25.85  | | | | | | | | |   (3995)   ~ (all_4_0 = e2)
% 171.17/25.85  | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.85  | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | |   (3996)   ~ (all_28_0 = e3)
% 171.17/25.85  | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | REDUCE: (776), (3996) imply:
% 171.17/25.85  | | | | | | | | | |   (3997)   ~ (all_6_0 = e3)
% 171.17/25.85  | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.85  | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | |   (3998)   ~ (all_34_0 = e1)
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | REDUCE: (773), (3998) imply:
% 171.17/25.85  | | | | | | | | | | |   (3999)   ~ (all_4_0 = e1)
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | |   (4000)  all_58_15 = e0
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | COMBINE_EQS: (532), (4000) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4001)  all_6_2 = e0
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (597), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4002)   ~ (all_52_7 = e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (600), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4003)   ~ (all_52_23 = e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (564), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4004)   ~ (all_52_25 = e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (582), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4005)   ~ (all_52_27 = e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (594), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4006)   ~ (all_52_29 = e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (43), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4007)  op(all_6_1, e0) = all_6_0
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (42), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4008)  op(e0, e0) = all_6_1
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (41), (4001) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4009)  op(e0, e0) = e0
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (52), (61), (154),
% 171.17/25.85  | | | | | | | | | | | |            (155), (156), (160), (161), (163), (164), (165),
% 171.17/25.85  | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 171.17/25.85  | | | | | | | | | | | |            (182), (185), (269), (270), (271), (272), (273),
% 171.17/25.85  | | | | | | | | | | | |            (274), (278), (280), (283), (302), (303), (304),
% 171.17/25.85  | | | | | | | | | | | |            (305), (306), (307), (308), (310), (311), (313),
% 171.17/25.85  | | | | | | | | | | | |            (323), (325), (326), (330), (331), (341), (344),
% 171.17/25.85  | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (386),
% 171.17/25.85  | | | | | | | | | | | |            (391), (403), (419), (429), (530), (531), (532),
% 171.17/25.85  | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (540),
% 171.17/25.85  | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (558),
% 171.17/25.85  | | | | | | | | | | | |            (562), (563), (565), (566), (567), (569), (571),
% 171.17/25.85  | | | | | | | | | | | |            (573), (575), (578), (579), (580), (581), (584),
% 171.17/25.85  | | | | | | | | | | | |            (585), (586), (591), (595), (596), (597), (661),
% 171.17/25.85  | | | | | | | | | | | |            (720), (796), (797), (3239), (3991), (3992),
% 171.17/25.85  | | | | | | | | | | | |            (3993), (3997), (4000), (4002), (4003), (4004),
% 171.17/25.85  | | | | | | | | | | | |            (4005), (4006), (4007), (4008), (4009),
% 171.17/25.85  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.85  | | | | | | | | | | | |            #236.
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | |   (4010)   ~ (all_58_15 = e0)
% 171.17/25.85  | | | | | | | | | | | |   (4011)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.85  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.85  | | | | | | | | | | | |             e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | ALPHA: (4011) implies:
% 171.17/25.85  | | | | | | | | | | | |   (4012)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.85  | | | | | | | | | | | |   (4013)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | REDUCE: (532), (4010) imply:
% 171.17/25.85  | | | | | | | | | | | |   (4014)   ~ (all_6_2 = e0)
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | |   (4015)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.85  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.85  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | BETA: splitting (4015) gives:
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | |   (4016)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.85  | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | ALPHA: (4016) implies:
% 171.17/25.85  | | | | | | | | | | | | | |   (4017)  all_52_6 = e0
% 171.17/25.85  | | | | | | | | | | | | | |   (4018)  all_52_4 = e1
% 171.17/25.85  | | | | | | | | | | | | | |   (4019)  all_52_2 = e2
% 171.17/25.85  | | | | | | | | | | | | | |   (4020)  all_52_0 = e3
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | COMBINE_EQS: (720), (4020) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4021)  all_4_1 = e3
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (38), (4021) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4022)  op(e3, all_4_2) = all_4_0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (37), (4021) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4023)  op(e3, all_4_2) = e3
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (176), (4019) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4024)  op(e2, all_52_3) = e2
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (168), (4018) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4025)  op(e1, all_52_5) = e1
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (160), (4017) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4026)  op(e0, all_52_7) = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (42), (43), (51), (52), (61),
% 171.17/25.85  | | | | | | | | | | | | | |            (154), (156), (158), (159), (161), (163), (164),
% 171.17/25.85  | | | | | | | | | | | | | |            (165), (170), (172), (173), (174), (177), (178),
% 171.17/25.85  | | | | | | | | | | | | | |            (179), (181), (182), (268), (269), (270), (271),
% 171.17/25.85  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (279), (280),
% 171.17/25.85  | | | | | | | | | | | | | |            (281), (282), (283), (302), (303), (304), (305),
% 171.17/25.85  | | | | | | | | | | | | | |            (306), (307), (309), (310), (311), (312), (313),
% 171.17/25.85  | | | | | | | | | | | | | |            (314), (315), (317), (318), (319), (321), (322),
% 171.17/25.85  | | | | | | | | | | | | | |            (323), (324), (326), (327), (328), (329), (330),
% 171.17/25.85  | | | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 171.17/25.85  | | | | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 171.17/25.85  | | | | | | | | | | | | | |            (403), (409), (413), (419), (425), (429), (529),
% 171.17/25.85  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.85  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.85  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.85  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.85  | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 171.17/25.85  | | | | | | | | | | | | | |            (575), (578), (579), (580), (581), (582), (583),
% 171.17/25.85  | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (589), (591),
% 171.17/25.85  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 171.17/25.85  | | | | | | | | | | | | | |            (600), (797), (3239), (3993), (3995), (3999),
% 171.17/25.85  | | | | | | | | | | | | | |            (4012), (4013), (4014), (4022), (4023), (4024),
% 171.17/25.85  | | | | | | | | | | | | | |            (4025), (4026), (function-axioms) are inconsistent
% 171.17/25.85  | | | | | | | | | | | | | |            by sub-proof #235.
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | |   (4027)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.85  | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | ALPHA: (4027) implies:
% 171.17/25.85  | | | | | | | | | | | | | |   (4028)  all_52_10 = e2
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | COMBINE_EQS: (661), (4028) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4029)  all_10_1 = e2
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (4029), (function-axioms) are
% 171.17/25.85  | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | |   (4030)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.85  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.85  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | BETA: splitting (4030) gives:
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | Case 1:
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | |   (4031)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.85  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REF_CLOSE: (8), (3991), (4031) are inconsistent by sub-proof
% 171.17/25.85  | | | | | | | | | | | | | |            #427.
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | |   (4032)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.85  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | ALPHA: (4032) implies:
% 171.17/25.85  | | | | | | | | | | | | | |   (4033)  all_52_30 = e0
% 171.17/25.85  | | | | | | | | | | | | | |   (4034)  all_52_28 = e1
% 171.17/25.85  | | | | | | | | | | | | | |   (4035)  all_52_26 = e2
% 171.17/25.85  | | | | | | | | | | | | | |   (4036)  all_52_24 = e3
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | COMBINE_EQS: (649), (4033) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4037)  all_6_1 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | SIMP: (4037) implies:
% 171.17/25.85  | | | | | | | | | | | | | |   (4038)  all_6_1 = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (43), (4038) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4039)  op(e0, all_6_2) = all_6_0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (181), (4036) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4040)  op(e3, all_52_25) = e3
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (173), (4035) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4041)  op(e2, all_52_27) = e2
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (165), (4034) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4042)  op(e1, all_52_29) = e1
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REDUCE: (42), (4038) imply:
% 171.17/25.85  | | | | | | | | | | | | | |   (4043)  op(e0, all_6_2) = e0
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (61), (154), (155),
% 171.17/25.85  | | | | | | | | | | | | | |            (156), (163), (164), (172), (177), (178), (179),
% 171.17/25.85  | | | | | | | | | | | | | |            (182), (183), (268), (269), (270), (271), (272),
% 171.17/25.85  | | | | | | | | | | | | | |            (277), (281), (283), (303), (304), (305), (306),
% 171.17/25.85  | | | | | | | | | | | | | |            (307), (311), (313), (314), (315), (321), (322),
% 171.17/25.85  | | | | | | | | | | | | | |            (323), (324), (325), (326), (328), (330), (341),
% 171.17/25.85  | | | | | | | | | | | | | |            (344), (349), (350), (364), (370), (373), (385),
% 171.17/25.85  | | | | | | | | | | | | | |            (391), (403), (413), (415), (429), (529), (531),
% 171.17/25.85  | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 171.17/25.85  | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 171.17/25.85  | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.85  | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (567),
% 171.17/25.85  | | | | | | | | | | | | | |            (568), (569), (571), (577), (578), (580), (581),
% 171.17/25.85  | | | | | | | | | | | | | |            (582), (585), (586), (587), (589), (591), (594),
% 171.17/25.85  | | | | | | | | | | | | | |            (596), (597), (797), (799), (3993), (3995),
% 171.17/25.85  | | | | | | | | | | | | | |            (3997), (3999), (4012), (4014), (4039), (4040),
% 171.17/25.85  | | | | | | | | | | | | | |            (4041), (4042), (4043), (function-axioms) are
% 171.17/25.85  | | | | | | | | | | | | | |            inconsistent by sub-proof #370.
% 171.17/25.85  | | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | | End of split
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | Case 2:
% 171.17/25.85  | | | | | | | | | | | 
% 171.17/25.85  | | | | | | | | | | |   (4044)  all_34_0 = e1
% 171.17/25.86  | | | | | | | | | | |   (4045)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | COMBINE_EQS: (773), (4044) imply:
% 171.17/25.86  | | | | | | | | | | |   (4046)  all_4_0 = e1
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | SIMP: (4046) implies:
% 171.17/25.86  | | | | | | | | | | |   (4047)  all_4_0 = e1
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | REDUCE: (38), (4047) imply:
% 171.17/25.86  | | | | | | | | | | |   (4048)  op(all_4_1, all_4_2) = e1
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | |   (4049)  all_58_15 = e0
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (41), (42), (43),
% 171.17/25.86  | | | | | | | | | | | |            (52), (61), (154), (155), (156), (160), (161),
% 171.17/25.86  | | | | | | | | | | | |            (163), (164), (165), (170), (172), (173), (177),
% 171.17/25.86  | | | | | | | | | | | |            (178), (179), (181), (182), (185), (269), (270),
% 171.17/25.86  | | | | | | | | | | | |            (271), (272), (273), (274), (278), (280), (283),
% 171.17/25.86  | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (308),
% 171.17/25.86  | | | | | | | | | | | |            (310), (311), (313), (323), (325), (326), (330),
% 171.17/25.86  | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 171.17/25.86  | | | | | | | | | | | |            (370), (373), (386), (391), (403), (419), (429),
% 171.17/25.86  | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 171.17/25.86  | | | | | | | | | | | |            (537), (538), (540), (546), (548), (550), (552),
% 171.17/25.86  | | | | | | | | | | | |            (553), (554), (558), (562), (563), (564), (565),
% 171.17/25.86  | | | | | | | | | | | |            (566), (567), (569), (571), (573), (575), (578),
% 171.17/25.86  | | | | | | | | | | | |            (579), (580), (581), (582), (584), (585), (586),
% 171.17/25.86  | | | | | | | | | | | |            (591), (594), (595), (596), (597), (600), (661),
% 171.17/25.86  | | | | | | | | | | | |            (720), (796), (797), (3239), (3991), (3992),
% 171.17/25.86  | | | | | | | | | | | |            (3993), (3997), (4049), (function-axioms) are
% 171.17/25.86  | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | |   (4050)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.86  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.86  | | | | | | | | | | | |             e0)
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | ALPHA: (4050) implies:
% 171.17/25.86  | | | | | | | | | | | |   (4051)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | |   (4052)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.86  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.86  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.86  | | | | | | | | | | | | |            (4048), (4052), (function-axioms) are inconsistent
% 171.17/25.86  | | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | |   (4053)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.86  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.86  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | BETA: splitting (4053) gives:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | |   (4054)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.86  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REF_CLOSE: (8), (3991), (4054) are inconsistent by sub-proof
% 171.17/25.86  | | | | | | | | | | | | | |            #373.
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | |   (4055)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.86  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | ALPHA: (4055) implies:
% 171.17/25.86  | | | | | | | | | | | | | |   (4056)  all_52_30 = e0
% 171.17/25.86  | | | | | | | | | | | | | |   (4057)  all_52_28 = e1
% 171.17/25.86  | | | | | | | | | | | | | |   (4058)  all_52_26 = e2
% 171.17/25.86  | | | | | | | | | | | | | |   (4059)  all_52_24 = e3
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | COMBINE_EQS: (649), (4056) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4060)  all_6_1 = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (43), (4060) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4061)  op(e0, all_6_2) = all_6_0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (181), (4059) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4062)  op(e3, all_52_25) = e3
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (173), (4058) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4063)  op(e2, all_52_27) = e2
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (165), (4057) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4064)  op(e1, all_52_29) = e1
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (42), (4060) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4065)  op(e0, all_6_2) = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (61), (154), (155), (156),
% 171.17/25.86  | | | | | | | | | | | | | |            (161), (163), (164), (172), (177), (178), (179),
% 171.17/25.86  | | | | | | | | | | | | | |            (183), (268), (270), (271), (280), (281), (282),
% 171.17/25.86  | | | | | | | | | | | | | |            (283), (303), (304), (306), (307), (315), (322),
% 171.17/25.86  | | | | | | | | | | | | | |            (325), (326), (327), (328), (330), (344), (349),
% 171.17/25.86  | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 171.17/25.86  | | | | | | | | | | | | | |            (403), (413), (429), (494), (529), (531), (532),
% 171.17/25.86  | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 171.17/25.86  | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (552), (554),
% 171.17/25.86  | | | | | | | | | | | | | |            (555), (556), (557), (559), (560), (561), (562),
% 171.17/25.86  | | | | | | | | | | | | | |            (566), (568), (580), (581), (582), (586), (588),
% 171.17/25.86  | | | | | | | | | | | | | |            (589), (591), (596), (597), (663), (796), (797),
% 171.17/25.86  | | | | | | | | | | | | | |            (799), (3993), (3997), (4045), (4048), (4051),
% 171.17/25.86  | | | | | | | | | | | | | |            (4061), (4062), (4063), (4064), (4065),
% 171.17/25.86  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.86  | | | | | | | | | | | | | |            #355.
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | |   (4066)  all_28_0 = e3
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | COMBINE_EQS: (776), (4066) imply:
% 171.17/25.86  | | | | | | | | | |   (4067)  all_6_0 = e3
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | SIMP: (4067) implies:
% 171.17/25.86  | | | | | | | | | |   (4068)  all_6_0 = e3
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | REDUCE: (43), (4068) imply:
% 171.17/25.86  | | | | | | | | | |   (4069)  op(all_6_1, all_6_2) = e3
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | |   (4070)   ~ (all_34_0 = e1)
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | REDUCE: (773), (4070) imply:
% 171.17/25.86  | | | | | | | | | | |   (4071)   ~ (all_4_0 = e1)
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | |   (4072)  all_58_15 = e0
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (4069), (4072),
% 171.17/25.86  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.86  | | | | | | | | | | | |            #510.
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | |   (4073)   ~ (all_58_15 = e0)
% 171.17/25.86  | | | | | | | | | | | |   (4074)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.86  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.86  | | | | | | | | | | | |             e0)
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | ALPHA: (4074) implies:
% 171.17/25.86  | | | | | | | | | | | |   (4075)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.86  | | | | | | | | | | | |   (4076)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | REDUCE: (532), (4073) imply:
% 171.17/25.86  | | | | | | | | | | | |   (4077)   ~ (all_6_2 = e0)
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | |   (4078)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.86  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.86  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | BETA: splitting (4078) gives:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | |   (4079)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.86  | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | ALPHA: (4079) implies:
% 171.17/25.86  | | | | | | | | | | | | | |   (4080)  all_52_6 = e0
% 171.17/25.86  | | | | | | | | | | | | | |   (4081)  all_52_4 = e1
% 171.17/25.86  | | | | | | | | | | | | | |   (4082)  all_52_2 = e2
% 171.17/25.86  | | | | | | | | | | | | | |   (4083)  all_52_0 = e3
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | COMBINE_EQS: (720), (4083) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4084)  all_4_1 = e3
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (38), (4084) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4085)  op(e3, all_4_2) = all_4_0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (37), (4084) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4086)  op(e3, all_4_2) = e3
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (176), (4082) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4087)  op(e2, all_52_3) = e2
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (168), (4081) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4088)  op(e1, all_52_5) = e1
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REDUCE: (160), (4080) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4089)  op(e0, all_52_7) = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (42), (43), (51), (52), (61),
% 171.17/25.86  | | | | | | | | | | | | | |            (154), (156), (158), (159), (161), (163), (164),
% 171.17/25.86  | | | | | | | | | | | | | |            (165), (170), (172), (173), (174), (177), (178),
% 171.17/25.86  | | | | | | | | | | | | | |            (179), (181), (182), (268), (269), (270), (271),
% 171.17/25.86  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (279), (280),
% 171.17/25.86  | | | | | | | | | | | | | |            (281), (282), (283), (302), (303), (304), (305),
% 171.17/25.86  | | | | | | | | | | | | | |            (306), (307), (309), (310), (311), (312), (313),
% 171.17/25.86  | | | | | | | | | | | | | |            (314), (315), (317), (318), (319), (321), (322),
% 171.17/25.86  | | | | | | | | | | | | | |            (323), (324), (326), (327), (328), (329), (330),
% 171.17/25.86  | | | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 171.17/25.86  | | | | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 171.17/25.86  | | | | | | | | | | | | | |            (403), (409), (413), (419), (425), (429), (529),
% 171.17/25.86  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.86  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.86  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.86  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.86  | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 171.17/25.86  | | | | | | | | | | | | | |            (575), (578), (579), (580), (581), (582), (583),
% 171.17/25.86  | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (589), (591),
% 171.17/25.86  | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 171.17/25.86  | | | | | | | | | | | | | |            (600), (797), (3239), (3993), (3995), (4071),
% 171.17/25.86  | | | | | | | | | | | | | |            (4075), (4076), (4077), (4085), (4086), (4087),
% 171.17/25.86  | | | | | | | | | | | | | |            (4088), (4089), (function-axioms) are inconsistent
% 171.17/25.86  | | | | | | | | | | | | | |            by sub-proof #235.
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | |   (4090)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.86  | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | ALPHA: (4090) implies:
% 171.17/25.86  | | | | | | | | | | | | | |   (4091)  all_52_10 = e2
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | COMBINE_EQS: (661), (4091) imply:
% 171.17/25.86  | | | | | | | | | | | | | |   (4092)  all_10_1 = e2
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (4092), (function-axioms) are
% 171.17/25.86  | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | |   (4093)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.86  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.86  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | BETA: splitting (4093) gives:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | |   (4094)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.86  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REF_CLOSE: (8), (3991), (4094) are inconsistent by sub-proof
% 171.17/25.86  | | | | | | | | | | | | | |            #373.
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | |   (4095)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.86  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (4069), (4095),
% 171.17/25.86  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.86  | | | | | | | | | | | | | |            #501.
% 171.17/25.86  | | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | |   (4096)  all_34_0 = e1
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | COMBINE_EQS: (773), (4096) imply:
% 171.17/25.86  | | | | | | | | | | |   (4097)  all_4_0 = e1
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | SIMP: (4097) implies:
% 171.17/25.86  | | | | | | | | | | |   (4098)  all_4_0 = e1
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | REDUCE: (38), (4098) imply:
% 171.17/25.86  | | | | | | | | | | |   (4099)  op(all_4_1, all_4_2) = e1
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | |   (4100)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.86  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.86  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.86  | | | | | | | | | | | |            (4099), (4100), (function-axioms) are inconsistent
% 171.17/25.86  | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | |   (4101)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.86  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.86  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | BETA: splitting (4101) gives:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | |   (4102)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.86  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | REF_CLOSE: (8), (3991), (4102) are inconsistent by sub-proof
% 171.17/25.86  | | | | | | | | | | | | |            #373.
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | |   (4103)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.86  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | ALPHA: (4103) implies:
% 171.17/25.86  | | | | | | | | | | | | |   (4104)  all_52_30 = e0
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | COMBINE_EQS: (649), (4104) imply:
% 171.17/25.86  | | | | | | | | | | | | |   (4105)  all_6_1 = e0
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | SIMP: (4105) implies:
% 171.17/25.86  | | | | | | | | | | | | |   (4106)  all_6_1 = e0
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | REDUCE: (4069), (4106) imply:
% 171.17/25.86  | | | | | | | | | | | | |   (4107)  op(e0, all_6_2) = e3
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | REDUCE: (42), (4106) imply:
% 171.17/25.86  | | | | | | | | | | | | |   (4108)  op(e0, all_6_2) = e0
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3,
% 171.17/25.86  | | | | | | | | | | | | |              all_6_2, e0, simplifying with (4107), (4108)
% 171.17/25.86  | | | | | | | | | | | | |              gives:
% 171.17/25.86  | | | | | | | | | | | | |   (4109)  e3 = e0
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | REDUCE: (7), (4109) imply:
% 171.17/25.86  | | | | | | | | | | | | |   (4110)  $false
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | | CLOSE: (4110) is inconsistent.
% 171.17/25.86  | | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | End of split
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | |   (4111)  all_26_0 = e2
% 171.17/25.86  | | | | | | | | |   (4112)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | COMBINE_EQS: (779), (4111) imply:
% 171.17/25.86  | | | | | | | | |   (4113)  all_4_0 = e2
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | SIMP: (4113) implies:
% 171.17/25.86  | | | | | | | | |   (4114)  all_4_0 = e2
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | COMBINE_EQS: (742), (4114) imply:
% 171.17/25.86  | | | | | | | | |   (4115)  all_50_0 = e2
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | REDUCE: (38), (4114) imply:
% 171.17/25.86  | | | | | | | | |   (4116)  op(all_4_1, all_4_2) = e2
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.86  | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | |   (4117)   ~ (all_28_0 = e3)
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | REDUCE: (776), (4117) imply:
% 171.17/25.86  | | | | | | | | | |   (4118)   ~ (all_6_0 = e3)
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.86  | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | |   (4119)   ~ (all_50_0 = e2)
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | REDUCE: (4115), (4119) imply:
% 171.17/25.86  | | | | | | | | | | |   (4120)  $false
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | CLOSE: (4120) is inconsistent.
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | Case 2:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | |   (4121)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.86  | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | Case 1:
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.86  | | | | | | | | | | | |   (4122)  all_58_15 = e0
% 171.17/25.86  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (41), (42), (43),
% 171.17/25.87  | | | | | | | | | | | |            (52), (61), (154), (155), (156), (160), (161),
% 171.17/25.87  | | | | | | | | | | | |            (163), (164), (165), (170), (172), (173), (177),
% 171.17/25.87  | | | | | | | | | | | |            (178), (179), (181), (182), (185), (269), (270),
% 171.17/25.87  | | | | | | | | | | | |            (271), (272), (273), (274), (278), (280), (283),
% 171.17/25.87  | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (308),
% 171.17/25.87  | | | | | | | | | | | |            (310), (311), (313), (323), (325), (326), (330),
% 171.17/25.87  | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 171.17/25.87  | | | | | | | | | | | |            (370), (373), (386), (391), (403), (419), (429),
% 171.17/25.87  | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 171.17/25.87  | | | | | | | | | | | |            (537), (538), (540), (546), (548), (550), (552),
% 171.17/25.87  | | | | | | | | | | | |            (553), (554), (558), (562), (563), (564), (565),
% 171.17/25.87  | | | | | | | | | | | |            (566), (567), (569), (571), (573), (575), (578),
% 171.17/25.87  | | | | | | | | | | | |            (579), (580), (581), (582), (584), (585), (586),
% 171.17/25.87  | | | | | | | | | | | |            (591), (594), (595), (596), (597), (600), (661),
% 171.17/25.87  | | | | | | | | | | | |            (720), (796), (797), (3239), (3991), (3992),
% 171.17/25.87  | | | | | | | | | | | |            (3993), (4118), (4122), (function-axioms) are
% 171.17/25.87  | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | |   (4123)   ~ (all_58_15 = e0)
% 171.17/25.87  | | | | | | | | | | | |   (4124)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.87  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.87  | | | | | | | | | | | |             e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | ALPHA: (4124) implies:
% 171.17/25.87  | | | | | | | | | | | |   (4125)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (532), (4123) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4126)   ~ (all_6_2 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | |   (4127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.87  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.87  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.87  | | | | | | | | | | | | |            (4116), (4127), (function-axioms) are inconsistent
% 171.17/25.87  | | | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | |   (4128)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.87  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.87  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | BETA: splitting (4128) gives:
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | |   (4129)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.87  | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | REF_CLOSE: (8), (3991), (4129) are inconsistent by sub-proof
% 171.17/25.87  | | | | | | | | | | | | | |            #373.
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | |   (4130)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.87  | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | ALPHA: (4130) implies:
% 171.17/25.87  | | | | | | | | | | | | | |   (4131)  all_52_30 = e0
% 171.17/25.87  | | | | | | | | | | | | | |   (4132)  all_52_28 = e1
% 171.17/25.87  | | | | | | | | | | | | | |   (4133)  all_52_26 = e2
% 171.17/25.87  | | | | | | | | | | | | | |   (4134)  all_52_24 = e3
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | COMBINE_EQS: (649), (4131) imply:
% 171.17/25.87  | | | | | | | | | | | | | |   (4135)  all_6_1 = e0
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | SIMP: (4135) implies:
% 171.17/25.87  | | | | | | | | | | | | | |   (4136)  all_6_1 = e0
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | REDUCE: (43), (4136) imply:
% 171.17/25.87  | | | | | | | | | | | | | |   (4137)  op(e0, all_6_2) = all_6_0
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | REDUCE: (181), (4134) imply:
% 171.17/25.87  | | | | | | | | | | | | | |   (4138)  op(e3, all_52_25) = e3
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | REDUCE: (173), (4133) imply:
% 171.17/25.87  | | | | | | | | | | | | | |   (4139)  op(e2, all_52_27) = e2
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | REDUCE: (165), (4132) imply:
% 171.17/25.87  | | | | | | | | | | | | | |   (4140)  op(e1, all_52_29) = e1
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | REDUCE: (42), (4136) imply:
% 171.17/25.87  | | | | | | | | | | | | | |   (4141)  op(e0, all_6_2) = e0
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (51), (61), (154), (155),
% 171.17/25.87  | | | | | | | | | | | | | |            (156), (163), (164), (172), (177), (178), (179),
% 171.17/25.87  | | | | | | | | | | | | | |            (182), (183), (268), (270), (271), (280), (283),
% 171.17/25.87  | | | | | | | | | | | | | |            (303), (304), (305), (306), (307), (313), (314),
% 171.17/25.87  | | | | | | | | | | | | | |            (322), (323), (325), (326), (327), (328), (329),
% 171.17/25.87  | | | | | | | | | | | | | |            (330), (344), (349), (364), (370), (373), (385),
% 171.17/25.87  | | | | | | | | | | | | | |            (386), (391), (403), (429), (503), (521), (529),
% 171.17/25.87  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.87  | | | | | | | | | | | | | |            (538), (539), (540), (542), (546), (548), (550),
% 171.17/25.87  | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.87  | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (568), (569),
% 171.17/25.87  | | | | | | | | | | | | | |            (573), (578), (580), (581), (589), (591), (594),
% 171.17/25.87  | | | | | | | | | | | | | |            (597), (698), (718), (796), (797), (799), (3993),
% 171.17/25.87  | | | | | | | | | | | | | |            (4112), (4116), (4118), (4121), (4125), (4126),
% 171.17/25.87  | | | | | | | | | | | | | |            (4137), (4138), (4139), (4140), (4141),
% 171.17/25.87  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.87  | | | | | | | | | | | | | |            #348.
% 171.17/25.87  | | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | |   (4142)  all_28_0 = e3
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | COMBINE_EQS: (776), (4142) imply:
% 171.17/25.87  | | | | | | | | | |   (4143)  all_6_0 = e3
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | SIMP: (4143) implies:
% 171.17/25.87  | | | | | | | | | |   (4144)  all_6_0 = e3
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | REDUCE: (43), (4144) imply:
% 171.17/25.87  | | | | | | | | | |   (4145)  op(all_6_1, all_6_2) = e3
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | |   (4146)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.87  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.87  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.87  | | | | | | | | | | |            (4116), (4146), (function-axioms) are inconsistent
% 171.17/25.87  | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | |   (4147)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.87  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.87  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | BETA: splitting (4147) gives:
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | |   (4148)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.87  | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REF_CLOSE: (8), (3991), (4148) are inconsistent by sub-proof
% 171.17/25.87  | | | | | | | | | | | |            #427.
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | |   (4149)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.87  | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (4145), (4149),
% 171.17/25.87  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.87  | | | | | | | | | | | |            #501.
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | 
% 171.17/25.87  | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | 
% 171.17/25.87  | | | | | | | End of split
% 171.17/25.87  | | | | | | | 
% 171.17/25.87  | | | | | | Case 2:
% 171.17/25.87  | | | | | | | 
% 171.17/25.87  | | | | | | |   (4150)  all_18_0 = e3
% 171.17/25.87  | | | | | | | 
% 171.17/25.87  | | | | | | | COMBINE_EQS: (789), (4150) imply:
% 171.17/25.87  | | | | | | |   (4151)  all_14_0 = e3
% 171.17/25.87  | | | | | | | 
% 171.17/25.87  | | | | | | | SIMP: (4151) implies:
% 171.17/25.87  | | | | | | |   (4152)  all_14_0 = e3
% 171.17/25.87  | | | | | | | 
% 171.17/25.87  | | | | | | | REDUCE: (63), (4152) imply:
% 171.17/25.87  | | | | | | |   (4153)  op(all_14_1, all_14_2) = e3
% 171.17/25.87  | | | | | | | 
% 171.17/25.87  | | | | | | | BETA: splitting (93) gives:
% 171.17/25.87  | | | | | | | 
% 171.17/25.87  | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | 
% 171.17/25.87  | | | | | | | |   (4154)   ~ (all_26_0 = e2)
% 171.17/25.87  | | | | | | | | 
% 171.17/25.87  | | | | | | | | REDUCE: (779), (4154) imply:
% 171.17/25.87  | | | | | | | |   (4155)   ~ (all_4_0 = e2)
% 171.17/25.87  | | | | | | | | 
% 171.17/25.87  | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.87  | | | | | | | | 
% 171.17/25.87  | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | 
% 171.17/25.87  | | | | | | | | |   (4156)   ~ (all_28_0 = e3)
% 171.17/25.87  | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | REDUCE: (776), (4156) imply:
% 171.17/25.87  | | | | | | | | |   (4157)   ~ (all_6_0 = e3)
% 171.17/25.87  | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.87  | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | |   (4158)   ~ (all_34_0 = e1)
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | REDUCE: (773), (4158) imply:
% 171.17/25.87  | | | | | | | | | |   (4159)   ~ (all_4_0 = e1)
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.87  | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | |   (4160)   ~ (all_40_1 = e1)
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | REDUCE: (715), (4160) imply:
% 171.17/25.87  | | | | | | | | | | |   (4161)   ~ (all_4_1 = e1)
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | |   (4162)  all_58_15 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | COMBINE_EQS: (532), (4162) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4163)  all_6_2 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (597), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4164)   ~ (all_52_7 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (600), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4165)   ~ (all_52_23 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (564), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4166)   ~ (all_52_25 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (582), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4167)   ~ (all_52_27 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (594), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4168)   ~ (all_52_29 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (43), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4169)  op(all_6_1, e0) = all_6_0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (42), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4170)  op(e0, e0) = all_6_1
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (41), (4163) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4171)  op(e0, e0) = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.87  | | | | | | | | | | | |              e0, e0, simplifying with (4170), (4171) gives:
% 171.17/25.87  | | | | | | | | | | | |   (4172)  all_6_1 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (4169), (4172) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4173)  op(e0, e0) = all_6_0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.87  | | | | | | | | | | | |              e0, e0, simplifying with (4171), (4173) gives:
% 171.17/25.87  | | | | | | | | | | | |   (4174)  all_6_0 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (4157), (4174) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4175)   ~ (e3 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (797), (4174) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4176)   ~ (e1 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | |   (4177)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.87  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.87  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | REF_CLOSE: (7), (9), (37), (38), (52), (154), (155), (156),
% 171.17/25.87  | | | | | | | | | | | | |            (160), (178), (179), (270), (271), (280), (283),
% 171.17/25.87  | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (323),
% 171.17/25.87  | | | | | | | | | | | | |            (326), (330), (331), (344), (349), (370), (386),
% 171.17/25.87  | | | | | | | | | | | | |            (391), (403), (429), (531), (532), (533), (534),
% 171.17/25.87  | | | | | | | | | | | | |            (535), (536), (540), (546), (552), (562), (569),
% 171.17/25.87  | | | | | | | | | | | | |            (585), (586), (595), (596), (597), (661), (720),
% 171.17/25.87  | | | | | | | | | | | | |            (3239), (4162), (4164), (4166), (4167), (4168),
% 171.17/25.87  | | | | | | | | | | | | |            (4177), (function-axioms) are inconsistent by
% 171.17/25.87  | | | | | | | | | | | | |            sub-proof #240.
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | |   (4178)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.87  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.87  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (62), (163), (164),
% 171.17/25.87  | | | | | | | | | | | | |            (165), (170), (172), (173), (177), (178), (179),
% 171.17/25.87  | | | | | | | | | | | | |            (181), (182), (183), (269), (270), (271), (275),
% 171.17/25.87  | | | | | | | | | | | | |            (278), (280), (283), (302), (304), (305), (306),
% 171.17/25.87  | | | | | | | | | | | | |            (310), (322), (324), (329), (330), (341), (344),
% 171.17/25.87  | | | | | | | | | | | | |            (349), (364), (365), (385), (386), (391), (403),
% 171.17/25.87  | | | | | | | | | | | | |            (429), (530), (531), (533), (534), (535), (536),
% 171.17/25.87  | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 171.17/25.87  | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (558),
% 171.17/25.87  | | | | | | | | | | | | |            (561), (562), (563), (569), (571), (573), (580),
% 171.17/25.87  | | | | | | | | | | | | |            (581), (583), (585), (586), (588), (591), (593),
% 171.17/25.87  | | | | | | | | | | | | |            (719), (796), (4153), (4161), (4162), (4165),
% 171.17/25.87  | | | | | | | | | | | | |            (4166), (4168), (4178), (function-axioms) are
% 171.17/25.87  | | | | | | | | | | | | |            inconsistent by sub-proof #320.
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | |   (4179)   ~ (all_58_15 = e0)
% 171.17/25.87  | | | | | | | | | | | |   (4180)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.87  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.87  | | | | | | | | | | | |             e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | ALPHA: (4180) implies:
% 171.17/25.87  | | | | | | | | | | | |   (4181)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.87  | | | | | | | | | | | |   (4182)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (532), (4179) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4183)   ~ (all_6_2 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (38), (42),
% 171.17/25.87  | | | | | | | | | | | |            (43), (51), (52), (61), (62), (154), (155), (156),
% 171.17/25.87  | | | | | | | | | | | |            (158), (159), (160), (161), (163), (164), (165),
% 171.17/25.87  | | | | | | | | | | | |            (168), (169), (170), (172), (173), (174), (176),
% 171.17/25.87  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 171.17/25.87  | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (274),
% 171.17/25.87  | | | | | | | | | | | |            (275), (276), (279), (280), (281), (282), (283),
% 171.17/25.87  | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (309),
% 171.17/25.87  | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 171.17/25.87  | | | | | | | | | | | |            (318), (319), (321), (322), (323), (324), (325),
% 171.17/25.87  | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (341),
% 171.17/25.87  | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 171.17/25.87  | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 171.17/25.87  | | | | | | | | | | | |            (413), (419), (425), (429), (529), (531), (532),
% 171.17/25.87  | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 171.17/25.87  | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 171.17/25.87  | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 171.17/25.87  | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 171.17/25.87  | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (577),
% 171.17/25.87  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 171.17/25.87  | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 171.17/25.87  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 171.17/25.87  | | | | | | | | | | | |            (649), (661), (719), (720), (797), (799), (3239),
% 171.17/25.87  | | | | | | | | | | | |            (4153), (4155), (4157), (4159), (4181), (4182),
% 171.17/25.87  | | | | | | | | | | | |            (4183), (function-axioms) are inconsistent by
% 171.17/25.87  | | | | | | | | | | | |            sub-proof #231.
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | End of split
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | Case 2:
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | |   (4184)  all_40_1 = e1
% 171.17/25.87  | | | | | | | | | | |   (4185)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | COMBINE_EQS: (715), (4184) imply:
% 171.17/25.87  | | | | | | | | | | |   (4186)  all_4_1 = e1
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | SIMP: (4186) implies:
% 171.17/25.87  | | | | | | | | | | |   (4187)  all_4_1 = e1
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | COMBINE_EQS: (720), (4187) imply:
% 171.17/25.87  | | | | | | | | | | |   (4188)  all_52_0 = e1
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | REDUCE: (796), (4187) imply:
% 171.17/25.87  | | | | | | | | | | |   (4189)   ~ (e2 = e1)
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | REDUCE: (38), (4187) imply:
% 171.17/25.87  | | | | | | | | | | |   (4190)  op(e1, all_4_2) = all_4_0
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | REDUCE: (37), (4187) imply:
% 171.17/25.87  | | | | | | | | | | |   (4191)  op(e3, all_4_2) = e1
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.87  | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | |   (4192)  all_58_15 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | COMBINE_EQS: (532), (4192) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4193)  all_6_2 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (597), (4193) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4194)   ~ (all_52_7 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (564), (4193) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4195)   ~ (all_52_25 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (594), (4193) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4196)   ~ (all_52_29 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (43), (4193) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4197)  op(all_6_1, e0) = all_6_0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (42), (4193) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4198)  op(e0, e0) = all_6_1
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (41), (4193) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4199)  op(e0, e0) = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.87  | | | | | | | | | | | |              e0, e0, simplifying with (4198), (4199) gives:
% 171.17/25.87  | | | | | | | | | | | |   (4200)  all_6_1 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (4197), (4200) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4201)  op(e0, e0) = all_6_0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.87  | | | | | | | | | | | |              e0, e0, simplifying with (4199), (4201) gives:
% 171.17/25.87  | | | | | | | | | | | |   (4202)  all_6_0 = e0
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (4157), (4202) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4203)   ~ (e3 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | REDUCE: (797), (4202) imply:
% 171.17/25.87  | | | | | | | | | | | |   (4204)   ~ (e1 = e0)
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.87  | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | Case 1:
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.87  | | | | | | | | | | | | |   (4205)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.87  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.87  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.87  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (661), (3239), (4188), (4205),
% 171.17/25.88  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.88  | | | | | | | | | | | | |            #247.
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | |   (4206)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.88  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.88  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (62), (161), (163), (164),
% 171.17/25.88  | | | | | | | | | | | | |            (165), (170), (172), (173), (177), (178), (179),
% 171.17/25.88  | | | | | | | | | | | | |            (181), (182), (269), (270), (271), (274), (280),
% 171.17/25.88  | | | | | | | | | | | | |            (283), (302), (303), (304), (306), (310), (313),
% 171.17/25.88  | | | | | | | | | | | | |            (325), (341), (344), (349), (364), (373), (386),
% 171.17/25.88  | | | | | | | | | | | | |            (391), (403), (419), (429), (518), (531), (533),
% 171.17/25.88  | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (542), (546),
% 171.17/25.88  | | | | | | | | | | | | |            (548), (550), (553), (554), (558), (560), (562),
% 171.17/25.88  | | | | | | | | | | | | |            (563), (566), (567), (569), (581), (586), (591),
% 171.17/25.88  | | | | | | | | | | | | |            (719), (770), (4153), (4155), (4185), (4190),
% 171.17/25.88  | | | | | | | | | | | | |            (4191), (4192), (4194), (4195), (4196), (4206),
% 171.17/25.88  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.88  | | | | | | | | | | | | |            #336.
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4207)   ~ (all_58_15 = e0)
% 171.17/25.88  | | | | | | | | | | | |   (4208)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.88  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.88  | | | | | | | | | | | |             e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | ALPHA: (4208) implies:
% 171.17/25.88  | | | | | | | | | | | |   (4209)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.88  | | | | | | | | | | | |   (4210)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REDUCE: (532), (4207) imply:
% 171.17/25.88  | | | | | | | | | | | |   (4211)   ~ (all_6_2 = e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (38), (42),
% 171.17/25.88  | | | | | | | | | | | |            (43), (51), (52), (61), (62), (154), (155), (156),
% 171.17/25.88  | | | | | | | | | | | |            (158), (159), (160), (161), (163), (164), (165),
% 171.17/25.88  | | | | | | | | | | | |            (168), (169), (170), (172), (173), (174), (176),
% 171.17/25.88  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 171.17/25.88  | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (274),
% 171.17/25.88  | | | | | | | | | | | |            (275), (276), (279), (280), (281), (282), (283),
% 171.17/25.88  | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (309),
% 171.17/25.88  | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 171.17/25.88  | | | | | | | | | | | |            (318), (319), (321), (322), (323), (324), (325),
% 171.17/25.88  | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (341),
% 171.17/25.88  | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 171.17/25.88  | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 171.17/25.88  | | | | | | | | | | | |            (413), (419), (425), (429), (529), (531), (532),
% 171.17/25.88  | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 171.17/25.88  | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 171.17/25.88  | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 171.17/25.88  | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 171.17/25.88  | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (577),
% 171.17/25.88  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 171.17/25.88  | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 171.17/25.88  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 171.17/25.88  | | | | | | | | | | | |            (649), (661), (719), (720), (797), (799), (3239),
% 171.17/25.88  | | | | | | | | | | | |            (4153), (4155), (4157), (4159), (4209), (4210),
% 171.17/25.88  | | | | | | | | | | | |            (4211), (function-axioms) are inconsistent by
% 171.17/25.88  | | | | | | | | | | | |            sub-proof #231.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | |   (4212)  all_34_0 = e1
% 171.17/25.88  | | | | | | | | | |   (4213)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | COMBINE_EQS: (773), (4212) imply:
% 171.17/25.88  | | | | | | | | | |   (4214)  all_4_0 = e1
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | REDUCE: (38), (4214) imply:
% 171.17/25.88  | | | | | | | | | |   (4215)  op(all_4_1, all_4_2) = e1
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | |   (4216)  all_58_15 = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | COMBINE_EQS: (532), (4216) imply:
% 171.17/25.88  | | | | | | | | | | |   (4217)  all_6_2 = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REDUCE: (564), (4217) imply:
% 171.17/25.88  | | | | | | | | | | |   (4218)   ~ (all_52_25 = e0)
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REDUCE: (43), (4217) imply:
% 171.17/25.88  | | | | | | | | | | |   (4219)  op(all_6_1, e0) = all_6_0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REDUCE: (42), (4217) imply:
% 171.17/25.88  | | | | | | | | | | |   (4220)  op(e0, e0) = all_6_1
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REDUCE: (41), (4217) imply:
% 171.17/25.88  | | | | | | | | | | |   (4221)  op(e0, e0) = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.88  | | | | | | | | | | |              e0, e0, simplifying with (4220), (4221) gives:
% 171.17/25.88  | | | | | | | | | | |   (4222)  all_6_1 = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REDUCE: (4219), (4222) imply:
% 171.17/25.88  | | | | | | | | | | |   (4223)  op(e0, e0) = all_6_0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.88  | | | | | | | | | | |              e0, e0, simplifying with (4221), (4223) gives:
% 171.17/25.88  | | | | | | | | | | |   (4224)  all_6_0 = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REDUCE: (4157), (4224) imply:
% 171.17/25.88  | | | | | | | | | | |   (4225)   ~ (e3 = e0)
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4226)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.88  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.88  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.88  | | | | | | | | | | | |            (4215), (4226), (function-axioms) are inconsistent
% 171.17/25.88  | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4227)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.88  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.88  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (7), (8), (36), (37), (62), (161), (163), (164),
% 171.17/25.88  | | | | | | | | | | | |            (165), (172), (173), (177), (179), (181), (270),
% 171.17/25.88  | | | | | | | | | | | |            (271), (280), (282), (283), (304), (328), (330),
% 171.17/25.88  | | | | | | | | | | | |            (344), (349), (386), (392), (403), (429), (494),
% 171.17/25.88  | | | | | | | | | | | |            (531), (533), (534), (544), (546), (548), (552),
% 171.17/25.88  | | | | | | | | | | | |            (554), (562), (566), (596), (663), (719), (796),
% 171.17/25.88  | | | | | | | | | | | |            (4153), (4213), (4215), (4216), (4218), (4227),
% 171.17/25.88  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.88  | | | | | | | | | | | |            #329.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | |   (4228)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.88  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.88  | | | | | | | | | | |             e0)
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | ALPHA: (4228) implies:
% 171.17/25.88  | | | | | | | | | | |   (4229)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4230)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.88  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.88  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.88  | | | | | | | | | | | |            (4215), (4230), (function-axioms) are inconsistent
% 171.17/25.88  | | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4231)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.88  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.88  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (61), (62),
% 171.17/25.88  | | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 171.17/25.88  | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 171.17/25.88  | | | | | | | | | | | |            (268), (270), (280), (281), (282), (283), (303),
% 171.17/25.88  | | | | | | | | | | | |            (304), (306), (307), (322), (324), (325), (326),
% 171.17/25.88  | | | | | | | | | | | |            (328), (330), (344), (349), (364), (370), (385),
% 171.17/25.88  | | | | | | | | | | | |            (386), (391), (392), (403), (413), (494), (529),
% 171.17/25.88  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (538),
% 171.17/25.88  | | | | | | | | | | | |            (539), (540), (544), (546), (548), (552), (554),
% 171.17/25.88  | | | | | | | | | | | |            (555), (557), (558), (559), (562), (565), (566),
% 171.17/25.88  | | | | | | | | | | | |            (567), (568), (569), (578), (580), (581), (586),
% 171.17/25.88  | | | | | | | | | | | |            (591), (595), (596), (597), (649), (663), (719),
% 171.17/25.88  | | | | | | | | | | | |            (796), (797), (799), (4153), (4157), (4213),
% 171.17/25.88  | | | | | | | | | | | |            (4215), (4229), (4231), (function-axioms) are
% 171.17/25.88  | | | | | | | | | | | |            inconsistent by sub-proof #318.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | |   (4232)  all_28_0 = e3
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | COMBINE_EQS: (776), (4232) imply:
% 171.17/25.88  | | | | | | | | |   (4233)  all_6_0 = e3
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | SIMP: (4233) implies:
% 171.17/25.88  | | | | | | | | |   (4234)  all_6_0 = e3
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | REDUCE: (43), (4234) imply:
% 171.17/25.88  | | | | | | | | |   (4235)  op(all_6_1, all_6_2) = e3
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | |   (4236)   ~ (all_34_0 = e1)
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | REDUCE: (773), (4236) imply:
% 171.17/25.88  | | | | | | | | | |   (4237)   ~ (all_4_0 = e1)
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | |   (4238)  all_58_15 = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (4235), (4238),
% 171.17/25.88  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.88  | | | | | | | | | | |            #510.
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | |   (4239)   ~ (all_58_15 = e0)
% 171.17/25.88  | | | | | | | | | | |   (4240)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.88  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.88  | | | | | | | | | | |             e0)
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | ALPHA: (4240) implies:
% 171.17/25.88  | | | | | | | | | | |   (4241)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REDUCE: (532), (4239) imply:
% 171.17/25.88  | | | | | | | | | | |   (4242)   ~ (all_6_2 = e0)
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4243)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.88  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.88  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | BETA: splitting (4243) gives:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | |   (4244)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.88  | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (37), (38), (42), (61), (154), (156),
% 171.17/25.88  | | | | | | | | | | | | |            (158), (159), (160), (161), (163), (164), (165),
% 171.17/25.88  | | | | | | | | | | | | |            (168), (169), (170), (172), (173), (176), (177),
% 171.17/25.88  | | | | | | | | | | | | |            (178), (179), (268), (269), (270), (271), (272),
% 171.17/25.88  | | | | | | | | | | | | |            (273), (276), (279), (281), (282), (283), (302),
% 171.17/25.88  | | | | | | | | | | | | |            (303), (304), (305), (307), (310), (311), (312),
% 171.17/25.88  | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (323), (324),
% 171.17/25.88  | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (341), (344),
% 171.17/25.88  | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 171.17/25.88  | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 171.17/25.88  | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 171.17/25.88  | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 171.17/25.88  | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 171.17/25.88  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.88  | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (575), (578),
% 171.17/25.88  | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 171.17/25.88  | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 171.17/25.88  | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (720),
% 171.17/25.88  | | | | | | | | | | | | |            (4155), (4235), (4237), (4241), (4242), (4244),
% 171.17/25.88  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.88  | | | | | | | | | | | | |            #436.
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | |   (4245)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.88  | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | | ALPHA: (4245) implies:
% 171.17/25.88  | | | | | | | | | | | | |   (4246)  all_52_10 = e2
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | | COMBINE_EQS: (661), (4246) imply:
% 171.17/25.88  | | | | | | | | | | | | |   (4247)  all_10_1 = e2
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (4247), (function-axioms) are
% 171.17/25.88  | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.88  | | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4248)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.88  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.88  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (7), (8), (42), (62), (649), (719), (4153),
% 171.17/25.88  | | | | | | | | | | | |            (4235), (4248), (function-axioms) are inconsistent
% 171.17/25.88  | | | | | | | | | | | |            by sub-proof #326.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | |   (4249)  all_34_0 = e1
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | COMBINE_EQS: (773), (4249) imply:
% 171.17/25.88  | | | | | | | | | |   (4250)  all_4_0 = e1
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | SIMP: (4250) implies:
% 171.17/25.88  | | | | | | | | | |   (4251)  all_4_0 = e1
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | REDUCE: (38), (4251) imply:
% 171.17/25.88  | | | | | | | | | |   (4252)  op(all_4_1, all_4_2) = e1
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | |   (4253)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.88  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.88  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.88  | | | | | | | | | | |            (4252), (4253), (function-axioms) are inconsistent
% 171.17/25.88  | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | |   (4254)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.88  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.88  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | BETA: splitting (4254) gives:
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 1:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4255)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.88  | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (8), (62), (719), (4153), (4255),
% 171.17/25.88  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.88  | | | | | | | | | | | |            #343.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | |   (4256)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.88  | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (4235), (4256),
% 171.17/25.88  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.88  | | | | | | | | | | | |            #501.
% 171.17/25.88  | | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | | 
% 171.17/25.88  | | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | | 
% 171.17/25.88  | | | | | | | | End of split
% 171.17/25.88  | | | | | | | | 
% 171.17/25.88  | | | | | | | Case 2:
% 171.17/25.88  | | | | | | | | 
% 171.17/25.88  | | | | | | | |   (4257)  all_26_0 = e2
% 171.17/25.88  | | | | | | | |   (4258)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 171.17/25.88  | | | | | | | | 
% 171.17/25.88  | | | | | | | | COMBINE_EQS: (779), (4257) imply:
% 171.17/25.88  | | | | | | | |   (4259)  all_4_0 = e2
% 171.17/25.88  | | | | | | | | 
% 171.17/25.88  | | | | | | | | SIMP: (4259) implies:
% 171.17/25.88  | | | | | | | |   (4260)  all_4_0 = e2
% 171.17/25.88  | | | | | | | | 
% 171.17/25.88  | | | | | | | | COMBINE_EQS: (742), (4260) imply:
% 171.17/25.88  | | | | | | | |   (4261)  all_50_0 = e2
% 171.17/25.88  | | | | | | | | 
% 171.17/25.88  | | | | | | | | REDUCE: (38), (4260) imply:
% 171.17/25.89  | | | | | | | |   (4262)  op(all_4_1, all_4_2) = e2
% 171.17/25.89  | | | | | | | | 
% 171.17/25.89  | | | | | | | | BETA: splitting (98) gives:
% 171.17/25.89  | | | | | | | | 
% 171.17/25.89  | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | |   (4263)   ~ (all_28_0 = e3)
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | REDUCE: (776), (4263) imply:
% 171.17/25.89  | | | | | | | | |   (4264)   ~ (all_6_0 = e3)
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | |   (4265)   ~ (all_50_0 = e2)
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | REDUCE: (4261), (4265) imply:
% 171.17/25.89  | | | | | | | | | |   (4266)  $false
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | CLOSE: (4266) is inconsistent.
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | |   (4267)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | |   (4268)  all_58_15 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | COMBINE_EQS: (532), (4268) imply:
% 171.17/25.89  | | | | | | | | | | |   (4269)  all_6_2 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (564), (4269) imply:
% 171.17/25.89  | | | | | | | | | | |   (4270)   ~ (all_52_25 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (43), (4269) imply:
% 171.17/25.89  | | | | | | | | | | |   (4271)  op(all_6_1, e0) = all_6_0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (42), (4269) imply:
% 171.17/25.89  | | | | | | | | | | |   (4272)  op(e0, e0) = all_6_1
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (41), (4269) imply:
% 171.17/25.89  | | | | | | | | | | |   (4273)  op(e0, e0) = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.89  | | | | | | | | | | |              e0, e0, simplifying with (4272), (4273) gives:
% 171.17/25.89  | | | | | | | | | | |   (4274)  all_6_1 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (4271), (4274) imply:
% 171.17/25.89  | | | | | | | | | | |   (4275)  op(e0, e0) = all_6_0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.89  | | | | | | | | | | |              e0, e0, simplifying with (4273), (4275) gives:
% 171.17/25.89  | | | | | | | | | | |   (4276)  all_6_0 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (4264), (4276) imply:
% 171.17/25.89  | | | | | | | | | | |   (4277)   ~ (e3 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (799), (4276) imply:
% 171.17/25.89  | | | | | | | | | | |   (4278)   ~ (e2 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | |   (4279)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.89  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.89  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.89  | | | | | | | | | | | |            (4262), (4279), (function-axioms) are inconsistent
% 171.17/25.89  | | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | |   (4280)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.89  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.89  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (36), (37), (62), (164),
% 171.17/25.89  | | | | | | | | | | | |            (165), (172), (173), (177), (178), (179), (181),
% 171.17/25.89  | | | | | | | | | | | |            (270), (271), (280), (283), (303), (304), (326),
% 171.17/25.89  | | | | | | | | | | | |            (344), (349), (386), (403), (429), (503), (531),
% 171.17/25.89  | | | | | | | | | | | |            (533), (534), (542), (544), (546), (548), (550),
% 171.17/25.89  | | | | | | | | | | | |            (552), (554), (558), (562), (563), (586), (698),
% 171.17/25.89  | | | | | | | | | | | |            (719), (796), (4153), (4258), (4262), (4268),
% 171.17/25.89  | | | | | | | | | | | |            (4270), (4280), (function-axioms) are inconsistent
% 171.17/25.89  | | | | | | | | | | | |            by sub-proof #324.
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | |   (4281)   ~ (all_58_15 = e0)
% 171.17/25.89  | | | | | | | | | | |   (4282)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.89  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.89  | | | | | | | | | | |             e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | ALPHA: (4282) implies:
% 171.17/25.89  | | | | | | | | | | |   (4283)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (532), (4281) imply:
% 171.17/25.89  | | | | | | | | | | |   (4284)   ~ (all_6_2 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | |   (4285)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.89  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.89  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.89  | | | | | | | | | | | |            (4262), (4285), (function-axioms) are inconsistent
% 171.17/25.89  | | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | |   (4286)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.89  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.89  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (51), (62),
% 171.17/25.89  | | | | | | | | | | | |            (154), (155), (156), (164), (165), (172), (173),
% 171.17/25.89  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 171.17/25.89  | | | | | | | | | | | |            (270), (271), (280), (283), (303), (304), (305),
% 171.17/25.89  | | | | | | | | | | | |            (306), (307), (313), (322), (323), (324), (325),
% 171.17/25.89  | | | | | | | | | | | |            (326), (328), (330), (344), (349), (364), (370),
% 171.17/25.89  | | | | | | | | | | | |            (373), (385), (386), (391), (403), (429), (503),
% 171.17/25.89  | | | | | | | | | | | |            (521), (529), (531), (532), (533), (534), (535),
% 171.17/25.89  | | | | | | | | | | | |            (536), (537), (538), (539), (540), (544), (546),
% 171.17/25.89  | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (557),
% 171.17/25.89  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.89  | | | | | | | | | | | |            (569), (573), (580), (581), (588), (589), (594),
% 171.17/25.89  | | | | | | | | | | | |            (597), (649), (698), (718), (719), (796), (797),
% 171.17/25.89  | | | | | | | | | | | |            (799), (4153), (4258), (4262), (4264), (4267),
% 171.17/25.89  | | | | | | | | | | | |            (4283), (4284), (4286), (function-axioms) are
% 171.17/25.89  | | | | | | | | | | | |            inconsistent by sub-proof #322.
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | |   (4287)  all_28_0 = e3
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | COMBINE_EQS: (776), (4287) imply:
% 171.17/25.89  | | | | | | | | |   (4288)  all_6_0 = e3
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | SIMP: (4288) implies:
% 171.17/25.89  | | | | | | | | |   (4289)  all_6_0 = e3
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | REDUCE: (43), (4289) imply:
% 171.17/25.89  | | | | | | | | |   (4290)  op(all_6_1, all_6_2) = e3
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | |   (4291)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.89  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.89  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.89  | | | | | | | | | |            (4262), (4291), (function-axioms) are inconsistent
% 171.17/25.89  | | | | | | | | | |            by sub-proof #237.
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | |   (4292)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.89  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.89  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | REF_CLOSE: (7), (8), (42), (62), (649), (719), (4153),
% 171.17/25.89  | | | | | | | | | |            (4290), (4292), (function-axioms) are inconsistent
% 171.17/25.89  | | | | | | | | | |            by sub-proof #326.
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | 
% 171.17/25.89  | | | | | | | End of split
% 171.17/25.89  | | | | | | | 
% 171.17/25.89  | | | | | | End of split
% 171.17/25.89  | | | | | | 
% 171.17/25.89  | | | | | Case 2:
% 171.17/25.89  | | | | | | 
% 171.17/25.89  | | | | | |   (4293)  all_14_0 = e2
% 171.17/25.89  | | | | | |   (4294)   ~ (all_14_1 = e0) |  ~ (all_14_2 = e3)
% 171.17/25.89  | | | | | | 
% 171.17/25.89  | | | | | | REDUCE: (63), (4293) imply:
% 171.17/25.89  | | | | | |   (4295)  op(all_14_1, all_14_2) = e2
% 171.17/25.89  | | | | | | 
% 171.17/25.89  | | | | | | BETA: splitting (93) gives:
% 171.17/25.89  | | | | | | 
% 171.17/25.89  | | | | | | Case 1:
% 171.17/25.89  | | | | | | | 
% 171.17/25.89  | | | | | | |   (4296)   ~ (all_26_0 = e2)
% 171.17/25.89  | | | | | | | 
% 171.17/25.89  | | | | | | | REDUCE: (779), (4296) imply:
% 171.17/25.89  | | | | | | |   (4297)   ~ (all_4_0 = e2)
% 171.17/25.89  | | | | | | | 
% 171.17/25.89  | | | | | | | BETA: splitting (98) gives:
% 171.17/25.89  | | | | | | | 
% 171.17/25.89  | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | 
% 171.17/25.89  | | | | | | | |   (4298)   ~ (all_28_0 = e3)
% 171.17/25.89  | | | | | | | | 
% 171.17/25.89  | | | | | | | | REDUCE: (776), (4298) imply:
% 171.17/25.89  | | | | | | | |   (4299)   ~ (all_6_0 = e3)
% 171.17/25.89  | | | | | | | | 
% 171.17/25.89  | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.89  | | | | | | | | 
% 171.17/25.89  | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | |   (4300)   ~ (all_34_0 = e1)
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | REDUCE: (773), (4300) imply:
% 171.17/25.89  | | | | | | | | |   (4301)   ~ (all_4_0 = e1)
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.89  | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | |   (4302)   ~ (all_40_1 = e1)
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | REDUCE: (715), (4302) imply:
% 171.17/25.89  | | | | | | | | | |   (4303)   ~ (all_4_1 = e1)
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.89  | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | |   (4304)  all_58_15 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | COMBINE_EQS: (532), (4304) imply:
% 171.17/25.89  | | | | | | | | | | |   (4305)  all_6_2 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (597), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4306)   ~ (all_52_7 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (600), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4307)   ~ (all_52_23 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (564), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4308)   ~ (all_52_25 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (582), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4309)   ~ (all_52_27 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (594), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4310)   ~ (all_52_29 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (43), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4311)  op(all_6_1, e0) = all_6_0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (42), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4312)  op(e0, e0) = all_6_1
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (41), (4305) imply:
% 171.17/25.89  | | | | | | | | | | |   (4313)  op(e0, e0) = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.89  | | | | | | | | | | |              e0, e0, simplifying with (4312), (4313) gives:
% 171.17/25.89  | | | | | | | | | | |   (4314)  all_6_1 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (4311), (4314) imply:
% 171.17/25.89  | | | | | | | | | | |   (4315)  op(e0, e0) = all_6_0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.89  | | | | | | | | | | |              e0, e0, simplifying with (4313), (4315) gives:
% 171.17/25.89  | | | | | | | | | | |   (4316)  all_6_0 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (4299), (4316) imply:
% 171.17/25.89  | | | | | | | | | | |   (4317)   ~ (e3 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (797), (4316) imply:
% 171.17/25.89  | | | | | | | | | | |   (4318)   ~ (e1 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | |   (4319)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.89  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.89  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | REF_CLOSE: (7), (9), (37), (38), (52), (154), (155), (156),
% 171.17/25.89  | | | | | | | | | | | |            (160), (178), (179), (270), (271), (280), (283),
% 171.17/25.89  | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (323),
% 171.17/25.89  | | | | | | | | | | | |            (326), (330), (331), (344), (349), (370), (386),
% 171.17/25.89  | | | | | | | | | | | |            (391), (403), (429), (531), (532), (533), (534),
% 171.17/25.89  | | | | | | | | | | | |            (535), (536), (540), (546), (552), (562), (569),
% 171.17/25.89  | | | | | | | | | | | |            (585), (586), (595), (596), (597), (661), (720),
% 171.17/25.89  | | | | | | | | | | | |            (3239), (4304), (4306), (4308), (4309), (4310),
% 171.17/25.89  | | | | | | | | | | | |            (4319), (function-axioms) are inconsistent by
% 171.17/25.89  | | | | | | | | | | | |            sub-proof #240.
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | |   (4320)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.89  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.89  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | BETA: splitting (4320) gives:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | |   (4321)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.89  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (4295), (4321),
% 171.17/25.89  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.89  | | | | | | | | | | | | |            #314.
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | |   (4322)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.89  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (163), (164), (165),
% 171.17/25.89  | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 171.17/25.89  | | | | | | | | | | | | |            (182), (183), (269), (270), (271), (275), (278),
% 171.17/25.89  | | | | | | | | | | | | |            (280), (283), (302), (304), (305), (306), (310),
% 171.17/25.89  | | | | | | | | | | | | |            (322), (324), (329), (330), (341), (344), (349),
% 171.17/25.89  | | | | | | | | | | | | |            (364), (365), (385), (386), (391), (403), (429),
% 171.17/25.89  | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 171.17/25.89  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.89  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (558), (561),
% 171.17/25.89  | | | | | | | | | | | | |            (562), (563), (569), (571), (573), (580), (581),
% 171.17/25.89  | | | | | | | | | | | | |            (583), (585), (586), (588), (591), (593), (796),
% 171.17/25.89  | | | | | | | | | | | | |            (4303), (4304), (4307), (4308), (4310), (4322),
% 171.17/25.89  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.89  | | | | | | | | | | | | |            #878.
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | End of split
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | Case 2:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | |   (4323)   ~ (all_58_15 = e0)
% 171.17/25.89  | | | | | | | | | | |   (4324)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.89  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.89  | | | | | | | | | | |             e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | ALPHA: (4324) implies:
% 171.17/25.89  | | | | | | | | | | |   (4325)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.89  | | | | | | | | | | |   (4326)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | REDUCE: (532), (4323) imply:
% 171.17/25.89  | | | | | | | | | | |   (4327)   ~ (all_6_2 = e0)
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.89  | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | |   (4328)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.89  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.89  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | BETA: splitting (4328) gives:
% 171.17/25.89  | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | Case 1:
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | |   (4329)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.89  | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | ALPHA: (4329) implies:
% 171.17/25.89  | | | | | | | | | | | | |   (4330)  all_52_6 = e0
% 171.17/25.89  | | | | | | | | | | | | |   (4331)  all_52_4 = e1
% 171.17/25.89  | | | | | | | | | | | | |   (4332)  all_52_2 = e2
% 171.17/25.89  | | | | | | | | | | | | |   (4333)  all_52_0 = e3
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | COMBINE_EQS: (720), (4333) imply:
% 171.17/25.89  | | | | | | | | | | | | |   (4334)  all_4_1 = e3
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REDUCE: (38), (4334) imply:
% 171.17/25.89  | | | | | | | | | | | | |   (4335)  op(e3, all_4_2) = all_4_0
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REDUCE: (37), (4334) imply:
% 171.17/25.89  | | | | | | | | | | | | |   (4336)  op(e3, all_4_2) = e3
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REDUCE: (176), (4332) imply:
% 171.17/25.89  | | | | | | | | | | | | |   (4337)  op(e2, all_52_3) = e2
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REDUCE: (168), (4331) imply:
% 171.17/25.89  | | | | | | | | | | | | |   (4338)  op(e1, all_52_5) = e1
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REDUCE: (160), (4330) imply:
% 171.17/25.89  | | | | | | | | | | | | |   (4339)  op(e0, all_52_7) = e0
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.89  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (42), (43), (51), (52), (61), (62),
% 171.17/25.89  | | | | | | | | | | | | |            (154), (155), (156), (158), (159), (161), (163),
% 171.17/25.89  | | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (174),
% 171.17/25.89  | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 171.17/25.89  | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 171.17/25.89  | | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 171.17/25.89  | | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (309),
% 171.17/25.89  | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 171.17/25.89  | | | | | | | | | | | | |            (318), (319), (321), (322), (323), (324), (325),
% 171.17/25.89  | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (341),
% 171.17/25.89  | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 171.17/25.89  | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 171.17/25.89  | | | | | | | | | | | | |            (413), (415), (419), (425), (429), (529), (531),
% 171.17/25.89  | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 171.17/25.89  | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 171.17/25.89  | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.89  | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 171.17/25.89  | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 171.17/25.89  | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 171.17/25.89  | | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 171.17/25.89  | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 171.17/25.89  | | | | | | | | | | | | |            (797), (799), (3239), (4294), (4295), (4297),
% 171.17/25.89  | | | | | | | | | | | | |            (4301), (4325), (4326), (4327), (4335), (4336),
% 171.17/25.89  | | | | | | | | | | | | |            (4337), (4338), (4339), (function-axioms) are
% 171.17/25.89  | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 171.17/25.89  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | |   (4340)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.90  | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | ALPHA: (4340) implies:
% 171.17/25.90  | | | | | | | | | | | | |   (4341)  all_52_10 = e2
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | COMBINE_EQS: (661), (4341) imply:
% 171.17/25.90  | | | | | | | | | | | | |   (4342)  all_10_1 = e2
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (4342), (function-axioms) are
% 171.17/25.90  | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | |   (4343)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.90  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.90  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | BETA: splitting (4343) gives:
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | |   (4344)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.90  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (4295), (4344),
% 171.17/25.90  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.90  | | | | | | | | | | | | |            #314.
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | |   (4345)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.90  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43),
% 171.17/25.90  | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 171.17/25.90  | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 171.17/25.90  | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (276), (281),
% 171.17/25.90  | | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 171.17/25.90  | | | | | | | | | | | | |            (311), (313), (315), (319), (321), (322), (323),
% 171.17/25.90  | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (330), (331),
% 171.17/25.90  | | | | | | | | | | | | |            (341), (344), (349), (350), (364), (370), (373),
% 171.17/25.90  | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (429), (529),
% 171.17/25.90  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.90  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.90  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.90  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.90  | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 171.17/25.90  | | | | | | | | | | | | |            (578), (580), (581), (582), (585), (586), (587),
% 171.17/25.90  | | | | | | | | | | | | |            (588), (589), (594), (595), (596), (597), (600),
% 171.17/25.90  | | | | | | | | | | | | |            (649), (797), (799), (4297), (4299), (4301),
% 171.17/25.90  | | | | | | | | | | | | |            (4325), (4326), (4327), (4345), (function-axioms)
% 171.17/25.90  | | | | | | | | | | | | |            are inconsistent by sub-proof #634.
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | |   (4346)  all_40_1 = e1
% 171.17/25.90  | | | | | | | | | |   (4347)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | COMBINE_EQS: (715), (4346) imply:
% 171.17/25.90  | | | | | | | | | |   (4348)  all_4_1 = e1
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | COMBINE_EQS: (720), (4348) imply:
% 171.17/25.90  | | | | | | | | | |   (4349)  all_52_0 = e1
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (796), (4348) imply:
% 171.17/25.90  | | | | | | | | | |   (4350)   ~ (e2 = e1)
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (38), (4348) imply:
% 171.17/25.90  | | | | | | | | | |   (4351)  op(e1, all_4_2) = all_4_0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (37), (4348) imply:
% 171.17/25.90  | | | | | | | | | |   (4352)  op(e3, all_4_2) = e1
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | |   (4353)  all_58_15 = e0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | COMBINE_EQS: (532), (4353) imply:
% 171.17/25.90  | | | | | | | | | | |   (4354)  all_6_2 = e0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (597), (4354) imply:
% 171.17/25.90  | | | | | | | | | | |   (4355)   ~ (all_52_7 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (564), (4354) imply:
% 171.17/25.90  | | | | | | | | | | |   (4356)   ~ (all_52_25 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (594), (4354) imply:
% 171.17/25.90  | | | | | | | | | | |   (4357)   ~ (all_52_29 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (43), (4354) imply:
% 171.17/25.90  | | | | | | | | | | |   (4358)  op(all_6_1, e0) = all_6_0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (42), (4354) imply:
% 171.17/25.90  | | | | | | | | | | |   (4359)  op(e0, e0) = all_6_1
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (41), (4354) imply:
% 171.17/25.90  | | | | | | | | | | |   (4360)  op(e0, e0) = e0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.90  | | | | | | | | | | |              e0, e0, simplifying with (4359), (4360) gives:
% 171.17/25.90  | | | | | | | | | | |   (4361)  all_6_1 = e0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (4358), (4361) imply:
% 171.17/25.90  | | | | | | | | | | |   (4362)  op(e0, e0) = all_6_0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.90  | | | | | | | | | | |              e0, e0, simplifying with (4360), (4362) gives:
% 171.17/25.90  | | | | | | | | | | |   (4363)  all_6_0 = e0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (4299), (4363) imply:
% 171.17/25.90  | | | | | | | | | | |   (4364)   ~ (e3 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (797), (4363) imply:
% 171.17/25.90  | | | | | | | | | | |   (4365)   ~ (e1 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | |   (4366)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.90  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.90  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (661), (3239), (4349), (4366),
% 171.17/25.90  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.90  | | | | | | | | | | | |            #247.
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | |   (4367)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.90  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.90  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (62), (161), (163),
% 171.17/25.90  | | | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 171.17/25.90  | | | | | | | | | | | |            (179), (181), (182), (269), (270), (271), (274),
% 171.17/25.90  | | | | | | | | | | | |            (280), (283), (302), (303), (304), (306), (310),
% 171.17/25.90  | | | | | | | | | | | |            (313), (325), (341), (344), (349), (364), (373),
% 171.17/25.90  | | | | | | | | | | | |            (386), (391), (403), (419), (429), (518), (531),
% 171.17/25.90  | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (542),
% 171.17/25.90  | | | | | | | | | | | |            (546), (548), (550), (553), (554), (558), (560),
% 171.17/25.90  | | | | | | | | | | | |            (562), (563), (566), (567), (569), (581), (586),
% 171.17/25.90  | | | | | | | | | | | |            (591), (719), (770), (4295), (4297), (4347),
% 171.17/25.90  | | | | | | | | | | | |            (4351), (4352), (4353), (4355), (4356), (4357),
% 171.17/25.90  | | | | | | | | | | | |            (4367), (function-axioms) are inconsistent by
% 171.17/25.90  | | | | | | | | | | | |            sub-proof #292.
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | |   (4368)   ~ (all_58_15 = e0)
% 171.17/25.90  | | | | | | | | | | |   (4369)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.90  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.90  | | | | | | | | | | |             e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | ALPHA: (4369) implies:
% 171.17/25.90  | | | | | | | | | | |   (4370)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.90  | | | | | | | | | | |   (4371)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REDUCE: (532), (4368) imply:
% 171.17/25.90  | | | | | | | | | | |   (4372)   ~ (all_6_2 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | |   (4373)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.90  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.90  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (661), (3239), (4349), (4373),
% 171.17/25.90  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.90  | | | | | | | | | | | |            #247.
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | |   (4374)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.90  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.90  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | BETA: splitting (4374) gives:
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | |   (4375)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.90  | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | ALPHA: (4375) implies:
% 171.17/25.90  | | | | | | | | | | | | |   (4376)  all_52_20 = e1
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | COMBINE_EQS: (719), (4376) imply:
% 171.17/25.90  | | | | | | | | | | | | |   (4377)  all_14_1 = e1
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (4295), (4377), (function-axioms) are
% 171.17/25.90  | | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | |   (4378)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.90  | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | ALPHA: (4378) implies:
% 171.17/25.90  | | | | | | | | | | | | |   (4379)  all_52_30 = e0
% 171.17/25.90  | | | | | | | | | | | | |   (4380)  all_52_28 = e1
% 171.17/25.90  | | | | | | | | | | | | |   (4381)  all_52_26 = e2
% 171.17/25.90  | | | | | | | | | | | | |   (4382)  all_52_24 = e3
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | COMBINE_EQS: (649), (4379) imply:
% 171.17/25.90  | | | | | | | | | | | | |   (4383)  all_6_1 = e0
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (38), (42),
% 171.17/25.90  | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (165), (172),
% 171.17/25.90  | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (182), (183),
% 171.17/25.90  | | | | | | | | | | | | |            (268), (270), (271), (283), (304), (305), (307),
% 171.17/25.90  | | | | | | | | | | | | |            (311), (313), (319), (321), (323), (324), (325),
% 171.17/25.90  | | | | | | | | | | | | |            (326), (327), (328), (330), (331), (344), (349),
% 171.17/25.90  | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (429),
% 171.17/25.90  | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 171.17/25.90  | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 171.17/25.90  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 171.17/25.90  | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (567),
% 171.17/25.90  | | | | | | | | | | | | |            (568), (569), (571), (573), (577), (580), (581),
% 171.17/25.90  | | | | | | | | | | | | |            (582), (583), (585), (586), (588), (589), (594),
% 171.17/25.90  | | | | | | | | | | | | |            (597), (4297), (4301), (4352), (4370), (4371),
% 171.17/25.90  | | | | | | | | | | | | |            (4372), (4380), (4381), (4382), (4383),
% 171.17/25.90  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.90  | | | | | | | | | | | | |            #602.
% 171.17/25.90  | | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | |   (4384)  all_34_0 = e1
% 171.17/25.90  | | | | | | | | |   (4385)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | COMBINE_EQS: (773), (4384) imply:
% 171.17/25.90  | | | | | | | | |   (4386)  all_4_0 = e1
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | SIMP: (4386) implies:
% 171.17/25.90  | | | | | | | | |   (4387)  all_4_0 = e1
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | REDUCE: (4297), (4387) imply:
% 171.17/25.90  | | | | | | | | |   (4388)   ~ (e2 = e1)
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | REDUCE: (38), (4387) imply:
% 171.17/25.90  | | | | | | | | |   (4389)  op(all_4_1, all_4_2) = e1
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | |   (4390)  all_58_15 = e0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | COMBINE_EQS: (532), (4390) imply:
% 171.17/25.90  | | | | | | | | | |   (4391)  all_6_2 = e0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (564), (4391) imply:
% 171.17/25.90  | | | | | | | | | |   (4392)   ~ (all_52_25 = e0)
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (43), (4391) imply:
% 171.17/25.90  | | | | | | | | | |   (4393)  op(all_6_1, e0) = all_6_0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (42), (4391) imply:
% 171.17/25.90  | | | | | | | | | |   (4394)  op(e0, e0) = all_6_1
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (41), (4391) imply:
% 171.17/25.90  | | | | | | | | | |   (4395)  op(e0, e0) = e0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.90  | | | | | | | | | |              e0, e0, simplifying with (4394), (4395) gives:
% 171.17/25.90  | | | | | | | | | |   (4396)  all_6_1 = e0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (4393), (4396) imply:
% 171.17/25.90  | | | | | | | | | |   (4397)  op(e0, e0) = all_6_0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.90  | | | | | | | | | |              e0, e0, simplifying with (4395), (4397) gives:
% 171.17/25.90  | | | | | | | | | |   (4398)  all_6_0 = e0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REDUCE: (4299), (4398) imply:
% 171.17/25.90  | | | | | | | | | |   (4399)   ~ (e3 = e0)
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | |   (4400)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.90  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.90  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.90  | | | | | | | | | | |            (4389), (4400), (function-axioms) are inconsistent
% 171.17/25.90  | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | |   (4401)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.90  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.90  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (37), (62), (161), (163),
% 171.17/25.90  | | | | | | | | | | |            (164), (165), (172), (173), (177), (179), (181),
% 171.17/25.90  | | | | | | | | | | |            (270), (271), (280), (282), (283), (304), (328),
% 171.17/25.90  | | | | | | | | | | |            (330), (344), (349), (386), (392), (403), (429),
% 171.17/25.90  | | | | | | | | | | |            (494), (531), (533), (534), (544), (546), (548),
% 171.17/25.90  | | | | | | | | | | |            (552), (554), (562), (566), (596), (663), (719),
% 171.17/25.90  | | | | | | | | | | |            (796), (4295), (4385), (4389), (4390), (4392),
% 171.17/25.90  | | | | | | | | | | |            (4401), (function-axioms) are inconsistent by
% 171.17/25.90  | | | | | | | | | | |            sub-proof #291.
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | |   (4402)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.90  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.90  | | | | | | | | | |             e0)
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | ALPHA: (4402) implies:
% 171.17/25.90  | | | | | | | | | |   (4403)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | |   (4404)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.90  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.90  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.90  | | | | | | | | | | |            (4389), (4404), (function-axioms) are inconsistent
% 171.17/25.90  | | | | | | | | | | |            by sub-proof #243.
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | |   (4405)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.90  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.90  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (42), (43), (61), (62),
% 171.17/25.90  | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 171.17/25.90  | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 171.17/25.90  | | | | | | | | | | |            (268), (270), (280), (281), (282), (283), (303),
% 171.17/25.90  | | | | | | | | | | |            (304), (306), (307), (322), (324), (325), (326),
% 171.17/25.90  | | | | | | | | | | |            (328), (330), (344), (349), (364), (370), (385),
% 171.17/25.90  | | | | | | | | | | |            (386), (391), (392), (403), (413), (494), (529),
% 171.17/25.90  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (538),
% 171.17/25.90  | | | | | | | | | | |            (539), (540), (544), (546), (548), (552), (554),
% 171.17/25.90  | | | | | | | | | | |            (555), (557), (558), (559), (562), (565), (566),
% 171.17/25.90  | | | | | | | | | | |            (567), (568), (569), (578), (580), (581), (586),
% 171.17/25.90  | | | | | | | | | | |            (591), (595), (596), (597), (649), (663), (719),
% 171.17/25.90  | | | | | | | | | | |            (796), (797), (799), (4295), (4299), (4385),
% 171.17/25.90  | | | | | | | | | | |            (4389), (4403), (4405), (function-axioms) are
% 171.17/25.90  | | | | | | | | | | |            inconsistent by sub-proof #290.
% 171.17/25.90  | | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | End of split
% 171.17/25.90  | | | | | | | | 
% 171.17/25.90  | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | 
% 171.17/25.90  | | | | | | | |   (4406)  all_28_0 = e3
% 171.17/25.90  | | | | | | | | 
% 171.17/25.90  | | | | | | | | COMBINE_EQS: (776), (4406) imply:
% 171.17/25.90  | | | | | | | |   (4407)  all_6_0 = e3
% 171.17/25.90  | | | | | | | | 
% 171.17/25.90  | | | | | | | | REDUCE: (43), (4407) imply:
% 171.17/25.90  | | | | | | | |   (4408)  op(all_6_1, all_6_2) = e3
% 171.17/25.90  | | | | | | | | 
% 171.17/25.90  | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.90  | | | | | | | | 
% 171.17/25.90  | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | |   (4409)   ~ (all_34_0 = e1)
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | REDUCE: (773), (4409) imply:
% 171.17/25.90  | | | | | | | | |   (4410)   ~ (all_4_0 = e1)
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.90  | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | Case 1:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | |   (4411)  all_58_15 = e0
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (4408), (4411),
% 171.17/25.90  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.90  | | | | | | | | | |            #510.
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | Case 2:
% 171.17/25.90  | | | | | | | | | | 
% 171.17/25.90  | | | | | | | | | |   (4412)   ~ (all_58_15 = e0)
% 171.17/25.91  | | | | | | | | | |   (4413)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.91  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.91  | | | | | | | | | |             e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | ALPHA: (4413) implies:
% 171.17/25.91  | | | | | | | | | |   (4414)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.91  | | | | | | | | | |   (4415)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (532), (4412) imply:
% 171.17/25.91  | | | | | | | | | |   (4416)   ~ (all_6_2 = e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | |   (4417)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.91  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.91  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | BETA: splitting (4417) gives:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | |   (4418)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.91  | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | ALPHA: (4418) implies:
% 171.17/25.91  | | | | | | | | | | | |   (4419)  all_52_6 = e0
% 171.17/25.91  | | | | | | | | | | | |   (4420)  all_52_4 = e1
% 171.17/25.91  | | | | | | | | | | | |   (4421)  all_52_2 = e2
% 171.17/25.91  | | | | | | | | | | | |   (4422)  all_52_0 = e3
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | COMBINE_EQS: (720), (4422) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4423)  all_4_1 = e3
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REDUCE: (38), (4423) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4424)  op(e3, all_4_2) = all_4_0
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REDUCE: (37), (4423) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4425)  op(e3, all_4_2) = e3
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REDUCE: (176), (4421) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4426)  op(e2, all_52_3) = e2
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REDUCE: (168), (4420) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4427)  op(e1, all_52_5) = e1
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REDUCE: (160), (4419) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4428)  op(e0, all_52_7) = e0
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (42), (43), (51), (52), (61), (62),
% 171.17/25.91  | | | | | | | | | | | |            (154), (155), (156), (158), (159), (161), (163),
% 171.17/25.91  | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (174),
% 171.17/25.91  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 171.17/25.91  | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 171.17/25.91  | | | | | | | | | | | |            (276), (277), (279), (280), (281), (282), (283),
% 171.17/25.91  | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (309),
% 171.17/25.91  | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 171.17/25.91  | | | | | | | | | | | |            (318), (319), (321), (322), (323), (324), (325),
% 171.17/25.91  | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (341),
% 171.17/25.91  | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 171.17/25.91  | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 171.17/25.91  | | | | | | | | | | | |            (413), (415), (419), (425), (429), (529), (531),
% 171.17/25.91  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 171.17/25.91  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 171.17/25.91  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.91  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 171.17/25.91  | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 171.17/25.91  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 171.17/25.91  | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 171.17/25.91  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 171.17/25.91  | | | | | | | | | | | |            (797), (799), (3239), (4294), (4295), (4297),
% 171.17/25.91  | | | | | | | | | | | |            (4410), (4414), (4415), (4416), (4424), (4425),
% 171.17/25.91  | | | | | | | | | | | |            (4426), (4427), (4428), (function-axioms) are
% 171.17/25.91  | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | |   (4429)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.91  | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | ALPHA: (4429) implies:
% 171.17/25.91  | | | | | | | | | | | |   (4430)  all_52_10 = e2
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | COMBINE_EQS: (661), (4430) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4431)  all_10_1 = e2
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REF_CLOSE: (9), (52), (3239), (4431), (function-axioms) are
% 171.17/25.91  | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | |   (4432)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.91  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.91  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (4295),
% 171.17/25.91  | | | | | | | | | | |            (4408), (4432), (function-axioms) are inconsistent
% 171.17/25.91  | | | | | | | | | | |            by sub-proof #300.
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | |   (4433)  all_34_0 = e1
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | COMBINE_EQS: (773), (4433) imply:
% 171.17/25.91  | | | | | | | | |   (4434)  all_4_0 = e1
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | SIMP: (4434) implies:
% 171.17/25.91  | | | | | | | | |   (4435)  all_4_0 = e1
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | REDUCE: (4297), (4435) imply:
% 171.17/25.91  | | | | | | | | |   (4436)   ~ (e2 = e1)
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | REDUCE: (38), (4435) imply:
% 171.17/25.91  | | | | | | | | |   (4437)  op(all_4_1, all_4_2) = e1
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | |   (4438)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.91  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.91  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (3239),
% 171.17/25.91  | | | | | | | | | |            (4437), (4438), (function-axioms) are inconsistent
% 171.17/25.91  | | | | | | | | | |            by sub-proof #243.
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | |   (4439)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.91  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.91  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REF_CLOSE: (6), (7), (42), (62), (649), (719), (4295),
% 171.17/25.91  | | | | | | | | | |            (4408), (4439), (function-axioms) are inconsistent
% 171.17/25.91  | | | | | | | | | |            by sub-proof #300.
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | End of split
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | Case 2:
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | |   (4440)  all_26_0 = e2
% 171.17/25.91  | | | | | | |   (4441)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | | COMBINE_EQS: (779), (4440) imply:
% 171.17/25.91  | | | | | | |   (4442)  all_4_0 = e2
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | | COMBINE_EQS: (742), (4442) imply:
% 171.17/25.91  | | | | | | |   (4443)  all_50_0 = e2
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | | REDUCE: (38), (4442) imply:
% 171.17/25.91  | | | | | | |   (4444)  op(all_4_1, all_4_2) = e2
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | | BETA: splitting (98) gives:
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | |   (4445)   ~ (all_28_0 = e3)
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | REDUCE: (776), (4445) imply:
% 171.17/25.91  | | | | | | | |   (4446)   ~ (all_6_0 = e3)
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | BETA: splitting (151) gives:
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | |   (4447)   ~ (all_50_0 = e2)
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | REDUCE: (4443), (4447) imply:
% 171.17/25.91  | | | | | | | | |   (4448)  $false
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | CLOSE: (4448) is inconsistent.
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | |   (4449)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | |   (4450)  all_58_15 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | COMBINE_EQS: (532), (4450) imply:
% 171.17/25.91  | | | | | | | | | |   (4451)  all_6_2 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (564), (4451) imply:
% 171.17/25.91  | | | | | | | | | |   (4452)   ~ (all_52_25 = e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (43), (4451) imply:
% 171.17/25.91  | | | | | | | | | |   (4453)  op(all_6_1, e0) = all_6_0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (42), (4451) imply:
% 171.17/25.91  | | | | | | | | | |   (4454)  op(e0, e0) = all_6_1
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (41), (4451) imply:
% 171.17/25.91  | | | | | | | | | |   (4455)  op(e0, e0) = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 171.17/25.91  | | | | | | | | | |              e0, e0, simplifying with (4454), (4455) gives:
% 171.17/25.91  | | | | | | | | | |   (4456)  all_6_1 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (4453), (4456) imply:
% 171.17/25.91  | | | | | | | | | |   (4457)  op(e0, e0) = all_6_0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 171.17/25.91  | | | | | | | | | |              e0, e0, simplifying with (4455), (4457) gives:
% 171.17/25.91  | | | | | | | | | |   (4458)  all_6_0 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (4446), (4458) imply:
% 171.17/25.91  | | | | | | | | | |   (4459)   ~ (e3 = e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (799), (4458) imply:
% 171.17/25.91  | | | | | | | | | |   (4460)   ~ (e2 = e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | |   (4461)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.91  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.91  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.91  | | | | | | | | | | |            (4444), (4461), (function-axioms) are inconsistent
% 171.17/25.91  | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | |   (4462)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.91  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.91  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (36), (37), (62), (164),
% 171.17/25.91  | | | | | | | | | | |            (165), (172), (173), (177), (178), (179), (181),
% 171.17/25.91  | | | | | | | | | | |            (270), (271), (280), (283), (303), (304), (326),
% 171.17/25.91  | | | | | | | | | | |            (344), (349), (386), (403), (429), (503), (531),
% 171.17/25.91  | | | | | | | | | | |            (533), (534), (542), (544), (546), (548), (550),
% 171.17/25.91  | | | | | | | | | | |            (552), (554), (558), (562), (563), (586), (698),
% 171.17/25.91  | | | | | | | | | | |            (719), (796), (4295), (4441), (4444), (4450),
% 171.17/25.91  | | | | | | | | | | |            (4452), (4462), (function-axioms) are inconsistent
% 171.17/25.91  | | | | | | | | | | |            by sub-proof #298.
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | |   (4463)   ~ (all_58_15 = e0)
% 171.17/25.91  | | | | | | | | | |   (4464)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.91  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.91  | | | | | | | | | |             e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | ALPHA: (4464) implies:
% 171.17/25.91  | | | | | | | | | |   (4465)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (532), (4463) imply:
% 171.17/25.91  | | | | | | | | | |   (4466)   ~ (all_6_2 = e0)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | |   (4467)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.91  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.91  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.91  | | | | | | | | | | |            (4444), (4467), (function-axioms) are inconsistent
% 171.17/25.91  | | | | | | | | | | |            by sub-proof #237.
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | |   (4468)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.91  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.91  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | BETA: splitting (4468) gives:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | |   (4469)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.91  | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | ALPHA: (4469) implies:
% 171.17/25.91  | | | | | | | | | | | |   (4470)  all_52_20 = e1
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | COMBINE_EQS: (719), (4470) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4471)  all_14_1 = e1
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REF_CLOSE: (6), (62), (4295), (4471), (function-axioms) are
% 171.17/25.91  | | | | | | | | | | | |            inconsistent by sub-proof #315.
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | |   (4472)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.91  | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (42), (43), (51), (154),
% 171.17/25.91  | | | | | | | | | | | |            (155), (156), (164), (165), (172), (173), (177),
% 171.17/25.91  | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 171.17/25.91  | | | | | | | | | | | |            (271), (280), (283), (303), (304), (305), (306),
% 171.17/25.91  | | | | | | | | | | | |            (307), (313), (322), (323), (324), (325), (326),
% 171.17/25.91  | | | | | | | | | | | |            (328), (330), (344), (349), (364), (370), (373),
% 171.17/25.91  | | | | | | | | | | | |            (385), (386), (391), (403), (429), (503), (521),
% 171.17/25.91  | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 171.17/25.91  | | | | | | | | | | | |            (537), (538), (539), (540), (544), (546), (548),
% 171.17/25.91  | | | | | | | | | | | |            (550), (552), (553), (554), (555), (557), (558),
% 171.17/25.91  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (569),
% 171.17/25.91  | | | | | | | | | | | |            (573), (580), (581), (588), (589), (594), (597),
% 171.17/25.91  | | | | | | | | | | | |            (649), (698), (718), (796), (797), (799), (4441),
% 171.17/25.91  | | | | | | | | | | | |            (4444), (4446), (4449), (4465), (4466), (4472),
% 171.17/25.91  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.91  | | | | | | | | | | | |            #449.
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | |   (4473)  all_28_0 = e3
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | COMBINE_EQS: (776), (4473) imply:
% 171.17/25.91  | | | | | | | |   (4474)  all_6_0 = e3
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | SIMP: (4474) implies:
% 171.17/25.91  | | | | | | | |   (4475)  all_6_0 = e3
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | REDUCE: (43), (4475) imply:
% 171.17/25.91  | | | | | | | |   (4476)  op(all_6_1, all_6_2) = e3
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | |   (4477)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.91  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 171.17/25.91  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (3239),
% 171.17/25.91  | | | | | | | | |            (4444), (4477), (function-axioms) are inconsistent
% 171.17/25.91  | | | | | | | | |            by sub-proof #237.
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | |   (4478)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.91  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 171.17/25.91  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | BETA: splitting (4478) gives:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | |   (4479)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.91  | | | | | | | | | |           all_52_22 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REF_CLOSE: (6), (62), (719), (4295), (4479),
% 171.17/25.91  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.91  | | | | | | | | | |            #314.
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | |   (4480)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.91  | | | | | | | | | |           all_52_30 = e0
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REF_CLOSE: (7), (42), (649), (4476), (4480),
% 171.17/25.91  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.91  | | | | | | | | | |            #501.
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | End of split
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | End of split
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | End of split
% 171.17/25.91  | | | | | | 
% 171.17/25.91  | | | | | End of split
% 171.17/25.91  | | | | | 
% 171.17/25.91  | | | | End of split
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | Case 2:
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | |   (4481)  all_8_0 = e2
% 171.17/25.91  | | | |   (4482)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | | COMBINE_EQS: (791), (4481) imply:
% 171.17/25.91  | | | |   (4483)  all_6_0 = e2
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | | SIMP: (4483) implies:
% 171.17/25.91  | | | |   (4484)  all_6_0 = e2
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | | COMBINE_EQS: (785), (4484) imply:
% 171.17/25.91  | | | |   (4485)  all_16_0 = e2
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | | REDUCE: (43), (4484) imply:
% 171.17/25.91  | | | |   (4486)  op(all_6_1, all_6_2) = e2
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | | BETA: splitting (54) gives:
% 171.17/25.91  | | | | 
% 171.17/25.91  | | | | Case 1:
% 171.17/25.91  | | | | | 
% 171.17/25.91  | | | | |   (4487)   ~ (all_10_0 = e3)
% 171.17/25.91  | | | | | 
% 171.17/25.91  | | | | | BETA: splitting (59) gives:
% 171.17/25.91  | | | | | 
% 171.17/25.91  | | | | | Case 1:
% 171.17/25.91  | | | | | | 
% 171.17/25.91  | | | | | |   (4488)   ~ (all_12_1 = e3)
% 171.17/25.91  | | | | | | 
% 171.17/25.91  | | | | | | REDUCE: (705), (4488) imply:
% 171.17/25.91  | | | | | |   (4489)   ~ (all_10_1 = e3)
% 171.17/25.91  | | | | | | 
% 171.17/25.91  | | | | | | BETA: splitting (64) gives:
% 171.17/25.91  | | | | | | 
% 171.17/25.91  | | | | | | Case 1:
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | |   (4490)   ~ (all_14_0 = e2)
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | | BETA: splitting (69) gives:
% 171.17/25.91  | | | | | | | 
% 171.17/25.91  | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | |   (4491)   ~ (all_16_0 = e2)
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | REDUCE: (4485), (4491) imply:
% 171.17/25.91  | | | | | | | |   (4492)  $false
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | CLOSE: (4492) is inconsistent.
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | Case 2:
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | |   (4493)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | BETA: splitting (74) gives:
% 171.17/25.91  | | | | | | | | 
% 171.17/25.91  | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | |   (4494)   ~ (all_18_0 = e3)
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | REDUCE: (789), (4494) imply:
% 171.17/25.91  | | | | | | | | |   (4495)   ~ (all_14_0 = e3)
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | BETA: splitting (83) gives:
% 171.17/25.91  | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | |   (4496)   ~ (all_22_1 = e3)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | REDUCE: (711), (4496) imply:
% 171.17/25.91  | | | | | | | | | |   (4497)   ~ (all_14_1 = e3)
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | BETA: splitting (88) gives:
% 171.17/25.91  | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | |   (4498)   ~ (all_24_0 = e1)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | REDUCE: (751), (4498) imply:
% 171.17/25.91  | | | | | | | | | | |   (4499)   ~ (all_10_0 = e1)
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | BETA: splitting (93) gives:
% 171.17/25.91  | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | |   (4500)   ~ (all_26_0 = e2)
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | REDUCE: (779), (4500) imply:
% 171.17/25.91  | | | | | | | | | | | |   (4501)   ~ (all_4_0 = e2)
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | BETA: splitting (108) gives:
% 171.17/25.91  | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | |   (4502)   ~ (all_32_1 = e2)
% 171.17/25.91  | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | REDUCE: (713), (4502) imply:
% 171.17/25.91  | | | | | | | | | | | | |   (4503)   ~ (all_14_1 = e2)
% 171.17/25.91  | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.91  | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | |   (4504)   ~ (all_34_0 = e1)
% 171.17/25.91  | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | REDUCE: (773), (4504) imply:
% 171.17/25.91  | | | | | | | | | | | | | |   (4505)   ~ (all_4_0 = e1)
% 171.17/25.91  | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.91  | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | |   (4506)   ~ (all_40_1 = e1)
% 171.17/25.91  | | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | | REDUCE: (715), (4506) imply:
% 171.17/25.91  | | | | | | | | | | | | | | |   (4507)   ~ (all_4_1 = e1)
% 171.17/25.91  | | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.91  | | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.91  | | | | | | | | | | | | | | | | 
% 171.17/25.91  | | | | | | | | | | | | | | | |   (4508)  all_58_15 = e0
% 171.17/25.91  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (4508),
% 171.17/25.92  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.92  | | | | | | | | | | | | | | | |            #228.
% 171.17/25.92  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | |   (4509)   ~ (all_58_15 = e0)
% 171.17/25.92  | | | | | | | | | | | | | | | |   (4510)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.92  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.92  | | | | | | | | | | | | | | | |             e0)
% 171.17/25.92  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | ALPHA: (4510) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | |   (4511)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | |   (4512)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | REDUCE: (532), (4509) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | |   (4513)   ~ (all_6_2 = e0)
% 171.17/25.92  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | |   (4514)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.92  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.92  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | BETA: splitting (4514) gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4515)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.92  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (37), (38), (42), (61), (154), (156),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (158), (160), (161), (163), (164), (165), (168),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (176), (177), (178),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (179), (268), (269), (270), (271), (272), (273),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (276), (278), (279), (281), (282), (283), (303),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (501), (515), (529), (530), (531), (532), (533),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (561),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (569), (571), (573), (575), (578), (579), (580),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (597), (598), (600), (704), (710), (720), (4482),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (4486), (4493), (4501), (4505), (4511), (4512),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (4513), (4515), (function-axioms) are inconsistent
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            by sub-proof #220.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4516)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 171.17/25.92  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | ALPHA: (4516) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4517)  all_52_14 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4518)  all_52_12 = e1
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4519)  all_52_10 = e2
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4520)  all_52_8 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (4519) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4521)  all_10_1 = e2
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (53), (4521) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4522)  op(e2, all_10_2) = all_10_0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (183), (4520) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4523)  op(e3, all_52_9) = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (52), (4521) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4524)  op(e2, all_10_2) = e2
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (167), (4518) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4525)  op(e1, all_52_13) = e1
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (159), (4517) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4526)  op(e0, all_52_15) = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 171.17/25.92  | | | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (4522), (4524)
% 171.17/25.92  | | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4527)  all_10_0 = e2
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (4487), (4527) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4528)   ~ (e3 = e2)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |   (4529)  all_56_15 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (4529) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |   (4530)  all_6_2 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | SIMP: (4530) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |   (4531)  all_6_2 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |            (4531), (function-axioms) are inconsistent by
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |   (4532)   ~ (all_56_15 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |   (4533)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (4532) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | |   (4534)   ~ (all_6_2 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4535)  all_56_13 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (4535) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4536)  all_52_27 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | SIMP: (4536) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4537)  all_52_27 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (4537) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4538)  all_58_13 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4537) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4539)   ~ (all_52_3 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (4537) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4540)   ~ (all_52_19 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (4537) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4541)   ~ (all_52_29 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | SIMP: (4541) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4542)   ~ (all_52_29 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (4537) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4543)   ~ (all_10_2 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | SIMP: (4543) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4544)   ~ (all_10_2 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (4537) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4545)   ~ (all_6_2 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4537) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4546)  op(e2, e3) = all_52_26
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e2, simplifying with (172), (4546)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4547)  all_52_9 = all_52_26
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4548)  all_56_4 = all_52_26
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4549)  all_58_2 = all_52_26
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4550)   ~ (all_52_13 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | SIMP: (4550) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4551)   ~ (all_52_13 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4552)   ~ (all_52_15 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | SIMP: (4552) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4553)   ~ (all_52_15 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4554)   ~ (all_52_17 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | SIMP: (4554) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4555)   ~ (all_52_17 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4556)   ~ (all_52_25 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | SIMP: (4556) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4557)   ~ (all_52_25 = all_52_26)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4558)   ~ (all_52_26 = all_10_2)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4559)   ~ (all_52_26 = all_4_2)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (4523), (4547) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4560)  op(e3, all_52_26) = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | |   (4561)  all_56_1 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (4539), (4561) are inconsistent by
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | |   (4562)   ~ (all_56_1 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | |   (4563)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |   (4564)  all_56_10 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (4564) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |   (4565)  all_14_2 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | SIMP: (4565) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |   (4566)  all_14_2 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (36), (37), (62), (156), (164), (179),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (307), (311), (315), (319), (328), (330), (331),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (349), (364), (370), (373), (391), (403), (532),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (533), (535), (536), (537), (538), (539), (540),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (548), (552), (558), (560), (579), (584), (586),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (587), (588), (593), (595), (596), (796), (4503),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (4525), (4526), (4534), (4539), (4544), (4549),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (4551), (4559), (4560), (4566), (function-axioms)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #219.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |   (4567)   ~ (all_56_10 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (4567) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |   (4568)   ~ (all_14_2 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (36), (37), (38), (42), (155), (156),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (161), (164), (170), (177), (178), (179), (181),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (182), (279), (283), (307), (311), (313), (315),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (316), (319), (321), (326), (330), (331), (349),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (364), (370), (373), (391), (392), (403), (529),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (546), (548), (550), (558),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (559), (560), (561), (565), (568), (569), (580),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (582), (583), (584), (586), (593), (594), (596),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (598), (4486), (4501), (4505), (4507), (4511),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (4512), (4524), (4525), (4526), (4533), (4534),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (4538), (4539), (4540), (4542), (4544), (4548),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (4549), (4551), (4553), (4555), (4557), (4558),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            (4559), (4560), (4563), (4568), (function-axioms)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #214.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4569)   ~ (all_56_13 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (4569) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |   (4570)   ~ (all_52_27 = e3)
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (38), (42),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (62), (154), (156), (158), (161), (163), (164),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (165), (169), (170), (172), (174), (177), (178),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (179), (181), (182), (272), (273), (274), (277),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (279), (280), (283), (304), (307), (311), (313),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (315), (316), (319), (320), (321), (323), (326),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (349), (350), (359),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (403),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (409), (415), (419), (515), (529), (531), (532),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (553), (554), (556), (557), (558), (559), (560),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (568), (569), (571), (573), (579), (580), (581),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (582), (586), (587), (588), (591), (593), (594),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (710),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (796), (4482), (4497), (4501), (4512), (4513),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (4523), (4524), (4525), (4526), (4533), (4534),
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            (4570), (function-axioms) are inconsistent by
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | |            sub-proof #208.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | |   (4571)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 171.17/25.92  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 171.17/25.92  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | BETA: splitting (4571) gives:
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4572)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 171.17/25.92  | | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | ALPHA: (4572) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4573)  all_52_22 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4574)  all_52_20 = e1
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4575)  all_52_18 = e2
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4576)  all_52_16 = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (4574) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4577)  all_14_1 = e1
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | SIMP: (4577) implies:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4578)  all_14_1 = e1
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (63), (4578) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4579)  op(e1, all_14_2) = all_14_0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (182), (4576) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4580)  op(e3, all_52_17) = e3
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (174), (4575) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4581)  op(e2, all_52_19) = e2
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (62), (4578) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4582)  op(e1, all_14_2) = e1
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REDUCE: (158), (4573) imply:
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4583)  op(e0, all_52_23) = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (52),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (154), (156), (161), (163), (164), (165), (169),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (183), (268), (270), (271), (272), (273), (274),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (275), (276), (277), (278), (282), (283), (303),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (304), (307), (308), (310), (311), (312), (314),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (315), (317), (319), (320), (322), (323), (324),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (391), (392), (403), (415), (419), (425), (429),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (501), (515), (529), (530), (531), (532), (533),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (568), (571), (577), (578), (579), (580), (581),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (582), (583), (584), (586), (587), (588), (591),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (704), (710), (796), (4482), (4486), (4489),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (4490), (4493), (4495), (4501), (4505), (4507),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (4512), (4513), (4579), (4580), (4581), (4582),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (4583), (function-axioms) are inconsistent by
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            sub-proof #202.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | |   (4584)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 171.17/25.92  | | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (4584),
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.92  | | | | | | | | | | | | | | | | | |            #200.
% 171.17/25.92  | | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | End of split
% 171.17/25.92  | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | Case 2:
% 171.17/25.92  | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | |   (4585)  all_40_1 = e1
% 171.17/25.92  | | | | | | | | | | | | | | |   (4586)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 171.17/25.92  | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | COMBINE_EQS: (715), (4585) imply:
% 171.17/25.92  | | | | | | | | | | | | | | |   (4587)  all_4_1 = e1
% 171.17/25.92  | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (4587) imply:
% 171.17/25.92  | | | | | | | | | | | | | | |   (4588)  all_52_0 = e1
% 171.17/25.92  | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | REDUCE: (38), (4587) imply:
% 171.17/25.92  | | | | | | | | | | | | | | |   (4589)  op(e1, all_4_2) = all_4_0
% 171.17/25.92  | | | | | | | | | | | | | | | 
% 171.17/25.92  | | | | | | | | | | | | | | | REDUCE: (37), (4587) imply:
% 171.17/25.92  | | | | | | | | | | | | | | |   (4590)  op(e3, all_4_2) = e1
% 171.17/25.92  | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (38), (41),
% 171.17/25.93  | | | | | | | | | | | | | | |            (42), (52), (53), (62), (63), (154), (156), (158),
% 171.17/25.93  | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (169),
% 171.17/25.93  | | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 171.17/25.93  | | | | | | | | | | | | | | |            (181), (182), (183), (185), (268), (270), (271),
% 171.17/25.93  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 171.17/25.93  | | | | | | | | | | | | | | |            (279), (280), (283), (301), (303), (304), (307),
% 171.17/25.93  | | | | | | | | | | | | | | |            (308), (310), (311), (313), (314), (315), (316),
% 171.17/25.93  | | | | | | | | | | | | | | |            (317), (319), (320), (321), (322), (323), (324),
% 171.17/25.93  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 171.17/25.93  | | | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 171.17/25.93  | | | | | | | | | | | | | | |            (386), (391), (403), (409), (415), (419), (425),
% 171.17/25.93  | | | | | | | | | | | | | | |            (429), (501), (515), (518), (529), (530), (531),
% 171.17/25.93  | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 171.17/25.93  | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 171.17/25.93  | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 171.17/25.93  | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 171.17/25.93  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 171.17/25.93  | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 171.17/25.93  | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 171.17/25.93  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (649),
% 171.17/25.93  | | | | | | | | | | | | | | |            (661), (704), (710), (719), (770), (796), (4482),
% 171.17/25.93  | | | | | | | | | | | | | | |            (4486), (4487), (4489), (4490), (4493), (4495),
% 171.17/25.93  | | | | | | | | | | | | | | |            (4497), (4499), (4501), (4505), (4586), (4588),
% 171.17/25.93  | | | | | | | | | | | | | | |            (4589), (4590), (function-axioms) are inconsistent
% 171.17/25.93  | | | | | | | | | | | | | | |            by sub-proof #198.
% 171.17/25.93  | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | End of split
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | Case 2:
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | |   (4591)  all_34_0 = e1
% 171.17/25.93  | | | | | | | | | | | | | |   (4592)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | COMBINE_EQS: (773), (4591) imply:
% 171.17/25.93  | | | | | | | | | | | | | |   (4593)  all_4_0 = e1
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | SIMP: (4593) implies:
% 171.17/25.93  | | | | | | | | | | | | | |   (4594)  all_4_0 = e1
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | REDUCE: (38), (4594) imply:
% 171.17/25.93  | | | | | | | | | | | | | |   (4595)  op(all_4_1, all_4_2) = e1
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (36), (37), (41), (42), (52),
% 171.17/25.93  | | | | | | | | | | | | | |            (53), (62), (63), (154), (155), (156), (158),
% 171.17/25.93  | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (169),
% 171.17/25.93  | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 171.17/25.93  | | | | | | | | | | | | | |            (182), (183), (185), (268), (270), (271), (274),
% 171.17/25.93  | | | | | | | | | | | | | |            (275), (277), (279), (280), (281), (282), (283),
% 171.17/25.93  | | | | | | | | | | | | | |            (301), (303), (304), (307), (308), (311), (315),
% 171.17/25.93  | | | | | | | | | | | | | |            (319), (320), (323), (326), (328), (329), (330),
% 171.17/25.93  | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 171.17/25.93  | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 171.17/25.93  | | | | | | | | | | | | | |            (415), (419), (429), (494), (501), (515), (529),
% 171.17/25.93  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 171.17/25.93  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 171.17/25.93  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 171.17/25.93  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 171.17/25.93  | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (573), (579),
% 171.17/25.93  | | | | | | | | | | | | | |            (580), (581), (582), (584), (585), (586), (588),
% 171.17/25.93  | | | | | | | | | | | | | |            (591), (593), (594), (596), (597), (598), (599),
% 171.17/25.93  | | | | | | | | | | | | | |            (649), (661), (663), (704), (710), (719), (720),
% 171.17/25.93  | | | | | | | | | | | | | |            (796), (4482), (4486), (4487), (4493), (4495),
% 171.17/25.93  | | | | | | | | | | | | | |            (4499), (4592), (4595), (function-axioms) are
% 171.17/25.93  | | | | | | | | | | | | | |            inconsistent by sub-proof #190.
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | End of split
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | Case 2:
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | |   (4596)  all_32_1 = e2
% 171.17/25.93  | | | | | | | | | | | | |   (4597)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e3)
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | COMBINE_EQS: (713), (4596) imply:
% 171.17/25.93  | | | | | | | | | | | | |   (4598)  all_14_1 = e2
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | COMBINE_EQS: (719), (4598) imply:
% 171.17/25.93  | | | | | | | | | | | | |   (4599)  all_52_20 = e2
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | REDUCE: (4497), (4598) imply:
% 171.17/25.93  | | | | | | | | | | | | |   (4600)   ~ (e3 = e2)
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | REDUCE: (63), (4598) imply:
% 171.17/25.93  | | | | | | | | | | | | |   (4601)  op(e2, all_14_2) = all_14_0
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | REDUCE: (62), (4598) imply:
% 171.17/25.93  | | | | | | | | | | | | |   (4602)  op(e1, all_14_2) = e2
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 171.17/25.93  | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | |   (4603)   ~ (all_34_0 = e1)
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | REDUCE: (773), (4603) imply:
% 171.17/25.93  | | | | | | | | | | | | | |   (4604)   ~ (all_4_0 = e1)
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 171.17/25.93  | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | |   (4605)   ~ (all_40_1 = e1)
% 171.17/25.93  | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | REDUCE: (715), (4605) imply:
% 171.17/25.93  | | | | | | | | | | | | | | |   (4606)   ~ (all_4_1 = e1)
% 171.17/25.93  | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | |   (4607)  all_58_15 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (4607),
% 171.17/25.93  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 171.17/25.93  | | | | | | | | | | | | | | | |            #228.
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | Case 2:
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | |   (4608)   ~ (all_58_15 = e0)
% 171.17/25.93  | | | | | | | | | | | | | | | |   (4609)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 171.17/25.93  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 171.17/25.93  | | | | | | | | | | | | | | | |             e0)
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | ALPHA: (4609) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | |   (4610)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | |   (4611)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | REDUCE: (532), (4608) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | |   (4612)   ~ (all_6_2 = e0)
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | |   (4613)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.93  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 171.17/25.93  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 171.17/25.93  | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | BETA: splitting (4613) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4614)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 171.17/25.93  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | ALPHA: (4614) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4615)  all_52_6 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4616)  all_52_4 = e1
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4617)  all_52_2 = e2
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4618)  all_52_0 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (4618) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4619)  all_4_1 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | REDUCE: (38), (4619) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4620)  op(e3, all_4_2) = all_4_0
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | REDUCE: (37), (4619) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4621)  op(e3, all_4_2) = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | REDUCE: (176), (4617) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4622)  op(e2, all_52_3) = e2
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | REDUCE: (168), (4616) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4623)  op(e1, all_52_5) = e1
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | REDUCE: (160), (4615) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4624)  op(e0, all_52_7) = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 171.17/25.93  | | | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (4620), (4621)
% 171.17/25.93  | | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | |   (4625)  all_4_0 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |   (4626)  all_56_15 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (4626) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |   (4627)  all_6_2 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |            (4627), (function-axioms) are inconsistent by
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |   (4628)   ~ (all_56_15 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |   (4629)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (4628) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | |   (4630)   ~ (all_6_2 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4631)  all_56_13 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (4631) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4632)  all_52_27 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4632) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4633)   ~ (all_52_3 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (4632) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4634)   ~ (all_52_19 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (4632) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4635)   ~ (all_52_25 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (4632) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4636)   ~ (all_52_29 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | SIMP: (4636) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4637)   ~ (all_52_29 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (4632) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4638)   ~ (all_6_2 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4632) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4639)  op(e2, e3) = all_52_26
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (155), (4632) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4640)  op(e0, e2) = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e2, simplifying with (172), (4639)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |              gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4641)  all_52_9 = all_52_26
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4642)  all_56_4 = all_52_26
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4643)  all_58_2 = all_52_26
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4644)   ~ (all_52_13 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | SIMP: (4644) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4645)   ~ (all_52_13 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4646)   ~ (all_52_15 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | SIMP: (4646) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4647)   ~ (all_52_15 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4648)   ~ (all_52_17 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | SIMP: (4648) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4649)   ~ (all_52_17 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4650)   ~ (all_52_25 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | SIMP: (4650) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4651)   ~ (all_52_25 = all_52_26)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4652)   ~ (all_52_26 = all_4_2)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (4641) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | |   (4653)  op(e3, all_52_26) = all_52_8
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | |   (4654)  all_56_14 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (341), (4637), (4654) are inconsistent by
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | |            sub-proof #896.
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | |   (4655)   ~ (all_56_14 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | |   (4656)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | |   (4657)  all_56_12 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (429), (4635), (4657) are inconsistent by
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1040.
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | |   (4658)   ~ (all_56_12 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | |   (4659)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | |   (4660)  all_56_6 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (4660) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | |   (4661)  all_52_13 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4661) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | |   (4662)  all_52_13 = e3
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (4662) imply:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | |   (4663)   ~ (all_14_2 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4663) implies:
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | |   (4664)   ~ (all_14_2 = e3)
% 171.17/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (161),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (177), (178), (179), (279), (281),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (310), (311), (312), (313), (314),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (315), (317), (324), (326), (327), (328), (330),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (341), (349), (364), (370), (373), (391), (403),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (413), (429), (529), (531), (532), (533), (535),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (536), (537), (538), (540), (544), (546), (550),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (552), (558), (559), (561), (563), (564), (566),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (579), (584), (585), (586), (587),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (589), (591), (594), (600), (4611), (4612),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (4621), (4623), (4624), (4629), (4630), (4634),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (4635), (4637), (4642), (4643), (4645), (4647),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (4649), (4651), (4652), (4656), (4659), (4664),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |            #800.
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |   (4665)   ~ (all_56_6 = e3)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (4665) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | |   (4666)   ~ (all_52_13 = e3)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |   (4667)  all_58_4 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (4667) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |   (4668)  all_52_5 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4668) implies:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |   (4669)  all_52_5 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (4669) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |   (4670)   ~ (all_14_2 = e3)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4670) implies:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |   (4671)   ~ (all_14_2 = e3)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (161),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (177), (178), (179), (279), (281),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (310), (311), (312), (313), (314),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (315), (317), (324), (326), (327), (328), (330),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (341), (349), (364), (370), (373), (391), (403),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (413), (429), (529), (531), (532), (533), (535),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (536), (537), (538), (540), (544), (546), (550),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (552), (558), (559), (561), (563), (564), (566),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (568), (569), (579), (584), (585), (586), (587),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (589), (591), (594), (600), (4611), (4612),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (4621), (4623), (4624), (4629), (4630), (4634),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (4635), (4637), (4642), (4643), (4645), (4647),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (4649), (4651), (4652), (4656), (4659), (4671),
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |            #800.
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | |   (4672)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4672) gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (4673)  all_58_5 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (373), (4666), (4673) are inconsistent by
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #969.
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (4674)  all_58_8 = e3 | all_58_14 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4674) gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4675)  all_58_8 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (4675) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4676)  all_14_2 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (4676) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4677)  all_32_2 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (4676) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4678)   ~ (all_52_5 = e3)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4601), (4676) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4679)  op(e2, e3) = all_14_0
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4602), (4676) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4680)  op(e1, e3) = e2
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (4676) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4681)  op(e1, e1) = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4597) gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4682)   ~ (all_32_2 = e3)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4677), (4682) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4683)  $false
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4683) is inconsistent.
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4684)   ~ (all_32_0 = e0)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (793), (4684) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4685)   ~ (all_14_0 = e0)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, e1, simplifying with (164), (4680) gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4686)  all_52_17 = e2
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_26,
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e3, e2, simplifying with (4639), (4679)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4687)  all_52_26 = all_14_0
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4642), (4687) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4688)  all_56_4 = all_14_0
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4645), (4687) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4689)   ~ (all_52_13 = all_14_0)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (4686) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4690)   ~ (all_52_25 = e2)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4690) implies:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4691)   ~ (all_52_25 = e2)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4649), (4686), (4687) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4692)   ~ (all_14_0 = e2)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4651), (4687) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4693)   ~ (all_52_25 = all_14_0)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4652), (4687) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4694)   ~ (all_14_0 = all_4_2)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (4686) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4695)  op(e3, e2) = all_52_16
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4653), (4687) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4696)  op(e3, all_14_0) = all_52_8
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4697)  all_58_0 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (4697) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4698)  all_4_2 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (552), (4698) imply:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4699)   ~ (all_52_7 = e3)
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4700)  all_56_4 = e3
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4495), (4688), (4700) are inconsistent by
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #519.
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4701)   ~ (all_56_4 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4702)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4702) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4703)  all_56_4 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4490), (4688), (4703) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #518.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4704)  all_56_4 = e1 | all_56_4 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4704) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4705)  all_56_4 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4688), (4705) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4706)  all_14_0 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4706) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4707)  all_14_0 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4689), (4707) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4708)   ~ (all_52_13 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4693), (4707) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4709)   ~ (all_52_25 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4495), (4707) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4710)   ~ (e3 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4696), (4707) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4711)  op(e3, e1) = all_52_8
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4659) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4712)  all_56_12 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (429), (4691), (4712) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1032.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4713)  all_56_12 = e1 | all_56_12 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4713) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4714)  all_56_12 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (429), (4709), (4714) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1031.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4715)  all_56_12 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (4715) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4716)  all_52_25 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4716) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4717)  all_52_25 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (4717) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4718)   ~ (all_6_2 = e0)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (4717) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4719)  op(e3, e0) = all_52_24
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e0, e3, simplifying with (177), (4719)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4720)  all_52_7 = all_52_24
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_8, e1, e3, simplifying with (178), (4711)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4721)  all_52_5 = all_52_8
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_16, e2, e3, simplifying with (179), (4695)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4722)  all_52_3 = all_52_16
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (4720) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4723)  all_56_3 = all_52_24
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (4721) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4724)  all_56_2 = all_52_8
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (4721) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4725)  all_58_4 = all_52_8
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (4721), (4722) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4726)   ~ (all_52_8 = all_52_16)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4726) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4727)   ~ (all_52_8 = all_52_16)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (4720), (4722) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4728)   ~ (all_52_16 = all_52_24)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (4720), (4721) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4729)   ~ (all_52_8 = all_52_24)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (4721) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4730)   ~ (all_52_8 = all_52_29)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4678), (4721) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4731)   ~ (all_52_8 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (4720) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4732)   ~ (all_52_23 = all_52_24)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4732) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4733)   ~ (all_52_23 = all_52_24)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4699), (4720) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4734)   ~ (all_52_24 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4623), (4721) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4735)  op(e1, all_52_8) = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4736)  all_58_4 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4725), (4736) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4737)  all_52_8 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4735), (4737) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4738)  op(e1, e1) = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4681), (4738), (function-axioms) are
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #425.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4739)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4739) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4740)  all_58_5 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (4740) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4741)  all_52_13 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4708), (4741) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4742)  $false
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4742) is inconsistent.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4743)  all_58_8 = e1 | all_58_14 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4743) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4744)  all_58_8 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4675), (4744) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4745)  e3 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4745) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4746)  $false
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4746) is inconsistent.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4747)  all_58_14 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (4747) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4748)  all_52_29 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4748) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4749)  all_52_29 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4730), (4749) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4750)   ~ (all_52_8 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (4749) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4751)   ~ (all_6_2 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4751) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4752)   ~ (all_6_2 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4629) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4753)  all_56_15 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (4753) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4754)  all_6_2 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4754) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4755)  all_6_2 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4486), (4755) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4756)  op(all_6_1, e2) = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (4755) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4757)  op(e0, e2) = all_6_1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (4640), (4757) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4758)  all_6_1 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4756), (4758) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4759)  op(e3, e2) = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_16,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, e3, simplifying with (4695), (4759) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4760)  all_52_16 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4727), (4760) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4761)   ~ (all_52_8 = e2)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4728), (4760) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4762)   ~ (all_52_24 = e2)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4762) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4763)   ~ (all_52_24 = e2)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4764)  all_56_2 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4724), (4764) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4765)  all_52_8 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4765) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4766)  all_52_8 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4731), (4766) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4767)  $false
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4767) is inconsistent.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4768)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4768) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4769)  all_56_2 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4724), (4769) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4770)  all_52_8 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4770) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4771)  all_52_8 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4761), (4771) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4772)  $false
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4772) is inconsistent.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4773)  all_56_2 = e1 | all_56_2 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4773) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4774)  all_56_2 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4724), (4774) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4775)  all_52_8 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4775) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4776)  all_52_8 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4750), (4776) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4777)  $false
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4777) is inconsistent.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4778)  all_56_2 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4724), (4778) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4779)  all_52_8 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4779) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4780)  all_52_8 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4729), (4780) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4781)   ~ (all_52_24 = e0)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4781) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4782)   ~ (all_52_24 = e0)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4735), (4780) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4783)  op(e1, e0) = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (280), (4723), (4733), (4734), (4763),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4782), (4783), (function-axioms) are inconsistent
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #407.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4784)  all_56_15 = e1 | all_56_15 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (529), (4612), (4752), (4784) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4785)  all_56_4 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4685), (4688), (4785) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #512.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4786)   ~ (all_58_0 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (4786) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4787)   ~ (all_4_2 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (178), (179), (283), (307), (326), (331),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (370), (391), (403), (531), (532), (535), (536),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (540), (546), (552), (569), (586), (595), (596),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (597), (4621), (4624), (4633), (4678), (4787),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1012.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4788)  all_58_14 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (4637), (4788) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1000.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | |   (4789)   ~ (all_56_13 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (4789) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | |   (4790)   ~ (all_52_27 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4791)  all_58_12 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (4791) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4792)  all_52_25 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | SIMP: (4792) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4793)  all_52_25 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (4793) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4794)   ~ (all_52_9 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (4793) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4795)   ~ (all_52_29 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | SIMP: (4795) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4796)   ~ (all_52_29 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (4793) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4797)   ~ (all_4_2 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | SIMP: (4797) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4798)   ~ (all_4_2 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (4793) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | |   (4799)  op(e0, e3) = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | |   (4800)  all_56_4 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (409), (4794), (4800) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #782.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | |   (4801)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | |   (4802)  all_56_0 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (4802) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | |   (4803)  all_4_2 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4798), (4803) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | |   (4804)  $false
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4804) is inconsistent.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | |   (4805)   ~ (all_56_0 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | |   (4806)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4807)  all_56_6 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (4807) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4808)  all_52_13 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4808) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4809)  all_52_13 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (4809) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4810)   ~ (all_52_5 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (4809) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4811)   ~ (all_14_2 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4811) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4812)   ~ (all_14_2 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (172), (177), (178), (179), (283), (307),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |            (315), (326), (331), (370), (373), (391), (403),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (535), (536), (537), (540),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |            (542), (546), (552), (568), (569), (583), (586),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (4621), (4622), (4624),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |            (4796), (4798), (4806), (4810), (4812),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |            #865.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4813)   ~ (all_56_6 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (4813) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | |   (4814)   ~ (all_52_13 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (4815)  all_58_4 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (177), (179), (324), (391), (403), (531),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (544), (568), (586), (4621), (4623), (4806),
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (4815), (function-axioms) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #868.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (4816)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4816) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4817)  all_58_5 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (373), (4814), (4817) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #969.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4818)  all_58_8 = e3 | all_58_14 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4818) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4819)  all_58_8 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (4819) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4820)  all_14_2 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (4820) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4821)  all_32_2 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4601), (4820) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4822)  op(e2, e3) = all_14_0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4602), (4820) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4823)  op(e1, e3) = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4597) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4824)   ~ (all_32_2 = e3)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4821), (4824) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4825)  $false
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4825) is inconsistent.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4826)   ~ (all_32_0 = e0)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (793), (4826) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4827)   ~ (all_14_0 = e0)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, e1, simplifying with (164), (4823) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4828)  all_52_17 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e3, e2, simplifying with (172), (4822)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4829)  all_52_9 = all_14_0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (4829) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4830)  all_56_4 = all_14_0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (4829) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4831)   ~ (all_14_0 = all_4_2)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (4828) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4832)   ~ (all_4_2 = e2)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4832) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4833)   ~ (all_4_2 = e2)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4801) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4834)  all_56_4 = e2
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4490), (4830), (4834) are inconsistent by
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #518.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4835)  all_56_4 = e1 | all_56_4 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4835) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4836)  all_56_4 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4830), (4836) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4837)  all_14_0 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4837) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4838)  all_14_0 = e1
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4831), (4838) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4839)   ~ (all_4_2 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4839) implies:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4840)   ~ (all_4_2 = e1)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4841)  all_58_0 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (4841) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4842)  all_4_2 = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (552), (4842) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4843)   ~ (all_52_7 = e0)
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4621), (4842) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4844)  op(e3, e0) = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (177), (4844) gives:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4845)  all_52_7 = e3
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4624), (4845) imply:
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4846)  op(e0, e3) = e0
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4799), (4846), (function-axioms) are
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1027.
% 172.25/25.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4847)   ~ (all_58_0 = e0)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (4847) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4848)   ~ (all_4_2 = e0)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (531), (4806), (4833), (4840), (4848) are
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #882.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4849)  all_56_4 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4827), (4830), (4849) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #512.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4850)  all_58_14 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (4796), (4850) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1000.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |   (4851)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (42), (61), (154), (156), (158),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (170), (172), (178),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (179), (276), (278), (281), (283), (305), (307),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (311), (313), (314), (319), (323), (326), (327),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (329), (330), (331), (349), (364), (370), (373),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (385), (391), (403), (413), (425), (515), (529),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (548), (550), (552), (555), (565), (568), (569),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (571), (573), (583), (584), (585), (586), (588),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (591), (594), (595), (596), (597), (598), (710),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (4482), (4610), (4611), (4612), (4621), (4622),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (4623), (4624), (4629), (4630), (4790), (4851),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            #222.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4852)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.25/25.95  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | ALPHA: (4852) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4853)  all_52_14 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4854)  all_52_12 = e1
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4855)  all_52_10 = e2
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4856)  all_52_8 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (4855) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4857)  all_10_1 = e2
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | REDUCE: (53), (4857) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4858)  op(e2, all_10_2) = all_10_0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | REDUCE: (183), (4856) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4859)  op(e3, all_52_9) = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | REDUCE: (52), (4857) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4860)  op(e2, all_10_2) = e2
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | REDUCE: (167), (4854) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4861)  op(e1, all_52_13) = e1
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | REDUCE: (159), (4853) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4862)  op(e0, all_52_15) = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 172.25/25.95  | | | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (4858), (4860)
% 172.25/25.95  | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | |   (4863)  all_10_0 = e2
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |   (4864)  all_56_15 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (4864) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |   (4865)  all_6_2 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | SIMP: (4865) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |   (4866)  all_6_2 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |            (4866), (function-axioms) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |   (4867)   ~ (all_56_15 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |   (4868)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (4867) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | |   (4869)   ~ (all_6_2 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4870)  all_56_13 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (4870) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4871)  all_52_27 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | SIMP: (4871) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4872)  all_52_27 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (4872) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4873)  all_58_13 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4872) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4874)   ~ (all_52_3 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (4872) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4875)   ~ (all_52_19 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (4872) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4876)   ~ (all_52_29 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | SIMP: (4876) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4877)   ~ (all_52_29 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (4872) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4878)   ~ (all_10_2 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | SIMP: (4878) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4879)   ~ (all_10_2 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (4872) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4880)   ~ (all_6_2 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4872) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4881)  op(e2, e3) = all_52_26
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e2, simplifying with (172), (4881)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4882)  all_52_9 = all_52_26
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4883)  all_56_4 = all_52_26
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4884)  all_58_2 = all_52_26
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4885)   ~ (all_52_13 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | SIMP: (4885) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4886)   ~ (all_52_13 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4887)   ~ (all_52_15 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | SIMP: (4887) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4888)   ~ (all_52_15 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4889)   ~ (all_52_17 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | SIMP: (4889) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4890)   ~ (all_52_17 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4891)   ~ (all_52_25 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | SIMP: (4891) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4892)   ~ (all_52_25 = all_52_26)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4893)   ~ (all_52_26 = all_10_2)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4894)   ~ (all_52_26 = all_4_2)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (4859), (4882) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4895)  op(e3, all_52_26) = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |   (4896)  all_56_1 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (4874), (4896) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |   (4897)   ~ (all_56_1 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | |   (4898)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |   (4899)  all_56_6 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (36), (37), (38), (42), (155), (156),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (161), (164), (170), (177), (178), (179), (181),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (182), (279), (283), (307), (311), (313), (315),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (316), (319), (321), (326), (330), (331), (349),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (364), (370), (373), (391), (392), (403), (415),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (546), (548), (550),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (565), (568), (569),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (575), (580), (582), (583), (584), (586), (587),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (588), (593), (594), (596), (598), (4486), (4501),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (4604), (4606), (4610), (4611), (4860), (4861),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (4862), (4868), (4869), (4873), (4874), (4875),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (4883), (4884), (4886), (4888), (4890), (4892),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (4893), (4894), (4895), (4898), (4899),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |            #189.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |   (4900)   ~ (all_56_6 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (4900) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | |   (4901)   ~ (all_52_13 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |   (4902)  all_58_4 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (36), (37), (38), (42), (155), (156),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (161), (164), (170), (177), (178), (179), (181),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (182), (279), (283), (307), (311), (313), (315),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (316), (319), (321), (326), (330), (331), (349),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (364), (370), (373), (391), (392), (403), (529),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (546), (548), (550), (558),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (559), (560), (561), (565), (568), (569), (580),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (593), (594),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (596), (598), (4486), (4501), (4604), (4606),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (4610), (4611), (4860), (4861), (4862), (4868),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (4869), (4873), (4875), (4879), (4883), (4884),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (4886), (4888), (4890), (4892), (4893), (4894),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            (4895), (4898), (4902), (function-axioms) are
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #188.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | |   (4903)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4903) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | |   (4904)  all_58_5 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (373), (4901), (4904) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #969.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | |   (4905)  all_58_8 = e3 | all_58_14 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4905) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (4906)  all_58_8 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (4906) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (4907)  all_14_2 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (492), (4907) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (4908)  all_32_2 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (4907) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (4909)   ~ (all_52_5 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4601), (4907) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (4910)  op(e2, e3) = all_14_0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4602), (4907) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (4911)  op(e1, e3) = e2
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4597) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4912)   ~ (all_32_2 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4908), (4912) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4913)  $false
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4913) is inconsistent.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4914)   ~ (all_32_0 = e0)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (793), (4914) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4915)   ~ (all_14_0 = e0)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, e1, simplifying with (164), (4911) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4916)  all_52_17 = e2
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_26,
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e3, e2, simplifying with (4881), (4910)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4917)  all_52_26 = all_14_0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4883), (4917) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4918)  all_56_4 = all_14_0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4890), (4916), (4917) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4919)   ~ (all_14_0 = e2)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4895), (4917) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4920)  op(e3, all_14_0) = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4921)  all_56_4 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4495), (4918), (4921) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #519.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4922)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4922) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4923)  all_56_4 = e2
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4490), (4918), (4923) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #518.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4924)  all_56_4 = e1 | all_56_4 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4924) gives:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4925)  all_56_4 = e1
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4918), (4925) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4926)  all_14_0 = e1
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4926) implies:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4927)  all_14_0 = e1
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4920), (4927) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4928)  op(e3, e1) = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (4909), (4928), (function-axioms) are
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1023.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4929)  all_56_4 = e0
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4915), (4918), (4929) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #512.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (4930)  all_58_14 = e3
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (4877), (4930) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1000.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4931)   ~ (all_56_13 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (4931) imply:
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |   (4932)   ~ (all_52_27 = e3)
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (38), (42),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (62), (154), (156), (158), (161), (163), (164),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (165), (169), (170), (172), (174), (177), (178),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (179), (181), (182), (272), (273), (274), (277),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (279), (280), (283), (304), (307), (311), (313),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (315), (316), (319), (320), (321), (323), (326),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (349), (350), (359),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (403),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (409), (415), (419), (515), (529), (531), (532),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (553), (554), (556), (557), (558), (559), (560),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (568), (569), (571), (573), (579), (580), (581),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (582), (586), (587), (588), (591), (593), (594),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (710),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (796), (4482), (4497), (4501), (4611), (4612),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (4859), (4860), (4861), (4862), (4868), (4869),
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            (4932), (function-axioms) are inconsistent by
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | |            sub-proof #208.
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | |   (4933)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.25/25.95  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.25/25.95  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.25/25.95  | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (649), (4486), (4599), (4933),
% 172.25/25.95  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.25/25.95  | | | | | | | | | | | | | | | | |            #187.
% 172.25/25.95  | | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | End of split
% 172.25/25.95  | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | Case 2:
% 172.25/25.95  | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | |   (4934)  all_40_1 = e1
% 172.25/25.95  | | | | | | | | | | | | | | |   (4935)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 172.25/25.95  | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | COMBINE_EQS: (715), (4934) imply:
% 172.25/25.95  | | | | | | | | | | | | | | |   (4936)  all_4_1 = e1
% 172.25/25.95  | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (4936) imply:
% 172.25/25.95  | | | | | | | | | | | | | | |   (4937)  all_52_0 = e1
% 172.25/25.95  | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | REDUCE: (38), (4936) imply:
% 172.25/25.95  | | | | | | | | | | | | | | |   (4938)  op(e1, all_4_2) = all_4_0
% 172.25/25.95  | | | | | | | | | | | | | | | 
% 172.25/25.95  | | | | | | | | | | | | | | | REDUCE: (37), (4936) imply:
% 172.25/25.95  | | | | | | | | | | | | | | |   (4939)  op(e3, all_4_2) = e1
% 172.25/25.95  | | | | | | | | | | | | | | | 
% 172.25/25.96  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (37), (38), (41),
% 172.25/25.96  | | | | | | | | | | | | | | |            (42), (52), (53), (62), (63), (154), (156), (158),
% 172.25/25.96  | | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (169),
% 172.25/25.96  | | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 172.25/25.96  | | | | | | | | | | | | | | |            (181), (182), (183), (185), (268), (270), (271),
% 172.25/25.96  | | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (277), (278),
% 172.25/25.96  | | | | | | | | | | | | | | |            (279), (280), (283), (301), (303), (304), (307),
% 172.25/25.96  | | | | | | | | | | | | | | |            (308), (310), (311), (313), (314), (315), (316),
% 172.25/25.96  | | | | | | | | | | | | | | |            (317), (319), (320), (321), (322), (323), (324),
% 172.25/25.96  | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 172.25/25.96  | | | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 172.25/25.96  | | | | | | | | | | | | | | |            (386), (391), (403), (409), (415), (419), (425),
% 172.25/25.96  | | | | | | | | | | | | | | |            (429), (501), (515), (518), (529), (530), (531),
% 172.25/25.96  | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 172.25/25.96  | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 172.25/25.96  | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 172.25/25.96  | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 172.25/25.96  | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (577),
% 172.25/25.96  | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 172.25/25.96  | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 172.25/25.96  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (649),
% 172.25/25.96  | | | | | | | | | | | | | | |            (661), (704), (710), (719), (770), (796), (4482),
% 172.25/25.96  | | | | | | | | | | | | | | |            (4486), (4487), (4489), (4490), (4493), (4495),
% 172.25/25.96  | | | | | | | | | | | | | | |            (4497), (4499), (4501), (4604), (4935), (4937),
% 172.25/25.96  | | | | | | | | | | | | | | |            (4938), (4939), (function-axioms) are inconsistent
% 172.25/25.96  | | | | | | | | | | | | | | |            by sub-proof #198.
% 172.25/25.96  | | | | | | | | | | | | | | | 
% 172.25/25.96  | | | | | | | | | | | | | | End of split
% 172.25/25.96  | | | | | | | | | | | | | | 
% 172.25/25.96  | | | | | | | | | | | | | Case 2:
% 172.25/25.96  | | | | | | | | | | | | | | 
% 172.25/25.96  | | | | | | | | | | | | | |   (4940)  all_34_0 = e1
% 172.25/25.96  | | | | | | | | | | | | | |   (4941)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 172.25/25.96  | | | | | | | | | | | | | | 
% 172.25/25.96  | | | | | | | | | | | | | | COMBINE_EQS: (773), (4940) imply:
% 172.25/25.96  | | | | | | | | | | | | | |   (4942)  all_4_0 = e1
% 172.25/25.96  | | | | | | | | | | | | | | 
% 172.25/25.96  | | | | | | | | | | | | | | SIMP: (4942) implies:
% 172.25/25.96  | | | | | | | | | | | | | |   (4943)  all_4_0 = e1
% 172.25/25.96  | | | | | | | | | | | | | | 
% 172.25/25.96  | | | | | | | | | | | | | | REDUCE: (38), (4943) imply:
% 172.25/25.96  | | | | | | | | | | | | | |   (4944)  op(all_4_1, all_4_2) = e1
% 172.25/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (36), (37), (41), (42), (52),
% 172.43/25.96  | | | | | | | | | | | | | |            (53), (62), (63), (154), (155), (156), (158),
% 172.43/25.96  | | | | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (169),
% 172.43/25.96  | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 172.43/25.96  | | | | | | | | | | | | | |            (182), (183), (185), (268), (270), (271), (274),
% 172.43/25.96  | | | | | | | | | | | | | |            (275), (277), (279), (280), (281), (282), (283),
% 172.43/25.96  | | | | | | | | | | | | | |            (301), (303), (304), (307), (308), (311), (315),
% 172.43/25.96  | | | | | | | | | | | | | |            (319), (320), (323), (326), (328), (329), (330),
% 172.43/25.96  | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 172.43/25.96  | | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 172.43/25.96  | | | | | | | | | | | | | |            (415), (419), (429), (494), (501), (515), (529),
% 172.43/25.96  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.43/25.96  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 172.43/25.96  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 172.43/25.96  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 172.43/25.96  | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (573), (579),
% 172.43/25.96  | | | | | | | | | | | | | |            (580), (581), (582), (584), (585), (586), (588),
% 172.43/25.96  | | | | | | | | | | | | | |            (591), (593), (594), (596), (597), (598), (599),
% 172.43/25.96  | | | | | | | | | | | | | |            (649), (661), (663), (704), (710), (719), (720),
% 172.43/25.96  | | | | | | | | | | | | | |            (796), (4482), (4486), (4487), (4493), (4495),
% 172.43/25.96  | | | | | | | | | | | | | |            (4499), (4941), (4944), (function-axioms) are
% 172.43/25.96  | | | | | | | | | | | | | |            inconsistent by sub-proof #190.
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | End of split
% 172.43/25.96  | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | End of split
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | |   (4945)  all_26_0 = e2
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | COMBINE_EQS: (779), (4945) imply:
% 172.43/25.96  | | | | | | | | | | | |   (4946)  all_4_0 = e2
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | SIMP: (4946) implies:
% 172.43/25.96  | | | | | | | | | | | |   (4947)  all_4_0 = e2
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | COMBINE_EQS: (742), (4947) imply:
% 172.43/25.96  | | | | | | | | | | | |   (4948)  all_50_0 = e2
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | REDUCE: (38), (4947) imply:
% 172.43/25.96  | | | | | | | | | | | |   (4949)  op(all_4_1, all_4_2) = e2
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | BETA: splitting (108) gives:
% 172.43/25.96  | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | |   (4950)   ~ (all_32_1 = e2)
% 172.43/25.96  | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | REDUCE: (713), (4950) imply:
% 172.43/25.96  | | | | | | | | | | | | |   (4951)   ~ (all_14_1 = e2)
% 172.43/25.96  | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | BETA: splitting (151) gives:
% 172.43/25.96  | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | |   (4952)   ~ (all_50_0 = e2)
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | REDUCE: (4948), (4952) imply:
% 172.43/25.96  | | | | | | | | | | | | | |   (4953)  $false
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | CLOSE: (4953) is inconsistent.
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | |   (4954)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.43/25.96  | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | |   (4955)  all_58_15 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (4955),
% 172.43/25.96  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.96  | | | | | | | | | | | | | | |            #228.
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | |   (4956)   ~ (all_58_15 = e0)
% 172.43/25.96  | | | | | | | | | | | | | | |   (4957)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.43/25.96  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.43/25.96  | | | | | | | | | | | | | | |             e0)
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | ALPHA: (4957) implies:
% 172.43/25.96  | | | | | | | | | | | | | | |   (4958)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | REDUCE: (532), (4956) imply:
% 172.43/25.96  | | | | | | | | | | | | | | |   (4959)   ~ (all_6_2 = e0)
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | |   (4960)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.96  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.43/25.96  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.43/25.96  | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | BETA: splitting (4960) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4961)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.96  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (4949), (4961),
% 172.43/25.96  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.96  | | | | | | | | | | | | | | | | |            #494.
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4962)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.43/25.96  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | ALPHA: (4962) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4963)  all_52_14 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4964)  all_52_12 = e1
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4965)  all_52_10 = e2
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4966)  all_52_8 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (4965) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4967)  all_10_1 = e2
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | REDUCE: (53), (4967) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4968)  op(e2, all_10_2) = all_10_0
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | REDUCE: (183), (4966) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4969)  op(e3, all_52_9) = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | REDUCE: (52), (4967) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4970)  op(e2, all_10_2) = e2
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | REDUCE: (167), (4964) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4971)  op(e1, all_52_13) = e1
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | REDUCE: (159), (4963) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4972)  op(e0, all_52_15) = e0
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 172.43/25.96  | | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (4968), (4970)
% 172.43/25.96  | | | | | | | | | | | | | | | | |              gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4973)  all_10_0 = e2
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | REDUCE: (4487), (4973) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | |   (4974)   ~ (e3 = e2)
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | |   (4975)  all_56_15 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (4975) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | |   (4976)  all_6_2 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.43/25.96  | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.43/25.96  | | | | | | | | | | | | | | | | | |            (4976), (function-axioms) are inconsistent by
% 172.43/25.96  | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | |   (4977)   ~ (all_56_15 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | |   (4978)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | REDUCE: (529), (4977) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | |   (4979)   ~ (all_6_2 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4980)  all_56_13 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (4980) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4981)  all_52_27 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (4981) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4982)  all_58_13 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (567), (4981) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4983)   ~ (all_52_3 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (562), (4981) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4984)   ~ (all_52_25 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (581), (4981) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4985)   ~ (all_52_29 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | SIMP: (4985) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4986)   ~ (all_52_29 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (573), (4981) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4987)   ~ (all_10_2 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | SIMP: (4987) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4988)   ~ (all_10_2 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (582), (4981) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4989)   ~ (all_6_2 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (173), (4981) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4990)  op(e2, e3) = all_52_26
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e2, simplifying with (172), (4990)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |              gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4991)  all_52_9 = all_52_26
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4992)  all_56_4 = all_52_26
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4993)  all_58_2 = all_52_26
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (556), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4994)   ~ (all_52_13 = all_52_26)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | SIMP: (4994) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4995)   ~ (all_52_13 = all_52_26)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (557), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4996)   ~ (all_52_15 = all_52_26)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | SIMP: (4996) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4997)   ~ (all_52_15 = all_52_26)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (554), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4998)   ~ (all_52_25 = all_52_26)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | SIMP: (4998) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (4999)   ~ (all_52_25 = all_52_26)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (555), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (5000)   ~ (all_52_26 = all_10_2)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (542), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (5001)   ~ (all_52_26 = all_4_2)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | REDUCE: (4969), (4991) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | |   (5002)  op(e3, all_52_26) = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | |   (5003)  all_56_5 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (4988), (5003) are inconsistent by
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | |            sub-proof #895.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | |   (5004)   ~ (all_56_5 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | |   (5005)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | |   (5006)  all_56_1 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (5006) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | |   (5007)  all_52_3 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | REDUCE: (4983), (5007) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | |   (5008)  $false
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | CLOSE: (5008) is inconsistent.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | |   (5009)   ~ (all_56_1 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | |   (5010)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5011)  all_56_6 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (5011) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5012)  all_52_13 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5012) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5013)  all_52_13 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4995), (5013) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5014)   ~ (all_52_26 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5014) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5015)   ~ (all_52_26 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4971), (5013) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5016)  op(e1, e3) = e1
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |              e1, e3, e1, simplifying with (164), (5016) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5017)  all_52_17 = e1
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5017) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5018)  all_58_6 = e1
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5019)  all_58_0 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (403), (796), (4949), (5019),
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |            #489.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5020)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (349), (4984), (4993), (5015), (5018), (5020)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1001.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5021)   ~ (all_56_6 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (5021) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | |   (5022)   ~ (all_52_13 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5023)  all_58_4 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5023) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5024)  all_52_5 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5024) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5025)  all_52_5 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (5025) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5026)   ~ (all_52_7 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5026) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5027)   ~ (all_52_7 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (5025) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5028)   ~ (all_4_2 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5028) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | |   (5029)   ~ (all_4_2 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5030)  all_58_2 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4993), (5030) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5031)  all_52_26 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5031) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5032)  all_52_26 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5001), (5002), (5032), (function-axioms)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1005.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5033)   ~ (all_58_2 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4993), (5033) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5034)   ~ (all_52_26 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5035)  all_58_0 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5035) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5036)  all_4_2 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5029), (5036) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5037)  $false
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5037) is inconsistent.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5038)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5038) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5039)  all_58_2 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4993), (5034), (5039) are inconsistent by
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1004.
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5040)  all_58_6 = e3 | all_58_12 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5040) gives:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5041)  all_58_6 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5041) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5042)  all_52_17 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5042) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5043)  all_52_17 = e3
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5043) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5044)   ~ (all_52_19 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5044) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5045)   ~ (all_52_19 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (5043) imply:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5046)   ~ (all_52_23 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5046) implies:
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5047)   ~ (all_52_23 = e3)
% 172.43/25.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (37), (156), (161), (163), (169),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (177), (179), (181), (279), (283), (307), (316),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (321), (325), (326), (328), (349), (364), (370),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (392), (403), (530), (531), (532), (535),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (536), (539), (540), (546), (548), (565), (569),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (571), (580), (598), (4949), (4958), (4970),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4971), (4972), (4979), (4982), (4983), (4992),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4993), (4997), (4999), (5000), (5001), (5002),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5005), (5010), (5027), (5029), (5041), (5045),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5047), (function-axioms) are inconsistent by
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #465.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5048)  all_58_12 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (349), (4984), (5048) are inconsistent by
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1003.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | |   (5049)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5049) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | |   (5050)  all_58_5 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (373), (5022), (5050) are inconsistent by
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #969.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | |   (5051)  all_58_8 = e3 | all_58_14 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5051) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (5052)  all_58_8 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (5052) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (5053)  all_14_2 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (36), (37), (62), (156), (164), (179),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            (307), (311), (315), (319), (328), (330), (331),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (364), (370), (373), (391), (403), (532),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            (533), (535), (536), (537), (538), (539), (540),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            (548), (552), (558), (560), (579), (584), (586),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            (587), (588), (593), (595), (596), (796), (4951),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            (4971), (4972), (4979), (4983), (4988), (4993),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            (4995), (5001), (5002), (5053), (function-axioms)
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #219.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (5054)  all_58_14 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (4986), (5054) are inconsistent by
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1000.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |   (5055)   ~ (all_56_13 = e3)
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | REDUCE: (344), (5055) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |   (5056)   ~ (all_52_27 = e3)
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (42), (62),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (154), (156), (158), (163), (164), (165), (170),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (172), (174), (177), (178), (179), (181), (182),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (272), (273), (274), (277), (279), (280), (283),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (304), (307), (311), (313), (315), (319), (321),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (323), (326), (328), (329), (330), (349), (350),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (386), (391),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (403), (409), (415), (419), (515), (529), (531),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (539), (540), (542), (546), (550), (552), (553),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (554), (556), (557), (558), (559), (560), (561),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (568), (569),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (571), (573), (579), (580), (581), (582), (585),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (586), (587), (588), (593), (594), (595), (596),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (597), (600), (710), (796), (4482), (4497),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (4949), (4958), (4959), (4969), (4970), (4971),
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            (4972), (4978), (4979), (5056), (function-axioms)
% 172.43/25.97  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #185.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5057)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.43/25.97  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.43/25.97  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (154), (156), (158), (161), (163), (164), (165),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (172), (174), (177), (178), (179), (181), (182),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (268), (271), (273), (274), (275), (276), (280),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (282), (283), (303), (304), (307), (310), (311),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (315), (319), (321), (323), (324), (325), (326),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (349), (359), (364),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (403), (419), (425), (429), (501), (515), (521),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (564), (566),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (568), (569), (577), (579), (580), (584), (585),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (586), (593), (595), (596), (597), (598), (649),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (704), (710), (718), (719), (796), (4482), (4486),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (4490), (4493), (4495), (4949), (4954), (4958),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (5057), (function-axioms) are inconsistent by
% 172.43/25.97  | | | | | | | | | | | | | | | |            sub-proof #183.
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | |   (5058)  all_32_1 = e2
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | COMBINE_EQS: (713), (5058) imply:
% 172.43/25.97  | | | | | | | | | | | | |   (5059)  all_14_1 = e2
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | SIMP: (5059) implies:
% 172.43/25.97  | | | | | | | | | | | | |   (5060)  all_14_1 = e2
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | COMBINE_EQS: (719), (5060) imply:
% 172.43/25.97  | | | | | | | | | | | | |   (5061)  all_52_20 = e2
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | |   (5062)  all_58_15 = e0
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5062),
% 172.43/25.97  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.97  | | | | | | | | | | | | | |            #228.
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | |   (5063)   ~ (all_58_15 = e0)
% 172.43/25.97  | | | | | | | | | | | | | |   (5064)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.43/25.97  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.43/25.97  | | | | | | | | | | | | | |             e0)
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | ALPHA: (5064) implies:
% 172.43/25.97  | | | | | | | | | | | | | |   (5065)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | REDUCE: (532), (5063) imply:
% 172.43/25.97  | | | | | | | | | | | | | |   (5066)   ~ (all_6_2 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | |   (5067)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.97  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.43/25.97  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | BETA: splitting (5067) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5068)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.97  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (4949), (5068),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.97  | | | | | | | | | | | | | | | |            #494.
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5069)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.43/25.97  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | ALPHA: (5069) implies:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5070)  all_52_14 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5071)  all_52_12 = e1
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5072)  all_52_10 = e2
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5073)  all_52_8 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (5072) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5074)  all_10_1 = e2
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REDUCE: (53), (5074) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5075)  op(e2, all_10_2) = all_10_0
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REDUCE: (183), (5073) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5076)  op(e3, all_52_9) = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REDUCE: (52), (5074) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5077)  op(e2, all_10_2) = e2
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REDUCE: (167), (5071) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5078)  op(e1, all_52_13) = e1
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REDUCE: (159), (5070) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5079)  op(e0, all_52_15) = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 172.43/25.97  | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (5075), (5077)
% 172.43/25.97  | | | | | | | | | | | | | | | |              gives:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5080)  all_10_0 = e2
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REDUCE: (4487), (5080) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5081)   ~ (e3 = e2)
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5082)  all_56_15 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5082) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5083)  all_6_2 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | SIMP: (5083) implies:
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5084)  all_6_2 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.43/25.97  | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.43/25.97  | | | | | | | | | | | | | | | | |            (5084), (function-axioms) are inconsistent by
% 172.43/25.97  | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5085)   ~ (all_56_15 = e3)
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5086)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | REDUCE: (529), (5085) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5087)   ~ (all_6_2 = e3)
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | |   (5088)  all_56_13 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (37), (156), (161), (163),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (164), (169), (172), (173), (177), (179), (181),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (182), (275), (278), (279), (282), (283), (307),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (311), (315), (316), (319), (321), (325), (326),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (328), (330), (344), (349), (364), (365), (370),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (530),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (550), (554), (555), (556), (557), (558), (559),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (560), (561), (562), (565), (567), (568), (569),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (571), (573), (575), (580), (581), (582), (583),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (598), (796), (4949),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (5065), (5076), (5077), (5078), (5079), (5088),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            #464.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | |   (5089)   ~ (all_56_13 = e3)
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | REDUCE: (344), (5089) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | | | |   (5090)   ~ (all_52_27 = e3)
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (37), (42), (62),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (154), (156), (158), (163), (164), (165), (170),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (172), (174), (177), (178), (179), (181), (182),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (272), (273), (274), (277), (279), (280), (283),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (304), (307), (311), (313), (315), (319), (321),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (323), (326), (328), (329), (330), (349), (350),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (386), (391),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (403), (409), (415), (419), (515), (529), (531),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (539), (540), (542), (546), (550), (552), (553),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (554), (556), (557), (558), (559), (560), (561),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (568), (569),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (571), (573), (579), (580), (581), (582), (585),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (586), (587), (588), (593), (594), (595), (596),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (597), (600), (710), (796), (4482), (4497),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (4949), (5065), (5066), (5076), (5077), (5078),
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            (5079), (5086), (5087), (5090), (function-axioms)
% 172.43/25.97  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #185.
% 172.43/25.97  | | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | |   (5091)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.43/25.97  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.43/25.97  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | BETA: splitting (5091) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5092)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.43/25.97  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5061), (5092) are inconsistent by sub-proof
% 172.43/25.97  | | | | | | | | | | | | | | | |            #539.
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5093)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.43/25.97  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (5093),
% 172.43/25.97  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.97  | | | | | | | | | | | | | | | |            #200.
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | End of split
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | |   (5094)  all_24_0 = e1
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | COMBINE_EQS: (751), (5094) imply:
% 172.43/25.97  | | | | | | | | | | |   (5095)  all_10_0 = e1
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | SIMP: (5095) implies:
% 172.43/25.97  | | | | | | | | | | |   (5096)  all_10_0 = e1
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | REDUCE: (4487), (5096) imply:
% 172.43/25.97  | | | | | | | | | | |   (5097)   ~ (e3 = e1)
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | REDUCE: (53), (5096) imply:
% 172.43/25.97  | | | | | | | | | | |   (5098)  op(all_10_1, all_10_2) = e1
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | BETA: splitting (93) gives:
% 172.43/25.97  | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | |   (5099)   ~ (all_26_0 = e2)
% 172.43/25.97  | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | REDUCE: (779), (5099) imply:
% 172.43/25.97  | | | | | | | | | | | |   (5100)   ~ (all_4_0 = e2)
% 172.43/25.97  | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | BETA: splitting (113) gives:
% 172.43/25.97  | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | |   (5101)   ~ (all_34_0 = e1)
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | REDUCE: (773), (5101) imply:
% 172.43/25.97  | | | | | | | | | | | | |   (5102)   ~ (all_4_0 = e1)
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 172.43/25.97  | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | |   (5103)   ~ (all_40_1 = e1)
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | REDUCE: (715), (5103) imply:
% 172.43/25.97  | | | | | | | | | | | | | |   (5104)   ~ (all_4_1 = e1)
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.43/25.97  | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | |   (5105)  all_58_15 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5105),
% 172.43/25.97  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.97  | | | | | | | | | | | | | | |            #228.
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | Case 2:
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | |   (5106)   ~ (all_58_15 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | |   (5107)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.43/25.97  | | | | | | | | | | | | | | |             e0)
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | ALPHA: (5107) implies:
% 172.43/25.97  | | | | | | | | | | | | | | |   (5108)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.43/25.97  | | | | | | | | | | | | | | |   (5109)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | REDUCE: (532), (5106) imply:
% 172.43/25.97  | | | | | | | | | | | | | | |   (5110)   ~ (all_6_2 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | |   (5111)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.97  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.43/25.97  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | BETA: splitting (5111) gives:
% 172.43/25.97  | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5112)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.97  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | ALPHA: (5112) implies:
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5113)  all_52_6 = e0
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5114)  all_52_4 = e1
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5115)  all_52_2 = e2
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5116)  all_52_0 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (5116) imply:
% 172.43/25.97  | | | | | | | | | | | | | | | | |   (5117)  all_4_1 = e3
% 172.43/25.97  | | | | | | | | | | | | | | | | | 
% 172.43/25.97  | | | | | | | | | | | | | | | | | REDUCE: (38), (5117) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5118)  op(e3, all_4_2) = all_4_0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (37), (5117) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5119)  op(e3, all_4_2) = e3
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (176), (5115) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5120)  op(e2, all_52_3) = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (168), (5114) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5121)  op(e1, all_52_5) = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (160), (5113) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5122)  op(e0, all_52_7) = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (61), (154), (156), (158), (161),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (163), (164), (165), (169), (170), (172), (173),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (272), (273), (276), (278), (279), (281), (282),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (283), (303), (304), (305), (307), (310), (311),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (324), (326), (327), (328), (329), (330), (331),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (413),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (425), (429), (501), (515), (529), (530), (531),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (578),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (704), (710),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (4482), (4486), (4493), (5100), (5102), (5108),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (5109), (5110), (5118), (5119), (5120), (5121),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (5122), (function-axioms) are inconsistent by
% 172.43/25.98  | | | | | | | | | | | | | | | | |            sub-proof #221.
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5123)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | ALPHA: (5123) implies:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5124)  all_52_10 = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (5124) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5125)  all_10_1 = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (5098), (5125), (function-axioms) are
% 172.43/25.98  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #446.
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5126)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.43/25.98  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | BETA: splitting (5126) gives:
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5127)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | ALPHA: (5127) implies:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5128)  all_52_22 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5129)  all_52_20 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5130)  all_52_18 = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5131)  all_52_16 = e3
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (5129) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5132)  all_14_1 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (63), (5132) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5133)  op(e1, all_14_2) = all_14_0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (182), (5131) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5134)  op(e3, all_52_17) = e3
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (174), (5130) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5135)  op(e2, all_52_19) = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (62), (5132) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5136)  op(e1, all_14_2) = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (158), (5128) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5137)  op(e0, all_52_23) = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (52),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (154), (156), (161), (163), (164), (165), (169),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (183), (268), (270), (271), (272), (273), (274),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (275), (276), (277), (278), (282), (283), (303),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (304), (307), (308), (310), (311), (312), (314),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (315), (317), (319), (320), (322), (323), (324),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (391), (392), (403), (415), (419), (425), (429),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (501), (515), (529), (530), (531), (532), (533),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (568), (571), (577), (578), (579), (580), (581),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (582), (583), (584), (586), (587), (588), (591),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (704), (710), (796), (4482), (4486), (4489),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (4490), (4493), (4495), (5100), (5102), (5104),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (5109), (5110), (5133), (5134), (5135), (5136),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (5137), (function-axioms) are inconsistent by
% 172.43/25.98  | | | | | | | | | | | | | | | | |            sub-proof #202.
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5138)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | ALPHA: (5138) implies:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5139)  all_52_30 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (5139) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5140)  all_6_1 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (4486), (5140), (function-axioms) are
% 172.43/25.98  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | |   (5141)  all_40_1 = e1
% 172.43/25.98  | | | | | | | | | | | | | |   (5142)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | COMBINE_EQS: (715), (5141) imply:
% 172.43/25.98  | | | | | | | | | | | | | |   (5143)  all_4_1 = e1
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | COMBINE_EQS: (720), (5143) imply:
% 172.43/25.98  | | | | | | | | | | | | | |   (5144)  all_52_0 = e1
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | REDUCE: (796), (5143) imply:
% 172.43/25.98  | | | | | | | | | | | | | |   (5145)   ~ (e2 = e1)
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | REDUCE: (38), (5143) imply:
% 172.43/25.98  | | | | | | | | | | | | | |   (5146)  op(e1, all_4_2) = all_4_0
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | REDUCE: (37), (5143) imply:
% 172.43/25.98  | | | | | | | | | | | | | |   (5147)  op(e3, all_4_2) = e1
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | Case 1:
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | |   (5148)  all_58_15 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5148),
% 172.43/25.98  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.98  | | | | | | | | | | | | | | |            #228.
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | |   (5149)   ~ (all_58_15 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | |   (5150)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.43/25.98  | | | | | | | | | | | | | | |             e0)
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | ALPHA: (5150) implies:
% 172.43/25.98  | | | | | | | | | | | | | | |   (5151)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | REDUCE: (532), (5149) imply:
% 172.43/25.98  | | | | | | | | | | | | | | |   (5152)   ~ (all_6_2 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | Case 1:
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5153)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.43/25.98  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (52), (661), (5098), (5144), (5153),
% 172.43/25.98  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.98  | | | | | | | | | | | | | | | |            #445.
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5154)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.43/25.98  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | BETA: splitting (5154) gives:
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | Case 1:
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5155)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | ALPHA: (5155) implies:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5156)  all_52_22 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5157)  all_52_20 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5158)  all_52_18 = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5159)  all_52_16 = e3
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (5157) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5160)  all_14_1 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (63), (5160) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5161)  op(e1, all_14_2) = all_14_0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (182), (5159) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5162)  op(e3, all_52_17) = e3
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (174), (5158) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5163)  op(e2, all_52_19) = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (62), (5160) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5164)  op(e1, all_14_2) = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REDUCE: (158), (5156) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5165)  op(e0, all_52_23) = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (52),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (154), (156), (161), (163), (164), (165), (169),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (170), (172), (177), (178), (179), (181), (183),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (268), (270), (271), (272), (274), (275), (276),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (277), (278), (283), (303), (304), (307), (308),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (310), (311), (314), (315), (317), (319), (320),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (364), (365), (370),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (415), (419), (425),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (429), (501), (515), (518), (529), (530), (531),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (567), (568), (571), (577), (578), (580), (581),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (582), (584), (586), (587), (588), (591), (594),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (704), (710),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (770), (796), (4482), (4486), (4489), (4490),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (4493), (4495), (5100), (5102), (5142), (5146),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (5147), (5151), (5152), (5161), (5162), (5163),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (5164), (5165), (function-axioms) are inconsistent
% 172.43/25.98  | | | | | | | | | | | | | | | | |            by sub-proof #199.
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | |   (5166)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (5166),
% 172.43/25.98  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.98  | | | | | | | | | | | | | | | | |            #200.
% 172.43/25.98  | | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | End of split
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | |   (5167)  all_34_0 = e1
% 172.43/25.98  | | | | | | | | | | | | |   (5168)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | COMBINE_EQS: (773), (5167) imply:
% 172.43/25.98  | | | | | | | | | | | | |   (5169)  all_4_0 = e1
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | SIMP: (5169) implies:
% 172.43/25.98  | | | | | | | | | | | | |   (5170)  all_4_0 = e1
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | REDUCE: (5100), (5170) imply:
% 172.43/25.98  | | | | | | | | | | | | |   (5171)   ~ (e2 = e1)
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | REDUCE: (38), (5170) imply:
% 172.43/25.98  | | | | | | | | | | | | |   (5172)  op(all_4_1, all_4_2) = e1
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.43/25.98  | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | Case 1:
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | |   (5173)  all_58_15 = e0
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5173),
% 172.43/25.98  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.43/25.98  | | | | | | | | | | | | | |            #228.
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | |   (5174)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.43/25.98  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.43/25.98  | | | | | | | | | | | | | |             e0)
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | ALPHA: (5174) implies:
% 172.43/25.98  | | | | | | | | | | | | | |   (5175)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.43/25.98  | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | Case 1:
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | |   (5176)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.43/25.98  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (5098),
% 172.43/25.98  | | | | | | | | | | | | | | |            (5172), (5176), (function-axioms) are inconsistent
% 172.43/25.98  | | | | | | | | | | | | | | |            by sub-proof #441.
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | Case 2:
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | |   (5177)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.43/25.98  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.43/25.98  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | BETA: splitting (5177) gives:
% 172.43/25.98  | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | Case 1:
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5178)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.43/25.98  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | ALPHA: (5178) implies:
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5179)  all_52_22 = e0
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5180)  all_52_20 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5181)  all_52_18 = e2
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5182)  all_52_16 = e3
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (5180) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5183)  all_14_1 = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | REDUCE: (63), (5183) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5184)  op(e1, all_14_2) = all_14_0
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | REDUCE: (182), (5182) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5185)  op(e3, all_52_17) = e3
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | REDUCE: (174), (5181) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5186)  op(e2, all_52_19) = e2
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | REDUCE: (62), (5183) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5187)  op(e1, all_14_2) = e1
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.43/25.98  | | | | | | | | | | | | | | | | REDUCE: (158), (5179) imply:
% 172.43/25.98  | | | | | | | | | | | | | | | |   (5188)  op(e0, all_52_23) = e0
% 172.43/25.98  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (37), (42), (154), (155), (156),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (173),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (177), (178), (179), (181), (268), (270), (271),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (274), (275), (277), (280), (281), (282), (283),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (303), (304), (307), (308), (311), (315), (319),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (320), (323), (326), (328), (329), (330), (331),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (344), (349), (364), (365), (370), (373), (385),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (386), (391), (392), (403), (413), (415), (419),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (429), (494), (501), (515), (529), (531), (532),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (560),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (568), (569), (579), (580), (581), (582), (584),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (585), (586), (593), (594), (596), (597), (598),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (599), (663), (704), (710), (796), (4482), (4486),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (4493), (4495), (5168), (5172), (5175), (5184),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (5185), (5186), (5187), (5188), (function-axioms)
% 172.54/25.99  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #193.
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5189)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.54/25.99  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (5189),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/25.99  | | | | | | | | | | | | | | | |            #200.
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | |   (5190)  all_26_0 = e2
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | COMBINE_EQS: (779), (5190) imply:
% 172.54/25.99  | | | | | | | | | | | |   (5191)  all_4_0 = e2
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | SIMP: (5191) implies:
% 172.54/25.99  | | | | | | | | | | | |   (5192)  all_4_0 = e2
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | COMBINE_EQS: (742), (5192) imply:
% 172.54/25.99  | | | | | | | | | | | |   (5193)  all_50_0 = e2
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | REDUCE: (38), (5192) imply:
% 172.54/25.99  | | | | | | | | | | | |   (5194)  op(all_4_1, all_4_2) = e2
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | BETA: splitting (151) gives:
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | |   (5195)   ~ (all_50_0 = e2)
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | REDUCE: (5193), (5195) imply:
% 172.54/25.99  | | | | | | | | | | | | |   (5196)  $false
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | CLOSE: (5196) is inconsistent.
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | |   (5197)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | |   (5198)  all_58_15 = e0
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5198),
% 172.54/25.99  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/25.99  | | | | | | | | | | | | | |            #228.
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | |   (5199)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.54/25.99  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.54/25.99  | | | | | | | | | | | | | |             e0)
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | ALPHA: (5199) implies:
% 172.54/25.99  | | | | | | | | | | | | | |   (5200)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | |   (5201)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.54/25.99  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.54/25.99  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (5098),
% 172.54/25.99  | | | | | | | | | | | | | | |            (5194), (5201), (function-axioms) are inconsistent
% 172.54/25.99  | | | | | | | | | | | | | | |            by sub-proof #434.
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | |   (5202)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.54/25.99  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.54/25.99  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | BETA: splitting (5202) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5203)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.54/25.99  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | ALPHA: (5203) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5204)  all_52_22 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5205)  all_52_20 = e1
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5206)  all_52_18 = e2
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5207)  all_52_16 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (5205) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5208)  all_14_1 = e1
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REDUCE: (63), (5208) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5209)  op(e1, all_14_2) = all_14_0
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REDUCE: (182), (5207) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5210)  op(e3, all_52_17) = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REDUCE: (174), (5206) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5211)  op(e2, all_52_19) = e2
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REDUCE: (62), (5208) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5212)  op(e1, all_14_2) = e1
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REDUCE: (158), (5204) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5213)  op(e0, all_52_23) = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (154),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (156), (161), (163), (164), (165), (172), (177),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (178), (179), (181), (268), (271), (273), (274),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (275), (276), (280), (282), (283), (303), (304),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (307), (310), (311), (315), (319), (321), (323),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (324), (325), (326), (328), (329), (330), (331),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (349), (359), (364), (365), (370), (373), (385),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (386), (391), (392), (403), (419), (425), (429),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (501), (515), (521), (529), (531), (532), (533),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (554), (556), (557), (558), (559), (560), (561),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (562), (564), (566), (568), (569), (577), (579),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (580), (584), (585), (586), (593), (595), (596),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (597), (598), (704), (710), (718), (796), (4482),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (4486), (4490), (4493), (4495), (5194), (5197),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (5200), (5209), (5210), (5211), (5212), (5213),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/25.99  | | | | | | | | | | | | | | | |            #184.
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5214)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.54/25.99  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (5214),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/25.99  | | | | | | | | | | | | | | | |            #200.
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | End of split
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | |   (5215)  all_22_1 = e3
% 172.54/25.99  | | | | | | | | | |   (5216)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | COMBINE_EQS: (711), (5215) imply:
% 172.54/25.99  | | | | | | | | | |   (5217)  all_14_1 = e3
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | COMBINE_EQS: (719), (5217) imply:
% 172.54/25.99  | | | | | | | | | |   (5218)  all_52_20 = e3
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | REDUCE: (63), (5217) imply:
% 172.54/25.99  | | | | | | | | | |   (5219)  op(e3, all_14_2) = all_14_0
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | REDUCE: (62), (5217) imply:
% 172.54/25.99  | | | | | | | | | |   (5220)  op(e1, all_14_2) = e3
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | BETA: splitting (88) gives:
% 172.54/25.99  | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | |   (5221)   ~ (all_24_0 = e1)
% 172.54/25.99  | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | REDUCE: (751), (5221) imply:
% 172.54/25.99  | | | | | | | | | | |   (5222)   ~ (all_10_0 = e1)
% 172.54/25.99  | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | BETA: splitting (93) gives:
% 172.54/25.99  | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | |   (5223)   ~ (all_26_0 = e2)
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | REDUCE: (779), (5223) imply:
% 172.54/25.99  | | | | | | | | | | | |   (5224)   ~ (all_4_0 = e2)
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | BETA: splitting (103) gives:
% 172.54/25.99  | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | |   (5225)   ~ (all_30_1 = e1)
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | REDUCE: (712), (5225) imply:
% 172.54/25.99  | | | | | | | | | | | | |   (5226)   ~ (all_10_1 = e1)
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 172.54/25.99  | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | |   (5227)   ~ (all_34_0 = e1)
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | REDUCE: (773), (5227) imply:
% 172.54/25.99  | | | | | | | | | | | | | |   (5228)   ~ (all_4_0 = e1)
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 172.54/25.99  | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | |   (5229)   ~ (all_40_1 = e1)
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | REDUCE: (715), (5229) imply:
% 172.54/25.99  | | | | | | | | | | | | | | |   (5230)   ~ (all_4_1 = e1)
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5231)  all_58_15 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5231),
% 172.54/25.99  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/25.99  | | | | | | | | | | | | | | | |            #228.
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5232)   ~ (all_58_15 = e0)
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5233)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.54/25.99  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.54/25.99  | | | | | | | | | | | | | | | |             e0)
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | ALPHA: (5233) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5234)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5235)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | REDUCE: (532), (5232) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | |   (5236)   ~ (all_6_2 = e0)
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | |   (5237)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.54/25.99  | | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.54/25.99  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.54/25.99  | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | BETA: splitting (5237) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5238)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.54/25.99  | | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | ALPHA: (5238) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5239)  all_52_6 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5240)  all_52_4 = e1
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5241)  all_52_2 = e2
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5242)  all_52_0 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (5242) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5243)  all_4_1 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | REDUCE: (38), (5243) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5244)  op(e3, all_4_2) = all_4_0
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | REDUCE: (37), (5243) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5245)  op(e3, all_4_2) = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | REDUCE: (176), (5241) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5246)  op(e2, all_52_3) = e2
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | REDUCE: (168), (5240) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5247)  op(e1, all_52_5) = e1
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | REDUCE: (160), (5239) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5248)  op(e0, all_52_7) = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 172.54/25.99  | | | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (5244), (5245)
% 172.54/25.99  | | | | | | | | | | | | | | | | | |              gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | |   (5249)  all_4_0 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |   (5250)  all_56_15 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5250) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |   (5251)  all_6_2 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | SIMP: (5251) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |   (5252)  all_6_2 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |            (5252), (function-axioms) are inconsistent by
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |   (5253)   ~ (all_56_15 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |   (5254)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (5253) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | |   (5255)   ~ (all_6_2 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5256)  all_56_13 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (5256) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5257)  all_52_27 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | SIMP: (5257) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5258)  all_52_27 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (5258) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5259)   ~ (all_52_19 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (5258) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5260)   ~ (all_52_25 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (5258) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5261)   ~ (all_52_29 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | SIMP: (5261) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5262)   ~ (all_52_29 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | REDUCE: (582), (5258) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5263)   ~ (all_6_2 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (5258) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5264)  op(e2, e3) = all_52_26
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (161),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (163), (164), (172), (177), (178), (179), (269),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (271), (273), (279), (281), (283), (307), (310),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (317), (324),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (326), (327), (328), (330), (341), (349), (359),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (409),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (413), (429), (529), (531), (532), (533), (535),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (536), (537), (538), (540), (542), (544), (546),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (559), (560), (561), (563), (564), (566), (568),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (569), (579), (584), (585), (586), (587), (589),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (591), (594), (600), (5220), (5235), (5236),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (5245), (5247), (5248), (5254), (5255), (5259),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            (5260), (5262), (5264), (function-axioms) are
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5265)   ~ (all_56_13 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (5265) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | |   (5266)   ~ (all_52_27 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |   (5267)  all_58_12 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (156), (164), (172), (177), (178), (179),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            (272), (283), (307), (315), (323), (324), (326),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            (349), (350), (364), (370), (373), (391), (403),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (560), (562),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            (563), (564), (568), (569), (575), (580), (583),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            (586), (589), (593), (5220), (5245), (5246),
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            (5247), (5248), (5267), (function-axioms) are
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #402.
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | |   (5268)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5268) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | |   (5269)  all_58_13 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (534), (5266), (5269) are inconsistent by
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1026.
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | |   (5270)  all_58_14 = e3 | all_58_15 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5270) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5271)  all_58_14 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (5271) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5272)  all_52_29 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5272) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5273)  all_52_29 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (5273) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5274)   ~ (all_52_5 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (5273) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5275)   ~ (all_52_13 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (5273) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5276)   ~ (all_6_2 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (5273) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5277)  op(e1, e3) = all_52_28
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (5273) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5278)  op(e0, e1) = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e1, simplifying with (164), (5277)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5279)  all_52_17 = all_52_28
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5279) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5280)  all_58_6 = all_52_28
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5279) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5281)   ~ (all_52_19 = all_52_28)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5281) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5282)   ~ (all_52_19 = all_52_28)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (5279) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5283)   ~ (all_52_23 = all_52_28)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5283) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | |   (5284)   ~ (all_52_23 = all_52_28)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5285)  all_56_2 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (5274), (5285) are inconsistent by
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5286)   ~ (all_56_2 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5287)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (5288)  all_56_11 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (5288) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (5289)  all_52_23 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5289) implies:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (5290)  all_52_23 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (5290) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (5291)  all_58_11 = e3
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (5290) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (5292)   ~ (all_52_15 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (5290) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (5293)   ~ (all_52_19 = e3)
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (5290) imply:
% 172.54/25.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (5294)  op(e0, e3) = all_52_22
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_22, e3, e0, simplifying with (156), (5294)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (5295)  all_52_22 = all_52_25
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5296)  all_58_1 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (172), (319), (370), (373), (385), (539),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            (540), (565), (5246), (5275), (5292), (5296),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            #180.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5297)   ~ (all_58_1 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5298)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (5297) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5299)   ~ (all_52_3 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5300)  all_58_0 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5300) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5301)  all_4_2 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (552), (5301) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5302)   ~ (all_52_7 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5298) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5303)  all_58_3 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (5303) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5304)  all_10_2 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (5304) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5305)   ~ (all_52_9 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (5304) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5306)  op(e2, e3) = all_10_1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_1, e3, e2, simplifying with (172), (5306)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5307)  all_52_9 = all_10_1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (5307) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5308)  all_56_4 = all_10_1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (5307) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5309)  all_58_2 = all_10_1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (5307) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5310)   ~ (all_52_13 = all_10_1)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5310) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5311)   ~ (all_52_13 = all_10_1)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (5307) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5312)   ~ (all_52_15 = all_10_1)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5312) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5313)   ~ (all_52_15 = all_10_1)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5314)  all_56_4 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4489), (5308), (5314) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #311.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5315)   ~ (all_56_4 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5316)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5317)  all_56_1 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (5299), (5317) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5318)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5319)  all_56_3 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (5302), (5319) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5320)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5321)  all_58_9 = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (536), (5248), (5278), (5321),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #794.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5322)   ~ (all_58_9 = e1)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (536), (5322) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5323)   ~ (all_52_7 = e1)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5324)  all_58_0 = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5300), (5324) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5325)  e3 = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5325) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5326)  $false
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5326) is inconsistent.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5327)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5328)  all_58_4 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5328) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5329)  all_52_5 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5329) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5330)  all_52_5 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (5330) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5331)   ~ (all_52_3 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (5330) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5332)   ~ (all_52_7 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5332) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5333)   ~ (all_52_7 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5247), (5330) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5334)  op(e1, e2) = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (386), (392), (540), (566), (569), (5318),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5320), (5323), (5327), (5331), (5333), (5334),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #840.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5335)   ~ (all_58_4 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5336)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (5335) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5337)   ~ (all_52_5 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5338)  all_58_2 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5309), (5338) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5339)  all_10_1 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5339) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5340)  all_10_1 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5311), (5340) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5341)   ~ (all_52_13 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4489), (5340) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5342)   ~ (e3 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (163), (373), (537), (5220), (5271), (5293),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5336), (5341), (function-axioms) are inconsistent
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #378.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5343)   ~ (all_58_2 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5309), (5343) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5344)   ~ (all_10_1 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5316) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5345)  all_56_4 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5308), (5344), (5345) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #544.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5346)  all_56_4 = e1 | all_56_4 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5346) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5347)  all_56_4 = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5226), (5308), (5347) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #543.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5348)  all_56_4 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5308), (5348) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5349)  all_10_1 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5349) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5350)  all_10_1 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5313), (5350) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5351)   ~ (all_52_15 = e0)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4489), (5350) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5352)   ~ (e3 = e0)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5235) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5353)  all_58_9 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (5353) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5354)  all_52_7 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5354) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5355)  all_52_7 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (5355) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5356)   ~ (all_52_5 = e0)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5287) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5357)  all_56_2 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (5337), (5357) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #827.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5358)  all_56_2 = e1 | all_56_2 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (413), (584), (5247), (5356), (5358),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #858.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5359)  all_58_10 = e0 | all_58_11 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5359) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5360)  all_58_10 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (5351), (5360) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #741.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5361)  all_58_11 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5291), (5361) are inconsistent by sub-proof
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #804.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5362)  all_58_7 = e3 | all_58_13 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (364), (534), (5266), (5293), (5362) are
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5363)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (178), (179), (283), (307), (326), (370),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (403), (531), (532), (535), (536), (540),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (546), (552), (569), (586), (595), (596), (597),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5245), (5248), (5274), (5299), (5363),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1013.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (5364)   ~ (all_56_11 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (5364) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (5365)   ~ (all_52_23 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (41), (42), (61), (156), (159), (163),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (172), (174), (178), (179), (183), (278), (280),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (302), (305), (307), (313), (314), (317),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (323), (326), (329), (331), (349), (364), (370),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (515), (529),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (530), (531), (532), (534), (535), (536), (537),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (539), (540), (542), (546), (548), (550), (552),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (555), (556), (557), (564), (565), (568), (569),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (571), (573), (577), (579), (584), (586), (595),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (596), (597), (710), (4482), (5220), (5234),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (5235), (5236), (5245), (5246), (5247), (5248),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (5254), (5255), (5266), (5271), (5274), (5278),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (5280), (5282), (5284), (5365), (function-axioms)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #171.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |   (5366)  all_58_15 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (5366) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |   (5367)  all_6_2 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5255), (5367) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |   (5368)  $false
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5368) is inconsistent.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5369)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.54/26.00  | | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | ALPHA: (5369) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5370)  all_52_14 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5371)  all_52_12 = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5372)  all_52_10 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5373)  all_52_8 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (5372) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5374)  all_10_1 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | REDUCE: (53), (5374) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5375)  op(e2, all_10_2) = all_10_0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | REDUCE: (183), (5373) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5376)  op(e3, all_52_9) = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | REDUCE: (52), (5374) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5377)  op(e2, all_10_2) = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | REDUCE: (167), (5371) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5378)  op(e1, all_52_13) = e1
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | REDUCE: (159), (5370) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5379)  op(e0, all_52_15) = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 172.54/26.00  | | | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (5375), (5377)
% 172.54/26.00  | | | | | | | | | | | | | | | | | |              gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5380)  all_10_0 = e2
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | REDUCE: (4487), (5380) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | |   (5381)   ~ (e3 = e2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |   (5382)  all_56_15 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5382) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |   (5383)  all_6_2 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | SIMP: (5383) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |   (5384)  all_6_2 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |            (5384), (function-axioms) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |   (5385)   ~ (all_56_15 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |   (5386)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (5385) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | |   (5387)   ~ (all_6_2 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5388)  all_56_13 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (5388) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5389)  all_52_27 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | SIMP: (5389) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5390)  all_52_27 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (5390) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5391)  all_58_13 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (5390) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5392)   ~ (all_52_3 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (5390) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5393)   ~ (all_52_19 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (5390) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5394)   ~ (all_52_25 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (5390) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5395)   ~ (all_52_29 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | SIMP: (5395) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5396)   ~ (all_52_29 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (573), (5390) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5397)   ~ (all_10_2 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | SIMP: (5397) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5398)   ~ (all_10_2 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (5390) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5399)  op(e2, e3) = all_52_26
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e2, simplifying with (172), (5399)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |              gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5400)  all_52_9 = all_52_26
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (409), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5401)  all_56_4 = all_52_26
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5402)  all_58_2 = all_52_26
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (556), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5403)   ~ (all_52_13 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | SIMP: (5403) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5404)   ~ (all_52_13 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5405)   ~ (all_52_15 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | SIMP: (5405) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5406)   ~ (all_52_15 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5407)   ~ (all_52_17 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | SIMP: (5407) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5408)   ~ (all_52_17 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5409)   ~ (all_52_25 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | SIMP: (5409) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5410)   ~ (all_52_25 = all_52_26)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5411)   ~ (all_52_26 = all_10_2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5412)   ~ (all_52_26 = all_4_2)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | REDUCE: (5376), (5400) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | |   (5413)  op(e3, all_52_26) = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | |   (5414)  all_56_1 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (5392), (5414) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | |   (5415)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | |   (5416)  all_56_5 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (5398), (5416) are inconsistent by
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #895.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | |   (5417)   ~ (all_56_5 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | |   (5418)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |   (5419)  all_56_10 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (359), (560), (5220), (5419),
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |            #406.
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |   (5420)   ~ (all_56_10 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (5420) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | |   (5421)   ~ (all_14_2 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | |   (5422)  all_58_4 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5422) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | |   (5423)  all_52_5 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5423) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | |   (5424)  all_52_5 = e3
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (5424) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | |   (5425)   ~ (all_52_13 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5425) implies:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | |   (5426)   ~ (all_52_13 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (5424) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | |   (5427)   ~ (all_14_2 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (5424) imply:
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | |   (5428)   ~ (all_4_2 = e3)
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.00  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5428) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |   (5429)   ~ (all_4_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (36), (37), (156), (163), (177), (179),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (181), (279), (283), (311), (314), (319), (321),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (326), (327), (330), (349), (364), (370), (373),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (385), (392), (403), (529), (530), (531), (533),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (544), (546), (548), (559), (564), (565), (566),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (571), (575), (594), (595), (597), (598), (599),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (5220), (5230), (5376), (5379), (5386), (5391),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (5392), (5393), (5398), (5401), (5402), (5406),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (5408), (5410), (5411), (5412), (5413), (5415),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (5418), (5421), (5422), (5426), (5429),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            #389.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |   (5430)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (36), (37), (38), (42), (155), (164),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (170), (178), (179), (182), (279), (313), (321),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (330), (349), (364), (373), (391), (403), (529),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (533), (534), (537), (538), (539), (540), (548),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (559), (560), (568), (582), (594), (4486), (5224),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (5228), (5234), (5377), (5378), (5386), (5391),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (5394), (5396), (5401), (5402), (5404), (5408),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (5410), (5412), (5413), (5421), (5430),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            #215.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |   (5431)   ~ (all_56_13 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (5431) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |   (5432)   ~ (all_52_27 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5433)  all_58_12 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (5433) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5434)  all_52_25 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (5434) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5435)  all_52_25 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (5435) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5436)   ~ (all_52_9 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (5435) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5437)   ~ (all_52_27 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (5435) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5438)   ~ (all_52_29 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (5438) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5439)   ~ (all_52_29 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (5435) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5440)   ~ (all_6_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (5435) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5441)   ~ (all_4_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (5441) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5442)   ~ (all_4_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (5435) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5443)  op(e0, e3) = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (37), (42), (154), (155),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (158), (164), (170), (172), (174), (177), (178),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (179), (182), (269), (272), (273), (274), (279),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (280), (283), (307), (310), (313), (315), (321),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (323), (324), (325), (328), (329), (341), (350),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (386), (391),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (403), (409), (419), (505), (529), (531), (532),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (550), (552), (553), (556),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (557), (559), (560), (561), (565), (566), (568),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (569), (579), (580), (581), (582), (583), (585),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (586), (587), (588), (591), (593), (594), (596),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (597), (600), (756), (4486), (5216), (5219),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (5234), (5235), (5236), (5376), (5377), (5378),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (5379), (5386), (5387), (5432), (5433), (5436),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (5439), (5442), (5443), (function-axioms) are
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #170.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5444)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (37), (38), (42), (154),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (156), (158), (161), (164), (165), (169), (172),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (174), (177), (178), (179), (181), (182), (272),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (307), (311), (316), (319), (320), (323), (326),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (329), (330), (331), (349), (350), (364), (370),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (515), (529), (532),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (552), (554),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (580), (581), (586),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (591), (594), (597), (598), (599), (600), (710),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (796), (4482), (5224), (5235), (5376), (5377),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (5378), (5379), (5386), (5387), (5432), (5444),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |            #209.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5445)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.54/26.01  | | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.54/26.01  | | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (42), (649), (4486), (5218), (5445),
% 172.54/26.01  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.01  | | | | | | | | | | | | | | | | |            #169.
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | End of split
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | |   (5446)  all_40_1 = e1
% 172.54/26.01  | | | | | | | | | | | | | | |   (5447)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | COMBINE_EQS: (715), (5446) imply:
% 172.54/26.01  | | | | | | | | | | | | | | |   (5448)  all_4_1 = e1
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (5448) imply:
% 172.54/26.01  | | | | | | | | | | | | | | |   (5449)  all_52_0 = e1
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | REDUCE: (38), (5448) imply:
% 172.54/26.01  | | | | | | | | | | | | | | |   (5450)  op(e1, all_4_2) = all_4_0
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | REDUCE: (37), (5448) imply:
% 172.54/26.01  | | | | | | | | | | | | | | |   (5451)  op(e3, all_4_2) = e1
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | |   (5452)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.54/26.01  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.54/26.01  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.54/26.01  | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | BETA: splitting (5452) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5453)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.54/26.01  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5449), (5453) are inconsistent by sub-proof
% 172.54/26.01  | | | | | | | | | | | | | | | | |            #632.
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5454)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.54/26.01  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | ALPHA: (5454) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5455)  all_52_14 = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5456)  all_52_12 = e1
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5457)  all_52_10 = e2
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5458)  all_52_8 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (5457) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5459)  all_10_1 = e2
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REDUCE: (53), (5459) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5460)  op(e2, all_10_2) = all_10_0
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REDUCE: (183), (5458) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5461)  op(e3, all_52_9) = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REDUCE: (52), (5459) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5462)  op(e2, all_10_2) = e2
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REDUCE: (167), (5456) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5463)  op(e1, all_52_13) = e1
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REDUCE: (159), (5455) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5464)  op(e0, all_52_15) = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 172.54/26.01  | | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (5460), (5462)
% 172.54/26.01  | | | | | | | | | | | | | | | | |              gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5465)  all_10_0 = e2
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | REDUCE: (4487), (5465) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | |   (5466)   ~ (e3 = e2)
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | |   (5467)  all_58_15 = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5467),
% 172.54/26.01  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.01  | | | | | | | | | | | | | | | | | |            #228.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | |   (5468)   ~ (all_58_15 = e0)
% 172.54/26.01  | | | | | | | | | | | | | | | | | |   (5469)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.54/26.01  | | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.54/26.01  | | | | | | | | | | | | | | | | | |             e0)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | ALPHA: (5469) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | |   (5470)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | REDUCE: (532), (5468) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | |   (5471)   ~ (all_6_2 = e0)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |   (5472)  all_56_15 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5472) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |   (5473)  all_6_2 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |            (5473), (function-axioms) are inconsistent by
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |   (5474)   ~ (all_56_15 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |   (5475)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (5474) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | |   (5476)   ~ (all_6_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |   (5477)  all_56_13 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (5477) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |   (5478)  all_52_27 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (156), (163), (164), (172), (173),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (178), (179), (274), (279), (283), (307), (315),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (326), (330), (349), (370), (373), (385), (391),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (403), (409), (419), (518), (531), (532), (533),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (542), (546), (550),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (556), (558), (560), (561), (562), (566), (578),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (581), (582), (586), (589), (770), (5220), (5224),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (5447), (5450), (5451), (5461), (5463), (5464),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            (5478), (function-axioms) are inconsistent by
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |            sub-proof #364.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |   (5479)   ~ (all_56_13 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (5479) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | |   (5480)   ~ (all_52_27 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5481)  all_58_12 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (5481) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5482)  all_52_25 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (5482) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5483)  all_52_25 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (5483) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5484)   ~ (all_52_17 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (5483) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5485)   ~ (all_52_27 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (5483) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5486)   ~ (all_52_29 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (5486) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5487)   ~ (all_52_29 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (5483) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5488)   ~ (all_6_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (5483) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5489)   ~ (all_4_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (5489) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5490)   ~ (all_4_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (5483) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | |   (5491)  op(e0, e3) = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | |   (5492)  all_56_0 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (5492) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | |   (5493)  all_4_2 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5490), (5493) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | |   (5494)  $false
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5494) is inconsistent.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | |   (5495)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5496)  all_56_2 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (5496) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5497)  all_52_5 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5497) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5498)  all_52_5 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (5498) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5499)   ~ (all_52_3 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (5498) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5500)   ~ (all_52_7 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5500) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5501)   ~ (all_52_7 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (172), (179), (274), (307), (323), (364),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |            (370), (419), (532), (534), (535), (536), (539),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |            (540), (565), (580), (5461), (5462), (5464),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |            (5476), (5480), (5491), (5499), (5501),
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |            #385.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5502)   ~ (all_56_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (413), (5502) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | |   (5503)   ~ (all_52_5 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |   (5504)  all_58_4 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (391), (5503), (5504) are inconsistent by
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1025.
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | |   (5505)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5506)  all_56_6 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (5506) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5507)  all_52_13 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5507) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5508)  all_52_13 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (5508) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5509)  all_58_5 = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (5508) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5510)   ~ (all_52_15 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5510) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5511)   ~ (all_52_15 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (5508) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5512)   ~ (all_14_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5512) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5513)   ~ (all_14_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (5508) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5514)   ~ (all_10_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5514) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5515)   ~ (all_10_2 = e3)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (5508) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5516)  op(e2, e1) = e3
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5463), (5508) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5517)  op(e1, e3) = e1
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, e1, simplifying with (164), (5517) gives:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5518)  all_52_17 = e1
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5518) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5519)  all_58_6 = e1
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5518) imply:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5520)   ~ (all_52_19 = e1)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5520) implies:
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (5521)   ~ (all_52_19 = e1)
% 172.54/26.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (560), (5518) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5522)   ~ (all_14_2 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5522) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5523)   ~ (all_14_2 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5484), (5518) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5524)   ~ (e3 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (5518) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5525)  op(e3, e1) = all_52_16
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_16, e1, e3, simplifying with (178), (5525)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5526)  all_52_5 = all_52_16
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5526) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5527)  all_58_4 = all_52_16
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (5526) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5528)   ~ (all_52_3 = all_52_16)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (5526) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5529)   ~ (all_52_7 = all_52_16)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5529) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5530)   ~ (all_52_7 = all_52_16)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (5526) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5531)   ~ (all_52_16 = all_4_2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5532)  all_56_10 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (359), (5513), (5532) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #552.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5533)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5534)  all_58_1 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (5534) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5535)  all_52_3 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (5535) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5536)   ~ (all_52_7 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5536) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5537)   ~ (all_52_7 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5528), (5535) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5538)   ~ (all_52_16 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5538) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5539)   ~ (all_52_16 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (5535) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5540)  op(e3, e2) = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5541)  all_58_4 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5527), (5541) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5542)  all_52_16 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5542) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5543)  all_52_16 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5530), (5543) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5544)   ~ (all_52_7 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5531), (5543) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5545)   ~ (all_4_2 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5545) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5546)   ~ (all_4_2 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5547)  all_56_3 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (386), (5537), (5547) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5548)   ~ (all_56_3 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5549)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5550)  all_58_1 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5534), (5550) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5551)  e3 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5551) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5552)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5552) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5553)   ~ (all_58_1 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5554)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5555)  all_58_0 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5555) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5556)  all_4_2 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5451), (5556) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5557)  op(e3, e2) = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2,
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (5540), (5557) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5558)  e3 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5558) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5559)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5559) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5560)   ~ (all_58_0 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (364), (386), (403), (529), (531), (534), (539),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (552), (582), (597), (5462), (5471), (5475),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5495), (5516), (5521), (5537), (5544), (5546),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5549), (5554), (5560), (function-axioms) are
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #749.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5561)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (321), (364), (533), (534), (537),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (539), (581), (5462), (5487), (5509), (5516),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5521), (5523), (5534), (5561), (function-axioms)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #748.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5562)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5562) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5563)  all_58_3 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (5563) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5564)  all_10_2 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5515), (5564) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5565)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5565) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5566)  all_58_7 = e3 | all_58_13 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5566) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5567)  all_58_7 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (5567) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5568)  all_52_19 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (5568) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5569)   ~ (all_52_23 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5569) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5570)   ~ (all_52_23 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5571)  all_58_9 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (5571) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5572)  all_52_7 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5572) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5573)  all_52_7 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (5573) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5574)   ~ (all_52_3 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5530), (5573) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5575)   ~ (all_52_16 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5575) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5576)   ~ (all_52_16 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (177), (5573) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5577)  op(e3, e0) = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5578)  all_58_6 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5519), (5578) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5579)  e2 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (5579) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5580)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5580) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5581)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5582)  all_58_4 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5527), (5582) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5583)  all_52_16 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5583) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5584)  all_52_16 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5528), (5584) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5585)   ~ (all_52_3 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5531), (5584) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5586)   ~ (all_4_2 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5586) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5587)   ~ (all_4_2 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5588)  all_56_1 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (5574), (5588) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5589)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5590)  all_58_1 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (5590) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5591)  all_52_3 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5585), (5591) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5592)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5592) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5593)   ~ (all_58_1 = e1)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5594)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5595)  all_58_0 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5595) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5596)  all_4_2 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (5596) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5597)   ~ (all_52_3 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5451), (5596) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5598)  op(e3, e2) = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5589) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5599)  all_56_1 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (5597), (5599) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #857.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5600)  all_56_1 = e1 | all_56_1 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5600) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5601)  all_56_1 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (5585), (5601) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #841.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5602)  all_56_1 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (5602) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5603)  all_52_3 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5603) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5604)  all_52_3 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5585), (5604) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5605)   ~ (e1 = e0)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (179), (5604) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5606)  op(e3, e2) = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5533) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5607)  all_56_10 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (5607) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5608)  all_14_2 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5608) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5609)  all_14_2 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5219), (5609) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5610)  op(e3, e2) = all_14_0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (5598), (5610) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5611)  all_14_0 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_14_0,
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (5606), (5610) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5612)  all_14_0 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5611), (5612) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5613)  e1 = e0
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5613) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5614)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5614) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5615)   ~ (all_56_10 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (5615) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5616)   ~ (all_14_2 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5581) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5617)  all_58_7 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5567), (5617) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5618)  e3 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5618) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5619)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5619) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5620)  all_58_8 = e2 | all_58_11 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5620) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5621)  all_58_8 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (5621) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5622)  all_14_2 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5616), (5622) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5623)  $false
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5623) is inconsistent.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5624)  all_58_11 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (5624) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5625)  all_52_23 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5625) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5626)  all_52_23 = e2
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (600), (5626) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5627)   ~ (all_6_2 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5627) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5628)   ~ (all_6_2 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (364), (529), (534), (539), (582), (5462), (5466),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5471), (5475), (5516), (5521), (5594), (5628),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #750.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5629)   ~ (all_58_0 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (5629) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5630)   ~ (all_4_2 = e2)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (531), (5451), (5495), (5577), (5587),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5630), (function-axioms) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #604.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5631)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (42), (155), (529), (533), (534),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (537), (582), (594), (4486), (5470), (5475),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5481), (5509), (5523), (5631), (function-axioms)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #168.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5632)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (532), (535), (5476), (5511), (5570),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5632) are inconsistent by sub-proof #645.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5633)  all_58_13 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (534), (5480), (5633) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1026.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5634)   ~ (all_56_6 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (5634) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (5635)   ~ (all_52_13 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (373), (533), (537), (560), (5220), (5487),
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |            (5505), (5635), (function-axioms) are inconsistent
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #420.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | |   (5636)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5636) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | |   (5637)  all_58_13 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (534), (5480), (5637) are inconsistent by
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1026.
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | |   (5638)  all_58_14 = e3 | all_58_15 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5638) gives:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5639)  all_58_14 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (5639) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5640)  all_52_29 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5640) implies:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5641)  all_52_29 = e3
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (5641) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5642)   ~ (all_52_5 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (5641) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5643)   ~ (all_52_25 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (5641) imply:
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5644)   ~ (all_6_2 = e3)
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.54/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (5641) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5645)  op(e1, e3) = all_52_28
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (5641) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5646)  op(e0, e1) = e3
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e1, simplifying with (164), (5645)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5647)  all_52_17 = all_52_28
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5647) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5648)  all_58_6 = all_52_28
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5647) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5649)   ~ (all_52_19 = all_52_28)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5649) implies:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5650)   ~ (all_52_19 = all_52_28)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (5647) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5651)   ~ (all_52_23 = all_52_28)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5651) implies:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5652)   ~ (all_52_23 = all_52_28)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (5647) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5653)   ~ (all_52_25 = all_52_28)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5653) implies:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5654)   ~ (all_52_25 = all_52_28)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (5647) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | |   (5655)  op(e3, all_52_28) = all_52_16
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | |   (5656)  all_56_0 = e3
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (5656) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | |   (5657)  all_4_2 = e3
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (5451), (5657), (function-axioms) are
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #630.
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | |   (5658)   ~ (all_56_0 = e3)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (531), (5658) imply:
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | |   (5659)   ~ (all_4_2 = e3)
% 172.64/26.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (37), (42), (156),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (172), (177), (178), (179), (181), (307), (319),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (323), (326), (329), (330), (349), (364), (370),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (385), (391), (403), (515), (529), (532), (534),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (535), (536), (539), (540), (542), (552), (564),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (565), (569), (597), (710), (796), (4482), (5461),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (5462), (5464), (5475), (5476), (5480), (5642),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (5643), (5646), (5648), (5650), (5652), (5654),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            (5655), (5659), (function-axioms) are inconsistent
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #211.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | |   (5660)  all_58_15 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (5660) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | |   (5661)  all_6_2 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5476), (5661) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | |   (5662)  $false
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5662) is inconsistent.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5663)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.64/26.03  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.64/26.03  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | BETA: splitting (5663) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5664)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (5664) are inconsistent by sub-proof
% 172.64/26.03  | | | | | | | | | | | | | | | | |            #373.
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5665)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (5665),
% 172.64/26.03  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.64/26.03  | | | | | | | | | | | | | | | | |            #200.
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | |   (5666)  all_34_0 = e1
% 172.64/26.03  | | | | | | | | | | | | | |   (5667)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | COMBINE_EQS: (773), (5666) imply:
% 172.64/26.03  | | | | | | | | | | | | | |   (5668)  all_4_0 = e1
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | SIMP: (5668) implies:
% 172.64/26.03  | | | | | | | | | | | | | |   (5669)  all_4_0 = e1
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | REDUCE: (38), (5669) imply:
% 172.64/26.03  | | | | | | | | | | | | | |   (5670)  op(all_4_1, all_4_2) = e1
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | |   (5671)  all_58_15 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (5671),
% 172.64/26.03  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.64/26.03  | | | | | | | | | | | | | | |            #228.
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | |   (5672)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.64/26.03  | | | | | | | | | | | | | | |             e0)
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | ALPHA: (5672) implies:
% 172.64/26.03  | | | | | | | | | | | | | | |   (5673)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5674)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.64/26.03  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | BETA: splitting (5674) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5675)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (5670), (5675),
% 172.64/26.03  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.64/26.03  | | | | | | | | | | | | | | | | |            #600.
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5676)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | ALPHA: (5676) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5677)  all_52_14 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5678)  all_52_12 = e1
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5679)  all_52_10 = e2
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5680)  all_52_8 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (5679) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5681)  all_10_1 = e2
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (53), (5681) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5682)  op(e2, all_10_2) = all_10_0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (183), (5680) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5683)  op(e3, all_52_9) = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (52), (5681) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5684)  op(e2, all_10_2) = e2
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (167), (5678) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5685)  op(e1, all_52_13) = e1
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (159), (5677) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5686)  op(e0, all_52_15) = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 172.64/26.03  | | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (5682), (5684)
% 172.64/26.03  | | | | | | | | | | | | | | | | |              gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5687)  all_10_0 = e2
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (4487), (5687) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5688)   ~ (e3 = e2)
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5689)  all_56_15 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5689) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5690)  all_6_2 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.64/26.03  | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.64/26.03  | | | | | | | | | | | | | | | | | |            (5690), (function-axioms) are inconsistent by
% 172.64/26.03  | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5691)   ~ (all_56_15 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5692)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | REDUCE: (529), (5691) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5693)   ~ (all_6_2 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5694)  all_56_13 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (5694) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5695)  all_52_27 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (37), (156), (163), (164), (172),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (173), (179), (277), (279), (282), (283), (315),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (319), (328), (330), (349), (370), (373), (385),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (415), (494), (531),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (533), (537), (538), (539), (542), (544), (546),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (548), (550), (554), (556), (557), (560), (562),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (566), (567), (568), (573), (581), (583), (663),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (5220), (5667), (5670), (5683), (5685), (5686),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (5695), (function-axioms) are inconsistent by
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            sub-proof #362.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5696)   ~ (all_56_13 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (344), (5696) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5697)   ~ (all_52_27 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (37), (42), (154),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (155), (156), (161), (163), (164), (165), (172),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (177), (178), (179), (181), (280), (281), (282),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (283), (304), (307), (311), (319), (323), (326),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (349), (364), (370),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (413),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (494), (515), (529), (531), (532), (533), (534),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (546), (548), (550), (552), (559), (561), (563),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (568), (569), (581), (582),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (585), (588), (591), (594), (596), (597), (598),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (663), (710), (796), (4482), (4486), (5667),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (5670), (5673), (5683), (5684), (5686), (5692),
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            (5693), (5697), (function-axioms) are inconsistent
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |            by sub-proof #195.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5698)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.64/26.03  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.64/26.03  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | BETA: splitting (5698) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5699)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (5699) are inconsistent by sub-proof
% 172.64/26.03  | | | | | | | | | | | | | | | | |            #373.
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5700)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (5700),
% 172.64/26.03  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.64/26.03  | | | | | | | | | | | | | | | | |            #200.
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | End of split
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | |   (5701)  all_30_1 = e1
% 172.64/26.03  | | | | | | | | | | | | |   (5702)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e3)
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | COMBINE_EQS: (712), (5701) imply:
% 172.64/26.03  | | | | | | | | | | | | |   (5703)  all_10_1 = e1
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | COMBINE_EQS: (661), (5703) imply:
% 172.64/26.03  | | | | | | | | | | | | |   (5704)  all_52_10 = e1
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | REDUCE: (4489), (5703) imply:
% 172.64/26.03  | | | | | | | | | | | | |   (5705)   ~ (e3 = e1)
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | REDUCE: (53), (5703) imply:
% 172.64/26.03  | | | | | | | | | | | | |   (5706)  op(e1, all_10_2) = all_10_0
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | REDUCE: (52), (5703) imply:
% 172.64/26.03  | | | | | | | | | | | | |   (5707)  op(e2, all_10_2) = e1
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 172.64/26.03  | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | |   (5708)   ~ (all_34_0 = e1)
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | REDUCE: (773), (5708) imply:
% 172.64/26.03  | | | | | | | | | | | | | |   (5709)   ~ (all_4_0 = e1)
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.64/26.03  | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | |   (5710)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.64/26.03  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | BETA: splitting (5710) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5711)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.64/26.03  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | ALPHA: (5711) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5712)  all_52_6 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5713)  all_52_4 = e1
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5714)  all_52_2 = e2
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5715)  all_52_0 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (5715) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5716)  all_4_1 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | REDUCE: (38), (5716) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5717)  op(e3, all_4_2) = all_4_0
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | REDUCE: (37), (5716) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5718)  op(e3, all_4_2) = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | REDUCE: (176), (5714) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5719)  op(e2, all_52_3) = e2
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | REDUCE: (168), (5713) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5720)  op(e1, all_52_5) = e1
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | REDUCE: (160), (5712) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5721)  op(e0, all_52_7) = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 172.64/26.03  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (5717), (5718)
% 172.64/26.03  | | | | | | | | | | | | | | | |              gives:
% 172.64/26.03  | | | | | | | | | | | | | | | |   (5722)  all_4_0 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5723)  all_58_15 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (5723) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5724)  all_6_2 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (4486), (5724) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5725)  op(all_6_1, e0) = e2
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (42), (5724) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5726)  op(e0, e0) = all_6_1
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (41), (5724) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5727)  op(e0, e0) = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5725), (5726), (5727), (function-axioms) are
% 172.64/26.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #229.
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5728)   ~ (all_58_15 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5729)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.64/26.03  | | | | | | | | | | | | | | | | |             e0)
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | ALPHA: (5729) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5730)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5731)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | REDUCE: (532), (5728) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | |   (5732)   ~ (all_6_2 = e0)
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5733)  all_56_15 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5733) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5734)  all_6_2 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (501), (5734) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5735)  all_16_2 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | REDUCE: (564), (5734) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5736)   ~ (all_52_25 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | REDUCE: (4486), (5734) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5737)  op(all_6_1, e3) = e2
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | REDUCE: (42), (5734) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5738)  op(e0, e3) = all_6_1
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (172), (271), (303), (349), (429), (554),
% 172.64/26.03  | | | | | | | | | | | | | | | | | |            (704), (4493), (5735), (5736), (5737), (5738),
% 172.64/26.03  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.64/26.03  | | | | | | | | | | | | | | | | | |            #227.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5739)   ~ (all_56_15 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5740)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | REDUCE: (529), (5739) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | |   (5741)   ~ (all_6_2 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5742)  all_56_13 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (5742) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5743)  all_52_27 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5744)  all_58_13 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (567), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5745)   ~ (all_52_3 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (578), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5746)   ~ (all_52_19 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (562), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5747)   ~ (all_52_25 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (581), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5748)   ~ (all_52_29 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | SIMP: (5748) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5749)   ~ (all_52_29 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (573), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5750)   ~ (all_10_2 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | SIMP: (5750) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5751)   ~ (all_10_2 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (582), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5752)   ~ (all_6_2 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (173), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5753)  op(e2, e3) = all_52_26
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (155), (5743) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5754)  op(e0, e2) = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |              all_52_26, e3, e2, simplifying with (172), (5753)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |              gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5755)  all_52_9 = all_52_26
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (5755) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5756)  all_58_2 = all_52_26
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (556), (5755) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5757)   ~ (all_52_13 = all_52_26)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | SIMP: (5757) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5758)   ~ (all_52_13 = all_52_26)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (557), (5755) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5759)   ~ (all_52_15 = all_52_26)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | SIMP: (5759) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5760)   ~ (all_52_15 = all_52_26)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (554), (5755) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5761)   ~ (all_52_25 = all_52_26)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | SIMP: (5761) implies:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5762)   ~ (all_52_25 = all_52_26)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (555), (5755) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5763)   ~ (all_52_26 = all_10_2)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (542), (5755) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5764)   ~ (all_52_26 = all_4_2)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | REDUCE: (183), (5755) imply:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | |   (5765)  op(e3, all_52_26) = all_52_8
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | |   (5766)  all_56_9 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (419), (5746), (5766) are inconsistent by
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | |            sub-proof #700.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | |   (5767)   ~ (all_56_9 = e3)
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | |   (5768)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | |   (5769)  all_56_1 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (5745), (5769) are inconsistent by
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | |            sub-proof #862.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | |   (5770)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | |   (5771)  all_56_12 = e3
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (429), (5747), (5771) are inconsistent by
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1040.
% 172.64/26.03  | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | |   (5772)   ~ (all_56_12 = e3)
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | |   (5773)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5774)  all_56_10 = e3
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (5774) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5775)  all_14_2 = e3
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (560), (5775) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5776)   ~ (all_52_17 = e3)
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5220), (5775) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5777)  op(e1, e3) = e3
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, e1, simplifying with (164), (5777) gives:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5778)  all_52_17 = e3
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5776), (5778) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5779)  $false
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5779) is inconsistent.
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5780)   ~ (all_56_10 = e3)
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (5780) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | |   (5781)   ~ (all_14_2 = e3)
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5782)  all_58_4 = e3
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5782) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5783)  all_52_5 = e3
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5783) implies:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5784)  all_52_5 = e3
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (5784) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5785)   ~ (all_14_2 = e3)
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (5784) imply:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5786)   ~ (all_4_2 = e3)
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5786) implies:
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5787)   ~ (all_4_2 = e3)
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.64/26.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5720), (5784) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5788)  op(e1, e3) = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, e1, simplifying with (164), (5788) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5789)  all_52_17 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (5789) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5790)  all_58_6 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (5789) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5791)   ~ (all_52_19 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5791) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5792)   ~ (all_52_19 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (5789) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5793)   ~ (all_52_23 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5793) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5794)   ~ (all_52_23 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (560), (5789) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5795)   ~ (all_14_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5795) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | |   (5796)   ~ (all_14_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (5797)  all_58_6 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5790), (5797) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (5798)  e3 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5798) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (5799)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5799) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (5800)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5800) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5801)  all_58_7 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (5801) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5802)  all_52_19 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5746), (5802) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5803)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5803) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5804)  all_58_8 = e3 | all_58_11 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5804) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5805)  all_58_8 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (5805) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5806)  all_14_2 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5781), (5806) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5807)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5807) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5808)  all_58_11 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (5808) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5809)  all_52_23 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5809) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5810)  all_52_23 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (5810) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5811)   ~ (all_52_7 = e3)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (5810) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5812)   ~ (all_52_15 = e3)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5813)  all_58_0 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5813) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5814)  all_4_2 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5787), (5814) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5815)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5815) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5816)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5816) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5817)  all_58_2 = e3
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5818)  all_58_1 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (5818) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5819)  all_52_3 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (5819) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5820)   ~ (all_10_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5820) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5821)   ~ (all_10_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5719), (5819) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5822)  op(e2, e1) = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, e2, simplifying with (170), (5822) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5823)  all_52_13 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (5823) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5824)  all_58_5 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5825)  all_58_2 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5817), (5825) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5826)  e3 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5826) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5827)  e3 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5827) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5828)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5828) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5829)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5829) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5830)  all_58_3 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (5830) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5831)  all_10_2 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5821), (5831) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5832)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5832) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5833)  all_58_5 = e1 | all_58_10 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5833) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5834)  all_58_5 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5824), (5834) are inconsistent by sub-proof
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #672.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5835)  all_58_10 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (5835) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5836)  all_52_15 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5836) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5837)  all_52_15 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (5837) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5838)   ~ (all_52_7 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (599), (5837) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5839)   ~ (all_6_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5839) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5840)   ~ (all_6_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (280), (386), (529), (536), (597), (5721),
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5731), (5732), (5740), (5811), (5838), (5840),
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #178.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5841)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5841) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5842)  all_58_3 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (5842) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5843)  all_10_2 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (5843) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5844)   ~ (all_52_13 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5707), (5843) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5845)  op(e2, e1) = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5846)  all_58_4 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5782), (5846) are inconsistent by sub-proof
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #392.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5847)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5847) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5848)  all_58_5 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (5848) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5849)  all_52_13 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5849) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5850)  all_52_13 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5844), (5850) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5851)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5851) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5852)  all_58_8 = e1 | all_58_14 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5852) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5853)  all_58_8 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (5796), (5853) are inconsistent by
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #815.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5854)  all_58_14 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (5854) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5855)  all_52_29 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5855) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5856)  all_52_29 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (5856) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5857)   ~ (all_6_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5857) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5858)   ~ (all_6_2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5859)  all_58_0 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5859) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5860)  all_4_2 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (5860) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5861)   ~ (all_52_3 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5740) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5862)  all_56_15 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5862) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5863)  all_6_2 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (5863) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5864)   ~ (all_52_7 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (599), (5863) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5865)   ~ (all_52_15 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5741), (5863) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5866)   ~ (e3 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (5863) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5867)  op(e0, e0) = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5868)  all_58_9 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (5868) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5869)  all_52_7 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5869) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5870)  all_52_7 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (5870) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5871)   ~ (all_52_3 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (5870) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5872)   ~ (all_52_15 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5872) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5873)   ~ (all_52_15 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5864), (5870) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5874)   ~ (e2 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5731) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5875)  all_58_9 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5868), (5875) are inconsistent by sub-proof
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #809.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5876)  all_58_10 = e0 | all_58_11 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (169), (170), (318), (370), (373),
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (392), (5719), (5745), (5770), (5808), (5817),
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5842), (5845), (5861), (5865), (5871), (5873),
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5876), (function-axioms) are inconsistent by
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #167.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5877)   ~ (all_58_9 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (536), (5877) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5878)   ~ (all_52_7 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (386), (536), (5721), (5731), (5811),
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5864), (5867), (5878), (function-axioms) are
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #179.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5879)  all_56_15 = e1 | all_56_15 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (529), (5732), (5858), (5879) are inconsistent by
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5880)   ~ (all_58_0 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (5880) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5881)   ~ (all_4_2 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5882)  all_58_9 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (5882) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5883)  all_52_7 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5883) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5884)  all_52_7 = e1
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (5884) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5885)   ~ (all_52_3 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (5884) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5886)   ~ (all_52_15 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5886) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5887)   ~ (all_52_15 = e1)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5740) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5888)  all_56_15 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5888) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5889)  all_6_2 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (599), (5889) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5890)   ~ (all_52_15 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5741), (5889) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5891)   ~ (e3 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5731) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5892)  all_58_9 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5882), (5892) are inconsistent by sub-proof
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #809.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5893)  all_58_10 = e0 | all_58_11 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5894)  all_58_0 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5894) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5895)  all_4_2 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5881), (5895) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5896)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5896) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5897)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5897) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5898)  all_58_1 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (5898) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5899)  all_52_3 = e2
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (5899) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5900)   ~ (all_52_19 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5900) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5901)   ~ (all_52_19 = e2)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5893) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5902)  all_58_10 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (5902) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5903)  all_52_15 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5903) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5904)  all_52_15 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (5904) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5905)   ~ (all_52_13 = e0)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5812), (5904) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5906)   ~ (e3 = e0)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5887), (5904) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5907)   ~ (e1 = e0)
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5908)  all_58_4 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5782), (5908) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5909)  e3 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5909) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5910)  e3 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5910) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5911)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5911) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5912)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5912) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5913)  all_58_5 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (5913) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5914)  all_52_13 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5914) implies:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5915)  all_52_13 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5905), (5915) imply:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5916)  $false
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5916) is inconsistent.
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5917)  all_58_8 = e0 | all_58_14 = e0
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5768) gives:
% 172.67/26.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5918)  all_56_9 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (5918) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5919)  all_52_19 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5901), (5919) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5920)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5920) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5921)  all_56_9 = e1 | all_56_9 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5917) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5922)  all_58_8 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (5922) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5923)  all_14_2 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (5923) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5924)   ~ (all_52_19 = e0)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (419), (5792), (5921), (5924) are inconsistent by
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #688.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5925)  all_58_14 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5854), (5925) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #217.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5926)  all_58_11 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5808), (5926) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #804.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5927)   ~ (all_58_1 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (5927) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5928)   ~ (all_52_3 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (169), (170), (318), (370), (373),
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (392), (5719), (5745), (5770), (5808), (5817),
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5842), (5845), (5885), (5887), (5890), (5893),
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5928), (function-axioms) are inconsistent by
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #167.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5929)  all_56_15 = e1 | all_56_15 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (529), (5732), (5858), (5929) are inconsistent by
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5930)   ~ (all_58_9 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (536), (5930) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5931)   ~ (all_52_7 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (280), (386), (529), (536), (597), (5721),
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5731), (5732), (5740), (5811), (5858), (5931),
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #178.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5932)  all_58_7 = e1 | all_58_13 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (364), (5744), (5792), (5932) are
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #768.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5933)  all_58_6 = e3 | all_58_12 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (349), (5747), (5790), (5933) are
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1002.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | |   (5934)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5934) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5935)  all_58_5 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (5935) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5936)  all_52_13 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5936) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5937)  all_52_13 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (5937) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5938)   ~ (all_52_15 = e3)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5938) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5939)   ~ (all_52_15 = e3)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5758), (5937) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5940)   ~ (all_52_26 = e3)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5940) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5941)   ~ (all_52_26 = e3)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (5937) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5942)   ~ (all_14_2 = e3)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (5937) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (5943)  op(e2, e1) = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5944)  all_58_0 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (5944) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5945)  all_4_2 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (5945) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5946)   ~ (all_52_17 = e3)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5947)  all_58_6 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (5946), (5947) are inconsistent by
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5948)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5948) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5949)  all_58_7 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (5949) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5950)  all_52_19 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5746), (5950) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5951)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5951) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5952)  all_58_8 = e3 | all_58_11 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5952) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5953)  all_58_8 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (5953) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5954)  all_14_2 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5781), (5954) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5955)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5955) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5956)  all_58_11 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (5956) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5957)  all_52_23 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5957) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5958)  all_52_23 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (5958) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5959)   ~ (all_52_7 = e3)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5960)  all_56_7 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (5960) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5961)  all_52_15 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5961) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5962)  all_52_15 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5939), (5962) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5963)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5963) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5964)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5965)  all_58_12 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (5965) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5966)  all_52_25 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5966) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5967)  all_52_25 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (5967) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5968)   ~ (all_52_29 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5968) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5969)   ~ (all_52_29 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (5967) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5970)   ~ (all_6_2 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5970) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5971)   ~ (all_6_2 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (5967) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5972)  op(e3, e1) = all_52_24
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5740) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5973)  all_56_15 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (5973) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5974)  all_6_2 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (5974) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5975)   ~ (all_52_29 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4486), (5974) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5976)  op(all_6_1, e2) = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (5974) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5977)  op(e0, e2) = all_6_1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (5974) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5978)  op(e0, e0) = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5730) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5979)  all_58_12 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5965), (5979) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #907.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5980)  all_58_13 = e0 | all_58_14 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5980) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5981)  all_58_13 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5744), (5981) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #659.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5982)  all_58_14 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (5982) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5983)  all_52_29 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5983) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5984)  all_52_29 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5975), (5984) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5985)   ~ (e2 = e0)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5969), (5984) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5986)   ~ (e1 = e0)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_6_1,
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (5754), (5977) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5987)  all_6_1 = e3
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e1, e3, simplifying with (178), (5972)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5988)  all_52_5 = all_52_24
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (5988) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5989)  all_58_4 = all_52_24
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (5988) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5990)   ~ (all_52_3 = all_52_24)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (5988) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5991)   ~ (all_52_7 = all_52_24)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5991) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5992)   ~ (all_52_7 = all_52_24)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5976), (5987) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5993)  op(e3, e2) = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (179), (5993) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5994)  all_52_3 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (5994) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5995)   ~ (all_52_7 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5995) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5996)   ~ (all_52_7 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5990), (5994) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5997)   ~ (all_52_24 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5997) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5998)   ~ (all_52_24 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5745), (5994) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5999)   ~ (e3 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6000)  all_58_4 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5989), (6000) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6001)  all_52_24 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5998), (6001) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6002)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6002) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6003)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6003) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6004)  all_58_5 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5935), (6004) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #262.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6005)  all_58_8 = e2 | all_58_14 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6005) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6006)  all_58_8 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (6006) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6007)  all_14_2 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6008)  all_58_4 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5989), (6008) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6009)  all_52_24 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5992), (6009) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6010)   ~ (all_52_7 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (386), (536), (5721), (5731), (5959),
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5978), (5996), (6010), (function-axioms) are
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #179.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6011)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6011) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6012)  all_58_5 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5935), (6012) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #816.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6013)  all_58_8 = e1 | all_58_14 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6013) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6014)  all_58_8 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6006), (6014) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6015)  e2 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (6015) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6016)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6016) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6017)  all_58_14 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5982), (6017) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6018)  e1 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6018) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6019)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6019) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6020)  all_58_14 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5982), (6020) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6021)  e2 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (6021) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6022)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6022) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6023)  all_56_15 = e1 | all_56_15 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (529), (5732), (5971), (6023) are inconsistent by
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6024)   ~ (all_58_12 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (6024) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6025)   ~ (all_52_25 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6026)  all_58_0 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5944), (6026) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6027)  e3 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (6027) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6028)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6028) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6029)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6030)  all_58_1 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6030) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6031)  all_52_3 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5719), (6031) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6032)  op(e2, e1) = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e2, e1,
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (5943), (6032) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6033)  e3 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (6033) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6034)  $false
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6034) is inconsistent.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6035)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6036)  all_58_2 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5756), (6036) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6037)  all_52_26 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6037) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6038)  all_52_26 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5762), (6038) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6039)   ~ (all_52_25 = e2)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5773) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6040)  all_56_12 = e2
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (429), (6039), (6040) are inconsistent by
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1032.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6041)  all_56_12 = e1 | all_56_12 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6041) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6042)  all_56_12 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (429), (6025), (6042) are inconsistent by
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1031.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6043)  all_56_12 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (6043) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6044)  all_52_25 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6044) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6045)  all_52_25 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (6045) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6046)  all_58_12 = e0
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6025), (6045) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6047)   ~ (e1 = e0)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6029) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6048)  all_58_2 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6036), (6048) are inconsistent by sub-proof
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #921.
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6049)  all_58_6 = e1 | all_58_12 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6049) gives:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6050)  all_58_6 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (6050) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6051)  all_52_17 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6051) implies:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6052)  all_52_17 = e1
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (6052) imply:
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6053)   ~ (all_52_19 = e1)
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6053) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6054)   ~ (all_52_19 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6035) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6055)  all_58_3 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6055) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6056)  all_10_2 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5707), (5751), (5943), (6056), (function-axioms)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #165.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6057)  all_58_7 = e1 | all_58_13 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (364), (5744), (6054), (6057) are
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #768.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6058)  all_58_12 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6046), (6058) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6059)  e1 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6059) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6060)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6060) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6061)   ~ (all_58_2 = e2)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6062)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5756), (6061) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6063)   ~ (all_52_26 = e2)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6064)  all_58_0 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5944), (6064) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6065)  e3 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (6065) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6066)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6066) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6067)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6068)  all_58_2 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5756), (6068) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6069)  all_52_26 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6069) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6070)  all_52_26 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5760), (6070) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6071)   ~ (all_52_15 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5763), (6070) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6072)   ~ (all_10_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6072) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6073)   ~ (all_10_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5765), (6070) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6074)  op(e3, e1) = all_52_8
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6035) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6075)  all_58_3 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6075) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6076)  all_10_2 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6073), (6076) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6077)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6077) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6078)  all_58_7 = e1 | all_58_13 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6078) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6079)  all_58_7 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (6079) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6080)  all_52_19 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (579), (6080) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6081)   ~ (all_14_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6081) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6082)   ~ (all_14_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_8, e1, e3, simplifying with (178), (6074)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6083)  all_52_5 = all_52_8
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (6083) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6084)  all_58_4 = all_52_8
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (584), (6083) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6085)   ~ (all_52_8 = all_14_2)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5720), (6083) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6086)  op(e1, all_52_8) = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6087)  all_58_9 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (6087) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6088)  all_52_7 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (6088) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6089)   ~ (all_52_3 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (6088) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6090)   ~ (all_52_15 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (6088) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6091)   ~ (all_6_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6091) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6092)   ~ (all_6_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5740) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6093)  all_56_15 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (6093) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6094)  all_6_2 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (599), (6094) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6095)   ~ (all_52_15 = e2)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5741), (6094) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6096)   ~ (e3 = e2)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5964) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6097)  all_56_7 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (425), (6095), (6097) are inconsistent by
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #164.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6098)   ~ (all_56_7 = e2)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6099)  all_56_7 = e1 | all_56_7 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6062) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6100)  all_58_3 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6100) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6101)  all_10_2 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (6101) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6102)   ~ (all_52_3 = e2)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5707), (6101) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6103)  op(e2, e2) = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (6101) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6104)  op(e2, e2) = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6105)  all_58_1 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6105) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6106)  all_52_3 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5719), (6106) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6107)  op(e2, e0) = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6099) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6108)  all_56_7 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (6108) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6109)  all_52_15 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6109) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6110)  all_52_15 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6071), (6110) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6111)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6111) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6112)  all_56_7 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (6112) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6113)  all_52_15 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6113) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6114)  all_52_15 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6071), (6114) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6115)   ~ (e1 = e0)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (6114) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6116)  op(e2, e0) = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e0,
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (6107), (6116) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6117)  e2 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e2,
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (6103), (6104) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6118)  e2 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6117), (6118) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6119)  e1 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (6119) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6120)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6120) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6121)   ~ (all_58_1 = e0)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (6121) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6122)   ~ (all_52_3 = e0)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (392), (5770), (6089), (6102), (6122) are
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #833.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6123)  all_58_5 = e2 | all_58_10 = e2
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (370), (5935), (6095), (6123) are
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #261.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6124)  all_56_15 = e1 | all_56_15 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (529), (5732), (6092), (6124) are inconsistent by
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6125)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6125) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6126)  all_58_10 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (6126) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6127)  all_52_15 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6071), (6127) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6128)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6128) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6129)  all_58_11 = e1 | all_58_15 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6129) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6130)  all_58_11 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5956), (6130) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6131)  e3 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (6131) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6132)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6132) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6133)  all_58_15 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (6133) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6134)  all_6_2 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6134) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6135)  all_6_2 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (6135) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6136)   ~ (all_52_29 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (313) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6137)  all_58_4 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6084), (6137) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6138)  all_52_8 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6138) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6139)  all_52_8 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (6085), (6086), (6139), (function-axioms)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #177.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6140)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (533), (537), (5935), (6082), (6136), (6140)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #814.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6141)  all_58_13 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5744), (6141) are inconsistent by sub-proof
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #769.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6142)   ~ (all_58_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5756), (6142) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6143)   ~ (all_52_26 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6029) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6144)  all_58_2 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5756), (6144) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6145)  all_52_26 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6145) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6146)  all_52_26 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6143), (6146) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6147)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6147) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6148)  all_58_6 = e1 | all_58_12 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6148) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6149)  all_58_6 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (6149) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6150)  all_52_17 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6150) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6151)  all_52_17 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (560), (6151) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6152)   ~ (all_14_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6152) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6153)   ~ (all_14_2 = e1)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (61), (313), (349), (391), (529), (533),
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (537), (564), (584), (594), (5720), (5732),
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5741), (5756), (5935), (6063), (6067),
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6149), (6153), (function-axioms) are inconsistent
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #811.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6154)  all_58_12 = e1
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (349), (6025), (6154) are inconsistent by
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #883.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6155)   ~ (all_58_0 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (6155) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6156)   ~ (all_4_2 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (178), (179), (283), (307), (326), (330),
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (370), (403), (531), (532), (535), (536),
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (538), (546), (552), (561), (569), (586), (5718),
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5741), (5747), (5756), (5939), (5941),
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6156), (function-axioms) are inconsistent by
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #819.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6157)  all_58_8 = e3 | all_58_14 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (533), (537), (5749), (5781), (6157) are
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #999.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | |   (6158)   ~ (all_56_13 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | REDUCE: (344), (6158) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | |   (6159)   ~ (all_52_27 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6160)  all_58_12 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (6160) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6161)  all_52_25 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | SIMP: (6161) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6162)  all_52_25 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (6162) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6163)   ~ (all_52_17 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (6162) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6164)   ~ (all_52_29 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | SIMP: (6164) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6165)   ~ (all_52_29 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6162) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6166)   ~ (all_4_2 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | SIMP: (6166) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | |   (6167)   ~ (all_4_2 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | |   (6168)  all_56_0 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (6168) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | |   (6169)  all_4_2 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6167), (6169) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | |   (6170)  $false
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | CLOSE: (6170) is inconsistent.
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | |   (6171)   ~ (all_56_0 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | |   (6172)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | |   (6173)  all_56_6 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (6173) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | |   (6174)  all_52_13 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6174) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | |   (6175)  all_52_13 = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (6175) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | |   (6176)   ~ (all_52_5 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (6175) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | |   (6177)   ~ (all_14_2 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6177) implies:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | |   (6178)   ~ (all_14_2 = e3)
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (6175) imply:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | |   (6179)  op(e2, e1) = e3
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6180)  all_58_1 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6180) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6181)  all_52_3 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (6181) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6182)   ~ (all_52_5 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (566), (6181) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6183)   ~ (all_52_19 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6183) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6184)   ~ (all_52_19 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (565), (6181) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6185)   ~ (all_10_2 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6185) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6186)   ~ (all_10_2 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5719), (6181) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6187)  op(e2, e3) = e2
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6188)  all_58_6 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (6163), (6188) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6189)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6189) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6190)  all_58_7 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (6190) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6191)  all_52_19 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6184), (6191) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6192)  $false
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6192) is inconsistent.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6193)  all_58_8 = e3 | all_58_11 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6193) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6194)  all_58_8 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (537), (6194) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6195)  all_14_2 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6178), (6195) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6196)  $false
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6196) is inconsistent.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6197)  all_58_11 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (172), (6187) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6198)  all_52_9 = e2
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (6198) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6199)   ~ (all_10_2 = e2)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6199) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6200)   ~ (all_10_2 = e2)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (6198) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6201)   ~ (all_4_2 = e2)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6201) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6202)   ~ (all_4_2 = e2)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6203)  all_56_5 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (6186), (6203) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #895.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6204)   ~ (all_56_5 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6205)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6206)  all_58_0 = e1
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (6206) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6207)  all_4_2 = e1
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5718), (6207) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6208)  op(e3, e1) = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (178), (6176), (6208), (function-axioms) are
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1023.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6209)   ~ (all_58_0 = e1)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (403), (6209) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6210)   ~ (all_4_2 = e1)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6172) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6211)  all_56_0 = e2
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (531), (6202), (6211) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #904.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6212)  all_56_0 = e1 | all_56_0 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6212) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6213)  all_56_0 = e1
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (531), (6210), (6213) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1022.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6214)  all_56_0 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (6214) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6215)  all_4_2 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6215) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6216)  all_4_2 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (552), (6216) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6217)   ~ (all_52_7 = e0)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6167), (6216) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6218)   ~ (e3 = e0)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5731) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6219)  all_58_9 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (536), (6217), (6219) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #825.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6220)  all_58_10 = e0 | all_58_11 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6220) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6221)  all_58_10 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (6221) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6222)  all_52_15 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6222) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6223)  all_52_15 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (6223) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6224)   ~ (all_10_2 = e0)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6224) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6225)   ~ (all_10_2 = e0)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6205) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6226)  all_56_5 = e2
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (6200), (6226) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #710.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6227)  all_56_5 = e1 | all_56_5 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6227) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6228)  all_56_5 = e1
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (6228) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6229)  all_10_2 = e1
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6229) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6230)  all_10_2 = e1
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5707), (6179), (6186), (6230), (function-axioms)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #165.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6231)  all_56_5 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (6225), (6231) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #708.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6232)  all_58_11 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6197), (6232) are inconsistent by sub-proof
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #804.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6233)   ~ (all_58_1 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (6233) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6234)   ~ (all_52_3 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (178), (179), (283), (307), (326), (331),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            (370), (391), (403), (531), (532), (535), (536),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            (540), (546), (552), (569), (586), (595), (596),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            (597), (5718), (5721), (6167), (6176), (6234),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            #1012.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6235)   ~ (all_56_6 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (6235) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6236)   ~ (all_52_13 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6237)  all_58_4 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (177), (179), (324), (391), (403), (531),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            (544), (568), (586), (5718), (5720), (6172),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            (6237), (function-axioms) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #868.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6238)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (373), (533), (537), (560), (5220), (6165),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            (6236), (6238), (function-axioms) are inconsistent
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #420.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | |   (6239)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6239) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | |   (6240)  all_58_13 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (534), (6159), (6240) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1026.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | |   (6241)  all_58_14 = e3 | all_58_15 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6241) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6242)  all_58_14 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (6242) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6243)  all_52_29 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6243) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6244)  all_52_29 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (6244) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6245)   ~ (all_52_5 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (6244) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6246)   ~ (all_52_13 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (6244) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6247)   ~ (all_52_25 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (591), (6244) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6248)   ~ (all_14_2 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6248) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6249)   ~ (all_14_2 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (6244) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6250)   ~ (all_6_2 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (6244) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6251)  op(e1, e3) = all_52_28
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (6244) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6252)  op(e0, e1) = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e1, simplifying with (164), (6251)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6253)  all_52_17 = all_52_28
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (6253) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6254)  all_56_8 = all_52_28
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (6253) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6255)  all_58_6 = all_52_28
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (6253) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6256)   ~ (all_52_9 = all_52_28)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (6253) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6257)   ~ (all_52_19 = all_52_28)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6257) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6258)   ~ (all_52_19 = all_52_28)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (6253) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6259)   ~ (all_52_23 = all_52_28)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6259) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6260)   ~ (all_52_23 = all_52_28)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (6253) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6261)   ~ (all_52_25 = all_52_28)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | SIMP: (6261) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6262)   ~ (all_52_25 = all_52_28)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (6253) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | |   (6263)   ~ (all_52_28 = all_4_2)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6264)  all_56_12 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (6264) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6265)  all_52_25 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6247), (6265) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6266)  $false
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6266) is inconsistent.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | |   (6267)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6268)  all_56_11 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (6268) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6269)  all_52_23 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6269) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6270)  all_52_23 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (6270) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6271)   ~ (all_52_15 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (6270) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6272)   ~ (all_52_19 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6260), (6270) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6273)   ~ (all_52_28 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6273) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6274)   ~ (all_52_28 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6275)  all_58_1 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (172), (319), (370), (373), (385), (539),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (540), (565), (5719), (6246), (6271), (6275),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            #180.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6276)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (172), (178), (183), (275), (313), (364),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (375), (391), (429), (534), (537), (539),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (554), (555), (556), (584), (792), (5220), (5702),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (5706), (5707), (5720), (6159), (6242), (6249),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (6251), (6254), (6256), (6262), (6267), (6272),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (6274), (6276), (function-axioms) are inconsistent
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #163.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6277)   ~ (all_56_11 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (6277) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | |   (6278)   ~ (all_52_23 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6279)  all_58_9 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (178), (179), (283), (307), (326), (370),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (403), (531), (532), (535), (536), (546), (552),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (569), (586), (595), (596), (597), (5718), (5721),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (6279), (function-axioms) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1014.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (6280)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6280) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6281)  all_58_10 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (6281) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6282)  all_52_15 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6282) implies:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6283)  all_52_15 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (6283) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6284)   ~ (all_52_9 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (6283) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6285)  op(e0, e3) = all_52_14
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_14, e3, e0, simplifying with (156), (6285)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6286)  all_52_14 = all_52_25
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6287)  all_58_0 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (6287) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6288)  all_4_2 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (6288) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6289)   ~ (all_52_3 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (552), (6288) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6290)   ~ (all_52_7 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6263), (6288) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6291)   ~ (all_52_28 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6292)  all_58_6 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6255), (6291), (6292) are inconsistent by
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #790.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6293)   ~ (all_58_6 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6294)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6294) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6295)  all_58_7 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (41), (42), (61), (172), (174), (178),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (183), (280), (302), (305), (313), (317), (326),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (349), (364), (373), (385), (386), (391), (515),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (529), (532), (535), (536), (537), (556), (564),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (579), (584), (597), (710), (4482), (5220),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5721), (5731), (5732), (5740), (6242),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6252), (6255), (6258), (6260), (6281), (6284),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6287), (6290), (6295), (function-axioms) are
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #173.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6296)   ~ (all_58_7 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (6296) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6297)   ~ (all_52_19 = e3)
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6298)  all_58_1 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6298) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6299)  all_52_3 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6289), (6299) imply:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6300)  $false
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6300) is inconsistent.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6301)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (172), (178), (183), (275), (313), (364),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (375), (391), (429), (534), (537), (539),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (554), (555), (556), (584), (792), (5220), (5702),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5706), (5707), (5720), (6159), (6242), (6249),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6251), (6254), (6256), (6262), (6267), (6291),
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6297), (6301), (function-axioms) are inconsistent
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #163.
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6302)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 172.67/26.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (163), (172), (178), (179), (278),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (314), (326), (329), (349), (370),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (403), (515), (529), (530), (531), (532),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (540), (542), (546), (548),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (550), (552), (555), (565), (568), (569), (571),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (573), (586), (595), (596), (597), (710), (4482),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5718), (5719), (5720), (5721), (5730), (5732),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (6242), (6245), (6252), (6284), (6302),
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #172.
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6303)  all_58_11 = e3 | all_58_15 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (532), (535), (5741), (6278), (6303) are
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1016.
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | |   (6304)  all_58_15 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (6304) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | |   (6305)  all_6_2 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5741), (6305) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | |   (6306)  $false
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6306) is inconsistent.
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6307)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5704), (6307) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | | |            #533.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | |   (6308)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.08  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.08  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | BETA: splitting (6308) gives:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6309)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (6309) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | | |            #373.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6310)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | ALPHA: (6310) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6311)  all_52_30 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (6311) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6312)  all_6_1 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | SIMP: (6312) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6313)  all_6_1 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REDUCE: (4486), (6313) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6314)  op(e0, all_6_2) = e2
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REDUCE: (42), (6313) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6315)  op(e0, all_6_2) = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2,
% 172.67/26.08  | | | | | | | | | | | | | | | |              all_6_2, e0, simplifying with (6314), (6315)
% 172.67/26.08  | | | | | | | | | | | | | | | |              gives:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6316)  e2 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REDUCE: (5), (6316) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6317)  $false
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | CLOSE: (6317) is inconsistent.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | |   (6318)  all_34_0 = e1
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | COMBINE_EQS: (773), (6318) imply:
% 172.67/26.08  | | | | | | | | | | | | | |   (6319)  all_4_0 = e1
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | REDUCE: (5224), (6319) imply:
% 172.67/26.08  | | | | | | | | | | | | | |   (6320)   ~ (e2 = e1)
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | REDUCE: (38), (6319) imply:
% 172.67/26.08  | | | | | | | | | | | | | |   (6321)  op(all_4_1, all_4_2) = e1
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | |   (6322)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.67/26.08  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | BETA: splitting (6322) gives:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6323)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | ALPHA: (6323) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6324)  all_52_0 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (6324) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6325)  all_4_1 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REDUCE: (6321), (6325) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6326)  op(e3, all_4_2) = e1
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REDUCE: (37), (6325) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6327)  op(e3, all_4_2) = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3,
% 172.67/26.08  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (6326), (6327)
% 172.67/26.08  | | | | | | | | | | | | | | | |              gives:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6328)  e3 = e1
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REDUCE: (8), (6328) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6329)  $false
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | CLOSE: (6329) is inconsistent.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6330)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5704), (6330) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | | |            #533.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | |   (6331)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.08  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.08  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | BETA: splitting (6331) gives:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6332)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (6332) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | | |            #373.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6333)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (6333),
% 172.67/26.08  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | | |            #200.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | |   (6334)  all_26_0 = e2
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | COMBINE_EQS: (779), (6334) imply:
% 172.67/26.08  | | | | | | | | | | | |   (6335)  all_4_0 = e2
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | SIMP: (6335) implies:
% 172.67/26.08  | | | | | | | | | | | |   (6336)  all_4_0 = e2
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | REDUCE: (38), (6336) imply:
% 172.67/26.08  | | | | | | | | | | | |   (6337)  op(all_4_1, all_4_2) = e2
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | |   (6338)  all_58_15 = e0
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (6338),
% 172.67/26.08  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | |            #228.
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | |   (6339)   ~ (all_58_15 = e0)
% 172.67/26.08  | | | | | | | | | | | | |   (6340)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.67/26.08  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.67/26.08  | | | | | | | | | | | | |             e0)
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | ALPHA: (6340) implies:
% 172.67/26.08  | | | | | | | | | | | | |   (6341)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.67/26.08  | | | | | | | | | | | | |   (6342)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | REDUCE: (532), (6339) imply:
% 172.67/26.08  | | | | | | | | | | | | |   (6343)   ~ (all_6_2 = e0)
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | |   (6344)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.67/26.08  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | BETA: splitting (6344) gives:
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | |   (6345)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (6337), (6345),
% 172.67/26.08  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | |            #494.
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | |   (6346)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | ALPHA: (6346) implies:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6347)  all_52_14 = e0
% 172.67/26.08  | | | | | | | | | | | | | | |   (6348)  all_52_12 = e1
% 172.67/26.08  | | | | | | | | | | | | | | |   (6349)  all_52_10 = e2
% 172.67/26.08  | | | | | | | | | | | | | | |   (6350)  all_52_8 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | COMBINE_EQS: (661), (6349) imply:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6351)  all_10_1 = e2
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REDUCE: (53), (6351) imply:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6352)  op(e2, all_10_2) = all_10_0
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REDUCE: (183), (6350) imply:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6353)  op(e3, all_52_9) = e3
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REDUCE: (52), (6351) imply:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6354)  op(e2, all_10_2) = e2
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REDUCE: (167), (6348) imply:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6355)  op(e1, all_52_13) = e1
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REDUCE: (159), (6347) imply:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6356)  op(e0, all_52_15) = e0
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 172.67/26.08  | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (6352), (6354)
% 172.67/26.08  | | | | | | | | | | | | | | |              gives:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6357)  all_10_0 = e2
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REDUCE: (4487), (6357) imply:
% 172.67/26.08  | | | | | | | | | | | | | | |   (6358)   ~ (e3 = e2)
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6359)  all_56_15 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (6359) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6360)  all_6_2 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | SIMP: (6360) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6361)  all_6_2 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.67/26.08  | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.67/26.08  | | | | | | | | | | | | | | | |            (6361), (function-axioms) are inconsistent by
% 172.67/26.08  | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6362)   ~ (all_56_15 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6363)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | REDUCE: (529), (6362) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | |   (6364)   ~ (all_6_2 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6365)  all_56_13 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (6365) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6366)  all_52_27 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | SIMP: (6366) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6367)  all_52_27 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | COMBINE_EQS: (534), (6367) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6368)  all_58_13 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | REDUCE: (567), (6367) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6369)   ~ (all_52_3 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | REDUCE: (578), (6367) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6370)   ~ (all_52_19 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | REDUCE: (573), (6367) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6371)   ~ (all_10_2 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | SIMP: (6371) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6372)   ~ (all_10_2 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | REDUCE: (582), (6367) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6373)   ~ (all_6_2 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | REDUCE: (173), (6367) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6374)  op(e2, e3) = all_52_26
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (37), (156), (163), (164), (169),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (172), (177), (179), (181), (278), (279), (282),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (283), (307), (311), (314), (315), (319), (321),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (325), (327), (328), (330), (331), (349), (364),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (370), (373), (385), (391), (392), (403), (409),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (535), (536),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (548), (550), (552), (554), (555), (556), (557),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (564), (565), (566),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (568), (571), (575), (583), (584), (586), (587),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (588), (594), (595), (596), (597), (598), (599),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (796), (5220), (6337), (6353), (6354), (6355),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (6356), (6363), (6364), (6368), (6369), (6370),
% 172.67/26.08  | | | | | | | | | | | | | | | | |            (6372), (6374), (function-axioms) are inconsistent
% 172.67/26.08  | | | | | | | | | | | | | | | | |            by sub-proof #350.
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6375)   ~ (all_56_13 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | REDUCE: (344), (6375) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | |   (6376)   ~ (all_52_27 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6377)  all_58_12 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (6377) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6378)  all_52_25 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | SIMP: (6378) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6379)  all_52_25 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REDUCE: (554), (6379) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6380)   ~ (all_52_9 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REDUCE: (562), (6379) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6381)   ~ (all_52_27 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REDUCE: (563), (6379) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6382)   ~ (all_52_29 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | SIMP: (6382) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6383)   ~ (all_52_29 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REDUCE: (564), (6379) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6384)   ~ (all_6_2 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REDUCE: (546), (6379) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6385)   ~ (all_4_2 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | SIMP: (6385) implies:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6386)   ~ (all_4_2 = e3)
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REDUCE: (156), (6379) imply:
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6387)  op(e0, e3) = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (37), (42), (154), (155),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (158), (164), (170), (172), (174), (177), (178),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (179), (182), (269), (272), (273), (274), (279),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (280), (283), (307), (310), (313), (315), (321),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (323), (324), (325), (328), (329), (341), (350),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (386), (391),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (403), (409), (419), (505), (529), (531), (532),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (540), (542), (544), (550), (552), (553), (556),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (557), (559), (560), (561), (565), (566), (568),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (569), (579), (580), (581), (582), (583), (585),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (586), (587), (588), (591), (593), (594), (596),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (597), (600), (756), (4486), (5216), (5219),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (6341), (6342), (6343), (6353), (6354), (6355),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (6356), (6363), (6364), (6376), (6377), (6380),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (6383), (6386), (6387), (function-axioms) are
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #170.
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | |   (6388)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (37), (42), (154),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (156), (164), (165), (172), (177), (178), (179),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (181), (182), (283), (307), (319), (323), (326),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (329), (330), (349), (364), (370), (385), (391),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (403), (515), (529), (531), (532), (533), (534),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (535), (536), (538), (539), (540), (542), (552),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (558), (559), (561), (563), (564), (565), (569),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (581), (585), (594), (597), (710), (796), (4482),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (6337), (6353), (6354), (6356), (6363), (6364),
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            (6376), (6388), (function-axioms) are inconsistent
% 172.67/26.08  | | | | | | | | | | | | | | | | | |            by sub-proof #186.
% 172.67/26.08  | | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | |   (6389)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.08  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.08  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | BETA: splitting (6389) gives:
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | Case 1:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | |   (6390)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (6390) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | |            #373.
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | |   (6391)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.67/26.08  | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (6391),
% 172.67/26.08  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.08  | | | | | | | | | | | | | | |            #200.
% 172.67/26.08  | | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | End of split
% 172.67/26.08  | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | Case 2:
% 172.67/26.08  | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | |   (6392)  all_24_0 = e1
% 172.67/26.08  | | | | | | | | | | | 
% 172.67/26.08  | | | | | | | | | | | COMBINE_EQS: (751), (6392) imply:
% 172.67/26.08  | | | | | | | | | | |   (6393)  all_10_0 = e1
% 172.67/26.08  | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | REDUCE: (4487), (6393) imply:
% 172.67/26.09  | | | | | | | | | | |   (6394)   ~ (e3 = e1)
% 172.67/26.09  | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | REDUCE: (53), (6393) imply:
% 172.67/26.09  | | | | | | | | | | |   (6395)  op(all_10_1, all_10_2) = e1
% 172.67/26.09  | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | BETA: splitting (93) gives:
% 172.67/26.09  | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | |   (6396)   ~ (all_26_0 = e2)
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | REDUCE: (779), (6396) imply:
% 172.67/26.09  | | | | | | | | | | | |   (6397)   ~ (all_4_0 = e2)
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | BETA: splitting (113) gives:
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | |   (6398)   ~ (all_34_0 = e1)
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | REDUCE: (773), (6398) imply:
% 172.67/26.09  | | | | | | | | | | | | |   (6399)   ~ (all_4_0 = e1)
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | |   (6400)  all_58_15 = e0
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (6400),
% 172.67/26.09  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.09  | | | | | | | | | | | | | |            #228.
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | |   (6401)   ~ (all_58_15 = e0)
% 172.67/26.09  | | | | | | | | | | | | | |   (6402)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.67/26.09  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.67/26.09  | | | | | | | | | | | | | |             e0)
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | ALPHA: (6402) implies:
% 172.67/26.09  | | | | | | | | | | | | | |   (6403)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.67/26.09  | | | | | | | | | | | | | |   (6404)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | REDUCE: (532), (6401) imply:
% 172.67/26.09  | | | | | | | | | | | | | |   (6405)   ~ (all_6_2 = e0)
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | |   (6406)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.67/26.09  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | BETA: splitting (6406) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6407)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | ALPHA: (6407) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6408)  all_52_6 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6409)  all_52_4 = e1
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6410)  all_52_2 = e2
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6411)  all_52_0 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (6411) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6412)  all_4_1 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (38), (6412) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6413)  op(e3, all_4_2) = all_4_0
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (37), (6412) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6414)  op(e3, all_4_2) = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (176), (6410) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6415)  op(e2, all_52_3) = e2
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (168), (6409) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6416)  op(e1, all_52_5) = e1
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (160), (6408) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6417)  op(e0, all_52_7) = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_4_0,
% 172.67/26.09  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (6413), (6414)
% 172.67/26.09  | | | | | | | | | | | | | | | |              gives:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6418)  all_4_0 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | |   (6419)  all_56_15 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (6419) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | |   (6420)  all_6_2 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.67/26.09  | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (4493),
% 172.67/26.09  | | | | | | | | | | | | | | | | |            (6420), (function-axioms) are inconsistent by
% 172.67/26.09  | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | |   (6421)   ~ (all_56_15 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | |   (6422)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | REDUCE: (529), (6421) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | |   (6423)   ~ (all_6_2 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | |   (6424)  all_56_13 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (6424) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | |   (6425)  all_52_27 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (61), (154), (156), (161),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (163), (164), (172), (173), (177), (178), (179),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (269), (271), (273), (279), (281), (283), (307),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (324), (326), (327), (328), (330), (341), (349),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (391), (403),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (409), (413), (429), (529), (531), (532), (533),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (540), (542), (544),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (546), (550), (552), (553), (554), (556), (557),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (566), (568), (569), (578), (579), (581), (582),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (589), (591), (594),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (600), (5220), (6404), (6405), (6414), (6416),
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            (6417), (6422), (6425), (function-axioms) are
% 172.67/26.09  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #404.
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | |   (6426)   ~ (all_56_13 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | REDUCE: (344), (6426) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | |   (6427)   ~ (all_52_27 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |   (6428)  all_58_12 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (156), (164), (172), (177), (178), (179),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            (272), (283), (307), (315), (323), (324), (326),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            (349), (350), (364), (370), (373), (391), (403),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (560), (562),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            (563), (564), (568), (569), (575), (580), (583),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            (586), (589), (593), (5220), (6414), (6415),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            (6416), (6417), (6428), (function-axioms) are
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #402.
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | |   (6429)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (6429) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | |   (6430)  all_58_13 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (534), (6427), (6430) are inconsistent by
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | |            sub-proof #1026.
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | |   (6431)  all_58_14 = e3 | all_58_15 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6431) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6432)  all_58_14 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (6432) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6433)  all_52_29 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | SIMP: (6433) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6434)  all_52_29 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (585), (6434) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6435)   ~ (all_52_5 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (588), (6434) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6436)   ~ (all_52_13 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (6434) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6437)   ~ (all_6_2 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (6434) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6438)  op(e1, e3) = all_52_28
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (154), (6434) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6439)  op(e0, e1) = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |              all_52_28, e3, e1, simplifying with (164), (6438)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6440)  all_52_17 = all_52_28
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (6440) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6441)  all_58_6 = all_52_28
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (559), (6440) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6442)   ~ (all_52_19 = all_52_28)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | SIMP: (6442) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6443)   ~ (all_52_19 = all_52_28)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (6440) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6444)   ~ (all_52_23 = all_52_28)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | SIMP: (6444) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6445)   ~ (all_52_23 = all_52_28)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | |   (6446)  all_56_2 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (6435), (6446) are inconsistent by
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | |   (6447)   ~ (all_56_2 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | |   (6448)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |   (6449)  all_56_7 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (6449) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |   (6450)  all_52_15 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6450) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |   (6451)  all_52_15 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (6451) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |   (6452)   ~ (all_52_23 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6452) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |   (6453)   ~ (all_52_23 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (41), (42), (61), (156), (159), (163),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (172), (174), (178), (179), (183), (278), (280),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (283), (302), (305), (307), (313), (314), (317),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (323), (326), (329), (331), (349), (364), (370),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (515), (529),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (530), (531), (532), (534), (535), (536), (537),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (539), (540), (542), (546), (548), (550), (552),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (555), (556), (557), (564), (565), (568), (569),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (571), (573), (577), (579), (584), (586), (595),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (596), (597), (710), (4482), (5220), (6403),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (6404), (6405), (6414), (6415), (6416), (6417),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (6422), (6423), (6427), (6432), (6435), (6439),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (6441), (6443), (6445), (6453), (function-axioms)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #171.
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |   (6454)   ~ (all_56_7 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (6454) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |   (6455)   ~ (all_52_15 = e3)
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (61), (156), (158), (161), (170),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (172), (178), (179), (283), (305), (307), (313),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (319), (323), (326), (327), (330), (331), (370),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (413), (531), (532),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (535), (536), (539), (540), (542), (546), (548),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (552), (565), (568), (569), (583), (584), (586),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (6414), (6415),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (6416), (6417), (6423), (6435), (6436), (6439),
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            (6448), (6455), (function-axioms) are inconsistent
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #791.
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6456)  all_58_15 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (6456) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6457)  all_6_2 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6423), (6457) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | |   (6458)  $false
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | CLOSE: (6458) is inconsistent.
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6459)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | ALPHA: (6459) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6460)  all_52_10 = e2
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (6460) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6461)  all_10_1 = e2
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (6395), (6461) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6462)  op(e2, all_10_2) = e1
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (52), (6461) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6463)  op(e2, all_10_2) = e2
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2,
% 172.67/26.09  | | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (6462), (6463)
% 172.67/26.09  | | | | | | | | | | | | | | | |              gives:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6464)  e2 = e1
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (6), (6464) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6465)  $false
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | CLOSE: (6465) is inconsistent.
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | |   (6466)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.09  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.09  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | BETA: splitting (6466) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6467)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (6467) are inconsistent by sub-proof
% 172.67/26.09  | | | | | | | | | | | | | | | |            #373.
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6468)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (6468),
% 172.67/26.09  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.09  | | | | | | | | | | | | | | | |            #200.
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | |   (6469)  all_34_0 = e1
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | COMBINE_EQS: (773), (6469) imply:
% 172.67/26.09  | | | | | | | | | | | | |   (6470)  all_4_0 = e1
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | REDUCE: (6397), (6470) imply:
% 172.67/26.09  | | | | | | | | | | | | |   (6471)   ~ (e2 = e1)
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | REDUCE: (38), (6470) imply:
% 172.67/26.09  | | | | | | | | | | | | |   (6472)  op(all_4_1, all_4_2) = e1
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | |   (6473)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.67/26.09  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (6395),
% 172.67/26.09  | | | | | | | | | | | | | |            (6472), (6473), (function-axioms) are inconsistent
% 172.67/26.09  | | | | | | | | | | | | | |            by sub-proof #441.
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | |   (6474)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.09  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.09  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | BETA: splitting (6474) gives:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | |   (6475)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (6475) are inconsistent by sub-proof
% 172.67/26.09  | | | | | | | | | | | | | | |            #373.
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | |   (6476)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (6476),
% 172.67/26.09  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.09  | | | | | | | | | | | | | | |            #200.
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | End of split
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | |   (6477)  all_26_0 = e2
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | COMBINE_EQS: (779), (6477) imply:
% 172.67/26.09  | | | | | | | | | | | |   (6478)  all_4_0 = e2
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | REDUCE: (38), (6478) imply:
% 172.67/26.09  | | | | | | | | | | | |   (6479)  op(all_4_1, all_4_2) = e2
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.67/26.09  | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | |   (6480)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.09  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.67/26.09  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | BETA: splitting (6480) gives:
% 172.67/26.09  | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | |   (6481)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | |           all_52_6 = e0
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (6479), (6481),
% 172.67/26.09  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.09  | | | | | | | | | | | | | |            #494.
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | Case 2:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | |   (6482)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | |           all_52_14 = e0
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | ALPHA: (6482) implies:
% 172.67/26.09  | | | | | | | | | | | | | |   (6483)  all_52_10 = e2
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | COMBINE_EQS: (661), (6483) imply:
% 172.67/26.09  | | | | | | | | | | | | | |   (6484)  all_10_1 = e2
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | REDUCE: (6395), (6484) imply:
% 172.67/26.09  | | | | | | | | | | | | | |   (6485)  op(e2, all_10_2) = e1
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | REDUCE: (52), (6484) imply:
% 172.67/26.09  | | | | | | | | | | | | | |   (6486)  op(e2, all_10_2) = e2
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2,
% 172.67/26.09  | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (6485), (6486)
% 172.67/26.09  | | | | | | | | | | | | | |              gives:
% 172.67/26.09  | | | | | | | | | | | | | |   (6487)  e2 = e1
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | COMBINE_EQS: (6483), (6487) imply:
% 172.67/26.09  | | | | | | | | | | | | | |   (6488)  all_52_10 = e1
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.67/26.09  | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | BETA: splitting (6480) gives:
% 172.67/26.09  | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6489)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.09  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | ALPHA: (6489) implies:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6490)  all_52_0 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (6490) imply:
% 172.67/26.09  | | | | | | | | | | | | | | | |   (6491)  all_4_1 = e3
% 172.67/26.09  | | | | | | | | | | | | | | | | 
% 172.67/26.09  | | | | | | | | | | | | | | | | REDUCE: (6479), (6491) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6492)  op(e3, all_4_2) = e2
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (37), (6491) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6493)  op(e3, all_4_2) = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3,
% 172.67/26.10  | | | | | | | | | | | | | | | |              all_4_2, e3, simplifying with (6492), (6493)
% 172.67/26.10  | | | | | | | | | | | | | | | |              gives:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6494)  e3 = e2
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (9), (6494) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6495)  $false
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | CLOSE: (6495) is inconsistent.
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6482), (6488) are inconsistent by sub-proof
% 172.67/26.10  | | | | | | | | | | | | | | | |            #533.
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | |   (6496)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.10  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.10  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | BETA: splitting (6496) gives:
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6497)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (6497) are inconsistent by sub-proof
% 172.67/26.10  | | | | | | | | | | | | | | | |            #427.
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6498)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (6498),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.10  | | | | | | | | | | | | | | | |            #200.
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | |   (6499)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.10  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.10  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | BETA: splitting (6499) gives:
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | |   (6500)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | REF_CLOSE: (8), (5218), (6500) are inconsistent by sub-proof
% 172.67/26.10  | | | | | | | | | | | | | |            #427.
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | |   (6501)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | |           all_52_30 = e0
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (6501),
% 172.67/26.10  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.10  | | | | | | | | | | | | | |            #200.
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | |   (6502)  all_18_0 = e3
% 172.67/26.10  | | | | | | | | |   (6503)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | COMBINE_EQS: (789), (6502) imply:
% 172.67/26.10  | | | | | | | | |   (6504)  all_14_0 = e3
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (37), (38), (41),
% 172.67/26.10  | | | | | | | | |            (42), (52), (53), (61), (62), (63), (88), (93),
% 172.67/26.10  | | | | | | | | |            (113), (128), (154), (155), (156), (158), (159),
% 172.67/26.10  | | | | | | | | |            (160), (161), (163), (164), (165), (167), (168),
% 172.67/26.10  | | | | | | | | |            (169), (170), (172), (173), (174), (176), (177),
% 172.67/26.10  | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 172.67/26.10  | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 172.67/26.10  | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 172.67/26.10  | | | | | | | | |            (283), (301), (303), (304), (305), (307), (310),
% 172.67/26.10  | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 172.67/26.10  | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 172.67/26.10  | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 172.67/26.10  | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 172.67/26.10  | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 172.67/26.10  | | | | | | | | |            (415), (419), (425), (429), (494), (501), (514),
% 172.67/26.10  | | | | | | | | |            (515), (518), (529), (530), (531), (532), (533),
% 172.67/26.10  | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.67/26.10  | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.67/26.10  | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 172.67/26.10  | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 172.67/26.10  | | | | | | | | |            (568), (569), (571), (573), (575), (578), (579),
% 172.67/26.10  | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 172.67/26.10  | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 172.67/26.10  | | | | | | | | |            (596), (597), (598), (599), (600), (649), (661),
% 172.67/26.10  | | | | | | | | |            (663), (704), (710), (715), (719), (720), (751),
% 172.67/26.10  | | | | | | | | |            (770), (773), (779), (796), (4482), (4486), (4487),
% 172.67/26.10  | | | | | | | | |            (4493), (6503), (6504), (function-axioms) are
% 172.67/26.10  | | | | | | | | |            inconsistent by sub-proof #157.
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | End of split
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | Case 2:
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | |   (6505)  all_14_0 = e2
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | | REDUCE: (63), (6505) imply:
% 172.67/26.10  | | | | | | |   (6506)  op(all_14_1, all_14_2) = e2
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (37), (38), (41), (42),
% 172.67/26.10  | | | | | | |            (52), (53), (61), (62), (69), (88), (93), (113), (128),
% 172.67/26.10  | | | | | | |            (151), (154), (155), (156), (158), (159), (160), (161),
% 172.67/26.10  | | | | | | |            (163), (164), (165), (167), (168), (169), (170), (172),
% 172.67/26.10  | | | | | | |            (173), (174), (176), (177), (178), (179), (181), (182),
% 172.67/26.10  | | | | | | |            (183), (185), (268), (269), (270), (271), (272), (273),
% 172.67/26.10  | | | | | | |            (274), (275), (276), (277), (278), (279), (280), (281),
% 172.67/26.10  | | | | | | |            (282), (283), (301), (303), (304), (305), (307), (310),
% 172.67/26.10  | | | | | | |            (311), (312), (313), (314), (315), (316), (317), (319),
% 172.67/26.10  | | | | | | |            (320), (321), (323), (324), (325), (326), (327), (328),
% 172.67/26.10  | | | | | | |            (329), (330), (331), (341), (344), (349), (350), (359),
% 172.67/26.10  | | | | | | |            (364), (365), (370), (373), (385), (386), (391), (392),
% 172.67/26.10  | | | | | | |            (403), (409), (413), (415), (419), (425), (429), (494),
% 172.67/26.10  | | | | | | |            (501), (503), (515), (518), (521), (529), (530), (531),
% 172.67/26.10  | | | | | | |            (532), (533), (534), (535), (536), (537), (538), (539),
% 172.67/26.10  | | | | | | |            (540), (542), (544), (546), (548), (550), (552), (553),
% 172.67/26.10  | | | | | | |            (554), (555), (556), (557), (558), (559), (560), (561),
% 172.67/26.10  | | | | | | |            (562), (563), (564), (565), (566), (567), (568), (569),
% 172.67/26.10  | | | | | | |            (571), (573), (575), (578), (579), (580), (581), (582),
% 172.67/26.10  | | | | | | |            (583), (584), (585), (586), (587), (588), (589), (591),
% 172.67/26.10  | | | | | | |            (593), (594), (595), (596), (597), (598), (599), (600),
% 172.67/26.10  | | | | | | |            (649), (661), (663), (698), (704), (710), (715), (718),
% 172.67/26.10  | | | | | | |            (719), (720), (742), (751), (770), (773), (779), (796),
% 172.67/26.10  | | | | | | |            (4482), (4485), (4486), (4487), (6506),
% 172.67/26.10  | | | | | | |            (function-axioms) are inconsistent by sub-proof #154.
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | End of split
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | Case 2:
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | |   (6507)  all_12_1 = e3
% 172.67/26.10  | | | | | |   (6508)   ~ (all_12_0 = e0) |  ~ (all_12_2 = e1)
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | COMBINE_EQS: (705), (6507) imply:
% 172.67/26.10  | | | | | |   (6509)  all_10_1 = e3
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | SIMP: (6509) implies:
% 172.67/26.10  | | | | | |   (6510)  all_10_1 = e3
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | COMBINE_EQS: (672), (6510) imply:
% 172.67/26.10  | | | | | |   (6511)  all_46_1 = e3
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | COMBINE_EQS: (661), (6510) imply:
% 172.67/26.10  | | | | | |   (6512)  all_52_10 = e3
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | REDUCE: (53), (6510) imply:
% 172.67/26.10  | | | | | |   (6513)  op(e3, all_10_2) = all_10_0
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | REDUCE: (52), (6510) imply:
% 172.67/26.10  | | | | | |   (6514)  op(e2, all_10_2) = e3
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | BETA: splitting (64) gives:
% 172.67/26.10  | | | | | | 
% 172.67/26.10  | | | | | | Case 1:
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | |   (6515)   ~ (all_14_0 = e2)
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | | BETA: splitting (69) gives:
% 172.67/26.10  | | | | | | | 
% 172.67/26.10  | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | |   (6516)   ~ (all_16_0 = e2)
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | | REDUCE: (4485), (6516) imply:
% 172.67/26.10  | | | | | | | |   (6517)  $false
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | | CLOSE: (6517) is inconsistent.
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | |   (6518)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | | BETA: splitting (74) gives:
% 172.67/26.10  | | | | | | | | 
% 172.67/26.10  | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | |   (6519)   ~ (all_18_0 = e3)
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | REDUCE: (789), (6519) imply:
% 172.67/26.10  | | | | | | | | |   (6520)   ~ (all_14_0 = e3)
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | BETA: splitting (93) gives:
% 172.67/26.10  | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | |   (6521)   ~ (all_26_0 = e2)
% 172.67/26.10  | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | REDUCE: (779), (6521) imply:
% 172.67/26.10  | | | | | | | | | |   (6522)   ~ (all_4_0 = e2)
% 172.67/26.10  | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | BETA: splitting (113) gives:
% 172.67/26.10  | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | |   (6523)   ~ (all_34_0 = e1)
% 172.67/26.10  | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | REDUCE: (773), (6523) imply:
% 172.67/26.10  | | | | | | | | | | |   (6524)   ~ (all_4_0 = e1)
% 172.67/26.10  | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | BETA: splitting (128) gives:
% 172.67/26.10  | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | |   (6525)   ~ (all_40_1 = e1)
% 172.67/26.10  | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | REDUCE: (715), (6525) imply:
% 172.67/26.10  | | | | | | | | | | | |   (6526)   ~ (all_4_1 = e1)
% 172.67/26.10  | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | BETA: splitting (142) gives:
% 172.67/26.10  | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | |   (6527)   ~ (all_46_0 = e1)
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | REDUCE: (795), (6527) imply:
% 172.67/26.10  | | | | | | | | | | | | |   (6528)   ~ (all_10_0 = e1)
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.67/26.10  | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | |   (6529)  all_58_15 = e0
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (6529),
% 172.67/26.10  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.10  | | | | | | | | | | | | | |            #228.
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | |   (6530)   ~ (all_58_15 = e0)
% 172.67/26.10  | | | | | | | | | | | | | |   (6531)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.67/26.10  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.67/26.10  | | | | | | | | | | | | | |             e0)
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | ALPHA: (6531) implies:
% 172.67/26.10  | | | | | | | | | | | | | |   (6532)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.67/26.10  | | | | | | | | | | | | | |   (6533)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | REDUCE: (532), (6530) imply:
% 172.67/26.10  | | | | | | | | | | | | | |   (6534)   ~ (all_6_2 = e0)
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.67/26.10  | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | |   (6535)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.67/26.10  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | BETA: splitting (6535) gives:
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6536)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (37), (38), (42), (61), (154), (156),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (158), (160), (161), (163), (164), (165), (168),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (176), (177), (178),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (179), (268), (269), (270), (271), (272), (273),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (276), (278), (279), (281), (282), (283), (303),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (501), (515), (529), (530), (531), (532), (533),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (561),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (569), (571), (573), (575), (578), (579), (580),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (597), (598), (600), (704), (710), (720), (4482),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (4486), (6518), (6522), (6524), (6532), (6533),
% 172.67/26.10  | | | | | | | | | | | | | | | |            (6534), (6536), (function-axioms) are inconsistent
% 172.67/26.10  | | | | | | | | | | | | | | | |            by sub-proof #220.
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6537)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6512), (6537) are inconsistent by sub-proof
% 172.67/26.10  | | | | | | | | | | | | | | | |            #289.
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | End of split
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | |   (6538)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.67/26.10  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.67/26.10  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | BETA: splitting (6538) gives:
% 172.67/26.10  | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6539)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.67/26.10  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | ALPHA: (6539) implies:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6540)  all_52_22 = e0
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6541)  all_52_20 = e1
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6542)  all_52_18 = e2
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6543)  all_52_16 = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (6541) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6544)  all_14_1 = e1
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (63), (6544) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6545)  op(e1, all_14_2) = all_14_0
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (182), (6543) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6546)  op(e3, all_52_17) = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (174), (6542) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6547)  op(e2, all_52_19) = e2
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (62), (6544) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6548)  op(e1, all_14_2) = e1
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (158), (6540) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6549)  op(e0, all_52_23) = e0
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 172.67/26.10  | | | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (6545), (6548)
% 172.67/26.10  | | | | | | | | | | | | | | | |              gives:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6550)  all_14_0 = e1
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (6520), (6550) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6551)   ~ (e3 = e1)
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | REDUCE: (6515), (6550) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | |   (6552)   ~ (e2 = e1)
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.67/26.10  | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | |   (6553)  all_56_15 = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (6553) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | | |   (6554)  all_6_2 = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | SIMP: (6554) implies:
% 172.67/26.10  | | | | | | | | | | | | | | | | |   (6555)  all_6_2 = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.67/26.10  | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (6518),
% 172.67/26.10  | | | | | | | | | | | | | | | | |            (6555), (function-axioms) are inconsistent by
% 172.67/26.10  | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | |   (6556)   ~ (all_56_15 = e3)
% 172.67/26.10  | | | | | | | | | | | | | | | | |   (6557)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | REDUCE: (529), (6556) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | | |   (6558)   ~ (all_6_2 = e3)
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.67/26.10  | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.10  | | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | |   (6559)  all_56_13 = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (6559) imply:
% 172.67/26.10  | | | | | | | | | | | | | | | | | |   (6560)  all_52_27 = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | | | 
% 172.67/26.10  | | | | | | | | | | | | | | | | | | SIMP: (6560) implies:
% 172.67/26.10  | | | | | | | | | | | | | | | | | |   (6561)  all_52_27 = e3
% 172.67/26.10  | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (37), (38), (156),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (161), (164), (169), (172), (173), (177), (178),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (179), (181), (273), (274), (282), (308), (311),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (312), (315), (326), (328), (330), (349), (359),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (392), (403),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (419), (533), (535), (536), (537), (538), (544),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (546), (548), (550), (553), (558), (559), (560),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (562), (563), (566), (567), (578), (579), (580),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (581), (583), (584), (586), (593), (6524), (6526),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (6533), (6546), (6547), (6548), (6549), (6561),
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.67/26.11  | | | | | | | | | | | | | | | | | |            #686.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | |   (6562)   ~ (all_56_13 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | REDUCE: (344), (6562) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | |   (6563)   ~ (all_52_27 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6564)  all_58_12 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (6564) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6565)  all_52_25 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | SIMP: (6565) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6566)  all_52_25 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | REDUCE: (554), (6566) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6567)   ~ (all_52_9 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | REDUCE: (558), (6566) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6568)   ~ (all_52_17 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | REDUCE: (562), (6566) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6569)   ~ (all_52_27 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | REDUCE: (564), (6566) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6570)   ~ (all_6_2 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6566) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6571)   ~ (all_4_2 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | SIMP: (6571) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6572)   ~ (all_4_2 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | REDUCE: (181), (6566) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6573)  op(e3, e3) = all_52_24
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | REDUCE: (156), (6566) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6574)  op(e0, e3) = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (36), (6573)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |              gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | |   (6575)  all_52_24 = all_4_2
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | |   (6576)  all_56_0 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (6576) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | |   (6577)  all_4_2 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | REDUCE: (6572), (6577) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | |   (6578)  $false
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | CLOSE: (6578) is inconsistent.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | |   (6579)   ~ (all_56_0 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | |   (6580)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | |   (6581)  all_58_9 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (6581) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | |   (6582)  all_52_7 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | SIMP: (6582) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | |   (6583)  all_52_7 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (6583) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | |   (6584)   ~ (all_52_5 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (6583) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | |   (6585)   ~ (all_52_23 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | SIMP: (6585) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | |   (6586)   ~ (all_52_23 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | |   (6587)  all_58_6 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (6568), (6587) are inconsistent by
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | |   (6588)   ~ (all_58_6 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | |   (6589)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | |   (6590)  all_58_4 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (391), (6584), (6590) are inconsistent by
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1025.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | |   (6591)   ~ (all_58_4 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | |   (6592)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | |   (6593)  all_56_2 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (413), (6584), (6593) are inconsistent by
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #931.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | |   (6594)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6595)  all_56_6 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (6595) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6596)  all_52_13 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6596) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6597)  all_52_13 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (6597) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6598)   ~ (all_14_2 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6598) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6599)   ~ (all_14_2 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6589) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6600)  all_58_7 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (6600) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6601)  all_52_19 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (6601) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6602)   ~ (all_10_2 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6602) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6603)   ~ (all_10_2 = e3)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6547), (6601) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6604)  op(e2, e3) = e2
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (6601) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6605)  op(e1, e2) = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (172), (6604) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6606)  all_52_9 = e2
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (6606) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6607)  all_58_2 = e2
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (6606) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6608)   ~ (all_52_17 = e2)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6608) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6609)   ~ (all_52_17 = e2)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (6606) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6610)   ~ (all_10_2 = e2)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6610) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6611)   ~ (all_10_2 = e2)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (6606) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6612)   ~ (all_4_2 = e2)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6612) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6613)   ~ (all_4_2 = e2)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6567), (6606) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6614)   ~ (e3 = e2)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6615)  all_56_5 = e3
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (6603), (6615) are inconsistent by
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #895.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6616)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6617)  all_58_6 = e2
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (6609), (6617) are inconsistent by
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #894.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6618)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6619)  all_58_0 = e1
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (6619) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6620)  all_4_2 = e1
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (6620) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6621)  op(e3, e1) = all_4_1
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6533) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6622)  all_58_9 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6581), (6622) are inconsistent by sub-proof
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #928.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6623)  all_58_10 = e0 | all_58_11 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6623) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6624)  all_58_10 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (6624) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6625)  all_52_15 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6625) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6626)  all_52_15 = e0
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (6626) imply:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6627)   ~ (all_10_2 = e0)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6627) implies:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6628)   ~ (all_10_2 = e0)
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6629)  all_58_2 = e1
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6607), (6629) are inconsistent by sub-proof
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #921.
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.67/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6630)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6616) gives:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6631)  all_56_5 = e2
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (6611), (6631) are inconsistent by
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #710.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6632)  all_56_5 = e1 | all_56_5 = e0
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6630) gives:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6633)  all_58_3 = e1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6633) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6634)  all_10_2 = e1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (510), (6634) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6635)  all_12_2 = e1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6513), (6634) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6636)  op(e3, e1) = all_10_0
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6508) gives:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6637)   ~ (all_12_2 = e1)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6635), (6637) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6638)  $false
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6638) is inconsistent.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6639)   ~ (all_12_0 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (786), (6639) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6640)   ~ (all_10_0 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_1, e1, e3, simplifying with (178), (6621)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6641)  all_52_5 = all_4_1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e1, e3, simplifying with (178), (6636)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6642)  all_52_5 = all_10_0
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6641), (6642) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6643)  all_10_0 = all_4_1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (6641) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6644)  all_56_2 = all_4_1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6640), (6643) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6645)   ~ (all_4_1 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (796), (6526), (6594), (6644), (6645) are
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6646)   ~ (all_58_3 = e1)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (6646) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6647)   ~ (all_10_2 = e1)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (6628), (6632), (6647) are inconsistent by
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #707.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6648)  all_58_11 = e0
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (537), (6548), (6600), (6605),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6618), (6648), (function-axioms) are inconsistent
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #685.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6649)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (178), (538), (6546), (6564), (6584),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6607), (6649), (function-axioms) are inconsistent
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #919.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6650)  all_58_8 = e3 | all_58_11 = e3
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (537), (6586), (6599), (6650) are
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #997.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6651)   ~ (all_56_6 = e3)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (6651) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6652)   ~ (all_52_13 = e3)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (42), (154), (163), (164),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (172), (178), (179), (183), (269), (311), (314),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (322), (330), (341), (349), (364), (373), (385),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (403), (515), (529), (533), (534), (535),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (544), (550), (555),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (556), (560), (563), (568), (579), (582), (584),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (710), (4482), (6522), (6524),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (6534), (6546), (6547), (6548), (6557), (6567),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (6568), (6586), (6592), (6652), (function-axioms)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #153.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |   (6653)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (163), (164), (172),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (177), (178), (276), (310), (311), (315), (323),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (324), (326), (331), (364), (370), (385), (391),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (403), (425), (531), (532), (534), (535), (536),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (550),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (552), (553), (557), (559), (566), (577), (584),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (586), (595), (598), (6533), (6546), (6547),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (6548), (6549), (6558), (6563), (6564), (6568),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            (6572), (6574), (6580), (6653), (function-axioms)
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #678.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |   (6654)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (272), (274), (275),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (283), (307), (308), (311), (314), (319), (320),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (322), (323), (326), (328), (329), (330), (349),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (350), (364), (365), (370), (373), (385), (391),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (403), (419), (515), (529), (531), (532), (533),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (561), (562), (563),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (568), (580), (581), (582),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (584), (588), (591), (594), (596), (597), (598),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (599), (710), (796), (4482), (6522), (6524),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (6534), (6546), (6547), (6548), (6549), (6557),
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            (6558), (6563), (6654), (function-axioms) are
% 172.94/26.11  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #203.
% 172.94/26.11  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | |   (6655)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.94/26.11  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.94/26.11  | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | ALPHA: (6655) implies:
% 172.94/26.11  | | | | | | | | | | | | | | | |   (6656)  all_52_30 = e0
% 172.94/26.11  | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (6656) imply:
% 172.94/26.11  | | | | | | | | | | | | | | | |   (6657)  all_6_1 = e0
% 172.94/26.11  | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (4486), (6657), (function-axioms) are
% 172.94/26.11  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 172.94/26.11  | | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | End of split
% 172.94/26.11  | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | |   (6658)  all_46_0 = e1
% 172.94/26.11  | | | | | | | | | | | | |   (6659)   ~ (all_46_1 = e3) |  ~ (all_46_2 = e0)
% 172.94/26.11  | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | COMBINE_EQS: (795), (6658) imply:
% 172.94/26.11  | | | | | | | | | | | | |   (6660)  all_10_0 = e1
% 172.94/26.11  | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | REDUCE: (6513), (6660) imply:
% 172.94/26.11  | | | | | | | | | | | | |   (6661)  op(e3, all_10_2) = e1
% 172.94/26.11  | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | BETA: splitting (6659) gives:
% 172.94/26.11  | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | Case 1:
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | |   (6662)   ~ (all_46_1 = e3)
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | REDUCE: (6511), (6662) imply:
% 172.94/26.11  | | | | | | | | | | | | | |   (6663)  $false
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | CLOSE: (6663) is inconsistent.
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | |   (6664)   ~ (all_46_2 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | REDUCE: (519), (6664) imply:
% 172.94/26.11  | | | | | | | | | | | | | |   (6665)   ~ (all_10_2 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.94/26.11  | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | Case 1:
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | |   (6666)  all_58_15 = e0
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (6666),
% 172.94/26.11  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.11  | | | | | | | | | | | | | | |            #228.
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | Case 2:
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | |   (6667)   ~ (all_58_15 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | |   (6668)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.94/26.11  | | | | | | | | | | | | | | |             e0)
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | ALPHA: (6668) implies:
% 172.94/26.11  | | | | | | | | | | | | | | |   (6669)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.94/26.11  | | | | | | | | | | | | | | |   (6670)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | REDUCE: (532), (6667) imply:
% 172.94/26.11  | | | | | | | | | | | | | | |   (6671)   ~ (all_6_2 = e0)
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.94/26.11  | | | | | | | | | | | | | | | 
% 172.94/26.11  | | | | | | | | | | | | | | | Case 1:
% 172.94/26.11  | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | |   (6672)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.12  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.94/26.12  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.94/26.12  | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | BETA: splitting (6672) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6673)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.12  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (37), (38), (42), (61), (154), (156),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (158), (160), (161), (163), (164), (165), (168),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (169), (170), (172), (173), (176), (177), (178),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (179), (268), (269), (270), (271), (272), (273),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (276), (278), (279), (281), (282), (283), (303),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (425), (429),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (501), (515), (529), (530), (531), (532), (533),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (561),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (569), (571), (573), (575), (578), (579), (580),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (597), (598), (600), (704), (710), (720), (4482),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (4486), (6518), (6522), (6524), (6669), (6670),
% 172.94/26.12  | | | | | | | | | | | | | | | | |            (6671), (6673), (function-axioms) are inconsistent
% 172.94/26.12  | | | | | | | | | | | | | | | | |            by sub-proof #220.
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6674)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.94/26.12  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6512), (6674) are inconsistent by sub-proof
% 172.94/26.12  | | | | | | | | | | | | | | | | |            #289.
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | |   (6675)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.94/26.12  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.94/26.12  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.94/26.12  | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | BETA: splitting (6675) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6676)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.94/26.12  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | ALPHA: (6676) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6677)  all_52_22 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6678)  all_52_20 = e1
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6679)  all_52_18 = e2
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6680)  all_52_16 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (6678) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6681)  all_14_1 = e1
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | SIMP: (6681) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6682)  all_14_1 = e1
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REDUCE: (63), (6682) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6683)  op(e1, all_14_2) = all_14_0
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REDUCE: (182), (6680) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6684)  op(e3, all_52_17) = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REDUCE: (174), (6679) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6685)  op(e2, all_52_19) = e2
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REDUCE: (62), (6682) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6686)  op(e1, all_14_2) = e1
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REDUCE: (158), (6677) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6687)  op(e0, all_52_23) = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 172.94/26.12  | | | | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (6683), (6686)
% 172.94/26.12  | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6688)  all_14_0 = e1
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REDUCE: (6520), (6688) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6689)   ~ (e3 = e1)
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | REDUCE: (6515), (6688) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | |   (6690)   ~ (e2 = e1)
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | |   (6691)  all_56_5 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (530), (555), (6514), (6691),
% 172.94/26.12  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.12  | | | | | | | | | | | | | | | | | |            #271.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | |   (6692)   ~ (all_56_5 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | |   (6693)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | REDUCE: (530), (6692) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | |   (6694)   ~ (all_10_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |   (6695)  all_56_15 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (6695) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |   (6696)  all_6_2 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | SIMP: (6696) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |   (6697)  all_6_2 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (6518),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |            (6697), (function-axioms) are inconsistent by
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |   (6698)   ~ (all_56_15 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |   (6699)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (6698) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | |   (6700)   ~ (all_6_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6701)  all_56_7 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (425), (6701) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6702)  all_52_15 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | SIMP: (6702) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6703)  all_52_15 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (6703) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6704)  all_58_10 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (557), (6703) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6705)   ~ (all_52_9 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (589), (6703) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6706)   ~ (all_52_13 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (598), (6703) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6707)   ~ (all_52_23 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | SIMP: (6707) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6708)   ~ (all_52_23 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (6703) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6709)   ~ (all_10_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (6703) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6710)  op(e0, e3) = all_52_14
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |              all_52_14, e3, e0, simplifying with (156), (6710)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6711)  all_52_14 = all_52_25
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6712)  all_58_2 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (6712) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6713)  all_52_9 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | SIMP: (6713) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6714)  all_52_9 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (6714) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6715)   ~ (all_52_25 = e0)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | SIMP: (6715) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6716)   ~ (all_52_25 = e0)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6705), (6714) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6717)   ~ (e3 = e0)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6718)  all_56_8 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (6718) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6719)  all_52_17 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (544), (6684), (6719), (function-axioms) are
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #948.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6720)   ~ (all_56_8 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (6720) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6721)   ~ (all_52_17 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6722)  all_58_0 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (6722) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6723)  all_4_2 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (550), (6723) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6724)   ~ (all_52_5 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6725)  all_58_4 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (391), (6724), (6725) are inconsistent by
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1025.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6726)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (37), (38), (42), (154), (163), (164),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (172), (178), (179), (183), (269), (311), (314),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (322), (330), (341), (349), (364), (373), (385),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (391), (403), (515), (529), (533), (534), (535),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (544), (550), (555),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (556), (560), (563), (568), (579), (582), (584),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (591), (593), (710), (4482), (6522), (6524),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (6671), (6684), (6685), (6686), (6699), (6705),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            (6706), (6708), (6721), (6726), (function-axioms)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #153.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6727)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6727) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6728)  all_58_2 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6712), (6728) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6729)  e3 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (6729) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6730)  $false
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6730) is inconsistent.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6731)  all_58_6 = e3 | all_58_12 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6731) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6732)  all_58_6 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (6721), (6732) are inconsistent by
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6733)  all_58_12 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (6733) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6734)  all_52_25 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6734) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6735)  all_52_25 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (6735) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6736)   ~ (all_52_27 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6736) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6737)   ~ (all_52_27 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (6735) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6738)   ~ (all_52_29 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6738) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6739)   ~ (all_52_29 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (6735) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6740)   ~ (all_6_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (6735) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6741)  op(e0, e3) = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (163), (164), (172),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (177), (178), (276), (283), (307), (310), (311),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (315), (323), (324), (326), (331), (364), (370),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (425), (531), (532),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (550), (552), (553), (557),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (559), (560), (566), (577), (579), (584), (586),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (593), (595), (598), (6670), (6684), (6685),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (6686), (6687), (6700), (6706), (6721), (6733),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (6737), (6739), (6741), (function-axioms) are
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #282.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6742)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6742) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6743)  all_58_3 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6743) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6744)  all_10_2 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6665), (6744) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6745)  $false
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6745) is inconsistent.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6746)  all_58_5 = e0 | all_58_10 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6746) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6747)  all_58_5 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (6747) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6748)  all_52_13 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6748) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6749)  all_52_13 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (6749) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6750)   ~ (all_10_2 = e0)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6706), (6749) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6751)   ~ (e3 = e0)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (6749) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6752)  op(e2, e1) = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (51), (317), (318), (385), (530), (539),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |            (555), (6514), (6665), (6693), (6694), (6752),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |            #151.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6753)  all_58_10 = e0
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6704), (6753) are inconsistent by sub-proof
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |            #824.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6754)   ~ (all_56_7 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (6754) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | |   (6755)   ~ (all_52_15 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6756)  all_58_9 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (6756) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6757)  all_52_7 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | SIMP: (6757) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6758)  all_52_7 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (6758) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6759)   ~ (all_52_3 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (6758) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6760)   ~ (all_52_15 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (596), (6758) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6761)   ~ (all_52_23 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | SIMP: (6761) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6762)   ~ (all_52_23 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (597), (6758) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6763)   ~ (all_6_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (6758) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6764)  op(e0, e3) = all_52_6
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |              all_52_6, e3, e0, simplifying with (156), (6764)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | |   (6765)  all_52_6 = all_52_25
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6766)  all_58_2 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (164), (172), (178), (274), (311),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |            (319), (330), (349), (364), (385), (403), (419),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |            (535), (537), (538), (542), (544), (553), (554),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |            (584), (6684), (6685), (6686), (6762), (6766),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |            #150.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | |   (6767)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6767) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6768)  all_58_3 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6768) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6769)  all_10_2 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6694), (6769) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6770)  $false
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6770) is inconsistent.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | |   (6771)  all_58_5 = e3 | all_58_10 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6771) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6772)  all_58_5 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (6772) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6773)  all_52_13 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6773) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6774)  all_52_13 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (587), (6774) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6775)   ~ (all_14_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6775) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6776)   ~ (all_14_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (6774) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6777)  op(e1, e3) = all_52_12
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_12, e3, e1, simplifying with (164), (6777)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | |   (6778)  all_52_12 = all_52_17
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6779)  all_58_1 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6779) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6780)  all_52_3 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6759), (6780) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6781)  $false
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6781) is inconsistent.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (6782)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6783)  all_58_6 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (6783) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6784)  all_52_17 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (544), (6684), (6784), (function-axioms) are
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #948.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6785)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6785) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6786)  all_58_7 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (6786) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6787)  all_52_19 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (578), (6787) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6788)   ~ (all_52_27 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6788) implies:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6789)   ~ (all_52_27 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (571), (6787) imply:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6790)   ~ (all_10_2 = e3)
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6791)  all_58_12 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (172), (178), (326), (364), (385), (403),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (530), (534), (538), (539), (550), (555), (559),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (575), (6514), (6661), (6665), (6684), (6685),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6693), (6694), (6782), (6789), (6791),
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #149.
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6792)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.94/26.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (272), (274), (275),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (308), (311), (314), (319), (320),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (322), (323), (326), (328), (329), (330), (349),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (350), (364), (365), (370), (373), (385), (391),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (403), (419), (515), (529), (531), (532), (533),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (561), (562), (563),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (568), (580), (581), (582),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (584), (588), (591), (594), (596), (597), (598),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (599), (710), (796), (4482), (6522), (6524),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6671), (6684), (6685), (6686), (6687), (6699),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6700), (6789), (6792), (function-axioms) are
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #203.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6793)  all_58_8 = e3 | all_58_11 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (537), (6762), (6776), (6793) are
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #997.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |   (6794)  all_58_10 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (6755), (6794) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1018.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | |   (6795)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6795) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | |   (6796)  all_58_10 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (6755), (6796) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1018.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | |   (6797)  all_58_11 = e3 | all_58_15 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6797) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6798)  all_58_11 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (535), (6798) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6799)  all_52_23 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6799) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6800)  all_52_23 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (6800) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6801)   ~ (all_52_19 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (593), (6800) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6802)   ~ (all_14_2 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6802) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6803)   ~ (all_14_2 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (6800) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6804)  op(e1, e0) = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6687), (6800) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6805)  op(e0, e3) = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, e0, simplifying with (156), (6805) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6806)  all_52_25 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (6806) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6807)  all_58_12 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (554), (6806) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6808)   ~ (all_52_9 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (558), (6806) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6809)   ~ (all_52_17 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (563), (6806) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6810)   ~ (all_52_29 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6810) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6811)   ~ (all_52_29 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (564), (6806) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6812)   ~ (all_6_2 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6806) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6813)   ~ (all_4_2 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6813) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6814)   ~ (all_4_2 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (181), (6806) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6815)  op(e3, e0) = all_52_24
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |              all_52_24, e0, e3, simplifying with (177), (6815)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6816)  all_52_7 = all_52_24
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (6816) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6817)  all_58_9 = all_52_24
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (6816) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6818)   ~ (all_52_3 = all_52_24)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (586), (6816) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6819)   ~ (all_52_5 = all_52_24)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |   (6820)  all_58_12 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6807), (6820) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |   (6821)  e3 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (6821) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |   (6822)  $false
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6822) is inconsistent.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |   (6823)   ~ (all_58_12 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |   (6824)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6807), (6823) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | |   (6825)   ~ (e3 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6826)  all_58_2 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (6826) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6827)  all_52_9 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6827) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6828)  all_52_9 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (6828) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6829)   ~ (all_52_17 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6829) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6830)   ~ (all_52_17 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (6828) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6831)   ~ (all_4_2 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6831) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6832)   ~ (all_4_2 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (6828) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6833)  op(e3, e3) = all_52_8
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_8, e3, e3, simplifying with (36), (6833)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6834)  all_52_8 = all_4_2
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6835)  all_56_0 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (531), (6832), (6835) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1024.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6836)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6837)  all_58_4 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (6837) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6838)  all_52_5 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6838) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6839)  all_52_5 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (6839) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6840)   ~ (all_52_3 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6841)  all_58_0 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (179), (328), (538), (6684),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6807), (6826), (6840), (6841), (function-axioms)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #692.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6842)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6842) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6843)  all_58_2 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6826), (6843) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6844)  e3 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (6844) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6845)  $false
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6845) is inconsistent.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6846)  all_58_6 = e1 | all_58_12 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6846) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6847)  all_58_6 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (538), (6847) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6848)  all_52_17 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (6848) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6849)   ~ (all_4_2 = e1)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6849) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6850)   ~ (all_4_2 = e1)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6836) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6851)  all_56_0 = e2
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (6851) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6852)  all_4_2 = e2
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6852) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6853)  all_4_2 = e2
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (548), (6853) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6854)   ~ (all_52_3 = e2)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (6853) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6855)  op(e3, e2) = all_4_1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_1, e2, e3, simplifying with (179), (6855)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6856)  all_52_3 = all_4_1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (392), (6856) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6857)  all_56_1 = all_4_1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6818), (6856) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6858)   ~ (all_52_24 = all_4_1)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6858) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6859)   ~ (all_52_24 = all_4_1)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6840), (6856) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6860)   ~ (all_4_1 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6861)  all_56_1 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6857), (6860), (6861) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #459.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6862)   ~ (all_56_1 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6863)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6863) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6864)  all_56_1 = e2
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (796), (6857), (6864) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #762.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6865)   ~ (all_56_1 = e2)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6866)  all_56_1 = e1 | all_56_1 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6866) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6867)  all_56_1 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6526), (6857), (6867) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #761.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6868)  all_56_1 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6857), (6868) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6869)  all_4_1 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6869) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6870)  all_4_1 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6859), (6870) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6871)   ~ (all_52_24 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (796), (6870) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6872)   ~ (e2 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6526), (6870) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6873)   ~ (e1 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6874)  all_58_6 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6847), (6874) are inconsistent by sub-proof
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #426.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6875)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (169), (364), (370), (537), (6670),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6685), (6686), (6798), (6801), (6804), (6817),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6871), (6875), (function-axioms) are inconsistent
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #697.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6876)  all_56_0 = e1 | all_56_0 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (531), (6814), (6850), (6876) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1020.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6877)  all_58_12 = e1
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6807), (6877) are inconsistent by sub-proof
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #907.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6878)   ~ (all_58_4 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6879)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (6878) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6880)   ~ (all_52_5 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6879) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6881)  all_58_5 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (169), (308), (312), (364), (370),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (533), (537), (538), (6670), (6685),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6686), (6798), (6801), (6804), (6809), (6811),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6817), (6819), (6880), (6881), (function-axioms)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #695.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6882)  all_58_8 = e3 | all_58_14 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6882) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6883)  all_58_8 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (537), (6803), (6883) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #901.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6884)  all_58_14 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (6884) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6885)  all_52_29 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6885) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6886)  all_52_29 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (581), (6886) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6887)   ~ (all_52_27 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (594), (6886) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6888)   ~ (all_6_2 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (272), (274), (275),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (307), (308), (311), (314), (319), (320),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (322), (323), (326), (328), (329), (330), (349),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (350), (364), (365), (370), (373), (385), (391),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (403), (419), (515), (529), (531), (532), (533),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (561), (562), (563),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (568), (580), (581), (582),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (584), (588), (591), (594), (596), (597), (598),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (599), (710), (796), (4482), (6522), (6524),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6671), (6684), (6685), (6686), (6687), (6699),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6700), (6824), (6887), (function-axioms) are
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #203.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (6889)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6889) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6890)  all_58_3 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6890) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6891)  all_10_2 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6694), (6891) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6892)  $false
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6892) is inconsistent.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6893)  all_58_5 = e3 | all_58_10 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6893) gives:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6894)  all_58_5 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (373), (6894) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6895)  all_52_13 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6895) implies:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6896)  all_52_13 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (6896) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6897)   ~ (all_52_5 = e3)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (169), (308), (312), (364), (370),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (533), (537), (538), (6670), (6685),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6686), (6798), (6801), (6804), (6809), (6811),
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6817), (6819), (6894), (6897), (function-axioms)
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #695.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6898)  all_58_10 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (370), (6755), (6898) are inconsistent by
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1018.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6899)  all_58_15 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (532), (6899) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6900)  all_6_2 = e3
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6700), (6900) imply:
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | |   (6901)  $false
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6901) is inconsistent.
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | |   (6902)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.94/26.13  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (6902),
% 172.94/26.13  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.13  | | | | | | | | | | | | | | | | |            #200.
% 172.94/26.13  | | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | |   (6903)  all_40_1 = e1
% 172.94/26.13  | | | | | | | | | | | |   (6904)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | COMBINE_EQS: (715), (6903) imply:
% 172.94/26.13  | | | | | | | | | | | |   (6905)  all_4_1 = e1
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | SIMP: (6905) implies:
% 172.94/26.13  | | | | | | | | | | | |   (6906)  all_4_1 = e1
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | COMBINE_EQS: (720), (6906) imply:
% 172.94/26.13  | | | | | | | | | | | |   (6907)  all_52_0 = e1
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | REDUCE: (38), (6906) imply:
% 172.94/26.13  | | | | | | | | | | | |   (6908)  op(e1, all_4_2) = all_4_0
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | REDUCE: (37), (6906) imply:
% 172.94/26.13  | | | | | | | | | | | |   (6909)  op(e3, all_4_2) = e1
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | BETA: splitting (142) gives:
% 172.94/26.13  | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | |   (6910)   ~ (all_46_0 = e1)
% 172.94/26.13  | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | REDUCE: (795), (6910) imply:
% 172.94/26.13  | | | | | | | | | | | | |   (6911)   ~ (all_10_0 = e1)
% 172.94/26.13  | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.94/26.13  | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | |   (6912)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.13  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.94/26.13  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | BETA: splitting (6912) gives:
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | |   (6913)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.13  | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | REF_CLOSE: (8), (6907), (6913) are inconsistent by sub-proof
% 172.94/26.13  | | | | | | | | | | | | | | |            #632.
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | |   (6914)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.94/26.13  | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | REF_CLOSE: (9), (6512), (6914) are inconsistent by sub-proof
% 172.94/26.13  | | | | | | | | | | | | | | |            #289.
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | End of split
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | Case 2:
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | |   (6915)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.94/26.13  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.94/26.13  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | BETA: splitting (6915) gives:
% 172.94/26.13  | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | Case 1:
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | |   (6916)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.94/26.13  | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.94/26.13  | | | | | | | | | | | | | | | 
% 172.94/26.13  | | | | | | | | | | | | | | | ALPHA: (6916) implies:
% 172.94/26.13  | | | | | | | | | | | | | | |   (6917)  all_52_22 = e0
% 172.94/26.14  | | | | | | | | | | | | | | |   (6918)  all_52_20 = e1
% 172.94/26.14  | | | | | | | | | | | | | | |   (6919)  all_52_18 = e2
% 172.94/26.14  | | | | | | | | | | | | | | |   (6920)  all_52_16 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (6918) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6921)  all_14_1 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | REDUCE: (63), (6921) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6922)  op(e1, all_14_2) = all_14_0
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | REDUCE: (182), (6920) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6923)  op(e3, all_52_17) = e3
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | REDUCE: (174), (6919) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6924)  op(e2, all_52_19) = e2
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | REDUCE: (62), (6921) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6925)  op(e1, all_14_2) = e1
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | REDUCE: (158), (6917) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6926)  op(e0, all_52_23) = e0
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 172.94/26.14  | | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (6922), (6925)
% 172.94/26.14  | | | | | | | | | | | | | | |              gives:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6927)  all_14_0 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | REDUCE: (6520), (6927) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6928)   ~ (e3 = e1)
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | REDUCE: (6515), (6927) imply:
% 172.94/26.14  | | | | | | | | | | | | | | |   (6929)   ~ (e2 = e1)
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | |   (6930)  all_58_15 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (6930),
% 172.94/26.14  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.14  | | | | | | | | | | | | | | | |            #228.
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | |   (6931)   ~ (all_58_15 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | |   (6932)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.94/26.14  | | | | | | | | | | | | | | | |             e0)
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | ALPHA: (6932) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | |   (6933)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | REDUCE: (532), (6931) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | |   (6934)   ~ (all_6_2 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | |   (6935)  all_56_15 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (6935) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | |   (6936)  all_6_2 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.94/26.14  | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (6518),
% 172.94/26.14  | | | | | | | | | | | | | | | | |            (6936), (function-axioms) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | |   (6937)   ~ (all_56_15 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | |   (6938)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | REDUCE: (529), (6937) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | |   (6939)   ~ (all_6_2 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | |   (6940)  all_56_13 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (6940) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | |   (6941)  all_52_27 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | REDUCE: (562), (6941) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | |   (6942)   ~ (all_52_25 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | REDUCE: (582), (6941) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | |   (6943)   ~ (all_6_2 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (270), (272), (274),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (275), (276), (283), (304), (307), (308), (311),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (314), (315), (319), (320), (322), (323), (326),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (350),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (403),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (419), (425), (515), (518), (529), (531), (532),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (553), (555), (556), (557), (558), (561), (562),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (578),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (580), (581), (582), (584), (588), (591), (594),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (710), (770), (796),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (4482), (6522), (6524), (6904), (6908), (6909),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (6923), (6924), (6925), (6926), (6934), (6938),
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            (6939), (6942), (function-axioms) are inconsistent
% 172.94/26.14  | | | | | | | | | | | | | | | | | |            by sub-proof #147.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | |   (6944)   ~ (all_56_13 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | REDUCE: (344), (6944) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | |   (6945)   ~ (all_52_27 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6946)  all_58_12 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (6946) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6947)  all_52_25 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | SIMP: (6947) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6948)  all_52_25 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | REDUCE: (558), (6948) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6949)   ~ (all_52_17 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | REDUCE: (562), (6948) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6950)   ~ (all_52_27 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | REDUCE: (563), (6948) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6951)   ~ (all_52_29 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | SIMP: (6951) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6952)   ~ (all_52_29 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | REDUCE: (564), (6948) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6953)   ~ (all_6_2 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | REDUCE: (546), (6948) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6954)   ~ (all_4_2 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | SIMP: (6954) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6955)   ~ (all_4_2 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | REDUCE: (181), (6948) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6956)  op(e3, e3) = all_52_24
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | REDUCE: (156), (6948) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6957)  op(e0, e3) = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |              all_52_24, e3, e3, simplifying with (36), (6956)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | |   (6958)  all_52_24 = all_4_2
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | |   (6959)  all_56_8 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (365), (6949), (6959) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | |            sub-proof #461.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | |   (6960)   ~ (all_56_8 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | |   (6961)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6962)  all_56_6 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (415), (6962) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6963)  all_52_13 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | SIMP: (6963) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6964)  all_52_13 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | REDUCE: (583), (6964) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6965)   ~ (all_52_5 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | REDUCE: (575), (6964) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6966)   ~ (all_10_2 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | SIMP: (6966) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6967)   ~ (all_10_2 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (6964) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6968)  op(e1, e3) = all_52_12
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |              all_52_12, e3, e1, simplifying with (164), (6968)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | |   (6969)  all_52_12 = all_52_17
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | |   (6970)  all_58_6 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (6949), (6970) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | |   (6971)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6972)  all_58_1 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6972) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6973)  all_52_3 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (6973) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6974)   ~ (all_52_7 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6974) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6975)   ~ (all_52_7 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (6973) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6976)  op(e2, e3) = all_52_2
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (42), (154), (156), (161), (163), (164), (165),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (169), (172), (177), (178), (179), (181), (183),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (272), (274), (275), (276), (283), (304), (307),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (308), (310), (311), (314), (315), (319), (320),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (331), (349), (350), (364), (365), (370), (373),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (385), (391), (403), (419), (425), (515), (529),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (550), (552), (553), (555), (556), (557), (558),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (568), (577), (580), (581), (582), (584), (586),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (588), (591), (594), (595), (596), (597), (598),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (599), (710), (796), (4482), (6522), (6524),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (6923), (6924), (6925), (6926), (6933), (6934),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (6938), (6939), (6945), (6975), (6976),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |            #146.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6977)   ~ (all_58_1 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6978)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (540), (6977) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | |   (6979)   ~ (all_52_3 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | |   (6980)  all_58_0 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (6980) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | |   (6981)  all_4_2 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6955), (6981) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | |   (6982)  $false
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6982) is inconsistent.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | |   (6983)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6983) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (6984)  all_58_1 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (6984) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (6985)  all_52_3 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6979), (6985) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (6986)  $false
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6986) is inconsistent.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (6987)  all_58_4 = e3 | all_58_9 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6987) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6988)  all_58_4 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (391), (6965), (6988) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1025.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6989)  all_58_9 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (6989) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6990)  all_52_7 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6990) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6991)  all_52_7 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6978) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6992)  all_58_3 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (6992) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6993)  all_10_2 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6967), (6993) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6994)  $false
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6994) is inconsistent.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6995)  all_58_7 = e3 | all_58_13 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6995) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6996)  all_58_7 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (364), (6996) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6997)  all_52_19 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (580), (6997) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6998)   ~ (all_52_23 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6998) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6999)   ~ (all_52_23 = e3)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6924), (6997) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7000)  op(e2, e3) = e2
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (172), (7000) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7001)  all_52_9 = e2
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (385), (7001) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7002)  all_58_2 = e2
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (553), (7001) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7003)   ~ (all_52_17 = e2)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7003) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7004)   ~ (all_52_17 = e2)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (555), (7001) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7005)   ~ (all_10_2 = e2)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7005) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7006)   ~ (all_10_2 = e2)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (542), (7001) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7007)   ~ (all_4_2 = e2)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7007) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7008)   ~ (all_4_2 = e2)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7009)  all_56_5 = e3
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (6967), (7009) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #895.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7010)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7011)  all_58_0 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (7011) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7012)  all_4_2 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (544), (7012) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7013)   ~ (all_52_17 = e1)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6909), (7012) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7014)  op(e3, e1) = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6961) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7015)  all_56_8 = e2
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (365), (7004), (7015) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #460.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7016)  all_56_8 = e1 | all_56_8 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7016) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7017)  all_56_8 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (365), (7013), (7017) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #287.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7018)  all_56_8 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (7018) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7019)  all_52_17 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7019) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7020)  all_52_17 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (561), (7020) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7021)   ~ (all_52_23 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7021) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7022)   ~ (all_52_23 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6949), (7020) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7023)   ~ (e3 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6933) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7024)  all_58_9 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6989), (7024) are inconsistent by sub-proof
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #928.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7025)  all_58_10 = e0 | all_58_11 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7025) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7026)  all_58_10 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (7026) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7027)  all_52_15 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7027) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7028)  all_52_15 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (577), (7028) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7029)   ~ (all_10_2 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7029) implies:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7030)   ~ (all_10_2 = e0)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7010) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7031)  all_56_5 = e2
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (7006), (7031) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #710.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7032)  all_56_5 = e1 | all_56_5 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7033)  all_58_2 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7002), (7033) are inconsistent by sub-proof
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #921.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7034)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7034) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7035)  all_58_3 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (7035) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7036)  all_10_2 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6513), (7036) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7037)  op(e3, e1) = all_10_0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5, e1,
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (178), (7014) gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7038)  all_52_5 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5,
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e1, e3, simplifying with (178), (7037)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7039)  all_52_5 = all_10_0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7038), (7039) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7040)  all_10_0 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6911), (7040) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7041)  $false
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7041) is inconsistent.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7042)   ~ (all_58_3 = e1)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (7042) imply:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7043)   ~ (all_10_2 = e1)
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (530), (7030), (7032), (7043) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #707.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7044)  all_58_11 = e0
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (535), (7022), (7044) are inconsistent by
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #252.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7045)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (172), (178), (273), (359),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (385), (535), (537), (538), (579), (584),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (593), (6923), (6924), (6925), (6946), (6965),
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6971), (6999), (7045), (function-axioms) are
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #918.
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7046)  all_58_13 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (534), (6945), (7046) are inconsistent by
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1026.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7047)   ~ (all_56_6 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (415), (7047) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7048)   ~ (all_52_13 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (163), (164), (172),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (177), (178), (276), (283), (307), (310), (311),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (315), (323), (324), (326), (331), (364), (370),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (425), (531), (532),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (550), (552), (553), (557),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (559), (560), (566), (577), (579), (584), (586),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (593), (595), (598), (6923), (6924), (6925),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (6926), (6933), (6939), (6945), (6946), (6949),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (6952), (6957), (7048), (function-axioms) are
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #282.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |   (7049)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (272), (274), (275),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (283), (307), (308), (311), (314), (319), (320),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (322), (323), (326), (328), (329), (330), (349),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (350), (364), (365), (370), (373), (385), (391),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (403), (419), (515), (529), (531), (532), (533),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (561), (562), (563),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (564), (565), (566), (568), (580), (581), (582),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (584), (588), (591), (594), (596), (597), (598),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (599), (710), (796), (4482), (6522), (6524),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (6923), (6924), (6925), (6926), (6934), (6938),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (6939), (6945), (7049), (function-axioms) are
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #203.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | |   (7050)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (7050),
% 172.94/26.15  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | | |            #200.
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | |   (7051)  all_46_0 = e1
% 172.94/26.15  | | | | | | | | | | | | |   (7052)   ~ (all_46_1 = e3) |  ~ (all_46_2 = e0)
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | COMBINE_EQS: (795), (7051) imply:
% 172.94/26.15  | | | | | | | | | | | | |   (7053)  all_10_0 = e1
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | SIMP: (7053) implies:
% 172.94/26.15  | | | | | | | | | | | | |   (7054)  all_10_0 = e1
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | REDUCE: (4487), (7054) imply:
% 172.94/26.15  | | | | | | | | | | | | |   (7055)   ~ (e3 = e1)
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | REDUCE: (6513), (7054) imply:
% 172.94/26.15  | | | | | | | | | | | | |   (7056)  op(e3, all_10_2) = e1
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | BETA: splitting (7052) gives:
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | |   (7057)   ~ (all_46_1 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | REDUCE: (6511), (7057) imply:
% 172.94/26.15  | | | | | | | | | | | | | |   (7058)  $false
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | CLOSE: (7058) is inconsistent.
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | |   (7059)   ~ (all_46_2 = e0)
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | REDUCE: (519), (7059) imply:
% 172.94/26.15  | | | | | | | | | | | | | |   (7060)   ~ (all_10_2 = e0)
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | |   (7061)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.94/26.15  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | BETA: splitting (7061) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7062)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6907), (7062) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | | | |            #632.
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7063)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6512), (7063) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | | | |            #289.
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | |   (7064)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.94/26.15  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.94/26.15  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | BETA: splitting (7064) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7065)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | ALPHA: (7065) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7066)  all_52_22 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7067)  all_52_20 = e1
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7068)  all_52_18 = e2
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7069)  all_52_16 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (7067) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7070)  all_14_1 = e1
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REDUCE: (63), (7070) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7071)  op(e1, all_14_2) = all_14_0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REDUCE: (182), (7069) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7072)  op(e3, all_52_17) = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REDUCE: (174), (7068) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7073)  op(e2, all_52_19) = e2
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REDUCE: (62), (7070) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7074)  op(e1, all_14_2) = e1
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REDUCE: (158), (7066) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7075)  op(e0, all_52_23) = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 172.94/26.15  | | | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (7071), (7074)
% 172.94/26.15  | | | | | | | | | | | | | | | |              gives:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7076)  all_14_0 = e1
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REDUCE: (6515), (7076) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7077)   ~ (e2 = e1)
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | |   (7078)  all_58_15 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7078),
% 172.94/26.15  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | | | | |            #228.
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | |   (7079)   ~ (all_58_15 = e0)
% 172.94/26.15  | | | | | | | | | | | | | | | | |   (7080)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.94/26.15  | | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.94/26.15  | | | | | | | | | | | | | | | | |             e0)
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | ALPHA: (7080) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | | |   (7081)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | REDUCE: (532), (7079) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | |   (7082)   ~ (all_6_2 = e0)
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7083)  all_56_5 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (530), (7083) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7084)  all_10_2 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | SIMP: (7084) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7085)  all_10_2 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | REDUCE: (555), (7085) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7086)   ~ (all_52_9 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | REDUCE: (6514), (7085) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7087)  op(e2, e3) = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 172.94/26.15  | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (172), (7087) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7088)  all_52_9 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | REDUCE: (7086), (7088) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7089)  $false
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | CLOSE: (7089) is inconsistent.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7090)   ~ (all_56_5 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7091)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | REDUCE: (530), (7090) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | |   (7092)   ~ (all_10_2 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |   (7093)  all_56_15 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (529), (7093) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |   (7094)  all_6_2 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | SIMP: (7094) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |   (7095)  all_6_2 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (6518),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            (7095), (function-axioms) are inconsistent by
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |            sub-proof #226.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |   (7096)   ~ (all_56_15 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |   (7097)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | REDUCE: (529), (7096) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | |   (7098)   ~ (all_6_2 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7099)  all_58_1 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (540), (7099) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7100)  all_52_3 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | REDUCE: (569), (7100) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7101)   ~ (all_52_7 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | SIMP: (7101) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7102)   ~ (all_52_7 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | REDUCE: (567), (7100) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7103)   ~ (all_52_27 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | SIMP: (7103) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7104)   ~ (all_52_27 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | REDUCE: (176), (7100) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7105)  op(e2, e3) = all_52_2
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (42), (154), (156), (161), (163), (164), (165),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (169), (172), (177), (178), (179), (181), (183),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (272), (274), (275), (276), (283), (304), (307),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (308), (310), (311), (314), (315), (319), (320),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (331), (349), (350), (364), (365), (370), (373),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (385), (391), (403), (419), (425), (515), (529),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (550), (552), (553), (555), (556), (557), (558),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (568), (577), (580), (581), (582), (584), (586),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (588), (591), (594), (595), (596), (597), (598),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (599), (710), (796), (4482), (6522), (6524),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (7072), (7073), (7074), (7075), (7081), (7082),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (7097), (7098), (7102), (7104), (7105),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |            #146.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | |   (7106)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7107)  all_56_12 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (429), (7107) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7108)  all_52_25 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | SIMP: (7108) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7109)  all_52_25 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (7109) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7110)  all_58_12 = e3
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (562), (7109) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7111)   ~ (all_52_27 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | SIMP: (7111) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7112)   ~ (all_52_27 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (172), (178), (326), (364), (385), (403),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (530), (534), (538), (539), (550), (555), (559),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (575), (6514), (7056), (7060), (7072), (7073),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (7091), (7092), (7106), (7110), (7112),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            #149.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7113)   ~ (all_56_12 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | REDUCE: (429), (7113) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |   (7114)   ~ (all_52_25 = e3)
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (270), (272), (274),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (275), (276), (283), (304), (307), (308), (311),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (314), (315), (319), (320), (322), (323), (326),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (350),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (403),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (419), (425), (515), (518), (529), (531), (532),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (553), (555), (556), (557), (558), (561), (562),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (578),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (580), (581), (582), (584), (588), (591), (594),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (710), (770), (796),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (4482), (6522), (6524), (6904), (6908), (6909),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (7072), (7073), (7074), (7075), (7082), (7097),
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            (7098), (7114), (function-axioms) are inconsistent
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #147.
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7115)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | ALPHA: (7115) implies:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7116)  all_52_30 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (7116) imply:
% 172.94/26.15  | | | | | | | | | | | | | | | |   (7117)  all_6_1 = e0
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (4486), (7117), (function-axioms) are
% 172.94/26.15  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 172.94/26.15  | | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | |   (7118)  all_34_0 = e1
% 172.94/26.15  | | | | | | | | | | |   (7119)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | COMBINE_EQS: (773), (7118) imply:
% 172.94/26.15  | | | | | | | | | | |   (7120)  all_4_0 = e1
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | SIMP: (7120) implies:
% 172.94/26.15  | | | | | | | | | | |   (7121)  all_4_0 = e1
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | REDUCE: (38), (7121) imply:
% 172.94/26.15  | | | | | | | | | | |   (7122)  op(all_4_1, all_4_2) = e1
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | BETA: splitting (301) gives:
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | |   (7123)  all_58_15 = e0
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7123),
% 172.94/26.15  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | |            #228.
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | |   (7124)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.94/26.15  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.94/26.15  | | | | | | | | | | | |             e0)
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | ALPHA: (7124) implies:
% 172.94/26.15  | | | | | | | | | | | |   (7125)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | |   (7126)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.15  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.94/26.15  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | BETA: splitting (7126) gives:
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | Case 1:
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | |   (7127)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | |           all_52_6 = e0
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (7122), (7127),
% 172.94/26.15  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | |            #600.
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | |   (7128)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.94/26.15  | | | | | | | | | | | | | |           all_52_14 = e0
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | | REF_CLOSE: (9), (6512), (7128) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | | |            #289.
% 172.94/26.15  | | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | |   (7129)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.94/26.15  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.94/26.15  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (37), (42), (62), (63), (154),
% 172.94/26.15  | | | | | | | | | | | | |            (155), (156), (158), (161), (163), (164), (165),
% 172.94/26.15  | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (179),
% 172.94/26.15  | | | | | | | | | | | | |            (181), (182), (268), (270), (271), (274), (275),
% 172.94/26.15  | | | | | | | | | | | | |            (277), (280), (281), (282), (283), (303), (304),
% 172.94/26.15  | | | | | | | | | | | | |            (307), (308), (311), (315), (319), (320), (323),
% 172.94/26.15  | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 172.94/26.15  | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 172.94/26.15  | | | | | | | | | | | | |            (392), (403), (413), (415), (419), (429), (494),
% 172.94/26.15  | | | | | | | | | | | | |            (501), (515), (529), (531), (532), (533), (534),
% 172.94/26.15  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 172.94/26.15  | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 172.94/26.15  | | | | | | | | | | | | |            (555), (556), (557), (558), (560), (561), (562),
% 172.94/26.15  | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 172.94/26.15  | | | | | | | | | | | | |            (579), (580), (581), (582), (584), (585), (586),
% 172.94/26.15  | | | | | | | | | | | | |            (593), (594), (596), (597), (598), (599), (649),
% 172.94/26.15  | | | | | | | | | | | | |            (663), (704), (710), (719), (796), (4482), (4486),
% 172.94/26.15  | | | | | | | | | | | | |            (6518), (6520), (7119), (7122), (7125), (7129),
% 172.94/26.15  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.15  | | | | | | | | | | | | |            #191.
% 172.94/26.15  | | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | End of split
% 172.94/26.15  | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | Case 2:
% 172.94/26.15  | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | |   (7130)  all_26_0 = e2
% 172.94/26.15  | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | COMBINE_EQS: (779), (7130) imply:
% 172.94/26.15  | | | | | | | | | |   (7131)  all_4_0 = e2
% 172.94/26.15  | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | COMBINE_EQS: (742), (7131) imply:
% 172.94/26.15  | | | | | | | | | |   (7132)  all_50_0 = e2
% 172.94/26.15  | | | | | | | | | | 
% 172.94/26.15  | | | | | | | | | | REDUCE: (38), (7131) imply:
% 172.94/26.15  | | | | | | | | | |   (7133)  op(all_4_1, all_4_2) = e2
% 172.94/26.15  | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | BETA: splitting (151) gives:
% 172.94/26.16  | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | |   (7134)   ~ (all_50_0 = e2)
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | REDUCE: (7132), (7134) imply:
% 172.94/26.16  | | | | | | | | | | |   (7135)  $false
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | CLOSE: (7135) is inconsistent.
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | |   (7136)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | BETA: splitting (301) gives:
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | |   (7137)  all_58_15 = e0
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7137),
% 172.94/26.16  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.16  | | | | | | | | | | | |            #228.
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | |   (7138)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.94/26.16  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.94/26.16  | | | | | | | | | | | |             e0)
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | ALPHA: (7138) implies:
% 172.94/26.16  | | | | | | | | | | | |   (7139)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | |   (7140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.16  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.94/26.16  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | BETA: splitting (7140) gives:
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | |   (7141)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.16  | | | | | | | | | | | | | |           all_52_6 = e0
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REF_CLOSE: (37), (720), (796), (7133), (7141),
% 172.94/26.16  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.16  | | | | | | | | | | | | | |            #494.
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | |   (7142)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 172.94/26.16  | | | | | | | | | | | | | |           all_52_14 = e0
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REF_CLOSE: (9), (6512), (7142) are inconsistent by sub-proof
% 172.94/26.16  | | | | | | | | | | | | | |            #289.
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | End of split
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | |   (7143)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.94/26.16  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.94/26.16  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 172.94/26.16  | | | | | | | | | | | | |            (154), (156), (158), (161), (163), (164), (165),
% 172.94/26.16  | | | | | | | | | | | | |            (172), (174), (177), (178), (179), (181), (182),
% 172.94/26.16  | | | | | | | | | | | | |            (268), (271), (273), (274), (275), (276), (280),
% 172.94/26.16  | | | | | | | | | | | | |            (282), (283), (303), (304), (307), (310), (311),
% 172.94/26.16  | | | | | | | | | | | | |            (315), (319), (321), (323), (324), (325), (326),
% 172.94/26.16  | | | | | | | | | | | | |            (328), (329), (330), (331), (349), (359), (364),
% 172.94/26.16  | | | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 172.94/26.16  | | | | | | | | | | | | |            (403), (419), (425), (429), (501), (515), (521),
% 172.94/26.16  | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 172.94/26.16  | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 172.94/26.16  | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 172.94/26.16  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (564), (566),
% 172.94/26.16  | | | | | | | | | | | | |            (568), (569), (577), (579), (580), (584), (585),
% 172.94/26.16  | | | | | | | | | | | | |            (586), (593), (595), (596), (597), (598), (649),
% 172.94/26.16  | | | | | | | | | | | | |            (704), (710), (718), (719), (796), (4482), (4486),
% 172.94/26.16  | | | | | | | | | | | | |            (6515), (6518), (6520), (7133), (7136), (7139),
% 172.94/26.16  | | | | | | | | | | | | |            (7143), (function-axioms) are inconsistent by
% 172.94/26.16  | | | | | | | | | | | | |            sub-proof #183.
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | End of split
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | End of split
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | End of split
% 172.94/26.16  | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | End of split
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | |   (7144)  all_18_0 = e3
% 172.94/26.16  | | | | | | | | |   (7145)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | COMBINE_EQS: (789), (7144) imply:
% 172.94/26.16  | | | | | | | | |   (7146)  all_14_0 = e3
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | SIMP: (7146) implies:
% 172.94/26.16  | | | | | | | | |   (7147)  all_14_0 = e3
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (37), (38), (41),
% 172.94/26.16  | | | | | | | | |            (42), (52), (53), (61), (62), (63), (88), (93),
% 172.94/26.16  | | | | | | | | |            (113), (128), (154), (155), (156), (158), (159),
% 172.94/26.16  | | | | | | | | |            (160), (161), (163), (164), (165), (167), (168),
% 172.94/26.16  | | | | | | | | |            (169), (170), (172), (173), (174), (176), (177),
% 172.94/26.16  | | | | | | | | |            (178), (179), (181), (182), (183), (185), (268),
% 172.94/26.16  | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 172.94/26.16  | | | | | | | | |            (276), (277), (278), (279), (280), (281), (282),
% 172.94/26.16  | | | | | | | | |            (283), (301), (303), (304), (305), (307), (310),
% 172.94/26.16  | | | | | | | | |            (311), (312), (313), (314), (315), (316), (317),
% 172.94/26.16  | | | | | | | | |            (319), (320), (321), (323), (324), (325), (326),
% 172.94/26.16  | | | | | | | | |            (327), (328), (329), (330), (331), (341), (344),
% 172.94/26.16  | | | | | | | | |            (349), (350), (359), (364), (365), (370), (373),
% 172.94/26.16  | | | | | | | | |            (385), (386), (391), (392), (403), (409), (413),
% 172.94/26.16  | | | | | | | | |            (415), (419), (425), (429), (494), (501), (514),
% 172.94/26.16  | | | | | | | | |            (515), (518), (529), (530), (531), (532), (533),
% 172.94/26.16  | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.94/26.16  | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.16  | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 172.94/26.16  | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 172.94/26.16  | | | | | | | | |            (568), (569), (571), (573), (575), (578), (579),
% 172.94/26.16  | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 172.94/26.16  | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 172.94/26.16  | | | | | | | | |            (596), (597), (598), (599), (600), (649), (661),
% 172.94/26.16  | | | | | | | | |            (663), (704), (710), (715), (719), (720), (751),
% 172.94/26.16  | | | | | | | | |            (770), (773), (779), (796), (4482), (4486), (4487),
% 172.94/26.16  | | | | | | | | |            (6518), (7145), (7147), (function-axioms) are
% 172.94/26.16  | | | | | | | | |            inconsistent by sub-proof #157.
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | End of split
% 172.94/26.16  | | | | | | | | 
% 172.94/26.16  | | | | | | | End of split
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | Case 2:
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | |   (7148)  all_14_0 = e2
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | | REDUCE: (63), (7148) imply:
% 172.94/26.16  | | | | | | |   (7149)  op(all_14_1, all_14_2) = e2
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (37), (38), (41), (42),
% 172.94/26.16  | | | | | | |            (52), (53), (61), (62), (69), (88), (93), (113), (128),
% 172.94/26.16  | | | | | | |            (151), (154), (155), (156), (158), (159), (160), (161),
% 172.94/26.16  | | | | | | |            (163), (164), (165), (167), (168), (169), (170), (172),
% 172.94/26.16  | | | | | | |            (173), (174), (176), (177), (178), (179), (181), (182),
% 172.94/26.16  | | | | | | |            (183), (185), (268), (269), (270), (271), (272), (273),
% 172.94/26.16  | | | | | | |            (274), (275), (276), (277), (278), (279), (280), (281),
% 172.94/26.16  | | | | | | |            (282), (283), (301), (303), (304), (305), (307), (310),
% 172.94/26.16  | | | | | | |            (311), (312), (313), (314), (315), (316), (317), (319),
% 172.94/26.16  | | | | | | |            (320), (321), (323), (324), (325), (326), (327), (328),
% 172.94/26.16  | | | | | | |            (329), (330), (331), (341), (344), (349), (350), (359),
% 172.94/26.16  | | | | | | |            (364), (365), (370), (373), (385), (386), (391), (392),
% 172.94/26.16  | | | | | | |            (403), (409), (413), (415), (419), (425), (429), (494),
% 172.94/26.16  | | | | | | |            (501), (503), (515), (518), (521), (529), (530), (531),
% 172.94/26.16  | | | | | | |            (532), (533), (534), (535), (536), (537), (538), (539),
% 172.94/26.16  | | | | | | |            (540), (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.16  | | | | | | |            (554), (555), (556), (557), (558), (559), (560), (561),
% 172.94/26.16  | | | | | | |            (562), (563), (564), (565), (566), (567), (568), (569),
% 172.94/26.16  | | | | | | |            (571), (573), (575), (578), (579), (580), (581), (582),
% 172.94/26.16  | | | | | | |            (583), (584), (585), (586), (587), (588), (589), (591),
% 172.94/26.16  | | | | | | |            (593), (594), (595), (596), (597), (598), (599), (600),
% 172.94/26.16  | | | | | | |            (649), (661), (663), (698), (704), (710), (715), (718),
% 172.94/26.16  | | | | | | |            (719), (720), (742), (751), (770), (773), (779), (796),
% 172.94/26.16  | | | | | | |            (4482), (4485), (4486), (4487), (7149),
% 172.94/26.16  | | | | | | |            (function-axioms) are inconsistent by sub-proof #154.
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | End of split
% 172.94/26.16  | | | | | | 
% 172.94/26.16  | | | | | End of split
% 172.94/26.16  | | | | | 
% 172.94/26.16  | | | | Case 2:
% 172.94/26.16  | | | | | 
% 172.94/26.16  | | | | |   (7150)  all_10_0 = e3
% 172.94/26.16  | | | | | 
% 172.94/26.16  | | | | | REDUCE: (53), (7150) imply:
% 172.94/26.16  | | | | |   (7151)  op(all_10_1, all_10_2) = e3
% 172.94/26.16  | | | | | 
% 172.94/26.16  | | | | | BETA: splitting (64) gives:
% 172.94/26.16  | | | | | 
% 172.94/26.16  | | | | | Case 1:
% 172.94/26.16  | | | | | | 
% 172.94/26.16  | | | | | |   (7152)   ~ (all_14_0 = e2)
% 172.94/26.16  | | | | | | 
% 172.94/26.16  | | | | | | BETA: splitting (69) gives:
% 172.94/26.16  | | | | | | 
% 172.94/26.16  | | | | | | Case 1:
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | |   (7153)   ~ (all_16_0 = e2)
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | | REDUCE: (4485), (7153) imply:
% 172.94/26.16  | | | | | | |   (7154)  $false
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | | CLOSE: (7154) is inconsistent.
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | Case 2:
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | |   (7155)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | | BETA: splitting (74) gives:
% 172.94/26.16  | | | | | | | 
% 172.94/26.16  | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | 
% 172.94/26.16  | | | | | | | |   (7156)   ~ (all_18_0 = e3)
% 172.94/26.16  | | | | | | | | 
% 172.94/26.16  | | | | | | | | REDUCE: (789), (7156) imply:
% 172.94/26.16  | | | | | | | |   (7157)   ~ (all_14_0 = e3)
% 172.94/26.16  | | | | | | | | 
% 172.94/26.16  | | | | | | | | BETA: splitting (93) gives:
% 172.94/26.16  | | | | | | | | 
% 172.94/26.16  | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | |   (7158)   ~ (all_26_0 = e2)
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | REDUCE: (779), (7158) imply:
% 172.94/26.16  | | | | | | | | |   (7159)   ~ (all_4_0 = e2)
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | BETA: splitting (113) gives:
% 172.94/26.16  | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | |   (7160)   ~ (all_34_0 = e1)
% 172.94/26.16  | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | REDUCE: (773), (7160) imply:
% 172.94/26.16  | | | | | | | | | |   (7161)   ~ (all_4_0 = e1)
% 172.94/26.16  | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | BETA: splitting (128) gives:
% 172.94/26.16  | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | |   (7162)   ~ (all_40_1 = e1)
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | REDUCE: (715), (7162) imply:
% 172.94/26.16  | | | | | | | | | | |   (7163)   ~ (all_4_1 = e1)
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | BETA: splitting (301) gives:
% 172.94/26.16  | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | |   (7164)  all_58_15 = e0
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7164),
% 172.94/26.16  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.16  | | | | | | | | | | | |            #228.
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | |   (7165)   ~ (all_58_15 = e0)
% 172.94/26.16  | | | | | | | | | | | |   (7166)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.94/26.16  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.94/26.16  | | | | | | | | | | | |             e0)
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | ALPHA: (7166) implies:
% 172.94/26.16  | | | | | | | | | | | |   (7167)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 172.94/26.16  | | | | | | | | | | | |   (7168)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | REDUCE: (532), (7165) imply:
% 172.94/26.16  | | | | | | | | | | | |   (7169)   ~ (all_6_2 = e0)
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.94/26.16  | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | |   (7170)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.16  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.94/26.16  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (38), (42), (52), (61),
% 172.94/26.16  | | | | | | | | | | | | |            (154), (156), (158), (160), (161), (163), (164),
% 172.94/26.16  | | | | | | | | | | | | |            (165), (168), (169), (170), (172), (173), (176),
% 172.94/26.16  | | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 172.94/26.16  | | | | | | | | | | | | |            (272), (273), (276), (278), (279), (281), (282),
% 172.94/26.16  | | | | | | | | | | | | |            (283), (303), (304), (305), (307), (310), (311),
% 172.94/26.16  | | | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 172.94/26.16  | | | | | | | | | | | | |            (324), (326), (327), (328), (329), (330), (331),
% 172.94/26.16  | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 172.94/26.16  | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (413),
% 172.94/26.16  | | | | | | | | | | | | |            (425), (429), (501), (515), (529), (530), (531),
% 172.94/26.16  | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 172.94/26.16  | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 172.94/26.16  | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 172.94/26.16  | | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 172.94/26.16  | | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (578),
% 172.94/26.16  | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 172.94/26.16  | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 172.94/26.16  | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (661), (704),
% 172.94/26.16  | | | | | | | | | | | | |            (710), (720), (4482), (4486), (7151), (7155),
% 172.94/26.16  | | | | | | | | | | | | |            (7159), (7161), (7167), (7168), (7169), (7170),
% 172.94/26.16  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.16  | | | | | | | | | | | | |            #145.
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | |   (7171)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.94/26.16  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.94/26.16  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | BETA: splitting (7171) gives:
% 172.94/26.16  | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | |   (7172)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.94/26.16  | | | | | | | | | | | | | |           all_52_22 = e0
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | ALPHA: (7172) implies:
% 172.94/26.16  | | | | | | | | | | | | | |   (7173)  all_52_22 = e0
% 172.94/26.16  | | | | | | | | | | | | | |   (7174)  all_52_20 = e1
% 172.94/26.16  | | | | | | | | | | | | | |   (7175)  all_52_18 = e2
% 172.94/26.16  | | | | | | | | | | | | | |   (7176)  all_52_16 = e3
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | COMBINE_EQS: (719), (7174) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7177)  all_14_1 = e1
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REDUCE: (63), (7177) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7178)  op(e1, all_14_2) = all_14_0
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REDUCE: (182), (7176) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7179)  op(e3, all_52_17) = e3
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REDUCE: (174), (7175) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7180)  op(e2, all_52_19) = e2
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REDUCE: (62), (7177) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7181)  op(e1, all_14_2) = e1
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REDUCE: (158), (7173) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7182)  op(e0, all_52_23) = e0
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 172.94/26.16  | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (7178), (7181)
% 172.94/26.16  | | | | | | | | | | | | | |              gives:
% 172.94/26.16  | | | | | | | | | | | | | |   (7183)  all_14_0 = e1
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REDUCE: (7157), (7183) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7184)   ~ (e3 = e1)
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | REDUCE: (7152), (7183) imply:
% 172.94/26.16  | | | | | | | | | | | | | |   (7185)   ~ (e2 = e1)
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.94/26.16  | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | |   (7186)  all_56_15 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | COMBINE_EQS: (529), (7186) imply:
% 172.94/26.16  | | | | | | | | | | | | | | |   (7187)  all_6_2 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | SIMP: (7187) implies:
% 172.94/26.16  | | | | | | | | | | | | | | |   (7188)  all_6_2 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.94/26.16  | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (7155),
% 172.94/26.16  | | | | | | | | | | | | | | |            (7188), (function-axioms) are inconsistent by
% 172.94/26.16  | | | | | | | | | | | | | | |            sub-proof #226.
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | |   (7189)   ~ (all_56_15 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | |   (7190)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | REDUCE: (529), (7189) imply:
% 172.94/26.16  | | | | | | | | | | | | | | |   (7191)   ~ (all_6_2 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 172.94/26.16  | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | |   (7192)  all_56_13 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | COMBINE_EQS: (344), (7192) imply:
% 172.94/26.16  | | | | | | | | | | | | | | | |   (7193)  all_52_27 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | SIMP: (7193) implies:
% 172.94/26.16  | | | | | | | | | | | | | | | |   (7194)  all_52_27 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (37), (38), (156),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (161), (164), (169), (172), (173), (177), (178),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (179), (181), (273), (274), (282), (308), (311),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (312), (315), (326), (328), (330), (349), (359),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (392), (403),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (419), (533), (535), (536), (537), (538), (544),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (546), (548), (550), (553), (558), (559), (560),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (562), (563), (566), (567), (578), (579), (580),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (581), (583), (584), (586), (593), (7161), (7163),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (7168), (7179), (7180), (7181), (7182), (7194),
% 172.94/26.16  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.16  | | | | | | | | | | | | | | | |            #686.
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | Case 2:
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | |   (7195)   ~ (all_56_13 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | REDUCE: (344), (7195) imply:
% 172.94/26.16  | | | | | | | | | | | | | | | |   (7196)   ~ (all_52_27 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.94/26.16  | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7197)  all_58_12 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (7197) imply:
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7198)  all_52_25 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | SIMP: (7198) implies:
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7199)  all_52_25 = e3
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | REDUCE: (554), (7199) imply:
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7200)   ~ (all_52_9 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | REDUCE: (558), (7199) imply:
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7201)   ~ (all_52_17 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | REDUCE: (562), (7199) imply:
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7202)   ~ (all_52_27 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | REDUCE: (563), (7199) imply:
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7203)   ~ (all_52_29 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | SIMP: (7203) implies:
% 172.94/26.16  | | | | | | | | | | | | | | | | |   (7204)   ~ (all_52_29 = e3)
% 172.94/26.16  | | | | | | | | | | | | | | | | | 
% 172.94/26.16  | | | | | | | | | | | | | | | | | REDUCE: (564), (7199) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7205)   ~ (all_6_2 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | REDUCE: (546), (7199) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7206)   ~ (all_4_2 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | SIMP: (7206) implies:
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7207)   ~ (all_4_2 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | REDUCE: (156), (7199) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7208)  op(e0, e3) = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (52), (163), (164),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (170), (172), (177), (178), (275), (276), (278),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (281), (283), (307), (310), (311), (315), (319),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (323), (324), (326), (331), (364), (365), (370),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (373), (385), (391), (403), (413), (425), (530),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (548), (550),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (552), (553), (555), (557), (559), (560), (561),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (566), (567), (569), (571), (575), (577), (579),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (583), (584), (585), (586), (593), (595), (598),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (7151), (7168), (7179), (7180), (7181), (7182),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (7191), (7196), (7197), (7200), (7201), (7204),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (7207), (7208), (function-axioms) are inconsistent
% 172.94/26.17  | | | | | | | | | | | | | | | | |            by sub-proof #251.
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7209)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (272), (274), (275),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (283), (307), (308), (311), (314), (319), (320),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (322), (323), (326), (328), (329), (330), (349),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (350), (364), (365), (370), (373), (385), (391),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (403), (419), (515), (529), (531), (532), (533),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (561), (562), (563),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (564), (565), (566), (568), (580), (581), (582),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (584), (588), (591), (594), (596), (597), (598),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (599), (710), (796), (4482), (7159), (7161),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (7169), (7179), (7180), (7181), (7182), (7190),
% 172.94/26.17  | | | | | | | | | | | | | | | | |            (7191), (7196), (7209), (function-axioms) are
% 172.94/26.17  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #203.
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | End of split
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | End of split
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | End of split
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | Case 2:
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | |   (7210)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 172.94/26.17  | | | | | | | | | | | | | |           all_52_30 = e0
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | ALPHA: (7210) implies:
% 172.94/26.17  | | | | | | | | | | | | | |   (7211)  all_52_30 = e0
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | COMBINE_EQS: (649), (7211) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7212)  all_6_1 = e0
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (4486), (7212), (function-axioms) are
% 172.94/26.17  | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | End of split
% 172.94/26.17  | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | End of split
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | End of split
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | Case 2:
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | |   (7213)  all_40_1 = e1
% 172.94/26.17  | | | | | | | | | | |   (7214)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | COMBINE_EQS: (715), (7213) imply:
% 172.94/26.17  | | | | | | | | | | |   (7215)  all_4_1 = e1
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | SIMP: (7215) implies:
% 172.94/26.17  | | | | | | | | | | |   (7216)  all_4_1 = e1
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | COMBINE_EQS: (720), (7216) imply:
% 172.94/26.17  | | | | | | | | | | |   (7217)  all_52_0 = e1
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | REDUCE: (38), (7216) imply:
% 172.94/26.17  | | | | | | | | | | |   (7218)  op(e1, all_4_2) = all_4_0
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | REDUCE: (37), (7216) imply:
% 172.94/26.17  | | | | | | | | | | |   (7219)  op(e3, all_4_2) = e1
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | BETA: splitting (301) gives:
% 172.94/26.17  | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | Case 1:
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | |   (7220)  all_58_15 = e0
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7220),
% 172.94/26.17  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.17  | | | | | | | | | | | |            #228.
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | Case 2:
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | |   (7221)   ~ (all_58_15 = e0)
% 172.94/26.17  | | | | | | | | | | | |   (7222)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 172.94/26.17  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 172.94/26.17  | | | | | | | | | | | |             e0)
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | ALPHA: (7222) implies:
% 172.94/26.17  | | | | | | | | | | | |   (7223)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | REDUCE: (532), (7221) imply:
% 172.94/26.17  | | | | | | | | | | | |   (7224)   ~ (all_6_2 = e0)
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | BETA: splitting (185) gives:
% 172.94/26.17  | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | Case 1:
% 172.94/26.17  | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | |   (7225)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 172.94/26.17  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 172.94/26.17  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 172.94/26.17  | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (52), (661), (7151), (7217), (7225),
% 172.94/26.17  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 172.94/26.17  | | | | | | | | | | | | |            #247.
% 172.94/26.17  | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | Case 2:
% 172.94/26.17  | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | |   (7226)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 172.94/26.17  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 172.94/26.17  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 172.94/26.17  | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | BETA: splitting (7226) gives:
% 172.94/26.17  | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | Case 1:
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | |   (7227)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 172.94/26.17  | | | | | | | | | | | | | |           all_52_22 = e0
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | ALPHA: (7227) implies:
% 172.94/26.17  | | | | | | | | | | | | | |   (7228)  all_52_22 = e0
% 172.94/26.17  | | | | | | | | | | | | | |   (7229)  all_52_20 = e1
% 172.94/26.17  | | | | | | | | | | | | | |   (7230)  all_52_18 = e2
% 172.94/26.17  | | | | | | | | | | | | | |   (7231)  all_52_16 = e3
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | COMBINE_EQS: (719), (7229) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7232)  all_14_1 = e1
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REDUCE: (63), (7232) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7233)  op(e1, all_14_2) = all_14_0
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REDUCE: (182), (7231) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7234)  op(e3, all_52_17) = e3
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REDUCE: (174), (7230) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7235)  op(e2, all_52_19) = e2
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REDUCE: (62), (7232) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7236)  op(e1, all_14_2) = e1
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REDUCE: (158), (7228) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7237)  op(e0, all_52_23) = e0
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 172.94/26.17  | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (7233), (7236)
% 172.94/26.17  | | | | | | | | | | | | | |              gives:
% 172.94/26.17  | | | | | | | | | | | | | |   (7238)  all_14_0 = e1
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REDUCE: (7157), (7238) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7239)   ~ (e3 = e1)
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | REDUCE: (7152), (7238) imply:
% 172.94/26.17  | | | | | | | | | | | | | |   (7240)   ~ (e2 = e1)
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 172.94/26.17  | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | Case 1:
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | |   (7241)  all_56_15 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | COMBINE_EQS: (529), (7241) imply:
% 172.94/26.17  | | | | | | | | | | | | | | |   (7242)  all_6_2 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 172.94/26.17  | | | | | | | | | | | | | | |            (501), (554), (564), (704), (4486), (7155),
% 172.94/26.17  | | | | | | | | | | | | | | |            (7242), (function-axioms) are inconsistent by
% 172.94/26.17  | | | | | | | | | | | | | | |            sub-proof #226.
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | Case 2:
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | |   (7243)   ~ (all_56_15 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | |   (7244)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | REDUCE: (529), (7243) imply:
% 172.94/26.17  | | | | | | | | | | | | | | |   (7245)   ~ (all_6_2 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 172.94/26.17  | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | Case 1:
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7246)  all_58_12 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (7246) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7247)  all_52_25 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | SIMP: (7247) implies:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7248)  all_52_25 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | REDUCE: (554), (7248) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7249)   ~ (all_52_9 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | REDUCE: (558), (7248) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7250)   ~ (all_52_17 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | REDUCE: (562), (7248) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7251)   ~ (all_52_27 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | SIMP: (7251) implies:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7252)   ~ (all_52_27 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | REDUCE: (564), (7248) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7253)   ~ (all_6_2 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | REDUCE: (546), (7248) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7254)   ~ (all_4_2 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | SIMP: (7254) implies:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7255)   ~ (all_4_2 = e3)
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | REDUCE: (156), (7248) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | |   (7256)  op(e0, e3) = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 172.94/26.17  | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | Case 1:
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7257)  all_56_0 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | COMBINE_EQS: (531), (7257) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7258)  all_4_2 = e3
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | REDUCE: (7255), (7258) imply:
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7259)  $false
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | | CLOSE: (7259) is inconsistent.
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | Case 2:
% 172.94/26.17  | | | | | | | | | | | | | | | | | 
% 172.94/26.17  | | | | | | | | | | | | | | | | |   (7260)   ~ (all_56_0 = e3)
% 173.03/26.17  | | | | | | | | | | | | | | | | |   (7261)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.03/26.17  | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 173.03/26.17  | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | Case 1:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | |   (7262)  all_58_0 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (403), (7262) imply:
% 173.03/26.17  | | | | | | | | | | | | | | | | | |   (7263)  all_4_2 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | REDUCE: (7255), (7263) imply:
% 173.03/26.17  | | | | | | | | | | | | | | | | | |   (7264)  $false
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | CLOSE: (7264) is inconsistent.
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | |   (7265)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | Case 1:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7266)  all_58_9 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (536), (7266) imply:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7267)  all_52_7 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | SIMP: (7267) implies:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7268)  all_52_7 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | REDUCE: (595), (7268) imply:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7269)   ~ (all_52_15 = e3)
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | SIMP: (7269) implies:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7270)   ~ (all_52_15 = e3)
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | REDUCE: (596), (7268) imply:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7271)   ~ (all_52_23 = e3)
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | SIMP: (7271) implies:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7272)   ~ (all_52_23 = e3)
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |   (7273)  all_58_6 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (7250), (7273) are inconsistent by
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |            sub-proof #981.
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |   (7274)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (172), (178), (277), (319),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |            (326), (364), (370), (373), (385), (403), (415),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |            (535), (537), (538), (539), (550), (571), (583),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |            (584), (587), (7219), (7234), (7235), (7236),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |            (7246), (7249), (7270), (7272), (7274),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | |            #625.
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |   (7275)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (163), (164), (172),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (177), (178), (276), (310), (311), (315), (323),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (324), (326), (364), (370), (385), (391), (403),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (425), (531), (532), (534), (535), (536), (537),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (550), (552),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (553), (557), (559), (566), (577), (584), (586),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (595), (598), (7223), (7234), (7235), (7236),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (7237), (7245), (7246), (7250), (7252), (7256),
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            (7261), (7265), (7275), (function-axioms) are
% 173.03/26.17  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #679.
% 173.03/26.17  | | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | |   (7276)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.03/26.17  | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (37), (38), (42), (154), (156),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (172), (177),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (178), (179), (181), (183), (270), (272), (274),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (275), (276), (283), (307), (308), (311), (314),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (315), (319), (320), (322), (323), (326), (328),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (364),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (403), (419),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (425), (515), (518), (529), (531), (532), (533),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (555), (556), (557), (558), (561), (562), (563),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (578), (580),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (581), (582), (584), (588), (591), (594), (596),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (597), (598), (599), (710), (770), (796), (4482),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (7159), (7161), (7214), (7218), (7219), (7224),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (7234), (7235), (7236), (7237), (7244), (7245),
% 173.03/26.17  | | | | | | | | | | | | | | | |            (7276), (function-axioms) are inconsistent by
% 173.03/26.17  | | | | | | | | | | | | | | | |            sub-proof #148.
% 173.03/26.17  | | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | |   (7277)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.17  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.17  | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (7277),
% 173.03/26.17  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.17  | | | | | | | | | | | | | |            #200.
% 173.03/26.17  | | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | |   (7278)  all_34_0 = e1
% 173.03/26.17  | | | | | | | | | |   (7279)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | COMBINE_EQS: (773), (7278) imply:
% 173.03/26.17  | | | | | | | | | |   (7280)  all_4_0 = e1
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | REDUCE: (38), (7280) imply:
% 173.03/26.17  | | | | | | | | | |   (7281)  op(all_4_1, all_4_2) = e1
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | Case 1:
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | |   (7282)  all_58_15 = e0
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7282),
% 173.03/26.17  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.17  | | | | | | | | | | |            #228.
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | |   (7283)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.17  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.17  | | | | | | | | | | |             e0)
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | ALPHA: (7283) implies:
% 173.03/26.17  | | | | | | | | | | |   (7284)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | Case 1:
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | |   (7285)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.17  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.17  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (7151),
% 173.03/26.17  | | | | | | | | | | | |            (7281), (7285), (function-axioms) are inconsistent
% 173.03/26.17  | | | | | | | | | | | |            by sub-proof #243.
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | |   (7286)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.17  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.17  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | BETA: splitting (7286) gives:
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | Case 1:
% 173.03/26.17  | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | |   (7287)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.17  | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.17  | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (37), (42), (62), (63), (154),
% 173.03/26.17  | | | | | | | | | | | | |            (155), (156), (158), (161), (163), (164), (165),
% 173.03/26.17  | | | | | | | | | | | | |            (169), (172), (173), (174), (177), (178), (179),
% 173.03/26.17  | | | | | | | | | | | | |            (181), (182), (268), (270), (271), (274), (275),
% 173.03/26.17  | | | | | | | | | | | | |            (277), (280), (281), (282), (283), (303), (304),
% 173.03/26.17  | | | | | | | | | | | | |            (307), (308), (311), (315), (319), (320), (323),
% 173.03/26.17  | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 173.03/26.17  | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 173.03/26.17  | | | | | | | | | | | | |            (392), (403), (413), (415), (419), (429), (494),
% 173.03/26.17  | | | | | | | | | | | | |            (501), (515), (529), (531), (532), (533), (534),
% 173.03/26.17  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.03/26.17  | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.03/26.17  | | | | | | | | | | | | |            (555), (556), (557), (558), (560), (561), (562),
% 173.03/26.17  | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.03/26.17  | | | | | | | | | | | | |            (579), (580), (581), (582), (584), (585), (586),
% 173.03/26.17  | | | | | | | | | | | | |            (593), (594), (596), (597), (598), (599), (663),
% 173.03/26.17  | | | | | | | | | | | | |            (704), (710), (719), (796), (4482), (4486),
% 173.03/26.17  | | | | | | | | | | | | |            (7155), (7157), (7279), (7281), (7284), (7287),
% 173.03/26.17  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.17  | | | | | | | | | | | | |            #192.
% 173.03/26.17  | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | |   (7288)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.17  | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.17  | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (7288),
% 173.03/26.17  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.17  | | | | | | | | | | | | |            #200.
% 173.03/26.17  | | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | End of split
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | Case 2:
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | |   (7289)  all_26_0 = e2
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | COMBINE_EQS: (779), (7289) imply:
% 173.03/26.17  | | | | | | | | |   (7290)  all_4_0 = e2
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | SIMP: (7290) implies:
% 173.03/26.17  | | | | | | | | |   (7291)  all_4_0 = e2
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | COMBINE_EQS: (742), (7291) imply:
% 173.03/26.17  | | | | | | | | |   (7292)  all_50_0 = e2
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | REDUCE: (38), (7291) imply:
% 173.03/26.17  | | | | | | | | |   (7293)  op(all_4_1, all_4_2) = e2
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | BETA: splitting (151) gives:
% 173.03/26.17  | | | | | | | | | 
% 173.03/26.17  | | | | | | | | | Case 1:
% 173.03/26.17  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7294)   ~ (all_50_0 = e2)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REDUCE: (7292), (7294) imply:
% 173.03/26.18  | | | | | | | | | |   (7295)  $false
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | CLOSE: (7295) is inconsistent.
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7296)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7297)  all_58_15 = e0
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7297),
% 173.03/26.18  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | | |            #228.
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7298)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.18  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.18  | | | | | | | | | | |             e0)
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | ALPHA: (7298) implies:
% 173.03/26.18  | | | | | | | | | | |   (7299)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | |   (7300)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.18  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (7151),
% 173.03/26.18  | | | | | | | | | | | |            (7293), (7300), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | | | | |            by sub-proof #237.
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | |   (7301)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.18  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.18  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 173.03/26.18  | | | | | | | | | | | |            (154), (156), (158), (161), (163), (164), (165),
% 173.03/26.18  | | | | | | | | | | | |            (172), (174), (177), (178), (179), (181), (182),
% 173.03/26.18  | | | | | | | | | | | |            (268), (271), (273), (274), (275), (276), (280),
% 173.03/26.18  | | | | | | | | | | | |            (282), (283), (303), (304), (307), (310), (311),
% 173.03/26.18  | | | | | | | | | | | |            (315), (319), (321), (323), (324), (325), (326),
% 173.03/26.18  | | | | | | | | | | | |            (328), (329), (330), (331), (349), (359), (364),
% 173.03/26.18  | | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 173.03/26.18  | | | | | | | | | | | |            (403), (419), (425), (429), (501), (515), (521),
% 173.03/26.18  | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.03/26.18  | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.03/26.18  | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 173.03/26.18  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (564), (566),
% 173.03/26.18  | | | | | | | | | | | |            (568), (569), (577), (579), (580), (584), (585),
% 173.03/26.18  | | | | | | | | | | | |            (586), (593), (595), (596), (597), (598), (649),
% 173.03/26.18  | | | | | | | | | | | |            (704), (710), (718), (719), (796), (4482), (4486),
% 173.03/26.18  | | | | | | | | | | | |            (7152), (7155), (7157), (7293), (7296), (7299),
% 173.03/26.18  | | | | | | | | | | | |            (7301), (function-axioms) are inconsistent by
% 173.03/26.18  | | | | | | | | | | | |            sub-proof #183.
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | |   (7302)  all_18_0 = e3
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | COMBINE_EQS: (789), (7302) imply:
% 173.03/26.18  | | | | | | | |   (7303)  all_14_0 = e3
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | REDUCE: (63), (7303) imply:
% 173.03/26.18  | | | | | | | |   (7304)  op(all_14_1, all_14_2) = e3
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | BETA: splitting (93) gives:
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | |   (7305)   ~ (all_26_0 = e2)
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | REDUCE: (779), (7305) imply:
% 173.03/26.18  | | | | | | | | |   (7306)   ~ (all_4_0 = e2)
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7307)   ~ (all_34_0 = e1)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REDUCE: (773), (7307) imply:
% 173.03/26.18  | | | | | | | | | |   (7308)   ~ (all_4_0 = e1)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7309)  all_58_15 = e0
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7309),
% 173.03/26.18  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | | |            #228.
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7310)   ~ (all_58_15 = e0)
% 173.03/26.18  | | | | | | | | | | |   (7311)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.18  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.18  | | | | | | | | | | |             e0)
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | ALPHA: (7311) implies:
% 173.03/26.18  | | | | | | | | | | |   (7312)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.18  | | | | | | | | | | |   (7313)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REDUCE: (532), (7310) imply:
% 173.03/26.18  | | | | | | | | | | |   (7314)   ~ (all_6_2 = e0)
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | |   (7315)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.18  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (38), (42), (52), (61),
% 173.03/26.18  | | | | | | | | | | | |            (154), (156), (158), (160), (161), (163), (164),
% 173.03/26.18  | | | | | | | | | | | |            (165), (168), (169), (170), (172), (173), (176),
% 173.03/26.18  | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 173.03/26.18  | | | | | | | | | | | |            (272), (273), (276), (278), (279), (281), (282),
% 173.03/26.18  | | | | | | | | | | | |            (283), (303), (304), (305), (307), (310), (311),
% 173.03/26.18  | | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 173.03/26.18  | | | | | | | | | | | |            (324), (326), (327), (328), (329), (330), (331),
% 173.03/26.18  | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 173.03/26.18  | | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (413),
% 173.03/26.18  | | | | | | | | | | | |            (425), (429), (501), (515), (529), (530), (531),
% 173.03/26.18  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.03/26.18  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.18  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.03/26.18  | | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 173.03/26.18  | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (578),
% 173.03/26.18  | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 173.03/26.18  | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.03/26.18  | | | | | | | | | | | |            (595), (596), (597), (598), (600), (661), (704),
% 173.03/26.18  | | | | | | | | | | | |            (710), (720), (4482), (4486), (7151), (7155),
% 173.03/26.18  | | | | | | | | | | | |            (7306), (7308), (7312), (7313), (7314), (7315),
% 173.03/26.18  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | | | |            #145.
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | |   (7316)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.18  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.18  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | | REF_CLOSE: (5), (8), (42), (62), (649), (719), (4486),
% 173.03/26.18  | | | | | | | | | | | |            (7304), (7316), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | | | | |            by sub-proof #160.
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7317)  all_34_0 = e1
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | COMBINE_EQS: (773), (7317) imply:
% 173.03/26.18  | | | | | | | | | |   (7318)  all_4_0 = e1
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | SIMP: (7318) implies:
% 173.03/26.18  | | | | | | | | | |   (7319)  all_4_0 = e1
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REDUCE: (38), (7319) imply:
% 173.03/26.18  | | | | | | | | | |   (7320)  op(all_4_1, all_4_2) = e1
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7321)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.18  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (7151),
% 173.03/26.18  | | | | | | | | | | |            (7320), (7321), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | | | |            by sub-proof #243.
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7322)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.18  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.18  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | BETA: splitting (7322) gives:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | |   (7323)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.18  | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | | REF_CLOSE: (8), (62), (719), (7304), (7323),
% 173.03/26.18  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | | | |            #343.
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | |   (7324)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.18  | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (7324),
% 173.03/26.18  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | | | |            #200.
% 173.03/26.18  | | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | |   (7325)  all_26_0 = e2
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | COMBINE_EQS: (779), (7325) imply:
% 173.03/26.18  | | | | | | | | |   (7326)  all_4_0 = e2
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | SIMP: (7326) implies:
% 173.03/26.18  | | | | | | | | |   (7327)  all_4_0 = e2
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | REDUCE: (38), (7327) imply:
% 173.03/26.18  | | | | | | | | |   (7328)  op(all_4_1, all_4_2) = e2
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7329)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.18  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (7151),
% 173.03/26.18  | | | | | | | | | |            (7328), (7329), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | | |            by sub-proof #237.
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7330)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.18  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.18  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REF_CLOSE: (5), (8), (42), (62), (649), (719), (4486),
% 173.03/26.18  | | | | | | | | | |            (7304), (7330), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | | |            by sub-proof #160.
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | End of split
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | End of split
% 173.03/26.18  | | | | | | 
% 173.03/26.18  | | | | | Case 2:
% 173.03/26.18  | | | | | | 
% 173.03/26.18  | | | | | |   (7331)  all_14_0 = e2
% 173.03/26.18  | | | | | | 
% 173.03/26.18  | | | | | | REDUCE: (63), (7331) imply:
% 173.03/26.18  | | | | | |   (7332)  op(all_14_1, all_14_2) = e2
% 173.03/26.18  | | | | | | 
% 173.03/26.18  | | | | | | BETA: splitting (69) gives:
% 173.03/26.18  | | | | | | 
% 173.03/26.18  | | | | | | Case 1:
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | |   (7333)   ~ (all_16_0 = e2)
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | | REDUCE: (4485), (7333) imply:
% 173.03/26.18  | | | | | | |   (7334)  $false
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | | CLOSE: (7334) is inconsistent.
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | Case 2:
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | |   (7335)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | | BETA: splitting (93) gives:
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | |   (7336)   ~ (all_26_0 = e2)
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | REDUCE: (779), (7336) imply:
% 173.03/26.18  | | | | | | | |   (7337)   ~ (all_4_0 = e2)
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | |   (7338)   ~ (all_34_0 = e1)
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | REDUCE: (773), (7338) imply:
% 173.03/26.18  | | | | | | | | |   (7339)   ~ (all_4_0 = e1)
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7340)  all_58_15 = e0
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (4486), (7340),
% 173.03/26.18  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | |            #228.
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7341)   ~ (all_58_15 = e0)
% 173.03/26.18  | | | | | | | | | |   (7342)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.18  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.18  | | | | | | | | | |             e0)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | ALPHA: (7342) implies:
% 173.03/26.18  | | | | | | | | | |   (7343)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.18  | | | | | | | | | |   (7344)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REDUCE: (532), (7341) imply:
% 173.03/26.18  | | | | | | | | | |   (7345)   ~ (all_6_2 = e0)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7346)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.18  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (38), (42), (52), (61),
% 173.03/26.18  | | | | | | | | | | |            (154), (156), (158), (160), (161), (163), (164),
% 173.03/26.18  | | | | | | | | | | |            (165), (168), (169), (170), (172), (173), (176),
% 173.03/26.18  | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 173.03/26.18  | | | | | | | | | | |            (272), (273), (276), (278), (279), (281), (282),
% 173.03/26.18  | | | | | | | | | | |            (283), (303), (304), (305), (307), (310), (311),
% 173.03/26.18  | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 173.03/26.18  | | | | | | | | | | |            (324), (326), (327), (328), (329), (330), (331),
% 173.03/26.18  | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (370),
% 173.03/26.18  | | | | | | | | | | |            (373), (385), (391), (392), (403), (409), (413),
% 173.03/26.18  | | | | | | | | | | |            (425), (429), (501), (515), (529), (530), (531),
% 173.03/26.18  | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.03/26.18  | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.18  | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.03/26.18  | | | | | | | | | | |            (559), (561), (562), (563), (564), (565), (566),
% 173.03/26.18  | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (578),
% 173.03/26.18  | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 173.03/26.18  | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.03/26.18  | | | | | | | | | | |            (595), (596), (597), (598), (600), (661), (704),
% 173.03/26.18  | | | | | | | | | | |            (710), (720), (4482), (4486), (7151), (7335),
% 173.03/26.18  | | | | | | | | | | |            (7337), (7339), (7343), (7344), (7345), (7346),
% 173.03/26.18  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | | |            #145.
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7347)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.18  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.18  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (62), (649), (719), (4486),
% 173.03/26.18  | | | | | | | | | | |            (7332), (7347), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | | | |            by sub-proof #155.
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | |   (7348)  all_34_0 = e1
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | COMBINE_EQS: (773), (7348) imply:
% 173.03/26.18  | | | | | | | | |   (7349)  all_4_0 = e1
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | SIMP: (7349) implies:
% 173.03/26.18  | | | | | | | | |   (7350)  all_4_0 = e1
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | REDUCE: (7337), (7350) imply:
% 173.03/26.18  | | | | | | | | |   (7351)   ~ (e2 = e1)
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | REDUCE: (38), (7350) imply:
% 173.03/26.18  | | | | | | | | |   (7352)  op(all_4_1, all_4_2) = e1
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7353)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.18  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | BETA: splitting (7353) gives:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7354)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (7352), (7354),
% 173.03/26.18  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | | |            #600.
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | |   (7355)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.18  | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | ALPHA: (7355) implies:
% 173.03/26.18  | | | | | | | | | | |   (7356)  all_52_10 = e2
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | COMBINE_EQS: (661), (7356) imply:
% 173.03/26.18  | | | | | | | | | | |   (7357)  all_10_1 = e2
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REDUCE: (7151), (7357) imply:
% 173.03/26.18  | | | | | | | | | | |   (7358)  op(e2, all_10_2) = e3
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REDUCE: (52), (7357) imply:
% 173.03/26.18  | | | | | | | | | | |   (7359)  op(e2, all_10_2) = e2
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3,
% 173.03/26.18  | | | | | | | | | | |              all_10_2, e2, simplifying with (7358), (7359)
% 173.03/26.18  | | | | | | | | | | |              gives:
% 173.03/26.18  | | | | | | | | | | |   (7360)  e3 = e2
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | REDUCE: (9), (7360) imply:
% 173.03/26.18  | | | | | | | | | | |   (7361)  $false
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | | CLOSE: (7361) is inconsistent.
% 173.03/26.18  | | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7362)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.18  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.18  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REF_CLOSE: (5), (6), (42), (62), (649), (719), (4486),
% 173.03/26.18  | | | | | | | | | |            (7332), (7362), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | | |            by sub-proof #155.
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | |   (7363)  all_26_0 = e2
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | COMBINE_EQS: (779), (7363) imply:
% 173.03/26.18  | | | | | | | |   (7364)  all_4_0 = e2
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | SIMP: (7364) implies:
% 173.03/26.18  | | | | | | | |   (7365)  all_4_0 = e2
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | REDUCE: (38), (7365) imply:
% 173.03/26.18  | | | | | | | |   (7366)  op(all_4_1, all_4_2) = e2
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | |   (7367)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.18  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.03/26.18  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (7151),
% 173.03/26.18  | | | | | | | | |            (7366), (7367), (function-axioms) are inconsistent
% 173.03/26.18  | | | | | | | | |            by sub-proof #237.
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | |   (7368)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.18  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 173.03/26.18  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | BETA: splitting (7368) gives:
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 1:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7369)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.18  | | | | | | | | | |           all_52_22 = e0
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REF_CLOSE: (6), (62), (719), (7332), (7369),
% 173.03/26.18  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | |            #314.
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | Case 2:
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | |   (7370)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.18  | | | | | | | | | |           all_52_30 = e0
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | | REF_CLOSE: (5), (42), (649), (4486), (7370),
% 173.03/26.18  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.18  | | | | | | | | | |            #200.
% 173.03/26.18  | | | | | | | | | | 
% 173.03/26.18  | | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | | 
% 173.03/26.18  | | | | | | | | End of split
% 173.03/26.18  | | | | | | | | 
% 173.03/26.18  | | | | | | | End of split
% 173.03/26.18  | | | | | | | 
% 173.03/26.18  | | | | | | End of split
% 173.03/26.18  | | | | | | 
% 173.03/26.18  | | | | | End of split
% 173.03/26.18  | | | | | 
% 173.03/26.18  | | | | End of split
% 173.03/26.18  | | | | 
% 173.03/26.18  | | | End of split
% 173.03/26.18  | | | 
% 173.03/26.18  | | Case 2:
% 173.03/26.18  | | | 
% 173.03/26.18  | | |   (7371)  all_6_0 = e1
% 173.03/26.18  | | | 
% 173.03/26.18  | | | COMBINE_EQS: (794), (7371) imply:
% 173.03/26.18  | | |   (7372)  all_38_0 = e1
% 173.03/26.18  | | | 
% 173.03/26.18  | | | REDUCE: (43), (7371) imply:
% 173.03/26.18  | | |   (7373)  op(all_6_1, all_6_2) = e1
% 173.03/26.18  | | | 
% 173.03/26.18  | | | BETA: splitting (54) gives:
% 173.03/26.18  | | | 
% 173.03/26.18  | | | Case 1:
% 173.03/26.18  | | | | 
% 173.03/26.18  | | | |   (7374)   ~ (all_10_0 = e3)
% 173.03/26.18  | | | | 
% 173.03/26.18  | | | | BETA: splitting (59) gives:
% 173.03/26.18  | | | | 
% 173.03/26.18  | | | | Case 1:
% 173.03/26.18  | | | | | 
% 173.03/26.18  | | | | |   (7375)   ~ (all_12_1 = e3)
% 173.03/26.18  | | | | | 
% 173.03/26.18  | | | | | REDUCE: (705), (7375) imply:
% 173.03/26.18  | | | | |   (7376)   ~ (all_10_1 = e3)
% 173.03/26.18  | | | | | 
% 173.03/26.18  | | | | | BETA: splitting (64) gives:
% 173.03/26.18  | | | | | 
% 173.03/26.18  | | | | | Case 1:
% 173.03/26.18  | | | | | | 
% 173.03/26.19  | | | | | |   (7377)   ~ (all_14_0 = e2)
% 173.03/26.19  | | | | | | 
% 173.03/26.19  | | | | | | BETA: splitting (74) gives:
% 173.03/26.19  | | | | | | 
% 173.03/26.19  | | | | | | Case 1:
% 173.03/26.19  | | | | | | | 
% 173.03/26.19  | | | | | | |   (7378)   ~ (all_18_0 = e3)
% 173.03/26.19  | | | | | | | 
% 173.03/26.19  | | | | | | | REDUCE: (789), (7378) imply:
% 173.03/26.19  | | | | | | |   (7379)   ~ (all_14_0 = e3)
% 173.03/26.19  | | | | | | | 
% 173.03/26.19  | | | | | | | BETA: splitting (83) gives:
% 173.03/26.19  | | | | | | | 
% 173.03/26.19  | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | 
% 173.03/26.19  | | | | | | | |   (7380)   ~ (all_22_1 = e3)
% 173.03/26.19  | | | | | | | | 
% 173.03/26.19  | | | | | | | | REDUCE: (711), (7380) imply:
% 173.03/26.19  | | | | | | | |   (7381)   ~ (all_14_1 = e3)
% 173.03/26.19  | | | | | | | | 
% 173.03/26.19  | | | | | | | | BETA: splitting (88) gives:
% 173.03/26.19  | | | | | | | | 
% 173.03/26.19  | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | 
% 173.03/26.19  | | | | | | | | |   (7382)   ~ (all_24_0 = e1)
% 173.03/26.19  | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | REDUCE: (751), (7382) imply:
% 173.03/26.19  | | | | | | | | |   (7383)   ~ (all_10_0 = e1)
% 173.03/26.19  | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | BETA: splitting (93) gives:
% 173.03/26.19  | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | |   (7384)   ~ (all_26_0 = e2)
% 173.03/26.19  | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | REDUCE: (779), (7384) imply:
% 173.03/26.19  | | | | | | | | | |   (7385)   ~ (all_4_0 = e2)
% 173.03/26.19  | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | BETA: splitting (103) gives:
% 173.03/26.19  | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | |   (7386)   ~ (all_30_1 = e1)
% 173.03/26.19  | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | REDUCE: (712), (7386) imply:
% 173.03/26.19  | | | | | | | | | | |   (7387)   ~ (all_10_1 = e1)
% 173.03/26.19  | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.19  | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | |   (7388)   ~ (all_34_0 = e1)
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | REDUCE: (773), (7388) imply:
% 173.03/26.19  | | | | | | | | | | | |   (7389)   ~ (all_4_0 = e1)
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | BETA: splitting (123) gives:
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | |   (7390)   ~ (all_38_0 = e1)
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | REDUCE: (7372), (7390) imply:
% 173.03/26.19  | | | | | | | | | | | | |   (7391)  $false
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | CLOSE: (7391) is inconsistent.
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | |   (7392)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | |   (7393)   ~ (all_40_1 = e1)
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | REDUCE: (715), (7393) imply:
% 173.03/26.19  | | | | | | | | | | | | | |   (7394)   ~ (all_4_1 = e1)
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | |   (7395)  all_58_15 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7395),
% 173.03/26.19  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.19  | | | | | | | | | | | | | | |            #143.
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | |   (7396)   ~ (all_58_15 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | |   (7397)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.19  | | | | | | | | | | | | | | |             e0)
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | ALPHA: (7397) implies:
% 173.03/26.19  | | | | | | | | | | | | | | |   (7398)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.19  | | | | | | | | | | | | | | |   (7399)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | REDUCE: (532), (7396) imply:
% 173.03/26.19  | | | | | | | | | | | | | | |   (7400)   ~ (all_6_2 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | |   (7401)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.19  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.19  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | BETA: splitting (7401) gives:
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7402)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.19  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (37), (38), (42), (61), (154), (156),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (158), (159), (160), (161), (163), (164), (165),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (168), (169), (170), (172), (173), (176), (177),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (178), (179), (268), (269), (270), (271), (272),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (273), (276), (279), (281), (282), (283), (302),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (327), (328), (330), (331), (341), (344), (349),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (350), (359), (364), (370), (373), (385), (391),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (392), (403), (409), (413), (425), (429), (517),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (558), (559), (561), (562), (563), (564), (565),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (596), (597), (598), (599), (600), (714), (720),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (7373), (7385), (7389), (7392), (7399), (7400),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (7402), (function-axioms) are inconsistent by
% 173.03/26.19  | | | | | | | | | | | | | | | | |            sub-proof #140.
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7403)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.19  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | ALPHA: (7403) implies:
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7404)  all_52_14 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7405)  all_52_12 = e1
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7406)  all_52_10 = e2
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7407)  all_52_8 = e3
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (7406) imply:
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7408)  all_10_1 = e2
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (38), (42), (52), (53),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (61), (62), (154), (156), (158), (159), (161),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (163), (164), (165), (167), (169), (170), (172),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (183), (268), (270), (272), (273), (274), (277),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (279), (280), (281), (282), (283), (303), (304),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (307), (311), (313), (315), (316), (317), (319),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (320), (321), (323), (326), (328), (329), (330),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (359), (364), (370),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (413), (415), (419), (529), (531), (532), (533),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (568), (569), (571), (573), (578), (579), (580),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (598), (599), (600), (796), (7374), (7381),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (7383), (7385), (7389), (7394), (7399), (7400),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (7404), (7405), (7407), (7408), (function-axioms)
% 173.03/26.19  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #715.
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | End of split
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | |   (7409)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.19  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.19  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | BETA: splitting (7409) gives:
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7410)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.19  | | | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | ALPHA: (7410) implies:
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7411)  all_52_22 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7412)  all_52_20 = e1
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7413)  all_52_18 = e2
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7414)  all_52_16 = e3
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (719), (7412) imply:
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7415)  all_14_1 = e1
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (62),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (63), (155), (156), (158), (161), (163), (164),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (165), (169), (170), (172), (173), (174), (177),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (271), (273), (274), (275), (276), (277), (278),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (282), (283), (304), (306), (307), (308), (310),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (311), (312), (313), (314), (315), (317), (319),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (326), (328),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (359), (364),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (392), (403),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (415), (419), (425), (429), (529), (530), (531),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (566), (567), (568), (571), (573), (575), (577),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (796), (7376),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (7377), (7379), (7385), (7389), (7394), (7398),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (7399), (7400), (7411), (7413), (7414), (7415),
% 173.03/26.19  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.19  | | | | | | | | | | | | | | | | |            #666.
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7416)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.19  | | | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | ALPHA: (7416) implies:
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7417)  all_52_30 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (7417) imply:
% 173.03/26.19  | | | | | | | | | | | | | | | | |   (7418)  all_6_1 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (42), (7373), (7418), (function-axioms) are
% 173.03/26.19  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #139.
% 173.03/26.19  | | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | | End of split
% 173.03/26.19  | | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | End of split
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | End of split
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | |   (7419)  all_40_1 = e1
% 173.03/26.19  | | | | | | | | | | | | | |   (7420)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | COMBINE_EQS: (715), (7419) imply:
% 173.03/26.19  | | | | | | | | | | | | | |   (7421)  all_4_1 = e1
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | SIMP: (7421) implies:
% 173.03/26.19  | | | | | | | | | | | | | |   (7422)  all_4_1 = e1
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | COMBINE_EQS: (720), (7422) imply:
% 173.03/26.19  | | | | | | | | | | | | | |   (7423)  all_52_0 = e1
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | REDUCE: (796), (7422) imply:
% 173.03/26.19  | | | | | | | | | | | | | |   (7424)   ~ (e2 = e1)
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | REDUCE: (38), (7422) imply:
% 173.03/26.19  | | | | | | | | | | | | | |   (7425)  op(e1, all_4_2) = all_4_0
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | REDUCE: (37), (7422) imply:
% 173.03/26.19  | | | | | | | | | | | | | |   (7426)  op(e3, all_4_2) = e1
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | |   (7427)  all_58_15 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7427),
% 173.03/26.19  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.19  | | | | | | | | | | | | | | |            #143.
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | |   (7428)   ~ (all_58_15 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | |   (7429)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.19  | | | | | | | | | | | | | | |             e0)
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.03/26.19  | | | | | | | | | | | | | | |            (42), (52), (61), (62), (63), (154), (155), (156),
% 173.03/26.19  | | | | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.03/26.19  | | | | | | | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 173.03/26.19  | | | | | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (270),
% 173.03/26.19  | | | | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.03/26.19  | | | | | | | | | | | | | | |            (278), (279), (280), (281), (283), (303), (304),
% 173.03/26.19  | | | | | | | | | | | | | | |            (305), (307), (310), (311), (313), (314), (315),
% 173.03/26.19  | | | | | | | | | | | | | | |            (316), (317), (319), (320), (321), (322), (323),
% 173.03/26.19  | | | | | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 173.03/26.19  | | | | | | | | | | | | | | |            (331), (344), (349), (350), (359), (364), (365),
% 173.03/26.19  | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (403), (409),
% 173.03/26.19  | | | | | | | | | | | | | | |            (413), (415), (419), (425), (429), (518), (529),
% 173.03/26.19  | | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 173.03/26.19  | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.03/26.19  | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.03/26.19  | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.03/26.19  | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.03/26.19  | | | | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.03/26.19  | | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.03/26.19  | | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.03/26.19  | | | | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (770),
% 173.03/26.19  | | | | | | | | | | | | | | |            (796), (7376), (7377), (7379), (7381), (7385),
% 173.03/26.19  | | | | | | | | | | | | | | |            (7387), (7389), (7420), (7423), (7425), (7426),
% 173.03/26.19  | | | | | | | | | | | | | | |            (7428), (7429), (function-axioms) are inconsistent
% 173.03/26.19  | | | | | | | | | | | | | | |            by sub-proof #500.
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | End of split
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | End of split
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | End of split
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | |   (7430)  all_34_0 = e1
% 173.03/26.19  | | | | | | | | | | | |   (7431)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | COMBINE_EQS: (773), (7430) imply:
% 173.03/26.19  | | | | | | | | | | | |   (7432)  all_4_0 = e1
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | REDUCE: (38), (7432) imply:
% 173.03/26.19  | | | | | | | | | | | |   (7433)  op(all_4_1, all_4_2) = e1
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.19  | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | |   (7434)  all_58_15 = e0
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7434),
% 173.03/26.19  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.19  | | | | | | | | | | | | |            #143.
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | |   (7435)   ~ (all_58_15 = e0)
% 173.03/26.19  | | | | | | | | | | | | |   (7436)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.19  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.19  | | | | | | | | | | | | |             e0)
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | ALPHA: (7436) implies:
% 173.03/26.19  | | | | | | | | | | | | |   (7437)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | REDUCE: (532), (7435) imply:
% 173.03/26.19  | | | | | | | | | | | | |   (7438)   ~ (all_6_2 = e0)
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.19  | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | |   (7439)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.19  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.19  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (42), (52), (53), (61),
% 173.03/26.19  | | | | | | | | | | | | | |            (62), (156), (158), (159), (163), (164), (165),
% 173.03/26.19  | | | | | | | | | | | | | |            (167), (170), (172), (173), (174), (177), (178),
% 173.03/26.19  | | | | | | | | | | | | | |            (179), (182), (183), (268), (270), (272), (273),
% 173.03/26.19  | | | | | | | | | | | | | |            (274), (277), (279), (280), (281), (282), (283),
% 173.03/26.19  | | | | | | | | | | | | | |            (304), (307), (311), (313), (315), (319), (321),
% 173.03/26.19  | | | | | | | | | | | | | |            (323), (326), (328), (329), (330), (331), (344),
% 173.03/26.19  | | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 173.03/26.19  | | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 173.03/26.19  | | | | | | | | | | | | | |            (419), (494), (529), (531), (532), (533), (534),
% 173.03/26.19  | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.03/26.19  | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.03/26.19  | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.03/26.19  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.03/26.19  | | | | | | | | | | | | | |            (571), (573), (579), (580), (581), (582), (583),
% 173.03/26.19  | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 173.03/26.19  | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (661),
% 173.03/26.19  | | | | | | | | | | | | | |            (663), (720), (796), (7374), (7381), (7383),
% 173.03/26.19  | | | | | | | | | | | | | |            (7431), (7433), (7437), (7438), (7439),
% 173.03/26.19  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.19  | | | | | | | | | | | | | |            #570.
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | Case 2:
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | |   (7440)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.19  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.19  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | BETA: splitting (7440) gives:
% 173.03/26.19  | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | Case 1:
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.19  | | | | | | | | | | | | | | |   (7441)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.19  | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.19  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (62), (63),
% 173.03/26.20  | | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (169), (170),
% 173.03/26.20  | | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.03/26.20  | | | | | | | | | | | | | | |            (182), (268), (270), (274), (275), (276), (277),
% 173.03/26.20  | | | | | | | | | | | | | | |            (278), (282), (283), (304), (307), (310), (311),
% 173.03/26.20  | | | | | | | | | | | | | | |            (313), (314), (315), (317), (319), (320), (321),
% 173.03/26.20  | | | | | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 173.03/26.20  | | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 173.03/26.20  | | | | | | | | | | | | | | |            (385), (391), (392), (403), (415), (419), (425),
% 173.03/26.20  | | | | | | | | | | | | | | |            (494), (529), (530), (531), (532), (533), (534),
% 173.03/26.20  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.03/26.20  | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.03/26.20  | | | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.03/26.20  | | | | | | | | | | | | | | |            (562), (563), (564), (566), (568), (571), (575),
% 173.03/26.20  | | | | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 173.03/26.20  | | | | | | | | | | | | | | |            (584), (585), (586), (587), (591), (593), (595),
% 173.03/26.20  | | | | | | | | | | | | | | |            (596), (597), (598), (600), (663), (719), (796),
% 173.03/26.20  | | | | | | | | | | | | | | |            (7376), (7377), (7379), (7431), (7433), (7437),
% 173.03/26.20  | | | | | | | | | | | | | | |            (7441), (function-axioms) are inconsistent by
% 173.03/26.20  | | | | | | | | | | | | | | |            sub-proof #440.
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | |   (7442)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7442),
% 173.03/26.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | |            #138.
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | |   (7443)  all_30_1 = e1
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | COMBINE_EQS: (712), (7443) imply:
% 173.03/26.20  | | | | | | | | | | |   (7444)  all_10_1 = e1
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | SIMP: (7444) implies:
% 173.03/26.20  | | | | | | | | | | |   (7445)  all_10_1 = e1
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | COMBINE_EQS: (661), (7445) imply:
% 173.03/26.20  | | | | | | | | | | |   (7446)  all_52_10 = e1
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | REDUCE: (7376), (7445) imply:
% 173.03/26.20  | | | | | | | | | | |   (7447)   ~ (e3 = e1)
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | |   (7448)   ~ (all_34_0 = e1)
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | REDUCE: (773), (7448) imply:
% 173.03/26.20  | | | | | | | | | | | |   (7449)   ~ (all_4_0 = e1)
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | BETA: splitting (123) gives:
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | |   (7450)   ~ (all_38_0 = e1)
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | REDUCE: (7372), (7450) imply:
% 173.03/26.20  | | | | | | | | | | | | |   (7451)  $false
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | CLOSE: (7451) is inconsistent.
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | |   (7452)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | BETA: splitting (128) gives:
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | |   (7453)   ~ (all_40_1 = e1)
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | REDUCE: (715), (7453) imply:
% 173.03/26.20  | | | | | | | | | | | | | |   (7454)   ~ (all_4_1 = e1)
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | |   (7455)  all_58_15 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7455),
% 173.03/26.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | |            #143.
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | |   (7456)   ~ (all_58_15 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | |   (7457)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.20  | | | | | | | | | | | | | | |             e0)
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | ALPHA: (7457) implies:
% 173.03/26.20  | | | | | | | | | | | | | | |   (7458)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.20  | | | | | | | | | | | | | | |   (7459)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | REDUCE: (532), (7456) imply:
% 173.03/26.20  | | | | | | | | | | | | | | |   (7460)   ~ (all_6_2 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7461)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.20  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | BETA: splitting (7461) gives:
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7462)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | ALPHA: (7462) implies:
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7463)  all_52_6 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7464)  all_52_4 = e1
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7465)  all_52_2 = e2
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7466)  all_52_0 = e3
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (7466) imply:
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7467)  all_4_1 = e3
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | REDUCE: (38), (7467) imply:
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7468)  op(e3, all_4_2) = all_4_0
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | REDUCE: (37), (7467) imply:
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7469)  op(e3, all_4_2) = e3
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | REDUCE: (176), (7465) imply:
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7470)  op(e2, all_52_3) = e2
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | REDUCE: (168), (7464) imply:
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7471)  op(e1, all_52_5) = e1
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | REDUCE: (160), (7463) imply:
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7472)  op(e0, all_52_7) = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (61), (154), (156), (158), (159),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (169), (170), (172),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (173), (177), (178), (179), (268), (269), (270),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (283), (302), (304), (305), (307), (310), (311),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (324), (326), (327), (328), (330), (331), (341),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (385), (391), (392), (403), (409), (413), (425),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (429), (517), (529), (531), (532), (533), (534),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (575),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (714), (7373), (7385), (7449), (7452), (7459),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (7460), (7468), (7469), (7470), (7471), (7472),
% 173.03/26.20  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | | | |            #141.
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | |   (7473)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7446), (7473) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | | | |            #533.
% 173.03/26.20  | | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7474)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.20  | | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.20  | | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (52),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (62), (63), (155), (156), (158), (161), (163),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (174),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (277),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (278), (282), (283), (304), (306), (307), (308),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (326),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (359),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (392),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (403), (415), (419), (425), (429), (529), (530),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (565), (566), (567), (568), (571), (573), (575),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (591), (593),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (649),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (719), (796), (7373), (7376), (7377), (7379),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (7385), (7449), (7454), (7458), (7459), (7460),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (7474), (function-axioms) are inconsistent by
% 173.03/26.20  | | | | | | | | | | | | | | | |            sub-proof #137.
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | |   (7475)  all_40_1 = e1
% 173.03/26.20  | | | | | | | | | | | | | |   (7476)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | COMBINE_EQS: (715), (7475) imply:
% 173.03/26.20  | | | | | | | | | | | | | |   (7477)  all_4_1 = e1
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | COMBINE_EQS: (720), (7477) imply:
% 173.03/26.20  | | | | | | | | | | | | | |   (7478)  all_52_0 = e1
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | REDUCE: (796), (7477) imply:
% 173.03/26.20  | | | | | | | | | | | | | |   (7479)   ~ (e2 = e1)
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | REDUCE: (38), (7477) imply:
% 173.03/26.20  | | | | | | | | | | | | | |   (7480)  op(e1, all_4_2) = all_4_0
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | REDUCE: (37), (7477) imply:
% 173.03/26.20  | | | | | | | | | | | | | |   (7481)  op(e3, all_4_2) = e1
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | |   (7482)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.20  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | BETA: splitting (7482) gives:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7483)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7478), (7483) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | | |            #632.
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7484)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7446), (7484) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | | |            #533.
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | |   (7485)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.20  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.20  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | BETA: splitting (7485) gives:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7486)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (62),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (63), (154), (155), (156), (158), (163), (164),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (165), (169), (170), (172), (174), (177), (178),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (179), (181), (182), (183), (268), (270), (271),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (272), (274), (275), (276), (277), (278), (283),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (310), (311), (313), (314), (315), (317), (319),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (326), (328),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (329), (330), (331), (344), (349), (350), (364),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (365), (370), (373), (385), (391), (403), (415),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (419), (425), (429), (518), (529), (530), (531),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (566), (567), (568), (571), (575), (577), (578),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (586), (587), (588), (591), (593), (594), (595),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (596), (597), (598), (600), (719), (770), (796),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (7376), (7377), (7379), (7385), (7449), (7476),
% 173.03/26.20  | | | | | | | | | | | | | | | |            (7480), (7481), (7486), (function-axioms) are
% 173.03/26.20  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #499.
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7487)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | ALPHA: (7487) implies:
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7488)  all_52_30 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | COMBINE_EQS: (649), (7488) imply:
% 173.03/26.20  | | | | | | | | | | | | | | | |   (7489)  all_6_1 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (42), (7373), (7489), (function-axioms) are
% 173.03/26.20  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #139.
% 173.03/26.20  | | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | |   (7490)  all_34_0 = e1
% 173.03/26.20  | | | | | | | | | | | |   (7491)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | COMBINE_EQS: (773), (7490) imply:
% 173.03/26.20  | | | | | | | | | | | |   (7492)  all_4_0 = e1
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | SIMP: (7492) implies:
% 173.03/26.20  | | | | | | | | | | | |   (7493)  all_4_0 = e1
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | REDUCE: (7385), (7493) imply:
% 173.03/26.20  | | | | | | | | | | | |   (7494)   ~ (e2 = e1)
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | REDUCE: (38), (7493) imply:
% 173.03/26.20  | | | | | | | | | | | |   (7495)  op(all_4_1, all_4_2) = e1
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | |   (7496)  all_58_15 = e0
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7496),
% 173.03/26.20  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | |            #143.
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | |   (7497)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.20  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.20  | | | | | | | | | | | | |             e0)
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | ALPHA: (7497) implies:
% 173.03/26.20  | | | | | | | | | | | | |   (7498)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | |   (7499)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.20  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | BETA: splitting (7499) gives:
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | |   (7500)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | REF_CLOSE: (8), (37), (720), (7495), (7500),
% 173.03/26.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | |            #600.
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | |   (7501)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.20  | | | | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7446), (7501) are inconsistent by sub-proof
% 173.03/26.20  | | | | | | | | | | | | | | |            #533.
% 173.03/26.20  | | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | |   (7502)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.20  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.20  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (52), (62),
% 173.03/26.20  | | | | | | | | | | | | | |            (63), (156), (158), (163), (164), (165), (169),
% 173.03/26.20  | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.03/26.20  | | | | | | | | | | | | | |            (181), (182), (268), (270), (274), (275), (276),
% 173.03/26.20  | | | | | | | | | | | | | |            (277), (278), (282), (283), (304), (307), (310),
% 173.03/26.20  | | | | | | | | | | | | | |            (311), (313), (314), (315), (317), (319), (320),
% 173.03/26.20  | | | | | | | | | | | | | |            (321), (322), (323), (324), (326), (328), (329),
% 173.03/26.20  | | | | | | | | | | | | | |            (330), (331), (344), (349), (364), (365), (370),
% 173.03/26.20  | | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (415), (419),
% 173.03/26.20  | | | | | | | | | | | | | |            (425), (494), (529), (530), (531), (532), (533),
% 173.03/26.20  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.03/26.20  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.03/26.20  | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 173.03/26.20  | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (568), (571),
% 173.03/26.20  | | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.03/26.20  | | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (591), (593),
% 173.03/26.20  | | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (649), (663),
% 173.03/26.20  | | | | | | | | | | | | | |            (719), (796), (7373), (7376), (7377), (7379),
% 173.03/26.20  | | | | | | | | | | | | | |            (7491), (7495), (7498), (7502), (function-axioms)
% 173.03/26.20  | | | | | | | | | | | | | |            are inconsistent by sub-proof #136.
% 173.03/26.20  | | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | End of split
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | |   (7503)  all_26_0 = e2
% 173.03/26.20  | | | | | | | | | |   (7504)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | COMBINE_EQS: (779), (7503) imply:
% 173.03/26.20  | | | | | | | | | |   (7505)  all_4_0 = e2
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | SIMP: (7505) implies:
% 173.03/26.20  | | | | | | | | | |   (7506)  all_4_0 = e2
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | COMBINE_EQS: (742), (7506) imply:
% 173.03/26.20  | | | | | | | | | |   (7507)  all_50_0 = e2
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | REDUCE: (38), (7506) imply:
% 173.03/26.20  | | | | | | | | | |   (7508)  op(all_4_1, all_4_2) = e2
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | BETA: splitting (151) gives:
% 173.03/26.20  | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | |   (7509)   ~ (all_50_0 = e2)
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | REDUCE: (7507), (7509) imply:
% 173.03/26.20  | | | | | | | | | | |   (7510)  $false
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | CLOSE: (7510) is inconsistent.
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | Case 2:
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | |   (7511)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.20  | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | Case 1:
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.20  | | | | | | | | | | | |   (7512)  all_58_15 = e0
% 173.03/26.20  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7512),
% 173.03/26.21  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.21  | | | | | | | | | | | |            #143.
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | |   (7513)   ~ (all_58_15 = e0)
% 173.03/26.21  | | | | | | | | | | | |   (7514)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.21  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.21  | | | | | | | | | | | |             e0)
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | ALPHA: (7514) implies:
% 173.03/26.21  | | | | | | | | | | | |   (7515)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | REDUCE: (532), (7513) imply:
% 173.03/26.21  | | | | | | | | | | | |   (7516)   ~ (all_6_2 = e0)
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | |   (7517)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.21  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.21  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (52), (53), (62),
% 173.03/26.21  | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 173.03/26.21  | | | | | | | | | | | | |            (167), (169), (170), (172), (173), (174), (177),
% 173.03/26.21  | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (270),
% 173.03/26.21  | | | | | | | | | | | | |            (272), (273), (274), (275), (277), (278), (279),
% 173.03/26.21  | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (311),
% 173.03/26.21  | | | | | | | | | | | | |            (313), (315), (316), (319), (321), (323), (325),
% 173.03/26.21  | | | | | | | | | | | | |            (326), (328), (329), (330), (344), (349), (350),
% 173.03/26.21  | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.03/26.21  | | | | | | | | | | | | |            (391), (392), (403), (409), (413), (415), (419),
% 173.03/26.21  | | | | | | | | | | | | |            (503), (521), (529), (530), (531), (532), (533),
% 173.03/26.21  | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.03/26.21  | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.03/26.21  | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 173.03/26.21  | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 173.03/26.21  | | | | | | | | | | | | |            (568), (569), (571), (573), (575), (579), (580),
% 173.03/26.21  | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 173.03/26.21  | | | | | | | | | | | | |            (589), (593), (594), (595), (596), (597), (598),
% 173.03/26.21  | | | | | | | | | | | | |            (599), (600), (661), (698), (718), (720), (796),
% 173.03/26.21  | | | | | | | | | | | | |            (7374), (7381), (7383), (7504), (7508), (7511),
% 173.03/26.21  | | | | | | | | | | | | |            (7515), (7516), (7517), (function-axioms) are
% 173.03/26.21  | | | | | | | | | | | | |            inconsistent by sub-proof #462.
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | |   (7518)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.21  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.21  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 173.03/26.21  | | | | | | | | | | | | |            (156), (158), (161), (163), (164), (165), (172),
% 173.03/26.21  | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.03/26.21  | | | | | | | | | | | | |            (183), (268), (270), (273), (274), (275), (276),
% 173.03/26.21  | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (310),
% 173.03/26.21  | | | | | | | | | | | | |            (311), (315), (319), (321), (323), (324), (325),
% 173.03/26.21  | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 173.03/26.21  | | | | | | | | | | | | |            (359), (364), (365), (370), (385), (386), (391),
% 173.03/26.21  | | | | | | | | | | | | |            (392), (403), (413), (419), (425), (521), (529),
% 173.03/26.21  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.21  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.21  | | | | | | | | | | | | |            (550), (552), (553), (554), (557), (558), (559),
% 173.03/26.21  | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 173.03/26.21  | | | | | | | | | | | | |            (568), (569), (577), (579), (580), (582), (584),
% 173.03/26.21  | | | | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (598),
% 173.03/26.21  | | | | | | | | | | | | |            (600), (649), (718), (719), (796), (7373), (7377),
% 173.03/26.21  | | | | | | | | | | | | |            (7379), (7508), (7511), (7515), (7518),
% 173.03/26.21  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.21  | | | | | | | | | | | | |            #135.
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | 
% 173.03/26.21  | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | 
% 173.03/26.21  | | | | | | | | |   (7519)  all_24_0 = e1
% 173.03/26.21  | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | COMBINE_EQS: (751), (7519) imply:
% 173.03/26.21  | | | | | | | | |   (7520)  all_10_0 = e1
% 173.03/26.21  | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | REDUCE: (7374), (7520) imply:
% 173.03/26.21  | | | | | | | | |   (7521)   ~ (e3 = e1)
% 173.03/26.21  | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | REDUCE: (53), (7520) imply:
% 173.03/26.21  | | | | | | | | |   (7522)  op(all_10_1, all_10_2) = e1
% 173.03/26.21  | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | BETA: splitting (93) gives:
% 173.03/26.21  | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | |   (7523)   ~ (all_26_0 = e2)
% 173.03/26.21  | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | REDUCE: (779), (7523) imply:
% 173.03/26.21  | | | | | | | | | |   (7524)   ~ (all_4_0 = e2)
% 173.03/26.21  | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.21  | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | |   (7525)   ~ (all_34_0 = e1)
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | REDUCE: (773), (7525) imply:
% 173.03/26.21  | | | | | | | | | | |   (7526)   ~ (all_4_0 = e1)
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | BETA: splitting (123) gives:
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | |   (7527)   ~ (all_38_0 = e1)
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | REDUCE: (7372), (7527) imply:
% 173.03/26.21  | | | | | | | | | | | |   (7528)  $false
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | CLOSE: (7528) is inconsistent.
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | |   (7529)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | BETA: splitting (128) gives:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | |   (7530)   ~ (all_40_1 = e1)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | REDUCE: (715), (7530) imply:
% 173.03/26.21  | | | | | | | | | | | | |   (7531)   ~ (all_4_1 = e1)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | |   (7532)  all_58_15 = e0
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7532),
% 173.03/26.21  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.21  | | | | | | | | | | | | | |            #143.
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | |   (7533)   ~ (all_58_15 = e0)
% 173.03/26.21  | | | | | | | | | | | | | |   (7534)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.21  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.21  | | | | | | | | | | | | | |             e0)
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | ALPHA: (7534) implies:
% 173.03/26.21  | | | | | | | | | | | | | |   (7535)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.21  | | | | | | | | | | | | | |   (7536)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | REDUCE: (532), (7533) imply:
% 173.03/26.21  | | | | | | | | | | | | | |   (7537)   ~ (all_6_2 = e0)
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | |   (7538)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.21  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.21  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.21  | | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (37), (38), (42), (52), (61),
% 173.03/26.21  | | | | | | | | | | | | | | |            (154), (156), (158), (159), (160), (161), (163),
% 173.03/26.21  | | | | | | | | | | | | | | |            (164), (165), (168), (169), (170), (172), (173),
% 173.03/26.21  | | | | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 173.03/26.21  | | | | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 173.03/26.21  | | | | | | | | | | | | | | |            (283), (302), (304), (305), (307), (310), (311),
% 173.03/26.21  | | | | | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 173.03/26.21  | | | | | | | | | | | | | | |            (324), (326), (327), (328), (330), (331), (341),
% 173.03/26.21  | | | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 173.03/26.21  | | | | | | | | | | | | | | |            (385), (391), (392), (403), (409), (413), (425),
% 173.03/26.21  | | | | | | | | | | | | | | |            (429), (517), (529), (531), (532), (533), (534),
% 173.03/26.21  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.03/26.21  | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.03/26.21  | | | | | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.03/26.21  | | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (575),
% 173.03/26.21  | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.03/26.21  | | | | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 173.03/26.21  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.03/26.21  | | | | | | | | | | | | | | |            (661), (714), (720), (7373), (7522), (7524),
% 173.03/26.21  | | | | | | | | | | | | | | |            (7526), (7529), (7536), (7537), (7538),
% 173.03/26.21  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.21  | | | | | | | | | | | | | | |            #134.
% 173.03/26.21  | | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | |   (7539)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.21  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.21  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.21  | | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (52),
% 173.03/26.21  | | | | | | | | | | | | | | |            (62), (63), (155), (156), (158), (161), (163),
% 173.03/26.21  | | | | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (174),
% 173.03/26.21  | | | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (268),
% 173.03/26.21  | | | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (277),
% 173.03/26.21  | | | | | | | | | | | | | | |            (278), (282), (283), (304), (306), (307), (308),
% 173.03/26.21  | | | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 173.03/26.21  | | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (326),
% 173.03/26.21  | | | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (359),
% 173.03/26.21  | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (392),
% 173.03/26.21  | | | | | | | | | | | | | | |            (403), (415), (419), (425), (429), (529), (530),
% 173.03/26.21  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.21  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.21  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.03/26.21  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.03/26.21  | | | | | | | | | | | | | | |            (565), (566), (567), (568), (571), (573), (575),
% 173.03/26.21  | | | | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 173.03/26.21  | | | | | | | | | | | | | | |            (584), (585), (586), (587), (588), (591), (593),
% 173.03/26.21  | | | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (649),
% 173.03/26.21  | | | | | | | | | | | | | | |            (719), (796), (7373), (7376), (7377), (7379),
% 173.03/26.21  | | | | | | | | | | | | | | |            (7524), (7526), (7531), (7535), (7536), (7537),
% 173.03/26.21  | | | | | | | | | | | | | | |            (7539), (function-axioms) are inconsistent by
% 173.03/26.21  | | | | | | | | | | | | | | |            sub-proof #137.
% 173.03/26.21  | | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | |   (7540)  all_40_1 = e1
% 173.03/26.21  | | | | | | | | | | | | |   (7541)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | COMBINE_EQS: (715), (7540) imply:
% 173.03/26.21  | | | | | | | | | | | | |   (7542)  all_4_1 = e1
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | COMBINE_EQS: (720), (7542) imply:
% 173.03/26.21  | | | | | | | | | | | | |   (7543)  all_52_0 = e1
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | REDUCE: (796), (7542) imply:
% 173.03/26.21  | | | | | | | | | | | | |   (7544)   ~ (e2 = e1)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | REDUCE: (38), (7542) imply:
% 173.03/26.21  | | | | | | | | | | | | |   (7545)  op(e1, all_4_2) = all_4_0
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | REDUCE: (37), (7542) imply:
% 173.03/26.21  | | | | | | | | | | | | |   (7546)  op(e3, all_4_2) = e1
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | |   (7547)  all_58_15 = e0
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7547),
% 173.03/26.21  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.21  | | | | | | | | | | | | | |            #143.
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | |   (7548)   ~ (all_58_15 = e0)
% 173.03/26.21  | | | | | | | | | | | | | |   (7549)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.21  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.21  | | | | | | | | | | | | | |             e0)
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.03/26.21  | | | | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 173.03/26.21  | | | | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (170),
% 173.03/26.21  | | | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.03/26.21  | | | | | | | | | | | | | |            (182), (183), (185), (268), (270), (271), (274),
% 173.03/26.21  | | | | | | | | | | | | | |            (275), (276), (277), (278), (283), (304), (305),
% 173.03/26.21  | | | | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (317),
% 173.03/26.21  | | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 173.03/26.21  | | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (344),
% 173.03/26.21  | | | | | | | | | | | | | |            (349), (364), (365), (370), (373), (385), (391),
% 173.03/26.21  | | | | | | | | | | | | | |            (403), (415), (419), (425), (429), (518), (529),
% 173.03/26.21  | | | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 173.03/26.21  | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.03/26.21  | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.03/26.21  | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.03/26.21  | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.03/26.21  | | | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.03/26.21  | | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.03/26.21  | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.03/26.21  | | | | | | | | | | | | | |            (598), (600), (649), (661), (719), (770), (796),
% 173.03/26.21  | | | | | | | | | | | | | |            (7376), (7377), (7379), (7522), (7524), (7526),
% 173.03/26.21  | | | | | | | | | | | | | |            (7541), (7543), (7545), (7546), (7548), (7549),
% 173.03/26.21  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.21  | | | | | | | | | | | | | |            #442.
% 173.03/26.21  | | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | End of split
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | |   (7550)  all_34_0 = e1
% 173.03/26.21  | | | | | | | | | | |   (7551)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | COMBINE_EQS: (773), (7550) imply:
% 173.03/26.21  | | | | | | | | | | |   (7552)  all_4_0 = e1
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | SIMP: (7552) implies:
% 173.03/26.21  | | | | | | | | | | |   (7553)  all_4_0 = e1
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | REDUCE: (7524), (7553) imply:
% 173.03/26.21  | | | | | | | | | | |   (7554)   ~ (e2 = e1)
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | REDUCE: (38), (7553) imply:
% 173.03/26.21  | | | | | | | | | | |   (7555)  op(all_4_1, all_4_2) = e1
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.21  | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | |   (7556)  all_58_15 = e0
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7556),
% 173.03/26.21  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.21  | | | | | | | | | | | |            #143.
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | |   (7557)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.21  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.21  | | | | | | | | | | | |             e0)
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | ALPHA: (7557) implies:
% 173.03/26.21  | | | | | | | | | | | |   (7558)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.21  | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | Case 1:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | |   (7559)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.21  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.21  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (7522),
% 173.03/26.21  | | | | | | | | | | | | |            (7555), (7559), (function-axioms) are inconsistent
% 173.03/26.21  | | | | | | | | | | | | |            by sub-proof #441.
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | Case 2:
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.21  | | | | | | | | | | | | |   (7560)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.21  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.21  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.21  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (52), (62),
% 173.03/26.22  | | | | | | | | | | | | |            (63), (156), (158), (163), (164), (165), (169),
% 173.03/26.22  | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.03/26.22  | | | | | | | | | | | | |            (181), (182), (268), (270), (274), (275), (276),
% 173.03/26.22  | | | | | | | | | | | | |            (277), (278), (282), (283), (304), (307), (310),
% 173.03/26.22  | | | | | | | | | | | | |            (311), (313), (314), (315), (317), (319), (320),
% 173.03/26.22  | | | | | | | | | | | | |            (321), (322), (323), (324), (326), (328), (329),
% 173.03/26.22  | | | | | | | | | | | | |            (330), (331), (344), (349), (364), (365), (370),
% 173.03/26.22  | | | | | | | | | | | | |            (373), (385), (391), (392), (403), (415), (419),
% 173.03/26.22  | | | | | | | | | | | | |            (425), (494), (529), (530), (531), (532), (533),
% 173.03/26.22  | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.03/26.22  | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.03/26.22  | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 173.03/26.22  | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (568), (571),
% 173.03/26.22  | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.03/26.22  | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (591), (593),
% 173.03/26.22  | | | | | | | | | | | | |            (595), (596), (597), (598), (600), (649), (663),
% 173.03/26.22  | | | | | | | | | | | | |            (719), (796), (7373), (7376), (7377), (7379),
% 173.03/26.22  | | | | | | | | | | | | |            (7551), (7555), (7558), (7560), (function-axioms)
% 173.03/26.22  | | | | | | | | | | | | |            are inconsistent by sub-proof #136.
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | |   (7561)  all_26_0 = e2
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | COMBINE_EQS: (779), (7561) imply:
% 173.03/26.22  | | | | | | | | | |   (7562)  all_4_0 = e2
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | COMBINE_EQS: (742), (7562) imply:
% 173.03/26.22  | | | | | | | | | |   (7563)  all_50_0 = e2
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | REDUCE: (38), (7562) imply:
% 173.03/26.22  | | | | | | | | | |   (7564)  op(all_4_1, all_4_2) = e2
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | BETA: splitting (151) gives:
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | |   (7565)   ~ (all_50_0 = e2)
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | REDUCE: (7563), (7565) imply:
% 173.03/26.22  | | | | | | | | | | |   (7566)  $false
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | CLOSE: (7566) is inconsistent.
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | |   (7567)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | |   (7568)  all_58_15 = e0
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7568),
% 173.03/26.22  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.22  | | | | | | | | | | | |            #143.
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | |   (7569)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.22  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.22  | | | | | | | | | | | |             e0)
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | ALPHA: (7569) implies:
% 173.03/26.22  | | | | | | | | | | | |   (7570)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | |   (7571)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.22  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.22  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (7522),
% 173.03/26.22  | | | | | | | | | | | | |            (7564), (7571), (function-axioms) are inconsistent
% 173.03/26.22  | | | | | | | | | | | | |            by sub-proof #434.
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | |   (7572)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.22  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.22  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 173.03/26.22  | | | | | | | | | | | | |            (156), (158), (161), (163), (164), (165), (172),
% 173.03/26.22  | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.03/26.22  | | | | | | | | | | | | |            (183), (268), (270), (273), (274), (275), (276),
% 173.03/26.22  | | | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (310),
% 173.03/26.22  | | | | | | | | | | | | |            (311), (315), (319), (321), (323), (324), (325),
% 173.03/26.22  | | | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 173.03/26.22  | | | | | | | | | | | | |            (359), (364), (365), (370), (385), (386), (391),
% 173.03/26.22  | | | | | | | | | | | | |            (392), (403), (413), (419), (425), (521), (529),
% 173.03/26.22  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.22  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.22  | | | | | | | | | | | | |            (550), (552), (553), (554), (557), (558), (559),
% 173.03/26.22  | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 173.03/26.22  | | | | | | | | | | | | |            (568), (569), (577), (579), (580), (582), (584),
% 173.03/26.22  | | | | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (598),
% 173.03/26.22  | | | | | | | | | | | | |            (600), (649), (718), (719), (796), (7373), (7377),
% 173.03/26.22  | | | | | | | | | | | | |            (7379), (7564), (7567), (7570), (7572),
% 173.03/26.22  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.22  | | | | | | | | | | | | |            #133.
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | 
% 173.03/26.22  | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | |   (7573)  all_22_1 = e3
% 173.03/26.22  | | | | | | | |   (7574)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | | COMBINE_EQS: (711), (7573) imply:
% 173.03/26.22  | | | | | | | |   (7575)  all_14_1 = e3
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | | COMBINE_EQS: (719), (7575) imply:
% 173.03/26.22  | | | | | | | |   (7576)  all_52_20 = e3
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | | REDUCE: (63), (7575) imply:
% 173.03/26.22  | | | | | | | |   (7577)  op(e3, all_14_2) = all_14_0
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | | REDUCE: (62), (7575) imply:
% 173.03/26.22  | | | | | | | |   (7578)  op(e1, all_14_2) = e3
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | | BETA: splitting (88) gives:
% 173.03/26.22  | | | | | | | | 
% 173.03/26.22  | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | 
% 173.03/26.22  | | | | | | | | |   (7579)   ~ (all_24_0 = e1)
% 173.03/26.22  | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | REDUCE: (751), (7579) imply:
% 173.03/26.22  | | | | | | | | |   (7580)   ~ (all_10_0 = e1)
% 173.03/26.22  | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | BETA: splitting (93) gives:
% 173.03/26.22  | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | |   (7581)   ~ (all_26_0 = e2)
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | REDUCE: (779), (7581) imply:
% 173.03/26.22  | | | | | | | | | |   (7582)   ~ (all_4_0 = e2)
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.22  | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | |   (7583)   ~ (all_34_0 = e1)
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | REDUCE: (773), (7583) imply:
% 173.03/26.22  | | | | | | | | | | |   (7584)   ~ (all_4_0 = e1)
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | BETA: splitting (123) gives:
% 173.03/26.22  | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | |   (7585)   ~ (all_38_0 = e1)
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | REDUCE: (7372), (7585) imply:
% 173.03/26.22  | | | | | | | | | | | |   (7586)  $false
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | CLOSE: (7586) is inconsistent.
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | |   (7587)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | BETA: splitting (128) gives:
% 173.03/26.22  | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | |   (7588)   ~ (all_40_1 = e1)
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | REDUCE: (715), (7588) imply:
% 173.03/26.22  | | | | | | | | | | | | |   (7589)   ~ (all_4_1 = e1)
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | |   (7590)  all_58_15 = e0
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7590),
% 173.03/26.22  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.22  | | | | | | | | | | | | | |            #143.
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | |   (7591)   ~ (all_58_15 = e0)
% 173.03/26.22  | | | | | | | | | | | | | |   (7592)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.22  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.22  | | | | | | | | | | | | | |             e0)
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | ALPHA: (7592) implies:
% 173.03/26.22  | | | | | | | | | | | | | |   (7593)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.22  | | | | | | | | | | | | | |   (7594)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | REDUCE: (532), (7591) imply:
% 173.03/26.22  | | | | | | | | | | | | | |   (7595)   ~ (all_6_2 = e0)
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | |   (7596)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.22  | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | BETA: splitting (7596) gives:
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7597)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | ALPHA: (7597) implies:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7598)  all_52_6 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7599)  all_52_4 = e1
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7600)  all_52_2 = e2
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7601)  all_52_0 = e3
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | COMBINE_EQS: (720), (7601) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7602)  all_4_1 = e3
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (38), (7602) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7603)  op(e3, all_4_2) = all_4_0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (37), (7602) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7604)  op(e3, all_4_2) = e3
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (176), (7600) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7605)  op(e2, all_52_3) = e2
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (168), (7599) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7606)  op(e1, all_52_5) = e1
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (160), (7598) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7607)  op(e0, all_52_7) = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (61), (154), (156), (158), (159),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (170), (172), (173),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (272), (273), (276), (279), (281), (283), (302),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (327), (328), (330), (331), (341), (344), (349),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (350), (359), (364), (370), (373), (385), (391),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (403), (409), (413), (425), (429), (517), (529),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (566), (568), (569), (575), (578), (579), (580),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (597), (598), (599), (600), (714), (7373), (7578),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (7582), (7584), (7587), (7594), (7595), (7603),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (7604), (7605), (7606), (7607), (function-axioms)
% 173.03/26.22  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #132.
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7608)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | ALPHA: (7608) implies:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7609)  all_52_14 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7610)  all_52_12 = e1
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7611)  all_52_10 = e2
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7612)  all_52_8 = e3
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | COMBINE_EQS: (661), (7611) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7613)  all_10_1 = e2
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (53), (7613) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7614)  op(e2, all_10_2) = all_10_0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (183), (7612) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7615)  op(e3, all_52_9) = e3
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (52), (7613) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7616)  op(e2, all_10_2) = e2
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (167), (7610) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7617)  op(e1, all_52_13) = e1
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (159), (7609) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7618)  op(e0, all_52_15) = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (38), (42), (62),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (154), (155), (156), (158), (161), (163), (164),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (165), (169), (170), (172), (173), (174), (177),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (178), (179), (181), (182), (268), (270), (272),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (273), (274), (276), (277), (278), (279), (280),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (281), (282), (283), (303), (304), (307), (311),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (313), (314), (315), (316), (317), (319), (320),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (321), (323), (326), (327), (328), (329), (330),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (331), (344), (349), (350), (359), (364), (370),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (413), (415), (419), (425), (529), (530), (531),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (796),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (7374), (7578), (7580), (7582), (7584), (7589),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (7593), (7594), (7595), (7614), (7615), (7616),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (7617), (7618), (function-axioms) are inconsistent
% 173.03/26.22  | | | | | | | | | | | | | | | |            by sub-proof #374.
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | |   (7619)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.22  | | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.22  | | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | BETA: splitting (7619) gives:
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7620)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7576), (7620) are inconsistent by sub-proof
% 173.03/26.22  | | | | | | | | | | | | | | | |            #427.
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7621)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7621),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.22  | | | | | | | | | | | | | | | |            #138.
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | End of split
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | |   (7622)  all_40_1 = e1
% 173.03/26.22  | | | | | | | | | | | | |   (7623)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | COMBINE_EQS: (715), (7622) imply:
% 173.03/26.22  | | | | | | | | | | | | |   (7624)  all_4_1 = e1
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | COMBINE_EQS: (720), (7624) imply:
% 173.03/26.22  | | | | | | | | | | | | |   (7625)  all_52_0 = e1
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | REDUCE: (38), (7624) imply:
% 173.03/26.22  | | | | | | | | | | | | |   (7626)  op(e1, all_4_2) = all_4_0
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | REDUCE: (37), (7624) imply:
% 173.03/26.22  | | | | | | | | | | | | |   (7627)  op(e3, all_4_2) = e1
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.22  | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | |   (7628)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.22  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | BETA: splitting (7628) gives:
% 173.03/26.22  | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | |   (7629)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | REF_CLOSE: (8), (7625), (7629) are inconsistent by sub-proof
% 173.03/26.22  | | | | | | | | | | | | | | |            #632.
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | |   (7630)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.22  | | | | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | ALPHA: (7630) implies:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7631)  all_52_14 = e0
% 173.03/26.22  | | | | | | | | | | | | | | |   (7632)  all_52_12 = e1
% 173.03/26.22  | | | | | | | | | | | | | | |   (7633)  all_52_10 = e2
% 173.03/26.22  | | | | | | | | | | | | | | |   (7634)  all_52_8 = e3
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | COMBINE_EQS: (661), (7633) imply:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7635)  all_10_1 = e2
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | REDUCE: (53), (7635) imply:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7636)  op(e2, all_10_2) = all_10_0
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | REDUCE: (183), (7634) imply:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7637)  op(e3, all_52_9) = e3
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | REDUCE: (52), (7635) imply:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7638)  op(e2, all_10_2) = e2
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | REDUCE: (167), (7632) imply:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7639)  op(e1, all_52_13) = e1
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | REDUCE: (159), (7631) imply:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7640)  op(e0, all_52_15) = e0
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 173.03/26.22  | | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (7636), (7638)
% 173.03/26.22  | | | | | | | | | | | | | | |              gives:
% 173.03/26.22  | | | | | | | | | | | | | | |   (7641)  all_10_0 = e2
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.22  | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | Case 1:
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7642)  all_58_15 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7642),
% 173.03/26.22  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.22  | | | | | | | | | | | | | | | |            #143.
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | Case 2:
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7643)   ~ (all_58_15 = e0)
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7644)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.22  | | | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.22  | | | | | | | | | | | | | | | |             e0)
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | ALPHA: (7644) implies:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7645)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7646)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.22  | | | | | | | | | | | | | | | | REDUCE: (532), (7643) imply:
% 173.03/26.22  | | | | | | | | | | | | | | | |   (7647)   ~ (all_6_2 = e0)
% 173.03/26.22  | | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (37), (38), (42), (61),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (62), (154), (156), (158), (160), (161), (163),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (174),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (268), (270),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (272), (273), (274), (276), (277), (278), (279),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (280), (281), (283), (303), (304), (305), (307),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (311), (313), (315), (316), (317), (319), (320),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (321), (322), (323), (325), (326), (328), (329),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (330), (331), (344), (349), (350), (359), (364),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (403), (409),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (413), (415), (419), (425), (518), (529), (530),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (770),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (796), (7374), (7580), (7582), (7623), (7626),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (7627), (7636), (7637), (7638), (7639), (7640),
% 173.03/26.23  | | | | | | | | | | | | | | | |            (7645), (7646), (7647), (function-axioms) are
% 173.03/26.23  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #308.
% 173.03/26.23  | | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | |   (7648)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.23  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.23  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (42), (649), (7373), (7576), (7648),
% 173.03/26.23  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | | |            #131.
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | |   (7649)  all_34_0 = e1
% 173.03/26.23  | | | | | | | | | | |   (7650)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | COMBINE_EQS: (773), (7649) imply:
% 173.03/26.23  | | | | | | | | | | |   (7651)  all_4_0 = e1
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | SIMP: (7651) implies:
% 173.03/26.23  | | | | | | | | | | |   (7652)  all_4_0 = e1
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | REDUCE: (38), (7652) imply:
% 173.03/26.23  | | | | | | | | | | |   (7653)  op(all_4_1, all_4_2) = e1
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7654)  all_58_15 = e0
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7654),
% 173.03/26.23  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | |            #143.
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7655)   ~ (all_58_15 = e0)
% 173.03/26.23  | | | | | | | | | | | |   (7656)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.23  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.23  | | | | | | | | | | | |             e0)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | ALPHA: (7656) implies:
% 173.03/26.23  | | | | | | | | | | | |   (7657)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REDUCE: (532), (7655) imply:
% 173.03/26.23  | | | | | | | | | | | |   (7658)   ~ (all_6_2 = e0)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7659)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.23  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.23  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (52), (53), (62),
% 173.03/26.23  | | | | | | | | | | | | |            (156), (158), (159), (161), (163), (164), (165),
% 173.03/26.23  | | | | | | | | | | | | |            (167), (170), (172), (173), (174), (177), (178),
% 173.03/26.23  | | | | | | | | | | | | |            (179), (182), (183), (268), (270), (272), (273),
% 173.03/26.23  | | | | | | | | | | | | |            (274), (277), (279), (280), (282), (283), (304),
% 173.03/26.23  | | | | | | | | | | | | |            (307), (311), (313), (314), (315), (319), (321),
% 173.03/26.23  | | | | | | | | | | | | |            (323), (326), (328), (329), (330), (331), (344),
% 173.03/26.23  | | | | | | | | | | | | |            (349), (350), (359), (364), (370), (373), (385),
% 173.03/26.23  | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (415), (419),
% 173.03/26.23  | | | | | | | | | | | | |            (494), (529), (531), (532), (533), (534), (535),
% 173.03/26.23  | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.03/26.23  | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.03/26.23  | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.03/26.23  | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.03/26.23  | | | | | | | | | | | | |            (573), (579), (580), (581), (582), (583), (586),
% 173.03/26.23  | | | | | | | | | | | | |            (587), (588), (591), (593), (594), (595), (596),
% 173.03/26.23  | | | | | | | | | | | | |            (597), (598), (599), (600), (661), (663), (720),
% 173.03/26.23  | | | | | | | | | | | | |            (796), (7374), (7578), (7580), (7650), (7653),
% 173.03/26.23  | | | | | | | | | | | | |            (7657), (7658), (7659), (function-axioms) are
% 173.03/26.23  | | | | | | | | | | | | |            inconsistent by sub-proof #356.
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7660)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.23  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.23  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | REF_CLOSE: (4), (8), (42), (649), (7373), (7576), (7660),
% 173.03/26.23  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | |            #131.
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | |   (7661)  all_26_0 = e2
% 173.03/26.23  | | | | | | | | | |   (7662)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | COMBINE_EQS: (779), (7661) imply:
% 173.03/26.23  | | | | | | | | | |   (7663)  all_4_0 = e2
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | COMBINE_EQS: (742), (7663) imply:
% 173.03/26.23  | | | | | | | | | |   (7664)  all_50_0 = e2
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | REDUCE: (38), (7663) imply:
% 173.03/26.23  | | | | | | | | | |   (7665)  op(all_4_1, all_4_2) = e2
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | BETA: splitting (151) gives:
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | |   (7666)   ~ (all_50_0 = e2)
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | REDUCE: (7664), (7666) imply:
% 173.03/26.23  | | | | | | | | | | |   (7667)  $false
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | CLOSE: (7667) is inconsistent.
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | |   (7668)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7669)  all_58_15 = e0
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | COMBINE_EQS: (532), (7669) imply:
% 173.03/26.23  | | | | | | | | | | | |   (7670)  all_6_2 = e0
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REDUCE: (7373), (7670) imply:
% 173.03/26.23  | | | | | | | | | | | |   (7671)  op(all_6_1, e0) = e1
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REDUCE: (42), (7670) imply:
% 173.03/26.23  | | | | | | | | | | | |   (7672)  op(e0, e0) = all_6_1
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REDUCE: (41), (7670) imply:
% 173.03/26.23  | | | | | | | | | | | |   (7673)  op(e0, e0) = e0
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REF_CLOSE: (4), (7671), (7672), (7673), (function-axioms) are
% 173.03/26.23  | | | | | | | | | | | |            inconsistent by sub-proof #144.
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7674)   ~ (all_58_15 = e0)
% 173.03/26.23  | | | | | | | | | | | |   (7675)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.23  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.23  | | | | | | | | | | | |             e0)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | ALPHA: (7675) implies:
% 173.03/26.23  | | | | | | | | | | | |   (7676)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REDUCE: (532), (7674) imply:
% 173.03/26.23  | | | | | | | | | | | |   (7677)   ~ (all_6_2 = e0)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7678)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.23  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.23  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (37), (52), (53), (62),
% 173.03/26.23  | | | | | | | | | | | | |            (156), (158), (159), (163), (164), (165), (167),
% 173.03/26.23  | | | | | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 173.03/26.23  | | | | | | | | | | | | |            (179), (181), (182), (183), (268), (270), (272),
% 173.03/26.23  | | | | | | | | | | | | |            (273), (274), (275), (277), (278), (279), (280),
% 173.03/26.23  | | | | | | | | | | | | |            (281), (282), (283), (304), (307), (311), (313),
% 173.03/26.23  | | | | | | | | | | | | |            (314), (315), (319), (321), (323), (325), (326),
% 173.03/26.23  | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (344), (349),
% 173.03/26.23  | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.03/26.23  | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 173.03/26.23  | | | | | | | | | | | | |            (419), (503), (505), (521), (529), (530), (531),
% 173.03/26.23  | | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.03/26.23  | | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.23  | | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.03/26.23  | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.23  | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.03/26.23  | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.03/26.23  | | | | | | | | | | | | |            (585), (586), (587), (588), (591), (593), (594),
% 173.03/26.23  | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (661),
% 173.03/26.23  | | | | | | | | | | | | |            (698), (718), (720), (756), (796), (7374), (7377),
% 173.03/26.23  | | | | | | | | | | | | |            (7574), (7577), (7578), (7580), (7662), (7665),
% 173.03/26.23  | | | | | | | | | | | | |            (7668), (7676), (7677), (7678), (function-axioms)
% 173.03/26.23  | | | | | | | | | | | | |            are inconsistent by sub-proof #346.
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7679)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.23  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.23  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | BETA: splitting (7679) gives:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | |   (7680)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.23  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | REF_CLOSE: (8), (7576), (7680) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | | |            #373.
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | |   (7681)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.23  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7681),
% 173.03/26.23  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | | |            #138.
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | |   (7682)  all_24_0 = e1
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | COMBINE_EQS: (751), (7682) imply:
% 173.03/26.23  | | | | | | | | |   (7683)  all_10_0 = e1
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | SIMP: (7683) implies:
% 173.03/26.23  | | | | | | | | |   (7684)  all_10_0 = e1
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | REDUCE: (7374), (7684) imply:
% 173.03/26.23  | | | | | | | | |   (7685)   ~ (e3 = e1)
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | REDUCE: (53), (7684) imply:
% 173.03/26.23  | | | | | | | | |   (7686)  op(all_10_1, all_10_2) = e1
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | BETA: splitting (93) gives:
% 173.03/26.23  | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | |   (7687)   ~ (all_26_0 = e2)
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | REDUCE: (779), (7687) imply:
% 173.03/26.23  | | | | | | | | | |   (7688)   ~ (all_4_0 = e2)
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | |   (7689)   ~ (all_34_0 = e1)
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | REDUCE: (773), (7689) imply:
% 173.03/26.23  | | | | | | | | | | |   (7690)   ~ (all_4_0 = e1)
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | BETA: splitting (123) gives:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7691)   ~ (all_38_0 = e1)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REDUCE: (7372), (7691) imply:
% 173.03/26.23  | | | | | | | | | | | |   (7692)  $false
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | CLOSE: (7692) is inconsistent.
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7693)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7694)  all_58_15 = e0
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7694),
% 173.03/26.23  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | |            #143.
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7695)   ~ (all_58_15 = e0)
% 173.03/26.23  | | | | | | | | | | | | |   (7696)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.23  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.23  | | | | | | | | | | | | |             e0)
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | ALPHA: (7696) implies:
% 173.03/26.23  | | | | | | | | | | | | |   (7697)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | REDUCE: (532), (7695) imply:
% 173.03/26.23  | | | | | | | | | | | | |   (7698)   ~ (all_6_2 = e0)
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | |   (7699)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.23  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.23  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | BETA: splitting (7699) gives:
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | |   (7700)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.23  | | | | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | ALPHA: (7700) implies:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7701)  all_52_6 = e0
% 173.03/26.23  | | | | | | | | | | | | | | |   (7702)  all_52_4 = e1
% 173.03/26.23  | | | | | | | | | | | | | | |   (7703)  all_52_2 = e2
% 173.03/26.23  | | | | | | | | | | | | | | |   (7704)  all_52_0 = e3
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | COMBINE_EQS: (720), (7704) imply:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7705)  all_4_1 = e3
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | REDUCE: (38), (7705) imply:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7706)  op(e3, all_4_2) = all_4_0
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | REDUCE: (37), (7705) imply:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7707)  op(e3, all_4_2) = e3
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | REDUCE: (176), (7703) imply:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7708)  op(e2, all_52_3) = e2
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | REDUCE: (168), (7702) imply:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7709)  op(e1, all_52_5) = e1
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | REDUCE: (160), (7701) imply:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7710)  op(e0, all_52_7) = e0
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (42), (61), (154), (156), (158), (159),
% 173.03/26.23  | | | | | | | | | | | | | | |            (161), (163), (164), (165), (170), (172), (173),
% 173.03/26.23  | | | | | | | | | | | | | | |            (177), (178), (179), (268), (269), (270), (271),
% 173.03/26.23  | | | | | | | | | | | | | | |            (272), (273), (276), (279), (281), (283), (302),
% 173.03/26.23  | | | | | | | | | | | | | | |            (304), (305), (307), (310), (311), (312), (313),
% 173.03/26.23  | | | | | | | | | | | | | | |            (314), (315), (317), (319), (323), (324), (326),
% 173.03/26.23  | | | | | | | | | | | | | | |            (327), (328), (330), (331), (341), (344), (349),
% 173.03/26.23  | | | | | | | | | | | | | | |            (350), (359), (364), (370), (373), (385), (391),
% 173.03/26.23  | | | | | | | | | | | | | | |            (403), (409), (413), (425), (429), (517), (529),
% 173.03/26.23  | | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.23  | | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.23  | | | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 173.03/26.23  | | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.23  | | | | | | | | | | | | | | |            (566), (568), (569), (575), (578), (579), (580),
% 173.03/26.23  | | | | | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 173.03/26.23  | | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.03/26.23  | | | | | | | | | | | | | | |            (597), (598), (599), (600), (714), (7373), (7578),
% 173.03/26.23  | | | | | | | | | | | | | | |            (7688), (7690), (7693), (7697), (7698), (7706),
% 173.03/26.23  | | | | | | | | | | | | | | |            (7707), (7708), (7709), (7710), (function-axioms)
% 173.03/26.23  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #132.
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | |   (7711)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.23  | | | | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | ALPHA: (7711) implies:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7712)  all_52_10 = e2
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | COMBINE_EQS: (661), (7712) imply:
% 173.03/26.23  | | | | | | | | | | | | | | |   (7713)  all_10_1 = e2
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (7686), (7713), (function-axioms) are
% 173.03/26.23  | | | | | | | | | | | | | | |            inconsistent by sub-proof #446.
% 173.03/26.23  | | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | |   (7714)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.23  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.23  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (42), (649), (7373), (7576), (7714),
% 173.03/26.23  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | | |            #131.
% 173.03/26.23  | | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | |   (7715)  all_34_0 = e1
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | COMBINE_EQS: (773), (7715) imply:
% 173.03/26.23  | | | | | | | | | | |   (7716)  all_4_0 = e1
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | REDUCE: (7688), (7716) imply:
% 173.03/26.23  | | | | | | | | | | |   (7717)   ~ (e2 = e1)
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | REDUCE: (38), (7716) imply:
% 173.03/26.23  | | | | | | | | | | |   (7718)  op(all_4_1, all_4_2) = e1
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7719)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.23  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.23  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (52), (661), (720), (7686),
% 173.03/26.23  | | | | | | | | | | | |            (7718), (7719), (function-axioms) are inconsistent
% 173.03/26.23  | | | | | | | | | | | |            by sub-proof #441.
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | |   (7720)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.23  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.23  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | BETA: splitting (7720) gives:
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7721)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.23  | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | REF_CLOSE: (8), (7576), (7721) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | |            #373.
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | |   (7722)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.23  | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7722),
% 173.03/26.23  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.23  | | | | | | | | | | | | |            #138.
% 173.03/26.23  | | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | End of split
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | Case 2:
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | |   (7723)  all_26_0 = e2
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | COMBINE_EQS: (779), (7723) imply:
% 173.03/26.23  | | | | | | | | | |   (7724)  all_4_0 = e2
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | SIMP: (7724) implies:
% 173.03/26.23  | | | | | | | | | |   (7725)  all_4_0 = e2
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | REDUCE: (38), (7725) imply:
% 173.03/26.23  | | | | | | | | | |   (7726)  op(all_4_1, all_4_2) = e2
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.23  | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | Case 1:
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.23  | | | | | | | | | | |   (7727)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.23  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.23  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.23  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | REF_CLOSE: (6), (37), (52), (661), (720), (796), (7686),
% 173.03/26.24  | | | | | | | | | | |            (7726), (7727), (function-axioms) are inconsistent
% 173.03/26.24  | | | | | | | | | | |            by sub-proof #434.
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | |   (7728)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.24  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.24  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | BETA: splitting (7728) gives:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7729)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.24  | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | REF_CLOSE: (8), (7576), (7729) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | | |            #373.
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7730)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.24  | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7730),
% 173.03/26.24  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | | |            #138.
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | 
% 173.03/26.24  | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | 
% 173.03/26.24  | | | | | | | End of split
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | Case 2:
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | |   (7731)  all_18_0 = e3
% 173.03/26.24  | | | | | | |   (7732)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (37), (38), (41), (42), (52),
% 173.03/26.24  | | | | | | |            (53), (61), (62), (63), (88), (93), (113), (123),
% 173.03/26.24  | | | | | | |            (128), (151), (154), (155), (156), (158), (159), (160),
% 173.03/26.24  | | | | | | |            (161), (163), (164), (165), (167), (168), (169), (170),
% 173.03/26.24  | | | | | | |            (172), (173), (174), (176), (177), (178), (179), (181),
% 173.03/26.24  | | | | | | |            (182), (183), (185), (268), (269), (270), (271), (272),
% 173.03/26.24  | | | | | | |            (273), (274), (275), (276), (277), (278), (279), (280),
% 173.03/26.24  | | | | | | |            (281), (282), (283), (301), (302), (303), (304), (305),
% 173.03/26.24  | | | | | | |            (307), (310), (311), (312), (313), (314), (315), (316),
% 173.03/26.24  | | | | | | |            (317), (319), (320), (321), (323), (324), (325), (326),
% 173.03/26.24  | | | | | | |            (327), (328), (329), (330), (331), (341), (344), (349),
% 173.03/26.24  | | | | | | |            (350), (359), (364), (365), (370), (373), (385), (386),
% 173.03/26.24  | | | | | | |            (391), (392), (403), (409), (413), (415), (419), (425),
% 173.03/26.24  | | | | | | |            (429), (494), (503), (514), (517), (518), (521), (529),
% 173.03/26.24  | | | | | | |            (530), (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.24  | | | | | | |            (538), (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.24  | | | | | | |            (552), (553), (554), (555), (556), (557), (558), (559),
% 173.03/26.24  | | | | | | |            (560), (561), (562), (563), (564), (565), (566), (567),
% 173.03/26.24  | | | | | | |            (568), (569), (571), (573), (575), (577), (578), (579),
% 173.03/26.24  | | | | | | |            (580), (581), (582), (583), (584), (585), (586), (587),
% 173.03/26.24  | | | | | | |            (588), (589), (591), (593), (594), (595), (596), (597),
% 173.03/26.24  | | | | | | |            (598), (599), (600), (649), (661), (663), (698), (714),
% 173.03/26.24  | | | | | | |            (715), (718), (719), (720), (742), (751), (770), (773),
% 173.03/26.24  | | | | | | |            (779), (789), (796), (7372), (7373), (7374), (7377),
% 173.03/26.24  | | | | | | |            (7731), (7732), (function-axioms) are inconsistent by
% 173.03/26.24  | | | | | | |            sub-proof #129.
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | End of split
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | Case 2:
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | |   (7733)  all_14_0 = e2
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | | REDUCE: (63), (7733) imply:
% 173.03/26.24  | | | | | |   (7734)  op(all_14_1, all_14_2) = e2
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41),
% 173.03/26.24  | | | | | |            (42), (52), (53), (61), (62), (88), (93), (113), (123),
% 173.03/26.24  | | | | | |            (128), (151), (154), (155), (156), (158), (159), (160),
% 173.03/26.24  | | | | | |            (161), (163), (164), (165), (167), (168), (169), (170),
% 173.03/26.24  | | | | | |            (172), (173), (174), (176), (177), (178), (179), (181),
% 173.03/26.24  | | | | | |            (182), (183), (185), (268), (269), (270), (271), (272),
% 173.03/26.24  | | | | | |            (273), (274), (275), (276), (277), (278), (279), (280),
% 173.03/26.24  | | | | | |            (281), (282), (283), (301), (302), (303), (304), (305),
% 173.03/26.24  | | | | | |            (307), (310), (311), (312), (313), (314), (315), (316),
% 173.03/26.24  | | | | | |            (317), (319), (320), (321), (322), (323), (324), (325),
% 173.03/26.24  | | | | | |            (326), (327), (328), (329), (330), (331), (341), (344),
% 173.03/26.24  | | | | | |            (349), (350), (359), (364), (365), (370), (373), (385),
% 173.03/26.24  | | | | | |            (386), (391), (392), (403), (409), (413), (415), (419),
% 173.03/26.24  | | | | | |            (425), (429), (494), (503), (517), (518), (521), (529),
% 173.03/26.24  | | | | | |            (530), (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.24  | | | | | |            (538), (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.24  | | | | | |            (552), (553), (554), (555), (556), (557), (558), (559),
% 173.03/26.24  | | | | | |            (560), (561), (562), (563), (564), (565), (566), (567),
% 173.03/26.24  | | | | | |            (568), (569), (571), (573), (575), (577), (578), (579),
% 173.03/26.24  | | | | | |            (580), (581), (582), (583), (584), (585), (586), (587),
% 173.03/26.24  | | | | | |            (588), (589), (591), (593), (594), (595), (596), (597),
% 173.03/26.24  | | | | | |            (598), (599), (600), (649), (661), (663), (698), (714),
% 173.03/26.24  | | | | | |            (715), (718), (719), (720), (742), (751), (770), (773),
% 173.03/26.24  | | | | | |            (779), (796), (7372), (7373), (7374), (7734),
% 173.03/26.24  | | | | | |            (function-axioms) are inconsistent by sub-proof #126.
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | End of split
% 173.03/26.24  | | | | | 
% 173.03/26.24  | | | | Case 2:
% 173.03/26.24  | | | | | 
% 173.03/26.24  | | | | |   (7735)  all_12_1 = e3
% 173.03/26.24  | | | | | 
% 173.03/26.24  | | | | | COMBINE_EQS: (705), (7735) imply:
% 173.03/26.24  | | | | |   (7736)  all_10_1 = e3
% 173.03/26.24  | | | | | 
% 173.03/26.24  | | | | | COMBINE_EQS: (661), (7736) imply:
% 173.03/26.24  | | | | |   (7737)  all_52_10 = e3
% 173.03/26.24  | | | | | 
% 173.03/26.24  | | | | | REDUCE: (52), (7736) imply:
% 173.03/26.24  | | | | |   (7738)  op(e2, all_10_2) = e3
% 173.03/26.24  | | | | | 
% 173.03/26.24  | | | | | BETA: splitting (64) gives:
% 173.03/26.24  | | | | | 
% 173.03/26.24  | | | | | Case 1:
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | |   (7739)   ~ (all_14_0 = e2)
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | | BETA: splitting (74) gives:
% 173.03/26.24  | | | | | | 
% 173.03/26.24  | | | | | | Case 1:
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | |   (7740)   ~ (all_18_0 = e3)
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | | REDUCE: (789), (7740) imply:
% 173.03/26.24  | | | | | | |   (7741)   ~ (all_14_0 = e3)
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | | BETA: splitting (93) gives:
% 173.03/26.24  | | | | | | | 
% 173.03/26.24  | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | 
% 173.03/26.24  | | | | | | | |   (7742)   ~ (all_26_0 = e2)
% 173.03/26.24  | | | | | | | | 
% 173.03/26.24  | | | | | | | | REDUCE: (779), (7742) imply:
% 173.03/26.24  | | | | | | | |   (7743)   ~ (all_4_0 = e2)
% 173.03/26.24  | | | | | | | | 
% 173.03/26.24  | | | | | | | | BETA: splitting (113) gives:
% 173.03/26.24  | | | | | | | | 
% 173.03/26.24  | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | 
% 173.03/26.24  | | | | | | | | |   (7744)   ~ (all_34_0 = e1)
% 173.03/26.24  | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | REDUCE: (773), (7744) imply:
% 173.03/26.24  | | | | | | | | |   (7745)   ~ (all_4_0 = e1)
% 173.03/26.24  | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | BETA: splitting (128) gives:
% 173.03/26.24  | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | |   (7746)   ~ (all_40_1 = e1)
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | REDUCE: (715), (7746) imply:
% 173.03/26.24  | | | | | | | | | |   (7747)   ~ (all_4_1 = e1)
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | |   (7748)  all_58_15 = e0
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7748),
% 173.03/26.24  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | |            #143.
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | |   (7749)   ~ (all_58_15 = e0)
% 173.03/26.24  | | | | | | | | | | |   (7750)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.24  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.24  | | | | | | | | | | |             e0)
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | ALPHA: (7750) implies:
% 173.03/26.24  | | | | | | | | | | |   (7751)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.24  | | | | | | | | | | |   (7752)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | REDUCE: (532), (7749) imply:
% 173.03/26.24  | | | | | | | | | | |   (7753)   ~ (all_6_2 = e0)
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7754)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.24  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.24  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (41), (61), (154), (155),
% 173.03/26.24  | | | | | | | | | | | |            (156), (158), (159), (160), (161), (163), (164),
% 173.03/26.24  | | | | | | | | | | | |            (165), (167), (168), (169), (170), (172), (173),
% 173.03/26.24  | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 173.03/26.24  | | | | | | | | | | | |            (271), (272), (273), (276), (278), (279), (280),
% 173.03/26.24  | | | | | | | | | | | |            (281), (282), (283), (304), (305), (306), (307),
% 173.03/26.24  | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (317),
% 173.03/26.24  | | | | | | | | | | | |            (319), (323), (324), (326), (327), (328), (330),
% 173.03/26.24  | | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.03/26.24  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.03/26.24  | | | | | | | | | | | |            (409), (413), (425), (429), (529), (530), (531),
% 173.03/26.24  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.03/26.24  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.24  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.03/26.24  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.03/26.24  | | | | | | | | | | | |            (566), (567), (568), (569), (575), (578), (579),
% 173.03/26.24  | | | | | | | | | | | |            (580), (581), (582), (583), (584), (585), (586),
% 173.03/26.24  | | | | | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 173.03/26.24  | | | | | | | | | | | |            (596), (597), (598), (599), (600), (720), (796),
% 173.03/26.24  | | | | | | | | | | | |            (7737), (7738), (7747), (7752), (7753), (7754),
% 173.03/26.24  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | | |            #268.
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7755)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.24  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.24  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | BETA: splitting (7755) gives:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | |   (7756)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.24  | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | | ALPHA: (7756) implies:
% 173.03/26.24  | | | | | | | | | | | | |   (7757)  all_52_22 = e0
% 173.03/26.24  | | | | | | | | | | | | |   (7758)  all_52_20 = e1
% 173.03/26.24  | | | | | | | | | | | | |   (7759)  all_52_18 = e2
% 173.03/26.24  | | | | | | | | | | | | |   (7760)  all_52_16 = e3
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | | COMBINE_EQS: (719), (7758) imply:
% 173.03/26.24  | | | | | | | | | | | | |   (7761)  all_14_1 = e1
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | | SIMP: (7761) implies:
% 173.03/26.24  | | | | | | | | | | | | |   (7762)  all_14_1 = e1
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (42), (62),
% 173.03/26.24  | | | | | | | | | | | | |            (63), (154), (155), (156), (158), (161), (163),
% 173.03/26.24  | | | | | | | | | | | | |            (164), (165), (169), (172), (173), (174), (177),
% 173.03/26.24  | | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (269),
% 173.03/26.24  | | | | | | | | | | | | |            (270), (271), (273), (274), (275), (276), (277),
% 173.03/26.24  | | | | | | | | | | | | |            (281), (282), (283), (304), (306), (307), (308),
% 173.03/26.24  | | | | | | | | | | | | |            (310), (311), (312), (313), (314), (315), (319),
% 173.03/26.24  | | | | | | | | | | | | |            (320), (321), (322), (323), (324), (325), (326),
% 173.03/26.24  | | | | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 173.03/26.24  | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (391),
% 173.03/26.24  | | | | | | | | | | | | |            (392), (403), (413), (415), (419), (425), (429),
% 173.03/26.24  | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.03/26.24  | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.03/26.24  | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.03/26.24  | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.03/26.24  | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.03/26.24  | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.03/26.24  | | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 173.03/26.24  | | | | | | | | | | | | |            (593), (595), (596), (597), (598), (599), (600),
% 173.03/26.24  | | | | | | | | | | | | |            (796), (7738), (7739), (7741), (7743), (7745),
% 173.03/26.24  | | | | | | | | | | | | |            (7747), (7751), (7752), (7753), (7757), (7759),
% 173.03/26.24  | | | | | | | | | | | | |            (7760), (7762), (function-axioms) are inconsistent
% 173.03/26.24  | | | | | | | | | | | | |            by sub-proof #267.
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | |   (7763)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.24  | | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7763),
% 173.03/26.24  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | | | |            #138.
% 173.03/26.24  | | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | |   (7764)  all_40_1 = e1
% 173.03/26.24  | | | | | | | | | |   (7765)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | COMBINE_EQS: (715), (7764) imply:
% 173.03/26.24  | | | | | | | | | |   (7766)  all_4_1 = e1
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | SIMP: (7766) implies:
% 173.03/26.24  | | | | | | | | | |   (7767)  all_4_1 = e1
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | COMBINE_EQS: (720), (7767) imply:
% 173.03/26.24  | | | | | | | | | |   (7768)  all_52_0 = e1
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | REDUCE: (38), (7767) imply:
% 173.03/26.24  | | | | | | | | | |   (7769)  op(e1, all_4_2) = all_4_0
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | REDUCE: (37), (7767) imply:
% 173.03/26.24  | | | | | | | | | |   (7770)  op(e3, all_4_2) = e1
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | |   (7771)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.24  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.24  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | BETA: splitting (7771) gives:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7772)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.24  | | | | | | | | | | | |           all_52_6 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | REF_CLOSE: (8), (7768), (7772) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | | |            #632.
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7773)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.03/26.24  | | | | | | | | | | | |           all_52_14 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | REF_CLOSE: (9), (7737), (7773) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | | |            #289.
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | |   (7774)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.24  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.24  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | BETA: splitting (7774) gives:
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 1:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7775)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.24  | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (62), (63),
% 173.03/26.24  | | | | | | | | | | | |            (154), (155), (156), (158), (163), (164), (165),
% 173.03/26.24  | | | | | | | | | | | |            (169), (172), (174), (177), (178), (179), (181),
% 173.03/26.24  | | | | | | | | | | | |            (182), (183), (268), (269), (270), (271), (272),
% 173.03/26.24  | | | | | | | | | | | |            (273), (274), (275), (276), (277), (281), (283),
% 173.03/26.24  | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.03/26.24  | | | | | | | | | | | |            (310), (311), (313), (314), (315), (319), (320),
% 173.03/26.24  | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 173.03/26.24  | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.03/26.24  | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (391),
% 173.03/26.24  | | | | | | | | | | | |            (403), (413), (415), (419), (425), (429), (518),
% 173.03/26.24  | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.03/26.24  | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.03/26.24  | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.03/26.24  | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.03/26.24  | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.03/26.24  | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.03/26.24  | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (591),
% 173.03/26.24  | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 173.03/26.24  | | | | | | | | | | | |            (719), (770), (796), (7738), (7739), (7741),
% 173.03/26.24  | | | | | | | | | | | |            (7743), (7745), (7765), (7769), (7770), (7775),
% 173.03/26.24  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.24  | | | | | | | | | | | |            #266.
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | Case 2:
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | |   (7776)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.24  | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | ALPHA: (7776) implies:
% 173.03/26.24  | | | | | | | | | | | |   (7777)  all_52_30 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | COMBINE_EQS: (649), (7777) imply:
% 173.03/26.24  | | | | | | | | | | | |   (7778)  all_6_1 = e0
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | | REF_CLOSE: (4), (42), (7373), (7778), (function-axioms) are
% 173.03/26.24  | | | | | | | | | | | |            inconsistent by sub-proof #139.
% 173.03/26.24  | | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | | 
% 173.03/26.24  | | | | | | | | | End of split
% 173.03/26.24  | | | | | | | | | 
% 173.03/26.24  | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | |   (7779)  all_34_0 = e1
% 173.03/26.25  | | | | | | | | |   (7780)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | COMBINE_EQS: (773), (7779) imply:
% 173.03/26.25  | | | | | | | | |   (7781)  all_4_0 = e1
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | REDUCE: (38), (7781) imply:
% 173.03/26.25  | | | | | | | | |   (7782)  op(all_4_1, all_4_2) = e1
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | |   (7783)  all_58_15 = e0
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7783),
% 173.03/26.25  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.25  | | | | | | | | | |            #143.
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | |   (7784)   ~ (all_58_15 = e0)
% 173.03/26.25  | | | | | | | | | |   (7785)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.25  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.25  | | | | | | | | | |             e0)
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | ALPHA: (7785) implies:
% 173.03/26.25  | | | | | | | | | |   (7786)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | REDUCE: (532), (7784) imply:
% 173.03/26.25  | | | | | | | | | |   (7787)   ~ (all_6_2 = e0)
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | |   (7788)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.25  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.25  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (37), (41), (61), (154),
% 173.03/26.25  | | | | | | | | | | |            (155), (156), (158), (159), (160), (161), (163),
% 173.03/26.25  | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (172),
% 173.03/26.25  | | | | | | | | | | |            (173), (176), (177), (178), (179), (268), (269),
% 173.03/26.25  | | | | | | | | | | |            (270), (271), (272), (273), (276), (278), (279),
% 173.03/26.25  | | | | | | | | | | |            (280), (281), (282), (283), (304), (305), (306),
% 173.03/26.25  | | | | | | | | | | |            (307), (310), (311), (312), (313), (314), (315),
% 173.03/26.25  | | | | | | | | | | |            (317), (319), (323), (324), (326), (327), (328),
% 173.03/26.25  | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 173.03/26.25  | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 173.03/26.25  | | | | | | | | | | |            (403), (409), (413), (425), (429), (529), (530),
% 173.03/26.25  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.25  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.25  | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.03/26.25  | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.03/26.25  | | | | | | | | | | |            (565), (566), (567), (568), (569), (575), (578),
% 173.03/26.25  | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 173.03/26.25  | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.03/26.25  | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (720),
% 173.03/26.25  | | | | | | | | | | |            (796), (7737), (7738), (7786), (7787), (7788),
% 173.03/26.25  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.25  | | | | | | | | | | |            #265.
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | |   (7789)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.25  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.25  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | BETA: splitting (7789) gives:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | |   (7790)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.25  | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | | ALPHA: (7790) implies:
% 173.03/26.25  | | | | | | | | | | | |   (7791)  all_52_22 = e0
% 173.03/26.25  | | | | | | | | | | | |   (7792)  all_52_20 = e1
% 173.03/26.25  | | | | | | | | | | | |   (7793)  all_52_18 = e2
% 173.03/26.25  | | | | | | | | | | | |   (7794)  all_52_16 = e3
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | | COMBINE_EQS: (719), (7792) imply:
% 173.03/26.25  | | | | | | | | | | | |   (7795)  all_14_1 = e1
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | | SIMP: (7795) implies:
% 173.03/26.25  | | | | | | | | | | | |   (7796)  all_14_1 = e1
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (37), (62), (63), (154), (156),
% 173.03/26.25  | | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (172),
% 173.03/26.25  | | | | | | | | | | | |            (174), (177), (178), (179), (181), (182), (183),
% 173.03/26.25  | | | | | | | | | | | |            (268), (274), (275), (280), (281), (282), (283),
% 173.03/26.25  | | | | | | | | | | | |            (304), (307), (310), (311), (313), (314), (319),
% 173.03/26.25  | | | | | | | | | | | |            (320), (321), (322), (323), (326), (328), (329),
% 173.03/26.25  | | | | | | | | | | | |            (330), (331), (349), (364), (365), (370), (373),
% 173.03/26.25  | | | | | | | | | | | |            (385), (386), (391), (392), (403), (413), (419),
% 173.03/26.25  | | | | | | | | | | | |            (494), (529), (531), (532), (533), (534), (535),
% 173.03/26.25  | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.03/26.25  | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.03/26.25  | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.03/26.25  | | | | | | | | | | | |            (564), (566), (567), (568), (575), (578), (579),
% 173.03/26.25  | | | | | | | | | | | |            (580), (582), (583), (584), (585), (586), (591),
% 173.03/26.25  | | | | | | | | | | | |            (593), (594), (596), (597), (600), (663), (796),
% 173.03/26.25  | | | | | | | | | | | |            (7741), (7780), (7782), (7786), (7787), (7791),
% 173.03/26.25  | | | | | | | | | | | |            (7793), (7794), (7796), (function-axioms) are
% 173.03/26.25  | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | |   (7797)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.03/26.25  | | | | | | | | | | | |           all_52_30 = e0
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7797),
% 173.03/26.25  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.25  | | | | | | | | | | | |            #138.
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | End of split
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | End of split
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | End of split
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | End of split
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | |   (7798)  all_26_0 = e2
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | COMBINE_EQS: (779), (7798) imply:
% 173.03/26.25  | | | | | | | |   (7799)  all_4_0 = e2
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | SIMP: (7799) implies:
% 173.03/26.25  | | | | | | | |   (7800)  all_4_0 = e2
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | COMBINE_EQS: (742), (7800) imply:
% 173.03/26.25  | | | | | | | |   (7801)  all_50_0 = e2
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | REDUCE: (38), (7800) imply:
% 173.03/26.25  | | | | | | | |   (7802)  op(all_4_1, all_4_2) = e2
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | BETA: splitting (151) gives:
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | |   (7803)   ~ (all_50_0 = e2)
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | REDUCE: (7801), (7803) imply:
% 173.03/26.25  | | | | | | | | |   (7804)  $false
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | CLOSE: (7804) is inconsistent.
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | |   (7805)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | |   (7806)  all_58_15 = e0
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7806),
% 173.03/26.25  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.25  | | | | | | | | | |            #143.
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | |   (7807)   ~ (all_58_15 = e0)
% 173.03/26.25  | | | | | | | | | |   (7808)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.25  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.25  | | | | | | | | | |             e0)
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | ALPHA: (7808) implies:
% 173.03/26.25  | | | | | | | | | |   (7809)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | REDUCE: (532), (7807) imply:
% 173.03/26.25  | | | | | | | | | |   (7810)   ~ (all_6_2 = e0)
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | |   (7811)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.25  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.25  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (37), (41), (61), (154),
% 173.03/26.25  | | | | | | | | | | |            (155), (156), (158), (159), (160), (161), (163),
% 173.03/26.25  | | | | | | | | | | |            (164), (165), (167), (168), (169), (170), (172),
% 173.03/26.25  | | | | | | | | | | |            (173), (176), (177), (178), (179), (268), (269),
% 173.03/26.25  | | | | | | | | | | |            (270), (271), (272), (273), (276), (278), (279),
% 173.03/26.25  | | | | | | | | | | |            (280), (281), (282), (283), (304), (305), (306),
% 173.03/26.25  | | | | | | | | | | |            (307), (310), (311), (312), (313), (314), (315),
% 173.03/26.25  | | | | | | | | | | |            (317), (319), (323), (324), (326), (327), (328),
% 173.03/26.25  | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 173.03/26.25  | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 173.03/26.25  | | | | | | | | | | |            (403), (409), (413), (425), (429), (529), (530),
% 173.03/26.25  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.25  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.25  | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.03/26.25  | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.03/26.25  | | | | | | | | | | |            (565), (566), (567), (568), (569), (575), (578),
% 173.03/26.25  | | | | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 173.03/26.25  | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.03/26.25  | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (720),
% 173.03/26.25  | | | | | | | | | | |            (796), (7737), (7738), (7809), (7810), (7811),
% 173.03/26.25  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.25  | | | | | | | | | | |            #265.
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | |   (7812)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.25  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.25  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 173.03/26.25  | | | | | | | | | | |            (156), (158), (161), (163), (164), (165), (172),
% 173.03/26.25  | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.03/26.25  | | | | | | | | | | |            (183), (268), (270), (273), (274), (275), (276),
% 173.03/26.25  | | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (310),
% 173.03/26.25  | | | | | | | | | | |            (311), (315), (319), (321), (323), (324), (325),
% 173.03/26.25  | | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 173.03/26.25  | | | | | | | | | | |            (359), (364), (365), (370), (385), (386), (391),
% 173.03/26.25  | | | | | | | | | | |            (392), (403), (413), (419), (425), (521), (529),
% 173.03/26.25  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.25  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.25  | | | | | | | | | | |            (550), (552), (553), (554), (557), (558), (559),
% 173.03/26.25  | | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 173.03/26.25  | | | | | | | | | | |            (568), (569), (577), (579), (580), (582), (584),
% 173.03/26.25  | | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (598),
% 173.03/26.25  | | | | | | | | | | |            (600), (649), (718), (719), (796), (7373), (7739),
% 173.03/26.25  | | | | | | | | | | |            (7741), (7802), (7805), (7809), (7812),
% 173.03/26.25  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.25  | | | | | | | | | | |            #135.
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | End of split
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | End of split
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | End of split
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | End of split
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | Case 2:
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | |   (7813)  all_18_0 = e3
% 173.03/26.25  | | | | | | |   (7814)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (37), (38), (41), (42), (52),
% 173.03/26.25  | | | | | | |            (53), (61), (62), (63), (88), (93), (113), (123),
% 173.03/26.25  | | | | | | |            (128), (151), (154), (155), (156), (158), (159), (160),
% 173.03/26.25  | | | | | | |            (161), (163), (164), (165), (167), (168), (169), (170),
% 173.03/26.25  | | | | | | |            (172), (173), (174), (176), (177), (178), (179), (181),
% 173.03/26.25  | | | | | | |            (182), (183), (185), (268), (269), (270), (271), (272),
% 173.03/26.25  | | | | | | |            (273), (274), (275), (276), (277), (278), (279), (280),
% 173.03/26.25  | | | | | | |            (281), (282), (283), (301), (302), (303), (304), (305),
% 173.03/26.25  | | | | | | |            (307), (310), (311), (312), (313), (314), (315), (316),
% 173.03/26.25  | | | | | | |            (317), (319), (320), (321), (323), (324), (325), (326),
% 173.03/26.25  | | | | | | |            (327), (328), (329), (330), (331), (341), (344), (349),
% 173.03/26.25  | | | | | | |            (350), (359), (364), (365), (370), (373), (385), (386),
% 173.03/26.25  | | | | | | |            (391), (392), (403), (409), (413), (415), (419), (425),
% 173.03/26.25  | | | | | | |            (429), (494), (503), (514), (517), (518), (521), (529),
% 173.03/26.25  | | | | | | |            (530), (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.25  | | | | | | |            (538), (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.25  | | | | | | |            (552), (553), (554), (555), (556), (557), (558), (559),
% 173.03/26.25  | | | | | | |            (560), (561), (562), (563), (564), (565), (566), (567),
% 173.03/26.25  | | | | | | |            (568), (569), (571), (573), (575), (577), (578), (579),
% 173.03/26.25  | | | | | | |            (580), (581), (582), (583), (584), (585), (586), (587),
% 173.03/26.25  | | | | | | |            (588), (589), (591), (593), (594), (595), (596), (597),
% 173.03/26.25  | | | | | | |            (598), (599), (600), (649), (661), (663), (698), (714),
% 173.03/26.25  | | | | | | |            (715), (718), (719), (720), (742), (751), (770), (773),
% 173.03/26.25  | | | | | | |            (779), (789), (796), (7372), (7373), (7374), (7739),
% 173.03/26.25  | | | | | | |            (7813), (7814), (function-axioms) are inconsistent by
% 173.03/26.25  | | | | | | |            sub-proof #129.
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | End of split
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | Case 2:
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | |   (7815)  all_14_0 = e2
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | | REDUCE: (63), (7815) imply:
% 173.03/26.25  | | | | | |   (7816)  op(all_14_1, all_14_2) = e2
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (41),
% 173.03/26.25  | | | | | |            (42), (52), (53), (61), (62), (88), (93), (113), (123),
% 173.03/26.25  | | | | | |            (128), (151), (154), (155), (156), (158), (159), (160),
% 173.03/26.25  | | | | | |            (161), (163), (164), (165), (167), (168), (169), (170),
% 173.03/26.25  | | | | | |            (172), (173), (174), (176), (177), (178), (179), (181),
% 173.03/26.25  | | | | | |            (182), (183), (185), (268), (269), (270), (271), (272),
% 173.03/26.25  | | | | | |            (273), (274), (275), (276), (277), (278), (279), (280),
% 173.03/26.25  | | | | | |            (281), (282), (283), (301), (302), (303), (304), (305),
% 173.03/26.25  | | | | | |            (307), (310), (311), (312), (313), (314), (315), (316),
% 173.03/26.25  | | | | | |            (317), (319), (320), (321), (322), (323), (324), (325),
% 173.03/26.25  | | | | | |            (326), (327), (328), (329), (330), (331), (341), (344),
% 173.03/26.25  | | | | | |            (349), (350), (359), (364), (365), (370), (373), (385),
% 173.03/26.25  | | | | | |            (386), (391), (392), (403), (409), (413), (415), (419),
% 173.03/26.25  | | | | | |            (425), (429), (494), (503), (517), (518), (521), (529),
% 173.03/26.25  | | | | | |            (530), (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.25  | | | | | |            (538), (539), (540), (542), (544), (546), (548), (550),
% 173.03/26.25  | | | | | |            (552), (553), (554), (555), (556), (557), (558), (559),
% 173.03/26.25  | | | | | |            (560), (561), (562), (563), (564), (565), (566), (567),
% 173.03/26.25  | | | | | |            (568), (569), (571), (573), (575), (577), (578), (579),
% 173.03/26.25  | | | | | |            (580), (581), (582), (583), (584), (585), (586), (587),
% 173.03/26.25  | | | | | |            (588), (589), (591), (593), (594), (595), (596), (597),
% 173.03/26.25  | | | | | |            (598), (599), (600), (649), (661), (663), (698), (714),
% 173.03/26.25  | | | | | |            (715), (718), (719), (720), (742), (751), (770), (773),
% 173.03/26.25  | | | | | |            (779), (796), (7372), (7373), (7374), (7816),
% 173.03/26.25  | | | | | |            (function-axioms) are inconsistent by sub-proof #126.
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | End of split
% 173.03/26.25  | | | | | 
% 173.03/26.25  | | | | End of split
% 173.03/26.25  | | | | 
% 173.03/26.25  | | | Case 2:
% 173.03/26.25  | | | | 
% 173.03/26.25  | | | |   (7817)  all_10_0 = e3
% 173.03/26.25  | | | | 
% 173.03/26.25  | | | | REDUCE: (53), (7817) imply:
% 173.03/26.25  | | | |   (7818)  op(all_10_1, all_10_2) = e3
% 173.03/26.25  | | | | 
% 173.03/26.25  | | | | BETA: splitting (64) gives:
% 173.03/26.25  | | | | 
% 173.03/26.25  | | | | Case 1:
% 173.03/26.25  | | | | | 
% 173.03/26.25  | | | | |   (7819)   ~ (all_14_0 = e2)
% 173.03/26.25  | | | | | 
% 173.03/26.25  | | | | | BETA: splitting (74) gives:
% 173.03/26.25  | | | | | 
% 173.03/26.25  | | | | | Case 1:
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | |   (7820)   ~ (all_18_0 = e3)
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | | REDUCE: (789), (7820) imply:
% 173.03/26.25  | | | | | |   (7821)   ~ (all_14_0 = e3)
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | | BETA: splitting (93) gives:
% 173.03/26.25  | | | | | | 
% 173.03/26.25  | | | | | | Case 1:
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | |   (7822)   ~ (all_26_0 = e2)
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | | REDUCE: (779), (7822) imply:
% 173.03/26.25  | | | | | | |   (7823)   ~ (all_4_0 = e2)
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | | BETA: splitting (113) gives:
% 173.03/26.25  | | | | | | | 
% 173.03/26.25  | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | |   (7824)   ~ (all_34_0 = e1)
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | REDUCE: (773), (7824) imply:
% 173.03/26.25  | | | | | | | |   (7825)   ~ (all_4_0 = e1)
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | BETA: splitting (123) gives:
% 173.03/26.25  | | | | | | | | 
% 173.03/26.25  | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | |   (7826)   ~ (all_38_0 = e1)
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | REDUCE: (7372), (7826) imply:
% 173.03/26.25  | | | | | | | | |   (7827)  $false
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | CLOSE: (7827) is inconsistent.
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | |   (7828)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | BETA: splitting (128) gives:
% 173.03/26.25  | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | |   (7829)   ~ (all_40_1 = e1)
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | REDUCE: (715), (7829) imply:
% 173.03/26.25  | | | | | | | | | |   (7830)   ~ (all_4_1 = e1)
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | BETA: splitting (301) gives:
% 173.03/26.25  | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | |   (7831)  all_58_15 = e0
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7831),
% 173.03/26.25  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.25  | | | | | | | | | | |            #143.
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | Case 2:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | |   (7832)   ~ (all_58_15 = e0)
% 173.03/26.25  | | | | | | | | | | |   (7833)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.03/26.25  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.03/26.25  | | | | | | | | | | |             e0)
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | ALPHA: (7833) implies:
% 173.03/26.25  | | | | | | | | | | |   (7834)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.03/26.25  | | | | | | | | | | |   (7835)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | REDUCE: (532), (7832) imply:
% 173.03/26.25  | | | | | | | | | | |   (7836)   ~ (all_6_2 = e0)
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.03/26.25  | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | Case 1:
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.25  | | | | | | | | | | | |   (7837)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.03/26.25  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.03/26.25  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.03/26.25  | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (38), (42), (52), (61),
% 173.03/26.26  | | | | | | | | | | | |            (154), (156), (158), (159), (160), (161), (163),
% 173.03/26.26  | | | | | | | | | | | |            (164), (165), (168), (169), (170), (172), (173),
% 173.03/26.26  | | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 173.03/26.26  | | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 173.03/26.26  | | | | | | | | | | | |            (283), (302), (304), (305), (307), (310), (311),
% 173.03/26.26  | | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 173.03/26.26  | | | | | | | | | | | |            (324), (326), (327), (328), (330), (331), (341),
% 173.03/26.26  | | | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 173.03/26.26  | | | | | | | | | | | |            (385), (391), (392), (403), (409), (413), (425),
% 173.03/26.26  | | | | | | | | | | | |            (429), (517), (529), (531), (532), (533), (534),
% 173.03/26.26  | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.03/26.26  | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.03/26.26  | | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.03/26.26  | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (575),
% 173.03/26.26  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.03/26.26  | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 173.03/26.26  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.03/26.26  | | | | | | | | | | | |            (661), (714), (720), (7373), (7818), (7823),
% 173.03/26.26  | | | | | | | | | | | |            (7825), (7828), (7835), (7836), (7837),
% 173.03/26.26  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.03/26.26  | | | | | | | | | | | |            #125.
% 173.03/26.26  | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | Case 2:
% 173.03/26.26  | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | |   (7838)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.03/26.26  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.03/26.26  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.03/26.26  | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | BETA: splitting (7838) gives:
% 173.03/26.26  | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | Case 1:
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | |   (7839)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.03/26.26  | | | | | | | | | | | | |           all_52_22 = e0
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | ALPHA: (7839) implies:
% 173.03/26.26  | | | | | | | | | | | | |   (7840)  all_52_22 = e0
% 173.03/26.26  | | | | | | | | | | | | |   (7841)  all_52_20 = e1
% 173.03/26.26  | | | | | | | | | | | | |   (7842)  all_52_18 = e2
% 173.03/26.26  | | | | | | | | | | | | |   (7843)  all_52_16 = e3
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | COMBINE_EQS: (719), (7841) imply:
% 173.03/26.26  | | | | | | | | | | | | |   (7844)  all_14_1 = e1
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | SIMP: (7844) implies:
% 173.03/26.26  | | | | | | | | | | | | |   (7845)  all_14_1 = e1
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | REDUCE: (63), (7845) imply:
% 173.03/26.26  | | | | | | | | | | | | |   (7846)  op(e1, all_14_2) = all_14_0
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | REDUCE: (182), (7843) imply:
% 173.03/26.26  | | | | | | | | | | | | |   (7847)  op(e3, all_52_17) = e3
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | REDUCE: (174), (7842) imply:
% 173.03/26.26  | | | | | | | | | | | | |   (7848)  op(e2, all_52_19) = e2
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | REDUCE: (62), (7845) imply:
% 173.03/26.26  | | | | | | | | | | | | |   (7849)  op(e1, all_14_2) = e1
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | REDUCE: (158), (7840) imply:
% 173.03/26.26  | | | | | | | | | | | | |   (7850)  op(e0, all_52_23) = e0
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (38), (52), (155),
% 173.03/26.26  | | | | | | | | | | | | |            (156), (161), (163), (164), (165), (169), (170),
% 173.03/26.26  | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (183),
% 173.03/26.26  | | | | | | | | | | | | |            (268), (270), (271), (273), (274), (275), (276),
% 173.03/26.26  | | | | | | | | | | | | |            (278), (281), (282), (283), (304), (306), (307),
% 173.03/26.26  | | | | | | | | | | | | |            (308), (310), (311), (312), (313), (314), (315),
% 173.03/26.26  | | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (326),
% 173.03/26.26  | | | | | | | | | | | | |            (328), (329), (330), (331), (344), (349), (359),
% 173.03/26.26  | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (392),
% 173.03/26.26  | | | | | | | | | | | | |            (403), (413), (419), (425), (429), (529), (530),
% 173.03/26.26  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.03/26.26  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.03/26.26  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.03/26.26  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.03/26.26  | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.03/26.26  | | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.03/26.26  | | | | | | | | | | | | |            (583), (584), (585), (586), (588), (591), (593),
% 173.03/26.26  | | | | | | | | | | | | |            (594), (595), (596), (597), (598), (600), (796),
% 173.03/26.26  | | | | | | | | | | | | |            (7818), (7819), (7821), (7823), (7825), (7830),
% 173.03/26.26  | | | | | | | | | | | | |            (7834), (7835), (7836), (7846), (7847), (7848),
% 173.03/26.26  | | | | | | | | | | | | |            (7849), (7850), (function-axioms) are inconsistent
% 173.03/26.26  | | | | | | | | | | | | |            by sub-proof #248.
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | Case 2:
% 173.03/26.26  | | | | | | | | | | | | | 
% 173.03/26.26  | | | | | | | | | | | | |   (7851)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.24/26.26  | | | | | | | | | | | | |           all_52_30 = e0
% 173.24/26.26  | | | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7851),
% 173.24/26.26  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.26  | | | | | | | | | | | | |            #138.
% 173.24/26.26  | | | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | |   (7852)  all_40_1 = e1
% 173.24/26.26  | | | | | | | | | |   (7853)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | COMBINE_EQS: (715), (7852) imply:
% 173.24/26.26  | | | | | | | | | |   (7854)  all_4_1 = e1
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | COMBINE_EQS: (720), (7854) imply:
% 173.24/26.26  | | | | | | | | | |   (7855)  all_52_0 = e1
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | REDUCE: (796), (7854) imply:
% 173.24/26.26  | | | | | | | | | |   (7856)   ~ (e2 = e1)
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | REDUCE: (38), (7854) imply:
% 173.24/26.26  | | | | | | | | | |   (7857)  op(e1, all_4_2) = all_4_0
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | REDUCE: (37), (7854) imply:
% 173.24/26.26  | | | | | | | | | |   (7858)  op(e3, all_4_2) = e1
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | |   (7859)  all_58_15 = e0
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7859),
% 173.24/26.26  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.26  | | | | | | | | | | |            #143.
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | |   (7860)   ~ (all_58_15 = e0)
% 173.24/26.26  | | | | | | | | | | |   (7861)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.24/26.26  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.24/26.26  | | | | | | | | | | |             e0)
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | ALPHA: (7861) implies:
% 173.24/26.26  | | | | | | | | | | |   (7862)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.24/26.26  | | | | | | | | | | |   (7863)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | REDUCE: (532), (7860) imply:
% 173.24/26.26  | | | | | | | | | | |   (7864)   ~ (all_6_2 = e0)
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.24/26.26  | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 173.24/26.26  | | | | | | | | | | |            (158), (161), (163), (164), (165), (169), (170),
% 173.24/26.26  | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.24/26.26  | | | | | | | | | | |            (182), (183), (185), (268), (270), (271), (274),
% 173.24/26.26  | | | | | | | | | | |            (275), (276), (278), (281), (283), (304), (305),
% 173.24/26.26  | | | | | | | | | | |            (307), (310), (311), (313), (314), (315), (319),
% 173.24/26.26  | | | | | | | | | | |            (320), (321), (322), (323), (324), (325), (326),
% 173.24/26.26  | | | | | | | | | | |            (327), (328), (329), (330), (331), (344), (349),
% 173.24/26.26  | | | | | | | | | | |            (364), (365), (370), (373), (385), (391), (403),
% 173.24/26.26  | | | | | | | | | | |            (413), (419), (425), (429), (518), (529), (530),
% 173.24/26.26  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.24/26.26  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.24/26.26  | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.24/26.26  | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.24/26.26  | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.24/26.26  | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.24/26.26  | | | | | | | | | | |            (583), (584), (585), (586), (588), (589), (591),
% 173.24/26.26  | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 173.24/26.26  | | | | | | | | | | |            (649), (661), (719), (770), (796), (7818), (7819),
% 173.24/26.26  | | | | | | | | | | |            (7821), (7823), (7825), (7853), (7855), (7857),
% 173.24/26.26  | | | | | | | | | | |            (7858), (7862), (7863), (7864), (function-axioms)
% 173.24/26.26  | | | | | | | | | | |            are inconsistent by sub-proof #244.
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | |   (7865)  all_34_0 = e1
% 173.24/26.26  | | | | | | | |   (7866)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | COMBINE_EQS: (773), (7865) imply:
% 173.24/26.26  | | | | | | | |   (7867)  all_4_0 = e1
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | SIMP: (7867) implies:
% 173.24/26.26  | | | | | | | |   (7868)  all_4_0 = e1
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | REDUCE: (38), (7868) imply:
% 173.24/26.26  | | | | | | | |   (7869)  op(all_4_1, all_4_2) = e1
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | |   (7870)  all_58_15 = e0
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7870),
% 173.24/26.26  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.26  | | | | | | | | |            #143.
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | |   (7871)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.24/26.26  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | ALPHA: (7871) implies:
% 173.24/26.26  | | | | | | | | |   (7872)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | BETA: splitting (185) gives:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | |   (7873)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.26  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.24/26.26  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (7818),
% 173.24/26.26  | | | | | | | | | |            (7869), (7873), (function-axioms) are inconsistent
% 173.24/26.26  | | | | | | | | | |            by sub-proof #243.
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | |   (7874)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.24/26.26  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.24/26.26  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | BETA: splitting (7874) gives:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | |   (7875)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.24/26.26  | | | | | | | | | | |           all_52_22 = e0
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | ALPHA: (7875) implies:
% 173.24/26.26  | | | | | | | | | | |   (7876)  all_52_22 = e0
% 173.24/26.26  | | | | | | | | | | |   (7877)  all_52_20 = e1
% 173.24/26.26  | | | | | | | | | | |   (7878)  all_52_18 = e2
% 173.24/26.26  | | | | | | | | | | |   (7879)  all_52_16 = e3
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | COMBINE_EQS: (719), (7877) imply:
% 173.24/26.26  | | | | | | | | | | |   (7880)  all_14_1 = e1
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (52), (62), (63),
% 173.24/26.26  | | | | | | | | | | |            (156), (158), (163), (164), (165), (169), (170),
% 173.24/26.26  | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.24/26.26  | | | | | | | | | | |            (182), (268), (270), (274), (275), (276), (277),
% 173.24/26.26  | | | | | | | | | | |            (278), (281), (282), (283), (304), (307), (310),
% 173.24/26.26  | | | | | | | | | | |            (311), (313), (314), (315), (319), (320), (321),
% 173.24/26.26  | | | | | | | | | | |            (322), (323), (324), (326), (328), (329), (330),
% 173.24/26.26  | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 173.24/26.26  | | | | | | | | | | |            (385), (391), (392), (403), (413), (415), (419),
% 173.24/26.26  | | | | | | | | | | |            (425), (494), (529), (530), (531), (532), (533),
% 173.24/26.26  | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.24/26.26  | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.24/26.26  | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 173.24/26.26  | | | | | | | | | | |            (561), (562), (563), (564), (566), (567), (568),
% 173.24/26.26  | | | | | | | | | | |            (569), (571), (575), (577), (578), (579), (580),
% 173.24/26.26  | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (591),
% 173.24/26.26  | | | | | | | | | | |            (593), (595), (596), (597), (598), (600), (663),
% 173.24/26.26  | | | | | | | | | | |            (796), (7818), (7819), (7821), (7866), (7869),
% 173.24/26.26  | | | | | | | | | | |            (7872), (7876), (7878), (7879), (7880),
% 173.24/26.26  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.26  | | | | | | | | | | |            #241.
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | |   (7881)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.24/26.26  | | | | | | | | | | |           all_52_30 = e0
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | ALPHA: (7881) implies:
% 173.24/26.26  | | | | | | | | | | |   (7882)  all_52_30 = e0
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | COMBINE_EQS: (649), (7882) imply:
% 173.24/26.26  | | | | | | | | | | |   (7883)  all_6_1 = e0
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | | REF_CLOSE: (4), (42), (7373), (7883), (function-axioms) are
% 173.24/26.26  | | | | | | | | | | |            inconsistent by sub-proof #139.
% 173.24/26.26  | | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | End of split
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | Case 2:
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | |   (7884)  all_26_0 = e2
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | COMBINE_EQS: (779), (7884) imply:
% 173.24/26.26  | | | | | | |   (7885)  all_4_0 = e2
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | SIMP: (7885) implies:
% 173.24/26.26  | | | | | | |   (7886)  all_4_0 = e2
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | COMBINE_EQS: (742), (7886) imply:
% 173.24/26.26  | | | | | | |   (7887)  all_50_0 = e2
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | REDUCE: (38), (7886) imply:
% 173.24/26.26  | | | | | | |   (7888)  op(all_4_1, all_4_2) = e2
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | BETA: splitting (151) gives:
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | |   (7889)   ~ (all_50_0 = e2)
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | REDUCE: (7887), (7889) imply:
% 173.24/26.26  | | | | | | | |   (7890)  $false
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | CLOSE: (7890) is inconsistent.
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | |   (7891)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | |   (7892)  all_58_15 = e0
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7892),
% 173.24/26.26  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.26  | | | | | | | | |            #143.
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | |   (7893)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.24/26.26  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | ALPHA: (7893) implies:
% 173.24/26.26  | | | | | | | | |   (7894)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | BETA: splitting (185) gives:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | |   (7895)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.26  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.24/26.26  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (7818),
% 173.24/26.26  | | | | | | | | | |            (7888), (7895), (function-axioms) are inconsistent
% 173.24/26.26  | | | | | | | | | |            by sub-proof #237.
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | |   (7896)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.24/26.26  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.24/26.26  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (37), (42), (62), (63),
% 173.24/26.26  | | | | | | | | | |            (156), (158), (161), (163), (164), (165), (172),
% 173.24/26.26  | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.24/26.26  | | | | | | | | | |            (183), (268), (270), (273), (274), (275), (276),
% 173.24/26.26  | | | | | | | | | |            (280), (281), (282), (283), (304), (307), (310),
% 173.24/26.26  | | | | | | | | | |            (311), (315), (319), (321), (323), (324), (325),
% 173.24/26.26  | | | | | | | | | |            (326), (328), (329), (330), (331), (344), (349),
% 173.24/26.26  | | | | | | | | | |            (359), (364), (365), (370), (385), (386), (391),
% 173.24/26.26  | | | | | | | | | |            (392), (403), (413), (419), (425), (521), (529),
% 173.24/26.26  | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.24/26.26  | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.24/26.26  | | | | | | | | | |            (550), (552), (553), (554), (557), (558), (559),
% 173.24/26.26  | | | | | | | | | |            (560), (561), (562), (563), (564), (566), (567),
% 173.24/26.26  | | | | | | | | | |            (568), (569), (577), (579), (580), (582), (584),
% 173.24/26.26  | | | | | | | | | |            (585), (586), (591), (593), (595), (596), (598),
% 173.24/26.26  | | | | | | | | | |            (600), (649), (718), (719), (796), (7373), (7819),
% 173.24/26.26  | | | | | | | | | |            (7821), (7888), (7891), (7894), (7896),
% 173.24/26.26  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.26  | | | | | | | | | |            #133.
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | End of split
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | End of split
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | End of split
% 173.24/26.26  | | | | | | 
% 173.24/26.26  | | | | | Case 2:
% 173.24/26.26  | | | | | | 
% 173.24/26.26  | | | | | |   (7897)  all_18_0 = e3
% 173.24/26.26  | | | | | | 
% 173.24/26.26  | | | | | | COMBINE_EQS: (789), (7897) imply:
% 173.24/26.26  | | | | | |   (7898)  all_14_0 = e3
% 173.24/26.26  | | | | | | 
% 173.24/26.26  | | | | | | SIMP: (7898) implies:
% 173.24/26.26  | | | | | |   (7899)  all_14_0 = e3
% 173.24/26.26  | | | | | | 
% 173.24/26.26  | | | | | | REDUCE: (63), (7899) imply:
% 173.24/26.26  | | | | | |   (7900)  op(all_14_1, all_14_2) = e3
% 173.24/26.26  | | | | | | 
% 173.24/26.26  | | | | | | BETA: splitting (93) gives:
% 173.24/26.26  | | | | | | 
% 173.24/26.26  | | | | | | Case 1:
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | |   (7901)   ~ (all_26_0 = e2)
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | REDUCE: (779), (7901) imply:
% 173.24/26.26  | | | | | | |   (7902)   ~ (all_4_0 = e2)
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | BETA: splitting (113) gives:
% 173.24/26.26  | | | | | | | 
% 173.24/26.26  | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | |   (7903)   ~ (all_34_0 = e1)
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | REDUCE: (773), (7903) imply:
% 173.24/26.26  | | | | | | | |   (7904)   ~ (all_4_0 = e1)
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | BETA: splitting (123) gives:
% 173.24/26.26  | | | | | | | | 
% 173.24/26.26  | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | |   (7905)   ~ (all_38_0 = e1)
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | REDUCE: (7372), (7905) imply:
% 173.24/26.26  | | | | | | | | |   (7906)  $false
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | CLOSE: (7906) is inconsistent.
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | |   (7907)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.26  | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | Case 1:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | |   (7908)  all_58_15 = e0
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7908),
% 173.24/26.26  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.26  | | | | | | | | | |            #143.
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | Case 2:
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | |   (7909)   ~ (all_58_15 = e0)
% 173.24/26.26  | | | | | | | | | |   (7910)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.24/26.26  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.24/26.26  | | | | | | | | | |             e0)
% 173.24/26.26  | | | | | | | | | | 
% 173.24/26.26  | | | | | | | | | | ALPHA: (7910) implies:
% 173.24/26.26  | | | | | | | | | |   (7911)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | REDUCE: (532), (7909) imply:
% 173.24/26.27  | | | | | | | | | |   (7912)   ~ (all_6_2 = e0)
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | BETA: splitting (185) gives:
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | |   (7913)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.27  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.24/26.27  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (38), (42), (52), (61),
% 173.24/26.27  | | | | | | | | | | |            (154), (156), (158), (159), (160), (161), (163),
% 173.24/26.27  | | | | | | | | | | |            (164), (165), (168), (169), (170), (172), (173),
% 173.24/26.27  | | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 173.24/26.27  | | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 173.24/26.27  | | | | | | | | | | |            (283), (302), (304), (305), (307), (310), (311),
% 173.24/26.27  | | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 173.24/26.27  | | | | | | | | | | |            (324), (326), (327), (328), (330), (331), (341),
% 173.24/26.27  | | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 173.24/26.27  | | | | | | | | | | |            (385), (391), (392), (403), (409), (413), (425),
% 173.24/26.27  | | | | | | | | | | |            (429), (517), (529), (531), (532), (533), (534),
% 173.24/26.27  | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.24/26.27  | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.24/26.27  | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.24/26.27  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (575),
% 173.24/26.27  | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.24/26.27  | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 173.24/26.27  | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.24/26.27  | | | | | | | | | | |            (661), (714), (720), (7373), (7818), (7902),
% 173.24/26.27  | | | | | | | | | | |            (7904), (7907), (7911), (7912), (7913),
% 173.24/26.27  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.27  | | | | | | | | | | |            #125.
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | |   (7914)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.24/26.27  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.24/26.27  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | REF_CLOSE: (4), (8), (42), (62), (649), (719), (7373),
% 173.24/26.27  | | | | | | | | | | |            (7900), (7914), (function-axioms) are inconsistent
% 173.24/26.27  | | | | | | | | | | |            by sub-proof #130.
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7915)  all_34_0 = e1
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | COMBINE_EQS: (773), (7915) imply:
% 173.24/26.27  | | | | | | | |   (7916)  all_4_0 = e1
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | SIMP: (7916) implies:
% 173.24/26.27  | | | | | | | |   (7917)  all_4_0 = e1
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | REDUCE: (38), (7917) imply:
% 173.24/26.27  | | | | | | | |   (7918)  op(all_4_1, all_4_2) = e1
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | BETA: splitting (185) gives:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | |   (7919)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.27  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.24/26.27  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (7818), (7918),
% 173.24/26.27  | | | | | | | | |            (7919), (function-axioms) are inconsistent by
% 173.24/26.27  | | | | | | | | |            sub-proof #243.
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | |   (7920)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.24/26.27  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 173.24/26.27  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | REF_CLOSE: (4), (8), (42), (62), (649), (719), (7373), (7900),
% 173.24/26.27  | | | | | | | | |            (7920), (function-axioms) are inconsistent by
% 173.24/26.27  | | | | | | | | |            sub-proof #130.
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | End of split
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | Case 2:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | |   (7921)  all_26_0 = e2
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | COMBINE_EQS: (779), (7921) imply:
% 173.24/26.27  | | | | | | |   (7922)  all_4_0 = e2
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | SIMP: (7922) implies:
% 173.24/26.27  | | | | | | |   (7923)  all_4_0 = e2
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | REDUCE: (38), (7923) imply:
% 173.24/26.27  | | | | | | |   (7924)  op(all_4_1, all_4_2) = e2
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | BETA: splitting (185) gives:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7925)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.27  | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.24/26.27  | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (7818), (7924),
% 173.24/26.27  | | | | | | | |            (7925), (function-axioms) are inconsistent by
% 173.24/26.27  | | | | | | | |            sub-proof #237.
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7926)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.24/26.27  | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 173.24/26.27  | | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | BETA: splitting (7926) gives:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | |   (7927)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.24/26.27  | | | | | | | | |           all_52_22 = e0
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | REF_CLOSE: (8), (62), (719), (7900), (7927), (function-axioms)
% 173.24/26.27  | | | | | | | | |            are inconsistent by sub-proof #343.
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | |   (7928)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.24/26.27  | | | | | | | | |           all_52_30 = e0
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | REF_CLOSE: (4), (42), (649), (7373), (7928), (function-axioms)
% 173.24/26.27  | | | | | | | | |            are inconsistent by sub-proof #138.
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | End of split
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | End of split
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | End of split
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | Case 2:
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | |   (7929)  all_14_0 = e2
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | | REDUCE: (63), (7929) imply:
% 173.24/26.27  | | | | |   (7930)  op(all_14_1, all_14_2) = e2
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | | BETA: splitting (93) gives:
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | | Case 1:
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | |   (7931)   ~ (all_26_0 = e2)
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | REDUCE: (779), (7931) imply:
% 173.24/26.27  | | | | | |   (7932)   ~ (all_4_0 = e2)
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | BETA: splitting (113) gives:
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | Case 1:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | |   (7933)   ~ (all_34_0 = e1)
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | REDUCE: (773), (7933) imply:
% 173.24/26.27  | | | | | | |   (7934)   ~ (all_4_0 = e1)
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | BETA: splitting (123) gives:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7935)   ~ (all_38_0 = e1)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | REDUCE: (7372), (7935) imply:
% 173.24/26.27  | | | | | | | |   (7936)  $false
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | CLOSE: (7936) is inconsistent.
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7937)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | |   (7938)  all_58_15 = e0
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (7373), (7938),
% 173.24/26.27  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.27  | | | | | | | | |            #143.
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | |   (7939)   ~ (all_58_15 = e0)
% 173.24/26.27  | | | | | | | | |   (7940)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.24/26.27  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | ALPHA: (7940) implies:
% 173.24/26.27  | | | | | | | | |   (7941)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | REDUCE: (532), (7939) imply:
% 173.24/26.27  | | | | | | | | |   (7942)   ~ (all_6_2 = e0)
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | BETA: splitting (185) gives:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | |   (7943)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.27  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.24/26.27  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | REF_CLOSE: (4), (7), (9), (37), (38), (42), (52), (61),
% 173.24/26.27  | | | | | | | | | |            (154), (156), (158), (159), (160), (161), (163),
% 173.24/26.27  | | | | | | | | | |            (164), (165), (168), (169), (170), (172), (173),
% 173.24/26.27  | | | | | | | | | |            (176), (177), (178), (179), (268), (269), (270),
% 173.24/26.27  | | | | | | | | | |            (271), (272), (273), (276), (279), (281), (282),
% 173.24/26.27  | | | | | | | | | |            (283), (302), (304), (305), (307), (310), (311),
% 173.24/26.27  | | | | | | | | | |            (312), (313), (314), (315), (317), (319), (323),
% 173.24/26.27  | | | | | | | | | |            (324), (326), (327), (328), (330), (331), (341),
% 173.24/26.27  | | | | | | | | | |            (344), (349), (350), (359), (364), (370), (373),
% 173.24/26.27  | | | | | | | | | |            (385), (391), (392), (403), (409), (413), (425),
% 173.24/26.27  | | | | | | | | | |            (429), (517), (529), (531), (532), (533), (534),
% 173.24/26.27  | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.24/26.27  | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.24/26.27  | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.24/26.27  | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (575),
% 173.24/26.27  | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.24/26.27  | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 173.24/26.27  | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.24/26.27  | | | | | | | | | |            (661), (714), (720), (7373), (7818), (7932),
% 173.24/26.27  | | | | | | | | | |            (7934), (7937), (7941), (7942), (7943),
% 173.24/26.27  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.27  | | | | | | | | | |            #125.
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | |   (7944)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.24/26.27  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.24/26.27  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | REF_CLOSE: (4), (6), (42), (62), (649), (719), (7373),
% 173.24/26.27  | | | | | | | | | |            (7930), (7944), (function-axioms) are inconsistent
% 173.24/26.27  | | | | | | | | | |            by sub-proof #128.
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | End of split
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | Case 2:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | |   (7945)  all_34_0 = e1
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | COMBINE_EQS: (773), (7945) imply:
% 173.24/26.27  | | | | | | |   (7946)  all_4_0 = e1
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | REDUCE: (7932), (7946) imply:
% 173.24/26.27  | | | | | | |   (7947)   ~ (e2 = e1)
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | REDUCE: (38), (7946) imply:
% 173.24/26.27  | | | | | | |   (7948)  op(all_4_1, all_4_2) = e1
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | BETA: splitting (185) gives:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7949)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.27  | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.24/26.27  | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | REF_CLOSE: (8), (9), (37), (52), (661), (720), (7818), (7948),
% 173.24/26.27  | | | | | | | |            (7949), (function-axioms) are inconsistent by
% 173.24/26.27  | | | | | | | |            sub-proof #243.
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7950)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.24/26.27  | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 173.24/26.27  | | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | REF_CLOSE: (4), (6), (42), (62), (649), (719), (7373), (7930),
% 173.24/26.27  | | | | | | | |            (7950), (function-axioms) are inconsistent by
% 173.24/26.27  | | | | | | | |            sub-proof #127.
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | End of split
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | End of split
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | Case 2:
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | |   (7951)  all_26_0 = e2
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | COMBINE_EQS: (779), (7951) imply:
% 173.24/26.27  | | | | | |   (7952)  all_4_0 = e2
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | SIMP: (7952) implies:
% 173.24/26.27  | | | | | |   (7953)  all_4_0 = e2
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | REDUCE: (38), (7953) imply:
% 173.24/26.27  | | | | | |   (7954)  op(all_4_1, all_4_2) = e2
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | BETA: splitting (185) gives:
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | Case 1:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | |   (7955)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.24/26.27  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.24/26.27  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | REF_CLOSE: (9), (37), (52), (661), (720), (796), (7818), (7954),
% 173.24/26.27  | | | | | | |            (7955), (function-axioms) are inconsistent by sub-proof
% 173.24/26.27  | | | | | | |            #237.
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | Case 2:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | |   (7956)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.24/26.27  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 173.24/26.27  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | REF_CLOSE: (4), (6), (42), (62), (649), (719), (7373), (7930),
% 173.24/26.27  | | | | | | |            (7956), (function-axioms) are inconsistent by sub-proof
% 173.24/26.27  | | | | | | |            #127.
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | End of split
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | End of split
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | End of split
% 173.24/26.27  | | | | 
% 173.24/26.27  | | | End of split
% 173.24/26.27  | | | 
% 173.24/26.27  | | End of split
% 173.24/26.27  | | 
% 173.24/26.27  | Case 2:
% 173.24/26.27  | | 
% 173.24/26.27  | |   (7957)  all_4_1 = e2
% 173.24/26.27  | |   (7958)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 173.24/26.27  | | 
% 173.24/26.27  | | COMBINE_EQS: (716), (7957) imply:
% 173.24/26.27  | |   (7959)  all_42_1 = e2
% 173.24/26.27  | | 
% 173.24/26.27  | | COMBINE_EQS: (720), (7957) imply:
% 173.24/26.27  | |   (7960)  all_52_0 = e2
% 173.24/26.27  | | 
% 173.24/26.27  | | REDUCE: (38), (7957) imply:
% 173.24/26.27  | |   (7961)  op(e2, all_4_2) = all_4_0
% 173.24/26.27  | | 
% 173.24/26.27  | | REDUCE: (37), (7957) imply:
% 173.24/26.27  | |   (7962)  op(e3, all_4_2) = e2
% 173.24/26.27  | | 
% 173.24/26.27  | | BETA: splitting (44) gives:
% 173.24/26.27  | | 
% 173.24/26.27  | | Case 1:
% 173.24/26.27  | | | 
% 173.24/26.27  | | |   (7963)   ~ (all_6_0 = e1)
% 173.24/26.27  | | | 
% 173.24/26.27  | | | BETA: splitting (49) gives:
% 173.24/26.27  | | | 
% 173.24/26.27  | | | Case 1:
% 173.24/26.27  | | | | 
% 173.24/26.27  | | | |   (7964)   ~ (all_8_0 = e2)
% 173.24/26.27  | | | | 
% 173.24/26.27  | | | | REDUCE: (791), (7964) imply:
% 173.24/26.27  | | | |   (7965)   ~ (all_6_0 = e2)
% 173.24/26.27  | | | | 
% 173.24/26.27  | | | | BETA: splitting (54) gives:
% 173.24/26.27  | | | | 
% 173.24/26.27  | | | | Case 1:
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | |   (7966)   ~ (all_10_0 = e3)
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | | BETA: splitting (59) gives:
% 173.24/26.27  | | | | | 
% 173.24/26.27  | | | | | Case 1:
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | |   (7967)   ~ (all_12_1 = e3)
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | REDUCE: (705), (7967) imply:
% 173.24/26.27  | | | | | |   (7968)   ~ (all_10_1 = e3)
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | BETA: splitting (64) gives:
% 173.24/26.27  | | | | | | 
% 173.24/26.27  | | | | | | Case 1:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | |   (7969)   ~ (all_14_0 = e2)
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | BETA: splitting (74) gives:
% 173.24/26.27  | | | | | | | 
% 173.24/26.27  | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | |   (7970)   ~ (all_18_0 = e3)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | REDUCE: (789), (7970) imply:
% 173.24/26.27  | | | | | | | |   (7971)   ~ (all_14_0 = e3)
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | BETA: splitting (88) gives:
% 173.24/26.27  | | | | | | | | 
% 173.24/26.27  | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | |   (7972)   ~ (all_24_0 = e1)
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | REDUCE: (751), (7972) imply:
% 173.24/26.27  | | | | | | | | |   (7973)   ~ (all_10_0 = e1)
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | BETA: splitting (98) gives:
% 173.24/26.27  | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | |   (7974)   ~ (all_28_0 = e3)
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | REDUCE: (776), (7974) imply:
% 173.24/26.27  | | | | | | | | | |   (7975)   ~ (all_6_0 = e3)
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | BETA: splitting (133) gives:
% 173.24/26.27  | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | |   (7976)   ~ (all_42_0 = e1)
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | REDUCE: (761), (7976) imply:
% 173.24/26.27  | | | | | | | | | | |   (7977)   ~ (all_4_0 = e1)
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | Case 1:
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | |   (7978)  all_58_15 = e0
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (52), (62),
% 173.24/26.27  | | | | | | | | | | | |            (154), (155), (156), (158), (159), (163), (164),
% 173.24/26.27  | | | | | | | | | | | |            (165), (167), (169), (170), (172), (173), (174),
% 173.24/26.27  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 173.24/26.27  | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 173.24/26.27  | | | | | | | | | | | |            (276), (278), (280), (283), (302), (303), (304),
% 173.24/26.27  | | | | | | | | | | | |            (305), (306), (307), (310), (311), (313), (315),
% 173.24/26.27  | | | | | | | | | | | |            (316), (319), (322), (323), (324), (325), (326),
% 173.24/26.27  | | | | | | | | | | | |            (328), (330), (331), (341), (344), (349), (350),
% 173.24/26.27  | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.24/26.27  | | | | | | | | | | | |            (391), (403), (419), (425), (429), (530), (531),
% 173.24/26.27  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.24/26.27  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.24/26.27  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.24/26.27  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.24/26.27  | | | | | | | | | | | |            (566), (567), (569), (571), (573), (575), (577),
% 173.24/26.27  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.24/26.27  | | | | | | | | | | | |            (585), (586), (588), (591), (593), (594), (595),
% 173.24/26.27  | | | | | | | | | | | |            (596), (598), (599), (600), (661), (719), (7960),
% 173.24/26.27  | | | | | | | | | | | |            (7961), (7962), (7963), (7965), (7968), (7975),
% 173.24/26.27  | | | | | | | | | | | |            (7977), (7978), (function-axioms) are inconsistent
% 173.24/26.27  | | | | | | | | | | | |            by sub-proof #107.
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | |   (7979)   ~ (all_58_15 = e0)
% 173.24/26.27  | | | | | | | | | | | |   (7980)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.24/26.27  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.24/26.27  | | | | | | | | | | | |             e0)
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | | ALPHA: (7980) implies:
% 173.24/26.27  | | | | | | | | | | | |   (7981)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.24/26.27  | | | | | | | | | | | |   (7982)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | | REDUCE: (532), (7979) imply:
% 173.24/26.27  | | | | | | | | | | | |   (7983)   ~ (all_6_2 = e0)
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.24/26.27  | | | | | | | | | | | |            (42), (52), (53), (62), (63), (154), (155), (156),
% 173.24/26.27  | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.24/26.27  | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.24/26.27  | | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.24/26.27  | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.24/26.27  | | | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (303),
% 173.24/26.27  | | | | | | | | | | | |            (304), (305), (306), (307), (310), (311), (313),
% 173.24/26.27  | | | | | | | | | | | |            (315), (317), (319), (321), (322), (323), (324),
% 173.24/26.27  | | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 173.24/26.27  | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 173.24/26.27  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.24/26.27  | | | | | | | | | | | |            (409), (413), (415), (419), (425), (429), (529),
% 173.24/26.27  | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 173.24/26.27  | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.24/26.27  | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.24/26.27  | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.24/26.27  | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.24/26.27  | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.24/26.27  | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.24/26.27  | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.24/26.27  | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.24/26.27  | | | | | | | | | | | |            (7960), (7961), (7962), (7966), (7968), (7969),
% 173.24/26.27  | | | | | | | | | | | |            (7971), (7973), (7977), (7981), (7982), (7983),
% 173.24/26.27  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.27  | | | | | | | | | | | |            #86.
% 173.24/26.27  | | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | End of split
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | Case 2:
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | |   (7984)  all_42_0 = e1
% 173.24/26.27  | | | | | | | | | | |   (7985)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | COMBINE_EQS: (761), (7984) imply:
% 173.24/26.27  | | | | | | | | | | |   (7986)  all_4_0 = e1
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | SIMP: (7986) implies:
% 173.24/26.27  | | | | | | | | | | |   (7987)  all_4_0 = e1
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.27  | | | | | | | | | | | REDUCE: (7961), (7987) imply:
% 173.24/26.27  | | | | | | | | | | |   (7988)  op(e2, all_4_2) = e1
% 173.24/26.27  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.24/26.28  | | | | | | | | | | |            (43), (52), (53), (61), (62), (154), (155), (156),
% 173.24/26.28  | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.24/26.28  | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.24/26.28  | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.24/26.28  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.24/26.28  | | | | | | | | | | |            (278), (279), (280), (282), (283), (301), (302),
% 173.24/26.28  | | | | | | | | | | |            (303), (304), (305), (306), (307), (310), (311),
% 173.24/26.28  | | | | | | | | | | |            (313), (315), (317), (319), (321), (322), (323),
% 173.24/26.28  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 173.24/26.28  | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.24/26.28  | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 173.24/26.28  | | | | | | | | | | |            (403), (409), (415), (419), (425), (429), (477),
% 173.24/26.28  | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.24/26.28  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.24/26.28  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.24/26.28  | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.24/26.28  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.24/26.28  | | | | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 173.24/26.28  | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 173.24/26.28  | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.24/26.28  | | | | | | | | | | |            (597), (598), (599), (600), (649), (661), (719),
% 173.24/26.28  | | | | | | | | | | |            (7959), (7960), (7962), (7963), (7965), (7966),
% 173.24/26.28  | | | | | | | | | | |            (7973), (7975), (7985), (7988), (function-axioms)
% 173.24/26.28  | | | | | | | | | | |            are inconsistent by sub-proof #72.
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | End of split
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | |   (7989)  all_28_0 = e3
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | COMBINE_EQS: (776), (7989) imply:
% 173.24/26.28  | | | | | | | | | |   (7990)  all_6_0 = e3
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | REDUCE: (43), (7990) imply:
% 173.24/26.28  | | | | | | | | | |   (7991)  op(all_6_1, all_6_2) = e3
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | BETA: splitting (133) gives:
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | Case 1:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | |   (7992)   ~ (all_42_0 = e1)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REDUCE: (761), (7992) imply:
% 173.24/26.28  | | | | | | | | | | |   (7993)   ~ (all_4_0 = e1)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | Case 1:
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | |   (7994)  all_58_15 = e0
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (7991), (7994),
% 173.24/26.28  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.28  | | | | | | | | | | | |            #510.
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | |   (7995)   ~ (all_58_15 = e0)
% 173.24/26.28  | | | | | | | | | | | |   (7996)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.24/26.28  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.24/26.28  | | | | | | | | | | | |             e0)
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.24/26.28  | | | | | | | | | | | |            (42), (52), (53), (62), (63), (154), (155), (156),
% 173.24/26.28  | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.24/26.28  | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.24/26.28  | | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.24/26.28  | | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.24/26.28  | | | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (303),
% 173.24/26.28  | | | | | | | | | | | |            (304), (305), (306), (307), (310), (311), (313),
% 173.24/26.28  | | | | | | | | | | | |            (315), (317), (319), (321), (322), (323), (324),
% 173.24/26.28  | | | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 173.24/26.28  | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 173.24/26.28  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.24/26.28  | | | | | | | | | | | |            (409), (413), (415), (419), (425), (429), (529),
% 173.24/26.28  | | | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 173.24/26.28  | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.24/26.28  | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.24/26.28  | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.24/26.28  | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.24/26.28  | | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.24/26.28  | | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.24/26.28  | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.24/26.28  | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.24/26.28  | | | | | | | | | | | |            (7960), (7961), (7962), (7966), (7968), (7969),
% 173.24/26.28  | | | | | | | | | | | |            (7971), (7973), (7993), (7995), (7996),
% 173.24/26.28  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.28  | | | | | | | | | | | |            #71.
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | End of split
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | |   (7997)  all_42_0 = e1
% 173.24/26.28  | | | | | | | | | | |   (7998)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | COMBINE_EQS: (761), (7997) imply:
% 173.24/26.28  | | | | | | | | | | |   (7999)  all_4_0 = e1
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REDUCE: (7961), (7999) imply:
% 173.24/26.28  | | | | | | | | | | |   (8000)  op(e2, all_4_2) = e1
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.24/26.28  | | | | | | | | | | |            (52), (53), (61), (62), (154), (156), (158),
% 173.24/26.28  | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.24/26.28  | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (182),
% 173.24/26.28  | | | | | | | | | | |            (183), (185), (268), (269), (272), (273), (274),
% 173.24/26.28  | | | | | | | | | | |            (275), (276), (277), (279), (280), (282), (283),
% 173.24/26.28  | | | | | | | | | | |            (301), (304), (307), (310), (311), (313), (315),
% 173.24/26.28  | | | | | | | | | | |            (317), (319), (321), (323), (324), (326), (327),
% 173.24/26.28  | | | | | | | | | | |            (328), (329), (330), (331), (341), (349), (350),
% 173.24/26.28  | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.24/26.28  | | | | | | | | | | |            (391), (392), (403), (409), (415), (419), (425),
% 173.24/26.28  | | | | | | | | | | |            (477), (529), (531), (532), (533), (534), (535),
% 173.24/26.28  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.24/26.28  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.24/26.28  | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.24/26.28  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.24/26.28  | | | | | | | | | | |            (573), (575), (577), (579), (580), (581), (582),
% 173.24/26.28  | | | | | | | | | | |            (584), (586), (587), (588), (589), (591), (593),
% 173.24/26.28  | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.24/26.28  | | | | | | | | | | |            (649), (661), (719), (7959), (7960), (7962),
% 173.24/26.28  | | | | | | | | | | |            (7966), (7973), (7991), (7998), (8000),
% 173.24/26.28  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.28  | | | | | | | | | | |            #70.
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | End of split
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | End of split
% 173.24/26.28  | | | | | | | | | 
% 173.24/26.28  | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | 
% 173.24/26.28  | | | | | | | | |   (8001)  all_24_0 = e1
% 173.24/26.28  | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | COMBINE_EQS: (751), (8001) imply:
% 173.24/26.28  | | | | | | | | |   (8002)  all_10_0 = e1
% 173.24/26.28  | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | REDUCE: (7966), (8002) imply:
% 173.24/26.28  | | | | | | | | |   (8003)   ~ (e3 = e1)
% 173.24/26.28  | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | REDUCE: (53), (8002) imply:
% 173.24/26.28  | | | | | | | | |   (8004)  op(all_10_1, all_10_2) = e1
% 173.24/26.28  | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | BETA: splitting (98) gives:
% 173.24/26.28  | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | Case 1:
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | |   (8005)   ~ (all_28_0 = e3)
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | REDUCE: (776), (8005) imply:
% 173.24/26.28  | | | | | | | | | |   (8006)   ~ (all_6_0 = e3)
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | BETA: splitting (133) gives:
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | Case 1:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | |   (8007)   ~ (all_42_0 = e1)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REDUCE: (761), (8007) imply:
% 173.24/26.28  | | | | | | | | | | |   (8008)   ~ (all_4_0 = e1)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | Case 1:
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | |   (8009)  all_58_15 = e0
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (52), (62),
% 173.24/26.28  | | | | | | | | | | | |            (154), (155), (156), (158), (159), (163), (164),
% 173.24/26.28  | | | | | | | | | | | |            (165), (167), (169), (170), (172), (173), (174),
% 173.24/26.28  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 173.24/26.28  | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 173.24/26.28  | | | | | | | | | | | |            (276), (278), (280), (283), (302), (303), (304),
% 173.24/26.28  | | | | | | | | | | | |            (305), (306), (307), (310), (311), (313), (315),
% 173.24/26.28  | | | | | | | | | | | |            (316), (319), (322), (323), (324), (325), (326),
% 173.24/26.28  | | | | | | | | | | | |            (328), (330), (331), (341), (344), (349), (350),
% 173.24/26.28  | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.24/26.28  | | | | | | | | | | | |            (391), (403), (419), (425), (429), (530), (531),
% 173.24/26.28  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.24/26.28  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.24/26.28  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.24/26.28  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.24/26.28  | | | | | | | | | | | |            (566), (567), (569), (571), (573), (575), (577),
% 173.24/26.28  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.24/26.28  | | | | | | | | | | | |            (585), (586), (588), (591), (593), (594), (595),
% 173.24/26.28  | | | | | | | | | | | |            (596), (598), (599), (600), (661), (719), (7960),
% 173.24/26.28  | | | | | | | | | | | |            (7961), (7962), (7963), (7965), (7968), (8006),
% 173.24/26.28  | | | | | | | | | | | |            (8008), (8009), (function-axioms) are inconsistent
% 173.24/26.28  | | | | | | | | | | | |            by sub-proof #107.
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | |   (8010)   ~ (all_58_15 = e0)
% 173.24/26.28  | | | | | | | | | | | |   (8011)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.24/26.28  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.24/26.28  | | | | | | | | | | | |             e0)
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | ALPHA: (8011) implies:
% 173.24/26.28  | | | | | | | | | | | |   (8012)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.24/26.28  | | | | | | | | | | | |   (8013)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | REDUCE: (532), (8010) imply:
% 173.24/26.28  | | | | | | | | | | | |   (8014)   ~ (all_6_2 = e0)
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.24/26.28  | | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 173.24/26.28  | | | | | | | | | | | |            (158), (161), (163), (164), (165), (170), (172),
% 173.24/26.28  | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.24/26.28  | | | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (274),
% 173.24/26.28  | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 173.24/26.28  | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 173.24/26.28  | | | | | | | | | | | |            (311), (313), (315), (317), (319), (321), (322),
% 173.24/26.28  | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 173.24/26.28  | | | | | | | | | | | |            (330), (331), (341), (344), (349), (364), (365),
% 173.24/26.28  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.24/26.28  | | | | | | | | | | | |            (413), (415), (419), (425), (429), (529), (530),
% 173.24/26.28  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.24/26.28  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.24/26.28  | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.24/26.28  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.24/26.28  | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.24/26.28  | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.24/26.28  | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 173.24/26.28  | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 173.24/26.28  | | | | | | | | | | | |            (649), (661), (719), (7958), (7960), (7961),
% 173.24/26.28  | | | | | | | | | | | |            (7962), (7968), (7969), (7971), (8004), (8008),
% 173.24/26.28  | | | | | | | | | | | |            (8012), (8013), (8014), (function-axioms) are
% 173.24/26.28  | | | | | | | | | | | |            inconsistent by sub-proof #68.
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | End of split
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | |   (8015)  all_42_0 = e1
% 173.24/26.28  | | | | | | | | | | |   (8016)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | COMBINE_EQS: (761), (8015) imply:
% 173.24/26.28  | | | | | | | | | | |   (8017)  all_4_0 = e1
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | SIMP: (8017) implies:
% 173.24/26.28  | | | | | | | | | | |   (8018)  all_4_0 = e1
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REDUCE: (7961), (8018) imply:
% 173.24/26.28  | | | | | | | | | | |   (8019)  op(e2, all_4_2) = e1
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.24/26.28  | | | | | | | | | | |            (43), (52), (62), (154), (155), (156), (158),
% 173.24/26.28  | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.24/26.28  | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.24/26.28  | | | | | | | | | | |            (182), (183), (185), (268), (269), (270), (271),
% 173.24/26.28  | | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 173.24/26.28  | | | | | | | | | | |            (282), (283), (301), (302), (303), (304), (305),
% 173.24/26.28  | | | | | | | | | | |            (306), (307), (310), (311), (313), (315), (319),
% 173.24/26.28  | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 173.24/26.28  | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.24/26.28  | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.24/26.28  | | | | | | | | | | |            (391), (392), (403), (419), (425), (429), (477),
% 173.24/26.28  | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.24/26.28  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.24/26.28  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.24/26.28  | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.24/26.28  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.24/26.28  | | | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 173.24/26.28  | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.24/26.28  | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.24/26.28  | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7959),
% 173.24/26.28  | | | | | | | | | | |            (7960), (7962), (7963), (7965), (7968), (8004),
% 173.24/26.28  | | | | | | | | | | |            (8006), (8016), (8019), (function-axioms) are
% 173.24/26.28  | | | | | | | | | | |            inconsistent by sub-proof #64.
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | End of split
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | |   (8020)  all_28_0 = e3
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | COMBINE_EQS: (776), (8020) imply:
% 173.24/26.28  | | | | | | | | | |   (8021)  all_6_0 = e3
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | REDUCE: (43), (8021) imply:
% 173.24/26.28  | | | | | | | | | |   (8022)  op(all_6_1, all_6_2) = e3
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | BETA: splitting (133) gives:
% 173.24/26.28  | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | Case 1:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | |   (8023)   ~ (all_42_0 = e1)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REDUCE: (761), (8023) imply:
% 173.24/26.28  | | | | | | | | | | |   (8024)   ~ (all_4_0 = e1)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | Case 1:
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | |   (8025)  all_58_15 = e0
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8022), (8025),
% 173.24/26.28  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.24/26.28  | | | | | | | | | | | |            #510.
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | |   (8026)   ~ (all_58_15 = e0)
% 173.24/26.28  | | | | | | | | | | | |   (8027)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.24/26.28  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.24/26.28  | | | | | | | | | | | |             e0)
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.24/26.28  | | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 173.24/26.28  | | | | | | | | | | | |            (158), (161), (163), (164), (165), (170), (172),
% 173.24/26.28  | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.24/26.28  | | | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (274),
% 173.24/26.28  | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 173.24/26.28  | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 173.24/26.28  | | | | | | | | | | | |            (311), (313), (315), (317), (319), (321), (322),
% 173.24/26.28  | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 173.24/26.28  | | | | | | | | | | | |            (330), (331), (341), (344), (349), (364), (365),
% 173.24/26.28  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.24/26.28  | | | | | | | | | | | |            (413), (415), (419), (425), (429), (529), (530),
% 173.24/26.28  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.24/26.28  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.24/26.28  | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.24/26.28  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.24/26.28  | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.24/26.28  | | | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.24/26.28  | | | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 173.24/26.28  | | | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 173.24/26.28  | | | | | | | | | | | |            (649), (661), (719), (7958), (7960), (7961),
% 173.24/26.28  | | | | | | | | | | | |            (7962), (7968), (7969), (7971), (8004), (8024),
% 173.24/26.28  | | | | | | | | | | | |            (8026), (8027), (function-axioms) are inconsistent
% 173.24/26.28  | | | | | | | | | | | |            by sub-proof #63.
% 173.24/26.28  | | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | End of split
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | Case 2:
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | |   (8028)  all_42_0 = e1
% 173.24/26.28  | | | | | | | | | | |   (8029)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | COMBINE_EQS: (761), (8028) imply:
% 173.24/26.28  | | | | | | | | | | |   (8030)  all_4_0 = e1
% 173.24/26.28  | | | | | | | | | | | 
% 173.24/26.28  | | | | | | | | | | | REDUCE: (7961), (8030) imply:
% 173.24/26.28  | | | | | | | | | | |   (8031)  op(e2, all_4_2) = e1
% 173.24/26.28  | | | | | | | | | | | 
% 173.28/26.28  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.28  | | | | | | | | | | |            (52), (62), (156), (158), (161), (163), (164),
% 173.28/26.28  | | | | | | | | | | |            (170), (172), (174), (177), (178), (179), (182),
% 173.28/26.28  | | | | | | | | | | |            (185), (268), (273), (274), (276), (283), (301),
% 173.28/26.28  | | | | | | | | | | |            (304), (307), (310), (311), (315), (319), (323),
% 173.28/26.28  | | | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.28/26.28  | | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (419),
% 173.28/26.29  | | | | | | | | | | |            (425), (477), (529), (531), (532), (533), (534),
% 173.28/26.29  | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.28/26.29  | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.28/26.29  | | | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.28/26.29  | | | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.28/26.29  | | | | | | | | | | |            (595), (596), (598), (600), (649), (661), (719),
% 173.28/26.29  | | | | | | | | | | |            (7959), (7960), (7962), (8004), (8022), (8029),
% 173.28/26.29  | | | | | | | | | | |            (8031), (function-axioms) are inconsistent by
% 173.28/26.29  | | | | | | | | | | |            sub-proof #61.
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | 
% 173.28/26.29  | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | 
% 173.28/26.29  | | | | | | | |   (8032)  all_18_0 = e3
% 173.28/26.29  | | | | | | | | 
% 173.28/26.29  | | | | | | | | COMBINE_EQS: (789), (8032) imply:
% 173.28/26.29  | | | | | | | |   (8033)  all_14_0 = e3
% 173.28/26.29  | | | | | | | | 
% 173.28/26.29  | | | | | | | | REDUCE: (63), (8033) imply:
% 173.28/26.29  | | | | | | | |   (8034)  op(all_14_1, all_14_2) = e3
% 173.28/26.29  | | | | | | | | 
% 173.28/26.29  | | | | | | | | BETA: splitting (88) gives:
% 173.28/26.29  | | | | | | | | 
% 173.28/26.29  | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | |   (8035)   ~ (all_24_0 = e1)
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | REDUCE: (751), (8035) imply:
% 173.28/26.29  | | | | | | | | |   (8036)   ~ (all_10_0 = e1)
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | BETA: splitting (98) gives:
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | |   (8037)   ~ (all_28_0 = e3)
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | REDUCE: (776), (8037) imply:
% 173.28/26.29  | | | | | | | | | |   (8038)   ~ (all_6_0 = e3)
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | |   (8039)   ~ (all_42_0 = e1)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | REDUCE: (761), (8039) imply:
% 173.28/26.29  | | | | | | | | | | |   (8040)   ~ (all_4_0 = e1)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | |   (8041)  all_58_15 = e0
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (52), (62),
% 173.28/26.29  | | | | | | | | | | | |            (154), (155), (156), (158), (159), (163), (164),
% 173.28/26.29  | | | | | | | | | | | |            (165), (167), (169), (170), (172), (173), (174),
% 173.28/26.29  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 173.28/26.29  | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 173.28/26.29  | | | | | | | | | | | |            (276), (278), (280), (283), (302), (303), (304),
% 173.28/26.29  | | | | | | | | | | | |            (305), (306), (307), (310), (311), (313), (315),
% 173.28/26.29  | | | | | | | | | | | |            (316), (319), (322), (323), (324), (325), (326),
% 173.28/26.29  | | | | | | | | | | | |            (328), (330), (331), (341), (344), (349), (350),
% 173.28/26.29  | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.28/26.29  | | | | | | | | | | | |            (391), (403), (419), (425), (429), (530), (531),
% 173.28/26.29  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.28/26.29  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.28/26.29  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.28/26.29  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.28/26.29  | | | | | | | | | | | |            (566), (567), (569), (571), (573), (575), (577),
% 173.28/26.29  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.28/26.29  | | | | | | | | | | | |            (585), (586), (588), (591), (593), (594), (595),
% 173.28/26.29  | | | | | | | | | | | |            (596), (598), (599), (600), (661), (719), (7960),
% 173.28/26.29  | | | | | | | | | | | |            (7961), (7962), (7963), (7965), (7968), (8038),
% 173.28/26.29  | | | | | | | | | | | |            (8040), (8041), (function-axioms) are inconsistent
% 173.28/26.29  | | | | | | | | | | | |            by sub-proof #107.
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | |   (8042)   ~ (all_58_15 = e0)
% 173.28/26.29  | | | | | | | | | | | |   (8043)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.29  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.29  | | | | | | | | | | | |             e0)
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | ALPHA: (8043) implies:
% 173.28/26.29  | | | | | | | | | | | |   (8044)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.28/26.29  | | | | | | | | | | | |   (8045)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | REDUCE: (532), (8042) imply:
% 173.28/26.29  | | | | | | | | | | | |   (8046)   ~ (all_6_2 = e0)
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.28/26.29  | | | | | | | | | | | |            (42), (52), (53), (62), (154), (155), (156),
% 173.28/26.29  | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.28/26.29  | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.28/26.29  | | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.28/26.29  | | | | | | | | | | | |            (271), (272), (273), (274), (275), (277), (279),
% 173.28/26.29  | | | | | | | | | | | |            (280), (281), (282), (283), (303), (304), (305),
% 173.28/26.29  | | | | | | | | | | | |            (306), (307), (311), (313), (315), (317), (319),
% 173.28/26.29  | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (327),
% 173.28/26.29  | | | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 173.28/26.29  | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.28/26.29  | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 173.28/26.29  | | | | | | | | | | | |            (419), (429), (529), (531), (532), (533), (534),
% 173.28/26.29  | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.28/26.29  | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.28/26.29  | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.28/26.29  | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 173.28/26.29  | | | | | | | | | | | |            (569), (571), (573), (575), (577), (579), (580),
% 173.28/26.29  | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 173.28/26.29  | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.28/26.29  | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.28/26.29  | | | | | | | | | | | |            (7960), (7961), (7962), (7966), (8034), (8036),
% 173.28/26.29  | | | | | | | | | | | |            (8040), (8044), (8045), (8046), (function-axioms)
% 173.28/26.29  | | | | | | | | | | | |            are inconsistent by sub-proof #60.
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | |   (8047)  all_42_0 = e1
% 173.28/26.29  | | | | | | | | | | |   (8048)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.29  | | | | | | | | | | |            (43), (52), (53), (61), (62), (154), (155), (156),
% 173.28/26.29  | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.28/26.29  | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.28/26.29  | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.28/26.29  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.28/26.29  | | | | | | | | | | |            (278), (279), (280), (282), (283), (301), (302),
% 173.28/26.29  | | | | | | | | | | |            (303), (304), (305), (306), (307), (310), (311),
% 173.28/26.29  | | | | | | | | | | |            (313), (315), (317), (319), (321), (322), (323),
% 173.28/26.29  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 173.28/26.29  | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.28/26.29  | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 173.28/26.29  | | | | | | | | | | |            (403), (409), (415), (419), (425), (429), (477),
% 173.28/26.29  | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.28/26.29  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.28/26.29  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.28/26.29  | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.28/26.29  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.28/26.29  | | | | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 173.28/26.29  | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 173.28/26.29  | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.28/26.29  | | | | | | | | | | |            (597), (598), (599), (600), (649), (661), (719),
% 173.28/26.29  | | | | | | | | | | |            (761), (7959), (7960), (7961), (7962), (7963),
% 173.28/26.29  | | | | | | | | | | |            (7965), (7966), (8036), (8038), (8047), (8048),
% 173.28/26.29  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.29  | | | | | | | | | | |            #59.
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | |   (8049)  all_28_0 = e3
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | COMBINE_EQS: (776), (8049) imply:
% 173.28/26.29  | | | | | | | | | |   (8050)  all_6_0 = e3
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | SIMP: (8050) implies:
% 173.28/26.29  | | | | | | | | | |   (8051)  all_6_0 = e3
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | REDUCE: (43), (8051) imply:
% 173.28/26.29  | | | | | | | | | |   (8052)  op(all_6_1, all_6_2) = e3
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | |   (8053)   ~ (all_42_0 = e1)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | REDUCE: (761), (8053) imply:
% 173.28/26.29  | | | | | | | | | | |   (8054)   ~ (all_4_0 = e1)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | |   (8055)  all_58_15 = e0
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8052), (8055),
% 173.28/26.29  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.29  | | | | | | | | | | | |            #510.
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | |   (8056)   ~ (all_58_15 = e0)
% 173.28/26.29  | | | | | | | | | | | |   (8057)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.29  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.29  | | | | | | | | | | | |             e0)
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | ALPHA: (8057) implies:
% 173.28/26.29  | | | | | | | | | | | |   (8058)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.28/26.29  | | | | | | | | | | | |   (8059)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | REDUCE: (532), (8056) imply:
% 173.28/26.29  | | | | | | | | | | | |   (8060)   ~ (all_6_2 = e0)
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | |   (8061)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.28/26.29  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.28/26.29  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.28/26.29  | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | BETA: splitting (8061) gives:
% 173.28/26.29  | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | |   (8062)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.28/26.29  | | | | | | | | | | | | | |           all_52_6 = e0
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8062) are inconsistent by sub-proof
% 173.28/26.29  | | | | | | | | | | | | | |            #124.
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | |   (8063)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.28/26.29  | | | | | | | | | | | | | |           all_52_14 = e0
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | ALPHA: (8063) implies:
% 173.28/26.29  | | | | | | | | | | | | | |   (8064)  all_52_14 = e0
% 173.28/26.29  | | | | | | | | | | | | | |   (8065)  all_52_12 = e1
% 173.28/26.29  | | | | | | | | | | | | | |   (8066)  all_52_10 = e2
% 173.28/26.29  | | | | | | | | | | | | | |   (8067)  all_52_8 = e3
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | COMBINE_EQS: (661), (8066) imply:
% 173.28/26.29  | | | | | | | | | | | | | |   (8068)  all_10_1 = e2
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | REDUCE: (53), (8068) imply:
% 173.28/26.29  | | | | | | | | | | | | | |   (8069)  op(e2, all_10_2) = all_10_0
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | REDUCE: (183), (8067) imply:
% 173.28/26.29  | | | | | | | | | | | | | |   (8070)  op(e3, all_52_9) = e3
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | REDUCE: (52), (8068) imply:
% 173.28/26.29  | | | | | | | | | | | | | |   (8071)  op(e2, all_10_2) = e2
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | REDUCE: (167), (8065) imply:
% 173.28/26.29  | | | | | | | | | | | | | |   (8072)  op(e1, all_52_13) = e1
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | REDUCE: (159), (8064) imply:
% 173.28/26.29  | | | | | | | | | | | | | |   (8073)  op(e0, all_52_15) = e0
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 173.28/26.29  | | | | | | | | | | | | | |              all_10_2, e2, simplifying with (8069), (8071)
% 173.28/26.29  | | | | | | | | | | | | | |              gives:
% 173.28/26.29  | | | | | | | | | | | | | |   (8074)  all_10_0 = e2
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | |   (8075)  all_58_15 = e0
% 173.28/26.29  | | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8052), (8075),
% 173.28/26.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.29  | | | | | | | | | | | | | | |            #510.
% 173.28/26.29  | | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (42), (62), (154), (156),
% 173.28/26.29  | | | | | | | | | | | | | | |            (158), (163), (164), (165), (170), (172), (173),
% 173.28/26.29  | | | | | | | | | | | | | | |            (174), (177), (178), (179), (182), (268), (269),
% 173.28/26.29  | | | | | | | | | | | | | | |            (270), (272), (273), (274), (275), (277), (279),
% 173.28/26.29  | | | | | | | | | | | | | | |            (280), (282), (283), (304), (307), (311), (313),
% 173.28/26.29  | | | | | | | | | | | | | | |            (315), (317), (319), (321), (323), (326), (327),
% 173.28/26.29  | | | | | | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 173.28/26.29  | | | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.28/26.29  | | | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (415), (419),
% 173.28/26.29  | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.28/26.29  | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.28/26.29  | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 173.28/26.29  | | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.28/26.29  | | | | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.28/26.29  | | | | | | | | | | | | | | |            (575), (579), (580), (581), (582), (583), (585),
% 173.28/26.29  | | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.28/26.29  | | | | | | | | | | | | | | |            (595), (596), (597), (598), (599), (600), (7958),
% 173.28/26.29  | | | | | | | | | | | | | | |            (7961), (7962), (7966), (8036), (8054), (8059),
% 173.28/26.29  | | | | | | | | | | | | | | |            (8060), (8069), (8070), (8071), (8072), (8073),
% 173.28/26.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.29  | | | | | | | | | | | | | | |            #98.
% 173.28/26.29  | | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | |   (8076)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.28/26.29  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.28/26.29  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.28/26.29  | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.28/26.29  | | | | | | | | | | | | |            (42), (62), (154), (155), (156), (161), (164),
% 173.28/26.29  | | | | | | | | | | | | |            (165), (170), (172), (173), (177), (178), (179),
% 173.28/26.29  | | | | | | | | | | | | |            (181), (182), (183), (268), (269), (270), (271),
% 173.28/26.29  | | | | | | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 173.28/26.29  | | | | | | | | | | | | |            (307), (313), (315), (321), (322), (323), (324),
% 173.28/26.29  | | | | | | | | | | | | |            (325), (326), (327), (329), (330), (331), (341),
% 173.28/26.29  | | | | | | | | | | | | |            (344), (349), (364), (370), (373), (385), (391),
% 173.28/26.29  | | | | | | | | | | | | |            (392), (403), (413), (429), (529), (531), (532),
% 173.28/26.29  | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.28/26.29  | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.28/26.29  | | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 173.28/26.29  | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (567),
% 173.28/26.29  | | | | | | | | | | | | |            (568), (569), (571), (577), (580), (581), (582),
% 173.28/26.29  | | | | | | | | | | | | |            (585), (586), (589), (594), (595), (596), (597),
% 173.28/26.29  | | | | | | | | | | | | |            (649), (719), (7961), (7962), (8034), (8054),
% 173.28/26.29  | | | | | | | | | | | | |            (8058), (8059), (8060), (8076), (function-axioms)
% 173.28/26.29  | | | | | | | | | | | | |            are inconsistent by sub-proof #58.
% 173.28/26.29  | | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | |   (8077)  all_42_0 = e1
% 173.28/26.29  | | | | | | | | | | |   (8078)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | COMBINE_EQS: (761), (8077) imply:
% 173.28/26.29  | | | | | | | | | | |   (8079)  all_4_0 = e1
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | SIMP: (8079) implies:
% 173.28/26.29  | | | | | | | | | | |   (8080)  all_4_0 = e1
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | REDUCE: (7961), (8080) imply:
% 173.28/26.29  | | | | | | | | | | |   (8081)  op(e2, all_4_2) = e1
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.29  | | | | | | | | | | |            (52), (53), (61), (62), (154), (156), (158),
% 173.28/26.29  | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.28/26.29  | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (182),
% 173.28/26.29  | | | | | | | | | | |            (183), (185), (268), (269), (272), (273), (274),
% 173.28/26.29  | | | | | | | | | | |            (275), (276), (277), (279), (280), (282), (283),
% 173.28/26.29  | | | | | | | | | | |            (301), (304), (307), (310), (311), (313), (315),
% 173.28/26.29  | | | | | | | | | | |            (317), (319), (321), (323), (324), (326), (327),
% 173.28/26.29  | | | | | | | | | | |            (328), (329), (330), (331), (341), (349), (350),
% 173.28/26.29  | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.28/26.29  | | | | | | | | | | |            (391), (392), (403), (409), (415), (419), (425),
% 173.28/26.29  | | | | | | | | | | |            (477), (529), (531), (532), (533), (534), (535),
% 173.28/26.29  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.28/26.29  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.28/26.29  | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.28/26.29  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.28/26.29  | | | | | | | | | | |            (573), (575), (577), (579), (580), (581), (582),
% 173.28/26.29  | | | | | | | | | | |            (584), (586), (587), (588), (589), (591), (593),
% 173.28/26.29  | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.28/26.29  | | | | | | | | | | |            (649), (661), (719), (7959), (7960), (7962),
% 173.28/26.29  | | | | | | | | | | |            (7966), (8036), (8052), (8078), (8081),
% 173.28/26.29  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.29  | | | | | | | | | | |            #70.
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | End of split
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | Case 2:
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | |   (8082)  all_24_0 = e1
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | COMBINE_EQS: (751), (8082) imply:
% 173.28/26.29  | | | | | | | | |   (8083)  all_10_0 = e1
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | SIMP: (8083) implies:
% 173.28/26.29  | | | | | | | | |   (8084)  all_10_0 = e1
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | REDUCE: (7966), (8084) imply:
% 173.28/26.29  | | | | | | | | |   (8085)   ~ (e3 = e1)
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | REDUCE: (53), (8084) imply:
% 173.28/26.29  | | | | | | | | |   (8086)  op(all_10_1, all_10_2) = e1
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | BETA: splitting (98) gives:
% 173.28/26.29  | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | |   (8087)   ~ (all_28_0 = e3)
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | REDUCE: (776), (8087) imply:
% 173.28/26.29  | | | | | | | | | |   (8088)   ~ (all_6_0 = e3)
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.29  | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | |   (8089)   ~ (all_42_0 = e1)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | REDUCE: (761), (8089) imply:
% 173.28/26.29  | | | | | | | | | | |   (8090)   ~ (all_4_0 = e1)
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.29  | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | Case 1:
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.29  | | | | | | | | | | | |   (8091)  all_58_15 = e0
% 173.28/26.29  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (41), (42), (43), (52), (62),
% 173.28/26.30  | | | | | | | | | | | |            (154), (155), (156), (158), (159), (163), (164),
% 173.28/26.30  | | | | | | | | | | | |            (165), (167), (169), (170), (172), (173), (174),
% 173.28/26.30  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 173.28/26.30  | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 173.28/26.30  | | | | | | | | | | | |            (276), (278), (280), (283), (302), (303), (304),
% 173.28/26.30  | | | | | | | | | | | |            (305), (306), (307), (310), (311), (313), (315),
% 173.28/26.30  | | | | | | | | | | | |            (316), (319), (322), (323), (324), (325), (326),
% 173.28/26.30  | | | | | | | | | | | |            (328), (330), (331), (341), (344), (349), (350),
% 173.28/26.30  | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.28/26.30  | | | | | | | | | | | |            (391), (403), (419), (425), (429), (530), (531),
% 173.28/26.30  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.28/26.30  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.28/26.30  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.28/26.30  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.28/26.30  | | | | | | | | | | | |            (566), (567), (569), (571), (573), (575), (577),
% 173.28/26.30  | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.28/26.30  | | | | | | | | | | | |            (585), (586), (588), (591), (593), (594), (595),
% 173.28/26.30  | | | | | | | | | | | |            (596), (598), (599), (600), (661), (719), (7960),
% 173.28/26.30  | | | | | | | | | | | |            (7961), (7962), (7963), (7965), (7968), (8088),
% 173.28/26.30  | | | | | | | | | | | |            (8090), (8091), (function-axioms) are inconsistent
% 173.28/26.30  | | | | | | | | | | | |            by sub-proof #107.
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | |   (8092)   ~ (all_58_15 = e0)
% 173.28/26.30  | | | | | | | | | | | |   (8093)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.30  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.30  | | | | | | | | | | | |             e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.28/26.30  | | | | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.28/26.30  | | | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.28/26.30  | | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.28/26.30  | | | | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.28/26.30  | | | | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.28/26.30  | | | | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.28/26.30  | | | | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.28/26.30  | | | | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.28/26.30  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.28/26.30  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.28/26.30  | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.28/26.30  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.28/26.30  | | | | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.28/26.30  | | | | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.28/26.30  | | | | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.28/26.30  | | | | | | | | | | | |            (7962), (8034), (8086), (8090), (8092), (8093),
% 173.28/26.30  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.30  | | | | | | | | | | | |            #57.
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | |   (8094)  all_42_0 = e1
% 173.28/26.30  | | | | | | | | | | |   (8095)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | COMBINE_EQS: (761), (8094) imply:
% 173.28/26.30  | | | | | | | | | | |   (8096)  all_4_0 = e1
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | REDUCE: (7961), (8096) imply:
% 173.28/26.30  | | | | | | | | | | |   (8097)  op(e2, all_4_2) = e1
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.30  | | | | | | | | | | |            (43), (52), (62), (154), (155), (156), (158),
% 173.28/26.30  | | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.28/26.30  | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.28/26.30  | | | | | | | | | | |            (182), (183), (185), (268), (269), (270), (271),
% 173.28/26.30  | | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 173.28/26.30  | | | | | | | | | | |            (282), (283), (301), (302), (303), (304), (305),
% 173.28/26.30  | | | | | | | | | | |            (306), (307), (310), (311), (313), (315), (319),
% 173.28/26.30  | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 173.28/26.30  | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.28/26.30  | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.28/26.30  | | | | | | | | | | |            (391), (392), (403), (419), (425), (429), (477),
% 173.28/26.30  | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.28/26.30  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.28/26.30  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.28/26.30  | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.28/26.30  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.28/26.30  | | | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 173.28/26.30  | | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.28/26.30  | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.28/26.30  | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7959),
% 173.28/26.30  | | | | | | | | | | |            (7960), (7962), (7963), (7965), (7968), (8086),
% 173.28/26.30  | | | | | | | | | | |            (8088), (8095), (8097), (function-axioms) are
% 173.28/26.30  | | | | | | | | | | |            inconsistent by sub-proof #64.
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | |   (8098)  all_28_0 = e3
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | COMBINE_EQS: (776), (8098) imply:
% 173.28/26.30  | | | | | | | | | |   (8099)  all_6_0 = e3
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | SIMP: (8099) implies:
% 173.28/26.30  | | | | | | | | | |   (8100)  all_6_0 = e3
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | REDUCE: (43), (8100) imply:
% 173.28/26.30  | | | | | | | | | |   (8101)  op(all_6_1, all_6_2) = e3
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | |   (8102)   ~ (all_42_0 = e1)
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | REDUCE: (761), (8102) imply:
% 173.28/26.30  | | | | | | | | | | |   (8103)   ~ (all_4_0 = e1)
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | |   (8104)  all_58_15 = e0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8101), (8104),
% 173.28/26.30  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.30  | | | | | | | | | | | |            #510.
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | |   (8105)   ~ (all_58_15 = e0)
% 173.28/26.30  | | | | | | | | | | | |   (8106)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.30  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.30  | | | | | | | | | | | |             e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | ALPHA: (8106) implies:
% 173.28/26.30  | | | | | | | | | | | |   (8107)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.28/26.30  | | | | | | | | | | | |   (8108)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (532), (8105) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8109)   ~ (all_6_2 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | |   (8110)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.28/26.30  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.28/26.30  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | REF_CLOSE: (6), (9), (52), (661), (7960), (8086), (8110),
% 173.28/26.30  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.30  | | | | | | | | | | | | |            #69.
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | |   (8111)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.28/26.30  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.28/26.30  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.28/26.30  | | | | | | | | | | | | |            (42), (62), (154), (155), (156), (161), (164),
% 173.28/26.30  | | | | | | | | | | | | |            (165), (170), (172), (173), (177), (178), (179),
% 173.28/26.30  | | | | | | | | | | | | |            (181), (182), (183), (268), (269), (270), (271),
% 173.28/26.30  | | | | | | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 173.28/26.30  | | | | | | | | | | | | |            (307), (313), (315), (321), (322), (323), (324),
% 173.28/26.30  | | | | | | | | | | | | |            (325), (326), (327), (329), (330), (331), (341),
% 173.28/26.30  | | | | | | | | | | | | |            (344), (349), (364), (370), (373), (385), (391),
% 173.28/26.30  | | | | | | | | | | | | |            (392), (403), (413), (429), (529), (531), (532),
% 173.28/26.30  | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.28/26.30  | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.28/26.30  | | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 173.28/26.30  | | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (567),
% 173.28/26.30  | | | | | | | | | | | | |            (568), (569), (571), (577), (580), (581), (582),
% 173.28/26.30  | | | | | | | | | | | | |            (585), (586), (589), (594), (595), (596), (597),
% 173.28/26.30  | | | | | | | | | | | | |            (649), (719), (7961), (7962), (8034), (8103),
% 173.28/26.30  | | | | | | | | | | | | |            (8107), (8108), (8109), (8111), (function-axioms)
% 173.28/26.30  | | | | | | | | | | | | |            are inconsistent by sub-proof #58.
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | |   (8112)  all_42_0 = e1
% 173.28/26.30  | | | | | | | | | | |   (8113)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | COMBINE_EQS: (761), (8112) imply:
% 173.28/26.30  | | | | | | | | | | |   (8114)  all_4_0 = e1
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | SIMP: (8114) implies:
% 173.28/26.30  | | | | | | | | | | |   (8115)  all_4_0 = e1
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | REDUCE: (7961), (8115) imply:
% 173.28/26.30  | | | | | | | | | | |   (8116)  op(e2, all_4_2) = e1
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.30  | | | | | | | | | | |            (52), (62), (156), (158), (161), (163), (164),
% 173.28/26.30  | | | | | | | | | | |            (170), (172), (174), (177), (178), (179), (182),
% 173.28/26.30  | | | | | | | | | | |            (185), (268), (273), (274), (276), (283), (301),
% 173.28/26.30  | | | | | | | | | | |            (304), (307), (310), (311), (315), (319), (323),
% 173.28/26.30  | | | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.28/26.30  | | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (419),
% 173.28/26.30  | | | | | | | | | | |            (425), (477), (529), (531), (532), (533), (534),
% 173.28/26.30  | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.28/26.30  | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.28/26.30  | | | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.28/26.30  | | | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.28/26.30  | | | | | | | | | | |            (595), (596), (598), (600), (649), (661), (719),
% 173.28/26.30  | | | | | | | | | | |            (7959), (7960), (7962), (8086), (8101), (8113),
% 173.28/26.30  | | | | | | | | | | |            (8116), (function-axioms) are inconsistent by
% 173.28/26.30  | | | | | | | | | | |            sub-proof #61.
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | | 
% 173.28/26.30  | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | 
% 173.28/26.30  | | | | | | | End of split
% 173.28/26.30  | | | | | | | 
% 173.28/26.30  | | | | | | Case 2:
% 173.28/26.30  | | | | | | | 
% 173.28/26.30  | | | | | | |   (8117)  all_14_0 = e2
% 173.28/26.30  | | | | | | | 
% 173.28/26.30  | | | | | | | REDUCE: (63), (8117) imply:
% 173.28/26.30  | | | | | | |   (8118)  op(all_14_1, all_14_2) = e2
% 173.28/26.30  | | | | | | | 
% 173.28/26.30  | | | | | | | BETA: splitting (88) gives:
% 173.28/26.30  | | | | | | | 
% 173.28/26.30  | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | 
% 173.28/26.30  | | | | | | | |   (8119)   ~ (all_24_0 = e1)
% 173.28/26.30  | | | | | | | | 
% 173.28/26.30  | | | | | | | | REDUCE: (751), (8119) imply:
% 173.28/26.30  | | | | | | | |   (8120)   ~ (all_10_0 = e1)
% 173.28/26.30  | | | | | | | | 
% 173.28/26.30  | | | | | | | | BETA: splitting (98) gives:
% 173.28/26.30  | | | | | | | | 
% 173.28/26.30  | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | 
% 173.28/26.30  | | | | | | | | |   (8121)   ~ (all_28_0 = e3)
% 173.28/26.30  | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | REDUCE: (776), (8121) imply:
% 173.28/26.30  | | | | | | | | |   (8122)   ~ (all_6_0 = e3)
% 173.28/26.30  | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | BETA: splitting (103) gives:
% 173.28/26.30  | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | |   (8123)   ~ (all_30_1 = e1)
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | REDUCE: (712), (8123) imply:
% 173.28/26.30  | | | | | | | | | |   (8124)   ~ (all_10_1 = e1)
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.30  | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | |   (8125)   ~ (all_42_0 = e1)
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | REDUCE: (761), (8125) imply:
% 173.28/26.30  | | | | | | | | | | |   (8126)   ~ (all_4_0 = e1)
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.30  | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | |   (8127)  all_58_15 = e0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | COMBINE_EQS: (532), (8127) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8128)  all_6_2 = e0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (599), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8129)   ~ (all_52_15 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (600), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8130)   ~ (all_52_23 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (564), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8131)   ~ (all_52_25 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (582), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8132)   ~ (all_52_27 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (594), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8133)   ~ (all_52_29 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (43), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8134)  op(all_6_1, e0) = all_6_0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (42), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8135)  op(e0, e0) = all_6_1
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (41), (8128) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8136)  op(e0, e0) = e0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 173.28/26.30  | | | | | | | | | | | |              e0, e0, simplifying with (8135), (8136) gives:
% 173.28/26.30  | | | | | | | | | | | |   (8137)  all_6_1 = e0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (8134), (8137) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8138)  op(e0, e0) = all_6_0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 173.28/26.30  | | | | | | | | | | | |              e0, e0, simplifying with (8136), (8138) gives:
% 173.28/26.30  | | | | | | | | | | | |   (8139)  all_6_0 = e0
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (8122), (8139) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8140)   ~ (e3 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (7965), (8139) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8141)   ~ (e2 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | REDUCE: (7963), (8139) imply:
% 173.28/26.30  | | | | | | | | | | | |   (8142)   ~ (e1 = e0)
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.28/26.30  | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | |   (8143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.28/26.30  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.28/26.30  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | BETA: splitting (8143) gives:
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | |   (8144)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.28/26.30  | | | | | | | | | | | | | |           all_52_6 = e0
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8144) are inconsistent by sub-proof
% 173.28/26.30  | | | | | | | | | | | | | |            #124.
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | |   (8145)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.28/26.30  | | | | | | | | | | | | | |           all_52_14 = e0
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | ALPHA: (8145) implies:
% 173.28/26.30  | | | | | | | | | | | | | |   (8146)  all_52_14 = e0
% 173.28/26.30  | | | | | | | | | | | | | |   (8147)  all_52_12 = e1
% 173.28/26.30  | | | | | | | | | | | | | |   (8148)  all_52_10 = e2
% 173.28/26.30  | | | | | | | | | | | | | |   (8149)  all_52_8 = e3
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | COMBINE_EQS: (661), (8148) imply:
% 173.28/26.30  | | | | | | | | | | | | | |   (8150)  all_10_1 = e2
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | SIMP: (8150) implies:
% 173.28/26.30  | | | | | | | | | | | | | |   (8151)  all_10_1 = e2
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | REDUCE: (7968), (8151) imply:
% 173.28/26.30  | | | | | | | | | | | | | |   (8152)   ~ (e3 = e2)
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (52), (154),
% 173.28/26.30  | | | | | | | | | | | | | |            (155), (156), (159), (164), (167), (172), (179),
% 173.28/26.30  | | | | | | | | | | | | | |            (183), (269), (273), (276), (304), (305), (306),
% 173.28/26.30  | | | | | | | | | | | | | |            (307), (311), (315), (319), (323), (330), (341),
% 173.28/26.30  | | | | | | | | | | | | | |            (349), (359), (364), (370), (373), (385), (391),
% 173.28/26.30  | | | | | | | | | | | | | |            (403), (425), (533), (534), (535), (536), (537),
% 173.28/26.30  | | | | | | | | | | | | | |            (538), (539), (540), (542), (552), (553), (554),
% 173.28/26.30  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (565), (569),
% 173.28/26.30  | | | | | | | | | | | | | |            (571), (579), (581), (586), (595), (596), (8127),
% 173.28/26.30  | | | | | | | | | | | | | |            (8131), (8132), (8133), (8146), (8147), (8149),
% 173.28/26.30  | | | | | | | | | | | | | |            (8151), (function-axioms) are inconsistent by
% 173.28/26.30  | | | | | | | | | | | | | |            sub-proof #121.
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | End of split
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | |   (8153)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.28/26.30  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.28/26.30  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | BETA: splitting (8153) gives:
% 173.28/26.30  | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | Case 1:
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | |   (8154)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.28/26.30  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (62), (154), (155), (156),
% 173.28/26.30  | | | | | | | | | | | | | |            (158), (164), (165), (172), (174), (177), (178),
% 173.28/26.30  | | | | | | | | | | | | | |            (179), (182), (270), (271), (272), (273), (274),
% 173.28/26.30  | | | | | | | | | | | | | |            (275), (276), (278), (280), (283), (302), (303),
% 173.28/26.30  | | | | | | | | | | | | | |            (304), (305), (306), (307), (311), (319), (323),
% 173.28/26.30  | | | | | | | | | | | | | |            (324), (326), (330), (331), (344), (349), (350),
% 173.28/26.30  | | | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.28/26.30  | | | | | | | | | | | | | |            (403), (419), (425), (429), (530), (531), (533),
% 173.28/26.30  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.28/26.30  | | | | | | | | | | | | | |            (542), (544), (546), (548), (552), (553), (554),
% 173.28/26.30  | | | | | | | | | | | | | |            (555), (557), (558), (561), (562), (563), (565),
% 173.28/26.30  | | | | | | | | | | | | | |            (569), (571), (578), (579), (580), (581), (584),
% 173.28/26.30  | | | | | | | | | | | | | |            (585), (588), (591), (593), (596), (598), (719),
% 173.28/26.30  | | | | | | | | | | | | | |            (7963), (7965), (8122), (8127), (8129), (8130),
% 173.28/26.30  | | | | | | | | | | | | | |            (8131), (8132), (8133), (8134), (8135), (8136),
% 173.28/26.30  | | | | | | | | | | | | | |            (8154), (function-axioms) are inconsistent by
% 173.28/26.30  | | | | | | | | | | | | | |            sub-proof #117.
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | Case 2:
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | |   (8155)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.28/26.30  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | ALPHA: (8155) implies:
% 173.28/26.30  | | | | | | | | | | | | | |   (8156)  all_52_28 = e1
% 173.28/26.30  | | | | | | | | | | | | | |   (8157)  all_52_26 = e2
% 173.28/26.30  | | | | | | | | | | | | | |   (8158)  all_52_24 = e3
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | REDUCE: (181), (8158) imply:
% 173.28/26.30  | | | | | | | | | | | | | |   (8159)  op(e3, all_52_25) = e3
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | REDUCE: (173), (8157) imply:
% 173.28/26.30  | | | | | | | | | | | | | |   (8160)  op(e2, all_52_27) = e2
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.30  | | | | | | | | | | | | | | REDUCE: (165), (8156) imply:
% 173.28/26.30  | | | | | | | | | | | | | |   (8161)  op(e1, all_52_29) = e1
% 173.28/26.30  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (52), (163), (164),
% 173.28/26.31  | | | | | | | | | | | | | |            (169), (170), (172), (177), (178), (179), (182),
% 173.28/26.31  | | | | | | | | | | | | | |            (183), (270), (271), (272), (278), (280), (283),
% 173.28/26.31  | | | | | | | | | | | | | |            (302), (303), (304), (305), (310), (311), (313),
% 173.28/26.31  | | | | | | | | | | | | | |            (315), (316), (319), (322), (324), (325), (328),
% 173.28/26.31  | | | | | | | | | | | | | |            (344), (349), (350), (364), (370), (373), (385),
% 173.28/26.31  | | | | | | | | | | | | | |            (386), (391), (403), (429), (530), (531), (533),
% 173.28/26.31  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.28/26.31  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.28/26.31  | | | | | | | | | | | | | |            (554), (555), (556), (558), (560), (562), (563),
% 173.28/26.31  | | | | | | | | | | | | | |            (565), (566), (567), (569), (571), (573), (575),
% 173.28/26.31  | | | | | | | | | | | | | |            (577), (580), (583), (585), (586), (588), (591),
% 173.28/26.31  | | | | | | | | | | | | | |            (593), (595), (598), (7961), (7962), (8126),
% 173.28/26.31  | | | | | | | | | | | | | |            (8127), (8130), (8131), (8159), (8160), (8161),
% 173.28/26.31  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.31  | | | | | | | | | | | | | |            #110.
% 173.28/26.31  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | |   (8162)   ~ (all_58_15 = e0)
% 173.28/26.31  | | | | | | | | | | | |   (8163)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.31  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.31  | | | | | | | | | | | |             e0)
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.28/26.31  | | | | | | | | | | | |            (42), (52), (53), (62), (154), (155), (156),
% 173.28/26.31  | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.28/26.31  | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.28/26.31  | | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.28/26.31  | | | | | | | | | | | |            (271), (272), (273), (274), (275), (277), (279),
% 173.28/26.31  | | | | | | | | | | | |            (280), (281), (282), (283), (303), (304), (305),
% 173.28/26.31  | | | | | | | | | | | |            (306), (307), (311), (313), (315), (317), (319),
% 173.28/26.31  | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (327),
% 173.28/26.31  | | | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 173.28/26.31  | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.28/26.31  | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 173.28/26.31  | | | | | | | | | | | |            (419), (429), (529), (531), (532), (533), (534),
% 173.28/26.31  | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.28/26.31  | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.28/26.31  | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.28/26.31  | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 173.28/26.31  | | | | | | | | | | | |            (569), (571), (573), (575), (577), (579), (580),
% 173.28/26.31  | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 173.28/26.31  | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.28/26.31  | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.28/26.31  | | | | | | | | | | | |            (7960), (7961), (7962), (7966), (8118), (8120),
% 173.28/26.31  | | | | | | | | | | | |            (8126), (8162), (8163), (function-axioms) are
% 173.28/26.31  | | | | | | | | | | | |            inconsistent by sub-proof #55.
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | |   (8164)  all_42_0 = e1
% 173.28/26.31  | | | | | | | | | | |   (8165)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | COMBINE_EQS: (761), (8164) imply:
% 173.28/26.31  | | | | | | | | | | |   (8166)  all_4_0 = e1
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | REDUCE: (7961), (8166) imply:
% 173.28/26.31  | | | | | | | | | | |   (8167)  op(e2, all_4_2) = e1
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.31  | | | | | | | | | | |            (43), (52), (53), (61), (62), (154), (155), (156),
% 173.28/26.31  | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.28/26.31  | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.28/26.31  | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.28/26.31  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.28/26.31  | | | | | | | | | | |            (278), (279), (280), (282), (283), (301), (302),
% 173.28/26.31  | | | | | | | | | | |            (303), (304), (305), (306), (307), (310), (311),
% 173.28/26.31  | | | | | | | | | | |            (313), (315), (317), (319), (321), (322), (323),
% 173.28/26.31  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 173.28/26.31  | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.28/26.31  | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 173.28/26.31  | | | | | | | | | | |            (403), (409), (415), (419), (425), (429), (477),
% 173.28/26.31  | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.28/26.31  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.28/26.31  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.28/26.31  | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.28/26.31  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.28/26.31  | | | | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 173.28/26.31  | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 173.28/26.31  | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.28/26.31  | | | | | | | | | | |            (597), (598), (599), (600), (649), (661), (719),
% 173.28/26.31  | | | | | | | | | | |            (7959), (7960), (7962), (7963), (7965), (7966),
% 173.28/26.31  | | | | | | | | | | |            (8120), (8122), (8165), (8167), (function-axioms)
% 173.28/26.31  | | | | | | | | | | |            are inconsistent by sub-proof #72.
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | |   (8168)  all_30_1 = e1
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | COMBINE_EQS: (712), (8168) imply:
% 173.28/26.31  | | | | | | | | | |   (8169)  all_10_1 = e1
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | COMBINE_EQS: (661), (8169) imply:
% 173.28/26.31  | | | | | | | | | |   (8170)  all_52_10 = e1
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | REDUCE: (7968), (8169) imply:
% 173.28/26.31  | | | | | | | | | |   (8171)   ~ (e3 = e1)
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | Case 1:
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | |   (8172)   ~ (all_42_0 = e1)
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | REDUCE: (761), (8172) imply:
% 173.28/26.31  | | | | | | | | | | |   (8173)   ~ (all_4_0 = e1)
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | Case 1:
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | |   (8174)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.28/26.31  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.28/26.31  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | BETA: splitting (8174) gives:
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | Case 1:
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | |   (8175)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.28/26.31  | | | | | | | | | | | | |           all_52_6 = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8175) are inconsistent by sub-proof
% 173.28/26.31  | | | | | | | | | | | | |            #124.
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | |   (8176)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.28/26.31  | | | | | | | | | | | | |           all_52_14 = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REF_CLOSE: (6), (8170), (8176) are inconsistent by sub-proof
% 173.28/26.31  | | | | | | | | | | | | |            #533.
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | |   (8177)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.28/26.31  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.28/26.31  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | BETA: splitting (8177) gives:
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | Case 1:
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | |   (8178)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.28/26.31  | | | | | | | | | | | | |           all_52_22 = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REF_CLOSE: (6), (62), (719), (8118), (8178),
% 173.28/26.31  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.31  | | | | | | | | | | | | |            #314.
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | |   (8179)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.28/26.31  | | | | | | | | | | | | |           all_52_30 = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | ALPHA: (8179) implies:
% 173.28/26.31  | | | | | | | | | | | | |   (8180)  all_52_30 = e0
% 173.28/26.31  | | | | | | | | | | | | |   (8181)  all_52_28 = e1
% 173.28/26.31  | | | | | | | | | | | | |   (8182)  all_52_26 = e2
% 173.28/26.31  | | | | | | | | | | | | |   (8183)  all_52_24 = e3
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | COMBINE_EQS: (649), (8180) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8184)  all_6_1 = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | SIMP: (8184) implies:
% 173.28/26.31  | | | | | | | | | | | | |   (8185)  all_6_1 = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (43), (8185) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8186)  op(e0, all_6_2) = all_6_0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (181), (8183) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8187)  op(e3, all_52_25) = e3
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (173), (8182) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8188)  op(e2, all_52_27) = e2
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (165), (8181) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8189)  op(e1, all_52_29) = e1
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (42), (8185) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8190)  op(e0, all_6_2) = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 173.28/26.31  | | | | | | | | | | | | |              all_6_2, e0, simplifying with (8186), (8190)
% 173.28/26.31  | | | | | | | | | | | | |              gives:
% 173.28/26.31  | | | | | | | | | | | | |   (8191)  all_6_0 = e0
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (8122), (8191) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8192)   ~ (e3 = e0)
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (7965), (8191) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8193)   ~ (e2 = e0)
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | REDUCE: (7963), (8191) imply:
% 173.28/26.31  | | | | | | | | | | | | |   (8194)   ~ (e1 = e0)
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | Case 1:
% 173.28/26.31  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | |   (8195)  all_58_15 = e0
% 173.28/26.31  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (52), (163), (164),
% 173.28/26.31  | | | | | | | | | | | | | |            (169), (170), (172), (177), (178), (179), (182),
% 173.28/26.31  | | | | | | | | | | | | | |            (183), (270), (271), (272), (278), (280), (283),
% 173.28/26.31  | | | | | | | | | | | | | |            (302), (303), (304), (305), (310), (311), (313),
% 173.28/26.31  | | | | | | | | | | | | | |            (315), (316), (319), (322), (324), (325), (328),
% 173.28/26.31  | | | | | | | | | | | | | |            (344), (349), (350), (364), (370), (373), (385),
% 173.28/26.31  | | | | | | | | | | | | | |            (386), (391), (403), (429), (530), (531), (532),
% 173.28/26.31  | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.28/26.31  | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.28/26.31  | | | | | | | | | | | | | |            (553), (554), (555), (556), (558), (560), (562),
% 173.28/26.31  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (569), (571),
% 173.28/26.31  | | | | | | | | | | | | | |            (573), (575), (577), (580), (583), (585), (586),
% 173.28/26.31  | | | | | | | | | | | | | |            (588), (591), (593), (595), (598), (600), (7961),
% 173.28/26.31  | | | | | | | | | | | | | |            (7962), (8173), (8187), (8188), (8189), (8195),
% 173.28/26.31  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.31  | | | | | | | | | | | | | |            #54.
% 173.28/26.31  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | |   (8196)   ~ (all_58_15 = e0)
% 173.28/26.31  | | | | | | | | | | | | | |   (8197)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.31  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.31  | | | | | | | | | | | | | |             e0)
% 173.28/26.31  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.28/26.31  | | | | | | | | | | | | | |            (42), (52), (53), (62), (154), (155), (156),
% 173.28/26.31  | | | | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.28/26.31  | | | | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.28/26.31  | | | | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.28/26.31  | | | | | | | | | | | | | |            (271), (272), (273), (274), (275), (277), (279),
% 173.28/26.31  | | | | | | | | | | | | | |            (280), (281), (282), (283), (303), (304), (305),
% 173.28/26.31  | | | | | | | | | | | | | |            (306), (307), (311), (313), (315), (317), (319),
% 173.28/26.31  | | | | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (327),
% 173.28/26.31  | | | | | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 173.28/26.31  | | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.28/26.31  | | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 173.28/26.31  | | | | | | | | | | | | | |            (419), (429), (529), (531), (532), (533), (534),
% 173.28/26.31  | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.28/26.31  | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.28/26.31  | | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.28/26.31  | | | | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 173.28/26.31  | | | | | | | | | | | | | |            (569), (571), (573), (575), (577), (579), (580),
% 173.28/26.31  | | | | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 173.28/26.31  | | | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.28/26.31  | | | | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.28/26.31  | | | | | | | | | | | | | |            (7960), (7961), (7962), (7966), (8118), (8120),
% 173.28/26.31  | | | | | | | | | | | | | |            (8173), (8196), (8197), (function-axioms) are
% 173.28/26.31  | | | | | | | | | | | | | |            inconsistent by sub-proof #55.
% 173.28/26.31  | | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | |   (8198)  all_42_0 = e1
% 173.28/26.31  | | | | | | | | | | |   (8199)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.31  | | | | | | | | | | |            (43), (52), (53), (61), (62), (154), (155), (156),
% 173.28/26.31  | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.28/26.31  | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.28/26.31  | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.28/26.31  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.28/26.31  | | | | | | | | | | |            (278), (279), (280), (282), (283), (301), (302),
% 173.28/26.31  | | | | | | | | | | |            (303), (304), (305), (306), (307), (310), (311),
% 173.28/26.31  | | | | | | | | | | |            (313), (315), (317), (319), (321), (322), (323),
% 173.28/26.31  | | | | | | | | | | |            (324), (325), (326), (327), (328), (329), (330),
% 173.28/26.31  | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.28/26.31  | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 173.28/26.31  | | | | | | | | | | |            (403), (409), (415), (419), (425), (429), (477),
% 173.28/26.31  | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.28/26.31  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.28/26.31  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.28/26.31  | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.28/26.31  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.28/26.31  | | | | | | | | | | |            (571), (573), (575), (577), (578), (579), (580),
% 173.28/26.31  | | | | | | | | | | |            (581), (582), (583), (584), (585), (586), (587),
% 173.28/26.31  | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.28/26.31  | | | | | | | | | | |            (597), (598), (599), (600), (649), (661), (719),
% 173.28/26.31  | | | | | | | | | | |            (761), (7959), (7960), (7961), (7962), (7963),
% 173.28/26.31  | | | | | | | | | | |            (7965), (7966), (8120), (8122), (8198), (8199),
% 173.28/26.31  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.31  | | | | | | | | | | |            #59.
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | 
% 173.28/26.31  | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | 
% 173.28/26.31  | | | | | | | | |   (8200)  all_28_0 = e3
% 173.28/26.31  | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | COMBINE_EQS: (776), (8200) imply:
% 173.28/26.31  | | | | | | | | |   (8201)  all_6_0 = e3
% 173.28/26.31  | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | REDUCE: (43), (8201) imply:
% 173.28/26.31  | | | | | | | | |   (8202)  op(all_6_1, all_6_2) = e3
% 173.28/26.31  | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.31  | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | Case 1:
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | |   (8203)   ~ (all_42_0 = e1)
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | REDUCE: (761), (8203) imply:
% 173.28/26.31  | | | | | | | | | |   (8204)   ~ (all_4_0 = e1)
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | Case 1:
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | |   (8205)  all_58_15 = e0
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8202), (8205),
% 173.28/26.31  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.31  | | | | | | | | | | |            #510.
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | |   (8206)   ~ (all_58_15 = e0)
% 173.28/26.31  | | | | | | | | | | |   (8207)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.31  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.31  | | | | | | | | | | |             e0)
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | ALPHA: (8207) implies:
% 173.28/26.31  | | | | | | | | | | |   (8208)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.28/26.31  | | | | | | | | | | |   (8209)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | REDUCE: (532), (8206) imply:
% 173.28/26.31  | | | | | | | | | | |   (8210)   ~ (all_6_2 = e0)
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.28/26.31  | | | | | | | | | | |            (42), (52), (53), (62), (154), (155), (156),
% 173.28/26.31  | | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.28/26.31  | | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.28/26.31  | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.28/26.31  | | | | | | | | | | |            (271), (272), (273), (274), (275), (277), (279),
% 173.28/26.31  | | | | | | | | | | |            (280), (281), (282), (283), (303), (304), (305),
% 173.28/26.31  | | | | | | | | | | |            (306), (307), (311), (313), (315), (317), (319),
% 173.28/26.31  | | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (327),
% 173.28/26.31  | | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 173.28/26.31  | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.28/26.31  | | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 173.28/26.31  | | | | | | | | | | |            (419), (429), (529), (531), (532), (533), (534),
% 173.28/26.31  | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.28/26.31  | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.28/26.31  | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.28/26.31  | | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 173.28/26.31  | | | | | | | | | | |            (569), (571), (573), (575), (577), (579), (580),
% 173.28/26.31  | | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 173.28/26.31  | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.28/26.31  | | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.28/26.31  | | | | | | | | | | |            (7960), (7961), (7962), (7966), (8118), (8120),
% 173.28/26.31  | | | | | | | | | | |            (8204), (8208), (8209), (8210), (function-axioms)
% 173.28/26.31  | | | | | | | | | | |            are inconsistent by sub-proof #56.
% 173.28/26.31  | | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | | End of split
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | Case 2:
% 173.28/26.31  | | | | | | | | | | 
% 173.28/26.31  | | | | | | | | | |   (8211)  all_42_0 = e1
% 173.28/26.32  | | | | | | | | | |   (8212)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | COMBINE_EQS: (761), (8211) imply:
% 173.28/26.32  | | | | | | | | | |   (8213)  all_4_0 = e1
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | SIMP: (8213) implies:
% 173.28/26.32  | | | | | | | | | |   (8214)  all_4_0 = e1
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | REDUCE: (7961), (8214) imply:
% 173.28/26.32  | | | | | | | | | |   (8215)  op(e2, all_4_2) = e1
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.28/26.32  | | | | | | | | | |            (52), (53), (61), (62), (154), (156), (158),
% 173.28/26.32  | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.28/26.32  | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (182),
% 173.28/26.32  | | | | | | | | | |            (183), (185), (268), (269), (272), (273), (274),
% 173.28/26.32  | | | | | | | | | |            (275), (276), (277), (279), (280), (282), (283),
% 173.28/26.32  | | | | | | | | | |            (301), (304), (307), (310), (311), (313), (315),
% 173.28/26.32  | | | | | | | | | |            (317), (319), (321), (323), (324), (326), (327),
% 173.28/26.32  | | | | | | | | | |            (328), (329), (330), (331), (341), (349), (350),
% 173.28/26.32  | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.28/26.32  | | | | | | | | | |            (391), (392), (403), (409), (415), (419), (425),
% 173.28/26.32  | | | | | | | | | |            (477), (529), (531), (532), (533), (534), (535),
% 173.28/26.32  | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.28/26.32  | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.28/26.32  | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.28/26.32  | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.28/26.32  | | | | | | | | | |            (573), (575), (577), (579), (580), (581), (582),
% 173.28/26.32  | | | | | | | | | |            (584), (586), (587), (588), (589), (591), (593),
% 173.28/26.32  | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.28/26.32  | | | | | | | | | |            (649), (661), (719), (7959), (7960), (7962),
% 173.28/26.32  | | | | | | | | | |            (7966), (8120), (8202), (8212), (8215),
% 173.28/26.32  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.28/26.32  | | | | | | | | | |            #70.
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | End of split
% 173.28/26.32  | | | | | | | | | 
% 173.28/26.32  | | | | | | | | End of split
% 173.28/26.32  | | | | | | | | 
% 173.28/26.32  | | | | | | | Case 2:
% 173.28/26.32  | | | | | | | | 
% 173.28/26.32  | | | | | | | |   (8216)  all_24_0 = e1
% 173.28/26.32  | | | | | | | | 
% 173.28/26.32  | | | | | | | | COMBINE_EQS: (751), (8216) imply:
% 173.28/26.32  | | | | | | | |   (8217)  all_10_0 = e1
% 173.28/26.32  | | | | | | | | 
% 173.28/26.32  | | | | | | | | REDUCE: (7966), (8217) imply:
% 173.28/26.32  | | | | | | | |   (8218)   ~ (e3 = e1)
% 173.28/26.32  | | | | | | | | 
% 173.28/26.32  | | | | | | | | REDUCE: (53), (8217) imply:
% 173.28/26.32  | | | | | | | |   (8219)  op(all_10_1, all_10_2) = e1
% 173.28/26.32  | | | | | | | | 
% 173.28/26.32  | | | | | | | | BETA: splitting (98) gives:
% 173.28/26.32  | | | | | | | | 
% 173.28/26.32  | | | | | | | | Case 1:
% 173.28/26.32  | | | | | | | | | 
% 173.28/26.32  | | | | | | | | |   (8220)   ~ (all_28_0 = e3)
% 173.28/26.32  | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | REDUCE: (776), (8220) imply:
% 173.28/26.32  | | | | | | | | |   (8221)   ~ (all_6_0 = e3)
% 173.28/26.32  | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | BETA: splitting (133) gives:
% 173.28/26.32  | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | Case 1:
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | |   (8222)   ~ (all_42_0 = e1)
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | REDUCE: (761), (8222) imply:
% 173.28/26.32  | | | | | | | | | |   (8223)   ~ (all_4_0 = e1)
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | BETA: splitting (301) gives:
% 173.28/26.32  | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | Case 1:
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | |   (8224)  all_58_15 = e0
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | COMBINE_EQS: (532), (8224) imply:
% 173.28/26.32  | | | | | | | | | | |   (8225)  all_6_2 = e0
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (599), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8226)   ~ (all_52_15 = e0)
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (600), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8227)   ~ (all_52_23 = e0)
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (564), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8228)   ~ (all_52_25 = e0)
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (582), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8229)   ~ (all_52_27 = e0)
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (594), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8230)   ~ (all_52_29 = e0)
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (43), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8231)  op(all_6_1, e0) = all_6_0
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (42), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8232)  op(e0, e0) = all_6_1
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (41), (8225) imply:
% 173.28/26.32  | | | | | | | | | | |   (8233)  op(e0, e0) = e0
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (52), (62), (154), (155),
% 173.28/26.32  | | | | | | | | | | |            (156), (158), (159), (163), (164), (165), (167),
% 173.28/26.32  | | | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 173.28/26.32  | | | | | | | | | | |            (179), (181), (182), (183), (185), (269), (270),
% 173.28/26.32  | | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (278),
% 173.28/26.32  | | | | | | | | | | |            (280), (283), (302), (303), (304), (305), (306),
% 173.28/26.32  | | | | | | | | | | |            (307), (310), (311), (313), (315), (316), (319),
% 173.28/26.32  | | | | | | | | | | |            (322), (323), (324), (325), (326), (328), (330),
% 173.28/26.32  | | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.28/26.32  | | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (403),
% 173.28/26.32  | | | | | | | | | | |            (419), (425), (429), (530), (531), (533), (534),
% 173.28/26.32  | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.28/26.32  | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.28/26.32  | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.28/26.32  | | | | | | | | | | |            (562), (563), (565), (566), (567), (569), (571),
% 173.28/26.32  | | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.28/26.32  | | | | | | | | | | |            (583), (584), (585), (586), (588), (591), (593),
% 173.28/26.32  | | | | | | | | | | |            (595), (596), (598), (661), (719), (7960), (7961),
% 173.28/26.32  | | | | | | | | | | |            (7962), (7963), (7965), (7968), (8221), (8223),
% 173.28/26.32  | | | | | | | | | | |            (8224), (8226), (8227), (8228), (8229), (8230),
% 173.28/26.32  | | | | | | | | | | |            (8231), (8232), (8233), (function-axioms) are
% 173.28/26.32  | | | | | | | | | | |            inconsistent by sub-proof #108.
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | Case 2:
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | |   (8234)   ~ (all_58_15 = e0)
% 173.28/26.32  | | | | | | | | | | |   (8235)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.28/26.32  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.28/26.32  | | | | | | | | | | |             e0)
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | ALPHA: (8235) implies:
% 173.28/26.32  | | | | | | | | | | |   (8236)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.28/26.32  | | | | | | | | | | |   (8237)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.28/26.32  | | | | | | | | | | | 
% 173.28/26.32  | | | | | | | | | | | REDUCE: (532), (8234) imply:
% 173.28/26.32  | | | | | | | | | | |   (8238)   ~ (all_6_2 = e0)
% 173.28/26.32  | | | | | | | | | | | 
% 173.46/26.34  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.34  | | | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.34  | | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.34  | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.34  | | | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.34  | | | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.34  | | | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.34  | | | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.34  | | | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.34  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.34  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.34  | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.34  | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.34  | | | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.34  | | | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.34  | | | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.34  | | | | | | | | | | |            (7962), (8118), (8219), (8223), (8236), (8237),
% 173.46/26.34  | | | | | | | | | | |            (8238), (function-axioms) are inconsistent by
% 173.46/26.34  | | | | | | | | | | |            sub-proof #53.
% 173.46/26.34  | | | | | | | | | | | 
% 173.46/26.34  | | | | | | | | | | End of split
% 173.46/26.34  | | | | | | | | | | 
% 173.46/26.34  | | | | | | | | | Case 2:
% 173.46/26.34  | | | | | | | | | | 
% 173.46/26.34  | | | | | | | | | |   (8239)  all_42_0 = e1
% 173.46/26.34  | | | | | | | | | |   (8240)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.34  | | | | | | | | | | 
% 173.46/26.34  | | | | | | | | | | COMBINE_EQS: (761), (8239) imply:
% 173.46/26.34  | | | | | | | | | |   (8241)  all_4_0 = e1
% 173.46/26.34  | | | | | | | | | | 
% 173.46/26.34  | | | | | | | | | | REDUCE: (7961), (8241) imply:
% 173.46/26.34  | | | | | | | | | |   (8242)  op(e2, all_4_2) = e1
% 173.46/26.34  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.35  | | | | | | | | | |            (43), (52), (62), (154), (155), (156), (158),
% 173.46/26.35  | | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.46/26.35  | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.46/26.35  | | | | | | | | | |            (182), (183), (185), (268), (269), (270), (271),
% 173.46/26.35  | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 173.46/26.35  | | | | | | | | | |            (282), (283), (301), (302), (303), (304), (305),
% 173.46/26.35  | | | | | | | | | |            (306), (307), (310), (311), (313), (315), (319),
% 173.46/26.35  | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 173.46/26.35  | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.46/26.35  | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.46/26.35  | | | | | | | | | |            (391), (392), (403), (419), (425), (429), (477),
% 173.46/26.35  | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.46/26.35  | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.35  | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.35  | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.35  | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.46/26.35  | | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 173.46/26.35  | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.46/26.35  | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.46/26.35  | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7959),
% 173.46/26.35  | | | | | | | | | |            (7960), (7962), (7963), (7965), (7968), (8219),
% 173.46/26.35  | | | | | | | | | |            (8221), (8240), (8242), (function-axioms) are
% 173.46/26.35  | | | | | | | | | |            inconsistent by sub-proof #64.
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | |   (8243)  all_28_0 = e3
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | COMBINE_EQS: (776), (8243) imply:
% 173.46/26.35  | | | | | | | | |   (8244)  all_6_0 = e3
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | REDUCE: (43), (8244) imply:
% 173.46/26.35  | | | | | | | | |   (8245)  op(all_6_1, all_6_2) = e3
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | |   (8246)   ~ (all_42_0 = e1)
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | REDUCE: (761), (8246) imply:
% 173.46/26.35  | | | | | | | | | |   (8247)   ~ (all_4_0 = e1)
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | |   (8248)  all_58_15 = e0
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8245), (8248),
% 173.46/26.35  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | |            #510.
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | |   (8249)   ~ (all_58_15 = e0)
% 173.46/26.35  | | | | | | | | | | |   (8250)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.35  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.35  | | | | | | | | | | |             e0)
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.35  | | | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.35  | | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.35  | | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.35  | | | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.35  | | | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.35  | | | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.35  | | | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.35  | | | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.35  | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.35  | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.35  | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.35  | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.35  | | | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.35  | | | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.35  | | | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.35  | | | | | | | | | | |            (7962), (8118), (8219), (8247), (8249), (8250),
% 173.46/26.35  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | |            #52.
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | |   (8251)  all_42_0 = e1
% 173.46/26.35  | | | | | | | | | |   (8252)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | COMBINE_EQS: (761), (8251) imply:
% 173.46/26.35  | | | | | | | | | |   (8253)  all_4_0 = e1
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | SIMP: (8253) implies:
% 173.46/26.35  | | | | | | | | | |   (8254)  all_4_0 = e1
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | REDUCE: (7961), (8254) imply:
% 173.46/26.35  | | | | | | | | | |   (8255)  op(e2, all_4_2) = e1
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.35  | | | | | | | | | |            (52), (62), (156), (158), (161), (163), (164),
% 173.46/26.35  | | | | | | | | | |            (170), (172), (174), (177), (178), (179), (182),
% 173.46/26.35  | | | | | | | | | |            (185), (268), (273), (274), (276), (283), (301),
% 173.46/26.35  | | | | | | | | | |            (304), (307), (310), (311), (315), (319), (323),
% 173.46/26.35  | | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.46/26.35  | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (419),
% 173.46/26.35  | | | | | | | | | |            (425), (477), (529), (531), (532), (533), (534),
% 173.46/26.35  | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.35  | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.35  | | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.46/26.35  | | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.46/26.35  | | | | | | | | | |            (595), (596), (598), (600), (649), (661), (719),
% 173.46/26.35  | | | | | | | | | |            (7959), (7960), (7962), (8219), (8245), (8252),
% 173.46/26.35  | | | | | | | | | |            (8255), (function-axioms) are inconsistent by
% 173.46/26.35  | | | | | | | | | |            sub-proof #61.
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | 
% 173.46/26.35  | | | | | | | End of split
% 173.46/26.35  | | | | | | | 
% 173.46/26.35  | | | | | | End of split
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | Case 2:
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | |   (8256)  all_12_1 = e3
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | | COMBINE_EQS: (705), (8256) imply:
% 173.46/26.35  | | | | | |   (8257)  all_10_1 = e3
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | | SIMP: (8257) implies:
% 173.46/26.35  | | | | | |   (8258)  all_10_1 = e3
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | | COMBINE_EQS: (661), (8258) imply:
% 173.46/26.35  | | | | | |   (8259)  all_52_10 = e3
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | | REDUCE: (53), (8258) imply:
% 173.46/26.35  | | | | | |   (8260)  op(e3, all_10_2) = all_10_0
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | | REDUCE: (52), (8258) imply:
% 173.46/26.35  | | | | | |   (8261)  op(e2, all_10_2) = e3
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | | BETA: splitting (64) gives:
% 173.46/26.35  | | | | | | 
% 173.46/26.35  | | | | | | Case 1:
% 173.46/26.35  | | | | | | | 
% 173.46/26.35  | | | | | | |   (8262)   ~ (all_14_0 = e2)
% 173.46/26.35  | | | | | | | 
% 173.46/26.35  | | | | | | | BETA: splitting (74) gives:
% 173.46/26.35  | | | | | | | 
% 173.46/26.35  | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | 
% 173.46/26.35  | | | | | | | |   (8263)   ~ (all_18_0 = e3)
% 173.46/26.35  | | | | | | | | 
% 173.46/26.35  | | | | | | | | REDUCE: (789), (8263) imply:
% 173.46/26.35  | | | | | | | |   (8264)   ~ (all_14_0 = e3)
% 173.46/26.35  | | | | | | | | 
% 173.46/26.35  | | | | | | | | BETA: splitting (98) gives:
% 173.46/26.35  | | | | | | | | 
% 173.46/26.35  | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | |   (8265)   ~ (all_28_0 = e3)
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | REDUCE: (776), (8265) imply:
% 173.46/26.35  | | | | | | | | |   (8266)   ~ (all_6_0 = e3)
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.35  | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | |   (8267)   ~ (all_42_0 = e1)
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | REDUCE: (761), (8267) imply:
% 173.46/26.35  | | | | | | | | | |   (8268)   ~ (all_4_0 = e1)
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | |   (8269)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.35  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.35  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | BETA: splitting (8269) gives:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | |   (8270)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.35  | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8270) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | | |            #124.
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | |   (8271)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.35  | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REF_CLOSE: (9), (8259), (8271) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | | |            #289.
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | |   (8272)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.35  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.35  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | BETA: splitting (8272) gives:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | |   (8273)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.35  | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | ALPHA: (8273) implies:
% 173.46/26.35  | | | | | | | | | | | |   (8274)  all_52_22 = e0
% 173.46/26.35  | | | | | | | | | | | |   (8275)  all_52_20 = e1
% 173.46/26.35  | | | | | | | | | | | |   (8276)  all_52_18 = e2
% 173.46/26.35  | | | | | | | | | | | |   (8277)  all_52_16 = e3
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | COMBINE_EQS: (719), (8275) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8278)  all_14_1 = e1
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REDUCE: (63), (8278) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8279)  op(e1, all_14_2) = all_14_0
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REDUCE: (182), (8277) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8280)  op(e3, all_52_17) = e3
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REDUCE: (174), (8276) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8281)  op(e2, all_52_19) = e2
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REDUCE: (62), (8278) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8282)  op(e1, all_14_2) = e1
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REDUCE: (158), (8274) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8283)  op(e0, all_52_23) = e0
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.35  | | | | | | | | | | | |              all_14_2, e1, simplifying with (8279), (8282)
% 173.46/26.35  | | | | | | | | | | | |              gives:
% 173.46/26.35  | | | | | | | | | | | |   (8284)  all_14_0 = e1
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REDUCE: (8264), (8284) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8285)   ~ (e3 = e1)
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REDUCE: (8262), (8284) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8286)   ~ (e2 = e1)
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | |   (8287)  all_58_15 = e0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | COMBINE_EQS: (532), (8287) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8288)  all_6_2 = e0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (599), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8289)   ~ (all_52_15 = e0)
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (600), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8290)   ~ (all_52_23 = e0)
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (564), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8291)   ~ (all_52_25 = e0)
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (582), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8292)   ~ (all_52_27 = e0)
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (594), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8293)   ~ (all_52_29 = e0)
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (43), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8294)  op(all_6_1, e0) = all_6_0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (42), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8295)  op(e0, e0) = all_6_1
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (41), (8288) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8296)  op(e0, e0) = e0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (154), (155), (156), (164),
% 173.46/26.35  | | | | | | | | | | | | |            (165), (172), (177), (178), (179), (270), (271),
% 173.46/26.35  | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 173.46/26.35  | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (306), (307),
% 173.46/26.35  | | | | | | | | | | | | |            (311), (319), (323), (324), (326), (330), (331),
% 173.46/26.35  | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 173.46/26.35  | | | | | | | | | | | | |            (373), (385), (386), (403), (419), (425), (429),
% 173.46/26.35  | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 173.46/26.35  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.35  | | | | | | | | | | | | |            (552), (553), (554), (555), (557), (558), (561),
% 173.46/26.35  | | | | | | | | | | | | |            (562), (563), (565), (569), (571), (578), (579),
% 173.46/26.35  | | | | | | | | | | | | |            (580), (581), (584), (585), (588), (591), (593),
% 173.46/26.35  | | | | | | | | | | | | |            (596), (598), (7963), (7965), (8266), (8280),
% 173.46/26.35  | | | | | | | | | | | | |            (8281), (8282), (8283), (8287), (8289), (8290),
% 173.46/26.35  | | | | | | | | | | | | |            (8291), (8292), (8293), (8294), (8295), (8296),
% 173.46/26.35  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | | | |            #119.
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | |   (8297)   ~ (all_58_15 = e0)
% 173.46/26.35  | | | | | | | | | | | | |   (8298)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.35  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.35  | | | | | | | | | | | | |             e0)
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | ALPHA: (8298) implies:
% 173.46/26.35  | | | | | | | | | | | | |   (8299)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.35  | | | | | | | | | | | | |   (8300)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (532), (8297) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8301)   ~ (all_6_2 = e0)
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.35  | | | | | | | | | | | | |            (42), (51), (155), (156), (163), (164), (165),
% 173.46/26.35  | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (183),
% 173.46/26.35  | | | | | | | | | | | | |            (268), (270), (271), (274), (275), (276), (277),
% 173.46/26.35  | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (304), (306),
% 173.46/26.35  | | | | | | | | | | | | |            (307), (310), (311), (314), (315), (316), (317),
% 173.46/26.35  | | | | | | | | | | | | |            (319), (321), (322), (323), (324), (325), (326),
% 173.46/26.35  | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (344), (349),
% 173.46/26.35  | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 173.46/26.35  | | | | | | | | | | | | |            (392), (403), (413), (415), (419), (425), (429),
% 173.46/26.35  | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.46/26.35  | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.35  | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.35  | | | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.46/26.35  | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.46/26.35  | | | | | | | | | | | | |            (573), (577), (578), (582), (583), (584), (585),
% 173.46/26.35  | | | | | | | | | | | | |            (586), (587), (588), (594), (595), (596), (598),
% 173.46/26.35  | | | | | | | | | | | | |            (599), (600), (7958), (7961), (7962), (8260),
% 173.46/26.35  | | | | | | | | | | | | |            (8261), (8268), (8280), (8281), (8282), (8283),
% 173.46/26.35  | | | | | | | | | | | | |            (8299), (8300), (8301), (function-axioms) are
% 173.46/26.35  | | | | | | | | | | | | |            inconsistent by sub-proof #47.
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | |   (8302)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.35  | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | ALPHA: (8302) implies:
% 173.46/26.35  | | | | | | | | | | | |   (8303)  all_52_30 = e0
% 173.46/26.35  | | | | | | | | | | | |   (8304)  all_52_28 = e1
% 173.46/26.35  | | | | | | | | | | | |   (8305)  all_52_26 = e2
% 173.46/26.35  | | | | | | | | | | | |   (8306)  all_52_24 = e3
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | COMBINE_EQS: (649), (8303) imply:
% 173.46/26.35  | | | | | | | | | | | |   (8307)  all_6_1 = e0
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.35  | | | | | | | | | | | |            (42), (51), (154), (155), (156), (161), (163),
% 173.46/26.35  | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (177),
% 173.46/26.35  | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (269),
% 173.46/26.35  | | | | | | | | | | | |            (270), (271), (278), (280), (281), (282), (283),
% 173.46/26.35  | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.46/26.35  | | | | | | | | | | | |            (310), (311), (313), (315), (316), (317), (318),
% 173.46/26.35  | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 173.46/26.35  | | | | | | | | | | | |            (326), (327), (329), (330), (331), (341), (344),
% 173.46/26.35  | | | | | | | | | | | |            (349), (364), (370), (373), (385), (386), (391),
% 173.46/26.35  | | | | | | | | | | | |            (392), (403), (413), (429), (529), (530), (531),
% 173.46/26.35  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.46/26.35  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.46/26.35  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.46/26.35  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.46/26.35  | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.35  | | | | | | | | | | | |            (577), (580), (581), (582), (583), (585), (586),
% 173.46/26.35  | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.46/26.35  | | | | | | | | | | | |            (597), (598), (599), (600), (7961), (7962),
% 173.46/26.35  | | | | | | | | | | | |            (8261), (8268), (8304), (8305), (8306), (8307),
% 173.46/26.35  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | | |            #44.
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | |   (8308)  all_42_0 = e1
% 173.46/26.35  | | | | | | | | | |   (8309)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | COMBINE_EQS: (761), (8308) imply:
% 173.46/26.35  | | | | | | | | | |   (8310)  all_4_0 = e1
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | REDUCE: (7961), (8310) imply:
% 173.46/26.35  | | | | | | | | | |   (8311)  op(e2, all_4_2) = e1
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | BETA: splitting (8309) gives:
% 173.46/26.35  | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | |   (8312)   ~ (all_42_1 = e2)
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | REDUCE: (7959), (8312) imply:
% 173.46/26.35  | | | | | | | | | | |   (8313)  $false
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | CLOSE: (8313) is inconsistent.
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | |   (8314)   ~ (all_42_2 = e0)
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | REDUCE: (477), (8314) imply:
% 173.46/26.35  | | | | | | | | | | |   (8315)   ~ (all_4_2 = e0)
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.35  | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | |   (8316)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.35  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.35  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | BETA: splitting (8316) gives:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | |   (8317)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.35  | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8317) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | | | |            #124.
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | |   (8318)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.35  | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REF_CLOSE: (9), (8259), (8318) are inconsistent by sub-proof
% 173.46/26.35  | | | | | | | | | | | | |            #289.
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | End of split
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | Case 2:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | |   (8319)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.35  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.35  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | BETA: splitting (8319) gives:
% 173.46/26.35  | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | Case 1:
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | |   (8320)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.35  | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | ALPHA: (8320) implies:
% 173.46/26.35  | | | | | | | | | | | | |   (8321)  all_52_22 = e0
% 173.46/26.35  | | | | | | | | | | | | |   (8322)  all_52_20 = e1
% 173.46/26.35  | | | | | | | | | | | | |   (8323)  all_52_18 = e2
% 173.46/26.35  | | | | | | | | | | | | |   (8324)  all_52_16 = e3
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | COMBINE_EQS: (719), (8322) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8325)  all_14_1 = e1
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (63), (8325) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8326)  op(e1, all_14_2) = all_14_0
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (182), (8324) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8327)  op(e3, all_52_17) = e3
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (174), (8323) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8328)  op(e2, all_52_19) = e2
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (62), (8325) imply:
% 173.46/26.35  | | | | | | | | | | | | |   (8329)  op(e1, all_14_2) = e1
% 173.46/26.35  | | | | | | | | | | | | | 
% 173.46/26.35  | | | | | | | | | | | | | REDUCE: (158), (8321) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8330)  op(e0, all_52_23) = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.36  | | | | | | | | | | | | |              all_14_2, e1, simplifying with (8326), (8329)
% 173.46/26.36  | | | | | | | | | | | | |              gives:
% 173.46/26.36  | | | | | | | | | | | | |   (8331)  all_14_0 = e1
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (8264), (8331) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8332)   ~ (e3 = e1)
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (8262), (8331) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8333)   ~ (e2 = e1)
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | |   (8334)  all_58_15 = e0
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | COMBINE_EQS: (532), (8334) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8335)  all_6_2 = e0
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (599), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8336)   ~ (all_52_15 = e0)
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (600), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8337)   ~ (all_52_23 = e0)
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (564), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8338)   ~ (all_52_25 = e0)
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (582), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8339)   ~ (all_52_27 = e0)
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (594), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8340)   ~ (all_52_29 = e0)
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (43), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8341)  op(all_6_1, e0) = all_6_0
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (42), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8342)  op(e0, e0) = all_6_1
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REDUCE: (41), (8335) imply:
% 173.46/26.36  | | | | | | | | | | | | | |   (8343)  op(e0, e0) = e0
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (154), (155), (156), (164),
% 173.46/26.36  | | | | | | | | | | | | | |            (165), (172), (177), (178), (179), (270), (271),
% 173.46/26.36  | | | | | | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 173.46/26.36  | | | | | | | | | | | | | |            (283), (302), (303), (304), (305), (306), (307),
% 173.46/26.36  | | | | | | | | | | | | | |            (311), (319), (323), (324), (326), (330), (331),
% 173.46/26.36  | | | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 173.46/26.36  | | | | | | | | | | | | | |            (373), (385), (386), (403), (419), (425), (429),
% 173.46/26.36  | | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 173.46/26.36  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.36  | | | | | | | | | | | | | |            (552), (553), (554), (555), (557), (558), (561),
% 173.46/26.36  | | | | | | | | | | | | | |            (562), (563), (565), (569), (571), (578), (579),
% 173.46/26.36  | | | | | | | | | | | | | |            (580), (581), (584), (585), (588), (591), (593),
% 173.46/26.36  | | | | | | | | | | | | | |            (596), (598), (7963), (7965), (8266), (8327),
% 173.46/26.36  | | | | | | | | | | | | | |            (8328), (8329), (8330), (8334), (8336), (8337),
% 173.46/26.36  | | | | | | | | | | | | | |            (8338), (8339), (8340), (8341), (8342), (8343),
% 173.46/26.36  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.36  | | | | | | | | | | | | | |            #119.
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | |   (8344)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.36  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.36  | | | | | | | | | | | | | |             e0)
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | ALPHA: (8344) implies:
% 173.46/26.36  | | | | | | | | | | | | | |   (8345)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (156), (161),
% 173.46/26.36  | | | | | | | | | | | | | |            (163), (164), (170), (172), (177), (178), (179),
% 173.46/26.36  | | | | | | | | | | | | | |            (268), (273), (274), (276), (283), (304), (307),
% 173.46/26.36  | | | | | | | | | | | | | |            (310), (311), (315), (319), (323), (324), (326),
% 173.46/26.36  | | | | | | | | | | | | | |            (328), (330), (331), (349), (359), (364), (370),
% 173.46/26.36  | | | | | | | | | | | | | |            (373), (385), (391), (403), (419), (425), (529),
% 173.46/26.36  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.36  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.36  | | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (558), (559),
% 173.46/26.36  | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (577), (579),
% 173.46/26.36  | | | | | | | | | | | | | |            (584), (586), (587), (593), (595), (596), (598),
% 173.46/26.36  | | | | | | | | | | | | | |            (600), (7962), (8311), (8315), (8327), (8328),
% 173.46/26.36  | | | | | | | | | | | | | |            (8329), (8330), (8345), (function-axioms) are
% 173.46/26.36  | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | |   (8346)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.36  | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | ALPHA: (8346) implies:
% 173.46/26.36  | | | | | | | | | | | | |   (8347)  all_52_30 = e0
% 173.46/26.36  | | | | | | | | | | | | |   (8348)  all_52_28 = e1
% 173.46/26.36  | | | | | | | | | | | | |   (8349)  all_52_26 = e2
% 173.46/26.36  | | | | | | | | | | | | |   (8350)  all_52_24 = e3
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | COMBINE_EQS: (649), (8347) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8351)  all_6_1 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (42), (51), (156), (164), (165), (170),
% 173.46/26.36  | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (268),
% 173.46/26.36  | | | | | | | | | | | | |            (276), (278), (282), (283), (304), (307), (315),
% 173.46/26.36  | | | | | | | | | | | | |            (319), (323), (325), (327), (328), (330), (349),
% 173.46/26.36  | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (392), (403),
% 173.46/26.36  | | | | | | | | | | | | |            (425), (477), (529), (530), (531), (532), (533),
% 173.46/26.36  | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.46/26.36  | | | | | | | | | | | | |            (544), (546), (548), (554), (555), (556), (557),
% 173.46/26.36  | | | | | | | | | | | | |            (560), (561), (565), (568), (569), (573), (575),
% 173.46/26.36  | | | | | | | | | | | | |            (580), (589), (593), (597), (7959), (7962),
% 173.46/26.36  | | | | | | | | | | | | |            (8261), (8309), (8311), (8348), (8349), (8350),
% 173.46/26.36  | | | | | | | | | | | | |            (8351), (function-axioms) are inconsistent by
% 173.46/26.36  | | | | | | | | | | | | |            sub-proof #41.
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | 
% 173.46/26.36  | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | 
% 173.46/26.36  | | | | | | | | |   (8352)  all_28_0 = e3
% 173.46/26.36  | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | COMBINE_EQS: (776), (8352) imply:
% 173.46/26.36  | | | | | | | | |   (8353)  all_6_0 = e3
% 173.46/26.36  | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | SIMP: (8353) implies:
% 173.46/26.36  | | | | | | | | |   (8354)  all_6_0 = e3
% 173.46/26.36  | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | REDUCE: (43), (8354) imply:
% 173.46/26.36  | | | | | | | | |   (8355)  op(all_6_1, all_6_2) = e3
% 173.46/26.36  | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.36  | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | |   (8356)   ~ (all_42_0 = e1)
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | REDUCE: (761), (8356) imply:
% 173.46/26.36  | | | | | | | | | |   (8357)   ~ (all_4_0 = e1)
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | |   (8358)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.36  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.36  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | BETA: splitting (8358) gives:
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | |   (8359)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.36  | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8359) are inconsistent by sub-proof
% 173.46/26.36  | | | | | | | | | | | |            #124.
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | |   (8360)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.36  | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REF_CLOSE: (9), (8259), (8360) are inconsistent by sub-proof
% 173.46/26.36  | | | | | | | | | | | |            #289.
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | |   (8361)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.36  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.36  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | BETA: splitting (8361) gives:
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | |   (8362)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.36  | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | ALPHA: (8362) implies:
% 173.46/26.36  | | | | | | | | | | | |   (8363)  all_52_22 = e0
% 173.46/26.36  | | | | | | | | | | | |   (8364)  all_52_20 = e1
% 173.46/26.36  | | | | | | | | | | | |   (8365)  all_52_18 = e2
% 173.46/26.36  | | | | | | | | | | | |   (8366)  all_52_16 = e3
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | COMBINE_EQS: (719), (8364) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8367)  all_14_1 = e1
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | SIMP: (8367) implies:
% 173.46/26.36  | | | | | | | | | | | |   (8368)  all_14_1 = e1
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REDUCE: (63), (8368) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8369)  op(e1, all_14_2) = all_14_0
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REDUCE: (182), (8366) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8370)  op(e3, all_52_17) = e3
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REDUCE: (174), (8365) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8371)  op(e2, all_52_19) = e2
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REDUCE: (62), (8368) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8372)  op(e1, all_14_2) = e1
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REDUCE: (158), (8363) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8373)  op(e0, all_52_23) = e0
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.36  | | | | | | | | | | | |              all_14_2, e1, simplifying with (8369), (8372)
% 173.46/26.36  | | | | | | | | | | | |              gives:
% 173.46/26.36  | | | | | | | | | | | |   (8374)  all_14_0 = e1
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REDUCE: (8264), (8374) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8375)   ~ (e3 = e1)
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REDUCE: (8262), (8374) imply:
% 173.46/26.36  | | | | | | | | | | | |   (8376)   ~ (e2 = e1)
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | |   (8377)  all_58_15 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8355), (8377),
% 173.46/26.36  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.36  | | | | | | | | | | | | |            #510.
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | |   (8378)   ~ (all_58_15 = e0)
% 173.46/26.36  | | | | | | | | | | | | |   (8379)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.36  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.36  | | | | | | | | | | | | |             e0)
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.36  | | | | | | | | | | | | |            (42), (51), (155), (156), (163), (164), (165),
% 173.46/26.36  | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (183),
% 173.46/26.36  | | | | | | | | | | | | |            (268), (270), (271), (274), (275), (276), (277),
% 173.46/26.36  | | | | | | | | | | | | |            (278), (280), (281), (282), (283), (304), (306),
% 173.46/26.36  | | | | | | | | | | | | |            (307), (310), (311), (314), (315), (316), (317),
% 173.46/26.36  | | | | | | | | | | | | |            (319), (321), (322), (323), (324), (325), (326),
% 173.46/26.36  | | | | | | | | | | | | |            (327), (328), (329), (330), (331), (344), (349),
% 173.46/26.36  | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 173.46/26.36  | | | | | | | | | | | | |            (392), (403), (413), (415), (419), (425), (429),
% 173.46/26.36  | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.46/26.36  | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.36  | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.36  | | | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.46/26.36  | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.46/26.36  | | | | | | | | | | | | |            (573), (577), (578), (582), (583), (584), (585),
% 173.46/26.36  | | | | | | | | | | | | |            (586), (587), (588), (594), (595), (596), (598),
% 173.46/26.36  | | | | | | | | | | | | |            (599), (600), (7958), (7961), (7962), (8260),
% 173.46/26.36  | | | | | | | | | | | | |            (8261), (8357), (8370), (8371), (8372), (8373),
% 173.46/26.36  | | | | | | | | | | | | |            (8378), (8379), (function-axioms) are inconsistent
% 173.46/26.36  | | | | | | | | | | | | |            by sub-proof #40.
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | |   (8380)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.36  | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.36  | | | | | | | | | | | |            (42), (51), (154), (155), (156), (161), (163),
% 173.46/26.36  | | | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (177),
% 173.46/26.36  | | | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (269),
% 173.46/26.36  | | | | | | | | | | | |            (270), (271), (278), (280), (281), (282), (283),
% 173.46/26.36  | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.46/26.36  | | | | | | | | | | | |            (310), (311), (313), (315), (316), (317), (318),
% 173.46/26.36  | | | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 173.46/26.36  | | | | | | | | | | | |            (326), (327), (329), (330), (331), (341), (344),
% 173.46/26.36  | | | | | | | | | | | |            (349), (364), (370), (373), (385), (386), (391),
% 173.46/26.36  | | | | | | | | | | | |            (392), (403), (413), (429), (529), (530), (531),
% 173.46/26.36  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.46/26.36  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.46/26.36  | | | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.46/26.36  | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.46/26.36  | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.36  | | | | | | | | | | | |            (577), (580), (581), (582), (583), (585), (586),
% 173.46/26.36  | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.46/26.36  | | | | | | | | | | | |            (597), (598), (599), (600), (649), (7961), (7962),
% 173.46/26.36  | | | | | | | | | | | |            (8261), (8357), (8380), (function-axioms) are
% 173.46/26.36  | | | | | | | | | | | |            inconsistent by sub-proof #39.
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | |   (8381)  all_42_0 = e1
% 173.46/26.36  | | | | | | | | | |   (8382)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | COMBINE_EQS: (761), (8381) imply:
% 173.46/26.36  | | | | | | | | | |   (8383)  all_4_0 = e1
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | SIMP: (8383) implies:
% 173.46/26.36  | | | | | | | | | |   (8384)  all_4_0 = e1
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | REDUCE: (7961), (8384) imply:
% 173.46/26.36  | | | | | | | | | |   (8385)  op(e2, all_4_2) = e1
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | BETA: splitting (8382) gives:
% 173.46/26.36  | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | |   (8386)   ~ (all_42_1 = e2)
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | REDUCE: (7959), (8386) imply:
% 173.46/26.36  | | | | | | | | | | |   (8387)  $false
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | CLOSE: (8387) is inconsistent.
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | |   (8388)   ~ (all_42_2 = e0)
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | REDUCE: (477), (8388) imply:
% 173.46/26.36  | | | | | | | | | | |   (8389)   ~ (all_4_2 = e0)
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.36  | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | |   (8390)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.36  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.36  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | BETA: splitting (8390) gives:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | |   (8391)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.36  | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8391) are inconsistent by sub-proof
% 173.46/26.36  | | | | | | | | | | | | |            #124.
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | |   (8392)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.36  | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REF_CLOSE: (9), (8259), (8392) are inconsistent by sub-proof
% 173.46/26.36  | | | | | | | | | | | | |            #289.
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | |   (8393)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.36  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.36  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | BETA: splitting (8393) gives:
% 173.46/26.36  | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | |   (8394)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.36  | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | ALPHA: (8394) implies:
% 173.46/26.36  | | | | | | | | | | | | |   (8395)  all_52_22 = e0
% 173.46/26.36  | | | | | | | | | | | | |   (8396)  all_52_20 = e1
% 173.46/26.36  | | | | | | | | | | | | |   (8397)  all_52_18 = e2
% 173.46/26.36  | | | | | | | | | | | | |   (8398)  all_52_16 = e3
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | COMBINE_EQS: (719), (8396) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8399)  all_14_1 = e1
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (63), (8399) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8400)  op(e1, all_14_2) = all_14_0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (182), (8398) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8401)  op(e3, all_52_17) = e3
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (174), (8397) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8402)  op(e2, all_52_19) = e2
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (62), (8399) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8403)  op(e1, all_14_2) = e1
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (158), (8395) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8404)  op(e0, all_52_23) = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.36  | | | | | | | | | | | | |              all_14_2, e1, simplifying with (8400), (8403)
% 173.46/26.36  | | | | | | | | | | | | |              gives:
% 173.46/26.36  | | | | | | | | | | | | |   (8405)  all_14_0 = e1
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (8264), (8405) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8406)   ~ (e3 = e1)
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REDUCE: (8262), (8405) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8407)   ~ (e2 = e1)
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | Case 1:
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | |   (8408)  all_58_15 = e0
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8355), (8408),
% 173.46/26.36  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.36  | | | | | | | | | | | | | |            #510.
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | |   (8409)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.36  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.36  | | | | | | | | | | | | | |             e0)
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | ALPHA: (8409) implies:
% 173.46/26.36  | | | | | | | | | | | | | |   (8410)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (156), (161),
% 173.46/26.36  | | | | | | | | | | | | | |            (163), (164), (170), (172), (177), (178), (179),
% 173.46/26.36  | | | | | | | | | | | | | |            (268), (273), (274), (276), (283), (304), (307),
% 173.46/26.36  | | | | | | | | | | | | | |            (310), (311), (315), (319), (323), (324), (326),
% 173.46/26.36  | | | | | | | | | | | | | |            (328), (330), (331), (349), (359), (364), (370),
% 173.46/26.36  | | | | | | | | | | | | | |            (373), (385), (391), (403), (419), (425), (529),
% 173.46/26.36  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.36  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.36  | | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (558), (559),
% 173.46/26.36  | | | | | | | | | | | | | |            (561), (562), (563), (564), (566), (577), (579),
% 173.46/26.36  | | | | | | | | | | | | | |            (584), (586), (587), (593), (595), (596), (598),
% 173.46/26.36  | | | | | | | | | | | | | |            (600), (7962), (8385), (8389), (8401), (8402),
% 173.46/26.36  | | | | | | | | | | | | | |            (8403), (8404), (8410), (function-axioms) are
% 173.46/26.36  | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 173.46/26.36  | | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | End of split
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | Case 2:
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | |   (8411)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.36  | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | ALPHA: (8411) implies:
% 173.46/26.36  | | | | | | | | | | | | |   (8412)  all_52_30 = e0
% 173.46/26.36  | | | | | | | | | | | | |   (8413)  all_52_28 = e1
% 173.46/26.36  | | | | | | | | | | | | |   (8414)  all_52_26 = e2
% 173.46/26.36  | | | | | | | | | | | | |   (8415)  all_52_24 = e3
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | COMBINE_EQS: (649), (8412) imply:
% 173.46/26.36  | | | | | | | | | | | | |   (8416)  all_6_1 = e0
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (42), (51), (156), (164), (165), (170),
% 173.46/26.36  | | | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (268),
% 173.46/26.36  | | | | | | | | | | | | |            (276), (278), (282), (283), (304), (307), (315),
% 173.46/26.36  | | | | | | | | | | | | |            (319), (323), (325), (327), (328), (330), (349),
% 173.46/26.36  | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (392), (403),
% 173.46/26.36  | | | | | | | | | | | | |            (425), (477), (529), (530), (531), (532), (533),
% 173.46/26.36  | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.46/26.36  | | | | | | | | | | | | |            (544), (546), (548), (554), (555), (556), (557),
% 173.46/26.36  | | | | | | | | | | | | |            (560), (561), (565), (568), (569), (573), (575),
% 173.46/26.36  | | | | | | | | | | | | |            (580), (589), (593), (597), (7959), (7962),
% 173.46/26.36  | | | | | | | | | | | | |            (8261), (8382), (8385), (8413), (8414), (8415),
% 173.46/26.36  | | | | | | | | | | | | |            (8416), (function-axioms) are inconsistent by
% 173.46/26.36  | | | | | | | | | | | | |            sub-proof #41.
% 173.46/26.36  | | | | | | | | | | | | | 
% 173.46/26.36  | | | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | |   (8417)  all_18_0 = e3
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | | COMBINE_EQS: (789), (8417) imply:
% 173.46/26.37  | | | | | | | |   (8418)  all_14_0 = e3
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | | REDUCE: (63), (8418) imply:
% 173.46/26.37  | | | | | | | |   (8419)  op(all_14_1, all_14_2) = e3
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | | BETA: splitting (98) gives:
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | |   (8420)   ~ (all_28_0 = e3)
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | REDUCE: (776), (8420) imply:
% 173.46/26.37  | | | | | | | | |   (8421)   ~ (all_6_0 = e3)
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | |   (8422)   ~ (all_42_0 = e1)
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | REDUCE: (761), (8422) imply:
% 173.46/26.37  | | | | | | | | | |   (8423)   ~ (all_4_0 = e1)
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | |   (8424)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.37  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.37  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | BETA: splitting (8424) gives:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | |   (8425)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.37  | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8425) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | | | |            #124.
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | |   (8426)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.37  | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REF_CLOSE: (9), (8259), (8426) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | | | |            #289.
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | |   (8427)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.37  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.37  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | BETA: splitting (8427) gives:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | |   (8428)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.37  | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | ALPHA: (8428) implies:
% 173.46/26.37  | | | | | | | | | | | |   (8429)  all_52_20 = e1
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | COMBINE_EQS: (719), (8429) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8430)  all_14_1 = e1
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REF_CLOSE: (8), (62), (8419), (8430), (function-axioms) are
% 173.46/26.37  | | | | | | | | | | | |            inconsistent by sub-proof #344.
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | |   (8431)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.37  | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | ALPHA: (8431) implies:
% 173.46/26.37  | | | | | | | | | | | |   (8432)  all_52_30 = e0
% 173.46/26.37  | | | | | | | | | | | |   (8433)  all_52_28 = e1
% 173.46/26.37  | | | | | | | | | | | |   (8434)  all_52_26 = e2
% 173.46/26.37  | | | | | | | | | | | |   (8435)  all_52_24 = e3
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | COMBINE_EQS: (649), (8432) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8436)  all_6_1 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (43), (8436) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8437)  op(e0, all_6_2) = all_6_0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (181), (8435) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8438)  op(e3, all_52_25) = e3
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (173), (8434) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8439)  op(e2, all_52_27) = e2
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (165), (8433) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8440)  op(e1, all_52_29) = e1
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (42), (8436) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8441)  op(e0, all_6_2) = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 173.46/26.37  | | | | | | | | | | | |              all_6_2, e0, simplifying with (8437), (8441)
% 173.46/26.37  | | | | | | | | | | | |              gives:
% 173.46/26.37  | | | | | | | | | | | |   (8442)  all_6_0 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (8421), (8442) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8443)   ~ (e3 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (7965), (8442) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8444)   ~ (e2 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (7963), (8442) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8445)   ~ (e1 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | |   (8446)  all_58_15 = e0
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | COMBINE_EQS: (532), (8446) imply:
% 173.46/26.37  | | | | | | | | | | | | |   (8447)  all_6_2 = e0
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REDUCE: (597), (8447) imply:
% 173.46/26.37  | | | | | | | | | | | | |   (8448)   ~ (all_52_7 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REDUCE: (599), (8447) imply:
% 173.46/26.37  | | | | | | | | | | | | |   (8449)   ~ (all_52_15 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REDUCE: (600), (8447) imply:
% 173.46/26.37  | | | | | | | | | | | | |   (8450)   ~ (all_52_23 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REDUCE: (564), (8447) imply:
% 173.46/26.37  | | | | | | | | | | | | |   (8451)   ~ (all_52_25 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REDUCE: (594), (8447) imply:
% 173.46/26.37  | | | | | | | | | | | | |   (8452)   ~ (all_52_29 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (51), (163), (164),
% 173.46/26.37  | | | | | | | | | | | | |            (169), (170), (172), (177), (178), (179), (183),
% 173.46/26.37  | | | | | | | | | | | | |            (270), (271), (278), (280), (283), (302), (303),
% 173.46/26.37  | | | | | | | | | | | | |            (304), (305), (310), (311), (316), (317), (318),
% 173.46/26.37  | | | | | | | | | | | | |            (319), (320), (322), (324), (325), (327), (329),
% 173.46/26.37  | | | | | | | | | | | | |            (344), (349), (364), (370), (373), (385), (386),
% 173.46/26.37  | | | | | | | | | | | | |            (391), (403), (429), (530), (531), (533), (534),
% 173.46/26.37  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.37  | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.37  | | | | | | | | | | | | |            (557), (558), (562), (563), (565), (566), (567),
% 173.46/26.37  | | | | | | | | | | | | |            (569), (571), (573), (575), (580), (583), (585),
% 173.46/26.37  | | | | | | | | | | | | |            (588), (589), (591), (593), (595), (598), (7961),
% 173.46/26.37  | | | | | | | | | | | | |            (7962), (8261), (8438), (8439), (8440), (8446),
% 173.46/26.37  | | | | | | | | | | | | |            (8448), (8449), (8450), (8451), (8452),
% 173.46/26.37  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | | | | |            #46.
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | |   (8453)   ~ (all_58_15 = e0)
% 173.46/26.37  | | | | | | | | | | | | |   (8454)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.37  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.37  | | | | | | | | | | | | |             e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | ALPHA: (8454) implies:
% 173.46/26.37  | | | | | | | | | | | | |   (8455)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.37  | | | | | | | | | | | | |   (8456)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REDUCE: (532), (8453) imply:
% 173.46/26.37  | | | | | | | | | | | | |   (8457)   ~ (all_6_2 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.37  | | | | | | | | | | | | |            (154), (155), (156), (161), (164), (170), (172),
% 173.46/26.37  | | | | | | | | | | | | |            (177), (178), (179), (182), (183), (268), (269),
% 173.46/26.37  | | | | | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.37  | | | | | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.37  | | | | | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.37  | | | | | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.37  | | | | | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.37  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.37  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.37  | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.37  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.37  | | | | | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.37  | | | | | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.37  | | | | | | | | | | | | |            (596), (597), (7961), (7962), (8423), (8438),
% 173.46/26.37  | | | | | | | | | | | | |            (8439), (8440), (8441), (8455), (8456), (8457),
% 173.46/26.37  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | | | | |            #89.
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | |   (8458)  all_42_0 = e1
% 173.46/26.37  | | | | | | | | | |   (8459)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | COMBINE_EQS: (761), (8458) imply:
% 173.46/26.37  | | | | | | | | | |   (8460)  all_4_0 = e1
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | SIMP: (8460) implies:
% 173.46/26.37  | | | | | | | | | |   (8461)  all_4_0 = e1
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | REDUCE: (7961), (8461) imply:
% 173.46/26.37  | | | | | | | | | |   (8462)  op(e2, all_4_2) = e1
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | REF_CLOSE: (8), (9), (36), (42), (43), (51), (62), (156),
% 173.46/26.37  | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.37  | | | | | | | | | |            (179), (181), (185), (268), (276), (278), (282),
% 173.46/26.37  | | | | | | | | | |            (283), (304), (307), (315), (319), (323), (325),
% 173.46/26.37  | | | | | | | | | |            (327), (328), (330), (349), (364), (370), (373),
% 173.46/26.37  | | | | | | | | | |            (385), (391), (392), (403), (425), (477), (529),
% 173.46/26.37  | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 173.46/26.37  | | | | | | | | | |            (537), (538), (539), (540), (544), (546), (548),
% 173.46/26.37  | | | | | | | | | |            (554), (555), (556), (557), (560), (561), (565),
% 173.46/26.37  | | | | | | | | | |            (568), (569), (573), (575), (580), (589), (593),
% 173.46/26.37  | | | | | | | | | |            (597), (649), (719), (7959), (7960), (7962),
% 173.46/26.37  | | | | | | | | | |            (8259), (8261), (8419), (8459), (8462),
% 173.46/26.37  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | |            #38.
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | |   (8463)  all_28_0 = e3
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | COMBINE_EQS: (776), (8463) imply:
% 173.46/26.37  | | | | | | | | |   (8464)  all_6_0 = e3
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | SIMP: (8464) implies:
% 173.46/26.37  | | | | | | | | |   (8465)  all_6_0 = e3
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | REDUCE: (43), (8465) imply:
% 173.46/26.37  | | | | | | | | |   (8466)  op(all_6_1, all_6_2) = e3
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | |   (8467)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.37  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.37  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | BETA: splitting (8467) gives:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | |   (8468)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.37  | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | REF_CLOSE: (9), (7960), (8468) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | | |            #124.
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | |   (8469)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.37  | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | REF_CLOSE: (9), (8259), (8469) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | | |            #289.
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | |   (8470)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.37  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.37  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | REF_CLOSE: (7), (8), (42), (62), (649), (719), (8419),
% 173.46/26.37  | | | | | | | | | |            (8466), (8470), (function-axioms) are inconsistent
% 173.46/26.37  | | | | | | | | | |            by sub-proof #326.
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | End of split
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | End of split
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | Case 2:
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | |   (8471)  all_14_0 = e2
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (42),
% 173.46/26.37  | | | | | | |            (51), (62), (63), (133), (154), (155), (156), (161),
% 173.46/26.37  | | | | | | |            (163), (164), (165), (169), (170), (172), (173), (177),
% 173.46/26.37  | | | | | | |            (178), (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.37  | | | | | | |            (270), (271), (276), (278), (280), (281), (282), (283),
% 173.46/26.37  | | | | | | |            (301), (302), (303), (304), (305), (306), (307), (310),
% 173.46/26.37  | | | | | | |            (311), (313), (315), (316), (317), (318), (319), (320),
% 173.46/26.37  | | | | | | |            (321), (322), (323), (324), (325), (326), (327), (328),
% 173.46/26.37  | | | | | | |            (329), (330), (331), (341), (344), (349), (364), (370),
% 173.46/26.37  | | | | | | |            (373), (385), (386), (391), (392), (403), (413), (425),
% 173.46/26.37  | | | | | | |            (429), (477), (529), (530), (531), (532), (533), (534),
% 173.46/26.37  | | | | | | |            (535), (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.37  | | | | | | |            (546), (548), (550), (552), (553), (554), (555), (556),
% 173.46/26.37  | | | | | | |            (557), (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.37  | | | | | | |            (565), (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.37  | | | | | | |            (577), (580), (581), (582), (583), (585), (586), (588),
% 173.46/26.37  | | | | | | |            (589), (591), (593), (594), (595), (596), (597), (598),
% 173.46/26.37  | | | | | | |            (599), (600), (649), (719), (761), (7959), (7960),
% 173.46/26.37  | | | | | | |            (7961), (7962), (8259), (8261), (8471),
% 173.46/26.37  | | | | | | |            (function-axioms) are inconsistent by sub-proof #36.
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | End of split
% 173.46/26.37  | | | | | | 
% 173.46/26.37  | | | | | End of split
% 173.46/26.37  | | | | | 
% 173.46/26.37  | | | | Case 2:
% 173.46/26.37  | | | | | 
% 173.46/26.37  | | | | |   (8472)  all_10_0 = e3
% 173.46/26.37  | | | | | 
% 173.46/26.37  | | | | | REDUCE: (53), (8472) imply:
% 173.46/26.37  | | | | |   (8473)  op(all_10_1, all_10_2) = e3
% 173.46/26.37  | | | | | 
% 173.46/26.37  | | | | | BETA: splitting (64) gives:
% 173.46/26.37  | | | | | 
% 173.46/26.37  | | | | | Case 1:
% 173.46/26.37  | | | | | | 
% 173.46/26.37  | | | | | |   (8474)   ~ (all_14_0 = e2)
% 173.46/26.37  | | | | | | 
% 173.46/26.37  | | | | | | BETA: splitting (74) gives:
% 173.46/26.37  | | | | | | 
% 173.46/26.37  | | | | | | Case 1:
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | |   (8475)   ~ (all_18_0 = e3)
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | | REDUCE: (789), (8475) imply:
% 173.46/26.37  | | | | | | |   (8476)   ~ (all_14_0 = e3)
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | | BETA: splitting (83) gives:
% 173.46/26.37  | | | | | | | 
% 173.46/26.37  | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | |   (8477)   ~ (all_22_1 = e3)
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | | REDUCE: (711), (8477) imply:
% 173.46/26.37  | | | | | | | |   (8478)   ~ (all_14_1 = e3)
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | | BETA: splitting (98) gives:
% 173.46/26.37  | | | | | | | | 
% 173.46/26.37  | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | |   (8479)   ~ (all_28_0 = e3)
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | REDUCE: (776), (8479) imply:
% 173.46/26.37  | | | | | | | | |   (8480)   ~ (all_6_0 = e3)
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | BETA: splitting (108) gives:
% 173.46/26.37  | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | |   (8481)   ~ (all_32_1 = e2)
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | REDUCE: (713), (8481) imply:
% 173.46/26.37  | | | | | | | | | |   (8482)   ~ (all_14_1 = e2)
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.37  | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | |   (8483)   ~ (all_42_0 = e1)
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | REDUCE: (761), (8483) imply:
% 173.46/26.37  | | | | | | | | | | |   (8484)   ~ (all_4_0 = e1)
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.37  | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | |   (8485)  all_58_15 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | COMBINE_EQS: (532), (8485) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8486)  all_6_2 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (599), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8487)   ~ (all_52_15 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (600), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8488)   ~ (all_52_23 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (564), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8489)   ~ (all_52_25 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (582), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8490)   ~ (all_52_27 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (594), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8491)   ~ (all_52_29 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (43), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8492)  op(all_6_1, e0) = all_6_0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (42), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8493)  op(e0, e0) = all_6_1
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (41), (8486) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8494)  op(e0, e0) = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 173.46/26.37  | | | | | | | | | | | |              e0, e0, simplifying with (8493), (8494) gives:
% 173.46/26.37  | | | | | | | | | | | |   (8495)  all_6_1 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (8492), (8495) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8496)  op(e0, e0) = all_6_0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 173.46/26.37  | | | | | | | | | | | |              e0, e0, simplifying with (8494), (8496) gives:
% 173.46/26.37  | | | | | | | | | | | |   (8497)  all_6_0 = e0
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (8480), (8497) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8498)   ~ (e3 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (7965), (8497) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8499)   ~ (e2 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | REDUCE: (7963), (8497) imply:
% 173.46/26.37  | | | | | | | | | | | |   (8500)   ~ (e1 = e0)
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.37  | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | |   (8501)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.37  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.37  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (52), (154),
% 173.46/26.37  | | | | | | | | | | | | |            (155), (156), (159), (164), (167), (172), (179),
% 173.46/26.37  | | | | | | | | | | | | |            (183), (269), (273), (276), (304), (305), (306),
% 173.46/26.37  | | | | | | | | | | | | |            (307), (311), (315), (319), (323), (330), (341),
% 173.46/26.37  | | | | | | | | | | | | |            (349), (359), (364), (370), (373), (385), (391),
% 173.46/26.37  | | | | | | | | | | | | |            (403), (425), (533), (534), (535), (536), (537),
% 173.46/26.37  | | | | | | | | | | | | |            (538), (539), (540), (542), (552), (553), (554),
% 173.46/26.37  | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (565), (569),
% 173.46/26.37  | | | | | | | | | | | | |            (571), (579), (581), (586), (595), (596), (661),
% 173.46/26.37  | | | | | | | | | | | | |            (7960), (8485), (8489), (8490), (8491), (8501),
% 173.46/26.37  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.37  | | | | | | | | | | | | |            #35.
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | |   (8502)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.37  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.37  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | BETA: splitting (8502) gives:
% 173.46/26.37  | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | Case 1:
% 173.46/26.37  | | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | |   (8503)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.37  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.37  | | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (62), (154), (155), (156), (158),
% 173.46/26.37  | | | | | | | | | | | | | |            (164), (165), (172), (174), (177), (178), (179),
% 173.46/26.37  | | | | | | | | | | | | | |            (182), (270), (271), (272), (273), (274), (275),
% 173.46/26.37  | | | | | | | | | | | | | |            (276), (278), (280), (283), (302), (303), (304),
% 173.46/26.37  | | | | | | | | | | | | | |            (305), (306), (307), (311), (319), (323), (324),
% 173.46/26.37  | | | | | | | | | | | | | |            (326), (330), (331), (344), (349), (350), (359),
% 173.46/26.37  | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (403),
% 173.46/26.37  | | | | | | | | | | | | | |            (419), (425), (429), (530), (531), (533), (534),
% 173.46/26.37  | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.37  | | | | | | | | | | | | | |            (544), (546), (548), (552), (553), (554), (555),
% 173.46/26.37  | | | | | | | | | | | | | |            (557), (558), (561), (562), (563), (565), (569),
% 173.46/26.37  | | | | | | | | | | | | | |            (571), (578), (579), (580), (581), (584), (585),
% 173.46/26.37  | | | | | | | | | | | | | |            (588), (591), (593), (596), (598), (719), (7963),
% 173.46/26.37  | | | | | | | | | | | | | |            (7965), (8478), (8480), (8482), (8485), (8487),
% 173.46/26.37  | | | | | | | | | | | | | |            (8488), (8489), (8490), (8491), (8492), (8493),
% 173.46/26.37  | | | | | | | | | | | | | |            (8494), (8503), (function-axioms) are inconsistent
% 173.46/26.37  | | | | | | | | | | | | | |            by sub-proof #34.
% 173.46/26.37  | | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | Case 2:
% 173.46/26.37  | | | | | | | | | | | | | | 
% 173.46/26.37  | | | | | | | | | | | | | |   (8504)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.37  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.37  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (52), (163), (164),
% 173.46/26.38  | | | | | | | | | | | | | |            (165), (169), (170), (172), (173), (177), (178),
% 173.46/26.38  | | | | | | | | | | | | | |            (179), (181), (182), (183), (270), (271), (272),
% 173.46/26.38  | | | | | | | | | | | | | |            (278), (280), (283), (302), (303), (304), (305),
% 173.46/26.38  | | | | | | | | | | | | | |            (310), (311), (313), (315), (316), (319), (322),
% 173.46/26.38  | | | | | | | | | | | | | |            (324), (325), (328), (344), (349), (350), (364),
% 173.46/26.38  | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (403), (429),
% 173.46/26.38  | | | | | | | | | | | | | |            (530), (531), (533), (534), (535), (536), (537),
% 173.46/26.38  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.38  | | | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (558),
% 173.46/26.38  | | | | | | | | | | | | | |            (560), (562), (563), (565), (566), (567), (569),
% 173.46/26.38  | | | | | | | | | | | | | |            (571), (573), (575), (577), (580), (583), (585),
% 173.46/26.38  | | | | | | | | | | | | | |            (586), (588), (591), (593), (595), (598), (7961),
% 173.46/26.38  | | | | | | | | | | | | | |            (7962), (8484), (8485), (8488), (8489), (8504),
% 173.46/26.38  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.38  | | | | | | | | | | | | | |            #109.
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | |   (8505)   ~ (all_58_15 = e0)
% 173.46/26.38  | | | | | | | | | | | |   (8506)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.38  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.38  | | | | | | | | | | | |             e0)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | ALPHA: (8506) implies:
% 173.46/26.38  | | | | | | | | | | | |   (8507)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.38  | | | | | | | | | | | |   (8508)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | REDUCE: (532), (8505) imply:
% 173.46/26.38  | | | | | | | | | | | |   (8509)   ~ (all_6_2 = e0)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.38  | | | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 173.46/26.38  | | | | | | | | | | | |            (158), (161), (163), (164), (165), (170), (172),
% 173.46/26.38  | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.46/26.38  | | | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (274),
% 173.46/26.38  | | | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 173.46/26.38  | | | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 173.46/26.38  | | | | | | | | | | | |            (311), (313), (314), (315), (319), (321), (322),
% 173.46/26.38  | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 173.46/26.38  | | | | | | | | | | | |            (330), (331), (341), (344), (349), (364), (365),
% 173.46/26.38  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.38  | | | | | | | | | | | |            (413), (415), (419), (425), (429), (529), (530),
% 173.46/26.38  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.38  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.38  | | | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.38  | | | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.38  | | | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (575),
% 173.46/26.38  | | | | | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 173.46/26.38  | | | | | | | | | | | |            (584), (585), (586), (587), (588), (589), (593),
% 173.46/26.38  | | | | | | | | | | | |            (594), (595), (596), (597), (598), (599), (600),
% 173.46/26.38  | | | | | | | | | | | |            (649), (661), (719), (7958), (7960), (7961),
% 173.46/26.38  | | | | | | | | | | | |            (7962), (8473), (8474), (8476), (8484), (8507),
% 173.46/26.38  | | | | | | | | | | | |            (8508), (8509), (function-axioms) are inconsistent
% 173.46/26.38  | | | | | | | | | | | |            by sub-proof #31.
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | |   (8510)  all_42_0 = e1
% 173.46/26.38  | | | | | | | | | | |   (8511)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | COMBINE_EQS: (761), (8510) imply:
% 173.46/26.38  | | | | | | | | | | |   (8512)  all_4_0 = e1
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | REDUCE: (7961), (8512) imply:
% 173.46/26.38  | | | | | | | | | | |   (8513)  op(e2, all_4_2) = e1
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | BETA: splitting (8511) gives:
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | |   (8514)   ~ (all_42_1 = e2)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | REDUCE: (7959), (8514) imply:
% 173.46/26.38  | | | | | | | | | | | |   (8515)  $false
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | CLOSE: (8515) is inconsistent.
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | |   (8516)   ~ (all_42_2 = e0)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | REDUCE: (477), (8516) imply:
% 173.46/26.38  | | | | | | | | | | | |   (8517)   ~ (all_4_2 = e0)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | |   (8518)  all_58_15 = e0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | COMBINE_EQS: (532), (8518) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8519)  all_6_2 = e0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (599), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8520)   ~ (all_52_15 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (600), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8521)   ~ (all_52_23 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (564), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8522)   ~ (all_52_25 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (582), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8523)   ~ (all_52_27 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (594), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8524)   ~ (all_52_29 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (43), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8525)  op(all_6_1, e0) = all_6_0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (42), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8526)  op(e0, e0) = all_6_1
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (41), (8519) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8527)  op(e0, e0) = e0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_1,
% 173.46/26.38  | | | | | | | | | | | | |              e0, e0, simplifying with (8526), (8527) gives:
% 173.46/26.38  | | | | | | | | | | | | |   (8528)  all_6_1 = e0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (8525), (8528) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8529)  op(e0, e0) = all_6_0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_6_0,
% 173.46/26.38  | | | | | | | | | | | | |              e0, e0, simplifying with (8527), (8529) gives:
% 173.46/26.38  | | | | | | | | | | | | |   (8530)  all_6_0 = e0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (8480), (8530) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8531)   ~ (e3 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (7965), (8530) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8532)   ~ (e2 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (7963), (8530) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8533)   ~ (e1 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | |   (8534)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.38  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.38  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (52), (154),
% 173.46/26.38  | | | | | | | | | | | | | |            (155), (156), (159), (164), (167), (172), (179),
% 173.46/26.38  | | | | | | | | | | | | | |            (183), (269), (273), (276), (304), (305), (306),
% 173.46/26.38  | | | | | | | | | | | | | |            (307), (311), (315), (319), (323), (330), (341),
% 173.46/26.38  | | | | | | | | | | | | | |            (349), (359), (364), (370), (373), (385), (391),
% 173.46/26.38  | | | | | | | | | | | | | |            (403), (425), (533), (534), (535), (536), (537),
% 173.46/26.38  | | | | | | | | | | | | | |            (538), (539), (540), (542), (552), (553), (554),
% 173.46/26.38  | | | | | | | | | | | | | |            (558), (559), (560), (561), (562), (565), (569),
% 173.46/26.38  | | | | | | | | | | | | | |            (571), (579), (581), (586), (595), (596), (661),
% 173.46/26.38  | | | | | | | | | | | | | |            (7960), (8518), (8522), (8523), (8524), (8534),
% 173.46/26.38  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.38  | | | | | | | | | | | | | |            #35.
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | |   (8535)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.38  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.38  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | BETA: splitting (8535) gives:
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | |   (8536)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.38  | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (62), (154), (155), (156), (158),
% 173.46/26.38  | | | | | | | | | | | | | | |            (164), (165), (172), (174), (177), (178), (179),
% 173.46/26.38  | | | | | | | | | | | | | | |            (182), (270), (271), (272), (273), (274), (275),
% 173.46/26.38  | | | | | | | | | | | | | | |            (276), (278), (280), (283), (302), (303), (304),
% 173.46/26.38  | | | | | | | | | | | | | | |            (305), (306), (307), (311), (319), (323), (324),
% 173.46/26.38  | | | | | | | | | | | | | | |            (326), (330), (331), (344), (349), (350), (359),
% 173.46/26.38  | | | | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (403),
% 173.46/26.38  | | | | | | | | | | | | | | |            (419), (425), (429), (530), (531), (533), (534),
% 173.46/26.38  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.38  | | | | | | | | | | | | | | |            (544), (546), (548), (552), (553), (554), (555),
% 173.46/26.38  | | | | | | | | | | | | | | |            (557), (558), (561), (562), (563), (565), (569),
% 173.46/26.38  | | | | | | | | | | | | | | |            (571), (578), (579), (580), (581), (584), (585),
% 173.46/26.38  | | | | | | | | | | | | | | |            (588), (591), (593), (596), (598), (719), (7963),
% 173.46/26.38  | | | | | | | | | | | | | | |            (7965), (8478), (8480), (8482), (8518), (8520),
% 173.46/26.38  | | | | | | | | | | | | | | |            (8521), (8522), (8523), (8524), (8525), (8526),
% 173.46/26.38  | | | | | | | | | | | | | | |            (8527), (8536), (function-axioms) are inconsistent
% 173.46/26.38  | | | | | | | | | | | | | | |            by sub-proof #34.
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | |   (8537)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.38  | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (163), (164), (165), (172),
% 173.46/26.38  | | | | | | | | | | | | | | |            (173), (177), (178), (179), (181), (183), (270),
% 173.46/26.38  | | | | | | | | | | | | | | |            (271), (278), (280), (283), (303), (304), (305),
% 173.46/26.38  | | | | | | | | | | | | | | |            (310), (315), (319), (322), (325), (328), (344),
% 173.46/26.38  | | | | | | | | | | | | | | |            (349), (364), (370), (373), (385), (386), (391),
% 173.46/26.38  | | | | | | | | | | | | | | |            (403), (429), (530), (531), (533), (534), (535),
% 173.46/26.38  | | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.38  | | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.38  | | | | | | | | | | | | | | |            (562), (563), (569), (571), (573), (580), (583),
% 173.46/26.38  | | | | | | | | | | | | | | |            (585), (588), (591), (593), (595), (598), (7962),
% 173.46/26.38  | | | | | | | | | | | | | | |            (8517), (8518), (8521), (8522), (8537),
% 173.46/26.38  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.38  | | | | | | | | | | | | | | |            #67.
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | |   (8538)   ~ (all_58_15 = e0)
% 173.46/26.38  | | | | | | | | | | | | |   (8539)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.38  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.38  | | | | | | | | | | | | |             e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | ALPHA: (8539) implies:
% 173.46/26.38  | | | | | | | | | | | | |   (8540)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.38  | | | | | | | | | | | | |   (8541)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | REDUCE: (532), (8538) imply:
% 173.46/26.38  | | | | | | | | | | | | |   (8542)   ~ (all_6_2 = e0)
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | |   (8543)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.38  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.38  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (661), (7960), (8473), (8543),
% 173.46/26.38  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.38  | | | | | | | | | | | | | |            #33.
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | |   (8544)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.38  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.38  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | BETA: splitting (8544) gives:
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | |   (8545)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.38  | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (62), (156), (158),
% 173.46/26.38  | | | | | | | | | | | | | | |            (161), (163), (164), (170), (172), (174), (177),
% 173.46/26.38  | | | | | | | | | | | | | | |            (178), (179), (182), (268), (273), (274), (276),
% 173.46/26.38  | | | | | | | | | | | | | | |            (283), (304), (307), (310), (311), (315), (319),
% 173.46/26.38  | | | | | | | | | | | | | | |            (323), (324), (326), (328), (330), (331), (349),
% 173.46/26.38  | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (391), (403),
% 173.46/26.38  | | | | | | | | | | | | | | |            (419), (425), (529), (531), (532), (533), (534),
% 173.46/26.38  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.38  | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.38  | | | | | | | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.46/26.38  | | | | | | | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.46/26.38  | | | | | | | | | | | | | | |            (595), (596), (598), (600), (719), (7962), (8478),
% 173.46/26.38  | | | | | | | | | | | | | | |            (8482), (8513), (8517), (8541), (8545),
% 173.46/26.38  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.38  | | | | | | | | | | | | | | |            #30.
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | |   (8546)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.38  | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | | ALPHA: (8546) implies:
% 173.46/26.38  | | | | | | | | | | | | | | |   (8547)  all_52_30 = e0
% 173.46/26.38  | | | | | | | | | | | | | | |   (8548)  all_52_28 = e1
% 173.46/26.38  | | | | | | | | | | | | | | |   (8549)  all_52_26 = e2
% 173.46/26.38  | | | | | | | | | | | | | | |   (8550)  all_52_24 = e3
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | | COMBINE_EQS: (649), (8547) imply:
% 173.46/26.38  | | | | | | | | | | | | | | |   (8551)  all_6_1 = e0
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (42), (43), (154), (156), (164),
% 173.46/26.38  | | | | | | | | | | | | | | |            (165), (170), (172), (173), (177), (178), (179),
% 173.46/26.38  | | | | | | | | | | | | | | |            (181), (182), (268), (271), (273), (274), (276),
% 173.46/26.38  | | | | | | | | | | | | | | |            (282), (283), (304), (305), (307), (311), (313),
% 173.46/26.38  | | | | | | | | | | | | | | |            (315), (319), (321), (323), (324), (328), (329),
% 173.46/26.38  | | | | | | | | | | | | | | |            (330), (331), (349), (359), (364), (370), (373),
% 173.46/26.38  | | | | | | | | | | | | | | |            (385), (391), (392), (403), (419), (425), (429),
% 173.46/26.38  | | | | | | | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.46/26.38  | | | | | | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.46/26.38  | | | | | | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.46/26.38  | | | | | | | | | | | | | | |            (557), (558), (559), (560), (561), (563), (564),
% 173.46/26.38  | | | | | | | | | | | | | | |            (565), (567), (568), (569), (571), (573), (577),
% 173.46/26.38  | | | | | | | | | | | | | | |            (578), (579), (580), (581), (582), (583), (584),
% 173.46/26.38  | | | | | | | | | | | | | | |            (585), (586), (589), (593), (594), (595), (597),
% 173.46/26.38  | | | | | | | | | | | | | | |            (598), (599), (7962), (7965), (8480), (8513),
% 173.46/26.38  | | | | | | | | | | | | | | |            (8517), (8540), (8542), (8548), (8549), (8550),
% 173.46/26.38  | | | | | | | | | | | | | | |            (8551), (function-axioms) are inconsistent by
% 173.46/26.38  | | | | | | | | | | | | | | |            sub-proof #65.
% 173.46/26.38  | | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | End of split
% 173.46/26.38  | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | |   (8552)  all_32_1 = e2
% 173.46/26.38  | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | COMBINE_EQS: (713), (8552) imply:
% 173.46/26.38  | | | | | | | | | |   (8553)  all_14_1 = e2
% 173.46/26.38  | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | COMBINE_EQS: (719), (8553) imply:
% 173.46/26.38  | | | | | | | | | |   (8554)  all_52_20 = e2
% 173.46/26.38  | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | REDUCE: (8478), (8553) imply:
% 173.46/26.38  | | | | | | | | | |   (8555)   ~ (e3 = e2)
% 173.46/26.38  | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.38  | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | |   (8556)   ~ (all_42_0 = e1)
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | REDUCE: (761), (8556) imply:
% 173.46/26.38  | | | | | | | | | | |   (8557)   ~ (all_4_0 = e1)
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43), (52),
% 173.46/26.38  | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 173.46/26.38  | | | | | | | | | | |            (169), (170), (172), (173), (177), (178), (179),
% 173.46/26.38  | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.46/26.38  | | | | | | | | | | |            (271), (272), (278), (280), (281), (282), (283),
% 173.46/26.38  | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.46/26.38  | | | | | | | | | | |            (310), (311), (313), (315), (316), (319), (321),
% 173.46/26.38  | | | | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 173.46/26.38  | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.46/26.38  | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 173.46/26.38  | | | | | | | | | | |            (403), (413), (429), (529), (530), (531), (532),
% 173.46/26.38  | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.38  | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.38  | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 173.46/26.38  | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 173.46/26.38  | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (577),
% 173.46/26.38  | | | | | | | | | | |            (580), (581), (582), (583), (585), (586), (588),
% 173.46/26.38  | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.46/26.38  | | | | | | | | | | |            (598), (600), (649), (661), (7960), (7961),
% 173.46/26.38  | | | | | | | | | | |            (7962), (7963), (7965), (8473), (8480), (8554),
% 173.46/26.38  | | | | | | | | | | |            (8557), (function-axioms) are inconsistent by
% 173.46/26.38  | | | | | | | | | | |            sub-proof #28.
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | |   (8558)  all_42_0 = e1
% 173.46/26.38  | | | | | | | | | | |   (8559)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | COMBINE_EQS: (761), (8558) imply:
% 173.46/26.38  | | | | | | | | | | |   (8560)  all_4_0 = e1
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | REDUCE: (7961), (8560) imply:
% 173.46/26.38  | | | | | | | | | | |   (8561)  op(e2, all_4_2) = e1
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | BETA: splitting (8559) gives:
% 173.46/26.38  | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | Case 1:
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | |   (8562)   ~ (all_42_1 = e2)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | REDUCE: (7959), (8562) imply:
% 173.46/26.38  | | | | | | | | | | | |   (8563)  $false
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | CLOSE: (8563) is inconsistent.
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | Case 2:
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | |   (8564)   ~ (all_42_2 = e0)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | REDUCE: (477), (8564) imply:
% 173.46/26.38  | | | | | | | | | | | |   (8565)   ~ (all_4_2 = e0)
% 173.46/26.38  | | | | | | | | | | | | 
% 173.46/26.38  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (42), (43), (52), (154),
% 173.46/26.38  | | | | | | | | | | | |            (156), (163), (164), (165), (170), (172), (173),
% 173.46/26.38  | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 173.46/26.38  | | | | | | | | | | | |            (268), (270), (271), (273), (274), (276), (278),
% 173.46/26.38  | | | | | | | | | | | |            (280), (282), (283), (301), (303), (304), (305),
% 173.46/26.38  | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 173.46/26.38  | | | | | | | | | | | |            (322), (323), (324), (325), (328), (329), (330),
% 173.46/26.38  | | | | | | | | | | | |            (331), (344), (349), (359), (364), (370), (373),
% 173.46/26.38  | | | | | | | | | | | |            (385), (386), (391), (392), (403), (419), (425),
% 173.46/26.38  | | | | | | | | | | | |            (429), (529), (530), (531), (532), (533), (534),
% 173.46/26.38  | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.38  | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.39  | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.46/26.39  | | | | | | | | | | | |            (562), (563), (564), (565), (567), (568), (569),
% 173.46/26.39  | | | | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 173.46/26.39  | | | | | | | | | | | |            (582), (583), (584), (585), (586), (588), (589),
% 173.46/26.39  | | | | | | | | | | | |            (591), (593), (594), (595), (597), (598), (599),
% 173.46/26.39  | | | | | | | | | | | |            (600), (649), (661), (7960), (7962), (7965),
% 173.46/26.39  | | | | | | | | | | | |            (8473), (8480), (8554), (8561), (8565),
% 173.46/26.39  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | |            #26.
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | |   (8566)  all_28_0 = e3
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | COMBINE_EQS: (776), (8566) imply:
% 173.46/26.39  | | | | | | | | |   (8567)  all_6_0 = e3
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | REDUCE: (43), (8567) imply:
% 173.46/26.39  | | | | | | | | |   (8568)  op(all_6_1, all_6_2) = e3
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | BETA: splitting (108) gives:
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | |   (8569)   ~ (all_32_1 = e2)
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | REDUCE: (713), (8569) imply:
% 173.46/26.39  | | | | | | | | | |   (8570)   ~ (all_14_1 = e2)
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | |   (8571)   ~ (all_42_0 = e1)
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | REDUCE: (761), (8571) imply:
% 173.46/26.39  | | | | | | | | | | |   (8572)   ~ (all_4_0 = e1)
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8573)  all_58_15 = e0
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8568), (8573),
% 173.46/26.39  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | |            #510.
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8574)   ~ (all_58_15 = e0)
% 173.46/26.39  | | | | | | | | | | | |   (8575)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.39  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.39  | | | | | | | | | | | |             e0)
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | ALPHA: (8575) implies:
% 173.46/26.39  | | | | | | | | | | | |   (8576)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.39  | | | | | | | | | | | |   (8577)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REDUCE: (532), (8574) imply:
% 173.46/26.39  | | | | | | | | | | | |   (8578)   ~ (all_6_2 = e0)
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | |   (8579)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.39  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.39  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | REF_CLOSE: (9), (52), (661), (7960), (8473), (8579),
% 173.46/26.39  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | | |            #33.
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | |   (8580)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.39  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.39  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | BETA: splitting (8580) gives:
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | |   (8581)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.39  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | ALPHA: (8581) implies:
% 173.46/26.39  | | | | | | | | | | | | | |   (8582)  all_52_22 = e0
% 173.46/26.39  | | | | | | | | | | | | | |   (8583)  all_52_20 = e1
% 173.46/26.39  | | | | | | | | | | | | | |   (8584)  all_52_18 = e2
% 173.46/26.39  | | | | | | | | | | | | | |   (8585)  all_52_16 = e3
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | COMBINE_EQS: (719), (8583) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8586)  all_14_1 = e1
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REDUCE: (63), (8586) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8587)  op(e1, all_14_2) = all_14_0
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REDUCE: (182), (8585) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8588)  op(e3, all_52_17) = e3
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REDUCE: (174), (8584) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8589)  op(e2, all_52_19) = e2
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REDUCE: (62), (8586) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8590)  op(e1, all_14_2) = e1
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REDUCE: (158), (8582) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8591)  op(e0, all_52_23) = e0
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.39  | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (8587), (8590)
% 173.46/26.39  | | | | | | | | | | | | | |              gives:
% 173.46/26.39  | | | | | | | | | | | | | |   (8592)  all_14_0 = e1
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REDUCE: (8476), (8592) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8593)   ~ (e3 = e1)
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REDUCE: (8474), (8592) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8594)   ~ (e2 = e1)
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | |   (8595)  all_56_15 = e3
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (42), (156), (164), (172), (178),
% 173.46/26.39  | | | | | | | | | | | | | | |            (271), (274), (302), (303), (311), (319), (330),
% 173.46/26.39  | | | | | | | | | | | | | | |            (349), (364), (385), (403), (419), (429), (529),
% 173.46/26.39  | | | | | | | | | | | | | | |            (535), (537), (538), (544), (546), (553), (564),
% 173.46/26.39  | | | | | | | | | | | | | | |            (584), (600), (8568), (8588), (8589), (8590),
% 173.46/26.39  | | | | | | | | | | | | | | |            (8595), (function-axioms) are inconsistent by
% 173.46/26.39  | | | | | | | | | | | | | | |            sub-proof #504.
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | |   (8596)   ~ (all_56_15 = e3)
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | | REDUCE: (529), (8596) imply:
% 173.46/26.39  | | | | | | | | | | | | | | |   (8597)   ~ (all_6_2 = e3)
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (52), (156),
% 173.46/26.39  | | | | | | | | | | | | | | |            (163), (164), (165), (170), (172), (173), (177),
% 173.46/26.39  | | | | | | | | | | | | | | |            (178), (179), (270), (274), (275), (276), (277),
% 173.46/26.39  | | | | | | | | | | | | | | |            (278), (280), (281), (283), (304), (307), (310),
% 173.46/26.39  | | | | | | | | | | | | | | |            (311), (315), (319), (323), (324), (326), (328),
% 173.46/26.39  | | | | | | | | | | | | | | |            (330), (331), (344), (349), (364), (365), (370),
% 173.46/26.39  | | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (413), (415),
% 173.46/26.39  | | | | | | | | | | | | | | |            (419), (425), (530), (531), (532), (533), (534),
% 173.46/26.39  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.39  | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.39  | | | | | | | | | | | | | | |            (555), (557), (558), (559), (560), (561), (562),
% 173.46/26.39  | | | | | | | | | | | | | | |            (563), (564), (566), (567), (569), (571), (575),
% 173.46/26.39  | | | | | | | | | | | | | | |            (577), (578), (579), (582), (583), (584), (585),
% 173.46/26.39  | | | | | | | | | | | | | | |            (586), (588), (593), (594), (595), (596), (598),
% 173.46/26.39  | | | | | | | | | | | | | | |            (7958), (7961), (7962), (8473), (8572), (8577),
% 173.46/26.39  | | | | | | | | | | | | | | |            (8588), (8589), (8590), (8591), (8597),
% 173.46/26.39  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | | | | |            #32.
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | |   (8598)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.39  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | ALPHA: (8598) implies:
% 173.46/26.39  | | | | | | | | | | | | | |   (8599)  all_52_30 = e0
% 173.46/26.39  | | | | | | | | | | | | | |   (8600)  all_52_28 = e1
% 173.46/26.39  | | | | | | | | | | | | | |   (8601)  all_52_26 = e2
% 173.46/26.39  | | | | | | | | | | | | | |   (8602)  all_52_24 = e3
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | COMBINE_EQS: (649), (8599) imply:
% 173.46/26.39  | | | | | | | | | | | | | |   (8603)  all_6_1 = e0
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.39  | | | | | | | | | | | | | |            (42), (154), (155), (156), (161), (164), (165),
% 173.46/26.39  | | | | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 173.46/26.39  | | | | | | | | | | | | | |            (182), (183), (268), (269), (270), (271), (281),
% 173.46/26.39  | | | | | | | | | | | | | |            (282), (283), (303), (304), (305), (306), (307),
% 173.46/26.39  | | | | | | | | | | | | | |            (313), (315), (321), (322), (323), (324), (325),
% 173.46/26.39  | | | | | | | | | | | | | |            (326), (327), (329), (330), (331), (341), (344),
% 173.46/26.39  | | | | | | | | | | | | | |            (349), (364), (370), (373), (385), (391), (392),
% 173.46/26.39  | | | | | | | | | | | | | |            (403), (413), (429), (529), (531), (532), (533),
% 173.46/26.39  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.46/26.39  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.46/26.39  | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 173.46/26.39  | | | | | | | | | | | | | |            (561), (562), (563), (564), (565), (567), (568),
% 173.46/26.39  | | | | | | | | | | | | | |            (569), (571), (577), (580), (581), (582), (585),
% 173.46/26.39  | | | | | | | | | | | | | |            (586), (589), (594), (595), (596), (597), (7961),
% 173.46/26.39  | | | | | | | | | | | | | |            (7962), (8572), (8576), (8577), (8578), (8600),
% 173.46/26.39  | | | | | | | | | | | | | |            (8601), (8602), (8603), (function-axioms) are
% 173.46/26.39  | | | | | | | | | | | | | |            inconsistent by sub-proof #88.
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | |   (8604)  all_42_0 = e1
% 173.46/26.39  | | | | | | | | | | |   (8605)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | COMBINE_EQS: (761), (8604) imply:
% 173.46/26.39  | | | | | | | | | | |   (8606)  all_4_0 = e1
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | SIMP: (8606) implies:
% 173.46/26.39  | | | | | | | | | | |   (8607)  all_4_0 = e1
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | REDUCE: (7961), (8607) imply:
% 173.46/26.39  | | | | | | | | | | |   (8608)  op(e2, all_4_2) = e1
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | BETA: splitting (8605) gives:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8609)   ~ (all_42_1 = e2)
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REDUCE: (7959), (8609) imply:
% 173.46/26.39  | | | | | | | | | | | |   (8610)  $false
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | CLOSE: (8610) is inconsistent.
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8611)   ~ (all_42_2 = e0)
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REDUCE: (477), (8611) imply:
% 173.46/26.39  | | | | | | | | | | | |   (8612)   ~ (all_4_2 = e0)
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | |   (8613)  all_58_15 = e0
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8568), (8613),
% 173.46/26.39  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | | |            #510.
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | |   (8614)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.39  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.39  | | | | | | | | | | | | |             e0)
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | ALPHA: (8614) implies:
% 173.46/26.39  | | | | | | | | | | | | |   (8615)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | |   (8616)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.39  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.39  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (661), (7960), (8473), (8616),
% 173.46/26.39  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | | | |            #33.
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | |   (8617)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.39  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.39  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | BETA: splitting (8617) gives:
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | |   (8618)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.39  | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (62), (156), (158),
% 173.46/26.39  | | | | | | | | | | | | | | |            (161), (163), (164), (170), (172), (174), (177),
% 173.46/26.39  | | | | | | | | | | | | | | |            (178), (179), (182), (268), (273), (274), (276),
% 173.46/26.39  | | | | | | | | | | | | | | |            (283), (304), (307), (310), (311), (315), (319),
% 173.46/26.39  | | | | | | | | | | | | | | |            (323), (324), (326), (328), (330), (331), (349),
% 173.46/26.39  | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (391), (403),
% 173.46/26.39  | | | | | | | | | | | | | | |            (419), (425), (529), (531), (532), (533), (534),
% 173.46/26.39  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.39  | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.39  | | | | | | | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.46/26.39  | | | | | | | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.46/26.39  | | | | | | | | | | | | | | |            (595), (596), (598), (600), (719), (7962), (8478),
% 173.46/26.39  | | | | | | | | | | | | | | |            (8570), (8608), (8612), (8615), (8618),
% 173.46/26.39  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | | | | |            #30.
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | |   (8619)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.39  | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | | ALPHA: (8619) implies:
% 173.46/26.39  | | | | | | | | | | | | | | |   (8620)  all_52_30 = e0
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | | COMBINE_EQS: (649), (8620) imply:
% 173.46/26.39  | | | | | | | | | | | | | | |   (8621)  all_6_1 = e0
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | | REF_CLOSE: (7), (42), (8568), (8621), (function-axioms) are
% 173.46/26.39  | | | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 173.46/26.39  | | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | |   (8622)  all_32_1 = e2
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | COMBINE_EQS: (713), (8622) imply:
% 173.46/26.39  | | | | | | | | | |   (8623)  all_14_1 = e2
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | SIMP: (8623) implies:
% 173.46/26.39  | | | | | | | | | |   (8624)  all_14_1 = e2
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | COMBINE_EQS: (719), (8624) imply:
% 173.46/26.39  | | | | | | | | | |   (8625)  all_52_20 = e2
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | REDUCE: (8478), (8624) imply:
% 173.46/26.39  | | | | | | | | | |   (8626)   ~ (e3 = e2)
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | REF_CLOSE: (6), (7), (9), (42), (52), (185), (649), (661),
% 173.46/26.39  | | | | | | | | | |            (7960), (8473), (8568), (8625), (function-axioms)
% 173.46/26.39  | | | | | | | | | |            are inconsistent by sub-proof #25.
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | 
% 173.46/26.39  | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | 
% 173.46/26.39  | | | | | | | |   (8627)  all_22_1 = e3
% 173.46/26.39  | | | | | | | | 
% 173.46/26.39  | | | | | | | | COMBINE_EQS: (711), (8627) imply:
% 173.46/26.39  | | | | | | | |   (8628)  all_14_1 = e3
% 173.46/26.39  | | | | | | | | 
% 173.46/26.39  | | | | | | | | SIMP: (8628) implies:
% 173.46/26.39  | | | | | | | |   (8629)  all_14_1 = e3
% 173.46/26.39  | | | | | | | | 
% 173.46/26.39  | | | | | | | | COMBINE_EQS: (719), (8629) imply:
% 173.46/26.39  | | | | | | | |   (8630)  all_52_20 = e3
% 173.46/26.39  | | | | | | | | 
% 173.46/26.39  | | | | | | | | BETA: splitting (98) gives:
% 173.46/26.39  | | | | | | | | 
% 173.46/26.39  | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | |   (8631)   ~ (all_28_0 = e3)
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | REDUCE: (776), (8631) imply:
% 173.46/26.39  | | | | | | | | |   (8632)   ~ (all_6_0 = e3)
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.39  | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | |   (8633)   ~ (all_42_0 = e1)
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | REDUCE: (761), (8633) imply:
% 173.46/26.39  | | | | | | | | | |   (8634)   ~ (all_4_0 = e1)
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | |   (8635)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.39  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.39  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | BETA: splitting (8635) gives:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8636)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.39  | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | ALPHA: (8636) implies:
% 173.46/26.39  | | | | | | | | | | | |   (8637)  all_52_0 = e3
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | COMBINE_EQS: (7960), (8637) imply:
% 173.46/26.39  | | | | | | | | | | | |   (8638)  e3 = e2
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | SIMP: (8638) implies:
% 173.46/26.39  | | | | | | | | | | | |   (8639)  e3 = e2
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | COMBINE_EQS: (8630), (8639) imply:
% 173.46/26.39  | | | | | | | | | | | |   (8640)  all_52_20 = e2
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43), (52),
% 173.46/26.39  | | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 173.46/26.39  | | | | | | | | | | | |            (169), (170), (172), (173), (177), (178), (179),
% 173.46/26.39  | | | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.46/26.39  | | | | | | | | | | | |            (271), (272), (278), (280), (281), (282), (283),
% 173.46/26.39  | | | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.46/26.39  | | | | | | | | | | | |            (310), (311), (313), (315), (316), (319), (321),
% 173.46/26.39  | | | | | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 173.46/26.39  | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.46/26.39  | | | | | | | | | | | |            (364), (370), (373), (385), (386), (391), (392),
% 173.46/26.39  | | | | | | | | | | | |            (403), (413), (429), (529), (530), (531), (532),
% 173.46/26.39  | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.39  | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.39  | | | | | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 173.46/26.39  | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 173.46/26.39  | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (577),
% 173.46/26.39  | | | | | | | | | | | |            (580), (581), (582), (583), (585), (586), (588),
% 173.46/26.39  | | | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.46/26.39  | | | | | | | | | | | |            (598), (600), (649), (661), (7960), (7961),
% 173.46/26.39  | | | | | | | | | | | |            (7962), (7963), (7965), (8473), (8632), (8634),
% 173.46/26.39  | | | | | | | | | | | |            (8640), (function-axioms) are inconsistent by
% 173.46/26.39  | | | | | | | | | | | |            sub-proof #28.
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8641)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.39  | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | ALPHA: (8641) implies:
% 173.46/26.39  | | | | | | | | | | | |   (8642)  all_52_10 = e2
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | COMBINE_EQS: (661), (8642) imply:
% 173.46/26.39  | | | | | | | | | | | |   (8643)  all_10_1 = e2
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REF_CLOSE: (9), (52), (8473), (8643), (function-axioms) are
% 173.46/26.39  | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | |   (8644)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.39  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.39  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | BETA: splitting (8644) gives:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8645)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.39  | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REF_CLOSE: (8), (8630), (8645) are inconsistent by sub-proof
% 173.46/26.39  | | | | | | | | | | | |            #427.
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | |   (8646)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.39  | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (37), (38), (42), (43), (52),
% 173.46/26.39  | | | | | | | | | | | |            (154), (155), (156), (161), (163), (164), (165),
% 173.46/26.39  | | | | | | | | | | | |            (169), (170), (172), (173), (177), (178), (179),
% 173.46/26.39  | | | | | | | | | | | |            (181), (182), (183), (268), (269), (270), (271),
% 173.46/26.39  | | | | | | | | | | | |            (272), (278), (280), (281), (282), (283), (301),
% 173.46/26.39  | | | | | | | | | | | |            (302), (303), (304), (305), (306), (307), (310),
% 173.46/26.39  | | | | | | | | | | | |            (311), (313), (315), (316), (319), (321), (322),
% 173.46/26.39  | | | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 173.46/26.39  | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (364),
% 173.46/26.39  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.39  | | | | | | | | | | | |            (413), (429), (529), (530), (531), (532), (533),
% 173.46/26.39  | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.46/26.39  | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.46/26.39  | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (560),
% 173.46/26.39  | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 173.46/26.39  | | | | | | | | | | | |            (568), (569), (571), (573), (575), (577), (580),
% 173.46/26.39  | | | | | | | | | | | |            (581), (582), (583), (585), (586), (588), (589),
% 173.46/26.39  | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 173.46/26.39  | | | | | | | | | | | |            (600), (649), (7961), (7962), (7963), (7965),
% 173.46/26.39  | | | | | | | | | | | |            (8632), (8634), (8646), (function-axioms) are
% 173.46/26.39  | | | | | | | | | | | |            inconsistent by sub-proof #29.
% 173.46/26.39  | | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | End of split
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | Case 2:
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | |   (8647)  all_42_0 = e1
% 173.46/26.39  | | | | | | | | | |   (8648)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | COMBINE_EQS: (761), (8647) imply:
% 173.46/26.39  | | | | | | | | | |   (8649)  all_4_0 = e1
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | REDUCE: (7961), (8649) imply:
% 173.46/26.39  | | | | | | | | | |   (8650)  op(e2, all_4_2) = e1
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | BETA: splitting (8648) gives:
% 173.46/26.39  | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | Case 1:
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | |   (8651)   ~ (all_42_1 = e2)
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | REDUCE: (7959), (8651) imply:
% 173.46/26.39  | | | | | | | | | | |   (8652)  $false
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.39  | | | | | | | | | | | CLOSE: (8652) is inconsistent.
% 173.46/26.39  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | |   (8653)   ~ (all_42_2 = e0)
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | REDUCE: (477), (8653) imply:
% 173.46/26.40  | | | | | | | | | | |   (8654)   ~ (all_4_2 = e0)
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | |   (8655)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.40  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.40  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | BETA: splitting (8655) gives:
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | |   (8656)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.40  | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | ALPHA: (8656) implies:
% 173.46/26.40  | | | | | | | | | | | | |   (8657)  all_52_0 = e3
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | COMBINE_EQS: (7960), (8657) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8658)  e3 = e2
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | SIMP: (8658) implies:
% 173.46/26.40  | | | | | | | | | | | | |   (8659)  e3 = e2
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | COMBINE_EQS: (8630), (8659) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8660)  all_52_20 = e2
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (42), (43), (52), (154),
% 173.46/26.40  | | | | | | | | | | | | |            (156), (163), (164), (165), (170), (172), (173),
% 173.46/26.40  | | | | | | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 173.46/26.40  | | | | | | | | | | | | |            (268), (270), (271), (273), (274), (276), (278),
% 173.46/26.40  | | | | | | | | | | | | |            (280), (282), (283), (301), (303), (304), (305),
% 173.46/26.40  | | | | | | | | | | | | |            (307), (310), (311), (313), (315), (319), (321),
% 173.46/26.40  | | | | | | | | | | | | |            (322), (323), (324), (325), (328), (329), (330),
% 173.46/26.40  | | | | | | | | | | | | |            (331), (344), (349), (359), (364), (370), (373),
% 173.46/26.40  | | | | | | | | | | | | |            (385), (386), (391), (392), (403), (419), (425),
% 173.46/26.40  | | | | | | | | | | | | |            (429), (529), (530), (531), (532), (533), (534),
% 173.46/26.40  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.40  | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.40  | | | | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.46/26.40  | | | | | | | | | | | | |            (562), (563), (564), (565), (567), (568), (569),
% 173.46/26.40  | | | | | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 173.46/26.40  | | | | | | | | | | | | |            (582), (583), (584), (585), (586), (588), (589),
% 173.46/26.40  | | | | | | | | | | | | |            (591), (593), (594), (595), (597), (598), (599),
% 173.46/26.40  | | | | | | | | | | | | |            (600), (649), (661), (7960), (7962), (7965),
% 173.46/26.40  | | | | | | | | | | | | |            (8473), (8632), (8650), (8654), (8660),
% 173.46/26.40  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.40  | | | | | | | | | | | | |            #26.
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | |   (8661)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.40  | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | ALPHA: (8661) implies:
% 173.46/26.40  | | | | | | | | | | | | |   (8662)  all_52_10 = e2
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | COMBINE_EQS: (661), (8662) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8663)  all_10_1 = e2
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REF_CLOSE: (9), (52), (8473), (8663), (function-axioms) are
% 173.46/26.40  | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | |   (8664)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.40  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.40  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | BETA: splitting (8664) gives:
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | |   (8665)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.40  | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REF_CLOSE: (8), (8630), (8665) are inconsistent by sub-proof
% 173.46/26.40  | | | | | | | | | | | | |            #427.
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | |   (8666)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.40  | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | ALPHA: (8666) implies:
% 173.46/26.40  | | | | | | | | | | | | |   (8667)  all_52_30 = e0
% 173.46/26.40  | | | | | | | | | | | | |   (8668)  all_52_28 = e1
% 173.46/26.40  | | | | | | | | | | | | |   (8669)  all_52_26 = e2
% 173.46/26.40  | | | | | | | | | | | | |   (8670)  all_52_24 = e3
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | COMBINE_EQS: (649), (8667) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8671)  all_6_1 = e0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | SIMP: (8671) implies:
% 173.46/26.40  | | | | | | | | | | | | |   (8672)  all_6_1 = e0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REDUCE: (43), (8672) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8673)  op(e0, all_6_2) = all_6_0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REDUCE: (181), (8670) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8674)  op(e3, all_52_25) = e3
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REDUCE: (173), (8669) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8675)  op(e2, all_52_27) = e2
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REDUCE: (165), (8668) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8676)  op(e1, all_52_29) = e1
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REDUCE: (42), (8672) imply:
% 173.46/26.40  | | | | | | | | | | | | |   (8677)  op(e0, all_6_2) = e0
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (154), (156), (163), (164), (170),
% 173.46/26.40  | | | | | | | | | | | | |            (172), (177), (178), (179), (182), (183), (268),
% 173.46/26.40  | | | | | | | | | | | | |            (270), (271), (273), (274), (276), (278), (280),
% 173.46/26.40  | | | | | | | | | | | | |            (282), (283), (301), (303), (304), (305), (307),
% 173.46/26.40  | | | | | | | | | | | | |            (310), (311), (313), (315), (319), (321), (322),
% 173.46/26.40  | | | | | | | | | | | | |            (323), (324), (325), (328), (329), (330), (331),
% 173.46/26.40  | | | | | | | | | | | | |            (344), (349), (359), (364), (370), (373), (385),
% 173.46/26.40  | | | | | | | | | | | | |            (386), (391), (392), (403), (419), (425), (429),
% 173.46/26.40  | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.46/26.40  | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.40  | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.40  | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.40  | | | | | | | | | | | | |            (563), (564), (565), (567), (568), (569), (571),
% 173.46/26.40  | | | | | | | | | | | | |            (573), (577), (578), (579), (580), (581), (582),
% 173.46/26.40  | | | | | | | | | | | | |            (583), (584), (585), (586), (588), (589), (591),
% 173.46/26.40  | | | | | | | | | | | | |            (593), (594), (595), (597), (598), (599), (600),
% 173.46/26.40  | | | | | | | | | | | | |            (7962), (7965), (8632), (8650), (8654), (8673),
% 173.46/26.40  | | | | | | | | | | | | |            (8674), (8675), (8676), (8677), (function-axioms)
% 173.46/26.40  | | | | | | | | | | | | |            are inconsistent by sub-proof #27.
% 173.46/26.40  | | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | |   (8678)  all_28_0 = e3
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | COMBINE_EQS: (776), (8678) imply:
% 173.46/26.40  | | | | | | | | |   (8679)  all_6_0 = e3
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | REDUCE: (43), (8679) imply:
% 173.46/26.40  | | | | | | | | |   (8680)  op(all_6_1, all_6_2) = e3
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | |   (8681)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.40  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.40  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | BETA: splitting (8681) gives:
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | |   (8682)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.40  | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | ALPHA: (8682) implies:
% 173.46/26.40  | | | | | | | | | | |   (8683)  all_52_0 = e3
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | COMBINE_EQS: (7960), (8683) imply:
% 173.46/26.40  | | | | | | | | | | |   (8684)  e3 = e2
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | SIMP: (8684) implies:
% 173.46/26.40  | | | | | | | | | | |   (8685)  e3 = e2
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | COMBINE_EQS: (8630), (8685) imply:
% 173.46/26.40  | | | | | | | | | | |   (8686)  all_52_20 = e2
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (42), (52), (185), (649), (661),
% 173.46/26.40  | | | | | | | | | | |            (7960), (8473), (8680), (8686), (function-axioms)
% 173.46/26.40  | | | | | | | | | | |            are inconsistent by sub-proof #25.
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | |   (8687)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.40  | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | ALPHA: (8687) implies:
% 173.46/26.40  | | | | | | | | | | |   (8688)  all_52_10 = e2
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | COMBINE_EQS: (661), (8688) imply:
% 173.46/26.40  | | | | | | | | | | |   (8689)  all_10_1 = e2
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | REF_CLOSE: (9), (52), (8473), (8689), (function-axioms) are
% 173.46/26.40  | | | | | | | | | | |            inconsistent by sub-proof #263.
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | |   (8690)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.40  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.40  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | BETA: splitting (8690) gives:
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | |   (8691)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.40  | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | REF_CLOSE: (8), (8630), (8691) are inconsistent by sub-proof
% 173.46/26.40  | | | | | | | | | | |            #373.
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | |   (8692)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.40  | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | | REF_CLOSE: (7), (42), (649), (8680), (8692),
% 173.46/26.40  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.40  | | | | | | | | | | |            #501.
% 173.46/26.40  | | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | 
% 173.46/26.40  | | | | | | | End of split
% 173.46/26.40  | | | | | | | 
% 173.46/26.40  | | | | | | Case 2:
% 173.46/26.40  | | | | | | | 
% 173.46/26.40  | | | | | | |   (8693)  all_18_0 = e3
% 173.46/26.40  | | | | | | | 
% 173.46/26.40  | | | | | | | COMBINE_EQS: (789), (8693) imply:
% 173.46/26.40  | | | | | | |   (8694)  all_14_0 = e3
% 173.46/26.40  | | | | | | | 
% 173.46/26.40  | | | | | | | REDUCE: (63), (8694) imply:
% 173.46/26.40  | | | | | | |   (8695)  op(all_14_1, all_14_2) = e3
% 173.46/26.40  | | | | | | | 
% 173.46/26.40  | | | | | | | BETA: splitting (98) gives:
% 173.46/26.40  | | | | | | | 
% 173.46/26.40  | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | 
% 173.46/26.40  | | | | | | | |   (8696)   ~ (all_28_0 = e3)
% 173.46/26.40  | | | | | | | | 
% 173.46/26.40  | | | | | | | | REDUCE: (776), (8696) imply:
% 173.46/26.40  | | | | | | | |   (8697)   ~ (all_6_0 = e3)
% 173.46/26.40  | | | | | | | | 
% 173.46/26.40  | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.40  | | | | | | | | 
% 173.46/26.40  | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | |   (8698)   ~ (all_42_0 = e1)
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | REDUCE: (761), (8698) imply:
% 173.46/26.40  | | | | | | | | |   (8699)   ~ (all_4_0 = e1)
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | Case 1:
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | |   (8700)  all_58_15 = e0
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | COMBINE_EQS: (532), (8700) imply:
% 173.46/26.40  | | | | | | | | | |   (8701)  all_6_2 = e0
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (599), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8702)   ~ (all_52_15 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (600), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8703)   ~ (all_52_23 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (564), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8704)   ~ (all_52_25 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (582), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8705)   ~ (all_52_27 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (594), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8706)   ~ (all_52_29 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (43), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8707)  op(all_6_1, e0) = all_6_0
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (42), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8708)  op(e0, e0) = all_6_1
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (41), (8701) imply:
% 173.46/26.40  | | | | | | | | | |   (8709)  op(e0, e0) = e0
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (52), (62), (154), (155),
% 173.46/26.40  | | | | | | | | | |            (156), (158), (159), (163), (164), (165), (167),
% 173.46/26.40  | | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 173.46/26.40  | | | | | | | | | |            (179), (181), (182), (183), (185), (269), (270),
% 173.46/26.40  | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (278),
% 173.46/26.40  | | | | | | | | | |            (280), (283), (302), (303), (304), (305), (306),
% 173.46/26.40  | | | | | | | | | |            (307), (310), (311), (313), (315), (316), (319),
% 173.46/26.40  | | | | | | | | | |            (322), (323), (324), (325), (326), (328), (330),
% 173.46/26.40  | | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.46/26.40  | | | | | | | | | |            (365), (370), (373), (385), (386), (391), (403),
% 173.46/26.40  | | | | | | | | | |            (419), (425), (429), (530), (531), (533), (534),
% 173.46/26.40  | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.40  | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.40  | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.46/26.40  | | | | | | | | | |            (562), (563), (565), (566), (567), (569), (571),
% 173.46/26.40  | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.46/26.40  | | | | | | | | | |            (583), (584), (585), (586), (588), (591), (593),
% 173.46/26.40  | | | | | | | | | |            (595), (596), (598), (661), (719), (7960), (7961),
% 173.46/26.40  | | | | | | | | | |            (7962), (7963), (7965), (8697), (8699), (8700),
% 173.46/26.40  | | | | | | | | | |            (8702), (8703), (8704), (8705), (8706), (8707),
% 173.46/26.40  | | | | | | | | | |            (8708), (8709), (function-axioms) are inconsistent
% 173.46/26.40  | | | | | | | | | |            by sub-proof #23.
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | |   (8710)   ~ (all_58_15 = e0)
% 173.46/26.40  | | | | | | | | | |   (8711)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.40  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.40  | | | | | | | | | |             e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | ALPHA: (8711) implies:
% 173.46/26.40  | | | | | | | | | |   (8712)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.40  | | | | | | | | | |   (8713)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REDUCE: (532), (8710) imply:
% 173.46/26.40  | | | | | | | | | |   (8714)   ~ (all_6_2 = e0)
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.40  | | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.40  | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.40  | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.40  | | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.40  | | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.40  | | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.40  | | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.40  | | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.40  | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.40  | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.40  | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.40  | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.40  | | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.40  | | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.40  | | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.40  | | | | | | | | | |            (7962), (8473), (8695), (8699), (8712), (8713),
% 173.46/26.40  | | | | | | | | | |            (8714), (function-axioms) are inconsistent by
% 173.46/26.40  | | | | | | | | | |            sub-proof #22.
% 173.46/26.40  | | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | End of split
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | Case 2:
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | |   (8715)  all_42_0 = e1
% 173.46/26.40  | | | | | | | | |   (8716)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | COMBINE_EQS: (761), (8715) imply:
% 173.46/26.40  | | | | | | | | |   (8717)  all_4_0 = e1
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | SIMP: (8717) implies:
% 173.46/26.40  | | | | | | | | |   (8718)  all_4_0 = e1
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | REDUCE: (7961), (8718) imply:
% 173.46/26.40  | | | | | | | | |   (8719)  op(e2, all_4_2) = e1
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.40  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.40  | | | | | | | | |            (43), (52), (62), (154), (155), (156), (158),
% 173.46/26.40  | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.46/26.40  | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.46/26.40  | | | | | | | | |            (182), (183), (185), (268), (269), (270), (271),
% 173.46/26.40  | | | | | | | | |            (272), (273), (274), (275), (276), (278), (280),
% 173.46/26.40  | | | | | | | | |            (282), (283), (301), (302), (303), (304), (305),
% 173.46/26.40  | | | | | | | | |            (306), (307), (310), (311), (313), (315), (319),
% 173.46/26.40  | | | | | | | | |            (321), (322), (323), (324), (325), (326), (328),
% 173.46/26.40  | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.46/26.40  | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.46/26.40  | | | | | | | | |            (391), (392), (403), (419), (425), (429), (477),
% 173.46/26.40  | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.46/26.40  | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.40  | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.40  | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.40  | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.46/26.40  | | | | | | | | |            (571), (573), (577), (578), (579), (580), (581),
% 173.46/26.40  | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.46/26.40  | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.46/26.40  | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7959),
% 173.46/26.40  | | | | | | | | |            (7960), (7962), (7963), (7965), (8473), (8697),
% 173.46/26.40  | | | | | | | | |            (8716), (8719), (function-axioms) are inconsistent
% 173.46/26.40  | | | | | | | | |            by sub-proof #21.
% 173.46/26.40  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | End of split
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | Case 2:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | |   (8720)  all_28_0 = e3
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | COMBINE_EQS: (776), (8720) imply:
% 173.46/26.41  | | | | | | | |   (8721)  all_6_0 = e3
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | SIMP: (8721) implies:
% 173.46/26.41  | | | | | | | |   (8722)  all_6_0 = e3
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | REDUCE: (43), (8722) imply:
% 173.46/26.41  | | | | | | | |   (8723)  op(all_6_1, all_6_2) = e3
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | Case 1:
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | |   (8724)   ~ (all_42_0 = e1)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (761), (8724) imply:
% 173.46/26.41  | | | | | | | | |   (8725)   ~ (all_4_0 = e1)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | Case 1:
% 173.46/26.41  | | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | |   (8726)  all_58_15 = e0
% 173.46/26.41  | | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8723), (8726),
% 173.46/26.41  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.41  | | | | | | | | | |            #510.
% 173.46/26.41  | | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | Case 2:
% 173.46/26.41  | | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | |   (8727)   ~ (all_58_15 = e0)
% 173.46/26.41  | | | | | | | | | |   (8728)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.41  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.41  | | | | | | | | | |             e0)
% 173.46/26.41  | | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.41  | | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.41  | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.41  | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.41  | | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.41  | | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.41  | | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.41  | | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.41  | | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.41  | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.41  | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.41  | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.41  | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.41  | | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.41  | | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.41  | | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.41  | | | | | | | | | |            (7962), (8473), (8695), (8725), (8727), (8728),
% 173.46/26.41  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.41  | | | | | | | | | |            #20.
% 173.46/26.41  | | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | End of split
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | Case 2:
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | |   (8729)  all_42_0 = e1
% 173.46/26.41  | | | | | | | | |   (8730)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | COMBINE_EQS: (761), (8729) imply:
% 173.46/26.41  | | | | | | | | |   (8731)  all_4_0 = e1
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (7961), (8731) imply:
% 173.46/26.41  | | | | | | | | |   (8732)  op(e2, all_4_2) = e1
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.41  | | | | | | | | |            (52), (62), (156), (158), (161), (163), (164),
% 173.46/26.41  | | | | | | | | |            (170), (172), (174), (177), (178), (179), (182),
% 173.46/26.41  | | | | | | | | |            (185), (268), (273), (274), (276), (283), (301),
% 173.46/26.41  | | | | | | | | |            (304), (307), (310), (311), (315), (319), (323),
% 173.46/26.41  | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.46/26.41  | | | | | | | | |            (364), (370), (373), (385), (391), (403), (419),
% 173.46/26.41  | | | | | | | | |            (425), (477), (529), (531), (532), (533), (534),
% 173.46/26.41  | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.41  | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.41  | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.46/26.41  | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.46/26.41  | | | | | | | | |            (595), (596), (598), (600), (649), (661), (719),
% 173.46/26.41  | | | | | | | | |            (7959), (7960), (7962), (8473), (8723), (8730),
% 173.46/26.41  | | | | | | | | |            (8732), (function-axioms) are inconsistent by
% 173.46/26.41  | | | | | | | | |            sub-proof #19.
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | End of split
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | End of split
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | End of split
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | Case 2:
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | |   (8733)  all_14_0 = e2
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | | REDUCE: (63), (8733) imply:
% 173.46/26.41  | | | | | |   (8734)  op(all_14_1, all_14_2) = e2
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | | BETA: splitting (98) gives:
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | | Case 1:
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | |   (8735)   ~ (all_28_0 = e3)
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | | REDUCE: (776), (8735) imply:
% 173.46/26.41  | | | | | | |   (8736)   ~ (all_6_0 = e3)
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | | BETA: splitting (133) gives:
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | | Case 1:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | |   (8737)   ~ (all_42_0 = e1)
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | REDUCE: (761), (8737) imply:
% 173.46/26.41  | | | | | | | |   (8738)   ~ (all_4_0 = e1)
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | Case 1:
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | |   (8739)  all_58_15 = e0
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | COMBINE_EQS: (532), (8739) imply:
% 173.46/26.41  | | | | | | | | |   (8740)  all_6_2 = e0
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (599), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8741)   ~ (all_52_15 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (600), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8742)   ~ (all_52_23 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (564), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8743)   ~ (all_52_25 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (582), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8744)   ~ (all_52_27 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (594), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8745)   ~ (all_52_29 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (43), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8746)  op(all_6_1, e0) = all_6_0
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (42), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8747)  op(e0, e0) = all_6_1
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (41), (8740) imply:
% 173.46/26.41  | | | | | | | | |   (8748)  op(e0, e0) = e0
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (52), (62), (154), (155),
% 173.46/26.41  | | | | | | | | |            (156), (158), (159), (163), (164), (165), (167),
% 173.46/26.41  | | | | | | | | |            (169), (170), (172), (173), (174), (177), (178),
% 173.46/26.41  | | | | | | | | |            (179), (181), (182), (183), (185), (269), (270),
% 173.46/26.41  | | | | | | | | |            (271), (272), (273), (274), (275), (276), (278),
% 173.46/26.41  | | | | | | | | |            (280), (283), (302), (303), (304), (305), (306),
% 173.46/26.41  | | | | | | | | |            (307), (310), (311), (313), (315), (316), (319),
% 173.46/26.41  | | | | | | | | |            (322), (323), (324), (325), (326), (328), (330),
% 173.46/26.41  | | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.46/26.41  | | | | | | | | |            (365), (370), (373), (385), (386), (391), (403),
% 173.46/26.41  | | | | | | | | |            (419), (425), (429), (530), (531), (533), (534),
% 173.46/26.41  | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.41  | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.41  | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.46/26.41  | | | | | | | | |            (562), (563), (565), (566), (567), (569), (571),
% 173.46/26.41  | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.46/26.41  | | | | | | | | |            (583), (584), (585), (586), (588), (591), (593),
% 173.46/26.41  | | | | | | | | |            (595), (596), (598), (661), (719), (7960), (7961),
% 173.46/26.41  | | | | | | | | |            (7962), (7963), (7965), (8736), (8738), (8739),
% 173.46/26.41  | | | | | | | | |            (8741), (8742), (8743), (8744), (8745), (8746),
% 173.46/26.41  | | | | | | | | |            (8747), (8748), (function-axioms) are inconsistent
% 173.46/26.41  | | | | | | | | |            by sub-proof #23.
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | Case 2:
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | |   (8749)   ~ (all_58_15 = e0)
% 173.46/26.41  | | | | | | | | |   (8750)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.41  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.41  | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.41  | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.41  | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.41  | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.41  | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.41  | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.41  | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.41  | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.41  | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.41  | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.41  | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.41  | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.41  | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.41  | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.41  | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.41  | | | | | | | | |            (7962), (8473), (8734), (8738), (8749), (8750),
% 173.46/26.41  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.41  | | | | | | | | |            #17.
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | End of split
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | Case 2:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | |   (8751)  all_42_0 = e1
% 173.46/26.41  | | | | | | | |   (8752)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | COMBINE_EQS: (761), (8751) imply:
% 173.46/26.41  | | | | | | | |   (8753)  all_4_0 = e1
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | REDUCE: (7961), (8753) imply:
% 173.46/26.41  | | | | | | | |   (8754)  op(e2, all_4_2) = e1
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42), (43),
% 173.46/26.41  | | | | | | | |            (52), (62), (154), (155), (156), (158), (159), (161),
% 173.46/26.41  | | | | | | | |            (163), (164), (165), (167), (170), (172), (173),
% 173.46/26.41  | | | | | | | |            (174), (177), (178), (179), (181), (182), (183),
% 173.46/26.41  | | | | | | | |            (185), (268), (269), (270), (271), (272), (273),
% 173.46/26.41  | | | | | | | |            (274), (275), (276), (278), (280), (282), (283),
% 173.46/26.41  | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.46/26.41  | | | | | | | |            (310), (311), (313), (315), (319), (321), (322),
% 173.46/26.41  | | | | | | | |            (323), (324), (325), (326), (328), (329), (330),
% 173.46/26.41  | | | | | | | |            (331), (341), (344), (349), (350), (359), (364),
% 173.46/26.41  | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 173.46/26.41  | | | | | | | |            (403), (419), (425), (429), (477), (529), (530),
% 173.46/26.41  | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.41  | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.41  | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.41  | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.41  | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.46/26.41  | | | | | | | |            (577), (578), (579), (580), (581), (582), (583),
% 173.46/26.41  | | | | | | | |            (584), (585), (586), (587), (588), (589), (591),
% 173.46/26.41  | | | | | | | |            (593), (594), (595), (596), (597), (598), (599),
% 173.46/26.41  | | | | | | | |            (600), (649), (661), (719), (7959), (7960), (7962),
% 173.46/26.41  | | | | | | | |            (7963), (7965), (8473), (8736), (8752), (8754),
% 173.46/26.41  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #21.
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | End of split
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | Case 2:
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | |   (8755)  all_28_0 = e3
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | | COMBINE_EQS: (776), (8755) imply:
% 173.46/26.41  | | | | | | |   (8756)  all_6_0 = e3
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | | REDUCE: (43), (8756) imply:
% 173.46/26.41  | | | | | | |   (8757)  op(all_6_1, all_6_2) = e3
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | | BETA: splitting (133) gives:
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | | Case 1:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | |   (8758)   ~ (all_42_0 = e1)
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | REDUCE: (761), (8758) imply:
% 173.46/26.41  | | | | | | | |   (8759)   ~ (all_4_0 = e1)
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | Case 1:
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | |   (8760)  all_58_15 = e0
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REF_CLOSE: (7), (41), (42), (532), (8757), (8760),
% 173.46/26.41  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.41  | | | | | | | | |            #510.
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | Case 2:
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | |   (8761)   ~ (all_58_15 = e0)
% 173.46/26.41  | | | | | | | | |   (8762)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.41  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | ALPHA: (8762) implies:
% 173.46/26.41  | | | | | | | | |   (8763)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.41  | | | | | | | | |   (8764)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REDUCE: (532), (8761) imply:
% 173.46/26.41  | | | | | | | | |   (8765)   ~ (all_6_2 = e0)
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.41  | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.41  | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.41  | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.41  | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.41  | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.41  | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.41  | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.41  | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.41  | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.41  | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.41  | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.41  | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.41  | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.41  | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.41  | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.41  | | | | | | | | |            (7962), (8473), (8734), (8759), (8763), (8764),
% 173.46/26.41  | | | | | | | | |            (8765), (function-axioms) are inconsistent by
% 173.46/26.41  | | | | | | | | |            sub-proof #18.
% 173.46/26.41  | | | | | | | | | 
% 173.46/26.41  | | | | | | | | End of split
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | Case 2:
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | |   (8766)  all_42_0 = e1
% 173.46/26.41  | | | | | | | |   (8767)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | COMBINE_EQS: (761), (8766) imply:
% 173.46/26.41  | | | | | | | |   (8768)  all_4_0 = e1
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | REDUCE: (7961), (8768) imply:
% 173.46/26.41  | | | | | | | |   (8769)  op(e2, all_4_2) = e1
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42), (52),
% 173.46/26.41  | | | | | | | |            (62), (156), (158), (161), (163), (164), (170),
% 173.46/26.41  | | | | | | | |            (172), (174), (177), (178), (179), (182), (185),
% 173.46/26.41  | | | | | | | |            (268), (273), (274), (276), (283), (301), (304),
% 173.46/26.41  | | | | | | | |            (307), (310), (311), (315), (319), (323), (324),
% 173.46/26.41  | | | | | | | |            (326), (328), (330), (331), (349), (359), (364),
% 173.46/26.41  | | | | | | | |            (370), (373), (385), (391), (403), (419), (425),
% 173.46/26.41  | | | | | | | |            (477), (529), (531), (532), (533), (534), (535),
% 173.46/26.41  | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.41  | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.46/26.41  | | | | | | | |            (558), (559), (561), (562), (563), (564), (566),
% 173.46/26.41  | | | | | | | |            (577), (579), (584), (586), (587), (593), (595),
% 173.46/26.41  | | | | | | | |            (596), (598), (600), (649), (661), (719), (7959),
% 173.46/26.41  | | | | | | | |            (7960), (7962), (8473), (8757), (8767), (8769),
% 173.46/26.41  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #19.
% 173.46/26.41  | | | | | | | | 
% 173.46/26.41  | | | | | | | End of split
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | End of split
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | End of split
% 173.46/26.41  | | | | | 
% 173.46/26.41  | | | | End of split
% 173.46/26.41  | | | | 
% 173.46/26.41  | | | Case 2:
% 173.46/26.41  | | | | 
% 173.46/26.41  | | | |   (8770)  all_8_0 = e2
% 173.46/26.41  | | | |   (8771)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 173.46/26.41  | | | | 
% 173.46/26.41  | | | | COMBINE_EQS: (791), (8770) imply:
% 173.46/26.41  | | | |   (8772)  all_6_0 = e2
% 173.46/26.41  | | | | 
% 173.46/26.41  | | | | COMBINE_EQS: (785), (8772) imply:
% 173.46/26.41  | | | |   (8773)  all_16_0 = e2
% 173.46/26.41  | | | | 
% 173.46/26.41  | | | | REDUCE: (43), (8772) imply:
% 173.46/26.41  | | | |   (8774)  op(all_6_1, all_6_2) = e2
% 173.46/26.41  | | | | 
% 173.46/26.41  | | | | BETA: splitting (54) gives:
% 173.46/26.41  | | | | 
% 173.46/26.41  | | | | Case 1:
% 173.46/26.41  | | | | | 
% 173.46/26.41  | | | | |   (8775)   ~ (all_10_0 = e3)
% 173.46/26.41  | | | | | 
% 173.46/26.41  | | | | | BETA: splitting (59) gives:
% 173.46/26.41  | | | | | 
% 173.46/26.41  | | | | | Case 1:
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | |   (8776)   ~ (all_12_1 = e3)
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | | REDUCE: (705), (8776) imply:
% 173.46/26.41  | | | | | |   (8777)   ~ (all_10_1 = e3)
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | | BETA: splitting (69) gives:
% 173.46/26.41  | | | | | | 
% 173.46/26.41  | | | | | | Case 1:
% 173.46/26.41  | | | | | | | 
% 173.46/26.41  | | | | | | |   (8778)   ~ (all_16_0 = e2)
% 173.46/26.42  | | | | | | | 
% 173.46/26.42  | | | | | | | REDUCE: (8773), (8778) imply:
% 173.46/26.42  | | | | | | |   (8779)  $false
% 173.46/26.42  | | | | | | | 
% 173.46/26.42  | | | | | | | CLOSE: (8779) is inconsistent.
% 173.46/26.42  | | | | | | | 
% 173.46/26.42  | | | | | | Case 2:
% 173.46/26.42  | | | | | | | 
% 173.46/26.42  | | | | | | |   (8780)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.42  | | | | | | | 
% 173.46/26.42  | | | | | | | BETA: splitting (83) gives:
% 173.46/26.42  | | | | | | | 
% 173.46/26.42  | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | 
% 173.46/26.42  | | | | | | | |   (8781)   ~ (all_22_1 = e3)
% 173.46/26.42  | | | | | | | | 
% 173.46/26.42  | | | | | | | | REDUCE: (711), (8781) imply:
% 173.46/26.42  | | | | | | | |   (8782)   ~ (all_14_1 = e3)
% 173.46/26.42  | | | | | | | | 
% 173.46/26.42  | | | | | | | | BETA: splitting (88) gives:
% 173.46/26.42  | | | | | | | | 
% 173.46/26.42  | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | 
% 173.46/26.42  | | | | | | | | |   (8783)   ~ (all_24_0 = e1)
% 173.46/26.42  | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | REDUCE: (751), (8783) imply:
% 173.46/26.42  | | | | | | | | |   (8784)   ~ (all_10_0 = e1)
% 173.46/26.42  | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | BETA: splitting (108) gives:
% 173.46/26.42  | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | |   (8785)   ~ (all_32_1 = e2)
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | REDUCE: (713), (8785) imply:
% 173.46/26.42  | | | | | | | | | |   (8786)   ~ (all_14_1 = e2)
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | |   (8787)   ~ (all_42_0 = e1)
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | REDUCE: (761), (8787) imply:
% 173.46/26.42  | | | | | | | | | | |   (8788)   ~ (all_4_0 = e1)
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | |   (8789)  all_58_15 = e0
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (8789),
% 173.46/26.42  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | |            #228.
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | |   (8790)   ~ (all_58_15 = e0)
% 173.46/26.42  | | | | | | | | | | | |   (8791)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.42  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.42  | | | | | | | | | | | |             e0)
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | ALPHA: (8791) implies:
% 173.46/26.42  | | | | | | | | | | | |   (8792)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.42  | | | | | | | | | | | |   (8793)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | REDUCE: (532), (8790) imply:
% 173.46/26.42  | | | | | | | | | | | |   (8794)   ~ (all_6_2 = e0)
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | |   (8795)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.42  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.42  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | BETA: splitting (8795) gives:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8796)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8796) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | | | |            #124.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8797)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | ALPHA: (8797) implies:
% 173.46/26.42  | | | | | | | | | | | | | |   (8798)  all_52_14 = e0
% 173.46/26.42  | | | | | | | | | | | | | |   (8799)  all_52_12 = e1
% 173.46/26.42  | | | | | | | | | | | | | |   (8800)  all_52_10 = e2
% 173.46/26.42  | | | | | | | | | | | | | |   (8801)  all_52_8 = e3
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | COMBINE_EQS: (661), (8800) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8802)  all_10_1 = e2
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (53), (8802) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8803)  op(e2, all_10_2) = all_10_0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (183), (8801) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8804)  op(e3, all_52_9) = e3
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (52), (8802) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8805)  op(e2, all_10_2) = e2
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (167), (8799) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8806)  op(e1, all_52_13) = e1
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (159), (8798) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8807)  op(e0, all_52_15) = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (42), (62), (154), (155),
% 173.46/26.42  | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (170), (172),
% 173.46/26.42  | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.46/26.42  | | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (274),
% 173.46/26.42  | | | | | | | | | | | | | |            (275), (277), (279), (280), (282), (283), (303),
% 173.46/26.42  | | | | | | | | | | | | | |            (304), (305), (307), (311), (313), (315), (319),
% 173.46/26.42  | | | | | | | | | | | | | |            (321), (323), (326), (328), (329), (330), (331),
% 173.46/26.42  | | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 173.46/26.42  | | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.42  | | | | | | | | | | | | | |            (409), (415), (419), (429), (501), (515), (529),
% 173.46/26.42  | | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.42  | | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.42  | | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 173.46/26.42  | | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.46/26.42  | | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.42  | | | | | | | | | | | | | |            (579), (580), (581), (582), (585), (586), (587),
% 173.46/26.42  | | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.46/26.42  | | | | | | | | | | | | | |            (597), (600), (704), (710), (7961), (7962),
% 173.46/26.42  | | | | | | | | | | | | | |            (8771), (8774), (8775), (8780), (8784), (8788),
% 173.46/26.42  | | | | | | | | | | | | | |            (8792), (8793), (8794), (8803), (8804), (8805),
% 173.46/26.42  | | | | | | | | | | | | | |            (8806), (8807), (function-axioms) are inconsistent
% 173.46/26.42  | | | | | | | | | | | | | |            by sub-proof #15.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | |   (8808)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.42  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.42  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | BETA: splitting (8808) gives:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8809)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | ALPHA: (8809) implies:
% 173.46/26.42  | | | | | | | | | | | | | |   (8810)  all_52_22 = e0
% 173.46/26.42  | | | | | | | | | | | | | |   (8811)  all_52_20 = e1
% 173.46/26.42  | | | | | | | | | | | | | |   (8812)  all_52_18 = e2
% 173.46/26.42  | | | | | | | | | | | | | |   (8813)  all_52_16 = e3
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | COMBINE_EQS: (719), (8811) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8814)  all_14_1 = e1
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | SIMP: (8814) implies:
% 173.46/26.42  | | | | | | | | | | | | | |   (8815)  all_14_1 = e1
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (42), (52), (62), (156),
% 173.46/26.42  | | | | | | | | | | | | | |            (158), (163), (164), (165), (170), (172), (173),
% 173.46/26.42  | | | | | | | | | | | | | |            (174), (177), (178), (179), (182), (268), (270),
% 173.46/26.42  | | | | | | | | | | | | | |            (271), (274), (275), (276), (277), (278), (280),
% 173.46/26.42  | | | | | | | | | | | | | |            (283), (303), (304), (307), (310), (311), (315),
% 173.46/26.42  | | | | | | | | | | | | | |            (317), (319), (323), (324), (326), (328), (330),
% 173.46/26.42  | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 173.46/26.42  | | | | | | | | | | | | | |            (385), (386), (391), (403), (415), (419), (425),
% 173.46/26.42  | | | | | | | | | | | | | |            (429), (501), (529), (530), (531), (532), (533),
% 173.46/26.42  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.46/26.42  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.46/26.42  | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (561),
% 173.46/26.42  | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (571), (577),
% 173.46/26.42  | | | | | | | | | | | | | |            (578), (582), (583), (584), (585), (586), (587),
% 173.46/26.42  | | | | | | | | | | | | | |            (588), (594), (595), (596), (598), (704), (7958),
% 173.46/26.42  | | | | | | | | | | | | | |            (7961), (7962), (8774), (8777), (8780), (8782),
% 173.46/26.42  | | | | | | | | | | | | | |            (8786), (8788), (8793), (8810), (8812), (8813),
% 173.46/26.42  | | | | | | | | | | | | | |            (8815), (function-axioms) are inconsistent by
% 173.46/26.42  | | | | | | | | | | | | | |            sub-proof #14.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8816)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (8774), (8816),
% 173.46/26.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | | | |            #200.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | |   (8817)  all_42_0 = e1
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | COMBINE_EQS: (761), (8817) imply:
% 173.46/26.42  | | | | | | | | | | |   (8818)  all_4_0 = e1
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | REDUCE: (7961), (8818) imply:
% 173.46/26.42  | | | | | | | | | | |   (8819)  op(e2, all_4_2) = e1
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | |   (8820)  all_58_15 = e0
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (8820),
% 173.46/26.42  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | |            #228.
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | |   (8821)   ~ (all_58_15 = e0)
% 173.46/26.42  | | | | | | | | | | | |   (8822)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.42  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.42  | | | | | | | | | | | |             e0)
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | ALPHA: (8822) implies:
% 173.46/26.42  | | | | | | | | | | | |   (8823)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.42  | | | | | | | | | | | |   (8824)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | REDUCE: (532), (8821) imply:
% 173.46/26.42  | | | | | | | | | | | |   (8825)   ~ (all_6_2 = e0)
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | |   (8826)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.42  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.42  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | BETA: splitting (8826) gives:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8827)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8827) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | | | |            #124.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8828)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | ALPHA: (8828) implies:
% 173.46/26.42  | | | | | | | | | | | | | |   (8829)  all_52_14 = e0
% 173.46/26.42  | | | | | | | | | | | | | |   (8830)  all_52_12 = e1
% 173.46/26.42  | | | | | | | | | | | | | |   (8831)  all_52_10 = e2
% 173.46/26.42  | | | | | | | | | | | | | |   (8832)  all_52_8 = e3
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | COMBINE_EQS: (661), (8831) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8833)  all_10_1 = e2
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (53), (8833) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8834)  op(e2, all_10_2) = all_10_0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (183), (8832) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8835)  op(e3, all_52_9) = e3
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (52), (8833) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8836)  op(e2, all_10_2) = e2
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (167), (8830) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8837)  op(e1, all_52_13) = e1
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REDUCE: (159), (8829) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8838)  op(e0, all_52_15) = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (42), (61), (62), (155),
% 173.46/26.42  | | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (170), (172),
% 173.46/26.42  | | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (182), (268),
% 173.46/26.42  | | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 173.46/26.42  | | | | | | | | | | | | | |            (277), (279), (280), (282), (283), (303), (304),
% 173.46/26.42  | | | | | | | | | | | | | |            (307), (311), (313), (315), (319), (321), (323),
% 173.46/26.42  | | | | | | | | | | | | | |            (326), (328), (329), (330), (341), (344), (349),
% 173.46/26.42  | | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.46/26.42  | | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (415), (419),
% 173.46/26.42  | | | | | | | | | | | | | |            (429), (501), (529), (531), (532), (533), (534),
% 173.46/26.42  | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.42  | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.42  | | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.42  | | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.46/26.42  | | | | | | | | | | | | | |            (571), (573), (575), (579), (580), (581), (582),
% 173.46/26.42  | | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.46/26.42  | | | | | | | | | | | | | |            (595), (596), (597), (600), (704), (7962), (8774),
% 173.46/26.42  | | | | | | | | | | | | | |            (8775), (8780), (8784), (8819), (8823), (8824),
% 173.46/26.42  | | | | | | | | | | | | | |            (8825), (8834), (8835), (8836), (8837), (8838),
% 173.46/26.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | | | |            #13.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | |   (8839)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.42  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.42  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | BETA: splitting (8839) gives:
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8840)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | ALPHA: (8840) implies:
% 173.46/26.42  | | | | | | | | | | | | | |   (8841)  all_52_22 = e0
% 173.46/26.42  | | | | | | | | | | | | | |   (8842)  all_52_20 = e1
% 173.46/26.42  | | | | | | | | | | | | | |   (8843)  all_52_18 = e2
% 173.46/26.42  | | | | | | | | | | | | | |   (8844)  all_52_16 = e3
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | COMBINE_EQS: (719), (8842) imply:
% 173.46/26.42  | | | | | | | | | | | | | |   (8845)  all_14_1 = e1
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | SIMP: (8845) implies:
% 173.46/26.42  | | | | | | | | | | | | | |   (8846)  all_14_1 = e1
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (42), (52), (62), (156),
% 173.46/26.42  | | | | | | | | | | | | | |            (158), (161), (163), (164), (170), (172), (174),
% 173.46/26.42  | | | | | | | | | | | | | |            (177), (178), (179), (182), (268), (271), (273),
% 173.46/26.42  | | | | | | | | | | | | | |            (274), (276), (277), (278), (283), (303), (304),
% 173.46/26.42  | | | | | | | | | | | | | |            (307), (310), (311), (315), (317), (319), (323),
% 173.46/26.42  | | | | | | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.46/26.42  | | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (415),
% 173.46/26.42  | | | | | | | | | | | | | |            (419), (425), (429), (501), (529), (530), (531),
% 173.46/26.42  | | | | | | | | | | | | | |            (532), (534), (535), (536), (537), (538), (539),
% 173.46/26.42  | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.42  | | | | | | | | | | | | | |            (553), (554), (555), (556), (558), (559), (561),
% 173.46/26.42  | | | | | | | | | | | | | |            (562), (564), (566), (571), (577), (584), (586),
% 173.46/26.42  | | | | | | | | | | | | | |            (587), (593), (595), (596), (598), (704), (7962),
% 173.46/26.42  | | | | | | | | | | | | | |            (8774), (8777), (8780), (8782), (8786), (8819),
% 173.46/26.42  | | | | | | | | | | | | | |            (8824), (8841), (8843), (8844), (8846),
% 173.46/26.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | | | |            #12.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | |   (8847)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.42  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (8774), (8847),
% 173.46/26.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | | | | |            #200.
% 173.46/26.42  | | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | End of split
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | |   (8848)  all_32_1 = e2
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | COMBINE_EQS: (713), (8848) imply:
% 173.46/26.42  | | | | | | | | | |   (8849)  all_14_1 = e2
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | SIMP: (8849) implies:
% 173.46/26.42  | | | | | | | | | |   (8850)  all_14_1 = e2
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | COMBINE_EQS: (719), (8850) imply:
% 173.46/26.42  | | | | | | | | | |   (8851)  all_52_20 = e2
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | REDUCE: (8782), (8850) imply:
% 173.46/26.42  | | | | | | | | | |   (8852)   ~ (e3 = e2)
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.42  | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | Case 1:
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | |   (8853)   ~ (all_42_0 = e1)
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | REDUCE: (761), (8853) imply:
% 173.46/26.42  | | | | | | | | | | |   (8854)   ~ (all_4_0 = e1)
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.42  | | | | | | | | | | |            (52), (53), (62), (154), (155), (156), (158),
% 173.46/26.42  | | | | | | | | | | |            (159), (163), (164), (165), (167), (170), (172),
% 173.46/26.42  | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.46/26.42  | | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (272),
% 173.46/26.42  | | | | | | | | | | |            (273), (274), (275), (277), (279), (280), (282),
% 173.46/26.42  | | | | | | | | | | |            (283), (301), (303), (304), (305), (307), (311),
% 173.46/26.42  | | | | | | | | | | |            (313), (315), (319), (321), (323), (326), (328),
% 173.46/26.42  | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.46/26.42  | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.46/26.42  | | | | | | | | | | |            (391), (392), (403), (409), (415), (419), (429),
% 173.46/26.42  | | | | | | | | | | |            (501), (515), (529), (531), (532), (533), (534),
% 173.46/26.42  | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.42  | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.42  | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.42  | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.46/26.42  | | | | | | | | | | |            (571), (573), (575), (579), (580), (581), (582),
% 173.46/26.42  | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 173.46/26.42  | | | | | | | | | | |            (594), (595), (596), (597), (600), (649), (661),
% 173.46/26.42  | | | | | | | | | | |            (704), (710), (7960), (7961), (7962), (8771),
% 173.46/26.42  | | | | | | | | | | |            (8774), (8775), (8780), (8784), (8851), (8854),
% 173.46/26.42  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.42  | | | | | | | | | | |            #10.
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | Case 2:
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | |   (8855)  all_42_0 = e1
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | COMBINE_EQS: (761), (8855) imply:
% 173.46/26.42  | | | | | | | | | | |   (8856)  all_4_0 = e1
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.42  | | | | | | | | | | | REDUCE: (7961), (8856) imply:
% 173.46/26.42  | | | | | | | | | | |   (8857)  op(e2, all_4_2) = e1
% 173.46/26.42  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.43  | | | | | | | | | | |            (52), (53), (61), (62), (155), (156), (158),
% 173.46/26.43  | | | | | | | | | | |            (159), (163), (164), (165), (167), (170), (172),
% 173.46/26.43  | | | | | | | | | | |            (173), (174), (177), (178), (179), (182), (183),
% 173.46/26.43  | | | | | | | | | | |            (185), (268), (269), (270), (271), (272), (273),
% 173.46/26.43  | | | | | | | | | | |            (274), (275), (277), (279), (280), (282), (283),
% 173.46/26.43  | | | | | | | | | | |            (301), (303), (304), (307), (311), (313), (315),
% 173.46/26.43  | | | | | | | | | | |            (319), (321), (323), (326), (328), (329), (330),
% 173.46/26.43  | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 173.46/26.43  | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.43  | | | | | | | | | | |            (409), (415), (419), (429), (501), (529), (531),
% 173.46/26.43  | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.46/26.43  | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.46/26.43  | | | | | | | | | | |            (552), (553), (554), (556), (557), (558), (559),
% 173.46/26.43  | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 173.46/26.43  | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (579),
% 173.46/26.43  | | | | | | | | | | |            (580), (581), (582), (586), (587), (588), (589),
% 173.46/26.43  | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (600),
% 173.46/26.43  | | | | | | | | | | |            (649), (661), (704), (7960), (7962), (8774),
% 173.46/26.43  | | | | | | | | | | |            (8775), (8780), (8784), (8851), (8857),
% 173.46/26.43  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | |            #8.
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | |   (8858)  all_24_0 = e1
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | COMBINE_EQS: (751), (8858) imply:
% 173.46/26.43  | | | | | | | | |   (8859)  all_10_0 = e1
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | SIMP: (8859) implies:
% 173.46/26.43  | | | | | | | | |   (8860)  all_10_0 = e1
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | REDUCE: (53), (8860) imply:
% 173.46/26.43  | | | | | | | | |   (8861)  op(all_10_1, all_10_2) = e1
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | BETA: splitting (108) gives:
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | |   (8862)   ~ (all_32_1 = e2)
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | REDUCE: (713), (8862) imply:
% 173.46/26.43  | | | | | | | | | |   (8863)   ~ (all_14_1 = e2)
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | |   (8864)   ~ (all_42_0 = e1)
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | REDUCE: (761), (8864) imply:
% 173.46/26.43  | | | | | | | | | | |   (8865)   ~ (all_4_0 = e1)
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | |   (8866)  all_58_15 = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (8866),
% 173.46/26.43  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | | |            #228.
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | |   (8867)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.43  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.43  | | | | | | | | | | | |             e0)
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | ALPHA: (8867) implies:
% 173.46/26.43  | | | | | | | | | | | |   (8868)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | |   (8869)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.43  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.43  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | REF_CLOSE: (6), (9), (52), (661), (7960), (8861), (8869),
% 173.46/26.43  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | | | |            #69.
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | |   (8870)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.43  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.43  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | BETA: splitting (8870) gives:
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | |   (8871)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.43  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | ALPHA: (8871) implies:
% 173.46/26.43  | | | | | | | | | | | | | |   (8872)  all_52_22 = e0
% 173.46/26.43  | | | | | | | | | | | | | |   (8873)  all_52_20 = e1
% 173.46/26.43  | | | | | | | | | | | | | |   (8874)  all_52_18 = e2
% 173.46/26.43  | | | | | | | | | | | | | |   (8875)  all_52_16 = e3
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | COMBINE_EQS: (719), (8873) imply:
% 173.46/26.43  | | | | | | | | | | | | | |   (8876)  all_14_1 = e1
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (42), (52), (62), (156),
% 173.46/26.43  | | | | | | | | | | | | | |            (158), (163), (164), (165), (170), (172), (173),
% 173.46/26.43  | | | | | | | | | | | | | |            (174), (177), (178), (179), (182), (268), (270),
% 173.46/26.43  | | | | | | | | | | | | | |            (271), (274), (275), (276), (277), (278), (280),
% 173.46/26.43  | | | | | | | | | | | | | |            (283), (303), (304), (307), (310), (311), (315),
% 173.46/26.43  | | | | | | | | | | | | | |            (317), (319), (323), (324), (326), (328), (330),
% 173.46/26.43  | | | | | | | | | | | | | |            (331), (344), (349), (364), (365), (370), (373),
% 173.46/26.43  | | | | | | | | | | | | | |            (385), (386), (391), (403), (415), (419), (425),
% 173.46/26.43  | | | | | | | | | | | | | |            (429), (501), (529), (530), (531), (532), (533),
% 173.46/26.43  | | | | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.46/26.43  | | | | | | | | | | | | | |            (542), (544), (546), (548), (550), (552), (553),
% 173.46/26.43  | | | | | | | | | | | | | |            (554), (555), (556), (557), (558), (559), (561),
% 173.46/26.43  | | | | | | | | | | | | | |            (562), (563), (564), (566), (567), (571), (577),
% 173.46/26.43  | | | | | | | | | | | | | |            (578), (582), (583), (584), (585), (586), (587),
% 173.46/26.43  | | | | | | | | | | | | | |            (588), (594), (595), (596), (598), (704), (7958),
% 173.46/26.43  | | | | | | | | | | | | | |            (7961), (7962), (8774), (8777), (8780), (8782),
% 173.46/26.43  | | | | | | | | | | | | | |            (8863), (8865), (8868), (8872), (8874), (8875),
% 173.46/26.43  | | | | | | | | | | | | | |            (8876), (function-axioms) are inconsistent by
% 173.46/26.43  | | | | | | | | | | | | | |            sub-proof #14.
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | |   (8877)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.43  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | ALPHA: (8877) implies:
% 173.46/26.43  | | | | | | | | | | | | | |   (8878)  all_52_30 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | COMBINE_EQS: (649), (8878) imply:
% 173.46/26.43  | | | | | | | | | | | | | |   (8879)  all_6_1 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (8774), (8879), (function-axioms) are
% 173.46/26.43  | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | |   (8880)  all_42_0 = e1
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | COMBINE_EQS: (761), (8880) imply:
% 173.46/26.43  | | | | | | | | | | |   (8881)  all_4_0 = e1
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | REDUCE: (7961), (8881) imply:
% 173.46/26.43  | | | | | | | | | | |   (8882)  op(e2, all_4_2) = e1
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | |   (8883)  all_58_15 = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (8883),
% 173.46/26.43  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | | |            #228.
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | |   (8884)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.43  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.43  | | | | | | | | | | | |             e0)
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | ALPHA: (8884) implies:
% 173.46/26.43  | | | | | | | | | | | |   (8885)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | |   (8886)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.43  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.43  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | REF_CLOSE: (6), (9), (52), (661), (7960), (8861), (8886),
% 173.46/26.43  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | | | |            #69.
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | |   (8887)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.43  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.43  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | BETA: splitting (8887) gives:
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | |   (8888)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.43  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | ALPHA: (8888) implies:
% 173.46/26.43  | | | | | | | | | | | | | |   (8889)  all_52_22 = e0
% 173.46/26.43  | | | | | | | | | | | | | |   (8890)  all_52_20 = e1
% 173.46/26.43  | | | | | | | | | | | | | |   (8891)  all_52_18 = e2
% 173.46/26.43  | | | | | | | | | | | | | |   (8892)  all_52_16 = e3
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | COMBINE_EQS: (719), (8890) imply:
% 173.46/26.43  | | | | | | | | | | | | | |   (8893)  all_14_1 = e1
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (42), (52), (62), (156),
% 173.46/26.43  | | | | | | | | | | | | | |            (158), (161), (163), (164), (170), (172), (174),
% 173.46/26.43  | | | | | | | | | | | | | |            (177), (178), (179), (182), (268), (271), (273),
% 173.46/26.43  | | | | | | | | | | | | | |            (274), (276), (277), (278), (283), (303), (304),
% 173.46/26.43  | | | | | | | | | | | | | |            (307), (310), (311), (315), (317), (319), (323),
% 173.46/26.43  | | | | | | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.46/26.43  | | | | | | | | | | | | | |            (364), (370), (373), (385), (391), (403), (415),
% 173.46/26.43  | | | | | | | | | | | | | |            (419), (425), (429), (501), (529), (530), (531),
% 173.46/26.43  | | | | | | | | | | | | | |            (532), (534), (535), (536), (537), (538), (539),
% 173.46/26.43  | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.43  | | | | | | | | | | | | | |            (553), (554), (555), (556), (558), (559), (561),
% 173.46/26.43  | | | | | | | | | | | | | |            (562), (564), (566), (571), (577), (584), (586),
% 173.46/26.43  | | | | | | | | | | | | | |            (587), (593), (595), (596), (598), (704), (7962),
% 173.46/26.43  | | | | | | | | | | | | | |            (8774), (8777), (8780), (8782), (8863), (8882),
% 173.46/26.43  | | | | | | | | | | | | | |            (8885), (8889), (8891), (8892), (8893),
% 173.46/26.43  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | | | | |            #12.
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | |   (8894)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.43  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | ALPHA: (8894) implies:
% 173.46/26.43  | | | | | | | | | | | | | |   (8895)  all_52_30 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | COMBINE_EQS: (649), (8895) imply:
% 173.46/26.43  | | | | | | | | | | | | | |   (8896)  all_6_1 = e0
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (8774), (8896), (function-axioms) are
% 173.46/26.43  | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 173.46/26.43  | | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | |   (8897)  all_32_1 = e2
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | COMBINE_EQS: (713), (8897) imply:
% 173.46/26.43  | | | | | | | | | |   (8898)  all_14_1 = e2
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | SIMP: (8898) implies:
% 173.46/26.43  | | | | | | | | | |   (8899)  all_14_1 = e2
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | COMBINE_EQS: (719), (8899) imply:
% 173.46/26.43  | | | | | | | | | |   (8900)  all_52_20 = e2
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | REDUCE: (8782), (8899) imply:
% 173.46/26.43  | | | | | | | | | |   (8901)   ~ (e3 = e2)
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | REF_CLOSE: (5), (6), (9), (42), (52), (185), (649), (661),
% 173.46/26.43  | | | | | | | | | |            (7960), (8774), (8861), (8900), (function-axioms)
% 173.46/26.43  | | | | | | | | | |            are inconsistent by sub-proof #7.
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | 
% 173.46/26.43  | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | 
% 173.46/26.43  | | | | | | | |   (8902)  all_22_1 = e3
% 173.46/26.43  | | | | | | | | 
% 173.46/26.43  | | | | | | | | COMBINE_EQS: (711), (8902) imply:
% 173.46/26.43  | | | | | | | |   (8903)  all_14_1 = e3
% 173.46/26.43  | | | | | | | | 
% 173.46/26.43  | | | | | | | | SIMP: (8903) implies:
% 173.46/26.43  | | | | | | | |   (8904)  all_14_1 = e3
% 173.46/26.43  | | | | | | | | 
% 173.46/26.43  | | | | | | | | COMBINE_EQS: (719), (8904) imply:
% 173.46/26.43  | | | | | | | |   (8905)  all_52_20 = e3
% 173.46/26.43  | | | | | | | | 
% 173.46/26.43  | | | | | | | | BETA: splitting (88) gives:
% 173.46/26.43  | | | | | | | | 
% 173.46/26.43  | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | |   (8906)   ~ (all_24_0 = e1)
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | REDUCE: (751), (8906) imply:
% 173.46/26.43  | | | | | | | | |   (8907)   ~ (all_10_0 = e1)
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.43  | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | |   (8908)   ~ (all_42_0 = e1)
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | REDUCE: (761), (8908) imply:
% 173.46/26.43  | | | | | | | | | |   (8909)   ~ (all_4_0 = e1)
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | |   (8910)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.43  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.43  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | BETA: splitting (8910) gives:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | |   (8911)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.43  | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | ALPHA: (8911) implies:
% 173.46/26.43  | | | | | | | | | | | |   (8912)  all_52_0 = e3
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | COMBINE_EQS: (7960), (8912) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8913)  e3 = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | SIMP: (8913) implies:
% 173.46/26.43  | | | | | | | | | | | |   (8914)  e3 = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | COMBINE_EQS: (8905), (8914) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8915)  all_52_20 = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.43  | | | | | | | | | | | |            (52), (53), (62), (154), (155), (156), (158),
% 173.46/26.43  | | | | | | | | | | | |            (159), (163), (164), (165), (167), (170), (172),
% 173.46/26.43  | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.46/26.43  | | | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (272),
% 173.46/26.43  | | | | | | | | | | | |            (273), (274), (275), (277), (279), (280), (282),
% 173.46/26.43  | | | | | | | | | | | |            (283), (301), (303), (304), (305), (307), (311),
% 173.46/26.43  | | | | | | | | | | | |            (313), (315), (319), (321), (323), (326), (328),
% 173.46/26.43  | | | | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.46/26.43  | | | | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.46/26.43  | | | | | | | | | | | |            (391), (392), (403), (409), (415), (419), (429),
% 173.46/26.43  | | | | | | | | | | | |            (501), (515), (529), (531), (532), (533), (534),
% 173.46/26.43  | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.43  | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.43  | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.43  | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.46/26.43  | | | | | | | | | | | |            (571), (573), (575), (579), (580), (581), (582),
% 173.46/26.43  | | | | | | | | | | | |            (585), (586), (587), (588), (589), (591), (593),
% 173.46/26.43  | | | | | | | | | | | |            (594), (595), (596), (597), (600), (649), (661),
% 173.46/26.43  | | | | | | | | | | | |            (704), (710), (7960), (7961), (7962), (8771),
% 173.46/26.43  | | | | | | | | | | | |            (8774), (8775), (8780), (8907), (8909), (8915),
% 173.46/26.43  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | | |            #10.
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | |   (8916)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.43  | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | ALPHA: (8916) implies:
% 173.46/26.43  | | | | | | | | | | | |   (8917)  all_52_14 = e0
% 173.46/26.43  | | | | | | | | | | | |   (8918)  all_52_12 = e1
% 173.46/26.43  | | | | | | | | | | | |   (8919)  all_52_10 = e2
% 173.46/26.43  | | | | | | | | | | | |   (8920)  all_52_8 = e3
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | COMBINE_EQS: (661), (8919) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8921)  all_10_1 = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REDUCE: (53), (8921) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8922)  op(e2, all_10_2) = all_10_0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REDUCE: (183), (8920) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8923)  op(e3, all_52_9) = e3
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REDUCE: (52), (8921) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8924)  op(e2, all_10_2) = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REDUCE: (167), (8918) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8925)  op(e1, all_52_13) = e1
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REDUCE: (159), (8917) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8926)  op(e0, all_52_15) = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (41), (42), (62), (154),
% 173.46/26.43  | | | | | | | | | | | |            (155), (156), (158), (163), (164), (165), (170),
% 173.46/26.43  | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.46/26.43  | | | | | | | | | | | |            (182), (268), (269), (270), (271), (272), (273),
% 173.46/26.43  | | | | | | | | | | | |            (274), (275), (277), (279), (280), (282), (283),
% 173.46/26.43  | | | | | | | | | | | |            (301), (303), (304), (305), (307), (311), (313),
% 173.46/26.43  | | | | | | | | | | | |            (315), (319), (321), (323), (326), (328), (329),
% 173.46/26.43  | | | | | | | | | | | |            (330), (331), (341), (344), (349), (350), (359),
% 173.46/26.43  | | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 173.46/26.43  | | | | | | | | | | | |            (392), (403), (409), (415), (419), (429), (501),
% 173.46/26.43  | | | | | | | | | | | |            (515), (529), (531), (532), (533), (534), (535),
% 173.46/26.43  | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.43  | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.46/26.43  | | | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.46/26.43  | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.46/26.43  | | | | | | | | | | | |            (573), (575), (579), (580), (581), (582), (585),
% 173.46/26.43  | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.46/26.43  | | | | | | | | | | | |            (595), (596), (597), (600), (704), (710), (7961),
% 173.46/26.43  | | | | | | | | | | | |            (7962), (8771), (8774), (8775), (8780), (8907),
% 173.46/26.43  | | | | | | | | | | | |            (8909), (8922), (8923), (8924), (8925), (8926),
% 173.46/26.43  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | | |            #11.
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | |   (8927)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.43  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.43  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | REF_CLOSE: (5), (8), (42), (649), (8774), (8905), (8927),
% 173.46/26.43  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.43  | | | | | | | | | | |            #169.
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | End of split
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | Case 2:
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | |   (8928)  all_42_0 = e1
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | COMBINE_EQS: (761), (8928) imply:
% 173.46/26.43  | | | | | | | | | |   (8929)  all_4_0 = e1
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | REDUCE: (7961), (8929) imply:
% 173.46/26.43  | | | | | | | | | |   (8930)  op(e2, all_4_2) = e1
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.43  | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | |   (8931)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.43  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.43  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | BETA: splitting (8931) gives:
% 173.46/26.43  | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | Case 1:
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | |   (8932)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.43  | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | ALPHA: (8932) implies:
% 173.46/26.43  | | | | | | | | | | | |   (8933)  all_52_0 = e3
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | COMBINE_EQS: (7960), (8933) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8934)  e3 = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | SIMP: (8934) implies:
% 173.46/26.43  | | | | | | | | | | | |   (8935)  e3 = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.43  | | | | | | | | | | | | COMBINE_EQS: (8905), (8935) imply:
% 173.46/26.43  | | | | | | | | | | | |   (8936)  all_52_20 = e2
% 173.46/26.43  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.44  | | | | | | | | | | | |            (52), (53), (61), (62), (155), (156), (158),
% 173.46/26.44  | | | | | | | | | | | |            (159), (163), (164), (165), (167), (170), (172),
% 173.46/26.44  | | | | | | | | | | | |            (173), (174), (177), (178), (179), (182), (183),
% 173.46/26.44  | | | | | | | | | | | |            (185), (268), (269), (270), (271), (272), (273),
% 173.46/26.44  | | | | | | | | | | | |            (274), (275), (277), (279), (280), (282), (283),
% 173.46/26.44  | | | | | | | | | | | |            (301), (303), (304), (307), (311), (313), (315),
% 173.46/26.44  | | | | | | | | | | | |            (319), (321), (323), (326), (328), (329), (330),
% 173.46/26.44  | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 173.46/26.44  | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.44  | | | | | | | | | | | |            (409), (415), (419), (429), (501), (529), (531),
% 173.46/26.44  | | | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.46/26.44  | | | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.46/26.44  | | | | | | | | | | | |            (552), (553), (554), (556), (557), (558), (559),
% 173.46/26.44  | | | | | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 173.46/26.44  | | | | | | | | | | | |            (567), (568), (569), (571), (573), (575), (579),
% 173.46/26.44  | | | | | | | | | | | |            (580), (581), (582), (586), (587), (588), (589),
% 173.46/26.44  | | | | | | | | | | | |            (591), (593), (594), (595), (596), (597), (600),
% 173.46/26.44  | | | | | | | | | | | |            (649), (661), (704), (7960), (7962), (8774),
% 173.46/26.44  | | | | | | | | | | | |            (8775), (8780), (8907), (8930), (8936),
% 173.46/26.44  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | |            #8.
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | |   (8937)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.44  | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | ALPHA: (8937) implies:
% 173.46/26.44  | | | | | | | | | | | |   (8938)  all_52_14 = e0
% 173.46/26.44  | | | | | | | | | | | |   (8939)  all_52_12 = e1
% 173.46/26.44  | | | | | | | | | | | |   (8940)  all_52_10 = e2
% 173.46/26.44  | | | | | | | | | | | |   (8941)  all_52_8 = e3
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | COMBINE_EQS: (661), (8940) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8942)  all_10_1 = e2
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (53), (8942) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8943)  op(e2, all_10_2) = all_10_0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (183), (8941) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8944)  op(e3, all_52_9) = e3
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (52), (8942) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8945)  op(e2, all_10_2) = e2
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (167), (8939) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8946)  op(e1, all_52_13) = e1
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (159), (8938) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8947)  op(e0, all_52_15) = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (41), (42), (61), (62),
% 173.46/26.44  | | | | | | | | | | | |            (155), (156), (158), (163), (164), (165), (170),
% 173.46/26.44  | | | | | | | | | | | |            (172), (173), (174), (177), (178), (179), (182),
% 173.46/26.44  | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (274),
% 173.46/26.44  | | | | | | | | | | | |            (275), (277), (279), (280), (282), (283), (301),
% 173.46/26.44  | | | | | | | | | | | |            (303), (304), (307), (311), (313), (315), (319),
% 173.46/26.44  | | | | | | | | | | | |            (321), (323), (326), (328), (329), (330), (341),
% 173.46/26.44  | | | | | | | | | | | |            (344), (349), (350), (359), (364), (365), (370),
% 173.46/26.44  | | | | | | | | | | | |            (373), (385), (386), (391), (392), (403), (409),
% 173.46/26.44  | | | | | | | | | | | |            (415), (419), (429), (501), (529), (531), (532),
% 173.46/26.44  | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.44  | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.44  | | | | | | | | | | | |            (553), (554), (556), (557), (558), (559), (560),
% 173.46/26.44  | | | | | | | | | | | |            (561), (562), (563), (564), (565), (566), (567),
% 173.46/26.44  | | | | | | | | | | | |            (568), (569), (571), (573), (575), (579), (580),
% 173.46/26.44  | | | | | | | | | | | |            (581), (582), (586), (587), (588), (589), (591),
% 173.46/26.44  | | | | | | | | | | | |            (593), (594), (595), (596), (597), (600), (704),
% 173.46/26.44  | | | | | | | | | | | |            (7962), (8774), (8775), (8780), (8907), (8930),
% 173.46/26.44  | | | | | | | | | | | |            (8943), (8944), (8945), (8946), (8947),
% 173.46/26.44  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | |            #9.
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (8948)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.44  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.44  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | REF_CLOSE: (5), (8), (42), (649), (8774), (8905), (8948),
% 173.46/26.44  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | |            #169.
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | |   (8949)  all_24_0 = e1
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | COMBINE_EQS: (751), (8949) imply:
% 173.46/26.44  | | | | | | | | |   (8950)  all_10_0 = e1
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | SIMP: (8950) implies:
% 173.46/26.44  | | | | | | | | |   (8951)  all_10_0 = e1
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | REDUCE: (8775), (8951) imply:
% 173.46/26.44  | | | | | | | | |   (8952)   ~ (e3 = e1)
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | REDUCE: (53), (8951) imply:
% 173.46/26.44  | | | | | | | | |   (8953)  op(all_10_1, all_10_2) = e1
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | |   (8954)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.44  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.44  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | BETA: splitting (8954) gives:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (8955)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.44  | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | ALPHA: (8955) implies:
% 173.46/26.44  | | | | | | | | | | |   (8956)  all_52_0 = e3
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | COMBINE_EQS: (7960), (8956) imply:
% 173.46/26.44  | | | | | | | | | | |   (8957)  e3 = e2
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | SIMP: (8957) implies:
% 173.46/26.44  | | | | | | | | | | |   (8958)  e3 = e2
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | COMBINE_EQS: (8905), (8958) imply:
% 173.46/26.44  | | | | | | | | | | |   (8959)  all_52_20 = e2
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (42), (52), (185), (649), (661),
% 173.46/26.44  | | | | | | | | | | |            (7960), (8774), (8953), (8959), (function-axioms)
% 173.46/26.44  | | | | | | | | | | |            are inconsistent by sub-proof #7.
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (8960)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.44  | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | ALPHA: (8960) implies:
% 173.46/26.44  | | | | | | | | | | |   (8961)  all_52_10 = e2
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | COMBINE_EQS: (661), (8961) imply:
% 173.46/26.44  | | | | | | | | | | |   (8962)  all_10_1 = e2
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | REF_CLOSE: (6), (52), (8953), (8962), (function-axioms) are
% 173.46/26.44  | | | | | | | | | | |            inconsistent by sub-proof #446.
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | |   (8963)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.44  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.44  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | BETA: splitting (8963) gives:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (8964)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.44  | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | REF_CLOSE: (8), (8905), (8964) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | |            #373.
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (8965)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.44  | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (8774), (8965),
% 173.46/26.44  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | |            #200.
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | End of split
% 173.46/26.44  | | | | | | | 
% 173.46/26.44  | | | | | | End of split
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | Case 2:
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | |   (8966)  all_12_1 = e3
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | | COMBINE_EQS: (705), (8966) imply:
% 173.46/26.44  | | | | | |   (8967)  all_10_1 = e3
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | | SIMP: (8967) implies:
% 173.46/26.44  | | | | | |   (8968)  all_10_1 = e3
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | | COMBINE_EQS: (661), (8968) imply:
% 173.46/26.44  | | | | | |   (8969)  all_52_10 = e3
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | | REDUCE: (53), (8968) imply:
% 173.46/26.44  | | | | | |   (8970)  op(e3, all_10_2) = all_10_0
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | | REDUCE: (52), (8968) imply:
% 173.46/26.44  | | | | | |   (8971)  op(e2, all_10_2) = e3
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | | BETA: splitting (64) gives:
% 173.46/26.44  | | | | | | 
% 173.46/26.44  | | | | | | Case 1:
% 173.46/26.44  | | | | | | | 
% 173.46/26.44  | | | | | | |   (8972)   ~ (all_14_0 = e2)
% 173.46/26.44  | | | | | | | 
% 173.46/26.44  | | | | | | | BETA: splitting (69) gives:
% 173.46/26.44  | | | | | | | 
% 173.46/26.44  | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | |   (8973)   ~ (all_16_0 = e2)
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | | REDUCE: (8773), (8973) imply:
% 173.46/26.44  | | | | | | | |   (8974)  $false
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | | CLOSE: (8974) is inconsistent.
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | |   (8975)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | | BETA: splitting (74) gives:
% 173.46/26.44  | | | | | | | | 
% 173.46/26.44  | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | |   (8976)   ~ (all_18_0 = e3)
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | REDUCE: (789), (8976) imply:
% 173.46/26.44  | | | | | | | | |   (8977)   ~ (all_14_0 = e3)
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | |   (8978)   ~ (all_42_0 = e1)
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | REDUCE: (761), (8978) imply:
% 173.46/26.44  | | | | | | | | | |   (8979)   ~ (all_4_0 = e1)
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (8980)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.44  | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.44  | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | BETA: splitting (8980) gives:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | |   (8981)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.44  | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REF_CLOSE: (9), (7960), (8981) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | |            #124.
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | |   (8982)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.44  | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REF_CLOSE: (9), (8969), (8982) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | |            #289.
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (8983)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.44  | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.44  | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | BETA: splitting (8983) gives:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | |   (8984)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.44  | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | ALPHA: (8984) implies:
% 173.46/26.44  | | | | | | | | | | | |   (8985)  all_52_22 = e0
% 173.46/26.44  | | | | | | | | | | | |   (8986)  all_52_20 = e1
% 173.46/26.44  | | | | | | | | | | | |   (8987)  all_52_18 = e2
% 173.46/26.44  | | | | | | | | | | | |   (8988)  all_52_16 = e3
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | COMBINE_EQS: (719), (8986) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8989)  all_14_1 = e1
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (63), (8989) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8990)  op(e1, all_14_2) = all_14_0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (182), (8988) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8991)  op(e3, all_52_17) = e3
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (174), (8987) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8992)  op(e2, all_52_19) = e2
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (62), (8989) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8993)  op(e1, all_14_2) = e1
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (158), (8985) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8994)  op(e0, all_52_23) = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.44  | | | | | | | | | | | |              all_14_2, e1, simplifying with (8990), (8993)
% 173.46/26.44  | | | | | | | | | | | |              gives:
% 173.46/26.44  | | | | | | | | | | | |   (8995)  all_14_0 = e1
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (8977), (8995) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8996)   ~ (e3 = e1)
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REDUCE: (8972), (8995) imply:
% 173.46/26.44  | | | | | | | | | | | |   (8997)   ~ (e2 = e1)
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | |   (8998)  all_58_15 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (8998),
% 173.46/26.44  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | | |            #228.
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | |   (8999)   ~ (all_58_15 = e0)
% 173.46/26.44  | | | | | | | | | | | | |   (9000)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.44  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.44  | | | | | | | | | | | | |             e0)
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | ALPHA: (9000) implies:
% 173.46/26.44  | | | | | | | | | | | | |   (9001)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.44  | | | | | | | | | | | | |   (9002)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (532), (8999) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9003)   ~ (all_6_2 = e0)
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | BETA: splitting (268) gives:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | |   (9004)  all_56_15 = e3
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | COMBINE_EQS: (529), (9004) imply:
% 173.46/26.44  | | | | | | | | | | | | | |   (9005)  all_6_2 = e3
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | SIMP: (9005) implies:
% 173.46/26.44  | | | | | | | | | | | | | |   (9006)  all_6_2 = e3
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 173.46/26.44  | | | | | | | | | | | | | |            (501), (554), (564), (704), (8774), (8975),
% 173.46/26.44  | | | | | | | | | | | | | |            (9006), (function-axioms) are inconsistent by
% 173.46/26.44  | | | | | | | | | | | | | |            sub-proof #226.
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | |   (9007)   ~ (all_56_15 = e3)
% 173.46/26.44  | | | | | | | | | | | | | |   (9008)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | REDUCE: (529), (9007) imply:
% 173.46/26.44  | | | | | | | | | | | | | |   (9009)   ~ (all_6_2 = e3)
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (51), (155),
% 173.46/26.44  | | | | | | | | | | | | | |            (156), (163), (164), (165), (170), (172), (173),
% 173.46/26.44  | | | | | | | | | | | | | |            (177), (178), (179), (183), (270), (274), (275),
% 173.46/26.44  | | | | | | | | | | | | | |            (276), (277), (278), (280), (281), (282), (283),
% 173.46/26.44  | | | | | | | | | | | | | |            (304), (306), (307), (310), (311), (315), (316),
% 173.46/26.44  | | | | | | | | | | | | | |            (317), (319), (321), (322), (323), (324), (325),
% 173.46/26.44  | | | | | | | | | | | | | |            (326), (327), (328), (329), (330), (331), (344),
% 173.46/26.44  | | | | | | | | | | | | | |            (349), (364), (365), (370), (373), (385), (386),
% 173.46/26.44  | | | | | | | | | | | | | |            (391), (392), (403), (413), (415), (419), (425),
% 173.46/26.44  | | | | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.46/26.44  | | | | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.44  | | | | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.44  | | | | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.46/26.44  | | | | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.46/26.44  | | | | | | | | | | | | | |            (573), (577), (578), (582), (583), (584), (585),
% 173.46/26.44  | | | | | | | | | | | | | |            (586), (587), (588), (594), (595), (596), (598),
% 173.46/26.44  | | | | | | | | | | | | | |            (7958), (7961), (7962), (8970), (8971), (8979),
% 173.46/26.44  | | | | | | | | | | | | | |            (8991), (8992), (8993), (8994), (9001), (9002),
% 173.46/26.44  | | | | | | | | | | | | | |            (9003), (9008), (9009), (function-axioms) are
% 173.46/26.44  | | | | | | | | | | | | | |            inconsistent by sub-proof #48.
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | |   (9010)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.44  | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | ALPHA: (9010) implies:
% 173.46/26.44  | | | | | | | | | | | |   (9011)  all_52_30 = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | COMBINE_EQS: (649), (9011) imply:
% 173.46/26.44  | | | | | | | | | | | |   (9012)  all_6_1 = e0
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | REF_CLOSE: (5), (42), (8774), (9012), (function-axioms) are
% 173.46/26.44  | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | |   (9013)  all_42_0 = e1
% 173.46/26.44  | | | | | | | | | |   (9014)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | COMBINE_EQS: (761), (9013) imply:
% 173.46/26.44  | | | | | | | | | |   (9015)  all_4_0 = e1
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | SIMP: (9015) implies:
% 173.46/26.44  | | | | | | | | | |   (9016)  all_4_0 = e1
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | REDUCE: (7961), (9016) imply:
% 173.46/26.44  | | | | | | | | | |   (9017)  op(e2, all_4_2) = e1
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | BETA: splitting (9014) gives:
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (9018)   ~ (all_42_1 = e2)
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | REDUCE: (7959), (9018) imply:
% 173.46/26.44  | | | | | | | | | | |   (9019)  $false
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | CLOSE: (9019) is inconsistent.
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | |   (9020)   ~ (all_42_2 = e0)
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | REDUCE: (477), (9020) imply:
% 173.46/26.44  | | | | | | | | | | |   (9021)   ~ (all_4_2 = e0)
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | |   (9022)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.44  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.44  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | BETA: splitting (9022) gives:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | |   (9023)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.44  | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (9023) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | | |            #124.
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | |   (9024)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.44  | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REF_CLOSE: (9), (8969), (9024) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | | |            #289.
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | |   (9025)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.44  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.44  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | BETA: splitting (9025) gives:
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | |   (9026)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.44  | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | ALPHA: (9026) implies:
% 173.46/26.44  | | | | | | | | | | | | |   (9027)  all_52_22 = e0
% 173.46/26.44  | | | | | | | | | | | | |   (9028)  all_52_20 = e1
% 173.46/26.44  | | | | | | | | | | | | |   (9029)  all_52_18 = e2
% 173.46/26.44  | | | | | | | | | | | | |   (9030)  all_52_16 = e3
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | COMBINE_EQS: (719), (9028) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9031)  all_14_1 = e1
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (63), (9031) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9032)  op(e1, all_14_2) = all_14_0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (182), (9030) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9033)  op(e3, all_52_17) = e3
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (174), (9029) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9034)  op(e2, all_52_19) = e2
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (62), (9031) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9035)  op(e1, all_14_2) = e1
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (158), (9027) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9036)  op(e0, all_52_23) = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.44  | | | | | | | | | | | | |              all_14_2, e1, simplifying with (9032), (9035)
% 173.46/26.44  | | | | | | | | | | | | |              gives:
% 173.46/26.44  | | | | | | | | | | | | |   (9037)  all_14_0 = e1
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (8977), (9037) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9038)   ~ (e3 = e1)
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REDUCE: (8972), (9037) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9039)   ~ (e2 = e1)
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | Case 1:
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | |   (9040)  all_58_15 = e0
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (9040),
% 173.46/26.44  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.44  | | | | | | | | | | | | | |            #228.
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | |   (9041)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.44  | | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.44  | | | | | | | | | | | | | |             e0)
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | ALPHA: (9041) implies:
% 173.46/26.44  | | | | | | | | | | | | | |   (9042)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (156),
% 173.46/26.44  | | | | | | | | | | | | | |            (161), (163), (164), (170), (172), (177), (178),
% 173.46/26.44  | | | | | | | | | | | | | |            (179), (268), (271), (273), (274), (276), (283),
% 173.46/26.44  | | | | | | | | | | | | | |            (303), (304), (307), (310), (311), (315), (319),
% 173.46/26.44  | | | | | | | | | | | | | |            (323), (324), (326), (328), (330), (331), (349),
% 173.46/26.44  | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (391), (403),
% 173.46/26.44  | | | | | | | | | | | | | |            (419), (425), (429), (501), (529), (531), (532),
% 173.46/26.44  | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.44  | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.44  | | | | | | | | | | | | | |            (553), (554), (556), (558), (559), (561), (562),
% 173.46/26.44  | | | | | | | | | | | | | |            (563), (564), (566), (577), (579), (584), (586),
% 173.46/26.44  | | | | | | | | | | | | | |            (587), (593), (595), (596), (598), (704), (7962),
% 173.46/26.44  | | | | | | | | | | | | | |            (8774), (8975), (9017), (9021), (9033), (9034),
% 173.46/26.44  | | | | | | | | | | | | | |            (9035), (9036), (9042), (function-axioms) are
% 173.46/26.44  | | | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 173.46/26.44  | | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | |   (9043)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.44  | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | ALPHA: (9043) implies:
% 173.46/26.44  | | | | | | | | | | | | |   (9044)  all_52_30 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | COMBINE_EQS: (649), (9044) imply:
% 173.46/26.44  | | | | | | | | | | | | |   (9045)  all_6_1 = e0
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | | REF_CLOSE: (5), (42), (8774), (9045), (function-axioms) are
% 173.46/26.44  | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 173.46/26.44  | | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | | 
% 173.46/26.44  | | | | | | | | | End of split
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | Case 2:
% 173.46/26.44  | | | | | | | | | 
% 173.46/26.44  | | | | | | | | |   (9046)  all_18_0 = e3
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | COMBINE_EQS: (789), (9046) imply:
% 173.46/26.45  | | | | | | | | |   (9047)  all_14_0 = e3
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | REDUCE: (63), (9047) imply:
% 173.46/26.45  | | | | | | | | |   (9048)  op(all_14_1, all_14_2) = e3
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | |   (9049)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.45  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | BETA: splitting (9049) gives:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9050)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | REF_CLOSE: (9), (7960), (9050) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | |            #124.
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9051)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.45  | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | REF_CLOSE: (9), (8969), (9051) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | |            #289.
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | |   (9052)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.45  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.45  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | REF_CLOSE: (5), (8), (42), (62), (649), (719), (8774),
% 173.46/26.45  | | | | | | | | | |            (9048), (9052), (function-axioms) are inconsistent
% 173.46/26.45  | | | | | | | | | |            by sub-proof #160.
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | End of split
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | Case 2:
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | |   (9053)  all_14_0 = e2
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | | REDUCE: (63), (9053) imply:
% 173.46/26.45  | | | | | | |   (9054)  op(all_14_1, all_14_2) = e2
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | | BETA: splitting (69) gives:
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | |   (9055)   ~ (all_16_0 = e2)
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | | REDUCE: (8773), (9055) imply:
% 173.46/26.45  | | | | | | | |   (9056)  $false
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | | CLOSE: (9056) is inconsistent.
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | |   (9057)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | | BETA: splitting (88) gives:
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | |   (9058)   ~ (all_24_0 = e1)
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | REDUCE: (751), (9058) imply:
% 173.46/26.45  | | | | | | | | |   (9059)   ~ (all_10_0 = e1)
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | |   (9060)   ~ (all_42_0 = e1)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | REDUCE: (761), (9060) imply:
% 173.46/26.45  | | | | | | | | | |   (9061)   ~ (all_4_0 = e1)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9062)  all_58_15 = e0
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (9062),
% 173.46/26.45  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | |            #228.
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9063)   ~ (all_58_15 = e0)
% 173.46/26.45  | | | | | | | | | | |   (9064)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.45  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.45  | | | | | | | | | | |             e0)
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | ALPHA: (9064) implies:
% 173.46/26.45  | | | | | | | | | | |   (9065)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.45  | | | | | | | | | | |   (9066)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | REDUCE: (532), (9063) imply:
% 173.46/26.45  | | | | | | | | | | |   (9067)   ~ (all_6_2 = e0)
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | |   (9068)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.45  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | BETA: splitting (9068) gives:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | |   (9069)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (9069) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | | | |            #124.
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | |   (9070)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.45  | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | ALPHA: (9070) implies:
% 173.46/26.45  | | | | | | | | | | | | |   (9071)  all_52_14 = e0
% 173.46/26.45  | | | | | | | | | | | | |   (9072)  all_52_12 = e1
% 173.46/26.45  | | | | | | | | | | | | |   (9073)  all_52_10 = e2
% 173.46/26.45  | | | | | | | | | | | | |   (9074)  all_52_8 = e3
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | COMBINE_EQS: (661), (9073) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9075)  all_10_1 = e2
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (53), (9075) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9076)  op(e2, all_10_2) = all_10_0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (183), (9074) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9077)  op(e3, all_52_9) = e3
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (52), (9075) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9078)  op(e2, all_10_2) = e2
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (167), (9072) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9079)  op(e1, all_52_13) = e1
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (159), (9071) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9080)  op(e0, all_52_15) = e0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (42), (62), (154), (155),
% 173.46/26.45  | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (170), (172),
% 173.46/26.45  | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.46/26.45  | | | | | | | | | | | | |            (268), (269), (270), (271), (272), (273), (274),
% 173.46/26.45  | | | | | | | | | | | | |            (275), (277), (279), (280), (282), (283), (303),
% 173.46/26.45  | | | | | | | | | | | | |            (304), (305), (307), (311), (313), (315), (319),
% 173.46/26.45  | | | | | | | | | | | | |            (321), (323), (326), (328), (329), (330), (331),
% 173.46/26.45  | | | | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 173.46/26.45  | | | | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.45  | | | | | | | | | | | | |            (409), (415), (419), (429), (501), (515), (529),
% 173.46/26.45  | | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.45  | | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.45  | | | | | | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 173.46/26.45  | | | | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.46/26.45  | | | | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.45  | | | | | | | | | | | | |            (579), (580), (581), (582), (585), (586), (587),
% 173.46/26.45  | | | | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.46/26.45  | | | | | | | | | | | | |            (597), (600), (704), (710), (7961), (7962),
% 173.46/26.45  | | | | | | | | | | | | |            (8771), (8774), (8775), (9057), (9059), (9061),
% 173.46/26.45  | | | | | | | | | | | | |            (9065), (9066), (9067), (9076), (9077), (9078),
% 173.46/26.45  | | | | | | | | | | | | |            (9079), (9080), (function-axioms) are inconsistent
% 173.46/26.45  | | | | | | | | | | | | |            by sub-proof #15.
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | |   (9081)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.45  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.45  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (62), (649), (719), (8774),
% 173.46/26.45  | | | | | | | | | | | |            (9054), (9081), (function-axioms) are inconsistent
% 173.46/26.45  | | | | | | | | | | | |            by sub-proof #156.
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | |   (9082)  all_42_0 = e1
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | COMBINE_EQS: (761), (9082) imply:
% 173.46/26.45  | | | | | | | | | |   (9083)  all_4_0 = e1
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | SIMP: (9083) implies:
% 173.46/26.45  | | | | | | | | | |   (9084)  all_4_0 = e1
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | REDUCE: (7961), (9084) imply:
% 173.46/26.45  | | | | | | | | | |   (9085)  op(e2, all_4_2) = e1
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9086)  all_58_15 = e0
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (9086),
% 173.46/26.45  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | |            #228.
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9087)   ~ (all_58_15 = e0)
% 173.46/26.45  | | | | | | | | | | |   (9088)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.45  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.45  | | | | | | | | | | |             e0)
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | ALPHA: (9088) implies:
% 173.46/26.45  | | | | | | | | | | |   (9089)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.45  | | | | | | | | | | |   (9090)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | REDUCE: (532), (9087) imply:
% 173.46/26.45  | | | | | | | | | | |   (9091)   ~ (all_6_2 = e0)
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | |   (9092)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.45  | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | BETA: splitting (9092) gives:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | |   (9093)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REF_CLOSE: (9), (7960), (9093) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | | | |            #124.
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | |   (9094)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.45  | | | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | ALPHA: (9094) implies:
% 173.46/26.45  | | | | | | | | | | | | |   (9095)  all_52_14 = e0
% 173.46/26.45  | | | | | | | | | | | | |   (9096)  all_52_12 = e1
% 173.46/26.45  | | | | | | | | | | | | |   (9097)  all_52_10 = e2
% 173.46/26.45  | | | | | | | | | | | | |   (9098)  all_52_8 = e3
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | COMBINE_EQS: (661), (9097) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9099)  all_10_1 = e2
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (53), (9099) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9100)  op(e2, all_10_2) = all_10_0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (183), (9098) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9101)  op(e3, all_52_9) = e3
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (52), (9099) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9102)  op(e2, all_10_2) = e2
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (167), (9096) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9103)  op(e1, all_52_13) = e1
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REDUCE: (159), (9095) imply:
% 173.46/26.45  | | | | | | | | | | | | |   (9104)  op(e0, all_52_15) = e0
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (42), (61), (62), (155),
% 173.46/26.45  | | | | | | | | | | | | |            (156), (158), (163), (164), (165), (170), (172),
% 173.46/26.45  | | | | | | | | | | | | |            (173), (174), (177), (178), (179), (182), (268),
% 173.46/26.45  | | | | | | | | | | | | |            (269), (270), (271), (272), (273), (274), (275),
% 173.46/26.45  | | | | | | | | | | | | |            (277), (279), (280), (282), (283), (303), (304),
% 173.46/26.45  | | | | | | | | | | | | |            (307), (311), (313), (315), (319), (321), (323),
% 173.46/26.45  | | | | | | | | | | | | |            (326), (328), (329), (330), (341), (344), (349),
% 173.46/26.45  | | | | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.46/26.45  | | | | | | | | | | | | |            (386), (391), (392), (403), (409), (415), (419),
% 173.46/26.45  | | | | | | | | | | | | |            (429), (501), (529), (531), (532), (533), (534),
% 173.46/26.45  | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.45  | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.45  | | | | | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.45  | | | | | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.46/26.45  | | | | | | | | | | | | |            (571), (573), (575), (579), (580), (581), (582),
% 173.46/26.45  | | | | | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.46/26.45  | | | | | | | | | | | | |            (595), (596), (597), (600), (704), (7962), (8774),
% 173.46/26.45  | | | | | | | | | | | | |            (8775), (9057), (9059), (9085), (9089), (9090),
% 173.46/26.45  | | | | | | | | | | | | |            (9091), (9100), (9101), (9102), (9103), (9104),
% 173.46/26.45  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | | | |            #13.
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | |   (9105)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.45  | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.45  | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | REF_CLOSE: (5), (6), (42), (62), (649), (719), (8774),
% 173.46/26.45  | | | | | | | | | | | |            (9054), (9105), (function-axioms) are inconsistent
% 173.46/26.45  | | | | | | | | | | | |            by sub-proof #156.
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | |   (9106)  all_24_0 = e1
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | COMBINE_EQS: (751), (9106) imply:
% 173.46/26.45  | | | | | | | | |   (9107)  all_10_0 = e1
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | SIMP: (9107) implies:
% 173.46/26.45  | | | | | | | | |   (9108)  all_10_0 = e1
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | REDUCE: (53), (9108) imply:
% 173.46/26.45  | | | | | | | | |   (9109)  op(all_10_1, all_10_2) = e1
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | |   (9110)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.45  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | REF_CLOSE: (6), (9), (52), (661), (7960), (9109), (9110),
% 173.46/26.45  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | |            #69.
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | |   (9111)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.45  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.45  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | REF_CLOSE: (5), (6), (42), (62), (649), (719), (8774),
% 173.46/26.45  | | | | | | | | | |            (9054), (9111), (function-axioms) are inconsistent
% 173.46/26.45  | | | | | | | | | |            by sub-proof #155.
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | End of split
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | End of split
% 173.46/26.45  | | | | | | 
% 173.46/26.45  | | | | | End of split
% 173.46/26.45  | | | | | 
% 173.46/26.45  | | | | Case 2:
% 173.46/26.45  | | | | | 
% 173.46/26.45  | | | | |   (9112)  all_10_0 = e3
% 173.46/26.45  | | | | | 
% 173.46/26.45  | | | | | REDUCE: (53), (9112) imply:
% 173.46/26.45  | | | | |   (9113)  op(all_10_1, all_10_2) = e3
% 173.46/26.45  | | | | | 
% 173.46/26.45  | | | | | BETA: splitting (64) gives:
% 173.46/26.45  | | | | | 
% 173.46/26.45  | | | | | Case 1:
% 173.46/26.45  | | | | | | 
% 173.46/26.45  | | | | | |   (9114)   ~ (all_14_0 = e2)
% 173.46/26.45  | | | | | | 
% 173.46/26.45  | | | | | | BETA: splitting (69) gives:
% 173.46/26.45  | | | | | | 
% 173.46/26.45  | | | | | | Case 1:
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | |   (9115)   ~ (all_16_0 = e2)
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | | REDUCE: (8773), (9115) imply:
% 173.46/26.45  | | | | | | |   (9116)  $false
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | | CLOSE: (9116) is inconsistent.
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | Case 2:
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | |   (9117)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | | BETA: splitting (74) gives:
% 173.46/26.45  | | | | | | | 
% 173.46/26.45  | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | |   (9118)   ~ (all_18_0 = e3)
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | | REDUCE: (789), (9118) imply:
% 173.46/26.45  | | | | | | | |   (9119)   ~ (all_14_0 = e3)
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | | BETA: splitting (83) gives:
% 173.46/26.45  | | | | | | | | 
% 173.46/26.45  | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | |   (9120)   ~ (all_22_1 = e3)
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | REDUCE: (711), (9120) imply:
% 173.46/26.45  | | | | | | | | |   (9121)   ~ (all_14_1 = e3)
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | BETA: splitting (108) gives:
% 173.46/26.45  | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | |   (9122)   ~ (all_32_1 = e2)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | REDUCE: (713), (9122) imply:
% 173.46/26.45  | | | | | | | | | |   (9123)   ~ (all_14_1 = e2)
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.45  | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9124)   ~ (all_42_0 = e1)
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | REDUCE: (761), (9124) imply:
% 173.46/26.45  | | | | | | | | | | |   (9125)   ~ (all_4_0 = e1)
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | |   (9126)  all_58_15 = e0
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (9126),
% 173.46/26.45  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | | |            #228.
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | |   (9127)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.45  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.45  | | | | | | | | | | | |             e0)
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | ALPHA: (9127) implies:
% 173.46/26.45  | | | | | | | | | | | |   (9128)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | |   (9129)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.45  | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.45  | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | REF_CLOSE: (9), (52), (661), (7960), (9113), (9129),
% 173.46/26.45  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | | | |            #33.
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | |   (9130)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.45  | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.45  | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | BETA: splitting (9130) gives:
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | |   (9131)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.45  | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | ALPHA: (9131) implies:
% 173.46/26.45  | | | | | | | | | | | | | |   (9132)  all_52_22 = e0
% 173.46/26.45  | | | | | | | | | | | | | |   (9133)  all_52_20 = e1
% 173.46/26.45  | | | | | | | | | | | | | |   (9134)  all_52_18 = e2
% 173.46/26.45  | | | | | | | | | | | | | |   (9135)  all_52_16 = e3
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | COMBINE_EQS: (719), (9133) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9136)  all_14_1 = e1
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REDUCE: (63), (9136) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9137)  op(e1, all_14_2) = all_14_0
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REDUCE: (182), (9135) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9138)  op(e3, all_52_17) = e3
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REDUCE: (174), (9134) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9139)  op(e2, all_52_19) = e2
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REDUCE: (62), (9136) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9140)  op(e1, all_14_2) = e1
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REDUCE: (158), (9132) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9141)  op(e0, all_52_23) = e0
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.45  | | | | | | | | | | | | | |              all_14_2, e1, simplifying with (9137), (9140)
% 173.46/26.45  | | | | | | | | | | | | | |              gives:
% 173.46/26.45  | | | | | | | | | | | | | |   (9142)  all_14_0 = e1
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REDUCE: (9119), (9142) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9143)   ~ (e3 = e1)
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REDUCE: (9114), (9142) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9144)   ~ (e2 = e1)
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | Case 1:
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | |   (9145)  all_56_15 = e3
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | | COMBINE_EQS: (529), (9145) imply:
% 173.46/26.45  | | | | | | | | | | | | | | |   (9146)  all_6_2 = e3
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | | SIMP: (9146) implies:
% 173.46/26.45  | | | | | | | | | | | | | | |   (9147)  all_6_2 = e3
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | | REF_CLOSE: (42), (156), (172), (271), (303), (349), (429),
% 173.46/26.45  | | | | | | | | | | | | | | |            (501), (554), (564), (704), (8774), (9117),
% 173.46/26.45  | | | | | | | | | | | | | | |            (9147), (function-axioms) are inconsistent by
% 173.46/26.45  | | | | | | | | | | | | | | |            sub-proof #226.
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | |   (9148)   ~ (all_56_15 = e3)
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | | REDUCE: (529), (9148) imply:
% 173.46/26.45  | | | | | | | | | | | | | | |   (9149)   ~ (all_6_2 = e3)
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (52), (156),
% 173.46/26.45  | | | | | | | | | | | | | | |            (163), (164), (165), (170), (172), (173), (177),
% 173.46/26.45  | | | | | | | | | | | | | | |            (178), (179), (270), (274), (275), (276), (277),
% 173.46/26.45  | | | | | | | | | | | | | | |            (278), (280), (281), (283), (304), (307), (310),
% 173.46/26.45  | | | | | | | | | | | | | | |            (311), (315), (319), (323), (324), (326), (328),
% 173.46/26.45  | | | | | | | | | | | | | | |            (330), (331), (344), (349), (364), (365), (370),
% 173.46/26.45  | | | | | | | | | | | | | | |            (373), (385), (386), (391), (403), (413), (415),
% 173.46/26.45  | | | | | | | | | | | | | | |            (419), (425), (530), (531), (532), (533), (534),
% 173.46/26.45  | | | | | | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.45  | | | | | | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.45  | | | | | | | | | | | | | | |            (555), (557), (558), (559), (560), (561), (562),
% 173.46/26.45  | | | | | | | | | | | | | | |            (563), (564), (566), (567), (569), (571), (575),
% 173.46/26.45  | | | | | | | | | | | | | | |            (577), (578), (579), (582), (583), (584), (585),
% 173.46/26.45  | | | | | | | | | | | | | | |            (586), (588), (593), (594), (595), (596), (598),
% 173.46/26.45  | | | | | | | | | | | | | | |            (7958), (7961), (7962), (9113), (9125), (9128),
% 173.46/26.45  | | | | | | | | | | | | | | |            (9138), (9139), (9140), (9141), (9149),
% 173.46/26.45  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.45  | | | | | | | | | | | | | | |            #32.
% 173.46/26.45  | | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | |   (9150)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.45  | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | ALPHA: (9150) implies:
% 173.46/26.45  | | | | | | | | | | | | | |   (9151)  all_52_30 = e0
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | COMBINE_EQS: (649), (9151) imply:
% 173.46/26.45  | | | | | | | | | | | | | |   (9152)  all_6_1 = e0
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (8774), (9152), (function-axioms) are
% 173.46/26.45  | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 173.46/26.45  | | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | | End of split
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | Case 2:
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.45  | | | | | | | | | | |   (9153)  all_42_0 = e1
% 173.46/26.45  | | | | | | | | | | |   (9154)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.45  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | COMBINE_EQS: (761), (9153) imply:
% 173.46/26.46  | | | | | | | | | | |   (9155)  all_4_0 = e1
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | SIMP: (9155) implies:
% 173.46/26.46  | | | | | | | | | | |   (9156)  all_4_0 = e1
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | REDUCE: (7961), (9156) imply:
% 173.46/26.46  | | | | | | | | | | |   (9157)  op(e2, all_4_2) = e1
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | BETA: splitting (9154) gives:
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | |   (9158)   ~ (all_42_1 = e2)
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | REDUCE: (7959), (9158) imply:
% 173.46/26.46  | | | | | | | | | | | |   (9159)  $false
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | CLOSE: (9159) is inconsistent.
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | |   (9160)   ~ (all_42_2 = e0)
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | REDUCE: (477), (9160) imply:
% 173.46/26.46  | | | | | | | | | | | |   (9161)   ~ (all_4_2 = e0)
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | |   (9162)  all_58_15 = e0
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | REF_CLOSE: (5), (41), (42), (532), (8774), (9162),
% 173.46/26.46  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | | | | | |            #228.
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | |   (9163)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.46  | | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.46  | | | | | | | | | | | | |             e0)
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | ALPHA: (9163) implies:
% 173.46/26.46  | | | | | | | | | | | | |   (9164)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | |   (9165)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.46  | | | | | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.46  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.46  | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | REF_CLOSE: (9), (52), (661), (7960), (9113), (9165),
% 173.46/26.46  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | | | | | | |            #33.
% 173.46/26.46  | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | |   (9166)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.46  | | | | | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.46  | | | | | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.46  | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | BETA: splitting (9166) gives:
% 173.46/26.46  | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | |   (9167)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.46  | | | | | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | ALPHA: (9167) implies:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9168)  all_52_22 = e0
% 173.46/26.46  | | | | | | | | | | | | | | |   (9169)  all_52_20 = e1
% 173.46/26.46  | | | | | | | | | | | | | | |   (9170)  all_52_18 = e2
% 173.46/26.46  | | | | | | | | | | | | | | |   (9171)  all_52_16 = e3
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | COMBINE_EQS: (719), (9169) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9172)  all_14_1 = e1
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REDUCE: (9121), (9172) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9173)   ~ (e3 = e1)
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REDUCE: (9123), (9172) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9174)   ~ (e2 = e1)
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REDUCE: (182), (9171) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9175)  op(e3, all_52_17) = e3
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REDUCE: (174), (9170) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9176)  op(e2, all_52_19) = e2
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REDUCE: (62), (9172) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9177)  op(e1, all_14_2) = e1
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REDUCE: (158), (9168) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9178)  op(e0, all_52_23) = e0
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (156),
% 173.46/26.46  | | | | | | | | | | | | | | |            (161), (163), (164), (170), (172), (177), (178),
% 173.46/26.46  | | | | | | | | | | | | | | |            (179), (268), (271), (273), (274), (276), (283),
% 173.46/26.46  | | | | | | | | | | | | | | |            (303), (304), (307), (310), (311), (315), (319),
% 173.46/26.46  | | | | | | | | | | | | | | |            (323), (324), (326), (328), (330), (331), (349),
% 173.46/26.46  | | | | | | | | | | | | | | |            (359), (364), (370), (373), (385), (391), (403),
% 173.46/26.46  | | | | | | | | | | | | | | |            (419), (425), (429), (501), (529), (531), (532),
% 173.46/26.46  | | | | | | | | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.46  | | | | | | | | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.46  | | | | | | | | | | | | | | |            (553), (554), (556), (558), (559), (561), (562),
% 173.46/26.46  | | | | | | | | | | | | | | |            (563), (564), (566), (577), (579), (584), (586),
% 173.46/26.46  | | | | | | | | | | | | | | |            (587), (593), (595), (596), (598), (704), (7962),
% 173.46/26.46  | | | | | | | | | | | | | | |            (8774), (9117), (9157), (9161), (9164), (9175),
% 173.46/26.46  | | | | | | | | | | | | | | |            (9176), (9177), (9178), (function-axioms) are
% 173.46/26.46  | | | | | | | | | | | | | | |            inconsistent by sub-proof #6.
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | |   (9179)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.46  | | | | | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | ALPHA: (9179) implies:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9180)  all_52_30 = e0
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | COMBINE_EQS: (649), (9180) imply:
% 173.46/26.46  | | | | | | | | | | | | | | |   (9181)  all_6_1 = e0
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (8774), (9181), (function-axioms) are
% 173.46/26.46  | | | | | | | | | | | | | | |            inconsistent by sub-proof #201.
% 173.46/26.46  | | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | |   (9182)  all_32_1 = e2
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | COMBINE_EQS: (713), (9182) imply:
% 173.46/26.46  | | | | | | | | | |   (9183)  all_14_1 = e2
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | COMBINE_EQS: (719), (9183) imply:
% 173.46/26.46  | | | | | | | | | |   (9184)  all_52_20 = e2
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | REDUCE: (9121), (9183) imply:
% 173.46/26.46  | | | | | | | | | |   (9185)   ~ (e3 = e2)
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | REF_CLOSE: (5), (6), (9), (42), (52), (185), (649), (661),
% 173.46/26.46  | | | | | | | | | |            (7960), (8774), (9113), (9184), (function-axioms)
% 173.46/26.46  | | | | | | | | | |            are inconsistent by sub-proof #5.
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | |   (9186)  all_22_1 = e3
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | COMBINE_EQS: (711), (9186) imply:
% 173.46/26.46  | | | | | | | | |   (9187)  all_14_1 = e3
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | SIMP: (9187) implies:
% 173.46/26.46  | | | | | | | | |   (9188)  all_14_1 = e3
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | COMBINE_EQS: (719), (9188) imply:
% 173.46/26.46  | | | | | | | | |   (9189)  all_52_20 = e3
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | |   (9190)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.46  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.46  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | BETA: splitting (9190) gives:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | |   (9191)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.46  | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | ALPHA: (9191) implies:
% 173.46/26.46  | | | | | | | | | | |   (9192)  all_52_0 = e3
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | COMBINE_EQS: (7960), (9192) imply:
% 173.46/26.46  | | | | | | | | | | |   (9193)  e3 = e2
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | SIMP: (9193) implies:
% 173.46/26.46  | | | | | | | | | | |   (9194)  e3 = e2
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | COMBINE_EQS: (9189), (9194) imply:
% 173.46/26.46  | | | | | | | | | | |   (9195)  all_52_20 = e2
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (42), (52), (185), (649), (661),
% 173.46/26.46  | | | | | | | | | | |            (7960), (8774), (9113), (9195), (function-axioms)
% 173.46/26.46  | | | | | | | | | | |            are inconsistent by sub-proof #5.
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | |   (9196)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.46  | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | ALPHA: (9196) implies:
% 173.46/26.46  | | | | | | | | | | |   (9197)  all_52_10 = e2
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | COMBINE_EQS: (661), (9197) imply:
% 173.46/26.46  | | | | | | | | | | |   (9198)  all_10_1 = e2
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | REF_CLOSE: (9), (52), (9113), (9198), (function-axioms) are
% 173.46/26.46  | | | | | | | | | | |            inconsistent by sub-proof #263.
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | |   (9199)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.46  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.46  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | BETA: splitting (9199) gives:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | |   (9200)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.46  | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | REF_CLOSE: (8), (9189), (9200) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | | | |            #373.
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | |   (9201)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.46  | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | | REF_CLOSE: (5), (42), (649), (8774), (9201),
% 173.46/26.46  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | | | |            #200.
% 173.46/26.46  | | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | |   (9202)  all_18_0 = e3
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | COMBINE_EQS: (789), (9202) imply:
% 173.46/26.46  | | | | | | | |   (9203)  all_14_0 = e3
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | SIMP: (9203) implies:
% 173.46/26.46  | | | | | | | |   (9204)  all_14_0 = e3
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | REDUCE: (63), (9204) imply:
% 173.46/26.46  | | | | | | | |   (9205)  op(all_14_1, all_14_2) = e3
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | |   (9206)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.46  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.46/26.46  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | REF_CLOSE: (9), (52), (661), (7960), (9113), (9206),
% 173.46/26.46  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | |            #33.
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | |   (9207)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.46  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 173.46/26.46  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | REF_CLOSE: (5), (8), (42), (62), (649), (719), (8774), (9205),
% 173.46/26.46  | | | | | | | | |            (9207), (function-axioms) are inconsistent by
% 173.46/26.46  | | | | | | | | |            sub-proof #160.
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | End of split
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | End of split
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | Case 2:
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | |   (9208)  all_14_0 = e2
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | | REDUCE: (63), (9208) imply:
% 173.46/26.46  | | | | | |   (9209)  op(all_14_1, all_14_2) = e2
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | | BETA: splitting (185) gives:
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | | Case 1:
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | |   (9210)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.46  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.46/26.46  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | | REF_CLOSE: (9), (52), (661), (7960), (9113), (9210),
% 173.46/26.46  | | | | | | |            (function-axioms) are inconsistent by sub-proof #33.
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | Case 2:
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | |   (9211)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.46  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 173.46/26.46  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | | REF_CLOSE: (5), (6), (42), (62), (649), (719), (8774), (9209),
% 173.46/26.46  | | | | | | |            (9211), (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | |            #155.
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | End of split
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | End of split
% 173.46/26.46  | | | | | 
% 173.46/26.46  | | | | End of split
% 173.46/26.46  | | | | 
% 173.46/26.46  | | | End of split
% 173.46/26.46  | | | 
% 173.46/26.46  | | Case 2:
% 173.46/26.46  | | | 
% 173.46/26.46  | | |   (9212)  all_6_0 = e1
% 173.46/26.46  | | | 
% 173.46/26.46  | | | REDUCE: (43), (9212) imply:
% 173.46/26.46  | | |   (9213)  op(all_6_1, all_6_2) = e1
% 173.46/26.46  | | | 
% 173.46/26.46  | | | BETA: splitting (54) gives:
% 173.46/26.46  | | | 
% 173.46/26.46  | | | Case 1:
% 173.46/26.46  | | | | 
% 173.46/26.46  | | | |   (9214)   ~ (all_10_0 = e3)
% 173.46/26.46  | | | | 
% 173.46/26.46  | | | | BETA: splitting (59) gives:
% 173.46/26.46  | | | | 
% 173.46/26.46  | | | | Case 1:
% 173.46/26.46  | | | | | 
% 173.46/26.46  | | | | |   (9215)   ~ (all_12_1 = e3)
% 173.46/26.46  | | | | | 
% 173.46/26.46  | | | | | REDUCE: (705), (9215) imply:
% 173.46/26.46  | | | | |   (9216)   ~ (all_10_1 = e3)
% 173.46/26.46  | | | | | 
% 173.46/26.46  | | | | | BETA: splitting (64) gives:
% 173.46/26.46  | | | | | 
% 173.46/26.46  | | | | | Case 1:
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | |   (9217)   ~ (all_14_0 = e2)
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | | BETA: splitting (74) gives:
% 173.46/26.46  | | | | | | 
% 173.46/26.46  | | | | | | Case 1:
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | |   (9218)   ~ (all_18_0 = e3)
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | | REDUCE: (789), (9218) imply:
% 173.46/26.46  | | | | | | |   (9219)   ~ (all_14_0 = e3)
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | | BETA: splitting (88) gives:
% 173.46/26.46  | | | | | | | 
% 173.46/26.46  | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | |   (9220)   ~ (all_24_0 = e1)
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | REDUCE: (751), (9220) imply:
% 173.46/26.46  | | | | | | | |   (9221)   ~ (all_10_0 = e1)
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | |   (9222)   ~ (all_42_0 = e1)
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | REDUCE: (761), (9222) imply:
% 173.46/26.46  | | | | | | | | |   (9223)   ~ (all_4_0 = e1)
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | |   (9224)  all_58_15 = e0
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9224),
% 173.46/26.46  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | | |            #143.
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | |   (9225)   ~ (all_58_15 = e0)
% 173.46/26.46  | | | | | | | | | |   (9226)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.46  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.46  | | | | | | | | | |             e0)
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.46  | | | | | | | | | |            (42), (52), (53), (62), (63), (154), (155), (156),
% 173.46/26.46  | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.46/26.46  | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.46/26.46  | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.46/26.46  | | | | | | | | | |            (271), (272), (273), (274), (275), (276), (277),
% 173.46/26.46  | | | | | | | | | |            (278), (279), (280), (281), (282), (283), (303),
% 173.46/26.46  | | | | | | | | | |            (304), (305), (306), (307), (310), (311), (313),
% 173.46/26.46  | | | | | | | | | |            (315), (317), (319), (321), (322), (323), (324),
% 173.46/26.46  | | | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 173.46/26.46  | | | | | | | | | |            (341), (344), (349), (350), (359), (364), (365),
% 173.46/26.46  | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.46  | | | | | | | | | |            (409), (413), (415), (419), (425), (429), (529),
% 173.46/26.46  | | | | | | | | | |            (530), (531), (532), (533), (534), (535), (536),
% 173.46/26.46  | | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.46/26.46  | | | | | | | | | |            (548), (550), (552), (553), (554), (555), (556),
% 173.46/26.46  | | | | | | | | | |            (557), (558), (559), (560), (561), (562), (563),
% 173.46/26.46  | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.46/26.46  | | | | | | | | | |            (573), (575), (577), (578), (579), (580), (581),
% 173.46/26.46  | | | | | | | | | |            (582), (583), (584), (585), (586), (587), (588),
% 173.46/26.46  | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.46/26.46  | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.46/26.46  | | | | | | | | | |            (7960), (7961), (7962), (9214), (9216), (9217),
% 173.46/26.46  | | | | | | | | | |            (9219), (9221), (9223), (9225), (9226),
% 173.46/26.46  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | | |            #71.
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | |   (9227)  all_42_0 = e1
% 173.46/26.46  | | | | | | | | |   (9228)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | COMBINE_EQS: (761), (9227) imply:
% 173.46/26.46  | | | | | | | | |   (9229)  all_4_0 = e1
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | SIMP: (9229) implies:
% 173.46/26.46  | | | | | | | | |   (9230)  all_4_0 = e1
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | REDUCE: (7961), (9230) imply:
% 173.46/26.46  | | | | | | | | |   (9231)  op(e2, all_4_2) = e1
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.46  | | | | | | | | |            (52), (53), (61), (62), (154), (156), (158), (159),
% 173.46/26.46  | | | | | | | | |            (161), (163), (164), (165), (167), (170), (172),
% 173.46/26.46  | | | | | | | | |            (173), (174), (177), (178), (179), (182), (183),
% 173.46/26.46  | | | | | | | | |            (185), (268), (269), (272), (273), (274), (275),
% 173.46/26.46  | | | | | | | | |            (276), (277), (279), (280), (282), (283), (301),
% 173.46/26.46  | | | | | | | | |            (304), (307), (310), (311), (313), (315), (317),
% 173.46/26.46  | | | | | | | | |            (319), (321), (323), (324), (326), (327), (328),
% 173.46/26.46  | | | | | | | | |            (329), (330), (331), (341), (349), (350), (359),
% 173.46/26.46  | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 173.46/26.46  | | | | | | | | |            (392), (403), (409), (415), (419), (425), (477),
% 173.46/26.46  | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.46/26.46  | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.46/26.46  | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 173.46/26.46  | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.46  | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.46/26.46  | | | | | | | | |            (575), (577), (579), (580), (581), (582), (584),
% 173.46/26.46  | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.46/26.46  | | | | | | | | |            (595), (596), (597), (598), (599), (600), (649),
% 173.46/26.46  | | | | | | | | |            (661), (719), (7959), (7960), (7962), (9213),
% 173.46/26.46  | | | | | | | | |            (9214), (9221), (9228), (9231), (function-axioms)
% 173.46/26.46  | | | | | | | | |            are inconsistent by sub-proof #4.
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | End of split
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | |   (9232)  all_24_0 = e1
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | COMBINE_EQS: (751), (9232) imply:
% 173.46/26.46  | | | | | | | |   (9233)  all_10_0 = e1
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | REDUCE: (9214), (9233) imply:
% 173.46/26.46  | | | | | | | |   (9234)   ~ (e3 = e1)
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | REDUCE: (53), (9233) imply:
% 173.46/26.46  | | | | | | | |   (9235)  op(all_10_1, all_10_2) = e1
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.46  | | | | | | | | 
% 173.46/26.46  | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | |   (9236)   ~ (all_42_0 = e1)
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | REDUCE: (761), (9236) imply:
% 173.46/26.46  | | | | | | | | |   (9237)   ~ (all_4_0 = e1)
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.46  | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | Case 1:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | |   (9238)  all_58_15 = e0
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9238),
% 173.46/26.46  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.46  | | | | | | | | | |            #143.
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | Case 2:
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.46  | | | | | | | | | |   (9239)   ~ (all_58_15 = e0)
% 173.46/26.46  | | | | | | | | | |   (9240)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.46  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.46  | | | | | | | | | |             e0)
% 173.46/26.46  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.47  | | | | | | | | | |            (42), (52), (62), (63), (154), (155), (156),
% 173.46/26.47  | | | | | | | | | |            (158), (161), (163), (164), (165), (170), (172),
% 173.46/26.47  | | | | | | | | | |            (173), (174), (177), (178), (179), (181), (182),
% 173.46/26.47  | | | | | | | | | |            (183), (185), (268), (269), (270), (271), (274),
% 173.46/26.47  | | | | | | | | | |            (275), (276), (277), (278), (280), (281), (282),
% 173.46/26.47  | | | | | | | | | |            (283), (303), (304), (305), (306), (307), (310),
% 173.46/26.47  | | | | | | | | | |            (311), (313), (315), (317), (319), (321), (322),
% 173.46/26.47  | | | | | | | | | |            (323), (324), (325), (326), (327), (328), (329),
% 173.46/26.47  | | | | | | | | | |            (330), (331), (341), (344), (349), (364), (365),
% 173.46/26.47  | | | | | | | | | |            (370), (373), (385), (386), (391), (392), (403),
% 173.46/26.47  | | | | | | | | | |            (413), (415), (419), (425), (429), (529), (530),
% 173.46/26.47  | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.47  | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.47  | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.47  | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.47  | | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.46/26.47  | | | | | | | | | |            (575), (577), (578), (579), (580), (581), (582),
% 173.46/26.47  | | | | | | | | | |            (583), (584), (585), (586), (587), (588), (589),
% 173.46/26.47  | | | | | | | | | |            (593), (594), (595), (596), (597), (598), (600),
% 173.46/26.47  | | | | | | | | | |            (649), (661), (719), (7958), (7960), (7961),
% 173.46/26.47  | | | | | | | | | |            (7962), (9216), (9217), (9219), (9235), (9237),
% 173.46/26.47  | | | | | | | | | |            (9239), (9240), (function-axioms) are inconsistent
% 173.46/26.47  | | | | | | | | | |            by sub-proof #63.
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | End of split
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | |   (9241)  all_42_0 = e1
% 173.46/26.47  | | | | | | | | |   (9242)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | COMBINE_EQS: (761), (9241) imply:
% 173.46/26.47  | | | | | | | | |   (9243)  all_4_0 = e1
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REDUCE: (7961), (9243) imply:
% 173.46/26.47  | | | | | | | | |   (9244)  op(e2, all_4_2) = e1
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.47  | | | | | | | | |            (52), (62), (156), (158), (161), (163), (164),
% 173.46/26.47  | | | | | | | | |            (170), (172), (174), (177), (178), (179), (182),
% 173.46/26.47  | | | | | | | | |            (185), (268), (273), (274), (276), (283), (301),
% 173.46/26.47  | | | | | | | | |            (304), (307), (310), (311), (315), (319), (323),
% 173.46/26.47  | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.46/26.47  | | | | | | | | |            (364), (370), (373), (385), (391), (403), (419),
% 173.46/26.47  | | | | | | | | |            (425), (477), (529), (531), (532), (533), (534),
% 173.46/26.47  | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.47  | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.47  | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.46/26.47  | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.46/26.47  | | | | | | | | |            (595), (596), (598), (600), (649), (661), (719),
% 173.46/26.47  | | | | | | | | |            (7959), (7960), (7962), (9213), (9235), (9242),
% 173.46/26.47  | | | | | | | | |            (9244), (function-axioms) are inconsistent by
% 173.46/26.47  | | | | | | | | |            sub-proof #2.
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | End of split
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | End of split
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | Case 2:
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | |   (9245)  all_18_0 = e3
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | | COMBINE_EQS: (789), (9245) imply:
% 173.46/26.47  | | | | | | |   (9246)  all_14_0 = e3
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | | REDUCE: (63), (9246) imply:
% 173.46/26.47  | | | | | | |   (9247)  op(all_14_1, all_14_2) = e3
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | | BETA: splitting (88) gives:
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | | Case 1:
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | |   (9248)   ~ (all_24_0 = e1)
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | REDUCE: (751), (9248) imply:
% 173.46/26.47  | | | | | | | |   (9249)   ~ (all_10_0 = e1)
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | Case 1:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | |   (9250)   ~ (all_42_0 = e1)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REDUCE: (761), (9250) imply:
% 173.46/26.47  | | | | | | | | |   (9251)   ~ (all_4_0 = e1)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | Case 1:
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | |   (9252)  all_58_15 = e0
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9252),
% 173.46/26.47  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.47  | | | | | | | | | |            #143.
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | |   (9253)   ~ (all_58_15 = e0)
% 173.46/26.47  | | | | | | | | | |   (9254)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.47  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.47  | | | | | | | | | |             e0)
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | | ALPHA: (9254) implies:
% 173.46/26.47  | | | | | | | | | |   (9255)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.47  | | | | | | | | | |   (9256)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | | REDUCE: (532), (9253) imply:
% 173.46/26.47  | | | | | | | | | |   (9257)   ~ (all_6_2 = e0)
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.47  | | | | | | | | | |            (42), (52), (53), (62), (154), (155), (156),
% 173.46/26.47  | | | | | | | | | |            (158), (159), (161), (163), (164), (165), (167),
% 173.46/26.47  | | | | | | | | | |            (170), (172), (173), (174), (177), (178), (179),
% 173.46/26.47  | | | | | | | | | |            (181), (182), (183), (185), (268), (269), (270),
% 173.46/26.47  | | | | | | | | | |            (271), (272), (273), (274), (275), (277), (279),
% 173.46/26.47  | | | | | | | | | |            (280), (281), (282), (283), (303), (304), (305),
% 173.46/26.47  | | | | | | | | | |            (306), (307), (311), (313), (315), (317), (319),
% 173.46/26.47  | | | | | | | | | |            (321), (322), (323), (324), (325), (326), (327),
% 173.46/26.47  | | | | | | | | | |            (328), (329), (330), (331), (341), (344), (349),
% 173.46/26.47  | | | | | | | | | |            (350), (359), (364), (365), (370), (373), (385),
% 173.46/26.47  | | | | | | | | | |            (386), (391), (392), (403), (409), (413), (415),
% 173.46/26.47  | | | | | | | | | |            (419), (429), (529), (531), (532), (533), (534),
% 173.46/26.47  | | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.47  | | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.47  | | | | | | | | | |            (555), (556), (557), (558), (559), (560), (561),
% 173.46/26.47  | | | | | | | | | |            (562), (563), (564), (565), (566), (567), (568),
% 173.46/26.47  | | | | | | | | | |            (569), (571), (573), (575), (577), (579), (580),
% 173.46/26.47  | | | | | | | | | |            (581), (582), (583), (585), (586), (587), (588),
% 173.46/26.47  | | | | | | | | | |            (589), (591), (593), (594), (595), (596), (597),
% 173.46/26.47  | | | | | | | | | |            (598), (599), (600), (649), (661), (719), (7958),
% 173.46/26.47  | | | | | | | | | |            (7960), (7961), (7962), (9214), (9247), (9249),
% 173.46/26.47  | | | | | | | | | |            (9251), (9255), (9256), (9257), (function-axioms)
% 173.46/26.47  | | | | | | | | | |            are inconsistent by sub-proof #60.
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | End of split
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | |   (9258)  all_42_0 = e1
% 173.46/26.47  | | | | | | | | |   (9259)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | COMBINE_EQS: (761), (9258) imply:
% 173.46/26.47  | | | | | | | | |   (9260)  all_4_0 = e1
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REDUCE: (7961), (9260) imply:
% 173.46/26.47  | | | | | | | | |   (9261)  op(e2, all_4_2) = e1
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.47  | | | | | | | | |            (52), (53), (61), (62), (154), (156), (158), (159),
% 173.46/26.47  | | | | | | | | |            (161), (163), (164), (165), (167), (170), (172),
% 173.46/26.47  | | | | | | | | |            (173), (174), (177), (178), (179), (182), (183),
% 173.46/26.47  | | | | | | | | |            (185), (268), (269), (272), (273), (274), (275),
% 173.46/26.47  | | | | | | | | |            (276), (277), (279), (280), (282), (283), (301),
% 173.46/26.47  | | | | | | | | |            (304), (307), (310), (311), (313), (315), (317),
% 173.46/26.47  | | | | | | | | |            (319), (321), (323), (324), (326), (327), (328),
% 173.46/26.47  | | | | | | | | |            (329), (330), (331), (341), (349), (350), (359),
% 173.46/26.47  | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 173.46/26.47  | | | | | | | | |            (392), (403), (409), (415), (419), (425), (477),
% 173.46/26.47  | | | | | | | | |            (529), (531), (532), (533), (534), (535), (536),
% 173.46/26.47  | | | | | | | | |            (537), (538), (539), (540), (542), (544), (546),
% 173.46/26.47  | | | | | | | | |            (548), (550), (552), (553), (554), (556), (557),
% 173.46/26.47  | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.47  | | | | | | | | |            (565), (566), (567), (568), (569), (571), (573),
% 173.46/26.47  | | | | | | | | |            (575), (577), (579), (580), (581), (582), (584),
% 173.46/26.47  | | | | | | | | |            (586), (587), (588), (589), (591), (593), (594),
% 173.46/26.47  | | | | | | | | |            (595), (596), (597), (598), (599), (600), (649),
% 173.46/26.47  | | | | | | | | |            (661), (719), (7959), (7960), (7962), (9213),
% 173.46/26.47  | | | | | | | | |            (9214), (9249), (9259), (9261), (function-axioms)
% 173.46/26.47  | | | | | | | | |            are inconsistent by sub-proof #4.
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | End of split
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | |   (9262)  all_24_0 = e1
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | COMBINE_EQS: (751), (9262) imply:
% 173.46/26.47  | | | | | | | |   (9263)  all_10_0 = e1
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | SIMP: (9263) implies:
% 173.46/26.47  | | | | | | | |   (9264)  all_10_0 = e1
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | REDUCE: (9214), (9264) imply:
% 173.46/26.47  | | | | | | | |   (9265)   ~ (e3 = e1)
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | REDUCE: (53), (9264) imply:
% 173.46/26.47  | | | | | | | |   (9266)  op(all_10_1, all_10_2) = e1
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | BETA: splitting (133) gives:
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | Case 1:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | |   (9267)   ~ (all_42_0 = e1)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REDUCE: (761), (9267) imply:
% 173.46/26.47  | | | | | | | | |   (9268)   ~ (all_4_0 = e1)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | Case 1:
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | |   (9269)  all_58_15 = e0
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9269),
% 173.46/26.47  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.47  | | | | | | | | | |            #143.
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | |   (9270)   ~ (all_58_15 = e0)
% 173.46/26.47  | | | | | | | | | |   (9271)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.47  | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.47  | | | | | | | | | |             e0)
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.47  | | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.47  | | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.47  | | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.47  | | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.47  | | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.47  | | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.47  | | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.47  | | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.47  | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.47  | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.47  | | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.47  | | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.47  | | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.47  | | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.47  | | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.47  | | | | | | | | | |            (7962), (9247), (9266), (9268), (9270), (9271),
% 173.46/26.47  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.47  | | | | | | | | | |            #57.
% 173.46/26.47  | | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | End of split
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | |   (9272)  all_42_0 = e1
% 173.46/26.47  | | | | | | | | |   (9273)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | COMBINE_EQS: (761), (9272) imply:
% 173.46/26.47  | | | | | | | | |   (9274)  all_4_0 = e1
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | SIMP: (9274) implies:
% 173.46/26.47  | | | | | | | | |   (9275)  all_4_0 = e1
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REDUCE: (7961), (9275) imply:
% 173.46/26.47  | | | | | | | | |   (9276)  op(e2, all_4_2) = e1
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42),
% 173.46/26.47  | | | | | | | | |            (52), (62), (156), (158), (161), (163), (164),
% 173.46/26.47  | | | | | | | | |            (170), (172), (174), (177), (178), (179), (182),
% 173.46/26.47  | | | | | | | | |            (185), (268), (273), (274), (276), (283), (301),
% 173.46/26.47  | | | | | | | | |            (304), (307), (310), (311), (315), (319), (323),
% 173.46/26.47  | | | | | | | | |            (324), (326), (328), (330), (331), (349), (359),
% 173.46/26.47  | | | | | | | | |            (364), (370), (373), (385), (391), (403), (419),
% 173.46/26.47  | | | | | | | | |            (425), (477), (529), (531), (532), (533), (534),
% 173.46/26.47  | | | | | | | | |            (535), (536), (537), (538), (539), (540), (542),
% 173.46/26.47  | | | | | | | | |            (544), (546), (548), (550), (552), (553), (554),
% 173.46/26.47  | | | | | | | | |            (556), (558), (559), (561), (562), (563), (564),
% 173.46/26.47  | | | | | | | | |            (566), (577), (579), (584), (586), (587), (593),
% 173.46/26.47  | | | | | | | | |            (595), (596), (598), (600), (649), (661), (719),
% 173.46/26.47  | | | | | | | | |            (7959), (7960), (7962), (9213), (9266), (9273),
% 173.46/26.47  | | | | | | | | |            (9276), (function-axioms) are inconsistent by
% 173.46/26.47  | | | | | | | | |            sub-proof #2.
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | End of split
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | End of split
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | End of split
% 173.46/26.47  | | | | | | 
% 173.46/26.47  | | | | | Case 2:
% 173.46/26.47  | | | | | | 
% 173.46/26.47  | | | | | |   (9277)  all_14_0 = e2
% 173.46/26.47  | | | | | | 
% 173.46/26.47  | | | | | | REDUCE: (63), (9277) imply:
% 173.46/26.47  | | | | | |   (9278)  op(all_14_1, all_14_2) = e2
% 173.46/26.47  | | | | | | 
% 173.46/26.47  | | | | | | BETA: splitting (88) gives:
% 173.46/26.47  | | | | | | 
% 173.46/26.47  | | | | | | Case 1:
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | |   (9279)   ~ (all_24_0 = e1)
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | | REDUCE: (751), (9279) imply:
% 173.46/26.47  | | | | | | |   (9280)   ~ (all_10_0 = e1)
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | | BETA: splitting (133) gives:
% 173.46/26.47  | | | | | | | 
% 173.46/26.47  | | | | | | | Case 1:
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | |   (9281)   ~ (all_42_0 = e1)
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | REDUCE: (761), (9281) imply:
% 173.46/26.47  | | | | | | | |   (9282)   ~ (all_4_0 = e1)
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | Case 1:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | |   (9283)  all_58_15 = e0
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9283),
% 173.46/26.47  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.47  | | | | | | | | |            #143.
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | |   (9284)   ~ (all_58_15 = e0)
% 173.46/26.47  | | | | | | | | |   (9285)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.47  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.47  | | | | | | | | |            (42), (52), (53), (62), (154), (155), (156), (158),
% 173.46/26.47  | | | | | | | | |            (159), (161), (163), (164), (165), (167), (170),
% 173.46/26.47  | | | | | | | | |            (172), (173), (174), (177), (178), (179), (181),
% 173.46/26.47  | | | | | | | | |            (182), (183), (185), (268), (269), (270), (271),
% 173.46/26.47  | | | | | | | | |            (272), (273), (274), (275), (277), (279), (280),
% 173.46/26.47  | | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 173.46/26.47  | | | | | | | | |            (307), (311), (313), (315), (317), (319), (321),
% 173.46/26.47  | | | | | | | | |            (322), (323), (324), (325), (326), (327), (328),
% 173.46/26.47  | | | | | | | | |            (329), (330), (331), (341), (344), (349), (350),
% 173.46/26.47  | | | | | | | | |            (359), (364), (365), (370), (373), (385), (386),
% 173.46/26.47  | | | | | | | | |            (391), (392), (403), (409), (413), (415), (419),
% 173.46/26.47  | | | | | | | | |            (429), (529), (531), (532), (533), (534), (535),
% 173.46/26.47  | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.47  | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.47  | | | | | | | | |            (556), (557), (558), (559), (560), (561), (562),
% 173.46/26.47  | | | | | | | | |            (563), (564), (565), (566), (567), (568), (569),
% 173.46/26.47  | | | | | | | | |            (571), (573), (575), (577), (579), (580), (581),
% 173.46/26.47  | | | | | | | | |            (582), (583), (585), (586), (587), (588), (589),
% 173.46/26.47  | | | | | | | | |            (591), (593), (594), (595), (596), (597), (598),
% 173.46/26.47  | | | | | | | | |            (599), (600), (649), (661), (719), (7958), (7960),
% 173.46/26.47  | | | | | | | | |            (7961), (7962), (9214), (9278), (9280), (9282),
% 173.46/26.47  | | | | | | | | |            (9284), (9285), (function-axioms) are inconsistent
% 173.46/26.47  | | | | | | | | |            by sub-proof #55.
% 173.46/26.47  | | | | | | | | | 
% 173.46/26.47  | | | | | | | | End of split
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | Case 2:
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | |   (9286)  all_42_0 = e1
% 173.46/26.47  | | | | | | | |   (9287)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | COMBINE_EQS: (761), (9286) imply:
% 173.46/26.47  | | | | | | | |   (9288)  all_4_0 = e1
% 173.46/26.47  | | | | | | | | 
% 173.46/26.47  | | | | | | | | REDUCE: (7961), (9288) imply:
% 173.46/26.47  | | | | | | | |   (9289)  op(e2, all_4_2) = e1
% 173.46/26.47  | | | | | | | | 
% 173.46/26.48  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42), (52),
% 173.46/26.48  | | | | | | | |            (53), (61), (62), (154), (156), (158), (159), (161),
% 173.46/26.48  | | | | | | | |            (163), (164), (165), (167), (170), (172), (173),
% 173.46/26.48  | | | | | | | |            (174), (177), (178), (179), (182), (183), (185),
% 173.46/26.48  | | | | | | | |            (268), (269), (272), (273), (274), (275), (276),
% 173.46/26.48  | | | | | | | |            (277), (279), (280), (282), (283), (301), (304),
% 173.46/26.48  | | | | | | | |            (307), (310), (311), (313), (315), (317), (319),
% 173.46/26.48  | | | | | | | |            (321), (323), (324), (326), (327), (328), (329),
% 173.46/26.48  | | | | | | | |            (330), (331), (341), (349), (350), (359), (364),
% 173.46/26.48  | | | | | | | |            (365), (370), (373), (385), (386), (391), (392),
% 173.46/26.48  | | | | | | | |            (403), (409), (415), (419), (425), (477), (529),
% 173.46/26.48  | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.48  | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.48  | | | | | | | |            (550), (552), (553), (554), (556), (557), (558),
% 173.46/26.48  | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.46/26.48  | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.48  | | | | | | | |            (577), (579), (580), (581), (582), (584), (586),
% 173.46/26.48  | | | | | | | |            (587), (588), (589), (591), (593), (594), (595),
% 173.46/26.48  | | | | | | | |            (596), (597), (598), (599), (600), (649), (661),
% 173.46/26.48  | | | | | | | |            (719), (7959), (7960), (7962), (9213), (9214),
% 173.46/26.48  | | | | | | | |            (9280), (9287), (9289), (function-axioms) are
% 173.46/26.48  | | | | | | | |            inconsistent by sub-proof #4.
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | End of split
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | Case 2:
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | |   (9290)  all_24_0 = e1
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | COMBINE_EQS: (751), (9290) imply:
% 173.46/26.48  | | | | | | |   (9291)  all_10_0 = e1
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | REDUCE: (9214), (9291) imply:
% 173.46/26.48  | | | | | | |   (9292)   ~ (e3 = e1)
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | REDUCE: (53), (9291) imply:
% 173.46/26.48  | | | | | | |   (9293)  op(all_10_1, all_10_2) = e1
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | BETA: splitting (133) gives:
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | |   (9294)   ~ (all_42_0 = e1)
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | REDUCE: (761), (9294) imply:
% 173.46/26.48  | | | | | | | |   (9295)   ~ (all_4_0 = e1)
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | |   (9296)  all_58_15 = e0
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9296),
% 173.46/26.48  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | |            #143.
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | |   (9297)   ~ (all_58_15 = e0)
% 173.46/26.48  | | | | | | | | |   (9298)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.48  | | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.48  | | | | | | | | |            (42), (52), (62), (154), (155), (156), (161),
% 173.46/26.48  | | | | | | | | |            (164), (165), (170), (172), (173), (177), (178),
% 173.46/26.48  | | | | | | | | |            (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.48  | | | | | | | | |            (270), (271), (281), (282), (283), (303), (304),
% 173.46/26.48  | | | | | | | | |            (305), (306), (307), (313), (315), (321), (322),
% 173.46/26.48  | | | | | | | | |            (323), (324), (325), (326), (327), (329), (330),
% 173.46/26.48  | | | | | | | | |            (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.48  | | | | | | | | |            (385), (391), (392), (403), (413), (429), (529),
% 173.46/26.48  | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.48  | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.48  | | | | | | | | |            (550), (552), (553), (554), (555), (556), (557),
% 173.46/26.48  | | | | | | | | |            (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.48  | | | | | | | | |            (565), (567), (568), (569), (571), (577), (580),
% 173.46/26.48  | | | | | | | | |            (581), (582), (585), (586), (589), (594), (595),
% 173.46/26.48  | | | | | | | | |            (596), (597), (649), (661), (719), (7960), (7961),
% 173.46/26.48  | | | | | | | | |            (7962), (9278), (9293), (9295), (9297), (9298),
% 173.46/26.48  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | |            #52.
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | End of split
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | |   (9299)  all_42_0 = e1
% 173.46/26.48  | | | | | | | |   (9300)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | COMBINE_EQS: (761), (9299) imply:
% 173.46/26.48  | | | | | | | |   (9301)  all_4_0 = e1
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | SIMP: (9301) implies:
% 173.46/26.48  | | | | | | | |   (9302)  all_4_0 = e1
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | REDUCE: (7961), (9302) imply:
% 173.46/26.48  | | | | | | | |   (9303)  op(e2, all_4_2) = e1
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42), (52),
% 173.46/26.48  | | | | | | | |            (62), (156), (158), (161), (163), (164), (170),
% 173.46/26.48  | | | | | | | |            (172), (174), (177), (178), (179), (182), (185),
% 173.46/26.48  | | | | | | | |            (268), (273), (274), (276), (283), (301), (304),
% 173.46/26.48  | | | | | | | |            (307), (310), (311), (315), (319), (323), (324),
% 173.46/26.48  | | | | | | | |            (326), (328), (330), (331), (349), (359), (364),
% 173.46/26.48  | | | | | | | |            (370), (373), (385), (391), (403), (419), (425),
% 173.46/26.48  | | | | | | | |            (477), (529), (531), (532), (533), (534), (535),
% 173.46/26.48  | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.48  | | | | | | | |            (546), (548), (550), (552), (553), (554), (556),
% 173.46/26.48  | | | | | | | |            (558), (559), (561), (562), (563), (564), (566),
% 173.46/26.48  | | | | | | | |            (577), (579), (584), (586), (587), (593), (595),
% 173.46/26.48  | | | | | | | |            (596), (598), (600), (649), (661), (719), (7959),
% 173.46/26.48  | | | | | | | |            (7960), (7962), (9213), (9293), (9300), (9303),
% 173.46/26.48  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #2.
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | End of split
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | End of split
% 173.46/26.48  | | | | | | 
% 173.46/26.48  | | | | | End of split
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | Case 2:
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | |   (9304)  all_12_1 = e3
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | | COMBINE_EQS: (705), (9304) imply:
% 173.46/26.48  | | | | |   (9305)  all_10_1 = e3
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | | COMBINE_EQS: (661), (9305) imply:
% 173.46/26.48  | | | | |   (9306)  all_52_10 = e3
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | | REDUCE: (53), (9305) imply:
% 173.46/26.48  | | | | |   (9307)  op(e3, all_10_2) = all_10_0
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | | REDUCE: (52), (9305) imply:
% 173.46/26.48  | | | | |   (9308)  op(e2, all_10_2) = e3
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | | BETA: splitting (64) gives:
% 173.46/26.48  | | | | | 
% 173.46/26.48  | | | | | Case 1:
% 173.46/26.48  | | | | | | 
% 173.46/26.48  | | | | | |   (9309)   ~ (all_14_0 = e2)
% 173.46/26.48  | | | | | | 
% 173.46/26.48  | | | | | | BETA: splitting (74) gives:
% 173.46/26.48  | | | | | | 
% 173.46/26.48  | | | | | | Case 1:
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | |   (9310)   ~ (all_18_0 = e3)
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | REDUCE: (789), (9310) imply:
% 173.46/26.48  | | | | | | |   (9311)   ~ (all_14_0 = e3)
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | BETA: splitting (133) gives:
% 173.46/26.48  | | | | | | | 
% 173.46/26.48  | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | |   (9312)   ~ (all_42_0 = e1)
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | REDUCE: (761), (9312) imply:
% 173.46/26.48  | | | | | | | |   (9313)   ~ (all_4_0 = e1)
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | |   (9314)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.48  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.46/26.48  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | BETA: splitting (9314) gives:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | |   (9315)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.48  | | | | | | | | | |           all_52_6 = e0
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REF_CLOSE: (9), (7960), (9315) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | | |            #124.
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | |   (9316)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.48  | | | | | | | | | |           all_52_14 = e0
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REF_CLOSE: (9), (9306), (9316) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | | |            #289.
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | End of split
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | |   (9317)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.48  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 173.46/26.48  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | BETA: splitting (9317) gives:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | |   (9318)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.48  | | | | | | | | | |           all_52_22 = e0
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | ALPHA: (9318) implies:
% 173.46/26.48  | | | | | | | | | |   (9319)  all_52_22 = e0
% 173.46/26.48  | | | | | | | | | |   (9320)  all_52_20 = e1
% 173.46/26.48  | | | | | | | | | |   (9321)  all_52_18 = e2
% 173.46/26.48  | | | | | | | | | |   (9322)  all_52_16 = e3
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | COMBINE_EQS: (719), (9320) imply:
% 173.46/26.48  | | | | | | | | | |   (9323)  all_14_1 = e1
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | SIMP: (9323) implies:
% 173.46/26.48  | | | | | | | | | |   (9324)  all_14_1 = e1
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REDUCE: (63), (9324) imply:
% 173.46/26.48  | | | | | | | | | |   (9325)  op(e1, all_14_2) = all_14_0
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REDUCE: (182), (9322) imply:
% 173.46/26.48  | | | | | | | | | |   (9326)  op(e3, all_52_17) = e3
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REDUCE: (174), (9321) imply:
% 173.46/26.48  | | | | | | | | | |   (9327)  op(e2, all_52_19) = e2
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REDUCE: (62), (9324) imply:
% 173.46/26.48  | | | | | | | | | |   (9328)  op(e1, all_14_2) = e1
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REDUCE: (158), (9319) imply:
% 173.46/26.48  | | | | | | | | | |   (9329)  op(e0, all_52_23) = e0
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.48  | | | | | | | | | |              all_14_2, e1, simplifying with (9325), (9328)
% 173.46/26.48  | | | | | | | | | |              gives:
% 173.46/26.48  | | | | | | | | | |   (9330)  all_14_0 = e1
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REDUCE: (9311), (9330) imply:
% 173.46/26.48  | | | | | | | | | |   (9331)   ~ (e3 = e1)
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REDUCE: (9309), (9330) imply:
% 173.46/26.48  | | | | | | | | | |   (9332)   ~ (e2 = e1)
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | |   (9333)  all_58_15 = e0
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9333),
% 173.46/26.48  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | | | |            #143.
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | |   (9334)   ~ (all_58_15 = e0)
% 173.46/26.48  | | | | | | | | | | |   (9335)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.48  | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.48  | | | | | | | | | | |             e0)
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.48  | | | | | | | | | | |            (42), (51), (155), (156), (163), (164), (165),
% 173.46/26.48  | | | | | | | | | | |            (170), (172), (173), (177), (178), (179), (183),
% 173.46/26.48  | | | | | | | | | | |            (268), (270), (271), (274), (275), (276), (277),
% 173.46/26.48  | | | | | | | | | | |            (278), (280), (281), (282), (283), (304), (306),
% 173.46/26.48  | | | | | | | | | | |            (307), (310), (311), (314), (315), (316), (317),
% 173.46/26.48  | | | | | | | | | | |            (319), (321), (322), (323), (324), (325), (326),
% 173.46/26.48  | | | | | | | | | | |            (327), (328), (329), (330), (331), (344), (349),
% 173.46/26.48  | | | | | | | | | | |            (364), (365), (370), (373), (385), (386), (391),
% 173.46/26.48  | | | | | | | | | | |            (392), (403), (413), (415), (419), (425), (429),
% 173.46/26.48  | | | | | | | | | | |            (529), (530), (531), (532), (533), (534), (535),
% 173.46/26.48  | | | | | | | | | | |            (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.48  | | | | | | | | | | |            (546), (548), (550), (552), (553), (554), (555),
% 173.46/26.48  | | | | | | | | | | |            (556), (557), (558), (559), (561), (562), (563),
% 173.46/26.48  | | | | | | | | | | |            (564), (565), (566), (567), (568), (569), (571),
% 173.46/26.48  | | | | | | | | | | |            (573), (577), (578), (582), (583), (584), (585),
% 173.46/26.48  | | | | | | | | | | |            (586), (587), (588), (594), (595), (596), (598),
% 173.46/26.48  | | | | | | | | | | |            (599), (600), (7958), (7961), (7962), (9307),
% 173.46/26.48  | | | | | | | | | | |            (9308), (9313), (9326), (9327), (9328), (9329),
% 173.46/26.48  | | | | | | | | | | |            (9334), (9335), (function-axioms) are inconsistent
% 173.46/26.48  | | | | | | | | | | |            by sub-proof #40.
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | End of split
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | |   (9336)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.48  | | | | | | | | | |           all_52_30 = e0
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.48  | | | | | | | | | |            (42), (51), (154), (155), (156), (161), (163),
% 173.46/26.48  | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (177),
% 173.46/26.48  | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (269),
% 173.46/26.48  | | | | | | | | | |            (270), (271), (278), (280), (281), (282), (283),
% 173.46/26.48  | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.46/26.48  | | | | | | | | | |            (310), (311), (313), (315), (316), (317), (318),
% 173.46/26.48  | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 173.46/26.48  | | | | | | | | | |            (326), (327), (329), (330), (331), (341), (344),
% 173.46/26.48  | | | | | | | | | |            (349), (364), (370), (373), (385), (386), (391),
% 173.46/26.48  | | | | | | | | | |            (392), (403), (413), (429), (529), (530), (531),
% 173.46/26.48  | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.46/26.48  | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.46/26.48  | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.46/26.48  | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.46/26.48  | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.48  | | | | | | | | | |            (577), (580), (581), (582), (583), (585), (586),
% 173.46/26.48  | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.46/26.48  | | | | | | | | | |            (597), (598), (599), (600), (649), (7961), (7962),
% 173.46/26.48  | | | | | | | | | |            (9308), (9313), (9336), (function-axioms) are
% 173.46/26.48  | | | | | | | | | |            inconsistent by sub-proof #39.
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | End of split
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | End of split
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | |   (9337)  all_42_0 = e1
% 173.46/26.48  | | | | | | | |   (9338)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | COMBINE_EQS: (761), (9337) imply:
% 173.46/26.48  | | | | | | | |   (9339)  all_4_0 = e1
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | SIMP: (9339) implies:
% 173.46/26.48  | | | | | | | |   (9340)  all_4_0 = e1
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | REDUCE: (7961), (9340) imply:
% 173.46/26.48  | | | | | | | |   (9341)  op(e2, all_4_2) = e1
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | BETA: splitting (9338) gives:
% 173.46/26.48  | | | | | | | | 
% 173.46/26.48  | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | |   (9342)   ~ (all_42_1 = e2)
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | REDUCE: (7959), (9342) imply:
% 173.46/26.48  | | | | | | | | |   (9343)  $false
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | CLOSE: (9343) is inconsistent.
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | |   (9344)   ~ (all_42_2 = e0)
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | REDUCE: (477), (9344) imply:
% 173.46/26.48  | | | | | | | | |   (9345)   ~ (all_4_2 = e0)
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.48  | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | |   (9346)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.48  | | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2
% 173.46/26.48  | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | BETA: splitting (9346) gives:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | |   (9347)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.48  | | | | | | | | | | |           all_52_6 = e0
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REF_CLOSE: (9), (7960), (9347) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | | | |            #124.
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | |   (9348)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.48  | | | | | | | | | | |           all_52_14 = e0
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REF_CLOSE: (9), (9306), (9348) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | | | |            #289.
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | End of split
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | |   (9349)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 173.46/26.48  | | | | | | | | | |             & all_52_22 = e0) | (all_52_24 = e3 & all_52_26
% 173.46/26.48  | | | | | | | | | |             = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | BETA: splitting (9349) gives:
% 173.46/26.48  | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | |   (9350)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.48  | | | | | | | | | | |           all_52_22 = e0
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | ALPHA: (9350) implies:
% 173.46/26.48  | | | | | | | | | | |   (9351)  all_52_22 = e0
% 173.46/26.48  | | | | | | | | | | |   (9352)  all_52_20 = e1
% 173.46/26.48  | | | | | | | | | | |   (9353)  all_52_18 = e2
% 173.46/26.48  | | | | | | | | | | |   (9354)  all_52_16 = e3
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | COMBINE_EQS: (719), (9352) imply:
% 173.46/26.48  | | | | | | | | | | |   (9355)  all_14_1 = e1
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | SIMP: (9355) implies:
% 173.46/26.48  | | | | | | | | | | |   (9356)  all_14_1 = e1
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REDUCE: (63), (9356) imply:
% 173.46/26.48  | | | | | | | | | | |   (9357)  op(e1, all_14_2) = all_14_0
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REDUCE: (182), (9354) imply:
% 173.46/26.48  | | | | | | | | | | |   (9358)  op(e3, all_52_17) = e3
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REDUCE: (174), (9353) imply:
% 173.46/26.48  | | | | | | | | | | |   (9359)  op(e2, all_52_19) = e2
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REDUCE: (62), (9356) imply:
% 173.46/26.48  | | | | | | | | | | |   (9360)  op(e1, all_14_2) = e1
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REDUCE: (158), (9351) imply:
% 173.46/26.48  | | | | | | | | | | |   (9361)  op(e0, all_52_23) = e0
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_14_0,
% 173.46/26.48  | | | | | | | | | | |              all_14_2, e1, simplifying with (9357), (9360)
% 173.46/26.48  | | | | | | | | | | |              gives:
% 173.46/26.48  | | | | | | | | | | |   (9362)  all_14_0 = e1
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REDUCE: (9311), (9362) imply:
% 173.46/26.48  | | | | | | | | | | |   (9363)   ~ (e3 = e1)
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | REDUCE: (9309), (9362) imply:
% 173.46/26.48  | | | | | | | | | | |   (9364)   ~ (e2 = e1)
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | BETA: splitting (301) gives:
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | Case 1:
% 173.46/26.48  | | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | |   (9365)  all_58_15 = e0
% 173.46/26.48  | | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9365),
% 173.46/26.48  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.48  | | | | | | | | | | | |            #143.
% 173.46/26.48  | | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | |   (9366)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0)
% 173.46/26.48  | | | | | | | | | | | |           & (all_58_12 = e0 | all_58_13 = e0 | all_58_14 =
% 173.46/26.48  | | | | | | | | | | | |             e0)
% 173.46/26.48  | | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | | ALPHA: (9366) implies:
% 173.46/26.48  | | | | | | | | | | | |   (9367)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.48  | | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (156), (161),
% 173.46/26.48  | | | | | | | | | | | |            (163), (164), (170), (172), (177), (178), (179),
% 173.46/26.48  | | | | | | | | | | | |            (268), (273), (274), (276), (283), (304), (307),
% 173.46/26.48  | | | | | | | | | | | |            (310), (311), (315), (319), (323), (324), (326),
% 173.46/26.48  | | | | | | | | | | | |            (328), (330), (331), (349), (359), (364), (370),
% 173.46/26.48  | | | | | | | | | | | |            (373), (385), (391), (403), (419), (425), (529),
% 173.46/26.48  | | | | | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.48  | | | | | | | | | | | |            (538), (539), (540), (542), (544), (546), (548),
% 173.46/26.48  | | | | | | | | | | | |            (550), (552), (553), (554), (556), (558), (559),
% 173.46/26.48  | | | | | | | | | | | |            (561), (562), (563), (564), (566), (577), (579),
% 173.46/26.48  | | | | | | | | | | | |            (584), (586), (587), (593), (595), (596), (598),
% 173.46/26.48  | | | | | | | | | | | |            (600), (7962), (9341), (9345), (9358), (9359),
% 173.46/26.48  | | | | | | | | | | | |            (9360), (9361), (9367), (function-axioms) are
% 173.46/26.48  | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 173.46/26.48  | | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | | End of split
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | Case 2:
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.48  | | | | | | | | | | |   (9368)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.48  | | | | | | | | | | |           all_52_30 = e0
% 173.46/26.48  | | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | | REF_CLOSE: (9), (36), (42), (51), (156), (164), (165), (170),
% 173.46/26.49  | | | | | | | | | | |            (172), (173), (177), (178), (179), (181), (268),
% 173.46/26.49  | | | | | | | | | | |            (276), (278), (282), (283), (304), (307), (315),
% 173.46/26.49  | | | | | | | | | | |            (319), (323), (325), (327), (328), (330), (349),
% 173.46/26.49  | | | | | | | | | | |            (364), (370), (373), (385), (391), (392), (403),
% 173.46/26.49  | | | | | | | | | | |            (425), (477), (529), (530), (531), (532), (533),
% 173.46/26.49  | | | | | | | | | | |            (534), (535), (536), (537), (538), (539), (540),
% 173.46/26.49  | | | | | | | | | | |            (544), (546), (548), (554), (555), (556), (557),
% 173.46/26.49  | | | | | | | | | | |            (560), (561), (565), (568), (569), (573), (575),
% 173.46/26.49  | | | | | | | | | | |            (580), (589), (593), (597), (649), (7959), (7962),
% 173.46/26.49  | | | | | | | | | | |            (9308), (9338), (9341), (9368), (function-axioms)
% 173.46/26.49  | | | | | | | | | | |            are inconsistent by sub-proof #37.
% 173.46/26.49  | | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | End of split
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | End of split
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | End of split
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | End of split
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | Case 2:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | |   (9369)  all_18_0 = e3
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | COMBINE_EQS: (789), (9369) imply:
% 173.46/26.49  | | | | | | |   (9370)  all_14_0 = e3
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | SIMP: (9370) implies:
% 173.46/26.49  | | | | | | |   (9371)  all_14_0 = e3
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REDUCE: (63), (9371) imply:
% 173.46/26.49  | | | | | | |   (9372)  op(all_14_1, all_14_2) = e3
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | BETA: splitting (133) gives:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | Case 1:
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | |   (9373)   ~ (all_42_0 = e1)
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REDUCE: (761), (9373) imply:
% 173.46/26.49  | | | | | | | |   (9374)   ~ (all_4_0 = e1)
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | BETA: splitting (185) gives:
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | Case 1:
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | |   (9375)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.49  | | | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 173.46/26.49  | | | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | BETA: splitting (9375) gives:
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | Case 1:
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | |   (9376)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 173.46/26.49  | | | | | | | | | |           all_52_6 = e0
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | REF_CLOSE: (9), (7960), (9376) are inconsistent by sub-proof
% 173.46/26.49  | | | | | | | | | |            #124.
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | Case 2:
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | |   (9377)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 173.46/26.49  | | | | | | | | | |           all_52_14 = e0
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | REF_CLOSE: (9), (9306), (9377) are inconsistent by sub-proof
% 173.46/26.49  | | | | | | | | | |            #289.
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | End of split
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | Case 2:
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | |   (9378)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.49  | | | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 173.46/26.49  | | | | | | | | |             & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | BETA: splitting (9378) gives:
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | Case 1:
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | |   (9379)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 173.46/26.49  | | | | | | | | | |           all_52_22 = e0
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | ALPHA: (9379) implies:
% 173.46/26.49  | | | | | | | | | |   (9380)  all_52_20 = e1
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | COMBINE_EQS: (719), (9380) imply:
% 173.46/26.49  | | | | | | | | | |   (9381)  all_14_1 = e1
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | REF_CLOSE: (8), (62), (9372), (9381), (function-axioms) are
% 173.46/26.49  | | | | | | | | | |            inconsistent by sub-proof #344.
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | Case 2:
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | |   (9382)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.49  | | | | | | | | | |           all_52_30 = e0
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | ALPHA: (9382) implies:
% 173.46/26.49  | | | | | | | | | |   (9383)  all_52_30 = e0
% 173.46/26.49  | | | | | | | | | |   (9384)  all_52_28 = e1
% 173.46/26.49  | | | | | | | | | |   (9385)  all_52_26 = e2
% 173.46/26.49  | | | | | | | | | |   (9386)  all_52_24 = e3
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | COMBINE_EQS: (649), (9383) imply:
% 173.46/26.49  | | | | | | | | | |   (9387)  all_6_1 = e0
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38),
% 173.46/26.49  | | | | | | | | | |            (42), (51), (154), (155), (156), (161), (163),
% 173.46/26.49  | | | | | | | | | |            (164), (165), (169), (170), (172), (173), (177),
% 173.46/26.49  | | | | | | | | | |            (178), (179), (181), (182), (183), (268), (269),
% 173.46/26.49  | | | | | | | | | |            (270), (271), (278), (280), (281), (282), (283),
% 173.46/26.49  | | | | | | | | | |            (301), (302), (303), (304), (305), (306), (307),
% 173.46/26.49  | | | | | | | | | |            (310), (311), (313), (315), (316), (317), (318),
% 173.46/26.49  | | | | | | | | | |            (319), (320), (321), (322), (323), (324), (325),
% 173.46/26.49  | | | | | | | | | |            (326), (327), (329), (330), (331), (341), (344),
% 173.46/26.49  | | | | | | | | | |            (349), (364), (370), (373), (385), (386), (391),
% 173.46/26.49  | | | | | | | | | |            (392), (403), (413), (429), (529), (530), (531),
% 173.46/26.49  | | | | | | | | | |            (532), (533), (534), (535), (536), (537), (538),
% 173.46/26.49  | | | | | | | | | |            (539), (540), (542), (544), (546), (548), (550),
% 173.46/26.49  | | | | | | | | | |            (552), (553), (554), (555), (556), (557), (558),
% 173.46/26.49  | | | | | | | | | |            (559), (560), (561), (562), (563), (564), (565),
% 173.46/26.49  | | | | | | | | | |            (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.49  | | | | | | | | | |            (577), (580), (581), (582), (583), (585), (586),
% 173.46/26.49  | | | | | | | | | |            (588), (589), (591), (593), (594), (595), (596),
% 173.46/26.49  | | | | | | | | | |            (597), (598), (599), (600), (7961), (7962),
% 173.46/26.49  | | | | | | | | | |            (9308), (9374), (9384), (9385), (9386), (9387),
% 173.46/26.49  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 173.46/26.49  | | | | | | | | | |            #44.
% 173.46/26.49  | | | | | | | | | | 
% 173.46/26.49  | | | | | | | | | End of split
% 173.46/26.49  | | | | | | | | | 
% 173.46/26.49  | | | | | | | | End of split
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | Case 2:
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | |   (9388)  all_42_0 = e1
% 173.46/26.49  | | | | | | | |   (9389)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | COMBINE_EQS: (761), (9388) imply:
% 173.46/26.49  | | | | | | | |   (9390)  all_4_0 = e1
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REDUCE: (7961), (9390) imply:
% 173.46/26.49  | | | | | | | |   (9391)  op(e2, all_4_2) = e1
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REF_CLOSE: (8), (9), (36), (42), (43), (51), (62), (156), (164),
% 173.46/26.49  | | | | | | | |            (165), (170), (172), (173), (177), (178), (179),
% 173.46/26.49  | | | | | | | |            (181), (185), (268), (276), (278), (282), (283),
% 173.46/26.49  | | | | | | | |            (304), (307), (315), (319), (323), (325), (327),
% 173.46/26.49  | | | | | | | |            (328), (330), (349), (364), (370), (373), (385),
% 173.46/26.49  | | | | | | | |            (391), (392), (403), (425), (477), (529), (530),
% 173.46/26.49  | | | | | | | |            (531), (532), (533), (534), (535), (536), (537),
% 173.46/26.49  | | | | | | | |            (538), (539), (540), (544), (546), (548), (554),
% 173.46/26.49  | | | | | | | |            (555), (556), (557), (560), (561), (565), (568),
% 173.46/26.49  | | | | | | | |            (569), (573), (575), (580), (589), (593), (597),
% 173.46/26.49  | | | | | | | |            (649), (719), (7959), (7960), (7962), (9306), (9308),
% 173.46/26.49  | | | | | | | |            (9372), (9389), (9391), (function-axioms) are
% 173.46/26.49  | | | | | | | |            inconsistent by sub-proof #38.
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | End of split
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | End of split
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | Case 2:
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | |   (9392)  all_14_0 = e2
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (42),
% 173.46/26.49  | | | | | |            (51), (62), (63), (133), (154), (155), (156), (161),
% 173.46/26.49  | | | | | |            (163), (164), (165), (169), (170), (172), (173), (177),
% 173.46/26.49  | | | | | |            (178), (179), (181), (182), (183), (185), (268), (269),
% 173.46/26.49  | | | | | |            (270), (271), (276), (278), (280), (281), (282), (283),
% 173.46/26.49  | | | | | |            (301), (302), (303), (304), (305), (306), (307), (310),
% 173.46/26.49  | | | | | |            (311), (313), (315), (316), (317), (318), (319), (320),
% 173.46/26.49  | | | | | |            (321), (322), (323), (324), (325), (326), (327), (328),
% 173.46/26.49  | | | | | |            (329), (330), (331), (341), (344), (349), (364), (370),
% 173.46/26.49  | | | | | |            (373), (385), (386), (391), (392), (403), (413), (425),
% 173.46/26.49  | | | | | |            (429), (477), (529), (530), (531), (532), (533), (534),
% 173.46/26.49  | | | | | |            (535), (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.49  | | | | | |            (546), (548), (550), (552), (553), (554), (555), (556),
% 173.46/26.49  | | | | | |            (557), (558), (559), (560), (561), (562), (563), (564),
% 173.46/26.49  | | | | | |            (565), (566), (567), (568), (569), (571), (573), (575),
% 173.46/26.49  | | | | | |            (577), (580), (581), (582), (583), (585), (586), (588),
% 173.46/26.49  | | | | | |            (589), (591), (593), (594), (595), (596), (597), (598),
% 173.46/26.49  | | | | | |            (599), (600), (649), (719), (761), (7959), (7960),
% 173.46/26.49  | | | | | |            (7961), (7962), (9306), (9308), (9392), (function-axioms)
% 173.46/26.49  | | | | | |            are inconsistent by sub-proof #36.
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | End of split
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | End of split
% 173.46/26.49  | | | | 
% 173.46/26.49  | | | Case 2:
% 173.46/26.49  | | | | 
% 173.46/26.49  | | | |   (9393)  all_10_0 = e3
% 173.46/26.49  | | | | 
% 173.46/26.49  | | | | REDUCE: (53), (9393) imply:
% 173.46/26.49  | | | |   (9394)  op(all_10_1, all_10_2) = e3
% 173.46/26.49  | | | | 
% 173.46/26.49  | | | | BETA: splitting (64) gives:
% 173.46/26.49  | | | | 
% 173.46/26.49  | | | | Case 1:
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | |   (9395)   ~ (all_14_0 = e2)
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | | BETA: splitting (74) gives:
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | | Case 1:
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | |   (9396)   ~ (all_18_0 = e3)
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | REDUCE: (789), (9396) imply:
% 173.46/26.49  | | | | | |   (9397)   ~ (all_14_0 = e3)
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | BETA: splitting (133) gives:
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | Case 1:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | |   (9398)   ~ (all_42_0 = e1)
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REDUCE: (761), (9398) imply:
% 173.46/26.49  | | | | | | |   (9399)   ~ (all_4_0 = e1)
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | BETA: splitting (301) gives:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | Case 1:
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | |   (9400)  all_58_15 = e0
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9400),
% 173.46/26.49  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #143.
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | Case 2:
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | |   (9401)   ~ (all_58_15 = e0)
% 173.46/26.49  | | | | | | | |   (9402)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.49  | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | ALPHA: (9402) implies:
% 173.46/26.49  | | | | | | | |   (9403)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.49  | | | | | | | |   (9404)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REDUCE: (532), (9401) imply:
% 173.46/26.49  | | | | | | | |   (9405)   ~ (all_6_2 = e0)
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (42),
% 173.46/26.49  | | | | | | | |            (52), (62), (63), (154), (155), (156), (158), (161),
% 173.46/26.49  | | | | | | | |            (163), (164), (165), (170), (172), (173), (174),
% 173.46/26.49  | | | | | | | |            (177), (178), (179), (181), (182), (183), (185),
% 173.46/26.49  | | | | | | | |            (268), (269), (270), (271), (274), (275), (276),
% 173.46/26.49  | | | | | | | |            (277), (278), (280), (281), (282), (283), (303),
% 173.46/26.49  | | | | | | | |            (304), (305), (306), (307), (310), (311), (313),
% 173.46/26.49  | | | | | | | |            (314), (315), (319), (321), (322), (323), (324),
% 173.46/26.49  | | | | | | | |            (325), (326), (327), (328), (329), (330), (331),
% 173.46/26.49  | | | | | | | |            (341), (344), (349), (364), (365), (370), (373),
% 173.46/26.49  | | | | | | | |            (385), (386), (391), (392), (403), (413), (415),
% 173.46/26.49  | | | | | | | |            (419), (425), (429), (529), (530), (531), (532),
% 173.46/26.49  | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.49  | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.49  | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 173.46/26.49  | | | | | | | |            (560), (561), (562), (563), (564), (565), (566),
% 173.46/26.49  | | | | | | | |            (567), (568), (569), (571), (575), (577), (578),
% 173.46/26.49  | | | | | | | |            (579), (580), (581), (582), (583), (584), (585),
% 173.46/26.49  | | | | | | | |            (586), (587), (588), (589), (593), (594), (595),
% 173.46/26.49  | | | | | | | |            (596), (597), (598), (599), (600), (649), (661),
% 173.46/26.49  | | | | | | | |            (719), (7958), (7960), (7961), (7962), (9394),
% 173.46/26.49  | | | | | | | |            (9395), (9397), (9399), (9403), (9404), (9405),
% 173.46/26.49  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #31.
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | End of split
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | Case 2:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | |   (9406)  all_42_0 = e1
% 173.46/26.49  | | | | | | |   (9407)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | COMBINE_EQS: (761), (9406) imply:
% 173.46/26.49  | | | | | | |   (9408)  all_4_0 = e1
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REDUCE: (7961), (9408) imply:
% 173.46/26.49  | | | | | | |   (9409)  op(e2, all_4_2) = e1
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42), (52),
% 173.46/26.49  | | | | | | |            (62), (156), (158), (161), (163), (164), (170), (172),
% 173.46/26.49  | | | | | | |            (174), (177), (178), (179), (182), (185), (268), (273),
% 173.46/26.49  | | | | | | |            (274), (276), (283), (301), (304), (307), (310), (311),
% 173.46/26.49  | | | | | | |            (315), (319), (323), (324), (326), (328), (330), (331),
% 173.46/26.49  | | | | | | |            (349), (359), (364), (370), (373), (385), (391), (403),
% 173.46/26.49  | | | | | | |            (419), (425), (477), (529), (531), (532), (533), (534),
% 173.46/26.49  | | | | | | |            (535), (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.49  | | | | | | |            (546), (548), (550), (552), (553), (554), (556), (558),
% 173.46/26.49  | | | | | | |            (559), (561), (562), (563), (564), (566), (577), (579),
% 173.46/26.49  | | | | | | |            (584), (586), (587), (593), (595), (596), (598), (600),
% 173.46/26.49  | | | | | | |            (649), (661), (719), (7959), (7960), (7962), (9213),
% 173.46/26.49  | | | | | | |            (9394), (9407), (9409), (function-axioms) are
% 173.46/26.49  | | | | | | |            inconsistent by sub-proof #1.
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | End of split
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | Case 2:
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | |   (9410)  all_18_0 = e3
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | COMBINE_EQS: (789), (9410) imply:
% 173.46/26.49  | | | | | |   (9411)  all_14_0 = e3
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | SIMP: (9411) implies:
% 173.46/26.49  | | | | | |   (9412)  all_14_0 = e3
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | REDUCE: (63), (9412) imply:
% 173.46/26.49  | | | | | |   (9413)  op(all_14_1, all_14_2) = e3
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | BETA: splitting (133) gives:
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | Case 1:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | |   (9414)   ~ (all_42_0 = e1)
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REDUCE: (761), (9414) imply:
% 173.46/26.49  | | | | | | |   (9415)   ~ (all_4_0 = e1)
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | BETA: splitting (301) gives:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | Case 1:
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | |   (9416)  all_58_15 = e0
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9416),
% 173.46/26.49  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #143.
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | Case 2:
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | |   (9417)   ~ (all_58_15 = e0)
% 173.46/26.49  | | | | | | | |   (9418)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.49  | | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (42),
% 173.46/26.49  | | | | | | | |            (52), (62), (154), (155), (156), (161), (164), (165),
% 173.46/26.49  | | | | | | | |            (170), (172), (173), (177), (178), (179), (181),
% 173.46/26.49  | | | | | | | |            (182), (183), (185), (268), (269), (270), (271),
% 173.46/26.49  | | | | | | | |            (281), (282), (283), (303), (304), (305), (306),
% 173.46/26.49  | | | | | | | |            (307), (313), (315), (321), (322), (323), (324),
% 173.46/26.49  | | | | | | | |            (325), (326), (327), (329), (330), (331), (341),
% 173.46/26.49  | | | | | | | |            (344), (349), (364), (370), (373), (385), (391),
% 173.46/26.49  | | | | | | | |            (392), (403), (413), (429), (529), (531), (532),
% 173.46/26.49  | | | | | | | |            (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.49  | | | | | | | |            (540), (542), (544), (546), (548), (550), (552),
% 173.46/26.49  | | | | | | | |            (553), (554), (555), (556), (557), (558), (559),
% 173.46/26.49  | | | | | | | |            (560), (561), (562), (563), (564), (565), (567),
% 173.46/26.49  | | | | | | | |            (568), (569), (571), (577), (580), (581), (582),
% 173.46/26.49  | | | | | | | |            (585), (586), (589), (594), (595), (596), (597),
% 173.46/26.49  | | | | | | | |            (649), (661), (719), (7960), (7961), (7962), (9394),
% 173.46/26.49  | | | | | | | |            (9413), (9415), (9417), (9418), (function-axioms) are
% 173.46/26.49  | | | | | | | |            inconsistent by sub-proof #20.
% 173.46/26.49  | | | | | | | | 
% 173.46/26.49  | | | | | | | End of split
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | Case 2:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | |   (9419)  all_42_0 = e1
% 173.46/26.49  | | | | | | |   (9420)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | COMBINE_EQS: (761), (9419) imply:
% 173.46/26.49  | | | | | | |   (9421)  all_4_0 = e1
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | SIMP: (9421) implies:
% 173.46/26.49  | | | | | | |   (9422)  all_4_0 = e1
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REDUCE: (7961), (9422) imply:
% 173.46/26.49  | | | | | | |   (9423)  op(e2, all_4_2) = e1
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42), (52),
% 173.46/26.49  | | | | | | |            (62), (156), (158), (161), (163), (164), (170), (172),
% 173.46/26.49  | | | | | | |            (174), (177), (178), (179), (182), (185), (268), (273),
% 173.46/26.49  | | | | | | |            (274), (276), (283), (301), (304), (307), (310), (311),
% 173.46/26.49  | | | | | | |            (315), (319), (323), (324), (326), (328), (330), (331),
% 173.46/26.49  | | | | | | |            (349), (359), (364), (370), (373), (385), (391), (403),
% 173.46/26.49  | | | | | | |            (419), (425), (477), (529), (531), (532), (533), (534),
% 173.46/26.49  | | | | | | |            (535), (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.49  | | | | | | |            (546), (548), (550), (552), (553), (554), (556), (558),
% 173.46/26.49  | | | | | | |            (559), (561), (562), (563), (564), (566), (577), (579),
% 173.46/26.49  | | | | | | |            (584), (586), (587), (593), (595), (596), (598), (600),
% 173.46/26.49  | | | | | | |            (649), (661), (719), (7959), (7960), (7962), (9213),
% 173.46/26.49  | | | | | | |            (9394), (9420), (9423), (function-axioms) are
% 173.46/26.49  | | | | | | |            inconsistent by sub-proof #1.
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | End of split
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | End of split
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | Case 2:
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | |   (9424)  all_14_0 = e2
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | | REDUCE: (63), (9424) imply:
% 173.46/26.49  | | | | |   (9425)  op(all_14_1, all_14_2) = e2
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | | BETA: splitting (133) gives:
% 173.46/26.49  | | | | | 
% 173.46/26.49  | | | | | Case 1:
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | |   (9426)   ~ (all_42_0 = e1)
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | REDUCE: (761), (9426) imply:
% 173.46/26.49  | | | | | |   (9427)   ~ (all_4_0 = e1)
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | BETA: splitting (301) gives:
% 173.46/26.49  | | | | | | 
% 173.46/26.49  | | | | | | Case 1:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | |   (9428)  all_58_15 = e0
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | | REF_CLOSE: (4), (41), (42), (532), (9213), (9428),
% 173.46/26.49  | | | | | | |            (function-axioms) are inconsistent by sub-proof #143.
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | Case 2:
% 173.46/26.49  | | | | | | | 
% 173.46/26.49  | | | | | | |   (9429)   ~ (all_58_15 = e0)
% 173.46/26.49  | | | | | | |   (9430)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.49  | | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.49  | | | | | | | 
% 173.46/26.50  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (37), (38), (42),
% 173.46/26.50  | | | | | | |            (52), (62), (154), (155), (156), (161), (164), (165),
% 173.46/26.50  | | | | | | |            (170), (172), (173), (177), (178), (179), (181), (182),
% 173.46/26.50  | | | | | | |            (183), (185), (268), (269), (270), (271), (281), (282),
% 173.46/26.50  | | | | | | |            (283), (303), (304), (305), (306), (307), (313), (315),
% 173.46/26.50  | | | | | | |            (321), (322), (323), (324), (325), (326), (327), (329),
% 173.46/26.50  | | | | | | |            (330), (331), (341), (344), (349), (364), (370), (373),
% 173.46/26.50  | | | | | | |            (385), (391), (392), (403), (413), (429), (529), (531),
% 173.46/26.50  | | | | | | |            (532), (533), (534), (535), (536), (537), (538), (539),
% 173.46/26.50  | | | | | | |            (540), (542), (544), (546), (548), (550), (552), (553),
% 173.46/26.50  | | | | | | |            (554), (555), (556), (557), (558), (559), (560), (561),
% 173.46/26.50  | | | | | | |            (562), (563), (564), (565), (567), (568), (569), (571),
% 173.46/26.50  | | | | | | |            (577), (580), (581), (582), (585), (586), (589), (594),
% 173.46/26.50  | | | | | | |            (595), (596), (597), (649), (661), (719), (7960),
% 173.46/26.50  | | | | | | |            (7961), (7962), (9394), (9425), (9427), (9429), (9430),
% 173.46/26.50  | | | | | | |            (function-axioms) are inconsistent by sub-proof #17.
% 173.46/26.50  | | | | | | | 
% 173.46/26.50  | | | | | | End of split
% 173.46/26.50  | | | | | | 
% 173.46/26.50  | | | | | Case 2:
% 173.46/26.50  | | | | | | 
% 173.46/26.50  | | | | | |   (9431)  all_42_0 = e1
% 173.46/26.50  | | | | | |   (9432)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.50  | | | | | | 
% 173.46/26.50  | | | | | | COMBINE_EQS: (761), (9431) imply:
% 173.46/26.50  | | | | | |   (9433)  all_4_0 = e1
% 173.46/26.50  | | | | | | 
% 173.46/26.50  | | | | | | SIMP: (9433) implies:
% 173.46/26.50  | | | | | |   (9434)  all_4_0 = e1
% 173.46/26.50  | | | | | | 
% 173.46/26.50  | | | | | | REDUCE: (7961), (9434) imply:
% 173.46/26.50  | | | | | |   (9435)  op(e2, all_4_2) = e1
% 173.46/26.50  | | | | | | 
% 173.46/26.50  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (41), (42), (52),
% 173.46/26.50  | | | | | |            (62), (156), (158), (161), (163), (164), (170), (172),
% 173.46/26.50  | | | | | |            (174), (177), (178), (179), (182), (185), (268), (273),
% 173.46/26.50  | | | | | |            (274), (276), (283), (301), (304), (307), (310), (311),
% 173.46/26.50  | | | | | |            (315), (319), (323), (324), (326), (328), (330), (331),
% 173.46/26.50  | | | | | |            (349), (359), (364), (370), (373), (385), (391), (403),
% 173.46/26.50  | | | | | |            (419), (425), (477), (529), (531), (532), (533), (534),
% 173.46/26.50  | | | | | |            (535), (536), (537), (538), (539), (540), (542), (544),
% 173.46/26.50  | | | | | |            (546), (548), (550), (552), (553), (554), (556), (558),
% 173.46/26.50  | | | | | |            (559), (561), (562), (563), (564), (566), (577), (579),
% 173.46/26.50  | | | | | |            (584), (586), (587), (593), (595), (596), (598), (600),
% 173.46/26.50  | | | | | |            (649), (661), (719), (7959), (7960), (7962), (9213),
% 173.46/26.50  | | | | | |            (9394), (9432), (9435), (function-axioms) are
% 173.46/26.50  | | | | | |            inconsistent by sub-proof #1.
% 173.46/26.50  | | | | | | 
% 173.46/26.50  | | | | | End of split
% 173.46/26.50  | | | | | 
% 173.46/26.50  | | | | End of split
% 173.46/26.50  | | | | 
% 173.46/26.50  | | | End of split
% 173.46/26.50  | | | 
% 173.46/26.50  | | End of split
% 173.46/26.50  | | 
% 173.46/26.50  | End of split
% 173.46/26.50  | 
% 173.46/26.50  End of proof
% 173.46/26.50  
% 173.46/26.50  Sub-proof #1 shows that the following formulas are inconsistent:
% 173.46/26.50  ----------------------------------------------------------------
% 173.46/26.50    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.50    (2)   ~ (all_52_17 = all_52_23)
% 173.46/26.50    (3)  op(e2, all_10_2) = all_10_1
% 173.46/26.50    (4)  all_42_1 = e2
% 173.46/26.50    (5)  op(e3, e2) = all_52_3
% 173.46/26.50    (6)   ~ (all_52_9 = all_52_25)
% 173.46/26.50    (7)  op(e1, e2) = all_52_19
% 173.46/26.50    (8)  op(all_6_1, all_6_2) = e1
% 173.46/26.50    (9)  all_58_5 = all_52_13
% 173.46/26.50    (10)   ~ (all_52_25 = all_52_29)
% 173.46/26.50    (11)  all_56_15 = all_6_2
% 173.46/26.50    (12)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.50    (13)  all_58_3 = all_10_2
% 173.46/26.50    (14)  all_56_9 = all_52_19
% 173.46/26.50    (15)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.50    (16)  all_58_15 = all_6_2
% 173.46/26.50    (17)  op(e2, all_4_2) = e1
% 173.46/26.50    (18)   ~ (all_52_9 = all_4_2)
% 173.46/26.50    (19)   ~ (all_52_5 = all_52_7)
% 173.46/26.50    (20)  all_58_10 = all_52_15
% 173.46/26.50    (21)   ~ (all_52_5 = all_4_2)
% 173.46/26.50    (22)  all_58_7 = all_52_19
% 173.46/26.50    (23)   ~ (all_52_17 = all_52_25)
% 173.46/26.50    (24)  all_58_4 = all_52_5
% 173.46/26.50    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.50    (26)   ~ (e3 = e1)
% 173.46/26.50    (27)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.50    (28)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.50    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.50    (30)   ~ (all_52_7 = all_4_2)
% 173.46/26.50    (31)  all_58_1 = all_52_3
% 173.46/26.50    (32)  all_58_0 = all_4_2
% 173.46/26.50    (33)  all_52_0 = e2
% 173.46/26.50    (34)  op(e0, e0) = all_6_2
% 173.46/26.50    (35)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.50    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.50    (37)  all_58_14 = all_52_29
% 173.46/26.50    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.50    (39)  op(e2, e1) = all_52_13
% 173.46/26.50    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.50    (41)  all_58_8 = all_14_2
% 173.46/26.50    (42)   ~ (all_52_5 = all_14_2)
% 173.46/26.50    (43)   ~ (all_52_3 = all_4_2)
% 173.46/26.50    (44)  op(e0, e3) = all_52_25
% 173.46/26.50    (45)  op(e0, all_6_2) = all_6_1
% 173.46/26.50    (46)  op(e3, all_52_17) = all_52_16
% 173.46/26.50    (47)  all_52_10 = all_10_1
% 173.46/26.50    (48)   ~ (all_52_13 = all_14_2)
% 173.46/26.50    (49)   ~ (e3 = e0)
% 173.46/26.50    (50)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 173.46/26.50    (51)   ~ (all_52_9 = all_52_13)
% 173.46/26.50    (52)  op(e0, all_52_23) = all_52_22
% 173.46/26.50    (53)   ~ (all_52_15 = all_52_23)
% 173.46/26.50    (54)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.50    (55)  op(e1, e0) = all_52_23
% 173.46/26.50    (56)  all_58_13 = all_52_27
% 173.46/26.50    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.50    (58)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 173.46/26.50    (59)   ~ (all_52_9 = all_52_17)
% 173.46/26.50    (60)  all_58_6 = all_52_17
% 173.46/26.50    (61)  op(all_10_1, all_10_2) = e3
% 173.46/26.50    (62)  op(e2, all_52_19) = all_52_18
% 173.46/26.50    (63)   ~ (e1 = e0)
% 173.46/26.50    (64)  all_56_0 = all_4_2
% 173.46/26.50    (65)  all_58_11 = all_52_23
% 173.46/26.50    (66)   ~ (all_52_3 = all_52_19)
% 173.46/26.50    (67)   ~ (all_52_7 = all_52_15)
% 173.46/26.50    (68)  op(e3, all_4_2) = e2
% 173.46/26.50    (69)   ~ (all_52_23 = all_6_2)
% 173.46/26.50    (70)  all_58_2 = all_52_9
% 173.46/26.50    (71)  op(e3, e1) = all_52_5
% 173.46/26.50    (72)   ~ (e2 = e1)
% 173.46/26.50    (73)  all_56_10 = all_14_2
% 173.46/26.50    (74)   ~ (all_52_25 = all_6_2)
% 173.46/26.50    (75)  op(e1, e3) = all_52_17
% 173.46/26.50    (76)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 173.46/26.50    (77)   ~ (all_52_25 = all_4_2)
% 173.46/26.50    (78)  op(e3, e0) = all_52_7
% 173.46/26.50    (79)  op(e3, e3) = all_4_2
% 173.46/26.50    (80)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.50            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 173.46/26.50    (81)   ~ (all_52_17 = all_4_2)
% 173.46/26.50    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.50    (83)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.50          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 173.46/26.50          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.50          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.50    (84)   ~ (all_52_25 = all_52_27)
% 173.46/26.50    (85)   ~ (all_52_15 = all_10_2)
% 173.46/26.50    (86)  all_42_2 = all_4_2
% 173.46/26.50    (87)  all_56_7 = all_52_15
% 173.46/26.50    (88)   ~ (all_52_7 = all_52_23)
% 173.46/26.50    (89)  all_52_20 = all_14_1
% 173.46/26.50    (90)   ~ (all_52_17 = all_52_19)
% 173.46/26.50    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.50    (92)  all_52_30 = all_6_1
% 173.46/26.50    (93)  op(e1, all_14_2) = all_14_1
% 173.46/26.50    (94)  all_58_9 = all_52_7
% 173.46/26.50    (95)   ~ (e2 = e0)
% 173.46/26.50    (96)  all_58_12 = all_52_25
% 173.46/26.50    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.50    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.50    (99)   ~ (e3 = e2)
% 173.46/26.50    (100)   ~ (all_52_19 = all_14_2)
% 173.46/26.50    (101)  op(e2, e3) = all_52_9
% 173.46/26.50  
% 173.46/26.50  Begin of proof
% 173.46/26.50  | 
% 173.46/26.50  | BETA: splitting (27) gives:
% 173.46/26.50  | 
% 173.46/26.50  | Case 1:
% 173.46/26.50  | | 
% 173.46/26.50  | |   (102)   ~ (all_42_1 = e2)
% 173.46/26.50  | | 
% 173.46/26.50  | | REDUCE: (4), (102) imply:
% 173.46/26.50  | |   (103)  $false
% 173.46/26.50  | | 
% 173.46/26.50  | | CLOSE: (103) is inconsistent.
% 173.46/26.50  | | 
% 173.46/26.50  | Case 2:
% 173.46/26.50  | | 
% 173.46/26.50  | |   (104)   ~ (all_42_2 = e0)
% 173.46/26.50  | | 
% 173.46/26.50  | | REDUCE: (86), (104) imply:
% 173.46/26.50  | |   (105)   ~ (all_4_2 = e0)
% 173.46/26.50  | | 
% 173.46/26.50  | | BETA: splitting (80) gives:
% 173.46/26.50  | | 
% 173.46/26.50  | | Case 1:
% 173.46/26.50  | | | 
% 173.46/26.50  | | |   (106)  all_58_15 = e0
% 173.46/26.50  | | | 
% 173.46/26.50  | | | REF_CLOSE: (8), (16), (34), (45), (63), (82), (106) are inconsistent by
% 173.46/26.50  | | |            sub-proof #143.
% 173.46/26.50  | | | 
% 173.46/26.50  | | Case 2:
% 173.46/26.50  | | | 
% 173.46/26.50  | | |   (107)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 173.46/26.50  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.50  | | | 
% 173.46/26.50  | | | ALPHA: (107) implies:
% 173.46/26.50  | | |   (108)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.50  | | | 
% 173.46/26.50  | | | BETA: splitting (83) gives:
% 173.46/26.50  | | | 
% 173.46/26.50  | | | Case 1:
% 173.46/26.50  | | | | 
% 173.46/26.50  | | | |   (109)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 173.46/26.50  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 173.46/26.50  | | | |            = e0)
% 173.46/26.50  | | | | 
% 173.46/26.50  | | | | REF_CLOSE: (3), (33), (47), (61), (82), (99), (109) are inconsistent by
% 173.46/26.50  | | | |            sub-proof #33.
% 173.46/26.50  | | | | 
% 173.46/26.50  | | | Case 2:
% 173.46/26.50  | | | | 
% 173.46/26.50  | | | |   (110)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 173.46/26.50  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.50  | | | |            all_52_30 = e0)
% 173.46/26.50  | | | | 
% 173.46/26.50  | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 173.46/26.50  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 173.46/26.50  | | | |            (24), (25), (26), (28), (29), (30), (31), (32), (35), (36),
% 173.46/26.50  | | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 173.46/26.50  | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 173.46/26.50  | | | |            (58), (59), (60), (62), (63), (64), (65), (66), (67), (68),
% 173.46/26.50  | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 173.46/26.50  | | | |            (79), (81), (82), (84), (85), (87), (88), (89), (90), (91),
% 173.46/26.50  | | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 173.46/26.50  | | | |            (105), (108), (110) are inconsistent by sub-proof #3.
% 173.46/26.50  | | | | 
% 173.46/26.50  | | | End of split
% 173.46/26.50  | | | 
% 173.46/26.50  | | End of split
% 173.46/26.50  | | 
% 173.46/26.50  | End of split
% 173.46/26.50  | 
% 173.46/26.50  End of proof
% 173.46/26.50  
% 173.46/26.50  Sub-proof #2 shows that the following formulas are inconsistent:
% 173.46/26.50  ----------------------------------------------------------------
% 173.46/26.50    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.50    (2)   ~ (all_52_17 = all_52_23)
% 173.46/26.50    (3)  op(e2, all_10_2) = all_10_1
% 173.46/26.50    (4)  all_42_1 = e2
% 173.46/26.50    (5)  op(all_10_1, all_10_2) = e1
% 173.46/26.50    (6)  op(e3, e2) = all_52_3
% 173.46/26.50    (7)   ~ (all_52_9 = all_52_25)
% 173.46/26.50    (8)  op(e1, e2) = all_52_19
% 173.46/26.50    (9)  op(all_6_1, all_6_2) = e1
% 173.46/26.50    (10)  all_58_5 = all_52_13
% 173.46/26.50    (11)   ~ (all_52_25 = all_52_29)
% 173.46/26.50    (12)  all_56_15 = all_6_2
% 173.46/26.50    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.50    (14)  all_58_3 = all_10_2
% 173.46/26.50    (15)  all_56_9 = all_52_19
% 173.46/26.50    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.50    (17)  all_58_15 = all_6_2
% 173.46/26.50    (18)  op(e2, all_4_2) = e1
% 173.46/26.50    (19)   ~ (all_52_9 = all_4_2)
% 173.46/26.50    (20)   ~ (all_52_5 = all_52_7)
% 173.46/26.50    (21)  all_58_10 = all_52_15
% 173.46/26.50    (22)   ~ (all_52_5 = all_4_2)
% 173.46/26.50    (23)  all_58_7 = all_52_19
% 173.46/26.50    (24)   ~ (all_52_17 = all_52_25)
% 173.46/26.50    (25)  all_58_4 = all_52_5
% 173.46/26.50    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.50    (27)   ~ (e3 = e1)
% 173.46/26.50    (28)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.50    (29)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.50    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.50    (31)   ~ (all_52_7 = all_4_2)
% 173.46/26.50    (32)  all_58_1 = all_52_3
% 173.46/26.50    (33)  all_58_0 = all_4_2
% 173.46/26.50    (34)  all_52_0 = e2
% 173.46/26.50    (35)  op(e0, e0) = all_6_2
% 173.46/26.50    (36)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.50    (37)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.50    (38)  all_58_14 = all_52_29
% 173.46/26.50    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.50    (40)  op(e2, e1) = all_52_13
% 173.46/26.50    (41)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.50    (42)  all_58_8 = all_14_2
% 173.46/26.50    (43)   ~ (all_52_5 = all_14_2)
% 173.46/26.50    (44)   ~ (all_52_3 = all_4_2)
% 173.46/26.50    (45)  op(e0, e3) = all_52_25
% 173.46/26.50    (46)  op(e0, all_6_2) = all_6_1
% 173.46/26.50    (47)  op(e3, all_52_17) = all_52_16
% 173.46/26.50    (48)  all_52_10 = all_10_1
% 173.46/26.50    (49)   ~ (all_52_13 = all_14_2)
% 173.46/26.50    (50)   ~ (e3 = e0)
% 173.46/26.50    (51)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 173.46/26.50    (52)   ~ (all_52_9 = all_52_13)
% 173.46/26.50    (53)  op(e0, all_52_23) = all_52_22
% 173.46/26.50    (54)   ~ (all_52_15 = all_52_23)
% 173.46/26.50    (55)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.50    (56)  op(e1, e0) = all_52_23
% 173.46/26.50    (57)  all_58_13 = all_52_27
% 173.46/26.50    (58)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.50    (59)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 173.46/26.50    (60)   ~ (all_52_9 = all_52_17)
% 173.46/26.50    (61)  all_58_6 = all_52_17
% 173.46/26.50    (62)  op(e2, all_52_19) = all_52_18
% 173.46/26.50    (63)   ~ (e1 = e0)
% 173.46/26.50    (64)  all_56_0 = all_4_2
% 173.46/26.50    (65)  all_58_11 = all_52_23
% 173.46/26.50    (66)   ~ (all_52_3 = all_52_19)
% 173.46/26.50    (67)   ~ (all_52_7 = all_52_15)
% 173.46/26.50    (68)  op(e3, all_4_2) = e2
% 173.46/26.50    (69)   ~ (all_52_23 = all_6_2)
% 173.46/26.50    (70)  all_58_2 = all_52_9
% 173.46/26.50    (71)  op(e3, e1) = all_52_5
% 173.46/26.50    (72)   ~ (e2 = e1)
% 173.46/26.50    (73)  all_56_10 = all_14_2
% 173.46/26.50    (74)   ~ (all_52_25 = all_6_2)
% 173.46/26.50    (75)  op(e1, e3) = all_52_17
% 173.46/26.50    (76)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 173.46/26.50    (77)   ~ (all_52_25 = all_4_2)
% 173.46/26.50    (78)  op(e3, e0) = all_52_7
% 173.46/26.50    (79)  op(e3, e3) = all_4_2
% 173.46/26.50    (80)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.50            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 173.46/26.50    (81)   ~ (all_52_17 = all_4_2)
% 173.46/26.50    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.50    (83)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.50          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 173.46/26.50          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.50          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.50    (84)   ~ (all_52_25 = all_52_27)
% 173.46/26.50    (85)   ~ (all_52_15 = all_10_2)
% 173.46/26.50    (86)  all_42_2 = all_4_2
% 173.46/26.50    (87)  all_56_7 = all_52_15
% 173.46/26.50    (88)   ~ (all_52_7 = all_52_23)
% 173.46/26.50    (89)  all_52_20 = all_14_1
% 173.46/26.50    (90)   ~ (all_52_17 = all_52_19)
% 173.46/26.50    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.50    (92)  all_52_30 = all_6_1
% 173.46/26.50    (93)  op(e1, all_14_2) = all_14_1
% 173.46/26.50    (94)  all_58_9 = all_52_7
% 173.46/26.50    (95)   ~ (e2 = e0)
% 173.46/26.50    (96)  all_58_12 = all_52_25
% 173.46/26.50    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.50    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.50    (99)   ~ (e3 = e2)
% 173.46/26.50    (100)   ~ (all_52_19 = all_14_2)
% 173.46/26.50    (101)  op(e2, e3) = all_52_9
% 173.46/26.50  
% 173.46/26.50  Begin of proof
% 173.46/26.50  | 
% 173.46/26.50  | BETA: splitting (28) gives:
% 173.46/26.50  | 
% 173.46/26.50  | Case 1:
% 173.46/26.50  | | 
% 173.46/26.50  | |   (102)   ~ (all_42_1 = e2)
% 173.46/26.50  | | 
% 173.46/26.50  | | REDUCE: (4), (102) imply:
% 173.46/26.50  | |   (103)  $false
% 173.46/26.50  | | 
% 173.46/26.50  | | CLOSE: (103) is inconsistent.
% 173.46/26.50  | | 
% 173.46/26.50  | Case 2:
% 173.46/26.50  | | 
% 173.46/26.50  | |   (104)   ~ (all_42_2 = e0)
% 173.46/26.50  | | 
% 173.46/26.50  | | REDUCE: (86), (104) imply:
% 173.46/26.50  | |   (105)   ~ (all_4_2 = e0)
% 173.46/26.50  | | 
% 173.46/26.50  | | BETA: splitting (80) gives:
% 173.46/26.50  | | 
% 173.46/26.50  | | Case 1:
% 173.46/26.50  | | | 
% 173.46/26.50  | | |   (106)  all_58_15 = e0
% 173.46/26.51  | | | 
% 173.46/26.51  | | | REF_CLOSE: (9), (17), (35), (46), (63), (82), (106) are inconsistent by
% 173.46/26.51  | | |            sub-proof #143.
% 173.46/26.51  | | | 
% 173.46/26.51  | | Case 2:
% 173.46/26.51  | | | 
% 173.46/26.51  | | |   (107)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 173.46/26.51  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.51  | | | 
% 173.46/26.51  | | | ALPHA: (107) implies:
% 173.46/26.51  | | |   (108)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.51  | | | 
% 173.46/26.51  | | | BETA: splitting (83) gives:
% 173.46/26.51  | | | 
% 173.46/26.51  | | | Case 1:
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | |   (109)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 173.46/26.51  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 173.46/26.51  | | | |            = e0)
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | | REF_CLOSE: (3), (5), (34), (48), (72), (82), (99), (109) are
% 173.46/26.51  | | | |            inconsistent by sub-proof #69.
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | Case 2:
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | |   (110)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 173.46/26.51  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.51  | | | |            all_52_30 = e0)
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 173.46/26.51  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 173.46/26.51  | | | |            (25), (26), (27), (29), (30), (31), (32), (33), (36), (37),
% 173.46/26.51  | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 173.46/26.51  | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 173.46/26.51  | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 173.46/26.51  | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 173.46/26.51  | | | |            (79), (81), (82), (84), (85), (87), (88), (89), (90), (91),
% 173.46/26.51  | | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 173.46/26.51  | | | |            (105), (108), (110) are inconsistent by sub-proof #3.
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | End of split
% 173.46/26.51  | | | 
% 173.46/26.51  | | End of split
% 173.46/26.51  | | 
% 173.46/26.51  | End of split
% 173.46/26.51  | 
% 173.46/26.51  End of proof
% 173.46/26.51  
% 173.46/26.51  Sub-proof #3 shows that the following formulas are inconsistent:
% 173.46/26.51  ----------------------------------------------------------------
% 173.46/26.51    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.51    (2)   ~ (all_52_17 = all_52_23)
% 173.46/26.51    (3)  op(e3, e2) = all_52_3
% 173.46/26.51    (4)   ~ (all_52_9 = all_52_25)
% 173.46/26.51    (5)  op(e1, e2) = all_52_19
% 173.46/26.51    (6)  op(all_6_1, all_6_2) = e1
% 173.46/26.51    (7)  all_58_5 = all_52_13
% 173.46/26.51    (8)   ~ (all_52_25 = all_52_29)
% 173.46/26.51    (9)  all_56_15 = all_6_2
% 173.46/26.51    (10)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.51    (11)  all_58_3 = all_10_2
% 173.46/26.51    (12)  all_56_9 = all_52_19
% 173.46/26.51    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.51    (14)  all_58_15 = all_6_2
% 173.46/26.51    (15)  op(e2, all_4_2) = e1
% 173.46/26.51    (16)   ~ (all_52_9 = all_4_2)
% 173.46/26.51    (17)   ~ (all_52_5 = all_52_7)
% 173.46/26.51    (18)  all_58_10 = all_52_15
% 173.46/26.51    (19)   ~ (all_52_5 = all_4_2)
% 173.46/26.51    (20)  all_58_7 = all_52_19
% 173.46/26.51    (21)   ~ (all_52_17 = all_52_25)
% 173.46/26.51    (22)  all_58_4 = all_52_5
% 173.46/26.51    (23)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.51    (24)   ~ (e3 = e1)
% 173.46/26.51    (25)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.51    (26)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.51    (27)   ~ (all_52_7 = all_4_2)
% 173.46/26.51    (28)  all_58_1 = all_52_3
% 173.46/26.51    (29)  all_58_0 = all_4_2
% 173.46/26.51    (30)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.51    (31)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.51    (32)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.51    (33)  all_58_14 = all_52_29
% 173.46/26.51    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.51    (35)  op(e2, e1) = all_52_13
% 173.46/26.51    (36)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.51    (37)  all_58_8 = all_14_2
% 173.46/26.51    (38)   ~ (all_52_5 = all_14_2)
% 173.46/26.51    (39)   ~ (all_52_3 = all_4_2)
% 173.46/26.51    (40)  op(e0, e3) = all_52_25
% 173.46/26.51    (41)  op(e0, all_6_2) = all_6_1
% 173.46/26.51    (42)  op(e3, all_52_17) = all_52_16
% 173.46/26.51    (43)   ~ (all_52_13 = all_14_2)
% 173.46/26.51    (44)   ~ (e3 = e0)
% 173.46/26.51    (45)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 173.46/26.51    (46)   ~ (all_52_9 = all_52_13)
% 173.46/26.51    (47)  op(e0, all_52_23) = all_52_22
% 173.46/26.51    (48)   ~ (all_52_15 = all_52_23)
% 173.46/26.51    (49)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.51    (50)  op(e1, e0) = all_52_23
% 173.46/26.51    (51)  all_58_13 = all_52_27
% 173.46/26.51    (52)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.51    (53)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 173.46/26.51    (54)   ~ (all_52_9 = all_52_17)
% 173.46/26.51    (55)  all_58_6 = all_52_17
% 173.46/26.51    (56)  op(e2, all_52_19) = all_52_18
% 173.46/26.51    (57)   ~ (e1 = e0)
% 173.46/26.51    (58)  all_56_0 = all_4_2
% 173.46/26.51    (59)  all_58_11 = all_52_23
% 173.46/26.51    (60)   ~ (all_52_3 = all_52_19)
% 173.46/26.51    (61)   ~ (all_52_7 = all_52_15)
% 173.46/26.51    (62)  op(e3, all_4_2) = e2
% 173.46/26.51    (63)   ~ (all_52_23 = all_6_2)
% 173.46/26.51    (64)  all_58_2 = all_52_9
% 173.46/26.51    (65)  op(e3, e1) = all_52_5
% 173.46/26.51    (66)   ~ (e2 = e1)
% 173.46/26.51    (67)  all_56_10 = all_14_2
% 173.46/26.51    (68)   ~ (all_52_25 = all_6_2)
% 173.46/26.51    (69)  op(e1, e3) = all_52_17
% 173.46/26.51    (70)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 173.46/26.51    (71)   ~ (all_52_25 = all_4_2)
% 173.46/26.51    (72)  op(e3, e0) = all_52_7
% 173.46/26.51    (73)  op(e3, e3) = all_4_2
% 173.46/26.51    (74)   ~ (all_52_17 = all_4_2)
% 173.46/26.51    (75)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.51    (76)   ~ (all_52_25 = all_52_27)
% 173.46/26.51    (77)   ~ (all_52_15 = all_10_2)
% 173.46/26.51    (78)  all_56_7 = all_52_15
% 173.46/26.51    (79)   ~ (all_4_2 = e0)
% 173.46/26.51    (80)   ~ (all_52_7 = all_52_23)
% 173.46/26.51    (81)  all_52_20 = all_14_1
% 173.46/26.51    (82)   ~ (all_52_17 = all_52_19)
% 173.46/26.51    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.51    (84)  all_52_30 = all_6_1
% 173.46/26.51    (85)  op(e1, all_14_2) = all_14_1
% 173.46/26.51    (86)  all_58_9 = all_52_7
% 173.46/26.51    (87)   ~ (e2 = e0)
% 173.46/26.51    (88)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.51          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.51    (89)  all_58_12 = all_52_25
% 173.46/26.51    (90)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.51    (91)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.51    (92)   ~ (e3 = e2)
% 173.46/26.51    (93)   ~ (all_52_19 = all_14_2)
% 173.46/26.51    (94)  op(e2, e3) = all_52_9
% 173.46/26.51  
% 173.46/26.51  Begin of proof
% 173.46/26.51  | 
% 173.46/26.51  | BETA: splitting (88) gives:
% 173.46/26.51  | 
% 173.46/26.51  | Case 1:
% 173.46/26.51  | | 
% 173.46/26.51  | |   (95)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 173.46/26.51  | | 
% 173.46/26.51  | | ALPHA: (95) implies:
% 173.46/26.51  | |   (96)  all_52_22 = e0
% 173.46/26.51  | |   (97)  all_52_20 = e1
% 173.46/26.51  | |   (98)  all_52_18 = e2
% 173.46/26.51  | |   (99)  all_52_16 = e3
% 173.46/26.51  | | 
% 173.46/26.51  | | COMBINE_EQS: (81), (97) imply:
% 173.46/26.51  | |   (100)  all_14_1 = e1
% 173.46/26.51  | | 
% 173.46/26.51  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 173.46/26.51  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 173.46/26.51  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 173.46/26.51  | |            (36), (37), (38), (39), (40), (42), (43), (44), (45), (46), (47),
% 173.46/26.51  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 173.46/26.51  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 173.46/26.51  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 173.46/26.51  | |            (82), (83), (85), (86), (87), (89), (90), (91), (92), (93), (94),
% 173.46/26.51  | |            (96), (98), (99), (100) are inconsistent by sub-proof #77.
% 173.46/26.51  | | 
% 173.46/26.51  | Case 2:
% 173.46/26.51  | | 
% 173.46/26.51  | |   (101)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 173.46/26.51  | | 
% 173.46/26.51  | | ALPHA: (101) implies:
% 173.46/26.51  | |   (102)  all_52_30 = e0
% 173.46/26.51  | | 
% 173.46/26.51  | | COMBINE_EQS: (84), (102) imply:
% 173.46/26.51  | |   (103)  all_6_1 = e0
% 173.46/26.51  | | 
% 173.46/26.51  | | REF_CLOSE: (6), (41), (57), (75), (103) are inconsistent by sub-proof #139.
% 173.46/26.51  | | 
% 173.46/26.51  | End of split
% 173.46/26.51  | 
% 173.46/26.51  End of proof
% 173.46/26.51  
% 173.46/26.51  Sub-proof #4 shows that the following formulas are inconsistent:
% 173.46/26.51  ----------------------------------------------------------------
% 173.46/26.51    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.51    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.51    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.51    (4)   ~ (all_52_27 = all_10_2)
% 173.46/26.51    (5)   ~ (all_52_17 = all_52_23)
% 173.46/26.51    (6)  op(e2, all_10_2) = all_10_1
% 173.46/26.51    (7)   ~ (all_52_13 = all_52_29)
% 173.46/26.51    (8)  all_42_1 = e2
% 173.46/26.51    (9)  all_56_3 = all_52_7
% 173.46/26.51    (10)  op(e3, e2) = all_52_3
% 173.46/26.51    (11)   ~ (all_52_9 = all_52_25)
% 173.46/26.51    (12)   ~ (all_52_19 = all_52_23)
% 173.46/26.51    (13)  all_56_11 = all_52_23
% 173.46/26.51    (14)  op(e1, e2) = all_52_19
% 173.46/26.51    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 173.46/26.51    (16)  op(e3, all_52_9) = all_52_8
% 173.46/26.51    (17)  op(all_6_1, all_6_2) = e1
% 173.46/26.51    (18)   ~ (all_52_3 = all_10_2)
% 173.46/26.51    (19)  all_58_5 = all_52_13
% 173.46/26.51    (20)   ~ (all_52_25 = all_52_29)
% 173.46/26.51    (21)  all_56_15 = all_6_2
% 173.46/26.51    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.51    (23)  all_58_3 = all_10_2
% 173.46/26.51    (24)  all_56_9 = all_52_19
% 173.46/26.51    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.51    (26)  all_58_15 = all_6_2
% 173.46/26.51    (27)  op(e2, all_4_2) = e1
% 173.46/26.51    (28)   ~ (all_52_9 = all_4_2)
% 173.46/26.51    (29)   ~ (all_52_5 = all_52_7)
% 173.46/26.51    (30)  all_58_10 = all_52_15
% 173.46/26.51    (31)   ~ (all_52_5 = all_4_2)
% 173.46/26.51    (32)  all_58_7 = all_52_19
% 173.46/26.51    (33)  all_56_4 = all_52_9
% 173.46/26.51    (34)   ~ (all_52_15 = all_6_2)
% 173.46/26.51    (35)   ~ (all_52_17 = all_52_25)
% 173.46/26.51    (36)  op(e0, e1) = all_52_29
% 173.46/26.51    (37)  all_58_4 = all_52_5
% 173.46/26.51    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.51    (39)   ~ (e3 = e1)
% 173.46/26.51    (40)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 173.46/26.51    (41)   ~ (all_52_27 = all_52_29)
% 173.46/26.51    (42)   ~ (all_52_17 = all_14_2)
% 173.46/26.51    (43)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.51    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.51    (45)   ~ (all_52_7 = all_4_2)
% 173.46/26.51    (46)  all_58_1 = all_52_3
% 173.46/26.51    (47)   ~ (all_52_13 = all_52_15)
% 173.46/26.51    (48)  all_58_0 = all_4_2
% 173.46/26.51    (49)  op(e1, all_52_13) = all_52_12
% 173.46/26.51    (50)  all_52_0 = e2
% 173.46/26.51    (51)  op(e0, e0) = all_6_2
% 173.46/26.51    (52)  op(e1, all_52_29) = all_52_28
% 173.46/26.51    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.51    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.51    (55)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 173.46/26.51    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.51    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.51    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.51    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 173.46/26.51    (60)  all_58_14 = all_52_29
% 173.46/26.51    (61)   ~ (all_52_3 = all_52_5)
% 173.46/26.51    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.51    (63)  op(e2, e1) = all_52_13
% 173.46/26.51    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.51    (65)  all_58_8 = all_14_2
% 173.46/26.51    (66)  all_56_1 = all_52_3
% 173.46/26.51    (67)  all_56_14 = all_52_29
% 173.46/26.51    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.51    (69)   ~ (all_52_5 = all_14_2)
% 173.46/26.51    (70)   ~ (all_52_3 = all_52_27)
% 173.46/26.51    (71)   ~ (all_52_3 = all_4_2)
% 173.46/26.51    (72)  op(e0, e3) = all_52_25
% 173.46/26.51    (73)  op(e0, all_6_2) = all_6_1
% 173.46/26.51    (74)  op(e3, all_52_17) = all_52_16
% 173.46/26.51    (75)  all_52_10 = all_10_1
% 173.46/26.51    (76)   ~ (all_52_13 = all_14_2)
% 173.46/26.51    (77)   ~ (e3 = e0)
% 173.46/26.51    (78)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 173.46/26.51    (79)   ~ (all_52_9 = all_52_13)
% 173.46/26.51    (80)  op(e0, all_52_23) = all_52_22
% 173.46/26.51    (81)   ~ (all_52_15 = all_52_23)
% 173.46/26.51    (82)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.51    (83)  op(all_10_1, all_10_2) = all_10_0
% 173.46/26.51    (84)  op(e1, e0) = all_52_23
% 173.46/26.51    (85)  all_58_13 = all_52_27
% 173.46/26.51    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.51    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 173.46/26.51    (88)   ~ (all_52_9 = all_52_17)
% 173.46/26.51    (89)  all_58_6 = all_52_17
% 173.46/26.51    (90)   ~ (all_52_3 = all_52_7)
% 173.46/26.51    (91)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.51    (92)  op(e2, all_52_19) = all_52_18
% 173.46/26.51    (93)   ~ (e1 = e0)
% 173.46/26.51    (94)  all_56_0 = all_4_2
% 173.46/26.51    (95)  all_58_11 = all_52_23
% 173.46/26.51    (96)   ~ (all_52_3 = all_52_19)
% 173.46/26.51    (97)   ~ (all_52_7 = all_52_15)
% 173.46/26.51    (98)  op(e0, all_52_15) = all_52_14
% 173.46/26.51    (99)   ~ (all_52_29 = all_14_2)
% 173.46/26.51    (100)   ~ (all_52_19 = all_10_2)
% 173.46/26.51    (101)  op(e3, all_4_2) = e2
% 173.46/26.51    (102)   ~ (all_52_23 = all_6_2)
% 173.46/26.51    (103)   ~ (all_52_29 = all_6_2)
% 173.46/26.51    (104)  all_58_2 = all_52_9
% 173.46/26.51    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.51    (106)  op(e3, e1) = all_52_5
% 173.46/26.51    (107)   ~ (e2 = e1)
% 173.46/26.51    (108)  all_56_10 = all_14_2
% 173.46/26.51    (109)   ~ (all_52_25 = all_6_2)
% 173.46/26.51    (110)  op(e1, e1) = all_14_2
% 173.46/26.51    (111)  op(e1, e3) = all_52_17
% 173.46/26.51    (112)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 173.46/26.51    (113)   ~ (all_52_25 = all_4_2)
% 173.46/26.51    (114)  op(e3, e0) = all_52_7
% 173.46/26.51    (115)  op(e3, e3) = all_4_2
% 173.46/26.51    (116)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.51             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 173.46/26.51    (117)  all_56_8 = all_52_17
% 173.46/26.51    (118)   ~ (all_52_17 = all_4_2)
% 173.46/26.51    (119)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.51             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.51    (120)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.51           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 173.46/26.51           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.51           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.51    (121)   ~ (all_52_25 = all_52_27)
% 173.46/26.51    (122)   ~ (all_52_27 = all_6_2)
% 173.46/26.51    (123)   ~ (all_52_7 = all_6_2)
% 173.46/26.51    (124)   ~ (all_10_0 = e3)
% 173.46/26.51    (125)   ~ (all_52_15 = all_10_2)
% 173.46/26.51    (126)  all_42_2 = all_4_2
% 173.46/26.51    (127)  all_56_7 = all_52_15
% 173.46/26.51    (128)   ~ (all_52_7 = all_52_23)
% 173.46/26.51    (129)   ~ (all_52_13 = all_10_2)
% 173.46/26.51    (130)  op(e2, all_52_27) = all_52_26
% 173.46/26.51    (131)  all_52_20 = all_14_1
% 173.46/26.51    (132)   ~ (all_52_17 = all_52_19)
% 173.46/26.51    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.51    (134)  all_52_30 = all_6_1
% 173.46/26.51    (135)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.51    (136)  op(e1, all_14_2) = all_14_1
% 173.46/26.51    (137)  all_58_9 = all_52_7
% 173.46/26.51    (138)   ~ (e2 = e0)
% 173.46/26.51    (139)  all_58_12 = all_52_25
% 173.46/26.51    (140)   ~ (all_10_0 = e1)
% 173.46/26.51    (141)  all_56_6 = all_52_13
% 173.46/26.51    (142)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.51    (143)   ~ (all_52_9 = all_52_15)
% 173.46/26.51    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.51    (145)   ~ (e3 = e2)
% 173.46/26.51    (146)   ~ (all_52_19 = all_14_2)
% 173.46/26.51    (147)  op(e2, e3) = all_52_9
% 173.46/26.51  
% 173.46/26.51  Begin of proof
% 173.46/26.51  | 
% 173.46/26.51  | BETA: splitting (40) gives:
% 173.46/26.51  | 
% 173.46/26.51  | Case 1:
% 173.46/26.51  | | 
% 173.46/26.51  | |   (148)   ~ (all_42_1 = e2)
% 173.46/26.51  | | 
% 173.46/26.51  | | REDUCE: (8), (148) imply:
% 173.46/26.51  | |   (149)  $false
% 173.46/26.51  | | 
% 173.46/26.51  | | CLOSE: (149) is inconsistent.
% 173.46/26.51  | | 
% 173.46/26.51  | Case 2:
% 173.46/26.51  | | 
% 173.46/26.51  | |   (150)   ~ (all_42_2 = e0)
% 173.46/26.51  | | 
% 173.46/26.51  | | REDUCE: (126), (150) imply:
% 173.46/26.51  | |   (151)   ~ (all_4_2 = e0)
% 173.46/26.51  | | 
% 173.46/26.51  | | BETA: splitting (116) gives:
% 173.46/26.51  | | 
% 173.46/26.51  | | Case 1:
% 173.46/26.51  | | | 
% 173.46/26.51  | | |   (152)  all_58_15 = e0
% 173.46/26.51  | | | 
% 173.46/26.51  | | | REF_CLOSE: (17), (26), (51), (73), (93), (119), (152) are inconsistent by
% 173.46/26.51  | | |            sub-proof #143.
% 173.46/26.51  | | | 
% 173.46/26.51  | | Case 2:
% 173.46/26.51  | | | 
% 173.46/26.51  | | |   (153)   ~ (all_58_15 = e0)
% 173.46/26.51  | | |   (154)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 173.46/26.51  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.51  | | | 
% 173.46/26.51  | | | ALPHA: (154) implies:
% 173.46/26.51  | | |   (155)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.51  | | | 
% 173.46/26.51  | | | REDUCE: (26), (153) imply:
% 173.46/26.51  | | |   (156)   ~ (all_6_2 = e0)
% 173.46/26.51  | | | 
% 173.46/26.51  | | | BETA: splitting (120) gives:
% 173.46/26.51  | | | 
% 173.46/26.51  | | | Case 1:
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | |   (157)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 173.46/26.51  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 173.46/26.51  | | | |            = e0)
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 173.46/26.51  | | | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23),
% 173.46/26.51  | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 173.46/26.51  | | | |            (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 173.46/26.51  | | | |            (45), (46), (47), (48), (49), (50), (52), (53), (54), (55),
% 173.46/26.51  | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 173.46/26.51  | | | |            (66), (67), (68), (70), (71), (72), (73), (74), (75), (76),
% 173.46/26.51  | | | |            (77), (79), (80), (82), (83), (85), (86), (88), (89), (90),
% 173.46/26.51  | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 173.46/26.51  | | | |            (101), (102), (103), (104), (105), (106), (108), (109),
% 173.46/26.51  | | | |            (110), (111), (113), (114), (115), (117), (118), (119),
% 173.46/26.51  | | | |            (121), (122), (123), (124), (128), (129), (130), (132),
% 173.46/26.51  | | | |            (133), (135), (136), (137), (139), (140), (141), (143),
% 173.46/26.51  | | | |            (144), (145), (146), (147), (155), (156), (157) are
% 173.46/26.51  | | | |            inconsistent by sub-proof #82.
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | Case 2:
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | |   (158)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 173.46/26.51  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 173.46/26.51  | | | |            all_52_30 = e0)
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | | BETA: splitting (158) gives:
% 173.46/26.51  | | | | 
% 173.46/26.51  | | | | Case 1:
% 173.46/26.51  | | | | | 
% 173.46/26.51  | | | | |   (159)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 173.46/26.51  | | | | |          = e0
% 173.46/26.51  | | | | | 
% 173.46/26.52  | | | | | REF_CLOSE: (1), (5), (10), (11), (14), (19), (20), (21), (22), (23),
% 173.46/26.52  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (35),
% 173.46/26.52  | | | | |            (37), (38), (39), (43), (44), (45), (46), (48), (54), (57),
% 173.46/26.52  | | | | |            (60), (62), (63), (64), (65), (69), (71), (72), (74), (76),
% 173.46/26.52  | | | | |            (77), (78), (79), (80), (81), (82), (84), (85), (86), (87),
% 173.46/26.52  | | | | |            (88), (89), (92), (93), (94), (95), (96), (97), (101),
% 173.46/26.52  | | | | |            (102), (104), (106), (107), (108), (109), (111), (112),
% 173.46/26.52  | | | | |            (113), (114), (115), (118), (119), (121), (125), (127),
% 173.46/26.52  | | | | |            (128), (131), (132), (133), (136), (137), (138), (139),
% 173.46/26.52  | | | | |            (142), (144), (145), (146), (147), (151), (155), (159) are
% 173.46/26.52  | | | | |            inconsistent by sub-proof #66.
% 173.46/26.52  | | | | | 
% 173.46/26.52  | | | | Case 2:
% 173.46/26.52  | | | | | 
% 173.46/26.52  | | | | |   (160)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 173.46/26.52  | | | | |          = e0
% 173.46/26.52  | | | | | 
% 173.46/26.52  | | | | | REF_CLOSE: (17), (73), (93), (119), (134), (160) are inconsistent by
% 173.46/26.52  | | | | |            sub-proof #138.
% 173.46/26.52  | | | | | 
% 173.46/26.52  | | | | End of split
% 173.46/26.52  | | | | 
% 173.46/26.52  | | | End of split
% 173.46/26.52  | | | 
% 173.46/26.52  | | End of split
% 173.46/26.52  | | 
% 173.46/26.52  | End of split
% 173.46/26.52  | 
% 173.46/26.52  End of proof
% 173.46/26.52  
% 173.46/26.52  Sub-proof #5 shows that the following formulas are inconsistent:
% 173.46/26.52  ----------------------------------------------------------------
% 173.46/26.52    (1)  op(e2, all_10_2) = all_10_1
% 173.46/26.52    (2)  all_52_0 = e2
% 173.46/26.52    (3)  op(e0, all_6_2) = all_6_1
% 173.46/26.52    (4)  op(all_6_1, all_6_2) = e2
% 173.46/26.52    (5)  all_52_10 = all_10_1
% 173.46/26.52    (6)  all_52_20 = e2
% 173.46/26.52    (7)  op(all_10_1, all_10_2) = e3
% 173.46/26.52    (8)   ~ (e2 = e1)
% 173.46/26.52    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.52    (10)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.52          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 173.46/26.52          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.52          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.52    (11)  all_52_30 = all_6_1
% 173.46/26.52    (12)   ~ (e2 = e0)
% 173.46/26.52    (13)   ~ (e3 = e2)
% 173.46/26.52  
% 173.46/26.52  Begin of proof
% 173.46/26.52  | 
% 173.46/26.52  | BETA: splitting (10) gives:
% 173.46/26.52  | 
% 173.46/26.52  | Case 1:
% 173.46/26.52  | | 
% 173.46/26.52  | |   (14)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.52  | |         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.52  | | 
% 173.46/26.52  | | REF_CLOSE: (1), (2), (5), (7), (9), (13), (14) are inconsistent by sub-proof
% 173.46/26.52  | |            #33.
% 173.46/26.52  | | 
% 173.46/26.52  | Case 2:
% 173.46/26.52  | | 
% 173.46/26.52  | |   (15)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 173.46/26.52  | |         | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 173.46/26.52  | |           e0)
% 173.46/26.52  | | 
% 173.46/26.52  | | BETA: splitting (15) gives:
% 173.46/26.52  | | 
% 173.46/26.52  | | Case 1:
% 173.46/26.52  | | | 
% 173.46/26.52  | | |   (16)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 173.46/26.52  | | | 
% 173.46/26.52  | | | REF_CLOSE: (6), (8), (16) are inconsistent by sub-proof #539.
% 173.46/26.52  | | | 
% 173.46/26.52  | | Case 2:
% 173.46/26.52  | | | 
% 173.46/26.52  | | |   (17)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 173.46/26.52  | | | 
% 173.46/26.52  | | | REF_CLOSE: (3), (4), (9), (11), (12), (17) are inconsistent by sub-proof
% 173.46/26.52  | | |            #200.
% 173.46/26.52  | | | 
% 173.46/26.52  | | End of split
% 173.46/26.52  | | 
% 173.46/26.52  | End of split
% 173.46/26.52  | 
% 173.46/26.52  End of proof
% 173.46/26.52  
% 173.46/26.52  Sub-proof #6 shows that the following formulas are inconsistent:
% 173.46/26.52  ----------------------------------------------------------------
% 173.46/26.52    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.52    (2)   ~ (all_52_17 = all_52_23)
% 173.46/26.52    (3)  op(e3, e2) = all_52_3
% 173.46/26.52    (4)   ~ (all_52_9 = all_52_25)
% 173.46/26.52    (5)  op(e1, e2) = all_52_19
% 173.46/26.52    (6)  all_16_1 = all_6_1
% 173.46/26.52    (7)  all_58_5 = all_52_13
% 173.46/26.52    (8)   ~ (all_52_25 = all_52_29)
% 173.46/26.52    (9)  all_16_2 = all_6_2
% 173.46/26.52    (10)  all_56_15 = all_6_2
% 173.46/26.52    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.52    (12)  all_58_3 = all_10_2
% 173.46/26.52    (13)  all_56_9 = all_52_19
% 173.46/26.52    (14)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.52    (15)  all_58_15 = all_6_2
% 173.46/26.52    (16)  op(e2, all_4_2) = e1
% 173.46/26.52    (17)   ~ (all_52_9 = all_4_2)
% 173.46/26.52    (18)   ~ (all_52_5 = all_52_7)
% 173.46/26.52    (19)  all_58_10 = all_52_15
% 173.46/26.52    (20)   ~ (all_52_5 = all_4_2)
% 173.46/26.52    (21)  all_58_7 = all_52_19
% 173.46/26.52    (22)   ~ (all_52_17 = all_52_25)
% 173.46/26.52    (23)  all_58_4 = all_52_5
% 173.46/26.52    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.52    (25)   ~ (e3 = e1)
% 173.46/26.52    (26)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.52    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.52    (28)   ~ (all_52_7 = all_4_2)
% 173.46/26.52    (29)  all_58_1 = all_52_3
% 173.46/26.52    (30)  all_58_0 = all_4_2
% 173.46/26.52    (31)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.52    (32)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.52    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.52    (34)  all_58_14 = all_52_29
% 173.46/26.52    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.52    (36)  op(e2, e1) = all_52_13
% 173.46/26.52    (37)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.52    (38)  all_58_8 = all_14_2
% 173.46/26.52    (39)   ~ (all_52_5 = all_14_2)
% 173.46/26.52    (40)   ~ (all_52_3 = all_4_2)
% 173.46/26.52    (41)  op(e0, e3) = all_52_25
% 173.46/26.52    (42)  op(e0, all_6_2) = all_6_1
% 173.46/26.52    (43)  op(all_6_1, all_6_2) = e2
% 173.46/26.52    (44)   ~ (all_52_13 = all_14_2)
% 173.46/26.52    (45)   ~ (e3 = e0)
% 173.46/26.52    (46)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 173.46/26.52    (47)   ~ (all_52_9 = all_52_13)
% 173.46/26.52    (48)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.52    (49)   ~ (all_52_15 = all_52_23)
% 173.46/26.52    (50)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.52    (51)  op(e1, e0) = all_52_23
% 173.46/26.52    (52)  all_56_12 = all_52_25
% 173.46/26.52    (53)  all_58_13 = all_52_27
% 173.46/26.52    (54)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.52    (55)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 173.46/26.52    (56)   ~ (all_52_9 = all_52_17)
% 173.46/26.52    (57)  all_58_6 = all_52_17
% 173.46/26.52    (58)  op(e2, all_52_19) = e2
% 173.46/26.52    (59)  op(e3, all_52_17) = e3
% 173.46/26.52    (60)   ~ (e1 = e0)
% 173.46/26.52    (61)  all_56_0 = all_4_2
% 173.46/26.52    (62)  all_58_11 = all_52_23
% 173.46/26.52    (63)   ~ (all_52_3 = all_52_19)
% 173.46/26.52    (64)   ~ (all_52_7 = all_52_15)
% 173.46/26.52    (65)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.52    (66)  op(e3, all_4_2) = e2
% 173.46/26.52    (67)  all_58_2 = all_52_9
% 173.46/26.52    (68)  op(e3, e1) = all_52_5
% 173.46/26.52    (69)   ~ (e2 = e1)
% 173.46/26.52    (70)  all_56_10 = all_14_2
% 173.46/26.52    (71)   ~ (all_52_25 = all_6_2)
% 173.46/26.52    (72)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.52    (73)  op(e1, e3) = all_52_17
% 173.46/26.52    (74)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 173.46/26.52    (75)   ~ (all_52_25 = all_4_2)
% 173.46/26.52    (76)  op(e3, e0) = all_52_7
% 173.46/26.52    (77)  op(e3, e3) = all_4_2
% 173.46/26.52    (78)   ~ (all_52_17 = all_4_2)
% 173.46/26.52    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.52    (80)   ~ (all_52_25 = all_52_27)
% 173.46/26.52    (81)  op(e0, all_52_23) = e0
% 173.46/26.52    (82)   ~ (all_52_15 = all_10_2)
% 173.46/26.52    (83)  all_56_7 = all_52_15
% 173.46/26.52    (84)  op(e1, all_14_2) = e1
% 173.46/26.52    (85)   ~ (all_4_2 = e0)
% 173.46/26.52    (86)   ~ (all_52_7 = all_52_23)
% 173.46/26.52    (87)   ~ (all_52_17 = all_52_19)
% 173.46/26.52    (88)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.52    (89)  all_58_9 = all_52_7
% 173.46/26.52    (90)   ~ (e2 = e0)
% 173.46/26.52    (91)  all_58_12 = all_52_25
% 173.46/26.52    (92)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.52    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.52    (94)   ~ (e3 = e2)
% 173.46/26.52    (95)   ~ (all_52_19 = all_14_2)
% 173.46/26.52    (96)  op(e2, e3) = all_52_9
% 173.46/26.52  
% 173.46/26.52  Begin of proof
% 173.46/26.52  | 
% 173.46/26.52  | BETA: splitting (14) gives:
% 173.46/26.52  | 
% 173.46/26.52  | Case 1:
% 173.46/26.52  | | 
% 173.46/26.52  | |   (97)  all_56_0 = e3
% 173.46/26.52  | | 
% 173.46/26.52  | | COMBINE_EQS: (61), (97) imply:
% 173.46/26.52  | |   (98)  all_4_2 = e3
% 173.46/26.52  | | 
% 173.46/26.52  | | REF_CLOSE: (66), (77), (79), (94), (98) are inconsistent by sub-proof #106.
% 173.46/26.52  | | 
% 173.46/26.52  | Case 2:
% 173.46/26.52  | | 
% 173.46/26.52  | |   (99)   ~ (all_56_0 = e3)
% 173.46/26.52  | |   (100)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.52  | | 
% 173.46/26.52  | | REDUCE: (61), (99) imply:
% 173.46/26.52  | |   (101)   ~ (all_4_2 = e3)
% 173.46/26.52  | | 
% 173.46/26.52  | | BETA: splitting (26) gives:
% 173.46/26.52  | | 
% 173.46/26.52  | | Case 1:
% 173.46/26.52  | | | 
% 173.46/26.52  | | |   (102)  all_56_15 = e3
% 173.46/26.52  | | | 
% 173.46/26.52  | | | COMBINE_EQS: (10), (102) imply:
% 173.46/26.52  | | |   (103)  all_6_2 = e3
% 173.46/26.52  | | | 
% 173.46/26.52  | | | SIMP: (103) implies:
% 173.46/26.52  | | |   (104)  all_6_2 = e3
% 173.46/26.52  | | | 
% 173.46/26.52  | | | REF_CLOSE: (4), (6), (9), (41), (42), (43), (48), (52), (65), (71), (72),
% 173.46/26.52  | | |            (79), (91), (96), (104) are inconsistent by sub-proof #226.
% 173.46/26.52  | | | 
% 173.46/26.52  | | Case 2:
% 173.46/26.52  | | | 
% 173.46/26.52  | | |   (105)   ~ (all_56_15 = e3)
% 173.46/26.52  | | | 
% 173.46/26.52  | | | REDUCE: (10), (105) imply:
% 173.46/26.52  | | |   (106)   ~ (all_6_2 = e3)
% 173.46/26.52  | | | 
% 173.46/26.52  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (12), (13), (15),
% 173.46/26.52  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 173.46/26.52  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 173.46/26.52  | | |            (37), (38), (39), (40), (41), (44), (45), (46), (47), (49),
% 173.46/26.52  | | |            (50), (51), (53), (54), (55), (56), (57), (58), (59), (60),
% 173.46/26.52  | | |            (61), (62), (63), (64), (66), (67), (68), (69), (70), (73),
% 173.46/26.52  | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 173.46/26.52  | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 173.46/26.52  | | |            (94), (95), (96), (100), (101), (106) are inconsistent by
% 173.46/26.52  | | |            sub-proof #79.
% 173.46/26.52  | | | 
% 173.46/26.52  | | End of split
% 173.46/26.52  | | 
% 173.46/26.52  | End of split
% 173.46/26.52  | 
% 173.46/26.52  End of proof
% 173.46/26.52  
% 173.46/26.52  Sub-proof #7 shows that the following formulas are inconsistent:
% 173.46/26.52  ----------------------------------------------------------------
% 173.46/26.52    (1)  op(e2, all_10_2) = all_10_1
% 173.46/26.52    (2)  op(all_10_1, all_10_2) = e1
% 173.46/26.52    (3)  all_52_0 = e2
% 173.46/26.52    (4)  op(e0, all_6_2) = all_6_1
% 173.46/26.52    (5)  op(all_6_1, all_6_2) = e2
% 173.46/26.52    (6)  all_52_10 = all_10_1
% 173.46/26.52    (7)  all_52_20 = e2
% 173.46/26.52    (8)   ~ (e2 = e1)
% 173.46/26.52    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.52    (10)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.52          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 173.46/26.52          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.52          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.52    (11)  all_52_30 = all_6_1
% 173.46/26.52    (12)   ~ (e2 = e0)
% 173.46/26.52    (13)   ~ (e3 = e2)
% 173.46/26.52  
% 173.46/26.52  Begin of proof
% 173.46/26.52  | 
% 173.46/26.52  | BETA: splitting (10) gives:
% 173.46/26.52  | 
% 173.46/26.52  | Case 1:
% 173.46/26.52  | | 
% 173.46/26.52  | |   (14)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.52  | |         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.52  | | 
% 173.46/26.52  | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (13), (14) are inconsistent by
% 173.46/26.52  | |            sub-proof #69.
% 173.46/26.52  | | 
% 173.46/26.52  | Case 2:
% 173.46/26.52  | | 
% 173.46/26.52  | |   (15)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 173.46/26.52  | |         | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 173.46/26.52  | |           e0)
% 173.46/26.52  | | 
% 173.46/26.52  | | BETA: splitting (15) gives:
% 173.46/26.52  | | 
% 173.46/26.52  | | Case 1:
% 173.46/26.52  | | | 
% 173.46/26.52  | | |   (16)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 173.46/26.52  | | | 
% 173.46/26.52  | | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #539.
% 173.46/26.52  | | | 
% 173.46/26.52  | | Case 2:
% 173.46/26.52  | | | 
% 173.46/26.52  | | |   (17)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 173.46/26.52  | | | 
% 173.46/26.52  | | | REF_CLOSE: (4), (5), (9), (11), (12), (17) are inconsistent by sub-proof
% 173.46/26.52  | | |            #200.
% 173.46/26.52  | | | 
% 173.46/26.52  | | End of split
% 173.46/26.52  | | 
% 173.46/26.52  | End of split
% 173.46/26.52  | 
% 173.46/26.52  End of proof
% 173.46/26.52  
% 173.46/26.52  Sub-proof #8 shows that the following formulas are inconsistent:
% 173.46/26.52  ----------------------------------------------------------------
% 173.46/26.52    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.52    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.52    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.52    (4)   ~ (all_52_27 = all_10_2)
% 173.46/26.52    (5)   ~ (all_52_17 = all_52_23)
% 173.46/26.52    (6)  op(e2, all_10_2) = all_10_1
% 173.46/26.52    (7)   ~ (all_52_13 = all_52_29)
% 173.46/26.52    (8)  all_56_3 = all_52_7
% 173.46/26.52    (9)  op(e3, e2) = all_52_3
% 173.46/26.52    (10)   ~ (all_52_9 = all_52_25)
% 173.46/26.52    (11)   ~ (all_52_19 = all_52_23)
% 173.46/26.52    (12)  all_56_11 = all_52_23
% 173.46/26.52    (13)  op(e1, e2) = all_52_19
% 173.46/26.52    (14)  all_16_1 = all_6_1
% 173.46/26.52    (15)  op(e3, all_52_9) = all_52_8
% 173.46/26.52    (16)   ~ (all_52_3 = all_10_2)
% 173.46/26.52    (17)  all_58_5 = all_52_13
% 173.46/26.52    (18)   ~ (all_52_25 = all_52_29)
% 173.46/26.52    (19)  all_16_2 = all_6_2
% 173.46/26.52    (20)  all_56_15 = all_6_2
% 173.46/26.52    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.52    (22)  all_58_3 = all_10_2
% 173.46/26.52    (23)  all_56_9 = all_52_19
% 173.46/26.52    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.52    (25)  all_58_15 = all_6_2
% 173.46/26.52    (26)  op(e2, all_4_2) = e1
% 173.46/26.52    (27)   ~ (all_52_9 = all_4_2)
% 173.46/26.52    (28)   ~ (all_52_5 = all_52_7)
% 173.46/26.52    (29)  all_58_10 = all_52_15
% 173.46/26.52    (30)   ~ (all_52_5 = all_4_2)
% 173.46/26.52    (31)  all_58_7 = all_52_19
% 173.46/26.52    (32)  all_56_4 = all_52_9
% 173.46/26.52    (33)   ~ (all_52_17 = all_52_25)
% 173.46/26.52    (34)  all_58_4 = all_52_5
% 173.46/26.52    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.52    (36)   ~ (e3 = e1)
% 173.46/26.52    (37)   ~ (all_52_27 = all_52_29)
% 173.46/26.52    (38)   ~ (all_52_17 = all_14_2)
% 173.46/26.52    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.52    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.52    (41)   ~ (all_52_7 = all_4_2)
% 173.46/26.52    (42)  all_58_1 = all_52_3
% 173.46/26.52    (43)   ~ (all_52_13 = all_52_15)
% 173.46/26.52    (44)  all_58_0 = all_4_2
% 173.46/26.52    (45)  op(e1, all_52_13) = all_52_12
% 173.46/26.52    (46)  all_52_0 = e2
% 173.46/26.52    (47)  op(e0, e0) = all_6_2
% 173.46/26.52    (48)  op(e1, all_52_29) = all_52_28
% 173.46/26.52    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.52    (50)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.52    (51)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 173.46/26.52    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.52    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.52    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.52    (55)  all_58_14 = all_52_29
% 173.46/26.52    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 173.46/26.52    (57)   ~ (all_52_3 = all_52_5)
% 173.46/26.52    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.52    (59)  op(e2, e1) = all_52_13
% 173.46/26.52    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.52    (61)  all_58_8 = all_14_2
% 173.46/26.52    (62)  all_56_1 = all_52_3
% 173.46/26.52    (63)  op(e0, e2) = all_52_27
% 173.46/26.52    (64)  all_56_14 = all_52_29
% 173.46/26.52    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.52    (66)   ~ (all_52_3 = all_52_27)
% 173.46/26.52    (67)   ~ (all_52_3 = all_4_2)
% 173.46/26.52    (68)  op(e0, e3) = all_52_25
% 173.46/26.52    (69)  op(e0, all_6_2) = all_6_1
% 173.46/26.52    (70)  op(all_6_1, all_6_2) = e2
% 173.46/26.52    (71)  op(e3, all_52_17) = all_52_16
% 173.46/26.52    (72)  all_52_10 = all_10_1
% 173.46/26.52    (73)  all_52_20 = e2
% 173.46/26.52    (74)   ~ (all_52_13 = all_14_2)
% 173.46/26.52    (75)   ~ (e3 = e0)
% 173.46/26.52    (76)   ~ (all_52_9 = all_52_13)
% 173.46/26.52    (77)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.52    (78)  op(e0, all_52_23) = all_52_22
% 173.46/26.52    (79)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.52    (80)  op(all_10_1, all_10_2) = all_10_0
% 173.46/26.52    (81)  all_56_12 = all_52_25
% 173.46/26.52    (82)  all_58_13 = all_52_27
% 173.46/26.52    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.52    (84)   ~ (all_52_9 = all_52_17)
% 173.46/26.52    (85)  all_58_6 = all_52_17
% 173.46/26.52    (86)   ~ (all_52_3 = all_52_7)
% 173.46/26.52    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.52    (88)  op(e2, all_52_19) = all_52_18
% 173.46/26.52    (89)   ~ (e1 = e0)
% 173.46/26.52    (90)  all_56_0 = all_4_2
% 173.46/26.52    (91)  all_58_11 = all_52_23
% 173.46/26.52    (92)   ~ (all_52_3 = all_52_19)
% 173.46/26.52    (93)   ~ (all_52_7 = all_52_15)
% 173.46/26.52    (94)  op(e0, all_52_15) = all_52_14
% 173.46/26.52    (95)   ~ (all_52_29 = all_14_2)
% 173.46/26.52    (96)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.52    (97)   ~ (all_52_19 = all_10_2)
% 173.46/26.52    (98)  op(e3, all_4_2) = e2
% 173.46/26.52    (99)   ~ (all_52_23 = all_6_2)
% 173.46/26.52    (100)   ~ (all_52_29 = all_6_2)
% 173.46/26.52    (101)  all_58_2 = all_52_9
% 173.46/26.52    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.52    (103)  op(e3, e1) = all_52_5
% 173.46/26.52    (104)   ~ (e2 = e1)
% 173.46/26.52    (105)  all_56_10 = all_14_2
% 173.46/26.52    (106)   ~ (all_52_25 = all_6_2)
% 173.46/26.52    (107)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.52    (108)  op(e1, e1) = all_14_2
% 173.46/26.52    (109)  op(e1, e3) = all_52_17
% 173.46/26.52    (110)   ~ (all_52_25 = all_4_2)
% 173.46/26.52    (111)  op(e3, e0) = all_52_7
% 173.46/26.52    (112)  op(e3, e3) = all_4_2
% 173.46/26.52    (113)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.52             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 173.46/26.52    (114)  all_56_8 = all_52_17
% 173.46/26.52    (115)   ~ (all_52_17 = all_4_2)
% 173.46/26.53    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.53             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.53    (117)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.53           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 173.46/26.53           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.53           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.53    (118)   ~ (all_52_25 = all_52_27)
% 173.46/26.53    (119)   ~ (all_52_27 = all_6_2)
% 173.46/26.53    (120)   ~ (all_52_7 = all_6_2)
% 173.46/26.53    (121)   ~ (all_10_0 = e3)
% 173.46/26.53    (122)   ~ (all_52_7 = all_52_23)
% 173.46/26.53    (123)   ~ (all_52_13 = all_10_2)
% 173.46/26.53    (124)  op(e2, all_52_27) = all_52_26
% 173.46/26.53    (125)   ~ (all_52_17 = all_52_19)
% 173.46/26.53    (126)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.53    (127)  all_52_30 = all_6_1
% 173.46/26.53    (128)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.53    (129)  op(e1, all_14_2) = all_14_1
% 173.46/26.53    (130)  all_58_9 = all_52_7
% 173.46/26.53    (131)   ~ (e2 = e0)
% 173.46/26.53    (132)  all_58_12 = all_52_25
% 173.46/26.53    (133)   ~ (all_10_0 = e1)
% 173.46/26.53    (134)  all_56_6 = all_52_13
% 173.46/26.53    (135)   ~ (all_52_9 = all_52_15)
% 173.46/26.53    (136)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.53    (137)   ~ (e3 = e2)
% 173.46/26.53    (138)   ~ (all_52_19 = all_14_2)
% 173.46/26.53    (139)  op(e2, e3) = all_52_9
% 173.46/26.53    (140)  all_56_13 = all_52_27
% 173.46/26.53  
% 173.46/26.53  Begin of proof
% 173.46/26.53  | 
% 173.46/26.53  | BETA: splitting (117) gives:
% 173.46/26.53  | 
% 173.46/26.53  | Case 1:
% 173.46/26.53  | | 
% 173.46/26.53  | |   (141)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.53  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.53  | | 
% 173.46/26.53  | | BETA: splitting (141) gives:
% 173.46/26.53  | | 
% 173.46/26.53  | | Case 1:
% 173.46/26.53  | | | 
% 173.46/26.53  | | |   (142)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 173.46/26.53  | | | 
% 173.46/26.53  | | | REF_CLOSE: (46), (137), (142) are inconsistent by sub-proof #124.
% 173.46/26.53  | | | 
% 173.46/26.53  | | Case 2:
% 173.46/26.53  | | | 
% 173.46/26.53  | | |   (143)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 173.46/26.53  | | | 
% 173.46/26.53  | | | ALPHA: (143) implies:
% 173.46/26.53  | | |   (144)  all_52_14 = e0
% 173.46/26.53  | | |   (145)  all_52_12 = e1
% 173.46/26.53  | | |   (146)  all_52_10 = e2
% 173.46/26.53  | | |   (147)  all_52_8 = e3
% 173.46/26.53  | | | 
% 173.46/26.53  | | | COMBINE_EQS: (72), (146) imply:
% 173.46/26.53  | | |   (148)  all_10_1 = e2
% 173.46/26.53  | | | 
% 173.46/26.53  | | | REDUCE: (80), (148) imply:
% 173.46/26.53  | | |   (149)  op(e2, all_10_2) = all_10_0
% 173.46/26.53  | | | 
% 173.46/26.53  | | | REDUCE: (15), (147) imply:
% 173.46/26.53  | | |   (150)  op(e3, all_52_9) = e3
% 173.46/26.53  | | | 
% 173.46/26.53  | | | REDUCE: (6), (148) imply:
% 173.46/26.53  | | |   (151)  op(e2, all_10_2) = e2
% 173.46/26.53  | | | 
% 173.46/26.53  | | | REDUCE: (45), (145) imply:
% 173.46/26.53  | | |   (152)  op(e1, all_52_13) = e1
% 173.46/26.53  | | | 
% 173.46/26.53  | | | REDUCE: (94), (144) imply:
% 173.46/26.53  | | |   (153)  op(e0, all_52_15) = e0
% 173.46/26.53  | | | 
% 173.46/26.53  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 173.46/26.53  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 173.46/26.53  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 173.46/26.53  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 173.46/26.53  | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 173.46/26.53  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 173.46/26.53  | | |            (67), (68), (69), (70), (71), (74), (75), (76), (77), (78),
% 173.46/26.53  | | |            (79), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 173.46/26.53  | | |            (90), (91), (92), (93), (95), (96), (97), (98), (99), (100),
% 173.46/26.53  | | |            (101), (102), (103), (105), (106), (107), (108), (109), (110),
% 173.46/26.53  | | |            (111), (112), (113), (114), (115), (116), (118), (119), (120),
% 173.46/26.53  | | |            (121), (122), (123), (124), (125), (126), (128), (129), (130),
% 173.46/26.53  | | |            (131), (132), (133), (134), (135), (136), (138), (139), (140),
% 173.46/26.53  | | |            (149), (150), (151), (152), (153) are inconsistent by sub-proof
% 173.46/26.53  | | |            #9.
% 173.46/26.53  | | | 
% 173.46/26.53  | | End of split
% 173.46/26.53  | | 
% 173.46/26.53  | Case 2:
% 173.46/26.53  | | 
% 173.46/26.53  | |   (154)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 173.46/26.53  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 173.46/26.53  | |            e0)
% 173.46/26.53  | | 
% 173.46/26.53  | | REF_CLOSE: (69), (70), (73), (104), (116), (127), (131), (154) are
% 173.46/26.53  | |            inconsistent by sub-proof #187.
% 173.46/26.53  | | 
% 173.46/26.53  | End of split
% 173.46/26.53  | 
% 173.46/26.53  End of proof
% 173.46/26.53  
% 173.46/26.53  Sub-proof #9 shows that the following formulas are inconsistent:
% 173.46/26.53  ----------------------------------------------------------------
% 173.46/26.53    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.53    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.53    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.53    (4)   ~ (all_52_27 = all_10_2)
% 173.46/26.53    (5)   ~ (all_52_17 = all_52_23)
% 173.46/26.53    (6)   ~ (all_52_13 = all_52_29)
% 173.46/26.53    (7)  op(e2, all_10_2) = all_10_0
% 173.46/26.53    (8)  all_56_3 = all_52_7
% 173.46/26.53    (9)  op(e3, e2) = all_52_3
% 173.46/26.53    (10)   ~ (all_52_9 = all_52_25)
% 173.46/26.53    (11)   ~ (all_52_19 = all_52_23)
% 173.46/26.53    (12)  all_56_11 = all_52_23
% 173.46/26.53    (13)  op(e1, e2) = all_52_19
% 173.46/26.53    (14)  all_16_1 = all_6_1
% 173.46/26.53    (15)   ~ (all_52_3 = all_10_2)
% 173.46/26.53    (16)  all_58_5 = all_52_13
% 173.46/26.53    (17)   ~ (all_52_25 = all_52_29)
% 173.46/26.53    (18)  op(e1, all_52_13) = e1
% 173.46/26.53    (19)  op(e0, all_52_15) = e0
% 173.46/26.53    (20)  all_16_2 = all_6_2
% 173.46/26.53    (21)  all_56_15 = all_6_2
% 173.46/26.53    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.53    (23)  all_58_3 = all_10_2
% 173.46/26.53    (24)  all_56_9 = all_52_19
% 173.46/26.53    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.53    (26)  all_58_15 = all_6_2
% 173.46/26.53    (27)  op(e2, all_4_2) = e1
% 173.46/26.53    (28)   ~ (all_52_9 = all_4_2)
% 173.46/26.53    (29)   ~ (all_52_5 = all_52_7)
% 173.46/26.53    (30)  all_58_10 = all_52_15
% 173.46/26.53    (31)   ~ (all_52_5 = all_4_2)
% 173.46/26.53    (32)  all_58_7 = all_52_19
% 173.46/26.53    (33)  all_56_4 = all_52_9
% 173.46/26.53    (34)   ~ (all_52_17 = all_52_25)
% 173.46/26.53    (35)  all_58_4 = all_52_5
% 173.46/26.53    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.53    (37)   ~ (e3 = e1)
% 173.46/26.53    (38)   ~ (all_52_27 = all_52_29)
% 173.46/26.53    (39)   ~ (all_52_17 = all_14_2)
% 173.46/26.53    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.53    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.53    (42)   ~ (all_52_7 = all_4_2)
% 173.46/26.53    (43)  all_58_1 = all_52_3
% 173.46/26.53    (44)   ~ (all_52_13 = all_52_15)
% 173.46/26.53    (45)  all_58_0 = all_4_2
% 173.46/26.53    (46)  op(e0, e0) = all_6_2
% 173.46/26.53    (47)  op(e1, all_52_29) = all_52_28
% 173.46/26.53    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.53    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.53    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 173.46/26.53    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.53    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.53    (53)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.53    (54)  all_58_14 = all_52_29
% 173.46/26.53    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 173.46/26.53    (56)   ~ (all_52_3 = all_52_5)
% 173.46/26.53    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.53    (58)  op(e2, e1) = all_52_13
% 173.46/26.53    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.53    (60)  all_58_8 = all_14_2
% 173.46/26.53    (61)  all_56_1 = all_52_3
% 173.46/26.53    (62)  op(e0, e2) = all_52_27
% 173.46/26.53    (63)  all_56_14 = all_52_29
% 173.46/26.53    (64)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.53    (65)   ~ (all_52_3 = all_52_27)
% 173.46/26.53    (66)   ~ (all_52_3 = all_4_2)
% 173.46/26.53    (67)  op(e0, e3) = all_52_25
% 173.46/26.53    (68)  op(e0, all_6_2) = all_6_1
% 173.46/26.53    (69)  op(all_6_1, all_6_2) = e2
% 173.46/26.53    (70)  op(e3, all_52_17) = all_52_16
% 173.46/26.53    (71)   ~ (all_52_13 = all_14_2)
% 173.46/26.53    (72)  op(e3, all_52_9) = e3
% 173.46/26.53    (73)   ~ (e3 = e0)
% 173.46/26.53    (74)   ~ (all_52_9 = all_52_13)
% 173.46/26.53    (75)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.53    (76)  op(e0, all_52_23) = all_52_22
% 173.46/26.53    (77)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.53    (78)  all_56_12 = all_52_25
% 173.46/26.53    (79)  all_58_13 = all_52_27
% 173.46/26.53    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.53    (81)   ~ (all_52_9 = all_52_17)
% 173.46/26.53    (82)  all_58_6 = all_52_17
% 173.46/26.53    (83)   ~ (all_52_3 = all_52_7)
% 173.46/26.53    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.53    (85)  op(e2, all_52_19) = all_52_18
% 173.46/26.53    (86)   ~ (e1 = e0)
% 173.46/26.53    (87)  all_56_0 = all_4_2
% 173.46/26.53    (88)  all_58_11 = all_52_23
% 173.46/26.53    (89)   ~ (all_52_3 = all_52_19)
% 173.46/26.53    (90)   ~ (all_52_7 = all_52_15)
% 173.46/26.53    (91)   ~ (all_52_29 = all_14_2)
% 173.46/26.53    (92)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.53    (93)   ~ (all_52_19 = all_10_2)
% 173.46/26.53    (94)  op(e3, all_4_2) = e2
% 173.46/26.53    (95)   ~ (all_52_23 = all_6_2)
% 173.46/26.53    (96)   ~ (all_52_29 = all_6_2)
% 173.46/26.53    (97)  all_58_2 = all_52_9
% 173.46/26.53    (98)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.53    (99)  op(e3, e1) = all_52_5
% 173.46/26.53    (100)  all_56_10 = all_14_2
% 173.46/26.53    (101)   ~ (all_52_25 = all_6_2)
% 173.46/26.53    (102)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.53    (103)  op(e1, e1) = all_14_2
% 173.46/26.53    (104)  op(e1, e3) = all_52_17
% 173.46/26.53    (105)   ~ (all_52_25 = all_4_2)
% 173.46/26.53    (106)  op(e3, e0) = all_52_7
% 173.46/26.53    (107)  op(e2, all_10_2) = e2
% 173.46/26.53    (108)  op(e3, e3) = all_4_2
% 173.46/26.53    (109)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.53             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 173.46/26.53    (110)  all_56_8 = all_52_17
% 173.46/26.53    (111)   ~ (all_52_17 = all_4_2)
% 173.46/26.53    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.53             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.53    (113)   ~ (all_52_25 = all_52_27)
% 173.46/26.53    (114)   ~ (all_52_27 = all_6_2)
% 173.46/26.53    (115)   ~ (all_52_7 = all_6_2)
% 173.46/26.53    (116)   ~ (all_10_0 = e3)
% 173.46/26.53    (117)   ~ (all_52_7 = all_52_23)
% 173.46/26.53    (118)   ~ (all_52_13 = all_10_2)
% 173.46/26.53    (119)  op(e2, all_52_27) = all_52_26
% 173.46/26.53    (120)   ~ (all_52_17 = all_52_19)
% 173.46/26.53    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.53    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.53    (123)  op(e1, all_14_2) = all_14_1
% 173.46/26.53    (124)  all_58_9 = all_52_7
% 173.46/26.53    (125)   ~ (e2 = e0)
% 173.46/26.53    (126)  all_58_12 = all_52_25
% 173.46/26.53    (127)   ~ (all_10_0 = e1)
% 173.46/26.53    (128)  all_56_6 = all_52_13
% 173.46/26.53    (129)   ~ (all_52_9 = all_52_15)
% 173.46/26.53    (130)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.53    (131)   ~ (all_52_19 = all_14_2)
% 173.46/26.53    (132)  op(e2, e3) = all_52_9
% 173.46/26.53    (133)  all_56_13 = all_52_27
% 173.46/26.53  
% 173.46/26.53  Begin of proof
% 173.46/26.53  | 
% 173.46/26.53  | GROUND_INST: instantiating (112) with e2, all_10_0, all_10_2, e2, simplifying
% 173.46/26.53  |              with (7), (107) gives:
% 173.46/26.53  |   (134)  all_10_0 = e2
% 173.46/26.53  | 
% 173.46/26.53  | BETA: splitting (109) gives:
% 173.46/26.53  | 
% 173.46/26.53  | Case 1:
% 173.46/26.53  | | 
% 173.46/26.53  | |   (135)  all_58_15 = e0
% 173.46/26.53  | | 
% 173.46/26.53  | | REF_CLOSE: (26), (46), (68), (69), (112), (125), (135) are inconsistent by
% 173.46/26.53  | |            sub-proof #228.
% 173.46/26.53  | | 
% 173.46/26.53  | Case 2:
% 173.46/26.53  | | 
% 173.46/26.53  | |   (136)   ~ (all_58_15 = e0)
% 173.46/26.53  | |   (137)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 173.46/26.53  | |            | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.53  | | 
% 173.46/26.53  | | ALPHA: (137) implies:
% 173.46/26.53  | |   (138)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.53  | |   (139)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.53  | | 
% 173.46/26.53  | | REDUCE: (26), (136) imply:
% 173.46/26.53  | |   (140)   ~ (all_6_2 = e0)
% 173.46/26.53  | | 
% 173.46/26.53  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 173.46/26.53  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 173.46/26.53  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 173.46/26.53  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 173.46/26.53  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 173.46/26.53  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 173.46/26.53  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 173.46/26.53  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 173.46/26.53  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 173.46/26.53  | |            (101), (102), (103), (104), (105), (106), (107), (108), (110),
% 173.46/26.53  | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 173.46/26.53  | |            (120), (121), (122), (123), (124), (126), (127), (128), (129),
% 173.46/26.53  | |            (130), (131), (132), (133), (138), (139), (140) are inconsistent
% 173.46/26.53  | |            by sub-proof #13.
% 173.46/26.53  | | 
% 173.46/26.53  | End of split
% 173.46/26.53  | 
% 173.46/26.53  End of proof
% 173.46/26.53  
% 173.46/26.53  Sub-proof #10 shows that the following formulas are inconsistent:
% 173.46/26.53  ----------------------------------------------------------------
% 173.46/26.53    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.53    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.53    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.53    (4)   ~ (all_52_27 = all_10_2)
% 173.46/26.53    (5)   ~ (all_52_17 = all_52_23)
% 173.46/26.53    (6)  op(e2, all_10_2) = all_10_1
% 173.46/26.53    (7)   ~ (all_52_13 = all_52_29)
% 173.46/26.53    (8)  all_56_3 = all_52_7
% 173.46/26.53    (9)  op(e3, e2) = all_52_3
% 173.46/26.53    (10)   ~ (all_52_9 = all_52_25)
% 173.46/26.53    (11)  op(e3, all_52_25) = all_52_24
% 173.46/26.53    (12)   ~ (all_52_19 = all_52_23)
% 173.46/26.53    (13)  all_56_11 = all_52_23
% 173.46/26.53    (14)  op(e1, e2) = all_52_19
% 173.46/26.53    (15)  all_16_1 = all_6_1
% 173.46/26.53    (16)  op(e3, all_52_9) = all_52_8
% 173.46/26.53    (17)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 173.46/26.53    (18)   ~ (all_52_3 = all_10_2)
% 173.46/26.53    (19)  all_58_5 = all_52_13
% 173.46/26.53    (20)   ~ (all_52_25 = all_52_29)
% 173.46/26.53    (21)  all_16_2 = all_6_2
% 173.46/26.53    (22)  all_56_15 = all_6_2
% 173.46/26.53    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.53    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 173.46/26.53    (25)  all_58_3 = all_10_2
% 173.46/26.53    (26)  all_56_9 = all_52_19
% 173.46/26.53    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.53    (28)  all_58_15 = all_6_2
% 173.46/26.53    (29)   ~ (all_52_9 = all_4_2)
% 173.46/26.53    (30)   ~ (all_52_5 = all_52_7)
% 173.46/26.53    (31)  all_58_10 = all_52_15
% 173.46/26.53    (32)  all_8_2 = all_6_2
% 173.46/26.53    (33)   ~ (all_52_5 = all_4_2)
% 173.46/26.53    (34)  all_58_7 = all_52_19
% 173.46/26.53    (35)  all_56_4 = all_52_9
% 173.46/26.53    (36)   ~ (all_52_17 = all_52_25)
% 173.46/26.53    (37)  op(e0, e1) = all_52_29
% 173.46/26.53    (38)  all_58_4 = all_52_5
% 173.46/26.53    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.53    (40)   ~ (e3 = e1)
% 173.46/26.53    (41)   ~ (all_52_27 = all_52_29)
% 173.46/26.53    (42)   ~ (all_52_17 = all_14_2)
% 173.46/26.53    (43)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.53    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.53    (45)   ~ (all_52_7 = all_4_2)
% 173.46/26.53    (46)  all_58_1 = all_52_3
% 173.46/26.53    (47)   ~ (all_52_13 = all_52_15)
% 173.46/26.53    (48)  all_58_0 = all_4_2
% 173.46/26.53    (49)  op(e1, all_52_13) = all_52_12
% 173.46/26.53    (50)  all_52_0 = e2
% 173.46/26.53    (51)  op(e0, e0) = all_6_2
% 173.46/26.53    (52)  op(e1, all_52_29) = all_52_28
% 173.46/26.53    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.53    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.53    (55)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 173.46/26.53    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.53    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.53    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.53    (59)  all_58_14 = all_52_29
% 173.46/26.53    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 173.46/26.53    (61)  op(e2, all_4_2) = all_4_0
% 173.46/26.53    (62)   ~ (all_52_3 = all_52_5)
% 173.46/26.53    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.53    (64)  op(e2, e1) = all_52_13
% 173.46/26.53    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.53    (66)  all_58_8 = all_14_2
% 173.46/26.53    (67)  all_56_1 = all_52_3
% 173.46/26.53    (68)  op(e0, e2) = all_52_27
% 173.46/26.53    (69)  all_56_14 = all_52_29
% 173.46/26.53    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.53    (71)   ~ (all_52_3 = all_52_27)
% 173.46/26.53    (72)   ~ (all_52_3 = all_4_2)
% 173.46/26.53    (73)  op(e0, e3) = all_52_25
% 173.46/26.53    (74)  op(e0, all_6_2) = all_6_1
% 173.46/26.53    (75)  op(all_6_1, all_6_2) = e2
% 173.46/26.53    (76)  op(e3, all_52_17) = all_52_16
% 173.46/26.53    (77)  all_52_10 = all_10_1
% 173.46/26.53    (78)  all_52_20 = e2
% 173.46/26.53    (79)   ~ (all_52_13 = all_14_2)
% 173.46/26.53    (80)   ~ (e3 = e0)
% 173.46/26.53    (81)   ~ (all_52_9 = all_52_13)
% 173.46/26.53    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.53    (83)  op(e0, all_52_23) = all_52_22
% 173.46/26.53    (84)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.53    (85)  op(all_10_1, all_10_2) = all_10_0
% 173.46/26.53    (86)   ~ (all_52_5 = all_52_29)
% 173.46/26.53    (87)  all_56_12 = all_52_25
% 173.46/26.53    (88)  all_58_13 = all_52_27
% 173.46/26.53    (89)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.53    (90)   ~ (all_52_9 = all_52_17)
% 173.46/26.53    (91)  all_58_6 = all_52_17
% 173.46/26.53    (92)   ~ (all_52_3 = all_52_7)
% 173.46/26.53    (93)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.53    (94)  op(e2, all_52_19) = all_52_18
% 173.46/26.53    (95)   ~ (e1 = e0)
% 173.46/26.53    (96)  all_56_0 = all_4_2
% 173.46/26.53    (97)  all_58_11 = all_52_23
% 173.46/26.53    (98)   ~ (all_52_3 = all_52_19)
% 173.46/26.53    (99)   ~ (all_52_7 = all_52_15)
% 173.46/26.53    (100)  op(e0, all_52_15) = all_52_14
% 173.46/26.53    (101)   ~ (all_52_29 = all_14_2)
% 173.46/26.53    (102)   ~ (all_4_0 = e1)
% 173.46/26.53    (103)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.54    (104)   ~ (all_52_19 = all_10_2)
% 173.46/26.54    (105)  op(e3, all_4_2) = e2
% 173.46/26.54    (106)   ~ (all_52_23 = all_6_2)
% 173.46/26.54    (107)   ~ (all_52_29 = all_6_2)
% 173.46/26.54    (108)  all_58_2 = all_52_9
% 173.46/26.54    (109)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.54    (110)  op(e3, e1) = all_52_5
% 173.46/26.54    (111)   ~ (e2 = e1)
% 173.46/26.54    (112)  all_56_10 = all_14_2
% 173.46/26.54    (113)   ~ (all_52_25 = all_6_2)
% 173.46/26.54    (114)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.54    (115)  op(e1, e3) = all_52_17
% 173.46/26.54    (116)   ~ (all_52_25 = all_4_2)
% 173.46/26.54    (117)  op(e3, e0) = all_52_7
% 173.46/26.54    (118)  op(e3, e3) = all_4_2
% 173.46/26.54    (119)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.54             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 173.46/26.54    (120)  all_56_8 = all_52_17
% 173.46/26.54    (121)   ~ (all_52_17 = all_4_2)
% 173.46/26.54    (122)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.54             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.54    (123)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.54           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 173.46/26.54           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 173.46/26.54           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 173.46/26.54    (124)   ~ (all_52_25 = all_52_27)
% 173.46/26.54    (125)   ~ (all_52_27 = all_6_2)
% 173.46/26.54    (126)  all_8_1 = all_6_1
% 173.46/26.54    (127)   ~ (all_52_7 = all_6_2)
% 173.46/26.54    (128)   ~ (all_10_0 = e3)
% 173.46/26.54    (129)   ~ (all_52_7 = all_52_23)
% 173.46/26.54    (130)   ~ (all_52_13 = all_10_2)
% 173.46/26.54    (131)  op(e2, all_52_27) = all_52_26
% 173.46/26.54    (132)   ~ (all_52_17 = all_52_19)
% 173.46/26.54    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.54    (134)  all_52_30 = all_6_1
% 173.46/26.54    (135)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.54    (136)  op(e1, all_14_2) = all_14_1
% 173.46/26.54    (137)  all_58_9 = all_52_7
% 173.46/26.54    (138)   ~ (e2 = e0)
% 173.46/26.54    (139)  all_58_12 = all_52_25
% 173.46/26.54    (140)   ~ (all_10_0 = e1)
% 173.46/26.54    (141)  all_56_6 = all_52_13
% 173.46/26.54    (142)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.54    (143)   ~ (all_52_9 = all_52_15)
% 173.46/26.54    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.54    (145)   ~ (e3 = e2)
% 173.46/26.54    (146)   ~ (all_52_19 = all_14_2)
% 173.46/26.54    (147)  op(e2, e3) = all_52_9
% 173.46/26.54    (148)  all_56_13 = all_52_27
% 173.46/26.54  
% 173.46/26.54  Begin of proof
% 173.46/26.54  | 
% 173.46/26.54  | BETA: splitting (123) gives:
% 173.46/26.54  | 
% 173.46/26.54  | Case 1:
% 173.46/26.54  | | 
% 173.46/26.54  | |   (149)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 173.46/26.54  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 173.46/26.54  | | 
% 173.46/26.54  | | BETA: splitting (149) gives:
% 173.46/26.54  | | 
% 173.46/26.54  | | Case 1:
% 173.46/26.54  | | | 
% 173.46/26.54  | | |   (150)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 173.46/26.54  | | | 
% 173.46/26.54  | | | REF_CLOSE: (50), (145), (150) are inconsistent by sub-proof #124.
% 173.46/26.54  | | | 
% 173.46/26.54  | | Case 2:
% 173.46/26.54  | | | 
% 173.46/26.54  | | |   (151)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 173.46/26.54  | | | 
% 173.46/26.54  | | | ALPHA: (151) implies:
% 173.46/26.54  | | |   (152)  all_52_14 = e0
% 173.46/26.54  | | |   (153)  all_52_12 = e1
% 173.46/26.54  | | |   (154)  all_52_10 = e2
% 173.46/26.54  | | |   (155)  all_52_8 = e3
% 173.46/26.54  | | | 
% 173.46/26.54  | | | COMBINE_EQS: (77), (154) imply:
% 173.46/26.54  | | |   (156)  all_10_1 = e2
% 173.46/26.54  | | | 
% 173.46/26.54  | | | REDUCE: (85), (156) imply:
% 173.46/26.54  | | |   (157)  op(e2, all_10_2) = all_10_0
% 173.46/26.54  | | | 
% 173.46/26.54  | | | REDUCE: (16), (155) imply:
% 173.46/26.54  | | |   (158)  op(e3, all_52_9) = e3
% 173.46/26.54  | | | 
% 173.46/26.54  | | | REDUCE: (6), (156) imply:
% 173.46/26.54  | | |   (159)  op(e2, all_10_2) = e2
% 173.46/26.54  | | | 
% 173.46/26.54  | | | REDUCE: (49), (153) imply:
% 173.46/26.54  | | |   (160)  op(e1, all_52_13) = e1
% 173.46/26.54  | | | 
% 173.46/26.54  | | | REDUCE: (100), (152) imply:
% 173.46/26.54  | | |   (161)  op(e0, all_52_15) = e0
% 173.46/26.54  | | | 
% 173.46/26.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 173.46/26.54  | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 173.46/26.54  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 173.46/26.54  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 173.46/26.54  | | |            (45), (46), (47), (48), (51), (52), (53), (54), (55), (56),
% 173.46/26.54  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 173.46/26.54  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 173.46/26.54  | | |            (79), (80), (81), (82), (83), (84), (86), (87), (88), (89),
% 173.46/26.54  | | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 173.46/26.54  | | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 173.46/26.54  | | |            (110), (112), (113), (114), (115), (116), (117), (118), (119),
% 173.46/26.54  | | |            (120), (121), (122), (124), (125), (126), (127), (128), (129),
% 173.46/26.54  | | |            (130), (131), (132), (133), (135), (136), (137), (138), (139),
% 173.46/26.54  | | |            (140), (141), (142), (143), (144), (146), (147), (148), (157),
% 173.46/26.54  | | |            (158), (159), (160), (161) are inconsistent by sub-proof #11.
% 173.46/26.54  | | | 
% 173.46/26.54  | | End of split
% 173.46/26.54  | | 
% 173.46/26.54  | Case 2:
% 173.46/26.54  | | 
% 173.46/26.54  | |   (162)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 173.46/26.54  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 173.46/26.54  | |            e0)
% 173.46/26.54  | | 
% 173.46/26.54  | | REF_CLOSE: (74), (75), (78), (111), (122), (134), (138), (162) are
% 173.46/26.54  | |            inconsistent by sub-proof #187.
% 173.46/26.54  | | 
% 173.46/26.54  | End of split
% 173.46/26.54  | 
% 173.46/26.54  End of proof
% 173.46/26.54  
% 173.46/26.54  Sub-proof #11 shows that the following formulas are inconsistent:
% 173.46/26.54  ----------------------------------------------------------------
% 173.46/26.54    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.54    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.54    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.54    (4)   ~ (all_52_27 = all_10_2)
% 173.46/26.54    (5)   ~ (all_52_17 = all_52_23)
% 173.46/26.54    (6)   ~ (all_52_13 = all_52_29)
% 173.46/26.54    (7)  op(e2, all_10_2) = all_10_0
% 173.46/26.54    (8)  all_56_3 = all_52_7
% 173.46/26.54    (9)  op(e3, e2) = all_52_3
% 173.46/26.54    (10)   ~ (all_52_9 = all_52_25)
% 173.46/26.54    (11)  op(e3, all_52_25) = all_52_24
% 173.46/26.54    (12)   ~ (all_52_19 = all_52_23)
% 173.46/26.54    (13)  all_56_11 = all_52_23
% 173.46/26.54    (14)  op(e1, e2) = all_52_19
% 173.46/26.54    (15)  all_16_1 = all_6_1
% 173.46/26.54    (16)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 173.46/26.54    (17)   ~ (all_52_3 = all_10_2)
% 173.46/26.54    (18)  all_58_5 = all_52_13
% 173.46/26.54    (19)   ~ (all_52_25 = all_52_29)
% 173.46/26.54    (20)  op(e1, all_52_13) = e1
% 173.46/26.54    (21)  op(e0, all_52_15) = e0
% 173.46/26.54    (22)  all_16_2 = all_6_2
% 173.46/26.54    (23)  all_56_15 = all_6_2
% 173.46/26.54    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.54    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 173.46/26.54    (26)  all_58_3 = all_10_2
% 173.46/26.54    (27)  all_56_9 = all_52_19
% 173.46/26.54    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.54    (29)  all_58_15 = all_6_2
% 173.46/26.54    (30)   ~ (all_52_9 = all_4_2)
% 173.46/26.54    (31)   ~ (all_52_5 = all_52_7)
% 173.46/26.54    (32)  all_58_10 = all_52_15
% 173.46/26.54    (33)  all_8_2 = all_6_2
% 173.46/26.54    (34)   ~ (all_52_5 = all_4_2)
% 173.46/26.54    (35)  all_58_7 = all_52_19
% 173.46/26.54    (36)  all_56_4 = all_52_9
% 173.46/26.54    (37)   ~ (all_52_17 = all_52_25)
% 173.46/26.54    (38)  op(e0, e1) = all_52_29
% 173.46/26.54    (39)  all_58_4 = all_52_5
% 173.46/26.54    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.54    (41)   ~ (e3 = e1)
% 173.46/26.54    (42)   ~ (all_52_27 = all_52_29)
% 173.46/26.54    (43)   ~ (all_52_17 = all_14_2)
% 173.46/26.54    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.54    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.54    (46)   ~ (all_52_7 = all_4_2)
% 173.46/26.54    (47)  all_58_1 = all_52_3
% 173.46/26.54    (48)   ~ (all_52_13 = all_52_15)
% 173.46/26.54    (49)  all_58_0 = all_4_2
% 173.46/26.54    (50)  op(e0, e0) = all_6_2
% 173.46/26.54    (51)  op(e1, all_52_29) = all_52_28
% 173.46/26.54    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.54    (53)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.54    (54)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 173.46/26.54    (55)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.54    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.54    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.54    (58)  all_58_14 = all_52_29
% 173.46/26.54    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 173.46/26.54    (60)  op(e2, all_4_2) = all_4_0
% 173.46/26.54    (61)   ~ (all_52_3 = all_52_5)
% 173.46/26.54    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.54    (63)  op(e2, e1) = all_52_13
% 173.46/26.54    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.54    (65)  all_58_8 = all_14_2
% 173.46/26.54    (66)  all_56_1 = all_52_3
% 173.46/26.54    (67)  op(e0, e2) = all_52_27
% 173.46/26.54    (68)  all_56_14 = all_52_29
% 173.46/26.54    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.54    (70)   ~ (all_52_3 = all_52_27)
% 173.46/26.54    (71)   ~ (all_52_3 = all_4_2)
% 173.46/26.54    (72)  op(e0, e3) = all_52_25
% 173.46/26.54    (73)  op(e0, all_6_2) = all_6_1
% 173.46/26.54    (74)  op(all_6_1, all_6_2) = e2
% 173.46/26.54    (75)  op(e3, all_52_17) = all_52_16
% 173.46/26.54    (76)   ~ (all_52_13 = all_14_2)
% 173.46/26.54    (77)  op(e3, all_52_9) = e3
% 173.46/26.54    (78)   ~ (e3 = e0)
% 173.46/26.54    (79)   ~ (all_52_9 = all_52_13)
% 173.46/26.54    (80)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.54    (81)  op(e0, all_52_23) = all_52_22
% 173.46/26.54    (82)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.54    (83)   ~ (all_52_5 = all_52_29)
% 173.46/26.54    (84)  all_56_12 = all_52_25
% 173.46/26.54    (85)  all_58_13 = all_52_27
% 173.46/26.54    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.54    (87)   ~ (all_52_9 = all_52_17)
% 173.46/26.54    (88)  all_58_6 = all_52_17
% 173.46/26.54    (89)   ~ (all_52_3 = all_52_7)
% 173.46/26.54    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.54    (91)  op(e2, all_52_19) = all_52_18
% 173.46/26.54    (92)   ~ (e1 = e0)
% 173.46/26.54    (93)  all_56_0 = all_4_2
% 173.46/26.54    (94)  all_58_11 = all_52_23
% 173.46/26.54    (95)   ~ (all_52_3 = all_52_19)
% 173.46/26.54    (96)   ~ (all_52_7 = all_52_15)
% 173.46/26.54    (97)   ~ (all_52_29 = all_14_2)
% 173.46/26.54    (98)   ~ (all_4_0 = e1)
% 173.46/26.54    (99)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.54    (100)   ~ (all_52_19 = all_10_2)
% 173.46/26.54    (101)  op(e3, all_4_2) = e2
% 173.46/26.54    (102)   ~ (all_52_23 = all_6_2)
% 173.46/26.54    (103)   ~ (all_52_29 = all_6_2)
% 173.46/26.54    (104)  all_58_2 = all_52_9
% 173.46/26.54    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.54    (106)  op(e3, e1) = all_52_5
% 173.46/26.54    (107)  all_56_10 = all_14_2
% 173.46/26.54    (108)   ~ (all_52_25 = all_6_2)
% 173.46/26.54    (109)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.54    (110)  op(e1, e3) = all_52_17
% 173.46/26.54    (111)   ~ (all_52_25 = all_4_2)
% 173.46/26.54    (112)  op(e3, e0) = all_52_7
% 173.46/26.54    (113)  op(e2, all_10_2) = e2
% 173.46/26.54    (114)  op(e3, e3) = all_4_2
% 173.46/26.54    (115)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 173.46/26.54             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 173.46/26.54    (116)  all_56_8 = all_52_17
% 173.46/26.54    (117)   ~ (all_52_17 = all_4_2)
% 173.46/26.54    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.54             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.54    (119)   ~ (all_52_25 = all_52_27)
% 173.46/26.54    (120)   ~ (all_52_27 = all_6_2)
% 173.46/26.54    (121)  all_8_1 = all_6_1
% 173.46/26.54    (122)   ~ (all_52_7 = all_6_2)
% 173.46/26.54    (123)   ~ (all_10_0 = e3)
% 173.46/26.54    (124)   ~ (all_52_7 = all_52_23)
% 173.46/26.54    (125)   ~ (all_52_13 = all_10_2)
% 173.46/26.54    (126)  op(e2, all_52_27) = all_52_26
% 173.46/26.54    (127)   ~ (all_52_17 = all_52_19)
% 173.46/26.54    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.54    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.54    (130)  op(e1, all_14_2) = all_14_1
% 173.46/26.54    (131)  all_58_9 = all_52_7
% 173.46/26.54    (132)   ~ (e2 = e0)
% 173.46/26.54    (133)  all_58_12 = all_52_25
% 173.46/26.54    (134)   ~ (all_10_0 = e1)
% 173.46/26.54    (135)  all_56_6 = all_52_13
% 173.46/26.54    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.54    (137)   ~ (all_52_9 = all_52_15)
% 173.46/26.54    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.54    (139)   ~ (all_52_19 = all_14_2)
% 173.46/26.54    (140)  op(e2, e3) = all_52_9
% 173.46/26.54    (141)  all_56_13 = all_52_27
% 173.46/26.54  
% 173.46/26.54  Begin of proof
% 173.46/26.54  | 
% 173.46/26.54  | GROUND_INST: instantiating (118) with e2, all_10_0, all_10_2, e2, simplifying
% 173.46/26.54  |              with (7), (113) gives:
% 173.46/26.54  |   (142)  all_10_0 = e2
% 173.46/26.54  | 
% 173.46/26.54  | BETA: splitting (115) gives:
% 173.46/26.54  | 
% 173.46/26.54  | Case 1:
% 173.46/26.54  | | 
% 173.46/26.54  | |   (143)  all_58_15 = e0
% 173.46/26.54  | | 
% 173.46/26.54  | | REF_CLOSE: (29), (50), (73), (74), (118), (132), (143) are inconsistent by
% 173.46/26.54  | |            sub-proof #228.
% 173.46/26.54  | | 
% 173.46/26.54  | Case 2:
% 173.46/26.54  | | 
% 173.46/26.54  | |   (144)   ~ (all_58_15 = e0)
% 173.46/26.54  | |   (145)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 173.46/26.54  | |            | all_58_13 = e0 | all_58_14 = e0)
% 173.46/26.54  | | 
% 173.46/26.54  | | ALPHA: (145) implies:
% 173.46/26.54  | |   (146)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.54  | |   (147)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.54  | | 
% 173.46/26.54  | | REDUCE: (29), (144) imply:
% 173.46/26.54  | |   (148)   ~ (all_6_2 = e0)
% 173.46/26.54  | | 
% 173.46/26.54  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 173.46/26.54  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 173.46/26.54  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 173.46/26.54  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 173.46/26.54  | |            (46), (47), (48), (49), (51), (52), (53), (54), (55), (56), (57),
% 173.46/26.54  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 173.46/26.54  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 173.46/26.54  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 173.46/26.54  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 173.46/26.54  | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 173.46/26.54  | |            (110), (111), (112), (113), (114), (116), (117), (118), (119),
% 173.46/26.54  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 173.46/26.54  | |            (129), (130), (131), (133), (134), (135), (136), (137), (138),
% 173.46/26.54  | |            (139), (140), (141), (146), (147), (148) are inconsistent by
% 173.46/26.54  | |            sub-proof #15.
% 173.46/26.54  | | 
% 173.46/26.54  | End of split
% 173.46/26.54  | 
% 173.46/26.54  End of proof
% 173.46/26.54  
% 173.46/26.54  Sub-proof #12 shows that the following formulas are inconsistent:
% 173.46/26.54  ----------------------------------------------------------------
% 173.46/26.54    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.54    (2)   ~ (all_52_17 = all_52_23)
% 173.46/26.54    (3)  op(e2, all_10_2) = all_10_1
% 173.46/26.54    (4)  all_52_16 = e3
% 173.46/26.54    (5)  op(e3, e2) = all_52_3
% 173.46/26.54    (6)   ~ (all_52_9 = all_52_25)
% 173.46/26.54    (7)  op(e1, e2) = all_52_19
% 173.46/26.54    (8)  all_16_1 = all_6_1
% 173.46/26.54    (9)   ~ (all_14_1 = e2)
% 173.46/26.54    (10)  all_58_5 = all_52_13
% 173.46/26.54    (11)  all_16_2 = all_6_2
% 173.46/26.54    (12)  all_56_15 = all_6_2
% 173.46/26.54    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.54    (14)  all_58_3 = all_10_2
% 173.46/26.54    (15)  all_56_9 = all_52_19
% 173.46/26.54    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.54    (17)  all_58_15 = all_6_2
% 173.46/26.54    (18)  op(e2, all_4_2) = e1
% 173.46/26.54    (19)   ~ (all_52_9 = all_4_2)
% 173.46/26.54    (20)   ~ (all_52_5 = all_52_7)
% 173.46/26.54    (21)  all_58_10 = all_52_15
% 173.46/26.54    (22)   ~ (all_52_5 = all_4_2)
% 173.46/26.54    (23)  all_58_7 = all_52_19
% 173.46/26.54    (24)   ~ (all_52_17 = all_52_25)
% 173.46/26.54    (25)  all_58_4 = all_52_5
% 173.46/26.54    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.54    (27)  all_52_18 = e2
% 173.46/26.54    (28)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.54    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.54    (30)   ~ (all_52_7 = all_4_2)
% 173.46/26.54    (31)  all_58_1 = all_52_3
% 173.46/26.54    (32)  all_58_0 = all_4_2
% 173.46/26.54    (33)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.54    (34)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.54    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.54    (36)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.54    (37)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 173.46/26.54    (38)   ~ (all_14_1 = e3)
% 173.46/26.54    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.54    (40)  op(e2, e1) = all_52_13
% 173.46/26.54    (41)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.54    (42)  all_58_8 = all_14_2
% 173.46/26.54    (43)   ~ (all_52_5 = all_14_2)
% 173.46/26.54    (44)   ~ (all_52_3 = all_4_2)
% 173.46/26.54    (45)  op(e0, e3) = all_52_25
% 173.46/26.54    (46)  op(e0, all_6_2) = all_6_1
% 173.46/26.54    (47)   ~ (all_52_9 = all_10_2)
% 173.46/26.54    (48)  op(all_6_1, all_6_2) = e2
% 173.46/26.54    (49)  op(e3, all_52_17) = all_52_16
% 173.46/26.54    (50)   ~ (all_52_13 = all_14_2)
% 173.46/26.54    (51)   ~ (e3 = e0)
% 173.46/26.54    (52)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 173.46/26.54    (53)   ~ (all_52_9 = all_52_13)
% 173.46/26.54    (54)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.54    (55)  op(e0, all_52_23) = all_52_22
% 173.46/26.54    (56)   ~ (all_52_15 = all_52_23)
% 173.46/26.54    (57)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.54    (58)  op(e1, e0) = all_52_23
% 173.46/26.54    (59)  all_56_12 = all_52_25
% 173.46/26.54    (60)  all_58_13 = all_52_27
% 173.46/26.54    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.54    (62)  all_56_5 = all_10_2
% 173.46/26.54    (63)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 173.46/26.54    (64)   ~ (all_52_9 = all_52_17)
% 173.46/26.54    (65)  all_58_6 = all_52_17
% 173.46/26.54    (66)  op(e2, all_52_19) = all_52_18
% 173.46/26.54    (67)   ~ (e1 = e0)
% 173.46/26.54    (68)  all_56_0 = all_4_2
% 173.46/26.54    (69)  all_58_11 = all_52_23
% 173.46/26.54    (70)   ~ (all_52_3 = all_52_19)
% 173.46/26.54    (71)   ~ (all_52_7 = all_52_15)
% 173.46/26.54    (72)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.54    (73)   ~ (all_52_19 = all_10_2)
% 173.46/26.54    (74)  op(e3, all_4_2) = e2
% 173.46/26.54    (75)  all_58_2 = all_52_9
% 173.46/26.54    (76)  op(e3, e1) = all_52_5
% 173.46/26.54    (77)  all_56_10 = all_14_2
% 173.46/26.54    (78)   ~ (all_52_25 = all_6_2)
% 173.46/26.54    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 173.46/26.54    (80)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.54    (81)  op(e1, e3) = all_52_17
% 173.46/26.54    (82)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 173.46/26.54    (83)   ~ (all_52_25 = all_4_2)
% 173.46/26.54    (84)  op(e3, e0) = all_52_7
% 173.46/26.54    (85)  op(e3, e3) = all_4_2
% 173.46/26.54    (86)   ~ (all_10_1 = e3)
% 173.46/26.54    (87)   ~ (all_52_17 = all_4_2)
% 173.46/26.54    (88)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.54    (89)   ~ (all_52_25 = all_52_27)
% 173.46/26.54    (90)   ~ (all_52_15 = all_10_2)
% 173.46/26.54    (91)  all_56_7 = all_52_15
% 173.46/26.54    (92)   ~ (all_52_7 = all_52_23)
% 173.46/26.54    (93)   ~ (all_52_17 = all_52_19)
% 173.46/26.54    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.54    (95)  all_52_22 = e0
% 173.46/26.54    (96)  op(e1, all_14_2) = all_14_1
% 173.46/26.54    (97)  all_58_9 = all_52_7
% 173.46/26.54    (98)   ~ (e2 = e0)
% 173.46/26.54    (99)  all_58_12 = all_52_25
% 173.46/26.54    (100)  all_14_1 = e1
% 173.46/26.54    (101)  all_56_6 = all_52_13
% 173.46/26.55    (102)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.55    (103)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.55    (104)   ~ (e3 = e2)
% 173.46/26.55    (105)  op(e2, e3) = all_52_9
% 173.46/26.55  
% 173.46/26.55  Begin of proof
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (38), (100) imply:
% 173.46/26.55  |   (106)   ~ (e3 = e1)
% 173.46/26.55  | 
% 173.46/26.55  | SIMP: (106) implies:
% 173.46/26.55  |   (107)   ~ (e3 = e1)
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (9), (100) imply:
% 173.46/26.55  |   (108)   ~ (e2 = e1)
% 173.46/26.55  | 
% 173.46/26.55  | SIMP: (108) implies:
% 173.46/26.55  |   (109)   ~ (e2 = e1)
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (4), (49) imply:
% 173.46/26.55  |   (110)  op(e3, all_52_17) = e3
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (27), (66) imply:
% 173.46/26.55  |   (111)  op(e2, all_52_19) = e2
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (96), (100) imply:
% 173.46/26.55  |   (112)  op(e1, all_14_2) = e1
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (55), (95) imply:
% 173.46/26.55  |   (113)  op(e0, all_52_23) = e0
% 173.46/26.55  | 
% 173.46/26.55  | BETA: splitting (16) gives:
% 173.46/26.55  | 
% 173.46/26.55  | Case 1:
% 173.46/26.55  | | 
% 173.46/26.55  | |   (114)  all_56_0 = e3
% 173.46/26.55  | | 
% 173.46/26.55  | | COMBINE_EQS: (68), (114) imply:
% 173.46/26.55  | |   (115)  all_4_2 = e3
% 173.46/26.55  | | 
% 173.46/26.55  | | REF_CLOSE: (74), (85), (88), (104), (115) are inconsistent by sub-proof
% 173.46/26.55  | |            #106.
% 173.46/26.55  | | 
% 173.46/26.55  | Case 2:
% 173.46/26.55  | | 
% 173.46/26.55  | |   (116)   ~ (all_56_0 = e3)
% 173.46/26.55  | |   (117)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.55  | | 
% 173.46/26.55  | | REDUCE: (68), (116) imply:
% 173.46/26.55  | |   (118)   ~ (all_4_2 = e3)
% 173.46/26.55  | | 
% 173.46/26.55  | | BETA: splitting (28) gives:
% 173.46/26.55  | | 
% 173.46/26.55  | | Case 1:
% 173.46/26.55  | | | 
% 173.46/26.55  | | |   (119)  all_56_15 = e3
% 173.46/26.55  | | | 
% 173.46/26.55  | | | COMBINE_EQS: (12), (119) imply:
% 173.46/26.55  | | |   (120)  all_6_2 = e3
% 173.46/26.55  | | | 
% 173.46/26.55  | | | SIMP: (120) implies:
% 173.46/26.55  | | |   (121)  all_6_2 = e3
% 173.46/26.55  | | | 
% 173.46/26.55  | | | REF_CLOSE: (6), (8), (11), (45), (46), (48), (54), (59), (72), (78), (80),
% 173.46/26.55  | | |            (88), (99), (105), (121) are inconsistent by sub-proof #226.
% 173.46/26.55  | | | 
% 173.46/26.55  | | Case 2:
% 173.46/26.55  | | | 
% 173.46/26.55  | | |   (122)   ~ (all_56_15 = e3)
% 173.46/26.55  | | | 
% 173.46/26.55  | | | REDUCE: (12), (122) imply:
% 173.46/26.55  | | |   (123)   ~ (all_6_2 = e3)
% 173.46/26.55  | | | 
% 173.46/26.55  | | | BETA: splitting (82) gives:
% 173.46/26.55  | | | 
% 173.46/26.55  | | | Case 1:
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | |   (124)  all_56_7 = e3
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | COMBINE_EQS: (91), (124) imply:
% 173.46/26.55  | | | |   (125)  all_52_15 = e3
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | SIMP: (125) implies:
% 173.46/26.55  | | | |   (126)  all_52_15 = e3
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | COMBINE_EQS: (21), (126) imply:
% 173.46/26.55  | | | |   (127)  all_58_10 = e3
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | REDUCE: (71), (126) imply:
% 173.46/26.55  | | | |   (128)   ~ (all_52_7 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | REDUCE: (56), (126) imply:
% 173.46/26.55  | | | |   (129)   ~ (all_52_23 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | SIMP: (129) implies:
% 173.46/26.55  | | | |   (130)   ~ (all_52_23 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | REDUCE: (90), (126) imply:
% 173.46/26.55  | | | |   (131)   ~ (all_10_2 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | SIMP: (131) implies:
% 173.46/26.55  | | | |   (132)   ~ (all_10_2 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | REF_CLOSE: (6), (7), (14), (15), (19), (20), (22), (23), (24), (25),
% 173.46/26.55  | | | |            (26), (29), (30), (31), (32), (33), (34), (35), (39), (41),
% 173.46/26.55  | | | |            (42), (43), (51), (52), (60), (61), (63), (64), (65), (67),
% 173.46/26.55  | | | |            (68), (69), (70), (75), (76), (81), (84), (85), (87), (88),
% 173.46/26.55  | | | |            (89), (93), (97), (98), (99), (102), (103), (104), (105),
% 173.46/26.55  | | | |            (107), (109), (110), (111), (112), (117), (118), (127),
% 173.46/26.55  | | | |            (128), (130), (132) are inconsistent by sub-proof #81.
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | Case 2:
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | |   (133)   ~ (all_56_7 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | REDUCE: (91), (133) imply:
% 173.46/26.55  | | | |   (134)   ~ (all_52_15 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | BETA: splitting (94) gives:
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | Case 1:
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | |   (135)  all_58_9 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | COMBINE_EQS: (97), (135) imply:
% 173.46/26.55  | | | | |   (136)  all_52_7 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | SIMP: (136) implies:
% 173.46/26.55  | | | | |   (137)  all_52_7 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (71), (137) imply:
% 173.46/26.55  | | | | |   (138)   ~ (all_52_15 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (92), (137) imply:
% 173.46/26.55  | | | | |   (139)   ~ (all_52_23 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | SIMP: (139) implies:
% 173.46/26.55  | | | | |   (140)   ~ (all_52_23 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | BETA: splitting (36) gives:
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | Case 1:
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | |   (141)  all_56_6 = e3
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | COMBINE_EQS: (101), (141) imply:
% 173.46/26.55  | | | | | |   (142)  all_52_13 = e3
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | SIMP: (142) implies:
% 173.46/26.55  | | | | | |   (143)  all_52_13 = e3
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | REDUCE: (53), (143) imply:
% 173.46/26.55  | | | | | |   (144)   ~ (all_52_9 = e3)
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | REDUCE: (50), (143) imply:
% 173.46/26.55  | | | | | |   (145)   ~ (all_14_2 = e3)
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | SIMP: (145) implies:
% 173.46/26.55  | | | | | |   (146)   ~ (all_14_2 = e3)
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | REDUCE: (40), (143) imply:
% 173.46/26.55  | | | | | |   (147)  op(e2, e1) = e3
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | BETA: splitting (26) gives:
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | Case 1:
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | |   (148)  all_58_6 = e3
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | | COMBINE_EQS: (65), (148) imply:
% 173.46/26.55  | | | | | | |   (149)  all_52_17 = e3
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | | REF_CLOSE: (85), (87), (88), (110), (149) are inconsistent by
% 173.46/26.55  | | | | | | |            sub-proof #948.
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | Case 2:
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | |   (150)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | | REF_CLOSE: (3), (7), (14), (21), (23), (33), (37), (42), (47),
% 173.46/26.55  | | | | | | |            (51), (62), (63), (64), (65), (69), (73), (75), (79),
% 173.46/26.55  | | | | | | |            (86), (88), (90), (98), (105), (107), (109), (111),
% 173.46/26.55  | | | | | | |            (112), (135), (140), (144), (146), (147), (150) are
% 173.46/26.55  | | | | | | |            inconsistent by sub-proof #684.
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | End of split
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | Case 2:
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | |   (151)   ~ (all_56_6 = e3)
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | REDUCE: (101), (151) imply:
% 173.46/26.55  | | | | | |   (152)   ~ (all_52_13 = e3)
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | BETA: splitting (29) gives:
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | | Case 1:
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | |   (153)  all_58_2 = e3
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | | REF_CLOSE: (6), (15), (19), (23), (26), (29), (32), (34), (39),
% 173.46/26.55  | | | | | | |            (42), (43), (64), (65), (69), (75), (76), (81), (85),
% 173.46/26.55  | | | | | | |            (87), (88), (99), (104), (105), (110), (111), (112),
% 173.46/26.55  | | | | | | |            (140), (153) are inconsistent by sub-proof #150.
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | Case 2:
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | |   (154)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | | BETA: splitting (154) gives:
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | | Case 1:
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | |   (155)  all_58_3 = e3
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | | COMBINE_EQS: (14), (155) imply:
% 173.46/26.55  | | | | | | | |   (156)  all_10_2 = e3
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | | REDUCE: (73), (156) imply:
% 173.46/26.55  | | | | | | | |   (157)   ~ (all_52_19 = e3)
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | | REF_CLOSE: (23), (26), (42), (43), (65), (69), (76), (81), (85),
% 173.46/26.55  | | | | | | | |            (87), (88), (110), (112), (140), (157) are
% 173.46/26.55  | | | | | | | |            inconsistent by sub-proof #702.
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | Case 2:
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | |   (158)  all_58_5 = e3 | all_58_10 = e3
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | | REF_CLOSE: (10), (21), (134), (152), (158) are inconsistent by
% 173.46/26.55  | | | | | | | |            sub-proof #958.
% 173.46/26.55  | | | | | | | | 
% 173.46/26.55  | | | | | | | End of split
% 173.46/26.55  | | | | | | | 
% 173.46/26.55  | | | | | | End of split
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | End of split
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | Case 2:
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | |   (159)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REF_CLOSE: (1), (2), (5), (13), (17), (18), (21), (32), (39), (40),
% 173.46/26.55  | | | | |            (43), (44), (45), (50), (51), (53), (57), (58), (61), (65),
% 173.46/26.55  | | | | |            (68), (69), (74), (75), (76), (77), (83), (88), (98), (99),
% 173.46/26.55  | | | | |            (104), (109), (112), (113), (117), (118), (123), (134),
% 173.46/26.55  | | | | |            (159) are inconsistent by sub-proof #80.
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | End of split
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | End of split
% 173.46/26.55  | | | 
% 173.46/26.55  | | End of split
% 173.46/26.55  | | 
% 173.46/26.55  | End of split
% 173.46/26.55  | 
% 173.46/26.55  End of proof
% 173.46/26.55  
% 173.46/26.55  Sub-proof #13 shows that the following formulas are inconsistent:
% 173.46/26.55  ----------------------------------------------------------------
% 173.46/26.55    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.55    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.55    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.55    (4)   ~ (all_52_27 = all_10_2)
% 173.46/26.55    (5)   ~ (all_52_17 = all_52_23)
% 173.46/26.55    (6)   ~ (all_52_13 = all_52_29)
% 173.46/26.55    (7)  op(e2, all_10_2) = all_10_0
% 173.46/26.55    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.55    (9)  all_56_3 = all_52_7
% 173.46/26.55    (10)  op(e3, e2) = all_52_3
% 173.46/26.55    (11)   ~ (all_52_9 = all_52_25)
% 173.46/26.55    (12)   ~ (all_52_19 = all_52_23)
% 173.46/26.55    (13)  all_56_11 = all_52_23
% 173.46/26.55    (14)  op(e1, e2) = all_52_19
% 173.46/26.55    (15)  all_16_1 = all_6_1
% 173.46/26.55    (16)   ~ (all_52_3 = all_10_2)
% 173.46/26.55    (17)  all_58_5 = all_52_13
% 173.46/26.55    (18)   ~ (all_6_2 = e0)
% 173.46/26.55    (19)   ~ (all_52_25 = all_52_29)
% 173.46/26.55    (20)  op(e1, all_52_13) = e1
% 173.46/26.55    (21)  op(e0, all_52_15) = e0
% 173.46/26.55    (22)  all_16_2 = all_6_2
% 173.46/26.55    (23)  all_56_15 = all_6_2
% 173.46/26.55    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.55    (25)  all_58_3 = all_10_2
% 173.46/26.55    (26)  all_56_9 = all_52_19
% 173.46/26.55    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.55    (28)  all_58_15 = all_6_2
% 173.46/26.55    (29)  op(e2, all_4_2) = e1
% 173.46/26.55    (30)   ~ (all_52_9 = all_4_2)
% 173.46/26.55    (31)   ~ (all_52_5 = all_52_7)
% 173.46/26.55    (32)  all_58_10 = all_52_15
% 173.46/26.55    (33)   ~ (all_52_5 = all_4_2)
% 173.46/26.55    (34)  all_58_7 = all_52_19
% 173.46/26.55    (35)  all_56_4 = all_52_9
% 173.46/26.55    (36)   ~ (all_52_17 = all_52_25)
% 173.46/26.55    (37)  all_58_4 = all_52_5
% 173.46/26.55    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.55    (39)   ~ (e3 = e1)
% 173.46/26.55    (40)   ~ (all_52_27 = all_52_29)
% 173.46/26.55    (41)   ~ (all_52_17 = all_14_2)
% 173.46/26.55    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.55    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.55    (44)   ~ (all_52_7 = all_4_2)
% 173.46/26.55    (45)  all_58_1 = all_52_3
% 173.46/26.55    (46)   ~ (all_52_13 = all_52_15)
% 173.46/26.55    (47)  all_58_0 = all_4_2
% 173.46/26.55    (48)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.55    (49)  op(e1, all_52_29) = all_52_28
% 173.46/26.55    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.55    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.55    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 173.46/26.55    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.55    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.55    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.55    (56)  all_58_14 = all_52_29
% 173.46/26.55    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 173.46/26.55    (58)   ~ (all_52_3 = all_52_5)
% 173.46/26.55    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.55    (60)  op(e2, e1) = all_52_13
% 173.46/26.55    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.55    (62)  all_58_8 = all_14_2
% 173.46/26.55    (63)  all_56_1 = all_52_3
% 173.46/26.55    (64)  op(e0, e2) = all_52_27
% 173.46/26.55    (65)  all_56_14 = all_52_29
% 173.46/26.55    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.55    (67)   ~ (all_52_3 = all_52_27)
% 173.46/26.55    (68)   ~ (all_52_3 = all_4_2)
% 173.46/26.55    (69)  op(e0, e3) = all_52_25
% 173.46/26.55    (70)  op(e0, all_6_2) = all_6_1
% 173.46/26.55    (71)  op(all_6_1, all_6_2) = e2
% 173.46/26.55    (72)  op(e3, all_52_17) = all_52_16
% 173.46/26.55    (73)   ~ (all_52_13 = all_14_2)
% 173.46/26.55    (74)  op(e3, all_52_9) = e3
% 173.46/26.55    (75)   ~ (e3 = e0)
% 173.46/26.55    (76)   ~ (all_52_9 = all_52_13)
% 173.46/26.55    (77)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.55    (78)  op(e0, all_52_23) = all_52_22
% 173.46/26.55    (79)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.55    (80)  all_56_12 = all_52_25
% 173.46/26.55    (81)  all_58_13 = all_52_27
% 173.46/26.55    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.55    (83)   ~ (all_52_9 = all_52_17)
% 173.46/26.55    (84)  all_58_6 = all_52_17
% 173.46/26.55    (85)   ~ (all_52_3 = all_52_7)
% 173.46/26.55    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.55    (87)  op(e2, all_52_19) = all_52_18
% 173.46/26.55    (88)   ~ (e1 = e0)
% 173.46/26.55    (89)  all_56_0 = all_4_2
% 173.46/26.55    (90)  all_58_11 = all_52_23
% 173.46/26.55    (91)   ~ (all_52_3 = all_52_19)
% 173.46/26.55    (92)   ~ (all_52_7 = all_52_15)
% 173.46/26.55    (93)   ~ (all_52_29 = all_14_2)
% 173.46/26.55    (94)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.55    (95)   ~ (all_52_19 = all_10_2)
% 173.46/26.55    (96)  op(e3, all_4_2) = e2
% 173.46/26.55    (97)   ~ (all_52_23 = all_6_2)
% 173.46/26.55    (98)   ~ (all_52_29 = all_6_2)
% 173.46/26.55    (99)  all_58_2 = all_52_9
% 173.46/26.55    (100)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.55    (101)  op(e3, e1) = all_52_5
% 173.46/26.55    (102)  all_56_10 = all_14_2
% 173.46/26.55    (103)   ~ (all_52_25 = all_6_2)
% 173.46/26.55    (104)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.55    (105)  op(e1, e1) = all_14_2
% 173.46/26.55    (106)  op(e1, e3) = all_52_17
% 173.46/26.55    (107)   ~ (all_52_25 = all_4_2)
% 173.46/26.55    (108)  op(e3, e0) = all_52_7
% 173.46/26.55    (109)  op(e2, all_10_2) = e2
% 173.46/26.55    (110)  op(e3, e3) = all_4_2
% 173.46/26.55    (111)  all_56_8 = all_52_17
% 173.46/26.55    (112)   ~ (all_52_17 = all_4_2)
% 173.46/26.55    (113)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.55             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.55    (114)   ~ (all_52_25 = all_52_27)
% 173.46/26.55    (115)   ~ (all_52_27 = all_6_2)
% 173.46/26.55    (116)   ~ (all_52_7 = all_6_2)
% 173.46/26.55    (117)   ~ (all_10_0 = e3)
% 173.46/26.55    (118)   ~ (all_52_7 = all_52_23)
% 173.46/26.55    (119)   ~ (all_52_13 = all_10_2)
% 173.46/26.55    (120)  op(e2, all_52_27) = all_52_26
% 173.46/26.55    (121)   ~ (all_52_17 = all_52_19)
% 173.46/26.55    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.55    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.55    (124)  op(e1, all_14_2) = all_14_1
% 173.46/26.55    (125)  all_58_9 = all_52_7
% 173.46/26.55    (126)  all_58_12 = all_52_25
% 173.46/26.55    (127)   ~ (all_10_0 = e1)
% 173.46/26.55    (128)  all_56_6 = all_52_13
% 173.46/26.55    (129)   ~ (all_52_9 = all_52_15)
% 173.46/26.55    (130)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.55    (131)   ~ (all_52_19 = all_14_2)
% 173.46/26.55    (132)  op(e2, e3) = all_52_9
% 173.46/26.55    (133)  all_56_13 = all_52_27
% 173.46/26.55  
% 173.46/26.55  Begin of proof
% 173.46/26.55  | 
% 173.46/26.55  | GROUND_INST: instantiating (113) with e2, all_10_0, all_10_2, e2, simplifying
% 173.46/26.55  |              with (7), (109) gives:
% 173.46/26.55  |   (134)  all_10_0 = e2
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (117), (134) imply:
% 173.46/26.55  |   (135)   ~ (e3 = e2)
% 173.46/26.55  | 
% 173.46/26.55  | SIMP: (135) implies:
% 173.46/26.55  |   (136)   ~ (e3 = e2)
% 173.46/26.55  | 
% 173.46/26.55  | REDUCE: (127), (134) imply:
% 173.46/26.55  |   (137)   ~ (e2 = e1)
% 173.46/26.55  | 
% 173.46/26.55  | BETA: splitting (27) gives:
% 173.46/26.55  | 
% 173.46/26.55  | Case 1:
% 173.46/26.55  | | 
% 173.46/26.55  | |   (138)  all_56_0 = e3
% 173.46/26.55  | | 
% 173.46/26.55  | | COMBINE_EQS: (89), (138) imply:
% 173.46/26.55  | |   (139)  all_4_2 = e3
% 173.46/26.55  | | 
% 173.46/26.55  | | REF_CLOSE: (96), (110), (113), (136), (139) are inconsistent by sub-proof
% 173.46/26.55  | |            #106.
% 173.46/26.55  | | 
% 173.46/26.55  | Case 2:
% 173.46/26.55  | | 
% 173.46/26.55  | |   (140)   ~ (all_56_0 = e3)
% 173.46/26.55  | | 
% 173.46/26.55  | | REDUCE: (89), (140) imply:
% 173.46/26.55  | |   (141)   ~ (all_4_2 = e3)
% 173.46/26.55  | | 
% 173.46/26.55  | | BETA: splitting (42) gives:
% 173.46/26.55  | | 
% 173.46/26.55  | | Case 1:
% 173.46/26.55  | | | 
% 173.46/26.55  | | |   (142)  all_56_15 = e3
% 173.46/26.55  | | | 
% 173.46/26.55  | | | COMBINE_EQS: (23), (142) imply:
% 173.46/26.55  | | |   (143)  all_6_2 = e3
% 173.46/26.55  | | | 
% 173.46/26.55  | | | SIMP: (143) implies:
% 173.46/26.55  | | |   (144)  all_6_2 = e3
% 173.46/26.55  | | | 
% 173.46/26.55  | | | REF_CLOSE: (11), (15), (22), (69), (70), (71), (77), (80), (94), (103),
% 173.46/26.55  | | |            (104), (113), (126), (132), (144) are inconsistent by sub-proof
% 173.46/26.55  | | |            #226.
% 173.46/26.55  | | | 
% 173.46/26.55  | | Case 2:
% 173.46/26.55  | | | 
% 173.46/26.55  | | |   (145)   ~ (all_56_15 = e3)
% 173.46/26.55  | | |   (146)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.55  | | | 
% 173.46/26.55  | | | REDUCE: (23), (145) imply:
% 173.46/26.55  | | |   (147)   ~ (all_6_2 = e3)
% 173.46/26.55  | | | 
% 173.46/26.55  | | | BETA: splitting (57) gives:
% 173.46/26.55  | | | 
% 173.46/26.55  | | | Case 1:
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | |   (148)  all_56_13 = e3
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | COMBINE_EQS: (133), (148) imply:
% 173.46/26.55  | | | |   (149)  all_52_27 = e3
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | SIMP: (149) implies:
% 173.46/26.55  | | | |   (150)  all_52_27 = e3
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | REF_CLOSE: (2), (5), (10), (11), (16), (17), (20), (21), (24), (25),
% 173.46/26.55  | | | |            (27), (28), (30), (31), (32), (34), (35), (36), (37), (38),
% 173.46/26.55  | | | |            (39), (40), (41), (43), (44), (45), (47), (52), (54), (56),
% 173.46/26.55  | | | |            (59), (62), (65), (67), (68), (69), (72), (74), (81), (82),
% 173.46/26.55  | | | |            (83), (84), (86), (89), (90), (92), (96), (99), (106), (107),
% 173.46/26.55  | | | |            (109), (110), (111), (112), (113), (114), (115), (120),
% 173.46/26.55  | | | |            (121), (122), (125), (126), (129), (130), (132), (136), (150)
% 173.46/26.55  | | | |            are inconsistent by sub-proof #103.
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | Case 2:
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | |   (151)   ~ (all_56_13 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | REDUCE: (133), (151) imply:
% 173.46/26.55  | | | |   (152)   ~ (all_52_27 = e3)
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | BETA: splitting (61) gives:
% 173.46/26.55  | | | | 
% 173.46/26.55  | | | | Case 1:
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | |   (153)  all_58_12 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | COMBINE_EQS: (126), (153) imply:
% 173.46/26.55  | | | | |   (154)  all_52_25 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | SIMP: (154) implies:
% 173.46/26.55  | | | | |   (155)  all_52_25 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (11), (155) imply:
% 173.46/26.55  | | | | |   (156)   ~ (all_52_9 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (114), (155) imply:
% 173.46/26.55  | | | | |   (157)   ~ (all_52_27 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (19), (155) imply:
% 173.46/26.55  | | | | |   (158)   ~ (all_52_29 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | SIMP: (158) implies:
% 173.46/26.55  | | | | |   (159)   ~ (all_52_29 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (103), (155) imply:
% 173.46/26.55  | | | | |   (160)   ~ (all_6_2 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (107), (155) imply:
% 173.46/26.55  | | | | |   (161)   ~ (all_4_2 = e3)
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REDUCE: (69), (155) imply:
% 173.46/26.55  | | | | |   (162)  op(e0, e3) = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 173.46/26.55  | | | | |            (16), (17), (18), (20), (21), (23), (24), (25), (26), (27),
% 173.46/26.55  | | | | |            (28), (30), (31), (32), (33), (34), (35), (37), (38), (40),
% 173.46/26.55  | | | | |            (41), (43), (44), (45), (46), (47), (48), (50), (51), (53),
% 173.46/26.55  | | | | |            (54), (55), (56), (58), (60), (62), (63), (64), (66), (68),
% 173.46/26.55  | | | | |            (70), (71), (72), (73), (74), (75), (76), (78), (79), (81),
% 173.46/26.55  | | | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 173.46/26.55  | | | | |            (93), (95), (96), (97), (98), (99), (100), (101), (102),
% 173.46/26.55  | | | | |            (106), (108), (109), (113), (115), (116), (118), (119),
% 173.46/26.55  | | | | |            (121), (122), (123), (124), (125), (128), (129), (130),
% 173.46/26.55  | | | | |            (131), (132), (136), (137), (141), (146), (147), (152),
% 173.46/26.55  | | | | |            (153), (156), (159), (162) are inconsistent by sub-proof
% 173.46/26.55  | | | | |            #16.
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | Case 2:
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | |   (163)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | BETA: splitting (163) gives:
% 173.46/26.55  | | | | | 
% 173.46/26.55  | | | | | Case 1:
% 173.46/26.55  | | | | | | 
% 173.46/26.55  | | | | | |   (164)  all_58_13 = e3
% 173.46/26.55  | | | | | | 
% 173.46/26.56  | | | | | | REF_CLOSE: (81), (152), (164) are inconsistent by sub-proof #1026.
% 173.46/26.56  | | | | | | 
% 173.46/26.56  | | | | | Case 2:
% 173.46/26.56  | | | | | | 
% 173.46/26.56  | | | | | |   (165)  all_58_14 = e3 | all_58_15 = e3
% 173.46/26.56  | | | | | | 
% 173.46/26.56  | | | | | | REF_CLOSE: (5), (10), (16), (17), (19), (20), (21), (25), (28),
% 173.46/26.56  | | | | | |            (29), (30), (32), (34), (35), (36), (39), (40), (43),
% 173.46/26.56  | | | | | |            (45), (47), (49), (54), (56), (58), (59), (60), (69),
% 173.46/26.56  | | | | | |            (73), (74), (81), (82), (83), (84), (86), (88), (90),
% 173.46/26.56  | | | | | |            (92), (98), (99), (101), (105), (106), (109), (110),
% 173.46/26.56  | | | | | |            (113), (121), (122), (125), (126), (132), (141), (147),
% 173.46/26.56  | | | | | |            (165) are inconsistent by sub-proof #84.
% 173.46/26.56  | | | | | | 
% 173.46/26.56  | | | | | End of split
% 173.46/26.56  | | | | | 
% 173.46/26.56  | | | | End of split
% 173.46/26.56  | | | | 
% 173.46/26.56  | | | End of split
% 173.46/26.56  | | | 
% 173.46/26.56  | | End of split
% 173.46/26.56  | | 
% 173.46/26.56  | End of split
% 173.46/26.56  | 
% 173.46/26.56  End of proof
% 173.46/26.56  
% 173.46/26.56  Sub-proof #14 shows that the following formulas are inconsistent:
% 173.46/26.56  ----------------------------------------------------------------
% 173.46/26.56    (1)   ~ (all_52_5 = all_52_13)
% 173.46/26.56    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.56    (3)   ~ (all_52_17 = all_52_23)
% 173.46/26.56    (4)  op(e2, all_10_2) = all_10_1
% 173.46/26.56    (5)   ~ (all_52_13 = all_52_29)
% 173.46/26.56    (6)  all_56_3 = all_52_7
% 173.46/26.56    (7)  all_52_16 = e3
% 173.46/26.56    (8)  op(e3, e2) = all_52_3
% 173.46/26.56    (9)   ~ (all_52_9 = all_52_25)
% 173.46/26.56    (10)  op(e1, e2) = all_52_19
% 173.46/26.56    (11)  all_16_1 = all_6_1
% 173.46/26.56    (12)   ~ (all_14_1 = e2)
% 173.46/26.56    (13)  all_58_5 = all_52_13
% 173.46/26.56    (14)   ~ (all_52_25 = all_52_29)
% 173.46/26.56    (15)  all_16_2 = all_6_2
% 173.46/26.56    (16)  all_56_15 = all_6_2
% 173.46/26.56    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.56    (18)  all_58_3 = all_10_2
% 173.46/26.56    (19)  all_56_9 = all_52_19
% 173.46/26.56    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.56    (21)  all_58_15 = all_6_2
% 173.46/26.56    (22)   ~ (all_52_9 = all_4_2)
% 173.46/26.56    (23)   ~ (all_52_5 = all_52_7)
% 173.46/26.56    (24)  all_58_10 = all_52_15
% 173.46/26.56    (25)   ~ (all_52_5 = all_4_2)
% 173.46/26.56    (26)  all_58_7 = all_52_19
% 173.46/26.56    (27)   ~ (all_52_17 = all_52_25)
% 173.46/26.56    (28)  all_58_4 = all_52_5
% 173.46/26.56    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.56    (30)  all_52_18 = e2
% 173.46/26.56    (31)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.56    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.56    (33)   ~ (all_52_7 = all_4_2)
% 173.46/26.56    (34)  all_58_1 = all_52_3
% 173.46/26.56    (35)  all_58_0 = all_4_2
% 173.46/26.56    (36)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 173.46/26.56    (37)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.56    (38)  op(e1, all_52_29) = all_52_28
% 173.46/26.56    (39)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.56    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.56    (41)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.56    (42)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 173.46/26.56    (43)   ~ (all_14_1 = e3)
% 173.46/26.56    (44)  all_58_14 = all_52_29
% 173.46/26.56    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 173.46/26.56    (46)  op(e2, all_4_2) = all_4_0
% 173.46/26.56    (47)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.56    (48)  op(e2, e1) = all_52_13
% 173.46/26.56    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.56    (50)  all_58_8 = all_14_2
% 173.46/26.56    (51)   ~ (all_52_5 = all_14_2)
% 173.46/26.56    (52)   ~ (all_52_3 = all_52_27)
% 173.46/26.56    (53)   ~ (all_52_3 = all_4_2)
% 173.46/26.56    (54)  op(e0, e3) = all_52_25
% 173.46/26.56    (55)  op(e0, all_6_2) = all_6_1
% 173.46/26.56    (56)   ~ (all_52_9 = all_10_2)
% 173.46/26.56    (57)  op(all_6_1, all_6_2) = e2
% 173.46/26.56    (58)  op(e3, all_52_17) = all_52_16
% 173.46/26.56    (59)   ~ (all_52_13 = all_14_2)
% 173.46/26.56    (60)   ~ (e3 = e0)
% 173.46/26.56    (61)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 173.46/26.56    (62)   ~ (all_52_9 = all_52_13)
% 173.46/26.56    (63)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.56    (64)  op(e0, all_52_23) = all_52_22
% 173.46/26.56    (65)   ~ (all_52_15 = all_52_23)
% 173.46/26.56    (66)   ~ (all_52_5 = all_52_29)
% 173.46/26.56    (67)  all_56_12 = all_52_25
% 173.46/26.56    (68)  all_58_13 = all_52_27
% 173.46/26.56    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.56    (70)  all_56_5 = all_10_2
% 173.46/26.56    (71)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 173.46/26.56    (72)   ~ (all_52_9 = all_52_17)
% 173.46/26.56    (73)  all_58_6 = all_52_17
% 173.46/26.56    (74)  op(e2, all_52_19) = all_52_18
% 173.46/26.56    (75)   ~ (e1 = e0)
% 173.46/26.56    (76)  all_56_0 = all_4_2
% 173.46/26.56    (77)  all_58_11 = all_52_23
% 173.46/26.56    (78)   ~ (all_52_3 = all_52_19)
% 173.46/26.56    (79)   ~ (all_52_7 = all_52_15)
% 173.46/26.56    (80)   ~ (all_4_0 = e1)
% 173.46/26.56    (81)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.56    (82)   ~ (all_52_19 = all_10_2)
% 173.46/26.56    (83)  op(e3, all_4_2) = e2
% 173.46/26.56    (84)   ~ (all_52_29 = all_6_2)
% 173.46/26.56    (85)  all_58_2 = all_52_9
% 173.46/26.56    (86)  op(e3, e1) = all_52_5
% 173.46/26.56    (87)   ~ (all_52_25 = all_6_2)
% 173.46/26.56    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 173.46/26.56    (89)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.56    (90)  op(e1, e3) = all_52_17
% 173.46/26.56    (91)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 173.46/26.56    (92)   ~ (all_52_25 = all_4_2)
% 173.46/26.56    (93)  op(e3, e0) = all_52_7
% 173.46/26.56    (94)  op(e3, e3) = all_4_2
% 173.46/26.56    (95)   ~ (all_10_1 = e3)
% 173.46/26.56    (96)  all_56_8 = all_52_17
% 173.46/26.56    (97)   ~ (all_52_17 = all_4_2)
% 173.46/26.56    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.56    (99)   ~ (all_52_25 = all_52_27)
% 173.46/26.56    (100)   ~ (all_52_27 = all_6_2)
% 173.46/26.56    (101)   ~ (all_52_15 = all_10_2)
% 173.46/26.56    (102)   ~ (all_52_19 = all_52_27)
% 173.46/26.56    (103)  all_56_7 = all_52_15
% 173.46/26.56    (104)   ~ (all_52_7 = all_52_23)
% 173.46/26.56    (105)  op(e2, all_52_27) = all_52_26
% 173.46/26.56    (106)   ~ (all_52_17 = all_52_19)
% 173.46/26.56    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.56    (108)  all_52_22 = e0
% 173.46/26.56    (109)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.56    (110)  op(e1, all_14_2) = all_14_1
% 173.46/26.56    (111)  all_58_9 = all_52_7
% 173.46/26.56    (112)   ~ (e2 = e0)
% 173.46/26.56    (113)  all_58_12 = all_52_25
% 173.46/26.56    (114)  all_14_1 = e1
% 173.46/26.56    (115)  all_56_6 = all_52_13
% 173.46/26.56    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.56    (117)   ~ (all_52_9 = all_52_15)
% 173.46/26.56    (118)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.56    (119)   ~ (e3 = e2)
% 173.46/26.56    (120)  op(e2, e3) = all_52_9
% 173.46/26.56    (121)  all_56_13 = all_52_27
% 173.46/26.56  
% 173.46/26.56  Begin of proof
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (43), (114) imply:
% 173.46/26.56  |   (122)   ~ (e3 = e1)
% 173.46/26.56  | 
% 173.46/26.56  | SIMP: (122) implies:
% 173.46/26.56  |   (123)   ~ (e3 = e1)
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (12), (114) imply:
% 173.46/26.56  |   (124)   ~ (e2 = e1)
% 173.46/26.56  | 
% 173.46/26.56  | SIMP: (124) implies:
% 173.46/26.56  |   (125)   ~ (e2 = e1)
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (7), (58) imply:
% 173.46/26.56  |   (126)  op(e3, all_52_17) = e3
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (30), (74) imply:
% 173.46/26.56  |   (127)  op(e2, all_52_19) = e2
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (110), (114) imply:
% 173.46/26.56  |   (128)  op(e1, all_14_2) = e1
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (64), (108) imply:
% 173.46/26.56  |   (129)  op(e0, all_52_23) = e0
% 173.46/26.56  | 
% 173.46/26.56  | BETA: splitting (31) gives:
% 173.46/26.56  | 
% 173.46/26.56  | Case 1:
% 173.46/26.56  | | 
% 173.46/26.56  | |   (130)  all_56_15 = e3
% 173.46/26.56  | | 
% 173.46/26.56  | | COMBINE_EQS: (16), (130) imply:
% 173.46/26.56  | |   (131)  all_6_2 = e3
% 173.46/26.56  | | 
% 173.46/26.56  | | SIMP: (131) implies:
% 173.46/26.56  | |   (132)  all_6_2 = e3
% 173.46/26.56  | | 
% 173.46/26.56  | | REF_CLOSE: (9), (11), (15), (54), (55), (57), (63), (67), (81), (87), (89),
% 173.46/26.56  | |            (98), (113), (120), (132) are inconsistent by sub-proof #226.
% 173.46/26.56  | | 
% 173.46/26.56  | Case 2:
% 173.46/26.56  | | 
% 173.46/26.56  | |   (133)   ~ (all_56_15 = e3)
% 173.46/26.56  | | 
% 173.46/26.56  | | REDUCE: (16), (133) imply:
% 173.46/26.56  | |   (134)   ~ (all_6_2 = e3)
% 173.46/26.56  | | 
% 173.46/26.56  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (13), (14), (17),
% 173.46/26.56  | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 173.46/26.56  | |            (29), (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 173.46/26.56  | |            (42), (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 173.46/26.56  | |            (54), (56), (59), (60), (61), (62), (65), (66), (68), (69), (70),
% 173.46/26.56  | |            (71), (72), (73), (75), (76), (77), (78), (79), (80), (82), (83),
% 173.46/26.56  | |            (84), (85), (86), (87), (88), (90), (91), (92), (93), (94), (95),
% 173.46/26.56  | |            (96), (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 173.46/26.56  | |            (106), (107), (109), (111), (112), (113), (115), (116), (117),
% 173.46/26.56  | |            (118), (119), (120), (121), (123), (125), (126), (127), (128),
% 173.46/26.56  | |            (129), (134) are inconsistent by sub-proof #94.
% 173.46/26.56  | | 
% 173.46/26.56  | End of split
% 173.46/26.56  | 
% 173.46/26.56  End of proof
% 173.46/26.56  
% 173.46/26.56  Sub-proof #15 shows that the following formulas are inconsistent:
% 173.46/26.56  ----------------------------------------------------------------
% 173.46/26.56    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.56    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 173.46/26.56    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.56    (4)   ~ (all_52_27 = all_10_2)
% 173.46/26.56    (5)   ~ (all_52_17 = all_52_23)
% 173.46/26.56    (6)   ~ (all_52_13 = all_52_29)
% 173.46/26.56    (7)  op(e2, all_10_2) = all_10_0
% 173.46/26.56    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.56    (9)  all_56_3 = all_52_7
% 173.46/26.56    (10)  op(e3, e2) = all_52_3
% 173.46/26.56    (11)   ~ (all_52_9 = all_52_25)
% 173.46/26.56    (12)  op(e3, all_52_25) = all_52_24
% 173.46/26.56    (13)   ~ (all_52_19 = all_52_23)
% 173.46/26.56    (14)  all_56_11 = all_52_23
% 173.46/26.56    (15)  op(e1, e2) = all_52_19
% 173.46/26.56    (16)  all_16_1 = all_6_1
% 173.46/26.56    (17)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 173.46/26.56    (18)   ~ (all_52_3 = all_10_2)
% 173.46/26.56    (19)  all_58_5 = all_52_13
% 173.46/26.56    (20)   ~ (all_6_2 = e0)
% 173.46/26.56    (21)   ~ (all_52_25 = all_52_29)
% 173.46/26.56    (22)  op(e1, all_52_13) = e1
% 173.46/26.56    (23)  op(e0, all_52_15) = e0
% 173.46/26.56    (24)  all_16_2 = all_6_2
% 173.46/26.56    (25)  all_56_15 = all_6_2
% 173.46/26.56    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.56    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 173.46/26.56    (28)  all_58_3 = all_10_2
% 173.46/26.56    (29)  all_56_9 = all_52_19
% 173.46/26.56    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.56    (31)  all_58_15 = all_6_2
% 173.46/26.56    (32)   ~ (all_52_9 = all_4_2)
% 173.46/26.56    (33)   ~ (all_52_5 = all_52_7)
% 173.46/26.56    (34)  all_58_10 = all_52_15
% 173.46/26.56    (35)  all_8_2 = all_6_2
% 173.46/26.56    (36)   ~ (all_52_5 = all_4_2)
% 173.46/26.56    (37)  all_58_7 = all_52_19
% 173.46/26.56    (38)  all_56_4 = all_52_9
% 173.46/26.56    (39)   ~ (all_52_17 = all_52_25)
% 173.46/26.56    (40)  op(e0, e1) = all_52_29
% 173.46/26.56    (41)  all_58_4 = all_52_5
% 173.46/26.56    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.56    (43)   ~ (e3 = e1)
% 173.46/26.56    (44)   ~ (all_52_27 = all_52_29)
% 173.46/26.56    (45)   ~ (all_52_17 = all_14_2)
% 173.46/26.56    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.56    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.56    (48)   ~ (all_52_7 = all_4_2)
% 173.46/26.56    (49)  all_58_1 = all_52_3
% 173.46/26.56    (50)   ~ (all_52_13 = all_52_15)
% 173.46/26.56    (51)  all_58_0 = all_4_2
% 173.46/26.56    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.56    (53)  op(e1, all_52_29) = all_52_28
% 173.46/26.56    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.56    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.56    (56)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 173.46/26.56    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.56    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.56    (59)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.56    (60)  all_58_14 = all_52_29
% 173.46/26.56    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 173.46/26.56    (62)  op(e2, all_4_2) = all_4_0
% 173.46/26.56    (63)   ~ (all_52_3 = all_52_5)
% 173.46/26.56    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.56    (65)  op(e2, e1) = all_52_13
% 173.46/26.56    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.56    (67)  all_58_8 = all_14_2
% 173.46/26.56    (68)  all_56_1 = all_52_3
% 173.46/26.56    (69)  op(e0, e2) = all_52_27
% 173.46/26.56    (70)  all_56_14 = all_52_29
% 173.46/26.56    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.56    (72)   ~ (all_52_3 = all_52_27)
% 173.46/26.56    (73)   ~ (all_52_3 = all_4_2)
% 173.46/26.56    (74)  op(e0, e3) = all_52_25
% 173.46/26.56    (75)  op(e0, all_6_2) = all_6_1
% 173.46/26.56    (76)  op(all_6_1, all_6_2) = e2
% 173.46/26.56    (77)  op(e3, all_52_17) = all_52_16
% 173.46/26.56    (78)   ~ (all_52_13 = all_14_2)
% 173.46/26.56    (79)  op(e3, all_52_9) = e3
% 173.46/26.56    (80)   ~ (e3 = e0)
% 173.46/26.56    (81)   ~ (all_52_9 = all_52_13)
% 173.46/26.56    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 173.46/26.56    (83)  op(e0, all_52_23) = all_52_22
% 173.46/26.56    (84)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.56    (85)   ~ (all_52_5 = all_52_29)
% 173.46/26.56    (86)  all_56_12 = all_52_25
% 173.46/26.56    (87)  all_58_13 = all_52_27
% 173.46/26.56    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.56    (89)   ~ (all_52_9 = all_52_17)
% 173.46/26.56    (90)  all_58_6 = all_52_17
% 173.46/26.56    (91)   ~ (all_52_3 = all_52_7)
% 173.46/26.56    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.56    (93)  op(e2, all_52_19) = all_52_18
% 173.46/26.56    (94)   ~ (e1 = e0)
% 173.46/26.56    (95)  all_56_0 = all_4_2
% 173.46/26.56    (96)  all_58_11 = all_52_23
% 173.46/26.56    (97)   ~ (all_52_3 = all_52_19)
% 173.46/26.56    (98)   ~ (all_52_7 = all_52_15)
% 173.46/26.56    (99)   ~ (all_52_29 = all_14_2)
% 173.46/26.56    (100)   ~ (all_4_0 = e1)
% 173.46/26.56    (101)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 173.46/26.56    (102)   ~ (all_52_19 = all_10_2)
% 173.46/26.56    (103)  op(e3, all_4_2) = e2
% 173.46/26.56    (104)   ~ (all_52_23 = all_6_2)
% 173.46/26.56    (105)   ~ (all_52_29 = all_6_2)
% 173.46/26.56    (106)  all_58_2 = all_52_9
% 173.46/26.56    (107)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.56    (108)  op(e3, e1) = all_52_5
% 173.46/26.56    (109)  all_56_10 = all_14_2
% 173.46/26.56    (110)   ~ (all_52_25 = all_6_2)
% 173.46/26.56    (111)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 173.46/26.56    (112)  op(e1, e3) = all_52_17
% 173.46/26.56    (113)   ~ (all_52_25 = all_4_2)
% 173.46/26.56    (114)  op(e3, e0) = all_52_7
% 173.46/26.56    (115)  op(e2, all_10_2) = e2
% 173.46/26.56    (116)  op(e3, e3) = all_4_2
% 173.46/26.56    (117)  all_56_8 = all_52_17
% 173.46/26.56    (118)   ~ (all_52_17 = all_4_2)
% 173.46/26.56    (119)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.56             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.56    (120)   ~ (all_52_25 = all_52_27)
% 173.46/26.56    (121)   ~ (all_52_27 = all_6_2)
% 173.46/26.56    (122)  all_8_1 = all_6_1
% 173.46/26.56    (123)   ~ (all_52_7 = all_6_2)
% 173.46/26.56    (124)   ~ (all_10_0 = e3)
% 173.46/26.56    (125)   ~ (all_52_7 = all_52_23)
% 173.46/26.56    (126)   ~ (all_52_13 = all_10_2)
% 173.46/26.56    (127)  op(e2, all_52_27) = all_52_26
% 173.46/26.56    (128)   ~ (all_52_17 = all_52_19)
% 173.46/26.56    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.56    (130)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.56    (131)  op(e1, all_14_2) = all_14_1
% 173.46/26.56    (132)  all_58_9 = all_52_7
% 173.46/26.56    (133)  all_58_12 = all_52_25
% 173.46/26.56    (134)   ~ (all_10_0 = e1)
% 173.46/26.56    (135)  all_56_6 = all_52_13
% 173.46/26.56    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 173.46/26.56    (137)   ~ (all_52_9 = all_52_15)
% 173.46/26.56    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.56    (139)   ~ (all_52_19 = all_14_2)
% 173.46/26.56    (140)  op(e2, e3) = all_52_9
% 173.46/26.56    (141)  all_56_13 = all_52_27
% 173.46/26.56  
% 173.46/26.56  Begin of proof
% 173.46/26.56  | 
% 173.46/26.56  | GROUND_INST: instantiating (119) with e2, all_10_0, all_10_2, e2, simplifying
% 173.46/26.56  |              with (7), (115) gives:
% 173.46/26.56  |   (142)  all_10_0 = e2
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (124), (142) imply:
% 173.46/26.56  |   (143)   ~ (e3 = e2)
% 173.46/26.56  | 
% 173.46/26.56  | SIMP: (143) implies:
% 173.46/26.56  |   (144)   ~ (e3 = e2)
% 173.46/26.56  | 
% 173.46/26.56  | REDUCE: (134), (142) imply:
% 173.46/26.56  |   (145)   ~ (e2 = e1)
% 173.46/26.56  | 
% 173.46/26.56  | BETA: splitting (46) gives:
% 173.46/26.56  | 
% 173.46/26.56  | Case 1:
% 173.46/26.56  | | 
% 173.46/26.56  | |   (146)  all_56_15 = e3
% 173.46/26.56  | | 
% 173.46/26.56  | | COMBINE_EQS: (25), (146) imply:
% 173.46/26.56  | |   (147)  all_6_2 = e3
% 173.46/26.56  | | 
% 173.46/26.56  | | SIMP: (147) implies:
% 173.46/26.56  | |   (148)  all_6_2 = e3
% 173.46/26.56  | | 
% 173.46/26.56  | | REF_CLOSE: (11), (16), (24), (74), (75), (76), (82), (86), (101), (110),
% 173.46/26.56  | |            (111), (119), (133), (140), (148) are inconsistent by sub-proof
% 173.46/26.56  | |            #226.
% 173.46/26.56  | | 
% 173.46/26.56  | Case 2:
% 173.46/26.56  | | 
% 173.46/26.56  | |   (149)   ~ (all_56_15 = e3)
% 173.46/26.56  | |   (150)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.56  | | 
% 173.46/26.56  | | REDUCE: (25), (149) imply:
% 173.46/26.56  | |   (151)   ~ (all_6_2 = e3)
% 173.46/26.56  | | 
% 173.46/26.56  | | BETA: splitting (61) gives:
% 173.46/26.56  | | 
% 173.46/26.56  | | Case 1:
% 173.46/26.56  | | | 
% 173.46/26.56  | | |   (152)  all_56_13 = e3
% 173.46/26.56  | | | 
% 173.46/26.56  | | | COMBINE_EQS: (141), (152) imply:
% 173.46/26.56  | | |   (153)  all_52_27 = e3
% 173.46/26.56  | | | 
% 173.46/26.56  | | | SIMP: (153) implies:
% 173.46/26.56  | | |   (154)  all_52_27 = e3
% 173.46/26.56  | | | 
% 173.46/26.57  | | | REF_CLOSE: (2), (5), (10), (11), (18), (19), (22), (23), (26), (28), (30),
% 173.46/26.57  | | |            (31), (32), (33), (34), (37), (38), (39), (41), (42), (43),
% 173.46/26.57  | | |            (44), (45), (47), (48), (49), (51), (56), (58), (60), (64),
% 173.46/26.57  | | |            (67), (70), (72), (73), (74), (77), (79), (87), (88), (89),
% 173.46/26.57  | | |            (90), (92), (95), (96), (98), (103), (106), (112), (113),
% 173.46/26.57  | | |            (115), (116), (117), (118), (119), (120), (121), (127), (128),
% 173.46/26.57  | | |            (129), (132), (133), (137), (138), (140), (144), (154) are
% 173.46/26.57  | | |            inconsistent by sub-proof #103.
% 173.46/26.57  | | | 
% 173.46/26.57  | | Case 2:
% 173.46/26.57  | | | 
% 173.46/26.57  | | |   (155)   ~ (all_56_13 = e3)
% 173.46/26.57  | | | 
% 173.46/26.57  | | | REDUCE: (141), (155) imply:
% 173.46/26.57  | | |   (156)   ~ (all_52_27 = e3)
% 173.46/26.57  | | | 
% 173.46/26.57  | | | BETA: splitting (66) gives:
% 173.46/26.57  | | | 
% 173.46/26.57  | | | Case 1:
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | |   (157)  all_58_12 = e3
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | COMBINE_EQS: (133), (157) imply:
% 173.46/26.57  | | | |   (158)  all_52_25 = e3
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | SIMP: (158) implies:
% 173.46/26.57  | | | |   (159)  all_52_25 = e3
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | REDUCE: (11), (159) imply:
% 173.46/26.57  | | | |   (160)   ~ (all_52_9 = e3)
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | REDUCE: (120), (159) imply:
% 173.46/26.57  | | | |   (161)   ~ (all_52_27 = e3)
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | REDUCE: (21), (159) imply:
% 173.46/26.57  | | | |   (162)   ~ (all_52_29 = e3)
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | SIMP: (162) implies:
% 173.46/26.57  | | | |   (163)   ~ (all_52_29 = e3)
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | REDUCE: (110), (159) imply:
% 173.46/26.57  | | | |   (164)   ~ (all_6_2 = e3)
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | REDUCE: (113), (159) imply:
% 173.46/26.57  | | | |   (165)   ~ (all_4_2 = e3)
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | SIMP: (165) implies:
% 173.46/26.57  | | | |   (166)   ~ (all_4_2 = e3)
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | REDUCE: (74), (159) imply:
% 173.46/26.57  | | | |   (167)  op(e0, e3) = e3
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (13), (14), (15),
% 173.46/26.57  | | | |            (18), (19), (20), (22), (23), (25), (26), (28), (29), (30),
% 173.46/26.57  | | | |            (31), (32), (33), (34), (36), (37), (38), (41), (42), (44),
% 173.46/26.57  | | | |            (45), (47), (48), (49), (50), (51), (52), (54), (55), (57),
% 173.46/26.57  | | | |            (58), (59), (60), (63), (65), (67), (68), (69), (71), (73),
% 173.46/26.57  | | | |            (75), (76), (77), (78), (79), (80), (81), (83), (84), (87),
% 173.46/26.57  | | | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 173.46/26.57  | | | |            (99), (102), (103), (104), (105), (106), (107), (108), (109),
% 173.46/26.57  | | | |            (112), (114), (115), (119), (121), (123), (125), (126),
% 173.46/26.57  | | | |            (128), (129), (130), (131), (132), (135), (137), (138),
% 173.46/26.57  | | | |            (139), (140), (144), (145), (150), (151), (156), (157),
% 173.46/26.57  | | | |            (160), (163), (166), (167) are inconsistent by sub-proof #16.
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | Case 2:
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | |   (168)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | BETA: splitting (168) gives:
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | | Case 1:
% 173.46/26.57  | | | | | 
% 173.46/26.57  | | | | |   (169)  all_58_13 = e3
% 173.46/26.57  | | | | | 
% 173.46/26.57  | | | | | REF_CLOSE: (87), (156), (169) are inconsistent by sub-proof #1026.
% 173.46/26.57  | | | | | 
% 173.46/26.57  | | | | Case 2:
% 173.46/26.57  | | | | | 
% 173.46/26.57  | | | | |   (170)  all_58_14 = e3 | all_58_15 = e3
% 173.46/26.57  | | | | | 
% 173.46/26.57  | | | | | BETA: splitting (170) gives:
% 173.46/26.57  | | | | | 
% 173.46/26.57  | | | | | Case 1:
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | |   (171)  all_58_14 = e3
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | COMBINE_EQS: (60), (171) imply:
% 173.46/26.57  | | | | | |   (172)  all_52_29 = e3
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | SIMP: (172) implies:
% 173.46/26.57  | | | | | |   (173)  all_52_29 = e3
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (85), (173) imply:
% 173.46/26.57  | | | | | |   (174)   ~ (all_52_5 = e3)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (21), (173) imply:
% 173.46/26.57  | | | | | |   (175)   ~ (all_52_25 = e3)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (105), (173) imply:
% 173.46/26.57  | | | | | |   (176)   ~ (all_6_2 = e3)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (53), (173) imply:
% 173.46/26.57  | | | | | |   (177)  op(e1, e3) = all_52_28
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (40), (173) imply:
% 173.46/26.57  | | | | | |   (178)  op(e0, e1) = e3
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | GROUND_INST: instantiating (119) with all_52_17, all_52_28, e3, e1,
% 173.46/26.57  | | | | | |              simplifying with (112), (177) gives:
% 173.46/26.57  | | | | | |   (179)  all_52_17 = all_52_28
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | COMBINE_EQS: (90), (179) imply:
% 173.46/26.57  | | | | | |   (180)  all_58_6 = all_52_28
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (5), (179) imply:
% 173.46/26.57  | | | | | |   (181)   ~ (all_52_23 = all_52_28)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | SIMP: (181) implies:
% 173.46/26.57  | | | | | |   (182)   ~ (all_52_23 = all_52_28)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (39), (179) imply:
% 173.46/26.57  | | | | | |   (183)   ~ (all_52_25 = all_52_28)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | SIMP: (183) implies:
% 173.46/26.57  | | | | | |   (184)   ~ (all_52_25 = all_52_28)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (45), (179) imply:
% 173.46/26.57  | | | | | |   (185)   ~ (all_52_28 = all_14_2)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (118), (179) imply:
% 173.46/26.57  | | | | | |   (186)   ~ (all_52_28 = all_4_2)
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | BETA: splitting (130) gives:
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | Case 1:
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | |   (187)  all_56_3 = e3
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | | COMBINE_EQS: (9), (187) imply:
% 173.46/26.57  | | | | | | |   (188)  all_52_7 = e3
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | | REF_CLOSE: (10), (18), (19), (22), (28), (32), (33), (34), (37),
% 173.46/26.57  | | | | | | |            (41), (42), (43), (44), (45), (47), (48), (49), (51),
% 173.46/26.57  | | | | | | |            (56), (58), (60), (64), (67), (70), (79), (87), (89),
% 173.46/26.57  | | | | | | |            (90), (98), (106), (112), (115), (116), (119), (128),
% 173.46/26.57  | | | | | | |            (133), (138), (140), (175), (188) are inconsistent by
% 173.46/26.57  | | | | | | |            sub-proof #104.
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | Case 2:
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | |   (189)   ~ (all_56_3 = e3)
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | | REDUCE: (9), (189) imply:
% 173.46/26.57  | | | | | | |   (190)   ~ (all_52_7 = e3)
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | | BETA: splitting (129) gives:
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | 
% 173.46/26.57  | | | | | | | |   (191)  all_58_9 = e3
% 173.46/26.57  | | | | | | | | 
% 173.46/26.57  | | | | | | | | REF_CLOSE: (132), (190), (191) are inconsistent by sub-proof
% 173.46/26.57  | | | | | | | |            #972.
% 173.46/26.57  | | | | | | | | 
% 173.46/26.57  | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | 
% 173.46/26.57  | | | | | | | |   (192)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.57  | | | | | | | | 
% 173.46/26.57  | | | | | | | | BETA: splitting (136) gives:
% 173.46/26.57  | | | | | | | | 
% 173.46/26.57  | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | |   (193)  all_58_0 = e3
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | COMBINE_EQS: (51), (193) imply:
% 173.46/26.57  | | | | | | | | |   (194)  all_4_2 = e3
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | REDUCE: (103), (194) imply:
% 173.46/26.57  | | | | | | | | |   (195)  op(e3, e3) = e2
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | REDUCE: (116), (194) imply:
% 173.46/26.57  | | | | | | | | |   (196)  op(e3, e3) = e3
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | GROUND_INST: instantiating (119) with e2, e3, e3, e3,
% 173.46/26.57  | | | | | | | | |              simplifying with (195), (196) gives:
% 173.46/26.57  | | | | | | | | |   (197)  e3 = e2
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | REDUCE: (144), (197) imply:
% 173.46/26.57  | | | | | | | | |   (198)  $false
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | CLOSE: (198) is inconsistent.
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | |   (199)   ~ (all_58_0 = e3)
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | REDUCE: (51), (199) imply:
% 173.46/26.57  | | | | | | | | |   (200)   ~ (all_4_2 = e3)
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | BETA: splitting (47) gives:
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | |   (201)  all_58_2 = e3
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | COMBINE_EQS: (106), (201) imply:
% 173.46/26.57  | | | | | | | | | |   (202)  all_52_9 = e3
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | REF_CLOSE: (32), (79), (116), (119), (202) are inconsistent
% 173.46/26.57  | | | | | | | | | |            by sub-proof #967.
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | |   (203)   ~ (all_58_2 = e3)
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | REDUCE: (106), (203) imply:
% 173.46/26.57  | | | | | | | | | |   (204)   ~ (all_52_9 = e3)
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | BETA: splitting (64) gives:
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | |   (205)  all_58_0 = e3
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | COMBINE_EQS: (51), (205) imply:
% 173.46/26.57  | | | | | | | | | | |   (206)  all_4_2 = e3
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | REDUCE: (200), (206) imply:
% 173.46/26.57  | | | | | | | | | | |   (207)  $false
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | |   (208)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | BETA: splitting (208) gives:
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | |   (209)  all_58_2 = e3
% 173.46/26.57  | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | REF_CLOSE: (106), (204), (209) are inconsistent by sub-proof
% 173.46/26.57  | | | | | | | | | | | |            #980.
% 173.46/26.57  | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | |   (210)  all_58_6 = e3 | all_58_12 = e3
% 173.46/26.57  | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | BETA: splitting (210) gives:
% 173.46/26.57  | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | |   (211)  all_58_6 = e3
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | COMBINE_EQS: (180), (211) imply:
% 173.46/26.57  | | | | | | | | | | | | |   (212)  all_52_28 = e3
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | SIMP: (212) implies:
% 173.46/26.57  | | | | | | | | | | | | |   (213)  all_52_28 = e3
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | REDUCE: (182), (213) imply:
% 173.46/26.57  | | | | | | | | | | | | |   (214)   ~ (all_52_23 = e3)
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | REDUCE: (185), (213) imply:
% 173.46/26.57  | | | | | | | | | | | | |   (215)   ~ (all_14_2 = e3)
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | SIMP: (215) implies:
% 173.46/26.57  | | | | | | | | | | | | |   (216)   ~ (all_14_2 = e3)
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | REDUCE: (186), (213) imply:
% 173.46/26.57  | | | | | | | | | | | | |   (217)   ~ (all_4_2 = e3)
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | BETA: splitting (192) gives:
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | |   (218)  all_58_10 = e3
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | COMBINE_EQS: (34), (218) imply:
% 173.46/26.57  | | | | | | | | | | | | | |   (219)  all_52_15 = e3
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | SIMP: (219) implies:
% 173.46/26.57  | | | | | | | | | | | | | |   (220)  all_52_15 = e3
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | REDUCE: (23), (220) imply:
% 173.46/26.57  | | | | | | | | | | | | | |   (221)  op(e0, e3) = e0
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | GROUND_INST: instantiating (119) with all_52_25, e0, e3, e0,
% 173.46/26.57  | | | | | | | | | | | | | |              simplifying with (74), (221) gives:
% 173.46/26.57  | | | | | | | | | | | | | |   (222)  all_52_25 = e0
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | COMBINE_EQS: (133), (222) imply:
% 173.46/26.57  | | | | | | | | | | | | | |   (223)  all_58_12 = e0
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | REDUCE: (12), (222) imply:
% 173.46/26.57  | | | | | | | | | | | | | |   (224)  op(e3, e0) = all_52_24
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | GROUND_INST: instantiating (119) with all_52_7, all_52_24, e0,
% 173.46/26.57  | | | | | | | | | | | | | |              e3, simplifying with (114), (224) gives:
% 173.46/26.57  | | | | | | | | | | | | | |   (225)  all_52_7 = all_52_24
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | COMBINE_EQS: (132), (225) imply:
% 173.46/26.57  | | | | | | | | | | | | | |   (226)  all_58_9 = all_52_24
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | REDUCE: (48), (225) imply:
% 173.46/26.57  | | | | | | | | | | | | | |   (227)   ~ (all_52_24 = all_4_2)
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | |   (228)  all_58_0 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | COMBINE_EQS: (51), (228) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (229)  all_4_2 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | REDUCE: (36), (229) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (230)   ~ (all_52_5 = e1)
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | REDUCE: (227), (229) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (231)   ~ (all_52_24 = e1)
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | REDUCE: (200), (229) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (232)   ~ (e3 = e1)
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | REDUCE: (103), (229) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (233)  op(e3, e1) = e2
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | REDUCE: (62), (229) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (234)  op(e2, e1) = all_4_0
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (119) with all_52_13, all_4_0, e1,
% 173.46/26.57  | | | | | | | | | | | | | | |              e2, simplifying with (65), (234) gives:
% 173.46/26.57  | | | | | | | | | | | | | | |   (235)  all_52_13 = all_4_0
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | GROUND_INST: instantiating (119) with all_52_5, e2, e1, e3,
% 173.46/26.57  | | | | | | | | | | | | | | |              simplifying with (108), (233) gives:
% 173.46/26.57  | | | | | | | | | | | | | | |   (236)  all_52_5 = e2
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | COMBINE_EQS: (19), (235) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (237)  all_58_5 = all_4_0
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | COMBINE_EQS: (41), (236) imply:
% 173.46/26.57  | | | | | | | | | | | | | | |   (238)  all_58_4 = e2
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | |   (239)  all_58_4 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (239) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | |   (240)  e2 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | SIMP: (240) implies:
% 173.46/26.57  | | | | | | | | | | | | | | | |   (241)  e2 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | REDUCE: (145), (241) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | |   (242)  $false
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | |   (243)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | |   (244)  all_58_5 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (244) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | |   (245)  all_4_0 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | SIMP: (245) implies:
% 173.46/26.57  | | | | | | | | | | | | | | | | |   (246)  all_4_0 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | REDUCE: (100), (246) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | |   (247)  $false
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | |   (248)  all_58_8 = e1 | all_58_14 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | |   (249)  all_58_8 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (67), (249) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | | |   (250)  all_14_2 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | REDUCE: (1), (250) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | | |   (251)   ~ (all_52_23 = e1)
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | Case 1:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | |   (252)  all_58_9 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (226), (252) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | |   (253)  all_52_24 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | SIMP: (253) implies:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | |   (254)  all_52_24 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | REDUCE: (231), (254) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | |   (255)  $false
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | CLOSE: (255) is inconsistent.
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | |   (256)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (31), (35), (43), (75), (96), (119), (122),
% 173.46/26.57  | | | | | | | | | | | | | | | | | | |            (178), (218), (251), (256) are inconsistent by
% 173.46/26.57  | | | | | | | | | | | | | | | | | | |            sub-proof #174.
% 173.46/26.57  | | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | |   (257)  all_58_14 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (257) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | | |   (258)  e3 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | SIMP: (258) implies:
% 173.46/26.57  | | | | | | | | | | | | | | | | | |   (259)  e3 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (259) imply:
% 173.46/26.57  | | | | | | | | | | | | | | | | | |   (260)  all_58_6 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (133), (175), (210), (260) are inconsistent
% 173.46/26.57  | | | | | | | | | | | | | | | | | |            by sub-proof #1002.
% 173.46/26.57  | | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | |   (261)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | | REF_CLOSE: (43), (79), (94), (106), (108), (119), (174),
% 173.46/26.57  | | | | | | | | | | | | | | |            (211), (223), (261) are inconsistent by sub-proof
% 173.46/26.57  | | | | | | | | | | | | | | |            #725.
% 173.46/26.57  | | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | |   (262)  all_58_11 = e3 | all_58_15 = e3
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | | REF_CLOSE: (31), (96), (151), (214), (262) are inconsistent
% 173.46/26.57  | | | | | | | | | | | | | |            by sub-proof #1016.
% 173.46/26.57  | | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | Case 2:
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | |   (263)  all_58_12 = e3
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | | REF_CLOSE: (133), (175), (263) are inconsistent by sub-proof
% 173.46/26.57  | | | | | | | | | | | | |            #1003.
% 173.46/26.57  | | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | | 
% 173.46/26.57  | | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | | 
% 173.46/26.57  | | | | | | | | End of split
% 173.46/26.57  | | | | | | | | 
% 173.46/26.57  | | | | | | | End of split
% 173.46/26.57  | | | | | | | 
% 173.46/26.57  | | | | | | End of split
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | Case 2:
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | |   (264)  all_58_15 = e3
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | COMBINE_EQS: (31), (264) imply:
% 173.46/26.57  | | | | | |   (265)  all_6_2 = e3
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | REDUCE: (151), (265) imply:
% 173.46/26.57  | | | | | |   (266)  $false
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | | CLOSE: (266) is inconsistent.
% 173.46/26.57  | | | | | | 
% 173.46/26.57  | | | | | End of split
% 173.46/26.57  | | | | | 
% 173.46/26.57  | | | | End of split
% 173.46/26.57  | | | | 
% 173.46/26.57  | | | End of split
% 173.46/26.57  | | | 
% 173.46/26.57  | | End of split
% 173.46/26.57  | | 
% 173.46/26.57  | End of split
% 173.46/26.57  | 
% 173.46/26.57  End of proof
% 173.46/26.57  
% 173.46/26.57  Sub-proof #16 shows that the following formulas are inconsistent:
% 173.46/26.57  ----------------------------------------------------------------
% 173.46/26.57    (1)   ~ (all_52_23 = all_14_2)
% 173.46/26.57    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 173.46/26.57    (3)   ~ (all_52_27 = all_10_2)
% 173.46/26.57    (4)   ~ (all_52_17 = all_52_23)
% 173.46/26.57    (5)   ~ (all_52_13 = all_52_29)
% 173.46/26.57    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 173.46/26.57    (7)  all_56_3 = all_52_7
% 173.46/26.57    (8)  op(e3, e2) = all_52_3
% 173.46/26.57    (9)   ~ (all_52_19 = all_52_23)
% 173.46/26.57    (10)  all_56_11 = all_52_23
% 173.46/26.57    (11)  op(e1, e2) = all_52_19
% 173.46/26.57    (12)   ~ (all_52_27 = e3)
% 173.46/26.57    (13)   ~ (all_6_2 = e3)
% 173.46/26.57    (14)   ~ (all_52_3 = all_10_2)
% 173.46/26.57    (15)  all_58_5 = all_52_13
% 173.46/26.57    (16)   ~ (all_6_2 = e0)
% 173.46/26.57    (17)  op(e1, all_52_13) = e1
% 173.46/26.57    (18)  op(e0, all_52_15) = e0
% 173.46/26.57    (19)  all_56_15 = all_6_2
% 173.46/26.57    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 173.46/26.57    (21)   ~ (all_4_2 = e3)
% 173.46/26.57    (22)  all_58_3 = all_10_2
% 173.46/26.57    (23)  all_56_9 = all_52_19
% 173.46/26.57    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.57    (25)  all_58_15 = all_6_2
% 173.46/26.57    (26)   ~ (all_52_9 = all_4_2)
% 173.46/26.57    (27)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 173.46/26.57    (28)   ~ (all_52_5 = all_52_7)
% 173.46/26.57    (29)  all_58_10 = all_52_15
% 173.46/26.57    (30)   ~ (all_52_5 = all_4_2)
% 173.46/26.57    (31)  all_58_7 = all_52_19
% 173.46/26.57    (32)  all_56_4 = all_52_9
% 173.46/26.57    (33)  all_58_4 = all_52_5
% 173.46/26.57    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 173.46/26.57    (35)   ~ (all_52_27 = all_52_29)
% 173.46/26.57    (36)   ~ (all_52_17 = all_14_2)
% 173.46/26.57    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 173.46/26.57    (38)   ~ (all_52_7 = all_4_2)
% 173.46/26.57    (39)  all_58_1 = all_52_3
% 173.46/26.57    (40)   ~ (all_52_13 = all_52_15)
% 173.46/26.57    (41)  all_58_0 = all_4_2
% 173.46/26.57    (42)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 173.46/26.57    (43)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 173.46/26.57    (44)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 173.46/26.57    (45)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 173.46/26.57    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 173.46/26.57    (47)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 173.46/26.57    (48)  all_58_14 = all_52_29
% 173.46/26.57    (49)  op(e0, e3) = e3
% 173.46/26.57    (50)   ~ (all_52_3 = all_52_5)
% 173.46/26.57    (51)  op(e2, e1) = all_52_13
% 173.46/26.57    (52)  all_58_8 = all_14_2
% 173.46/26.57    (53)  all_56_1 = all_52_3
% 173.46/26.57    (54)  op(e0, e2) = all_52_27
% 173.46/26.57    (55)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 173.46/26.57    (56)   ~ (all_52_3 = all_4_2)
% 173.46/26.57    (57)  op(e0, all_6_2) = all_6_1
% 173.46/26.57    (58)  op(all_6_1, all_6_2) = e2
% 173.46/26.57    (59)  op(e3, all_52_17) = all_52_16
% 173.46/26.57    (60)   ~ (all_52_29 = e3)
% 173.46/26.57    (61)   ~ (all_52_13 = all_14_2)
% 173.46/26.57    (62)  op(e3, all_52_9) = e3
% 173.46/26.57    (63)   ~ (e3 = e0)
% 173.46/26.57    (64)   ~ (all_52_9 = all_52_13)
% 173.46/26.57    (65)  op(e0, all_52_23) = all_52_22
% 173.46/26.57    (66)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 173.46/26.57    (67)  all_58_13 = all_52_27
% 173.46/26.57    (68)  all_58_12 = e3
% 173.46/26.57    (69)   ~ (all_52_9 = all_52_17)
% 173.46/26.57    (70)  all_58_6 = all_52_17
% 173.46/26.57    (71)   ~ (all_52_3 = all_52_7)
% 173.46/26.57    (72)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.57    (73)  op(e2, all_52_19) = all_52_18
% 173.46/26.57    (74)   ~ (e1 = e0)
% 173.46/26.57    (75)  all_56_0 = all_4_2
% 173.46/26.57    (76)  all_58_11 = all_52_23
% 173.46/26.57    (77)   ~ (all_52_3 = all_52_19)
% 173.46/26.57    (78)   ~ (all_52_7 = all_52_15)
% 173.46/26.57    (79)   ~ (all_52_29 = all_14_2)
% 173.46/26.57    (80)   ~ (all_52_19 = all_10_2)
% 173.46/26.57    (81)   ~ (all_52_9 = e3)
% 173.46/26.57    (82)  op(e3, all_4_2) = e2
% 173.46/26.57    (83)   ~ (all_52_23 = all_6_2)
% 173.46/26.57    (84)   ~ (all_52_29 = all_6_2)
% 173.46/26.57    (85)  all_58_2 = all_52_9
% 173.46/26.57    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 173.46/26.57    (87)  op(e3, e1) = all_52_5
% 173.46/26.57    (88)   ~ (e2 = e1)
% 173.46/26.57    (89)  all_56_10 = all_14_2
% 173.46/26.57    (90)  op(e1, e3) = all_52_17
% 173.46/26.57    (91)  op(e3, e0) = all_52_7
% 173.46/26.57    (92)  op(e2, all_10_2) = e2
% 173.46/26.57    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 173.46/26.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 173.46/26.57    (94)   ~ (all_52_27 = all_6_2)
% 173.46/26.57    (95)   ~ (all_52_7 = all_6_2)
% 173.46/26.57    (96)   ~ (all_52_7 = all_52_23)
% 173.46/26.57    (97)   ~ (all_52_13 = all_10_2)
% 173.46/26.57    (98)   ~ (all_52_17 = all_52_19)
% 173.46/26.57    (99)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 173.46/26.58    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 173.46/26.58    (101)  op(e1, all_14_2) = all_14_1
% 173.46/26.58    (102)  all_58_9 = all_52_7
% 173.46/26.58    (103)  all_56_6 = all_52_13
% 173.46/26.58    (104)   ~ (all_52_9 = all_52_15)
% 173.46/26.58    (105)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 173.46/26.58    (106)   ~ (e3 = e2)
% 173.46/26.58    (107)   ~ (all_52_19 = all_14_2)
% 173.46/26.58    (108)  op(e2, e3) = all_52_9
% 173.46/26.58  
% 173.46/26.58  Begin of proof
% 173.46/26.58  | 
% 173.46/26.58  | BETA: splitting (72) gives:
% 173.46/26.58  | 
% 173.46/26.58  | Case 1:
% 173.46/26.58  | | 
% 173.46/26.58  | |   (109)  all_56_4 = e3
% 173.46/26.58  | | 
% 173.46/26.58  | | REF_CLOSE: (32), (81), (109) are inconsistent by sub-proof #782.
% 173.46/26.58  | | 
% 173.46/26.58  | Case 2:
% 173.46/26.58  | | 
% 173.46/26.58  | |   (110)   ~ (all_56_4 = e3)
% 173.46/26.58  | |   (111)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 173.46/26.58  | | 
% 173.46/26.58  | | BETA: splitting (24) gives:
% 173.46/26.58  | | 
% 173.46/26.58  | | Case 1:
% 173.46/26.58  | | | 
% 173.46/26.58  | | |   (112)  all_56_0 = e3
% 173.46/26.58  | | | 
% 173.46/26.58  | | | COMBINE_EQS: (75), (112) imply:
% 173.46/26.58  | | |   (113)  all_4_2 = e3
% 173.46/26.58  | | | 
% 173.46/26.58  | | | REDUCE: (21), (113) imply:
% 173.46/26.58  | | |   (114)  $false
% 173.46/26.58  | | | 
% 173.46/26.58  | | | CLOSE: (114) is inconsistent.
% 173.46/26.58  | | | 
% 173.46/26.58  | | Case 2:
% 173.46/26.58  | | | 
% 173.46/26.58  | | |   (115)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 173.46/26.58  | | | 
% 173.46/26.58  | | | BETA: splitting (47) gives:
% 173.46/26.58  | | | 
% 173.46/26.58  | | | Case 1:
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | |   (116)  all_56_6 = e3
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | | COMBINE_EQS: (103), (116) imply:
% 173.46/26.58  | | | |   (117)  all_52_13 = e3
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | | SIMP: (117) implies:
% 173.46/26.58  | | | |   (118)  all_52_13 = e3
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | | COMBINE_EQS: (15), (118) imply:
% 173.46/26.58  | | | |   (119)  all_58_5 = e3
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | | REDUCE: (40), (118) imply:
% 173.46/26.58  | | | |   (120)   ~ (all_52_15 = e3)
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | | SIMP: (120) implies:
% 173.46/26.58  | | | |   (121)   ~ (all_52_15 = e3)
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | | REDUCE: (5), (118) imply:
% 173.46/26.58  | | | |   (122)   ~ (all_52_29 = e3)
% 173.46/26.58  | | | | 
% 173.46/26.58  | | | | REDUCE: (97), (118) imply:
% 174.00/26.58  | | | |   (123)   ~ (all_10_2 = e3)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | SIMP: (123) implies:
% 174.00/26.58  | | | |   (124)   ~ (all_10_2 = e3)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | REDUCE: (17), (118) imply:
% 174.00/26.58  | | | |   (125)  op(e1, e3) = e1
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | GROUND_INST: instantiating (93) with all_52_17, e1, e3, e1, simplifying
% 174.00/26.58  | | | |              with (90), (125) gives:
% 174.00/26.58  | | | |   (126)  all_52_17 = e1
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | COMBINE_EQS: (70), (126) imply:
% 174.00/26.58  | | | |   (127)  all_58_6 = e1
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | REDUCE: (98), (126) imply:
% 174.00/26.58  | | | |   (128)   ~ (all_52_19 = e1)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | SIMP: (128) implies:
% 174.00/26.58  | | | |   (129)   ~ (all_52_19 = e1)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | REDUCE: (36), (126) imply:
% 174.00/26.58  | | | |   (130)   ~ (all_14_2 = e1)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | SIMP: (130) implies:
% 174.00/26.58  | | | |   (131)   ~ (all_14_2 = e1)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | REDUCE: (59), (126) imply:
% 174.00/26.58  | | | |   (132)  op(e3, e1) = all_52_16
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | GROUND_INST: instantiating (93) with all_52_5, all_52_16, e1, e3,
% 174.00/26.58  | | | |              simplifying with (87), (132) gives:
% 174.00/26.58  | | | |   (133)  all_52_5 = all_52_16
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | COMBINE_EQS: (33), (133) imply:
% 174.00/26.58  | | | |   (134)  all_58_4 = all_52_16
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | REDUCE: (50), (133) imply:
% 174.00/26.58  | | | |   (135)   ~ (all_52_3 = all_52_16)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | BETA: splitting (99) gives:
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | Case 1:
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | |   (136)  all_58_9 = e3
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | | COMBINE_EQS: (102), (136) imply:
% 174.00/26.58  | | | | |   (137)  all_52_7 = e3
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | | SIMP: (137) implies:
% 174.00/26.58  | | | | |   (138)  all_52_7 = e3
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | | REDUCE: (71), (138) imply:
% 174.00/26.58  | | | | |   (139)   ~ (all_52_3 = e3)
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | | BETA: splitting (46) gives:
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | | Case 1:
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | |   (140)  all_58_1 = e3
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | | COMBINE_EQS: (39), (140) imply:
% 174.00/26.58  | | | | | |   (141)  all_52_3 = e3
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | | REDUCE: (139), (141) imply:
% 174.00/26.58  | | | | | |   (142)  $false
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | | CLOSE: (142) is inconsistent.
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | Case 2:
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | |   (143)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | | BETA: splitting (143) gives:
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | | Case 1:
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | |   (144)  all_58_3 = e3
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | | COMBINE_EQS: (22), (144) imply:
% 174.00/26.58  | | | | | | |   (145)  all_10_2 = e3
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | | REDUCE: (124), (145) imply:
% 174.00/26.58  | | | | | | |   (146)  $false
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | | CLOSE: (146) is inconsistent.
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | Case 2:
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | |   (147)  all_58_7 = e3 | all_58_13 = e3
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | | BETA: splitting (147) gives:
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | | Case 1:
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | |   (148)  all_58_7 = e3
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | COMBINE_EQS: (31), (148) imply:
% 174.00/26.58  | | | | | | | |   (149)  all_52_19 = e3
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | REDUCE: (129), (149) imply:
% 174.00/26.58  | | | | | | | |   (150)   ~ (e3 = e1)
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | REDUCE: (73), (149) imply:
% 174.00/26.58  | | | | | | | |   (151)  op(e2, e3) = all_52_18
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | GROUND_INST: instantiating (93) with all_52_9, all_52_18, e3,
% 174.00/26.58  | | | | | | | |              e2, simplifying with (108), (151) gives:
% 174.00/26.58  | | | | | | | |   (152)  all_52_9 = all_52_18
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | COMBINE_EQS: (85), (152) imply:
% 174.00/26.58  | | | | | | | |   (153)  all_58_2 = all_52_18
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | REDUCE: (62), (152) imply:
% 174.00/26.58  | | | | | | | |   (154)  op(e3, all_52_18) = e3
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | BETA: splitting (45) gives:
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | Case 1:
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | |   (155)  all_58_4 = e1
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | | COMBINE_EQS: (134), (155) imply:
% 174.00/26.58  | | | | | | | | |   (156)  all_52_16 = e1
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | | SIMP: (156) implies:
% 174.00/26.58  | | | | | | | | |   (157)  all_52_16 = e1
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | | REDUCE: (135), (157) imply:
% 174.00/26.58  | | | | | | | | |   (158)   ~ (all_52_3 = e1)
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | | REF_CLOSE: (8), (20), (41), (43), (53), (56), (68), (82),
% 174.00/26.58  | | | | | | | | |            (88), (93), (106), (127), (139), (153), (154),
% 174.00/26.58  | | | | | | | | |            (158) are inconsistent by sub-proof #101.
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | Case 2:
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | |   (159)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | | REF_CLOSE: (6), (19), (27), (48), (52), (54), (57), (58),
% 174.00/26.58  | | | | | | | | |            (63), (67), (68), (74), (84), (93), (94), (119),
% 174.00/26.58  | | | | | | | | |            (131), (150), (159) are inconsistent by sub-proof
% 174.00/26.58  | | | | | | | | |            #168.
% 174.00/26.58  | | | | | | | | | 
% 174.00/26.58  | | | | | | | | End of split
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | Case 2:
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | |   (160)  all_58_13 = e3
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | | REF_CLOSE: (12), (67), (160) are inconsistent by sub-proof
% 174.00/26.58  | | | | | | | |            #1026.
% 174.00/26.58  | | | | | | | | 
% 174.00/26.58  | | | | | | | End of split
% 174.00/26.58  | | | | | | | 
% 174.00/26.58  | | | | | | End of split
% 174.00/26.58  | | | | | | 
% 174.00/26.58  | | | | | End of split
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | Case 2:
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | |   (161)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (12), (13), (14), (15),
% 174.00/26.58  | | | | |            (16), (17), (18), (19), (22), (23), (25), (26), (27), (28),
% 174.00/26.58  | | | | |            (29), (30), (31), (32), (33), (35), (36), (38), (39), (41),
% 174.00/26.58  | | | | |            (44), (45), (46), (48), (49), (50), (51), (52), (55), (59),
% 174.00/26.58  | | | | |            (60), (62), (63), (65), (67), (69), (71), (75), (76), (83),
% 174.00/26.58  | | | | |            (87), (90), (91), (92), (93), (94), (95), (96), (98), (99),
% 174.00/26.58  | | | | |            (100), (102), (105), (106), (108), (111), (115), (121),
% 174.00/26.58  | | | | |            (161) are inconsistent by sub-proof #366.
% 174.00/26.58  | | | | | 
% 174.00/26.58  | | | | End of split
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | Case 2:
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | |   (162)   ~ (all_56_6 = e3)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | REDUCE: (103), (162) imply:
% 174.00/26.58  | | | |   (163)   ~ (all_52_13 = e3)
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 174.00/26.58  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 174.00/26.58  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.00/26.58  | | | |            (35), (36), (37), (38), (39), (41), (42), (44), (45), (46),
% 174.00/26.58  | | | |            (47), (48), (49), (50), (51), (52), (55), (59), (60), (61),
% 174.00/26.58  | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 174.00/26.58  | | | |            (72), (73), (75), (76), (77), (78), (79), (80), (81), (83),
% 174.00/26.58  | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 174.00/26.58  | | | |            (95), (96), (98), (99), (100), (101), (102), (103), (104),
% 174.00/26.58  | | | |            (105), (106), (107), (108), (115), (163) are inconsistent by
% 174.00/26.58  | | | |            sub-proof #382.
% 174.00/26.58  | | | | 
% 174.00/26.58  | | | End of split
% 174.00/26.58  | | | 
% 174.00/26.58  | | End of split
% 174.00/26.58  | | 
% 174.00/26.58  | End of split
% 174.00/26.58  | 
% 174.00/26.58  End of proof
% 174.00/26.58  
% 174.00/26.58  Sub-proof #17 shows that the following formulas are inconsistent:
% 174.00/26.58  ----------------------------------------------------------------
% 174.00/26.58    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.58    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.58    (3)   ~ (all_52_17 = all_52_23)
% 174.00/26.58    (4)  op(e2, all_10_2) = all_10_1
% 174.00/26.58    (5)  op(e3, e2) = all_52_3
% 174.00/26.58    (6)   ~ (all_52_9 = all_52_25)
% 174.00/26.58    (7)  op(e3, all_52_25) = all_52_24
% 174.00/26.58    (8)   ~ (all_52_19 = all_52_23)
% 174.00/26.58    (9)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.00/26.58    (10)  op(e3, all_52_9) = all_52_8
% 174.00/26.58    (11)   ~ (all_52_3 = all_10_2)
% 174.00/26.58    (12)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.58    (13)  all_58_5 = all_52_13
% 174.00/26.58    (14)   ~ (all_52_25 = all_52_29)
% 174.00/26.58    (15)  all_56_15 = all_6_2
% 174.00/26.58    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.58    (17)  all_58_3 = all_10_2
% 174.00/26.58    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.58    (19)  all_58_15 = all_6_2
% 174.00/26.58    (20)   ~ (all_52_9 = all_4_2)
% 174.00/26.58    (21)   ~ (all_52_5 = all_52_7)
% 174.00/26.58    (22)  all_58_10 = all_52_15
% 174.00/26.58    (23)   ~ (all_52_5 = all_4_2)
% 174.00/26.58    (24)  all_58_7 = all_52_19
% 174.00/26.58    (25)   ~ (all_52_17 = all_52_25)
% 174.00/26.58    (26)  op(e0, e1) = all_52_29
% 174.00/26.58    (27)  all_58_4 = all_52_5
% 174.00/26.58    (28)   ~ (e3 = e1)
% 174.00/26.58    (29)   ~ (all_52_27 = all_52_29)
% 174.00/26.58    (30)   ~ (all_52_17 = all_14_2)
% 174.00/26.58    (31)  op(e3, all_4_2) = all_4_1
% 174.00/26.58    (32)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.58    (33)   ~ (all_52_7 = all_4_2)
% 174.00/26.58    (34)  all_58_1 = all_52_3
% 174.00/26.58    (35)   ~ (all_52_13 = all_52_15)
% 174.00/26.58    (36)  all_58_0 = all_4_2
% 174.00/26.58    (37)  all_52_0 = e2
% 174.00/26.58    (38)  op(e1, all_52_29) = all_52_28
% 174.00/26.58    (39)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.58    (40)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.58    (41)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.58    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.58    (43)  all_58_14 = all_52_29
% 174.00/26.58    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.58    (45)  op(e2, all_4_2) = all_4_0
% 174.00/26.58    (46)   ~ (all_52_3 = all_52_5)
% 174.00/26.58    (47)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.58    (48)  op(e2, e1) = all_52_13
% 174.00/26.58    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.58    (50)  all_58_8 = all_14_2
% 174.00/26.58    (51)  all_56_1 = all_52_3
% 174.00/26.58    (52)  op(e0, e2) = all_52_27
% 174.00/26.58    (53)  all_56_14 = all_52_29
% 174.00/26.58    (54)  op(all_4_1, all_4_2) = all_4_0
% 174.00/26.58    (55)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.58    (56)   ~ (all_52_3 = all_52_27)
% 174.00/26.58    (57)   ~ (all_52_3 = all_4_2)
% 174.00/26.58    (58)  op(e0, e3) = all_52_25
% 174.00/26.58    (59)  op(e0, all_6_2) = all_6_1
% 174.00/26.58    (60)   ~ (all_52_9 = all_10_2)
% 174.00/26.58    (61)  op(e3, all_52_17) = all_52_16
% 174.00/26.58    (62)  all_52_10 = all_10_1
% 174.00/26.58    (63)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.58    (64)   ~ (e3 = e0)
% 174.00/26.58    (65)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.58    (66)  op(all_14_1, all_14_2) = e2
% 174.00/26.58    (67)   ~ (all_52_9 = all_52_13)
% 174.00/26.58    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.58    (69)   ~ (all_52_5 = all_52_29)
% 174.00/26.58    (70)  all_56_2 = all_52_5
% 174.00/26.58    (71)  op(e1, e0) = all_52_23
% 174.00/26.58    (72)  all_56_12 = all_52_25
% 174.00/26.58    (73)  all_58_13 = all_52_27
% 174.00/26.58    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.58    (75)   ~ (all_52_9 = all_52_17)
% 174.00/26.58    (76)  all_58_6 = all_52_17
% 174.00/26.58    (77)   ~ (all_52_3 = all_52_7)
% 174.00/26.58    (78)  op(all_10_1, all_10_2) = e3
% 174.00/26.58    (79)   ~ (e1 = e0)
% 174.00/26.58    (80)  all_56_0 = all_4_2
% 174.00/26.58    (81)  all_58_11 = all_52_23
% 174.00/26.58    (82)   ~ (all_52_7 = all_52_15)
% 174.00/26.58    (83)   ~ (all_4_0 = e1)
% 174.00/26.58    (84)   ~ (all_52_19 = all_10_2)
% 174.00/26.58    (85)   ~ (all_58_15 = e0)
% 174.00/26.58    (86)  op(e3, all_4_2) = e2
% 174.00/26.58    (87)   ~ (all_52_29 = all_6_2)
% 174.00/26.58    (88)  all_58_2 = all_52_9
% 174.00/26.58    (89)  op(e3, e1) = all_52_5
% 174.00/26.58    (90)   ~ (e2 = e1)
% 174.00/26.58    (91)   ~ (all_52_25 = all_6_2)
% 174.00/26.58    (92)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.58    (93)  op(e1, e3) = all_52_17
% 174.00/26.58    (94)   ~ (all_52_25 = all_4_2)
% 174.00/26.58    (95)  op(e3, e0) = all_52_7
% 174.00/26.58    (96)  op(e3, e3) = all_4_2
% 174.00/26.58    (97)   ~ (all_52_17 = all_4_2)
% 174.00/26.58    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.58    (99)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.58          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.58          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.58          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.58    (100)   ~ (all_52_25 = all_52_27)
% 174.00/26.58    (101)   ~ (all_52_27 = all_6_2)
% 174.00/26.58    (102)   ~ (all_52_7 = all_6_2)
% 174.00/26.58    (103)   ~ (all_52_15 = all_10_2)
% 174.00/26.58    (104)   ~ (all_52_7 = all_52_23)
% 174.00/26.58    (105)  op(e2, all_52_27) = all_52_26
% 174.00/26.58    (106)  all_52_20 = all_14_1
% 174.00/26.58    (107)   ~ (all_52_17 = all_52_19)
% 174.00/26.58    (108)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.58    (109)  all_52_30 = all_6_1
% 174.00/26.58    (110)  op(e1, all_14_2) = all_14_1
% 174.00/26.58    (111)  all_58_9 = all_52_7
% 174.00/26.58    (112)   ~ (e2 = e0)
% 174.00/26.58    (113)  all_58_12 = all_52_25
% 174.00/26.58    (114)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.00/26.58             all_58_13 = e0 | all_58_14 = e0)
% 174.00/26.58    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.58    (116)   ~ (all_52_9 = all_52_15)
% 174.00/26.58    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.58    (118)   ~ (e3 = e2)
% 174.00/26.58    (119)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.00/26.58    (120)  op(e2, e3) = all_52_9
% 174.00/26.58    (121)  all_56_13 = all_52_27
% 174.00/26.58  
% 174.00/26.58  Begin of proof
% 174.00/26.58  | 
% 174.00/26.58  | ALPHA: (114) implies:
% 174.00/26.58  |   (122)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.00/26.58  |   (123)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.00/26.58  | 
% 174.00/26.58  | REDUCE: (19), (85) imply:
% 174.00/26.58  |   (124)   ~ (all_6_2 = e0)
% 174.00/26.58  | 
% 174.00/26.58  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.00/26.58  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.00/26.58  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.00/26.58  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.00/26.58  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.00/26.58  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.00/26.58  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.00/26.58  |            (79), (80), (81), (82), (83), (84), (86), (87), (88), (89), (90),
% 174.00/26.58  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.00/26.58  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 174.00/26.58  |            (111), (112), (113), (115), (116), (117), (118), (119), (120),
% 174.00/26.58  |            (121), (122), (123), (124) are inconsistent by sub-proof #18.
% 174.00/26.58  | 
% 174.00/26.58  End of proof
% 174.00/26.58  
% 174.00/26.58  Sub-proof #18 shows that the following formulas are inconsistent:
% 174.00/26.58  ----------------------------------------------------------------
% 174.00/26.58    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.58    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.58    (3)   ~ (all_52_17 = all_52_23)
% 174.00/26.58    (4)  op(e2, all_10_2) = all_10_1
% 174.00/26.58    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.00/26.58    (6)  op(e3, e2) = all_52_3
% 174.00/26.58    (7)   ~ (all_52_9 = all_52_25)
% 174.00/26.58    (8)  op(e3, all_52_25) = all_52_24
% 174.00/26.58    (9)   ~ (all_52_19 = all_52_23)
% 174.00/26.58    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.00/26.58    (11)  op(e3, all_52_9) = all_52_8
% 174.00/26.58    (12)   ~ (all_52_3 = all_10_2)
% 174.00/26.58    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.58    (14)  all_58_5 = all_52_13
% 174.00/26.58    (15)   ~ (all_6_2 = e0)
% 174.00/26.58    (16)   ~ (all_52_25 = all_52_29)
% 174.00/26.58    (17)  all_56_15 = all_6_2
% 174.00/26.58    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.58    (19)  all_58_3 = all_10_2
% 174.00/26.58    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.58    (21)  all_58_15 = all_6_2
% 174.00/26.58    (22)   ~ (all_52_9 = all_4_2)
% 174.00/26.58    (23)   ~ (all_52_5 = all_52_7)
% 174.00/26.58    (24)  all_58_10 = all_52_15
% 174.00/26.58    (25)   ~ (all_52_5 = all_4_2)
% 174.00/26.58    (26)  all_58_7 = all_52_19
% 174.00/26.58    (27)   ~ (all_52_17 = all_52_25)
% 174.00/26.58    (28)  op(e0, e1) = all_52_29
% 174.00/26.58    (29)  all_58_4 = all_52_5
% 174.00/26.58    (30)   ~ (e3 = e1)
% 174.00/26.58    (31)   ~ (all_52_27 = all_52_29)
% 174.00/26.58    (32)   ~ (all_52_17 = all_14_2)
% 174.00/26.58    (33)  op(e3, all_4_2) = all_4_1
% 174.00/26.58    (34)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.58    (35)   ~ (all_52_7 = all_4_2)
% 174.00/26.58    (36)  all_58_1 = all_52_3
% 174.00/26.58    (37)   ~ (all_52_13 = all_52_15)
% 174.00/26.58    (38)  all_58_0 = all_4_2
% 174.00/26.58    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.00/26.58    (40)  all_52_0 = e2
% 174.00/26.58    (41)  op(e1, all_52_29) = all_52_28
% 174.00/26.58    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.58    (43)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.58    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.58    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.58    (46)  all_58_14 = all_52_29
% 174.00/26.58    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.58    (48)  op(e2, all_4_2) = all_4_0
% 174.00/26.58    (49)   ~ (all_52_3 = all_52_5)
% 174.00/26.58    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.58    (51)  op(e2, e1) = all_52_13
% 174.00/26.58    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.58    (53)  all_58_8 = all_14_2
% 174.00/26.58    (54)  all_56_1 = all_52_3
% 174.00/26.58    (55)  op(e0, e2) = all_52_27
% 174.00/26.58    (56)  all_56_14 = all_52_29
% 174.00/26.58    (57)  op(all_4_1, all_4_2) = all_4_0
% 174.00/26.58    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.58    (59)   ~ (all_52_3 = all_52_27)
% 174.00/26.58    (60)   ~ (all_52_3 = all_4_2)
% 174.00/26.58    (61)  op(e0, e3) = all_52_25
% 174.00/26.58    (62)  op(e0, all_6_2) = all_6_1
% 174.00/26.58    (63)   ~ (all_52_9 = all_10_2)
% 174.00/26.58    (64)  op(e3, all_52_17) = all_52_16
% 174.00/26.58    (65)  all_52_10 = all_10_1
% 174.00/26.58    (66)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.58    (67)   ~ (e3 = e0)
% 174.00/26.58    (68)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.58    (69)  op(all_14_1, all_14_2) = e2
% 174.00/26.58    (70)   ~ (all_52_9 = all_52_13)
% 174.00/26.58    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.58    (72)   ~ (all_52_5 = all_52_29)
% 174.00/26.58    (73)  all_56_2 = all_52_5
% 174.00/26.58    (74)  op(e1, e0) = all_52_23
% 174.00/26.58    (75)  all_56_12 = all_52_25
% 174.00/26.58    (76)  all_58_13 = all_52_27
% 174.00/26.58    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.58    (78)   ~ (all_52_9 = all_52_17)
% 174.00/26.58    (79)  all_58_6 = all_52_17
% 174.00/26.58    (80)   ~ (all_52_3 = all_52_7)
% 174.00/26.58    (81)  op(all_10_1, all_10_2) = e3
% 174.00/26.58    (82)   ~ (e1 = e0)
% 174.00/26.58    (83)  all_56_0 = all_4_2
% 174.00/26.58    (84)  all_58_11 = all_52_23
% 174.00/26.58    (85)   ~ (all_52_7 = all_52_15)
% 174.00/26.58    (86)   ~ (all_4_0 = e1)
% 174.00/26.58    (87)   ~ (all_52_19 = all_10_2)
% 174.00/26.58    (88)  op(e3, all_4_2) = e2
% 174.00/26.58    (89)   ~ (all_52_29 = all_6_2)
% 174.00/26.58    (90)  all_58_2 = all_52_9
% 174.00/26.58    (91)  op(e3, e1) = all_52_5
% 174.00/26.58    (92)   ~ (e2 = e1)
% 174.00/26.58    (93)   ~ (all_52_25 = all_6_2)
% 174.00/26.58    (94)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.58    (95)  op(e1, e3) = all_52_17
% 174.00/26.58    (96)   ~ (all_52_25 = all_4_2)
% 174.00/26.59    (97)  op(e3, e0) = all_52_7
% 174.00/26.59    (98)  op(e3, e3) = all_4_2
% 174.00/26.59    (99)   ~ (all_52_17 = all_4_2)
% 174.00/26.59    (100)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.59             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.59    (101)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.59           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.59           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.59           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.59    (102)   ~ (all_52_25 = all_52_27)
% 174.00/26.59    (103)   ~ (all_52_27 = all_6_2)
% 174.00/26.59    (104)   ~ (all_52_7 = all_6_2)
% 174.00/26.59    (105)   ~ (all_52_15 = all_10_2)
% 174.00/26.59    (106)   ~ (all_52_7 = all_52_23)
% 174.00/26.59    (107)  op(e2, all_52_27) = all_52_26
% 174.00/26.59    (108)  all_52_20 = all_14_1
% 174.00/26.59    (109)   ~ (all_52_17 = all_52_19)
% 174.00/26.59    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.59    (111)  all_52_30 = all_6_1
% 174.00/26.59    (112)  op(e1, all_14_2) = all_14_1
% 174.00/26.59    (113)  all_58_9 = all_52_7
% 174.00/26.59    (114)   ~ (e2 = e0)
% 174.00/26.59    (115)  all_58_12 = all_52_25
% 174.00/26.59    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.59    (117)   ~ (all_52_9 = all_52_15)
% 174.00/26.59    (118)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.59    (119)   ~ (e3 = e2)
% 174.00/26.59    (120)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.00/26.59    (121)  op(e2, e3) = all_52_9
% 174.00/26.59    (122)  all_56_13 = all_52_27
% 174.00/26.59  
% 174.00/26.59  Begin of proof
% 174.00/26.59  | 
% 174.00/26.59  | BETA: splitting (101) gives:
% 174.00/26.59  | 
% 174.00/26.59  | Case 1:
% 174.00/26.59  | | 
% 174.00/26.59  | |   (123)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.59  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.00/26.59  | | 
% 174.00/26.59  | | REF_CLOSE: (4), (40), (65), (81), (100), (119), (123) are inconsistent by
% 174.00/26.59  | |            sub-proof #33.
% 174.00/26.59  | | 
% 174.00/26.59  | Case 2:
% 174.00/26.59  | | 
% 174.00/26.59  | |   (124)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.00/26.59  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.00/26.59  | |            e0)
% 174.00/26.59  | | 
% 174.00/26.59  | | BETA: splitting (124) gives:
% 174.00/26.59  | | 
% 174.00/26.59  | | Case 1:
% 174.00/26.59  | | | 
% 174.00/26.59  | | |   (125)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.00/26.59  | | | 
% 174.00/26.59  | | | ALPHA: (125) implies:
% 174.00/26.59  | | |   (126)  all_52_20 = e1
% 174.00/26.59  | | | 
% 174.00/26.59  | | | COMBINE_EQS: (108), (126) imply:
% 174.00/26.59  | | |   (127)  all_14_1 = e1
% 174.00/26.59  | | | 
% 174.00/26.59  | | | REF_CLOSE: (69), (92), (100), (112), (127) are inconsistent by sub-proof
% 174.00/26.59  | | |            #315.
% 174.00/26.59  | | | 
% 174.00/26.59  | | Case 2:
% 174.00/26.59  | | | 
% 174.00/26.59  | | |   (128)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.00/26.59  | | | 
% 174.00/26.59  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 174.00/26.59  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.00/26.59  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 174.00/26.59  | | |            (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 174.00/26.59  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 174.00/26.59  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 174.00/26.59  | | |            (66), (67), (68), (70), (71), (72), (73), (74), (75), (76),
% 174.00/26.59  | | |            (77), (78), (79), (80), (82), (83), (84), (85), (86), (87),
% 174.00/26.59  | | |            (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 174.00/26.59  | | |            (98), (99), (100), (102), (103), (104), (105), (106), (107),
% 174.00/26.59  | | |            (109), (110), (111), (113), (114), (115), (116), (117), (118),
% 174.00/26.59  | | |            (119), (120), (121), (122), (128) are inconsistent by sub-proof
% 174.00/26.59  | | |            #87.
% 174.00/26.59  | | | 
% 174.00/26.59  | | End of split
% 174.00/26.59  | | 
% 174.00/26.59  | End of split
% 174.00/26.59  | 
% 174.00/26.59  End of proof
% 174.00/26.59  
% 174.00/26.59  Sub-proof #19 shows that the following formulas are inconsistent:
% 174.00/26.59  ----------------------------------------------------------------
% 174.00/26.59    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.59    (2)   ~ (all_52_17 = all_52_23)
% 174.00/26.59    (3)  op(e2, all_10_2) = all_10_1
% 174.00/26.59    (4)  all_42_1 = e2
% 174.00/26.59    (5)  op(e3, e2) = all_52_3
% 174.00/26.59    (6)   ~ (all_52_9 = all_52_25)
% 174.00/26.59    (7)  op(e1, e2) = all_52_19
% 174.00/26.59    (8)  all_58_5 = all_52_13
% 174.00/26.59    (9)   ~ (all_52_25 = all_52_29)
% 174.00/26.59    (10)  all_56_15 = all_6_2
% 174.00/26.59    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.00/26.59    (12)  all_58_3 = all_10_2
% 174.00/26.59    (13)  all_56_9 = all_52_19
% 174.00/26.59    (14)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.59    (15)  all_58_15 = all_6_2
% 174.00/26.59    (16)  op(e2, all_4_2) = e1
% 174.00/26.59    (17)   ~ (all_52_9 = all_4_2)
% 174.00/26.59    (18)   ~ (all_52_5 = all_52_7)
% 174.00/26.59    (19)  all_58_10 = all_52_15
% 174.00/26.59    (20)   ~ (all_52_5 = all_4_2)
% 174.00/26.59    (21)  all_58_7 = all_52_19
% 174.00/26.59    (22)   ~ (all_52_17 = all_52_25)
% 174.00/26.59    (23)  all_58_4 = all_52_5
% 174.00/26.59    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.59    (25)   ~ (e3 = e1)
% 174.00/26.59    (26)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.00/26.59    (27)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.59    (28)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.59    (29)   ~ (all_52_7 = all_4_2)
% 174.00/26.59    (30)  all_58_1 = all_52_3
% 174.00/26.59    (31)  all_58_0 = all_4_2
% 174.00/26.59    (32)  all_52_0 = e2
% 174.00/26.59    (33)  op(e0, e0) = all_6_2
% 174.00/26.59    (34)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.00/26.59    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.59    (36)  all_58_14 = all_52_29
% 174.00/26.59    (37)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.59    (38)  op(e2, e1) = all_52_13
% 174.00/26.59    (39)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.59    (40)  all_58_8 = all_14_2
% 174.00/26.59    (41)   ~ (all_52_5 = all_14_2)
% 174.00/26.59    (42)   ~ (all_52_3 = all_4_2)
% 174.00/26.59    (43)  op(e0, e3) = all_52_25
% 174.00/26.59    (44)  op(e0, all_6_2) = all_6_1
% 174.00/26.59    (45)  op(e3, all_52_17) = all_52_16
% 174.00/26.59    (46)  all_52_10 = all_10_1
% 174.00/26.59    (47)   ~ (all_52_13 = all_14_2)
% 174.00/26.59    (48)   ~ (e3 = e0)
% 174.00/26.59    (49)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.59    (50)   ~ (all_52_9 = all_52_13)
% 174.00/26.59    (51)  op(e0, all_52_23) = all_52_22
% 174.00/26.59    (52)   ~ (all_52_15 = all_52_23)
% 174.00/26.59    (53)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.00/26.59    (54)  op(e1, e0) = all_52_23
% 174.00/26.59    (55)  all_58_13 = all_52_27
% 174.00/26.59    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.59    (57)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.00/26.59    (58)   ~ (all_52_9 = all_52_17)
% 174.00/26.59    (59)  all_58_6 = all_52_17
% 174.00/26.59    (60)  op(all_10_1, all_10_2) = e3
% 174.00/26.59    (61)  op(e2, all_52_19) = all_52_18
% 174.00/26.59    (62)   ~ (e1 = e0)
% 174.00/26.59    (63)  all_56_0 = all_4_2
% 174.00/26.59    (64)  all_58_11 = all_52_23
% 174.00/26.59    (65)   ~ (all_52_3 = all_52_19)
% 174.00/26.59    (66)   ~ (all_52_7 = all_52_15)
% 174.00/26.59    (67)  op(e3, all_4_2) = e2
% 174.00/26.59    (68)   ~ (all_52_23 = all_6_2)
% 174.00/26.59    (69)  all_58_2 = all_52_9
% 174.00/26.59    (70)  op(e3, e1) = all_52_5
% 174.00/26.59    (71)   ~ (e2 = e1)
% 174.00/26.59    (72)  all_56_10 = all_14_2
% 174.00/26.59    (73)   ~ (all_52_25 = all_6_2)
% 174.00/26.59    (74)  op(e1, e3) = all_52_17
% 174.00/26.59    (75)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.00/26.59    (76)   ~ (all_52_25 = all_4_2)
% 174.00/26.59    (77)  op(e3, e0) = all_52_7
% 174.00/26.59    (78)  op(e3, e3) = all_4_2
% 174.00/26.59    (79)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.00/26.59            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.00/26.59    (80)   ~ (all_52_17 = all_4_2)
% 174.00/26.59    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.59    (82)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.59          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.59          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.59          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.59    (83)   ~ (all_52_25 = all_52_27)
% 174.00/26.59    (84)   ~ (all_52_15 = all_10_2)
% 174.00/26.59    (85)  all_42_2 = all_4_2
% 174.00/26.59    (86)  all_56_7 = all_52_15
% 174.00/26.59    (87)   ~ (all_52_7 = all_52_23)
% 174.00/26.59    (88)  all_52_20 = all_14_1
% 174.00/26.59    (89)   ~ (all_52_17 = all_52_19)
% 174.00/26.59    (90)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.59    (91)  all_52_30 = all_6_1
% 174.00/26.59    (92)  op(e1, all_14_2) = all_14_1
% 174.00/26.59    (93)  all_58_9 = all_52_7
% 174.00/26.59    (94)   ~ (e2 = e0)
% 174.00/26.59    (95)  all_58_12 = all_52_25
% 174.00/26.59    (96)  op(all_6_1, all_6_2) = e3
% 174.00/26.59    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.59    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.59    (99)   ~ (e3 = e2)
% 174.00/26.59    (100)   ~ (all_52_19 = all_14_2)
% 174.00/26.59    (101)  op(e2, e3) = all_52_9
% 174.00/26.59  
% 174.00/26.59  Begin of proof
% 174.00/26.59  | 
% 174.00/26.59  | BETA: splitting (26) gives:
% 174.00/26.59  | 
% 174.00/26.59  | Case 1:
% 174.00/26.59  | | 
% 174.00/26.59  | |   (102)   ~ (all_42_1 = e2)
% 174.00/26.59  | | 
% 174.00/26.59  | | REDUCE: (4), (102) imply:
% 174.00/26.59  | |   (103)  $false
% 174.00/26.59  | | 
% 174.00/26.59  | | CLOSE: (103) is inconsistent.
% 174.00/26.59  | | 
% 174.00/26.59  | Case 2:
% 174.00/26.59  | | 
% 174.00/26.59  | |   (104)   ~ (all_42_2 = e0)
% 174.00/26.59  | | 
% 174.00/26.59  | | REDUCE: (85), (104) imply:
% 174.00/26.59  | |   (105)   ~ (all_4_2 = e0)
% 174.00/26.59  | | 
% 174.00/26.59  | | BETA: splitting (79) gives:
% 174.00/26.59  | | 
% 174.00/26.59  | | Case 1:
% 174.00/26.59  | | | 
% 174.00/26.59  | | |   (106)  all_58_15 = e0
% 174.00/26.59  | | | 
% 174.00/26.59  | | | REF_CLOSE: (15), (33), (44), (48), (81), (96), (106) are inconsistent by
% 174.00/26.59  | | |            sub-proof #510.
% 174.00/26.59  | | | 
% 174.00/26.59  | | Case 2:
% 174.00/26.59  | | | 
% 174.00/26.59  | | |   (107)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 174.00/26.59  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 174.00/26.59  | | | 
% 174.00/26.59  | | | ALPHA: (107) implies:
% 174.00/26.59  | | |   (108)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.00/26.59  | | | 
% 174.00/26.59  | | | BETA: splitting (82) gives:
% 174.00/26.59  | | | 
% 174.00/26.59  | | | Case 1:
% 174.00/26.59  | | | | 
% 174.00/26.59  | | | |   (109)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.00/26.59  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.00/26.59  | | | |            = e0)
% 174.00/26.59  | | | | 
% 174.00/26.59  | | | | REF_CLOSE: (3), (32), (46), (60), (81), (99), (109) are inconsistent by
% 174.00/26.59  | | | |            sub-proof #33.
% 174.00/26.59  | | | | 
% 174.00/26.59  | | | Case 2:
% 174.00/26.59  | | | | 
% 174.00/26.59  | | | |   (110)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.00/26.59  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.00/26.59  | | | |            all_52_30 = e0)
% 174.00/26.59  | | | | 
% 174.00/26.59  | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 174.00/26.59  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.00/26.59  | | | |            (24), (25), (27), (28), (29), (30), (31), (34), (35), (36),
% 174.00/26.59  | | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 174.00/26.59  | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 174.00/26.59  | | | |            (58), (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.00/26.59  | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.00/26.59  | | | |            (80), (81), (83), (84), (86), (87), (88), (89), (90), (91),
% 174.00/26.59  | | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.00/26.59  | | | |            (105), (108), (110) are inconsistent by sub-proof #62.
% 174.00/26.59  | | | | 
% 174.00/26.59  | | | End of split
% 174.00/26.59  | | | 
% 174.00/26.59  | | End of split
% 174.00/26.59  | | 
% 174.00/26.59  | End of split
% 174.00/26.59  | 
% 174.00/26.59  End of proof
% 174.00/26.59  
% 174.00/26.59  Sub-proof #20 shows that the following formulas are inconsistent:
% 174.00/26.59  ----------------------------------------------------------------
% 174.00/26.59    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.59    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.59    (3)   ~ (all_52_17 = all_52_23)
% 174.00/26.59    (4)  op(e2, all_10_2) = all_10_1
% 174.00/26.59    (5)  op(e3, e2) = all_52_3
% 174.00/26.59    (6)   ~ (all_52_9 = all_52_25)
% 174.00/26.59    (7)  op(e3, all_52_25) = all_52_24
% 174.00/26.59    (8)   ~ (all_52_19 = all_52_23)
% 174.00/26.59    (9)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.00/26.59    (10)  op(e3, all_52_9) = all_52_8
% 174.00/26.59    (11)   ~ (all_52_3 = all_10_2)
% 174.00/26.59    (12)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.59    (13)  all_58_5 = all_52_13
% 174.00/26.59    (14)   ~ (all_52_25 = all_52_29)
% 174.00/26.59    (15)  all_56_15 = all_6_2
% 174.00/26.59    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.59    (17)  all_58_3 = all_10_2
% 174.00/26.59    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.59    (19)  all_58_15 = all_6_2
% 174.00/26.59    (20)   ~ (all_52_9 = all_4_2)
% 174.00/26.59    (21)   ~ (all_52_5 = all_52_7)
% 174.00/26.59    (22)  all_58_10 = all_52_15
% 174.00/26.59    (23)   ~ (all_52_5 = all_4_2)
% 174.00/26.59    (24)  all_58_7 = all_52_19
% 174.00/26.59    (25)   ~ (all_52_17 = all_52_25)
% 174.00/26.59    (26)  op(e0, e1) = all_52_29
% 174.00/26.59    (27)  all_58_4 = all_52_5
% 174.00/26.59    (28)   ~ (e3 = e1)
% 174.00/26.59    (29)   ~ (all_52_27 = all_52_29)
% 174.00/26.59    (30)   ~ (all_52_17 = all_14_2)
% 174.00/26.59    (31)  op(e3, all_4_2) = all_4_1
% 174.00/26.59    (32)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.59    (33)   ~ (all_52_7 = all_4_2)
% 174.00/26.59    (34)  all_58_1 = all_52_3
% 174.00/26.59    (35)   ~ (all_52_13 = all_52_15)
% 174.00/26.59    (36)  all_58_0 = all_4_2
% 174.00/26.59    (37)  all_52_0 = e2
% 174.00/26.59    (38)  op(e1, all_52_29) = all_52_28
% 174.00/26.59    (39)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.59    (40)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.59    (41)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.59    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.59    (43)  all_58_14 = all_52_29
% 174.00/26.59    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.59    (45)  op(e2, all_4_2) = all_4_0
% 174.00/26.59    (46)   ~ (all_52_3 = all_52_5)
% 174.00/26.59    (47)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.59    (48)  op(e2, e1) = all_52_13
% 174.00/26.59    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.59    (50)  all_58_8 = all_14_2
% 174.00/26.59    (51)  all_56_1 = all_52_3
% 174.00/26.59    (52)  op(e0, e2) = all_52_27
% 174.00/26.59    (53)  all_56_14 = all_52_29
% 174.00/26.59    (54)  op(all_14_1, all_14_2) = e3
% 174.00/26.59    (55)  op(all_4_1, all_4_2) = all_4_0
% 174.00/26.59    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.59    (57)   ~ (all_52_3 = all_52_27)
% 174.00/26.59    (58)   ~ (all_52_3 = all_4_2)
% 174.00/26.59    (59)  op(e0, e3) = all_52_25
% 174.00/26.59    (60)  op(e0, all_6_2) = all_6_1
% 174.00/26.59    (61)   ~ (all_52_9 = all_10_2)
% 174.00/26.59    (62)  op(e3, all_52_17) = all_52_16
% 174.00/26.59    (63)  all_52_10 = all_10_1
% 174.00/26.59    (64)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.59    (65)   ~ (e3 = e0)
% 174.00/26.59    (66)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.59    (67)   ~ (all_52_9 = all_52_13)
% 174.00/26.59    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.59    (69)   ~ (all_52_5 = all_52_29)
% 174.00/26.59    (70)  all_56_2 = all_52_5
% 174.00/26.59    (71)  op(e1, e0) = all_52_23
% 174.00/26.59    (72)  all_56_12 = all_52_25
% 174.00/26.59    (73)  all_58_13 = all_52_27
% 174.00/26.59    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.59    (75)   ~ (all_52_9 = all_52_17)
% 174.00/26.59    (76)  all_58_6 = all_52_17
% 174.00/26.59    (77)   ~ (all_52_3 = all_52_7)
% 174.00/26.59    (78)  op(all_10_1, all_10_2) = e3
% 174.00/26.59    (79)   ~ (e1 = e0)
% 174.00/26.59    (80)  all_56_0 = all_4_2
% 174.00/26.59    (81)  all_58_11 = all_52_23
% 174.00/26.59    (82)   ~ (all_52_7 = all_52_15)
% 174.00/26.59    (83)   ~ (all_4_0 = e1)
% 174.00/26.59    (84)   ~ (all_52_19 = all_10_2)
% 174.00/26.59    (85)   ~ (all_58_15 = e0)
% 174.00/26.59    (86)  op(e3, all_4_2) = e2
% 174.00/26.59    (87)   ~ (all_52_29 = all_6_2)
% 174.00/26.59    (88)  all_58_2 = all_52_9
% 174.00/26.59    (89)  op(e3, e1) = all_52_5
% 174.00/26.59    (90)   ~ (e2 = e1)
% 174.00/26.59    (91)   ~ (all_52_25 = all_6_2)
% 174.00/26.59    (92)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.59    (93)  op(e1, e3) = all_52_17
% 174.00/26.59    (94)   ~ (all_52_25 = all_4_2)
% 174.00/26.59    (95)  op(e3, e0) = all_52_7
% 174.00/26.59    (96)  op(e3, e3) = all_4_2
% 174.00/26.59    (97)   ~ (all_52_17 = all_4_2)
% 174.00/26.59    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.59    (99)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.59          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.59          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.59          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.59    (100)   ~ (all_52_25 = all_52_27)
% 174.00/26.59    (101)   ~ (all_52_27 = all_6_2)
% 174.00/26.59    (102)   ~ (all_52_7 = all_6_2)
% 174.00/26.59    (103)   ~ (all_52_15 = all_10_2)
% 174.00/26.59    (104)   ~ (all_52_7 = all_52_23)
% 174.00/26.59    (105)  op(e2, all_52_27) = all_52_26
% 174.00/26.59    (106)  all_52_20 = all_14_1
% 174.00/26.59    (107)   ~ (all_52_17 = all_52_19)
% 174.00/26.59    (108)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.59    (109)  all_52_30 = all_6_1
% 174.00/26.59    (110)  op(e1, all_14_2) = all_14_1
% 174.00/26.59    (111)  all_58_9 = all_52_7
% 174.00/26.59    (112)   ~ (e2 = e0)
% 174.00/26.59    (113)  all_58_12 = all_52_25
% 174.00/26.59    (114)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.00/26.59             all_58_13 = e0 | all_58_14 = e0)
% 174.00/26.59    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.59    (116)   ~ (all_52_9 = all_52_15)
% 174.00/26.59    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.59    (118)   ~ (e3 = e2)
% 174.00/26.59    (119)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.00/26.59    (120)  op(e2, e3) = all_52_9
% 174.00/26.59    (121)  all_56_13 = all_52_27
% 174.00/26.59  
% 174.00/26.59  Begin of proof
% 174.00/26.59  | 
% 174.00/26.59  | ALPHA: (114) implies:
% 174.00/26.59  |   (122)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.00/26.59  |   (123)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.00/26.59  | 
% 174.00/26.59  | REDUCE: (19), (85) imply:
% 174.00/26.59  |   (124)   ~ (all_6_2 = e0)
% 174.00/26.59  | 
% 174.00/26.60  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.00/26.60  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.00/26.60  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.00/26.60  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.00/26.60  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.00/26.60  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.00/26.60  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.00/26.60  |            (79), (80), (81), (82), (83), (84), (86), (87), (88), (89), (90),
% 174.00/26.60  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.00/26.60  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 174.00/26.60  |            (111), (112), (113), (115), (116), (117), (118), (119), (120),
% 174.00/26.60  |            (121), (122), (123), (124) are inconsistent by sub-proof #22.
% 174.00/26.60  | 
% 174.00/26.60  End of proof
% 174.00/26.60  
% 174.00/26.60  Sub-proof #21 shows that the following formulas are inconsistent:
% 174.00/26.60  ----------------------------------------------------------------
% 174.00/26.60    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.60    (2)   ~ (all_52_5 = all_52_13)
% 174.00/26.60    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.00/26.60    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.60    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.60    (6)   ~ (all_52_27 = all_10_2)
% 174.00/26.60    (7)   ~ (all_52_17 = all_52_23)
% 174.00/26.60    (8)   ~ (all_6_0 = e3)
% 174.00/26.60    (9)  op(e2, all_10_2) = all_10_1
% 174.00/26.60    (10)   ~ (all_52_13 = all_52_29)
% 174.00/26.60    (11)  all_42_1 = e2
% 174.00/26.60    (12)  all_56_3 = all_52_7
% 174.00/26.60    (13)  op(e3, e2) = all_52_3
% 174.00/26.60    (14)   ~ (all_52_9 = all_52_25)
% 174.00/26.60    (15)  op(e3, all_52_25) = all_52_24
% 174.00/26.60    (16)   ~ (all_52_19 = all_52_23)
% 174.00/26.60    (17)  all_56_11 = all_52_23
% 174.00/26.60    (18)  op(e1, e2) = all_52_19
% 174.00/26.60    (19)  op(e3, all_52_9) = all_52_8
% 174.00/26.60    (20)   ~ (all_52_3 = all_10_2)
% 174.00/26.60    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.60    (22)  all_58_5 = all_52_13
% 174.00/26.60    (23)   ~ (all_52_25 = all_52_29)
% 174.00/26.60    (24)  all_56_15 = all_6_2
% 174.00/26.60    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.00/26.60    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.60    (27)  all_58_3 = all_10_2
% 174.00/26.60    (28)  all_56_9 = all_52_19
% 174.00/26.60    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.60    (30)  all_58_15 = all_6_2
% 174.00/26.60    (31)  op(e2, all_4_2) = e1
% 174.00/26.60    (32)   ~ (all_52_9 = all_4_2)
% 174.00/26.60    (33)   ~ (all_52_5 = all_52_7)
% 174.00/26.60    (34)  all_58_10 = all_52_15
% 174.00/26.60    (35)   ~ (all_52_5 = all_4_2)
% 174.00/26.60    (36)  all_58_7 = all_52_19
% 174.00/26.60    (37)   ~ (all_52_15 = all_6_2)
% 174.00/26.60    (38)   ~ (all_52_17 = all_52_25)
% 174.00/26.60    (39)  op(e0, e1) = all_52_29
% 174.00/26.60    (40)  all_58_4 = all_52_5
% 174.00/26.60    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.60    (42)   ~ (e3 = e1)
% 174.00/26.60    (43)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.00/26.60    (44)   ~ (all_52_27 = all_52_29)
% 174.00/26.60    (45)   ~ (all_52_17 = all_14_2)
% 174.00/26.60    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.60    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.60    (48)   ~ (all_52_7 = all_4_2)
% 174.00/26.60    (49)  all_58_1 = all_52_3
% 174.00/26.60    (50)   ~ (all_52_13 = all_52_15)
% 174.00/26.60    (51)  all_58_0 = all_4_2
% 174.00/26.60    (52)  op(e1, all_52_13) = all_52_12
% 174.00/26.60    (53)  all_52_0 = e2
% 174.00/26.60    (54)  op(e0, e0) = all_6_2
% 174.00/26.60    (55)  op(e1, all_52_29) = all_52_28
% 174.00/26.60    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.60    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.00/26.60    (58)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.60    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.60    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.60    (61)  all_58_14 = all_52_29
% 174.00/26.60    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.60    (63)   ~ (all_52_3 = all_52_5)
% 174.00/26.60    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.60    (65)  op(e2, e1) = all_52_13
% 174.00/26.60    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.60    (67)  all_58_8 = all_14_2
% 174.00/26.60    (68)  all_56_1 = all_52_3
% 174.00/26.60    (69)  op(e0, e2) = all_52_27
% 174.00/26.60    (70)  all_56_14 = all_52_29
% 174.00/26.60    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.60    (72)   ~ (all_52_5 = all_14_2)
% 174.00/26.60    (73)   ~ (all_52_3 = all_52_27)
% 174.00/26.60    (74)   ~ (all_52_3 = all_4_2)
% 174.00/26.60    (75)  op(all_6_1, all_6_2) = all_6_0
% 174.00/26.60    (76)  op(e0, e3) = all_52_25
% 174.00/26.60    (77)  op(e0, all_6_2) = all_6_1
% 174.00/26.60    (78)   ~ (all_52_9 = all_10_2)
% 174.00/26.60    (79)  op(e3, all_52_17) = all_52_16
% 174.00/26.60    (80)  all_52_10 = all_10_1
% 174.00/26.60    (81)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.60    (82)   ~ (all_52_13 = all_14_2)
% 174.00/26.60    (83)   ~ (e3 = e0)
% 174.00/26.60    (84)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.60    (85)   ~ (all_52_9 = all_52_13)
% 174.00/26.60    (86)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.60    (87)  op(e0, all_52_23) = all_52_22
% 174.00/26.60    (88)   ~ (all_52_15 = all_52_23)
% 174.00/26.60    (89)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.00/26.60    (90)   ~ (all_52_5 = all_52_29)
% 174.00/26.60    (91)  op(e1, e0) = all_52_23
% 174.00/26.60    (92)  all_56_12 = all_52_25
% 174.00/26.60    (93)  all_58_13 = all_52_27
% 174.00/26.60    (94)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.60    (95)  all_56_5 = all_10_2
% 174.00/26.60    (96)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.00/26.60    (97)   ~ (all_52_9 = all_52_17)
% 174.00/26.60    (98)  all_58_6 = all_52_17
% 174.00/26.60    (99)   ~ (all_52_3 = all_52_7)
% 174.00/26.60    (100)  op(all_10_1, all_10_2) = e3
% 174.00/26.60    (101)  op(e2, all_52_19) = all_52_18
% 174.00/26.60    (102)   ~ (e1 = e0)
% 174.00/26.60    (103)  all_56_0 = all_4_2
% 174.00/26.60    (104)  all_58_11 = all_52_23
% 174.00/26.60    (105)   ~ (all_52_3 = all_52_19)
% 174.00/26.60    (106)   ~ (all_52_7 = all_52_15)
% 174.00/26.60    (107)  op(e0, all_52_15) = all_52_14
% 174.00/26.60    (108)   ~ (all_52_29 = all_14_2)
% 174.00/26.60    (109)   ~ (all_52_19 = all_10_2)
% 174.00/26.60    (110)  op(e3, all_4_2) = e2
% 174.00/26.60    (111)   ~ (all_52_23 = all_6_2)
% 174.00/26.60    (112)   ~ (all_6_0 = e2)
% 174.00/26.60    (113)   ~ (all_52_29 = all_6_2)
% 174.00/26.60    (114)  all_58_2 = all_52_9
% 174.00/26.60    (115)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.00/26.60    (116)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.00/26.60    (117)  op(e3, e1) = all_52_5
% 174.00/26.60    (118)   ~ (e2 = e1)
% 174.00/26.60    (119)  all_56_10 = all_14_2
% 174.00/26.60    (120)   ~ (all_52_25 = all_6_2)
% 174.00/26.60    (121)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.00/26.60    (122)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.60    (123)  op(e1, e3) = all_52_17
% 174.00/26.60    (124)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.00/26.60    (125)   ~ (all_52_25 = all_4_2)
% 174.00/26.60    (126)  op(e3, e0) = all_52_7
% 174.00/26.60    (127)  op(e3, e3) = all_4_2
% 174.00/26.60    (128)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.00/26.60             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.00/26.60    (129)  all_56_8 = all_52_17
% 174.00/26.60    (130)   ~ (all_52_17 = all_4_2)
% 174.00/26.60    (131)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.60             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.60    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.60           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.60           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.60           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.60    (133)   ~ (all_52_25 = all_52_27)
% 174.00/26.60    (134)   ~ (all_52_27 = all_6_2)
% 174.00/26.60    (135)   ~ (all_52_7 = all_6_2)
% 174.00/26.60    (136)   ~ (all_52_15 = all_10_2)
% 174.00/26.60    (137)   ~ (all_52_19 = all_52_27)
% 174.00/26.60    (138)  all_42_2 = all_4_2
% 174.00/26.60    (139)  all_56_7 = all_52_15
% 174.00/26.60    (140)   ~ (all_52_7 = all_52_23)
% 174.00/26.60    (141)   ~ (all_6_0 = e1)
% 174.00/26.60    (142)  op(e2, all_52_27) = all_52_26
% 174.00/26.60    (143)  all_52_20 = all_14_1
% 174.00/26.60    (144)   ~ (all_52_17 = all_52_19)
% 174.00/26.60    (145)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.60    (146)  all_52_30 = all_6_1
% 174.00/26.60    (147)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.00/26.60    (148)  op(e1, all_14_2) = all_14_1
% 174.00/26.60    (149)  all_58_9 = all_52_7
% 174.00/26.60    (150)   ~ (e2 = e0)
% 174.00/26.60    (151)  all_58_12 = all_52_25
% 174.00/26.60    (152)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.60    (153)   ~ (all_52_9 = all_52_15)
% 174.00/26.60    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.60    (155)   ~ (e3 = e2)
% 174.00/26.60    (156)   ~ (all_52_19 = all_14_2)
% 174.00/26.60    (157)  op(e2, e3) = all_52_9
% 174.00/26.60    (158)  all_56_13 = all_52_27
% 174.00/26.60  
% 174.00/26.60  Begin of proof
% 174.00/26.60  | 
% 174.00/26.60  | BETA: splitting (43) gives:
% 174.00/26.60  | 
% 174.00/26.60  | Case 1:
% 174.00/26.60  | | 
% 174.00/26.60  | |   (159)   ~ (all_42_1 = e2)
% 174.00/26.60  | | 
% 174.00/26.60  | | REDUCE: (11), (159) imply:
% 174.00/26.60  | |   (160)  $false
% 174.00/26.60  | | 
% 174.00/26.60  | | CLOSE: (160) is inconsistent.
% 174.00/26.60  | | 
% 174.00/26.60  | Case 2:
% 174.00/26.60  | | 
% 174.00/26.60  | |   (161)   ~ (all_42_2 = e0)
% 174.00/26.60  | | 
% 174.00/26.60  | | REDUCE: (138), (161) imply:
% 174.00/26.60  | |   (162)   ~ (all_4_2 = e0)
% 174.00/26.60  | | 
% 174.00/26.60  | | BETA: splitting (128) gives:
% 174.00/26.60  | | 
% 174.00/26.60  | | Case 1:
% 174.00/26.60  | | | 
% 174.00/26.60  | | |   (163)  all_58_15 = e0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | COMBINE_EQS: (30), (163) imply:
% 174.00/26.60  | | |   (164)  all_6_2 = e0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (37), (164) imply:
% 174.00/26.60  | | |   (165)   ~ (all_52_15 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (111), (164) imply:
% 174.00/26.60  | | |   (166)   ~ (all_52_23 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (120), (164) imply:
% 174.00/26.60  | | |   (167)   ~ (all_52_25 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (134), (164) imply:
% 174.00/26.60  | | |   (168)   ~ (all_52_27 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (113), (164) imply:
% 174.00/26.60  | | |   (169)   ~ (all_52_29 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (75), (164) imply:
% 174.00/26.60  | | |   (170)  op(all_6_1, e0) = all_6_0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (77), (164) imply:
% 174.00/26.60  | | |   (171)  op(e0, e0) = all_6_1
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (54), (164) imply:
% 174.00/26.60  | | |   (172)  op(e0, e0) = e0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | GROUND_INST: instantiating (131) with e0, all_6_1, e0, e0, simplifying
% 174.00/26.60  | | |              with (171), (172) gives:
% 174.00/26.60  | | |   (173)  all_6_1 = e0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (170), (173) imply:
% 174.00/26.60  | | |   (174)  op(e0, e0) = all_6_0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | GROUND_INST: instantiating (131) with e0, all_6_0, e0, e0, simplifying
% 174.00/26.60  | | |              with (172), (174) gives:
% 174.00/26.60  | | |   (175)  all_6_0 = e0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (8), (175) imply:
% 174.00/26.60  | | |   (176)   ~ (e3 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (112), (175) imply:
% 174.00/26.60  | | |   (177)   ~ (e2 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (141), (175) imply:
% 174.00/26.60  | | |   (178)   ~ (e1 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | BETA: splitting (132) gives:
% 174.00/26.60  | | | 
% 174.00/26.60  | | | Case 1:
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | |   (179)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.00/26.60  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.00/26.60  | | | |            = e0)
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | | REF_CLOSE: (7), (9), (13), (14), (19), (20), (22), (26), (27), (32),
% 174.00/26.60  | | | |            (33), (34), (36), (38), (39), (40), (41), (42), (44), (45),
% 174.00/26.60  | | | |            (47), (48), (49), (51), (52), (53), (58), (60), (61), (64),
% 174.00/26.60  | | | |            (66), (67), (69), (70), (76), (80), (81), (83), (89), (93),
% 174.00/26.60  | | | |            (97), (98), (99), (102), (104), (106), (107), (109), (114),
% 174.00/26.60  | | | |            (118), (119), (123), (124), (127), (131), (133), (139),
% 174.00/26.60  | | | |            (140), (144), (145), (149), (150), (151), (154), (155),
% 174.00/26.60  | | | |            (156), (157), (163), (167), (168), (169), (179) are
% 174.00/26.60  | | | |            inconsistent by sub-proof #24.
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | Case 2:
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | |   (180)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.00/26.60  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.00/26.60  | | | |            all_52_30 = e0)
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | | BETA: splitting (180) gives:
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | | Case 1:
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | |   (181)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 174.00/26.60  | | | | |          = e0
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | ALPHA: (181) implies:
% 174.00/26.60  | | | | |   (182)  all_52_22 = e0
% 174.00/26.60  | | | | |   (183)  all_52_20 = e1
% 174.00/26.60  | | | | |   (184)  all_52_18 = e2
% 174.00/26.60  | | | | |   (185)  all_52_16 = e3
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | COMBINE_EQS: (143), (183) imply:
% 174.00/26.60  | | | | |   (186)  all_14_1 = e1
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | REF_CLOSE: (1), (3), (7), (8), (10), (12), (13), (14), (16), (17),
% 174.00/26.60  | | | | |            (20), (22), (23), (26), (27), (28), (29), (32), (34), (36),
% 174.00/26.60  | | | | |            (38), (39), (41), (42), (44), (47), (48), (49), (51), (55),
% 174.00/26.60  | | | | |            (57), (60), (61), (62), (64), (66), (67), (69), (72), (74),
% 174.00/26.60  | | | | |            (76), (78), (79), (81), (84), (86), (87), (88), (89), (90),
% 174.00/26.60  | | | | |            (92), (93), (94), (95), (97), (98), (99), (101), (103),
% 174.00/26.60  | | | | |            (104), (108), (109), (112), (114), (115), (116), (117),
% 174.00/26.60  | | | | |            (118), (119), (121), (122), (123), (124), (125), (126),
% 174.00/26.60  | | | | |            (127), (129), (130), (131), (133), (137), (139), (140),
% 174.00/26.60  | | | | |            (141), (145), (147), (148), (149), (151), (152), (153),
% 174.00/26.60  | | | | |            (155), (156), (157), (158), (163), (165), (166), (167),
% 174.00/26.60  | | | | |            (168), (169), (170), (171), (172), (182), (184), (185),
% 174.00/26.60  | | | | |            (186) are inconsistent by sub-proof #118.
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | Case 2:
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | |   (187)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 174.00/26.60  | | | | |          = e0
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | REF_CLOSE: (1), (2), (4), (6), (10), (12), (13), (14), (15), (16),
% 174.00/26.60  | | | | |            (18), (19), (21), (22), (23), (25), (26), (27), (29), (32),
% 174.00/26.60  | | | | |            (34), (35), (36), (40), (47), (48), (49), (51), (55), (61),
% 174.00/26.60  | | | | |            (62), (66), (67), (74), (78), (83), (86), (88), (90), (92),
% 174.00/26.60  | | | | |            (93), (95), (96), (97), (98), (99), (103), (104), (106),
% 174.00/26.60  | | | | |            (108), (109), (110), (114), (117), (121), (122), (123),
% 174.00/26.60  | | | | |            (125), (126), (127), (130), (131), (133), (142), (147),
% 174.00/26.60  | | | | |            (149), (150), (151), (154), (155), (157), (158), (162),
% 174.00/26.60  | | | | |            (163), (166), (167), (187) are inconsistent by sub-proof
% 174.00/26.60  | | | | |            #67.
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | End of split
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | End of split
% 174.00/26.60  | | | 
% 174.00/26.60  | | Case 2:
% 174.00/26.60  | | | 
% 174.00/26.60  | | |   (188)   ~ (all_58_15 = e0)
% 174.00/26.60  | | |   (189)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 174.00/26.60  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | ALPHA: (189) implies:
% 174.00/26.60  | | |   (190)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.00/26.60  | | |   (191)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.00/26.60  | | | 
% 174.00/26.60  | | | REDUCE: (30), (188) imply:
% 174.00/26.60  | | |   (192)   ~ (all_6_2 = e0)
% 174.00/26.60  | | | 
% 174.00/26.60  | | | BETA: splitting (132) gives:
% 174.00/26.60  | | | 
% 174.00/26.60  | | | Case 1:
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | |   (193)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.00/26.60  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.00/26.60  | | | |            = e0)
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | | REF_CLOSE: (9), (53), (80), (100), (131), (155), (193) are inconsistent
% 174.00/26.60  | | | |            by sub-proof #33.
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | Case 2:
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | |   (194)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.00/26.60  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.00/26.60  | | | |            all_52_30 = e0)
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | | BETA: splitting (194) gives:
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | | Case 1:
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | |   (195)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 174.00/26.60  | | | | |          = e0
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | ALPHA: (195) implies:
% 174.00/26.60  | | | | |   (196)  all_52_22 = e0
% 174.00/26.60  | | | | |   (197)  all_52_20 = e1
% 174.00/26.60  | | | | |   (198)  all_52_18 = e2
% 174.00/26.60  | | | | |   (199)  all_52_16 = e3
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | COMBINE_EQS: (143), (197) imply:
% 174.00/26.60  | | | | |   (200)  all_14_1 = e1
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | REF_CLOSE: (1), (7), (13), (14), (18), (22), (23), (24), (25), (27),
% 174.00/26.60  | | | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (38),
% 174.00/26.60  | | | | |            (40), (41), (42), (46), (47), (48), (49), (51), (57), (60),
% 174.00/26.60  | | | | |            (61), (64), (65), (66), (67), (72), (74), (76), (79), (82),
% 174.00/26.60  | | | | |            (83), (84), (85), (87), (88), (89), (91), (93), (94), (96),
% 174.00/26.60  | | | | |            (97), (98), (101), (102), (103), (104), (105), (106),
% 174.00/26.60  | | | | |            (110), (111), (114), (117), (118), (119), (120), (123),
% 174.00/26.60  | | | | |            (124), (125), (126), (127), (130), (131), (133), (136),
% 174.00/26.60  | | | | |            (139), (140), (144), (145), (148), (149), (150), (151),
% 174.00/26.60  | | | | |            (152), (154), (155), (156), (157), (162), (191), (196),
% 174.00/26.60  | | | | |            (198), (199), (200) are inconsistent by sub-proof #77.
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | Case 2:
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | |   (201)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 174.00/26.60  | | | | |          = e0
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | ALPHA: (201) implies:
% 174.00/26.60  | | | | |   (202)  all_52_30 = e0
% 174.00/26.60  | | | | |   (203)  all_52_28 = e1
% 174.00/26.60  | | | | |   (204)  all_52_26 = e2
% 174.00/26.60  | | | | |   (205)  all_52_24 = e3
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | COMBINE_EQS: (146), (202) imply:
% 174.00/26.60  | | | | |   (206)  all_6_1 = e0
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (13), (14), (15), (16), (20),
% 174.00/26.60  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 174.00/26.60  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 174.00/26.60  | | | | |            (42), (44), (45), (46), (47), (48), (49), (50), (51), (55),
% 174.00/26.60  | | | | |            (56), (57), (59), (60), (61), (63), (64), (65), (66), (67),
% 174.00/26.60  | | | | |            (68), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 174.00/26.60  | | | | |            (84), (85), (86), (88), (89), (90), (92), (93), (97), (98),
% 174.00/26.60  | | | | |            (99), (103), (104), (106), (109), (110), (112), (113),
% 174.00/26.60  | | | | |            (114), (117), (119), (120), (123), (124), (125), (126),
% 174.00/26.60  | | | | |            (127), (130), (131), (134), (135), (136), (137), (139),
% 174.00/26.60  | | | | |            (142), (144), (145), (149), (151), (152), (153), (154),
% 174.00/26.60  | | | | |            (155), (156), (157), (162), (190), (192), (203), (204),
% 174.00/26.60  | | | | |            (205), (206) are inconsistent by sub-proof #65.
% 174.00/26.60  | | | | | 
% 174.00/26.60  | | | | End of split
% 174.00/26.60  | | | | 
% 174.00/26.60  | | | End of split
% 174.00/26.60  | | | 
% 174.00/26.60  | | End of split
% 174.00/26.60  | | 
% 174.00/26.60  | End of split
% 174.00/26.60  | 
% 174.00/26.60  End of proof
% 174.00/26.60  
% 174.00/26.60  Sub-proof #22 shows that the following formulas are inconsistent:
% 174.00/26.60  ----------------------------------------------------------------
% 174.00/26.60    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.60    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.60    (3)   ~ (all_52_17 = all_52_23)
% 174.00/26.60    (4)  op(e2, all_10_2) = all_10_1
% 174.00/26.60    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.00/26.60    (6)  op(e3, e2) = all_52_3
% 174.00/26.60    (7)   ~ (all_52_9 = all_52_25)
% 174.00/26.60    (8)  op(e3, all_52_25) = all_52_24
% 174.00/26.60    (9)   ~ (all_52_19 = all_52_23)
% 174.00/26.60    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.00/26.60    (11)  op(e3, all_52_9) = all_52_8
% 174.00/26.60    (12)   ~ (all_52_3 = all_10_2)
% 174.00/26.60    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.60    (14)  all_58_5 = all_52_13
% 174.00/26.60    (15)   ~ (all_6_2 = e0)
% 174.00/26.60    (16)   ~ (all_52_25 = all_52_29)
% 174.00/26.60    (17)  all_56_15 = all_6_2
% 174.00/26.60    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.60    (19)  all_58_3 = all_10_2
% 174.00/26.60    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.60    (21)  all_58_15 = all_6_2
% 174.00/26.60    (22)   ~ (all_52_9 = all_4_2)
% 174.00/26.60    (23)   ~ (all_52_5 = all_52_7)
% 174.00/26.60    (24)  all_58_10 = all_52_15
% 174.00/26.60    (25)   ~ (all_52_5 = all_4_2)
% 174.00/26.60    (26)  all_58_7 = all_52_19
% 174.00/26.60    (27)   ~ (all_52_17 = all_52_25)
% 174.00/26.61    (28)  op(e0, e1) = all_52_29
% 174.00/26.61    (29)  all_58_4 = all_52_5
% 174.00/26.61    (30)   ~ (e3 = e1)
% 174.00/26.61    (31)   ~ (all_52_27 = all_52_29)
% 174.00/26.61    (32)   ~ (all_52_17 = all_14_2)
% 174.00/26.61    (33)  op(e3, all_4_2) = all_4_1
% 174.00/26.61    (34)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.61    (35)   ~ (all_52_7 = all_4_2)
% 174.00/26.61    (36)  all_58_1 = all_52_3
% 174.00/26.61    (37)   ~ (all_52_13 = all_52_15)
% 174.00/26.61    (38)  all_58_0 = all_4_2
% 174.00/26.61    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.00/26.61    (40)  all_52_0 = e2
% 174.00/26.61    (41)  op(e1, all_52_29) = all_52_28
% 174.00/26.61    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.61    (43)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.61    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.61    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.61    (46)  all_58_14 = all_52_29
% 174.00/26.61    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.61    (48)  op(e2, all_4_2) = all_4_0
% 174.00/26.61    (49)   ~ (all_52_3 = all_52_5)
% 174.00/26.61    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.61    (51)  op(e2, e1) = all_52_13
% 174.00/26.61    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.61    (53)  all_58_8 = all_14_2
% 174.00/26.61    (54)  all_56_1 = all_52_3
% 174.00/26.61    (55)  op(e0, e2) = all_52_27
% 174.00/26.61    (56)  all_56_14 = all_52_29
% 174.00/26.61    (57)  op(all_14_1, all_14_2) = e3
% 174.00/26.61    (58)  op(all_4_1, all_4_2) = all_4_0
% 174.00/26.61    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.61    (60)   ~ (all_52_3 = all_52_27)
% 174.00/26.61    (61)   ~ (all_52_3 = all_4_2)
% 174.00/26.61    (62)  op(e0, e3) = all_52_25
% 174.00/26.61    (63)  op(e0, all_6_2) = all_6_1
% 174.00/26.61    (64)   ~ (all_52_9 = all_10_2)
% 174.00/26.61    (65)  op(e3, all_52_17) = all_52_16
% 174.00/26.61    (66)  all_52_10 = all_10_1
% 174.00/26.61    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.61    (68)   ~ (e3 = e0)
% 174.00/26.61    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.61    (70)   ~ (all_52_9 = all_52_13)
% 174.00/26.61    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.61    (72)   ~ (all_52_5 = all_52_29)
% 174.00/26.61    (73)  all_56_2 = all_52_5
% 174.00/26.61    (74)  op(e1, e0) = all_52_23
% 174.00/26.61    (75)  all_56_12 = all_52_25
% 174.00/26.61    (76)  all_58_13 = all_52_27
% 174.00/26.61    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.61    (78)   ~ (all_52_9 = all_52_17)
% 174.00/26.61    (79)  all_58_6 = all_52_17
% 174.00/26.61    (80)   ~ (all_52_3 = all_52_7)
% 174.00/26.61    (81)  op(all_10_1, all_10_2) = e3
% 174.00/26.61    (82)   ~ (e1 = e0)
% 174.00/26.61    (83)  all_56_0 = all_4_2
% 174.00/26.61    (84)  all_58_11 = all_52_23
% 174.00/26.61    (85)   ~ (all_52_7 = all_52_15)
% 174.00/26.61    (86)   ~ (all_4_0 = e1)
% 174.00/26.61    (87)   ~ (all_52_19 = all_10_2)
% 174.00/26.61    (88)  op(e3, all_4_2) = e2
% 174.00/26.61    (89)   ~ (all_52_29 = all_6_2)
% 174.00/26.61    (90)  all_58_2 = all_52_9
% 174.00/26.61    (91)  op(e3, e1) = all_52_5
% 174.00/26.61    (92)   ~ (e2 = e1)
% 174.00/26.61    (93)   ~ (all_52_25 = all_6_2)
% 174.00/26.61    (94)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.61    (95)  op(e1, e3) = all_52_17
% 174.00/26.61    (96)   ~ (all_52_25 = all_4_2)
% 174.00/26.61    (97)  op(e3, e0) = all_52_7
% 174.00/26.61    (98)  op(e3, e3) = all_4_2
% 174.00/26.61    (99)   ~ (all_52_17 = all_4_2)
% 174.00/26.61    (100)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.61             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.61    (101)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.61           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.61           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.61           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.61    (102)   ~ (all_52_25 = all_52_27)
% 174.00/26.61    (103)   ~ (all_52_27 = all_6_2)
% 174.00/26.61    (104)   ~ (all_52_7 = all_6_2)
% 174.00/26.61    (105)   ~ (all_52_15 = all_10_2)
% 174.00/26.61    (106)   ~ (all_52_7 = all_52_23)
% 174.00/26.61    (107)  op(e2, all_52_27) = all_52_26
% 174.00/26.61    (108)  all_52_20 = all_14_1
% 174.00/26.61    (109)   ~ (all_52_17 = all_52_19)
% 174.00/26.61    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.61    (111)  all_52_30 = all_6_1
% 174.00/26.61    (112)  op(e1, all_14_2) = all_14_1
% 174.00/26.61    (113)  all_58_9 = all_52_7
% 174.00/26.61    (114)   ~ (e2 = e0)
% 174.00/26.61    (115)  all_58_12 = all_52_25
% 174.00/26.61    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.61    (117)   ~ (all_52_9 = all_52_15)
% 174.00/26.61    (118)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.61    (119)   ~ (e3 = e2)
% 174.00/26.61    (120)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.00/26.61    (121)  op(e2, e3) = all_52_9
% 174.00/26.61    (122)  all_56_13 = all_52_27
% 174.00/26.61  
% 174.00/26.61  Begin of proof
% 174.00/26.61  | 
% 174.00/26.61  | BETA: splitting (101) gives:
% 174.00/26.61  | 
% 174.00/26.61  | Case 1:
% 174.00/26.61  | | 
% 174.00/26.61  | |   (123)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.61  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.00/26.61  | | 
% 174.00/26.61  | | REF_CLOSE: (4), (40), (66), (81), (100), (119), (123) are inconsistent by
% 174.00/26.61  | |            sub-proof #33.
% 174.00/26.61  | | 
% 174.00/26.61  | Case 2:
% 174.00/26.61  | | 
% 174.00/26.61  | |   (124)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.00/26.61  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.00/26.61  | |            e0)
% 174.00/26.61  | | 
% 174.00/26.61  | | BETA: splitting (124) gives:
% 174.00/26.61  | | 
% 174.00/26.61  | | Case 1:
% 174.00/26.61  | | | 
% 174.00/26.61  | | |   (125)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.00/26.61  | | | 
% 174.00/26.61  | | | ALPHA: (125) implies:
% 174.00/26.61  | | |   (126)  all_52_20 = e1
% 174.00/26.61  | | | 
% 174.00/26.61  | | | COMBINE_EQS: (108), (126) imply:
% 174.00/26.61  | | |   (127)  all_14_1 = e1
% 174.00/26.61  | | | 
% 174.00/26.61  | | | REF_CLOSE: (30), (57), (100), (112), (127) are inconsistent by sub-proof
% 174.00/26.61  | | |            #344.
% 174.00/26.61  | | | 
% 174.00/26.61  | | Case 2:
% 174.00/26.61  | | | 
% 174.00/26.61  | | |   (128)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.00/26.61  | | | 
% 174.00/26.61  | | | ALPHA: (128) implies:
% 174.00/26.61  | | |   (129)  all_52_30 = e0
% 174.00/26.61  | | |   (130)  all_52_28 = e1
% 174.00/26.61  | | |   (131)  all_52_26 = e2
% 174.00/26.61  | | |   (132)  all_52_24 = e3
% 174.00/26.61  | | | 
% 174.00/26.61  | | | COMBINE_EQS: (111), (129) imply:
% 174.00/26.61  | | |   (133)  all_6_1 = e0
% 174.00/26.61  | | | 
% 174.00/26.61  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 174.00/26.61  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.00/26.61  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 174.00/26.61  | | |            (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 174.00/26.61  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 174.00/26.61  | | |            (55), (56), (58), (59), (60), (61), (62), (63), (64), (65),
% 174.00/26.61  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 174.00/26.61  | | |            (77), (78), (79), (80), (82), (83), (84), (85), (86), (87),
% 174.00/26.61  | | |            (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 174.00/26.61  | | |            (98), (99), (100), (102), (103), (104), (105), (106), (107),
% 174.00/26.61  | | |            (109), (110), (113), (114), (115), (116), (117), (118), (119),
% 174.00/26.61  | | |            (120), (121), (122), (130), (131), (132), (133) are
% 174.00/26.61  | | |            inconsistent by sub-proof #88.
% 174.00/26.61  | | | 
% 174.00/26.61  | | End of split
% 174.00/26.61  | | 
% 174.00/26.61  | End of split
% 174.00/26.61  | 
% 174.00/26.61  End of proof
% 174.00/26.61  
% 174.00/26.61  Sub-proof #23 shows that the following formulas are inconsistent:
% 174.00/26.61  ----------------------------------------------------------------
% 174.00/26.61    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.61    (2)   ~ (all_52_5 = all_52_13)
% 174.00/26.61    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.00/26.61    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.61    (5)   ~ (all_52_27 = all_10_2)
% 174.00/26.61    (6)   ~ (all_52_17 = all_52_23)
% 174.00/26.61    (7)   ~ (all_6_0 = e3)
% 174.00/26.61    (8)  op(e2, all_10_2) = all_10_1
% 174.00/26.61    (9)   ~ (all_52_13 = all_52_29)
% 174.00/26.61    (10)  all_56_3 = all_52_7
% 174.00/26.61    (11)  op(e3, e2) = all_52_3
% 174.00/26.61    (12)   ~ (all_52_9 = all_52_25)
% 174.00/26.61    (13)  op(e3, all_52_25) = all_52_24
% 174.00/26.61    (14)   ~ (all_52_19 = all_52_23)
% 174.00/26.61    (15)  all_56_11 = all_52_23
% 174.00/26.61    (16)  op(e1, e2) = all_52_19
% 174.00/26.61    (17)   ~ (all_52_27 = e0)
% 174.00/26.61    (18)  op(e3, all_52_9) = all_52_8
% 174.00/26.61    (19)   ~ (all_52_23 = e0)
% 174.00/26.61    (20)   ~ (all_52_3 = all_10_2)
% 174.00/26.61    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.61    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.00/26.61    (23)  all_58_5 = all_52_13
% 174.00/26.61    (24)   ~ (all_52_25 = all_52_29)
% 174.00/26.61    (25)  op(e0, e0) = all_6_1
% 174.00/26.61    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.00/26.61    (27)  op(e2, e0) = all_52_15
% 174.00/26.61    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.61    (29)  all_58_3 = all_10_2
% 174.00/26.61    (30)  all_56_9 = all_52_19
% 174.00/26.61    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.61    (32)   ~ (all_52_9 = all_4_2)
% 174.00/26.61    (33)   ~ (all_52_5 = all_52_7)
% 174.00/26.61    (34)  all_58_10 = all_52_15
% 174.00/26.61    (35)   ~ (all_52_5 = all_4_2)
% 174.00/26.61    (36)  all_58_7 = all_52_19
% 174.00/26.61    (37)   ~ (all_52_17 = all_52_25)
% 174.00/26.61    (38)  op(e0, e1) = all_52_29
% 174.00/26.61    (39)  all_58_4 = all_52_5
% 174.00/26.61    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.61    (41)   ~ (e3 = e1)
% 174.00/26.61    (42)   ~ (all_52_27 = all_52_29)
% 174.00/26.61    (43)   ~ (all_52_17 = all_14_2)
% 174.00/26.61    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.61    (45)   ~ (all_52_7 = all_4_2)
% 174.00/26.61    (46)  all_58_1 = all_52_3
% 174.00/26.61    (47)  all_58_0 = all_4_2
% 174.00/26.61    (48)  op(e1, all_52_13) = all_52_12
% 174.00/26.61    (49)  all_52_0 = e2
% 174.00/26.61    (50)  op(e1, all_52_29) = all_52_28
% 174.00/26.61    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.00/26.61    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.61    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.61    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.61    (55)  all_58_14 = all_52_29
% 174.00/26.61    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.61    (57)  op(e2, all_4_2) = all_4_0
% 174.00/26.61    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.61    (59)  op(e2, e1) = all_52_13
% 174.00/26.61    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.61    (61)  all_58_8 = all_14_2
% 174.00/26.61    (62)  op(e0, e2) = all_52_27
% 174.00/26.61    (63)  all_56_14 = all_52_29
% 174.00/26.61    (64)   ~ (all_52_5 = all_14_2)
% 174.00/26.61    (65)   ~ (all_52_3 = all_52_27)
% 174.00/26.61    (66)   ~ (all_52_3 = all_4_2)
% 174.00/26.61    (67)  op(e0, e3) = all_52_25
% 174.00/26.61    (68)   ~ (all_52_9 = all_10_2)
% 174.00/26.61    (69)  op(e3, all_52_17) = all_52_16
% 174.00/26.61    (70)  all_52_10 = all_10_1
% 174.00/26.61    (71)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.61    (72)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.61    (73)   ~ (all_52_9 = all_52_13)
% 174.00/26.61    (74)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.61    (75)  op(e0, all_52_23) = all_52_22
% 174.00/26.61    (76)   ~ (all_52_15 = all_52_23)
% 174.00/26.61    (77)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.00/26.61    (78)   ~ (all_52_5 = all_52_29)
% 174.00/26.61    (79)  all_56_12 = all_52_25
% 174.00/26.61    (80)  all_58_13 = all_52_27
% 174.00/26.61    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.61    (82)  all_56_5 = all_10_2
% 174.00/26.61    (83)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.00/26.61    (84)  op(e0, e0) = e0
% 174.00/26.61    (85)   ~ (all_52_25 = e0)
% 174.00/26.61    (86)   ~ (all_52_9 = all_52_17)
% 174.00/26.61    (87)  all_58_6 = all_52_17
% 174.00/26.61    (88)   ~ (all_52_3 = all_52_7)
% 174.00/26.61    (89)  op(e2, all_52_19) = all_52_18
% 174.00/26.61    (90)  all_56_0 = all_4_2
% 174.00/26.61    (91)  all_58_11 = all_52_23
% 174.00/26.61    (92)   ~ (all_52_3 = all_52_19)
% 174.00/26.61    (93)   ~ (all_52_7 = all_52_15)
% 174.00/26.61    (94)  op(e0, all_52_15) = all_52_14
% 174.00/26.61    (95)   ~ (all_52_29 = all_14_2)
% 174.00/26.61    (96)   ~ (all_4_0 = e1)
% 174.00/26.61    (97)   ~ (all_52_19 = all_10_2)
% 174.00/26.61    (98)  all_58_15 = e0
% 174.00/26.61    (99)  op(e3, all_4_2) = e2
% 174.00/26.61    (100)   ~ (all_6_0 = e2)
% 174.00/26.61    (101)  all_58_2 = all_52_9
% 174.00/26.61    (102)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.00/26.61    (103)   ~ (all_52_29 = e0)
% 174.00/26.61    (104)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.00/26.61    (105)  op(e3, e1) = all_52_5
% 174.00/26.61    (106)   ~ (e2 = e1)
% 174.00/26.61    (107)  all_56_10 = all_14_2
% 174.00/26.61    (108)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.00/26.61    (109)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.61    (110)  op(e1, e3) = all_52_17
% 174.00/26.61    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.00/26.61    (112)   ~ (all_52_25 = all_4_2)
% 174.00/26.61    (113)  op(e3, e0) = all_52_7
% 174.00/26.61    (114)  op(e3, e3) = all_4_2
% 174.00/26.61    (115)  all_56_8 = all_52_17
% 174.00/26.61    (116)   ~ (all_52_17 = all_4_2)
% 174.00/26.61    (117)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.61             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.61    (118)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.61           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.61           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.61           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.61    (119)   ~ (all_52_25 = all_52_27)
% 174.00/26.61    (120)   ~ (all_52_15 = all_10_2)
% 174.00/26.61    (121)   ~ (all_52_19 = all_52_27)
% 174.00/26.61    (122)  all_56_7 = all_52_15
% 174.00/26.61    (123)   ~ (all_52_15 = e0)
% 174.00/26.61    (124)  op(all_6_1, e0) = all_6_0
% 174.00/26.61    (125)   ~ (all_52_7 = all_52_23)
% 174.00/26.61    (126)   ~ (all_52_13 = all_10_2)
% 174.00/26.61    (127)   ~ (all_6_0 = e1)
% 174.00/26.61    (128)  op(e2, all_52_27) = all_52_26
% 174.00/26.61    (129)  all_52_20 = all_14_1
% 174.00/26.61    (130)   ~ (all_52_17 = all_52_19)
% 174.00/26.61    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.61    (132)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.00/26.61    (133)  op(e1, all_14_2) = all_14_1
% 174.00/26.61    (134)  all_58_9 = all_52_7
% 174.00/26.61    (135)  all_58_12 = all_52_25
% 174.00/26.61    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.61    (137)   ~ (all_52_9 = all_52_15)
% 174.00/26.61    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.61    (139)   ~ (e3 = e2)
% 174.00/26.61    (140)   ~ (all_52_19 = all_14_2)
% 174.00/26.61    (141)  op(e2, e3) = all_52_9
% 174.00/26.61    (142)  all_56_13 = all_52_27
% 174.00/26.61  
% 174.00/26.61  Begin of proof
% 174.00/26.61  | 
% 174.00/26.61  | GROUND_INST: instantiating (117) with e0, all_6_1, e0, e0, simplifying with
% 174.00/26.61  |              (25), (84) gives:
% 174.00/26.61  |   (143)  all_6_1 = e0
% 174.00/26.61  | 
% 174.00/26.61  | REDUCE: (124), (143) imply:
% 174.00/26.61  |   (144)  op(e0, e0) = all_6_0
% 174.00/26.61  | 
% 174.00/26.61  | GROUND_INST: instantiating (117) with e0, all_6_0, e0, e0, simplifying with
% 174.00/26.61  |              (84), (144) gives:
% 174.00/26.61  |   (145)  all_6_0 = e0
% 174.00/26.61  | 
% 174.00/26.61  | REDUCE: (7), (145) imply:
% 174.00/26.61  |   (146)   ~ (e3 = e0)
% 174.00/26.61  | 
% 174.00/26.61  | SIMP: (146) implies:
% 174.00/26.61  |   (147)   ~ (e3 = e0)
% 174.00/26.61  | 
% 174.00/26.61  | REDUCE: (100), (145) imply:
% 174.00/26.61  |   (148)   ~ (e2 = e0)
% 174.00/26.61  | 
% 174.00/26.61  | SIMP: (148) implies:
% 174.00/26.61  |   (149)   ~ (e2 = e0)
% 174.00/26.61  | 
% 174.00/26.61  | REDUCE: (127), (145) imply:
% 174.00/26.61  |   (150)   ~ (e1 = e0)
% 174.00/26.61  | 
% 174.00/26.61  | SIMP: (150) implies:
% 174.00/26.61  |   (151)   ~ (e1 = e0)
% 174.00/26.61  | 
% 174.00/26.61  | BETA: splitting (118) gives:
% 174.00/26.61  | 
% 174.00/26.61  | Case 1:
% 174.00/26.61  | | 
% 174.00/26.61  | |   (152)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.61  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.00/26.61  | | 
% 174.00/26.61  | | REF_CLOSE: (6), (8), (11), (12), (17), (18), (20), (23), (28), (29), (32),
% 174.00/26.61  | |            (33), (34), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 174.00/26.61  | |            (45), (46), (47), (48), (49), (52), (54), (55), (58), (60), (61),
% 174.00/26.61  | |            (62), (63), (67), (70), (71), (77), (80), (85), (86), (87), (88),
% 174.00/26.61  | |            (91), (93), (94), (97), (98), (101), (103), (106), (107), (110),
% 174.00/26.61  | |            (111), (114), (117), (119), (122), (125), (130), (131), (134),
% 174.00/26.61  | |            (135), (138), (139), (140), (141), (147), (149), (151), (152) are
% 174.00/26.61  | |            inconsistent by sub-proof #24.
% 174.00/26.61  | | 
% 174.00/26.61  | Case 2:
% 174.00/26.61  | | 
% 174.00/26.61  | |   (153)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.00/26.61  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.00/26.61  | |            e0)
% 174.00/26.61  | | 
% 174.00/26.61  | | BETA: splitting (153) gives:
% 174.00/26.61  | | 
% 174.00/26.61  | | Case 1:
% 174.00/26.61  | | | 
% 174.00/26.61  | | |   (154)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.00/26.61  | | | 
% 174.00/26.61  | | | ALPHA: (154) implies:
% 174.00/26.61  | | |   (155)  all_52_22 = e0
% 174.00/26.61  | | |   (156)  all_52_20 = e1
% 174.00/26.61  | | |   (157)  all_52_18 = e2
% 174.00/26.61  | | |   (158)  all_52_16 = e3
% 174.00/26.61  | | | 
% 174.00/26.61  | | | COMBINE_EQS: (129), (156) imply:
% 174.00/26.61  | | |   (159)  all_14_1 = e1
% 174.00/26.61  | | | 
% 174.00/26.61  | | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (11), (12), (14), (15), (17),
% 174.00/26.61  | | |            (19), (20), (23), (24), (25), (28), (29), (30), (31), (32),
% 174.00/26.61  | | |            (34), (36), (37), (38), (40), (41), (42), (44), (45), (46),
% 174.00/26.61  | | |            (47), (50), (51), (54), (55), (56), (58), (60), (61), (62),
% 174.00/26.61  | | |            (64), (66), (67), (68), (69), (71), (72), (74), (75), (76),
% 174.00/26.61  | | |            (77), (78), (79), (80), (81), (82), (84), (85), (86), (87),
% 174.00/26.61  | | |            (88), (89), (90), (91), (95), (97), (98), (100), (101), (102),
% 174.00/26.61  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 174.00/26.61  | | |            (112), (113), (114), (115), (116), (117), (119), (121), (122),
% 174.00/26.61  | | |            (123), (124), (125), (127), (131), (132), (133), (134), (135),
% 174.00/26.61  | | |            (136), (137), (139), (140), (141), (142), (155), (157), (158),
% 174.00/26.61  | | |            (159) are inconsistent by sub-proof #118.
% 174.00/26.61  | | | 
% 174.00/26.61  | | Case 2:
% 174.00/26.61  | | | 
% 174.00/26.61  | | |   (160)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.00/26.61  | | | 
% 174.00/26.61  | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 174.00/26.61  | | |            (15), (16), (18), (19), (20), (21), (22), (23), (24), (26),
% 174.00/26.61  | | |            (27), (28), (29), (31), (32), (33), (34), (35), (36), (37),
% 174.00/26.61  | | |            (39), (40), (41), (43), (44), (45), (46), (47), (50), (53),
% 174.00/26.61  | | |            (55), (56), (57), (59), (60), (61), (65), (66), (68), (69),
% 174.00/26.61  | | |            (72), (73), (74), (76), (78), (79), (80), (82), (83), (85),
% 174.00/26.61  | | |            (86), (87), (88), (90), (91), (92), (93), (95), (96), (97),
% 174.00/26.61  | | |            (98), (99), (101), (102), (104), (105), (108), (109), (110),
% 174.00/26.61  | | |            (112), (113), (114), (116), (117), (119), (120), (126), (128),
% 174.00/26.61  | | |            (132), (134), (135), (138), (139), (141), (142), (147), (149),
% 174.00/26.61  | | |            (151), (160) are inconsistent by sub-proof #109.
% 174.00/26.61  | | | 
% 174.00/26.61  | | End of split
% 174.00/26.61  | | 
% 174.00/26.61  | End of split
% 174.00/26.61  | 
% 174.00/26.61  End of proof
% 174.00/26.61  
% 174.00/26.61  Sub-proof #24 shows that the following formulas are inconsistent:
% 174.00/26.61  ----------------------------------------------------------------
% 174.00/26.61    (1)   ~ (all_52_17 = all_52_23)
% 174.00/26.61    (2)  op(e2, all_10_2) = all_10_1
% 174.00/26.61    (3)  op(e3, e2) = all_52_3
% 174.00/26.61    (4)   ~ (all_52_9 = all_52_25)
% 174.00/26.61    (5)   ~ (all_52_27 = e0)
% 174.00/26.61    (6)  op(e3, all_52_9) = all_52_8
% 174.00/26.61    (7)   ~ (all_52_3 = all_10_2)
% 174.00/26.61    (8)  all_58_5 = all_52_13
% 174.00/26.61    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.61    (10)  all_58_3 = all_10_2
% 174.00/26.61    (11)   ~ (all_52_9 = all_4_2)
% 174.00/26.61    (12)   ~ (all_52_5 = all_52_7)
% 174.00/26.61    (13)  all_58_10 = all_52_15
% 174.00/26.61    (14)  all_58_7 = all_52_19
% 174.00/26.61    (15)   ~ (all_52_17 = all_52_25)
% 174.00/26.61    (16)  op(e0, e1) = all_52_29
% 174.00/26.62    (17)  all_58_4 = all_52_5
% 174.00/26.62    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.62    (19)   ~ (e3 = e1)
% 174.00/26.62    (20)   ~ (all_52_27 = all_52_29)
% 174.00/26.62    (21)   ~ (all_52_17 = all_14_2)
% 174.00/26.62    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.62    (23)   ~ (all_52_7 = all_4_2)
% 174.00/26.62    (24)  all_58_1 = all_52_3
% 174.00/26.62    (25)  all_58_0 = all_4_2
% 174.00/26.62    (26)  op(e1, all_52_13) = all_52_12
% 174.00/26.62    (27)  all_52_0 = e2
% 174.00/26.62    (28)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.62          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.00/26.62    (29)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.62    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.62    (31)  all_58_14 = all_52_29
% 174.00/26.62    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.62    (33)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.62    (34)  all_58_8 = all_14_2
% 174.00/26.62    (35)  op(e0, e2) = all_52_27
% 174.00/26.62    (36)  all_56_14 = all_52_29
% 174.00/26.62    (37)  op(e0, e3) = all_52_25
% 174.00/26.62    (38)  all_52_10 = all_10_1
% 174.00/26.62    (39)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.62    (40)   ~ (e3 = e0)
% 174.00/26.62    (41)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.00/26.62    (42)  all_58_13 = all_52_27
% 174.00/26.62    (43)   ~ (all_52_25 = e0)
% 174.00/26.62    (44)   ~ (all_52_9 = all_52_17)
% 174.00/26.62    (45)  all_58_6 = all_52_17
% 174.00/26.62    (46)   ~ (all_52_3 = all_52_7)
% 174.00/26.62    (47)   ~ (e1 = e0)
% 174.00/26.62    (48)  all_58_11 = all_52_23
% 174.00/26.62    (49)   ~ (all_52_7 = all_52_15)
% 174.00/26.62    (50)  op(e0, all_52_15) = all_52_14
% 174.00/26.62    (51)   ~ (all_52_19 = all_10_2)
% 174.00/26.62    (52)  all_58_15 = e0
% 174.00/26.62    (53)  all_58_2 = all_52_9
% 174.00/26.62    (54)   ~ (all_52_29 = e0)
% 174.00/26.62    (55)   ~ (e2 = e1)
% 174.00/26.62    (56)  all_56_10 = all_14_2
% 174.00/26.62    (57)  op(e1, e3) = all_52_17
% 174.00/26.62    (58)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.00/26.62    (59)  op(e3, e3) = all_4_2
% 174.00/26.62    (60)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.62    (61)   ~ (all_52_25 = all_52_27)
% 174.00/26.62    (62)  all_56_7 = all_52_15
% 174.00/26.62    (63)   ~ (all_52_7 = all_52_23)
% 174.00/26.62    (64)   ~ (all_52_17 = all_52_19)
% 174.00/26.62    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.62    (66)  all_58_9 = all_52_7
% 174.00/26.62    (67)   ~ (e2 = e0)
% 174.00/26.62    (68)  all_58_12 = all_52_25
% 174.00/26.62    (69)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.62    (70)   ~ (e3 = e2)
% 174.00/26.62    (71)   ~ (all_52_19 = all_14_2)
% 174.00/26.62    (72)  op(e2, e3) = all_52_9
% 174.00/26.62  
% 174.00/26.62  Begin of proof
% 174.00/26.62  | 
% 174.00/26.62  | BETA: splitting (28) gives:
% 174.00/26.62  | 
% 174.00/26.62  | Case 1:
% 174.00/26.62  | | 
% 174.00/26.62  | |   (73)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.00/26.62  | | 
% 174.00/26.62  | | REF_CLOSE: (27), (70), (73) are inconsistent by sub-proof #124.
% 174.00/26.62  | | 
% 174.00/26.62  | Case 2:
% 174.00/26.62  | | 
% 174.00/26.62  | |   (74)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 174.00/26.62  | | 
% 174.00/26.62  | | ALPHA: (74) implies:
% 174.00/26.62  | |   (75)  all_52_14 = e0
% 174.00/26.62  | |   (76)  all_52_12 = e1
% 174.00/26.62  | |   (77)  all_52_10 = e2
% 174.00/26.62  | |   (78)  all_52_8 = e3
% 174.00/26.62  | | 
% 174.00/26.62  | | COMBINE_EQS: (38), (77) imply:
% 174.00/26.62  | |   (79)  all_10_1 = e2
% 174.00/26.62  | | 
% 174.00/26.62  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.00/26.62  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.00/26.62  | |            (24), (25), (26), (29), (30), (31), (32), (33), (34), (35), (36),
% 174.00/26.62  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 174.00/26.62  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 174.00/26.62  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 174.00/26.62  | |            (71), (72), (75), (76), (78), (79) are inconsistent by sub-proof
% 174.00/26.62  | |            #121.
% 174.00/26.62  | | 
% 174.00/26.62  | End of split
% 174.00/26.62  | 
% 174.00/26.62  End of proof
% 174.00/26.62  
% 174.00/26.62  Sub-proof #25 shows that the following formulas are inconsistent:
% 174.00/26.62  ----------------------------------------------------------------
% 174.00/26.62    (1)  op(e2, all_10_2) = all_10_1
% 174.00/26.62    (2)  all_52_0 = e2
% 174.00/26.62    (3)  op(e0, all_6_2) = all_6_1
% 174.00/26.62    (4)  all_52_10 = all_10_1
% 174.00/26.62    (5)  all_52_20 = e2
% 174.00/26.62    (6)   ~ (e3 = e0)
% 174.00/26.62    (7)  op(all_10_1, all_10_2) = e3
% 174.00/26.62    (8)   ~ (e2 = e1)
% 174.00/26.62    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.62    (10)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.62          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.62          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.62          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.62    (11)  all_52_30 = all_6_1
% 174.00/26.62    (12)  op(all_6_1, all_6_2) = e3
% 174.00/26.62    (13)   ~ (e3 = e2)
% 174.00/26.62  
% 174.00/26.62  Begin of proof
% 174.00/26.62  | 
% 174.00/26.62  | BETA: splitting (10) gives:
% 174.00/26.62  | 
% 174.00/26.62  | Case 1:
% 174.00/26.62  | | 
% 174.00/26.62  | |   (14)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.62  | |         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.00/26.62  | | 
% 174.00/26.62  | | REF_CLOSE: (1), (2), (4), (7), (9), (13), (14) are inconsistent by sub-proof
% 174.00/26.62  | |            #33.
% 174.00/26.62  | | 
% 174.00/26.62  | Case 2:
% 174.00/26.62  | | 
% 174.00/26.62  | |   (15)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.00/26.62  | |         | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.00/26.62  | |           e0)
% 174.00/26.62  | | 
% 174.00/26.62  | | BETA: splitting (15) gives:
% 174.00/26.62  | | 
% 174.00/26.62  | | Case 1:
% 174.00/26.62  | | | 
% 174.00/26.62  | | |   (16)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REF_CLOSE: (5), (8), (16) are inconsistent by sub-proof #539.
% 174.00/26.62  | | | 
% 174.00/26.62  | | Case 2:
% 174.00/26.62  | | | 
% 174.00/26.62  | | |   (17)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REF_CLOSE: (3), (6), (9), (11), (12), (17) are inconsistent by sub-proof
% 174.00/26.62  | | |            #501.
% 174.00/26.62  | | | 
% 174.00/26.62  | | End of split
% 174.00/26.62  | | 
% 174.00/26.62  | End of split
% 174.00/26.62  | 
% 174.00/26.62  End of proof
% 174.00/26.62  
% 174.00/26.62  Sub-proof #26 shows that the following formulas are inconsistent:
% 174.00/26.62  ----------------------------------------------------------------
% 174.00/26.62    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.62    (2)   ~ (all_52_5 = all_52_13)
% 174.00/26.62    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.62    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.62    (5)   ~ (all_52_27 = all_10_2)
% 174.00/26.62    (6)   ~ (all_52_17 = all_52_23)
% 174.00/26.62    (7)   ~ (all_6_0 = e3)
% 174.00/26.62    (8)  op(e2, all_10_2) = all_10_1
% 174.00/26.62    (9)   ~ (all_52_13 = all_52_29)
% 174.00/26.62    (10)  all_56_3 = all_52_7
% 174.00/26.62    (11)  op(e3, e2) = all_52_3
% 174.00/26.62    (12)   ~ (all_52_9 = all_52_25)
% 174.00/26.62    (13)  op(e3, all_52_25) = all_52_24
% 174.00/26.62    (14)   ~ (all_52_19 = all_52_23)
% 174.00/26.62    (15)  op(e1, e2) = all_52_19
% 174.00/26.62    (16)  op(e3, all_52_9) = all_52_8
% 174.00/26.62    (17)   ~ (all_52_3 = all_10_2)
% 174.00/26.62    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.62    (19)  all_58_5 = all_52_13
% 174.00/26.62    (20)   ~ (all_52_25 = all_52_29)
% 174.00/26.62    (21)  all_56_15 = all_6_2
% 174.00/26.62    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.00/26.62    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.62    (24)  all_58_3 = all_10_2
% 174.00/26.62    (25)  all_56_9 = all_52_19
% 174.00/26.62    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.62    (27)  all_58_15 = all_6_2
% 174.00/26.62    (28)  op(e2, all_4_2) = e1
% 174.00/26.62    (29)   ~ (all_52_9 = all_4_2)
% 174.00/26.62    (30)   ~ (all_52_5 = all_52_7)
% 174.00/26.62    (31)  all_58_10 = all_52_15
% 174.00/26.62    (32)   ~ (all_52_5 = all_4_2)
% 174.00/26.62    (33)  all_58_7 = all_52_19
% 174.00/26.62    (34)   ~ (all_52_15 = all_6_2)
% 174.00/26.62    (35)   ~ (all_52_17 = all_52_25)
% 174.00/26.62    (36)  op(e0, e1) = all_52_29
% 174.00/26.62    (37)  all_58_4 = all_52_5
% 174.00/26.62    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.62    (39)   ~ (e3 = e1)
% 174.00/26.62    (40)   ~ (all_52_27 = all_52_29)
% 174.00/26.62    (41)   ~ (all_52_17 = all_14_2)
% 174.00/26.62    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.62    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.62    (44)   ~ (all_52_7 = all_4_2)
% 174.00/26.62    (45)  all_58_1 = all_52_3
% 174.00/26.62    (46)   ~ (all_52_13 = all_52_15)
% 174.00/26.62    (47)  all_58_0 = all_4_2
% 174.00/26.62    (48)  all_52_0 = e2
% 174.00/26.62    (49)  op(e1, all_52_29) = all_52_28
% 174.00/26.62    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.62    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.00/26.62    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.62    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.62    (54)  all_58_14 = all_52_29
% 174.00/26.62    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.62    (56)   ~ (all_52_3 = all_52_5)
% 174.00/26.62    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.62    (58)  op(e2, e1) = all_52_13
% 174.00/26.62    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.62    (60)  all_58_8 = all_14_2
% 174.00/26.62    (61)  all_56_1 = all_52_3
% 174.00/26.62    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.62    (63)   ~ (all_52_5 = all_14_2)
% 174.00/26.62    (64)   ~ (all_52_3 = all_52_27)
% 174.00/26.62    (65)   ~ (all_52_3 = all_4_2)
% 174.00/26.62    (66)  op(all_6_1, all_6_2) = all_6_0
% 174.00/26.62    (67)  op(e0, e3) = all_52_25
% 174.00/26.62    (68)  op(e0, all_6_2) = all_6_1
% 174.00/26.62    (69)   ~ (all_52_9 = all_10_2)
% 174.00/26.62    (70)  op(e3, all_52_17) = all_52_16
% 174.00/26.62    (71)  all_52_10 = all_10_1
% 174.00/26.62    (72)  all_52_20 = e2
% 174.00/26.62    (73)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.62    (74)   ~ (all_52_9 = all_52_13)
% 174.00/26.62    (75)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.62    (76)   ~ (all_52_15 = all_52_23)
% 174.00/26.62    (77)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.00/26.62    (78)   ~ (all_52_5 = all_52_29)
% 174.00/26.62    (79)  all_56_12 = all_52_25
% 174.00/26.62    (80)  all_58_13 = all_52_27
% 174.00/26.62    (81)  all_56_5 = all_10_2
% 174.00/26.62    (82)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.00/26.62    (83)   ~ (all_52_9 = all_52_17)
% 174.00/26.62    (84)  all_58_6 = all_52_17
% 174.00/26.62    (85)   ~ (all_52_3 = all_52_7)
% 174.00/26.62    (86)  op(all_10_1, all_10_2) = e3
% 174.00/26.62    (87)  all_56_0 = all_4_2
% 174.00/26.62    (88)  all_58_11 = all_52_23
% 174.00/26.62    (89)   ~ (all_52_7 = all_52_15)
% 174.00/26.62    (90)   ~ (all_52_29 = all_14_2)
% 174.00/26.62    (91)   ~ (all_52_19 = all_10_2)
% 174.00/26.62    (92)  op(e3, all_4_2) = e2
% 174.00/26.62    (93)   ~ (all_52_23 = all_6_2)
% 174.00/26.62    (94)   ~ (all_6_0 = e2)
% 174.00/26.62    (95)   ~ (all_52_29 = all_6_2)
% 174.00/26.62    (96)  all_58_2 = all_52_9
% 174.00/26.62    (97)  op(e3, e1) = all_52_5
% 174.00/26.62    (98)   ~ (e2 = e1)
% 174.00/26.62    (99)  all_56_10 = all_14_2
% 174.00/26.62    (100)   ~ (all_52_25 = all_6_2)
% 174.00/26.62    (101)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.00/26.62    (102)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.62    (103)  op(e1, e3) = all_52_17
% 174.00/26.62    (104)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.00/26.62    (105)   ~ (all_52_25 = all_4_2)
% 174.00/26.62    (106)  op(e3, e0) = all_52_7
% 174.00/26.62    (107)  op(e3, e3) = all_4_2
% 174.00/26.62    (108)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.00/26.62             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.00/26.62    (109)   ~ (all_52_17 = all_4_2)
% 174.00/26.62    (110)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.62             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.62    (111)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.62           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.62           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.62           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.62    (112)   ~ (all_52_25 = all_52_27)
% 174.00/26.62    (113)   ~ (all_52_27 = all_6_2)
% 174.00/26.62    (114)   ~ (all_52_7 = all_6_2)
% 174.00/26.62    (115)   ~ (all_52_15 = all_10_2)
% 174.00/26.62    (116)   ~ (all_52_19 = all_52_27)
% 174.00/26.62    (117)  all_56_7 = all_52_15
% 174.00/26.62    (118)   ~ (all_4_2 = e0)
% 174.00/26.62    (119)  op(e2, all_52_27) = all_52_26
% 174.00/26.62    (120)   ~ (all_52_17 = all_52_19)
% 174.00/26.62    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.62    (122)  all_52_30 = all_6_1
% 174.00/26.62    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.00/26.62    (124)  all_58_9 = all_52_7
% 174.00/26.62    (125)  all_58_12 = all_52_25
% 174.00/26.62    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.62    (127)   ~ (all_52_9 = all_52_15)
% 174.00/26.62    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.62    (129)   ~ (e3 = e2)
% 174.00/26.62    (130)   ~ (all_52_19 = all_14_2)
% 174.00/26.62    (131)  op(e2, e3) = all_52_9
% 174.00/26.62    (132)  all_56_13 = all_52_27
% 174.00/26.62  
% 174.00/26.62  Begin of proof
% 174.00/26.62  | 
% 174.00/26.62  | BETA: splitting (111) gives:
% 174.00/26.62  | 
% 174.00/26.62  | Case 1:
% 174.00/26.62  | | 
% 174.00/26.62  | |   (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.62  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.00/26.62  | | 
% 174.00/26.62  | | REF_CLOSE: (8), (48), (71), (86), (110), (129), (133) are inconsistent by
% 174.00/26.62  | |            sub-proof #33.
% 174.00/26.62  | | 
% 174.00/26.62  | Case 2:
% 174.00/26.62  | | 
% 174.00/26.62  | |   (134)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.00/26.62  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.00/26.62  | |            e0)
% 174.00/26.62  | | 
% 174.00/26.62  | | BETA: splitting (134) gives:
% 174.00/26.62  | | 
% 174.00/26.62  | | Case 1:
% 174.00/26.62  | | | 
% 174.00/26.62  | | |   (135)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REF_CLOSE: (72), (98), (135) are inconsistent by sub-proof #553.
% 174.00/26.62  | | | 
% 174.00/26.62  | | Case 2:
% 174.00/26.62  | | | 
% 174.00/26.62  | | |   (136)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | ALPHA: (136) implies:
% 174.00/26.62  | | |   (137)  all_52_30 = e0
% 174.00/26.62  | | |   (138)  all_52_28 = e1
% 174.00/26.62  | | |   (139)  all_52_26 = e2
% 174.00/26.62  | | |   (140)  all_52_24 = e3
% 174.00/26.62  | | | 
% 174.00/26.62  | | | COMBINE_EQS: (122), (137) imply:
% 174.00/26.62  | | |   (141)  all_6_1 = e0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | SIMP: (141) implies:
% 174.00/26.62  | | |   (142)  all_6_1 = e0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REDUCE: (66), (142) imply:
% 174.00/26.62  | | |   (143)  op(e0, all_6_2) = all_6_0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REDUCE: (13), (140) imply:
% 174.00/26.62  | | |   (144)  op(e3, all_52_25) = e3
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REDUCE: (119), (139) imply:
% 174.00/26.62  | | |   (145)  op(e2, all_52_27) = e2
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REDUCE: (49), (138) imply:
% 174.00/26.62  | | |   (146)  op(e1, all_52_29) = e1
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REDUCE: (68), (142) imply:
% 174.00/26.62  | | |   (147)  op(e0, all_6_2) = e0
% 174.00/26.62  | | | 
% 174.00/26.62  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 174.00/26.62  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.00/26.62  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.00/26.62  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 174.00/26.62  | | |            (45), (46), (47), (50), (51), (52), (53), (54), (55), (56),
% 174.00/26.62  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (67),
% 174.00/26.62  | | |            (69), (70), (73), (74), (75), (76), (77), (78), (79), (80),
% 174.00/26.62  | | |            (81), (82), (83), (84), (85), (87), (88), (89), (90), (91),
% 174.00/26.62  | | |            (92), (93), (94), (95), (96), (97), (99), (100), (101), (102),
% 174.00/26.62  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (112),
% 174.00/26.62  | | |            (113), (114), (115), (116), (117), (118), (120), (121), (123),
% 174.00/26.62  | | |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 174.00/26.62  | | |            (143), (144), (145), (146), (147) are inconsistent by sub-proof
% 174.00/26.62  | | |            #27.
% 174.00/26.62  | | | 
% 174.00/26.62  | | End of split
% 174.00/26.62  | | 
% 174.00/26.62  | End of split
% 174.00/26.62  | 
% 174.00/26.62  End of proof
% 174.00/26.62  
% 174.00/26.62  Sub-proof #27 shows that the following formulas are inconsistent:
% 174.00/26.62  ----------------------------------------------------------------
% 174.00/26.62    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.62    (2)   ~ (all_52_5 = all_52_13)
% 174.00/26.62    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.62    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.62    (5)   ~ (all_52_27 = all_10_2)
% 174.00/26.62    (6)   ~ (all_52_17 = all_52_23)
% 174.00/26.62    (7)   ~ (all_6_0 = e3)
% 174.00/26.62    (8)   ~ (all_52_13 = all_52_29)
% 174.00/26.62    (9)  all_56_3 = all_52_7
% 174.00/26.62    (10)  op(e3, e2) = all_52_3
% 174.00/26.62    (11)   ~ (all_52_9 = all_52_25)
% 174.00/26.62    (12)   ~ (all_52_19 = all_52_23)
% 174.00/26.62    (13)  op(e1, e2) = all_52_19
% 174.00/26.62    (14)  op(e3, all_52_9) = all_52_8
% 174.00/26.62    (15)   ~ (all_52_3 = all_10_2)
% 174.00/26.62    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.62    (17)  all_58_5 = all_52_13
% 174.00/26.62    (18)   ~ (all_52_25 = all_52_29)
% 174.00/26.62    (19)  all_56_15 = all_6_2
% 174.00/26.62    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.00/26.62    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.62    (22)  all_58_3 = all_10_2
% 174.00/26.62    (23)  all_56_9 = all_52_19
% 174.00/26.62    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.62    (25)  all_58_15 = all_6_2
% 174.00/26.62    (26)  op(e2, all_4_2) = e1
% 174.00/26.62    (27)  op(e0, all_6_2) = e0
% 174.00/26.62    (28)   ~ (all_52_9 = all_4_2)
% 174.00/26.62    (29)   ~ (all_52_5 = all_52_7)
% 174.00/26.62    (30)  all_58_10 = all_52_15
% 174.00/26.62    (31)   ~ (all_52_5 = all_4_2)
% 174.00/26.62    (32)  all_58_7 = all_52_19
% 174.00/26.62    (33)   ~ (all_52_15 = all_6_2)
% 174.00/26.62    (34)   ~ (all_52_17 = all_52_25)
% 174.00/26.62    (35)  op(e0, e1) = all_52_29
% 174.00/26.62    (36)  all_58_4 = all_52_5
% 174.00/26.62    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.62    (38)   ~ (e3 = e1)
% 174.00/26.62    (39)   ~ (all_52_27 = all_52_29)
% 174.00/26.62    (40)   ~ (all_52_17 = all_14_2)
% 174.00/26.62    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.62    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.62    (43)   ~ (all_52_7 = all_4_2)
% 174.00/26.62    (44)  all_58_1 = all_52_3
% 174.00/26.62    (45)   ~ (all_52_13 = all_52_15)
% 174.00/26.62    (46)  all_58_0 = all_4_2
% 174.00/26.62    (47)  op(e2, all_52_27) = e2
% 174.00/26.62    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.62    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.00/26.62    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.62    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.62    (52)  all_58_14 = all_52_29
% 174.00/26.62    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.62    (54)   ~ (all_52_3 = all_52_5)
% 174.00/26.62    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.62    (56)  op(e2, e1) = all_52_13
% 174.00/26.62    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.62    (58)  all_58_8 = all_14_2
% 174.00/26.62    (59)  all_56_1 = all_52_3
% 174.00/26.62    (60)  op(e1, all_52_29) = e1
% 174.00/26.62    (61)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.62    (62)   ~ (all_52_5 = all_14_2)
% 174.00/26.62    (63)   ~ (all_52_3 = all_52_27)
% 174.00/26.62    (64)   ~ (all_52_3 = all_4_2)
% 174.00/26.62    (65)  op(e0, e3) = all_52_25
% 174.00/26.62    (66)   ~ (all_52_9 = all_10_2)
% 174.00/26.62    (67)  op(e3, all_52_17) = all_52_16
% 174.00/26.62    (68)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.62    (69)   ~ (all_52_9 = all_52_13)
% 174.00/26.62    (70)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.62    (71)   ~ (all_52_15 = all_52_23)
% 174.00/26.62    (72)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.00/26.62    (73)   ~ (all_52_5 = all_52_29)
% 174.00/26.62    (74)  all_56_12 = all_52_25
% 174.00/26.62    (75)  all_58_13 = all_52_27
% 174.00/26.62    (76)  all_56_5 = all_10_2
% 174.00/26.63    (77)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.00/26.63    (78)   ~ (all_52_9 = all_52_17)
% 174.00/26.63    (79)  all_58_6 = all_52_17
% 174.00/26.63    (80)   ~ (all_52_3 = all_52_7)
% 174.00/26.63    (81)  all_56_0 = all_4_2
% 174.00/26.63    (82)  all_58_11 = all_52_23
% 174.00/26.63    (83)   ~ (all_52_7 = all_52_15)
% 174.00/26.63    (84)   ~ (all_52_29 = all_14_2)
% 174.00/26.63    (85)  op(e3, all_52_25) = e3
% 174.00/26.63    (86)   ~ (all_52_19 = all_10_2)
% 174.00/26.63    (87)  op(e3, all_4_2) = e2
% 174.00/26.63    (88)   ~ (all_52_23 = all_6_2)
% 174.00/26.63    (89)   ~ (all_6_0 = e2)
% 174.00/26.63    (90)   ~ (all_52_29 = all_6_2)
% 174.00/26.63    (91)  all_58_2 = all_52_9
% 174.00/26.63    (92)  op(e3, e1) = all_52_5
% 174.00/26.63    (93)  all_56_10 = all_14_2
% 174.00/26.63    (94)   ~ (all_52_25 = all_6_2)
% 174.00/26.63    (95)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.00/26.63    (96)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.63    (97)  op(e1, e3) = all_52_17
% 174.00/26.63    (98)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.00/26.63    (99)   ~ (all_52_25 = all_4_2)
% 174.00/26.63    (100)  op(e3, e0) = all_52_7
% 174.00/26.63    (101)  op(e3, e3) = all_4_2
% 174.00/26.63    (102)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.00/26.63             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.00/26.63    (103)   ~ (all_52_17 = all_4_2)
% 174.00/26.63    (104)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.63             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.63    (105)   ~ (all_52_25 = all_52_27)
% 174.00/26.63    (106)  op(e0, all_6_2) = all_6_0
% 174.00/26.63    (107)   ~ (all_52_27 = all_6_2)
% 174.00/26.63    (108)   ~ (all_52_7 = all_6_2)
% 174.00/26.63    (109)   ~ (all_52_15 = all_10_2)
% 174.00/26.63    (110)   ~ (all_52_19 = all_52_27)
% 174.00/26.63    (111)  all_56_7 = all_52_15
% 174.00/26.63    (112)   ~ (all_4_2 = e0)
% 174.00/26.63    (113)   ~ (all_52_17 = all_52_19)
% 174.00/26.63    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.63    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.00/26.63    (116)  all_58_9 = all_52_7
% 174.00/26.63    (117)  all_58_12 = all_52_25
% 174.00/26.63    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.63    (119)   ~ (all_52_9 = all_52_15)
% 174.00/26.63    (120)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.63    (121)   ~ (e3 = e2)
% 174.00/26.63    (122)   ~ (all_52_19 = all_14_2)
% 174.00/26.63    (123)  op(e2, e3) = all_52_9
% 174.00/26.63    (124)  all_56_13 = all_52_27
% 174.00/26.63  
% 174.00/26.63  Begin of proof
% 174.00/26.63  | 
% 174.00/26.63  | GROUND_INST: instantiating (104) with e0, all_6_0, all_6_2, e0, simplifying
% 174.00/26.63  |              with (27), (106) gives:
% 174.00/26.63  |   (125)  all_6_0 = e0
% 174.00/26.63  | 
% 174.00/26.63  | REDUCE: (7), (125) imply:
% 174.00/26.63  |   (126)   ~ (e3 = e0)
% 174.00/26.63  | 
% 174.00/26.63  | SIMP: (126) implies:
% 174.00/26.63  |   (127)   ~ (e3 = e0)
% 174.00/26.63  | 
% 174.00/26.63  | REDUCE: (89), (125) imply:
% 174.00/26.63  |   (128)   ~ (e2 = e0)
% 174.00/26.63  | 
% 174.00/26.63  | SIMP: (128) implies:
% 174.00/26.63  |   (129)   ~ (e2 = e0)
% 174.00/26.63  | 
% 174.00/26.63  | BETA: splitting (102) gives:
% 174.00/26.63  | 
% 174.00/26.63  | Case 1:
% 174.00/26.63  | | 
% 174.00/26.63  | |   (130)  all_58_15 = e0
% 174.00/26.63  | | 
% 174.00/26.63  | | COMBINE_EQS: (25), (130) imply:
% 174.00/26.63  | |   (131)  all_6_2 = e0
% 174.00/26.63  | | 
% 174.00/26.63  | | REDUCE: (88), (131) imply:
% 174.00/26.63  | |   (132)   ~ (all_52_23 = e0)
% 174.00/26.63  | | 
% 174.00/26.63  | | REDUCE: (94), (131) imply:
% 174.00/26.63  | |   (133)   ~ (all_52_25 = e0)
% 174.00/26.63  | | 
% 174.00/26.63  | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (11), (12), (13), (14), (16),
% 174.00/26.63  | |            (17), (18), (20), (21), (22), (24), (28), (30), (31), (32), (36),
% 174.00/26.63  | |            (42), (43), (44), (46), (47), (52), (53), (57), (58), (60), (64),
% 174.00/26.63  | |            (66), (70), (71), (73), (74), (75), (76), (77), (78), (79), (80),
% 174.00/26.63  | |            (81), (82), (83), (84), (85), (86), (87), (91), (92), (95), (96),
% 174.00/26.63  | |            (97), (99), (100), (101), (103), (104), (105), (112), (115),
% 174.00/26.63  | |            (116), (117), (120), (121), (123), (124), (127), (129), (130),
% 174.00/26.63  | |            (132), (133) are inconsistent by sub-proof #85.
% 174.00/26.63  | | 
% 174.00/26.63  | Case 2:
% 174.00/26.63  | | 
% 174.00/26.63  | |   (134)   ~ (all_58_15 = e0)
% 174.00/26.63  | |   (135)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 174.00/26.63  | |            | all_58_13 = e0 | all_58_14 = e0)
% 174.00/26.63  | | 
% 174.00/26.63  | | ALPHA: (135) implies:
% 174.00/26.63  | |   (136)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.00/26.63  | | 
% 174.00/26.63  | | REDUCE: (25), (134) imply:
% 174.00/26.63  | |   (137)   ~ (all_6_2 = e0)
% 174.00/26.63  | | 
% 174.00/26.63  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (12), (15), (17), (18),
% 174.00/26.63  | |            (19), (20), (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 174.00/26.63  | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 174.00/26.63  | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 174.00/26.63  | |            (52), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 174.00/26.63  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 174.00/26.63  | |            (75), (78), (79), (80), (81), (82), (83), (85), (86), (87), (89),
% 174.00/26.63  | |            (90), (91), (92), (93), (94), (97), (98), (99), (100), (101),
% 174.00/26.63  | |            (103), (104), (106), (107), (108), (109), (110), (111), (112),
% 174.00/26.63  | |            (113), (114), (116), (117), (118), (119), (120), (121), (122),
% 174.00/26.63  | |            (123), (136), (137) are inconsistent by sub-proof #73.
% 174.00/26.63  | | 
% 174.00/26.63  | End of split
% 174.00/26.63  | 
% 174.00/26.63  End of proof
% 174.00/26.63  
% 174.00/26.63  Sub-proof #28 shows that the following formulas are inconsistent:
% 174.00/26.63  ----------------------------------------------------------------
% 174.00/26.63    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.63    (2)   ~ (all_52_5 = all_52_13)
% 174.00/26.63    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.63    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.63    (5)   ~ (all_52_27 = all_10_2)
% 174.00/26.63    (6)   ~ (all_52_17 = all_52_23)
% 174.00/26.63    (7)   ~ (all_6_0 = e3)
% 174.00/26.63    (8)  op(e2, all_10_2) = all_10_1
% 174.00/26.63    (9)   ~ (all_52_13 = all_52_29)
% 174.00/26.63    (10)  all_56_3 = all_52_7
% 174.00/26.63    (11)  op(e3, e2) = all_52_3
% 174.00/26.63    (12)   ~ (all_52_9 = all_52_25)
% 174.00/26.63    (13)  op(e3, all_52_25) = all_52_24
% 174.00/26.63    (14)   ~ (all_52_19 = all_52_23)
% 174.00/26.63    (15)  all_56_11 = all_52_23
% 174.00/26.63    (16)  op(e1, e2) = all_52_19
% 174.00/26.63    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.00/26.63    (18)  op(e3, all_52_9) = all_52_8
% 174.00/26.63    (19)   ~ (all_52_3 = all_10_2)
% 174.00/26.63    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.63    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.00/26.63    (22)  all_58_5 = all_52_13
% 174.00/26.63    (23)   ~ (all_52_25 = all_52_29)
% 174.00/26.63    (24)  all_56_15 = all_6_2
% 174.00/26.63    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.00/26.63    (26)  op(e2, e0) = all_52_15
% 174.00/26.63    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.63    (28)  all_58_3 = all_10_2
% 174.00/26.63    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.63    (30)  all_58_15 = all_6_2
% 174.00/26.63    (31)   ~ (all_52_9 = all_4_2)
% 174.00/26.63    (32)   ~ (all_52_5 = all_52_7)
% 174.00/26.63    (33)  all_58_10 = all_52_15
% 174.00/26.63    (34)   ~ (all_52_5 = all_4_2)
% 174.00/26.63    (35)  all_58_7 = all_52_19
% 174.00/26.63    (36)   ~ (all_52_17 = all_52_25)
% 174.00/26.63    (37)  op(e0, e1) = all_52_29
% 174.00/26.63    (38)  all_58_4 = all_52_5
% 174.00/26.63    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.63    (40)   ~ (e3 = e1)
% 174.00/26.63    (41)   ~ (all_52_27 = all_52_29)
% 174.00/26.63    (42)   ~ (all_52_17 = all_14_2)
% 174.00/26.63    (43)  op(e3, all_4_2) = all_4_1
% 174.00/26.63    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.63    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.63    (46)   ~ (all_52_7 = all_4_2)
% 174.00/26.63    (47)  all_58_1 = all_52_3
% 174.00/26.63    (48)   ~ (all_52_13 = all_52_15)
% 174.00/26.63    (49)  all_58_0 = all_4_2
% 174.00/26.63    (50)  all_52_0 = e2
% 174.00/26.63    (51)  op(e1, all_52_29) = all_52_28
% 174.00/26.63    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.63    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.63    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.63    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.63    (56)  all_58_14 = all_52_29
% 174.00/26.63    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.63    (58)  op(e2, all_4_2) = all_4_0
% 174.00/26.63    (59)   ~ (all_52_3 = all_52_5)
% 174.00/26.63    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.63    (61)  op(e2, e1) = all_52_13
% 174.00/26.63    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.63    (63)  all_58_8 = all_14_2
% 174.00/26.63    (64)  all_56_1 = all_52_3
% 174.00/26.63    (65)  op(e0, e2) = all_52_27
% 174.00/26.63    (66)  all_56_14 = all_52_29
% 174.00/26.63    (67)  op(all_4_1, all_4_2) = all_4_0
% 174.00/26.63    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.63    (69)   ~ (all_52_3 = all_52_27)
% 174.00/26.63    (70)   ~ (all_52_3 = all_4_2)
% 174.00/26.63    (71)  op(all_6_1, all_6_2) = all_6_0
% 174.00/26.63    (72)  op(e0, e3) = all_52_25
% 174.00/26.63    (73)  op(e0, all_6_2) = all_6_1
% 174.00/26.63    (74)   ~ (all_52_9 = all_10_2)
% 174.00/26.63    (75)  op(e3, all_52_17) = all_52_16
% 174.00/26.63    (76)  all_52_10 = all_10_1
% 174.00/26.63    (77)  all_52_20 = e2
% 174.00/26.63    (78)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.63    (79)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.63    (80)   ~ (all_52_9 = all_52_13)
% 174.00/26.63    (81)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.63    (82)   ~ (all_52_15 = all_52_23)
% 174.00/26.63    (83)   ~ (all_52_5 = all_52_29)
% 174.00/26.63    (84)  all_56_2 = all_52_5
% 174.00/26.63    (85)  op(e1, e0) = all_52_23
% 174.00/26.63    (86)  all_56_12 = all_52_25
% 174.00/26.63    (87)  all_58_13 = all_52_27
% 174.00/26.63    (88)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.63    (89)  all_56_5 = all_10_2
% 174.00/26.63    (90)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.00/26.63    (91)   ~ (all_52_9 = all_52_17)
% 174.00/26.63    (92)  all_58_6 = all_52_17
% 174.00/26.63    (93)   ~ (all_52_3 = all_52_7)
% 174.00/26.63    (94)  op(all_10_1, all_10_2) = e3
% 174.00/26.63    (95)  all_56_0 = all_4_2
% 174.00/26.63    (96)  all_58_11 = all_52_23
% 174.00/26.63    (97)   ~ (all_52_3 = all_52_19)
% 174.00/26.63    (98)   ~ (all_52_7 = all_52_15)
% 174.00/26.63    (99)   ~ (all_52_29 = all_14_2)
% 174.00/26.63    (100)   ~ (all_4_0 = e1)
% 174.00/26.63    (101)   ~ (all_52_19 = all_10_2)
% 174.00/26.63    (102)  op(e3, all_4_2) = e2
% 174.00/26.63    (103)   ~ (all_52_23 = all_6_2)
% 174.00/26.63    (104)   ~ (all_6_0 = e2)
% 174.00/26.63    (105)   ~ (all_52_29 = all_6_2)
% 174.00/26.63    (106)  all_58_2 = all_52_9
% 174.00/26.63    (107)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.00/26.63    (108)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.00/26.63    (109)  op(e3, e1) = all_52_5
% 174.00/26.63    (110)   ~ (e2 = e1)
% 174.00/26.63    (111)   ~ (all_52_25 = all_6_2)
% 174.00/26.63    (112)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.00/26.63    (113)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.63    (114)  op(e1, e3) = all_52_17
% 174.00/26.63    (115)   ~ (all_52_25 = all_4_2)
% 174.00/26.63    (116)  op(e3, e0) = all_52_7
% 174.00/26.63    (117)  op(e3, e3) = all_4_2
% 174.00/26.63    (118)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.00/26.63             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.00/26.63    (119)   ~ (all_52_17 = all_4_2)
% 174.00/26.63    (120)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.63             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.63    (121)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.63           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.00/26.63           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.00/26.63           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.00/26.63    (122)   ~ (all_52_25 = all_52_27)
% 174.00/26.63    (123)   ~ (all_52_27 = all_6_2)
% 174.00/26.63    (124)   ~ (all_52_7 = all_6_2)
% 174.00/26.63    (125)   ~ (all_52_15 = all_10_2)
% 174.00/26.63    (126)   ~ (all_52_7 = all_52_23)
% 174.00/26.63    (127)   ~ (all_52_13 = all_10_2)
% 174.00/26.63    (128)   ~ (all_6_0 = e1)
% 174.00/26.63    (129)  op(e2, all_52_27) = all_52_26
% 174.00/26.63    (130)   ~ (all_52_17 = all_52_19)
% 174.00/26.63    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.63    (132)  all_52_30 = all_6_1
% 174.00/26.63    (133)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.00/26.63    (134)  all_58_9 = all_52_7
% 174.00/26.63    (135)  all_58_12 = all_52_25
% 174.00/26.63    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.63    (137)   ~ (all_52_9 = all_52_15)
% 174.00/26.63    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.63    (139)   ~ (e3 = e2)
% 174.00/26.63    (140)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.00/26.63    (141)  op(e2, e3) = all_52_9
% 174.00/26.63    (142)  all_56_13 = all_52_27
% 174.00/26.63  
% 174.00/26.63  Begin of proof
% 174.00/26.63  | 
% 174.00/26.63  | BETA: splitting (121) gives:
% 174.00/26.63  | 
% 174.00/26.63  | Case 1:
% 174.00/26.63  | | 
% 174.00/26.63  | |   (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.00/26.63  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.00/26.63  | | 
% 174.00/26.63  | | REF_CLOSE: (8), (50), (76), (94), (120), (139), (143) are inconsistent by
% 174.00/26.63  | |            sub-proof #33.
% 174.00/26.63  | | 
% 174.00/26.63  | Case 2:
% 174.00/26.63  | | 
% 174.00/26.63  | |   (144)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.00/26.63  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.00/26.63  | |            e0)
% 174.00/26.63  | | 
% 174.00/26.63  | | BETA: splitting (144) gives:
% 174.00/26.63  | | 
% 174.00/26.63  | | Case 1:
% 174.00/26.63  | | | 
% 174.00/26.63  | | |   (145)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.00/26.63  | | | 
% 174.00/26.63  | | | REF_CLOSE: (77), (110), (145) are inconsistent by sub-proof #553.
% 174.00/26.63  | | | 
% 174.00/26.63  | | Case 2:
% 174.00/26.63  | | | 
% 174.00/26.63  | | |   (146)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.00/26.63  | | | 
% 174.00/26.63  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.00/26.63  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 174.00/26.63  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 174.00/26.63  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 174.00/26.63  | | |            (43), (44), (45), (46), (47), (48), (49), (51), (52), (53),
% 174.00/26.63  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 174.00/26.63  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 174.00/26.63  | | |            (74), (75), (78), (79), (80), (81), (82), (83), (84), (85),
% 174.00/26.63  | | |            (86), (87), (88), (89), (90), (91), (92), (93), (95), (96),
% 174.00/26.63  | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 174.00/26.63  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 174.00/26.63  | | |            (115), (116), (117), (118), (119), (120), (122), (123), (124),
% 174.00/26.63  | | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 174.00/26.63  | | |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 174.00/26.63  | | |            (146) are inconsistent by sub-proof #29.
% 174.00/26.63  | | | 
% 174.00/26.63  | | End of split
% 174.00/26.63  | | 
% 174.00/26.63  | End of split
% 174.00/26.63  | 
% 174.00/26.63  End of proof
% 174.00/26.63  
% 174.00/26.63  Sub-proof #29 shows that the following formulas are inconsistent:
% 174.00/26.63  ----------------------------------------------------------------
% 174.00/26.63    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.63    (2)   ~ (all_52_5 = all_52_13)
% 174.00/26.63    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.00/26.63    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.00/26.63    (5)   ~ (all_52_27 = all_10_2)
% 174.00/26.63    (6)   ~ (all_52_17 = all_52_23)
% 174.00/26.63    (7)   ~ (all_6_0 = e3)
% 174.00/26.63    (8)  op(e2, all_10_2) = all_10_1
% 174.00/26.63    (9)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.00/26.63    (10)   ~ (all_52_13 = all_52_29)
% 174.00/26.63    (11)  all_56_3 = all_52_7
% 174.00/26.63    (12)  op(e3, e2) = all_52_3
% 174.00/26.63    (13)   ~ (all_52_9 = all_52_25)
% 174.00/26.63    (14)  op(e3, all_52_25) = all_52_24
% 174.00/26.63    (15)   ~ (all_52_19 = all_52_23)
% 174.00/26.63    (16)  all_56_11 = all_52_23
% 174.00/26.63    (17)  op(e1, e2) = all_52_19
% 174.00/26.63    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.00/26.63    (19)  op(e3, all_52_9) = all_52_8
% 174.00/26.63    (20)   ~ (all_52_3 = all_10_2)
% 174.00/26.63    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.00/26.63    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.00/26.63    (23)  all_58_5 = all_52_13
% 174.00/26.63    (24)   ~ (all_52_25 = all_52_29)
% 174.00/26.63    (25)  all_56_15 = all_6_2
% 174.00/26.63    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.00/26.63    (27)  op(e2, e0) = all_52_15
% 174.00/26.63    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.00/26.63    (29)  all_58_3 = all_10_2
% 174.00/26.63    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.00/26.63    (31)  all_58_15 = all_6_2
% 174.00/26.63    (32)   ~ (all_52_9 = all_4_2)
% 174.00/26.63    (33)   ~ (all_52_5 = all_52_7)
% 174.00/26.63    (34)  all_58_10 = all_52_15
% 174.00/26.63    (35)   ~ (all_52_5 = all_4_2)
% 174.00/26.63    (36)  all_58_7 = all_52_19
% 174.00/26.63    (37)   ~ (all_52_17 = all_52_25)
% 174.00/26.63    (38)  op(e0, e1) = all_52_29
% 174.00/26.63    (39)  all_58_4 = all_52_5
% 174.00/26.63    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.00/26.63    (41)   ~ (e3 = e1)
% 174.00/26.63    (42)   ~ (all_52_27 = all_52_29)
% 174.00/26.63    (43)   ~ (all_52_17 = all_14_2)
% 174.00/26.63    (44)  op(e3, all_4_2) = all_4_1
% 174.00/26.63    (45)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.00/26.63    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.00/26.63    (47)   ~ (all_52_7 = all_4_2)
% 174.00/26.63    (48)  all_58_1 = all_52_3
% 174.00/26.63    (49)   ~ (all_52_13 = all_52_15)
% 174.00/26.63    (50)  all_58_0 = all_4_2
% 174.00/26.63    (51)  op(e1, all_52_29) = all_52_28
% 174.00/26.63    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.00/26.63    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.00/26.63    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.00/26.63    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.00/26.63    (56)  all_58_14 = all_52_29
% 174.00/26.63    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.00/26.63    (58)  op(e2, all_4_2) = all_4_0
% 174.00/26.63    (59)   ~ (all_52_3 = all_52_5)
% 174.00/26.63    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.00/26.63    (61)  op(e2, e1) = all_52_13
% 174.00/26.63    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.00/26.63    (63)  all_58_8 = all_14_2
% 174.00/26.63    (64)  all_56_1 = all_52_3
% 174.00/26.63    (65)  op(e0, e2) = all_52_27
% 174.00/26.63    (66)  all_56_14 = all_52_29
% 174.00/26.63    (67)  op(all_4_1, all_4_2) = all_4_0
% 174.00/26.63    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.00/26.63    (69)   ~ (all_52_3 = all_52_27)
% 174.00/26.63    (70)   ~ (all_52_3 = all_4_2)
% 174.00/26.63    (71)  op(all_6_1, all_6_2) = all_6_0
% 174.00/26.63    (72)  op(e0, e3) = all_52_25
% 174.00/26.63    (73)  op(e0, all_6_2) = all_6_1
% 174.00/26.63    (74)   ~ (all_52_9 = all_10_2)
% 174.00/26.63    (75)  op(e3, all_52_17) = all_52_16
% 174.00/26.63    (76)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.00/26.63    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.00/26.63    (78)   ~ (all_52_9 = all_52_13)
% 174.00/26.63    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.00/26.63    (80)   ~ (all_52_15 = all_52_23)
% 174.00/26.63    (81)   ~ (all_52_5 = all_52_29)
% 174.00/26.63    (82)  all_56_2 = all_52_5
% 174.00/26.63    (83)  op(e1, e0) = all_52_23
% 174.00/26.63    (84)  all_56_12 = all_52_25
% 174.00/26.63    (85)  all_58_13 = all_52_27
% 174.00/26.63    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.00/26.63    (87)  all_56_5 = all_10_2
% 174.00/26.63    (88)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.00/26.63    (89)   ~ (all_52_9 = all_52_17)
% 174.00/26.63    (90)  all_58_6 = all_52_17
% 174.00/26.63    (91)   ~ (all_52_3 = all_52_7)
% 174.00/26.63    (92)  all_56_0 = all_4_2
% 174.00/26.63    (93)  all_58_11 = all_52_23
% 174.00/26.63    (94)   ~ (all_52_3 = all_52_19)
% 174.00/26.63    (95)   ~ (all_52_7 = all_52_15)
% 174.00/26.63    (96)   ~ (all_52_29 = all_14_2)
% 174.00/26.63    (97)   ~ (all_4_0 = e1)
% 174.00/26.63    (98)   ~ (all_52_19 = all_10_2)
% 174.00/26.63    (99)  op(e3, all_4_2) = e2
% 174.00/26.63    (100)   ~ (all_52_23 = all_6_2)
% 174.00/26.63    (101)   ~ (all_6_0 = e2)
% 174.00/26.63    (102)   ~ (all_52_29 = all_6_2)
% 174.00/26.63    (103)  all_58_2 = all_52_9
% 174.00/26.63    (104)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.00/26.63    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.00/26.63    (106)  op(e3, e1) = all_52_5
% 174.00/26.63    (107)   ~ (e2 = e1)
% 174.00/26.63    (108)   ~ (all_52_25 = all_6_2)
% 174.00/26.63    (109)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.00/26.63    (110)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.00/26.64    (111)  op(e1, e3) = all_52_17
% 174.00/26.64    (112)   ~ (all_52_25 = all_4_2)
% 174.00/26.64    (113)  op(e3, e0) = all_52_7
% 174.00/26.64    (114)  op(e3, e3) = all_4_2
% 174.00/26.64    (115)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.00/26.64             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.00/26.64    (116)   ~ (all_52_17 = all_4_2)
% 174.00/26.64    (117)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.00/26.64             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.00/26.64    (118)   ~ (all_52_25 = all_52_27)
% 174.00/26.64    (119)   ~ (all_52_27 = all_6_2)
% 174.00/26.64    (120)   ~ (all_52_7 = all_6_2)
% 174.00/26.64    (121)   ~ (all_52_15 = all_10_2)
% 174.00/26.64    (122)   ~ (all_52_7 = all_52_23)
% 174.00/26.64    (123)   ~ (all_52_13 = all_10_2)
% 174.00/26.64    (124)   ~ (all_6_0 = e1)
% 174.00/26.64    (125)  op(e2, all_52_27) = all_52_26
% 174.00/26.64    (126)   ~ (all_52_17 = all_52_19)
% 174.00/26.64    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.00/26.64    (128)  all_52_30 = all_6_1
% 174.00/26.64    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.00/26.64    (130)  all_58_9 = all_52_7
% 174.00/26.64    (131)  all_58_12 = all_52_25
% 174.00/26.64    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.00/26.64    (133)   ~ (all_52_9 = all_52_15)
% 174.00/26.64    (134)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.00/26.64    (135)   ~ (e3 = e2)
% 174.00/26.64    (136)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.00/26.64    (137)  op(e2, e3) = all_52_9
% 174.00/26.64    (138)  all_56_13 = all_52_27
% 174.00/26.64  
% 174.00/26.64  Begin of proof
% 174.00/26.64  | 
% 174.00/26.64  | ALPHA: (9) implies:
% 174.00/26.64  |   (139)  all_52_30 = e0
% 174.00/26.64  |   (140)  all_52_28 = e1
% 174.00/26.64  |   (141)  all_52_26 = e2
% 174.00/26.64  |   (142)  all_52_24 = e3
% 174.00/26.64  | 
% 174.00/26.64  | COMBINE_EQS: (128), (139) imply:
% 174.00/26.64  |   (143)  all_6_1 = e0
% 174.00/26.64  | 
% 174.00/26.64  | SIMP: (143) implies:
% 174.00/26.64  |   (144)  all_6_1 = e0
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (71), (144) imply:
% 174.00/26.64  |   (145)  op(e0, all_6_2) = all_6_0
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (14), (142) imply:
% 174.00/26.64  |   (146)  op(e3, all_52_25) = e3
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (125), (141) imply:
% 174.00/26.64  |   (147)  op(e2, all_52_27) = e2
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (51), (140) imply:
% 174.00/26.64  |   (148)  op(e1, all_52_29) = e1
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (73), (144) imply:
% 174.00/26.64  |   (149)  op(e0, all_6_2) = e0
% 174.00/26.64  | 
% 174.00/26.64  | GROUND_INST: instantiating (117) with e0, all_6_0, all_6_2, e0, simplifying
% 174.00/26.64  |              with (145), (149) gives:
% 174.00/26.64  |   (150)  all_6_0 = e0
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (7), (150) imply:
% 174.00/26.64  |   (151)   ~ (e3 = e0)
% 174.00/26.64  | 
% 174.00/26.64  | SIMP: (151) implies:
% 174.00/26.64  |   (152)   ~ (e3 = e0)
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (101), (150) imply:
% 174.00/26.64  |   (153)   ~ (e2 = e0)
% 174.00/26.64  | 
% 174.00/26.64  | SIMP: (153) implies:
% 174.00/26.64  |   (154)   ~ (e2 = e0)
% 174.00/26.64  | 
% 174.00/26.64  | REDUCE: (124), (150) imply:
% 174.00/26.64  |   (155)   ~ (e1 = e0)
% 174.00/26.64  | 
% 174.00/26.64  | SIMP: (155) implies:
% 174.00/26.64  |   (156)   ~ (e1 = e0)
% 174.00/26.64  | 
% 174.00/26.64  | BETA: splitting (115) gives:
% 174.00/26.64  | 
% 174.00/26.64  | Case 1:
% 174.00/26.64  | | 
% 174.00/26.64  | |   (157)  all_58_15 = e0
% 174.00/26.64  | | 
% 174.00/26.64  | | REF_CLOSE: (1), (2), (3), (5), (8), (10), (11), (12), (13), (15), (16),
% 174.00/26.64  | |            (17), (19), (20), (21), (22), (23), (24), (26), (27), (28), (29),
% 174.00/26.64  | |            (30), (31), (32), (33), (34), (35), (36), (37), (39), (40), (41),
% 174.00/26.64  | |            (43), (46), (47), (48), (50), (54), (56), (57), (58), (61), (62),
% 174.00/26.64  | |            (63), (69), (70), (74), (75), (77), (78), (79), (80), (81), (84),
% 174.00/26.64  | |            (85), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 174.00/26.64  | |            (97), (98), (99), (100), (103), (104), (105), (106), (108),
% 174.00/26.64  | |            (109), (110), (111), (112), (113), (114), (116), (117), (118),
% 174.00/26.64  | |            (121), (123), (129), (130), (131), (134), (135), (137), (138),
% 174.00/26.64  | |            (146), (147), (148), (152), (154), (156), (157) are inconsistent
% 174.00/26.64  | |            by sub-proof #54.
% 174.00/26.64  | | 
% 174.00/26.64  | Case 2:
% 174.00/26.64  | | 
% 174.00/26.64  | |   (158)   ~ (all_58_15 = e0)
% 174.00/26.64  | |   (159)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 174.00/26.64  | |            | all_58_13 = e0 | all_58_14 = e0)
% 174.00/26.64  | | 
% 174.00/26.64  | | REF_CLOSE: (3), (4), (6), (12), (13), (15), (18), (19), (20), (21), (23),
% 174.00/26.64  | |            (24), (25), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 174.00/26.64  | |            (37), (38), (39), (41), (42), (43), (44), (45), (47), (48), (49),
% 174.00/26.64  | |            (50), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 174.00/26.64  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (72), (74),
% 174.00/26.64  | |            (75), (76), (77), (78), (79), (81), (82), (83), (84), (85), (86),
% 174.00/26.64  | |            (89), (90), (91), (92), (93), (95), (97), (98), (99), (102),
% 174.00/26.64  | |            (103), (106), (107), (108), (110), (111), (112), (113), (114),
% 174.00/26.64  | |            (116), (117), (118), (119), (120), (121), (122), (126), (127),
% 174.00/26.64  | |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 174.00/26.64  | |            (146), (147), (148), (149), (152), (154), (156), (158), (159) are
% 174.00/26.64  | |            inconsistent by sub-proof #45.
% 174.00/26.64  | | 
% 174.00/26.64  | End of split
% 174.00/26.64  | 
% 174.00/26.64  End of proof
% 174.00/26.64  
% 174.00/26.64  Sub-proof #30 shows that the following formulas are inconsistent:
% 174.00/26.64  ----------------------------------------------------------------
% 174.00/26.64    (1)   ~ (all_52_23 = all_14_2)
% 174.00/26.64    (2)   ~ (all_52_17 = all_52_23)
% 174.00/26.64    (3)  op(e3, e2) = all_52_3
% 174.00/26.64    (4)   ~ (all_52_9 = all_52_25)
% 174.00/26.64    (5)  op(e1, e2) = all_52_19
% 174.00/26.64    (6)   ~ (all_14_1 = e2)
% 174.00/26.64    (7)  all_58_5 = all_52_13
% 174.00/26.64    (8)   ~ (all_52_25 = all_52_29)
% 174.00/26.64    (9)  all_56_15 = all_6_2
% 174.24/26.64    (10)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.64    (11)  all_58_3 = all_10_2
% 174.24/26.64    (12)  all_56_9 = all_52_19
% 174.24/26.64    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.64    (14)  all_58_15 = all_6_2
% 174.24/26.64    (15)  op(e2, all_4_2) = e1
% 174.24/26.64    (16)   ~ (all_52_9 = all_4_2)
% 174.24/26.64    (17)   ~ (all_52_5 = all_52_7)
% 174.24/26.64    (18)  all_58_10 = all_52_15
% 174.24/26.64    (19)   ~ (all_52_5 = all_4_2)
% 174.24/26.64    (20)  all_58_7 = all_52_19
% 174.24/26.64    (21)   ~ (all_52_17 = all_52_25)
% 174.24/26.64    (22)  all_58_4 = all_52_5
% 174.24/26.64    (23)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.64    (24)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.64    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.64    (26)   ~ (all_52_7 = all_4_2)
% 174.24/26.64    (27)  all_58_1 = all_52_3
% 174.24/26.64    (28)  all_58_0 = all_4_2
% 174.24/26.64    (29)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.24/26.64    (30)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.24/26.64    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.64    (32)   ~ (all_14_1 = e3)
% 174.24/26.64    (33)  all_58_14 = all_52_29
% 174.24/26.64    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.64    (35)  op(e2, e1) = all_52_13
% 174.24/26.64    (36)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.64    (37)  all_58_8 = all_14_2
% 174.24/26.64    (38)   ~ (all_52_5 = all_14_2)
% 174.24/26.64    (39)   ~ (all_52_3 = all_4_2)
% 174.24/26.64    (40)  op(e0, e3) = all_52_25
% 174.24/26.64    (41)  op(e3, all_52_17) = all_52_16
% 174.24/26.64    (42)   ~ (all_52_13 = all_14_2)
% 174.24/26.64    (43)   ~ (e3 = e0)
% 174.24/26.64    (44)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.64    (45)   ~ (all_52_9 = all_52_13)
% 174.24/26.64    (46)  op(e0, all_52_23) = all_52_22
% 174.24/26.64    (47)   ~ (all_52_15 = all_52_23)
% 174.24/26.64    (48)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.24/26.64    (49)  op(e1, e0) = all_52_23
% 174.24/26.64    (50)  all_58_13 = all_52_27
% 174.24/26.64    (51)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.64    (52)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.64    (53)   ~ (all_52_9 = all_52_17)
% 174.24/26.64    (54)  all_58_6 = all_52_17
% 174.24/26.64    (55)  op(e2, all_52_19) = all_52_18
% 174.24/26.64    (56)   ~ (e1 = e0)
% 174.24/26.64    (57)  all_56_0 = all_4_2
% 174.24/26.64    (58)  all_58_11 = all_52_23
% 174.24/26.64    (59)   ~ (all_52_3 = all_52_19)
% 174.24/26.64    (60)   ~ (all_52_7 = all_52_15)
% 174.24/26.64    (61)  op(e3, all_4_2) = e2
% 174.24/26.64    (62)   ~ (all_52_23 = all_6_2)
% 174.24/26.64    (63)  all_58_2 = all_52_9
% 174.24/26.64    (64)  op(e3, e1) = all_52_5
% 174.24/26.64    (65)  all_56_10 = all_14_2
% 174.24/26.64    (66)   ~ (all_52_25 = all_6_2)
% 174.24/26.64    (67)  op(e1, e3) = all_52_17
% 174.24/26.64    (68)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.64    (69)   ~ (all_52_25 = all_4_2)
% 174.24/26.64    (70)  op(e3, e0) = all_52_7
% 174.24/26.64    (71)  op(e3, e3) = all_4_2
% 174.24/26.64    (72)   ~ (all_52_17 = all_4_2)
% 174.24/26.64    (73)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.64    (74)   ~ (all_52_25 = all_52_27)
% 174.24/26.64    (75)   ~ (all_52_15 = all_10_2)
% 174.24/26.64    (76)  all_56_7 = all_52_15
% 174.24/26.64    (77)   ~ (all_4_2 = e0)
% 174.24/26.64    (78)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.24/26.64    (79)   ~ (all_52_7 = all_52_23)
% 174.24/26.64    (80)  all_52_20 = all_14_1
% 174.24/26.64    (81)   ~ (all_52_17 = all_52_19)
% 174.24/26.64    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.64    (83)  op(e1, all_14_2) = all_14_1
% 174.24/26.64    (84)  all_58_9 = all_52_7
% 174.24/26.64    (85)   ~ (e2 = e0)
% 174.24/26.64    (86)  all_58_12 = all_52_25
% 174.24/26.64    (87)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.64    (88)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.64    (89)   ~ (e3 = e2)
% 174.24/26.64    (90)   ~ (all_52_19 = all_14_2)
% 174.24/26.64    (91)  op(e2, e3) = all_52_9
% 174.24/26.64  
% 174.24/26.64  Begin of proof
% 174.24/26.64  | 
% 174.24/26.64  | ALPHA: (78) implies:
% 174.24/26.64  |   (92)  all_52_22 = e0
% 174.24/26.64  |   (93)  all_52_20 = e1
% 174.24/26.64  |   (94)  all_52_18 = e2
% 174.24/26.64  |   (95)  all_52_16 = e3
% 174.24/26.64  | 
% 174.24/26.64  | COMBINE_EQS: (80), (93) imply:
% 174.24/26.64  |   (96)  all_14_1 = e1
% 174.24/26.64  | 
% 174.24/26.64  | REDUCE: (32), (96) imply:
% 174.24/26.64  |   (97)   ~ (e3 = e1)
% 174.24/26.64  | 
% 174.24/26.64  | SIMP: (97) implies:
% 174.24/26.64  |   (98)   ~ (e3 = e1)
% 174.24/26.64  | 
% 174.24/26.64  | REDUCE: (6), (96) imply:
% 174.24/26.64  |   (99)   ~ (e2 = e1)
% 174.24/26.64  | 
% 174.24/26.64  | SIMP: (99) implies:
% 174.24/26.64  |   (100)   ~ (e2 = e1)
% 174.24/26.64  | 
% 174.24/26.64  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 174.24/26.64  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.24/26.64  |            (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 174.24/26.64  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 174.24/26.64  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 174.24/26.64  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 174.24/26.64  |            (70), (71), (72), (73), (74), (75), (76), (77), (79), (81), (82),
% 174.24/26.64  |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (94),
% 174.24/26.64  |            (95), (96), (98), (100) are inconsistent by sub-proof #77.
% 174.24/26.64  | 
% 174.24/26.64  End of proof
% 174.24/26.64  
% 174.24/26.64  Sub-proof #31 shows that the following formulas are inconsistent:
% 174.24/26.64  ----------------------------------------------------------------
% 174.24/26.64    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.64    (2)   ~ (all_52_5 = all_52_13)
% 174.24/26.64    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.24/26.64    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.64    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.64    (6)   ~ (all_52_17 = all_52_23)
% 174.24/26.64    (7)  op(e2, all_10_2) = all_10_1
% 174.24/26.64    (8)   ~ (all_52_13 = all_52_29)
% 174.24/26.64    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.24/26.64    (10)  all_56_3 = all_52_7
% 174.24/26.64    (11)  op(e3, e2) = all_52_3
% 174.24/26.64    (12)   ~ (all_52_9 = all_52_25)
% 174.24/26.64    (13)  op(e3, all_52_25) = all_52_24
% 174.24/26.64    (14)   ~ (all_52_19 = all_52_23)
% 174.24/26.64    (15)  op(e1, e2) = all_52_19
% 174.24/26.64    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.64    (17)  op(e3, all_52_9) = all_52_8
% 174.24/26.64    (18)   ~ (all_52_3 = all_10_2)
% 174.24/26.64    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.64    (20)  all_58_5 = all_52_13
% 174.24/26.64    (21)   ~ (all_6_2 = e0)
% 174.24/26.64    (22)   ~ (all_52_25 = all_52_29)
% 174.24/26.64    (23)  all_56_15 = all_6_2
% 174.24/26.64    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.64    (25)  op(all_14_1, all_14_2) = all_14_0
% 174.24/26.64    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.64    (27)  all_58_3 = all_10_2
% 174.24/26.64    (28)  all_56_9 = all_52_19
% 174.24/26.64    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.64    (30)  all_58_15 = all_6_2
% 174.24/26.64    (31)   ~ (all_52_9 = all_4_2)
% 174.24/26.64    (32)   ~ (all_52_5 = all_52_7)
% 174.24/26.64    (33)  all_58_10 = all_52_15
% 174.24/26.64    (34)   ~ (all_52_5 = all_4_2)
% 174.24/26.64    (35)  all_58_7 = all_52_19
% 174.24/26.64    (36)   ~ (all_52_15 = all_6_2)
% 174.24/26.64    (37)   ~ (all_52_17 = all_52_25)
% 174.24/26.64    (38)  op(e0, e1) = all_52_29
% 174.24/26.64    (39)  all_58_4 = all_52_5
% 174.24/26.64    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.64    (41)   ~ (e3 = e1)
% 174.24/26.64    (42)   ~ (all_52_27 = all_52_29)
% 174.24/26.64    (43)   ~ (all_52_17 = all_14_2)
% 174.24/26.64    (44)  op(e3, all_4_2) = all_4_1
% 174.24/26.64    (45)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.64    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.64    (47)   ~ (all_52_7 = all_4_2)
% 174.24/26.64    (48)  all_58_1 = all_52_3
% 174.24/26.64    (49)   ~ (all_52_13 = all_52_15)
% 174.24/26.64    (50)  all_58_0 = all_4_2
% 174.24/26.64    (51)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.24/26.64    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.24/26.64    (53)  all_52_0 = e2
% 174.24/26.64    (54)  op(e1, all_52_29) = all_52_28
% 174.24/26.64    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.64    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.24/26.64    (57)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.24/26.64    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.24/26.64    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.64    (60)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.24/26.64    (61)  all_58_14 = all_52_29
% 174.24/26.64    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.64    (63)  op(e2, all_4_2) = all_4_0
% 174.24/26.64    (64)   ~ (all_52_3 = all_52_5)
% 174.24/26.64    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.64    (66)  op(e2, e1) = all_52_13
% 174.24/26.64    (67)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.64    (68)  all_58_8 = all_14_2
% 174.24/26.64    (69)  all_56_1 = all_52_3
% 174.24/26.64    (70)  op(e0, e2) = all_52_27
% 174.24/26.64    (71)  all_56_14 = all_52_29
% 174.24/26.64    (72)   ~ (all_14_0 = e3)
% 174.24/26.64    (73)  op(all_4_1, all_4_2) = all_4_0
% 174.24/26.64    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.64    (75)   ~ (all_52_5 = all_14_2)
% 174.24/26.64    (76)   ~ (all_52_3 = all_52_27)
% 174.24/26.64    (77)   ~ (all_52_3 = all_4_2)
% 174.24/26.64    (78)  op(e0, e3) = all_52_25
% 174.24/26.64    (79)  op(e0, all_6_2) = all_6_1
% 174.24/26.64    (80)   ~ (all_52_9 = all_10_2)
% 174.24/26.64    (81)  op(e3, all_52_17) = all_52_16
% 174.24/26.64    (82)  all_52_10 = all_10_1
% 174.24/26.64    (83)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.64    (84)   ~ (all_52_13 = all_14_2)
% 174.24/26.64    (85)   ~ (e3 = e0)
% 174.24/26.64    (86)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.64    (87)   ~ (all_52_9 = all_52_13)
% 174.24/26.64    (88)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.64    (89)  op(e0, all_52_23) = all_52_22
% 174.24/26.64    (90)   ~ (all_52_15 = all_52_23)
% 174.24/26.64    (91)   ~ (all_52_5 = all_52_29)
% 174.24/26.64    (92)  all_56_2 = all_52_5
% 174.24/26.64    (93)  op(e1, e0) = all_52_23
% 174.24/26.64    (94)  all_56_12 = all_52_25
% 174.24/26.64    (95)  all_58_13 = all_52_27
% 174.24/26.64    (96)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.64    (97)  all_56_5 = all_10_2
% 174.24/26.64    (98)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.64    (99)   ~ (all_52_9 = all_52_17)
% 174.24/26.64    (100)   ~ (all_14_0 = e2)
% 174.24/26.64    (101)  all_58_6 = all_52_17
% 174.24/26.64    (102)   ~ (all_52_3 = all_52_7)
% 174.24/26.64    (103)  op(all_10_1, all_10_2) = e3
% 174.24/26.64    (104)  op(e2, all_52_19) = all_52_18
% 174.24/26.64    (105)   ~ (e1 = e0)
% 174.24/26.64    (106)  all_56_0 = all_4_2
% 174.24/26.64    (107)  all_58_11 = all_52_23
% 174.24/26.64    (108)   ~ (all_52_3 = all_52_19)
% 174.24/26.64    (109)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 174.24/26.64    (110)   ~ (all_52_7 = all_52_15)
% 174.24/26.64    (111)   ~ (all_4_0 = e1)
% 174.24/26.64    (112)   ~ (all_52_19 = all_10_2)
% 174.24/26.64    (113)  op(e3, all_4_2) = e2
% 174.24/26.64    (114)   ~ (all_52_23 = all_6_2)
% 174.24/26.64    (115)   ~ (all_52_29 = all_6_2)
% 174.24/26.64    (116)  all_58_2 = all_52_9
% 174.24/26.64    (117)  op(e3, e1) = all_52_5
% 174.24/26.64    (118)   ~ (e2 = e1)
% 174.24/26.64    (119)   ~ (all_52_25 = all_6_2)
% 174.24/26.64    (120)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.64    (121)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.24/26.64    (122)  op(e1, e3) = all_52_17
% 174.24/26.64    (123)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.64    (124)   ~ (all_52_25 = all_4_2)
% 174.24/26.64    (125)  op(e3, e0) = all_52_7
% 174.24/26.64    (126)  op(e3, e3) = all_4_2
% 174.24/26.64    (127)  all_56_8 = all_52_17
% 174.24/26.64    (128)   ~ (all_52_17 = all_4_2)
% 174.24/26.64    (129)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.64             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.64    (130)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.64           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.24/26.64           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.24/26.64           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.24/26.64    (131)   ~ (all_52_25 = all_52_27)
% 174.24/26.64    (132)   ~ (all_52_27 = all_6_2)
% 174.24/26.64    (133)   ~ (all_52_7 = all_6_2)
% 174.24/26.64    (134)   ~ (all_52_15 = all_10_2)
% 174.24/26.64    (135)   ~ (all_52_19 = all_52_27)
% 174.24/26.64    (136)  all_56_7 = all_52_15
% 174.24/26.64    (137)   ~ (all_52_7 = all_52_23)
% 174.24/26.64    (138)   ~ (all_52_13 = all_10_2)
% 174.24/26.64    (139)  op(e2, all_52_27) = all_52_26
% 174.24/26.64    (140)  all_52_20 = all_14_1
% 174.24/26.64    (141)   ~ (all_52_17 = all_52_19)
% 174.24/26.64    (142)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.64    (143)  all_52_30 = all_6_1
% 174.24/26.64    (144)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.64    (145)  op(e1, all_14_2) = all_14_1
% 174.24/26.64    (146)  all_58_9 = all_52_7
% 174.24/26.64    (147)   ~ (e2 = e0)
% 174.24/26.64    (148)  all_58_12 = all_52_25
% 174.24/26.64    (149)  all_56_6 = all_52_13
% 174.24/26.64    (150)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.64    (151)   ~ (all_52_9 = all_52_15)
% 174.24/26.65    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.65    (153)   ~ (e3 = e2)
% 174.24/26.65    (154)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.65    (155)   ~ (all_52_19 = all_14_2)
% 174.24/26.65    (156)  op(e2, e3) = all_52_9
% 174.24/26.65    (157)  all_56_13 = all_52_27
% 174.24/26.65  
% 174.24/26.65  Begin of proof
% 174.24/26.65  | 
% 174.24/26.65  | BETA: splitting (130) gives:
% 174.24/26.65  | 
% 174.24/26.65  | Case 1:
% 174.24/26.65  | | 
% 174.24/26.65  | |   (158)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.65  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.24/26.65  | | 
% 174.24/26.65  | | REF_CLOSE: (7), (53), (82), (103), (129), (153), (158) are inconsistent by
% 174.24/26.65  | |            sub-proof #33.
% 174.24/26.65  | | 
% 174.24/26.65  | Case 2:
% 174.24/26.65  | | 
% 174.24/26.65  | |   (159)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.24/26.65  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.24/26.65  | |            e0)
% 174.24/26.65  | | 
% 174.24/26.65  | | BETA: splitting (159) gives:
% 174.24/26.65  | | 
% 174.24/26.65  | | Case 1:
% 174.24/26.65  | | | 
% 174.24/26.65  | | |   (160)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.24/26.65  | | | 
% 174.24/26.65  | | | ALPHA: (160) implies:
% 174.24/26.65  | | |   (161)  all_52_22 = e0
% 174.24/26.65  | | |   (162)  all_52_20 = e1
% 174.24/26.65  | | |   (163)  all_52_18 = e2
% 174.24/26.65  | | |   (164)  all_52_16 = e3
% 174.24/26.65  | | | 
% 174.24/26.65  | | | COMBINE_EQS: (140), (162) imply:
% 174.24/26.65  | | |   (165)  all_14_1 = e1
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REDUCE: (25), (165) imply:
% 174.24/26.65  | | |   (166)  op(e1, all_14_2) = all_14_0
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REDUCE: (81), (164) imply:
% 174.24/26.65  | | |   (167)  op(e3, all_52_17) = e3
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REDUCE: (104), (163) imply:
% 174.24/26.65  | | |   (168)  op(e2, all_52_19) = e2
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REDUCE: (145), (165) imply:
% 174.24/26.65  | | |   (169)  op(e1, all_14_2) = e1
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REDUCE: (89), (161) imply:
% 174.24/26.65  | | |   (170)  op(e0, all_52_23) = e0
% 174.24/26.65  | | | 
% 174.24/26.65  | | | GROUND_INST: instantiating (129) with e1, all_14_0, all_14_2, e1,
% 174.24/26.65  | | |              simplifying with (166), (169) gives:
% 174.24/26.65  | | |   (171)  all_14_0 = e1
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REDUCE: (72), (171) imply:
% 174.24/26.65  | | |   (172)   ~ (e3 = e1)
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REDUCE: (100), (171) imply:
% 174.24/26.65  | | |   (173)   ~ (e2 = e1)
% 174.24/26.65  | | | 
% 174.24/26.65  | | | BETA: splitting (45) gives:
% 174.24/26.65  | | | 
% 174.24/26.65  | | | Case 1:
% 174.24/26.65  | | | | 
% 174.24/26.65  | | | |   (174)  all_56_15 = e3
% 174.24/26.65  | | | | 
% 174.24/26.65  | | | | REF_CLOSE: (2), (3), (6), (11), (12), (15), (17), (19), (20), (23),
% 174.24/26.65  | | | |            (27), (28), (30), (31), (33), (35), (36), (37), (39), (40),
% 174.24/26.65  | | | |            (44), (46), (47), (48), (50), (56), (60), (65), (68), (70),
% 174.24/26.65  | | | |            (73), (74), (75), (76), (78), (79), (80), (83), (84), (87),
% 174.24/26.65  | | | |            (88), (94), (95), (98), (99), (101), (102), (107), (108),
% 174.24/26.65  | | | |            (109), (111), (112), (114), (116), (117), (119), (122),
% 174.24/26.65  | | | |            (125), (126), (127), (128), (129), (131), (135), (137),
% 174.24/26.65  | | | |            (146), (147), (148), (149), (151), (153), (156), (167),
% 174.24/26.65  | | | |            (168), (169), (170), (174) are inconsistent by sub-proof
% 174.24/26.65  | | | |            #284.
% 174.24/26.65  | | | | 
% 174.24/26.65  | | | Case 2:
% 174.24/26.65  | | | | 
% 174.24/26.65  | | | |   (175)   ~ (all_56_15 = e3)
% 174.24/26.65  | | | | 
% 174.24/26.65  | | | | REDUCE: (23), (175) imply:
% 174.24/26.65  | | | |   (176)   ~ (all_6_2 = e3)
% 174.24/26.65  | | | | 
% 174.24/26.65  | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (11), (12), (15), (20),
% 174.24/26.65  | | | |            (22), (24), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.24/26.65  | | | |            (35), (37), (39), (40), (41), (43), (46), (47), (48), (50),
% 174.24/26.65  | | | |            (51), (52), (54), (56), (59), (60), (61), (62), (63), (65),
% 174.24/26.65  | | | |            (66), (67), (68), (75), (76), (77), (78), (80), (85), (86),
% 174.24/26.65  | | | |            (90), (91), (92), (95), (96), (97), (98), (99), (101), (102),
% 174.24/26.65  | | | |            (103), (105), (106), (107), (108), (110), (111), (112),
% 174.24/26.65  | | | |            (113), (115), (116), (117), (118), (119), (120), (122),
% 174.24/26.65  | | | |            (123), (124), (125), (126), (127), (128), (129), (131),
% 174.24/26.65  | | | |            (132), (134), (135), (136), (137), (138), (139), (141),
% 174.24/26.65  | | | |            (142), (144), (146), (147), (148), (149), (150), (151),
% 174.24/26.65  | | | |            (152), (153), (154), (155), (156), (157), (167), (168),
% 174.24/26.65  | | | |            (169), (170), (176) are inconsistent by sub-proof #32.
% 174.24/26.65  | | | | 
% 174.24/26.65  | | | End of split
% 174.24/26.65  | | | 
% 174.24/26.65  | | Case 2:
% 174.24/26.65  | | | 
% 174.24/26.65  | | |   (177)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.24/26.65  | | | 
% 174.24/26.65  | | | ALPHA: (177) implies:
% 174.24/26.65  | | |   (178)  all_52_30 = e0
% 174.24/26.65  | | |   (179)  all_52_28 = e1
% 174.24/26.65  | | |   (180)  all_52_26 = e2
% 174.24/26.65  | | |   (181)  all_52_24 = e3
% 174.24/26.65  | | | 
% 174.24/26.65  | | | COMBINE_EQS: (143), (178) imply:
% 174.24/26.65  | | |   (182)  all_6_1 = e0
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REF_CLOSE: (4), (5), (6), (9), (11), (12), (13), (14), (16), (17), (18),
% 174.24/26.65  | | |            (19), (20), (21), (22), (23), (26), (27), (29), (30), (31),
% 174.24/26.65  | | |            (32), (33), (34), (35), (37), (38), (39), (41), (42), (43),
% 174.24/26.65  | | |            (44), (45), (47), (48), (49), (50), (52), (54), (55), (57),
% 174.24/26.65  | | |            (58), (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.24/26.65  | | |            (69), (70), (71), (73), (74), (76), (77), (78), (79), (80),
% 174.24/26.65  | | |            (81), (83), (85), (86), (87), (88), (91), (92), (93), (94),
% 174.24/26.65  | | |            (95), (96), (99), (101), (102), (105), (106), (107), (110),
% 174.24/26.65  | | |            (111), (112), (113), (115), (116), (117), (118), (119), (121),
% 174.24/26.65  | | |            (122), (124), (125), (126), (128), (129), (131), (132), (133),
% 174.24/26.65  | | |            (134), (137), (139), (141), (142), (146), (147), (148), (150),
% 174.24/26.65  | | |            (151), (152), (153), (154), (156), (157), (179), (180), (181),
% 174.24/26.65  | | |            (182) are inconsistent by sub-proof #88.
% 174.24/26.65  | | | 
% 174.24/26.65  | | End of split
% 174.24/26.65  | | 
% 174.24/26.65  | End of split
% 174.24/26.65  | 
% 174.24/26.65  End of proof
% 174.24/26.65  
% 174.24/26.65  Sub-proof #32 shows that the following formulas are inconsistent:
% 174.24/26.65  ----------------------------------------------------------------
% 174.24/26.65    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.65    (2)   ~ (all_52_5 = all_52_13)
% 174.24/26.65    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.24/26.65    (4)   ~ (all_52_17 = all_52_23)
% 174.24/26.65    (5)  op(e2, all_10_2) = all_10_1
% 174.24/26.65    (6)   ~ (all_52_13 = all_52_29)
% 174.24/26.65    (7)  all_56_3 = all_52_7
% 174.24/26.65    (8)  op(e3, e2) = all_52_3
% 174.24/26.65    (9)   ~ (all_52_9 = all_52_25)
% 174.24/26.65    (10)  op(e1, e2) = all_52_19
% 174.24/26.65    (11)   ~ (all_6_2 = e3)
% 174.24/26.65    (12)  all_58_5 = all_52_13
% 174.24/26.65    (13)   ~ (all_52_25 = all_52_29)
% 174.24/26.65    (14)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.65    (15)  all_58_3 = all_10_2
% 174.24/26.65    (16)  all_56_9 = all_52_19
% 174.24/26.65    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.65    (18)  all_58_15 = all_6_2
% 174.24/26.65    (19)   ~ (all_52_9 = all_4_2)
% 174.24/26.65    (20)   ~ (all_52_5 = all_52_7)
% 174.24/26.65    (21)  all_58_10 = all_52_15
% 174.24/26.65    (22)   ~ (all_52_5 = all_4_2)
% 174.24/26.65    (23)  all_58_7 = all_52_19
% 174.24/26.65    (24)   ~ (all_52_17 = all_52_25)
% 174.24/26.65    (25)  all_58_4 = all_52_5
% 174.24/26.65    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.65    (27)   ~ (e3 = e1)
% 174.24/26.65    (28)   ~ (all_52_17 = all_14_2)
% 174.24/26.65    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.65    (30)   ~ (all_52_7 = all_4_2)
% 174.24/26.65    (31)  all_58_1 = all_52_3
% 174.24/26.65    (32)  all_58_0 = all_4_2
% 174.24/26.65    (33)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.24/26.65    (34)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.24/26.65    (35)  op(e1, all_52_29) = all_52_28
% 174.24/26.65    (36)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.24/26.65    (37)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.65    (38)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.24/26.65    (39)  all_58_14 = all_52_29
% 174.24/26.65    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.65    (41)  op(e2, all_4_2) = all_4_0
% 174.24/26.65    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.65    (43)  op(e2, e1) = all_52_13
% 174.24/26.65    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.65    (45)  all_58_8 = all_14_2
% 174.24/26.65    (46)   ~ (all_52_5 = all_14_2)
% 174.24/26.65    (47)   ~ (all_52_3 = all_52_27)
% 174.24/26.65    (48)   ~ (all_52_3 = all_4_2)
% 174.24/26.65    (49)  op(e0, e3) = all_52_25
% 174.24/26.65    (50)   ~ (all_52_9 = all_10_2)
% 174.24/26.65    (51)   ~ (e3 = e0)
% 174.24/26.65    (52)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.65    (53)   ~ (all_52_15 = all_52_23)
% 174.24/26.65    (54)   ~ (all_52_5 = all_52_29)
% 174.24/26.65    (55)  all_56_2 = all_52_5
% 174.24/26.65    (56)  all_58_13 = all_52_27
% 174.24/26.65    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.65    (58)  all_56_5 = all_10_2
% 174.24/26.65    (59)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.65    (60)   ~ (all_52_9 = all_52_17)
% 174.24/26.65    (61)  all_58_6 = all_52_17
% 174.24/26.65    (62)   ~ (all_52_3 = all_52_7)
% 174.24/26.65    (63)  op(e2, all_52_19) = e2
% 174.24/26.65    (64)  op(all_10_1, all_10_2) = e3
% 174.24/26.65    (65)  op(e3, all_52_17) = e3
% 174.24/26.65    (66)   ~ (e1 = e0)
% 174.24/26.65    (67)  all_56_0 = all_4_2
% 174.24/26.65    (68)  all_58_11 = all_52_23
% 174.24/26.65    (69)   ~ (all_52_3 = all_52_19)
% 174.24/26.65    (70)   ~ (all_52_7 = all_52_15)
% 174.24/26.65    (71)   ~ (all_4_0 = e1)
% 174.24/26.65    (72)   ~ (all_52_19 = all_10_2)
% 174.24/26.65    (73)  op(e3, all_4_2) = e2
% 174.24/26.65    (74)   ~ (all_52_29 = all_6_2)
% 174.24/26.65    (75)  all_58_2 = all_52_9
% 174.24/26.65    (76)  op(e3, e1) = all_52_5
% 174.24/26.65    (77)   ~ (e2 = e1)
% 174.24/26.65    (78)   ~ (all_52_25 = all_6_2)
% 174.24/26.65    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.65    (80)  op(e1, e3) = all_52_17
% 174.24/26.65    (81)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.65    (82)   ~ (all_52_25 = all_4_2)
% 174.24/26.65    (83)  op(e3, e0) = all_52_7
% 174.24/26.65    (84)  op(e3, e3) = all_4_2
% 174.24/26.65    (85)  all_56_8 = all_52_17
% 174.24/26.65    (86)   ~ (all_52_17 = all_4_2)
% 174.24/26.65    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.65    (88)   ~ (all_52_25 = all_52_27)
% 174.24/26.65    (89)   ~ (all_52_27 = all_6_2)
% 174.24/26.65    (90)  op(e0, all_52_23) = e0
% 174.24/26.65    (91)   ~ (all_52_15 = all_10_2)
% 174.24/26.65    (92)   ~ (all_52_19 = all_52_27)
% 174.24/26.65    (93)  all_56_7 = all_52_15
% 174.24/26.65    (94)  op(e1, all_14_2) = e1
% 174.24/26.65    (95)   ~ (all_52_7 = all_52_23)
% 174.24/26.65    (96)   ~ (all_52_13 = all_10_2)
% 174.24/26.65    (97)  op(e2, all_52_27) = all_52_26
% 174.24/26.65    (98)   ~ (all_52_17 = all_52_19)
% 174.24/26.65    (99)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.65    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.65    (101)  all_58_9 = all_52_7
% 174.24/26.65    (102)   ~ (e2 = e0)
% 174.24/26.65    (103)  all_58_12 = all_52_25
% 174.24/26.65    (104)  all_56_6 = all_52_13
% 174.24/26.65    (105)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.65    (106)   ~ (all_52_9 = all_52_15)
% 174.24/26.65    (107)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.65    (108)   ~ (e3 = e2)
% 174.24/26.65    (109)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.65    (110)   ~ (all_52_19 = all_14_2)
% 174.24/26.65    (111)  op(e2, e3) = all_52_9
% 174.24/26.65    (112)  all_56_13 = all_52_27
% 174.24/26.65  
% 174.24/26.65  Begin of proof
% 174.24/26.65  | 
% 174.24/26.65  | BETA: splitting (40) gives:
% 174.24/26.65  | 
% 174.24/26.65  | Case 1:
% 174.24/26.65  | | 
% 174.24/26.65  | |   (113)  all_56_13 = e3
% 174.24/26.65  | | 
% 174.24/26.65  | | REF_CLOSE: (8), (14), (17), (18), (19), (21), (23), (26), (29), (32), (42),
% 174.24/26.65  | |            (45), (46), (47), (48), (49), (57), (61), (65), (67), (68), (73),
% 174.24/26.65  | |            (75), (76), (77), (80), (82), (84), (86), (87), (88), (89), (90),
% 174.24/26.65  | |            (92), (94), (95), (97), (99), (101), (102), (103), (105), (106),
% 174.24/26.65  | |            (108), (111), (112), (113) are inconsistent by sub-proof #96.
% 174.24/26.65  | | 
% 174.24/26.65  | Case 2:
% 174.24/26.65  | | 
% 174.24/26.65  | |   (114)   ~ (all_56_13 = e3)
% 174.24/26.65  | | 
% 174.24/26.65  | | REDUCE: (112), (114) imply:
% 174.24/26.65  | |   (115)   ~ (all_52_27 = e3)
% 174.24/26.65  | | 
% 174.24/26.65  | | BETA: splitting (44) gives:
% 174.24/26.65  | | 
% 174.24/26.65  | | Case 1:
% 174.24/26.65  | | | 
% 174.24/26.65  | | |   (116)  all_58_12 = e3
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (12), (13), (15), (17),
% 174.24/26.65  | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 174.24/26.65  | | |            (28), (29), (30), (31), (32), (34), (37), (39), (43), (45),
% 174.24/26.65  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 174.24/26.65  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 174.24/26.65  | | |            (66), (67), (68), (69), (70), (72), (75), (76), (77), (78),
% 174.24/26.65  | | |            (79), (80), (81), (82), (83), (85), (86), (87), (88), (90),
% 174.24/26.65  | | |            (91), (93), (94), (96), (98), (99), (101), (102), (103), (105),
% 174.24/26.65  | | |            (106), (107), (109), (110), (111), (116) are inconsistent by
% 174.24/26.65  | | |            sub-proof #250.
% 174.24/26.65  | | | 
% 174.24/26.65  | | Case 2:
% 174.24/26.65  | | | 
% 174.24/26.65  | | |   (117)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.65  | | | 
% 174.24/26.65  | | | REF_CLOSE: (2), (3), (4), (6), (7), (11), (13), (14), (16), (17), (18),
% 174.24/26.65  | | |            (19), (21), (23), (24), (26), (29), (30), (32), (33), (35),
% 174.24/26.65  | | |            (36), (38), (39), (41), (42), (43), (45), (46), (49), (54),
% 174.24/26.65  | | |            (56), (57), (60), (61), (63), (65), (67), (68), (71), (73),
% 174.24/26.65  | | |            (74), (75), (76), (80), (82), (84), (85), (86), (87), (90),
% 174.24/26.65  | | |            (94), (95), (99), (100), (101), (103), (104), (105), (106),
% 174.24/26.65  | | |            (108), (111), (115), (117) are inconsistent by sub-proof #95.
% 174.24/26.65  | | | 
% 174.24/26.65  | | End of split
% 174.24/26.65  | | 
% 174.24/26.65  | End of split
% 174.24/26.65  | 
% 174.24/26.65  End of proof
% 174.24/26.65  
% 174.24/26.65  Sub-proof #33 shows that the following formulas are inconsistent:
% 174.24/26.65  ----------------------------------------------------------------
% 174.24/26.65    (1)  op(e2, all_10_2) = all_10_1
% 174.24/26.65    (2)  all_52_0 = e2
% 174.24/26.65    (3)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.65         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.24/26.65    (4)  all_52_10 = all_10_1
% 174.24/26.65    (5)  op(all_10_1, all_10_2) = e3
% 174.24/26.65    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.65    (7)   ~ (e3 = e2)
% 174.24/26.65  
% 174.24/26.65  Begin of proof
% 174.24/26.65  | 
% 174.24/26.65  | BETA: splitting (3) gives:
% 174.24/26.65  | 
% 174.24/26.65  | Case 1:
% 174.24/26.65  | | 
% 174.24/26.65  | |   (8)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.24/26.65  | | 
% 174.24/26.65  | | REF_CLOSE: (2), (7), (8) are inconsistent by sub-proof #124.
% 174.24/26.65  | | 
% 174.24/26.65  | Case 2:
% 174.24/26.65  | | 
% 174.24/26.65  | |   (9)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 174.24/26.65  | | 
% 174.24/26.65  | | ALPHA: (9) implies:
% 174.24/26.65  | |   (10)  all_52_10 = e2
% 174.24/26.65  | | 
% 174.24/26.65  | | COMBINE_EQS: (4), (10) imply:
% 174.24/26.65  | |   (11)  all_10_1 = e2
% 174.24/26.65  | | 
% 174.24/26.65  | | REF_CLOSE: (1), (5), (6), (7), (11) are inconsistent by sub-proof #263.
% 174.24/26.65  | | 
% 174.24/26.65  | End of split
% 174.24/26.65  | 
% 174.24/26.65  End of proof
% 174.24/26.65  
% 174.24/26.65  Sub-proof #34 shows that the following formulas are inconsistent:
% 174.24/26.65  ----------------------------------------------------------------
% 174.24/26.65    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.65    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.24/26.65    (3)   ~ (all_52_17 = all_52_23)
% 174.24/26.65    (4)   ~ (all_6_0 = e3)
% 174.24/26.65    (5)   ~ (all_52_13 = all_52_29)
% 174.24/26.65    (6)  all_56_3 = all_52_7
% 174.24/26.65    (7)  op(e3, e2) = all_52_3
% 174.24/26.65    (8)   ~ (all_52_9 = all_52_25)
% 174.24/26.65    (9)   ~ (all_52_19 = all_52_23)
% 174.24/26.65    (10)  all_56_11 = all_52_23
% 174.24/26.65    (11)   ~ (all_52_27 = e0)
% 174.24/26.65    (12)   ~ (all_14_1 = e2)
% 174.24/26.65    (13)   ~ (all_52_23 = e0)
% 174.24/26.65    (14)   ~ (all_52_3 = all_10_2)
% 174.24/26.65    (15)  all_58_5 = all_52_13
% 174.24/26.65    (16)   ~ (all_52_25 = all_52_29)
% 174.24/26.65    (17)  op(e0, e0) = all_6_1
% 174.24/26.65    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.65    (19)  all_58_3 = all_10_2
% 174.24/26.65    (20)  all_56_9 = all_52_19
% 174.24/26.65    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.65    (22)   ~ (all_52_9 = all_4_2)
% 174.24/26.65    (23)  all_58_10 = all_52_15
% 174.24/26.65    (24)  all_58_7 = all_52_19
% 174.24/26.65    (25)   ~ (all_52_17 = all_52_25)
% 174.24/26.65    (26)  op(e0, e1) = all_52_29
% 174.24/26.65    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.65    (28)   ~ (all_52_27 = all_52_29)
% 174.24/26.65    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.65    (30)   ~ (all_52_7 = all_4_2)
% 174.24/26.65    (31)  all_58_1 = all_52_3
% 174.24/26.65    (32)  all_58_0 = all_4_2
% 174.24/26.65    (33)  op(e1, all_52_29) = all_52_28
% 174.24/26.65    (34)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.24/26.65    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.65    (36)   ~ (all_14_1 = e3)
% 174.24/26.65    (37)  all_58_14 = all_52_29
% 174.24/26.65    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.65    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.65    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.65    (41)  all_58_8 = all_14_2
% 174.24/26.65    (42)  op(e0, e2) = all_52_27
% 174.24/26.65    (43)   ~ (all_52_5 = all_14_2)
% 174.24/26.65    (44)   ~ (all_52_3 = all_4_2)
% 174.24/26.65    (45)  op(e0, e3) = all_52_25
% 174.24/26.65    (46)   ~ (all_52_9 = all_10_2)
% 174.24/26.65    (47)  op(e3, all_52_17) = all_52_16
% 174.24/26.65    (48)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.65    (49)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.65    (50)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.65    (51)  op(e0, all_52_23) = all_52_22
% 174.24/26.65    (52)   ~ (all_52_15 = all_52_23)
% 174.24/26.65    (53)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.24/26.65    (54)   ~ (all_52_5 = all_52_29)
% 174.24/26.65    (55)  all_56_12 = all_52_25
% 174.24/26.65    (56)  all_58_13 = all_52_27
% 174.24/26.65    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.65    (58)  all_56_5 = all_10_2
% 174.24/26.65    (59)  op(e0, e0) = e0
% 174.24/26.65    (60)   ~ (all_52_25 = e0)
% 174.24/26.65    (61)   ~ (all_52_9 = all_52_17)
% 174.24/26.65    (62)  all_58_6 = all_52_17
% 174.24/26.65    (63)   ~ (all_52_3 = all_52_7)
% 174.24/26.65    (64)  op(e2, all_52_19) = all_52_18
% 174.24/26.65    (65)  all_56_0 = all_4_2
% 174.24/26.65    (66)  all_58_11 = all_52_23
% 174.24/26.65    (67)   ~ (all_52_29 = all_14_2)
% 174.24/26.65    (68)   ~ (all_52_19 = all_10_2)
% 174.24/26.65    (69)  all_58_15 = e0
% 174.24/26.65    (70)   ~ (all_6_0 = e2)
% 174.24/26.65    (71)  all_58_2 = all_52_9
% 174.24/26.65    (72)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.24/26.65    (73)   ~ (all_52_29 = e0)
% 174.24/26.65    (74)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.24/26.65    (75)  op(e3, e1) = all_52_5
% 174.24/26.65    (76)  all_56_10 = all_14_2
% 174.24/26.65    (77)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.65    (78)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.24/26.65    (79)  op(e1, e3) = all_52_17
% 174.24/26.65    (80)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.65    (81)   ~ (all_52_25 = all_4_2)
% 174.24/26.65    (82)  op(e3, e0) = all_52_7
% 174.24/26.65    (83)  op(e3, e3) = all_4_2
% 174.24/26.65    (84)  all_56_8 = all_52_17
% 174.24/26.65    (85)   ~ (all_52_17 = all_4_2)
% 174.24/26.65    (86)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.65    (87)   ~ (all_52_25 = all_52_27)
% 174.24/26.65    (88)   ~ (all_52_19 = all_52_27)
% 174.24/26.65    (89)  all_56_7 = all_52_15
% 174.24/26.65    (90)   ~ (all_52_15 = e0)
% 174.24/26.65    (91)  op(all_6_1, e0) = all_6_0
% 174.24/26.65    (92)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.24/26.65    (93)   ~ (all_52_7 = all_52_23)
% 174.24/26.65    (94)   ~ (all_6_0 = e1)
% 174.24/26.65    (95)  all_52_20 = all_14_1
% 174.24/26.65    (96)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.65    (97)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.65    (98)  op(e1, all_14_2) = all_14_1
% 174.24/26.65    (99)  all_58_9 = all_52_7
% 174.24/26.65    (100)  all_58_12 = all_52_25
% 174.24/26.65    (101)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.65    (102)   ~ (all_52_9 = all_52_15)
% 174.24/26.65    (103)   ~ (e3 = e2)
% 174.24/26.65    (104)   ~ (all_52_19 = all_14_2)
% 174.24/26.65    (105)  op(e2, e3) = all_52_9
% 174.24/26.65    (106)  all_56_13 = all_52_27
% 174.24/26.65  
% 174.24/26.65  Begin of proof
% 174.24/26.65  | 
% 174.24/26.65  | ALPHA: (92) implies:
% 174.24/26.65  |   (107)  all_52_22 = e0
% 174.24/26.65  |   (108)  all_52_20 = e1
% 174.24/26.65  |   (109)  all_52_18 = e2
% 174.24/26.65  |   (110)  all_52_16 = e3
% 174.24/26.65  | 
% 174.24/26.65  | COMBINE_EQS: (95), (108) imply:
% 174.24/26.65  |   (111)  all_14_1 = e1
% 174.24/26.65  | 
% 174.24/26.65  | SIMP: (111) implies:
% 174.24/26.65  |   (112)  all_14_1 = e1
% 174.24/26.65  | 
% 174.24/26.65  | REDUCE: (36), (112) imply:
% 174.24/26.65  |   (113)   ~ (e3 = e1)
% 174.24/26.65  | 
% 174.24/26.65  | SIMP: (113) implies:
% 174.24/26.65  |   (114)   ~ (e3 = e1)
% 174.24/26.65  | 
% 174.24/26.65  | REDUCE: (12), (112) imply:
% 174.24/26.65  |   (115)   ~ (e2 = e1)
% 174.24/26.65  | 
% 174.24/26.65  | SIMP: (115) implies:
% 174.24/26.65  |   (116)   ~ (e2 = e1)
% 174.24/26.65  | 
% 174.24/26.66  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 174.24/26.66  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.24/26.66  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 174.24/26.66  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 174.24/26.66  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 174.24/26.66  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 174.24/26.66  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 174.24/26.66  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 174.24/26.66  |            (93), (94), (96), (97), (98), (99), (100), (101), (102), (103),
% 174.24/26.66  |            (104), (105), (106), (107), (109), (110), (112), (114), (116) are
% 174.24/26.66  |            inconsistent by sub-proof #118.
% 174.24/26.66  | 
% 174.24/26.66  End of proof
% 174.24/26.66  
% 174.24/26.66  Sub-proof #35 shows that the following formulas are inconsistent:
% 174.24/26.66  ----------------------------------------------------------------
% 174.24/26.66    (1)   ~ (all_52_17 = all_52_23)
% 174.24/26.66    (2)  op(e2, all_10_2) = all_10_1
% 174.24/26.66    (3)  op(e3, e2) = all_52_3
% 174.24/26.66    (4)   ~ (all_52_9 = all_52_25)
% 174.24/26.66    (5)   ~ (all_52_27 = e0)
% 174.24/26.66    (6)  op(e3, all_52_9) = all_52_8
% 174.24/26.66    (7)   ~ (all_52_3 = all_10_2)
% 174.24/26.66    (8)  all_58_5 = all_52_13
% 174.24/26.66    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.66    (10)  all_58_3 = all_10_2
% 174.24/26.66    (11)   ~ (all_52_9 = all_4_2)
% 174.24/26.66    (12)   ~ (all_52_5 = all_52_7)
% 174.24/26.66    (13)  all_58_10 = all_52_15
% 174.24/26.66    (14)  all_58_7 = all_52_19
% 174.24/26.66    (15)   ~ (all_52_17 = all_52_25)
% 174.24/26.66    (16)  op(e0, e1) = all_52_29
% 174.24/26.66    (17)  all_58_4 = all_52_5
% 174.24/26.66    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.66    (19)   ~ (e3 = e1)
% 174.24/26.66    (20)   ~ (all_52_27 = all_52_29)
% 174.24/26.66    (21)   ~ (all_52_17 = all_14_2)
% 174.24/26.66    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.66    (23)   ~ (all_52_7 = all_4_2)
% 174.24/26.66    (24)  all_58_1 = all_52_3
% 174.24/26.66    (25)  all_58_0 = all_4_2
% 174.24/26.66    (26)  op(e1, all_52_13) = all_52_12
% 174.24/26.66    (27)  all_52_0 = e2
% 174.24/26.66    (28)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.66          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.24/26.66    (29)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.24/26.66    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.66    (31)  all_58_14 = all_52_29
% 174.24/26.66    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.66    (33)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.66    (34)  all_58_8 = all_14_2
% 174.24/26.66    (35)  op(e0, e2) = all_52_27
% 174.24/26.66    (36)  all_56_14 = all_52_29
% 174.24/26.66    (37)  op(e0, e3) = all_52_25
% 174.24/26.66    (38)  all_52_10 = all_10_1
% 174.24/26.66    (39)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.66    (40)   ~ (e3 = e0)
% 174.24/26.66    (41)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.24/26.66    (42)  all_58_13 = all_52_27
% 174.24/26.66    (43)   ~ (all_52_25 = e0)
% 174.24/26.66    (44)   ~ (all_52_9 = all_52_17)
% 174.24/26.66    (45)  all_58_6 = all_52_17
% 174.24/26.66    (46)   ~ (all_52_3 = all_52_7)
% 174.24/26.66    (47)   ~ (e1 = e0)
% 174.24/26.66    (48)  all_58_11 = all_52_23
% 174.24/26.66    (49)   ~ (all_52_7 = all_52_15)
% 174.24/26.66    (50)  op(e0, all_52_15) = all_52_14
% 174.24/26.66    (51)   ~ (all_52_19 = all_10_2)
% 174.24/26.66    (52)  all_58_15 = e0
% 174.24/26.66    (53)  all_58_2 = all_52_9
% 174.24/26.66    (54)   ~ (all_52_29 = e0)
% 174.24/26.66    (55)   ~ (e2 = e1)
% 174.24/26.66    (56)  all_56_10 = all_14_2
% 174.24/26.66    (57)  op(e1, e3) = all_52_17
% 174.24/26.66    (58)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.66    (59)  op(e3, e3) = all_4_2
% 174.24/26.66    (60)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.66    (61)   ~ (all_52_25 = all_52_27)
% 174.24/26.66    (62)  all_56_7 = all_52_15
% 174.24/26.66    (63)   ~ (all_52_7 = all_52_23)
% 174.24/26.66    (64)   ~ (all_52_17 = all_52_19)
% 174.24/26.66    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.66    (66)  all_58_9 = all_52_7
% 174.24/26.66    (67)   ~ (e2 = e0)
% 174.24/26.66    (68)  all_58_12 = all_52_25
% 174.24/26.66    (69)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.66    (70)   ~ (e3 = e2)
% 174.24/26.66    (71)   ~ (all_52_19 = all_14_2)
% 174.24/26.66    (72)  op(e2, e3) = all_52_9
% 174.24/26.66  
% 174.24/26.66  Begin of proof
% 174.24/26.66  | 
% 174.24/26.66  | BETA: splitting (28) gives:
% 174.24/26.66  | 
% 174.24/26.66  | Case 1:
% 174.24/26.66  | | 
% 174.24/26.66  | |   (73)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.24/26.66  | | 
% 174.24/26.66  | | REF_CLOSE: (27), (70), (73) are inconsistent by sub-proof #124.
% 174.24/26.66  | | 
% 174.24/26.66  | Case 2:
% 174.24/26.66  | | 
% 174.24/26.66  | |   (74)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 174.24/26.66  | | 
% 174.24/26.66  | | ALPHA: (74) implies:
% 174.24/26.66  | |   (75)  all_52_14 = e0
% 174.24/26.66  | |   (76)  all_52_12 = e1
% 174.24/26.66  | |   (77)  all_52_10 = e2
% 174.24/26.66  | |   (78)  all_52_8 = e3
% 174.24/26.66  | | 
% 174.24/26.66  | | COMBINE_EQS: (38), (77) imply:
% 174.24/26.66  | |   (79)  all_10_1 = e2
% 174.24/26.66  | | 
% 174.24/26.66  | | SIMP: (79) implies:
% 174.24/26.66  | |   (80)  all_10_1 = e2
% 174.24/26.66  | | 
% 174.24/26.66  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.24/26.66  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.24/26.66  | |            (24), (25), (26), (29), (30), (31), (32), (33), (34), (35), (36),
% 174.24/26.66  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 174.24/26.66  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 174.24/26.66  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 174.24/26.66  | |            (71), (72), (75), (76), (78), (80) are inconsistent by sub-proof
% 174.24/26.66  | |            #121.
% 174.24/26.66  | | 
% 174.24/26.66  | End of split
% 174.24/26.66  | 
% 174.24/26.66  End of proof
% 174.24/26.66  
% 174.24/26.66  Sub-proof #36 shows that the following formulas are inconsistent:
% 174.24/26.66  ----------------------------------------------------------------
% 174.24/26.66    (1)  all_52_10 = e3
% 174.24/26.66    (2)   ~ (all_52_23 = all_14_2)
% 174.24/26.66    (3)   ~ (all_52_5 = all_52_13)
% 174.24/26.66    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.66    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.66    (6)   ~ (all_52_27 = all_10_2)
% 174.24/26.66    (7)  op(e2, e2) = all_10_2
% 174.24/26.66    (8)   ~ (all_52_17 = all_52_23)
% 174.24/26.66    (9)   ~ (all_52_13 = all_52_29)
% 174.24/26.66    (10)  all_42_1 = e2
% 174.24/26.66    (11)  all_56_3 = all_52_7
% 174.24/26.66    (12)  op(e3, e2) = all_52_3
% 174.24/26.66    (13)   ~ (all_52_9 = all_52_25)
% 174.24/26.66    (14)  op(e3, all_52_25) = all_52_24
% 174.24/26.66    (15)   ~ (all_52_19 = all_52_23)
% 174.24/26.66    (16)  op(e1, e2) = all_52_19
% 174.24/26.66    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.66    (18)  op(e3, all_52_9) = all_52_8
% 174.24/26.66    (19)   ~ (all_52_3 = all_10_2)
% 174.24/26.66    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.66    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.66    (22)  all_58_5 = all_52_13
% 174.24/26.66    (23)   ~ (all_52_25 = all_52_29)
% 174.24/26.66    (24)  all_56_15 = all_6_2
% 174.24/26.66    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.66    (26)  op(e2, e0) = all_52_15
% 174.24/26.66    (27)  op(all_14_1, all_14_2) = all_14_0
% 174.24/26.66    (28)   ~ (all_42_0 = e1) |  ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.24/26.66    (29)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.66    (30)  all_58_3 = all_10_2
% 174.24/26.66    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.66    (32)  all_58_15 = all_6_2
% 174.24/26.66    (33)   ~ (all_52_9 = all_4_2)
% 174.24/26.66    (34)   ~ (all_52_5 = all_52_7)
% 174.24/26.66    (35)  all_58_10 = all_52_15
% 174.24/26.66    (36)   ~ (all_52_5 = all_4_2)
% 174.24/26.66    (37)  all_58_7 = all_52_19
% 174.24/26.66    (38)   ~ (all_52_15 = all_6_2)
% 174.24/26.66    (39)   ~ (all_52_17 = all_52_25)
% 174.24/26.66    (40)  op(e0, e1) = all_52_29
% 174.24/26.66    (41)  all_58_4 = all_52_5
% 174.24/26.66    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.66    (43)   ~ (e3 = e1)
% 174.24/26.66    (44)   ~ (all_52_27 = all_52_29)
% 174.24/26.66    (45)   ~ (all_52_17 = all_14_2)
% 174.24/26.66    (46)  op(e3, all_4_2) = all_4_1
% 174.24/26.66    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.66    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.66    (49)   ~ (all_52_7 = all_4_2)
% 174.24/26.66    (50)  all_58_1 = all_52_3
% 174.24/26.66    (51)   ~ (all_52_13 = all_52_15)
% 174.24/26.66    (52)  all_58_0 = all_4_2
% 174.24/26.66    (53)  all_52_0 = e2
% 174.24/26.66    (54)  op(e1, all_52_29) = all_52_28
% 174.24/26.66    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.66    (56)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.24/26.66    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.24/26.66    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.66    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.66    (60)  all_58_14 = all_52_29
% 174.24/26.66    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.66    (62)  op(e2, all_4_2) = all_4_0
% 174.24/26.66    (63)   ~ (all_52_3 = all_52_5)
% 174.24/26.66    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.66    (65)  op(e2, e1) = all_52_13
% 174.24/26.66    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.66    (67)  all_58_8 = all_14_2
% 174.24/26.66    (68)  all_56_1 = all_52_3
% 174.24/26.66    (69)  op(e0, e2) = all_52_27
% 174.24/26.66    (70)  all_56_14 = all_52_29
% 174.24/26.66    (71)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 174.24/26.66    (72)  op(all_4_1, all_4_2) = all_4_0
% 174.24/26.66    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.66    (74)   ~ (all_52_3 = all_52_27)
% 174.24/26.66    (75)   ~ (all_52_3 = all_4_2)
% 174.24/26.66    (76)  op(e0, e3) = all_52_25
% 174.24/26.66    (77)  op(e0, all_6_2) = all_6_1
% 174.24/26.66    (78)   ~ (all_52_9 = all_10_2)
% 174.24/26.66    (79)  op(e3, all_52_17) = all_52_16
% 174.24/26.66    (80)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.66    (81)   ~ (e3 = e0)
% 174.24/26.66    (82)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.66    (83)   ~ (all_52_9 = all_52_13)
% 174.24/26.66    (84)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.66    (85)   ~ (all_52_15 = all_52_23)
% 174.24/26.66    (86)   ~ (all_52_5 = all_52_29)
% 174.24/26.66    (87)  all_56_2 = all_52_5
% 174.24/26.66    (88)  op(e1, e0) = all_52_23
% 174.24/26.66    (89)  all_56_12 = all_52_25
% 174.24/26.66    (90)  all_58_13 = all_52_27
% 174.24/26.66    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.66    (92)  all_56_5 = all_10_2
% 174.24/26.66    (93)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.66    (94)   ~ (all_52_9 = all_52_17)
% 174.24/26.66    (95)  all_14_0 = e2
% 174.24/26.66    (96)  all_58_6 = all_52_17
% 174.24/26.66    (97)   ~ (all_52_3 = all_52_7)
% 174.24/26.66    (98)   ~ (e1 = e0)
% 174.24/26.66    (99)  all_56_0 = all_4_2
% 174.24/26.66    (100)  all_58_11 = all_52_23
% 174.24/26.66    (101)   ~ (all_52_3 = all_52_19)
% 174.24/26.66    (102)   ~ (all_52_7 = all_52_15)
% 174.24/26.66    (103)  all_42_0 = all_4_0
% 174.24/26.66    (104)   ~ (all_52_29 = all_14_2)
% 174.24/26.66    (105)   ~ (all_52_19 = all_10_2)
% 174.24/26.66    (106)  op(e3, all_4_2) = e2
% 174.24/26.66    (107)   ~ (all_52_23 = all_6_2)
% 174.24/26.66    (108)   ~ (all_52_29 = all_6_2)
% 174.24/26.66    (109)  all_58_2 = all_52_9
% 174.24/26.66    (110)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.24/26.66    (111)  op(e3, e1) = all_52_5
% 174.24/26.66    (112)   ~ (e2 = e1)
% 174.24/26.66    (113)   ~ (all_52_25 = all_6_2)
% 174.24/26.66    (114)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.66    (115)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.24/26.66    (116)  op(e1, e3) = all_52_17
% 174.24/26.66    (117)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.66    (118)   ~ (all_52_25 = all_4_2)
% 174.24/26.66    (119)  op(e3, e0) = all_52_7
% 174.24/26.66    (120)  op(e3, e3) = all_4_2
% 174.24/26.66    (121)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.24/26.66             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.24/26.66    (122)   ~ (all_52_17 = all_4_2)
% 174.24/26.66    (123)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.66             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.66    (124)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.66           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.24/26.66           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.24/26.66           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.24/26.66    (125)   ~ (all_52_25 = all_52_27)
% 174.24/26.66    (126)   ~ (all_52_27 = all_6_2)
% 174.24/26.66    (127)   ~ (all_52_7 = all_6_2)
% 174.24/26.66    (128)   ~ (all_52_15 = all_10_2)
% 174.24/26.66    (129)  all_42_2 = all_4_2
% 174.24/26.66    (130)  all_56_7 = all_52_15
% 174.24/26.66    (131)   ~ (all_52_7 = all_52_23)
% 174.24/26.66    (132)   ~ (all_52_13 = all_10_2)
% 174.24/26.66    (133)  op(e2, all_52_27) = all_52_26
% 174.24/26.66    (134)  all_52_20 = all_14_1
% 174.24/26.66    (135)   ~ (all_52_17 = all_52_19)
% 174.24/26.66    (136)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.66    (137)  all_52_30 = all_6_1
% 174.24/26.66    (138)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.66    (139)  op(e2, all_10_2) = e3
% 174.24/26.66    (140)  op(e1, all_14_2) = all_14_1
% 174.24/26.66    (141)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 174.24/26.66    (142)  all_58_9 = all_52_7
% 174.24/26.66    (143)   ~ (e2 = e0)
% 174.24/26.66    (144)  all_58_12 = all_52_25
% 174.24/26.66    (145)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.66    (146)   ~ (all_52_9 = all_52_15)
% 174.24/26.66    (147)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.66    (148)   ~ (e3 = e2)
% 174.24/26.66    (149)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.66    (150)  op(e2, e3) = all_52_9
% 174.24/26.66    (151)  all_56_13 = all_52_27
% 174.24/26.66  
% 174.24/26.66  Begin of proof
% 174.24/26.66  | 
% 174.24/26.66  | REDUCE: (27), (95) imply:
% 174.24/26.66  |   (152)  op(all_14_1, all_14_2) = e2
% 174.24/26.66  | 
% 174.24/26.66  | BETA: splitting (28) gives:
% 174.24/26.66  | 
% 174.24/26.66  | Case 1:
% 174.24/26.66  | | 
% 174.24/26.66  | |   (153)   ~ (all_42_0 = e1)
% 174.24/26.66  | | 
% 174.24/26.66  | | REDUCE: (103), (153) imply:
% 174.24/26.66  | |   (154)   ~ (all_4_0 = e1)
% 174.24/26.66  | | 
% 174.24/26.66  | | BETA: splitting (124) gives:
% 174.24/26.66  | | 
% 174.24/26.66  | | Case 1:
% 174.24/26.66  | | | 
% 174.24/26.66  | | |   (155)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.66  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 174.24/26.66  | | |            e0)
% 174.24/26.66  | | | 
% 174.24/26.66  | | | BETA: splitting (155) gives:
% 174.24/26.66  | | | 
% 174.24/26.66  | | | Case 1:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (156)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (53), (148), (156) are inconsistent by sub-proof #124.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | Case 2:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (157)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 174.24/26.66  | | | |          e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (1), (148), (157) are inconsistent by sub-proof #289.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | End of split
% 174.24/26.66  | | | 
% 174.24/26.66  | | Case 2:
% 174.24/26.66  | | | 
% 174.24/26.66  | | |   (158)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.24/26.66  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.24/26.66  | | |            all_52_30 = e0)
% 174.24/26.66  | | | 
% 174.24/26.66  | | | BETA: splitting (158) gives:
% 174.24/26.66  | | | 
% 174.24/26.66  | | | Case 1:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (159)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.24/26.66  | | | |          e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (112), (123), (134), (140), (152), (159) are inconsistent by
% 174.24/26.66  | | | |            sub-proof #314.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | Case 2:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (160)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.24/26.66  | | | |          e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 174.24/26.66  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.24/26.66  | | | |            (24), (26), (29), (30), (31), (32), (33), (34), (35), (36),
% 174.24/26.66  | | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 174.24/26.66  | | | |            (47), (48), (49), (50), (51), (52), (54), (55), (56), (57),
% 174.24/26.66  | | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.24/26.66  | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 174.24/26.66  | | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 174.24/26.66  | | | |            (88), (89), (90), (91), (92), (93), (94), (96), (97), (98),
% 174.24/26.66  | | | |            (99), (100), (101), (102), (104), (105), (106), (107), (108),
% 174.24/26.66  | | | |            (109), (110), (111), (112), (113), (114), (115), (116),
% 174.24/26.66  | | | |            (118), (119), (120), (121), (122), (123), (125), (126),
% 174.24/26.66  | | | |            (127), (128), (131), (132), (133), (135), (136), (137),
% 174.24/26.66  | | | |            (138), (139), (141), (142), (143), (144), (145), (146),
% 174.24/26.66  | | | |            (147), (148), (149), (150), (151), (154), (160) are
% 174.24/26.66  | | | |            inconsistent by sub-proof #39.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | End of split
% 174.24/26.66  | | | 
% 174.24/26.66  | | End of split
% 174.24/26.66  | | 
% 174.24/26.66  | Case 2:
% 174.24/26.66  | | 
% 174.24/26.66  | |   (161)  all_42_0 = e1
% 174.24/26.66  | |   (162)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.24/26.66  | | 
% 174.24/26.66  | | COMBINE_EQS: (103), (161) imply:
% 174.24/26.66  | |   (163)  all_4_0 = e1
% 174.24/26.66  | | 
% 174.24/26.66  | | SIMP: (163) implies:
% 174.24/26.66  | |   (164)  all_4_0 = e1
% 174.24/26.66  | | 
% 174.24/26.66  | | REDUCE: (62), (164) imply:
% 174.24/26.66  | |   (165)  op(e2, all_4_2) = e1
% 174.24/26.66  | | 
% 174.24/26.66  | | BETA: splitting (124) gives:
% 174.24/26.66  | | 
% 174.24/26.66  | | Case 1:
% 174.24/26.66  | | | 
% 174.24/26.66  | | |   (166)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.66  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 174.24/26.66  | | |            e0)
% 174.24/26.66  | | | 
% 174.24/26.66  | | | BETA: splitting (166) gives:
% 174.24/26.66  | | | 
% 174.24/26.66  | | | Case 1:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (167)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (53), (148), (167) are inconsistent by sub-proof #124.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | Case 2:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (168)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 174.24/26.66  | | | |          e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (1), (148), (168) are inconsistent by sub-proof #289.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | End of split
% 174.24/26.66  | | | 
% 174.24/26.66  | | Case 2:
% 174.24/26.66  | | | 
% 174.24/26.66  | | |   (169)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.24/26.66  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.24/26.66  | | |            all_52_30 = e0)
% 174.24/26.66  | | | 
% 174.24/26.66  | | | BETA: splitting (169) gives:
% 174.24/26.66  | | | 
% 174.24/26.66  | | | Case 1:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (170)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.24/26.66  | | | |          e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (112), (123), (134), (140), (152), (170) are inconsistent by
% 174.24/26.66  | | | |            sub-proof #314.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | Case 2:
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | |   (171)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.24/26.66  | | | |          e0
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (12), (13), (14), (15), (17),
% 174.24/26.66  | | | |            (19), (22), (24), (25), (30), (31), (32), (35), (37), (41),
% 174.24/26.66  | | | |            (45), (47), (48), (50), (51), (52), (54), (55), (58), (60),
% 174.24/26.66  | | | |            (63), (64), (65), (66), (67), (68), (75), (76), (77), (78),
% 174.24/26.66  | | | |            (83), (90), (92), (96), (97), (99), (100), (106), (109),
% 174.24/26.66  | | | |            (111), (114), (116), (117), (118), (119), (120), (122),
% 174.24/26.66  | | | |            (123), (127), (129), (130), (132), (133), (136), (137),
% 174.24/26.66  | | | |            (139), (142), (144), (146), (147), (148), (150), (162),
% 174.24/26.66  | | | |            (165), (171) are inconsistent by sub-proof #37.
% 174.24/26.66  | | | | 
% 174.24/26.66  | | | End of split
% 174.24/26.66  | | | 
% 174.24/26.66  | | End of split
% 174.24/26.66  | | 
% 174.24/26.66  | End of split
% 174.24/26.66  | 
% 174.24/26.66  End of proof
% 174.24/26.66  
% 174.24/26.66  Sub-proof #37 shows that the following formulas are inconsistent:
% 174.24/26.66  ----------------------------------------------------------------
% 174.24/26.66    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.66    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.66    (3)   ~ (all_52_27 = all_10_2)
% 174.24/26.66    (4)  op(e2, e2) = all_10_2
% 174.24/26.66    (5)   ~ (all_52_17 = all_52_23)
% 174.24/26.66    (6)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.24/26.66    (7)  all_42_1 = e2
% 174.24/26.66    (8)  op(e3, e2) = all_52_3
% 174.24/26.66    (9)   ~ (all_52_9 = all_52_25)
% 174.24/26.66    (10)  op(e3, all_52_25) = all_52_24
% 174.24/26.66    (11)   ~ (all_52_19 = all_52_23)
% 174.24/26.66    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.66    (13)   ~ (all_52_3 = all_10_2)
% 174.24/26.66    (14)  all_58_5 = all_52_13
% 174.24/26.66    (15)  all_56_15 = all_6_2
% 174.24/26.66    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.66    (17)  all_58_3 = all_10_2
% 174.24/26.66    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.66    (19)  all_58_15 = all_6_2
% 174.24/26.66    (20)  op(e2, all_4_2) = e1
% 174.24/26.66    (21)  all_58_10 = all_52_15
% 174.24/26.66    (22)  all_58_7 = all_52_19
% 174.24/26.66    (23)  all_58_4 = all_52_5
% 174.24/26.66    (24)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.24/26.66    (25)   ~ (all_52_17 = all_14_2)
% 174.24/26.66    (26)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.66    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.66    (28)  all_58_1 = all_52_3
% 174.24/26.66    (29)   ~ (all_52_13 = all_52_15)
% 174.24/26.66    (30)  all_58_0 = all_4_2
% 174.24/26.66    (31)  op(e1, all_52_29) = all_52_28
% 174.24/26.66    (32)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.66    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.66    (34)  all_58_14 = all_52_29
% 174.24/26.66    (35)   ~ (all_52_3 = all_52_5)
% 174.24/26.66    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.66    (37)  op(e2, e1) = all_52_13
% 174.24/26.66    (38)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.66    (39)  all_58_8 = all_14_2
% 174.24/26.66    (40)  all_56_1 = all_52_3
% 174.24/26.66    (41)   ~ (all_52_3 = all_4_2)
% 174.24/26.66    (42)  op(e0, e3) = all_52_25
% 174.24/26.66    (43)  op(e0, all_6_2) = all_6_1
% 174.24/26.66    (44)   ~ (all_52_9 = all_10_2)
% 174.24/26.66    (45)   ~ (all_52_9 = all_52_13)
% 174.24/26.66    (46)  all_58_13 = all_52_27
% 174.24/26.66    (47)  all_56_5 = all_10_2
% 174.24/26.66    (48)  all_58_6 = all_52_17
% 174.24/26.66    (49)   ~ (all_52_3 = all_52_7)
% 174.24/26.66    (50)  all_56_0 = all_4_2
% 174.24/26.66    (51)  all_58_11 = all_52_23
% 174.24/26.66    (52)  op(e3, all_4_2) = e2
% 174.24/26.66    (53)  all_58_2 = all_52_9
% 174.24/26.66    (54)  op(e3, e1) = all_52_5
% 174.24/26.66    (55)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.66    (56)  op(e1, e3) = all_52_17
% 174.24/26.66    (57)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.66    (58)   ~ (all_52_25 = all_4_2)
% 174.24/26.66    (59)  op(e3, e0) = all_52_7
% 174.24/26.66    (60)  op(e3, e3) = all_4_2
% 174.24/26.67    (61)   ~ (all_52_17 = all_4_2)
% 174.24/26.67    (62)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.67    (63)   ~ (all_52_7 = all_6_2)
% 174.24/26.67    (64)  all_42_2 = all_4_2
% 174.24/26.67    (65)  all_56_7 = all_52_15
% 174.24/26.67    (66)   ~ (all_52_13 = all_10_2)
% 174.24/26.67    (67)  op(e2, all_52_27) = all_52_26
% 174.24/26.67    (68)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.67    (69)  all_52_30 = all_6_1
% 174.24/26.67    (70)  op(e2, all_10_2) = e3
% 174.24/26.67    (71)  all_58_9 = all_52_7
% 174.24/26.67    (72)  all_58_12 = all_52_25
% 174.24/26.67    (73)   ~ (all_52_9 = all_52_15)
% 174.24/26.67    (74)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.67    (75)   ~ (e3 = e2)
% 174.24/26.67    (76)  op(e2, e3) = all_52_9
% 174.24/26.67  
% 174.24/26.67  Begin of proof
% 174.24/26.67  | 
% 174.24/26.67  | ALPHA: (6) implies:
% 174.24/26.67  |   (77)  all_52_30 = e0
% 174.24/26.67  |   (78)  all_52_28 = e1
% 174.24/26.67  |   (79)  all_52_26 = e2
% 174.24/26.67  |   (80)  all_52_24 = e3
% 174.24/26.67  | 
% 174.24/26.67  | COMBINE_EQS: (69), (77) imply:
% 174.24/26.67  |   (81)  all_6_1 = e0
% 174.24/26.67  | 
% 174.24/26.67  | SIMP: (81) implies:
% 174.24/26.67  |   (82)  all_6_1 = e0
% 174.24/26.67  | 
% 174.24/26.67  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 174.24/26.67  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.24/26.67  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 174.24/26.67  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 174.24/26.67  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 174.24/26.67  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.24/26.67  |            (70), (71), (72), (73), (74), (75), (76), (78), (79), (80), (82)
% 174.24/26.67  |            are inconsistent by sub-proof #41.
% 174.24/26.67  | 
% 174.24/26.67  End of proof
% 174.24/26.67  
% 174.24/26.67  Sub-proof #38 shows that the following formulas are inconsistent:
% 174.24/26.67  ----------------------------------------------------------------
% 174.24/26.67    (1)  all_52_10 = e3
% 174.24/26.67    (2)   ~ (all_52_23 = all_14_2)
% 174.24/26.67    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.67    (4)   ~ (all_52_27 = all_10_2)
% 174.24/26.67    (5)  op(e2, e2) = all_10_2
% 174.24/26.67    (6)   ~ (all_52_17 = all_52_23)
% 174.24/26.67    (7)  all_42_1 = e2
% 174.24/26.67    (8)  op(e3, e2) = all_52_3
% 174.24/26.67    (9)   ~ (all_52_9 = all_52_25)
% 174.24/26.67    (10)  op(e3, all_52_25) = all_52_24
% 174.24/26.67    (11)   ~ (all_52_19 = all_52_23)
% 174.24/26.67    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.67    (13)   ~ (all_52_3 = all_10_2)
% 174.24/26.67    (14)  all_58_5 = all_52_13
% 174.24/26.67    (15)  all_56_15 = all_6_2
% 174.24/26.67    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.67    (17)  all_58_3 = all_10_2
% 174.24/26.67    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.67    (19)  all_58_15 = all_6_2
% 174.24/26.67    (20)  op(e2, all_4_2) = e1
% 174.24/26.67    (21)  all_58_10 = all_52_15
% 174.24/26.67    (22)  all_58_7 = all_52_19
% 174.24/26.67    (23)  all_58_4 = all_52_5
% 174.24/26.67    (24)   ~ (e3 = e1)
% 174.24/26.67    (25)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.24/26.67    (26)   ~ (all_52_17 = all_14_2)
% 174.24/26.67    (27)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.67    (28)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.67    (29)  all_58_1 = all_52_3
% 174.24/26.67    (30)   ~ (all_52_13 = all_52_15)
% 174.24/26.67    (31)  all_58_0 = all_4_2
% 174.24/26.67    (32)  all_52_0 = e2
% 174.24/26.67    (33)  op(e1, all_52_29) = all_52_28
% 174.24/26.67    (34)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.67    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.67    (36)  all_58_14 = all_52_29
% 174.24/26.67    (37)   ~ (all_52_3 = all_52_5)
% 174.24/26.67    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.67    (39)  op(e2, e1) = all_52_13
% 174.24/26.67    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.67    (41)  all_58_8 = all_14_2
% 174.24/26.67    (42)  all_56_1 = all_52_3
% 174.24/26.67    (43)  op(all_14_1, all_14_2) = e3
% 174.24/26.67    (44)   ~ (all_52_3 = all_4_2)
% 174.24/26.67    (45)  op(all_6_1, all_6_2) = all_6_0
% 174.24/26.67    (46)  op(e0, e3) = all_52_25
% 174.24/26.67    (47)  op(e0, all_6_2) = all_6_1
% 174.24/26.67    (48)   ~ (all_52_9 = all_10_2)
% 174.24/26.67    (49)   ~ (all_52_9 = all_52_13)
% 174.24/26.67    (50)  all_58_13 = all_52_27
% 174.24/26.67    (51)  all_56_5 = all_10_2
% 174.24/26.67    (52)  all_58_6 = all_52_17
% 174.24/26.67    (53)   ~ (all_52_3 = all_52_7)
% 174.24/26.67    (54)  all_56_0 = all_4_2
% 174.24/26.67    (55)  all_58_11 = all_52_23
% 174.24/26.67    (56)  op(e3, all_4_2) = e2
% 174.24/26.67    (57)  all_58_2 = all_52_9
% 174.24/26.67    (58)  op(e3, e1) = all_52_5
% 174.24/26.67    (59)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.67    (60)  op(e1, e3) = all_52_17
% 174.24/26.67    (61)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.67    (62)   ~ (all_52_25 = all_4_2)
% 174.24/26.67    (63)  op(e3, e0) = all_52_7
% 174.24/26.67    (64)  op(e3, e3) = all_4_2
% 174.24/26.67    (65)   ~ (all_52_17 = all_4_2)
% 174.24/26.67    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.67    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.67          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.24/26.67          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.24/26.67          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.24/26.67    (68)   ~ (all_52_7 = all_6_2)
% 174.24/26.67    (69)  all_42_2 = all_4_2
% 174.24/26.67    (70)  all_56_7 = all_52_15
% 174.24/26.67    (71)   ~ (all_52_13 = all_10_2)
% 174.24/26.67    (72)  op(e2, all_52_27) = all_52_26
% 174.24/26.67    (73)  all_52_20 = all_14_1
% 174.24/26.67    (74)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.67    (75)  all_52_30 = all_6_1
% 174.24/26.67    (76)  op(e2, all_10_2) = e3
% 174.24/26.67    (77)  op(e1, all_14_2) = all_14_1
% 174.24/26.67    (78)  all_58_9 = all_52_7
% 174.24/26.67    (79)  all_58_12 = all_52_25
% 174.24/26.67    (80)   ~ (all_52_9 = all_52_15)
% 174.24/26.67    (81)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.67    (82)   ~ (e3 = e2)
% 174.24/26.67    (83)  op(e2, e3) = all_52_9
% 174.24/26.67  
% 174.24/26.67  Begin of proof
% 174.24/26.67  | 
% 174.24/26.67  | BETA: splitting (25) gives:
% 174.24/26.67  | 
% 174.24/26.67  | Case 1:
% 174.24/26.67  | | 
% 174.24/26.67  | |   (84)   ~ (all_42_1 = e2)
% 174.24/26.67  | | 
% 174.24/26.67  | | REDUCE: (7), (84) imply:
% 174.24/26.67  | |   (85)  $false
% 174.24/26.67  | | 
% 174.24/26.67  | | CLOSE: (85) is inconsistent.
% 174.24/26.67  | | 
% 174.24/26.67  | Case 2:
% 174.24/26.67  | | 
% 174.24/26.67  | |   (86)   ~ (all_42_2 = e0)
% 174.24/26.67  | | 
% 174.24/26.67  | | REDUCE: (69), (86) imply:
% 174.24/26.67  | |   (87)   ~ (all_4_2 = e0)
% 174.24/26.67  | | 
% 174.24/26.67  | | BETA: splitting (67) gives:
% 174.24/26.67  | | 
% 174.24/26.67  | | Case 1:
% 174.24/26.67  | | | 
% 174.24/26.67  | | |   (88)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.24/26.67  | | |         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.24/26.67  | | | 
% 174.24/26.67  | | | BETA: splitting (88) gives:
% 174.24/26.67  | | | 
% 174.24/26.67  | | | Case 1:
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | |   (89)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REF_CLOSE: (32), (82), (89) are inconsistent by sub-proof #124.
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | Case 2:
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | |   (90)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REF_CLOSE: (1), (82), (90) are inconsistent by sub-proof #289.
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | End of split
% 174.24/26.67  | | | 
% 174.24/26.67  | | Case 2:
% 174.24/26.67  | | | 
% 174.24/26.67  | | |   (91)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.24/26.67  | | |           e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.24/26.67  | | |           all_52_30 = e0)
% 174.24/26.67  | | | 
% 174.24/26.67  | | | BETA: splitting (91) gives:
% 174.24/26.67  | | | 
% 174.24/26.67  | | | Case 1:
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | |   (92)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.24/26.67  | | | |         e0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | ALPHA: (92) implies:
% 174.24/26.67  | | | |   (93)  all_52_20 = e1
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | COMBINE_EQS: (73), (93) imply:
% 174.24/26.67  | | | |   (94)  all_14_1 = e1
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REF_CLOSE: (24), (43), (66), (77), (94) are inconsistent by sub-proof
% 174.24/26.67  | | | |            #344.
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | Case 2:
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | |   (95)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.24/26.67  | | | |         e0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | ALPHA: (95) implies:
% 174.24/26.67  | | | |   (96)  all_52_30 = e0
% 174.24/26.67  | | | |   (97)  all_52_28 = e1
% 174.24/26.67  | | | |   (98)  all_52_26 = e2
% 174.24/26.67  | | | |   (99)  all_52_24 = e3
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | COMBINE_EQS: (75), (96) imply:
% 174.24/26.67  | | | |   (100)  all_6_1 = e0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REDUCE: (45), (100) imply:
% 174.24/26.67  | | | |   (101)  op(e0, all_6_2) = all_6_0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REDUCE: (10), (99) imply:
% 174.24/26.67  | | | |   (102)  op(e3, all_52_25) = e3
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REDUCE: (72), (98) imply:
% 174.24/26.67  | | | |   (103)  op(e2, all_52_27) = e2
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REDUCE: (33), (97) imply:
% 174.24/26.67  | | | |   (104)  op(e1, all_52_29) = e1
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REDUCE: (47), (100) imply:
% 174.24/26.67  | | | |   (105)  op(e0, all_6_2) = e0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | GROUND_INST: instantiating (66) with e0, all_6_0, all_6_2, e0,
% 174.24/26.67  | | | |              simplifying with (101), (105) gives:
% 174.24/26.67  | | | |   (106)  all_6_0 = e0
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 174.24/26.67  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 174.24/26.67  | | | |            (27), (28), (29), (30), (31), (34), (35), (36), (37), (38),
% 174.24/26.67  | | | |            (39), (40), (41), (42), (44), (46), (48), (49), (50), (51),
% 174.24/26.67  | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 174.24/26.67  | | | |            (62), (63), (64), (65), (66), (68), (70), (71), (74), (76),
% 174.24/26.67  | | | |            (78), (79), (80), (81), (82), (83), (87), (102), (103),
% 174.24/26.67  | | | |            (104), (105) are inconsistent by sub-proof #42.
% 174.24/26.67  | | | | 
% 174.24/26.67  | | | End of split
% 174.24/26.67  | | | 
% 174.24/26.67  | | End of split
% 174.24/26.67  | | 
% 174.24/26.67  | End of split
% 174.24/26.67  | 
% 174.24/26.67  End of proof
% 174.24/26.67  
% 174.24/26.67  Sub-proof #39 shows that the following formulas are inconsistent:
% 174.24/26.67  ----------------------------------------------------------------
% 174.24/26.67    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.67    (2)   ~ (all_52_5 = all_52_13)
% 174.24/26.67    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.67    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.67    (5)   ~ (all_52_27 = all_10_2)
% 174.24/26.67    (6)  op(e2, e2) = all_10_2
% 174.24/26.67    (7)   ~ (all_52_17 = all_52_23)
% 174.24/26.67    (8)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.24/26.67    (9)   ~ (all_52_13 = all_52_29)
% 174.24/26.67    (10)  all_56_3 = all_52_7
% 174.24/26.67    (11)  op(e3, e2) = all_52_3
% 174.24/26.67    (12)   ~ (all_52_9 = all_52_25)
% 174.24/26.67    (13)  op(e3, all_52_25) = all_52_24
% 174.24/26.67    (14)   ~ (all_52_19 = all_52_23)
% 174.24/26.67    (15)  op(e1, e2) = all_52_19
% 174.24/26.67    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.67    (17)  op(e3, all_52_9) = all_52_8
% 174.24/26.67    (18)   ~ (all_52_3 = all_10_2)
% 174.24/26.67    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.67    (20)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.67    (21)  all_58_5 = all_52_13
% 174.24/26.67    (22)   ~ (all_52_25 = all_52_29)
% 174.24/26.67    (23)  all_56_15 = all_6_2
% 174.24/26.67    (24)  op(e2, e0) = all_52_15
% 174.24/26.67    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.67    (26)  all_58_3 = all_10_2
% 174.24/26.67    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.67    (28)  all_58_15 = all_6_2
% 174.24/26.67    (29)   ~ (all_52_9 = all_4_2)
% 174.24/26.67    (30)   ~ (all_52_5 = all_52_7)
% 174.24/26.67    (31)  all_58_10 = all_52_15
% 174.24/26.67    (32)   ~ (all_52_5 = all_4_2)
% 174.24/26.67    (33)  all_58_7 = all_52_19
% 174.24/26.67    (34)   ~ (all_52_15 = all_6_2)
% 174.24/26.67    (35)   ~ (all_52_17 = all_52_25)
% 174.24/26.67    (36)  op(e0, e1) = all_52_29
% 174.24/26.67    (37)  all_58_4 = all_52_5
% 174.24/26.67    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.67    (39)   ~ (e3 = e1)
% 174.24/26.67    (40)   ~ (all_52_27 = all_52_29)
% 174.24/26.67    (41)   ~ (all_52_17 = all_14_2)
% 174.24/26.67    (42)  op(e3, all_4_2) = all_4_1
% 174.24/26.67    (43)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.67    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.67    (45)   ~ (all_52_7 = all_4_2)
% 174.24/26.67    (46)  all_58_1 = all_52_3
% 174.24/26.67    (47)   ~ (all_52_13 = all_52_15)
% 174.24/26.67    (48)  all_58_0 = all_4_2
% 174.24/26.67    (49)  op(e1, all_52_29) = all_52_28
% 174.24/26.67    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.67    (51)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.24/26.67    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.24/26.67    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.67    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.67    (55)  all_58_14 = all_52_29
% 174.24/26.67    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.67    (57)  op(e2, all_4_2) = all_4_0
% 174.24/26.67    (58)   ~ (all_52_3 = all_52_5)
% 174.24/26.67    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.67    (60)  op(e2, e1) = all_52_13
% 174.24/26.67    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.67    (62)  all_58_8 = all_14_2
% 174.24/26.67    (63)  all_56_1 = all_52_3
% 174.24/26.67    (64)  op(e0, e2) = all_52_27
% 174.24/26.67    (65)  all_56_14 = all_52_29
% 174.24/26.67    (66)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 174.24/26.67    (67)  op(all_4_1, all_4_2) = all_4_0
% 174.24/26.67    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.67    (69)   ~ (all_52_3 = all_52_27)
% 174.24/26.67    (70)   ~ (all_52_3 = all_4_2)
% 174.24/26.67    (71)  op(e0, e3) = all_52_25
% 174.24/26.67    (72)  op(e0, all_6_2) = all_6_1
% 174.24/26.67    (73)   ~ (all_52_9 = all_10_2)
% 174.24/26.67    (74)  op(e3, all_52_17) = all_52_16
% 174.24/26.67    (75)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.67    (76)   ~ (e3 = e0)
% 174.24/26.67    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.67    (78)   ~ (all_52_9 = all_52_13)
% 174.24/26.67    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.67    (80)   ~ (all_52_15 = all_52_23)
% 174.24/26.67    (81)   ~ (all_52_5 = all_52_29)
% 174.24/26.67    (82)  all_56_2 = all_52_5
% 174.24/26.67    (83)  op(e1, e0) = all_52_23
% 174.24/26.67    (84)  all_56_12 = all_52_25
% 174.24/26.67    (85)  all_58_13 = all_52_27
% 174.24/26.67    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.67    (87)  all_56_5 = all_10_2
% 174.24/26.67    (88)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.67    (89)   ~ (all_52_9 = all_52_17)
% 174.24/26.67    (90)  all_58_6 = all_52_17
% 174.24/26.67    (91)   ~ (all_52_3 = all_52_7)
% 174.24/26.67    (92)   ~ (e1 = e0)
% 174.24/26.67    (93)  all_56_0 = all_4_2
% 174.24/26.67    (94)  all_58_11 = all_52_23
% 174.24/26.67    (95)   ~ (all_52_3 = all_52_19)
% 174.24/26.67    (96)   ~ (all_52_7 = all_52_15)
% 174.24/26.67    (97)   ~ (all_52_29 = all_14_2)
% 174.24/26.67    (98)   ~ (all_4_0 = e1)
% 174.24/26.67    (99)   ~ (all_52_19 = all_10_2)
% 174.24/26.67    (100)  op(e3, all_4_2) = e2
% 174.24/26.67    (101)   ~ (all_52_23 = all_6_2)
% 174.24/26.67    (102)   ~ (all_52_29 = all_6_2)
% 174.24/26.67    (103)  all_58_2 = all_52_9
% 174.24/26.67    (104)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.24/26.67    (105)  op(e3, e1) = all_52_5
% 174.24/26.67    (106)   ~ (e2 = e1)
% 174.24/26.67    (107)   ~ (all_52_25 = all_6_2)
% 174.24/26.67    (108)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.67    (109)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.24/26.67    (110)  op(e1, e3) = all_52_17
% 174.24/26.67    (111)   ~ (all_52_25 = all_4_2)
% 174.24/26.67    (112)  op(e3, e0) = all_52_7
% 174.24/26.67    (113)  op(e3, e3) = all_4_2
% 174.24/26.67    (114)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.24/26.67             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.24/26.67    (115)   ~ (all_52_17 = all_4_2)
% 174.24/26.67    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.67             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.67    (117)   ~ (all_52_25 = all_52_27)
% 174.24/26.67    (118)   ~ (all_52_27 = all_6_2)
% 174.24/26.67    (119)   ~ (all_52_7 = all_6_2)
% 174.24/26.67    (120)   ~ (all_52_15 = all_10_2)
% 174.24/26.67    (121)   ~ (all_52_7 = all_52_23)
% 174.24/26.67    (122)   ~ (all_52_13 = all_10_2)
% 174.24/26.67    (123)  op(e2, all_52_27) = all_52_26
% 174.24/26.67    (124)   ~ (all_52_17 = all_52_19)
% 174.24/26.67    (125)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.67    (126)  all_52_30 = all_6_1
% 174.24/26.67    (127)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.67    (128)  op(e2, all_10_2) = e3
% 174.24/26.67    (129)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 174.24/26.67    (130)  all_58_9 = all_52_7
% 174.24/26.67    (131)   ~ (e2 = e0)
% 174.24/26.67    (132)  all_58_12 = all_52_25
% 174.24/26.67    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.67    (134)   ~ (all_52_9 = all_52_15)
% 174.24/26.67    (135)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.67    (136)   ~ (e3 = e2)
% 174.24/26.67    (137)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.67    (138)  op(e2, e3) = all_52_9
% 174.24/26.67    (139)  all_56_13 = all_52_27
% 174.24/26.67  
% 174.24/26.67  Begin of proof
% 174.24/26.67  | 
% 174.24/26.67  | ALPHA: (8) implies:
% 174.24/26.67  |   (140)  all_52_30 = e0
% 174.24/26.67  |   (141)  all_52_28 = e1
% 174.24/26.67  |   (142)  all_52_26 = e2
% 174.24/26.67  |   (143)  all_52_24 = e3
% 174.24/26.67  | 
% 174.24/26.67  | COMBINE_EQS: (126), (140) imply:
% 174.24/26.67  |   (144)  all_6_1 = e0
% 174.24/26.67  | 
% 174.24/26.67  | SIMP: (144) implies:
% 174.24/26.67  |   (145)  all_6_1 = e0
% 174.24/26.67  | 
% 174.24/26.67  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 174.24/26.67  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.24/26.67  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 174.24/26.67  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 174.24/26.67  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 174.24/26.67  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.24/26.67  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 174.24/26.67  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 174.24/26.67  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.24/26.67  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 174.24/26.67  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 174.24/26.67  |            (120), (121), (122), (123), (124), (125), (127), (128), (129),
% 174.24/26.67  |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 174.24/26.67  |            (139), (141), (142), (143), (145) are inconsistent by sub-proof
% 174.24/26.67  |            #44.
% 174.24/26.67  | 
% 174.24/26.67  End of proof
% 174.24/26.67  
% 174.24/26.67  Sub-proof #40 shows that the following formulas are inconsistent:
% 174.24/26.67  ----------------------------------------------------------------
% 174.24/26.67    (1)   ~ (all_52_5 = all_52_13)
% 174.24/26.67    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.24/26.67    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.67    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.67    (5)   ~ (all_52_27 = all_10_2)
% 174.24/26.67    (6)  op(e2, e2) = all_10_2
% 174.24/26.67    (7)   ~ (all_52_17 = all_52_23)
% 174.24/26.67    (8)   ~ (all_52_13 = all_52_29)
% 174.24/26.67    (9)  all_56_3 = all_52_7
% 174.24/26.67    (10)  op(e3, e2) = all_52_3
% 174.24/26.67    (11)   ~ (all_52_9 = all_52_25)
% 174.24/26.67    (12)  op(e1, e2) = all_52_19
% 174.24/26.67    (13)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.67    (14)  op(e3, all_52_9) = all_52_8
% 174.24/26.67    (15)   ~ (all_52_3 = all_10_2)
% 174.24/26.67    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.67    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.67    (18)  all_58_5 = all_52_13
% 174.24/26.67    (19)   ~ (all_52_25 = all_52_29)
% 174.24/26.67    (20)  all_56_15 = all_6_2
% 174.24/26.67    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.67    (22)  all_58_3 = all_10_2
% 174.24/26.67    (23)  all_56_9 = all_52_19
% 174.24/26.67    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.67    (25)  all_58_15 = all_6_2
% 174.24/26.67    (26)   ~ (all_52_9 = all_4_2)
% 174.24/26.67    (27)   ~ (all_52_5 = all_52_7)
% 174.24/26.67    (28)  all_58_10 = all_52_15
% 174.24/26.67    (29)   ~ (all_52_5 = all_4_2)
% 174.24/26.67    (30)  all_58_7 = all_52_19
% 174.24/26.67    (31)   ~ (all_52_15 = all_6_2)
% 174.24/26.67    (32)   ~ (all_52_17 = all_52_25)
% 174.24/26.67    (33)  all_58_4 = all_52_5
% 174.24/26.67    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.67    (35)   ~ (e3 = e1)
% 174.24/26.67    (36)  op(e3, all_4_2) = all_4_1
% 174.24/26.67    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.67    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.67    (39)   ~ (all_52_7 = all_4_2)
% 174.24/26.67    (40)  all_58_1 = all_52_3
% 174.24/26.67    (41)  all_58_0 = all_4_2
% 174.24/26.67    (42)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.24/26.67    (43)  op(e1, all_52_29) = all_52_28
% 174.24/26.67    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.67    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.24/26.67    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.67    (47)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.24/26.67    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.67    (49)  all_58_14 = all_52_29
% 174.24/26.68    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.68    (51)  op(e2, all_4_2) = all_4_0
% 174.24/26.68    (52)   ~ (all_52_3 = all_52_5)
% 174.24/26.68    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.68    (54)  op(e2, e1) = all_52_13
% 174.24/26.68    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.68    (56)  all_58_8 = all_14_2
% 174.24/26.68    (57)  all_56_1 = all_52_3
% 174.24/26.68    (58)  op(e0, e2) = all_52_27
% 174.24/26.68    (59)  op(all_4_1, all_4_2) = all_4_0
% 174.24/26.68    (60)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.68    (61)   ~ (all_52_5 = all_14_2)
% 174.24/26.68    (62)   ~ (all_52_3 = all_52_27)
% 174.24/26.68    (63)   ~ (all_52_3 = all_4_2)
% 174.24/26.68    (64)  op(e0, e3) = all_52_25
% 174.24/26.68    (65)  op(e0, all_6_2) = all_6_1
% 174.24/26.68    (66)   ~ (all_52_9 = all_10_2)
% 174.24/26.68    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.68    (68)   ~ (all_52_13 = all_14_2)
% 174.24/26.68    (69)   ~ (e3 = e0)
% 174.24/26.68    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.68    (71)   ~ (all_52_9 = all_52_13)
% 174.24/26.68    (72)  op(e3, all_10_2) = all_10_0
% 174.24/26.68    (73)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.68    (74)   ~ (all_52_15 = all_52_23)
% 174.24/26.68    (75)   ~ (all_52_5 = all_52_29)
% 174.24/26.68    (76)  all_56_2 = all_52_5
% 174.24/26.68    (77)  all_56_12 = all_52_25
% 174.24/26.68    (78)  all_58_13 = all_52_27
% 174.24/26.68    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.68    (80)  all_56_5 = all_10_2
% 174.24/26.68    (81)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.68    (82)   ~ (all_52_9 = all_52_17)
% 174.24/26.68    (83)  all_58_6 = all_52_17
% 174.24/26.68    (84)   ~ (all_52_3 = all_52_7)
% 174.24/26.68    (85)  op(e2, all_52_19) = e2
% 174.24/26.68    (86)  op(e3, all_52_17) = e3
% 174.24/26.68    (87)   ~ (e1 = e0)
% 174.24/26.68    (88)  all_56_0 = all_4_2
% 174.24/26.68    (89)  all_58_11 = all_52_23
% 174.24/26.68    (90)   ~ (all_52_3 = all_52_19)
% 174.24/26.68    (91)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 174.24/26.68    (92)   ~ (all_52_7 = all_52_15)
% 174.24/26.68    (93)   ~ (all_4_0 = e1)
% 174.24/26.68    (94)   ~ (all_52_19 = all_10_2)
% 174.24/26.68    (95)   ~ (all_58_15 = e0)
% 174.24/26.68    (96)  op(e3, all_4_2) = e2
% 174.24/26.68    (97)   ~ (all_52_23 = all_6_2)
% 174.24/26.68    (98)   ~ (all_52_29 = all_6_2)
% 174.24/26.68    (99)  all_58_2 = all_52_9
% 174.24/26.68    (100)  op(e3, e1) = all_52_5
% 174.24/26.68    (101)   ~ (e2 = e1)
% 174.24/26.68    (102)   ~ (all_52_25 = all_6_2)
% 174.24/26.68    (103)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.68    (104)  op(e1, e3) = all_52_17
% 174.24/26.68    (105)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.68    (106)   ~ (all_52_25 = all_4_2)
% 174.24/26.68    (107)  op(e3, e0) = all_52_7
% 174.24/26.68    (108)  op(e3, e3) = all_4_2
% 174.24/26.68    (109)  all_56_8 = all_52_17
% 174.24/26.68    (110)   ~ (all_52_17 = all_4_2)
% 174.24/26.68    (111)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.68             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.68    (112)   ~ (all_52_25 = all_52_27)
% 174.24/26.68    (113)   ~ (all_52_27 = all_6_2)
% 174.24/26.68    (114)  op(e0, all_52_23) = e0
% 174.24/26.68    (115)   ~ (all_52_15 = all_10_2)
% 174.24/26.68    (116)   ~ (all_52_19 = all_52_27)
% 174.24/26.68    (117)  all_56_7 = all_52_15
% 174.24/26.68    (118)  op(e1, all_14_2) = e1
% 174.24/26.68    (119)   ~ (all_52_7 = all_52_23)
% 174.24/26.68    (120)  op(e2, all_52_27) = all_52_26
% 174.24/26.68    (121)   ~ (all_52_17 = all_52_19)
% 174.24/26.68    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.68    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.68    (124)  op(e2, all_10_2) = e3
% 174.24/26.68    (125)  all_58_9 = all_52_7
% 174.24/26.68    (126)   ~ (e2 = e0)
% 174.24/26.68    (127)  all_58_12 = all_52_25
% 174.24/26.68    (128)  all_56_6 = all_52_13
% 174.24/26.68    (129)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.24/26.68             all_58_13 = e0 | all_58_14 = e0)
% 174.24/26.68    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.68    (131)   ~ (all_52_9 = all_52_15)
% 174.24/26.68    (132)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.68    (133)   ~ (e3 = e2)
% 174.24/26.68    (134)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.68    (135)  op(e2, e3) = all_52_9
% 174.24/26.68    (136)  all_56_13 = all_52_27
% 174.24/26.68  
% 174.24/26.68  Begin of proof
% 174.24/26.68  | 
% 174.24/26.68  | ALPHA: (129) implies:
% 174.24/26.68  |   (137)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.24/26.68  |   (138)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.24/26.68  | 
% 174.24/26.68  | REDUCE: (25), (95) imply:
% 174.24/26.68  |   (139)   ~ (all_6_2 = e0)
% 174.24/26.68  | 
% 174.24/26.68  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.24/26.68  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.24/26.68  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.24/26.68  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.24/26.68  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.24/26.68  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.24/26.68  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.24/26.68  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 174.24/26.68  |            (90), (91), (92), (93), (94), (96), (97), (98), (99), (100), (101),
% 174.24/26.68  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 174.24/26.68  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 174.24/26.68  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 174.24/26.68  |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 174.24/26.68  |            (139) are inconsistent by sub-proof #47.
% 174.24/26.68  | 
% 174.24/26.68  End of proof
% 174.24/26.68  
% 174.24/26.68  Sub-proof #41 shows that the following formulas are inconsistent:
% 174.24/26.68  ----------------------------------------------------------------
% 174.24/26.68    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.68    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.68    (3)   ~ (all_52_27 = all_10_2)
% 174.24/26.68    (4)  op(e2, e2) = all_10_2
% 174.24/26.68    (5)   ~ (all_52_17 = all_52_23)
% 174.24/26.68    (6)  all_52_26 = e2
% 174.24/26.68    (7)  all_42_1 = e2
% 174.24/26.68    (8)  op(e3, e2) = all_52_3
% 174.24/26.68    (9)   ~ (all_52_9 = all_52_25)
% 174.24/26.68    (10)  op(e3, all_52_25) = all_52_24
% 174.24/26.68    (11)   ~ (all_52_19 = all_52_23)
% 174.24/26.68    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.68    (13)   ~ (all_52_3 = all_10_2)
% 174.24/26.68    (14)  all_58_5 = all_52_13
% 174.24/26.68    (15)  all_56_15 = all_6_2
% 174.24/26.68    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.68    (17)  all_6_1 = e0
% 174.24/26.68    (18)  all_58_3 = all_10_2
% 174.24/26.68    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.68    (20)  all_58_15 = all_6_2
% 174.24/26.68    (21)  op(e2, all_4_2) = e1
% 174.24/26.68    (22)  all_58_10 = all_52_15
% 174.24/26.68    (23)  all_58_7 = all_52_19
% 174.24/26.68    (24)  all_58_4 = all_52_5
% 174.24/26.68    (25)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.24/26.68    (26)   ~ (all_52_17 = all_14_2)
% 174.24/26.68    (27)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.68    (28)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.68    (29)  all_58_1 = all_52_3
% 174.24/26.68    (30)   ~ (all_52_13 = all_52_15)
% 174.24/26.68    (31)  all_58_0 = all_4_2
% 174.24/26.68    (32)  op(e1, all_52_29) = all_52_28
% 174.24/26.68    (33)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.68    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.68    (35)  all_58_14 = all_52_29
% 174.24/26.68    (36)   ~ (all_52_3 = all_52_5)
% 174.24/26.68    (37)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.68    (38)  op(e2, e1) = all_52_13
% 174.24/26.68    (39)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.68    (40)  all_58_8 = all_14_2
% 174.24/26.68    (41)  all_56_1 = all_52_3
% 174.24/26.68    (42)   ~ (all_52_3 = all_4_2)
% 174.24/26.68    (43)  op(e0, e3) = all_52_25
% 174.24/26.68    (44)  op(e0, all_6_2) = all_6_1
% 174.24/26.68    (45)   ~ (all_52_9 = all_10_2)
% 174.24/26.68    (46)   ~ (all_52_9 = all_52_13)
% 174.24/26.68    (47)  all_58_13 = all_52_27
% 174.24/26.68    (48)  all_56_5 = all_10_2
% 174.24/26.68    (49)  all_58_6 = all_52_17
% 174.24/26.68    (50)   ~ (all_52_3 = all_52_7)
% 174.24/26.68    (51)  all_56_0 = all_4_2
% 174.24/26.68    (52)  all_58_11 = all_52_23
% 174.24/26.68    (53)  op(e3, all_4_2) = e2
% 174.24/26.68    (54)  all_58_2 = all_52_9
% 174.24/26.68    (55)  op(e3, e1) = all_52_5
% 174.24/26.68    (56)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.68    (57)  op(e1, e3) = all_52_17
% 174.24/26.68    (58)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.68    (59)   ~ (all_52_25 = all_4_2)
% 174.24/26.68    (60)  op(e3, e0) = all_52_7
% 174.24/26.68    (61)  all_52_28 = e1
% 174.24/26.68    (62)  op(e3, e3) = all_4_2
% 174.24/26.68    (63)   ~ (all_52_17 = all_4_2)
% 174.24/26.68    (64)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.68    (65)   ~ (all_52_7 = all_6_2)
% 174.24/26.68    (66)  all_42_2 = all_4_2
% 174.24/26.68    (67)  all_56_7 = all_52_15
% 174.24/26.68    (68)   ~ (all_52_13 = all_10_2)
% 174.24/26.68    (69)  op(e2, all_52_27) = all_52_26
% 174.24/26.68    (70)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.68    (71)  op(e2, all_10_2) = e3
% 174.24/26.68    (72)  all_58_9 = all_52_7
% 174.24/26.68    (73)  all_52_24 = e3
% 174.24/26.68    (74)  all_58_12 = all_52_25
% 174.24/26.68    (75)   ~ (all_52_9 = all_52_15)
% 174.24/26.68    (76)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.68    (77)   ~ (e3 = e2)
% 174.24/26.68    (78)  op(e2, e3) = all_52_9
% 174.24/26.68  
% 174.24/26.68  Begin of proof
% 174.24/26.68  | 
% 174.24/26.68  | REDUCE: (10), (73) imply:
% 174.24/26.68  |   (79)  op(e3, all_52_25) = e3
% 174.24/26.68  | 
% 174.24/26.68  | REDUCE: (6), (69) imply:
% 174.24/26.68  |   (80)  op(e2, all_52_27) = e2
% 174.24/26.68  | 
% 174.24/26.68  | REDUCE: (32), (61) imply:
% 174.24/26.68  |   (81)  op(e1, all_52_29) = e1
% 174.24/26.68  | 
% 174.24/26.68  | REDUCE: (17), (44) imply:
% 174.24/26.68  |   (82)  op(e0, all_6_2) = e0
% 174.24/26.68  | 
% 174.24/26.68  | BETA: splitting (25) gives:
% 174.24/26.68  | 
% 174.24/26.68  | Case 1:
% 174.24/26.68  | | 
% 174.24/26.68  | |   (83)   ~ (all_42_1 = e2)
% 174.24/26.68  | | 
% 174.24/26.68  | | REDUCE: (7), (83) imply:
% 174.24/26.68  | |   (84)  $false
% 174.24/26.68  | | 
% 174.24/26.68  | | CLOSE: (84) is inconsistent.
% 174.24/26.68  | | 
% 174.24/26.68  | Case 2:
% 174.24/26.68  | | 
% 174.24/26.68  | |   (85)   ~ (all_42_2 = e0)
% 174.24/26.68  | | 
% 174.24/26.68  | | REDUCE: (66), (85) imply:
% 174.24/26.68  | |   (86)   ~ (all_4_2 = e0)
% 174.24/26.68  | | 
% 174.24/26.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12), (13), (14), (15),
% 174.24/26.68  | |            (16), (18), (19), (20), (21), (22), (23), (24), (26), (27), (28),
% 174.24/26.68  | |            (29), (30), (31), (33), (34), (35), (36), (37), (38), (39), (40),
% 174.24/26.68  | |            (41), (42), (43), (45), (46), (47), (48), (49), (50), (51), (52),
% 174.24/26.68  | |            (53), (54), (55), (56), (57), (58), (59), (60), (62), (63), (64),
% 174.24/26.68  | |            (65), (67), (68), (70), (71), (72), (74), (75), (76), (77), (78),
% 174.24/26.68  | |            (79), (80), (81), (82), (86) are inconsistent by sub-proof #42.
% 174.24/26.68  | | 
% 174.24/26.68  | End of split
% 174.24/26.68  | 
% 174.24/26.68  End of proof
% 174.24/26.68  
% 174.24/26.68  Sub-proof #42 shows that the following formulas are inconsistent:
% 174.24/26.68  ----------------------------------------------------------------
% 174.24/26.68    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.68    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.68    (3)   ~ (all_52_27 = all_10_2)
% 174.24/26.68    (4)  op(e2, e2) = all_10_2
% 174.24/26.68    (5)   ~ (all_52_17 = all_52_23)
% 174.24/26.68    (6)  op(e3, e2) = all_52_3
% 174.24/26.68    (7)   ~ (all_52_9 = all_52_25)
% 174.24/26.68    (8)   ~ (all_52_19 = all_52_23)
% 174.24/26.68    (9)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.68    (10)   ~ (all_52_3 = all_10_2)
% 174.24/26.68    (11)  all_58_5 = all_52_13
% 174.24/26.68    (12)  all_56_15 = all_6_2
% 174.24/26.68    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.68    (14)  all_58_3 = all_10_2
% 174.24/26.68    (15)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.68    (16)  all_58_15 = all_6_2
% 174.24/26.68    (17)  op(e2, all_4_2) = e1
% 174.24/26.68    (18)  op(e0, all_6_2) = e0
% 174.24/26.68    (19)  all_58_10 = all_52_15
% 174.24/26.68    (20)  all_58_7 = all_52_19
% 174.24/26.68    (21)  all_58_4 = all_52_5
% 174.24/26.68    (22)   ~ (all_52_17 = all_14_2)
% 174.24/26.68    (23)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.68    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.68    (25)  all_58_1 = all_52_3
% 174.24/26.68    (26)   ~ (all_52_13 = all_52_15)
% 174.24/26.68    (27)  all_58_0 = all_4_2
% 174.24/26.68    (28)  op(e2, all_52_27) = e2
% 174.24/26.68    (29)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.68    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.68    (31)  all_58_14 = all_52_29
% 174.24/26.68    (32)   ~ (all_52_3 = all_52_5)
% 174.24/26.68    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.68    (34)  op(e2, e1) = all_52_13
% 174.24/26.68    (35)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.68    (36)  all_58_8 = all_14_2
% 174.24/26.68    (37)  all_56_1 = all_52_3
% 174.24/26.68    (38)  op(e1, all_52_29) = e1
% 174.24/26.68    (39)   ~ (all_52_3 = all_4_2)
% 174.24/26.68    (40)  op(e0, e3) = all_52_25
% 174.24/26.68    (41)   ~ (all_52_9 = all_10_2)
% 174.24/26.68    (42)   ~ (all_52_9 = all_52_13)
% 174.24/26.68    (43)  all_58_13 = all_52_27
% 174.24/26.68    (44)  all_56_5 = all_10_2
% 174.24/26.68    (45)  all_58_6 = all_52_17
% 174.24/26.68    (46)   ~ (all_52_3 = all_52_7)
% 174.24/26.68    (47)  all_56_0 = all_4_2
% 174.24/26.68    (48)  all_58_11 = all_52_23
% 174.24/26.68    (49)  op(e3, all_52_25) = e3
% 174.24/26.68    (50)  op(e3, all_4_2) = e2
% 174.24/26.68    (51)  all_58_2 = all_52_9
% 174.24/26.68    (52)  op(e3, e1) = all_52_5
% 174.24/26.68    (53)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.68    (54)  op(e1, e3) = all_52_17
% 174.24/26.68    (55)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.68    (56)   ~ (all_52_25 = all_4_2)
% 174.24/26.68    (57)  op(e3, e0) = all_52_7
% 174.24/26.68    (58)  op(e3, e3) = all_4_2
% 174.24/26.68    (59)   ~ (all_52_17 = all_4_2)
% 174.24/26.68    (60)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.68    (61)   ~ (all_52_7 = all_6_2)
% 174.24/26.68    (62)  all_56_7 = all_52_15
% 174.24/26.68    (63)   ~ (all_4_2 = e0)
% 174.24/26.68    (64)   ~ (all_52_13 = all_10_2)
% 174.24/26.68    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.68    (66)  op(e2, all_10_2) = e3
% 174.24/26.68    (67)  all_58_9 = all_52_7
% 174.24/26.68    (68)  all_58_12 = all_52_25
% 174.24/26.68    (69)   ~ (all_52_9 = all_52_15)
% 174.24/26.68    (70)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.68    (71)   ~ (e3 = e2)
% 174.24/26.68    (72)  op(e2, e3) = all_52_9
% 174.24/26.68  
% 174.24/26.68  Begin of proof
% 174.24/26.68  | 
% 174.24/26.68  | BETA: splitting (15) gives:
% 174.24/26.68  | 
% 174.24/26.68  | Case 1:
% 174.24/26.68  | | 
% 174.24/26.68  | |   (73)  all_56_0 = e3
% 174.24/26.68  | | 
% 174.24/26.68  | | COMBINE_EQS: (47), (73) imply:
% 174.24/26.68  | |   (74)  all_4_2 = e3
% 174.24/26.68  | | 
% 174.24/26.68  | | REF_CLOSE: (50), (58), (60), (71), (74) are inconsistent by sub-proof #106.
% 174.24/26.68  | | 
% 174.24/26.68  | Case 2:
% 174.24/26.68  | | 
% 174.24/26.68  | |   (75)   ~ (all_56_0 = e3)
% 174.24/26.68  | |   (76)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.68  | | 
% 174.24/26.68  | | REDUCE: (47), (75) imply:
% 174.24/26.68  | |   (77)   ~ (all_4_2 = e3)
% 174.24/26.68  | | 
% 174.24/26.68  | | BETA: splitting (23) gives:
% 174.24/26.68  | | 
% 174.24/26.68  | | Case 1:
% 174.24/26.68  | | | 
% 174.24/26.68  | | |   (78)  all_56_15 = e3
% 174.24/26.68  | | | 
% 174.24/26.68  | | | COMBINE_EQS: (12), (78) imply:
% 174.24/26.68  | | |   (79)  all_6_2 = e3
% 174.24/26.68  | | | 
% 174.24/26.68  | | | SIMP: (79) implies:
% 174.24/26.68  | | |   (80)  all_6_2 = e3
% 174.24/26.68  | | | 
% 174.24/26.68  | | | REF_CLOSE: (18), (40), (49), (57), (60), (61), (80) are inconsistent by
% 174.24/26.68  | | |            sub-proof #665.
% 174.24/26.68  | | | 
% 174.24/26.68  | | Case 2:
% 174.24/26.68  | | | 
% 174.24/26.68  | | |   (81)   ~ (all_56_15 = e3)
% 174.24/26.68  | | | 
% 174.24/26.68  | | | REDUCE: (12), (81) imply:
% 174.24/26.68  | | |   (82)   ~ (all_6_2 = e3)
% 174.24/26.68  | | | 
% 174.24/26.68  | | | BETA: splitting (33) gives:
% 174.24/26.68  | | | 
% 174.24/26.68  | | | Case 1:
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | |   (83)  all_58_0 = e3
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | | COMBINE_EQS: (27), (83) imply:
% 174.24/26.68  | | | |   (84)  all_4_2 = e3
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | | REDUCE: (77), (84) imply:
% 174.24/26.68  | | | |   (85)  $false
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | | CLOSE: (85) is inconsistent.
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | Case 2:
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | |   (86)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | | BETA: splitting (55) gives:
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | | Case 1:
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | |   (87)  all_56_7 = e3
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | COMBINE_EQS: (62), (87) imply:
% 174.24/26.68  | | | | |   (88)  all_52_15 = e3
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | SIMP: (88) implies:
% 174.24/26.68  | | | | |   (89)  all_52_15 = e3
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | REDUCE: (69), (89) imply:
% 174.24/26.68  | | | | |   (90)   ~ (all_52_9 = e3)
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | REDUCE: (26), (89) imply:
% 174.24/26.68  | | | | |   (91)   ~ (all_52_13 = e3)
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | BETA: splitting (29) gives:
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | Case 1:
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | |   (92)  all_56_1 = e3
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | COMBINE_EQS: (37), (92) imply:
% 174.24/26.68  | | | | | |   (93)  all_52_3 = e3
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | REDUCE: (32), (93) imply:
% 174.24/26.68  | | | | | |   (94)   ~ (all_52_5 = e3)
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | SIMP: (94) implies:
% 174.24/26.68  | | | | | |   (95)   ~ (all_52_5 = e3)
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | BETA: splitting (35) gives:
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | Case 1:
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | |   (96)  all_58_12 = e3
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | REF_CLOSE: (49), (56), (58), (60), (68), (96) are inconsistent by
% 174.24/26.68  | | | | | | |            sub-proof #884.
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | Case 2:
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | |   (97)   ~ (all_58_12 = e3)
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | REDUCE: (68), (97) imply:
% 174.24/26.68  | | | | | | |   (98)   ~ (all_52_25 = e3)
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | BETA: splitting (86) gives:
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | Case 1:
% 174.24/26.68  | | | | | | | | 
% 174.24/26.68  | | | | | | | |   (99)  all_58_2 = e3
% 174.24/26.68  | | | | | | | | 
% 174.24/26.68  | | | | | | | | REF_CLOSE: (51), (90), (99) are inconsistent by sub-proof #980.
% 174.24/26.68  | | | | | | | | 
% 174.24/26.68  | | | | | | | Case 2:
% 174.24/26.68  | | | | | | | | 
% 174.24/26.68  | | | | | | | |   (100)  all_58_6 = e3 | all_58_12 = e3
% 174.24/26.68  | | | | | | | | 
% 174.24/26.68  | | | | | | | | BETA: splitting (100) gives:
% 174.24/26.68  | | | | | | | | 
% 174.24/26.68  | | | | | | | | Case 1:
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | |   (101)  all_58_6 = e3
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | | COMBINE_EQS: (45), (101) imply:
% 174.24/26.68  | | | | | | | | |   (102)  all_52_17 = e3
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | | SIMP: (102) implies:
% 174.24/26.68  | | | | | | | | |   (103)  all_52_17 = e3
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | | REDUCE: (22), (103) imply:
% 174.24/26.68  | | | | | | | | |   (104)   ~ (all_14_2 = e3)
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | | SIMP: (104) implies:
% 174.24/26.68  | | | | | | | | |   (105)   ~ (all_14_2 = e3)
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | | REF_CLOSE: (6), (11), (13), (21), (27), (31), (36), (38),
% 174.24/26.68  | | | | | | | | |            (39), (47), (50), (54), (59), (60), (63), (70),
% 174.24/26.68  | | | | | | | | |            (76), (91), (95), (105) are inconsistent by
% 174.24/26.68  | | | | | | | | |            sub-proof #112.
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | Case 2:
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | |   (106)  all_58_12 = e3
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | | REF_CLOSE: (68), (98), (106) are inconsistent by sub-proof
% 174.24/26.68  | | | | | | | | |            #1003.
% 174.24/26.68  | | | | | | | | | 
% 174.24/26.68  | | | | | | | | End of split
% 174.24/26.68  | | | | | | | | 
% 174.24/26.68  | | | | | | | End of split
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | End of split
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | Case 2:
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | |   (107)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (13), (17), (25), (27), (32),
% 174.24/26.68  | | | | | |            (34), (37), (39), (41), (44), (47), (50), (52), (53),
% 174.24/26.68  | | | | | |            (60), (63), (64), (66), (72), (76), (107) are
% 174.24/26.68  | | | | | |            inconsistent by sub-proof #43.
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | End of split
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | Case 2:
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | |   (108)   ~ (all_56_7 = e3)
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | REDUCE: (62), (108) imply:
% 174.24/26.68  | | | | |   (109)   ~ (all_52_15 = e3)
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | BETA: splitting (65) gives:
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | | Case 1:
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | |   (110)  all_58_9 = e3
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | COMBINE_EQS: (67), (110) imply:
% 174.24/26.68  | | | | | |   (111)  all_52_7 = e3
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | SIMP: (111) implies:
% 174.24/26.68  | | | | | |   (112)  all_52_7 = e3
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | REDUCE: (46), (112) imply:
% 174.24/26.68  | | | | | |   (113)   ~ (all_52_3 = e3)
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | BETA: splitting (29) gives:
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | Case 1:
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | |   (114)  all_56_1 = e3
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | COMBINE_EQS: (37), (114) imply:
% 174.24/26.68  | | | | | | |   (115)  all_52_3 = e3
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | REDUCE: (113), (115) imply:
% 174.24/26.68  | | | | | | |   (116)  $false
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | CLOSE: (116) is inconsistent.
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | Case 2:
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | |   (117)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (13), (17), (25), (27), (32),
% 174.24/26.68  | | | | | | |            (34), (37), (39), (41), (44), (47), (50), (52), (53),
% 174.24/26.68  | | | | | | |            (60), (63), (64), (66), (72), (76), (117) are
% 174.24/26.68  | | | | | | |            inconsistent by sub-proof #43.
% 174.24/26.68  | | | | | | | 
% 174.24/26.68  | | | | | | End of split
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | Case 2:
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | |   (118)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (11), (13), (14), (16),
% 174.24/26.68  | | | | | |            (19), (20), (21), (24), (25), (27), (28), (29), (30),
% 174.24/26.68  | | | | | |            (31), (32), (35), (36), (37), (38), (39), (41), (42),
% 174.24/26.68  | | | | | |            (43), (45), (47), (48), (49), (50), (51), (54), (56),
% 174.24/26.68  | | | | | |            (58), (59), (60), (63), (68), (69), (70), (71), (72),
% 174.24/26.68  | | | | | |            (76), (82), (86), (109), (118) are inconsistent by
% 174.24/26.68  | | | | | |            sub-proof #74.
% 174.24/26.68  | | | | | | 
% 174.24/26.68  | | | | | End of split
% 174.24/26.68  | | | | | 
% 174.24/26.68  | | | | End of split
% 174.24/26.68  | | | | 
% 174.24/26.68  | | | End of split
% 174.24/26.68  | | | 
% 174.24/26.68  | | End of split
% 174.24/26.68  | | 
% 174.24/26.68  | End of split
% 174.24/26.68  | 
% 174.24/26.68  End of proof
% 174.24/26.68  
% 174.24/26.68  Sub-proof #43 shows that the following formulas are inconsistent:
% 174.24/26.68  ----------------------------------------------------------------
% 174.24/26.68    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.68    (2)  op(e2, e2) = all_10_2
% 174.24/26.69    (3)  op(e3, e2) = all_52_3
% 174.24/26.69    (4)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.69    (5)   ~ (all_52_3 = all_10_2)
% 174.24/26.69    (6)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.69    (7)  op(e2, all_4_2) = e1
% 174.24/26.69    (8)  all_58_1 = all_52_3
% 174.24/26.69    (9)  all_58_0 = all_4_2
% 174.24/26.69    (10)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.69    (11)   ~ (all_52_3 = all_52_5)
% 174.24/26.69    (12)  op(e2, e1) = all_52_13
% 174.24/26.69    (13)  all_56_1 = all_52_3
% 174.24/26.69    (14)   ~ (all_52_3 = all_4_2)
% 174.24/26.69    (15)   ~ (all_52_9 = all_10_2)
% 174.24/26.69    (16)  all_56_5 = all_10_2
% 174.24/26.69    (17)  all_56_0 = all_4_2
% 174.24/26.69    (18)  op(e3, all_4_2) = e2
% 174.24/26.69    (19)  op(e3, e1) = all_52_5
% 174.24/26.69    (20)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.69    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.69    (22)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.69    (23)   ~ (all_4_2 = e0)
% 174.24/26.69    (24)   ~ (all_52_13 = all_10_2)
% 174.24/26.69    (25)  op(e2, all_10_2) = e3
% 174.24/26.69    (26)  op(e2, e3) = all_52_9
% 174.24/26.69  
% 174.24/26.69  Begin of proof
% 174.24/26.69  | 
% 174.24/26.69  | BETA: splitting (1) gives:
% 174.24/26.69  | 
% 174.24/26.69  | Case 1:
% 174.24/26.69  | | 
% 174.24/26.69  | |   (27)  all_58_0 = e0
% 174.24/26.69  | | 
% 174.24/26.69  | | COMBINE_EQS: (9), (27) imply:
% 174.24/26.69  | |   (28)  all_4_2 = e0
% 174.24/26.69  | | 
% 174.24/26.69  | | REDUCE: (23), (28) imply:
% 174.24/26.69  | |   (29)  $false
% 174.24/26.69  | | 
% 174.24/26.69  | | CLOSE: (29) is inconsistent.
% 174.24/26.69  | | 
% 174.24/26.69  | Case 2:
% 174.24/26.69  | | 
% 174.24/26.69  | |   (30)   ~ (all_58_0 = e0)
% 174.24/26.69  | |   (31)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.69  | | 
% 174.24/26.69  | | BETA: splitting (20) gives:
% 174.24/26.69  | | 
% 174.24/26.69  | | Case 1:
% 174.24/26.69  | | | 
% 174.24/26.69  | | |   (32)  all_56_5 = e3
% 174.24/26.69  | | | 
% 174.24/26.69  | | | REF_CLOSE: (15), (16), (21), (25), (26), (32) are inconsistent by
% 174.24/26.69  | | |            sub-proof #271.
% 174.24/26.69  | | | 
% 174.24/26.69  | | Case 2:
% 174.24/26.69  | | | 
% 174.24/26.69  | | |   (33)   ~ (all_56_5 = e3)
% 174.24/26.69  | | |   (34)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.69  | | | 
% 174.24/26.69  | | | REDUCE: (16), (33) imply:
% 174.24/26.69  | | |   (35)   ~ (all_10_2 = e3)
% 174.24/26.69  | | | 
% 174.24/26.69  | | | BETA: splitting (4) gives:
% 174.24/26.69  | | | 
% 174.24/26.69  | | | Case 1:
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | |   (36)  all_58_0 = e1
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | COMBINE_EQS: (9), (36) imply:
% 174.24/26.69  | | | |   (37)  all_4_2 = e1
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | REDUCE: (14), (37) imply:
% 174.24/26.69  | | | |   (38)   ~ (all_52_3 = e1)
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | REDUCE: (18), (37) imply:
% 174.24/26.69  | | | |   (39)  op(e3, e1) = e2
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | REDUCE: (7), (37) imply:
% 174.24/26.69  | | | |   (40)  op(e2, e1) = e1
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | GROUND_INST: instantiating (21) with all_52_13, e1, e1, e2, simplifying
% 174.24/26.69  | | | |              with (12), (40) gives:
% 174.24/26.69  | | | |   (41)  all_52_13 = e1
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | GROUND_INST: instantiating (21) with all_52_5, e2, e1, e3, simplifying
% 174.24/26.69  | | | |              with (19), (39) gives:
% 174.24/26.69  | | | |   (42)  all_52_5 = e2
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | REDUCE: (11), (42) imply:
% 174.24/26.69  | | | |   (43)   ~ (all_52_3 = e2)
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | REDUCE: (24), (41) imply:
% 174.24/26.69  | | | |   (44)   ~ (all_10_2 = e1)
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | SIMP: (44) implies:
% 174.24/26.69  | | | |   (45)   ~ (all_10_2 = e1)
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | BETA: splitting (10) gives:
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | Case 1:
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | |   (46)  all_56_1 = e2
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | | COMBINE_EQS: (13), (46) imply:
% 174.24/26.69  | | | | |   (47)  all_52_3 = e2
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | | REDUCE: (43), (47) imply:
% 174.24/26.69  | | | | |   (48)  $false
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | | CLOSE: (48) is inconsistent.
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | Case 2:
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | |   (49)  all_56_1 = e1 | all_56_1 = e0
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | | BETA: splitting (31) gives:
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | | Case 1:
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | |   (50)  all_58_1 = e0
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | | COMBINE_EQS: (8), (50) imply:
% 174.24/26.69  | | | | | |   (51)  all_52_3 = e0
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | | REDUCE: (5), (51) imply:
% 174.24/26.69  | | | | | |   (52)   ~ (all_10_2 = e0)
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | | SIMP: (52) implies:
% 174.24/26.69  | | | | | |   (53)   ~ (all_10_2 = e0)
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | | REF_CLOSE: (2), (16), (21), (25), (34), (35), (45), (53) are
% 174.24/26.69  | | | | | |            inconsistent by sub-proof #152.
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | Case 2:
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | |   (54)   ~ (all_58_1 = e0)
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | | REDUCE: (8), (54) imply:
% 174.24/26.69  | | | | | |   (55)   ~ (all_52_3 = e0)
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | | REF_CLOSE: (13), (38), (49), (55) are inconsistent by sub-proof
% 174.24/26.69  | | | | | |            #843.
% 174.24/26.69  | | | | | | 
% 174.24/26.69  | | | | | End of split
% 174.24/26.69  | | | | | 
% 174.24/26.69  | | | | End of split
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | Case 2:
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | |   (56)   ~ (all_58_0 = e1)
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | REDUCE: (9), (56) imply:
% 174.24/26.69  | | | |   (57)   ~ (all_4_2 = e1)
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | | REF_CLOSE: (3), (6), (9), (14), (17), (18), (21), (22), (23), (57) are
% 174.24/26.69  | | | |            inconsistent by sub-proof #114.
% 174.24/26.69  | | | | 
% 174.24/26.69  | | | End of split
% 174.24/26.69  | | | 
% 174.24/26.69  | | End of split
% 174.24/26.69  | | 
% 174.24/26.69  | End of split
% 174.24/26.69  | 
% 174.24/26.69  End of proof
% 174.24/26.69  
% 174.24/26.69  Sub-proof #44 shows that the following formulas are inconsistent:
% 174.24/26.69  ----------------------------------------------------------------
% 174.24/26.69    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.69    (2)   ~ (all_52_5 = all_52_13)
% 174.24/26.69    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.69    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.69    (5)   ~ (all_52_27 = all_10_2)
% 174.24/26.69    (6)  op(e2, e2) = all_10_2
% 174.24/26.69    (7)   ~ (all_52_17 = all_52_23)
% 174.24/26.69    (8)  all_52_26 = e2
% 174.24/26.69    (9)   ~ (all_52_13 = all_52_29)
% 174.24/26.69    (10)  all_56_3 = all_52_7
% 174.24/26.69    (11)  op(e3, e2) = all_52_3
% 174.24/26.69    (12)   ~ (all_52_9 = all_52_25)
% 174.24/26.69    (13)  op(e3, all_52_25) = all_52_24
% 174.24/26.69    (14)   ~ (all_52_19 = all_52_23)
% 174.24/26.69    (15)  op(e1, e2) = all_52_19
% 174.24/26.69    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.69    (17)  op(e3, all_52_9) = all_52_8
% 174.24/26.69    (18)   ~ (all_52_3 = all_10_2)
% 174.24/26.69    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.69    (20)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.69    (21)  all_58_5 = all_52_13
% 174.24/26.69    (22)   ~ (all_52_25 = all_52_29)
% 174.24/26.69    (23)  all_56_15 = all_6_2
% 174.24/26.69    (24)  op(e2, e0) = all_52_15
% 174.24/26.69    (25)  all_6_1 = e0
% 174.24/26.69    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.69    (27)  all_58_3 = all_10_2
% 174.24/26.69    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.69    (29)  all_58_15 = all_6_2
% 174.24/26.69    (30)   ~ (all_52_9 = all_4_2)
% 174.24/26.69    (31)   ~ (all_52_5 = all_52_7)
% 174.24/26.69    (32)  all_58_10 = all_52_15
% 174.24/26.69    (33)   ~ (all_52_5 = all_4_2)
% 174.24/26.69    (34)  all_58_7 = all_52_19
% 174.24/26.69    (35)   ~ (all_52_15 = all_6_2)
% 174.24/26.69    (36)   ~ (all_52_17 = all_52_25)
% 174.24/26.69    (37)  op(e0, e1) = all_52_29
% 174.24/26.69    (38)  all_58_4 = all_52_5
% 174.24/26.69    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.69    (40)   ~ (e3 = e1)
% 174.24/26.69    (41)   ~ (all_52_27 = all_52_29)
% 174.24/26.69    (42)   ~ (all_52_17 = all_14_2)
% 174.24/26.69    (43)  op(e3, all_4_2) = all_4_1
% 174.24/26.69    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.69    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.69    (46)   ~ (all_52_7 = all_4_2)
% 174.24/26.69    (47)  all_58_1 = all_52_3
% 174.24/26.69    (48)   ~ (all_52_13 = all_52_15)
% 174.24/26.69    (49)  all_58_0 = all_4_2
% 174.24/26.69    (50)  op(e1, all_52_29) = all_52_28
% 174.24/26.69    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.69    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.24/26.69    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.24/26.69    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.69    (55)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.69    (56)  all_58_14 = all_52_29
% 174.24/26.69    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.69    (58)  op(e2, all_4_2) = all_4_0
% 174.24/26.69    (59)   ~ (all_52_3 = all_52_5)
% 174.24/26.69    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.69    (61)  op(e2, e1) = all_52_13
% 174.24/26.69    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.69    (63)  all_58_8 = all_14_2
% 174.24/26.69    (64)  all_56_1 = all_52_3
% 174.24/26.69    (65)  op(e0, e2) = all_52_27
% 174.24/26.69    (66)  all_56_14 = all_52_29
% 174.24/26.69    (67)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 174.24/26.69    (68)  op(all_4_1, all_4_2) = all_4_0
% 174.24/26.69    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.69    (70)   ~ (all_52_3 = all_52_27)
% 174.24/26.69    (71)   ~ (all_52_3 = all_4_2)
% 174.24/26.69    (72)  op(e0, e3) = all_52_25
% 174.24/26.69    (73)  op(e0, all_6_2) = all_6_1
% 174.24/26.69    (74)   ~ (all_52_9 = all_10_2)
% 174.24/26.69    (75)  op(e3, all_52_17) = all_52_16
% 174.24/26.69    (76)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.69    (77)   ~ (e3 = e0)
% 174.24/26.69    (78)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.69    (79)   ~ (all_52_9 = all_52_13)
% 174.24/26.69    (80)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.69    (81)   ~ (all_52_15 = all_52_23)
% 174.24/26.69    (82)   ~ (all_52_5 = all_52_29)
% 174.24/26.69    (83)  all_56_2 = all_52_5
% 174.24/26.69    (84)  op(e1, e0) = all_52_23
% 174.24/26.69    (85)  all_56_12 = all_52_25
% 174.24/26.69    (86)  all_58_13 = all_52_27
% 174.24/26.69    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.69    (88)  all_56_5 = all_10_2
% 174.24/26.69    (89)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.69    (90)   ~ (all_52_9 = all_52_17)
% 174.24/26.69    (91)  all_58_6 = all_52_17
% 174.24/26.69    (92)   ~ (all_52_3 = all_52_7)
% 174.24/26.69    (93)   ~ (e1 = e0)
% 174.24/26.69    (94)  all_56_0 = all_4_2
% 174.24/26.69    (95)  all_58_11 = all_52_23
% 174.24/26.69    (96)   ~ (all_52_3 = all_52_19)
% 174.24/26.69    (97)   ~ (all_52_7 = all_52_15)
% 174.24/26.69    (98)   ~ (all_52_29 = all_14_2)
% 174.24/26.69    (99)   ~ (all_4_0 = e1)
% 174.24/26.69    (100)   ~ (all_52_19 = all_10_2)
% 174.24/26.69    (101)  op(e3, all_4_2) = e2
% 174.24/26.69    (102)   ~ (all_52_23 = all_6_2)
% 174.24/26.69    (103)   ~ (all_52_29 = all_6_2)
% 174.24/26.69    (104)  all_58_2 = all_52_9
% 174.24/26.69    (105)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.24/26.69    (106)  op(e3, e1) = all_52_5
% 174.24/26.69    (107)   ~ (e2 = e1)
% 174.24/26.69    (108)   ~ (all_52_25 = all_6_2)
% 174.24/26.69    (109)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.69    (110)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.24/26.69    (111)  op(e1, e3) = all_52_17
% 174.24/26.69    (112)   ~ (all_52_25 = all_4_2)
% 174.24/26.69    (113)  op(e3, e0) = all_52_7
% 174.24/26.69    (114)  all_52_28 = e1
% 174.24/26.69    (115)  op(e3, e3) = all_4_2
% 174.24/26.69    (116)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.24/26.69             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.24/26.69    (117)   ~ (all_52_17 = all_4_2)
% 174.24/26.69    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.69             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.69    (119)   ~ (all_52_25 = all_52_27)
% 174.24/26.69    (120)   ~ (all_52_27 = all_6_2)
% 174.24/26.69    (121)   ~ (all_52_7 = all_6_2)
% 174.24/26.69    (122)   ~ (all_52_15 = all_10_2)
% 174.24/26.69    (123)   ~ (all_52_7 = all_52_23)
% 174.24/26.69    (124)   ~ (all_52_13 = all_10_2)
% 174.24/26.69    (125)  op(e2, all_52_27) = all_52_26
% 174.24/26.69    (126)   ~ (all_52_17 = all_52_19)
% 174.24/26.69    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.69    (128)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.69    (129)  op(e2, all_10_2) = e3
% 174.24/26.69    (130)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 174.24/26.69    (131)  all_58_9 = all_52_7
% 174.24/26.69    (132)   ~ (e2 = e0)
% 174.24/26.69    (133)  all_52_24 = e3
% 174.24/26.69    (134)  all_58_12 = all_52_25
% 174.24/26.69    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.69    (136)   ~ (all_52_9 = all_52_15)
% 174.24/26.69    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.69    (138)   ~ (e3 = e2)
% 174.24/26.69    (139)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.69    (140)  op(e2, e3) = all_52_9
% 174.24/26.69    (141)  all_56_13 = all_52_27
% 174.24/26.69  
% 174.24/26.69  Begin of proof
% 174.24/26.69  | 
% 174.24/26.69  | REDUCE: (13), (133) imply:
% 174.24/26.69  |   (142)  op(e3, all_52_25) = e3
% 174.24/26.69  | 
% 174.24/26.69  | REDUCE: (8), (125) imply:
% 174.24/26.69  |   (143)  op(e2, all_52_27) = e2
% 174.24/26.69  | 
% 174.24/26.69  | REDUCE: (50), (114) imply:
% 174.24/26.69  |   (144)  op(e1, all_52_29) = e1
% 174.24/26.69  | 
% 174.24/26.69  | REDUCE: (25), (73) imply:
% 174.24/26.69  |   (145)  op(e0, all_6_2) = e0
% 174.24/26.69  | 
% 174.24/26.69  | BETA: splitting (116) gives:
% 174.24/26.69  | 
% 174.24/26.69  | Case 1:
% 174.24/26.69  | | 
% 174.24/26.69  | |   (146)  all_58_15 = e0
% 174.24/26.69  | | 
% 174.24/26.69  | | COMBINE_EQS: (29), (146) imply:
% 174.24/26.69  | |   (147)  all_6_2 = e0
% 174.24/26.69  | | 
% 174.24/26.69  | | REDUCE: (121), (147) imply:
% 174.24/26.69  | |   (148)   ~ (all_52_7 = e0)
% 174.24/26.69  | | 
% 174.24/26.69  | | REDUCE: (35), (147) imply:
% 174.24/26.69  | |   (149)   ~ (all_52_15 = e0)
% 174.24/26.69  | | 
% 174.24/26.69  | | REDUCE: (102), (147) imply:
% 174.24/26.69  | |   (150)   ~ (all_52_23 = e0)
% 174.24/26.69  | | 
% 174.24/26.69  | | REDUCE: (108), (147) imply:
% 174.24/26.69  | |   (151)   ~ (all_52_25 = e0)
% 174.24/26.69  | | 
% 174.24/26.69  | | REDUCE: (103), (147) imply:
% 174.24/26.69  | |   (152)   ~ (all_52_29 = e0)
% 174.24/26.69  | | 
% 174.24/26.69  | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (12), (14), (15), (16),
% 174.24/26.69  | |            (17), (18), (19), (20), (21), (22), (24), (26), (27), (28), (30),
% 174.24/26.69  | |            (32), (33), (34), (36), (38), (39), (40), (45), (46), (47), (48),
% 174.24/26.69  | |            (49), (55), (56), (57), (58), (61), (62), (63), (67), (69), (70),
% 174.24/26.69  | |            (71), (74), (77), (78), (80), (81), (82), (85), (86), (88), (89),
% 174.24/26.69  | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (100),
% 174.24/26.69  | |            (101), (104), (105), (106), (109), (110), (111), (112), (113),
% 174.24/26.69  | |            (115), (118), (119), (124), (128), (129), (130), (131), (132),
% 174.24/26.69  | |            (134), (136), (138), (140), (141), (142), (143), (144), (146),
% 174.24/26.69  | |            (148), (149), (150), (151), (152) are inconsistent by sub-proof
% 174.24/26.69  | |            #46.
% 174.24/26.69  | | 
% 174.24/26.69  | Case 2:
% 174.24/26.69  | | 
% 174.24/26.69  | |   (153)   ~ (all_58_15 = e0)
% 174.24/26.69  | |   (154)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 174.24/26.69  | |            | all_58_13 = e0 | all_58_14 = e0)
% 174.24/26.69  | | 
% 174.24/26.69  | | REF_CLOSE: (3), (4), (7), (11), (12), (14), (16), (17), (18), (19), (21),
% 174.24/26.69  | |            (22), (23), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.24/26.69  | |            (36), (37), (38), (40), (41), (42), (43), (44), (46), (47), (48),
% 174.24/26.69  | |            (49), (51), (52), (53), (54), (56), (57), (58), (59), (60), (61),
% 174.24/26.69  | |            (62), (63), (64), (65), (66), (68), (69), (70), (71), (72), (74),
% 174.24/26.69  | |            (75), (76), (77), (78), (79), (80), (82), (83), (84), (85), (86),
% 174.24/26.69  | |            (87), (90), (91), (92), (93), (94), (95), (97), (99), (100),
% 174.24/26.69  | |            (101), (103), (104), (106), (107), (108), (110), (111), (112),
% 174.24/26.69  | |            (113), (115), (117), (118), (119), (120), (121), (122), (123),
% 174.24/26.69  | |            (126), (127), (131), (132), (134), (135), (136), (137), (138),
% 174.24/26.69  | |            (139), (140), (141), (142), (143), (144), (145), (153), (154) are
% 174.24/26.69  | |            inconsistent by sub-proof #45.
% 174.24/26.69  | | 
% 174.24/26.69  | End of split
% 174.24/26.69  | 
% 174.24/26.69  End of proof
% 174.24/26.69  
% 174.24/26.69  Sub-proof #45 shows that the following formulas are inconsistent:
% 174.24/26.69  ----------------------------------------------------------------
% 174.24/26.69    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.69    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.69    (3)   ~ (all_52_17 = all_52_23)
% 174.24/26.69    (4)  op(e3, e2) = all_52_3
% 174.24/26.69    (5)   ~ (all_52_9 = all_52_25)
% 174.24/26.69    (6)   ~ (all_52_19 = all_52_23)
% 174.24/26.69    (7)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.69    (8)  op(e3, all_52_9) = all_52_8
% 174.24/26.69    (9)   ~ (all_52_3 = all_10_2)
% 174.24/26.69    (10)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.69    (11)  all_58_5 = all_52_13
% 174.24/26.69    (12)   ~ (all_52_25 = all_52_29)
% 174.24/26.69    (13)  all_56_15 = all_6_2
% 174.24/26.69    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.69    (15)  all_58_3 = all_10_2
% 174.24/26.69    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.69    (17)  all_58_15 = all_6_2
% 174.24/26.69    (18)  op(e0, all_6_2) = e0
% 174.24/26.69    (19)   ~ (all_52_9 = all_4_2)
% 174.24/26.69    (20)   ~ (all_52_5 = all_52_7)
% 174.24/26.69    (21)  all_58_10 = all_52_15
% 174.24/26.69    (22)   ~ (all_52_5 = all_4_2)
% 174.24/26.69    (23)  all_58_7 = all_52_19
% 174.24/26.69    (24)   ~ (all_52_17 = all_52_25)
% 174.24/26.69    (25)  op(e0, e1) = all_52_29
% 174.24/26.69    (26)  all_58_4 = all_52_5
% 174.24/26.69    (27)   ~ (e3 = e1)
% 174.24/26.69    (28)   ~ (all_52_27 = all_52_29)
% 174.24/26.69    (29)   ~ (all_52_17 = all_14_2)
% 174.24/26.69    (30)  op(e3, all_4_2) = all_4_1
% 174.24/26.69    (31)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.69    (32)   ~ (all_52_7 = all_4_2)
% 174.24/26.69    (33)  all_58_1 = all_52_3
% 174.24/26.69    (34)   ~ (all_52_13 = all_52_15)
% 174.24/26.69    (35)  all_58_0 = all_4_2
% 174.24/26.69    (36)  op(e2, all_52_27) = e2
% 174.24/26.69    (37)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.69    (38)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.24/26.69    (39)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.24/26.69    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.69    (41)  all_58_14 = all_52_29
% 174.24/26.69    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.69    (43)  op(e2, all_4_2) = all_4_0
% 174.24/26.69    (44)   ~ (all_52_3 = all_52_5)
% 174.24/26.69    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.69    (46)  op(e2, e1) = all_52_13
% 174.24/26.69    (47)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.69    (48)  all_58_8 = all_14_2
% 174.24/26.69    (49)  all_56_1 = all_52_3
% 174.24/26.69    (50)  op(e0, e2) = all_52_27
% 174.24/26.69    (51)  all_56_14 = all_52_29
% 174.24/26.69    (52)  op(e1, all_52_29) = e1
% 174.24/26.69    (53)  op(all_4_1, all_4_2) = all_4_0
% 174.24/26.69    (54)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.69    (55)   ~ (all_52_3 = all_52_27)
% 174.24/26.69    (56)   ~ (all_52_3 = all_4_2)
% 174.24/26.69    (57)  op(e0, e3) = all_52_25
% 174.24/26.69    (58)   ~ (all_52_9 = all_10_2)
% 174.24/26.69    (59)  op(e3, all_52_17) = all_52_16
% 174.24/26.69    (60)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.69    (61)   ~ (e3 = e0)
% 174.24/26.69    (62)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.69    (63)   ~ (all_52_9 = all_52_13)
% 174.24/26.69    (64)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.69    (65)   ~ (all_52_5 = all_52_29)
% 174.24/26.69    (66)  all_56_2 = all_52_5
% 174.24/26.69    (67)  op(e1, e0) = all_52_23
% 174.24/26.69    (68)  all_56_12 = all_52_25
% 174.24/26.69    (69)  all_58_13 = all_52_27
% 174.24/26.69    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.69    (71)   ~ (all_52_9 = all_52_17)
% 174.24/26.69    (72)  all_58_6 = all_52_17
% 174.24/26.69    (73)   ~ (all_52_3 = all_52_7)
% 174.24/26.69    (74)   ~ (e1 = e0)
% 174.24/26.69    (75)  all_56_0 = all_4_2
% 174.24/26.69    (76)  all_58_11 = all_52_23
% 174.24/26.69    (77)   ~ (all_52_7 = all_52_15)
% 174.24/26.69    (78)  op(e3, all_52_25) = e3
% 174.24/26.69    (79)   ~ (all_4_0 = e1)
% 174.24/26.69    (80)   ~ (all_52_19 = all_10_2)
% 174.24/26.69    (81)   ~ (all_58_15 = e0)
% 174.24/26.69    (82)  op(e3, all_4_2) = e2
% 174.24/26.69    (83)   ~ (all_52_29 = all_6_2)
% 174.24/26.69    (84)  all_58_2 = all_52_9
% 174.24/26.69    (85)  op(e3, e1) = all_52_5
% 174.24/26.69    (86)   ~ (e2 = e1)
% 174.24/26.69    (87)   ~ (all_52_25 = all_6_2)
% 174.24/26.69    (88)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.24/26.69    (89)  op(e1, e3) = all_52_17
% 174.24/26.69    (90)   ~ (all_52_25 = all_4_2)
% 174.24/26.69    (91)  op(e3, e0) = all_52_7
% 174.24/26.69    (92)  op(e3, e3) = all_4_2
% 174.24/26.69    (93)   ~ (all_52_17 = all_4_2)
% 174.24/26.69    (94)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.69    (95)   ~ (all_52_25 = all_52_27)
% 174.24/26.69    (96)   ~ (all_52_27 = all_6_2)
% 174.24/26.69    (97)   ~ (all_52_7 = all_6_2)
% 174.24/26.69    (98)   ~ (all_52_15 = all_10_2)
% 174.24/26.69    (99)   ~ (all_52_7 = all_52_23)
% 174.24/26.69    (100)   ~ (all_52_17 = all_52_19)
% 174.24/26.69    (101)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.69    (102)  all_58_9 = all_52_7
% 174.24/26.69    (103)   ~ (e2 = e0)
% 174.24/26.69    (104)  all_58_12 = all_52_25
% 174.24/26.69    (105)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.24/26.69             all_58_13 = e0 | all_58_14 = e0)
% 174.24/26.69    (106)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.69    (107)   ~ (all_52_9 = all_52_15)
% 174.24/26.69    (108)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.69    (109)   ~ (e3 = e2)
% 174.24/26.69    (110)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.70    (111)  op(e2, e3) = all_52_9
% 174.24/26.70    (112)  all_56_13 = all_52_27
% 174.24/26.70  
% 174.24/26.70  Begin of proof
% 174.24/26.70  | 
% 174.24/26.70  | ALPHA: (105) implies:
% 174.24/26.70  |   (113)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.24/26.70  |   (114)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.24/26.70  | 
% 174.24/26.70  | REDUCE: (17), (81) imply:
% 174.24/26.70  |   (115)   ~ (all_6_2 = e0)
% 174.24/26.70  | 
% 174.24/26.70  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.24/26.70  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.24/26.70  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.24/26.70  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.24/26.70  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.24/26.70  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.24/26.70  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.24/26.70  |            (79), (80), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 174.24/26.70  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.24/26.70  |            (102), (103), (104), (106), (107), (108), (109), (110), (111),
% 174.24/26.70  |            (112), (113), (114), (115) are inconsistent by sub-proof #89.
% 174.24/26.70  | 
% 174.24/26.70  End of proof
% 174.24/26.70  
% 174.24/26.70  Sub-proof #46 shows that the following formulas are inconsistent:
% 174.24/26.70  ----------------------------------------------------------------
% 174.24/26.70    (1)   ~ (all_52_23 = all_14_2)
% 174.24/26.70    (2)   ~ (all_52_5 = all_52_13)
% 174.24/26.70    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.70    (4)   ~ (all_52_27 = all_10_2)
% 174.24/26.70    (5)  op(e2, e2) = all_10_2
% 174.24/26.70    (6)   ~ (all_52_13 = all_52_29)
% 174.24/26.70    (7)  all_56_3 = all_52_7
% 174.24/26.70    (8)  op(e3, e2) = all_52_3
% 174.24/26.70    (9)   ~ (all_52_9 = all_52_25)
% 174.24/26.70    (10)   ~ (all_52_19 = all_52_23)
% 174.24/26.70    (11)  op(e1, e2) = all_52_19
% 174.24/26.70    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.70    (13)  op(e3, all_52_9) = all_52_8
% 174.24/26.70    (14)   ~ (all_52_23 = e0)
% 174.24/26.70    (15)   ~ (all_52_3 = all_10_2)
% 174.24/26.70    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.70    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.70    (18)  all_58_5 = all_52_13
% 174.24/26.70    (19)   ~ (all_52_25 = all_52_29)
% 174.24/26.70    (20)  op(e2, e0) = all_52_15
% 174.24/26.70    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.24/26.70    (22)  all_58_3 = all_10_2
% 174.24/26.70    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.70    (24)   ~ (all_52_9 = all_4_2)
% 174.24/26.70    (25)  all_58_10 = all_52_15
% 174.24/26.70    (26)   ~ (all_52_5 = all_4_2)
% 174.24/26.70    (27)  all_58_7 = all_52_19
% 174.24/26.70    (28)   ~ (all_52_17 = all_52_25)
% 174.24/26.70    (29)  all_58_4 = all_52_5
% 174.24/26.70    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.70    (31)   ~ (e3 = e1)
% 174.24/26.70    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.70    (33)   ~ (all_52_7 = all_4_2)
% 174.24/26.70    (34)  all_58_1 = all_52_3
% 174.24/26.70    (35)   ~ (all_52_13 = all_52_15)
% 174.24/26.70    (36)  all_58_0 = all_4_2
% 174.24/26.70    (37)  op(e2, all_52_27) = e2
% 174.24/26.70    (38)   ~ (all_52_7 = e0)
% 174.24/26.70    (39)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.70    (40)  all_58_14 = all_52_29
% 174.24/26.70    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.70    (42)  op(e2, all_4_2) = all_4_0
% 174.24/26.70    (43)  op(e2, e1) = all_52_13
% 174.24/26.70    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.70    (45)  all_58_8 = all_14_2
% 174.24/26.70    (46)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 174.24/26.70    (47)  op(e1, all_52_29) = e1
% 174.24/26.70    (48)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.70    (49)   ~ (all_52_3 = all_52_27)
% 174.24/26.70    (50)   ~ (all_52_3 = all_4_2)
% 174.24/26.70    (51)   ~ (all_52_9 = all_10_2)
% 174.24/26.70    (52)   ~ (e3 = e0)
% 174.24/26.70    (53)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.70    (54)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.70    (55)   ~ (all_52_15 = all_52_23)
% 174.24/26.70    (56)   ~ (all_52_5 = all_52_29)
% 174.24/26.70    (57)  all_56_12 = all_52_25
% 174.24/26.70    (58)  all_58_13 = all_52_27
% 174.24/26.70    (59)  all_56_5 = all_10_2
% 174.24/26.70    (60)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.70    (61)   ~ (all_52_25 = e0)
% 174.24/26.70    (62)   ~ (all_52_9 = all_52_17)
% 174.24/26.70    (63)  all_58_6 = all_52_17
% 174.24/26.70    (64)   ~ (all_52_3 = all_52_7)
% 174.24/26.70    (65)   ~ (e1 = e0)
% 174.24/26.70    (66)  all_56_0 = all_4_2
% 174.24/26.70    (67)  all_58_11 = all_52_23
% 174.24/26.70    (68)   ~ (all_52_3 = all_52_19)
% 174.24/26.70    (69)   ~ (all_52_7 = all_52_15)
% 174.24/26.70    (70)   ~ (all_52_29 = all_14_2)
% 174.24/26.70    (71)  op(e3, all_52_25) = e3
% 174.24/26.70    (72)   ~ (all_52_19 = all_10_2)
% 174.24/26.70    (73)  all_58_15 = e0
% 174.24/26.70    (74)  op(e3, all_4_2) = e2
% 174.24/26.70    (75)  all_58_2 = all_52_9
% 174.24/26.70    (76)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.24/26.70    (77)   ~ (all_52_29 = e0)
% 174.24/26.70    (78)  op(e3, e1) = all_52_5
% 174.24/26.70    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.70    (80)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.24/26.70    (81)  op(e1, e3) = all_52_17
% 174.24/26.70    (82)   ~ (all_52_25 = all_4_2)
% 174.24/26.70    (83)  op(e3, e0) = all_52_7
% 174.24/26.70    (84)  op(e3, e3) = all_4_2
% 174.24/26.70    (85)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.70    (86)   ~ (all_52_25 = all_52_27)
% 174.24/26.70    (87)   ~ (all_52_15 = e0)
% 174.24/26.70    (88)   ~ (all_52_13 = all_10_2)
% 174.24/26.70    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.70    (90)  op(e2, all_10_2) = e3
% 174.24/26.70    (91)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 174.24/26.70    (92)  all_58_9 = all_52_7
% 174.24/26.70    (93)   ~ (e2 = e0)
% 174.24/26.70    (94)  all_58_12 = all_52_25
% 174.24/26.70    (95)   ~ (all_52_9 = all_52_15)
% 174.24/26.70    (96)   ~ (e3 = e2)
% 174.24/26.70    (97)  op(e2, e3) = all_52_9
% 174.24/26.70    (98)  all_56_13 = all_52_27
% 174.24/26.70  
% 174.24/26.70  Begin of proof
% 174.24/26.70  | 
% 174.24/26.70  | BETA: splitting (41) gives:
% 174.24/26.70  | 
% 174.24/26.70  | Case 1:
% 174.24/26.70  | | 
% 174.24/26.70  | |   (99)  all_56_13 = e3
% 174.24/26.70  | | 
% 174.24/26.70  | | COMBINE_EQS: (98), (99) imply:
% 174.24/26.70  | |   (100)  all_52_27 = e3
% 174.24/26.70  | | 
% 174.24/26.70  | | SIMP: (100) implies:
% 174.24/26.70  | |   (101)  all_52_27 = e3
% 174.24/26.70  | | 
% 174.24/26.70  | | COMBINE_EQS: (58), (101) imply:
% 174.24/26.70  | |   (102)  all_58_13 = e3
% 174.24/26.70  | | 
% 174.24/26.70  | | REDUCE: (86), (101) imply:
% 174.24/26.70  | |   (103)   ~ (all_52_25 = e3)
% 174.24/26.70  | | 
% 174.24/26.70  | | REDUCE: (4), (101) imply:
% 174.24/26.70  | |   (104)   ~ (all_10_2 = e3)
% 174.24/26.70  | | 
% 174.24/26.70  | | SIMP: (104) implies:
% 174.24/26.70  | |   (105)   ~ (all_10_2 = e3)
% 174.24/26.70  | | 
% 174.24/26.70  | | REDUCE: (37), (101) imply:
% 174.24/26.70  | |   (106)  op(e2, e3) = e2
% 174.24/26.70  | | 
% 174.24/26.70  | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (11), (13), (14), (16), (18),
% 174.24/26.70  | |            (19), (21), (22), (23), (24), (25), (26), (27), (32), (33), (34),
% 174.24/26.70  | |            (36), (40), (45), (47), (51), (54), (55), (56), (57), (59), (60),
% 174.24/26.70  | |            (61), (62), (63), (64), (66), (67), (69), (70), (71), (72), (73),
% 174.24/26.70  | |            (74), (75), (78), (79), (80), (82), (83), (85), (89), (92), (93),
% 174.24/26.70  | |            (94), (96), (97), (102), (103), (105), (106) are inconsistent by
% 174.24/26.70  | |            sub-proof #116.
% 174.24/26.70  | | 
% 174.24/26.70  | Case 2:
% 174.24/26.70  | | 
% 174.24/26.70  | |   (107)   ~ (all_56_13 = e3)
% 174.24/26.70  | | 
% 174.24/26.70  | | REDUCE: (98), (107) imply:
% 174.24/26.70  | |   (108)   ~ (all_52_27 = e3)
% 174.24/26.70  | | 
% 174.24/26.70  | | BETA: splitting (44) gives:
% 174.24/26.70  | | 
% 174.24/26.70  | | Case 1:
% 174.24/26.70  | | | 
% 174.24/26.70  | | |   (109)  all_58_12 = e3
% 174.24/26.70  | | | 
% 174.24/26.70  | | | REF_CLOSE: (71), (82), (84), (85), (94), (109) are inconsistent by
% 174.24/26.70  | | |            sub-proof #884.
% 174.24/26.70  | | | 
% 174.24/26.70  | | Case 2:
% 174.24/26.70  | | | 
% 174.24/26.70  | | |   (110)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.70  | | | 
% 174.24/26.70  | | | BETA: splitting (110) gives:
% 174.24/26.70  | | | 
% 174.24/26.70  | | | Case 1:
% 174.24/26.70  | | | | 
% 174.24/26.70  | | | |   (111)  all_58_13 = e3
% 174.24/26.70  | | | | 
% 174.24/26.70  | | | | REF_CLOSE: (58), (108), (111) are inconsistent by sub-proof #1026.
% 174.24/26.70  | | | | 
% 174.24/26.70  | | | Case 2:
% 174.24/26.70  | | | | 
% 174.24/26.70  | | | |   (112)  all_58_14 = e3 | all_58_15 = e3
% 174.24/26.70  | | | | 
% 174.24/26.70  | | | | BETA: splitting (112) gives:
% 174.24/26.70  | | | | 
% 174.24/26.70  | | | | Case 1:
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | |   (113)  all_58_14 = e3
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | COMBINE_EQS: (40), (113) imply:
% 174.24/26.70  | | | | |   (114)  all_52_29 = e3
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | SIMP: (114) implies:
% 174.24/26.70  | | | | |   (115)  all_52_29 = e3
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | REDUCE: (6), (115) imply:
% 174.24/26.70  | | | | |   (116)   ~ (all_52_13 = e3)
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | REDUCE: (19), (115) imply:
% 174.24/26.70  | | | | |   (117)   ~ (all_52_25 = e3)
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | REDUCE: (70), (115) imply:
% 174.24/26.70  | | | | |   (118)   ~ (all_14_2 = e3)
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | SIMP: (118) implies:
% 174.24/26.70  | | | | |   (119)   ~ (all_14_2 = e3)
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | REDUCE: (47), (115) imply:
% 174.24/26.70  | | | | |   (120)  op(e1, e3) = e1
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | GROUND_INST: instantiating (85) with all_52_17, e1, e3, e1,
% 174.24/26.70  | | | | |              simplifying with (81), (120) gives:
% 174.24/26.70  | | | | |   (121)  all_52_17 = e1
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | COMBINE_EQS: (63), (121) imply:
% 174.24/26.70  | | | | |   (122)  all_58_6 = e1
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | REDUCE: (62), (121) imply:
% 174.24/26.70  | | | | |   (123)   ~ (all_52_9 = e1)
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | REDUCE: (28), (121) imply:
% 174.24/26.70  | | | | |   (124)   ~ (all_52_25 = e1)
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | SIMP: (124) implies:
% 174.24/26.70  | | | | |   (125)   ~ (all_52_25 = e1)
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | BETA: splitting (54) gives:
% 174.24/26.70  | | | | | 
% 174.24/26.70  | | | | | Case 1:
% 174.24/26.70  | | | | | | 
% 174.24/26.70  | | | | | |   (126)  all_56_12 = e3
% 174.24/26.70  | | | | | | 
% 174.24/26.70  | | | | | | REF_CLOSE: (57), (117), (126) are inconsistent by sub-proof #1040.
% 174.24/26.70  | | | | | | 
% 174.24/26.70  | | | | | Case 2:
% 174.24/26.70  | | | | | | 
% 174.24/26.70  | | | | | |   (127)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.70  | | | | | | 
% 174.24/26.70  | | | | | | BETA: splitting (76) gives:
% 174.24/26.70  | | | | | | 
% 174.24/26.70  | | | | | | Case 1:
% 174.24/26.70  | | | | | | | 
% 174.24/26.70  | | | | | | |   (128)  all_58_12 = e1
% 174.24/26.70  | | | | | | | 
% 174.24/26.70  | | | | | | | REF_CLOSE: (94), (125), (128) are inconsistent by sub-proof #883.
% 174.24/26.70  | | | | | | | 
% 174.24/26.70  | | | | | | Case 2:
% 174.24/26.70  | | | | | | | 
% 174.24/26.70  | | | | | | |   (129)   ~ (all_58_12 = e1)
% 174.24/26.70  | | | | | | |   (130)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.24/26.70  | | | | | | | 
% 174.24/26.70  | | | | | | | BETA: splitting (127) gives:
% 174.24/26.70  | | | | | | | 
% 174.24/26.70  | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | |   (131)  all_56_12 = e2
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | | COMBINE_EQS: (57), (131) imply:
% 174.24/26.70  | | | | | | | |   (132)  all_52_25 = e2
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | | SIMP: (132) implies:
% 174.24/26.70  | | | | | | | |   (133)  all_52_25 = e2
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | | REDUCE: (86), (133) imply:
% 174.24/26.70  | | | | | | | |   (134)   ~ (all_52_27 = e2)
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | | SIMP: (134) implies:
% 174.24/26.70  | | | | | | | |   (135)   ~ (all_52_27 = e2)
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | | REDUCE: (71), (133) imply:
% 174.24/26.70  | | | | | | | |   (136)  op(e3, e2) = e3
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | | BETA: splitting (130) gives:
% 174.24/26.70  | | | | | | | | 
% 174.24/26.70  | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | |   (137)  all_58_13 = e1
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | COMBINE_EQS: (58), (137) imply:
% 174.24/26.70  | | | | | | | | |   (138)  all_52_27 = e1
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | SIMP: (138) implies:
% 174.24/26.70  | | | | | | | | |   (139)  all_52_27 = e1
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (49), (139) imply:
% 174.24/26.70  | | | | | | | | |   (140)   ~ (all_52_3 = e1)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (4), (139) imply:
% 174.24/26.70  | | | | | | | | |   (141)   ~ (all_10_2 = e1)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | SIMP: (141) implies:
% 174.24/26.70  | | | | | | | | |   (142)   ~ (all_10_2 = e1)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (135), (139) imply:
% 174.24/26.70  | | | | | | | | |   (143)   ~ (e2 = e1)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | SIMP: (143) implies:
% 174.24/26.70  | | | | | | | | |   (144)   ~ (e2 = e1)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (37), (139) imply:
% 174.24/26.70  | | | | | | | | |   (145)  op(e2, e1) = e2
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | GROUND_INST: instantiating (85) with all_52_13, e2, e1, e2,
% 174.24/26.70  | | | | | | | | |              simplifying with (43), (145) gives:
% 174.24/26.70  | | | | | | | | |   (146)  all_52_13 = e2
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | GROUND_INST: instantiating (85) with all_52_3, e3, e2, e3,
% 174.24/26.70  | | | | | | | | |              simplifying with (8), (136) gives:
% 174.24/26.70  | | | | | | | | |   (147)  all_52_3 = e3
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | COMBINE_EQS: (18), (146) imply:
% 174.24/26.70  | | | | | | | | |   (148)  all_58_5 = e2
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | COMBINE_EQS: (34), (147) imply:
% 174.24/26.70  | | | | | | | | |   (149)  all_58_1 = e3
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (68), (147) imply:
% 174.24/26.70  | | | | | | | | |   (150)   ~ (all_52_19 = e3)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | SIMP: (150) implies:
% 174.24/26.70  | | | | | | | | |   (151)   ~ (all_52_19 = e3)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (15), (147) imply:
% 174.24/26.70  | | | | | | | | |   (152)   ~ (all_10_2 = e3)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | SIMP: (152) implies:
% 174.24/26.70  | | | | | | | | |   (153)   ~ (all_10_2 = e3)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (50), (147) imply:
% 174.24/26.70  | | | | | | | | |   (154)   ~ (all_4_2 = e3)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | SIMP: (154) implies:
% 174.24/26.70  | | | | | | | | |   (155)   ~ (all_4_2 = e3)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | REDUCE: (35), (146) imply:
% 174.24/26.70  | | | | | | | | |   (156)   ~ (all_52_15 = e2)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | SIMP: (156) implies:
% 174.24/26.70  | | | | | | | | |   (157)   ~ (all_52_15 = e2)
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | BETA: splitting (23) gives:
% 174.24/26.70  | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | |   (158)  all_56_0 = e3
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | COMBINE_EQS: (66), (158) imply:
% 174.24/26.70  | | | | | | | | | |   (159)  all_4_2 = e3
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | REDUCE: (155), (159) imply:
% 174.24/26.70  | | | | | | | | | |   (160)  $false
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | CLOSE: (160) is inconsistent.
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | |   (161)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | BETA: splitting (39) gives:
% 174.24/26.70  | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | |   (162)  all_58_2 = e1
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | COMBINE_EQS: (75), (162) imply:
% 174.24/26.70  | | | | | | | | | | |   (163)  all_52_9 = e1
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | SIMP: (163) implies:
% 174.24/26.70  | | | | | | | | | | |   (164)  all_52_9 = e1
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | REDUCE: (123), (164) imply:
% 174.24/26.70  | | | | | | | | | | |   (165)  $false
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | |   (166)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | BETA: splitting (166) gives:
% 174.24/26.70  | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | |   (167)  all_58_3 = e1
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | COMBINE_EQS: (22), (167) imply:
% 174.24/26.70  | | | | | | | | | | | |   (168)  all_10_2 = e1
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | REDUCE: (142), (168) imply:
% 174.24/26.70  | | | | | | | | | | | |   (169)  $false
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | |   (170)  all_58_5 = e1 | all_58_10 = e1
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | BETA: splitting (170) gives:
% 174.24/26.70  | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | |   (171)  all_58_5 = e1
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | REF_CLOSE: (144), (148), (171) are inconsistent by sub-proof
% 174.24/26.70  | | | | | | | | | | | | |            #672.
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | |   (172)  all_58_10 = e1
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | COMBINE_EQS: (25), (172) imply:
% 174.24/26.70  | | | | | | | | | | | | |   (173)  all_52_15 = e1
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | REDUCE: (20), (173) imply:
% 174.24/26.70  | | | | | | | | | | | | |   (174)  op(e2, e0) = e1
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | BETA: splitting (30) gives:
% 174.24/26.70  | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | |   (175)  all_58_6 = e3
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | COMBINE_EQS: (122), (175) imply:
% 174.24/26.70  | | | | | | | | | | | | | |   (176)  e3 = e1
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | REDUCE: (31), (176) imply:
% 174.24/26.70  | | | | | | | | | | | | | |   (177)  $false
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | |   (178)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 174.24/26.70  | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | |   (179)  all_56_5 = e3
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | COMBINE_EQS: (59), (179) imply:
% 174.24/26.70  | | | | | | | | | | | | | | |   (180)  all_10_2 = e3
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | REDUCE: (153), (180) imply:
% 174.24/26.70  | | | | | | | | | | | | | | |   (181)  $false
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | |   (182)   ~ (all_56_5 = e3)
% 174.24/26.70  | | | | | | | | | | | | | | |   (183)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | |   (184)  all_58_2 = e3
% 174.24/26.70  | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (184) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | |   (185)  all_52_9 = e3
% 174.24/26.70  | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 174.24/26.70  | | | | | | | | | | | | | | | |   (186)  all_52_9 = e3
% 174.24/26.70  | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | |   (187)  all_58_0 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (187) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | |   (188)  all_4_2 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | REDUCE: (155), (188) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | |   (189)   ~ (e3 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | REDUCE: (42), (188) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | |   (190)  op(e2, e0) = all_4_0
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (191)  all_58_2 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (184), (191) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (192)  e3 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | REDUCE: (52), (192) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (193)  $false
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | CLOSE: (193) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (194)   ~ (all_58_2 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (195)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (196)  all_58_1 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (196) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (197)  e3 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | REDUCE: (52), (197) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (198)  $false
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (199)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (200)  all_58_3 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (200) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (201)  all_10_2 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | REDUCE: (90), (201) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (202)  op(e2, e0) = e3
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with e3, all_4_0, e0, e2,
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |              simplifying with (190), (202) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (203)  all_4_0 = e3
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with e1, all_4_0, e0, e2,
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |              simplifying with (174), (190) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (204)  all_4_0 = e1
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (204) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (205)  e3 = e1
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (206)  e3 = e1
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (206) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (207)  $false
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (208)   ~ (all_58_3 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (208) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (209)   ~ (all_10_2 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |   (210)  all_58_3 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (22), (210) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |   (211)  all_10_2 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | REDUCE: (209), (211) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |   (212)  $false
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |   (213)  all_58_5 = e0 | all_58_10 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |   (214)  all_58_5 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (214) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |   (215)  all_52_13 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |   (216)  all_52_13 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (88), (216) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |   (217)   ~ (all_10_2 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (216) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |   (218)  op(e2, e1) = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22), (39), (51), (52), (59), (75), (85),
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |            (90), (91), (144), (153), (183), (209), (218) are
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #151.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |   (219)  all_58_10 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (87), (219) are inconsistent by sub-proof
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | |            #741.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | End of split
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | |   (220)   ~ (all_58_0 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | REDUCE: (36), (220) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | |   (221)   ~ (all_4_2 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (222)  all_58_0 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (222) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (223)  all_4_2 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | REDUCE: (221), (223) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (224)  $false
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | |   (225)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (226)  all_58_1 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (226) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (227)  e3 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | REDUCE: (52), (227) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (228)  $false
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | |   (229)  all_58_4 = e0 | all_58_9 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (230)  all_58_4 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (230) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (231)  all_52_5 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | SIMP: (231) implies:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (232)  all_52_5 = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | REDUCE: (26), (232) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (233)   ~ (all_4_2 = e0)
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (232) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | |   (234)  op(e3, e1) = e0
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |   (235)  all_58_0 = e2
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (74), (85), (136), (155), (235) are
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #92.
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |   (236)   ~ (all_58_0 = e2)
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (236) imply:
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | |   (237)   ~ (all_4_2 = e2)
% 174.24/26.70  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | |   (238)  all_56_0 = e2
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (237), (238) are inconsistent by sub-proof
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | |            #904.
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | |   (239)  all_56_0 = e1 | all_56_0 = e0
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_58_0 = e1
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (240) imply:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_4_2 = e1
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (241) imply:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |   (242)  op(e3, e1) = e2
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (85) with e0, e2, e1, e3,
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (234), (242) gives:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |   (243)  e2 = e0
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (243) imply:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |   (244)  $false
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |   (245)   ~ (all_58_0 = e1)
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (245) imply:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |   (246)   ~ (all_4_2 = e1)
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (221), (239), (246) are inconsistent by
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #892.
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | |   (247)  all_58_9 = e0
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (92), (247) are inconsistent by sub-proof
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | |            #825.
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | Case 2:
% 174.24/26.71  | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | |   (248)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.71  | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | | REF_CLOSE: (18), (22), (25), (27), (45), (55), (67), (116),
% 174.24/26.71  | | | | | | | | | | | | | | | |            (119), (151), (153), (178), (248) are inconsistent
% 174.24/26.71  | | | | | | | | | | | | | | | |            by sub-proof #966.
% 174.24/26.71  | | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | | 
% 174.24/26.71  | | | | | | | | Case 2:
% 174.24/26.71  | | | | | | | | | 
% 174.24/26.71  | | | | | | | | |   (249)  all_58_14 = e1 | all_58_15 = e1
% 174.24/26.71  | | | | | | | | | 
% 174.24/26.71  | | | | | | | | | REF_CLOSE: (31), (65), (73), (113), (249) are inconsistent by
% 174.24/26.71  | | | | | | | | |            sub-proof #880.
% 174.24/26.71  | | | | | | | | | 
% 174.24/26.71  | | | | | | | | End of split
% 174.24/26.71  | | | | | | | | 
% 174.24/26.71  | | | | | | | Case 2:
% 174.24/26.71  | | | | | | | | 
% 174.24/26.71  | | | | | | | |   (250)  all_56_12 = e1 | all_56_12 = e0
% 174.24/26.71  | | | | | | | | 
% 174.24/26.71  | | | | | | | | REF_CLOSE: (57), (61), (125), (250) are inconsistent by
% 174.24/26.71  | | | | | | | |            sub-proof #1029.
% 174.24/26.71  | | | | | | | | 
% 174.24/26.71  | | | | | | | End of split
% 174.24/26.71  | | | | | | | 
% 174.24/26.71  | | | | | | End of split
% 174.24/26.71  | | | | | | 
% 174.24/26.71  | | | | | End of split
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | Case 2:
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | |   (251)  all_58_15 = e3
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | | REF_CLOSE: (52), (73), (251) are inconsistent by sub-proof #1010.
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | End of split
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | End of split
% 174.24/26.71  | | | 
% 174.24/26.71  | | End of split
% 174.24/26.71  | | 
% 174.24/26.71  | End of split
% 174.24/26.71  | 
% 174.24/26.71  End of proof
% 174.24/26.71  
% 174.24/26.71  Sub-proof #47 shows that the following formulas are inconsistent:
% 174.24/26.71  ----------------------------------------------------------------
% 174.24/26.71    (1)   ~ (all_52_5 = all_52_13)
% 174.24/26.71    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.24/26.71    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.71    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.71    (5)   ~ (all_52_27 = all_10_2)
% 174.24/26.71    (6)  op(e2, e2) = all_10_2
% 174.24/26.71    (7)   ~ (all_52_17 = all_52_23)
% 174.24/26.71    (8)   ~ (all_52_13 = all_52_29)
% 174.24/26.71    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.24/26.71    (10)  all_56_3 = all_52_7
% 174.24/26.71    (11)  op(e3, e2) = all_52_3
% 174.24/26.71    (12)   ~ (all_52_9 = all_52_25)
% 174.24/26.71    (13)  op(e1, e2) = all_52_19
% 174.24/26.71    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.71    (15)  op(e3, all_52_9) = all_52_8
% 174.24/26.71    (16)   ~ (all_52_3 = all_10_2)
% 174.24/26.71    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.71    (18)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.71    (19)  all_58_5 = all_52_13
% 174.24/26.71    (20)   ~ (all_6_2 = e0)
% 174.24/26.71    (21)   ~ (all_52_25 = all_52_29)
% 174.24/26.71    (22)  all_56_15 = all_6_2
% 174.24/26.71    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.71    (24)  all_58_3 = all_10_2
% 174.24/26.71    (25)  all_56_9 = all_52_19
% 174.24/26.71    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.71    (27)  all_58_15 = all_6_2
% 174.24/26.71    (28)   ~ (all_52_9 = all_4_2)
% 174.24/26.71    (29)   ~ (all_52_5 = all_52_7)
% 174.24/26.71    (30)  all_58_10 = all_52_15
% 174.24/26.71    (31)   ~ (all_52_5 = all_4_2)
% 174.24/26.71    (32)  all_58_7 = all_52_19
% 174.24/26.71    (33)   ~ (all_52_15 = all_6_2)
% 174.24/26.71    (34)   ~ (all_52_17 = all_52_25)
% 174.24/26.71    (35)  all_58_4 = all_52_5
% 174.24/26.71    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.71    (37)   ~ (e3 = e1)
% 174.24/26.71    (38)  op(e3, all_4_2) = all_4_1
% 174.24/26.71    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.71    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.71    (41)   ~ (all_52_7 = all_4_2)
% 174.24/26.71    (42)  all_58_1 = all_52_3
% 174.24/26.71    (43)  all_58_0 = all_4_2
% 174.24/26.71    (44)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.24/26.71    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.24/26.71    (46)  op(e1, all_52_29) = all_52_28
% 174.24/26.71    (47)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.71    (48)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.24/26.71    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.71    (50)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.24/26.71    (51)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.71    (52)  all_58_14 = all_52_29
% 174.24/26.71    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.71    (54)  op(e2, all_4_2) = all_4_0
% 174.24/26.71    (55)   ~ (all_52_3 = all_52_5)
% 174.24/26.71    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.71    (57)  op(e2, e1) = all_52_13
% 174.24/26.71    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.71    (59)  all_58_8 = all_14_2
% 174.24/26.71    (60)  all_56_1 = all_52_3
% 174.24/26.71    (61)  op(e0, e2) = all_52_27
% 174.24/26.71    (62)  op(all_4_1, all_4_2) = all_4_0
% 174.24/26.71    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.71    (64)   ~ (all_52_5 = all_14_2)
% 174.24/26.71    (65)   ~ (all_52_3 = all_52_27)
% 174.24/26.71    (66)   ~ (all_52_3 = all_4_2)
% 174.24/26.71    (67)  op(e0, e3) = all_52_25
% 174.24/26.71    (68)  op(e0, all_6_2) = all_6_1
% 174.24/26.71    (69)   ~ (all_52_9 = all_10_2)
% 174.24/26.71    (70)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.71    (71)   ~ (all_52_13 = all_14_2)
% 174.24/26.71    (72)   ~ (e3 = e0)
% 174.24/26.71    (73)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.71    (74)   ~ (all_52_9 = all_52_13)
% 174.24/26.71    (75)  op(e3, all_10_2) = all_10_0
% 174.24/26.71    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.24/26.71    (77)   ~ (all_52_15 = all_52_23)
% 174.24/26.71    (78)   ~ (all_52_5 = all_52_29)
% 174.24/26.71    (79)  all_56_2 = all_52_5
% 174.24/26.71    (80)  all_56_12 = all_52_25
% 174.24/26.71    (81)  all_58_13 = all_52_27
% 174.24/26.71    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.71    (83)  all_56_5 = all_10_2
% 174.24/26.71    (84)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.71    (85)   ~ (all_52_9 = all_52_17)
% 174.24/26.71    (86)  all_58_6 = all_52_17
% 174.24/26.71    (87)   ~ (all_52_3 = all_52_7)
% 174.24/26.71    (88)  op(e2, all_52_19) = e2
% 174.24/26.71    (89)  op(e3, all_52_17) = e3
% 174.24/26.71    (90)   ~ (e1 = e0)
% 174.24/26.71    (91)  all_56_0 = all_4_2
% 174.24/26.71    (92)  all_58_11 = all_52_23
% 174.24/26.71    (93)   ~ (all_52_3 = all_52_19)
% 174.24/26.71    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 174.24/26.71    (95)   ~ (all_52_7 = all_52_15)
% 174.24/26.71    (96)   ~ (all_4_0 = e1)
% 174.24/26.71    (97)   ~ (all_52_19 = all_10_2)
% 174.24/26.71    (98)  op(e3, all_4_2) = e2
% 174.24/26.71    (99)   ~ (all_52_23 = all_6_2)
% 174.24/26.71    (100)   ~ (all_52_29 = all_6_2)
% 174.24/26.71    (101)  all_58_2 = all_52_9
% 174.24/26.71    (102)  op(e3, e1) = all_52_5
% 174.24/26.71    (103)   ~ (e2 = e1)
% 174.24/26.71    (104)   ~ (all_52_25 = all_6_2)
% 174.24/26.71    (105)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.71    (106)  op(e1, e3) = all_52_17
% 174.24/26.71    (107)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.71    (108)   ~ (all_52_25 = all_4_2)
% 174.24/26.71    (109)  op(e3, e0) = all_52_7
% 174.24/26.71    (110)  op(e3, e3) = all_4_2
% 174.24/26.71    (111)  all_56_8 = all_52_17
% 174.24/26.71    (112)   ~ (all_52_17 = all_4_2)
% 174.24/26.71    (113)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.71             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.71    (114)   ~ (all_52_25 = all_52_27)
% 174.24/26.71    (115)   ~ (all_52_27 = all_6_2)
% 174.24/26.71    (116)  op(e0, all_52_23) = e0
% 174.24/26.71    (117)   ~ (all_52_15 = all_10_2)
% 174.24/26.71    (118)   ~ (all_52_19 = all_52_27)
% 174.24/26.71    (119)  all_56_7 = all_52_15
% 174.24/26.71    (120)  op(e1, all_14_2) = e1
% 174.24/26.71    (121)   ~ (all_52_7 = all_52_23)
% 174.24/26.71    (122)  op(e2, all_52_27) = all_52_26
% 174.24/26.71    (123)   ~ (all_52_17 = all_52_19)
% 174.24/26.71    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.71    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.71    (126)  op(e2, all_10_2) = e3
% 174.24/26.71    (127)  all_58_9 = all_52_7
% 174.24/26.71    (128)   ~ (e2 = e0)
% 174.24/26.71    (129)  all_58_12 = all_52_25
% 174.24/26.71    (130)  all_56_6 = all_52_13
% 174.24/26.71    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.71    (132)   ~ (all_52_9 = all_52_15)
% 174.24/26.71    (133)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.71    (134)   ~ (e3 = e2)
% 174.24/26.71    (135)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.71    (136)  op(e2, e3) = all_52_9
% 174.24/26.71    (137)  all_56_13 = all_52_27
% 174.24/26.71  
% 174.24/26.71  Begin of proof
% 174.24/26.71  | 
% 174.24/26.71  | BETA: splitting (39) gives:
% 174.24/26.71  | 
% 174.24/26.71  | Case 1:
% 174.24/26.71  | | 
% 174.24/26.71  | |   (138)  all_56_15 = e3
% 174.24/26.71  | | 
% 174.24/26.71  | | REF_CLOSE: (1), (2), (7), (11), (12), (13), (15), (17), (19), (22), (24),
% 174.24/26.71  | |            (25), (27), (28), (30), (32), (33), (34), (35), (36), (38), (40),
% 174.24/26.71  | |            (41), (42), (43), (48), (50), (56), (59), (61), (62), (63), (64),
% 174.24/26.71  | |            (65), (67), (68), (69), (70), (71), (74), (76), (80), (81), (84),
% 174.24/26.71  | |            (85), (86), (87), (88), (89), (92), (93), (94), (96), (97), (99),
% 174.24/26.71  | |            (101), (102), (104), (106), (109), (110), (111), (112), (113),
% 174.24/26.71  | |            (114), (116), (118), (120), (121), (127), (128), (129), (130),
% 174.24/26.71  | |            (132), (134), (136), (138) are inconsistent by sub-proof #284.
% 174.24/26.71  | | 
% 174.24/26.71  | Case 2:
% 174.24/26.71  | | 
% 174.24/26.71  | |   (139)   ~ (all_56_15 = e3)
% 174.24/26.71  | |   (140)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.71  | | 
% 174.24/26.71  | | REDUCE: (22), (139) imply:
% 174.24/26.71  | |   (141)   ~ (all_6_2 = e3)
% 174.24/26.71  | | 
% 174.24/26.71  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.24/26.71  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.24/26.71  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 174.24/26.71  | |            (36), (37), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 174.24/26.71  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 174.24/26.71  | |            (60), (61), (63), (64), (65), (66), (67), (69), (70), (71), (72),
% 174.24/26.71  | |            (73), (74), (75), (77), (78), (79), (81), (82), (83), (84), (85),
% 174.24/26.71  | |            (86), (87), (88), (89), (90), (91), (92), (93), (95), (96), (97),
% 174.24/26.71  | |            (98), (100), (101), (102), (103), (104), (105), (106), (107),
% 174.24/26.71  | |            (108), (109), (110), (111), (112), (113), (114), (115), (116),
% 174.24/26.71  | |            (117), (118), (119), (120), (121), (122), (123), (124), (125),
% 174.24/26.71  | |            (126), (127), (128), (129), (130), (131), (132), (133), (134),
% 174.24/26.71  | |            (135), (136), (137), (140), (141) are inconsistent by sub-proof
% 174.24/26.71  | |            #48.
% 174.24/26.71  | | 
% 174.24/26.71  | End of split
% 174.24/26.71  | 
% 174.24/26.71  End of proof
% 174.24/26.71  
% 174.24/26.71  Sub-proof #48 shows that the following formulas are inconsistent:
% 174.24/26.71  ----------------------------------------------------------------
% 174.24/26.71    (1)   ~ (all_52_5 = all_52_13)
% 174.24/26.71    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.24/26.71    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.71    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.71    (5)   ~ (all_52_27 = all_10_2)
% 174.24/26.71    (6)  op(e2, e2) = all_10_2
% 174.24/26.71    (7)   ~ (all_52_17 = all_52_23)
% 174.24/26.71    (8)   ~ (all_52_13 = all_52_29)
% 174.24/26.71    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.24/26.71    (10)  all_56_3 = all_52_7
% 174.24/26.71    (11)  op(e3, e2) = all_52_3
% 174.24/26.71    (12)   ~ (all_52_9 = all_52_25)
% 174.24/26.71    (13)  op(e1, e2) = all_52_19
% 174.24/26.71    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.24/26.71    (15)   ~ (all_6_2 = e3)
% 174.24/26.71    (16)  op(e3, all_52_9) = all_52_8
% 174.24/26.71    (17)   ~ (all_52_3 = all_10_2)
% 174.24/26.71    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.71    (19)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.71    (20)  all_58_5 = all_52_13
% 174.24/26.71    (21)   ~ (all_6_2 = e0)
% 174.24/26.71    (22)   ~ (all_52_25 = all_52_29)
% 174.24/26.71    (23)  all_56_15 = all_6_2
% 174.24/26.71    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.24/26.71    (25)  all_58_3 = all_10_2
% 174.24/26.71    (26)  all_56_9 = all_52_19
% 174.24/26.71    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.24/26.71    (28)  all_58_15 = all_6_2
% 174.24/26.71    (29)   ~ (all_52_9 = all_4_2)
% 174.24/26.71    (30)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.24/26.71    (31)   ~ (all_52_5 = all_52_7)
% 174.24/26.71    (32)  all_58_10 = all_52_15
% 174.24/26.71    (33)   ~ (all_52_5 = all_4_2)
% 174.24/26.71    (34)  all_58_7 = all_52_19
% 174.24/26.71    (35)   ~ (all_52_17 = all_52_25)
% 174.24/26.71    (36)  all_58_4 = all_52_5
% 174.24/26.71    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.71    (38)   ~ (e3 = e1)
% 174.24/26.71    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.71    (40)   ~ (all_52_7 = all_4_2)
% 174.24/26.71    (41)  all_58_1 = all_52_3
% 174.24/26.71    (42)  all_58_0 = all_4_2
% 174.24/26.71    (43)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.24/26.71    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.24/26.71    (45)  op(e1, all_52_29) = all_52_28
% 174.24/26.71    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.71    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.24/26.71    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.24/26.71    (49)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.24/26.71    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.71    (51)  all_58_14 = all_52_29
% 174.24/26.71    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.24/26.71    (53)  op(e2, all_4_2) = all_4_0
% 174.24/26.71    (54)   ~ (all_52_3 = all_52_5)
% 174.24/26.71    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.24/26.71    (56)  op(e2, e1) = all_52_13
% 174.24/26.71    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.24/26.71    (58)  all_58_8 = all_14_2
% 174.24/26.71    (59)  all_56_1 = all_52_3
% 174.24/26.71    (60)  op(e0, e2) = all_52_27
% 174.24/26.71    (61)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.71    (62)   ~ (all_52_5 = all_14_2)
% 174.24/26.71    (63)   ~ (all_52_3 = all_52_27)
% 174.24/26.71    (64)   ~ (all_52_3 = all_4_2)
% 174.24/26.71    (65)  op(e0, e3) = all_52_25
% 174.24/26.71    (66)   ~ (all_52_9 = all_10_2)
% 174.24/26.71    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.71    (68)   ~ (all_52_13 = all_14_2)
% 174.24/26.71    (69)   ~ (e3 = e0)
% 174.24/26.71    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.24/26.71    (71)   ~ (all_52_9 = all_52_13)
% 174.24/26.71    (72)  op(e3, all_10_2) = all_10_0
% 174.24/26.71    (73)   ~ (all_52_15 = all_52_23)
% 174.24/26.71    (74)   ~ (all_52_5 = all_52_29)
% 174.24/26.71    (75)  all_56_2 = all_52_5
% 174.24/26.71    (76)  all_58_13 = all_52_27
% 174.24/26.71    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.24/26.71    (78)  all_56_5 = all_10_2
% 174.24/26.71    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.71    (80)   ~ (all_52_9 = all_52_17)
% 174.24/26.71    (81)  all_58_6 = all_52_17
% 174.24/26.71    (82)   ~ (all_52_3 = all_52_7)
% 174.24/26.71    (83)  op(e2, all_52_19) = e2
% 174.24/26.71    (84)  op(e3, all_52_17) = e3
% 174.24/26.71    (85)   ~ (e1 = e0)
% 174.24/26.71    (86)  all_56_0 = all_4_2
% 174.24/26.71    (87)  all_58_11 = all_52_23
% 174.24/26.71    (88)   ~ (all_52_3 = all_52_19)
% 174.24/26.71    (89)   ~ (all_52_7 = all_52_15)
% 174.24/26.71    (90)   ~ (all_4_0 = e1)
% 174.24/26.71    (91)   ~ (all_52_19 = all_10_2)
% 174.24/26.71    (92)  op(e3, all_4_2) = e2
% 174.24/26.71    (93)   ~ (all_52_29 = all_6_2)
% 174.24/26.71    (94)  all_58_2 = all_52_9
% 174.24/26.71    (95)  op(e3, e1) = all_52_5
% 174.24/26.71    (96)   ~ (e2 = e1)
% 174.24/26.71    (97)   ~ (all_52_25 = all_6_2)
% 174.24/26.71    (98)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.71    (99)  op(e1, e3) = all_52_17
% 174.24/26.71    (100)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.24/26.71    (101)   ~ (all_52_25 = all_4_2)
% 174.24/26.71    (102)  op(e3, e0) = all_52_7
% 174.24/26.71    (103)  op(e3, e3) = all_4_2
% 174.24/26.71    (104)  all_56_8 = all_52_17
% 174.24/26.71    (105)   ~ (all_52_17 = all_4_2)
% 174.24/26.71    (106)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.24/26.71             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.24/26.71    (107)   ~ (all_52_25 = all_52_27)
% 174.24/26.71    (108)   ~ (all_52_27 = all_6_2)
% 174.24/26.71    (109)  op(e0, all_52_23) = e0
% 174.24/26.71    (110)   ~ (all_52_15 = all_10_2)
% 174.24/26.71    (111)   ~ (all_52_19 = all_52_27)
% 174.24/26.71    (112)  all_56_7 = all_52_15
% 174.24/26.71    (113)  op(e1, all_14_2) = e1
% 174.24/26.71    (114)   ~ (all_52_7 = all_52_23)
% 174.24/26.71    (115)  op(e2, all_52_27) = all_52_26
% 174.24/26.71    (116)   ~ (all_52_17 = all_52_19)
% 174.24/26.71    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.24/26.71    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.24/26.71    (119)  op(e2, all_10_2) = e3
% 174.24/26.71    (120)  all_58_9 = all_52_7
% 174.24/26.71    (121)   ~ (e2 = e0)
% 174.24/26.71    (122)  all_58_12 = all_52_25
% 174.24/26.71    (123)  all_56_6 = all_52_13
% 174.24/26.71    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.24/26.71    (125)   ~ (all_52_9 = all_52_15)
% 174.24/26.71    (126)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.24/26.71    (127)   ~ (e3 = e2)
% 174.24/26.71    (128)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.71    (129)  op(e2, e3) = all_52_9
% 174.24/26.71    (130)  all_56_13 = all_52_27
% 174.24/26.71  
% 174.24/26.71  Begin of proof
% 174.24/26.71  | 
% 174.24/26.71  | BETA: splitting (52) gives:
% 174.24/26.71  | 
% 174.24/26.71  | Case 1:
% 174.24/26.71  | | 
% 174.24/26.71  | |   (131)  all_56_13 = e3
% 174.24/26.71  | | 
% 174.24/26.71  | | REF_CLOSE: (11), (24), (27), (28), (29), (32), (34), (37), (39), (42), (55),
% 174.24/26.71  | |            (58), (62), (63), (64), (65), (77), (81), (84), (86), (87), (92),
% 174.24/26.71  | |            (94), (95), (96), (99), (101), (103), (105), (106), (107), (108),
% 174.24/26.71  | |            (109), (111), (113), (114), (115), (117), (120), (121), (122),
% 174.24/26.71  | |            (124), (125), (127), (129), (130), (131) are inconsistent by
% 174.24/26.71  | |            sub-proof #96.
% 174.24/26.71  | | 
% 174.24/26.71  | Case 2:
% 174.24/26.71  | | 
% 174.24/26.71  | |   (132)   ~ (all_56_13 = e3)
% 174.24/26.71  | | 
% 174.24/26.71  | | REDUCE: (130), (132) imply:
% 174.24/26.71  | |   (133)   ~ (all_52_27 = e3)
% 174.24/26.71  | | 
% 174.24/26.71  | | BETA: splitting (57) gives:
% 174.24/26.71  | | 
% 174.24/26.71  | | Case 1:
% 174.24/26.71  | | | 
% 174.24/26.71  | | |   (134)  all_58_12 = e3
% 174.24/26.71  | | | 
% 174.24/26.71  | | | COMBINE_EQS: (122), (134) imply:
% 174.24/26.71  | | |   (135)  all_52_25 = e3
% 174.24/26.71  | | | 
% 174.24/26.71  | | | SIMP: (135) implies:
% 174.24/26.71  | | |   (136)  all_52_25 = e3
% 174.24/26.71  | | | 
% 174.24/26.71  | | | REDUCE: (12), (136) imply:
% 174.24/26.71  | | |   (137)   ~ (all_52_9 = e3)
% 174.24/26.71  | | | 
% 174.24/26.71  | | | REDUCE: (35), (136) imply:
% 174.24/26.71  | | |   (138)   ~ (all_52_17 = e3)
% 174.24/26.71  | | | 
% 174.24/26.71  | | | REDUCE: (107), (136) imply:
% 174.24/26.71  | | |   (139)   ~ (all_52_27 = e3)
% 174.24/26.71  | | | 
% 174.24/26.71  | | | REDUCE: (97), (136) imply:
% 174.24/26.71  | | |   (140)   ~ (all_6_2 = e3)
% 174.24/26.71  | | | 
% 174.24/26.71  | | | REDUCE: (101), (136) imply:
% 174.24/26.71  | | |   (141)   ~ (all_4_2 = e3)
% 174.24/26.71  | | | 
% 174.24/26.71  | | | SIMP: (141) implies:
% 174.24/26.71  | | |   (142)   ~ (all_4_2 = e3)
% 174.24/26.71  | | | 
% 174.24/26.71  | | | REDUCE: (65), (136) imply:
% 174.24/26.71  | | |   (143)  op(e0, e3) = e3
% 174.24/26.71  | | | 
% 174.24/26.71  | | | BETA: splitting (118) gives:
% 174.24/26.71  | | | 
% 174.24/26.71  | | | Case 1:
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | |   (144)  all_56_3 = e3
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | COMBINE_EQS: (10), (144) imply:
% 174.24/26.71  | | | |   (145)  all_52_7 = e3
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | SIMP: (145) implies:
% 174.24/26.71  | | | |   (146)  all_52_7 = e3
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | COMBINE_EQS: (120), (146) imply:
% 174.24/26.71  | | | |   (147)  all_58_9 = e3
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | REDUCE: (82), (146) imply:
% 174.24/26.71  | | | |   (148)   ~ (all_52_3 = e3)
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | REDUCE: (31), (146) imply:
% 174.24/26.71  | | | |   (149)   ~ (all_52_5 = e3)
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | REDUCE: (89), (146) imply:
% 174.24/26.71  | | | |   (150)   ~ (all_52_15 = e3)
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | SIMP: (150) implies:
% 174.24/26.71  | | | |   (151)   ~ (all_52_15 = e3)
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | REDUCE: (114), (146) imply:
% 174.24/26.71  | | | |   (152)   ~ (all_52_23 = e3)
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | SIMP: (152) implies:
% 174.24/26.71  | | | |   (153)   ~ (all_52_23 = e3)
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | BETA: splitting (37) gives:
% 174.24/26.71  | | | | 
% 174.24/26.71  | | | | Case 1:
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | |   (154)  all_58_6 = e3
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | | REF_CLOSE: (81), (138), (154) are inconsistent by sub-proof #981.
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | Case 2:
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | |   (155)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | | BETA: splitting (39) gives:
% 174.24/26.71  | | | | | 
% 174.24/26.71  | | | | | Case 1:
% 174.24/26.71  | | | | | | 
% 174.24/26.71  | | | | | |   (156)  all_58_2 = e3
% 174.24/26.71  | | | | | | 
% 174.24/26.71  | | | | | | REF_CLOSE: (94), (137), (156) are inconsistent by sub-proof #980.
% 174.24/26.71  | | | | | | 
% 174.24/26.71  | | | | | Case 2:
% 174.24/26.71  | | | | | | 
% 174.24/26.71  | | | | | |   (157)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.24/26.71  | | | | | | 
% 174.24/26.71  | | | | | | BETA: splitting (128) gives:
% 174.24/26.71  | | | | | | 
% 174.24/26.71  | | | | | | Case 1:
% 174.24/26.71  | | | | | | | 
% 174.24/26.71  | | | | | | |   (158)  all_56_2 = e3
% 174.24/26.71  | | | | | | | 
% 174.24/26.71  | | | | | | | REF_CLOSE: (75), (149), (158) are inconsistent by sub-proof #931.
% 174.24/26.71  | | | | | | | 
% 174.24/26.71  | | | | | | Case 2:
% 174.24/26.71  | | | | | | | 
% 174.24/26.71  | | | | | | |   (159)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.24/26.71  | | | | | | | 
% 174.24/26.71  | | | | | | | BETA: splitting (46) gives:
% 174.24/26.71  | | | | | | | 
% 174.24/26.71  | | | | | | | Case 1:
% 174.24/26.71  | | | | | | | | 
% 174.24/26.71  | | | | | | | |   (160)  all_56_1 = e3
% 174.24/26.71  | | | | | | | | 
% 174.24/26.72  | | | | | | | | REF_CLOSE: (59), (148), (160) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | |            #862.
% 174.24/26.72  | | | | | | | | 
% 174.24/26.72  | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | 
% 174.24/26.72  | | | | | | | |   (161)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.24/26.72  | | | | | | | | 
% 174.24/26.72  | | | | | | | | BETA: splitting (98) gives:
% 174.24/26.72  | | | | | | | | 
% 174.24/26.72  | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | |   (162)  all_56_5 = e3
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | COMBINE_EQS: (78), (162) imply:
% 174.24/26.72  | | | | | | | | |   (163)  all_10_2 = e3
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | SIMP: (163) implies:
% 174.24/26.72  | | | | | | | | |   (164)  all_10_2 = e3
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | REDUCE: (119), (164) imply:
% 174.24/26.72  | | | | | | | | |   (165)  op(e2, e3) = e3
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | REF_CLOSE: (26), (34), (47), (58), (62), (83), (84), (87),
% 174.24/26.72  | | | | | | | | |            (95), (99), (106), (113), (127), (153), (155),
% 174.24/26.72  | | | | | | | | |            (165) are inconsistent by sub-proof #949.
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | |   (166)   ~ (all_56_5 = e3)
% 174.24/26.72  | | | | | | | | |   (167)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | REDUCE: (78), (166) imply:
% 174.24/26.72  | | | | | | | | |   (168)   ~ (all_10_2 = e3)
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | BETA: splitting (157) gives:
% 174.24/26.72  | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | |   (169)  all_58_3 = e3
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | COMBINE_EQS: (25), (169) imply:
% 174.24/26.72  | | | | | | | | | |   (170)  all_10_2 = e3
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | REDUCE: (168), (170) imply:
% 174.24/26.72  | | | | | | | | | |   (171)  $false
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | CLOSE: (171) is inconsistent.
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | |   (172)  all_58_5 = e3 | all_58_10 = e3
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | BETA: splitting (172) gives:
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | |   (173)  all_58_5 = e3
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | COMBINE_EQS: (20), (173) imply:
% 174.24/26.72  | | | | | | | | | | |   (174)  all_52_13 = e3
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | SIMP: (174) implies:
% 174.24/26.72  | | | | | | | | | | |   (175)  all_52_13 = e3
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | REDUCE: (68), (175) imply:
% 174.24/26.72  | | | | | | | | | | |   (176)   ~ (all_14_2 = e3)
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | SIMP: (176) implies:
% 174.24/26.72  | | | | | | | | | | |   (177)   ~ (all_14_2 = e3)
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | BETA: splitting (155) gives:
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | |   (178)  all_58_7 = e3
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | COMBINE_EQS: (34), (178) imply:
% 174.24/26.72  | | | | | | | | | | | |   (179)  all_52_19 = e3
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (91), (179) imply:
% 174.24/26.72  | | | | | | | | | | | |   (180)   ~ (all_10_2 = e3)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (83), (179) imply:
% 174.24/26.72  | | | | | | | | | | | |   (181)  op(e2, e3) = e2
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | GROUND_INST: instantiating (106) with all_52_9, e2, e3, e2,
% 174.24/26.72  | | | | | | | | | | | |              simplifying with (129), (181) gives:
% 174.24/26.72  | | | | | | | | | | | |   (182)  all_52_9 = e2
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | COMBINE_EQS: (94), (182) imply:
% 174.24/26.72  | | | | | | | | | | | |   (183)  all_58_2 = e2
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (125), (182) imply:
% 174.24/26.72  | | | | | | | | | | | |   (184)   ~ (all_52_15 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | SIMP: (184) implies:
% 174.24/26.72  | | | | | | | | | | | |   (185)   ~ (all_52_15 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (80), (182) imply:
% 174.24/26.72  | | | | | | | | | | | |   (186)   ~ (all_52_17 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | SIMP: (186) implies:
% 174.24/26.72  | | | | | | | | | | | |   (187)   ~ (all_52_17 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (66), (182) imply:
% 174.24/26.72  | | | | | | | | | | | |   (188)   ~ (all_10_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | SIMP: (188) implies:
% 174.24/26.72  | | | | | | | | | | | |   (189)   ~ (all_10_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (29), (182) imply:
% 174.24/26.72  | | | | | | | | | | | |   (190)   ~ (all_4_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | SIMP: (190) implies:
% 174.24/26.72  | | | | | | | | | | | |   (191)   ~ (all_4_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (137), (182) imply:
% 174.24/26.72  | | | | | | | | | | | |   (192)   ~ (e3 = e2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (16), (182) imply:
% 174.24/26.72  | | | | | | | | | | | |   (193)  op(e3, e2) = all_52_8
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | GROUND_INST: instantiating (106) with all_52_3, all_52_8, e2,
% 174.24/26.72  | | | | | | | | | | | |              e3, simplifying with (11), (193) gives:
% 174.24/26.72  | | | | | | | | | | | |   (194)  all_52_3 = all_52_8
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | COMBINE_EQS: (59), (194) imply:
% 174.24/26.72  | | | | | | | | | | | |   (195)  all_56_1 = all_52_8
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | COMBINE_EQS: (41), (194) imply:
% 174.24/26.72  | | | | | | | | | | | |   (196)  all_58_1 = all_52_8
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (54), (194) imply:
% 174.24/26.72  | | | | | | | | | | | |   (197)   ~ (all_52_5 = all_52_8)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | SIMP: (197) implies:
% 174.24/26.72  | | | | | | | | | | | |   (198)   ~ (all_52_5 = all_52_8)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (63), (194) imply:
% 174.24/26.72  | | | | | | | | | | | |   (199)   ~ (all_52_8 = all_52_27)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (17), (194) imply:
% 174.24/26.72  | | | | | | | | | | | |   (200)   ~ (all_52_8 = all_10_2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (64), (194) imply:
% 174.24/26.72  | | | | | | | | | | | |   (201)   ~ (all_52_8 = all_4_2)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REDUCE: (148), (194) imply:
% 174.24/26.72  | | | | | | | | | | | |   (202)   ~ (all_52_8 = e3)
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | BETA: splitting (67) gives:
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | |   (203)  all_58_9 = e2
% 174.24/26.72  | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | REF_CLOSE: (127), (147), (203) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | |            #51.
% 174.24/26.72  | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | |   (204)   ~ (all_58_9 = e2)
% 174.24/26.72  | | | | | | | | | | | | |   (205)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.24/26.72  | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 174.24/26.72  | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | |   (206)  all_58_6 = e2
% 174.24/26.72  | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | REF_CLOSE: (81), (187), (206) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | |            #894.
% 174.24/26.72  | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | |   (207)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.24/26.72  | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 174.24/26.72  | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | |   (208)  all_58_1 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | COMBINE_EQS: (196), (208) imply:
% 174.24/26.72  | | | | | | | | | | | | | | |   (209)  all_52_8 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | REDUCE: (198), (209) imply:
% 174.24/26.72  | | | | | | | | | | | | | | |   (210)   ~ (all_52_5 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | REDUCE: (199), (209) imply:
% 174.24/26.72  | | | | | | | | | | | | | | |   (211)   ~ (all_52_27 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | SIMP: (211) implies:
% 174.24/26.72  | | | | | | | | | | | | | | |   (212)   ~ (all_52_27 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | |   (213)  all_58_0 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (213) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | |   (214)  all_4_2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | REDUCE: (191), (214) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | |   (215)   ~ (e2 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | REDUCE: (92), (214) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | |   (216)  op(e3, e1) = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (217)  all_58_0 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (217) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (218)  e1 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | REDUCE: (85), (218) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (219)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (220)   ~ (all_58_0 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (221)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (222)  all_58_1 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (222) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (223)  e2 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | REDUCE: (121), (223) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (224)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (225)  all_58_4 = e0 | all_58_9 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | |   (226)  all_56_2 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (210), (226) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | |            #827.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | |   (227)  all_56_2 = e1 | all_56_2 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (228)  all_56_2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (69), (75), (85), (147), (225), (228) are
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #926.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (229)  all_56_2 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (229) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (230)  all_52_5 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | SIMP: (230) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (231)  all_52_5 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (231) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (232)   ~ (all_52_29 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (233)   ~ (all_52_29 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (231) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (234)   ~ (e3 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (95), (231) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (235)  op(e3, e1) = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | |   (236)  all_58_12 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (134), (236) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | |            #682.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | |   (237)  all_58_13 = e0 | all_58_14 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (238)  all_58_13 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (238) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (239)  all_52_27 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | SIMP: (239) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (240)  all_52_27 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (240) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (241)   ~ (all_10_2 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | SIMP: (241) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (242)   ~ (all_10_2 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (212), (240) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (243)   ~ (e2 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_58_1 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (244) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (245)  e2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (245) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (246)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (248)  all_58_3 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (248) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_10_2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (249) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (250)  op(e3, e1) = all_10_0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (106) with e2, all_10_0, e1, e3,
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (216), (250) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_10_0 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (106) with e0, all_10_0, e1, e3,
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (235), (250) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_10_0 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (252) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (253)  e2 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (253) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (254)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (254) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (255)   ~ (all_58_3 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (255) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (256)   ~ (all_10_2 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (167), (189), (242), (256) are inconsistent
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #367.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (257)  all_58_14 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (233), (257) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |            #696.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | |   (258)   ~ (all_58_0 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | REDUCE: (42), (258) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | |   (259)   ~ (all_4_2 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | REF_CLOSE: (38), (42), (77), (81), (84), (95), (96), (106),
% 174.24/26.72  | | | | | | | | | | | | | | | |            (134), (149), (183), (259) are inconsistent by
% 174.24/26.72  | | | | | | | | | | | | | | | |            sub-proof #50.
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | |   (260)   ~ (all_58_1 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | |   (261)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | REDUCE: (196), (260) imply:
% 174.24/26.72  | | | | | | | | | | | | | | |   (262)   ~ (all_52_8 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | |   (263)  all_58_0 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (263) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | |   (264)  all_4_2 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | REDUCE: (191), (264) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | |   (265)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | |   (266)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (267)  all_58_1 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (267) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (268)  all_52_8 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | REDUCE: (262), (268) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (269)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | CLOSE: (269) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | |   (270)  all_58_4 = e2 | all_58_9 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (271)  all_58_4 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (271) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (272)  all_52_5 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | SIMP: (272) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (273)  all_52_5 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | REDUCE: (62), (273) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (274)   ~ (all_14_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | SIMP: (274) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (275)   ~ (all_14_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | |   (276)  all_58_3 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (276) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | |   (277)  all_10_2 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | REDUCE: (189), (277) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | |   (278)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | |   (279)  all_58_7 = e2 | all_58_13 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (280)  all_58_7 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (280) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (281)  e3 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (281) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (282)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | CLOSE: (282) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (283)  all_58_13 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (283) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (284)  all_52_27 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (285)  all_52_27 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (285) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (286)   ~ (all_6_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | SIMP: (286) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (287)   ~ (all_6_2 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (60), (285) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | |   (288)  op(e0, e2) = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | |   (289)  all_58_10 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (185), (289) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | |            #711.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | |   (290)  all_58_11 = e2 | all_58_15 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (291)  all_56_15 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (287), (291) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |            #817.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (292)   ~ (all_56_15 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | |   (293)  all_56_15 = e1 | all_56_15 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_56_15 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (294) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_6_2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (295) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_6_2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (296) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_58_15 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (287), (296) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (298)   ~ (e2 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_58_2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (299) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (300)  e2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (127), (178), (279), (283), (300) are
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #49.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_58_3 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (302) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_10_2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_58_2 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (121), (183), (304) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            #909.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_58_7 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (306) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  e3 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (307) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)   ~ (all_58_7 = e2)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_58_8 = e2 | all_58_11 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_58_11 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (311) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_52_23 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (312) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_52_23 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (313) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  op(e0, e2) = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_58_3 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (315) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  e1 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (316) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (317) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_58_5 = e0 | all_58_10 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_58_5 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (173), (319) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #810.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_58_10 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (320) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_52_15 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (321) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  all_52_15 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (185), (322) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)   ~ (e2 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (106) with e0, e2, e2, e0,
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (288), (314) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  e2 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (324) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_58_11 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (121), (275), (310), (325) are inconsistent
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #890.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_58_15 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (326) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  e2 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (127), (178), (279), (283), (327) are
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #49.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (328)   ~ (all_58_3 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (328) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (329)   ~ (all_10_2 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_58_1 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (330) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_52_8 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (331) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)   ~ (all_4_2 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (332) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)   ~ (all_4_2 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (202), (331) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)   ~ (e3 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (42), (77), (81), (84), (95), (96), (106),
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (149), (183), (333) are inconsistent by
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #50.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)   ~ (all_58_1 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (196), (335) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)   ~ (all_52_8 = e1)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_56_1 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (337) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  all_52_8 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  all_52_8 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (262), (339) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_56_1 = e1 | all_56_1 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  all_56_1 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (342) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_52_8 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (343) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  all_52_8 = e1
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (344) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  $false
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (345) is inconsistent.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)  all_56_1 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (346) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  all_52_8 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (347) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_52_8 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (348) imply:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)   ~ (all_10_2 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (349) implies:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)   ~ (all_10_2 = e0)
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (78), (106), (119), (167), (168), (329),
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (350) are inconsistent by sub-proof #152.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |   (351)  all_56_15 = e0
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (23), (351) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | |            #812.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | |   (352)  all_58_9 = e2
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (147), (352) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | | | | | | | | |            #51.
% 174.24/26.72  | | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | |   (353)  all_58_8 = e3 | all_58_11 = e3
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | | REF_CLOSE: (58), (87), (153), (177), (353) are inconsistent
% 174.24/26.72  | | | | | | | | | | | |            by sub-proof #997.
% 174.24/26.72  | | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | Case 2:
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | |   (354)  all_58_10 = e3
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | | REF_CLOSE: (32), (151), (354) are inconsistent by sub-proof
% 174.24/26.72  | | | | | | | | | | |            #1018.
% 174.24/26.72  | | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | | 
% 174.24/26.72  | | | | | | | | | End of split
% 174.24/26.72  | | | | | | | | | 
% 174.59/26.72  | | | | | | | | End of split
% 174.59/26.72  | | | | | | | | 
% 174.59/26.72  | | | | | | | End of split
% 174.59/26.72  | | | | | | | 
% 174.59/26.72  | | | | | | End of split
% 174.59/26.72  | | | | | | 
% 174.59/26.72  | | | | | End of split
% 174.59/26.72  | | | | | 
% 174.59/26.72  | | | | End of split
% 174.59/26.72  | | | | 
% 174.59/26.72  | | | Case 2:
% 174.59/26.72  | | | | 
% 174.59/26.72  | | | |   (355)   ~ (all_56_3 = e3)
% 174.59/26.72  | | | | 
% 174.59/26.72  | | | | REDUCE: (10), (355) imply:
% 174.59/26.72  | | | |   (356)   ~ (all_52_7 = e3)
% 174.59/26.73  | | | | 
% 174.59/26.73  | | | | REF_CLOSE: (13), (15), (25), (27), (28), (29), (31), (32), (33), (34),
% 174.59/26.73  | | | |            (36), (37), (38), (40), (41), (42), (44), (48), (58), (62),
% 174.59/26.73  | | | |            (69), (70), (73), (76), (77), (79), (80), (81), (83), (84),
% 174.59/26.73  | | | |            (85), (86), (87), (88), (89), (94), (95), (96), (99), (100),
% 174.59/26.73  | | | |            (102), (105), (106), (109), (110), (112), (113), (116),
% 174.59/26.73  | | | |            (117), (120), (121), (124), (125), (126), (129), (133),
% 174.59/26.73  | | | |            (134), (138), (142), (143), (356) are inconsistent by
% 174.59/26.73  | | | |            sub-proof #283.
% 174.59/26.73  | | | | 
% 174.59/26.73  | | | End of split
% 174.59/26.73  | | | 
% 174.59/26.73  | | Case 2:
% 174.59/26.73  | | | 
% 174.59/26.73  | | |   (357)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.73  | | | 
% 174.59/26.73  | | | REF_CLOSE: (1), (2), (7), (8), (10), (15), (22), (24), (26), (27), (28),
% 174.59/26.73  | | |            (29), (32), (34), (35), (37), (39), (40), (42), (43), (45),
% 174.59/26.73  | | |            (47), (49), (51), (53), (55), (56), (58), (62), (65), (74),
% 174.59/26.73  | | |            (76), (77), (80), (81), (83), (84), (86), (87), (90), (92),
% 174.59/26.73  | | |            (93), (94), (95), (99), (101), (103), (104), (105), (106),
% 174.59/26.73  | | |            (109), (113), (114), (117), (118), (120), (122), (123), (124),
% 174.59/26.73  | | |            (125), (127), (129), (133), (357) are inconsistent by sub-proof
% 174.59/26.73  | | |            #95.
% 174.59/26.73  | | | 
% 174.59/26.73  | | End of split
% 174.59/26.73  | | 
% 174.59/26.73  | End of split
% 174.59/26.73  | 
% 174.59/26.73  End of proof
% 174.59/26.73  
% 174.59/26.73  Sub-proof #49 shows that the following formulas are inconsistent:
% 174.59/26.73  ----------------------------------------------------------------
% 174.59/26.73    (1)  all_58_7 = e3
% 174.59/26.73    (2)  e2 = e1
% 174.59/26.73    (3)  all_58_13 = e2
% 174.59/26.73    (4)   ~ (e2 = e1)
% 174.59/26.73    (5)  all_58_7 = e2 | all_58_13 = e2
% 174.59/26.73    (6)   ~ (e3 = e2)
% 174.59/26.73  
% 174.59/26.73  Begin of proof
% 174.59/26.73  | 
% 174.59/26.73  | SIMP: (2) implies:
% 174.59/26.73  |   (7)  e2 = e1
% 174.59/26.73  | 
% 174.59/26.73  | COMBINE_EQS: (3), (7) imply:
% 174.59/26.73  |   (8)  all_58_13 = e1
% 174.59/26.73  | 
% 174.59/26.73  | REF_CLOSE: (1), (4), (5), (6), (8) are inconsistent by sub-proof #259.
% 174.59/26.73  | 
% 174.59/26.73  End of proof
% 174.59/26.73  
% 174.59/26.73  Sub-proof #50 shows that the following formulas are inconsistent:
% 174.59/26.73  ----------------------------------------------------------------
% 174.59/26.73    (1)  all_58_2 = e2
% 174.59/26.73    (2)   ~ (e3 = e1)
% 174.59/26.73    (3)  all_58_0 = all_4_2
% 174.59/26.73    (4)   ~ (all_52_5 = e3)
% 174.59/26.73    (5)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.73    (6)  all_58_12 = e3
% 174.59/26.73    (7)  all_58_6 = all_52_17
% 174.59/26.73    (8)  op(e3, all_52_17) = e3
% 174.59/26.73    (9)  op(e3, e1) = all_52_5
% 174.59/26.73    (10)   ~ (e2 = e1)
% 174.59/26.73    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.73    (12)   ~ (all_4_2 = e1)
% 174.59/26.73  
% 174.59/26.73  Begin of proof
% 174.59/26.73  | 
% 174.59/26.73  | BETA: splitting (5) gives:
% 174.59/26.73  | 
% 174.59/26.73  | Case 1:
% 174.59/26.73  | | 
% 174.59/26.73  | |   (13)  all_58_0 = e1
% 174.59/26.73  | | 
% 174.59/26.73  | | COMBINE_EQS: (3), (13) imply:
% 174.59/26.73  | |   (14)  all_4_2 = e1
% 174.59/26.73  | | 
% 174.59/26.73  | | REDUCE: (12), (14) imply:
% 174.59/26.73  | |   (15)  $false
% 174.59/26.73  | | 
% 174.59/26.73  | | CLOSE: (15) is inconsistent.
% 174.59/26.73  | | 
% 174.59/26.73  | Case 2:
% 174.59/26.73  | | 
% 174.59/26.73  | |   (16)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.73  | | 
% 174.59/26.73  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (16) are
% 174.59/26.73  | |            inconsistent by sub-proof #919.
% 174.59/26.73  | | 
% 174.59/26.73  | End of split
% 174.59/26.73  | 
% 174.59/26.73  End of proof
% 174.59/26.73  
% 174.59/26.73  Sub-proof #51 shows that the following formulas are inconsistent:
% 174.59/26.73  ----------------------------------------------------------------
% 174.59/26.73    (1)  all_58_9 = e3
% 174.59/26.73    (2)  all_58_9 = e2
% 174.59/26.73    (3)   ~ (e3 = e2)
% 174.59/26.73  
% 174.59/26.73  Begin of proof
% 174.59/26.73  | 
% 174.59/26.73  | COMBINE_EQS: (1), (2) imply:
% 174.59/26.73  |   (4)  e3 = e2
% 174.59/26.73  | 
% 174.59/26.73  | SIMP: (4) implies:
% 174.59/26.73  |   (5)  e3 = e2
% 174.59/26.73  | 
% 174.59/26.73  | REDUCE: (3), (5) imply:
% 174.59/26.73  |   (6)  $false
% 174.59/26.73  | 
% 174.59/26.73  | CLOSE: (6) is inconsistent.
% 174.59/26.73  | 
% 174.59/26.73  End of proof
% 174.59/26.73  
% 174.59/26.73  Sub-proof #52 shows that the following formulas are inconsistent:
% 174.59/26.73  ----------------------------------------------------------------
% 174.59/26.73    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.73    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.73    (3)   ~ (all_52_17 = all_52_23)
% 174.59/26.73    (4)  op(e2, all_10_2) = all_10_1
% 174.59/26.73    (5)  op(all_10_1, all_10_2) = e1
% 174.59/26.73    (6)  op(e3, e2) = all_52_3
% 174.59/26.73    (7)   ~ (all_52_9 = all_52_25)
% 174.59/26.73    (8)  op(e3, all_52_25) = all_52_24
% 174.59/26.73    (9)   ~ (all_52_19 = all_52_23)
% 174.59/26.73    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.73    (11)  op(e3, all_52_9) = all_52_8
% 174.59/26.73    (12)   ~ (all_52_3 = all_10_2)
% 174.59/26.73    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.73    (14)  all_58_5 = all_52_13
% 174.59/26.73    (15)   ~ (all_52_25 = all_52_29)
% 174.59/26.73    (16)  all_56_15 = all_6_2
% 174.59/26.73    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.73    (18)  all_58_3 = all_10_2
% 174.59/26.73    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.73    (20)  all_58_15 = all_6_2
% 174.59/26.73    (21)   ~ (all_52_9 = all_4_2)
% 174.59/26.73    (22)   ~ (all_52_5 = all_52_7)
% 174.59/26.73    (23)  all_58_10 = all_52_15
% 174.59/26.73    (24)   ~ (all_52_5 = all_4_2)
% 174.59/26.73    (25)  all_58_7 = all_52_19
% 174.59/26.73    (26)   ~ (all_52_17 = all_52_25)
% 174.59/26.73    (27)  op(e0, e1) = all_52_29
% 174.59/26.73    (28)  all_58_4 = all_52_5
% 174.59/26.73    (29)   ~ (e3 = e1)
% 174.59/26.73    (30)   ~ (all_52_27 = all_52_29)
% 174.59/26.73    (31)   ~ (all_52_17 = all_14_2)
% 174.59/26.73    (32)  op(e3, all_4_2) = all_4_1
% 174.59/26.73    (33)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.73    (34)   ~ (all_52_7 = all_4_2)
% 174.59/26.73    (35)  all_58_1 = all_52_3
% 174.59/26.73    (36)   ~ (all_52_13 = all_52_15)
% 174.59/26.73    (37)  all_58_0 = all_4_2
% 174.59/26.73    (38)  all_52_0 = e2
% 174.59/26.73    (39)  op(e1, all_52_29) = all_52_28
% 174.59/26.73    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.73    (41)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.73    (42)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.73    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.73    (44)  all_58_14 = all_52_29
% 174.59/26.73    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.73    (46)  op(e2, all_4_2) = all_4_0
% 174.59/26.73    (47)   ~ (all_52_3 = all_52_5)
% 174.59/26.73    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.73    (49)  op(e2, e1) = all_52_13
% 174.59/26.73    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.73    (51)  all_58_8 = all_14_2
% 174.59/26.73    (52)  all_56_1 = all_52_3
% 174.59/26.73    (53)  op(e0, e2) = all_52_27
% 174.59/26.73    (54)  all_56_14 = all_52_29
% 174.59/26.73    (55)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.73    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.73    (57)   ~ (all_52_3 = all_52_27)
% 174.59/26.73    (58)   ~ (all_52_3 = all_4_2)
% 174.59/26.73    (59)  op(e0, e3) = all_52_25
% 174.59/26.73    (60)  op(e0, all_6_2) = all_6_1
% 174.59/26.73    (61)   ~ (all_52_9 = all_10_2)
% 174.59/26.73    (62)  op(e3, all_52_17) = all_52_16
% 174.59/26.73    (63)  all_52_10 = all_10_1
% 174.59/26.73    (64)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.73    (65)   ~ (e3 = e0)
% 174.59/26.73    (66)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.73    (67)  op(all_14_1, all_14_2) = e2
% 174.59/26.73    (68)   ~ (all_52_9 = all_52_13)
% 174.59/26.73    (69)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.73    (70)   ~ (all_52_5 = all_52_29)
% 174.59/26.73    (71)  all_56_2 = all_52_5
% 174.59/26.73    (72)  op(e1, e0) = all_52_23
% 174.59/26.73    (73)  all_56_12 = all_52_25
% 174.59/26.73    (74)  all_58_13 = all_52_27
% 174.59/26.73    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.73    (76)   ~ (all_52_9 = all_52_17)
% 174.59/26.73    (77)  all_58_6 = all_52_17
% 174.59/26.73    (78)   ~ (all_52_3 = all_52_7)
% 174.59/26.73    (79)   ~ (e1 = e0)
% 174.59/26.73    (80)  all_56_0 = all_4_2
% 174.59/26.73    (81)  all_58_11 = all_52_23
% 174.59/26.73    (82)   ~ (all_52_7 = all_52_15)
% 174.59/26.73    (83)   ~ (all_4_0 = e1)
% 174.59/26.73    (84)   ~ (all_52_19 = all_10_2)
% 174.59/26.73    (85)   ~ (all_58_15 = e0)
% 174.59/26.73    (86)  op(e3, all_4_2) = e2
% 174.59/26.73    (87)   ~ (all_52_29 = all_6_2)
% 174.59/26.73    (88)  all_58_2 = all_52_9
% 174.59/26.73    (89)  op(e3, e1) = all_52_5
% 174.59/26.73    (90)   ~ (e2 = e1)
% 174.59/26.73    (91)   ~ (all_52_25 = all_6_2)
% 174.59/26.73    (92)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.73    (93)  op(e1, e3) = all_52_17
% 174.59/26.73    (94)   ~ (all_52_25 = all_4_2)
% 174.59/26.73    (95)  op(e3, e0) = all_52_7
% 174.59/26.73    (96)  op(e3, e3) = all_4_2
% 174.59/26.73    (97)   ~ (all_52_17 = all_4_2)
% 174.59/26.73    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.73    (99)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.73          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.73          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.73          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.73    (100)   ~ (all_52_25 = all_52_27)
% 174.59/26.73    (101)   ~ (all_52_27 = all_6_2)
% 174.59/26.73    (102)   ~ (all_52_7 = all_6_2)
% 174.59/26.73    (103)   ~ (all_52_15 = all_10_2)
% 174.59/26.73    (104)   ~ (all_52_7 = all_52_23)
% 174.59/26.73    (105)  op(e2, all_52_27) = all_52_26
% 174.59/26.73    (106)  all_52_20 = all_14_1
% 174.59/26.73    (107)   ~ (all_52_17 = all_52_19)
% 174.59/26.73    (108)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.73    (109)  all_52_30 = all_6_1
% 174.59/26.73    (110)  op(e1, all_14_2) = all_14_1
% 174.59/26.73    (111)  all_58_9 = all_52_7
% 174.59/26.73    (112)   ~ (e2 = e0)
% 174.59/26.73    (113)  all_58_12 = all_52_25
% 174.59/26.73    (114)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.59/26.73             all_58_13 = e0 | all_58_14 = e0)
% 174.59/26.73    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.73    (116)   ~ (all_52_9 = all_52_15)
% 174.59/26.73    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.73    (118)   ~ (e3 = e2)
% 174.59/26.73    (119)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.73    (120)  op(e2, e3) = all_52_9
% 174.59/26.73    (121)  all_56_13 = all_52_27
% 174.59/26.73  
% 174.59/26.73  Begin of proof
% 174.59/26.73  | 
% 174.59/26.73  | ALPHA: (114) implies:
% 174.59/26.73  |   (122)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.73  |   (123)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.73  | 
% 174.59/26.73  | REDUCE: (20), (85) imply:
% 174.59/26.73  |   (124)   ~ (all_6_2 = e0)
% 174.59/26.73  | 
% 174.59/26.73  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.59/26.73  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.73  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.59/26.73  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.59/26.73  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.59/26.73  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.59/26.73  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.59/26.73  |            (79), (80), (81), (82), (83), (84), (86), (87), (88), (89), (90),
% 174.59/26.73  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.59/26.73  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 174.59/26.73  |            (111), (112), (113), (115), (116), (117), (118), (119), (120),
% 174.59/26.73  |            (121), (122), (123), (124) are inconsistent by sub-proof #53.
% 174.59/26.73  | 
% 174.59/26.73  End of proof
% 174.59/26.73  
% 174.59/26.73  Sub-proof #53 shows that the following formulas are inconsistent:
% 174.59/26.73  ----------------------------------------------------------------
% 174.59/26.73    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.73    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.73    (3)   ~ (all_52_17 = all_52_23)
% 174.59/26.73    (4)  op(e2, all_10_2) = all_10_1
% 174.59/26.73    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.73    (6)  op(all_10_1, all_10_2) = e1
% 174.59/26.73    (7)  op(e3, e2) = all_52_3
% 174.59/26.73    (8)   ~ (all_52_9 = all_52_25)
% 174.59/26.73    (9)  op(e3, all_52_25) = all_52_24
% 174.59/26.73    (10)   ~ (all_52_19 = all_52_23)
% 174.59/26.73    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.73    (12)  op(e3, all_52_9) = all_52_8
% 174.59/26.73    (13)   ~ (all_52_3 = all_10_2)
% 174.59/26.73    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.73    (15)  all_58_5 = all_52_13
% 174.59/26.73    (16)   ~ (all_6_2 = e0)
% 174.59/26.73    (17)   ~ (all_52_25 = all_52_29)
% 174.59/26.73    (18)  all_56_15 = all_6_2
% 174.59/26.73    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.73    (20)  all_58_3 = all_10_2
% 174.59/26.73    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.73    (22)  all_58_15 = all_6_2
% 174.59/26.73    (23)   ~ (all_52_9 = all_4_2)
% 174.59/26.73    (24)   ~ (all_52_5 = all_52_7)
% 174.59/26.73    (25)  all_58_10 = all_52_15
% 174.59/26.73    (26)   ~ (all_52_5 = all_4_2)
% 174.59/26.73    (27)  all_58_7 = all_52_19
% 174.59/26.73    (28)   ~ (all_52_17 = all_52_25)
% 174.59/26.73    (29)  op(e0, e1) = all_52_29
% 174.59/26.73    (30)  all_58_4 = all_52_5
% 174.59/26.73    (31)   ~ (e3 = e1)
% 174.59/26.73    (32)   ~ (all_52_27 = all_52_29)
% 174.59/26.73    (33)   ~ (all_52_17 = all_14_2)
% 174.59/26.73    (34)  op(e3, all_4_2) = all_4_1
% 174.59/26.73    (35)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.73    (36)   ~ (all_52_7 = all_4_2)
% 174.59/26.73    (37)  all_58_1 = all_52_3
% 174.59/26.73    (38)   ~ (all_52_13 = all_52_15)
% 174.59/26.73    (39)  all_58_0 = all_4_2
% 174.59/26.73    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.73    (41)  all_52_0 = e2
% 174.59/26.73    (42)  op(e1, all_52_29) = all_52_28
% 174.59/26.73    (43)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.73    (44)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.73    (45)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.73    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.73    (47)  all_58_14 = all_52_29
% 174.59/26.73    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.73    (49)  op(e2, all_4_2) = all_4_0
% 174.59/26.73    (50)   ~ (all_52_3 = all_52_5)
% 174.59/26.73    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.73    (52)  op(e2, e1) = all_52_13
% 174.59/26.73    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.73    (54)  all_58_8 = all_14_2
% 174.59/26.73    (55)  all_56_1 = all_52_3
% 174.59/26.73    (56)  op(e0, e2) = all_52_27
% 174.59/26.73    (57)  all_56_14 = all_52_29
% 174.59/26.73    (58)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.73    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.73    (60)   ~ (all_52_3 = all_52_27)
% 174.59/26.73    (61)   ~ (all_52_3 = all_4_2)
% 174.59/26.73    (62)  op(e0, e3) = all_52_25
% 174.59/26.73    (63)  op(e0, all_6_2) = all_6_1
% 174.59/26.73    (64)   ~ (all_52_9 = all_10_2)
% 174.59/26.73    (65)  op(e3, all_52_17) = all_52_16
% 174.59/26.73    (66)  all_52_10 = all_10_1
% 174.59/26.73    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.73    (68)   ~ (e3 = e0)
% 174.59/26.73    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.73    (70)  op(all_14_1, all_14_2) = e2
% 174.59/26.73    (71)   ~ (all_52_9 = all_52_13)
% 174.59/26.73    (72)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.73    (73)   ~ (all_52_5 = all_52_29)
% 174.59/26.73    (74)  all_56_2 = all_52_5
% 174.59/26.73    (75)  op(e1, e0) = all_52_23
% 174.59/26.73    (76)  all_56_12 = all_52_25
% 174.59/26.73    (77)  all_58_13 = all_52_27
% 174.59/26.73    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.73    (79)   ~ (all_52_9 = all_52_17)
% 174.59/26.73    (80)  all_58_6 = all_52_17
% 174.59/26.73    (81)   ~ (all_52_3 = all_52_7)
% 174.59/26.73    (82)   ~ (e1 = e0)
% 174.59/26.73    (83)  all_56_0 = all_4_2
% 174.59/26.73    (84)  all_58_11 = all_52_23
% 174.59/26.73    (85)   ~ (all_52_7 = all_52_15)
% 174.59/26.73    (86)   ~ (all_4_0 = e1)
% 174.59/26.73    (87)   ~ (all_52_19 = all_10_2)
% 174.59/26.73    (88)  op(e3, all_4_2) = e2
% 174.59/26.73    (89)   ~ (all_52_29 = all_6_2)
% 174.59/26.73    (90)  all_58_2 = all_52_9
% 174.59/26.73    (91)  op(e3, e1) = all_52_5
% 174.59/26.73    (92)   ~ (e2 = e1)
% 174.59/26.73    (93)   ~ (all_52_25 = all_6_2)
% 174.59/26.73    (94)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.73    (95)  op(e1, e3) = all_52_17
% 174.59/26.73    (96)   ~ (all_52_25 = all_4_2)
% 174.59/26.73    (97)  op(e3, e0) = all_52_7
% 174.59/26.73    (98)  op(e3, e3) = all_4_2
% 174.59/26.73    (99)   ~ (all_52_17 = all_4_2)
% 174.59/26.73    (100)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.73             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.73    (101)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.73           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.73           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.73           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.73    (102)   ~ (all_52_25 = all_52_27)
% 174.59/26.73    (103)   ~ (all_52_27 = all_6_2)
% 174.59/26.73    (104)   ~ (all_52_7 = all_6_2)
% 174.59/26.73    (105)   ~ (all_52_15 = all_10_2)
% 174.59/26.73    (106)   ~ (all_52_7 = all_52_23)
% 174.59/26.73    (107)  op(e2, all_52_27) = all_52_26
% 174.59/26.73    (108)  all_52_20 = all_14_1
% 174.59/26.73    (109)   ~ (all_52_17 = all_52_19)
% 174.59/26.73    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.73    (111)  all_52_30 = all_6_1
% 174.59/26.73    (112)  op(e1, all_14_2) = all_14_1
% 174.59/26.73    (113)  all_58_9 = all_52_7
% 174.59/26.73    (114)   ~ (e2 = e0)
% 174.59/26.73    (115)  all_58_12 = all_52_25
% 174.59/26.73    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.73    (117)   ~ (all_52_9 = all_52_15)
% 174.59/26.73    (118)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.73    (119)   ~ (e3 = e2)
% 174.59/26.73    (120)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.73    (121)  op(e2, e3) = all_52_9
% 174.59/26.73    (122)  all_56_13 = all_52_27
% 174.59/26.73  
% 174.59/26.73  Begin of proof
% 174.59/26.73  | 
% 174.59/26.73  | BETA: splitting (101) gives:
% 174.59/26.73  | 
% 174.59/26.73  | Case 1:
% 174.59/26.73  | | 
% 174.59/26.73  | |   (123)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.73  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.59/26.73  | | 
% 174.59/26.73  | | REF_CLOSE: (4), (6), (41), (66), (92), (100), (119), (123) are inconsistent
% 174.59/26.73  | |            by sub-proof #69.
% 174.59/26.73  | | 
% 174.59/26.73  | Case 2:
% 174.59/26.73  | | 
% 174.59/26.73  | |   (124)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.59/26.73  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.59/26.73  | |            e0)
% 174.59/26.73  | | 
% 174.59/26.73  | | BETA: splitting (124) gives:
% 174.59/26.73  | | 
% 174.59/26.73  | | Case 1:
% 174.59/26.73  | | | 
% 174.59/26.73  | | |   (125)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.59/26.73  | | | 
% 174.59/26.73  | | | REF_CLOSE: (70), (92), (100), (108), (112), (125) are inconsistent by
% 174.59/26.73  | | |            sub-proof #314.
% 174.59/26.73  | | | 
% 174.59/26.73  | | Case 2:
% 174.59/26.73  | | | 
% 174.59/26.73  | | |   (126)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.59/26.73  | | | 
% 174.59/26.73  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 174.59/26.73  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.73  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 174.59/26.73  | | |            (34), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 174.59/26.73  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 174.59/26.73  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 174.59/26.73  | | |            (65), (67), (68), (69), (71), (72), (73), (74), (75), (76),
% 174.59/26.73  | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 174.59/26.73  | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 174.59/26.73  | | |            (97), (98), (99), (100), (102), (103), (104), (105), (106),
% 174.59/26.73  | | |            (107), (109), (110), (111), (113), (114), (115), (116), (117),
% 174.59/26.73  | | |            (118), (119), (120), (121), (122), (126) are inconsistent by
% 174.59/26.73  | | |            sub-proof #87.
% 174.59/26.73  | | | 
% 174.59/26.73  | | End of split
% 174.59/26.73  | | 
% 174.59/26.73  | End of split
% 174.59/26.73  | 
% 174.59/26.73  End of proof
% 174.59/26.73  
% 174.59/26.73  Sub-proof #54 shows that the following formulas are inconsistent:
% 174.59/26.73  ----------------------------------------------------------------
% 174.59/26.73    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.73    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.73    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.73    (4)   ~ (all_52_27 = all_10_2)
% 174.59/26.73    (5)  op(e2, all_10_2) = all_10_1
% 174.59/26.73    (6)   ~ (all_52_13 = all_52_29)
% 174.59/26.73    (7)  all_56_3 = all_52_7
% 174.59/26.73    (8)  op(e3, e2) = all_52_3
% 174.59/26.73    (9)   ~ (all_52_9 = all_52_25)
% 174.59/26.73    (10)   ~ (all_52_19 = all_52_23)
% 174.59/26.73    (11)  all_56_11 = all_52_23
% 174.59/26.73    (12)  op(e1, e2) = all_52_19
% 174.59/26.73    (13)  op(e3, all_52_9) = all_52_8
% 174.59/26.73    (14)   ~ (all_52_3 = all_10_2)
% 174.59/26.73    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.73    (16)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 174.59/26.73    (17)  all_58_5 = all_52_13
% 174.59/26.73    (18)   ~ (all_52_25 = all_52_29)
% 174.59/26.73    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.73    (20)  op(e2, e0) = all_52_15
% 174.59/26.74    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.74    (22)  all_58_3 = all_10_2
% 174.59/26.74    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.74    (24)  all_58_15 = all_6_2
% 174.59/26.74    (25)   ~ (all_52_9 = all_4_2)
% 174.59/26.74    (26)   ~ (all_52_5 = all_52_7)
% 174.59/26.74    (27)  all_58_10 = all_52_15
% 174.59/26.74    (28)   ~ (all_52_5 = all_4_2)
% 174.59/26.74    (29)  all_58_7 = all_52_19
% 174.59/26.74    (30)   ~ (all_52_17 = all_52_25)
% 174.59/26.74    (31)  all_58_4 = all_52_5
% 174.59/26.74    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.74    (33)   ~ (e3 = e1)
% 174.59/26.74    (34)   ~ (all_52_17 = all_14_2)
% 174.59/26.74    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.74    (36)   ~ (all_52_7 = all_4_2)
% 174.59/26.74    (37)  all_58_1 = all_52_3
% 174.59/26.74    (38)  all_58_0 = all_4_2
% 174.59/26.74    (39)  op(e2, all_52_27) = e2
% 174.59/26.74    (40)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.74    (41)  all_58_14 = all_52_29
% 174.59/26.74    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.74    (43)  op(e2, all_4_2) = all_4_0
% 174.59/26.74    (44)  op(e2, e1) = all_52_13
% 174.59/26.74    (45)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.74    (46)  all_58_8 = all_14_2
% 174.59/26.74    (47)  op(e1, all_52_29) = e1
% 174.59/26.74    (48)   ~ (all_52_3 = all_52_27)
% 174.59/26.74    (49)   ~ (all_52_3 = all_4_2)
% 174.59/26.74    (50)   ~ (all_52_9 = all_10_2)
% 174.59/26.74    (51)  op(e3, all_52_17) = all_52_16
% 174.59/26.74    (52)   ~ (e3 = e0)
% 174.59/26.74    (53)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.74    (54)   ~ (all_52_9 = all_52_13)
% 174.59/26.74    (55)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.74    (56)   ~ (all_52_15 = all_52_23)
% 174.59/26.74    (57)   ~ (all_52_5 = all_52_29)
% 174.59/26.74    (58)  all_56_12 = all_52_25
% 174.59/26.74    (59)  all_58_13 = all_52_27
% 174.59/26.74    (60)  all_56_5 = all_10_2
% 174.59/26.74    (61)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.59/26.74    (62)   ~ (all_52_9 = all_52_17)
% 174.59/26.74    (63)  all_58_6 = all_52_17
% 174.59/26.74    (64)   ~ (all_52_3 = all_52_7)
% 174.59/26.74    (65)   ~ (e1 = e0)
% 174.59/26.74    (66)  all_56_0 = all_4_2
% 174.59/26.74    (67)  all_58_11 = all_52_23
% 174.59/26.74    (68)   ~ (all_52_3 = all_52_19)
% 174.59/26.74    (69)   ~ (all_52_7 = all_52_15)
% 174.59/26.74    (70)   ~ (all_52_29 = all_14_2)
% 174.59/26.74    (71)  op(e3, all_52_25) = e3
% 174.59/26.74    (72)   ~ (all_4_0 = e1)
% 174.59/26.74    (73)   ~ (all_52_19 = all_10_2)
% 174.59/26.74    (74)  all_58_15 = e0
% 174.59/26.74    (75)  op(e3, all_4_2) = e2
% 174.59/26.74    (76)   ~ (all_52_23 = all_6_2)
% 174.59/26.74    (77)  all_58_2 = all_52_9
% 174.59/26.74    (78)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.59/26.74    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.59/26.74    (80)  op(e3, e1) = all_52_5
% 174.59/26.74    (81)   ~ (all_52_25 = all_6_2)
% 174.59/26.74    (82)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.59/26.74    (83)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.74    (84)  op(e1, e3) = all_52_17
% 174.59/26.74    (85)   ~ (all_52_25 = all_4_2)
% 174.59/26.74    (86)  op(e3, e0) = all_52_7
% 174.59/26.74    (87)  op(e3, e3) = all_4_2
% 174.59/26.74    (88)   ~ (all_52_17 = all_4_2)
% 174.59/26.74    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.74    (90)   ~ (all_52_25 = all_52_27)
% 174.59/26.74    (91)   ~ (all_52_15 = all_10_2)
% 174.59/26.74    (92)   ~ (all_52_13 = all_10_2)
% 174.59/26.74    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.59/26.74    (94)  all_58_9 = all_52_7
% 174.59/26.74    (95)   ~ (e2 = e0)
% 174.59/26.74    (96)  all_58_12 = all_52_25
% 174.59/26.74    (97)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.74    (98)   ~ (e3 = e2)
% 174.59/26.74    (99)  op(e2, e3) = all_52_9
% 174.59/26.74    (100)  all_56_13 = all_52_27
% 174.59/26.74  
% 174.59/26.74  Begin of proof
% 174.59/26.74  | 
% 174.59/26.74  | COMBINE_EQS: (24), (74) imply:
% 174.59/26.74  |   (101)  all_6_2 = e0
% 174.59/26.74  | 
% 174.59/26.74  | REDUCE: (76), (101) imply:
% 174.59/26.74  |   (102)   ~ (all_52_23 = e0)
% 174.59/26.74  | 
% 174.59/26.74  | REDUCE: (81), (101) imply:
% 174.59/26.74  |   (103)   ~ (all_52_25 = e0)
% 174.59/26.74  | 
% 174.59/26.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.59/26.74  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.74  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 174.59/26.74  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 174.59/26.74  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 174.59/26.74  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.59/26.74  |            (69), (70), (71), (72), (73), (74), (75), (77), (78), (79), (80),
% 174.59/26.74  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 174.59/26.74  |            (93), (94), (95), (96), (97), (98), (99), (100), (102), (103) are
% 174.59/26.74  |            inconsistent by sub-proof #110.
% 174.59/26.74  | 
% 174.59/26.74  End of proof
% 174.59/26.74  
% 174.59/26.74  Sub-proof #55 shows that the following formulas are inconsistent:
% 174.59/26.74  ----------------------------------------------------------------
% 174.59/26.74    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.74    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.74    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.59/26.74    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.74    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.74    (6)   ~ (all_52_27 = all_10_2)
% 174.59/26.74    (7)   ~ (all_52_17 = all_52_23)
% 174.59/26.74    (8)  op(e2, all_10_2) = all_10_1
% 174.59/26.74    (9)   ~ (all_52_13 = all_52_29)
% 174.59/26.74    (10)  all_56_3 = all_52_7
% 174.59/26.74    (11)  op(e3, e2) = all_52_3
% 174.59/26.74    (12)   ~ (all_52_9 = all_52_25)
% 174.59/26.74    (13)  op(e3, all_52_25) = all_52_24
% 174.59/26.74    (14)   ~ (all_52_19 = all_52_23)
% 174.59/26.74    (15)  all_56_11 = all_52_23
% 174.59/26.74    (16)  op(e1, e2) = all_52_19
% 174.59/26.74    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.74    (18)  op(e3, all_52_9) = all_52_8
% 174.59/26.74    (19)   ~ (all_52_3 = all_10_2)
% 174.59/26.74    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.74    (21)  all_58_5 = all_52_13
% 174.59/26.74    (22)   ~ (all_52_25 = all_52_29)
% 174.59/26.74    (23)  all_56_15 = all_6_2
% 174.59/26.74    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.74    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.74    (26)  all_58_3 = all_10_2
% 174.59/26.74    (27)  all_56_9 = all_52_19
% 174.59/26.74    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.74    (29)  all_58_15 = all_6_2
% 174.59/26.74    (30)   ~ (all_52_9 = all_4_2)
% 174.59/26.74    (31)   ~ (all_52_5 = all_52_7)
% 174.59/26.74    (32)  all_58_10 = all_52_15
% 174.59/26.74    (33)   ~ (all_52_5 = all_4_2)
% 174.59/26.74    (34)  all_58_7 = all_52_19
% 174.59/26.74    (35)  all_56_4 = all_52_9
% 174.59/26.74    (36)   ~ (all_52_15 = all_6_2)
% 174.59/26.74    (37)   ~ (all_52_17 = all_52_25)
% 174.59/26.74    (38)  op(e0, e1) = all_52_29
% 174.59/26.74    (39)  all_58_4 = all_52_5
% 174.59/26.74    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.74    (41)   ~ (e3 = e1)
% 174.59/26.74    (42)   ~ (all_52_27 = all_52_29)
% 174.59/26.74    (43)   ~ (all_52_17 = all_14_2)
% 174.59/26.74    (44)  op(e3, all_4_2) = all_4_1
% 174.59/26.74    (45)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.74    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.74    (47)   ~ (all_52_7 = all_4_2)
% 174.59/26.74    (48)  all_58_1 = all_52_3
% 174.59/26.74    (49)   ~ (all_52_13 = all_52_15)
% 174.59/26.74    (50)  all_58_0 = all_4_2
% 174.59/26.74    (51)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.59/26.74    (52)  op(e1, all_52_13) = all_52_12
% 174.59/26.74    (53)  all_52_0 = e2
% 174.59/26.74    (54)  op(e1, all_52_29) = all_52_28
% 174.59/26.74    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.74    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.74    (57)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.74    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.74    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.74    (60)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.59/26.74    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.59/26.74    (62)  all_58_14 = all_52_29
% 174.59/26.74    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.74    (64)  op(e2, all_4_2) = all_4_0
% 174.59/26.74    (65)   ~ (all_52_3 = all_52_5)
% 174.59/26.74    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.74    (67)  op(e2, e1) = all_52_13
% 174.59/26.74    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.74    (69)  all_58_8 = all_14_2
% 174.59/26.74    (70)  all_56_1 = all_52_3
% 174.59/26.74    (71)  op(e0, e2) = all_52_27
% 174.59/26.74    (72)  all_56_14 = all_52_29
% 174.59/26.74    (73)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.74    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.74    (75)   ~ (all_52_3 = all_52_27)
% 174.59/26.74    (76)   ~ (all_52_3 = all_4_2)
% 174.59/26.74    (77)  op(e0, e3) = all_52_25
% 174.59/26.74    (78)  op(e0, all_6_2) = all_6_1
% 174.59/26.74    (79)   ~ (all_52_9 = all_10_2)
% 174.59/26.74    (80)  op(e3, all_52_17) = all_52_16
% 174.59/26.74    (81)  all_52_10 = all_10_1
% 174.59/26.74    (82)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.74    (83)   ~ (all_52_13 = all_14_2)
% 174.59/26.74    (84)   ~ (e3 = e0)
% 174.59/26.74    (85)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.74    (86)  op(all_14_1, all_14_2) = e2
% 174.59/26.74    (87)   ~ (all_52_9 = all_52_13)
% 174.59/26.74    (88)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.74    (89)  op(e0, all_52_23) = all_52_22
% 174.59/26.74    (90)   ~ (all_52_15 = all_52_23)
% 174.59/26.74    (91)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.59/26.74    (92)  op(all_10_1, all_10_2) = all_10_0
% 174.59/26.74    (93)   ~ (all_52_5 = all_52_29)
% 174.59/26.74    (94)  all_56_2 = all_52_5
% 174.59/26.74    (95)  op(e1, e0) = all_52_23
% 174.59/26.74    (96)  all_56_12 = all_52_25
% 174.59/26.74    (97)  all_58_13 = all_52_27
% 174.59/26.74    (98)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.74    (99)   ~ (all_52_9 = all_52_17)
% 174.59/26.74    (100)  all_58_6 = all_52_17
% 174.59/26.74    (101)   ~ (all_52_3 = all_52_7)
% 174.59/26.74    (102)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.59/26.74    (103)  op(e2, all_52_19) = all_52_18
% 174.59/26.74    (104)   ~ (e1 = e0)
% 174.59/26.74    (105)  all_56_0 = all_4_2
% 174.59/26.74    (106)  all_58_11 = all_52_23
% 174.59/26.74    (107)   ~ (all_52_3 = all_52_19)
% 174.59/26.74    (108)   ~ (all_52_7 = all_52_15)
% 174.59/26.74    (109)  op(e0, all_52_15) = all_52_14
% 174.59/26.74    (110)   ~ (all_52_29 = all_14_2)
% 174.59/26.74    (111)   ~ (all_4_0 = e1)
% 174.59/26.74    (112)   ~ (all_52_19 = all_10_2)
% 174.59/26.74    (113)   ~ (all_58_15 = e0)
% 174.59/26.74    (114)  op(e3, all_4_2) = e2
% 174.59/26.74    (115)   ~ (all_52_23 = all_6_2)
% 174.59/26.74    (116)   ~ (all_52_29 = all_6_2)
% 174.59/26.74    (117)  all_58_2 = all_52_9
% 174.59/26.74    (118)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.59/26.74    (119)  op(e3, e1) = all_52_5
% 174.59/26.74    (120)   ~ (e2 = e1)
% 174.59/26.74    (121)  all_56_10 = all_14_2
% 174.59/26.74    (122)   ~ (all_52_25 = all_6_2)
% 174.59/26.74    (123)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.74    (124)  op(e1, e3) = all_52_17
% 174.59/26.74    (125)   ~ (all_52_25 = all_4_2)
% 174.59/26.74    (126)  op(e3, e0) = all_52_7
% 174.59/26.74    (127)  op(e3, e3) = all_4_2
% 174.59/26.74    (128)  all_56_8 = all_52_17
% 174.59/26.74    (129)   ~ (all_52_17 = all_4_2)
% 174.59/26.74    (130)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.74             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.74    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.74    (132)   ~ (all_52_25 = all_52_27)
% 174.59/26.74    (133)   ~ (all_52_27 = all_6_2)
% 174.59/26.74    (134)   ~ (all_52_7 = all_6_2)
% 174.59/26.74    (135)   ~ (all_10_0 = e3)
% 174.59/26.74    (136)   ~ (all_52_15 = all_10_2)
% 174.59/26.74    (137)   ~ (all_52_7 = all_52_23)
% 174.59/26.74    (138)   ~ (all_52_13 = all_10_2)
% 174.59/26.74    (139)  op(e2, all_52_27) = all_52_26
% 174.59/26.74    (140)  all_52_20 = all_14_1
% 174.59/26.74    (141)   ~ (all_52_17 = all_52_19)
% 174.59/26.74    (142)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.74    (143)  all_52_30 = all_6_1
% 174.59/26.74    (144)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.59/26.74    (145)  op(e1, all_14_2) = all_14_1
% 174.59/26.74    (146)  all_58_9 = all_52_7
% 174.59/26.74    (147)   ~ (e2 = e0)
% 174.59/26.74    (148)  all_58_12 = all_52_25
% 174.59/26.74    (149)   ~ (all_10_0 = e1)
% 174.59/26.74    (150)  all_56_6 = all_52_13
% 174.59/26.74    (151)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.59/26.74             all_58_13 = e0 | all_58_14 = e0)
% 174.59/26.74    (152)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.74    (153)   ~ (all_52_9 = all_52_15)
% 174.59/26.74    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.74    (155)   ~ (e3 = e2)
% 174.59/26.74    (156)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.74    (157)   ~ (all_52_19 = all_14_2)
% 174.59/26.74    (158)  op(e2, e3) = all_52_9
% 174.59/26.74    (159)  all_56_13 = all_52_27
% 174.59/26.74  
% 174.59/26.74  Begin of proof
% 174.59/26.74  | 
% 174.59/26.74  | ALPHA: (151) implies:
% 174.59/26.74  |   (160)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.74  |   (161)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.74  | 
% 174.59/26.74  | REDUCE: (29), (113) imply:
% 174.59/26.74  |   (162)   ~ (all_6_2 = e0)
% 174.59/26.74  | 
% 174.59/26.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.59/26.74  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.74  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.59/26.74  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.59/26.74  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.59/26.74  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.59/26.74  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.59/26.74  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 174.59/26.74  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 174.59/26.74  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 174.59/26.74  |            (110), (111), (112), (114), (115), (116), (117), (118), (119),
% 174.59/26.74  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 174.59/26.74  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 174.59/26.74  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 174.59/26.74  |            (147), (148), (149), (150), (152), (153), (154), (155), (156),
% 174.59/26.74  |            (157), (158), (159), (160), (161), (162) are inconsistent by
% 174.59/26.74  |            sub-proof #56.
% 174.59/26.74  | 
% 174.59/26.74  End of proof
% 174.59/26.74  
% 174.59/26.74  Sub-proof #56 shows that the following formulas are inconsistent:
% 174.59/26.74  ----------------------------------------------------------------
% 174.59/26.74    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.74    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.74    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.59/26.74    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.74    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.74    (6)   ~ (all_52_27 = all_10_2)
% 174.59/26.74    (7)   ~ (all_52_17 = all_52_23)
% 174.59/26.74    (8)  op(e2, all_10_2) = all_10_1
% 174.59/26.74    (9)   ~ (all_52_13 = all_52_29)
% 174.59/26.74    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.74    (11)  all_56_3 = all_52_7
% 174.59/26.74    (12)  op(e3, e2) = all_52_3
% 174.59/26.74    (13)   ~ (all_52_9 = all_52_25)
% 174.59/26.74    (14)  op(e3, all_52_25) = all_52_24
% 174.59/26.74    (15)   ~ (all_52_19 = all_52_23)
% 174.59/26.74    (16)  all_56_11 = all_52_23
% 174.59/26.74    (17)  op(e1, e2) = all_52_19
% 174.59/26.74    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.74    (19)  op(e3, all_52_9) = all_52_8
% 174.59/26.74    (20)   ~ (all_52_3 = all_10_2)
% 174.59/26.74    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.74    (22)  all_58_5 = all_52_13
% 174.59/26.74    (23)   ~ (all_6_2 = e0)
% 174.59/26.74    (24)   ~ (all_52_25 = all_52_29)
% 174.59/26.74    (25)  all_56_15 = all_6_2
% 174.59/26.74    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.74    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.74    (28)  all_58_3 = all_10_2
% 174.59/26.74    (29)  all_56_9 = all_52_19
% 174.59/26.74    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.74    (31)  all_58_15 = all_6_2
% 174.59/26.74    (32)   ~ (all_52_9 = all_4_2)
% 174.59/26.74    (33)   ~ (all_52_5 = all_52_7)
% 174.59/26.74    (34)  all_58_10 = all_52_15
% 174.59/26.74    (35)   ~ (all_52_5 = all_4_2)
% 174.59/26.74    (36)  all_58_7 = all_52_19
% 174.59/26.74    (37)  all_56_4 = all_52_9
% 174.59/26.74    (38)   ~ (all_52_15 = all_6_2)
% 174.59/26.74    (39)   ~ (all_52_17 = all_52_25)
% 174.59/26.74    (40)  op(e0, e1) = all_52_29
% 174.59/26.74    (41)  all_58_4 = all_52_5
% 174.59/26.74    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.74    (43)   ~ (e3 = e1)
% 174.59/26.74    (44)   ~ (all_52_27 = all_52_29)
% 174.59/26.74    (45)   ~ (all_52_17 = all_14_2)
% 174.59/26.74    (46)  op(e3, all_4_2) = all_4_1
% 174.59/26.74    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.74    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.74    (49)   ~ (all_52_7 = all_4_2)
% 174.59/26.74    (50)  all_58_1 = all_52_3
% 174.59/26.74    (51)   ~ (all_52_13 = all_52_15)
% 174.59/26.74    (52)  all_58_0 = all_4_2
% 174.59/26.74    (53)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.59/26.74    (54)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.74    (55)  op(e1, all_52_13) = all_52_12
% 174.59/26.74    (56)  all_52_0 = e2
% 174.59/26.74    (57)  op(e1, all_52_29) = all_52_28
% 174.59/26.74    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.74    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.74    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.74    (61)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.74    (62)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.74    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.59/26.74    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.59/26.74    (65)  all_58_14 = all_52_29
% 174.59/26.74    (66)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.74    (67)  op(e2, all_4_2) = all_4_0
% 174.59/26.74    (68)   ~ (all_52_3 = all_52_5)
% 174.59/26.74    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.74    (70)  op(e2, e1) = all_52_13
% 174.59/26.74    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.74    (72)  all_58_8 = all_14_2
% 174.59/26.74    (73)  all_56_1 = all_52_3
% 174.59/26.74    (74)  op(e0, e2) = all_52_27
% 174.59/26.74    (75)  all_56_14 = all_52_29
% 174.59/26.74    (76)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.74    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.74    (78)   ~ (all_52_3 = all_52_27)
% 174.59/26.74    (79)   ~ (all_52_3 = all_4_2)
% 174.59/26.74    (80)  op(e0, e3) = all_52_25
% 174.59/26.74    (81)  op(e0, all_6_2) = all_6_1
% 174.59/26.74    (82)   ~ (all_52_9 = all_10_2)
% 174.59/26.74    (83)  op(e3, all_52_17) = all_52_16
% 174.59/26.74    (84)  all_52_10 = all_10_1
% 174.59/26.74    (85)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.74    (86)   ~ (all_52_13 = all_14_2)
% 174.59/26.74    (87)   ~ (e3 = e0)
% 174.59/26.74    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.74    (89)  op(all_14_1, all_14_2) = e2
% 174.59/26.74    (90)   ~ (all_52_9 = all_52_13)
% 174.59/26.74    (91)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.74    (92)  op(e0, all_52_23) = all_52_22
% 174.59/26.74    (93)   ~ (all_52_15 = all_52_23)
% 174.59/26.74    (94)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.59/26.74    (95)  op(all_10_1, all_10_2) = all_10_0
% 174.59/26.74    (96)   ~ (all_52_5 = all_52_29)
% 174.59/26.74    (97)  all_56_2 = all_52_5
% 174.59/26.74    (98)  op(e1, e0) = all_52_23
% 174.59/26.74    (99)  all_56_12 = all_52_25
% 174.59/26.74    (100)  all_58_13 = all_52_27
% 174.59/26.74    (101)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.74    (102)   ~ (all_52_9 = all_52_17)
% 174.59/26.74    (103)  all_58_6 = all_52_17
% 174.59/26.74    (104)   ~ (all_52_3 = all_52_7)
% 174.59/26.74    (105)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.59/26.74    (106)  op(e2, all_52_19) = all_52_18
% 174.59/26.74    (107)   ~ (e1 = e0)
% 174.59/26.74    (108)  all_56_0 = all_4_2
% 174.59/26.74    (109)  all_58_11 = all_52_23
% 174.59/26.74    (110)   ~ (all_52_3 = all_52_19)
% 174.59/26.74    (111)   ~ (all_52_7 = all_52_15)
% 174.59/26.74    (112)  op(e0, all_52_15) = all_52_14
% 174.59/26.74    (113)   ~ (all_52_29 = all_14_2)
% 174.59/26.74    (114)   ~ (all_4_0 = e1)
% 174.59/26.74    (115)   ~ (all_52_19 = all_10_2)
% 174.59/26.74    (116)  op(e3, all_4_2) = e2
% 174.59/26.74    (117)   ~ (all_52_23 = all_6_2)
% 174.59/26.74    (118)   ~ (all_52_29 = all_6_2)
% 174.59/26.74    (119)  all_58_2 = all_52_9
% 174.59/26.74    (120)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.59/26.74    (121)  op(e3, e1) = all_52_5
% 174.59/26.74    (122)   ~ (e2 = e1)
% 174.59/26.74    (123)  all_56_10 = all_14_2
% 174.59/26.74    (124)   ~ (all_52_25 = all_6_2)
% 174.59/26.74    (125)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.74    (126)  op(e1, e3) = all_52_17
% 174.59/26.74    (127)   ~ (all_52_25 = all_4_2)
% 174.59/26.75    (128)  op(e3, e0) = all_52_7
% 174.59/26.75    (129)  op(e3, e3) = all_4_2
% 174.59/26.75    (130)  all_56_8 = all_52_17
% 174.59/26.75    (131)   ~ (all_52_17 = all_4_2)
% 174.59/26.75    (132)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.75             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.75    (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.75           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.75           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.75           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.75    (134)   ~ (all_52_25 = all_52_27)
% 174.59/26.75    (135)   ~ (all_52_27 = all_6_2)
% 174.59/26.75    (136)   ~ (all_52_7 = all_6_2)
% 174.59/26.75    (137)   ~ (all_10_0 = e3)
% 174.59/26.75    (138)   ~ (all_52_15 = all_10_2)
% 174.59/26.75    (139)   ~ (all_52_7 = all_52_23)
% 174.59/26.75    (140)   ~ (all_52_13 = all_10_2)
% 174.59/26.75    (141)  op(e2, all_52_27) = all_52_26
% 174.59/26.75    (142)  all_52_20 = all_14_1
% 174.59/26.75    (143)   ~ (all_52_17 = all_52_19)
% 174.59/26.75    (144)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.75    (145)  all_52_30 = all_6_1
% 174.59/26.75    (146)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.59/26.75    (147)  op(e1, all_14_2) = all_14_1
% 174.59/26.75    (148)  all_58_9 = all_52_7
% 174.59/26.75    (149)   ~ (e2 = e0)
% 174.59/26.75    (150)  all_58_12 = all_52_25
% 174.59/26.75    (151)   ~ (all_10_0 = e1)
% 174.59/26.75    (152)  all_56_6 = all_52_13
% 174.59/26.75    (153)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.75    (154)   ~ (all_52_9 = all_52_15)
% 174.59/26.75    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.75    (156)   ~ (e3 = e2)
% 174.59/26.75    (157)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.75    (158)   ~ (all_52_19 = all_14_2)
% 174.59/26.75    (159)  op(e2, e3) = all_52_9
% 174.59/26.75    (160)  all_56_13 = all_52_27
% 174.59/26.75  
% 174.59/26.75  Begin of proof
% 174.59/26.75  | 
% 174.59/26.75  | BETA: splitting (133) gives:
% 174.59/26.75  | 
% 174.59/26.75  | Case 1:
% 174.59/26.75  | | 
% 174.59/26.75  | |   (161)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.75  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.59/26.75  | | 
% 174.59/26.75  | | BETA: splitting (161) gives:
% 174.59/26.75  | | 
% 174.59/26.75  | | Case 1:
% 174.59/26.75  | | | 
% 174.59/26.75  | | |   (162)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REF_CLOSE: (56), (156), (162) are inconsistent by sub-proof #124.
% 174.59/26.75  | | | 
% 174.59/26.75  | | Case 2:
% 174.59/26.75  | | | 
% 174.59/26.75  | | |   (163)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 174.59/26.75  | | | 
% 174.59/26.75  | | | ALPHA: (163) implies:
% 174.59/26.75  | | |   (164)  all_52_14 = e0
% 174.59/26.75  | | |   (165)  all_52_12 = e1
% 174.59/26.75  | | |   (166)  all_52_10 = e2
% 174.59/26.75  | | |   (167)  all_52_8 = e3
% 174.59/26.75  | | | 
% 174.59/26.75  | | | COMBINE_EQS: (84), (166) imply:
% 174.59/26.75  | | |   (168)  all_10_1 = e2
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REDUCE: (95), (168) imply:
% 174.59/26.75  | | |   (169)  op(e2, all_10_2) = all_10_0
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REDUCE: (19), (167) imply:
% 174.59/26.75  | | |   (170)  op(e3, all_52_9) = e3
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REDUCE: (8), (168) imply:
% 174.59/26.75  | | |   (171)  op(e2, all_10_2) = e2
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REDUCE: (55), (165) imply:
% 174.59/26.75  | | |   (172)  op(e1, all_52_13) = e1
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REDUCE: (112), (164) imply:
% 174.59/26.75  | | |   (173)  op(e0, all_52_15) = e0
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11), (12), (13), (15),
% 174.59/26.75  | | |            (16), (17), (18), (20), (22), (23), (24), (25), (26), (28),
% 174.59/26.75  | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 174.59/26.75  | | |            (39), (40), (41), (42), (43), (44), (45), (47), (48), (49),
% 174.59/26.75  | | |            (50), (51), (52), (53), (54), (57), (58), (59), (60), (61),
% 174.59/26.75  | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 174.59/26.75  | | |            (72), (73), (75), (77), (78), (79), (80), (81), (83), (86),
% 174.59/26.75  | | |            (87), (90), (92), (93), (94), (96), (100), (101), (102), (103),
% 174.59/26.75  | | |            (104), (105), (106), (107), (108), (109), (110), (111), (113),
% 174.59/26.75  | | |            (114), (115), (116), (117), (118), (119), (120), (121), (123),
% 174.59/26.75  | | |            (124), (126), (127), (128), (129), (130), (131), (132), (134),
% 174.59/26.75  | | |            (135), (136), (137), (139), (140), (141), (143), (144), (146),
% 174.59/26.75  | | |            (147), (148), (150), (151), (152), (153), (154), (155), (158),
% 174.59/26.75  | | |            (159), (160), (169), (170), (171), (172), (173) are
% 174.59/26.75  | | |            inconsistent by sub-proof #98.
% 174.59/26.75  | | | 
% 174.59/26.75  | | End of split
% 174.59/26.75  | | 
% 174.59/26.75  | Case 2:
% 174.59/26.75  | | 
% 174.59/26.75  | |   (174)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.59/26.75  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.59/26.75  | |            e0)
% 174.59/26.75  | | 
% 174.59/26.75  | | BETA: splitting (174) gives:
% 174.59/26.75  | | 
% 174.59/26.75  | | Case 1:
% 174.59/26.75  | | | 
% 174.59/26.75  | | |   (175)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.59/26.75  | | | 
% 174.59/26.75  | | | ALPHA: (175) implies:
% 174.59/26.75  | | |   (176)  all_52_20 = e1
% 174.59/26.75  | | | 
% 174.59/26.75  | | | COMBINE_EQS: (142), (176) imply:
% 174.59/26.75  | | |   (177)  all_14_1 = e1
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REF_CLOSE: (89), (122), (132), (147), (177) are inconsistent by sub-proof
% 174.59/26.75  | | |            #315.
% 174.59/26.75  | | | 
% 174.59/26.75  | | Case 2:
% 174.59/26.75  | | | 
% 174.59/26.75  | | |   (178)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.59/26.75  | | | 
% 174.59/26.75  | | | ALPHA: (178) implies:
% 174.59/26.75  | | |   (179)  all_52_30 = e0
% 174.59/26.75  | | |   (180)  all_52_28 = e1
% 174.59/26.75  | | |   (181)  all_52_26 = e2
% 174.59/26.75  | | |   (182)  all_52_24 = e3
% 174.59/26.75  | | | 
% 174.59/26.75  | | | COMBINE_EQS: (145), (179) imply:
% 174.59/26.75  | | |   (183)  all_6_1 = e0
% 174.59/26.75  | | | 
% 174.59/26.75  | | | REF_CLOSE: (4), (5), (7), (10), (12), (13), (14), (15), (18), (19), (20),
% 174.59/26.75  | | |            (21), (22), (23), (24), (25), (27), (28), (30), (31), (32),
% 174.59/26.75  | | |            (33), (34), (35), (36), (39), (40), (41), (43), (44), (45),
% 174.59/26.75  | | |            (46), (47), (49), (50), (51), (52), (54), (57), (58), (60),
% 174.59/26.75  | | |            (61), (62), (65), (66), (67), (68), (69), (70), (71), (72),
% 174.59/26.75  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 174.59/26.75  | | |            (83), (85), (87), (88), (90), (91), (96), (97), (98), (99),
% 174.59/26.75  | | |            (100), (101), (102), (103), (104), (107), (108), (109), (111),
% 174.59/26.75  | | |            (114), (115), (116), (118), (119), (121), (122), (124), (125),
% 174.59/26.75  | | |            (126), (127), (128), (129), (131), (132), (134), (135), (136),
% 174.59/26.75  | | |            (138), (139), (141), (143), (144), (148), (149), (150), (153),
% 174.59/26.75  | | |            (154), (155), (156), (157), (159), (160), (180), (181), (182),
% 174.59/26.75  | | |            (183) are inconsistent by sub-proof #88.
% 174.59/26.75  | | | 
% 174.59/26.75  | | End of split
% 174.59/26.75  | | 
% 174.59/26.75  | End of split
% 174.59/26.75  | 
% 174.59/26.75  End of proof
% 174.59/26.75  
% 174.59/26.75  Sub-proof #57 shows that the following formulas are inconsistent:
% 174.59/26.75  ----------------------------------------------------------------
% 174.59/26.75    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.75    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.75    (3)   ~ (all_52_17 = all_52_23)
% 174.59/26.75    (4)  op(e2, all_10_2) = all_10_1
% 174.59/26.75    (5)  op(all_10_1, all_10_2) = e1
% 174.59/26.75    (6)  op(e3, e2) = all_52_3
% 174.59/26.75    (7)   ~ (all_52_9 = all_52_25)
% 174.59/26.75    (8)  op(e3, all_52_25) = all_52_24
% 174.59/26.75    (9)   ~ (all_52_19 = all_52_23)
% 174.59/26.75    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.75    (11)  op(e3, all_52_9) = all_52_8
% 174.59/26.75    (12)   ~ (all_52_3 = all_10_2)
% 174.59/26.75    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.75    (14)  all_58_5 = all_52_13
% 174.59/26.75    (15)   ~ (all_52_25 = all_52_29)
% 174.59/26.75    (16)  all_56_15 = all_6_2
% 174.59/26.75    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.75    (18)  all_58_3 = all_10_2
% 174.59/26.75    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.75    (20)  all_58_15 = all_6_2
% 174.59/26.75    (21)   ~ (all_52_9 = all_4_2)
% 174.59/26.75    (22)   ~ (all_52_5 = all_52_7)
% 174.59/26.75    (23)  all_58_10 = all_52_15
% 174.59/26.75    (24)   ~ (all_52_5 = all_4_2)
% 174.59/26.75    (25)  all_58_7 = all_52_19
% 174.59/26.75    (26)   ~ (all_52_17 = all_52_25)
% 174.59/26.75    (27)  op(e0, e1) = all_52_29
% 174.59/26.75    (28)  all_58_4 = all_52_5
% 174.59/26.75    (29)   ~ (e3 = e1)
% 174.59/26.75    (30)   ~ (all_52_27 = all_52_29)
% 174.59/26.75    (31)   ~ (all_52_17 = all_14_2)
% 174.59/26.75    (32)  op(e3, all_4_2) = all_4_1
% 174.59/26.75    (33)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.75    (34)   ~ (all_52_7 = all_4_2)
% 174.59/26.75    (35)  all_58_1 = all_52_3
% 174.59/26.75    (36)   ~ (all_52_13 = all_52_15)
% 174.59/26.75    (37)  all_58_0 = all_4_2
% 174.59/26.75    (38)  all_52_0 = e2
% 174.59/26.75    (39)  op(e1, all_52_29) = all_52_28
% 174.59/26.75    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.75    (41)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.75    (42)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.75    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.75    (44)  all_58_14 = all_52_29
% 174.59/26.75    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.75    (46)  op(e2, all_4_2) = all_4_0
% 174.59/26.75    (47)   ~ (all_52_3 = all_52_5)
% 174.59/26.75    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.75    (49)  op(e2, e1) = all_52_13
% 174.59/26.75    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.75    (51)  all_58_8 = all_14_2
% 174.59/26.75    (52)  all_56_1 = all_52_3
% 174.59/26.75    (53)  op(e0, e2) = all_52_27
% 174.59/26.75    (54)  all_56_14 = all_52_29
% 174.59/26.75    (55)  op(all_14_1, all_14_2) = e3
% 174.59/26.75    (56)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.75    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.75    (58)   ~ (all_52_3 = all_52_27)
% 174.59/26.75    (59)   ~ (all_52_3 = all_4_2)
% 174.59/26.75    (60)  op(e0, e3) = all_52_25
% 174.59/26.75    (61)  op(e0, all_6_2) = all_6_1
% 174.59/26.75    (62)   ~ (all_52_9 = all_10_2)
% 174.59/26.75    (63)  op(e3, all_52_17) = all_52_16
% 174.59/26.75    (64)  all_52_10 = all_10_1
% 174.59/26.75    (65)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.75    (66)   ~ (e3 = e0)
% 174.59/26.75    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.75    (68)   ~ (all_52_9 = all_52_13)
% 174.59/26.75    (69)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.75    (70)   ~ (all_52_5 = all_52_29)
% 174.59/26.75    (71)  all_56_2 = all_52_5
% 174.59/26.75    (72)  op(e1, e0) = all_52_23
% 174.59/26.75    (73)  all_56_12 = all_52_25
% 174.59/26.75    (74)  all_58_13 = all_52_27
% 174.59/26.75    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.75    (76)   ~ (all_52_9 = all_52_17)
% 174.59/26.75    (77)  all_58_6 = all_52_17
% 174.59/26.75    (78)   ~ (all_52_3 = all_52_7)
% 174.59/26.75    (79)   ~ (e1 = e0)
% 174.59/26.75    (80)  all_56_0 = all_4_2
% 174.59/26.75    (81)  all_58_11 = all_52_23
% 174.59/26.75    (82)   ~ (all_52_7 = all_52_15)
% 174.59/26.75    (83)   ~ (all_4_0 = e1)
% 174.59/26.75    (84)   ~ (all_52_19 = all_10_2)
% 174.59/26.75    (85)   ~ (all_58_15 = e0)
% 174.59/26.75    (86)  op(e3, all_4_2) = e2
% 174.59/26.75    (87)   ~ (all_52_29 = all_6_2)
% 174.59/26.75    (88)  all_58_2 = all_52_9
% 174.59/26.75    (89)  op(e3, e1) = all_52_5
% 174.59/26.75    (90)   ~ (e2 = e1)
% 174.59/26.75    (91)   ~ (all_52_25 = all_6_2)
% 174.59/26.75    (92)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.75    (93)  op(e1, e3) = all_52_17
% 174.59/26.75    (94)   ~ (all_52_25 = all_4_2)
% 174.59/26.75    (95)  op(e3, e0) = all_52_7
% 174.59/26.75    (96)  op(e3, e3) = all_4_2
% 174.59/26.75    (97)   ~ (all_52_17 = all_4_2)
% 174.59/26.75    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.75    (99)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.75          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.75          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.75          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.75    (100)   ~ (all_52_25 = all_52_27)
% 174.59/26.75    (101)   ~ (all_52_27 = all_6_2)
% 174.59/26.75    (102)   ~ (all_52_7 = all_6_2)
% 174.59/26.75    (103)   ~ (all_52_15 = all_10_2)
% 174.59/26.75    (104)   ~ (all_52_7 = all_52_23)
% 174.59/26.75    (105)  op(e2, all_52_27) = all_52_26
% 174.59/26.75    (106)  all_52_20 = all_14_1
% 174.59/26.75    (107)   ~ (all_52_17 = all_52_19)
% 174.59/26.75    (108)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.75    (109)  all_52_30 = all_6_1
% 174.59/26.75    (110)  op(e1, all_14_2) = all_14_1
% 174.59/26.75    (111)  all_58_9 = all_52_7
% 174.59/26.75    (112)   ~ (e2 = e0)
% 174.59/26.75    (113)  all_58_12 = all_52_25
% 174.59/26.75    (114)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.59/26.75             all_58_13 = e0 | all_58_14 = e0)
% 174.59/26.75    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.75    (116)   ~ (all_52_9 = all_52_15)
% 174.59/26.75    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.75    (118)   ~ (e3 = e2)
% 174.59/26.75    (119)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.75    (120)  op(e2, e3) = all_52_9
% 174.59/26.75    (121)  all_56_13 = all_52_27
% 174.59/26.75  
% 174.59/26.75  Begin of proof
% 174.59/26.75  | 
% 174.59/26.75  | ALPHA: (114) implies:
% 174.59/26.75  |   (122)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.75  |   (123)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.75  | 
% 174.59/26.75  | REDUCE: (20), (85) imply:
% 174.59/26.75  |   (124)   ~ (all_6_2 = e0)
% 174.59/26.75  | 
% 174.59/26.75  | BETA: splitting (99) gives:
% 174.59/26.75  | 
% 174.59/26.75  | Case 1:
% 174.59/26.75  | | 
% 174.59/26.75  | |   (125)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.75  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.59/26.75  | | 
% 174.59/26.75  | | REF_CLOSE: (4), (5), (38), (64), (90), (98), (118), (125) are inconsistent
% 174.59/26.75  | |            by sub-proof #69.
% 174.59/26.75  | | 
% 174.59/26.75  | Case 2:
% 174.59/26.75  | | 
% 174.59/26.75  | |   (126)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.59/26.75  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.59/26.75  | |            e0)
% 174.59/26.75  | | 
% 174.59/26.75  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 174.59/26.75  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 174.59/26.75  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 174.59/26.75  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 174.59/26.75  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 174.59/26.75  | |            (60), (61), (62), (63), (65), (66), (67), (68), (69), (70), (71),
% 174.59/26.75  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 174.59/26.75  | |            (83), (84), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 174.59/26.75  | |            (95), (96), (97), (98), (100), (101), (102), (103), (104), (105),
% 174.59/26.75  | |            (106), (107), (108), (109), (110), (111), (112), (113), (115),
% 174.59/26.75  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 174.59/26.75  | |            (126) are inconsistent by sub-proof #58.
% 174.59/26.75  | | 
% 174.59/26.75  | End of split
% 174.59/26.75  | 
% 174.59/26.75  End of proof
% 174.59/26.75  
% 174.59/26.75  Sub-proof #58 shows that the following formulas are inconsistent:
% 174.59/26.75  ----------------------------------------------------------------
% 174.59/26.75    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.75    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.75    (3)   ~ (all_52_17 = all_52_23)
% 174.59/26.75    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.75    (5)  op(e3, e2) = all_52_3
% 174.59/26.75    (6)   ~ (all_52_9 = all_52_25)
% 174.59/26.75    (7)  op(e3, all_52_25) = all_52_24
% 174.59/26.75    (8)   ~ (all_52_19 = all_52_23)
% 174.59/26.75    (9)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.75    (10)  op(e3, all_52_9) = all_52_8
% 174.59/26.75    (11)   ~ (all_52_3 = all_10_2)
% 174.59/26.75    (12)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.75    (13)  all_58_5 = all_52_13
% 174.59/26.75    (14)   ~ (all_6_2 = e0)
% 174.59/26.75    (15)   ~ (all_52_25 = all_52_29)
% 174.59/26.75    (16)  all_56_15 = all_6_2
% 174.59/26.75    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.75    (18)  all_58_3 = all_10_2
% 174.59/26.75    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.75    (20)  all_58_15 = all_6_2
% 174.59/26.75    (21)   ~ (all_52_9 = all_4_2)
% 174.59/26.75    (22)   ~ (all_52_5 = all_52_7)
% 174.59/26.75    (23)  all_58_10 = all_52_15
% 174.59/26.75    (24)   ~ (all_52_5 = all_4_2)
% 174.59/26.75    (25)  all_58_7 = all_52_19
% 174.59/26.75    (26)   ~ (all_52_17 = all_52_25)
% 174.59/26.75    (27)  op(e0, e1) = all_52_29
% 174.59/26.75    (28)  all_58_4 = all_52_5
% 174.59/26.75    (29)   ~ (e3 = e1)
% 174.59/26.75    (30)   ~ (all_52_27 = all_52_29)
% 174.59/26.75    (31)   ~ (all_52_17 = all_14_2)
% 174.59/26.75    (32)  op(e3, all_4_2) = all_4_1
% 174.59/26.75    (33)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.75    (34)   ~ (all_52_7 = all_4_2)
% 174.59/26.75    (35)  all_58_1 = all_52_3
% 174.59/26.75    (36)   ~ (all_52_13 = all_52_15)
% 174.59/26.75    (37)  all_58_0 = all_4_2
% 174.59/26.75    (38)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.75    (39)  op(e1, all_52_29) = all_52_28
% 174.59/26.75    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.75    (41)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.75    (42)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.75    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.75    (44)  all_58_14 = all_52_29
% 174.59/26.75    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.75    (46)  op(e2, all_4_2) = all_4_0
% 174.59/26.75    (47)   ~ (all_52_3 = all_52_5)
% 174.59/26.75    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.75    (49)  op(e2, e1) = all_52_13
% 174.59/26.75    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.75    (51)  all_58_8 = all_14_2
% 174.59/26.75    (52)  all_56_1 = all_52_3
% 174.59/26.75    (53)  op(e0, e2) = all_52_27
% 174.59/26.75    (54)  all_56_14 = all_52_29
% 174.59/26.75    (55)  op(all_14_1, all_14_2) = e3
% 174.59/26.75    (56)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.75    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.75    (58)   ~ (all_52_3 = all_52_27)
% 174.59/26.75    (59)   ~ (all_52_3 = all_4_2)
% 174.59/26.75    (60)  op(e0, e3) = all_52_25
% 174.59/26.75    (61)  op(e0, all_6_2) = all_6_1
% 174.59/26.75    (62)   ~ (all_52_9 = all_10_2)
% 174.59/26.75    (63)  op(e3, all_52_17) = all_52_16
% 174.59/26.75    (64)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.75    (65)   ~ (e3 = e0)
% 174.59/26.75    (66)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.75    (67)   ~ (all_52_9 = all_52_13)
% 174.59/26.75    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.75    (69)   ~ (all_52_5 = all_52_29)
% 174.59/26.75    (70)  all_56_2 = all_52_5
% 174.59/26.75    (71)  op(e1, e0) = all_52_23
% 174.59/26.75    (72)  all_56_12 = all_52_25
% 174.59/26.75    (73)  all_58_13 = all_52_27
% 174.59/26.75    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.75    (75)   ~ (all_52_9 = all_52_17)
% 174.59/26.75    (76)  all_58_6 = all_52_17
% 174.59/26.75    (77)   ~ (all_52_3 = all_52_7)
% 174.59/26.75    (78)   ~ (e1 = e0)
% 174.59/26.75    (79)  all_56_0 = all_4_2
% 174.59/26.75    (80)  all_58_11 = all_52_23
% 174.59/26.75    (81)   ~ (all_52_7 = all_52_15)
% 174.59/26.75    (82)   ~ (all_4_0 = e1)
% 174.59/26.75    (83)   ~ (all_52_19 = all_10_2)
% 174.59/26.75    (84)  op(e3, all_4_2) = e2
% 174.59/26.75    (85)   ~ (all_52_29 = all_6_2)
% 174.59/26.75    (86)  all_58_2 = all_52_9
% 174.59/26.75    (87)  op(e3, e1) = all_52_5
% 174.59/26.75    (88)   ~ (e2 = e1)
% 174.59/26.75    (89)   ~ (all_52_25 = all_6_2)
% 174.59/26.75    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.75    (91)  op(e1, e3) = all_52_17
% 174.59/26.75    (92)   ~ (all_52_25 = all_4_2)
% 174.59/26.75    (93)  op(e3, e0) = all_52_7
% 174.59/26.75    (94)  op(e3, e3) = all_4_2
% 174.59/26.75    (95)   ~ (all_52_17 = all_4_2)
% 174.59/26.75    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.75    (97)   ~ (all_52_25 = all_52_27)
% 174.59/26.75    (98)   ~ (all_52_27 = all_6_2)
% 174.59/26.75    (99)   ~ (all_52_7 = all_6_2)
% 174.59/26.75    (100)   ~ (all_52_15 = all_10_2)
% 174.59/26.75    (101)   ~ (all_52_7 = all_52_23)
% 174.59/26.75    (102)  op(e2, all_52_27) = all_52_26
% 174.59/26.75    (103)  all_52_20 = all_14_1
% 174.59/26.75    (104)   ~ (all_52_17 = all_52_19)
% 174.59/26.75    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.75    (106)  all_52_30 = all_6_1
% 174.59/26.75    (107)  op(e1, all_14_2) = all_14_1
% 174.59/26.75    (108)  all_58_9 = all_52_7
% 174.59/26.75    (109)   ~ (e2 = e0)
% 174.59/26.75    (110)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.75           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.75    (111)  all_58_12 = all_52_25
% 174.59/26.75    (112)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.75    (113)   ~ (all_52_9 = all_52_15)
% 174.59/26.75    (114)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.75    (115)   ~ (e3 = e2)
% 174.59/26.75    (116)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.75    (117)  op(e2, e3) = all_52_9
% 174.59/26.75    (118)  all_56_13 = all_52_27
% 174.59/26.75  
% 174.59/26.75  Begin of proof
% 174.59/26.75  | 
% 174.59/26.75  | BETA: splitting (110) gives:
% 174.59/26.75  | 
% 174.59/26.75  | Case 1:
% 174.59/26.75  | | 
% 174.59/26.75  | |   (119)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.59/26.75  | | 
% 174.59/26.75  | | ALPHA: (119) implies:
% 174.59/26.75  | |   (120)  all_52_20 = e1
% 174.59/26.75  | | 
% 174.59/26.75  | | COMBINE_EQS: (103), (120) imply:
% 174.59/26.75  | |   (121)  all_14_1 = e1
% 174.59/26.75  | | 
% 174.59/26.75  | | REF_CLOSE: (29), (55), (96), (107), (121) are inconsistent by sub-proof
% 174.59/26.75  | |            #344.
% 174.59/26.75  | | 
% 174.59/26.75  | Case 2:
% 174.59/26.75  | | 
% 174.59/26.75  | |   (122)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.59/26.75  | | 
% 174.59/26.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.59/26.76  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.76  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.59/26.76  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.59/26.76  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (56), (57),
% 174.59/26.76  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.59/26.76  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 174.59/26.76  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 174.59/26.76  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 174.59/26.76  | |            (101), (102), (104), (105), (106), (108), (109), (111), (112),
% 174.59/26.76  | |            (113), (114), (115), (116), (117), (118), (122) are inconsistent
% 174.59/26.76  | |            by sub-proof #87.
% 174.59/26.76  | | 
% 174.59/26.76  | End of split
% 174.59/26.76  | 
% 174.59/26.76  End of proof
% 174.59/26.76  
% 174.59/26.76  Sub-proof #59 shows that the following formulas are inconsistent:
% 174.59/26.76  ----------------------------------------------------------------
% 174.59/26.76    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.76    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.76    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.59/26.76    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.76    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.76    (6)   ~ (all_52_27 = all_10_2)
% 174.59/26.76    (7)   ~ (all_52_17 = all_52_23)
% 174.59/26.76    (8)   ~ (all_6_0 = e3)
% 174.59/26.76    (9)  op(e2, all_10_2) = all_10_1
% 174.59/26.76    (10)   ~ (all_52_13 = all_52_29)
% 174.59/26.76    (11)  all_42_1 = e2
% 174.59/26.76    (12)  all_56_3 = all_52_7
% 174.59/26.76    (13)  op(e3, e2) = all_52_3
% 174.59/26.76    (14)   ~ (all_52_9 = all_52_25)
% 174.59/26.76    (15)  op(e3, all_52_25) = all_52_24
% 174.59/26.76    (16)   ~ (all_52_19 = all_52_23)
% 174.59/26.76    (17)  all_56_11 = all_52_23
% 174.59/26.76    (18)  op(e1, e2) = all_52_19
% 174.59/26.76    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.76    (20)  op(e3, all_52_9) = all_52_8
% 174.59/26.76    (21)   ~ (all_52_3 = all_10_2)
% 174.59/26.76    (22)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.76    (23)  all_58_5 = all_52_13
% 174.59/26.76    (24)   ~ (all_52_25 = all_52_29)
% 174.59/26.76    (25)  all_56_15 = all_6_2
% 174.59/26.76    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.76    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.76    (28)  all_58_3 = all_10_2
% 174.59/26.76    (29)  all_56_9 = all_52_19
% 174.59/26.76    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.76    (31)  all_58_15 = all_6_2
% 174.59/26.76    (32)   ~ (all_52_9 = all_4_2)
% 174.59/26.76    (33)   ~ (all_52_5 = all_52_7)
% 174.59/26.76    (34)  all_58_10 = all_52_15
% 174.59/26.76    (35)   ~ (all_52_5 = all_4_2)
% 174.59/26.76    (36)  all_58_7 = all_52_19
% 174.59/26.76    (37)  all_56_4 = all_52_9
% 174.59/26.76    (38)   ~ (all_52_15 = all_6_2)
% 174.59/26.76    (39)   ~ (all_52_17 = all_52_25)
% 174.59/26.76    (40)  op(e0, e1) = all_52_29
% 174.59/26.76    (41)  all_58_4 = all_52_5
% 174.59/26.76    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.76    (43)   ~ (e3 = e1)
% 174.59/26.76    (44)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.59/26.76    (45)   ~ (all_52_27 = all_52_29)
% 174.59/26.76    (46)   ~ (all_52_17 = all_14_2)
% 174.59/26.76    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.76    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.76    (49)   ~ (all_52_7 = all_4_2)
% 174.59/26.76    (50)  all_58_1 = all_52_3
% 174.59/26.76    (51)   ~ (all_52_13 = all_52_15)
% 174.59/26.76    (52)  all_58_0 = all_4_2
% 174.59/26.76    (53)  op(e1, all_52_13) = all_52_12
% 174.59/26.76    (54)  all_52_0 = e2
% 174.59/26.76    (55)  op(e0, e0) = all_6_2
% 174.59/26.76    (56)  op(e1, all_52_29) = all_52_28
% 174.59/26.76    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.76    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.76    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.76    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.76    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.76    (62)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.59/26.76    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.59/26.76    (64)  all_58_14 = all_52_29
% 174.59/26.76    (65)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.76    (66)  op(e2, all_4_2) = all_4_0
% 174.59/26.76    (67)   ~ (all_52_3 = all_52_5)
% 174.59/26.76    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.76    (69)  op(e2, e1) = all_52_13
% 174.59/26.76    (70)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.76    (71)  all_58_8 = all_14_2
% 174.59/26.76    (72)  all_56_1 = all_52_3
% 174.59/26.76    (73)  op(e0, e2) = all_52_27
% 174.59/26.76    (74)  all_56_14 = all_52_29
% 174.59/26.76    (75)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.76    (76)   ~ (all_52_5 = all_14_2)
% 174.59/26.76    (77)   ~ (all_52_3 = all_52_27)
% 174.59/26.76    (78)   ~ (all_52_3 = all_4_2)
% 174.59/26.76    (79)  op(all_6_1, all_6_2) = all_6_0
% 174.59/26.76    (80)  op(e0, e3) = all_52_25
% 174.59/26.76    (81)  op(e0, all_6_2) = all_6_1
% 174.59/26.76    (82)   ~ (all_52_9 = all_10_2)
% 174.59/26.76    (83)  op(e3, all_52_17) = all_52_16
% 174.59/26.76    (84)  all_52_10 = all_10_1
% 174.59/26.76    (85)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.76    (86)   ~ (all_52_13 = all_14_2)
% 174.59/26.76    (87)   ~ (e3 = e0)
% 174.59/26.76    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.76    (89)   ~ (all_52_9 = all_52_13)
% 174.59/26.76    (90)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.76    (91)  op(e0, all_52_23) = all_52_22
% 174.59/26.76    (92)   ~ (all_52_15 = all_52_23)
% 174.59/26.76    (93)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.59/26.76    (94)  op(all_10_1, all_10_2) = all_10_0
% 174.59/26.76    (95)   ~ (all_52_5 = all_52_29)
% 174.59/26.76    (96)  op(e1, e0) = all_52_23
% 174.59/26.76    (97)  all_56_12 = all_52_25
% 174.59/26.76    (98)  all_58_13 = all_52_27
% 174.59/26.76    (99)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.76    (100)  all_56_5 = all_10_2
% 174.59/26.76    (101)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.59/26.76    (102)   ~ (all_52_9 = all_52_17)
% 174.59/26.76    (103)  all_58_6 = all_52_17
% 174.59/26.76    (104)   ~ (all_52_3 = all_52_7)
% 174.59/26.76    (105)  all_42_0 = e1
% 174.59/26.76    (106)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.59/26.76    (107)  op(e2, all_52_19) = all_52_18
% 174.59/26.76    (108)   ~ (e1 = e0)
% 174.59/26.76    (109)  all_56_0 = all_4_2
% 174.59/26.76    (110)  all_58_11 = all_52_23
% 174.59/26.76    (111)   ~ (all_52_3 = all_52_19)
% 174.59/26.76    (112)   ~ (all_52_7 = all_52_15)
% 174.59/26.76    (113)  all_42_0 = all_4_0
% 174.59/26.76    (114)  op(e0, all_52_15) = all_52_14
% 174.59/26.76    (115)   ~ (all_52_29 = all_14_2)
% 174.59/26.76    (116)   ~ (all_52_19 = all_10_2)
% 174.59/26.76    (117)  op(e3, all_4_2) = e2
% 174.59/26.76    (118)   ~ (all_52_23 = all_6_2)
% 174.59/26.76    (119)   ~ (all_6_0 = e2)
% 174.59/26.76    (120)   ~ (all_52_29 = all_6_2)
% 174.59/26.76    (121)  all_58_2 = all_52_9
% 174.59/26.76    (122)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.59/26.76    (123)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.59/26.76    (124)  op(e3, e1) = all_52_5
% 174.59/26.76    (125)   ~ (e2 = e1)
% 174.59/26.76    (126)  all_56_10 = all_14_2
% 174.59/26.76    (127)   ~ (all_52_25 = all_6_2)
% 174.59/26.76    (128)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.59/26.76    (129)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.76    (130)  op(e1, e1) = all_14_2
% 174.59/26.76    (131)  op(e1, e3) = all_52_17
% 174.59/26.76    (132)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.59/26.76    (133)   ~ (all_52_25 = all_4_2)
% 174.59/26.76    (134)  op(e3, e0) = all_52_7
% 174.59/26.76    (135)  op(e3, e3) = all_4_2
% 174.59/26.76    (136)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.59/26.76             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.59/26.76    (137)  all_56_8 = all_52_17
% 174.59/26.76    (138)   ~ (all_52_17 = all_4_2)
% 174.59/26.76    (139)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.76             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.76    (140)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.76           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.76           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.76           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.76    (141)   ~ (all_52_25 = all_52_27)
% 174.59/26.76    (142)   ~ (all_52_27 = all_6_2)
% 174.59/26.76    (143)   ~ (all_52_7 = all_6_2)
% 174.59/26.76    (144)   ~ (all_10_0 = e3)
% 174.59/26.76    (145)   ~ (all_52_15 = all_10_2)
% 174.59/26.76    (146)   ~ (all_52_19 = all_52_27)
% 174.59/26.76    (147)  all_42_2 = all_4_2
% 174.59/26.76    (148)  all_56_7 = all_52_15
% 174.59/26.76    (149)   ~ (all_52_7 = all_52_23)
% 174.59/26.76    (150)   ~ (all_52_13 = all_10_2)
% 174.59/26.76    (151)   ~ (all_6_0 = e1)
% 174.59/26.76    (152)  op(e2, all_52_27) = all_52_26
% 174.59/26.76    (153)  all_52_20 = all_14_1
% 174.59/26.76    (154)   ~ (all_52_17 = all_52_19)
% 174.59/26.76    (155)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.76    (156)  all_52_30 = all_6_1
% 174.59/26.76    (157)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.59/26.76    (158)  op(e1, all_14_2) = all_14_1
% 174.59/26.76    (159)  all_58_9 = all_52_7
% 174.59/26.76    (160)   ~ (e2 = e0)
% 174.59/26.76    (161)  all_58_12 = all_52_25
% 174.59/26.76    (162)   ~ (all_10_0 = e1)
% 174.59/26.76    (163)  all_56_6 = all_52_13
% 174.59/26.76    (164)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.76    (165)   ~ (all_52_9 = all_52_15)
% 174.59/26.76    (166)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.76    (167)   ~ (e3 = e2)
% 174.59/26.76    (168)   ~ (all_52_19 = all_14_2)
% 174.59/26.76    (169)  op(e2, e3) = all_52_9
% 174.59/26.76    (170)  all_56_13 = all_52_27
% 174.59/26.76  
% 174.59/26.76  Begin of proof
% 174.59/26.76  | 
% 174.59/26.76  | COMBINE_EQS: (105), (113) imply:
% 174.59/26.76  |   (171)  all_4_0 = e1
% 174.59/26.76  | 
% 174.59/26.76  | REDUCE: (66), (171) imply:
% 174.59/26.76  |   (172)  op(e2, all_4_2) = e1
% 174.59/26.76  | 
% 174.59/26.76  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.59/26.76  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.76  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.59/26.76  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.59/26.76  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.59/26.76  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (67), (68),
% 174.59/26.76  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 174.59/26.76  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 174.59/26.76  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.59/26.76  |            (102), (103), (104), (106), (107), (108), (109), (110), (111),
% 174.59/26.76  |            (112), (114), (115), (116), (117), (118), (119), (120), (121),
% 174.59/26.76  |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 174.59/26.76  |            (131), (132), (133), (134), (135), (136), (137), (138), (139),
% 174.59/26.76  |            (140), (141), (142), (143), (144), (145), (146), (147), (148),
% 174.59/26.76  |            (149), (150), (151), (152), (153), (154), (155), (156), (157),
% 174.59/26.76  |            (158), (159), (160), (161), (162), (163), (164), (165), (166),
% 174.59/26.76  |            (167), (168), (169), (170), (172) are inconsistent by sub-proof
% 174.59/26.76  |            #72.
% 174.59/26.76  | 
% 174.59/26.76  End of proof
% 174.59/26.76  
% 174.59/26.76  Sub-proof #60 shows that the following formulas are inconsistent:
% 174.59/26.76  ----------------------------------------------------------------
% 174.59/26.76    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.76    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.76    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.59/26.76    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.76    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.76    (6)   ~ (all_52_27 = all_10_2)
% 174.59/26.76    (7)   ~ (all_52_17 = all_52_23)
% 174.59/26.76    (8)  op(e2, all_10_2) = all_10_1
% 174.59/26.76    (9)   ~ (all_52_13 = all_52_29)
% 174.59/26.76    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.76    (11)  all_56_3 = all_52_7
% 174.59/26.76    (12)  op(e3, e2) = all_52_3
% 174.59/26.76    (13)   ~ (all_52_9 = all_52_25)
% 174.59/26.76    (14)  op(e3, all_52_25) = all_52_24
% 174.59/26.76    (15)   ~ (all_52_19 = all_52_23)
% 174.59/26.76    (16)  all_56_11 = all_52_23
% 174.59/26.76    (17)  op(e1, e2) = all_52_19
% 174.59/26.76    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.76    (19)  op(e3, all_52_9) = all_52_8
% 174.59/26.76    (20)   ~ (all_52_3 = all_10_2)
% 174.59/26.76    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.76    (22)  all_58_5 = all_52_13
% 174.59/26.76    (23)   ~ (all_6_2 = e0)
% 174.59/26.76    (24)   ~ (all_52_25 = all_52_29)
% 174.59/26.76    (25)  all_56_15 = all_6_2
% 174.59/26.76    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.76    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.76    (28)  all_58_3 = all_10_2
% 174.59/26.76    (29)  all_56_9 = all_52_19
% 174.59/26.76    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.76    (31)  all_58_15 = all_6_2
% 174.59/26.76    (32)   ~ (all_52_9 = all_4_2)
% 174.59/26.76    (33)   ~ (all_52_5 = all_52_7)
% 174.59/26.76    (34)  all_58_10 = all_52_15
% 174.59/26.76    (35)   ~ (all_52_5 = all_4_2)
% 174.59/26.76    (36)  all_58_7 = all_52_19
% 174.59/26.76    (37)  all_56_4 = all_52_9
% 174.59/26.76    (38)   ~ (all_52_15 = all_6_2)
% 174.59/26.76    (39)   ~ (all_52_17 = all_52_25)
% 174.59/26.76    (40)  op(e0, e1) = all_52_29
% 174.59/26.76    (41)  all_58_4 = all_52_5
% 174.59/26.76    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.76    (43)   ~ (e3 = e1)
% 174.59/26.76    (44)   ~ (all_52_27 = all_52_29)
% 174.59/26.76    (45)   ~ (all_52_17 = all_14_2)
% 174.59/26.76    (46)  op(e3, all_4_2) = all_4_1
% 174.59/26.76    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.76    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.76    (49)   ~ (all_52_7 = all_4_2)
% 174.59/26.76    (50)  all_58_1 = all_52_3
% 174.59/26.76    (51)   ~ (all_52_13 = all_52_15)
% 174.59/26.76    (52)  all_58_0 = all_4_2
% 174.59/26.76    (53)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.59/26.76    (54)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.76    (55)  op(e1, all_52_13) = all_52_12
% 174.59/26.76    (56)  all_52_0 = e2
% 174.59/26.76    (57)  op(e1, all_52_29) = all_52_28
% 174.59/26.76    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.76    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.76    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.76    (61)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.76    (62)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.76    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.59/26.76    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.59/26.76    (65)  all_58_14 = all_52_29
% 174.59/26.76    (66)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.76    (67)  op(e2, all_4_2) = all_4_0
% 174.59/26.76    (68)   ~ (all_52_3 = all_52_5)
% 174.59/26.76    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.76    (70)  op(e2, e1) = all_52_13
% 174.59/26.76    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.76    (72)  all_58_8 = all_14_2
% 174.59/26.76    (73)  all_56_1 = all_52_3
% 174.59/26.76    (74)  op(e0, e2) = all_52_27
% 174.59/26.76    (75)  all_56_14 = all_52_29
% 174.59/26.76    (76)  op(all_14_1, all_14_2) = e3
% 174.59/26.76    (77)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.76    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.76    (79)   ~ (all_52_3 = all_52_27)
% 174.59/26.76    (80)   ~ (all_52_3 = all_4_2)
% 174.59/26.76    (81)  op(e0, e3) = all_52_25
% 174.59/26.76    (82)  op(e0, all_6_2) = all_6_1
% 174.59/26.76    (83)   ~ (all_52_9 = all_10_2)
% 174.59/26.76    (84)  op(e3, all_52_17) = all_52_16
% 174.59/26.76    (85)  all_52_10 = all_10_1
% 174.59/26.76    (86)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.76    (87)   ~ (all_52_13 = all_14_2)
% 174.59/26.76    (88)   ~ (e3 = e0)
% 174.59/26.76    (89)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.76    (90)   ~ (all_52_9 = all_52_13)
% 174.59/26.76    (91)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.76    (92)  op(e0, all_52_23) = all_52_22
% 174.59/26.76    (93)   ~ (all_52_15 = all_52_23)
% 174.59/26.76    (94)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.59/26.76    (95)  op(all_10_1, all_10_2) = all_10_0
% 174.59/26.76    (96)   ~ (all_52_5 = all_52_29)
% 174.59/26.76    (97)  all_56_2 = all_52_5
% 174.59/26.76    (98)  op(e1, e0) = all_52_23
% 174.59/26.76    (99)  all_56_12 = all_52_25
% 174.59/26.76    (100)  all_58_13 = all_52_27
% 174.59/26.76    (101)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.76    (102)   ~ (all_52_9 = all_52_17)
% 174.59/26.76    (103)  all_58_6 = all_52_17
% 174.59/26.76    (104)   ~ (all_52_3 = all_52_7)
% 174.59/26.76    (105)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.59/26.76    (106)  op(e2, all_52_19) = all_52_18
% 174.59/26.76    (107)   ~ (e1 = e0)
% 174.59/26.76    (108)  all_56_0 = all_4_2
% 174.59/26.76    (109)  all_58_11 = all_52_23
% 174.59/26.76    (110)   ~ (all_52_3 = all_52_19)
% 174.59/26.76    (111)   ~ (all_52_7 = all_52_15)
% 174.59/26.76    (112)  op(e0, all_52_15) = all_52_14
% 174.59/26.76    (113)   ~ (all_52_29 = all_14_2)
% 174.59/26.76    (114)   ~ (all_4_0 = e1)
% 174.59/26.76    (115)   ~ (all_52_19 = all_10_2)
% 174.59/26.76    (116)  op(e3, all_4_2) = e2
% 174.59/26.76    (117)   ~ (all_52_23 = all_6_2)
% 174.59/26.76    (118)   ~ (all_52_29 = all_6_2)
% 174.59/26.76    (119)  all_58_2 = all_52_9
% 174.59/26.76    (120)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.59/26.76    (121)  op(e3, e1) = all_52_5
% 174.59/26.76    (122)   ~ (e2 = e1)
% 174.59/26.76    (123)  all_56_10 = all_14_2
% 174.59/26.76    (124)   ~ (all_52_25 = all_6_2)
% 174.59/26.76    (125)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.76    (126)  op(e1, e3) = all_52_17
% 174.59/26.76    (127)   ~ (all_52_25 = all_4_2)
% 174.59/26.76    (128)  op(e3, e0) = all_52_7
% 174.59/26.76    (129)  op(e3, e3) = all_4_2
% 174.59/26.76    (130)  all_56_8 = all_52_17
% 174.59/26.76    (131)   ~ (all_52_17 = all_4_2)
% 174.59/26.76    (132)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.76             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.76    (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.76           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.76           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.76           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.76    (134)   ~ (all_52_25 = all_52_27)
% 174.59/26.76    (135)   ~ (all_52_27 = all_6_2)
% 174.59/26.76    (136)   ~ (all_52_7 = all_6_2)
% 174.59/26.76    (137)   ~ (all_10_0 = e3)
% 174.59/26.76    (138)   ~ (all_52_15 = all_10_2)
% 174.59/26.76    (139)   ~ (all_52_7 = all_52_23)
% 174.59/26.76    (140)   ~ (all_52_13 = all_10_2)
% 174.59/26.76    (141)  op(e2, all_52_27) = all_52_26
% 174.59/26.76    (142)  all_52_20 = all_14_1
% 174.59/26.76    (143)   ~ (all_52_17 = all_52_19)
% 174.59/26.76    (144)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.76    (145)  all_52_30 = all_6_1
% 174.59/26.76    (146)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.59/26.76    (147)  op(e1, all_14_2) = all_14_1
% 174.59/26.76    (148)  all_58_9 = all_52_7
% 174.59/26.76    (149)   ~ (e2 = e0)
% 174.59/26.76    (150)  all_58_12 = all_52_25
% 174.59/26.76    (151)   ~ (all_10_0 = e1)
% 174.59/26.76    (152)  all_56_6 = all_52_13
% 174.59/26.76    (153)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.76    (154)   ~ (all_52_9 = all_52_15)
% 174.59/26.76    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.76    (156)   ~ (e3 = e2)
% 174.59/26.76    (157)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.76    (158)   ~ (all_52_19 = all_14_2)
% 174.59/26.76    (159)  op(e2, e3) = all_52_9
% 174.59/26.76    (160)  all_56_13 = all_52_27
% 174.59/26.76  
% 174.59/26.76  Begin of proof
% 174.59/26.76  | 
% 174.59/26.76  | BETA: splitting (133) gives:
% 174.59/26.76  | 
% 174.59/26.76  | Case 1:
% 174.59/26.76  | | 
% 174.59/26.76  | |   (161)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.76  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.59/26.76  | | 
% 174.59/26.76  | | BETA: splitting (161) gives:
% 174.59/26.76  | | 
% 174.59/26.76  | | Case 1:
% 174.59/26.76  | | | 
% 174.59/26.76  | | |   (162)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.59/26.76  | | | 
% 174.59/26.76  | | | REF_CLOSE: (56), (156), (162) are inconsistent by sub-proof #124.
% 174.59/26.76  | | | 
% 174.59/26.76  | | Case 2:
% 174.59/26.76  | | | 
% 174.59/26.76  | | |   (163)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 174.59/26.76  | | | 
% 174.59/26.76  | | | ALPHA: (163) implies:
% 174.59/26.76  | | |   (164)  all_52_14 = e0
% 174.59/26.76  | | |   (165)  all_52_12 = e1
% 174.59/26.76  | | |   (166)  all_52_10 = e2
% 174.59/26.76  | | |   (167)  all_52_8 = e3
% 174.59/26.76  | | | 
% 174.59/26.76  | | | COMBINE_EQS: (85), (166) imply:
% 174.59/26.76  | | |   (168)  all_10_1 = e2
% 174.59/26.76  | | | 
% 174.59/26.76  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 174.59/26.76  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 174.59/26.76  | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 174.59/26.76  | | |            (38), (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 174.59/26.76  | | |            (49), (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 174.59/26.76  | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 174.59/26.76  | | |            (70), (71), (72), (73), (75), (78), (79), (80), (81), (82),
% 174.59/26.76  | | |            (84), (87), (88), (90), (92), (93), (94), (95), (96), (100),
% 174.59/26.76  | | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 174.59/26.76  | | |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 174.59/26.76  | | |            (119), (120), (121), (123), (124), (126), (127), (128), (129),
% 174.59/26.76  | | |            (130), (131), (132), (134), (135), (136), (137), (139), (140),
% 174.59/26.76  | | |            (141), (143), (144), (146), (147), (148), (150), (151), (152),
% 174.59/26.76  | | |            (153), (154), (155), (158), (159), (160), (164), (165), (167),
% 174.59/26.76  | | |            (168) are inconsistent by sub-proof #97.
% 174.59/26.76  | | | 
% 174.59/26.76  | | End of split
% 174.59/26.76  | | 
% 174.59/26.76  | Case 2:
% 174.59/26.76  | | 
% 174.59/26.76  | |   (169)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.59/26.76  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.59/26.76  | |            e0)
% 174.59/26.76  | | 
% 174.59/26.76  | | BETA: splitting (169) gives:
% 174.59/26.76  | | 
% 174.59/26.76  | | Case 1:
% 174.59/26.76  | | | 
% 174.59/26.76  | | |   (170)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.59/26.76  | | | 
% 174.59/26.76  | | | REF_CLOSE: (43), (76), (132), (142), (147), (170) are inconsistent by
% 174.59/26.76  | | |            sub-proof #343.
% 174.59/26.76  | | | 
% 174.59/26.76  | | Case 2:
% 174.59/26.76  | | | 
% 174.59/26.76  | | |   (171)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.59/26.76  | | | 
% 174.59/26.76  | | | REF_CLOSE: (4), (5), (7), (10), (12), (13), (14), (15), (18), (19), (20),
% 174.59/26.76  | | |            (21), (22), (23), (24), (25), (27), (28), (30), (31), (32),
% 174.59/26.76  | | |            (33), (34), (35), (36), (39), (40), (41), (43), (44), (45),
% 174.59/26.76  | | |            (46), (47), (49), (50), (51), (52), (54), (57), (58), (60),
% 174.59/26.76  | | |            (61), (62), (65), (66), (67), (68), (69), (70), (71), (72),
% 174.59/26.76  | | |            (73), (74), (75), (77), (78), (79), (80), (81), (82), (83),
% 174.59/26.76  | | |            (84), (86), (88), (89), (90), (91), (96), (97), (98), (99),
% 174.59/26.76  | | |            (100), (101), (102), (103), (104), (107), (108), (109), (111),
% 174.59/26.76  | | |            (114), (115), (116), (118), (119), (121), (122), (124), (125),
% 174.59/26.76  | | |            (126), (127), (128), (129), (131), (132), (134), (135), (136),
% 174.59/26.76  | | |            (138), (139), (141), (143), (144), (145), (148), (149), (150),
% 174.59/26.76  | | |            (153), (154), (155), (156), (157), (159), (160), (171) are
% 174.59/26.76  | | |            inconsistent by sub-proof #87.
% 174.59/26.76  | | | 
% 174.59/26.76  | | End of split
% 174.59/26.76  | | 
% 174.59/26.76  | End of split
% 174.59/26.76  | 
% 174.59/26.76  End of proof
% 174.59/26.76  
% 174.59/26.76  Sub-proof #61 shows that the following formulas are inconsistent:
% 174.59/26.76  ----------------------------------------------------------------
% 174.59/26.77    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.77    (2)   ~ (all_52_17 = all_52_23)
% 174.59/26.77    (3)  op(e2, all_10_2) = all_10_1
% 174.59/26.77    (4)  all_42_1 = e2
% 174.59/26.77    (5)  op(all_10_1, all_10_2) = e1
% 174.59/26.77    (6)  op(e3, e2) = all_52_3
% 174.59/26.77    (7)   ~ (all_52_9 = all_52_25)
% 174.59/26.77    (8)  op(e1, e2) = all_52_19
% 174.59/26.77    (9)  all_58_5 = all_52_13
% 174.59/26.77    (10)   ~ (all_52_25 = all_52_29)
% 174.59/26.77    (11)  all_56_15 = all_6_2
% 174.59/26.77    (12)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.77    (13)  all_58_3 = all_10_2
% 174.59/26.77    (14)  all_56_9 = all_52_19
% 174.59/26.77    (15)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.77    (16)  all_58_15 = all_6_2
% 174.59/26.77    (17)  op(e2, all_4_2) = e1
% 174.59/26.77    (18)   ~ (all_52_9 = all_4_2)
% 174.59/26.77    (19)   ~ (all_52_5 = all_52_7)
% 174.59/26.77    (20)  all_58_10 = all_52_15
% 174.59/26.77    (21)   ~ (all_52_5 = all_4_2)
% 174.59/26.77    (22)  all_58_7 = all_52_19
% 174.59/26.77    (23)   ~ (all_52_17 = all_52_25)
% 174.59/26.77    (24)  all_58_4 = all_52_5
% 174.59/26.77    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.77    (26)   ~ (e3 = e1)
% 174.59/26.77    (27)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.59/26.77    (28)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.77    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.77    (30)   ~ (all_52_7 = all_4_2)
% 174.59/26.77    (31)  all_58_1 = all_52_3
% 174.59/26.77    (32)  all_58_0 = all_4_2
% 174.59/26.77    (33)  all_52_0 = e2
% 174.59/26.77    (34)  op(e0, e0) = all_6_2
% 174.59/26.77    (35)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.77    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.77    (37)  all_58_14 = all_52_29
% 174.59/26.77    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.77    (39)  op(e2, e1) = all_52_13
% 174.59/26.77    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.77    (41)  all_58_8 = all_14_2
% 174.59/26.77    (42)   ~ (all_52_5 = all_14_2)
% 174.59/26.77    (43)   ~ (all_52_3 = all_4_2)
% 174.59/26.77    (44)  op(e0, e3) = all_52_25
% 174.59/26.77    (45)  op(e0, all_6_2) = all_6_1
% 174.59/26.77    (46)  op(e3, all_52_17) = all_52_16
% 174.59/26.77    (47)  all_52_10 = all_10_1
% 174.59/26.77    (48)   ~ (all_52_13 = all_14_2)
% 174.59/26.77    (49)   ~ (e3 = e0)
% 174.59/26.77    (50)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.77    (51)   ~ (all_52_9 = all_52_13)
% 174.59/26.77    (52)  op(e0, all_52_23) = all_52_22
% 174.59/26.77    (53)   ~ (all_52_15 = all_52_23)
% 174.59/26.77    (54)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.59/26.77    (55)  op(e1, e0) = all_52_23
% 174.59/26.77    (56)  all_58_13 = all_52_27
% 174.59/26.77    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.77    (58)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.59/26.77    (59)   ~ (all_52_9 = all_52_17)
% 174.59/26.77    (60)  all_58_6 = all_52_17
% 174.59/26.77    (61)  op(e2, all_52_19) = all_52_18
% 174.59/26.77    (62)   ~ (e1 = e0)
% 174.59/26.77    (63)  all_56_0 = all_4_2
% 174.59/26.77    (64)  all_58_11 = all_52_23
% 174.59/26.77    (65)   ~ (all_52_3 = all_52_19)
% 174.59/26.77    (66)   ~ (all_52_7 = all_52_15)
% 174.59/26.77    (67)  op(e3, all_4_2) = e2
% 174.59/26.77    (68)   ~ (all_52_23 = all_6_2)
% 174.59/26.77    (69)  all_58_2 = all_52_9
% 174.59/26.77    (70)  op(e3, e1) = all_52_5
% 174.59/26.77    (71)   ~ (e2 = e1)
% 174.59/26.77    (72)  all_56_10 = all_14_2
% 174.59/26.77    (73)   ~ (all_52_25 = all_6_2)
% 174.59/26.77    (74)  op(e1, e3) = all_52_17
% 174.59/26.77    (75)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.59/26.77    (76)   ~ (all_52_25 = all_4_2)
% 174.59/26.77    (77)  op(e3, e0) = all_52_7
% 174.59/26.77    (78)  op(e3, e3) = all_4_2
% 174.59/26.77    (79)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.59/26.77            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.59/26.77    (80)   ~ (all_52_17 = all_4_2)
% 174.59/26.77    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.77    (82)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.77          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.77          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.77          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.77    (83)   ~ (all_52_25 = all_52_27)
% 174.59/26.77    (84)   ~ (all_52_15 = all_10_2)
% 174.59/26.77    (85)  all_42_2 = all_4_2
% 174.59/26.77    (86)  all_56_7 = all_52_15
% 174.59/26.77    (87)   ~ (all_52_7 = all_52_23)
% 174.59/26.77    (88)  all_52_20 = all_14_1
% 174.59/26.77    (89)   ~ (all_52_17 = all_52_19)
% 174.59/26.77    (90)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.77    (91)  all_52_30 = all_6_1
% 174.59/26.77    (92)  op(e1, all_14_2) = all_14_1
% 174.59/26.77    (93)  all_58_9 = all_52_7
% 174.59/26.77    (94)   ~ (e2 = e0)
% 174.59/26.77    (95)  all_58_12 = all_52_25
% 174.59/26.77    (96)  op(all_6_1, all_6_2) = e3
% 174.59/26.77    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.77    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.77    (99)   ~ (e3 = e2)
% 174.59/26.77    (100)   ~ (all_52_19 = all_14_2)
% 174.59/26.77    (101)  op(e2, e3) = all_52_9
% 174.59/26.77  
% 174.59/26.77  Begin of proof
% 174.59/26.77  | 
% 174.59/26.77  | BETA: splitting (27) gives:
% 174.59/26.77  | 
% 174.59/26.77  | Case 1:
% 174.59/26.77  | | 
% 174.59/26.77  | |   (102)   ~ (all_42_1 = e2)
% 174.59/26.77  | | 
% 174.59/26.77  | | REDUCE: (4), (102) imply:
% 174.59/26.77  | |   (103)  $false
% 174.59/26.77  | | 
% 174.59/26.77  | | CLOSE: (103) is inconsistent.
% 174.59/26.77  | | 
% 174.59/26.77  | Case 2:
% 174.59/26.77  | | 
% 174.59/26.77  | |   (104)   ~ (all_42_2 = e0)
% 174.59/26.77  | | 
% 174.59/26.77  | | REDUCE: (85), (104) imply:
% 174.59/26.77  | |   (105)   ~ (all_4_2 = e0)
% 174.59/26.77  | | 
% 174.59/26.77  | | BETA: splitting (79) gives:
% 174.59/26.77  | | 
% 174.59/26.77  | | Case 1:
% 174.59/26.77  | | | 
% 174.59/26.77  | | |   (106)  all_58_15 = e0
% 174.59/26.77  | | | 
% 174.59/26.77  | | | REF_CLOSE: (16), (34), (45), (49), (81), (96), (106) are inconsistent by
% 174.59/26.77  | | |            sub-proof #510.
% 174.59/26.77  | | | 
% 174.59/26.77  | | Case 2:
% 174.59/26.77  | | | 
% 174.59/26.77  | | |   (107)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 174.59/26.77  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 174.59/26.77  | | | 
% 174.59/26.77  | | | ALPHA: (107) implies:
% 174.59/26.77  | | |   (108)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.77  | | | 
% 174.59/26.77  | | | BETA: splitting (82) gives:
% 174.59/26.77  | | | 
% 174.59/26.77  | | | Case 1:
% 174.59/26.77  | | | | 
% 174.59/26.77  | | | |   (109)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.59/26.77  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.59/26.77  | | | |            = e0)
% 174.59/26.77  | | | | 
% 174.59/26.77  | | | | REF_CLOSE: (3), (5), (33), (47), (71), (81), (99), (109) are
% 174.59/26.77  | | | |            inconsistent by sub-proof #69.
% 174.59/26.77  | | | | 
% 174.59/26.77  | | | Case 2:
% 174.59/26.77  | | | | 
% 174.59/26.77  | | | |   (110)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.59/26.77  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.59/26.77  | | | |            all_52_30 = e0)
% 174.59/26.77  | | | | 
% 174.59/26.77  | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 174.59/26.77  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.59/26.77  | | | |            (25), (26), (28), (29), (30), (31), (32), (35), (36), (37),
% 174.59/26.77  | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (48),
% 174.59/26.77  | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 174.59/26.77  | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.59/26.77  | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.59/26.77  | | | |            (80), (81), (83), (84), (86), (87), (88), (89), (90), (91),
% 174.59/26.77  | | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 174.59/26.77  | | | |            (105), (108), (110) are inconsistent by sub-proof #62.
% 174.59/26.77  | | | | 
% 174.59/26.77  | | | End of split
% 174.59/26.77  | | | 
% 174.59/26.77  | | End of split
% 174.59/26.77  | | 
% 174.59/26.77  | End of split
% 174.59/26.77  | 
% 174.59/26.77  End of proof
% 174.59/26.77  
% 174.59/26.77  Sub-proof #62 shows that the following formulas are inconsistent:
% 174.59/26.77  ----------------------------------------------------------------
% 174.59/26.77    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.77    (2)   ~ (all_52_17 = all_52_23)
% 174.59/26.77    (3)  op(e3, e2) = all_52_3
% 174.59/26.77    (4)   ~ (all_52_9 = all_52_25)
% 174.59/26.77    (5)  op(e1, e2) = all_52_19
% 174.59/26.77    (6)  all_58_5 = all_52_13
% 174.59/26.77    (7)   ~ (all_52_25 = all_52_29)
% 174.59/26.77    (8)  all_56_15 = all_6_2
% 174.59/26.77    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.77    (10)  all_58_3 = all_10_2
% 174.59/26.77    (11)  all_56_9 = all_52_19
% 174.59/26.77    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.77    (13)  all_58_15 = all_6_2
% 174.59/26.77    (14)  op(e2, all_4_2) = e1
% 174.59/26.77    (15)   ~ (all_52_9 = all_4_2)
% 174.59/26.77    (16)   ~ (all_52_5 = all_52_7)
% 174.59/26.77    (17)  all_58_10 = all_52_15
% 174.59/26.77    (18)   ~ (all_52_5 = all_4_2)
% 174.59/26.77    (19)  all_58_7 = all_52_19
% 174.59/26.77    (20)   ~ (all_52_17 = all_52_25)
% 174.59/26.77    (21)  all_58_4 = all_52_5
% 174.59/26.77    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.77    (23)   ~ (e3 = e1)
% 174.59/26.77    (24)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.77    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.77    (26)   ~ (all_52_7 = all_4_2)
% 174.59/26.77    (27)  all_58_1 = all_52_3
% 174.59/26.77    (28)  all_58_0 = all_4_2
% 174.59/26.77    (29)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.77    (30)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.77    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.77    (32)  all_58_14 = all_52_29
% 174.59/26.77    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.77    (34)  op(e2, e1) = all_52_13
% 174.59/26.77    (35)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.77    (36)  all_58_8 = all_14_2
% 174.59/26.77    (37)   ~ (all_52_5 = all_14_2)
% 174.59/26.77    (38)   ~ (all_52_3 = all_4_2)
% 174.59/26.77    (39)  op(e0, e3) = all_52_25
% 174.59/26.77    (40)  op(e0, all_6_2) = all_6_1
% 174.59/26.77    (41)  op(e3, all_52_17) = all_52_16
% 174.59/26.77    (42)   ~ (all_52_13 = all_14_2)
% 174.59/26.77    (43)   ~ (e3 = e0)
% 174.59/26.77    (44)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.77    (45)   ~ (all_52_9 = all_52_13)
% 174.59/26.77    (46)  op(e0, all_52_23) = all_52_22
% 174.59/26.77    (47)   ~ (all_52_15 = all_52_23)
% 174.59/26.77    (48)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.59/26.77    (49)  op(e1, e0) = all_52_23
% 174.59/26.77    (50)  all_58_13 = all_52_27
% 174.59/26.77    (51)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.77    (52)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.59/26.77    (53)   ~ (all_52_9 = all_52_17)
% 174.59/26.77    (54)  all_58_6 = all_52_17
% 174.59/26.77    (55)  op(e2, all_52_19) = all_52_18
% 174.59/26.77    (56)   ~ (e1 = e0)
% 174.59/26.77    (57)  all_56_0 = all_4_2
% 174.59/26.77    (58)  all_58_11 = all_52_23
% 174.59/26.77    (59)   ~ (all_52_3 = all_52_19)
% 174.59/26.77    (60)   ~ (all_52_7 = all_52_15)
% 174.59/26.77    (61)  op(e3, all_4_2) = e2
% 174.59/26.77    (62)   ~ (all_52_23 = all_6_2)
% 174.59/26.77    (63)  all_58_2 = all_52_9
% 174.59/26.77    (64)  op(e3, e1) = all_52_5
% 174.59/26.77    (65)   ~ (e2 = e1)
% 174.59/26.77    (66)  all_56_10 = all_14_2
% 174.59/26.77    (67)   ~ (all_52_25 = all_6_2)
% 174.59/26.77    (68)  op(e1, e3) = all_52_17
% 174.59/26.77    (69)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.59/26.77    (70)   ~ (all_52_25 = all_4_2)
% 174.59/26.77    (71)  op(e3, e0) = all_52_7
% 174.59/26.77    (72)  op(e3, e3) = all_4_2
% 174.59/26.77    (73)   ~ (all_52_17 = all_4_2)
% 174.59/26.77    (74)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.77    (75)   ~ (all_52_25 = all_52_27)
% 174.59/26.77    (76)   ~ (all_52_15 = all_10_2)
% 174.59/26.77    (77)  all_56_7 = all_52_15
% 174.59/26.77    (78)   ~ (all_4_2 = e0)
% 174.59/26.77    (79)   ~ (all_52_7 = all_52_23)
% 174.59/26.77    (80)  all_52_20 = all_14_1
% 174.59/26.77    (81)   ~ (all_52_17 = all_52_19)
% 174.59/26.77    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.77    (83)  all_52_30 = all_6_1
% 174.59/26.77    (84)  op(e1, all_14_2) = all_14_1
% 174.59/26.77    (85)  all_58_9 = all_52_7
% 174.59/26.77    (86)   ~ (e2 = e0)
% 174.59/26.77    (87)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.77          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.77    (88)  all_58_12 = all_52_25
% 174.59/26.77    (89)  op(all_6_1, all_6_2) = e3
% 174.59/26.77    (90)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.77    (91)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.77    (92)   ~ (e3 = e2)
% 174.59/26.77    (93)   ~ (all_52_19 = all_14_2)
% 174.59/26.77    (94)  op(e2, e3) = all_52_9
% 174.59/26.77  
% 174.59/26.77  Begin of proof
% 174.59/26.77  | 
% 174.59/26.77  | BETA: splitting (87) gives:
% 174.59/26.77  | 
% 174.59/26.77  | Case 1:
% 174.59/26.77  | | 
% 174.59/26.77  | |   (95)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.59/26.77  | | 
% 174.59/26.77  | | ALPHA: (95) implies:
% 174.59/26.77  | |   (96)  all_52_22 = e0
% 174.59/26.77  | |   (97)  all_52_20 = e1
% 174.59/26.77  | |   (98)  all_52_18 = e2
% 174.59/26.77  | |   (99)  all_52_16 = e3
% 174.59/26.77  | | 
% 174.59/26.77  | | COMBINE_EQS: (80), (97) imply:
% 174.59/26.77  | |   (100)  all_14_1 = e1
% 174.59/26.77  | | 
% 174.59/26.77  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.59/26.77  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.77  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.59/26.77  | |            (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 174.59/26.77  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 174.59/26.77  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 174.59/26.77  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 174.59/26.77  | |            (81), (82), (84), (85), (86), (88), (90), (91), (92), (93), (94),
% 174.59/26.77  | |            (96), (98), (99), (100) are inconsistent by sub-proof #77.
% 174.59/26.77  | | 
% 174.59/26.77  | Case 2:
% 174.59/26.77  | | 
% 174.59/26.77  | |   (101)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.59/26.77  | | 
% 174.59/26.77  | | REF_CLOSE: (40), (43), (74), (83), (89), (101) are inconsistent by sub-proof
% 174.59/26.77  | |            #501.
% 174.59/26.77  | | 
% 174.59/26.77  | End of split
% 174.59/26.77  | 
% 174.59/26.77  End of proof
% 174.59/26.77  
% 174.59/26.77  Sub-proof #63 shows that the following formulas are inconsistent:
% 174.59/26.77  ----------------------------------------------------------------
% 174.59/26.77    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.77    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.77    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.59/26.77    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.77    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.77    (6)   ~ (all_52_27 = all_10_2)
% 174.59/26.77    (7)   ~ (all_52_17 = all_52_23)
% 174.59/26.77    (8)  op(e2, all_10_2) = all_10_1
% 174.59/26.77    (9)   ~ (all_52_13 = all_52_29)
% 174.59/26.77    (10)  all_56_3 = all_52_7
% 174.59/26.77    (11)  op(all_10_1, all_10_2) = e1
% 174.59/26.77    (12)  op(e3, e2) = all_52_3
% 174.59/26.77    (13)   ~ (all_52_9 = all_52_25)
% 174.59/26.77    (14)  op(e3, all_52_25) = all_52_24
% 174.59/26.77    (15)   ~ (all_52_19 = all_52_23)
% 174.59/26.77    (16)  op(e1, e2) = all_52_19
% 174.59/26.77    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.59/26.77    (18)  op(e3, all_52_9) = all_52_8
% 174.59/26.77    (19)   ~ (all_52_3 = all_10_2)
% 174.59/26.77    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.77    (21)  all_58_5 = all_52_13
% 174.59/26.77    (22)   ~ (all_52_25 = all_52_29)
% 174.59/26.77    (23)  all_56_15 = all_6_2
% 174.59/26.77    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.77    (25)  op(all_14_1, all_14_2) = all_14_0
% 174.59/26.77    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.77    (27)  all_58_3 = all_10_2
% 174.59/26.77    (28)  all_56_9 = all_52_19
% 174.59/26.77    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.77    (30)  all_58_15 = all_6_2
% 174.59/26.77    (31)   ~ (all_52_9 = all_4_2)
% 174.59/26.77    (32)   ~ (all_52_5 = all_52_7)
% 174.59/26.77    (33)  all_58_10 = all_52_15
% 174.59/26.77    (34)   ~ (all_52_5 = all_4_2)
% 174.59/26.77    (35)  all_58_7 = all_52_19
% 174.59/26.77    (36)   ~ (all_52_17 = all_52_25)
% 174.59/26.77    (37)  op(e0, e1) = all_52_29
% 174.59/26.77    (38)  all_58_4 = all_52_5
% 174.59/26.77    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.77    (40)   ~ (e3 = e1)
% 174.59/26.77    (41)   ~ (all_52_27 = all_52_29)
% 174.59/26.77    (42)   ~ (all_52_17 = all_14_2)
% 174.59/26.77    (43)  op(e3, all_4_2) = all_4_1
% 174.59/26.77    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.77    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.77    (46)   ~ (all_52_7 = all_4_2)
% 174.59/26.77    (47)  all_58_1 = all_52_3
% 174.59/26.77    (48)   ~ (all_52_13 = all_52_15)
% 174.59/26.77    (49)  all_58_0 = all_4_2
% 174.59/26.77    (50)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.59/26.77    (51)  all_52_0 = e2
% 174.59/26.77    (52)  op(e1, all_52_29) = all_52_28
% 174.59/26.77    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.77    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.77    (55)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.77    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.77    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.77    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.59/26.77    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.59/26.77    (60)  all_58_14 = all_52_29
% 174.59/26.77    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.77    (62)  op(e2, all_4_2) = all_4_0
% 174.59/26.77    (63)   ~ (all_52_3 = all_52_5)
% 174.59/26.77    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.77    (65)  op(e2, e1) = all_52_13
% 174.59/26.77    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.77    (67)  all_58_8 = all_14_2
% 174.59/26.77    (68)  all_56_1 = all_52_3
% 174.59/26.77    (69)  op(e0, e2) = all_52_27
% 174.59/26.77    (70)  all_56_14 = all_52_29
% 174.59/26.77    (71)   ~ (all_14_0 = e3)
% 174.59/26.77    (72)  op(all_4_1, all_4_2) = all_4_0
% 174.59/26.77    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.77    (74)   ~ (all_52_5 = all_14_2)
% 174.59/26.77    (75)   ~ (all_52_3 = all_52_27)
% 174.59/26.77    (76)   ~ (all_52_3 = all_4_2)
% 174.59/26.77    (77)  op(e0, e3) = all_52_25
% 174.59/26.77    (78)  op(e0, all_6_2) = all_6_1
% 174.59/26.77    (79)   ~ (all_52_9 = all_10_2)
% 174.59/26.77    (80)  op(e3, all_52_17) = all_52_16
% 174.59/26.77    (81)  all_52_10 = all_10_1
% 174.59/26.77    (82)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.77    (83)   ~ (all_52_13 = all_14_2)
% 174.59/26.77    (84)   ~ (e3 = e0)
% 174.59/26.77    (85)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.77    (86)   ~ (all_52_9 = all_52_13)
% 174.59/26.77    (87)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.77    (88)  op(e0, all_52_23) = all_52_22
% 174.59/26.77    (89)   ~ (all_52_15 = all_52_23)
% 174.59/26.77    (90)   ~ (all_52_5 = all_52_29)
% 174.59/26.77    (91)  all_56_2 = all_52_5
% 174.59/26.77    (92)  op(e1, e0) = all_52_23
% 174.59/26.77    (93)  all_56_12 = all_52_25
% 174.59/26.77    (94)  all_58_13 = all_52_27
% 174.59/26.77    (95)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.77    (96)  all_56_5 = all_10_2
% 174.59/26.77    (97)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.59/26.77    (98)   ~ (all_52_9 = all_52_17)
% 174.59/26.77    (99)   ~ (all_14_0 = e2)
% 174.59/26.77    (100)  all_58_6 = all_52_17
% 174.59/26.77    (101)   ~ (all_52_3 = all_52_7)
% 174.59/26.77    (102)  op(e2, all_52_19) = all_52_18
% 174.59/26.77    (103)   ~ (e1 = e0)
% 174.59/26.77    (104)  all_56_0 = all_4_2
% 174.59/26.77    (105)  all_58_11 = all_52_23
% 174.59/26.77    (106)   ~ (all_52_3 = all_52_19)
% 174.59/26.77    (107)   ~ (all_52_7 = all_52_15)
% 174.59/26.77    (108)   ~ (all_4_0 = e1)
% 174.59/26.77    (109)   ~ (all_52_19 = all_10_2)
% 174.59/26.77    (110)   ~ (all_58_15 = e0)
% 174.59/26.77    (111)  op(e3, all_4_2) = e2
% 174.59/26.77    (112)   ~ (all_52_23 = all_6_2)
% 174.59/26.77    (113)   ~ (all_52_29 = all_6_2)
% 174.59/26.77    (114)  all_58_2 = all_52_9
% 174.59/26.77    (115)  op(e3, e1) = all_52_5
% 174.59/26.77    (116)   ~ (e2 = e1)
% 174.59/26.77    (117)   ~ (all_52_25 = all_6_2)
% 174.59/26.77    (118)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.59/26.77    (119)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.77    (120)  op(e1, e3) = all_52_17
% 174.59/26.77    (121)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.59/26.77    (122)   ~ (all_52_25 = all_4_2)
% 174.59/26.77    (123)  op(e3, e0) = all_52_7
% 174.59/26.77    (124)  op(e3, e3) = all_4_2
% 174.59/26.77    (125)   ~ (all_10_1 = e3)
% 174.59/26.77    (126)  all_56_8 = all_52_17
% 174.59/26.77    (127)   ~ (all_52_17 = all_4_2)
% 174.59/26.77    (128)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.77             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.77    (129)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.77           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.77           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.77           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.77    (130)   ~ (all_52_25 = all_52_27)
% 174.59/26.77    (131)   ~ (all_52_27 = all_6_2)
% 174.59/26.77    (132)   ~ (all_52_7 = all_6_2)
% 174.59/26.77    (133)   ~ (all_52_15 = all_10_2)
% 174.59/26.77    (134)   ~ (all_52_19 = all_52_27)
% 174.59/26.77    (135)  all_56_7 = all_52_15
% 174.59/26.77    (136)   ~ (all_52_7 = all_52_23)
% 174.59/26.77    (137)   ~ (all_52_13 = all_10_2)
% 174.59/26.77    (138)  op(e2, all_52_27) = all_52_26
% 174.59/26.77    (139)  all_52_20 = all_14_1
% 174.59/26.77    (140)   ~ (all_52_17 = all_52_19)
% 174.59/26.77    (141)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.77    (142)  all_52_30 = all_6_1
% 174.59/26.77    (143)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.59/26.77    (144)  op(e1, all_14_2) = all_14_1
% 174.59/26.77    (145)  all_58_9 = all_52_7
% 174.59/26.77    (146)   ~ (e2 = e0)
% 174.59/26.77    (147)  all_58_12 = all_52_25
% 174.59/26.77    (148)  all_56_6 = all_52_13
% 174.59/26.77    (149)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.59/26.77             all_58_13 = e0 | all_58_14 = e0)
% 174.59/26.77    (150)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.77    (151)   ~ (all_52_9 = all_52_15)
% 174.59/26.77    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.77    (153)   ~ (e3 = e2)
% 174.59/26.77    (154)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.59/26.77    (155)   ~ (all_52_19 = all_14_2)
% 174.59/26.77    (156)  op(e2, e3) = all_52_9
% 174.59/26.77    (157)  all_56_13 = all_52_27
% 174.59/26.77  
% 174.59/26.77  Begin of proof
% 174.59/26.77  | 
% 174.59/26.77  | ALPHA: (149) implies:
% 174.59/26.77  |   (158)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.78  |   (159)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.78  | 
% 174.59/26.78  | REDUCE: (30), (110) imply:
% 174.59/26.78  |   (160)   ~ (all_6_2 = e0)
% 174.59/26.78  | 
% 174.59/26.78  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.59/26.78  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.59/26.78  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.59/26.78  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.59/26.78  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.59/26.78  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.59/26.78  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.59/26.78  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 174.59/26.78  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 174.59/26.78  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 174.59/26.78  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 174.59/26.78  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 174.59/26.78  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 174.59/26.78  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 174.59/26.78  |            (147), (148), (150), (151), (152), (153), (154), (155), (156),
% 174.59/26.78  |            (157), (158), (159), (160) are inconsistent by sub-proof #68.
% 174.59/26.78  | 
% 174.59/26.78  End of proof
% 174.59/26.78  
% 174.59/26.78  Sub-proof #64 shows that the following formulas are inconsistent:
% 174.59/26.78  ----------------------------------------------------------------
% 174.59/26.78    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.78    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.78    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.59/26.78    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.59/26.78    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.78    (6)   ~ (all_52_27 = all_10_2)
% 174.59/26.78    (7)   ~ (all_52_17 = all_52_23)
% 174.59/26.78    (8)   ~ (all_6_0 = e3)
% 174.59/26.78    (9)  op(e2, all_10_2) = all_10_1
% 174.59/26.78    (10)   ~ (all_52_13 = all_52_29)
% 174.59/26.78    (11)  all_42_1 = e2
% 174.59/26.78    (12)  all_56_3 = all_52_7
% 174.59/26.78    (13)  op(all_10_1, all_10_2) = e1
% 174.59/26.78    (14)  op(e3, e2) = all_52_3
% 174.59/26.78    (15)   ~ (all_52_9 = all_52_25)
% 174.59/26.78    (16)  op(e3, all_52_25) = all_52_24
% 174.59/26.78    (17)   ~ (all_52_19 = all_52_23)
% 174.59/26.78    (18)  all_56_11 = all_52_23
% 174.59/26.78    (19)  op(e1, e2) = all_52_19
% 174.59/26.78    (20)  op(e3, all_52_9) = all_52_8
% 174.59/26.78    (21)   ~ (all_52_3 = all_10_2)
% 174.59/26.78    (22)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.59/26.78    (23)  all_58_5 = all_52_13
% 174.59/26.78    (24)   ~ (all_52_25 = all_52_29)
% 174.59/26.78    (25)  all_56_15 = all_6_2
% 174.59/26.78    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.78    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.59/26.78    (28)  all_58_3 = all_10_2
% 174.59/26.78    (29)  all_56_9 = all_52_19
% 174.59/26.78    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.59/26.78    (31)  all_58_15 = all_6_2
% 174.59/26.78    (32)  op(e2, all_4_2) = e1
% 174.59/26.78    (33)   ~ (all_52_9 = all_4_2)
% 174.59/26.78    (34)   ~ (all_52_5 = all_52_7)
% 174.59/26.78    (35)  all_58_10 = all_52_15
% 174.59/26.78    (36)   ~ (all_52_5 = all_4_2)
% 174.59/26.78    (37)  all_58_7 = all_52_19
% 174.59/26.78    (38)   ~ (all_52_15 = all_6_2)
% 174.59/26.78    (39)   ~ (all_52_17 = all_52_25)
% 174.59/26.78    (40)  op(e0, e1) = all_52_29
% 174.59/26.78    (41)  all_58_4 = all_52_5
% 174.59/26.78    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.59/26.78    (43)   ~ (e3 = e1)
% 174.59/26.78    (44)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.59/26.78    (45)   ~ (all_52_27 = all_52_29)
% 174.59/26.78    (46)   ~ (all_52_17 = all_14_2)
% 174.59/26.78    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.59/26.78    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.59/26.78    (49)   ~ (all_52_7 = all_4_2)
% 174.59/26.78    (50)  all_58_1 = all_52_3
% 174.59/26.78    (51)   ~ (all_52_13 = all_52_15)
% 174.59/26.78    (52)  all_58_0 = all_4_2
% 174.59/26.78    (53)  op(e1, all_52_13) = all_52_12
% 174.59/26.78    (54)  all_52_0 = e2
% 174.59/26.78    (55)  op(e0, e0) = all_6_2
% 174.59/26.78    (56)  op(e1, all_52_29) = all_52_28
% 174.59/26.78    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.59/26.78    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.59/26.78    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.59/26.78    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.59/26.78    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.59/26.78    (62)  all_58_14 = all_52_29
% 174.59/26.78    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.59/26.78    (64)   ~ (all_52_3 = all_52_5)
% 174.59/26.78    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.59/26.78    (66)  op(e2, e1) = all_52_13
% 174.59/26.78    (67)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.59/26.78    (68)  all_58_8 = all_14_2
% 174.59/26.78    (69)  all_56_1 = all_52_3
% 174.59/26.78    (70)  op(e0, e2) = all_52_27
% 174.59/26.78    (71)  all_56_14 = all_52_29
% 174.59/26.78    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.59/26.78    (73)   ~ (all_52_5 = all_14_2)
% 174.59/26.78    (74)   ~ (all_52_3 = all_52_27)
% 174.59/26.78    (75)   ~ (all_52_3 = all_4_2)
% 174.59/26.78    (76)  op(all_6_1, all_6_2) = all_6_0
% 174.59/26.78    (77)  op(e0, e3) = all_52_25
% 174.59/26.78    (78)  op(e0, all_6_2) = all_6_1
% 174.59/26.78    (79)   ~ (all_52_9 = all_10_2)
% 174.59/26.78    (80)  op(e3, all_52_17) = all_52_16
% 174.59/26.78    (81)  all_52_10 = all_10_1
% 174.59/26.78    (82)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.59/26.78    (83)   ~ (all_52_13 = all_14_2)
% 174.59/26.78    (84)   ~ (e3 = e0)
% 174.59/26.78    (85)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.59/26.78    (86)   ~ (all_52_9 = all_52_13)
% 174.59/26.78    (87)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.59/26.78    (88)  op(e0, all_52_23) = all_52_22
% 174.59/26.78    (89)   ~ (all_52_15 = all_52_23)
% 174.59/26.78    (90)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.59/26.78    (91)   ~ (all_52_5 = all_52_29)
% 174.59/26.78    (92)  op(e1, e0) = all_52_23
% 174.59/26.78    (93)  all_56_12 = all_52_25
% 174.59/26.78    (94)  all_58_13 = all_52_27
% 174.59/26.78    (95)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.59/26.78    (96)  all_56_5 = all_10_2
% 174.59/26.78    (97)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.59/26.78    (98)   ~ (all_52_9 = all_52_17)
% 174.59/26.78    (99)  all_58_6 = all_52_17
% 174.59/26.78    (100)   ~ (all_52_3 = all_52_7)
% 174.59/26.78    (101)  op(e2, all_52_19) = all_52_18
% 174.59/26.78    (102)   ~ (e1 = e0)
% 174.59/26.78    (103)  all_56_0 = all_4_2
% 174.59/26.78    (104)  all_58_11 = all_52_23
% 174.59/26.78    (105)   ~ (all_52_3 = all_52_19)
% 174.59/26.78    (106)   ~ (all_52_7 = all_52_15)
% 174.59/26.78    (107)  op(e0, all_52_15) = all_52_14
% 174.59/26.78    (108)   ~ (all_52_29 = all_14_2)
% 174.59/26.78    (109)   ~ (all_52_19 = all_10_2)
% 174.59/26.78    (110)  op(e3, all_4_2) = e2
% 174.59/26.78    (111)   ~ (all_52_23 = all_6_2)
% 174.59/26.78    (112)   ~ (all_6_0 = e2)
% 174.59/26.78    (113)   ~ (all_52_29 = all_6_2)
% 174.59/26.78    (114)  all_58_2 = all_52_9
% 174.59/26.78    (115)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.59/26.78    (116)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.59/26.78    (117)  op(e3, e1) = all_52_5
% 174.59/26.78    (118)   ~ (e2 = e1)
% 174.59/26.78    (119)  all_56_10 = all_14_2
% 174.59/26.78    (120)   ~ (all_52_25 = all_6_2)
% 174.59/26.78    (121)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.59/26.78    (122)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.59/26.78    (123)  op(e1, e3) = all_52_17
% 174.59/26.78    (124)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.59/26.78    (125)   ~ (all_52_25 = all_4_2)
% 174.59/26.78    (126)  op(e3, e0) = all_52_7
% 174.59/26.78    (127)  op(e3, e3) = all_4_2
% 174.59/26.78    (128)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.59/26.78             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.59/26.78    (129)   ~ (all_10_1 = e3)
% 174.59/26.78    (130)  all_56_8 = all_52_17
% 174.59/26.78    (131)   ~ (all_52_17 = all_4_2)
% 174.59/26.78    (132)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.59/26.78             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.59/26.78    (133)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.59/26.78           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.59/26.78           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.59/26.78           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.59/26.78    (134)   ~ (all_52_25 = all_52_27)
% 174.59/26.78    (135)   ~ (all_52_27 = all_6_2)
% 174.59/26.78    (136)   ~ (all_52_7 = all_6_2)
% 174.59/26.78    (137)   ~ (all_52_15 = all_10_2)
% 174.59/26.78    (138)   ~ (all_52_19 = all_52_27)
% 174.59/26.78    (139)  all_42_2 = all_4_2
% 174.59/26.78    (140)  all_56_7 = all_52_15
% 174.59/26.78    (141)   ~ (all_52_7 = all_52_23)
% 174.59/26.78    (142)   ~ (all_6_0 = e1)
% 174.59/26.78    (143)  op(e2, all_52_27) = all_52_26
% 174.59/26.78    (144)  all_52_20 = all_14_1
% 174.59/26.78    (145)   ~ (all_52_17 = all_52_19)
% 174.59/26.78    (146)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.59/26.78    (147)  all_52_30 = all_6_1
% 174.59/26.78    (148)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.59/26.78    (149)  op(e1, all_14_2) = all_14_1
% 174.59/26.78    (150)  all_58_9 = all_52_7
% 174.59/26.78    (151)   ~ (e2 = e0)
% 174.59/26.78    (152)  all_58_12 = all_52_25
% 174.59/26.78    (153)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.59/26.78    (154)   ~ (all_52_9 = all_52_15)
% 174.59/26.78    (155)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.59/26.78    (156)   ~ (e3 = e2)
% 174.59/26.78    (157)   ~ (all_52_19 = all_14_2)
% 174.59/26.78    (158)  op(e2, e3) = all_52_9
% 174.59/26.78    (159)  all_56_13 = all_52_27
% 174.59/26.78  
% 174.59/26.78  Begin of proof
% 174.59/26.78  | 
% 174.59/26.78  | BETA: splitting (44) gives:
% 174.59/26.78  | 
% 174.59/26.78  | Case 1:
% 174.59/26.78  | | 
% 174.59/26.78  | |   (160)   ~ (all_42_1 = e2)
% 174.59/26.78  | | 
% 174.59/26.78  | | REDUCE: (11), (160) imply:
% 174.59/26.78  | |   (161)  $false
% 174.59/26.78  | | 
% 174.59/26.78  | | CLOSE: (161) is inconsistent.
% 174.59/26.78  | | 
% 174.59/26.78  | Case 2:
% 174.59/26.78  | | 
% 174.59/26.78  | |   (162)   ~ (all_42_2 = e0)
% 174.59/26.78  | | 
% 174.59/26.78  | | REDUCE: (139), (162) imply:
% 174.59/26.78  | |   (163)   ~ (all_4_2 = e0)
% 174.59/26.78  | | 
% 174.59/26.78  | | BETA: splitting (128) gives:
% 174.59/26.78  | | 
% 174.59/26.78  | | Case 1:
% 174.59/26.78  | | | 
% 174.59/26.78  | | |   (164)  all_58_15 = e0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | COMBINE_EQS: (31), (164) imply:
% 174.59/26.78  | | |   (165)  all_6_2 = e0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (38), (165) imply:
% 174.59/26.78  | | |   (166)   ~ (all_52_15 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (111), (165) imply:
% 174.59/26.78  | | |   (167)   ~ (all_52_23 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (120), (165) imply:
% 174.59/26.78  | | |   (168)   ~ (all_52_25 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (135), (165) imply:
% 174.59/26.78  | | |   (169)   ~ (all_52_27 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (113), (165) imply:
% 174.59/26.78  | | |   (170)   ~ (all_52_29 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (76), (165) imply:
% 174.59/26.78  | | |   (171)  op(all_6_1, e0) = all_6_0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (78), (165) imply:
% 174.59/26.78  | | |   (172)  op(e0, e0) = all_6_1
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (55), (165) imply:
% 174.59/26.78  | | |   (173)  op(e0, e0) = e0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | GROUND_INST: instantiating (132) with e0, all_6_1, e0, e0, simplifying
% 174.59/26.78  | | |              with (172), (173) gives:
% 174.59/26.78  | | |   (174)  all_6_1 = e0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (171), (174) imply:
% 174.59/26.78  | | |   (175)  op(e0, e0) = all_6_0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | GROUND_INST: instantiating (132) with e0, all_6_0, e0, e0, simplifying
% 174.59/26.78  | | |              with (173), (175) gives:
% 174.59/26.78  | | |   (176)  all_6_0 = e0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (8), (176) imply:
% 174.59/26.78  | | |   (177)   ~ (e3 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (112), (176) imply:
% 174.59/26.78  | | |   (178)   ~ (e2 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (142), (176) imply:
% 174.59/26.78  | | |   (179)   ~ (e1 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | BETA: splitting (133) gives:
% 174.59/26.78  | | | 
% 174.59/26.78  | | | Case 1:
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | |   (180)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.59/26.78  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.59/26.78  | | | |            = e0)
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | | REF_CLOSE: (7), (9), (14), (15), (20), (21), (23), (27), (28), (33),
% 174.59/26.78  | | | |            (34), (35), (37), (39), (40), (41), (42), (43), (45), (46),
% 174.59/26.78  | | | |            (48), (49), (50), (52), (53), (54), (59), (61), (62), (65),
% 174.59/26.78  | | | |            (67), (68), (70), (71), (77), (81), (82), (84), (90), (94),
% 174.59/26.78  | | | |            (98), (99), (100), (102), (104), (106), (107), (109), (114),
% 174.59/26.78  | | | |            (118), (119), (123), (124), (127), (129), (132), (134),
% 174.59/26.78  | | | |            (140), (141), (145), (146), (150), (151), (152), (155),
% 174.59/26.78  | | | |            (156), (157), (158), (164), (168), (169), (170), (180) are
% 174.59/26.78  | | | |            inconsistent by sub-proof #120.
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | Case 2:
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | |   (181)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.59/26.78  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.59/26.78  | | | |            all_52_30 = e0)
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | | BETA: splitting (181) gives:
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | | Case 1:
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | |   (182)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 174.59/26.78  | | | | |          = e0
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | | REF_CLOSE: (1), (3), (7), (8), (10), (12), (14), (15), (17), (18),
% 174.59/26.78  | | | | |            (21), (23), (24), (27), (28), (29), (30), (33), (35), (37),
% 174.59/26.78  | | | | |            (39), (40), (42), (43), (45), (48), (49), (50), (52), (56),
% 174.59/26.78  | | | | |            (58), (61), (62), (63), (65), (67), (68), (70), (73), (75),
% 174.59/26.78  | | | | |            (77), (79), (80), (82), (85), (87), (88), (89), (90), (91),
% 174.59/26.78  | | | | |            (93), (94), (95), (96), (98), (99), (100), (101), (103),
% 174.59/26.78  | | | | |            (104), (108), (109), (112), (114), (115), (116), (117),
% 174.59/26.78  | | | | |            (118), (119), (121), (122), (123), (124), (125), (126),
% 174.59/26.78  | | | | |            (127), (130), (131), (132), (134), (138), (140), (141),
% 174.59/26.78  | | | | |            (142), (144), (146), (148), (149), (150), (152), (153),
% 174.59/26.78  | | | | |            (154), (156), (157), (158), (159), (164), (166), (167),
% 174.59/26.78  | | | | |            (168), (169), (170), (171), (172), (173), (182) are
% 174.59/26.78  | | | | |            inconsistent by sub-proof #117.
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | Case 2:
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | |   (183)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 174.59/26.78  | | | | |          = e0
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | | REF_CLOSE: (1), (2), (4), (6), (10), (12), (14), (15), (16), (17),
% 174.59/26.78  | | | | |            (19), (20), (22), (23), (24), (26), (27), (28), (30), (33),
% 174.59/26.78  | | | | |            (35), (36), (37), (41), (48), (49), (50), (52), (56), (62),
% 174.59/26.78  | | | | |            (63), (67), (68), (75), (79), (84), (87), (89), (91), (93),
% 174.59/26.78  | | | | |            (94), (96), (97), (98), (99), (100), (103), (104), (106),
% 174.59/26.78  | | | | |            (108), (109), (110), (114), (117), (121), (122), (123),
% 174.59/26.78  | | | | |            (125), (126), (127), (131), (132), (134), (143), (148),
% 174.59/26.78  | | | | |            (150), (151), (152), (155), (156), (158), (159), (163),
% 174.59/26.78  | | | | |            (164), (167), (168), (183) are inconsistent by sub-proof
% 174.59/26.78  | | | | |            #67.
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | End of split
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | End of split
% 174.59/26.78  | | | 
% 174.59/26.78  | | Case 2:
% 174.59/26.78  | | | 
% 174.59/26.78  | | |   (184)   ~ (all_58_15 = e0)
% 174.59/26.78  | | |   (185)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 174.59/26.78  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | ALPHA: (185) implies:
% 174.59/26.78  | | |   (186)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.78  | | |   (187)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.59/26.78  | | | 
% 174.59/26.78  | | | REDUCE: (31), (184) imply:
% 174.59/26.78  | | |   (188)   ~ (all_6_2 = e0)
% 174.59/26.78  | | | 
% 174.59/26.78  | | | BETA: splitting (133) gives:
% 174.59/26.78  | | | 
% 174.59/26.78  | | | Case 1:
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | |   (189)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.59/26.78  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.59/26.78  | | | |            = e0)
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | | REF_CLOSE: (9), (13), (54), (81), (118), (132), (156), (189) are
% 174.59/26.78  | | | |            inconsistent by sub-proof #69.
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | Case 2:
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | |   (190)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.59/26.78  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.59/26.78  | | | |            all_52_30 = e0)
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | | BETA: splitting (190) gives:
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | | Case 1:
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | |   (191)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 174.59/26.78  | | | | |          = e0
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | | REF_CLOSE: (1), (7), (14), (15), (19), (23), (24), (25), (26), (28),
% 174.59/26.78  | | | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (39),
% 174.59/26.78  | | | | |            (41), (42), (43), (47), (48), (49), (50), (52), (58), (61),
% 174.59/26.78  | | | | |            (62), (65), (66), (67), (68), (73), (75), (77), (80), (83),
% 174.59/26.78  | | | | |            (84), (85), (86), (88), (89), (90), (92), (94), (95), (97),
% 174.59/26.78  | | | | |            (98), (99), (101), (102), (103), (104), (105), (106),
% 174.59/26.78  | | | | |            (110), (111), (114), (117), (118), (119), (120), (123),
% 174.59/26.78  | | | | |            (124), (125), (126), (127), (131), (132), (134), (137),
% 174.59/26.78  | | | | |            (140), (141), (144), (145), (146), (149), (150), (151),
% 174.59/26.78  | | | | |            (152), (153), (155), (156), (157), (158), (163), (187),
% 174.59/26.78  | | | | |            (191) are inconsistent by sub-proof #66.
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | Case 2:
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | |   (192)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 174.59/26.78  | | | | |          = e0
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | | ALPHA: (192) implies:
% 174.59/26.78  | | | | |   (193)  all_52_30 = e0
% 174.59/26.78  | | | | |   (194)  all_52_28 = e1
% 174.59/26.78  | | | | |   (195)  all_52_26 = e2
% 174.59/26.78  | | | | |   (196)  all_52_24 = e3
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | | COMBINE_EQS: (147), (193) imply:
% 174.59/26.78  | | | | |   (197)  all_6_1 = e0
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | | SIMP: (197) implies:
% 174.59/26.78  | | | | |   (198)  all_6_1 = e0
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (14), (15), (16), (17), (21),
% 174.59/26.78  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 174.59/26.78  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 174.59/26.78  | | | | |            (43), (45), (46), (47), (48), (49), (50), (51), (52), (56),
% 174.59/26.78  | | | | |            (57), (58), (60), (61), (62), (64), (65), (66), (67), (68),
% 174.59/26.78  | | | | |            (69), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 174.59/26.78  | | | | |            (85), (86), (87), (89), (90), (91), (93), (94), (98), (99),
% 174.59/26.78  | | | | |            (100), (103), (104), (106), (109), (110), (112), (113),
% 174.59/26.78  | | | | |            (114), (117), (119), (120), (123), (124), (125), (126),
% 174.59/26.78  | | | | |            (127), (131), (132), (135), (136), (137), (138), (140),
% 174.59/26.78  | | | | |            (143), (145), (146), (150), (152), (153), (154), (155),
% 174.59/26.78  | | | | |            (156), (157), (158), (163), (186), (188), (194), (195),
% 174.59/26.78  | | | | |            (196), (198) are inconsistent by sub-proof #65.
% 174.59/26.78  | | | | | 
% 174.59/26.78  | | | | End of split
% 174.59/26.78  | | | | 
% 174.59/26.78  | | | End of split
% 174.59/26.78  | | | 
% 174.59/26.78  | | End of split
% 174.59/26.78  | | 
% 174.59/26.78  | End of split
% 174.59/26.78  | 
% 174.59/26.78  End of proof
% 174.59/26.78  
% 174.59/26.78  Sub-proof #65 shows that the following formulas are inconsistent:
% 174.59/26.78  ----------------------------------------------------------------
% 174.59/26.78    (1)   ~ (all_52_23 = all_14_2)
% 174.59/26.78    (2)   ~ (all_52_5 = all_52_13)
% 174.59/26.78    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.59/26.78    (4)   ~ (all_52_27 = all_10_2)
% 174.59/26.78    (5)   ~ (all_52_17 = all_52_23)
% 174.59/26.78    (6)  all_52_26 = e2
% 174.59/26.78    (7)   ~ (all_6_0 = e3)
% 174.59/26.78    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.59/26.78    (9)  op(e3, e2) = all_52_3
% 174.59/26.78    (10)   ~ (all_52_9 = all_52_25)
% 174.59/26.78    (11)  op(e3, all_52_25) = all_52_24
% 174.59/26.78    (12)   ~ (all_52_19 = all_52_23)
% 174.59/26.78    (13)   ~ (all_52_3 = all_10_2)
% 174.59/26.78    (14)  all_58_5 = all_52_13
% 174.59/26.78    (15)   ~ (all_6_2 = e0)
% 174.59/26.78    (16)   ~ (all_52_25 = all_52_29)
% 174.59/26.78    (17)  all_56_15 = all_6_2
% 174.59/26.78    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.59/26.78    (19)  all_6_1 = e0
% 174.80/26.78    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.80/26.78    (21)  all_58_3 = all_10_2
% 174.80/26.78    (22)  all_56_9 = all_52_19
% 174.80/26.78    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.78    (24)  all_58_15 = all_6_2
% 174.80/26.78    (25)  op(e2, all_4_2) = e1
% 174.80/26.78    (26)   ~ (all_52_9 = all_4_2)
% 174.80/26.78    (27)   ~ (all_52_5 = all_52_7)
% 174.80/26.78    (28)  all_58_10 = all_52_15
% 174.80/26.78    (29)   ~ (all_52_5 = all_4_2)
% 174.80/26.78    (30)  all_58_7 = all_52_19
% 174.80/26.78    (31)   ~ (all_52_15 = all_6_2)
% 174.80/26.78    (32)   ~ (all_52_17 = all_52_25)
% 174.80/26.78    (33)  op(e0, e1) = all_52_29
% 174.80/26.78    (34)  all_58_4 = all_52_5
% 174.80/26.78    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.78    (36)   ~ (e3 = e1)
% 174.80/26.78    (37)   ~ (all_52_27 = all_52_29)
% 174.80/26.78    (38)   ~ (all_52_17 = all_14_2)
% 174.80/26.78    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.78    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.78    (41)   ~ (all_52_7 = all_4_2)
% 174.80/26.78    (42)  all_58_1 = all_52_3
% 174.80/26.78    (43)   ~ (all_52_13 = all_52_15)
% 174.80/26.78    (44)  all_58_0 = all_4_2
% 174.80/26.78    (45)  op(e1, all_52_29) = all_52_28
% 174.80/26.78    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.79    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.79    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.80/26.79    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.79    (50)  all_58_14 = all_52_29
% 174.80/26.79    (51)   ~ (all_52_3 = all_52_5)
% 174.80/26.79    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.79    (53)  op(e2, e1) = all_52_13
% 174.80/26.79    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.79    (55)  all_58_8 = all_14_2
% 174.80/26.79    (56)  all_56_1 = all_52_3
% 174.80/26.79    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.80/26.79    (58)   ~ (all_52_5 = all_14_2)
% 174.80/26.79    (59)   ~ (all_52_3 = all_52_27)
% 174.80/26.79    (60)   ~ (all_52_3 = all_4_2)
% 174.80/26.79    (61)  op(all_6_1, all_6_2) = all_6_0
% 174.80/26.79    (62)  op(e0, e3) = all_52_25
% 174.80/26.79    (63)  op(e0, all_6_2) = all_6_1
% 174.80/26.79    (64)   ~ (all_52_9 = all_10_2)
% 174.80/26.79    (65)  op(e3, all_52_17) = all_52_16
% 174.80/26.79    (66)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.79    (67)   ~ (all_52_9 = all_52_13)
% 174.80/26.79    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.80/26.79    (69)   ~ (all_52_15 = all_52_23)
% 174.80/26.79    (70)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.79    (71)   ~ (all_52_5 = all_52_29)
% 174.80/26.79    (72)  all_56_12 = all_52_25
% 174.80/26.79    (73)  all_58_13 = all_52_27
% 174.80/26.79    (74)   ~ (all_52_9 = all_52_17)
% 174.80/26.79    (75)  all_58_6 = all_52_17
% 174.80/26.79    (76)   ~ (all_52_3 = all_52_7)
% 174.80/26.79    (77)  all_56_0 = all_4_2
% 174.80/26.79    (78)  all_58_11 = all_52_23
% 174.80/26.79    (79)   ~ (all_52_7 = all_52_15)
% 174.80/26.79    (80)   ~ (all_52_19 = all_10_2)
% 174.80/26.79    (81)  op(e3, all_4_2) = e2
% 174.80/26.79    (82)   ~ (all_6_0 = e2)
% 174.80/26.79    (83)   ~ (all_52_29 = all_6_2)
% 174.80/26.79    (84)  all_58_2 = all_52_9
% 174.80/26.79    (85)  op(e3, e1) = all_52_5
% 174.80/26.79    (86)  all_56_10 = all_14_2
% 174.80/26.79    (87)   ~ (all_52_25 = all_6_2)
% 174.80/26.79    (88)  op(e1, e3) = all_52_17
% 174.80/26.79    (89)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.79    (90)   ~ (all_52_25 = all_4_2)
% 174.80/26.79    (91)  op(e3, e0) = all_52_7
% 174.80/26.79    (92)  all_52_28 = e1
% 174.80/26.79    (93)  op(e3, e3) = all_4_2
% 174.80/26.79    (94)   ~ (all_52_17 = all_4_2)
% 174.80/26.79    (95)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.79    (96)   ~ (all_52_27 = all_6_2)
% 174.80/26.79    (97)   ~ (all_52_7 = all_6_2)
% 174.80/26.79    (98)   ~ (all_52_15 = all_10_2)
% 174.80/26.79    (99)   ~ (all_52_19 = all_52_27)
% 174.80/26.79    (100)  all_56_7 = all_52_15
% 174.80/26.79    (101)   ~ (all_4_2 = e0)
% 174.80/26.79    (102)  op(e2, all_52_27) = all_52_26
% 174.80/26.79    (103)   ~ (all_52_17 = all_52_19)
% 174.80/26.79    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.79    (105)  all_58_9 = all_52_7
% 174.80/26.79    (106)  all_52_24 = e3
% 174.80/26.79    (107)  all_58_12 = all_52_25
% 174.80/26.79    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.79    (109)   ~ (all_52_9 = all_52_15)
% 174.80/26.79    (110)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.79    (111)   ~ (e3 = e2)
% 174.80/26.79    (112)   ~ (all_52_19 = all_14_2)
% 174.80/26.79    (113)  op(e2, e3) = all_52_9
% 174.80/26.79  
% 174.80/26.79  Begin of proof
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (19), (61) imply:
% 174.80/26.79  |   (114)  op(e0, all_6_2) = all_6_0
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (11), (106) imply:
% 174.80/26.79  |   (115)  op(e3, all_52_25) = e3
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (6), (102) imply:
% 174.80/26.79  |   (116)  op(e2, all_52_27) = e2
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (45), (92) imply:
% 174.80/26.79  |   (117)  op(e1, all_52_29) = e1
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (19), (63) imply:
% 174.80/26.79  |   (118)  op(e0, all_6_2) = e0
% 174.80/26.79  | 
% 174.80/26.79  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 174.80/26.79  |            (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 174.80/26.79  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 174.80/26.79  |            (38), (39), (40), (41), (42), (43), (44), (46), (47), (48), (49),
% 174.80/26.79  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 174.80/26.79  |            (62), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 174.80/26.79  |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 174.80/26.79  |            (85), (86), (87), (88), (89), (90), (91), (93), (94), (95), (96),
% 174.80/26.79  |            (97), (98), (99), (100), (101), (103), (104), (105), (107), (108),
% 174.80/26.79  |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 174.80/26.79  |            (118) are inconsistent by sub-proof #73.
% 174.80/26.79  | 
% 174.80/26.79  End of proof
% 174.80/26.79  
% 174.80/26.79  Sub-proof #66 shows that the following formulas are inconsistent:
% 174.80/26.79  ----------------------------------------------------------------
% 174.80/26.79    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.79    (2)   ~ (all_52_17 = all_52_23)
% 174.80/26.79    (3)  op(e3, e2) = all_52_3
% 174.80/26.79    (4)   ~ (all_52_9 = all_52_25)
% 174.80/26.79    (5)  op(e1, e2) = all_52_19
% 174.80/26.79    (6)  all_58_5 = all_52_13
% 174.80/26.79    (7)   ~ (all_52_25 = all_52_29)
% 174.80/26.79    (8)  all_56_15 = all_6_2
% 174.80/26.79    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.79    (10)  all_58_3 = all_10_2
% 174.80/26.79    (11)  all_56_9 = all_52_19
% 174.80/26.79    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.79    (13)  all_58_15 = all_6_2
% 174.80/26.79    (14)  op(e2, all_4_2) = e1
% 174.80/26.79    (15)   ~ (all_52_9 = all_4_2)
% 174.80/26.79    (16)   ~ (all_52_5 = all_52_7)
% 174.80/26.79    (17)  all_58_10 = all_52_15
% 174.80/26.79    (18)   ~ (all_52_5 = all_4_2)
% 174.80/26.79    (19)  all_58_7 = all_52_19
% 174.80/26.79    (20)   ~ (all_52_17 = all_52_25)
% 174.80/26.79    (21)  all_58_4 = all_52_5
% 174.80/26.79    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.79    (23)   ~ (e3 = e1)
% 174.80/26.79    (24)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.79    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.79    (26)   ~ (all_52_7 = all_4_2)
% 174.80/26.79    (27)  all_58_1 = all_52_3
% 174.80/26.79    (28)  all_58_0 = all_4_2
% 174.80/26.79    (29)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.79    (30)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.79    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.79    (32)  all_58_14 = all_52_29
% 174.80/26.79    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.79    (34)  op(e2, e1) = all_52_13
% 174.80/26.79    (35)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.79    (36)  all_58_8 = all_14_2
% 174.80/26.79    (37)   ~ (all_52_5 = all_14_2)
% 174.80/26.79    (38)   ~ (all_52_3 = all_4_2)
% 174.80/26.79    (39)  op(e0, e3) = all_52_25
% 174.80/26.79    (40)  op(e3, all_52_17) = all_52_16
% 174.80/26.79    (41)   ~ (all_52_13 = all_14_2)
% 174.80/26.79    (42)   ~ (e3 = e0)
% 174.80/26.79    (43)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.79    (44)   ~ (all_52_9 = all_52_13)
% 174.80/26.79    (45)  op(e0, all_52_23) = all_52_22
% 174.80/26.79    (46)   ~ (all_52_15 = all_52_23)
% 174.80/26.79    (47)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.79    (48)  op(e1, e0) = all_52_23
% 174.80/26.79    (49)  all_58_13 = all_52_27
% 174.80/26.79    (50)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.79    (51)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.79    (52)   ~ (all_52_9 = all_52_17)
% 174.80/26.79    (53)  all_58_6 = all_52_17
% 174.80/26.79    (54)  op(e2, all_52_19) = all_52_18
% 174.80/26.79    (55)   ~ (e1 = e0)
% 174.80/26.79    (56)  all_56_0 = all_4_2
% 174.80/26.79    (57)  all_58_11 = all_52_23
% 174.80/26.79    (58)   ~ (all_52_3 = all_52_19)
% 174.80/26.79    (59)   ~ (all_52_7 = all_52_15)
% 174.80/26.79    (60)  op(e3, all_4_2) = e2
% 174.80/26.79    (61)   ~ (all_52_23 = all_6_2)
% 174.80/26.79    (62)  all_58_2 = all_52_9
% 174.80/26.79    (63)  op(e3, e1) = all_52_5
% 174.80/26.79    (64)   ~ (e2 = e1)
% 174.80/26.79    (65)  all_56_10 = all_14_2
% 174.80/26.79    (66)   ~ (all_52_25 = all_6_2)
% 174.80/26.79    (67)  op(e1, e3) = all_52_17
% 174.80/26.79    (68)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.79    (69)   ~ (all_52_25 = all_4_2)
% 174.80/26.79    (70)  op(e3, e0) = all_52_7
% 174.80/26.79    (71)  op(e3, e3) = all_4_2
% 174.80/26.79    (72)   ~ (all_52_17 = all_4_2)
% 174.80/26.79    (73)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.79    (74)   ~ (all_52_25 = all_52_27)
% 174.80/26.79    (75)   ~ (all_52_15 = all_10_2)
% 174.80/26.79    (76)  all_56_7 = all_52_15
% 174.80/26.79    (77)   ~ (all_4_2 = e0)
% 174.80/26.79    (78)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.80/26.79    (79)   ~ (all_52_7 = all_52_23)
% 174.80/26.79    (80)  all_52_20 = all_14_1
% 174.80/26.79    (81)   ~ (all_52_17 = all_52_19)
% 174.80/26.79    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.79    (83)  op(e1, all_14_2) = all_14_1
% 174.80/26.79    (84)  all_58_9 = all_52_7
% 174.80/26.79    (85)   ~ (e2 = e0)
% 174.80/26.79    (86)  all_58_12 = all_52_25
% 174.80/26.79    (87)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.79    (88)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.79    (89)   ~ (e3 = e2)
% 174.80/26.79    (90)   ~ (all_52_19 = all_14_2)
% 174.80/26.79    (91)  op(e2, e3) = all_52_9
% 174.80/26.79  
% 174.80/26.79  Begin of proof
% 174.80/26.79  | 
% 174.80/26.79  | ALPHA: (78) implies:
% 174.80/26.79  |   (92)  all_52_22 = e0
% 174.80/26.79  |   (93)  all_52_20 = e1
% 174.80/26.79  |   (94)  all_52_18 = e2
% 174.80/26.79  |   (95)  all_52_16 = e3
% 174.80/26.79  | 
% 174.80/26.79  | COMBINE_EQS: (80), (93) imply:
% 174.80/26.79  |   (96)  all_14_1 = e1
% 174.80/26.79  | 
% 174.80/26.79  | SIMP: (96) implies:
% 174.80/26.79  |   (97)  all_14_1 = e1
% 174.80/26.79  | 
% 174.80/26.79  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.80/26.79  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.80/26.79  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.80/26.79  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.80/26.79  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.80/26.79  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.80/26.79  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (79),
% 174.80/26.79  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 174.80/26.79  |            (92), (94), (95), (97) are inconsistent by sub-proof #77.
% 174.80/26.79  | 
% 174.80/26.79  End of proof
% 174.80/26.79  
% 174.80/26.79  Sub-proof #67 shows that the following formulas are inconsistent:
% 174.80/26.79  ----------------------------------------------------------------
% 174.80/26.79    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.79    (2)   ~ (all_52_5 = all_52_13)
% 174.80/26.79    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.80/26.79    (4)   ~ (all_52_27 = all_10_2)
% 174.80/26.79    (5)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.80/26.79    (6)   ~ (all_52_13 = all_52_29)
% 174.80/26.79    (7)  all_56_3 = all_52_7
% 174.80/26.79    (8)  op(e3, e2) = all_52_3
% 174.80/26.79    (9)   ~ (all_52_9 = all_52_25)
% 174.80/26.79    (10)  op(e3, all_52_25) = all_52_24
% 174.80/26.79    (11)   ~ (all_52_19 = all_52_23)
% 174.80/26.79    (12)  op(e1, e2) = all_52_19
% 174.80/26.79    (13)  op(e3, all_52_9) = all_52_8
% 174.80/26.79    (14)   ~ (all_52_23 = e0)
% 174.80/26.79    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.80/26.79    (16)  all_58_5 = all_52_13
% 174.80/26.79    (17)   ~ (all_52_25 = all_52_29)
% 174.80/26.79    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.79    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.80/26.79    (20)  all_58_3 = all_10_2
% 174.80/26.79    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.79    (22)   ~ (all_52_9 = all_4_2)
% 174.80/26.79    (23)  all_58_10 = all_52_15
% 174.80/26.79    (24)   ~ (all_52_5 = all_4_2)
% 174.80/26.79    (25)  all_58_7 = all_52_19
% 174.80/26.79    (26)  all_58_4 = all_52_5
% 174.80/26.79    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.79    (28)   ~ (all_52_7 = all_4_2)
% 174.80/26.79    (29)  all_58_1 = all_52_3
% 174.80/26.79    (30)  all_58_0 = all_4_2
% 174.80/26.79    (31)  op(e1, all_52_29) = all_52_28
% 174.80/26.79    (32)  all_58_14 = all_52_29
% 174.80/26.79    (33)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.80/26.79    (34)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.79    (35)  all_58_8 = all_14_2
% 174.80/26.79    (36)   ~ (all_52_3 = all_4_2)
% 174.80/26.79    (37)   ~ (all_52_9 = all_10_2)
% 174.80/26.79    (38)   ~ (e3 = e0)
% 174.80/26.79    (39)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.80/26.79    (40)   ~ (all_52_15 = all_52_23)
% 174.80/26.79    (41)   ~ (all_52_5 = all_52_29)
% 174.80/26.79    (42)  all_56_12 = all_52_25
% 174.80/26.79    (43)  all_58_13 = all_52_27
% 174.80/26.79    (44)  all_56_5 = all_10_2
% 174.80/26.79    (45)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.79    (46)   ~ (all_52_25 = e0)
% 174.80/26.79    (47)   ~ (all_52_9 = all_52_17)
% 174.80/26.79    (48)  all_58_6 = all_52_17
% 174.80/26.79    (49)   ~ (all_52_3 = all_52_7)
% 174.80/26.79    (50)  all_56_0 = all_4_2
% 174.80/26.79    (51)  all_58_11 = all_52_23
% 174.80/26.79    (52)   ~ (all_52_7 = all_52_15)
% 174.80/26.79    (53)   ~ (all_52_29 = all_14_2)
% 174.80/26.79    (54)   ~ (all_52_19 = all_10_2)
% 174.80/26.79    (55)  all_58_15 = e0
% 174.80/26.79    (56)  op(e3, all_4_2) = e2
% 174.80/26.79    (57)  all_58_2 = all_52_9
% 174.80/26.79    (58)  op(e3, e1) = all_52_5
% 174.80/26.79    (59)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.80/26.79    (60)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.80/26.79    (61)  op(e1, e3) = all_52_17
% 174.80/26.79    (62)   ~ (all_52_25 = all_4_2)
% 174.80/26.79    (63)  op(e3, e0) = all_52_7
% 174.80/26.79    (64)  op(e3, e3) = all_4_2
% 174.80/26.79    (65)   ~ (all_52_17 = all_4_2)
% 174.80/26.79    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.79    (67)   ~ (all_52_25 = all_52_27)
% 174.80/26.79    (68)   ~ (all_4_2 = e0)
% 174.80/26.79    (69)  op(e2, all_52_27) = all_52_26
% 174.80/26.79    (70)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.80/26.79    (71)  all_58_9 = all_52_7
% 174.80/26.79    (72)   ~ (e2 = e0)
% 174.80/26.79    (73)  all_58_12 = all_52_25
% 174.80/26.79    (74)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.79    (75)   ~ (e3 = e2)
% 174.80/26.79    (76)  op(e2, e3) = all_52_9
% 174.80/26.79    (77)  all_56_13 = all_52_27
% 174.80/26.79  
% 174.80/26.79  Begin of proof
% 174.80/26.79  | 
% 174.80/26.79  | ALPHA: (5) implies:
% 174.80/26.79  |   (78)  all_52_28 = e1
% 174.80/26.79  |   (79)  all_52_26 = e2
% 174.80/26.79  |   (80)  all_52_24 = e3
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (10), (80) imply:
% 174.80/26.79  |   (81)  op(e3, all_52_25) = e3
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (69), (79) imply:
% 174.80/26.79  |   (82)  op(e2, all_52_27) = e2
% 174.80/26.79  | 
% 174.80/26.79  | REDUCE: (31), (78) imply:
% 174.80/26.79  |   (83)  op(e1, all_52_29) = e1
% 174.80/26.79  | 
% 174.80/26.79  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14),
% 174.80/26.79  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 174.80/26.79  |            (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (37),
% 174.80/26.79  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 174.80/26.79  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 174.80/26.79  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (70), (71),
% 174.80/26.79  |            (72), (73), (74), (75), (76), (77), (81), (82), (83) are
% 174.80/26.79  |            inconsistent by sub-proof #85.
% 174.80/26.79  | 
% 174.80/26.79  End of proof
% 174.80/26.79  
% 174.80/26.79  Sub-proof #68 shows that the following formulas are inconsistent:
% 174.80/26.79  ----------------------------------------------------------------
% 174.80/26.79    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.79    (2)   ~ (all_52_5 = all_52_13)
% 174.80/26.79    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.80/26.79    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.80/26.79    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.80/26.79    (6)   ~ (all_52_27 = all_10_2)
% 174.80/26.79    (7)   ~ (all_52_17 = all_52_23)
% 174.80/26.79    (8)  op(e2, all_10_2) = all_10_1
% 174.80/26.79    (9)   ~ (all_52_13 = all_52_29)
% 174.80/26.79    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.80/26.79    (11)  all_56_3 = all_52_7
% 174.80/26.79    (12)  op(all_10_1, all_10_2) = e1
% 174.80/26.79    (13)  op(e3, e2) = all_52_3
% 174.80/26.80    (14)   ~ (all_52_9 = all_52_25)
% 174.80/26.80    (15)  op(e3, all_52_25) = all_52_24
% 174.80/26.80    (16)   ~ (all_52_19 = all_52_23)
% 174.80/26.80    (17)  op(e1, e2) = all_52_19
% 174.80/26.80    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.80/26.80    (19)  op(e3, all_52_9) = all_52_8
% 174.80/26.80    (20)   ~ (all_52_3 = all_10_2)
% 174.80/26.80    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.80/26.80    (22)  all_58_5 = all_52_13
% 174.80/26.80    (23)   ~ (all_6_2 = e0)
% 174.80/26.80    (24)   ~ (all_52_25 = all_52_29)
% 174.80/26.80    (25)  all_56_15 = all_6_2
% 174.80/26.80    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.80    (27)  op(all_14_1, all_14_2) = all_14_0
% 174.80/26.80    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.80/26.80    (29)  all_58_3 = all_10_2
% 174.80/26.80    (30)  all_56_9 = all_52_19
% 174.80/26.80    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.80    (32)  all_58_15 = all_6_2
% 174.80/26.80    (33)   ~ (all_52_9 = all_4_2)
% 174.80/26.80    (34)   ~ (all_52_5 = all_52_7)
% 174.80/26.80    (35)  all_58_10 = all_52_15
% 174.80/26.80    (36)   ~ (all_52_5 = all_4_2)
% 174.80/26.80    (37)  all_58_7 = all_52_19
% 174.80/26.80    (38)   ~ (all_52_17 = all_52_25)
% 174.80/26.80    (39)  op(e0, e1) = all_52_29
% 174.80/26.80    (40)  all_58_4 = all_52_5
% 174.80/26.80    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.80    (42)   ~ (e3 = e1)
% 174.80/26.80    (43)   ~ (all_52_27 = all_52_29)
% 174.80/26.80    (44)   ~ (all_52_17 = all_14_2)
% 174.80/26.80    (45)  op(e3, all_4_2) = all_4_1
% 174.80/26.80    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.80    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.80    (48)   ~ (all_52_7 = all_4_2)
% 174.80/26.80    (49)  all_58_1 = all_52_3
% 174.80/26.80    (50)   ~ (all_52_13 = all_52_15)
% 174.80/26.80    (51)  all_58_0 = all_4_2
% 174.80/26.80    (52)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.80/26.80    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.80    (54)  all_52_0 = e2
% 174.80/26.80    (55)  op(e1, all_52_29) = all_52_28
% 174.80/26.80    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.80    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.80    (58)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.80/26.80    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.80/26.80    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.80    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.80/26.80    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.80/26.80    (63)  all_58_14 = all_52_29
% 174.80/26.80    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.80/26.80    (65)  op(e2, all_4_2) = all_4_0
% 174.80/26.80    (66)   ~ (all_52_3 = all_52_5)
% 174.80/26.80    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.80    (68)  op(e2, e1) = all_52_13
% 174.80/26.80    (69)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.80    (70)  all_58_8 = all_14_2
% 174.80/26.80    (71)  all_56_1 = all_52_3
% 174.80/26.80    (72)  op(e0, e2) = all_52_27
% 174.80/26.80    (73)  all_56_14 = all_52_29
% 174.80/26.80    (74)   ~ (all_14_0 = e3)
% 174.80/26.80    (75)  op(all_4_1, all_4_2) = all_4_0
% 174.80/26.80    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.80/26.80    (77)   ~ (all_52_5 = all_14_2)
% 174.80/26.80    (78)   ~ (all_52_3 = all_52_27)
% 174.80/26.80    (79)   ~ (all_52_3 = all_4_2)
% 174.80/26.80    (80)  op(e0, e3) = all_52_25
% 174.80/26.80    (81)  op(e0, all_6_2) = all_6_1
% 174.80/26.80    (82)   ~ (all_52_9 = all_10_2)
% 174.80/26.80    (83)  op(e3, all_52_17) = all_52_16
% 174.80/26.80    (84)  all_52_10 = all_10_1
% 174.80/26.80    (85)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.80/26.80    (86)   ~ (all_52_13 = all_14_2)
% 174.80/26.80    (87)   ~ (e3 = e0)
% 174.80/26.80    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.80    (89)   ~ (all_52_9 = all_52_13)
% 174.80/26.80    (90)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.80/26.80    (91)  op(e0, all_52_23) = all_52_22
% 174.80/26.80    (92)   ~ (all_52_15 = all_52_23)
% 174.80/26.80    (93)   ~ (all_52_5 = all_52_29)
% 174.80/26.80    (94)  all_56_2 = all_52_5
% 174.80/26.80    (95)  op(e1, e0) = all_52_23
% 174.80/26.80    (96)  all_56_12 = all_52_25
% 174.80/26.80    (97)  all_58_13 = all_52_27
% 174.80/26.80    (98)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.80    (99)  all_56_5 = all_10_2
% 174.80/26.80    (100)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.80    (101)   ~ (all_52_9 = all_52_17)
% 174.80/26.80    (102)   ~ (all_14_0 = e2)
% 174.80/26.80    (103)  all_58_6 = all_52_17
% 174.80/26.80    (104)   ~ (all_52_3 = all_52_7)
% 174.80/26.80    (105)  op(e2, all_52_19) = all_52_18
% 174.80/26.80    (106)   ~ (e1 = e0)
% 174.80/26.80    (107)  all_56_0 = all_4_2
% 174.80/26.80    (108)  all_58_11 = all_52_23
% 174.80/26.80    (109)   ~ (all_52_3 = all_52_19)
% 174.80/26.80    (110)   ~ (all_52_7 = all_52_15)
% 174.80/26.80    (111)   ~ (all_4_0 = e1)
% 174.80/26.80    (112)   ~ (all_52_19 = all_10_2)
% 174.80/26.80    (113)  op(e3, all_4_2) = e2
% 174.80/26.80    (114)   ~ (all_52_23 = all_6_2)
% 174.80/26.80    (115)   ~ (all_52_29 = all_6_2)
% 174.80/26.80    (116)  all_58_2 = all_52_9
% 174.80/26.80    (117)  op(e3, e1) = all_52_5
% 174.80/26.80    (118)   ~ (e2 = e1)
% 174.80/26.80    (119)   ~ (all_52_25 = all_6_2)
% 174.80/26.80    (120)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.80/26.80    (121)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.80/26.80    (122)  op(e1, e3) = all_52_17
% 174.80/26.80    (123)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.80    (124)   ~ (all_52_25 = all_4_2)
% 174.80/26.80    (125)  op(e3, e0) = all_52_7
% 174.80/26.80    (126)  op(e3, e3) = all_4_2
% 174.80/26.80    (127)   ~ (all_10_1 = e3)
% 174.80/26.80    (128)  all_56_8 = all_52_17
% 174.80/26.80    (129)   ~ (all_52_17 = all_4_2)
% 174.80/26.80    (130)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.80             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.80    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.80/26.80           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.80/26.80           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.80/26.80           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.80/26.80    (132)   ~ (all_52_25 = all_52_27)
% 174.80/26.80    (133)   ~ (all_52_27 = all_6_2)
% 174.80/26.80    (134)   ~ (all_52_7 = all_6_2)
% 174.80/26.80    (135)   ~ (all_52_15 = all_10_2)
% 174.80/26.80    (136)   ~ (all_52_19 = all_52_27)
% 174.80/26.80    (137)  all_56_7 = all_52_15
% 174.80/26.80    (138)   ~ (all_52_7 = all_52_23)
% 174.80/26.80    (139)   ~ (all_52_13 = all_10_2)
% 174.80/26.80    (140)  op(e2, all_52_27) = all_52_26
% 174.80/26.80    (141)  all_52_20 = all_14_1
% 174.80/26.80    (142)   ~ (all_52_17 = all_52_19)
% 174.80/26.80    (143)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.80    (144)  all_52_30 = all_6_1
% 174.80/26.80    (145)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.80/26.80    (146)  op(e1, all_14_2) = all_14_1
% 174.80/26.80    (147)  all_58_9 = all_52_7
% 174.80/26.80    (148)   ~ (e2 = e0)
% 174.80/26.80    (149)  all_58_12 = all_52_25
% 174.80/26.80    (150)  all_56_6 = all_52_13
% 174.80/26.80    (151)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.80    (152)   ~ (all_52_9 = all_52_15)
% 174.80/26.80    (153)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.80    (154)   ~ (e3 = e2)
% 174.80/26.80    (155)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.80/26.80    (156)   ~ (all_52_19 = all_14_2)
% 174.80/26.80    (157)  op(e2, e3) = all_52_9
% 174.80/26.80    (158)  all_56_13 = all_52_27
% 174.80/26.80  
% 174.80/26.80  Begin of proof
% 174.80/26.80  | 
% 174.80/26.80  | BETA: splitting (131) gives:
% 174.80/26.80  | 
% 174.80/26.80  | Case 1:
% 174.80/26.80  | | 
% 174.80/26.80  | |   (159)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.80/26.80  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.80/26.80  | | 
% 174.80/26.80  | | REF_CLOSE: (8), (12), (54), (84), (118), (130), (154), (159) are
% 174.80/26.80  | |            inconsistent by sub-proof #69.
% 174.80/26.80  | | 
% 174.80/26.80  | Case 2:
% 174.80/26.80  | | 
% 174.80/26.80  | |   (160)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 174.80/26.80  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 174.80/26.80  | |            e0)
% 174.80/26.80  | | 
% 174.80/26.80  | | BETA: splitting (160) gives:
% 174.80/26.80  | | 
% 174.80/26.80  | | Case 1:
% 174.80/26.80  | | | 
% 174.80/26.80  | | |   (161)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 174.80/26.80  | | | 
% 174.80/26.80  | | | ALPHA: (161) implies:
% 174.80/26.80  | | |   (162)  all_52_22 = e0
% 174.80/26.80  | | |   (163)  all_52_20 = e1
% 174.80/26.80  | | |   (164)  all_52_18 = e2
% 174.80/26.80  | | |   (165)  all_52_16 = e3
% 174.80/26.80  | | | 
% 174.80/26.80  | | | COMBINE_EQS: (141), (163) imply:
% 174.80/26.80  | | |   (166)  all_14_1 = e1
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REDUCE: (27), (166) imply:
% 174.80/26.80  | | |   (167)  op(e1, all_14_2) = all_14_0
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REDUCE: (83), (165) imply:
% 174.80/26.80  | | |   (168)  op(e3, all_52_17) = e3
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REDUCE: (105), (164) imply:
% 174.80/26.80  | | |   (169)  op(e2, all_52_19) = e2
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REDUCE: (146), (166) imply:
% 174.80/26.80  | | |   (170)  op(e1, all_14_2) = e1
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REDUCE: (91), (162) imply:
% 174.80/26.80  | | |   (171)  op(e0, all_52_23) = e0
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11), (13), (14), (16),
% 174.80/26.80  | | |            (17), (22), (24), (25), (26), (29), (30), (31), (32), (33),
% 174.80/26.80  | | |            (34), (35), (36), (37), (38), (40), (41), (44), (45), (46),
% 174.80/26.80  | | |            (47), (48), (49), (51), (52), (53), (55), (57), (60), (61),
% 174.80/26.80  | | |            (62), (63), (64), (65), (67), (68), (69), (70), (72), (74),
% 174.80/26.80  | | |            (75), (77), (78), (79), (80), (82), (85), (86), (87), (88),
% 174.80/26.80  | | |            (89), (92), (93), (97), (98), (99), (100), (101), (102), (103),
% 174.80/26.80  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 174.80/26.80  | | |            (115), (116), (117), (119), (120), (122), (123), (124), (125),
% 174.80/26.80  | | |            (126), (127), (128), (129), (130), (132), (133), (134), (135),
% 174.80/26.80  | | |            (136), (137), (138), (139), (140), (142), (143), (145), (147),
% 174.80/26.80  | | |            (148), (149), (150), (151), (152), (153), (154), (156), (157),
% 174.80/26.80  | | |            (158), (167), (168), (169), (170), (171) are inconsistent by
% 174.80/26.80  | | |            sub-proof #93.
% 174.80/26.80  | | | 
% 174.80/26.80  | | Case 2:
% 174.80/26.80  | | | 
% 174.80/26.80  | | |   (172)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 174.80/26.80  | | | 
% 174.80/26.80  | | | ALPHA: (172) implies:
% 174.80/26.80  | | |   (173)  all_52_30 = e0
% 174.80/26.80  | | |   (174)  all_52_28 = e1
% 174.80/26.80  | | |   (175)  all_52_26 = e2
% 174.80/26.80  | | |   (176)  all_52_24 = e3
% 174.80/26.80  | | | 
% 174.80/26.80  | | | COMBINE_EQS: (144), (173) imply:
% 174.80/26.80  | | |   (177)  all_6_1 = e0
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REF_CLOSE: (4), (5), (7), (10), (13), (14), (15), (16), (18), (19), (20),
% 174.80/26.80  | | |            (21), (22), (23), (24), (25), (28), (29), (31), (32), (33),
% 174.80/26.80  | | |            (34), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 174.80/26.80  | | |            (45), (46), (48), (49), (50), (51), (53), (55), (56), (58),
% 174.80/26.80  | | |            (59), (60), (63), (64), (65), (66), (67), (68), (69), (70),
% 174.80/26.80  | | |            (71), (72), (73), (75), (76), (78), (79), (80), (81), (82),
% 174.80/26.80  | | |            (83), (85), (87), (88), (89), (90), (93), (94), (95), (96),
% 174.80/26.80  | | |            (97), (98), (101), (103), (104), (106), (107), (108), (110),
% 174.80/26.80  | | |            (111), (112), (113), (115), (116), (117), (118), (119), (121),
% 174.80/26.80  | | |            (122), (124), (125), (126), (129), (130), (132), (133), (134),
% 174.80/26.80  | | |            (135), (138), (140), (142), (143), (147), (148), (149), (151),
% 174.80/26.80  | | |            (152), (153), (154), (155), (157), (158), (174), (175), (176),
% 174.80/26.80  | | |            (177) are inconsistent by sub-proof #88.
% 174.80/26.80  | | | 
% 174.80/26.80  | | End of split
% 174.80/26.80  | | 
% 174.80/26.80  | End of split
% 174.80/26.80  | 
% 174.80/26.80  End of proof
% 174.80/26.80  
% 174.80/26.80  Sub-proof #69 shows that the following formulas are inconsistent:
% 174.80/26.80  ----------------------------------------------------------------
% 174.80/26.80    (1)  op(e2, all_10_2) = all_10_1
% 174.80/26.80    (2)  op(all_10_1, all_10_2) = e1
% 174.80/26.80    (3)  all_52_0 = e2
% 174.80/26.80    (4)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.80/26.80         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.80/26.80    (5)  all_52_10 = all_10_1
% 174.80/26.80    (6)   ~ (e2 = e1)
% 174.80/26.80    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.80    (8)   ~ (e3 = e2)
% 174.80/26.80  
% 174.80/26.80  Begin of proof
% 174.80/26.80  | 
% 174.80/26.80  | BETA: splitting (4) gives:
% 174.80/26.80  | 
% 174.80/26.80  | Case 1:
% 174.80/26.80  | | 
% 174.80/26.80  | |   (9)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.80/26.80  | | 
% 174.80/26.80  | | REF_CLOSE: (3), (8), (9) are inconsistent by sub-proof #124.
% 174.80/26.80  | | 
% 174.80/26.80  | Case 2:
% 174.80/26.80  | | 
% 174.80/26.80  | |   (10)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 174.80/26.80  | | 
% 174.80/26.80  | | ALPHA: (10) implies:
% 174.80/26.80  | |   (11)  all_52_10 = e2
% 174.80/26.80  | | 
% 174.80/26.80  | | COMBINE_EQS: (5), (11) imply:
% 174.80/26.80  | |   (12)  all_10_1 = e2
% 174.80/26.80  | | 
% 174.80/26.80  | | REF_CLOSE: (1), (2), (6), (7), (12) are inconsistent by sub-proof #446.
% 174.80/26.80  | | 
% 174.80/26.80  | End of split
% 174.80/26.80  | 
% 174.80/26.80  End of proof
% 174.80/26.80  
% 174.80/26.80  Sub-proof #70 shows that the following formulas are inconsistent:
% 174.80/26.80  ----------------------------------------------------------------
% 174.80/26.80    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.80    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.80/26.80    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.80/26.80    (4)   ~ (all_52_27 = all_10_2)
% 174.80/26.80    (5)   ~ (all_52_17 = all_52_23)
% 174.80/26.80    (6)  op(e2, all_10_2) = all_10_1
% 174.80/26.80    (7)   ~ (all_52_13 = all_52_29)
% 174.80/26.80    (8)  all_42_1 = e2
% 174.80/26.80    (9)  all_56_3 = all_52_7
% 174.80/26.80    (10)  op(e3, e2) = all_52_3
% 174.80/26.80    (11)   ~ (all_52_9 = all_52_25)
% 174.80/26.80    (12)   ~ (all_52_19 = all_52_23)
% 174.80/26.80    (13)  all_56_11 = all_52_23
% 174.80/26.80    (14)  op(e1, e2) = all_52_19
% 174.80/26.80    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.80/26.80    (16)  op(e3, all_52_9) = all_52_8
% 174.80/26.80    (17)   ~ (all_52_3 = all_10_2)
% 174.80/26.80    (18)  all_58_5 = all_52_13
% 174.80/26.80    (19)   ~ (all_52_25 = all_52_29)
% 174.80/26.80    (20)  all_56_15 = all_6_2
% 174.80/26.80    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.80    (22)  all_58_3 = all_10_2
% 174.80/26.80    (23)  all_56_9 = all_52_19
% 174.80/26.80    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.80    (25)  all_58_15 = all_6_2
% 174.80/26.80    (26)  op(e2, all_4_2) = e1
% 174.80/26.80    (27)   ~ (all_52_9 = all_4_2)
% 174.80/26.80    (28)   ~ (all_52_5 = all_52_7)
% 174.80/26.80    (29)  all_58_10 = all_52_15
% 174.80/26.80    (30)   ~ (all_52_5 = all_4_2)
% 174.80/26.80    (31)  all_58_7 = all_52_19
% 174.80/26.80    (32)  all_56_4 = all_52_9
% 174.80/26.80    (33)   ~ (all_52_15 = all_6_2)
% 174.80/26.80    (34)   ~ (all_52_17 = all_52_25)
% 174.80/26.80    (35)  op(e0, e1) = all_52_29
% 174.80/26.80    (36)  all_58_4 = all_52_5
% 174.80/26.80    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.80    (38)   ~ (e3 = e1)
% 174.80/26.80    (39)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.80/26.80    (40)   ~ (all_52_27 = all_52_29)
% 174.80/26.80    (41)   ~ (all_52_17 = all_14_2)
% 174.80/26.80    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.80    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.80    (44)   ~ (all_52_7 = all_4_2)
% 174.80/26.80    (45)  all_58_1 = all_52_3
% 174.80/26.80    (46)   ~ (all_52_13 = all_52_15)
% 174.80/26.80    (47)  all_58_0 = all_4_2
% 174.80/26.80    (48)  op(e1, all_52_13) = all_52_12
% 174.80/26.80    (49)  all_52_0 = e2
% 174.80/26.80    (50)  op(e0, e0) = all_6_2
% 174.80/26.80    (51)  op(e1, all_52_29) = all_52_28
% 174.80/26.80    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.80    (53)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.80    (54)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.80/26.80    (55)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.80/26.80    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.80    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.80/26.80    (58)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.80/26.80    (59)  all_58_14 = all_52_29
% 174.80/26.80    (60)   ~ (all_52_3 = all_52_5)
% 174.80/26.80    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.80    (62)  op(e2, e1) = all_52_13
% 174.80/26.80    (63)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.80    (64)  all_58_8 = all_14_2
% 174.80/26.80    (65)  all_56_1 = all_52_3
% 174.80/26.80    (66)  all_56_14 = all_52_29
% 174.80/26.80    (67)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.80/26.80    (68)   ~ (all_52_5 = all_14_2)
% 174.80/26.80    (69)   ~ (all_52_3 = all_52_27)
% 174.80/26.80    (70)   ~ (all_52_3 = all_4_2)
% 174.80/26.80    (71)  op(e0, e3) = all_52_25
% 174.80/26.80    (72)  op(e0, all_6_2) = all_6_1
% 174.80/26.80    (73)  op(e3, all_52_17) = all_52_16
% 174.80/26.80    (74)  all_52_10 = all_10_1
% 174.80/26.80    (75)   ~ (all_52_13 = all_14_2)
% 174.80/26.80    (76)   ~ (e3 = e0)
% 174.80/26.80    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.80    (78)   ~ (all_52_9 = all_52_13)
% 174.80/26.80    (79)  op(e0, all_52_23) = all_52_22
% 174.80/26.80    (80)   ~ (all_52_15 = all_52_23)
% 174.80/26.80    (81)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.80    (82)  op(all_10_1, all_10_2) = all_10_0
% 174.80/26.80    (83)  op(e1, e0) = all_52_23
% 174.80/26.80    (84)  all_58_13 = all_52_27
% 174.80/26.80    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.80    (86)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.80    (87)   ~ (all_52_9 = all_52_17)
% 174.80/26.80    (88)  all_58_6 = all_52_17
% 174.80/26.80    (89)   ~ (all_52_3 = all_52_7)
% 174.80/26.80    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.80/26.80    (91)  op(e2, all_52_19) = all_52_18
% 174.80/26.80    (92)   ~ (e1 = e0)
% 174.80/26.80    (93)  all_56_0 = all_4_2
% 174.80/26.80    (94)  all_58_11 = all_52_23
% 174.80/26.80    (95)   ~ (all_52_3 = all_52_19)
% 174.80/26.80    (96)   ~ (all_52_7 = all_52_15)
% 174.80/26.80    (97)  op(e0, all_52_15) = all_52_14
% 174.80/26.80    (98)   ~ (all_52_29 = all_14_2)
% 174.80/26.80    (99)   ~ (all_52_19 = all_10_2)
% 174.80/26.80    (100)  op(e3, all_4_2) = e2
% 174.80/26.80    (101)   ~ (all_52_23 = all_6_2)
% 174.80/26.80    (102)   ~ (all_52_29 = all_6_2)
% 174.80/26.80    (103)  all_58_2 = all_52_9
% 174.80/26.80    (104)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.80/26.80    (105)  op(e3, e1) = all_52_5
% 174.80/26.80    (106)   ~ (e2 = e1)
% 174.80/26.80    (107)  all_56_10 = all_14_2
% 174.80/26.80    (108)   ~ (all_52_25 = all_6_2)
% 174.80/26.80    (109)  op(e1, e1) = all_14_2
% 174.80/26.80    (110)  op(e1, e3) = all_52_17
% 174.80/26.80    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.80    (112)   ~ (all_52_25 = all_4_2)
% 174.80/26.80    (113)  op(e3, e0) = all_52_7
% 174.80/26.80    (114)  op(e3, e3) = all_4_2
% 174.80/26.80    (115)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.80/26.80             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.80/26.80    (116)  all_56_8 = all_52_17
% 174.80/26.80    (117)   ~ (all_52_17 = all_4_2)
% 174.80/26.80    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.80             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.80    (119)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.80/26.80           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.80/26.80           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.80/26.80           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.80/26.80    (120)   ~ (all_52_25 = all_52_27)
% 174.80/26.80    (121)   ~ (all_52_27 = all_6_2)
% 174.80/26.80    (122)   ~ (all_52_7 = all_6_2)
% 174.80/26.80    (123)   ~ (all_10_0 = e3)
% 174.80/26.80    (124)   ~ (all_52_15 = all_10_2)
% 174.80/26.80    (125)  all_42_2 = all_4_2
% 174.80/26.80    (126)  all_56_7 = all_52_15
% 174.80/26.80    (127)   ~ (all_52_7 = all_52_23)
% 174.80/26.80    (128)   ~ (all_52_13 = all_10_2)
% 174.80/26.80    (129)  op(e2, all_52_27) = all_52_26
% 174.80/26.80    (130)  all_52_20 = all_14_1
% 174.80/26.80    (131)   ~ (all_52_17 = all_52_19)
% 174.80/26.80    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.80    (133)  all_52_30 = all_6_1
% 174.80/26.80    (134)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.80/26.80    (135)  op(e1, all_14_2) = all_14_1
% 174.80/26.80    (136)  all_58_9 = all_52_7
% 174.80/26.80    (137)   ~ (e2 = e0)
% 174.80/26.80    (138)  all_58_12 = all_52_25
% 174.80/26.80    (139)  op(all_6_1, all_6_2) = e3
% 174.80/26.80    (140)   ~ (all_10_0 = e1)
% 174.80/26.80    (141)  all_56_6 = all_52_13
% 174.80/26.80    (142)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.80    (143)   ~ (all_52_9 = all_52_15)
% 174.80/26.80    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.80    (145)   ~ (e3 = e2)
% 174.80/26.80    (146)   ~ (all_52_19 = all_14_2)
% 174.80/26.80    (147)  op(e2, e3) = all_52_9
% 174.80/26.80  
% 174.80/26.80  Begin of proof
% 174.80/26.80  | 
% 174.80/26.80  | BETA: splitting (39) gives:
% 174.80/26.80  | 
% 174.80/26.80  | Case 1:
% 174.80/26.80  | | 
% 174.80/26.80  | |   (148)   ~ (all_42_1 = e2)
% 174.80/26.80  | | 
% 174.80/26.80  | | REDUCE: (8), (148) imply:
% 174.80/26.80  | |   (149)  $false
% 174.80/26.80  | | 
% 174.80/26.80  | | CLOSE: (149) is inconsistent.
% 174.80/26.80  | | 
% 174.80/26.80  | Case 2:
% 174.80/26.80  | | 
% 174.80/26.80  | |   (150)   ~ (all_42_2 = e0)
% 174.80/26.80  | | 
% 174.80/26.80  | | REDUCE: (125), (150) imply:
% 174.80/26.80  | |   (151)   ~ (all_4_2 = e0)
% 174.80/26.80  | | 
% 174.80/26.80  | | BETA: splitting (115) gives:
% 174.80/26.80  | | 
% 174.80/26.80  | | Case 1:
% 174.80/26.80  | | | 
% 174.80/26.80  | | |   (152)  all_58_15 = e0
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REF_CLOSE: (25), (50), (72), (76), (118), (139), (152) are inconsistent by
% 174.80/26.80  | | |            sub-proof #510.
% 174.80/26.80  | | | 
% 174.80/26.80  | | Case 2:
% 174.80/26.80  | | | 
% 174.80/26.80  | | |   (153)   ~ (all_58_15 = e0)
% 174.80/26.80  | | |   (154)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 174.80/26.80  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 174.80/26.80  | | | 
% 174.80/26.80  | | | ALPHA: (154) implies:
% 174.80/26.80  | | |   (155)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.80  | | | 
% 174.80/26.80  | | | REDUCE: (25), (153) imply:
% 174.80/26.80  | | |   (156)   ~ (all_6_2 = e0)
% 174.80/26.80  | | | 
% 174.80/26.80  | | | BETA: splitting (119) gives:
% 174.80/26.80  | | | 
% 174.80/26.80  | | | Case 1:
% 174.80/26.80  | | | | 
% 174.80/26.80  | | | |   (157)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.80/26.81  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.80/26.81  | | | |            = e0)
% 174.80/26.81  | | | | 
% 174.80/26.81  | | | | BETA: splitting (157) gives:
% 174.80/26.81  | | | | 
% 174.80/26.81  | | | | Case 1:
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | |   (158)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REF_CLOSE: (49), (145), (158) are inconsistent by sub-proof #124.
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | Case 2:
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | |   (159)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 174.80/26.81  | | | | |          e0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | ALPHA: (159) implies:
% 174.80/26.81  | | | | |   (160)  all_52_14 = e0
% 174.80/26.81  | | | | |   (161)  all_52_12 = e1
% 174.80/26.81  | | | | |   (162)  all_52_10 = e2
% 174.80/26.81  | | | | |   (163)  all_52_8 = e3
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | COMBINE_EQS: (74), (162) imply:
% 174.80/26.81  | | | | |   (164)  all_10_1 = e2
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REDUCE: (82), (164) imply:
% 174.80/26.81  | | | | |   (165)  op(e2, all_10_2) = all_10_0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REDUCE: (16), (163) imply:
% 174.80/26.81  | | | | |   (166)  op(e3, all_52_9) = e3
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REDUCE: (6), (164) imply:
% 174.80/26.81  | | | | |   (167)  op(e2, all_10_2) = e2
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REDUCE: (48), (161) imply:
% 174.80/26.81  | | | | |   (168)  op(e1, all_52_13) = e1
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REDUCE: (97), (160) imply:
% 174.80/26.81  | | | | |   (169)  op(e0, all_52_15) = e0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13),
% 174.80/26.81  | | | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.80/26.81  | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.80/26.81  | | | | |            (35), (36), (37), (38), (40), (41), (42), (43), (44), (45),
% 174.80/26.81  | | | | |            (46), (47), (51), (52), (53), (54), (55), (56), (57), (58),
% 174.80/26.81  | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (69),
% 174.80/26.81  | | | | |            (70), (71), (72), (73), (75), (76), (78), (79), (81), (84),
% 174.80/26.81  | | | | |            (85), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 174.80/26.81  | | | | |            (96), (98), (99), (100), (101), (102), (103), (104), (105),
% 174.80/26.81  | | | | |            (107), (108), (109), (110), (112), (113), (114), (116),
% 174.80/26.81  | | | | |            (117), (118), (120), (121), (122), (123), (127), (128),
% 174.80/26.81  | | | | |            (129), (131), (132), (134), (135), (136), (138), (140),
% 174.80/26.81  | | | | |            (141), (143), (144), (146), (147), (155), (156), (165),
% 174.80/26.81  | | | | |            (166), (167), (168), (169) are inconsistent by sub-proof
% 174.80/26.81  | | | | |            #83.
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | End of split
% 174.80/26.81  | | | | 
% 174.80/26.81  | | | Case 2:
% 174.80/26.81  | | | | 
% 174.80/26.81  | | | |   (170)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.80/26.81  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.80/26.81  | | | |            all_52_30 = e0)
% 174.80/26.81  | | | | 
% 174.80/26.81  | | | | BETA: splitting (170) gives:
% 174.80/26.81  | | | | 
% 174.80/26.81  | | | | Case 1:
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | |   (171)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 174.80/26.81  | | | | |          = e0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | ALPHA: (171) implies:
% 174.80/26.81  | | | | |   (172)  all_52_22 = e0
% 174.80/26.81  | | | | |   (173)  all_52_20 = e1
% 174.80/26.81  | | | | |   (174)  all_52_18 = e2
% 174.80/26.81  | | | | |   (175)  all_52_16 = e3
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | COMBINE_EQS: (130), (173) imply:
% 174.80/26.81  | | | | |   (176)  all_14_1 = e1
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REF_CLOSE: (1), (5), (10), (11), (14), (18), (19), (20), (21), (22),
% 174.80/26.81  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (34),
% 174.80/26.81  | | | | |            (36), (37), (38), (42), (43), (44), (45), (47), (53), (56),
% 174.80/26.81  | | | | |            (59), (61), (62), (63), (64), (68), (70), (71), (73), (75),
% 174.80/26.81  | | | | |            (76), (77), (78), (79), (80), (81), (83), (84), (85), (86),
% 174.80/26.81  | | | | |            (87), (88), (91), (92), (93), (94), (95), (96), (100),
% 174.80/26.81  | | | | |            (101), (103), (105), (106), (107), (108), (110), (111),
% 174.80/26.81  | | | | |            (112), (113), (114), (117), (118), (120), (124), (126),
% 174.80/26.81  | | | | |            (127), (131), (132), (135), (136), (137), (138), (142),
% 174.80/26.81  | | | | |            (144), (145), (146), (147), (151), (155), (172), (174),
% 174.80/26.81  | | | | |            (175), (176) are inconsistent by sub-proof #77.
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | Case 2:
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | |   (177)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 174.80/26.81  | | | | |          = e0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | ALPHA: (177) implies:
% 174.80/26.81  | | | | |   (178)  all_52_30 = e0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | COMBINE_EQS: (133), (178) imply:
% 174.80/26.81  | | | | |   (179)  all_6_1 = e0
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | | REF_CLOSE: (72), (76), (118), (139), (179) are inconsistent by
% 174.80/26.81  | | | | |            sub-proof #502.
% 174.80/26.81  | | | | | 
% 174.80/26.81  | | | | End of split
% 174.80/26.81  | | | | 
% 174.80/26.81  | | | End of split
% 174.80/26.81  | | | 
% 174.80/26.81  | | End of split
% 174.80/26.81  | | 
% 174.80/26.81  | End of split
% 174.80/26.81  | 
% 174.80/26.81  End of proof
% 174.80/26.81  
% 174.80/26.81  Sub-proof #71 shows that the following formulas are inconsistent:
% 174.80/26.81  ----------------------------------------------------------------
% 174.80/26.81    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.81    (2)   ~ (all_52_5 = all_52_13)
% 174.80/26.81    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.80/26.81    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.80/26.81    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.80/26.81    (6)   ~ (all_52_27 = all_10_2)
% 174.80/26.81    (7)   ~ (all_52_17 = all_52_23)
% 174.80/26.81    (8)  op(e2, all_10_2) = all_10_1
% 174.80/26.81    (9)   ~ (all_52_13 = all_52_29)
% 174.80/26.81    (10)  all_56_3 = all_52_7
% 174.80/26.81    (11)  op(e3, e2) = all_52_3
% 174.80/26.81    (12)   ~ (all_52_9 = all_52_25)
% 174.80/26.81    (13)  op(e3, all_52_25) = all_52_24
% 174.80/26.81    (14)   ~ (all_52_19 = all_52_23)
% 174.80/26.81    (15)  all_56_11 = all_52_23
% 174.80/26.81    (16)  op(e1, e2) = all_52_19
% 174.80/26.81    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.80/26.81    (18)  op(e3, all_52_9) = all_52_8
% 174.80/26.81    (19)   ~ (all_52_3 = all_10_2)
% 174.80/26.81    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.80/26.81    (21)  all_58_5 = all_52_13
% 174.80/26.81    (22)   ~ (all_52_25 = all_52_29)
% 174.80/26.81    (23)  all_56_15 = all_6_2
% 174.80/26.81    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.81    (25)  op(all_14_1, all_14_2) = all_14_0
% 174.80/26.81    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.80/26.81    (27)  all_58_3 = all_10_2
% 174.80/26.81    (28)  all_56_9 = all_52_19
% 174.80/26.81    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.81    (30)  all_58_15 = all_6_2
% 174.80/26.81    (31)   ~ (all_52_9 = all_4_2)
% 174.80/26.81    (32)   ~ (all_52_5 = all_52_7)
% 174.80/26.81    (33)  all_58_10 = all_52_15
% 174.80/26.81    (34)   ~ (all_52_5 = all_4_2)
% 174.80/26.81    (35)  all_58_7 = all_52_19
% 174.80/26.81    (36)  all_56_4 = all_52_9
% 174.80/26.81    (37)   ~ (all_52_15 = all_6_2)
% 174.80/26.81    (38)   ~ (all_52_17 = all_52_25)
% 174.80/26.81    (39)  op(e0, e1) = all_52_29
% 174.80/26.81    (40)  all_58_4 = all_52_5
% 174.80/26.81    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.81    (42)   ~ (e3 = e1)
% 174.80/26.81    (43)   ~ (all_52_27 = all_52_29)
% 174.80/26.81    (44)   ~ (all_52_17 = all_14_2)
% 174.80/26.81    (45)  op(e3, all_4_2) = all_4_1
% 174.80/26.81    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.81    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.81    (48)   ~ (all_52_7 = all_4_2)
% 174.80/26.81    (49)  all_58_1 = all_52_3
% 174.80/26.81    (50)   ~ (all_52_13 = all_52_15)
% 174.80/26.81    (51)  all_58_0 = all_4_2
% 174.80/26.81    (52)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 174.80/26.81    (53)  op(e1, all_52_13) = all_52_12
% 174.80/26.81    (54)  all_52_0 = e2
% 174.80/26.81    (55)  op(e1, all_52_29) = all_52_28
% 174.80/26.81    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.81    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.81    (58)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.80/26.81    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.80/26.81    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.81    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.80/26.81    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.80/26.81    (63)  all_58_14 = all_52_29
% 174.80/26.81    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.80/26.81    (65)  op(e2, all_4_2) = all_4_0
% 174.80/26.81    (66)   ~ (all_52_3 = all_52_5)
% 174.80/26.81    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.81    (68)  op(e2, e1) = all_52_13
% 174.80/26.81    (69)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.81    (70)  all_58_8 = all_14_2
% 174.80/26.81    (71)  all_56_1 = all_52_3
% 174.80/26.81    (72)  op(e0, e2) = all_52_27
% 174.80/26.81    (73)  all_56_14 = all_52_29
% 174.80/26.81    (74)   ~ (all_14_0 = e3)
% 174.80/26.81    (75)  op(all_4_1, all_4_2) = all_4_0
% 174.80/26.81    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.80/26.81    (77)   ~ (all_52_5 = all_14_2)
% 174.80/26.81    (78)   ~ (all_52_3 = all_52_27)
% 174.80/26.81    (79)   ~ (all_52_3 = all_4_2)
% 174.80/26.81    (80)  op(e0, e3) = all_52_25
% 174.80/26.81    (81)  op(e0, all_6_2) = all_6_1
% 174.80/26.81    (82)   ~ (all_52_9 = all_10_2)
% 174.80/26.81    (83)  op(e3, all_52_17) = all_52_16
% 174.80/26.81    (84)  all_52_10 = all_10_1
% 174.80/26.81    (85)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.80/26.81    (86)   ~ (all_52_13 = all_14_2)
% 174.80/26.81    (87)   ~ (e3 = e0)
% 174.80/26.81    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.81    (89)   ~ (all_52_9 = all_52_13)
% 174.80/26.81    (90)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.80/26.81    (91)  op(e0, all_52_23) = all_52_22
% 174.80/26.81    (92)   ~ (all_52_15 = all_52_23)
% 174.80/26.81    (93)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.81    (94)  op(all_10_1, all_10_2) = all_10_0
% 174.80/26.81    (95)   ~ (all_52_5 = all_52_29)
% 174.80/26.81    (96)  all_56_2 = all_52_5
% 174.80/26.81    (97)  op(e1, e0) = all_52_23
% 174.80/26.81    (98)  all_56_12 = all_52_25
% 174.80/26.81    (99)  all_58_13 = all_52_27
% 174.80/26.81    (100)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.81    (101)  all_56_5 = all_10_2
% 174.80/26.81    (102)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.81    (103)   ~ (all_52_9 = all_52_17)
% 174.80/26.81    (104)   ~ (all_14_0 = e2)
% 174.80/26.81    (105)  all_58_6 = all_52_17
% 174.80/26.81    (106)   ~ (all_52_3 = all_52_7)
% 174.80/26.81    (107)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.80/26.81    (108)  op(e2, all_52_19) = all_52_18
% 174.80/26.81    (109)   ~ (e1 = e0)
% 174.80/26.81    (110)  all_56_0 = all_4_2
% 174.80/26.81    (111)  all_58_11 = all_52_23
% 174.80/26.81    (112)   ~ (all_52_3 = all_52_19)
% 174.80/26.81    (113)   ~ (all_52_7 = all_52_15)
% 174.80/26.81    (114)  op(e0, all_52_15) = all_52_14
% 174.80/26.81    (115)   ~ (all_52_29 = all_14_2)
% 174.80/26.81    (116)   ~ (all_4_0 = e1)
% 174.80/26.81    (117)   ~ (all_52_19 = all_10_2)
% 174.80/26.81    (118)   ~ (all_58_15 = e0)
% 174.80/26.81    (119)  op(e3, all_4_2) = e2
% 174.80/26.81    (120)   ~ (all_52_23 = all_6_2)
% 174.80/26.81    (121)   ~ (all_52_29 = all_6_2)
% 174.80/26.81    (122)  all_58_2 = all_52_9
% 174.80/26.81    (123)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.80/26.81    (124)  op(e3, e1) = all_52_5
% 174.80/26.81    (125)   ~ (e2 = e1)
% 174.80/26.81    (126)  all_56_10 = all_14_2
% 174.80/26.81    (127)   ~ (all_52_25 = all_6_2)
% 174.80/26.81    (128)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.80/26.81    (129)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.80/26.81    (130)  op(e1, e3) = all_52_17
% 174.80/26.81    (131)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.81    (132)   ~ (all_52_25 = all_4_2)
% 174.80/26.81    (133)  op(e3, e0) = all_52_7
% 174.80/26.81    (134)  op(e3, e3) = all_4_2
% 174.80/26.81    (135)   ~ (all_10_1 = e3)
% 174.80/26.81    (136)  all_56_8 = all_52_17
% 174.80/26.81    (137)   ~ (all_52_17 = all_4_2)
% 174.80/26.81    (138)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.81             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.81    (139)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.80/26.81           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.80/26.81           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.80/26.81           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.80/26.81    (140)   ~ (all_52_25 = all_52_27)
% 174.80/26.81    (141)   ~ (all_52_27 = all_6_2)
% 174.80/26.81    (142)   ~ (all_52_7 = all_6_2)
% 174.80/26.81    (143)   ~ (all_10_0 = e3)
% 174.80/26.81    (144)   ~ (all_52_15 = all_10_2)
% 174.80/26.81    (145)   ~ (all_52_19 = all_52_27)
% 174.80/26.81    (146)  all_56_7 = all_52_15
% 174.80/26.81    (147)   ~ (all_52_7 = all_52_23)
% 174.80/26.81    (148)   ~ (all_52_13 = all_10_2)
% 174.80/26.81    (149)  op(e2, all_52_27) = all_52_26
% 174.80/26.81    (150)  all_52_20 = all_14_1
% 174.80/26.81    (151)   ~ (all_52_17 = all_52_19)
% 174.80/26.81    (152)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.81    (153)  all_52_30 = all_6_1
% 174.80/26.81    (154)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.80/26.81    (155)  op(e1, all_14_2) = all_14_1
% 174.80/26.81    (156)  all_58_9 = all_52_7
% 174.80/26.81    (157)   ~ (e2 = e0)
% 174.80/26.81    (158)  all_58_12 = all_52_25
% 174.80/26.81    (159)   ~ (all_10_0 = e1)
% 174.80/26.81    (160)  all_56_6 = all_52_13
% 174.80/26.81    (161)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 174.80/26.81             all_58_13 = e0 | all_58_14 = e0)
% 174.80/26.81    (162)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.81    (163)   ~ (all_52_9 = all_52_15)
% 174.80/26.81    (164)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.81    (165)   ~ (e3 = e2)
% 174.80/26.81    (166)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 174.80/26.81    (167)   ~ (all_52_19 = all_14_2)
% 174.80/26.81    (168)  op(e2, e3) = all_52_9
% 174.80/26.81    (169)  all_56_13 = all_52_27
% 174.80/26.81  
% 174.80/26.81  Begin of proof
% 174.80/26.81  | 
% 174.80/26.81  | ALPHA: (161) implies:
% 174.80/26.81  |   (170)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.80/26.81  |   (171)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.81  | 
% 174.80/26.81  | REDUCE: (30), (118) imply:
% 174.80/26.81  |   (172)   ~ (all_6_2 = e0)
% 174.80/26.81  | 
% 174.80/26.81  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 174.80/26.81  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 174.80/26.81  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 174.80/26.81  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.80/26.81  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 174.80/26.81  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 174.80/26.81  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 174.80/26.81  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 174.80/26.81  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 174.80/26.81  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 174.80/26.81  |            (110), (111), (112), (113), (114), (115), (116), (117), (119),
% 174.80/26.81  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 174.80/26.81  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 174.80/26.81  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 174.80/26.81  |            (147), (148), (149), (150), (151), (152), (153), (154), (155),
% 174.80/26.81  |            (156), (157), (158), (159), (160), (162), (163), (164), (165),
% 174.80/26.81  |            (166), (167), (168), (169), (170), (171), (172) are inconsistent by
% 174.80/26.81  |            sub-proof #86.
% 174.80/26.81  | 
% 174.80/26.81  End of proof
% 174.80/26.81  
% 174.80/26.81  Sub-proof #72 shows that the following formulas are inconsistent:
% 174.80/26.81  ----------------------------------------------------------------
% 174.80/26.81    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.81    (2)   ~ (all_52_5 = all_52_13)
% 174.80/26.81    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.80/26.81    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 174.80/26.81    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.80/26.81    (6)   ~ (all_52_27 = all_10_2)
% 174.80/26.81    (7)   ~ (all_52_17 = all_52_23)
% 174.80/26.81    (8)   ~ (all_6_0 = e3)
% 174.80/26.81    (9)  op(e2, all_10_2) = all_10_1
% 174.80/26.81    (10)   ~ (all_52_13 = all_52_29)
% 174.80/26.81    (11)  all_42_1 = e2
% 174.80/26.81    (12)  all_56_3 = all_52_7
% 174.80/26.81    (13)  op(e3, e2) = all_52_3
% 174.80/26.81    (14)   ~ (all_52_9 = all_52_25)
% 174.80/26.81    (15)  op(e3, all_52_25) = all_52_24
% 174.80/26.81    (16)   ~ (all_52_19 = all_52_23)
% 174.80/26.81    (17)  all_56_11 = all_52_23
% 174.80/26.81    (18)  op(e1, e2) = all_52_19
% 174.80/26.81    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.80/26.81    (20)  op(e3, all_52_9) = all_52_8
% 174.80/26.81    (21)   ~ (all_52_3 = all_10_2)
% 174.80/26.81    (22)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 174.80/26.81    (23)  all_58_5 = all_52_13
% 174.80/26.81    (24)   ~ (all_52_25 = all_52_29)
% 174.80/26.81    (25)  all_56_15 = all_6_2
% 174.80/26.81    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.81    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.80/26.81    (28)  all_58_3 = all_10_2
% 174.80/26.81    (29)  all_56_9 = all_52_19
% 174.80/26.81    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.81    (31)  all_58_15 = all_6_2
% 174.80/26.81    (32)  op(e2, all_4_2) = e1
% 174.80/26.81    (33)   ~ (all_52_9 = all_4_2)
% 174.80/26.81    (34)   ~ (all_52_5 = all_52_7)
% 174.80/26.81    (35)  all_58_10 = all_52_15
% 174.80/26.81    (36)   ~ (all_52_5 = all_4_2)
% 174.80/26.81    (37)  all_58_7 = all_52_19
% 174.80/26.81    (38)  all_56_4 = all_52_9
% 174.80/26.81    (39)   ~ (all_52_15 = all_6_2)
% 174.80/26.81    (40)   ~ (all_52_17 = all_52_25)
% 174.80/26.81    (41)  op(e0, e1) = all_52_29
% 174.80/26.81    (42)  all_58_4 = all_52_5
% 174.80/26.81    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.81    (44)   ~ (e3 = e1)
% 174.80/26.81    (45)   ~ (all_42_1 = e2) |  ~ (all_42_2 = e0)
% 174.80/26.81    (46)   ~ (all_52_27 = all_52_29)
% 174.80/26.81    (47)   ~ (all_52_17 = all_14_2)
% 174.80/26.81    (48)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.81    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.81    (50)   ~ (all_52_7 = all_4_2)
% 174.80/26.81    (51)  all_58_1 = all_52_3
% 174.80/26.81    (52)   ~ (all_52_13 = all_52_15)
% 174.80/26.81    (53)  all_58_0 = all_4_2
% 174.80/26.81    (54)  op(e1, all_52_13) = all_52_12
% 174.80/26.81    (55)  all_52_0 = e2
% 174.80/26.81    (56)  op(e0, e0) = all_6_2
% 174.80/26.81    (57)  op(e1, all_52_29) = all_52_28
% 174.80/26.81    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.81    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.81    (60)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.80/26.81    (61)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.80/26.81    (62)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.81    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.80/26.81    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.80/26.81    (65)  all_58_14 = all_52_29
% 174.80/26.81    (66)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 174.80/26.81    (67)   ~ (all_52_3 = all_52_5)
% 174.80/26.81    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.81    (69)  op(e2, e1) = all_52_13
% 174.80/26.81    (70)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.81    (71)  all_58_8 = all_14_2
% 174.80/26.81    (72)  all_56_1 = all_52_3
% 174.80/26.81    (73)  op(e0, e2) = all_52_27
% 174.80/26.81    (74)  all_56_14 = all_52_29
% 174.80/26.81    (75)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.80/26.81    (76)   ~ (all_52_5 = all_14_2)
% 174.80/26.81    (77)   ~ (all_52_3 = all_52_27)
% 174.80/26.81    (78)   ~ (all_52_3 = all_4_2)
% 174.80/26.81    (79)  op(all_6_1, all_6_2) = all_6_0
% 174.80/26.81    (80)  op(e0, e3) = all_52_25
% 174.80/26.81    (81)  op(e0, all_6_2) = all_6_1
% 174.80/26.81    (82)   ~ (all_52_9 = all_10_2)
% 174.80/26.81    (83)  op(e3, all_52_17) = all_52_16
% 174.80/26.81    (84)  all_52_10 = all_10_1
% 174.80/26.81    (85)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 174.80/26.81    (86)   ~ (all_52_13 = all_14_2)
% 174.80/26.81    (87)   ~ (e3 = e0)
% 174.80/26.81    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.81    (89)   ~ (all_52_9 = all_52_13)
% 174.80/26.81    (90)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.80/26.81    (91)  op(e0, all_52_23) = all_52_22
% 174.80/26.81    (92)   ~ (all_52_15 = all_52_23)
% 174.80/26.81    (93)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.81    (94)  op(all_10_1, all_10_2) = all_10_0
% 174.80/26.81    (95)   ~ (all_52_5 = all_52_29)
% 174.80/26.81    (96)  op(e1, e0) = all_52_23
% 174.80/26.81    (97)  all_56_12 = all_52_25
% 174.80/26.81    (98)  all_58_13 = all_52_27
% 174.80/26.81    (99)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.81    (100)  all_56_5 = all_10_2
% 174.80/26.81    (101)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.81    (102)   ~ (all_52_9 = all_52_17)
% 174.80/26.81    (103)  all_58_6 = all_52_17
% 174.80/26.81    (104)   ~ (all_52_3 = all_52_7)
% 174.80/26.81    (105)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.80/26.81    (106)  op(e2, all_52_19) = all_52_18
% 174.80/26.81    (107)   ~ (e1 = e0)
% 174.80/26.81    (108)  all_56_0 = all_4_2
% 174.80/26.81    (109)  all_58_11 = all_52_23
% 174.80/26.81    (110)   ~ (all_52_3 = all_52_19)
% 174.80/26.81    (111)   ~ (all_52_7 = all_52_15)
% 174.80/26.81    (112)  op(e0, all_52_15) = all_52_14
% 174.80/26.81    (113)   ~ (all_52_29 = all_14_2)
% 174.80/26.81    (114)   ~ (all_52_19 = all_10_2)
% 174.80/26.81    (115)  op(e3, all_4_2) = e2
% 174.80/26.81    (116)   ~ (all_52_23 = all_6_2)
% 174.80/26.81    (117)   ~ (all_6_0 = e2)
% 174.80/26.81    (118)   ~ (all_52_29 = all_6_2)
% 174.80/26.81    (119)  all_58_2 = all_52_9
% 174.80/26.81    (120)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 174.80/26.81    (121)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.80/26.81    (122)  op(e3, e1) = all_52_5
% 174.80/26.81    (123)   ~ (e2 = e1)
% 174.80/26.81    (124)  all_56_10 = all_14_2
% 174.80/26.81    (125)   ~ (all_52_25 = all_6_2)
% 174.80/26.81    (126)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 174.80/26.81    (127)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 174.80/26.81    (128)  op(e1, e1) = all_14_2
% 174.80/26.81    (129)  op(e1, e3) = all_52_17
% 174.80/26.81    (130)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.81    (131)   ~ (all_52_25 = all_4_2)
% 174.80/26.81    (132)  op(e3, e0) = all_52_7
% 174.80/26.81    (133)  op(e3, e3) = all_4_2
% 174.80/26.81    (134)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 174.80/26.81             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 174.80/26.81    (135)  all_56_8 = all_52_17
% 174.80/26.81    (136)   ~ (all_52_17 = all_4_2)
% 174.80/26.82    (137)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.82             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.82    (138)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.80/26.82           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 174.80/26.82           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 174.80/26.82           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 174.80/26.82    (139)   ~ (all_52_25 = all_52_27)
% 174.80/26.82    (140)   ~ (all_52_27 = all_6_2)
% 174.80/26.82    (141)   ~ (all_52_7 = all_6_2)
% 174.80/26.82    (142)   ~ (all_10_0 = e3)
% 174.80/26.82    (143)   ~ (all_52_15 = all_10_2)
% 174.80/26.82    (144)   ~ (all_52_19 = all_52_27)
% 174.80/26.82    (145)  all_42_2 = all_4_2
% 174.80/26.82    (146)  all_56_7 = all_52_15
% 174.80/26.82    (147)   ~ (all_52_7 = all_52_23)
% 174.80/26.82    (148)   ~ (all_52_13 = all_10_2)
% 174.80/26.82    (149)   ~ (all_6_0 = e1)
% 174.80/26.82    (150)  op(e2, all_52_27) = all_52_26
% 174.80/26.82    (151)  all_52_20 = all_14_1
% 174.80/26.82    (152)   ~ (all_52_17 = all_52_19)
% 174.80/26.82    (153)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.82    (154)  all_52_30 = all_6_1
% 174.80/26.82    (155)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 174.80/26.82    (156)  op(e1, all_14_2) = all_14_1
% 174.80/26.82    (157)  all_58_9 = all_52_7
% 174.80/26.82    (158)   ~ (e2 = e0)
% 174.80/26.82    (159)  all_58_12 = all_52_25
% 174.80/26.82    (160)   ~ (all_10_0 = e1)
% 174.80/26.82    (161)  all_56_6 = all_52_13
% 174.80/26.82    (162)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.82    (163)   ~ (all_52_9 = all_52_15)
% 174.80/26.82    (164)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.82    (165)   ~ (e3 = e2)
% 174.80/26.82    (166)   ~ (all_52_19 = all_14_2)
% 174.80/26.82    (167)  op(e2, e3) = all_52_9
% 174.80/26.82    (168)  all_56_13 = all_52_27
% 174.80/26.82  
% 174.80/26.82  Begin of proof
% 174.80/26.82  | 
% 174.80/26.82  | BETA: splitting (45) gives:
% 174.80/26.82  | 
% 174.80/26.82  | Case 1:
% 174.80/26.82  | | 
% 174.80/26.82  | |   (169)   ~ (all_42_1 = e2)
% 174.80/26.82  | | 
% 174.80/26.82  | | REDUCE: (11), (169) imply:
% 174.80/26.82  | |   (170)  $false
% 174.80/26.82  | | 
% 174.80/26.82  | | CLOSE: (170) is inconsistent.
% 174.80/26.82  | | 
% 174.80/26.82  | Case 2:
% 174.80/26.82  | | 
% 174.80/26.82  | |   (171)   ~ (all_42_2 = e0)
% 174.80/26.82  | | 
% 174.80/26.82  | | REDUCE: (145), (171) imply:
% 174.80/26.82  | |   (172)   ~ (all_4_2 = e0)
% 174.80/26.82  | | 
% 174.80/26.82  | | BETA: splitting (134) gives:
% 174.80/26.82  | | 
% 174.80/26.82  | | Case 1:
% 174.80/26.82  | | | 
% 174.80/26.82  | | |   (173)  all_58_15 = e0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | COMBINE_EQS: (31), (173) imply:
% 174.80/26.82  | | |   (174)  all_6_2 = e0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (39), (174) imply:
% 174.80/26.82  | | |   (175)   ~ (all_52_15 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (116), (174) imply:
% 174.80/26.82  | | |   (176)   ~ (all_52_23 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (125), (174) imply:
% 174.80/26.82  | | |   (177)   ~ (all_52_25 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (140), (174) imply:
% 174.80/26.82  | | |   (178)   ~ (all_52_27 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (118), (174) imply:
% 174.80/26.82  | | |   (179)   ~ (all_52_29 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (79), (174) imply:
% 174.80/26.82  | | |   (180)  op(all_6_1, e0) = all_6_0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (81), (174) imply:
% 174.80/26.82  | | |   (181)  op(e0, e0) = all_6_1
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (56), (174) imply:
% 174.80/26.82  | | |   (182)  op(e0, e0) = e0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | GROUND_INST: instantiating (137) with e0, all_6_1, e0, e0, simplifying
% 174.80/26.82  | | |              with (181), (182) gives:
% 174.80/26.82  | | |   (183)  all_6_1 = e0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (180), (183) imply:
% 174.80/26.82  | | |   (184)  op(e0, e0) = all_6_0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | GROUND_INST: instantiating (137) with e0, all_6_0, e0, e0, simplifying
% 174.80/26.82  | | |              with (182), (184) gives:
% 174.80/26.82  | | |   (185)  all_6_0 = e0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (8), (185) imply:
% 174.80/26.82  | | |   (186)   ~ (e3 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (117), (185) imply:
% 174.80/26.82  | | |   (187)   ~ (e2 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (149), (185) imply:
% 174.80/26.82  | | |   (188)   ~ (e1 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | BETA: splitting (138) gives:
% 174.80/26.82  | | | 
% 174.80/26.82  | | | Case 1:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | |   (189)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.80/26.82  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.80/26.82  | | | |            = e0)
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | BETA: splitting (189) gives:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | Case 1:
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | |   (190)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REF_CLOSE: (55), (165), (190) are inconsistent by sub-proof #124.
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | Case 2:
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | |   (191)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 174.80/26.82  | | | | |          e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | ALPHA: (191) implies:
% 174.80/26.82  | | | | |   (192)  all_52_14 = e0
% 174.80/26.82  | | | | |   (193)  all_52_12 = e1
% 174.80/26.82  | | | | |   (194)  all_52_10 = e2
% 174.80/26.82  | | | | |   (195)  all_52_8 = e3
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | COMBINE_EQS: (84), (194) imply:
% 174.80/26.82  | | | | |   (196)  all_10_1 = e2
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | SIMP: (196) implies:
% 174.80/26.82  | | | | |   (197)  all_10_1 = e2
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (94), (197) imply:
% 174.80/26.82  | | | | |   (198)  op(e2, all_10_2) = all_10_0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (20), (195) imply:
% 174.80/26.82  | | | | |   (199)  op(e3, all_52_9) = e3
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (9), (197) imply:
% 174.80/26.82  | | | | |   (200)  op(e2, all_10_2) = e2
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (54), (193) imply:
% 174.80/26.82  | | | | |   (201)  op(e1, all_52_13) = e1
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (112), (192) imply:
% 174.80/26.82  | | | | |   (202)  op(e0, all_52_15) = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | GROUND_INST: instantiating (137) with e2, all_10_0, all_10_2, e2,
% 174.80/26.82  | | | | |              simplifying with (198), (200) gives:
% 174.80/26.82  | | | | |   (203)  all_10_0 = e2
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (142), (203) imply:
% 174.80/26.82  | | | | |   (204)   ~ (e3 = e2)
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REF_CLOSE: (7), (13), (14), (21), (23), (27), (28), (33), (34), (35),
% 174.80/26.82  | | | | |            (37), (40), (41), (42), (43), (44), (46), (47), (49), (50),
% 174.80/26.82  | | | | |            (51), (53), (60), (62), (65), (68), (70), (71), (73), (74),
% 174.80/26.82  | | | | |            (80), (85), (87), (93), (98), (102), (103), (104), (107),
% 174.80/26.82  | | | | |            (109), (111), (114), (119), (123), (124), (129), (130),
% 174.80/26.82  | | | | |            (133), (137), (139), (146), (147), (152), (153), (157),
% 174.80/26.82  | | | | |            (158), (159), (164), (165), (166), (167), (173), (177),
% 174.80/26.82  | | | | |            (178), (179), (199), (200), (201), (202) are inconsistent
% 174.80/26.82  | | | | |            by sub-proof #122.
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | End of split
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | Case 2:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | |   (205)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.80/26.82  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.80/26.82  | | | |            all_52_30 = e0)
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | BETA: splitting (205) gives:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | Case 1:
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | |   (206)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 174.80/26.82  | | | | |          = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REF_CLOSE: (1), (3), (7), (8), (10), (12), (13), (14), (16), (17),
% 174.80/26.82  | | | | |            (21), (23), (24), (27), (28), (29), (30), (33), (35), (37),
% 174.80/26.82  | | | | |            (40), (41), (43), (44), (46), (49), (50), (51), (53), (57),
% 174.80/26.82  | | | | |            (59), (62), (65), (66), (68), (70), (71), (73), (76), (78),
% 174.80/26.82  | | | | |            (80), (82), (83), (85), (88), (90), (91), (92), (93), (95),
% 174.80/26.82  | | | | |            (97), (98), (99), (100), (102), (103), (104), (106), (108),
% 174.80/26.82  | | | | |            (109), (113), (114), (117), (119), (120), (121), (122),
% 174.80/26.82  | | | | |            (123), (124), (126), (127), (129), (130), (131), (132),
% 174.80/26.82  | | | | |            (133), (135), (136), (137), (139), (144), (146), (147),
% 174.80/26.82  | | | | |            (149), (151), (153), (155), (156), (157), (159), (162),
% 174.80/26.82  | | | | |            (163), (165), (166), (167), (168), (173), (175), (176),
% 174.80/26.82  | | | | |            (177), (178), (179), (180), (181), (182), (206) are
% 174.80/26.82  | | | | |            inconsistent by sub-proof #117.
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | Case 2:
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | |   (207)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 174.80/26.82  | | | | |          = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | ALPHA: (207) implies:
% 174.80/26.82  | | | | |   (208)  all_52_28 = e1
% 174.80/26.82  | | | | |   (209)  all_52_26 = e2
% 174.80/26.82  | | | | |   (210)  all_52_24 = e3
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (15), (210) imply:
% 174.80/26.82  | | | | |   (211)  op(e3, all_52_25) = e3
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (150), (209) imply:
% 174.80/26.82  | | | | |   (212)  op(e2, all_52_27) = e2
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (57), (208) imply:
% 174.80/26.82  | | | | |   (213)  op(e1, all_52_29) = e1
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REF_CLOSE: (1), (2), (4), (6), (10), (12), (13), (14), (16), (18),
% 174.80/26.82  | | | | |            (20), (22), (23), (24), (26), (27), (28), (30), (33), (35),
% 174.80/26.82  | | | | |            (36), (37), (42), (49), (50), (51), (53), (65), (66), (70),
% 174.80/26.82  | | | | |            (71), (78), (82), (87), (90), (92), (95), (97), (98),
% 174.80/26.82  | | | | |            (100), (101), (102), (103), (104), (108), (109), (111),
% 174.80/26.82  | | | | |            (113), (114), (115), (119), (122), (126), (127), (129),
% 174.80/26.82  | | | | |            (131), (132), (133), (136), (137), (139), (155), (157),
% 174.80/26.82  | | | | |            (158), (159), (164), (165), (167), (168), (172), (173),
% 174.80/26.82  | | | | |            (176), (177), (211), (212), (213) are inconsistent by
% 174.80/26.82  | | | | |            sub-proof #85.
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | End of split
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | End of split
% 174.80/26.82  | | | 
% 174.80/26.82  | | Case 2:
% 174.80/26.82  | | | 
% 174.80/26.82  | | |   (214)   ~ (all_58_15 = e0)
% 174.80/26.82  | | |   (215)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 =
% 174.80/26.82  | | |            e0 | all_58_13 = e0 | all_58_14 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | ALPHA: (215) implies:
% 174.80/26.82  | | |   (216)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.80/26.82  | | |   (217)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (31), (214) imply:
% 174.80/26.82  | | |   (218)   ~ (all_6_2 = e0)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | BETA: splitting (138) gives:
% 174.80/26.82  | | | 
% 174.80/26.82  | | | Case 1:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | |   (219)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 174.80/26.82  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 174.80/26.82  | | | |            = e0)
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (12), (13), (14), (16),
% 174.80/26.82  | | | |            (17), (18), (19), (20), (21), (23), (24), (25), (26), (28),
% 174.80/26.82  | | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 174.80/26.82  | | | |            (39), (40), (41), (42), (43), (44), (46), (47), (48), (49),
% 174.80/26.82  | | | |            (50), (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 174.80/26.82  | | | |            (61), (62), (63), (64), (65), (67), (68), (69), (70), (71),
% 174.80/26.82  | | | |            (72), (74), (75), (77), (78), (80), (81), (83), (84), (86),
% 174.80/26.82  | | | |            (87), (89), (91), (93), (94), (98), (99), (102), (103),
% 174.80/26.82  | | | |            (104), (105), (106), (107), (108), (109), (110), (111),
% 174.80/26.82  | | | |            (112), (113), (114), (115), (116), (118), (119), (121),
% 174.80/26.82  | | | |            (122), (124), (125), (128), (129), (131), (132), (133),
% 174.80/26.82  | | | |            (135), (136), (137), (139), (140), (141), (142), (147),
% 174.80/26.82  | | | |            (148), (150), (152), (153), (155), (156), (157), (159),
% 174.80/26.82  | | | |            (160), (161), (163), (164), (165), (166), (167), (217),
% 174.80/26.82  | | | |            (218), (219) are inconsistent by sub-proof #82.
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | Case 2:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | |   (220)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 174.80/26.82  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 174.80/26.82  | | | |            all_52_30 = e0)
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | BETA: splitting (220) gives:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | Case 1:
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | |   (221)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 174.80/26.82  | | | | |          = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | ALPHA: (221) implies:
% 174.80/26.82  | | | | |   (222)  all_52_22 = e0
% 174.80/26.82  | | | | |   (223)  all_52_20 = e1
% 174.80/26.82  | | | | |   (224)  all_52_18 = e2
% 174.80/26.82  | | | | |   (225)  all_52_16 = e3
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | COMBINE_EQS: (151), (223) imply:
% 174.80/26.82  | | | | |   (226)  all_14_1 = e1
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REF_CLOSE: (1), (7), (13), (14), (18), (23), (24), (25), (26), (28),
% 174.80/26.82  | | | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (40),
% 174.80/26.82  | | | | |            (42), (43), (44), (48), (49), (50), (51), (53), (59), (62),
% 174.80/26.82  | | | | |            (65), (68), (69), (70), (71), (76), (78), (80), (83), (86),
% 174.80/26.82  | | | | |            (87), (88), (89), (91), (92), (93), (96), (98), (99),
% 174.80/26.82  | | | | |            (101), (102), (103), (106), (107), (108), (109), (110),
% 174.80/26.82  | | | | |            (111), (115), (116), (119), (122), (123), (124), (125),
% 174.80/26.82  | | | | |            (129), (130), (131), (132), (133), (136), (137), (139),
% 174.80/26.82  | | | | |            (143), (146), (147), (152), (153), (156), (157), (158),
% 174.80/26.82  | | | | |            (159), (162), (164), (165), (166), (167), (172), (217),
% 174.80/26.82  | | | | |            (222), (224), (225), (226) are inconsistent by sub-proof
% 174.80/26.82  | | | | |            #77.
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | Case 2:
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | |   (227)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 174.80/26.82  | | | | |          = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | ALPHA: (227) implies:
% 174.80/26.82  | | | | |   (228)  all_52_30 = e0
% 174.80/26.82  | | | | |   (229)  all_52_28 = e1
% 174.80/26.82  | | | | |   (230)  all_52_26 = e2
% 174.80/26.82  | | | | |   (231)  all_52_24 = e3
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | COMBINE_EQS: (154), (228) imply:
% 174.80/26.82  | | | | |   (232)  all_6_1 = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (79), (232) imply:
% 174.80/26.82  | | | | |   (233)  op(e0, all_6_2) = all_6_0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (15), (231) imply:
% 174.80/26.82  | | | | |   (234)  op(e3, all_52_25) = e3
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (150), (230) imply:
% 174.80/26.82  | | | | |   (235)  op(e2, all_52_27) = e2
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (57), (229) imply:
% 174.80/26.82  | | | | |   (236)  op(e1, all_52_29) = e1
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REDUCE: (81), (232) imply:
% 174.80/26.82  | | | | |   (237)  op(e0, all_6_2) = e0
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (13), (14), (16), (21), (23),
% 174.80/26.82  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 174.80/26.82  | | | | |            (34), (35), (36), (37), (39), (40), (41), (42), (43), (44),
% 174.80/26.82  | | | | |            (46), (47), (48), (49), (50), (51), (52), (53), (58), (59),
% 174.80/26.82  | | | | |            (61), (62), (65), (67), (68), (69), (70), (71), (72), (75),
% 174.80/26.82  | | | | |            (76), (77), (78), (80), (82), (83), (88), (89), (90), (92),
% 174.80/26.82  | | | | |            (93), (95), (97), (98), (102), (103), (104), (108), (109),
% 174.80/26.82  | | | | |            (111), (114), (115), (117), (118), (119), (122), (124),
% 174.80/26.82  | | | | |            (125), (129), (130), (131), (132), (133), (136), (137),
% 174.80/26.82  | | | | |            (140), (141), (143), (144), (146), (152), (153), (157),
% 174.80/26.82  | | | | |            (159), (162), (163), (164), (165), (166), (167), (172),
% 174.80/26.82  | | | | |            (216), (218), (233), (234), (235), (236), (237) are
% 174.80/26.82  | | | | |            inconsistent by sub-proof #73.
% 174.80/26.82  | | | | | 
% 174.80/26.82  | | | | End of split
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | End of split
% 174.80/26.82  | | | 
% 174.80/26.82  | | End of split
% 174.80/26.82  | | 
% 174.80/26.82  | End of split
% 174.80/26.82  | 
% 174.80/26.82  End of proof
% 174.80/26.82  
% 174.80/26.82  Sub-proof #73 shows that the following formulas are inconsistent:
% 174.80/26.82  ----------------------------------------------------------------
% 174.80/26.82    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.82    (2)   ~ (all_52_5 = all_52_13)
% 174.80/26.82    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.80/26.82    (4)   ~ (all_52_27 = all_10_2)
% 174.80/26.82    (5)   ~ (all_52_17 = all_52_23)
% 174.80/26.82    (6)   ~ (all_6_0 = e3)
% 174.80/26.82    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 174.80/26.82    (8)  op(e3, e2) = all_52_3
% 174.80/26.82    (9)   ~ (all_52_9 = all_52_25)
% 174.80/26.82    (10)   ~ (all_52_19 = all_52_23)
% 174.80/26.82    (11)   ~ (all_52_3 = all_10_2)
% 174.80/26.82    (12)  all_58_5 = all_52_13
% 174.80/26.82    (13)   ~ (all_6_2 = e0)
% 174.80/26.82    (14)   ~ (all_52_25 = all_52_29)
% 174.80/26.82    (15)  all_56_15 = all_6_2
% 174.80/26.82    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.82    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 174.80/26.82    (18)  all_58_3 = all_10_2
% 174.80/26.82    (19)  all_56_9 = all_52_19
% 174.80/26.82    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.82    (21)  all_58_15 = all_6_2
% 174.80/26.82    (22)  op(e2, all_4_2) = e1
% 174.80/26.82    (23)  op(e0, all_6_2) = e0
% 174.80/26.82    (24)   ~ (all_52_9 = all_4_2)
% 174.80/26.82    (25)   ~ (all_52_5 = all_52_7)
% 174.80/26.82    (26)  all_58_10 = all_52_15
% 174.80/26.82    (27)   ~ (all_52_5 = all_4_2)
% 174.80/26.82    (28)  all_58_7 = all_52_19
% 174.80/26.82    (29)   ~ (all_52_15 = all_6_2)
% 174.80/26.82    (30)   ~ (all_52_17 = all_52_25)
% 174.80/26.82    (31)  op(e0, e1) = all_52_29
% 174.80/26.82    (32)  all_58_4 = all_52_5
% 174.80/26.82    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.82    (34)   ~ (e3 = e1)
% 174.80/26.82    (35)   ~ (all_52_27 = all_52_29)
% 174.80/26.82    (36)   ~ (all_52_17 = all_14_2)
% 174.80/26.82    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.82    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.82    (39)   ~ (all_52_7 = all_4_2)
% 174.80/26.82    (40)  all_58_1 = all_52_3
% 174.80/26.82    (41)   ~ (all_52_13 = all_52_15)
% 174.80/26.82    (42)  all_58_0 = all_4_2
% 174.80/26.82    (43)  op(e2, all_52_27) = e2
% 174.80/26.82    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.82    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.82    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.80/26.82    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.82    (48)  all_58_14 = all_52_29
% 174.80/26.82    (49)   ~ (all_52_3 = all_52_5)
% 174.80/26.82    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.82    (51)  op(e2, e1) = all_52_13
% 174.80/26.82    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.82    (53)  all_58_8 = all_14_2
% 174.80/26.82    (54)  all_56_1 = all_52_3
% 174.80/26.82    (55)  op(e1, all_52_29) = e1
% 174.80/26.82    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.80/26.82    (57)   ~ (all_52_5 = all_14_2)
% 174.80/26.82    (58)   ~ (all_52_3 = all_52_27)
% 174.80/26.82    (59)   ~ (all_52_3 = all_4_2)
% 174.80/26.82    (60)  op(e0, e3) = all_52_25
% 174.80/26.82    (61)   ~ (all_52_9 = all_10_2)
% 174.80/26.82    (62)  op(e3, all_52_17) = all_52_16
% 174.80/26.82    (63)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.82    (64)   ~ (all_52_9 = all_52_13)
% 174.80/26.82    (65)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 174.80/26.82    (66)   ~ (all_52_15 = all_52_23)
% 174.80/26.82    (67)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.82    (68)   ~ (all_52_5 = all_52_29)
% 174.80/26.82    (69)  all_56_12 = all_52_25
% 174.80/26.82    (70)  all_58_13 = all_52_27
% 174.80/26.82    (71)   ~ (all_52_9 = all_52_17)
% 174.80/26.82    (72)  all_58_6 = all_52_17
% 174.80/26.82    (73)   ~ (all_52_3 = all_52_7)
% 174.80/26.82    (74)  all_56_0 = all_4_2
% 174.80/26.82    (75)  all_58_11 = all_52_23
% 174.80/26.82    (76)   ~ (all_52_7 = all_52_15)
% 174.80/26.82    (77)  op(e3, all_52_25) = e3
% 174.80/26.82    (78)   ~ (all_52_19 = all_10_2)
% 174.80/26.82    (79)  op(e3, all_4_2) = e2
% 174.80/26.82    (80)   ~ (all_6_0 = e2)
% 174.80/26.82    (81)   ~ (all_52_29 = all_6_2)
% 174.80/26.82    (82)  all_58_2 = all_52_9
% 174.80/26.82    (83)  op(e3, e1) = all_52_5
% 174.80/26.82    (84)  all_56_10 = all_14_2
% 174.80/26.82    (85)   ~ (all_52_25 = all_6_2)
% 174.80/26.82    (86)  op(e1, e3) = all_52_17
% 174.80/26.82    (87)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.82    (88)   ~ (all_52_25 = all_4_2)
% 174.80/26.82    (89)  op(e3, e0) = all_52_7
% 174.80/26.82    (90)  op(e3, e3) = all_4_2
% 174.80/26.82    (91)   ~ (all_52_17 = all_4_2)
% 174.80/26.82    (92)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.82    (93)  op(e0, all_6_2) = all_6_0
% 174.80/26.82    (94)   ~ (all_52_27 = all_6_2)
% 174.80/26.82    (95)   ~ (all_52_7 = all_6_2)
% 174.80/26.82    (96)   ~ (all_52_15 = all_10_2)
% 174.80/26.82    (97)   ~ (all_52_19 = all_52_27)
% 174.80/26.82    (98)  all_56_7 = all_52_15
% 174.80/26.82    (99)   ~ (all_4_2 = e0)
% 174.80/26.82    (100)   ~ (all_52_17 = all_52_19)
% 174.80/26.82    (101)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.82    (102)  all_58_9 = all_52_7
% 174.80/26.82    (103)  all_58_12 = all_52_25
% 174.80/26.82    (104)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.82    (105)   ~ (all_52_9 = all_52_15)
% 174.80/26.82    (106)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.82    (107)   ~ (e3 = e2)
% 174.80/26.82    (108)   ~ (all_52_19 = all_14_2)
% 174.80/26.82    (109)  op(e2, e3) = all_52_9
% 174.80/26.82  
% 174.80/26.82  Begin of proof
% 174.80/26.82  | 
% 174.80/26.82  | GROUND_INST: instantiating (92) with e0, all_6_0, all_6_2, e0, simplifying
% 174.80/26.82  |              with (23), (93) gives:
% 174.80/26.82  |   (110)  all_6_0 = e0
% 174.80/26.82  | 
% 174.80/26.82  | REDUCE: (6), (110) imply:
% 174.80/26.82  |   (111)   ~ (e3 = e0)
% 174.80/26.82  | 
% 174.80/26.82  | SIMP: (111) implies:
% 174.80/26.82  |   (112)   ~ (e3 = e0)
% 174.80/26.82  | 
% 174.80/26.82  | REDUCE: (80), (110) imply:
% 174.80/26.82  |   (113)   ~ (e2 = e0)
% 174.80/26.82  | 
% 174.80/26.82  | SIMP: (113) implies:
% 174.80/26.82  |   (114)   ~ (e2 = e0)
% 174.80/26.82  | 
% 174.80/26.82  | BETA: splitting (20) gives:
% 174.80/26.82  | 
% 174.80/26.82  | Case 1:
% 174.80/26.82  | | 
% 174.80/26.82  | |   (115)  all_56_0 = e3
% 174.80/26.82  | | 
% 174.80/26.82  | | COMBINE_EQS: (74), (115) imply:
% 174.80/26.82  | |   (116)  all_4_2 = e3
% 174.80/26.82  | | 
% 174.80/26.82  | | SIMP: (116) implies:
% 174.80/26.82  | |   (117)  all_4_2 = e3
% 174.80/26.82  | | 
% 174.80/26.82  | | REF_CLOSE: (79), (90), (92), (107), (117) are inconsistent by sub-proof
% 174.80/26.82  | |            #106.
% 174.80/26.82  | | 
% 174.80/26.82  | Case 2:
% 174.80/26.82  | | 
% 174.80/26.82  | |   (118)   ~ (all_56_0 = e3)
% 174.80/26.82  | |   (119)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.82  | | 
% 174.80/26.82  | | REDUCE: (74), (118) imply:
% 174.80/26.82  | |   (120)   ~ (all_4_2 = e3)
% 174.80/26.82  | | 
% 174.80/26.82  | | BETA: splitting (37) gives:
% 174.80/26.82  | | 
% 174.80/26.82  | | Case 1:
% 174.80/26.82  | | | 
% 174.80/26.82  | | |   (121)  all_56_15 = e3
% 174.80/26.82  | | | 
% 174.80/26.82  | | | COMBINE_EQS: (15), (121) imply:
% 174.80/26.82  | | |   (122)  all_6_2 = e3
% 174.80/26.82  | | | 
% 174.80/26.82  | | | SIMP: (122) implies:
% 174.80/26.82  | | |   (123)  all_6_2 = e3
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REF_CLOSE: (23), (60), (77), (89), (92), (95), (123) are inconsistent by
% 174.80/26.82  | | |            sub-proof #665.
% 174.80/26.82  | | | 
% 174.80/26.82  | | Case 2:
% 174.80/26.82  | | | 
% 174.80/26.82  | | |   (124)   ~ (all_56_15 = e3)
% 174.80/26.82  | | |   (125)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.82  | | | 
% 174.80/26.82  | | | REDUCE: (15), (124) imply:
% 174.80/26.82  | | |   (126)   ~ (all_6_2 = e3)
% 174.80/26.82  | | | 
% 174.80/26.82  | | | BETA: splitting (50) gives:
% 174.80/26.82  | | | 
% 174.80/26.82  | | | Case 1:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | |   (127)  all_58_0 = e3
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | COMBINE_EQS: (42), (127) imply:
% 174.80/26.82  | | | |   (128)  all_4_2 = e3
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | REDUCE: (120), (128) imply:
% 174.80/26.82  | | | |   (129)  $false
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | | CLOSE: (129) is inconsistent.
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | Case 2:
% 174.80/26.82  | | | | 
% 174.80/26.82  | | | |   (130)   ~ (all_58_0 = e3)
% 174.80/26.83  | | | |   (131)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | BETA: splitting (104) gives:
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | Case 1:
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | |   (132)  all_58_0 = e3
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | COMBINE_EQS: (42), (132) imply:
% 174.80/26.83  | | | | |   (133)  all_4_2 = e3
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | REDUCE: (120), (133) imply:
% 174.80/26.83  | | | | |   (134)  $false
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | CLOSE: (134) is inconsistent.
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | Case 2:
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | |   (135)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | BETA: splitting (87) gives:
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | Case 1:
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | |   (136)  all_56_7 = e3
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | COMBINE_EQS: (98), (136) imply:
% 174.80/26.83  | | | | | |   (137)  all_52_15 = e3
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | SIMP: (137) implies:
% 174.80/26.83  | | | | | |   (138)  all_52_15 = e3
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | REDUCE: (76), (138) imply:
% 174.80/26.83  | | | | | |   (139)   ~ (all_52_7 = e3)
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | REDUCE: (105), (138) imply:
% 174.80/26.83  | | | | | |   (140)   ~ (all_52_9 = e3)
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | REDUCE: (96), (138) imply:
% 174.80/26.83  | | | | | |   (141)   ~ (all_10_2 = e3)
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | SIMP: (141) implies:
% 174.80/26.83  | | | | | |   (142)   ~ (all_10_2 = e3)
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | REDUCE: (29), (138) imply:
% 174.80/26.83  | | | | | |   (143)   ~ (all_6_2 = e3)
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | BETA: splitting (45) gives:
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | Case 1:
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | |   (144)  all_56_9 = e3
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | COMBINE_EQS: (19), (144) imply:
% 174.80/26.83  | | | | | | |   (145)  all_52_19 = e3
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | REDUCE: (97), (145) imply:
% 174.80/26.83  | | | | | | |   (146)   ~ (all_52_27 = e3)
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | SIMP: (146) implies:
% 174.80/26.83  | | | | | | |   (147)   ~ (all_52_27 = e3)
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 174.80/26.83  | | | | | | |            (15), (17), (18), (20), (21), (23), (24), (26), (27),
% 174.80/26.83  | | | | | | |            (28), (30), (31), (32), (34), (35), (36), (39), (40),
% 174.80/26.83  | | | | | | |            (41), (42), (44), (46), (47), (48), (49), (50), (52),
% 174.80/26.83  | | | | | | |            (53), (54), (55), (56), (58), (59), (61), (62), (64),
% 174.80/26.83  | | | | | | |            (65), (68), (69), (70), (71), (72), (73), (74), (75),
% 174.80/26.83  | | | | | | |            (76), (77), (78), (79), (81), (82), (83), (85), (86),
% 174.80/26.83  | | | | | | |            (88), (89), (90), (92), (94), (95), (96), (100), (101),
% 174.80/26.83  | | | | | | |            (102), (103), (104), (105), (107), (112), (125), (126),
% 174.80/26.83  | | | | | | |            (147) are inconsistent by sub-proof #90.
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | Case 2:
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | |   (148)   ~ (all_56_9 = e3)
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | REDUCE: (19), (148) imply:
% 174.80/26.83  | | | | | | |   (149)   ~ (all_52_19 = e3)
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | BETA: splitting (47) gives:
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | |   (150)  all_58_1 = e3
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | COMBINE_EQS: (40), (150) imply:
% 174.80/26.83  | | | | | | | |   (151)  all_52_3 = e3
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | REDUCE: (58), (151) imply:
% 174.80/26.83  | | | | | | | |   (152)   ~ (all_52_27 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | SIMP: (152) implies:
% 174.80/26.83  | | | | | | | |   (153)   ~ (all_52_27 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 174.80/26.83  | | | | | | | |            (14), (15), (17), (18), (20), (21), (23), (24), (26),
% 174.80/26.83  | | | | | | | |            (27), (28), (30), (31), (32), (34), (35), (36), (39),
% 174.80/26.83  | | | | | | | |            (40), (41), (42), (44), (46), (47), (48), (49), (50),
% 174.80/26.83  | | | | | | | |            (52), (53), (54), (55), (56), (58), (59), (61), (62),
% 174.80/26.83  | | | | | | | |            (64), (65), (68), (69), (70), (71), (72), (73), (74),
% 174.80/26.83  | | | | | | | |            (75), (76), (77), (78), (79), (81), (82), (83), (85),
% 174.80/26.83  | | | | | | | |            (86), (88), (89), (90), (92), (94), (95), (96),
% 174.80/26.83  | | | | | | | |            (100), (101), (102), (103), (104), (105), (107),
% 174.80/26.83  | | | | | | | |            (112), (125), (126), (153) are inconsistent by
% 174.80/26.83  | | | | | | | |            sub-proof #90.
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | |   (154)   ~ (all_58_1 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | REDUCE: (40), (154) imply:
% 174.80/26.83  | | | | | | | |   (155)   ~ (all_52_3 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | BETA: splitting (135) gives:
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | |   (156)  all_58_1 = e3
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | COMBINE_EQS: (40), (156) imply:
% 174.80/26.83  | | | | | | | | |   (157)  all_52_3 = e3
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | REDUCE: (155), (157) imply:
% 174.80/26.83  | | | | | | | | |   (158)  $false
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | CLOSE: (158) is inconsistent.
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | |   (159)  all_58_4 = e3 | all_58_9 = e3
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | BETA: splitting (159) gives:
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | |   (160)  all_58_4 = e3
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | COMBINE_EQS: (32), (160) imply:
% 174.80/26.83  | | | | | | | | | |   (161)  all_52_5 = e3
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | SIMP: (161) implies:
% 174.80/26.83  | | | | | | | | | |   (162)  all_52_5 = e3
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REDUCE: (25), (162) imply:
% 174.80/26.83  | | | | | | | | | |   (163)   ~ (all_52_7 = e3)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REDUCE: (2), (162) imply:
% 174.80/26.83  | | | | | | | | | |   (164)   ~ (all_52_13 = e3)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | SIMP: (164) implies:
% 174.80/26.83  | | | | | | | | | |   (165)   ~ (all_52_13 = e3)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REDUCE: (57), (162) imply:
% 174.80/26.83  | | | | | | | | | |   (166)   ~ (all_14_2 = e3)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | SIMP: (166) implies:
% 174.80/26.83  | | | | | | | | | |   (167)   ~ (all_14_2 = e3)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | BETA: splitting (33) gives:
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | |   (168)  all_58_6 = e3
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | COMBINE_EQS: (72), (168) imply:
% 174.80/26.83  | | | | | | | | | | |   (169)  all_52_17 = e3
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | SIMP: (169) implies:
% 174.80/26.83  | | | | | | | | | | |   (170)  all_52_17 = e3
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | REDUCE: (30), (170) imply:
% 174.80/26.83  | | | | | | | | | | |   (171)   ~ (all_52_25 = e3)
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | SIMP: (171) implies:
% 174.80/26.83  | | | | | | | | | | |   (172)   ~ (all_52_25 = e3)
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | BETA: splitting (52) gives:
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | |   (173)  all_58_12 = e3
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | REF_CLOSE: (103), (172), (173) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | | | | |            #1003.
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | |   (174)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | BETA: splitting (174) gives:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | |   (175)  all_58_13 = e3
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | COMBINE_EQS: (70), (175) imply:
% 174.80/26.83  | | | | | | | | | | | | |   (176)  all_52_27 = e3
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | SIMP: (176) implies:
% 174.80/26.83  | | | | | | | | | | | | |   (177)  all_52_27 = e3
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | REDUCE: (43), (177) imply:
% 174.80/26.83  | | | | | | | | | | | | |   (178)  op(e2, e3) = e2
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | GROUND_INST: instantiating (92) with all_52_9, e2, e3, e2,
% 174.80/26.83  | | | | | | | | | | | | |              simplifying with (109), (178) gives:
% 174.80/26.83  | | | | | | | | | | | | |   (179)  all_52_9 = e2
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | COMBINE_EQS: (82), (179) imply:
% 174.80/26.83  | | | | | | | | | | | | |   (180)  all_58_2 = e2
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | BETA: splitting (63) gives:
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | |   (181)  all_58_0 = e0
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | COMBINE_EQS: (42), (181) imply:
% 174.80/26.83  | | | | | | | | | | | | | |   (182)  all_4_2 = e0
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | REDUCE: (99), (182) imply:
% 174.80/26.83  | | | | | | | | | | | | | |   (183)  $false
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | |   (184)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | |   (185)  all_58_2 = e0
% 174.80/26.83  | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | REF_CLOSE: (114), (180), (185) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | | | | | | | |            #909.
% 174.80/26.83  | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | |   (186)  all_58_6 = e0 | all_58_12 = e0
% 174.80/26.83  | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 174.80/26.83  | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | |   (187)  all_58_6 = e0
% 174.80/26.83  | | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | | REF_CLOSE: (112), (168), (187) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | | | | | | | | |            #559.
% 174.80/26.83  | | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | |   (188)  all_58_12 = e0
% 174.80/26.83  | | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | | REF_CLOSE: (77), (89), (92), (103), (139), (188) are
% 174.80/26.83  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #654.
% 174.80/26.83  | | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | |   (189)  all_58_14 = e3 | all_58_15 = e3
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 174.80/26.83  | | | | | | | | | | | | |            (14), (15), (17), (18), (20), (21), (23), (24),
% 174.80/26.83  | | | | | | | | | | | | |            (26), (27), (28), (30), (31), (32), (34), (35),
% 174.80/26.83  | | | | | | | | | | | | |            (36), (39), (40), (41), (42), (44), (46), (47),
% 174.80/26.83  | | | | | | | | | | | | |            (48), (49), (50), (53), (54), (55), (56), (58),
% 174.80/26.83  | | | | | | | | | | | | |            (59), (61), (62), (64), (65), (68), (69), (70),
% 174.80/26.83  | | | | | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (78),
% 174.80/26.83  | | | | | | | | | | | | |            (79), (81), (82), (83), (85), (86), (88), (89),
% 174.80/26.83  | | | | | | | | | | | | |            (90), (92), (94), (95), (96), (100), (101), (102),
% 174.80/26.83  | | | | | | | | | | | | |            (103), (104), (105), (107), (112), (125), (126),
% 174.80/26.83  | | | | | | | | | | | | |            (189) are inconsistent by sub-proof #91.
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | |   (190)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | BETA: splitting (38) gives:
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | |   (191)  all_58_2 = e3
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | REF_CLOSE: (82), (140), (191) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | | | | |            #980.
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | |   (192)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | REF_CLOSE: (12), (18), (26), (28), (53), (66), (75), (142),
% 174.80/26.83  | | | | | | | | | | | |            (149), (165), (167), (190), (192) are inconsistent
% 174.80/26.83  | | | | | | | | | | | |            by sub-proof #966.
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | |   (193)  all_58_9 = e3
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REF_CLOSE: (102), (139), (193) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | | |            #972.
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | End of split
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | End of split
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | Case 2:
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | |   (194)   ~ (all_56_7 = e3)
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | REDUCE: (98), (194) imply:
% 174.80/26.83  | | | | | |   (195)   ~ (all_52_15 = e3)
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | BETA: splitting (101) gives:
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | | Case 1:
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | |   (196)  all_58_9 = e3
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | COMBINE_EQS: (102), (196) imply:
% 174.80/26.83  | | | | | | |   (197)  all_52_7 = e3
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | SIMP: (197) implies:
% 174.80/26.83  | | | | | | |   (198)  all_52_7 = e3
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | REDUCE: (73), (198) imply:
% 174.80/26.83  | | | | | | |   (199)   ~ (all_52_3 = e3)
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | REDUCE: (25), (198) imply:
% 174.80/26.83  | | | | | | |   (200)   ~ (all_52_5 = e3)
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | REDUCE: (39), (198) imply:
% 174.80/26.83  | | | | | | |   (201)   ~ (all_4_2 = e3)
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | BETA: splitting (67) gives:
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | |   (202)  all_56_10 = e3
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | COMBINE_EQS: (84), (202) imply:
% 174.80/26.83  | | | | | | | |   (203)  all_14_2 = e3
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | SIMP: (203) implies:
% 174.80/26.83  | | | | | | | |   (204)  all_14_2 = e3
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | REDUCE: (36), (204) imply:
% 174.80/26.83  | | | | | | | |   (205)   ~ (all_52_17 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | REDUCE: (108), (204) imply:
% 174.80/26.83  | | | | | | | |   (206)   ~ (all_52_19 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | REF_CLOSE: (4), (9), (12), (18), (26), (28), (38), (40), (43),
% 174.80/26.83  | | | | | | | |            (47), (52), (61), (64), (70), (72), (77), (82), (88),
% 174.80/26.83  | | | | | | | |            (90), (92), (103), (105), (107), (109), (131), (199),
% 174.80/26.83  | | | | | | | |            (205), (206) are inconsistent by sub-proof #75.
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | |   (207)   ~ (all_56_10 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | REDUCE: (84), (207) imply:
% 174.80/26.83  | | | | | | | |   (208)   ~ (all_14_2 = e3)
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | BETA: splitting (106) gives:
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | |   (209)  all_58_4 = e3
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | REF_CLOSE: (32), (200), (209) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | |            #1025.
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | |   (210)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | BETA: splitting (56) gives:
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | |   (211)  all_58_0 = e2
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | COMBINE_EQS: (42), (211) imply:
% 174.80/26.83  | | | | | | | | | |   (212)  all_4_2 = e2
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REDUCE: (59), (212) imply:
% 174.80/26.83  | | | | | | | | | |   (213)   ~ (all_52_3 = e2)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REDUCE: (79), (212) imply:
% 174.80/26.83  | | | | | | | | | |   (214)  op(e3, e2) = e2
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | GROUND_INST: instantiating (92) with all_52_3, e2, e2, e3,
% 174.80/26.83  | | | | | | | | | |              simplifying with (8), (214) gives:
% 174.80/26.83  | | | | | | | | | |   (215)  all_52_3 = e2
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REDUCE: (213), (215) imply:
% 174.80/26.83  | | | | | | | | | |   (216)  $false
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | CLOSE: (216) is inconsistent.
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | |   (217)   ~ (all_58_0 = e2)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | REDUCE: (42), (217) imply:
% 174.80/26.83  | | | | | | | | | |   (218)   ~ (all_4_2 = e2)
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | BETA: splitting (119) gives:
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | |   (219)  all_56_0 = e2
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | REF_CLOSE: (74), (218), (219) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | | | |            #904.
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | |   (220)  all_56_0 = e1 | all_56_0 = e0
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | BETA: splitting (220) gives:
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | |   (221)  all_56_0 = e1
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | COMBINE_EQS: (74), (221) imply:
% 174.80/26.83  | | | | | | | | | | | |   (222)  all_4_2 = e1
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | SIMP: (222) implies:
% 174.80/26.83  | | | | | | | | | | | |   (223)  all_4_2 = e1
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | REDUCE: (120), (223) imply:
% 174.80/26.83  | | | | | | | | | | | |   (224)   ~ (e3 = e1)
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | REDUCE: (22), (223) imply:
% 174.80/26.83  | | | | | | | | | | | |   (225)  op(e2, e1) = e1
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | GROUND_INST: instantiating (92) with all_52_13, e1, e1, e2,
% 174.80/26.83  | | | | | | | | | | | |              simplifying with (51), (225) gives:
% 174.80/26.83  | | | | | | | | | | | |   (226)  all_52_13 = e1
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | COMBINE_EQS: (12), (226) imply:
% 174.80/26.83  | | | | | | | | | | | |   (227)  all_58_5 = e1
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | BETA: splitting (210) gives:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | Case 1:
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | |   (228)  all_58_5 = e3
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | COMBINE_EQS: (227), (228) imply:
% 174.80/26.83  | | | | | | | | | | | | |   (229)  e3 = e1
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | REDUCE: (34), (229) imply:
% 174.80/26.83  | | | | | | | | | | | | |   (230)  $false
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | CLOSE: (230) is inconsistent.
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | |   (231)  all_58_8 = e3 | all_58_14 = e3
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | | REF_CLOSE: (8), (16), (42), (48), (53), (55), (59), (74),
% 174.80/26.83  | | | | | | | | | | | | |            (79), (86), (91), (92), (99), (119), (208), (231)
% 174.80/26.83  | | | | | | | | | | | | |            are inconsistent by sub-proof #113.
% 174.80/26.83  | | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | Case 2:
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | |   (232)  all_56_0 = e0
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | | REF_CLOSE: (74), (99), (232) are inconsistent by sub-proof
% 174.80/26.83  | | | | | | | | | | | |            #1021.
% 174.80/26.83  | | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | | 
% 174.80/26.83  | | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | | 
% 174.80/26.83  | | | | | | | | End of split
% 174.80/26.83  | | | | | | | | 
% 174.80/26.83  | | | | | | | End of split
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | Case 2:
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | |   (233)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | | REF_CLOSE: (1), (4), (5), (8), (9), (10), (12), (16), (18), (21),
% 174.80/26.83  | | | | | | |            (26), (28), (32), (38), (40), (42), (43), (44), (47),
% 174.80/26.83  | | | | | | |            (48), (49), (52), (53), (54), (55), (59), (61), (64),
% 174.80/26.83  | | | | | | |            (70), (72), (74), (75), (77), (79), (82), (86), (88),
% 174.80/26.83  | | | | | | |            (90), (91), (92), (99), (103), (105), (106), (107),
% 174.80/26.83  | | | | | | |            (109), (119), (126), (131), (195), (233) are
% 174.80/26.83  | | | | | | |            inconsistent by sub-proof #74.
% 174.80/26.83  | | | | | | | 
% 174.80/26.83  | | | | | | End of split
% 174.80/26.83  | | | | | | 
% 174.80/26.83  | | | | | End of split
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | End of split
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | End of split
% 174.80/26.83  | | | 
% 174.80/26.83  | | End of split
% 174.80/26.83  | | 
% 174.80/26.83  | End of split
% 174.80/26.83  | 
% 174.80/26.83  End of proof
% 174.80/26.83  
% 174.80/26.83  Sub-proof #74 shows that the following formulas are inconsistent:
% 174.80/26.83  ----------------------------------------------------------------
% 174.80/26.83    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.83    (2)   ~ (all_52_27 = all_10_2)
% 174.80/26.83    (3)   ~ (all_52_17 = all_52_23)
% 174.80/26.83    (4)  op(e3, e2) = all_52_3
% 174.80/26.83    (5)   ~ (all_52_9 = all_52_25)
% 174.80/26.83    (6)   ~ (all_52_19 = all_52_23)
% 174.80/26.83    (7)   ~ (all_6_2 = e3)
% 174.80/26.83    (8)  all_58_5 = all_52_13
% 174.80/26.83    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.83    (10)  all_58_3 = all_10_2
% 174.80/26.83    (11)  all_58_15 = all_6_2
% 174.80/26.83    (12)  all_58_10 = all_52_15
% 174.80/26.83    (13)  all_58_7 = all_52_19
% 174.80/26.83    (14)  all_58_4 = all_52_5
% 174.80/26.83    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.83    (16)  all_58_1 = all_52_3
% 174.80/26.83    (17)  all_58_0 = all_4_2
% 174.80/26.83    (18)  op(e2, all_52_27) = e2
% 174.80/26.83    (19)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.83    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.83    (21)  all_58_14 = all_52_29
% 174.80/26.83    (22)   ~ (all_52_3 = all_52_5)
% 174.80/26.83    (23)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.83    (24)  all_58_8 = all_14_2
% 174.80/26.83    (25)  all_56_1 = all_52_3
% 174.80/26.83    (26)  op(e1, all_52_29) = e1
% 174.80/26.83    (27)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.83    (28)   ~ (all_52_3 = all_4_2)
% 174.80/26.83    (29)   ~ (all_52_9 = all_10_2)
% 174.80/26.83    (30)   ~ (all_52_9 = all_52_13)
% 174.80/26.83    (31)   ~ (all_52_15 = e3)
% 174.80/26.83    (32)  all_58_13 = all_52_27
% 174.80/26.83    (33)  all_58_6 = all_52_17
% 174.80/26.83    (34)  all_56_0 = all_4_2
% 174.80/26.83    (35)  all_58_11 = all_52_23
% 174.80/26.83    (36)  op(e3, all_52_25) = e3
% 174.80/26.83    (37)  op(e3, all_4_2) = e2
% 174.80/26.83    (38)  all_58_2 = all_52_9
% 174.80/26.83    (39)  op(e1, e3) = all_52_17
% 174.80/26.83    (40)   ~ (all_52_25 = all_4_2)
% 174.80/26.83    (41)  op(e3, e3) = all_4_2
% 174.80/26.83    (42)   ~ (all_52_17 = all_4_2)
% 174.80/26.83    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.83    (44)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.83    (45)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.83    (46)   ~ (all_4_2 = e0)
% 174.80/26.83    (47)  all_58_12 = all_52_25
% 174.80/26.83    (48)   ~ (all_52_9 = all_52_15)
% 174.80/26.83    (49)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.83    (50)   ~ (e3 = e2)
% 174.80/26.83    (51)  op(e2, e3) = all_52_9
% 174.80/26.83  
% 174.80/26.83  Begin of proof
% 174.80/26.83  | 
% 174.80/26.83  | BETA: splitting (27) gives:
% 174.80/26.83  | 
% 174.80/26.83  | Case 1:
% 174.80/26.83  | | 
% 174.80/26.83  | |   (52)  all_58_10 = e3
% 174.80/26.83  | | 
% 174.80/26.83  | | REF_CLOSE: (12), (31), (52) are inconsistent by sub-proof #1018.
% 174.80/26.83  | | 
% 174.80/26.83  | Case 2:
% 174.80/26.83  | | 
% 174.80/26.83  | |   (53)  all_58_11 = e3 | all_58_15 = e3
% 174.80/26.83  | | 
% 174.80/26.83  | | BETA: splitting (53) gives:
% 174.80/26.83  | | 
% 174.80/26.83  | | Case 1:
% 174.80/26.83  | | | 
% 174.80/26.83  | | |   (54)  all_58_11 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | COMBINE_EQS: (35), (54) imply:
% 174.80/26.83  | | |   (55)  all_52_23 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | SIMP: (55) implies:
% 174.80/26.83  | | |   (56)  all_52_23 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | REDUCE: (3), (56) imply:
% 174.80/26.83  | | |   (57)   ~ (all_52_17 = e3)
% 174.80/26.83  | | | 
% 174.80/26.83  | | | REDUCE: (6), (56) imply:
% 174.80/26.83  | | |   (58)   ~ (all_52_19 = e3)
% 174.80/26.83  | | | 
% 174.80/26.83  | | | REDUCE: (1), (56) imply:
% 174.80/26.83  | | |   (59)   ~ (all_14_2 = e3)
% 174.80/26.83  | | | 
% 174.80/26.83  | | | SIMP: (59) implies:
% 174.80/26.83  | | |   (60)   ~ (all_14_2 = e3)
% 174.80/26.83  | | | 
% 174.80/26.83  | | | BETA: splitting (19) gives:
% 174.80/26.83  | | | 
% 174.80/26.83  | | | Case 1:
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | |   (61)  all_56_1 = e3
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | COMBINE_EQS: (25), (61) imply:
% 174.80/26.83  | | | |   (62)  all_52_3 = e3
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | REDUCE: (22), (62) imply:
% 174.80/26.83  | | | |   (63)   ~ (all_52_5 = e3)
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | SIMP: (63) implies:
% 174.80/26.83  | | | |   (64)   ~ (all_52_5 = e3)
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | BETA: splitting (15) gives:
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | Case 1:
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | |   (65)  all_58_2 = e3
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | COMBINE_EQS: (38), (65) imply:
% 174.80/26.83  | | | | |   (66)  all_52_9 = e3
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | SIMP: (66) implies:
% 174.80/26.83  | | | | |   (67)  all_52_9 = e3
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | REDUCE: (30), (67) imply:
% 174.80/26.83  | | | | |   (68)   ~ (all_52_13 = e3)
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | SIMP: (68) implies:
% 174.80/26.83  | | | | |   (69)   ~ (all_52_13 = e3)
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | REF_CLOSE: (4), (8), (9), (14), (17), (21), (24), (26), (28), (34),
% 174.80/26.83  | | | | |            (37), (39), (42), (43), (45), (46), (49), (60), (64), (69)
% 174.80/26.83  | | | | |            are inconsistent by sub-proof #112.
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | Case 2:
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | |   (70)   ~ (all_58_2 = e3)
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | | REF_CLOSE: (23), (33), (36), (38), (40), (41), (43), (44), (47), (57),
% 174.80/26.83  | | | | |            (70) are inconsistent by sub-proof #76.
% 174.80/26.83  | | | | | 
% 174.80/26.83  | | | | End of split
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | Case 2:
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | |   (71)   ~ (all_56_1 = e3)
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | REDUCE: (25), (71) imply:
% 174.80/26.83  | | | |   (72)   ~ (all_52_3 = e3)
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | | REF_CLOSE: (2), (5), (8), (10), (12), (13), (15), (16), (18), (20),
% 174.80/26.83  | | | |            (23), (29), (30), (32), (33), (36), (38), (40), (41), (43),
% 174.80/26.83  | | | |            (44), (47), (48), (50), (51), (57), (58), (72) are
% 174.80/26.83  | | | |            inconsistent by sub-proof #75.
% 174.80/26.83  | | | | 
% 174.80/26.83  | | | End of split
% 174.80/26.83  | | | 
% 174.80/26.83  | | Case 2:
% 174.80/26.83  | | | 
% 174.80/26.83  | | |   (73)  all_58_15 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | COMBINE_EQS: (11), (73) imply:
% 174.80/26.83  | | |   (74)  all_6_2 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | REDUCE: (7), (74) imply:
% 174.80/26.83  | | |   (75)  $false
% 174.80/26.83  | | | 
% 174.80/26.83  | | | CLOSE: (75) is inconsistent.
% 174.80/26.83  | | | 
% 174.80/26.83  | | End of split
% 174.80/26.83  | | 
% 174.80/26.83  | End of split
% 174.80/26.83  | 
% 174.80/26.83  End of proof
% 174.80/26.83  
% 174.80/26.83  Sub-proof #75 shows that the following formulas are inconsistent:
% 174.80/26.83  ----------------------------------------------------------------
% 174.80/26.83    (1)   ~ (all_52_27 = all_10_2)
% 174.80/26.83    (2)   ~ (all_52_9 = all_52_25)
% 174.80/26.83    (3)   ~ (all_52_17 = e3)
% 174.80/26.83    (4)  all_58_5 = all_52_13
% 174.80/26.83    (5)  all_58_3 = all_10_2
% 174.80/26.83    (6)  all_58_10 = all_52_15
% 174.80/26.83    (7)  all_58_7 = all_52_19
% 174.80/26.83    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.83    (9)  all_58_1 = all_52_3
% 174.80/26.83    (10)  op(e2, all_52_27) = e2
% 174.80/26.83    (11)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.83    (12)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.83    (13)   ~ (all_52_9 = all_10_2)
% 174.80/26.83    (14)   ~ (all_52_9 = all_52_13)
% 174.80/26.83    (15)  all_58_13 = all_52_27
% 174.80/26.83    (16)   ~ (all_52_3 = e3)
% 174.80/26.83    (17)  all_58_6 = all_52_17
% 174.80/26.83    (18)  op(e3, all_52_25) = e3
% 174.80/26.83    (19)  all_58_2 = all_52_9
% 174.80/26.83    (20)   ~ (all_52_19 = e3)
% 174.80/26.83    (21)   ~ (all_52_25 = all_4_2)
% 174.80/26.83    (22)  op(e3, e3) = all_4_2
% 174.80/26.83    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.83    (24)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.83    (25)  all_58_12 = all_52_25
% 174.80/26.83    (26)   ~ (all_52_9 = all_52_15)
% 174.80/26.83    (27)   ~ (e3 = e2)
% 174.80/26.83    (28)  op(e2, e3) = all_52_9
% 174.80/26.83  
% 174.80/26.83  Begin of proof
% 174.80/26.83  | 
% 174.80/26.83  | BETA: splitting (11) gives:
% 174.80/26.83  | 
% 174.80/26.83  | Case 1:
% 174.80/26.83  | | 
% 174.80/26.83  | |   (29)  all_58_1 = e3
% 174.80/26.83  | | 
% 174.80/26.83  | | COMBINE_EQS: (9), (29) imply:
% 174.80/26.83  | |   (30)  all_52_3 = e3
% 174.80/26.83  | | 
% 174.80/26.83  | | REDUCE: (16), (30) imply:
% 174.80/26.83  | |   (31)  $false
% 174.80/26.83  | | 
% 174.80/26.83  | | CLOSE: (31) is inconsistent.
% 174.80/26.83  | | 
% 174.80/26.83  | Case 2:
% 174.80/26.83  | | 
% 174.80/26.83  | |   (32)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.83  | | 
% 174.80/26.83  | | BETA: splitting (8) gives:
% 174.80/26.83  | | 
% 174.80/26.83  | | Case 1:
% 174.80/26.83  | | | 
% 174.80/26.83  | | |   (33)  all_58_2 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | COMBINE_EQS: (19), (33) imply:
% 174.80/26.83  | | |   (34)  all_52_9 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | SIMP: (34) implies:
% 174.80/26.83  | | |   (35)  all_52_9 = e3
% 174.80/26.83  | | | 
% 174.80/26.83  | | | REDUCE: (14), (35) imply:
% 174.80/26.83  | | |   (36)   ~ (all_52_13 = e3)
% 174.80/26.83  | | | 
% 174.80/26.83  | | | SIMP: (36) implies:
% 174.80/26.83  | | |   (37)   ~ (all_52_13 = e3)
% 174.80/26.83  | | | 
% 174.80/26.83  | | | REDUCE: (26), (35) imply:
% 174.80/26.83  | | |   (38)   ~ (all_52_15 = e3)
% 174.80/26.83  | | | 
% 174.80/26.83  | | | SIMP: (38) implies:
% 174.80/26.84  | | |   (39)   ~ (all_52_15 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REDUCE: (2), (35) imply:
% 174.80/26.84  | | |   (40)   ~ (all_52_25 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | SIMP: (40) implies:
% 174.80/26.84  | | |   (41)   ~ (all_52_25 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REDUCE: (13), (35) imply:
% 174.80/26.84  | | |   (42)   ~ (all_10_2 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | SIMP: (42) implies:
% 174.80/26.84  | | |   (43)   ~ (all_10_2 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | BETA: splitting (12) gives:
% 174.80/26.84  | | | 
% 174.80/26.84  | | | Case 1:
% 174.80/26.84  | | | | 
% 174.80/26.84  | | | |   (44)  all_58_12 = e3
% 174.80/26.84  | | | | 
% 174.80/26.84  | | | | REF_CLOSE: (25), (41), (44) are inconsistent by sub-proof #1003.
% 174.80/26.84  | | | | 
% 174.80/26.84  | | | Case 2:
% 174.80/26.84  | | | | 
% 174.80/26.84  | | | |   (45)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.84  | | | | 
% 174.80/26.84  | | | | BETA: splitting (45) gives:
% 174.80/26.84  | | | | 
% 174.80/26.84  | | | | Case 1:
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | |   (46)  all_58_13 = e3
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | | COMBINE_EQS: (15), (46) imply:
% 174.80/26.84  | | | | |   (47)  all_52_27 = e3
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | | SIMP: (47) implies:
% 174.80/26.84  | | | | |   (48)  all_52_27 = e3
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | | REDUCE: (10), (48) imply:
% 174.80/26.84  | | | | |   (49)  op(e2, e3) = e2
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | | REF_CLOSE: (4), (5), (6), (8), (19), (23), (27), (28), (37), (39),
% 174.80/26.84  | | | | |            (43), (49) are inconsistent by sub-proof #181.
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | Case 2:
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | |   (50)   ~ (all_58_13 = e3)
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | | REDUCE: (15), (50) imply:
% 174.80/26.84  | | | | |   (51)   ~ (all_52_27 = e3)
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | | REF_CLOSE: (5), (7), (15), (20), (32), (43), (51) are inconsistent by
% 174.80/26.84  | | | | |            sub-proof #206.
% 174.80/26.84  | | | | | 
% 174.80/26.84  | | | | End of split
% 174.80/26.84  | | | | 
% 174.80/26.84  | | | End of split
% 174.80/26.84  | | | 
% 174.80/26.84  | | Case 2:
% 174.80/26.84  | | | 
% 174.80/26.84  | | |   (52)   ~ (all_58_2 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REF_CLOSE: (3), (12), (17), (18), (19), (21), (22), (23), (24), (25), (52)
% 174.80/26.84  | | |            are inconsistent by sub-proof #76.
% 174.80/26.84  | | | 
% 174.80/26.84  | | End of split
% 174.80/26.84  | | 
% 174.80/26.84  | End of split
% 174.80/26.84  | 
% 174.80/26.84  End of proof
% 174.80/26.84  
% 174.80/26.84  Sub-proof #76 shows that the following formulas are inconsistent:
% 174.80/26.84  ----------------------------------------------------------------
% 174.80/26.84    (1)   ~ (all_52_17 = e3)
% 174.80/26.84    (2)   ~ (all_58_2 = e3)
% 174.80/26.84    (3)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.84    (4)  all_58_6 = all_52_17
% 174.80/26.84    (5)  op(e3, all_52_25) = e3
% 174.80/26.84    (6)  all_58_2 = all_52_9
% 174.80/26.84    (7)   ~ (all_52_25 = all_4_2)
% 174.80/26.84    (8)  op(e3, e3) = all_4_2
% 174.80/26.84    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.84    (10)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.84    (11)  all_58_12 = all_52_25
% 174.80/26.84  
% 174.80/26.84  Begin of proof
% 174.80/26.84  | 
% 174.80/26.84  | REDUCE: (2), (6) imply:
% 174.80/26.84  |   (12)   ~ (all_52_9 = e3)
% 174.80/26.84  | 
% 174.80/26.84  | BETA: splitting (10) gives:
% 174.80/26.84  | 
% 174.80/26.84  | Case 1:
% 174.80/26.84  | | 
% 174.80/26.84  | |   (13)  all_58_2 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | REF_CLOSE: (6), (12), (13) are inconsistent by sub-proof #980.
% 174.80/26.84  | | 
% 174.80/26.84  | Case 2:
% 174.80/26.84  | | 
% 174.80/26.84  | |   (14)  all_58_6 = e3 | all_58_12 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | BETA: splitting (3) gives:
% 174.80/26.84  | | 
% 174.80/26.84  | | Case 1:
% 174.80/26.84  | | | 
% 174.80/26.84  | | |   (15)  all_58_12 = e3
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REF_CLOSE: (5), (7), (8), (9), (11), (15) are inconsistent by sub-proof
% 174.80/26.84  | | |            #884.
% 174.80/26.84  | | | 
% 174.80/26.84  | | Case 2:
% 174.80/26.84  | | | 
% 174.80/26.84  | | |   (16)   ~ (all_58_12 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REDUCE: (11), (16) imply:
% 174.80/26.84  | | |   (17)   ~ (all_52_25 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REF_CLOSE: (1), (4), (11), (14), (17) are inconsistent by sub-proof #888.
% 174.80/26.84  | | | 
% 174.80/26.84  | | End of split
% 174.80/26.84  | | 
% 174.80/26.84  | End of split
% 174.80/26.84  | 
% 174.80/26.84  End of proof
% 174.80/26.84  
% 174.80/26.84  Sub-proof #77 shows that the following formulas are inconsistent:
% 174.80/26.84  ----------------------------------------------------------------
% 174.80/26.84    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.84    (2)   ~ (all_52_17 = all_52_23)
% 174.80/26.84    (3)  all_52_16 = e3
% 174.80/26.84    (4)  op(e3, e2) = all_52_3
% 174.80/26.84    (5)   ~ (all_52_9 = all_52_25)
% 174.80/26.84    (6)  op(e1, e2) = all_52_19
% 174.80/26.84    (7)  all_58_5 = all_52_13
% 174.80/26.84    (8)   ~ (all_52_25 = all_52_29)
% 174.80/26.84    (9)  all_56_15 = all_6_2
% 174.80/26.84    (10)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.84    (11)  all_58_3 = all_10_2
% 174.80/26.84    (12)  all_56_9 = all_52_19
% 174.80/26.84    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.84    (14)  all_58_15 = all_6_2
% 174.80/26.84    (15)  op(e2, all_4_2) = e1
% 174.80/26.84    (16)   ~ (all_52_9 = all_4_2)
% 174.80/26.84    (17)   ~ (all_52_5 = all_52_7)
% 174.80/26.84    (18)  all_58_10 = all_52_15
% 174.80/26.84    (19)   ~ (all_52_5 = all_4_2)
% 174.80/26.84    (20)  all_58_7 = all_52_19
% 174.80/26.84    (21)   ~ (all_52_17 = all_52_25)
% 174.80/26.84    (22)  all_58_4 = all_52_5
% 174.80/26.84    (23)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.84    (24)   ~ (e3 = e1)
% 174.80/26.84    (25)  all_52_18 = e2
% 174.80/26.84    (26)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.84    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.84    (28)   ~ (all_52_7 = all_4_2)
% 174.80/26.84    (29)  all_58_1 = all_52_3
% 174.80/26.84    (30)  all_58_0 = all_4_2
% 174.80/26.84    (31)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.84    (32)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.84    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.84    (34)  all_58_14 = all_52_29
% 174.80/26.84    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.84    (36)  op(e2, e1) = all_52_13
% 174.80/26.84    (37)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.84    (38)  all_58_8 = all_14_2
% 174.80/26.84    (39)   ~ (all_52_5 = all_14_2)
% 174.80/26.84    (40)   ~ (all_52_3 = all_4_2)
% 174.80/26.84    (41)  op(e0, e3) = all_52_25
% 174.80/26.84    (42)  op(e3, all_52_17) = all_52_16
% 174.80/26.84    (43)   ~ (all_52_13 = all_14_2)
% 174.80/26.84    (44)   ~ (e3 = e0)
% 174.80/26.84    (45)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.84    (46)   ~ (all_52_9 = all_52_13)
% 174.80/26.84    (47)  op(e0, all_52_23) = all_52_22
% 174.80/26.84    (48)   ~ (all_52_15 = all_52_23)
% 174.80/26.84    (49)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.84    (50)  op(e1, e0) = all_52_23
% 174.80/26.84    (51)  all_58_13 = all_52_27
% 174.80/26.84    (52)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.84    (53)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.84    (54)   ~ (all_52_9 = all_52_17)
% 174.80/26.84    (55)  all_58_6 = all_52_17
% 174.80/26.84    (56)  op(e2, all_52_19) = all_52_18
% 174.80/26.84    (57)   ~ (e1 = e0)
% 174.80/26.84    (58)  all_56_0 = all_4_2
% 174.80/26.84    (59)  all_58_11 = all_52_23
% 174.80/26.84    (60)   ~ (all_52_3 = all_52_19)
% 174.80/26.84    (61)   ~ (all_52_7 = all_52_15)
% 174.80/26.84    (62)  op(e3, all_4_2) = e2
% 174.80/26.84    (63)   ~ (all_52_23 = all_6_2)
% 174.80/26.84    (64)  all_58_2 = all_52_9
% 174.80/26.84    (65)  op(e3, e1) = all_52_5
% 174.80/26.84    (66)   ~ (e2 = e1)
% 174.80/26.84    (67)  all_56_10 = all_14_2
% 174.80/26.84    (68)   ~ (all_52_25 = all_6_2)
% 174.80/26.84    (69)  op(e1, e3) = all_52_17
% 174.80/26.84    (70)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.84    (71)   ~ (all_52_25 = all_4_2)
% 174.80/26.84    (72)  op(e3, e0) = all_52_7
% 174.80/26.84    (73)  op(e3, e3) = all_4_2
% 174.80/26.84    (74)   ~ (all_52_17 = all_4_2)
% 174.80/26.84    (75)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.84    (76)   ~ (all_52_25 = all_52_27)
% 174.80/26.84    (77)   ~ (all_52_15 = all_10_2)
% 174.80/26.84    (78)  all_56_7 = all_52_15
% 174.80/26.84    (79)   ~ (all_4_2 = e0)
% 174.80/26.84    (80)   ~ (all_52_7 = all_52_23)
% 174.80/26.84    (81)   ~ (all_52_17 = all_52_19)
% 174.80/26.84    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.84    (83)  all_52_22 = e0
% 174.80/26.84    (84)  op(e1, all_14_2) = all_14_1
% 174.80/26.84    (85)  all_58_9 = all_52_7
% 174.80/26.84    (86)   ~ (e2 = e0)
% 174.80/26.84    (87)  all_58_12 = all_52_25
% 174.80/26.84    (88)  all_14_1 = e1
% 174.80/26.84    (89)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.84    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.84    (91)   ~ (e3 = e2)
% 174.80/26.84    (92)   ~ (all_52_19 = all_14_2)
% 174.80/26.84    (93)  op(e2, e3) = all_52_9
% 174.80/26.84  
% 174.80/26.84  Begin of proof
% 174.80/26.84  | 
% 174.80/26.84  | REDUCE: (3), (42) imply:
% 174.80/26.84  |   (94)  op(e3, all_52_17) = e3
% 174.80/26.84  | 
% 174.80/26.84  | REDUCE: (25), (56) imply:
% 174.80/26.84  |   (95)  op(e2, all_52_19) = e2
% 174.80/26.84  | 
% 174.80/26.84  | REDUCE: (84), (88) imply:
% 174.80/26.84  |   (96)  op(e1, all_14_2) = e1
% 174.80/26.84  | 
% 174.80/26.84  | REDUCE: (47), (83) imply:
% 174.80/26.84  |   (97)  op(e0, all_52_23) = e0
% 174.80/26.84  | 
% 174.80/26.84  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 174.80/26.84  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 174.80/26.84  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 174.80/26.84  |            (37), (38), (39), (40), (41), (43), (44), (45), (46), (48), (49),
% 174.80/26.84  |            (50), (51), (52), (53), (54), (55), (57), (58), (59), (60), (61),
% 174.80/26.84  |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 174.80/26.84  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (85),
% 174.80/26.84  |            (86), (87), (89), (90), (91), (92), (93), (94), (95), (96), (97)
% 174.80/26.84  |            are inconsistent by sub-proof #78.
% 174.80/26.84  | 
% 174.80/26.84  End of proof
% 174.80/26.84  
% 174.80/26.84  Sub-proof #78 shows that the following formulas are inconsistent:
% 174.80/26.84  ----------------------------------------------------------------
% 174.80/26.84    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.84    (2)   ~ (all_52_17 = all_52_23)
% 174.80/26.84    (3)  op(e3, e2) = all_52_3
% 174.80/26.84    (4)   ~ (all_52_9 = all_52_25)
% 174.80/26.84    (5)  op(e1, e2) = all_52_19
% 174.80/26.84    (6)  all_58_5 = all_52_13
% 174.80/26.84    (7)   ~ (all_52_25 = all_52_29)
% 174.80/26.84    (8)  all_56_15 = all_6_2
% 174.80/26.84    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.84    (10)  all_58_3 = all_10_2
% 174.80/26.84    (11)  all_56_9 = all_52_19
% 174.80/26.84    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.84    (13)  all_58_15 = all_6_2
% 174.80/26.84    (14)  op(e2, all_4_2) = e1
% 174.80/26.84    (15)   ~ (all_52_9 = all_4_2)
% 174.80/26.84    (16)   ~ (all_52_5 = all_52_7)
% 174.80/26.84    (17)  all_58_10 = all_52_15
% 174.80/26.84    (18)   ~ (all_52_5 = all_4_2)
% 174.80/26.84    (19)  all_58_7 = all_52_19
% 174.80/26.84    (20)   ~ (all_52_17 = all_52_25)
% 174.80/26.84    (21)  all_58_4 = all_52_5
% 174.80/26.84    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.84    (23)   ~ (e3 = e1)
% 174.80/26.84    (24)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.84    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.84    (26)   ~ (all_52_7 = all_4_2)
% 174.80/26.84    (27)  all_58_1 = all_52_3
% 174.80/26.84    (28)  all_58_0 = all_4_2
% 174.80/26.84    (29)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.84    (30)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.84    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.84    (32)  all_58_14 = all_52_29
% 174.80/26.84    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.84    (34)  op(e2, e1) = all_52_13
% 174.80/26.84    (35)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.84    (36)  all_58_8 = all_14_2
% 174.80/26.84    (37)   ~ (all_52_5 = all_14_2)
% 174.80/26.84    (38)   ~ (all_52_3 = all_4_2)
% 174.80/26.84    (39)  op(e0, e3) = all_52_25
% 174.80/26.84    (40)   ~ (all_52_13 = all_14_2)
% 174.80/26.84    (41)   ~ (e3 = e0)
% 174.80/26.84    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.84    (43)   ~ (all_52_9 = all_52_13)
% 174.80/26.84    (44)   ~ (all_52_15 = all_52_23)
% 174.80/26.84    (45)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.84    (46)  op(e1, e0) = all_52_23
% 174.80/26.84    (47)  all_58_13 = all_52_27
% 174.80/26.84    (48)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.84    (49)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.84    (50)   ~ (all_52_9 = all_52_17)
% 174.80/26.84    (51)  all_58_6 = all_52_17
% 174.80/26.84    (52)  op(e2, all_52_19) = e2
% 174.80/26.84    (53)  op(e3, all_52_17) = e3
% 174.80/26.84    (54)   ~ (e1 = e0)
% 174.80/26.84    (55)  all_56_0 = all_4_2
% 174.80/26.84    (56)  all_58_11 = all_52_23
% 174.80/26.84    (57)   ~ (all_52_3 = all_52_19)
% 174.80/26.84    (58)   ~ (all_52_7 = all_52_15)
% 174.80/26.84    (59)  op(e3, all_4_2) = e2
% 174.80/26.84    (60)   ~ (all_52_23 = all_6_2)
% 174.80/26.84    (61)  all_58_2 = all_52_9
% 174.80/26.84    (62)  op(e3, e1) = all_52_5
% 174.80/26.84    (63)   ~ (e2 = e1)
% 174.80/26.84    (64)  all_56_10 = all_14_2
% 174.80/26.84    (65)   ~ (all_52_25 = all_6_2)
% 174.80/26.84    (66)  op(e1, e3) = all_52_17
% 174.80/26.84    (67)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.84    (68)   ~ (all_52_25 = all_4_2)
% 174.80/26.84    (69)  op(e3, e0) = all_52_7
% 174.80/26.84    (70)  op(e3, e3) = all_4_2
% 174.80/26.84    (71)   ~ (all_52_17 = all_4_2)
% 174.80/26.84    (72)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.84    (73)   ~ (all_52_25 = all_52_27)
% 174.80/26.84    (74)  op(e0, all_52_23) = e0
% 174.80/26.84    (75)   ~ (all_52_15 = all_10_2)
% 174.80/26.84    (76)  all_56_7 = all_52_15
% 174.80/26.84    (77)  op(e1, all_14_2) = e1
% 174.80/26.84    (78)   ~ (all_4_2 = e0)
% 174.80/26.84    (79)   ~ (all_52_7 = all_52_23)
% 174.80/26.84    (80)   ~ (all_52_17 = all_52_19)
% 174.80/26.84    (81)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.84    (82)  all_58_9 = all_52_7
% 174.80/26.84    (83)   ~ (e2 = e0)
% 174.80/26.84    (84)  all_58_12 = all_52_25
% 174.80/26.84    (85)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.84    (86)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.84    (87)   ~ (e3 = e2)
% 174.80/26.84    (88)   ~ (all_52_19 = all_14_2)
% 174.80/26.84    (89)  op(e2, e3) = all_52_9
% 174.80/26.84  
% 174.80/26.84  Begin of proof
% 174.80/26.84  | 
% 174.80/26.84  | BETA: splitting (12) gives:
% 174.80/26.84  | 
% 174.80/26.84  | Case 1:
% 174.80/26.84  | | 
% 174.80/26.84  | |   (90)  all_56_0 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | COMBINE_EQS: (55), (90) imply:
% 174.80/26.84  | |   (91)  all_4_2 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | SIMP: (91) implies:
% 174.80/26.84  | |   (92)  all_4_2 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | REF_CLOSE: (59), (70), (72), (87), (92) are inconsistent by sub-proof #106.
% 174.80/26.84  | | 
% 174.80/26.84  | Case 2:
% 174.80/26.84  | | 
% 174.80/26.84  | |   (93)   ~ (all_56_0 = e3)
% 174.80/26.84  | |   (94)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.84  | | 
% 174.80/26.84  | | REDUCE: (55), (93) imply:
% 174.80/26.84  | |   (95)   ~ (all_4_2 = e3)
% 174.80/26.84  | | 
% 174.80/26.84  | | BETA: splitting (24) gives:
% 174.80/26.84  | | 
% 174.80/26.84  | | Case 1:
% 174.80/26.84  | | | 
% 174.80/26.84  | | |   (96)  all_56_15 = e3
% 174.80/26.84  | | | 
% 174.80/26.84  | | | COMBINE_EQS: (8), (96) imply:
% 174.80/26.84  | | |   (97)  all_6_2 = e3
% 174.80/26.84  | | | 
% 174.80/26.84  | | | SIMP: (97) implies:
% 174.80/26.84  | | |   (98)  all_6_2 = e3
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REDUCE: (60), (98) imply:
% 174.80/26.84  | | |   (99)   ~ (all_52_23 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REDUCE: (65), (98) imply:
% 174.80/26.84  | | |   (100)   ~ (all_52_25 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REF_CLOSE: (11), (19), (22), (25), (28), (30), (33), (36), (37), (50),
% 174.80/26.84  | | |            (51), (52), (53), (56), (61), (62), (66), (70), (71), (72),
% 174.80/26.84  | | |            (77), (84), (87), (89), (95), (99), (100) are inconsistent by
% 174.80/26.84  | | |            sub-proof #944.
% 174.80/26.84  | | | 
% 174.80/26.84  | | Case 2:
% 174.80/26.84  | | | 
% 174.80/26.84  | | |   (101)   ~ (all_56_15 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REDUCE: (8), (101) imply:
% 174.80/26.84  | | |   (102)   ~ (all_6_2 = e3)
% 174.80/26.84  | | | 
% 174.80/26.84  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 174.80/26.84  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 174.80/26.84  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 174.80/26.84  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 174.80/26.84  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 174.80/26.84  | | |            (56), (57), (58), (59), (61), (62), (63), (64), (66), (67),
% 174.80/26.84  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 174.80/26.84  | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 174.80/26.84  | | |            (88), (89), (94), (95), (102) are inconsistent by sub-proof
% 174.80/26.84  | | |            #79.
% 174.80/26.84  | | | 
% 174.80/26.84  | | End of split
% 174.80/26.84  | | 
% 174.80/26.84  | End of split
% 174.80/26.84  | 
% 174.80/26.84  End of proof
% 174.80/26.84  
% 174.80/26.84  Sub-proof #79 shows that the following formulas are inconsistent:
% 174.80/26.84  ----------------------------------------------------------------
% 174.80/26.84    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.84    (2)   ~ (all_52_17 = all_52_23)
% 174.80/26.84    (3)  op(e3, e2) = all_52_3
% 174.80/26.84    (4)   ~ (all_52_9 = all_52_25)
% 174.80/26.84    (5)  op(e1, e2) = all_52_19
% 174.80/26.84    (6)   ~ (all_6_2 = e3)
% 174.80/26.84    (7)  all_58_5 = all_52_13
% 174.80/26.84    (8)   ~ (all_52_25 = all_52_29)
% 174.80/26.84    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.84    (10)   ~ (all_4_2 = e3)
% 174.80/26.84    (11)  all_58_3 = all_10_2
% 174.80/26.84    (12)  all_56_9 = all_52_19
% 174.80/26.84    (13)  all_58_15 = all_6_2
% 174.80/26.84    (14)  op(e2, all_4_2) = e1
% 174.80/26.84    (15)   ~ (all_52_9 = all_4_2)
% 174.80/26.84    (16)   ~ (all_52_5 = all_52_7)
% 174.80/26.84    (17)  all_58_10 = all_52_15
% 174.80/26.84    (18)   ~ (all_52_5 = all_4_2)
% 174.80/26.84    (19)  all_58_7 = all_52_19
% 174.80/26.84    (20)   ~ (all_52_17 = all_52_25)
% 174.80/26.84    (21)  all_58_4 = all_52_5
% 174.80/26.84    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.84    (23)   ~ (e3 = e1)
% 174.80/26.84    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.84    (25)   ~ (all_52_7 = all_4_2)
% 174.80/26.84    (26)  all_58_1 = all_52_3
% 174.80/26.84    (27)  all_58_0 = all_4_2
% 174.80/26.84    (28)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.84    (29)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.84    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.84    (31)  all_58_14 = all_52_29
% 174.80/26.84    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.84    (33)  op(e2, e1) = all_52_13
% 174.80/26.84    (34)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.84    (35)  all_58_8 = all_14_2
% 174.80/26.84    (36)   ~ (all_52_5 = all_14_2)
% 174.80/26.84    (37)   ~ (all_52_3 = all_4_2)
% 174.80/26.84    (38)  op(e0, e3) = all_52_25
% 174.80/26.84    (39)   ~ (all_52_13 = all_14_2)
% 174.80/26.84    (40)   ~ (e3 = e0)
% 174.80/26.84    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.84    (42)   ~ (all_52_9 = all_52_13)
% 174.80/26.84    (43)   ~ (all_52_15 = all_52_23)
% 174.80/26.84    (44)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.84    (45)  op(e1, e0) = all_52_23
% 174.80/26.84    (46)  all_58_13 = all_52_27
% 174.80/26.84    (47)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.84    (48)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.84    (49)   ~ (all_52_9 = all_52_17)
% 174.80/26.84    (50)  all_58_6 = all_52_17
% 174.80/26.84    (51)  op(e2, all_52_19) = e2
% 174.80/26.84    (52)  op(e3, all_52_17) = e3
% 174.80/26.84    (53)   ~ (e1 = e0)
% 174.80/26.84    (54)  all_56_0 = all_4_2
% 174.80/26.84    (55)  all_58_11 = all_52_23
% 174.80/26.84    (56)   ~ (all_52_3 = all_52_19)
% 174.80/26.84    (57)   ~ (all_52_7 = all_52_15)
% 174.80/26.84    (58)  op(e3, all_4_2) = e2
% 174.80/26.84    (59)  all_58_2 = all_52_9
% 174.80/26.84    (60)  op(e3, e1) = all_52_5
% 174.80/26.84    (61)   ~ (e2 = e1)
% 174.80/26.84    (62)  all_56_10 = all_14_2
% 174.80/26.84    (63)  op(e1, e3) = all_52_17
% 174.80/26.84    (64)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 174.80/26.84    (65)   ~ (all_52_25 = all_4_2)
% 174.80/26.84    (66)  op(e3, e0) = all_52_7
% 174.80/26.84    (67)  op(e3, e3) = all_4_2
% 174.80/26.84    (68)   ~ (all_52_17 = all_4_2)
% 174.80/26.84    (69)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.84    (70)   ~ (all_52_25 = all_52_27)
% 174.80/26.84    (71)  op(e0, all_52_23) = e0
% 174.80/26.84    (72)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.84    (73)   ~ (all_52_15 = all_10_2)
% 174.80/26.84    (74)  all_56_7 = all_52_15
% 174.80/26.84    (75)  op(e1, all_14_2) = e1
% 174.80/26.84    (76)   ~ (all_4_2 = e0)
% 174.80/26.84    (77)   ~ (all_52_7 = all_52_23)
% 174.80/26.84    (78)   ~ (all_52_17 = all_52_19)
% 174.80/26.84    (79)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.84    (80)  all_58_9 = all_52_7
% 174.80/26.84    (81)   ~ (e2 = e0)
% 174.80/26.84    (82)  all_58_12 = all_52_25
% 174.80/26.84    (83)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.84    (84)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.84    (85)   ~ (e3 = e2)
% 174.80/26.84    (86)   ~ (all_52_19 = all_14_2)
% 174.80/26.84    (87)  op(e2, e3) = all_52_9
% 174.80/26.84  
% 174.80/26.84  Begin of proof
% 174.80/26.84  | 
% 174.80/26.84  | BETA: splitting (64) gives:
% 174.80/26.84  | 
% 174.80/26.84  | Case 1:
% 174.80/26.84  | | 
% 174.80/26.84  | |   (88)  all_56_7 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | COMBINE_EQS: (74), (88) imply:
% 174.80/26.84  | |   (89)  all_52_15 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | SIMP: (89) implies:
% 174.80/26.84  | |   (90)  all_52_15 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | COMBINE_EQS: (17), (90) imply:
% 174.80/26.84  | |   (91)  all_58_10 = e3
% 174.80/26.84  | | 
% 174.80/26.84  | | REDUCE: (57), (90) imply:
% 174.80/26.84  | |   (92)   ~ (all_52_7 = e3)
% 174.80/26.84  | | 
% 174.80/26.84  | | REDUCE: (43), (90) imply:
% 174.80/26.84  | |   (93)   ~ (all_52_23 = e3)
% 174.80/26.84  | | 
% 174.80/26.84  | | SIMP: (93) implies:
% 174.80/26.84  | |   (94)   ~ (all_52_23 = e3)
% 174.80/26.84  | | 
% 174.80/26.84  | | REDUCE: (73), (90) imply:
% 174.80/26.84  | |   (95)   ~ (all_10_2 = e3)
% 174.80/26.84  | | 
% 174.80/26.84  | | SIMP: (95) implies:
% 174.80/26.84  | |   (96)   ~ (all_10_2 = e3)
% 174.80/26.84  | | 
% 174.80/26.84  | | REF_CLOSE: (4), (5), (10), (11), (12), (15), (16), (18), (19), (20), (21),
% 174.80/26.84  | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (32), (34),
% 174.80/26.84  | |            (35), (36), (40), (41), (46), (47), (48), (49), (50), (51), (52),
% 174.80/26.84  | |            (53), (54), (55), (56), (59), (60), (61), (63), (66), (67), (68),
% 174.80/26.84  | |            (69), (70), (72), (75), (78), (80), (81), (82), (83), (84), (85),
% 174.80/26.84  | |            (87), (91), (92), (94), (96) are inconsistent by sub-proof #81.
% 174.80/26.84  | | 
% 174.80/26.84  | Case 2:
% 174.80/26.84  | | 
% 174.80/26.84  | |   (97)   ~ (all_56_7 = e3)
% 174.80/26.84  | | 
% 174.80/26.84  | | REDUCE: (74), (97) imply:
% 174.80/26.85  | |   (98)   ~ (all_52_15 = e3)
% 174.80/26.85  | | 
% 174.80/26.85  | | BETA: splitting (79) gives:
% 174.80/26.85  | | 
% 174.80/26.85  | | Case 1:
% 174.80/26.85  | | | 
% 174.80/26.85  | | |   (99)  all_58_9 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | COMBINE_EQS: (80), (99) imply:
% 174.80/26.85  | | |   (100)  all_52_7 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | SIMP: (100) implies:
% 174.80/26.85  | | |   (101)  all_52_7 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (16), (101) imply:
% 174.80/26.85  | | |   (102)   ~ (all_52_5 = e3)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (77), (101) imply:
% 174.80/26.85  | | |   (103)   ~ (all_52_23 = e3)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | SIMP: (103) implies:
% 174.80/26.85  | | |   (104)   ~ (all_52_23 = e3)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (25), (101) imply:
% 174.80/26.85  | | |   (105)   ~ (all_4_2 = e3)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | BETA: splitting (34) gives:
% 174.80/26.85  | | | 
% 174.80/26.85  | | | Case 1:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | |   (106)  all_58_12 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | COMBINE_EQS: (82), (106) imply:
% 174.80/26.85  | | | |   (107)  all_52_25 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | SIMP: (107) implies:
% 174.80/26.85  | | | |   (108)  all_52_25 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (20), (108) imply:
% 174.80/26.85  | | | |   (109)   ~ (all_52_17 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (8), (108) imply:
% 174.80/26.85  | | | |   (110)   ~ (all_52_29 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | SIMP: (110) implies:
% 174.80/26.85  | | | |   (111)   ~ (all_52_29 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | BETA: splitting (22) gives:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | Case 1:
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | |   (112)  all_58_6 = e3
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | REF_CLOSE: (50), (109), (112) are inconsistent by sub-proof #981.
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | Case 2:
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | |   (113)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | BETA: splitting (84) gives:
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | Case 1:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | |   (114)  all_58_4 = e3
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | REF_CLOSE: (21), (102), (114) are inconsistent by sub-proof #1025.
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | Case 2:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | |   (115)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | BETA: splitting (44) gives:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | Case 1:
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | |   (116)  all_56_10 = e3
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | | REF_CLOSE: (1), (19), (35), (36), (52), (55), (60), (62), (63),
% 174.80/26.85  | | | | | | |            (69), (75), (86), (113), (116) are inconsistent by
% 174.80/26.85  | | | | | | |            sub-proof #922.
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | Case 2:
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | |   (117)   ~ (all_56_10 = e3)
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | | REDUCE: (62), (117) imply:
% 174.80/26.85  | | | | | | |   (118)   ~ (all_14_2 = e3)
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | | BETA: splitting (115) gives:
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | | Case 1:
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | |   (119)  all_58_5 = e3
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | COMBINE_EQS: (7), (119) imply:
% 174.80/26.85  | | | | | | | |   (120)  all_52_13 = e3
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | SIMP: (120) implies:
% 174.80/26.85  | | | | | | | |   (121)  all_52_13 = e3
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | REDUCE: (39), (121) imply:
% 174.80/26.85  | | | | | | | |   (122)   ~ (all_14_2 = e3)
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | REDUCE: (33), (121) imply:
% 174.80/26.85  | | | | | | | |   (123)  op(e2, e1) = e3
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | BETA: splitting (113) gives:
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | Case 1:
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | |   (124)  all_58_7 = e3
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | COMBINE_EQS: (19), (124) imply:
% 174.80/26.85  | | | | | | | | |   (125)  all_52_19 = e3
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | REDUCE: (51), (125) imply:
% 174.80/26.85  | | | | | | | | |   (126)  op(e2, e3) = e2
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | GROUND_INST: instantiating (69) with all_52_9, e2, e3, e2,
% 174.80/26.85  | | | | | | | | |              simplifying with (87), (126) gives:
% 174.80/26.85  | | | | | | | | |   (127)  all_52_9 = e2
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | REDUCE: (15), (127) imply:
% 174.80/26.85  | | | | | | | | |   (128)   ~ (all_4_2 = e2)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | SIMP: (128) implies:
% 174.80/26.85  | | | | | | | | |   (129)   ~ (all_4_2 = e2)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | BETA: splitting (72) gives:
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | Case 1:
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | |   (130)  all_56_0 = e2
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | COMBINE_EQS: (54), (130) imply:
% 174.80/26.85  | | | | | | | | | |   (131)  all_4_2 = e2
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | REDUCE: (129), (131) imply:
% 174.80/26.85  | | | | | | | | | |   (132)  $false
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | CLOSE: (132) is inconsistent.
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | Case 2:
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | |   (133)  all_56_0 = e1 | all_56_0 = e0
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | BETA: splitting (133) gives:
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | Case 1:
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | |   (134)  all_56_0 = e1
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | | COMBINE_EQS: (54), (134) imply:
% 174.80/26.85  | | | | | | | | | | |   (135)  all_4_2 = e1
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | | REDUCE: (10), (135) imply:
% 174.80/26.85  | | | | | | | | | | |   (136)   ~ (e3 = e1)
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | | REDUCE: (14), (135) imply:
% 174.80/26.85  | | | | | | | | | | |   (137)  op(e2, e1) = e1
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | | REF_CLOSE: (23), (69), (123), (137) are inconsistent by
% 174.80/26.85  | | | | | | | | | | |            sub-proof #166.
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | Case 2:
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | |   (138)  all_56_0 = e0
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | | COMBINE_EQS: (54), (138) imply:
% 174.80/26.85  | | | | | | | | | | |   (139)  all_4_2 = e0
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | | REDUCE: (76), (139) imply:
% 174.80/26.85  | | | | | | | | | | |   (140)  $false
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 174.80/26.85  | | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | End of split
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | End of split
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | Case 2:
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | |   (141)  all_58_8 = e3 | all_58_11 = e3
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | REF_CLOSE: (35), (55), (104), (118), (141) are inconsistent by
% 174.80/26.85  | | | | | | | | |            sub-proof #997.
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | End of split
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | Case 2:
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | |   (142)  all_58_8 = e3 | all_58_14 = e3
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | REF_CLOSE: (31), (35), (111), (118), (142) are inconsistent by
% 174.80/26.85  | | | | | | | |            sub-proof #999.
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | End of split
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | End of split
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | End of split
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | End of split
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | Case 2:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | |   (143)   ~ (all_58_12 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (82), (143) imply:
% 174.80/26.85  | | | |   (144)   ~ (all_52_25 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REF_CLOSE: (10), (12), (19), (22), (24), (27), (29), (32), (35), (36),
% 174.80/26.85  | | | |            (49), (50), (51), (52), (55), (59), (60), (63), (67), (68),
% 174.80/26.85  | | | |            (69), (75), (82), (85), (87), (104), (144) are inconsistent
% 174.80/26.85  | | | |            by sub-proof #944.
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | End of split
% 174.80/26.85  | | | 
% 174.80/26.85  | | Case 2:
% 174.80/26.85  | | | 
% 174.80/26.85  | | |   (145)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REF_CLOSE: (1), (2), (3), (6), (9), (10), (13), (14), (17), (27), (32),
% 174.80/26.85  | | |            (33), (36), (37), (38), (39), (40), (42), (44), (45), (47),
% 174.80/26.85  | | |            (50), (54), (55), (58), (59), (60), (61), (62), (65), (69),
% 174.80/26.85  | | |            (71), (72), (75), (81), (82), (85), (98), (145) are
% 174.80/26.85  | | |            inconsistent by sub-proof #80.
% 174.80/26.85  | | | 
% 174.80/26.85  | | End of split
% 174.80/26.85  | | 
% 174.80/26.85  | End of split
% 174.80/26.85  | 
% 174.80/26.85  End of proof
% 174.80/26.85  
% 174.80/26.85  Sub-proof #80 shows that the following formulas are inconsistent:
% 174.80/26.85  ----------------------------------------------------------------
% 174.80/26.85    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.85    (2)   ~ (all_52_17 = all_52_23)
% 174.80/26.85    (3)  op(e3, e2) = all_52_3
% 174.80/26.85    (4)   ~ (all_6_2 = e3)
% 174.80/26.85    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.85    (6)   ~ (all_4_2 = e3)
% 174.80/26.85    (7)  all_58_15 = all_6_2
% 174.80/26.85    (8)  op(e2, all_4_2) = e1
% 174.80/26.85    (9)  all_58_10 = all_52_15
% 174.80/26.85    (10)  all_58_0 = all_4_2
% 174.80/26.85    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.85    (12)  op(e2, e1) = all_52_13
% 174.80/26.85    (13)   ~ (all_52_5 = all_14_2)
% 174.80/26.85    (14)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 174.80/26.85    (15)   ~ (all_52_3 = all_4_2)
% 174.80/26.85    (16)  op(e0, e3) = all_52_25
% 174.80/26.85    (17)   ~ (all_52_13 = all_14_2)
% 174.80/26.85    (18)   ~ (e3 = e0)
% 174.80/26.85    (19)   ~ (all_52_9 = all_52_13)
% 174.80/26.85    (20)   ~ (all_52_15 = e3)
% 174.80/26.85    (21)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.85    (22)  op(e1, e0) = all_52_23
% 174.80/26.85    (23)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.85    (24)  all_58_6 = all_52_17
% 174.80/26.85    (25)  all_56_0 = all_4_2
% 174.80/26.85    (26)  all_58_11 = all_52_23
% 174.80/26.85    (27)  op(e3, all_4_2) = e2
% 174.80/26.85    (28)  all_58_2 = all_52_9
% 174.80/26.85    (29)  op(e3, e1) = all_52_5
% 174.80/26.85    (30)   ~ (e2 = e1)
% 174.80/26.85    (31)  all_56_10 = all_14_2
% 174.80/26.85    (32)   ~ (all_52_25 = all_4_2)
% 174.80/26.85    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.85    (34)  op(e0, all_52_23) = e0
% 174.80/26.85    (35)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.85    (36)  op(e1, all_14_2) = e1
% 174.80/26.85    (37)   ~ (e2 = e0)
% 174.80/26.85    (38)  all_58_12 = all_52_25
% 174.80/26.85    (39)   ~ (e3 = e2)
% 174.80/26.85  
% 174.80/26.85  Begin of proof
% 174.80/26.85  | 
% 174.80/26.85  | BETA: splitting (14) gives:
% 174.80/26.85  | 
% 174.80/26.85  | Case 1:
% 174.80/26.85  | | 
% 174.80/26.85  | |   (40)  all_58_10 = e3
% 174.80/26.85  | | 
% 174.80/26.85  | | REF_CLOSE: (9), (20), (40) are inconsistent by sub-proof #1018.
% 174.80/26.85  | | 
% 174.80/26.85  | Case 2:
% 174.80/26.85  | | 
% 174.80/26.85  | |   (41)  all_58_11 = e3 | all_58_15 = e3
% 174.80/26.85  | | 
% 174.80/26.85  | | BETA: splitting (41) gives:
% 174.80/26.85  | | 
% 174.80/26.85  | | Case 1:
% 174.80/26.85  | | | 
% 174.80/26.85  | | |   (42)  all_58_11 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | COMBINE_EQS: (26), (42) imply:
% 174.80/26.85  | | |   (43)  all_52_23 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | SIMP: (43) implies:
% 174.80/26.85  | | |   (44)  all_52_23 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (2), (44) imply:
% 174.80/26.85  | | |   (45)   ~ (all_52_17 = e3)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (1), (44) imply:
% 174.80/26.85  | | |   (46)   ~ (all_14_2 = e3)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | SIMP: (46) implies:
% 174.80/26.85  | | |   (47)   ~ (all_14_2 = e3)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (22), (44) imply:
% 174.80/26.85  | | |   (48)  op(e1, e0) = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (34), (44) imply:
% 174.80/26.85  | | |   (49)  op(e0, e3) = e0
% 174.80/26.85  | | | 
% 174.80/26.85  | | | GROUND_INST: instantiating (33) with all_52_25, e0, e3, e0, simplifying
% 174.80/26.85  | | |              with (16), (49) gives:
% 174.80/26.85  | | |   (50)  all_52_25 = e0
% 174.80/26.85  | | | 
% 174.80/26.85  | | | COMBINE_EQS: (38), (50) imply:
% 174.80/26.85  | | |   (51)  all_58_12 = e0
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (32), (50) imply:
% 174.80/26.85  | | |   (52)   ~ (all_4_2 = e0)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | SIMP: (52) implies:
% 174.80/26.85  | | |   (53)   ~ (all_4_2 = e0)
% 174.80/26.85  | | | 
% 174.80/26.85  | | | BETA: splitting (11) gives:
% 174.80/26.85  | | | 
% 174.80/26.85  | | | Case 1:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | |   (54)  all_58_0 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | COMBINE_EQS: (10), (54) imply:
% 174.80/26.85  | | | |   (55)  all_4_2 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (6), (55) imply:
% 174.80/26.85  | | | |   (56)  $false
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | CLOSE: (56) is inconsistent.
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | Case 2:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | |   (57)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | BETA: splitting (57) gives:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | Case 1:
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | |   (58)  all_58_2 = e3
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | COMBINE_EQS: (28), (58) imply:
% 174.80/26.85  | | | | |   (59)  all_52_9 = e3
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | SIMP: (59) implies:
% 174.80/26.85  | | | | |   (60)  all_52_9 = e3
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | REDUCE: (19), (60) imply:
% 174.80/26.85  | | | | |   (61)   ~ (all_52_13 = e3)
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | SIMP: (61) implies:
% 174.80/26.85  | | | | |   (62)   ~ (all_52_13 = e3)
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | BETA: splitting (23) gives:
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | Case 1:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | |   (63)  all_58_0 = e1
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | COMBINE_EQS: (10), (63) imply:
% 174.80/26.85  | | | | | |   (64)  all_4_2 = e1
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | REDUCE: (27), (64) imply:
% 174.80/26.85  | | | | | |   (65)  op(e3, e1) = e2
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | REDUCE: (8), (64) imply:
% 174.80/26.85  | | | | | |   (66)  op(e2, e1) = e1
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | BETA: splitting (5) gives:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | Case 1:
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | |   (67)  all_58_0 = e2
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | | REF_CLOSE: (30), (63), (67) are inconsistent by sub-proof #930.
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | Case 2:
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | |   (68)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | | BETA: splitting (68) gives:
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | | Case 1:
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | |   (69)  all_58_2 = e2
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | COMBINE_EQS: (58), (69) imply:
% 174.80/26.85  | | | | | | | |   (70)  e3 = e2
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | REDUCE: (39), (70) imply:
% 174.80/26.85  | | | | | | | |   (71)  $false
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | CLOSE: (71) is inconsistent.
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | Case 2:
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | |   (72)  all_58_6 = e2 | all_58_12 = e2
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | BETA: splitting (72) gives:
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | | Case 1:
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | GROUND_INST: instantiating (33) with all_52_13, e1, e1, e2,
% 174.80/26.85  | | | | | | | | |              simplifying with (12), (66) gives:
% 174.80/26.85  | | | | | | | | |   (73)  all_52_13 = e1
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | GROUND_INST: instantiating (33) with all_52_5, e2, e1, e3,
% 174.80/26.85  | | | | | | | | |              simplifying with (29), (65) gives:
% 174.80/26.85  | | | | | | | | |   (74)  all_52_5 = e2
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | REDUCE: (13), (74) imply:
% 174.80/26.85  | | | | | | | | |   (75)   ~ (all_14_2 = e2)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | SIMP: (75) implies:
% 174.80/26.85  | | | | | | | | |   (76)   ~ (all_14_2 = e2)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | REDUCE: (17), (73) imply:
% 174.80/26.85  | | | | | | | | |   (77)   ~ (all_14_2 = e1)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | SIMP: (77) implies:
% 174.80/26.85  | | | | | | | | |   (78)   ~ (all_14_2 = e1)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | REDUCE: (62), (73) imply:
% 174.80/26.85  | | | | | | | | |   (79)   ~ (e3 = e1)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | SIMP: (79) implies:
% 174.80/26.85  | | | | | | | | |   (80)   ~ (e3 = e1)
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | BETA: splitting (21) gives:
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | Case 1:
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | |   (81)  all_56_10 = e3
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | COMBINE_EQS: (31), (81) imply:
% 174.80/26.85  | | | | | | | | | |   (82)  all_14_2 = e3
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | REDUCE: (47), (82) imply:
% 174.80/26.85  | | | | | | | | | |   (83)  $false
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | CLOSE: (83) is inconsistent.
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | Case 2:
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | |   (84)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | | REF_CLOSE: (31), (33), (36), (48), (76), (78), (80), (84) are
% 174.80/26.85  | | | | | | | | | |            inconsistent by sub-proof #690.
% 174.80/26.85  | | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | End of split
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | Case 2:
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | |   (85)  all_58_12 = e2
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | COMBINE_EQS: (51), (85) imply:
% 174.80/26.85  | | | | | | | | |   (86)  e2 = e0
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | SIMP: (86) implies:
% 174.80/26.85  | | | | | | | | |   (87)  e2 = e0
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | REDUCE: (37), (87) imply:
% 174.80/26.85  | | | | | | | | |   (88)  $false
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | | CLOSE: (88) is inconsistent.
% 174.80/26.85  | | | | | | | | | 
% 174.80/26.85  | | | | | | | | End of split
% 174.80/26.85  | | | | | | | | 
% 174.80/26.85  | | | | | | | End of split
% 174.80/26.85  | | | | | | | 
% 174.80/26.85  | | | | | | End of split
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | Case 2:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | |   (89)   ~ (all_58_0 = e1)
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | REDUCE: (10), (89) imply:
% 174.80/26.85  | | | | | |   (90)   ~ (all_4_2 = e1)
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | REF_CLOSE: (3), (5), (10), (15), (25), (27), (33), (35), (53), (90)
% 174.80/26.85  | | | | | |            are inconsistent by sub-proof #114.
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | End of split
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | Case 2:
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | |   (91)  all_58_6 = e3 | all_58_12 = e3
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | BETA: splitting (91) gives:
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | | Case 1:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | |   (92)  all_58_6 = e3
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | REF_CLOSE: (24), (45), (92) are inconsistent by sub-proof #981.
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | Case 2:
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | |   (93)  all_58_12 = e3
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | COMBINE_EQS: (51), (93) imply:
% 174.80/26.85  | | | | | |   (94)  e3 = e0
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | REDUCE: (18), (94) imply:
% 174.80/26.85  | | | | | |   (95)  $false
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | | CLOSE: (95) is inconsistent.
% 174.80/26.85  | | | | | | 
% 174.80/26.85  | | | | | End of split
% 174.80/26.85  | | | | | 
% 174.80/26.85  | | | | End of split
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | End of split
% 174.80/26.85  | | | 
% 174.80/26.85  | | Case 2:
% 174.80/26.85  | | | 
% 174.80/26.85  | | |   (96)  all_58_15 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | COMBINE_EQS: (7), (96) imply:
% 174.80/26.85  | | |   (97)  all_6_2 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (4), (97) imply:
% 174.80/26.85  | | |   (98)  $false
% 174.80/26.85  | | | 
% 174.80/26.85  | | | CLOSE: (98) is inconsistent.
% 174.80/26.85  | | | 
% 174.80/26.85  | | End of split
% 174.80/26.85  | | 
% 174.80/26.85  | End of split
% 174.80/26.85  | 
% 174.80/26.85  End of proof
% 174.80/26.85  
% 174.80/26.85  Sub-proof #81 shows that the following formulas are inconsistent:
% 174.80/26.85  ----------------------------------------------------------------
% 174.80/26.85    (1)   ~ (all_52_9 = all_52_25)
% 174.80/26.85    (2)  op(e1, e2) = all_52_19
% 174.80/26.85    (3)   ~ (all_4_2 = e3)
% 174.80/26.85    (4)  all_58_3 = all_10_2
% 174.80/26.85    (5)  all_56_9 = all_52_19
% 174.80/26.85    (6)   ~ (all_52_9 = all_4_2)
% 174.80/26.85    (7)   ~ (all_52_5 = all_52_7)
% 174.80/26.85    (8)   ~ (all_52_5 = all_4_2)
% 174.80/26.85    (9)  all_58_7 = all_52_19
% 174.80/26.85    (10)   ~ (all_52_17 = all_52_25)
% 174.80/26.85    (11)  all_58_4 = all_52_5
% 174.80/26.85    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.85    (13)   ~ (e3 = e1)
% 174.80/26.85    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.85    (15)   ~ (all_52_7 = all_4_2)
% 174.80/26.85    (16)  all_58_1 = all_52_3
% 174.80/26.85    (17)  all_58_0 = all_4_2
% 174.80/26.85    (18)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.85    (19)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.85    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.85    (21)   ~ (all_10_2 = e3)
% 174.80/26.85    (22)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.85    (23)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.85    (24)  all_58_8 = all_14_2
% 174.80/26.85    (25)   ~ (all_52_5 = all_14_2)
% 174.80/26.85    (26)   ~ (all_52_23 = e3)
% 174.80/26.85    (27)   ~ (e3 = e0)
% 174.80/26.85    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 174.80/26.85    (29)  all_58_13 = all_52_27
% 174.80/26.85    (30)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.85    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 174.80/26.85    (32)   ~ (all_52_9 = all_52_17)
% 174.80/26.85    (33)  all_58_6 = all_52_17
% 174.80/26.85    (34)  op(e2, all_52_19) = e2
% 174.80/26.85    (35)  op(e3, all_52_17) = e3
% 174.80/26.85    (36)  all_58_10 = e3
% 174.80/26.85    (37)   ~ (e1 = e0)
% 174.80/26.85    (38)  all_56_0 = all_4_2
% 174.80/26.85    (39)  all_58_11 = all_52_23
% 174.80/26.85    (40)   ~ (all_52_3 = all_52_19)
% 174.80/26.85    (41)  all_58_2 = all_52_9
% 174.80/26.85    (42)  op(e3, e1) = all_52_5
% 174.80/26.85    (43)   ~ (e2 = e1)
% 174.80/26.85    (44)  op(e1, e3) = all_52_17
% 174.80/26.85    (45)  op(e3, e0) = all_52_7
% 174.80/26.85    (46)  op(e3, e3) = all_4_2
% 174.80/26.85    (47)   ~ (all_52_17 = all_4_2)
% 174.80/26.85    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.85    (49)   ~ (all_52_25 = all_52_27)
% 174.80/26.85    (50)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.85    (51)  op(e1, all_14_2) = e1
% 174.80/26.85    (52)   ~ (all_52_7 = e3)
% 174.80/26.85    (53)   ~ (all_52_17 = all_52_19)
% 174.80/26.85    (54)  all_58_9 = all_52_7
% 174.80/26.85    (55)   ~ (e2 = e0)
% 174.80/26.85    (56)  all_58_12 = all_52_25
% 174.80/26.85    (57)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.85    (58)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 174.80/26.85    (59)   ~ (e3 = e2)
% 174.80/26.85    (60)  op(e2, e3) = all_52_9
% 174.80/26.85  
% 174.80/26.85  Begin of proof
% 174.80/26.85  | 
% 174.80/26.85  | BETA: splitting (22) gives:
% 174.80/26.85  | 
% 174.80/26.85  | Case 1:
% 174.80/26.85  | | 
% 174.80/26.85  | |   (61)  all_58_0 = e3
% 174.80/26.85  | | 
% 174.80/26.85  | | COMBINE_EQS: (17), (61) imply:
% 174.80/26.85  | |   (62)  all_4_2 = e3
% 174.80/26.85  | | 
% 174.80/26.85  | | REDUCE: (3), (62) imply:
% 174.80/26.85  | |   (63)  $false
% 174.80/26.85  | | 
% 174.80/26.85  | | CLOSE: (63) is inconsistent.
% 174.80/26.85  | | 
% 174.80/26.85  | Case 2:
% 174.80/26.85  | | 
% 174.80/26.85  | |   (64)   ~ (all_58_0 = e3)
% 174.80/26.85  | |   (65)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.85  | | 
% 174.80/26.85  | | BETA: splitting (57) gives:
% 174.80/26.85  | | 
% 174.80/26.85  | | Case 1:
% 174.80/26.85  | | | 
% 174.80/26.85  | | |   (66)  all_58_0 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | COMBINE_EQS: (17), (66) imply:
% 174.80/26.85  | | |   (67)  all_4_2 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | REDUCE: (3), (67) imply:
% 174.80/26.85  | | |   (68)  $false
% 174.80/26.85  | | | 
% 174.80/26.85  | | | CLOSE: (68) is inconsistent.
% 174.80/26.85  | | | 
% 174.80/26.85  | | Case 2:
% 174.80/26.85  | | | 
% 174.80/26.85  | | |   (69)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 174.80/26.85  | | | 
% 174.80/26.85  | | | BETA: splitting (23) gives:
% 174.80/26.85  | | | 
% 174.80/26.85  | | | Case 1:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | |   (70)  all_58_12 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | COMBINE_EQS: (56), (70) imply:
% 174.80/26.85  | | | |   (71)  all_52_25 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | SIMP: (71) implies:
% 174.80/26.85  | | | |   (72)  all_52_25 = e3
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (1), (72) imply:
% 174.80/26.85  | | | |   (73)   ~ (all_52_9 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (10), (72) imply:
% 174.80/26.85  | | | |   (74)   ~ (all_52_17 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (49), (72) imply:
% 174.80/26.85  | | | |   (75)   ~ (all_52_27 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | SIMP: (75) implies:
% 174.80/26.85  | | | |   (76)   ~ (all_52_27 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (11), (12), (13), (15), (16),
% 174.80/26.85  | | | |            (17), (18), (20), (21), (24), (25), (26), (27), (28), (29),
% 174.80/26.85  | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 174.80/26.85  | | | |            (40), (41), (42), (43), (44), (45), (47), (48), (50), (51),
% 174.80/26.85  | | | |            (52), (53), (54), (55), (58), (60), (69), (70), (73), (74),
% 174.80/26.85  | | | |            (76) are inconsistent by sub-proof #680.
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | Case 2:
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | |   (77)   ~ (all_58_12 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REDUCE: (56), (77) imply:
% 174.80/26.85  | | | |   (78)   ~ (all_52_25 = e3)
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | | REF_CLOSE: (5), (9), (12), (14), (19), (24), (25), (26), (32), (33),
% 174.80/26.85  | | | |            (34), (35), (39), (41), (42), (44), (46), (47), (48), (51),
% 174.80/26.85  | | | |            (56), (59), (60), (65), (78) are inconsistent by sub-proof
% 174.80/26.85  | | | |            #945.
% 174.80/26.85  | | | | 
% 174.80/26.85  | | | End of split
% 174.80/26.85  | | | 
% 174.80/26.85  | | End of split
% 174.80/26.85  | | 
% 174.80/26.85  | End of split
% 174.80/26.85  | 
% 174.80/26.85  End of proof
% 174.80/26.85  
% 174.80/26.85  Sub-proof #82 shows that the following formulas are inconsistent:
% 174.80/26.85  ----------------------------------------------------------------
% 174.80/26.85    (1)   ~ (all_52_23 = all_14_2)
% 174.80/26.85    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 174.80/26.85    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 174.80/26.85    (4)   ~ (all_52_27 = all_10_2)
% 174.80/26.85    (5)   ~ (all_52_17 = all_52_23)
% 174.80/26.85    (6)  op(e2, all_10_2) = all_10_1
% 174.80/26.85    (7)   ~ (all_52_13 = all_52_29)
% 174.80/26.85    (8)  all_56_3 = all_52_7
% 174.80/26.85    (9)  op(e3, e2) = all_52_3
% 174.80/26.85    (10)   ~ (all_52_9 = all_52_25)
% 174.80/26.85    (11)   ~ (all_52_19 = all_52_23)
% 174.80/26.85    (12)  all_56_11 = all_52_23
% 174.80/26.85    (13)  op(e1, e2) = all_52_19
% 174.80/26.85    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 174.80/26.85    (15)  op(e3, all_52_9) = all_52_8
% 174.80/26.85    (16)   ~ (all_52_3 = all_10_2)
% 174.80/26.85    (17)  all_58_5 = all_52_13
% 174.80/26.85    (18)   ~ (all_6_2 = e0)
% 174.80/26.85    (19)   ~ (all_52_25 = all_52_29)
% 174.80/26.85    (20)  all_56_15 = all_6_2
% 174.80/26.85    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 174.80/26.85    (22)  all_58_3 = all_10_2
% 174.80/26.85    (23)  all_56_9 = all_52_19
% 174.80/26.85    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 174.80/26.85    (25)  all_58_15 = all_6_2
% 174.80/26.85    (26)  op(e2, all_4_2) = e1
% 174.80/26.85    (27)   ~ (all_52_9 = all_4_2)
% 174.80/26.85    (28)   ~ (all_52_5 = all_52_7)
% 174.80/26.85    (29)  all_58_10 = all_52_15
% 174.80/26.85    (30)   ~ (all_52_5 = all_4_2)
% 174.80/26.85    (31)  all_58_7 = all_52_19
% 174.80/26.85    (32)  all_56_4 = all_52_9
% 174.80/26.85    (33)   ~ (all_52_15 = all_6_2)
% 174.80/26.85    (34)   ~ (all_52_17 = all_52_25)
% 174.80/26.85    (35)  op(e0, e1) = all_52_29
% 174.80/26.85    (36)  all_58_4 = all_52_5
% 174.80/26.85    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 174.80/26.85    (38)   ~ (e3 = e1)
% 174.80/26.85    (39)   ~ (all_52_27 = all_52_29)
% 174.80/26.85    (40)   ~ (all_52_17 = all_14_2)
% 174.80/26.85    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 174.80/26.85    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 174.80/26.85    (43)   ~ (all_52_7 = all_4_2)
% 174.80/26.85    (44)  all_58_1 = all_52_3
% 174.80/26.85    (45)   ~ (all_52_13 = all_52_15)
% 174.80/26.85    (46)  all_58_0 = all_4_2
% 174.80/26.85    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 174.80/26.85    (48)  op(e1, all_52_13) = all_52_12
% 174.80/26.85    (49)  all_52_0 = e2
% 174.80/26.86    (50)  op(e1, all_52_29) = all_52_28
% 174.80/26.86    (51)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 174.80/26.86          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 174.80/26.86    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 174.80/26.86    (53)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 174.80/26.86    (54)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 174.80/26.86    (55)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 174.80/26.86    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 174.80/26.86    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 174.80/26.86    (58)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 174.80/26.86    (59)  all_58_14 = all_52_29
% 174.80/26.86    (60)   ~ (all_52_3 = all_52_5)
% 174.80/26.86    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 174.80/26.86    (62)  op(e2, e1) = all_52_13
% 174.80/26.86    (63)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 174.80/26.86    (64)  all_58_8 = all_14_2
% 174.80/26.86    (65)  all_56_1 = all_52_3
% 174.80/26.86    (66)  all_56_14 = all_52_29
% 174.80/26.86    (67)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 174.80/26.86    (68)   ~ (all_52_3 = all_52_27)
% 174.80/26.86    (69)   ~ (all_52_3 = all_4_2)
% 174.80/26.86    (70)  op(e0, e3) = all_52_25
% 174.80/26.86    (71)  op(e0, all_6_2) = all_6_1
% 174.80/26.86    (72)  op(e3, all_52_17) = all_52_16
% 174.80/26.86    (73)  all_52_10 = all_10_1
% 174.80/26.86    (74)   ~ (all_52_13 = all_14_2)
% 174.80/26.86    (75)   ~ (e3 = e0)
% 174.80/26.86    (76)   ~ (all_52_9 = all_52_13)
% 174.80/26.86    (77)  op(e0, all_52_23) = all_52_22
% 174.80/26.86    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 174.80/26.86    (79)  op(all_10_1, all_10_2) = all_10_0
% 174.80/26.86    (80)  all_58_13 = all_52_27
% 174.80/26.86    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 174.80/26.86    (82)   ~ (all_52_9 = all_52_17)
% 174.80/26.86    (83)  all_58_6 = all_52_17
% 174.80/26.86    (84)   ~ (all_52_3 = all_52_7)
% 174.80/26.86    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 174.80/26.86    (86)  op(e2, all_52_19) = all_52_18
% 174.80/26.86    (87)   ~ (e1 = e0)
% 174.80/26.86    (88)  all_56_0 = all_4_2
% 174.80/26.86    (89)  all_58_11 = all_52_23
% 174.80/26.86    (90)   ~ (all_52_3 = all_52_19)
% 174.80/26.86    (91)   ~ (all_52_7 = all_52_15)
% 174.80/26.86    (92)  op(e0, all_52_15) = all_52_14
% 174.80/26.86    (93)   ~ (all_52_29 = all_14_2)
% 174.80/26.86    (94)   ~ (all_52_19 = all_10_2)
% 174.80/26.86    (95)  op(e3, all_4_2) = e2
% 174.80/26.86    (96)   ~ (all_52_23 = all_6_2)
% 174.80/26.86    (97)   ~ (all_52_29 = all_6_2)
% 174.80/26.86    (98)  all_58_2 = all_52_9
% 174.80/26.86    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 174.80/26.86    (100)  op(e3, e1) = all_52_5
% 174.80/26.86    (101)  all_56_10 = all_14_2
% 174.80/26.86    (102)   ~ (all_52_25 = all_6_2)
% 174.80/26.86    (103)  op(e1, e1) = all_14_2
% 174.80/26.86    (104)  op(e1, e3) = all_52_17
% 174.80/26.86    (105)   ~ (all_52_25 = all_4_2)
% 174.80/26.86    (106)  op(e3, e0) = all_52_7
% 174.80/26.86    (107)  op(e3, e3) = all_4_2
% 174.80/26.86    (108)  all_56_8 = all_52_17
% 174.80/26.86    (109)   ~ (all_52_17 = all_4_2)
% 174.80/26.86    (110)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 174.80/26.86             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 174.80/26.86    (111)   ~ (all_52_25 = all_52_27)
% 174.80/26.86    (112)   ~ (all_52_27 = all_6_2)
% 174.80/26.86    (113)   ~ (all_52_7 = all_6_2)
% 175.06/26.86    (114)   ~ (all_10_0 = e3)
% 175.06/26.86    (115)   ~ (all_52_7 = all_52_23)
% 175.06/26.86    (116)   ~ (all_52_13 = all_10_2)
% 175.06/26.86    (117)  op(e2, all_52_27) = all_52_26
% 175.06/26.86    (118)   ~ (all_52_17 = all_52_19)
% 175.06/26.86    (119)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.06/26.86    (120)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.06/26.86    (121)  op(e1, all_14_2) = all_14_1
% 175.06/26.86    (122)  all_58_9 = all_52_7
% 175.06/26.86    (123)  all_58_12 = all_52_25
% 175.06/26.86    (124)   ~ (all_10_0 = e1)
% 175.06/26.86    (125)  all_56_6 = all_52_13
% 175.06/26.86    (126)   ~ (all_52_9 = all_52_15)
% 175.06/26.86    (127)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.06/26.86    (128)   ~ (e3 = e2)
% 175.06/26.86    (129)   ~ (all_52_19 = all_14_2)
% 175.06/26.86    (130)  op(e2, e3) = all_52_9
% 175.06/26.86  
% 175.06/26.86  Begin of proof
% 175.06/26.86  | 
% 175.06/26.86  | BETA: splitting (51) gives:
% 175.06/26.86  | 
% 175.06/26.86  | Case 1:
% 175.06/26.86  | | 
% 175.06/26.86  | |   (131)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.06/26.86  | | 
% 175.06/26.86  | | REF_CLOSE: (49), (128), (131) are inconsistent by sub-proof #124.
% 175.06/26.86  | | 
% 175.06/26.86  | Case 2:
% 175.06/26.86  | | 
% 175.06/26.86  | |   (132)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.06/26.86  | | 
% 175.06/26.86  | | ALPHA: (132) implies:
% 175.06/26.86  | |   (133)  all_52_14 = e0
% 175.06/26.86  | |   (134)  all_52_12 = e1
% 175.06/26.86  | |   (135)  all_52_10 = e2
% 175.06/26.86  | |   (136)  all_52_8 = e3
% 175.06/26.86  | | 
% 175.06/26.86  | | COMBINE_EQS: (73), (135) imply:
% 175.06/26.86  | |   (137)  all_10_1 = e2
% 175.06/26.86  | | 
% 175.06/26.86  | | REDUCE: (79), (137) imply:
% 175.06/26.86  | |   (138)  op(e2, all_10_2) = all_10_0
% 175.06/26.86  | | 
% 175.06/26.86  | | REDUCE: (15), (136) imply:
% 175.06/26.86  | |   (139)  op(e3, all_52_9) = e3
% 175.06/26.86  | | 
% 175.06/26.86  | | REDUCE: (6), (137) imply:
% 175.06/26.86  | |   (140)  op(e2, all_10_2) = e2
% 175.06/26.86  | | 
% 175.06/26.86  | | REDUCE: (48), (134) imply:
% 175.06/26.86  | |   (141)  op(e1, all_52_13) = e1
% 175.06/26.86  | | 
% 175.06/26.86  | | REDUCE: (92), (133) imply:
% 175.06/26.86  | |   (142)  op(e0, all_52_15) = e0
% 175.06/26.86  | | 
% 175.06/26.86  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 175.06/26.86  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 175.06/26.86  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 175.06/26.86  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 175.06/26.86  | |            (50), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 175.06/26.86  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 175.06/26.86  | |            (74), (75), (76), (77), (78), (80), (81), (82), (83), (84), (85),
% 175.06/26.86  | |            (86), (87), (88), (89), (90), (91), (93), (94), (95), (96), (97),
% 175.06/26.86  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 175.06/26.86  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 175.06/26.86  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 175.06/26.86  | |            (125), (126), (127), (129), (130), (138), (139), (140), (141),
% 175.06/26.86  | |            (142) are inconsistent by sub-proof #83.
% 175.06/26.86  | | 
% 175.06/26.86  | End of split
% 175.06/26.86  | 
% 175.06/26.86  End of proof
% 175.06/26.86  
% 175.06/26.86  Sub-proof #83 shows that the following formulas are inconsistent:
% 175.06/26.86  ----------------------------------------------------------------
% 175.06/26.86    (1)   ~ (all_52_23 = all_14_2)
% 175.06/26.86    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.06/26.86    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.06/26.86    (4)   ~ (all_52_27 = all_10_2)
% 175.06/26.86    (5)   ~ (all_52_17 = all_52_23)
% 175.06/26.86    (6)   ~ (all_52_13 = all_52_29)
% 175.06/26.86    (7)  op(e2, all_10_2) = all_10_0
% 175.06/26.86    (8)  all_56_3 = all_52_7
% 175.06/26.86    (9)  op(e3, e2) = all_52_3
% 175.06/26.86    (10)   ~ (all_52_9 = all_52_25)
% 175.06/26.86    (11)   ~ (all_52_19 = all_52_23)
% 175.06/26.86    (12)  all_56_11 = all_52_23
% 175.06/26.86    (13)  op(e1, e2) = all_52_19
% 175.06/26.86    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.06/26.86    (15)   ~ (all_52_3 = all_10_2)
% 175.06/26.86    (16)  all_58_5 = all_52_13
% 175.06/26.86    (17)   ~ (all_6_2 = e0)
% 175.06/26.86    (18)   ~ (all_52_25 = all_52_29)
% 175.06/26.86    (19)  op(e1, all_52_13) = e1
% 175.06/26.86    (20)  op(e0, all_52_15) = e0
% 175.06/26.86    (21)  all_56_15 = all_6_2
% 175.06/26.86    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.06/26.86    (23)  all_58_3 = all_10_2
% 175.06/26.86    (24)  all_56_9 = all_52_19
% 175.06/26.86    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.06/26.86    (26)  all_58_15 = all_6_2
% 175.06/26.86    (27)  op(e2, all_4_2) = e1
% 175.06/26.86    (28)   ~ (all_52_9 = all_4_2)
% 175.06/26.86    (29)   ~ (all_52_5 = all_52_7)
% 175.06/26.86    (30)  all_58_10 = all_52_15
% 175.06/26.86    (31)   ~ (all_52_5 = all_4_2)
% 175.06/26.86    (32)  all_58_7 = all_52_19
% 175.06/26.86    (33)  all_56_4 = all_52_9
% 175.06/26.86    (34)   ~ (all_52_15 = all_6_2)
% 175.06/26.86    (35)   ~ (all_52_17 = all_52_25)
% 175.06/26.86    (36)  op(e0, e1) = all_52_29
% 175.06/26.86    (37)  all_58_4 = all_52_5
% 175.06/26.86    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.06/26.86    (39)   ~ (e3 = e1)
% 175.06/26.86    (40)   ~ (all_52_27 = all_52_29)
% 175.06/26.86    (41)   ~ (all_52_17 = all_14_2)
% 175.06/26.86    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.06/26.86    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.06/26.86    (44)   ~ (all_52_7 = all_4_2)
% 175.06/26.86    (45)  all_58_1 = all_52_3
% 175.06/26.86    (46)   ~ (all_52_13 = all_52_15)
% 175.06/26.86    (47)  all_58_0 = all_4_2
% 175.06/26.86    (48)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.06/26.86    (49)  op(e1, all_52_29) = all_52_28
% 175.06/26.86    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.06/26.86    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.06/26.86    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.06/26.86    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.06/26.86    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.06/26.86    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.06/26.86    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.06/26.86    (57)  all_58_14 = all_52_29
% 175.06/26.86    (58)   ~ (all_52_3 = all_52_5)
% 175.06/26.86    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.06/26.86    (60)  op(e2, e1) = all_52_13
% 175.06/26.86    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.06/26.86    (62)  all_58_8 = all_14_2
% 175.06/26.86    (63)  all_56_1 = all_52_3
% 175.06/26.86    (64)  all_56_14 = all_52_29
% 175.06/26.86    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.06/26.86    (66)   ~ (all_52_3 = all_52_27)
% 175.06/26.86    (67)   ~ (all_52_3 = all_4_2)
% 175.06/26.86    (68)  op(e0, e3) = all_52_25
% 175.06/26.86    (69)  op(e0, all_6_2) = all_6_1
% 175.06/26.86    (70)  op(e3, all_52_17) = all_52_16
% 175.06/26.86    (71)   ~ (all_52_13 = all_14_2)
% 175.06/26.86    (72)  op(e3, all_52_9) = e3
% 175.06/26.86    (73)   ~ (e3 = e0)
% 175.06/26.86    (74)   ~ (all_52_9 = all_52_13)
% 175.06/26.86    (75)  op(e0, all_52_23) = all_52_22
% 175.06/26.86    (76)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.06/26.86    (77)  all_58_13 = all_52_27
% 175.06/26.86    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.06/26.86    (79)   ~ (all_52_9 = all_52_17)
% 175.06/26.86    (80)  all_58_6 = all_52_17
% 175.06/26.86    (81)   ~ (all_52_3 = all_52_7)
% 175.06/26.86    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.06/26.86    (83)  op(e2, all_52_19) = all_52_18
% 175.06/26.86    (84)   ~ (e1 = e0)
% 175.06/26.86    (85)  all_56_0 = all_4_2
% 175.06/26.86    (86)  all_58_11 = all_52_23
% 175.06/26.86    (87)   ~ (all_52_3 = all_52_19)
% 175.06/26.86    (88)   ~ (all_52_7 = all_52_15)
% 175.06/26.86    (89)   ~ (all_52_29 = all_14_2)
% 175.06/26.86    (90)   ~ (all_52_19 = all_10_2)
% 175.06/26.86    (91)  op(e3, all_4_2) = e2
% 175.06/26.86    (92)   ~ (all_52_23 = all_6_2)
% 175.06/26.86    (93)   ~ (all_52_29 = all_6_2)
% 175.06/26.86    (94)  all_58_2 = all_52_9
% 175.06/26.86    (95)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.06/26.86    (96)  op(e3, e1) = all_52_5
% 175.06/26.86    (97)  all_56_10 = all_14_2
% 175.06/26.86    (98)   ~ (all_52_25 = all_6_2)
% 175.06/26.86    (99)  op(e1, e1) = all_14_2
% 175.06/26.86    (100)  op(e1, e3) = all_52_17
% 175.06/26.86    (101)   ~ (all_52_25 = all_4_2)
% 175.06/26.86    (102)  op(e3, e0) = all_52_7
% 175.06/26.86    (103)  op(e2, all_10_2) = e2
% 175.06/26.86    (104)  op(e3, e3) = all_4_2
% 175.06/26.86    (105)  all_56_8 = all_52_17
% 175.06/26.86    (106)   ~ (all_52_17 = all_4_2)
% 175.06/26.86    (107)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.06/26.86             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.06/26.86    (108)   ~ (all_52_25 = all_52_27)
% 175.06/26.86    (109)   ~ (all_52_27 = all_6_2)
% 175.06/26.86    (110)   ~ (all_52_7 = all_6_2)
% 175.06/26.86    (111)   ~ (all_10_0 = e3)
% 175.06/26.86    (112)   ~ (all_52_7 = all_52_23)
% 175.06/26.86    (113)   ~ (all_52_13 = all_10_2)
% 175.06/26.86    (114)  op(e2, all_52_27) = all_52_26
% 175.06/26.86    (115)   ~ (all_52_17 = all_52_19)
% 175.06/26.86    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.06/26.86    (117)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.06/26.86    (118)  op(e1, all_14_2) = all_14_1
% 175.06/26.86    (119)  all_58_9 = all_52_7
% 175.06/26.86    (120)  all_58_12 = all_52_25
% 175.06/26.86    (121)   ~ (all_10_0 = e1)
% 175.06/26.86    (122)  all_56_6 = all_52_13
% 175.06/26.86    (123)   ~ (all_52_9 = all_52_15)
% 175.06/26.86    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.06/26.86    (125)   ~ (all_52_19 = all_14_2)
% 175.06/26.86    (126)  op(e2, e3) = all_52_9
% 175.06/26.86  
% 175.06/26.86  Begin of proof
% 175.06/26.86  | 
% 175.06/26.86  | GROUND_INST: instantiating (107) with e2, all_10_0, all_10_2, e2, simplifying
% 175.06/26.86  |              with (7), (103) gives:
% 175.06/26.86  |   (127)  all_10_0 = e2
% 175.06/26.86  | 
% 175.06/26.86  | REDUCE: (111), (127) imply:
% 175.06/26.86  |   (128)   ~ (e3 = e2)
% 175.06/26.86  | 
% 175.06/26.86  | SIMP: (128) implies:
% 175.06/26.86  |   (129)   ~ (e3 = e2)
% 175.06/26.86  | 
% 175.06/26.86  | REDUCE: (121), (127) imply:
% 175.06/26.86  |   (130)   ~ (e2 = e1)
% 175.06/26.86  | 
% 175.06/26.86  | BETA: splitting (25) gives:
% 175.06/26.86  | 
% 175.06/26.86  | Case 1:
% 175.06/26.86  | | 
% 175.06/26.86  | |   (131)  all_56_0 = e3
% 175.06/26.86  | | 
% 175.06/26.86  | | COMBINE_EQS: (85), (131) imply:
% 175.06/26.86  | |   (132)  all_4_2 = e3
% 175.06/26.86  | | 
% 175.06/26.86  | | REF_CLOSE: (91), (104), (107), (129), (132) are inconsistent by sub-proof
% 175.06/26.86  | |            #106.
% 175.06/26.86  | | 
% 175.06/26.86  | Case 2:
% 175.06/26.86  | | 
% 175.06/26.86  | |   (133)   ~ (all_56_0 = e3)
% 175.06/26.86  | |   (134)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.06/26.86  | | 
% 175.06/26.86  | | REDUCE: (85), (133) imply:
% 175.06/26.86  | |   (135)   ~ (all_4_2 = e3)
% 175.06/26.86  | | 
% 175.06/26.86  | | BETA: splitting (42) gives:
% 175.06/26.86  | | 
% 175.06/26.86  | | Case 1:
% 175.06/26.86  | | | 
% 175.06/26.86  | | |   (136)  all_56_15 = e3
% 175.06/26.86  | | | 
% 175.06/26.86  | | | REF_CLOSE: (9), (15), (16), (19), (21), (23), (28), (30), (32), (34),
% 175.06/26.86  | | |            (39), (43), (45), (47), (54), (59), (68), (69), (72), (77),
% 175.06/26.86  | | |            (80), (91), (94), (98), (100), (103), (104), (107), (109),
% 175.06/26.86  | | |            (115), (120), (126), (129), (136) are inconsistent by sub-proof
% 175.06/26.86  | | |            #105.
% 175.06/26.86  | | | 
% 175.06/26.86  | | Case 2:
% 175.06/26.86  | | | 
% 175.06/26.86  | | |   (137)   ~ (all_56_15 = e3)
% 175.06/26.86  | | |   (138)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.06/26.86  | | | 
% 175.06/26.86  | | | REDUCE: (21), (137) imply:
% 175.06/26.86  | | |   (139)   ~ (all_6_2 = e3)
% 175.06/26.86  | | | 
% 175.06/26.86  | | | BETA: splitting (61) gives:
% 175.06/26.86  | | | 
% 175.06/26.86  | | | Case 1:
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | |   (140)  all_58_12 = e3
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | COMBINE_EQS: (120), (140) imply:
% 175.06/26.86  | | | |   (141)  all_52_25 = e3
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | SIMP: (141) implies:
% 175.06/26.86  | | | |   (142)  all_52_25 = e3
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | REDUCE: (10), (142) imply:
% 175.06/26.86  | | | |   (143)   ~ (all_52_9 = e3)
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | REDUCE: (108), (142) imply:
% 175.06/26.86  | | | |   (144)   ~ (all_52_27 = e3)
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | SIMP: (144) implies:
% 175.06/26.86  | | | |   (145)   ~ (all_52_27 = e3)
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | REDUCE: (18), (142) imply:
% 175.06/26.86  | | | |   (146)   ~ (all_52_29 = e3)
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | SIMP: (146) implies:
% 175.06/26.86  | | | |   (147)   ~ (all_52_29 = e3)
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | REDUCE: (98), (142) imply:
% 175.06/26.86  | | | |   (148)   ~ (all_6_2 = e3)
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | REDUCE: (68), (142) imply:
% 175.06/26.86  | | | |   (149)  op(e0, e3) = e3
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 175.06/26.86  | | | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (26),
% 175.06/26.86  | | | |            (28), (29), (30), (31), (32), (33), (36), (37), (38), (40),
% 175.06/26.86  | | | |            (41), (43), (44), (45), (46), (47), (48), (50), (51), (53),
% 175.06/26.86  | | | |            (54), (55), (56), (57), (58), (60), (62), (63), (65), (67),
% 175.06/26.86  | | | |            (70), (71), (72), (73), (74), (75), (76), (77), (79), (80),
% 175.06/26.86  | | | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 175.06/26.86  | | | |            (91), (92), (94), (95), (96), (97), (100), (102), (103),
% 175.06/26.86  | | | |            (106), (107), (109), (110), (112), (113), (115), (116),
% 175.06/26.86  | | | |            (117), (118), (119), (122), (123), (124), (125), (126),
% 175.06/26.86  | | | |            (129), (130), (134), (138), (139), (140), (143), (145),
% 175.06/26.86  | | | |            (147), (149) are inconsistent by sub-proof #100.
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | Case 2:
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | |   (150)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | BETA: splitting (150) gives:
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | | Case 1:
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | |   (151)  all_58_13 = e3
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | | COMBINE_EQS: (77), (151) imply:
% 175.06/26.86  | | | | |   (152)  all_52_27 = e3
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | | SIMP: (152) implies:
% 175.06/26.86  | | | | |   (153)  all_52_27 = e3
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | | REF_CLOSE: (2), (5), (9), (10), (15), (16), (19), (20), (22), (23),
% 175.06/26.86  | | | | |            (25), (26), (28), (29), (30), (32), (33), (35), (37), (38),
% 175.06/26.86  | | | | |            (39), (40), (41), (43), (44), (45), (47), (52), (54), (57),
% 175.06/26.86  | | | | |            (59), (62), (64), (66), (67), (68), (70), (72), (77), (78),
% 175.06/26.86  | | | | |            (79), (80), (82), (85), (86), (88), (91), (94), (100),
% 175.06/26.86  | | | | |            (101), (103), (104), (105), (106), (107), (108), (109),
% 175.06/26.86  | | | | |            (114), (115), (116), (119), (120), (123), (124), (126),
% 175.06/26.86  | | | | |            (129), (153) are inconsistent by sub-proof #103.
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | Case 2:
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | |   (154)  all_58_14 = e3 | all_58_15 = e3
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | | REF_CLOSE: (5), (9), (15), (16), (18), (19), (20), (23), (26), (27),
% 175.06/26.86  | | | | |            (28), (30), (32), (33), (35), (39), (40), (43), (45), (47),
% 175.06/26.86  | | | | |            (49), (54), (57), (58), (59), (60), (68), (71), (72), (77),
% 175.06/26.86  | | | | |            (78), (79), (80), (82), (84), (86), (88), (93), (94), (96),
% 175.06/26.86  | | | | |            (99), (100), (103), (104), (107), (115), (116), (119),
% 175.06/26.86  | | | | |            (120), (126), (135), (139), (154) are inconsistent by
% 175.06/26.86  | | | | |            sub-proof #84.
% 175.06/26.86  | | | | | 
% 175.06/26.86  | | | | End of split
% 175.06/26.86  | | | | 
% 175.06/26.86  | | | End of split
% 175.06/26.86  | | | 
% 175.06/26.86  | | End of split
% 175.06/26.86  | | 
% 175.06/26.86  | End of split
% 175.06/26.86  | 
% 175.06/26.86  End of proof
% 175.06/26.86  
% 175.06/26.86  Sub-proof #84 shows that the following formulas are inconsistent:
% 175.06/26.86  ----------------------------------------------------------------
% 175.06/26.86    (1)   ~ (all_52_17 = all_52_23)
% 175.06/26.86    (2)  all_58_14 = e3 | all_58_15 = e3
% 175.06/26.86    (3)  op(e3, e2) = all_52_3
% 175.06/26.86    (4)   ~ (all_6_2 = e3)
% 175.06/26.86    (5)   ~ (all_52_3 = all_10_2)
% 175.06/26.86    (6)  all_58_5 = all_52_13
% 175.06/26.86    (7)   ~ (all_52_25 = all_52_29)
% 175.06/26.86    (8)  op(e1, all_52_13) = e1
% 175.06/26.86    (9)  op(e0, all_52_15) = e0
% 175.06/26.86    (10)   ~ (all_4_2 = e3)
% 175.06/26.86    (11)  all_58_3 = all_10_2
% 175.06/26.86    (12)  all_58_15 = all_6_2
% 175.06/26.86    (13)  op(e2, all_4_2) = e1
% 175.06/26.86    (14)   ~ (all_52_9 = all_4_2)
% 175.06/26.86    (15)  all_58_10 = all_52_15
% 175.06/26.86    (16)  all_58_7 = all_52_19
% 175.06/26.86    (17)  all_56_4 = all_52_9
% 175.06/26.86    (18)   ~ (all_52_17 = all_52_25)
% 175.06/26.86    (19)   ~ (e3 = e1)
% 175.06/26.86    (20)   ~ (all_52_27 = all_52_29)
% 175.06/26.86    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.06/26.86    (22)  all_58_1 = all_52_3
% 175.06/26.86    (23)  all_58_0 = all_4_2
% 175.06/26.86    (24)  op(e1, all_52_29) = all_52_28
% 175.06/26.86    (25)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.06/26.86    (26)  all_58_14 = all_52_29
% 175.06/26.86    (27)   ~ (all_52_3 = all_52_5)
% 175.06/26.86    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.06/26.86    (29)  op(e2, e1) = all_52_13
% 175.06/26.86    (30)  op(e0, e3) = all_52_25
% 175.06/26.86    (31)   ~ (all_52_13 = all_14_2)
% 175.06/26.86    (32)  op(e3, all_52_9) = e3
% 175.06/26.86    (33)  all_58_13 = all_52_27
% 175.06/26.86    (34)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.06/26.86    (35)   ~ (all_52_9 = all_52_17)
% 175.06/26.86    (36)  all_58_6 = all_52_17
% 175.06/26.86    (37)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.06/26.86    (38)   ~ (e1 = e0)
% 175.06/26.86    (39)  all_58_11 = all_52_23
% 175.06/26.86    (40)   ~ (all_52_7 = all_52_15)
% 175.06/26.86    (41)   ~ (all_52_29 = all_6_2)
% 175.06/26.86    (42)  all_58_2 = all_52_9
% 175.06/26.86    (43)  op(e3, e1) = all_52_5
% 175.06/26.86    (44)  op(e1, e1) = all_14_2
% 175.06/26.86    (45)  op(e1, e3) = all_52_17
% 175.06/26.86    (46)  op(e2, all_10_2) = e2
% 175.06/26.86    (47)  op(e3, e3) = all_4_2
% 175.06/26.86    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.06/26.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.06/26.86    (49)   ~ (all_52_17 = all_52_19)
% 175.06/26.86    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.06/26.86    (51)  all_58_9 = all_52_7
% 175.06/26.86    (52)  all_58_12 = all_52_25
% 175.06/26.86    (53)  op(e2, e3) = all_52_9
% 175.06/26.86  
% 175.06/26.86  Begin of proof
% 175.06/26.86  | 
% 175.06/26.86  | BETA: splitting (2) gives:
% 175.06/26.86  | 
% 175.06/26.86  | Case 1:
% 175.06/26.86  | | 
% 175.06/26.86  | |   (54)  all_58_14 = e3
% 175.06/26.86  | | 
% 175.06/26.86  | | COMBINE_EQS: (26), (54) imply:
% 175.06/26.86  | |   (55)  all_52_29 = e3
% 175.06/26.86  | | 
% 175.06/26.86  | | SIMP: (55) implies:
% 175.06/26.86  | |   (56)  all_52_29 = e3
% 175.06/26.86  | | 
% 175.06/26.86  | | REDUCE: (7), (56) imply:
% 175.06/26.86  | |   (57)   ~ (all_52_25 = e3)
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (20), (56) imply:
% 175.06/26.87  | |   (58)   ~ (all_52_27 = e3)
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (41), (56) imply:
% 175.06/26.87  | |   (59)   ~ (all_6_2 = e3)
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (24), (56) imply:
% 175.06/26.87  | |   (60)  op(e1, e3) = all_52_28
% 175.06/26.87  | | 
% 175.06/26.87  | | GROUND_INST: instantiating (48) with all_52_17, all_52_28, e3, e1,
% 175.06/26.87  | |              simplifying with (45), (60) gives:
% 175.06/26.87  | |   (61)  all_52_17 = all_52_28
% 175.06/26.87  | | 
% 175.06/26.87  | | COMBINE_EQS: (36), (61) imply:
% 175.06/26.87  | |   (62)  all_58_6 = all_52_28
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (35), (61) imply:
% 175.06/26.87  | |   (63)   ~ (all_52_9 = all_52_28)
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (49), (61) imply:
% 175.06/26.87  | |   (64)   ~ (all_52_19 = all_52_28)
% 175.06/26.87  | | 
% 175.06/26.87  | | SIMP: (64) implies:
% 175.06/26.87  | |   (65)   ~ (all_52_19 = all_52_28)
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (1), (61) imply:
% 175.06/26.87  | |   (66)   ~ (all_52_23 = all_52_28)
% 175.06/26.87  | | 
% 175.06/26.87  | | SIMP: (66) implies:
% 175.06/26.87  | |   (67)   ~ (all_52_23 = all_52_28)
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (18), (61) imply:
% 175.06/26.87  | |   (68)   ~ (all_52_25 = all_52_28)
% 175.06/26.87  | | 
% 175.06/26.87  | | SIMP: (68) implies:
% 175.06/26.87  | |   (69)   ~ (all_52_25 = all_52_28)
% 175.06/26.87  | | 
% 175.06/26.87  | | BETA: splitting (28) gives:
% 175.06/26.87  | | 
% 175.06/26.87  | | Case 1:
% 175.06/26.87  | | | 
% 175.06/26.87  | | |   (70)  all_58_0 = e3
% 175.06/26.87  | | | 
% 175.06/26.87  | | | COMBINE_EQS: (23), (70) imply:
% 175.06/26.87  | | |   (71)  all_4_2 = e3
% 175.06/26.87  | | | 
% 175.06/26.87  | | | REDUCE: (10), (71) imply:
% 175.06/26.87  | | |   (72)  $false
% 175.06/26.87  | | | 
% 175.06/26.87  | | | CLOSE: (72) is inconsistent.
% 175.06/26.87  | | | 
% 175.06/26.87  | | Case 2:
% 175.06/26.87  | | | 
% 175.06/26.87  | | |   (73)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.06/26.87  | | | 
% 175.06/26.87  | | | BETA: splitting (37) gives:
% 175.06/26.87  | | | 
% 175.06/26.87  | | | Case 1:
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | |   (74)  all_56_4 = e3
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | | COMBINE_EQS: (17), (74) imply:
% 175.06/26.87  | | | |   (75)  all_52_9 = e3
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | | REF_CLOSE: (14), (32), (47), (48), (75) are inconsistent by sub-proof
% 175.06/26.87  | | | |            #967.
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | Case 2:
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | |   (76)   ~ (all_56_4 = e3)
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | | REDUCE: (17), (76) imply:
% 175.06/26.87  | | | |   (77)   ~ (all_52_9 = e3)
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | | BETA: splitting (73) gives:
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | | Case 1:
% 175.06/26.87  | | | | | 
% 175.06/26.87  | | | | |   (78)  all_58_2 = e3
% 175.06/26.87  | | | | | 
% 175.06/26.87  | | | | | REF_CLOSE: (42), (77), (78) are inconsistent by sub-proof #980.
% 175.06/26.87  | | | | | 
% 175.06/26.87  | | | | Case 2:
% 175.06/26.87  | | | | | 
% 175.06/26.87  | | | | |   (79)  all_58_6 = e3 | all_58_12 = e3
% 175.06/26.87  | | | | | 
% 175.06/26.87  | | | | | BETA: splitting (79) gives:
% 175.06/26.87  | | | | | 
% 175.06/26.87  | | | | | Case 1:
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | |   (80)  all_58_6 = e3
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | COMBINE_EQS: (62), (80) imply:
% 175.06/26.87  | | | | | |   (81)  all_52_28 = e3
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | SIMP: (81) implies:
% 175.06/26.87  | | | | | |   (82)  all_52_28 = e3
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | REDUCE: (65), (82) imply:
% 175.06/26.87  | | | | | |   (83)   ~ (all_52_19 = e3)
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | REDUCE: (67), (82) imply:
% 175.06/26.87  | | | | | |   (84)   ~ (all_52_23 = e3)
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | REDUCE: (60), (82) imply:
% 175.06/26.87  | | | | | |   (85)  op(e1, e3) = e3
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | BETA: splitting (21) gives:
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | Case 1:
% 175.06/26.87  | | | | | | | 
% 175.06/26.87  | | | | | | |   (86)  all_58_2 = e3
% 175.06/26.87  | | | | | | | 
% 175.06/26.87  | | | | | | | REF_CLOSE: (42), (77), (86) are inconsistent by sub-proof #980.
% 175.06/26.87  | | | | | | | 
% 175.06/26.87  | | | | | | Case 2:
% 175.06/26.87  | | | | | | | 
% 175.06/26.87  | | | | | | |   (87)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.06/26.87  | | | | | | | 
% 175.06/26.87  | | | | | | | BETA: splitting (50) gives:
% 175.06/26.87  | | | | | | | 
% 175.06/26.87  | | | | | | | Case 1:
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | |   (88)  all_58_9 = e3
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | | COMBINE_EQS: (51), (88) imply:
% 175.06/26.87  | | | | | | | |   (89)  all_52_7 = e3
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | | SIMP: (89) implies:
% 175.06/26.87  | | | | | | | |   (90)  all_52_7 = e3
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | | REDUCE: (40), (90) imply:
% 175.06/26.87  | | | | | | | |   (91)   ~ (all_52_15 = e3)
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | | SIMP: (91) implies:
% 175.06/26.87  | | | | | | | |   (92)   ~ (all_52_15 = e3)
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (11), (15), (16), (19), (22),
% 175.06/26.87  | | | | | | | |            (25), (32), (33), (46), (48), (53), (58), (83), (85),
% 175.06/26.87  | | | | | | | |            (87), (92) are inconsistent by sub-proof #775.
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | Case 2:
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | |   (93)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | | BETA: splitting (93) gives:
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | | Case 1:
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | |   (94)  all_58_10 = e3
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | COMBINE_EQS: (15), (94) imply:
% 175.06/26.87  | | | | | | | | |   (95)  all_52_15 = e3
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | SIMP: (95) implies:
% 175.06/26.87  | | | | | | | | |   (96)  all_52_15 = e3
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | REDUCE: (9), (96) imply:
% 175.06/26.87  | | | | | | | | |   (97)  op(e0, e3) = e0
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | BETA: splitting (25) gives:
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | Case 1:
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | |   (98)  all_58_1 = e3
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | COMBINE_EQS: (22), (98) imply:
% 175.06/26.87  | | | | | | | | | |   (99)  all_52_3 = e3
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | REDUCE: (27), (99) imply:
% 175.06/26.87  | | | | | | | | | |   (100)   ~ (all_52_5 = e3)
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | SIMP: (100) implies:
% 175.06/26.87  | | | | | | | | | |   (101)   ~ (all_52_5 = e3)
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | GROUND_INST: instantiating (48) with all_52_25, e0, e3, e0,
% 175.06/26.87  | | | | | | | | | |              simplifying with (30), (97) gives:
% 175.06/26.87  | | | | | | | | | |   (102)  all_52_25 = e0
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | COMBINE_EQS: (52), (102) imply:
% 175.06/26.87  | | | | | | | | | |   (103)  all_58_12 = e0
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | BETA: splitting (34) gives:
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | Case 1:
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | |   (104)  all_58_0 = e1
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | | COMBINE_EQS: (23), (104) imply:
% 175.06/26.87  | | | | | | | | | | |   (105)  all_4_2 = e1
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | | REDUCE: (13), (105) imply:
% 175.06/26.87  | | | | | | | | | | |   (106)  op(e2, e1) = e1
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | | GROUND_INST: instantiating (48) with all_52_13, e1, e1, e2,
% 175.06/26.87  | | | | | | | | | | |              simplifying with (29), (106) gives:
% 175.06/26.87  | | | | | | | | | | |   (107)  all_52_13 = e1
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | | REF_CLOSE: (8), (31), (44), (48), (107) are inconsistent by
% 175.06/26.87  | | | | | | | | | | |            sub-proof #721.
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | Case 2:
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | |   (108)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | | REF_CLOSE: (19), (32), (38), (42), (43), (48), (80), (101),
% 175.06/26.87  | | | | | | | | | | |            (103), (108) are inconsistent by sub-proof #725.
% 175.06/26.87  | | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | End of split
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | Case 2:
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | |   (109)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | | REF_CLOSE: (3), (5), (11), (16), (32), (33), (46), (48),
% 175.06/26.87  | | | | | | | | | |            (52), (53), (57), (58), (62), (65), (79), (109)
% 175.06/26.87  | | | | | | | | | |            are inconsistent by sub-proof #962.
% 175.06/26.87  | | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | End of split
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | Case 2:
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | |   (110)  all_58_11 = e3 | all_58_15 = e3
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | | REF_CLOSE: (4), (12), (39), (84), (110) are inconsistent by
% 175.06/26.87  | | | | | | | | |            sub-proof #1016.
% 175.06/26.87  | | | | | | | | | 
% 175.06/26.87  | | | | | | | | End of split
% 175.06/26.87  | | | | | | | | 
% 175.06/26.87  | | | | | | | End of split
% 175.06/26.87  | | | | | | | 
% 175.06/26.87  | | | | | | End of split
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | Case 2:
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | |   (111)  all_58_12 = e3
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | | REF_CLOSE: (52), (57), (111) are inconsistent by sub-proof #1003.
% 175.06/26.87  | | | | | | 
% 175.06/26.87  | | | | | End of split
% 175.06/26.87  | | | | | 
% 175.06/26.87  | | | | End of split
% 175.06/26.87  | | | | 
% 175.06/26.87  | | | End of split
% 175.06/26.87  | | | 
% 175.06/26.87  | | End of split
% 175.06/26.87  | | 
% 175.06/26.87  | Case 2:
% 175.06/26.87  | | 
% 175.06/26.87  | |   (112)  all_58_15 = e3
% 175.06/26.87  | | 
% 175.06/26.87  | | COMBINE_EQS: (12), (112) imply:
% 175.06/26.87  | |   (113)  all_6_2 = e3
% 175.06/26.87  | | 
% 175.06/26.87  | | REDUCE: (4), (113) imply:
% 175.06/26.87  | |   (114)  $false
% 175.06/26.87  | | 
% 175.06/26.87  | | CLOSE: (114) is inconsistent.
% 175.06/26.87  | | 
% 175.06/26.87  | End of split
% 175.06/26.87  | 
% 175.06/26.87  End of proof
% 175.06/26.87  
% 175.06/26.87  Sub-proof #85 shows that the following formulas are inconsistent:
% 175.06/26.87  ----------------------------------------------------------------
% 175.06/26.87    (1)   ~ (all_52_23 = all_14_2)
% 175.06/26.87    (2)   ~ (all_52_5 = all_52_13)
% 175.06/26.87    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.06/26.87    (4)   ~ (all_52_27 = all_10_2)
% 175.06/26.87    (5)   ~ (all_52_13 = all_52_29)
% 175.06/26.87    (6)  all_56_3 = all_52_7
% 175.06/26.87    (7)  op(e3, e2) = all_52_3
% 175.06/26.87    (8)   ~ (all_52_9 = all_52_25)
% 175.06/26.87    (9)   ~ (all_52_19 = all_52_23)
% 175.06/26.87    (10)  op(e1, e2) = all_52_19
% 175.06/26.87    (11)  op(e3, all_52_9) = all_52_8
% 175.06/26.87    (12)   ~ (all_52_23 = e0)
% 175.06/26.87    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.06/26.87    (14)  all_58_5 = all_52_13
% 175.06/26.87    (15)   ~ (all_52_25 = all_52_29)
% 175.06/26.87    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.06/26.87    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.06/26.87    (18)  all_58_3 = all_10_2
% 175.06/26.87    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.06/26.87    (20)   ~ (all_52_9 = all_4_2)
% 175.06/26.87    (21)  all_58_10 = all_52_15
% 175.06/26.87    (22)   ~ (all_52_5 = all_4_2)
% 175.06/26.87    (23)  all_58_7 = all_52_19
% 175.06/26.87    (24)  all_58_4 = all_52_5
% 175.06/26.87    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.06/26.87    (26)   ~ (all_52_7 = all_4_2)
% 175.06/26.87    (27)  all_58_1 = all_52_3
% 175.06/26.87    (28)  all_58_0 = all_4_2
% 175.06/26.87    (29)  op(e2, all_52_27) = e2
% 175.06/26.87    (30)  all_58_14 = all_52_29
% 175.06/26.87    (31)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.06/26.87    (32)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.06/26.87    (33)  all_58_8 = all_14_2
% 175.06/26.87    (34)  op(e1, all_52_29) = e1
% 175.06/26.87    (35)   ~ (all_52_3 = all_4_2)
% 175.06/26.87    (36)   ~ (all_52_9 = all_10_2)
% 175.06/26.87    (37)   ~ (e3 = e0)
% 175.06/26.87    (38)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.06/26.87    (39)   ~ (all_52_15 = all_52_23)
% 175.06/26.87    (40)   ~ (all_52_5 = all_52_29)
% 175.06/26.87    (41)  all_56_12 = all_52_25
% 175.06/26.87    (42)  all_58_13 = all_52_27
% 175.06/26.87    (43)  all_56_5 = all_10_2
% 175.06/26.87    (44)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.06/26.87    (45)   ~ (all_52_25 = e0)
% 175.06/26.87    (46)   ~ (all_52_9 = all_52_17)
% 175.06/26.87    (47)  all_58_6 = all_52_17
% 175.06/26.87    (48)   ~ (all_52_3 = all_52_7)
% 175.06/26.87    (49)  all_56_0 = all_4_2
% 175.11/26.87    (50)  all_58_11 = all_52_23
% 175.11/26.87    (51)   ~ (all_52_7 = all_52_15)
% 175.11/26.87    (52)   ~ (all_52_29 = all_14_2)
% 175.11/26.87    (53)  op(e3, all_52_25) = e3
% 175.11/26.87    (54)   ~ (all_52_19 = all_10_2)
% 175.11/26.87    (55)  all_58_15 = e0
% 175.11/26.87    (56)  op(e3, all_4_2) = e2
% 175.11/26.87    (57)  all_58_2 = all_52_9
% 175.11/26.87    (58)  op(e3, e1) = all_52_5
% 175.11/26.87    (59)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.11/26.87    (60)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.11/26.87    (61)  op(e1, e3) = all_52_17
% 175.11/26.87    (62)   ~ (all_52_25 = all_4_2)
% 175.11/26.87    (63)  op(e3, e0) = all_52_7
% 175.11/26.87    (64)  op(e3, e3) = all_4_2
% 175.11/26.87    (65)   ~ (all_52_17 = all_4_2)
% 175.11/26.87    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.87    (67)   ~ (all_52_25 = all_52_27)
% 175.11/26.87    (68)   ~ (all_4_2 = e0)
% 175.11/26.87    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.11/26.87    (70)  all_58_9 = all_52_7
% 175.11/26.87    (71)   ~ (e2 = e0)
% 175.11/26.87    (72)  all_58_12 = all_52_25
% 175.11/26.87    (73)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.11/26.87    (74)   ~ (e3 = e2)
% 175.11/26.87    (75)  op(e2, e3) = all_52_9
% 175.11/26.87    (76)  all_56_13 = all_52_27
% 175.11/26.87  
% 175.11/26.87  Begin of proof
% 175.11/26.87  | 
% 175.11/26.87  | BETA: splitting (19) gives:
% 175.11/26.87  | 
% 175.11/26.87  | Case 1:
% 175.11/26.87  | | 
% 175.11/26.87  | |   (77)  all_56_0 = e3
% 175.11/26.87  | | 
% 175.11/26.87  | | COMBINE_EQS: (49), (77) imply:
% 175.11/26.87  | |   (78)  all_4_2 = e3
% 175.11/26.87  | | 
% 175.11/26.87  | | SIMP: (78) implies:
% 175.11/26.87  | |   (79)  all_4_2 = e3
% 175.11/26.87  | | 
% 175.11/26.87  | | REF_CLOSE: (56), (64), (66), (74), (79) are inconsistent by sub-proof #106.
% 175.11/26.87  | | 
% 175.11/26.87  | Case 2:
% 175.11/26.87  | | 
% 175.11/26.87  | |   (80)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.87  | | 
% 175.11/26.87  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.11/26.87  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.11/26.87  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 175.11/26.87  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 175.11/26.87  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 175.11/26.87  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 175.11/26.87  | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (80) are
% 175.11/26.87  | |            inconsistent by sub-proof #111.
% 175.11/26.87  | | 
% 175.11/26.87  | End of split
% 175.11/26.87  | 
% 175.11/26.87  End of proof
% 175.11/26.87  
% 175.11/26.87  Sub-proof #86 shows that the following formulas are inconsistent:
% 175.11/26.87  ----------------------------------------------------------------
% 175.11/26.87    (1)   ~ (all_52_23 = all_14_2)
% 175.11/26.87    (2)   ~ (all_52_5 = all_52_13)
% 175.11/26.87    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.11/26.87    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.11/26.87    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.11/26.87    (6)   ~ (all_52_27 = all_10_2)
% 175.11/26.87    (7)   ~ (all_52_17 = all_52_23)
% 175.11/26.87    (8)  op(e2, all_10_2) = all_10_1
% 175.11/26.87    (9)   ~ (all_52_13 = all_52_29)
% 175.11/26.87    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.11/26.87    (11)  all_56_3 = all_52_7
% 175.11/26.87    (12)  op(e3, e2) = all_52_3
% 175.11/26.87    (13)   ~ (all_52_9 = all_52_25)
% 175.11/26.87    (14)  op(e3, all_52_25) = all_52_24
% 175.11/26.87    (15)   ~ (all_52_19 = all_52_23)
% 175.11/26.87    (16)  all_56_11 = all_52_23
% 175.11/26.87    (17)  op(e1, e2) = all_52_19
% 175.11/26.87    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.11/26.87    (19)  op(e3, all_52_9) = all_52_8
% 175.11/26.87    (20)   ~ (all_52_3 = all_10_2)
% 175.11/26.87    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.11/26.87    (22)  all_58_5 = all_52_13
% 175.11/26.87    (23)   ~ (all_6_2 = e0)
% 175.11/26.87    (24)   ~ (all_52_25 = all_52_29)
% 175.11/26.87    (25)  all_56_15 = all_6_2
% 175.11/26.87    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.11/26.87    (27)  op(all_14_1, all_14_2) = all_14_0
% 175.11/26.87    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.11/26.87    (29)  all_58_3 = all_10_2
% 175.11/26.87    (30)  all_56_9 = all_52_19
% 175.11/26.87    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.87    (32)  all_58_15 = all_6_2
% 175.11/26.87    (33)   ~ (all_52_9 = all_4_2)
% 175.11/26.87    (34)   ~ (all_52_5 = all_52_7)
% 175.11/26.87    (35)  all_58_10 = all_52_15
% 175.11/26.87    (36)   ~ (all_52_5 = all_4_2)
% 175.11/26.87    (37)  all_58_7 = all_52_19
% 175.11/26.87    (38)  all_56_4 = all_52_9
% 175.11/26.87    (39)   ~ (all_52_15 = all_6_2)
% 175.11/26.87    (40)   ~ (all_52_17 = all_52_25)
% 175.11/26.87    (41)  op(e0, e1) = all_52_29
% 175.11/26.87    (42)  all_58_4 = all_52_5
% 175.11/26.87    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.11/26.87    (44)   ~ (e3 = e1)
% 175.11/26.87    (45)   ~ (all_52_27 = all_52_29)
% 175.11/26.87    (46)   ~ (all_52_17 = all_14_2)
% 175.11/26.87    (47)  op(e3, all_4_2) = all_4_1
% 175.11/26.87    (48)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.87    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.11/26.87    (50)   ~ (all_52_7 = all_4_2)
% 175.11/26.87    (51)  all_58_1 = all_52_3
% 175.11/26.87    (52)   ~ (all_52_13 = all_52_15)
% 175.11/26.87    (53)  all_58_0 = all_4_2
% 175.11/26.87    (54)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 175.11/26.87    (55)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.11/26.87    (56)  op(e1, all_52_13) = all_52_12
% 175.11/26.87    (57)  all_52_0 = e2
% 175.11/26.87    (58)  op(e1, all_52_29) = all_52_28
% 175.11/26.87    (59)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.11/26.87    (60)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.11/26.87    (61)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.11/26.87    (62)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.11/26.87    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.87    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.11/26.87    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.11/26.87    (66)  all_58_14 = all_52_29
% 175.11/26.87    (67)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.11/26.87    (68)  op(e2, all_4_2) = all_4_0
% 175.11/26.87    (69)   ~ (all_52_3 = all_52_5)
% 175.11/26.87    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.87    (71)  op(e2, e1) = all_52_13
% 175.11/26.87    (72)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.87    (73)  all_58_8 = all_14_2
% 175.11/26.87    (74)  all_56_1 = all_52_3
% 175.11/26.87    (75)  op(e0, e2) = all_52_27
% 175.11/26.87    (76)  all_56_14 = all_52_29
% 175.11/26.87    (77)   ~ (all_14_0 = e3)
% 175.11/26.87    (78)  op(all_4_1, all_4_2) = all_4_0
% 175.11/26.87    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.11/26.87    (80)   ~ (all_52_5 = all_14_2)
% 175.11/26.87    (81)   ~ (all_52_3 = all_52_27)
% 175.11/26.87    (82)   ~ (all_52_3 = all_4_2)
% 175.11/26.87    (83)  op(e0, e3) = all_52_25
% 175.11/26.87    (84)  op(e0, all_6_2) = all_6_1
% 175.11/26.87    (85)   ~ (all_52_9 = all_10_2)
% 175.11/26.87    (86)  op(e3, all_52_17) = all_52_16
% 175.11/26.87    (87)  all_52_10 = all_10_1
% 175.11/26.87    (88)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.11/26.87    (89)   ~ (all_52_13 = all_14_2)
% 175.11/26.87    (90)   ~ (e3 = e0)
% 175.11/26.87    (91)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.11/26.87    (92)   ~ (all_52_9 = all_52_13)
% 175.11/26.87    (93)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.87    (94)  op(e0, all_52_23) = all_52_22
% 175.11/26.87    (95)   ~ (all_52_15 = all_52_23)
% 175.11/26.87    (96)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.11/26.87    (97)  op(all_10_1, all_10_2) = all_10_0
% 175.11/26.87    (98)   ~ (all_52_5 = all_52_29)
% 175.11/26.87    (99)  all_56_2 = all_52_5
% 175.11/26.87    (100)  op(e1, e0) = all_52_23
% 175.11/26.87    (101)  all_56_12 = all_52_25
% 175.11/26.87    (102)  all_58_13 = all_52_27
% 175.11/26.87    (103)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.87    (104)  all_56_5 = all_10_2
% 175.11/26.87    (105)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.11/26.87    (106)   ~ (all_52_9 = all_52_17)
% 175.11/26.87    (107)   ~ (all_14_0 = e2)
% 175.11/26.87    (108)  all_58_6 = all_52_17
% 175.11/26.87    (109)   ~ (all_52_3 = all_52_7)
% 175.11/26.87    (110)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.11/26.87    (111)  op(e2, all_52_19) = all_52_18
% 175.11/26.87    (112)   ~ (e1 = e0)
% 175.11/26.87    (113)  all_56_0 = all_4_2
% 175.11/26.87    (114)  all_58_11 = all_52_23
% 175.11/26.87    (115)   ~ (all_52_3 = all_52_19)
% 175.11/26.87    (116)   ~ (all_52_7 = all_52_15)
% 175.11/26.87    (117)  op(e0, all_52_15) = all_52_14
% 175.11/26.87    (118)   ~ (all_52_29 = all_14_2)
% 175.11/26.87    (119)   ~ (all_4_0 = e1)
% 175.11/26.87    (120)   ~ (all_52_19 = all_10_2)
% 175.11/26.87    (121)  op(e3, all_4_2) = e2
% 175.11/26.87    (122)   ~ (all_52_23 = all_6_2)
% 175.11/26.87    (123)   ~ (all_52_29 = all_6_2)
% 175.11/26.87    (124)  all_58_2 = all_52_9
% 175.11/26.87    (125)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.11/26.87    (126)  op(e3, e1) = all_52_5
% 175.11/26.87    (127)   ~ (e2 = e1)
% 175.11/26.87    (128)  all_56_10 = all_14_2
% 175.11/26.87    (129)   ~ (all_52_25 = all_6_2)
% 175.11/26.87    (130)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.11/26.87    (131)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.11/26.87    (132)  op(e1, e3) = all_52_17
% 175.11/26.87    (133)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.11/26.87    (134)   ~ (all_52_25 = all_4_2)
% 175.11/26.87    (135)  op(e3, e0) = all_52_7
% 175.11/26.87    (136)  op(e3, e3) = all_4_2
% 175.11/26.87    (137)   ~ (all_10_1 = e3)
% 175.11/26.87    (138)  all_56_8 = all_52_17
% 175.11/26.87    (139)   ~ (all_52_17 = all_4_2)
% 175.11/26.87    (140)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.87             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.87    (141)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.11/26.87           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 175.11/26.87           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.11/26.87           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.11/26.87    (142)   ~ (all_52_25 = all_52_27)
% 175.11/26.87    (143)   ~ (all_52_27 = all_6_2)
% 175.11/26.87    (144)   ~ (all_52_7 = all_6_2)
% 175.11/26.87    (145)   ~ (all_10_0 = e3)
% 175.11/26.87    (146)   ~ (all_52_15 = all_10_2)
% 175.11/26.87    (147)   ~ (all_52_19 = all_52_27)
% 175.11/26.87    (148)  all_56_7 = all_52_15
% 175.11/26.87    (149)   ~ (all_52_7 = all_52_23)
% 175.11/26.87    (150)   ~ (all_52_13 = all_10_2)
% 175.11/26.87    (151)  op(e2, all_52_27) = all_52_26
% 175.11/26.87    (152)  all_52_20 = all_14_1
% 175.11/26.87    (153)   ~ (all_52_17 = all_52_19)
% 175.11/26.87    (154)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.87    (155)  all_52_30 = all_6_1
% 175.11/26.87    (156)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.11/26.87    (157)  op(e1, all_14_2) = all_14_1
% 175.11/26.87    (158)  all_58_9 = all_52_7
% 175.11/26.87    (159)   ~ (e2 = e0)
% 175.11/26.87    (160)  all_58_12 = all_52_25
% 175.11/26.87    (161)   ~ (all_10_0 = e1)
% 175.11/26.87    (162)  all_56_6 = all_52_13
% 175.11/26.87    (163)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.87    (164)   ~ (all_52_9 = all_52_15)
% 175.11/26.87    (165)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.11/26.87    (166)   ~ (e3 = e2)
% 175.11/26.87    (167)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.11/26.87    (168)   ~ (all_52_19 = all_14_2)
% 175.11/26.87    (169)  op(e2, e3) = all_52_9
% 175.11/26.87    (170)  all_56_13 = all_52_27
% 175.11/26.87  
% 175.11/26.87  Begin of proof
% 175.11/26.87  | 
% 175.11/26.87  | BETA: splitting (141) gives:
% 175.11/26.87  | 
% 175.11/26.87  | Case 1:
% 175.11/26.87  | | 
% 175.11/26.87  | |   (171)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.11/26.87  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.11/26.87  | | 
% 175.11/26.87  | | BETA: splitting (171) gives:
% 175.11/26.87  | | 
% 175.11/26.87  | | Case 1:
% 175.11/26.87  | | | 
% 175.11/26.87  | | |   (172)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.11/26.87  | | | 
% 175.11/26.87  | | | ALPHA: (172) implies:
% 175.11/26.87  | | |   (173)  all_52_0 = e3
% 175.11/26.87  | | | 
% 175.11/26.87  | | | COMBINE_EQS: (57), (173) imply:
% 175.11/26.87  | | |   (174)  e3 = e2
% 175.11/26.87  | | | 
% 175.11/26.87  | | | REDUCE: (166), (174) imply:
% 175.11/26.87  | | |   (175)  $false
% 175.11/26.87  | | | 
% 175.11/26.87  | | | CLOSE: (175) is inconsistent.
% 175.11/26.87  | | | 
% 175.11/26.87  | | Case 2:
% 175.11/26.87  | | | 
% 175.11/26.87  | | |   (176)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.11/26.87  | | | 
% 175.11/26.87  | | | ALPHA: (176) implies:
% 175.11/26.87  | | |   (177)  all_52_14 = e0
% 175.11/26.87  | | |   (178)  all_52_12 = e1
% 175.11/26.87  | | |   (179)  all_52_10 = e2
% 175.11/26.87  | | |   (180)  all_52_8 = e3
% 175.11/26.87  | | | 
% 175.11/26.87  | | | COMBINE_EQS: (87), (179) imply:
% 175.11/26.87  | | |   (181)  all_10_1 = e2
% 175.11/26.87  | | | 
% 175.11/26.87  | | | SIMP: (181) implies:
% 175.11/26.87  | | |   (182)  all_10_1 = e2
% 175.11/26.87  | | | 
% 175.11/26.88  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 175.11/26.88  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 175.11/26.88  | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 175.11/26.88  | | |            (39), (40), (41), (42), (43), (44), (45), (46), (48), (49),
% 175.11/26.88  | | |            (50), (51), (52), (53), (54), (55), (56), (58), (59), (60),
% 175.11/26.88  | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 175.11/26.88  | | |            (71), (72), (73), (74), (76), (79), (81), (82), (83), (84),
% 175.11/26.88  | | |            (86), (89), (90), (92), (94), (95), (96), (97), (98), (102),
% 175.11/26.88  | | |            (103), (106), (108), (109), (110), (111), (112), (113), (114),
% 175.11/26.88  | | |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 175.11/26.88  | | |            (124), (125), (126), (128), (129), (132), (134), (135), (136),
% 175.11/26.88  | | |            (138), (139), (140), (142), (143), (144), (145), (149), (150),
% 175.11/26.88  | | |            (151), (153), (154), (156), (157), (158), (160), (161), (162),
% 175.11/26.88  | | |            (163), (164), (165), (168), (169), (170), (177), (178), (180),
% 175.11/26.88  | | |            (182) are inconsistent by sub-proof #97.
% 175.11/26.88  | | | 
% 175.11/26.88  | | End of split
% 175.11/26.88  | | 
% 175.11/26.88  | Case 2:
% 175.11/26.88  | | 
% 175.11/26.88  | |   (183)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 175.11/26.88  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 175.11/26.88  | |            e0)
% 175.11/26.88  | | 
% 175.11/26.88  | | BETA: splitting (183) gives:
% 175.11/26.88  | | 
% 175.11/26.88  | | Case 1:
% 175.11/26.88  | | | 
% 175.11/26.88  | | |   (184)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.11/26.88  | | | 
% 175.11/26.88  | | | ALPHA: (184) implies:
% 175.11/26.88  | | |   (185)  all_52_22 = e0
% 175.11/26.88  | | |   (186)  all_52_20 = e1
% 175.11/26.88  | | |   (187)  all_52_18 = e2
% 175.11/26.88  | | |   (188)  all_52_16 = e3
% 175.11/26.88  | | | 
% 175.11/26.88  | | | COMBINE_EQS: (152), (186) imply:
% 175.11/26.88  | | |   (189)  all_14_1 = e1
% 175.11/26.88  | | | 
% 175.11/26.88  | | | REDUCE: (27), (189) imply:
% 175.11/26.88  | | |   (190)  op(e1, all_14_2) = all_14_0
% 175.11/26.88  | | | 
% 175.11/26.88  | | | REDUCE: (86), (188) imply:
% 175.11/26.88  | | |   (191)  op(e3, all_52_17) = e3
% 175.11/26.88  | | | 
% 175.11/26.88  | | | REDUCE: (111), (187) imply:
% 175.11/26.88  | | |   (192)  op(e2, all_52_19) = e2
% 175.11/26.88  | | | 
% 175.11/26.88  | | | REDUCE: (157), (189) imply:
% 175.11/26.88  | | |   (193)  op(e1, all_14_2) = e1
% 175.11/26.88  | | | 
% 175.11/26.88  | | | REDUCE: (94), (185) imply:
% 175.11/26.88  | | |   (194)  op(e0, all_52_23) = e0
% 175.11/26.88  | | | 
% 175.11/26.88  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (11), (12), (13), (15),
% 175.11/26.88  | | |            (17), (22), (24), (25), (26), (29), (30), (31), (32), (33),
% 175.11/26.88  | | |            (34), (35), (36), (37), (40), (42), (43), (46), (47), (48),
% 175.11/26.88  | | |            (49), (50), (51), (53), (54), (55), (58), (60), (63), (64),
% 175.11/26.88  | | |            (65), (66), (67), (68), (70), (71), (72), (73), (75), (77),
% 175.11/26.88  | | |            (78), (80), (81), (82), (83), (85), (88), (89), (90), (91),
% 175.11/26.88  | | |            (92), (95), (98), (102), (103), (104), (105), (106), (107),
% 175.11/26.88  | | |            (108), (112), (113), (114), (115), (116), (119), (120), (121),
% 175.11/26.88  | | |            (122), (123), (124), (126), (129), (130), (132), (133), (134),
% 175.11/26.88  | | |            (135), (136), (137), (138), (139), (140), (142), (143), (144),
% 175.11/26.88  | | |            (146), (147), (148), (149), (150), (151), (153), (154), (156),
% 175.11/26.88  | | |            (158), (159), (160), (162), (163), (164), (165), (166), (168),
% 175.11/26.88  | | |            (169), (170), (190), (191), (192), (193), (194) are
% 175.11/26.88  | | |            inconsistent by sub-proof #93.
% 175.11/26.88  | | | 
% 175.11/26.88  | | Case 2:
% 175.11/26.88  | | | 
% 175.11/26.88  | | |   (195)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.11/26.88  | | | 
% 175.11/26.88  | | | REF_CLOSE: (4), (5), (7), (10), (12), (13), (14), (15), (18), (19), (20),
% 175.11/26.88  | | |            (21), (22), (23), (24), (25), (28), (29), (31), (32), (33),
% 175.11/26.88  | | |            (34), (35), (36), (37), (40), (41), (42), (44), (45), (46),
% 175.11/26.88  | | |            (47), (48), (50), (51), (52), (53), (55), (58), (59), (61),
% 175.11/26.88  | | |            (62), (63), (66), (67), (68), (69), (70), (71), (72), (73),
% 175.11/26.88  | | |            (74), (75), (76), (78), (79), (81), (82), (83), (84), (85),
% 175.11/26.88  | | |            (86), (88), (90), (91), (92), (93), (98), (99), (100), (101),
% 175.11/26.88  | | |            (102), (103), (106), (108), (109), (112), (113), (114), (116),
% 175.11/26.88  | | |            (119), (120), (121), (123), (124), (126), (127), (129), (131),
% 175.11/26.88  | | |            (132), (134), (135), (136), (139), (140), (142), (143), (144),
% 175.11/26.88  | | |            (146), (149), (151), (153), (154), (155), (158), (159), (160),
% 175.11/26.88  | | |            (163), (164), (165), (166), (167), (169), (170), (195) are
% 175.11/26.88  | | |            inconsistent by sub-proof #87.
% 175.11/26.88  | | | 
% 175.11/26.88  | | End of split
% 175.11/26.88  | | 
% 175.11/26.88  | End of split
% 175.11/26.88  | 
% 175.11/26.88  End of proof
% 175.11/26.88  
% 175.11/26.88  Sub-proof #87 shows that the following formulas are inconsistent:
% 175.11/26.88  ----------------------------------------------------------------
% 175.11/26.88    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.11/26.88    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.11/26.88    (3)   ~ (all_52_17 = all_52_23)
% 175.11/26.88    (4)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.11/26.88    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.11/26.88    (6)  op(e3, e2) = all_52_3
% 175.11/26.88    (7)   ~ (all_52_9 = all_52_25)
% 175.11/26.88    (8)  op(e3, all_52_25) = all_52_24
% 175.11/26.88    (9)   ~ (all_52_19 = all_52_23)
% 175.11/26.88    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.11/26.88    (11)  op(e3, all_52_9) = all_52_8
% 175.11/26.88    (12)   ~ (all_52_3 = all_10_2)
% 175.11/26.88    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.11/26.88    (14)  all_58_5 = all_52_13
% 175.11/26.88    (15)   ~ (all_6_2 = e0)
% 175.11/26.88    (16)   ~ (all_52_25 = all_52_29)
% 175.11/26.88    (17)  all_56_15 = all_6_2
% 175.11/26.88    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.11/26.88    (19)  all_58_3 = all_10_2
% 175.11/26.88    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.88    (21)  all_58_15 = all_6_2
% 175.11/26.88    (22)   ~ (all_52_9 = all_4_2)
% 175.11/26.88    (23)   ~ (all_52_5 = all_52_7)
% 175.11/26.88    (24)  all_58_10 = all_52_15
% 175.11/26.88    (25)   ~ (all_52_5 = all_4_2)
% 175.11/26.88    (26)  all_58_7 = all_52_19
% 175.11/26.88    (27)   ~ (all_52_17 = all_52_25)
% 175.11/26.88    (28)  op(e0, e1) = all_52_29
% 175.11/26.88    (29)  all_58_4 = all_52_5
% 175.11/26.88    (30)   ~ (e3 = e1)
% 175.11/26.88    (31)   ~ (all_52_27 = all_52_29)
% 175.11/26.88    (32)   ~ (all_52_17 = all_14_2)
% 175.11/26.88    (33)  op(e3, all_4_2) = all_4_1
% 175.11/26.88    (34)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.88    (35)   ~ (all_52_7 = all_4_2)
% 175.11/26.88    (36)  all_58_1 = all_52_3
% 175.11/26.88    (37)   ~ (all_52_13 = all_52_15)
% 175.11/26.88    (38)  all_58_0 = all_4_2
% 175.11/26.88    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.11/26.88    (40)  op(e1, all_52_29) = all_52_28
% 175.11/26.88    (41)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.11/26.88    (42)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.11/26.88    (43)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.11/26.88    (44)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.88    (45)  all_58_14 = all_52_29
% 175.11/26.88    (46)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.11/26.88    (47)  op(e2, all_4_2) = all_4_0
% 175.11/26.88    (48)   ~ (all_52_3 = all_52_5)
% 175.11/26.88    (49)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.88    (50)  op(e2, e1) = all_52_13
% 175.11/26.88    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.88    (52)  all_58_8 = all_14_2
% 175.11/26.88    (53)  all_56_1 = all_52_3
% 175.11/26.88    (54)  op(e0, e2) = all_52_27
% 175.11/26.88    (55)  all_56_14 = all_52_29
% 175.11/26.88    (56)  op(all_4_1, all_4_2) = all_4_0
% 175.11/26.88    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.11/26.88    (58)   ~ (all_52_3 = all_52_27)
% 175.11/26.88    (59)   ~ (all_52_3 = all_4_2)
% 175.11/26.88    (60)  op(e0, e3) = all_52_25
% 175.11/26.88    (61)  op(e0, all_6_2) = all_6_1
% 175.11/26.88    (62)   ~ (all_52_9 = all_10_2)
% 175.11/26.88    (63)  op(e3, all_52_17) = all_52_16
% 175.11/26.88    (64)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.11/26.88    (65)   ~ (e3 = e0)
% 175.11/26.88    (66)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.11/26.88    (67)   ~ (all_52_9 = all_52_13)
% 175.11/26.88    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.88    (69)   ~ (all_52_5 = all_52_29)
% 175.11/26.88    (70)  all_56_2 = all_52_5
% 175.11/26.88    (71)  op(e1, e0) = all_52_23
% 175.11/26.88    (72)  all_56_12 = all_52_25
% 175.11/26.88    (73)  all_58_13 = all_52_27
% 175.11/26.88    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.88    (75)   ~ (all_52_9 = all_52_17)
% 175.11/26.88    (76)  all_58_6 = all_52_17
% 175.11/26.88    (77)   ~ (all_52_3 = all_52_7)
% 175.11/26.88    (78)   ~ (e1 = e0)
% 175.11/26.88    (79)  all_56_0 = all_4_2
% 175.11/26.88    (80)  all_58_11 = all_52_23
% 175.11/26.88    (81)   ~ (all_52_7 = all_52_15)
% 175.11/26.88    (82)   ~ (all_4_0 = e1)
% 175.11/26.88    (83)   ~ (all_52_19 = all_10_2)
% 175.11/26.88    (84)  op(e3, all_4_2) = e2
% 175.11/26.88    (85)   ~ (all_52_29 = all_6_2)
% 175.11/26.88    (86)  all_58_2 = all_52_9
% 175.11/26.88    (87)  op(e3, e1) = all_52_5
% 175.11/26.88    (88)   ~ (e2 = e1)
% 175.11/26.88    (89)   ~ (all_52_25 = all_6_2)
% 175.11/26.88    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.11/26.88    (91)  op(e1, e3) = all_52_17
% 175.11/26.88    (92)   ~ (all_52_25 = all_4_2)
% 175.11/26.88    (93)  op(e3, e0) = all_52_7
% 175.11/26.88    (94)  op(e3, e3) = all_4_2
% 175.11/26.88    (95)   ~ (all_52_17 = all_4_2)
% 175.11/26.88    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.88    (97)   ~ (all_52_25 = all_52_27)
% 175.11/26.88    (98)   ~ (all_52_27 = all_6_2)
% 175.11/26.88    (99)   ~ (all_52_7 = all_6_2)
% 175.11/26.88    (100)   ~ (all_52_15 = all_10_2)
% 175.11/26.88    (101)   ~ (all_52_7 = all_52_23)
% 175.11/26.88    (102)  op(e2, all_52_27) = all_52_26
% 175.11/26.88    (103)   ~ (all_52_17 = all_52_19)
% 175.11/26.88    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.88    (105)  all_52_30 = all_6_1
% 175.11/26.88    (106)  all_58_9 = all_52_7
% 175.11/26.88    (107)   ~ (e2 = e0)
% 175.11/26.88    (108)  all_58_12 = all_52_25
% 175.11/26.88    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.88    (110)   ~ (all_52_9 = all_52_15)
% 175.11/26.88    (111)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.11/26.88    (112)   ~ (e3 = e2)
% 175.11/26.88    (113)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.11/26.88    (114)  op(e2, e3) = all_52_9
% 175.11/26.88    (115)  all_56_13 = all_52_27
% 175.11/26.88  
% 175.11/26.88  Begin of proof
% 175.11/26.88  | 
% 175.11/26.88  | ALPHA: (4) implies:
% 175.11/26.88  |   (116)  all_52_30 = e0
% 175.11/26.88  |   (117)  all_52_28 = e1
% 175.11/26.88  |   (118)  all_52_26 = e2
% 175.11/26.88  |   (119)  all_52_24 = e3
% 175.11/26.88  | 
% 175.11/26.88  | COMBINE_EQS: (105), (116) imply:
% 175.11/26.88  |   (120)  all_6_1 = e0
% 175.11/26.88  | 
% 175.11/26.88  | SIMP: (120) implies:
% 175.11/26.88  |   (121)  all_6_1 = e0
% 175.11/26.88  | 
% 175.11/26.88  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 175.11/26.88  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.11/26.88  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.11/26.88  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.11/26.88  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 175.11/26.88  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 175.11/26.88  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 175.11/26.88  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 175.11/26.88  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 175.11/26.88  |            (102), (103), (104), (106), (107), (108), (109), (110), (111),
% 175.11/26.88  |            (112), (113), (114), (115), (117), (118), (119), (121) are
% 175.11/26.88  |            inconsistent by sub-proof #88.
% 175.11/26.88  | 
% 175.11/26.88  End of proof
% 175.11/26.88  
% 175.11/26.88  Sub-proof #88 shows that the following formulas are inconsistent:
% 175.11/26.88  ----------------------------------------------------------------
% 175.11/26.88    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.11/26.88    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.11/26.88    (3)   ~ (all_52_17 = all_52_23)
% 175.11/26.88    (4)  all_52_26 = e2
% 175.11/26.88    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.11/26.88    (6)  op(e3, e2) = all_52_3
% 175.11/26.88    (7)   ~ (all_52_9 = all_52_25)
% 175.11/26.88    (8)  op(e3, all_52_25) = all_52_24
% 175.11/26.88    (9)   ~ (all_52_19 = all_52_23)
% 175.11/26.88    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.11/26.88    (11)  op(e3, all_52_9) = all_52_8
% 175.11/26.88    (12)   ~ (all_52_3 = all_10_2)
% 175.11/26.88    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.11/26.88    (14)  all_58_5 = all_52_13
% 175.11/26.88    (15)   ~ (all_6_2 = e0)
% 175.11/26.88    (16)   ~ (all_52_25 = all_52_29)
% 175.11/26.88    (17)  all_56_15 = all_6_2
% 175.11/26.88    (18)  all_6_1 = e0
% 175.11/26.88    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.11/26.88    (20)  all_58_3 = all_10_2
% 175.11/26.88    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.88    (22)  all_58_15 = all_6_2
% 175.11/26.88    (23)   ~ (all_52_9 = all_4_2)
% 175.11/26.88    (24)   ~ (all_52_5 = all_52_7)
% 175.11/26.88    (25)  all_58_10 = all_52_15
% 175.11/26.88    (26)   ~ (all_52_5 = all_4_2)
% 175.11/26.88    (27)  all_58_7 = all_52_19
% 175.11/26.88    (28)   ~ (all_52_17 = all_52_25)
% 175.11/26.88    (29)  op(e0, e1) = all_52_29
% 175.11/26.88    (30)  all_58_4 = all_52_5
% 175.11/26.88    (31)   ~ (e3 = e1)
% 175.11/26.88    (32)   ~ (all_52_27 = all_52_29)
% 175.11/26.88    (33)   ~ (all_52_17 = all_14_2)
% 175.11/26.88    (34)  op(e3, all_4_2) = all_4_1
% 175.11/26.88    (35)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.88    (36)   ~ (all_52_7 = all_4_2)
% 175.11/26.88    (37)  all_58_1 = all_52_3
% 175.11/26.88    (38)   ~ (all_52_13 = all_52_15)
% 175.11/26.88    (39)  all_58_0 = all_4_2
% 175.11/26.88    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.11/26.88    (41)  op(e1, all_52_29) = all_52_28
% 175.11/26.88    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.11/26.88    (43)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.11/26.88    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.11/26.88    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.88    (46)  all_58_14 = all_52_29
% 175.11/26.88    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.11/26.88    (48)  op(e2, all_4_2) = all_4_0
% 175.11/26.88    (49)   ~ (all_52_3 = all_52_5)
% 175.11/26.88    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.88    (51)  op(e2, e1) = all_52_13
% 175.11/26.88    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.88    (53)  all_58_8 = all_14_2
% 175.11/26.88    (54)  all_56_1 = all_52_3
% 175.11/26.88    (55)  op(e0, e2) = all_52_27
% 175.11/26.88    (56)  all_56_14 = all_52_29
% 175.11/26.88    (57)  op(all_4_1, all_4_2) = all_4_0
% 175.11/26.88    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.11/26.88    (59)   ~ (all_52_3 = all_52_27)
% 175.11/26.88    (60)   ~ (all_52_3 = all_4_2)
% 175.11/26.88    (61)  op(e0, e3) = all_52_25
% 175.11/26.88    (62)  op(e0, all_6_2) = all_6_1
% 175.11/26.88    (63)   ~ (all_52_9 = all_10_2)
% 175.11/26.88    (64)  op(e3, all_52_17) = all_52_16
% 175.11/26.88    (65)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.11/26.88    (66)   ~ (e3 = e0)
% 175.11/26.88    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.11/26.88    (68)   ~ (all_52_9 = all_52_13)
% 175.11/26.88    (69)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.88    (70)   ~ (all_52_5 = all_52_29)
% 175.11/26.88    (71)  all_56_2 = all_52_5
% 175.11/26.88    (72)  op(e1, e0) = all_52_23
% 175.11/26.88    (73)  all_56_12 = all_52_25
% 175.11/26.88    (74)  all_58_13 = all_52_27
% 175.11/26.88    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.88    (76)   ~ (all_52_9 = all_52_17)
% 175.11/26.88    (77)  all_58_6 = all_52_17
% 175.11/26.88    (78)   ~ (all_52_3 = all_52_7)
% 175.11/26.88    (79)   ~ (e1 = e0)
% 175.11/26.88    (80)  all_56_0 = all_4_2
% 175.11/26.88    (81)  all_58_11 = all_52_23
% 175.11/26.88    (82)   ~ (all_52_7 = all_52_15)
% 175.11/26.88    (83)   ~ (all_4_0 = e1)
% 175.11/26.88    (84)   ~ (all_52_19 = all_10_2)
% 175.11/26.88    (85)  op(e3, all_4_2) = e2
% 175.11/26.88    (86)   ~ (all_52_29 = all_6_2)
% 175.11/26.88    (87)  all_58_2 = all_52_9
% 175.11/26.88    (88)  op(e3, e1) = all_52_5
% 175.11/26.88    (89)   ~ (e2 = e1)
% 175.11/26.88    (90)   ~ (all_52_25 = all_6_2)
% 175.11/26.88    (91)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.11/26.88    (92)  op(e1, e3) = all_52_17
% 175.11/26.88    (93)   ~ (all_52_25 = all_4_2)
% 175.11/26.88    (94)  op(e3, e0) = all_52_7
% 175.11/26.88    (95)  all_52_28 = e1
% 175.11/26.88    (96)  op(e3, e3) = all_4_2
% 175.11/26.88    (97)   ~ (all_52_17 = all_4_2)
% 175.11/26.88    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.88    (99)   ~ (all_52_25 = all_52_27)
% 175.11/26.88    (100)   ~ (all_52_27 = all_6_2)
% 175.11/26.88    (101)   ~ (all_52_7 = all_6_2)
% 175.11/26.88    (102)   ~ (all_52_15 = all_10_2)
% 175.11/26.88    (103)   ~ (all_52_7 = all_52_23)
% 175.11/26.88    (104)  op(e2, all_52_27) = all_52_26
% 175.11/26.88    (105)   ~ (all_52_17 = all_52_19)
% 175.11/26.88    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.88    (107)  all_58_9 = all_52_7
% 175.11/26.88    (108)   ~ (e2 = e0)
% 175.11/26.88    (109)  all_52_24 = e3
% 175.11/26.88    (110)  all_58_12 = all_52_25
% 175.11/26.88    (111)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.88    (112)   ~ (all_52_9 = all_52_15)
% 175.11/26.88    (113)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.11/26.88    (114)   ~ (e3 = e2)
% 175.11/26.88    (115)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.11/26.88    (116)  op(e2, e3) = all_52_9
% 175.11/26.88    (117)  all_56_13 = all_52_27
% 175.11/26.88  
% 175.11/26.88  Begin of proof
% 175.11/26.88  | 
% 175.11/26.88  | REDUCE: (8), (109) imply:
% 175.11/26.88  |   (118)  op(e3, all_52_25) = e3
% 175.11/26.88  | 
% 175.11/26.88  | REDUCE: (4), (104) imply:
% 175.11/26.88  |   (119)  op(e2, all_52_27) = e2
% 175.11/26.88  | 
% 175.11/26.88  | REDUCE: (41), (95) imply:
% 175.11/26.88  |   (120)  op(e1, all_52_29) = e1
% 175.11/26.88  | 
% 175.11/26.88  | REDUCE: (18), (62) imply:
% 175.11/26.88  |   (121)  op(e0, all_6_2) = e0
% 175.11/26.88  | 
% 175.11/26.88  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 175.11/26.88  |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 175.11/26.88  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 175.11/26.88  |            (38), (39), (40), (42), (43), (44), (45), (46), (47), (48), (49),
% 175.11/26.88  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 175.11/26.88  |            (61), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 175.11/26.88  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 175.11/26.88  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 175.11/26.88  |            (96), (97), (98), (99), (100), (101), (102), (103), (105), (106),
% 175.11/26.88  |            (107), (108), (110), (111), (112), (113), (114), (115), (116),
% 175.11/26.88  |            (117), (118), (119), (120), (121) are inconsistent by sub-proof
% 175.11/26.88  |            #89.
% 175.11/26.88  | 
% 175.11/26.88  End of proof
% 175.11/26.88  
% 175.11/26.88  Sub-proof #89 shows that the following formulas are inconsistent:
% 175.11/26.88  ----------------------------------------------------------------
% 175.11/26.88    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.11/26.88    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.11/26.88    (3)   ~ (all_52_17 = all_52_23)
% 175.11/26.88    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.11/26.88    (5)  op(e3, e2) = all_52_3
% 175.11/26.88    (6)   ~ (all_52_9 = all_52_25)
% 175.11/26.88    (7)   ~ (all_52_19 = all_52_23)
% 175.11/26.88    (8)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.11/26.88    (9)  op(e3, all_52_9) = all_52_8
% 175.11/26.88    (10)   ~ (all_52_3 = all_10_2)
% 175.11/26.88    (11)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.11/26.88    (12)  all_58_5 = all_52_13
% 175.11/26.88    (13)   ~ (all_6_2 = e0)
% 175.11/26.88    (14)   ~ (all_52_25 = all_52_29)
% 175.11/26.88    (15)  all_56_15 = all_6_2
% 175.11/26.88    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.11/26.88    (17)  all_58_3 = all_10_2
% 175.11/26.88    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.88    (19)  all_58_15 = all_6_2
% 175.11/26.88    (20)  op(e0, all_6_2) = e0
% 175.11/26.88    (21)   ~ (all_52_9 = all_4_2)
% 175.11/26.88    (22)   ~ (all_52_5 = all_52_7)
% 175.11/26.88    (23)  all_58_10 = all_52_15
% 175.11/26.88    (24)   ~ (all_52_5 = all_4_2)
% 175.11/26.88    (25)  all_58_7 = all_52_19
% 175.11/26.88    (26)   ~ (all_52_17 = all_52_25)
% 175.11/26.88    (27)  op(e0, e1) = all_52_29
% 175.11/26.88    (28)  all_58_4 = all_52_5
% 175.11/26.88    (29)   ~ (e3 = e1)
% 175.11/26.88    (30)   ~ (all_52_27 = all_52_29)
% 175.11/26.88    (31)   ~ (all_52_17 = all_14_2)
% 175.11/26.88    (32)  op(e3, all_4_2) = all_4_1
% 175.11/26.88    (33)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.88    (34)   ~ (all_52_7 = all_4_2)
% 175.11/26.88    (35)  all_58_1 = all_52_3
% 175.11/26.88    (36)   ~ (all_52_13 = all_52_15)
% 175.11/26.88    (37)  all_58_0 = all_4_2
% 175.11/26.88    (38)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.11/26.88    (39)  op(e2, all_52_27) = e2
% 175.11/26.88    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.11/26.88    (41)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.11/26.88    (42)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.11/26.88    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.88    (44)  all_58_14 = all_52_29
% 175.11/26.88    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.11/26.88    (46)  op(e2, all_4_2) = all_4_0
% 175.11/26.88    (47)   ~ (all_52_3 = all_52_5)
% 175.11/26.88    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.88    (49)  op(e2, e1) = all_52_13
% 175.11/26.88    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.88    (51)  all_58_8 = all_14_2
% 175.11/26.88    (52)  all_56_1 = all_52_3
% 175.11/26.88    (53)  op(e0, e2) = all_52_27
% 175.11/26.88    (54)  all_56_14 = all_52_29
% 175.11/26.88    (55)  op(e1, all_52_29) = e1
% 175.11/26.88    (56)  op(all_4_1, all_4_2) = all_4_0
% 175.11/26.88    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.11/26.88    (58)   ~ (all_52_3 = all_52_27)
% 175.11/26.88    (59)   ~ (all_52_3 = all_4_2)
% 175.11/26.88    (60)  op(e0, e3) = all_52_25
% 175.11/26.88    (61)   ~ (all_52_9 = all_10_2)
% 175.11/26.88    (62)  op(e3, all_52_17) = all_52_16
% 175.11/26.88    (63)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.11/26.88    (64)   ~ (e3 = e0)
% 175.11/26.88    (65)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.11/26.88    (66)   ~ (all_52_9 = all_52_13)
% 175.11/26.88    (67)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.88    (68)   ~ (all_52_5 = all_52_29)
% 175.11/26.88    (69)  all_56_2 = all_52_5
% 175.11/26.89    (70)  op(e1, e0) = all_52_23
% 175.11/26.89    (71)  all_56_12 = all_52_25
% 175.11/26.89    (72)  all_58_13 = all_52_27
% 175.11/26.89    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.89    (74)   ~ (all_52_9 = all_52_17)
% 175.11/26.89    (75)  all_58_6 = all_52_17
% 175.11/26.89    (76)   ~ (all_52_3 = all_52_7)
% 175.11/26.89    (77)   ~ (e1 = e0)
% 175.11/26.89    (78)  all_56_0 = all_4_2
% 175.11/26.89    (79)  all_58_11 = all_52_23
% 175.11/26.89    (80)   ~ (all_52_7 = all_52_15)
% 175.11/26.89    (81)  op(e3, all_52_25) = e3
% 175.11/26.89    (82)   ~ (all_4_0 = e1)
% 175.11/26.89    (83)   ~ (all_52_19 = all_10_2)
% 175.11/26.89    (84)  op(e3, all_4_2) = e2
% 175.11/26.89    (85)   ~ (all_52_29 = all_6_2)
% 175.11/26.89    (86)  all_58_2 = all_52_9
% 175.11/26.89    (87)  op(e3, e1) = all_52_5
% 175.11/26.89    (88)   ~ (e2 = e1)
% 175.11/26.89    (89)   ~ (all_52_25 = all_6_2)
% 175.11/26.89    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.11/26.89    (91)  op(e1, e3) = all_52_17
% 175.11/26.89    (92)   ~ (all_52_25 = all_4_2)
% 175.11/26.89    (93)  op(e3, e0) = all_52_7
% 175.11/26.89    (94)  op(e3, e3) = all_4_2
% 175.11/26.89    (95)   ~ (all_52_17 = all_4_2)
% 175.11/26.89    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.89    (97)   ~ (all_52_25 = all_52_27)
% 175.11/26.89    (98)   ~ (all_52_27 = all_6_2)
% 175.11/26.89    (99)   ~ (all_52_7 = all_6_2)
% 175.11/26.89    (100)   ~ (all_52_15 = all_10_2)
% 175.11/26.89    (101)   ~ (all_52_7 = all_52_23)
% 175.11/26.89    (102)   ~ (all_52_17 = all_52_19)
% 175.11/26.89    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.89    (104)  all_58_9 = all_52_7
% 175.11/26.89    (105)   ~ (e2 = e0)
% 175.11/26.89    (106)  all_58_12 = all_52_25
% 175.11/26.89    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.89    (108)   ~ (all_52_9 = all_52_15)
% 175.11/26.89    (109)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.11/26.89    (110)   ~ (e3 = e2)
% 175.11/26.89    (111)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.11/26.89    (112)  op(e2, e3) = all_52_9
% 175.11/26.89    (113)  all_56_13 = all_52_27
% 175.11/26.89  
% 175.11/26.89  Begin of proof
% 175.11/26.89  | 
% 175.11/26.89  | BETA: splitting (33) gives:
% 175.11/26.89  | 
% 175.11/26.89  | Case 1:
% 175.11/26.89  | | 
% 175.11/26.89  | |   (114)  all_56_15 = e3
% 175.11/26.89  | | 
% 175.11/26.89  | | COMBINE_EQS: (15), (114) imply:
% 175.11/26.89  | |   (115)  all_6_2 = e3
% 175.11/26.89  | | 
% 175.11/26.89  | | SIMP: (115) implies:
% 175.11/26.89  | |   (116)  all_6_2 = e3
% 175.11/26.89  | | 
% 175.11/26.89  | | REF_CLOSE: (20), (60), (81), (93), (96), (99), (116) are inconsistent by
% 175.11/26.89  | |            sub-proof #665.
% 175.11/26.89  | | 
% 175.11/26.89  | Case 2:
% 175.11/26.89  | | 
% 175.11/26.89  | |   (117)   ~ (all_56_15 = e3)
% 175.11/26.89  | |   (118)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.89  | | 
% 175.11/26.89  | | REDUCE: (15), (117) imply:
% 175.11/26.89  | |   (119)   ~ (all_6_2 = e3)
% 175.11/26.89  | | 
% 175.11/26.89  | | BETA: splitting (45) gives:
% 175.11/26.89  | | 
% 175.11/26.89  | | Case 1:
% 175.11/26.89  | | | 
% 175.11/26.89  | | |   (120)  all_56_13 = e3
% 175.11/26.89  | | | 
% 175.11/26.89  | | | COMBINE_EQS: (113), (120) imply:
% 175.11/26.89  | | |   (121)  all_52_27 = e3
% 175.11/26.89  | | | 
% 175.11/26.89  | | | COMBINE_EQS: (72), (121) imply:
% 175.11/26.89  | | |   (122)  all_58_13 = e3
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (97), (121) imply:
% 175.11/26.89  | | |   (123)   ~ (all_52_25 = e3)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (30), (121) imply:
% 175.11/26.89  | | |   (124)   ~ (all_52_29 = e3)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (124) implies:
% 175.11/26.89  | | |   (125)   ~ (all_52_29 = e3)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (39), (121) imply:
% 175.11/26.89  | | |   (126)  op(e2, e3) = e2
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (53), (121) imply:
% 175.11/26.89  | | |   (127)  op(e0, e2) = e3
% 175.11/26.89  | | | 
% 175.11/26.89  | | | GROUND_INST: instantiating (96) with all_52_9, e2, e3, e2, simplifying
% 175.11/26.89  | | |              with (112), (126) gives:
% 175.11/26.89  | | |   (128)  all_52_9 = e2
% 175.11/26.89  | | | 
% 175.11/26.89  | | | COMBINE_EQS: (86), (128) imply:
% 175.11/26.89  | | |   (129)  all_58_2 = e2
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (66), (128) imply:
% 175.11/26.89  | | |   (130)   ~ (all_52_13 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (130) implies:
% 175.11/26.89  | | |   (131)   ~ (all_52_13 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (108), (128) imply:
% 175.11/26.89  | | |   (132)   ~ (all_52_15 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (132) implies:
% 175.11/26.89  | | |   (133)   ~ (all_52_15 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (6), (128) imply:
% 175.11/26.89  | | |   (134)   ~ (all_52_25 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (134) implies:
% 175.11/26.89  | | |   (135)   ~ (all_52_25 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (61), (128) imply:
% 175.11/26.89  | | |   (136)   ~ (all_10_2 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (136) implies:
% 175.11/26.89  | | |   (137)   ~ (all_10_2 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (21), (128) imply:
% 175.11/26.89  | | |   (138)   ~ (all_4_2 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (138) implies:
% 175.11/26.89  | | |   (139)   ~ (all_4_2 = e2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (9), (128) imply:
% 175.11/26.89  | | |   (140)  op(e3, e2) = all_52_8
% 175.11/26.89  | | | 
% 175.11/26.89  | | | GROUND_INST: instantiating (96) with all_52_3, all_52_8, e2, e3,
% 175.11/26.89  | | |              simplifying with (5), (140) gives:
% 175.11/26.89  | | |   (141)  all_52_3 = all_52_8
% 175.11/26.89  | | | 
% 175.11/26.89  | | | COMBINE_EQS: (35), (141) imply:
% 175.11/26.89  | | |   (142)  all_58_1 = all_52_8
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (47), (141) imply:
% 175.11/26.89  | | |   (143)   ~ (all_52_5 = all_52_8)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (143) implies:
% 175.11/26.89  | | |   (144)   ~ (all_52_5 = all_52_8)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (76), (141) imply:
% 175.11/26.89  | | |   (145)   ~ (all_52_7 = all_52_8)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | SIMP: (145) implies:
% 175.11/26.89  | | |   (146)   ~ (all_52_7 = all_52_8)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (59), (141) imply:
% 175.11/26.89  | | |   (147)   ~ (all_52_8 = all_4_2)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | BETA: splitting (67) gives:
% 175.11/26.89  | | | 
% 175.11/26.89  | | | Case 1:
% 175.11/26.89  | | | | 
% 175.11/26.89  | | | |   (148)  all_56_12 = e3
% 175.11/26.89  | | | | 
% 175.11/26.89  | | | | REF_CLOSE: (71), (123), (148) are inconsistent by sub-proof #1040.
% 175.11/26.89  | | | | 
% 175.11/26.89  | | | Case 2:
% 175.11/26.89  | | | | 
% 175.11/26.89  | | | |   (149)   ~ (all_56_12 = e3)
% 175.11/26.89  | | | |   (150)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.89  | | | | 
% 175.11/26.89  | | | | BETA: splitting (48) gives:
% 175.11/26.89  | | | | 
% 175.11/26.89  | | | | Case 1:
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | |   (151)  all_58_0 = e3
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | | COMBINE_EQS: (37), (151) imply:
% 175.11/26.89  | | | | |   (152)  all_4_2 = e3
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | | REF_CLOSE: (84), (94), (96), (110), (152) are inconsistent by
% 175.11/26.89  | | | | |            sub-proof #106.
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | Case 2:
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | |   (153)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | | BETA: splitting (153) gives:
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | | Case 1:
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | |   (154)  all_58_2 = e3
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | | COMBINE_EQS: (129), (154) imply:
% 175.11/26.89  | | | | | |   (155)  e3 = e2
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | | REDUCE: (110), (155) imply:
% 175.11/26.89  | | | | | |   (156)  $false
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | | CLOSE: (156) is inconsistent.
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | Case 2:
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | |   (157)  all_58_6 = e3 | all_58_12 = e3
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | | BETA: splitting (157) gives:
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | | Case 1:
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | |   (158)  all_58_6 = e3
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | COMBINE_EQS: (75), (158) imply:
% 175.11/26.89  | | | | | | |   (159)  all_52_17 = e3
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | SIMP: (159) implies:
% 175.11/26.89  | | | | | | |   (160)  all_52_17 = e3
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | REDUCE: (102), (160) imply:
% 175.11/26.89  | | | | | | |   (161)   ~ (all_52_19 = e3)
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | SIMP: (161) implies:
% 175.11/26.89  | | | | | | |   (162)   ~ (all_52_19 = e3)
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | REDUCE: (26), (160) imply:
% 175.11/26.89  | | | | | | |   (163)   ~ (all_52_25 = e3)
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | REDUCE: (95), (160) imply:
% 175.11/26.89  | | | | | | |   (164)   ~ (all_4_2 = e3)
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | SIMP: (164) implies:
% 175.11/26.89  | | | | | | |   (165)   ~ (all_4_2 = e3)
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | BETA: splitting (73) gives:
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | Case 1:
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | |   (166)  all_58_0 = e1
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | COMBINE_EQS: (37), (166) imply:
% 175.11/26.89  | | | | | | | |   (167)  all_4_2 = e1
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | REDUCE: (24), (167) imply:
% 175.11/26.89  | | | | | | | |   (168)   ~ (all_52_5 = e1)
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | REDUCE: (34), (167) imply:
% 175.11/26.89  | | | | | | | |   (169)   ~ (all_52_7 = e1)
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | REDUCE: (92), (167) imply:
% 175.11/26.89  | | | | | | | |   (170)   ~ (all_52_25 = e1)
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | REDUCE: (84), (167) imply:
% 175.11/26.89  | | | | | | | |   (171)  op(e3, e1) = e2
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | REDUCE: (46), (167) imply:
% 175.11/26.89  | | | | | | | |   (172)  op(e2, e1) = all_4_0
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | BETA: splitting (65) gives:
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | Case 1:
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | |   (173)  all_58_0 = e0
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | COMBINE_EQS: (166), (173) imply:
% 175.11/26.89  | | | | | | | | |   (174)  e1 = e0
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | REDUCE: (77), (174) imply:
% 175.11/26.89  | | | | | | | | |   (175)  $false
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | CLOSE: (175) is inconsistent.
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | Case 2:
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | |   (176)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | BETA: splitting (176) gives:
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | Case 1:
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | |   (177)  all_58_2 = e0
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | REF_CLOSE: (105), (129), (177) are inconsistent by sub-proof
% 175.11/26.89  | | | | | | | | | |            #909.
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | Case 2:
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | |   (178)  all_58_6 = e0 | all_58_12 = e0
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | BETA: splitting (178) gives:
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | Case 1:
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | |   (179)  all_58_6 = e0
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REF_CLOSE: (64), (158), (179) are inconsistent by sub-proof
% 175.11/26.89  | | | | | | | | | | |            #559.
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | Case 2:
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | |   (180)  all_58_12 = e0
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | COMBINE_EQS: (106), (180) imply:
% 175.11/26.89  | | | | | | | | | | |   (181)  all_52_25 = e0
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | SIMP: (181) implies:
% 175.11/26.89  | | | | | | | | | | |   (182)  all_52_25 = e0
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (123), (182) imply:
% 175.11/26.89  | | | | | | | | | | |   (183)   ~ (e3 = e0)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (135), (182) imply:
% 175.11/26.89  | | | | | | | | | | |   (184)   ~ (e2 = e0)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (170), (182) imply:
% 175.11/26.89  | | | | | | | | | | |   (185)   ~ (e1 = e0)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (81), (182) imply:
% 175.11/26.89  | | | | | | | | | | |   (186)  op(e3, e0) = e3
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | GROUND_INST: instantiating (96) with all_52_13, all_4_0, e1,
% 175.11/26.89  | | | | | | | | | | |              e2, simplifying with (49), (172) gives:
% 175.11/26.89  | | | | | | | | | | |   (187)  all_52_13 = all_4_0
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | GROUND_INST: instantiating (96) with all_52_7, e3, e0, e3,
% 175.11/26.89  | | | | | | | | | | |              simplifying with (93), (186) gives:
% 175.11/26.89  | | | | | | | | | | |   (188)  all_52_7 = e3
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | GROUND_INST: instantiating (96) with all_52_5, e2, e1, e3,
% 175.11/26.89  | | | | | | | | | | |              simplifying with (87), (171) gives:
% 175.11/26.89  | | | | | | | | | | |   (189)  all_52_5 = e2
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (22), (188), (189) imply:
% 175.11/26.89  | | | | | | | | | | |   (190)   ~ (e3 = e2)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (146), (188) imply:
% 175.11/26.89  | | | | | | | | | | |   (191)   ~ (all_52_8 = e3)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | SIMP: (191) implies:
% 175.11/26.89  | | | | | | | | | | |   (192)   ~ (all_52_8 = e3)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (101), (188) imply:
% 175.11/26.89  | | | | | | | | | | |   (193)   ~ (all_52_23 = e3)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | SIMP: (193) implies:
% 175.11/26.89  | | | | | | | | | | |   (194)   ~ (all_52_23 = e3)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (99), (188) imply:
% 175.11/26.89  | | | | | | | | | | |   (195)   ~ (all_6_2 = e3)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REDUCE: (131), (187) imply:
% 175.11/26.89  | | | | | | | | | | |   (196)   ~ (all_4_0 = e2)
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (8), (11), (17), (18), (19), (20),
% 175.11/26.89  | | | | | | | | | | |            (22), (23), (24), (25), (27), (28), (29), (32),
% 175.11/26.89  | | | | | | | | | | |            (34), (37), (38), (41), (44), (54), (55), (56),
% 175.11/26.89  | | | | | | | | | | |            (63), (64), (65), (68), (69), (70), (71), (73),
% 175.11/26.89  | | | | | | | | | | |            (77), (78), (79), (80), (81), (82), (87), (88),
% 175.11/26.89  | | | | | | | | | | |            (90), (92), (93), (96), (99), (103), (104), (105),
% 175.11/26.89  | | | | | | | | | | |            (106), (107), (109), (110), (111), (119), (122),
% 175.11/26.89  | | | | | | | | | | |            (123), (125), (127), (129), (133), (135), (137),
% 175.11/26.89  | | | | | | | | | | |            (142), (144), (147), (150), (157), (158), (162),
% 175.11/26.89  | | | | | | | | | | |            (165), (192), (194), (196) are inconsistent by
% 175.11/26.89  | | | | | | | | | | |            sub-proof #655.
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | End of split
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | End of split
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | End of split
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | Case 2:
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | |   (197)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | BETA: splitting (197) gives:
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | | Case 1:
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | |   (198)  all_58_2 = e1
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | REF_CLOSE: (88), (129), (198) are inconsistent by sub-proof
% 175.11/26.89  | | | | | | | | |            #921.
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | Case 2:
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | |   (199)  all_58_6 = e1 | all_58_12 = e1
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | BETA: splitting (199) gives:
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | Case 1:
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | |   (200)  all_58_6 = e1
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | REF_CLOSE: (29), (106), (123), (157), (200) are inconsistent
% 175.11/26.89  | | | | | | | | | |            by sub-proof #1002.
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | Case 2:
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | |   (201)  all_58_12 = e1
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | COMBINE_EQS: (106), (201) imply:
% 175.11/26.89  | | | | | | | | | |   (202)  all_52_25 = e1
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | SIMP: (202) implies:
% 175.11/26.89  | | | | | | | | | |   (203)  all_52_25 = e1
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | REDUCE: (89), (203) imply:
% 175.11/26.89  | | | | | | | | | |   (204)   ~ (all_6_2 = e1)
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | SIMP: (204) implies:
% 175.11/26.89  | | | | | | | | | |   (205)   ~ (all_6_2 = e1)
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | BETA: splitting (118) gives:
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | Case 1:
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | |   (206)  all_56_15 = e2
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | COMBINE_EQS: (15), (206) imply:
% 175.11/26.89  | | | | | | | | | | |   (207)  all_6_2 = e2
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | SIMP: (207) implies:
% 175.11/26.89  | | | | | | | | | | |   (208)  all_6_2 = e2
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REF_CLOSE: (20), (64), (96), (127), (208) are inconsistent by
% 175.11/26.89  | | | | | | | | | | |            sub-proof #662.
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | Case 2:
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | |   (209)  all_56_15 = e1 | all_56_15 = e0
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | | REF_CLOSE: (13), (15), (205), (209) are inconsistent by
% 175.11/26.89  | | | | | | | | | | |            sub-proof #653.
% 175.11/26.89  | | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | | End of split
% 175.11/26.89  | | | | | | | | | | 
% 175.11/26.89  | | | | | | | | | End of split
% 175.11/26.89  | | | | | | | | | 
% 175.11/26.89  | | | | | | | | End of split
% 175.11/26.89  | | | | | | | | 
% 175.11/26.89  | | | | | | | End of split
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | Case 2:
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | |   (210)  all_58_12 = e3
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | | REF_CLOSE: (106), (123), (210) are inconsistent by sub-proof
% 175.11/26.89  | | | | | | |            #1003.
% 175.11/26.89  | | | | | | | 
% 175.11/26.89  | | | | | | End of split
% 175.11/26.89  | | | | | | 
% 175.11/26.89  | | | | | End of split
% 175.11/26.89  | | | | | 
% 175.11/26.89  | | | | End of split
% 175.11/26.89  | | | | 
% 175.11/26.89  | | | End of split
% 175.11/26.89  | | | 
% 175.11/26.89  | | Case 2:
% 175.11/26.89  | | | 
% 175.11/26.89  | | |   (211)   ~ (all_56_13 = e3)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REDUCE: (113), (211) imply:
% 175.11/26.89  | | |   (212)   ~ (all_52_27 = e3)
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (12), (13), (14), (15),
% 175.11/26.89  | | |            (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 175.11/26.89  | | |            (27), (28), (29), (30), (31), (34), (35), (36), (37), (40),
% 175.11/26.89  | | |            (42), (43), (44), (47), (48), (50), (51), (52), (55), (57),
% 175.11/26.89  | | |            (58), (59), (61), (62), (64), (66), (67), (68), (71), (72),
% 175.11/26.89  | | |            (74), (75), (76), (78), (79), (80), (81), (83), (84), (85),
% 175.11/26.89  | | |            (86), (87), (89), (91), (92), (93), (94), (96), (98), (99),
% 175.11/26.89  | | |            (100), (102), (103), (104), (106), (107), (108), (110), (118),
% 175.11/26.89  | | |            (119), (212) are inconsistent by sub-proof #90.
% 175.11/26.89  | | | 
% 175.11/26.89  | | End of split
% 175.11/26.89  | | 
% 175.11/26.89  | End of split
% 175.11/26.89  | 
% 175.11/26.89  End of proof
% 175.11/26.89  
% 175.11/26.89  Sub-proof #90 shows that the following formulas are inconsistent:
% 175.11/26.89  ----------------------------------------------------------------
% 175.11/26.89    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.11/26.89    (2)   ~ (all_52_17 = all_52_23)
% 175.11/26.89    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.11/26.89    (4)  op(e3, e2) = all_52_3
% 175.11/26.89    (5)   ~ (all_52_9 = all_52_25)
% 175.11/26.89    (6)   ~ (all_52_19 = all_52_23)
% 175.11/26.89    (7)   ~ (all_52_27 = e3)
% 175.11/26.89    (8)   ~ (all_6_2 = e3)
% 175.11/26.89    (9)   ~ (all_52_3 = all_10_2)
% 175.11/26.89    (10)  all_58_5 = all_52_13
% 175.11/26.89    (11)   ~ (all_6_2 = e0)
% 175.11/26.89    (12)   ~ (all_52_25 = all_52_29)
% 175.11/26.89    (13)  all_56_15 = all_6_2
% 175.11/26.89    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.11/26.89    (15)  all_58_3 = all_10_2
% 175.11/26.89    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.89    (17)  all_58_15 = all_6_2
% 175.11/26.89    (18)  op(e0, all_6_2) = e0
% 175.11/26.89    (19)   ~ (all_52_9 = all_4_2)
% 175.11/26.89    (20)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.89    (21)  all_58_10 = all_52_15
% 175.11/26.89    (22)   ~ (all_52_5 = all_4_2)
% 175.11/26.89    (23)  all_58_7 = all_52_19
% 175.11/26.89    (24)   ~ (all_52_17 = all_52_25)
% 175.11/26.89    (25)  op(e0, e1) = all_52_29
% 175.11/26.89    (26)  all_58_4 = all_52_5
% 175.11/26.89    (27)   ~ (e3 = e1)
% 175.11/26.89    (28)   ~ (all_52_27 = all_52_29)
% 175.11/26.89    (29)   ~ (all_52_17 = all_14_2)
% 175.11/26.89    (30)   ~ (all_52_7 = all_4_2)
% 175.11/26.89    (31)  all_58_1 = all_52_3
% 175.11/26.89    (32)   ~ (all_52_13 = all_52_15)
% 175.11/26.89    (33)  all_58_0 = all_4_2
% 175.11/26.89    (34)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.11/26.89    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.11/26.89    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.89    (37)  all_58_14 = all_52_29
% 175.11/26.89    (38)   ~ (all_52_3 = all_52_5)
% 175.11/26.89    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.89    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.89    (41)  all_58_8 = all_14_2
% 175.11/26.89    (42)  all_56_1 = all_52_3
% 175.11/26.89    (43)  op(e1, all_52_29) = e1
% 175.11/26.89    (44)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.11/26.89    (45)   ~ (all_52_3 = all_52_27)
% 175.11/26.89    (46)   ~ (all_52_3 = all_4_2)
% 175.11/26.89    (47)   ~ (all_52_9 = all_10_2)
% 175.11/26.89    (48)  op(e3, all_52_17) = all_52_16
% 175.11/26.89    (49)   ~ (e3 = e0)
% 175.11/26.89    (50)   ~ (all_52_9 = all_52_13)
% 175.11/26.89    (51)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.89    (52)   ~ (all_52_5 = all_52_29)
% 175.11/26.89    (53)  all_56_12 = all_52_25
% 175.11/26.89    (54)  all_58_13 = all_52_27
% 175.11/26.89    (55)   ~ (all_52_9 = all_52_17)
% 175.11/26.89    (56)  all_58_6 = all_52_17
% 175.11/26.89    (57)   ~ (all_52_3 = all_52_7)
% 175.11/26.89    (58)  all_56_0 = all_4_2
% 175.11/26.89    (59)  all_58_11 = all_52_23
% 175.11/26.89    (60)   ~ (all_52_7 = all_52_15)
% 175.11/26.89    (61)  op(e3, all_52_25) = e3
% 175.11/26.89    (62)   ~ (all_52_19 = all_10_2)
% 175.11/26.89    (63)  op(e3, all_4_2) = e2
% 175.11/26.89    (64)   ~ (all_52_29 = all_6_2)
% 175.11/26.89    (65)  all_58_2 = all_52_9
% 175.11/26.89    (66)  op(e3, e1) = all_52_5
% 175.11/26.89    (67)   ~ (all_52_25 = all_6_2)
% 175.11/26.89    (68)  op(e1, e3) = all_52_17
% 175.11/26.89    (69)   ~ (all_52_25 = all_4_2)
% 175.11/26.89    (70)  op(e3, e0) = all_52_7
% 175.11/26.89    (71)  op(e3, e3) = all_4_2
% 175.11/26.89    (72)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.89    (73)   ~ (all_52_27 = all_6_2)
% 175.11/26.89    (74)   ~ (all_52_7 = all_6_2)
% 175.11/26.89    (75)   ~ (all_52_15 = all_10_2)
% 175.11/26.89    (76)   ~ (all_52_17 = all_52_19)
% 175.11/26.89    (77)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.89    (78)  all_58_9 = all_52_7
% 175.11/26.89    (79)  all_58_12 = all_52_25
% 175.11/26.89    (80)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.89    (81)   ~ (all_52_9 = all_52_15)
% 175.11/26.89    (82)   ~ (e3 = e2)
% 175.11/26.89  
% 175.11/26.89  Begin of proof
% 175.11/26.89  | 
% 175.11/26.89  | BETA: splitting (40) gives:
% 175.11/26.89  | 
% 175.11/26.89  | Case 1:
% 175.11/26.89  | | 
% 175.11/26.89  | |   (83)  all_58_12 = e3
% 175.11/26.89  | | 
% 175.11/26.89  | | REF_CLOSE: (61), (69), (71), (72), (79), (83) are inconsistent by sub-proof
% 175.11/26.89  | |            #884.
% 175.11/26.89  | | 
% 175.11/26.89  | Case 2:
% 175.11/26.89  | | 
% 175.11/26.89  | |   (84)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.89  | | 
% 175.11/26.89  | | BETA: splitting (84) gives:
% 175.11/26.89  | | 
% 175.11/26.89  | | Case 1:
% 175.11/26.89  | | | 
% 175.11/26.89  | | |   (85)  all_58_13 = e3
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REF_CLOSE: (7), (54), (85) are inconsistent by sub-proof #1026.
% 175.11/26.89  | | | 
% 175.11/26.89  | | Case 2:
% 175.11/26.89  | | | 
% 175.11/26.89  | | |   (86)  all_58_14 = e3 | all_58_15 = e3
% 175.11/26.89  | | | 
% 175.11/26.89  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 175.11/26.89  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.11/26.89  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 175.11/26.89  | | |            (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 175.11/26.89  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 175.11/26.89  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 175.11/26.89  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 175.11/26.89  | | |            (75), (76), (77), (78), (79), (80), (81), (82), (86) are
% 175.11/26.89  | | |            inconsistent by sub-proof #91.
% 175.11/26.89  | | | 
% 175.11/26.89  | | End of split
% 175.11/26.89  | | 
% 175.11/26.89  | End of split
% 175.11/26.89  | 
% 175.11/26.89  End of proof
% 175.11/26.89  
% 175.11/26.89  Sub-proof #91 shows that the following formulas are inconsistent:
% 175.11/26.89  ----------------------------------------------------------------
% 175.11/26.89    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.11/26.89    (2)   ~ (all_52_17 = all_52_23)
% 175.11/26.89    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.11/26.89    (4)  all_58_14 = e3 | all_58_15 = e3
% 175.11/26.89    (5)  op(e3, e2) = all_52_3
% 175.11/26.89    (6)   ~ (all_52_9 = all_52_25)
% 175.11/26.89    (7)   ~ (all_52_19 = all_52_23)
% 175.11/26.89    (8)   ~ (all_6_2 = e3)
% 175.11/26.89    (9)   ~ (all_52_3 = all_10_2)
% 175.11/26.89    (10)  all_58_5 = all_52_13
% 175.11/26.89    (11)   ~ (all_6_2 = e0)
% 175.11/26.89    (12)   ~ (all_52_25 = all_52_29)
% 175.11/26.89    (13)  all_56_15 = all_6_2
% 175.11/26.89    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.11/26.89    (15)  all_58_3 = all_10_2
% 175.11/26.89    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.89    (17)  all_58_15 = all_6_2
% 175.11/26.89    (18)  op(e0, all_6_2) = e0
% 175.11/26.89    (19)   ~ (all_52_9 = all_4_2)
% 175.11/26.89    (20)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.89    (21)  all_58_10 = all_52_15
% 175.11/26.89    (22)   ~ (all_52_5 = all_4_2)
% 175.11/26.89    (23)  all_58_7 = all_52_19
% 175.11/26.89    (24)   ~ (all_52_17 = all_52_25)
% 175.11/26.89    (25)  op(e0, e1) = all_52_29
% 175.11/26.89    (26)  all_58_4 = all_52_5
% 175.11/26.89    (27)   ~ (e3 = e1)
% 175.11/26.89    (28)   ~ (all_52_27 = all_52_29)
% 175.11/26.89    (29)   ~ (all_52_17 = all_14_2)
% 175.11/26.89    (30)   ~ (all_52_7 = all_4_2)
% 175.11/26.89    (31)  all_58_1 = all_52_3
% 175.11/26.89    (32)   ~ (all_52_13 = all_52_15)
% 175.11/26.89    (33)  all_58_0 = all_4_2
% 175.11/26.89    (34)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.11/26.89    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.11/26.89    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.89    (37)  all_58_14 = all_52_29
% 175.11/26.89    (38)   ~ (all_52_3 = all_52_5)
% 175.11/26.89    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.89    (40)  all_58_8 = all_14_2
% 175.11/26.89    (41)  all_56_1 = all_52_3
% 175.11/26.89    (42)  op(e1, all_52_29) = e1
% 175.11/26.89    (43)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.11/26.89    (44)   ~ (all_52_3 = all_52_27)
% 175.11/26.89    (45)   ~ (all_52_3 = all_4_2)
% 175.11/26.89    (46)   ~ (all_52_9 = all_10_2)
% 175.11/26.89    (47)  op(e3, all_52_17) = all_52_16
% 175.11/26.89    (48)   ~ (e3 = e0)
% 175.11/26.89    (49)   ~ (all_52_9 = all_52_13)
% 175.11/26.89    (50)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.89    (51)   ~ (all_52_5 = all_52_29)
% 175.11/26.89    (52)  all_56_12 = all_52_25
% 175.11/26.89    (53)  all_58_13 = all_52_27
% 175.11/26.89    (54)   ~ (all_52_9 = all_52_17)
% 175.11/26.89    (55)  all_58_6 = all_52_17
% 175.11/26.90    (56)   ~ (all_52_3 = all_52_7)
% 175.11/26.90    (57)  all_56_0 = all_4_2
% 175.11/26.90    (58)  all_58_11 = all_52_23
% 175.11/26.90    (59)   ~ (all_52_7 = all_52_15)
% 175.11/26.90    (60)  op(e3, all_52_25) = e3
% 175.11/26.90    (61)   ~ (all_52_19 = all_10_2)
% 175.11/26.90    (62)  op(e3, all_4_2) = e2
% 175.11/26.90    (63)   ~ (all_52_29 = all_6_2)
% 175.11/26.90    (64)  all_58_2 = all_52_9
% 175.11/26.90    (65)  op(e3, e1) = all_52_5
% 175.11/26.90    (66)   ~ (all_52_25 = all_6_2)
% 175.11/26.90    (67)  op(e1, e3) = all_52_17
% 175.11/26.90    (68)   ~ (all_52_25 = all_4_2)
% 175.11/26.90    (69)  op(e3, e0) = all_52_7
% 175.11/26.90    (70)  op(e3, e3) = all_4_2
% 175.11/26.90    (71)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.90    (72)   ~ (all_52_27 = all_6_2)
% 175.11/26.90    (73)   ~ (all_52_7 = all_6_2)
% 175.11/26.90    (74)   ~ (all_52_15 = all_10_2)
% 175.11/26.90    (75)   ~ (all_52_17 = all_52_19)
% 175.11/26.90    (76)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.90    (77)  all_58_9 = all_52_7
% 175.11/26.90    (78)  all_58_12 = all_52_25
% 175.11/26.90    (79)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.90    (80)   ~ (all_52_9 = all_52_15)
% 175.11/26.90    (81)   ~ (e3 = e2)
% 175.11/26.90  
% 175.11/26.90  Begin of proof
% 175.11/26.90  | 
% 175.11/26.90  | BETA: splitting (4) gives:
% 175.11/26.90  | 
% 175.11/26.90  | Case 1:
% 175.11/26.90  | | 
% 175.11/26.90  | |   (82)  all_58_14 = e3
% 175.11/26.90  | | 
% 175.11/26.90  | | COMBINE_EQS: (37), (82) imply:
% 175.11/26.90  | |   (83)  all_52_29 = e3
% 175.11/26.90  | | 
% 175.11/26.90  | | SIMP: (83) implies:
% 175.11/26.90  | |   (84)  all_52_29 = e3
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (51), (84) imply:
% 175.11/26.90  | |   (85)   ~ (all_52_5 = e3)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (12), (84) imply:
% 175.11/26.90  | |   (86)   ~ (all_52_25 = e3)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (28), (84) imply:
% 175.11/26.90  | |   (87)   ~ (all_52_27 = e3)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (63), (84) imply:
% 175.11/26.90  | |   (88)   ~ (all_6_2 = e3)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (42), (84) imply:
% 175.11/26.90  | |   (89)  op(e1, e3) = e1
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (25), (84) imply:
% 175.11/26.90  | |   (90)  op(e0, e1) = e3
% 175.11/26.90  | | 
% 175.11/26.90  | | GROUND_INST: instantiating (71) with all_52_17, e1, e3, e1, simplifying with
% 175.11/26.90  | |              (67), (89) gives:
% 175.11/26.90  | |   (91)  all_52_17 = e1
% 175.11/26.90  | | 
% 175.11/26.90  | | COMBINE_EQS: (55), (91) imply:
% 175.11/26.90  | |   (92)  all_58_6 = e1
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (54), (91) imply:
% 175.11/26.90  | |   (93)   ~ (all_52_9 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (75), (91) imply:
% 175.11/26.90  | |   (94)   ~ (all_52_19 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | SIMP: (94) implies:
% 175.11/26.90  | |   (95)   ~ (all_52_19 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (2), (91) imply:
% 175.11/26.90  | |   (96)   ~ (all_52_23 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | SIMP: (96) implies:
% 175.11/26.90  | |   (97)   ~ (all_52_23 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (24), (91) imply:
% 175.11/26.90  | |   (98)   ~ (all_52_25 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | SIMP: (98) implies:
% 175.11/26.90  | |   (99)   ~ (all_52_25 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (29), (91) imply:
% 175.11/26.90  | |   (100)   ~ (all_14_2 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | SIMP: (100) implies:
% 175.11/26.90  | |   (101)   ~ (all_14_2 = e1)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (47), (91) imply:
% 175.11/26.90  | |   (102)  op(e3, e1) = all_52_16
% 175.11/26.90  | | 
% 175.11/26.90  | | GROUND_INST: instantiating (71) with all_52_5, all_52_16, e1, e3,
% 175.11/26.90  | |              simplifying with (65), (102) gives:
% 175.11/26.90  | |   (103)  all_52_5 = all_52_16
% 175.11/26.90  | | 
% 175.11/26.90  | | COMBINE_EQS: (26), (103) imply:
% 175.11/26.90  | |   (104)  all_58_4 = all_52_16
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (38), (103) imply:
% 175.11/26.90  | |   (105)   ~ (all_52_3 = all_52_16)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (22), (103) imply:
% 175.11/26.90  | |   (106)   ~ (all_52_16 = all_4_2)
% 175.11/26.90  | | 
% 175.11/26.90  | | BETA: splitting (50) gives:
% 175.11/26.90  | | 
% 175.11/26.90  | | Case 1:
% 175.11/26.90  | | | 
% 175.11/26.90  | | |   (107)  all_56_12 = e3
% 175.11/26.90  | | | 
% 175.11/26.90  | | | REF_CLOSE: (52), (86), (107) are inconsistent by sub-proof #1040.
% 175.11/26.90  | | | 
% 175.11/26.90  | | Case 2:
% 175.11/26.90  | | | 
% 175.11/26.90  | | |   (108)   ~ (all_56_12 = e3)
% 175.11/26.90  | | |   (109)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.11/26.90  | | | 
% 175.11/26.90  | | | BETA: splitting (39) gives:
% 175.11/26.90  | | | 
% 175.11/26.90  | | | Case 1:
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | |   (110)  all_58_0 = e3
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | | COMBINE_EQS: (33), (110) imply:
% 175.11/26.90  | | | |   (111)  all_4_2 = e3
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | | REF_CLOSE: (62), (70), (71), (81), (111) are inconsistent by sub-proof
% 175.11/26.90  | | | |            #106.
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | Case 2:
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | |   (112)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | | BETA: splitting (112) gives:
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | | Case 1:
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | |   (113)  all_58_2 = e3
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | COMBINE_EQS: (64), (113) imply:
% 175.11/26.90  | | | | |   (114)  all_52_9 = e3
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | SIMP: (114) implies:
% 175.11/26.90  | | | | |   (115)  all_52_9 = e3
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | REDUCE: (49), (115) imply:
% 175.11/26.90  | | | | |   (116)   ~ (all_52_13 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | SIMP: (116) implies:
% 175.11/26.90  | | | | |   (117)   ~ (all_52_13 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | REDUCE: (80), (115) imply:
% 175.11/26.90  | | | | |   (118)   ~ (all_52_15 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | SIMP: (118) implies:
% 175.11/26.90  | | | | |   (119)   ~ (all_52_15 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | REDUCE: (6), (115) imply:
% 175.11/26.90  | | | | |   (120)   ~ (all_52_25 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | REDUCE: (46), (115) imply:
% 175.11/26.90  | | | | |   (121)   ~ (all_10_2 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | SIMP: (121) implies:
% 175.11/26.90  | | | | |   (122)   ~ (all_10_2 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | REDUCE: (19), (115) imply:
% 175.11/26.90  | | | | |   (123)   ~ (all_4_2 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | SIMP: (123) implies:
% 175.11/26.90  | | | | |   (124)   ~ (all_4_2 = e3)
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | BETA: splitting (16) gives:
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | Case 1:
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | |   (125)  all_56_0 = e3
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | | COMBINE_EQS: (57), (125) imply:
% 175.11/26.90  | | | | | |   (126)  all_4_2 = e3
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | | REDUCE: (124), (126) imply:
% 175.11/26.90  | | | | | |   (127)  $false
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | | CLOSE: (127) is inconsistent.
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | Case 2:
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | |   (128)   ~ (all_56_0 = e3)
% 175.11/26.90  | | | | | |   (129)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | | BETA: splitting (35) gives:
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | | Case 1:
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | |   (130)  all_58_4 = e1
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | COMBINE_EQS: (104), (130) imply:
% 175.11/26.90  | | | | | | |   (131)  all_52_16 = e1
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | SIMP: (131) implies:
% 175.11/26.90  | | | | | | |   (132)  all_52_16 = e1
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | REDUCE: (105), (132) imply:
% 175.11/26.90  | | | | | | |   (133)   ~ (all_52_3 = e1)
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | REDUCE: (106), (132) imply:
% 175.11/26.90  | | | | | | |   (134)   ~ (all_4_2 = e1)
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | SIMP: (134) implies:
% 175.11/26.90  | | | | | | |   (135)   ~ (all_4_2 = e1)
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | BETA: splitting (79) gives:
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | Case 1:
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | |   (136)  all_58_0 = e3
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | | COMBINE_EQS: (33), (136) imply:
% 175.11/26.90  | | | | | | | |   (137)  all_4_2 = e3
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | | REDUCE: (124), (137) imply:
% 175.11/26.90  | | | | | | | |   (138)  $false
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | | CLOSE: (138) is inconsistent.
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | Case 2:
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | |   (139)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | | BETA: splitting (76) gives:
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | | Case 1:
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | |   (140)  all_58_9 = e3
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | COMBINE_EQS: (77), (140) imply:
% 175.11/26.90  | | | | | | | | |   (141)  all_52_7 = e3
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | SIMP: (141) implies:
% 175.11/26.90  | | | | | | | | |   (142)  all_52_7 = e3
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | REDUCE: (56), (142) imply:
% 175.11/26.90  | | | | | | | | |   (143)   ~ (all_52_3 = e3)
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | BETA: splitting (34) gives:
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | Case 1:
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | |   (144)  all_56_1 = e3
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | REF_CLOSE: (41), (143), (144) are inconsistent by sub-proof
% 175.11/26.90  | | | | | | | | | |            #862.
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | Case 2:
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | |   (145)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | BETA: splitting (43) gives:
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | Case 1:
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | |   (146)  all_58_0 = e2
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | COMBINE_EQS: (33), (146) imply:
% 175.11/26.90  | | | | | | | | | | |   (147)  all_4_2 = e2
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REDUCE: (45), (147) imply:
% 175.11/26.90  | | | | | | | | | | |   (148)   ~ (all_52_3 = e2)
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REDUCE: (62), (147) imply:
% 175.11/26.90  | | | | | | | | | | |   (149)  op(e3, e2) = e2
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REF_CLOSE: (5), (41), (71), (133), (145), (148), (149) are
% 175.11/26.90  | | | | | | | | | | |            inconsistent by sub-proof #102.
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | Case 2:
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | |   (150)   ~ (all_58_0 = e2)
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REDUCE: (33), (150) imply:
% 175.11/26.90  | | | | | | | | | | |   (151)   ~ (all_4_2 = e2)
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (8), (13), (14), (15), (17), (18),
% 175.11/26.90  | | | | | | | | | | |            (20), (21), (23), (31), (36), (52), (53), (56),
% 175.11/26.90  | | | | | | | | | | |            (57), (58), (60), (61), (66), (68), (69), (71),
% 175.11/26.90  | | | | | | | | | | |            (72), (73), (74), (76), (77), (78), (82), (87),
% 175.11/26.90  | | | | | | | | | | |            (90), (95), (97), (99), (109), (119), (122),
% 175.11/26.90  | | | | | | | | | | |            (124), (129), (133), (135), (151) are inconsistent
% 175.11/26.90  | | | | | | | | | | |            by sub-proof #642.
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | End of split
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | End of split
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | Case 2:
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | |   (152)   ~ (all_58_9 = e3)
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | REDUCE: (77), (152) imply:
% 175.11/26.90  | | | | | | | | |   (153)   ~ (all_52_7 = e3)
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | BETA: splitting (139) gives:
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | Case 1:
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | |   (154)  all_58_1 = e3
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | COMBINE_EQS: (31), (154) imply:
% 175.11/26.90  | | | | | | | | | |   (155)  all_52_3 = e3
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | REDUCE: (44), (155) imply:
% 175.11/26.90  | | | | | | | | | |   (156)   ~ (all_52_27 = e3)
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | REDUCE: (5), (155) imply:
% 175.11/26.90  | | | | | | | | | |   (157)  op(e3, e2) = e3
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | BETA: splitting (43) gives:
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | Case 1:
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | |   (158)  all_58_0 = e2
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REF_CLOSE: (33), (62), (71), (124), (157), (158) are
% 175.11/26.90  | | | | | | | | | | |            inconsistent by sub-proof #92.
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | Case 2:
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | |   (159)   ~ (all_58_0 = e2)
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REDUCE: (33), (159) imply:
% 175.11/26.90  | | | | | | | | | | |   (160)   ~ (all_4_2 = e2)
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (8), (13), (14), (15), (17), (18),
% 175.11/26.90  | | | | | | | | | | |            (20), (21), (23), (31), (36), (52), (53), (56),
% 175.11/26.90  | | | | | | | | | | |            (57), (58), (60), (61), (66), (68), (69), (71),
% 175.11/26.90  | | | | | | | | | | |            (72), (73), (74), (76), (77), (78), (82), (87),
% 175.11/26.90  | | | | | | | | | | |            (90), (95), (97), (99), (109), (119), (122),
% 175.11/26.90  | | | | | | | | | | |            (124), (129), (133), (135), (160) are inconsistent
% 175.11/26.90  | | | | | | | | | | |            by sub-proof #642.
% 175.11/26.90  | | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | End of split
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | Case 2:
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | |   (161)  all_58_4 = e3 | all_58_9 = e3
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | | REF_CLOSE: (26), (77), (85), (153), (161) are inconsistent by
% 175.11/26.90  | | | | | | | | | |            sub-proof #729.
% 175.11/26.90  | | | | | | | | | | 
% 175.11/26.90  | | | | | | | | | End of split
% 175.11/26.90  | | | | | | | | | 
% 175.11/26.90  | | | | | | | | End of split
% 175.11/26.90  | | | | | | | | 
% 175.11/26.90  | | | | | | | End of split
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | Case 2:
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | |   (162)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | | REF_CLOSE: (7), (8), (10), (11), (13), (14), (15), (17), (18),
% 175.11/26.90  | | | | | | |            (20), (21), (23), (27), (30), (31), (32), (33), (36),
% 175.11/26.90  | | | | | | |            (39), (40), (46), (48), (52), (53), (56), (58), (60),
% 175.11/26.90  | | | | | | |            (64), (66), (69), (71), (73), (76), (77), (78), (80),
% 175.11/26.90  | | | | | | |            (82), (86), (87), (90), (92), (95), (97), (99), (101),
% 175.11/26.90  | | | | | | |            (109), (117), (162) are inconsistent by sub-proof #637.
% 175.11/26.90  | | | | | | | 
% 175.11/26.90  | | | | | | End of split
% 175.11/26.90  | | | | | | 
% 175.11/26.90  | | | | | End of split
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | Case 2:
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | |   (163)  all_58_6 = e3 | all_58_12 = e3
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | | REF_CLOSE: (27), (78), (86), (92), (163) are inconsistent by sub-proof
% 175.11/26.90  | | | | |            #1002.
% 175.11/26.90  | | | | | 
% 175.11/26.90  | | | | End of split
% 175.11/26.90  | | | | 
% 175.11/26.90  | | | End of split
% 175.11/26.90  | | | 
% 175.11/26.90  | | End of split
% 175.11/26.90  | | 
% 175.11/26.90  | Case 2:
% 175.11/26.90  | | 
% 175.11/26.90  | |   (164)  all_58_15 = e3
% 175.11/26.90  | | 
% 175.11/26.90  | | COMBINE_EQS: (17), (164) imply:
% 175.11/26.90  | |   (165)  all_6_2 = e3
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (8), (165) imply:
% 175.11/26.90  | |   (166)  $false
% 175.11/26.90  | | 
% 175.11/26.90  | | CLOSE: (166) is inconsistent.
% 175.11/26.90  | | 
% 175.11/26.90  | End of split
% 175.11/26.90  | 
% 175.11/26.90  End of proof
% 175.11/26.90  
% 175.11/26.90  Sub-proof #92 shows that the following formulas are inconsistent:
% 175.11/26.90  ----------------------------------------------------------------
% 175.11/26.90    (1)   ~ (all_4_2 = e3)
% 175.11/26.90    (2)  all_58_0 = all_4_2
% 175.11/26.90    (3)  op(e3, e2) = e3
% 175.11/26.90    (4)  op(e3, all_4_2) = e2
% 175.11/26.90    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.90    (6)  all_58_0 = e2
% 175.11/26.90  
% 175.11/26.90  Begin of proof
% 175.11/26.90  | 
% 175.11/26.90  | COMBINE_EQS: (2), (6) imply:
% 175.11/26.90  |   (7)  all_4_2 = e2
% 175.11/26.90  | 
% 175.11/26.90  | REDUCE: (1), (7) imply:
% 175.11/26.90  |   (8)   ~ (e3 = e2)
% 175.11/26.90  | 
% 175.11/26.90  | SIMP: (8) implies:
% 175.11/26.90  |   (9)   ~ (e3 = e2)
% 175.11/26.90  | 
% 175.11/26.90  | REDUCE: (4), (7) imply:
% 175.11/26.90  |   (10)  op(e3, e2) = e2
% 175.11/26.90  | 
% 175.11/26.90  | GROUND_INST: instantiating (5) with e3, e2, e2, e3, simplifying with (3), (10)
% 175.11/26.90  |              gives:
% 175.11/26.90  |   (11)  e3 = e2
% 175.11/26.90  | 
% 175.11/26.90  | REDUCE: (9), (11) imply:
% 175.11/26.90  |   (12)  $false
% 175.11/26.90  | 
% 175.11/26.90  | CLOSE: (12) is inconsistent.
% 175.11/26.90  | 
% 175.11/26.90  End of proof
% 175.11/26.90  
% 175.11/26.90  Sub-proof #93 shows that the following formulas are inconsistent:
% 175.11/26.90  ----------------------------------------------------------------
% 175.11/26.90    (1)   ~ (all_52_23 = all_14_2)
% 175.11/26.90    (2)   ~ (all_52_5 = all_52_13)
% 175.11/26.90    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.11/26.90    (4)   ~ (all_52_27 = all_10_2)
% 175.11/26.90    (5)   ~ (all_52_17 = all_52_23)
% 175.11/26.90    (6)  op(e2, all_10_2) = all_10_1
% 175.11/26.90    (7)   ~ (all_52_13 = all_52_29)
% 175.11/26.90    (8)  all_56_3 = all_52_7
% 175.11/26.90    (9)  op(e3, e2) = all_52_3
% 175.11/26.90    (10)   ~ (all_52_9 = all_52_25)
% 175.11/26.90    (11)   ~ (all_52_19 = all_52_23)
% 175.11/26.90    (12)  op(e1, e2) = all_52_19
% 175.11/26.90    (13)  all_58_5 = all_52_13
% 175.11/26.90    (14)   ~ (all_52_25 = all_52_29)
% 175.11/26.90    (15)  all_56_15 = all_6_2
% 175.11/26.90    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.11/26.90    (17)  all_58_3 = all_10_2
% 175.11/26.90    (18)  all_56_9 = all_52_19
% 175.11/26.90    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.90    (20)  all_58_15 = all_6_2
% 175.11/26.90    (21)   ~ (all_52_9 = all_4_2)
% 175.11/26.90    (22)   ~ (all_52_5 = all_52_7)
% 175.11/26.90    (23)  all_58_10 = all_52_15
% 175.11/26.90    (24)   ~ (all_52_5 = all_4_2)
% 175.11/26.90    (25)  all_58_7 = all_52_19
% 175.11/26.90    (26)   ~ (all_52_17 = all_52_25)
% 175.11/26.90    (27)  all_58_4 = all_52_5
% 175.11/26.90    (28)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.11/26.90    (29)   ~ (all_52_17 = all_14_2)
% 175.11/26.90    (30)  op(e3, all_4_2) = all_4_1
% 175.11/26.90    (31)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.11/26.90    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.11/26.90    (33)   ~ (all_52_7 = all_4_2)
% 175.11/26.90    (34)  all_58_1 = all_52_3
% 175.11/26.90    (35)  all_58_0 = all_4_2
% 175.11/26.90    (36)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 175.11/26.90    (37)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.11/26.90    (38)  op(e1, all_52_29) = all_52_28
% 175.11/26.90    (39)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.11/26.90    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.90    (41)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.11/26.90    (42)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.11/26.90    (43)  all_58_14 = all_52_29
% 175.11/26.90    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.11/26.90    (45)  op(e2, all_4_2) = all_4_0
% 175.11/26.90    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.90    (47)  op(e2, e1) = all_52_13
% 175.11/26.90    (48)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.90    (49)  all_58_8 = all_14_2
% 175.11/26.90    (50)  op(e0, e2) = all_52_27
% 175.11/26.90    (51)   ~ (all_14_0 = e3)
% 175.11/26.90    (52)  op(all_4_1, all_4_2) = all_4_0
% 175.11/26.90    (53)   ~ (all_52_5 = all_14_2)
% 175.11/26.90    (54)   ~ (all_52_3 = all_52_27)
% 175.11/26.90    (55)   ~ (all_52_3 = all_4_2)
% 175.11/26.90    (56)  op(e0, e3) = all_52_25
% 175.11/26.90    (57)   ~ (all_52_9 = all_10_2)
% 175.11/26.90    (58)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.11/26.90    (59)   ~ (all_52_13 = all_14_2)
% 175.11/26.90    (60)  op(e1, all_14_2) = all_14_0
% 175.11/26.90    (61)   ~ (e3 = e0)
% 175.11/26.90    (62)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.11/26.90    (63)   ~ (all_52_9 = all_52_13)
% 175.11/26.90    (64)   ~ (all_52_15 = all_52_23)
% 175.11/26.90    (65)   ~ (all_52_5 = all_52_29)
% 175.11/26.90    (66)  all_58_13 = all_52_27
% 175.11/26.90    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.90    (68)  all_56_5 = all_10_2
% 175.11/26.90    (69)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.11/26.90    (70)   ~ (all_52_9 = all_52_17)
% 175.11/26.90    (71)   ~ (all_14_0 = e2)
% 175.11/26.90    (72)  all_58_6 = all_52_17
% 175.11/26.90    (73)  op(e2, all_52_19) = e2
% 175.11/26.90    (74)  op(e3, all_52_17) = e3
% 175.11/26.90    (75)   ~ (e1 = e0)
% 175.11/26.90    (76)  all_56_0 = all_4_2
% 175.11/26.90    (77)  all_58_11 = all_52_23
% 175.11/26.90    (78)   ~ (all_52_3 = all_52_19)
% 175.11/26.90    (79)   ~ (all_52_7 = all_52_15)
% 175.11/26.90    (80)   ~ (all_4_0 = e1)
% 175.11/26.90    (81)   ~ (all_52_19 = all_10_2)
% 175.11/26.90    (82)  op(e3, all_4_2) = e2
% 175.11/26.90    (83)   ~ (all_52_23 = all_6_2)
% 175.11/26.90    (84)   ~ (all_52_29 = all_6_2)
% 175.11/26.90    (85)  all_58_2 = all_52_9
% 175.11/26.90    (86)  op(e3, e1) = all_52_5
% 175.11/26.90    (87)   ~ (all_52_25 = all_6_2)
% 175.11/26.90    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.11/26.90    (89)  op(e1, e3) = all_52_17
% 175.11/26.90    (90)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.11/26.90    (91)   ~ (all_52_25 = all_4_2)
% 175.11/26.90    (92)  op(e3, e0) = all_52_7
% 175.11/26.90    (93)  op(e3, e3) = all_4_2
% 175.11/26.90    (94)   ~ (all_10_1 = e3)
% 175.11/26.90    (95)  all_56_8 = all_52_17
% 175.11/26.90    (96)   ~ (all_52_17 = all_4_2)
% 175.11/26.90    (97)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.90    (98)   ~ (all_52_25 = all_52_27)
% 175.11/26.90    (99)   ~ (all_52_27 = all_6_2)
% 175.11/26.90    (100)   ~ (all_52_7 = all_6_2)
% 175.11/26.90    (101)  op(e0, all_52_23) = e0
% 175.11/26.90    (102)   ~ (all_52_15 = all_10_2)
% 175.11/26.90    (103)   ~ (all_52_19 = all_52_27)
% 175.11/26.90    (104)  all_56_7 = all_52_15
% 175.11/26.90    (105)  op(e1, all_14_2) = e1
% 175.11/26.90    (106)   ~ (all_52_7 = all_52_23)
% 175.11/26.90    (107)   ~ (all_52_13 = all_10_2)
% 175.11/26.90    (108)  op(e2, all_52_27) = all_52_26
% 175.11/26.90    (109)   ~ (all_52_17 = all_52_19)
% 175.11/26.90    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.90    (111)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.11/26.90    (112)  all_58_9 = all_52_7
% 175.11/26.90    (113)   ~ (e2 = e0)
% 175.11/26.90    (114)  all_58_12 = all_52_25
% 175.11/26.90    (115)  all_56_6 = all_52_13
% 175.11/26.90    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.90    (117)   ~ (all_52_9 = all_52_15)
% 175.11/26.90    (118)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.11/26.90    (119)   ~ (e3 = e2)
% 175.11/26.90    (120)   ~ (all_52_19 = all_14_2)
% 175.11/26.90    (121)  op(e2, e3) = all_52_9
% 175.11/26.90    (122)  all_56_13 = all_52_27
% 175.11/26.90  
% 175.11/26.90  Begin of proof
% 175.11/26.90  | 
% 175.11/26.90  | GROUND_INST: instantiating (97) with e1, all_14_0, all_14_2, e1, simplifying
% 175.11/26.90  |              with (60), (105) gives:
% 175.11/26.90  |   (123)  all_14_0 = e1
% 175.11/26.90  | 
% 175.11/26.90  | REDUCE: (51), (123) imply:
% 175.11/26.90  |   (124)   ~ (e3 = e1)
% 175.11/26.90  | 
% 175.11/26.90  | SIMP: (124) implies:
% 175.11/26.90  |   (125)   ~ (e3 = e1)
% 175.11/26.90  | 
% 175.11/26.90  | REDUCE: (71), (123) imply:
% 175.11/26.90  |   (126)   ~ (e2 = e1)
% 175.11/26.90  | 
% 175.11/26.90  | SIMP: (126) implies:
% 175.11/26.90  |   (127)   ~ (e2 = e1)
% 175.11/26.90  | 
% 175.11/26.90  | BETA: splitting (31) gives:
% 175.11/26.90  | 
% 175.11/26.90  | Case 1:
% 175.11/26.90  | | 
% 175.11/26.90  | |   (128)  all_56_15 = e3
% 175.11/26.90  | | 
% 175.11/26.90  | | REF_CLOSE: (1), (4), (6), (11), (12), (13), (15), (17), (18), (20), (21),
% 175.11/26.90  | |            (23), (24), (25), (27), (28), (29), (30), (32), (35), (39), (42),
% 175.11/26.90  | |            (43), (46), (47), (49), (50), (52), (53), (57), (58), (63), (68),
% 175.11/26.90  | |            (69), (70), (72), (73), (74), (77), (80), (83), (84), (85), (86),
% 175.11/26.90  | |            (87), (88), (89), (93), (94), (96), (97), (100), (101), (105),
% 175.11/26.90  | |            (106), (107), (112), (114), (116), (117), (118), (119), (120),
% 175.11/26.90  | |            (121), (127), (128) are inconsistent by sub-proof #701.
% 175.11/26.90  | | 
% 175.11/26.90  | Case 2:
% 175.11/26.90  | | 
% 175.11/26.90  | |   (129)   ~ (all_56_15 = e3)
% 175.11/26.90  | | 
% 175.11/26.90  | | REDUCE: (15), (129) imply:
% 175.11/26.90  | |   (130)   ~ (all_6_2 = e3)
% 175.11/26.90  | | 
% 175.11/26.90  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14), (16),
% 175.11/26.90  | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 175.11/26.90  | |            (28), (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 175.11/26.90  | |            (42), (43), (44), (45), (46), (47), (48), (49), (53), (54), (55),
% 175.11/26.90  | |            (56), (57), (59), (61), (62), (63), (64), (65), (66), (67), (68),
% 175.11/26.90  | |            (69), (70), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 175.11/26.90  | |            (81), (82), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 175.11/26.90  | |            (93), (94), (95), (96), (97), (98), (99), (101), (102), (103),
% 175.11/26.90  | |            (104), (105), (106), (108), (109), (110), (111), (112), (113),
% 175.11/26.90  | |            (114), (115), (116), (117), (118), (119), (121), (122), (125),
% 175.11/26.90  | |            (127), (130) are inconsistent by sub-proof #94.
% 175.11/26.90  | | 
% 175.11/26.90  | End of split
% 175.11/26.90  | 
% 175.11/26.90  End of proof
% 175.11/26.90  
% 175.11/26.90  Sub-proof #94 shows that the following formulas are inconsistent:
% 175.11/26.90  ----------------------------------------------------------------
% 175.11/26.90    (1)   ~ (all_52_5 = all_52_13)
% 175.11/26.90    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.11/26.90    (3)   ~ (all_52_17 = all_52_23)
% 175.11/26.90    (4)  op(e2, all_10_2) = all_10_1
% 175.11/26.90    (5)   ~ (all_52_13 = all_52_29)
% 175.11/26.90    (6)  all_56_3 = all_52_7
% 175.11/26.90    (7)  op(e3, e2) = all_52_3
% 175.11/26.90    (8)   ~ (all_52_9 = all_52_25)
% 175.11/26.91    (9)  op(e1, e2) = all_52_19
% 175.11/26.91    (10)   ~ (all_6_2 = e3)
% 175.11/26.91    (11)  all_58_5 = all_52_13
% 175.11/26.91    (12)   ~ (all_52_25 = all_52_29)
% 175.11/26.91    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.11/26.91    (14)  all_58_3 = all_10_2
% 175.11/26.91    (15)  all_56_9 = all_52_19
% 175.11/26.91    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.91    (17)  all_58_15 = all_6_2
% 175.11/26.91    (18)   ~ (all_52_9 = all_4_2)
% 175.11/26.91    (19)   ~ (all_52_5 = all_52_7)
% 175.11/26.91    (20)  all_58_10 = all_52_15
% 175.11/26.91    (21)   ~ (all_52_5 = all_4_2)
% 175.11/26.91    (22)  all_58_7 = all_52_19
% 175.11/26.91    (23)   ~ (all_52_17 = all_52_25)
% 175.11/26.91    (24)  all_58_4 = all_52_5
% 175.11/26.91    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.11/26.91    (26)   ~ (e3 = e1)
% 175.11/26.91    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.11/26.91    (28)   ~ (all_52_7 = all_4_2)
% 175.11/26.91    (29)  all_58_1 = all_52_3
% 175.11/26.91    (30)  all_58_0 = all_4_2
% 175.11/26.91    (31)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 175.11/26.91    (32)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.11/26.91    (33)  op(e1, all_52_29) = all_52_28
% 175.11/26.91    (34)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.11/26.91    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.11/26.91    (36)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.11/26.91    (37)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.11/26.91    (38)  all_58_14 = all_52_29
% 175.11/26.91    (39)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.11/26.91    (40)  op(e2, all_4_2) = all_4_0
% 175.11/26.91    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.91    (42)  op(e2, e1) = all_52_13
% 175.11/26.91    (43)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.91    (44)  all_58_8 = all_14_2
% 175.11/26.91    (45)   ~ (all_52_5 = all_14_2)
% 175.11/26.91    (46)   ~ (all_52_3 = all_52_27)
% 175.11/26.91    (47)   ~ (all_52_3 = all_4_2)
% 175.11/26.91    (48)  op(e0, e3) = all_52_25
% 175.11/26.91    (49)   ~ (all_52_9 = all_10_2)
% 175.11/26.91    (50)   ~ (all_52_13 = all_14_2)
% 175.11/26.91    (51)   ~ (e3 = e0)
% 175.11/26.91    (52)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.11/26.91    (53)   ~ (all_52_9 = all_52_13)
% 175.11/26.91    (54)   ~ (all_52_15 = all_52_23)
% 175.11/26.91    (55)   ~ (all_52_5 = all_52_29)
% 175.11/26.91    (56)  all_58_13 = all_52_27
% 175.11/26.91    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.91    (58)  all_56_5 = all_10_2
% 175.11/26.91    (59)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.11/26.91    (60)   ~ (all_52_9 = all_52_17)
% 175.11/26.91    (61)  all_58_6 = all_52_17
% 175.11/26.91    (62)  op(e2, all_52_19) = e2
% 175.11/26.91    (63)  op(e3, all_52_17) = e3
% 175.11/26.91    (64)   ~ (e1 = e0)
% 175.11/26.91    (65)  all_56_0 = all_4_2
% 175.11/26.91    (66)  all_58_11 = all_52_23
% 175.11/26.91    (67)   ~ (all_52_3 = all_52_19)
% 175.11/26.91    (68)   ~ (all_52_7 = all_52_15)
% 175.11/26.91    (69)   ~ (all_4_0 = e1)
% 175.11/26.91    (70)   ~ (all_52_19 = all_10_2)
% 175.11/26.91    (71)  op(e3, all_4_2) = e2
% 175.11/26.91    (72)   ~ (all_52_29 = all_6_2)
% 175.11/26.91    (73)  all_58_2 = all_52_9
% 175.11/26.91    (74)  op(e3, e1) = all_52_5
% 175.11/26.91    (75)   ~ (e2 = e1)
% 175.11/26.91    (76)   ~ (all_52_25 = all_6_2)
% 175.11/26.91    (77)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.11/26.91    (78)  op(e1, e3) = all_52_17
% 175.11/26.91    (79)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.11/26.91    (80)   ~ (all_52_25 = all_4_2)
% 175.11/26.91    (81)  op(e3, e0) = all_52_7
% 175.11/26.91    (82)  op(e3, e3) = all_4_2
% 175.11/26.91    (83)   ~ (all_10_1 = e3)
% 175.11/26.91    (84)  all_56_8 = all_52_17
% 175.11/26.91    (85)   ~ (all_52_17 = all_4_2)
% 175.11/26.91    (86)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.91    (87)   ~ (all_52_25 = all_52_27)
% 175.11/26.91    (88)   ~ (all_52_27 = all_6_2)
% 175.11/26.91    (89)  op(e0, all_52_23) = e0
% 175.11/26.91    (90)   ~ (all_52_15 = all_10_2)
% 175.11/26.91    (91)   ~ (all_52_19 = all_52_27)
% 175.11/26.91    (92)  all_56_7 = all_52_15
% 175.11/26.91    (93)  op(e1, all_14_2) = e1
% 175.11/26.91    (94)   ~ (all_52_7 = all_52_23)
% 175.11/26.91    (95)  op(e2, all_52_27) = all_52_26
% 175.11/26.91    (96)   ~ (all_52_17 = all_52_19)
% 175.11/26.91    (97)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.91    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.11/26.91    (99)  all_58_9 = all_52_7
% 175.11/26.91    (100)   ~ (e2 = e0)
% 175.11/26.91    (101)  all_58_12 = all_52_25
% 175.11/26.91    (102)  all_56_6 = all_52_13
% 175.11/26.91    (103)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.91    (104)   ~ (all_52_9 = all_52_15)
% 175.11/26.91    (105)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.11/26.91    (106)   ~ (e3 = e2)
% 175.11/26.91    (107)  op(e2, e3) = all_52_9
% 175.11/26.91    (108)  all_56_13 = all_52_27
% 175.11/26.91  
% 175.11/26.91  Begin of proof
% 175.11/26.91  | 
% 175.11/26.91  | BETA: splitting (39) gives:
% 175.11/26.91  | 
% 175.11/26.91  | Case 1:
% 175.11/26.91  | | 
% 175.11/26.91  | |   (109)  all_56_13 = e3
% 175.11/26.91  | | 
% 175.11/26.91  | | REF_CLOSE: (7), (13), (16), (17), (18), (20), (22), (25), (27), (30), (41),
% 175.11/26.91  | |            (44), (45), (46), (47), (48), (57), (61), (63), (65), (66), (71),
% 175.11/26.91  | |            (73), (74), (75), (78), (80), (82), (85), (86), (87), (88), (89),
% 175.11/26.91  | |            (91), (93), (94), (95), (97), (99), (100), (101), (103), (104),
% 175.11/26.91  | |            (106), (107), (108), (109) are inconsistent by sub-proof #96.
% 175.11/26.91  | | 
% 175.11/26.91  | Case 2:
% 175.11/26.91  | | 
% 175.11/26.91  | |   (110)   ~ (all_56_13 = e3)
% 175.11/26.91  | | 
% 175.11/26.91  | | REDUCE: (108), (110) imply:
% 175.11/26.91  | |   (111)   ~ (all_52_27 = e3)
% 175.11/26.91  | | 
% 175.11/26.91  | | BETA: splitting (43) gives:
% 175.11/26.91  | | 
% 175.11/26.91  | | Case 1:
% 175.11/26.91  | | | 
% 175.11/26.91  | | |   (112)  all_58_12 = e3
% 175.11/26.91  | | | 
% 175.11/26.91  | | | REF_CLOSE: (4), (8), (9), (11), (14), (16), (17), (18), (19), (20), (21),
% 175.11/26.91  | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (32),
% 175.11/26.91  | | |            (35), (36), (37), (42), (44), (45), (48), (49), (50), (51),
% 175.11/26.91  | | |            (52), (53), (54), (56), (57), (58), (59), (60), (61), (62),
% 175.11/26.91  | | |            (63), (64), (65), (66), (67), (68), (70), (73), (74), (75),
% 175.11/26.91  | | |            (76), (77), (78), (79), (80), (81), (83), (85), (86), (87),
% 175.11/26.91  | | |            (89), (90), (92), (93), (94), (96), (97), (99), (100), (101),
% 175.11/26.91  | | |            (102), (103), (104), (105), (107), (112) are inconsistent by
% 175.11/26.91  | | |            sub-proof #677.
% 175.11/26.91  | | | 
% 175.11/26.91  | | Case 2:
% 175.11/26.91  | | | 
% 175.11/26.91  | | |   (113)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.91  | | | 
% 175.11/26.91  | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (12), (13), (15), (16), (17),
% 175.11/26.91  | | |            (18), (20), (22), (23), (25), (27), (28), (30), (31), (33),
% 175.11/26.91  | | |            (34), (36), (38), (40), (41), (42), (44), (45), (48), (55),
% 175.11/26.91  | | |            (56), (57), (60), (61), (62), (63), (65), (66), (69), (71),
% 175.11/26.91  | | |            (72), (73), (74), (78), (80), (82), (84), (85), (86), (89),
% 175.11/26.91  | | |            (93), (94), (97), (98), (99), (101), (102), (103), (104),
% 175.11/26.91  | | |            (106), (107), (111), (113) are inconsistent by sub-proof #95.
% 175.11/26.91  | | | 
% 175.11/26.91  | | End of split
% 175.11/26.91  | | 
% 175.11/26.91  | End of split
% 175.11/26.91  | 
% 175.11/26.91  End of proof
% 175.11/26.91  
% 175.11/26.91  Sub-proof #95 shows that the following formulas are inconsistent:
% 175.11/26.91  ----------------------------------------------------------------
% 175.11/26.91    (1)   ~ (all_52_5 = all_52_13)
% 175.11/26.91    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.11/26.91    (3)   ~ (all_52_17 = all_52_23)
% 175.11/26.91    (4)   ~ (all_52_13 = all_52_29)
% 175.11/26.91    (5)  all_56_3 = all_52_7
% 175.11/26.91    (6)   ~ (all_52_27 = e3)
% 175.11/26.91    (7)   ~ (all_6_2 = e3)
% 175.11/26.91    (8)   ~ (all_52_25 = all_52_29)
% 175.11/26.91    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.11/26.91    (10)  all_56_9 = all_52_19
% 175.11/26.91    (11)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.11/26.91    (12)  all_58_15 = all_6_2
% 175.11/26.91    (13)   ~ (all_52_9 = all_4_2)
% 175.11/26.91    (14)  all_58_10 = all_52_15
% 175.11/26.91    (15)  all_58_7 = all_52_19
% 175.11/26.91    (16)   ~ (all_52_17 = all_52_25)
% 175.11/26.91    (17)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.11/26.91    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.11/26.91    (19)   ~ (all_52_7 = all_4_2)
% 175.11/26.91    (20)  all_58_0 = all_4_2
% 175.11/26.91    (21)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 175.11/26.91    (22)  op(e1, all_52_29) = all_52_28
% 175.11/26.91    (23)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.11/26.91    (24)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.11/26.91    (25)  all_58_14 = all_52_29
% 175.11/26.91    (26)  op(e2, all_4_2) = all_4_0
% 175.11/26.91    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.11/26.91    (28)  op(e2, e1) = all_52_13
% 175.11/26.91    (29)  all_58_8 = all_14_2
% 175.11/26.91    (30)   ~ (all_52_5 = all_14_2)
% 175.11/26.91    (31)  op(e0, e3) = all_52_25
% 175.11/26.91    (32)   ~ (all_52_5 = all_52_29)
% 175.11/26.91    (33)  all_58_13 = all_52_27
% 175.11/26.91    (34)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.11/26.91    (35)   ~ (all_52_9 = all_52_17)
% 175.11/26.91    (36)  all_58_6 = all_52_17
% 175.11/26.91    (37)  op(e2, all_52_19) = e2
% 175.11/26.91    (38)  op(e3, all_52_17) = e3
% 175.11/26.91    (39)  all_56_0 = all_4_2
% 175.11/26.91    (40)  all_58_11 = all_52_23
% 175.11/26.91    (41)   ~ (all_4_0 = e1)
% 175.11/26.91    (42)  op(e3, all_4_2) = e2
% 175.11/26.91    (43)   ~ (all_52_29 = all_6_2)
% 175.11/26.91    (44)  all_58_2 = all_52_9
% 175.11/26.91    (45)  op(e3, e1) = all_52_5
% 175.11/26.91    (46)  op(e1, e3) = all_52_17
% 175.11/26.91    (47)   ~ (all_52_25 = all_4_2)
% 175.11/26.91    (48)  op(e3, e3) = all_4_2
% 175.11/26.91    (49)  all_56_8 = all_52_17
% 175.11/26.91    (50)   ~ (all_52_17 = all_4_2)
% 175.11/26.91    (51)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.11/26.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.11/26.91    (52)  op(e0, all_52_23) = e0
% 175.11/26.91    (53)  op(e1, all_14_2) = e1
% 175.11/26.91    (54)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.11/26.91    (55)   ~ (all_52_7 = all_52_23)
% 175.11/26.91    (56)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.11/26.91    (57)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.11/26.91    (58)  all_58_9 = all_52_7
% 175.11/26.91    (59)  all_58_12 = all_52_25
% 175.11/26.91    (60)  all_56_6 = all_52_13
% 175.11/26.91    (61)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.11/26.91    (62)   ~ (all_52_9 = all_52_15)
% 175.11/26.91    (63)   ~ (e3 = e2)
% 175.11/26.91    (64)  op(e2, e3) = all_52_9
% 175.11/26.91  
% 175.11/26.91  Begin of proof
% 175.11/26.91  | 
% 175.11/26.91  | BETA: splitting (54) gives:
% 175.11/26.91  | 
% 175.11/26.91  | Case 1:
% 175.11/26.91  | | 
% 175.11/26.91  | |   (65)  all_58_13 = e3
% 175.11/26.91  | | 
% 175.11/26.91  | | REF_CLOSE: (6), (33), (65) are inconsistent by sub-proof #1026.
% 175.11/26.91  | | 
% 175.11/26.91  | Case 2:
% 175.11/26.91  | | 
% 175.11/26.91  | |   (66)  all_58_14 = e3 | all_58_15 = e3
% 175.11/26.91  | | 
% 175.11/26.91  | | BETA: splitting (66) gives:
% 175.11/26.91  | | 
% 175.11/26.91  | | Case 1:
% 175.11/26.91  | | | 
% 175.11/26.91  | | |   (67)  all_58_14 = e3
% 175.11/26.91  | | | 
% 175.11/26.91  | | | COMBINE_EQS: (25), (67) imply:
% 175.23/26.91  | | |   (68)  all_52_29 = e3
% 175.23/26.91  | | | 
% 175.23/26.91  | | | SIMP: (68) implies:
% 175.23/26.91  | | |   (69)  all_52_29 = e3
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (32), (69) imply:
% 175.23/26.91  | | |   (70)   ~ (all_52_5 = e3)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (4), (69) imply:
% 175.23/26.91  | | |   (71)   ~ (all_52_13 = e3)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (8), (69) imply:
% 175.23/26.91  | | |   (72)   ~ (all_52_25 = e3)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (43), (69) imply:
% 175.23/26.91  | | |   (73)   ~ (all_6_2 = e3)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (22), (69) imply:
% 175.23/26.91  | | |   (74)  op(e1, e3) = all_52_28
% 175.23/26.91  | | | 
% 175.23/26.91  | | | GROUND_INST: instantiating (51) with all_52_17, all_52_28, e3, e1,
% 175.23/26.91  | | |              simplifying with (46), (74) gives:
% 175.23/26.91  | | |   (75)  all_52_17 = all_52_28
% 175.23/26.91  | | | 
% 175.23/26.91  | | | COMBINE_EQS: (49), (75) imply:
% 175.23/26.91  | | |   (76)  all_56_8 = all_52_28
% 175.23/26.91  | | | 
% 175.23/26.91  | | | COMBINE_EQS: (36), (75) imply:
% 175.23/26.91  | | |   (77)  all_58_6 = all_52_28
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (3), (75) imply:
% 175.23/26.91  | | |   (78)   ~ (all_52_23 = all_52_28)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | SIMP: (78) implies:
% 175.23/26.91  | | |   (79)   ~ (all_52_23 = all_52_28)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (16), (75) imply:
% 175.23/26.91  | | |   (80)   ~ (all_52_25 = all_52_28)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | SIMP: (80) implies:
% 175.23/26.91  | | |   (81)   ~ (all_52_25 = all_52_28)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (50), (75) imply:
% 175.23/26.91  | | |   (82)   ~ (all_52_28 = all_4_2)
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (38), (75) imply:
% 175.23/26.91  | | |   (83)  op(e3, all_52_28) = e3
% 175.23/26.91  | | | 
% 175.23/26.91  | | | BETA: splitting (24) gives:
% 175.23/26.91  | | | 
% 175.23/26.91  | | | Case 1:
% 175.23/26.91  | | | | 
% 175.23/26.91  | | | |   (84)  all_56_6 = e3
% 175.23/26.91  | | | | 
% 175.23/26.91  | | | | REF_CLOSE: (60), (71), (84) are inconsistent by sub-proof #573.
% 175.23/26.91  | | | | 
% 175.23/26.91  | | | Case 2:
% 175.23/26.91  | | | | 
% 175.23/26.91  | | | |   (85)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.23/26.91  | | | | 
% 175.23/26.91  | | | | BETA: splitting (57) gives:
% 175.23/26.91  | | | | 
% 175.23/26.91  | | | | Case 1:
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | |   (86)  all_56_3 = e3
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | | COMBINE_EQS: (5), (86) imply:
% 175.23/26.91  | | | | |   (87)  all_52_7 = e3
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | | SIMP: (87) implies:
% 175.23/26.91  | | | | |   (88)  all_52_7 = e3
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | | REF_CLOSE: (10), (15), (17), (18), (19), (20), (23), (27), (29), (30),
% 175.23/26.91  | | | | |            (35), (36), (37), (38), (40), (44), (45), (46), (48), (50),
% 175.23/26.91  | | | | |            (51), (53), (55), (59), (63), (64), (72), (88) are
% 175.23/26.91  | | | | |            inconsistent by sub-proof #943.
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | Case 2:
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | |   (89)   ~ (all_56_3 = e3)
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | | REDUCE: (5), (89) imply:
% 175.23/26.91  | | | | |   (90)   ~ (all_52_7 = e3)
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | | BETA: splitting (61) gives:
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | | Case 1:
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | |   (91)  all_58_0 = e3
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | | COMBINE_EQS: (20), (91) imply:
% 175.23/26.91  | | | | | |   (92)  all_4_2 = e3
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | | REF_CLOSE: (42), (48), (51), (63), (92) are inconsistent by
% 175.23/26.91  | | | | | |            sub-proof #106.
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | Case 2:
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | |   (93)   ~ (all_58_0 = e3)
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | | REDUCE: (20), (93) imply:
% 175.23/26.91  | | | | | |   (94)   ~ (all_4_2 = e3)
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | | BETA: splitting (27) gives:
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | | Case 1:
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | |   (95)  all_58_0 = e3
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | | COMBINE_EQS: (20), (95) imply:
% 175.23/26.91  | | | | | | |   (96)  all_4_2 = e3
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | | REDUCE: (94), (96) imply:
% 175.23/26.91  | | | | | | |   (97)  $false
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | | CLOSE: (97) is inconsistent.
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | Case 2:
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | |   (98)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | | BETA: splitting (56) gives:
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | 
% 175.23/26.91  | | | | | | | |   (99)  all_58_9 = e3
% 175.23/26.91  | | | | | | | | 
% 175.23/26.91  | | | | | | | | REF_CLOSE: (58), (90), (99) are inconsistent by sub-proof #972.
% 175.23/26.91  | | | | | | | | 
% 175.23/26.91  | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | 
% 175.23/26.91  | | | | | | | |   (100)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.23/26.91  | | | | | | | | 
% 175.23/26.91  | | | | | | | | BETA: splitting (17) gives:
% 175.23/26.91  | | | | | | | | 
% 175.23/26.91  | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | |   (101)  all_58_6 = e3
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | COMBINE_EQS: (77), (101) imply:
% 175.23/26.91  | | | | | | | | |   (102)  all_52_28 = e3
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | SIMP: (102) implies:
% 175.23/26.91  | | | | | | | | |   (103)  all_52_28 = e3
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | REF_CLOSE: (48), (51), (82), (83), (103) are inconsistent by
% 175.23/26.91  | | | | | | | | |            sub-proof #902.
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | |   (104)   ~ (all_58_6 = e3)
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | REDUCE: (77), (104) imply:
% 175.23/26.91  | | | | | | | | |   (105)   ~ (all_52_28 = e3)
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | BETA: splitting (98) gives:
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | |   (106)  all_58_2 = e3
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | COMBINE_EQS: (44), (106) imply:
% 175.23/26.91  | | | | | | | | | |   (107)  all_52_9 = e3
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | SIMP: (107) implies:
% 175.23/26.91  | | | | | | | | | |   (108)  all_52_9 = e3
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | REDUCE: (62), (108) imply:
% 175.23/26.91  | | | | | | | | | |   (109)   ~ (all_52_15 = e3)
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | SIMP: (109) implies:
% 175.23/26.91  | | | | | | | | | |   (110)   ~ (all_52_15 = e3)
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | REDUCE: (13), (108) imply:
% 175.23/26.91  | | | | | | | | | |   (111)   ~ (all_4_2 = e3)
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | BETA: splitting (100) gives:
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | |   (112)  all_58_10 = e3
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | REF_CLOSE: (14), (110), (112) are inconsistent by sub-proof
% 175.23/26.91  | | | | | | | | | | |            #1018.
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | |   (113)  all_58_11 = e3 | all_58_15 = e3
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | BETA: splitting (113) gives:
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | |   (114)  all_58_11 = e3
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | COMBINE_EQS: (40), (114) imply:
% 175.23/26.91  | | | | | | | | | | | |   (115)  all_52_23 = e3
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | SIMP: (115) implies:
% 175.23/26.91  | | | | | | | | | | | |   (116)  all_52_23 = e3
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | REDUCE: (79), (116) imply:
% 175.23/26.91  | | | | | | | | | | | |   (117)   ~ (all_52_28 = e3)
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | REDUCE: (52), (116) imply:
% 175.23/26.91  | | | | | | | | | | | |   (118)  op(e0, e3) = e0
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | GROUND_INST: instantiating (51) with all_52_25, e0, e3, e0,
% 175.23/26.91  | | | | | | | | | | | |              simplifying with (31), (118) gives:
% 175.23/26.91  | | | | | | | | | | | |   (119)  all_52_25 = e0
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | REDUCE: (81), (119) imply:
% 175.23/26.91  | | | | | | | | | | | |   (120)   ~ (all_52_28 = e0)
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | SIMP: (120) implies:
% 175.23/26.91  | | | | | | | | | | | |   (121)   ~ (all_52_28 = e0)
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | REDUCE: (47), (119) imply:
% 175.23/26.91  | | | | | | | | | | | |   (122)   ~ (all_4_2 = e0)
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | SIMP: (122) implies:
% 175.23/26.91  | | | | | | | | | | | |   (123)   ~ (all_4_2 = e0)
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | BETA: splitting (11) gives:
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | |   (124)  all_56_0 = e3
% 175.23/26.91  | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | REF_CLOSE: (39), (94), (124) are inconsistent by sub-proof
% 175.23/26.91  | | | | | | | | | | | | |            #1024.
% 175.23/26.91  | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | |   (125)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.91  | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | BETA: splitting (2) gives:
% 175.23/26.91  | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | |   (126)  all_56_8 = e3
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | COMBINE_EQS: (76), (126) imply:
% 175.23/26.91  | | | | | | | | | | | | | |   (127)  all_52_28 = e3
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | REDUCE: (105), (127) imply:
% 175.23/26.91  | | | | | | | | | | | | | |   (128)  $false
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | CLOSE: (128) is inconsistent.
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | |   (129)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | |   (130)  all_58_0 = e2
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | | COMBINE_EQS: (20), (130) imply:
% 175.23/26.91  | | | | | | | | | | | | | | |   (131)  all_4_2 = e2
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | | REDUCE: (82), (131) imply:
% 175.23/26.91  | | | | | | | | | | | | | | |   (132)   ~ (all_52_28 = e2)
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | | REF_CLOSE: (45), (51), (70), (76), (83), (121), (129), (132)
% 175.23/26.91  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #903.
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | |   (133)   ~ (all_58_0 = e2)
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | | REF_CLOSE: (1), (20), (21), (26), (28), (34), (39), (41),
% 175.23/26.91  | | | | | | | | | | | | | | |            (42), (45), (51), (60), (85), (123), (125), (133)
% 175.23/26.91  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #99.
% 175.23/26.91  | | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | |   (134)  all_58_15 = e3
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | COMBINE_EQS: (12), (134) imply:
% 175.23/26.91  | | | | | | | | | | | |   (135)  all_6_2 = e3
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | REDUCE: (7), (135) imply:
% 175.23/26.91  | | | | | | | | | | | |   (136)  $false
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 175.23/26.91  | | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | |   (137)  all_58_6 = e3 | all_58_12 = e3
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | BETA: splitting (137) gives:
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | Case 1:
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | |   (138)  all_58_6 = e3
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | REF_CLOSE: (77), (105), (138) are inconsistent by sub-proof
% 175.23/26.91  | | | | | | | | | | |            #790.
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | Case 2:
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | |   (139)  all_58_12 = e3
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | | REF_CLOSE: (59), (72), (139) are inconsistent by sub-proof
% 175.23/26.91  | | | | | | | | | | |            #1003.
% 175.23/26.91  | | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | | | 
% 175.23/26.91  | | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | | 
% 175.23/26.91  | | | | | | | | End of split
% 175.23/26.91  | | | | | | | | 
% 175.23/26.91  | | | | | | | End of split
% 175.23/26.91  | | | | | | | 
% 175.23/26.91  | | | | | | End of split
% 175.23/26.91  | | | | | | 
% 175.23/26.91  | | | | | End of split
% 175.23/26.91  | | | | | 
% 175.23/26.91  | | | | End of split
% 175.23/26.91  | | | | 
% 175.23/26.91  | | | End of split
% 175.23/26.91  | | | 
% 175.23/26.91  | | Case 2:
% 175.23/26.91  | | | 
% 175.23/26.91  | | |   (140)  all_58_15 = e3
% 175.23/26.91  | | | 
% 175.23/26.91  | | | COMBINE_EQS: (12), (140) imply:
% 175.23/26.91  | | |   (141)  all_6_2 = e3
% 175.23/26.91  | | | 
% 175.23/26.91  | | | REDUCE: (7), (141) imply:
% 175.23/26.91  | | |   (142)  $false
% 175.23/26.91  | | | 
% 175.23/26.91  | | | CLOSE: (142) is inconsistent.
% 175.23/26.91  | | | 
% 175.23/26.91  | | End of split
% 175.23/26.91  | | 
% 175.23/26.91  | End of split
% 175.23/26.91  | 
% 175.23/26.91  End of proof
% 175.23/26.91  
% 175.23/26.91  Sub-proof #96 shows that the following formulas are inconsistent:
% 175.23/26.91  ----------------------------------------------------------------
% 175.23/26.91    (1)  op(e3, e2) = all_52_3
% 175.23/26.91    (2)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.23/26.91    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.91    (4)  all_58_15 = all_6_2
% 175.23/26.91    (5)   ~ (all_52_9 = all_4_2)
% 175.23/26.91    (6)  all_58_10 = all_52_15
% 175.23/26.91    (7)  all_58_7 = all_52_19
% 175.23/26.91    (8)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.23/26.91    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.23/26.91    (10)  all_58_0 = all_4_2
% 175.23/26.91    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.23/26.91    (12)  all_58_8 = all_14_2
% 175.23/26.91    (13)   ~ (all_52_5 = all_14_2)
% 175.23/26.91    (14)   ~ (all_52_3 = all_52_27)
% 175.23/26.91    (15)   ~ (all_52_3 = all_4_2)
% 175.23/26.91    (16)  op(e0, e3) = all_52_25
% 175.23/26.91    (17)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.23/26.91    (18)  all_58_6 = all_52_17
% 175.23/26.91    (19)  op(e3, all_52_17) = e3
% 175.23/26.91    (20)  all_56_0 = all_4_2
% 175.23/26.91    (21)  all_58_11 = all_52_23
% 175.23/26.91    (22)  op(e3, all_4_2) = e2
% 175.23/26.91    (23)  all_58_2 = all_52_9
% 175.23/26.91    (24)  op(e3, e1) = all_52_5
% 175.23/26.91    (25)   ~ (e2 = e1)
% 175.23/26.91    (26)  op(e1, e3) = all_52_17
% 175.23/26.91    (27)   ~ (all_52_25 = all_4_2)
% 175.23/26.91    (28)  op(e3, e3) = all_4_2
% 175.23/26.91    (29)   ~ (all_52_17 = all_4_2)
% 175.23/26.91    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.23/26.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.23/26.91    (31)   ~ (all_52_25 = all_52_27)
% 175.23/26.91    (32)  all_56_13 = e3
% 175.23/26.91    (33)   ~ (all_52_27 = all_6_2)
% 175.23/26.91    (34)  op(e0, all_52_23) = e0
% 175.23/26.91    (35)   ~ (all_52_19 = all_52_27)
% 175.23/26.91    (36)  op(e1, all_14_2) = e1
% 175.23/26.91    (37)   ~ (all_52_7 = all_52_23)
% 175.23/26.91    (38)  op(e2, all_52_27) = all_52_26
% 175.23/26.91    (39)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.23/26.91    (40)  all_58_9 = all_52_7
% 175.23/26.91    (41)   ~ (e2 = e0)
% 175.23/26.91    (42)  all_58_12 = all_52_25
% 175.23/26.91    (43)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.23/26.91    (44)   ~ (all_52_9 = all_52_15)
% 175.23/26.91    (45)   ~ (e3 = e2)
% 175.23/26.91    (46)  op(e2, e3) = all_52_9
% 175.23/26.91    (47)  all_56_13 = all_52_27
% 175.23/26.91  
% 175.23/26.91  Begin of proof
% 175.23/26.91  | 
% 175.23/26.91  | COMBINE_EQS: (32), (47) imply:
% 175.23/26.91  |   (48)  all_52_27 = e3
% 175.23/26.91  | 
% 175.23/26.91  | SIMP: (48) implies:
% 175.23/26.91  |   (49)  all_52_27 = e3
% 175.23/26.91  | 
% 175.23/26.91  | REDUCE: (14), (49) imply:
% 175.23/26.91  |   (50)   ~ (all_52_3 = e3)
% 175.23/26.91  | 
% 175.23/26.91  | REDUCE: (35), (49) imply:
% 175.23/26.91  |   (51)   ~ (all_52_19 = e3)
% 175.23/26.91  | 
% 175.23/26.91  | REDUCE: (31), (49) imply:
% 175.23/26.91  |   (52)   ~ (all_52_25 = e3)
% 175.23/26.91  | 
% 175.23/26.91  | REDUCE: (33), (49) imply:
% 175.23/26.91  |   (53)   ~ (all_6_2 = e3)
% 175.23/26.91  | 
% 175.23/26.91  | SIMP: (53) implies:
% 175.23/26.91  |   (54)   ~ (all_6_2 = e3)
% 175.23/26.91  | 
% 175.23/26.91  | REDUCE: (38), (49) imply:
% 175.23/26.91  |   (55)  op(e2, e3) = all_52_26
% 175.23/26.91  | 
% 175.23/26.91  | GROUND_INST: instantiating (30) with all_52_9, all_52_26, e3, e2, simplifying
% 175.23/26.91  |              with (46), (55) gives:
% 175.23/26.91  |   (56)  all_52_9 = all_52_26
% 175.23/26.91  | 
% 175.23/26.91  | COMBINE_EQS: (23), (56) imply:
% 175.23/26.91  |   (57)  all_58_2 = all_52_26
% 175.23/26.91  | 
% 175.23/26.91  | REDUCE: (44), (56) imply:
% 175.23/26.91  |   (58)   ~ (all_52_15 = all_52_26)
% 175.23/26.91  | 
% 175.23/26.91  | SIMP: (58) implies:
% 175.23/26.91  |   (59)   ~ (all_52_15 = all_52_26)
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (5), (56) imply:
% 175.23/26.92  |   (60)   ~ (all_52_26 = all_4_2)
% 175.23/26.92  | 
% 175.23/26.92  | BETA: splitting (39) gives:
% 175.23/26.92  | 
% 175.23/26.92  | Case 1:
% 175.23/26.92  | | 
% 175.23/26.92  | |   (61)  all_58_9 = e3
% 175.23/26.92  | | 
% 175.23/26.92  | | COMBINE_EQS: (40), (61) imply:
% 175.23/26.92  | |   (62)  all_52_7 = e3
% 175.23/26.92  | | 
% 175.23/26.92  | | SIMP: (62) implies:
% 175.23/26.92  | |   (63)  all_52_7 = e3
% 175.23/26.92  | | 
% 175.23/26.92  | | REDUCE: (37), (63) imply:
% 175.23/26.92  | |   (64)   ~ (all_52_23 = e3)
% 175.23/26.92  | | 
% 175.23/26.92  | | SIMP: (64) implies:
% 175.23/26.92  | |   (65)   ~ (all_52_23 = e3)
% 175.23/26.92  | | 
% 175.23/26.92  | | REF_CLOSE: (7), (8), (12), (13), (18), (19), (21), (24), (26), (28), (29),
% 175.23/26.92  | |            (30), (36), (51), (65) are inconsistent by sub-proof #702.
% 175.23/26.92  | | 
% 175.23/26.92  | Case 2:
% 175.23/26.92  | | 
% 175.23/26.92  | |   (66)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.23/26.92  | | 
% 175.23/26.92  | | BETA: splitting (43) gives:
% 175.23/26.92  | | 
% 175.23/26.92  | | Case 1:
% 175.23/26.92  | | | 
% 175.23/26.92  | | |   (67)  all_58_0 = e3
% 175.23/26.92  | | | 
% 175.23/26.92  | | | COMBINE_EQS: (10), (67) imply:
% 175.23/26.92  | | |   (68)  all_4_2 = e3
% 175.23/26.92  | | | 
% 175.23/26.92  | | | REF_CLOSE: (22), (28), (30), (45), (68) are inconsistent by sub-proof
% 175.23/26.92  | | |            #106.
% 175.23/26.92  | | | 
% 175.23/26.92  | | Case 2:
% 175.23/26.92  | | | 
% 175.23/26.92  | | |   (69)   ~ (all_58_0 = e3)
% 175.23/26.92  | | | 
% 175.23/26.92  | | | REDUCE: (10), (69) imply:
% 175.23/26.92  | | |   (70)   ~ (all_4_2 = e3)
% 175.23/26.92  | | | 
% 175.23/26.92  | | | BETA: splitting (11) gives:
% 175.23/26.92  | | | 
% 175.23/26.92  | | | Case 1:
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | |   (71)  all_58_0 = e3
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | | COMBINE_EQS: (10), (71) imply:
% 175.23/26.92  | | | |   (72)  all_4_2 = e3
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | | REDUCE: (70), (72) imply:
% 175.23/26.92  | | | |   (73)  $false
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | | CLOSE: (73) is inconsistent.
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | Case 2:
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | |   (74)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | | BETA: splitting (9) gives:
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | | Case 1:
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | |   (75)  all_58_2 = e3
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | COMBINE_EQS: (57), (75) imply:
% 175.23/26.92  | | | | |   (76)  all_52_26 = e3
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | SIMP: (76) implies:
% 175.23/26.92  | | | | |   (77)  all_52_26 = e3
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | REDUCE: (59), (77) imply:
% 175.23/26.92  | | | | |   (78)   ~ (all_52_15 = e3)
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | REDUCE: (60), (77) imply:
% 175.23/26.92  | | | | |   (79)   ~ (all_4_2 = e3)
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | BETA: splitting (66) gives:
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | Case 1:
% 175.23/26.92  | | | | | | 
% 175.23/26.92  | | | | | |   (80)  all_58_10 = e3
% 175.23/26.92  | | | | | | 
% 175.23/26.92  | | | | | | REF_CLOSE: (6), (78), (80) are inconsistent by sub-proof #1018.
% 175.23/26.92  | | | | | | 
% 175.23/26.92  | | | | | Case 2:
% 175.23/26.92  | | | | | | 
% 175.23/26.92  | | | | | |   (81)  all_58_11 = e3 | all_58_15 = e3
% 175.23/26.92  | | | | | | 
% 175.23/26.92  | | | | | | BETA: splitting (81) gives:
% 175.23/26.92  | | | | | | 
% 175.23/26.92  | | | | | | Case 1:
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | |   (82)  all_58_11 = e3
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | COMBINE_EQS: (21), (82) imply:
% 175.23/26.92  | | | | | | |   (83)  all_52_23 = e3
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | SIMP: (83) implies:
% 175.23/26.92  | | | | | | |   (84)  all_52_23 = e3
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | REDUCE: (34), (84) imply:
% 175.23/26.92  | | | | | | |   (85)  op(e0, e3) = e0
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | GROUND_INST: instantiating (30) with all_52_25, e0, e3, e0,
% 175.23/26.92  | | | | | | |              simplifying with (16), (85) gives:
% 175.23/26.92  | | | | | | |   (86)  all_52_25 = e0
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | COMBINE_EQS: (42), (86) imply:
% 175.23/26.92  | | | | | | |   (87)  all_58_12 = e0
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | REDUCE: (27), (86) imply:
% 175.23/26.92  | | | | | | |   (88)   ~ (all_4_2 = e0)
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | SIMP: (88) implies:
% 175.23/26.92  | | | | | | |   (89)   ~ (all_4_2 = e0)
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | BETA: splitting (3) gives:
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | Case 1:
% 175.23/26.92  | | | | | | | | 
% 175.23/26.92  | | | | | | | |   (90)  all_56_0 = e3
% 175.23/26.92  | | | | | | | | 
% 175.23/26.92  | | | | | | | | REF_CLOSE: (20), (70), (90) are inconsistent by sub-proof #1024.
% 175.23/26.92  | | | | | | | | 
% 175.23/26.92  | | | | | | | Case 2:
% 175.23/26.92  | | | | | | | | 
% 175.23/26.92  | | | | | | | |   (91)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.92  | | | | | | | | 
% 175.23/26.92  | | | | | | | | BETA: splitting (17) gives:
% 175.23/26.92  | | | | | | | | 
% 175.23/26.92  | | | | | | | | Case 1:
% 175.23/26.92  | | | | | | | | | 
% 175.23/26.92  | | | | | | | | |   (92)  all_58_0 = e1
% 175.23/26.92  | | | | | | | | | 
% 175.23/26.92  | | | | | | | | | REF_CLOSE: (1), (2), (18), (19), (25), (30), (41), (45), (50),
% 175.23/26.92  | | | | | | | | |            (75), (87), (92) are inconsistent by sub-proof
% 175.23/26.92  | | | | | | | | |            #692.
% 175.23/26.92  | | | | | | | | | 
% 175.23/26.92  | | | | | | | | Case 2:
% 175.23/26.92  | | | | | | | | | 
% 175.23/26.92  | | | | | | | | |   (93)   ~ (all_58_0 = e1)
% 175.23/26.92  | | | | | | | | | 
% 175.23/26.92  | | | | | | | | | REDUCE: (10), (93) imply:
% 175.23/26.92  | | | | | | | | |   (94)   ~ (all_4_2 = e1)
% 175.23/26.92  | | | | | | | | | 
% 175.23/26.92  | | | | | | | | | REF_CLOSE: (1), (2), (10), (15), (20), (22), (30), (89), (91),
% 175.23/26.92  | | | | | | | | |            (94) are inconsistent by sub-proof #114.
% 175.23/26.92  | | | | | | | | | 
% 175.23/26.92  | | | | | | | | End of split
% 175.23/26.92  | | | | | | | | 
% 175.23/26.92  | | | | | | | End of split
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | Case 2:
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | |   (95)  all_58_15 = e3
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | COMBINE_EQS: (4), (95) imply:
% 175.23/26.92  | | | | | | |   (96)  all_6_2 = e3
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | REDUCE: (54), (96) imply:
% 175.23/26.92  | | | | | | |   (97)  $false
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | | CLOSE: (97) is inconsistent.
% 175.23/26.92  | | | | | | | 
% 175.23/26.92  | | | | | | End of split
% 175.23/26.92  | | | | | | 
% 175.23/26.92  | | | | | End of split
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | Case 2:
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | |   (98)   ~ (all_58_2 = e3)
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | REDUCE: (57), (98) imply:
% 175.23/26.92  | | | | |   (99)   ~ (all_52_26 = e3)
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | | REF_CLOSE: (18), (19), (28), (29), (30), (42), (52), (57), (74), (99)
% 175.23/26.92  | | | | |            are inconsistent by sub-proof #567.
% 175.23/26.92  | | | | | 
% 175.23/26.92  | | | | End of split
% 175.23/26.92  | | | | 
% 175.23/26.92  | | | End of split
% 175.23/26.92  | | | 
% 175.23/26.92  | | End of split
% 175.23/26.92  | | 
% 175.23/26.92  | End of split
% 175.23/26.92  | 
% 175.23/26.92  End of proof
% 175.23/26.92  
% 175.23/26.92  Sub-proof #97 shows that the following formulas are inconsistent:
% 175.23/26.92  ----------------------------------------------------------------
% 175.23/26.92    (1)   ~ (all_52_23 = all_14_2)
% 175.23/26.92    (2)   ~ (all_52_5 = all_52_13)
% 175.23/26.92    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.23/26.92    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.23/26.92    (5)   ~ (all_52_27 = all_10_2)
% 175.23/26.92    (6)   ~ (all_52_17 = all_52_23)
% 175.23/26.92    (7)  op(e2, all_10_2) = all_10_1
% 175.23/26.92    (8)   ~ (all_52_13 = all_52_29)
% 175.23/26.92    (9)  all_56_3 = all_52_7
% 175.23/26.92    (10)  op(e3, e2) = all_52_3
% 175.23/26.92    (11)   ~ (all_52_9 = all_52_25)
% 175.23/26.92    (12)   ~ (all_52_19 = all_52_23)
% 175.23/26.92    (13)  all_56_11 = all_52_23
% 175.23/26.92    (14)  op(e1, e2) = all_52_19
% 175.23/26.92    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.23/26.92    (16)  op(e3, all_52_9) = all_52_8
% 175.23/26.92    (17)   ~ (all_52_3 = all_10_2)
% 175.23/26.92    (18)  all_58_5 = all_52_13
% 175.23/26.92    (19)   ~ (all_6_2 = e0)
% 175.23/26.92    (20)   ~ (all_52_25 = all_52_29)
% 175.23/26.92    (21)  all_56_15 = all_6_2
% 175.23/26.92    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.23/26.92    (23)  all_58_3 = all_10_2
% 175.23/26.92    (24)  all_56_9 = all_52_19
% 175.23/26.92    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.92    (26)  all_58_15 = all_6_2
% 175.23/26.92    (27)  all_52_12 = e1
% 175.23/26.92    (28)   ~ (all_52_9 = all_4_2)
% 175.23/26.92    (29)   ~ (all_52_5 = all_52_7)
% 175.23/26.92    (30)  all_58_10 = all_52_15
% 175.23/26.92    (31)   ~ (all_52_5 = all_4_2)
% 175.23/26.92    (32)  all_58_7 = all_52_19
% 175.23/26.92    (33)  all_56_4 = all_52_9
% 175.23/26.92    (34)   ~ (all_52_15 = all_6_2)
% 175.23/26.92    (35)   ~ (all_52_17 = all_52_25)
% 175.23/26.92    (36)  op(e0, e1) = all_52_29
% 175.23/26.92    (37)  all_58_4 = all_52_5
% 175.23/26.92    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.23/26.92    (39)   ~ (e3 = e1)
% 175.23/26.92    (40)  all_52_14 = e0
% 175.23/26.92    (41)   ~ (all_52_27 = all_52_29)
% 175.23/26.92    (42)   ~ (all_52_17 = all_14_2)
% 175.23/26.92    (43)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.23/26.92    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.23/26.92    (45)   ~ (all_52_7 = all_4_2)
% 175.23/26.92    (46)  all_58_1 = all_52_3
% 175.23/26.92    (47)   ~ (all_52_13 = all_52_15)
% 175.23/26.92    (48)  all_58_0 = all_4_2
% 175.23/26.92    (49)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 175.23/26.92    (50)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.23/26.92    (51)  op(e1, all_52_13) = all_52_12
% 175.23/26.92    (52)  op(e1, all_52_29) = all_52_28
% 175.23/26.92    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.23/26.92    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.23/26.92    (55)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.23/26.92    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.23/26.92    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.23/26.92    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.23/26.92    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.23/26.92    (60)  all_58_14 = all_52_29
% 175.23/26.92    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.23/26.92    (62)  op(e2, all_4_2) = all_4_0
% 175.23/26.92    (63)   ~ (all_52_3 = all_52_5)
% 175.23/26.92    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.23/26.92    (65)  op(e2, e1) = all_52_13
% 175.23/26.92    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.23/26.92    (67)  all_58_8 = all_14_2
% 175.23/26.92    (68)  all_56_1 = all_52_3
% 175.23/26.92    (69)  all_56_14 = all_52_29
% 175.23/26.92    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.23/26.92    (71)   ~ (all_52_3 = all_52_27)
% 175.23/26.92    (72)   ~ (all_52_3 = all_4_2)
% 175.23/26.92    (73)  op(e0, e3) = all_52_25
% 175.23/26.92    (74)  op(e0, all_6_2) = all_6_1
% 175.23/26.92    (75)  op(e3, all_52_17) = all_52_16
% 175.23/26.92    (76)   ~ (all_52_13 = all_14_2)
% 175.23/26.92    (77)   ~ (e3 = e0)
% 175.23/26.92    (78)   ~ (all_52_9 = all_52_13)
% 175.23/26.92    (79)  op(e0, all_52_23) = all_52_22
% 175.23/26.92    (80)   ~ (all_52_15 = all_52_23)
% 175.23/26.92    (81)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.23/26.92    (82)  op(all_10_1, all_10_2) = all_10_0
% 175.23/26.92    (83)   ~ (all_52_5 = all_52_29)
% 175.23/26.92    (84)  all_58_13 = all_52_27
% 175.23/26.92    (85)  all_52_8 = e3
% 175.23/26.92    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.23/26.92    (87)   ~ (all_52_9 = all_52_17)
% 175.23/26.92    (88)  all_58_6 = all_52_17
% 175.23/26.92    (89)   ~ (all_52_3 = all_52_7)
% 175.23/26.92    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.23/26.92    (91)  op(e2, all_52_19) = all_52_18
% 175.23/26.92    (92)   ~ (e1 = e0)
% 175.23/26.92    (93)  all_56_0 = all_4_2
% 175.23/26.92    (94)  all_58_11 = all_52_23
% 175.23/26.92    (95)   ~ (all_52_3 = all_52_19)
% 175.23/26.92    (96)   ~ (all_52_7 = all_52_15)
% 175.23/26.92    (97)  op(e0, all_52_15) = all_52_14
% 175.23/26.92    (98)   ~ (all_52_29 = all_14_2)
% 175.23/26.92    (99)   ~ (all_4_0 = e1)
% 175.23/26.92    (100)   ~ (all_52_19 = all_10_2)
% 175.23/26.92    (101)  op(e3, all_4_2) = e2
% 175.23/26.92    (102)   ~ (all_52_23 = all_6_2)
% 175.23/26.92    (103)   ~ (all_52_29 = all_6_2)
% 175.23/26.92    (104)  all_58_2 = all_52_9
% 175.23/26.92    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.23/26.92    (106)  op(e3, e1) = all_52_5
% 175.23/26.92    (107)  all_56_10 = all_14_2
% 175.23/26.92    (108)   ~ (all_52_25 = all_6_2)
% 175.23/26.92    (109)  op(e1, e3) = all_52_17
% 175.23/26.92    (110)   ~ (all_52_25 = all_4_2)
% 175.23/26.92    (111)  op(e3, e0) = all_52_7
% 175.23/26.92    (112)  op(e3, e3) = all_4_2
% 175.23/26.92    (113)  all_56_8 = all_52_17
% 175.23/26.92    (114)   ~ (all_52_17 = all_4_2)
% 175.23/26.92    (115)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.23/26.92             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.23/26.92    (116)   ~ (all_52_25 = all_52_27)
% 175.23/26.92    (117)   ~ (all_52_27 = all_6_2)
% 175.23/26.92    (118)   ~ (all_52_7 = all_6_2)
% 175.23/26.92    (119)   ~ (all_10_0 = e3)
% 175.23/26.92    (120)  all_10_1 = e2
% 175.23/26.92    (121)   ~ (all_52_7 = all_52_23)
% 175.23/26.92    (122)   ~ (all_52_13 = all_10_2)
% 175.23/26.92    (123)  op(e2, all_52_27) = all_52_26
% 175.23/26.92    (124)   ~ (all_52_17 = all_52_19)
% 175.23/26.92    (125)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.23/26.92    (126)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.23/26.92    (127)  op(e1, all_14_2) = all_14_1
% 175.23/26.92    (128)  all_58_9 = all_52_7
% 175.23/26.92    (129)  all_58_12 = all_52_25
% 175.23/26.92    (130)   ~ (all_10_0 = e1)
% 175.23/26.92    (131)  all_56_6 = all_52_13
% 175.23/26.92    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.23/26.92    (133)   ~ (all_52_9 = all_52_15)
% 175.23/26.92    (134)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.23/26.92    (135)   ~ (all_52_19 = all_14_2)
% 175.23/26.92    (136)  op(e2, e3) = all_52_9
% 175.23/26.92    (137)  all_56_13 = all_52_27
% 175.23/26.92  
% 175.23/26.92  Begin of proof
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (82), (120) imply:
% 175.23/26.92  |   (138)  op(e2, all_10_2) = all_10_0
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (16), (85) imply:
% 175.23/26.92  |   (139)  op(e3, all_52_9) = e3
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (7), (120) imply:
% 175.23/26.92  |   (140)  op(e2, all_10_2) = e2
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (27), (51) imply:
% 175.23/26.92  |   (141)  op(e1, all_52_13) = e1
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (40), (97) imply:
% 175.23/26.92  |   (142)  op(e0, all_52_15) = e0
% 175.23/26.92  | 
% 175.23/26.92  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 175.23/26.92  |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 175.23/26.92  |            (26), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 175.23/26.92  |            (38), (39), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 175.23/26.92  |            (50), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 175.23/26.92  |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 175.23/26.92  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (83), (84),
% 175.23/26.92  |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 175.23/26.92  |            (98), (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 175.23/26.92  |            (108), (109), (110), (111), (112), (113), (114), (115), (116),
% 175.23/26.92  |            (117), (118), (119), (121), (122), (123), (124), (125), (126),
% 175.23/26.92  |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 175.23/26.92  |            (136), (137), (138), (139), (140), (141), (142) are inconsistent by
% 175.23/26.92  |            sub-proof #98.
% 175.23/26.92  | 
% 175.23/26.92  End of proof
% 175.23/26.92  
% 175.23/26.92  Sub-proof #98 shows that the following formulas are inconsistent:
% 175.23/26.92  ----------------------------------------------------------------
% 175.23/26.92    (1)   ~ (all_52_23 = all_14_2)
% 175.23/26.92    (2)   ~ (all_52_5 = all_52_13)
% 175.23/26.92    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.23/26.92    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.23/26.92    (5)   ~ (all_52_27 = all_10_2)
% 175.23/26.92    (6)   ~ (all_52_17 = all_52_23)
% 175.23/26.92    (7)   ~ (all_52_13 = all_52_29)
% 175.23/26.92    (8)  op(e2, all_10_2) = all_10_0
% 175.23/26.92    (9)  all_56_3 = all_52_7
% 175.23/26.92    (10)  op(e3, e2) = all_52_3
% 175.23/26.92    (11)   ~ (all_52_9 = all_52_25)
% 175.23/26.92    (12)   ~ (all_52_19 = all_52_23)
% 175.23/26.92    (13)  all_56_11 = all_52_23
% 175.23/26.92    (14)  op(e1, e2) = all_52_19
% 175.23/26.92    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.23/26.92    (16)   ~ (all_52_3 = all_10_2)
% 175.23/26.92    (17)  all_58_5 = all_52_13
% 175.23/26.92    (18)   ~ (all_6_2 = e0)
% 175.23/26.92    (19)   ~ (all_52_25 = all_52_29)
% 175.23/26.92    (20)  op(e1, all_52_13) = e1
% 175.23/26.92    (21)  op(e0, all_52_15) = e0
% 175.23/26.92    (22)  all_56_15 = all_6_2
% 175.23/26.92    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.23/26.92    (24)  all_58_3 = all_10_2
% 175.23/26.92    (25)  all_56_9 = all_52_19
% 175.23/26.92    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.92    (27)  all_58_15 = all_6_2
% 175.23/26.92    (28)   ~ (all_52_9 = all_4_2)
% 175.23/26.92    (29)   ~ (all_52_5 = all_52_7)
% 175.23/26.92    (30)  all_58_10 = all_52_15
% 175.23/26.92    (31)   ~ (all_52_5 = all_4_2)
% 175.23/26.92    (32)  all_58_7 = all_52_19
% 175.23/26.92    (33)  all_56_4 = all_52_9
% 175.23/26.92    (34)   ~ (all_52_15 = all_6_2)
% 175.23/26.92    (35)   ~ (all_52_17 = all_52_25)
% 175.23/26.92    (36)  op(e0, e1) = all_52_29
% 175.23/26.92    (37)  all_58_4 = all_52_5
% 175.23/26.92    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.23/26.92    (39)   ~ (e3 = e1)
% 175.23/26.92    (40)   ~ (all_52_27 = all_52_29)
% 175.23/26.92    (41)   ~ (all_52_17 = all_14_2)
% 175.23/26.92    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.23/26.92    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.23/26.92    (44)   ~ (all_52_7 = all_4_2)
% 175.23/26.92    (45)  all_58_1 = all_52_3
% 175.23/26.92    (46)   ~ (all_52_13 = all_52_15)
% 175.23/26.92    (47)  all_58_0 = all_4_2
% 175.23/26.92    (48)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 175.23/26.92    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.23/26.92    (50)  op(e1, all_52_29) = all_52_28
% 175.23/26.92    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.23/26.92    (52)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.23/26.92    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.23/26.92    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.23/26.92    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.23/26.92    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.23/26.92    (57)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.23/26.92    (58)  all_58_14 = all_52_29
% 175.23/26.92    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.23/26.92    (60)  op(e2, all_4_2) = all_4_0
% 175.23/26.92    (61)   ~ (all_52_3 = all_52_5)
% 175.23/26.92    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.23/26.92    (63)  op(e2, e1) = all_52_13
% 175.23/26.92    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.23/26.92    (65)  all_58_8 = all_14_2
% 175.23/26.92    (66)  all_56_1 = all_52_3
% 175.23/26.92    (67)  all_56_14 = all_52_29
% 175.23/26.92    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.23/26.92    (69)   ~ (all_52_3 = all_52_27)
% 175.23/26.92    (70)   ~ (all_52_3 = all_4_2)
% 175.23/26.92    (71)  op(e0, e3) = all_52_25
% 175.23/26.92    (72)  op(e0, all_6_2) = all_6_1
% 175.23/26.92    (73)  op(e3, all_52_17) = all_52_16
% 175.23/26.92    (74)   ~ (all_52_13 = all_14_2)
% 175.23/26.92    (75)  op(e3, all_52_9) = e3
% 175.23/26.92    (76)   ~ (e3 = e0)
% 175.23/26.92    (77)   ~ (all_52_9 = all_52_13)
% 175.23/26.92    (78)  op(e0, all_52_23) = all_52_22
% 175.23/26.92    (79)   ~ (all_52_15 = all_52_23)
% 175.23/26.92    (80)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.23/26.92    (81)   ~ (all_52_5 = all_52_29)
% 175.23/26.92    (82)  all_58_13 = all_52_27
% 175.23/26.92    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.23/26.92    (84)   ~ (all_52_9 = all_52_17)
% 175.23/26.92    (85)  all_58_6 = all_52_17
% 175.23/26.92    (86)   ~ (all_52_3 = all_52_7)
% 175.23/26.92    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.23/26.92    (88)  op(e2, all_52_19) = all_52_18
% 175.23/26.92    (89)   ~ (e1 = e0)
% 175.23/26.92    (90)  all_56_0 = all_4_2
% 175.23/26.92    (91)  all_58_11 = all_52_23
% 175.23/26.92    (92)   ~ (all_52_3 = all_52_19)
% 175.23/26.92    (93)   ~ (all_52_7 = all_52_15)
% 175.23/26.92    (94)   ~ (all_52_29 = all_14_2)
% 175.23/26.92    (95)   ~ (all_4_0 = e1)
% 175.23/26.92    (96)   ~ (all_52_19 = all_10_2)
% 175.23/26.92    (97)  op(e3, all_4_2) = e2
% 175.23/26.92    (98)   ~ (all_52_23 = all_6_2)
% 175.23/26.92    (99)   ~ (all_52_29 = all_6_2)
% 175.23/26.92    (100)  all_58_2 = all_52_9
% 175.23/26.92    (101)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.23/26.92    (102)  op(e3, e1) = all_52_5
% 175.23/26.92    (103)  all_56_10 = all_14_2
% 175.23/26.92    (104)   ~ (all_52_25 = all_6_2)
% 175.23/26.92    (105)  op(e1, e3) = all_52_17
% 175.23/26.92    (106)   ~ (all_52_25 = all_4_2)
% 175.23/26.92    (107)  op(e3, e0) = all_52_7
% 175.23/26.92    (108)  op(e2, all_10_2) = e2
% 175.23/26.92    (109)  op(e3, e3) = all_4_2
% 175.23/26.92    (110)  all_56_8 = all_52_17
% 175.23/26.92    (111)   ~ (all_52_17 = all_4_2)
% 175.23/26.92    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.23/26.92             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.23/26.92    (113)   ~ (all_52_25 = all_52_27)
% 175.23/26.92    (114)   ~ (all_52_27 = all_6_2)
% 175.23/26.92    (115)   ~ (all_52_7 = all_6_2)
% 175.23/26.92    (116)   ~ (all_10_0 = e3)
% 175.23/26.92    (117)   ~ (all_52_7 = all_52_23)
% 175.23/26.92    (118)   ~ (all_52_13 = all_10_2)
% 175.23/26.92    (119)  op(e2, all_52_27) = all_52_26
% 175.23/26.92    (120)   ~ (all_52_17 = all_52_19)
% 175.23/26.92    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.23/26.92    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.23/26.92    (123)  op(e1, all_14_2) = all_14_1
% 175.23/26.92    (124)  all_58_9 = all_52_7
% 175.23/26.92    (125)  all_58_12 = all_52_25
% 175.23/26.92    (126)   ~ (all_10_0 = e1)
% 175.23/26.92    (127)  all_56_6 = all_52_13
% 175.23/26.92    (128)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.23/26.92    (129)   ~ (all_52_9 = all_52_15)
% 175.23/26.92    (130)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.23/26.92    (131)   ~ (all_52_19 = all_14_2)
% 175.23/26.92    (132)  op(e2, e3) = all_52_9
% 175.23/26.92    (133)  all_56_13 = all_52_27
% 175.23/26.92  
% 175.23/26.92  Begin of proof
% 175.23/26.92  | 
% 175.23/26.92  | GROUND_INST: instantiating (112) with e2, all_10_0, all_10_2, e2, simplifying
% 175.23/26.92  |              with (8), (108) gives:
% 175.23/26.92  |   (134)  all_10_0 = e2
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (116), (134) imply:
% 175.23/26.92  |   (135)   ~ (e3 = e2)
% 175.23/26.92  | 
% 175.23/26.92  | SIMP: (135) implies:
% 175.23/26.92  |   (136)   ~ (e3 = e2)
% 175.23/26.92  | 
% 175.23/26.92  | REDUCE: (126), (134) imply:
% 175.23/26.92  |   (137)   ~ (e2 = e1)
% 175.23/26.92  | 
% 175.23/26.92  | BETA: splitting (42) gives:
% 175.23/26.92  | 
% 175.23/26.92  | Case 1:
% 175.23/26.92  | | 
% 175.23/26.92  | |   (138)  all_56_15 = e3
% 175.23/26.92  | | 
% 175.23/26.92  | | REF_CLOSE: (10), (16), (17), (20), (22), (24), (28), (30), (32), (34), (39),
% 175.23/26.92  | |            (43), (45), (47), (55), (62), (71), (72), (75), (82), (85), (97),
% 175.23/26.92  | |            (100), (104), (105), (108), (109), (112), (114), (120), (125),
% 175.23/26.92  | |            (132), (136), (138) are inconsistent by sub-proof #105.
% 175.23/26.92  | | 
% 175.23/26.92  | Case 2:
% 175.23/26.92  | | 
% 175.23/26.92  | |   (139)   ~ (all_56_15 = e3)
% 175.23/26.92  | |   (140)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.23/26.92  | | 
% 175.23/26.92  | | REDUCE: (22), (139) imply:
% 175.23/26.92  | |   (141)   ~ (all_6_2 = e3)
% 175.23/26.92  | | 
% 175.23/26.92  | | BETA: splitting (59) gives:
% 175.23/26.92  | | 
% 175.23/26.92  | | Case 1:
% 175.23/26.92  | | | 
% 175.23/26.92  | | |   (142)  all_56_13 = e3
% 175.23/26.92  | | | 
% 175.23/26.92  | | | COMBINE_EQS: (133), (142) imply:
% 175.23/26.92  | | |   (143)  all_52_27 = e3
% 175.23/26.92  | | | 
% 175.23/26.93  | | | REF_CLOSE: (3), (6), (10), (11), (16), (17), (20), (21), (23), (24), (26),
% 175.23/26.93  | | |            (27), (28), (29), (30), (32), (33), (35), (37), (38), (39),
% 175.23/26.93  | | |            (40), (41), (43), (44), (45), (47), (53), (55), (58), (62),
% 175.23/26.93  | | |            (65), (67), (69), (70), (71), (73), (75), (82), (83), (84),
% 175.23/26.93  | | |            (85), (87), (90), (91), (93), (97), (100), (105), (106), (108),
% 175.23/26.93  | | |            (109), (110), (111), (112), (113), (114), (119), (120), (121),
% 175.23/26.93  | | |            (124), (125), (129), (130), (132), (136), (143) are
% 175.23/26.93  | | |            inconsistent by sub-proof #103.
% 175.23/26.93  | | | 
% 175.23/26.93  | | Case 2:
% 175.23/26.93  | | | 
% 175.23/26.93  | | |   (144)   ~ (all_56_13 = e3)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (133), (144) imply:
% 175.23/26.93  | | |   (145)   ~ (all_52_27 = e3)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | BETA: splitting (64) gives:
% 175.23/26.93  | | | 
% 175.23/26.93  | | | Case 1:
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | |   (146)  all_58_12 = e3
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | COMBINE_EQS: (125), (146) imply:
% 175.23/26.93  | | | |   (147)  all_52_25 = e3
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | SIMP: (147) implies:
% 175.23/26.93  | | | |   (148)  all_52_25 = e3
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REDUCE: (11), (148) imply:
% 175.23/26.93  | | | |   (149)   ~ (all_52_9 = e3)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REDUCE: (113), (148) imply:
% 175.23/26.93  | | | |   (150)   ~ (all_52_27 = e3)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REDUCE: (19), (148) imply:
% 175.23/26.93  | | | |   (151)   ~ (all_52_29 = e3)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | SIMP: (151) implies:
% 175.23/26.93  | | | |   (152)   ~ (all_52_29 = e3)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REDUCE: (104), (148) imply:
% 175.23/26.93  | | | |   (153)   ~ (all_6_2 = e3)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REDUCE: (106), (148) imply:
% 175.23/26.93  | | | |   (154)   ~ (all_4_2 = e3)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | SIMP: (154) implies:
% 175.23/26.93  | | | |   (155)   ~ (all_4_2 = e3)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REDUCE: (71), (148) imply:
% 175.23/26.93  | | | |   (156)  op(e0, e3) = e3
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | BETA: splitting (26) gives:
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | Case 1:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | |   (157)  all_56_0 = e3
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | COMBINE_EQS: (90), (157) imply:
% 175.23/26.93  | | | | |   (158)  all_4_2 = e3
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | REDUCE: (155), (158) imply:
% 175.23/26.93  | | | | |   (159)  $false
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | CLOSE: (159) is inconsistent.
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | Case 2:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | |   (160)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (12), (13), (14), (15),
% 175.23/26.93  | | | | |            (16), (17), (18), (20), (21), (22), (23), (24), (25), (27),
% 175.23/26.93  | | | | |            (28), (29), (30), (31), (32), (33), (36), (37), (38), (40),
% 175.23/26.93  | | | | |            (41), (43), (44), (45), (46), (47), (49), (51), (52), (54),
% 175.23/26.93  | | | | |            (55), (56), (57), (58), (61), (63), (65), (66), (68), (70),
% 175.23/26.93  | | | | |            (73), (74), (75), (76), (77), (78), (80), (82), (84), (85),
% 175.23/26.93  | | | | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (96),
% 175.23/26.93  | | | | |            (97), (98), (100), (101), (102), (103), (105), (107),
% 175.23/26.93  | | | | |            (108), (111), (112), (114), (115), (117), (118), (120),
% 175.23/26.93  | | | | |            (121), (122), (123), (124), (127), (129), (130), (131),
% 175.23/26.93  | | | | |            (132), (136), (137), (140), (141), (145), (146), (149),
% 175.23/26.93  | | | | |            (152), (156), (160) are inconsistent by sub-proof #100.
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | End of split
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | Case 2:
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | |   (161)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | BETA: splitting (161) gives:
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | Case 1:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | |   (162)  all_58_13 = e3
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | REF_CLOSE: (82), (145), (162) are inconsistent by sub-proof #1026.
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | Case 2:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | |   (163)  all_58_14 = e3 | all_58_15 = e3
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | BETA: splitting (163) gives:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | Case 1:
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | |   (164)  all_58_14 = e3
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | COMBINE_EQS: (58), (164) imply:
% 175.23/26.93  | | | | | |   (165)  all_52_29 = e3
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | SIMP: (165) implies:
% 175.23/26.93  | | | | | |   (166)  all_52_29 = e3
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (81), (166) imply:
% 175.23/26.93  | | | | | |   (167)   ~ (all_52_5 = e3)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (7), (166) imply:
% 175.23/26.93  | | | | | |   (168)   ~ (all_52_13 = e3)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (19), (166) imply:
% 175.23/26.93  | | | | | |   (169)   ~ (all_52_25 = e3)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (94), (166) imply:
% 175.23/26.93  | | | | | |   (170)   ~ (all_14_2 = e3)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | SIMP: (170) implies:
% 175.23/26.93  | | | | | |   (171)   ~ (all_14_2 = e3)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (99), (166) imply:
% 175.23/26.93  | | | | | |   (172)   ~ (all_6_2 = e3)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (50), (166) imply:
% 175.23/26.93  | | | | | |   (173)  op(e1, e3) = all_52_28
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | GROUND_INST: instantiating (112) with all_52_17, all_52_28, e3, e1,
% 175.23/26.93  | | | | | |              simplifying with (105), (173) gives:
% 175.23/26.93  | | | | | |   (174)  all_52_17 = all_52_28
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | COMBINE_EQS: (85), (174) imply:
% 175.23/26.93  | | | | | |   (175)  all_58_6 = all_52_28
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (6), (174) imply:
% 175.23/26.93  | | | | | |   (176)   ~ (all_52_23 = all_52_28)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | SIMP: (176) implies:
% 175.23/26.93  | | | | | |   (177)   ~ (all_52_23 = all_52_28)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (111), (174) imply:
% 175.23/26.93  | | | | | |   (178)   ~ (all_52_28 = all_4_2)
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | BETA: splitting (56) gives:
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | Case 1:
% 175.23/26.93  | | | | | | | 
% 175.23/26.93  | | | | | | |   (179)  all_56_6 = e3
% 175.23/26.93  | | | | | | | 
% 175.23/26.93  | | | | | | | REF_CLOSE: (127), (168), (179) are inconsistent by sub-proof #573.
% 175.23/26.93  | | | | | | | 
% 175.23/26.93  | | | | | | Case 2:
% 175.23/26.93  | | | | | | | 
% 175.23/26.93  | | | | | | |   (180)   ~ (all_56_6 = e3)
% 175.23/26.93  | | | | | | |   (181)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.23/26.93  | | | | | | | 
% 175.23/26.93  | | | | | | | BETA: splitting (121) gives:
% 175.23/26.93  | | | | | | | 
% 175.23/26.93  | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | |   (182)  all_58_9 = e3
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | | COMBINE_EQS: (124), (182) imply:
% 175.23/26.93  | | | | | | | |   (183)  all_52_7 = e3
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | | REF_CLOSE: (10), (16), (17), (20), (24), (28), (29), (30), (32),
% 175.23/26.93  | | | | | | | |            (37), (38), (39), (40), (41), (43), (44), (45), (47),
% 175.23/26.93  | | | | | | | |            (53), (55), (58), (62), (65), (67), (75), (82), (84),
% 175.23/26.93  | | | | | | | |            (85), (93), (100), (105), (108), (109), (112), (120),
% 175.23/26.93  | | | | | | | |            (125), (130), (132), (169), (183) are inconsistent by
% 175.23/26.93  | | | | | | | |            sub-proof #104.
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | |   (184)   ~ (all_58_9 = e3)
% 175.23/26.93  | | | | | | | |   (185)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | | REDUCE: (124), (184) imply:
% 175.23/26.93  | | | | | | | |   (186)   ~ (all_52_7 = e3)
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | | BETA: splitting (128) gives:
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | |   (187)  all_58_0 = e3
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | COMBINE_EQS: (47), (187) imply:
% 175.23/26.93  | | | | | | | | |   (188)  all_4_2 = e3
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | REF_CLOSE: (97), (109), (112), (136), (188) are inconsistent
% 175.23/26.93  | | | | | | | | |            by sub-proof #106.
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | |   (189)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | BETA: splitting (189) gives:
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | |   (190)  all_58_1 = e3
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | COMBINE_EQS: (45), (190) imply:
% 175.23/26.93  | | | | | | | | | |   (191)  all_52_3 = e3
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | REDUCE: (61), (191) imply:
% 175.23/26.93  | | | | | | | | | |   (192)   ~ (all_52_5 = e3)
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | REDUCE: (92), (191) imply:
% 175.23/26.93  | | | | | | | | | |   (193)   ~ (all_52_19 = e3)
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | SIMP: (193) implies:
% 175.23/26.93  | | | | | | | | | |   (194)   ~ (all_52_19 = e3)
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | REDUCE: (16), (191) imply:
% 175.23/26.93  | | | | | | | | | |   (195)   ~ (all_10_2 = e3)
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | SIMP: (195) implies:
% 175.23/26.93  | | | | | | | | | |   (196)   ~ (all_10_2 = e3)
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | REDUCE: (70), (191) imply:
% 175.23/26.93  | | | | | | | | | |   (197)   ~ (all_4_2 = e3)
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | SIMP: (197) implies:
% 175.23/26.93  | | | | | | | | | |   (198)   ~ (all_4_2 = e3)
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | BETA: splitting (62) gives:
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | |   (199)  all_58_0 = e3
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | COMBINE_EQS: (47), (199) imply:
% 175.23/26.93  | | | | | | | | | | |   (200)  all_4_2 = e3
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | REDUCE: (198), (200) imply:
% 175.23/26.93  | | | | | | | | | | |   (201)  $false
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | CLOSE: (201) is inconsistent.
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | |   (202)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | BETA: splitting (38) gives:
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | |   (203)  all_58_6 = e3
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | COMBINE_EQS: (175), (203) imply:
% 175.23/26.93  | | | | | | | | | | | |   (204)  all_52_28 = e3
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | SIMP: (204) implies:
% 175.23/26.93  | | | | | | | | | | | |   (205)  all_52_28 = e3
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | REDUCE: (177), (205) imply:
% 175.23/26.93  | | | | | | | | | | | |   (206)   ~ (all_52_23 = e3)
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | BETA: splitting (185) gives:
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | |   (207)  all_58_10 = e3
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | COMBINE_EQS: (30), (207) imply:
% 175.23/26.93  | | | | | | | | | | | | |   (208)  all_52_15 = e3
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | SIMP: (208) implies:
% 175.23/26.93  | | | | | | | | | | | | |   (209)  all_52_15 = e3
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | REDUCE: (21), (209) imply:
% 175.23/26.93  | | | | | | | | | | | | |   (210)  op(e0, e3) = e0
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | GROUND_INST: instantiating (112) with all_52_25, e0, e3, e0,
% 175.23/26.93  | | | | | | | | | | | | |              simplifying with (71), (210) gives:
% 175.23/26.93  | | | | | | | | | | | | |   (211)  all_52_25 = e0
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | COMBINE_EQS: (125), (211) imply:
% 175.23/26.93  | | | | | | | | | | | | |   (212)  all_58_12 = e0
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | REDUCE: (106), (211) imply:
% 175.23/26.93  | | | | | | | | | | | | |   (213)   ~ (all_4_2 = e0)
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | SIMP: (213) implies:
% 175.23/26.93  | | | | | | | | | | | | |   (214)   ~ (all_4_2 = e0)
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | BETA: splitting (26) gives:
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | |   (215)  all_56_0 = e3
% 175.23/26.93  | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | REF_CLOSE: (90), (198), (215) are inconsistent by sub-proof
% 175.23/26.93  | | | | | | | | | | | | | |            #1024.
% 175.23/26.93  | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | |   (216)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.93  | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 175.23/26.93  | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | Case 1:
% 175.23/26.93  | | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | |   (217)  all_58_0 = e2
% 175.23/26.93  | | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | | REF_CLOSE: (39), (75), (83), (89), (100), (102), (112),
% 175.23/26.93  | | | | | | | | | | | | | | |            (137), (167), (203), (212), (217) are inconsistent
% 175.23/26.93  | | | | | | | | | | | | | | |            by sub-proof #724.
% 175.23/26.93  | | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | |   (218)   ~ (all_58_0 = e2)
% 175.23/26.93  | | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | | REF_CLOSE: (2), (47), (48), (60), (63), (83), (90), (95),
% 175.23/26.93  | | | | | | | | | | | | | | |            (97), (102), (112), (127), (181), (214), (216),
% 175.23/26.93  | | | | | | | | | | | | | | |            (218) are inconsistent by sub-proof #99.
% 175.23/26.93  | | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | | End of split
% 175.23/26.93  | | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | End of split
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | |   (219)  all_58_11 = e3 | all_58_15 = e3
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | | REF_CLOSE: (27), (91), (141), (206), (219) are inconsistent
% 175.23/26.93  | | | | | | | | | | | | |            by sub-proof #1016.
% 175.23/26.93  | | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | End of split
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | |   (220)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | | REF_CLOSE: (17), (24), (28), (30), (32), (43), (65), (75),
% 175.23/26.93  | | | | | | | | | | | |            (79), (91), (100), (109), (112), (168), (171),
% 175.23/26.93  | | | | | | | | | | | |            (194), (196), (202), (220) are inconsistent by
% 175.23/26.93  | | | | | | | | | | | |            sub-proof #965.
% 175.23/26.93  | | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | | End of split
% 175.23/26.93  | | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | End of split
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | Case 2:
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | |   (221)  all_58_4 = e3 | all_58_9 = e3
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | | REF_CLOSE: (37), (124), (167), (186), (221) are inconsistent
% 175.23/26.93  | | | | | | | | | |            by sub-proof #729.
% 175.23/26.93  | | | | | | | | | | 
% 175.23/26.93  | | | | | | | | | End of split
% 175.23/26.93  | | | | | | | | | 
% 175.23/26.93  | | | | | | | | End of split
% 175.23/26.93  | | | | | | | | 
% 175.23/26.93  | | | | | | | End of split
% 175.23/26.93  | | | | | | | 
% 175.23/26.93  | | | | | | End of split
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | Case 2:
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | |   (222)  all_58_15 = e3
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | COMBINE_EQS: (27), (222) imply:
% 175.23/26.93  | | | | | |   (223)  all_6_2 = e3
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (141), (223) imply:
% 175.23/26.93  | | | | | |   (224)  $false
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | CLOSE: (224) is inconsistent.
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | End of split
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | End of split
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | End of split
% 175.23/26.93  | | | 
% 175.23/26.93  | | End of split
% 175.23/26.93  | | 
% 175.23/26.93  | End of split
% 175.23/26.93  | 
% 175.23/26.93  End of proof
% 175.23/26.93  
% 175.23/26.93  Sub-proof #99 shows that the following formulas are inconsistent:
% 175.23/26.93  ----------------------------------------------------------------
% 175.23/26.93    (1)   ~ (all_52_5 = all_52_13)
% 175.23/26.93    (2)  all_58_0 = all_4_2
% 175.23/26.93    (3)   ~ (all_4_0 = e0) |  ~ (all_4_2 = e1)
% 175.23/26.93    (4)  op(e2, all_4_2) = all_4_0
% 175.23/26.93    (5)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.23/26.93    (6)  op(e2, e1) = all_52_13
% 175.23/26.93    (7)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.23/26.93    (8)  all_56_0 = all_4_2
% 175.23/26.93    (9)   ~ (all_4_0 = e1)
% 175.23/26.93    (10)  op(e3, all_4_2) = e2
% 175.23/26.93    (11)  op(e3, e1) = all_52_5
% 175.23/26.93    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.23/26.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.23/26.93    (13)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.93    (14)   ~ (all_4_2 = e0)
% 175.23/26.93    (15)   ~ (all_58_0 = e2)
% 175.23/26.93    (16)  all_56_6 = all_52_13
% 175.23/26.93  
% 175.23/26.93  Begin of proof
% 175.23/26.93  | 
% 175.23/26.93  | REDUCE: (2), (15) imply:
% 175.23/26.93  |   (17)   ~ (all_4_2 = e2)
% 175.23/26.93  | 
% 175.23/26.93  | BETA: splitting (13) gives:
% 175.23/26.93  | 
% 175.23/26.93  | Case 1:
% 175.23/26.93  | | 
% 175.23/26.93  | |   (18)  all_56_0 = e2
% 175.23/26.93  | | 
% 175.23/26.93  | | REF_CLOSE: (8), (17), (18) are inconsistent by sub-proof #904.
% 175.23/26.93  | | 
% 175.23/26.93  | Case 2:
% 175.23/26.93  | | 
% 175.23/26.93  | |   (19)  all_56_0 = e1 | all_56_0 = e0
% 175.23/26.93  | | 
% 175.23/26.93  | | BETA: splitting (7) gives:
% 175.23/26.93  | | 
% 175.23/26.93  | | Case 1:
% 175.23/26.93  | | | 
% 175.23/26.93  | | |   (20)  all_58_0 = e1
% 175.23/26.93  | | | 
% 175.23/26.93  | | | COMBINE_EQS: (2), (20) imply:
% 175.23/26.93  | | |   (21)  all_4_2 = e1
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (10), (21) imply:
% 175.23/26.93  | | |   (22)  op(e3, e1) = e2
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (4), (21) imply:
% 175.23/26.93  | | |   (23)  op(e2, e1) = all_4_0
% 175.23/26.93  | | | 
% 175.23/26.93  | | | BETA: splitting (3) gives:
% 175.23/26.93  | | | 
% 175.23/26.93  | | | Case 1:
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | |   (24)   ~ (all_4_2 = e1)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REF_CLOSE: (8), (14), (19), (24) are inconsistent by sub-proof #1020.
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | Case 2:
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | |   (25)   ~ (all_4_0 = e0)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | GROUND_INST: instantiating (12) with all_52_13, all_4_0, e1, e2,
% 175.23/26.93  | | | |              simplifying with (6), (23) gives:
% 175.23/26.93  | | | |   (26)  all_52_13 = all_4_0
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | GROUND_INST: instantiating (12) with all_52_5, e2, e1, e3, simplifying
% 175.23/26.93  | | | |              with (11), (22) gives:
% 175.23/26.93  | | | |   (27)  all_52_5 = e2
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | COMBINE_EQS: (16), (26) imply:
% 175.23/26.93  | | | |   (28)  all_56_6 = all_4_0
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | REDUCE: (1), (26), (27) imply:
% 175.23/26.93  | | | |   (29)   ~ (all_4_0 = e2)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | SIMP: (29) implies:
% 175.23/26.93  | | | |   (30)   ~ (all_4_0 = e2)
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | BETA: splitting (5) gives:
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | | Case 1:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | |   (31)  all_56_6 = e2
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | COMBINE_EQS: (28), (31) imply:
% 175.23/26.93  | | | | |   (32)  all_4_0 = e2
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | SIMP: (32) implies:
% 175.23/26.93  | | | | |   (33)  all_4_0 = e2
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | REDUCE: (30), (33) imply:
% 175.23/26.93  | | | | |   (34)  $false
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | CLOSE: (34) is inconsistent.
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | Case 2:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | |   (35)  all_56_6 = e1 | all_56_6 = e0
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | BETA: splitting (35) gives:
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | | Case 1:
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | |   (36)  all_56_6 = e1
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | COMBINE_EQS: (28), (36) imply:
% 175.23/26.93  | | | | | |   (37)  all_4_0 = e1
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | SIMP: (37) implies:
% 175.23/26.93  | | | | | |   (38)  all_4_0 = e1
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (9), (38) imply:
% 175.23/26.93  | | | | | |   (39)  $false
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | CLOSE: (39) is inconsistent.
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | Case 2:
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | |   (40)  all_56_6 = e0
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | COMBINE_EQS: (28), (40) imply:
% 175.23/26.93  | | | | | |   (41)  all_4_0 = e0
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | SIMP: (41) implies:
% 175.23/26.93  | | | | | |   (42)  all_4_0 = e0
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | REDUCE: (25), (42) imply:
% 175.23/26.93  | | | | | |   (43)  $false
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | | CLOSE: (43) is inconsistent.
% 175.23/26.93  | | | | | | 
% 175.23/26.93  | | | | | End of split
% 175.23/26.93  | | | | | 
% 175.23/26.93  | | | | End of split
% 175.23/26.93  | | | | 
% 175.23/26.93  | | | End of split
% 175.23/26.93  | | | 
% 175.23/26.93  | | Case 2:
% 175.23/26.93  | | | 
% 175.23/26.93  | | |   (44)   ~ (all_58_0 = e1)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (2), (44) imply:
% 175.23/26.93  | | |   (45)   ~ (all_4_2 = e1)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REF_CLOSE: (8), (14), (19), (45) are inconsistent by sub-proof #892.
% 175.23/26.93  | | | 
% 175.23/26.93  | | End of split
% 175.23/26.93  | | 
% 175.23/26.93  | End of split
% 175.23/26.93  | 
% 175.23/26.93  End of proof
% 175.23/26.93  
% 175.23/26.93  Sub-proof #100 shows that the following formulas are inconsistent:
% 175.23/26.93  ----------------------------------------------------------------
% 175.23/26.93    (1)   ~ (all_52_23 = all_14_2)
% 175.23/26.93    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.23/26.93    (3)   ~ (all_52_27 = all_10_2)
% 175.23/26.93    (4)   ~ (all_52_17 = all_52_23)
% 175.23/26.93    (5)   ~ (all_52_13 = all_52_29)
% 175.23/26.93    (6)  all_56_3 = all_52_7
% 175.23/26.93    (7)  op(e3, e2) = all_52_3
% 175.23/26.93    (8)   ~ (all_52_19 = all_52_23)
% 175.23/26.93    (9)  all_56_11 = all_52_23
% 175.23/26.93    (10)  op(e1, e2) = all_52_19
% 175.23/26.93    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.23/26.93    (12)   ~ (all_52_27 = e3)
% 175.23/26.93    (13)   ~ (all_6_2 = e3)
% 175.23/26.93    (14)   ~ (all_52_3 = all_10_2)
% 175.23/26.93    (15)  all_58_5 = all_52_13
% 175.23/26.93    (16)   ~ (all_6_2 = e0)
% 175.23/26.93    (17)  op(e1, all_52_13) = e1
% 175.23/26.93    (18)  op(e0, all_52_15) = e0
% 175.23/26.93    (19)  all_56_15 = all_6_2
% 175.23/26.93    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.23/26.93    (21)  all_58_3 = all_10_2
% 175.23/26.93    (22)  all_56_9 = all_52_19
% 175.23/26.93    (23)  all_58_15 = all_6_2
% 175.23/26.93    (24)   ~ (all_52_9 = all_4_2)
% 175.23/26.93    (25)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.23/26.93    (26)   ~ (all_52_5 = all_52_7)
% 175.23/26.93    (27)  all_58_10 = all_52_15
% 175.23/26.93    (28)   ~ (all_52_5 = all_4_2)
% 175.23/26.93    (29)  all_58_7 = all_52_19
% 175.23/26.93    (30)  all_56_4 = all_52_9
% 175.23/26.93    (31)  op(e0, e1) = all_52_29
% 175.23/26.93    (32)  all_58_4 = all_52_5
% 175.23/26.93    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.23/26.93    (34)   ~ (all_52_27 = all_52_29)
% 175.23/26.93    (35)   ~ (all_52_17 = all_14_2)
% 175.23/26.93    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.23/26.93    (37)   ~ (all_52_7 = all_4_2)
% 175.23/26.93    (38)  all_58_1 = all_52_3
% 175.23/26.93    (39)   ~ (all_52_13 = all_52_15)
% 175.23/26.93    (40)  all_58_0 = all_4_2
% 175.23/26.93    (41)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.23/26.93    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.23/26.93    (43)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.23/26.93    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.23/26.93    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.23/26.93    (46)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.23/26.93    (47)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.23/26.93    (48)  all_58_14 = all_52_29
% 175.23/26.93    (49)  op(e0, e3) = e3
% 175.23/26.93    (50)   ~ (all_52_3 = all_52_5)
% 175.23/26.93    (51)  op(e2, e1) = all_52_13
% 175.23/26.93    (52)  all_58_8 = all_14_2
% 175.23/26.93    (53)  all_56_1 = all_52_3
% 175.23/26.93    (54)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.23/26.93    (55)   ~ (all_52_3 = all_4_2)
% 175.23/26.93    (56)  op(e3, all_52_17) = all_52_16
% 175.23/26.93    (57)   ~ (all_52_29 = e3)
% 175.23/26.93    (58)   ~ (all_52_13 = all_14_2)
% 175.23/26.93    (59)  op(e3, all_52_9) = e3
% 175.23/26.93    (60)   ~ (e3 = e0)
% 175.23/26.93    (61)   ~ (all_52_9 = all_52_13)
% 175.23/26.93    (62)  op(e0, all_52_23) = all_52_22
% 175.23/26.93    (63)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.23/26.93    (64)  all_58_13 = all_52_27
% 175.23/26.93    (65)  all_58_12 = e3
% 175.23/26.93    (66)   ~ (all_52_9 = all_52_17)
% 175.23/26.93    (67)  all_58_6 = all_52_17
% 175.23/26.93    (68)   ~ (all_52_3 = all_52_7)
% 175.23/26.93    (69)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.23/26.93    (70)  op(e2, all_52_19) = all_52_18
% 175.23/26.93    (71)   ~ (e1 = e0)
% 175.23/26.93    (72)  all_56_0 = all_4_2
% 175.23/26.93    (73)  all_58_11 = all_52_23
% 175.23/26.93    (74)   ~ (all_52_3 = all_52_19)
% 175.23/26.93    (75)   ~ (all_52_7 = all_52_15)
% 175.23/26.93    (76)   ~ (all_52_29 = all_14_2)
% 175.23/26.93    (77)   ~ (all_52_19 = all_10_2)
% 175.23/26.93    (78)   ~ (all_52_9 = e3)
% 175.23/26.93    (79)  op(e3, all_4_2) = e2
% 175.23/26.93    (80)   ~ (all_52_23 = all_6_2)
% 175.23/26.93    (81)  all_58_2 = all_52_9
% 175.23/26.93    (82)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.23/26.93    (83)  op(e3, e1) = all_52_5
% 175.23/26.93    (84)   ~ (e2 = e1)
% 175.23/26.93    (85)  all_56_10 = all_14_2
% 175.23/26.93    (86)  op(e1, e3) = all_52_17
% 175.23/26.93    (87)  op(e3, e0) = all_52_7
% 175.23/26.93    (88)  op(e2, all_10_2) = e2
% 175.23/26.93    (89)   ~ (all_52_17 = all_4_2)
% 175.23/26.93    (90)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.23/26.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.23/26.93    (91)   ~ (all_52_27 = all_6_2)
% 175.23/26.93    (92)   ~ (all_52_7 = all_6_2)
% 175.23/26.93    (93)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.23/26.93    (94)   ~ (all_52_7 = all_52_23)
% 175.23/26.93    (95)   ~ (all_52_13 = all_10_2)
% 175.23/26.93    (96)   ~ (all_52_17 = all_52_19)
% 175.23/26.93    (97)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.23/26.93    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.23/26.93    (99)  op(e1, all_14_2) = all_14_1
% 175.23/26.93    (100)  all_58_9 = all_52_7
% 175.23/26.93    (101)  all_56_6 = all_52_13
% 175.23/26.93    (102)   ~ (all_52_9 = all_52_15)
% 175.23/26.93    (103)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.23/26.93    (104)   ~ (e3 = e2)
% 175.23/26.93    (105)   ~ (all_52_19 = all_14_2)
% 175.23/26.93    (106)  op(e2, e3) = all_52_9
% 175.23/26.93  
% 175.23/26.93  Begin of proof
% 175.23/26.93  | 
% 175.23/26.93  | BETA: splitting (69) gives:
% 175.23/26.93  | 
% 175.23/26.93  | Case 1:
% 175.23/26.93  | | 
% 175.23/26.93  | |   (107)  all_56_4 = e3
% 175.23/26.93  | | 
% 175.23/26.93  | | REF_CLOSE: (30), (78), (107) are inconsistent by sub-proof #782.
% 175.23/26.93  | | 
% 175.23/26.93  | Case 2:
% 175.23/26.93  | | 
% 175.23/26.93  | |   (108)   ~ (all_56_4 = e3)
% 175.23/26.93  | |   (109)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.23/26.93  | | 
% 175.23/26.93  | | BETA: splitting (46) gives:
% 175.23/26.93  | | 
% 175.23/26.93  | | Case 1:
% 175.23/26.93  | | | 
% 175.23/26.93  | | |   (110)  all_56_6 = e3
% 175.23/26.93  | | | 
% 175.23/26.93  | | | COMBINE_EQS: (101), (110) imply:
% 175.23/26.93  | | |   (111)  all_52_13 = e3
% 175.23/26.93  | | | 
% 175.23/26.93  | | | SIMP: (111) implies:
% 175.23/26.93  | | |   (112)  all_52_13 = e3
% 175.23/26.93  | | | 
% 175.23/26.93  | | | COMBINE_EQS: (15), (112) imply:
% 175.23/26.93  | | |   (113)  all_58_5 = e3
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (39), (112) imply:
% 175.23/26.93  | | |   (114)   ~ (all_52_15 = e3)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | SIMP: (114) implies:
% 175.23/26.93  | | |   (115)   ~ (all_52_15 = e3)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (5), (112) imply:
% 175.23/26.93  | | |   (116)   ~ (all_52_29 = e3)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (95), (112) imply:
% 175.23/26.93  | | |   (117)   ~ (all_10_2 = e3)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | SIMP: (117) implies:
% 175.23/26.93  | | |   (118)   ~ (all_10_2 = e3)
% 175.23/26.93  | | | 
% 175.23/26.93  | | | REDUCE: (17), (112) imply:
% 175.23/26.93  | | |   (119)  op(e1, e3) = e1
% 175.23/26.93  | | | 
% 175.23/26.94  | | | GROUND_INST: instantiating (90) with all_52_17, e1, e3, e1, simplifying
% 175.23/26.94  | | |              with (86), (119) gives:
% 175.23/26.94  | | |   (120)  all_52_17 = e1
% 175.23/26.94  | | | 
% 175.23/26.94  | | | COMBINE_EQS: (67), (120) imply:
% 175.23/26.94  | | |   (121)  all_58_6 = e1
% 175.23/26.94  | | | 
% 175.23/26.94  | | | REDUCE: (66), (120) imply:
% 175.23/26.94  | | |   (122)   ~ (all_52_9 = e1)
% 175.23/26.94  | | | 
% 175.23/26.94  | | | REDUCE: (35), (120) imply:
% 175.23/26.94  | | |   (123)   ~ (all_14_2 = e1)
% 175.23/26.94  | | | 
% 175.23/26.94  | | | SIMP: (123) implies:
% 175.23/26.94  | | |   (124)   ~ (all_14_2 = e1)
% 175.23/26.94  | | | 
% 175.23/26.94  | | | REDUCE: (89), (120) imply:
% 175.23/26.94  | | |   (125)   ~ (all_4_2 = e1)
% 175.23/26.94  | | | 
% 175.23/26.94  | | | SIMP: (125) implies:
% 175.23/26.94  | | |   (126)   ~ (all_4_2 = e1)
% 175.23/26.94  | | | 
% 175.23/26.94  | | | REDUCE: (56), (120) imply:
% 175.23/26.94  | | |   (127)  op(e3, e1) = all_52_16
% 175.23/26.94  | | | 
% 175.23/26.94  | | | GROUND_INST: instantiating (90) with all_52_5, all_52_16, e1, e3,
% 175.23/26.94  | | |              simplifying with (83), (127) gives:
% 175.23/26.94  | | |   (128)  all_52_5 = all_52_16
% 175.23/26.94  | | | 
% 175.23/26.94  | | | COMBINE_EQS: (32), (128) imply:
% 175.23/26.94  | | |   (129)  all_58_4 = all_52_16
% 175.23/26.94  | | | 
% 175.23/26.94  | | | REDUCE: (50), (128) imply:
% 175.23/26.94  | | |   (130)   ~ (all_52_3 = all_52_16)
% 175.23/26.94  | | | 
% 175.23/26.94  | | | BETA: splitting (97) gives:
% 175.23/26.94  | | | 
% 175.23/26.94  | | | Case 1:
% 175.23/26.94  | | | | 
% 175.23/26.94  | | | |   (131)  all_58_9 = e3
% 175.23/26.94  | | | | 
% 175.23/26.94  | | | | COMBINE_EQS: (100), (131) imply:
% 175.23/26.94  | | | |   (132)  all_52_7 = e3
% 175.23/26.94  | | | | 
% 175.23/26.94  | | | | SIMP: (132) implies:
% 175.23/26.94  | | | |   (133)  all_52_7 = e3
% 175.23/26.94  | | | | 
% 175.23/26.94  | | | | REDUCE: (68), (133) imply:
% 175.23/26.94  | | | |   (134)   ~ (all_52_3 = e3)
% 175.23/26.94  | | | | 
% 175.23/26.94  | | | | BETA: splitting (45) gives:
% 175.23/26.94  | | | | 
% 175.23/26.94  | | | | Case 1:
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | |   (135)  all_58_1 = e3
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | | COMBINE_EQS: (38), (135) imply:
% 175.23/26.94  | | | | |   (136)  all_52_3 = e3
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | | REDUCE: (134), (136) imply:
% 175.23/26.94  | | | | |   (137)  $false
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | | CLOSE: (137) is inconsistent.
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | Case 2:
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | |   (138)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | | BETA: splitting (138) gives:
% 175.23/26.94  | | | | | 
% 175.23/26.94  | | | | | Case 1:
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | |   (139)  all_58_3 = e3
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | | COMBINE_EQS: (21), (139) imply:
% 175.23/26.94  | | | | | |   (140)  all_10_2 = e3
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | | REDUCE: (118), (140) imply:
% 175.23/26.94  | | | | | |   (141)  $false
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | | CLOSE: (141) is inconsistent.
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | Case 2:
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | |   (142)  all_58_7 = e3 | all_58_13 = e3
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | | BETA: splitting (142) gives:
% 175.23/26.94  | | | | | | 
% 175.23/26.94  | | | | | | Case 1:
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | |   (143)  all_58_7 = e3
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | COMBINE_EQS: (29), (143) imply:
% 175.23/26.94  | | | | | | |   (144)  all_52_19 = e3
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | REDUCE: (70), (144) imply:
% 175.23/26.94  | | | | | | |   (145)  op(e2, e3) = all_52_18
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | GROUND_INST: instantiating (90) with all_52_9, all_52_18, e3, e2,
% 175.23/26.94  | | | | | | |              simplifying with (106), (145) gives:
% 175.23/26.94  | | | | | | |   (146)  all_52_9 = all_52_18
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | COMBINE_EQS: (81), (146) imply:
% 175.23/26.94  | | | | | | |   (147)  all_58_2 = all_52_18
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | REDUCE: (122), (146) imply:
% 175.23/26.94  | | | | | | |   (148)   ~ (all_52_18 = e1)
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | REDUCE: (59), (146) imply:
% 175.23/26.94  | | | | | | |   (149)  op(e3, all_52_18) = e3
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | BETA: splitting (47) gives:
% 175.23/26.94  | | | | | | | 
% 175.23/26.94  | | | | | | | Case 1:
% 175.23/26.94  | | | | | | | | 
% 175.23/26.94  | | | | | | | |   (150)  all_58_2 = e1
% 175.23/26.94  | | | | | | | | 
% 175.23/26.94  | | | | | | | | REF_CLOSE: (147), (148), (150) are inconsistent by sub-proof
% 175.23/26.94  | | | | | | | |            #175.
% 175.23/26.94  | | | | | | | | 
% 175.23/26.94  | | | | | | | Case 2:
% 175.23/26.94  | | | | | | | | 
% 175.23/26.94  | | | | | | | |   (151)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.23/26.94  | | | | | | | | 
% 175.23/26.94  | | | | | | | | BETA: splitting (11) gives:
% 175.23/26.94  | | | | | | | | 
% 175.23/26.94  | | | | | | | | Case 1:
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | |   (152)  all_58_0 = e1
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | | COMBINE_EQS: (40), (152) imply:
% 175.23/26.94  | | | | | | | | |   (153)  all_4_2 = e1
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | | REDUCE: (126), (153) imply:
% 175.23/26.94  | | | | | | | | |   (154)  $false
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | | CLOSE: (154) is inconsistent.
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | Case 2:
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | |   (155)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | | BETA: splitting (155) gives:
% 175.23/26.94  | | | | | | | | | 
% 175.23/26.94  | | | | | | | | | Case 1:
% 175.23/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | |   (156)  all_58_1 = e1
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | COMBINE_EQS: (38), (156) imply:
% 175.30/26.94  | | | | | | | | | |   (157)  all_52_3 = e1
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | REDUCE: (130), (157) imply:
% 175.30/26.94  | | | | | | | | | |   (158)   ~ (all_52_16 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | SIMP: (158) implies:
% 175.30/26.94  | | | | | | | | | |   (159)   ~ (all_52_16 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | REDUCE: (14), (157) imply:
% 175.30/26.94  | | | | | | | | | |   (160)   ~ (all_10_2 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | SIMP: (160) implies:
% 175.30/26.94  | | | | | | | | | |   (161)   ~ (all_10_2 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | REDUCE: (134), (157) imply:
% 175.30/26.94  | | | | | | | | | |   (162)   ~ (e3 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | SIMP: (162) implies:
% 175.30/26.94  | | | | | | | | | |   (163)   ~ (e3 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | REF_CLOSE: (18), (21), (27), (31), (44), (48), (52), (71),
% 175.30/26.94  | | | | | | | | | |            (90), (113), (124), (129), (151), (159), (161),
% 175.30/26.94  | | | | | | | | | |            (163) are inconsistent by sub-proof #770.
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | Case 2:
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | |   (164)   ~ (all_58_1 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | REDUCE: (38), (164) imply:
% 175.30/26.94  | | | | | | | | | |   (165)   ~ (all_52_3 = e1)
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | | REF_CLOSE: (7), (20), (40), (42), (53), (55), (65), (79),
% 175.30/26.94  | | | | | | | | | |            (84), (90), (104), (121), (134), (147), (149),
% 175.30/26.94  | | | | | | | | | |            (165) are inconsistent by sub-proof #101.
% 175.30/26.94  | | | | | | | | | | 
% 175.30/26.94  | | | | | | | | | End of split
% 175.30/26.94  | | | | | | | | | 
% 175.30/26.94  | | | | | | | | End of split
% 175.30/26.94  | | | | | | | | 
% 175.30/26.94  | | | | | | | End of split
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | Case 2:
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | |   (166)  all_58_13 = e3
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | | REF_CLOSE: (12), (64), (166) are inconsistent by sub-proof #1026.
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | End of split
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | End of split
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | End of split
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | Case 2:
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | |   (167)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (12), (13), (14), (15),
% 175.30/26.94  | | | |            (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 175.30/26.94  | | | |            (27), (28), (29), (30), (32), (34), (35), (37), (38), (40),
% 175.30/26.94  | | | |            (43), (44), (45), (48), (49), (50), (51), (52), (54), (56),
% 175.30/26.94  | | | |            (57), (59), (60), (62), (64), (66), (68), (72), (73), (80),
% 175.30/26.94  | | | |            (83), (86), (87), (88), (90), (91), (92), (93), (94), (96),
% 175.30/26.94  | | | |            (97), (98), (100), (103), (104), (106), (109), (115), (167)
% 175.30/26.94  | | | |            are inconsistent by sub-proof #366.
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | End of split
% 175.30/26.94  | | | 
% 175.30/26.94  | | Case 2:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (168)   ~ (all_56_6 = e3)
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REDUCE: (101), (168) imply:
% 175.30/26.94  | | |   (169)   ~ (all_52_13 = e3)
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 175.30/26.94  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.30/26.94  | | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 175.30/26.94  | | |            (35), (36), (37), (38), (40), (41), (43), (44), (45), (46),
% 175.30/26.94  | | |            (48), (49), (50), (51), (52), (54), (56), (57), (58), (59),
% 175.30/26.94  | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 175.30/26.94  | | |            (70), (72), (73), (74), (75), (76), (77), (78), (80), (81),
% 175.30/26.94  | | |            (82), (83), (84), (85), (86), (87), (88), (90), (91), (92),
% 175.30/26.94  | | |            (93), (94), (96), (97), (98), (99), (100), (101), (102), (103),
% 175.30/26.94  | | |            (104), (105), (106), (169) are inconsistent by sub-proof #382.
% 175.30/26.94  | | | 
% 175.30/26.94  | | End of split
% 175.30/26.94  | | 
% 175.30/26.94  | End of split
% 175.30/26.94  | 
% 175.30/26.94  End of proof
% 175.30/26.94  
% 175.30/26.94  Sub-proof #101 shows that the following formulas are inconsistent:
% 175.30/26.94  ----------------------------------------------------------------
% 175.30/26.94    (1)  all_58_2 = all_52_18
% 175.30/26.94    (2)   ~ (all_52_3 = e1)
% 175.30/26.94    (3)  op(e3, e2) = all_52_3
% 175.30/26.94    (4)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.94    (5)  all_58_0 = all_4_2
% 175.30/26.94    (6)  all_58_6 = e1
% 175.30/26.94    (7)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.30/26.94    (8)  all_56_1 = all_52_3
% 175.30/26.94    (9)   ~ (all_52_3 = all_4_2)
% 175.30/26.94    (10)   ~ (all_52_3 = e3)
% 175.30/26.94    (11)  all_58_12 = e3
% 175.30/26.94    (12)  op(e3, all_4_2) = e2
% 175.30/26.94    (13)   ~ (e2 = e1)
% 175.30/26.94    (14)  op(e3, all_52_18) = e3
% 175.30/26.94    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.94    (16)   ~ (e3 = e2)
% 175.30/26.94  
% 175.30/26.94  Begin of proof
% 175.30/26.94  | 
% 175.30/26.94  | BETA: splitting (7) gives:
% 175.30/26.94  | 
% 175.30/26.94  | Case 1:
% 175.30/26.94  | | 
% 175.30/26.94  | |   (17)  all_56_1 = e3
% 175.30/26.94  | | 
% 175.30/26.94  | | REF_CLOSE: (8), (10), (17) are inconsistent by sub-proof #862.
% 175.30/26.94  | | 
% 175.30/26.94  | Case 2:
% 175.30/26.94  | | 
% 175.30/26.94  | |   (18)   ~ (all_56_1 = e3)
% 175.30/26.94  | |   (19)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.30/26.94  | | 
% 175.30/26.94  | | BETA: splitting (4) gives:
% 175.30/26.94  | | 
% 175.30/26.94  | | Case 1:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (20)  all_58_0 = e2
% 175.30/26.94  | | | 
% 175.30/26.94  | | | COMBINE_EQS: (5), (20) imply:
% 175.30/26.94  | | |   (21)  all_4_2 = e2
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REDUCE: (9), (21) imply:
% 175.30/26.94  | | |   (22)   ~ (all_52_3 = e2)
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REDUCE: (12), (21) imply:
% 175.30/26.94  | | |   (23)  op(e3, e2) = e2
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REF_CLOSE: (2), (3), (8), (15), (19), (22), (23) are inconsistent by
% 175.30/26.94  | | |            sub-proof #102.
% 175.30/26.94  | | | 
% 175.30/26.94  | | Case 2:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (24)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REF_CLOSE: (1), (3), (6), (10), (11), (13), (14), (15), (16), (24) are
% 175.30/26.94  | | |            inconsistent by sub-proof #737.
% 175.30/26.94  | | | 
% 175.30/26.94  | | End of split
% 175.30/26.94  | | 
% 175.30/26.94  | End of split
% 175.30/26.94  | 
% 175.30/26.94  End of proof
% 175.30/26.94  
% 175.30/26.94  Sub-proof #102 shows that the following formulas are inconsistent:
% 175.30/26.94  ----------------------------------------------------------------
% 175.30/26.94    (1)   ~ (all_52_3 = e1)
% 175.30/26.94    (2)  op(e3, e2) = all_52_3
% 175.30/26.94    (3)   ~ (all_52_3 = e2)
% 175.30/26.94    (4)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.30/26.94    (5)  all_56_1 = all_52_3
% 175.30/26.94    (6)  op(e3, e2) = e2
% 175.30/26.94    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.94  
% 175.30/26.94  Begin of proof
% 175.30/26.94  | 
% 175.30/26.94  | BETA: splitting (4) gives:
% 175.30/26.94  | 
% 175.30/26.94  | Case 1:
% 175.30/26.94  | | 
% 175.30/26.94  | |   (8)  all_56_1 = e2
% 175.30/26.94  | | 
% 175.30/26.94  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #857.
% 175.30/26.94  | | 
% 175.30/26.94  | Case 2:
% 175.30/26.94  | | 
% 175.30/26.94  | |   (9)   ~ (all_56_1 = e2)
% 175.30/26.94  | |   (10)  all_56_1 = e1 | all_56_1 = e0
% 175.30/26.94  | | 
% 175.30/26.94  | | BETA: splitting (10) gives:
% 175.30/26.94  | | 
% 175.30/26.94  | | Case 1:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (11)  all_56_1 = e1
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REF_CLOSE: (1), (5), (11) are inconsistent by sub-proof #841.
% 175.30/26.94  | | | 
% 175.30/26.94  | | Case 2:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (12)  all_56_1 = e0
% 175.30/26.94  | | | 
% 175.30/26.94  | | | COMBINE_EQS: (5), (12) imply:
% 175.30/26.94  | | |   (13)  all_52_3 = e0
% 175.30/26.94  | | | 
% 175.30/26.94  | | | SIMP: (13) implies:
% 175.30/26.94  | | |   (14)  all_52_3 = e0
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REDUCE: (3), (14) imply:
% 175.30/26.94  | | |   (15)   ~ (e2 = e0)
% 175.30/26.94  | | | 
% 175.30/26.94  | | | SIMP: (15) implies:
% 175.30/26.94  | | |   (16)   ~ (e2 = e0)
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REDUCE: (2), (14) imply:
% 175.30/26.94  | | |   (17)  op(e3, e2) = e0
% 175.30/26.94  | | | 
% 175.30/26.94  | | | GROUND_INST: instantiating (7) with e0, e2, e2, e3, simplifying with (6),
% 175.30/26.94  | | |              (17) gives:
% 175.30/26.94  | | |   (18)  e2 = e0
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REDUCE: (16), (18) imply:
% 175.30/26.94  | | |   (19)  $false
% 175.30/26.94  | | | 
% 175.30/26.94  | | | CLOSE: (19) is inconsistent.
% 175.30/26.94  | | | 
% 175.30/26.94  | | End of split
% 175.30/26.94  | | 
% 175.30/26.94  | End of split
% 175.30/26.94  | 
% 175.30/26.94  End of proof
% 175.30/26.94  
% 175.30/26.94  Sub-proof #103 shows that the following formulas are inconsistent:
% 175.30/26.94  ----------------------------------------------------------------
% 175.30/26.94    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.30/26.94    (2)   ~ (all_52_17 = all_52_23)
% 175.30/26.94    (3)  op(e3, e2) = all_52_3
% 175.30/26.94    (4)   ~ (all_52_9 = all_52_25)
% 175.30/26.94    (5)  all_52_27 = e3
% 175.30/26.94    (6)   ~ (all_52_3 = all_10_2)
% 175.30/26.94    (7)  all_58_5 = all_52_13
% 175.30/26.94    (8)  op(e1, all_52_13) = e1
% 175.30/26.94    (9)  op(e0, all_52_15) = e0
% 175.30/26.94    (10)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.94    (11)  all_58_3 = all_10_2
% 175.30/26.94    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.94    (13)  all_58_15 = all_6_2
% 175.30/26.94    (14)   ~ (all_52_9 = all_4_2)
% 175.30/26.94    (15)   ~ (all_52_5 = all_52_7)
% 175.30/26.94    (16)  all_58_10 = all_52_15
% 175.30/26.94    (17)  all_58_7 = all_52_19
% 175.30/26.94    (18)  all_56_4 = all_52_9
% 175.30/26.94    (19)   ~ (all_52_17 = all_52_25)
% 175.30/26.94    (20)  all_58_4 = all_52_5
% 175.30/26.94    (21)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.94    (22)   ~ (e3 = e1)
% 175.30/26.94    (23)   ~ (all_52_27 = all_52_29)
% 175.30/26.94    (24)   ~ (all_52_17 = all_14_2)
% 175.30/26.94    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.94    (26)   ~ (all_52_7 = all_4_2)
% 175.30/26.94    (27)  all_58_1 = all_52_3
% 175.30/26.94    (28)  all_58_0 = all_4_2
% 175.30/26.94    (29)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/26.94    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.94    (31)  all_58_14 = all_52_29
% 175.30/26.94    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.94    (33)  all_58_8 = all_14_2
% 175.30/26.94    (34)  all_56_14 = all_52_29
% 175.30/26.94    (35)   ~ (all_52_3 = all_52_27)
% 175.30/26.94    (36)   ~ (all_52_3 = all_4_2)
% 175.30/26.94    (37)  op(e0, e3) = all_52_25
% 175.30/26.94    (38)  op(e3, all_52_17) = all_52_16
% 175.30/26.94    (39)  op(e3, all_52_9) = e3
% 175.30/26.94    (40)  all_58_13 = all_52_27
% 175.30/26.94    (41)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/26.94    (42)   ~ (all_52_9 = all_52_17)
% 175.30/26.94    (43)  all_58_6 = all_52_17
% 175.30/26.94    (44)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.30/26.94    (45)  all_56_0 = all_4_2
% 175.30/26.94    (46)  all_58_11 = all_52_23
% 175.30/26.94    (47)   ~ (all_52_7 = all_52_15)
% 175.30/26.94    (48)  op(e3, all_4_2) = e2
% 175.30/26.94    (49)  all_58_2 = all_52_9
% 175.30/26.94    (50)  op(e1, e3) = all_52_17
% 175.30/26.94    (51)   ~ (all_52_25 = all_4_2)
% 175.30/26.94    (52)  op(e2, all_10_2) = e2
% 175.30/26.94    (53)  op(e3, e3) = all_4_2
% 175.30/26.94    (54)  all_56_8 = all_52_17
% 175.30/26.94    (55)   ~ (all_52_17 = all_4_2)
% 175.30/26.94    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.94    (57)   ~ (all_52_25 = all_52_27)
% 175.30/26.94    (58)   ~ (all_52_27 = all_6_2)
% 175.30/26.94    (59)  op(e2, all_52_27) = all_52_26
% 175.30/26.94    (60)   ~ (all_52_17 = all_52_19)
% 175.30/26.94    (61)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.94    (62)  all_58_9 = all_52_7
% 175.30/26.94    (63)  all_58_12 = all_52_25
% 175.30/26.94    (64)   ~ (all_52_9 = all_52_15)
% 175.30/26.94    (65)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.94    (66)   ~ (e3 = e2)
% 175.30/26.94    (67)  op(e2, e3) = all_52_9
% 175.30/26.94  
% 175.30/26.94  Begin of proof
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (5), (35) imply:
% 175.30/26.94  |   (68)   ~ (all_52_3 = e3)
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (5), (57) imply:
% 175.30/26.94  |   (69)   ~ (all_52_25 = e3)
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (5), (58) imply:
% 175.30/26.94  |   (70)   ~ (all_6_2 = e3)
% 175.30/26.94  | 
% 175.30/26.94  | SIMP: (70) implies:
% 175.30/26.94  |   (71)   ~ (all_6_2 = e3)
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (5), (59) imply:
% 175.30/26.94  |   (72)  op(e2, e3) = all_52_26
% 175.30/26.94  | 
% 175.30/26.94  | GROUND_INST: instantiating (56) with all_52_9, all_52_26, e3, e2, simplifying
% 175.30/26.94  |              with (67), (72) gives:
% 175.30/26.94  |   (73)  all_52_9 = all_52_26
% 175.30/26.94  | 
% 175.30/26.94  | COMBINE_EQS: (18), (73) imply:
% 175.30/26.94  |   (74)  all_56_4 = all_52_26
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (64), (73) imply:
% 175.30/26.94  |   (75)   ~ (all_52_15 = all_52_26)
% 175.30/26.94  | 
% 175.30/26.94  | SIMP: (75) implies:
% 175.30/26.94  |   (76)   ~ (all_52_15 = all_52_26)
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (4), (73) imply:
% 175.30/26.94  |   (77)   ~ (all_52_25 = all_52_26)
% 175.30/26.94  | 
% 175.30/26.94  | SIMP: (77) implies:
% 175.30/26.94  |   (78)   ~ (all_52_25 = all_52_26)
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (14), (73) imply:
% 175.30/26.94  |   (79)   ~ (all_52_26 = all_4_2)
% 175.30/26.94  | 
% 175.30/26.94  | REDUCE: (39), (73) imply:
% 175.30/26.94  |   (80)  op(e3, all_52_26) = e3
% 175.30/26.94  | 
% 175.30/26.94  | BETA: splitting (1) gives:
% 175.30/26.94  | 
% 175.30/26.94  | Case 1:
% 175.30/26.94  | | 
% 175.30/26.94  | |   (81)  all_56_8 = e3
% 175.30/26.94  | | 
% 175.30/26.94  | | COMBINE_EQS: (54), (81) imply:
% 175.30/26.94  | |   (82)  all_52_17 = e3
% 175.30/26.94  | | 
% 175.30/26.94  | | SIMP: (82) implies:
% 175.30/26.94  | |   (83)  all_52_17 = e3
% 175.30/26.94  | | 
% 175.30/26.94  | | REDUCE: (2), (83) imply:
% 175.30/26.94  | |   (84)   ~ (all_52_23 = e3)
% 175.30/26.94  | | 
% 175.30/26.94  | | SIMP: (84) implies:
% 175.30/26.94  | |   (85)   ~ (all_52_23 = e3)
% 175.30/26.94  | | 
% 175.30/26.94  | | REDUCE: (19), (83) imply:
% 175.30/26.94  | |   (86)   ~ (all_52_25 = e3)
% 175.30/26.94  | | 
% 175.30/26.94  | | REDUCE: (55), (83) imply:
% 175.30/26.94  | |   (87)   ~ (all_4_2 = e3)
% 175.30/26.94  | | 
% 175.30/26.94  | | SIMP: (87) implies:
% 175.30/26.94  | |   (88)   ~ (all_4_2 = e3)
% 175.30/26.94  | | 
% 175.30/26.94  | | REDUCE: (38), (83) imply:
% 175.30/26.94  | |   (89)  op(e3, e3) = all_52_16
% 175.30/26.94  | | 
% 175.30/26.94  | | GROUND_INST: instantiating (56) with all_4_2, all_52_16, e3, e3, simplifying
% 175.30/26.94  | |              with (53), (89) gives:
% 175.30/26.94  | |   (90)  all_52_16 = all_4_2
% 175.30/26.94  | | 
% 175.30/26.94  | | BETA: splitting (61) gives:
% 175.30/26.94  | | 
% 175.30/26.94  | | Case 1:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (91)  all_58_9 = e3
% 175.30/26.94  | | | 
% 175.30/26.94  | | | COMBINE_EQS: (62), (91) imply:
% 175.30/26.94  | | |   (92)  all_52_7 = e3
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REF_CLOSE: (3), (6), (7), (8), (11), (14), (15), (16), (17), (20), (21),
% 175.30/26.94  | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 175.30/26.94  | | |            (32), (33), (34), (39), (40), (42), (43), (47), (49), (50),
% 175.30/26.94  | | |            (52), (53), (56), (60), (63), (65), (67), (69), (92) are
% 175.30/26.94  | | |            inconsistent by sub-proof #104.
% 175.30/26.94  | | | 
% 175.30/26.94  | | Case 2:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (93)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.94  | | | 
% 175.30/26.94  | | | BETA: splitting (93) gives:
% 175.30/26.94  | | | 
% 175.30/26.94  | | | Case 1:
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | |   (94)  all_58_10 = e3
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | COMBINE_EQS: (16), (94) imply:
% 175.30/26.94  | | | |   (95)  all_52_15 = e3
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | SIMP: (95) implies:
% 175.30/26.94  | | | |   (96)  all_52_15 = e3
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | REDUCE: (76), (96) imply:
% 175.30/26.94  | | | |   (97)   ~ (all_52_26 = e3)
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | SIMP: (97) implies:
% 175.30/26.94  | | | |   (98)   ~ (all_52_26 = e3)
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | REDUCE: (9), (96) imply:
% 175.30/26.94  | | | |   (99)  op(e0, e3) = e0
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | GROUND_INST: instantiating (56) with all_52_25, e0, e3, e0, simplifying
% 175.30/26.94  | | | |              with (37), (99) gives:
% 175.30/26.94  | | | |   (100)  all_52_25 = e0
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | REDUCE: (78), (100) imply:
% 175.30/26.94  | | | |   (101)   ~ (all_52_26 = e0)
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | SIMP: (101) implies:
% 175.30/26.94  | | | |   (102)   ~ (all_52_26 = e0)
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | REDUCE: (51), (100) imply:
% 175.30/26.94  | | | |   (103)   ~ (all_4_2 = e0)
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | SIMP: (103) implies:
% 175.30/26.94  | | | |   (104)   ~ (all_4_2 = e0)
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | BETA: splitting (44) gives:
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | Case 1:
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | |   (105)  all_56_4 = e3
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | | REF_CLOSE: (74), (98), (105) are inconsistent by sub-proof #818.
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | Case 2:
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | |   (106)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | | BETA: splitting (12) gives:
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | | Case 1:
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | |   (107)  all_56_0 = e3
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | | REF_CLOSE: (45), (88), (107) are inconsistent by sub-proof #1024.
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | Case 2:
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | |   (108)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | | BETA: splitting (41) gives:
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | | Case 1:
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | |   (109)  all_58_0 = e1
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | | COMBINE_EQS: (28), (109) imply:
% 175.30/26.94  | | | | | | |   (110)  all_4_2 = e1
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | | REDUCE: (79), (110) imply:
% 175.30/26.94  | | | | | | |   (111)   ~ (all_52_26 = e1)
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | | REF_CLOSE: (3), (56), (68), (74), (80), (102), (106), (111) are
% 175.30/26.94  | | | | | | |            inconsistent by sub-proof #766.
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | Case 2:
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | |   (112)   ~ (all_58_0 = e1)
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | | REDUCE: (28), (112) imply:
% 175.30/26.94  | | | | | | |   (113)   ~ (all_4_2 = e1)
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | | REF_CLOSE: (3), (10), (28), (36), (45), (48), (56), (104), (108),
% 175.30/26.94  | | | | | | |            (113) are inconsistent by sub-proof #114.
% 175.30/26.94  | | | | | | | 
% 175.30/26.94  | | | | | | End of split
% 175.30/26.94  | | | | | | 
% 175.30/26.94  | | | | | End of split
% 175.30/26.94  | | | | | 
% 175.30/26.94  | | | | End of split
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | Case 2:
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | |   (114)  all_58_11 = e3 | all_58_15 = e3
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | | REF_CLOSE: (13), (46), (71), (85), (114) are inconsistent by sub-proof
% 175.30/26.94  | | | |            #1016.
% 175.30/26.94  | | | | 
% 175.30/26.94  | | | End of split
% 175.30/26.94  | | | 
% 175.30/26.94  | | End of split
% 175.30/26.94  | | 
% 175.30/26.94  | Case 2:
% 175.30/26.94  | | 
% 175.30/26.94  | |   (115)   ~ (all_56_8 = e3)
% 175.30/26.94  | | 
% 175.30/26.94  | | REDUCE: (54), (115) imply:
% 175.30/26.94  | |   (116)   ~ (all_52_17 = e3)
% 175.30/26.94  | | 
% 175.30/26.94  | | BETA: splitting (32) gives:
% 175.30/26.94  | | 
% 175.30/26.94  | | Case 1:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (117)  all_58_0 = e3
% 175.30/26.94  | | | 
% 175.30/26.94  | | | COMBINE_EQS: (28), (117) imply:
% 175.30/26.94  | | |   (118)  all_4_2 = e3
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REF_CLOSE: (48), (53), (56), (66), (118) are inconsistent by sub-proof
% 175.30/26.94  | | |            #106.
% 175.30/26.94  | | | 
% 175.30/26.94  | | Case 2:
% 175.30/26.94  | | | 
% 175.30/26.94  | | |   (119)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.94  | | | 
% 175.30/26.94  | | | REF_CLOSE: (14), (39), (43), (49), (53), (56), (63), (69), (116), (119)
% 175.30/26.94  | | |            are inconsistent by sub-proof #396.
% 175.30/26.94  | | | 
% 175.30/26.94  | | End of split
% 175.30/26.94  | | 
% 175.30/26.94  | End of split
% 175.30/26.94  | 
% 175.30/26.94  End of proof
% 175.30/26.94  
% 175.30/26.94  Sub-proof #104 shows that the following formulas are inconsistent:
% 175.30/26.94  ----------------------------------------------------------------
% 175.30/26.94    (1)   ~ (all_52_25 = e3)
% 175.30/26.94    (2)  op(e3, e2) = all_52_3
% 175.30/26.94    (3)   ~ (all_52_3 = all_10_2)
% 175.30/26.94    (4)  all_52_7 = e3
% 175.30/26.94    (5)  all_58_5 = all_52_13
% 175.30/26.94    (6)  op(e1, all_52_13) = e1
% 175.30/26.94    (7)  all_58_3 = all_10_2
% 175.30/26.94    (8)   ~ (all_52_9 = all_4_2)
% 175.30/26.94    (9)   ~ (all_52_5 = all_52_7)
% 175.30/26.94    (10)  all_58_10 = all_52_15
% 175.30/26.94    (11)  all_58_7 = all_52_19
% 175.30/26.94    (12)  all_58_4 = all_52_5
% 175.30/26.94    (13)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.94    (14)   ~ (e3 = e1)
% 175.30/26.94    (15)   ~ (all_52_27 = all_52_29)
% 175.30/26.94    (16)   ~ (all_52_17 = all_14_2)
% 175.30/26.94    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.94    (18)   ~ (all_52_7 = all_4_2)
% 175.30/26.94    (19)  all_58_1 = all_52_3
% 175.30/26.94    (20)  all_58_0 = all_4_2
% 175.30/26.94    (21)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/26.94    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.94    (23)  all_58_14 = all_52_29
% 175.30/26.94    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.94    (25)  all_58_8 = all_14_2
% 175.30/26.94    (26)  all_56_14 = all_52_29
% 175.30/26.94    (27)  op(e3, all_52_9) = e3
% 175.30/26.94    (28)  all_58_13 = all_52_27
% 175.30/26.94    (29)   ~ (all_52_9 = all_52_17)
% 175.30/26.94    (30)  all_58_6 = all_52_17
% 175.30/26.94    (31)   ~ (all_52_7 = all_52_15)
% 175.30/26.94    (32)  all_58_2 = all_52_9
% 175.30/26.94    (33)  op(e1, e3) = all_52_17
% 175.30/26.94    (34)  op(e2, all_10_2) = e2
% 175.30/26.94    (35)  op(e3, e3) = all_4_2
% 175.30/26.94    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.94    (37)   ~ (all_52_17 = all_52_19)
% 175.30/26.94    (38)  all_58_12 = all_52_25
% 175.30/26.94    (39)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.94    (40)  op(e2, e3) = all_52_9
% 175.30/26.94  
% 175.30/26.94  Begin of proof
% 175.30/26.94  | 
% 175.30/26.95  | SIMP: (4) implies:
% 175.30/26.95  |   (41)  all_52_7 = e3
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (9), (41) imply:
% 175.30/26.95  |   (42)   ~ (all_52_5 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (31), (41) imply:
% 175.30/26.95  |   (43)   ~ (all_52_15 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | SIMP: (43) implies:
% 175.30/26.95  |   (44)   ~ (all_52_15 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (18), (41) imply:
% 175.30/26.95  |   (45)   ~ (all_4_2 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | SIMP: (45) implies:
% 175.30/26.95  |   (46)   ~ (all_4_2 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 175.30/26.95  |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 175.30/26.95  |            (27), (28), (29), (30), (32), (33), (34), (35), (36), (37), (38),
% 175.30/26.95  |            (39), (40), (42), (44), (46) are inconsistent by sub-proof #123.
% 175.30/26.95  | 
% 175.30/26.95  End of proof
% 175.30/26.95  
% 175.30/26.95  Sub-proof #105 shows that the following formulas are inconsistent:
% 175.30/26.95  ----------------------------------------------------------------
% 175.30/26.95    (1)  op(e3, e2) = all_52_3
% 175.30/26.95    (2)   ~ (all_52_3 = all_10_2)
% 175.30/26.95    (3)  all_56_15 = e3
% 175.30/26.95    (4)  all_58_5 = all_52_13
% 175.30/26.95    (5)  op(e1, all_52_13) = e1
% 175.30/26.95    (6)  all_56_15 = all_6_2
% 175.30/26.95    (7)  all_58_3 = all_10_2
% 175.30/26.95    (8)   ~ (all_52_9 = all_4_2)
% 175.30/26.95    (9)  all_58_10 = all_52_15
% 175.30/26.95    (10)  all_58_7 = all_52_19
% 175.30/26.95    (11)   ~ (all_52_15 = all_6_2)
% 175.30/26.95    (12)   ~ (e3 = e1)
% 175.30/26.95    (13)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.95    (14)  all_58_1 = all_52_3
% 175.30/26.95    (15)  all_58_0 = all_4_2
% 175.30/26.95    (16)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.95    (17)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.95    (18)  op(e0, e3) = all_52_25
% 175.30/26.95    (19)  op(e0, all_6_2) = all_6_1
% 175.30/26.95    (20)  op(e3, all_52_9) = e3
% 175.30/26.95    (21)  all_58_13 = all_52_27
% 175.30/26.95    (22)  all_58_6 = all_52_17
% 175.30/26.95    (23)  op(e3, all_4_2) = e2
% 175.30/26.95    (24)  all_58_2 = all_52_9
% 175.30/26.95    (25)   ~ (all_52_25 = all_6_2)
% 175.30/26.95    (26)  op(e1, e3) = all_52_17
% 175.30/26.95    (27)  op(e2, all_10_2) = e2
% 175.30/26.95    (28)  op(e3, e3) = all_4_2
% 175.30/26.95    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.95    (30)   ~ (all_52_27 = all_6_2)
% 175.30/26.95    (31)   ~ (all_52_17 = all_52_19)
% 175.30/26.95    (32)  all_58_12 = all_52_25
% 175.30/26.95    (33)   ~ (e3 = e2)
% 175.30/26.95    (34)  op(e2, e3) = all_52_9
% 175.30/26.95  
% 175.30/26.95  Begin of proof
% 175.30/26.95  | 
% 175.30/26.95  | COMBINE_EQS: (3), (6) imply:
% 175.30/26.95  |   (35)  all_6_2 = e3
% 175.30/26.95  | 
% 175.30/26.95  | SIMP: (35) implies:
% 175.30/26.95  |   (36)  all_6_2 = e3
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (11), (36) imply:
% 175.30/26.95  |   (37)   ~ (all_52_15 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (25), (36) imply:
% 175.30/26.95  |   (38)   ~ (all_52_25 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (30), (36) imply:
% 175.30/26.95  |   (39)   ~ (all_52_27 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (19), (36) imply:
% 175.30/26.95  |   (40)  op(e0, e3) = all_6_1
% 175.30/26.95  | 
% 175.30/26.95  | GROUND_INST: instantiating (29) with all_52_25, all_6_1, e3, e0, simplifying
% 175.30/26.95  |              with (18), (40) gives:
% 175.30/26.95  |   (41)  all_52_25 = all_6_1
% 175.30/26.95  | 
% 175.30/26.95  | COMBINE_EQS: (32), (41) imply:
% 175.30/26.95  |   (42)  all_58_12 = all_6_1
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (38), (41) imply:
% 175.30/26.95  |   (43)   ~ (all_6_1 = e3)
% 175.30/26.95  | 
% 175.30/26.95  | BETA: splitting (17) gives:
% 175.30/26.95  | 
% 175.30/26.95  | Case 1:
% 175.30/26.95  | | 
% 175.30/26.95  | |   (44)  all_58_0 = e3
% 175.30/26.95  | | 
% 175.30/26.95  | | COMBINE_EQS: (15), (44) imply:
% 175.30/26.95  | |   (45)  all_4_2 = e3
% 175.30/26.95  | | 
% 175.30/26.95  | | REF_CLOSE: (23), (28), (29), (33), (45) are inconsistent by sub-proof #106.
% 175.30/26.95  | | 
% 175.30/26.95  | Case 2:
% 175.30/26.95  | | 
% 175.30/26.95  | |   (46)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.95  | | 
% 175.30/26.95  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (12), (13), (14), (16),
% 175.30/26.95  | |            (20), (21), (22), (24), (26), (27), (28), (29), (31), (34), (37),
% 175.30/26.95  | |            (39), (42), (43), (46) are inconsistent by sub-proof #774.
% 175.30/26.95  | | 
% 175.30/26.95  | End of split
% 175.30/26.95  | 
% 175.30/26.95  End of proof
% 175.30/26.95  
% 175.30/26.95  Sub-proof #106 shows that the following formulas are inconsistent:
% 175.30/26.95  ----------------------------------------------------------------
% 175.30/26.95    (1)  all_4_2 = e3
% 175.30/26.95    (2)  op(e3, all_4_2) = e2
% 175.30/26.95    (3)  op(e3, e3) = all_4_2
% 175.30/26.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.95    (5)   ~ (e3 = e2)
% 175.30/26.95  
% 175.30/26.95  Begin of proof
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (1), (2) imply:
% 175.30/26.95  |   (6)  op(e3, e3) = e2
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (1), (3) imply:
% 175.30/26.95  |   (7)  op(e3, e3) = e3
% 175.30/26.95  | 
% 175.30/26.95  | GROUND_INST: instantiating (4) with e2, e3, e3, e3, simplifying with (6), (7)
% 175.30/26.95  |              gives:
% 175.30/26.95  |   (8)  e3 = e2
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (5), (8) imply:
% 175.30/26.95  |   (9)  $false
% 175.30/26.95  | 
% 175.30/26.95  | CLOSE: (9) is inconsistent.
% 175.30/26.95  | 
% 175.30/26.95  End of proof
% 175.30/26.95  
% 175.30/26.95  Sub-proof #107 shows that the following formulas are inconsistent:
% 175.30/26.95  ----------------------------------------------------------------
% 175.30/26.95    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.95    (2)   ~ (all_52_5 = all_52_13)
% 175.30/26.95    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.30/26.95    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/26.95    (5)   ~ (all_52_27 = all_10_2)
% 175.30/26.95    (6)   ~ (all_52_17 = all_52_23)
% 175.30/26.95    (7)   ~ (all_6_0 = e3)
% 175.30/26.95    (8)  op(e2, all_10_2) = all_10_1
% 175.30/26.95    (9)   ~ (all_52_13 = all_52_29)
% 175.30/26.95    (10)  all_56_3 = all_52_7
% 175.30/26.95    (11)  op(e3, e2) = all_52_3
% 175.30/26.95    (12)   ~ (all_52_9 = all_52_25)
% 175.30/26.95    (13)  op(e3, all_52_25) = all_52_24
% 175.30/26.95    (14)   ~ (all_52_19 = all_52_23)
% 175.30/26.95    (15)  all_56_11 = all_52_23
% 175.30/26.95    (16)  op(e1, e2) = all_52_19
% 175.30/26.95    (17)  op(e3, all_52_9) = all_52_8
% 175.30/26.95    (18)   ~ (all_52_3 = all_10_2)
% 175.30/26.95    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.95    (20)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.30/26.95    (21)  all_58_5 = all_52_13
% 175.30/26.95    (22)   ~ (all_52_25 = all_52_29)
% 175.30/26.95    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.95    (24)  op(e2, e0) = all_52_15
% 175.30/26.95    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.95    (26)  all_58_3 = all_10_2
% 175.30/26.95    (27)  all_56_9 = all_52_19
% 175.30/26.95    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.95    (29)  all_58_15 = all_6_2
% 175.30/26.95    (30)   ~ (all_52_9 = all_4_2)
% 175.30/26.95    (31)   ~ (all_52_5 = all_52_7)
% 175.30/26.95    (32)  all_58_10 = all_52_15
% 175.30/26.95    (33)   ~ (all_52_5 = all_4_2)
% 175.30/26.95    (34)  all_58_7 = all_52_19
% 175.30/26.95    (35)   ~ (all_52_15 = all_6_2)
% 175.30/26.95    (36)   ~ (all_52_17 = all_52_25)
% 175.30/26.95    (37)  op(e0, e1) = all_52_29
% 175.30/26.95    (38)  all_58_4 = all_52_5
% 175.30/26.95    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.95    (40)   ~ (e3 = e1)
% 175.30/26.95    (41)   ~ (all_52_27 = all_52_29)
% 175.30/26.95    (42)   ~ (all_52_17 = all_14_2)
% 175.30/26.95    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.95    (44)   ~ (all_52_7 = all_4_2)
% 175.30/26.95    (45)  all_58_1 = all_52_3
% 175.30/26.95    (46)  all_58_0 = all_4_2
% 175.30/26.95    (47)  op(e1, all_52_13) = all_52_12
% 175.30/26.95    (48)  all_52_0 = e2
% 175.30/26.95    (49)  op(e0, e0) = all_6_2
% 175.30/26.95    (50)  op(e1, all_52_29) = all_52_28
% 175.30/26.95    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.30/26.95    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/26.95    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.30/26.95    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.95    (55)  all_58_14 = all_52_29
% 175.30/26.95    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.95    (57)  op(e2, all_4_2) = all_4_0
% 175.30/26.95    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.95    (59)  op(e2, e1) = all_52_13
% 175.30/26.95    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.95    (61)  all_58_8 = all_14_2
% 175.30/26.95    (62)  op(e0, e2) = all_52_27
% 175.30/26.95    (63)  all_56_14 = all_52_29
% 175.30/26.95    (64)   ~ (all_52_5 = all_14_2)
% 175.30/26.95    (65)   ~ (all_52_3 = all_52_27)
% 175.30/26.95    (66)   ~ (all_52_3 = all_4_2)
% 175.30/26.95    (67)  op(all_6_1, all_6_2) = all_6_0
% 175.30/26.95    (68)  op(e0, e3) = all_52_25
% 175.30/26.95    (69)  op(e0, all_6_2) = all_6_1
% 175.30/26.95    (70)   ~ (all_52_9 = all_10_2)
% 175.30/26.95    (71)  op(e3, all_52_17) = all_52_16
% 175.30/26.95    (72)  all_52_10 = all_10_1
% 175.30/26.95    (73)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/26.95    (74)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/26.95    (75)   ~ (all_52_9 = all_52_13)
% 175.30/26.95    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.95    (77)  op(e0, all_52_23) = all_52_22
% 175.30/26.95    (78)   ~ (all_52_15 = all_52_23)
% 175.30/26.95    (79)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/26.95    (80)   ~ (all_52_5 = all_52_29)
% 175.30/26.95    (81)  all_56_12 = all_52_25
% 175.30/26.95    (82)  all_58_13 = all_52_27
% 175.30/26.95    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/26.95    (84)  all_56_5 = all_10_2
% 175.30/26.95    (85)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.95    (86)   ~ (all_52_9 = all_52_17)
% 175.30/26.95    (87)  all_58_6 = all_52_17
% 175.30/26.95    (88)   ~ (all_52_3 = all_52_7)
% 175.30/26.95    (89)  op(e2, all_52_19) = all_52_18
% 175.30/26.95    (90)  all_56_0 = all_4_2
% 175.30/26.95    (91)  all_58_11 = all_52_23
% 175.30/26.95    (92)   ~ (all_52_3 = all_52_19)
% 175.30/26.95    (93)   ~ (all_52_7 = all_52_15)
% 175.30/26.95    (94)  op(e0, all_52_15) = all_52_14
% 175.30/26.95    (95)   ~ (all_52_29 = all_14_2)
% 175.30/26.95    (96)   ~ (all_4_0 = e1)
% 175.30/26.95    (97)   ~ (all_52_19 = all_10_2)
% 175.30/26.95    (98)  all_58_15 = e0
% 175.30/26.95    (99)  op(e3, all_4_2) = e2
% 175.30/26.95    (100)   ~ (all_52_23 = all_6_2)
% 175.30/26.95    (101)   ~ (all_6_0 = e2)
% 175.30/26.95    (102)   ~ (all_52_29 = all_6_2)
% 175.30/26.95    (103)  all_58_2 = all_52_9
% 175.30/26.95    (104)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.95    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.95    (106)  op(e3, e1) = all_52_5
% 175.30/26.95    (107)   ~ (e2 = e1)
% 175.30/26.95    (108)  all_56_10 = all_14_2
% 175.30/26.95    (109)   ~ (all_52_25 = all_6_2)
% 175.30/26.95    (110)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.95    (111)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.95    (112)  op(e1, e3) = all_52_17
% 175.30/26.95    (113)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/26.95    (114)   ~ (all_52_25 = all_4_2)
% 175.30/26.95    (115)  op(e3, e0) = all_52_7
% 175.30/26.95    (116)  op(e3, e3) = all_4_2
% 175.30/26.95    (117)   ~ (all_10_1 = e3)
% 175.30/26.95    (118)  all_56_8 = all_52_17
% 175.30/26.95    (119)   ~ (all_52_17 = all_4_2)
% 175.30/26.95    (120)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.95             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.95    (121)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.30/26.95           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 175.30/26.95           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.30/26.95           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.30/26.95    (122)   ~ (all_52_25 = all_52_27)
% 175.30/26.95    (123)   ~ (all_52_27 = all_6_2)
% 175.30/26.95    (124)   ~ (all_52_15 = all_10_2)
% 175.30/26.95    (125)   ~ (all_52_19 = all_52_27)
% 175.30/26.95    (126)  all_56_7 = all_52_15
% 175.30/26.95    (127)   ~ (all_52_7 = all_52_23)
% 175.30/26.95    (128)   ~ (all_52_13 = all_10_2)
% 175.30/26.95    (129)   ~ (all_6_0 = e1)
% 175.30/26.95    (130)  op(e2, all_52_27) = all_52_26
% 175.30/26.95    (131)  all_52_20 = all_14_1
% 175.30/26.95    (132)   ~ (all_52_17 = all_52_19)
% 175.30/26.95    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.95    (134)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.95    (135)  op(e1, all_14_2) = all_14_1
% 175.30/26.95    (136)  all_58_9 = all_52_7
% 175.30/26.95    (137)  all_58_12 = all_52_25
% 175.30/26.95    (138)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.30/26.95    (139)   ~ (all_52_9 = all_52_15)
% 175.30/26.95    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.95    (141)   ~ (e3 = e2)
% 175.30/26.95    (142)   ~ (all_52_19 = all_14_2)
% 175.30/26.95    (143)  op(e2, e3) = all_52_9
% 175.30/26.95    (144)  all_56_13 = all_52_27
% 175.30/26.95  
% 175.30/26.95  Begin of proof
% 175.30/26.95  | 
% 175.30/26.95  | COMBINE_EQS: (29), (98) imply:
% 175.30/26.95  |   (145)  all_6_2 = e0
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (35), (145) imply:
% 175.30/26.95  |   (146)   ~ (all_52_15 = e0)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (100), (145) imply:
% 175.30/26.95  |   (147)   ~ (all_52_23 = e0)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (109), (145) imply:
% 175.30/26.95  |   (148)   ~ (all_52_25 = e0)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (123), (145) imply:
% 175.30/26.95  |   (149)   ~ (all_52_27 = e0)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (102), (145) imply:
% 175.30/26.95  |   (150)   ~ (all_52_29 = e0)
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (67), (145) imply:
% 175.30/26.95  |   (151)  op(all_6_1, e0) = all_6_0
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (69), (145) imply:
% 175.30/26.95  |   (152)  op(e0, e0) = all_6_1
% 175.30/26.95  | 
% 175.30/26.95  | REDUCE: (49), (145) imply:
% 175.30/26.95  |   (153)  op(e0, e0) = e0
% 175.30/26.95  | 
% 175.30/26.95  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.30/26.95  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.30/26.95  |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34), (36),
% 175.30/26.95  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 175.30/26.95  |            (48), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 175.30/26.95  |            (60), (61), (62), (63), (64), (65), (66), (68), (70), (71), (72),
% 175.30/26.95  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 175.30/26.95  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 175.30/26.95  |            (95), (96), (97), (98), (99), (101), (103), (104), (105), (106),
% 175.30/26.95  |            (107), (108), (110), (111), (112), (113), (114), (115), (116),
% 175.30/26.95  |            (117), (118), (119), (120), (121), (122), (124), (125), (126),
% 175.30/26.95  |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 175.30/26.95  |            (136), (137), (138), (139), (140), (141), (142), (143), (144),
% 175.30/26.95  |            (146), (147), (148), (149), (150), (151), (152), (153) are
% 175.30/26.95  |            inconsistent by sub-proof #108.
% 175.30/26.95  | 
% 175.30/26.95  End of proof
% 175.30/26.95  
% 175.30/26.95  Sub-proof #108 shows that the following formulas are inconsistent:
% 175.30/26.95  ----------------------------------------------------------------
% 175.30/26.95    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.95    (2)   ~ (all_52_5 = all_52_13)
% 175.30/26.95    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.30/26.95    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/26.95    (5)   ~ (all_52_27 = all_10_2)
% 175.30/26.95    (6)   ~ (all_52_17 = all_52_23)
% 175.30/26.95    (7)   ~ (all_6_0 = e3)
% 175.30/26.95    (8)  op(e2, all_10_2) = all_10_1
% 175.30/26.95    (9)   ~ (all_52_13 = all_52_29)
% 175.30/26.95    (10)  all_56_3 = all_52_7
% 175.30/26.95    (11)  op(e3, e2) = all_52_3
% 175.30/26.95    (12)   ~ (all_52_9 = all_52_25)
% 175.30/26.95    (13)  op(e3, all_52_25) = all_52_24
% 175.30/26.95    (14)   ~ (all_52_19 = all_52_23)
% 175.30/26.95    (15)  all_56_11 = all_52_23
% 175.30/26.95    (16)  op(e1, e2) = all_52_19
% 175.30/26.95    (17)   ~ (all_52_27 = e0)
% 175.30/26.95    (18)  op(e3, all_52_9) = all_52_8
% 175.30/26.95    (19)   ~ (all_52_23 = e0)
% 175.30/26.95    (20)   ~ (all_52_3 = all_10_2)
% 175.30/26.95    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.95    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.30/26.95    (23)  all_58_5 = all_52_13
% 175.30/26.95    (24)   ~ (all_52_25 = all_52_29)
% 175.30/26.95    (25)  op(e0, e0) = all_6_1
% 175.30/26.95    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.95    (27)  op(e2, e0) = all_52_15
% 175.30/26.95    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.95    (29)  all_58_3 = all_10_2
% 175.30/26.95    (30)  all_56_9 = all_52_19
% 175.30/26.95    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.95    (32)   ~ (all_52_9 = all_4_2)
% 175.30/26.95    (33)   ~ (all_52_5 = all_52_7)
% 175.30/26.95    (34)  all_58_10 = all_52_15
% 175.30/26.95    (35)   ~ (all_52_5 = all_4_2)
% 175.30/26.95    (36)  all_58_7 = all_52_19
% 175.30/26.95    (37)   ~ (all_52_17 = all_52_25)
% 175.30/26.95    (38)  op(e0, e1) = all_52_29
% 175.30/26.95    (39)  all_58_4 = all_52_5
% 175.30/26.95    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.95    (41)   ~ (e3 = e1)
% 175.30/26.95    (42)   ~ (all_52_27 = all_52_29)
% 175.30/26.95    (43)   ~ (all_52_17 = all_14_2)
% 175.30/26.95    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.95    (45)   ~ (all_52_7 = all_4_2)
% 175.30/26.95    (46)  all_58_1 = all_52_3
% 175.30/26.95    (47)  all_58_0 = all_4_2
% 175.30/26.95    (48)  op(e1, all_52_13) = all_52_12
% 175.30/26.95    (49)  all_52_0 = e2
% 175.30/26.95    (50)  op(e1, all_52_29) = all_52_28
% 175.30/26.95    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.30/26.95    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/26.95    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.30/26.95    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.95    (55)  all_58_14 = all_52_29
% 175.30/26.95    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.95    (57)  op(e2, all_4_2) = all_4_0
% 175.30/26.95    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.95    (59)  op(e2, e1) = all_52_13
% 175.30/26.95    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.95    (61)  all_58_8 = all_14_2
% 175.30/26.95    (62)  op(e0, e2) = all_52_27
% 175.30/26.95    (63)  all_56_14 = all_52_29
% 175.30/26.95    (64)   ~ (all_52_5 = all_14_2)
% 175.30/26.95    (65)   ~ (all_52_3 = all_52_27)
% 175.30/26.95    (66)   ~ (all_52_3 = all_4_2)
% 175.30/26.95    (67)  op(e0, e3) = all_52_25
% 175.30/26.95    (68)   ~ (all_52_9 = all_10_2)
% 175.30/26.95    (69)  op(e3, all_52_17) = all_52_16
% 175.30/26.95    (70)  all_52_10 = all_10_1
% 175.30/26.95    (71)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/26.95    (72)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/26.95    (73)   ~ (all_52_9 = all_52_13)
% 175.30/26.95    (74)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.95    (75)  op(e0, all_52_23) = all_52_22
% 175.30/26.95    (76)   ~ (all_52_15 = all_52_23)
% 175.30/26.95    (77)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/26.95    (78)   ~ (all_52_5 = all_52_29)
% 175.30/26.95    (79)  all_56_12 = all_52_25
% 175.30/26.95    (80)  all_58_13 = all_52_27
% 175.30/26.95    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/26.95    (82)  all_56_5 = all_10_2
% 175.30/26.95    (83)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.95    (84)  op(e0, e0) = e0
% 175.30/26.95    (85)   ~ (all_52_25 = e0)
% 175.30/26.95    (86)   ~ (all_52_9 = all_52_17)
% 175.30/26.95    (87)  all_58_6 = all_52_17
% 175.30/26.95    (88)   ~ (all_52_3 = all_52_7)
% 175.30/26.95    (89)  op(e2, all_52_19) = all_52_18
% 175.30/26.95    (90)  all_56_0 = all_4_2
% 175.30/26.95    (91)  all_58_11 = all_52_23
% 175.30/26.95    (92)   ~ (all_52_3 = all_52_19)
% 175.30/26.95    (93)   ~ (all_52_7 = all_52_15)
% 175.30/26.95    (94)  op(e0, all_52_15) = all_52_14
% 175.30/26.95    (95)   ~ (all_52_29 = all_14_2)
% 175.30/26.95    (96)   ~ (all_4_0 = e1)
% 175.30/26.95    (97)   ~ (all_52_19 = all_10_2)
% 175.30/26.95    (98)  all_58_15 = e0
% 175.30/26.95    (99)  op(e3, all_4_2) = e2
% 175.30/26.95    (100)   ~ (all_6_0 = e2)
% 175.30/26.95    (101)  all_58_2 = all_52_9
% 175.30/26.95    (102)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.95    (103)   ~ (all_52_29 = e0)
% 175.30/26.95    (104)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.95    (105)  op(e3, e1) = all_52_5
% 175.30/26.95    (106)   ~ (e2 = e1)
% 175.30/26.95    (107)  all_56_10 = all_14_2
% 175.30/26.95    (108)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.95    (109)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.95    (110)  op(e1, e3) = all_52_17
% 175.30/26.95    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/26.95    (112)   ~ (all_52_25 = all_4_2)
% 175.30/26.95    (113)  op(e3, e0) = all_52_7
% 175.30/26.95    (114)  op(e3, e3) = all_4_2
% 175.30/26.95    (115)   ~ (all_10_1 = e3)
% 175.30/26.95    (116)  all_56_8 = all_52_17
% 175.30/26.95    (117)   ~ (all_52_17 = all_4_2)
% 175.30/26.95    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.95             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.95    (119)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.30/26.95           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 175.30/26.95           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.30/26.95           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.30/26.95    (120)   ~ (all_52_25 = all_52_27)
% 175.30/26.95    (121)   ~ (all_52_15 = all_10_2)
% 175.30/26.95    (122)   ~ (all_52_19 = all_52_27)
% 175.30/26.95    (123)  all_56_7 = all_52_15
% 175.30/26.95    (124)   ~ (all_52_15 = e0)
% 175.30/26.95    (125)  op(all_6_1, e0) = all_6_0
% 175.30/26.95    (126)   ~ (all_52_7 = all_52_23)
% 175.30/26.95    (127)   ~ (all_52_13 = all_10_2)
% 175.30/26.95    (128)   ~ (all_6_0 = e1)
% 175.30/26.95    (129)  op(e2, all_52_27) = all_52_26
% 175.30/26.95    (130)  all_52_20 = all_14_1
% 175.30/26.95    (131)   ~ (all_52_17 = all_52_19)
% 175.30/26.95    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.96    (133)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.96    (134)  op(e1, all_14_2) = all_14_1
% 175.30/26.96    (135)  all_58_9 = all_52_7
% 175.30/26.96    (136)  all_58_12 = all_52_25
% 175.30/26.96    (137)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.30/26.96    (138)   ~ (all_52_9 = all_52_15)
% 175.30/26.96    (139)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.96    (140)   ~ (e3 = e2)
% 175.30/26.96    (141)   ~ (all_52_19 = all_14_2)
% 175.30/26.96    (142)  op(e2, e3) = all_52_9
% 175.30/26.96    (143)  all_56_13 = all_52_27
% 175.30/26.96  
% 175.30/26.96  Begin of proof
% 175.30/26.96  | 
% 175.30/26.96  | GROUND_INST: instantiating (118) with e0, all_6_1, e0, e0, simplifying with
% 175.30/26.96  |              (25), (84) gives:
% 175.30/26.96  |   (144)  all_6_1 = e0
% 175.30/26.96  | 
% 175.30/26.96  | REDUCE: (125), (144) imply:
% 175.30/26.96  |   (145)  op(e0, e0) = all_6_0
% 175.30/26.96  | 
% 175.30/26.96  | GROUND_INST: instantiating (118) with e0, all_6_0, e0, e0, simplifying with
% 175.30/26.96  |              (84), (145) gives:
% 175.30/26.96  |   (146)  all_6_0 = e0
% 175.30/26.96  | 
% 175.30/26.96  | REDUCE: (7), (146) imply:
% 175.30/26.96  |   (147)   ~ (e3 = e0)
% 175.30/26.96  | 
% 175.30/26.96  | SIMP: (147) implies:
% 175.30/26.96  |   (148)   ~ (e3 = e0)
% 175.30/26.96  | 
% 175.30/26.96  | REDUCE: (100), (146) imply:
% 175.30/26.96  |   (149)   ~ (e2 = e0)
% 175.30/26.96  | 
% 175.30/26.96  | SIMP: (149) implies:
% 175.30/26.96  |   (150)   ~ (e2 = e0)
% 175.30/26.96  | 
% 175.30/26.96  | REDUCE: (128), (146) imply:
% 175.30/26.96  |   (151)   ~ (e1 = e0)
% 175.30/26.96  | 
% 175.30/26.96  | SIMP: (151) implies:
% 175.30/26.96  |   (152)   ~ (e1 = e0)
% 175.30/26.96  | 
% 175.30/26.96  | BETA: splitting (119) gives:
% 175.30/26.96  | 
% 175.30/26.96  | Case 1:
% 175.30/26.96  | | 
% 175.30/26.96  | |   (153)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.30/26.96  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.30/26.96  | | 
% 175.30/26.96  | | REF_CLOSE: (6), (8), (11), (12), (17), (18), (20), (23), (28), (29), (32),
% 175.30/26.96  | |            (33), (34), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 175.30/26.96  | |            (45), (46), (47), (48), (49), (52), (54), (55), (58), (60), (61),
% 175.30/26.96  | |            (62), (63), (67), (70), (71), (77), (80), (85), (86), (87), (88),
% 175.30/26.96  | |            (91), (93), (94), (97), (98), (101), (103), (106), (107), (110),
% 175.30/26.96  | |            (111), (114), (115), (118), (120), (123), (126), (131), (132),
% 175.30/26.96  | |            (135), (136), (139), (140), (141), (142), (148), (150), (152),
% 175.30/26.96  | |            (153) are inconsistent by sub-proof #120.
% 175.30/26.96  | | 
% 175.30/26.96  | Case 2:
% 175.30/26.96  | | 
% 175.30/26.96  | |   (154)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 175.30/26.96  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 175.30/26.96  | |            e0)
% 175.30/26.96  | | 
% 175.30/26.96  | | BETA: splitting (154) gives:
% 175.30/26.96  | | 
% 175.30/26.96  | | Case 1:
% 175.30/26.96  | | | 
% 175.30/26.96  | | |   (155)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.30/26.96  | | | 
% 175.30/26.96  | | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (11), (12), (14), (15), (17),
% 175.30/26.96  | | |            (19), (20), (23), (24), (25), (28), (29), (30), (31), (32),
% 175.30/26.96  | | |            (34), (36), (37), (38), (40), (41), (42), (44), (45), (46),
% 175.30/26.96  | | |            (47), (50), (51), (54), (55), (56), (58), (60), (61), (62),
% 175.30/26.96  | | |            (64), (66), (67), (68), (69), (71), (72), (74), (75), (76),
% 175.30/26.96  | | |            (77), (78), (79), (80), (81), (82), (84), (85), (86), (87),
% 175.30/26.96  | | |            (88), (89), (90), (91), (95), (97), (98), (100), (101), (102),
% 175.30/26.96  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 175.30/26.96  | | |            (112), (113), (114), (116), (117), (118), (120), (122), (123),
% 175.30/26.96  | | |            (124), (125), (126), (128), (130), (132), (133), (134), (135),
% 175.30/26.96  | | |            (136), (137), (138), (140), (141), (142), (143), (155) are
% 175.30/26.96  | | |            inconsistent by sub-proof #117.
% 175.30/26.96  | | | 
% 175.30/26.96  | | Case 2:
% 175.30/26.96  | | | 
% 175.30/26.96  | | |   (156)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.30/26.96  | | | 
% 175.30/26.96  | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 175.30/26.96  | | |            (15), (16), (18), (19), (20), (21), (22), (23), (24), (26),
% 175.30/26.96  | | |            (27), (28), (29), (31), (32), (33), (34), (35), (36), (37),
% 175.30/26.96  | | |            (39), (40), (41), (43), (44), (45), (46), (47), (50), (53),
% 175.30/26.96  | | |            (55), (56), (57), (59), (60), (61), (65), (66), (68), (69),
% 175.30/26.96  | | |            (72), (73), (74), (76), (78), (79), (80), (82), (83), (85),
% 175.30/26.96  | | |            (86), (87), (88), (90), (91), (92), (93), (95), (96), (97),
% 175.30/26.96  | | |            (98), (99), (101), (102), (104), (105), (108), (109), (110),
% 175.30/26.96  | | |            (112), (113), (114), (117), (118), (120), (121), (127), (129),
% 175.30/26.96  | | |            (133), (135), (136), (139), (140), (142), (143), (148), (150),
% 175.30/26.96  | | |            (152), (156) are inconsistent by sub-proof #109.
% 175.30/26.96  | | | 
% 175.30/26.96  | | End of split
% 175.30/26.96  | | 
% 175.30/26.96  | End of split
% 175.30/26.96  | 
% 175.30/26.96  End of proof
% 175.30/26.96  
% 175.30/26.96  Sub-proof #109 shows that the following formulas are inconsistent:
% 175.30/26.96  ----------------------------------------------------------------
% 175.30/26.96    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.96    (2)   ~ (all_52_5 = all_52_13)
% 175.30/26.96    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/26.96    (4)   ~ (all_52_27 = all_10_2)
% 175.30/26.96    (5)  op(e2, all_10_2) = all_10_1
% 175.30/26.96    (6)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.30/26.96    (7)   ~ (all_52_13 = all_52_29)
% 175.30/26.96    (8)  all_56_3 = all_52_7
% 175.30/26.96    (9)  op(e3, e2) = all_52_3
% 175.30/26.96    (10)   ~ (all_52_9 = all_52_25)
% 175.30/26.96    (11)  op(e3, all_52_25) = all_52_24
% 175.30/26.96    (12)   ~ (all_52_19 = all_52_23)
% 175.30/26.96    (13)  all_56_11 = all_52_23
% 175.30/26.96    (14)  op(e1, e2) = all_52_19
% 175.30/26.96    (15)  op(e3, all_52_9) = all_52_8
% 175.30/26.96    (16)   ~ (all_52_23 = e0)
% 175.30/26.96    (17)   ~ (all_52_3 = all_10_2)
% 175.30/26.96    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.96    (19)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.30/26.96    (20)  all_58_5 = all_52_13
% 175.30/26.96    (21)   ~ (all_52_25 = all_52_29)
% 175.30/26.96    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.96    (23)  op(e2, e0) = all_52_15
% 175.30/26.96    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.96    (25)  all_58_3 = all_10_2
% 175.30/26.96    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.96    (27)   ~ (all_52_9 = all_4_2)
% 175.30/26.96    (28)   ~ (all_52_5 = all_52_7)
% 175.30/26.96    (29)  all_58_10 = all_52_15
% 175.30/26.96    (30)   ~ (all_52_5 = all_4_2)
% 175.30/26.96    (31)  all_58_7 = all_52_19
% 175.30/26.96    (32)   ~ (all_52_17 = all_52_25)
% 175.30/26.96    (33)  all_58_4 = all_52_5
% 175.30/26.96    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.96    (35)   ~ (e3 = e1)
% 175.30/26.96    (36)   ~ (all_52_17 = all_14_2)
% 175.30/26.96    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.96    (38)   ~ (all_52_7 = all_4_2)
% 175.30/26.96    (39)  all_58_1 = all_52_3
% 175.30/26.96    (40)  all_58_0 = all_4_2
% 175.30/26.96    (41)  op(e1, all_52_29) = all_52_28
% 175.30/26.96    (42)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.30/26.96    (43)  all_58_14 = all_52_29
% 175.30/26.96    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.96    (45)  op(e2, all_4_2) = all_4_0
% 175.30/26.96    (46)  op(e2, e1) = all_52_13
% 175.30/26.96    (47)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.96    (48)  all_58_8 = all_14_2
% 175.30/26.96    (49)   ~ (all_52_3 = all_52_27)
% 175.30/26.96    (50)   ~ (all_52_3 = all_4_2)
% 175.30/26.96    (51)   ~ (all_52_9 = all_10_2)
% 175.30/26.96    (52)  op(e3, all_52_17) = all_52_16
% 175.30/26.96    (53)   ~ (e3 = e0)
% 175.30/26.96    (54)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/26.96    (55)   ~ (all_52_9 = all_52_13)
% 175.30/26.96    (56)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.96    (57)   ~ (all_52_15 = all_52_23)
% 175.30/26.96    (58)   ~ (all_52_5 = all_52_29)
% 175.30/26.96    (59)  all_56_12 = all_52_25
% 175.30/26.96    (60)  all_58_13 = all_52_27
% 175.30/26.96    (61)  all_56_5 = all_10_2
% 175.30/26.96    (62)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.96    (63)   ~ (all_52_25 = e0)
% 175.30/26.96    (64)   ~ (all_52_9 = all_52_17)
% 175.30/26.96    (65)  all_58_6 = all_52_17
% 175.30/26.96    (66)   ~ (all_52_3 = all_52_7)
% 175.30/26.96    (67)   ~ (e1 = e0)
% 175.30/26.96    (68)  all_56_0 = all_4_2
% 175.30/26.96    (69)  all_58_11 = all_52_23
% 175.30/26.96    (70)   ~ (all_52_3 = all_52_19)
% 175.30/26.96    (71)   ~ (all_52_7 = all_52_15)
% 175.30/26.96    (72)   ~ (all_52_29 = all_14_2)
% 175.30/26.96    (73)   ~ (all_4_0 = e1)
% 175.30/26.96    (74)   ~ (all_52_19 = all_10_2)
% 175.30/26.96    (75)  all_58_15 = e0
% 175.30/26.96    (76)  op(e3, all_4_2) = e2
% 175.30/26.96    (77)  all_58_2 = all_52_9
% 175.30/26.96    (78)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.96    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.96    (80)  op(e3, e1) = all_52_5
% 175.30/26.96    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.96    (82)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.96    (83)  op(e1, e3) = all_52_17
% 175.30/26.96    (84)   ~ (all_52_25 = all_4_2)
% 175.30/26.96    (85)  op(e3, e0) = all_52_7
% 175.30/26.96    (86)  op(e3, e3) = all_4_2
% 175.30/26.96    (87)   ~ (all_52_17 = all_4_2)
% 175.30/26.96    (88)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.96    (89)   ~ (all_52_25 = all_52_27)
% 175.30/26.96    (90)   ~ (all_52_15 = all_10_2)
% 175.30/26.96    (91)   ~ (all_52_13 = all_10_2)
% 175.30/26.96    (92)  op(e2, all_52_27) = all_52_26
% 175.30/26.96    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.96    (94)  all_58_9 = all_52_7
% 175.30/26.96    (95)   ~ (e2 = e0)
% 175.30/26.96    (96)  all_58_12 = all_52_25
% 175.30/26.96    (97)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.96    (98)   ~ (e3 = e2)
% 175.30/26.96    (99)  op(e2, e3) = all_52_9
% 175.30/26.96    (100)  all_56_13 = all_52_27
% 175.30/26.96  
% 175.30/26.96  Begin of proof
% 175.30/26.96  | 
% 175.30/26.96  | ALPHA: (6) implies:
% 175.30/26.96  |   (101)  all_52_28 = e1
% 175.30/26.96  |   (102)  all_52_26 = e2
% 175.30/26.96  |   (103)  all_52_24 = e3
% 175.30/26.96  | 
% 175.30/26.96  | REDUCE: (11), (103) imply:
% 175.30/26.96  |   (104)  op(e3, all_52_25) = e3
% 175.30/26.96  | 
% 175.30/26.96  | REDUCE: (92), (102) imply:
% 175.30/26.96  |   (105)  op(e2, all_52_27) = e2
% 175.30/26.96  | 
% 175.30/26.96  | REDUCE: (41), (101) imply:
% 175.30/26.96  |   (106)  op(e1, all_52_29) = e1
% 175.30/26.96  | 
% 175.30/26.96  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 175.30/26.96  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 175.30/26.96  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 175.30/26.96  |            (37), (38), (39), (40), (42), (43), (44), (45), (46), (47), (48),
% 175.30/26.96  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 175.30/26.96  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 175.30/26.96  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 175.30/26.96  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (93),
% 175.30/26.96  |            (94), (95), (96), (97), (98), (99), (100), (104), (105), (106) are
% 175.30/26.96  |            inconsistent by sub-proof #110.
% 175.30/26.96  | 
% 175.30/26.96  End of proof
% 175.30/26.96  
% 175.30/26.96  Sub-proof #110 shows that the following formulas are inconsistent:
% 175.30/26.96  ----------------------------------------------------------------
% 175.30/26.96    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.96    (2)   ~ (all_52_5 = all_52_13)
% 175.30/26.96    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/26.96    (4)   ~ (all_52_27 = all_10_2)
% 175.30/26.96    (5)  op(e2, all_10_2) = all_10_1
% 175.30/26.96    (6)   ~ (all_52_13 = all_52_29)
% 175.30/26.96    (7)  all_56_3 = all_52_7
% 175.30/26.96    (8)  op(e3, e2) = all_52_3
% 175.30/26.96    (9)   ~ (all_52_9 = all_52_25)
% 175.30/26.96    (10)   ~ (all_52_19 = all_52_23)
% 175.30/26.96    (11)  all_56_11 = all_52_23
% 175.30/26.96    (12)  op(e1, e2) = all_52_19
% 175.30/26.96    (13)  op(e3, all_52_9) = all_52_8
% 175.30/26.96    (14)   ~ (all_52_23 = e0)
% 175.30/26.96    (15)   ~ (all_52_3 = all_10_2)
% 175.30/26.96    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.96    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.30/26.96    (18)  all_58_5 = all_52_13
% 175.30/26.96    (19)   ~ (all_52_25 = all_52_29)
% 175.30/26.96    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.96    (21)  op(e2, e0) = all_52_15
% 175.30/26.96    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.96    (23)  all_58_3 = all_10_2
% 175.30/26.96    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.96    (25)   ~ (all_52_9 = all_4_2)
% 175.30/26.96    (26)   ~ (all_52_5 = all_52_7)
% 175.30/26.96    (27)  all_58_10 = all_52_15
% 175.30/26.96    (28)   ~ (all_52_5 = all_4_2)
% 175.30/26.96    (29)  all_58_7 = all_52_19
% 175.30/26.96    (30)   ~ (all_52_17 = all_52_25)
% 175.30/26.96    (31)  all_58_4 = all_52_5
% 175.30/26.96    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.96    (33)   ~ (e3 = e1)
% 175.30/26.96    (34)   ~ (all_52_17 = all_14_2)
% 175.30/26.96    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.96    (36)   ~ (all_52_7 = all_4_2)
% 175.30/26.96    (37)  all_58_1 = all_52_3
% 175.30/26.96    (38)  all_58_0 = all_4_2
% 175.30/26.96    (39)  op(e2, all_52_27) = e2
% 175.30/26.96    (40)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.30/26.96    (41)  all_58_14 = all_52_29
% 175.30/26.96    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.96    (43)  op(e2, all_4_2) = all_4_0
% 175.30/26.96    (44)  op(e2, e1) = all_52_13
% 175.30/26.96    (45)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.96    (46)  all_58_8 = all_14_2
% 175.30/26.96    (47)  op(e1, all_52_29) = e1
% 175.30/26.96    (48)   ~ (all_52_3 = all_52_27)
% 175.30/26.96    (49)   ~ (all_52_3 = all_4_2)
% 175.30/26.96    (50)   ~ (all_52_9 = all_10_2)
% 175.30/26.96    (51)  op(e3, all_52_17) = all_52_16
% 175.30/26.96    (52)   ~ (e3 = e0)
% 175.30/26.96    (53)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/26.96    (54)   ~ (all_52_9 = all_52_13)
% 175.30/26.96    (55)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.96    (56)   ~ (all_52_15 = all_52_23)
% 175.30/26.96    (57)   ~ (all_52_5 = all_52_29)
% 175.30/26.96    (58)  all_56_12 = all_52_25
% 175.30/26.96    (59)  all_58_13 = all_52_27
% 175.30/26.96    (60)  all_56_5 = all_10_2
% 175.30/26.96    (61)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.96    (62)   ~ (all_52_25 = e0)
% 175.30/26.96    (63)   ~ (all_52_9 = all_52_17)
% 175.30/26.96    (64)  all_58_6 = all_52_17
% 175.30/26.96    (65)   ~ (all_52_3 = all_52_7)
% 175.30/26.96    (66)   ~ (e1 = e0)
% 175.30/26.96    (67)  all_56_0 = all_4_2
% 175.30/26.96    (68)  all_58_11 = all_52_23
% 175.30/26.96    (69)   ~ (all_52_3 = all_52_19)
% 175.30/26.96    (70)   ~ (all_52_7 = all_52_15)
% 175.30/26.96    (71)   ~ (all_52_29 = all_14_2)
% 175.30/26.96    (72)  op(e3, all_52_25) = e3
% 175.30/26.96    (73)   ~ (all_4_0 = e1)
% 175.30/26.96    (74)   ~ (all_52_19 = all_10_2)
% 175.30/26.96    (75)  all_58_15 = e0
% 175.30/26.96    (76)  op(e3, all_4_2) = e2
% 175.30/26.96    (77)  all_58_2 = all_52_9
% 175.30/26.96    (78)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.96    (79)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.96    (80)  op(e3, e1) = all_52_5
% 175.30/26.96    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.96    (82)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.96    (83)  op(e1, e3) = all_52_17
% 175.30/26.96    (84)   ~ (all_52_25 = all_4_2)
% 175.30/26.96    (85)  op(e3, e0) = all_52_7
% 175.30/26.96    (86)  op(e3, e3) = all_4_2
% 175.30/26.96    (87)   ~ (all_52_17 = all_4_2)
% 175.30/26.96    (88)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.96    (89)   ~ (all_52_25 = all_52_27)
% 175.30/26.96    (90)   ~ (all_52_15 = all_10_2)
% 175.30/26.96    (91)   ~ (all_52_13 = all_10_2)
% 175.30/26.96    (92)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.96    (93)  all_58_9 = all_52_7
% 175.30/26.96    (94)   ~ (e2 = e0)
% 175.30/26.96    (95)  all_58_12 = all_52_25
% 175.30/26.96    (96)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.96    (97)   ~ (e3 = e2)
% 175.30/26.96    (98)  op(e2, e3) = all_52_9
% 175.30/26.96    (99)  all_56_13 = all_52_27
% 175.30/26.96  
% 175.30/26.96  Begin of proof
% 175.30/26.96  | 
% 175.30/26.96  | BETA: splitting (42) gives:
% 175.30/26.96  | 
% 175.30/26.96  | Case 1:
% 175.30/26.96  | | 
% 175.30/26.96  | |   (100)  all_56_13 = e3
% 175.30/26.96  | | 
% 175.30/26.96  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (12), (13), (14), (16),
% 175.30/26.96  | |            (18), (19), (22), (23), (24), (25), (27), (28), (29), (35), (36),
% 175.30/26.96  | |            (37), (38), (39), (41), (46), (47), (50), (55), (56), (57), (58),
% 175.30/26.96  | |            (59), (60), (61), (62), (63), (64), (65), (67), (68), (70), (71),
% 175.30/26.96  | |            (72), (74), (75), (76), (77), (80), (81), (82), (84), (85), (88),
% 175.30/26.96  | |            (89), (92), (93), (94), (95), (97), (98), (99), (100) are
% 175.30/26.96  | |            inconsistent by sub-proof #115.
% 175.30/26.96  | | 
% 175.30/26.96  | Case 2:
% 175.30/26.96  | | 
% 175.30/26.96  | |   (101)   ~ (all_56_13 = e3)
% 175.30/26.96  | | 
% 175.30/26.96  | | REDUCE: (99), (101) imply:
% 175.30/26.96  | |   (102)   ~ (all_52_27 = e3)
% 175.30/26.96  | | 
% 175.30/26.96  | | BETA: splitting (45) gives:
% 175.30/26.96  | | 
% 175.30/26.96  | | Case 1:
% 175.30/26.96  | | | 
% 175.30/26.96  | | |   (103)  all_58_12 = e3
% 175.30/26.96  | | | 
% 175.30/26.96  | | | REF_CLOSE: (72), (84), (86), (88), (95), (103) are inconsistent by
% 175.30/26.96  | | |            sub-proof #884.
% 175.30/26.96  | | | 
% 175.30/26.96  | | Case 2:
% 175.30/26.96  | | | 
% 175.30/26.96  | | |   (104)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.96  | | | 
% 175.30/26.96  | | | BETA: splitting (104) gives:
% 175.30/26.96  | | | 
% 175.30/26.96  | | | Case 1:
% 175.30/26.96  | | | | 
% 175.30/26.96  | | | |   (105)  all_58_13 = e3
% 175.30/26.96  | | | | 
% 175.30/26.96  | | | | REF_CLOSE: (59), (102), (105) are inconsistent by sub-proof #1026.
% 175.30/26.96  | | | | 
% 175.30/26.96  | | | Case 2:
% 175.30/26.96  | | | | 
% 175.30/26.96  | | | |   (106)  all_58_14 = e3 | all_58_15 = e3
% 175.30/26.96  | | | | 
% 175.30/26.96  | | | | BETA: splitting (106) gives:
% 175.30/26.96  | | | | 
% 175.30/26.96  | | | | Case 1:
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | |   (107)  all_58_14 = e3
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | COMBINE_EQS: (41), (107) imply:
% 175.30/26.96  | | | | |   (108)  all_52_29 = e3
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | SIMP: (108) implies:
% 175.30/26.96  | | | | |   (109)  all_52_29 = e3
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (57), (109) imply:
% 175.30/26.96  | | | | |   (110)   ~ (all_52_5 = e3)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (6), (109) imply:
% 175.30/26.96  | | | | |   (111)   ~ (all_52_13 = e3)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (19), (109) imply:
% 175.30/26.96  | | | | |   (112)   ~ (all_52_25 = e3)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (71), (109) imply:
% 175.30/26.96  | | | | |   (113)   ~ (all_14_2 = e3)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | SIMP: (113) implies:
% 175.30/26.96  | | | | |   (114)   ~ (all_14_2 = e3)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (47), (109) imply:
% 175.30/26.96  | | | | |   (115)  op(e1, e3) = e1
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | GROUND_INST: instantiating (88) with all_52_17, e1, e3, e1,
% 175.30/26.96  | | | | |              simplifying with (83), (115) gives:
% 175.30/26.96  | | | | |   (116)  all_52_17 = e1
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | COMBINE_EQS: (64), (116) imply:
% 175.30/26.96  | | | | |   (117)  all_58_6 = e1
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (63), (116) imply:
% 175.30/26.96  | | | | |   (118)   ~ (all_52_9 = e1)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (30), (116) imply:
% 175.30/26.96  | | | | |   (119)   ~ (all_52_25 = e1)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | SIMP: (119) implies:
% 175.30/26.96  | | | | |   (120)   ~ (all_52_25 = e1)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (34), (116) imply:
% 175.30/26.96  | | | | |   (121)   ~ (all_14_2 = e1)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | SIMP: (121) implies:
% 175.30/26.96  | | | | |   (122)   ~ (all_14_2 = e1)
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | REDUCE: (51), (116) imply:
% 175.30/26.96  | | | | |   (123)  op(e3, e1) = all_52_16
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | BETA: splitting (55) gives:
% 175.30/26.96  | | | | | 
% 175.30/26.96  | | | | | Case 1:
% 175.30/26.96  | | | | | | 
% 175.30/26.96  | | | | | |   (124)  all_56_12 = e3
% 175.30/26.96  | | | | | | 
% 175.30/26.96  | | | | | | REF_CLOSE: (58), (112), (124) are inconsistent by sub-proof #1040.
% 175.30/26.96  | | | | | | 
% 175.30/26.96  | | | | | Case 2:
% 175.30/26.96  | | | | | | 
% 175.30/26.96  | | | | | |   (125)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.96  | | | | | | 
% 175.30/26.96  | | | | | | BETA: splitting (78) gives:
% 175.30/26.96  | | | | | | 
% 175.30/26.96  | | | | | | Case 1:
% 175.30/26.96  | | | | | | | 
% 175.30/26.96  | | | | | | |   (126)  all_58_12 = e1
% 175.30/26.96  | | | | | | | 
% 175.30/26.96  | | | | | | | REF_CLOSE: (95), (120), (126) are inconsistent by sub-proof #883.
% 175.30/26.96  | | | | | | | 
% 175.30/26.96  | | | | | | Case 2:
% 175.30/26.96  | | | | | | | 
% 175.30/26.96  | | | | | | |   (127)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.96  | | | | | | | 
% 175.30/26.96  | | | | | | | BETA: splitting (127) gives:
% 175.30/26.96  | | | | | | | 
% 175.30/26.96  | | | | | | | Case 1:
% 175.30/26.96  | | | | | | | | 
% 175.30/26.96  | | | | | | | |   (128)  all_58_13 = e1
% 175.30/26.96  | | | | | | | | 
% 175.30/26.96  | | | | | | | | COMBINE_EQS: (59), (128) imply:
% 175.30/26.96  | | | | | | | |   (129)  all_52_27 = e1
% 175.30/26.96  | | | | | | | | 
% 175.30/26.96  | | | | | | | | SIMP: (129) implies:
% 175.30/26.96  | | | | | | | |   (130)  all_52_27 = e1
% 175.30/26.96  | | | | | | | | 
% 175.30/26.96  | | | | | | | | REDUCE: (48), (130) imply:
% 175.30/26.96  | | | | | | | |   (131)   ~ (all_52_3 = e1)
% 175.30/26.96  | | | | | | | | 
% 175.30/26.96  | | | | | | | | REDUCE: (39), (130) imply:
% 175.30/26.96  | | | | | | | |   (132)  op(e2, e1) = e2
% 175.30/26.96  | | | | | | | | 
% 175.30/26.96  | | | | | | | | BETA: splitting (82) gives:
% 175.30/26.96  | | | | | | | | 
% 175.30/26.96  | | | | | | | | Case 1:
% 175.30/26.96  | | | | | | | | | 
% 175.30/26.96  | | | | | | | | |   (133)  all_58_12 = e2
% 175.30/26.96  | | | | | | | | | 
% 175.30/26.96  | | | | | | | | | COMBINE_EQS: (95), (133) imply:
% 175.30/26.96  | | | | | | | | |   (134)  all_52_25 = e2
% 175.30/26.96  | | | | | | | | | 
% 175.30/26.96  | | | | | | | | | SIMP: (134) implies:
% 175.30/26.96  | | | | | | | | |   (135)  all_52_25 = e2
% 175.30/26.96  | | | | | | | | | 
% 175.30/26.96  | | | | | | | | | REDUCE: (120), (135) imply:
% 175.30/26.97  | | | | | | | | |   (136)   ~ (e2 = e1)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (72), (135) imply:
% 175.30/26.97  | | | | | | | | |   (137)  op(e3, e2) = e3
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | GROUND_INST: instantiating (88) with all_52_13, e2, e1, e2,
% 175.30/26.97  | | | | | | | | |              simplifying with (44), (132) gives:
% 175.30/26.97  | | | | | | | | |   (138)  all_52_13 = e2
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | GROUND_INST: instantiating (88) with all_52_5, all_52_16, e1,
% 175.30/26.97  | | | | | | | | |              e3, simplifying with (80), (123) gives:
% 175.30/26.97  | | | | | | | | |   (139)  all_52_5 = all_52_16
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | GROUND_INST: instantiating (88) with all_52_3, e3, e2, e3,
% 175.30/26.97  | | | | | | | | |              simplifying with (8), (137) gives:
% 175.30/26.97  | | | | | | | | |   (140)  all_52_3 = e3
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | COMBINE_EQS: (18), (138) imply:
% 175.30/26.97  | | | | | | | | |   (141)  all_58_5 = e2
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | COMBINE_EQS: (31), (139) imply:
% 175.30/26.97  | | | | | | | | |   (142)  all_58_4 = all_52_16
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (69), (140) imply:
% 175.30/26.97  | | | | | | | | |   (143)   ~ (all_52_19 = e3)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | SIMP: (143) implies:
% 175.30/26.97  | | | | | | | | |   (144)   ~ (all_52_19 = e3)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (15), (140) imply:
% 175.30/26.97  | | | | | | | | |   (145)   ~ (all_10_2 = e3)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | SIMP: (145) implies:
% 175.30/26.97  | | | | | | | | |   (146)   ~ (all_10_2 = e3)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (49), (140) imply:
% 175.30/26.97  | | | | | | | | |   (147)   ~ (all_4_2 = e3)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | SIMP: (147) implies:
% 175.30/26.97  | | | | | | | | |   (148)   ~ (all_4_2 = e3)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (26), (139) imply:
% 175.30/26.97  | | | | | | | | |   (149)   ~ (all_52_7 = all_52_16)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | SIMP: (149) implies:
% 175.30/26.97  | | | | | | | | |   (150)   ~ (all_52_7 = all_52_16)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (28), (139) imply:
% 175.30/26.97  | | | | | | | | |   (151)   ~ (all_52_16 = all_4_2)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (110), (139) imply:
% 175.30/26.97  | | | | | | | | |   (152)   ~ (all_52_16 = e3)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (54), (138) imply:
% 175.30/26.97  | | | | | | | | |   (153)   ~ (all_52_9 = e2)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (91), (138) imply:
% 175.30/26.97  | | | | | | | | |   (154)   ~ (all_10_2 = e2)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | SIMP: (154) implies:
% 175.30/26.97  | | | | | | | | |   (155)   ~ (all_10_2 = e2)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | BETA: splitting (24) gives:
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | |   (156)  all_56_0 = e3
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | COMBINE_EQS: (67), (156) imply:
% 175.30/26.97  | | | | | | | | | |   (157)  all_4_2 = e3
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | REDUCE: (148), (157) imply:
% 175.30/26.97  | | | | | | | | | |   (158)  $false
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | CLOSE: (158) is inconsistent.
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | |   (159)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | BETA: splitting (40) gives:
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | |   (160)  all_58_4 = e1
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | COMBINE_EQS: (142), (160) imply:
% 175.30/26.97  | | | | | | | | | | |   (161)  all_52_16 = e1
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | REDUCE: (150), (161) imply:
% 175.30/26.97  | | | | | | | | | | |   (162)   ~ (all_52_7 = e1)
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | REDUCE: (151), (161) imply:
% 175.30/26.97  | | | | | | | | | | |   (163)   ~ (all_4_2 = e1)
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | SIMP: (163) implies:
% 175.30/26.97  | | | | | | | | | | |   (164)   ~ (all_4_2 = e1)
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | REDUCE: (152), (161) imply:
% 175.30/26.97  | | | | | | | | | | |   (165)   ~ (e3 = e1)
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | BETA: splitting (22) gives:
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | |   (166)  all_58_9 = e1
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | COMBINE_EQS: (93), (166) imply:
% 175.30/26.97  | | | | | | | | | | | |   (167)  all_52_7 = e1
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | REDUCE: (162), (167) imply:
% 175.30/26.97  | | | | | | | | | | | |   (168)  $false
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | CLOSE: (168) is inconsistent.
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | |   (169)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | BETA: splitting (79) gives:
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | |   (170)  all_56_11 = e3
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | COMBINE_EQS: (11), (170) imply:
% 175.30/26.97  | | | | | | | | | | | | |   (171)  all_52_23 = e3
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | SIMP: (171) implies:
% 175.30/26.97  | | | | | | | | | | | | |   (172)  all_52_23 = e3
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | COMBINE_EQS: (68), (172) imply:
% 175.30/26.97  | | | | | | | | | | | | |   (173)  all_58_11 = e3
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | REDUCE: (56), (172) imply:
% 175.30/26.97  | | | | | | | | | | | | |   (174)   ~ (all_52_15 = e3)
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | BETA: splitting (35) gives:
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | |   (175)  all_58_2 = e3
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | COMBINE_EQS: (77), (175) imply:
% 175.30/26.97  | | | | | | | | | | | | | |   (176)  all_52_9 = e3
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | SIMP: (176) implies:
% 175.30/26.97  | | | | | | | | | | | | | |   (177)  all_52_9 = e3
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | |   (178)  all_58_0 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | COMBINE_EQS: (38), (178) imply:
% 175.30/26.97  | | | | | | | | | | | | | | |   (179)  all_4_2 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | REDUCE: (148), (179) imply:
% 175.30/26.97  | | | | | | | | | | | | | | |   (180)   ~ (e3 = e0)
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | REDUCE: (164), (179) imply:
% 175.30/26.97  | | | | | | | | | | | | | | |   (181)   ~ (e1 = e0)
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | REDUCE: (43), (179) imply:
% 175.30/26.97  | | | | | | | | | | | | | | |   (182)  op(e2, e0) = all_4_0
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | |   (183)  all_56_5 = e3
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (183) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | |   (184)  all_10_2 = e3
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | REDUCE: (146), (184) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | |   (185)  $false
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | |   (186)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | |   (187)  all_58_2 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (187) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | |   (188)  e3 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 175.30/26.97  | | | | | | | | | | | | | | | | |   (189)  e3 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | REDUCE: (52), (189) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | |   (190)  $false
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | |   (191)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | |   (192)  all_58_10 = e1
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (192) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | |   (193)  all_52_15 = e1
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | REDUCE: (90), (193) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | |   (194)   ~ (all_10_2 = e1)
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | SIMP: (194) implies:
% 175.30/26.97  | | | | | | | | | | | | | | | | | |   (195)   ~ (all_10_2 = e1)
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | REDUCE: (21), (193) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | |   (196)  op(e2, e0) = e1
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | |   (197)  all_56_5 = e2
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (197) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | |   (198)  all_10_2 = e2
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | REDUCE: (155), (198) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | |   (199)  $false
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | |   (200)  all_56_5 = e1 | all_56_5 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (201)  all_58_3 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (201) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (202)  all_10_2 = e0
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (202) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (203)  op(e2, e0) = all_10_1
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with all_4_0, all_10_1, e0, e2,
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |              simplifying with (182), (203) gives:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (204)  all_10_1 = all_4_0
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with e1, all_10_1, e0, e2,
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |              simplifying with (196), (203) gives:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (205)  all_10_1 = e1
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (204), (205) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (206)  all_4_0 = e1
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (206) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (207)  $false
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (208)   ~ (all_58_3 = e0)
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (208) imply:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |   (209)   ~ (all_10_2 = e0)
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (195), (200), (209) are inconsistent by
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | |            sub-proof #707.
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | |   (210)  all_58_11 = e1 | all_58_15 = e1
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (66), (75), (173), (210) are inconsistent by
% 175.30/26.97  | | | | | | | | | | | | | | | | | |            sub-proof #987.
% 175.30/26.97  | | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | |   (211)   ~ (all_58_0 = e0)
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | REDUCE: (38), (211) imply:
% 175.30/26.97  | | | | | | | | | | | | | | |   (212)   ~ (all_4_2 = e0)
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 175.30/26.97  | | | | | | | | | | | | | | |            (12), (13), (14), (16), (18), (19), (20), (22),
% 175.30/26.97  | | | | | | | | | | | | | | |            (23), (24), (25), (27), (28), (29), (31), (35),
% 175.30/26.97  | | | | | | | | | | | | | | |            (36), (37), (38), (39), (41), (42), (45), (46),
% 175.30/26.97  | | | | | | | | | | | | | | |            (47), (49), (50), (52), (55), (56), (57), (58),
% 175.30/26.97  | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (67),
% 175.30/26.97  | | | | | | | | | | | | | | |            (68), (70), (71), (72), (74), (75), (76), (77),
% 175.30/26.97  | | | | | | | | | | | | | | |            (80), (81), (82), (83), (84), (85), (86), (87),
% 175.30/26.97  | | | | | | | | | | | | | | |            (88), (89), (92), (93), (94), (95), (96), (97),
% 175.30/26.97  | | | | | | | | | | | | | | |            (98), (99), (159), (212) are inconsistent by
% 175.30/26.97  | | | | | | | | | | | | | | |            sub-proof #111.
% 175.30/26.97  | | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | |   (213)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (27), (111), (146), (174), (213) are
% 175.30/26.97  | | | | | | | | | | | | | |            inconsistent by sub-proof #182.
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | |   (214)   ~ (all_56_11 = e3)
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | REDUCE: (11), (214) imply:
% 175.30/26.97  | | | | | | | | | | | | |   (215)   ~ (all_52_23 = e3)
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | BETA: splitting (32) gives:
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | Case 1:
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | |   (216)  all_58_6 = e3
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | COMBINE_EQS: (117), (216) imply:
% 175.30/26.97  | | | | | | | | | | | | | |   (217)  e3 = e1
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | REDUCE: (33), (217) imply:
% 175.30/26.97  | | | | | | | | | | | | | |   (218)  $false
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | |   (219)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | | REF_CLOSE: (29), (46), (68), (114), (144), (215), (219) are
% 175.30/26.97  | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 175.30/26.97  | | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | |   (220)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | | REF_CLOSE: (33), (46), (107), (122), (136), (141), (220) are
% 175.30/26.97  | | | | | | | | | | |            inconsistent by sub-proof #617.
% 175.30/26.97  | | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | |   (221)   ~ (all_58_12 = e2)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REDUCE: (95), (221) imply:
% 175.30/26.97  | | | | | | | | |   (222)   ~ (all_52_25 = e2)
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | | REF_CLOSE: (58), (62), (120), (125), (222) are inconsistent by
% 175.30/26.97  | | | | | | | | |            sub-proof #1028.
% 175.30/26.97  | | | | | | | | | 
% 175.30/26.97  | | | | | | | | End of split
% 175.30/26.97  | | | | | | | | 
% 175.30/26.97  | | | | | | | Case 2:
% 175.30/26.97  | | | | | | | | 
% 175.30/26.97  | | | | | | | |   (223)  all_58_14 = e1 | all_58_15 = e1
% 175.30/26.97  | | | | | | | | 
% 175.30/26.97  | | | | | | | | REF_CLOSE: (33), (66), (75), (107), (223) are inconsistent by
% 175.30/26.97  | | | | | | | |            sub-proof #880.
% 175.30/26.97  | | | | | | | | 
% 175.30/26.97  | | | | | | | End of split
% 175.30/26.97  | | | | | | | 
% 175.30/26.97  | | | | | | End of split
% 175.30/26.97  | | | | | | 
% 175.30/26.97  | | | | | End of split
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | Case 2:
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | |   (224)  all_58_15 = e3
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | REF_CLOSE: (52), (75), (224) are inconsistent by sub-proof #1010.
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | End of split
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | End of split
% 175.30/26.97  | | | 
% 175.30/26.97  | | End of split
% 175.30/26.97  | | 
% 175.30/26.97  | End of split
% 175.30/26.97  | 
% 175.30/26.97  End of proof
% 175.30/26.97  
% 175.30/26.97  Sub-proof #111 shows that the following formulas are inconsistent:
% 175.30/26.97  ----------------------------------------------------------------
% 175.30/26.97    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.97    (2)   ~ (all_52_5 = all_52_13)
% 175.30/26.97    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/26.97    (4)   ~ (all_52_27 = all_10_2)
% 175.30/26.97    (5)   ~ (all_52_13 = all_52_29)
% 175.30/26.97    (6)  all_56_3 = all_52_7
% 175.30/26.97    (7)  op(e3, e2) = all_52_3
% 175.30/26.97    (8)   ~ (all_52_9 = all_52_25)
% 175.30/26.97    (9)   ~ (all_52_19 = all_52_23)
% 175.30/26.97    (10)  op(e1, e2) = all_52_19
% 175.30/26.97    (11)  op(e3, all_52_9) = all_52_8
% 175.30/26.97    (12)   ~ (all_52_23 = e0)
% 175.30/26.97    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.97    (14)  all_58_5 = all_52_13
% 175.30/26.97    (15)   ~ (all_52_25 = all_52_29)
% 175.30/26.97    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.97    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.97    (18)  all_58_3 = all_10_2
% 175.30/26.97    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.97    (20)   ~ (all_52_9 = all_4_2)
% 175.30/26.97    (21)  all_58_10 = all_52_15
% 175.30/26.97    (22)   ~ (all_52_5 = all_4_2)
% 175.30/26.97    (23)  all_58_7 = all_52_19
% 175.30/26.97    (24)  all_58_4 = all_52_5
% 175.30/26.97    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.97    (26)   ~ (all_52_7 = all_4_2)
% 175.30/26.97    (27)  all_58_1 = all_52_3
% 175.30/26.97    (28)  all_58_0 = all_4_2
% 175.30/26.97    (29)  op(e2, all_52_27) = e2
% 175.30/26.97    (30)  all_58_14 = all_52_29
% 175.30/26.97    (31)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.97    (32)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.97    (33)  all_58_8 = all_14_2
% 175.30/26.97    (34)  op(e1, all_52_29) = e1
% 175.30/26.97    (35)   ~ (all_52_3 = all_4_2)
% 175.30/26.97    (36)   ~ (all_52_9 = all_10_2)
% 175.30/26.97    (37)   ~ (e3 = e0)
% 175.30/26.97    (38)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.97    (39)   ~ (all_52_15 = all_52_23)
% 175.30/26.97    (40)   ~ (all_52_5 = all_52_29)
% 175.30/26.97    (41)  all_56_12 = all_52_25
% 175.30/26.97    (42)  all_58_13 = all_52_27
% 175.30/26.97    (43)  all_56_5 = all_10_2
% 175.30/26.97    (44)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.97    (45)   ~ (all_52_25 = e0)
% 175.30/26.97    (46)   ~ (all_52_9 = all_52_17)
% 175.30/26.97    (47)  all_58_6 = all_52_17
% 175.30/26.97    (48)   ~ (all_52_3 = all_52_7)
% 175.30/26.97    (49)  all_56_0 = all_4_2
% 175.30/26.97    (50)  all_58_11 = all_52_23
% 175.30/26.97    (51)   ~ (all_52_7 = all_52_15)
% 175.30/26.97    (52)   ~ (all_52_29 = all_14_2)
% 175.30/26.97    (53)  op(e3, all_52_25) = e3
% 175.30/26.97    (54)   ~ (all_52_19 = all_10_2)
% 175.30/26.97    (55)  all_58_15 = e0
% 175.30/26.97    (56)  op(e3, all_4_2) = e2
% 175.30/26.97    (57)  all_58_2 = all_52_9
% 175.30/26.97    (58)  op(e3, e1) = all_52_5
% 175.30/26.97    (59)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.97    (60)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.97    (61)  op(e1, e3) = all_52_17
% 175.30/26.97    (62)   ~ (all_52_25 = all_4_2)
% 175.30/26.97    (63)  op(e3, e0) = all_52_7
% 175.30/26.97    (64)  op(e3, e3) = all_4_2
% 175.30/26.97    (65)   ~ (all_52_17 = all_4_2)
% 175.30/26.97    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.97    (67)   ~ (all_52_25 = all_52_27)
% 175.30/26.97    (68)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.97    (69)   ~ (all_4_2 = e0)
% 175.30/26.97    (70)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.97    (71)  all_58_9 = all_52_7
% 175.30/26.97    (72)   ~ (e2 = e0)
% 175.30/26.97    (73)  all_58_12 = all_52_25
% 175.30/26.97    (74)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.97    (75)   ~ (e3 = e2)
% 175.30/26.97    (76)  op(e2, e3) = all_52_9
% 175.30/26.97    (77)  all_56_13 = all_52_27
% 175.30/26.97  
% 175.30/26.97  Begin of proof
% 175.30/26.97  | 
% 175.30/26.97  | BETA: splitting (31) gives:
% 175.30/26.97  | 
% 175.30/26.97  | Case 1:
% 175.30/26.97  | | 
% 175.30/26.97  | |   (78)  all_56_13 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 175.30/26.97  | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 175.30/26.97  | |            (27), (28), (29), (30), (33), (34), (36), (38), (39), (40), (41),
% 175.30/26.97  | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 175.30/26.97  | |            (53), (54), (55), (56), (57), (58), (59), (60), (62), (63), (66),
% 175.30/26.97  | |            (67), (70), (71), (72), (73), (75), (76), (77), (78) are
% 175.30/26.97  | |            inconsistent by sub-proof #115.
% 175.30/26.97  | | 
% 175.30/26.97  | Case 2:
% 175.30/26.97  | | 
% 175.30/26.97  | |   (79)   ~ (all_56_13 = e3)
% 175.30/26.97  | | 
% 175.30/26.97  | | REDUCE: (77), (79) imply:
% 175.30/26.97  | |   (80)   ~ (all_52_27 = e3)
% 175.30/26.97  | | 
% 175.30/26.97  | | BETA: splitting (32) gives:
% 175.30/26.97  | | 
% 175.30/26.97  | | Case 1:
% 175.30/26.97  | | | 
% 175.30/26.97  | | |   (81)  all_58_12 = e3
% 175.30/26.97  | | | 
% 175.30/26.97  | | | REF_CLOSE: (53), (62), (64), (66), (73), (81) are inconsistent by
% 175.30/26.97  | | |            sub-proof #884.
% 175.30/26.97  | | | 
% 175.30/26.97  | | Case 2:
% 175.30/26.97  | | | 
% 175.30/26.97  | | |   (82)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.97  | | | 
% 175.30/26.97  | | | BETA: splitting (82) gives:
% 175.30/26.97  | | | 
% 175.30/26.97  | | | Case 1:
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | |   (83)  all_58_13 = e3
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | | REF_CLOSE: (42), (80), (83) are inconsistent by sub-proof #1026.
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | Case 2:
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | |   (84)  all_58_14 = e3 | all_58_15 = e3
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | | BETA: splitting (84) gives:
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | | Case 1:
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | |   (85)  all_58_14 = e3
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | COMBINE_EQS: (30), (85) imply:
% 175.30/26.97  | | | | |   (86)  all_52_29 = e3
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | SIMP: (86) implies:
% 175.30/26.97  | | | | |   (87)  all_52_29 = e3
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | REDUCE: (40), (87) imply:
% 175.30/26.97  | | | | |   (88)   ~ (all_52_5 = e3)
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | REDUCE: (5), (87) imply:
% 175.30/26.97  | | | | |   (89)   ~ (all_52_13 = e3)
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | REDUCE: (52), (87) imply:
% 175.30/26.97  | | | | |   (90)   ~ (all_14_2 = e3)
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | SIMP: (90) implies:
% 175.30/26.97  | | | | |   (91)   ~ (all_14_2 = e3)
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | REF_CLOSE: (7), (14), (16), (24), (28), (30), (33), (34), (35), (49),
% 175.30/26.97  | | | | |            (56), (61), (65), (66), (68), (69), (74), (88), (89), (91)
% 175.30/26.97  | | | | |            are inconsistent by sub-proof #112.
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | Case 2:
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | |   (92)  all_58_15 = e3
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | COMBINE_EQS: (55), (92) imply:
% 175.30/26.97  | | | | |   (93)  e3 = e0
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | REDUCE: (37), (93) imply:
% 175.30/26.97  | | | | |   (94)  $false
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | | CLOSE: (94) is inconsistent.
% 175.30/26.97  | | | | | 
% 175.30/26.97  | | | | End of split
% 175.30/26.97  | | | | 
% 175.30/26.97  | | | End of split
% 175.30/26.97  | | | 
% 175.30/26.97  | | End of split
% 175.30/26.97  | | 
% 175.30/26.97  | End of split
% 175.30/26.97  | 
% 175.30/26.97  End of proof
% 175.30/26.97  
% 175.30/26.97  Sub-proof #112 shows that the following formulas are inconsistent:
% 175.30/26.97  ----------------------------------------------------------------
% 175.30/26.97    (1)  op(e3, e2) = all_52_3
% 175.30/26.97    (2)  all_58_5 = all_52_13
% 175.30/26.97    (3)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.97    (4)  all_58_4 = all_52_5
% 175.30/26.97    (5)  all_58_0 = all_4_2
% 175.30/26.97    (6)  all_58_14 = all_52_29
% 175.30/26.97    (7)  all_58_8 = all_14_2
% 175.30/26.97    (8)  op(e1, all_52_29) = e1
% 175.30/26.97    (9)   ~ (all_52_3 = all_4_2)
% 175.30/26.97    (10)   ~ (all_52_5 = e3)
% 175.30/26.97    (11)   ~ (all_52_13 = e3)
% 175.30/26.97    (12)  all_56_0 = all_4_2
% 175.30/26.97    (13)  op(e3, all_4_2) = e2
% 175.30/26.97    (14)  op(e1, e3) = all_52_17
% 175.30/26.97    (15)   ~ (all_14_2 = e3)
% 175.30/26.97    (16)   ~ (all_52_17 = all_4_2)
% 175.30/26.97    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.97    (18)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.97    (19)   ~ (all_4_2 = e0)
% 175.30/26.97    (20)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.97  
% 175.30/26.97  Begin of proof
% 175.30/26.97  | 
% 175.30/26.97  | BETA: splitting (20) gives:
% 175.30/26.97  | 
% 175.30/26.97  | Case 1:
% 175.30/26.97  | | 
% 175.30/26.97  | |   (21)  all_58_4 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | REF_CLOSE: (4), (10), (21) are inconsistent by sub-proof #1025.
% 175.30/26.97  | | 
% 175.30/26.97  | Case 2:
% 175.30/26.97  | | 
% 175.30/26.97  | |   (22)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | BETA: splitting (22) gives:
% 175.30/26.97  | | 
% 175.30/26.97  | | Case 1:
% 175.30/26.97  | | | 
% 175.30/26.97  | | |   (23)  all_58_5 = e3
% 175.30/26.97  | | | 
% 175.30/26.97  | | | REF_CLOSE: (2), (11), (23) are inconsistent by sub-proof #969.
% 175.30/26.97  | | | 
% 175.30/26.97  | | Case 2:
% 175.30/26.97  | | | 
% 175.30/26.97  | | |   (24)  all_58_8 = e3 | all_58_14 = e3
% 175.30/26.97  | | | 
% 175.30/26.97  | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (12), (13), (14), (15),
% 175.30/26.97  | | |            (16), (17), (18), (19), (24) are inconsistent by sub-proof
% 175.30/26.97  | | |            #113.
% 175.30/26.97  | | | 
% 175.30/26.97  | | End of split
% 175.30/26.97  | | 
% 175.30/26.97  | End of split
% 175.30/26.97  | 
% 175.30/26.97  End of proof
% 175.30/26.97  
% 175.30/26.97  Sub-proof #113 shows that the following formulas are inconsistent:
% 175.30/26.97  ----------------------------------------------------------------
% 175.30/26.97    (1)  op(e3, e2) = all_52_3
% 175.30/26.97    (2)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.97    (3)  all_58_0 = all_4_2
% 175.30/26.97    (4)  all_58_14 = all_52_29
% 175.30/26.97    (5)  all_58_8 = all_14_2
% 175.30/26.97    (6)  op(e1, all_52_29) = e1
% 175.30/26.97    (7)   ~ (all_52_3 = all_4_2)
% 175.30/26.97    (8)  all_56_0 = all_4_2
% 175.30/26.97    (9)  op(e3, all_4_2) = e2
% 175.30/26.97    (10)  all_58_8 = e3 | all_58_14 = e3
% 175.30/26.97    (11)  op(e1, e3) = all_52_17
% 175.30/26.97    (12)   ~ (all_14_2 = e3)
% 175.30/26.97    (13)   ~ (all_52_17 = all_4_2)
% 175.30/26.97    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.97    (15)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.97    (16)   ~ (all_4_2 = e0)
% 175.30/26.97  
% 175.30/26.97  Begin of proof
% 175.30/26.97  | 
% 175.30/26.97  | BETA: splitting (10) gives:
% 175.30/26.97  | 
% 175.30/26.97  | Case 1:
% 175.30/26.97  | | 
% 175.30/26.97  | |   (17)  all_58_8 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | COMBINE_EQS: (5), (17) imply:
% 175.30/26.97  | |   (18)  all_14_2 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | REDUCE: (12), (18) imply:
% 175.30/26.97  | |   (19)  $false
% 175.30/26.97  | | 
% 175.30/26.97  | | CLOSE: (19) is inconsistent.
% 175.30/26.97  | | 
% 175.30/26.97  | Case 2:
% 175.30/26.97  | | 
% 175.30/26.97  | |   (20)  all_58_14 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | COMBINE_EQS: (4), (20) imply:
% 175.30/26.97  | |   (21)  all_52_29 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | SIMP: (21) implies:
% 175.30/26.97  | |   (22)  all_52_29 = e3
% 175.30/26.97  | | 
% 175.30/26.97  | | REDUCE: (6), (22) imply:
% 175.30/26.97  | |   (23)  op(e1, e3) = e1
% 175.30/26.97  | | 
% 175.30/26.97  | | GROUND_INST: instantiating (14) with all_52_17, e1, e3, e1, simplifying with
% 175.30/26.97  | |              (11), (23) gives:
% 175.30/26.97  | |   (24)  all_52_17 = e1
% 175.30/26.97  | | 
% 175.30/26.97  | | REDUCE: (13), (24) imply:
% 175.30/26.97  | |   (25)   ~ (all_4_2 = e1)
% 175.30/26.97  | | 
% 175.30/26.97  | | SIMP: (25) implies:
% 175.30/26.97  | |   (26)   ~ (all_4_2 = e1)
% 175.30/26.97  | | 
% 175.30/26.97  | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (14), (15), (16), (26) are
% 175.30/26.97  | |            inconsistent by sub-proof #114.
% 175.30/26.97  | | 
% 175.30/26.97  | End of split
% 175.30/26.97  | 
% 175.30/26.97  End of proof
% 175.30/26.97  
% 175.30/26.97  Sub-proof #114 shows that the following formulas are inconsistent:
% 175.30/26.97  ----------------------------------------------------------------
% 175.30/26.97    (1)  op(e3, e2) = all_52_3
% 175.30/26.97    (2)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/26.97    (3)  all_58_0 = all_4_2
% 175.30/26.97    (4)   ~ (all_52_3 = all_4_2)
% 175.30/26.97    (5)  all_56_0 = all_4_2
% 175.30/26.97    (6)  op(e3, all_4_2) = e2
% 175.30/26.97    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.97    (8)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.97    (9)   ~ (all_4_2 = e1)
% 175.30/26.97    (10)   ~ (all_4_2 = e0)
% 175.30/26.97  
% 175.30/26.97  Begin of proof
% 175.30/26.97  | 
% 175.30/26.97  | BETA: splitting (2) gives:
% 175.30/26.97  | 
% 175.30/26.97  | Case 1:
% 175.30/26.97  | | 
% 175.30/26.97  | |   (11)  all_58_0 = e2
% 175.30/26.97  | | 
% 175.30/26.97  | | COMBINE_EQS: (3), (11) imply:
% 175.30/26.97  | |   (12)  all_4_2 = e2
% 175.30/26.97  | | 
% 175.30/26.97  | | REDUCE: (4), (12) imply:
% 175.30/26.97  | |   (13)   ~ (all_52_3 = e2)
% 175.30/26.97  | | 
% 175.30/26.97  | | REDUCE: (6), (12) imply:
% 175.30/26.97  | |   (14)  op(e3, e2) = e2
% 175.30/26.97  | | 
% 175.30/26.97  | | GROUND_INST: instantiating (7) with all_52_3, e2, e2, e3, simplifying with
% 175.30/26.97  | |              (1), (14) gives:
% 175.30/26.97  | |   (15)  all_52_3 = e2
% 175.30/26.97  | | 
% 175.30/26.98  | | REDUCE: (13), (15) imply:
% 175.30/26.98  | |   (16)  $false
% 175.30/26.98  | | 
% 175.30/26.98  | | CLOSE: (16) is inconsistent.
% 175.30/26.98  | | 
% 175.30/26.98  | Case 2:
% 175.30/26.98  | | 
% 175.30/26.98  | |   (17)   ~ (all_58_0 = e2)
% 175.30/26.98  | | 
% 175.30/26.98  | | REDUCE: (3), (17) imply:
% 175.30/26.98  | |   (18)   ~ (all_4_2 = e2)
% 175.30/26.98  | | 
% 175.30/26.98  | | REF_CLOSE: (5), (8), (9), (10), (18) are inconsistent by sub-proof #882.
% 175.30/26.98  | | 
% 175.30/26.98  | End of split
% 175.30/26.98  | 
% 175.30/26.98  End of proof
% 175.30/26.98  
% 175.30/26.98  Sub-proof #115 shows that the following formulas are inconsistent:
% 175.30/26.98  ----------------------------------------------------------------
% 175.30/26.98    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.98    (2)   ~ (all_52_5 = all_52_13)
% 175.30/26.98    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/26.98    (4)   ~ (all_52_27 = all_10_2)
% 175.30/26.98    (5)  all_56_3 = all_52_7
% 175.30/26.98    (6)  op(e3, e2) = all_52_3
% 175.30/26.98    (7)   ~ (all_52_9 = all_52_25)
% 175.30/26.98    (8)   ~ (all_52_19 = all_52_23)
% 175.30/26.98    (9)  op(e1, e2) = all_52_19
% 175.30/26.98    (10)  op(e3, all_52_9) = all_52_8
% 175.30/26.98    (11)   ~ (all_52_23 = e0)
% 175.30/26.98    (12)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.98    (13)  all_58_5 = all_52_13
% 175.30/26.98    (14)   ~ (all_52_25 = all_52_29)
% 175.30/26.98    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.98    (16)  all_58_3 = all_10_2
% 175.30/26.98    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.98    (18)   ~ (all_52_9 = all_4_2)
% 175.30/26.98    (19)  all_58_10 = all_52_15
% 175.30/26.98    (20)   ~ (all_52_5 = all_4_2)
% 175.30/26.98    (21)  all_58_7 = all_52_19
% 175.30/26.98    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.98    (23)   ~ (all_52_7 = all_4_2)
% 175.30/26.98    (24)  all_58_1 = all_52_3
% 175.30/26.98    (25)  all_58_0 = all_4_2
% 175.30/26.98    (26)  op(e2, all_52_27) = e2
% 175.30/26.98    (27)  all_58_14 = all_52_29
% 175.30/26.98    (28)  all_58_8 = all_14_2
% 175.30/26.98    (29)  op(e1, all_52_29) = e1
% 175.30/26.98    (30)   ~ (all_52_9 = all_10_2)
% 175.30/26.98    (31)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.98    (32)   ~ (all_52_15 = all_52_23)
% 175.30/26.98    (33)   ~ (all_52_5 = all_52_29)
% 175.30/26.98    (34)  all_56_12 = all_52_25
% 175.30/26.98    (35)  all_58_13 = all_52_27
% 175.30/26.98    (36)  all_56_5 = all_10_2
% 175.30/26.98    (37)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.98    (38)   ~ (all_52_25 = e0)
% 175.30/26.98    (39)   ~ (all_52_9 = all_52_17)
% 175.30/26.98    (40)  all_58_6 = all_52_17
% 175.30/26.98    (41)   ~ (all_52_3 = all_52_7)
% 175.30/26.98    (42)  all_56_0 = all_4_2
% 175.30/26.98    (43)  all_58_11 = all_52_23
% 175.30/26.98    (44)   ~ (all_52_7 = all_52_15)
% 175.30/26.98    (45)   ~ (all_52_29 = all_14_2)
% 175.30/26.98    (46)  op(e3, all_52_25) = e3
% 175.30/26.98    (47)   ~ (all_52_19 = all_10_2)
% 175.30/26.98    (48)  all_58_15 = e0
% 175.30/26.98    (49)  op(e3, all_4_2) = e2
% 175.30/26.98    (50)  all_58_2 = all_52_9
% 175.30/26.98    (51)  op(e3, e1) = all_52_5
% 175.30/26.98    (52)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.98    (53)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.98    (54)   ~ (all_52_25 = all_4_2)
% 175.30/26.98    (55)  op(e3, e0) = all_52_7
% 175.30/26.98    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.98    (57)   ~ (all_52_25 = all_52_27)
% 175.30/26.98    (58)  all_56_13 = e3
% 175.30/26.98    (59)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.98    (60)  all_58_9 = all_52_7
% 175.30/26.98    (61)   ~ (e2 = e0)
% 175.30/26.98    (62)  all_58_12 = all_52_25
% 175.30/26.98    (63)   ~ (e3 = e2)
% 175.30/26.98    (64)  op(e2, e3) = all_52_9
% 175.30/26.98    (65)  all_56_13 = all_52_27
% 175.30/26.98  
% 175.30/26.98  Begin of proof
% 175.30/26.98  | 
% 175.30/26.98  | COMBINE_EQS: (58), (65) imply:
% 175.30/26.98  |   (66)  all_52_27 = e3
% 175.30/26.98  | 
% 175.30/26.98  | SIMP: (66) implies:
% 175.30/26.98  |   (67)  all_52_27 = e3
% 175.30/26.98  | 
% 175.30/26.98  | COMBINE_EQS: (35), (67) imply:
% 175.30/26.98  |   (68)  all_58_13 = e3
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (57), (67) imply:
% 175.30/26.98  |   (69)   ~ (all_52_25 = e3)
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (4), (67) imply:
% 175.30/26.98  |   (70)   ~ (all_10_2 = e3)
% 175.30/26.98  | 
% 175.30/26.98  | SIMP: (70) implies:
% 175.30/26.98  |   (71)   ~ (all_10_2 = e3)
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (26), (67) imply:
% 175.30/26.98  |   (72)  op(e2, e3) = e2
% 175.30/26.98  | 
% 175.30/26.98  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 175.30/26.98  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.30/26.98  |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (36), (37),
% 175.30/26.98  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 175.30/26.98  |            (49), (50), (51), (52), (53), (54), (55), (56), (59), (60), (61),
% 175.30/26.98  |            (62), (63), (64), (68), (69), (71), (72) are inconsistent by
% 175.30/26.98  |            sub-proof #116.
% 175.30/26.98  | 
% 175.30/26.98  End of proof
% 175.30/26.98  
% 175.30/26.98  Sub-proof #116 shows that the following formulas are inconsistent:
% 175.30/26.98  ----------------------------------------------------------------
% 175.30/26.98    (1)   ~ (all_52_25 = e3)
% 175.30/26.98    (2)   ~ (all_52_23 = all_14_2)
% 175.30/26.98    (3)   ~ (all_52_5 = all_52_13)
% 175.30/26.98    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/26.98    (5)  all_56_3 = all_52_7
% 175.30/26.98    (6)  op(e2, e3) = e2
% 175.30/26.98    (7)  op(e3, e2) = all_52_3
% 175.30/26.98    (8)   ~ (all_52_9 = all_52_25)
% 175.30/26.98    (9)   ~ (all_52_19 = all_52_23)
% 175.30/26.98    (10)  op(e1, e2) = all_52_19
% 175.30/26.98    (11)  op(e3, all_52_9) = all_52_8
% 175.30/26.98    (12)   ~ (all_52_23 = e0)
% 175.30/26.98    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.98    (14)  all_58_5 = all_52_13
% 175.30/26.98    (15)   ~ (all_52_25 = all_52_29)
% 175.30/26.98    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.98    (17)  all_58_3 = all_10_2
% 175.30/26.98    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.98    (19)   ~ (all_52_9 = all_4_2)
% 175.30/26.98    (20)  all_58_10 = all_52_15
% 175.30/26.98    (21)   ~ (all_52_5 = all_4_2)
% 175.30/26.98    (22)  all_58_7 = all_52_19
% 175.30/26.98    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.98    (24)   ~ (all_52_7 = all_4_2)
% 175.30/26.98    (25)  all_58_1 = all_52_3
% 175.30/26.98    (26)  all_58_0 = all_4_2
% 175.30/26.98    (27)  all_58_14 = all_52_29
% 175.30/26.98    (28)   ~ (all_10_2 = e3)
% 175.30/26.98    (29)  all_58_8 = all_14_2
% 175.30/26.98    (30)  op(e1, all_52_29) = e1
% 175.30/26.98    (31)   ~ (all_52_9 = all_10_2)
% 175.30/26.98    (32)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.98    (33)   ~ (all_52_15 = all_52_23)
% 175.30/26.98    (34)   ~ (all_52_5 = all_52_29)
% 175.30/26.98    (35)  all_56_12 = all_52_25
% 175.30/26.98    (36)  all_56_5 = all_10_2
% 175.30/26.98    (37)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.98    (38)   ~ (all_52_25 = e0)
% 175.30/26.98    (39)   ~ (all_52_9 = all_52_17)
% 175.30/26.98    (40)  all_58_6 = all_52_17
% 175.30/26.98    (41)   ~ (all_52_3 = all_52_7)
% 175.30/26.98    (42)  all_56_0 = all_4_2
% 175.30/26.98    (43)  all_58_11 = all_52_23
% 175.30/26.98    (44)   ~ (all_52_7 = all_52_15)
% 175.30/26.98    (45)   ~ (all_52_29 = all_14_2)
% 175.30/26.98    (46)  op(e3, all_52_25) = e3
% 175.30/26.98    (47)   ~ (all_52_19 = all_10_2)
% 175.30/26.98    (48)  all_58_15 = e0
% 175.30/26.98    (49)  op(e3, all_4_2) = e2
% 175.30/26.98    (50)  all_58_2 = all_52_9
% 175.30/26.98    (51)  op(e3, e1) = all_52_5
% 175.30/26.98    (52)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.98    (53)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.98    (54)   ~ (all_52_25 = all_4_2)
% 175.30/26.98    (55)  op(e3, e0) = all_52_7
% 175.30/26.98    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.98    (57)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.98    (58)  all_58_9 = all_52_7
% 175.30/26.98    (59)   ~ (e2 = e0)
% 175.30/26.98    (60)  all_58_12 = all_52_25
% 175.30/26.98    (61)   ~ (e3 = e2)
% 175.30/26.98    (62)  all_58_13 = e3
% 175.30/26.98    (63)  op(e2, e3) = all_52_9
% 175.30/26.98  
% 175.30/26.98  Begin of proof
% 175.30/26.98  | 
% 175.30/26.98  | GROUND_INST: instantiating (56) with all_52_9, e2, e3, e2, simplifying with
% 175.30/26.98  |              (6), (63) gives:
% 175.30/26.98  |   (64)  all_52_9 = e2
% 175.30/26.98  | 
% 175.30/26.98  | COMBINE_EQS: (50), (64) imply:
% 175.30/26.98  |   (65)  all_58_2 = e2
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (39), (64) imply:
% 175.30/26.98  |   (66)   ~ (all_52_17 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | SIMP: (66) implies:
% 175.30/26.98  |   (67)   ~ (all_52_17 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (8), (64) imply:
% 175.30/26.98  |   (68)   ~ (all_52_25 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | SIMP: (68) implies:
% 175.30/26.98  |   (69)   ~ (all_52_25 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (31), (64) imply:
% 175.30/26.98  |   (70)   ~ (all_10_2 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | SIMP: (70) implies:
% 175.30/26.98  |   (71)   ~ (all_10_2 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (19), (64) imply:
% 175.30/26.98  |   (72)   ~ (all_4_2 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | SIMP: (72) implies:
% 175.30/26.98  |   (73)   ~ (all_4_2 = e2)
% 175.30/26.98  | 
% 175.30/26.98  | REDUCE: (11), (64) imply:
% 175.30/26.98  |   (74)  op(e3, e2) = all_52_8
% 175.30/26.98  | 
% 175.30/26.98  | BETA: splitting (32) gives:
% 175.30/26.98  | 
% 175.30/26.98  | Case 1:
% 175.30/26.98  | | 
% 175.30/26.98  | |   (75)  all_56_12 = e3
% 175.30/26.98  | | 
% 175.30/26.98  | | REF_CLOSE: (1), (35), (75) are inconsistent by sub-proof #1040.
% 175.30/26.98  | | 
% 175.30/26.98  | Case 2:
% 175.30/26.98  | | 
% 175.30/26.98  | |   (76)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.98  | | 
% 175.30/26.98  | | BETA: splitting (76) gives:
% 175.30/26.98  | | 
% 175.30/26.98  | | Case 1:
% 175.30/26.98  | | | 
% 175.30/26.98  | | |   (77)  all_56_12 = e2
% 175.30/26.98  | | | 
% 175.30/26.98  | | | REF_CLOSE: (35), (69), (77) are inconsistent by sub-proof #1032.
% 175.30/26.98  | | | 
% 175.30/26.98  | | Case 2:
% 175.30/26.98  | | | 
% 175.30/26.98  | | |   (78)   ~ (all_56_12 = e2)
% 175.30/26.98  | | |   (79)  all_56_12 = e1 | all_56_12 = e0
% 175.30/26.98  | | | 
% 175.30/26.98  | | | BETA: splitting (53) gives:
% 175.30/26.98  | | | 
% 175.30/26.98  | | | Case 1:
% 175.30/26.98  | | | | 
% 175.30/26.98  | | | |   (80)  all_58_12 = e2
% 175.30/26.98  | | | | 
% 175.30/26.98  | | | | REF_CLOSE: (60), (69), (80) are inconsistent by sub-proof #660.
% 175.30/26.98  | | | | 
% 175.30/26.98  | | | Case 2:
% 175.30/26.98  | | | | 
% 175.30/26.98  | | | |   (81)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.98  | | | | 
% 175.30/26.98  | | | | BETA: splitting (81) gives:
% 175.30/26.98  | | | | 
% 175.30/26.98  | | | | Case 1:
% 175.30/26.98  | | | | | 
% 175.30/26.98  | | | | |   (82)  all_58_13 = e2
% 175.30/26.98  | | | | | 
% 175.30/26.98  | | | | | REF_CLOSE: (61), (62), (82) are inconsistent by sub-proof #906.
% 175.30/26.98  | | | | | 
% 175.30/26.98  | | | | Case 2:
% 175.30/26.98  | | | | | 
% 175.30/26.98  | | | | |   (83)  all_58_14 = e2 | all_58_15 = e2
% 175.30/26.98  | | | | | 
% 175.30/26.98  | | | | | BETA: splitting (83) gives:
% 175.30/26.98  | | | | | 
% 175.30/26.98  | | | | | Case 1:
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | |   (84)  all_58_14 = e2
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | COMBINE_EQS: (27), (84) imply:
% 175.30/26.98  | | | | | |   (85)  all_52_29 = e2
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | SIMP: (85) implies:
% 175.30/26.98  | | | | | |   (86)  all_52_29 = e2
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | REDUCE: (34), (86) imply:
% 175.30/26.98  | | | | | |   (87)   ~ (all_52_5 = e2)
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | REDUCE: (45), (86) imply:
% 175.30/26.98  | | | | | |   (88)   ~ (all_14_2 = e2)
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | SIMP: (88) implies:
% 175.30/26.98  | | | | | |   (89)   ~ (all_14_2 = e2)
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | REDUCE: (30), (86) imply:
% 175.30/26.98  | | | | | |   (90)  op(e1, e2) = e1
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | BETA: splitting (79) gives:
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | Case 1:
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | |   (91)  all_56_12 = e1
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | COMBINE_EQS: (35), (91) imply:
% 175.30/26.98  | | | | | | |   (92)  all_52_25 = e1
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (92) implies:
% 175.30/26.98  | | | | | | |   (93)  all_52_25 = e1
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (54), (93) imply:
% 175.30/26.98  | | | | | | |   (94)   ~ (all_4_2 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (94) implies:
% 175.30/26.98  | | | | | | |   (95)   ~ (all_4_2 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (69), (93) imply:
% 175.30/26.98  | | | | | | |   (96)   ~ (e2 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (96) implies:
% 175.30/26.98  | | | | | | |   (97)   ~ (e2 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (46), (93) imply:
% 175.30/26.98  | | | | | | |   (98)  op(e3, e1) = e3
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | GROUND_INST: instantiating (56) with all_52_19, e1, e2, e1,
% 175.30/26.98  | | | | | | |              simplifying with (10), (90) gives:
% 175.30/26.98  | | | | | | |   (99)  all_52_19 = e1
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | GROUND_INST: instantiating (56) with all_52_5, e3, e1, e3,
% 175.30/26.98  | | | | | | |              simplifying with (51), (98) gives:
% 175.30/26.98  | | | | | | |   (100)  all_52_5 = e3
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | GROUND_INST: instantiating (56) with all_52_3, all_52_8, e2, e3,
% 175.30/26.98  | | | | | | |              simplifying with (7), (74) gives:
% 175.30/26.98  | | | | | | |   (101)  all_52_3 = all_52_8
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | COMBINE_EQS: (22), (99) imply:
% 175.30/26.98  | | | | | | |   (102)  all_58_7 = e1
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | COMBINE_EQS: (25), (101) imply:
% 175.30/26.98  | | | | | | |   (103)  all_58_1 = all_52_8
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (41), (101) imply:
% 175.30/26.98  | | | | | | |   (104)   ~ (all_52_7 = all_52_8)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (104) implies:
% 175.30/26.98  | | | | | | |   (105)   ~ (all_52_7 = all_52_8)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (3), (100) imply:
% 175.30/26.98  | | | | | | |   (106)   ~ (all_52_13 = e3)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (106) implies:
% 175.30/26.98  | | | | | | |   (107)   ~ (all_52_13 = e3)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (21), (100) imply:
% 175.30/26.98  | | | | | | |   (108)   ~ (all_4_2 = e3)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (108) implies:
% 175.30/26.98  | | | | | | |   (109)   ~ (all_4_2 = e3)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (9), (99) imply:
% 175.30/26.98  | | | | | | |   (110)   ~ (all_52_23 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (110) implies:
% 175.30/26.98  | | | | | | |   (111)   ~ (all_52_23 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REDUCE: (47), (99) imply:
% 175.30/26.98  | | | | | | |   (112)   ~ (all_10_2 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | SIMP: (112) implies:
% 175.30/26.98  | | | | | | |   (113)   ~ (all_10_2 = e1)
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | BETA: splitting (52) gives:
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | 
% 175.30/26.98  | | | | | | | |   (114)  all_56_5 = e3
% 175.30/26.98  | | | | | | | | 
% 175.30/26.98  | | | | | | | | REF_CLOSE: (28), (36), (114) are inconsistent by sub-proof #895.
% 175.30/26.98  | | | | | | | | 
% 175.30/26.98  | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | 
% 175.30/26.98  | | | | | | | |   (115)   ~ (all_56_5 = e3)
% 175.30/26.98  | | | | | | | |   (116)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.98  | | | | | | | | 
% 175.30/26.98  | | | | | | | | BETA: splitting (37) gives:
% 175.30/26.98  | | | | | | | | 
% 175.30/26.98  | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | 
% 175.30/26.98  | | | | | | | | |   (117)  all_58_6 = e2
% 175.30/26.98  | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | REF_CLOSE: (40), (67), (117) are inconsistent by sub-proof
% 175.30/26.98  | | | | | | | | |            #894.
% 175.30/26.98  | | | | | | | | | 
% 175.30/26.98  | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | 
% 175.30/26.98  | | | | | | | | |   (118)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/26.98  | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | BETA: splitting (18) gives:
% 175.30/26.98  | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | |   (119)  all_56_0 = e3
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | COMBINE_EQS: (42), (119) imply:
% 175.30/26.98  | | | | | | | | | |   (120)  all_4_2 = e3
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | REDUCE: (109), (120) imply:
% 175.30/26.98  | | | | | | | | | |   (121)  $false
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | CLOSE: (121) is inconsistent.
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | |   (122)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | BETA: splitting (23) gives:
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | |   (123)  all_58_2 = e3
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | COMBINE_EQS: (65), (123) imply:
% 175.30/26.98  | | | | | | | | | | |   (124)  e3 = e2
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | REDUCE: (61), (124) imply:
% 175.30/26.98  | | | | | | | | | | |   (125)  $false
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | CLOSE: (125) is inconsistent.
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | |   (126)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | BETA: splitting (126) gives:
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | |   (127)  all_58_3 = e3
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | COMBINE_EQS: (17), (127) imply:
% 175.30/26.98  | | | | | | | | | | | |   (128)  all_10_2 = e3
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | REDUCE: (28), (128) imply:
% 175.30/26.98  | | | | | | | | | | | |   (129)  $false
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | |   (130)  all_58_5 = e3 | all_58_10 = e3
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | BETA: splitting (130) gives:
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | |   (131)  all_58_5 = e3
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | REF_CLOSE: (14), (107), (131) are inconsistent by sub-proof
% 175.30/26.98  | | | | | | | | | | | | |            #969.
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | |   (132)  all_58_10 = e3
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | COMBINE_EQS: (20), (132) imply:
% 175.30/26.98  | | | | | | | | | | | | |   (133)  all_52_15 = e3
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | REDUCE: (44), (133) imply:
% 175.30/26.98  | | | | | | | | | | | | |   (134)   ~ (all_52_7 = e3)
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | REDUCE: (33), (133) imply:
% 175.30/26.98  | | | | | | | | | | | | |   (135)   ~ (all_52_23 = e3)
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | SIMP: (135) implies:
% 175.30/26.98  | | | | | | | | | | | | |   (136)   ~ (all_52_23 = e3)
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | BETA: splitting (4) gives:
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | |   (137)  all_58_0 = e0
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | COMBINE_EQS: (26), (137) imply:
% 175.30/26.98  | | | | | | | | | | | | | |   (138)  all_4_2 = e0
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | REDUCE: (24), (138) imply:
% 175.30/26.98  | | | | | | | | | | | | | |   (139)   ~ (all_52_7 = e0)
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | REDUCE: (49), (138) imply:
% 175.30/26.98  | | | | | | | | | | | | | |   (140)  op(e3, e0) = e2
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | |   (141)  all_58_9 = e1
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | COMBINE_EQS: (58), (141) imply:
% 175.30/26.98  | | | | | | | | | | | | | | |   (142)  all_52_7 = e1
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | REDUCE: (55), (142) imply:
% 175.30/26.98  | | | | | | | | | | | | | | |   (143)  op(e3, e0) = e1
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | REF_CLOSE: (56), (97), (140), (143) are inconsistent by
% 175.30/26.98  | | | | | | | | | | | | | | |            sub-proof #620.
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | |   (144)   ~ (all_58_9 = e1)
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | REDUCE: (58), (144) imply:
% 175.30/26.98  | | | | | | | | | | | | | | |   (145)   ~ (all_52_7 = e1)
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | |   (146)  all_58_1 = e2
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (146) imply:
% 175.30/26.98  | | | | | | | | | | | | | | | |   (147)  all_52_8 = e2
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | REDUCE: (105), (147) imply:
% 175.30/26.98  | | | | | | | | | | | | | | | |   (148)   ~ (all_52_7 = e2)
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | Case 1:
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | |   (149)  all_56_3 = e3
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (149) imply:
% 175.30/26.98  | | | | | | | | | | | | | | | | |   (150)  all_52_7 = e3
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | | REDUCE: (134), (150) imply:
% 175.30/26.98  | | | | | | | | | | | | | | | | |   (151)  $false
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | |   (152)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (139), (145), (148), (152) are inconsistent
% 175.30/26.98  | | | | | | | | | | | | | | | | |            by sub-proof #893.
% 175.30/26.98  | | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | |   (153)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (17), (29), (36), (43), (62), (71),
% 175.30/26.98  | | | | | | | | | | | | | | | |            (89), (97), (102), (111), (113), (116), (118),
% 175.30/26.98  | | | | | | | | | | | | | | | |            (136), (153) are inconsistent by sub-proof #889.
% 175.30/26.98  | | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | Case 2:
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | |   (154)   ~ (all_58_0 = e0)
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | REDUCE: (26), (154) imply:
% 175.30/26.98  | | | | | | | | | | | | | |   (155)   ~ (all_4_2 = e0)
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | | REF_CLOSE: (42), (73), (95), (122), (155) are inconsistent by
% 175.30/26.98  | | | | | | | | | | | | | |            sub-proof #882.
% 175.30/26.98  | | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | | 
% 175.30/26.98  | | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | | 
% 175.30/26.98  | | | | | | | | End of split
% 175.30/26.98  | | | | | | | | 
% 175.30/26.98  | | | | | | | End of split
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | Case 2:
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | |   (156)  all_56_12 = e0
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | | REF_CLOSE: (35), (38), (156) are inconsistent by sub-proof #1030.
% 175.30/26.98  | | | | | | | 
% 175.30/26.98  | | | | | | End of split
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | Case 2:
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | |   (157)  all_58_15 = e2
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | | REF_CLOSE: (48), (59), (157) are inconsistent by sub-proof #991.
% 175.30/26.98  | | | | | | 
% 175.30/26.98  | | | | | End of split
% 175.30/26.98  | | | | | 
% 175.30/26.98  | | | | End of split
% 175.30/26.98  | | | | 
% 175.30/26.98  | | | End of split
% 175.30/26.98  | | | 
% 175.30/26.98  | | End of split
% 175.30/26.98  | | 
% 175.30/26.98  | End of split
% 175.30/26.98  | 
% 175.30/26.98  End of proof
% 175.30/26.98  
% 175.30/26.98  Sub-proof #117 shows that the following formulas are inconsistent:
% 175.30/26.98  ----------------------------------------------------------------
% 175.30/26.98    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.98    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.30/26.98    (3)   ~ (all_52_17 = all_52_23)
% 175.30/26.98    (4)   ~ (all_6_0 = e3)
% 175.30/26.98    (5)   ~ (all_52_13 = all_52_29)
% 175.30/26.98    (6)  all_56_3 = all_52_7
% 175.30/26.98    (7)  op(e3, e2) = all_52_3
% 175.30/26.98    (8)   ~ (all_52_9 = all_52_25)
% 175.30/26.98    (9)   ~ (all_52_19 = all_52_23)
% 175.30/26.98    (10)  all_56_11 = all_52_23
% 175.30/26.98    (11)   ~ (all_52_27 = e0)
% 175.30/26.98    (12)   ~ (all_52_23 = e0)
% 175.30/26.98    (13)   ~ (all_52_3 = all_10_2)
% 175.30/26.98    (14)  all_58_5 = all_52_13
% 175.30/26.98    (15)   ~ (all_52_25 = all_52_29)
% 175.30/26.98    (16)  op(e0, e0) = all_6_1
% 175.30/26.98    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.98    (18)  all_58_3 = all_10_2
% 175.30/26.98    (19)  all_56_9 = all_52_19
% 175.30/26.98    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.98    (21)   ~ (all_52_9 = all_4_2)
% 175.30/26.98    (22)  all_58_10 = all_52_15
% 175.30/26.98    (23)  all_58_7 = all_52_19
% 175.30/26.98    (24)   ~ (all_52_17 = all_52_25)
% 175.30/26.98    (25)  op(e0, e1) = all_52_29
% 175.30/26.98    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.98    (27)   ~ (e3 = e1)
% 175.30/26.98    (28)   ~ (all_52_27 = all_52_29)
% 175.30/26.98    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.98    (30)   ~ (all_52_7 = all_4_2)
% 175.30/26.98    (31)  all_58_1 = all_52_3
% 175.30/26.98    (32)  all_58_0 = all_4_2
% 175.30/26.98    (33)  op(e1, all_52_29) = all_52_28
% 175.30/26.98    (34)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.30/26.98    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.98    (36)  all_58_14 = all_52_29
% 175.30/26.98    (37)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.98    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.98    (39)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.98    (40)  all_58_8 = all_14_2
% 175.30/26.98    (41)  op(e0, e2) = all_52_27
% 175.30/26.98    (42)   ~ (all_52_5 = all_14_2)
% 175.30/26.98    (43)   ~ (all_52_3 = all_4_2)
% 175.30/26.98    (44)  op(e0, e3) = all_52_25
% 175.30/26.98    (45)   ~ (all_52_9 = all_10_2)
% 175.30/26.98    (46)  op(e3, all_52_17) = all_52_16
% 175.30/26.98    (47)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/26.98    (48)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/26.98    (49)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.98    (50)  op(e0, all_52_23) = all_52_22
% 175.30/26.98    (51)   ~ (all_52_15 = all_52_23)
% 175.30/26.98    (52)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/26.98    (53)   ~ (all_52_5 = all_52_29)
% 175.30/26.98    (54)  all_56_12 = all_52_25
% 175.30/26.98    (55)  all_58_13 = all_52_27
% 175.30/26.98    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/26.98    (57)  all_56_5 = all_10_2
% 175.30/26.98    (58)  op(e0, e0) = e0
% 175.30/26.98    (59)   ~ (all_52_25 = e0)
% 175.30/26.98    (60)   ~ (all_52_9 = all_52_17)
% 175.30/26.98    (61)  all_58_6 = all_52_17
% 175.30/26.98    (62)   ~ (all_52_3 = all_52_7)
% 175.30/26.98    (63)  op(e2, all_52_19) = all_52_18
% 175.30/26.98    (64)  all_56_0 = all_4_2
% 175.30/26.98    (65)  all_58_11 = all_52_23
% 175.30/26.98    (66)   ~ (all_52_29 = all_14_2)
% 175.30/26.98    (67)   ~ (all_52_19 = all_10_2)
% 175.30/26.98    (68)  all_58_15 = e0
% 175.30/26.98    (69)   ~ (all_6_0 = e2)
% 175.30/26.98    (70)  all_58_2 = all_52_9
% 175.30/26.98    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.98    (72)   ~ (all_52_29 = e0)
% 175.30/26.98    (73)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.98    (74)  op(e3, e1) = all_52_5
% 175.30/26.98    (75)   ~ (e2 = e1)
% 175.30/26.98    (76)  all_56_10 = all_14_2
% 175.30/26.98    (77)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.98    (78)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.98    (79)  op(e1, e3) = all_52_17
% 175.30/26.98    (80)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/26.98    (81)   ~ (all_52_25 = all_4_2)
% 175.30/26.98    (82)  op(e3, e0) = all_52_7
% 175.30/26.99    (83)  op(e3, e3) = all_4_2
% 175.30/26.99    (84)  all_56_8 = all_52_17
% 175.30/26.99    (85)   ~ (all_52_17 = all_4_2)
% 175.30/26.99    (86)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.99    (87)   ~ (all_52_25 = all_52_27)
% 175.30/26.99    (88)   ~ (all_52_19 = all_52_27)
% 175.30/26.99    (89)  all_56_7 = all_52_15
% 175.30/26.99    (90)   ~ (all_52_15 = e0)
% 175.30/26.99    (91)  op(all_6_1, e0) = all_6_0
% 175.30/26.99    (92)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.30/26.99    (93)   ~ (all_52_7 = all_52_23)
% 175.30/26.99    (94)   ~ (all_6_0 = e1)
% 175.30/26.99    (95)  all_52_20 = all_14_1
% 175.30/26.99    (96)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.99    (97)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.99    (98)  op(e1, all_14_2) = all_14_1
% 175.30/26.99    (99)  all_58_9 = all_52_7
% 175.30/26.99    (100)  all_58_12 = all_52_25
% 175.30/26.99    (101)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.30/26.99    (102)   ~ (all_52_9 = all_52_15)
% 175.30/26.99    (103)   ~ (e3 = e2)
% 175.30/26.99    (104)   ~ (all_52_19 = all_14_2)
% 175.30/26.99    (105)  op(e2, e3) = all_52_9
% 175.30/26.99    (106)  all_56_13 = all_52_27
% 175.30/26.99  
% 175.30/26.99  Begin of proof
% 175.30/26.99  | 
% 175.30/26.99  | ALPHA: (92) implies:
% 175.30/26.99  |   (107)  all_52_22 = e0
% 175.30/26.99  |   (108)  all_52_20 = e1
% 175.30/26.99  |   (109)  all_52_18 = e2
% 175.30/26.99  |   (110)  all_52_16 = e3
% 175.30/26.99  | 
% 175.30/26.99  | COMBINE_EQS: (95), (108) imply:
% 175.30/26.99  |   (111)  all_14_1 = e1
% 175.30/26.99  | 
% 175.30/26.99  | SIMP: (111) implies:
% 175.30/26.99  |   (112)  all_14_1 = e1
% 175.30/26.99  | 
% 175.30/26.99  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.30/26.99  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.30/26.99  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 175.30/26.99  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 175.30/26.99  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 175.30/26.99  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 175.30/26.99  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 175.30/26.99  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 175.30/26.99  |            (90), (91), (93), (94), (96), (97), (98), (99), (100), (101),
% 175.30/26.99  |            (102), (103), (104), (105), (106), (107), (109), (110), (112) are
% 175.30/26.99  |            inconsistent by sub-proof #118.
% 175.30/26.99  | 
% 175.30/26.99  End of proof
% 175.30/26.99  
% 175.30/26.99  Sub-proof #118 shows that the following formulas are inconsistent:
% 175.30/26.99  ----------------------------------------------------------------
% 175.30/26.99    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.99    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.30/26.99    (3)   ~ (all_52_17 = all_52_23)
% 175.30/26.99    (4)   ~ (all_6_0 = e3)
% 175.30/26.99    (5)   ~ (all_52_13 = all_52_29)
% 175.30/26.99    (6)  all_56_3 = all_52_7
% 175.30/26.99    (7)  all_52_16 = e3
% 175.30/26.99    (8)  op(e3, e2) = all_52_3
% 175.30/26.99    (9)   ~ (all_52_9 = all_52_25)
% 175.30/26.99    (10)   ~ (all_52_19 = all_52_23)
% 175.30/26.99    (11)  all_56_11 = all_52_23
% 175.30/26.99    (12)   ~ (all_52_27 = e0)
% 175.30/26.99    (13)   ~ (all_52_23 = e0)
% 175.30/26.99    (14)   ~ (all_52_3 = all_10_2)
% 175.30/26.99    (15)  all_58_5 = all_52_13
% 175.30/26.99    (16)   ~ (all_52_25 = all_52_29)
% 175.30/26.99    (17)  op(e0, e0) = all_6_1
% 175.30/26.99    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.99    (19)  all_58_3 = all_10_2
% 175.30/26.99    (20)  all_56_9 = all_52_19
% 175.30/26.99    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.99    (22)   ~ (all_52_9 = all_4_2)
% 175.30/26.99    (23)  all_58_10 = all_52_15
% 175.30/26.99    (24)  all_58_7 = all_52_19
% 175.30/26.99    (25)   ~ (all_52_17 = all_52_25)
% 175.30/26.99    (26)  op(e0, e1) = all_52_29
% 175.30/26.99    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.99    (28)   ~ (e3 = e1)
% 175.30/26.99    (29)  all_52_18 = e2
% 175.30/26.99    (30)   ~ (all_52_27 = all_52_29)
% 175.30/26.99    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.99    (32)   ~ (all_52_7 = all_4_2)
% 175.30/26.99    (33)  all_58_1 = all_52_3
% 175.30/26.99    (34)  all_58_0 = all_4_2
% 175.30/26.99    (35)  op(e1, all_52_29) = all_52_28
% 175.30/26.99    (36)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.30/26.99    (37)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.99    (38)  all_58_14 = all_52_29
% 175.30/26.99    (39)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.99    (40)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.99    (41)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.99    (42)  all_58_8 = all_14_2
% 175.30/26.99    (43)  op(e0, e2) = all_52_27
% 175.30/26.99    (44)   ~ (all_52_5 = all_14_2)
% 175.30/26.99    (45)   ~ (all_52_3 = all_4_2)
% 175.30/26.99    (46)  op(e0, e3) = all_52_25
% 175.30/26.99    (47)   ~ (all_52_9 = all_10_2)
% 175.30/26.99    (48)  op(e3, all_52_17) = all_52_16
% 175.30/26.99    (49)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/26.99    (50)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/26.99    (51)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.99    (52)  op(e0, all_52_23) = all_52_22
% 175.30/26.99    (53)   ~ (all_52_15 = all_52_23)
% 175.30/26.99    (54)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/26.99    (55)   ~ (all_52_5 = all_52_29)
% 175.30/26.99    (56)  all_56_12 = all_52_25
% 175.30/26.99    (57)  all_58_13 = all_52_27
% 175.30/26.99    (58)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/26.99    (59)  all_56_5 = all_10_2
% 175.30/26.99    (60)  op(e0, e0) = e0
% 175.30/26.99    (61)   ~ (all_52_25 = e0)
% 175.30/26.99    (62)   ~ (all_52_9 = all_52_17)
% 175.30/26.99    (63)  all_58_6 = all_52_17
% 175.30/26.99    (64)   ~ (all_52_3 = all_52_7)
% 175.30/26.99    (65)  op(e2, all_52_19) = all_52_18
% 175.30/26.99    (66)  all_56_0 = all_4_2
% 175.30/26.99    (67)  all_58_11 = all_52_23
% 175.30/26.99    (68)   ~ (all_52_29 = all_14_2)
% 175.30/26.99    (69)   ~ (all_52_19 = all_10_2)
% 175.30/26.99    (70)  all_58_15 = e0
% 175.30/26.99    (71)   ~ (all_6_0 = e2)
% 175.30/26.99    (72)  all_58_2 = all_52_9
% 175.30/26.99    (73)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.99    (74)   ~ (all_52_29 = e0)
% 175.30/26.99    (75)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.99    (76)  op(e3, e1) = all_52_5
% 175.30/26.99    (77)   ~ (e2 = e1)
% 175.30/26.99    (78)  all_56_10 = all_14_2
% 175.30/26.99    (79)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.99    (80)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.99    (81)  op(e1, e3) = all_52_17
% 175.30/26.99    (82)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/26.99    (83)   ~ (all_52_25 = all_4_2)
% 175.30/26.99    (84)  op(e3, e0) = all_52_7
% 175.30/26.99    (85)  op(e3, e3) = all_4_2
% 175.30/26.99    (86)  all_56_8 = all_52_17
% 175.30/26.99    (87)   ~ (all_52_17 = all_4_2)
% 175.30/26.99    (88)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.99    (89)   ~ (all_52_25 = all_52_27)
% 175.30/26.99    (90)   ~ (all_52_19 = all_52_27)
% 175.30/26.99    (91)  all_56_7 = all_52_15
% 175.30/26.99    (92)   ~ (all_52_15 = e0)
% 175.30/26.99    (93)  op(all_6_1, e0) = all_6_0
% 175.30/26.99    (94)   ~ (all_52_7 = all_52_23)
% 175.30/26.99    (95)   ~ (all_6_0 = e1)
% 175.30/26.99    (96)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.99    (97)  all_52_22 = e0
% 175.30/26.99    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.99    (99)  op(e1, all_14_2) = all_14_1
% 175.30/26.99    (100)  all_58_9 = all_52_7
% 175.30/26.99    (101)  all_58_12 = all_52_25
% 175.30/26.99    (102)  all_14_1 = e1
% 175.30/26.99    (103)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.30/26.99    (104)   ~ (all_52_9 = all_52_15)
% 175.30/26.99    (105)   ~ (e3 = e2)
% 175.30/26.99    (106)   ~ (all_52_19 = all_14_2)
% 175.30/26.99    (107)  op(e2, e3) = all_52_9
% 175.30/26.99    (108)  all_56_13 = all_52_27
% 175.30/26.99  
% 175.30/26.99  Begin of proof
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (7), (48) imply:
% 175.30/26.99  |   (109)  op(e3, all_52_17) = e3
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (29), (65) imply:
% 175.30/26.99  |   (110)  op(e2, all_52_19) = e2
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (99), (102) imply:
% 175.30/26.99  |   (111)  op(e1, all_14_2) = e1
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (52), (97) imply:
% 175.30/26.99  |   (112)  op(e0, all_52_23) = e0
% 175.30/26.99  | 
% 175.30/26.99  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 175.30/26.99  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.30/26.99  |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 175.30/26.99  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 175.30/26.99  |            (49), (50), (51), (53), (54), (55), (56), (57), (58), (59), (60),
% 175.30/26.99  |            (61), (62), (63), (64), (66), (67), (68), (69), (70), (71), (72),
% 175.30/26.99  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 175.30/26.99  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 175.30/26.99  |            (95), (96), (98), (100), (101), (103), (104), (105), (106), (107),
% 175.30/26.99  |            (108), (109), (110), (111), (112) are inconsistent by sub-proof
% 175.30/26.99  |            #119.
% 175.30/26.99  | 
% 175.30/26.99  End of proof
% 175.30/26.99  
% 175.30/26.99  Sub-proof #119 shows that the following formulas are inconsistent:
% 175.30/26.99  ----------------------------------------------------------------
% 175.30/26.99    (1)   ~ (all_52_23 = all_14_2)
% 175.30/26.99    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.30/26.99    (3)   ~ (all_52_17 = all_52_23)
% 175.30/26.99    (4)   ~ (all_6_0 = e3)
% 175.30/26.99    (5)   ~ (all_52_13 = all_52_29)
% 175.30/26.99    (6)  all_56_3 = all_52_7
% 175.30/26.99    (7)  op(e3, e2) = all_52_3
% 175.30/26.99    (8)   ~ (all_52_9 = all_52_25)
% 175.30/26.99    (9)   ~ (all_52_19 = all_52_23)
% 175.30/26.99    (10)  all_56_11 = all_52_23
% 175.30/26.99    (11)   ~ (all_52_27 = e0)
% 175.30/26.99    (12)   ~ (all_52_23 = e0)
% 175.30/26.99    (13)   ~ (all_52_3 = all_10_2)
% 175.30/26.99    (14)  all_58_5 = all_52_13
% 175.30/26.99    (15)   ~ (all_52_25 = all_52_29)
% 175.30/26.99    (16)  op(e0, e0) = all_6_1
% 175.30/26.99    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/26.99    (18)  all_58_3 = all_10_2
% 175.30/26.99    (19)  all_56_9 = all_52_19
% 175.30/26.99    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/26.99    (21)   ~ (all_52_9 = all_4_2)
% 175.30/26.99    (22)  all_58_10 = all_52_15
% 175.30/26.99    (23)  all_58_7 = all_52_19
% 175.30/26.99    (24)   ~ (all_52_17 = all_52_25)
% 175.30/26.99    (25)  op(e0, e1) = all_52_29
% 175.30/26.99    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.99    (27)   ~ (e3 = e1)
% 175.30/26.99    (28)   ~ (all_52_27 = all_52_29)
% 175.30/26.99    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.99    (30)   ~ (all_52_7 = all_4_2)
% 175.30/26.99    (31)  all_58_1 = all_52_3
% 175.30/26.99    (32)  all_58_0 = all_4_2
% 175.30/26.99    (33)  op(e1, all_52_29) = all_52_28
% 175.30/26.99    (34)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.30/26.99    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/26.99    (36)  all_58_14 = all_52_29
% 175.30/26.99    (37)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/26.99    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/26.99    (39)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/26.99    (40)  all_58_8 = all_14_2
% 175.30/26.99    (41)  op(e0, e2) = all_52_27
% 175.30/26.99    (42)   ~ (all_52_5 = all_14_2)
% 175.30/26.99    (43)   ~ (all_52_3 = all_4_2)
% 175.30/26.99    (44)  op(e0, e3) = all_52_25
% 175.30/26.99    (45)   ~ (all_52_9 = all_10_2)
% 175.30/26.99    (46)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/26.99    (47)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/26.99    (48)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/26.99    (49)   ~ (all_52_15 = all_52_23)
% 175.30/26.99    (50)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/26.99    (51)   ~ (all_52_5 = all_52_29)
% 175.30/26.99    (52)  all_56_12 = all_52_25
% 175.30/26.99    (53)  all_58_13 = all_52_27
% 175.30/26.99    (54)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/26.99    (55)  all_56_5 = all_10_2
% 175.30/26.99    (56)  op(e0, e0) = e0
% 175.30/26.99    (57)   ~ (all_52_25 = e0)
% 175.30/26.99    (58)   ~ (all_52_9 = all_52_17)
% 175.30/26.99    (59)  all_58_6 = all_52_17
% 175.30/26.99    (60)   ~ (all_52_3 = all_52_7)
% 175.30/26.99    (61)  op(e2, all_52_19) = e2
% 175.30/26.99    (62)  op(e3, all_52_17) = e3
% 175.30/26.99    (63)  all_56_0 = all_4_2
% 175.30/26.99    (64)  all_58_11 = all_52_23
% 175.30/26.99    (65)   ~ (all_52_29 = all_14_2)
% 175.30/26.99    (66)   ~ (all_52_19 = all_10_2)
% 175.30/26.99    (67)  all_58_15 = e0
% 175.30/26.99    (68)   ~ (all_6_0 = e2)
% 175.30/26.99    (69)  all_58_2 = all_52_9
% 175.30/26.99    (70)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/26.99    (71)   ~ (all_52_29 = e0)
% 175.30/26.99    (72)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.99    (73)  op(e3, e1) = all_52_5
% 175.30/26.99    (74)   ~ (e2 = e1)
% 175.30/26.99    (75)  all_56_10 = all_14_2
% 175.30/26.99    (76)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/26.99    (77)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/26.99    (78)  op(e1, e3) = all_52_17
% 175.30/26.99    (79)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/26.99    (80)   ~ (all_52_25 = all_4_2)
% 175.30/26.99    (81)  op(e3, e0) = all_52_7
% 175.30/26.99    (82)  op(e3, e3) = all_4_2
% 175.30/26.99    (83)  all_56_8 = all_52_17
% 175.30/26.99    (84)   ~ (all_52_17 = all_4_2)
% 175.30/26.99    (85)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/26.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/26.99    (86)   ~ (all_52_25 = all_52_27)
% 175.30/26.99    (87)  op(e0, all_52_23) = e0
% 175.30/26.99    (88)   ~ (all_52_19 = all_52_27)
% 175.30/26.99    (89)  all_56_7 = all_52_15
% 175.30/26.99    (90)  op(e1, all_14_2) = e1
% 175.30/26.99    (91)   ~ (all_52_15 = e0)
% 175.30/26.99    (92)  op(all_6_1, e0) = all_6_0
% 175.30/26.99    (93)   ~ (all_52_7 = all_52_23)
% 175.30/26.99    (94)   ~ (all_6_0 = e1)
% 175.30/26.99    (95)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/26.99    (96)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/26.99    (97)  all_58_9 = all_52_7
% 175.30/26.99    (98)  all_58_12 = all_52_25
% 175.30/26.99    (99)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.30/26.99    (100)   ~ (all_52_9 = all_52_15)
% 175.30/26.99    (101)   ~ (e3 = e2)
% 175.30/26.99    (102)   ~ (all_52_19 = all_14_2)
% 175.30/26.99    (103)  op(e2, e3) = all_52_9
% 175.30/26.99    (104)  all_56_13 = all_52_27
% 175.30/26.99  
% 175.30/26.99  Begin of proof
% 175.30/26.99  | 
% 175.30/26.99  | GROUND_INST: instantiating (85) with e0, all_6_1, e0, e0, simplifying with
% 175.30/26.99  |              (16), (56) gives:
% 175.30/26.99  |   (105)  all_6_1 = e0
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (92), (105) imply:
% 175.30/26.99  |   (106)  op(e0, e0) = all_6_0
% 175.30/26.99  | 
% 175.30/26.99  | GROUND_INST: instantiating (85) with e0, all_6_0, e0, e0, simplifying with
% 175.30/26.99  |              (56), (106) gives:
% 175.30/26.99  |   (107)  all_6_0 = e0
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (4), (107) imply:
% 175.30/26.99  |   (108)   ~ (e3 = e0)
% 175.30/26.99  | 
% 175.30/26.99  | SIMP: (108) implies:
% 175.30/26.99  |   (109)   ~ (e3 = e0)
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (68), (107) imply:
% 175.30/26.99  |   (110)   ~ (e2 = e0)
% 175.30/26.99  | 
% 175.30/26.99  | SIMP: (110) implies:
% 175.30/26.99  |   (111)   ~ (e2 = e0)
% 175.30/26.99  | 
% 175.30/26.99  | REDUCE: (94), (107) imply:
% 175.30/26.99  |   (112)   ~ (e1 = e0)
% 175.30/26.99  | 
% 175.30/26.99  | SIMP: (112) implies:
% 175.30/26.99  |   (113)   ~ (e1 = e0)
% 175.30/26.99  | 
% 175.30/26.99  | BETA: splitting (37) gives:
% 175.30/26.99  | 
% 175.30/26.99  | Case 1:
% 175.30/26.99  | | 
% 175.30/26.99  | |   (114)  all_56_13 = e3
% 175.30/26.99  | | 
% 175.30/26.99  | | REF_CLOSE: (6), (10), (11), (17), (19), (22), (23), (25), (26), (27), (29),
% 175.30/26.99  | |            (30), (32), (34), (38), (40), (41), (42), (44), (46), (48), (49),
% 175.30/26.99  | |            (52), (57), (58), (59), (61), (62), (64), (67), (69), (70), (71),
% 175.30/26.99  | |            (72), (73), (77), (78), (79), (82), (84), (85), (86), (87), (88),
% 175.30/26.99  | |            (89), (90), (93), (95), (96), (97), (98), (99), (100), (101),
% 175.30/26.99  | |            (103), (104), (113), (114) are inconsistent by sub-proof #580.
% 175.30/26.99  | | 
% 175.30/26.99  | Case 2:
% 175.30/26.99  | | 
% 175.30/26.99  | |   (115)   ~ (all_56_13 = e3)
% 175.30/26.99  | | 
% 175.30/26.99  | | REDUCE: (104), (115) imply:
% 175.30/26.99  | |   (116)   ~ (all_52_27 = e3)
% 175.30/26.99  | | 
% 175.30/26.99  | | BETA: splitting (39) gives:
% 175.30/26.99  | | 
% 175.30/26.99  | | Case 1:
% 175.30/26.99  | | | 
% 175.30/26.99  | | |   (117)  all_58_12 = e3
% 175.30/26.99  | | | 
% 175.30/26.99  | | | COMBINE_EQS: (98), (117) imply:
% 175.30/26.99  | | |   (118)  all_52_25 = e3
% 175.30/26.99  | | | 
% 175.30/26.99  | | | SIMP: (118) implies:
% 175.30/26.99  | | |   (119)  all_52_25 = e3
% 175.30/26.99  | | | 
% 175.30/26.99  | | | REDUCE: (8), (119) imply:
% 175.30/26.99  | | |   (120)   ~ (all_52_9 = e3)
% 175.30/26.99  | | | 
% 175.30/26.99  | | | REDUCE: (24), (119) imply:
% 175.30/26.99  | | |   (121)   ~ (all_52_17 = e3)
% 175.30/26.99  | | | 
% 175.30/26.99  | | | REDUCE: (44), (119) imply:
% 175.30/26.99  | | |   (122)  op(e0, e3) = e3
% 175.30/26.99  | | | 
% 175.30/26.99  | | | BETA: splitting (79) gives:
% 175.30/26.99  | | | 
% 175.30/26.99  | | | Case 1:
% 175.30/26.99  | | | | 
% 175.30/26.99  | | | |   (123)  all_56_7 = e3
% 175.30/26.99  | | | | 
% 175.30/26.99  | | | | REF_CLOSE: (10), (11), (17), (22), (25), (27), (41), (46), (49), (64),
% 175.30/26.99  | | | |            (67), (71), (72), (74), (85), (87), (89), (101), (111),
% 175.30/26.99  | | | |            (113), (123) are inconsistent by sub-proof #933.
% 175.30/26.99  | | | | 
% 175.30/26.99  | | | Case 2:
% 175.30/26.99  | | | | 
% 175.30/26.99  | | | |   (124)   ~ (all_56_7 = e3)
% 175.30/26.99  | | | |   (125)  all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/26.99  | | | | 
% 175.30/26.99  | | | | REDUCE: (89), (124) imply:
% 175.30/26.99  | | | |   (126)   ~ (all_52_15 = e3)
% 175.30/26.99  | | | | 
% 175.30/26.99  | | | | BETA: splitting (29) gives:
% 175.30/26.99  | | | | 
% 175.30/26.99  | | | | Case 1:
% 175.30/26.99  | | | | | 
% 175.30/26.99  | | | | |   (127)  all_58_2 = e3
% 175.30/26.99  | | | | | 
% 175.30/26.99  | | | | | REF_CLOSE: (69), (120), (127) are inconsistent by sub-proof #980.
% 175.30/26.99  | | | | | 
% 175.30/26.99  | | | | Case 2:
% 175.30/26.99  | | | | | 
% 175.30/26.99  | | | | |   (128)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/26.99  | | | | | 
% 175.30/26.99  | | | | | BETA: splitting (95) gives:
% 175.30/26.99  | | | | | 
% 175.30/26.99  | | | | | Case 1:
% 175.30/26.99  | | | | | | 
% 175.30/26.99  | | | | | |   (129)  all_58_9 = e3
% 175.30/26.99  | | | | | | 
% 175.30/26.99  | | | | | | COMBINE_EQS: (97), (129) imply:
% 175.30/26.99  | | | | | |   (130)  all_52_7 = e3
% 175.30/26.99  | | | | | | 
% 175.30/26.99  | | | | | | SIMP: (130) implies:
% 175.30/26.99  | | | | | |   (131)  all_52_7 = e3
% 175.30/26.99  | | | | | | 
% 175.30/26.99  | | | | | | REDUCE: (93), (131) imply:
% 175.30/26.99  | | | | | |   (132)   ~ (all_52_23 = e3)
% 175.30/26.99  | | | | | | 
% 175.30/26.99  | | | | | | SIMP: (132) implies:
% 175.30/26.99  | | | | | |   (133)   ~ (all_52_23 = e3)
% 175.30/26.99  | | | | | | 
% 175.30/26.99  | | | | | | BETA: splitting (72) gives:
% 175.30/26.99  | | | | | | 
% 175.30/26.99  | | | | | | Case 1:
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | |   (134)  all_56_11 = e3
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | | COMBINE_EQS: (10), (134) imply:
% 175.30/26.99  | | | | | | |   (135)  all_52_23 = e3
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | | REDUCE: (133), (135) imply:
% 175.30/26.99  | | | | | | |   (136)  $false
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | | CLOSE: (136) is inconsistent.
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | Case 2:
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | |   (137)   ~ (all_56_11 = e3)
% 175.30/26.99  | | | | | | |   (138)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | | BETA: splitting (26) gives:
% 175.30/26.99  | | | | | | | 
% 175.30/26.99  | | | | | | | Case 1:
% 175.30/26.99  | | | | | | | | 
% 175.30/26.99  | | | | | | | |   (139)  all_58_6 = e3
% 175.30/26.99  | | | | | | | | 
% 175.30/26.99  | | | | | | | | REF_CLOSE: (59), (121), (139) are inconsistent by sub-proof
% 175.30/26.99  | | | | | | | |            #981.
% 175.30/26.99  | | | | | | | | 
% 175.30/26.99  | | | | | | | Case 2:
% 175.30/26.99  | | | | | | | | 
% 175.30/26.99  | | | | | | | |   (140)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/26.99  | | | | | | | | 
% 175.30/26.99  | | | | | | | | BETA: splitting (50) gives:
% 175.30/26.99  | | | | | | | | 
% 175.30/26.99  | | | | | | | | Case 1:
% 175.30/26.99  | | | | | | | | | 
% 175.30/26.99  | | | | | | | | |   (141)  all_56_10 = e3
% 175.30/26.99  | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | REF_CLOSE: (1), (23), (40), (42), (62), (64), (73), (75),
% 175.30/26.99  | | | | | | | | |            (78), (85), (90), (102), (140), (141) are
% 175.30/26.99  | | | | | | | | |            inconsistent by sub-proof #922.
% 175.30/26.99  | | | | | | | | | 
% 175.30/26.99  | | | | | | | | Case 2:
% 175.30/26.99  | | | | | | | | | 
% 175.30/26.99  | | | | | | | | |   (142)   ~ (all_56_10 = e3)
% 175.30/26.99  | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | REDUCE: (75), (142) imply:
% 175.30/26.99  | | | | | | | | |   (143)   ~ (all_14_2 = e3)
% 175.30/26.99  | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | BETA: splitting (140) gives:
% 175.30/26.99  | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | Case 1:
% 175.30/26.99  | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | |   (144)  all_58_7 = e3
% 175.30/26.99  | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | COMBINE_EQS: (23), (144) imply:
% 175.30/26.99  | | | | | | | | | |   (145)  all_52_19 = e3
% 175.30/26.99  | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | REDUCE: (66), (145) imply:
% 175.30/26.99  | | | | | | | | | |   (146)   ~ (all_10_2 = e3)
% 175.30/26.99  | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | SIMP: (146) implies:
% 175.30/26.99  | | | | | | | | | |   (147)   ~ (all_10_2 = e3)
% 175.30/26.99  | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | REDUCE: (61), (145) imply:
% 175.30/26.99  | | | | | | | | | |   (148)  op(e2, e3) = e2
% 175.30/26.99  | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | BETA: splitting (128) gives:
% 175.30/26.99  | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | Case 1:
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | |   (149)  all_58_3 = e3
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | COMBINE_EQS: (18), (149) imply:
% 175.30/26.99  | | | | | | | | | | |   (150)  all_10_2 = e3
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | REDUCE: (147), (150) imply:
% 175.30/26.99  | | | | | | | | | | |   (151)  $false
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | Case 2:
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | GROUND_INST: instantiating (85) with all_52_9, e2, e3, e2,
% 175.30/26.99  | | | | | | | | | | |              simplifying with (103), (148) gives:
% 175.30/26.99  | | | | | | | | | | |   (152)  all_52_9 = e2
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | REDUCE: (100), (152) imply:
% 175.30/26.99  | | | | | | | | | | |   (153)   ~ (all_52_15 = e2)
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | SIMP: (153) implies:
% 175.30/26.99  | | | | | | | | | | |   (154)   ~ (all_52_15 = e2)
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | BETA: splitting (125) gives:
% 175.30/26.99  | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | Case 1:
% 175.30/26.99  | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | |   (155)  all_56_7 = e2
% 175.30/26.99  | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | | REF_CLOSE: (89), (154), (155) are inconsistent by sub-proof
% 175.30/26.99  | | | | | | | | | | | |            #164.
% 175.30/26.99  | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | Case 2:
% 175.30/26.99  | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | |   (156)  all_56_7 = e1 | all_56_7 = e0
% 175.30/26.99  | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | | BETA: splitting (156) gives:
% 175.30/26.99  | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | | Case 1:
% 175.30/26.99  | | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | | |   (157)  all_56_7 = e1
% 175.30/26.99  | | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | | | COMBINE_EQS: (89), (157) imply:
% 175.30/26.99  | | | | | | | | | | | | |   (158)  all_52_15 = e1
% 175.30/26.99  | | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | | | SIMP: (158) implies:
% 175.30/26.99  | | | | | | | | | | | | |   (159)  all_52_15 = e1
% 175.30/26.99  | | | | | | | | | | | | | 
% 175.30/26.99  | | | | | | | | | | | | | REDUCE: (49), (159) imply:
% 175.30/26.99  | | | | | | | | | | | | |   (160)   ~ (all_52_23 = e1)
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | SIMP: (160) implies:
% 175.30/27.00  | | | | | | | | | | | | |   (161)   ~ (all_52_23 = e1)
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | BETA: splitting (138) gives:
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | Case 1:
% 175.30/27.00  | | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | |   (162)  all_56_11 = e2
% 175.30/27.00  | | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (41), (85), (87), (162) are
% 175.30/27.00  | | | | | | | | | | | | | |            inconsistent by sub-proof #936.
% 175.30/27.00  | | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | Case 2:
% 175.30/27.00  | | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | |   (163)  all_56_11 = e1 | all_56_11 = e0
% 175.30/27.00  | | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (161), (163) are inconsistent by
% 175.30/27.00  | | | | | | | | | | | | | |            sub-proof #431.
% 175.30/27.00  | | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | End of split
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | Case 2:
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | |   (164)  all_56_7 = e0
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | COMBINE_EQS: (89), (164) imply:
% 175.30/27.00  | | | | | | | | | | | | |   (165)  all_52_15 = e0
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | SIMP: (165) implies:
% 175.30/27.00  | | | | | | | | | | | | |   (166)  all_52_15 = e0
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | REDUCE: (91), (166) imply:
% 175.30/27.00  | | | | | | | | | | | | |   (167)  $false
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 175.30/27.00  | | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | | End of split
% 175.30/27.00  | | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | | End of split
% 175.30/27.00  | | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | End of split
% 175.30/27.00  | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | Case 2:
% 175.30/27.00  | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | |   (168)  all_58_8 = e3 | all_58_11 = e3
% 175.30/27.00  | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | | REF_CLOSE: (40), (64), (133), (143), (168) are inconsistent
% 175.30/27.00  | | | | | | | | | |            by sub-proof #997.
% 175.30/27.00  | | | | | | | | | | 
% 175.30/27.00  | | | | | | | | | End of split
% 175.30/27.00  | | | | | | | | | 
% 175.30/27.00  | | | | | | | | End of split
% 175.30/27.00  | | | | | | | | 
% 175.30/27.00  | | | | | | | End of split
% 175.30/27.00  | | | | | | | 
% 175.30/27.00  | | | | | | End of split
% 175.30/27.00  | | | | | | 
% 175.30/27.00  | | | | | Case 2:
% 175.30/27.00  | | | | | | 
% 175.30/27.00  | | | | | |   (169)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/27.00  | | | | | | 
% 175.30/27.00  | | | | | | REF_CLOSE: (12), (22), (64), (67), (85), (87), (109), (122), (126),
% 175.30/27.00  | | | | | |            (169) are inconsistent by sub-proof #914.
% 175.30/27.00  | | | | | | 
% 175.30/27.00  | | | | | End of split
% 175.30/27.00  | | | | | 
% 175.30/27.00  | | | | End of split
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | End of split
% 175.30/27.00  | | | 
% 175.30/27.00  | | Case 2:
% 175.30/27.00  | | | 
% 175.30/27.00  | | |   (170)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/27.00  | | | 
% 175.30/27.00  | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 175.30/27.00  | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 175.30/27.00  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 175.30/27.00  | | |            (38), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 175.30/27.00  | | |            (49), (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 175.30/27.00  | | |            (61), (62), (63), (64), (65), (66), (67), (69), (70), (71),
% 175.30/27.00  | | |            (72), (73), (74), (76), (77), (78), (79), (80), (81), (82),
% 175.30/27.00  | | |            (83), (84), (85), (87), (88), (89), (90), (93), (95), (97),
% 175.30/27.00  | | |            (98), (100), (101), (103), (109), (111), (113), (116), (170)
% 175.30/27.00  | | |            are inconsistent by sub-proof #898.
% 175.30/27.00  | | | 
% 175.30/27.00  | | End of split
% 175.30/27.00  | | 
% 175.30/27.00  | End of split
% 175.30/27.00  | 
% 175.30/27.00  End of proof
% 175.30/27.00  
% 175.30/27.00  Sub-proof #120 shows that the following formulas are inconsistent:
% 175.30/27.00  ----------------------------------------------------------------
% 175.30/27.00    (1)   ~ (all_52_17 = all_52_23)
% 175.30/27.00    (2)  op(e2, all_10_2) = all_10_1
% 175.30/27.00    (3)  op(e3, e2) = all_52_3
% 175.30/27.00    (4)   ~ (all_52_9 = all_52_25)
% 175.30/27.00    (5)   ~ (all_52_27 = e0)
% 175.30/27.00    (6)  op(e3, all_52_9) = all_52_8
% 175.30/27.00    (7)   ~ (all_52_3 = all_10_2)
% 175.30/27.00    (8)  all_58_5 = all_52_13
% 175.30/27.00    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/27.00    (10)  all_58_3 = all_10_2
% 175.30/27.00    (11)   ~ (all_52_9 = all_4_2)
% 175.30/27.00    (12)   ~ (all_52_5 = all_52_7)
% 175.30/27.00    (13)  all_58_10 = all_52_15
% 175.30/27.00    (14)  all_58_7 = all_52_19
% 175.30/27.00    (15)   ~ (all_52_17 = all_52_25)
% 175.30/27.00    (16)  op(e0, e1) = all_52_29
% 175.30/27.00    (17)  all_58_4 = all_52_5
% 175.30/27.00    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/27.00    (19)   ~ (e3 = e1)
% 175.30/27.00    (20)   ~ (all_52_27 = all_52_29)
% 175.30/27.00    (21)   ~ (all_52_17 = all_14_2)
% 175.30/27.00    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/27.00    (23)   ~ (all_52_7 = all_4_2)
% 175.30/27.00    (24)  all_58_1 = all_52_3
% 175.30/27.00    (25)  all_58_0 = all_4_2
% 175.30/27.00    (26)  op(e1, all_52_13) = all_52_12
% 175.30/27.00    (27)  all_52_0 = e2
% 175.30/27.00    (28)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.30/27.00          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.30/27.00    (29)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/27.00    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/27.00    (31)  all_58_14 = all_52_29
% 175.30/27.00    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/27.00    (33)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/27.00    (34)  all_58_8 = all_14_2
% 175.30/27.00    (35)  op(e0, e2) = all_52_27
% 175.30/27.00    (36)  all_56_14 = all_52_29
% 175.30/27.00    (37)  op(e0, e3) = all_52_25
% 175.30/27.00    (38)  all_52_10 = all_10_1
% 175.30/27.00    (39)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/27.00    (40)   ~ (e3 = e0)
% 175.30/27.00    (41)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/27.00    (42)  all_58_13 = all_52_27
% 175.30/27.00    (43)   ~ (all_52_25 = e0)
% 175.30/27.00    (44)   ~ (all_52_9 = all_52_17)
% 175.30/27.00    (45)  all_58_6 = all_52_17
% 175.30/27.00    (46)   ~ (all_52_3 = all_52_7)
% 175.30/27.00    (47)   ~ (e1 = e0)
% 175.30/27.00    (48)  all_58_11 = all_52_23
% 175.30/27.00    (49)   ~ (all_52_7 = all_52_15)
% 175.30/27.00    (50)  op(e0, all_52_15) = all_52_14
% 175.30/27.00    (51)   ~ (all_52_19 = all_10_2)
% 175.30/27.00    (52)  all_58_15 = e0
% 175.30/27.00    (53)  all_58_2 = all_52_9
% 175.30/27.00    (54)   ~ (all_52_29 = e0)
% 175.30/27.00    (55)   ~ (e2 = e1)
% 175.30/27.00    (56)  all_56_10 = all_14_2
% 175.30/27.00    (57)  op(e1, e3) = all_52_17
% 175.30/27.00    (58)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/27.00    (59)  op(e3, e3) = all_4_2
% 175.30/27.00    (60)   ~ (all_10_1 = e3)
% 175.30/27.00    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/27.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/27.00    (62)   ~ (all_52_25 = all_52_27)
% 175.30/27.00    (63)  all_56_7 = all_52_15
% 175.30/27.00    (64)   ~ (all_52_7 = all_52_23)
% 175.30/27.00    (65)   ~ (all_52_17 = all_52_19)
% 175.30/27.00    (66)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/27.00    (67)  all_58_9 = all_52_7
% 175.30/27.00    (68)   ~ (e2 = e0)
% 175.30/27.00    (69)  all_58_12 = all_52_25
% 175.30/27.00    (70)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/27.00    (71)   ~ (e3 = e2)
% 175.30/27.00    (72)   ~ (all_52_19 = all_14_2)
% 175.30/27.00    (73)  op(e2, e3) = all_52_9
% 175.30/27.00  
% 175.30/27.00  Begin of proof
% 175.30/27.00  | 
% 175.30/27.00  | BETA: splitting (28) gives:
% 175.30/27.00  | 
% 175.30/27.00  | Case 1:
% 175.30/27.00  | | 
% 175.30/27.00  | |   (74)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.30/27.00  | | 
% 175.30/27.00  | | REF_CLOSE: (27), (71), (74) are inconsistent by sub-proof #124.
% 175.30/27.00  | | 
% 175.30/27.00  | Case 2:
% 175.30/27.00  | | 
% 175.30/27.00  | |   (75)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.30/27.00  | | 
% 175.30/27.00  | | ALPHA: (75) implies:
% 175.30/27.00  | |   (76)  all_52_14 = e0
% 175.30/27.00  | |   (77)  all_52_12 = e1
% 175.30/27.00  | |   (78)  all_52_10 = e2
% 175.30/27.00  | |   (79)  all_52_8 = e3
% 175.30/27.00  | | 
% 175.30/27.00  | | COMBINE_EQS: (38), (78) imply:
% 175.30/27.00  | |   (80)  all_10_1 = e2
% 175.30/27.00  | | 
% 175.30/27.00  | | REDUCE: (60), (80) imply:
% 175.30/27.00  | |   (81)   ~ (e3 = e2)
% 175.30/27.00  | | 
% 175.30/27.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.30/27.00  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.30/27.00  | |            (24), (25), (26), (29), (30), (31), (32), (33), (34), (35), (36),
% 175.30/27.00  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 175.30/27.00  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 175.30/27.00  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 175.30/27.00  | |            (72), (73), (76), (77), (79), (80) are inconsistent by sub-proof
% 175.30/27.00  | |            #121.
% 175.30/27.00  | | 
% 175.30/27.00  | End of split
% 175.30/27.00  | 
% 175.30/27.00  End of proof
% 175.30/27.00  
% 175.30/27.00  Sub-proof #121 shows that the following formulas are inconsistent:
% 175.30/27.00  ----------------------------------------------------------------
% 175.30/27.00    (1)   ~ (all_52_17 = all_52_23)
% 175.30/27.00    (2)  op(e2, all_10_2) = all_10_1
% 175.30/27.00    (3)  op(e3, e2) = all_52_3
% 175.30/27.00    (4)   ~ (all_52_9 = all_52_25)
% 175.30/27.00    (5)   ~ (all_52_27 = e0)
% 175.30/27.00    (6)  op(e3, all_52_9) = all_52_8
% 175.30/27.00    (7)   ~ (all_52_3 = all_10_2)
% 175.30/27.00    (8)  all_58_5 = all_52_13
% 175.30/27.00    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/27.00    (10)  all_58_3 = all_10_2
% 175.30/27.00    (11)  all_52_12 = e1
% 175.30/27.00    (12)   ~ (all_52_9 = all_4_2)
% 175.30/27.00    (13)   ~ (all_52_5 = all_52_7)
% 175.30/27.00    (14)  all_58_10 = all_52_15
% 175.30/27.00    (15)  all_58_7 = all_52_19
% 175.30/27.00    (16)   ~ (all_52_17 = all_52_25)
% 175.30/27.00    (17)  op(e0, e1) = all_52_29
% 175.30/27.00    (18)  all_58_4 = all_52_5
% 175.30/27.00    (19)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/27.00    (20)   ~ (e3 = e1)
% 175.30/27.00    (21)  all_52_14 = e0
% 175.30/27.00    (22)   ~ (all_52_27 = all_52_29)
% 175.30/27.00    (23)   ~ (all_52_17 = all_14_2)
% 175.30/27.00    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/27.00    (25)   ~ (all_52_7 = all_4_2)
% 175.30/27.00    (26)  all_58_1 = all_52_3
% 175.30/27.00    (27)  all_58_0 = all_4_2
% 175.30/27.00    (28)  op(e1, all_52_13) = all_52_12
% 175.30/27.00    (29)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/27.00    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/27.00    (31)  all_58_14 = all_52_29
% 175.30/27.00    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/27.00    (33)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/27.00    (34)  all_58_8 = all_14_2
% 175.30/27.00    (35)  op(e0, e2) = all_52_27
% 175.30/27.00    (36)  all_56_14 = all_52_29
% 175.30/27.00    (37)  op(e0, e3) = all_52_25
% 175.30/27.00    (38)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/27.00    (39)   ~ (e3 = e0)
% 175.30/27.00    (40)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/27.00    (41)  all_58_13 = all_52_27
% 175.30/27.00    (42)  all_52_8 = e3
% 175.30/27.00    (43)   ~ (all_52_25 = e0)
% 175.30/27.00    (44)   ~ (all_52_9 = all_52_17)
% 175.30/27.00    (45)  all_58_6 = all_52_17
% 175.30/27.00    (46)   ~ (all_52_3 = all_52_7)
% 175.30/27.00    (47)   ~ (e1 = e0)
% 175.30/27.00    (48)  all_58_11 = all_52_23
% 175.30/27.00    (49)   ~ (all_52_7 = all_52_15)
% 175.30/27.00    (50)  op(e0, all_52_15) = all_52_14
% 175.30/27.00    (51)   ~ (all_52_19 = all_10_2)
% 175.30/27.00    (52)  all_58_15 = e0
% 175.30/27.00    (53)  all_58_2 = all_52_9
% 175.30/27.00    (54)   ~ (all_52_29 = e0)
% 175.30/27.00    (55)   ~ (e2 = e1)
% 175.30/27.00    (56)  all_56_10 = all_14_2
% 175.30/27.00    (57)  op(e1, e3) = all_52_17
% 175.30/27.00    (58)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/27.00    (59)  op(e3, e3) = all_4_2
% 175.30/27.00    (60)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/27.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/27.00    (61)   ~ (all_52_25 = all_52_27)
% 175.30/27.00    (62)  all_56_7 = all_52_15
% 175.30/27.00    (63)  all_10_1 = e2
% 175.30/27.00    (64)   ~ (all_52_7 = all_52_23)
% 175.30/27.00    (65)   ~ (all_52_17 = all_52_19)
% 175.30/27.00    (66)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/27.00    (67)  all_58_9 = all_52_7
% 175.30/27.00    (68)   ~ (e2 = e0)
% 175.30/27.00    (69)  all_58_12 = all_52_25
% 175.30/27.00    (70)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/27.00    (71)   ~ (e3 = e2)
% 175.30/27.00    (72)   ~ (all_52_19 = all_14_2)
% 175.30/27.00    (73)  op(e2, e3) = all_52_9
% 175.30/27.00  
% 175.30/27.00  Begin of proof
% 175.30/27.00  | 
% 175.30/27.00  | REDUCE: (6), (42) imply:
% 175.30/27.00  |   (74)  op(e3, all_52_9) = e3
% 175.30/27.00  | 
% 175.30/27.00  | REDUCE: (2), (63) imply:
% 175.30/27.00  |   (75)  op(e2, all_10_2) = e2
% 175.30/27.00  | 
% 175.30/27.00  | REDUCE: (11), (28) imply:
% 175.30/27.00  |   (76)  op(e1, all_52_13) = e1
% 175.30/27.00  | 
% 175.30/27.00  | REDUCE: (21), (50) imply:
% 175.30/27.00  |   (77)  op(e0, all_52_15) = e0
% 175.30/27.00  | 
% 175.30/27.00  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14), (15),
% 175.30/27.00  |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 175.30/27.00  |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 175.30/27.00  |            (40), (41), (43), (44), (45), (46), (47), (48), (49), (51), (52),
% 175.30/27.00  |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62), (64),
% 175.30/27.00  |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 175.30/27.00  |            (76), (77) are inconsistent by sub-proof #122.
% 175.30/27.00  | 
% 175.30/27.00  End of proof
% 175.30/27.00  
% 175.30/27.00  Sub-proof #122 shows that the following formulas are inconsistent:
% 175.30/27.00  ----------------------------------------------------------------
% 175.30/27.00    (1)   ~ (all_52_17 = all_52_23)
% 175.30/27.00    (2)  op(e3, e2) = all_52_3
% 175.30/27.00    (3)   ~ (all_52_9 = all_52_25)
% 175.30/27.00    (4)   ~ (all_52_27 = e0)
% 175.30/27.00    (5)   ~ (all_52_3 = all_10_2)
% 175.30/27.00    (6)  all_58_5 = all_52_13
% 175.30/27.00    (7)  op(e1, all_52_13) = e1
% 175.30/27.00    (8)  op(e0, all_52_15) = e0
% 175.30/27.00    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/27.00    (10)  all_58_3 = all_10_2
% 175.30/27.00    (11)   ~ (all_52_9 = all_4_2)
% 175.30/27.00    (12)   ~ (all_52_5 = all_52_7)
% 175.30/27.00    (13)  all_58_10 = all_52_15
% 175.30/27.00    (14)  all_58_7 = all_52_19
% 175.30/27.00    (15)   ~ (all_52_17 = all_52_25)
% 175.30/27.00    (16)  op(e0, e1) = all_52_29
% 175.30/27.00    (17)  all_58_4 = all_52_5
% 175.30/27.00    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/27.00    (19)   ~ (e3 = e1)
% 175.30/27.00    (20)   ~ (all_52_27 = all_52_29)
% 175.30/27.00    (21)   ~ (all_52_17 = all_14_2)
% 175.30/27.00    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/27.00    (23)   ~ (all_52_7 = all_4_2)
% 175.30/27.00    (24)  all_58_1 = all_52_3
% 175.30/27.00    (25)  all_58_0 = all_4_2
% 175.30/27.00    (26)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/27.00    (27)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/27.00    (28)  all_58_14 = all_52_29
% 175.30/27.00    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/27.00    (30)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/27.00    (31)  all_58_8 = all_14_2
% 175.30/27.00    (32)  op(e0, e2) = all_52_27
% 175.30/27.00    (33)  all_56_14 = all_52_29
% 175.30/27.00    (34)  op(e0, e3) = all_52_25
% 175.30/27.00    (35)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.30/27.00    (36)  op(e3, all_52_9) = e3
% 175.30/27.00    (37)   ~ (e3 = e0)
% 175.30/27.00    (38)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/27.00    (39)  all_58_13 = all_52_27
% 175.30/27.00    (40)   ~ (all_52_25 = e0)
% 175.30/27.00    (41)   ~ (all_52_9 = all_52_17)
% 175.30/27.00    (42)  all_58_6 = all_52_17
% 175.30/27.00    (43)   ~ (all_52_3 = all_52_7)
% 175.30/27.00    (44)   ~ (e1 = e0)
% 175.30/27.00    (45)  all_58_11 = all_52_23
% 175.30/27.00    (46)   ~ (all_52_7 = all_52_15)
% 175.30/27.00    (47)   ~ (all_52_19 = all_10_2)
% 175.30/27.00    (48)  all_58_15 = e0
% 175.30/27.00    (49)  all_58_2 = all_52_9
% 175.30/27.00    (50)   ~ (all_52_29 = e0)
% 175.30/27.00    (51)   ~ (e2 = e1)
% 175.30/27.00    (52)  all_56_10 = all_14_2
% 175.30/27.00    (53)  op(e1, e3) = all_52_17
% 175.30/27.00    (54)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/27.00    (55)  op(e2, all_10_2) = e2
% 175.30/27.00    (56)  op(e3, e3) = all_4_2
% 175.30/27.00    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/27.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/27.00    (58)   ~ (all_52_25 = all_52_27)
% 175.30/27.00    (59)  all_56_7 = all_52_15
% 175.30/27.00    (60)   ~ (all_52_7 = all_52_23)
% 175.30/27.00    (61)   ~ (all_52_17 = all_52_19)
% 175.30/27.00    (62)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/27.00    (63)  all_58_9 = all_52_7
% 175.30/27.00    (64)   ~ (e2 = e0)
% 175.30/27.00    (65)  all_58_12 = all_52_25
% 175.30/27.00    (66)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/27.00    (67)   ~ (e3 = e2)
% 175.30/27.00    (68)   ~ (all_52_19 = all_14_2)
% 175.30/27.00    (69)  op(e2, e3) = all_52_9
% 175.30/27.00  
% 175.30/27.00  Begin of proof
% 175.30/27.00  | 
% 175.30/27.00  | BETA: splitting (54) gives:
% 175.30/27.00  | 
% 175.30/27.00  | Case 1:
% 175.30/27.00  | | 
% 175.30/27.00  | |   (70)  all_56_7 = e3
% 175.30/27.00  | | 
% 175.30/27.00  | | COMBINE_EQS: (59), (70) imply:
% 175.30/27.00  | |   (71)  all_52_15 = e3
% 175.30/27.00  | | 
% 175.30/27.00  | | SIMP: (71) implies:
% 175.30/27.00  | |   (72)  all_52_15 = e3
% 175.30/27.00  | | 
% 175.30/27.00  | | REDUCE: (8), (72) imply:
% 175.30/27.00  | |   (73)  op(e0, e3) = e0
% 175.30/27.00  | | 
% 175.30/27.00  | | GROUND_INST: instantiating (57) with all_52_25, e0, e3, e0, simplifying with
% 175.30/27.00  | |              (34), (73) gives:
% 175.30/27.00  | |   (74)  all_52_25 = e0
% 175.30/27.00  | | 
% 175.30/27.00  | | REDUCE: (40), (74) imply:
% 175.30/27.00  | |   (75)  $false
% 175.30/27.00  | | 
% 175.30/27.00  | | CLOSE: (75) is inconsistent.
% 175.30/27.00  | | 
% 175.30/27.00  | Case 2:
% 175.30/27.00  | | 
% 175.30/27.00  | |   (76)   ~ (all_56_7 = e3)
% 175.30/27.00  | | 
% 175.30/27.00  | | REDUCE: (59), (76) imply:
% 175.30/27.00  | |   (77)   ~ (all_52_15 = e3)
% 175.30/27.00  | | 
% 175.30/27.00  | | BETA: splitting (62) gives:
% 175.30/27.00  | | 
% 175.30/27.00  | | Case 1:
% 175.30/27.00  | | | 
% 175.30/27.00  | | |   (78)  all_58_9 = e3
% 175.30/27.00  | | | 
% 175.30/27.00  | | | COMBINE_EQS: (63), (78) imply:
% 175.30/27.00  | | |   (79)  all_52_7 = e3
% 175.30/27.00  | | | 
% 175.30/27.00  | | | SIMP: (79) implies:
% 175.30/27.00  | | |   (80)  all_52_7 = e3
% 175.30/27.00  | | | 
% 175.30/27.00  | | | REDUCE: (43), (80) imply:
% 175.30/27.00  | | |   (81)   ~ (all_52_3 = e3)
% 175.30/27.00  | | | 
% 175.30/27.00  | | | REDUCE: (12), (80) imply:
% 175.30/27.00  | | |   (82)   ~ (all_52_5 = e3)
% 175.30/27.00  | | | 
% 175.30/27.00  | | | REDUCE: (46), (80) imply:
% 175.30/27.00  | | |   (83)   ~ (all_52_15 = e3)
% 175.30/27.00  | | | 
% 175.30/27.00  | | | REDUCE: (60), (80) imply:
% 175.30/27.00  | | |   (84)   ~ (all_52_23 = e3)
% 175.30/27.00  | | | 
% 175.30/27.00  | | | SIMP: (84) implies:
% 175.30/27.00  | | |   (85)   ~ (all_52_23 = e3)
% 175.30/27.00  | | | 
% 175.30/27.00  | | | REDUCE: (23), (80) imply:
% 175.30/27.00  | | |   (86)   ~ (all_4_2 = e3)
% 175.30/27.00  | | | 
% 175.30/27.00  | | | SIMP: (86) implies:
% 175.30/27.00  | | |   (87)   ~ (all_4_2 = e3)
% 175.30/27.00  | | | 
% 175.30/27.00  | | | BETA: splitting (30) gives:
% 175.30/27.00  | | | 
% 175.30/27.00  | | | Case 1:
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | |   (88)  all_58_12 = e3
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | COMBINE_EQS: (65), (88) imply:
% 175.30/27.00  | | | |   (89)  all_52_25 = e3
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | SIMP: (89) implies:
% 175.30/27.00  | | | |   (90)  all_52_25 = e3
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | REDUCE: (3), (90) imply:
% 175.30/27.00  | | | |   (91)   ~ (all_52_9 = e3)
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | REDUCE: (15), (90) imply:
% 175.30/27.00  | | | |   (92)   ~ (all_52_17 = e3)
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | REDUCE: (58), (90) imply:
% 175.30/27.00  | | | |   (93)   ~ (all_52_27 = e3)
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | SIMP: (93) implies:
% 175.30/27.00  | | | |   (94)   ~ (all_52_27 = e3)
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (13), (14), (16),
% 175.30/27.00  | | | |            (18), (19), (22), (24), (27), (31), (36), (38), (39), (42),
% 175.30/27.00  | | | |            (44), (45), (47), (48), (49), (50), (52), (53), (55), (57),
% 175.30/27.00  | | | |            (68), (69), (77), (78), (81), (85), (91), (92), (94) are
% 175.30/27.00  | | | |            inconsistent by sub-proof #973.
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | Case 2:
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | |   (95)   ~ (all_58_12 = e3)
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | REDUCE: (65), (95) imply:
% 175.30/27.00  | | | |   (96)   ~ (all_52_25 = e3)
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | | REF_CLOSE: (2), (5), (6), (7), (10), (11), (13), (14), (17), (18), (19),
% 175.30/27.00  | | | |            (20), (21), (22), (24), (25), (26), (27), (28), (29), (31),
% 175.30/27.00  | | | |            (33), (36), (39), (41), (42), (49), (53), (55), (56), (57),
% 175.30/27.00  | | | |            (61), (65), (66), (69), (77), (82), (87), (96) are
% 175.30/27.00  | | | |            inconsistent by sub-proof #123.
% 175.30/27.00  | | | | 
% 175.30/27.00  | | | End of split
% 175.30/27.00  | | | 
% 175.30/27.00  | | Case 2:
% 175.30/27.00  | | | 
% 175.30/27.00  | | |   (97)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/27.00  | | | 
% 175.30/27.00  | | | REF_CLOSE: (4), (8), (9), (13), (16), (19), (32), (35), (37), (44), (48),
% 175.30/27.00  | | |            (50), (51), (57), (64), (67), (77), (97) are inconsistent by
% 175.30/27.00  | | |            sub-proof #985.
% 175.30/27.00  | | | 
% 175.30/27.00  | | End of split
% 175.30/27.00  | | 
% 175.30/27.00  | End of split
% 175.30/27.00  | 
% 175.30/27.00  End of proof
% 175.30/27.00  
% 175.30/27.00  Sub-proof #123 shows that the following formulas are inconsistent:
% 175.30/27.00  ----------------------------------------------------------------
% 175.30/27.00    (1)   ~ (all_52_25 = e3)
% 175.30/27.00    (2)  op(e3, e2) = all_52_3
% 175.30/27.00    (3)   ~ (all_52_3 = all_10_2)
% 175.30/27.00    (4)  all_58_5 = all_52_13
% 175.30/27.00    (5)  op(e1, all_52_13) = e1
% 175.30/27.00    (6)   ~ (all_4_2 = e3)
% 175.30/27.00    (7)  all_58_3 = all_10_2
% 175.30/27.00    (8)   ~ (all_52_9 = all_4_2)
% 175.30/27.00    (9)  all_58_10 = all_52_15
% 175.30/27.00    (10)  all_58_7 = all_52_19
% 175.30/27.00    (11)  all_58_4 = all_52_5
% 175.30/27.00    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/27.00    (13)   ~ (e3 = e1)
% 175.30/27.00    (14)   ~ (all_52_27 = all_52_29)
% 175.30/27.00    (15)   ~ (all_52_17 = all_14_2)
% 175.30/27.00    (16)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/27.00    (17)  all_58_1 = all_52_3
% 175.30/27.00    (18)  all_58_0 = all_4_2
% 175.30/27.00    (19)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/27.00    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/27.00    (21)  all_58_14 = all_52_29
% 175.30/27.00    (22)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/27.00    (23)  all_58_8 = all_14_2
% 175.30/27.00    (24)  all_56_14 = all_52_29
% 175.30/27.00    (25)   ~ (all_52_5 = e3)
% 175.30/27.00    (26)  op(e3, all_52_9) = e3
% 175.30/27.00    (27)   ~ (all_52_15 = e3)
% 175.30/27.00    (28)  all_58_13 = all_52_27
% 175.30/27.00    (29)   ~ (all_52_9 = all_52_17)
% 175.30/27.00    (30)  all_58_6 = all_52_17
% 175.30/27.00    (31)  all_58_2 = all_52_9
% 175.30/27.00    (32)  op(e1, e3) = all_52_17
% 175.30/27.00    (33)  op(e2, all_10_2) = e2
% 175.30/27.00    (34)  op(e3, e3) = all_4_2
% 175.30/27.00    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/27.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/27.00    (36)   ~ (all_52_17 = all_52_19)
% 175.30/27.00    (37)  all_58_12 = all_52_25
% 175.30/27.00    (38)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/27.00    (39)  op(e2, e3) = all_52_9
% 175.30/27.00  
% 175.30/27.00  Begin of proof
% 175.30/27.00  | 
% 175.30/27.00  | BETA: splitting (22) gives:
% 175.30/27.00  | 
% 175.30/27.00  | Case 1:
% 175.30/27.00  | | 
% 175.30/27.00  | |   (40)  all_58_0 = e3
% 175.30/27.00  | | 
% 175.30/27.00  | | COMBINE_EQS: (18), (40) imply:
% 175.30/27.00  | |   (41)  all_4_2 = e3
% 175.30/27.00  | | 
% 175.30/27.00  | | REDUCE: (6), (41) imply:
% 175.30/27.00  | |   (42)  $false
% 175.30/27.00  | | 
% 175.30/27.00  | | CLOSE: (42) is inconsistent.
% 175.30/27.00  | | 
% 175.30/27.00  | Case 2:
% 175.30/27.00  | | 
% 175.30/27.00  | |   (43)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/27.00  | | 
% 175.30/27.00  | | BETA: splitting (12) gives:
% 175.30/27.00  | | 
% 175.30/27.00  | | Case 1:
% 175.30/27.00  | | | 
% 175.30/27.00  | | |   (44)  all_58_6 = e3
% 175.30/27.01  | | | 
% 175.30/27.01  | | | COMBINE_EQS: (30), (44) imply:
% 175.30/27.01  | | |   (45)  all_52_17 = e3
% 175.30/27.01  | | | 
% 175.30/27.01  | | | SIMP: (45) implies:
% 175.30/27.01  | | |   (46)  all_52_17 = e3
% 175.30/27.01  | | | 
% 175.30/27.01  | | | REDUCE: (29), (46) imply:
% 175.30/27.01  | | |   (47)   ~ (all_52_9 = e3)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | REDUCE: (36), (46) imply:
% 175.30/27.01  | | |   (48)   ~ (all_52_19 = e3)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | SIMP: (48) implies:
% 175.30/27.01  | | |   (49)   ~ (all_52_19 = e3)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | REDUCE: (15), (46) imply:
% 175.30/27.01  | | |   (50)   ~ (all_14_2 = e3)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | SIMP: (50) implies:
% 175.30/27.01  | | |   (51)   ~ (all_14_2 = e3)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | REDUCE: (32), (46) imply:
% 175.30/27.01  | | |   (52)  op(e1, e3) = e3
% 175.30/27.01  | | | 
% 175.30/27.01  | | | BETA: splitting (38) gives:
% 175.30/27.01  | | | 
% 175.30/27.01  | | | Case 1:
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | |   (53)  all_58_4 = e3
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | | COMBINE_EQS: (11), (53) imply:
% 175.30/27.01  | | | |   (54)  all_52_5 = e3
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | | REDUCE: (25), (54) imply:
% 175.30/27.01  | | | |   (55)  $false
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | | CLOSE: (55) is inconsistent.
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | Case 2:
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | |   (56)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | | BETA: splitting (16) gives:
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | | Case 1:
% 175.30/27.01  | | | | | 
% 175.30/27.01  | | | | |   (57)  all_58_2 = e3
% 175.30/27.01  | | | | | 
% 175.30/27.01  | | | | | REF_CLOSE: (31), (47), (57) are inconsistent by sub-proof #980.
% 175.30/27.01  | | | | | 
% 175.30/27.01  | | | | Case 2:
% 175.30/27.01  | | | | | 
% 175.30/27.01  | | | | |   (58)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/27.01  | | | | | 
% 175.30/27.01  | | | | | BETA: splitting (19) gives:
% 175.30/27.01  | | | | | 
% 175.30/27.01  | | | | | Case 1:
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | |   (59)  all_56_14 = e3
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | | COMBINE_EQS: (24), (59) imply:
% 175.30/27.01  | | | | | |   (60)  all_52_29 = e3
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | | SIMP: (60) implies:
% 175.30/27.01  | | | | | |   (61)  all_52_29 = e3
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | | REDUCE: (14), (61) imply:
% 175.30/27.01  | | | | | |   (62)   ~ (all_52_27 = e3)
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (13), (17), (20),
% 175.30/27.01  | | | | | |            (26), (27), (28), (33), (35), (39), (49), (52), (58),
% 175.30/27.01  | | | | | |            (62) are inconsistent by sub-proof #775.
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | Case 2:
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | |   (63)   ~ (all_56_14 = e3)
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | | REDUCE: (24), (63) imply:
% 175.30/27.01  | | | | | |   (64)   ~ (all_52_29 = e3)
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | | BETA: splitting (56) gives:
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | | Case 1:
% 175.30/27.01  | | | | | | | 
% 175.30/27.01  | | | | | | |   (65)  all_58_5 = e3
% 175.30/27.01  | | | | | | | 
% 175.30/27.01  | | | | | | | REF_CLOSE: (4), (5), (13), (35), (52), (65) are inconsistent by
% 175.30/27.01  | | | | | | |            sub-proof #776.
% 175.30/27.01  | | | | | | | 
% 175.30/27.01  | | | | | | Case 2:
% 175.30/27.01  | | | | | | | 
% 175.30/27.01  | | | | | | |   (66)  all_58_8 = e3 | all_58_14 = e3
% 175.30/27.01  | | | | | | | 
% 175.30/27.01  | | | | | | | REF_CLOSE: (21), (23), (51), (64), (66) are inconsistent by
% 175.30/27.01  | | | | | | |            sub-proof #999.
% 175.30/27.01  | | | | | | | 
% 175.30/27.01  | | | | | | End of split
% 175.30/27.01  | | | | | | 
% 175.30/27.01  | | | | | End of split
% 175.30/27.01  | | | | | 
% 175.30/27.01  | | | | End of split
% 175.30/27.01  | | | | 
% 175.30/27.01  | | | End of split
% 175.30/27.01  | | | 
% 175.30/27.01  | | Case 2:
% 175.30/27.01  | | | 
% 175.30/27.01  | | |   (67)   ~ (all_58_6 = e3)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | REDUCE: (30), (67) imply:
% 175.30/27.01  | | |   (68)   ~ (all_52_17 = e3)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | REF_CLOSE: (1), (8), (26), (30), (31), (34), (35), (37), (43), (68) are
% 175.30/27.01  | | |            inconsistent by sub-proof #396.
% 175.30/27.01  | | | 
% 175.30/27.01  | | End of split
% 175.30/27.01  | | 
% 175.30/27.01  | End of split
% 175.30/27.01  | 
% 175.30/27.01  End of proof
% 175.30/27.01  
% 175.30/27.01  Sub-proof #124 shows that the following formulas are inconsistent:
% 175.30/27.01  ----------------------------------------------------------------
% 175.30/27.01    (1)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.30/27.01    (2)  all_52_0 = e2
% 175.30/27.01    (3)   ~ (e3 = e2)
% 175.30/27.01  
% 175.30/27.01  Begin of proof
% 175.30/27.01  | 
% 175.30/27.01  | ALPHA: (1) implies:
% 175.30/27.01  |   (4)  all_52_0 = e3
% 175.30/27.01  | 
% 175.30/27.01  | COMBINE_EQS: (2), (4) imply:
% 175.30/27.01  |   (5)  e3 = e2
% 175.30/27.01  | 
% 175.30/27.01  | SIMP: (5) implies:
% 175.30/27.01  |   (6)  e3 = e2
% 175.30/27.01  | 
% 175.30/27.01  | REDUCE: (3), (6) imply:
% 175.30/27.01  |   (7)  $false
% 175.30/27.01  | 
% 175.30/27.01  | CLOSE: (7) is inconsistent.
% 175.30/27.01  | 
% 175.30/27.01  End of proof
% 175.30/27.01  
% 175.30/27.01  Sub-proof #125 shows that the following formulas are inconsistent:
% 175.30/27.01  ----------------------------------------------------------------
% 175.30/27.01    (1)   ~ (all_52_23 = all_14_2)
% 175.30/27.01    (2)   ~ (all_52_5 = all_52_13)
% 175.30/27.01    (3)   ~ (all_52_17 = all_52_23)
% 175.30/27.01    (4)  op(e2, all_10_2) = all_10_1
% 175.30/27.01    (5)   ~ (all_52_13 = all_52_29)
% 175.30/27.01    (6)  op(e3, e2) = all_52_3
% 175.30/27.01    (7)   ~ (all_52_9 = all_52_25)
% 175.30/27.01    (8)   ~ (all_52_19 = all_52_23)
% 175.30/27.01    (9)  all_56_11 = all_52_23
% 175.30/27.01    (10)  op(e1, e2) = all_52_19
% 175.30/27.01    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.30/27.01    (12)  op(all_6_1, all_6_2) = e1
% 175.30/27.01    (13)   ~ (all_52_3 = all_10_2)
% 175.30/27.01    (14)  all_58_5 = all_52_13
% 175.30/27.01    (15)   ~ (all_6_2 = e0)
% 175.30/27.01    (16)   ~ (all_52_25 = all_52_29)
% 175.30/27.01    (17)  all_56_15 = all_6_2
% 175.30/27.01    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/27.01    (19)  op(e2, e0) = all_52_15
% 175.30/27.01    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/27.01    (21)  all_58_3 = all_10_2
% 175.30/27.01    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/27.01    (23)  all_58_15 = all_6_2
% 175.30/27.01    (24)   ~ (all_52_9 = all_4_2)
% 175.30/27.01    (25)   ~ (all_52_5 = all_52_7)
% 175.30/27.01    (26)  all_58_10 = all_52_15
% 175.30/27.01    (27)   ~ (all_52_5 = all_4_2)
% 175.30/27.01    (28)  all_58_7 = all_52_19
% 175.30/27.01    (29)  all_56_4 = all_52_9
% 175.30/27.01    (30)   ~ (all_52_15 = all_6_2)
% 175.30/27.01    (31)   ~ (all_52_17 = all_52_25)
% 175.30/27.01    (32)  op(e0, e1) = all_52_29
% 175.30/27.01    (33)   ~ (all_4_0 = e2)
% 175.30/27.01    (34)  all_58_4 = all_52_5
% 175.30/27.01    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/27.01    (36)   ~ (all_52_27 = all_52_29)
% 175.30/27.01    (37)  op(e3, all_4_2) = all_4_1
% 175.30/27.01    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.30/27.01    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/27.01    (40)   ~ (all_52_7 = all_4_2)
% 175.30/27.01    (41)  all_58_1 = all_52_3
% 175.30/27.01    (42)   ~ (all_52_13 = all_52_15)
% 175.30/27.01    (43)  all_58_0 = all_4_2
% 175.30/27.01    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.30/27.01    (45)  op(e1, all_52_29) = all_52_28
% 175.30/27.01    (46)  op(e1, all_52_5) = all_52_4
% 175.30/27.01    (47)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.30/27.01          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.30/27.01    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.30/27.01    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/27.01    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.30/27.01    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/27.01    (52)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.30/27.01    (53)  all_58_14 = all_52_29
% 175.30/27.01    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/27.01    (55)   ~ (all_52_3 = all_52_5)
% 175.30/27.01    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/27.01    (57)  op(e2, e1) = all_52_13
% 175.30/27.01    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/27.01    (59)  all_58_8 = all_14_2
% 175.30/27.01    (60)  all_56_1 = all_52_3
% 175.30/27.01    (61)  all_56_14 = all_52_29
% 175.30/27.01    (62)  op(all_4_1, all_4_2) = all_4_0
% 175.30/27.01    (63)   ~ (all_52_5 = all_14_2)
% 175.30/27.01    (64)   ~ (all_52_3 = all_52_27)
% 175.30/27.01    (65)   ~ (all_52_3 = all_4_2)
% 175.30/27.01    (66)  all_38_2 = all_6_2
% 175.30/27.01    (67)  op(e0, e3) = all_52_25
% 175.30/27.01    (68)  op(e0, all_6_2) = all_6_1
% 175.30/27.01    (69)  all_52_0 = all_4_1
% 175.30/27.01    (70)  all_52_10 = all_10_1
% 175.30/27.01    (71)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.30/27.01    (72)   ~ (all_52_13 = all_14_2)
% 175.30/27.01    (73)   ~ (e3 = e0)
% 175.30/27.01    (74)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/27.01    (75)   ~ (all_52_9 = all_52_13)
% 175.30/27.01    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/27.01    (77)  op(e0, all_52_23) = all_52_22
% 175.30/27.01    (78)   ~ (all_52_15 = all_52_23)
% 175.30/27.01    (79)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/27.01    (80)   ~ (all_52_5 = all_52_29)
% 175.30/27.01    (81)  all_56_2 = all_52_5
% 175.30/27.01    (82)  op(e1, e0) = all_52_23
% 175.30/27.01    (83)  all_56_12 = all_52_25
% 175.30/27.01    (84)  all_58_13 = all_52_27
% 175.30/27.01    (85)  op(e2, all_52_3) = all_52_2
% 175.30/27.01    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/27.01    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/27.01    (88)   ~ (all_52_9 = all_52_17)
% 175.30/27.01    (89)  all_58_6 = all_52_17
% 175.30/27.01    (90)   ~ (all_52_3 = all_52_7)
% 175.30/27.01    (91)  op(all_10_1, all_10_2) = e3
% 175.30/27.01    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.30/27.01    (93)   ~ (e1 = e0)
% 175.30/27.01    (94)  all_56_0 = all_4_2
% 175.30/27.01    (95)  all_58_11 = all_52_23
% 175.30/27.01    (96)   ~ (all_52_3 = all_52_19)
% 175.30/27.01    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.30/27.01    (98)   ~ (all_52_7 = all_52_15)
% 175.30/27.01    (99)  op(e0, all_52_15) = all_52_14
% 175.30/27.01    (100)   ~ (all_52_29 = all_14_2)
% 175.30/27.01    (101)   ~ (all_4_0 = e1)
% 175.30/27.01    (102)   ~ (all_52_23 = all_6_2)
% 175.30/27.01    (103)   ~ (all_52_29 = all_6_2)
% 175.30/27.01    (104)  all_58_2 = all_52_9
% 175.30/27.01    (105)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/27.01    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/27.01    (107)  op(e3, e1) = all_52_5
% 175.30/27.01    (108)  all_56_10 = all_14_2
% 175.30/27.01    (109)   ~ (all_52_25 = all_6_2)
% 175.30/27.01    (110)  op(e1, e1) = all_14_2
% 175.30/27.01    (111)  op(e1, e3) = all_52_17
% 175.30/27.01    (112)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/27.01    (113)   ~ (all_52_25 = all_4_2)
% 175.30/27.01    (114)  op(e3, e0) = all_52_7
% 175.30/27.01    (115)   ~ (all_52_17 = all_4_2)
% 175.30/27.01    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/27.01             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/27.01    (117)   ~ (all_52_25 = all_52_27)
% 175.30/27.01    (118)   ~ (all_52_27 = all_6_2)
% 175.30/27.01    (119)   ~ (all_52_7 = all_6_2)
% 175.30/27.01    (120)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.30/27.01    (121)  all_38_1 = all_6_1
% 175.30/27.01    (122)   ~ (all_52_19 = all_52_27)
% 175.30/27.01    (123)  all_56_7 = all_52_15
% 175.30/27.01    (124)   ~ (all_52_7 = all_52_23)
% 175.30/27.01    (125)   ~ (all_52_13 = all_10_2)
% 175.30/27.01    (126)  op(e2, all_52_27) = all_52_26
% 175.30/27.01    (127)   ~ (all_52_17 = all_52_19)
% 175.30/27.01    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/27.01    (129)  all_58_9 = all_52_7
% 175.30/27.01    (130)  all_58_12 = all_52_25
% 175.30/27.01    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.30/27.01    (132)   ~ (all_52_9 = all_52_15)
% 175.30/27.01    (133)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/27.01    (134)   ~ (e3 = e2)
% 175.30/27.01    (135)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.30/27.01    (136)   ~ (all_52_19 = all_14_2)
% 175.30/27.01    (137)  op(e0, all_52_7) = all_52_6
% 175.30/27.01    (138)  op(e2, e3) = all_52_9
% 175.30/27.01    (139)  all_56_13 = all_52_27
% 175.30/27.01  
% 175.30/27.01  Begin of proof
% 175.30/27.01  | 
% 175.30/27.01  | BETA: splitting (47) gives:
% 175.30/27.01  | 
% 175.30/27.01  | Case 1:
% 175.30/27.01  | | 
% 175.30/27.01  | |   (140)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.30/27.01  | | 
% 175.30/27.01  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 175.30/27.01  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.30/27.01  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.30/27.01  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.30/27.01  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 175.30/27.01  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 175.30/27.01  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 175.30/27.01  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (92), (93),
% 175.30/27.01  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 175.30/27.01  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 175.30/27.01  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 175.30/27.01  | |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 175.30/27.01  | |            (131), (132), (133), (135), (136), (137), (138), (139), (140) are
% 175.30/27.01  | |            inconsistent by sub-proof #140.
% 175.30/27.01  | | 
% 175.30/27.01  | Case 2:
% 175.30/27.01  | | 
% 175.30/27.01  | |   (141)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.30/27.01  | | 
% 175.30/27.01  | | ALPHA: (141) implies:
% 175.30/27.01  | |   (142)  all_52_10 = e2
% 175.30/27.01  | | 
% 175.30/27.01  | | COMBINE_EQS: (70), (142) imply:
% 175.30/27.01  | |   (143)  all_10_1 = e2
% 175.30/27.01  | | 
% 175.30/27.01  | | REF_CLOSE: (4), (91), (116), (134), (143) are inconsistent by sub-proof
% 175.30/27.01  | |            #263.
% 175.30/27.01  | | 
% 175.30/27.01  | End of split
% 175.30/27.01  | 
% 175.30/27.01  End of proof
% 175.30/27.01  
% 175.30/27.01  Sub-proof #126 shows that the following formulas are inconsistent:
% 175.30/27.01  ----------------------------------------------------------------
% 175.30/27.01    (1)   ~ (all_52_23 = all_14_2)
% 175.30/27.01    (2)   ~ (all_52_5 = all_52_13)
% 175.30/27.01    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.30/27.01    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.30/27.01    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.30/27.01    (6)   ~ (all_52_27 = all_10_2)
% 175.30/27.01    (7)   ~ (all_52_17 = all_52_23)
% 175.30/27.01    (8)  op(e2, all_10_2) = all_10_1
% 175.30/27.01    (9)  all_40_2 = all_4_2
% 175.30/27.01    (10)   ~ (all_52_13 = all_52_29)
% 175.30/27.01    (11)  all_56_3 = all_52_7
% 175.30/27.01    (12)  op(e3, e2) = all_52_3
% 175.30/27.01    (13)   ~ (all_52_9 = all_52_25)
% 175.30/27.01    (14)  op(e3, all_52_25) = all_52_24
% 175.30/27.01    (15)   ~ (all_52_19 = all_52_23)
% 175.30/27.01    (16)  all_56_11 = all_52_23
% 175.30/27.01    (17)  op(e1, e2) = all_52_19
% 175.30/27.01    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.30/27.01    (19)  op(e3, all_52_9) = all_52_8
% 175.30/27.01    (20)  all_50_1 = all_4_1
% 175.30/27.01    (21)  op(all_6_1, all_6_2) = e1
% 175.30/27.01    (22)   ~ (all_52_3 = all_10_2)
% 175.30/27.01    (23)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.30/27.01    (24)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.30/27.01    (25)  all_58_5 = all_52_13
% 175.30/27.01    (26)   ~ (all_52_25 = all_52_29)
% 175.30/27.01    (27)  all_56_15 = all_6_2
% 175.30/27.01    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.30/27.01    (29)  op(e2, e0) = all_52_15
% 175.30/27.01    (30)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.30/27.01    (31)  all_58_3 = all_10_2
% 175.30/27.01    (32)  all_56_9 = all_52_19
% 175.30/27.01    (33)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.30/27.01    (34)  all_58_15 = all_6_2
% 175.30/27.01    (35)   ~ (all_52_9 = all_4_2)
% 175.30/27.01    (36)   ~ (all_52_5 = all_52_7)
% 175.30/27.01    (37)  all_58_10 = all_52_15
% 175.30/27.01    (38)   ~ (all_52_5 = all_4_2)
% 175.30/27.01    (39)  all_58_7 = all_52_19
% 175.30/27.01    (40)  all_56_4 = all_52_9
% 175.30/27.01    (41)   ~ (all_52_15 = all_6_2)
% 175.30/27.01    (42)   ~ (all_52_17 = all_52_25)
% 175.30/27.01    (43)  op(e0, e1) = all_52_29
% 175.30/27.01    (44)  all_58_4 = all_52_5
% 175.30/27.01    (45)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.30/27.01    (46)   ~ (e3 = e1)
% 175.30/27.01    (47)  all_34_1 = all_4_1
% 175.30/27.01    (48)   ~ (all_52_27 = all_52_29)
% 175.30/27.01    (49)   ~ (all_52_17 = all_14_2)
% 175.30/27.01    (50)  op(e3, all_4_2) = all_4_1
% 175.30/27.01    (51)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.30/27.01    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.30/27.01    (53)   ~ (all_52_7 = all_4_2)
% 175.30/27.01    (54)  all_58_1 = all_52_3
% 175.30/27.01    (55)   ~ (all_52_13 = all_52_15)
% 175.30/27.01    (56)  all_58_0 = all_4_2
% 175.30/27.01    (57)  op(e1, all_52_13) = all_52_12
% 175.30/27.01    (58)  op(e0, e0) = all_6_2
% 175.30/27.01    (59)  op(e1, all_52_29) = all_52_28
% 175.30/27.01    (60)  all_50_0 = all_4_0
% 175.30/27.01    (61)  op(e1, all_52_5) = all_52_4
% 175.30/27.01    (62)  all_50_2 = all_4_2
% 175.30/27.01    (63)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.30/27.01    (64)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.30/27.01    (65)   ~ (all_4_1 = e2)
% 175.30/27.01    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.30/27.01    (67)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.30/27.01    (68)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.30/27.01    (69)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.30/27.01    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.30/27.01    (71)  all_58_14 = all_52_29
% 175.30/27.01    (72)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.30/27.01    (73)  all_24_0 = all_10_0
% 175.30/27.01    (74)  all_40_1 = all_4_1
% 175.30/27.01    (75)  all_26_2 = all_4_2
% 175.30/27.01    (76)   ~ (all_52_3 = all_52_5)
% 175.30/27.01    (77)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.30/27.01    (78)  op(e2, e1) = all_52_13
% 175.30/27.01    (79)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.30/27.01    (80)  all_58_8 = all_14_2
% 175.30/27.01    (81)  all_56_1 = all_52_3
% 175.30/27.01    (82)  op(e0, e2) = all_52_27
% 175.30/27.01    (83)  all_56_14 = all_52_29
% 175.30/27.01    (84)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.30/27.01    (85)  op(all_4_1, all_4_2) = all_4_0
% 175.30/27.01    (86)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.30/27.01    (87)   ~ (all_52_5 = all_14_2)
% 175.30/27.01    (88)   ~ (all_52_3 = all_52_27)
% 175.30/27.01    (89)   ~ (all_52_3 = all_4_2)
% 175.30/27.01    (90)  all_38_2 = all_6_2
% 175.30/27.01    (91)  op(e0, e3) = all_52_25
% 175.30/27.01    (92)  op(e0, all_6_2) = all_6_1
% 175.30/27.01    (93)  all_52_0 = all_4_1
% 175.30/27.01    (94)   ~ (all_52_9 = all_10_2)
% 175.30/27.01    (95)  op(e3, all_52_17) = all_52_16
% 175.30/27.01    (96)  all_52_10 = all_10_1
% 175.30/27.01    (97)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.30/27.01    (98)   ~ (all_52_13 = all_14_2)
% 175.30/27.01    (99)   ~ (e3 = e0)
% 175.30/27.01    (100)  all_40_0 = all_4_0
% 175.30/27.01    (101)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.30/27.01    (102)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 175.30/27.01    (103)  op(all_14_1, all_14_2) = e2
% 175.30/27.01    (104)   ~ (all_52_9 = all_52_13)
% 175.30/27.01    (105)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.30/27.01    (106)  op(e0, all_52_23) = all_52_22
% 175.30/27.01    (107)   ~ (all_52_15 = all_52_23)
% 175.30/27.01    (108)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.30/27.01    (109)  op(all_10_1, all_10_2) = all_10_0
% 175.30/27.01    (110)   ~ (all_52_5 = all_52_29)
% 175.30/27.01    (111)  all_56_2 = all_52_5
% 175.30/27.01    (112)  op(e1, e0) = all_52_23
% 175.30/27.01    (113)  all_56_12 = all_52_25
% 175.30/27.01    (114)  all_58_13 = all_52_27
% 175.30/27.01    (115)  op(e2, all_52_3) = all_52_2
% 175.30/27.01    (116)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.30/27.01    (117)  all_56_5 = all_10_2
% 175.30/27.01    (118)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.30/27.01    (119)   ~ (all_52_9 = all_52_17)
% 175.30/27.01    (120)  all_58_6 = all_52_17
% 175.30/27.01    (121)   ~ (all_52_3 = all_52_7)
% 175.30/27.01    (122)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.30/27.01    (123)  op(e2, all_52_19) = all_52_18
% 175.30/27.01    (124)   ~ (e1 = e0)
% 175.30/27.01    (125)  all_56_0 = all_4_2
% 175.30/27.01    (126)  all_58_11 = all_52_23
% 175.30/27.01    (127)   ~ (all_52_3 = all_52_19)
% 175.30/27.01    (128)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.30/27.01    (129)   ~ (all_52_7 = all_52_15)
% 175.30/27.01    (130)  all_26_1 = all_4_1
% 175.30/27.01    (131)  op(e0, all_52_15) = all_52_14
% 175.30/27.01    (132)   ~ (all_52_29 = all_14_2)
% 175.30/27.01    (133)   ~ (all_52_19 = all_10_2)
% 175.30/27.01    (134)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.30/27.01    (135)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.30/27.01    (136)   ~ (all_52_23 = all_6_2)
% 175.30/27.01    (137)  all_38_0 = e1
% 175.30/27.01    (138)   ~ (all_52_29 = all_6_2)
% 175.30/27.01    (139)  all_58_2 = all_52_9
% 175.30/27.01    (140)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.30/27.01    (141)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.30/27.01    (142)  op(e3, e1) = all_52_5
% 175.30/27.01    (143)   ~ (e2 = e1)
% 175.30/27.01    (144)  all_56_10 = all_14_2
% 175.30/27.01    (145)   ~ (all_52_25 = all_6_2)
% 175.30/27.01    (146)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.30/27.01    (147)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.30/27.01    (148)  op(e1, e1) = all_14_2
% 175.30/27.01    (149)  op(e1, e3) = all_52_17
% 175.30/27.01    (150)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.30/27.01    (151)  all_26_0 = all_4_0
% 175.30/27.01    (152)   ~ (all_52_25 = all_4_2)
% 175.30/27.01    (153)  op(e3, e0) = all_52_7
% 175.30/27.01    (154)  op(e3, e3) = all_4_2
% 175.30/27.01    (155)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.30/27.01             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 175.30/27.01    (156)  all_56_8 = all_52_17
% 175.30/27.01    (157)   ~ (all_52_17 = all_4_2)
% 175.30/27.01    (158)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.30/27.01             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.30/27.01    (159)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.30/27.01           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 175.30/27.01           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.30/27.01           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.30/27.01    (160)   ~ (all_52_25 = all_52_27)
% 175.30/27.01    (161)  all_34_2 = all_4_2
% 175.30/27.01    (162)   ~ (all_52_27 = all_6_2)
% 175.30/27.01    (163)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.30/27.01    (164)   ~ (all_52_7 = all_6_2)
% 175.30/27.01    (165)   ~ (all_10_0 = e3)
% 175.30/27.01    (166)   ~ (all_52_15 = all_10_2)
% 175.30/27.01    (167)  all_38_1 = all_6_1
% 175.30/27.01    (168)   ~ (all_52_19 = all_52_27)
% 175.30/27.01    (169)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2)
% 175.30/27.01    (170)  all_56_7 = all_52_15
% 175.30/27.01    (171)   ~ (all_52_7 = all_52_23)
% 175.30/27.01    (172)   ~ (all_52_13 = all_10_2)
% 175.30/27.01    (173)  op(e2, all_52_27) = all_52_26
% 175.30/27.01    (174)  all_52_20 = all_14_1
% 175.30/27.01    (175)   ~ (all_52_17 = all_52_19)
% 175.30/27.01    (176)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.30/27.01    (177)  all_52_30 = all_6_1
% 175.30/27.01    (178)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.30/27.01    (179)  op(e1, all_14_2) = all_14_1
% 175.30/27.01    (180)  all_58_9 = all_52_7
% 175.30/27.01    (181)   ~ (e2 = e0)
% 175.30/27.01    (182)  all_58_12 = all_52_25
% 175.30/27.01    (183)  all_34_0 = all_4_0
% 175.30/27.01    (184)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 175.30/27.01    (185)  all_56_6 = all_52_13
% 175.30/27.01    (186)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.30/27.01    (187)   ~ (all_52_9 = all_52_15)
% 175.30/27.01    (188)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.30/27.01    (189)   ~ (e3 = e2)
% 175.30/27.01    (190)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.30/27.01    (191)   ~ (all_52_19 = all_14_2)
% 175.30/27.01    (192)  op(e0, all_52_7) = all_52_6
% 175.30/27.01    (193)  op(e2, e3) = all_52_9
% 175.30/27.01    (194)  all_56_13 = all_52_27
% 175.30/27.01  
% 175.30/27.01  Begin of proof
% 175.30/27.01  | 
% 175.30/27.01  | BETA: splitting (102) gives:
% 175.30/27.01  | 
% 175.30/27.01  | Case 1:
% 175.30/27.01  | | 
% 175.30/27.01  | |   (195)   ~ (all_24_0 = e1)
% 175.30/27.01  | | 
% 175.30/27.01  | | REDUCE: (73), (195) imply:
% 175.30/27.01  | |   (196)   ~ (all_10_0 = e1)
% 175.30/27.01  | | 
% 175.30/27.01  | | BETA: splitting (184) gives:
% 175.30/27.01  | | 
% 175.30/27.01  | | Case 1:
% 175.30/27.01  | | | 
% 175.30/27.01  | | |   (197)   ~ (all_26_0 = e2)
% 175.30/27.01  | | | 
% 175.30/27.01  | | | REDUCE: (151), (197) imply:
% 175.30/27.02  | | |   (198)   ~ (all_4_0 = e2)
% 175.30/27.02  | | | 
% 175.30/27.02  | | | BETA: splitting (134) gives:
% 175.30/27.02  | | | 
% 175.30/27.02  | | | Case 1:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (199)   ~ (all_34_0 = e1)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REDUCE: (183), (199) imply:
% 175.30/27.02  | | | |   (200)   ~ (all_4_0 = e1)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | BETA: splitting (163) gives:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | Case 1:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (201)   ~ (all_38_0 = e1)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REDUCE: (137), (201) imply:
% 175.30/27.02  | | | | |   (202)  $false
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | CLOSE: (202) is inconsistent.
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | Case 2:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (203)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | BETA: splitting (169) gives:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | Case 1:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (204)   ~ (all_40_1 = e1)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REDUCE: (74), (204) imply:
% 175.30/27.02  | | | | | |   (205)   ~ (all_4_1 = e1)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | BETA: splitting (155) gives:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | Case 1:
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | |   (206)  all_58_15 = e0
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | REF_CLOSE: (21), (34), (58), (92), (124), (158), (206) are
% 175.30/27.02  | | | | | | |            inconsistent by sub-proof #143.
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | Case 2:
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | |   (207)   ~ (all_58_15 = e0)
% 175.30/27.02  | | | | | | |   (208)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.30/27.02  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | ALPHA: (208) implies:
% 175.30/27.02  | | | | | | |   (209)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.30/27.02  | | | | | | |   (210)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | REDUCE: (34), (207) imply:
% 175.30/27.02  | | | | | | |   (211)   ~ (all_6_2 = e0)
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | BETA: splitting (159) gives:
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | Case 1:
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | |   (212)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.30/27.02  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 175.30/27.02  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | | BETA: splitting (212) gives:
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | | Case 1:
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | |   (213)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.30/27.02  | | | | | | | | |          all_52_6 = e0
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | | REF_CLOSE: (1), (2), (7), (10), (12), (13), (15), (16), (17),
% 175.30/27.02  | | | | | | | | |            (18), (21), (22), (25), (26), (27), (28), (29),
% 175.30/27.02  | | | | | | | | |            (30), (31), (33), (34), (35), (36), (37), (38),
% 175.30/27.02  | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (48),
% 175.30/27.02  | | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (59),
% 175.30/27.02  | | | | | | | | |            (61), (63), (66), (67), (68), (70), (71), (72),
% 175.30/27.02  | | | | | | | | |            (76), (77), (78), (79), (80), (81), (83), (85),
% 175.30/27.02  | | | | | | | | |            (87), (88), (89), (90), (91), (92), (93), (97),
% 175.30/27.02  | | | | | | | | |            (98), (99), (101), (104), (105), (106), (107),
% 175.30/27.02  | | | | | | | | |            (108), (110), (111), (112), (113), (114), (115),
% 175.30/27.02  | | | | | | | | |            (116), (118), (119), (120), (121), (122), (124),
% 175.30/27.02  | | | | | | | | |            (125), (126), (127), (128), (129), (131), (132),
% 175.30/27.02  | | | | | | | | |            (136), (138), (139), (140), (141), (142), (144),
% 175.30/27.02  | | | | | | | | |            (145), (148), (149), (150), (152), (153), (157),
% 175.30/27.02  | | | | | | | | |            (158), (160), (162), (164), (167), (168), (170),
% 175.30/27.02  | | | | | | | | |            (171), (172), (173), (175), (176), (180), (182),
% 175.30/27.02  | | | | | | | | |            (186), (187), (188), (190), (191), (192), (193),
% 175.30/27.02  | | | | | | | | |            (194), (198), (200), (203), (210), (211), (213) are
% 175.30/27.02  | | | | | | | | |            inconsistent by sub-proof #140.
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | Case 2:
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | |   (214)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.30/27.02  | | | | | | | | |          all_52_14 = e0
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12),
% 175.30/27.02  | | | | | | | | |            (13), (14), (15), (16), (17), (19), (22), (24),
% 175.30/27.02  | | | | | | | | |            (25), (26), (27), (28), (29), (31), (32), (33),
% 175.30/27.02  | | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41),
% 175.30/27.02  | | | | | | | | |            (42), (43), (44), (45), (46), (48), (49), (50),
% 175.30/27.02  | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (59),
% 175.30/27.02  | | | | | | | | |            (63), (64), (65), (67), (68), (69), (70), (71),
% 175.30/27.02  | | | | | | | | |            (72), (76), (77), (78), (79), (80), (81), (82),
% 175.30/27.02  | | | | | | | | |            (84), (85), (86), (88), (89), (91), (92), (94),
% 175.30/27.02  | | | | | | | | |            (95), (96), (98), (99), (104), (106), (107), (108),
% 175.30/27.02  | | | | | | | | |            (109), (110), (111), (112), (114), (116), (119),
% 175.30/27.02  | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 175.30/27.02  | | | | | | | | |            (127), (129), (131), (132), (133), (136), (138),
% 175.30/27.02  | | | | | | | | |            (139), (141), (142), (144), (145), (147), (148),
% 175.30/27.02  | | | | | | | | |            (149), (150), (152), (153), (154), (157), (158),
% 175.30/27.02  | | | | | | | | |            (160), (162), (164), (165), (168), (170), (171),
% 175.30/27.02  | | | | | | | | |            (173), (175), (176), (178), (179), (180), (182),
% 175.30/27.02  | | | | | | | | |            (185), (186), (187), (188), (190), (191), (193),
% 175.30/27.02  | | | | | | | | |            (194), (196), (198), (200), (205), (209), (210),
% 175.30/27.02  | | | | | | | | |            (211), (214) are inconsistent by sub-proof #338.
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | End of split
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | Case 2:
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | |   (215)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.30/27.02  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.30/27.02  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | | BETA: splitting (215) gives:
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | | Case 1:
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | |   (216)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.30/27.02  | | | | | | | | |          all_52_22 = e0
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | | REF_CLOSE: (103), (143), (158), (174), (179), (216) are
% 175.30/27.02  | | | | | | | | |            inconsistent by sub-proof #314.
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | Case 2:
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | |   (217)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.30/27.02  | | | | | | | | |          all_52_30 = e0
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | | REF_CLOSE: (21), (92), (124), (158), (177), (217) are
% 175.30/27.02  | | | | | | | | |            inconsistent by sub-proof #138.
% 175.30/27.02  | | | | | | | | | 
% 175.30/27.02  | | | | | | | | End of split
% 175.30/27.02  | | | | | | | | 
% 175.30/27.02  | | | | | | | End of split
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | End of split
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | Case 2:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (218)  all_40_1 = e1
% 175.30/27.02  | | | | | |   (219)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | COMBINE_EQS: (74), (218) imply:
% 175.30/27.02  | | | | | |   (220)  all_4_1 = e1
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | COMBINE_EQS: (93), (220) imply:
% 175.30/27.02  | | | | | |   (221)  all_52_0 = e1
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REDUCE: (65), (220) imply:
% 175.30/27.02  | | | | | |   (222)   ~ (e2 = e1)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REDUCE: (85), (220) imply:
% 175.30/27.02  | | | | | |   (223)  op(e1, all_4_2) = all_4_0
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REDUCE: (50), (220) imply:
% 175.30/27.02  | | | | | |   (224)  op(e3, all_4_2) = e1
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | BETA: splitting (155) gives:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | Case 1:
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | |   (225)  all_58_15 = e0
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | REF_CLOSE: (21), (34), (58), (92), (124), (158), (225) are
% 175.30/27.02  | | | | | | |            inconsistent by sub-proof #143.
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | Case 2:
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | |   (226)   ~ (all_58_15 = e0)
% 175.30/27.02  | | | | | | |   (227)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.30/27.02  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 175.30/27.02  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (22),
% 175.30/27.02  | | | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 175.30/27.02  | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 175.30/27.02  | | | | | | |            (41), (42), (43), (44), (45), (46), (48), (49), (50),
% 175.30/27.02  | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (59), (64),
% 175.30/27.02  | | | | | | |            (65), (67), (68), (69), (70), (71), (72), (76), (77),
% 175.30/27.02  | | | | | | |            (78), (79), (80), (82), (84), (85), (86), (87), (88),
% 175.30/27.02  | | | | | | |            (89), (91), (92), (94), (95), (96), (98), (99), (100),
% 175.30/27.02  | | | | | | |            (101), (103), (104), (105), (106), (107), (108), (109),
% 175.30/27.02  | | | | | | |            (110), (111), (112), (113), (114), (116), (117), (119),
% 175.30/27.02  | | | | | | |            (120), (121), (122), (123), (124), (125), (126), (127),
% 175.30/27.02  | | | | | | |            (129), (131), (132), (133), (136), (138), (139), (141),
% 175.30/27.02  | | | | | | |            (142), (143), (144), (145), (146), (147), (148), (149),
% 175.30/27.02  | | | | | | |            (150), (152), (153), (154), (157), (158), (159), (160),
% 175.30/27.02  | | | | | | |            (162), (164), (165), (166), (168), (170), (171), (172),
% 175.30/27.02  | | | | | | |            (173), (174), (175), (176), (177), (178), (179), (180),
% 175.30/27.02  | | | | | | |            (181), (182), (185), (186), (187), (188), (189), (190),
% 175.30/27.02  | | | | | | |            (191), (192), (193), (194), (196), (198), (200), (219),
% 175.30/27.02  | | | | | | |            (221), (223), (224), (226), (227) are inconsistent by
% 175.30/27.02  | | | | | | |            sub-proof #301.
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | End of split
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | End of split
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | End of split
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | Case 2:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (228)  all_34_0 = e1
% 175.30/27.02  | | | |   (229)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | COMBINE_EQS: (183), (228) imply:
% 175.30/27.02  | | | |   (230)  all_4_0 = e1
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | SIMP: (230) implies:
% 175.30/27.02  | | | |   (231)  all_4_0 = e1
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REDUCE: (198), (231) imply:
% 175.30/27.02  | | | |   (232)   ~ (e2 = e1)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REDUCE: (85), (231) imply:
% 175.30/27.02  | | | |   (233)  op(all_4_1, all_4_2) = e1
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | BETA: splitting (155) gives:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | Case 1:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (234)  all_58_15 = e0
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REF_CLOSE: (21), (34), (58), (92), (124), (158), (234) are
% 175.30/27.02  | | | | |            inconsistent by sub-proof #143.
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | Case 2:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (235)   ~ (all_58_15 = e0)
% 175.30/27.02  | | | | |   (236)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.30/27.02  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | ALPHA: (236) implies:
% 175.30/27.02  | | | | |   (237)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REDUCE: (34), (235) imply:
% 175.30/27.02  | | | | |   (238)   ~ (all_6_2 = e0)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | BETA: splitting (159) gives:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | Case 1:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (239)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.30/27.02  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.30/27.02  | | | | | |            all_52_14 = e0)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13),
% 175.30/27.02  | | | | | |            (15), (16), (17), (19), (22), (25), (26), (27), (28),
% 175.30/27.02  | | | | | |            (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 175.30/27.02  | | | | | |            (40), (41), (42), (44), (45), (46), (47), (48), (49),
% 175.30/27.02  | | | | | |            (50), (51), (52), (53), (54), (56), (57), (59), (63),
% 175.30/27.02  | | | | | |            (64), (65), (67), (68), (69), (71), (72), (76), (77),
% 175.30/27.02  | | | | | |            (78), (79), (80), (81), (86), (88), (89), (91), (92),
% 175.30/27.02  | | | | | |            (93), (95), (96), (98), (99), (104), (106), (107), (108),
% 175.30/27.02  | | | | | |            (109), (110), (111), (112), (114), (116), (119), (120),
% 175.30/27.02  | | | | | |            (121), (122), (123), (124), (125), (126), (127), (129),
% 175.30/27.02  | | | | | |            (131), (132), (133), (136), (138), (139), (141), (142),
% 175.30/27.02  | | | | | |            (144), (145), (148), (149), (152), (153), (154), (157),
% 175.30/27.02  | | | | | |            (158), (160), (161), (162), (164), (165), (171), (173),
% 175.30/27.02  | | | | | |            (175), (176), (178), (179), (180), (182), (185), (186),
% 175.30/27.02  | | | | | |            (187), (188), (190), (191), (193), (194), (196), (229),
% 175.30/27.02  | | | | | |            (233), (237), (238), (239) are inconsistent by sub-proof
% 175.30/27.02  | | | | | |            #327.
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | Case 2:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (240)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.30/27.02  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.30/27.02  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REF_CLOSE: (21), (92), (103), (124), (143), (158), (174), (177),
% 175.30/27.02  | | | | | |            (179), (240) are inconsistent by sub-proof #128.
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | End of split
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | End of split
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | End of split
% 175.30/27.02  | | | 
% 175.30/27.02  | | Case 2:
% 175.30/27.02  | | | 
% 175.30/27.02  | | |   (241)  all_26_0 = e2
% 175.30/27.02  | | |   (242)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 175.30/27.02  | | | 
% 175.30/27.02  | | | COMBINE_EQS: (151), (241) imply:
% 175.30/27.02  | | |   (243)  all_4_0 = e2
% 175.30/27.02  | | | 
% 175.30/27.02  | | | SIMP: (243) implies:
% 175.30/27.02  | | |   (244)  all_4_0 = e2
% 175.30/27.02  | | | 
% 175.30/27.02  | | | COMBINE_EQS: (60), (244) imply:
% 175.30/27.02  | | |   (245)  all_50_0 = e2
% 175.30/27.02  | | | 
% 175.30/27.02  | | | REDUCE: (85), (244) imply:
% 175.30/27.02  | | |   (246)  op(all_4_1, all_4_2) = e2
% 175.30/27.02  | | | 
% 175.30/27.02  | | | BETA: splitting (135) gives:
% 175.30/27.02  | | | 
% 175.30/27.02  | | | Case 1:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (247)   ~ (all_50_0 = e2)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REDUCE: (245), (247) imply:
% 175.30/27.02  | | | |   (248)  $false
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | CLOSE: (248) is inconsistent.
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | Case 2:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (249)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | BETA: splitting (155) gives:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | Case 1:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (250)  all_58_15 = e0
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REF_CLOSE: (21), (34), (58), (92), (124), (158), (250) are
% 175.30/27.02  | | | | |            inconsistent by sub-proof #143.
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | Case 2:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (251)   ~ (all_58_15 = e0)
% 175.30/27.02  | | | | |   (252)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.30/27.02  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | ALPHA: (252) implies:
% 175.30/27.02  | | | | |   (253)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REDUCE: (34), (251) imply:
% 175.30/27.02  | | | | |   (254)   ~ (all_6_2 = e0)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | BETA: splitting (159) gives:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | Case 1:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (255)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.30/27.02  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.30/27.02  | | | | | |            all_52_14 = e0)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 175.30/27.02  | | | | | |            (13), (14), (15), (16), (17), (19), (20), (22), (24),
% 175.30/27.02  | | | | | |            (25), (26), (27), (28), (29), (31), (32), (33), (34),
% 175.30/27.02  | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 175.30/27.02  | | | | | |            (45), (46), (48), (49), (50), (51), (52), (53), (54),
% 175.30/27.02  | | | | | |            (55), (56), (57), (59), (62), (63), (64), (65), (67),
% 175.30/27.02  | | | | | |            (68), (69), (71), (72), (75), (76), (77), (78), (79),
% 175.30/27.02  | | | | | |            (80), (81), (86), (88), (89), (91), (93), (94), (95),
% 175.30/27.02  | | | | | |            (96), (98), (99), (101), (103), (104), (106), (107),
% 175.30/27.02  | | | | | |            (108), (109), (110), (111), (112), (114), (116), (117),
% 175.30/27.02  | | | | | |            (119), (120), (121), (122), (123), (124), (125), (126),
% 175.30/27.02  | | | | | |            (127), (129), (130), (131), (132), (133), (136), (138),
% 175.30/27.02  | | | | | |            (139), (141), (142), (144), (145), (146), (149), (150),
% 175.30/27.02  | | | | | |            (152), (153), (154), (156), (157), (158), (160), (162),
% 175.30/27.02  | | | | | |            (164), (170), (171), (172), (173), (175), (176), (178),
% 175.30/27.02  | | | | | |            (179), (180), (181), (182), (185), (186), (187), (188),
% 175.30/27.02  | | | | | |            (190), (191), (193), (194), (196), (242), (246), (249),
% 175.30/27.02  | | | | | |            (253), (254), (255) are inconsistent by sub-proof #294.
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | Case 2:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (256)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.30/27.02  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.30/27.02  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REF_CLOSE: (21), (92), (103), (124), (143), (158), (174), (177),
% 175.30/27.02  | | | | | |            (179), (256) are inconsistent by sub-proof #127.
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | End of split
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | End of split
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | End of split
% 175.30/27.02  | | | 
% 175.30/27.02  | | End of split
% 175.30/27.02  | | 
% 175.30/27.02  | Case 2:
% 175.30/27.02  | | 
% 175.30/27.02  | |   (257)  all_24_0 = e1
% 175.30/27.02  | | 
% 175.30/27.02  | | COMBINE_EQS: (73), (257) imply:
% 175.30/27.02  | |   (258)  all_10_0 = e1
% 175.30/27.02  | | 
% 175.30/27.02  | | REDUCE: (165), (258) imply:
% 175.30/27.02  | |   (259)   ~ (e3 = e1)
% 175.30/27.02  | | 
% 175.30/27.02  | | REDUCE: (109), (258) imply:
% 175.30/27.02  | |   (260)  op(all_10_1, all_10_2) = e1
% 175.30/27.02  | | 
% 175.30/27.02  | | BETA: splitting (184) gives:
% 175.30/27.02  | | 
% 175.30/27.02  | | Case 1:
% 175.30/27.02  | | | 
% 175.30/27.02  | | |   (261)   ~ (all_26_0 = e2)
% 175.30/27.02  | | | 
% 175.30/27.02  | | | REDUCE: (151), (261) imply:
% 175.30/27.02  | | |   (262)   ~ (all_4_0 = e2)
% 175.30/27.02  | | | 
% 175.30/27.02  | | | BETA: splitting (134) gives:
% 175.30/27.02  | | | 
% 175.30/27.02  | | | Case 1:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (263)   ~ (all_34_0 = e1)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REDUCE: (183), (263) imply:
% 175.30/27.02  | | | |   (264)   ~ (all_4_0 = e1)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | BETA: splitting (163) gives:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | Case 1:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (265)   ~ (all_38_0 = e1)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REDUCE: (137), (265) imply:
% 175.30/27.02  | | | | |   (266)  $false
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | CLOSE: (266) is inconsistent.
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | Case 2:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (267)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | BETA: splitting (155) gives:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | Case 1:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (268)  all_58_15 = e0
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REF_CLOSE: (21), (34), (58), (92), (124), (158), (268) are
% 175.30/27.02  | | | | | |            inconsistent by sub-proof #143.
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | Case 2:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | |   (269)   ~ (all_58_15 = e0)
% 175.30/27.02  | | | | | |   (270)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.30/27.02  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | ALPHA: (270) implies:
% 175.30/27.02  | | | | | |   (271)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | REDUCE: (34), (269) imply:
% 175.30/27.02  | | | | | |   (272)   ~ (all_6_2 = e0)
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | BETA: splitting (159) gives:
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | | Case 1:
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | |   (273)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 175.30/27.02  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 175.30/27.02  | | | | | | |            e1 & all_52_14 = e0)
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | REF_CLOSE: (1), (2), (7), (8), (10), (12), (13), (15), (16), (17),
% 175.30/27.02  | | | | | | |            (18), (21), (22), (25), (26), (27), (28), (29), (30),
% 175.30/27.02  | | | | | | |            (31), (33), (34), (35), (36), (37), (38), (39), (40),
% 175.30/27.02  | | | | | | |            (41), (42), (43), (44), (45), (48), (50), (51), (52),
% 175.30/27.02  | | | | | | |            (53), (54), (55), (56), (59), (61), (63), (66), (67),
% 175.30/27.02  | | | | | | |            (68), (70), (71), (72), (76), (77), (78), (79), (80),
% 175.30/27.02  | | | | | | |            (81), (83), (85), (87), (88), (89), (90), (91), (92),
% 175.30/27.02  | | | | | | |            (93), (96), (97), (98), (99), (101), (104), (105),
% 175.30/27.02  | | | | | | |            (106), (107), (108), (110), (111), (112), (113), (114),
% 175.30/27.02  | | | | | | |            (115), (116), (118), (119), (120), (121), (122), (124),
% 175.30/27.02  | | | | | | |            (125), (126), (127), (128), (129), (131), (132), (136),
% 175.30/27.02  | | | | | | |            (138), (139), (140), (141), (142), (143), (144), (145),
% 175.30/27.02  | | | | | | |            (148), (149), (150), (152), (153), (157), (158), (160),
% 175.30/27.02  | | | | | | |            (162), (164), (167), (168), (170), (171), (172), (173),
% 175.30/27.02  | | | | | | |            (175), (176), (180), (182), (186), (187), (188), (190),
% 175.30/27.02  | | | | | | |            (191), (192), (193), (194), (260), (262), (264), (267),
% 175.30/27.02  | | | | | | |            (271), (272), (273) are inconsistent by sub-proof #134.
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | Case 2:
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | |   (274)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.30/27.02  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.30/27.02  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | | REF_CLOSE: (21), (92), (103), (124), (143), (158), (174), (177),
% 175.30/27.02  | | | | | | |            (179), (274) are inconsistent by sub-proof #128.
% 175.30/27.02  | | | | | | | 
% 175.30/27.02  | | | | | | End of split
% 175.30/27.02  | | | | | | 
% 175.30/27.02  | | | | | End of split
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | End of split
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | Case 2:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (275)  all_34_0 = e1
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | COMBINE_EQS: (183), (275) imply:
% 175.30/27.02  | | | |   (276)  all_4_0 = e1
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REDUCE: (262), (276) imply:
% 175.30/27.02  | | | |   (277)   ~ (e2 = e1)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REDUCE: (85), (276) imply:
% 175.30/27.02  | | | |   (278)  op(all_4_1, all_4_2) = e1
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | BETA: splitting (159) gives:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | Case 1:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (279)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.30/27.02  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.30/27.02  | | | | |            all_52_14 = e0)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REF_CLOSE: (8), (46), (50), (93), (96), (143), (158), (260), (278),
% 175.30/27.02  | | | | |            (279) are inconsistent by sub-proof #441.
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | Case 2:
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | |   (280)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 175.30/27.02  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.30/27.02  | | | | |            all_52_30 = e0)
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | | REF_CLOSE: (21), (92), (103), (124), (143), (158), (174), (177),
% 175.30/27.02  | | | | |            (179), (280) are inconsistent by sub-proof #127.
% 175.30/27.02  | | | | | 
% 175.30/27.02  | | | | End of split
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | End of split
% 175.30/27.02  | | | 
% 175.30/27.02  | | Case 2:
% 175.30/27.02  | | | 
% 175.30/27.02  | | |   (281)  all_26_0 = e2
% 175.30/27.02  | | | 
% 175.30/27.02  | | | COMBINE_EQS: (151), (281) imply:
% 175.30/27.02  | | |   (282)  all_4_0 = e2
% 175.30/27.02  | | | 
% 175.30/27.02  | | | REDUCE: (85), (282) imply:
% 175.30/27.02  | | |   (283)  op(all_4_1, all_4_2) = e2
% 175.30/27.02  | | | 
% 175.30/27.02  | | | BETA: splitting (159) gives:
% 175.30/27.02  | | | 
% 175.30/27.02  | | | Case 1:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (284)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 175.30/27.02  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 175.30/27.02  | | | |            = e0)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REF_CLOSE: (8), (50), (65), (93), (96), (143), (158), (260), (283),
% 175.30/27.02  | | | |            (284) are inconsistent by sub-proof #434.
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | Case 2:
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | |   (285)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 175.30/27.02  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.30/27.02  | | | |            all_52_30 = e0)
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | | REF_CLOSE: (21), (92), (103), (124), (143), (158), (174), (177), (179),
% 175.30/27.02  | | | |            (285) are inconsistent by sub-proof #127.
% 175.30/27.02  | | | | 
% 175.30/27.02  | | | End of split
% 175.30/27.02  | | | 
% 175.30/27.02  | | End of split
% 175.30/27.02  | | 
% 175.30/27.02  | End of split
% 175.30/27.02  | 
% 175.30/27.02  End of proof
% 175.30/27.02  
% 175.30/27.02  Sub-proof #127 shows that the following formulas are inconsistent:
% 175.30/27.02  ----------------------------------------------------------------
% 175.30/27.02    (1)  op(all_6_1, all_6_2) = e1
% 175.30/27.02    (2)  op(e0, all_6_2) = all_6_1
% 175.30/27.02    (3)  op(all_14_1, all_14_2) = e2
% 175.30/27.02    (4)   ~ (e1 = e0)
% 175.30/27.02    (5)   ~ (e2 = e1)
% 175.59/27.02    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.02    (7)  all_52_20 = all_14_1
% 175.59/27.02    (8)  all_52_30 = all_6_1
% 175.59/27.02    (9)  op(e1, all_14_2) = all_14_1
% 175.59/27.02    (10)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.02          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.02  
% 175.59/27.02  Begin of proof
% 175.59/27.02  | 
% 175.59/27.02  | BETA: splitting (10) gives:
% 175.59/27.02  | 
% 175.59/27.02  | Case 1:
% 175.59/27.02  | | 
% 175.59/27.02  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.02  | | 
% 175.59/27.02  | | ALPHA: (11) implies:
% 175.59/27.02  | |   (12)  all_52_20 = e1
% 175.59/27.02  | | 
% 175.59/27.02  | | COMBINE_EQS: (7), (12) imply:
% 175.59/27.02  | |   (13)  all_14_1 = e1
% 175.59/27.02  | | 
% 175.59/27.02  | | REF_CLOSE: (3), (5), (6), (9), (13) are inconsistent by sub-proof #315.
% 175.59/27.02  | | 
% 175.59/27.02  | Case 2:
% 175.59/27.02  | | 
% 175.59/27.02  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.02  | | 
% 175.59/27.02  | | REF_CLOSE: (1), (2), (4), (6), (8), (14) are inconsistent by sub-proof #138.
% 175.59/27.02  | | 
% 175.59/27.02  | End of split
% 175.59/27.02  | 
% 175.59/27.02  End of proof
% 175.59/27.02  
% 175.59/27.02  Sub-proof #128 shows that the following formulas are inconsistent:
% 175.59/27.02  ----------------------------------------------------------------
% 175.59/27.02    (1)  op(all_6_1, all_6_2) = e1
% 175.59/27.02    (2)  op(e0, all_6_2) = all_6_1
% 175.59/27.02    (3)  op(all_14_1, all_14_2) = e2
% 175.59/27.02    (4)   ~ (e1 = e0)
% 175.59/27.02    (5)   ~ (e2 = e1)
% 175.59/27.02    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.02    (7)  all_52_20 = all_14_1
% 175.59/27.02    (8)  all_52_30 = all_6_1
% 175.59/27.02    (9)  op(e1, all_14_2) = all_14_1
% 175.59/27.02    (10)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.02          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.02  
% 175.59/27.02  Begin of proof
% 175.59/27.02  | 
% 175.59/27.02  | BETA: splitting (10) gives:
% 175.59/27.02  | 
% 175.59/27.02  | Case 1:
% 175.59/27.02  | | 
% 175.59/27.02  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.02  | | 
% 175.59/27.02  | | ALPHA: (11) implies:
% 175.59/27.02  | |   (12)  all_52_20 = e1
% 175.59/27.02  | | 
% 175.59/27.02  | | COMBINE_EQS: (7), (12) imply:
% 175.59/27.02  | |   (13)  all_14_1 = e1
% 175.59/27.02  | | 
% 175.59/27.02  | | REF_CLOSE: (3), (5), (6), (9), (13) are inconsistent by sub-proof #315.
% 175.59/27.02  | | 
% 175.59/27.02  | Case 2:
% 175.59/27.02  | | 
% 175.59/27.02  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.02  | | 
% 175.59/27.02  | | ALPHA: (14) implies:
% 175.59/27.02  | |   (15)  all_52_30 = e0
% 175.59/27.02  | | 
% 175.59/27.02  | | COMBINE_EQS: (8), (15) imply:
% 175.59/27.02  | |   (16)  all_6_1 = e0
% 175.59/27.02  | | 
% 175.59/27.02  | | REF_CLOSE: (1), (2), (4), (6), (16) are inconsistent by sub-proof #139.
% 175.59/27.02  | | 
% 175.59/27.02  | End of split
% 175.59/27.02  | 
% 175.59/27.02  End of proof
% 175.59/27.02  
% 175.59/27.02  Sub-proof #129 shows that the following formulas are inconsistent:
% 175.59/27.02  ----------------------------------------------------------------
% 175.59/27.02    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.02    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.02    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.59/27.02    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.59/27.02    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.59/27.02    (6)   ~ (all_52_27 = all_10_2)
% 175.59/27.02    (7)   ~ (all_52_17 = all_52_23)
% 175.59/27.02    (8)  op(e2, all_10_2) = all_10_1
% 175.59/27.02    (9)  all_40_2 = all_4_2
% 175.59/27.02    (10)   ~ (all_52_13 = all_52_29)
% 175.59/27.02    (11)  all_56_3 = all_52_7
% 175.59/27.03    (12)  op(e3, e2) = all_52_3
% 175.59/27.03    (13)   ~ (all_52_9 = all_52_25)
% 175.59/27.03    (14)  op(e3, all_52_25) = all_52_24
% 175.59/27.03    (15)   ~ (all_52_19 = all_52_23)
% 175.59/27.03    (16)  all_56_11 = all_52_23
% 175.59/27.03    (17)  op(e1, e2) = all_52_19
% 175.59/27.03    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.59/27.03    (19)  op(e3, all_52_9) = all_52_8
% 175.59/27.03    (20)  all_50_1 = all_4_1
% 175.59/27.03    (21)  all_18_0 = all_14_0
% 175.59/27.03    (22)  op(all_6_1, all_6_2) = e1
% 175.59/27.03    (23)   ~ (all_52_3 = all_10_2)
% 175.59/27.03    (24)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.59/27.03    (25)  all_58_5 = all_52_13
% 175.59/27.03    (26)   ~ (all_52_25 = all_52_29)
% 175.59/27.03    (27)  all_56_15 = all_6_2
% 175.59/27.03    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.03    (29)  op(e2, e0) = all_52_15
% 175.59/27.03    (30)  op(all_14_1, all_14_2) = all_14_0
% 175.59/27.03    (31)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.59/27.03    (32)  all_58_3 = all_10_2
% 175.59/27.03    (33)  all_56_9 = all_52_19
% 175.59/27.03    (34)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.03    (35)  all_58_15 = all_6_2
% 175.59/27.03    (36)   ~ (all_52_9 = all_4_2)
% 175.59/27.03    (37)   ~ (all_52_5 = all_52_7)
% 175.59/27.03    (38)  all_58_10 = all_52_15
% 175.59/27.03    (39)   ~ (all_52_5 = all_4_2)
% 175.59/27.03    (40)  all_58_7 = all_52_19
% 175.59/27.03    (41)  all_56_4 = all_52_9
% 175.59/27.03    (42)   ~ (all_52_15 = all_6_2)
% 175.59/27.03    (43)   ~ (all_52_17 = all_52_25)
% 175.59/27.03    (44)  op(e0, e1) = all_52_29
% 175.59/27.03    (45)  all_58_4 = all_52_5
% 175.59/27.03    (46)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.03    (47)   ~ (e3 = e1)
% 175.59/27.03    (48)  all_34_1 = all_4_1
% 175.59/27.03    (49)   ~ (all_52_27 = all_52_29)
% 175.59/27.03    (50)   ~ (all_52_17 = all_14_2)
% 175.59/27.03    (51)  op(e3, all_4_2) = all_4_1
% 175.59/27.03    (52)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.03    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.03    (54)   ~ (all_52_7 = all_4_2)
% 175.59/27.03    (55)  all_58_1 = all_52_3
% 175.59/27.03    (56)   ~ (all_52_13 = all_52_15)
% 175.59/27.03    (57)  all_58_0 = all_4_2
% 175.59/27.03    (58)  op(e1, all_52_13) = all_52_12
% 175.59/27.03    (59)  op(e0, e0) = all_6_2
% 175.59/27.03    (60)  op(e1, all_52_29) = all_52_28
% 175.59/27.03    (61)  all_50_0 = all_4_0
% 175.59/27.03    (62)  op(e1, all_52_5) = all_52_4
% 175.59/27.03    (63)  all_50_2 = all_4_2
% 175.59/27.03    (64)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.03    (65)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.59/27.03    (66)   ~ (all_4_1 = e2)
% 175.59/27.03    (67)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.59/27.03    (68)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.03    (69)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.03    (70)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.59/27.03    (71)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.03    (72)  all_58_14 = all_52_29
% 175.59/27.03    (73)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.03    (74)  all_24_0 = all_10_0
% 175.59/27.03    (75)  all_40_1 = all_4_1
% 175.59/27.03    (76)  all_26_2 = all_4_2
% 175.59/27.03    (77)   ~ (all_52_3 = all_52_5)
% 175.59/27.03    (78)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.03    (79)  op(e2, e1) = all_52_13
% 175.59/27.03    (80)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.03    (81)  all_58_8 = all_14_2
% 175.59/27.03    (82)  all_56_1 = all_52_3
% 175.59/27.03    (83)  op(e0, e2) = all_52_27
% 175.59/27.03    (84)  all_56_14 = all_52_29
% 175.59/27.03    (85)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.59/27.03    (86)  op(all_4_1, all_4_2) = all_4_0
% 175.59/27.03    (87)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.59/27.03    (88)   ~ (all_52_5 = all_14_2)
% 175.59/27.03    (89)   ~ (all_52_3 = all_52_27)
% 175.59/27.03    (90)   ~ (all_52_3 = all_4_2)
% 175.59/27.03    (91)  all_38_2 = all_6_2
% 175.59/27.03    (92)  op(e0, e3) = all_52_25
% 175.59/27.03    (93)  op(e0, all_6_2) = all_6_1
% 175.59/27.03    (94)  all_52_0 = all_4_1
% 175.59/27.03    (95)   ~ (all_52_9 = all_10_2)
% 175.59/27.03    (96)  op(e3, all_52_17) = all_52_16
% 175.59/27.03    (97)  all_52_10 = all_10_1
% 175.59/27.03    (98)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.59/27.03    (99)   ~ (all_52_13 = all_14_2)
% 175.59/27.03    (100)   ~ (e3 = e0)
% 175.59/27.03    (101)  all_40_0 = all_4_0
% 175.59/27.03    (102)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.03    (103)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 175.59/27.03    (104)   ~ (all_52_9 = all_52_13)
% 175.59/27.03    (105)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.03    (106)  op(e0, all_52_23) = all_52_22
% 175.59/27.03    (107)   ~ (all_52_15 = all_52_23)
% 175.59/27.03    (108)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.03    (109)  op(all_10_1, all_10_2) = all_10_0
% 175.59/27.03    (110)   ~ (all_52_5 = all_52_29)
% 175.59/27.03    (111)  all_56_2 = all_52_5
% 175.59/27.03    (112)  op(e1, e0) = all_52_23
% 175.59/27.03    (113)  all_56_12 = all_52_25
% 175.59/27.03    (114)  all_58_13 = all_52_27
% 175.59/27.03    (115)  op(e2, all_52_3) = all_52_2
% 175.59/27.03    (116)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 175.59/27.03    (117)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.03    (118)  all_56_5 = all_10_2
% 175.59/27.03    (119)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.03    (120)   ~ (all_52_9 = all_52_17)
% 175.59/27.03    (121)   ~ (all_14_0 = e2)
% 175.59/27.03    (122)  all_58_6 = all_52_17
% 175.59/27.03    (123)   ~ (all_52_3 = all_52_7)
% 175.59/27.03    (124)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.59/27.03    (125)  op(e2, all_52_19) = all_52_18
% 175.59/27.03    (126)   ~ (e1 = e0)
% 175.59/27.03    (127)  all_56_0 = all_4_2
% 175.59/27.03    (128)  all_58_11 = all_52_23
% 175.59/27.03    (129)   ~ (all_52_3 = all_52_19)
% 175.59/27.03    (130)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.03    (131)   ~ (all_52_7 = all_52_15)
% 175.59/27.03    (132)  all_26_1 = all_4_1
% 175.59/27.03    (133)  op(e0, all_52_15) = all_52_14
% 175.59/27.03    (134)   ~ (all_52_29 = all_14_2)
% 175.59/27.03    (135)   ~ (all_52_19 = all_10_2)
% 175.59/27.03    (136)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.59/27.03    (137)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.59/27.03    (138)   ~ (all_52_23 = all_6_2)
% 175.59/27.03    (139)  all_38_0 = e1
% 175.59/27.03    (140)   ~ (all_52_29 = all_6_2)
% 175.59/27.03    (141)  all_58_2 = all_52_9
% 175.59/27.03    (142)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.59/27.03    (143)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.59/27.03    (144)  op(e3, e1) = all_52_5
% 175.59/27.03    (145)   ~ (e2 = e1)
% 175.59/27.03    (146)  all_56_10 = all_14_2
% 175.59/27.03    (147)   ~ (all_52_25 = all_6_2)
% 175.59/27.03    (148)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.59/27.03    (149)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.59/27.03    (150)  op(e1, e1) = all_14_2
% 175.59/27.03    (151)  op(e1, e3) = all_52_17
% 175.59/27.03    (152)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.03    (153)  all_26_0 = all_4_0
% 175.59/27.03    (154)   ~ (all_52_25 = all_4_2)
% 175.59/27.03    (155)  op(e3, e0) = all_52_7
% 175.59/27.03    (156)  op(e3, e3) = all_4_2
% 175.59/27.03    (157)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.59/27.03             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 175.59/27.03    (158)  all_56_8 = all_52_17
% 175.59/27.03    (159)   ~ (all_52_17 = all_4_2)
% 175.59/27.03    (160)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.03             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.03    (161)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.59/27.03           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 175.59/27.03           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.03           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.03    (162)   ~ (all_52_25 = all_52_27)
% 175.59/27.03    (163)  all_34_2 = all_4_2
% 175.59/27.03    (164)   ~ (all_52_27 = all_6_2)
% 175.59/27.03    (165)   ~ (all_38_0 = e1) |  ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.03    (166)   ~ (all_52_7 = all_6_2)
% 175.59/27.03    (167)   ~ (all_10_0 = e3)
% 175.59/27.03    (168)   ~ (all_52_15 = all_10_2)
% 175.59/27.03    (169)  all_38_1 = all_6_1
% 175.59/27.03    (170)   ~ (all_52_19 = all_52_27)
% 175.59/27.03    (171)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2)
% 175.59/27.03    (172)  all_56_7 = all_52_15
% 175.59/27.03    (173)  all_18_2 = all_14_2
% 175.59/27.03    (174)  all_18_0 = e3
% 175.59/27.03    (175)   ~ (all_52_7 = all_52_23)
% 175.59/27.03    (176)   ~ (all_52_13 = all_10_2)
% 175.59/27.03    (177)  op(e2, all_52_27) = all_52_26
% 175.59/27.03    (178)  all_52_20 = all_14_1
% 175.59/27.03    (179)   ~ (all_52_17 = all_52_19)
% 175.59/27.03    (180)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.03    (181)  all_52_30 = all_6_1
% 175.59/27.03    (182)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.59/27.03    (183)  op(e1, all_14_2) = all_14_1
% 175.59/27.03    (184)  all_58_9 = all_52_7
% 175.59/27.03    (185)  all_58_12 = all_52_25
% 175.59/27.03    (186)  all_34_0 = all_4_0
% 175.59/27.03    (187)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 175.59/27.03    (188)  all_56_6 = all_52_13
% 175.59/27.03    (189)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.03    (190)   ~ (all_52_9 = all_52_15)
% 175.59/27.03    (191)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.03    (192)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.03    (193)   ~ (all_52_19 = all_14_2)
% 175.59/27.03    (194)  op(e0, all_52_7) = all_52_6
% 175.59/27.03    (195)  op(e2, e3) = all_52_9
% 175.59/27.03    (196)  all_56_13 = all_52_27
% 175.59/27.03  
% 175.59/27.03  Begin of proof
% 175.59/27.03  | 
% 175.59/27.03  | COMBINE_EQS: (21), (174) imply:
% 175.59/27.03  |   (197)  all_14_0 = e3
% 175.59/27.03  | 
% 175.59/27.03  | SIMP: (197) implies:
% 175.59/27.03  |   (198)  all_14_0 = e3
% 175.59/27.03  | 
% 175.59/27.03  | REDUCE: (121), (198) imply:
% 175.59/27.03  |   (199)   ~ (e3 = e2)
% 175.59/27.03  | 
% 175.59/27.03  | REDUCE: (30), (198) imply:
% 175.59/27.03  |   (200)  op(all_14_1, all_14_2) = e3
% 175.59/27.03  | 
% 175.59/27.03  | BETA: splitting (103) gives:
% 175.59/27.03  | 
% 175.59/27.03  | Case 1:
% 175.59/27.03  | | 
% 175.59/27.03  | |   (201)   ~ (all_24_0 = e1)
% 175.59/27.03  | | 
% 175.59/27.03  | | REDUCE: (74), (201) imply:
% 175.59/27.03  | |   (202)   ~ (all_10_0 = e1)
% 175.59/27.03  | | 
% 175.59/27.03  | | BETA: splitting (187) gives:
% 175.59/27.03  | | 
% 175.59/27.03  | | Case 1:
% 175.59/27.03  | | | 
% 175.59/27.03  | | |   (203)   ~ (all_26_0 = e2)
% 175.59/27.03  | | | 
% 175.59/27.03  | | | REDUCE: (153), (203) imply:
% 175.59/27.03  | | |   (204)   ~ (all_4_0 = e2)
% 175.59/27.03  | | | 
% 175.59/27.03  | | | BETA: splitting (136) gives:
% 175.59/27.03  | | | 
% 175.59/27.03  | | | Case 1:
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | |   (205)   ~ (all_34_0 = e1)
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | | REDUCE: (186), (205) imply:
% 175.59/27.03  | | | |   (206)   ~ (all_4_0 = e1)
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | | BETA: splitting (165) gives:
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | | Case 1:
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | |   (207)   ~ (all_38_0 = e1)
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | REDUCE: (139), (207) imply:
% 175.59/27.03  | | | | |   (208)  $false
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | CLOSE: (208) is inconsistent.
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | Case 2:
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | |   (209)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | BETA: splitting (171) gives:
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | Case 1:
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | |   (210)   ~ (all_40_1 = e1)
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | REDUCE: (75), (210) imply:
% 175.59/27.03  | | | | | |   (211)   ~ (all_4_1 = e1)
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | BETA: splitting (157) gives:
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | Case 1:
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | |   (212)  all_58_15 = e0
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | | REF_CLOSE: (22), (35), (59), (93), (126), (160), (212) are
% 175.59/27.03  | | | | | | |            inconsistent by sub-proof #143.
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | Case 2:
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | |   (213)   ~ (all_58_15 = e0)
% 175.59/27.03  | | | | | | |   (214)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.59/27.03  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | | ALPHA: (214) implies:
% 175.59/27.03  | | | | | | |   (215)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.59/27.03  | | | | | | |   (216)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | | REDUCE: (35), (213) imply:
% 175.59/27.03  | | | | | | |   (217)   ~ (all_6_2 = e0)
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | | BETA: splitting (161) gives:
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | | Case 1:
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | |   (218)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.59/27.03  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 175.59/27.03  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | | BETA: splitting (218) gives:
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | | Case 1:
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | |   (219)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.59/27.03  | | | | | | | | |          all_52_6 = e0
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | REF_CLOSE: (1), (2), (7), (10), (12), (13), (15), (16), (17),
% 175.59/27.03  | | | | | | | | |            (18), (22), (23), (25), (26), (27), (28), (29),
% 175.59/27.03  | | | | | | | | |            (31), (32), (34), (35), (36), (37), (38), (39),
% 175.59/27.03  | | | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (49),
% 175.59/27.03  | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (60),
% 175.59/27.03  | | | | | | | | |            (62), (64), (67), (68), (69), (71), (72), (73),
% 175.59/27.03  | | | | | | | | |            (77), (78), (79), (80), (81), (82), (84), (86),
% 175.59/27.03  | | | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (98),
% 175.59/27.03  | | | | | | | | |            (99), (100), (102), (104), (105), (106), (107),
% 175.59/27.03  | | | | | | | | |            (108), (110), (111), (112), (113), (114), (115),
% 175.59/27.03  | | | | | | | | |            (117), (119), (120), (122), (123), (124), (126),
% 175.59/27.03  | | | | | | | | |            (127), (128), (129), (130), (131), (133), (134),
% 175.59/27.03  | | | | | | | | |            (138), (140), (141), (142), (143), (144), (146),
% 175.59/27.03  | | | | | | | | |            (147), (150), (151), (152), (154), (155), (159),
% 175.59/27.03  | | | | | | | | |            (160), (162), (164), (166), (169), (170), (172),
% 175.59/27.03  | | | | | | | | |            (175), (176), (177), (179), (180), (184), (185),
% 175.59/27.03  | | | | | | | | |            (189), (190), (191), (192), (193), (194), (195),
% 175.59/27.03  | | | | | | | | |            (196), (204), (206), (209), (216), (217), (219) are
% 175.59/27.03  | | | | | | | | |            inconsistent by sub-proof #140.
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | Case 2:
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | |   (220)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.59/27.03  | | | | | | | | |          all_52_14 = e0
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12),
% 175.59/27.03  | | | | | | | | |            (13), (14), (15), (16), (17), (19), (23), (24),
% 175.59/27.03  | | | | | | | | |            (25), (26), (27), (28), (29), (32), (33), (34),
% 175.59/27.03  | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 175.59/27.03  | | | | | | | | |            (43), (44), (45), (46), (47), (49), (50), (51),
% 175.59/27.03  | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (60),
% 175.59/27.03  | | | | | | | | |            (64), (65), (66), (68), (69), (70), (71), (72),
% 175.59/27.03  | | | | | | | | |            (73), (77), (78), (79), (80), (81), (82), (83),
% 175.59/27.03  | | | | | | | | |            (85), (86), (87), (89), (90), (92), (93), (95),
% 175.59/27.03  | | | | | | | | |            (96), (97), (99), (100), (104), (106), (107),
% 175.59/27.03  | | | | | | | | |            (108), (109), (110), (111), (112), (114), (117),
% 175.59/27.03  | | | | | | | | |            (120), (122), (123), (124), (125), (126), (127),
% 175.59/27.03  | | | | | | | | |            (128), (129), (131), (133), (134), (135), (138),
% 175.59/27.03  | | | | | | | | |            (140), (141), (143), (144), (146), (147), (149),
% 175.59/27.03  | | | | | | | | |            (150), (151), (152), (154), (155), (156), (159),
% 175.59/27.03  | | | | | | | | |            (160), (162), (164), (166), (167), (170), (172),
% 175.59/27.03  | | | | | | | | |            (175), (177), (179), (180), (182), (183), (184),
% 175.59/27.03  | | | | | | | | |            (185), (188), (189), (190), (191), (192), (193),
% 175.59/27.03  | | | | | | | | |            (195), (196), (202), (204), (206), (211), (215),
% 175.59/27.03  | | | | | | | | |            (216), (217), (220) are inconsistent by sub-proof
% 175.59/27.03  | | | | | | | | |            #338.
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | End of split
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | Case 2:
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | |   (221)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.59/27.03  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.59/27.03  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | | BETA: splitting (221) gives:
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | | Case 1:
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | |   (222)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.59/27.03  | | | | | | | | |          all_52_22 = e0
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | ALPHA: (222) implies:
% 175.59/27.03  | | | | | | | | |   (223)  all_52_20 = e1
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | COMBINE_EQS: (178), (223) imply:
% 175.59/27.03  | | | | | | | | |   (224)  all_14_1 = e1
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | REF_CLOSE: (47), (160), (183), (200), (224) are inconsistent
% 175.59/27.03  | | | | | | | | |            by sub-proof #344.
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | Case 2:
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | |   (225)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.59/27.03  | | | | | | | | |          all_52_30 = e0
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | ALPHA: (225) implies:
% 175.59/27.03  | | | | | | | | |   (226)  all_52_30 = e0
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | COMBINE_EQS: (181), (226) imply:
% 175.59/27.03  | | | | | | | | |   (227)  all_6_1 = e0
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | | REF_CLOSE: (22), (93), (126), (160), (227) are inconsistent by
% 175.59/27.03  | | | | | | | | |            sub-proof #139.
% 175.59/27.03  | | | | | | | | | 
% 175.59/27.03  | | | | | | | | End of split
% 175.59/27.03  | | | | | | | | 
% 175.59/27.03  | | | | | | | End of split
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | End of split
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | Case 2:
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | |   (228)  all_40_1 = e1
% 175.59/27.03  | | | | | |   (229)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | COMBINE_EQS: (75), (228) imply:
% 175.59/27.03  | | | | | |   (230)  all_4_1 = e1
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | COMBINE_EQS: (94), (230) imply:
% 175.59/27.03  | | | | | |   (231)  all_52_0 = e1
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | REDUCE: (66), (230) imply:
% 175.59/27.03  | | | | | |   (232)   ~ (e2 = e1)
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | REDUCE: (86), (230) imply:
% 175.59/27.03  | | | | | |   (233)  op(e1, all_4_2) = all_4_0
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | REDUCE: (51), (230) imply:
% 175.59/27.03  | | | | | |   (234)  op(e3, all_4_2) = e1
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | BETA: splitting (157) gives:
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | Case 1:
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | |   (235)  all_58_15 = e0
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | | REF_CLOSE: (22), (35), (59), (93), (126), (160), (235) are
% 175.59/27.03  | | | | | | |            inconsistent by sub-proof #143.
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | Case 2:
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | |   (236)   ~ (all_58_15 = e0)
% 175.59/27.03  | | | | | | |   (237)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.59/27.03  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 175.59/27.03  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (23),
% 175.59/27.03  | | | | | | |            (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 175.59/27.03  | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 175.59/27.03  | | | | | | |            (43), (44), (45), (46), (47), (49), (50), (51), (52),
% 175.59/27.03  | | | | | | |            (53), (54), (55), (56), (57), (58), (60), (65), (66),
% 175.59/27.03  | | | | | | |            (68), (69), (70), (72), (73), (77), (78), (79), (80),
% 175.59/27.03  | | | | | | |            (81), (83), (85), (86), (87), (88), (89), (90), (92),
% 175.59/27.03  | | | | | | |            (93), (95), (96), (97), (99), (100), (101), (102),
% 175.59/27.03  | | | | | | |            (104), (105), (106), (107), (108), (109), (110), (111),
% 175.59/27.03  | | | | | | |            (112), (113), (114), (116), (117), (119), (120), (122),
% 175.59/27.03  | | | | | | |            (123), (124), (125), (126), (127), (128), (129), (131),
% 175.59/27.03  | | | | | | |            (133), (134), (135), (138), (140), (141), (143), (144),
% 175.59/27.03  | | | | | | |            (145), (146), (147), (149), (150), (151), (154), (155),
% 175.59/27.03  | | | | | | |            (156), (159), (160), (161), (162), (164), (166), (167),
% 175.59/27.03  | | | | | | |            (168), (170), (173), (175), (177), (178), (179), (180),
% 175.59/27.03  | | | | | | |            (181), (182), (183), (184), (185), (188), (189), (190),
% 175.59/27.03  | | | | | | |            (191), (192), (193), (195), (196), (199), (200), (202),
% 175.59/27.03  | | | | | | |            (204), (206), (229), (231), (233), (234), (236), (237)
% 175.59/27.03  | | | | | | |            are inconsistent by sub-proof #331.
% 175.59/27.03  | | | | | | | 
% 175.59/27.03  | | | | | | End of split
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | End of split
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | End of split
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | Case 2:
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | |   (238)  all_34_0 = e1
% 175.59/27.03  | | | |   (239)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | | COMBINE_EQS: (186), (238) imply:
% 175.59/27.03  | | | |   (240)  all_4_0 = e1
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | | REDUCE: (86), (240) imply:
% 175.59/27.03  | | | |   (241)  op(all_4_1, all_4_2) = e1
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | | BETA: splitting (157) gives:
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | | Case 1:
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | |   (242)  all_58_15 = e0
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | REF_CLOSE: (22), (35), (59), (93), (126), (160), (242) are
% 175.59/27.03  | | | | |            inconsistent by sub-proof #143.
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | Case 2:
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | |   (243)   ~ (all_58_15 = e0)
% 175.59/27.03  | | | | |   (244)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.59/27.03  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | ALPHA: (244) implies:
% 175.59/27.03  | | | | |   (245)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | REDUCE: (35), (243) imply:
% 175.59/27.03  | | | | |   (246)   ~ (all_6_2 = e0)
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | BETA: splitting (161) gives:
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | | Case 1:
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | |   (247)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.59/27.03  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.59/27.03  | | | | | |            all_52_14 = e0)
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13),
% 175.59/27.03  | | | | | |            (15), (16), (17), (19), (23), (25), (26), (27), (28),
% 175.59/27.03  | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 175.59/27.03  | | | | | |            (41), (42), (43), (45), (46), (47), (48), (49), (50),
% 175.59/27.03  | | | | | |            (51), (52), (53), (54), (55), (57), (58), (60), (64),
% 175.59/27.03  | | | | | |            (65), (66), (68), (69), (70), (72), (73), (77), (78),
% 175.59/27.03  | | | | | |            (79), (80), (81), (82), (87), (89), (90), (92), (93),
% 175.59/27.03  | | | | | |            (94), (96), (97), (99), (100), (104), (106), (107),
% 175.59/27.03  | | | | | |            (108), (109), (110), (111), (112), (114), (117), (120),
% 175.59/27.03  | | | | | |            (122), (123), (124), (125), (126), (127), (128), (129),
% 175.59/27.03  | | | | | |            (131), (133), (134), (135), (138), (140), (141), (143),
% 175.59/27.03  | | | | | |            (144), (146), (147), (150), (151), (154), (155), (156),
% 175.59/27.03  | | | | | |            (159), (160), (162), (163), (164), (166), (167), (175),
% 175.59/27.03  | | | | | |            (177), (179), (180), (182), (183), (184), (185), (188),
% 175.59/27.03  | | | | | |            (189), (190), (191), (192), (193), (195), (196), (202),
% 175.59/27.03  | | | | | |            (239), (241), (245), (246), (247) are inconsistent by
% 175.59/27.03  | | | | | |            sub-proof #327.
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | Case 2:
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | |   (248)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.59/27.03  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.59/27.03  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | | REF_CLOSE: (22), (47), (93), (126), (160), (178), (181), (183),
% 175.59/27.03  | | | | | |            (200), (248) are inconsistent by sub-proof #130.
% 175.59/27.03  | | | | | | 
% 175.59/27.03  | | | | | End of split
% 175.59/27.03  | | | | | 
% 175.59/27.03  | | | | End of split
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | End of split
% 175.59/27.03  | | | 
% 175.59/27.03  | | Case 2:
% 175.59/27.03  | | | 
% 175.59/27.03  | | |   (249)  all_26_0 = e2
% 175.59/27.03  | | |   (250)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 175.59/27.03  | | | 
% 175.59/27.03  | | | COMBINE_EQS: (153), (249) imply:
% 175.59/27.03  | | |   (251)  all_4_0 = e2
% 175.59/27.03  | | | 
% 175.59/27.03  | | | SIMP: (251) implies:
% 175.59/27.03  | | |   (252)  all_4_0 = e2
% 175.59/27.03  | | | 
% 175.59/27.03  | | | COMBINE_EQS: (61), (252) imply:
% 175.59/27.03  | | |   (253)  all_50_0 = e2
% 175.59/27.03  | | | 
% 175.59/27.03  | | | REDUCE: (86), (252) imply:
% 175.59/27.03  | | |   (254)  op(all_4_1, all_4_2) = e2
% 175.59/27.03  | | | 
% 175.59/27.03  | | | BETA: splitting (137) gives:
% 175.59/27.03  | | | 
% 175.59/27.03  | | | Case 1:
% 175.59/27.03  | | | | 
% 175.59/27.03  | | | |   (255)   ~ (all_50_0 = e2)
% 175.59/27.03  | | | | 
% 175.59/27.04  | | | | REDUCE: (253), (255) imply:
% 175.59/27.04  | | | |   (256)  $false
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | CLOSE: (256) is inconsistent.
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | Case 2:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | |   (257)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | BETA: splitting (157) gives:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | Case 1:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (258)  all_58_15 = e0
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | REF_CLOSE: (22), (35), (59), (93), (126), (160), (258) are
% 175.59/27.04  | | | | |            inconsistent by sub-proof #143.
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | Case 2:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (259)   ~ (all_58_15 = e0)
% 175.59/27.04  | | | | |   (260)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.59/27.04  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | ALPHA: (260) implies:
% 175.59/27.04  | | | | |   (261)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | REDUCE: (35), (259) imply:
% 175.59/27.04  | | | | |   (262)   ~ (all_6_2 = e0)
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | BETA: splitting (161) gives:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | Case 1:
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | |   (263)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.59/27.04  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.59/27.04  | | | | | |            all_52_14 = e0)
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 175.59/27.04  | | | | | |            (13), (14), (15), (16), (17), (19), (20), (23), (24),
% 175.59/27.04  | | | | | |            (25), (26), (27), (28), (29), (32), (33), (34), (35),
% 175.59/27.04  | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (45),
% 175.59/27.04  | | | | | |            (46), (47), (49), (50), (51), (52), (53), (54), (55),
% 175.59/27.04  | | | | | |            (56), (57), (58), (60), (63), (64), (65), (66), (68),
% 175.59/27.04  | | | | | |            (69), (70), (72), (73), (76), (77), (78), (79), (80),
% 175.59/27.04  | | | | | |            (81), (82), (87), (89), (90), (92), (94), (95), (96),
% 175.59/27.04  | | | | | |            (97), (99), (100), (104), (106), (107), (108), (109),
% 175.59/27.04  | | | | | |            (110), (111), (112), (114), (116), (117), (118), (119),
% 175.59/27.04  | | | | | |            (120), (122), (123), (124), (125), (126), (127), (128),
% 175.59/27.04  | | | | | |            (129), (131), (132), (133), (134), (135), (138), (140),
% 175.59/27.04  | | | | | |            (141), (143), (144), (146), (147), (148), (151), (154),
% 175.59/27.04  | | | | | |            (155), (156), (158), (159), (160), (162), (164), (166),
% 175.59/27.04  | | | | | |            (167), (173), (175), (176), (177), (179), (180), (182),
% 175.59/27.04  | | | | | |            (183), (184), (185), (188), (189), (190), (191), (192),
% 175.59/27.04  | | | | | |            (193), (195), (196), (200), (202), (250), (254), (257),
% 175.59/27.04  | | | | | |            (261), (262), (263) are inconsistent by sub-proof #321.
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | Case 2:
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | |   (264)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.59/27.04  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.59/27.04  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | | REF_CLOSE: (22), (47), (93), (126), (160), (178), (181), (183),
% 175.59/27.04  | | | | | |            (200), (264) are inconsistent by sub-proof #130.
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | End of split
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | End of split
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | End of split
% 175.59/27.04  | | | 
% 175.59/27.04  | | End of split
% 175.59/27.04  | | 
% 175.59/27.04  | Case 2:
% 175.59/27.04  | | 
% 175.59/27.04  | |   (265)  all_24_0 = e1
% 175.59/27.04  | | 
% 175.59/27.04  | | COMBINE_EQS: (74), (265) imply:
% 175.59/27.04  | |   (266)  all_10_0 = e1
% 175.59/27.04  | | 
% 175.59/27.04  | | SIMP: (266) implies:
% 175.59/27.04  | |   (267)  all_10_0 = e1
% 175.59/27.04  | | 
% 175.59/27.04  | | REDUCE: (167), (267) imply:
% 175.59/27.04  | |   (268)   ~ (e3 = e1)
% 175.59/27.04  | | 
% 175.59/27.04  | | REDUCE: (109), (267) imply:
% 175.59/27.04  | |   (269)  op(all_10_1, all_10_2) = e1
% 175.59/27.04  | | 
% 175.59/27.04  | | BETA: splitting (187) gives:
% 175.59/27.04  | | 
% 175.59/27.04  | | Case 1:
% 175.59/27.04  | | | 
% 175.59/27.04  | | |   (270)   ~ (all_26_0 = e2)
% 175.59/27.04  | | | 
% 175.59/27.04  | | | REDUCE: (153), (270) imply:
% 175.59/27.04  | | |   (271)   ~ (all_4_0 = e2)
% 175.59/27.04  | | | 
% 175.59/27.04  | | | BETA: splitting (136) gives:
% 175.59/27.04  | | | 
% 175.59/27.04  | | | Case 1:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | |   (272)   ~ (all_34_0 = e1)
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | REDUCE: (186), (272) imply:
% 175.59/27.04  | | | |   (273)   ~ (all_4_0 = e1)
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | BETA: splitting (165) gives:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | Case 1:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (274)   ~ (all_38_0 = e1)
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | REDUCE: (139), (274) imply:
% 175.59/27.04  | | | | |   (275)  $false
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | CLOSE: (275) is inconsistent.
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | Case 2:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (276)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | BETA: splitting (157) gives:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | Case 1:
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | |   (277)  all_58_15 = e0
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | | REF_CLOSE: (22), (35), (59), (93), (126), (160), (277) are
% 175.59/27.04  | | | | | |            inconsistent by sub-proof #143.
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | Case 2:
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | |   (278)   ~ (all_58_15 = e0)
% 175.59/27.04  | | | | | |   (279)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.59/27.04  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | | ALPHA: (279) implies:
% 175.59/27.04  | | | | | |   (280)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | | REDUCE: (35), (278) imply:
% 175.59/27.04  | | | | | |   (281)   ~ (all_6_2 = e0)
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | | BETA: splitting (161) gives:
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | | Case 1:
% 175.59/27.04  | | | | | | | 
% 175.59/27.04  | | | | | | |   (282)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 175.59/27.04  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 175.59/27.04  | | | | | | |            e1 & all_52_14 = e0)
% 175.59/27.04  | | | | | | | 
% 175.59/27.04  | | | | | | | REF_CLOSE: (1), (2), (7), (8), (10), (12), (13), (15), (16), (17),
% 175.59/27.04  | | | | | | |            (18), (22), (23), (25), (26), (27), (28), (29), (31),
% 175.59/27.04  | | | | | | |            (32), (34), (35), (36), (37), (38), (39), (40), (41),
% 175.59/27.04  | | | | | | |            (42), (43), (44), (45), (46), (49), (51), (52), (53),
% 175.59/27.04  | | | | | | |            (54), (55), (56), (57), (60), (62), (64), (67), (68),
% 175.59/27.04  | | | | | | |            (69), (71), (72), (73), (77), (78), (79), (80), (81),
% 175.59/27.04  | | | | | | |            (82), (84), (86), (88), (89), (90), (91), (92), (93),
% 175.59/27.04  | | | | | | |            (94), (97), (98), (99), (100), (102), (104), (105),
% 175.59/27.04  | | | | | | |            (106), (107), (108), (110), (111), (112), (113), (114),
% 175.59/27.04  | | | | | | |            (115), (117), (119), (120), (122), (123), (124), (126),
% 175.59/27.04  | | | | | | |            (127), (128), (129), (130), (131), (133), (134), (138),
% 175.59/27.04  | | | | | | |            (140), (141), (142), (143), (144), (145), (146), (147),
% 175.59/27.04  | | | | | | |            (150), (151), (152), (154), (155), (159), (160), (162),
% 175.59/27.04  | | | | | | |            (164), (166), (169), (170), (172), (175), (176), (177),
% 175.59/27.04  | | | | | | |            (179), (180), (184), (185), (189), (190), (191), (192),
% 175.59/27.04  | | | | | | |            (193), (194), (195), (196), (269), (271), (273), (276),
% 175.59/27.04  | | | | | | |            (280), (281), (282) are inconsistent by sub-proof #134.
% 175.59/27.04  | | | | | | | 
% 175.59/27.04  | | | | | | Case 2:
% 175.59/27.04  | | | | | | | 
% 175.59/27.04  | | | | | | |   (283)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.59/27.04  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.59/27.04  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.04  | | | | | | | 
% 175.59/27.04  | | | | | | | REF_CLOSE: (22), (47), (93), (126), (160), (178), (181), (183),
% 175.59/27.04  | | | | | | |            (200), (283) are inconsistent by sub-proof #130.
% 175.59/27.04  | | | | | | | 
% 175.59/27.04  | | | | | | End of split
% 175.59/27.04  | | | | | | 
% 175.59/27.04  | | | | | End of split
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | End of split
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | Case 2:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | |   (284)  all_34_0 = e1
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | COMBINE_EQS: (186), (284) imply:
% 175.59/27.04  | | | |   (285)  all_4_0 = e1
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | SIMP: (285) implies:
% 175.59/27.04  | | | |   (286)  all_4_0 = e1
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | REDUCE: (271), (286) imply:
% 175.59/27.04  | | | |   (287)   ~ (e2 = e1)
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | REDUCE: (86), (286) imply:
% 175.59/27.04  | | | |   (288)  op(all_4_1, all_4_2) = e1
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | BETA: splitting (161) gives:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | Case 1:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (289)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.59/27.04  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.59/27.04  | | | | |            all_52_14 = e0)
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | REF_CLOSE: (8), (47), (51), (94), (97), (145), (160), (269), (288),
% 175.59/27.04  | | | | |            (289) are inconsistent by sub-proof #441.
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | Case 2:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (290)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 175.59/27.04  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.59/27.04  | | | | |            all_52_30 = e0)
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | REF_CLOSE: (22), (47), (93), (126), (160), (178), (181), (183), (200),
% 175.59/27.04  | | | | |            (290) are inconsistent by sub-proof #130.
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | End of split
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | End of split
% 175.59/27.04  | | | 
% 175.59/27.04  | | Case 2:
% 175.59/27.04  | | | 
% 175.59/27.04  | | |   (291)  all_26_0 = e2
% 175.59/27.04  | | | 
% 175.59/27.04  | | | COMBINE_EQS: (153), (291) imply:
% 175.59/27.04  | | |   (292)  all_4_0 = e2
% 175.59/27.04  | | | 
% 175.59/27.04  | | | SIMP: (292) implies:
% 175.59/27.04  | | |   (293)  all_4_0 = e2
% 175.59/27.04  | | | 
% 175.59/27.04  | | | REDUCE: (86), (293) imply:
% 175.59/27.04  | | |   (294)  op(all_4_1, all_4_2) = e2
% 175.59/27.04  | | | 
% 175.59/27.04  | | | BETA: splitting (161) gives:
% 175.59/27.04  | | | 
% 175.59/27.04  | | | Case 1:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | |   (295)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 175.59/27.04  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 175.59/27.04  | | | |            = e0)
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | REF_CLOSE: (8), (51), (66), (94), (97), (145), (160), (269), (294),
% 175.59/27.04  | | | |            (295) are inconsistent by sub-proof #434.
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | Case 2:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | |   (296)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 175.59/27.04  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.59/27.04  | | | |            all_52_30 = e0)
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | BETA: splitting (296) gives:
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | | Case 1:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (297)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 175.59/27.04  | | | | |          = e0
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | REF_CLOSE: (47), (160), (178), (183), (200), (297) are inconsistent by
% 175.59/27.04  | | | | |            sub-proof #343.
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | Case 2:
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | |   (298)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 175.59/27.04  | | | | |          = e0
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | | REF_CLOSE: (22), (93), (126), (160), (181), (298) are inconsistent by
% 175.59/27.04  | | | | |            sub-proof #138.
% 175.59/27.04  | | | | | 
% 175.59/27.04  | | | | End of split
% 175.59/27.04  | | | | 
% 175.59/27.04  | | | End of split
% 175.59/27.04  | | | 
% 175.59/27.04  | | End of split
% 175.59/27.04  | | 
% 175.59/27.04  | End of split
% 175.59/27.04  | 
% 175.59/27.04  End of proof
% 175.59/27.04  
% 175.59/27.04  Sub-proof #130 shows that the following formulas are inconsistent:
% 175.59/27.04  ----------------------------------------------------------------
% 175.59/27.04    (1)  op(all_6_1, all_6_2) = e1
% 175.59/27.04    (2)   ~ (e3 = e1)
% 175.59/27.04    (3)  op(all_14_1, all_14_2) = e3
% 175.59/27.04    (4)  op(e0, all_6_2) = all_6_1
% 175.59/27.04    (5)   ~ (e1 = e0)
% 175.59/27.04    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.04    (7)  all_52_20 = all_14_1
% 175.59/27.04    (8)  all_52_30 = all_6_1
% 175.59/27.04    (9)  op(e1, all_14_2) = all_14_1
% 175.59/27.04    (10)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.04          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.04  
% 175.59/27.04  Begin of proof
% 175.59/27.04  | 
% 175.59/27.04  | BETA: splitting (10) gives:
% 175.59/27.04  | 
% 175.59/27.04  | Case 1:
% 175.59/27.04  | | 
% 175.59/27.04  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.04  | | 
% 175.59/27.04  | | ALPHA: (11) implies:
% 175.59/27.04  | |   (12)  all_52_20 = e1
% 175.59/27.04  | | 
% 175.59/27.04  | | COMBINE_EQS: (7), (12) imply:
% 175.59/27.04  | |   (13)  all_14_1 = e1
% 175.59/27.04  | | 
% 175.59/27.04  | | REF_CLOSE: (2), (3), (6), (9), (13) are inconsistent by sub-proof #344.
% 175.59/27.04  | | 
% 175.59/27.04  | Case 2:
% 175.59/27.04  | | 
% 175.59/27.04  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.04  | | 
% 175.59/27.04  | | REF_CLOSE: (1), (4), (5), (6), (8), (14) are inconsistent by sub-proof #138.
% 175.59/27.04  | | 
% 175.59/27.04  | End of split
% 175.59/27.04  | 
% 175.59/27.04  End of proof
% 175.59/27.04  
% 175.59/27.04  Sub-proof #131 shows that the following formulas are inconsistent:
% 175.59/27.04  ----------------------------------------------------------------
% 175.59/27.04    (1)  op(all_6_1, all_6_2) = e1
% 175.59/27.04    (2)   ~ (e3 = e1)
% 175.59/27.04    (3)  op(e0, all_6_2) = all_6_1
% 175.59/27.04    (4)  all_52_20 = e3
% 175.59/27.04    (5)   ~ (e1 = e0)
% 175.59/27.04    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.04    (7)  all_52_30 = all_6_1
% 175.59/27.04    (8)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.04         (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.04  
% 175.59/27.04  Begin of proof
% 175.59/27.04  | 
% 175.59/27.04  | BETA: splitting (8) gives:
% 175.59/27.04  | 
% 175.59/27.04  | Case 1:
% 175.59/27.04  | | 
% 175.59/27.04  | |   (9)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.04  | | 
% 175.59/27.04  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #373.
% 175.59/27.04  | | 
% 175.59/27.04  | Case 2:
% 175.59/27.04  | | 
% 175.59/27.04  | |   (10)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.04  | | 
% 175.59/27.04  | | ALPHA: (10) implies:
% 175.59/27.04  | |   (11)  all_52_30 = e0
% 175.59/27.04  | | 
% 175.59/27.04  | | COMBINE_EQS: (7), (11) imply:
% 175.59/27.04  | |   (12)  all_6_1 = e0
% 175.59/27.04  | | 
% 175.59/27.04  | | REF_CLOSE: (1), (3), (5), (6), (12) are inconsistent by sub-proof #139.
% 175.59/27.04  | | 
% 175.59/27.04  | End of split
% 175.59/27.04  | 
% 175.59/27.04  End of proof
% 175.59/27.04  
% 175.59/27.04  Sub-proof #132 shows that the following formulas are inconsistent:
% 175.59/27.04  ----------------------------------------------------------------
% 175.59/27.04    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.04    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.04    (3)   ~ (all_52_17 = all_52_23)
% 175.59/27.04    (4)  op(e2, all_52_3) = e2
% 175.59/27.04    (5)   ~ (all_52_13 = all_52_29)
% 175.59/27.04    (6)  op(e3, e2) = all_52_3
% 175.59/27.04    (7)   ~ (all_52_9 = all_52_25)
% 175.59/27.04    (8)   ~ (all_52_19 = all_52_23)
% 175.59/27.04    (9)  all_56_11 = all_52_23
% 175.59/27.04    (10)  op(e1, e2) = all_52_19
% 175.59/27.04    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.59/27.04    (12)  op(all_6_1, all_6_2) = e1
% 175.59/27.04    (13)   ~ (all_52_3 = all_10_2)
% 175.59/27.04    (14)  all_58_5 = all_52_13
% 175.59/27.04    (15)   ~ (all_6_2 = e0)
% 175.59/27.04    (16)   ~ (all_52_25 = all_52_29)
% 175.59/27.04    (17)  all_56_15 = all_6_2
% 175.59/27.04    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.04    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.59/27.04    (20)  all_58_3 = all_10_2
% 175.59/27.04    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.04    (22)  all_58_15 = all_6_2
% 175.59/27.04    (23)   ~ (all_52_9 = all_4_2)
% 175.59/27.04    (24)   ~ (all_52_5 = all_52_7)
% 175.59/27.04    (25)  all_58_10 = all_52_15
% 175.59/27.04    (26)   ~ (all_52_5 = all_4_2)
% 175.59/27.04    (27)  all_58_7 = all_52_19
% 175.59/27.04    (28)  all_56_4 = all_52_9
% 175.59/27.04    (29)   ~ (all_52_15 = all_6_2)
% 175.59/27.04    (30)   ~ (all_52_17 = all_52_25)
% 175.59/27.04    (31)  op(e0, e1) = all_52_29
% 175.59/27.04    (32)   ~ (all_4_0 = e2)
% 175.59/27.04    (33)  all_58_4 = all_52_5
% 175.59/27.04    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.04    (35)   ~ (all_52_27 = all_52_29)
% 175.59/27.04    (36)   ~ (all_52_17 = all_14_2)
% 175.59/27.04    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.04    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.04    (39)   ~ (all_52_7 = all_4_2)
% 175.59/27.04    (40)  all_58_1 = all_52_3
% 175.59/27.04    (41)   ~ (all_52_13 = all_52_15)
% 175.59/27.04    (42)  all_58_0 = all_4_2
% 175.59/27.04    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.04    (44)  op(e1, all_52_29) = all_52_28
% 175.59/27.04    (45)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.59/27.04    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.04    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.04    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.04    (49)  all_58_14 = all_52_29
% 175.59/27.04    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.04    (51)   ~ (all_52_3 = all_52_5)
% 175.59/27.04    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.04    (53)  op(e2, e1) = all_52_13
% 175.59/27.04    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.04    (55)  all_58_8 = all_14_2
% 175.59/27.04    (56)  all_56_14 = all_52_29
% 175.59/27.04    (57)  op(e1, all_14_2) = e3
% 175.59/27.04    (58)   ~ (all_52_5 = all_14_2)
% 175.59/27.04    (59)   ~ (all_52_3 = all_4_2)
% 175.59/27.04    (60)  op(e3, all_4_2) = e3
% 175.59/27.04    (61)  all_38_2 = all_6_2
% 175.59/27.04    (62)  op(e0, e3) = all_52_25
% 175.59/27.04    (63)  op(e0, all_6_2) = all_6_1
% 175.59/27.04    (64)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.59/27.04    (65)   ~ (all_52_13 = all_14_2)
% 175.59/27.04    (66)   ~ (e3 = e0)
% 175.59/27.04    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.04    (68)   ~ (all_52_9 = all_52_13)
% 175.59/27.04    (69)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.04    (70)  op(e0, all_52_23) = all_52_22
% 175.59/27.04    (71)   ~ (all_52_15 = all_52_23)
% 175.59/27.04    (72)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.04    (73)   ~ (all_52_5 = all_52_29)
% 175.59/27.04    (74)  all_56_2 = all_52_5
% 175.59/27.04    (75)  op(e1, e0) = all_52_23
% 175.59/27.04    (76)  all_56_12 = all_52_25
% 175.59/27.04    (77)  all_58_13 = all_52_27
% 175.59/27.04    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.04    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.04    (80)   ~ (all_52_9 = all_52_17)
% 175.59/27.04    (81)  all_58_6 = all_52_17
% 175.59/27.04    (82)   ~ (all_52_3 = all_52_7)
% 175.59/27.04    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.59/27.04    (84)   ~ (e1 = e0)
% 175.59/27.04    (85)  all_56_0 = all_4_2
% 175.59/27.04    (86)  all_58_11 = all_52_23
% 175.59/27.04    (87)   ~ (all_52_3 = all_52_19)
% 175.59/27.04    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.04    (89)   ~ (all_52_7 = all_52_15)
% 175.59/27.04    (90)  op(e0, all_52_15) = all_52_14
% 175.59/27.04    (91)   ~ (all_52_29 = all_14_2)
% 175.59/27.04    (92)   ~ (all_4_0 = e1)
% 175.59/27.04    (93)   ~ (all_52_23 = all_6_2)
% 175.59/27.04    (94)   ~ (all_52_29 = all_6_2)
% 175.59/27.04    (95)  all_58_2 = all_52_9
% 175.59/27.04    (96)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.59/27.04    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.59/27.04    (98)  op(e3, e1) = all_52_5
% 175.59/27.04    (99)  all_56_10 = all_14_2
% 175.59/27.04    (100)   ~ (all_52_25 = all_6_2)
% 175.59/27.04    (101)  op(e1, e1) = all_14_2
% 175.59/27.04    (102)  op(e1, e3) = all_52_17
% 175.59/27.04    (103)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.04    (104)   ~ (all_52_25 = all_4_2)
% 175.59/27.04    (105)  op(e3, e0) = all_52_7
% 175.59/27.04    (106)   ~ (all_52_17 = all_4_2)
% 175.59/27.04    (107)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.04             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.04    (108)   ~ (all_52_25 = all_52_27)
% 175.59/27.04    (109)   ~ (all_52_27 = all_6_2)
% 175.59/27.04    (110)   ~ (all_52_7 = all_6_2)
% 175.59/27.04    (111)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.04    (112)  all_38_1 = all_6_1
% 175.59/27.04    (113)   ~ (all_52_19 = all_52_27)
% 175.59/27.04    (114)  all_56_7 = all_52_15
% 175.59/27.04    (115)  op(e1, all_52_5) = e1
% 175.59/27.04    (116)   ~ (all_52_7 = all_52_23)
% 175.59/27.04    (117)   ~ (all_52_13 = all_10_2)
% 175.59/27.04    (118)  op(e3, all_4_2) = all_4_0
% 175.59/27.04    (119)  op(e0, all_52_7) = e0
% 175.59/27.04    (120)  op(e2, all_52_27) = all_52_26
% 175.59/27.04    (121)   ~ (all_52_17 = all_52_19)
% 175.59/27.04    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.04    (123)  all_58_9 = all_52_7
% 175.59/27.04    (124)  all_58_12 = all_52_25
% 175.59/27.04    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.04    (126)   ~ (all_52_9 = all_52_15)
% 175.59/27.04    (127)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.04    (128)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.04    (129)   ~ (all_52_19 = all_14_2)
% 175.59/27.04    (130)  op(e2, e3) = all_52_9
% 175.59/27.04    (131)  all_56_13 = all_52_27
% 175.59/27.04  
% 175.59/27.04  Begin of proof
% 175.59/27.04  | 
% 175.59/27.04  | GROUND_INST: instantiating (107) with e3, all_4_0, all_4_2, e3, simplifying
% 175.59/27.04  |              with (60), (118) gives:
% 175.59/27.04  |   (132)  all_4_0 = e3
% 175.59/27.04  | 
% 175.59/27.04  | REDUCE: (32), (132) imply:
% 175.59/27.04  |   (133)   ~ (e3 = e2)
% 175.59/27.04  | 
% 175.59/27.04  | REDUCE: (92), (132) imply:
% 175.59/27.04  |   (134)   ~ (e3 = e1)
% 175.59/27.04  | 
% 175.59/27.04  | BETA: splitting (37) gives:
% 175.59/27.04  | 
% 175.59/27.04  | Case 1:
% 175.59/27.04  | | 
% 175.59/27.04  | |   (135)  all_56_15 = e3
% 175.59/27.04  | | 
% 175.59/27.04  | | COMBINE_EQS: (17), (135) imply:
% 175.59/27.04  | |   (136)  all_6_2 = e3
% 175.59/27.04  | | 
% 175.59/27.04  | | SIMP: (136) implies:
% 175.59/27.04  | |   (137)  all_6_2 = e3
% 175.59/27.04  | | 
% 175.59/27.04  | | COMBINE_EQS: (61), (137) imply:
% 175.59/27.04  | |   (138)  all_38_2 = e3
% 175.59/27.04  | | 
% 175.59/27.04  | | REDUCE: (100), (137) imply:
% 175.59/27.04  | |   (139)   ~ (all_52_25 = e3)
% 175.59/27.04  | | 
% 175.59/27.04  | | REDUCE: (12), (137) imply:
% 175.59/27.04  | |   (140)  op(all_6_1, e3) = e1
% 175.59/27.04  | | 
% 175.59/27.04  | | REDUCE: (63), (137) imply:
% 175.59/27.04  | |   (141)  op(e0, e3) = all_6_1
% 175.59/27.04  | | 
% 175.59/27.04  | | REF_CLOSE: (30), (62), (69), (76), (96), (102), (107), (111), (112), (124),
% 175.59/27.04  | |            (138), (139), (140), (141) are inconsistent by sub-proof #142.
% 175.59/27.04  | | 
% 175.59/27.04  | Case 2:
% 175.59/27.04  | | 
% 175.59/27.04  | |   (142)   ~ (all_56_15 = e3)
% 175.59/27.04  | |   (143)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.04  | | 
% 175.59/27.04  | | REDUCE: (17), (142) imply:
% 175.59/27.04  | |   (144)   ~ (all_6_2 = e3)
% 175.59/27.04  | | 
% 175.59/27.04  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 175.59/27.04  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.59/27.04  | |            (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 175.59/27.04  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 175.59/27.04  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 175.59/27.04  | |            (60), (62), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 175.59/27.04  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 175.59/27.04  | |            (84), (85), (86), (87), (88), (89), (90), (91), (93), (94), (95),
% 175.59/27.04  | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 175.59/27.04  | |            (106), (107), (108), (109), (110), (113), (114), (115), (116),
% 175.59/27.04  | |            (117), (119), (120), (121), (122), (123), (124), (125), (126),
% 175.59/27.04  | |            (127), (128), (129), (130), (131), (133), (134), (143), (144) are
% 175.59/27.04  | |            inconsistent by sub-proof #401.
% 175.59/27.04  | | 
% 175.59/27.04  | End of split
% 175.59/27.04  | 
% 175.59/27.04  End of proof
% 175.59/27.04  
% 175.59/27.04  Sub-proof #133 shows that the following formulas are inconsistent:
% 175.59/27.04  ----------------------------------------------------------------
% 175.59/27.04    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.04    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.59/27.04    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.59/27.04    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.59/27.04    (5)   ~ (all_52_17 = all_52_23)
% 175.59/27.04    (6)  all_56_3 = all_52_7
% 175.59/27.04    (7)  op(e3, e2) = all_52_3
% 175.59/27.04    (8)   ~ (all_52_9 = all_52_25)
% 175.59/27.04    (9)  op(e3, all_52_25) = all_52_24
% 175.59/27.04    (10)   ~ (all_52_19 = all_52_23)
% 175.59/27.04    (11)  op(e1, e2) = all_52_19
% 175.59/27.04    (12)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.59/27.04    (13)  op(e3, all_52_9) = all_52_8
% 175.59/27.04    (14)  all_50_1 = all_4_1
% 175.59/27.04    (15)  op(all_6_1, all_6_2) = e1
% 175.59/27.04    (16)   ~ (all_52_25 = all_52_29)
% 175.59/27.04    (17)  all_56_15 = all_6_2
% 175.59/27.04    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.04    (19)  op(all_14_1, all_14_2) = all_14_0
% 175.59/27.04    (20)  all_58_3 = all_10_2
% 175.59/27.04    (21)  all_56_9 = all_52_19
% 175.59/27.04    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.05    (23)  all_58_15 = all_6_2
% 175.59/27.05    (24)   ~ (all_52_9 = all_4_2)
% 175.59/27.05    (25)   ~ (all_52_5 = all_52_7)
% 175.59/27.05    (26)  all_58_10 = all_52_15
% 175.59/27.05    (27)   ~ (all_52_5 = all_4_2)
% 175.59/27.05    (28)  all_58_7 = all_52_19
% 175.59/27.05    (29)   ~ (all_52_17 = all_52_25)
% 175.59/27.05    (30)  all_58_4 = all_52_5
% 175.59/27.05    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.05    (32)   ~ (all_52_17 = all_14_2)
% 175.59/27.05    (33)  op(e3, all_4_2) = all_4_1
% 175.59/27.05    (34)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.05    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.05    (36)   ~ (all_52_7 = all_4_2)
% 175.59/27.05    (37)  all_58_1 = all_52_3
% 175.59/27.05    (38)  all_58_0 = all_4_2
% 175.59/27.05    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.05    (40)  op(e1, all_52_29) = all_52_28
% 175.59/27.05    (41)  all_50_2 = all_4_2
% 175.59/27.05    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.05    (43)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.59/27.05    (44)   ~ (all_4_1 = e2)
% 175.59/27.05    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.05    (46)  all_58_14 = all_52_29
% 175.59/27.05    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.05    (48)   ~ (all_52_3 = all_52_5)
% 175.59/27.05    (49)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.05    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.05    (51)  all_58_8 = all_14_2
% 175.59/27.05    (52)  all_56_1 = all_52_3
% 175.59/27.05    (53)   ~ (all_14_0 = e3)
% 175.59/27.05    (54)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.59/27.05    (55)   ~ (all_52_5 = all_14_2)
% 175.59/27.05    (56)   ~ (all_52_3 = all_52_27)
% 175.59/27.05    (57)   ~ (all_52_3 = all_4_2)
% 175.59/27.05    (58)  op(e0, e3) = all_52_25
% 175.59/27.05    (59)  op(e0, all_6_2) = all_6_1
% 175.59/27.05    (60)  op(all_4_1, all_4_2) = e2
% 175.59/27.05    (61)  op(e3, all_52_17) = all_52_16
% 175.59/27.05    (62)   ~ (e3 = e0)
% 175.59/27.05    (63)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.05    (64)  op(e0, all_52_23) = all_52_22
% 175.59/27.05    (65)   ~ (all_52_15 = all_52_23)
% 175.59/27.05    (66)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.05    (67)   ~ (all_52_5 = all_52_29)
% 175.59/27.05    (68)  all_56_2 = all_52_5
% 175.59/27.05    (69)  op(e1, e0) = all_52_23
% 175.59/27.05    (70)  all_58_13 = all_52_27
% 175.59/27.05    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.05    (72)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.05    (73)   ~ (all_52_9 = all_52_17)
% 175.59/27.05    (74)   ~ (all_14_0 = e2)
% 175.59/27.05    (75)  all_58_6 = all_52_17
% 175.59/27.05    (76)   ~ (all_52_3 = all_52_7)
% 175.59/27.05    (77)  op(e2, all_52_19) = all_52_18
% 175.59/27.05    (78)   ~ (e1 = e0)
% 175.59/27.05    (79)  all_56_0 = all_4_2
% 175.59/27.05    (80)  all_58_11 = all_52_23
% 175.59/27.05    (81)   ~ (all_52_3 = all_52_19)
% 175.59/27.05    (82)   ~ (all_52_7 = all_52_15)
% 175.59/27.05    (83)   ~ (all_52_29 = all_14_2)
% 175.59/27.05    (84)   ~ (all_52_23 = all_6_2)
% 175.59/27.05    (85)  all_58_2 = all_52_9
% 175.59/27.05    (86)  op(e3, e1) = all_52_5
% 175.59/27.05    (87)  all_56_10 = all_14_2
% 175.59/27.05    (88)   ~ (all_52_25 = all_6_2)
% 175.59/27.05    (89)  op(e1, e3) = all_52_17
% 175.59/27.05    (90)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.05    (91)   ~ (all_52_25 = all_4_2)
% 175.59/27.05    (92)  op(e3, e0) = all_52_7
% 175.59/27.05    (93)  op(e3, e3) = all_4_2
% 175.59/27.05    (94)  all_56_8 = all_52_17
% 175.59/27.05    (95)   ~ (all_52_17 = all_4_2)
% 175.59/27.05    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.05    (97)   ~ (all_52_25 = all_52_27)
% 175.59/27.05    (98)   ~ (all_52_27 = all_6_2)
% 175.59/27.05    (99)   ~ (all_52_15 = all_10_2)
% 175.59/27.05    (100)  all_56_7 = all_52_15
% 175.59/27.05    (101)   ~ (all_52_7 = all_52_23)
% 175.59/27.05    (102)  op(e2, all_52_27) = all_52_26
% 175.59/27.05    (103)  all_52_20 = all_14_1
% 175.59/27.05    (104)   ~ (all_52_17 = all_52_19)
% 175.59/27.05    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.05    (106)  all_52_30 = all_6_1
% 175.59/27.05    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.59/27.05    (108)  op(e1, all_14_2) = all_14_1
% 175.59/27.05    (109)  all_58_9 = all_52_7
% 175.59/27.05    (110)   ~ (e2 = e0)
% 175.59/27.05    (111)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.05           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.05    (112)  all_58_12 = all_52_25
% 175.59/27.05    (113)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.05    (114)   ~ (all_52_9 = all_52_15)
% 175.59/27.05    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.05    (116)   ~ (e3 = e2)
% 175.59/27.05    (117)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.05    (118)   ~ (all_52_19 = all_14_2)
% 175.59/27.05    (119)  op(e2, e3) = all_52_9
% 175.59/27.05    (120)  all_56_13 = all_52_27
% 175.59/27.05  
% 175.59/27.05  Begin of proof
% 175.59/27.05  | 
% 175.59/27.05  | BETA: splitting (111) gives:
% 175.59/27.05  | 
% 175.59/27.05  | Case 1:
% 175.59/27.05  | | 
% 175.59/27.05  | |   (121)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.05  | | 
% 175.59/27.05  | | ALPHA: (121) implies:
% 175.59/27.05  | |   (122)  all_52_22 = e0
% 175.59/27.05  | |   (123)  all_52_20 = e1
% 175.59/27.05  | |   (124)  all_52_18 = e2
% 175.59/27.05  | |   (125)  all_52_16 = e3
% 175.59/27.05  | | 
% 175.59/27.05  | | COMBINE_EQS: (103), (123) imply:
% 175.59/27.05  | |   (126)  all_14_1 = e1
% 175.59/27.05  | | 
% 175.59/27.05  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.59/27.05  | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.59/27.05  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.59/27.05  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.59/27.05  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 175.59/27.05  | |            (58), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 175.59/27.05  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 175.59/27.05  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 175.59/27.05  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 175.59/27.05  | |            (102), (104), (105), (107), (108), (109), (110), (112), (113),
% 175.59/27.05  | |            (114), (115), (116), (117), (118), (119), (120), (122), (124),
% 175.59/27.05  | |            (125), (126) are inconsistent by sub-proof #454.
% 175.59/27.05  | | 
% 175.59/27.05  | Case 2:
% 175.59/27.05  | | 
% 175.59/27.05  | |   (127)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.05  | | 
% 175.59/27.05  | | REF_CLOSE: (15), (59), (78), (96), (106), (127) are inconsistent by
% 175.59/27.05  | |            sub-proof #138.
% 175.59/27.05  | | 
% 175.59/27.05  | End of split
% 175.59/27.05  | 
% 175.59/27.05  End of proof
% 175.59/27.05  
% 175.59/27.05  Sub-proof #134 shows that the following formulas are inconsistent:
% 175.59/27.05  ----------------------------------------------------------------
% 175.59/27.05    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.05    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.05    (3)   ~ (all_52_17 = all_52_23)
% 175.59/27.05    (4)  op(e2, all_10_2) = all_10_1
% 175.59/27.05    (5)   ~ (all_52_13 = all_52_29)
% 175.59/27.05    (6)  op(all_10_1, all_10_2) = e1
% 175.59/27.05    (7)  op(e3, e2) = all_52_3
% 175.59/27.05    (8)   ~ (all_52_9 = all_52_25)
% 175.59/27.05    (9)   ~ (all_52_19 = all_52_23)
% 175.59/27.05    (10)  all_56_11 = all_52_23
% 175.59/27.05    (11)  op(e1, e2) = all_52_19
% 175.59/27.05    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.59/27.05    (13)  op(all_6_1, all_6_2) = e1
% 175.59/27.05    (14)   ~ (all_52_3 = all_10_2)
% 175.59/27.05    (15)  all_58_5 = all_52_13
% 175.59/27.05    (16)   ~ (all_6_2 = e0)
% 175.59/27.05    (17)   ~ (all_52_25 = all_52_29)
% 175.59/27.05    (18)  all_56_15 = all_6_2
% 175.59/27.05    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.05    (20)  op(e2, e0) = all_52_15
% 175.59/27.05    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.59/27.05    (22)  all_58_3 = all_10_2
% 175.59/27.05    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.05    (24)  all_58_15 = all_6_2
% 175.59/27.05    (25)   ~ (all_52_9 = all_4_2)
% 175.59/27.05    (26)   ~ (all_52_5 = all_52_7)
% 175.59/27.05    (27)  all_58_10 = all_52_15
% 175.59/27.05    (28)   ~ (all_52_5 = all_4_2)
% 175.59/27.05    (29)  all_58_7 = all_52_19
% 175.59/27.05    (30)  all_56_4 = all_52_9
% 175.59/27.05    (31)   ~ (all_52_15 = all_6_2)
% 175.59/27.05    (32)   ~ (all_52_17 = all_52_25)
% 175.59/27.05    (33)  op(e0, e1) = all_52_29
% 175.59/27.05    (34)   ~ (all_4_0 = e2)
% 175.59/27.05    (35)  all_58_4 = all_52_5
% 175.59/27.05    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.05    (37)   ~ (all_52_27 = all_52_29)
% 175.59/27.05    (38)  op(e3, all_4_2) = all_4_1
% 175.59/27.05    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.05    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.05    (41)   ~ (all_52_7 = all_4_2)
% 175.59/27.05    (42)  all_58_1 = all_52_3
% 175.59/27.05    (43)   ~ (all_52_13 = all_52_15)
% 175.59/27.05    (44)  all_58_0 = all_4_2
% 175.59/27.05    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.05    (46)  op(e1, all_52_29) = all_52_28
% 175.59/27.05    (47)  op(e1, all_52_5) = all_52_4
% 175.59/27.05    (48)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.59/27.05          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.59/27.05    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.05    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.59/27.05    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.05    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.05    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.05    (54)  all_58_14 = all_52_29
% 175.59/27.05    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.05    (56)   ~ (all_52_3 = all_52_5)
% 175.59/27.05    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.05    (58)  op(e2, e1) = all_52_13
% 175.59/27.05    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.05    (60)  all_58_8 = all_14_2
% 175.59/27.05    (61)  all_56_1 = all_52_3
% 175.59/27.05    (62)  all_56_14 = all_52_29
% 175.59/27.05    (63)  op(all_4_1, all_4_2) = all_4_0
% 175.59/27.05    (64)   ~ (all_52_5 = all_14_2)
% 175.59/27.05    (65)   ~ (all_52_3 = all_52_27)
% 175.59/27.05    (66)   ~ (all_52_3 = all_4_2)
% 175.59/27.05    (67)  all_38_2 = all_6_2
% 175.59/27.05    (68)  op(e0, e3) = all_52_25
% 175.59/27.05    (69)  op(e0, all_6_2) = all_6_1
% 175.59/27.05    (70)  all_52_0 = all_4_1
% 175.59/27.05    (71)  all_52_10 = all_10_1
% 175.59/27.05    (72)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.59/27.05    (73)   ~ (all_52_13 = all_14_2)
% 175.59/27.05    (74)   ~ (e3 = e0)
% 175.59/27.05    (75)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.05    (76)   ~ (all_52_9 = all_52_13)
% 175.59/27.05    (77)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.05    (78)  op(e0, all_52_23) = all_52_22
% 175.59/27.05    (79)   ~ (all_52_15 = all_52_23)
% 175.59/27.05    (80)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.05    (81)   ~ (all_52_5 = all_52_29)
% 175.59/27.05    (82)  all_56_2 = all_52_5
% 175.59/27.05    (83)  op(e1, e0) = all_52_23
% 175.59/27.05    (84)  all_56_12 = all_52_25
% 175.59/27.05    (85)  all_58_13 = all_52_27
% 175.59/27.05    (86)  op(e2, all_52_3) = all_52_2
% 175.59/27.05    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.05    (88)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.05    (89)   ~ (all_52_9 = all_52_17)
% 175.59/27.05    (90)  all_58_6 = all_52_17
% 175.59/27.05    (91)   ~ (all_52_3 = all_52_7)
% 175.59/27.05    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.59/27.05    (93)   ~ (e1 = e0)
% 175.59/27.05    (94)  all_56_0 = all_4_2
% 175.59/27.05    (95)  all_58_11 = all_52_23
% 175.59/27.05    (96)   ~ (all_52_3 = all_52_19)
% 175.59/27.05    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.05    (98)   ~ (all_52_7 = all_52_15)
% 175.59/27.05    (99)  op(e0, all_52_15) = all_52_14
% 175.59/27.05    (100)   ~ (all_52_29 = all_14_2)
% 175.59/27.05    (101)   ~ (all_4_0 = e1)
% 175.59/27.05    (102)   ~ (all_52_23 = all_6_2)
% 175.59/27.05    (103)   ~ (all_52_29 = all_6_2)
% 175.59/27.05    (104)  all_58_2 = all_52_9
% 175.59/27.05    (105)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.59/27.05    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.59/27.05    (107)  op(e3, e1) = all_52_5
% 175.59/27.05    (108)   ~ (e2 = e1)
% 175.59/27.05    (109)  all_56_10 = all_14_2
% 175.59/27.05    (110)   ~ (all_52_25 = all_6_2)
% 175.59/27.05    (111)  op(e1, e1) = all_14_2
% 175.59/27.05    (112)  op(e1, e3) = all_52_17
% 175.59/27.05    (113)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.05    (114)   ~ (all_52_25 = all_4_2)
% 175.59/27.05    (115)  op(e3, e0) = all_52_7
% 175.59/27.05    (116)   ~ (all_52_17 = all_4_2)
% 175.59/27.05    (117)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.05             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.05    (118)   ~ (all_52_25 = all_52_27)
% 175.59/27.05    (119)   ~ (all_52_27 = all_6_2)
% 175.59/27.05    (120)   ~ (all_52_7 = all_6_2)
% 175.59/27.05    (121)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.05    (122)  all_38_1 = all_6_1
% 175.59/27.05    (123)   ~ (all_52_19 = all_52_27)
% 175.59/27.05    (124)  all_56_7 = all_52_15
% 175.59/27.05    (125)   ~ (all_52_7 = all_52_23)
% 175.59/27.05    (126)   ~ (all_52_13 = all_10_2)
% 175.59/27.05    (127)  op(e2, all_52_27) = all_52_26
% 175.59/27.05    (128)   ~ (all_52_17 = all_52_19)
% 175.59/27.05    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.05    (130)  all_58_9 = all_52_7
% 175.59/27.05    (131)  all_58_12 = all_52_25
% 175.59/27.05    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.05    (133)   ~ (all_52_9 = all_52_15)
% 175.59/27.05    (134)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.05    (135)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.05    (136)   ~ (all_52_19 = all_14_2)
% 175.59/27.05    (137)  op(e0, all_52_7) = all_52_6
% 175.59/27.05    (138)  op(e2, e3) = all_52_9
% 175.59/27.05    (139)  all_56_13 = all_52_27
% 175.59/27.05  
% 175.59/27.05  Begin of proof
% 175.59/27.05  | 
% 175.59/27.05  | BETA: splitting (48) gives:
% 175.59/27.05  | 
% 175.59/27.05  | Case 1:
% 175.59/27.05  | | 
% 175.59/27.05  | |   (140)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.59/27.05  | | 
% 175.59/27.05  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 175.59/27.05  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 175.59/27.05  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 175.59/27.05  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 175.59/27.05  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 175.59/27.05  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 175.59/27.05  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 175.59/27.05  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 175.59/27.05  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 175.59/27.05  | |            (104), (105), (106), (107), (109), (110), (111), (112), (113),
% 175.59/27.05  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 175.59/27.05  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 175.59/27.05  | |            (132), (133), (134), (135), (136), (137), (138), (139), (140) are
% 175.59/27.05  | |            inconsistent by sub-proof #140.
% 175.59/27.05  | | 
% 175.59/27.05  | Case 2:
% 175.59/27.05  | | 
% 175.59/27.05  | |   (141)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.59/27.05  | | 
% 175.59/27.05  | | ALPHA: (141) implies:
% 175.59/27.05  | |   (142)  all_52_10 = e2
% 175.59/27.05  | | 
% 175.59/27.05  | | COMBINE_EQS: (71), (142) imply:
% 175.59/27.05  | |   (143)  all_10_1 = e2
% 175.59/27.05  | | 
% 175.59/27.05  | | REF_CLOSE: (4), (6), (108), (117), (143) are inconsistent by sub-proof #446.
% 175.59/27.05  | | 
% 175.59/27.05  | End of split
% 175.59/27.05  | 
% 175.59/27.05  End of proof
% 175.59/27.05  
% 175.59/27.05  Sub-proof #135 shows that the following formulas are inconsistent:
% 175.59/27.05  ----------------------------------------------------------------
% 175.59/27.05    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.05    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.59/27.05    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.59/27.05    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.59/27.05    (5)   ~ (all_52_17 = all_52_23)
% 175.59/27.05    (6)  all_56_3 = all_52_7
% 175.59/27.05    (7)  op(e3, e2) = all_52_3
% 175.59/27.05    (8)   ~ (all_52_9 = all_52_25)
% 175.59/27.05    (9)  op(e3, all_52_25) = all_52_24
% 175.59/27.05    (10)   ~ (all_52_19 = all_52_23)
% 175.59/27.05    (11)  op(e1, e2) = all_52_19
% 175.59/27.05    (12)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.59/27.05    (13)  op(e3, all_52_9) = all_52_8
% 175.59/27.05    (14)  all_50_1 = all_4_1
% 175.59/27.05    (15)  op(all_6_1, all_6_2) = e1
% 175.59/27.05    (16)   ~ (all_52_25 = all_52_29)
% 175.59/27.05    (17)  all_56_15 = all_6_2
% 175.59/27.05    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.05    (19)  op(all_14_1, all_14_2) = all_14_0
% 175.59/27.05    (20)  all_58_3 = all_10_2
% 175.59/27.05    (21)  all_56_9 = all_52_19
% 175.59/27.05    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.05    (23)  all_58_15 = all_6_2
% 175.59/27.05    (24)   ~ (all_52_9 = all_4_2)
% 175.59/27.05    (25)   ~ (all_52_5 = all_52_7)
% 175.59/27.05    (26)  all_58_10 = all_52_15
% 175.59/27.05    (27)   ~ (all_52_5 = all_4_2)
% 175.59/27.05    (28)  all_58_7 = all_52_19
% 175.59/27.05    (29)   ~ (all_52_17 = all_52_25)
% 175.59/27.05    (30)  all_58_4 = all_52_5
% 175.59/27.05    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.05    (32)   ~ (all_52_17 = all_14_2)
% 175.59/27.05    (33)  op(e3, all_4_2) = all_4_1
% 175.59/27.05    (34)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.05    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.05    (36)   ~ (all_52_7 = all_4_2)
% 175.59/27.05    (37)  all_58_1 = all_52_3
% 175.59/27.05    (38)  all_58_0 = all_4_2
% 175.59/27.05    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.05    (40)  op(e1, all_52_29) = all_52_28
% 175.59/27.05    (41)  all_50_2 = all_4_2
% 175.59/27.05    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.05    (43)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.59/27.05    (44)   ~ (all_4_1 = e2)
% 175.59/27.05    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.05    (46)  all_58_14 = all_52_29
% 175.59/27.05    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.05    (48)   ~ (all_52_3 = all_52_5)
% 175.59/27.05    (49)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.05    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.05    (51)  all_58_8 = all_14_2
% 175.59/27.05    (52)  all_56_1 = all_52_3
% 175.59/27.05    (53)   ~ (all_14_0 = e3)
% 175.59/27.05    (54)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.59/27.05    (55)   ~ (all_52_5 = all_14_2)
% 175.59/27.05    (56)   ~ (all_52_3 = all_52_27)
% 175.59/27.05    (57)   ~ (all_52_3 = all_4_2)
% 175.59/27.05    (58)  op(e0, e3) = all_52_25
% 175.59/27.05    (59)  op(e0, all_6_2) = all_6_1
% 175.59/27.05    (60)  op(all_4_1, all_4_2) = e2
% 175.59/27.05    (61)  op(e3, all_52_17) = all_52_16
% 175.59/27.05    (62)   ~ (e3 = e0)
% 175.59/27.05    (63)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.05    (64)  op(e0, all_52_23) = all_52_22
% 175.59/27.05    (65)   ~ (all_52_15 = all_52_23)
% 175.59/27.05    (66)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.05    (67)   ~ (all_52_5 = all_52_29)
% 175.59/27.05    (68)  all_56_2 = all_52_5
% 175.59/27.05    (69)  op(e1, e0) = all_52_23
% 175.59/27.05    (70)  all_58_13 = all_52_27
% 175.59/27.05    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.05    (72)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.05    (73)   ~ (all_52_9 = all_52_17)
% 175.59/27.05    (74)   ~ (all_14_0 = e2)
% 175.59/27.05    (75)  all_58_6 = all_52_17
% 175.59/27.05    (76)   ~ (all_52_3 = all_52_7)
% 175.59/27.05    (77)  op(e2, all_52_19) = all_52_18
% 175.59/27.05    (78)   ~ (e1 = e0)
% 175.59/27.05    (79)  all_56_0 = all_4_2
% 175.59/27.05    (80)  all_58_11 = all_52_23
% 175.59/27.05    (81)   ~ (all_52_3 = all_52_19)
% 175.59/27.05    (82)   ~ (all_52_7 = all_52_15)
% 175.59/27.05    (83)   ~ (all_52_29 = all_14_2)
% 175.59/27.05    (84)   ~ (all_52_23 = all_6_2)
% 175.59/27.05    (85)  all_58_2 = all_52_9
% 175.59/27.05    (86)  op(e3, e1) = all_52_5
% 175.59/27.05    (87)  all_56_10 = all_14_2
% 175.59/27.05    (88)   ~ (all_52_25 = all_6_2)
% 175.59/27.05    (89)  op(e1, e3) = all_52_17
% 175.59/27.05    (90)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.05    (91)   ~ (all_52_25 = all_4_2)
% 175.59/27.05    (92)  op(e3, e0) = all_52_7
% 175.59/27.05    (93)  op(e3, e3) = all_4_2
% 175.59/27.05    (94)  all_56_8 = all_52_17
% 175.59/27.05    (95)   ~ (all_52_17 = all_4_2)
% 175.59/27.05    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.05    (97)   ~ (all_52_25 = all_52_27)
% 175.59/27.05    (98)   ~ (all_52_27 = all_6_2)
% 175.59/27.05    (99)   ~ (all_52_15 = all_10_2)
% 175.59/27.05    (100)  all_56_7 = all_52_15
% 175.59/27.05    (101)   ~ (all_52_7 = all_52_23)
% 175.59/27.05    (102)  op(e2, all_52_27) = all_52_26
% 175.59/27.05    (103)  all_52_20 = all_14_1
% 175.59/27.05    (104)   ~ (all_52_17 = all_52_19)
% 175.59/27.05    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.05    (106)  all_52_30 = all_6_1
% 175.59/27.05    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.59/27.05    (108)  op(e1, all_14_2) = all_14_1
% 175.59/27.05    (109)  all_58_9 = all_52_7
% 175.59/27.05    (110)   ~ (e2 = e0)
% 175.59/27.05    (111)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.05           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.05    (112)  all_58_12 = all_52_25
% 175.59/27.05    (113)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.05    (114)   ~ (all_52_9 = all_52_15)
% 175.59/27.05    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.05    (116)   ~ (e3 = e2)
% 175.59/27.05    (117)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.05    (118)   ~ (all_52_19 = all_14_2)
% 175.59/27.05    (119)  op(e2, e3) = all_52_9
% 175.59/27.05    (120)  all_56_13 = all_52_27
% 175.59/27.05  
% 175.59/27.05  Begin of proof
% 175.59/27.05  | 
% 175.59/27.05  | BETA: splitting (111) gives:
% 175.59/27.05  | 
% 175.59/27.05  | Case 1:
% 175.59/27.05  | | 
% 175.59/27.05  | |   (121)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.05  | | 
% 175.59/27.05  | | ALPHA: (121) implies:
% 175.59/27.05  | |   (122)  all_52_22 = e0
% 175.59/27.05  | |   (123)  all_52_20 = e1
% 175.59/27.05  | |   (124)  all_52_18 = e2
% 175.59/27.05  | |   (125)  all_52_16 = e3
% 175.59/27.05  | | 
% 175.59/27.05  | | COMBINE_EQS: (103), (123) imply:
% 175.59/27.05  | |   (126)  all_14_1 = e1
% 175.59/27.05  | | 
% 175.59/27.05  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.59/27.05  | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.59/27.05  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.59/27.05  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.59/27.05  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 175.59/27.06  | |            (58), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 175.59/27.06  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 175.59/27.06  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 175.59/27.06  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 175.59/27.06  | |            (102), (104), (105), (107), (108), (109), (110), (112), (113),
% 175.59/27.06  | |            (114), (115), (116), (117), (118), (119), (120), (122), (124),
% 175.59/27.06  | |            (125), (126) are inconsistent by sub-proof #454.
% 175.59/27.06  | | 
% 175.59/27.06  | Case 2:
% 175.59/27.06  | | 
% 175.59/27.06  | |   (127)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | ALPHA: (127) implies:
% 175.59/27.06  | |   (128)  all_52_30 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | COMBINE_EQS: (106), (128) imply:
% 175.59/27.06  | |   (129)  all_6_1 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | REF_CLOSE: (15), (59), (78), (96), (129) are inconsistent by sub-proof #139.
% 175.59/27.06  | | 
% 175.59/27.06  | End of split
% 175.59/27.06  | 
% 175.59/27.06  End of proof
% 175.59/27.06  
% 175.59/27.06  Sub-proof #136 shows that the following formulas are inconsistent:
% 175.59/27.06  ----------------------------------------------------------------
% 175.59/27.06    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.06    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.06    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.59/27.06    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.59/27.06    (5)   ~ (all_52_17 = all_52_23)
% 175.59/27.06    (6)  op(e2, all_10_2) = all_10_1
% 175.59/27.06    (7)  op(e3, e2) = all_52_3
% 175.59/27.06    (8)   ~ (all_52_9 = all_52_25)
% 175.59/27.06    (9)  op(e3, all_52_25) = all_52_24
% 175.59/27.06    (10)   ~ (all_52_19 = all_52_23)
% 175.59/27.06    (11)  op(e1, e2) = all_52_19
% 175.59/27.06    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.59/27.06    (13)  op(all_6_1, all_6_2) = e1
% 175.59/27.06    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.59/27.06    (15)  all_58_5 = all_52_13
% 175.59/27.06    (16)   ~ (all_52_25 = all_52_29)
% 175.59/27.06    (17)  all_56_15 = all_6_2
% 175.59/27.06    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.06    (19)  op(e2, e0) = all_52_15
% 175.59/27.06    (20)  op(all_14_1, all_14_2) = all_14_0
% 175.59/27.06    (21)  all_58_3 = all_10_2
% 175.59/27.06    (22)  all_56_9 = all_52_19
% 175.59/27.06    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.06    (24)  all_58_15 = all_6_2
% 175.59/27.06    (25)   ~ (all_52_9 = all_4_2)
% 175.59/27.06    (26)   ~ (all_52_5 = all_52_7)
% 175.59/27.06    (27)  all_58_10 = all_52_15
% 175.59/27.06    (28)   ~ (all_52_5 = all_4_2)
% 175.59/27.06    (29)  all_58_7 = all_52_19
% 175.59/27.06    (30)   ~ (all_52_17 = all_52_25)
% 175.59/27.06    (31)  all_58_4 = all_52_5
% 175.59/27.06    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.06    (33)  all_34_1 = all_4_1
% 175.59/27.06    (34)   ~ (all_52_27 = all_52_29)
% 175.59/27.06    (35)   ~ (all_52_17 = all_14_2)
% 175.59/27.06    (36)  op(e3, all_4_2) = all_4_1
% 175.59/27.06    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.06    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.06    (39)   ~ (all_52_7 = all_4_2)
% 175.59/27.06    (40)  all_58_1 = all_52_3
% 175.59/27.06    (41)  all_58_0 = all_4_2
% 175.59/27.06    (42)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.06    (43)  op(all_4_1, all_4_2) = e1
% 175.59/27.06    (44)  op(e1, all_52_29) = all_52_28
% 175.59/27.06    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.06    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.59/27.06    (47)   ~ (all_4_1 = e2)
% 175.59/27.06    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.06    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.06    (50)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.59/27.06    (51)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.06    (52)  all_58_14 = all_52_29
% 175.59/27.06    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.06    (54)   ~ (all_52_3 = all_52_5)
% 175.59/27.06    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.06    (56)  op(e2, e1) = all_52_13
% 175.59/27.06    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.06    (58)  all_58_8 = all_14_2
% 175.59/27.06    (59)  all_56_1 = all_52_3
% 175.59/27.06    (60)   ~ (all_14_0 = e3)
% 175.59/27.06    (61)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.59/27.06    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.59/27.06    (63)   ~ (all_52_5 = all_14_2)
% 175.59/27.06    (64)   ~ (all_52_3 = all_4_2)
% 175.59/27.06    (65)  op(e0, e3) = all_52_25
% 175.59/27.06    (66)  op(e0, all_6_2) = all_6_1
% 175.59/27.06    (67)   ~ (all_52_9 = all_10_2)
% 175.59/27.06    (68)  op(e3, all_52_17) = all_52_16
% 175.59/27.06    (69)   ~ (all_52_13 = all_14_2)
% 175.59/27.06    (70)   ~ (e3 = e0)
% 175.59/27.06    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.06    (72)   ~ (all_52_9 = all_52_13)
% 175.59/27.06    (73)  op(e0, all_52_23) = all_52_22
% 175.59/27.06    (74)   ~ (all_52_15 = all_52_23)
% 175.59/27.06    (75)   ~ (all_52_5 = all_52_29)
% 175.59/27.06    (76)  all_58_13 = all_52_27
% 175.59/27.06    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.06    (78)  all_56_5 = all_10_2
% 175.59/27.06    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.06    (80)   ~ (all_52_9 = all_52_17)
% 175.59/27.06    (81)   ~ (all_14_0 = e2)
% 175.59/27.06    (82)  all_58_6 = all_52_17
% 175.59/27.06    (83)  op(e2, all_52_19) = all_52_18
% 175.59/27.06    (84)   ~ (e1 = e0)
% 175.59/27.06    (85)  all_56_0 = all_4_2
% 175.59/27.06    (86)  all_58_11 = all_52_23
% 175.59/27.06    (87)   ~ (all_52_3 = all_52_19)
% 175.59/27.06    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.06    (89)   ~ (all_52_7 = all_52_15)
% 175.59/27.06    (90)   ~ (all_52_29 = all_14_2)
% 175.59/27.06    (91)   ~ (all_52_19 = all_10_2)
% 175.59/27.06    (92)   ~ (all_52_23 = all_6_2)
% 175.59/27.06    (93)  all_58_2 = all_52_9
% 175.59/27.06    (94)  op(e3, e1) = all_52_5
% 175.59/27.06    (95)   ~ (all_52_25 = all_6_2)
% 175.59/27.06    (96)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.59/27.06    (97)  op(e1, e3) = all_52_17
% 175.59/27.06    (98)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.06    (99)   ~ (all_52_25 = all_4_2)
% 175.59/27.06    (100)  op(e3, e0) = all_52_7
% 175.59/27.06    (101)  op(e3, e3) = all_4_2
% 175.59/27.06    (102)   ~ (all_10_1 = e3)
% 175.59/27.06    (103)  all_56_8 = all_52_17
% 175.59/27.06    (104)   ~ (all_52_17 = all_4_2)
% 175.59/27.06    (105)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.06             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.06    (106)   ~ (all_52_25 = all_52_27)
% 175.59/27.06    (107)  all_34_2 = all_4_2
% 175.59/27.06    (108)   ~ (all_52_27 = all_6_2)
% 175.59/27.06    (109)   ~ (all_52_7 = all_6_2)
% 175.59/27.06    (110)   ~ (all_52_15 = all_10_2)
% 175.59/27.06    (111)   ~ (all_52_19 = all_52_27)
% 175.59/27.06    (112)  all_56_7 = all_52_15
% 175.59/27.06    (113)   ~ (all_52_7 = all_52_23)
% 175.59/27.06    (114)   ~ (all_52_13 = all_10_2)
% 175.59/27.06    (115)  op(e2, all_52_27) = all_52_26
% 175.59/27.06    (116)  all_52_20 = all_14_1
% 175.59/27.06    (117)   ~ (all_52_17 = all_52_19)
% 175.59/27.06    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.06    (119)  all_52_30 = all_6_1
% 175.59/27.06    (120)  op(e1, all_14_2) = all_14_1
% 175.59/27.06    (121)  all_58_9 = all_52_7
% 175.59/27.06    (122)   ~ (e2 = e0)
% 175.59/27.06    (123)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.06           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.06    (124)  all_58_12 = all_52_25
% 175.59/27.06    (125)  all_56_6 = all_52_13
% 175.59/27.06    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.06    (127)   ~ (all_52_9 = all_52_15)
% 175.59/27.06    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.06    (129)   ~ (e3 = e2)
% 175.59/27.06    (130)   ~ (all_52_19 = all_14_2)
% 175.59/27.06    (131)  op(e2, e3) = all_52_9
% 175.59/27.06    (132)  all_56_13 = all_52_27
% 175.59/27.06  
% 175.59/27.06  Begin of proof
% 175.59/27.06  | 
% 175.59/27.06  | BETA: splitting (123) gives:
% 175.59/27.06  | 
% 175.59/27.06  | Case 1:
% 175.59/27.06  | | 
% 175.59/27.06  | |   (133)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | ALPHA: (133) implies:
% 175.59/27.06  | |   (134)  all_52_22 = e0
% 175.59/27.06  | |   (135)  all_52_20 = e1
% 175.59/27.06  | |   (136)  all_52_18 = e2
% 175.59/27.06  | |   (137)  all_52_16 = e3
% 175.59/27.06  | | 
% 175.59/27.06  | | COMBINE_EQS: (116), (135) imply:
% 175.59/27.06  | |   (138)  all_14_1 = e1
% 175.59/27.06  | | 
% 175.59/27.06  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.59/27.06  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.59/27.06  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.59/27.06  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.59/27.06  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 175.59/27.06  | |            (58), (59), (60), (61), (62), (63), (64), (65), (67), (68), (69),
% 175.59/27.06  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 175.59/27.06  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 175.59/27.06  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 175.59/27.06  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 175.59/27.06  | |            (111), (112), (113), (114), (115), (117), (118), (120), (121),
% 175.59/27.06  | |            (122), (124), (125), (126), (127), (128), (129), (130), (131),
% 175.59/27.06  | |            (132), (134), (136), (137), (138) are inconsistent by sub-proof
% 175.59/27.06  | |            #560.
% 175.59/27.06  | | 
% 175.59/27.06  | Case 2:
% 175.59/27.06  | | 
% 175.59/27.06  | |   (139)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | ALPHA: (139) implies:
% 175.59/27.06  | |   (140)  all_52_30 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | COMBINE_EQS: (119), (140) imply:
% 175.59/27.06  | |   (141)  all_6_1 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | REF_CLOSE: (13), (66), (84), (105), (141) are inconsistent by sub-proof
% 175.59/27.06  | |            #139.
% 175.59/27.06  | | 
% 175.59/27.06  | End of split
% 175.59/27.06  | 
% 175.59/27.06  End of proof
% 175.59/27.06  
% 175.59/27.06  Sub-proof #137 shows that the following formulas are inconsistent:
% 175.59/27.06  ----------------------------------------------------------------
% 175.59/27.06    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.06    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.06    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.59/27.06    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.59/27.06    (5)   ~ (all_52_27 = all_10_2)
% 175.59/27.06    (6)   ~ (all_52_17 = all_52_23)
% 175.59/27.06    (7)  op(e2, all_10_2) = all_10_1
% 175.59/27.06    (8)   ~ (all_52_13 = all_52_29)
% 175.59/27.06    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.59/27.06    (10)  op(e3, e2) = all_52_3
% 175.59/27.06    (11)   ~ (all_52_9 = all_52_25)
% 175.59/27.06    (12)  op(e3, all_52_25) = all_52_24
% 175.59/27.06    (13)   ~ (all_52_19 = all_52_23)
% 175.59/27.06    (14)  op(e1, e2) = all_52_19
% 175.59/27.06    (15)  op(e3, all_52_9) = all_52_8
% 175.59/27.06    (16)  op(all_6_1, all_6_2) = e1
% 175.59/27.06    (17)   ~ (all_52_3 = all_10_2)
% 175.59/27.06    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.59/27.06    (19)  all_58_5 = all_52_13
% 175.59/27.06    (20)   ~ (all_6_2 = e0)
% 175.59/27.06    (21)   ~ (all_52_25 = all_52_29)
% 175.59/27.06    (22)  all_56_15 = all_6_2
% 175.59/27.06    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.06    (24)  op(e2, e0) = all_52_15
% 175.59/27.06    (25)  op(all_14_1, all_14_2) = all_14_0
% 175.59/27.06    (26)  all_58_3 = all_10_2
% 175.59/27.06    (27)  all_56_9 = all_52_19
% 175.59/27.06    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.06    (29)  all_58_15 = all_6_2
% 175.59/27.06    (30)   ~ (all_52_9 = all_4_2)
% 175.59/27.06    (31)   ~ (all_52_5 = all_52_7)
% 175.59/27.06    (32)  all_58_10 = all_52_15
% 175.59/27.06    (33)   ~ (all_52_5 = all_4_2)
% 175.59/27.06    (34)  all_58_7 = all_52_19
% 175.59/27.06    (35)   ~ (all_52_17 = all_52_25)
% 175.59/27.06    (36)   ~ (all_4_0 = e2)
% 175.59/27.06    (37)  all_58_4 = all_52_5
% 175.59/27.06    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.06    (39)   ~ (all_52_27 = all_52_29)
% 175.59/27.06    (40)   ~ (all_52_17 = all_14_2)
% 175.59/27.06    (41)  op(e3, all_4_2) = all_4_1
% 175.59/27.06    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.06    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.06    (44)   ~ (all_52_7 = all_4_2)
% 175.59/27.06    (45)  all_58_1 = all_52_3
% 175.59/27.06    (46)  all_58_0 = all_4_2
% 175.59/27.06    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.06    (48)  op(e1, all_52_29) = all_52_28
% 175.59/27.06    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.06    (50)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.59/27.06    (51)   ~ (all_4_1 = e2)
% 175.59/27.06    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.06    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.06    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.59/27.06    (55)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.06    (56)  all_58_14 = all_52_29
% 175.59/27.06    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.06    (58)   ~ (all_52_3 = all_52_5)
% 175.59/27.06    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.06    (60)  op(e2, e1) = all_52_13
% 175.59/27.06    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.06    (62)  all_58_8 = all_14_2
% 175.59/27.06    (63)  all_56_1 = all_52_3
% 175.59/27.06    (64)  op(e0, e2) = all_52_27
% 175.59/27.06    (65)   ~ (all_14_0 = e3)
% 175.59/27.06    (66)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.59/27.06    (67)  op(all_4_1, all_4_2) = all_4_0
% 175.59/27.06    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.59/27.06    (69)   ~ (all_52_5 = all_14_2)
% 175.59/27.06    (70)   ~ (all_52_3 = all_52_27)
% 175.59/27.06    (71)   ~ (all_52_3 = all_4_2)
% 175.59/27.06    (72)  op(e0, e3) = all_52_25
% 175.59/27.06    (73)  op(e0, all_6_2) = all_6_1
% 175.59/27.06    (74)   ~ (all_52_9 = all_10_2)
% 175.59/27.06    (75)  op(e3, all_52_17) = all_52_16
% 175.59/27.06    (76)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 175.59/27.06    (77)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.59/27.06    (78)   ~ (all_52_13 = all_14_2)
% 175.59/27.06    (79)   ~ (e3 = e0)
% 175.59/27.06    (80)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.06    (81)   ~ (all_52_9 = all_52_13)
% 175.59/27.06    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.06    (83)  op(e0, all_52_23) = all_52_22
% 175.59/27.06    (84)   ~ (all_52_15 = all_52_23)
% 175.59/27.06    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.06    (86)   ~ (all_52_5 = all_52_29)
% 175.59/27.06    (87)  op(e1, e0) = all_52_23
% 175.59/27.06    (88)  all_56_12 = all_52_25
% 175.59/27.06    (89)  all_58_13 = all_52_27
% 175.59/27.06    (90)   ~ (all_4_1 = e1)
% 175.59/27.06    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.06    (92)  all_56_5 = all_10_2
% 175.59/27.06    (93)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.06    (94)   ~ (all_52_9 = all_52_17)
% 175.59/27.06    (95)   ~ (all_14_0 = e2)
% 175.59/27.06    (96)  all_58_6 = all_52_17
% 175.59/27.06    (97)  op(e2, all_52_19) = all_52_18
% 175.59/27.06    (98)   ~ (e1 = e0)
% 175.59/27.06    (99)  all_56_0 = all_4_2
% 175.59/27.06    (100)  all_58_11 = all_52_23
% 175.59/27.06    (101)   ~ (all_52_3 = all_52_19)
% 175.59/27.06    (102)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.06    (103)   ~ (all_52_7 = all_52_15)
% 175.59/27.06    (104)   ~ (all_52_29 = all_14_2)
% 175.59/27.06    (105)   ~ (all_4_0 = e1)
% 175.59/27.06    (106)   ~ (all_52_19 = all_10_2)
% 175.59/27.06    (107)   ~ (all_52_23 = all_6_2)
% 175.59/27.06    (108)   ~ (all_52_29 = all_6_2)
% 175.59/27.06    (109)  all_58_2 = all_52_9
% 175.59/27.06    (110)  op(e3, e1) = all_52_5
% 175.59/27.06    (111)  all_56_10 = all_14_2
% 175.59/27.06    (112)   ~ (all_52_25 = all_6_2)
% 175.59/27.06    (113)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.59/27.06    (114)  op(e1, e3) = all_52_17
% 175.59/27.06    (115)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.06    (116)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 175.59/27.06    (117)   ~ (all_52_25 = all_4_2)
% 175.59/27.06    (118)  op(e3, e0) = all_52_7
% 175.59/27.06    (119)  op(e3, e3) = all_4_2
% 175.59/27.06    (120)   ~ (all_10_1 = e3)
% 175.59/27.06    (121)  all_56_8 = all_52_17
% 175.59/27.06    (122)   ~ (all_52_17 = all_4_2)
% 175.59/27.06    (123)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.06             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.06    (124)   ~ (all_52_25 = all_52_27)
% 175.59/27.06    (125)   ~ (all_52_27 = all_6_2)
% 175.59/27.06    (126)   ~ (all_52_7 = all_6_2)
% 175.59/27.06    (127)   ~ (all_52_15 = all_10_2)
% 175.59/27.06    (128)   ~ (all_52_19 = all_52_27)
% 175.59/27.06    (129)  all_56_7 = all_52_15
% 175.59/27.06    (130)   ~ (all_52_7 = all_52_23)
% 175.59/27.06    (131)   ~ (all_52_13 = all_10_2)
% 175.59/27.06    (132)  op(e2, all_52_27) = all_52_26
% 175.59/27.06    (133)  all_52_20 = all_14_1
% 175.59/27.06    (134)   ~ (all_52_17 = all_52_19)
% 175.59/27.06    (135)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.06    (136)  all_52_30 = all_6_1
% 175.59/27.06    (137)  op(e1, all_14_2) = all_14_1
% 175.59/27.06    (138)  all_58_9 = all_52_7
% 175.59/27.06    (139)   ~ (e2 = e0)
% 175.59/27.06    (140)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.59/27.06           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.59/27.06    (141)  all_58_12 = all_52_25
% 175.59/27.06    (142)  all_56_6 = all_52_13
% 175.59/27.06    (143)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.06    (144)   ~ (all_52_9 = all_52_15)
% 175.59/27.06    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.06    (146)   ~ (e3 = e2)
% 175.59/27.06    (147)   ~ (all_52_19 = all_14_2)
% 175.59/27.06    (148)  op(e2, e3) = all_52_9
% 175.59/27.06    (149)  all_56_13 = all_52_27
% 175.59/27.06  
% 175.59/27.06  Begin of proof
% 175.59/27.06  | 
% 175.59/27.06  | BETA: splitting (140) gives:
% 175.59/27.06  | 
% 175.59/27.06  | Case 1:
% 175.59/27.06  | | 
% 175.59/27.06  | |   (150)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | ALPHA: (150) implies:
% 175.59/27.06  | |   (151)  all_52_22 = e0
% 175.59/27.06  | |   (152)  all_52_20 = e1
% 175.59/27.06  | |   (153)  all_52_18 = e2
% 175.59/27.06  | |   (154)  all_52_16 = e3
% 175.59/27.06  | | 
% 175.59/27.06  | | COMBINE_EQS: (133), (152) imply:
% 175.59/27.06  | |   (155)  all_14_1 = e1
% 175.59/27.06  | | 
% 175.59/27.06  | | SIMP: (155) implies:
% 175.59/27.06  | |   (156)  all_14_1 = e1
% 175.59/27.06  | | 
% 175.59/27.06  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.59/27.06  | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.59/27.06  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.59/27.06  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.59/27.06  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 175.59/27.06  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 175.59/27.06  | |            (69), (70), (71), (72), (74), (75), (76), (77), (78), (79), (80),
% 175.59/27.06  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 175.59/27.06  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 175.59/27.06  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 175.59/27.06  | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 175.59/27.06  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 175.59/27.06  | |            (129), (130), (131), (132), (134), (135), (137), (138), (139),
% 175.59/27.06  | |            (141), (142), (143), (144), (145), (146), (147), (148), (149),
% 175.59/27.06  | |            (151), (153), (154), (156) are inconsistent by sub-proof #666.
% 175.59/27.06  | | 
% 175.59/27.06  | Case 2:
% 175.59/27.06  | | 
% 175.59/27.06  | |   (157)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.06  | | 
% 175.59/27.06  | | REF_CLOSE: (16), (73), (98), (123), (136), (157) are inconsistent by
% 175.59/27.06  | |            sub-proof #138.
% 175.59/27.06  | | 
% 175.59/27.06  | End of split
% 175.59/27.06  | 
% 175.59/27.06  End of proof
% 175.59/27.06  
% 175.59/27.06  Sub-proof #138 shows that the following formulas are inconsistent:
% 175.59/27.06  ----------------------------------------------------------------
% 175.59/27.06    (1)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.59/27.06    (2)  op(all_6_1, all_6_2) = e1
% 175.59/27.06    (3)  op(e0, all_6_2) = all_6_1
% 175.59/27.06    (4)   ~ (e1 = e0)
% 175.59/27.06    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.06    (6)  all_52_30 = all_6_1
% 175.59/27.06  
% 175.59/27.06  Begin of proof
% 175.59/27.06  | 
% 175.59/27.06  | ALPHA: (1) implies:
% 175.59/27.06  |   (7)  all_52_30 = e0
% 175.59/27.06  | 
% 175.59/27.06  | COMBINE_EQS: (6), (7) imply:
% 175.59/27.06  |   (8)  all_6_1 = e0
% 175.59/27.06  | 
% 175.59/27.06  | SIMP: (8) implies:
% 175.59/27.06  |   (9)  all_6_1 = e0
% 175.59/27.06  | 
% 175.59/27.06  | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #139.
% 175.59/27.06  | 
% 175.59/27.06  End of proof
% 175.59/27.06  
% 175.59/27.06  Sub-proof #139 shows that the following formulas are inconsistent:
% 175.59/27.06  ----------------------------------------------------------------
% 175.59/27.06    (1)  op(all_6_1, all_6_2) = e1
% 175.59/27.06    (2)  all_6_1 = e0
% 175.59/27.06    (3)  op(e0, all_6_2) = all_6_1
% 175.59/27.06    (4)   ~ (e1 = e0)
% 175.59/27.06    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.06  
% 175.59/27.06  Begin of proof
% 175.59/27.06  | 
% 175.59/27.06  | REDUCE: (1), (2) imply:
% 175.59/27.06  |   (6)  op(e0, all_6_2) = e1
% 175.59/27.06  | 
% 175.59/27.06  | REDUCE: (2), (3) imply:
% 175.59/27.06  |   (7)  op(e0, all_6_2) = e0
% 175.59/27.06  | 
% 175.59/27.06  | GROUND_INST: instantiating (5) with e0, e1, all_6_2, e0, simplifying with (6),
% 175.59/27.06  |              (7) gives:
% 175.59/27.06  |   (8)  e1 = e0
% 175.59/27.06  | 
% 175.59/27.06  | REDUCE: (4), (8) imply:
% 175.59/27.06  |   (9)  $false
% 175.59/27.06  | 
% 175.59/27.06  | CLOSE: (9) is inconsistent.
% 175.59/27.06  | 
% 175.59/27.06  End of proof
% 175.59/27.06  
% 175.59/27.06  Sub-proof #140 shows that the following formulas are inconsistent:
% 175.59/27.06  ----------------------------------------------------------------
% 175.59/27.06    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.06    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.06    (3)   ~ (all_52_17 = all_52_23)
% 175.59/27.06    (4)   ~ (all_52_13 = all_52_29)
% 175.59/27.06    (5)  op(e3, e2) = all_52_3
% 175.59/27.06    (6)   ~ (all_52_9 = all_52_25)
% 175.59/27.06    (7)   ~ (all_52_19 = all_52_23)
% 175.59/27.06    (8)  all_56_11 = all_52_23
% 175.59/27.06    (9)  op(e1, e2) = all_52_19
% 175.59/27.06    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.59/27.06    (11)  op(all_6_1, all_6_2) = e1
% 175.59/27.06    (12)   ~ (all_52_3 = all_10_2)
% 175.59/27.06    (13)  all_58_5 = all_52_13
% 175.59/27.06    (14)   ~ (all_6_2 = e0)
% 175.59/27.06    (15)   ~ (all_52_25 = all_52_29)
% 175.59/27.06    (16)  all_56_15 = all_6_2
% 175.59/27.06    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.06    (18)  op(e2, e0) = all_52_15
% 175.59/27.06    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.59/27.06    (20)  all_58_3 = all_10_2
% 175.59/27.06    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.06    (22)  all_58_15 = all_6_2
% 175.59/27.06    (23)   ~ (all_52_9 = all_4_2)
% 175.59/27.06    (24)   ~ (all_52_5 = all_52_7)
% 175.59/27.06    (25)  all_58_10 = all_52_15
% 175.59/27.06    (26)   ~ (all_52_5 = all_4_2)
% 175.59/27.06    (27)  all_58_7 = all_52_19
% 175.59/27.06    (28)  all_56_4 = all_52_9
% 175.59/27.06    (29)   ~ (all_52_15 = all_6_2)
% 175.59/27.06    (30)   ~ (all_52_17 = all_52_25)
% 175.59/27.06    (31)  op(e0, e1) = all_52_29
% 175.59/27.06    (32)   ~ (all_4_0 = e2)
% 175.59/27.06    (33)  all_58_4 = all_52_5
% 175.59/27.06    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.06    (35)   ~ (all_52_27 = all_52_29)
% 175.59/27.06    (36)  op(e3, all_4_2) = all_4_1
% 175.59/27.07    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.07    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.07    (39)   ~ (all_52_7 = all_4_2)
% 175.59/27.07    (40)  all_58_1 = all_52_3
% 175.59/27.07    (41)   ~ (all_52_13 = all_52_15)
% 175.59/27.07    (42)  all_58_0 = all_4_2
% 175.59/27.07    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.07    (44)  op(e1, all_52_29) = all_52_28
% 175.59/27.07    (45)  op(e1, all_52_5) = all_52_4
% 175.59/27.07    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.07    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.59/27.07    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.07    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.07    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.07    (51)  all_58_14 = all_52_29
% 175.59/27.07    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.07    (53)   ~ (all_52_3 = all_52_5)
% 175.59/27.07    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.07    (55)  op(e2, e1) = all_52_13
% 175.59/27.07    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.07    (57)  all_58_8 = all_14_2
% 175.59/27.07    (58)  all_56_1 = all_52_3
% 175.59/27.07    (59)  all_56_14 = all_52_29
% 175.59/27.07    (60)  op(all_4_1, all_4_2) = all_4_0
% 175.59/27.07    (61)   ~ (all_52_5 = all_14_2)
% 175.59/27.07    (62)   ~ (all_52_3 = all_52_27)
% 175.59/27.07    (63)   ~ (all_52_3 = all_4_2)
% 175.59/27.07    (64)  all_38_2 = all_6_2
% 175.59/27.07    (65)  op(e0, e3) = all_52_25
% 175.59/27.07    (66)  op(e0, all_6_2) = all_6_1
% 175.59/27.07    (67)  all_52_0 = all_4_1
% 175.59/27.07    (68)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.59/27.07    (69)   ~ (all_52_13 = all_14_2)
% 175.59/27.07    (70)   ~ (e3 = e0)
% 175.59/27.07    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.07    (72)   ~ (all_52_9 = all_52_13)
% 175.59/27.07    (73)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.07    (74)  op(e0, all_52_23) = all_52_22
% 175.59/27.07    (75)   ~ (all_52_15 = all_52_23)
% 175.59/27.07    (76)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.07    (77)   ~ (all_52_5 = all_52_29)
% 175.59/27.07    (78)  all_56_2 = all_52_5
% 175.59/27.07    (79)  op(e1, e0) = all_52_23
% 175.59/27.07    (80)  all_56_12 = all_52_25
% 175.59/27.07    (81)  all_58_13 = all_52_27
% 175.59/27.07    (82)  op(e2, all_52_3) = all_52_2
% 175.59/27.07    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.07    (84)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.07    (85)   ~ (all_52_9 = all_52_17)
% 175.59/27.07    (86)  all_58_6 = all_52_17
% 175.59/27.07    (87)   ~ (all_52_3 = all_52_7)
% 175.59/27.07    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.59/27.07    (89)   ~ (e1 = e0)
% 175.59/27.07    (90)  all_56_0 = all_4_2
% 175.59/27.07    (91)  all_58_11 = all_52_23
% 175.59/27.07    (92)   ~ (all_52_3 = all_52_19)
% 175.59/27.07    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.07    (94)   ~ (all_52_7 = all_52_15)
% 175.59/27.07    (95)  op(e0, all_52_15) = all_52_14
% 175.59/27.07    (96)   ~ (all_52_29 = all_14_2)
% 175.59/27.07    (97)   ~ (all_4_0 = e1)
% 175.59/27.07    (98)   ~ (all_52_23 = all_6_2)
% 175.59/27.07    (99)   ~ (all_52_29 = all_6_2)
% 175.59/27.07    (100)  all_58_2 = all_52_9
% 175.59/27.07    (101)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.59/27.07    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.59/27.07    (103)  op(e3, e1) = all_52_5
% 175.59/27.07    (104)  all_56_10 = all_14_2
% 175.59/27.07    (105)   ~ (all_52_25 = all_6_2)
% 175.59/27.07    (106)  op(e1, e1) = all_14_2
% 175.59/27.07    (107)  op(e1, e3) = all_52_17
% 175.59/27.07    (108)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.07    (109)   ~ (all_52_25 = all_4_2)
% 175.59/27.07    (110)  op(e3, e0) = all_52_7
% 175.59/27.07    (111)   ~ (all_52_17 = all_4_2)
% 175.59/27.07    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.07             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.07    (113)   ~ (all_52_25 = all_52_27)
% 175.59/27.07    (114)   ~ (all_52_27 = all_6_2)
% 175.59/27.07    (115)   ~ (all_52_7 = all_6_2)
% 175.59/27.07    (116)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.07    (117)  all_38_1 = all_6_1
% 175.59/27.07    (118)   ~ (all_52_19 = all_52_27)
% 175.59/27.07    (119)  all_56_7 = all_52_15
% 175.59/27.07    (120)   ~ (all_52_7 = all_52_23)
% 175.59/27.07    (121)   ~ (all_52_13 = all_10_2)
% 175.59/27.07    (122)  op(e2, all_52_27) = all_52_26
% 175.59/27.07    (123)   ~ (all_52_17 = all_52_19)
% 175.59/27.07    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.07    (125)  all_58_9 = all_52_7
% 175.59/27.07    (126)  all_58_12 = all_52_25
% 175.59/27.07    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.07    (128)   ~ (all_52_9 = all_52_15)
% 175.59/27.07    (129)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.07    (130)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.07    (131)   ~ (all_52_19 = all_14_2)
% 175.59/27.07    (132)  op(e0, all_52_7) = all_52_6
% 175.59/27.07    (133)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.59/27.07    (134)  op(e2, e3) = all_52_9
% 175.59/27.07    (135)  all_56_13 = all_52_27
% 175.59/27.07  
% 175.59/27.07  Begin of proof
% 175.59/27.07  | 
% 175.59/27.07  | ALPHA: (133) implies:
% 175.59/27.07  |   (136)  all_52_6 = e0
% 175.59/27.07  |   (137)  all_52_4 = e1
% 175.59/27.07  |   (138)  all_52_2 = e2
% 175.59/27.07  |   (139)  all_52_0 = e3
% 175.59/27.07  | 
% 175.59/27.07  | COMBINE_EQS: (67), (139) imply:
% 175.59/27.07  |   (140)  all_4_1 = e3
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (60), (140) imply:
% 175.59/27.07  |   (141)  op(e3, all_4_2) = all_4_0
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (36), (140) imply:
% 175.59/27.07  |   (142)  op(e3, all_4_2) = e3
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (82), (138) imply:
% 175.59/27.07  |   (143)  op(e2, all_52_3) = e2
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (45), (137) imply:
% 175.59/27.07  |   (144)  op(e1, all_52_5) = e1
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (132), (136) imply:
% 175.59/27.07  |   (145)  op(e0, all_52_7) = e0
% 175.59/27.07  | 
% 175.59/27.07  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.59/27.07  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.59/27.07  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 175.59/27.07  |            (35), (37), (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 175.59/27.07  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 175.59/27.07  |            (59), (61), (62), (63), (64), (65), (66), (68), (69), (70), (71),
% 175.59/27.07  |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (83),
% 175.59/27.07  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 175.59/27.07  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 175.59/27.07  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 175.59/27.07  |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 175.59/27.07  |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 175.59/27.07  |            (134), (135), (141), (142), (143), (144), (145) are inconsistent by
% 175.59/27.07  |            sub-proof #141.
% 175.59/27.07  | 
% 175.59/27.07  End of proof
% 175.59/27.07  
% 175.59/27.07  Sub-proof #141 shows that the following formulas are inconsistent:
% 175.59/27.07  ----------------------------------------------------------------
% 175.59/27.07    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.07    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.07    (3)   ~ (all_52_17 = all_52_23)
% 175.59/27.07    (4)  op(e2, all_52_3) = e2
% 175.59/27.07    (5)   ~ (all_52_13 = all_52_29)
% 175.59/27.07    (6)  op(e3, e2) = all_52_3
% 175.59/27.07    (7)   ~ (all_52_9 = all_52_25)
% 175.59/27.07    (8)   ~ (all_52_19 = all_52_23)
% 175.59/27.07    (9)  all_56_11 = all_52_23
% 175.59/27.07    (10)  op(e1, e2) = all_52_19
% 175.59/27.07    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.59/27.07    (12)  op(all_6_1, all_6_2) = e1
% 175.59/27.07    (13)   ~ (all_52_3 = all_10_2)
% 175.59/27.07    (14)  all_58_5 = all_52_13
% 175.59/27.07    (15)   ~ (all_6_2 = e0)
% 175.59/27.07    (16)   ~ (all_52_25 = all_52_29)
% 175.59/27.07    (17)  all_56_15 = all_6_2
% 175.59/27.07    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.07    (19)  op(e2, e0) = all_52_15
% 175.59/27.07    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.59/27.07    (21)  all_58_3 = all_10_2
% 175.59/27.07    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.07    (23)  all_58_15 = all_6_2
% 175.59/27.07    (24)   ~ (all_52_9 = all_4_2)
% 175.59/27.07    (25)   ~ (all_52_5 = all_52_7)
% 175.59/27.07    (26)  all_58_10 = all_52_15
% 175.59/27.07    (27)   ~ (all_52_5 = all_4_2)
% 175.59/27.07    (28)  all_58_7 = all_52_19
% 175.59/27.07    (29)  all_56_4 = all_52_9
% 175.59/27.07    (30)   ~ (all_52_15 = all_6_2)
% 175.59/27.07    (31)   ~ (all_52_17 = all_52_25)
% 175.59/27.07    (32)  op(e0, e1) = all_52_29
% 175.59/27.07    (33)   ~ (all_4_0 = e2)
% 175.59/27.07    (34)  all_58_4 = all_52_5
% 175.59/27.07    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.07    (36)   ~ (all_52_27 = all_52_29)
% 175.59/27.07    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.07    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.07    (39)   ~ (all_52_7 = all_4_2)
% 175.59/27.07    (40)  all_58_1 = all_52_3
% 175.59/27.07    (41)   ~ (all_52_13 = all_52_15)
% 175.59/27.07    (42)  all_58_0 = all_4_2
% 175.59/27.07    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.07    (44)  op(e1, all_52_29) = all_52_28
% 175.59/27.07    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.07    (46)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.59/27.07    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.07    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.07    (49)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.07    (50)  all_58_14 = all_52_29
% 175.59/27.07    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.07    (52)   ~ (all_52_3 = all_52_5)
% 175.59/27.07    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.07    (54)  op(e2, e1) = all_52_13
% 175.59/27.07    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.07    (56)  all_58_8 = all_14_2
% 175.59/27.07    (57)  all_56_1 = all_52_3
% 175.59/27.07    (58)  all_56_14 = all_52_29
% 175.59/27.07    (59)   ~ (all_52_5 = all_14_2)
% 175.59/27.07    (60)   ~ (all_52_3 = all_52_27)
% 175.59/27.07    (61)   ~ (all_52_3 = all_4_2)
% 175.59/27.07    (62)  op(e3, all_4_2) = e3
% 175.59/27.07    (63)  all_38_2 = all_6_2
% 175.59/27.07    (64)  op(e0, e3) = all_52_25
% 175.59/27.07    (65)  op(e0, all_6_2) = all_6_1
% 175.59/27.07    (66)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.59/27.07    (67)   ~ (all_52_13 = all_14_2)
% 175.59/27.07    (68)   ~ (e3 = e0)
% 175.59/27.07    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.07    (70)   ~ (all_52_9 = all_52_13)
% 175.59/27.07    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.07    (72)  op(e0, all_52_23) = all_52_22
% 175.59/27.07    (73)   ~ (all_52_15 = all_52_23)
% 175.59/27.07    (74)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.07    (75)   ~ (all_52_5 = all_52_29)
% 175.59/27.07    (76)  all_56_2 = all_52_5
% 175.59/27.07    (77)  op(e1, e0) = all_52_23
% 175.59/27.07    (78)  all_56_12 = all_52_25
% 175.59/27.07    (79)  all_58_13 = all_52_27
% 175.59/27.07    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.07    (81)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.07    (82)   ~ (all_52_9 = all_52_17)
% 175.59/27.07    (83)  all_58_6 = all_52_17
% 175.59/27.07    (84)   ~ (all_52_3 = all_52_7)
% 175.59/27.07    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.59/27.07    (86)   ~ (e1 = e0)
% 175.59/27.07    (87)  all_56_0 = all_4_2
% 175.59/27.07    (88)  all_58_11 = all_52_23
% 175.59/27.07    (89)   ~ (all_52_3 = all_52_19)
% 175.59/27.07    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.07    (91)   ~ (all_52_7 = all_52_15)
% 175.59/27.07    (92)  op(e0, all_52_15) = all_52_14
% 175.59/27.07    (93)   ~ (all_52_29 = all_14_2)
% 175.59/27.07    (94)   ~ (all_4_0 = e1)
% 175.59/27.07    (95)   ~ (all_52_23 = all_6_2)
% 175.59/27.07    (96)   ~ (all_52_29 = all_6_2)
% 175.59/27.07    (97)  all_58_2 = all_52_9
% 175.59/27.07    (98)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.59/27.07    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.59/27.07    (100)  op(e3, e1) = all_52_5
% 175.59/27.07    (101)  all_56_10 = all_14_2
% 175.59/27.07    (102)   ~ (all_52_25 = all_6_2)
% 175.59/27.07    (103)  op(e1, e1) = all_14_2
% 175.59/27.07    (104)  op(e1, e3) = all_52_17
% 175.59/27.07    (105)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.07    (106)   ~ (all_52_25 = all_4_2)
% 175.59/27.07    (107)  op(e3, e0) = all_52_7
% 175.59/27.07    (108)   ~ (all_52_17 = all_4_2)
% 175.59/27.07    (109)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.07             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.07    (110)   ~ (all_52_25 = all_52_27)
% 175.59/27.07    (111)   ~ (all_52_27 = all_6_2)
% 175.59/27.07    (112)   ~ (all_52_7 = all_6_2)
% 175.59/27.07    (113)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.07    (114)  all_38_1 = all_6_1
% 175.59/27.07    (115)   ~ (all_52_19 = all_52_27)
% 175.59/27.07    (116)  all_56_7 = all_52_15
% 175.59/27.07    (117)  op(e1, all_52_5) = e1
% 175.59/27.07    (118)   ~ (all_52_7 = all_52_23)
% 175.59/27.07    (119)   ~ (all_52_13 = all_10_2)
% 175.59/27.07    (120)  op(e3, all_4_2) = all_4_0
% 175.59/27.07    (121)  op(e0, all_52_7) = e0
% 175.59/27.07    (122)  op(e2, all_52_27) = all_52_26
% 175.59/27.07    (123)   ~ (all_52_17 = all_52_19)
% 175.59/27.07    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.07    (125)  all_58_9 = all_52_7
% 175.59/27.07    (126)  all_58_12 = all_52_25
% 175.59/27.07    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.07    (128)   ~ (all_52_9 = all_52_15)
% 175.59/27.07    (129)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.07    (130)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.07    (131)   ~ (all_52_19 = all_14_2)
% 175.59/27.07    (132)  op(e2, e3) = all_52_9
% 175.59/27.07    (133)  all_56_13 = all_52_27
% 175.59/27.07  
% 175.59/27.07  Begin of proof
% 175.59/27.07  | 
% 175.59/27.07  | GROUND_INST: instantiating (109) with e3, all_4_0, all_4_2, e3, simplifying
% 175.59/27.07  |              with (62), (120) gives:
% 175.59/27.07  |   (134)  all_4_0 = e3
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (33), (134) imply:
% 175.59/27.07  |   (135)   ~ (e3 = e2)
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (94), (134) imply:
% 175.59/27.07  |   (136)   ~ (e3 = e1)
% 175.59/27.07  | 
% 175.59/27.07  | BETA: splitting (37) gives:
% 175.59/27.07  | 
% 175.59/27.07  | Case 1:
% 175.59/27.07  | | 
% 175.59/27.07  | |   (137)  all_56_15 = e3
% 175.59/27.07  | | 
% 175.59/27.07  | | COMBINE_EQS: (17), (137) imply:
% 175.59/27.07  | |   (138)  all_6_2 = e3
% 175.59/27.07  | | 
% 175.59/27.07  | | SIMP: (138) implies:
% 175.59/27.07  | |   (139)  all_6_2 = e3
% 175.59/27.07  | | 
% 175.59/27.07  | | COMBINE_EQS: (63), (139) imply:
% 175.59/27.07  | |   (140)  all_38_2 = e3
% 175.59/27.07  | | 
% 175.59/27.07  | | REDUCE: (102), (139) imply:
% 175.59/27.07  | |   (141)   ~ (all_52_25 = e3)
% 175.59/27.07  | | 
% 175.59/27.07  | | REDUCE: (12), (139) imply:
% 175.59/27.07  | |   (142)  op(all_6_1, e3) = e1
% 175.59/27.07  | | 
% 175.59/27.07  | | REDUCE: (65), (139) imply:
% 175.59/27.07  | |   (143)  op(e0, e3) = all_6_1
% 175.59/27.07  | | 
% 175.59/27.07  | | REF_CLOSE: (31), (64), (71), (78), (98), (104), (109), (113), (114), (126),
% 175.59/27.07  | |            (140), (141), (142), (143) are inconsistent by sub-proof #142.
% 175.59/27.07  | | 
% 175.59/27.07  | Case 2:
% 175.59/27.07  | | 
% 175.59/27.07  | |   (144)   ~ (all_56_15 = e3)
% 175.59/27.07  | |   (145)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.07  | | 
% 175.59/27.07  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 175.59/27.07  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.59/27.07  | |            (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 175.59/27.07  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 175.59/27.07  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 175.59/27.07  | |            (60), (61), (62), (64), (66), (67), (68), (69), (70), (71), (72),
% 175.59/27.07  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 175.59/27.07  | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (95),
% 175.59/27.07  | |            (96), (97), (99), (100), (101), (102), (103), (104), (105),
% 175.59/27.07  | |            (106), (107), (108), (109), (110), (111), (112), (115), (116),
% 175.59/27.07  | |            (117), (118), (119), (121), (122), (123), (124), (125), (126),
% 175.59/27.07  | |            (127), (128), (129), (130), (131), (132), (133), (135), (136),
% 175.59/27.07  | |            (144), (145) are inconsistent by sub-proof #785.
% 175.59/27.07  | | 
% 175.59/27.07  | End of split
% 175.59/27.07  | 
% 175.59/27.07  End of proof
% 175.59/27.07  
% 175.59/27.07  Sub-proof #142 shows that the following formulas are inconsistent:
% 175.59/27.07  ----------------------------------------------------------------
% 175.59/27.07    (1)   ~ (all_52_25 = e3)
% 175.59/27.07    (2)   ~ (all_52_17 = all_52_25)
% 175.59/27.07    (3)  op(all_6_1, e3) = e1
% 175.59/27.07    (4)  op(e0, e3) = all_52_25
% 175.59/27.07    (5)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.07    (6)  all_56_12 = all_52_25
% 175.59/27.07    (7)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 175.59/27.07    (8)  op(e0, e3) = all_6_1
% 175.59/27.07    (9)  op(e1, e3) = all_52_17
% 175.59/27.07    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.07    (11)   ~ (all_38_1 = e2) |  ~ (all_38_2 = e3)
% 175.59/27.07    (12)  all_38_1 = all_6_1
% 175.59/27.07    (13)  all_58_12 = all_52_25
% 175.59/27.07    (14)  all_38_2 = e3
% 175.59/27.07  
% 175.59/27.07  Begin of proof
% 175.59/27.07  | 
% 175.59/27.07  | BETA: splitting (11) gives:
% 175.59/27.07  | 
% 175.59/27.07  | Case 1:
% 175.59/27.07  | | 
% 175.59/27.07  | |   (15)   ~ (all_38_1 = e2)
% 175.59/27.07  | | 
% 175.59/27.07  | | REDUCE: (12), (15) imply:
% 175.59/27.07  | |   (16)   ~ (all_6_1 = e2)
% 175.59/27.07  | | 
% 175.59/27.07  | | GROUND_INST: instantiating (10) with all_52_25, all_6_1, e3, e0, simplifying
% 175.59/27.07  | |              with (4), (8) gives:
% 175.59/27.07  | |   (17)  all_52_25 = all_6_1
% 175.59/27.07  | | 
% 175.59/27.07  | | COMBINE_EQS: (6), (17) imply:
% 175.59/27.07  | |   (18)  all_56_12 = all_6_1
% 175.59/27.07  | | 
% 175.59/27.07  | | COMBINE_EQS: (13), (17) imply:
% 175.59/27.07  | |   (19)  all_58_12 = all_6_1
% 175.59/27.07  | | 
% 175.59/27.07  | | REDUCE: (2), (17) imply:
% 175.59/27.07  | |   (20)   ~ (all_52_17 = all_6_1)
% 175.59/27.07  | | 
% 175.59/27.07  | | REDUCE: (1), (17) imply:
% 175.59/27.07  | |   (21)   ~ (all_6_1 = e3)
% 175.59/27.07  | | 
% 175.59/27.07  | | BETA: splitting (5) gives:
% 175.59/27.07  | | 
% 175.59/27.07  | | Case 1:
% 175.59/27.07  | | | 
% 175.59/27.07  | | |   (22)  all_56_12 = e3
% 175.59/27.07  | | | 
% 175.59/27.07  | | | REF_CLOSE: (18), (21), (22) are inconsistent by sub-proof #509.
% 175.59/27.07  | | | 
% 175.59/27.07  | | Case 2:
% 175.59/27.07  | | | 
% 175.59/27.07  | | |   (23)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.07  | | | 
% 175.59/27.07  | | | BETA: splitting (7) gives:
% 175.59/27.07  | | | 
% 175.59/27.07  | | | Case 1:
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | |   (24)  all_58_12 = e1
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | COMBINE_EQS: (19), (24) imply:
% 175.59/27.07  | | | |   (25)  all_6_1 = e1
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | SIMP: (25) implies:
% 175.59/27.07  | | | |   (26)  all_6_1 = e1
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | REDUCE: (20), (26) imply:
% 175.59/27.07  | | | |   (27)   ~ (all_52_17 = e1)
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | REDUCE: (3), (26) imply:
% 175.59/27.07  | | | |   (28)  op(e1, e3) = e1
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | GROUND_INST: instantiating (10) with all_52_17, e1, e3, e1, simplifying
% 175.59/27.07  | | | |              with (9), (28) gives:
% 175.59/27.07  | | | |   (29)  all_52_17 = e1
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | REDUCE: (27), (29) imply:
% 175.59/27.07  | | | |   (30)  $false
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | CLOSE: (30) is inconsistent.
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | Case 2:
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | |   (31)   ~ (all_58_12 = e1)
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | REDUCE: (19), (31) imply:
% 175.59/27.07  | | | |   (32)   ~ (all_6_1 = e1)
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | BETA: splitting (23) gives:
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | | Case 1:
% 175.59/27.07  | | | | | 
% 175.59/27.07  | | | | |   (33)  all_56_12 = e2
% 175.59/27.07  | | | | | 
% 175.59/27.07  | | | | | REF_CLOSE: (16), (18), (33) are inconsistent by sub-proof #507.
% 175.59/27.07  | | | | | 
% 175.59/27.07  | | | | Case 2:
% 175.59/27.07  | | | | | 
% 175.59/27.07  | | | | |   (34)  all_56_12 = e1 | all_56_12 = e0
% 175.59/27.07  | | | | | 
% 175.59/27.07  | | | | | BETA: splitting (34) gives:
% 175.59/27.07  | | | | | 
% 175.59/27.07  | | | | | Case 1:
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | |   (35)  all_56_12 = e1
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | REF_CLOSE: (18), (32), (35) are inconsistent by sub-proof #506.
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | Case 2:
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | |   (36)  all_56_12 = e0
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | COMBINE_EQS: (18), (36) imply:
% 175.59/27.07  | | | | | |   (37)  all_6_1 = e0
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | SIMP: (37) implies:
% 175.59/27.07  | | | | | |   (38)  all_6_1 = e0
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | REDUCE: (32), (38) imply:
% 175.59/27.07  | | | | | |   (39)   ~ (e1 = e0)
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | SIMP: (39) implies:
% 175.59/27.07  | | | | | |   (40)   ~ (e1 = e0)
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | REDUCE: (3), (38) imply:
% 175.59/27.07  | | | | | |   (41)  op(e0, e3) = e1
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | REDUCE: (8), (38) imply:
% 175.59/27.07  | | | | | |   (42)  op(e0, e3) = e0
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | | REF_CLOSE: (10), (40), (41), (42) are inconsistent by sub-proof
% 175.59/27.07  | | | | | |            #1007.
% 175.59/27.07  | | | | | | 
% 175.59/27.07  | | | | | End of split
% 175.59/27.07  | | | | | 
% 175.59/27.07  | | | | End of split
% 175.59/27.07  | | | | 
% 175.59/27.07  | | | End of split
% 175.59/27.07  | | | 
% 175.59/27.07  | | End of split
% 175.59/27.07  | | 
% 175.59/27.07  | Case 2:
% 175.59/27.07  | | 
% 175.59/27.07  | |   (43)   ~ (all_38_2 = e3)
% 175.59/27.07  | | 
% 175.59/27.07  | | REDUCE: (14), (43) imply:
% 175.59/27.07  | |   (44)  $false
% 175.59/27.07  | | 
% 175.59/27.07  | | CLOSE: (44) is inconsistent.
% 175.59/27.07  | | 
% 175.59/27.07  | End of split
% 175.59/27.07  | 
% 175.59/27.07  End of proof
% 175.59/27.07  
% 175.59/27.07  Sub-proof #143 shows that the following formulas are inconsistent:
% 175.59/27.07  ----------------------------------------------------------------
% 175.59/27.07    (1)  op(all_6_1, all_6_2) = e1
% 175.59/27.07    (2)  all_58_15 = all_6_2
% 175.59/27.07    (3)  op(e0, e0) = all_6_2
% 175.59/27.07    (4)  op(e0, all_6_2) = all_6_1
% 175.59/27.07    (5)   ~ (e1 = e0)
% 175.59/27.07    (6)  all_58_15 = e0
% 175.59/27.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.07  
% 175.59/27.07  Begin of proof
% 175.59/27.07  | 
% 175.59/27.07  | COMBINE_EQS: (2), (6) imply:
% 175.59/27.07  |   (8)  all_6_2 = e0
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (1), (8) imply:
% 175.59/27.07  |   (9)  op(all_6_1, e0) = e1
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (4), (8) imply:
% 175.59/27.07  |   (10)  op(e0, e0) = all_6_1
% 175.59/27.07  | 
% 175.59/27.07  | REDUCE: (3), (8) imply:
% 175.59/27.07  |   (11)  op(e0, e0) = e0
% 175.59/27.07  | 
% 175.59/27.07  | REF_CLOSE: (5), (7), (9), (10), (11) are inconsistent by sub-proof #144.
% 175.59/27.07  | 
% 175.59/27.07  End of proof
% 175.59/27.07  
% 175.59/27.07  Sub-proof #144 shows that the following formulas are inconsistent:
% 175.59/27.07  ----------------------------------------------------------------
% 175.59/27.07    (1)  op(all_6_1, e0) = e1
% 175.59/27.07    (2)  op(e0, e0) = all_6_1
% 175.59/27.07    (3)  op(e0, e0) = e0
% 175.59/27.07    (4)   ~ (e1 = e0)
% 175.59/27.08    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.08  
% 175.59/27.08  Begin of proof
% 175.59/27.08  | 
% 175.59/27.08  | GROUND_INST: instantiating (5) with e0, all_6_1, e0, e0, simplifying with (2),
% 175.59/27.08  |              (3) gives:
% 175.59/27.08  |   (6)  all_6_1 = e0
% 175.59/27.08  | 
% 175.59/27.08  | REDUCE: (1), (6) imply:
% 175.59/27.08  |   (7)  op(e0, e0) = e1
% 175.59/27.08  | 
% 175.59/27.08  | GROUND_INST: instantiating (5) with e0, e1, e0, e0, simplifying with (3), (7)
% 175.59/27.08  |              gives:
% 175.59/27.08  |   (8)  e1 = e0
% 175.59/27.08  | 
% 175.59/27.08  | REDUCE: (4), (8) imply:
% 175.59/27.08  |   (9)  $false
% 175.59/27.08  | 
% 175.59/27.08  | CLOSE: (9) is inconsistent.
% 175.59/27.08  | 
% 175.59/27.08  End of proof
% 175.59/27.08  
% 175.59/27.08  Sub-proof #145 shows that the following formulas are inconsistent:
% 175.59/27.08  ----------------------------------------------------------------
% 175.59/27.08    (1)   ~ (all_52_23 = all_14_2)
% 175.59/27.08    (2)   ~ (all_52_5 = all_52_13)
% 175.59/27.08    (3)   ~ (all_52_27 = all_10_2)
% 175.59/27.08    (4)   ~ (all_52_17 = all_52_23)
% 175.59/27.08    (5)  op(e2, all_10_2) = all_10_1
% 175.59/27.08    (6)   ~ (all_52_13 = all_52_29)
% 175.59/27.08    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.59/27.08    (8)  op(e3, e2) = all_52_3
% 175.59/27.08    (9)   ~ (all_52_9 = all_52_25)
% 175.59/27.08    (10)   ~ (all_52_19 = all_52_23)
% 175.59/27.08    (11)  all_56_11 = all_52_23
% 175.59/27.08    (12)  op(e1, e2) = all_52_19
% 175.59/27.08    (13)  all_16_1 = all_6_1
% 175.59/27.08    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.59/27.08    (15)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.59/27.08    (16)   ~ (all_52_3 = all_10_2)
% 175.59/27.08    (17)  all_58_5 = all_52_13
% 175.59/27.08    (18)   ~ (all_6_2 = e0)
% 175.59/27.08    (19)   ~ (all_52_25 = all_52_29)
% 175.59/27.08    (20)  all_16_2 = all_6_2
% 175.59/27.08    (21)  all_56_15 = all_6_2
% 175.59/27.08    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.08    (23)  op(e2, e0) = all_52_15
% 175.59/27.08    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.59/27.08    (25)  all_58_3 = all_10_2
% 175.59/27.08    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.08    (27)  all_58_15 = all_6_2
% 175.59/27.08    (28)   ~ (all_52_9 = all_4_2)
% 175.59/27.08    (29)   ~ (all_52_5 = all_52_7)
% 175.59/27.08    (30)  all_58_10 = all_52_15
% 175.59/27.08    (31)  all_8_2 = all_6_2
% 175.59/27.08    (32)   ~ (all_52_5 = all_4_2)
% 175.59/27.08    (33)  all_58_7 = all_52_19
% 175.59/27.08    (34)  all_56_4 = all_52_9
% 175.59/27.08    (35)   ~ (all_52_17 = all_52_25)
% 175.59/27.08    (36)  op(e0, e1) = all_52_29
% 175.59/27.08    (37)   ~ (all_4_0 = e2)
% 175.59/27.08    (38)  all_58_4 = all_52_5
% 175.59/27.08    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.08    (40)   ~ (all_52_27 = all_52_29)
% 175.59/27.08    (41)  op(e3, all_4_2) = all_4_1
% 175.59/27.08    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.08    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.08    (44)   ~ (all_52_7 = all_4_2)
% 175.59/27.08    (45)  all_58_1 = all_52_3
% 175.59/27.08    (46)   ~ (all_52_13 = all_52_15)
% 175.59/27.08    (47)  all_58_0 = all_4_2
% 175.59/27.08    (48)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.08    (49)  op(e1, all_52_29) = all_52_28
% 175.59/27.08    (50)  op(e1, all_52_5) = all_52_4
% 175.59/27.08    (51)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.59/27.08          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.59/27.08    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.59/27.08    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.59/27.08    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.59/27.08    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.08    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.59/27.08    (57)  all_58_14 = all_52_29
% 175.59/27.08    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.59/27.08    (59)   ~ (all_52_3 = all_52_5)
% 175.59/27.08    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.08    (61)  op(e2, e1) = all_52_13
% 175.59/27.08    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.08    (63)  all_58_8 = all_14_2
% 175.59/27.08    (64)  all_56_1 = all_52_3
% 175.59/27.08    (65)  all_56_14 = all_52_29
% 175.59/27.08    (66)  op(all_4_1, all_4_2) = all_4_0
% 175.59/27.08    (67)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.59/27.08    (68)   ~ (all_52_5 = all_14_2)
% 175.59/27.08    (69)   ~ (all_52_3 = all_52_27)
% 175.59/27.08    (70)   ~ (all_52_3 = all_4_2)
% 175.59/27.08    (71)  op(e0, e3) = all_52_25
% 175.59/27.08    (72)  op(e0, all_6_2) = all_6_1
% 175.59/27.08    (73)  all_52_0 = all_4_1
% 175.59/27.08    (74)   ~ (all_52_9 = all_10_2)
% 175.59/27.08    (75)  op(all_6_1, all_6_2) = e2
% 175.59/27.08    (76)  all_52_10 = all_10_1
% 175.59/27.08    (77)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.59/27.08    (78)   ~ (all_52_13 = all_14_2)
% 175.59/27.08    (79)   ~ (e3 = e0)
% 175.59/27.08    (80)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.08    (81)   ~ (all_52_9 = all_52_13)
% 175.59/27.08    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.59/27.08    (83)  op(e0, all_52_23) = all_52_22
% 175.59/27.08    (84)   ~ (all_52_15 = all_52_23)
% 175.59/27.08    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.59/27.08    (86)   ~ (all_52_5 = all_52_29)
% 175.59/27.08    (87)  all_56_2 = all_52_5
% 175.59/27.08    (88)  op(e1, e0) = all_52_23
% 175.59/27.08    (89)  all_56_12 = all_52_25
% 175.59/27.08    (90)  all_58_13 = all_52_27
% 175.59/27.08    (91)  op(e2, all_52_3) = all_52_2
% 175.59/27.08    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.08    (93)  all_56_5 = all_10_2
% 175.59/27.08    (94)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.08    (95)   ~ (all_52_9 = all_52_17)
% 175.59/27.08    (96)  all_58_6 = all_52_17
% 175.59/27.08    (97)   ~ (all_52_3 = all_52_7)
% 175.59/27.08    (98)  op(all_10_1, all_10_2) = e3
% 175.59/27.08    (99)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.59/27.08    (100)   ~ (e1 = e0)
% 175.59/27.08    (101)  all_56_0 = all_4_2
% 175.59/27.08    (102)  all_58_11 = all_52_23
% 175.59/27.08    (103)   ~ (all_52_3 = all_52_19)
% 175.59/27.08    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.08    (105)   ~ (all_52_7 = all_52_15)
% 175.59/27.08    (106)   ~ (all_52_29 = all_14_2)
% 175.59/27.08    (107)   ~ (all_4_0 = e1)
% 175.59/27.08    (108)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 175.59/27.08    (109)   ~ (all_52_19 = all_10_2)
% 175.59/27.08    (110)   ~ (all_52_23 = all_6_2)
% 175.59/27.08    (111)   ~ (all_52_29 = all_6_2)
% 175.59/27.08    (112)  all_58_2 = all_52_9
% 175.59/27.08    (113)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.59/27.08    (114)  op(e3, e1) = all_52_5
% 175.59/27.08    (115)  all_56_10 = all_14_2
% 175.59/27.08    (116)   ~ (all_52_25 = all_6_2)
% 175.59/27.08    (117)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.59/27.08    (118)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.59/27.08    (119)  op(e1, e1) = all_14_2
% 175.59/27.08    (120)  op(e1, e3) = all_52_17
% 175.59/27.08    (121)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.08    (122)   ~ (all_52_25 = all_4_2)
% 175.59/27.08    (123)  op(e3, e0) = all_52_7
% 175.59/27.08    (124)   ~ (all_52_17 = all_4_2)
% 175.59/27.08    (125)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.08             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.08    (126)   ~ (all_52_25 = all_52_27)
% 175.59/27.08    (127)   ~ (all_52_27 = all_6_2)
% 175.59/27.08    (128)  all_8_1 = all_6_1
% 175.59/27.08    (129)   ~ (all_52_7 = all_6_2)
% 175.59/27.08    (130)   ~ (all_52_19 = all_52_27)
% 175.59/27.08    (131)  all_56_7 = all_52_15
% 175.59/27.08    (132)   ~ (all_52_7 = all_52_23)
% 175.59/27.08    (133)   ~ (all_52_13 = all_10_2)
% 175.59/27.08    (134)  op(e2, all_52_27) = all_52_26
% 175.59/27.08    (135)   ~ (all_52_17 = all_52_19)
% 175.59/27.08    (136)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.08    (137)  all_58_9 = all_52_7
% 175.59/27.08    (138)  all_58_12 = all_52_25
% 175.59/27.08    (139)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.08    (140)   ~ (all_52_9 = all_52_15)
% 175.59/27.08    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.08    (142)   ~ (e3 = e2)
% 175.59/27.08    (143)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.59/27.08    (144)   ~ (all_52_19 = all_14_2)
% 175.59/27.08    (145)  op(e0, all_52_7) = all_52_6
% 175.59/27.08    (146)  op(e2, e3) = all_52_9
% 175.59/27.08    (147)  all_56_13 = all_52_27
% 175.59/27.08  
% 175.59/27.08  Begin of proof
% 175.59/27.08  | 
% 175.59/27.08  | BETA: splitting (51) gives:
% 175.59/27.08  | 
% 175.59/27.08  | Case 1:
% 175.59/27.08  | | 
% 175.59/27.08  | |   (148)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.59/27.08  | | 
% 175.59/27.08  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 175.59/27.08  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.59/27.08  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.59/27.08  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.59/27.08  | |            (47), (48), (49), (50), (52), (53), (54), (55), (56), (57), (58),
% 175.59/27.08  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 175.59/27.08  | |            (70), (71), (72), (73), (74), (75), (77), (78), (79), (80), (81),
% 175.59/27.08  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 175.59/27.08  | |            (93), (94), (95), (96), (97), (99), (100), (101), (102), (103),
% 175.59/27.08  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 175.59/27.08  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 175.59/27.08  | |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 175.59/27.08  | |            (131), (132), (133), (134), (135), (136), (137), (138), (139),
% 175.59/27.08  | |            (140), (141), (143), (144), (145), (146), (147), (148) are
% 175.59/27.08  | |            inconsistent by sub-proof #220.
% 175.59/27.08  | | 
% 175.59/27.08  | Case 2:
% 175.59/27.08  | | 
% 175.59/27.08  | |   (149)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.59/27.08  | | 
% 175.59/27.08  | | ALPHA: (149) implies:
% 175.59/27.08  | |   (150)  all_52_10 = e2
% 175.59/27.08  | | 
% 175.59/27.08  | | COMBINE_EQS: (76), (150) imply:
% 175.59/27.08  | |   (151)  all_10_1 = e2
% 175.59/27.08  | | 
% 175.59/27.08  | | REF_CLOSE: (5), (98), (125), (142), (151) are inconsistent by sub-proof
% 175.59/27.08  | |            #263.
% 175.59/27.08  | | 
% 175.59/27.08  | End of split
% 175.59/27.08  | 
% 175.59/27.08  End of proof
% 175.59/27.08  
% 175.59/27.08  Sub-proof #146 shows that the following formulas are inconsistent:
% 175.59/27.08  ----------------------------------------------------------------
% 175.59/27.08    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.59/27.08    (2)   ~ (all_52_17 = all_52_23)
% 175.59/27.08    (3)   ~ (all_52_13 = all_52_29)
% 175.59/27.08    (4)  op(e3, e2) = all_52_3
% 175.59/27.08    (5)  op(e3, all_52_25) = all_52_24
% 175.59/27.08    (6)   ~ (all_52_19 = all_52_23)
% 175.59/27.08    (7)  all_56_11 = all_52_23
% 175.59/27.08    (8)  op(e1, e2) = all_52_19
% 175.59/27.08    (9)   ~ (all_52_27 = e3)
% 175.59/27.08    (10)   ~ (all_6_2 = e3)
% 175.59/27.08    (11)  op(e3, all_52_9) = all_52_8
% 175.59/27.08    (12)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.59/27.08    (13)   ~ (all_52_3 = all_10_2)
% 175.59/27.08    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.59/27.08    (15)  all_58_5 = all_52_13
% 175.59/27.08    (16)   ~ (all_6_2 = e0)
% 175.59/27.08    (17)   ~ (all_52_25 = all_52_29)
% 175.59/27.08    (18)  all_56_15 = all_6_2
% 175.59/27.08    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.08    (20)  op(e2, e0) = all_52_15
% 175.59/27.08    (21)  all_58_3 = all_10_2
% 175.59/27.08    (22)  all_56_9 = all_52_19
% 175.59/27.08    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.08    (24)  all_58_15 = all_6_2
% 175.59/27.08    (25)   ~ (all_52_9 = all_4_2)
% 175.59/27.08    (26)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.08    (27)   ~ (all_52_5 = all_52_7)
% 175.59/27.08    (28)  all_58_10 = all_52_15
% 175.59/27.08    (29)  all_8_2 = all_6_2
% 175.59/27.08    (30)   ~ (all_52_5 = all_4_2)
% 175.59/27.08    (31)  all_58_7 = all_52_19
% 175.59/27.08    (32)   ~ (all_52_15 = all_6_2)
% 175.59/27.08    (33)   ~ (all_52_17 = all_52_25)
% 175.59/27.08    (34)  op(e0, e1) = all_52_29
% 175.59/27.08    (35)   ~ (all_4_0 = e2)
% 175.59/27.08    (36)  all_58_4 = all_52_5
% 175.59/27.08    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.59/27.08    (38)   ~ (e3 = e1)
% 175.59/27.08    (39)   ~ (all_52_27 = all_52_29)
% 175.59/27.08    (40)  op(e3, all_4_2) = all_4_1
% 175.59/27.08    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.59/27.08    (42)   ~ (all_52_7 = all_4_2)
% 175.59/27.08    (43)  all_58_1 = all_52_3
% 175.59/27.08    (44)  all_58_0 = all_4_2
% 175.59/27.08    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.59/27.08    (46)  op(e1, all_52_29) = all_52_28
% 175.59/27.08    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.59/27.08    (48)   ~ (all_4_1 = e2)
% 175.59/27.08    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.59/27.08    (50)  all_58_14 = all_52_29
% 175.59/27.08    (51)   ~ (all_52_3 = all_52_5)
% 175.59/27.08    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.59/27.08    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.08    (54)  all_58_8 = all_14_2
% 175.59/27.08    (55)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.59/27.08    (56)  op(all_4_1, all_4_2) = all_4_0
% 175.59/27.08    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.59/27.08    (58)   ~ (all_52_5 = all_14_2)
% 175.59/27.08    (59)   ~ (all_52_3 = all_4_2)
% 175.59/27.08    (60)  op(e0, e3) = all_52_25
% 175.59/27.08    (61)  op(e0, all_6_2) = all_6_1
% 175.59/27.08    (62)   ~ (all_52_9 = all_10_2)
% 175.59/27.08    (63)   ~ (e3 = e0)
% 175.59/27.08    (64)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.59/27.08    (65)   ~ (all_52_9 = all_52_13)
% 175.59/27.08    (66)   ~ (all_52_15 = all_52_23)
% 175.59/27.08    (67)  op(e1, e0) = all_52_23
% 175.59/27.08    (68)  all_58_13 = all_52_27
% 175.59/27.08    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.59/27.08    (70)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.59/27.08    (71)   ~ (all_52_9 = all_52_17)
% 175.59/27.08    (72)  all_58_6 = all_52_17
% 175.59/27.08    (73)  op(e2, all_52_19) = e2
% 175.59/27.08    (74)  op(e3, all_52_17) = e3
% 175.59/27.08    (75)   ~ (e1 = e0)
% 175.59/27.08    (76)  all_56_0 = all_4_2
% 175.59/27.08    (77)  all_58_11 = all_52_23
% 175.59/27.08    (78)   ~ (all_52_3 = all_52_19)
% 175.59/27.08    (79)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.59/27.08    (80)   ~ (all_52_7 = all_52_15)
% 175.59/27.08    (81)   ~ (all_52_29 = all_14_2)
% 175.59/27.08    (82)   ~ (all_4_0 = e1)
% 175.59/27.08    (83)   ~ (all_52_29 = all_6_2)
% 175.59/27.08    (84)  all_58_2 = all_52_9
% 175.59/27.08    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.59/27.08    (86)  op(e3, e1) = all_52_5
% 175.59/27.08    (87)   ~ (e2 = e1)
% 175.59/27.08    (88)   ~ (all_52_25 = all_6_2)
% 175.59/27.08    (89)  op(e1, e3) = all_52_17
% 175.59/27.08    (90)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.59/27.08    (91)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 175.59/27.08    (92)   ~ (all_52_25 = all_4_2)
% 175.59/27.08    (93)  op(e3, e0) = all_52_7
% 175.59/27.08    (94)  op(e3, e3) = all_4_2
% 175.59/27.08    (95)  all_56_8 = all_52_17
% 175.59/27.08    (96)   ~ (all_52_17 = all_4_2)
% 175.59/27.08    (97)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.59/27.08            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.59/27.08    (98)   ~ (all_52_25 = all_52_27)
% 175.59/27.08    (99)   ~ (all_52_27 = all_6_2)
% 175.59/27.08    (100)  all_8_1 = all_6_1
% 175.59/27.08    (101)   ~ (all_52_7 = all_6_2)
% 175.59/27.08    (102)  op(e0, all_52_23) = e0
% 175.59/27.08    (103)   ~ (all_52_15 = all_10_2)
% 175.59/27.08    (104)  all_56_7 = all_52_15
% 175.59/27.08    (105)  op(e1, all_14_2) = e1
% 175.59/27.08    (106)   ~ (all_52_7 = e3)
% 175.59/27.08    (107)   ~ (all_52_7 = all_52_23)
% 175.59/27.08    (108)   ~ (all_52_17 = all_52_19)
% 175.59/27.08    (109)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.59/27.08    (110)  all_58_9 = all_52_7
% 175.59/27.08    (111)   ~ (e2 = e0)
% 175.59/27.08    (112)  all_58_12 = all_52_25
% 175.59/27.08    (113)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.59/27.08    (114)   ~ (all_52_9 = all_52_15)
% 175.59/27.08    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.59/27.08    (116)   ~ (e3 = e2)
% 175.59/27.08    (117)  op(e2, e3) = all_52_2
% 175.59/27.08    (118)  op(e2, e3) = all_52_9
% 175.59/27.08  
% 175.59/27.08  Begin of proof
% 175.59/27.08  | 
% 175.59/27.08  | GROUND_INST: instantiating (97) with all_52_9, all_52_2, e3, e2, simplifying
% 175.59/27.08  |              with (117), (118) gives:
% 175.59/27.08  |   (119)  all_52_2 = all_52_9
% 175.59/27.08  | 
% 175.59/27.08  | BETA: splitting (53) gives:
% 175.59/27.08  | 
% 175.59/27.08  | Case 1:
% 175.59/27.08  | | 
% 175.59/27.08  | |   (120)  all_58_12 = e3
% 175.59/27.08  | | 
% 175.59/27.08  | | COMBINE_EQS: (112), (120) imply:
% 175.59/27.08  | |   (121)  all_52_25 = e3
% 175.59/27.08  | | 
% 175.59/27.08  | | SIMP: (121) implies:
% 175.59/27.08  | |   (122)  all_52_25 = e3
% 175.59/27.08  | | 
% 175.59/27.08  | | REDUCE: (33), (122) imply:
% 175.59/27.08  | |   (123)   ~ (all_52_17 = e3)
% 175.59/27.08  | | 
% 175.59/27.08  | | REDUCE: (98), (122) imply:
% 175.59/27.08  | |   (124)   ~ (all_52_27 = e3)
% 175.59/27.08  | | 
% 175.59/27.08  | | REDUCE: (88), (122) imply:
% 175.59/27.08  | |   (125)   ~ (all_6_2 = e3)
% 175.59/27.08  | | 
% 175.59/27.08  | | REDUCE: (92), (122) imply:
% 175.59/27.08  | |   (126)   ~ (all_4_2 = e3)
% 175.59/27.08  | | 
% 175.59/27.08  | | SIMP: (126) implies:
% 175.59/27.08  | |   (127)   ~ (all_4_2 = e3)
% 175.59/27.08  | | 
% 175.59/27.08  | | REDUCE: (60), (122) imply:
% 175.59/27.08  | |   (128)  op(e0, e3) = e3
% 175.59/27.08  | | 
% 175.59/27.08  | | REF_CLOSE: (8), (9), (10), (21), (23), (24), (25), (27), (28), (30), (31),
% 175.59/27.08  | |            (36), (37), (38), (42), (43), (44), (45), (49), (54), (58), (63),
% 175.59/27.08  | |            (64), (66), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 175.59/27.08  | |            (77), (78), (80), (84), (86), (87), (89), (90), (93), (96), (97),
% 175.59/27.08  | |            (102), (103), (104), (105), (106), (108), (109), (110), (111),
% 175.59/27.08  | |            (113), (114), (115), (118), (120), (123), (127), (128) are
% 175.59/27.08  | |            inconsistent by sub-proof #283.
% 175.59/27.08  | | 
% 175.59/27.08  | Case 2:
% 175.59/27.08  | | 
% 175.59/27.08  | |   (129)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.59/27.08  | | 
% 175.59/27.08  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 175.59/27.08  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 175.59/27.08  | |            (24), (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.59/27.08  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 175.59/27.08  | |            (48), (49), (50), (51), (52), (54), (55), (56), (57), (58), (59),
% 175.59/27.08  | |            (60), (61), (62), (65), (66), (67), (68), (69), (71), (72), (73),
% 175.59/27.08  | |            (74), (76), (77), (78), (79), (81), (82), (83), (84), (85), (86),
% 175.59/27.08  | |            (88), (89), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 175.59/27.08  | |            (100), (101), (102), (105), (107), (109), (110), (112), (114),
% 175.59/27.08  | |            (116), (118), (129) are inconsistent by sub-proof #203.
% 175.59/27.08  | | 
% 175.59/27.08  | End of split
% 175.59/27.08  | 
% 175.59/27.08  End of proof
% 175.59/27.08  
% 175.59/27.08  Sub-proof #147 shows that the following formulas are inconsistent:
% 175.59/27.08  ----------------------------------------------------------------
% 175.59/27.08    (1)   ~ (all_52_25 = e3)
% 175.59/27.08    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.59/27.08    (3)   ~ (all_52_17 = all_52_23)
% 175.59/27.08    (4)  all_40_2 = all_4_2
% 175.59/27.08    (5)   ~ (all_52_13 = all_52_29)
% 175.59/27.08    (6)  op(e3, e2) = all_52_3
% 175.59/27.08    (7)  op(e3, all_52_25) = all_52_24
% 175.59/27.08    (8)   ~ (all_52_19 = all_52_23)
% 175.59/27.08    (9)  all_56_11 = all_52_23
% 175.59/27.08    (10)  op(e1, e2) = all_52_19
% 175.59/27.08    (11)   ~ (all_6_2 = e3)
% 175.59/27.08    (12)  op(e3, all_52_9) = all_52_8
% 175.59/27.08    (13)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.59/27.08    (14)   ~ (all_52_3 = all_10_2)
% 175.59/27.08    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.59/27.08    (16)  all_58_5 = all_52_13
% 175.59/27.08    (17)   ~ (all_6_2 = e0)
% 175.59/27.08    (18)   ~ (all_52_25 = all_52_29)
% 175.59/27.08    (19)  all_56_15 = all_6_2
% 175.59/27.08    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.59/27.08    (21)  op(e2, e0) = all_52_15
% 175.59/27.08    (22)  all_58_3 = all_10_2
% 175.59/27.08    (23)  all_56_9 = all_52_19
% 175.59/27.08    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.59/27.08    (25)  all_58_15 = all_6_2
% 175.59/27.08    (26)   ~ (all_52_9 = all_4_2)
% 175.59/27.08    (27)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.59/27.08    (28)  all_58_10 = all_52_15
% 175.59/27.08    (29)  all_8_2 = all_6_2
% 175.59/27.08    (30)   ~ (all_52_5 = all_4_2)
% 175.59/27.08    (31)  all_58_7 = all_52_19
% 175.59/27.08    (32)   ~ (all_52_15 = all_6_2)
% 175.59/27.08    (33)   ~ (all_52_17 = all_52_25)
% 175.59/27.08    (34)  op(e0, e1) = all_52_29
% 175.59/27.08    (35)   ~ (all_4_0 = e2)
% 175.79/27.08    (36)  all_58_4 = all_52_5
% 175.79/27.08    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.08    (38)   ~ (e3 = e1)
% 175.79/27.08    (39)   ~ (all_52_27 = all_52_29)
% 175.79/27.08    (40)  op(e3, all_4_2) = all_4_1
% 175.79/27.08    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.08    (42)   ~ (all_52_7 = all_4_2)
% 175.79/27.08    (43)  all_58_1 = all_52_3
% 175.79/27.08    (44)  all_58_0 = all_4_2
% 175.79/27.08    (45)  op(e1, all_52_29) = all_52_28
% 175.79/27.08    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.79/27.08    (47)   ~ (all_4_1 = e2)
% 175.79/27.08    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.08    (49)  all_58_14 = all_52_29
% 175.79/27.08    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.79/27.08    (51)   ~ (all_52_3 = all_52_5)
% 175.79/27.08    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.08    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.08    (54)  all_58_8 = all_14_2
% 175.79/27.08    (55)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 175.79/27.08    (56)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.79/27.08    (57)  op(all_4_1, all_4_2) = all_4_0
% 175.79/27.08    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.79/27.08    (59)   ~ (all_52_5 = all_14_2)
% 175.79/27.08    (60)   ~ (all_52_3 = all_52_27)
% 175.79/27.08    (61)   ~ (all_52_3 = all_4_2)
% 175.79/27.08    (62)  op(e0, e3) = all_52_25
% 175.79/27.08    (63)  op(e0, all_6_2) = all_6_1
% 175.79/27.08    (64)   ~ (all_52_9 = all_10_2)
% 175.79/27.08    (65)  all_40_0 = all_4_0
% 175.79/27.08    (66)   ~ (all_52_9 = all_52_13)
% 175.79/27.08    (67)   ~ (all_52_15 = all_52_23)
% 175.79/27.08    (68)  op(e1, e0) = all_52_23
% 175.79/27.08    (69)  all_58_13 = all_52_27
% 175.79/27.08    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.08    (71)   ~ (all_52_9 = all_52_17)
% 175.79/27.08    (72)  all_58_6 = all_52_17
% 175.79/27.08    (73)  op(e2, all_52_19) = e2
% 175.79/27.08    (74)  op(e3, all_52_17) = e3
% 175.79/27.08    (75)  all_56_0 = all_4_2
% 175.79/27.08    (76)  all_58_11 = all_52_23
% 175.79/27.08    (77)   ~ (all_52_3 = all_52_19)
% 175.79/27.08    (78)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.79/27.08    (79)   ~ (all_52_29 = all_14_2)
% 175.79/27.08    (80)   ~ (all_4_0 = e1)
% 175.79/27.08    (81)  op(e1, all_4_2) = all_4_0
% 175.79/27.08    (82)   ~ (all_52_29 = all_6_2)
% 175.79/27.08    (83)  all_58_2 = all_52_9
% 175.79/27.09    (84)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.79/27.09    (85)  op(e3, e1) = all_52_5
% 175.79/27.09    (86)   ~ (all_52_25 = all_6_2)
% 175.79/27.09    (87)  op(e1, e3) = all_52_17
% 175.79/27.09    (88)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.79/27.09    (89)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 175.79/27.09    (90)   ~ (all_52_25 = all_4_2)
% 175.79/27.09    (91)  op(e3, e0) = all_52_7
% 175.79/27.09    (92)  op(e3, e3) = all_4_2
% 175.79/27.09    (93)  all_56_8 = all_52_17
% 175.79/27.09    (94)   ~ (all_52_17 = all_4_2)
% 175.79/27.09    (95)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.09    (96)   ~ (all_52_25 = all_52_27)
% 175.79/27.09    (97)   ~ (all_52_27 = all_6_2)
% 175.79/27.09    (98)  all_8_1 = all_6_1
% 175.79/27.09    (99)   ~ (all_52_7 = all_6_2)
% 175.79/27.09    (100)  op(e0, all_52_23) = e0
% 175.79/27.09    (101)   ~ (all_52_19 = all_52_27)
% 175.79/27.09    (102)  all_56_7 = all_52_15
% 175.79/27.09    (103)  op(e1, all_14_2) = e1
% 175.79/27.09    (104)   ~ (all_52_7 = all_52_23)
% 175.79/27.09    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.79/27.09    (106)  all_58_9 = all_52_7
% 175.79/27.09    (107)  all_58_12 = all_52_25
% 175.79/27.09    (108)  op(e3, all_4_2) = e1
% 175.79/27.09    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.79/27.09    (110)   ~ (all_52_9 = all_52_15)
% 175.79/27.09    (111)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.79/27.09    (112)   ~ (e3 = e2)
% 175.79/27.09    (113)  op(e2, e3) = all_52_9
% 175.79/27.09    (114)  all_56_13 = all_52_27
% 175.79/27.09  
% 175.79/27.09  Begin of proof
% 175.79/27.09  | 
% 175.79/27.09  | BETA: splitting (53) gives:
% 175.79/27.09  | 
% 175.79/27.09  | Case 1:
% 175.79/27.09  | | 
% 175.79/27.09  | |   (115)  all_58_12 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | REF_CLOSE: (1), (107), (115) are inconsistent by sub-proof #1003.
% 175.79/27.09  | | 
% 175.79/27.09  | Case 2:
% 175.79/27.09  | | 
% 175.79/27.09  | |   (116)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 175.79/27.09  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.79/27.09  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.79/27.09  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.79/27.09  | |            (47), (48), (49), (50), (51), (52), (54), (55), (56), (57), (58),
% 175.79/27.09  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 175.79/27.09  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 175.79/27.09  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 175.79/27.09  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 175.79/27.09  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 175.79/27.09  | |            (111), (112), (113), (114), (116) are inconsistent by sub-proof
% 175.79/27.09  | |            #148.
% 175.79/27.09  | | 
% 175.79/27.09  | End of split
% 175.79/27.09  | 
% 175.79/27.09  End of proof
% 175.79/27.09  
% 175.79/27.09  Sub-proof #148 shows that the following formulas are inconsistent:
% 175.79/27.09  ----------------------------------------------------------------
% 175.79/27.09    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.79/27.09    (2)   ~ (all_52_17 = all_52_23)
% 175.79/27.09    (3)  all_40_2 = all_4_2
% 175.79/27.09    (4)   ~ (all_52_13 = all_52_29)
% 175.79/27.09    (5)  op(e3, e2) = all_52_3
% 175.79/27.09    (6)  op(e3, all_52_25) = all_52_24
% 175.79/27.09    (7)   ~ (all_52_19 = all_52_23)
% 175.79/27.09    (8)  all_56_11 = all_52_23
% 175.79/27.09    (9)  op(e1, e2) = all_52_19
% 175.79/27.09    (10)   ~ (all_6_2 = e3)
% 175.79/27.09    (11)  op(e3, all_52_9) = all_52_8
% 175.79/27.09    (12)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.79/27.09    (13)   ~ (all_52_3 = all_10_2)
% 175.79/27.09    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.79/27.09    (15)  all_58_5 = all_52_13
% 175.79/27.09    (16)   ~ (all_6_2 = e0)
% 175.79/27.09    (17)   ~ (all_52_25 = all_52_29)
% 175.79/27.09    (18)  all_56_15 = all_6_2
% 175.79/27.09    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.79/27.09    (20)  op(e2, e0) = all_52_15
% 175.79/27.09    (21)  all_58_3 = all_10_2
% 175.79/27.09    (22)  all_56_9 = all_52_19
% 175.79/27.09    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.79/27.09    (24)  all_58_15 = all_6_2
% 175.79/27.09    (25)   ~ (all_52_9 = all_4_2)
% 175.79/27.09    (26)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.09    (27)  all_58_10 = all_52_15
% 175.79/27.09    (28)  all_8_2 = all_6_2
% 175.79/27.09    (29)   ~ (all_52_5 = all_4_2)
% 175.79/27.09    (30)  all_58_7 = all_52_19
% 175.79/27.09    (31)   ~ (all_52_15 = all_6_2)
% 175.79/27.09    (32)   ~ (all_52_17 = all_52_25)
% 175.79/27.09    (33)  op(e0, e1) = all_52_29
% 175.79/27.09    (34)   ~ (all_4_0 = e2)
% 175.79/27.09    (35)  all_58_4 = all_52_5
% 175.79/27.09    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.09    (37)   ~ (e3 = e1)
% 175.79/27.09    (38)   ~ (all_52_27 = all_52_29)
% 175.79/27.09    (39)  op(e3, all_4_2) = all_4_1
% 175.79/27.09    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.09    (41)   ~ (all_52_7 = all_4_2)
% 175.79/27.09    (42)  all_58_1 = all_52_3
% 175.79/27.09    (43)  all_58_0 = all_4_2
% 175.79/27.09    (44)  op(e1, all_52_29) = all_52_28
% 175.79/27.09    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.79/27.09    (46)   ~ (all_4_1 = e2)
% 175.79/27.09    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.09    (48)  all_58_14 = all_52_29
% 175.79/27.09    (49)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.79/27.09    (50)   ~ (all_52_3 = all_52_5)
% 175.79/27.09    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.09    (52)  all_58_8 = all_14_2
% 175.79/27.09    (53)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 175.79/27.09    (54)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.79/27.09    (55)  op(all_4_1, all_4_2) = all_4_0
% 175.79/27.09    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.79/27.09    (57)   ~ (all_52_5 = all_14_2)
% 175.79/27.09    (58)   ~ (all_52_3 = all_52_27)
% 175.79/27.09    (59)   ~ (all_52_3 = all_4_2)
% 175.79/27.09    (60)  op(e0, e3) = all_52_25
% 175.79/27.09    (61)  op(e0, all_6_2) = all_6_1
% 175.79/27.09    (62)   ~ (all_52_9 = all_10_2)
% 175.79/27.09    (63)  all_40_0 = all_4_0
% 175.79/27.09    (64)   ~ (all_52_9 = all_52_13)
% 175.79/27.09    (65)   ~ (all_52_15 = all_52_23)
% 175.79/27.09    (66)  op(e1, e0) = all_52_23
% 175.79/27.09    (67)  all_58_13 = all_52_27
% 175.79/27.09    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.09    (69)   ~ (all_52_9 = all_52_17)
% 175.79/27.09    (70)  all_58_6 = all_52_17
% 175.79/27.09    (71)  op(e2, all_52_19) = e2
% 175.79/27.09    (72)  op(e3, all_52_17) = e3
% 175.79/27.09    (73)  all_56_0 = all_4_2
% 175.79/27.09    (74)  all_58_11 = all_52_23
% 175.79/27.09    (75)   ~ (all_52_3 = all_52_19)
% 175.79/27.09    (76)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.79/27.09    (77)   ~ (all_52_29 = all_14_2)
% 175.79/27.09    (78)   ~ (all_4_0 = e1)
% 175.79/27.09    (79)  op(e1, all_4_2) = all_4_0
% 175.79/27.09    (80)   ~ (all_52_29 = all_6_2)
% 175.79/27.09    (81)  all_58_2 = all_52_9
% 175.79/27.09    (82)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.79/27.09    (83)  op(e3, e1) = all_52_5
% 175.79/27.09    (84)   ~ (all_52_25 = all_6_2)
% 175.79/27.09    (85)  op(e1, e3) = all_52_17
% 175.79/27.09    (86)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.79/27.09    (87)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 175.79/27.09    (88)   ~ (all_52_25 = all_4_2)
% 175.79/27.09    (89)  op(e3, e0) = all_52_7
% 175.79/27.09    (90)  op(e3, e3) = all_4_2
% 175.79/27.09    (91)  all_56_8 = all_52_17
% 175.79/27.09    (92)   ~ (all_52_17 = all_4_2)
% 175.79/27.09    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.09    (94)   ~ (all_52_25 = all_52_27)
% 175.79/27.09    (95)   ~ (all_52_27 = all_6_2)
% 175.79/27.09    (96)  all_8_1 = all_6_1
% 175.79/27.09    (97)   ~ (all_52_7 = all_6_2)
% 175.79/27.09    (98)  op(e0, all_52_23) = e0
% 175.79/27.09    (99)   ~ (all_52_19 = all_52_27)
% 175.79/27.09    (100)  all_56_7 = all_52_15
% 175.79/27.09    (101)  op(e1, all_14_2) = e1
% 175.79/27.09    (102)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.09    (103)   ~ (all_52_7 = all_52_23)
% 175.79/27.09    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.79/27.09    (105)  all_58_9 = all_52_7
% 175.79/27.09    (106)  all_58_12 = all_52_25
% 175.79/27.09    (107)  op(e3, all_4_2) = e1
% 175.79/27.09    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.79/27.09    (109)   ~ (all_52_9 = all_52_15)
% 175.79/27.09    (110)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.79/27.09    (111)   ~ (e3 = e2)
% 175.79/27.09    (112)  op(e2, e3) = all_52_9
% 175.79/27.09    (113)  all_56_13 = all_52_27
% 175.79/27.09  
% 175.79/27.09  Begin of proof
% 175.79/27.09  | 
% 175.79/27.09  | BETA: splitting (49) gives:
% 175.79/27.09  | 
% 175.79/27.09  | Case 1:
% 175.79/27.09  | | 
% 175.79/27.09  | |   (114)  all_56_13 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | COMBINE_EQS: (113), (114) imply:
% 175.79/27.09  | |   (115)  all_52_27 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | SIMP: (115) implies:
% 175.79/27.09  | |   (116)  all_52_27 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | REF_CLOSE: (3), (5), (9), (22), (23), (24), (27), (29), (30), (34), (35),
% 175.79/27.09  | |            (36), (37), (40), (41), (42), (43), (45), (51), (52), (53), (57),
% 175.79/27.09  | |            (58), (60), (63), (65), (68), (69), (70), (71), (72), (73), (74),
% 175.79/27.09  | |            (75), (79), (81), (83), (85), (86), (88), (90), (92), (93), (94),
% 175.79/27.09  | |            (95), (98), (99), (100), (101), (103), (104), (105), (106),
% 175.79/27.09  | |            (107), (108), (110), (111), (112), (116) are inconsistent by
% 175.79/27.09  | |            sub-proof #246.
% 175.79/27.09  | | 
% 175.79/27.09  | Case 2:
% 175.79/27.09  | | 
% 175.79/27.09  | |   (117)   ~ (all_56_13 = e3)
% 175.79/27.09  | | 
% 175.79/27.09  | | REDUCE: (113), (117) imply:
% 175.79/27.09  | |   (118)   ~ (all_52_27 = e3)
% 175.79/27.09  | | 
% 175.79/27.09  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 175.79/27.09  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 175.79/27.09  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 175.79/27.09  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 175.79/27.09  | |            (47), (48), (50), (51), (52), (54), (55), (56), (57), (59), (60),
% 175.79/27.09  | |            (61), (62), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 175.79/27.09  | |            (73), (74), (75), (76), (77), (78), (80), (81), (82), (83), (84),
% 175.79/27.09  | |            (85), (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 175.79/27.09  | |            (97), (98), (101), (102), (103), (104), (105), (106), (109),
% 175.79/27.09  | |            (111), (112), (118) are inconsistent by sub-proof #203.
% 175.79/27.09  | | 
% 175.79/27.09  | End of split
% 175.79/27.09  | 
% 175.79/27.09  End of proof
% 175.79/27.09  
% 175.79/27.09  Sub-proof #149 shows that the following formulas are inconsistent:
% 175.79/27.09  ----------------------------------------------------------------
% 175.79/27.09    (1)   ~ (all_10_2 = e0)
% 175.79/27.09    (2)   ~ (all_52_27 = e3)
% 175.79/27.09    (3)  all_58_3 = all_10_2
% 175.79/27.09    (4)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.09    (5)   ~ (all_52_5 = all_4_2)
% 175.79/27.09    (6)  all_58_7 = all_52_19
% 175.79/27.09    (7)  all_58_0 = all_4_2
% 175.79/27.09    (8)   ~ (all_10_2 = e3)
% 175.79/27.09    (9)  op(e2, e1) = all_52_13
% 175.79/27.09    (10)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.79/27.09    (11)   ~ (all_52_9 = all_10_2)
% 175.79/27.09    (12)  op(e3, all_10_2) = e1
% 175.79/27.09    (13)  all_58_13 = all_52_27
% 175.79/27.09    (14)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.09    (15)  all_56_5 = all_10_2
% 175.79/27.09    (16)  all_58_12 = e3
% 175.79/27.09    (17)  all_58_6 = all_52_17
% 175.79/27.09    (18)  op(e2, all_52_19) = e2
% 175.79/27.09    (19)  op(e3, all_52_17) = e3
% 175.79/27.09    (20)  all_58_2 = all_52_9
% 175.79/27.09    (21)  op(e3, e1) = all_52_5
% 175.79/27.09    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.09    (23)   ~ (all_52_13 = all_10_2)
% 175.79/27.09    (24)   ~ (all_52_17 = all_52_19)
% 175.79/27.09    (25)  op(e2, all_10_2) = e3
% 175.79/27.09    (26)  op(e2, e3) = all_52_9
% 175.79/27.09  
% 175.79/27.09  Begin of proof
% 175.79/27.09  | 
% 175.79/27.09  | BETA: splitting (4) gives:
% 175.79/27.09  | 
% 175.79/27.09  | Case 1:
% 175.79/27.09  | | 
% 175.79/27.09  | |   (27)  all_58_3 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | COMBINE_EQS: (3), (27) imply:
% 175.79/27.09  | |   (28)  all_10_2 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | REDUCE: (8), (28) imply:
% 175.79/27.09  | |   (29)  $false
% 175.79/27.09  | | 
% 175.79/27.09  | | CLOSE: (29) is inconsistent.
% 175.79/27.09  | | 
% 175.79/27.09  | Case 2:
% 175.79/27.09  | | 
% 175.79/27.09  | |   (30)  all_58_7 = e3 | all_58_13 = e3
% 175.79/27.09  | | 
% 175.79/27.09  | | BETA: splitting (30) gives:
% 175.79/27.09  | | 
% 175.79/27.09  | | Case 1:
% 175.79/27.09  | | | 
% 175.79/27.09  | | |   (31)  all_58_7 = e3
% 175.79/27.09  | | | 
% 175.79/27.09  | | | COMBINE_EQS: (6), (31) imply:
% 175.79/27.09  | | |   (32)  all_52_19 = e3
% 175.79/27.09  | | | 
% 175.79/27.09  | | | REDUCE: (24), (32) imply:
% 175.79/27.09  | | |   (33)   ~ (all_52_17 = e3)
% 175.79/27.09  | | | 
% 175.79/27.09  | | | REDUCE: (18), (32) imply:
% 175.79/27.09  | | |   (34)  op(e2, e3) = e2
% 175.79/27.09  | | | 
% 175.79/27.09  | | | GROUND_INST: instantiating (22) with all_52_9, e2, e3, e2, simplifying
% 175.79/27.09  | | |              with (26), (34) gives:
% 175.79/27.09  | | |   (35)  all_52_9 = e2
% 175.79/27.09  | | | 
% 175.79/27.09  | | | COMBINE_EQS: (20), (35) imply:
% 175.79/27.09  | | |   (36)  all_58_2 = e2
% 175.79/27.09  | | | 
% 175.79/27.09  | | | REDUCE: (11), (35) imply:
% 175.79/27.09  | | |   (37)   ~ (all_10_2 = e2)
% 175.79/27.09  | | | 
% 175.79/27.09  | | | SIMP: (37) implies:
% 175.79/27.09  | | |   (38)   ~ (all_10_2 = e2)
% 175.79/27.09  | | | 
% 175.79/27.09  | | | BETA: splitting (10) gives:
% 175.79/27.09  | | | 
% 175.79/27.09  | | | Case 1:
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | |   (39)  all_56_5 = e2
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | REF_CLOSE: (15), (38), (39) are inconsistent by sub-proof #710.
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | Case 2:
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | |   (40)   ~ (all_56_5 = e2)
% 175.79/27.09  | | | |   (41)  all_56_5 = e1 | all_56_5 = e0
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | BETA: splitting (41) gives:
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | Case 1:
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | |   (42)  all_56_5 = e1
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | COMBINE_EQS: (15), (42) imply:
% 175.79/27.09  | | | | |   (43)  all_10_2 = e1
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | SIMP: (43) implies:
% 175.79/27.09  | | | | |   (44)  all_10_2 = e1
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REDUCE: (23), (44) imply:
% 175.79/27.09  | | | | |   (45)   ~ (all_52_13 = e1)
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REDUCE: (38), (44) imply:
% 175.79/27.09  | | | | |   (46)   ~ (e2 = e1)
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | SIMP: (46) implies:
% 175.79/27.09  | | | | |   (47)   ~ (e2 = e1)
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REDUCE: (12), (44) imply:
% 175.79/27.09  | | | | |   (48)  op(e3, e1) = e1
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REDUCE: (25), (44) imply:
% 175.79/27.09  | | | | |   (49)  op(e2, e1) = e3
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | GROUND_INST: instantiating (22) with all_52_13, e3, e1, e2,
% 175.79/27.09  | | | | |              simplifying with (9), (49) gives:
% 175.79/27.09  | | | | |   (50)  all_52_13 = e3
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | GROUND_INST: instantiating (22) with all_52_5, e1, e1, e3, simplifying
% 175.79/27.09  | | | | |              with (21), (48) gives:
% 175.79/27.09  | | | | |   (51)  all_52_5 = e1
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REDUCE: (5), (51) imply:
% 175.79/27.09  | | | | |   (52)   ~ (all_4_2 = e1)
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | SIMP: (52) implies:
% 175.79/27.09  | | | | |   (53)   ~ (all_4_2 = e1)
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REDUCE: (45), (50) imply:
% 175.79/27.09  | | | | |   (54)   ~ (e3 = e1)
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | BETA: splitting (14) gives:
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | Case 1:
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | |   (55)  all_58_0 = e1
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | | COMBINE_EQS: (7), (55) imply:
% 175.79/27.09  | | | | | |   (56)  all_4_2 = e1
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | | REDUCE: (53), (56) imply:
% 175.79/27.09  | | | | | |   (57)  $false
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | | CLOSE: (57) is inconsistent.
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | Case 2:
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | |   (58)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | | BETA: splitting (58) gives:
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | | Case 1:
% 175.79/27.09  | | | | | | | 
% 175.79/27.09  | | | | | | |   (59)  all_58_2 = e1
% 175.79/27.09  | | | | | | | 
% 175.79/27.09  | | | | | | | REF_CLOSE: (36), (47), (59) are inconsistent by sub-proof #921.
% 175.79/27.09  | | | | | | | 
% 175.79/27.09  | | | | | | Case 2:
% 175.79/27.09  | | | | | | | 
% 175.79/27.09  | | | | | | |   (60)  all_58_6 = e1 | all_58_12 = e1
% 175.79/27.09  | | | | | | | 
% 175.79/27.09  | | | | | | | BETA: splitting (60) gives:
% 175.79/27.09  | | | | | | | 
% 175.79/27.09  | | | | | | | Case 1:
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | |   (61)  all_58_6 = e1
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | | COMBINE_EQS: (17), (61) imply:
% 175.79/27.09  | | | | | | | |   (62)  all_52_17 = e1
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | | SIMP: (62) implies:
% 175.79/27.09  | | | | | | | |   (63)  all_52_17 = e1
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | | REDUCE: (33), (63) imply:
% 175.79/27.09  | | | | | | | |   (64)   ~ (e3 = e1)
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | | REDUCE: (19), (63) imply:
% 175.79/27.09  | | | | | | | |   (65)  op(e3, e1) = e3
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | | REF_CLOSE: (22), (48), (54), (65) are inconsistent by sub-proof
% 175.79/27.09  | | | | | | | |            #613.
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | Case 2:
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | |   (66)  all_58_12 = e1
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | | REF_CLOSE: (16), (54), (66) are inconsistent by sub-proof #920.
% 175.79/27.09  | | | | | | | | 
% 175.79/27.09  | | | | | | | End of split
% 175.79/27.09  | | | | | | | 
% 175.79/27.09  | | | | | | End of split
% 175.79/27.09  | | | | | | 
% 175.79/27.09  | | | | | End of split
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | Case 2:
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | |   (67)  all_56_5 = e0
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REF_CLOSE: (1), (15), (67) are inconsistent by sub-proof #708.
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | End of split
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | End of split
% 175.79/27.09  | | | 
% 175.79/27.09  | | Case 2:
% 175.79/27.09  | | | 
% 175.79/27.09  | | |   (68)  all_58_13 = e3
% 175.79/27.09  | | | 
% 175.79/27.09  | | | REF_CLOSE: (2), (13), (68) are inconsistent by sub-proof #1026.
% 175.79/27.09  | | | 
% 175.79/27.09  | | End of split
% 175.79/27.09  | | 
% 175.79/27.09  | End of split
% 175.79/27.09  | 
% 175.79/27.09  End of proof
% 175.79/27.09  
% 175.79/27.09  Sub-proof #150 shows that the following formulas are inconsistent:
% 175.79/27.09  ----------------------------------------------------------------
% 175.79/27.09    (1)   ~ (all_52_9 = all_52_25)
% 175.79/27.09    (2)  all_56_9 = all_52_19
% 175.79/27.09    (3)  all_58_2 = e3
% 175.79/27.09    (4)   ~ (all_52_9 = all_4_2)
% 175.79/27.09    (5)  all_58_7 = all_52_19
% 175.79/27.09    (6)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.09    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.09    (8)  all_58_0 = all_4_2
% 175.79/27.09    (9)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.79/27.09    (10)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.09    (11)  all_58_8 = all_14_2
% 175.79/27.09    (12)   ~ (all_52_5 = all_14_2)
% 175.79/27.09    (13)   ~ (all_52_23 = e3)
% 175.79/27.09    (14)   ~ (all_52_9 = all_52_17)
% 175.79/27.09    (15)  all_58_6 = all_52_17
% 175.79/27.09    (16)  op(e2, all_52_19) = e2
% 175.79/27.09    (17)  op(e3, all_52_17) = e3
% 175.79/27.09    (18)  all_58_11 = all_52_23
% 175.79/27.09    (19)  all_58_2 = all_52_9
% 175.79/27.09    (20)  op(e3, e1) = all_52_5
% 175.79/27.09    (21)  op(e1, e3) = all_52_17
% 175.79/27.09    (22)  op(e3, e3) = all_4_2
% 175.79/27.09    (23)   ~ (all_52_17 = all_4_2)
% 175.79/27.09    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.09    (25)  op(e1, all_14_2) = e1
% 175.79/27.09    (26)  all_58_12 = all_52_25
% 175.79/27.09    (27)   ~ (e3 = e2)
% 175.79/27.09    (28)  op(e2, e3) = all_52_9
% 175.79/27.09  
% 175.79/27.09  Begin of proof
% 175.79/27.09  | 
% 175.79/27.09  | COMBINE_EQS: (3), (19) imply:
% 175.79/27.09  |   (29)  all_52_9 = e3
% 175.79/27.09  | 
% 175.79/27.09  | SIMP: (29) implies:
% 175.79/27.09  |   (30)  all_52_9 = e3
% 175.79/27.09  | 
% 175.79/27.09  | REDUCE: (1), (30) imply:
% 175.79/27.09  |   (31)   ~ (all_52_25 = e3)
% 175.79/27.09  | 
% 175.79/27.09  | SIMP: (31) implies:
% 175.79/27.09  |   (32)   ~ (all_52_25 = e3)
% 175.79/27.09  | 
% 175.79/27.09  | REDUCE: (4), (30) imply:
% 175.79/27.09  |   (33)   ~ (all_4_2 = e3)
% 175.79/27.09  | 
% 175.79/27.09  | SIMP: (33) implies:
% 175.79/27.09  |   (34)   ~ (all_4_2 = e3)
% 175.79/27.09  | 
% 175.79/27.09  | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 175.79/27.09  |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 175.79/27.09  |            (27), (28), (32), (34) are inconsistent by sub-proof #944.
% 175.79/27.09  | 
% 175.79/27.09  End of proof
% 175.79/27.09  
% 175.79/27.09  Sub-proof #151 shows that the following formulas are inconsistent:
% 175.79/27.09  ----------------------------------------------------------------
% 175.79/27.09    (1)  op(e2, e2) = all_10_2
% 175.79/27.09    (2)   ~ (all_10_2 = e0)
% 175.79/27.09    (3)  all_58_3 = all_10_2
% 175.79/27.09    (4)  op(e2, e1) = e0
% 175.79/27.09    (5)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.79/27.09    (6)   ~ (all_10_2 = e3)
% 175.79/27.09    (7)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.79/27.09    (8)   ~ (all_52_9 = all_10_2)
% 175.79/27.09    (9)   ~ (e3 = e0)
% 175.79/27.09    (10)  all_56_5 = all_10_2
% 175.79/27.09    (11)  all_58_2 = all_52_9
% 175.79/27.09    (12)   ~ (e2 = e1)
% 175.79/27.09    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.09    (14)  op(e2, all_10_2) = e3
% 175.79/27.09    (15)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 175.79/27.09  
% 175.79/27.09  Begin of proof
% 175.79/27.09  | 
% 175.79/27.09  | BETA: splitting (5) gives:
% 175.79/27.09  | 
% 175.79/27.09  | Case 1:
% 175.79/27.09  | | 
% 175.79/27.09  | |   (16)  all_58_2 = e1
% 175.79/27.09  | | 
% 175.79/27.09  | | COMBINE_EQS: (11), (16) imply:
% 175.79/27.09  | |   (17)  all_52_9 = e1
% 175.79/27.09  | | 
% 175.79/27.09  | | SIMP: (17) implies:
% 175.79/27.09  | |   (18)  all_52_9 = e1
% 175.79/27.09  | | 
% 175.79/27.09  | | REDUCE: (8), (18) imply:
% 175.79/27.09  | |   (19)   ~ (all_10_2 = e1)
% 175.79/27.09  | | 
% 175.79/27.09  | | SIMP: (19) implies:
% 175.79/27.09  | |   (20)   ~ (all_10_2 = e1)
% 175.79/27.09  | | 
% 175.79/27.09  | | BETA: splitting (15) gives:
% 175.79/27.09  | | 
% 175.79/27.09  | | Case 1:
% 175.79/27.09  | | | 
% 175.79/27.09  | | |   (21)  all_58_2 = e2
% 175.79/27.09  | | | 
% 175.79/27.09  | | | COMBINE_EQS: (16), (21) imply:
% 175.79/27.09  | | |   (22)  e2 = e1
% 175.79/27.09  | | | 
% 175.79/27.09  | | | REDUCE: (12), (22) imply:
% 175.79/27.09  | | |   (23)  $false
% 175.79/27.09  | | | 
% 175.79/27.09  | | | CLOSE: (23) is inconsistent.
% 175.79/27.09  | | | 
% 175.79/27.09  | | Case 2:
% 175.79/27.09  | | | 
% 175.79/27.09  | | |   (24)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 175.79/27.09  | | | 
% 175.79/27.09  | | | BETA: splitting (24) gives:
% 175.79/27.09  | | | 
% 175.79/27.09  | | | Case 1:
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | |   (25)  all_58_3 = e2
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | COMBINE_EQS: (3), (25) imply:
% 175.79/27.09  | | | |   (26)  all_10_2 = e2
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | REDUCE: (6), (26) imply:
% 175.79/27.09  | | | |   (27)   ~ (e3 = e2)
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | SIMP: (27) implies:
% 175.79/27.09  | | | |   (28)   ~ (e3 = e2)
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | REDUCE: (14), (26) imply:
% 175.79/27.09  | | | |   (29)  op(e2, e2) = e3
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | REDUCE: (1), (26) imply:
% 175.79/27.09  | | | |   (30)  op(e2, e2) = e2
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | GROUND_INST: instantiating (13) with e2, e3, e2, e2, simplifying with
% 175.79/27.09  | | | |              (29), (30) gives:
% 175.79/27.09  | | | |   (31)  e3 = e2
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | REDUCE: (28), (31) imply:
% 175.79/27.09  | | | |   (32)  $false
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | CLOSE: (32) is inconsistent.
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | Case 2:
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | |   (33)   ~ (all_58_3 = e2)
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | REDUCE: (3), (33) imply:
% 175.79/27.09  | | | |   (34)   ~ (all_10_2 = e2)
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | BETA: splitting (7) gives:
% 175.79/27.09  | | | | 
% 175.79/27.09  | | | | Case 1:
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | |   (35)  all_56_5 = e2
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | | REF_CLOSE: (10), (34), (35) are inconsistent by sub-proof #710.
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | Case 2:
% 175.79/27.09  | | | | | 
% 175.79/27.09  | | | | |   (36)  all_56_5 = e1 | all_56_5 = e0
% 175.79/27.10  | | | | | 
% 175.79/27.10  | | | | | REF_CLOSE: (2), (10), (20), (36) are inconsistent by sub-proof #527.
% 175.79/27.10  | | | | | 
% 175.79/27.10  | | | | End of split
% 175.79/27.10  | | | | 
% 175.79/27.10  | | | End of split
% 175.79/27.10  | | | 
% 175.79/27.10  | | End of split
% 175.79/27.10  | | 
% 175.79/27.10  | Case 2:
% 175.79/27.10  | | 
% 175.79/27.10  | |   (37)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.79/27.10  | | 
% 175.79/27.10  | | BETA: splitting (37) gives:
% 175.79/27.10  | | 
% 175.79/27.10  | | Case 1:
% 175.79/27.10  | | | 
% 175.79/27.10  | | |   (38)  all_58_3 = e1
% 175.79/27.10  | | | 
% 175.79/27.10  | | | COMBINE_EQS: (3), (38) imply:
% 175.79/27.10  | | |   (39)  all_10_2 = e1
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (14), (39) imply:
% 175.79/27.10  | | |   (40)  op(e2, e1) = e3
% 175.79/27.10  | | | 
% 175.79/27.10  | | | GROUND_INST: instantiating (13) with e0, e3, e1, e2, simplifying with (4),
% 175.79/27.10  | | |              (40) gives:
% 175.79/27.10  | | |   (41)  e3 = e0
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (9), (41) imply:
% 175.79/27.10  | | |   (42)  $false
% 175.79/27.10  | | | 
% 175.79/27.10  | | | CLOSE: (42) is inconsistent.
% 175.79/27.10  | | | 
% 175.79/27.10  | | Case 2:
% 175.79/27.10  | | | 
% 175.79/27.10  | | |   (43)   ~ (all_58_3 = e1)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (3), (43) imply:
% 175.79/27.10  | | |   (44)   ~ (all_10_2 = e1)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REF_CLOSE: (1), (2), (6), (7), (10), (13), (14), (44) are inconsistent by
% 175.79/27.10  | | |            sub-proof #152.
% 175.79/27.10  | | | 
% 175.79/27.10  | | End of split
% 175.79/27.10  | | 
% 175.79/27.10  | End of split
% 175.79/27.10  | 
% 175.79/27.10  End of proof
% 175.79/27.10  
% 175.79/27.10  Sub-proof #152 shows that the following formulas are inconsistent:
% 175.79/27.10  ----------------------------------------------------------------
% 175.79/27.10    (1)  op(e2, e2) = all_10_2
% 175.79/27.10    (2)   ~ (all_10_2 = e0)
% 175.79/27.10    (3)   ~ (all_10_2 = e1)
% 175.79/27.10    (4)   ~ (all_10_2 = e3)
% 175.79/27.10    (5)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.79/27.10    (6)  all_56_5 = all_10_2
% 175.79/27.10    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.10    (8)  op(e2, all_10_2) = e3
% 175.79/27.10  
% 175.79/27.10  Begin of proof
% 175.79/27.10  | 
% 175.79/27.10  | BETA: splitting (5) gives:
% 175.79/27.10  | 
% 175.79/27.10  | Case 1:
% 175.79/27.10  | | 
% 175.79/27.10  | |   (9)  all_56_5 = e2
% 175.79/27.10  | | 
% 175.79/27.10  | | COMBINE_EQS: (6), (9) imply:
% 175.79/27.10  | |   (10)  all_10_2 = e2
% 175.79/27.10  | | 
% 175.79/27.10  | | SIMP: (10) implies:
% 175.79/27.10  | |   (11)  all_10_2 = e2
% 175.79/27.10  | | 
% 175.79/27.10  | | REDUCE: (4), (11) imply:
% 175.79/27.10  | |   (12)   ~ (e3 = e2)
% 175.79/27.10  | | 
% 175.79/27.10  | | SIMP: (12) implies:
% 175.79/27.10  | |   (13)   ~ (e3 = e2)
% 175.79/27.10  | | 
% 175.79/27.10  | | REDUCE: (8), (11) imply:
% 175.79/27.10  | |   (14)  op(e2, e2) = e3
% 175.79/27.10  | | 
% 175.79/27.10  | | REDUCE: (1), (11) imply:
% 175.79/27.10  | |   (15)  op(e2, e2) = e2
% 175.79/27.10  | | 
% 175.79/27.10  | | REF_CLOSE: (7), (13), (14), (15) are inconsistent by sub-proof #848.
% 175.79/27.10  | | 
% 175.79/27.10  | Case 2:
% 175.79/27.10  | | 
% 175.79/27.10  | |   (16)  all_56_5 = e1 | all_56_5 = e0
% 175.79/27.10  | | 
% 175.79/27.10  | | REF_CLOSE: (2), (3), (6), (16) are inconsistent by sub-proof #527.
% 175.79/27.10  | | 
% 175.79/27.10  | End of split
% 175.79/27.10  | 
% 175.79/27.10  End of proof
% 175.79/27.10  
% 175.79/27.10  Sub-proof #153 shows that the following formulas are inconsistent:
% 175.79/27.10  ----------------------------------------------------------------
% 175.79/27.10    (1)   ~ (all_52_23 = all_14_2)
% 175.79/27.10    (2)  op(e3, e2) = all_52_3
% 175.79/27.10    (3)  op(e1, e2) = all_52_19
% 175.79/27.10    (4)   ~ (all_52_17 = e3)
% 175.79/27.10    (5)  op(e3, all_52_9) = all_52_8
% 175.79/27.10    (6)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.79/27.10    (7)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 175.79/27.10    (8)  all_58_5 = all_52_13
% 175.79/27.10    (9)   ~ (all_6_2 = e0)
% 175.79/27.10    (10)   ~ (all_52_25 = all_52_29)
% 175.79/27.10    (11)  all_56_15 = all_6_2
% 175.79/27.10    (12)  all_58_3 = all_10_2
% 175.79/27.10    (13)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.10    (14)  all_8_2 = all_6_2
% 175.79/27.10    (15)   ~ (all_52_5 = all_4_2)
% 175.79/27.10    (16)  all_58_7 = all_52_19
% 175.79/27.10    (17)  op(e0, e1) = all_52_29
% 175.79/27.10    (18)   ~ (all_4_0 = e2)
% 175.79/27.10    (19)  all_58_4 = all_52_5
% 175.79/27.10    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.10    (21)   ~ (all_52_17 = all_14_2)
% 175.79/27.10    (22)  op(e3, all_4_2) = all_4_1
% 175.79/27.10    (23)  all_58_1 = all_52_3
% 175.79/27.10    (24)  all_58_0 = all_4_2
% 175.79/27.10    (25)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.79/27.10    (26)  all_58_14 = all_52_29
% 175.79/27.10    (27)   ~ (all_52_3 = all_52_5)
% 175.79/27.10    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.10    (29)  all_58_8 = all_14_2
% 175.79/27.10    (30)  all_56_14 = all_52_29
% 175.79/27.10    (31)  op(all_4_1, all_4_2) = all_4_0
% 175.79/27.10    (32)   ~ (all_52_5 = all_14_2)
% 175.79/27.10    (33)   ~ (all_52_23 = e3)
% 175.79/27.10    (34)  op(e0, all_6_2) = all_6_1
% 175.79/27.10    (35)   ~ (all_52_9 = all_10_2)
% 175.79/27.10    (36)   ~ (all_52_13 = e3)
% 175.79/27.10    (37)   ~ (all_52_9 = all_52_13)
% 175.79/27.10    (38)  all_58_13 = all_52_27
% 175.79/27.10    (39)  all_58_6 = all_52_17
% 175.79/27.10    (40)  op(e2, all_52_19) = e2
% 175.79/27.10    (41)  op(e3, all_52_17) = e3
% 175.79/27.10    (42)  all_58_11 = all_52_23
% 175.79/27.10    (43)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.79/27.10    (44)   ~ (all_52_29 = all_14_2)
% 175.79/27.10    (45)   ~ (all_4_0 = e1)
% 175.79/27.10    (46)   ~ (all_52_9 = e3)
% 175.79/27.10    (47)  all_58_2 = all_52_9
% 175.79/27.10    (48)  op(e3, e1) = all_52_5
% 175.79/27.10    (49)  op(e1, e3) = all_52_17
% 175.79/27.10    (50)  op(e3, e3) = all_4_2
% 175.79/27.10    (51)   ~ (all_52_17 = all_4_2)
% 175.79/27.10    (52)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.79/27.10    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.10            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.10    (54)   ~ (all_52_27 = all_6_2)
% 175.79/27.10    (55)  all_8_1 = all_6_1
% 175.79/27.10    (56)  op(e1, all_14_2) = e1
% 175.79/27.10    (57)  all_58_12 = all_52_25
% 175.79/27.10    (58)   ~ (all_52_19 = all_14_2)
% 175.79/27.10    (59)  op(e2, e3) = all_52_9
% 175.79/27.10  
% 175.79/27.10  Begin of proof
% 175.79/27.10  | 
% 175.79/27.10  | BETA: splitting (20) gives:
% 175.79/27.10  | 
% 175.79/27.10  | Case 1:
% 175.79/27.10  | | 
% 175.79/27.10  | |   (60)  all_58_6 = e3
% 175.79/27.10  | | 
% 175.79/27.10  | | REF_CLOSE: (4), (39), (60) are inconsistent by sub-proof #981.
% 175.79/27.10  | | 
% 175.79/27.10  | Case 2:
% 175.79/27.10  | | 
% 175.79/27.10  | |   (61)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.10  | | 
% 175.79/27.10  | | BETA: splitting (25) gives:
% 175.79/27.10  | | 
% 175.79/27.10  | | Case 1:
% 175.79/27.10  | | | 
% 175.79/27.10  | | |   (62)  all_56_14 = e3
% 175.79/27.10  | | | 
% 175.79/27.10  | | | COMBINE_EQS: (30), (62) imply:
% 175.79/27.10  | | |   (63)  all_52_29 = e3
% 175.79/27.10  | | | 
% 175.79/27.10  | | | SIMP: (63) implies:
% 175.79/27.10  | | |   (64)  all_52_29 = e3
% 175.79/27.10  | | | 
% 175.79/27.10  | | | COMBINE_EQS: (26), (64) imply:
% 175.79/27.10  | | |   (65)  all_58_14 = e3
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (10), (64) imply:
% 175.79/27.10  | | |   (66)   ~ (all_52_25 = e3)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (44), (64) imply:
% 175.79/27.10  | | |   (67)   ~ (all_14_2 = e3)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | SIMP: (67) implies:
% 175.79/27.10  | | |   (68)   ~ (all_14_2 = e3)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (17), (64) imply:
% 175.79/27.10  | | |   (69)  op(e0, e1) = e3
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 175.79/27.10  | | |            (15), (16), (18), (19), (22), (23), (24), (27), (28), (29),
% 175.79/27.10  | | |            (31), (33), (34), (35), (37), (38), (39), (40), (41), (42),
% 175.79/27.10  | | |            (43), (45), (46), (47), (50), (51), (53), (54), (55), (56),
% 175.79/27.10  | | |            (57), (59), (61), (65), (66), (68), (69) are inconsistent by
% 175.79/27.10  | | |            sub-proof #204.
% 175.79/27.10  | | | 
% 175.79/27.10  | | Case 2:
% 175.79/27.10  | | | 
% 175.79/27.10  | | |   (70)   ~ (all_56_14 = e3)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (30), (70) imply:
% 175.79/27.10  | | |   (71)   ~ (all_52_29 = e3)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REF_CLOSE: (1), (8), (16), (20), (21), (26), (29), (32), (36), (39), (41),
% 175.79/27.10  | | |            (42), (48), (49), (52), (53), (56), (58), (71) are inconsistent
% 175.79/27.10  | | |            by sub-proof #253.
% 175.79/27.10  | | | 
% 175.79/27.10  | | End of split
% 175.79/27.10  | | 
% 175.79/27.10  | End of split
% 175.79/27.10  | 
% 175.79/27.10  End of proof
% 175.79/27.10  
% 175.79/27.10  Sub-proof #154 shows that the following formulas are inconsistent:
% 175.79/27.10  ----------------------------------------------------------------
% 175.79/27.10    (1)   ~ (all_52_23 = all_14_2)
% 175.79/27.10    (2)   ~ (all_52_5 = all_52_13)
% 175.79/27.10    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.79/27.10    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.79/27.10    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.79/27.10    (6)   ~ (all_52_27 = all_10_2)
% 175.79/27.10    (7)   ~ (all_52_17 = all_52_23)
% 175.79/27.10    (8)  op(e2, all_10_2) = all_10_1
% 175.79/27.10    (9)  all_40_2 = all_4_2
% 175.79/27.10    (10)   ~ (all_52_13 = all_52_29)
% 175.79/27.10    (11)  all_56_3 = all_52_7
% 175.79/27.10    (12)  op(e3, e2) = all_52_3
% 175.79/27.10    (13)   ~ (all_52_9 = all_52_25)
% 175.79/27.10    (14)  op(e3, all_52_25) = all_52_24
% 175.79/27.10    (15)   ~ (all_52_19 = all_52_23)
% 175.79/27.10    (16)  all_16_0 = e2
% 175.79/27.10    (17)  all_56_11 = all_52_23
% 175.79/27.10    (18)  op(e1, e2) = all_52_19
% 175.79/27.10    (19)  all_16_1 = all_6_1
% 175.79/27.10    (20)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.79/27.10    (21)  op(e3, all_52_9) = all_52_8
% 175.79/27.10    (22)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.79/27.10    (23)  all_50_1 = all_4_1
% 175.79/27.10    (24)   ~ (all_52_3 = all_10_2)
% 175.79/27.10    (25)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.79/27.10    (26)  all_58_5 = all_52_13
% 175.79/27.10    (27)   ~ (all_52_25 = all_52_29)
% 175.79/27.10    (28)  all_16_2 = all_6_2
% 175.79/27.10    (29)  all_56_15 = all_6_2
% 175.79/27.10    (30)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.79/27.10    (31)  op(e2, e0) = all_52_15
% 175.79/27.10    (32)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.79/27.10    (33)  all_58_3 = all_10_2
% 175.79/27.10    (34)  all_56_9 = all_52_19
% 175.79/27.10    (35)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.79/27.10    (36)  all_58_15 = all_6_2
% 175.79/27.10    (37)   ~ (all_52_9 = all_4_2)
% 175.79/27.10    (38)   ~ (all_52_5 = all_52_7)
% 175.79/27.10    (39)  all_58_10 = all_52_15
% 175.79/27.10    (40)  all_8_2 = all_6_2
% 175.79/27.10    (41)   ~ (all_52_5 = all_4_2)
% 175.79/27.10    (42)  all_58_7 = all_52_19
% 175.79/27.10    (43)  all_56_4 = all_52_9
% 175.79/27.10    (44)   ~ (all_52_15 = all_6_2)
% 175.79/27.10    (45)   ~ (all_52_17 = all_52_25)
% 175.79/27.10    (46)  op(e0, e1) = all_52_29
% 175.79/27.10    (47)  all_58_4 = all_52_5
% 175.79/27.10    (48)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.10    (49)   ~ (e3 = e1)
% 175.79/27.10    (50)  all_34_1 = all_4_1
% 175.79/27.10    (51)   ~ (all_52_27 = all_52_29)
% 175.79/27.10    (52)   ~ (all_52_17 = all_14_2)
% 175.79/27.10    (53)  op(e3, all_4_2) = all_4_1
% 175.79/27.10    (54)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.10    (55)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.10    (56)   ~ (all_52_7 = all_4_2)
% 175.79/27.10    (57)  all_58_1 = all_52_3
% 175.79/27.10    (58)   ~ (all_52_13 = all_52_15)
% 175.79/27.10    (59)  all_58_0 = all_4_2
% 175.79/27.10    (60)  op(e1, all_52_13) = all_52_12
% 175.79/27.10    (61)  op(e0, e0) = all_6_2
% 175.79/27.10    (62)  op(e1, all_52_29) = all_52_28
% 175.79/27.10    (63)  all_50_0 = all_4_0
% 175.79/27.10    (64)  op(e1, all_52_5) = all_52_4
% 175.79/27.10    (65)  all_50_2 = all_4_2
% 175.79/27.10    (66)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.79/27.10    (67)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.79/27.10    (68)   ~ (all_4_1 = e2)
% 175.79/27.10    (69)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.79/27.10    (70)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.79/27.10    (71)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.10    (72)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.79/27.10    (73)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.79/27.10    (74)  all_58_14 = all_52_29
% 175.79/27.10    (75)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.79/27.10    (76)  all_24_0 = all_10_0
% 175.79/27.10    (77)  all_40_1 = all_4_1
% 175.79/27.10    (78)  all_26_2 = all_4_2
% 175.79/27.10    (79)   ~ (all_52_3 = all_52_5)
% 175.79/27.10    (80)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.10    (81)  op(e2, e1) = all_52_13
% 175.79/27.10    (82)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.10    (83)  all_58_8 = all_14_2
% 175.79/27.10    (84)  all_56_1 = all_52_3
% 175.79/27.10    (85)  op(e0, e2) = all_52_27
% 175.79/27.10    (86)  all_56_14 = all_52_29
% 175.79/27.10    (87)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.79/27.10    (88)  op(all_4_1, all_4_2) = all_4_0
% 175.79/27.10    (89)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.79/27.10    (90)   ~ (all_52_5 = all_14_2)
% 175.79/27.10    (91)   ~ (all_52_3 = all_52_27)
% 175.79/27.10    (92)   ~ (all_52_3 = all_4_2)
% 175.79/27.10    (93)  op(e0, e3) = all_52_25
% 175.79/27.10    (94)  op(e0, all_6_2) = all_6_1
% 175.79/27.10    (95)  all_52_0 = all_4_1
% 175.79/27.10    (96)   ~ (all_52_9 = all_10_2)
% 175.79/27.10    (97)  op(all_6_1, all_6_2) = e2
% 175.79/27.10    (98)   ~ (all_16_0 = e2) |  ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 175.79/27.10    (99)  op(e3, all_52_17) = all_52_16
% 175.79/27.10    (100)  all_52_10 = all_10_1
% 175.79/27.10    (101)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.79/27.10    (102)   ~ (all_52_13 = all_14_2)
% 175.79/27.10    (103)   ~ (e3 = e0)
% 175.79/27.10    (104)  all_40_0 = all_4_0
% 175.79/27.10    (105)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.79/27.10    (106)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 175.79/27.10    (107)  op(all_14_1, all_14_2) = e2
% 175.79/27.10    (108)   ~ (all_52_9 = all_52_13)
% 175.79/27.10    (109)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.79/27.10    (110)  op(e0, all_52_23) = all_52_22
% 175.79/27.10    (111)   ~ (all_52_15 = all_52_23)
% 175.79/27.10    (112)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.79/27.10    (113)  op(all_10_1, all_10_2) = all_10_0
% 175.79/27.10    (114)   ~ (all_52_5 = all_52_29)
% 175.79/27.10    (115)  all_56_2 = all_52_5
% 175.79/27.10    (116)  op(e1, e0) = all_52_23
% 175.79/27.10    (117)  all_56_12 = all_52_25
% 175.79/27.10    (118)  all_58_13 = all_52_27
% 175.79/27.10    (119)  op(e2, all_52_3) = all_52_2
% 175.79/27.10    (120)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.10    (121)  all_56_5 = all_10_2
% 175.79/27.10    (122)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.79/27.10    (123)   ~ (all_52_9 = all_52_17)
% 175.79/27.10    (124)  all_58_6 = all_52_17
% 175.79/27.10    (125)   ~ (all_52_3 = all_52_7)
% 175.79/27.10    (126)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.79/27.10    (127)  op(e2, all_52_19) = all_52_18
% 175.79/27.10    (128)   ~ (e1 = e0)
% 175.79/27.10    (129)  all_56_0 = all_4_2
% 175.79/27.10    (130)  all_58_11 = all_52_23
% 175.79/27.10    (131)   ~ (all_52_3 = all_52_19)
% 175.79/27.10    (132)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.79/27.10    (133)   ~ (all_52_7 = all_52_15)
% 175.79/27.10    (134)  all_26_1 = all_4_1
% 175.79/27.10    (135)  op(e0, all_52_15) = all_52_14
% 175.79/27.10    (136)   ~ (all_52_29 = all_14_2)
% 175.79/27.10    (137)   ~ (all_52_19 = all_10_2)
% 175.79/27.10    (138)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.79/27.10    (139)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.79/27.10    (140)   ~ (all_52_23 = all_6_2)
% 175.79/27.10    (141)   ~ (all_52_29 = all_6_2)
% 175.79/27.10    (142)  all_58_2 = all_52_9
% 175.79/27.10    (143)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.79/27.10    (144)  op(e3, e1) = all_52_5
% 175.79/27.10    (145)   ~ (e2 = e1)
% 175.79/27.10    (146)  all_56_10 = all_14_2
% 175.79/27.10    (147)   ~ (all_52_25 = all_6_2)
% 175.79/27.10    (148)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.79/27.10    (149)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.79/27.10    (150)  op(e1, e1) = all_14_2
% 175.79/27.10    (151)  op(e1, e3) = all_52_17
% 175.79/27.10    (152)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.79/27.10    (153)  all_26_0 = all_4_0
% 175.79/27.10    (154)   ~ (all_52_25 = all_4_2)
% 175.79/27.10    (155)  op(e3, e0) = all_52_7
% 175.79/27.10    (156)  op(e3, e3) = all_4_2
% 175.79/27.10    (157)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.10             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 175.79/27.10    (158)  all_56_8 = all_52_17
% 175.79/27.10    (159)   ~ (all_52_17 = all_4_2)
% 175.79/27.10    (160)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.10             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.10    (161)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.79/27.10           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 175.79/27.10           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.79/27.10           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.10    (162)   ~ (all_52_25 = all_52_27)
% 175.79/27.10    (163)  all_34_2 = all_4_2
% 175.79/27.10    (164)   ~ (all_52_27 = all_6_2)
% 175.79/27.10    (165)  all_8_1 = all_6_1
% 175.79/27.10    (166)   ~ (all_52_7 = all_6_2)
% 175.79/27.10    (167)   ~ (all_10_0 = e3)
% 175.79/27.10    (168)   ~ (all_52_19 = all_52_27)
% 175.79/27.10    (169)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2)
% 175.79/27.10    (170)  all_56_7 = all_52_15
% 175.79/27.10    (171)   ~ (all_52_7 = all_52_23)
% 175.79/27.10    (172)   ~ (all_52_13 = all_10_2)
% 175.79/27.10    (173)  op(e2, all_52_27) = all_52_26
% 175.79/27.10    (174)  all_52_20 = all_14_1
% 175.79/27.10    (175)   ~ (all_52_17 = all_52_19)
% 175.79/27.10    (176)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.79/27.10    (177)  all_52_30 = all_6_1
% 175.79/27.10    (178)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.79/27.10    (179)  op(e1, all_14_2) = all_14_1
% 175.79/27.10    (180)  all_58_9 = all_52_7
% 175.79/27.10    (181)   ~ (e2 = e0)
% 175.79/27.10    (182)  all_58_12 = all_52_25
% 175.79/27.10    (183)  all_34_0 = all_4_0
% 175.79/27.10    (184)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 175.79/27.10    (185)  all_56_6 = all_52_13
% 175.79/27.10    (186)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.79/27.10    (187)   ~ (all_52_9 = all_52_15)
% 175.79/27.10    (188)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.79/27.10    (189)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.79/27.10    (190)   ~ (all_52_19 = all_14_2)
% 175.79/27.10    (191)  op(e0, all_52_7) = all_52_6
% 175.79/27.10    (192)  op(e2, e3) = all_52_9
% 175.79/27.10    (193)  all_56_13 = all_52_27
% 175.79/27.10  
% 175.79/27.10  Begin of proof
% 175.79/27.10  | 
% 175.79/27.10  | BETA: splitting (98) gives:
% 175.79/27.10  | 
% 175.79/27.10  | Case 1:
% 175.79/27.10  | | 
% 175.79/27.10  | |   (194)   ~ (all_16_0 = e2)
% 175.79/27.10  | | 
% 175.79/27.10  | | REDUCE: (16), (194) imply:
% 175.79/27.10  | |   (195)  $false
% 175.79/27.10  | | 
% 175.79/27.10  | | CLOSE: (195) is inconsistent.
% 175.79/27.10  | | 
% 175.79/27.10  | Case 2:
% 175.79/27.10  | | 
% 175.79/27.10  | |   (196)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 175.79/27.10  | | 
% 175.79/27.10  | | BETA: splitting (106) gives:
% 175.79/27.10  | | 
% 175.79/27.10  | | Case 1:
% 175.79/27.10  | | | 
% 175.79/27.10  | | |   (197)   ~ (all_24_0 = e1)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | REDUCE: (76), (197) imply:
% 175.79/27.10  | | |   (198)   ~ (all_10_0 = e1)
% 175.79/27.10  | | | 
% 175.79/27.10  | | | BETA: splitting (184) gives:
% 175.79/27.10  | | | 
% 175.79/27.10  | | | Case 1:
% 175.79/27.10  | | | | 
% 175.79/27.10  | | | |   (199)   ~ (all_26_0 = e2)
% 175.79/27.10  | | | | 
% 175.79/27.10  | | | | REDUCE: (153), (199) imply:
% 175.79/27.10  | | | |   (200)   ~ (all_4_0 = e2)
% 175.79/27.10  | | | | 
% 175.79/27.10  | | | | BETA: splitting (138) gives:
% 175.79/27.10  | | | | 
% 175.79/27.10  | | | | Case 1:
% 175.79/27.10  | | | | | 
% 175.79/27.10  | | | | |   (201)   ~ (all_34_0 = e1)
% 175.79/27.10  | | | | | 
% 175.79/27.10  | | | | | REDUCE: (183), (201) imply:
% 175.79/27.10  | | | | |   (202)   ~ (all_4_0 = e1)
% 175.79/27.10  | | | | | 
% 175.79/27.10  | | | | | BETA: splitting (169) gives:
% 175.79/27.10  | | | | | 
% 175.79/27.10  | | | | | Case 1:
% 175.79/27.10  | | | | | | 
% 175.79/27.10  | | | | | |   (203)   ~ (all_40_1 = e1)
% 175.79/27.10  | | | | | | 
% 175.79/27.10  | | | | | | REDUCE: (77), (203) imply:
% 175.79/27.10  | | | | | |   (204)   ~ (all_4_1 = e1)
% 175.79/27.10  | | | | | | 
% 175.79/27.10  | | | | | | BETA: splitting (157) gives:
% 175.79/27.10  | | | | | | 
% 175.79/27.10  | | | | | | Case 1:
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | |   (205)  all_58_15 = e0
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | | REF_CLOSE: (36), (61), (94), (97), (160), (181), (205) are
% 175.79/27.10  | | | | | | |            inconsistent by sub-proof #228.
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | Case 2:
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | |   (206)   ~ (all_58_15 = e0)
% 175.79/27.10  | | | | | | |   (207)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.10  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | | ALPHA: (207) implies:
% 175.79/27.10  | | | | | | |   (208)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.10  | | | | | | |   (209)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | | REDUCE: (36), (206) imply:
% 175.79/27.10  | | | | | | |   (210)   ~ (all_6_2 = e0)
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | | BETA: splitting (161) gives:
% 175.79/27.10  | | | | | | | 
% 175.79/27.10  | | | | | | | Case 1:
% 175.79/27.10  | | | | | | | | 
% 175.79/27.10  | | | | | | | |   (211)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.79/27.10  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 175.79/27.10  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 175.79/27.10  | | | | | | | | 
% 175.79/27.10  | | | | | | | | BETA: splitting (211) gives:
% 175.79/27.10  | | | | | | | | 
% 175.79/27.10  | | | | | | | | Case 1:
% 175.79/27.10  | | | | | | | | | 
% 175.79/27.10  | | | | | | | | |   (212)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.79/27.10  | | | | | | | | |          all_52_6 = e0
% 175.79/27.10  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (13), (15), (17),
% 175.79/27.11  | | | | | | | | |            (18), (19), (20), (22), (24), (26), (27), (28),
% 175.79/27.11  | | | | | | | | |            (29), (30), (31), (32), (33), (35), (36), (37),
% 175.79/27.11  | | | | | | | | |            (38), (39), (40), (41), (42), (43), (45), (46),
% 175.79/27.11  | | | | | | | | |            (47), (48), (51), (53), (54), (55), (56), (57),
% 175.79/27.11  | | | | | | | | |            (58), (59), (62), (64), (66), (69), (70), (71),
% 175.79/27.11  | | | | | | | | |            (73), (74), (75), (79), (80), (81), (82), (83),
% 175.79/27.11  | | | | | | | | |            (84), (86), (88), (89), (90), (91), (92), (93),
% 175.79/27.11  | | | | | | | | |            (94), (95), (96), (97), (101), (102), (103), (105),
% 175.79/27.11  | | | | | | | | |            (108), (109), (110), (111), (112), (114), (115),
% 175.79/27.11  | | | | | | | | |            (116), (117), (118), (119), (120), (121), (122),
% 175.79/27.11  | | | | | | | | |            (123), (124), (125), (126), (128), (129), (130),
% 175.79/27.11  | | | | | | | | |            (131), (132), (133), (136), (137), (140), (141),
% 175.79/27.11  | | | | | | | | |            (142), (143), (144), (146), (147), (148), (149),
% 175.79/27.11  | | | | | | | | |            (150), (151), (152), (154), (155), (159), (160),
% 175.79/27.11  | | | | | | | | |            (162), (164), (165), (166), (168), (170), (171),
% 175.79/27.11  | | | | | | | | |            (172), (173), (175), (176), (180), (182), (186),
% 175.79/27.11  | | | | | | | | |            (187), (188), (189), (190), (191), (192), (193),
% 175.79/27.11  | | | | | | | | |            (196), (200), (202), (208), (209), (210), (212) are
% 175.79/27.11  | | | | | | | | |            inconsistent by sub-proof #220.
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | |   (213)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.11  | | | | | | | | |          all_52_14 = e0
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | ALPHA: (213) implies:
% 175.79/27.11  | | | | | | | | |   (214)  all_52_14 = e0
% 175.79/27.11  | | | | | | | | |   (215)  all_52_12 = e1
% 175.79/27.11  | | | | | | | | |   (216)  all_52_10 = e2
% 175.79/27.11  | | | | | | | | |   (217)  all_52_8 = e3
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | COMBINE_EQS: (100), (216) imply:
% 175.79/27.11  | | | | | | | | |   (218)  all_10_1 = e2
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (113), (218) imply:
% 175.79/27.11  | | | | | | | | |   (219)  op(e2, all_10_2) = all_10_0
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (21), (217) imply:
% 175.79/27.11  | | | | | | | | |   (220)  op(e3, all_52_9) = e3
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (8), (218) imply:
% 175.79/27.11  | | | | | | | | |   (221)  op(e2, all_10_2) = e2
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (60), (215) imply:
% 175.79/27.11  | | | | | | | | |   (222)  op(e1, all_52_13) = e1
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (135), (214) imply:
% 175.79/27.11  | | | | | | | | |   (223)  op(e0, all_52_15) = e0
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | GROUND_INST: instantiating (160) with e2, all_10_0, all_10_2,
% 175.79/27.11  | | | | | | | | |              e2, simplifying with (219), (221) gives:
% 175.79/27.11  | | | | | | | | |   (224)  all_10_0 = e2
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (167), (224) imply:
% 175.79/27.11  | | | | | | | | |   (225)   ~ (e3 = e2)
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | SIMP: (225) implies:
% 175.79/27.11  | | | | | | | | |   (226)   ~ (e3 = e2)
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | BETA: splitting (54) gives:
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | |   (227)  all_56_15 = e3
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | COMBINE_EQS: (29), (227) imply:
% 175.79/27.11  | | | | | | | | | |   (228)  all_6_2 = e3
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | SIMP: (228) implies:
% 175.79/27.11  | | | | | | | | | |   (229)  all_6_2 = e3
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | REF_CLOSE: (13), (19), (28), (93), (94), (97), (109), (117),
% 175.79/27.11  | | | | | | | | | |            (147), (149), (160), (182), (192), (196), (229)
% 175.79/27.11  | | | | | | | | | |            are inconsistent by sub-proof #226.
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | |   (230)   ~ (all_56_15 = e3)
% 175.79/27.11  | | | | | | | | | |   (231)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | REDUCE: (29), (230) imply:
% 175.79/27.11  | | | | | | | | | |   (232)   ~ (all_6_2 = e3)
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | BETA: splitting (75) gives:
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | |   (233)  all_56_13 = e3
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | COMBINE_EQS: (193), (233) imply:
% 175.79/27.11  | | | | | | | | | | |   (234)  all_52_27 = e3
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | SIMP: (234) implies:
% 175.79/27.11  | | | | | | | | | | |   (235)  all_52_27 = e3
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (12), (13), (14),
% 175.79/27.11  | | | | | | | | | | |            (15), (24), (25), (26), (29), (33), (35), (36),
% 175.79/27.11  | | | | | | | | | | |            (37), (38), (39), (41), (42), (43), (45), (47),
% 175.79/27.11  | | | | | | | | | | |            (48), (49), (51), (52), (53), (55), (56), (57),
% 175.79/27.11  | | | | | | | | | | |            (59), (66), (70), (72), (74), (79), (80), (81),
% 175.79/27.11  | | | | | | | | | | |            (83), (84), (85), (88), (90), (91), (92), (93),
% 175.79/27.11  | | | | | | | | | | |            (94), (96), (97), (99), (102), (108), (111),
% 175.79/27.11  | | | | | | | | | | |            (114), (116), (118), (120), (123), (124), (125),
% 175.79/27.11  | | | | | | | | | | |            (126), (128), (129), (130), (141), (142), (144),
% 175.79/27.11  | | | | | | | | | | |            (151), (154), (155), (156), (160), (162), (164),
% 175.79/27.11  | | | | | | | | | | |            (168), (171), (172), (173), (175), (176), (180),
% 175.79/27.11  | | | | | | | | | | |            (182), (185), (186), (187), (188), (192), (200),
% 175.79/27.11  | | | | | | | | | | |            (202), (204), (208), (209), (220), (221), (222),
% 175.79/27.11  | | | | | | | | | | |            (223), (231), (235) are inconsistent by sub-proof
% 175.79/27.11  | | | | | | | | | | |            #162.
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | |   (236)   ~ (all_56_13 = e3)
% 175.79/27.11  | | | | | | | | | | |   (237)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | REDUCE: (193), (236) imply:
% 175.79/27.11  | | | | | | | | | | |   (238)   ~ (all_52_27 = e3)
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | BETA: splitting (82) gives:
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | |   (239)  all_58_12 = e3
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (13),
% 175.79/27.11  | | | | | | | | | | | |            (15), (17), (18), (24), (26), (27), (29), (30),
% 175.79/27.11  | | | | | | | | | | | |            (33), (34), (35), (36), (37), (38), (39), (41),
% 175.79/27.11  | | | | | | | | | | | |            (42), (43), (45), (47), (48), (51), (52), (53),
% 175.79/27.11  | | | | | | | | | | | |            (55), (56), (57), (59), (66), (67), (70), (71),
% 175.79/27.11  | | | | | | | | | | | |            (72), (74), (79), (81), (83), (84), (85), (88),
% 175.79/27.11  | | | | | | | | | | | |            (89), (91), (92), (93), (99), (102), (103), (108),
% 175.79/27.11  | | | | | | | | | | | |            (110), (112), (114), (115), (118), (123), (124),
% 175.79/27.11  | | | | | | | | | | | |            (125), (126), (127), (129), (130), (131), (133),
% 175.79/27.11  | | | | | | | | | | | |            (136), (137), (140), (142), (143), (144), (145),
% 175.79/27.11  | | | | | | | | | | | |            (146), (147), (151), (152), (154), (155), (160),
% 175.79/27.11  | | | | | | | | | | | |            (162), (164), (166), (170), (171), (175), (176),
% 175.79/27.11  | | | | | | | | | | | |            (178), (179), (180), (182), (185), (186), (187),
% 175.79/27.11  | | | | | | | | | | | |            (188), (189), (190), (192), (193), (200), (202),
% 175.79/27.11  | | | | | | | | | | | |            (204), (208), (209), (210), (220), (221), (222),
% 175.79/27.11  | | | | | | | | | | | |            (223), (226), (231), (237), (239) are inconsistent
% 175.79/27.11  | | | | | | | | | | | |            by sub-proof #380.
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | |   (240)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REF_CLOSE: (7), (12), (13), (14), (15), (17), (22), (24),
% 175.79/27.11  | | | | | | | | | | | |            (25), (26), (27), (29), (31), (33), (36), (37),
% 175.79/27.11  | | | | | | | | | | | |            (38), (39), (40), (42), (44), (45), (46), (47),
% 175.79/27.11  | | | | | | | | | | | |            (48), (49), (51), (53), (55), (56), (57), (59),
% 175.79/27.11  | | | | | | | | | | | |            (62), (68), (71), (74), (79), (80), (83), (87),
% 175.79/27.11  | | | | | | | | | | | |            (88), (89), (91), (92), (93), (94), (99), (110),
% 175.79/27.11  | | | | | | | | | | | |            (111), (116), (118), (120), (124), (125), (127),
% 175.79/27.11  | | | | | | | | | | | |            (128), (130), (131), (136), (140), (141), (142),
% 175.79/27.11  | | | | | | | | | | | |            (143), (144), (145), (147), (151), (154), (155),
% 175.79/27.11  | | | | | | | | | | | |            (156), (159), (160), (162), (165), (166), (175),
% 175.79/27.11  | | | | | | | | | | | |            (176), (180), (182), (186), (192), (200), (209),
% 175.79/27.11  | | | | | | | | | | | |            (220), (221), (222), (223), (226), (231), (232),
% 175.79/27.11  | | | | | | | | | | | |            (238), (240) are inconsistent by sub-proof #209.
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | End of split
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | End of split
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | End of split
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | End of split
% 175.79/27.11  | | | | | | | | 
% 175.79/27.11  | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | 
% 175.79/27.11  | | | | | | | |   (241)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.11  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.11  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.11  | | | | | | | | 
% 175.79/27.11  | | | | | | | | REF_CLOSE: (94), (97), (107), (145), (160), (174), (177), (179),
% 175.79/27.11  | | | | | | | |            (181), (241) are inconsistent by sub-proof #156.
% 175.79/27.11  | | | | | | | | 
% 175.79/27.11  | | | | | | | End of split
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | End of split
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | Case 2:
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | |   (242)  all_40_1 = e1
% 175.79/27.11  | | | | | |   (243)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | COMBINE_EQS: (77), (242) imply:
% 175.79/27.11  | | | | | |   (244)  all_4_1 = e1
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | SIMP: (244) implies:
% 175.79/27.11  | | | | | |   (245)  all_4_1 = e1
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | COMBINE_EQS: (95), (245) imply:
% 175.79/27.11  | | | | | |   (246)  all_52_0 = e1
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | REDUCE: (68), (245) imply:
% 175.79/27.11  | | | | | |   (247)   ~ (e2 = e1)
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | REDUCE: (88), (245) imply:
% 175.79/27.11  | | | | | |   (248)  op(e1, all_4_2) = all_4_0
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | REDUCE: (53), (245) imply:
% 175.79/27.11  | | | | | |   (249)  op(e3, all_4_2) = e1
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | BETA: splitting (157) gives:
% 175.79/27.11  | | | | | | 
% 175.79/27.11  | | | | | | Case 1:
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | |   (250)  all_58_15 = e0
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | | REF_CLOSE: (36), (61), (94), (97), (160), (181), (250) are
% 175.79/27.11  | | | | | | |            inconsistent by sub-proof #228.
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | Case 2:
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | |   (251)   ~ (all_58_15 = e0)
% 175.79/27.11  | | | | | | |   (252)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.11  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | | ALPHA: (252) implies:
% 175.79/27.11  | | | | | | |   (253)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.11  | | | | | | |   (254)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | | REDUCE: (36), (251) imply:
% 175.79/27.11  | | | | | | |   (255)   ~ (all_6_2 = e0)
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | | BETA: splitting (161) gives:
% 175.79/27.11  | | | | | | | 
% 175.79/27.11  | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | 
% 175.79/27.11  | | | | | | | |   (256)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.79/27.11  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 175.79/27.11  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 175.79/27.11  | | | | | | | | 
% 175.79/27.11  | | | | | | | | BETA: splitting (256) gives:
% 175.79/27.11  | | | | | | | | 
% 175.79/27.11  | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | |   (257)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.79/27.11  | | | | | | | | |          all_52_6 = e0
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REF_CLOSE: (49), (246), (257) are inconsistent by sub-proof
% 175.79/27.11  | | | | | | | | |            #632.
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | |   (258)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.11  | | | | | | | | |          all_52_14 = e0
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | ALPHA: (258) implies:
% 175.79/27.11  | | | | | | | | |   (259)  all_52_14 = e0
% 175.79/27.11  | | | | | | | | |   (260)  all_52_12 = e1
% 175.79/27.11  | | | | | | | | |   (261)  all_52_10 = e2
% 175.79/27.11  | | | | | | | | |   (262)  all_52_8 = e3
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | COMBINE_EQS: (100), (261) imply:
% 175.79/27.11  | | | | | | | | |   (263)  all_10_1 = e2
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (113), (263) imply:
% 175.79/27.11  | | | | | | | | |   (264)  op(e2, all_10_2) = all_10_0
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (21), (262) imply:
% 175.79/27.11  | | | | | | | | |   (265)  op(e3, all_52_9) = e3
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (8), (263) imply:
% 175.79/27.11  | | | | | | | | |   (266)  op(e2, all_10_2) = e2
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (60), (260) imply:
% 175.79/27.11  | | | | | | | | |   (267)  op(e1, all_52_13) = e1
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (135), (259) imply:
% 175.79/27.11  | | | | | | | | |   (268)  op(e0, all_52_15) = e0
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | GROUND_INST: instantiating (160) with e2, all_10_0, all_10_2,
% 175.79/27.11  | | | | | | | | |              e2, simplifying with (264), (266) gives:
% 175.79/27.11  | | | | | | | | |   (269)  all_10_0 = e2
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | REDUCE: (167), (269) imply:
% 175.79/27.11  | | | | | | | | |   (270)   ~ (e3 = e2)
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | SIMP: (270) implies:
% 175.79/27.11  | | | | | | | | |   (271)   ~ (e3 = e2)
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | BETA: splitting (54) gives:
% 175.79/27.11  | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | |   (272)  all_56_15 = e3
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | COMBINE_EQS: (29), (272) imply:
% 175.79/27.11  | | | | | | | | | |   (273)  all_6_2 = e3
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | REF_CLOSE: (13), (19), (28), (93), (94), (97), (109), (117),
% 175.79/27.11  | | | | | | | | | |            (147), (149), (160), (182), (192), (196), (273)
% 175.79/27.11  | | | | | | | | | |            are inconsistent by sub-proof #226.
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | |   (274)   ~ (all_56_15 = e3)
% 175.79/27.11  | | | | | | | | | |   (275)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | REDUCE: (29), (274) imply:
% 175.79/27.11  | | | | | | | | | |   (276)   ~ (all_6_2 = e3)
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | BETA: splitting (75) gives:
% 175.79/27.11  | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | |   (277)  all_56_13 = e3
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | COMBINE_EQS: (193), (277) imply:
% 175.79/27.11  | | | | | | | | | | |   (278)  all_52_27 = e3
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (11), (12), (18), (26),
% 175.79/27.11  | | | | | | | | | | |            (33), (34), (35), (36), (37), (38), (39), (41),
% 175.79/27.11  | | | | | | | | | | |            (42), (45), (47), (48), (49), (52), (55), (56),
% 175.79/27.11  | | | | | | | | | | |            (57), (59), (67), (74), (80), (83), (90), (91),
% 175.79/27.11  | | | | | | | | | | |            (93), (102), (104), (108), (111), (120), (124),
% 175.79/27.11  | | | | | | | | | | |            (129), (130), (131), (133), (142), (144), (151),
% 175.79/27.11  | | | | | | | | | | |            (154), (156), (159), (160), (164), (168), (171),
% 175.79/27.11  | | | | | | | | | | |            (173), (176), (178), (180), (182), (186), (188),
% 175.79/27.11  | | | | | | | | | | |            (192), (200), (243), (248), (249), (265), (267),
% 175.79/27.11  | | | | | | | | | | |            (268), (278) are inconsistent by sub-proof #610.
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | |   (279)   ~ (all_56_13 = e3)
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | REDUCE: (193), (279) imply:
% 175.79/27.11  | | | | | | | | | | |   (280)   ~ (all_52_27 = e3)
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | BETA: splitting (82) gives:
% 175.79/27.11  | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | |   (281)  all_58_12 = e3
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | COMBINE_EQS: (182), (281) imply:
% 175.79/27.11  | | | | | | | | | | | |   (282)  all_52_25 = e3
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | SIMP: (282) implies:
% 175.79/27.11  | | | | | | | | | | | |   (283)  all_52_25 = e3
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REDUCE: (13), (283) imply:
% 175.79/27.11  | | | | | | | | | | | |   (284)   ~ (all_52_9 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REDUCE: (45), (283) imply:
% 175.79/27.11  | | | | | | | | | | | |   (285)   ~ (all_52_17 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REDUCE: (162), (283) imply:
% 175.79/27.11  | | | | | | | | | | | |   (286)   ~ (all_52_27 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REDUCE: (27), (283) imply:
% 175.79/27.11  | | | | | | | | | | | |   (287)   ~ (all_52_29 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | SIMP: (287) implies:
% 175.79/27.11  | | | | | | | | | | | |   (288)   ~ (all_52_29 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REDUCE: (147), (283) imply:
% 175.79/27.11  | | | | | | | | | | | |   (289)   ~ (all_6_2 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REDUCE: (154), (283) imply:
% 175.79/27.11  | | | | | | | | | | | |   (290)   ~ (all_4_2 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | SIMP: (290) implies:
% 175.79/27.11  | | | | | | | | | | | |   (291)   ~ (all_4_2 = e3)
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | REDUCE: (93), (283) imply:
% 175.79/27.11  | | | | | | | | | | | |   (292)  op(e0, e3) = e3
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | BETA: splitting (126) gives:
% 175.79/27.11  | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | |   (293)  all_56_4 = e3
% 175.79/27.11  | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | REF_CLOSE: (43), (284), (293) are inconsistent by sub-proof
% 175.79/27.11  | | | | | | | | | | | | |            #782.
% 175.79/27.11  | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | |   (294)   ~ (all_56_4 = e3)
% 175.79/27.11  | | | | | | | | | | | | |   (295)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.79/27.11  | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | BETA: splitting (35) gives:
% 175.79/27.11  | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | |   (296)  all_56_0 = e3
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | COMBINE_EQS: (129), (296) imply:
% 175.79/27.11  | | | | | | | | | | | | | |   (297)  all_4_2 = e3
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | REDUCE: (291), (297) imply:
% 175.79/27.11  | | | | | | | | | | | | | |   (298)  $false
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | CLOSE: (298) is inconsistent.
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | |   (299)   ~ (all_56_0 = e3)
% 175.79/27.11  | | | | | | | | | | | | | |   (300)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 175.79/27.11  | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | |   (301)  all_56_6 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | COMBINE_EQS: (185), (301) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (302)  all_52_13 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | SIMP: (302) implies:
% 175.79/27.11  | | | | | | | | | | | | | | |   (303)  all_52_13 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | COMBINE_EQS: (26), (303) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (304)  all_58_5 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (2), (303) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (305)   ~ (all_52_5 = e3)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (102), (303) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (306)   ~ (all_14_2 = e3)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | SIMP: (306) implies:
% 175.79/27.11  | | | | | | | | | | | | | | |   (307)   ~ (all_14_2 = e3)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (81), (303) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (308)  op(e2, e1) = e3
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (267), (303) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (309)  op(e1, e3) = e1
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | GROUND_INST: instantiating (160) with all_52_17, e1, e3, e1,
% 175.79/27.11  | | | | | | | | | | | | | | |              simplifying with (151), (309) gives:
% 175.79/27.11  | | | | | | | | | | | | | | |   (310)  all_52_17 = e1
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | COMBINE_EQS: (124), (310) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (311)  all_58_6 = e1
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (123), (310) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (312)   ~ (all_52_9 = e1)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (175), (310) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (313)   ~ (all_52_19 = e1)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | SIMP: (313) implies:
% 175.79/27.11  | | | | | | | | | | | | | | |   (314)   ~ (all_52_19 = e1)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (52), (310) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (315)   ~ (all_14_2 = e1)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | SIMP: (315) implies:
% 175.79/27.11  | | | | | | | | | | | | | | |   (316)   ~ (all_14_2 = e1)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (285), (310) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (317)   ~ (e3 = e1)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (99), (310) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (318)  op(e3, e1) = all_52_16
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | GROUND_INST: instantiating (160) with all_52_5, all_52_16, e1,
% 175.79/27.11  | | | | | | | | | | | | | | |              e3, simplifying with (144), (318) gives:
% 175.79/27.11  | | | | | | | | | | | | | | |   (319)  all_52_5 = all_52_16
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | COMBINE_EQS: (47), (319) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (320)  all_58_4 = all_52_16
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (79), (319) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (321)   ~ (all_52_3 = all_52_16)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (38), (319) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (322)   ~ (all_52_7 = all_52_16)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | SIMP: (322) implies:
% 175.79/27.11  | | | | | | | | | | | | | | |   (323)   ~ (all_52_7 = all_52_16)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | REDUCE: (41), (319) imply:
% 175.79/27.11  | | | | | | | | | | | | | | |   (324)   ~ (all_52_16 = all_4_2)
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | |   (325)  all_58_9 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (325) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | |   (326)  all_52_7 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | SIMP: (326) implies:
% 175.79/27.11  | | | | | | | | | | | | | | | |   (327)  all_52_7 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | REDUCE: (171), (327) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | |   (328)   ~ (all_52_23 = e3)
% 175.79/27.11  | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | SIMP: (328) implies:
% 175.79/27.11  | | | | | | | | | | | | | | | |   (329)   ~ (all_52_23 = e3)
% 175.79/27.11  | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | |   (330)  all_58_6 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (330) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | |   (331)  e3 = e1
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | REDUCE: (49), (331) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | |   (332)  $false
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent.
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | |   (333)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | |   (334)  all_58_7 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (334) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | |   (335)  all_52_19 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | REDUCE: (131), (335) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | |   (336)   ~ (all_52_3 = e3)
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | REDUCE: (127), (335) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | |   (337)  op(e2, e3) = all_52_18
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (160) with all_52_9, all_52_18, e3,
% 175.79/27.11  | | | | | | | | | | | | | | | | | |              e2, simplifying with (192), (337) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | | | |   (338)  all_52_9 = all_52_18
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (338) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | |   (339)  all_58_2 = all_52_18
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | REDUCE: (265), (338) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | |   (340)  op(e3, all_52_18) = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | |   (341)  all_58_4 = e1
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (341) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | |   (342)  all_52_16 = e1
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | SIMP: (342) implies:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | |   (343)  all_52_16 = e1
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | REDUCE: (321), (343) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | |   (344)   ~ (all_52_3 = e1)
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | |   (345)  all_56_1 = e3
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (336), (345) are inconsistent by sub-proof
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | |            #862.
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | |   (346)   ~ (all_56_1 = e3)
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | |   (347)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | |   (348)  all_58_0 = e2
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (348) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | |   (349)  all_4_2 = e2
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (349) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | |   (350)   ~ (all_52_3 = e2)
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (349) imply:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | |   (351)  op(e3, e2) = e1
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.11  | | | | | | | | | | | | | | | | | | | | | |   (352)  all_56_1 = e2
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (350), (352) are inconsistent by sub-proof
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | |            #857.
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | |   (353)  all_56_1 = e1 | all_56_1 = e0
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_56_1 = e1
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (344), (354) are inconsistent by sub-proof
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |            #841.
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_56_1 = e0
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (355) imply:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_52_3 = e0
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (356) implies:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_52_3 = e0
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (344), (357) imply:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (358)   ~ (e1 = e0)
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (357) imply:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (359)  op(e3, e2) = e0
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (160) with e0, e1, e2, e3,
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (351), (359) gives:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (360)  e1 = e0
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (360) imply:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | |   (361)  $false
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (361) is inconsistent.
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | |   (362)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (145), (160), (271), (281), (311), (336),
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | |            (339), (340), (362) are inconsistent by sub-proof
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | |            #737.
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | |   (363)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (49), (74), (83), (85), (94), (97), (103),
% 175.79/27.12  | | | | | | | | | | | | | | | | | | |            (118), (128), (141), (160), (164), (253), (275),
% 175.79/27.12  | | | | | | | | | | | | | | | | | | |            (281), (304), (316), (363) are inconsistent by
% 175.79/27.12  | | | | | | | | | | | | | | | | | | |            sub-proof #168.
% 175.79/27.12  | | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | |   (364)  all_58_8 = e3 | all_58_11 = e3
% 175.79/27.12  | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (130), (307), (329), (364) are inconsistent
% 175.79/27.12  | | | | | | | | | | | | | | | | | |            by sub-proof #997.
% 175.79/27.12  | | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | |   (365)   ~ (all_58_9 = e3)
% 175.79/27.12  | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | REDUCE: (180), (365) imply:
% 175.79/27.12  | | | | | | | | | | | | | | | |   (366)   ~ (all_52_7 = e3)
% 175.79/27.12  | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (29), (33), (37), (42), (43), (47),
% 175.79/27.12  | | | | | | | | | | | | | | | |            (49), (51), (56), (59), (70), (74), (83), (89),
% 175.79/27.12  | | | | | | | | | | | | | | | |            (118), (129), (155), (160), (164), (166), (178),
% 175.79/27.12  | | | | | | | | | | | | | | | |            (180), (186), (255), (265), (266), (271), (275),
% 175.79/27.12  | | | | | | | | | | | | | | | |            (288), (291), (295), (300), (304), (305), (308),
% 175.79/27.12  | | | | | | | | | | | | | | | |            (312), (314), (316), (320), (323), (324), (366)
% 175.79/27.12  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #335.
% 175.79/27.12  | | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | |   (367)   ~ (all_56_6 = e3)
% 175.79/27.12  | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | REDUCE: (185), (367) imply:
% 175.79/27.12  | | | | | | | | | | | | | | |   (368)   ~ (all_52_13 = e3)
% 175.79/27.12  | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (10), (11), (12), (15), (17),
% 175.79/27.12  | | | | | | | | | | | | | | |            (18), (24), (26), (29), (30), (33), (34), (36),
% 175.79/27.12  | | | | | | | | | | | | | | |            (37), (38), (39), (41), (42), (43), (47), (48),
% 175.79/27.12  | | | | | | | | | | | | | | |            (51), (52), (55), (56), (57), (59), (67), (70),
% 175.79/27.12  | | | | | | | | | | | | | | |            (71), (72), (74), (79), (81), (83), (89), (99),
% 175.79/27.12  | | | | | | | | | | | | | | |            (102), (103), (108), (110), (112), (118), (123),
% 175.79/27.12  | | | | | | | | | | | | | | |            (124), (125), (126), (127), (129), (130), (131),
% 175.79/27.12  | | | | | | | | | | | | | | |            (133), (136), (137), (140), (142), (143), (144),
% 175.79/27.12  | | | | | | | | | | | | | | |            (145), (146), (151), (155), (160), (164), (166),
% 175.79/27.12  | | | | | | | | | | | | | | |            (171), (175), (176), (178), (179), (180), (185),
% 175.79/27.12  | | | | | | | | | | | | | | |            (187), (188), (190), (192), (254), (255), (265),
% 175.79/27.12  | | | | | | | | | | | | | | |            (266), (267), (268), (271), (275), (276), (280),
% 175.79/27.12  | | | | | | | | | | | | | | |            (281), (284), (288), (292), (300), (368) are
% 175.79/27.12  | | | | | | | | | | | | | | |            inconsistent by sub-proof #382.
% 175.79/27.12  | | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | |   (369)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.12  | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | | REF_CLOSE: (7), (12), (13), (14), (15), (17), (22), (24),
% 175.79/27.12  | | | | | | | | | | | |            (25), (26), (27), (29), (31), (33), (36), (37),
% 175.79/27.12  | | | | | | | | | | | |            (38), (39), (40), (42), (44), (45), (46), (47),
% 175.79/27.12  | | | | | | | | | | | |            (48), (49), (51), (53), (55), (56), (57), (59),
% 175.79/27.12  | | | | | | | | | | | |            (62), (68), (71), (74), (79), (80), (83), (87),
% 175.79/27.12  | | | | | | | | | | | |            (88), (89), (91), (92), (93), (94), (99), (110),
% 175.79/27.12  | | | | | | | | | | | |            (111), (116), (118), (120), (124), (125), (127),
% 175.79/27.12  | | | | | | | | | | | |            (128), (130), (131), (136), (140), (141), (142),
% 175.79/27.12  | | | | | | | | | | | |            (143), (144), (145), (147), (151), (154), (155),
% 175.79/27.12  | | | | | | | | | | | |            (156), (159), (160), (162), (165), (166), (175),
% 175.79/27.12  | | | | | | | | | | | |            (176), (180), (182), (186), (192), (200), (254),
% 175.79/27.12  | | | | | | | | | | | |            (265), (266), (267), (268), (271), (275), (276),
% 175.79/27.12  | | | | | | | | | | | |            (280), (369) are inconsistent by sub-proof #209.
% 175.79/27.12  | | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | |   (370)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.12  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.12  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REF_CLOSE: (94), (97), (107), (145), (160), (174), (177), (179),
% 175.79/27.12  | | | | | | | |            (181), (370) are inconsistent by sub-proof #155.
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | End of split
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | End of split
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | End of split
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | Case 2:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | |   (371)  all_34_0 = e1
% 175.79/27.12  | | | | |   (372)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | COMBINE_EQS: (183), (371) imply:
% 175.79/27.12  | | | | |   (373)  all_4_0 = e1
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | REDUCE: (200), (373) imply:
% 175.79/27.12  | | | | |   (374)   ~ (e2 = e1)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | REDUCE: (88), (373) imply:
% 175.79/27.12  | | | | |   (375)  op(all_4_1, all_4_2) = e1
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | BETA: splitting (157) gives:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | Case 1:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (376)  all_58_15 = e0
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REF_CLOSE: (36), (61), (94), (97), (160), (181), (376) are
% 175.79/27.12  | | | | | |            inconsistent by sub-proof #228.
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | Case 2:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (377)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.12  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | ALPHA: (377) implies:
% 175.79/27.12  | | | | | |   (378)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | BETA: splitting (161) gives:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | Case 1:
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | |   (379)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 175.79/27.12  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 175.79/27.12  | | | | | | |            e1 & all_52_14 = e0)
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (12), (13), (14), (18),
% 175.79/27.12  | | | | | | |            (19), (21), (22), (24), (26), (27), (28), (29), (30),
% 175.79/27.12  | | | | | | |            (33), (35), (36), (37), (39), (40), (41), (42), (43),
% 175.79/27.12  | | | | | | |            (46), (47), (48), (49), (50), (51), (53), (54), (55),
% 175.79/27.12  | | | | | | |            (56), (57), (59), (60), (62), (66), (68), (71), (72),
% 175.79/27.12  | | | | | | |            (74), (75), (79), (80), (82), (83), (84), (85), (89),
% 175.79/27.12  | | | | | | |            (91), (92), (93), (94), (95), (97), (100), (108),
% 175.79/27.12  | | | | | | |            (109), (111), (113), (114), (115), (116), (117), (118),
% 175.79/27.12  | | | | | | |            (120), (124), (125), (126), (128), (129), (130), (131),
% 175.79/27.12  | | | | | | |            (135), (136), (141), (142), (144), (147), (149), (151),
% 175.79/27.12  | | | | | | |            (154), (155), (156), (159), (160), (162), (163), (164),
% 175.79/27.12  | | | | | | |            (165), (166), (167), (171), (173), (175), (176), (178),
% 175.79/27.12  | | | | | | |            (180), (182), (185), (186), (187), (189), (192), (193),
% 175.79/27.12  | | | | | | |            (196), (198), (372), (375), (378), (379) are
% 175.79/27.12  | | | | | | |            inconsistent by sub-proof #159.
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | Case 2:
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | |   (380)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.12  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.12  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | | REF_CLOSE: (94), (97), (107), (145), (160), (174), (177), (179),
% 175.79/27.12  | | | | | | |            (181), (380) are inconsistent by sub-proof #155.
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | End of split
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | End of split
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | End of split
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | Case 2:
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | |   (381)  all_26_0 = e2
% 175.79/27.12  | | | |   (382)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | COMBINE_EQS: (153), (381) imply:
% 175.79/27.12  | | | |   (383)  all_4_0 = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | SIMP: (383) implies:
% 175.79/27.12  | | | |   (384)  all_4_0 = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | COMBINE_EQS: (63), (384) imply:
% 175.79/27.12  | | | |   (385)  all_50_0 = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | REDUCE: (88), (384) imply:
% 175.79/27.12  | | | |   (386)  op(all_4_1, all_4_2) = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | BETA: splitting (139) gives:
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | Case 1:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | |   (387)   ~ (all_50_0 = e2)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | REDUCE: (385), (387) imply:
% 175.79/27.12  | | | | |   (388)  $false
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | CLOSE: (388) is inconsistent.
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | Case 2:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | |   (389)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | BETA: splitting (157) gives:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | Case 1:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (390)  all_58_15 = e0
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REF_CLOSE: (36), (61), (94), (97), (160), (181), (390) are
% 175.79/27.12  | | | | | |            inconsistent by sub-proof #228.
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | Case 2:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (391)   ~ (all_58_15 = e0)
% 175.79/27.12  | | | | | |   (392)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.12  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | ALPHA: (392) implies:
% 175.79/27.12  | | | | | |   (393)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REDUCE: (36), (391) imply:
% 175.79/27.12  | | | | | |   (394)   ~ (all_6_2 = e0)
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | BETA: splitting (161) gives:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | Case 1:
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | |   (395)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 175.79/27.12  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 175.79/27.12  | | | | | | |            e1 & all_52_14 = e0)
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | | BETA: splitting (395) gives:
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | | Case 1:
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | |   (396)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.79/27.12  | | | | | | | |          all_52_6 = e0
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REF_CLOSE: (53), (68), (95), (160), (386), (396) are
% 175.79/27.12  | | | | | | | |            inconsistent by sub-proof #494.
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | |   (397)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.12  | | | | | | | |          all_52_14 = e0
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | ALPHA: (397) implies:
% 175.79/27.12  | | | | | | | |   (398)  all_52_14 = e0
% 175.79/27.12  | | | | | | | |   (399)  all_52_12 = e1
% 175.79/27.12  | | | | | | | |   (400)  all_52_10 = e2
% 175.79/27.12  | | | | | | | |   (401)  all_52_8 = e3
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | COMBINE_EQS: (100), (400) imply:
% 175.79/27.12  | | | | | | | |   (402)  all_10_1 = e2
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REDUCE: (113), (402) imply:
% 175.79/27.12  | | | | | | | |   (403)  op(e2, all_10_2) = all_10_0
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REDUCE: (21), (401) imply:
% 175.79/27.12  | | | | | | | |   (404)  op(e3, all_52_9) = e3
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REDUCE: (8), (402) imply:
% 175.79/27.12  | | | | | | | |   (405)  op(e2, all_10_2) = e2
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REDUCE: (60), (399) imply:
% 175.79/27.12  | | | | | | | |   (406)  op(e1, all_52_13) = e1
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REDUCE: (135), (398) imply:
% 175.79/27.12  | | | | | | | |   (407)  op(e0, all_52_15) = e0
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | GROUND_INST: instantiating (160) with e2, all_10_0, all_10_2,
% 175.79/27.12  | | | | | | | |              e2, simplifying with (403), (405) gives:
% 175.79/27.12  | | | | | | | |   (408)  all_10_0 = e2
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | REDUCE: (167), (408) imply:
% 175.79/27.12  | | | | | | | |   (409)   ~ (e3 = e2)
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | SIMP: (409) implies:
% 175.79/27.12  | | | | | | | |   (410)   ~ (e3 = e2)
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | BETA: splitting (54) gives:
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | | Case 1:
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | |   (411)  all_56_15 = e3
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | COMBINE_EQS: (29), (411) imply:
% 175.79/27.12  | | | | | | | | |   (412)  all_6_2 = e3
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | SIMP: (412) implies:
% 175.79/27.12  | | | | | | | | |   (413)  all_6_2 = e3
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | REF_CLOSE: (13), (19), (28), (93), (94), (97), (109), (117),
% 175.79/27.12  | | | | | | | | |            (147), (149), (160), (182), (192), (196), (413) are
% 175.79/27.12  | | | | | | | | |            inconsistent by sub-proof #226.
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | |   (414)   ~ (all_56_15 = e3)
% 175.79/27.12  | | | | | | | | |   (415)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | REDUCE: (29), (414) imply:
% 175.79/27.12  | | | | | | | | |   (416)   ~ (all_6_2 = e3)
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | BETA: splitting (75) gives:
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | Case 1:
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | |   (417)  all_56_13 = e3
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (12), (13),
% 175.79/27.12  | | | | | | | | | |            (14), (15), (18), (24), (25), (26), (30), (31),
% 175.79/27.12  | | | | | | | | | |            (33), (35), (36), (37), (38), (39), (41), (42),
% 175.79/27.12  | | | | | | | | | |            (43), (45), (47), (48), (49), (51), (52), (53),
% 175.79/27.12  | | | | | | | | | |            (55), (57), (58), (59), (66), (68), (74), (79),
% 175.79/27.12  | | | | | | | | | |            (80), (83), (84), (91), (92), (93), (96), (99),
% 175.79/27.12  | | | | | | | | | |            (102), (108), (111), (116), (118), (120), (121),
% 175.79/27.12  | | | | | | | | | |            (124), (125), (126), (128), (129), (130), (137),
% 175.79/27.12  | | | | | | | | | |            (142), (145), (148), (151), (154), (155), (156),
% 175.79/27.12  | | | | | | | | | |            (158), (159), (160), (162), (164), (172), (173),
% 175.79/27.12  | | | | | | | | | |            (175), (176), (180), (182), (187), (188), (192),
% 175.79/27.12  | | | | | | | | | |            (193), (386), (393), (404), (405), (406), (407),
% 175.79/27.12  | | | | | | | | | |            (417) are inconsistent by sub-proof #464.
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | |   (418)   ~ (all_56_13 = e3)
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | REDUCE: (193), (418) imply:
% 175.79/27.12  | | | | | | | | | |   (419)   ~ (all_52_27 = e3)
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | BETA: splitting (82) gives:
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | Case 1:
% 175.79/27.12  | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | |   (420)  all_58_12 = e3
% 175.79/27.12  | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (13),
% 175.79/27.12  | | | | | | | | | | |            (15), (17), (18), (23), (24), (26), (27), (29),
% 175.79/27.12  | | | | | | | | | | |            (30), (33), (34), (35), (36), (37), (38), (39),
% 175.79/27.12  | | | | | | | | | | |            (41), (42), (43), (45), (47), (48), (51), (52),
% 175.79/27.12  | | | | | | | | | | |            (53), (55), (56), (57), (59), (65), (67), (68),
% 175.79/27.12  | | | | | | | | | | |            (70), (71), (72), (74), (78), (79), (81), (83),
% 175.79/27.12  | | | | | | | | | | |            (89), (92), (93), (99), (102), (103), (105),
% 175.79/27.12  | | | | | | | | | | |            (107), (108), (110), (112), (114), (115), (118),
% 175.79/27.12  | | | | | | | | | | |            (120), (123), (124), (125), (126), (127), (129),
% 175.79/27.12  | | | | | | | | | | |            (130), (131), (133), (134), (136), (137), (140),
% 175.79/27.12  | | | | | | | | | | |            (142), (143), (144), (145), (146), (147), (151),
% 175.79/27.12  | | | | | | | | | | |            (152), (154), (155), (160), (162), (164), (166),
% 175.79/27.12  | | | | | | | | | | |            (170), (171), (175), (176), (178), (179), (180),
% 175.79/27.12  | | | | | | | | | | |            (181), (182), (185), (186), (187), (188), (189),
% 175.79/27.12  | | | | | | | | | | |            (190), (192), (382), (386), (389), (393), (394),
% 175.79/27.12  | | | | | | | | | | |            (404), (405), (406), (407), (415), (420) are
% 175.79/27.12  | | | | | | | | | | |            inconsistent by sub-proof #296.
% 175.79/27.12  | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | Case 2:
% 175.79/27.12  | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | |   (421)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.12  | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | | REF_CLOSE: (7), (12), (14), (22), (24), (27), (29), (33),
% 175.79/27.12  | | | | | | | | | | |            (35), (36), (37), (39), (40), (42), (45), (46),
% 175.79/27.12  | | | | | | | | | | |            (47), (49), (51), (53), (55), (56), (57), (59),
% 175.79/27.12  | | | | | | | | | | |            (62), (68), (71), (74), (80), (89), (93), (94),
% 175.79/27.12  | | | | | | | | | | |            (99), (114), (118), (120), (124), (125), (128),
% 175.79/27.12  | | | | | | | | | | |            (129), (130), (141), (142), (144), (145), (147),
% 175.79/27.12  | | | | | | | | | | |            (151), (155), (156), (160), (165), (166), (175),
% 175.79/27.12  | | | | | | | | | | |            (176), (180), (182), (192), (386), (404), (405),
% 175.79/27.12  | | | | | | | | | | |            (407), (410), (415), (416), (419), (421) are
% 175.79/27.12  | | | | | | | | | | |            inconsistent by sub-proof #186.
% 175.79/27.12  | | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | | 
% 175.79/27.12  | | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | | 
% 175.79/27.12  | | | | | | | | End of split
% 175.79/27.12  | | | | | | | | 
% 175.79/27.12  | | | | | | | End of split
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | Case 2:
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | |   (422)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.12  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.12  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | | REF_CLOSE: (94), (97), (107), (145), (160), (174), (177), (179),
% 175.79/27.12  | | | | | | |            (181), (422) are inconsistent by sub-proof #155.
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | End of split
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | End of split
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | End of split
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | End of split
% 175.79/27.12  | | | 
% 175.79/27.12  | | Case 2:
% 175.79/27.12  | | | 
% 175.79/27.12  | | |   (423)  all_24_0 = e1
% 175.79/27.12  | | | 
% 175.79/27.12  | | | COMBINE_EQS: (76), (423) imply:
% 175.79/27.12  | | |   (424)  all_10_0 = e1
% 175.79/27.12  | | | 
% 175.79/27.12  | | | SIMP: (424) implies:
% 175.79/27.12  | | |   (425)  all_10_0 = e1
% 175.79/27.12  | | | 
% 175.79/27.12  | | | REDUCE: (167), (425) imply:
% 175.79/27.12  | | |   (426)   ~ (e3 = e1)
% 175.79/27.12  | | | 
% 175.79/27.12  | | | REDUCE: (113), (425) imply:
% 175.79/27.12  | | |   (427)  op(all_10_1, all_10_2) = e1
% 175.79/27.12  | | | 
% 175.79/27.12  | | | BETA: splitting (184) gives:
% 175.79/27.12  | | | 
% 175.79/27.12  | | | Case 1:
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | |   (428)   ~ (all_26_0 = e2)
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | REDUCE: (153), (428) imply:
% 175.79/27.12  | | | |   (429)   ~ (all_4_0 = e2)
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | BETA: splitting (138) gives:
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | Case 1:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | |   (430)   ~ (all_34_0 = e1)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | REDUCE: (183), (430) imply:
% 175.79/27.12  | | | | |   (431)   ~ (all_4_0 = e1)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | BETA: splitting (157) gives:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | Case 1:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (432)  all_58_15 = e0
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REF_CLOSE: (36), (61), (94), (97), (160), (181), (432) are
% 175.79/27.12  | | | | | |            inconsistent by sub-proof #228.
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | Case 2:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (433)   ~ (all_58_15 = e0)
% 175.79/27.12  | | | | | |   (434)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.12  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | ALPHA: (434) implies:
% 175.79/27.12  | | | | | |   (435)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.12  | | | | | |   (436)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REDUCE: (36), (433) imply:
% 175.79/27.12  | | | | | |   (437)   ~ (all_6_2 = e0)
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | BETA: splitting (161) gives:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | Case 1:
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | |   (438)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 175.79/27.12  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 175.79/27.12  | | | | | | |            e1 & all_52_14 = e0)
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | | REF_CLOSE: (1), (2), (6), (7), (8), (10), (12), (13), (15), (17),
% 175.79/27.12  | | | | | | |            (18), (19), (20), (22), (24), (26), (27), (28), (29),
% 175.79/27.12  | | | | | | |            (30), (31), (32), (33), (35), (36), (37), (38), (39),
% 175.79/27.12  | | | | | | |            (40), (41), (42), (43), (45), (46), (47), (48), (51),
% 175.79/27.12  | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (62), (64),
% 175.79/27.12  | | | | | | |            (66), (69), (70), (71), (73), (74), (75), (79), (80),
% 175.79/27.12  | | | | | | |            (81), (82), (83), (84), (86), (88), (89), (90), (91),
% 175.79/27.12  | | | | | | |            (92), (93), (94), (95), (96), (97), (100), (101),
% 175.79/27.12  | | | | | | |            (102), (103), (105), (108), (109), (110), (111), (112),
% 175.79/27.12  | | | | | | |            (114), (115), (116), (117), (118), (119), (120), (121),
% 175.79/27.12  | | | | | | |            (122), (123), (124), (125), (126), (128), (129), (130),
% 175.79/27.12  | | | | | | |            (131), (132), (133), (136), (137), (140), (141), (142),
% 175.79/27.12  | | | | | | |            (143), (144), (145), (146), (147), (148), (149), (150),
% 175.79/27.12  | | | | | | |            (151), (152), (154), (155), (159), (160), (162), (164),
% 175.79/27.12  | | | | | | |            (165), (166), (168), (170), (171), (172), (173), (175),
% 175.79/27.12  | | | | | | |            (176), (180), (182), (186), (187), (188), (189), (190),
% 175.79/27.12  | | | | | | |            (191), (192), (193), (196), (427), (429), (431), (435),
% 175.79/27.12  | | | | | | |            (436), (437), (438) are inconsistent by sub-proof #158.
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | Case 2:
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | |   (439)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.12  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.12  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | | REF_CLOSE: (94), (97), (107), (145), (160), (174), (177), (179),
% 175.79/27.12  | | | | | | |            (181), (439) are inconsistent by sub-proof #155.
% 175.79/27.12  | | | | | | | 
% 175.79/27.12  | | | | | | End of split
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | End of split
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | Case 2:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | |   (440)  all_34_0 = e1
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | COMBINE_EQS: (183), (440) imply:
% 175.79/27.12  | | | | |   (441)  all_4_0 = e1
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | SIMP: (441) implies:
% 175.79/27.12  | | | | |   (442)  all_4_0 = e1
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | REDUCE: (429), (442) imply:
% 175.79/27.12  | | | | |   (443)   ~ (e2 = e1)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | REDUCE: (88), (442) imply:
% 175.79/27.12  | | | | |   (444)  op(all_4_1, all_4_2) = e1
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | BETA: splitting (161) gives:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | Case 1:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (445)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.79/27.12  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.12  | | | | | |            all_52_14 = e0)
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REF_CLOSE: (8), (49), (53), (95), (100), (145), (160), (427), (444),
% 175.79/27.12  | | | | | |            (445) are inconsistent by sub-proof #441.
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | Case 2:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (446)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.12  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.12  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REF_CLOSE: (94), (97), (107), (145), (160), (174), (177), (179),
% 175.79/27.12  | | | | | |            (181), (446) are inconsistent by sub-proof #155.
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | End of split
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | End of split
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | Case 2:
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | |   (447)  all_26_0 = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | COMBINE_EQS: (153), (447) imply:
% 175.79/27.12  | | | |   (448)  all_4_0 = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | SIMP: (448) implies:
% 175.79/27.12  | | | |   (449)  all_4_0 = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | REDUCE: (88), (449) imply:
% 175.79/27.12  | | | |   (450)  op(all_4_1, all_4_2) = e2
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | BETA: splitting (161) gives:
% 175.79/27.12  | | | | 
% 175.79/27.12  | | | | Case 1:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | |   (451)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.79/27.12  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.12  | | | | |            all_52_14 = e0)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | REF_CLOSE: (8), (53), (68), (95), (100), (145), (160), (427), (450),
% 175.79/27.12  | | | | |            (451) are inconsistent by sub-proof #434.
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | Case 2:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | |   (452)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 175.79/27.12  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.79/27.12  | | | | |            all_52_30 = e0)
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | BETA: splitting (452) gives:
% 175.79/27.12  | | | | | 
% 175.79/27.12  | | | | | Case 1:
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | |   (453)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.12  | | | | | |          all_52_22 = e0
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | ALPHA: (453) implies:
% 175.79/27.12  | | | | | |   (454)  all_52_20 = e1
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | COMBINE_EQS: (174), (454) imply:
% 175.79/27.12  | | | | | |   (455)  all_14_1 = e1
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | SIMP: (455) implies:
% 175.79/27.12  | | | | | |   (456)  all_14_1 = e1
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REDUCE: (107), (456) imply:
% 175.79/27.12  | | | | | |   (457)  op(e1, all_14_2) = e2
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | REDUCE: (179), (456) imply:
% 175.79/27.12  | | | | | |   (458)  op(e1, all_14_2) = e1
% 175.79/27.12  | | | | | | 
% 175.79/27.12  | | | | | | GROUND_INST: instantiating (160) with e1, e2, all_14_2, e1,
% 175.79/27.12  | | | | | |              simplifying with (457), (458) gives:
% 175.79/27.12  | | | | | |   (459)  e2 = e1
% 175.79/27.12  | | | | | | 
% 175.79/27.13  | | | | | | REDUCE: (145), (459) imply:
% 175.79/27.13  | | | | | |   (460)  $false
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | | CLOSE: (460) is inconsistent.
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | Case 2:
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | |   (461)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.79/27.13  | | | | | |          all_52_30 = e0
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | | REF_CLOSE: (94), (97), (160), (177), (181), (461) are inconsistent
% 175.79/27.13  | | | | | |            by sub-proof #200.
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | End of split
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | End of split
% 175.79/27.13  | | | | 
% 175.79/27.13  | | | End of split
% 175.79/27.13  | | | 
% 175.79/27.13  | | End of split
% 175.79/27.13  | | 
% 175.79/27.13  | End of split
% 175.79/27.13  | 
% 175.79/27.13  End of proof
% 175.79/27.13  
% 175.79/27.13  Sub-proof #155 shows that the following formulas are inconsistent:
% 175.79/27.13  ----------------------------------------------------------------
% 175.79/27.13    (1)  op(e0, all_6_2) = all_6_1
% 175.79/27.13    (2)  op(all_6_1, all_6_2) = e2
% 175.79/27.13    (3)  op(all_14_1, all_14_2) = e2
% 175.79/27.13    (4)   ~ (e2 = e1)
% 175.79/27.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.13    (6)  all_52_20 = all_14_1
% 175.79/27.13    (7)  all_52_30 = all_6_1
% 175.79/27.13    (8)  op(e1, all_14_2) = all_14_1
% 175.79/27.13    (9)   ~ (e2 = e0)
% 175.79/27.13    (10)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.79/27.13          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.13  
% 175.79/27.13  Begin of proof
% 175.79/27.13  | 
% 175.79/27.13  | BETA: splitting (10) gives:
% 175.79/27.13  | 
% 175.79/27.13  | Case 1:
% 175.79/27.13  | | 
% 175.79/27.13  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.79/27.13  | | 
% 175.79/27.13  | | ALPHA: (11) implies:
% 175.79/27.13  | |   (12)  all_52_20 = e1
% 175.79/27.13  | | 
% 175.79/27.13  | | COMBINE_EQS: (6), (12) imply:
% 175.79/27.13  | |   (13)  all_14_1 = e1
% 175.79/27.13  | | 
% 175.79/27.13  | | REF_CLOSE: (3), (4), (5), (8), (13) are inconsistent by sub-proof #315.
% 175.79/27.13  | | 
% 175.79/27.13  | Case 2:
% 175.79/27.13  | | 
% 175.79/27.13  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.79/27.13  | | 
% 175.79/27.13  | | REF_CLOSE: (1), (2), (5), (7), (9), (14) are inconsistent by sub-proof #200.
% 175.79/27.13  | | 
% 175.79/27.13  | End of split
% 175.79/27.13  | 
% 175.79/27.13  End of proof
% 175.79/27.13  
% 175.79/27.13  Sub-proof #156 shows that the following formulas are inconsistent:
% 175.79/27.13  ----------------------------------------------------------------
% 175.79/27.13    (1)  op(e0, all_6_2) = all_6_1
% 175.79/27.13    (2)  op(all_6_1, all_6_2) = e2
% 175.79/27.13    (3)  op(all_14_1, all_14_2) = e2
% 175.79/27.13    (4)   ~ (e2 = e1)
% 175.79/27.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.13    (6)  all_52_20 = all_14_1
% 175.79/27.13    (7)  all_52_30 = all_6_1
% 175.79/27.13    (8)  op(e1, all_14_2) = all_14_1
% 175.79/27.13    (9)   ~ (e2 = e0)
% 175.79/27.13    (10)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.79/27.13          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.13  
% 175.79/27.13  Begin of proof
% 175.79/27.13  | 
% 175.79/27.13  | BETA: splitting (10) gives:
% 175.79/27.13  | 
% 175.79/27.13  | Case 1:
% 175.79/27.13  | | 
% 175.79/27.13  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.79/27.13  | | 
% 175.79/27.13  | | ALPHA: (11) implies:
% 175.79/27.13  | |   (12)  all_52_20 = e1
% 175.79/27.13  | | 
% 175.79/27.13  | | COMBINE_EQS: (6), (12) imply:
% 175.79/27.13  | |   (13)  all_14_1 = e1
% 175.79/27.13  | | 
% 175.79/27.13  | | REF_CLOSE: (3), (4), (5), (8), (13) are inconsistent by sub-proof #315.
% 175.79/27.13  | | 
% 175.79/27.13  | Case 2:
% 175.79/27.13  | | 
% 175.79/27.13  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.79/27.13  | | 
% 175.79/27.13  | | ALPHA: (14) implies:
% 175.79/27.13  | |   (15)  all_52_30 = e0
% 175.79/27.13  | | 
% 175.79/27.13  | | COMBINE_EQS: (7), (15) imply:
% 175.79/27.13  | |   (16)  all_6_1 = e0
% 175.79/27.13  | | 
% 175.79/27.13  | | REF_CLOSE: (1), (2), (5), (9), (16) are inconsistent by sub-proof #201.
% 175.79/27.13  | | 
% 175.79/27.13  | End of split
% 175.79/27.13  | 
% 175.79/27.13  End of proof
% 175.79/27.13  
% 175.79/27.13  Sub-proof #157 shows that the following formulas are inconsistent:
% 175.79/27.13  ----------------------------------------------------------------
% 175.79/27.13    (1)   ~ (all_52_23 = all_14_2)
% 175.79/27.13    (2)   ~ (all_52_5 = all_52_13)
% 175.79/27.13    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 175.79/27.13    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 175.79/27.13    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.79/27.13    (6)   ~ (all_52_27 = all_10_2)
% 175.79/27.13    (7)   ~ (all_52_17 = all_52_23)
% 175.79/27.13    (8)  op(e2, all_10_2) = all_10_1
% 175.79/27.13    (9)  all_40_2 = all_4_2
% 175.79/27.13    (10)   ~ (all_52_13 = all_52_29)
% 175.79/27.13    (11)  all_56_3 = all_52_7
% 175.79/27.13    (12)  op(e3, e2) = all_52_3
% 175.79/27.13    (13)   ~ (all_52_9 = all_52_25)
% 175.79/27.13    (14)  op(e3, all_52_25) = all_52_24
% 175.79/27.13    (15)   ~ (all_52_19 = all_52_23)
% 175.79/27.13    (16)  all_56_11 = all_52_23
% 175.79/27.13    (17)  op(e1, e2) = all_52_19
% 175.79/27.13    (18)  all_16_1 = all_6_1
% 175.79/27.13    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.79/27.13    (20)  op(e3, all_52_9) = all_52_8
% 175.79/27.13    (21)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.79/27.13    (22)   ~ (all_52_3 = all_10_2)
% 175.79/27.13    (23)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.79/27.13    (24)  all_58_5 = all_52_13
% 175.79/27.13    (25)   ~ (all_52_25 = all_52_29)
% 175.79/27.13    (26)  all_16_2 = all_6_2
% 175.79/27.13    (27)  all_56_15 = all_6_2
% 175.79/27.13    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.79/27.13    (29)  op(e2, e0) = all_52_15
% 175.79/27.13    (30)  op(all_14_1, all_14_2) = all_14_0
% 175.79/27.13    (31)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.79/27.13    (32)  all_58_3 = all_10_2
% 175.79/27.13    (33)  all_56_9 = all_52_19
% 175.79/27.13    (34)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.79/27.13    (35)  all_58_15 = all_6_2
% 175.79/27.13    (36)   ~ (all_52_9 = all_4_2)
% 175.79/27.13    (37)   ~ (all_52_5 = all_52_7)
% 175.79/27.13    (38)  all_58_10 = all_52_15
% 175.79/27.13    (39)  all_8_2 = all_6_2
% 175.79/27.13    (40)   ~ (all_52_5 = all_4_2)
% 175.79/27.13    (41)  all_58_7 = all_52_19
% 175.79/27.13    (42)  all_56_4 = all_52_9
% 175.79/27.13    (43)   ~ (all_52_15 = all_6_2)
% 175.79/27.13    (44)   ~ (all_52_17 = all_52_25)
% 175.79/27.13    (45)  op(e0, e1) = all_52_29
% 175.79/27.13    (46)  all_58_4 = all_52_5
% 175.79/27.13    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.13    (48)   ~ (e3 = e1)
% 175.79/27.13    (49)  all_34_1 = all_4_1
% 175.79/27.13    (50)   ~ (all_52_27 = all_52_29)
% 175.79/27.13    (51)   ~ (all_52_17 = all_14_2)
% 175.79/27.13    (52)  op(e3, all_4_2) = all_4_1
% 175.79/27.13    (53)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.13    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.13    (55)   ~ (all_52_7 = all_4_2)
% 175.79/27.13    (56)  all_58_1 = all_52_3
% 175.79/27.13    (57)   ~ (all_52_13 = all_52_15)
% 175.79/27.13    (58)  all_58_0 = all_4_2
% 175.79/27.13    (59)  op(e1, all_52_13) = all_52_12
% 175.79/27.13    (60)  op(e0, e0) = all_6_2
% 175.79/27.13    (61)  op(e1, all_52_29) = all_52_28
% 175.79/27.13    (62)  op(e1, all_52_5) = all_52_4
% 175.79/27.13    (63)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.79/27.13    (64)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.79/27.13    (65)   ~ (all_4_1 = e2)
% 175.79/27.13    (66)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.79/27.13    (67)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.79/27.13    (68)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.13    (69)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.79/27.13    (70)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.79/27.13    (71)  all_58_14 = all_52_29
% 175.79/27.13    (72)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.79/27.13    (73)  all_24_0 = all_10_0
% 175.79/27.13    (74)  all_40_1 = all_4_1
% 175.79/27.13    (75)   ~ (all_52_3 = all_52_5)
% 175.79/27.13    (76)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.13    (77)  op(e2, e1) = all_52_13
% 175.79/27.13    (78)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.13    (79)  all_58_8 = all_14_2
% 175.79/27.13    (80)  all_56_1 = all_52_3
% 175.79/27.13    (81)  op(e0, e2) = all_52_27
% 175.79/27.13    (82)  all_56_14 = all_52_29
% 175.79/27.13    (83)  all_14_0 = e3
% 175.79/27.13    (84)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.79/27.13    (85)  op(all_4_1, all_4_2) = all_4_0
% 175.79/27.13    (86)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.79/27.13    (87)   ~ (all_52_5 = all_14_2)
% 175.79/27.13    (88)   ~ (all_52_3 = all_52_27)
% 175.79/27.13    (89)   ~ (all_52_3 = all_4_2)
% 175.79/27.13    (90)  op(e0, e3) = all_52_25
% 175.79/27.13    (91)  op(e0, all_6_2) = all_6_1
% 175.79/27.13    (92)  all_52_0 = all_4_1
% 175.79/27.13    (93)   ~ (all_52_9 = all_10_2)
% 175.79/27.13    (94)  op(all_6_1, all_6_2) = e2
% 175.79/27.13    (95)  op(e3, all_52_17) = all_52_16
% 175.79/27.13    (96)  all_52_10 = all_10_1
% 175.79/27.13    (97)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.79/27.13    (98)   ~ (all_52_13 = all_14_2)
% 175.79/27.13    (99)   ~ (e3 = e0)
% 175.79/27.13    (100)  all_40_0 = all_4_0
% 175.79/27.13    (101)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.79/27.13    (102)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 175.79/27.13    (103)   ~ (all_52_9 = all_52_13)
% 175.79/27.13    (104)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.79/27.13    (105)  op(e0, all_52_23) = all_52_22
% 175.79/27.13    (106)   ~ (all_52_15 = all_52_23)
% 175.79/27.13    (107)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.79/27.13    (108)  op(all_10_1, all_10_2) = all_10_0
% 175.79/27.13    (109)   ~ (all_52_5 = all_52_29)
% 175.79/27.13    (110)  all_56_2 = all_52_5
% 175.79/27.13    (111)  op(e1, e0) = all_52_23
% 175.79/27.13    (112)  all_56_12 = all_52_25
% 175.79/27.13    (113)  all_58_13 = all_52_27
% 175.79/27.13    (114)  op(e2, all_52_3) = all_52_2
% 175.79/27.13    (115)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 175.79/27.13    (116)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.13    (117)  all_56_5 = all_10_2
% 175.79/27.13    (118)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.79/27.13    (119)   ~ (all_52_9 = all_52_17)
% 175.79/27.13    (120)  all_58_6 = all_52_17
% 175.79/27.13    (121)   ~ (all_52_3 = all_52_7)
% 175.79/27.13    (122)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.79/27.13    (123)  op(e2, all_52_19) = all_52_18
% 175.79/27.13    (124)   ~ (e1 = e0)
% 175.79/27.13    (125)  all_56_0 = all_4_2
% 175.79/27.13    (126)  all_58_11 = all_52_23
% 175.79/27.13    (127)   ~ (all_52_3 = all_52_19)
% 175.79/27.13    (128)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.79/27.13    (129)   ~ (all_52_7 = all_52_15)
% 175.79/27.13    (130)  op(e0, all_52_15) = all_52_14
% 175.79/27.13    (131)   ~ (all_52_29 = all_14_2)
% 175.79/27.13    (132)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 175.79/27.13    (133)   ~ (all_52_19 = all_10_2)
% 175.79/27.13    (134)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.79/27.13    (135)   ~ (all_52_23 = all_6_2)
% 175.79/27.13    (136)   ~ (all_52_29 = all_6_2)
% 175.79/27.13    (137)  all_58_2 = all_52_9
% 175.79/27.13    (138)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.79/27.13    (139)  op(e3, e1) = all_52_5
% 175.79/27.13    (140)   ~ (e2 = e1)
% 175.79/27.13    (141)  all_56_10 = all_14_2
% 175.79/27.13    (142)   ~ (all_52_25 = all_6_2)
% 175.79/27.13    (143)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.79/27.13    (144)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.79/27.13    (145)  op(e1, e1) = all_14_2
% 175.79/27.13    (146)  op(e1, e3) = all_52_17
% 175.79/27.13    (147)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.79/27.13    (148)  all_26_0 = all_4_0
% 175.79/27.13    (149)   ~ (all_52_25 = all_4_2)
% 175.79/27.13    (150)  op(e3, e0) = all_52_7
% 175.79/27.13    (151)  op(e3, e3) = all_4_2
% 175.79/27.13    (152)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.13             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 175.79/27.13    (153)  all_56_8 = all_52_17
% 175.79/27.13    (154)   ~ (all_52_17 = all_4_2)
% 175.79/27.13    (155)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.13             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.13    (156)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.79/27.13           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 175.79/27.13           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.79/27.13           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.13    (157)   ~ (all_52_25 = all_52_27)
% 175.79/27.13    (158)  all_34_2 = all_4_2
% 175.79/27.13    (159)   ~ (all_52_27 = all_6_2)
% 175.79/27.13    (160)  all_8_1 = all_6_1
% 175.79/27.13    (161)   ~ (all_52_7 = all_6_2)
% 175.79/27.13    (162)   ~ (all_10_0 = e3)
% 175.79/27.13    (163)   ~ (all_52_19 = all_52_27)
% 175.79/27.13    (164)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2)
% 175.79/27.13    (165)  all_56_7 = all_52_15
% 175.79/27.13    (166)  all_18_2 = all_14_2
% 175.79/27.13    (167)   ~ (all_52_7 = all_52_23)
% 175.79/27.13    (168)   ~ (all_52_13 = all_10_2)
% 175.79/27.13    (169)  op(e2, all_52_27) = all_52_26
% 175.79/27.13    (170)  all_52_20 = all_14_1
% 175.79/27.13    (171)   ~ (all_52_17 = all_52_19)
% 175.79/27.13    (172)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.79/27.13    (173)  all_52_30 = all_6_1
% 175.79/27.13    (174)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.79/27.13    (175)  op(e1, all_14_2) = all_14_1
% 175.79/27.13    (176)  all_58_9 = all_52_7
% 175.79/27.13    (177)   ~ (e2 = e0)
% 175.79/27.13    (178)  all_58_12 = all_52_25
% 175.79/27.13    (179)  all_34_0 = all_4_0
% 175.79/27.13    (180)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 175.79/27.13    (181)  all_56_6 = all_52_13
% 175.79/27.13    (182)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.79/27.13    (183)   ~ (all_52_9 = all_52_15)
% 175.79/27.13    (184)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.79/27.13    (185)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.79/27.13    (186)   ~ (all_52_19 = all_14_2)
% 175.79/27.13    (187)  op(e0, all_52_7) = all_52_6
% 175.79/27.13    (188)  op(e2, e3) = all_52_9
% 175.79/27.13    (189)  all_56_13 = all_52_27
% 175.79/27.13  
% 175.79/27.13  Begin of proof
% 175.79/27.13  | 
% 175.79/27.13  | REDUCE: (30), (83) imply:
% 175.79/27.13  |   (190)  op(all_14_1, all_14_2) = e3
% 175.79/27.13  | 
% 175.79/27.13  | BETA: splitting (102) gives:
% 175.79/27.13  | 
% 175.79/27.13  | Case 1:
% 175.79/27.13  | | 
% 175.79/27.13  | |   (191)   ~ (all_24_0 = e1)
% 175.79/27.13  | | 
% 175.79/27.13  | | REDUCE: (73), (191) imply:
% 175.79/27.13  | |   (192)   ~ (all_10_0 = e1)
% 175.79/27.13  | | 
% 175.79/27.13  | | BETA: splitting (180) gives:
% 175.79/27.13  | | 
% 175.79/27.13  | | Case 1:
% 175.79/27.13  | | | 
% 175.79/27.13  | | |   (193)   ~ (all_26_0 = e2)
% 175.79/27.13  | | | 
% 175.79/27.13  | | | REDUCE: (148), (193) imply:
% 175.79/27.13  | | |   (194)   ~ (all_4_0 = e2)
% 175.79/27.13  | | | 
% 175.79/27.13  | | | BETA: splitting (134) gives:
% 175.79/27.13  | | | 
% 175.79/27.13  | | | Case 1:
% 175.79/27.13  | | | | 
% 175.79/27.13  | | | |   (195)   ~ (all_34_0 = e1)
% 175.79/27.13  | | | | 
% 175.79/27.13  | | | | REDUCE: (179), (195) imply:
% 175.79/27.13  | | | |   (196)   ~ (all_4_0 = e1)
% 175.79/27.13  | | | | 
% 175.79/27.13  | | | | BETA: splitting (164) gives:
% 175.79/27.13  | | | | 
% 175.79/27.13  | | | | Case 1:
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | |   (197)   ~ (all_40_1 = e1)
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | | REDUCE: (74), (197) imply:
% 175.79/27.13  | | | | |   (198)   ~ (all_4_1 = e1)
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | | BETA: splitting (152) gives:
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | | Case 1:
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | |   (199)  all_58_15 = e0
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | | REF_CLOSE: (35), (60), (91), (94), (155), (177), (199) are
% 175.79/27.13  | | | | | |            inconsistent by sub-proof #228.
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | Case 2:
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | |   (200)   ~ (all_58_15 = e0)
% 175.79/27.13  | | | | | |   (201)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.13  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | | ALPHA: (201) implies:
% 175.79/27.13  | | | | | |   (202)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.13  | | | | | |   (203)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | | REDUCE: (35), (200) imply:
% 175.79/27.13  | | | | | |   (204)   ~ (all_6_2 = e0)
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | | BETA: splitting (156) gives:
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | | Case 1:
% 175.79/27.13  | | | | | | | 
% 175.79/27.13  | | | | | | |   (205)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 175.79/27.13  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 175.79/27.13  | | | | | | |            e1 & all_52_14 = e0)
% 175.79/27.13  | | | | | | | 
% 175.79/27.13  | | | | | | | BETA: splitting (205) gives:
% 175.79/27.13  | | | | | | | 
% 175.79/27.13  | | | | | | | Case 1:
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | |   (206)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.79/27.13  | | | | | | | |          all_52_6 = e0
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (13), (15), (16),
% 175.79/27.13  | | | | | | | |            (17), (18), (19), (21), (22), (24), (25), (26), (27),
% 175.79/27.13  | | | | | | | |            (28), (29), (31), (32), (34), (35), (36), (37), (38),
% 175.79/27.13  | | | | | | | |            (39), (40), (41), (42), (44), (45), (46), (47), (50),
% 175.79/27.13  | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (61), (62),
% 175.79/27.13  | | | | | | | |            (63), (66), (67), (68), (70), (71), (72), (75), (76),
% 175.79/27.13  | | | | | | | |            (77), (78), (79), (80), (82), (85), (86), (87), (88),
% 175.79/27.13  | | | | | | | |            (89), (90), (91), (92), (93), (94), (97), (98), (99),
% 175.79/27.13  | | | | | | | |            (101), (103), (104), (105), (106), (107), (109),
% 175.79/27.13  | | | | | | | |            (110), (111), (112), (113), (114), (116), (117),
% 175.79/27.13  | | | | | | | |            (118), (119), (120), (121), (122), (124), (125),
% 175.79/27.13  | | | | | | | |            (126), (127), (128), (129), (131), (132), (133),
% 175.79/27.13  | | | | | | | |            (135), (136), (137), (138), (139), (141), (142),
% 175.79/27.13  | | | | | | | |            (143), (144), (145), (146), (147), (149), (150),
% 175.79/27.13  | | | | | | | |            (154), (155), (157), (159), (160), (161), (163),
% 175.79/27.13  | | | | | | | |            (165), (167), (168), (169), (171), (172), (176),
% 175.79/27.13  | | | | | | | |            (178), (182), (183), (184), (185), (186), (187),
% 175.79/27.13  | | | | | | | |            (188), (189), (194), (196), (202), (203), (204),
% 175.79/27.13  | | | | | | | |            (206) are inconsistent by sub-proof #220.
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | Case 2:
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | |   (207)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.13  | | | | | | | |          all_52_14 = e0
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | ALPHA: (207) implies:
% 175.79/27.13  | | | | | | | |   (208)  all_52_14 = e0
% 175.79/27.13  | | | | | | | |   (209)  all_52_12 = e1
% 175.79/27.13  | | | | | | | |   (210)  all_52_10 = e2
% 175.79/27.13  | | | | | | | |   (211)  all_52_8 = e3
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | COMBINE_EQS: (96), (210) imply:
% 175.79/27.13  | | | | | | | |   (212)  all_10_1 = e2
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | REDUCE: (108), (212) imply:
% 175.79/27.13  | | | | | | | |   (213)  op(e2, all_10_2) = all_10_0
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | REDUCE: (20), (211) imply:
% 175.79/27.13  | | | | | | | |   (214)  op(e3, all_52_9) = e3
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | REDUCE: (8), (212) imply:
% 175.79/27.13  | | | | | | | |   (215)  op(e2, all_10_2) = e2
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | REDUCE: (59), (209) imply:
% 175.79/27.13  | | | | | | | |   (216)  op(e1, all_52_13) = e1
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | REDUCE: (130), (208) imply:
% 175.79/27.13  | | | | | | | |   (217)  op(e0, all_52_15) = e0
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | GROUND_INST: instantiating (155) with e2, all_10_0, all_10_2,
% 175.79/27.13  | | | | | | | |              e2, simplifying with (213), (215) gives:
% 175.79/27.13  | | | | | | | |   (218)  all_10_0 = e2
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | REDUCE: (162), (218) imply:
% 175.79/27.13  | | | | | | | |   (219)   ~ (e3 = e2)
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | SIMP: (219) implies:
% 175.79/27.13  | | | | | | | |   (220)   ~ (e3 = e2)
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | BETA: splitting (53) gives:
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | | Case 1:
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | |   (221)  all_56_15 = e3
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | COMBINE_EQS: (27), (221) imply:
% 175.79/27.13  | | | | | | | | |   (222)  all_6_2 = e3
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | REF_CLOSE: (13), (18), (26), (90), (91), (94), (104), (112),
% 175.79/27.13  | | | | | | | | |            (132), (142), (144), (155), (178), (188), (222) are
% 175.79/27.13  | | | | | | | | |            inconsistent by sub-proof #226.
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | Case 2:
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | |   (223)   ~ (all_56_15 = e3)
% 175.79/27.13  | | | | | | | | |   (224)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | REDUCE: (27), (223) imply:
% 175.79/27.13  | | | | | | | | |   (225)   ~ (all_6_2 = e3)
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | BETA: splitting (72) gives:
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | Case 1:
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | |   (226)  all_56_13 = e3
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | | COMBINE_EQS: (189), (226) imply:
% 175.79/27.13  | | | | | | | | | |   (227)  all_52_27 = e3
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (12), (13), (14),
% 175.79/27.13  | | | | | | | | | |            (15), (22), (23), (24), (27), (32), (34), (35),
% 175.79/27.13  | | | | | | | | | |            (36), (37), (38), (40), (41), (42), (44), (46),
% 175.79/27.13  | | | | | | | | | |            (47), (48), (50), (51), (52), (54), (55), (56),
% 175.79/27.13  | | | | | | | | | |            (58), (63), (67), (69), (71), (75), (76), (77),
% 175.79/27.13  | | | | | | | | | |            (79), (80), (81), (85), (87), (88), (89), (90),
% 175.79/27.13  | | | | | | | | | |            (91), (93), (94), (95), (98), (103), (106), (109),
% 175.79/27.13  | | | | | | | | | |            (111), (113), (116), (119), (120), (121), (122),
% 175.79/27.13  | | | | | | | | | |            (124), (125), (126), (136), (137), (139), (146),
% 175.79/27.13  | | | | | | | | | |            (149), (150), (151), (155), (157), (159), (163),
% 175.79/27.13  | | | | | | | | | |            (167), (168), (169), (171), (172), (176), (178),
% 175.79/27.13  | | | | | | | | | |            (181), (182), (183), (184), (188), (194), (196),
% 175.79/27.13  | | | | | | | | | |            (198), (202), (203), (214), (215), (216), (217),
% 175.79/27.13  | | | | | | | | | |            (224), (227) are inconsistent by sub-proof #162.
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | Case 2:
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | |   (228)   ~ (all_56_13 = e3)
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | | REDUCE: (189), (228) imply:
% 175.79/27.13  | | | | | | | | | |   (229)   ~ (all_52_27 = e3)
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (13),
% 175.79/27.13  | | | | | | | | | |            (14), (15), (16), (17), (21), (22), (23), (24),
% 175.79/27.13  | | | | | | | | | |            (25), (27), (28), (29), (32), (33), (34), (35),
% 175.79/27.13  | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 175.79/27.13  | | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 175.79/27.13  | | | | | | | | | |            (54), (55), (56), (58), (61), (64), (65), (67),
% 175.79/27.13  | | | | | | | | | |            (68), (69), (71), (75), (76), (77), (78), (79),
% 175.79/27.13  | | | | | | | | | |            (84), (85), (86), (88), (89), (90), (91), (95),
% 175.79/27.13  | | | | | | | | | |            (98), (99), (103), (105), (106), (107), (111),
% 175.79/27.13  | | | | | | | | | |            (113), (115), (116), (118), (119), (120), (121),
% 175.79/27.13  | | | | | | | | | |            (122), (123), (124), (125), (126), (127), (129),
% 175.79/27.13  | | | | | | | | | |            (131), (133), (135), (136), (137), (138), (139),
% 175.79/27.13  | | | | | | | | | |            (140), (141), (142), (146), (149), (150), (151),
% 175.79/27.13  | | | | | | | | | |            (154), (155), (157), (159), (160), (161), (166),
% 175.79/27.13  | | | | | | | | | |            (167), (171), (172), (174), (175), (176), (178),
% 175.79/27.13  | | | | | | | | | |            (181), (182), (183), (184), (186), (188), (190),
% 175.79/27.13  | | | | | | | | | |            (194), (203), (204), (214), (215), (216), (217),
% 175.79/27.13  | | | | | | | | | |            (220), (224), (225), (229) are inconsistent by
% 175.79/27.13  | | | | | | | | | |            sub-proof #161.
% 175.79/27.13  | | | | | | | | | | 
% 175.79/27.13  | | | | | | | | | End of split
% 175.79/27.13  | | | | | | | | | 
% 175.79/27.13  | | | | | | | | End of split
% 175.79/27.13  | | | | | | | | 
% 175.79/27.13  | | | | | | | End of split
% 175.79/27.13  | | | | | | | 
% 175.79/27.13  | | | | | | Case 2:
% 175.79/27.13  | | | | | | | 
% 175.79/27.13  | | | | | | |   (230)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.13  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.13  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.13  | | | | | | | 
% 175.79/27.13  | | | | | | | REF_CLOSE: (48), (91), (94), (155), (170), (173), (175), (177),
% 175.79/27.13  | | | | | | |            (190), (230) are inconsistent by sub-proof #160.
% 175.79/27.13  | | | | | | | 
% 175.79/27.13  | | | | | | End of split
% 175.79/27.13  | | | | | | 
% 175.79/27.13  | | | | | End of split
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | Case 2:
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | |   (231)  all_40_1 = e1
% 175.79/27.13  | | | | |   (232)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | | COMBINE_EQS: (74), (231) imply:
% 175.79/27.13  | | | | |   (233)  all_4_1 = e1
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | | SIMP: (233) implies:
% 175.79/27.13  | | | | |   (234)  all_4_1 = e1
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | | COMBINE_EQS: (92), (234) imply:
% 175.79/27.13  | | | | |   (235)  all_52_0 = e1
% 175.79/27.13  | | | | | 
% 175.79/27.13  | | | | | REDUCE: (85), (234) imply:
% 175.79/27.13  | | | | |   (236)  op(e1, all_4_2) = all_4_0
% 175.79/27.13  | | | | | 
% 175.79/27.14  | | | | | REDUCE: (52), (234) imply:
% 175.79/27.14  | | | | |   (237)  op(e3, all_4_2) = e1
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | BETA: splitting (152) gives:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | Case 1:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (238)  all_58_15 = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (35), (60), (91), (94), (155), (177), (238) are
% 175.79/27.14  | | | | | |            inconsistent by sub-proof #228.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | Case 2:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (239)   ~ (all_58_15 = e0)
% 175.79/27.14  | | | | | |   (240)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.14  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | ALPHA: (240) implies:
% 175.79/27.14  | | | | | |   (241)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REDUCE: (35), (239) imply:
% 175.79/27.14  | | | | | |   (242)   ~ (all_6_2 = e0)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | BETA: splitting (156) gives:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | Case 1:
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | |   (243)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 175.79/27.14  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 175.79/27.14  | | | | | | |            e1 & all_52_14 = e0)
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | BETA: splitting (243) gives:
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | Case 1:
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | |   (244)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 175.79/27.14  | | | | | | | |          all_52_6 = e0
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REF_CLOSE: (48), (235), (244) are inconsistent by sub-proof
% 175.79/27.14  | | | | | | | |            #632.
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | Case 2:
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | |   (245)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.14  | | | | | | | |          all_52_14 = e0
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | ALPHA: (245) implies:
% 175.79/27.14  | | | | | | | |   (246)  all_52_14 = e0
% 175.79/27.14  | | | | | | | |   (247)  all_52_12 = e1
% 175.79/27.14  | | | | | | | |   (248)  all_52_10 = e2
% 175.79/27.14  | | | | | | | |   (249)  all_52_8 = e3
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | COMBINE_EQS: (96), (248) imply:
% 175.79/27.14  | | | | | | | |   (250)  all_10_1 = e2
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REDUCE: (108), (250) imply:
% 175.79/27.14  | | | | | | | |   (251)  op(e2, all_10_2) = all_10_0
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REDUCE: (20), (249) imply:
% 175.79/27.14  | | | | | | | |   (252)  op(e3, all_52_9) = e3
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REDUCE: (8), (250) imply:
% 175.79/27.14  | | | | | | | |   (253)  op(e2, all_10_2) = e2
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REDUCE: (59), (247) imply:
% 175.79/27.14  | | | | | | | |   (254)  op(e1, all_52_13) = e1
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REDUCE: (130), (246) imply:
% 175.79/27.14  | | | | | | | |   (255)  op(e0, all_52_15) = e0
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | GROUND_INST: instantiating (155) with e2, all_10_0, all_10_2,
% 175.79/27.14  | | | | | | | |              e2, simplifying with (251), (253) gives:
% 175.79/27.14  | | | | | | | |   (256)  all_10_0 = e2
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REDUCE: (162), (256) imply:
% 175.79/27.14  | | | | | | | |   (257)   ~ (e3 = e2)
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | SIMP: (257) implies:
% 175.79/27.14  | | | | | | | |   (258)   ~ (e3 = e2)
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | BETA: splitting (53) gives:
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | Case 1:
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | |   (259)  all_56_15 = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | COMBINE_EQS: (27), (259) imply:
% 175.79/27.14  | | | | | | | | |   (260)  all_6_2 = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | SIMP: (260) implies:
% 175.79/27.14  | | | | | | | | |   (261)  all_6_2 = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REF_CLOSE: (13), (18), (26), (90), (91), (94), (104), (112),
% 175.79/27.14  | | | | | | | | |            (132), (142), (144), (155), (178), (188), (261) are
% 175.79/27.14  | | | | | | | | |            inconsistent by sub-proof #226.
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | Case 2:
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | |   (262)   ~ (all_56_15 = e3)
% 175.79/27.14  | | | | | | | | |   (263)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (27), (262) imply:
% 175.79/27.14  | | | | | | | | |   (264)   ~ (all_6_2 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | BETA: splitting (72) gives:
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | Case 1:
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | |   (265)  all_56_13 = e3
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | | COMBINE_EQS: (189), (265) imply:
% 175.79/27.14  | | | | | | | | | |   (266)  all_52_27 = e3
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | | SIMP: (266) implies:
% 175.79/27.14  | | | | | | | | | |   (267)  all_52_27 = e3
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (11), (12), (17), (24),
% 175.79/27.14  | | | | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (40),
% 175.79/27.14  | | | | | | | | | |            (41), (44), (46), (47), (48), (51), (54), (55),
% 175.79/27.14  | | | | | | | | | |            (56), (58), (64), (71), (76), (79), (87), (88),
% 175.79/27.14  | | | | | | | | | |            (90), (98), (100), (103), (106), (116), (120),
% 175.79/27.14  | | | | | | | | | |            (125), (126), (127), (129), (137), (139), (146),
% 175.79/27.14  | | | | | | | | | |            (149), (151), (154), (155), (159), (163), (167),
% 175.79/27.14  | | | | | | | | | |            (169), (172), (174), (176), (178), (182), (184),
% 175.79/27.14  | | | | | | | | | |            (188), (194), (232), (236), (237), (252), (254),
% 175.79/27.14  | | | | | | | | | |            (255), (267) are inconsistent by sub-proof #610.
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | Case 2:
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | |   (268)   ~ (all_56_13 = e3)
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | | REDUCE: (189), (268) imply:
% 175.79/27.14  | | | | | | | | | |   (269)   ~ (all_52_27 = e3)
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (13),
% 175.79/27.14  | | | | | | | | | |            (14), (15), (16), (17), (21), (22), (23), (24),
% 175.79/27.14  | | | | | | | | | |            (25), (27), (28), (29), (32), (33), (34), (35),
% 175.79/27.14  | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 175.79/27.14  | | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 175.79/27.14  | | | | | | | | | |            (54), (55), (56), (58), (61), (64), (65), (67),
% 175.79/27.14  | | | | | | | | | |            (68), (69), (71), (75), (76), (77), (78), (79),
% 175.79/27.14  | | | | | | | | | |            (84), (85), (86), (88), (89), (90), (91), (95),
% 175.79/27.14  | | | | | | | | | |            (98), (99), (103), (105), (106), (107), (111),
% 175.79/27.14  | | | | | | | | | |            (113), (115), (116), (118), (119), (120), (121),
% 175.79/27.14  | | | | | | | | | |            (122), (123), (124), (125), (126), (127), (129),
% 175.79/27.14  | | | | | | | | | |            (131), (133), (135), (136), (137), (138), (139),
% 175.79/27.14  | | | | | | | | | |            (140), (141), (142), (146), (149), (150), (151),
% 175.79/27.14  | | | | | | | | | |            (154), (155), (157), (159), (160), (161), (166),
% 175.79/27.14  | | | | | | | | | |            (167), (171), (172), (174), (175), (176), (178),
% 175.79/27.14  | | | | | | | | | |            (181), (182), (183), (184), (186), (188), (190),
% 175.79/27.14  | | | | | | | | | |            (194), (241), (242), (252), (253), (254), (255),
% 175.79/27.14  | | | | | | | | | |            (258), (263), (264), (269) are inconsistent by
% 175.79/27.14  | | | | | | | | | |            sub-proof #161.
% 175.79/27.14  | | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | End of split
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | End of split
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | End of split
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | Case 2:
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | |   (270)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.14  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.14  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | REF_CLOSE: (48), (91), (94), (155), (170), (173), (175), (177),
% 175.79/27.14  | | | | | | |            (190), (270) are inconsistent by sub-proof #160.
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | End of split
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | End of split
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | End of split
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | Case 2:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | |   (271)  all_34_0 = e1
% 175.79/27.14  | | | |   (272)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | COMBINE_EQS: (179), (271) imply:
% 175.79/27.14  | | | |   (273)  all_4_0 = e1
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REDUCE: (85), (273) imply:
% 175.79/27.14  | | | |   (274)  op(all_4_1, all_4_2) = e1
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | BETA: splitting (152) gives:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | Case 1:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (275)  all_58_15 = e0
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | REF_CLOSE: (35), (60), (91), (94), (155), (177), (275) are
% 175.79/27.14  | | | | |            inconsistent by sub-proof #228.
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | Case 2:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (276)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.14  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | ALPHA: (276) implies:
% 175.79/27.14  | | | | |   (277)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | BETA: splitting (156) gives:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | Case 1:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (278)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.79/27.14  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.14  | | | | | |            all_52_14 = e0)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (12), (13), (14), (17), (18),
% 175.79/27.14  | | | | | |            (20), (21), (22), (24), (25), (26), (27), (28), (32),
% 175.79/27.14  | | | | | |            (34), (35), (36), (38), (39), (40), (41), (42), (45),
% 175.79/27.14  | | | | | |            (46), (47), (48), (49), (50), (52), (53), (54), (55),
% 175.79/27.14  | | | | | |            (56), (58), (59), (61), (63), (65), (68), (69), (71),
% 175.79/27.14  | | | | | |            (72), (75), (76), (78), (79), (80), (81), (86), (88),
% 175.79/27.14  | | | | | |            (89), (90), (91), (92), (94), (96), (103), (104), (106),
% 175.79/27.14  | | | | | |            (108), (109), (110), (111), (112), (113), (116), (120),
% 175.79/27.14  | | | | | |            (121), (122), (124), (125), (126), (127), (130), (131),
% 175.79/27.14  | | | | | |            (132), (136), (137), (139), (142), (144), (146), (149),
% 175.79/27.14  | | | | | |            (150), (151), (154), (155), (157), (158), (159), (160),
% 175.79/27.14  | | | | | |            (161), (162), (167), (169), (171), (172), (174), (176),
% 175.79/27.14  | | | | | |            (178), (181), (182), (183), (185), (188), (189), (192),
% 175.79/27.14  | | | | | |            (272), (274), (277), (278) are inconsistent by sub-proof
% 175.79/27.14  | | | | | |            #159.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | Case 2:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (279)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.14  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.14  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (48), (91), (94), (155), (170), (173), (175), (177),
% 175.79/27.14  | | | | | |            (190), (279) are inconsistent by sub-proof #160.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | End of split
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | End of split
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | End of split
% 175.79/27.14  | | | 
% 175.79/27.14  | | Case 2:
% 175.79/27.14  | | | 
% 175.79/27.14  | | |   (280)  all_26_0 = e2
% 175.79/27.14  | | | 
% 175.79/27.14  | | | COMBINE_EQS: (148), (280) imply:
% 175.79/27.14  | | |   (281)  all_4_0 = e2
% 175.79/27.14  | | | 
% 175.79/27.14  | | | SIMP: (281) implies:
% 175.79/27.14  | | |   (282)  all_4_0 = e2
% 175.79/27.14  | | | 
% 175.79/27.14  | | | REDUCE: (85), (282) imply:
% 175.79/27.14  | | |   (283)  op(all_4_1, all_4_2) = e2
% 175.79/27.14  | | | 
% 175.79/27.14  | | | BETA: splitting (152) gives:
% 175.79/27.14  | | | 
% 175.79/27.14  | | | Case 1:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | |   (284)  all_58_15 = e0
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REF_CLOSE: (35), (60), (91), (94), (155), (177), (284) are inconsistent
% 175.79/27.14  | | | |            by sub-proof #228.
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | Case 2:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | |   (285)   ~ (all_58_15 = e0)
% 175.79/27.14  | | | |   (286)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12
% 175.79/27.14  | | | |            = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | ALPHA: (286) implies:
% 175.79/27.14  | | | |   (287)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REDUCE: (35), (285) imply:
% 175.79/27.14  | | | |   (288)   ~ (all_6_2 = e0)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | BETA: splitting (156) gives:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | Case 1:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (289)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.79/27.14  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.14  | | | | |            all_52_14 = e0)
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | BETA: splitting (289) gives:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | Case 1:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (290)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.79/27.14  | | | | | |          e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (52), (65), (92), (155), (283), (290) are inconsistent by
% 175.79/27.14  | | | | | |            sub-proof #494.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | Case 2:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (291)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 175.79/27.14  | | | | | |          = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | ALPHA: (291) implies:
% 175.79/27.14  | | | | | |   (292)  all_52_14 = e0
% 175.79/27.14  | | | | | |   (293)  all_52_12 = e1
% 175.79/27.14  | | | | | |   (294)  all_52_10 = e2
% 175.79/27.14  | | | | | |   (295)  all_52_8 = e3
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | COMBINE_EQS: (96), (294) imply:
% 175.79/27.14  | | | | | |   (296)  all_10_1 = e2
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REDUCE: (108), (296) imply:
% 175.79/27.14  | | | | | |   (297)  op(e2, all_10_2) = all_10_0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REDUCE: (20), (295) imply:
% 175.79/27.14  | | | | | |   (298)  op(e3, all_52_9) = e3
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REDUCE: (8), (296) imply:
% 175.79/27.14  | | | | | |   (299)  op(e2, all_10_2) = e2
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REDUCE: (59), (293) imply:
% 175.79/27.14  | | | | | |   (300)  op(e1, all_52_13) = e1
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REDUCE: (130), (292) imply:
% 175.79/27.14  | | | | | |   (301)  op(e0, all_52_15) = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | GROUND_INST: instantiating (155) with e2, all_10_0, all_10_2, e2,
% 175.79/27.14  | | | | | |              simplifying with (297), (299) gives:
% 175.79/27.14  | | | | | |   (302)  all_10_0 = e2
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REDUCE: (162), (302) imply:
% 175.79/27.14  | | | | | |   (303)   ~ (e3 = e2)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | SIMP: (303) implies:
% 175.79/27.14  | | | | | |   (304)   ~ (e3 = e2)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | BETA: splitting (53) gives:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | Case 1:
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | |   (305)  all_56_15 = e3
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | COMBINE_EQS: (27), (305) imply:
% 175.79/27.14  | | | | | | |   (306)  all_6_2 = e3
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | SIMP: (306) implies:
% 175.79/27.14  | | | | | | |   (307)  all_6_2 = e3
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | REF_CLOSE: (13), (18), (26), (90), (91), (94), (104), (112),
% 175.79/27.14  | | | | | | |            (132), (142), (144), (155), (178), (188), (307) are
% 175.79/27.14  | | | | | | |            inconsistent by sub-proof #226.
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | Case 2:
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | |   (308)   ~ (all_56_15 = e3)
% 175.79/27.14  | | | | | | |   (309)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | REDUCE: (27), (308) imply:
% 175.79/27.14  | | | | | | |   (310)   ~ (all_6_2 = e3)
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | BETA: splitting (72) gives:
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | | Case 1:
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | |   (311)  all_56_13 = e3
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (12), (13), (14),
% 175.79/27.14  | | | | | | | |            (15), (17), (22), (23), (24), (28), (29), (32), (34),
% 175.79/27.14  | | | | | | | |            (35), (36), (37), (38), (40), (41), (42), (44), (46),
% 175.79/27.14  | | | | | | | |            (47), (48), (50), (51), (52), (54), (56), (57), (58),
% 175.79/27.14  | | | | | | | |            (63), (65), (71), (75), (76), (79), (80), (88), (89),
% 175.79/27.14  | | | | | | | |            (90), (93), (95), (98), (103), (106), (111), (113),
% 175.79/27.14  | | | | | | | |            (116), (117), (120), (121), (122), (124), (125),
% 175.79/27.14  | | | | | | | |            (126), (133), (137), (140), (143), (146), (149),
% 175.79/27.14  | | | | | | | |            (150), (151), (153), (154), (155), (157), (159),
% 175.79/27.14  | | | | | | | |            (168), (169), (171), (172), (176), (178), (183),
% 175.79/27.14  | | | | | | | |            (184), (188), (189), (283), (287), (298), (299),
% 175.79/27.14  | | | | | | | |            (300), (301), (311) are inconsistent by sub-proof
% 175.79/27.14  | | | | | | | |            #464.
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | Case 2:
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | |   (312)   ~ (all_56_13 = e3)
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | REDUCE: (189), (312) imply:
% 175.79/27.14  | | | | | | | |   (313)   ~ (all_52_27 = e3)
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | BETA: splitting (78) gives:
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | | Case 1:
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | |   (314)  all_58_12 = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | COMBINE_EQS: (178), (314) imply:
% 175.79/27.14  | | | | | | | | |   (315)  all_52_25 = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | SIMP: (315) implies:
% 175.79/27.14  | | | | | | | | |   (316)  all_52_25 = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (13), (316) imply:
% 175.79/27.14  | | | | | | | | |   (317)   ~ (all_52_9 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (44), (316) imply:
% 175.79/27.14  | | | | | | | | |   (318)   ~ (all_52_17 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (157), (316) imply:
% 175.79/27.14  | | | | | | | | |   (319)   ~ (all_52_27 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (25), (316) imply:
% 175.79/27.14  | | | | | | | | |   (320)   ~ (all_52_29 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | SIMP: (320) implies:
% 175.79/27.14  | | | | | | | | |   (321)   ~ (all_52_29 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (142), (316) imply:
% 175.79/27.14  | | | | | | | | |   (322)   ~ (all_6_2 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (149), (316) imply:
% 175.79/27.14  | | | | | | | | |   (323)   ~ (all_4_2 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | SIMP: (323) implies:
% 175.79/27.14  | | | | | | | | |   (324)   ~ (all_4_2 = e3)
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REDUCE: (90), (316) imply:
% 175.79/27.14  | | | | | | | | |   (325)  op(e0, e3) = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (15),
% 175.79/27.14  | | | | | | | | |            (16), (17), (22), (24), (27), (28), (32), (33),
% 175.79/27.14  | | | | | | | | |            (34), (35), (36), (37), (38), (40), (41), (42),
% 175.79/27.14  | | | | | | | | |            (46), (47), (50), (51), (54), (55), (56), (58),
% 175.79/27.14  | | | | | | | | |            (64), (67), (68), (69), (71), (75), (77), (79),
% 175.79/27.14  | | | | | | | | |            (86), (95), (98), (99), (103), (105), (107), (113),
% 175.79/27.14  | | | | | | | | |            (115), (118), (119), (120), (121), (122), (123),
% 175.79/27.14  | | | | | | | | |            (125), (126), (127), (129), (131), (133), (135),
% 175.79/27.14  | | | | | | | | |            (137), (138), (139), (140), (141), (146), (150),
% 175.79/27.14  | | | | | | | | |            (154), (155), (159), (161), (166), (167), (171),
% 175.79/27.14  | | | | | | | | |            (172), (174), (175), (176), (181), (182), (183),
% 175.79/27.14  | | | | | | | | |            (184), (186), (188), (190), (287), (288), (298),
% 175.79/27.14  | | | | | | | | |            (299), (300), (301), (304), (309), (310), (313),
% 175.79/27.14  | | | | | | | | |            (314), (317), (318), (321), (324), (325) are
% 175.79/27.14  | | | | | | | | |            inconsistent by sub-proof #334.
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | Case 2:
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | |   (326)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | | REF_CLOSE: (7), (12), (14), (21), (22), (25), (27), (32),
% 175.79/27.14  | | | | | | | | |            (34), (35), (36), (38), (39), (41), (44), (45),
% 175.79/27.14  | | | | | | | | |            (46), (48), (50), (52), (54), (55), (56), (58),
% 175.79/27.14  | | | | | | | | |            (61), (65), (68), (71), (76), (86), (90), (91),
% 175.79/27.14  | | | | | | | | |            (95), (109), (113), (116), (120), (121), (124),
% 175.79/27.14  | | | | | | | | |            (125), (126), (136), (137), (139), (140), (142),
% 175.79/27.14  | | | | | | | | |            (146), (150), (151), (155), (160), (161), (171),
% 175.79/27.14  | | | | | | | | |            (172), (176), (178), (188), (283), (298), (299),
% 175.79/27.14  | | | | | | | | |            (301), (304), (309), (310), (313), (326) are
% 175.79/27.14  | | | | | | | | |            inconsistent by sub-proof #186.
% 175.79/27.14  | | | | | | | | | 
% 175.79/27.14  | | | | | | | | End of split
% 175.79/27.14  | | | | | | | | 
% 175.79/27.14  | | | | | | | End of split
% 175.79/27.14  | | | | | | | 
% 175.79/27.14  | | | | | | End of split
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | End of split
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | Case 2:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (327)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 175.79/27.14  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.79/27.14  | | | | |            all_52_30 = e0)
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | BETA: splitting (327) gives:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | Case 1:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (328)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.14  | | | | | |          all_52_22 = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (48), (155), (170), (175), (190), (328) are inconsistent
% 175.79/27.14  | | | | | |            by sub-proof #343.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | Case 2:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (329)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.79/27.14  | | | | | |          all_52_30 = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (91), (94), (155), (173), (177), (329) are inconsistent
% 175.79/27.14  | | | | | |            by sub-proof #200.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | End of split
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | End of split
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | End of split
% 175.79/27.14  | | | 
% 175.79/27.14  | | End of split
% 175.79/27.14  | | 
% 175.79/27.14  | Case 2:
% 175.79/27.14  | | 
% 175.79/27.14  | |   (330)  all_24_0 = e1
% 175.79/27.14  | | 
% 175.79/27.14  | | COMBINE_EQS: (73), (330) imply:
% 175.79/27.14  | |   (331)  all_10_0 = e1
% 175.79/27.14  | | 
% 175.79/27.14  | | SIMP: (331) implies:
% 175.79/27.14  | |   (332)  all_10_0 = e1
% 175.79/27.14  | | 
% 175.79/27.14  | | REDUCE: (162), (332) imply:
% 175.79/27.14  | |   (333)   ~ (e3 = e1)
% 175.79/27.14  | | 
% 175.79/27.14  | | REDUCE: (108), (332) imply:
% 175.79/27.14  | |   (334)  op(all_10_1, all_10_2) = e1
% 175.79/27.14  | | 
% 175.79/27.14  | | BETA: splitting (180) gives:
% 175.79/27.14  | | 
% 175.79/27.14  | | Case 1:
% 175.79/27.14  | | | 
% 175.79/27.14  | | |   (335)   ~ (all_26_0 = e2)
% 175.79/27.14  | | | 
% 175.79/27.14  | | | REDUCE: (148), (335) imply:
% 175.79/27.14  | | |   (336)   ~ (all_4_0 = e2)
% 175.79/27.14  | | | 
% 175.79/27.14  | | | BETA: splitting (134) gives:
% 175.79/27.14  | | | 
% 175.79/27.14  | | | Case 1:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | |   (337)   ~ (all_34_0 = e1)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REDUCE: (179), (337) imply:
% 175.79/27.14  | | | |   (338)   ~ (all_4_0 = e1)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | BETA: splitting (152) gives:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | Case 1:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (339)  all_58_15 = e0
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | REF_CLOSE: (35), (60), (91), (94), (155), (177), (339) are
% 175.79/27.14  | | | | |            inconsistent by sub-proof #228.
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | Case 2:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (340)   ~ (all_58_15 = e0)
% 175.79/27.14  | | | | |   (341)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 175.79/27.14  | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | ALPHA: (341) implies:
% 175.79/27.14  | | | | |   (342)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.14  | | | | |   (343)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | REDUCE: (35), (340) imply:
% 175.79/27.14  | | | | |   (344)   ~ (all_6_2 = e0)
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | BETA: splitting (156) gives:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | Case 1:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (345)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.79/27.14  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.14  | | | | | |            all_52_14 = e0)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (1), (2), (6), (7), (8), (10), (12), (13), (15), (16),
% 175.79/27.14  | | | | | |            (17), (18), (19), (21), (22), (24), (25), (26), (27),
% 175.79/27.14  | | | | | |            (28), (29), (31), (32), (34), (35), (36), (37), (38),
% 175.79/27.14  | | | | | |            (39), (40), (41), (42), (44), (45), (46), (47), (50),
% 175.79/27.14  | | | | | |            (52), (53), (54), (55), (56), (57), (58), (61), (62),
% 175.79/27.14  | | | | | |            (63), (66), (67), (68), (70), (71), (72), (75), (76),
% 175.79/27.14  | | | | | |            (77), (78), (79), (80), (82), (85), (86), (87), (88),
% 175.79/27.14  | | | | | |            (89), (90), (91), (92), (93), (94), (96), (97), (98),
% 175.79/27.14  | | | | | |            (99), (101), (103), (104), (105), (106), (107), (109),
% 175.79/27.14  | | | | | |            (110), (111), (112), (113), (114), (116), (117), (118),
% 175.79/27.14  | | | | | |            (119), (120), (121), (122), (124), (125), (126), (127),
% 175.79/27.14  | | | | | |            (128), (129), (131), (132), (133), (135), (136), (137),
% 175.79/27.14  | | | | | |            (138), (139), (140), (141), (142), (143), (144), (145),
% 175.79/27.14  | | | | | |            (146), (147), (149), (150), (154), (155), (157), (159),
% 175.79/27.14  | | | | | |            (160), (161), (163), (165), (167), (168), (169), (171),
% 175.79/27.14  | | | | | |            (172), (176), (178), (182), (183), (184), (185), (186),
% 175.79/27.14  | | | | | |            (187), (188), (189), (334), (336), (338), (342), (343),
% 175.79/27.14  | | | | | |            (344), (345) are inconsistent by sub-proof #158.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | Case 2:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (346)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.14  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 175.79/27.14  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (48), (91), (94), (155), (170), (173), (175), (177),
% 175.79/27.14  | | | | | |            (190), (346) are inconsistent by sub-proof #160.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | End of split
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | End of split
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | Case 2:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | |   (347)  all_34_0 = e1
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | COMBINE_EQS: (179), (347) imply:
% 175.79/27.14  | | | |   (348)  all_4_0 = e1
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | SIMP: (348) implies:
% 175.79/27.14  | | | |   (349)  all_4_0 = e1
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REDUCE: (336), (349) imply:
% 175.79/27.14  | | | |   (350)   ~ (e2 = e1)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REDUCE: (85), (349) imply:
% 175.79/27.14  | | | |   (351)  op(all_4_1, all_4_2) = e1
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | BETA: splitting (156) gives:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | Case 1:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (352)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 175.79/27.14  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 175.79/27.14  | | | | |            all_52_14 = e0)
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | REF_CLOSE: (8), (48), (52), (92), (96), (140), (155), (334), (351),
% 175.79/27.14  | | | | |            (352) are inconsistent by sub-proof #441.
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | Case 2:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | |   (353)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 175.79/27.14  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.79/27.14  | | | | |            all_52_30 = e0)
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | BETA: splitting (353) gives:
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | | Case 1:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (354)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 175.79/27.14  | | | | | |          all_52_22 = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (48), (155), (170), (175), (190), (354) are inconsistent
% 175.79/27.14  | | | | | |            by sub-proof #343.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | Case 2:
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | |   (355)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.79/27.14  | | | | | |          all_52_30 = e0
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | | REF_CLOSE: (91), (94), (155), (173), (177), (355) are inconsistent
% 175.79/27.14  | | | | | |            by sub-proof #200.
% 175.79/27.14  | | | | | | 
% 175.79/27.14  | | | | | End of split
% 175.79/27.14  | | | | | 
% 175.79/27.14  | | | | End of split
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | End of split
% 175.79/27.14  | | | 
% 175.79/27.14  | | Case 2:
% 175.79/27.14  | | | 
% 175.79/27.14  | | |   (356)  all_26_0 = e2
% 175.79/27.14  | | | 
% 175.79/27.14  | | | COMBINE_EQS: (148), (356) imply:
% 175.79/27.14  | | |   (357)  all_4_0 = e2
% 175.79/27.14  | | | 
% 175.79/27.14  | | | REDUCE: (85), (357) imply:
% 175.79/27.14  | | |   (358)  op(all_4_1, all_4_2) = e2
% 175.79/27.14  | | | 
% 175.79/27.14  | | | BETA: splitting (156) gives:
% 175.79/27.14  | | | 
% 175.79/27.14  | | | Case 1:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | |   (359)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0)
% 175.79/27.14  | | | |          | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 175.79/27.14  | | | |            = e0)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REF_CLOSE: (8), (52), (65), (92), (96), (140), (155), (334), (358),
% 175.79/27.14  | | | |            (359) are inconsistent by sub-proof #434.
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | Case 2:
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | |   (360)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 175.79/27.14  | | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 175.79/27.14  | | | |            all_52_30 = e0)
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | | REF_CLOSE: (48), (91), (94), (155), (170), (173), (175), (177), (190),
% 175.79/27.14  | | | |            (360) are inconsistent by sub-proof #160.
% 175.79/27.14  | | | | 
% 175.79/27.14  | | | End of split
% 175.79/27.14  | | | 
% 175.79/27.14  | | End of split
% 175.79/27.14  | | 
% 175.79/27.14  | End of split
% 175.79/27.14  | 
% 175.79/27.14  End of proof
% 175.79/27.14  
% 175.79/27.14  Sub-proof #158 shows that the following formulas are inconsistent:
% 175.79/27.14  ----------------------------------------------------------------
% 175.79/27.14    (1)   ~ (all_52_23 = all_14_2)
% 175.79/27.14    (2)   ~ (all_52_5 = all_52_13)
% 175.79/27.14    (3)   ~ (all_52_27 = all_10_2)
% 175.79/27.14    (4)   ~ (all_52_17 = all_52_23)
% 175.79/27.14    (5)  op(e2, all_10_2) = all_10_1
% 175.79/27.14    (6)   ~ (all_52_13 = all_52_29)
% 175.79/27.14    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.14    (8)  op(all_10_1, all_10_2) = e1
% 175.79/27.14    (9)  op(e3, e2) = all_52_3
% 175.79/27.14    (10)   ~ (all_52_9 = all_52_25)
% 175.79/27.14    (11)   ~ (all_52_19 = all_52_23)
% 175.79/27.14    (12)  all_56_11 = all_52_23
% 175.79/27.14    (13)  op(e1, e2) = all_52_19
% 175.79/27.14    (14)  all_16_1 = all_6_1
% 175.79/27.14    (15)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 175.79/27.14    (16)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.79/27.14    (17)   ~ (all_52_3 = all_10_2)
% 175.79/27.14    (18)  all_58_5 = all_52_13
% 175.79/27.15    (19)   ~ (all_6_2 = e0)
% 175.79/27.15    (20)   ~ (all_52_25 = all_52_29)
% 175.79/27.15    (21)  all_16_2 = all_6_2
% 175.79/27.15    (22)  all_56_15 = all_6_2
% 175.79/27.15    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.79/27.15    (24)  op(e2, e0) = all_52_15
% 175.79/27.15    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 175.79/27.15    (26)  all_58_3 = all_10_2
% 175.79/27.15    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.79/27.15    (28)  all_58_15 = all_6_2
% 175.79/27.15    (29)   ~ (all_52_9 = all_4_2)
% 175.79/27.15    (30)   ~ (all_52_5 = all_52_7)
% 175.79/27.15    (31)  all_58_10 = all_52_15
% 175.79/27.15    (32)  all_8_2 = all_6_2
% 175.79/27.15    (33)   ~ (all_52_5 = all_4_2)
% 175.79/27.15    (34)  all_58_7 = all_52_19
% 175.79/27.15    (35)  all_56_4 = all_52_9
% 175.79/27.15    (36)   ~ (all_52_17 = all_52_25)
% 175.79/27.15    (37)  op(e0, e1) = all_52_29
% 175.79/27.15    (38)   ~ (all_4_0 = e2)
% 175.79/27.15    (39)  all_58_4 = all_52_5
% 175.79/27.15    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.15    (41)   ~ (all_52_27 = all_52_29)
% 175.79/27.15    (42)  op(e3, all_4_2) = all_4_1
% 175.79/27.15    (43)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.15    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.15    (45)   ~ (all_52_7 = all_4_2)
% 175.79/27.15    (46)  all_58_1 = all_52_3
% 175.79/27.15    (47)   ~ (all_52_13 = all_52_15)
% 175.79/27.15    (48)  all_58_0 = all_4_2
% 175.79/27.15    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.15    (50)  op(e1, all_52_29) = all_52_28
% 175.79/27.15    (51)  op(e1, all_52_5) = all_52_4
% 175.79/27.15    (52)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.79/27.15          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.79/27.15    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.79/27.15    (54)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 175.79/27.15    (55)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.79/27.15    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.15    (57)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 175.79/27.15    (58)  all_58_14 = all_52_29
% 175.79/27.15    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.79/27.15    (60)   ~ (all_52_3 = all_52_5)
% 175.79/27.15    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.15    (62)  op(e2, e1) = all_52_13
% 175.79/27.15    (63)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.15    (64)  all_58_8 = all_14_2
% 175.79/27.15    (65)  all_56_1 = all_52_3
% 175.79/27.15    (66)  all_56_14 = all_52_29
% 175.79/27.15    (67)  op(all_4_1, all_4_2) = all_4_0
% 175.79/27.15    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.79/27.15    (69)   ~ (all_52_5 = all_14_2)
% 175.79/27.15    (70)   ~ (all_52_3 = all_52_27)
% 175.79/27.15    (71)   ~ (all_52_3 = all_4_2)
% 175.79/27.15    (72)  op(e0, e3) = all_52_25
% 175.79/27.15    (73)  op(e0, all_6_2) = all_6_1
% 175.79/27.15    (74)  all_52_0 = all_4_1
% 175.79/27.15    (75)   ~ (all_52_9 = all_10_2)
% 175.79/27.15    (76)  op(all_6_1, all_6_2) = e2
% 175.79/27.15    (77)  all_52_10 = all_10_1
% 175.79/27.15    (78)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 175.79/27.15    (79)   ~ (all_52_13 = all_14_2)
% 175.79/27.15    (80)   ~ (e3 = e0)
% 175.79/27.15    (81)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 175.79/27.15    (82)   ~ (all_52_9 = all_52_13)
% 175.79/27.15    (83)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.79/27.15    (84)  op(e0, all_52_23) = all_52_22
% 175.79/27.15    (85)   ~ (all_52_15 = all_52_23)
% 175.79/27.15    (86)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.79/27.15    (87)   ~ (all_52_5 = all_52_29)
% 175.79/27.15    (88)  all_56_2 = all_52_5
% 175.79/27.15    (89)  op(e1, e0) = all_52_23
% 175.79/27.15    (90)  all_56_12 = all_52_25
% 175.79/27.15    (91)  all_58_13 = all_52_27
% 175.79/27.15    (92)  op(e2, all_52_3) = all_52_2
% 175.79/27.15    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.15    (94)  all_56_5 = all_10_2
% 175.79/27.15    (95)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.79/27.15    (96)   ~ (all_52_9 = all_52_17)
% 175.79/27.15    (97)  all_58_6 = all_52_17
% 175.79/27.15    (98)   ~ (all_52_3 = all_52_7)
% 175.79/27.15    (99)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.79/27.15    (100)   ~ (e1 = e0)
% 175.79/27.15    (101)  all_56_0 = all_4_2
% 175.79/27.15    (102)  all_58_11 = all_52_23
% 175.79/27.15    (103)   ~ (all_52_3 = all_52_19)
% 175.79/27.15    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 175.79/27.15    (105)   ~ (all_52_7 = all_52_15)
% 175.79/27.15    (106)   ~ (all_52_29 = all_14_2)
% 175.79/27.15    (107)   ~ (all_4_0 = e1)
% 175.79/27.15    (108)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 175.79/27.15    (109)   ~ (all_52_19 = all_10_2)
% 175.79/27.15    (110)   ~ (all_52_23 = all_6_2)
% 175.79/27.15    (111)   ~ (all_52_29 = all_6_2)
% 175.79/27.15    (112)  all_58_2 = all_52_9
% 175.79/27.15    (113)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.79/27.15    (114)  op(e3, e1) = all_52_5
% 175.79/27.15    (115)   ~ (e2 = e1)
% 175.79/27.15    (116)  all_56_10 = all_14_2
% 175.79/27.15    (117)   ~ (all_52_25 = all_6_2)
% 175.79/27.15    (118)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 175.79/27.15    (119)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.79/27.15    (120)  op(e1, e1) = all_14_2
% 175.79/27.15    (121)  op(e1, e3) = all_52_17
% 175.79/27.15    (122)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 175.79/27.15    (123)   ~ (all_52_25 = all_4_2)
% 175.79/27.15    (124)  op(e3, e0) = all_52_7
% 175.79/27.15    (125)   ~ (all_52_17 = all_4_2)
% 175.79/27.15    (126)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.15             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.15    (127)   ~ (all_52_25 = all_52_27)
% 175.79/27.15    (128)   ~ (all_52_27 = all_6_2)
% 175.79/27.15    (129)  all_8_1 = all_6_1
% 175.79/27.15    (130)   ~ (all_52_7 = all_6_2)
% 175.79/27.15    (131)   ~ (all_52_19 = all_52_27)
% 175.79/27.15    (132)  all_56_7 = all_52_15
% 175.79/27.15    (133)   ~ (all_52_7 = all_52_23)
% 175.79/27.15    (134)   ~ (all_52_13 = all_10_2)
% 175.79/27.15    (135)  op(e2, all_52_27) = all_52_26
% 175.79/27.15    (136)   ~ (all_52_17 = all_52_19)
% 175.79/27.15    (137)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.79/27.15    (138)  all_58_9 = all_52_7
% 175.79/27.15    (139)  all_58_12 = all_52_25
% 175.79/27.15    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.79/27.15    (141)   ~ (all_52_9 = all_52_15)
% 175.79/27.15    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.79/27.15    (143)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.79/27.15    (144)   ~ (all_52_19 = all_14_2)
% 175.79/27.15    (145)  op(e0, all_52_7) = all_52_6
% 175.79/27.15    (146)  op(e2, e3) = all_52_9
% 175.79/27.15    (147)  all_56_13 = all_52_27
% 175.79/27.15  
% 175.79/27.15  Begin of proof
% 175.79/27.15  | 
% 175.79/27.15  | BETA: splitting (52) gives:
% 175.79/27.15  | 
% 175.79/27.15  | Case 1:
% 175.79/27.15  | | 
% 175.79/27.15  | |   (148)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.79/27.15  | | 
% 175.79/27.15  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 175.79/27.15  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 175.79/27.15  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 175.79/27.15  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 175.79/27.15  | |            (48), (49), (50), (51), (53), (54), (55), (56), (57), (58), (59),
% 175.79/27.15  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 175.79/27.15  | |            (71), (72), (73), (74), (75), (76), (78), (79), (80), (81), (82),
% 175.79/27.15  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 175.79/27.15  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 175.79/27.15  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 175.79/27.15  | |            (113), (114), (116), (117), (118), (119), (120), (121), (122),
% 175.79/27.15  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 175.79/27.15  | |            (132), (133), (134), (135), (136), (137), (138), (139), (140),
% 175.79/27.15  | |            (141), (142), (143), (144), (145), (146), (147), (148) are
% 175.79/27.15  | |            inconsistent by sub-proof #220.
% 175.79/27.15  | | 
% 175.79/27.15  | Case 2:
% 175.79/27.15  | | 
% 175.79/27.15  | |   (149)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.79/27.15  | | 
% 175.79/27.15  | | ALPHA: (149) implies:
% 175.79/27.15  | |   (150)  all_52_10 = e2
% 175.79/27.15  | | 
% 175.79/27.15  | | COMBINE_EQS: (77), (150) imply:
% 175.79/27.15  | |   (151)  all_10_1 = e2
% 175.79/27.15  | | 
% 175.79/27.15  | | REF_CLOSE: (5), (8), (115), (126), (151) are inconsistent by sub-proof #446.
% 175.79/27.15  | | 
% 175.79/27.15  | End of split
% 175.79/27.15  | 
% 175.79/27.15  End of proof
% 175.79/27.15  
% 175.79/27.15  Sub-proof #159 shows that the following formulas are inconsistent:
% 175.79/27.15  ----------------------------------------------------------------
% 175.79/27.15    (1)   ~ (all_52_27 = all_10_2)
% 175.79/27.15    (2)   ~ (all_52_17 = all_52_23)
% 175.79/27.15    (3)  op(e2, all_10_2) = all_10_1
% 175.79/27.15    (4)   ~ (all_52_13 = all_52_29)
% 175.79/27.15    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 175.79/27.15    (6)  all_56_3 = all_52_7
% 175.79/27.15    (7)  op(e3, e2) = all_52_3
% 175.79/27.15    (8)   ~ (all_52_9 = all_52_25)
% 175.79/27.15    (9)  op(e3, all_52_25) = all_52_24
% 175.79/27.15    (10)  op(e1, e2) = all_52_19
% 175.79/27.15    (11)  all_16_1 = all_6_1
% 175.79/27.15    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 175.79/27.15    (13)  op(e3, all_52_9) = all_52_8
% 175.79/27.15    (14)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.79/27.15    (15)   ~ (all_52_3 = all_10_2)
% 175.79/27.15    (16)  all_58_5 = all_52_13
% 175.79/27.15    (17)   ~ (all_52_25 = all_52_29)
% 175.79/27.15    (18)  all_16_2 = all_6_2
% 175.79/27.15    (19)  all_56_15 = all_6_2
% 175.79/27.15    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.79/27.15    (21)  all_58_3 = all_10_2
% 175.79/27.15    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.79/27.15    (23)  all_58_15 = all_6_2
% 175.79/27.15    (24)   ~ (all_52_9 = all_4_2)
% 175.79/27.15    (25)  all_58_10 = all_52_15
% 175.79/27.15    (26)  all_8_2 = all_6_2
% 175.79/27.15    (27)   ~ (all_52_5 = all_4_2)
% 175.79/27.15    (28)  all_58_7 = all_52_19
% 175.79/27.15    (29)  all_56_4 = all_52_9
% 175.79/27.15    (30)  op(e0, e1) = all_52_29
% 175.79/27.15    (31)  all_58_4 = all_52_5
% 175.79/27.15    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.15    (33)   ~ (e3 = e1)
% 175.79/27.15    (34)  all_34_1 = all_4_1
% 175.79/27.15    (35)   ~ (all_52_27 = all_52_29)
% 175.79/27.15    (36)  op(e3, all_4_2) = all_4_1
% 175.79/27.15    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.15    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.15    (39)   ~ (all_52_7 = all_4_2)
% 175.79/27.15    (40)  all_58_1 = all_52_3
% 175.79/27.15    (41)  all_58_0 = all_4_2
% 175.79/27.15    (42)  op(e1, all_52_13) = all_52_12
% 175.79/27.15    (43)  op(all_4_1, all_4_2) = e1
% 175.79/27.15    (44)  op(e1, all_52_29) = all_52_28
% 175.79/27.15    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 175.79/27.15          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 175.79/27.15    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 175.79/27.15    (47)   ~ (all_4_1 = e2)
% 175.79/27.15    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.15    (49)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.79/27.15    (50)  all_58_14 = all_52_29
% 175.79/27.15    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 175.79/27.15    (52)   ~ (all_52_3 = all_52_5)
% 175.79/27.15    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.15    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.15    (55)  all_58_8 = all_14_2
% 175.79/27.15    (56)  all_56_1 = all_52_3
% 175.79/27.15    (57)  op(e0, e2) = all_52_27
% 175.79/27.15    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.79/27.15    (59)   ~ (all_52_3 = all_52_27)
% 175.79/27.15    (60)   ~ (all_52_3 = all_4_2)
% 175.79/27.15    (61)  op(e0, e3) = all_52_25
% 175.79/27.15    (62)  op(e0, all_6_2) = all_6_1
% 175.79/27.15    (63)  all_52_0 = all_4_1
% 175.79/27.15    (64)  op(all_6_1, all_6_2) = e2
% 175.79/27.15    (65)  all_52_10 = all_10_1
% 175.79/27.15    (66)   ~ (all_52_9 = all_52_13)
% 175.79/27.15    (67)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 175.79/27.15    (68)   ~ (all_52_15 = all_52_23)
% 175.79/27.15    (69)  op(all_10_1, all_10_2) = all_10_0
% 175.79/27.15    (70)   ~ (all_52_5 = all_52_29)
% 175.79/27.15    (71)  all_56_2 = all_52_5
% 175.79/27.15    (72)  op(e1, e0) = all_52_23
% 175.79/27.15    (73)  all_56_12 = all_52_25
% 175.79/27.15    (74)  all_58_13 = all_52_27
% 175.79/27.15    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.15    (76)  all_58_6 = all_52_17
% 175.79/27.15    (77)   ~ (all_52_3 = all_52_7)
% 175.79/27.15    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.79/27.15    (79)   ~ (e1 = e0)
% 175.79/27.15    (80)  all_56_0 = all_4_2
% 175.79/27.15    (81)  all_58_11 = all_52_23
% 175.79/27.15    (82)   ~ (all_52_3 = all_52_19)
% 175.79/27.15    (83)  op(e0, all_52_15) = all_52_14
% 175.79/27.15    (84)   ~ (all_52_29 = all_14_2)
% 175.79/27.15    (85)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 175.79/27.15    (86)   ~ (all_52_29 = all_6_2)
% 175.79/27.15    (87)  all_58_2 = all_52_9
% 175.79/27.15    (88)  op(e3, e1) = all_52_5
% 175.79/27.15    (89)   ~ (all_52_25 = all_6_2)
% 175.79/27.15    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 175.79/27.15    (91)  op(e1, e3) = all_52_17
% 175.79/27.15    (92)   ~ (all_52_25 = all_4_2)
% 175.79/27.15    (93)  op(e3, e0) = all_52_7
% 175.79/27.15    (94)  op(e3, e3) = all_4_2
% 175.79/27.15    (95)   ~ (all_52_17 = all_4_2)
% 175.79/27.15    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.15    (97)   ~ (all_52_25 = all_52_27)
% 175.79/27.15    (98)  all_34_2 = all_4_2
% 175.79/27.15    (99)   ~ (all_52_27 = all_6_2)
% 175.79/27.15    (100)  all_8_1 = all_6_1
% 175.79/27.15    (101)   ~ (all_52_7 = all_6_2)
% 175.79/27.15    (102)   ~ (all_10_0 = e3)
% 175.79/27.15    (103)   ~ (all_52_7 = all_52_23)
% 175.79/27.15    (104)  op(e2, all_52_27) = all_52_26
% 175.79/27.15    (105)   ~ (all_52_17 = all_52_19)
% 175.79/27.15    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.79/27.15    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.79/27.15    (108)  all_58_9 = all_52_7
% 175.79/27.15    (109)  all_58_12 = all_52_25
% 175.79/27.15    (110)   ~ (all_10_0 = e1)
% 175.79/27.15    (111)  all_56_6 = all_52_13
% 175.79/27.15    (112)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.79/27.15    (113)   ~ (all_52_9 = all_52_15)
% 175.79/27.15    (114)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 175.79/27.15    (115)  op(e2, e3) = all_52_9
% 175.79/27.15    (116)  all_56_13 = all_52_27
% 175.79/27.15  
% 175.79/27.15  Begin of proof
% 175.79/27.15  | 
% 175.79/27.15  | BETA: splitting (45) gives:
% 175.79/27.15  | 
% 175.79/27.15  | Case 1:
% 175.79/27.15  | | 
% 175.79/27.15  | |   (117)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 175.79/27.15  | | 
% 175.79/27.15  | | REF_CLOSE: (33), (36), (43), (63), (96), (117) are inconsistent by sub-proof
% 175.79/27.15  | |            #600.
% 175.79/27.15  | | 
% 175.79/27.15  | Case 2:
% 175.79/27.15  | | 
% 175.79/27.15  | |   (118)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 175.79/27.15  | | 
% 175.79/27.15  | | ALPHA: (118) implies:
% 175.79/27.15  | |   (119)  all_52_14 = e0
% 175.79/27.15  | |   (120)  all_52_12 = e1
% 175.79/27.15  | |   (121)  all_52_10 = e2
% 175.79/27.15  | |   (122)  all_52_8 = e3
% 175.79/27.15  | | 
% 175.79/27.15  | | COMBINE_EQS: (65), (121) imply:
% 175.79/27.15  | |   (123)  all_10_1 = e2
% 175.79/27.15  | | 
% 175.79/27.15  | | REDUCE: (69), (123) imply:
% 175.79/27.15  | |   (124)  op(e2, all_10_2) = all_10_0
% 175.79/27.15  | | 
% 175.79/27.15  | | REDUCE: (13), (122) imply:
% 175.79/27.15  | |   (125)  op(e3, all_52_9) = e3
% 175.79/27.15  | | 
% 175.79/27.15  | | REDUCE: (3), (123) imply:
% 175.79/27.15  | |   (126)  op(e2, all_10_2) = e2
% 175.79/27.15  | | 
% 175.79/27.15  | | REDUCE: (42), (120) imply:
% 175.79/27.15  | |   (127)  op(e1, all_52_13) = e1
% 175.79/27.15  | | 
% 175.79/27.15  | | REDUCE: (83), (119) imply:
% 175.79/27.15  | |   (128)  op(e0, all_52_15) = e0
% 175.79/27.15  | | 
% 175.79/27.15  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 175.79/27.15  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 175.79/27.15  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 175.79/27.15  | |            (37), (38), (39), (40), (41), (43), (44), (46), (47), (48), (49),
% 175.79/27.15  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 175.79/27.15  | |            (61), (62), (64), (66), (67), (68), (70), (71), (72), (73), (74),
% 175.79/27.15  | |            (75), (76), (77), (78), (79), (80), (81), (82), (84), (85), (86),
% 175.79/27.15  | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 175.79/27.15  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 175.79/27.15  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 175.79/27.15  | |            (116), (124), (125), (126), (127), (128) are inconsistent by
% 175.79/27.15  | |            sub-proof #194.
% 175.79/27.15  | | 
% 175.79/27.15  | End of split
% 175.79/27.15  | 
% 175.79/27.15  End of proof
% 175.79/27.15  
% 175.79/27.15  Sub-proof #160 shows that the following formulas are inconsistent:
% 175.79/27.15  ----------------------------------------------------------------
% 175.79/27.15    (1)   ~ (e3 = e1)
% 175.79/27.15    (2)  op(all_14_1, all_14_2) = e3
% 175.79/27.15    (3)  op(e0, all_6_2) = all_6_1
% 175.79/27.15    (4)  op(all_6_1, all_6_2) = e2
% 175.79/27.15    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.15    (6)  all_52_20 = all_14_1
% 175.79/27.15    (7)  all_52_30 = all_6_1
% 175.79/27.15    (8)  op(e1, all_14_2) = all_14_1
% 175.79/27.15    (9)   ~ (e2 = e0)
% 175.79/27.15    (10)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 175.79/27.15          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 175.79/27.15  
% 175.79/27.15  Begin of proof
% 175.79/27.15  | 
% 175.79/27.15  | BETA: splitting (10) gives:
% 175.79/27.15  | 
% 175.79/27.15  | Case 1:
% 175.79/27.15  | | 
% 175.79/27.15  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 175.79/27.15  | | 
% 175.79/27.15  | | ALPHA: (11) implies:
% 175.79/27.15  | |   (12)  all_52_20 = e1
% 175.79/27.15  | | 
% 175.79/27.15  | | COMBINE_EQS: (6), (12) imply:
% 175.79/27.15  | |   (13)  all_14_1 = e1
% 175.79/27.15  | | 
% 175.79/27.15  | | REF_CLOSE: (1), (2), (5), (8), (13) are inconsistent by sub-proof #344.
% 175.79/27.15  | | 
% 175.79/27.15  | Case 2:
% 175.79/27.15  | | 
% 175.79/27.15  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 175.79/27.15  | | 
% 175.79/27.15  | | REF_CLOSE: (3), (4), (5), (7), (9), (14) are inconsistent by sub-proof #200.
% 175.79/27.15  | | 
% 175.79/27.15  | End of split
% 175.79/27.15  | 
% 175.79/27.15  End of proof
% 175.79/27.15  
% 175.79/27.15  Sub-proof #161 shows that the following formulas are inconsistent:
% 175.79/27.15  ----------------------------------------------------------------
% 175.79/27.15    (1)   ~ (all_52_23 = all_14_2)
% 175.79/27.15    (2)   ~ (all_52_5 = all_52_13)
% 175.79/27.15    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 175.79/27.15    (4)   ~ (all_52_27 = all_10_2)
% 175.79/27.15    (5)   ~ (all_52_17 = all_52_23)
% 175.79/27.15    (6)   ~ (all_52_13 = all_52_29)
% 175.79/27.15    (7)  all_56_3 = all_52_7
% 175.79/27.15    (8)  op(e3, e2) = all_52_3
% 175.79/27.15    (9)   ~ (all_52_9 = all_52_25)
% 175.79/27.15    (10)  op(e3, all_52_25) = all_52_24
% 175.79/27.15    (11)   ~ (all_52_19 = all_52_23)
% 175.79/27.15    (12)  all_56_11 = all_52_23
% 175.79/27.15    (13)  op(e1, e2) = all_52_19
% 175.79/27.15    (14)   ~ (all_52_27 = e3)
% 175.79/27.15    (15)   ~ (all_6_2 = e3)
% 175.79/27.15    (16)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 175.79/27.15    (17)   ~ (all_52_3 = all_10_2)
% 175.79/27.15    (18)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 175.79/27.15    (19)  all_58_5 = all_52_13
% 175.79/27.15    (20)   ~ (all_6_2 = e0)
% 175.79/27.15    (21)   ~ (all_52_25 = all_52_29)
% 175.79/27.15    (22)  op(e1, all_52_13) = e1
% 175.79/27.15    (23)  op(e0, all_52_15) = e0
% 175.79/27.15    (24)  all_56_15 = all_6_2
% 175.79/27.15    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 175.79/27.15    (26)  op(e2, e0) = all_52_15
% 175.79/27.15    (27)  all_58_3 = all_10_2
% 175.79/27.15    (28)  all_56_9 = all_52_19
% 175.79/27.15    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 175.79/27.15    (30)  all_58_15 = all_6_2
% 175.79/27.15    (31)   ~ (all_52_9 = all_4_2)
% 175.79/27.15    (32)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 175.79/27.15    (33)   ~ (all_52_5 = all_52_7)
% 175.79/27.15    (34)  all_58_10 = all_52_15
% 175.79/27.15    (35)  all_8_2 = all_6_2
% 175.79/27.15    (36)   ~ (all_52_5 = all_4_2)
% 175.79/27.15    (37)  all_58_7 = all_52_19
% 175.79/27.15    (38)  all_56_4 = all_52_9
% 175.79/27.15    (39)   ~ (all_52_15 = all_6_2)
% 175.79/27.15    (40)   ~ (all_52_17 = all_52_25)
% 175.79/27.15    (41)  op(e0, e1) = all_52_29
% 175.79/27.15    (42)   ~ (all_4_0 = e2)
% 175.79/27.15    (43)  all_58_4 = all_52_5
% 175.79/27.15    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 175.79/27.15    (45)   ~ (e3 = e1)
% 175.79/27.15    (46)   ~ (all_52_27 = all_52_29)
% 175.79/27.15    (47)   ~ (all_52_17 = all_14_2)
% 175.79/27.15    (48)  op(e3, all_4_2) = all_4_1
% 175.79/27.15    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 175.79/27.15    (50)   ~ (all_52_7 = all_4_2)
% 175.79/27.15    (51)  all_58_1 = all_52_3
% 175.79/27.15    (52)  all_58_0 = all_4_2
% 175.79/27.15    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 175.79/27.15    (54)  op(e1, all_52_29) = all_52_28
% 175.79/27.15    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 175.79/27.15    (56)   ~ (all_4_1 = e2)
% 175.79/27.15    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 175.79/27.15    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 175.79/27.15    (59)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 175.79/27.15    (60)  all_58_14 = all_52_29
% 175.79/27.15    (61)   ~ (all_52_3 = all_52_5)
% 175.79/27.15    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 175.79/27.15    (63)  op(e2, e1) = all_52_13
% 175.79/27.15    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.15    (65)  all_58_8 = all_14_2
% 175.79/27.15    (66)  op(all_14_1, all_14_2) = e3
% 175.79/27.15    (67)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 175.79/27.15    (68)  op(all_4_1, all_4_2) = all_4_0
% 175.79/27.15    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 175.79/27.15    (70)   ~ (all_52_3 = all_52_27)
% 175.79/27.15    (71)   ~ (all_52_3 = all_4_2)
% 175.79/27.15    (72)  op(e0, e3) = all_52_25
% 175.79/27.15    (73)  op(e0, all_6_2) = all_6_1
% 175.79/27.15    (74)  op(e3, all_52_17) = all_52_16
% 175.79/27.15    (75)   ~ (all_52_13 = all_14_2)
% 175.79/27.15    (76)  op(e3, all_52_9) = e3
% 175.79/27.15    (77)   ~ (e3 = e0)
% 175.79/27.15    (78)   ~ (all_52_9 = all_52_13)
% 175.79/27.15    (79)  op(e0, all_52_23) = all_52_22
% 175.79/27.15    (80)   ~ (all_52_15 = all_52_23)
% 175.79/27.15    (81)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 175.79/27.15    (82)  op(e1, e0) = all_52_23
% 175.79/27.15    (83)  all_58_13 = all_52_27
% 175.79/27.16    (84)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 175.79/27.16    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 175.79/27.16    (86)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 175.79/27.16    (87)   ~ (all_52_9 = all_52_17)
% 175.79/27.16    (88)  all_58_6 = all_52_17
% 175.79/27.16    (89)   ~ (all_52_3 = all_52_7)
% 175.79/27.16    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 175.79/27.16    (91)  op(e2, all_52_19) = all_52_18
% 175.79/27.16    (92)   ~ (e1 = e0)
% 175.79/27.16    (93)  all_56_0 = all_4_2
% 175.79/27.16    (94)  all_58_11 = all_52_23
% 175.79/27.16    (95)   ~ (all_52_3 = all_52_19)
% 175.79/27.16    (96)   ~ (all_52_7 = all_52_15)
% 175.79/27.16    (97)   ~ (all_52_29 = all_14_2)
% 175.79/27.16    (98)   ~ (all_52_19 = all_10_2)
% 175.79/27.16    (99)   ~ (all_52_23 = all_6_2)
% 175.79/27.16    (100)   ~ (all_52_29 = all_6_2)
% 175.79/27.16    (101)  all_58_2 = all_52_9
% 175.79/27.16    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 175.79/27.16    (103)  op(e3, e1) = all_52_5
% 175.79/27.16    (104)   ~ (e2 = e1)
% 175.79/27.16    (105)  all_56_10 = all_14_2
% 175.79/27.16    (106)   ~ (all_52_25 = all_6_2)
% 175.79/27.16    (107)  op(e1, e3) = all_52_17
% 175.79/27.16    (108)   ~ (all_52_25 = all_4_2)
% 175.79/27.16    (109)  op(e3, e0) = all_52_7
% 175.79/27.16    (110)  op(e2, all_10_2) = e2
% 175.79/27.16    (111)  op(e3, e3) = all_4_2
% 175.79/27.16    (112)   ~ (all_52_17 = all_4_2)
% 175.79/27.16    (113)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 175.79/27.16             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 175.79/27.16    (114)   ~ (all_52_25 = all_52_27)
% 175.79/27.16    (115)   ~ (all_52_27 = all_6_2)
% 175.79/27.16    (116)  all_8_1 = all_6_1
% 175.79/27.16    (117)   ~ (all_52_7 = all_6_2)
% 175.79/27.16    (118)  all_18_2 = all_14_2
% 175.79/27.16    (119)   ~ (all_52_7 = all_52_23)
% 175.79/27.16    (120)   ~ (all_52_17 = all_52_19)
% 175.79/27.16    (121)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 175.79/27.16    (122)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 175.79/27.16    (123)  op(e1, all_14_2) = all_14_1
% 175.79/27.16    (124)  all_58_9 = all_52_7
% 175.79/27.16    (125)  all_58_12 = all_52_25
% 175.79/27.16    (126)  all_56_6 = all_52_13
% 175.79/27.16    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 175.79/27.16    (128)   ~ (all_52_9 = all_52_15)
% 175.79/27.16    (129)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 175.79/27.16    (130)   ~ (e3 = e2)
% 175.79/27.16    (131)   ~ (all_52_19 = all_14_2)
% 175.79/27.16    (132)  op(e2, e3) = all_52_9
% 175.79/27.16  
% 175.79/27.16  Begin of proof
% 175.79/27.16  | 
% 175.79/27.16  | BETA: splitting (64) gives:
% 175.79/27.16  | 
% 175.79/27.16  | Case 1:
% 175.79/27.16  | | 
% 175.79/27.16  | |   (133)  all_58_12 = e3
% 175.79/27.16  | | 
% 175.79/27.16  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 175.79/27.16  | |            (17), (19), (20), (21), (22), (23), (24), (25), (27), (28), (29),
% 175.79/27.16  | |            (30), (31), (32), (33), (34), (36), (37), (38), (40), (43), (44),
% 175.79/27.16  | |            (46), (47), (49), (50), (51), (52), (53), (55), (57), (58), (59),
% 175.79/27.16  | |            (60), (61), (63), (65), (66), (69), (72), (74), (75), (76), (77),
% 175.79/27.16  | |            (78), (79), (81), (83), (84), (86), (87), (88), (89), (90), (91),
% 175.79/27.16  | |            (93), (94), (95), (96), (97), (98), (99), (101), (102), (103),
% 175.79/27.16  | |            (104), (105), (106), (107), (108), (109), (110), (112), (113),
% 175.79/27.16  | |            (114), (115), (117), (118), (119), (120), (121), (122), (123),
% 175.79/27.16  | |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 175.79/27.16  | |            (133) are inconsistent by sub-proof #333.
% 175.79/27.16  | | 
% 175.79/27.16  | Case 2:
% 175.79/27.16  | | 
% 175.79/27.16  | |   (134)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 175.79/27.16  | | 
% 176.00/27.16  | | REF_CLOSE: (5), (8), (9), (10), (11), (12), (14), (15), (16), (17), (18),
% 176.00/27.16  | |            (19), (21), (22), (23), (24), (26), (27), (30), (31), (32), (33),
% 176.00/27.16  | |            (34), (35), (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.00/27.16  | |            (48), (49), (50), (51), (52), (53), (54), (56), (58), (60), (61),
% 176.00/27.16  | |            (62), (65), (67), (68), (69), (70), (71), (72), (73), (74), (76),
% 176.00/27.16  | |            (79), (80), (82), (83), (85), (88), (89), (91), (92), (94), (95),
% 176.00/27.16  | |            (97), (99), (100), (101), (102), (103), (104), (106), (107),
% 176.00/27.16  | |            (108), (109), (110), (111), (112), (113), (114), (116), (117),
% 176.00/27.16  | |            (120), (121), (124), (125), (127), (130), (132), (134) are
% 176.00/27.16  | |            inconsistent by sub-proof #209.
% 176.00/27.16  | | 
% 176.00/27.16  | End of split
% 176.00/27.16  | 
% 176.00/27.16  End of proof
% 176.00/27.16  
% 176.00/27.16  Sub-proof #162 shows that the following formulas are inconsistent:
% 176.00/27.16  ----------------------------------------------------------------
% 176.00/27.16    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.16    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.16    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.16    (4)   ~ (all_52_27 = all_10_2)
% 176.00/27.16    (5)   ~ (all_52_17 = all_52_23)
% 176.00/27.16    (6)   ~ (all_52_13 = all_52_29)
% 176.00/27.16    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.16    (8)  op(e3, e2) = all_52_3
% 176.00/27.16    (9)   ~ (all_52_9 = all_52_25)
% 176.00/27.16    (10)  op(e3, all_52_25) = all_52_24
% 176.00/27.16    (11)   ~ (all_52_19 = all_52_23)
% 176.00/27.16    (12)  all_52_27 = e3
% 176.00/27.16    (13)   ~ (all_52_3 = all_10_2)
% 176.00/27.16    (14)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 176.00/27.16    (15)  all_58_5 = all_52_13
% 176.00/27.16    (16)  op(e1, all_52_13) = e1
% 176.00/27.16    (17)  op(e0, all_52_15) = e0
% 176.00/27.16    (18)  all_56_15 = all_6_2
% 176.00/27.16    (19)  all_58_3 = all_10_2
% 176.00/27.16    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.16    (21)  all_58_15 = all_6_2
% 176.00/27.16    (22)   ~ (all_52_9 = all_4_2)
% 176.00/27.16    (23)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.16    (24)   ~ (all_52_5 = all_52_7)
% 176.00/27.16    (25)  all_58_10 = all_52_15
% 176.00/27.16    (26)   ~ (all_52_5 = all_4_2)
% 176.00/27.16    (27)  all_58_7 = all_52_19
% 176.00/27.16    (28)  all_56_4 = all_52_9
% 176.00/27.16    (29)   ~ (all_52_17 = all_52_25)
% 176.00/27.16    (30)   ~ (all_4_0 = e2)
% 176.00/27.16    (31)  all_58_4 = all_52_5
% 176.00/27.16    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.16    (33)   ~ (e3 = e1)
% 176.00/27.16    (34)   ~ (all_52_27 = all_52_29)
% 176.00/27.16    (35)   ~ (all_52_17 = all_14_2)
% 176.00/27.16    (36)  op(e3, all_4_2) = all_4_1
% 176.00/27.16    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.16    (38)   ~ (all_52_7 = all_4_2)
% 176.00/27.16    (39)  all_58_1 = all_52_3
% 176.00/27.16    (40)  all_58_0 = all_4_2
% 176.00/27.16    (41)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.16    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.16    (43)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.16    (44)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.16    (45)  all_58_14 = all_52_29
% 176.00/27.16    (46)   ~ (all_52_3 = all_52_5)
% 176.00/27.16    (47)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.16    (48)  op(e2, e1) = all_52_13
% 176.00/27.16    (49)  all_58_8 = all_14_2
% 176.00/27.16    (50)  all_56_1 = all_52_3
% 176.00/27.16    (51)  op(e0, e2) = all_52_27
% 176.00/27.16    (52)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.16    (53)   ~ (all_52_5 = all_14_2)
% 176.00/27.16    (54)   ~ (all_52_3 = all_52_27)
% 176.00/27.16    (55)   ~ (all_52_3 = all_4_2)
% 176.00/27.16    (56)  op(e0, e3) = all_52_25
% 176.00/27.16    (57)  op(e0, all_6_2) = all_6_1
% 176.00/27.16    (58)   ~ (all_52_9 = all_10_2)
% 176.00/27.16    (59)  op(all_6_1, all_6_2) = e2
% 176.00/27.16    (60)  op(e3, all_52_17) = all_52_16
% 176.00/27.16    (61)   ~ (all_52_13 = all_14_2)
% 176.00/27.16    (62)  op(e3, all_52_9) = e3
% 176.00/27.16    (63)   ~ (all_52_9 = all_52_13)
% 176.00/27.16    (64)   ~ (all_52_15 = all_52_23)
% 176.00/27.16    (65)   ~ (all_52_5 = all_52_29)
% 176.00/27.16    (66)  op(e1, e0) = all_52_23
% 176.00/27.16    (67)  all_58_13 = all_52_27
% 176.00/27.16    (68)   ~ (all_4_1 = e1)
% 176.00/27.16    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.16    (70)   ~ (all_52_9 = all_52_17)
% 176.00/27.16    (71)  all_58_6 = all_52_17
% 176.00/27.16    (72)   ~ (all_52_3 = all_52_7)
% 176.00/27.16    (73)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.16    (74)   ~ (e1 = e0)
% 176.00/27.16    (75)  all_56_0 = all_4_2
% 176.00/27.16    (76)  all_58_11 = all_52_23
% 176.00/27.16    (77)   ~ (all_4_0 = e1)
% 176.00/27.16    (78)   ~ (all_52_29 = all_6_2)
% 176.00/27.16    (79)  all_58_2 = all_52_9
% 176.00/27.16    (80)  op(e3, e1) = all_52_5
% 176.00/27.16    (81)  op(e1, e3) = all_52_17
% 176.00/27.16    (82)   ~ (all_52_25 = all_4_2)
% 176.00/27.16    (83)  op(e3, e0) = all_52_7
% 176.00/27.16    (84)  op(e2, all_10_2) = e2
% 176.00/27.16    (85)  op(e3, e3) = all_4_2
% 176.00/27.16    (86)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.16    (87)   ~ (all_52_25 = all_52_27)
% 176.00/27.16    (88)   ~ (all_52_27 = all_6_2)
% 176.00/27.16    (89)   ~ (all_52_19 = all_52_27)
% 176.00/27.16    (90)   ~ (all_52_7 = all_52_23)
% 176.00/27.16    (91)   ~ (all_52_13 = all_10_2)
% 176.00/27.16    (92)  op(e2, all_52_27) = all_52_26
% 176.00/27.16    (93)   ~ (all_52_17 = all_52_19)
% 176.00/27.16    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.16    (95)  all_58_9 = all_52_7
% 176.00/27.16    (96)  all_58_12 = all_52_25
% 176.00/27.16    (97)  all_56_6 = all_52_13
% 176.00/27.16    (98)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.16    (99)   ~ (all_52_9 = all_52_15)
% 176.00/27.16    (100)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.16    (101)  op(e2, e3) = all_52_9
% 176.00/27.16  
% 176.00/27.16  Begin of proof
% 176.00/27.16  | 
% 176.00/27.16  | COMBINE_EQS: (12), (67) imply:
% 176.00/27.16  |   (102)  all_58_13 = e3
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (12), (54) imply:
% 176.00/27.16  |   (103)   ~ (all_52_3 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (12), (89) imply:
% 176.00/27.16  |   (104)   ~ (all_52_19 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (12), (87) imply:
% 176.00/27.16  |   (105)   ~ (all_52_25 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (12), (34) imply:
% 176.00/27.16  |   (106)   ~ (all_52_29 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (106) implies:
% 176.00/27.16  |   (107)   ~ (all_52_29 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (4), (12) imply:
% 176.00/27.16  |   (108)   ~ (all_10_2 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (108) implies:
% 176.00/27.16  |   (109)   ~ (all_10_2 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (12), (88) imply:
% 176.00/27.16  |   (110)   ~ (all_6_2 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (110) implies:
% 176.00/27.16  |   (111)   ~ (all_6_2 = e3)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (12), (92) imply:
% 176.00/27.16  |   (112)  op(e2, e3) = all_52_26
% 176.00/27.16  | 
% 176.00/27.16  | GROUND_INST: instantiating (86) with all_52_9, all_52_26, e3, e2, simplifying
% 176.00/27.16  |              with (101), (112) gives:
% 176.00/27.16  |   (113)  all_52_9 = all_52_26
% 176.00/27.16  | 
% 176.00/27.16  | COMBINE_EQS: (28), (113) imply:
% 176.00/27.16  |   (114)  all_56_4 = all_52_26
% 176.00/27.16  | 
% 176.00/27.16  | COMBINE_EQS: (79), (113) imply:
% 176.00/27.16  |   (115)  all_58_2 = all_52_26
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (63), (113) imply:
% 176.00/27.16  |   (116)   ~ (all_52_13 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (116) implies:
% 176.00/27.16  |   (117)   ~ (all_52_13 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (99), (113) imply:
% 176.00/27.16  |   (118)   ~ (all_52_15 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (118) implies:
% 176.00/27.16  |   (119)   ~ (all_52_15 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (70), (113) imply:
% 176.00/27.16  |   (120)   ~ (all_52_17 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (120) implies:
% 176.00/27.16  |   (121)   ~ (all_52_17 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (9), (113) imply:
% 176.00/27.16  |   (122)   ~ (all_52_25 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (122) implies:
% 176.00/27.16  |   (123)   ~ (all_52_25 = all_52_26)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (58), (113) imply:
% 176.00/27.16  |   (124)   ~ (all_52_26 = all_10_2)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (22), (113) imply:
% 176.00/27.16  |   (125)   ~ (all_52_26 = all_4_2)
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (62), (113) imply:
% 176.00/27.16  |   (126)  op(e3, all_52_26) = e3
% 176.00/27.16  | 
% 176.00/27.16  | BETA: splitting (42) gives:
% 176.00/27.16  | 
% 176.00/27.16  | Case 1:
% 176.00/27.16  | | 
% 176.00/27.16  | |   (127)  all_56_1 = e3
% 176.00/27.16  | | 
% 176.00/27.16  | | COMBINE_EQS: (50), (127) imply:
% 176.00/27.16  | |   (128)  all_52_3 = e3
% 176.00/27.16  | | 
% 176.00/27.16  | | REDUCE: (103), (128) imply:
% 176.00/27.16  | |   (129)  $false
% 176.00/27.16  | | 
% 176.00/27.16  | | CLOSE: (129) is inconsistent.
% 176.00/27.16  | | 
% 176.00/27.16  | Case 2:
% 176.00/27.16  | | 
% 176.00/27.16  | |   (130)   ~ (all_56_1 = e3)
% 176.00/27.16  | |   (131)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.16  | | 
% 176.00/27.16  | | BETA: splitting (44) gives:
% 176.00/27.16  | | 
% 176.00/27.16  | | Case 1:
% 176.00/27.16  | | | 
% 176.00/27.16  | | |   (132)  all_56_6 = e3
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13), (14),
% 176.00/27.16  | | |            (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 176.00/27.16  | | |            (26), (27), (29), (30), (31), (32), (33), (35), (36), (37),
% 176.00/27.16  | | |            (39), (40), (41), (43), (45), (46), (47), (48), (49), (50),
% 176.00/27.16  | | |            (51), (52), (53), (55), (56), (57), (59), (60), (61), (64),
% 176.00/27.16  | | |            (66), (67), (68), (69), (71), (72), (73), (74), (75), (76),
% 176.00/27.16  | | |            (77), (78), (80), (81), (82), (83), (84), (85), (86), (88),
% 176.00/27.16  | | |            (90), (91), (93), (94), (95), (96), (97), (98), (100), (102),
% 176.00/27.16  | | |            (103), (104), (111), (114), (115), (117), (119), (121), (123),
% 176.00/27.16  | | |            (124), (125), (126), (131), (132) are inconsistent by sub-proof
% 176.00/27.16  | | |            #189.
% 176.00/27.16  | | | 
% 176.00/27.16  | | Case 2:
% 176.00/27.16  | | | 
% 176.00/27.16  | | |   (133)   ~ (all_56_6 = e3)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (97), (133) imply:
% 176.00/27.16  | | |   (134)   ~ (all_52_13 = e3)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | BETA: splitting (100) gives:
% 176.00/27.16  | | | 
% 176.00/27.16  | | | Case 1:
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | |   (135)  all_58_4 = e3
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (13), (14), (15),
% 176.00/27.16  | | | |            (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 176.00/27.16  | | | |            (27), (29), (30), (31), (32), (33), (35), (36), (37), (39),
% 176.00/27.16  | | | |            (40), (41), (43), (45), (46), (47), (48), (49), (50), (51),
% 176.00/27.16  | | | |            (52), (53), (55), (56), (57), (59), (60), (64), (65), (66),
% 176.00/27.16  | | | |            (67), (68), (69), (71), (72), (73), (74), (75), (76), (77),
% 176.00/27.16  | | | |            (78), (80), (81), (82), (83), (84), (85), (86), (88), (90),
% 176.00/27.16  | | | |            (93), (94), (95), (96), (98), (100), (102), (104), (109),
% 176.00/27.16  | | | |            (111), (114), (115), (117), (119), (121), (123), (124),
% 176.00/27.16  | | | |            (125), (126), (131), (135) are inconsistent by sub-proof
% 176.00/27.16  | | | |            #188.
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | Case 2:
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | |   (136)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | BETA: splitting (136) gives:
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | Case 1:
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | |   (137)  all_58_5 = e3
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | REF_CLOSE: (15), (134), (137) are inconsistent by sub-proof #969.
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | Case 2:
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | |   (138)  all_58_8 = e3 | all_58_14 = e3
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | REF_CLOSE: (1), (8), (17), (21), (25), (26), (35), (36), (38), (40),
% 176.00/27.16  | | | | |            (45), (47), (49), (52), (55), (56), (69), (71), (73), (76),
% 176.00/27.16  | | | | |            (77), (80), (85), (86), (94), (95), (96), (105), (107),
% 176.00/27.16  | | | | |            (111), (114), (115), (119), (123), (125), (126), (138) are
% 176.00/27.16  | | | | |            inconsistent by sub-proof #764.
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | End of split
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | End of split
% 176.00/27.16  | | | 
% 176.00/27.16  | | End of split
% 176.00/27.16  | | 
% 176.00/27.16  | End of split
% 176.00/27.16  | 
% 176.00/27.16  End of proof
% 176.00/27.16  
% 176.00/27.16  Sub-proof #163 shows that the following formulas are inconsistent:
% 176.00/27.16  ----------------------------------------------------------------
% 176.00/27.16    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.16    (2)  op(e1, e3) = all_52_28
% 176.00/27.16    (3)   ~ (all_52_9 = all_52_25)
% 176.00/27.16    (4)   ~ (all_52_27 = e3)
% 176.00/27.16    (5)  op(e3, all_52_9) = all_52_8
% 176.00/27.16    (6)   ~ (all_52_25 = all_52_28)
% 176.00/27.16    (7)  all_58_5 = all_52_13
% 176.00/27.16    (8)  all_58_3 = all_10_2
% 176.00/27.16    (9)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.16    (10)  all_56_8 = all_52_28
% 176.00/27.16    (11)  all_58_7 = all_52_19
% 176.00/27.16    (12)  all_58_4 = all_52_5
% 176.00/27.16    (13)   ~ (all_52_9 = all_52_28)
% 176.00/27.16    (14)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.16    (15)  all_58_8 = all_14_2
% 176.00/27.16    (16)  op(e1, all_14_2) = e3
% 176.00/27.16    (17)   ~ (all_52_28 = e3)
% 176.00/27.16    (18)   ~ (all_52_5 = all_14_2)
% 176.00/27.16    (19)   ~ (all_52_9 = all_10_2)
% 176.00/27.16    (20)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.16    (21)   ~ (all_52_9 = all_52_13)
% 176.00/27.16    (22)  all_30_2 = all_10_2
% 176.00/27.16    (23)  all_56_12 = all_52_25
% 176.00/27.16    (24)  all_58_13 = all_52_27
% 176.00/27.16    (25)  op(e1, all_10_2) = all_10_0
% 176.00/27.16    (26)  op(e3, e1) = all_52_5
% 176.00/27.16    (27)  op(e2, all_10_2) = e1
% 176.00/27.16    (28)   ~ (all_30_0 = e0) |  ~ (all_30_2 = e3)
% 176.00/27.16    (29)  op(e1, e1) = all_14_2
% 176.00/27.16    (30)   ~ (all_52_19 = e3)
% 176.00/27.16    (31)   ~ (all_14_2 = e3)
% 176.00/27.16    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.16    (33)  all_58_14 = e3
% 176.00/27.16    (34)  op(e1, all_52_5) = e1
% 176.00/27.16    (35)  all_30_0 = all_10_0
% 176.00/27.16    (36)  op(e2, e3) = all_52_9
% 176.00/27.16  
% 176.00/27.16  Begin of proof
% 176.00/27.16  | 
% 176.00/27.16  | BETA: splitting (9) gives:
% 176.00/27.16  | 
% 176.00/27.16  | Case 1:
% 176.00/27.16  | | 
% 176.00/27.16  | |   (37)  all_58_3 = e3
% 176.00/27.16  | | 
% 176.00/27.16  | | COMBINE_EQS: (8), (37) imply:
% 176.00/27.16  | |   (38)  all_10_2 = e3
% 176.00/27.16  | | 
% 176.00/27.16  | | COMBINE_EQS: (22), (38) imply:
% 176.00/27.16  | |   (39)  all_30_2 = e3
% 176.00/27.16  | | 
% 176.00/27.16  | | REDUCE: (19), (38) imply:
% 176.00/27.16  | |   (40)   ~ (all_52_9 = e3)
% 176.00/27.16  | | 
% 176.00/27.16  | | REDUCE: (27), (38) imply:
% 176.00/27.16  | |   (41)  op(e2, e3) = e1
% 176.00/27.16  | | 
% 176.00/27.16  | | REDUCE: (25), (38) imply:
% 176.00/27.16  | |   (42)  op(e1, e3) = all_10_0
% 176.00/27.16  | | 
% 176.00/27.16  | | BETA: splitting (28) gives:
% 176.00/27.16  | | 
% 176.00/27.16  | | Case 1:
% 176.00/27.16  | | | 
% 176.00/27.16  | | |   (43)   ~ (all_30_2 = e3)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (39), (43) imply:
% 176.00/27.16  | | |   (44)  $false
% 176.00/27.16  | | | 
% 176.00/27.16  | | | CLOSE: (44) is inconsistent.
% 176.00/27.16  | | | 
% 176.00/27.16  | | Case 2:
% 176.00/27.16  | | | 
% 176.00/27.16  | | |   (45)   ~ (all_30_0 = e0)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (35), (45) imply:
% 176.00/27.16  | | |   (46)   ~ (all_10_0 = e0)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | GROUND_INST: instantiating (32) with all_52_28, all_10_0, e3, e1,
% 176.00/27.16  | | |              simplifying with (2), (42) gives:
% 176.00/27.16  | | |   (47)  all_52_28 = all_10_0
% 176.00/27.16  | | | 
% 176.00/27.16  | | | GROUND_INST: instantiating (32) with all_52_9, e1, e3, e2, simplifying
% 176.00/27.16  | | |              with (36), (41) gives:
% 176.00/27.16  | | |   (48)  all_52_9 = e1
% 176.00/27.16  | | | 
% 176.00/27.16  | | | COMBINE_EQS: (10), (47) imply:
% 176.00/27.16  | | |   (49)  all_56_8 = all_10_0
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (21), (48) imply:
% 176.00/27.16  | | |   (50)   ~ (all_52_13 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | SIMP: (50) implies:
% 176.00/27.16  | | |   (51)   ~ (all_52_13 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (3), (48) imply:
% 176.00/27.16  | | |   (52)   ~ (all_52_25 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | SIMP: (52) implies:
% 176.00/27.16  | | |   (53)   ~ (all_52_25 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (13), (47), (48) imply:
% 176.00/27.16  | | |   (54)   ~ (all_10_0 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | SIMP: (54) implies:
% 176.00/27.16  | | |   (55)   ~ (all_10_0 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (40), (48) imply:
% 176.00/27.16  | | |   (56)   ~ (e3 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | SIMP: (56) implies:
% 176.00/27.16  | | |   (57)   ~ (e3 = e1)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (6), (47) imply:
% 176.00/27.16  | | |   (58)   ~ (all_52_25 = all_10_0)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (17), (47) imply:
% 176.00/27.16  | | |   (59)   ~ (all_10_0 = e3)
% 176.00/27.16  | | | 
% 176.00/27.16  | | | REDUCE: (5), (48) imply:
% 176.00/27.16  | | |   (60)  op(e3, e1) = all_52_8
% 176.00/27.16  | | | 
% 176.00/27.16  | | | BETA: splitting (1) gives:
% 176.00/27.16  | | | 
% 176.00/27.16  | | | Case 1:
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | |   (61)  all_56_8 = e3
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | COMBINE_EQS: (49), (61) imply:
% 176.00/27.16  | | | |   (62)  all_10_0 = e3
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | SIMP: (62) implies:
% 176.00/27.16  | | | |   (63)  all_10_0 = e3
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | REDUCE: (59), (63) imply:
% 176.00/27.16  | | | |   (64)  $false
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | CLOSE: (64) is inconsistent.
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | Case 2:
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | |   (65)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | BETA: splitting (65) gives:
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | | Case 1:
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | |   (66)  all_56_8 = e2
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | COMBINE_EQS: (49), (66) imply:
% 176.00/27.16  | | | | |   (67)  all_10_0 = e2
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | SIMP: (67) implies:
% 176.00/27.16  | | | | |   (68)  all_10_0 = e2
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | REDUCE: (58), (68) imply:
% 176.00/27.16  | | | | |   (69)   ~ (all_52_25 = e2)
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | BETA: splitting (20) gives:
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | Case 1:
% 176.00/27.16  | | | | | | 
% 176.00/27.16  | | | | | |   (70)  all_56_12 = e2
% 176.00/27.16  | | | | | | 
% 176.00/27.16  | | | | | | REF_CLOSE: (23), (69), (70) are inconsistent by sub-proof #1032.
% 176.00/27.16  | | | | | | 
% 176.00/27.16  | | | | | Case 2:
% 176.00/27.16  | | | | | | 
% 176.00/27.16  | | | | | |   (71)  all_56_12 = e1 | all_56_12 = e0
% 176.00/27.16  | | | | | | 
% 176.00/27.16  | | | | | | BETA: splitting (71) gives:
% 176.00/27.16  | | | | | | 
% 176.00/27.16  | | | | | | Case 1:
% 176.00/27.16  | | | | | | | 
% 176.00/27.16  | | | | | | |   (72)  all_56_12 = e1
% 176.00/27.16  | | | | | | | 
% 176.00/27.16  | | | | | | | REF_CLOSE: (23), (53), (72) are inconsistent by sub-proof #1031.
% 176.00/27.16  | | | | | | | 
% 176.00/27.16  | | | | | | Case 2:
% 176.00/27.16  | | | | | | | 
% 176.00/27.16  | | | | | | | 
% 176.00/27.16  | | | | | | | GROUND_INST: instantiating (32) with all_52_5, all_52_8, e1, e3,
% 176.00/27.16  | | | | | | |              simplifying with (26), (60) gives:
% 176.00/27.16  | | | | | | |   (73)  all_52_5 = all_52_8
% 176.00/27.16  | | | | | | | 
% 176.00/27.16  | | | | | | | REF_CLOSE: (7), (12), (14), (15), (16), (18), (29), (31), (32),
% 176.00/27.16  | | | | | | |            (33), (34), (51), (57), (73) are inconsistent by
% 176.00/27.16  | | | | | | |            sub-proof #176.
% 176.00/27.16  | | | | | | | 
% 176.00/27.16  | | | | | | End of split
% 176.00/27.16  | | | | | | 
% 176.00/27.16  | | | | | End of split
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | Case 2:
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | |   (74)  all_56_8 = e1 | all_56_8 = e0
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | | REF_CLOSE: (46), (49), (55), (74) are inconsistent by sub-proof #302.
% 176.00/27.16  | | | | | 
% 176.00/27.16  | | | | End of split
% 176.00/27.16  | | | | 
% 176.00/27.16  | | | End of split
% 176.00/27.16  | | | 
% 176.00/27.16  | | End of split
% 176.00/27.16  | | 
% 176.00/27.16  | Case 2:
% 176.00/27.16  | | 
% 176.00/27.16  | |   (75)  all_58_7 = e3 | all_58_13 = e3
% 176.00/27.16  | | 
% 176.00/27.16  | | REF_CLOSE: (4), (11), (24), (30), (75) are inconsistent by sub-proof #976.
% 176.00/27.16  | | 
% 176.00/27.16  | End of split
% 176.00/27.16  | 
% 176.00/27.16  End of proof
% 176.00/27.16  
% 176.00/27.16  Sub-proof #164 shows that the following formulas are inconsistent:
% 176.00/27.16  ----------------------------------------------------------------
% 176.00/27.16    (1)  all_56_7 = all_52_15
% 176.00/27.16    (2)  all_56_7 = e2
% 176.00/27.16    (3)   ~ (all_52_15 = e2)
% 176.00/27.16  
% 176.00/27.16  Begin of proof
% 176.00/27.16  | 
% 176.00/27.16  | COMBINE_EQS: (1), (2) imply:
% 176.00/27.16  |   (4)  all_52_15 = e2
% 176.00/27.16  | 
% 176.00/27.16  | SIMP: (4) implies:
% 176.00/27.16  |   (5)  all_52_15 = e2
% 176.00/27.16  | 
% 176.00/27.16  | REDUCE: (3), (5) imply:
% 176.00/27.16  |   (6)  $false
% 176.00/27.16  | 
% 176.00/27.16  | CLOSE: (6) is inconsistent.
% 176.00/27.16  | 
% 176.00/27.16  End of proof
% 176.00/27.16  
% 176.00/27.16  Sub-proof #165 shows that the following formulas are inconsistent:
% 176.00/27.16  ----------------------------------------------------------------
% 176.00/27.16    (1)  all_10_2 = e1
% 176.00/27.16    (2)   ~ (all_10_2 = e3)
% 176.00/27.17    (3)  op(e2, e1) = e3
% 176.00/27.17    (4)  op(e2, all_10_2) = e1
% 176.00/27.17    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.17  
% 176.00/27.17  Begin of proof
% 176.00/27.17  | 
% 176.00/27.17  | REDUCE: (1), (2) imply:
% 176.00/27.17  |   (6)   ~ (e3 = e1)
% 176.00/27.17  | 
% 176.00/27.17  | SIMP: (6) implies:
% 176.00/27.17  |   (7)   ~ (e3 = e1)
% 176.00/27.17  | 
% 176.00/27.17  | REDUCE: (1), (4) imply:
% 176.00/27.17  |   (8)  op(e2, e1) = e1
% 176.00/27.17  | 
% 176.00/27.17  | REF_CLOSE: (3), (5), (7), (8) are inconsistent by sub-proof #166.
% 176.00/27.17  | 
% 176.00/27.17  End of proof
% 176.00/27.17  
% 176.00/27.17  Sub-proof #166 shows that the following formulas are inconsistent:
% 176.00/27.17  ----------------------------------------------------------------
% 176.00/27.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.17    (2)  op(e2, e1) = e3
% 176.00/27.17    (3)  op(e2, e1) = e1
% 176.00/27.17    (4)   ~ (e3 = e1)
% 176.00/27.17  
% 176.00/27.17  Begin of proof
% 176.00/27.17  | 
% 176.00/27.17  | GROUND_INST: instantiating (1) with e3, e1, e1, e2, simplifying with (2), (3)
% 176.00/27.17  |              gives:
% 176.00/27.17  |   (5)  e3 = e1
% 176.00/27.17  | 
% 176.00/27.17  | REDUCE: (4), (5) imply:
% 176.00/27.17  |   (6)  $false
% 176.00/27.17  | 
% 176.00/27.17  | CLOSE: (6) is inconsistent.
% 176.00/27.17  | 
% 176.00/27.17  End of proof
% 176.00/27.17  
% 176.00/27.17  Sub-proof #167 shows that the following formulas are inconsistent:
% 176.00/27.17  ----------------------------------------------------------------
% 176.00/27.17    (1)  op(e2, all_52_3) = e2
% 176.00/27.17    (2)  all_58_10 = e0 | all_58_11 = e0
% 176.00/27.17    (3)   ~ (all_52_3 = e1)
% 176.00/27.17    (4)  all_58_5 = all_52_13
% 176.00/27.17    (5)   ~ (all_52_3 = e2)
% 176.00/27.17    (6)  op(e2, e0) = all_52_15
% 176.00/27.17    (7)  all_58_2 = e3
% 176.00/27.17    (8)  all_58_10 = all_52_15
% 176.00/27.17    (9)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.17    (10)  all_58_11 = e3
% 176.00/27.17    (11)   ~ (all_52_15 = e2)
% 176.00/27.17    (12)  op(e2, e1) = all_52_13
% 176.00/27.17    (13)  all_56_1 = all_52_3
% 176.00/27.17    (14)  all_58_3 = e1
% 176.00/27.17    (15)   ~ (all_52_3 = e3)
% 176.00/27.17    (16)   ~ (e2 = e1)
% 176.00/27.17    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.17    (18)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.00/27.17    (19)  op(e2, e1) = e1
% 176.00/27.17    (20)   ~ (e3 = e2)
% 176.00/27.17    (21)   ~ (all_52_15 = e1)
% 176.00/27.17  
% 176.00/27.17  Begin of proof
% 176.00/27.17  | 
% 176.00/27.17  | BETA: splitting (18) gives:
% 176.00/27.17  | 
% 176.00/27.17  | Case 1:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (22)  all_58_2 = e2
% 176.00/27.17  | | 
% 176.00/27.17  | | REF_CLOSE: (7), (20), (22) are inconsistent by sub-proof #694.
% 176.00/27.17  | | 
% 176.00/27.17  | Case 2:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (23)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.00/27.17  | | 
% 176.00/27.17  | | BETA: splitting (23) gives:
% 176.00/27.17  | | 
% 176.00/27.17  | | Case 1:
% 176.00/27.17  | | | 
% 176.00/27.17  | | |   (24)  all_58_3 = e2
% 176.00/27.17  | | | 
% 176.00/27.17  | | | COMBINE_EQS: (14), (24) imply:
% 176.00/27.17  | | |   (25)  e2 = e1
% 176.00/27.17  | | | 
% 176.00/27.17  | | | SIMP: (25) implies:
% 176.00/27.17  | | |   (26)  e2 = e1
% 176.00/27.17  | | | 
% 176.00/27.17  | | | REDUCE: (16), (26) imply:
% 176.00/27.17  | | |   (27)  $false
% 176.00/27.17  | | | 
% 176.00/27.17  | | | CLOSE: (27) is inconsistent.
% 176.00/27.17  | | | 
% 176.00/27.17  | | Case 2:
% 176.00/27.17  | | | 
% 176.00/27.17  | | |   (28)  all_58_5 = e2 | all_58_10 = e2
% 176.00/27.17  | | | 
% 176.00/27.17  | | | BETA: splitting (9) gives:
% 176.00/27.17  | | | 
% 176.00/27.17  | | | Case 1:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | |   (29)  all_56_1 = e2
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | COMBINE_EQS: (13), (29) imply:
% 176.00/27.17  | | | |   (30)  all_52_3 = e2
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | REDUCE: (5), (30) imply:
% 176.00/27.17  | | | |   (31)  $false
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | CLOSE: (31) is inconsistent.
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | Case 2:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | |   (32)  all_56_1 = e1 | all_56_1 = e0
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | BETA: splitting (32) gives:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | Case 1:
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | |   (33)  all_56_1 = e1
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | COMBINE_EQS: (13), (33) imply:
% 176.00/27.17  | | | | |   (34)  all_52_3 = e1
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (3), (34) imply:
% 176.00/27.17  | | | | |   (35)  $false
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | CLOSE: (35) is inconsistent.
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | Case 2:
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | |   (36)  all_56_1 = e0
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | COMBINE_EQS: (13), (36) imply:
% 176.00/27.17  | | | | |   (37)  all_52_3 = e0
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (15), (37) imply:
% 176.00/27.17  | | | | |   (38)   ~ (e3 = e0)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | SIMP: (38) implies:
% 176.00/27.17  | | | | |   (39)   ~ (e3 = e0)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (1), (37) imply:
% 176.00/27.17  | | | | |   (40)  op(e2, e0) = e2
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | BETA: splitting (28) gives:
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | Case 1:
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | |   (41)  all_58_5 = e2
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | COMBINE_EQS: (4), (41) imply:
% 176.00/27.17  | | | | | |   (42)  all_52_13 = e2
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | SIMP: (42) implies:
% 176.00/27.17  | | | | | |   (43)  all_52_13 = e2
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | REDUCE: (12), (43) imply:
% 176.00/27.17  | | | | | |   (44)  op(e2, e1) = e2
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | BETA: splitting (2) gives:
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | Case 1:
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | |   (45)  all_58_10 = e0
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | COMBINE_EQS: (8), (45) imply:
% 176.00/27.17  | | | | | | |   (46)  all_52_15 = e0
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | SIMP: (46) implies:
% 176.00/27.17  | | | | | | |   (47)  all_52_15 = e0
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | REDUCE: (21), (47) imply:
% 176.00/27.17  | | | | | | |   (48)   ~ (e1 = e0)
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | SIMP: (48) implies:
% 176.00/27.17  | | | | | | |   (49)   ~ (e1 = e0)
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | REDUCE: (6), (47) imply:
% 176.00/27.17  | | | | | | |   (50)  op(e2, e0) = e0
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | GROUND_INST: instantiating (17) with e0, e2, e0, e2, simplifying
% 176.00/27.17  | | | | | | |              with (40), (50) gives:
% 176.00/27.17  | | | | | | |   (51)  e2 = e0
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | GROUND_INST: instantiating (17) with e1, e2, e1, e2, simplifying
% 176.00/27.17  | | | | | | |              with (19), (44) gives:
% 176.00/27.17  | | | | | | |   (52)  e2 = e1
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | COMBINE_EQS: (51), (52) imply:
% 176.00/27.17  | | | | | | |   (53)  e1 = e0
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | REDUCE: (49), (53) imply:
% 176.00/27.17  | | | | | | |   (54)  $false
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | CLOSE: (54) is inconsistent.
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | Case 2:
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | |   (55)  all_58_11 = e0
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | REF_CLOSE: (10), (39), (55) are inconsistent by sub-proof #804.
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | End of split
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | Case 2:
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | |   (56)  all_58_10 = e2
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | REF_CLOSE: (8), (11), (56) are inconsistent by sub-proof #711.
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | End of split
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | End of split
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | End of split
% 176.00/27.17  | | | 
% 176.00/27.17  | | End of split
% 176.00/27.17  | | 
% 176.00/27.17  | End of split
% 176.00/27.17  | 
% 176.00/27.17  End of proof
% 176.00/27.17  
% 176.00/27.17  Sub-proof #168 shows that the following formulas are inconsistent:
% 176.00/27.17  ----------------------------------------------------------------
% 176.00/27.17    (1)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.17    (2)  all_56_15 = all_6_2
% 176.00/27.17    (3)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.17    (4)   ~ (e3 = e1)
% 176.00/27.17    (5)  all_58_5 = e3
% 176.00/27.17    (6)   ~ (all_14_2 = e1)
% 176.00/27.17    (7)  all_58_14 = all_52_29
% 176.00/27.17    (8)  all_58_8 = all_14_2
% 176.00/27.17    (9)  op(e0, e2) = all_52_27
% 176.00/27.17    (10)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.17    (11)  op(e0, all_6_2) = all_6_1
% 176.00/27.17    (12)  op(all_6_1, all_6_2) = e2
% 176.00/27.17    (13)   ~ (e3 = e0)
% 176.00/27.17    (14)  all_58_13 = all_52_27
% 176.00/27.17    (15)  all_58_12 = e3
% 176.00/27.17    (16)   ~ (e1 = e0)
% 176.00/27.17    (17)   ~ (all_52_29 = all_6_2)
% 176.00/27.17    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.17    (19)   ~ (all_52_27 = all_6_2)
% 176.00/27.17  
% 176.00/27.17  Begin of proof
% 176.00/27.17  | 
% 176.00/27.17  | BETA: splitting (10) gives:
% 176.00/27.17  | 
% 176.00/27.17  | Case 1:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (20)  all_58_5 = e1
% 176.00/27.17  | | 
% 176.00/27.17  | | REF_CLOSE: (4), (5), (20) are inconsistent by sub-proof #816.
% 176.00/27.17  | | 
% 176.00/27.17  | Case 2:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (21)  all_58_8 = e1 | all_58_14 = e1
% 176.00/27.17  | | 
% 176.00/27.17  | | BETA: splitting (21) gives:
% 176.00/27.17  | | 
% 176.00/27.17  | | Case 1:
% 176.00/27.17  | | | 
% 176.00/27.17  | | |   (22)  all_58_8 = e1
% 176.00/27.17  | | | 
% 176.00/27.17  | | | REF_CLOSE: (6), (8), (22) are inconsistent by sub-proof #815.
% 176.00/27.17  | | | 
% 176.00/27.17  | | Case 2:
% 176.00/27.17  | | | 
% 176.00/27.17  | | |   (23)  all_58_14 = e1
% 176.00/27.17  | | | 
% 176.00/27.17  | | | COMBINE_EQS: (7), (23) imply:
% 176.00/27.17  | | |   (24)  all_52_29 = e1
% 176.00/27.17  | | | 
% 176.00/27.17  | | | SIMP: (24) implies:
% 176.00/27.17  | | |   (25)  all_52_29 = e1
% 176.00/27.17  | | | 
% 176.00/27.17  | | | REDUCE: (17), (25) imply:
% 176.00/27.17  | | |   (26)   ~ (all_6_2 = e1)
% 176.00/27.17  | | | 
% 176.00/27.17  | | | SIMP: (26) implies:
% 176.00/27.17  | | |   (27)   ~ (all_6_2 = e1)
% 176.00/27.17  | | | 
% 176.00/27.17  | | | BETA: splitting (1) gives:
% 176.00/27.17  | | | 
% 176.00/27.17  | | | Case 1:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | |   (28)  all_58_12 = e0
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | REF_CLOSE: (13), (15), (28) are inconsistent by sub-proof #682.
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | Case 2:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | |   (29)  all_58_13 = e0 | all_58_14 = e0
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | REF_CLOSE: (2), (3), (9), (11), (12), (14), (16), (18), (19), (23),
% 176.00/27.17  | | | |            (27), (29) are inconsistent by sub-proof #216.
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | End of split
% 176.00/27.17  | | | 
% 176.00/27.17  | | End of split
% 176.00/27.17  | | 
% 176.00/27.17  | End of split
% 176.00/27.17  | 
% 176.00/27.17  End of proof
% 176.00/27.17  
% 176.00/27.17  Sub-proof #169 shows that the following formulas are inconsistent:
% 176.00/27.17  ----------------------------------------------------------------
% 176.00/27.17    (1)   ~ (e3 = e1)
% 176.00/27.17    (2)  op(e0, all_6_2) = all_6_1
% 176.00/27.17    (3)  op(all_6_1, all_6_2) = e2
% 176.00/27.17    (4)  all_52_20 = e3
% 176.00/27.17    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.17    (6)  all_52_30 = all_6_1
% 176.00/27.17    (7)   ~ (e2 = e0)
% 176.00/27.17    (8)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.00/27.17         (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.00/27.17  
% 176.00/27.17  Begin of proof
% 176.00/27.17  | 
% 176.00/27.17  | BETA: splitting (8) gives:
% 176.00/27.17  | 
% 176.00/27.17  | Case 1:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (9)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.00/27.17  | | 
% 176.00/27.17  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #373.
% 176.00/27.17  | | 
% 176.00/27.17  | Case 2:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (10)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.00/27.17  | | 
% 176.00/27.17  | | ALPHA: (10) implies:
% 176.00/27.17  | |   (11)  all_52_30 = e0
% 176.00/27.17  | | 
% 176.00/27.17  | | COMBINE_EQS: (6), (11) imply:
% 176.00/27.17  | |   (12)  all_6_1 = e0
% 176.00/27.17  | | 
% 176.00/27.17  | | REF_CLOSE: (2), (3), (5), (7), (12) are inconsistent by sub-proof #201.
% 176.00/27.17  | | 
% 176.00/27.17  | End of split
% 176.00/27.17  | 
% 176.00/27.17  End of proof
% 176.00/27.17  
% 176.00/27.17  Sub-proof #170 shows that the following formulas are inconsistent:
% 176.00/27.17  ----------------------------------------------------------------
% 176.00/27.17    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.17    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.17    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.00/27.17    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.17    (5)   ~ (all_52_17 = all_52_23)
% 176.00/27.17    (6)  all_22_2 = all_14_2
% 176.00/27.17    (7)   ~ (all_52_13 = all_52_29)
% 176.00/27.17    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.17    (9)  all_56_3 = all_52_7
% 176.00/27.17    (10)  op(e3, e2) = all_52_3
% 176.00/27.17    (11)   ~ (all_52_19 = all_52_23)
% 176.00/27.17    (12)  all_56_11 = all_52_23
% 176.00/27.17    (13)   ~ (all_52_27 = e3)
% 176.00/27.17    (14)   ~ (all_6_2 = e3)
% 176.00/27.17    (15)   ~ (all_52_3 = all_10_2)
% 176.00/27.17    (16)  all_58_5 = all_52_13
% 176.00/27.17    (17)   ~ (all_6_2 = e0)
% 176.00/27.17    (18)  op(e1, all_52_13) = e1
% 176.00/27.17    (19)  op(e0, all_52_15) = e0
% 176.00/27.17    (20)  all_56_15 = all_6_2
% 176.00/27.17    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.17    (22)   ~ (all_4_2 = e3)
% 176.00/27.17    (23)  all_58_3 = all_10_2
% 176.00/27.17    (24)  all_56_9 = all_52_19
% 176.00/27.17    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.17    (26)  all_58_15 = all_6_2
% 176.00/27.17    (27)   ~ (all_52_9 = all_4_2)
% 176.00/27.17    (28)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.17    (29)   ~ (all_52_5 = all_52_7)
% 176.00/27.17    (30)  all_58_10 = all_52_15
% 176.00/27.17    (31)   ~ (all_52_5 = all_4_2)
% 176.00/27.17    (32)  all_58_7 = all_52_19
% 176.00/27.17    (33)  all_56_4 = all_52_9
% 176.00/27.17    (34)  op(e0, e1) = all_52_29
% 176.00/27.17    (35)  all_58_4 = all_52_5
% 176.00/27.17    (36)   ~ (all_52_27 = all_52_29)
% 176.00/27.17    (37)   ~ (all_52_17 = all_14_2)
% 176.00/27.17    (38)  op(e3, all_4_2) = all_4_1
% 176.00/27.17    (39)   ~ (all_52_7 = all_4_2)
% 176.00/27.17    (40)  all_58_1 = all_52_3
% 176.00/27.17    (41)  all_58_0 = all_4_2
% 176.00/27.17    (42)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.17    (43)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.17    (44)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.00/27.17    (45)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.17    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.17    (47)  all_58_14 = all_52_29
% 176.00/27.17    (48)  op(e0, e3) = e3
% 176.00/27.17    (49)   ~ (all_52_3 = all_52_5)
% 176.00/27.17    (50)  op(e2, e1) = all_52_13
% 176.00/27.17    (51)  all_58_8 = all_14_2
% 176.00/27.17    (52)  op(e0, e2) = all_52_27
% 176.00/27.17    (53)  all_56_14 = all_52_29
% 176.00/27.17    (54)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.17    (55)  op(e0, all_6_2) = all_6_1
% 176.00/27.17    (56)  op(all_6_1, all_6_2) = e2
% 176.00/27.17    (57)  op(e3, all_52_17) = all_52_16
% 176.00/27.17    (58)   ~ (all_52_29 = e3)
% 176.00/27.17    (59)   ~ (all_52_13 = all_14_2)
% 176.00/27.17    (60)  op(e3, all_52_9) = e3
% 176.00/27.17    (61)   ~ (e3 = e0)
% 176.00/27.17    (62)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.17    (63)  all_22_0 = all_14_0
% 176.00/27.17    (64)   ~ (all_52_9 = all_52_13)
% 176.00/27.17    (65)  op(e0, all_52_23) = all_52_22
% 176.00/27.17    (66)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.17    (67)   ~ (all_52_5 = all_52_29)
% 176.00/27.17    (68)  all_58_13 = all_52_27
% 176.00/27.17    (69)  all_58_12 = e3
% 176.00/27.17    (70)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.00/27.17    (71)   ~ (all_52_9 = all_52_17)
% 176.00/27.17    (72)  all_58_6 = all_52_17
% 176.00/27.17    (73)   ~ (all_52_3 = all_52_7)
% 176.00/27.17    (74)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.17    (75)  op(e2, all_52_19) = all_52_18
% 176.00/27.17    (76)  all_56_0 = all_4_2
% 176.00/27.17    (77)  all_58_11 = all_52_23
% 176.00/27.17    (78)   ~ (all_52_3 = all_52_19)
% 176.00/27.17    (79)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 176.00/27.17    (80)   ~ (all_52_29 = all_14_2)
% 176.00/27.17    (81)   ~ (all_52_9 = e3)
% 176.00/27.17    (82)   ~ (all_52_23 = all_6_2)
% 176.00/27.17    (83)   ~ (all_52_29 = all_6_2)
% 176.00/27.17    (84)  all_58_2 = all_52_9
% 176.00/27.17    (85)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.17    (86)  op(e3, e1) = all_52_5
% 176.00/27.17    (87)   ~ (e2 = e1)
% 176.00/27.17    (88)  all_56_10 = all_14_2
% 176.00/27.17    (89)  op(e1, e3) = all_52_17
% 176.00/27.17    (90)  op(e3, e0) = all_52_7
% 176.00/27.17    (91)  op(e2, all_10_2) = e2
% 176.00/27.17    (92)   ~ (all_52_17 = all_4_2)
% 176.00/27.17    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.17    (94)   ~ (all_52_27 = all_6_2)
% 176.00/27.17    (95)   ~ (all_52_7 = all_6_2)
% 176.00/27.17    (96)   ~ (all_52_7 = all_52_23)
% 176.00/27.17    (97)   ~ (all_52_17 = all_52_19)
% 176.00/27.17    (98)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.17    (99)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.17    (100)  op(e3, all_14_2) = all_14_0
% 176.00/27.17    (101)  all_58_9 = all_52_7
% 176.00/27.17    (102)   ~ (e2 = e0)
% 176.00/27.17    (103)   ~ (all_52_9 = all_52_15)
% 176.00/27.17    (104)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.17    (105)   ~ (e3 = e2)
% 176.00/27.17    (106)   ~ (all_52_19 = all_14_2)
% 176.00/27.17    (107)  op(e2, e3) = all_52_9
% 176.00/27.17  
% 176.00/27.17  Begin of proof
% 176.00/27.17  | 
% 176.00/27.17  | BETA: splitting (44) gives:
% 176.00/27.17  | 
% 176.00/27.17  | Case 1:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (108)  all_56_14 = e3
% 176.00/27.17  | | 
% 176.00/27.17  | | REF_CLOSE: (53), (58), (108) are inconsistent by sub-proof #896.
% 176.00/27.17  | | 
% 176.00/27.17  | Case 2:
% 176.00/27.17  | | 
% 176.00/27.17  | |   (109)   ~ (all_56_14 = e3)
% 176.00/27.17  | |   (110)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.00/27.17  | | 
% 176.00/27.17  | | BETA: splitting (25) gives:
% 176.00/27.17  | | 
% 176.00/27.17  | | Case 1:
% 176.00/27.17  | | | 
% 176.00/27.17  | | |   (111)  all_56_0 = e3
% 176.00/27.17  | | | 
% 176.00/27.17  | | | COMBINE_EQS: (76), (111) imply:
% 176.00/27.17  | | |   (112)  all_4_2 = e3
% 176.00/27.17  | | | 
% 176.00/27.17  | | | REDUCE: (22), (112) imply:
% 176.00/27.17  | | |   (113)  $false
% 176.00/27.17  | | | 
% 176.00/27.17  | | | CLOSE: (113) is inconsistent.
% 176.00/27.17  | | | 
% 176.00/27.17  | | Case 2:
% 176.00/27.17  | | | 
% 176.00/27.17  | | |   (114)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.17  | | | 
% 176.00/27.17  | | | BETA: splitting (74) gives:
% 176.00/27.17  | | | 
% 176.00/27.17  | | | Case 1:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | |   (115)  all_56_4 = e3
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | REF_CLOSE: (33), (81), (115) are inconsistent by sub-proof #782.
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | Case 2:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | |   (116)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | BETA: splitting (85) gives:
% 176.00/27.17  | | | | 
% 176.00/27.17  | | | | Case 1:
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | |   (117)  all_56_11 = e3
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | COMBINE_EQS: (12), (117) imply:
% 176.00/27.17  | | | | |   (118)  all_52_23 = e3
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | SIMP: (118) implies:
% 176.00/27.17  | | | | |   (119)  all_52_23 = e3
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (96), (119) imply:
% 176.00/27.17  | | | | |   (120)   ~ (all_52_7 = e3)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (5), (119) imply:
% 176.00/27.17  | | | | |   (121)   ~ (all_52_17 = e3)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (1), (119) imply:
% 176.00/27.17  | | | | |   (122)   ~ (all_14_2 = e3)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | SIMP: (122) implies:
% 176.00/27.17  | | | | |   (123)   ~ (all_14_2 = e3)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (82), (119) imply:
% 176.00/27.17  | | | | |   (124)   ~ (all_6_2 = e3)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (65), (119) imply:
% 176.00/27.17  | | | | |   (125)  op(e0, e3) = all_52_22
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REF_CLOSE: (4), (7), (9), (10), (11), (13), (14), (15), (16), (17),
% 176.00/27.17  | | | | |            (18), (19), (20), (23), (24), (26), (27), (28), (29), (30),
% 176.00/27.17  | | | | |            (31), (32), (33), (35), (36), (37), (39), (40), (41), (43),
% 176.00/27.17  | | | | |            (45), (46), (47), (48), (49), (50), (51), (54), (57), (58),
% 176.00/27.17  | | | | |            (60), (61), (68), (71), (73), (76), (77), (86), (89), (90),
% 176.00/27.17  | | | | |            (91), (93), (94), (95), (97), (98), (99), (101), (104),
% 176.00/27.17  | | | | |            (105), (107), (114), (116), (120), (121), (123), (125) are
% 176.00/27.17  | | | | |            inconsistent by sub-proof #743.
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | Case 2:
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | |   (126)   ~ (all_56_11 = e3)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | REDUCE: (12), (126) imply:
% 176.00/27.17  | | | | |   (127)   ~ (all_52_23 = e3)
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | BETA: splitting (98) gives:
% 176.00/27.17  | | | | | 
% 176.00/27.17  | | | | | Case 1:
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | |   (128)  all_58_9 = e3
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | COMBINE_EQS: (101), (128) imply:
% 176.00/27.17  | | | | | |   (129)  all_52_7 = e3
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | SIMP: (129) implies:
% 176.00/27.17  | | | | | |   (130)  all_52_7 = e3
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | REDUCE: (73), (130) imply:
% 176.00/27.17  | | | | | |   (131)   ~ (all_52_3 = e3)
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | REDUCE: (29), (130) imply:
% 176.00/27.17  | | | | | |   (132)   ~ (all_52_5 = e3)
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | REDUCE: (39), (130) imply:
% 176.00/27.17  | | | | | |   (133)   ~ (all_4_2 = e3)
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | BETA: splitting (46) gives:
% 176.00/27.17  | | | | | | 
% 176.00/27.17  | | | | | | Case 1:
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | |   (134)  all_58_1 = e3
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | COMBINE_EQS: (40), (134) imply:
% 176.00/27.17  | | | | | | |   (135)  all_52_3 = e3
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | REDUCE: (131), (135) imply:
% 176.00/27.17  | | | | | | |   (136)  $false
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | CLOSE: (136) is inconsistent.
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | Case 2:
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | |   (137)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | BETA: splitting (104) gives:
% 176.00/27.17  | | | | | | | 
% 176.00/27.17  | | | | | | | Case 1:
% 176.00/27.17  | | | | | | | | 
% 176.00/27.17  | | | | | | | |   (138)  all_58_4 = e3
% 176.00/27.17  | | | | | | | | 
% 176.00/27.17  | | | | | | | | REF_CLOSE: (35), (132), (138) are inconsistent by sub-proof
% 176.00/27.17  | | | | | | | |            #1025.
% 176.00/27.17  | | | | | | | | 
% 176.00/27.17  | | | | | | | Case 2:
% 176.00/27.17  | | | | | | | | 
% 176.00/27.17  | | | | | | | |   (139)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.17  | | | | | | | | 
% 176.00/27.17  | | | | | | | | BETA: splitting (43) gives:
% 176.00/27.17  | | | | | | | | 
% 176.00/27.17  | | | | | | | | Case 1:
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | |   (140)  all_56_9 = e3
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | COMBINE_EQS: (24), (140) imply:
% 176.00/27.17  | | | | | | | | |   (141)  all_52_19 = e3
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | SIMP: (141) implies:
% 176.00/27.17  | | | | | | | | |   (142)  all_52_19 = e3
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | COMBINE_EQS: (32), (142) imply:
% 176.00/27.17  | | | | | | | | |   (143)  all_58_7 = e3
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | REDUCE: (11), (142) imply:
% 176.00/27.17  | | | | | | | | |   (144)   ~ (all_52_23 = e3)
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | REDUCE: (106), (142) imply:
% 176.00/27.17  | | | | | | | | |   (145)   ~ (all_14_2 = e3)
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | SIMP: (145) implies:
% 176.00/27.17  | | | | | | | | |   (146)   ~ (all_14_2 = e3)
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | REDUCE: (75), (142) imply:
% 176.00/27.17  | | | | | | | | |   (147)  op(e2, e3) = all_52_18
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | BETA: splitting (139) gives:
% 176.00/27.17  | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | Case 1:
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | |   (148)  all_58_5 = e3
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | COMBINE_EQS: (16), (148) imply:
% 176.00/27.17  | | | | | | | | | |   (149)  all_52_13 = e3
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | SIMP: (149) implies:
% 176.00/27.17  | | | | | | | | | |   (150)  all_52_13 = e3
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (18), (150) imply:
% 176.00/27.17  | | | | | | | | | |   (151)  op(e1, e3) = e1
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | GROUND_INST: instantiating (93) with all_52_17, e1, e3, e1,
% 176.00/27.17  | | | | | | | | | |              simplifying with (89), (151) gives:
% 176.00/27.17  | | | | | | | | | |   (152)  all_52_17 = e1
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | GROUND_INST: instantiating (93) with all_52_9, all_52_18, e3,
% 176.00/27.17  | | | | | | | | | |              e2, simplifying with (107), (147) gives:
% 176.00/27.17  | | | | | | | | | |   (153)  all_52_9 = all_52_18
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | COMBINE_EQS: (33), (153) imply:
% 176.00/27.17  | | | | | | | | | |   (154)  all_56_4 = all_52_18
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | COMBINE_EQS: (72), (152) imply:
% 176.00/27.17  | | | | | | | | | |   (155)  all_58_6 = e1
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | COMBINE_EQS: (84), (153) imply:
% 176.00/27.17  | | | | | | | | | |   (156)  all_58_2 = all_52_18
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (103), (153) imply:
% 176.00/27.17  | | | | | | | | | |   (157)   ~ (all_52_15 = all_52_18)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | SIMP: (157) implies:
% 176.00/27.17  | | | | | | | | | |   (158)   ~ (all_52_15 = all_52_18)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (71), (152), (153) imply:
% 176.00/27.17  | | | | | | | | | |   (159)   ~ (all_52_18 = e1)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (27), (153) imply:
% 176.00/27.17  | | | | | | | | | |   (160)   ~ (all_52_18 = all_4_2)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (81), (153) imply:
% 176.00/27.17  | | | | | | | | | |   (161)   ~ (all_52_18 = e3)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (92), (152) imply:
% 176.00/27.17  | | | | | | | | | |   (162)   ~ (all_4_2 = e1)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | SIMP: (162) implies:
% 176.00/27.17  | | | | | | | | | |   (163)   ~ (all_4_2 = e1)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (60), (153) imply:
% 176.00/27.17  | | | | | | | | | |   (164)  op(e3, all_52_18) = e3
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (57), (152) imply:
% 176.00/27.17  | | | | | | | | | |   (165)  op(e3, e1) = all_52_16
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | GROUND_INST: instantiating (93) with all_52_5, all_52_16, e1,
% 176.00/27.17  | | | | | | | | | |              e3, simplifying with (86), (165) gives:
% 176.00/27.17  | | | | | | | | | |   (166)  all_52_5 = all_52_16
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | COMBINE_EQS: (35), (166) imply:
% 176.00/27.17  | | | | | | | | | |   (167)  all_58_4 = all_52_16
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (67), (166) imply:
% 176.00/27.17  | | | | | | | | | |   (168)   ~ (all_52_16 = all_52_29)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | REDUCE: (132), (166) imply:
% 176.00/27.17  | | | | | | | | | |   (169)   ~ (all_52_16 = e3)
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | BETA: splitting (66) gives:
% 176.00/27.17  | | | | | | | | | | 
% 176.00/27.17  | | | | | | | | | | Case 1:
% 176.00/27.17  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | |   (170)  all_56_10 = e3
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | COMBINE_EQS: (88), (170) imply:
% 176.00/27.18  | | | | | | | | | | |   (171)  all_14_2 = e3
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | REDUCE: (146), (171) imply:
% 176.00/27.18  | | | | | | | | | | |   (172)  $false
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | |   (173)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | BETA: splitting (21) gives:
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | |   (174)  all_58_0 = e2
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | COMBINE_EQS: (41), (174) imply:
% 176.00/27.18  | | | | | | | | | | | |   (175)  all_4_2 = e2
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | REDUCE: (160), (175) imply:
% 176.00/27.18  | | | | | | | | | | | |   (176)   ~ (all_52_18 = e2)
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | REDUCE: (22), (175) imply:
% 176.00/27.18  | | | | | | | | | | | |   (177)   ~ (e3 = e2)
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | REDUCE: (38), (175) imply:
% 176.00/27.18  | | | | | | | | | | | |   (178)  op(e3, e2) = all_4_1
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | BETA: splitting (62) gives:
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | |   (179)  all_58_0 = e0
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | COMBINE_EQS: (174), (179) imply:
% 176.00/27.18  | | | | | | | | | | | | |   (180)  e2 = e0
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | REDUCE: (102), (180) imply:
% 176.00/27.18  | | | | | | | | | | | | |   (181)  $false
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | |   (182)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | BETA: splitting (182) gives:
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | |   (183)  all_58_2 = e0
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | COMBINE_EQS: (156), (183) imply:
% 176.00/27.18  | | | | | | | | | | | | | |   (184)  all_52_18 = e0
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | SIMP: (184) implies:
% 176.00/27.18  | | | | | | | | | | | | | |   (185)  all_52_18 = e0
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | REDUCE: (158), (185) imply:
% 176.00/27.18  | | | | | | | | | | | | | |   (186)   ~ (all_52_15 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | REDUCE: (161), (185) imply:
% 176.00/27.18  | | | | | | | | | | | | | |   (187)   ~ (e3 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | REDUCE: (176), (185) imply:
% 176.00/27.18  | | | | | | | | | | | | | |   (188)   ~ (e2 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | |   (189)  all_58_9 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | REF_CLOSE: (61), (128), (189) are inconsistent by sub-proof
% 176.00/27.18  | | | | | | | | | | | | | | |            #928.
% 176.00/27.18  | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | |   (190)  all_58_10 = e0 | all_58_11 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | |   (191)  all_58_10 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | REF_CLOSE: (30), (186), (191) are inconsistent by sub-proof
% 176.00/27.18  | | | | | | | | | | | | | | | |            #741.
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | |   (192)  all_58_11 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (192) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | |   (193)  all_52_23 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | SIMP: (193) implies:
% 176.00/27.18  | | | | | | | | | | | | | | | |   (194)  all_52_23 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | REDUCE: (1), (194) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | |   (195)   ~ (all_14_2 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | SIMP: (195) implies:
% 176.00/27.18  | | | | | | | | | | | | | | | |   (196)   ~ (all_14_2 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | |   (197)  all_58_6 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (197) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | |   (198)  e2 = e1
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | REDUCE: (87), (198) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | |   (199)  $false
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | |   (200)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | |   (201)  all_58_7 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (201) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | |   (202)  e3 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | REDUCE: (105), (202) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | |   (203)  $false
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | |   (204)  all_58_8 = e2 | all_58_11 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (205)  all_56_10 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (205) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (206)  all_14_2 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | SIMP: (206) implies:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (207)  all_14_2 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (207) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (208)  all_22_2 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | REDUCE: (80), (207) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (209)   ~ (all_52_29 = e2)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | REDUCE: (100), (207) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (210)  op(e3, e2) = all_14_0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (211)   ~ (all_22_2 = e2)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | REDUCE: (208), (211) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (212)  $false
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | CLOSE: (212) is inconsistent.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (213)   ~ (all_22_0 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (213) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (214)   ~ (all_14_0 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (93) with all_52_3, all_4_1, e2, e3,
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |              simplifying with (10), (178) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (215)  all_52_3 = all_4_1
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (93) with all_52_3, all_14_0, e2,
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (10), (210) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (216)  all_52_3 = all_14_0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (216) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (217)  all_14_0 = all_4_1
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (215) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (218)  all_58_1 = all_4_1
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (217) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | |   (219)   ~ (all_4_1 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | |   (220)  all_58_0 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (174), (220) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | |   (221)  e2 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (221) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | |   (222)  $false
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | |   (223)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | |   (224)  all_58_1 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (224) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | |   (225)  all_4_1 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (219), (225) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | |   (226)  $false
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | |   (227)  all_58_4 = e0 | all_58_9 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_58_4 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (228) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_52_16 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (229) implies:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_52_16 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (230) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | |   (231)   ~ (all_52_29 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (231) implies:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | |   (232)   ~ (all_52_29 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_56_14 = e2
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (209), (233) are inconsistent by sub-proof
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | |            #837.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | |   (234)  all_56_14 = e1 | all_56_14 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_56_14 = e1
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (53), (235) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_52_29 = e1
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (236) implies:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_52_29 = e1
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (34), (237) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  op(e0, e1) = e1
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (20), (28), (34), (47), (52), (55), (56),
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (68), (69), (83), (93), (94), (232), (238)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #197.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_56_14 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (232), (239) are inconsistent by sub-proof
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | |            #887.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_58_9 = e0
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (128), (240) are inconsistent by sub-proof
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | |            #928.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (241)   ~ (all_56_10 = e2)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | REDUCE: (88), (241) imply:
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |   (242)   ~ (all_14_2 = e2)
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (102), (192), (204), (242) are inconsistent
% 176.00/27.18  | | | | | | | | | | | | | | | | | | |            by sub-proof #890.
% 176.00/27.18  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | |   (243)   ~ (all_58_2 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | REDUCE: (156), (243) imply:
% 176.00/27.18  | | | | | | | | | | | | | |   (244)   ~ (all_52_18 = e0)
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | | REF_CLOSE: (116), (154), (159), (176), (244) are inconsistent
% 176.00/27.18  | | | | | | | | | | | | | |            by sub-proof #297.
% 176.00/27.18  | | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | |   (245)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | | REF_CLOSE: (10), (69), (87), (93), (105), (131), (155),
% 176.00/27.18  | | | | | | | | | | | |            (156), (164), (245) are inconsistent by sub-proof
% 176.00/27.18  | | | | | | | | | | | |            #737.
% 176.00/27.18  | | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | |   (246)  all_58_8 = e3 | all_58_14 = e3
% 176.00/27.18  | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | | REF_CLOSE: (47), (51), (58), (146), (246) are inconsistent by
% 176.00/27.18  | | | | | | | | | |            sub-proof #999.
% 176.00/27.18  | | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | | 
% 176.00/27.18  | | | | | | | | Case 2:
% 176.00/27.18  | | | | | | | | | 
% 176.00/27.18  | | | | | | | | |   (247)   ~ (all_56_9 = e3)
% 176.00/27.18  | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | REDUCE: (24), (247) imply:
% 176.00/27.18  | | | | | | | | |   (248)   ~ (all_52_19 = e3)
% 176.00/27.18  | | | | | | | | | 
% 176.00/27.18  | | | | | | | | | REF_CLOSE: (10), (13), (15), (23), (32), (60), (68), (91),
% 176.00/27.18  | | | | | | | | |            (93), (107), (137), (248) are inconsistent by
% 176.00/27.18  | | | | | | | | |            sub-proof #975.
% 176.00/27.18  | | | | | | | | | 
% 176.00/27.18  | | | | | | | | End of split
% 176.00/27.18  | | | | | | | | 
% 176.00/27.18  | | | | | | | End of split
% 176.00/27.18  | | | | | | | 
% 176.00/27.18  | | | | | | End of split
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | Case 2:
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | |   (249)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | | REF_CLOSE: (14), (19), (26), (30), (48), (61), (77), (93), (127),
% 176.00/27.18  | | | | | |            (249) are inconsistent by sub-proof #745.
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | End of split
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | End of split
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | End of split
% 176.00/27.18  | | | 
% 176.00/27.18  | | End of split
% 176.00/27.18  | | 
% 176.00/27.18  | End of split
% 176.00/27.18  | 
% 176.00/27.18  End of proof
% 176.00/27.18  
% 176.00/27.18  Sub-proof #171 shows that the following formulas are inconsistent:
% 176.00/27.18  ----------------------------------------------------------------
% 176.00/27.18    (1)   ~ (all_52_27 = all_10_2)
% 176.00/27.18    (2)   ~ (all_52_23 = all_52_28)
% 176.00/27.18    (3)  op(e2, all_52_3) = e2
% 176.00/27.18    (4)  all_58_6 = all_52_28
% 176.00/27.18    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.18    (6)  all_56_3 = all_52_7
% 176.00/27.18    (7)  op(e3, e2) = all_52_3
% 176.00/27.18    (8)  op(e1, e2) = all_52_19
% 176.00/27.18    (9)   ~ (all_52_27 = e3)
% 176.00/27.18    (10)   ~ (all_6_2 = e3)
% 176.00/27.18    (11)  op(e3, all_52_9) = all_52_8
% 176.00/27.18    (12)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.18    (13)   ~ (all_52_3 = all_10_2)
% 176.00/27.18    (14)  all_58_5 = all_52_13
% 176.00/27.18    (15)   ~ (all_6_2 = e0)
% 176.00/27.18    (16)  all_56_15 = all_6_2
% 176.00/27.18    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.00/27.18    (18)  all_58_3 = all_10_2
% 176.00/27.18    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.18    (20)  all_58_15 = all_6_2
% 176.00/27.18    (21)   ~ (all_52_9 = all_4_2)
% 176.00/27.18    (22)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.18    (23)   ~ (all_52_5 = all_52_7)
% 176.00/27.18    (24)  all_58_10 = all_52_15
% 176.00/27.18    (25)  all_8_2 = all_6_2
% 176.00/27.18    (26)   ~ (all_52_5 = all_4_2)
% 176.00/27.18    (27)  all_58_7 = all_52_19
% 176.00/27.18    (28)  all_58_4 = all_52_5
% 176.00/27.18    (29)   ~ (e3 = e1)
% 176.00/27.18    (30)   ~ (all_52_7 = all_4_2)
% 176.00/27.18    (31)  all_58_1 = all_52_3
% 176.00/27.18    (32)  all_58_0 = all_4_2
% 176.00/27.18    (33)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.18    (34)  op(e0, e0) = all_6_2
% 176.00/27.18    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.18    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.18    (37)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.00/27.18    (38)   ~ (all_52_3 = all_52_5)
% 176.00/27.18    (39)  all_58_8 = all_14_2
% 176.00/27.18    (40)  op(e1, all_14_2) = e3
% 176.00/27.18    (41)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.18    (42)   ~ (all_52_5 = all_14_2)
% 176.00/27.18    (43)   ~ (all_52_23 = e3)
% 176.00/27.18    (44)   ~ (all_52_3 = all_4_2)
% 176.00/27.18    (45)  op(e3, all_4_2) = e3
% 176.00/27.18    (46)  op(e0, e3) = all_52_25
% 176.00/27.18    (47)  op(e0, all_6_2) = all_6_1
% 176.00/27.18    (48)   ~ (all_52_9 = all_10_2)
% 176.00/27.18    (49)   ~ (all_52_5 = e3)
% 176.00/27.18    (50)   ~ (e3 = e0)
% 176.00/27.18    (51)   ~ (all_52_9 = all_52_13)
% 176.00/27.18    (52)   ~ (all_52_19 = all_52_28)
% 176.00/27.18    (53)  all_58_13 = all_52_27
% 176.00/27.18    (54)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.18    (55)  all_56_5 = all_10_2
% 176.00/27.18    (56)   ~ (all_52_3 = all_52_7)
% 176.00/27.18    (57)  op(e2, all_52_19) = all_52_18
% 176.00/27.18    (58)  all_56_0 = all_4_2
% 176.00/27.18    (59)  all_58_11 = all_52_23
% 176.00/27.18    (60)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.18    (61)   ~ (all_52_7 = all_52_15)
% 176.00/27.18    (62)  op(e0, all_52_15) = all_52_14
% 176.00/27.18    (63)   ~ (all_52_19 = all_10_2)
% 176.00/27.18    (64)  all_58_2 = all_52_9
% 176.00/27.18    (65)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.00/27.18    (66)  op(e3, e1) = all_52_5
% 176.00/27.18    (67)   ~ (all_52_25 = all_6_2)
% 176.00/27.18    (68)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.00/27.18    (69)  op(e1, e1) = all_14_2
% 176.00/27.18    (70)   ~ (all_52_25 = all_4_2)
% 176.00/27.18    (71)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.18    (72)  op(e0, e1) = e3
% 176.00/27.18    (73)  all_8_1 = all_6_1
% 176.00/27.18    (74)   ~ (all_52_7 = all_6_2)
% 176.00/27.18    (75)   ~ (all_52_15 = all_10_2)
% 176.00/27.18    (76)  all_58_14 = e3
% 176.00/27.18    (77)  op(e1, all_52_5) = e1
% 176.00/27.18    (78)   ~ (all_52_7 = all_52_23)
% 176.00/27.18    (79)  op(e0, all_52_7) = e0
% 176.00/27.18    (80)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.18    (81)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.18    (82)  all_58_9 = all_52_7
% 176.00/27.18    (83)  all_58_12 = all_52_25
% 176.00/27.18    (84)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.18    (85)   ~ (all_52_9 = all_52_15)
% 176.00/27.18    (86)   ~ (all_52_19 = all_14_2)
% 176.00/27.18    (87)  op(e2, e3) = all_52_9
% 176.00/27.18  
% 176.00/27.18  Begin of proof
% 176.00/27.18  | 
% 176.00/27.18  | BETA: splitting (80) gives:
% 176.00/27.18  | 
% 176.00/27.18  | Case 1:
% 176.00/27.18  | | 
% 176.00/27.18  | |   (88)  all_58_9 = e3
% 176.00/27.18  | | 
% 176.00/27.18  | | REF_CLOSE: (7), (19), (20), (23), (24), (30), (32), (45), (46), (54), (56),
% 176.00/27.18  | |            (58), (59), (61), (66), (70), (71), (74), (78), (79), (80), (82),
% 176.00/27.18  | |            (88) are inconsistent by sub-proof #1014.
% 176.00/27.18  | | 
% 176.00/27.18  | Case 2:
% 176.00/27.18  | | 
% 176.00/27.18  | |   (89)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.18  | | 
% 176.00/27.18  | | BETA: splitting (89) gives:
% 176.00/27.18  | | 
% 176.00/27.18  | | Case 1:
% 176.00/27.18  | | | 
% 176.00/27.18  | | |   (90)  all_58_10 = e3
% 176.00/27.18  | | | 
% 176.00/27.18  | | | COMBINE_EQS: (24), (90) imply:
% 176.00/27.18  | | |   (91)  all_52_15 = e3
% 176.00/27.18  | | | 
% 176.00/27.18  | | | SIMP: (91) implies:
% 176.00/27.18  | | |   (92)  all_52_15 = e3
% 176.00/27.18  | | | 
% 176.00/27.18  | | | REDUCE: (85), (92) imply:
% 176.00/27.18  | | |   (93)   ~ (all_52_9 = e3)
% 176.00/27.18  | | | 
% 176.00/27.18  | | | REDUCE: (75), (92) imply:
% 176.00/27.18  | | |   (94)   ~ (all_10_2 = e3)
% 176.00/27.18  | | | 
% 176.00/27.18  | | | SIMP: (94) implies:
% 176.00/27.18  | | |   (95)   ~ (all_10_2 = e3)
% 176.00/27.18  | | | 
% 176.00/27.18  | | | REDUCE: (62), (92) imply:
% 176.00/27.18  | | |   (96)  op(e0, e3) = all_52_14
% 176.00/27.18  | | | 
% 176.00/27.18  | | | GROUND_INST: instantiating (71) with all_52_25, all_52_14, e3, e0,
% 176.00/27.18  | | |              simplifying with (46), (96) gives:
% 176.00/27.18  | | |   (97)  all_52_14 = all_52_25
% 176.00/27.18  | | | 
% 176.00/27.18  | | | BETA: splitting (84) gives:
% 176.00/27.18  | | | 
% 176.00/27.18  | | | Case 1:
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | |   (98)  all_58_0 = e3
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | | COMBINE_EQS: (32), (98) imply:
% 176.00/27.18  | | | |   (99)  all_4_2 = e3
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | | REDUCE: (44), (99) imply:
% 176.00/27.18  | | | |   (100)   ~ (all_52_3 = e3)
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | | REDUCE: (30), (99) imply:
% 176.00/27.18  | | | |   (101)   ~ (all_52_7 = e3)
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | | BETA: splitting (36) gives:
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | | Case 1:
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | |   (102)  all_58_1 = e3
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | | COMBINE_EQS: (31), (102) imply:
% 176.00/27.18  | | | | |   (103)  all_52_3 = e3
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | | REDUCE: (100), (103) imply:
% 176.00/27.18  | | | | |   (104)  $false
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | | CLOSE: (104) is inconsistent.
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | Case 2:
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | |   (105)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | | BETA: splitting (105) gives:
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | | Case 1:
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | |   (106)  all_58_3 = e3
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | | COMBINE_EQS: (18), (106) imply:
% 176.00/27.18  | | | | | |   (107)  all_10_2 = e3
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | | REDUCE: (95), (107) imply:
% 176.00/27.18  | | | | | |   (108)  $false
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | | CLOSE: (108) is inconsistent.
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | Case 2:
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | |   (109)  all_58_7 = e3 | all_58_13 = e3
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | | BETA: splitting (109) gives:
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | | Case 1:
% 176.00/27.18  | | | | | | | 
% 176.00/27.18  | | | | | | |   (110)  all_58_7 = e3
% 176.00/27.18  | | | | | | | 
% 176.00/27.18  | | | | | | | REF_CLOSE: (2), (4), (6), (11), (12), (14), (15), (16), (17),
% 176.00/27.18  | | | | | | |            (20), (22), (25), (27), (28), (29), (33), (34), (35),
% 176.00/27.18  | | | | | | |            (37), (39), (40), (42), (47), (50), (51), (52), (54),
% 176.00/27.18  | | | | | | |            (57), (59), (64), (65), (66), (67), (69), (71), (72),
% 176.00/27.18  | | | | | | |            (73), (74), (76), (77), (79), (81), (82), (83), (86),
% 176.00/27.18  | | | | | | |            (87), (90), (93), (98), (101), (110) are inconsistent
% 176.00/27.18  | | | | | | |            by sub-proof #173.
% 176.00/27.18  | | | | | | | 
% 176.00/27.18  | | | | | | Case 2:
% 176.00/27.18  | | | | | | | 
% 176.00/27.18  | | | | | | |   (111)  all_58_13 = e3
% 176.00/27.18  | | | | | | | 
% 176.00/27.18  | | | | | | | REF_CLOSE: (9), (53), (111) are inconsistent by sub-proof #1026.
% 176.00/27.18  | | | | | | | 
% 176.00/27.18  | | | | | | End of split
% 176.00/27.18  | | | | | | 
% 176.00/27.18  | | | | | End of split
% 176.00/27.18  | | | | | 
% 176.00/27.18  | | | | End of split
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | Case 2:
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | |   (112)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | | REF_CLOSE: (1), (3), (5), (7), (8), (12), (13), (15), (16), (19), (20),
% 176.00/27.18  | | | |            (21), (22), (23), (24), (25), (26), (28), (30), (31), (32),
% 176.00/27.18  | | | |            (38), (41), (44), (45), (46), (47), (48), (49), (53), (54),
% 176.00/27.18  | | | |            (55), (56), (58), (59), (60), (61), (63), (66), (68), (70),
% 176.00/27.18  | | | |            (71), (72), (73), (74), (76), (77), (78), (79), (80), (82),
% 176.00/27.18  | | | |            (83), (87), (93), (112) are inconsistent by sub-proof #172.
% 176.00/27.18  | | | | 
% 176.00/27.18  | | | End of split
% 176.00/27.18  | | | 
% 176.00/27.18  | | Case 2:
% 176.00/27.18  | | | 
% 176.00/27.18  | | |   (113)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.18  | | | 
% 176.00/27.18  | | | REF_CLOSE: (10), (20), (43), (59), (113) are inconsistent by sub-proof
% 176.00/27.18  | | |            #1016.
% 176.00/27.18  | | | 
% 176.00/27.18  | | End of split
% 176.00/27.18  | | 
% 176.00/27.18  | End of split
% 176.00/27.18  | 
% 176.00/27.18  End of proof
% 176.00/27.18  
% 176.00/27.18  Sub-proof #172 shows that the following formulas are inconsistent:
% 176.00/27.18  ----------------------------------------------------------------
% 176.00/27.18    (1)   ~ (all_52_27 = all_10_2)
% 176.00/27.18    (2)  op(e2, all_52_3) = e2
% 176.00/27.18    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.18    (4)  op(e3, e2) = all_52_3
% 176.00/27.18    (5)  op(e1, e2) = all_52_19
% 176.00/27.18    (6)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.18    (7)   ~ (all_52_3 = all_10_2)
% 176.00/27.18    (8)   ~ (all_6_2 = e0)
% 176.00/27.18    (9)  all_56_15 = all_6_2
% 176.00/27.18    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.18    (11)  all_58_15 = all_6_2
% 176.00/27.18    (12)   ~ (all_52_9 = all_4_2)
% 176.00/27.18    (13)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.18    (14)   ~ (all_52_5 = all_52_7)
% 176.00/27.18    (15)  all_58_10 = all_52_15
% 176.00/27.18    (16)  all_8_2 = all_6_2
% 176.00/27.18    (17)   ~ (all_52_5 = all_4_2)
% 176.00/27.18    (18)  all_58_4 = all_52_5
% 176.00/27.18    (19)   ~ (all_52_7 = all_4_2)
% 176.00/27.18    (20)  all_58_1 = all_52_3
% 176.00/27.18    (21)  all_58_0 = all_4_2
% 176.00/27.18    (22)   ~ (all_52_3 = all_52_5)
% 176.00/27.18    (23)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.18    (24)   ~ (all_52_3 = all_4_2)
% 176.00/27.18    (25)  op(e3, all_4_2) = e3
% 176.00/27.18    (26)  op(e0, e3) = all_52_25
% 176.00/27.18    (27)  op(e0, all_6_2) = all_6_1
% 176.00/27.18    (28)   ~ (all_52_9 = all_10_2)
% 176.00/27.18    (29)   ~ (all_52_5 = e3)
% 176.00/27.18    (30)  all_58_13 = all_52_27
% 176.00/27.18    (31)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.18    (32)  all_56_5 = all_10_2
% 176.00/27.18    (33)   ~ (all_52_3 = all_52_7)
% 176.00/27.18    (34)  all_56_0 = all_4_2
% 176.00/27.18    (35)  all_58_11 = all_52_23
% 176.00/27.18    (36)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.18    (37)   ~ (all_52_7 = all_52_15)
% 176.00/27.18    (38)   ~ (all_52_19 = all_10_2)
% 176.00/27.18    (39)   ~ (all_52_9 = e3)
% 176.00/27.18    (40)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.18    (41)  op(e3, e1) = all_52_5
% 176.00/27.18    (42)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.00/27.18    (43)   ~ (all_52_25 = all_4_2)
% 176.00/27.18    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.18    (45)  op(e0, e1) = e3
% 176.00/27.18    (46)  all_8_1 = all_6_1
% 176.00/27.18    (47)   ~ (all_52_7 = all_6_2)
% 176.00/27.18    (48)  all_58_14 = e3
% 176.00/27.18    (49)  op(e1, all_52_5) = e1
% 176.00/27.18    (50)   ~ (all_52_7 = all_52_23)
% 176.00/27.18    (51)  op(e0, all_52_7) = e0
% 176.00/27.18    (52)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.18    (53)  all_58_9 = all_52_7
% 176.00/27.18    (54)  all_58_12 = all_52_25
% 176.00/27.18    (55)  op(e2, e3) = all_52_9
% 176.00/27.18  
% 176.00/27.18  Begin of proof
% 176.00/27.18  | 
% 176.00/27.18  | BETA: splitting (40) gives:
% 176.00/27.18  | 
% 176.00/27.18  | Case 1:
% 176.00/27.18  | | 
% 176.00/27.18  | |   (56)  all_58_1 = e3
% 176.00/27.18  | | 
% 176.00/27.18  | | COMBINE_EQS: (20), (56) imply:
% 176.00/27.18  | |   (57)  all_52_3 = e3
% 176.00/27.18  | | 
% 176.00/27.18  | | REDUCE: (22), (57) imply:
% 176.00/27.18  | |   (58)   ~ (all_52_5 = e3)
% 176.00/27.18  | | 
% 176.00/27.18  | | REDUCE: (7), (57) imply:
% 176.00/27.18  | |   (59)   ~ (all_10_2 = e3)
% 176.00/27.18  | | 
% 176.00/27.18  | | SIMP: (59) implies:
% 176.00/27.18  | |   (60)   ~ (all_10_2 = e3)
% 176.00/27.18  | | 
% 176.00/27.18  | | REDUCE: (24), (57) imply:
% 176.00/27.18  | |   (61)   ~ (all_4_2 = e3)
% 176.00/27.18  | | 
% 176.00/27.18  | | SIMP: (61) implies:
% 176.00/27.18  | |   (62)   ~ (all_4_2 = e3)
% 176.00/27.18  | | 
% 176.00/27.18  | | REDUCE: (2), (57) imply:
% 176.00/27.18  | |   (63)  op(e2, e3) = e2
% 176.00/27.18  | | 
% 176.00/27.18  | | GROUND_INST: instantiating (44) with all_52_9, e2, e3, e2, simplifying with
% 176.00/27.18  | |              (55), (63) gives:
% 176.00/27.18  | |   (64)  all_52_9 = e2
% 176.00/27.18  | | 
% 176.00/27.18  | | REDUCE: (28), (64) imply:
% 176.00/27.18  | |   (65)   ~ (all_10_2 = e2)
% 176.00/27.18  | | 
% 176.00/27.18  | | SIMP: (65) implies:
% 176.00/27.18  | |   (66)   ~ (all_10_2 = e2)
% 176.00/27.18  | | 
% 176.00/27.18  | | REDUCE: (12), (64) imply:
% 176.00/27.18  | |   (67)   ~ (all_4_2 = e2)
% 176.00/27.18  | | 
% 176.00/27.18  | | SIMP: (67) implies:
% 176.00/27.18  | |   (68)   ~ (all_4_2 = e2)
% 176.00/27.18  | | 
% 176.00/27.18  | | REDUCE: (39), (64) imply:
% 176.00/27.18  | |   (69)   ~ (e3 = e2)
% 176.00/27.18  | | 
% 176.00/27.18  | | SIMP: (69) implies:
% 176.00/27.18  | |   (70)   ~ (e3 = e2)
% 176.00/27.18  | | 
% 176.00/27.18  | | BETA: splitting (42) gives:
% 176.00/27.18  | | 
% 176.00/27.18  | | Case 1:
% 176.00/27.18  | | | 
% 176.00/27.18  | | |   (71)  all_56_5 = e3
% 176.00/27.18  | | | 
% 176.00/27.18  | | | REF_CLOSE: (32), (60), (71) are inconsistent by sub-proof #895.
% 176.00/27.18  | | | 
% 176.00/27.18  | | Case 2:
% 176.00/27.18  | | | 
% 176.00/27.19  | | |   (72)   ~ (all_56_5 = e3)
% 176.00/27.19  | | |   (73)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (13), (16), (17), (18),
% 176.00/27.19  | | |            (21), (23), (25), (27), (29), (30), (31), (32), (34), (36),
% 176.00/27.19  | | |            (38), (41), (43), (44), (45), (46), (47), (48), (49), (53),
% 176.00/27.19  | | |            (54), (56), (60), (62), (66), (68), (70), (73) are inconsistent
% 176.00/27.19  | | |            by sub-proof #223.
% 176.00/27.19  | | | 
% 176.00/27.19  | | End of split
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (74)  all_58_4 = e3 | all_58_9 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (4), (10), (11), (14), (15), (18), (19), (21), (25), (26), (29),
% 176.00/27.19  | |            (31), (33), (34), (35), (37), (41), (43), (44), (47), (50), (51),
% 176.00/27.19  | |            (52), (53), (74) are inconsistent by sub-proof #871.
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #173 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)   ~ (all_52_23 = all_52_28)
% 176.00/27.19    (2)  all_58_6 = all_52_28
% 176.00/27.19    (3)  all_56_3 = all_52_7
% 176.00/27.19    (4)  op(e3, all_52_9) = all_52_8
% 176.00/27.19    (5)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.19    (6)  all_58_5 = all_52_13
% 176.00/27.19    (7)   ~ (all_6_2 = e0)
% 176.00/27.19    (8)  all_56_15 = all_6_2
% 176.00/27.19    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.00/27.19    (10)  all_58_15 = all_6_2
% 176.00/27.19    (11)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.19    (12)  all_8_2 = all_6_2
% 176.00/27.19    (13)  all_58_7 = all_52_19
% 176.00/27.19    (14)  all_58_4 = all_52_5
% 176.00/27.19    (15)   ~ (e3 = e1)
% 176.00/27.19    (16)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.19    (17)  op(e0, e0) = all_6_2
% 176.00/27.19    (18)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.19    (19)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.00/27.19    (20)  all_58_7 = e3
% 176.00/27.19    (21)  all_58_8 = all_14_2
% 176.00/27.19    (22)  op(e1, all_14_2) = e3
% 176.00/27.19    (23)   ~ (all_52_5 = all_14_2)
% 176.00/27.19    (24)  op(e0, all_6_2) = all_6_1
% 176.00/27.19    (25)   ~ (e3 = e0)
% 176.00/27.19    (26)   ~ (all_52_9 = all_52_13)
% 176.00/27.19    (27)   ~ (all_52_19 = all_52_28)
% 176.00/27.19    (28)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.19    (29)  all_58_10 = e3
% 176.00/27.19    (30)  op(e2, all_52_19) = all_52_18
% 176.00/27.19    (31)  all_58_11 = all_52_23
% 176.00/27.19    (32)   ~ (all_52_9 = e3)
% 176.00/27.19    (33)  all_58_2 = all_52_9
% 176.00/27.19    (34)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.00/27.19    (35)  op(e3, e1) = all_52_5
% 176.00/27.19    (36)   ~ (all_52_25 = all_6_2)
% 176.00/27.19    (37)  op(e1, e1) = all_14_2
% 176.00/27.19    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (39)  op(e0, e1) = e3
% 176.00/27.19    (40)  all_8_1 = all_6_1
% 176.00/27.19    (41)   ~ (all_52_7 = all_6_2)
% 176.00/27.19    (42)  all_58_14 = e3
% 176.00/27.19    (43)   ~ (all_52_7 = e3)
% 176.00/27.19    (44)  op(e1, all_52_5) = e1
% 176.00/27.19    (45)  op(e0, all_52_7) = e0
% 176.00/27.19    (46)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.19    (47)  all_58_9 = all_52_7
% 176.00/27.19    (48)  all_58_12 = all_52_25
% 176.00/27.19    (49)  all_58_0 = e3
% 176.00/27.19    (50)   ~ (all_52_19 = all_14_2)
% 176.00/27.19    (51)  op(e2, e3) = all_52_9
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | COMBINE_EQS: (13), (20) imply:
% 176.00/27.19  |   (52)  all_52_19 = e3
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (27), (52) imply:
% 176.00/27.19  |   (53)   ~ (all_52_28 = e3)
% 176.00/27.19  | 
% 176.00/27.19  | SIMP: (53) implies:
% 176.00/27.19  |   (54)   ~ (all_52_28 = e3)
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (50), (52) imply:
% 176.00/27.19  |   (55)   ~ (all_14_2 = e3)
% 176.00/27.19  | 
% 176.00/27.19  | SIMP: (55) implies:
% 176.00/27.19  |   (56)   ~ (all_14_2 = e3)
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (30), (52) imply:
% 176.00/27.19  |   (57)  op(e2, e3) = all_52_18
% 176.00/27.19  | 
% 176.00/27.19  | GROUND_INST: instantiating (38) with all_52_9, all_52_18, e3, e2, simplifying
% 176.00/27.19  |              with (51), (57) gives:
% 176.00/27.19  |   (58)  all_52_9 = all_52_18
% 176.00/27.19  | 
% 176.00/27.19  | COMBINE_EQS: (33), (58) imply:
% 176.00/27.19  |   (59)  all_58_2 = all_52_18
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (26), (58) imply:
% 176.00/27.19  |   (60)   ~ (all_52_13 = all_52_18)
% 176.00/27.19  | 
% 176.00/27.19  | SIMP: (60) implies:
% 176.00/27.19  |   (61)   ~ (all_52_13 = all_52_18)
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (32), (58) imply:
% 176.00/27.19  |   (62)   ~ (all_52_18 = e3)
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (4), (58) imply:
% 176.00/27.19  |   (63)  op(e3, all_52_18) = all_52_8
% 176.00/27.19  | 
% 176.00/27.19  | BETA: splitting (9) gives:
% 176.00/27.19  | 
% 176.00/27.19  | Case 1:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (64)  all_58_9 = e1
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (25), (38), (39), (45), (47), (64) are inconsistent by sub-proof
% 176.00/27.19  | |            #794.
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (65)   ~ (all_58_9 = e1)
% 176.00/27.19  | |   (66)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.00/27.19  | | 
% 176.00/27.19  | | REDUCE: (47), (65) imply:
% 176.00/27.19  | |   (67)   ~ (all_52_7 = e1)
% 176.00/27.19  | | 
% 176.00/27.19  | | BETA: splitting (28) gives:
% 176.00/27.19  | | 
% 176.00/27.19  | | Case 1:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (68)  all_58_0 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | COMBINE_EQS: (49), (68) imply:
% 176.00/27.19  | | |   (69)  e3 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REDUCE: (15), (69) imply:
% 176.00/27.19  | | |   (70)  $false
% 176.00/27.19  | | | 
% 176.00/27.19  | | | CLOSE: (70) is inconsistent.
% 176.00/27.19  | | | 
% 176.00/27.19  | | Case 2:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (71)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | BETA: splitting (34) gives:
% 176.00/27.19  | | | 
% 176.00/27.19  | | | Case 1:
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | |   (72)  all_58_12 = e1
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | COMBINE_EQS: (48), (72) imply:
% 176.00/27.19  | | | |   (73)  all_52_25 = e1
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | SIMP: (73) implies:
% 176.00/27.19  | | | |   (74)  all_52_25 = e1
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | REDUCE: (36), (74) imply:
% 176.00/27.19  | | | |   (75)   ~ (all_6_2 = e1)
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | SIMP: (75) implies:
% 176.00/27.19  | | | |   (76)   ~ (all_6_2 = e1)
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | REF_CLOSE: (3), (7), (8), (11), (16), (17), (38), (41), (43), (45),
% 176.00/27.19  | | | |            (46), (47), (67), (76) are inconsistent by sub-proof #178.
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | Case 2:
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | |   (77)   ~ (all_58_12 = e1)
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | REDUCE: (48), (77) imply:
% 176.00/27.19  | | | |   (78)   ~ (all_52_25 = e1)
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | BETA: splitting (19) gives:
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | | Case 1:
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | |   (79)  all_58_2 = e1
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | COMBINE_EQS: (59), (79) imply:
% 176.00/27.19  | | | | |   (80)  all_52_18 = e1
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | SIMP: (80) implies:
% 176.00/27.19  | | | | |   (81)  all_52_18 = e1
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | REDUCE: (61), (81) imply:
% 176.00/27.19  | | | | |   (82)   ~ (all_52_13 = e1)
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | REDUCE: (62), (81) imply:
% 176.00/27.19  | | | | |   (83)   ~ (e3 = e1)
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | REDUCE: (63), (81) imply:
% 176.00/27.19  | | | | |   (84)  op(e3, e1) = all_52_8
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | GROUND_INST: instantiating (38) with all_52_5, all_52_8, e1, e3,
% 176.00/27.19  | | | | |              simplifying with (35), (84) gives:
% 176.00/27.19  | | | | |   (85)  all_52_5 = all_52_8
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | REF_CLOSE: (6), (14), (15), (18), (21), (22), (23), (37), (38), (42),
% 176.00/27.19  | | | | |            (44), (56), (82), (85) are inconsistent by sub-proof #176.
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | Case 2:
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | |   (86)   ~ (all_58_2 = e1)
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | REDUCE: (59), (86) imply:
% 176.00/27.19  | | | | |   (87)   ~ (all_52_18 = e1)
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | BETA: splitting (71) gives:
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | | Case 1:
% 176.00/27.19  | | | | | | 
% 176.00/27.19  | | | | | |   (88)  all_58_2 = e1
% 176.00/27.19  | | | | | | 
% 176.00/27.19  | | | | | | REF_CLOSE: (59), (87), (88) are inconsistent by sub-proof #175.
% 176.00/27.19  | | | | | | 
% 176.00/27.19  | | | | | Case 2:
% 176.00/27.19  | | | | | | 
% 176.00/27.19  | | | | | |   (89)  all_58_6 = e1 | all_58_12 = e1
% 176.00/27.19  | | | | | | 
% 176.00/27.19  | | | | | | BETA: splitting (89) gives:
% 176.00/27.19  | | | | | | 
% 176.00/27.19  | | | | | | Case 1:
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | |   (90)  all_58_6 = e1
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | | COMBINE_EQS: (2), (90) imply:
% 176.00/27.19  | | | | | | |   (91)  all_52_28 = e1
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | | SIMP: (91) implies:
% 176.00/27.19  | | | | | | |   (92)  all_52_28 = e1
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | | REDUCE: (1), (92) imply:
% 176.00/27.19  | | | | | | |   (93)   ~ (all_52_23 = e1)
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | | REDUCE: (54), (92) imply:
% 176.00/27.19  | | | | | | |   (94)   ~ (e3 = e1)
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | | REF_CLOSE: (5), (10), (12), (15), (24), (29), (31), (38), (39),
% 176.00/27.19  | | | | | | |            (40), (66), (93) are inconsistent by sub-proof #174.
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | Case 2:
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | |   (95)  all_58_12 = e1
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | | REF_CLOSE: (48), (78), (95) are inconsistent by sub-proof #883.
% 176.00/27.19  | | | | | | | 
% 176.00/27.19  | | | | | | End of split
% 176.00/27.19  | | | | | | 
% 176.00/27.19  | | | | | End of split
% 176.00/27.19  | | | | | 
% 176.00/27.19  | | | | End of split
% 176.00/27.19  | | | | 
% 176.00/27.19  | | | End of split
% 176.00/27.19  | | | 
% 176.00/27.19  | | End of split
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #174 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.19    (2)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.00/27.19    (3)  all_58_15 = all_6_2
% 176.00/27.19    (4)  all_8_2 = all_6_2
% 176.00/27.19    (5)   ~ (e3 = e1)
% 176.00/27.19    (6)  op(e0, all_6_2) = all_6_1
% 176.00/27.19    (7)   ~ (all_52_23 = e1)
% 176.00/27.19    (8)  all_58_10 = e3
% 176.00/27.19    (9)  all_58_11 = all_52_23
% 176.00/27.19    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (11)  op(e0, e1) = e3
% 176.00/27.19    (12)  all_8_1 = all_6_1
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | BETA: splitting (2) gives:
% 176.00/27.19  | 
% 176.00/27.19  | Case 1:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (13)  all_58_10 = e1
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #937.
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (14)  all_58_11 = e1 | all_58_15 = e1
% 176.00/27.19  | | 
% 176.00/27.19  | | BETA: splitting (14) gives:
% 176.00/27.19  | | 
% 176.00/27.19  | | Case 1:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (15)  all_58_11 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REF_CLOSE: (7), (9), (15) are inconsistent by sub-proof #974.
% 176.00/27.19  | | | 
% 176.00/27.19  | | Case 2:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (16)  all_58_15 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | COMBINE_EQS: (3), (16) imply:
% 176.00/27.19  | | |   (17)  all_6_2 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | COMBINE_EQS: (4), (17) imply:
% 176.00/27.19  | | |   (18)  all_8_2 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REDUCE: (6), (17) imply:
% 176.00/27.19  | | |   (19)  op(e0, e1) = all_6_1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REF_CLOSE: (1), (10), (11), (12), (18), (19) are inconsistent by sub-proof
% 176.00/27.19  | | |            #225.
% 176.00/27.19  | | | 
% 176.00/27.19  | | End of split
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #175 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)  all_58_2 = all_52_18
% 176.00/27.19    (2)  all_58_2 = e1
% 176.00/27.19    (3)   ~ (all_52_18 = e1)
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | COMBINE_EQS: (1), (2) imply:
% 176.00/27.19  |   (4)  all_52_18 = e1
% 176.00/27.19  | 
% 176.00/27.19  | SIMP: (4) implies:
% 176.00/27.19  |   (5)  all_52_18 = e1
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (3), (5) imply:
% 176.00/27.19  |   (6)  $false
% 176.00/27.19  | 
% 176.00/27.19  | CLOSE: (6) is inconsistent.
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #176 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)   ~ (all_52_13 = e1)
% 176.00/27.19    (2)  all_58_5 = all_52_13
% 176.00/27.19    (3)  all_58_4 = all_52_5
% 176.00/27.19    (4)   ~ (e3 = e1)
% 176.00/27.19    (5)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.19    (6)  all_58_8 = all_14_2
% 176.00/27.19    (7)  op(e1, all_14_2) = e3
% 176.00/27.19    (8)   ~ (all_52_5 = all_14_2)
% 176.00/27.19    (9)  all_52_5 = all_52_8
% 176.00/27.19    (10)  op(e1, e1) = all_14_2
% 176.00/27.19    (11)   ~ (all_14_2 = e3)
% 176.00/27.19    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (13)  all_58_14 = e3
% 176.00/27.19    (14)  op(e1, all_52_5) = e1
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | COMBINE_EQS: (3), (9) imply:
% 176.00/27.19  |   (15)  all_58_4 = all_52_8
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (8), (9) imply:
% 176.00/27.19  |   (16)   ~ (all_52_8 = all_14_2)
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (9), (14) imply:
% 176.00/27.19  |   (17)  op(e1, all_52_8) = e1
% 176.00/27.19  | 
% 176.00/27.19  | BETA: splitting (5) gives:
% 176.00/27.19  | 
% 176.00/27.19  | Case 1:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (18)  all_58_4 = e1
% 176.00/27.19  | | 
% 176.00/27.19  | | COMBINE_EQS: (15), (18) imply:
% 176.00/27.19  | |   (19)  all_52_8 = e1
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (10), (12), (16), (17), (19) are inconsistent by sub-proof #177.
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (20)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.19  | | 
% 176.00/27.19  | | BETA: splitting (20) gives:
% 176.00/27.19  | | 
% 176.00/27.19  | | Case 1:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (21)  all_58_5 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | COMBINE_EQS: (2), (21) imply:
% 176.00/27.19  | | |   (22)  all_52_13 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REDUCE: (1), (22) imply:
% 176.00/27.19  | | |   (23)  $false
% 176.00/27.19  | | | 
% 176.00/27.19  | | | CLOSE: (23) is inconsistent.
% 176.00/27.19  | | | 
% 176.00/27.19  | | Case 2:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (24)  all_58_8 = e1 | all_58_14 = e1
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REF_CLOSE: (4), (6), (7), (10), (11), (12), (13), (24) are inconsistent by
% 176.00/27.19  | | |            sub-proof #423.
% 176.00/27.19  | | | 
% 176.00/27.19  | | End of split
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #177 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)  all_52_8 = e1
% 176.00/27.19    (2)  op(e1, all_52_8) = e1
% 176.00/27.19    (3)  op(e1, e1) = all_14_2
% 176.00/27.19    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (5)   ~ (all_52_8 = all_14_2)
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (1), (5) imply:
% 176.00/27.19  |   (6)   ~ (all_14_2 = e1)
% 176.00/27.19  | 
% 176.00/27.19  | SIMP: (6) implies:
% 176.00/27.19  |   (7)   ~ (all_14_2 = e1)
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (1), (2) imply:
% 176.00/27.19  |   (8)  op(e1, e1) = e1
% 176.00/27.19  | 
% 176.00/27.19  | REF_CLOSE: (3), (4), (7), (8) are inconsistent by sub-proof #860.
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #178 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)  all_56_3 = all_52_7
% 176.00/27.19    (2)   ~ (all_6_2 = e0)
% 176.00/27.19    (3)  all_56_15 = all_6_2
% 176.00/27.19    (4)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.19    (5)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.19    (6)  op(e0, e0) = all_6_2
% 176.00/27.19    (7)   ~ (all_52_7 = e1)
% 176.00/27.19    (8)   ~ (all_6_2 = e1)
% 176.00/27.19    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (10)   ~ (all_52_7 = all_6_2)
% 176.00/27.19    (11)   ~ (all_52_7 = e3)
% 176.00/27.19    (12)  op(e0, all_52_7) = e0
% 176.00/27.19    (13)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.19    (14)  all_58_9 = all_52_7
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | BETA: splitting (4) gives:
% 176.00/27.19  | 
% 176.00/27.19  | Case 1:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (15)  all_56_15 = e2
% 176.00/27.19  | | 
% 176.00/27.19  | | COMBINE_EQS: (3), (15) imply:
% 176.00/27.19  | |   (16)  all_6_2 = e2
% 176.00/27.19  | | 
% 176.00/27.19  | | REDUCE: (10), (16) imply:
% 176.00/27.19  | |   (17)   ~ (all_52_7 = e2)
% 176.00/27.19  | | 
% 176.00/27.19  | | REDUCE: (6), (16) imply:
% 176.00/27.19  | |   (18)  op(e0, e0) = e2
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (1), (5), (7), (9), (11), (12), (13), (14), (17), (18) are
% 176.00/27.19  | |            inconsistent by sub-proof #179.
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (19)  all_56_15 = e1 | all_56_15 = e0
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (2), (3), (8), (19) are inconsistent by sub-proof #653.
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #179 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)  all_56_3 = all_52_7
% 176.00/27.19    (2)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.19    (3)   ~ (all_52_7 = e1)
% 176.00/27.19    (4)  op(e0, e0) = e2
% 176.00/27.19    (5)   ~ (all_52_7 = e2)
% 176.00/27.19    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (7)   ~ (all_52_7 = e3)
% 176.00/27.19    (8)  op(e0, all_52_7) = e0
% 176.00/27.19    (9)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.19    (10)  all_58_9 = all_52_7
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | BETA: splitting (9) gives:
% 176.00/27.19  | 
% 176.00/27.19  | Case 1:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (11)  all_56_3 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #1034.
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (12)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.19  | | 
% 176.00/27.19  | | BETA: splitting (2) gives:
% 176.00/27.19  | | 
% 176.00/27.19  | | Case 1:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (13)  all_58_9 = e0
% 176.00/27.19  | | | 
% 176.00/27.19  | | | COMBINE_EQS: (10), (13) imply:
% 176.00/27.19  | | |   (14)  all_52_7 = e0
% 176.00/27.19  | | | 
% 176.00/27.19  | | | SIMP: (14) implies:
% 176.00/27.19  | | |   (15)  all_52_7 = e0
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REDUCE: (5), (15) imply:
% 176.00/27.19  | | |   (16)   ~ (e2 = e0)
% 176.00/27.19  | | | 
% 176.00/27.19  | | | SIMP: (16) implies:
% 176.00/27.19  | | |   (17)   ~ (e2 = e0)
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REDUCE: (8), (15) imply:
% 176.00/27.19  | | |   (18)  op(e0, e0) = e0
% 176.00/27.19  | | | 
% 176.00/27.19  | | | GROUND_INST: instantiating (6) with e0, e2, e0, e0, simplifying with (4),
% 176.00/27.19  | | |              (18) gives:
% 176.00/27.19  | | |   (19)  e2 = e0
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REDUCE: (17), (19) imply:
% 176.00/27.19  | | |   (20)  $false
% 176.00/27.19  | | | 
% 176.00/27.19  | | | CLOSE: (20) is inconsistent.
% 176.00/27.19  | | | 
% 176.00/27.19  | | Case 2:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (21)   ~ (all_58_9 = e0)
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REDUCE: (10), (21) imply:
% 176.00/27.19  | | |   (22)   ~ (all_52_7 = e0)
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REF_CLOSE: (1), (3), (5), (12), (22) are inconsistent by sub-proof #893.
% 176.00/27.19  | | | 
% 176.00/27.19  | | End of split
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #180 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)  op(e2, all_52_3) = e2
% 176.00/27.19    (2)   ~ (all_52_3 = all_10_2)
% 176.00/27.19    (3)  all_58_5 = all_52_13
% 176.00/27.19    (4)  all_58_3 = all_10_2
% 176.00/27.19    (5)  all_58_10 = all_52_15
% 176.00/27.19    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.19    (7)  all_58_1 = all_52_3
% 176.00/27.19    (8)   ~ (all_52_13 = e3)
% 176.00/27.19    (9)   ~ (all_52_15 = e3)
% 176.00/27.19    (10)  all_58_1 = e3
% 176.00/27.19    (11)  all_58_2 = all_52_9
% 176.00/27.19    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (13)   ~ (e3 = e2)
% 176.00/27.19    (14)  op(e2, e3) = all_52_9
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | COMBINE_EQS: (7), (10) imply:
% 176.00/27.19  |   (15)  all_52_3 = e3
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (2), (15) imply:
% 176.00/27.19  |   (16)   ~ (all_10_2 = e3)
% 176.00/27.19  | 
% 176.00/27.19  | SIMP: (16) implies:
% 176.00/27.19  |   (17)   ~ (all_10_2 = e3)
% 176.00/27.19  | 
% 176.00/27.19  | REDUCE: (1), (15) imply:
% 176.00/27.19  |   (18)  op(e2, e3) = e2
% 176.00/27.19  | 
% 176.00/27.19  | REF_CLOSE: (3), (4), (5), (6), (8), (9), (11), (12), (13), (14), (17), (18)
% 176.00/27.19  |            are inconsistent by sub-proof #181.
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #181 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)  op(e2, e3) = e2
% 176.00/27.19    (2)  all_58_5 = all_52_13
% 176.00/27.19    (3)  all_58_3 = all_10_2
% 176.00/27.19    (4)  all_58_10 = all_52_15
% 176.00/27.19    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.19    (6)   ~ (all_10_2 = e3)
% 176.00/27.19    (7)   ~ (all_52_13 = e3)
% 176.00/27.19    (8)   ~ (all_52_15 = e3)
% 176.00/27.19    (9)  all_58_2 = all_52_9
% 176.00/27.19    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.19    (11)   ~ (e3 = e2)
% 176.00/27.19    (12)  op(e2, e3) = all_52_9
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | BETA: splitting (5) gives:
% 176.00/27.19  | 
% 176.00/27.19  | Case 1:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (13)  all_58_2 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | COMBINE_EQS: (9), (13) imply:
% 176.00/27.19  | |   (14)  all_52_9 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | SIMP: (14) implies:
% 176.00/27.19  | |   (15)  all_52_9 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | REDUCE: (12), (15) imply:
% 176.00/27.19  | |   (16)  op(e2, e3) = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | GROUND_INST: instantiating (10) with e2, e3, e3, e2, simplifying with (1),
% 176.00/27.19  | |              (16) gives:
% 176.00/27.19  | |   (17)  e3 = e2
% 176.00/27.19  | | 
% 176.00/27.19  | | REDUCE: (11), (17) imply:
% 176.00/27.19  | |   (18)  $false
% 176.00/27.19  | | 
% 176.00/27.19  | | CLOSE: (18) is inconsistent.
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (19)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (19) are inconsistent by sub-proof
% 176.00/27.19  | |            #182.
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #182 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)  all_58_5 = all_52_13
% 176.00/27.19    (2)  all_58_3 = all_10_2
% 176.00/27.19    (3)  all_58_10 = all_52_15
% 176.00/27.19    (4)   ~ (all_10_2 = e3)
% 176.00/27.19    (5)   ~ (all_52_13 = e3)
% 176.00/27.19    (6)   ~ (all_52_15 = e3)
% 176.00/27.19    (7)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.19  
% 176.00/27.19  Begin of proof
% 176.00/27.19  | 
% 176.00/27.19  | BETA: splitting (7) gives:
% 176.00/27.19  | 
% 176.00/27.19  | Case 1:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (8)  all_58_3 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | COMBINE_EQS: (2), (8) imply:
% 176.00/27.19  | |   (9)  all_10_2 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | REDUCE: (4), (9) imply:
% 176.00/27.19  | |   (10)  $false
% 176.00/27.19  | | 
% 176.00/27.19  | | CLOSE: (10) is inconsistent.
% 176.00/27.19  | | 
% 176.00/27.19  | Case 2:
% 176.00/27.19  | | 
% 176.00/27.19  | |   (11)  all_58_5 = e3 | all_58_10 = e3
% 176.00/27.19  | | 
% 176.00/27.19  | | BETA: splitting (11) gives:
% 176.00/27.19  | | 
% 176.00/27.19  | | Case 1:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (12)  all_58_5 = e3
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #969.
% 176.00/27.19  | | | 
% 176.00/27.19  | | Case 2:
% 176.00/27.19  | | | 
% 176.00/27.19  | | |   (13)  all_58_10 = e3
% 176.00/27.19  | | | 
% 176.00/27.19  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #1018.
% 176.00/27.19  | | | 
% 176.00/27.19  | | End of split
% 176.00/27.19  | | 
% 176.00/27.19  | End of split
% 176.00/27.19  | 
% 176.00/27.19  End of proof
% 176.00/27.19  
% 176.00/27.19  Sub-proof #183 shows that the following formulas are inconsistent:
% 176.00/27.19  ----------------------------------------------------------------
% 176.00/27.19    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.19    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.19    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.00/27.19    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.19    (5)   ~ (all_52_17 = all_52_23)
% 176.00/27.19    (6)  all_56_3 = all_52_7
% 176.00/27.19    (7)  op(e3, e2) = all_52_3
% 176.00/27.19    (8)   ~ (all_52_9 = all_52_25)
% 176.00/27.19    (9)  op(e3, all_52_25) = all_52_24
% 176.00/27.19    (10)   ~ (all_52_19 = all_52_23)
% 176.00/27.19    (11)  op(e1, e2) = all_52_19
% 176.00/27.19    (12)  all_16_1 = all_6_1
% 176.00/27.19    (13)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 176.00/27.19    (14)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.19    (15)  all_50_1 = all_4_1
% 176.00/27.19    (16)  all_58_5 = all_52_13
% 176.00/27.19    (17)  all_16_2 = all_6_2
% 176.00/27.19    (18)  all_56_15 = all_6_2
% 176.00/27.19    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.19    (20)  op(all_14_1, all_14_2) = all_14_0
% 176.00/27.19    (21)  all_58_3 = all_10_2
% 176.00/27.19    (22)  all_56_9 = all_52_19
% 176.00/27.19    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.19    (24)  all_58_15 = all_6_2
% 176.00/27.19    (25)   ~ (all_52_9 = all_4_2)
% 176.00/27.19    (26)   ~ (all_52_5 = all_52_7)
% 176.00/27.19    (27)  all_58_10 = all_52_15
% 176.00/27.19    (28)  all_8_2 = all_6_2
% 176.00/27.19    (29)   ~ (all_52_5 = all_4_2)
% 176.00/27.19    (30)  all_58_7 = all_52_19
% 176.00/27.19    (31)   ~ (all_52_17 = all_52_25)
% 176.00/27.19    (32)  op(e0, e1) = all_52_29
% 176.00/27.19    (33)  all_58_4 = all_52_5
% 176.00/27.19    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.19    (35)   ~ (all_52_17 = all_14_2)
% 176.00/27.19    (36)  op(e3, all_4_2) = all_4_1
% 176.00/27.19    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.19    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.19    (39)   ~ (all_52_7 = all_4_2)
% 176.00/27.19    (40)  all_58_1 = all_52_3
% 176.00/27.19    (41)  all_58_0 = all_4_2
% 176.00/27.19    (42)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.19    (43)  op(e1, all_52_29) = all_52_28
% 176.00/27.19    (44)  all_50_2 = all_4_2
% 176.00/27.20    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.20    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.20    (47)   ~ (all_4_1 = e2)
% 176.00/27.20    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.20    (49)  all_58_14 = all_52_29
% 176.00/27.20    (50)   ~ (all_52_3 = all_52_5)
% 176.00/27.20    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.20    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.20    (53)  all_58_8 = all_14_2
% 176.00/27.20    (54)  all_56_1 = all_52_3
% 176.00/27.20    (55)   ~ (all_14_0 = e3)
% 176.00/27.20    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.20    (57)   ~ (all_52_5 = all_14_2)
% 176.00/27.20    (58)   ~ (all_52_3 = all_4_2)
% 176.00/27.20    (59)  op(e0, e3) = all_52_25
% 176.00/27.20    (60)  op(e0, all_6_2) = all_6_1
% 176.00/27.20    (61)  op(all_6_1, all_6_2) = e2
% 176.00/27.20    (62)  op(all_4_1, all_4_2) = e2
% 176.00/27.20    (63)  op(e3, all_52_17) = all_52_16
% 176.00/27.20    (64)   ~ (e3 = e0)
% 176.00/27.20    (65)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.20    (66)   ~ (all_52_9 = all_52_13)
% 176.00/27.20    (67)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.20    (68)  op(e0, all_52_23) = all_52_22
% 176.00/27.20    (69)   ~ (all_52_15 = all_52_23)
% 176.00/27.20    (70)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.20    (71)   ~ (all_52_5 = all_52_29)
% 176.00/27.20    (72)  op(e1, e0) = all_52_23
% 176.00/27.20    (73)  all_56_12 = all_52_25
% 176.00/27.20    (74)  all_58_13 = all_52_27
% 176.00/27.20    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.20    (76)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.00/27.20    (77)   ~ (all_52_9 = all_52_17)
% 176.00/27.20    (78)   ~ (all_14_0 = e2)
% 176.00/27.20    (79)  all_58_6 = all_52_17
% 176.00/27.20    (80)   ~ (all_52_3 = all_52_7)
% 176.00/27.20    (81)  op(e2, all_52_19) = all_52_18
% 176.00/27.20    (82)   ~ (e1 = e0)
% 176.00/27.20    (83)  all_56_0 = all_4_2
% 176.00/27.20    (84)  all_58_11 = all_52_23
% 176.00/27.20    (85)   ~ (all_52_3 = all_52_19)
% 176.00/27.20    (86)   ~ (all_52_7 = all_52_15)
% 176.00/27.20    (87)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.20    (88)  all_58_2 = all_52_9
% 176.00/27.20    (89)  op(e3, e1) = all_52_5
% 176.00/27.20    (90)  all_56_10 = all_14_2
% 176.00/27.20    (91)   ~ (all_52_25 = all_6_2)
% 176.00/27.20    (92)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.20    (93)  op(e1, e3) = all_52_17
% 176.00/27.20    (94)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.00/27.20    (95)   ~ (all_52_25 = all_4_2)
% 176.00/27.20    (96)  op(e3, e0) = all_52_7
% 176.00/27.20    (97)  op(e3, e3) = all_4_2
% 176.00/27.20    (98)  all_56_8 = all_52_17
% 176.00/27.20    (99)   ~ (all_52_17 = all_4_2)
% 176.00/27.20    (100)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.20             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.20    (101)   ~ (all_52_25 = all_52_27)
% 176.00/27.20    (102)  all_8_1 = all_6_1
% 176.00/27.20    (103)   ~ (all_52_7 = all_6_2)
% 176.00/27.20    (104)   ~ (all_52_15 = all_10_2)
% 176.00/27.20    (105)  all_56_7 = all_52_15
% 176.00/27.20    (106)   ~ (all_52_7 = all_52_23)
% 176.00/27.20    (107)  all_52_20 = all_14_1
% 176.00/27.20    (108)   ~ (all_52_17 = all_52_19)
% 176.00/27.20    (109)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.20    (110)  all_52_30 = all_6_1
% 176.00/27.20    (111)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.20    (112)  op(e1, all_14_2) = all_14_1
% 176.00/27.20    (113)  all_58_9 = all_52_7
% 176.00/27.20    (114)   ~ (e2 = e0)
% 176.00/27.20    (115)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.00/27.20           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.00/27.20    (116)  all_58_12 = all_52_25
% 176.00/27.20    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.20    (118)   ~ (all_52_9 = all_52_15)
% 176.00/27.20    (119)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.20    (120)   ~ (e3 = e2)
% 176.00/27.20    (121)   ~ (all_52_19 = all_14_2)
% 176.00/27.20    (122)  op(e2, e3) = all_52_9
% 176.00/27.20  
% 176.00/27.20  Begin of proof
% 176.00/27.20  | 
% 176.00/27.20  | BETA: splitting (115) gives:
% 176.00/27.20  | 
% 176.00/27.20  | Case 1:
% 176.00/27.20  | | 
% 176.00/27.20  | |   (123)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.00/27.20  | | 
% 176.00/27.20  | | ALPHA: (123) implies:
% 176.00/27.20  | |   (124)  all_52_22 = e0
% 176.00/27.20  | |   (125)  all_52_20 = e1
% 176.00/27.20  | |   (126)  all_52_18 = e2
% 176.00/27.20  | |   (127)  all_52_16 = e3
% 176.00/27.20  | | 
% 176.00/27.20  | | COMBINE_EQS: (107), (125) imply:
% 176.00/27.20  | |   (128)  all_14_1 = e1
% 176.00/27.20  | | 
% 176.00/27.20  | | REDUCE: (20), (128) imply:
% 176.00/27.20  | |   (129)  op(e1, all_14_2) = all_14_0
% 176.00/27.20  | | 
% 176.00/27.20  | | REDUCE: (63), (127) imply:
% 176.00/27.20  | |   (130)  op(e3, all_52_17) = e3
% 176.00/27.20  | | 
% 176.00/27.20  | | REDUCE: (81), (126) imply:
% 176.00/27.20  | |   (131)  op(e2, all_52_19) = e2
% 176.00/27.20  | | 
% 176.00/27.20  | | REDUCE: (112), (128) imply:
% 176.00/27.20  | |   (132)  op(e1, all_14_2) = e1
% 176.00/27.20  | | 
% 176.00/27.20  | | REDUCE: (68), (124) imply:
% 176.00/27.20  | |   (133)  op(e0, all_52_23) = e0
% 176.00/27.20  | | 
% 176.00/27.20  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.00/27.20  | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 176.00/27.20  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.00/27.20  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.00/27.20  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 176.00/27.20  | |            (58), (59), (60), (61), (62), (64), (65), (66), (67), (69), (70),
% 176.00/27.20  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (82),
% 176.00/27.20  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 176.00/27.20  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 176.00/27.20  | |            (104), (105), (106), (108), (109), (111), (113), (114), (116),
% 176.00/27.20  | |            (117), (118), (119), (120), (121), (122), (129), (130), (131),
% 176.00/27.20  | |            (132), (133) are inconsistent by sub-proof #184.
% 176.00/27.20  | | 
% 176.00/27.20  | Case 2:
% 176.00/27.20  | | 
% 176.00/27.20  | |   (134)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.00/27.20  | | 
% 176.00/27.20  | | REF_CLOSE: (60), (61), (100), (110), (114), (134) are inconsistent by
% 176.00/27.20  | |            sub-proof #200.
% 176.00/27.20  | | 
% 176.00/27.20  | End of split
% 176.00/27.20  | 
% 176.00/27.20  End of proof
% 176.00/27.20  
% 176.00/27.20  Sub-proof #184 shows that the following formulas are inconsistent:
% 176.00/27.20  ----------------------------------------------------------------
% 176.00/27.20    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.20    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.20    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.00/27.20    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.20    (5)   ~ (all_52_17 = all_52_23)
% 176.00/27.20    (6)  all_56_3 = all_52_7
% 176.00/27.20    (7)  op(e3, e2) = all_52_3
% 176.00/27.20    (8)   ~ (all_52_9 = all_52_25)
% 176.00/27.20    (9)  op(e3, all_52_25) = all_52_24
% 176.00/27.20    (10)   ~ (all_52_19 = all_52_23)
% 176.00/27.20    (11)  op(e1, e2) = all_52_19
% 176.00/27.20    (12)  all_16_1 = all_6_1
% 176.00/27.20    (13)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 176.00/27.20    (14)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.20    (15)  all_50_1 = all_4_1
% 176.00/27.20    (16)  all_58_5 = all_52_13
% 176.00/27.20    (17)  all_16_2 = all_6_2
% 176.00/27.20    (18)  all_56_15 = all_6_2
% 176.00/27.20    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.20    (20)  all_58_3 = all_10_2
% 176.00/27.20    (21)  all_56_9 = all_52_19
% 176.00/27.20    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.20    (23)  all_58_15 = all_6_2
% 176.00/27.20    (24)   ~ (all_52_9 = all_4_2)
% 176.00/27.20    (25)   ~ (all_52_5 = all_52_7)
% 176.00/27.20    (26)  all_58_10 = all_52_15
% 176.00/27.20    (27)  all_8_2 = all_6_2
% 176.00/27.20    (28)   ~ (all_52_5 = all_4_2)
% 176.00/27.20    (29)  all_58_7 = all_52_19
% 176.00/27.20    (30)   ~ (all_52_17 = all_52_25)
% 176.00/27.20    (31)  op(e0, e1) = all_52_29
% 176.00/27.20    (32)  all_58_4 = all_52_5
% 176.00/27.20    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.20    (34)   ~ (all_52_17 = all_14_2)
% 176.00/27.20    (35)  op(e3, all_4_2) = all_4_1
% 176.00/27.20    (36)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.20    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.20    (38)   ~ (all_52_7 = all_4_2)
% 176.00/27.20    (39)  all_58_1 = all_52_3
% 176.00/27.20    (40)  all_58_0 = all_4_2
% 176.00/27.20    (41)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.20    (42)  op(e1, all_52_29) = all_52_28
% 176.00/27.20    (43)  all_50_2 = all_4_2
% 176.00/27.20    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.20    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.20    (46)   ~ (all_4_1 = e2)
% 176.00/27.20    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.20    (48)  all_58_14 = all_52_29
% 176.00/27.20    (49)   ~ (all_52_3 = all_52_5)
% 176.00/27.20    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.20    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.20    (52)  all_58_8 = all_14_2
% 176.00/27.20    (53)  all_56_1 = all_52_3
% 176.00/27.20    (54)   ~ (all_14_0 = e3)
% 176.00/27.20    (55)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.20    (56)   ~ (all_52_5 = all_14_2)
% 176.00/27.20    (57)   ~ (all_52_3 = all_4_2)
% 176.00/27.20    (58)  op(e0, e3) = all_52_25
% 176.00/27.20    (59)  op(e0, all_6_2) = all_6_1
% 176.00/27.20    (60)  op(all_6_1, all_6_2) = e2
% 176.00/27.20    (61)  op(all_4_1, all_4_2) = e2
% 176.00/27.20    (62)  op(e1, all_14_2) = all_14_0
% 176.00/27.20    (63)   ~ (e3 = e0)
% 176.00/27.20    (64)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.20    (65)   ~ (all_52_9 = all_52_13)
% 176.00/27.20    (66)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.20    (67)   ~ (all_52_15 = all_52_23)
% 176.00/27.20    (68)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.20    (69)   ~ (all_52_5 = all_52_29)
% 176.00/27.20    (70)  op(e1, e0) = all_52_23
% 176.00/27.20    (71)  all_56_12 = all_52_25
% 176.00/27.20    (72)  all_58_13 = all_52_27
% 176.00/27.20    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.20    (74)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.00/27.20    (75)   ~ (all_52_9 = all_52_17)
% 176.00/27.20    (76)   ~ (all_14_0 = e2)
% 176.00/27.20    (77)  all_58_6 = all_52_17
% 176.00/27.20    (78)   ~ (all_52_3 = all_52_7)
% 176.00/27.20    (79)  op(e2, all_52_19) = e2
% 176.00/27.20    (80)  op(e3, all_52_17) = e3
% 176.00/27.20    (81)   ~ (e1 = e0)
% 176.00/27.20    (82)  all_56_0 = all_4_2
% 176.00/27.20    (83)  all_58_11 = all_52_23
% 176.00/27.20    (84)   ~ (all_52_3 = all_52_19)
% 176.00/27.20    (85)   ~ (all_52_7 = all_52_15)
% 176.00/27.20    (86)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.20    (87)  all_58_2 = all_52_9
% 176.00/27.20    (88)  op(e3, e1) = all_52_5
% 176.00/27.20    (89)  all_56_10 = all_14_2
% 176.00/27.20    (90)   ~ (all_52_25 = all_6_2)
% 176.00/27.20    (91)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.20    (92)  op(e1, e3) = all_52_17
% 176.00/27.20    (93)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.00/27.20    (94)   ~ (all_52_25 = all_4_2)
% 176.00/27.20    (95)  op(e3, e0) = all_52_7
% 176.00/27.20    (96)  op(e3, e3) = all_4_2
% 176.00/27.20    (97)  all_56_8 = all_52_17
% 176.00/27.20    (98)   ~ (all_52_17 = all_4_2)
% 176.00/27.20    (99)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.20    (100)   ~ (all_52_25 = all_52_27)
% 176.00/27.20    (101)  all_8_1 = all_6_1
% 176.00/27.20    (102)   ~ (all_52_7 = all_6_2)
% 176.00/27.20    (103)  op(e0, all_52_23) = e0
% 176.00/27.20    (104)   ~ (all_52_15 = all_10_2)
% 176.00/27.20    (105)  all_56_7 = all_52_15
% 176.00/27.20    (106)  op(e1, all_14_2) = e1
% 176.00/27.20    (107)   ~ (all_52_7 = all_52_23)
% 176.00/27.20    (108)   ~ (all_52_17 = all_52_19)
% 176.00/27.20    (109)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.20    (110)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.20    (111)  all_58_9 = all_52_7
% 176.00/27.20    (112)   ~ (e2 = e0)
% 176.00/27.20    (113)  all_58_12 = all_52_25
% 176.00/27.20    (114)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.20    (115)   ~ (all_52_9 = all_52_15)
% 176.00/27.20    (116)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.20    (117)   ~ (e3 = e2)
% 176.00/27.20    (118)   ~ (all_52_19 = all_14_2)
% 176.00/27.20    (119)  op(e2, e3) = all_52_9
% 176.00/27.20  
% 176.00/27.20  Begin of proof
% 176.00/27.20  | 
% 176.00/27.20  | GROUND_INST: instantiating (99) with e1, all_14_0, all_14_2, e1, simplifying
% 176.00/27.20  |              with (62), (106) gives:
% 176.00/27.20  |   (120)  all_14_0 = e1
% 176.00/27.20  | 
% 176.00/27.20  | REDUCE: (54), (120) imply:
% 176.00/27.20  |   (121)   ~ (e3 = e1)
% 176.00/27.20  | 
% 176.00/27.20  | SIMP: (121) implies:
% 176.00/27.20  |   (122)   ~ (e3 = e1)
% 176.00/27.20  | 
% 176.00/27.20  | REDUCE: (76), (120) imply:
% 176.00/27.20  |   (123)   ~ (e2 = e1)
% 176.00/27.20  | 
% 176.00/27.20  | SIMP: (123) implies:
% 176.00/27.20  |   (124)   ~ (e2 = e1)
% 176.00/27.20  | 
% 176.00/27.20  | BETA: splitting (36) gives:
% 176.00/27.20  | 
% 176.00/27.20  | Case 1:
% 176.00/27.20  | | 
% 176.00/27.20  | |   (125)  all_56_15 = e3
% 176.00/27.20  | | 
% 176.00/27.20  | | COMBINE_EQS: (18), (125) imply:
% 176.00/27.20  | |   (126)  all_6_2 = e3
% 176.00/27.20  | | 
% 176.00/27.20  | | SIMP: (126) implies:
% 176.00/27.20  | |   (127)  all_6_2 = e3
% 176.00/27.20  | | 
% 176.00/27.20  | | REF_CLOSE: (8), (12), (17), (58), (59), (60), (66), (71), (86), (90), (91),
% 176.00/27.20  | |            (99), (113), (119), (127) are inconsistent by sub-proof #226.
% 176.00/27.20  | | 
% 176.00/27.20  | Case 2:
% 176.00/27.20  | | 
% 176.00/27.20  | |   (128)   ~ (all_56_15 = e3)
% 176.00/27.20  | |   (129)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.20  | | 
% 176.00/27.20  | | REDUCE: (18), (128) imply:
% 176.00/27.20  | |   (130)   ~ (all_6_2 = e3)
% 176.00/27.20  | | 
% 176.00/27.20  | | BETA: splitting (51) gives:
% 176.00/27.20  | | 
% 176.00/27.20  | | Case 1:
% 176.00/27.20  | | | 
% 176.00/27.20  | | |   (131)  all_58_12 = e3
% 176.00/27.20  | | | 
% 176.00/27.20  | | | REF_CLOSE: (1), (3), (11), (13), (15), (20), (22), (23), (24), (25), (26),
% 176.00/27.20  | | |            (28), (29), (30), (32), (33), (35), (38), (39), (40), (41),
% 176.00/27.20  | | |            (43), (46), (47), (52), (55), (56), (58), (63), (64), (67),
% 176.00/27.20  | | |            (68), (72), (73), (74), (75), (77), (79), (80), (81), (82),
% 176.00/27.20  | | |            (83), (84), (85), (87), (88), (89), (90), (92), (93), (94),
% 176.00/27.20  | | |            (95), (98), (99), (100), (103), (104), (105), (106), (107),
% 176.00/27.20  | | |            (108), (109), (111), (112), (113), (114), (115), (116), (117),
% 176.00/27.20  | | |            (118), (119), (122), (124), (131) are inconsistent by sub-proof
% 176.00/27.20  | | |            #456.
% 176.00/27.20  | | | 
% 176.00/27.20  | | Case 2:
% 176.00/27.20  | | | 
% 176.00/27.20  | | |   (132)   ~ (all_58_12 = e3)
% 176.00/27.20  | | | 
% 176.00/27.20  | | | REDUCE: (113), (132) imply:
% 176.00/27.20  | | |   (133)   ~ (all_52_25 = e3)
% 176.00/27.20  | | | 
% 176.00/27.20  | | | BETA: splitting (93) gives:
% 176.00/27.20  | | | 
% 176.00/27.20  | | | Case 1:
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | |   (134)  all_56_7 = e3
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | | COMBINE_EQS: (105), (134) imply:
% 176.00/27.20  | | | |   (135)  all_52_15 = e3
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | | SIMP: (135) implies:
% 176.00/27.20  | | | |   (136)  all_52_15 = e3
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | | REDUCE: (115), (136) imply:
% 176.00/27.20  | | | |   (137)   ~ (all_52_9 = e3)
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | | REF_CLOSE: (35), (40), (46), (50), (61), (77), (80), (87), (96), (98),
% 176.00/27.20  | | | |            (99), (113), (133), (137) are inconsistent by sub-proof #476.
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | Case 2:
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | |   (138)   ~ (all_56_7 = e3)
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | | REDUCE: (105), (138) imply:
% 176.00/27.20  | | | |   (139)   ~ (all_52_15 = e3)
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | | BETA: splitting (109) gives:
% 176.00/27.20  | | | | 
% 176.00/27.20  | | | | Case 1:
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | |   (140)  all_58_9 = e3
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | COMBINE_EQS: (111), (140) imply:
% 176.00/27.20  | | | | |   (141)  all_52_7 = e3
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | REDUCE: (107), (141) imply:
% 176.00/27.20  | | | | |   (142)   ~ (all_52_23 = e3)
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | SIMP: (142) implies:
% 176.00/27.20  | | | | |   (143)   ~ (all_52_23 = e3)
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | REDUCE: (38), (141) imply:
% 176.00/27.20  | | | | |   (144)   ~ (all_4_2 = e3)
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | SIMP: (144) implies:
% 176.00/27.20  | | | | |   (145)   ~ (all_4_2 = e3)
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | REF_CLOSE: (21), (29), (33), (37), (40), (45), (50), (52), (56), (75),
% 176.00/27.20  | | | | |            (77), (79), (80), (83), (87), (88), (92), (96), (98), (99),
% 176.00/27.20  | | | | |            (106), (113), (117), (119), (133), (143), (145) are
% 176.00/27.20  | | | | |            inconsistent by sub-proof #944.
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | Case 2:
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | |   (146)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | BETA: splitting (146) gives:
% 176.00/27.20  | | | | | 
% 176.00/27.20  | | | | | Case 1:
% 176.00/27.20  | | | | | | 
% 176.00/27.20  | | | | | |   (147)  all_58_10 = e3
% 176.00/27.20  | | | | | | 
% 176.00/27.20  | | | | | | REF_CLOSE: (26), (139), (147) are inconsistent by sub-proof #1018.
% 176.00/27.20  | | | | | | 
% 176.00/27.20  | | | | | Case 2:
% 176.00/27.20  | | | | | | 
% 176.00/27.20  | | | | | |   (148)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.20  | | | | | | 
% 176.00/27.20  | | | | | | BETA: splitting (148) gives:
% 176.00/27.20  | | | | | | 
% 176.00/27.20  | | | | | | Case 1:
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | |   (149)  all_58_11 = e3
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | COMBINE_EQS: (83), (149) imply:
% 176.00/27.20  | | | | | | |   (150)  all_52_23 = e3
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | SIMP: (150) implies:
% 176.00/27.20  | | | | | | |   (151)  all_52_23 = e3
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (107), (151) imply:
% 176.00/27.20  | | | | | | |   (152)   ~ (all_52_7 = e3)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (5), (151) imply:
% 176.00/27.20  | | | | | | |   (153)   ~ (all_52_17 = e3)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (10), (151) imply:
% 176.00/27.20  | | | | | | |   (154)   ~ (all_52_19 = e3)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (1), (151) imply:
% 176.00/27.20  | | | | | | |   (155)   ~ (all_14_2 = e3)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | SIMP: (155) implies:
% 176.00/27.20  | | | | | | |   (156)   ~ (all_14_2 = e3)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (70), (151) imply:
% 176.00/27.20  | | | | | | |   (157)  op(e1, e0) = e3
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (103), (151) imply:
% 176.00/27.20  | | | | | | |   (158)  op(e0, e3) = e0
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | GROUND_INST: instantiating (99) with all_52_25, e0, e3, e0,
% 176.00/27.20  | | | | | | |              simplifying with (58), (158) gives:
% 176.00/27.20  | | | | | | |   (159)  all_52_25 = e0
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | COMBINE_EQS: (113), (159) imply:
% 176.00/27.20  | | | | | | |   (160)  all_58_12 = e0
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (30), (159) imply:
% 176.00/27.20  | | | | | | |   (161)   ~ (all_52_17 = e0)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (90), (159) imply:
% 176.00/27.20  | | | | | | |   (162)   ~ (all_6_2 = e0)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | SIMP: (162) implies:
% 176.00/27.20  | | | | | | |   (163)   ~ (all_6_2 = e0)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (94), (159) imply:
% 176.00/27.20  | | | | | | |   (164)   ~ (all_4_2 = e0)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | SIMP: (164) implies:
% 176.00/27.20  | | | | | | |   (165)   ~ (all_4_2 = e0)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (9), (159) imply:
% 176.00/27.20  | | | | | | |   (166)  op(e3, e0) = all_52_24
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | GROUND_INST: instantiating (99) with all_52_7, all_52_24, e0, e3,
% 176.00/27.20  | | | | | | |              simplifying with (95), (166) gives:
% 176.00/27.20  | | | | | | |   (167)  all_52_7 = all_52_24
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | COMBINE_EQS: (6), (167) imply:
% 176.00/27.20  | | | | | | |   (168)  all_56_3 = all_52_24
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | COMBINE_EQS: (111), (167) imply:
% 176.00/27.20  | | | | | | |   (169)  all_58_9 = all_52_24
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (78), (167) imply:
% 176.00/27.20  | | | | | | |   (170)   ~ (all_52_3 = all_52_24)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (25), (167) imply:
% 176.00/27.20  | | | | | | |   (171)   ~ (all_52_5 = all_52_24)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (102), (167) imply:
% 176.00/27.20  | | | | | | |   (172)   ~ (all_52_24 = all_6_2)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | REDUCE: (38), (167) imply:
% 176.00/27.20  | | | | | | |   (173)   ~ (all_52_24 = all_4_2)
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | BETA: splitting (2) gives:
% 176.00/27.20  | | | | | | | 
% 176.00/27.20  | | | | | | | Case 1:
% 176.00/27.20  | | | | | | | | 
% 176.00/27.20  | | | | | | | |   (174)  all_56_8 = e3
% 176.00/27.20  | | | | | | | | 
% 176.00/27.20  | | | | | | | | REF_CLOSE: (97), (153), (174) are inconsistent by sub-proof
% 176.00/27.20  | | | | | | | |            #461.
% 176.00/27.20  | | | | | | | | 
% 176.00/27.20  | | | | | | | Case 2:
% 176.00/27.20  | | | | | | | | 
% 176.00/27.20  | | | | | | | |   (175)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.20  | | | | | | | | 
% 176.00/27.20  | | | | | | | | BETA: splitting (50) gives:
% 176.00/27.20  | | | | | | | | 
% 176.00/27.20  | | | | | | | | Case 1:
% 176.00/27.20  | | | | | | | | | 
% 176.00/27.20  | | | | | | | | |   (176)  all_58_0 = e3
% 176.00/27.20  | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | REF_CLOSE: (35), (40), (46), (61), (96), (99), (176) are
% 176.00/27.20  | | | | | | | | |            inconsistent by sub-proof #489.
% 176.00/27.20  | | | | | | | | | 
% 176.00/27.20  | | | | | | | | Case 2:
% 176.00/27.20  | | | | | | | | | 
% 176.00/27.20  | | | | | | | | |   (177)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.20  | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | BETA: splitting (177) gives:
% 176.00/27.20  | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | Case 1:
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | |   (178)  all_58_2 = e3
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | COMBINE_EQS: (87), (178) imply:
% 176.00/27.20  | | | | | | | | | |   (179)  all_52_9 = e3
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | SIMP: (179) implies:
% 176.00/27.20  | | | | | | | | | |   (180)  all_52_9 = e3
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | REDUCE: (65), (180) imply:
% 176.00/27.20  | | | | | | | | | |   (181)   ~ (all_52_13 = e3)
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | SIMP: (181) implies:
% 176.00/27.20  | | | | | | | | | |   (182)   ~ (all_52_13 = e3)
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | REDUCE: (75), (180) imply:
% 176.00/27.20  | | | | | | | | | |   (183)   ~ (all_52_17 = e3)
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | REDUCE: (24), (180) imply:
% 176.00/27.20  | | | | | | | | | |   (184)   ~ (all_4_2 = e3)
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | SIMP: (184) implies:
% 176.00/27.20  | | | | | | | | | |   (185)   ~ (all_4_2 = e3)
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | BETA: splitting (22) gives:
% 176.00/27.20  | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | Case 1:
% 176.00/27.20  | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | |   (186)  all_56_0 = e3
% 176.00/27.20  | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | REF_CLOSE: (82), (185), (186) are inconsistent by sub-proof
% 176.00/27.20  | | | | | | | | | | |            #1024.
% 176.00/27.20  | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | Case 2:
% 176.00/27.20  | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | |   (187)   ~ (all_56_0 = e3)
% 176.00/27.20  | | | | | | | | | | |   (188)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.20  | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | BETA: splitting (114) gives:
% 176.00/27.20  | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | Case 1:
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | |   (189)  all_58_0 = e3
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | COMBINE_EQS: (40), (189) imply:
% 176.00/27.20  | | | | | | | | | | | |   (190)  all_4_2 = e3
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | REDUCE: (185), (190) imply:
% 176.00/27.20  | | | | | | | | | | | |   (191)  $false
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | Case 2:
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | |   (192)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | BETA: splitting (116) gives:
% 176.00/27.20  | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | Case 1:
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | |   (193)  all_58_4 = e3
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | COMBINE_EQS: (32), (193) imply:
% 176.00/27.20  | | | | | | | | | | | | |   (194)  all_52_5 = e3
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | SIMP: (194) implies:
% 176.00/27.20  | | | | | | | | | | | | |   (195)  all_52_5 = e3
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | REDUCE: (49), (195) imply:
% 176.00/27.20  | | | | | | | | | | | | |   (196)   ~ (all_52_3 = e3)
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | REDUCE: (171), (195) imply:
% 176.00/27.20  | | | | | | | | | | | | |   (197)   ~ (all_52_24 = e3)
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | SIMP: (197) implies:
% 176.00/27.20  | | | | | | | | | | | | |   (198)   ~ (all_52_24 = e3)
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | REF_CLOSE: (4), (7), (11), (19), (21), (34), (35), (39),
% 176.00/27.20  | | | | | | | | | | | | |            (40), (44), (45), (53), (57), (61), (68), (77),
% 176.00/27.20  | | | | | | | | | | | | |            (80), (84), (89), (97), (98), (99), (106), (108),
% 176.00/27.20  | | | | | | | | | | | | |            (110), (112), (117), (118), (153), (154), (156),
% 176.00/27.20  | | | | | | | | | | | | |            (157), (160), (161), (168), (170), (173), (175),
% 176.00/27.20  | | | | | | | | | | | | |            (178), (196), (198) are inconsistent by sub-proof
% 176.00/27.20  | | | | | | | | | | | | |            #457.
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | Case 2:
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | |   (199)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 176.00/27.20  | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | Case 1:
% 176.00/27.20  | | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | |   (200)  all_58_5 = e3
% 176.00/27.20  | | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | | REF_CLOSE: (16), (182), (200) are inconsistent by sub-proof
% 176.00/27.20  | | | | | | | | | | | | | |            #969.
% 176.00/27.20  | | | | | | | | | | | | | | 
% 176.00/27.20  | | | | | | | | | | | | | Case 2:
% 176.00/27.20  | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | |   (201)  all_58_8 = e3 | all_58_14 = e3
% 176.00/27.21  | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 176.00/27.21  | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | Case 1:
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | |   (202)  all_58_8 = e3
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | REF_CLOSE: (52), (156), (202) are inconsistent by sub-proof
% 176.00/27.21  | | | | | | | | | | | | | | |            #901.
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | Case 2:
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | |   (203)  all_58_14 = e3
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | COMBINE_EQS: (48), (203) imply:
% 176.00/27.21  | | | | | | | | | | | | | | |   (204)  all_52_29 = e3
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | SIMP: (204) implies:
% 176.00/27.21  | | | | | | | | | | | | | | |   (205)  all_52_29 = e3
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | REDUCE: (69), (205) imply:
% 176.00/27.21  | | | | | | | | | | | | | | |   (206)   ~ (all_52_5 = e3)
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | REDUCE: (42), (205) imply:
% 176.00/27.21  | | | | | | | | | | | | | | |   (207)  op(e1, e3) = all_52_28
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | REDUCE: (31), (205) imply:
% 176.00/27.21  | | | | | | | | | | | | | | |   (208)  op(e0, e1) = e3
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | Case 1:
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | |   (209)  all_58_1 = e3
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (209) imply:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (210)  all_52_3 = e3
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | REDUCE: (49), (210) imply:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (211)   ~ (all_52_5 = e3)
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (99) with all_52_17, all_52_28, e3,
% 176.00/27.21  | | | | | | | | | | | | | | | |              e1, simplifying with (92), (207) gives:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (212)  all_52_17 = all_52_28
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (212) imply:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (213)  all_56_8 = all_52_28
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | REDUCE: (98), (212) imply:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (214)   ~ (all_52_28 = all_4_2)
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | REDUCE: (161), (212) imply:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (215)   ~ (all_52_28 = e0)
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | REDUCE: (80), (212) imply:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (216)  op(e3, all_52_28) = e3
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | REF_CLOSE: (14), (18), (19), (27), (32), (35), (40), (46),
% 176.00/27.21  | | | | | | | | | | | | | | | |            (55), (59), (73), (82), (88), (99), (101), (117),
% 176.00/27.21  | | | | | | | | | | | | | | | |            (129), (163), (165), (169), (172), (175), (188),
% 176.00/27.21  | | | | | | | | | | | | | | | |            (206), (208), (209), (213), (214), (215), (216)
% 176.00/27.21  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #207.
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | Case 2:
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | |   (217)   ~ (all_58_1 = e3)
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | REDUCE: (39), (217) imply:
% 176.00/27.21  | | | | | | | | | | | | | | | |   (218)   ~ (all_52_3 = e3)
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | | REF_CLOSE: (32), (39), (111), (152), (192), (206), (218) are
% 176.00/27.21  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #728.
% 176.00/27.21  | | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | Case 2:
% 176.00/27.21  | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | |   (219)  all_58_6 = e3 | all_58_12 = e3
% 176.00/27.21  | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | | REF_CLOSE: (77), (80), (96), (98), (99), (113), (133), (219)
% 176.00/27.21  | | | | | | | | | |            are inconsistent by sub-proof #947.
% 176.00/27.21  | | | | | | | | | | 
% 176.00/27.21  | | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | | 
% 176.00/27.21  | | | | | | | | End of split
% 176.00/27.21  | | | | | | | | 
% 176.00/27.21  | | | | | | | End of split
% 176.00/27.21  | | | | | | | 
% 176.00/27.21  | | | | | | Case 2:
% 176.00/27.21  | | | | | | | 
% 176.00/27.21  | | | | | | |   (220)  all_58_15 = e3
% 176.00/27.21  | | | | | | | 
% 176.00/27.21  | | | | | | | COMBINE_EQS: (23), (220) imply:
% 176.00/27.21  | | | | | | |   (221)  all_6_2 = e3
% 176.00/27.21  | | | | | | | 
% 176.00/27.21  | | | | | | | REDUCE: (130), (221) imply:
% 176.00/27.21  | | | | | | |   (222)  $false
% 176.00/27.21  | | | | | | | 
% 176.00/27.21  | | | | | | | CLOSE: (222) is inconsistent.
% 176.00/27.21  | | | | | | | 
% 176.00/27.21  | | | | | | End of split
% 176.00/27.21  | | | | | | 
% 176.00/27.21  | | | | | End of split
% 176.00/27.21  | | | | | 
% 176.00/27.21  | | | | End of split
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | End of split
% 176.00/27.21  | | | 
% 176.00/27.21  | | End of split
% 176.00/27.21  | | 
% 176.00/27.21  | End of split
% 176.00/27.21  | 
% 176.00/27.21  End of proof
% 176.00/27.21  
% 176.00/27.21  Sub-proof #185 shows that the following formulas are inconsistent:
% 176.00/27.21  ----------------------------------------------------------------
% 176.00/27.21    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.21    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.21    (3)   ~ (all_52_27 = all_10_2)
% 176.00/27.21    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.21    (5)   ~ (all_52_13 = all_52_29)
% 176.00/27.21    (6)  all_56_3 = all_52_7
% 176.00/27.21    (7)  op(e3, e2) = all_52_3
% 176.00/27.21    (8)   ~ (all_52_9 = all_52_25)
% 176.00/27.21    (9)  op(e3, all_52_25) = all_52_24
% 176.00/27.21    (10)   ~ (all_52_19 = all_52_23)
% 176.00/27.21    (11)  all_56_11 = all_52_23
% 176.00/27.21    (12)  op(e1, e2) = all_52_19
% 176.00/27.21    (13)   ~ (all_52_27 = e3)
% 176.00/27.21    (14)   ~ (all_6_2 = e3)
% 176.00/27.21    (15)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.21    (16)   ~ (all_52_3 = all_10_2)
% 176.00/27.21    (17)  all_58_5 = all_52_13
% 176.00/27.21    (18)   ~ (all_6_2 = e0)
% 176.00/27.21    (19)   ~ (all_52_25 = all_52_29)
% 176.00/27.21    (20)  op(e1, all_52_13) = e1
% 176.00/27.21    (21)  op(e0, all_52_15) = e0
% 176.00/27.21    (22)  all_56_15 = all_6_2
% 176.00/27.21    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.21    (24)  all_58_3 = all_10_2
% 176.00/27.21    (25)  all_56_9 = all_52_19
% 176.00/27.21    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.21    (27)  all_58_15 = all_6_2
% 176.00/27.21    (28)   ~ (all_52_9 = all_4_2)
% 176.00/27.21    (29)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.21    (30)   ~ (all_52_5 = all_52_7)
% 176.00/27.21    (31)  all_58_10 = all_52_15
% 176.00/27.21    (32)  all_8_2 = all_6_2
% 176.00/27.21    (33)   ~ (all_52_5 = all_4_2)
% 176.00/27.21    (34)  all_58_7 = all_52_19
% 176.00/27.21    (35)  all_56_4 = all_52_9
% 176.00/27.21    (36)   ~ (all_52_17 = all_52_25)
% 176.00/27.21    (37)  op(e0, e1) = all_52_29
% 176.00/27.21    (38)  all_58_4 = all_52_5
% 176.00/27.21    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.21    (40)   ~ (e3 = e1)
% 176.00/27.21    (41)   ~ (all_52_27 = all_52_29)
% 176.00/27.21    (42)   ~ (all_52_17 = all_14_2)
% 176.00/27.21    (43)  op(e3, all_4_2) = all_4_1
% 176.00/27.21    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.21    (45)   ~ (all_52_7 = all_4_2)
% 176.00/27.21    (46)  all_58_1 = all_52_3
% 176.00/27.21    (47)  all_58_0 = all_4_2
% 176.00/27.21    (48)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.21    (49)  op(e1, all_52_29) = all_52_28
% 176.00/27.21    (50)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.21    (51)   ~ (all_4_1 = e2)
% 176.00/27.21    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.21    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.21    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.21    (55)   ~ (all_14_1 = e3)
% 176.00/27.21    (56)  all_58_14 = all_52_29
% 176.00/27.21    (57)   ~ (all_52_3 = all_52_5)
% 176.00/27.21    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.21    (59)  op(e2, e1) = all_52_13
% 176.00/27.21    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.21    (61)  all_58_8 = all_14_2
% 176.00/27.21    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.21    (63)  op(e0, e3) = all_52_25
% 176.00/27.21    (64)  op(e0, all_6_2) = all_6_1
% 176.00/27.21    (65)  op(all_4_1, all_4_2) = e2
% 176.00/27.21    (66)  op(e3, all_52_17) = all_52_16
% 176.00/27.21    (67)   ~ (all_52_13 = all_14_2)
% 176.00/27.21    (68)  op(e3, all_52_9) = e3
% 176.00/27.21    (69)   ~ (e3 = e0)
% 176.00/27.21    (70)   ~ (all_52_9 = all_52_13)
% 176.00/27.21    (71)  op(e0, all_52_23) = all_52_22
% 176.00/27.21    (72)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.21    (73)   ~ (all_52_5 = all_52_29)
% 176.00/27.21    (74)  all_58_13 = all_52_27
% 176.00/27.21    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.21    (76)   ~ (all_52_9 = all_52_17)
% 176.00/27.21    (77)  all_58_6 = all_52_17
% 176.00/27.21    (78)   ~ (all_52_3 = all_52_7)
% 176.00/27.21    (79)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.21    (80)  op(e2, all_52_19) = all_52_18
% 176.00/27.21    (81)   ~ (e1 = e0)
% 176.00/27.21    (82)  all_56_0 = all_4_2
% 176.00/27.21    (83)  all_58_11 = all_52_23
% 176.00/27.21    (84)   ~ (all_52_3 = all_52_19)
% 176.00/27.21    (85)   ~ (all_52_7 = all_52_15)
% 176.00/27.21    (86)   ~ (all_52_19 = all_10_2)
% 176.00/27.21    (87)   ~ (all_52_23 = all_6_2)
% 176.00/27.21    (88)   ~ (all_52_29 = all_6_2)
% 176.00/27.21    (89)  all_58_2 = all_52_9
% 176.00/27.21    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.21    (91)  op(e3, e1) = all_52_5
% 176.00/27.21    (92)   ~ (e2 = e1)
% 176.00/27.21    (93)  all_56_10 = all_14_2
% 176.00/27.21    (94)   ~ (all_52_25 = all_6_2)
% 176.00/27.21    (95)  op(e1, e3) = all_52_17
% 176.00/27.21    (96)   ~ (all_52_25 = all_4_2)
% 176.00/27.21    (97)  op(e3, e0) = all_52_7
% 176.00/27.21    (98)  op(e2, all_10_2) = e2
% 176.00/27.21    (99)  op(e3, e3) = all_4_2
% 176.00/27.21    (100)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.21             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.21    (101)   ~ (all_52_25 = all_52_27)
% 176.00/27.21    (102)   ~ (all_52_27 = all_6_2)
% 176.00/27.21    (103)  all_8_1 = all_6_1
% 176.00/27.21    (104)   ~ (all_52_7 = all_6_2)
% 176.00/27.21    (105)   ~ (all_52_7 = all_52_23)
% 176.00/27.21    (106)   ~ (all_52_17 = all_52_19)
% 176.00/27.21    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.21    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.21    (109)  op(e1, all_14_2) = all_14_1
% 176.00/27.21    (110)  all_58_9 = all_52_7
% 176.00/27.21    (111)  all_58_12 = all_52_25
% 176.00/27.21    (112)  all_56_6 = all_52_13
% 176.00/27.21    (113)   ~ (all_52_9 = all_52_15)
% 176.00/27.21    (114)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.21    (115)   ~ (e3 = e2)
% 176.00/27.21    (116)   ~ (all_52_19 = all_14_2)
% 176.00/27.21    (117)  op(e2, e3) = all_52_9
% 176.00/27.21  
% 176.00/27.21  Begin of proof
% 176.00/27.21  | 
% 176.00/27.21  | BETA: splitting (60) gives:
% 176.00/27.21  | 
% 176.00/27.21  | Case 1:
% 176.00/27.21  | | 
% 176.00/27.21  | |   (118)  all_58_12 = e3
% 176.00/27.21  | | 
% 176.00/27.21  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (16),
% 176.00/27.21  | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 176.00/27.21  | |            (28), (29), (30), (31), (33), (34), (35), (36), (38), (39), (41),
% 176.00/27.21  | |            (42), (44), (45), (46), (47), (48), (50), (52), (53), (54), (55),
% 176.00/27.21  | |            (56), (57), (59), (61), (62), (63), (66), (67), (68), (69), (70),
% 176.00/27.21  | |            (71), (72), (74), (76), (77), (78), (79), (80), (82), (83), (84),
% 176.00/27.21  | |            (85), (86), (87), (89), (90), (91), (92), (93), (94), (95), (96),
% 176.00/27.21  | |            (97), (98), (100), (101), (102), (104), (105), (106), (107),
% 176.00/27.21  | |            (108), (109), (110), (111), (112), (113), (114), (115), (116),
% 176.00/27.21  | |            (117), (118) are inconsistent by sub-proof #734.
% 176.00/27.21  | | 
% 176.00/27.21  | Case 2:
% 176.00/27.21  | | 
% 176.00/27.21  | |   (119)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.21  | | 
% 176.00/27.21  | | REF_CLOSE: (4), (7), (9), (13), (14), (15), (16), (19), (21), (22), (24),
% 176.00/27.21  | |            (26), (27), (28), (29), (31), (32), (34), (36), (37), (38), (40),
% 176.00/27.21  | |            (41), (43), (44), (45), (46), (47), (49), (51), (53), (56), (58),
% 176.00/27.21  | |            (62), (63), (64), (65), (66), (68), (73), (74), (75), (77), (78),
% 176.00/27.21  | |            (81), (82), (83), (88), (89), (91), (92), (94), (95), (97), (98),
% 176.00/27.21  | |            (99), (100), (103), (104), (106), (107), (110), (111), (115),
% 176.00/27.21  | |            (117), (119) are inconsistent by sub-proof #186.
% 176.00/27.21  | | 
% 176.00/27.21  | End of split
% 176.00/27.21  | 
% 176.00/27.21  End of proof
% 176.00/27.21  
% 176.00/27.21  Sub-proof #186 shows that the following formulas are inconsistent:
% 176.00/27.21  ----------------------------------------------------------------
% 176.00/27.21    (1)   ~ (all_52_17 = all_52_23)
% 176.00/27.21    (2)  op(e3, e2) = all_52_3
% 176.00/27.21    (3)  op(e3, all_52_25) = all_52_24
% 176.00/27.21    (4)   ~ (all_52_27 = e3)
% 176.00/27.21    (5)   ~ (all_6_2 = e3)
% 176.00/27.21    (6)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.21    (7)   ~ (all_52_3 = all_10_2)
% 176.00/27.21    (8)   ~ (all_52_25 = all_52_29)
% 176.00/27.21    (9)  op(e0, all_52_15) = e0
% 176.00/27.21    (10)  all_56_15 = all_6_2
% 176.00/27.21    (11)  all_58_3 = all_10_2
% 176.00/27.21    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.21    (13)  all_58_15 = all_6_2
% 176.00/27.21    (14)   ~ (all_52_9 = all_4_2)
% 176.00/27.21    (15)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.21    (16)  all_58_10 = all_52_15
% 176.00/27.21    (17)  all_8_2 = all_6_2
% 176.00/27.21    (18)  all_58_7 = all_52_19
% 176.00/27.21    (19)   ~ (all_52_17 = all_52_25)
% 176.00/27.21    (20)  op(e0, e1) = all_52_29
% 176.00/27.21    (21)  all_58_4 = all_52_5
% 176.00/27.21    (22)   ~ (e3 = e1)
% 176.00/27.21    (23)   ~ (all_52_27 = all_52_29)
% 176.00/27.21    (24)  op(e3, all_4_2) = all_4_1
% 176.00/27.21    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.21    (26)   ~ (all_52_7 = all_4_2)
% 176.00/27.21    (27)  all_58_1 = all_52_3
% 176.00/27.21    (28)  all_58_0 = all_4_2
% 176.00/27.21    (29)  op(e1, all_52_29) = all_52_28
% 176.00/27.21    (30)   ~ (all_4_1 = e2)
% 176.00/27.21    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.21    (32)  all_58_14 = all_52_29
% 176.00/27.21    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.21    (34)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.21    (35)  op(e0, e3) = all_52_25
% 176.00/27.21    (36)  op(e0, all_6_2) = all_6_1
% 176.00/27.21    (37)  op(all_4_1, all_4_2) = e2
% 176.00/27.21    (38)  op(e3, all_52_17) = all_52_16
% 176.00/27.21    (39)  op(e3, all_52_9) = e3
% 176.00/27.21    (40)   ~ (all_52_5 = all_52_29)
% 176.00/27.21    (41)  all_58_13 = all_52_27
% 176.00/27.21    (42)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.21    (43)  all_58_6 = all_52_17
% 176.00/27.21    (44)   ~ (all_52_3 = all_52_7)
% 176.00/27.21    (45)   ~ (e1 = e0)
% 176.00/27.21    (46)  all_56_0 = all_4_2
% 176.00/27.21    (47)  all_58_11 = all_52_23
% 176.00/27.21    (48)   ~ (all_52_29 = all_6_2)
% 176.00/27.21    (49)  all_58_2 = all_52_9
% 176.00/27.21    (50)  op(e3, e1) = all_52_5
% 176.00/27.21    (51)   ~ (e2 = e1)
% 176.00/27.21    (52)   ~ (all_52_25 = all_6_2)
% 176.00/27.21    (53)  op(e1, e3) = all_52_17
% 176.00/27.21    (54)  op(e3, e0) = all_52_7
% 176.00/27.21    (55)  op(e2, all_10_2) = e2
% 176.00/27.21    (56)  op(e3, e3) = all_4_2
% 176.00/27.21    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.21    (58)  all_8_1 = all_6_1
% 176.00/27.21    (59)   ~ (all_52_7 = all_6_2)
% 176.00/27.21    (60)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.21    (61)   ~ (all_52_17 = all_52_19)
% 176.00/27.21    (62)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.21    (63)  all_58_9 = all_52_7
% 176.00/27.21    (64)  all_58_12 = all_52_25
% 176.00/27.21    (65)   ~ (e3 = e2)
% 176.00/27.21    (66)  op(e2, e3) = all_52_9
% 176.00/27.21  
% 176.00/27.21  Begin of proof
% 176.00/27.21  | 
% 176.00/27.21  | BETA: splitting (60) gives:
% 176.00/27.21  | 
% 176.00/27.21  | Case 1:
% 176.00/27.21  | | 
% 176.00/27.21  | |   (67)  all_58_13 = e3
% 176.00/27.21  | | 
% 176.00/27.21  | | REF_CLOSE: (4), (41), (67) are inconsistent by sub-proof #1026.
% 176.00/27.21  | | 
% 176.00/27.21  | Case 2:
% 176.00/27.21  | | 
% 176.00/27.21  | |   (68)  all_58_14 = e3 | all_58_15 = e3
% 176.00/27.21  | | 
% 176.00/27.21  | | BETA: splitting (68) gives:
% 176.00/27.21  | | 
% 176.00/27.21  | | Case 1:
% 176.00/27.21  | | | 
% 176.00/27.21  | | |   (69)  all_58_14 = e3
% 176.00/27.21  | | | 
% 176.00/27.21  | | | COMBINE_EQS: (32), (69) imply:
% 176.00/27.21  | | |   (70)  all_52_29 = e3
% 176.00/27.21  | | | 
% 176.00/27.21  | | | SIMP: (70) implies:
% 176.00/27.21  | | |   (71)  all_52_29 = e3
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (40), (71) imply:
% 176.00/27.21  | | |   (72)   ~ (all_52_5 = e3)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (8), (71) imply:
% 176.00/27.21  | | |   (73)   ~ (all_52_25 = e3)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (48), (71) imply:
% 176.00/27.21  | | |   (74)   ~ (all_6_2 = e3)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (29), (71) imply:
% 176.00/27.21  | | |   (75)  op(e1, e3) = all_52_28
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (20), (71) imply:
% 176.00/27.21  | | |   (76)  op(e0, e1) = e3
% 176.00/27.21  | | | 
% 176.00/27.21  | | | GROUND_INST: instantiating (57) with all_52_17, all_52_28, e3, e1,
% 176.00/27.21  | | |              simplifying with (53), (75) gives:
% 176.00/27.21  | | |   (77)  all_52_17 = all_52_28
% 176.00/27.21  | | | 
% 176.00/27.21  | | | COMBINE_EQS: (43), (77) imply:
% 176.00/27.21  | | |   (78)  all_58_6 = all_52_28
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (61), (77) imply:
% 176.00/27.21  | | |   (79)   ~ (all_52_19 = all_52_28)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | SIMP: (79) implies:
% 176.00/27.21  | | |   (80)   ~ (all_52_19 = all_52_28)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (1), (77) imply:
% 176.00/27.21  | | |   (81)   ~ (all_52_23 = all_52_28)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | SIMP: (81) implies:
% 176.00/27.21  | | |   (82)   ~ (all_52_23 = all_52_28)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (19), (77) imply:
% 176.00/27.21  | | |   (83)   ~ (all_52_25 = all_52_28)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | SIMP: (83) implies:
% 176.00/27.21  | | |   (84)   ~ (all_52_25 = all_52_28)
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (38), (77) imply:
% 176.00/27.21  | | |   (85)  op(e3, all_52_28) = all_52_16
% 176.00/27.21  | | | 
% 176.00/27.21  | | | BETA: splitting (12) gives:
% 176.00/27.21  | | | 
% 176.00/27.21  | | | Case 1:
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | |   (86)  all_56_0 = e3
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | | COMBINE_EQS: (46), (86) imply:
% 176.00/27.21  | | | |   (87)  all_4_2 = e3
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | | REDUCE: (37), (87) imply:
% 176.00/27.21  | | | |   (88)  op(all_4_1, e3) = e2
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | | REDUCE: (24), (87) imply:
% 176.00/27.21  | | | |   (89)  op(e3, e3) = all_4_1
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | | REDUCE: (56), (87) imply:
% 176.00/27.21  | | | |   (90)  op(e3, e3) = e3
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | | REF_CLOSE: (30), (57), (88), (89), (90) are inconsistent by sub-proof
% 176.00/27.21  | | | |            #490.
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | Case 2:
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | |   (91)   ~ (all_56_0 = e3)
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | | REDUCE: (46), (91) imply:
% 176.00/27.21  | | | |   (92)   ~ (all_4_2 = e3)
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 176.00/27.21  | | | |            (15), (16), (17), (18), (21), (22), (24), (25), (26), (27),
% 176.00/27.21  | | | |            (28), (30), (31), (33), (34), (35), (36), (39), (41), (42),
% 176.00/27.21  | | | |            (44), (45), (47), (49), (50), (51), (52), (54), (55), (56),
% 176.00/27.21  | | | |            (57), (58), (59), (62), (63), (64), (65), (66), (72), (73),
% 176.00/27.21  | | | |            (76), (78), (80), (82), (84), (85), (92) are inconsistent by
% 176.00/27.21  | | | |            sub-proof #211.
% 176.00/27.21  | | | | 
% 176.00/27.21  | | | End of split
% 176.00/27.21  | | | 
% 176.00/27.21  | | Case 2:
% 176.00/27.21  | | | 
% 176.00/27.21  | | |   (93)  all_58_15 = e3
% 176.00/27.21  | | | 
% 176.00/27.21  | | | COMBINE_EQS: (13), (93) imply:
% 176.00/27.21  | | |   (94)  all_6_2 = e3
% 176.00/27.21  | | | 
% 176.00/27.21  | | | REDUCE: (5), (94) imply:
% 176.00/27.21  | | |   (95)  $false
% 176.00/27.21  | | | 
% 176.00/27.21  | | | CLOSE: (95) is inconsistent.
% 176.00/27.21  | | | 
% 176.00/27.21  | | End of split
% 176.00/27.21  | | 
% 176.00/27.21  | End of split
% 176.00/27.21  | 
% 176.00/27.21  End of proof
% 176.00/27.21  
% 176.00/27.21  Sub-proof #187 shows that the following formulas are inconsistent:
% 176.00/27.21  ----------------------------------------------------------------
% 176.00/27.21    (1)  op(e0, all_6_2) = all_6_1
% 176.00/27.21    (2)  op(all_6_1, all_6_2) = e2
% 176.00/27.21    (3)  all_52_20 = e2
% 176.00/27.21    (4)   ~ (e2 = e1)
% 176.00/27.21    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.21    (6)  all_52_30 = all_6_1
% 176.00/27.21    (7)   ~ (e2 = e0)
% 176.00/27.21    (8)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.00/27.21         (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.00/27.21  
% 176.00/27.21  Begin of proof
% 176.00/27.21  | 
% 176.00/27.21  | BETA: splitting (8) gives:
% 176.00/27.21  | 
% 176.00/27.21  | Case 1:
% 176.00/27.21  | | 
% 176.00/27.21  | |   (9)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.00/27.21  | | 
% 176.00/27.21  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #539.
% 176.00/27.21  | | 
% 176.00/27.21  | Case 2:
% 176.00/27.21  | | 
% 176.00/27.21  | |   (10)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.00/27.21  | | 
% 176.00/27.21  | | ALPHA: (10) implies:
% 176.00/27.21  | |   (11)  all_52_30 = e0
% 176.00/27.21  | | 
% 176.00/27.21  | | COMBINE_EQS: (6), (11) imply:
% 176.00/27.21  | |   (12)  all_6_1 = e0
% 176.00/27.21  | | 
% 176.00/27.21  | | REF_CLOSE: (1), (2), (5), (7), (12) are inconsistent by sub-proof #201.
% 176.00/27.21  | | 
% 176.00/27.21  | End of split
% 176.00/27.21  | 
% 176.00/27.21  End of proof
% 176.00/27.21  
% 176.00/27.21  Sub-proof #188 shows that the following formulas are inconsistent:
% 176.00/27.21  ----------------------------------------------------------------
% 176.00/27.21    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.21    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.21    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.21    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.21    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.21    (6)  op(e3, e2) = all_52_3
% 176.00/27.21    (7)  op(e3, all_52_25) = all_52_24
% 176.00/27.21    (8)   ~ (all_52_19 = all_52_23)
% 176.00/27.21    (9)   ~ (all_6_2 = e3)
% 176.00/27.21    (10)   ~ (all_52_3 = all_10_2)
% 176.00/27.21    (11)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 176.00/27.21    (12)  all_58_5 = all_52_13
% 176.00/27.21    (13)  all_58_4 = e3
% 176.00/27.21    (14)  op(e1, all_52_13) = e1
% 176.00/27.21    (15)  op(e0, all_52_15) = e0
% 176.00/27.21    (16)  all_56_15 = all_6_2
% 176.00/27.21    (17)   ~ (all_52_26 = all_10_2)
% 176.00/27.21    (18)  all_58_3 = all_10_2
% 176.00/27.21    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.21    (20)  all_58_15 = all_6_2
% 176.00/27.21    (21)   ~ (all_52_26 = all_4_2)
% 176.00/27.21    (22)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.21    (23)   ~ (all_52_5 = all_52_7)
% 176.00/27.21    (24)  all_58_10 = all_52_15
% 176.00/27.21    (25)   ~ (all_52_5 = all_4_2)
% 176.00/27.21    (26)  all_58_7 = all_52_19
% 176.00/27.21    (27)   ~ (all_52_17 = all_52_25)
% 176.00/27.21    (28)   ~ (all_4_0 = e2)
% 176.00/27.21    (29)  all_58_4 = all_52_5
% 176.00/27.21    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.21    (31)   ~ (e3 = e1)
% 176.00/27.21    (32)   ~ (all_52_17 = all_14_2)
% 176.00/27.21    (33)  op(e3, all_4_2) = all_4_1
% 176.00/27.21    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.21    (35)  all_58_1 = all_52_3
% 176.00/27.21    (36)  all_58_0 = all_4_2
% 176.00/27.21    (37)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.21    (38)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.21    (39)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.21    (40)  all_58_14 = all_52_29
% 176.00/27.21    (41)   ~ (all_10_2 = e3)
% 176.00/27.21    (42)   ~ (all_52_13 = all_52_26)
% 176.00/27.21    (43)   ~ (all_52_3 = all_52_5)
% 176.00/27.21    (44)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.21    (45)  op(e2, e1) = all_52_13
% 176.00/27.21    (46)  all_58_8 = all_14_2
% 176.00/27.21    (47)  all_56_1 = all_52_3
% 176.00/27.21    (48)  op(e0, e2) = all_52_27
% 176.00/27.21    (49)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.21    (50)   ~ (all_52_5 = all_14_2)
% 176.00/27.21    (51)   ~ (all_52_3 = all_4_2)
% 176.00/27.21    (52)  op(e0, e3) = all_52_25
% 176.00/27.21    (53)  op(e0, all_6_2) = all_6_1
% 176.00/27.21    (54)  op(all_6_1, all_6_2) = e2
% 176.00/27.21    (55)  op(e3, all_52_17) = all_52_16
% 176.00/27.21    (56)   ~ (all_52_15 = all_52_23)
% 176.00/27.21    (57)   ~ (all_52_5 = all_52_29)
% 176.00/27.21    (58)  op(e1, e0) = all_52_23
% 176.00/27.21    (59)  all_58_13 = all_52_27
% 176.00/27.21    (60)   ~ (all_4_1 = e1)
% 176.00/27.21    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.21    (62)  all_58_6 = all_52_17
% 176.00/27.21    (63)   ~ (all_52_3 = all_52_7)
% 176.00/27.21    (64)  all_58_2 = all_52_26
% 176.00/27.21    (65)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.21    (66)   ~ (e1 = e0)
% 176.00/27.21    (67)  all_56_0 = all_4_2
% 176.00/27.21    (68)  all_58_11 = all_52_23
% 176.00/27.21    (69)   ~ (all_4_0 = e1)
% 176.00/27.21    (70)   ~ (all_52_29 = all_6_2)
% 176.00/27.21    (71)  op(e3, e1) = all_52_5
% 176.00/27.21    (72)   ~ (all_52_19 = e3)
% 176.00/27.21    (73)  op(e1, e3) = all_52_17
% 176.00/27.21    (74)   ~ (all_52_25 = all_4_2)
% 176.00/27.21    (75)  op(e3, e0) = all_52_7
% 176.00/27.21    (76)  op(e2, all_10_2) = e2
% 176.00/27.21    (77)  op(e3, e3) = all_4_2
% 176.00/27.21    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.21    (79)   ~ (all_52_27 = all_6_2)
% 176.00/27.21    (80)   ~ (all_52_7 = all_52_23)
% 176.00/27.21    (81)   ~ (all_52_25 = all_52_26)
% 176.00/27.21    (82)   ~ (all_52_17 = all_52_19)
% 176.00/27.21    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.21    (84)  all_56_4 = all_52_26
% 176.00/27.21    (85)  all_58_9 = all_52_7
% 176.00/27.21    (86)   ~ (all_52_15 = all_52_26)
% 176.00/27.21    (87)  all_58_12 = all_52_25
% 176.00/27.21    (88)   ~ (all_52_17 = all_52_26)
% 176.00/27.21    (89)  op(e3, all_52_26) = e3
% 176.00/27.21    (90)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.22    (91)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.22    (92)  all_58_13 = e3
% 176.00/27.22  
% 176.00/27.22  Begin of proof
% 176.00/27.22  | 
% 176.00/27.22  | COMBINE_EQS: (13), (29) imply:
% 176.00/27.22  |   (93)  all_52_5 = e3
% 176.00/27.22  | 
% 176.00/27.22  | SIMP: (93) implies:
% 176.00/27.22  |   (94)  all_52_5 = e3
% 176.00/27.22  | 
% 176.00/27.22  | REDUCE: (43), (94) imply:
% 176.00/27.22  |   (95)   ~ (all_52_3 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | REDUCE: (57), (94) imply:
% 176.00/27.22  |   (96)   ~ (all_52_29 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | SIMP: (96) implies:
% 176.00/27.22  |   (97)   ~ (all_52_29 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | REDUCE: (50), (94) imply:
% 176.00/27.22  |   (98)   ~ (all_14_2 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | SIMP: (98) implies:
% 176.00/27.22  |   (99)   ~ (all_14_2 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.00/27.22  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.00/27.22  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.00/27.22  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.00/27.22  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (58),
% 176.00/27.22  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 176.00/27.22  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 176.00/27.22  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 176.00/27.22  |            (92), (95), (97), (99) are inconsistent by sub-proof #214.
% 176.00/27.22  | 
% 176.00/27.22  End of proof
% 176.00/27.22  
% 176.00/27.22  Sub-proof #189 shows that the following formulas are inconsistent:
% 176.00/27.22  ----------------------------------------------------------------
% 176.00/27.22    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.22    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.22    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.22    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.22    (5)   ~ (all_52_13 = all_52_29)
% 176.00/27.22    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.22    (7)  all_56_6 = e3
% 176.00/27.22    (8)  op(e3, e2) = all_52_3
% 176.00/27.22    (9)  op(e3, all_52_25) = all_52_24
% 176.00/27.22    (10)   ~ (all_52_19 = all_52_23)
% 176.00/27.22    (11)   ~ (all_6_2 = e3)
% 176.00/27.22    (12)   ~ (all_52_3 = all_10_2)
% 176.00/27.22    (13)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 176.00/27.22    (14)  all_58_5 = all_52_13
% 176.00/27.22    (15)  op(e1, all_52_13) = e1
% 176.00/27.22    (16)  op(e0, all_52_15) = e0
% 176.00/27.22    (17)  all_56_15 = all_6_2
% 176.00/27.22    (18)   ~ (all_52_26 = all_10_2)
% 176.00/27.22    (19)  all_58_3 = all_10_2
% 176.00/27.22    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.22    (21)  all_58_15 = all_6_2
% 176.00/27.22    (22)   ~ (all_52_26 = all_4_2)
% 176.00/27.22    (23)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.22    (24)   ~ (all_52_5 = all_52_7)
% 176.00/27.22    (25)  all_58_10 = all_52_15
% 176.00/27.22    (26)   ~ (all_52_5 = all_4_2)
% 176.00/27.22    (27)  all_58_7 = all_52_19
% 176.00/27.22    (28)   ~ (all_52_17 = all_52_25)
% 176.00/27.22    (29)   ~ (all_4_0 = e2)
% 176.00/27.22    (30)  all_58_4 = all_52_5
% 176.00/27.22    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.22    (32)   ~ (e3 = e1)
% 176.00/27.22    (33)   ~ (all_52_17 = all_14_2)
% 176.00/27.22    (34)  op(e3, all_4_2) = all_4_1
% 176.00/27.22    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.22    (36)  all_58_1 = all_52_3
% 176.00/27.22    (37)  all_58_0 = all_4_2
% 176.00/27.22    (38)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.22    (39)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.22    (40)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.22    (41)  all_58_14 = all_52_29
% 176.00/27.22    (42)   ~ (all_52_13 = all_52_26)
% 176.00/27.22    (43)   ~ (all_52_3 = all_52_5)
% 176.00/27.22    (44)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.22    (45)  op(e2, e1) = all_52_13
% 176.00/27.22    (46)  all_58_8 = all_14_2
% 176.00/27.22    (47)  all_56_1 = all_52_3
% 176.00/27.22    (48)  op(e0, e2) = all_52_27
% 176.00/27.22    (49)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.22    (50)   ~ (all_52_5 = all_14_2)
% 176.00/27.22    (51)   ~ (all_52_3 = all_4_2)
% 176.00/27.22    (52)  op(e0, e3) = all_52_25
% 176.00/27.22    (53)  op(e0, all_6_2) = all_6_1
% 176.00/27.22    (54)  op(all_6_1, all_6_2) = e2
% 176.00/27.22    (55)  op(e3, all_52_17) = all_52_16
% 176.00/27.22    (56)   ~ (all_52_13 = all_14_2)
% 176.00/27.22    (57)   ~ (all_52_15 = all_52_23)
% 176.00/27.22    (58)  op(e1, e0) = all_52_23
% 176.00/27.22    (59)  all_58_13 = all_52_27
% 176.00/27.22    (60)   ~ (all_4_1 = e1)
% 176.00/27.22    (61)   ~ (all_52_3 = e3)
% 176.00/27.22    (62)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.22    (63)  all_58_6 = all_52_17
% 176.00/27.22    (64)   ~ (all_52_3 = all_52_7)
% 176.00/27.22    (65)  all_58_2 = all_52_26
% 176.00/27.22    (66)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.22    (67)   ~ (e1 = e0)
% 176.00/27.22    (68)  all_56_0 = all_4_2
% 176.00/27.22    (69)  all_58_11 = all_52_23
% 176.00/27.22    (70)   ~ (all_4_0 = e1)
% 176.00/27.22    (71)   ~ (all_52_29 = all_6_2)
% 176.00/27.22    (72)  op(e3, e1) = all_52_5
% 176.00/27.22    (73)   ~ (all_52_19 = e3)
% 176.00/27.22    (74)  op(e1, e3) = all_52_17
% 176.00/27.22    (75)   ~ (all_52_25 = all_4_2)
% 176.00/27.22    (76)  op(e3, e0) = all_52_7
% 176.00/27.22    (77)  op(e2, all_10_2) = e2
% 176.00/27.22    (78)  op(e3, e3) = all_4_2
% 176.00/27.22    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.22    (80)   ~ (all_52_27 = all_6_2)
% 176.00/27.22    (81)   ~ (all_52_7 = all_52_23)
% 176.00/27.22    (82)   ~ (all_52_13 = all_10_2)
% 176.00/27.22    (83)   ~ (all_52_25 = all_52_26)
% 176.00/27.22    (84)   ~ (all_52_17 = all_52_19)
% 176.00/27.22    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.22    (86)  all_56_4 = all_52_26
% 176.00/27.22    (87)  all_58_9 = all_52_7
% 176.00/27.22    (88)   ~ (all_52_15 = all_52_26)
% 176.00/27.22    (89)  all_58_12 = all_52_25
% 176.00/27.22    (90)   ~ (all_52_17 = all_52_26)
% 176.00/27.22    (91)  all_56_6 = all_52_13
% 176.00/27.22    (92)  op(e3, all_52_26) = e3
% 176.00/27.22    (93)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.22    (94)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.22    (95)  all_58_13 = e3
% 176.00/27.22  
% 176.00/27.22  Begin of proof
% 176.00/27.22  | 
% 176.00/27.22  | COMBINE_EQS: (7), (91) imply:
% 176.00/27.22  |   (96)  all_52_13 = e3
% 176.00/27.22  | 
% 176.00/27.22  | SIMP: (96) implies:
% 176.00/27.22  |   (97)  all_52_13 = e3
% 176.00/27.22  | 
% 176.00/27.22  | REDUCE: (5), (97) imply:
% 176.00/27.22  |   (98)   ~ (all_52_29 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | SIMP: (98) implies:
% 176.00/27.22  |   (99)   ~ (all_52_29 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | REDUCE: (56), (97) imply:
% 176.00/27.22  |   (100)   ~ (all_14_2 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | SIMP: (100) implies:
% 176.00/27.22  |   (101)   ~ (all_14_2 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | REDUCE: (82), (97) imply:
% 176.00/27.22  |   (102)   ~ (all_10_2 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | SIMP: (102) implies:
% 176.00/27.22  |   (103)   ~ (all_10_2 = e3)
% 176.00/27.22  | 
% 176.00/27.22  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 176.00/27.22  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 176.00/27.22  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 176.00/27.22  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 176.00/27.22  |            (48), (49), (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 176.00/27.22  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 176.00/27.22  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 176.00/27.22  |            (83), (84), (85), (86), (87), (88), (89), (90), (92), (93), (94),
% 176.00/27.22  |            (95), (99), (101), (103) are inconsistent by sub-proof #214.
% 176.00/27.22  | 
% 176.00/27.22  End of proof
% 176.00/27.22  
% 176.00/27.22  Sub-proof #190 shows that the following formulas are inconsistent:
% 176.00/27.22  ----------------------------------------------------------------
% 176.00/27.22    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.22    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.22    (3)   ~ (all_52_27 = all_10_2)
% 176.00/27.22    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.22    (5)  op(e2, all_10_2) = all_10_1
% 176.00/27.22    (6)   ~ (all_52_13 = all_52_29)
% 176.00/27.22    (7)  all_56_3 = all_52_7
% 176.00/27.22    (8)  op(e3, e2) = all_52_3
% 176.00/27.22    (9)   ~ (all_52_9 = all_52_25)
% 176.00/27.22    (10)  op(e3, all_52_25) = all_52_24
% 176.00/27.22    (11)   ~ (all_52_19 = all_52_23)
% 176.00/27.22    (12)  op(e1, e2) = all_52_19
% 176.00/27.22    (13)  all_16_1 = all_6_1
% 176.00/27.22    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.00/27.22    (15)  op(e3, all_52_9) = all_52_8
% 176.00/27.22    (16)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.22    (17)   ~ (all_52_3 = all_10_2)
% 176.00/27.22    (18)  all_58_5 = all_52_13
% 176.00/27.22    (19)   ~ (all_52_25 = all_52_29)
% 176.00/27.22    (20)  all_16_2 = all_6_2
% 176.00/27.22    (21)  all_56_15 = all_6_2
% 176.00/27.22    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.22    (23)  op(e2, e0) = all_52_15
% 176.00/27.22    (24)  op(all_14_1, all_14_2) = all_14_0
% 176.00/27.22    (25)  all_58_3 = all_10_2
% 176.00/27.22    (26)  all_56_9 = all_52_19
% 176.00/27.22    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.22    (28)  all_58_15 = all_6_2
% 176.00/27.22    (29)   ~ (all_52_9 = all_4_2)
% 176.00/27.22    (30)   ~ (all_52_5 = all_52_7)
% 176.00/27.22    (31)  all_58_10 = all_52_15
% 176.00/27.22    (32)  all_8_2 = all_6_2
% 176.00/27.22    (33)   ~ (all_52_5 = all_4_2)
% 176.00/27.22    (34)  all_58_7 = all_52_19
% 176.00/27.22    (35)  all_56_4 = all_52_9
% 176.00/27.22    (36)   ~ (all_52_15 = all_6_2)
% 176.00/27.22    (37)   ~ (all_52_17 = all_52_25)
% 176.00/27.22    (38)  op(e0, e1) = all_52_29
% 176.00/27.22    (39)  all_58_4 = all_52_5
% 176.00/27.22    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.22    (41)   ~ (e3 = e1)
% 176.00/27.22    (42)  all_34_1 = all_4_1
% 176.00/27.22    (43)   ~ (all_52_27 = all_52_29)
% 176.00/27.22    (44)   ~ (all_52_17 = all_14_2)
% 176.00/27.22    (45)  op(e3, all_4_2) = all_4_1
% 176.00/27.22    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.22    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.22    (48)   ~ (all_52_7 = all_4_2)
% 176.00/27.22    (49)  all_58_1 = all_52_3
% 176.00/27.22    (50)  all_58_0 = all_4_2
% 176.00/27.22    (51)  op(e1, all_52_13) = all_52_12
% 176.00/27.22    (52)  op(all_4_1, all_4_2) = e1
% 176.00/27.22    (53)  op(e0, e0) = all_6_2
% 176.00/27.22    (54)  op(e1, all_52_29) = all_52_28
% 176.00/27.22    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.22    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.22    (57)   ~ (all_4_1 = e2)
% 176.00/27.22    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.22    (59)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.22    (60)  all_58_14 = all_52_29
% 176.00/27.22    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.22    (62)   ~ (all_52_3 = all_52_5)
% 176.00/27.22    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.22    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.22    (65)  all_58_8 = all_14_2
% 176.00/27.22    (66)  all_56_1 = all_52_3
% 176.00/27.22    (67)  op(e0, e2) = all_52_27
% 176.00/27.22    (68)   ~ (all_14_0 = e3)
% 176.00/27.22    (69)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.22    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.22    (71)   ~ (all_52_5 = all_14_2)
% 176.00/27.22    (72)   ~ (all_52_3 = all_52_27)
% 176.00/27.22    (73)   ~ (all_52_3 = all_4_2)
% 176.00/27.22    (74)  op(e0, e3) = all_52_25
% 176.00/27.22    (75)  op(e0, all_6_2) = all_6_1
% 176.00/27.22    (76)  all_52_0 = all_4_1
% 176.00/27.22    (77)   ~ (all_52_9 = all_10_2)
% 176.00/27.22    (78)  op(all_6_1, all_6_2) = e2
% 176.00/27.22    (79)  op(e3, all_52_17) = all_52_16
% 176.00/27.22    (80)  all_52_10 = all_10_1
% 176.00/27.22    (81)   ~ (all_52_9 = all_52_13)
% 176.00/27.22    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.22    (83)  op(e0, all_52_23) = all_52_22
% 176.00/27.22    (84)   ~ (all_52_15 = all_52_23)
% 176.00/27.22    (85)  op(all_10_1, all_10_2) = all_10_0
% 176.00/27.22    (86)   ~ (all_52_5 = all_52_29)
% 176.00/27.22    (87)  all_56_2 = all_52_5
% 176.00/27.22    (88)  op(e1, e0) = all_52_23
% 176.00/27.22    (89)  all_56_12 = all_52_25
% 176.00/27.22    (90)  all_58_13 = all_52_27
% 176.00/27.22    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.22    (92)   ~ (all_52_9 = all_52_17)
% 176.00/27.22    (93)  all_58_6 = all_52_17
% 176.00/27.22    (94)   ~ (all_52_3 = all_52_7)
% 176.00/27.22    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.22    (96)  op(e2, all_52_19) = all_52_18
% 176.00/27.22    (97)   ~ (e1 = e0)
% 176.00/27.22    (98)  all_56_0 = all_4_2
% 176.00/27.22    (99)  all_58_11 = all_52_23
% 176.00/27.22    (100)   ~ (all_52_3 = all_52_19)
% 176.00/27.22    (101)  op(e0, all_52_15) = all_52_14
% 176.00/27.22    (102)   ~ (all_52_29 = all_14_2)
% 176.00/27.22    (103)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.22    (104)   ~ (all_52_29 = all_6_2)
% 176.00/27.22    (105)  all_58_2 = all_52_9
% 176.00/27.22    (106)  op(e3, e1) = all_52_5
% 176.00/27.22    (107)   ~ (all_52_25 = all_6_2)
% 176.00/27.22    (108)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.22    (109)  op(e1, e3) = all_52_17
% 176.00/27.22    (110)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.22    (111)   ~ (all_52_25 = all_4_2)
% 176.00/27.22    (112)  op(e3, e0) = all_52_7
% 176.00/27.22    (113)  op(e3, e3) = all_4_2
% 176.00/27.22    (114)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 176.00/27.22             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 176.00/27.22    (115)  all_56_8 = all_52_17
% 176.00/27.22    (116)   ~ (all_52_17 = all_4_2)
% 176.00/27.22    (117)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.22             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.22    (118)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.00/27.22           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.00/27.22           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.00/27.22           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.00/27.22    (119)   ~ (all_52_25 = all_52_27)
% 176.00/27.22    (120)  all_34_2 = all_4_2
% 176.00/27.22    (121)   ~ (all_52_27 = all_6_2)
% 176.00/27.22    (122)  all_8_1 = all_6_1
% 176.00/27.22    (123)   ~ (all_52_7 = all_6_2)
% 176.00/27.22    (124)   ~ (all_10_0 = e3)
% 176.00/27.22    (125)   ~ (all_52_7 = all_52_23)
% 176.00/27.22    (126)  op(e2, all_52_27) = all_52_26
% 176.00/27.22    (127)  all_52_20 = all_14_1
% 176.00/27.22    (128)   ~ (all_52_17 = all_52_19)
% 176.00/27.22    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.22    (130)  all_52_30 = all_6_1
% 176.00/27.22    (131)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.22    (132)  op(e1, all_14_2) = all_14_1
% 176.00/27.22    (133)  all_58_9 = all_52_7
% 176.00/27.22    (134)   ~ (e2 = e0)
% 176.00/27.22    (135)  all_58_12 = all_52_25
% 176.00/27.22    (136)   ~ (all_10_0 = e1)
% 176.00/27.22    (137)  all_56_6 = all_52_13
% 176.00/27.22    (138)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.22    (139)   ~ (all_52_9 = all_52_15)
% 176.00/27.22    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.22    (141)   ~ (e3 = e2)
% 176.00/27.22    (142)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.22    (143)   ~ (all_52_19 = all_14_2)
% 176.00/27.22    (144)  op(e2, e3) = all_52_9
% 176.00/27.22    (145)  all_56_13 = all_52_27
% 176.00/27.22  
% 176.00/27.22  Begin of proof
% 176.00/27.22  | 
% 176.00/27.22  | BETA: splitting (114) gives:
% 176.00/27.22  | 
% 176.00/27.22  | Case 1:
% 176.00/27.22  | | 
% 176.00/27.22  | |   (146)  all_58_15 = e0
% 176.00/27.22  | | 
% 176.00/27.22  | | REF_CLOSE: (28), (53), (75), (78), (117), (134), (146) are inconsistent by
% 176.00/27.22  | |            sub-proof #228.
% 176.00/27.22  | | 
% 176.00/27.22  | Case 2:
% 176.00/27.22  | | 
% 176.00/27.22  | |   (147)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 176.00/27.22  | |            | all_58_13 = e0 | all_58_14 = e0)
% 176.00/27.22  | | 
% 176.00/27.22  | | ALPHA: (147) implies:
% 176.00/27.22  | |   (148)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.22  | | 
% 176.00/27.22  | | BETA: splitting (118) gives:
% 176.00/27.22  | | 
% 176.00/27.22  | | Case 1:
% 176.00/27.22  | | | 
% 176.00/27.22  | | |   (149)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.00/27.22  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.00/27.22  | | |            e0)
% 176.00/27.22  | | | 
% 176.00/27.22  | | | BETA: splitting (149) gives:
% 176.00/27.22  | | | 
% 176.00/27.22  | | | Case 1:
% 176.00/27.22  | | | | 
% 176.00/27.23  | | | |   (150)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | REF_CLOSE: (41), (45), (52), (76), (117), (150) are inconsistent by
% 176.00/27.23  | | | |            sub-proof #600.
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | Case 2:
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | |   (151)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.00/27.23  | | | |          e0
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | ALPHA: (151) implies:
% 176.00/27.23  | | | |   (152)  all_52_14 = e0
% 176.00/27.23  | | | |   (153)  all_52_12 = e1
% 176.00/27.23  | | | |   (154)  all_52_10 = e2
% 176.00/27.23  | | | |   (155)  all_52_8 = e3
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | COMBINE_EQS: (80), (154) imply:
% 176.00/27.23  | | | |   (156)  all_10_1 = e2
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | REDUCE: (85), (156) imply:
% 176.00/27.23  | | | |   (157)  op(e2, all_10_2) = all_10_0
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | REDUCE: (15), (155) imply:
% 176.00/27.23  | | | |   (158)  op(e3, all_52_9) = e3
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | REDUCE: (5), (156) imply:
% 176.00/27.23  | | | |   (159)  op(e2, all_10_2) = e2
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | REDUCE: (51), (153) imply:
% 176.00/27.23  | | | |   (160)  op(e1, all_52_13) = e1
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | REDUCE: (101), (152) imply:
% 176.00/27.23  | | | |   (161)  op(e0, all_52_15) = e0
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13), (14), (16),
% 176.00/27.23  | | | |            (17), (18), (19), (20), (21), (22), (25), (27), (28), (29),
% 176.00/27.23  | | | |            (31), (32), (33), (34), (35), (38), (39), (40), (41), (42),
% 176.00/27.23  | | | |            (43), (45), (46), (47), (48), (49), (50), (52), (54), (55),
% 176.00/27.23  | | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 176.00/27.23  | | | |            (67), (70), (72), (73), (74), (75), (78), (81), (82), (84),
% 176.00/27.23  | | | |            (86), (87), (88), (89), (90), (91), (93), (94), (95), (97),
% 176.00/27.23  | | | |            (98), (99), (100), (102), (103), (104), (105), (106), (107),
% 176.00/27.23  | | | |            (108), (109), (111), (112), (113), (116), (117), (119),
% 176.00/27.23  | | | |            (120), (121), (122), (123), (124), (125), (126), (128),
% 176.00/27.23  | | | |            (129), (131), (133), (135), (136), (137), (138), (139),
% 176.00/27.23  | | | |            (142), (144), (145), (148), (157), (158), (159), (160), (161)
% 176.00/27.23  | | | |            are inconsistent by sub-proof #194.
% 176.00/27.23  | | | | 
% 176.00/27.23  | | | End of split
% 176.00/27.23  | | | 
% 176.00/27.23  | | Case 2:
% 176.00/27.23  | | | 
% 176.00/27.23  | | |   (162)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 176.00/27.23  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 176.00/27.23  | | |            all_52_30 = e0)
% 176.00/27.23  | | | 
% 176.00/27.23  | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 176.00/27.23  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 176.00/27.23  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 176.00/27.23  | | |            (37), (38), (39), (40), (42), (43), (44), (45), (46), (47),
% 176.00/27.23  | | |            (48), (49), (50), (52), (54), (55), (56), (57), (58), (59),
% 176.00/27.23  | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 176.00/27.23  | | |            (70), (71), (72), (73), (74), (75), (77), (78), (79), (81),
% 176.00/27.23  | | |            (82), (83), (84), (86), (87), (88), (89), (90), (91), (92),
% 176.00/27.23  | | |            (93), (94), (96), (98), (99), (100), (103), (104), (105),
% 176.00/27.23  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (115),
% 176.00/27.23  | | |            (116), (117), (119), (120), (121), (122), (123), (125), (126),
% 176.00/27.23  | | |            (127), (129), (130), (131), (132), (133), (134), (135), (137),
% 176.00/27.23  | | |            (138), (139), (140), (141), (142), (143), (144), (145), (148),
% 176.00/27.23  | | |            (162) are inconsistent by sub-proof #191.
% 176.00/27.23  | | | 
% 176.00/27.23  | | End of split
% 176.00/27.23  | | 
% 176.00/27.23  | End of split
% 176.00/27.23  | 
% 176.00/27.23  End of proof
% 176.00/27.23  
% 176.00/27.23  Sub-proof #191 shows that the following formulas are inconsistent:
% 176.00/27.23  ----------------------------------------------------------------
% 176.00/27.23    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.23    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.23    (3)   ~ (all_52_17 = all_52_23)
% 176.00/27.23    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.23    (5)  all_56_3 = all_52_7
% 176.00/27.23    (6)  op(e3, e2) = all_52_3
% 176.00/27.23    (7)   ~ (all_52_9 = all_52_25)
% 176.00/27.23    (8)  op(e3, all_52_25) = all_52_24
% 176.00/27.23    (9)   ~ (all_52_19 = all_52_23)
% 176.00/27.23    (10)  op(e1, e2) = all_52_19
% 176.00/27.23    (11)  all_16_1 = all_6_1
% 176.00/27.23    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.00/27.23    (13)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.23    (14)   ~ (all_52_3 = all_10_2)
% 176.00/27.23    (15)  all_58_5 = all_52_13
% 176.00/27.23    (16)   ~ (all_52_25 = all_52_29)
% 176.00/27.23    (17)  all_16_2 = all_6_2
% 176.00/27.23    (18)  all_56_15 = all_6_2
% 176.00/27.23    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.23    (20)  op(e2, e0) = all_52_15
% 176.00/27.23    (21)  op(all_14_1, all_14_2) = all_14_0
% 176.00/27.23    (22)  all_58_3 = all_10_2
% 176.00/27.23    (23)  all_56_9 = all_52_19
% 176.00/27.23    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.23    (25)  all_58_15 = all_6_2
% 176.00/27.23    (26)   ~ (all_52_9 = all_4_2)
% 176.00/27.23    (27)   ~ (all_52_5 = all_52_7)
% 176.00/27.23    (28)  all_58_10 = all_52_15
% 176.00/27.23    (29)  all_8_2 = all_6_2
% 176.00/27.23    (30)   ~ (all_52_5 = all_4_2)
% 176.00/27.23    (31)  all_58_7 = all_52_19
% 176.00/27.23    (32)   ~ (all_52_15 = all_6_2)
% 176.00/27.23    (33)   ~ (all_52_17 = all_52_25)
% 176.00/27.23    (34)  op(e0, e1) = all_52_29
% 176.00/27.23    (35)  all_58_4 = all_52_5
% 176.00/27.23    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.23    (37)  all_34_1 = all_4_1
% 176.00/27.23    (38)   ~ (all_52_27 = all_52_29)
% 176.00/27.23    (39)   ~ (all_52_17 = all_14_2)
% 176.00/27.23    (40)  op(e3, all_4_2) = all_4_1
% 176.00/27.23    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.23    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.23    (43)   ~ (all_52_7 = all_4_2)
% 176.00/27.23    (44)  all_58_1 = all_52_3
% 176.00/27.23    (45)  all_58_0 = all_4_2
% 176.00/27.23    (46)  op(all_4_1, all_4_2) = e1
% 176.00/27.23    (47)  op(e1, all_52_29) = all_52_28
% 176.00/27.23    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.23    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.23    (50)   ~ (all_4_1 = e2)
% 176.00/27.23    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.23    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.23    (53)  all_58_14 = all_52_29
% 176.00/27.23    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.23    (55)   ~ (all_52_3 = all_52_5)
% 176.00/27.23    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.23    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.23    (58)  all_58_8 = all_14_2
% 176.00/27.23    (59)  all_56_1 = all_52_3
% 176.00/27.23    (60)  op(e0, e2) = all_52_27
% 176.00/27.23    (61)   ~ (all_14_0 = e3)
% 176.00/27.23    (62)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.23    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.23    (64)   ~ (all_52_5 = all_14_2)
% 176.00/27.23    (65)   ~ (all_52_3 = all_52_27)
% 176.00/27.23    (66)   ~ (all_52_3 = all_4_2)
% 176.00/27.23    (67)  op(e0, e3) = all_52_25
% 176.00/27.23    (68)  op(e0, all_6_2) = all_6_1
% 176.00/27.23    (69)   ~ (all_52_9 = all_10_2)
% 176.00/27.23    (70)  op(all_6_1, all_6_2) = e2
% 176.00/27.23    (71)  op(e3, all_52_17) = all_52_16
% 176.00/27.23    (72)   ~ (all_52_9 = all_52_13)
% 176.00/27.23    (73)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.23    (74)  op(e0, all_52_23) = all_52_22
% 176.00/27.23    (75)   ~ (all_52_15 = all_52_23)
% 176.00/27.23    (76)   ~ (all_52_5 = all_52_29)
% 176.00/27.23    (77)  all_56_2 = all_52_5
% 176.00/27.23    (78)  op(e1, e0) = all_52_23
% 176.00/27.23    (79)  all_56_12 = all_52_25
% 176.00/27.23    (80)  all_58_13 = all_52_27
% 176.00/27.23    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.23    (82)   ~ (all_52_9 = all_52_17)
% 176.00/27.23    (83)  all_58_6 = all_52_17
% 176.00/27.23    (84)   ~ (all_52_3 = all_52_7)
% 176.00/27.23    (85)  op(e2, all_52_19) = all_52_18
% 176.00/27.23    (86)  all_56_0 = all_4_2
% 176.00/27.23    (87)  all_58_11 = all_52_23
% 176.00/27.23    (88)   ~ (all_52_3 = all_52_19)
% 176.00/27.23    (89)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.23    (90)   ~ (all_52_29 = all_6_2)
% 176.00/27.23    (91)  all_58_2 = all_52_9
% 176.00/27.23    (92)  op(e3, e1) = all_52_5
% 176.00/27.23    (93)   ~ (all_52_25 = all_6_2)
% 176.00/27.23    (94)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.23    (95)  op(e1, e3) = all_52_17
% 176.00/27.23    (96)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.23    (97)   ~ (all_52_25 = all_4_2)
% 176.00/27.23    (98)  op(e3, e0) = all_52_7
% 176.00/27.23    (99)  op(e3, e3) = all_4_2
% 176.00/27.23    (100)  all_56_8 = all_52_17
% 176.00/27.23    (101)   ~ (all_52_17 = all_4_2)
% 176.00/27.23    (102)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.23             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.23    (103)   ~ (all_52_25 = all_52_27)
% 176.00/27.23    (104)  all_34_2 = all_4_2
% 176.00/27.23    (105)   ~ (all_52_27 = all_6_2)
% 176.00/27.23    (106)  all_8_1 = all_6_1
% 176.00/27.23    (107)   ~ (all_52_7 = all_6_2)
% 176.00/27.23    (108)   ~ (all_52_7 = all_52_23)
% 176.00/27.23    (109)  op(e2, all_52_27) = all_52_26
% 176.00/27.23    (110)  all_52_20 = all_14_1
% 176.00/27.23    (111)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.23    (112)  all_52_30 = all_6_1
% 176.00/27.23    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.23    (114)  op(e1, all_14_2) = all_14_1
% 176.00/27.23    (115)  all_58_9 = all_52_7
% 176.00/27.23    (116)   ~ (e2 = e0)
% 176.00/27.23    (117)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.00/27.23           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.00/27.23    (118)  all_58_12 = all_52_25
% 176.00/27.23    (119)  all_56_6 = all_52_13
% 176.00/27.23    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.23    (121)   ~ (all_52_9 = all_52_15)
% 176.00/27.23    (122)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.23    (123)   ~ (e3 = e2)
% 176.00/27.23    (124)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.23    (125)   ~ (all_52_19 = all_14_2)
% 176.00/27.23    (126)  op(e2, e3) = all_52_9
% 176.00/27.23    (127)  all_56_13 = all_52_27
% 176.00/27.23  
% 176.00/27.23  Begin of proof
% 176.00/27.23  | 
% 176.00/27.23  | BETA: splitting (117) gives:
% 176.00/27.23  | 
% 176.00/27.23  | Case 1:
% 176.00/27.23  | | 
% 176.00/27.23  | |   (128)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.00/27.23  | | 
% 176.00/27.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.00/27.23  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.00/27.23  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 176.00/27.23  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 176.00/27.23  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 176.00/27.23  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 176.00/27.23  | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 176.00/27.23  | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 176.00/27.23  | |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 176.00/27.23  | |            (100), (101), (102), (103), (104), (105), (106), (107), (108),
% 176.00/27.23  | |            (109), (110), (111), (113), (114), (115), (116), (118), (119),
% 176.00/27.23  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128) are
% 176.00/27.23  | |            inconsistent by sub-proof #192.
% 176.00/27.23  | | 
% 176.00/27.23  | Case 2:
% 176.00/27.23  | | 
% 176.00/27.23  | |   (129)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.00/27.23  | | 
% 176.00/27.23  | | ALPHA: (129) implies:
% 176.00/27.23  | |   (130)  all_52_30 = e0
% 176.00/27.23  | | 
% 176.00/27.23  | | COMBINE_EQS: (112), (130) imply:
% 176.00/27.23  | |   (131)  all_6_1 = e0
% 176.00/27.23  | | 
% 176.00/27.23  | | REF_CLOSE: (68), (70), (102), (116), (131) are inconsistent by sub-proof
% 176.00/27.23  | |            #201.
% 176.00/27.23  | | 
% 176.00/27.23  | End of split
% 176.00/27.23  | 
% 176.00/27.23  End of proof
% 176.00/27.23  
% 176.00/27.23  Sub-proof #192 shows that the following formulas are inconsistent:
% 176.00/27.23  ----------------------------------------------------------------
% 176.00/27.23    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.23    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.23    (3)   ~ (all_52_17 = all_52_23)
% 176.00/27.23    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.23    (5)  all_56_3 = all_52_7
% 176.00/27.23    (6)  op(e3, e2) = all_52_3
% 176.00/27.23    (7)   ~ (all_52_9 = all_52_25)
% 176.00/27.23    (8)  op(e3, all_52_25) = all_52_24
% 176.00/27.23    (9)   ~ (all_52_19 = all_52_23)
% 176.00/27.23    (10)  op(e1, e2) = all_52_19
% 176.00/27.23    (11)  all_16_1 = all_6_1
% 176.00/27.23    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.00/27.23    (13)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.23    (14)   ~ (all_52_3 = all_10_2)
% 176.00/27.23    (15)  all_58_5 = all_52_13
% 176.00/27.23    (16)   ~ (all_52_25 = all_52_29)
% 176.00/27.23    (17)  all_16_2 = all_6_2
% 176.00/27.23    (18)  all_56_15 = all_6_2
% 176.00/27.23    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.23    (20)  op(e2, e0) = all_52_15
% 176.00/27.23    (21)  op(all_14_1, all_14_2) = all_14_0
% 176.00/27.23    (22)  all_58_3 = all_10_2
% 176.00/27.23    (23)  all_56_9 = all_52_19
% 176.00/27.23    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.23    (25)  all_58_15 = all_6_2
% 176.00/27.23    (26)   ~ (all_52_9 = all_4_2)
% 176.00/27.23    (27)   ~ (all_52_5 = all_52_7)
% 176.00/27.23    (28)  all_58_10 = all_52_15
% 176.00/27.23    (29)  all_8_2 = all_6_2
% 176.00/27.23    (30)   ~ (all_52_5 = all_4_2)
% 176.00/27.23    (31)  all_58_7 = all_52_19
% 176.00/27.23    (32)   ~ (all_52_15 = all_6_2)
% 176.00/27.23    (33)   ~ (all_52_17 = all_52_25)
% 176.00/27.23    (34)  op(e0, e1) = all_52_29
% 176.00/27.23    (35)  all_58_4 = all_52_5
% 176.00/27.23    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.23    (37)  all_34_1 = all_4_1
% 176.00/27.23    (38)   ~ (all_52_27 = all_52_29)
% 176.00/27.23    (39)   ~ (all_52_17 = all_14_2)
% 176.00/27.23    (40)  op(e3, all_4_2) = all_4_1
% 176.00/27.23    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.23    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.23    (43)   ~ (all_52_7 = all_4_2)
% 176.00/27.23    (44)  all_58_1 = all_52_3
% 176.00/27.23    (45)  all_58_0 = all_4_2
% 176.00/27.23    (46)  op(all_4_1, all_4_2) = e1
% 176.00/27.23    (47)  op(e1, all_52_29) = all_52_28
% 176.00/27.23    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.23    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.23    (50)   ~ (all_4_1 = e2)
% 176.00/27.23    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.23    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.23    (53)  all_58_14 = all_52_29
% 176.00/27.23    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.23    (55)   ~ (all_52_3 = all_52_5)
% 176.00/27.23    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.23    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.23    (58)  all_58_8 = all_14_2
% 176.00/27.23    (59)  all_56_1 = all_52_3
% 176.00/27.23    (60)  op(e0, e2) = all_52_27
% 176.00/27.23    (61)   ~ (all_14_0 = e3)
% 176.00/27.23    (62)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.23    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.23    (64)   ~ (all_52_5 = all_14_2)
% 176.00/27.23    (65)   ~ (all_52_3 = all_52_27)
% 176.00/27.23    (66)   ~ (all_52_3 = all_4_2)
% 176.00/27.23    (67)  op(e0, e3) = all_52_25
% 176.00/27.23    (68)  op(e0, all_6_2) = all_6_1
% 176.00/27.23    (69)   ~ (all_52_9 = all_10_2)
% 176.00/27.23    (70)  op(all_6_1, all_6_2) = e2
% 176.00/27.23    (71)  op(e3, all_52_17) = all_52_16
% 176.00/27.23    (72)   ~ (all_52_9 = all_52_13)
% 176.00/27.23    (73)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.23    (74)  op(e0, all_52_23) = all_52_22
% 176.00/27.23    (75)   ~ (all_52_15 = all_52_23)
% 176.00/27.23    (76)   ~ (all_52_5 = all_52_29)
% 176.00/27.23    (77)  all_56_2 = all_52_5
% 176.00/27.23    (78)  op(e1, e0) = all_52_23
% 176.00/27.23    (79)  all_56_12 = all_52_25
% 176.00/27.23    (80)  all_58_13 = all_52_27
% 176.00/27.23    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.23    (82)   ~ (all_52_9 = all_52_17)
% 176.00/27.23    (83)  all_58_6 = all_52_17
% 176.00/27.23    (84)   ~ (all_52_3 = all_52_7)
% 176.00/27.23    (85)  op(e2, all_52_19) = all_52_18
% 176.00/27.23    (86)  all_56_0 = all_4_2
% 176.00/27.23    (87)  all_58_11 = all_52_23
% 176.00/27.23    (88)   ~ (all_52_3 = all_52_19)
% 176.00/27.23    (89)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.23    (90)   ~ (all_52_29 = all_6_2)
% 176.00/27.23    (91)  all_58_2 = all_52_9
% 176.00/27.23    (92)  op(e3, e1) = all_52_5
% 176.00/27.23    (93)   ~ (all_52_25 = all_6_2)
% 176.00/27.23    (94)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.23    (95)  op(e1, e3) = all_52_17
% 176.00/27.23    (96)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.23    (97)   ~ (all_52_25 = all_4_2)
% 176.00/27.23    (98)  op(e3, e0) = all_52_7
% 176.00/27.23    (99)  op(e3, e3) = all_4_2
% 176.00/27.23    (100)  all_56_8 = all_52_17
% 176.00/27.23    (101)   ~ (all_52_17 = all_4_2)
% 176.00/27.23    (102)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.23             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.23    (103)   ~ (all_52_25 = all_52_27)
% 176.00/27.23    (104)  all_34_2 = all_4_2
% 176.00/27.23    (105)   ~ (all_52_27 = all_6_2)
% 176.00/27.23    (106)  all_8_1 = all_6_1
% 176.00/27.23    (107)   ~ (all_52_7 = all_6_2)
% 176.00/27.23    (108)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.00/27.23    (109)   ~ (all_52_7 = all_52_23)
% 176.00/27.23    (110)  op(e2, all_52_27) = all_52_26
% 176.00/27.23    (111)  all_52_20 = all_14_1
% 176.00/27.23    (112)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.23    (113)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.23    (114)  op(e1, all_14_2) = all_14_1
% 176.00/27.23    (115)  all_58_9 = all_52_7
% 176.00/27.23    (116)   ~ (e2 = e0)
% 176.00/27.23    (117)  all_58_12 = all_52_25
% 176.00/27.23    (118)  all_56_6 = all_52_13
% 176.00/27.23    (119)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.23    (120)   ~ (all_52_9 = all_52_15)
% 176.00/27.23    (121)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.23    (122)   ~ (e3 = e2)
% 176.00/27.23    (123)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.23    (124)   ~ (all_52_19 = all_14_2)
% 176.00/27.23    (125)  op(e2, e3) = all_52_9
% 176.00/27.23    (126)  all_56_13 = all_52_27
% 176.00/27.23  
% 176.00/27.23  Begin of proof
% 176.00/27.23  | 
% 176.00/27.23  | ALPHA: (108) implies:
% 176.00/27.23  |   (127)  all_52_22 = e0
% 176.00/27.23  |   (128)  all_52_20 = e1
% 176.00/27.23  |   (129)  all_52_18 = e2
% 176.00/27.23  |   (130)  all_52_16 = e3
% 176.00/27.23  | 
% 176.00/27.23  | COMBINE_EQS: (111), (128) imply:
% 176.00/27.23  |   (131)  all_14_1 = e1
% 176.00/27.23  | 
% 176.00/27.23  | REDUCE: (21), (131) imply:
% 176.00/27.23  |   (132)  op(e1, all_14_2) = all_14_0
% 176.00/27.23  | 
% 176.00/27.23  | REDUCE: (71), (130) imply:
% 176.00/27.23  |   (133)  op(e3, all_52_17) = e3
% 176.00/27.23  | 
% 176.00/27.23  | REDUCE: (85), (129) imply:
% 176.00/27.23  |   (134)  op(e2, all_52_19) = e2
% 176.00/27.23  | 
% 176.00/27.23  | REDUCE: (114), (131) imply:
% 176.00/27.23  |   (135)  op(e1, all_14_2) = e1
% 176.00/27.23  | 
% 176.00/27.23  | REDUCE: (74), (127) imply:
% 176.00/27.23  |   (136)  op(e0, all_52_23) = e0
% 176.00/27.23  | 
% 176.00/27.23  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.00/27.23  |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 176.00/27.23  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.00/27.23  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.00/27.23  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 176.00/27.23  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 176.00/27.23  |            (69), (70), (72), (73), (75), (76), (77), (78), (79), (80), (81),
% 176.00/27.23  |            (82), (83), (84), (86), (87), (88), (89), (90), (91), (92), (93),
% 176.00/27.23  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 176.00/27.23  |            (104), (105), (106), (107), (109), (110), (112), (113), (115),
% 176.00/27.23  |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 176.00/27.23  |            (125), (126), (132), (133), (134), (135), (136) are inconsistent by
% 176.00/27.23  |            sub-proof #193.
% 176.00/27.23  | 
% 176.00/27.23  End of proof
% 176.00/27.23  
% 176.00/27.23  Sub-proof #193 shows that the following formulas are inconsistent:
% 176.00/27.23  ----------------------------------------------------------------
% 176.00/27.23    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.23    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.23    (3)   ~ (all_52_17 = all_52_23)
% 176.00/27.23    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.23    (5)  all_56_3 = all_52_7
% 176.00/27.23    (6)  op(e3, e2) = all_52_3
% 176.00/27.23    (7)   ~ (all_52_9 = all_52_25)
% 176.00/27.23    (8)  op(e3, all_52_25) = all_52_24
% 176.00/27.23    (9)   ~ (all_52_19 = all_52_23)
% 176.00/27.23    (10)  op(e1, e2) = all_52_19
% 176.00/27.23    (11)  all_16_1 = all_6_1
% 176.00/27.23    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.00/27.23    (13)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.23    (14)   ~ (all_52_3 = all_10_2)
% 176.00/27.23    (15)  all_58_5 = all_52_13
% 176.00/27.23    (16)   ~ (all_52_25 = all_52_29)
% 176.00/27.23    (17)  all_16_2 = all_6_2
% 176.00/27.23    (18)  all_56_15 = all_6_2
% 176.00/27.23    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.23    (20)  op(e2, e0) = all_52_15
% 176.00/27.23    (21)  all_58_3 = all_10_2
% 176.00/27.23    (22)  all_56_9 = all_52_19
% 176.00/27.23    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.23    (24)  all_58_15 = all_6_2
% 176.00/27.23    (25)   ~ (all_52_9 = all_4_2)
% 176.00/27.23    (26)   ~ (all_52_5 = all_52_7)
% 176.00/27.23    (27)  all_58_10 = all_52_15
% 176.00/27.23    (28)  all_8_2 = all_6_2
% 176.00/27.23    (29)   ~ (all_52_5 = all_4_2)
% 176.00/27.23    (30)  all_58_7 = all_52_19
% 176.00/27.23    (31)   ~ (all_52_15 = all_6_2)
% 176.00/27.23    (32)   ~ (all_52_17 = all_52_25)
% 176.00/27.23    (33)  op(e0, e1) = all_52_29
% 176.00/27.23    (34)  all_58_4 = all_52_5
% 176.00/27.23    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.23    (36)  all_34_1 = all_4_1
% 176.00/27.23    (37)   ~ (all_52_27 = all_52_29)
% 176.00/27.23    (38)   ~ (all_52_17 = all_14_2)
% 176.00/27.23    (39)  op(e3, all_4_2) = all_4_1
% 176.00/27.23    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.23    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.23    (42)   ~ (all_52_7 = all_4_2)
% 176.00/27.23    (43)  all_58_1 = all_52_3
% 176.00/27.23    (44)  all_58_0 = all_4_2
% 176.00/27.23    (45)  op(all_4_1, all_4_2) = e1
% 176.00/27.23    (46)  op(e1, all_52_29) = all_52_28
% 176.00/27.23    (47)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.23    (48)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.23    (49)   ~ (all_4_1 = e2)
% 176.00/27.23    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.23    (51)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.23    (52)  all_58_14 = all_52_29
% 176.00/27.23    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.23    (54)   ~ (all_52_3 = all_52_5)
% 176.00/27.23    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.23    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.24    (57)  all_58_8 = all_14_2
% 176.00/27.24    (58)  all_56_1 = all_52_3
% 176.00/27.24    (59)  op(e0, e2) = all_52_27
% 176.00/27.24    (60)   ~ (all_14_0 = e3)
% 176.00/27.24    (61)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.24    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.24    (63)   ~ (all_52_5 = all_14_2)
% 176.00/27.24    (64)   ~ (all_52_3 = all_52_27)
% 176.00/27.24    (65)   ~ (all_52_3 = all_4_2)
% 176.00/27.24    (66)  op(e0, e3) = all_52_25
% 176.00/27.24    (67)  op(e0, all_6_2) = all_6_1
% 176.00/27.24    (68)   ~ (all_52_9 = all_10_2)
% 176.00/27.24    (69)  op(all_6_1, all_6_2) = e2
% 176.00/27.24    (70)  op(e1, all_14_2) = all_14_0
% 176.00/27.24    (71)   ~ (all_52_9 = all_52_13)
% 176.00/27.24    (72)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.24    (73)   ~ (all_52_15 = all_52_23)
% 176.00/27.24    (74)   ~ (all_52_5 = all_52_29)
% 176.00/27.24    (75)  all_56_2 = all_52_5
% 176.00/27.24    (76)  op(e1, e0) = all_52_23
% 176.00/27.24    (77)  all_56_12 = all_52_25
% 176.00/27.24    (78)  all_58_13 = all_52_27
% 176.00/27.24    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.24    (80)   ~ (all_52_9 = all_52_17)
% 176.00/27.24    (81)  all_58_6 = all_52_17
% 176.00/27.24    (82)   ~ (all_52_3 = all_52_7)
% 176.00/27.24    (83)  op(e2, all_52_19) = e2
% 176.00/27.24    (84)  op(e3, all_52_17) = e3
% 176.00/27.24    (85)  all_56_0 = all_4_2
% 176.00/27.24    (86)  all_58_11 = all_52_23
% 176.00/27.24    (87)   ~ (all_52_3 = all_52_19)
% 176.00/27.24    (88)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.24    (89)   ~ (all_52_29 = all_6_2)
% 176.00/27.24    (90)  all_58_2 = all_52_9
% 176.00/27.24    (91)  op(e3, e1) = all_52_5
% 176.00/27.24    (92)   ~ (all_52_25 = all_6_2)
% 176.00/27.24    (93)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.24    (94)  op(e1, e3) = all_52_17
% 176.00/27.24    (95)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.24    (96)   ~ (all_52_25 = all_4_2)
% 176.00/27.24    (97)  op(e3, e0) = all_52_7
% 176.00/27.24    (98)  op(e3, e3) = all_4_2
% 176.00/27.24    (99)  all_56_8 = all_52_17
% 176.00/27.24    (100)   ~ (all_52_17 = all_4_2)
% 176.00/27.24    (101)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.24             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.24    (102)   ~ (all_52_25 = all_52_27)
% 176.00/27.24    (103)  all_34_2 = all_4_2
% 176.00/27.24    (104)   ~ (all_52_27 = all_6_2)
% 176.00/27.24    (105)  all_8_1 = all_6_1
% 176.00/27.24    (106)   ~ (all_52_7 = all_6_2)
% 176.00/27.24    (107)  op(e0, all_52_23) = e0
% 176.00/27.24    (108)  op(e1, all_14_2) = e1
% 176.00/27.24    (109)   ~ (all_52_7 = all_52_23)
% 176.00/27.24    (110)  op(e2, all_52_27) = all_52_26
% 176.00/27.24    (111)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.24    (112)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.24    (113)  all_58_9 = all_52_7
% 176.00/27.24    (114)   ~ (e2 = e0)
% 176.00/27.24    (115)  all_58_12 = all_52_25
% 176.00/27.24    (116)  all_56_6 = all_52_13
% 176.00/27.24    (117)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.24    (118)   ~ (all_52_9 = all_52_15)
% 176.00/27.24    (119)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.24    (120)   ~ (e3 = e2)
% 176.00/27.24    (121)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.24    (122)   ~ (all_52_19 = all_14_2)
% 176.00/27.24    (123)  op(e2, e3) = all_52_9
% 176.00/27.24    (124)  all_56_13 = all_52_27
% 176.00/27.24  
% 176.00/27.24  Begin of proof
% 176.00/27.24  | 
% 176.00/27.24  | GROUND_INST: instantiating (101) with e1, all_14_0, all_14_2, e1, simplifying
% 176.00/27.24  |              with (70), (108) gives:
% 176.00/27.24  |   (125)  all_14_0 = e1
% 176.00/27.24  | 
% 176.00/27.24  | REDUCE: (60), (125) imply:
% 176.00/27.24  |   (126)   ~ (e3 = e1)
% 176.00/27.24  | 
% 176.00/27.24  | SIMP: (126) implies:
% 176.00/27.24  |   (127)   ~ (e3 = e1)
% 176.00/27.24  | 
% 176.00/27.24  | BETA: splitting (40) gives:
% 176.00/27.24  | 
% 176.00/27.24  | Case 1:
% 176.00/27.24  | | 
% 176.00/27.24  | |   (128)  all_56_15 = e3
% 176.00/27.24  | | 
% 176.00/27.24  | | COMBINE_EQS: (18), (128) imply:
% 176.00/27.24  | |   (129)  all_6_2 = e3
% 176.00/27.24  | | 
% 176.00/27.24  | | REF_CLOSE: (7), (11), (17), (66), (67), (69), (72), (77), (88), (92), (93),
% 176.00/27.24  | |            (101), (115), (123), (129) are inconsistent by sub-proof #226.
% 176.00/27.24  | | 
% 176.00/27.24  | Case 2:
% 176.00/27.24  | | 
% 176.00/27.24  | |   (130)   ~ (all_56_15 = e3)
% 176.00/27.24  | |   (131)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.24  | | 
% 176.00/27.24  | | REDUCE: (18), (130) imply:
% 176.00/27.24  | |   (132)   ~ (all_6_2 = e3)
% 176.00/27.24  | | 
% 176.00/27.24  | | BETA: splitting (53) gives:
% 176.00/27.24  | | 
% 176.00/27.24  | | Case 1:
% 176.00/27.24  | | | 
% 176.00/27.24  | | |   (133)  all_56_13 = e3
% 176.00/27.24  | | | 
% 176.00/27.24  | | | COMBINE_EQS: (124), (133) imply:
% 176.00/27.24  | | |   (134)  all_52_27 = e3
% 176.00/27.24  | | | 
% 176.00/27.24  | | | REF_CLOSE: (1), (6), (10), (12), (15), (19), (24), (26), (27), (29), (30),
% 176.00/27.24  | | |            (34), (35), (36), (37), (38), (39), (41), (44), (45), (47),
% 176.00/27.24  | | |            (51), (52), (54), (55), (57), (58), (63), (65), (66), (71),
% 176.00/27.24  | | |            (81), (84), (86), (87), (90), (91), (94), (98), (100), (101),
% 176.00/27.24  | | |            (102), (103), (104), (107), (108), (110), (111), (113), (114),
% 176.00/27.24  | | |            (115), (116), (118), (119), (120), (122), (123), (127), (134)
% 176.00/27.24  | | |            are inconsistent by sub-proof #565.
% 176.00/27.24  | | | 
% 176.00/27.24  | | Case 2:
% 176.00/27.24  | | | 
% 176.00/27.24  | | |   (135)   ~ (all_56_13 = e3)
% 176.00/27.24  | | | 
% 176.00/27.24  | | | REDUCE: (124), (135) imply:
% 176.00/27.24  | | |   (136)   ~ (all_52_27 = e3)
% 176.00/27.24  | | | 
% 176.00/27.24  | | | BETA: splitting (56) gives:
% 176.00/27.24  | | | 
% 176.00/27.24  | | | Case 1:
% 176.00/27.24  | | | | 
% 176.00/27.24  | | | |   (137)  all_58_12 = e3
% 176.00/27.24  | | | | 
% 176.00/27.24  | | | | REF_CLOSE: (4), (5), (6), (10), (12), (18), (19), (23), (29), (33),
% 176.00/27.24  | | | |            (36), (39), (42), (44), (45), (47), (49), (52), (58), (59),
% 176.00/27.24  | | | |            (65), (67), (69), (74), (75), (76), (78), (79), (85), (87),
% 176.00/27.24  | | | |            (89), (91), (96), (97), (101), (103), (104), (109), (112),
% 176.00/27.24  | | | |            (115), (121), (127), (131), (137) are inconsistent by
% 176.00/27.24  | | | |            sub-proof #196.
% 176.00/27.24  | | | | 
% 176.00/27.24  | | | Case 2:
% 176.00/27.24  | | | | 
% 176.00/27.24  | | | |   (138)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.24  | | | | 
% 176.00/27.24  | | | | BETA: splitting (138) gives:
% 176.00/27.24  | | | | 
% 176.00/27.24  | | | | Case 1:
% 176.00/27.24  | | | | | 
% 176.00/27.24  | | | | |   (139)  all_58_13 = e3
% 176.00/27.24  | | | | | 
% 176.00/27.24  | | | | | REF_CLOSE: (78), (136), (139) are inconsistent by sub-proof #1026.
% 176.00/27.24  | | | | | 
% 176.00/27.24  | | | | Case 2:
% 176.00/27.24  | | | | | 
% 176.00/27.24  | | | | |   (140)  all_58_14 = e3 | all_58_15 = e3
% 176.00/27.24  | | | | | 
% 176.00/27.24  | | | | | BETA: splitting (140) gives:
% 176.00/27.24  | | | | | 
% 176.00/27.24  | | | | | Case 1:
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | |   (141)  all_58_14 = e3
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | COMBINE_EQS: (52), (141) imply:
% 176.00/27.24  | | | | | |   (142)  all_52_29 = e3
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | SIMP: (142) implies:
% 176.00/27.24  | | | | | |   (143)  all_52_29 = e3
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (74), (143) imply:
% 176.00/27.24  | | | | | |   (144)   ~ (all_52_5 = e3)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (16), (143) imply:
% 176.00/27.24  | | | | | |   (145)   ~ (all_52_25 = e3)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (89), (143) imply:
% 176.00/27.24  | | | | | |   (146)   ~ (all_6_2 = e3)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (46), (143) imply:
% 176.00/27.24  | | | | | |   (147)  op(e1, e3) = all_52_28
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (33), (143) imply:
% 176.00/27.24  | | | | | |   (148)  op(e0, e1) = e3
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | GROUND_INST: instantiating (101) with all_52_17, all_52_28, e3, e1,
% 176.00/27.24  | | | | | |              simplifying with (94), (147) gives:
% 176.00/27.24  | | | | | |   (149)  all_52_17 = all_52_28
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | COMBINE_EQS: (99), (149) imply:
% 176.00/27.24  | | | | | |   (150)  all_56_8 = all_52_28
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | COMBINE_EQS: (81), (149) imply:
% 176.00/27.24  | | | | | |   (151)  all_58_6 = all_52_28
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (3), (149) imply:
% 176.00/27.24  | | | | | |   (152)   ~ (all_52_23 = all_52_28)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | SIMP: (152) implies:
% 176.00/27.24  | | | | | |   (153)   ~ (all_52_23 = all_52_28)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (32), (149) imply:
% 176.00/27.24  | | | | | |   (154)   ~ (all_52_25 = all_52_28)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | SIMP: (154) implies:
% 176.00/27.24  | | | | | |   (155)   ~ (all_52_25 = all_52_28)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (100), (149) imply:
% 176.00/27.24  | | | | | |   (156)   ~ (all_52_28 = all_4_2)
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (84), (149) imply:
% 176.00/27.24  | | | | | |   (157)  op(e3, all_52_28) = e3
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | BETA: splitting (50) gives:
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | Case 1:
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | |   (158)  all_58_1 = e3
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | COMBINE_EQS: (43), (158) imply:
% 176.00/27.24  | | | | | | |   (159)  all_52_3 = e3
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | REDUCE: (82), (159) imply:
% 176.00/27.24  | | | | | | |   (160)   ~ (all_52_7 = e3)
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | SIMP: (160) implies:
% 176.00/27.24  | | | | | | |   (161)   ~ (all_52_7 = e3)
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | REDUCE: (64), (159) imply:
% 176.00/27.24  | | | | | | |   (162)   ~ (all_52_27 = e3)
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | REDUCE: (65), (159) imply:
% 176.00/27.24  | | | | | | |   (163)   ~ (all_4_2 = e3)
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | SIMP: (163) implies:
% 176.00/27.24  | | | | | | |   (164)   ~ (all_4_2 = e3)
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | BETA: splitting (41) gives:
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | Case 1:
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | |   (165)  all_58_2 = e3
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | COMBINE_EQS: (90), (165) imply:
% 176.00/27.24  | | | | | | | |   (166)  all_52_9 = e3
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | SIMP: (166) implies:
% 176.00/27.24  | | | | | | | |   (167)  all_52_9 = e3
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | REDUCE: (71), (167) imply:
% 176.00/27.24  | | | | | | | |   (168)   ~ (all_52_13 = e3)
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | SIMP: (168) implies:
% 176.00/27.24  | | | | | | | |   (169)   ~ (all_52_13 = e3)
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | REDUCE: (118), (167) imply:
% 176.00/27.24  | | | | | | | |   (170)   ~ (all_52_15 = e3)
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | SIMP: (170) implies:
% 176.00/27.24  | | | | | | | |   (171)   ~ (all_52_15 = e3)
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | REDUCE: (7), (167) imply:
% 176.00/27.24  | | | | | | | |   (172)   ~ (all_52_25 = e3)
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | BETA: splitting (111) gives:
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | Case 1:
% 176.00/27.24  | | | | | | | | | 
% 176.00/27.24  | | | | | | | | |   (173)  all_58_9 = e3
% 176.00/27.24  | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | REF_CLOSE: (113), (161), (173) are inconsistent by sub-proof
% 176.00/27.24  | | | | | | | | |            #972.
% 176.00/27.24  | | | | | | | | | 
% 176.00/27.24  | | | | | | | | Case 2:
% 176.00/27.24  | | | | | | | | | 
% 176.00/27.24  | | | | | | | | |   (174)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.24  | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | BETA: splitting (174) gives:
% 176.00/27.24  | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | Case 1:
% 176.00/27.24  | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | |   (175)  all_58_10 = e3
% 176.00/27.24  | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | REF_CLOSE: (27), (171), (175) are inconsistent by sub-proof
% 176.00/27.24  | | | | | | | | | |            #1018.
% 176.00/27.24  | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | Case 2:
% 176.00/27.24  | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | |   (176)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.24  | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | BETA: splitting (176) gives:
% 176.00/27.24  | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | Case 1:
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | |   (177)  all_58_11 = e3
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | COMBINE_EQS: (86), (177) imply:
% 176.00/27.24  | | | | | | | | | | |   (178)  all_52_23 = e3
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | SIMP: (178) implies:
% 176.00/27.24  | | | | | | | | | | |   (179)  all_52_23 = e3
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | REDUCE: (9), (179) imply:
% 176.00/27.24  | | | | | | | | | | |   (180)   ~ (all_52_19 = e3)
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | REDUCE: (153), (179) imply:
% 176.00/27.24  | | | | | | | | | | |   (181)   ~ (all_52_28 = e3)
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | SIMP: (181) implies:
% 176.00/27.24  | | | | | | | | | | |   (182)   ~ (all_52_28 = e3)
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | REDUCE: (76), (179) imply:
% 176.00/27.24  | | | | | | | | | | |   (183)  op(e1, e0) = e3
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | REDUCE: (107), (179) imply:
% 176.00/27.24  | | | | | | | | | | |   (184)  op(e0, e3) = e0
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (14), (15), (18), (19), (20),
% 176.00/27.24  | | | | | | | | | | |            (21), (23), (25), (27), (28), (30), (31), (34),
% 176.00/27.24  | | | | | | | | | | |            (39), (41), (43), (44), (49), (50), (54), (55),
% 176.00/27.24  | | | | | | | | | | |            (57), (61), (62), (65), (66), (67), (68), (78),
% 176.00/27.24  | | | | | | | | | | |            (79), (81), (83), (84), (85), (87), (90), (91),
% 176.00/27.24  | | | | | | | | | | |            (92), (95), (96), (97), (98), (100), (101), (102),
% 176.00/27.24  | | | | | | | | | | |            (105), (106), (108), (113), (115), (120), (127),
% 176.00/27.24  | | | | | | | | | | |            (131), (136), (145), (148), (150), (151), (155),
% 176.00/27.24  | | | | | | | | | | |            (156), (157), (169), (171), (177), (180), (182),
% 176.00/27.24  | | | | | | | | | | |            (183), (184) are inconsistent by sub-proof #205.
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | Case 2:
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | |   (185)  all_58_15 = e3
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | COMBINE_EQS: (24), (185) imply:
% 176.00/27.24  | | | | | | | | | | |   (186)  all_6_2 = e3
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | REDUCE: (132), (186) imply:
% 176.00/27.24  | | | | | | | | | | |   (187)  $false
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | | CLOSE: (187) is inconsistent.
% 176.00/27.24  | | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | | End of split
% 176.00/27.24  | | | | | | | | | | 
% 176.00/27.24  | | | | | | | | | End of split
% 176.00/27.24  | | | | | | | | | 
% 176.00/27.24  | | | | | | | | End of split
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | Case 2:
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | |   (188)   ~ (all_58_2 = e3)
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | REDUCE: (90), (188) imply:
% 176.00/27.24  | | | | | | | |   (189)   ~ (all_52_9 = e3)
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | | REF_CLOSE: (44), (55), (81), (84), (90), (98), (100), (101),
% 176.00/27.24  | | | | | | | |            (115), (145), (164), (189) are inconsistent by
% 176.00/27.24  | | | | | | | |            sub-proof #912.
% 176.00/27.24  | | | | | | | | 
% 176.00/27.24  | | | | | | | End of split
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | Case 2:
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | |   (190)   ~ (all_58_1 = e3)
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | REDUCE: (43), (190) imply:
% 176.00/27.24  | | | | | | |   (191)   ~ (all_52_3 = e3)
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | | REF_CLOSE: (22), (30), (34), (35), (39), (41), (42), (43), (44),
% 176.00/27.24  | | | | | | |            (45), (48), (55), (57), (63), (80), (81), (83), (84),
% 176.00/27.24  | | | | | | |            (86), (90), (91), (94), (98), (100), (101), (108),
% 176.00/27.24  | | | | | | |            (109), (113), (115), (117), (120), (123), (127), (144),
% 176.00/27.24  | | | | | | |            (145), (191) are inconsistent by sub-proof #563.
% 176.00/27.24  | | | | | | | 
% 176.00/27.24  | | | | | | End of split
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | Case 2:
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | |   (192)  all_58_15 = e3
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | COMBINE_EQS: (24), (192) imply:
% 176.00/27.24  | | | | | |   (193)  all_6_2 = e3
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | REDUCE: (132), (193) imply:
% 176.00/27.24  | | | | | |   (194)  $false
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | | CLOSE: (194) is inconsistent.
% 176.00/27.24  | | | | | | 
% 176.00/27.24  | | | | | End of split
% 176.00/27.24  | | | | | 
% 176.00/27.24  | | | | End of split
% 176.00/27.24  | | | | 
% 176.00/27.24  | | | End of split
% 176.00/27.24  | | | 
% 176.00/27.24  | | End of split
% 176.00/27.24  | | 
% 176.00/27.24  | End of split
% 176.00/27.24  | 
% 176.00/27.24  End of proof
% 176.00/27.24  
% 176.00/27.24  Sub-proof #194 shows that the following formulas are inconsistent:
% 176.00/27.24  ----------------------------------------------------------------
% 176.00/27.24    (1)   ~ (all_52_27 = all_10_2)
% 176.00/27.24    (2)   ~ (all_52_17 = all_52_23)
% 176.00/27.24    (3)   ~ (all_52_13 = all_52_29)
% 176.00/27.24    (4)  op(e2, all_10_2) = all_10_0
% 176.00/27.24    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.24    (6)  all_56_3 = all_52_7
% 176.00/27.24    (7)  op(e3, e2) = all_52_3
% 176.00/27.24    (8)   ~ (all_52_9 = all_52_25)
% 176.00/27.24    (9)  op(e3, all_52_25) = all_52_24
% 176.00/27.24    (10)  op(e1, e2) = all_52_19
% 176.00/27.24    (11)  all_16_1 = all_6_1
% 176.00/27.24    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.00/27.24    (13)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.24    (14)   ~ (all_52_3 = all_10_2)
% 176.00/27.24    (15)  all_58_5 = all_52_13
% 176.00/27.24    (16)   ~ (all_52_25 = all_52_29)
% 176.00/27.24    (17)  op(e1, all_52_13) = e1
% 176.00/27.24    (18)  op(e0, all_52_15) = e0
% 176.00/27.24    (19)  all_16_2 = all_6_2
% 176.00/27.24    (20)  all_56_15 = all_6_2
% 176.00/27.24    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.24    (22)  all_58_3 = all_10_2
% 176.00/27.24    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.24    (24)  all_58_15 = all_6_2
% 176.00/27.24    (25)   ~ (all_52_9 = all_4_2)
% 176.00/27.24    (26)  all_58_10 = all_52_15
% 176.00/27.24    (27)  all_8_2 = all_6_2
% 176.00/27.24    (28)   ~ (all_52_5 = all_4_2)
% 176.00/27.24    (29)  all_58_7 = all_52_19
% 176.00/27.24    (30)  all_56_4 = all_52_9
% 176.00/27.24    (31)  op(e0, e1) = all_52_29
% 176.00/27.24    (32)  all_58_4 = all_52_5
% 176.00/27.24    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.24    (34)   ~ (e3 = e1)
% 176.00/27.24    (35)  all_34_1 = all_4_1
% 176.00/27.24    (36)   ~ (all_52_27 = all_52_29)
% 176.00/27.24    (37)  op(e3, all_4_2) = all_4_1
% 176.00/27.24    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.24    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.24    (40)   ~ (all_52_7 = all_4_2)
% 176.00/27.24    (41)  all_58_1 = all_52_3
% 176.00/27.24    (42)  all_58_0 = all_4_2
% 176.00/27.24    (43)  op(all_4_1, all_4_2) = e1
% 176.00/27.24    (44)  op(e1, all_52_29) = all_52_28
% 176.00/27.24    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.24    (46)   ~ (all_4_1 = e2)
% 176.00/27.24    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.24    (48)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.24    (49)  all_58_14 = all_52_29
% 176.00/27.24    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.24    (51)   ~ (all_52_3 = all_52_5)
% 176.00/27.24    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.24    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.24    (54)  all_58_8 = all_14_2
% 176.00/27.24    (55)  all_56_1 = all_52_3
% 176.00/27.24    (56)  op(e0, e2) = all_52_27
% 176.00/27.24    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.24    (58)   ~ (all_52_3 = all_52_27)
% 176.00/27.24    (59)   ~ (all_52_3 = all_4_2)
% 176.00/27.24    (60)  op(e0, e3) = all_52_25
% 176.00/27.24    (61)  op(e0, all_6_2) = all_6_1
% 176.00/27.24    (62)  op(all_6_1, all_6_2) = e2
% 176.00/27.24    (63)  op(e3, all_52_9) = e3
% 176.00/27.24    (64)   ~ (all_52_9 = all_52_13)
% 176.00/27.24    (65)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.24    (66)   ~ (all_52_15 = all_52_23)
% 176.00/27.24    (67)   ~ (all_52_5 = all_52_29)
% 176.00/27.24    (68)  all_56_2 = all_52_5
% 176.00/27.24    (69)  op(e1, e0) = all_52_23
% 176.00/27.24    (70)  all_56_12 = all_52_25
% 176.00/27.24    (71)  all_58_13 = all_52_27
% 176.00/27.24    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.24    (73)  all_58_6 = all_52_17
% 176.00/27.24    (74)   ~ (all_52_3 = all_52_7)
% 176.00/27.24    (75)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.24    (76)   ~ (e1 = e0)
% 176.00/27.24    (77)  all_56_0 = all_4_2
% 176.00/27.24    (78)  all_58_11 = all_52_23
% 176.00/27.24    (79)   ~ (all_52_3 = all_52_19)
% 176.00/27.24    (80)   ~ (all_52_29 = all_14_2)
% 176.00/27.24    (81)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.24    (82)   ~ (all_52_29 = all_6_2)
% 176.00/27.24    (83)  all_58_2 = all_52_9
% 176.00/27.24    (84)  op(e3, e1) = all_52_5
% 176.00/27.24    (85)   ~ (all_52_25 = all_6_2)
% 176.00/27.24    (86)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.24    (87)  op(e1, e3) = all_52_17
% 176.00/27.24    (88)   ~ (all_52_25 = all_4_2)
% 176.00/27.24    (89)  op(e3, e0) = all_52_7
% 176.00/27.24    (90)  op(e2, all_10_2) = e2
% 176.00/27.24    (91)  op(e3, e3) = all_4_2
% 176.00/27.24    (92)   ~ (all_52_17 = all_4_2)
% 176.00/27.24    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.24    (94)   ~ (all_52_25 = all_52_27)
% 176.00/27.24    (95)  all_34_2 = all_4_2
% 176.00/27.24    (96)   ~ (all_52_27 = all_6_2)
% 176.00/27.24    (97)  all_8_1 = all_6_1
% 176.00/27.24    (98)   ~ (all_52_7 = all_6_2)
% 176.00/27.24    (99)   ~ (all_10_0 = e3)
% 176.00/27.24    (100)   ~ (all_52_7 = all_52_23)
% 176.00/27.24    (101)  op(e2, all_52_27) = all_52_26
% 176.00/27.24    (102)   ~ (all_52_17 = all_52_19)
% 176.00/27.24    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.24    (104)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.24    (105)  all_58_9 = all_52_7
% 176.00/27.24    (106)  all_58_12 = all_52_25
% 176.00/27.24    (107)   ~ (all_10_0 = e1)
% 176.00/27.24    (108)  all_56_6 = all_52_13
% 176.00/27.24    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.24    (110)   ~ (all_52_9 = all_52_15)
% 176.00/27.24    (111)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.24    (112)  op(e2, e3) = all_52_9
% 176.00/27.24    (113)  all_56_13 = all_52_27
% 176.00/27.24  
% 176.00/27.24  Begin of proof
% 176.00/27.24  | 
% 176.00/27.24  | GROUND_INST: instantiating (93) with e2, all_10_0, all_10_2, e2, simplifying
% 176.00/27.24  |              with (4), (90) gives:
% 176.00/27.24  |   (114)  all_10_0 = e2
% 176.00/27.24  | 
% 176.00/27.24  | REDUCE: (99), (114) imply:
% 176.00/27.24  |   (115)   ~ (e3 = e2)
% 176.00/27.24  | 
% 176.00/27.24  | SIMP: (115) implies:
% 176.00/27.24  |   (116)   ~ (e3 = e2)
% 176.00/27.24  | 
% 176.00/27.24  | REDUCE: (107), (114) imply:
% 176.00/27.24  |   (117)   ~ (e2 = e1)
% 176.00/27.24  | 
% 176.00/27.24  | BETA: splitting (38) gives:
% 176.00/27.24  | 
% 176.00/27.24  | Case 1:
% 176.00/27.24  | | 
% 176.00/27.24  | |   (118)  all_56_15 = e3
% 176.00/27.24  | | 
% 176.00/27.24  | | COMBINE_EQS: (20), (118) imply:
% 176.00/27.24  | |   (119)  all_6_2 = e3
% 176.00/27.24  | | 
% 176.00/27.24  | | SIMP: (119) implies:
% 176.00/27.24  | |   (120)  all_6_2 = e3
% 176.00/27.24  | | 
% 176.00/27.24  | | REF_CLOSE: (8), (11), (19), (60), (61), (62), (65), (70), (81), (85), (86),
% 176.00/27.24  | |            (93), (106), (112), (120) are inconsistent by sub-proof #226.
% 176.00/27.24  | | 
% 176.00/27.24  | Case 2:
% 176.00/27.24  | | 
% 176.00/27.24  | |   (121)   ~ (all_56_15 = e3)
% 176.00/27.24  | |   (122)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.24  | | 
% 176.00/27.24  | | REDUCE: (20), (121) imply:
% 176.00/27.24  | |   (123)   ~ (all_6_2 = e3)
% 176.00/27.24  | | 
% 176.00/27.24  | | BETA: splitting (50) gives:
% 176.00/27.24  | | 
% 176.00/27.24  | | Case 1:
% 176.00/27.24  | | | 
% 176.00/27.24  | | |   (124)  all_56_13 = e3
% 176.00/27.24  | | | 
% 176.00/27.24  | | | REF_CLOSE: (1), (7), (8), (10), (12), (15), (17), (18), (21), (22), (23),
% 176.00/27.24  | | |            (25), (26), (30), (34), (35), (37), (39), (42), (43), (45),
% 176.00/27.24  | | |            (48), (52), (55), (58), (59), (60), (63), (64), (73), (75),
% 176.00/27.24  | | |            (77), (79), (83), (87), (88), (91), (92), (93), (94), (95),
% 176.00/27.24  | | |            (101), (106), (108), (109), (110), (112), (113), (124) are
% 176.00/27.24  | | |            inconsistent by sub-proof #593.
% 176.00/27.24  | | | 
% 176.00/27.24  | | Case 2:
% 176.00/27.24  | | | 
% 176.00/27.24  | | |   (125)   ~ (all_56_13 = e3)
% 176.00/27.24  | | | 
% 176.00/27.24  | | | REDUCE: (113), (125) imply:
% 176.00/27.24  | | |   (126)   ~ (all_52_27 = e3)
% 176.00/27.24  | | | 
% 176.00/27.24  | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (12), (13), (14), (15),
% 176.00/27.24  | | |            (16), (18), (20), (21), (22), (23), (24), (25), (26), (27),
% 176.00/27.24  | | |            (28), (29), (31), (32), (33), (34), (35), (36), (37), (39),
% 176.00/27.24  | | |            (40), (41), (42), (43), (44), (45), (46), (47), (49), (51),
% 176.00/27.24  | | |            (52), (53), (54), (55), (56), (57), (59), (60), (61), (62),
% 176.00/27.24  | | |            (63), (66), (67), (68), (69), (71), (72), (73), (74), (76),
% 176.00/27.24  | | |            (77), (78), (79), (80), (82), (83), (84), (85), (87), (88),
% 176.00/27.24  | | |            (89), (90), (91), (93), (95), (96), (97), (98), (100), (102),
% 176.00/27.24  | | |            (103), (104), (105), (106), (109), (111), (112), (116), (117),
% 176.00/27.24  | | |            (122), (123), (126) are inconsistent by sub-proof #195.
% 176.00/27.24  | | | 
% 176.00/27.24  | | End of split
% 176.00/27.24  | | 
% 176.00/27.24  | End of split
% 176.00/27.24  | 
% 176.00/27.24  End of proof
% 176.00/27.24  
% 176.00/27.24  Sub-proof #195 shows that the following formulas are inconsistent:
% 176.00/27.24  ----------------------------------------------------------------
% 176.00/27.24    (1)   ~ (all_52_17 = all_52_23)
% 176.00/27.24    (2)   ~ (all_52_13 = all_52_29)
% 176.00/27.24    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.24    (4)  all_56_3 = all_52_7
% 176.00/27.24    (5)  op(e3, e2) = all_52_3
% 176.00/27.24    (6)  op(e3, all_52_25) = all_52_24
% 176.00/27.24    (7)  op(e1, e2) = all_52_19
% 176.00/27.24    (8)   ~ (all_52_27 = e3)
% 176.00/27.24    (9)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.00/27.24    (10)   ~ (all_6_2 = e3)
% 176.00/27.24    (11)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.24    (12)   ~ (all_52_3 = all_10_2)
% 176.00/27.24    (13)  all_58_5 = all_52_13
% 176.00/27.24    (14)   ~ (all_52_25 = all_52_29)
% 176.00/27.24    (15)  op(e0, all_52_15) = e0
% 176.00/27.24    (16)  all_56_15 = all_6_2
% 176.00/27.24    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.24    (18)  all_58_3 = all_10_2
% 176.00/27.24    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.24    (20)  all_58_15 = all_6_2
% 176.00/27.24    (21)   ~ (all_52_9 = all_4_2)
% 176.00/27.24    (22)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.24    (23)  all_58_10 = all_52_15
% 176.00/27.24    (24)  all_8_2 = all_6_2
% 176.00/27.24    (25)   ~ (all_52_5 = all_4_2)
% 176.00/27.24    (26)  all_58_7 = all_52_19
% 176.00/27.24    (27)  op(e0, e1) = all_52_29
% 176.00/27.24    (28)  all_58_4 = all_52_5
% 176.00/27.24    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.24    (30)   ~ (e3 = e1)
% 176.00/27.24    (31)  all_34_1 = all_4_1
% 176.00/27.24    (32)   ~ (all_52_27 = all_52_29)
% 176.00/27.24    (33)  op(e3, all_4_2) = all_4_1
% 176.00/27.24    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.24    (35)   ~ (all_52_7 = all_4_2)
% 176.00/27.24    (36)  all_58_1 = all_52_3
% 176.00/27.24    (37)  all_58_0 = all_4_2
% 176.00/27.24    (38)  op(all_4_1, all_4_2) = e1
% 176.00/27.24    (39)  op(e1, all_52_29) = all_52_28
% 176.00/27.24    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.24    (41)   ~ (all_4_1 = e2)
% 176.00/27.24    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.25    (43)  all_58_14 = all_52_29
% 176.00/27.25    (44)   ~ (all_52_3 = all_52_5)
% 176.00/27.25    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.25    (46)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.25    (47)  all_58_8 = all_14_2
% 176.00/27.25    (48)  all_56_1 = all_52_3
% 176.00/27.25    (49)  op(e0, e2) = all_52_27
% 176.00/27.25    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.25    (51)   ~ (all_52_3 = all_4_2)
% 176.00/27.25    (52)  op(e0, e3) = all_52_25
% 176.00/27.25    (53)  op(e0, all_6_2) = all_6_1
% 176.00/27.25    (54)  op(all_6_1, all_6_2) = e2
% 176.00/27.25    (55)  op(e3, all_52_9) = e3
% 176.00/27.25    (56)   ~ (all_52_15 = all_52_23)
% 176.00/27.25    (57)   ~ (all_52_5 = all_52_29)
% 176.00/27.25    (58)  all_56_2 = all_52_5
% 176.00/27.25    (59)  op(e1, e0) = all_52_23
% 176.00/27.25    (60)  all_58_13 = all_52_27
% 176.00/27.25    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.25    (62)  all_58_6 = all_52_17
% 176.00/27.25    (63)   ~ (all_52_3 = all_52_7)
% 176.00/27.25    (64)   ~ (e1 = e0)
% 176.00/27.25    (65)  all_56_0 = all_4_2
% 176.00/27.25    (66)  all_58_11 = all_52_23
% 176.00/27.25    (67)   ~ (all_52_3 = all_52_19)
% 176.00/27.25    (68)   ~ (all_52_29 = all_14_2)
% 176.00/27.25    (69)   ~ (all_52_29 = all_6_2)
% 176.00/27.25    (70)  all_58_2 = all_52_9
% 176.00/27.25    (71)  op(e3, e1) = all_52_5
% 176.00/27.25    (72)   ~ (e2 = e1)
% 176.00/27.25    (73)   ~ (all_52_25 = all_6_2)
% 176.00/27.25    (74)  op(e1, e3) = all_52_17
% 176.00/27.25    (75)   ~ (all_52_25 = all_4_2)
% 176.00/27.25    (76)  op(e3, e0) = all_52_7
% 176.00/27.25    (77)  op(e2, all_10_2) = e2
% 176.00/27.25    (78)  op(e3, e3) = all_4_2
% 176.00/27.25    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.25    (80)  all_34_2 = all_4_2
% 176.00/27.25    (81)   ~ (all_52_27 = all_6_2)
% 176.00/27.25    (82)  all_8_1 = all_6_1
% 176.00/27.25    (83)   ~ (all_52_7 = all_6_2)
% 176.00/27.25    (84)   ~ (all_52_7 = all_52_23)
% 176.00/27.25    (85)   ~ (all_52_17 = all_52_19)
% 176.00/27.25    (86)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.25    (87)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.25    (88)  all_58_9 = all_52_7
% 176.00/27.25    (89)  all_58_12 = all_52_25
% 176.00/27.25    (90)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.25    (91)   ~ (e3 = e2)
% 176.00/27.25    (92)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.25    (93)  op(e2, e3) = all_52_9
% 176.00/27.25  
% 176.00/27.25  Begin of proof
% 176.00/27.25  | 
% 176.00/27.25  | BETA: splitting (46) gives:
% 176.00/27.25  | 
% 176.00/27.25  | Case 1:
% 176.00/27.25  | | 
% 176.00/27.25  | |   (94)  all_58_12 = e3
% 176.00/27.25  | | 
% 176.00/27.25  | | REF_CLOSE: (3), (4), (5), (7), (9), (16), (17), (19), (22), (25), (27),
% 176.00/27.25  | |            (30), (31), (33), (35), (37), (38), (40), (41), (43), (48), (49),
% 176.00/27.25  | |            (51), (53), (54), (57), (58), (59), (60), (61), (65), (67), (69),
% 176.00/27.25  | |            (71), (75), (76), (79), (80), (81), (84), (87), (89), (92), (94)
% 176.00/27.25  | |            are inconsistent by sub-proof #196.
% 176.00/27.25  | | 
% 176.00/27.25  | Case 2:
% 176.00/27.25  | | 
% 176.00/27.25  | |   (95)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.25  | | 
% 176.00/27.25  | | BETA: splitting (95) gives:
% 176.00/27.25  | | 
% 176.00/27.25  | | Case 1:
% 176.00/27.25  | | | 
% 176.00/27.25  | | |   (96)  all_58_13 = e3
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REF_CLOSE: (8), (60), (96) are inconsistent by sub-proof #1026.
% 176.00/27.25  | | | 
% 176.00/27.25  | | Case 2:
% 176.00/27.25  | | | 
% 176.00/27.25  | | |   (97)  all_58_14 = e3 | all_58_15 = e3
% 176.00/27.25  | | | 
% 176.00/27.25  | | | BETA: splitting (97) gives:
% 176.00/27.25  | | | 
% 176.00/27.25  | | | Case 1:
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | |   (98)  all_58_14 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | COMBINE_EQS: (43), (98) imply:
% 176.00/27.25  | | | |   (99)  all_52_29 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | SIMP: (99) implies:
% 176.00/27.25  | | | |   (100)  all_52_29 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (2), (100) imply:
% 176.00/27.25  | | | |   (101)   ~ (all_52_13 = e3)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (14), (100) imply:
% 176.00/27.25  | | | |   (102)   ~ (all_52_25 = e3)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (68), (100) imply:
% 176.00/27.25  | | | |   (103)   ~ (all_14_2 = e3)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | SIMP: (103) implies:
% 176.00/27.25  | | | |   (104)   ~ (all_14_2 = e3)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (69), (100) imply:
% 176.00/27.25  | | | |   (105)   ~ (all_6_2 = e3)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (39), (100) imply:
% 176.00/27.25  | | | |   (106)  op(e1, e3) = all_52_28
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (27), (100) imply:
% 176.00/27.25  | | | |   (107)  op(e0, e1) = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | GROUND_INST: instantiating (79) with all_52_17, all_52_28, e3, e1,
% 176.00/27.25  | | | |              simplifying with (74), (106) gives:
% 176.00/27.25  | | | |   (108)  all_52_17 = all_52_28
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | COMBINE_EQS: (62), (108) imply:
% 176.00/27.25  | | | |   (109)  all_58_6 = all_52_28
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (85), (108) imply:
% 176.00/27.25  | | | |   (110)   ~ (all_52_19 = all_52_28)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | SIMP: (110) implies:
% 176.00/27.25  | | | |   (111)   ~ (all_52_19 = all_52_28)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (1), (108) imply:
% 176.00/27.25  | | | |   (112)   ~ (all_52_23 = all_52_28)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | SIMP: (112) implies:
% 176.00/27.25  | | | |   (113)   ~ (all_52_23 = all_52_28)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | BETA: splitting (40) gives:
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | Case 1:
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | |   (114)  all_56_1 = e3
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | COMBINE_EQS: (48), (114) imply:
% 176.00/27.25  | | | | |   (115)  all_52_3 = e3
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | COMBINE_EQS: (36), (115) imply:
% 176.00/27.25  | | | | |   (116)  all_58_1 = e3
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REDUCE: (44), (115) imply:
% 176.00/27.25  | | | | |   (117)   ~ (all_52_5 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | SIMP: (117) implies:
% 176.00/27.25  | | | | |   (118)   ~ (all_52_5 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REDUCE: (63), (115) imply:
% 176.00/27.25  | | | | |   (119)   ~ (all_52_7 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | SIMP: (119) implies:
% 176.00/27.25  | | | | |   (120)   ~ (all_52_7 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REDUCE: (67), (115) imply:
% 176.00/27.25  | | | | |   (121)   ~ (all_52_19 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | SIMP: (121) implies:
% 176.00/27.25  | | | | |   (122)   ~ (all_52_19 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REDUCE: (12), (115) imply:
% 176.00/27.25  | | | | |   (123)   ~ (all_10_2 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | SIMP: (123) implies:
% 176.00/27.25  | | | | |   (124)   ~ (all_10_2 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REDUCE: (51), (115) imply:
% 176.00/27.25  | | | | |   (125)   ~ (all_4_2 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | SIMP: (125) implies:
% 176.00/27.25  | | | | |   (126)   ~ (all_4_2 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | BETA: splitting (86) gives:
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | Case 1:
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | |   (127)  all_58_9 = e3
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | REF_CLOSE: (88), (120), (127) are inconsistent by sub-proof #972.
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | Case 2:
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | |   (128)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | BETA: splitting (45) gives:
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | Case 1:
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | |   (129)  all_58_0 = e3
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | | COMBINE_EQS: (37), (129) imply:
% 176.00/27.25  | | | | | | |   (130)  all_4_2 = e3
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | | REDUCE: (126), (130) imply:
% 176.00/27.25  | | | | | | |   (131)  $false
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | | CLOSE: (131) is inconsistent.
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | Case 2:
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | |   (132)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | | BETA: splitting (29) gives:
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | | Case 1:
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | |   (133)  all_58_6 = e3
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | | COMBINE_EQS: (109), (133) imply:
% 176.00/27.25  | | | | | | | |   (134)  all_52_28 = e3
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | | SIMP: (134) implies:
% 176.00/27.25  | | | | | | | |   (135)  all_52_28 = e3
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | | REDUCE: (113), (135) imply:
% 176.00/27.25  | | | | | | | |   (136)   ~ (all_52_23 = e3)
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | | REF_CLOSE: (6), (10), (11), (15), (16), (20), (22), (23), (24),
% 176.00/27.25  | | | | | | | |            (28), (30), (33), (37), (41), (50), (52), (53), (55),
% 176.00/27.25  | | | | | | | |            (61), (64), (66), (70), (71), (72), (73), (76), (79),
% 176.00/27.25  | | | | | | | |            (82), (83), (88), (89), (91), (107), (116), (118),
% 176.00/27.25  | | | | | | | |            (128), (133), (136) are inconsistent by sub-proof
% 176.00/27.25  | | | | | | | |            #212.
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | Case 2:
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | |   (137)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | | REF_CLOSE: (13), (18), (21), (23), (26), (34), (47), (55), (56),
% 176.00/27.25  | | | | | | | |            (66), (70), (78), (79), (101), (104), (122), (124),
% 176.00/27.25  | | | | | | | |            (132), (137) are inconsistent by sub-proof #965.
% 176.00/27.25  | | | | | | | | 
% 176.00/27.25  | | | | | | | End of split
% 176.00/27.25  | | | | | | | 
% 176.00/27.25  | | | | | | End of split
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | End of split
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | Case 2:
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | |   (138)   ~ (all_56_1 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REDUCE: (48), (138) imply:
% 176.00/27.25  | | | | |   (139)   ~ (all_52_3 = e3)
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REF_CLOSE: (5), (8), (12), (18), (21), (26), (30), (33), (34), (36),
% 176.00/27.25  | | | | |            (37), (38), (42), (45), (55), (60), (70), (77), (78), (79),
% 176.00/27.25  | | | | |            (89), (90), (93), (102), (109), (111), (139) are
% 176.00/27.25  | | | | |            inconsistent by sub-proof #358.
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | End of split
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | Case 2:
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | |   (140)  all_58_15 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | COMBINE_EQS: (20), (140) imply:
% 176.00/27.25  | | | |   (141)  all_6_2 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (10), (141) imply:
% 176.00/27.25  | | | |   (142)  $false
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | CLOSE: (142) is inconsistent.
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | End of split
% 176.00/27.25  | | | 
% 176.00/27.25  | | End of split
% 176.00/27.25  | | 
% 176.00/27.25  | End of split
% 176.00/27.25  | 
% 176.00/27.25  End of proof
% 176.00/27.25  
% 176.00/27.25  Sub-proof #196 shows that the following formulas are inconsistent:
% 176.00/27.25  ----------------------------------------------------------------
% 176.00/27.25    (1)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.25    (2)  all_56_3 = all_52_7
% 176.00/27.25    (3)  op(e3, e2) = all_52_3
% 176.00/27.25    (4)  op(e1, e2) = all_52_19
% 176.00/27.25    (5)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.00/27.25    (6)  all_56_15 = all_6_2
% 176.00/27.25    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.25    (8)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.25    (9)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.25    (10)   ~ (all_52_5 = all_4_2)
% 176.00/27.25    (11)  op(e0, e1) = all_52_29
% 176.00/27.25    (12)   ~ (e3 = e1)
% 176.00/27.25    (13)  all_34_1 = all_4_1
% 176.00/27.25    (14)  op(e3, all_4_2) = all_4_1
% 176.00/27.25    (15)   ~ (all_52_7 = all_4_2)
% 176.00/27.25    (16)  all_58_0 = all_4_2
% 176.00/27.25    (17)  op(all_4_1, all_4_2) = e1
% 176.00/27.25    (18)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.25    (19)   ~ (all_4_1 = e2)
% 176.00/27.25    (20)  all_58_14 = all_52_29
% 176.00/27.25    (21)  all_56_1 = all_52_3
% 176.00/27.25    (22)  op(e0, e2) = all_52_27
% 176.00/27.25    (23)   ~ (all_52_3 = all_4_2)
% 176.00/27.25    (24)  op(e0, all_6_2) = all_6_1
% 176.00/27.25    (25)  op(all_6_1, all_6_2) = e2
% 176.00/27.25    (26)   ~ (all_52_5 = all_52_29)
% 176.00/27.25    (27)  all_56_2 = all_52_5
% 176.00/27.25    (28)  op(e1, e0) = all_52_23
% 176.00/27.25    (29)  all_58_13 = all_52_27
% 176.00/27.25    (30)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.25    (31)  all_58_12 = e3
% 176.00/27.25    (32)  all_56_0 = all_4_2
% 176.00/27.25    (33)   ~ (all_52_3 = all_52_19)
% 176.00/27.25    (34)   ~ (all_52_29 = all_6_2)
% 176.00/27.25    (35)  op(e3, e1) = all_52_5
% 176.00/27.25    (36)   ~ (all_52_25 = all_4_2)
% 176.00/27.25    (37)  op(e3, e0) = all_52_7
% 176.00/27.25    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.25    (39)  all_34_2 = all_4_2
% 176.00/27.25    (40)   ~ (all_52_27 = all_6_2)
% 176.00/27.25    (41)   ~ (all_52_7 = all_52_23)
% 176.00/27.25    (42)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.25    (43)  all_58_12 = all_52_25
% 176.00/27.25    (44)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.25  
% 176.00/27.25  Begin of proof
% 176.00/27.25  | 
% 176.00/27.25  | COMBINE_EQS: (31), (43) imply:
% 176.00/27.25  |   (45)  all_52_25 = e3
% 176.00/27.25  | 
% 176.00/27.25  | SIMP: (45) implies:
% 176.00/27.25  |   (46)  all_52_25 = e3
% 176.00/27.25  | 
% 176.00/27.25  | REDUCE: (36), (46) imply:
% 176.00/27.25  |   (47)   ~ (all_4_2 = e3)
% 176.00/27.25  | 
% 176.00/27.25  | SIMP: (47) implies:
% 176.00/27.25  |   (48)   ~ (all_4_2 = e3)
% 176.00/27.25  | 
% 176.00/27.25  | BETA: splitting (8) gives:
% 176.00/27.25  | 
% 176.00/27.25  | Case 1:
% 176.00/27.25  | | 
% 176.00/27.25  | |   (49)  all_56_0 = e3
% 176.00/27.25  | | 
% 176.00/27.25  | | COMBINE_EQS: (32), (49) imply:
% 176.00/27.25  | |   (50)  all_4_2 = e3
% 176.00/27.25  | | 
% 176.00/27.25  | | REDUCE: (48), (50) imply:
% 176.00/27.25  | |   (51)  $false
% 176.00/27.25  | | 
% 176.00/27.25  | | CLOSE: (51) is inconsistent.
% 176.00/27.25  | | 
% 176.00/27.25  | Case 2:
% 176.00/27.25  | | 
% 176.00/27.25  | |   (52)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.25  | | 
% 176.00/27.25  | | BETA: splitting (30) gives:
% 176.00/27.25  | | 
% 176.00/27.25  | | Case 1:
% 176.00/27.25  | | | 
% 176.00/27.25  | | |   (53)  all_58_0 = e1
% 176.00/27.25  | | | 
% 176.00/27.25  | | | COMBINE_EQS: (16), (53) imply:
% 176.00/27.25  | | |   (54)  all_4_2 = e1
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (10), (54) imply:
% 176.00/27.25  | | |   (55)   ~ (all_52_5 = e1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (17), (54) imply:
% 176.00/27.25  | | |   (56)  op(all_4_1, e1) = e1
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (14), (54) imply:
% 176.00/27.25  | | |   (57)  op(e3, e1) = all_4_1
% 176.00/27.25  | | | 
% 176.00/27.25  | | | GROUND_INST: instantiating (38) with all_52_5, all_4_1, e1, e3,
% 176.00/27.25  | | |              simplifying with (35), (57) gives:
% 176.00/27.25  | | |   (58)  all_52_5 = all_4_1
% 176.00/27.25  | | | 
% 176.00/27.25  | | | COMBINE_EQS: (27), (58) imply:
% 176.00/27.25  | | |   (59)  all_56_2 = all_4_1
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (26), (58) imply:
% 176.00/27.25  | | |   (60)   ~ (all_52_29 = all_4_1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | SIMP: (60) implies:
% 176.00/27.25  | | |   (61)   ~ (all_52_29 = all_4_1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (55), (58) imply:
% 176.00/27.25  | | |   (62)   ~ (all_4_1 = e1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | BETA: splitting (44) gives:
% 176.00/27.25  | | | 
% 176.00/27.25  | | | Case 1:
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | |   (63)  all_56_2 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | COMBINE_EQS: (59), (63) imply:
% 176.00/27.25  | | | |   (64)  all_4_1 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | SIMP: (64) implies:
% 176.00/27.25  | | | |   (65)  all_4_1 = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (56), (65) imply:
% 176.00/27.25  | | | |   (66)  op(e3, e1) = e1
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (57), (65) imply:
% 176.00/27.25  | | | |   (67)  op(e3, e1) = e3
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | GROUND_INST: instantiating (38) with e1, e3, e1, e3, simplifying with
% 176.00/27.25  | | | |              (66), (67) gives:
% 176.00/27.25  | | | |   (68)  e3 = e1
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (12), (68) imply:
% 176.00/27.25  | | | |   (69)  $false
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | CLOSE: (69) is inconsistent.
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | Case 2:
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | |   (70)   ~ (all_56_2 = e3)
% 176.00/27.25  | | | |   (71)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | REDUCE: (59), (70) imply:
% 176.00/27.25  | | | |   (72)   ~ (all_4_1 = e3)
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | BETA: splitting (71) gives:
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | | Case 1:
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | |   (73)  all_56_2 = e2
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | REF_CLOSE: (19), (59), (73) are inconsistent by sub-proof #929.
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | Case 2:
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | |   (74)  all_56_2 = e1 | all_56_2 = e0
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | BETA: splitting (74) gives:
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | | Case 1:
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | |   (75)  all_56_2 = e1
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | REF_CLOSE: (59), (62), (75) are inconsistent by sub-proof #723.
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | Case 2:
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | |   (76)  all_56_2 = e0
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | COMBINE_EQS: (59), (76) imply:
% 176.00/27.25  | | | | | |   (77)  all_4_1 = e0
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | SIMP: (77) implies:
% 176.00/27.25  | | | | | |   (78)  all_4_1 = e0
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | REDUCE: (61), (78) imply:
% 176.00/27.25  | | | | | |   (79)   ~ (all_52_29 = e0)
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | REDUCE: (72), (78) imply:
% 176.00/27.25  | | | | | |   (80)   ~ (e3 = e0)
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | SIMP: (80) implies:
% 176.00/27.25  | | | | | |   (81)   ~ (e3 = e0)
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | REDUCE: (56), (78) imply:
% 176.00/27.25  | | | | | |   (82)  op(e0, e1) = e1
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | | REF_CLOSE: (1), (6), (9), (11), (20), (22), (24), (25), (29), (31),
% 176.00/27.25  | | | | | |            (34), (38), (40), (79), (81), (82) are inconsistent by
% 176.00/27.25  | | | | | |            sub-proof #197.
% 176.00/27.25  | | | | | | 
% 176.00/27.25  | | | | | End of split
% 176.00/27.25  | | | | | 
% 176.00/27.25  | | | | End of split
% 176.00/27.25  | | | | 
% 176.00/27.25  | | | End of split
% 176.00/27.25  | | | 
% 176.00/27.25  | | Case 2:
% 176.00/27.25  | | | 
% 176.00/27.25  | | |   (83)   ~ (all_58_0 = e1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (16), (83) imply:
% 176.00/27.25  | | |   (84)   ~ (all_4_2 = e1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REF_CLOSE: (2), (3), (4), (5), (7), (12), (13), (14), (15), (16), (17),
% 176.00/27.25  | | |            (18), (19), (21), (23), (28), (32), (33), (37), (38), (39),
% 176.00/27.25  | | |            (41), (42), (52), (84) are inconsistent by sub-proof #587.
% 176.00/27.25  | | | 
% 176.00/27.25  | | End of split
% 176.00/27.25  | | 
% 176.00/27.25  | End of split
% 176.00/27.25  | 
% 176.00/27.25  End of proof
% 176.00/27.25  
% 176.00/27.25  Sub-proof #197 shows that the following formulas are inconsistent:
% 176.00/27.25  ----------------------------------------------------------------
% 176.00/27.25    (1)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.25    (2)  op(e0, e1) = e1
% 176.00/27.25    (3)  all_56_15 = all_6_2
% 176.00/27.25    (4)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.25    (5)  op(e0, e1) = all_52_29
% 176.00/27.25    (6)  all_58_14 = all_52_29
% 176.00/27.25    (7)  op(e0, e2) = all_52_27
% 176.00/27.25    (8)  op(e0, all_6_2) = all_6_1
% 176.00/27.25    (9)  op(all_6_1, all_6_2) = e2
% 176.00/27.25    (10)   ~ (e3 = e0)
% 176.00/27.25    (11)  all_58_13 = all_52_27
% 176.00/27.25    (12)  all_58_12 = e3
% 176.00/27.25    (13)   ~ (all_52_29 = all_6_2)
% 176.00/27.25    (14)   ~ (all_52_29 = e0)
% 176.00/27.25    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.25    (16)   ~ (all_52_27 = all_6_2)
% 176.00/27.25  
% 176.00/27.25  Begin of proof
% 176.00/27.25  | 
% 176.00/27.25  | BETA: splitting (1) gives:
% 176.00/27.25  | 
% 176.00/27.25  | Case 1:
% 176.00/27.25  | | 
% 176.00/27.25  | |   (17)  all_58_12 = e0
% 176.00/27.25  | | 
% 176.00/27.25  | | REF_CLOSE: (10), (12), (17) are inconsistent by sub-proof #682.
% 176.00/27.25  | | 
% 176.00/27.25  | Case 2:
% 176.00/27.25  | | 
% 176.00/27.25  | |   (18)  all_58_13 = e0 | all_58_14 = e0
% 176.00/27.25  | | 
% 176.00/27.25  | | BETA: splitting (18) gives:
% 176.00/27.25  | | 
% 176.00/27.25  | | Case 1:
% 176.00/27.25  | | | 
% 176.00/27.25  | | |   (19)  all_58_13 = e0
% 176.00/27.25  | | | 
% 176.00/27.25  | | | COMBINE_EQS: (11), (19) imply:
% 176.00/27.25  | | |   (20)  all_52_27 = e0
% 176.00/27.25  | | | 
% 176.00/27.25  | | | SIMP: (20) implies:
% 176.00/27.25  | | |   (21)  all_52_27 = e0
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (16), (21) imply:
% 176.00/27.25  | | |   (22)   ~ (all_6_2 = e0)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | SIMP: (22) implies:
% 176.00/27.25  | | |   (23)   ~ (all_6_2 = e0)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (7), (21) imply:
% 176.00/27.25  | | |   (24)  op(e0, e2) = e0
% 176.00/27.25  | | | 
% 176.00/27.25  | | | GROUND_INST: instantiating (15) with all_52_29, e1, e1, e0, simplifying
% 176.00/27.25  | | |              with (2), (5) gives:
% 176.00/27.25  | | |   (25)  all_52_29 = e1
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REDUCE: (13), (25) imply:
% 176.00/27.25  | | |   (26)   ~ (all_6_2 = e1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | SIMP: (26) implies:
% 176.00/27.25  | | |   (27)   ~ (all_6_2 = e1)
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REF_CLOSE: (3), (4), (8), (9), (15), (23), (24), (27) are inconsistent by
% 176.00/27.25  | | |            sub-proof #218.
% 176.00/27.25  | | | 
% 176.00/27.25  | | Case 2:
% 176.00/27.25  | | | 
% 176.00/27.25  | | |   (28)  all_58_14 = e0
% 176.00/27.25  | | | 
% 176.00/27.25  | | | REF_CLOSE: (6), (14), (28) are inconsistent by sub-proof #696.
% 176.00/27.25  | | | 
% 176.00/27.25  | | End of split
% 176.00/27.25  | | 
% 176.00/27.25  | End of split
% 176.00/27.25  | 
% 176.00/27.25  End of proof
% 176.00/27.25  
% 176.00/27.25  Sub-proof #198 shows that the following formulas are inconsistent:
% 176.00/27.25  ----------------------------------------------------------------
% 176.00/27.25    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.25    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.25    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.25    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.25    (5)   ~ (all_52_27 = all_10_2)
% 176.00/27.25    (6)   ~ (all_52_17 = all_52_23)
% 176.00/27.25    (7)  op(e2, all_10_2) = all_10_1
% 176.00/27.25    (8)  all_40_2 = all_4_2
% 176.00/27.25    (9)   ~ (all_52_13 = all_52_29)
% 176.00/27.25    (10)  all_56_3 = all_52_7
% 176.00/27.25    (11)  op(e3, e2) = all_52_3
% 176.00/27.25    (12)   ~ (all_52_9 = all_52_25)
% 176.00/27.25    (13)  op(e3, all_52_25) = all_52_24
% 176.00/27.25    (14)   ~ (all_52_19 = all_52_23)
% 176.00/27.25    (15)  all_56_11 = all_52_23
% 176.00/27.25    (16)  op(e1, e2) = all_52_19
% 176.00/27.25    (17)  all_16_1 = all_6_1
% 176.00/27.25    (18)  op(e3, all_52_9) = all_52_8
% 176.00/27.25    (19)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.25    (20)   ~ (all_52_3 = all_10_2)
% 176.00/27.25    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.00/27.25    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 176.00/27.25    (23)  all_58_5 = all_52_13
% 176.00/27.25    (24)   ~ (all_52_25 = all_52_29)
% 176.00/27.25    (25)  all_16_2 = all_6_2
% 176.00/27.25    (26)  all_56_15 = all_6_2
% 176.00/27.25    (27)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.25    (28)  op(e2, e0) = all_52_15
% 176.00/27.25    (29)  op(all_14_1, all_14_2) = all_14_0
% 176.00/27.25    (30)  all_58_3 = all_10_2
% 176.00/27.25    (31)  all_56_9 = all_52_19
% 176.00/27.25    (32)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.25    (33)  all_58_15 = all_6_2
% 176.00/27.25    (34)   ~ (all_52_9 = all_4_2)
% 176.00/27.25    (35)   ~ (all_52_5 = all_52_7)
% 176.00/27.25    (36)  all_58_10 = all_52_15
% 176.00/27.25    (37)  all_8_2 = all_6_2
% 176.00/27.25    (38)   ~ (all_52_5 = all_4_2)
% 176.00/27.25    (39)  all_58_7 = all_52_19
% 176.00/27.25    (40)  all_56_4 = all_52_9
% 176.00/27.25    (41)   ~ (all_52_15 = all_6_2)
% 176.00/27.25    (42)   ~ (all_52_17 = all_52_25)
% 176.00/27.25    (43)  op(e0, e1) = all_52_29
% 176.00/27.25    (44)   ~ (all_4_0 = e2)
% 176.00/27.25    (45)  all_58_4 = all_52_5
% 176.00/27.25    (46)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.25    (47)   ~ (e3 = e1)
% 176.00/27.25    (48)   ~ (all_52_27 = all_52_29)
% 176.00/27.25    (49)   ~ (all_52_17 = all_14_2)
% 176.00/27.25    (50)  op(e3, all_4_2) = all_4_1
% 176.00/27.25    (51)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.25    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.25    (53)   ~ (all_52_7 = all_4_2)
% 176.00/27.25    (54)  all_58_1 = all_52_3
% 176.00/27.25    (55)   ~ (all_52_13 = all_52_15)
% 176.00/27.25    (56)  all_58_0 = all_4_2
% 176.00/27.25    (57)  all_52_0 = e1
% 176.00/27.25    (58)  op(e1, all_52_13) = all_52_12
% 176.00/27.25    (59)  op(e0, e0) = all_6_2
% 176.00/27.25    (60)  op(e1, all_52_29) = all_52_28
% 176.00/27.25    (61)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.25    (62)   ~ (all_4_1 = e2)
% 176.00/27.25    (63)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.25    (64)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.25    (65)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.25    (66)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.00/27.25    (67)   ~ (all_14_1 = e3)
% 176.00/27.25    (68)  all_58_14 = all_52_29
% 176.00/27.25    (69)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.25    (70)   ~ (all_52_3 = all_52_5)
% 176.00/27.25    (71)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.25    (72)  op(e2, e1) = all_52_13
% 176.00/27.25    (73)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.25    (74)  all_58_8 = all_14_2
% 176.00/27.25    (75)   ~ (all_14_0 = e3)
% 176.00/27.25    (76)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.00/27.25    (77)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.25    (78)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.25    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.25    (80)   ~ (all_52_5 = all_14_2)
% 176.00/27.25    (81)   ~ (all_52_3 = all_52_27)
% 176.00/27.25    (82)   ~ (all_52_3 = all_4_2)
% 176.00/27.25    (83)  op(e0, e3) = all_52_25
% 176.00/27.25    (84)  op(e0, all_6_2) = all_6_1
% 176.00/27.25    (85)   ~ (all_52_9 = all_10_2)
% 176.00/27.25    (86)  op(all_6_1, all_6_2) = e2
% 176.00/27.25    (87)  op(e3, all_52_17) = all_52_16
% 176.00/27.25    (88)  all_52_10 = all_10_1
% 176.00/27.25    (89)   ~ (all_52_13 = all_14_2)
% 176.00/27.26    (90)   ~ (e3 = e0)
% 176.00/27.26    (91)  all_40_0 = all_4_0
% 176.00/27.26    (92)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.26    (93)   ~ (all_52_9 = all_52_13)
% 176.00/27.26    (94)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.26    (95)  op(e0, all_52_23) = all_52_22
% 176.00/27.26    (96)   ~ (all_52_15 = all_52_23)
% 176.00/27.26    (97)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.26    (98)  op(all_10_1, all_10_2) = all_10_0
% 176.00/27.26    (99)  op(e1, e0) = all_52_23
% 176.00/27.26    (100)  all_56_12 = all_52_25
% 176.00/27.26    (101)  all_58_13 = all_52_27
% 176.00/27.26    (102)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.26    (103)  all_56_5 = all_10_2
% 176.00/27.26    (104)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.00/27.26    (105)   ~ (all_52_9 = all_52_17)
% 176.00/27.26    (106)   ~ (all_14_0 = e2)
% 176.00/27.26    (107)  all_58_6 = all_52_17
% 176.00/27.26    (108)   ~ (all_52_3 = all_52_7)
% 176.00/27.26    (109)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.26    (110)  op(e2, all_52_19) = all_52_18
% 176.00/27.26    (111)   ~ (e1 = e0)
% 176.00/27.26    (112)  all_56_0 = all_4_2
% 176.00/27.26    (113)  all_58_11 = all_52_23
% 176.00/27.26    (114)   ~ (all_52_3 = all_52_19)
% 176.00/27.26    (115)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.26    (116)   ~ (all_52_7 = all_52_15)
% 176.00/27.26    (117)  op(e0, all_52_15) = all_52_14
% 176.00/27.26    (118)   ~ (all_52_29 = all_14_2)
% 176.00/27.26    (119)   ~ (all_4_0 = e1)
% 176.00/27.26    (120)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.26    (121)   ~ (all_52_19 = all_10_2)
% 176.00/27.26    (122)   ~ (all_52_23 = all_6_2)
% 176.00/27.26    (123)  op(e1, all_4_2) = all_4_0
% 176.00/27.26    (124)   ~ (all_52_29 = all_6_2)
% 176.00/27.26    (125)  all_58_2 = all_52_9
% 176.00/27.26    (126)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.26    (127)  op(e3, e1) = all_52_5
% 176.00/27.26    (128)  all_56_10 = all_14_2
% 176.00/27.26    (129)   ~ (all_52_25 = all_6_2)
% 176.00/27.26    (130)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.00/27.26    (131)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.26    (132)  op(e1, e3) = all_52_17
% 176.00/27.26    (133)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.00/27.26    (134)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.26    (135)   ~ (all_52_25 = all_4_2)
% 176.00/27.26    (136)  op(e3, e0) = all_52_7
% 176.00/27.26    (137)  op(e3, e3) = all_4_2
% 176.00/27.26    (138)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 176.00/27.26             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 176.00/27.26    (139)   ~ (all_10_1 = e3)
% 176.00/27.26    (140)  all_56_8 = all_52_17
% 176.00/27.26    (141)   ~ (all_52_17 = all_4_2)
% 176.00/27.26    (142)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.26             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.26    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.00/27.26           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.00/27.26           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.00/27.26           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.00/27.26    (144)   ~ (all_52_25 = all_52_27)
% 176.00/27.26    (145)   ~ (all_52_27 = all_6_2)
% 176.00/27.26    (146)  all_8_1 = all_6_1
% 176.00/27.26    (147)   ~ (all_52_7 = all_6_2)
% 176.00/27.26    (148)   ~ (all_10_0 = e3)
% 176.00/27.26    (149)   ~ (all_52_15 = all_10_2)
% 176.00/27.26    (150)   ~ (all_52_19 = all_52_27)
% 176.00/27.26    (151)  all_56_7 = all_52_15
% 176.00/27.26    (152)   ~ (all_52_7 = all_52_23)
% 176.00/27.26    (153)  op(e2, all_52_27) = all_52_26
% 176.00/27.26    (154)  all_52_20 = all_14_1
% 176.00/27.26    (155)   ~ (all_52_17 = all_52_19)
% 176.00/27.26    (156)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.26    (157)  all_52_30 = all_6_1
% 176.00/27.26    (158)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.26    (159)  op(e1, all_14_2) = all_14_1
% 176.00/27.26    (160)  all_58_9 = all_52_7
% 176.00/27.26    (161)   ~ (e2 = e0)
% 176.00/27.26    (162)  all_58_12 = all_52_25
% 176.00/27.26    (163)  op(e3, all_4_2) = e1
% 176.00/27.26    (164)   ~ (all_10_0 = e1)
% 176.00/27.26    (165)  all_56_6 = all_52_13
% 176.00/27.26    (166)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.26    (167)   ~ (all_52_9 = all_52_15)
% 176.00/27.26    (168)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.26    (169)   ~ (e3 = e2)
% 176.00/27.26    (170)   ~ (all_52_19 = all_14_2)
% 176.00/27.26    (171)  op(e2, e3) = all_52_9
% 176.00/27.26    (172)  all_56_13 = all_52_27
% 176.00/27.26  
% 176.00/27.26  Begin of proof
% 176.00/27.26  | 
% 176.00/27.26  | BETA: splitting (138) gives:
% 176.00/27.26  | 
% 176.00/27.26  | Case 1:
% 176.00/27.26  | | 
% 176.00/27.26  | |   (173)  all_58_15 = e0
% 176.00/27.26  | | 
% 176.00/27.26  | | REF_CLOSE: (33), (59), (84), (86), (142), (161), (173) are inconsistent by
% 176.00/27.26  | |            sub-proof #228.
% 176.00/27.26  | | 
% 176.00/27.26  | Case 2:
% 176.00/27.26  | | 
% 176.00/27.26  | |   (174)   ~ (all_58_15 = e0)
% 176.00/27.26  | |   (175)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 176.00/27.26  | |            | all_58_13 = e0 | all_58_14 = e0)
% 176.00/27.26  | | 
% 176.00/27.26  | | ALPHA: (175) implies:
% 176.00/27.26  | |   (176)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.26  | | 
% 176.00/27.26  | | REDUCE: (33), (174) imply:
% 176.00/27.26  | |   (177)   ~ (all_6_2 = e0)
% 176.00/27.26  | | 
% 176.00/27.26  | | BETA: splitting (143) gives:
% 176.00/27.26  | | 
% 176.00/27.26  | | Case 1:
% 176.00/27.26  | | | 
% 176.00/27.26  | | |   (178)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.00/27.26  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.00/27.26  | | |            e0)
% 176.00/27.26  | | | 
% 176.00/27.26  | | | BETA: splitting (178) gives:
% 176.00/27.26  | | | 
% 176.00/27.26  | | | Case 1:
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | |   (179)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REF_CLOSE: (47), (57), (179) are inconsistent by sub-proof #632.
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | Case 2:
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | |   (180)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.00/27.26  | | | |          e0
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | ALPHA: (180) implies:
% 176.00/27.26  | | | |   (181)  all_52_14 = e0
% 176.00/27.26  | | | |   (182)  all_52_12 = e1
% 176.00/27.26  | | | |   (183)  all_52_10 = e2
% 176.00/27.26  | | | |   (184)  all_52_8 = e3
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | COMBINE_EQS: (88), (183) imply:
% 176.00/27.26  | | | |   (185)  all_10_1 = e2
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REDUCE: (98), (185) imply:
% 176.00/27.26  | | | |   (186)  op(e2, all_10_2) = all_10_0
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REDUCE: (18), (184) imply:
% 176.00/27.26  | | | |   (187)  op(e3, all_52_9) = e3
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REDUCE: (7), (185) imply:
% 176.00/27.26  | | | |   (188)  op(e2, all_10_2) = e2
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REDUCE: (58), (182) imply:
% 176.00/27.26  | | | |   (189)  op(e1, all_52_13) = e1
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REDUCE: (117), (181) imply:
% 176.00/27.26  | | | |   (190)  op(e0, all_52_15) = e0
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | GROUND_INST: instantiating (142) with e2, all_10_0, all_10_2, e2,
% 176.00/27.26  | | | |              simplifying with (186), (188) gives:
% 176.00/27.26  | | | |   (191)  all_10_0 = e2
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REDUCE: (148), (191) imply:
% 176.00/27.26  | | | |   (192)   ~ (e3 = e2)
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | REDUCE: (164), (191) imply:
% 176.00/27.26  | | | |   (193)   ~ (e2 = e1)
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | BETA: splitting (51) gives:
% 176.00/27.26  | | | | 
% 176.00/27.26  | | | | Case 1:
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | |   (194)  all_56_15 = e3
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | | COMBINE_EQS: (26), (194) imply:
% 176.00/27.26  | | | | |   (195)  all_6_2 = e3
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | | SIMP: (195) implies:
% 176.00/27.26  | | | | |   (196)  all_6_2 = e3
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | | REF_CLOSE: (12), (17), (25), (83), (84), (86), (94), (100), (120),
% 176.00/27.26  | | | | |            (129), (131), (142), (162), (171), (196) are inconsistent
% 176.00/27.26  | | | | |            by sub-proof #226.
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | Case 2:
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | |   (197)   ~ (all_56_15 = e3)
% 176.00/27.26  | | | | |   (198)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | | REDUCE: (26), (197) imply:
% 176.00/27.26  | | | | |   (199)   ~ (all_6_2 = e3)
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | | BETA: splitting (69) gives:
% 176.00/27.26  | | | | | 
% 176.00/27.26  | | | | | Case 1:
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | |   (200)  all_56_13 = e3
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | | COMBINE_EQS: (172), (200) imply:
% 176.00/27.26  | | | | | |   (201)  all_52_27 = e3
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | | SIMP: (201) implies:
% 176.00/27.26  | | | | | |   (202)  all_52_27 = e3
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (10), (11), (16), (23), (30),
% 176.00/27.26  | | | | | |            (31), (32), (33), (34), (35), (36), (38), (39), (42),
% 176.00/27.26  | | | | | |            (44), (45), (46), (47), (49), (52), (53), (54), (56),
% 176.00/27.26  | | | | | |            (61), (68), (71), (74), (76), (80), (81), (83), (89),
% 176.00/27.26  | | | | | |            (91), (93), (96), (102), (107), (112), (113), (114),
% 176.00/27.26  | | | | | |            (116), (123), (125), (127), (132), (135), (137), (141),
% 176.00/27.26  | | | | | |            (142), (145), (150), (152), (153), (156), (158), (160),
% 176.00/27.26  | | | | | |            (162), (163), (166), (168), (171), (187), (189), (190),
% 176.00/27.26  | | | | | |            (202) are inconsistent by sub-proof #610.
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | Case 2:
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | |   (203)   ~ (all_56_13 = e3)
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | | REDUCE: (172), (203) imply:
% 176.00/27.26  | | | | | |   (204)   ~ (all_52_27 = e3)
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | | BETA: splitting (73) gives:
% 176.00/27.26  | | | | | | 
% 176.00/27.26  | | | | | | Case 1:
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | |   (205)  all_58_12 = e3
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | COMBINE_EQS: (162), (205) imply:
% 176.00/27.26  | | | | | | |   (206)  all_52_25 = e3
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | SIMP: (206) implies:
% 176.00/27.26  | | | | | | |   (207)  all_52_25 = e3
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | REDUCE: (12), (207) imply:
% 176.00/27.26  | | | | | | |   (208)   ~ (all_52_9 = e3)
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | REDUCE: (144), (207) imply:
% 176.00/27.26  | | | | | | |   (209)   ~ (all_52_27 = e3)
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | REDUCE: (24), (207) imply:
% 176.00/27.26  | | | | | | |   (210)   ~ (all_52_29 = e3)
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | SIMP: (210) implies:
% 176.00/27.26  | | | | | | |   (211)   ~ (all_52_29 = e3)
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | REDUCE: (129), (207) imply:
% 176.00/27.26  | | | | | | |   (212)   ~ (all_6_2 = e3)
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | REDUCE: (135), (207) imply:
% 176.00/27.26  | | | | | | |   (213)   ~ (all_4_2 = e3)
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | SIMP: (213) implies:
% 176.00/27.26  | | | | | | |   (214)   ~ (all_4_2 = e3)
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | REDUCE: (83), (207) imply:
% 176.00/27.26  | | | | | | |   (215)  op(e0, e3) = e3
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | BETA: splitting (32) gives:
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | |   (216)  all_56_0 = e3
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | | COMBINE_EQS: (112), (216) imply:
% 176.00/27.26  | | | | | | | |   (217)  all_4_2 = e3
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | | REDUCE: (214), (217) imply:
% 176.00/27.26  | | | | | | | |   (218)  $false
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | | CLOSE: (218) is inconsistent.
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | |   (219)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | | BETA: splitting (109) gives:
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | 
% 176.00/27.26  | | | | | | | | |   (220)  all_56_4 = e3
% 176.00/27.26  | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | REF_CLOSE: (40), (208), (220) are inconsistent by sub-proof
% 176.00/27.26  | | | | | | | | |            #782.
% 176.00/27.26  | | | | | | | | | 
% 176.00/27.26  | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | 
% 176.00/27.26  | | | | | | | | |   (221)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.26  | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | BETA: splitting (130) gives:
% 176.00/27.26  | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | |   (222)  all_56_5 = e3
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | COMBINE_EQS: (103), (222) imply:
% 176.00/27.26  | | | | | | | | | |   (223)  all_10_2 = e3
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | SIMP: (223) implies:
% 176.00/27.26  | | | | | | | | | |   (224)  all_10_2 = e3
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | REF_CLOSE: (11), (20), (142), (171), (187), (188), (224) are
% 176.00/27.26  | | | | | | | | | |            inconsistent by sub-proof #977.
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | |   (225)   ~ (all_56_5 = e3)
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | REDUCE: (103), (225) imply:
% 176.00/27.26  | | | | | | | | | |   (226)   ~ (all_10_2 = e3)
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | BETA: splitting (64) gives:
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | |   (227)  all_58_1 = e3
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | COMBINE_EQS: (54), (227) imply:
% 176.00/27.26  | | | | | | | | | | |   (228)  all_52_3 = e3
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (9), (10), (23), (26), (30), (33),
% 176.00/27.26  | | | | | | | | | | |            (34), (35), (36), (38), (39), (40), (45), (48),
% 176.00/27.26  | | | | | | | | | | |            (49), (53), (54), (56), (63), (68), (70), (72),
% 176.00/27.26  | | | | | | | | | | |            (74), (79), (87), (90), (101), (105), (108),
% 176.00/27.26  | | | | | | | | | | |            (112), (113), (127), (132), (133), (136), (142),
% 176.00/27.26  | | | | | | | | | | |            (145), (147), (151), (152), (155), (156), (158),
% 176.00/27.26  | | | | | | | | | | |            (160), (168), (169), (177), (187), (188), (189),
% 176.00/27.26  | | | | | | | | | | |            (190), (198), (199), (211), (215), (219), (221),
% 176.00/27.26  | | | | | | | | | | |            (228) are inconsistent by sub-proof #386.
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | |   (229)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | BETA: splitting (229) gives:
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | |   (230)  all_58_3 = e3
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | COMBINE_EQS: (30), (230) imply:
% 176.00/27.26  | | | | | | | | | | | |   (231)  all_10_2 = e3
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | REDUCE: (226), (231) imply:
% 176.00/27.26  | | | | | | | | | | | |   (232)  $false
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | |   (233)  all_58_7 = e3 | all_58_13 = e3
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | BETA: splitting (233) gives:
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | |   (234)  all_58_7 = e3
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | COMBINE_EQS: (39), (234) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (235)  all_52_19 = e3
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (14), (235) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (236)   ~ (all_52_23 = e3)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | SIMP: (236) implies:
% 176.00/27.26  | | | | | | | | | | | | |   (237)   ~ (all_52_23 = e3)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (170), (235) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (238)   ~ (all_14_2 = e3)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | SIMP: (238) implies:
% 176.00/27.26  | | | | | | | | | | | | |   (239)   ~ (all_14_2 = e3)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (110), (235) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (240)  op(e2, e3) = all_52_18
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (16), (235) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (241)  op(e1, e2) = e3
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | GROUND_INST: instantiating (142) with all_52_9, all_52_18, e3,
% 176.00/27.26  | | | | | | | | | | | | |              e2, simplifying with (171), (240) gives:
% 176.00/27.26  | | | | | | | | | | | | |   (242)  all_52_9 = all_52_18
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | COMBINE_EQS: (40), (242) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (243)  all_56_4 = all_52_18
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | COMBINE_EQS: (125), (242) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (244)  all_58_2 = all_52_18
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (93), (242) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (245)   ~ (all_52_13 = all_52_18)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | SIMP: (245) implies:
% 176.00/27.26  | | | | | | | | | | | | |   (246)   ~ (all_52_13 = all_52_18)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (167), (242) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (247)   ~ (all_52_15 = all_52_18)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | SIMP: (247) implies:
% 176.00/27.26  | | | | | | | | | | | | |   (248)   ~ (all_52_15 = all_52_18)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (105), (242) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (249)   ~ (all_52_17 = all_52_18)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | SIMP: (249) implies:
% 176.00/27.26  | | | | | | | | | | | | |   (250)   ~ (all_52_17 = all_52_18)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (34), (242) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (251)   ~ (all_52_18 = all_4_2)
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REDUCE: (187), (242) imply:
% 176.00/27.26  | | | | | | | | | | | | |   (252)  op(e3, all_52_18) = e3
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | BETA: splitting (168) gives:
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | |   (253)  all_58_4 = e3
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | COMBINE_EQS: (45), (253) imply:
% 176.00/27.26  | | | | | | | | | | | | | |   (254)  all_52_5 = e3
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | SIMP: (254) implies:
% 176.00/27.26  | | | | | | | | | | | | | |   (255)  all_52_5 = e3
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (20), (30), (31), (33), (35), (36),
% 176.00/27.26  | | | | | | | | | | | | | |            (39), (54), (61), (64), (70), (90), (101), (113),
% 176.00/27.26  | | | | | | | | | | | | | |            (142), (156), (160), (171), (187), (188), (190),
% 176.00/27.26  | | | | | | | | | | | | | |            (199), (204), (215), (255) are inconsistent by
% 176.00/27.26  | | | | | | | | | | | | | |            sub-proof #384.
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | |   (256)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | |   (257)  all_58_5 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | COMBINE_EQS: (23), (257) imply:
% 176.00/27.26  | | | | | | | | | | | | | | |   (258)  all_52_13 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | SIMP: (258) implies:
% 176.00/27.26  | | | | | | | | | | | | | | |   (259)  all_52_13 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | REDUCE: (55), (259) imply:
% 176.00/27.26  | | | | | | | | | | | | | | |   (260)   ~ (all_52_15 = e3)
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | SIMP: (260) implies:
% 176.00/27.26  | | | | | | | | | | | | | | |   (261)   ~ (all_52_15 = e3)
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | REDUCE: (246), (259) imply:
% 176.00/27.26  | | | | | | | | | | | | | | |   (262)   ~ (all_52_18 = e3)
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | SIMP: (262) implies:
% 176.00/27.26  | | | | | | | | | | | | | | |   (263)   ~ (all_52_18 = e3)
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | REDUCE: (189), (259) imply:
% 176.00/27.26  | | | | | | | | | | | | | | |   (264)  op(e1, e3) = e1
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | |   (265)  all_58_9 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (265) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (266)  all_52_7 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (267)  all_52_7 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | REDUCE: (108), (267) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (268)   ~ (all_52_3 = e3)
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (142) with all_52_17, e1, e3, e1,
% 176.00/27.26  | | | | | | | | | | | | | | | |              simplifying with (132), (264) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (269)  all_52_17 = e1
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (269) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (270)  all_58_6 = e1
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | REDUCE: (250), (269) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (271)   ~ (all_52_18 = e1)
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | SIMP: (271) implies:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (272)   ~ (all_52_18 = e1)
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | REDUCE: (49), (269) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (273)   ~ (all_14_2 = e1)
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | SIMP: (273) implies:
% 176.00/27.26  | | | | | | | | | | | | | | | |   (274)   ~ (all_14_2 = e1)
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | |   (275)  all_56_10 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (275) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | |   (276)  all_14_2 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | REDUCE: (239), (276) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | |   (277)  $false
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent.
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | |   (278)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | |   (279)  all_58_0 = e2
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (279) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | |   (280)  all_4_2 = e2
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | REDUCE: (251), (280) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | |   (281)   ~ (all_52_18 = e2)
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | REDUCE: (123), (280) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | |   (282)  op(e1, e2) = all_4_0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | |   (283)  all_58_0 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (283) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | |   (284)  e2 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | REDUCE: (161), (284) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | |   (285)  $false
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | |   (286)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |   (287)  all_58_2 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (287) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |   (288)  all_52_18 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | SIMP: (288) implies:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |   (289)  all_52_18 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (248), (289) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |   (290)   ~ (all_52_15 = e0)
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (289) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |   (291)   ~ (e3 = e0)
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | |   (292)  all_58_9 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (265), (292) are inconsistent by sub-proof
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | |            #928.
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | |   (293)  all_58_10 = e0 | all_58_11 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | |   (294)  all_58_10 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (290), (294) are inconsistent by sub-proof
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | |            #741.
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | |   (295)  all_58_11 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (295) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | |   (296)  all_52_23 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | |   (297)  all_52_23 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (297) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | |   (298)   ~ (all_14_2 = e0)
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | |   (299)   ~ (all_14_2 = e0)
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_56_10 = e2
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (300) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_14_2 = e2
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (301) implies:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_14_2 = e2
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (302) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (303)  op(e1, e2) = all_14_1
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (142) with e3, all_14_1, e2, e1,
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (241), (303) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_14_1 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (142) with all_4_0, all_14_1, e2,
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (282), (303) gives:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_14_1 = all_4_0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (305) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_4_0 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (304) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (307)  $false
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_56_10 = e1 | all_56_10 = e0
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (274), (299), (308) are inconsistent by
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #738.
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |   (309)   ~ (all_58_2 = e0)
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (244), (309) imply:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |   (310)   ~ (all_52_18 = e0)
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (221), (243), (272), (281), (310) are inconsistent
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | |            by sub-proof #297.
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | |   (311)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (142), (169), (193), (205), (244), (252),
% 176.00/27.26  | | | | | | | | | | | | | | | | | |            (268), (270), (311) are inconsistent by sub-proof
% 176.00/27.26  | | | | | | | | | | | | | | | | | |            #737.
% 176.00/27.26  | | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | |   (312)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | | REF_CLOSE: (33), (36), (113), (199), (237), (261), (312) are
% 176.00/27.26  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #645.
% 176.00/27.26  | | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | |   (313)  all_58_8 = e3 | all_58_14 = e3
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | | REF_CLOSE: (68), (74), (211), (239), (313) are inconsistent
% 176.00/27.26  | | | | | | | | | | | | | | |            by sub-proof #999.
% 176.00/27.26  | | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | Case 2:
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | |   (314)  all_58_13 = e3
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | | REF_CLOSE: (101), (204), (314) are inconsistent by sub-proof
% 176.00/27.26  | | | | | | | | | | | | |            #1026.
% 176.00/27.26  | | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | | 
% 176.00/27.26  | | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | | 
% 176.00/27.26  | | | | | | | | End of split
% 176.00/27.26  | | | | | | | | 
% 176.00/27.26  | | | | | | | End of split
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | Case 2:
% 176.00/27.26  | | | | | | | 
% 176.00/27.26  | | | | | | |   (315)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.26  | | | | | | | 
% 176.00/27.27  | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (19), (20), (22),
% 176.00/27.27  | | | | | | |            (23), (24), (26), (28), (30), (33), (34), (35), (36),
% 176.00/27.27  | | | | | | |            (37), (39), (41), (42), (43), (44), (45), (46), (47),
% 176.00/27.27  | | | | | | |            (48), (50), (52), (53), (54), (56), (60), (62), (64),
% 176.00/27.27  | | | | | | |            (68), (70), (71), (74), (77), (78), (79), (81), (82),
% 176.00/27.27  | | | | | | |            (83), (84), (87), (95), (96), (99), (101), (102),
% 176.00/27.27  | | | | | | |            (107), (108), (110), (111), (113), (114), (118), (122),
% 176.00/27.27  | | | | | | |            (124), (125), (126), (127), (129), (132), (135), (136),
% 176.00/27.27  | | | | | | |            (137), (141), (142), (144), (146), (147), (155), (156),
% 176.00/27.27  | | | | | | |            (160), (162), (166), (169), (171), (176), (187), (188),
% 176.00/27.27  | | | | | | |            (189), (190), (193), (198), (199), (204), (315) are
% 176.00/27.27  | | | | | | |            inconsistent by sub-proof #209.
% 176.00/27.27  | | | | | | | 
% 176.00/27.27  | | | | | | End of split
% 176.00/27.27  | | | | | | 
% 176.00/27.27  | | | | | End of split
% 176.00/27.27  | | | | | 
% 176.00/27.27  | | | | End of split
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | End of split
% 176.00/27.27  | | | 
% 176.00/27.27  | | Case 2:
% 176.00/27.27  | | | 
% 176.00/27.27  | | |   (316)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 176.00/27.27  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 176.00/27.27  | | |            all_52_30 = e0)
% 176.00/27.27  | | | 
% 176.00/27.27  | | | BETA: splitting (316) gives:
% 176.00/27.27  | | | 
% 176.00/27.27  | | | Case 1:
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | |   (317)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 176.00/27.27  | | | |          e0
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | ALPHA: (317) implies:
% 176.00/27.27  | | | |   (318)  all_52_22 = e0
% 176.00/27.27  | | | |   (319)  all_52_20 = e1
% 176.00/27.27  | | | |   (320)  all_52_18 = e2
% 176.00/27.27  | | | |   (321)  all_52_16 = e3
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | COMBINE_EQS: (154), (319) imply:
% 176.00/27.27  | | | |   (322)  all_14_1 = e1
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REDUCE: (29), (322) imply:
% 176.00/27.27  | | | |   (323)  op(e1, all_14_2) = all_14_0
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REDUCE: (87), (321) imply:
% 176.00/27.27  | | | |   (324)  op(e3, all_52_17) = e3
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REDUCE: (110), (320) imply:
% 176.00/27.27  | | | |   (325)  op(e2, all_52_19) = e2
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REDUCE: (159), (322) imply:
% 176.00/27.27  | | | |   (326)  op(e1, all_14_2) = e1
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REDUCE: (95), (318) imply:
% 176.00/27.27  | | | |   (327)  op(e0, all_52_23) = e0
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (12), (13), (14), (15), (16),
% 176.00/27.27  | | | |            (17), (18), (19), (20), (21), (23), (24), (25), (26), (27),
% 176.00/27.27  | | | |            (28), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 176.00/27.27  | | | |            (39), (41), (42), (43), (44), (45), (46), (48), (50), (51),
% 176.00/27.27  | | | |            (52), (53), (54), (56), (60), (61), (62), (64), (65), (66),
% 176.00/27.27  | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 176.00/27.27  | | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (89),
% 176.00/27.27  | | | |            (90), (91), (92), (93), (94), (96), (99), (100), (101),
% 176.00/27.27  | | | |            (102), (103), (104), (105), (106), (107), (111), (112),
% 176.00/27.27  | | | |            (113), (114), (115), (116), (118), (119), (120), (121),
% 176.00/27.27  | | | |            (123), (124), (125), (126), (127), (129), (130), (131),
% 176.00/27.27  | | | |            (132), (133), (134), (135), (136), (137), (139), (140),
% 176.00/27.27  | | | |            (141), (142), (144), (145), (146), (147), (149), (150),
% 176.00/27.27  | | | |            (151), (152), (155), (156), (160), (161), (162), (163),
% 176.00/27.27  | | | |            (165), (166), (167), (168), (169), (171), (172), (176),
% 176.00/27.27  | | | |            (177), (323), (324), (325), (326), (327) are inconsistent by
% 176.00/27.27  | | | |            sub-proof #199.
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | Case 2:
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | |   (328)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 176.00/27.27  | | | |          e0
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | ALPHA: (328) implies:
% 176.00/27.27  | | | |   (329)  all_52_30 = e0
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | COMBINE_EQS: (157), (329) imply:
% 176.00/27.27  | | | |   (330)  all_6_1 = e0
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REF_CLOSE: (84), (86), (142), (161), (330) are inconsistent by sub-proof
% 176.00/27.27  | | | |            #201.
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | End of split
% 176.00/27.27  | | | 
% 176.00/27.27  | | End of split
% 176.00/27.27  | | 
% 176.00/27.27  | End of split
% 176.00/27.27  | 
% 176.00/27.27  End of proof
% 176.00/27.27  
% 176.00/27.27  Sub-proof #199 shows that the following formulas are inconsistent:
% 176.00/27.27  ----------------------------------------------------------------
% 176.00/27.27    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.27    (2)   ~ (all_52_17 = all_52_23)
% 176.00/27.27    (3)  op(e2, all_10_2) = all_10_1
% 176.00/27.27    (4)  all_40_2 = all_4_2
% 176.00/27.27    (5)   ~ (all_52_13 = all_52_29)
% 176.00/27.27    (6)  op(e3, e2) = all_52_3
% 176.00/27.27    (7)   ~ (all_52_9 = all_52_25)
% 176.00/27.27    (8)  op(e3, all_52_25) = all_52_24
% 176.00/27.27    (9)   ~ (all_52_19 = all_52_23)
% 176.00/27.27    (10)  all_56_11 = all_52_23
% 176.00/27.27    (11)  op(e1, e2) = all_52_19
% 176.00/27.27    (12)  all_16_1 = all_6_1
% 176.00/27.27    (13)  op(e3, all_52_9) = all_52_8
% 176.00/27.27    (14)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.27    (15)   ~ (all_52_3 = all_10_2)
% 176.00/27.27    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.00/27.27    (17)  all_58_5 = all_52_13
% 176.00/27.27    (18)   ~ (all_6_2 = e0)
% 176.00/27.27    (19)   ~ (all_52_25 = all_52_29)
% 176.00/27.27    (20)  all_16_2 = all_6_2
% 176.00/27.27    (21)  all_56_15 = all_6_2
% 176.00/27.27    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.27    (23)  op(e2, e0) = all_52_15
% 176.00/27.27    (24)  all_58_3 = all_10_2
% 176.00/27.27    (25)  all_56_9 = all_52_19
% 176.00/27.27    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.27    (27)  all_58_15 = all_6_2
% 176.00/27.27    (28)   ~ (all_52_9 = all_4_2)
% 176.00/27.27    (29)   ~ (all_52_5 = all_52_7)
% 176.00/27.27    (30)  all_58_10 = all_52_15
% 176.00/27.27    (31)  all_8_2 = all_6_2
% 176.00/27.27    (32)   ~ (all_52_5 = all_4_2)
% 176.00/27.27    (33)  all_58_7 = all_52_19
% 176.00/27.27    (34)   ~ (all_52_15 = all_6_2)
% 176.00/27.27    (35)   ~ (all_52_17 = all_52_25)
% 176.00/27.27    (36)  op(e0, e1) = all_52_29
% 176.00/27.27    (37)   ~ (all_4_0 = e2)
% 176.00/27.27    (38)  all_58_4 = all_52_5
% 176.00/27.27    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.27    (40)   ~ (all_52_27 = all_52_29)
% 176.00/27.27    (41)  op(e3, all_4_2) = all_4_1
% 176.00/27.27    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.27    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.27    (44)   ~ (all_52_7 = all_4_2)
% 176.00/27.27    (45)  all_58_1 = all_52_3
% 176.00/27.27    (46)  all_58_0 = all_4_2
% 176.00/27.27    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.27    (48)  op(e1, all_52_29) = all_52_28
% 176.00/27.27    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.27    (50)   ~ (all_4_1 = e2)
% 176.00/27.27    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.27    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.27    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.00/27.27    (54)  all_58_14 = all_52_29
% 176.00/27.27    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.27    (56)   ~ (all_52_3 = all_52_5)
% 176.00/27.27    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.27    (58)  op(e2, e1) = all_52_13
% 176.00/27.27    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.27    (60)  all_58_8 = all_14_2
% 176.00/27.27    (61)   ~ (all_14_0 = e3)
% 176.00/27.27    (62)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.00/27.27    (63)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.27    (64)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.27    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.27    (66)   ~ (all_52_5 = all_14_2)
% 176.00/27.27    (67)   ~ (all_52_3 = all_52_27)
% 176.00/27.27    (68)   ~ (all_52_3 = all_4_2)
% 176.00/27.27    (69)  op(e0, e3) = all_52_25
% 176.00/27.27    (70)  op(e0, all_6_2) = all_6_1
% 176.00/27.27    (71)   ~ (all_52_9 = all_10_2)
% 176.00/27.27    (72)  op(all_6_1, all_6_2) = e2
% 176.00/27.27    (73)   ~ (all_52_13 = all_14_2)
% 176.00/27.27    (74)  op(e1, all_14_2) = all_14_0
% 176.00/27.27    (75)   ~ (e3 = e0)
% 176.00/27.27    (76)  all_40_0 = all_4_0
% 176.00/27.27    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.27    (78)   ~ (all_52_9 = all_52_13)
% 176.00/27.27    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.27    (80)   ~ (all_52_15 = all_52_23)
% 176.00/27.27    (81)  op(e1, e0) = all_52_23
% 176.00/27.27    (82)  all_56_12 = all_52_25
% 176.00/27.27    (83)  all_58_13 = all_52_27
% 176.00/27.27    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.27    (85)  all_56_5 = all_10_2
% 176.00/27.27    (86)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.00/27.27    (87)   ~ (all_52_9 = all_52_17)
% 176.00/27.27    (88)   ~ (all_14_0 = e2)
% 176.00/27.27    (89)  all_58_6 = all_52_17
% 176.00/27.27    (90)  op(e2, all_52_19) = e2
% 176.00/27.27    (91)  op(e3, all_52_17) = e3
% 176.00/27.27    (92)   ~ (e1 = e0)
% 176.00/27.27    (93)  all_56_0 = all_4_2
% 176.00/27.27    (94)  all_58_11 = all_52_23
% 176.00/27.27    (95)   ~ (all_52_3 = all_52_19)
% 176.00/27.27    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.27    (97)   ~ (all_52_7 = all_52_15)
% 176.00/27.27    (98)   ~ (all_52_29 = all_14_2)
% 176.00/27.27    (99)   ~ (all_4_0 = e1)
% 176.00/27.27    (100)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.27    (101)   ~ (all_52_19 = all_10_2)
% 176.00/27.27    (102)  op(e1, all_4_2) = all_4_0
% 176.00/27.27    (103)   ~ (all_52_29 = all_6_2)
% 176.00/27.27    (104)  all_58_2 = all_52_9
% 176.00/27.27    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.27    (106)  op(e3, e1) = all_52_5
% 176.00/27.27    (107)   ~ (all_52_25 = all_6_2)
% 176.00/27.27    (108)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.00/27.27    (109)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.27    (110)  op(e1, e3) = all_52_17
% 176.00/27.27    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.00/27.27    (112)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.27    (113)   ~ (all_52_25 = all_4_2)
% 176.00/27.27    (114)  op(e3, e0) = all_52_7
% 176.00/27.27    (115)  op(e3, e3) = all_4_2
% 176.00/27.27    (116)   ~ (all_10_1 = e3)
% 176.00/27.27    (117)  all_56_8 = all_52_17
% 176.00/27.27    (118)   ~ (all_52_17 = all_4_2)
% 176.00/27.27    (119)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.27             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.27    (120)   ~ (all_52_25 = all_52_27)
% 176.00/27.27    (121)   ~ (all_52_27 = all_6_2)
% 176.00/27.27    (122)  all_8_1 = all_6_1
% 176.00/27.27    (123)   ~ (all_52_7 = all_6_2)
% 176.00/27.27    (124)  op(e0, all_52_23) = e0
% 176.00/27.27    (125)   ~ (all_52_15 = all_10_2)
% 176.00/27.27    (126)   ~ (all_52_19 = all_52_27)
% 176.00/27.27    (127)  all_56_7 = all_52_15
% 176.00/27.27    (128)  op(e1, all_14_2) = e1
% 176.00/27.27    (129)   ~ (all_52_7 = all_52_23)
% 176.00/27.27    (130)   ~ (all_52_17 = all_52_19)
% 176.00/27.27    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.27    (132)  all_58_9 = all_52_7
% 176.00/27.27    (133)   ~ (e2 = e0)
% 176.00/27.27    (134)  all_58_12 = all_52_25
% 176.00/27.27    (135)  op(e3, all_4_2) = e1
% 176.00/27.27    (136)  all_56_6 = all_52_13
% 176.00/27.27    (137)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.27    (138)   ~ (all_52_9 = all_52_15)
% 176.00/27.27    (139)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.27    (140)   ~ (e3 = e2)
% 176.00/27.27    (141)  op(e2, e3) = all_52_9
% 176.00/27.27    (142)  all_56_13 = all_52_27
% 176.00/27.27  
% 176.00/27.27  Begin of proof
% 176.00/27.27  | 
% 176.00/27.27  | GROUND_INST: instantiating (119) with e1, all_14_0, all_14_2, e1, simplifying
% 176.00/27.27  |              with (74), (128) gives:
% 176.00/27.27  |   (143)  all_14_0 = e1
% 176.00/27.27  | 
% 176.00/27.27  | REDUCE: (61), (143) imply:
% 176.00/27.27  |   (144)   ~ (e3 = e1)
% 176.00/27.27  | 
% 176.00/27.27  | SIMP: (144) implies:
% 176.00/27.27  |   (145)   ~ (e3 = e1)
% 176.00/27.27  | 
% 176.00/27.27  | REDUCE: (88), (143) imply:
% 176.00/27.27  |   (146)   ~ (e2 = e1)
% 176.00/27.27  | 
% 176.00/27.27  | SIMP: (146) implies:
% 176.00/27.27  |   (147)   ~ (e2 = e1)
% 176.00/27.27  | 
% 176.00/27.27  | BETA: splitting (42) gives:
% 176.00/27.27  | 
% 176.00/27.27  | Case 1:
% 176.00/27.27  | | 
% 176.00/27.27  | |   (148)  all_56_15 = e3
% 176.00/27.27  | | 
% 176.00/27.27  | | COMBINE_EQS: (21), (148) imply:
% 176.00/27.27  | |   (149)  all_6_2 = e3
% 176.00/27.27  | | 
% 176.00/27.27  | | REF_CLOSE: (7), (12), (20), (69), (70), (72), (79), (82), (100), (107),
% 176.00/27.27  | |            (109), (119), (134), (141), (149) are inconsistent by sub-proof
% 176.00/27.27  | |            #226.
% 176.00/27.27  | | 
% 176.00/27.27  | Case 2:
% 176.00/27.27  | | 
% 176.00/27.27  | |   (150)   ~ (all_56_15 = e3)
% 176.00/27.27  | |   (151)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.27  | | 
% 176.00/27.27  | | REDUCE: (21), (150) imply:
% 176.00/27.27  | |   (152)   ~ (all_6_2 = e3)
% 176.00/27.27  | | 
% 176.00/27.27  | | BETA: splitting (55) gives:
% 176.00/27.27  | | 
% 176.00/27.27  | | Case 1:
% 176.00/27.27  | | | 
% 176.00/27.27  | | |   (153)  all_56_13 = e3
% 176.00/27.27  | | | 
% 176.00/27.27  | | | COMBINE_EQS: (142), (153) imply:
% 176.00/27.27  | | |   (154)  all_52_27 = e3
% 176.00/27.27  | | | 
% 176.00/27.27  | | | REF_CLOSE: (4), (6), (11), (25), (26), (27), (30), (32), (33), (37), (38),
% 176.00/27.27  | | |            (39), (43), (44), (45), (46), (49), (57), (60), (62), (66),
% 176.00/27.27  | | |            (67), (69), (76), (80), (84), (87), (89), (90), (91), (93),
% 176.00/27.27  | | |            (94), (95), (102), (104), (106), (110), (111), (113), (115),
% 176.00/27.27  | | |            (118), (119), (120), (121), (124), (126), (127), (128), (129),
% 176.00/27.27  | | |            (131), (132), (134), (135), (137), (139), (140), (141), (145),
% 176.00/27.27  | | |            (154) are inconsistent by sub-proof #246.
% 176.00/27.27  | | | 
% 176.00/27.27  | | Case 2:
% 176.00/27.27  | | | 
% 176.00/27.27  | | |   (155)   ~ (all_56_13 = e3)
% 176.00/27.27  | | | 
% 176.00/27.27  | | | REDUCE: (142), (155) imply:
% 176.00/27.27  | | |   (156)   ~ (all_52_27 = e3)
% 176.00/27.27  | | | 
% 176.00/27.27  | | | BETA: splitting (59) gives:
% 176.00/27.27  | | | 
% 176.00/27.27  | | | Case 1:
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | |   (157)  all_58_12 = e3
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REF_CLOSE: (3), (7), (11), (17), (24), (26), (27), (28), (29), (30),
% 176.00/27.27  | | | |            (32), (33), (35), (38), (39), (43), (44), (45), (46), (47),
% 176.00/27.27  | | | |            (51), (52), (53), (58), (60), (66), (69), (71), (73), (75),
% 176.00/27.27  | | | |            (77), (78), (80), (83), (84), (85), (86), (87), (89), (90),
% 176.00/27.27  | | | |            (91), (92), (93), (94), (95), (97), (101), (104), (106),
% 176.00/27.27  | | | |            (107), (108), (110), (111), (113), (114), (116), (118),
% 176.00/27.27  | | | |            (119), (120), (124), (125), (127), (128), (129), (130),
% 176.00/27.27  | | | |            (131), (132), (133), (134), (136), (137), (138), (139),
% 176.00/27.27  | | | |            (141), (145), (147), (157) are inconsistent by sub-proof
% 176.00/27.27  | | | |            #677.
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | Case 2:
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | |   (158)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (13), (14), (15),
% 176.00/27.27  | | | |            (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 176.00/27.27  | | | |            (27), (28), (30), (31), (32), (33), (34), (35), (36), (37),
% 176.00/27.27  | | | |            (38), (39), (40), (41), (43), (44), (45), (46), (48), (49),
% 176.00/27.27  | | | |            (50), (51), (54), (56), (57), (60), (63), (64), (65), (66),
% 176.00/27.27  | | | |            (68), (69), (70), (71), (78), (80), (81), (83), (84), (87),
% 176.00/27.27  | | | |            (89), (90), (91), (93), (94), (95), (96), (98), (99), (103),
% 176.00/27.27  | | | |            (104), (105), (106), (107), (110), (112), (113), (114),
% 176.00/27.27  | | | |            (115), (117), (118), (119), (120), (121), (122), (123),
% 176.00/27.27  | | | |            (124), (128), (129), (131), (132), (134), (138), (140),
% 176.00/27.27  | | | |            (141), (145), (151), (152), (156), (158) are inconsistent by
% 176.00/27.27  | | | |            sub-proof #203.
% 176.00/27.27  | | | | 
% 176.00/27.27  | | | End of split
% 176.00/27.27  | | | 
% 176.00/27.27  | | End of split
% 176.00/27.27  | | 
% 176.00/27.27  | End of split
% 176.00/27.27  | 
% 176.00/27.27  End of proof
% 176.00/27.27  
% 176.00/27.27  Sub-proof #200 shows that the following formulas are inconsistent:
% 176.00/27.27  ----------------------------------------------------------------
% 176.00/27.27    (1)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.00/27.27    (2)  op(e0, all_6_2) = all_6_1
% 176.00/27.27    (3)  op(all_6_1, all_6_2) = e2
% 176.00/27.27    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.27    (5)  all_52_30 = all_6_1
% 176.00/27.27    (6)   ~ (e2 = e0)
% 176.00/27.27  
% 176.00/27.27  Begin of proof
% 176.00/27.27  | 
% 176.00/27.27  | ALPHA: (1) implies:
% 176.00/27.27  |   (7)  all_52_30 = e0
% 176.00/27.27  | 
% 176.00/27.27  | COMBINE_EQS: (5), (7) imply:
% 176.00/27.27  |   (8)  all_6_1 = e0
% 176.00/27.27  | 
% 176.00/27.27  | SIMP: (8) implies:
% 176.00/27.27  |   (9)  all_6_1 = e0
% 176.00/27.27  | 
% 176.00/27.27  | REF_CLOSE: (2), (3), (4), (6), (9) are inconsistent by sub-proof #201.
% 176.00/27.27  | 
% 176.00/27.27  End of proof
% 176.00/27.27  
% 176.00/27.27  Sub-proof #201 shows that the following formulas are inconsistent:
% 176.00/27.27  ----------------------------------------------------------------
% 176.00/27.27    (1)  all_6_1 = e0
% 176.00/27.27    (2)  op(e0, all_6_2) = all_6_1
% 176.00/27.27    (3)  op(all_6_1, all_6_2) = e2
% 176.00/27.27    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.27    (5)   ~ (e2 = e0)
% 176.00/27.27  
% 176.00/27.27  Begin of proof
% 176.00/27.27  | 
% 176.00/27.27  | REDUCE: (1), (3) imply:
% 176.00/27.27  |   (6)  op(e0, all_6_2) = e2
% 176.00/27.27  | 
% 176.00/27.27  | REDUCE: (1), (2) imply:
% 176.00/27.27  |   (7)  op(e0, all_6_2) = e0
% 176.00/27.27  | 
% 176.00/27.27  | GROUND_INST: instantiating (4) with e0, e2, all_6_2, e0, simplifying with (6),
% 176.00/27.27  |              (7) gives:
% 176.00/27.27  |   (8)  e2 = e0
% 176.00/27.27  | 
% 176.00/27.27  | REDUCE: (5), (8) imply:
% 176.00/27.27  |   (9)  $false
% 176.00/27.27  | 
% 176.00/27.27  | CLOSE: (9) is inconsistent.
% 176.00/27.27  | 
% 176.00/27.27  End of proof
% 176.00/27.27  
% 176.00/27.27  Sub-proof #202 shows that the following formulas are inconsistent:
% 176.00/27.27  ----------------------------------------------------------------
% 176.00/27.27    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.27    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.27    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.27    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.27    (5)  op(e2, all_10_2) = all_10_1
% 176.00/27.27    (6)   ~ (all_52_13 = all_52_29)
% 176.00/27.27    (7)  op(e3, e2) = all_52_3
% 176.00/27.27    (8)   ~ (all_52_9 = all_52_25)
% 176.00/27.27    (9)  op(e3, all_52_25) = all_52_24
% 176.00/27.27    (10)   ~ (all_52_19 = all_52_23)
% 176.00/27.27    (11)  all_56_11 = all_52_23
% 176.00/27.27    (12)  op(e1, e2) = all_52_19
% 176.00/27.27    (13)  all_16_1 = all_6_1
% 176.00/27.27    (14)  op(e3, all_52_9) = all_52_8
% 176.00/27.27    (15)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.27    (16)   ~ (all_52_3 = all_10_2)
% 176.00/27.27    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.00/27.27    (18)  all_58_5 = all_52_13
% 176.00/27.27    (19)   ~ (all_6_2 = e0)
% 176.00/27.27    (20)   ~ (all_52_25 = all_52_29)
% 176.00/27.27    (21)  all_16_2 = all_6_2
% 176.00/27.27    (22)  all_56_15 = all_6_2
% 176.00/27.27    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.27    (24)  op(e2, e0) = all_52_15
% 176.00/27.27    (25)  all_58_3 = all_10_2
% 176.00/27.27    (26)  all_56_9 = all_52_19
% 176.00/27.27    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.27    (28)  all_58_15 = all_6_2
% 176.00/27.27    (29)   ~ (all_52_9 = all_4_2)
% 176.00/27.27    (30)   ~ (all_52_5 = all_52_7)
% 176.00/27.27    (31)  all_58_10 = all_52_15
% 176.00/27.27    (32)  all_8_2 = all_6_2
% 176.00/27.27    (33)   ~ (all_52_5 = all_4_2)
% 176.00/27.27    (34)  all_58_7 = all_52_19
% 176.00/27.27    (35)   ~ (all_52_15 = all_6_2)
% 176.00/27.27    (36)   ~ (all_52_17 = all_52_25)
% 176.00/27.27    (37)  op(e0, e1) = all_52_29
% 176.00/27.27    (38)   ~ (all_4_0 = e2)
% 176.00/27.27    (39)  all_58_4 = all_52_5
% 176.00/27.27    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.27    (41)   ~ (all_52_27 = all_52_29)
% 176.00/27.27    (42)   ~ (all_52_17 = all_14_2)
% 176.00/27.27    (43)  op(e3, all_4_2) = all_4_1
% 176.00/27.27    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.27    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.27    (46)   ~ (all_52_7 = all_4_2)
% 176.00/27.27    (47)  all_58_1 = all_52_3
% 176.00/27.27    (48)  all_58_0 = all_4_2
% 176.00/27.27    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.27    (50)  op(e1, all_52_29) = all_52_28
% 176.00/27.27    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.27    (52)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.27    (53)   ~ (all_4_1 = e2)
% 176.00/27.27    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.27    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.27    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.00/27.27    (57)  all_58_14 = all_52_29
% 176.00/27.27    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.27    (59)   ~ (all_52_3 = all_52_5)
% 176.00/27.27    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.27    (61)  op(e2, e1) = all_52_13
% 176.00/27.27    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.27    (63)  all_58_8 = all_14_2
% 176.00/27.27    (64)  all_56_1 = all_52_3
% 176.00/27.27    (65)   ~ (all_14_0 = e3)
% 176.00/27.27    (66)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.27    (67)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.27    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.27    (69)   ~ (all_52_5 = all_14_2)
% 176.00/27.27    (70)   ~ (all_52_3 = all_52_27)
% 176.00/27.27    (71)   ~ (all_52_3 = all_4_2)
% 176.00/27.27    (72)  op(e0, e3) = all_52_25
% 176.00/27.27    (73)  op(e0, all_6_2) = all_6_1
% 176.00/27.27    (74)   ~ (all_52_9 = all_10_2)
% 176.00/27.27    (75)  op(all_6_1, all_6_2) = e2
% 176.00/27.27    (76)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.00/27.27    (77)   ~ (all_52_13 = all_14_2)
% 176.00/27.27    (78)  op(e1, all_14_2) = all_14_0
% 176.00/27.27    (79)   ~ (e3 = e0)
% 176.00/27.27    (80)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.00/27.27    (81)   ~ (all_52_9 = all_52_13)
% 176.00/27.27    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.00/27.27    (83)   ~ (all_52_15 = all_52_23)
% 176.00/27.27    (84)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.27    (85)  op(e1, e0) = all_52_23
% 176.00/27.27    (86)  all_56_12 = all_52_25
% 176.00/27.27    (87)  all_58_13 = all_52_27
% 176.00/27.27    (88)   ~ (all_4_1 = e1)
% 176.00/27.27    (89)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.27    (90)  all_56_5 = all_10_2
% 176.00/27.27    (91)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.00/27.27    (92)   ~ (all_52_9 = all_52_17)
% 176.00/27.27    (93)   ~ (all_14_0 = e2)
% 176.00/27.27    (94)  all_58_6 = all_52_17
% 176.00/27.27    (95)  op(e2, all_52_19) = e2
% 176.00/27.27    (96)  op(e3, all_52_17) = e3
% 176.00/27.27    (97)   ~ (e1 = e0)
% 176.00/27.27    (98)  all_56_0 = all_4_2
% 176.00/27.27    (99)  all_58_11 = all_52_23
% 176.00/27.27    (100)   ~ (all_52_3 = all_52_19)
% 176.00/27.27    (101)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.27    (102)   ~ (all_52_7 = all_52_15)
% 176.00/27.27    (103)   ~ (all_52_29 = all_14_2)
% 176.00/27.27    (104)   ~ (all_4_0 = e1)
% 176.00/27.27    (105)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.00/27.27    (106)   ~ (all_52_19 = all_10_2)
% 176.00/27.27    (107)   ~ (all_52_29 = all_6_2)
% 176.00/27.27    (108)  all_58_2 = all_52_9
% 176.00/27.27    (109)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.27    (110)  op(e3, e1) = all_52_5
% 176.00/27.27    (111)  all_56_10 = all_14_2
% 176.00/27.27    (112)   ~ (all_52_25 = all_6_2)
% 176.00/27.27    (113)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.00/27.27    (114)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.00/27.27    (115)  op(e1, e3) = all_52_17
% 176.00/27.27    (116)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.00/27.27    (117)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.28    (118)   ~ (all_52_25 = all_4_2)
% 176.00/27.28    (119)  op(e3, e0) = all_52_7
% 176.00/27.28    (120)  op(e3, e3) = all_4_2
% 176.00/27.28    (121)   ~ (all_10_1 = e3)
% 176.00/27.28    (122)  all_56_8 = all_52_17
% 176.00/27.28    (123)   ~ (all_52_17 = all_4_2)
% 176.00/27.28    (124)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.28             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.28    (125)   ~ (all_52_25 = all_52_27)
% 176.00/27.28    (126)   ~ (all_52_27 = all_6_2)
% 176.00/27.28    (127)  all_8_1 = all_6_1
% 176.00/27.28    (128)   ~ (all_52_7 = all_6_2)
% 176.00/27.28    (129)  op(e0, all_52_23) = e0
% 176.00/27.28    (130)   ~ (all_52_15 = all_10_2)
% 176.00/27.28    (131)   ~ (all_52_19 = all_52_27)
% 176.00/27.28    (132)  all_56_7 = all_52_15
% 176.00/27.28    (133)  op(e1, all_14_2) = e1
% 176.00/27.28    (134)   ~ (all_52_7 = all_52_23)
% 176.00/27.28    (135)  op(e2, all_52_27) = all_52_26
% 176.00/27.28    (136)   ~ (all_52_17 = all_52_19)
% 176.00/27.28    (137)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.28    (138)  all_58_9 = all_52_7
% 176.00/27.28    (139)   ~ (e2 = e0)
% 176.00/27.28    (140)  all_58_12 = all_52_25
% 176.00/27.28    (141)  all_56_6 = all_52_13
% 176.00/27.28    (142)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.28    (143)   ~ (all_52_9 = all_52_15)
% 176.00/27.28    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.28    (145)   ~ (e3 = e2)
% 176.00/27.28    (146)   ~ (all_52_19 = all_14_2)
% 176.00/27.28    (147)  op(e2, e3) = all_52_9
% 176.00/27.28    (148)  all_56_13 = all_52_27
% 176.00/27.28  
% 176.00/27.28  Begin of proof
% 176.00/27.28  | 
% 176.00/27.28  | GROUND_INST: instantiating (124) with e1, all_14_0, all_14_2, e1, simplifying
% 176.00/27.28  |              with (78), (133) gives:
% 176.00/27.28  |   (149)  all_14_0 = e1
% 176.00/27.28  | 
% 176.00/27.28  | REDUCE: (65), (149) imply:
% 176.00/27.28  |   (150)   ~ (e3 = e1)
% 176.00/27.28  | 
% 176.00/27.28  | SIMP: (150) implies:
% 176.00/27.28  |   (151)   ~ (e3 = e1)
% 176.00/27.28  | 
% 176.00/27.28  | REDUCE: (93), (149) imply:
% 176.00/27.28  |   (152)   ~ (e2 = e1)
% 176.00/27.28  | 
% 176.00/27.28  | SIMP: (152) implies:
% 176.00/27.28  |   (153)   ~ (e2 = e1)
% 176.00/27.28  | 
% 176.00/27.28  | BETA: splitting (44) gives:
% 176.00/27.28  | 
% 176.00/27.28  | Case 1:
% 176.00/27.28  | | 
% 176.00/27.28  | |   (154)  all_56_15 = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | COMBINE_EQS: (22), (154) imply:
% 176.00/27.28  | |   (155)  all_6_2 = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | SIMP: (155) implies:
% 176.00/27.28  | |   (156)  all_6_2 = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | REF_CLOSE: (8), (13), (21), (72), (73), (75), (82), (86), (105), (112),
% 176.00/27.28  | |            (114), (124), (140), (147), (156) are inconsistent by sub-proof
% 176.00/27.28  | |            #226.
% 176.00/27.28  | | 
% 176.00/27.28  | Case 2:
% 176.00/27.28  | | 
% 176.00/27.28  | |   (157)   ~ (all_56_15 = e3)
% 176.00/27.28  | |   (158)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.28  | | 
% 176.00/27.28  | | REDUCE: (22), (157) imply:
% 176.00/27.28  | |   (159)   ~ (all_6_2 = e3)
% 176.00/27.28  | | 
% 176.00/27.28  | | BETA: splitting (58) gives:
% 176.00/27.28  | | 
% 176.00/27.28  | | Case 1:
% 176.00/27.28  | | | 
% 176.00/27.28  | | |   (160)  all_56_13 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | COMBINE_EQS: (148), (160) imply:
% 176.00/27.28  | | |   (161)  all_52_27 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (161) implies:
% 176.00/27.28  | | |   (162)  all_52_27 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REF_CLOSE: (1), (2), (7), (9), (10), (18), (20), (23), (24), (26), (30),
% 176.00/27.28  | | |            (31), (33), (34), (36), (39), (40), (41), (42), (43), (48),
% 176.00/27.28  | | |            (49), (51), (52), (57), (60), (63), (64), (67), (69), (70),
% 176.00/27.28  | | |            (71), (72), (76), (84), (85), (88), (89), (92), (94), (95),
% 176.00/27.28  | | |            (96), (97), (99), (100), (104), (108), (110), (111), (115),
% 176.00/27.28  | | |            (117), (118), (119), (120), (123), (124), (125), (129), (131),
% 176.00/27.28  | | |            (133), (135), (136), (138), (139), (140), (144), (145), (146),
% 176.00/27.28  | | |            (147), (151), (153), (162) are inconsistent by sub-proof #686.
% 176.00/27.28  | | | 
% 176.00/27.28  | | Case 2:
% 176.00/27.28  | | | 
% 176.00/27.28  | | |   (163)   ~ (all_56_13 = e3)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (148), (163) imply:
% 176.00/27.28  | | |   (164)   ~ (all_52_27 = e3)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | BETA: splitting (62) gives:
% 176.00/27.28  | | | 
% 176.00/27.28  | | | Case 1:
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | |   (165)  all_58_12 = e3
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REF_CLOSE: (5), (8), (12), (18), (25), (27), (28), (29), (30), (31),
% 176.00/27.28  | | | |            (33), (34), (36), (39), (40), (45), (46), (47), (48), (49),
% 176.00/27.28  | | | |            (54), (55), (56), (61), (63), (69), (72), (74), (77), (79),
% 176.00/27.28  | | | |            (80), (81), (83), (87), (89), (90), (91), (92), (94), (95),
% 176.00/27.28  | | | |            (96), (97), (98), (99), (100), (102), (106), (108), (110),
% 176.00/27.28  | | | |            (112), (113), (115), (116), (118), (119), (121), (123),
% 176.00/27.28  | | | |            (124), (125), (129), (130), (132), (133), (134), (136),
% 176.00/27.28  | | | |            (137), (138), (139), (140), (141), (142), (143), (144),
% 176.00/27.28  | | | |            (147), (151), (153), (165) are inconsistent by sub-proof
% 176.00/27.28  | | | |            #677.
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | Case 2:
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | |   (166)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (14), (15), (16),
% 176.00/27.28  | | | |            (17), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 176.00/27.28  | | | |            (28), (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 176.00/27.28  | | | |            (39), (40), (41), (43), (45), (46), (47), (48), (50), (52),
% 176.00/27.28  | | | |            (53), (54), (57), (59), (60), (63), (66), (67), (68), (69),
% 176.00/27.28  | | | |            (71), (72), (73), (74), (81), (83), (85), (87), (89), (92),
% 176.00/27.28  | | | |            (94), (95), (96), (98), (99), (100), (101), (103), (104),
% 176.00/27.28  | | | |            (107), (108), (109), (110), (112), (115), (117), (118),
% 176.00/27.28  | | | |            (119), (120), (122), (123), (124), (125), (126), (127),
% 176.00/27.28  | | | |            (128), (129), (133), (134), (137), (138), (140), (143),
% 176.00/27.28  | | | |            (145), (147), (151), (158), (159), (164), (166) are
% 176.00/27.28  | | | |            inconsistent by sub-proof #203.
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | End of split
% 176.00/27.28  | | | 
% 176.00/27.28  | | End of split
% 176.00/27.28  | | 
% 176.00/27.28  | End of split
% 176.00/27.28  | 
% 176.00/27.28  End of proof
% 176.00/27.28  
% 176.00/27.28  Sub-proof #203 shows that the following formulas are inconsistent:
% 176.00/27.28  ----------------------------------------------------------------
% 176.00/27.28    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.28    (2)   ~ (all_52_17 = all_52_23)
% 176.00/27.28    (3)   ~ (all_52_13 = all_52_29)
% 176.00/27.28    (4)  op(e3, e2) = all_52_3
% 176.00/27.28    (5)  op(e3, all_52_25) = all_52_24
% 176.00/27.28    (6)   ~ (all_52_19 = all_52_23)
% 176.00/27.28    (7)  all_56_11 = all_52_23
% 176.00/27.28    (8)  op(e1, e2) = all_52_19
% 176.00/27.28    (9)   ~ (all_52_27 = e3)
% 176.00/27.28    (10)   ~ (all_6_2 = e3)
% 176.00/27.28    (11)  op(e3, all_52_9) = all_52_8
% 176.00/27.28    (12)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.28    (13)   ~ (all_52_3 = all_10_2)
% 176.00/27.28    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.00/27.28    (15)  all_58_5 = all_52_13
% 176.00/27.28    (16)   ~ (all_6_2 = e0)
% 176.00/27.28    (17)   ~ (all_52_25 = all_52_29)
% 176.00/27.28    (18)  all_56_15 = all_6_2
% 176.00/27.28    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.28    (20)  op(e2, e0) = all_52_15
% 176.00/27.28    (21)  all_58_3 = all_10_2
% 176.00/27.28    (22)  all_56_9 = all_52_19
% 176.00/27.28    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.28    (24)  all_58_15 = all_6_2
% 176.00/27.28    (25)   ~ (all_52_9 = all_4_2)
% 176.00/27.28    (26)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.28    (27)  all_58_10 = all_52_15
% 176.00/27.28    (28)  all_8_2 = all_6_2
% 176.00/27.28    (29)   ~ (all_52_5 = all_4_2)
% 176.00/27.28    (30)  all_58_7 = all_52_19
% 176.00/27.28    (31)   ~ (all_52_15 = all_6_2)
% 176.00/27.28    (32)   ~ (all_52_17 = all_52_25)
% 176.00/27.28    (33)  op(e0, e1) = all_52_29
% 176.00/27.28    (34)   ~ (all_4_0 = e2)
% 176.00/27.28    (35)  all_58_4 = all_52_5
% 176.00/27.28    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.28    (37)   ~ (e3 = e1)
% 176.00/27.28    (38)   ~ (all_52_27 = all_52_29)
% 176.00/27.28    (39)  op(e3, all_4_2) = all_4_1
% 176.00/27.28    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.28    (41)   ~ (all_52_7 = all_4_2)
% 176.00/27.28    (42)  all_58_1 = all_52_3
% 176.00/27.28    (43)  all_58_0 = all_4_2
% 176.00/27.28    (44)  op(e1, all_52_29) = all_52_28
% 176.00/27.28    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.28    (46)   ~ (all_4_1 = e2)
% 176.00/27.28    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.28    (48)  all_58_14 = all_52_29
% 176.00/27.28    (49)   ~ (all_52_3 = all_52_5)
% 176.00/27.28    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.28    (51)  all_58_8 = all_14_2
% 176.00/27.28    (52)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.28    (53)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.28    (54)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.28    (55)   ~ (all_52_5 = all_14_2)
% 176.00/27.28    (56)   ~ (all_52_3 = all_4_2)
% 176.00/27.28    (57)  op(e0, e3) = all_52_25
% 176.00/27.28    (58)  op(e0, all_6_2) = all_6_1
% 176.00/27.28    (59)   ~ (all_52_9 = all_10_2)
% 176.00/27.28    (60)   ~ (all_52_9 = all_52_13)
% 176.00/27.28    (61)   ~ (all_52_15 = all_52_23)
% 176.00/27.28    (62)  op(e1, e0) = all_52_23
% 176.00/27.28    (63)  all_58_13 = all_52_27
% 176.00/27.28    (64)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.28    (65)   ~ (all_52_9 = all_52_17)
% 176.00/27.28    (66)  all_58_6 = all_52_17
% 176.00/27.28    (67)  op(e2, all_52_19) = e2
% 176.00/27.28    (68)  op(e3, all_52_17) = e3
% 176.00/27.28    (69)  all_56_0 = all_4_2
% 176.00/27.28    (70)  all_58_11 = all_52_23
% 176.00/27.28    (71)   ~ (all_52_3 = all_52_19)
% 176.00/27.28    (72)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.28    (73)   ~ (all_52_29 = all_14_2)
% 176.00/27.28    (74)   ~ (all_4_0 = e1)
% 176.00/27.28    (75)   ~ (all_52_29 = all_6_2)
% 176.00/27.28    (76)  all_58_2 = all_52_9
% 176.00/27.28    (77)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.28    (78)  op(e3, e1) = all_52_5
% 176.00/27.28    (79)   ~ (all_52_25 = all_6_2)
% 176.00/27.28    (80)  op(e1, e3) = all_52_17
% 176.00/27.28    (81)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.28    (82)   ~ (all_52_25 = all_4_2)
% 176.00/27.28    (83)  op(e3, e0) = all_52_7
% 176.00/27.28    (84)  op(e3, e3) = all_4_2
% 176.00/27.28    (85)  all_56_8 = all_52_17
% 176.00/27.28    (86)   ~ (all_52_17 = all_4_2)
% 176.00/27.28    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.28    (88)   ~ (all_52_25 = all_52_27)
% 176.00/27.28    (89)   ~ (all_52_27 = all_6_2)
% 176.00/27.28    (90)  all_8_1 = all_6_1
% 176.00/27.28    (91)   ~ (all_52_7 = all_6_2)
% 176.00/27.28    (92)  op(e0, all_52_23) = e0
% 176.00/27.28    (93)  op(e1, all_14_2) = e1
% 176.00/27.28    (94)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.28    (95)   ~ (all_52_7 = all_52_23)
% 176.00/27.28    (96)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.28    (97)  all_58_9 = all_52_7
% 176.00/27.28    (98)  all_58_12 = all_52_25
% 176.00/27.28    (99)   ~ (all_52_9 = all_52_15)
% 176.00/27.28    (100)   ~ (e3 = e2)
% 176.00/27.28    (101)  op(e2, e3) = all_52_9
% 176.00/27.28  
% 176.00/27.28  Begin of proof
% 176.00/27.28  | 
% 176.00/27.28  | BETA: splitting (94) gives:
% 176.00/27.28  | 
% 176.00/27.28  | Case 1:
% 176.00/27.28  | | 
% 176.00/27.28  | |   (102)  all_58_13 = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | REF_CLOSE: (9), (63), (102) are inconsistent by sub-proof #1026.
% 176.00/27.28  | | 
% 176.00/27.28  | Case 2:
% 176.00/27.28  | | 
% 176.00/27.28  | |   (103)  all_58_14 = e3 | all_58_15 = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | BETA: splitting (103) gives:
% 176.00/27.28  | | 
% 176.00/27.28  | | Case 1:
% 176.00/27.28  | | | 
% 176.00/27.28  | | |   (104)  all_58_14 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | COMBINE_EQS: (48), (104) imply:
% 176.00/27.28  | | |   (105)  all_52_29 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (105) implies:
% 176.00/27.28  | | |   (106)  all_52_29 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (3), (106) imply:
% 176.00/27.28  | | |   (107)   ~ (all_52_13 = e3)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (17), (106) imply:
% 176.00/27.28  | | |   (108)   ~ (all_52_25 = e3)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (73), (106) imply:
% 176.00/27.28  | | |   (109)   ~ (all_14_2 = e3)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (109) implies:
% 176.00/27.28  | | |   (110)   ~ (all_14_2 = e3)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (75), (106) imply:
% 176.00/27.28  | | |   (111)   ~ (all_6_2 = e3)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (44), (106) imply:
% 176.00/27.28  | | |   (112)  op(e1, e3) = all_52_28
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (33), (106) imply:
% 176.00/27.28  | | |   (113)  op(e0, e1) = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | GROUND_INST: instantiating (87) with all_52_17, all_52_28, e3, e1,
% 176.00/27.28  | | |              simplifying with (80), (112) gives:
% 176.00/27.28  | | |   (114)  all_52_17 = all_52_28
% 176.00/27.28  | | | 
% 176.00/27.28  | | | COMBINE_EQS: (85), (114) imply:
% 176.00/27.28  | | |   (115)  all_56_8 = all_52_28
% 176.00/27.28  | | | 
% 176.00/27.28  | | | COMBINE_EQS: (66), (114) imply:
% 176.00/27.28  | | |   (116)  all_58_6 = all_52_28
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (2), (114) imply:
% 176.00/27.28  | | |   (117)   ~ (all_52_23 = all_52_28)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (117) implies:
% 176.00/27.28  | | |   (118)   ~ (all_52_23 = all_52_28)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (32), (114) imply:
% 176.00/27.28  | | |   (119)   ~ (all_52_25 = all_52_28)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (119) implies:
% 176.00/27.28  | | |   (120)   ~ (all_52_25 = all_52_28)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (86), (114) imply:
% 176.00/27.28  | | |   (121)   ~ (all_52_28 = all_4_2)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (68), (114) imply:
% 176.00/27.28  | | |   (122)  op(e3, all_52_28) = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | BETA: splitting (77) gives:
% 176.00/27.28  | | | 
% 176.00/27.28  | | | Case 1:
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | |   (123)  all_56_11 = e3
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | COMBINE_EQS: (7), (123) imply:
% 176.00/27.28  | | | |   (124)  all_52_23 = e3
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | SIMP: (124) implies:
% 176.00/27.28  | | | |   (125)  all_52_23 = e3
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | COMBINE_EQS: (70), (125) imply:
% 176.00/27.28  | | | |   (126)  all_58_11 = e3
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REDUCE: (61), (125) imply:
% 176.00/27.28  | | | |   (127)   ~ (all_52_15 = e3)
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REDUCE: (6), (125) imply:
% 176.00/27.28  | | | |   (128)   ~ (all_52_19 = e3)
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REDUCE: (118), (125) imply:
% 176.00/27.28  | | | |   (129)   ~ (all_52_28 = e3)
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | SIMP: (129) implies:
% 176.00/27.28  | | | |   (130)   ~ (all_52_28 = e3)
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REDUCE: (62), (125) imply:
% 176.00/27.28  | | | |   (131)  op(e1, e0) = e3
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REDUCE: (92), (125) imply:
% 176.00/27.28  | | | |   (132)  op(e0, e3) = e0
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REF_CLOSE: (1), (5), (9), (12), (13), (15), (18), (19), (20), (21),
% 176.00/27.28  | | | |            (23), (25), (26), (27), (28), (30), (31), (35), (37), (39),
% 176.00/27.28  | | | |            (40), (42), (43), (46), (47), (49), (50), (51), (52), (54),
% 176.00/27.28  | | | |            (56), (57), (58), (59), (63), (64), (66), (67), (68), (69),
% 176.00/27.28  | | | |            (71), (76), (78), (79), (81), (82), (83), (84), (86), (87),
% 176.00/27.28  | | | |            (88), (90), (91), (93), (97), (98), (100), (107), (108),
% 176.00/27.28  | | | |            (113), (115), (116), (120), (121), (122), (126), (127),
% 176.00/27.28  | | | |            (128), (130), (131), (132) are inconsistent by sub-proof
% 176.00/27.28  | | | |            #205.
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | Case 2:
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | |   (133)   ~ (all_56_11 = e3)
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | REDUCE: (7), (133) imply:
% 176.00/27.28  | | | |   (134)   ~ (all_52_23 = e3)
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | BETA: splitting (96) gives:
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | | Case 1:
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | |   (135)  all_58_9 = e3
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | | COMBINE_EQS: (97), (135) imply:
% 176.00/27.28  | | | | |   (136)  all_52_7 = e3
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | | SIMP: (136) implies:
% 176.00/27.28  | | | | |   (137)  all_52_7 = e3
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | | REF_CLOSE: (22), (30), (36), (40), (41), (43), (45), (50), (51), (55),
% 176.00/27.28  | | | | |            (65), (66), (67), (68), (70), (76), (78), (80), (84), (86),
% 176.00/27.28  | | | | |            (87), (93), (95), (98), (100), (101), (108), (137) are
% 176.00/27.28  | | | | |            inconsistent by sub-proof #943.
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | Case 2:
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | |   (138)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | | BETA: splitting (138) gives:
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | | Case 1:
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | |   (139)  all_58_10 = e3
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | | COMBINE_EQS: (27), (139) imply:
% 176.00/27.28  | | | | | |   (140)  all_52_15 = e3
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | | SIMP: (140) implies:
% 176.00/27.28  | | | | | |   (141)  all_52_15 = e3
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | | REDUCE: (99), (141) imply:
% 176.00/27.28  | | | | | |   (142)   ~ (all_52_9 = e3)
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | | REDUCE: (61), (141) imply:
% 176.00/27.28  | | | | | |   (143)   ~ (all_52_23 = e3)
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | | BETA: splitting (36) gives:
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | | Case 1:
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | |   (144)  all_58_6 = e3
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | | COMBINE_EQS: (116), (144) imply:
% 176.00/27.28  | | | | | | |   (145)  all_52_28 = e3
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | | SIMP: (145) implies:
% 176.00/27.28  | | | | | | |   (146)  all_52_28 = e3
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | | REF_CLOSE: (84), (87), (121), (122), (146) are inconsistent by
% 176.00/27.28  | | | | | | |            sub-proof #902.
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | Case 2:
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | |   (147)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | | REF_CLOSE: (4), (8), (11), (12), (14), (15), (16), (18), (21),
% 176.00/27.28  | | | | | | |            (26), (28), (29), (30), (34), (35), (39), (42), (43),
% 176.00/27.28  | | | | | | |            (49), (50), (51), (53), (58), (59), (60), (63), (66),
% 176.00/27.28  | | | | | | |            (67), (68), (70), (72), (74), (76), (84), (86), (87),
% 176.00/27.28  | | | | | | |            (89), (90), (93), (98), (101), (104), (108), (110),
% 176.00/27.28  | | | | | | |            (113), (134), (142), (147) are inconsistent by
% 176.00/27.28  | | | | | | |            sub-proof #204.
% 176.00/27.28  | | | | | | | 
% 176.00/27.28  | | | | | | End of split
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | Case 2:
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | |   (148)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | | REF_CLOSE: (10), (24), (70), (134), (148) are inconsistent by
% 176.00/27.28  | | | | | |            sub-proof #1016.
% 176.00/27.28  | | | | | | 
% 176.00/27.28  | | | | | End of split
% 176.00/27.28  | | | | | 
% 176.00/27.28  | | | | End of split
% 176.00/27.28  | | | | 
% 176.00/27.28  | | | End of split
% 176.00/27.28  | | | 
% 176.00/27.28  | | Case 2:
% 176.00/27.28  | | | 
% 176.00/27.28  | | |   (149)  all_58_15 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | COMBINE_EQS: (24), (149) imply:
% 176.00/27.28  | | |   (150)  all_6_2 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (10), (150) imply:
% 176.00/27.28  | | |   (151)  $false
% 176.00/27.28  | | | 
% 176.00/27.28  | | | CLOSE: (151) is inconsistent.
% 176.00/27.28  | | | 
% 176.00/27.28  | | End of split
% 176.00/27.28  | | 
% 176.00/27.28  | End of split
% 176.00/27.28  | 
% 176.00/27.28  End of proof
% 176.00/27.28  
% 176.00/27.28  Sub-proof #204 shows that the following formulas are inconsistent:
% 176.00/27.28  ----------------------------------------------------------------
% 176.00/27.28    (1)   ~ (all_52_25 = e3)
% 176.00/27.28    (2)  op(e3, e2) = all_52_3
% 176.00/27.28    (3)  op(e1, e2) = all_52_19
% 176.00/27.28    (4)  op(e3, all_52_9) = all_52_8
% 176.00/27.28    (5)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.28    (6)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.00/27.28    (7)  all_58_5 = all_52_13
% 176.00/27.28    (8)   ~ (all_6_2 = e0)
% 176.00/27.28    (9)  all_56_15 = all_6_2
% 176.00/27.28    (10)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.28    (11)  all_58_3 = all_10_2
% 176.00/27.28    (12)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.28    (13)  all_8_2 = all_6_2
% 176.00/27.28    (14)   ~ (all_52_5 = all_4_2)
% 176.00/27.28    (15)  all_58_7 = all_52_19
% 176.00/27.28    (16)   ~ (all_4_0 = e2)
% 176.00/27.28    (17)  all_58_4 = all_52_5
% 176.00/27.28    (18)  op(e3, all_4_2) = all_4_1
% 176.00/27.28    (19)  all_58_1 = all_52_3
% 176.00/27.28    (20)  all_58_0 = all_4_2
% 176.00/27.28    (21)   ~ (all_52_3 = all_52_5)
% 176.00/27.28    (22)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.28    (23)  all_58_8 = all_14_2
% 176.00/27.28    (24)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.28    (25)   ~ (all_52_23 = e3)
% 176.00/27.28    (26)  op(e0, all_6_2) = all_6_1
% 176.00/27.28    (27)   ~ (all_52_9 = all_10_2)
% 176.00/27.28    (28)   ~ (all_52_9 = all_52_13)
% 176.00/27.28    (29)  all_58_13 = all_52_27
% 176.00/27.28    (30)  all_58_6 = all_52_17
% 176.00/27.28    (31)  op(e2, all_52_19) = e2
% 176.00/27.28    (32)  op(e3, all_52_17) = e3
% 176.00/27.28    (33)  all_58_11 = all_52_23
% 176.00/27.28    (34)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.28    (35)   ~ (all_4_0 = e1)
% 176.00/27.28    (36)   ~ (all_52_9 = e3)
% 176.00/27.28    (37)  all_58_2 = all_52_9
% 176.00/27.28    (38)  op(e3, e3) = all_4_2
% 176.00/27.28    (39)   ~ (all_14_2 = e3)
% 176.00/27.28    (40)   ~ (all_52_17 = all_4_2)
% 176.00/27.28    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.28    (42)   ~ (all_52_27 = all_6_2)
% 176.00/27.28    (43)  op(e0, e1) = e3
% 176.00/27.28    (44)  all_8_1 = all_6_1
% 176.00/27.28    (45)  all_58_14 = e3
% 176.00/27.28    (46)  op(e1, all_14_2) = e1
% 176.00/27.28    (47)  all_58_12 = all_52_25
% 176.00/27.28    (48)  op(e2, e3) = all_52_9
% 176.00/27.28  
% 176.00/27.28  Begin of proof
% 176.00/27.28  | 
% 176.00/27.28  | BETA: splitting (22) gives:
% 176.00/27.28  | 
% 176.00/27.28  | Case 1:
% 176.00/27.28  | | 
% 176.00/27.28  | |   (49)  all_58_0 = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | COMBINE_EQS: (20), (49) imply:
% 176.00/27.28  | |   (50)  all_4_2 = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | REDUCE: (14), (50) imply:
% 176.00/27.28  | |   (51)   ~ (all_52_5 = e3)
% 176.00/27.28  | | 
% 176.00/27.28  | | REDUCE: (24), (50) imply:
% 176.00/27.28  | |   (52)  op(all_4_1, e3) = all_4_0
% 176.00/27.28  | | 
% 176.00/27.28  | | REDUCE: (18), (50) imply:
% 176.00/27.28  | |   (53)  op(e3, e3) = all_4_1
% 176.00/27.28  | | 
% 176.00/27.28  | | REDUCE: (38), (50) imply:
% 176.00/27.28  | |   (54)  op(e3, e3) = e3
% 176.00/27.28  | | 
% 176.00/27.28  | | BETA: splitting (10) gives:
% 176.00/27.28  | | 
% 176.00/27.28  | | Case 1:
% 176.00/27.28  | | | 
% 176.00/27.28  | | |   (55)  all_58_7 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | COMBINE_EQS: (15), (55) imply:
% 176.00/27.28  | | |   (56)  all_52_19 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (31), (56) imply:
% 176.00/27.28  | | |   (57)  op(e2, e3) = e2
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (3), (56) imply:
% 176.00/27.28  | | |   (58)  op(e1, e2) = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | GROUND_INST: instantiating (41) with all_52_9, e2, e3, e2, simplifying
% 176.00/27.28  | | |              with (48), (57) gives:
% 176.00/27.28  | | |   (59)  all_52_9 = e2
% 176.00/27.28  | | | 
% 176.00/27.28  | | | GROUND_INST: instantiating (41) with e3, all_4_1, e3, e3, simplifying with
% 176.00/27.28  | | |              (53), (54) gives:
% 176.00/27.28  | | |   (60)  all_4_1 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (28), (59) imply:
% 176.00/27.28  | | |   (61)   ~ (all_52_13 = e2)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (61) implies:
% 176.00/27.28  | | |   (62)   ~ (all_52_13 = e2)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (27), (59) imply:
% 176.00/27.28  | | |   (63)   ~ (all_10_2 = e2)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (63) implies:
% 176.00/27.28  | | |   (64)   ~ (all_10_2 = e2)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (52), (60) imply:
% 176.00/27.28  | | |   (65)  op(e3, e3) = all_4_0
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (4), (59) imply:
% 176.00/27.28  | | |   (66)  op(e3, e2) = all_52_8
% 176.00/27.28  | | | 
% 176.00/27.28  | | | GROUND_INST: instantiating (41) with all_52_3, all_52_8, e2, e3,
% 176.00/27.28  | | |              simplifying with (2), (66) gives:
% 176.00/27.28  | | |   (67)  all_52_3 = all_52_8
% 176.00/27.28  | | | 
% 176.00/27.28  | | | GROUND_INST: instantiating (41) with e3, all_4_0, e3, e3, simplifying with
% 176.00/27.28  | | |              (54), (65) gives:
% 176.00/27.28  | | |   (68)  all_4_0 = e3
% 176.00/27.28  | | | 
% 176.00/27.28  | | | COMBINE_EQS: (19), (67) imply:
% 176.00/27.28  | | |   (69)  all_58_1 = all_52_8
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (21), (67) imply:
% 176.00/27.28  | | |   (70)   ~ (all_52_5 = all_52_8)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | SIMP: (70) implies:
% 176.00/27.28  | | |   (71)   ~ (all_52_5 = all_52_8)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (16), (68) imply:
% 176.00/27.28  | | |   (72)   ~ (e3 = e2)
% 176.00/27.28  | | | 
% 176.00/27.28  | | | REDUCE: (35), (68) imply:
% 176.00/27.28  | | |   (73)   ~ (e3 = e1)
% 176.00/27.28  | | | 
% 176.00/27.29  | | | BETA: splitting (34) gives:
% 176.00/27.29  | | | 
% 176.00/27.29  | | | Case 1:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | |   (74)  all_58_4 = e2
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | COMBINE_EQS: (17), (74) imply:
% 176.00/27.29  | | | |   (75)  all_52_5 = e2
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | REDUCE: (71), (75) imply:
% 176.00/27.29  | | | |   (76)   ~ (all_52_8 = e2)
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | SIMP: (76) implies:
% 176.00/27.29  | | | |   (77)   ~ (all_52_8 = e2)
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | REDUCE: (51), (75) imply:
% 176.00/27.29  | | | |   (78)   ~ (e3 = e2)
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | BETA: splitting (6) gives:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | Case 1:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | |   (79)  all_58_1 = e2
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | COMBINE_EQS: (69), (79) imply:
% 176.00/27.29  | | | | |   (80)  all_52_8 = e2
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | REDUCE: (77), (80) imply:
% 176.00/27.29  | | | | |   (81)  $false
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | CLOSE: (81) is inconsistent.
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | Case 2:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | |   (82)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | BETA: splitting (82) gives:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | Case 1:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | |   (83)  all_58_3 = e2
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | COMBINE_EQS: (11), (83) imply:
% 176.00/27.29  | | | | | |   (84)  all_10_2 = e2
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | REDUCE: (64), (84) imply:
% 176.00/27.29  | | | | | |   (85)  $false
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | CLOSE: (85) is inconsistent.
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | Case 2:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | |   (86)  all_58_7 = e2 | all_58_13 = e2
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | BETA: splitting (86) gives:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | Case 1:
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | |   (87)  all_58_7 = e2
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | COMBINE_EQS: (55), (87) imply:
% 176.00/27.29  | | | | | | |   (88)  e3 = e2
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | REDUCE: (72), (88) imply:
% 176.00/27.29  | | | | | | |   (89)  $false
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | CLOSE: (89) is inconsistent.
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | Case 2:
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | |   (90)  all_58_13 = e2
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | COMBINE_EQS: (29), (90) imply:
% 176.00/27.29  | | | | | | |   (91)  all_52_27 = e2
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | REDUCE: (42), (91) imply:
% 176.00/27.29  | | | | | | |   (92)   ~ (all_6_2 = e2)
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | REF_CLOSE: (5), (8), (9), (12), (13), (26), (41), (43), (44), (92)
% 176.00/27.29  | | | | | | |            are inconsistent by sub-proof #224.
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | End of split
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | End of split
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | End of split
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | Case 2:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | |   (93)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | REF_CLOSE: (7), (23), (41), (45), (46), (58), (62), (72), (73), (93) are
% 176.00/27.29  | | | |            inconsistent by sub-proof #674.
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | End of split
% 176.00/27.29  | | | 
% 176.00/27.29  | | Case 2:
% 176.00/27.29  | | | 
% 176.00/27.29  | | |   (94)  all_58_8 = e3 | all_58_11 = e3
% 176.00/27.29  | | | 
% 176.00/27.29  | | | REF_CLOSE: (23), (25), (33), (39), (94) are inconsistent by sub-proof
% 176.00/27.29  | | |            #997.
% 176.00/27.29  | | | 
% 176.00/27.29  | | End of split
% 176.00/27.29  | | 
% 176.00/27.29  | Case 2:
% 176.00/27.29  | | 
% 176.00/27.29  | |   (95)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.29  | | 
% 176.00/27.29  | | REF_CLOSE: (1), (30), (32), (36), (37), (38), (40), (41), (47), (95) are
% 176.00/27.29  | |            inconsistent by sub-proof #913.
% 176.00/27.29  | | 
% 176.00/27.29  | End of split
% 176.00/27.29  | 
% 176.00/27.29  End of proof
% 176.00/27.29  
% 176.00/27.29  Sub-proof #205 shows that the following formulas are inconsistent:
% 176.00/27.29  ----------------------------------------------------------------
% 176.00/27.29    (1)   ~ (all_52_25 = e3)
% 176.00/27.29    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.29    (3)  all_58_6 = all_52_28
% 176.00/27.29    (4)  op(e3, all_52_25) = all_52_24
% 176.00/27.29    (5)   ~ (all_52_27 = e3)
% 176.00/27.29    (6)  op(e3, all_52_28) = e3
% 176.00/27.29    (7)   ~ (all_52_25 = all_52_28)
% 176.00/27.29    (8)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.29    (9)   ~ (all_52_3 = all_10_2)
% 176.00/27.29    (10)  all_58_5 = all_52_13
% 176.00/27.29    (11)  all_56_15 = all_6_2
% 176.00/27.29    (12)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.29    (13)  op(e2, e0) = all_52_15
% 176.00/27.29    (14)  all_58_3 = all_10_2
% 176.00/27.29    (15)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.29    (16)  all_56_8 = all_52_28
% 176.00/27.29    (17)   ~ (all_52_9 = all_4_2)
% 176.00/27.29    (18)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.29    (19)  all_58_10 = all_52_15
% 176.00/27.29    (20)  all_8_2 = all_6_2
% 176.00/27.29    (21)   ~ (all_52_28 = all_4_2)
% 176.00/27.29    (22)  all_58_7 = all_52_19
% 176.00/27.29    (23)   ~ (all_52_15 = all_6_2)
% 176.00/27.29    (24)  all_58_4 = all_52_5
% 176.00/27.29    (25)   ~ (e3 = e1)
% 176.00/27.29    (26)  op(e3, all_4_2) = all_4_1
% 176.00/27.29    (27)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.29    (28)  all_58_1 = all_52_3
% 176.00/27.29    (29)  all_58_0 = all_4_2
% 176.00/27.29    (30)   ~ (all_4_1 = e2)
% 176.00/27.29    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.29    (32)  all_58_11 = e3
% 176.00/27.29    (33)   ~ (all_52_3 = all_52_5)
% 176.00/27.29    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.29    (35)  all_58_8 = all_14_2
% 176.00/27.29    (36)  op(e0, e3) = e0
% 176.00/27.29    (37)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.29    (38)   ~ (all_52_28 = e3)
% 176.00/27.29    (39)  op(e1, e0) = e3
% 176.00/27.29    (40)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.29    (41)   ~ (all_52_3 = all_4_2)
% 176.00/27.29    (42)  op(e0, e3) = all_52_25
% 176.00/27.29    (43)  op(e0, all_6_2) = all_6_1
% 176.00/27.29    (44)   ~ (all_52_9 = all_10_2)
% 176.00/27.29    (45)   ~ (all_52_13 = e3)
% 176.00/27.29    (46)   ~ (all_52_15 = e3)
% 176.00/27.29    (47)  all_58_13 = all_52_27
% 176.00/27.29    (48)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.29    (49)  all_58_6 = all_52_17
% 176.00/27.29    (50)  op(e2, all_52_19) = e2
% 176.00/27.29    (51)  op(e3, all_52_17) = e3
% 176.00/27.29    (52)  all_56_0 = all_4_2
% 176.00/27.29    (53)   ~ (all_52_3 = all_52_19)
% 176.00/27.29    (54)  all_58_2 = all_52_9
% 176.00/27.29    (55)  op(e3, e1) = all_52_5
% 176.00/27.29    (56)   ~ (all_52_25 = all_6_2)
% 176.00/27.29    (57)   ~ (all_52_19 = e3)
% 176.00/27.29    (58)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.29    (59)   ~ (all_52_25 = all_4_2)
% 176.00/27.29    (60)  op(e3, e0) = all_52_7
% 176.00/27.29    (61)  op(e3, e3) = all_4_2
% 176.00/27.29    (62)   ~ (all_52_17 = all_4_2)
% 176.00/27.29    (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.29    (64)   ~ (all_52_25 = all_52_27)
% 176.00/27.29    (65)  op(e0, e1) = e3
% 176.00/27.29    (66)  all_8_1 = all_6_1
% 176.00/27.29    (67)   ~ (all_52_7 = all_6_2)
% 176.00/27.29    (68)  op(e1, all_14_2) = e1
% 176.00/27.29    (69)  all_58_9 = all_52_7
% 176.00/27.29    (70)  all_58_12 = all_52_25
% 176.00/27.29    (71)   ~ (e3 = e2)
% 176.00/27.29  
% 176.00/27.29  Begin of proof
% 176.00/27.29  | 
% 176.00/27.29  | GROUND_INST: instantiating (63) with all_52_25, e0, e3, e0, simplifying with
% 176.00/27.29  |              (36), (42) gives:
% 176.00/27.29  |   (72)  all_52_25 = e0
% 176.00/27.29  | 
% 176.00/27.29  | REDUCE: (64), (72) imply:
% 176.00/27.29  |   (73)   ~ (all_52_27 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | SIMP: (73) implies:
% 176.00/27.29  |   (74)   ~ (all_52_27 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | REDUCE: (7), (72) imply:
% 176.00/27.29  |   (75)   ~ (all_52_28 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | SIMP: (75) implies:
% 176.00/27.29  |   (76)   ~ (all_52_28 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | REDUCE: (56), (72) imply:
% 176.00/27.29  |   (77)   ~ (all_6_2 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | SIMP: (77) implies:
% 176.00/27.29  |   (78)   ~ (all_6_2 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | REDUCE: (59), (72) imply:
% 176.00/27.29  |   (79)   ~ (all_4_2 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | SIMP: (79) implies:
% 176.00/27.29  |   (80)   ~ (all_4_2 = e0)
% 176.00/27.29  | 
% 176.00/27.29  | REDUCE: (4), (72) imply:
% 176.00/27.29  |   (81)  op(e3, e0) = all_52_24
% 176.00/27.29  | 
% 176.00/27.29  | GROUND_INST: instantiating (63) with all_52_7, all_52_24, e0, e3, simplifying
% 176.00/27.29  |              with (60), (81) gives:
% 176.00/27.29  |   (82)  all_52_7 = all_52_24
% 176.00/27.29  | 
% 176.00/27.29  | COMBINE_EQS: (69), (82) imply:
% 176.00/27.29  |   (83)  all_58_9 = all_52_24
% 176.00/27.29  | 
% 176.00/27.29  | REDUCE: (67), (82) imply:
% 176.00/27.29  |   (84)   ~ (all_52_24 = all_6_2)
% 176.00/27.29  | 
% 176.00/27.29  | BETA: splitting (2) gives:
% 176.00/27.29  | 
% 176.00/27.29  | Case 1:
% 176.00/27.29  | | 
% 176.00/27.29  | |   (85)  all_56_8 = e3
% 176.00/27.29  | | 
% 176.00/27.29  | | COMBINE_EQS: (16), (85) imply:
% 176.00/27.29  | |   (86)  all_52_28 = e3
% 176.00/27.29  | | 
% 176.00/27.29  | | REDUCE: (38), (86) imply:
% 176.00/27.29  | |   (87)  $false
% 176.00/27.29  | | 
% 176.00/27.29  | | CLOSE: (87) is inconsistent.
% 176.00/27.29  | | 
% 176.00/27.29  | Case 2:
% 176.00/27.29  | | 
% 176.00/27.29  | |   (88)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.29  | | 
% 176.00/27.29  | | BETA: splitting (34) gives:
% 176.00/27.29  | | 
% 176.00/27.29  | | Case 1:
% 176.00/27.29  | | | 
% 176.00/27.29  | | |   (89)  all_58_0 = e3
% 176.00/27.29  | | | 
% 176.00/27.29  | | | COMBINE_EQS: (29), (89) imply:
% 176.00/27.29  | | |   (90)  all_4_2 = e3
% 176.00/27.29  | | | 
% 176.00/27.29  | | | REDUCE: (17), (90) imply:
% 176.00/27.29  | | |   (91)   ~ (all_52_9 = e3)
% 176.00/27.29  | | | 
% 176.00/27.29  | | | REDUCE: (80), (90) imply:
% 176.00/27.29  | | |   (92)   ~ (e3 = e0)
% 176.00/27.29  | | | 
% 176.00/27.29  | | | BETA: splitting (27) gives:
% 176.00/27.29  | | | 
% 176.00/27.29  | | | Case 1:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | |   (93)  all_58_2 = e3
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | REF_CLOSE: (54), (91), (93) are inconsistent by sub-proof #980.
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | Case 2:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | |   (94)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | BETA: splitting (94) gives:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | Case 1:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | |   (95)  all_58_3 = e3
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | COMBINE_EQS: (14), (95) imply:
% 176.00/27.29  | | | | |   (96)  all_10_2 = e3
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | REDUCE: (9), (96) imply:
% 176.00/27.29  | | | | |   (97)   ~ (all_52_3 = e3)
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | BETA: splitting (58) gives:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | Case 1:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | |   (98)  all_58_6 = e0
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | COMBINE_EQS: (3), (98) imply:
% 176.00/27.29  | | | | | |   (99)  all_52_28 = e0
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | REDUCE: (76), (99) imply:
% 176.00/27.29  | | | | | |   (100)  $false
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | CLOSE: (100) is inconsistent.
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | Case 2:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | |   (101)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | BETA: splitting (37) gives:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | Case 1:
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | |   (102)  all_58_1 = e0
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | COMBINE_EQS: (28), (102) imply:
% 176.00/27.29  | | | | | | |   (103)  all_52_3 = e0
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | REDUCE: (53), (103) imply:
% 176.00/27.29  | | | | | | |   (104)   ~ (all_52_19 = e0)
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | SIMP: (104) implies:
% 176.00/27.29  | | | | | | |   (105)   ~ (all_52_19 = e0)
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | REDUCE: (97), (103) imply:
% 176.00/27.29  | | | | | | |   (106)   ~ (e3 = e0)
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | BETA: splitting (101) gives:
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | Case 1:
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | |   (107)  all_58_7 = e0
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | COMBINE_EQS: (22), (107) imply:
% 176.00/27.29  | | | | | | | |   (108)  all_52_19 = e0
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | REDUCE: (105), (108) imply:
% 176.00/27.29  | | | | | | | |   (109)  $false
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | CLOSE: (109) is inconsistent.
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | Case 2:
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | |   (110)  all_58_8 = e0 | all_58_11 = e0
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | REF_CLOSE: (25), (32), (35), (39), (63), (68), (92), (110) are
% 176.00/27.29  | | | | | | | |            inconsistent by sub-proof #698.
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | End of split
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | Case 2:
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | |   (111)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | BETA: splitting (111) gives:
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | | Case 1:
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | |   (112)  all_58_3 = e0
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | COMBINE_EQS: (95), (112) imply:
% 176.00/27.29  | | | | | | | |   (113)  e3 = e0
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | REDUCE: (92), (113) imply:
% 176.00/27.29  | | | | | | | |   (114)  $false
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | CLOSE: (114) is inconsistent.
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | Case 2:
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | |   (115)  all_58_7 = e0 | all_58_13 = e0
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | BETA: splitting (115) gives:
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | | Case 1:
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | |   (116)  all_58_7 = e0
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | COMBINE_EQS: (22), (116) imply:
% 176.00/27.29  | | | | | | | | |   (117)  all_52_19 = e0
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | REDUCE: (50), (117) imply:
% 176.00/27.29  | | | | | | | | |   (118)  op(e2, e0) = e2
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | GROUND_INST: instantiating (63) with all_52_15, e2, e0, e2,
% 176.00/27.29  | | | | | | | | |              simplifying with (13), (118) gives:
% 176.00/27.29  | | | | | | | | |   (119)  all_52_15 = e2
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | REDUCE: (23), (119) imply:
% 176.00/27.29  | | | | | | | | |   (120)   ~ (all_6_2 = e2)
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | REF_CLOSE: (8), (11), (18), (20), (43), (63), (65), (66),
% 176.00/27.29  | | | | | | | | |            (78), (120) are inconsistent by sub-proof #224.
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | Case 2:
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | |   (121)  all_58_13 = e0
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | COMBINE_EQS: (47), (121) imply:
% 176.00/27.29  | | | | | | | | |   (122)  all_52_27 = e0
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | REDUCE: (74), (122) imply:
% 176.00/27.29  | | | | | | | | |   (123)  $false
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | | CLOSE: (123) is inconsistent.
% 176.00/27.29  | | | | | | | | | 
% 176.00/27.29  | | | | | | | | End of split
% 176.00/27.29  | | | | | | | | 
% 176.00/27.29  | | | | | | | End of split
% 176.00/27.29  | | | | | | | 
% 176.00/27.29  | | | | | | End of split
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | End of split
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | Case 2:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | |   (124)  all_58_5 = e3 | all_58_10 = e3
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | REF_CLOSE: (10), (19), (45), (46), (124) are inconsistent by sub-proof
% 176.00/27.29  | | | | |            #958.
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | End of split
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | End of split
% 176.00/27.29  | | | 
% 176.00/27.29  | | Case 2:
% 176.00/27.29  | | | 
% 176.00/27.29  | | |   (125)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.29  | | | 
% 176.00/27.29  | | | BETA: splitting (125) gives:
% 176.00/27.29  | | | 
% 176.00/27.29  | | | Case 1:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | |   (126)  all_58_2 = e3
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | COMBINE_EQS: (54), (126) imply:
% 176.00/27.29  | | | |   (127)  all_52_9 = e3
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | SIMP: (127) implies:
% 176.00/27.29  | | | |   (128)  all_52_9 = e3
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | REDUCE: (44), (128) imply:
% 176.00/27.29  | | | |   (129)   ~ (all_10_2 = e3)
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | SIMP: (129) implies:
% 176.00/27.29  | | | |   (130)   ~ (all_10_2 = e3)
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | BETA: splitting (31) gives:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | Case 1:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | |   (131)  all_58_1 = e3
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | COMBINE_EQS: (28), (131) imply:
% 176.00/27.29  | | | | |   (132)  all_52_3 = e3
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | REDUCE: (33), (132) imply:
% 176.00/27.29  | | | | |   (133)   ~ (all_52_5 = e3)
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | SIMP: (133) implies:
% 176.00/27.29  | | | | |   (134)   ~ (all_52_5 = e3)
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | REDUCE: (41), (132) imply:
% 176.00/27.29  | | | | |   (135)   ~ (all_4_2 = e3)
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | SIMP: (135) implies:
% 176.00/27.29  | | | | |   (136)   ~ (all_4_2 = e3)
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | BETA: splitting (15) gives:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | Case 1:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | |   (137)  all_56_0 = e3
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | REF_CLOSE: (52), (136), (137) are inconsistent by sub-proof #1024.
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | Case 2:
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | |   (138)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | | REF_CLOSE: (6), (8), (11), (12), (16), (18), (20), (21), (24), (26),
% 176.00/27.29  | | | | | |            (29), (30), (40), (43), (48), (52), (55), (63), (65),
% 176.00/27.29  | | | | | |            (66), (71), (76), (78), (80), (83), (84), (88), (131),
% 176.00/27.29  | | | | | |            (134), (138) are inconsistent by sub-proof #207.
% 176.00/27.29  | | | | | | 
% 176.00/27.29  | | | | | End of split
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | Case 2:
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | |   (139)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | | REF_CLOSE: (5), (14), (22), (47), (57), (130), (139) are inconsistent
% 176.00/27.29  | | | | |            by sub-proof #206.
% 176.00/27.29  | | | | | 
% 176.00/27.29  | | | | End of split
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | Case 2:
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | |   (140)  all_58_6 = e3 | all_58_12 = e3
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | | REF_CLOSE: (1), (49), (51), (61), (62), (63), (70), (140) are
% 176.00/27.29  | | | |            inconsistent by sub-proof #947.
% 176.00/27.29  | | | | 
% 176.00/27.29  | | | End of split
% 176.00/27.29  | | | 
% 176.00/27.29  | | End of split
% 176.00/27.29  | | 
% 176.00/27.29  | End of split
% 176.00/27.29  | 
% 176.00/27.29  End of proof
% 176.00/27.29  
% 176.00/27.29  Sub-proof #206 shows that the following formulas are inconsistent:
% 176.00/27.29  ----------------------------------------------------------------
% 176.00/27.29    (1)   ~ (all_52_27 = e3)
% 176.00/27.29    (2)  all_58_3 = all_10_2
% 176.00/27.29    (3)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.29    (4)  all_58_7 = all_52_19
% 176.00/27.29    (5)   ~ (all_10_2 = e3)
% 176.00/27.29    (6)  all_58_13 = all_52_27
% 176.00/27.29    (7)   ~ (all_52_19 = e3)
% 176.00/27.29  
% 176.00/27.29  Begin of proof
% 176.00/27.29  | 
% 176.00/27.29  | BETA: splitting (3) gives:
% 176.00/27.29  | 
% 176.00/27.29  | Case 1:
% 176.00/27.29  | | 
% 176.00/27.29  | |   (8)  all_58_3 = e3
% 176.00/27.29  | | 
% 176.00/27.29  | | COMBINE_EQS: (2), (8) imply:
% 176.00/27.29  | |   (9)  all_10_2 = e3
% 176.00/27.29  | | 
% 176.00/27.29  | | REDUCE: (5), (9) imply:
% 176.00/27.29  | |   (10)  $false
% 176.00/27.29  | | 
% 176.00/27.29  | | CLOSE: (10) is inconsistent.
% 176.00/27.29  | | 
% 176.00/27.29  | Case 2:
% 176.00/27.29  | | 
% 176.00/27.29  | |   (11)  all_58_7 = e3 | all_58_13 = e3
% 176.00/27.29  | | 
% 176.00/27.29  | | REF_CLOSE: (1), (4), (6), (7), (11) are inconsistent by sub-proof #976.
% 176.00/27.29  | | 
% 176.00/27.29  | End of split
% 176.00/27.29  | 
% 176.00/27.29  End of proof
% 176.00/27.29  
% 176.00/27.29  Sub-proof #207 shows that the following formulas are inconsistent:
% 176.00/27.29  ----------------------------------------------------------------
% 176.00/27.29    (1)  op(e3, all_52_28) = e3
% 176.00/27.29    (2)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.29    (3)   ~ (all_6_2 = e0)
% 176.00/27.29    (4)  all_56_15 = all_6_2
% 176.00/27.29    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.29    (6)  all_56_8 = all_52_28
% 176.00/27.29    (7)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.29    (8)  all_8_2 = all_6_2
% 176.00/27.29    (9)   ~ (all_52_28 = all_4_2)
% 176.00/27.29    (10)  all_58_4 = all_52_5
% 176.00/27.29    (11)  op(e3, all_4_2) = all_4_1
% 176.00/27.29    (12)  all_58_0 = all_4_2
% 176.00/27.29    (13)   ~ (all_4_1 = e2)
% 176.00/27.29    (14)   ~ (all_52_24 = all_6_2)
% 176.00/27.29    (15)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.29    (16)   ~ (all_52_28 = e0)
% 176.00/27.29    (17)  op(e0, all_6_2) = all_6_1
% 176.00/27.29    (18)   ~ (all_52_5 = e3)
% 176.00/27.29    (19)  all_58_1 = e3
% 176.00/27.29    (20)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.29    (21)  all_56_0 = all_4_2
% 176.00/27.29    (22)  op(e3, e1) = all_52_5
% 176.00/27.29    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.29    (24)  op(e0, e1) = e3
% 176.00/27.29    (25)  all_8_1 = all_6_1
% 176.00/27.29    (26)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.29    (27)   ~ (all_4_2 = e0)
% 176.00/27.29    (28)  all_58_9 = all_52_24
% 176.00/27.29    (29)   ~ (e3 = e2)
% 176.00/27.29    (30)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.00/27.29  
% 176.00/27.29  Begin of proof
% 176.00/27.29  | 
% 176.00/27.29  | BETA: splitting (5) gives:
% 176.00/27.29  | 
% 176.00/27.29  | Case 1:
% 176.00/27.29  | | 
% 176.00/27.29  | |   (31)  all_58_0 = e2
% 176.00/27.29  | | 
% 176.00/27.29  | | COMBINE_EQS: (12), (31) imply:
% 176.00/27.29  | |   (32)  all_4_2 = e2
% 176.00/27.29  | | 
% 176.00/27.29  | | REDUCE: (9), (32) imply:
% 176.00/27.29  | |   (33)   ~ (all_52_28 = e2)
% 176.00/27.29  | | 
% 176.00/27.29  | | REF_CLOSE: (1), (6), (16), (18), (22), (23), (30), (33) are inconsistent by
% 176.00/27.29  | |            sub-proof #903.
% 176.00/27.29  | | 
% 176.00/27.29  | Case 2:
% 176.00/27.29  | | 
% 176.00/27.29  | |   (34)   ~ (all_58_0 = e2)
% 176.00/27.29  | | 
% 176.00/27.29  | | REDUCE: (12), (34) imply:
% 176.00/27.29  | |   (35)   ~ (all_4_2 = e2)
% 176.00/27.29  | | 
% 176.00/27.29  | | BETA: splitting (20) gives:
% 176.00/27.29  | | 
% 176.00/27.29  | | Case 1:
% 176.00/27.29  | | | 
% 176.00/27.29  | | |   (36)  all_58_0 = e1
% 176.00/27.29  | | | 
% 176.00/27.29  | | | COMBINE_EQS: (12), (36) imply:
% 176.00/27.29  | | |   (37)  all_4_2 = e1
% 176.00/27.29  | | | 
% 176.00/27.29  | | | REDUCE: (35), (37) imply:
% 176.00/27.29  | | |   (38)   ~ (e2 = e1)
% 176.00/27.29  | | | 
% 176.00/27.29  | | | SIMP: (38) implies:
% 176.00/27.29  | | |   (39)   ~ (e2 = e1)
% 176.00/27.29  | | | 
% 176.00/27.29  | | | REF_CLOSE: (2), (3), (4), (7), (8), (10), (11), (13), (14), (15), (17),
% 176.00/27.29  | | |            (19), (22), (23), (24), (25), (28), (29), (36), (37), (39) are
% 176.00/27.29  | | |            inconsistent by sub-proof #213.
% 176.00/27.29  | | | 
% 176.00/27.29  | | Case 2:
% 176.00/27.29  | | | 
% 176.00/27.29  | | |   (40)   ~ (all_58_0 = e1)
% 176.00/27.29  | | | 
% 176.00/27.29  | | | REDUCE: (12), (40) imply:
% 176.00/27.29  | | |   (41)   ~ (all_4_2 = e1)
% 176.00/27.29  | | | 
% 176.00/27.29  | | | REF_CLOSE: (21), (26), (27), (35), (41) are inconsistent by sub-proof
% 176.00/27.29  | | |            #882.
% 176.00/27.29  | | | 
% 176.00/27.29  | | End of split
% 176.00/27.29  | | 
% 176.00/27.29  | End of split
% 176.00/27.29  | 
% 176.00/27.29  End of proof
% 176.00/27.29  
% 176.00/27.29  Sub-proof #208 shows that the following formulas are inconsistent:
% 176.00/27.29  ----------------------------------------------------------------
% 176.00/27.29    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.29    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.29    (3)   ~ (all_52_27 = all_10_2)
% 176.00/27.29    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.29    (5)   ~ (all_52_13 = all_52_29)
% 176.00/27.29    (6)  all_56_3 = all_52_7
% 176.00/27.29    (7)  op(e3, e2) = all_52_3
% 176.00/27.29    (8)   ~ (all_52_9 = all_52_25)
% 176.00/27.29    (9)  op(e3, all_52_25) = all_52_24
% 176.00/27.29    (10)   ~ (all_52_19 = all_52_23)
% 176.00/27.29    (11)  all_56_11 = all_52_23
% 176.00/27.29    (12)  op(e1, e2) = all_52_19
% 176.00/27.29    (13)   ~ (all_52_27 = e3)
% 176.00/27.29    (14)   ~ (all_6_2 = e3)
% 176.00/27.29    (15)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.29    (16)   ~ (all_52_3 = all_10_2)
% 176.00/27.29    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 176.00/27.29    (18)  all_58_5 = all_52_13
% 176.00/27.29    (19)   ~ (all_6_2 = e0)
% 176.00/27.29    (20)   ~ (all_52_25 = all_52_29)
% 176.00/27.29    (21)  op(e1, all_52_13) = e1
% 176.00/27.29    (22)  op(e0, all_52_15) = e0
% 176.00/27.29    (23)  all_56_15 = all_6_2
% 176.00/27.29    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.29    (25)  op(e2, e0) = all_52_15
% 176.00/27.29    (26)  all_58_3 = all_10_2
% 176.00/27.29    (27)  all_56_9 = all_52_19
% 176.00/27.29    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.29    (29)  all_58_15 = all_6_2
% 176.00/27.29    (30)   ~ (all_52_9 = all_4_2)
% 176.00/27.29    (31)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.29    (32)   ~ (all_52_5 = all_52_7)
% 176.00/27.29    (33)  all_58_10 = all_52_15
% 176.00/27.29    (34)  all_8_2 = all_6_2
% 176.00/27.29    (35)   ~ (all_52_5 = all_4_2)
% 176.00/27.29    (36)  all_58_7 = all_52_19
% 176.00/27.29    (37)  all_56_4 = all_52_9
% 176.00/27.29    (38)   ~ (all_52_15 = all_6_2)
% 176.00/27.29    (39)   ~ (all_52_17 = all_52_25)
% 176.00/27.29    (40)  op(e0, e1) = all_52_29
% 176.00/27.29    (41)   ~ (all_4_0 = e2)
% 176.00/27.29    (42)  all_58_4 = all_52_5
% 176.00/27.29    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.29    (44)   ~ (e3 = e1)
% 176.00/27.29    (45)   ~ (all_52_27 = all_52_29)
% 176.00/27.29    (46)   ~ (all_52_17 = all_14_2)
% 176.00/27.29    (47)  op(e3, all_4_2) = all_4_1
% 176.00/27.29    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.29    (49)   ~ (all_52_7 = all_4_2)
% 176.00/27.29    (50)  all_58_1 = all_52_3
% 176.00/27.29    (51)  all_58_0 = all_4_2
% 176.00/27.29    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.29    (53)  op(e1, all_52_29) = all_52_28
% 176.00/27.29    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.00/27.29    (55)   ~ (all_4_1 = e2)
% 176.00/27.29    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.29    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.29    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.00/27.29    (59)   ~ (all_14_1 = e3)
% 176.00/27.29    (60)  all_58_14 = all_52_29
% 176.00/27.29    (61)   ~ (all_52_3 = all_52_5)
% 176.00/27.29    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.29    (63)  op(e2, e1) = all_52_13
% 176.00/27.29    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.29    (65)  all_58_8 = all_14_2
% 176.00/27.29    (66)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.29    (67)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.29    (68)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.29    (69)   ~ (all_52_3 = all_52_27)
% 176.00/27.29    (70)   ~ (all_52_3 = all_4_2)
% 176.00/27.29    (71)  op(e0, e3) = all_52_25
% 176.00/27.29    (72)  op(e0, all_6_2) = all_6_1
% 176.00/27.29    (73)  op(e3, all_52_17) = all_52_16
% 176.00/27.29    (74)   ~ (all_52_13 = all_14_2)
% 176.00/27.29    (75)  op(e3, all_52_9) = e3
% 176.00/27.29    (76)   ~ (e3 = e0)
% 176.00/27.29    (77)   ~ (all_52_9 = all_52_13)
% 176.00/27.29    (78)  op(e0, all_52_23) = all_52_22
% 176.00/27.29    (79)   ~ (all_52_15 = all_52_23)
% 176.00/27.29    (80)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.00/27.29    (81)  op(e1, e0) = all_52_23
% 176.00/27.29    (82)  all_58_13 = all_52_27
% 176.00/27.29    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.29    (84)   ~ (all_52_9 = all_52_17)
% 176.00/27.29    (85)  all_58_6 = all_52_17
% 176.00/27.29    (86)   ~ (all_52_3 = all_52_7)
% 176.00/27.29    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.29    (88)  op(e2, all_52_19) = all_52_18
% 176.00/27.29    (89)   ~ (e1 = e0)
% 176.00/27.29    (90)  all_56_0 = all_4_2
% 176.00/27.29    (91)  all_58_11 = all_52_23
% 176.00/27.29    (92)   ~ (all_52_3 = all_52_19)
% 176.00/27.29    (93)   ~ (all_52_7 = all_52_15)
% 176.00/27.29    (94)   ~ (all_52_29 = all_14_2)
% 176.00/27.29    (95)   ~ (all_52_19 = all_10_2)
% 176.00/27.29    (96)   ~ (all_52_23 = all_6_2)
% 176.00/27.29    (97)   ~ (all_52_29 = all_6_2)
% 176.00/27.29    (98)  all_58_2 = all_52_9
% 176.00/27.29    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.29    (100)  op(e3, e1) = all_52_5
% 176.00/27.29    (101)   ~ (e2 = e1)
% 176.00/27.29    (102)  all_56_10 = all_14_2
% 176.00/27.29    (103)   ~ (all_52_25 = all_6_2)
% 176.00/27.30    (104)  op(e1, e3) = all_52_17
% 176.00/27.30    (105)   ~ (all_52_25 = all_4_2)
% 176.00/27.30    (106)  op(e3, e0) = all_52_7
% 176.00/27.30    (107)  op(e2, all_10_2) = e2
% 176.00/27.30    (108)  op(e3, e3) = all_4_2
% 176.00/27.30    (109)   ~ (all_52_17 = all_4_2)
% 176.00/27.30    (110)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.30             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.30    (111)   ~ (all_52_25 = all_52_27)
% 176.00/27.30    (112)   ~ (all_52_27 = all_6_2)
% 176.00/27.30    (113)  all_8_1 = all_6_1
% 176.00/27.30    (114)   ~ (all_52_7 = all_6_2)
% 176.00/27.30    (115)   ~ (all_52_7 = all_52_23)
% 176.00/27.30    (116)   ~ (all_52_17 = all_52_19)
% 176.00/27.30    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.30    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.00/27.30    (119)  op(e1, all_14_2) = all_14_1
% 176.00/27.30    (120)  all_58_9 = all_52_7
% 176.00/27.30    (121)  all_58_12 = all_52_25
% 176.00/27.30    (122)  all_56_6 = all_52_13
% 176.00/27.30    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.30    (124)   ~ (all_52_9 = all_52_15)
% 176.00/27.30    (125)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.30    (126)   ~ (e3 = e2)
% 176.00/27.30    (127)   ~ (all_52_19 = all_14_2)
% 176.00/27.30    (128)  op(e2, e3) = all_52_9
% 176.00/27.30  
% 176.00/27.30  Begin of proof
% 176.00/27.30  | 
% 176.00/27.30  | BETA: splitting (64) gives:
% 176.00/27.30  | 
% 176.00/27.30  | Case 1:
% 176.00/27.30  | | 
% 176.00/27.30  | |   (129)  all_58_12 = e3
% 176.00/27.30  | | 
% 176.00/27.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (16),
% 176.00/27.30  | |            (18), (19), (20), (21), (22), (23), (24), (26), (27), (28), (29),
% 176.00/27.30  | |            (30), (31), (32), (33), (35), (36), (37), (39), (42), (43), (45),
% 176.00/27.30  | |            (46), (48), (49), (50), (51), (52), (54), (56), (57), (58), (59),
% 176.00/27.30  | |            (60), (61), (63), (65), (68), (71), (73), (74), (75), (76), (77),
% 176.00/27.30  | |            (78), (80), (82), (84), (85), (86), (87), (88), (90), (91), (92),
% 176.00/27.30  | |            (93), (95), (96), (98), (99), (100), (101), (102), (103), (104),
% 176.00/27.30  | |            (105), (106), (107), (110), (111), (112), (114), (115), (116),
% 176.00/27.30  | |            (117), (118), (119), (120), (121), (122), (124), (125), (126),
% 176.00/27.30  | |            (127), (128), (129) are inconsistent by sub-proof #734.
% 176.00/27.30  | | 
% 176.00/27.30  | Case 2:
% 176.00/27.30  | | 
% 176.00/27.30  | |   (130)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.30  | | 
% 176.00/27.30  | | REF_CLOSE: (4), (7), (8), (9), (10), (11), (13), (14), (15), (16), (17),
% 176.00/27.30  | |            (18), (20), (21), (22), (23), (25), (26), (29), (30), (31), (32),
% 176.00/27.30  | |            (33), (34), (36), (38), (39), (40), (41), (42), (43), (44), (45),
% 176.00/27.30  | |            (47), (48), (49), (50), (51), (52), (53), (55), (57), (60), (61),
% 176.00/27.30  | |            (62), (65), (66), (67), (68), (69), (70), (71), (72), (73), (75),
% 176.00/27.30  | |            (78), (79), (81), (82), (83), (85), (86), (88), (89), (91), (92),
% 176.00/27.30  | |            (94), (96), (97), (98), (99), (100), (101), (103), (104), (105),
% 176.00/27.30  | |            (106), (107), (108), (109), (110), (111), (113), (114), (116),
% 176.00/27.30  | |            (117), (120), (121), (123), (126), (128), (130) are inconsistent
% 176.00/27.30  | |            by sub-proof #209.
% 176.00/27.30  | | 
% 176.00/27.30  | End of split
% 176.00/27.30  | 
% 176.00/27.30  End of proof
% 176.00/27.30  
% 176.00/27.30  Sub-proof #209 shows that the following formulas are inconsistent:
% 176.00/27.30  ----------------------------------------------------------------
% 176.00/27.30    (1)   ~ (all_52_17 = all_52_23)
% 176.00/27.30    (2)  op(e3, e2) = all_52_3
% 176.00/27.30    (3)   ~ (all_52_9 = all_52_25)
% 176.00/27.30    (4)  op(e3, all_52_25) = all_52_24
% 176.00/27.30    (5)   ~ (all_52_19 = all_52_23)
% 176.00/27.30    (6)  all_56_11 = all_52_23
% 176.00/27.30    (7)   ~ (all_52_27 = e3)
% 176.00/27.30    (8)   ~ (all_6_2 = e3)
% 176.00/27.30    (9)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.30    (10)   ~ (all_52_3 = all_10_2)
% 176.00/27.30    (11)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 176.00/27.30    (12)  all_58_5 = all_52_13
% 176.00/27.30    (13)   ~ (all_52_25 = all_52_29)
% 176.00/27.30    (14)  op(e1, all_52_13) = e1
% 176.00/27.30    (15)  op(e0, all_52_15) = e0
% 176.00/27.30    (16)  all_56_15 = all_6_2
% 176.00/27.30    (17)  op(e2, e0) = all_52_15
% 176.00/27.30    (18)  all_58_3 = all_10_2
% 176.00/27.30    (19)  all_58_15 = all_6_2
% 176.00/27.30    (20)   ~ (all_52_9 = all_4_2)
% 176.00/27.30    (21)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.30    (22)   ~ (all_52_5 = all_52_7)
% 176.00/27.30    (23)  all_58_10 = all_52_15
% 176.00/27.30    (24)  all_8_2 = all_6_2
% 176.00/27.30    (25)  all_58_7 = all_52_19
% 176.00/27.30    (26)   ~ (all_52_15 = all_6_2)
% 176.00/27.30    (27)   ~ (all_52_17 = all_52_25)
% 176.00/27.30    (28)  op(e0, e1) = all_52_29
% 176.00/27.30    (29)   ~ (all_4_0 = e2)
% 176.00/27.30    (30)  all_58_4 = all_52_5
% 176.00/27.30    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.30    (32)   ~ (e3 = e1)
% 176.00/27.30    (33)   ~ (all_52_27 = all_52_29)
% 176.00/27.30    (34)  op(e3, all_4_2) = all_4_1
% 176.00/27.30    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.30    (36)   ~ (all_52_7 = all_4_2)
% 176.00/27.30    (37)  all_58_1 = all_52_3
% 176.00/27.30    (38)  all_58_0 = all_4_2
% 176.00/27.30    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.30    (40)  op(e1, all_52_29) = all_52_28
% 176.00/27.30    (41)   ~ (all_4_1 = e2)
% 176.00/27.30    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.30    (43)  all_58_14 = all_52_29
% 176.00/27.30    (44)   ~ (all_52_3 = all_52_5)
% 176.00/27.30    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.30    (46)  all_58_8 = all_14_2
% 176.00/27.30    (47)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.00/27.30    (48)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.30    (49)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.30    (50)   ~ (all_52_3 = all_52_27)
% 176.00/27.30    (51)   ~ (all_52_3 = all_4_2)
% 176.00/27.30    (52)  op(e0, e3) = all_52_25
% 176.00/27.30    (53)  op(e0, all_6_2) = all_6_1
% 176.00/27.30    (54)  op(e3, all_52_17) = all_52_16
% 176.00/27.30    (55)  op(e3, all_52_9) = e3
% 176.00/27.30    (56)  op(e0, all_52_23) = all_52_22
% 176.00/27.30    (57)   ~ (all_52_15 = all_52_23)
% 176.00/27.30    (58)  op(e1, e0) = all_52_23
% 176.00/27.30    (59)  all_58_13 = all_52_27
% 176.00/27.30    (60)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.30    (61)  all_58_6 = all_52_17
% 176.00/27.30    (62)   ~ (all_52_3 = all_52_7)
% 176.00/27.30    (63)  op(e2, all_52_19) = all_52_18
% 176.00/27.30    (64)   ~ (e1 = e0)
% 176.00/27.30    (65)  all_58_11 = all_52_23
% 176.00/27.30    (66)   ~ (all_52_3 = all_52_19)
% 176.00/27.30    (67)   ~ (all_52_29 = all_14_2)
% 176.00/27.30    (68)   ~ (all_52_23 = all_6_2)
% 176.00/27.30    (69)   ~ (all_52_29 = all_6_2)
% 176.00/27.30    (70)  all_58_2 = all_52_9
% 176.00/27.30    (71)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.00/27.30    (72)  op(e3, e1) = all_52_5
% 176.00/27.30    (73)   ~ (e2 = e1)
% 176.00/27.30    (74)   ~ (all_52_25 = all_6_2)
% 176.00/27.30    (75)  op(e1, e3) = all_52_17
% 176.00/27.30    (76)   ~ (all_52_25 = all_4_2)
% 176.00/27.30    (77)  op(e3, e0) = all_52_7
% 176.00/27.30    (78)  op(e2, all_10_2) = e2
% 176.00/27.30    (79)  op(e3, e3) = all_4_2
% 176.00/27.30    (80)   ~ (all_52_17 = all_4_2)
% 176.00/27.30    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.30    (82)   ~ (all_52_25 = all_52_27)
% 176.00/27.30    (83)  all_8_1 = all_6_1
% 176.00/27.30    (84)   ~ (all_52_7 = all_6_2)
% 176.00/27.30    (85)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.30    (86)   ~ (all_52_17 = all_52_19)
% 176.00/27.30    (87)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.30    (88)  all_58_9 = all_52_7
% 176.00/27.30    (89)  all_58_12 = all_52_25
% 176.00/27.30    (90)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.30    (91)   ~ (e3 = e2)
% 176.00/27.30    (92)  op(e2, e3) = all_52_9
% 176.00/27.30  
% 176.00/27.30  Begin of proof
% 176.00/27.30  | 
% 176.00/27.30  | BETA: splitting (85) gives:
% 176.00/27.30  | 
% 176.00/27.30  | Case 1:
% 176.00/27.30  | | 
% 176.00/27.30  | |   (93)  all_58_13 = e3
% 176.00/27.30  | | 
% 176.00/27.30  | | REF_CLOSE: (7), (59), (93) are inconsistent by sub-proof #1026.
% 176.00/27.30  | | 
% 176.00/27.30  | Case 2:
% 176.00/27.30  | | 
% 176.00/27.30  | |   (94)  all_58_14 = e3 | all_58_15 = e3
% 176.00/27.30  | | 
% 176.00/27.30  | | BETA: splitting (94) gives:
% 176.00/27.30  | | 
% 176.00/27.30  | | Case 1:
% 176.00/27.30  | | | 
% 176.00/27.30  | | |   (95)  all_58_14 = e3
% 176.00/27.30  | | | 
% 176.00/27.30  | | | COMBINE_EQS: (43), (95) imply:
% 176.00/27.30  | | |   (96)  all_52_29 = e3
% 176.00/27.30  | | | 
% 176.00/27.30  | | | SIMP: (96) implies:
% 176.00/27.30  | | |   (97)  all_52_29 = e3
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (13), (97) imply:
% 176.00/27.30  | | |   (98)   ~ (all_52_25 = e3)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (67), (97) imply:
% 176.00/27.30  | | |   (99)   ~ (all_14_2 = e3)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | SIMP: (99) implies:
% 176.00/27.30  | | |   (100)   ~ (all_14_2 = e3)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (69), (97) imply:
% 176.00/27.30  | | |   (101)   ~ (all_6_2 = e3)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (40), (97) imply:
% 176.00/27.30  | | |   (102)  op(e1, e3) = all_52_28
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (28), (97) imply:
% 176.00/27.30  | | |   (103)  op(e0, e1) = e3
% 176.00/27.30  | | | 
% 176.00/27.30  | | | GROUND_INST: instantiating (81) with all_52_17, all_52_28, e3, e1,
% 176.00/27.30  | | |              simplifying with (75), (102) gives:
% 176.00/27.30  | | |   (104)  all_52_17 = all_52_28
% 176.00/27.30  | | | 
% 176.00/27.30  | | | COMBINE_EQS: (61), (104) imply:
% 176.00/27.30  | | |   (105)  all_58_6 = all_52_28
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (86), (104) imply:
% 176.00/27.30  | | |   (106)   ~ (all_52_19 = all_52_28)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | SIMP: (106) implies:
% 176.00/27.30  | | |   (107)   ~ (all_52_19 = all_52_28)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (1), (104) imply:
% 176.00/27.30  | | |   (108)   ~ (all_52_23 = all_52_28)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | SIMP: (108) implies:
% 176.00/27.30  | | |   (109)   ~ (all_52_23 = all_52_28)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (27), (104) imply:
% 176.00/27.30  | | |   (110)   ~ (all_52_25 = all_52_28)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | SIMP: (110) implies:
% 176.00/27.30  | | |   (111)   ~ (all_52_25 = all_52_28)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (80), (104) imply:
% 176.00/27.30  | | |   (112)   ~ (all_52_28 = all_4_2)
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (54), (104) imply:
% 176.00/27.30  | | |   (113)  op(e3, all_52_28) = all_52_16
% 176.00/27.30  | | | 
% 176.00/27.30  | | | BETA: splitting (71) gives:
% 176.00/27.30  | | | 
% 176.00/27.30  | | | Case 1:
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | |   (114)  all_56_11 = e3
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | COMBINE_EQS: (6), (114) imply:
% 176.00/27.30  | | | |   (115)  all_52_23 = e3
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | SIMP: (115) implies:
% 176.00/27.30  | | | |   (116)  all_52_23 = e3
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | REDUCE: (5), (116) imply:
% 176.00/27.30  | | | |   (117)   ~ (all_52_19 = e3)
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | REDUCE: (56), (116) imply:
% 176.00/27.30  | | | |   (118)  op(e0, e3) = all_52_22
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | GROUND_INST: instantiating (81) with all_52_25, all_52_22, e3, e0,
% 176.00/27.30  | | | |              simplifying with (52), (118) gives:
% 176.00/27.30  | | | |   (119)  all_52_22 = all_52_25
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | BETA: splitting (42) gives:
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | Case 1:
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | |   (120)  all_58_1 = e3
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (15), (16), (18), (19), (20),
% 176.00/27.30  | | | | |            (21), (23), (24), (25), (30), (32), (34), (35), (36), (37),
% 176.00/27.30  | | | | |            (38), (41), (42), (44), (45), (49), (50), (51), (52), (53),
% 176.00/27.30  | | | | |            (55), (59), (60), (62), (64), (65), (70), (72), (73), (74),
% 176.00/27.30  | | | | |            (77), (78), (79), (81), (83), (84), (87), (88), (89), (91),
% 176.00/27.30  | | | | |            (92), (98), (103), (105), (107), (109), (111), (113), (120)
% 176.00/27.30  | | | | |            are inconsistent by sub-proof #210.
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | Case 2:
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | |   (121)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | REF_CLOSE: (2), (7), (10), (18), (25), (55), (59), (78), (81), (92),
% 176.00/27.30  | | | | |            (117), (121) are inconsistent by sub-proof #975.
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | End of split
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | Case 2:
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | |   (122)   ~ (all_56_11 = e3)
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | REDUCE: (6), (122) imply:
% 176.00/27.30  | | | |   (123)   ~ (all_52_23 = e3)
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | BETA: splitting (87) gives:
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | | Case 1:
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | |   (124)  all_58_9 = e3
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | COMBINE_EQS: (88), (124) imply:
% 176.00/27.30  | | | | |   (125)  all_52_7 = e3
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | SIMP: (125) implies:
% 176.00/27.30  | | | | |   (126)  all_52_7 = e3
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | REDUCE: (22), (126) imply:
% 176.00/27.30  | | | | |   (127)   ~ (all_52_5 = e3)
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | REDUCE: (36), (126) imply:
% 176.00/27.30  | | | | |   (128)   ~ (all_4_2 = e3)
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | SIMP: (128) implies:
% 176.00/27.30  | | | | |   (129)   ~ (all_4_2 = e3)
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | REF_CLOSE: (2), (4), (7), (8), (9), (10), (15), (16), (18), (19),
% 176.00/27.30  | | | | |            (20), (21), (23), (24), (25), (30), (32), (34), (35), (36),
% 176.00/27.30  | | | | |            (37), (38), (41), (42), (45), (49), (52), (53), (55), (59),
% 176.00/27.30  | | | | |            (60), (62), (64), (65), (70), (72), (73), (74), (77), (78),
% 176.00/27.30  | | | | |            (79), (81), (83), (84), (87), (88), (89), (91), (92), (98),
% 176.00/27.30  | | | | |            (103), (105), (107), (109), (111), (113), (127), (129) are
% 176.00/27.30  | | | | |            inconsistent by sub-proof #211.
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | Case 2:
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | |   (130)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | BETA: splitting (130) gives:
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | | Case 1:
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | |   (131)  all_58_10 = e3
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | COMBINE_EQS: (23), (131) imply:
% 176.00/27.30  | | | | | |   (132)  all_52_15 = e3
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | SIMP: (132) implies:
% 176.00/27.30  | | | | | |   (133)  all_52_15 = e3
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (57), (133) imply:
% 176.00/27.30  | | | | | |   (134)   ~ (all_52_23 = e3)
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (17), (133) imply:
% 176.00/27.30  | | | | | |   (135)  op(e2, e0) = e3
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (15), (133) imply:
% 176.00/27.30  | | | | | |   (136)  op(e0, e3) = e0
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | GROUND_INST: instantiating (81) with all_52_25, e0, e3, e0,
% 176.00/27.30  | | | | | |              simplifying with (52), (136) gives:
% 176.00/27.30  | | | | | |   (137)  all_52_25 = e0
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (3), (137) imply:
% 176.00/27.30  | | | | | |   (138)   ~ (all_52_9 = e0)
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (82), (137) imply:
% 176.00/27.30  | | | | | |   (139)   ~ (all_52_27 = e0)
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | SIMP: (139) implies:
% 176.00/27.30  | | | | | |   (140)   ~ (all_52_27 = e0)
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (76), (137) imply:
% 176.00/27.30  | | | | | |   (141)   ~ (all_4_2 = e0)
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | SIMP: (141) implies:
% 176.00/27.30  | | | | | |   (142)   ~ (all_4_2 = e0)
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (4), (137) imply:
% 176.00/27.30  | | | | | |   (143)  op(e3, e0) = all_52_24
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | GROUND_INST: instantiating (81) with all_52_7, all_52_24, e0, e3,
% 176.00/27.30  | | | | | |              simplifying with (77), (143) gives:
% 176.00/27.30  | | | | | |   (144)  all_52_7 = all_52_24
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | COMBINE_EQS: (88), (144) imply:
% 176.00/27.30  | | | | | |   (145)  all_58_9 = all_52_24
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REDUCE: (62), (144) imply:
% 176.00/27.30  | | | | | |   (146)   ~ (all_52_3 = all_52_24)
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | BETA: splitting (42) gives:
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | Case 1:
% 176.00/27.30  | | | | | | | 
% 176.00/27.30  | | | | | | |   (147)  all_58_1 = e3
% 176.00/27.30  | | | | | | | 
% 176.00/27.30  | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (15), (16), (18), (19), (20),
% 176.00/27.30  | | | | | | |            (21), (23), (24), (25), (30), (32), (34), (35), (36),
% 176.00/27.30  | | | | | | |            (37), (38), (41), (42), (44), (45), (49), (50), (51),
% 176.00/27.30  | | | | | | |            (52), (53), (55), (59), (60), (62), (64), (65), (70),
% 176.00/27.30  | | | | | | |            (72), (73), (74), (77), (78), (79), (81), (83), (84),
% 176.00/27.30  | | | | | | |            (87), (88), (89), (91), (92), (98), (103), (105),
% 176.00/27.30  | | | | | | |            (107), (109), (111), (113), (147) are inconsistent by
% 176.00/27.30  | | | | | | |            sub-proof #210.
% 176.00/27.30  | | | | | | | 
% 176.00/27.30  | | | | | | Case 2:
% 176.00/27.30  | | | | | | | 
% 176.00/27.30  | | | | | | |   (148)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.30  | | | | | | | 
% 176.00/27.30  | | | | | | | BETA: splitting (90) gives:
% 176.00/27.30  | | | | | | | 
% 176.00/27.30  | | | | | | | Case 1:
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | |   (149)  all_58_0 = e3
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | COMBINE_EQS: (38), (149) imply:
% 176.00/27.30  | | | | | | | |   (150)  all_4_2 = e3
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | REDUCE: (112), (150) imply:
% 176.00/27.30  | | | | | | | |   (151)   ~ (all_52_28 = e3)
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | REDUCE: (142), (150) imply:
% 176.00/27.30  | | | | | | | |   (152)   ~ (e3 = e0)
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | REDUCE: (48), (150) imply:
% 176.00/27.30  | | | | | | | |   (153)  op(all_4_1, e3) = all_4_0
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | REDUCE: (34), (150) imply:
% 176.00/27.30  | | | | | | | |   (154)  op(e3, e3) = all_4_1
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | REDUCE: (79), (150) imply:
% 176.00/27.30  | | | | | | | |   (155)  op(e3, e3) = e3
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | BETA: splitting (31) gives:
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | Case 1:
% 176.00/27.30  | | | | | | | | | 
% 176.00/27.30  | | | | | | | | |   (156)  all_58_6 = e3
% 176.00/27.30  | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | REF_CLOSE: (105), (151), (156) are inconsistent by sub-proof
% 176.00/27.30  | | | | | | | | |            #790.
% 176.00/27.30  | | | | | | | | | 
% 176.00/27.30  | | | | | | | | Case 2:
% 176.00/27.30  | | | | | | | | | 
% 176.00/27.30  | | | | | | | | |   (157)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.30  | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | BETA: splitting (157) gives:
% 176.00/27.30  | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | Case 1:
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | |   (158)  all_58_7 = e3
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | COMBINE_EQS: (25), (158) imply:
% 176.00/27.30  | | | | | | | | | |   (159)  all_52_19 = e3
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | REDUCE: (66), (159) imply:
% 176.00/27.30  | | | | | | | | | |   (160)   ~ (all_52_3 = e3)
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | REDUCE: (63), (159) imply:
% 176.00/27.30  | | | | | | | | | |   (161)  op(e2, e3) = all_52_18
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | GROUND_INST: instantiating (81) with all_52_9, all_52_18, e3,
% 176.00/27.30  | | | | | | | | | |              e2, simplifying with (92), (161) gives:
% 176.00/27.30  | | | | | | | | | |   (162)  all_52_9 = all_52_18
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | GROUND_INST: instantiating (81) with e3, all_4_1, e3, e3,
% 176.00/27.30  | | | | | | | | | |              simplifying with (154), (155) gives:
% 176.00/27.30  | | | | | | | | | |   (163)  all_4_1 = e3
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | COMBINE_EQS: (70), (162) imply:
% 176.00/27.30  | | | | | | | | | |   (164)  all_58_2 = all_52_18
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | REDUCE: (138), (162) imply:
% 176.00/27.30  | | | | | | | | | |   (165)   ~ (all_52_18 = e0)
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | REDUCE: (153), (163) imply:
% 176.00/27.30  | | | | | | | | | |   (166)  op(e3, e3) = all_4_0
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | GROUND_INST: instantiating (81) with e3, all_4_0, e3, e3,
% 176.00/27.30  | | | | | | | | | |              simplifying with (155), (166) gives:
% 176.00/27.30  | | | | | | | | | |   (167)  all_4_0 = e3
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | REF_CLOSE: (10), (11), (12), (14), (18), (29), (37), (39),
% 176.00/27.30  | | | | | | | | | |            (47), (58), (59), (64), (65), (78), (81), (123),
% 176.00/27.30  | | | | | | | | | |            (131), (135), (140), (145), (146), (152), (158),
% 176.00/27.30  | | | | | | | | | |            (160), (164), (165), (167) are inconsistent by
% 176.00/27.30  | | | | | | | | | |            sub-proof #730.
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | Case 2:
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | |   (168)  all_58_8 = e3 | all_58_11 = e3
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | | REF_CLOSE: (46), (65), (100), (123), (168) are inconsistent
% 176.00/27.30  | | | | | | | | | |            by sub-proof #997.
% 176.00/27.30  | | | | | | | | | | 
% 176.00/27.30  | | | | | | | | | End of split
% 176.00/27.30  | | | | | | | | | 
% 176.00/27.30  | | | | | | | | End of split
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | Case 2:
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | |   (169)   ~ (all_58_0 = e3)
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | REDUCE: (38), (169) imply:
% 176.00/27.30  | | | | | | | |   (170)   ~ (all_4_2 = e3)
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | | REF_CLOSE: (2), (7), (10), (18), (20), (25), (35), (38), (45),
% 176.00/27.30  | | | | | | | |            (55), (59), (70), (78), (79), (81), (89), (92), (98),
% 176.00/27.30  | | | | | | | |            (105), (107), (148), (170) are inconsistent by
% 176.00/27.30  | | | | | | | |            sub-proof #961.
% 176.00/27.30  | | | | | | | | 
% 176.00/27.30  | | | | | | | End of split
% 176.00/27.30  | | | | | | | 
% 176.00/27.30  | | | | | | End of split
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | Case 2:
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | |   (171)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | | REF_CLOSE: (8), (19), (65), (123), (171) are inconsistent by
% 176.00/27.30  | | | | | |            sub-proof #1016.
% 176.00/27.30  | | | | | | 
% 176.00/27.30  | | | | | End of split
% 176.00/27.30  | | | | | 
% 176.00/27.30  | | | | End of split
% 176.00/27.30  | | | | 
% 176.00/27.30  | | | End of split
% 176.00/27.30  | | | 
% 176.00/27.30  | | Case 2:
% 176.00/27.30  | | | 
% 176.00/27.30  | | |   (172)  all_58_15 = e3
% 176.00/27.30  | | | 
% 176.00/27.30  | | | COMBINE_EQS: (19), (172) imply:
% 176.00/27.30  | | |   (173)  all_6_2 = e3
% 176.00/27.30  | | | 
% 176.00/27.30  | | | REDUCE: (8), (173) imply:
% 176.00/27.30  | | |   (174)  $false
% 176.00/27.30  | | | 
% 176.00/27.30  | | | CLOSE: (174) is inconsistent.
% 176.00/27.30  | | | 
% 176.00/27.30  | | End of split
% 176.00/27.30  | | 
% 176.00/27.30  | End of split
% 176.00/27.30  | 
% 176.00/27.30  End of proof
% 176.00/27.30  
% 176.00/27.30  Sub-proof #210 shows that the following formulas are inconsistent:
% 176.00/27.30  ----------------------------------------------------------------
% 176.00/27.30    (1)   ~ (all_52_25 = e3)
% 176.00/27.30    (2)   ~ (all_52_23 = all_52_28)
% 176.00/27.30    (3)  all_58_6 = all_52_28
% 176.00/27.30    (4)  op(e3, e2) = all_52_3
% 176.00/27.30    (5)  op(e3, all_52_25) = all_52_24
% 176.00/27.30    (6)  op(e3, all_52_28) = all_52_16
% 176.00/27.30    (7)   ~ (all_6_2 = e3)
% 176.00/27.30    (8)   ~ (all_52_25 = all_52_28)
% 176.00/27.30    (9)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.30    (10)   ~ (all_52_3 = all_10_2)
% 176.00/27.30    (11)  op(e0, all_52_15) = e0
% 176.00/27.30    (12)  all_56_15 = all_6_2
% 176.00/27.30    (13)  all_58_3 = all_10_2
% 176.00/27.30    (14)  all_58_15 = all_6_2
% 176.00/27.30    (15)   ~ (all_52_9 = all_4_2)
% 176.00/27.30    (16)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.30    (17)  all_58_10 = all_52_15
% 176.00/27.30    (18)  all_8_2 = all_6_2
% 176.00/27.30    (19)  all_58_7 = all_52_19
% 176.00/27.30    (20)  all_58_4 = all_52_5
% 176.00/27.30    (21)   ~ (e3 = e1)
% 176.00/27.30    (22)  op(e3, all_4_2) = all_4_1
% 176.00/27.30    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.30    (24)   ~ (all_52_7 = all_4_2)
% 176.00/27.30    (25)  all_58_1 = all_52_3
% 176.00/27.30    (26)  all_58_0 = all_4_2
% 176.00/27.30    (27)   ~ (all_4_1 = e2)
% 176.00/27.30    (28)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.30    (29)   ~ (all_52_3 = all_52_5)
% 176.00/27.30    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.30    (31)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.30    (32)   ~ (all_52_3 = all_52_27)
% 176.00/27.30    (33)   ~ (all_52_3 = all_4_2)
% 176.00/27.30    (34)  op(e0, e3) = all_52_25
% 176.00/27.30    (35)  op(e0, all_6_2) = all_6_1
% 176.00/27.30    (36)  op(e3, all_52_9) = e3
% 176.00/27.30    (37)   ~ (all_52_19 = all_52_28)
% 176.00/27.30    (38)  all_58_13 = all_52_27
% 176.00/27.30    (39)  all_58_1 = e3
% 176.00/27.30    (40)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.30    (41)   ~ (all_52_3 = all_52_7)
% 176.00/27.30    (42)   ~ (e1 = e0)
% 176.00/27.30    (43)  all_58_11 = all_52_23
% 176.00/27.30    (44)  all_58_2 = all_52_9
% 176.00/27.30    (45)  op(e3, e1) = all_52_5
% 176.00/27.30    (46)   ~ (e2 = e1)
% 176.00/27.30    (47)   ~ (all_52_25 = all_6_2)
% 176.00/27.30    (48)  op(e3, e0) = all_52_7
% 176.00/27.30    (49)  op(e2, all_10_2) = e2
% 176.00/27.30    (50)  op(e3, e3) = all_4_2
% 176.00/27.30    (51)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.30    (52)  op(e0, e1) = e3
% 176.00/27.30    (53)  all_8_1 = all_6_1
% 176.00/27.30    (54)   ~ (all_52_7 = all_6_2)
% 176.00/27.30    (55)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.30    (56)  all_58_9 = all_52_7
% 176.00/27.30    (57)  all_58_12 = all_52_25
% 176.00/27.30    (58)   ~ (e3 = e2)
% 176.00/27.30    (59)  op(e2, e3) = all_52_9
% 176.00/27.30  
% 176.00/27.30  Begin of proof
% 176.00/27.30  | 
% 176.00/27.30  | COMBINE_EQS: (25), (39) imply:
% 176.00/27.30  |   (60)  all_52_3 = e3
% 176.00/27.30  | 
% 176.00/27.30  | REDUCE: (29), (60) imply:
% 176.00/27.30  |   (61)   ~ (all_52_5 = e3)
% 176.00/27.30  | 
% 176.00/27.30  | SIMP: (61) implies:
% 176.00/27.30  |   (62)   ~ (all_52_5 = e3)
% 176.00/27.30  | 
% 176.00/27.30  | REDUCE: (32), (60) imply:
% 176.00/27.30  |   (63)   ~ (all_52_27 = e3)
% 176.00/27.30  | 
% 176.00/27.30  | SIMP: (63) implies:
% 176.00/27.30  |   (64)   ~ (all_52_27 = e3)
% 176.00/27.30  | 
% 176.00/27.30  | REDUCE: (33), (60) imply:
% 176.00/27.30  |   (65)   ~ (all_4_2 = e3)
% 176.00/27.30  | 
% 176.00/27.30  | SIMP: (65) implies:
% 176.00/27.31  |   (66)   ~ (all_4_2 = e3)
% 176.00/27.31  | 
% 176.00/27.31  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.00/27.31  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.00/27.31  |            (24), (25), (26), (27), (28), (30), (31), (34), (35), (36), (37),
% 176.00/27.31  |            (38), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 176.00/27.31  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (62),
% 176.00/27.31  |            (64), (66) are inconsistent by sub-proof #211.
% 176.00/27.31  | 
% 176.00/27.31  End of proof
% 176.00/27.31  
% 176.00/27.31  Sub-proof #211 shows that the following formulas are inconsistent:
% 176.00/27.31  ----------------------------------------------------------------
% 176.00/27.31    (1)   ~ (all_52_25 = e3)
% 176.00/27.31    (2)   ~ (all_52_23 = all_52_28)
% 176.00/27.31    (3)  all_58_6 = all_52_28
% 176.00/27.31    (4)  op(e3, e2) = all_52_3
% 176.00/27.31    (5)  op(e3, all_52_25) = all_52_24
% 176.00/27.31    (6)   ~ (all_52_27 = e3)
% 176.00/27.31    (7)  op(e3, all_52_28) = all_52_16
% 176.00/27.31    (8)   ~ (all_6_2 = e3)
% 176.00/27.31    (9)   ~ (all_52_25 = all_52_28)
% 176.00/27.31    (10)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.31    (11)   ~ (all_52_3 = all_10_2)
% 176.00/27.31    (12)  op(e0, all_52_15) = e0
% 176.00/27.31    (13)  all_56_15 = all_6_2
% 176.00/27.31    (14)   ~ (all_4_2 = e3)
% 176.00/27.31    (15)  all_58_3 = all_10_2
% 176.00/27.31    (16)  all_58_15 = all_6_2
% 176.00/27.31    (17)   ~ (all_52_9 = all_4_2)
% 176.00/27.31    (18)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.31    (19)  all_58_10 = all_52_15
% 176.00/27.31    (20)  all_8_2 = all_6_2
% 176.00/27.31    (21)  all_58_7 = all_52_19
% 176.00/27.31    (22)  all_58_4 = all_52_5
% 176.00/27.31    (23)   ~ (e3 = e1)
% 176.00/27.31    (24)  op(e3, all_4_2) = all_4_1
% 176.00/27.31    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.31    (26)   ~ (all_52_7 = all_4_2)
% 176.00/27.31    (27)  all_58_1 = all_52_3
% 176.00/27.31    (28)  all_58_0 = all_4_2
% 176.00/27.31    (29)   ~ (all_4_1 = e2)
% 176.00/27.31    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.31    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.31    (32)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.31    (33)  op(e0, e3) = all_52_25
% 176.00/27.31    (34)  op(e0, all_6_2) = all_6_1
% 176.00/27.31    (35)   ~ (all_52_5 = e3)
% 176.00/27.31    (36)  op(e3, all_52_9) = e3
% 176.00/27.31    (37)   ~ (all_52_19 = all_52_28)
% 176.00/27.31    (38)  all_58_13 = all_52_27
% 176.00/27.31    (39)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.31    (40)   ~ (all_52_3 = all_52_7)
% 176.00/27.31    (41)   ~ (e1 = e0)
% 176.00/27.31    (42)  all_58_11 = all_52_23
% 176.00/27.31    (43)  all_58_2 = all_52_9
% 176.00/27.31    (44)  op(e3, e1) = all_52_5
% 176.00/27.31    (45)   ~ (e2 = e1)
% 176.00/27.31    (46)   ~ (all_52_25 = all_6_2)
% 176.00/27.31    (47)  op(e3, e0) = all_52_7
% 176.00/27.31    (48)  op(e2, all_10_2) = e2
% 176.00/27.31    (49)  op(e3, e3) = all_4_2
% 176.00/27.31    (50)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.31    (51)  op(e0, e1) = e3
% 176.00/27.31    (52)  all_8_1 = all_6_1
% 176.00/27.31    (53)   ~ (all_52_7 = all_6_2)
% 176.00/27.31    (54)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.31    (55)  all_58_9 = all_52_7
% 176.00/27.31    (56)  all_58_12 = all_52_25
% 176.00/27.31    (57)   ~ (e3 = e2)
% 176.00/27.31    (58)  op(e2, e3) = all_52_9
% 176.00/27.31  
% 176.00/27.31  Begin of proof
% 176.00/27.31  | 
% 176.00/27.31  | BETA: splitting (31) gives:
% 176.00/27.31  | 
% 176.00/27.31  | Case 1:
% 176.00/27.31  | | 
% 176.00/27.31  | |   (59)  all_58_0 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | COMBINE_EQS: (28), (59) imply:
% 176.00/27.31  | |   (60)  all_4_2 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (14), (60) imply:
% 176.00/27.31  | |   (61)  $false
% 176.00/27.31  | | 
% 176.00/27.31  | | CLOSE: (61) is inconsistent.
% 176.00/27.31  | | 
% 176.00/27.31  | Case 2:
% 176.00/27.31  | | 
% 176.00/27.31  | |   (62)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | BETA: splitting (25) gives:
% 176.00/27.31  | | 
% 176.00/27.31  | | Case 1:
% 176.00/27.31  | | | 
% 176.00/27.31  | | |   (63)  all_58_2 = e3
% 176.00/27.31  | | | 
% 176.00/27.31  | | | COMBINE_EQS: (43), (63) imply:
% 176.00/27.31  | | |   (64)  all_52_9 = e3
% 176.00/27.31  | | | 
% 176.00/27.31  | | | REF_CLOSE: (17), (36), (49), (50), (64) are inconsistent by sub-proof
% 176.00/27.31  | | |            #967.
% 176.00/27.31  | | | 
% 176.00/27.31  | | Case 2:
% 176.00/27.31  | | | 
% 176.00/27.31  | | |   (65)   ~ (all_58_2 = e3)
% 176.00/27.31  | | | 
% 176.00/27.31  | | | REDUCE: (43), (65) imply:
% 176.00/27.31  | | |   (66)   ~ (all_52_9 = e3)
% 176.00/27.31  | | | 
% 176.00/27.31  | | | BETA: splitting (62) gives:
% 176.00/27.31  | | | 
% 176.00/27.31  | | | Case 1:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | |   (67)  all_58_2 = e3
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | REF_CLOSE: (43), (66), (67) are inconsistent by sub-proof #980.
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | Case 2:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | |   (68)  all_58_6 = e3 | all_58_12 = e3
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | BETA: splitting (68) gives:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | Case 1:
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | |   (69)  all_58_6 = e3
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | COMBINE_EQS: (3), (69) imply:
% 176.00/27.31  | | | | |   (70)  all_52_28 = e3
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | SIMP: (70) implies:
% 176.00/27.31  | | | | |   (71)  all_52_28 = e3
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (2), (71) imply:
% 176.00/27.31  | | | | |   (72)   ~ (all_52_23 = e3)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (7), (71) imply:
% 176.00/27.31  | | | | |   (73)  op(e3, e3) = all_52_16
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | GROUND_INST: instantiating (50) with all_4_2, all_52_16, e3, e3,
% 176.00/27.31  | | | | |              simplifying with (49), (73) gives:
% 176.00/27.31  | | | | |   (74)  all_52_16 = all_4_2
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | BETA: splitting (54) gives:
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | Case 1:
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | |   (75)  all_58_9 = e3
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | | REF_CLOSE: (1), (3), (4), (6), (11), (15), (17), (21), (25), (26),
% 176.00/27.31  | | | | | |            (27), (28), (30), (31), (36), (37), (38), (40), (43),
% 176.00/27.31  | | | | | |            (48), (49), (50), (55), (56), (58), (75) are inconsistent
% 176.00/27.31  | | | | | |            by sub-proof #732.
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | Case 2:
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | |   (76)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | | BETA: splitting (30) gives:
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | | Case 1:
% 176.00/27.31  | | | | | | | 
% 176.00/27.31  | | | | | | |   (77)  all_58_1 = e3
% 176.00/27.31  | | | | | | | 
% 176.00/27.31  | | | | | | | REF_CLOSE: (5), (8), (10), (12), (13), (16), (18), (19), (20),
% 176.00/27.31  | | | | | | |            (22), (23), (24), (28), (29), (32), (33), (34), (35),
% 176.00/27.31  | | | | | | |            (36), (39), (41), (42), (43), (44), (45), (46), (47),
% 176.00/27.31  | | | | | | |            (50), (51), (52), (53), (55), (56), (57), (69), (72),
% 176.00/27.31  | | | | | | |            (76), (77) are inconsistent by sub-proof #212.
% 176.00/27.31  | | | | | | | 
% 176.00/27.31  | | | | | | Case 2:
% 176.00/27.31  | | | | | | | 
% 176.00/27.31  | | | | | | |   (78)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.31  | | | | | | | 
% 176.00/27.31  | | | | | | | REF_CLOSE: (1), (3), (4), (6), (11), (15), (21), (36), (37), (38),
% 176.00/27.31  | | | | | | |            (48), (50), (56), (58), (68), (78) are inconsistent by
% 176.00/27.31  | | | | | | |            sub-proof #962.
% 176.00/27.31  | | | | | | | 
% 176.00/27.31  | | | | | | End of split
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | End of split
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | Case 2:
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | |   (79)  all_58_12 = e3
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REF_CLOSE: (1), (56), (79) are inconsistent by sub-proof #1003.
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | End of split
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | End of split
% 176.00/27.31  | | | 
% 176.00/27.31  | | End of split
% 176.00/27.31  | | 
% 176.00/27.31  | End of split
% 176.00/27.31  | 
% 176.00/27.31  End of proof
% 176.00/27.31  
% 176.00/27.31  Sub-proof #212 shows that the following formulas are inconsistent:
% 176.00/27.31  ----------------------------------------------------------------
% 176.00/27.31    (1)  op(e3, all_52_25) = all_52_24
% 176.00/27.31    (2)   ~ (all_6_2 = e3)
% 176.00/27.31    (3)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.31    (4)  op(e0, all_52_15) = e0
% 176.00/27.31    (5)  all_56_15 = all_6_2
% 176.00/27.31    (6)  all_58_15 = all_6_2
% 176.00/27.31    (7)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.31    (8)  all_58_10 = all_52_15
% 176.00/27.31    (9)  all_8_2 = all_6_2
% 176.00/27.31    (10)  all_58_4 = all_52_5
% 176.00/27.31    (11)   ~ (e3 = e1)
% 176.00/27.31    (12)  op(e3, all_4_2) = all_4_1
% 176.00/27.31    (13)  all_58_0 = all_4_2
% 176.00/27.31    (14)   ~ (all_4_1 = e2)
% 176.00/27.31    (15)  all_58_6 = e3
% 176.00/27.31    (16)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.31    (17)   ~ (all_52_23 = e3)
% 176.00/27.31    (18)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.31    (19)  op(e0, e3) = all_52_25
% 176.00/27.31    (20)  op(e0, all_6_2) = all_6_1
% 176.00/27.31    (21)   ~ (all_52_5 = e3)
% 176.00/27.31    (22)  op(e3, all_52_9) = e3
% 176.00/27.31    (23)  all_58_1 = e3
% 176.00/27.31    (24)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.31    (25)   ~ (e1 = e0)
% 176.00/27.31    (26)  all_58_11 = all_52_23
% 176.00/27.31    (27)  all_58_2 = all_52_9
% 176.00/27.31    (28)  op(e3, e1) = all_52_5
% 176.00/27.31    (29)   ~ (e2 = e1)
% 176.00/27.31    (30)   ~ (all_52_25 = all_6_2)
% 176.00/27.31    (31)  op(e3, e0) = all_52_7
% 176.00/27.31    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.31    (33)  op(e0, e1) = e3
% 176.00/27.31    (34)  all_8_1 = all_6_1
% 176.00/27.31    (35)   ~ (all_52_7 = all_6_2)
% 176.00/27.31    (36)  all_58_9 = all_52_7
% 176.00/27.31    (37)  all_58_12 = all_52_25
% 176.00/27.31    (38)   ~ (e3 = e2)
% 176.00/27.31  
% 176.00/27.31  Begin of proof
% 176.00/27.31  | 
% 176.00/27.31  | BETA: splitting (18) gives:
% 176.00/27.31  | 
% 176.00/27.31  | Case 1:
% 176.00/27.31  | | 
% 176.00/27.31  | |   (39)  all_58_10 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | COMBINE_EQS: (8), (39) imply:
% 176.00/27.31  | |   (40)  all_52_15 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | SIMP: (40) implies:
% 176.00/27.31  | |   (41)  all_52_15 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (4), (41) imply:
% 176.00/27.31  | |   (42)  op(e0, e3) = e0
% 176.00/27.31  | | 
% 176.00/27.31  | | GROUND_INST: instantiating (32) with all_52_25, e0, e3, e0, simplifying with
% 176.00/27.31  | |              (19), (42) gives:
% 176.00/27.31  | |   (43)  all_52_25 = e0
% 176.00/27.31  | | 
% 176.00/27.31  | | COMBINE_EQS: (37), (43) imply:
% 176.00/27.31  | |   (44)  all_58_12 = e0
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (30), (43) imply:
% 176.00/27.31  | |   (45)   ~ (all_6_2 = e0)
% 176.00/27.31  | | 
% 176.00/27.31  | | SIMP: (45) implies:
% 176.00/27.31  | |   (46)   ~ (all_6_2 = e0)
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (1), (43) imply:
% 176.00/27.31  | |   (47)  op(e3, e0) = all_52_24
% 176.00/27.31  | | 
% 176.00/27.31  | | GROUND_INST: instantiating (32) with all_52_7, all_52_24, e0, e3,
% 176.00/27.31  | |              simplifying with (31), (47) gives:
% 176.00/27.31  | |   (48)  all_52_7 = all_52_24
% 176.00/27.31  | | 
% 176.00/27.31  | | COMBINE_EQS: (36), (48) imply:
% 176.00/27.31  | |   (49)  all_58_9 = all_52_24
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (35), (48) imply:
% 176.00/27.31  | |   (50)   ~ (all_52_24 = all_6_2)
% 176.00/27.31  | | 
% 176.00/27.31  | | BETA: splitting (24) gives:
% 176.00/27.31  | | 
% 176.00/27.31  | | Case 1:
% 176.00/27.31  | | | 
% 176.00/27.31  | | |   (51)  all_58_0 = e1
% 176.00/27.31  | | | 
% 176.00/27.31  | | | COMBINE_EQS: (13), (51) imply:
% 176.00/27.31  | | |   (52)  all_4_2 = e1
% 176.00/27.31  | | | 
% 176.00/27.31  | | | REF_CLOSE: (3), (5), (7), (9), (10), (12), (14), (16), (20), (23), (28),
% 176.00/27.31  | | |            (29), (32), (33), (34), (38), (46), (49), (50), (51), (52) are
% 176.00/27.31  | | |            inconsistent by sub-proof #213.
% 176.00/27.31  | | | 
% 176.00/27.31  | | Case 2:
% 176.00/27.31  | | | 
% 176.00/27.31  | | |   (53)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.31  | | | 
% 176.00/27.31  | | | REF_CLOSE: (11), (15), (21), (22), (25), (27), (28), (32), (44), (53) are
% 176.00/27.31  | | |            inconsistent by sub-proof #725.
% 176.00/27.31  | | | 
% 176.00/27.31  | | End of split
% 176.00/27.31  | | 
% 176.00/27.31  | Case 2:
% 176.00/27.31  | | 
% 176.00/27.31  | |   (54)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | REF_CLOSE: (2), (6), (17), (26), (54) are inconsistent by sub-proof #1016.
% 176.00/27.31  | | 
% 176.00/27.31  | End of split
% 176.00/27.31  | 
% 176.00/27.31  End of proof
% 176.00/27.31  
% 176.00/27.31  Sub-proof #213 shows that the following formulas are inconsistent:
% 176.00/27.31  ----------------------------------------------------------------
% 176.00/27.31    (1)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.31    (2)   ~ (all_6_2 = e0)
% 176.00/27.31    (3)  all_56_15 = all_6_2
% 176.00/27.31    (4)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.31    (5)  all_8_2 = all_6_2
% 176.00/27.31    (6)  all_58_4 = all_52_5
% 176.00/27.31    (7)  op(e3, all_4_2) = all_4_1
% 176.00/27.31    (8)   ~ (all_4_1 = e2)
% 176.00/27.31    (9)   ~ (all_52_24 = all_6_2)
% 176.00/27.31    (10)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.31    (11)  op(e0, all_6_2) = all_6_1
% 176.00/27.31    (12)  all_58_0 = e1
% 176.00/27.31    (13)  all_58_1 = e3
% 176.00/27.31    (14)  op(e3, e1) = all_52_5
% 176.00/27.31    (15)   ~ (e2 = e1)
% 176.00/27.31    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.31    (17)  op(e0, e1) = e3
% 176.00/27.31    (18)  all_8_1 = all_6_1
% 176.00/27.31    (19)  all_4_2 = e1
% 176.00/27.31    (20)  all_58_9 = all_52_24
% 176.00/27.31    (21)   ~ (e3 = e2)
% 176.00/27.31  
% 176.00/27.31  Begin of proof
% 176.00/27.31  | 
% 176.00/27.31  | REDUCE: (7), (19) imply:
% 176.00/27.31  |   (22)  op(e3, e1) = all_4_1
% 176.00/27.31  | 
% 176.00/27.31  | GROUND_INST: instantiating (16) with all_52_5, all_4_1, e1, e3, simplifying
% 176.00/27.31  |              with (14), (22) gives:
% 176.00/27.31  |   (23)  all_52_5 = all_4_1
% 176.00/27.31  | 
% 176.00/27.31  | COMBINE_EQS: (6), (23) imply:
% 176.00/27.31  |   (24)  all_58_4 = all_4_1
% 176.00/27.31  | 
% 176.00/27.31  | BETA: splitting (10) gives:
% 176.00/27.31  | 
% 176.00/27.31  | Case 1:
% 176.00/27.31  | | 
% 176.00/27.31  | |   (25)  all_58_0 = e2
% 176.00/27.31  | | 
% 176.00/27.31  | | REF_CLOSE: (12), (15), (25) are inconsistent by sub-proof #930.
% 176.00/27.31  | | 
% 176.00/27.31  | Case 2:
% 176.00/27.31  | | 
% 176.00/27.31  | |   (26)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.31  | | 
% 176.00/27.31  | | BETA: splitting (26) gives:
% 176.00/27.31  | | 
% 176.00/27.31  | | Case 1:
% 176.00/27.31  | | | 
% 176.00/27.31  | | |   (27)  all_58_1 = e2
% 176.00/27.31  | | | 
% 176.00/27.31  | | | COMBINE_EQS: (13), (27) imply:
% 176.00/27.31  | | |   (28)  e3 = e2
% 176.00/27.31  | | | 
% 176.00/27.31  | | | REDUCE: (21), (28) imply:
% 176.00/27.31  | | |   (29)  $false
% 176.00/27.31  | | | 
% 176.00/27.31  | | | CLOSE: (29) is inconsistent.
% 176.00/27.31  | | | 
% 176.00/27.31  | | Case 2:
% 176.00/27.31  | | | 
% 176.00/27.31  | | |   (30)  all_58_4 = e2 | all_58_9 = e2
% 176.00/27.31  | | | 
% 176.00/27.31  | | | BETA: splitting (30) gives:
% 176.00/27.31  | | | 
% 176.00/27.31  | | | Case 1:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | |   (31)  all_58_4 = e2
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | REF_CLOSE: (8), (24), (31) are inconsistent by sub-proof #673.
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | Case 2:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | |   (32)  all_58_9 = e2
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | COMBINE_EQS: (20), (32) imply:
% 176.00/27.31  | | | |   (33)  all_52_24 = e2
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | SIMP: (33) implies:
% 176.00/27.31  | | | |   (34)  all_52_24 = e2
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | REDUCE: (9), (34) imply:
% 176.00/27.31  | | | |   (35)   ~ (all_6_2 = e2)
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (11), (16), (17), (18), (35) are
% 176.00/27.31  | | | |            inconsistent by sub-proof #224.
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | End of split
% 176.00/27.31  | | | 
% 176.00/27.31  | | End of split
% 176.00/27.31  | | 
% 176.00/27.31  | End of split
% 176.00/27.31  | 
% 176.00/27.31  End of proof
% 176.00/27.31  
% 176.00/27.31  Sub-proof #214 shows that the following formulas are inconsistent:
% 176.00/27.31  ----------------------------------------------------------------
% 176.00/27.31    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.31    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.31    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.31    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.31    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.31    (6)  op(e3, e2) = all_52_3
% 176.00/27.31    (7)  op(e3, all_52_25) = all_52_24
% 176.00/27.31    (8)   ~ (all_52_19 = all_52_23)
% 176.00/27.31    (9)   ~ (all_6_2 = e3)
% 176.00/27.31    (10)   ~ (all_52_3 = all_10_2)
% 176.00/27.31    (11)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 176.00/27.31    (12)  all_58_5 = all_52_13
% 176.00/27.31    (13)  op(e1, all_52_13) = e1
% 176.00/27.31    (14)  op(e0, all_52_15) = e0
% 176.00/27.31    (15)  all_56_15 = all_6_2
% 176.00/27.31    (16)   ~ (all_52_26 = all_10_2)
% 176.00/27.31    (17)  all_58_3 = all_10_2
% 176.00/27.31    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.31    (19)  all_58_15 = all_6_2
% 176.00/27.31    (20)   ~ (all_52_26 = all_4_2)
% 176.00/27.31    (21)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.31    (22)   ~ (all_52_5 = all_52_7)
% 176.00/27.31    (23)  all_58_10 = all_52_15
% 176.00/27.31    (24)   ~ (all_52_5 = all_4_2)
% 176.00/27.31    (25)  all_58_7 = all_52_19
% 176.00/27.31    (26)   ~ (all_52_17 = all_52_25)
% 176.00/27.31    (27)   ~ (all_4_0 = e2)
% 176.00/27.31    (28)  all_58_4 = all_52_5
% 176.00/27.31    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.31    (30)   ~ (e3 = e1)
% 176.00/27.31    (31)   ~ (all_52_17 = all_14_2)
% 176.00/27.31    (32)  op(e3, all_4_2) = all_4_1
% 176.00/27.31    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.31    (34)  all_58_1 = all_52_3
% 176.00/27.31    (35)  all_58_0 = all_4_2
% 176.00/27.31    (36)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.31    (37)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.31    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.31    (39)  all_58_14 = all_52_29
% 176.00/27.31    (40)   ~ (all_10_2 = e3)
% 176.00/27.31    (41)   ~ (all_52_13 = all_52_26)
% 176.00/27.31    (42)   ~ (all_52_3 = all_52_5)
% 176.00/27.31    (43)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.31    (44)  op(e2, e1) = all_52_13
% 176.00/27.31    (45)  all_58_8 = all_14_2
% 176.00/27.31    (46)  all_56_1 = all_52_3
% 176.00/27.31    (47)  op(e0, e2) = all_52_27
% 176.00/27.31    (48)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.31    (49)   ~ (all_52_5 = all_14_2)
% 176.00/27.31    (50)   ~ (all_52_3 = all_4_2)
% 176.00/27.31    (51)  op(e0, e3) = all_52_25
% 176.00/27.31    (52)  op(e0, all_6_2) = all_6_1
% 176.00/27.31    (53)  op(all_6_1, all_6_2) = e2
% 176.00/27.31    (54)  op(e3, all_52_17) = all_52_16
% 176.00/27.31    (55)   ~ (all_52_29 = e3)
% 176.00/27.31    (56)   ~ (all_52_15 = all_52_23)
% 176.00/27.31    (57)  op(e1, e0) = all_52_23
% 176.00/27.31    (58)  all_58_13 = all_52_27
% 176.00/27.31    (59)   ~ (all_4_1 = e1)
% 176.00/27.31    (60)   ~ (all_52_3 = e3)
% 176.00/27.31    (61)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.00/27.31    (62)  all_58_6 = all_52_17
% 176.00/27.31    (63)   ~ (all_52_3 = all_52_7)
% 176.00/27.31    (64)  all_58_2 = all_52_26
% 176.00/27.31    (65)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.31    (66)   ~ (e1 = e0)
% 176.00/27.31    (67)  all_56_0 = all_4_2
% 176.00/27.31    (68)  all_58_11 = all_52_23
% 176.00/27.31    (69)   ~ (all_4_0 = e1)
% 176.00/27.31    (70)   ~ (all_52_29 = all_6_2)
% 176.00/27.31    (71)  op(e3, e1) = all_52_5
% 176.00/27.31    (72)   ~ (all_52_19 = e3)
% 176.00/27.31    (73)  op(e1, e3) = all_52_17
% 176.00/27.31    (74)   ~ (all_52_25 = all_4_2)
% 176.00/27.31    (75)  op(e3, e0) = all_52_7
% 176.00/27.31    (76)  op(e2, all_10_2) = e2
% 176.00/27.31    (77)  op(e3, e3) = all_4_2
% 176.00/27.31    (78)   ~ (all_14_2 = e3)
% 176.00/27.31    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.31    (80)   ~ (all_52_27 = all_6_2)
% 176.00/27.31    (81)   ~ (all_52_7 = all_52_23)
% 176.00/27.31    (82)   ~ (all_52_25 = all_52_26)
% 176.00/27.31    (83)   ~ (all_52_17 = all_52_19)
% 176.00/27.31    (84)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.31    (85)  all_56_4 = all_52_26
% 176.00/27.31    (86)  all_58_9 = all_52_7
% 176.00/27.31    (87)   ~ (all_52_15 = all_52_26)
% 176.00/27.31    (88)  all_58_12 = all_52_25
% 176.00/27.31    (89)   ~ (all_52_17 = all_52_26)
% 176.00/27.31    (90)  op(e3, all_52_26) = e3
% 176.00/27.31    (91)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.31    (92)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.31    (93)  all_58_13 = e3
% 176.00/27.31  
% 176.00/27.31  Begin of proof
% 176.00/27.31  | 
% 176.00/27.31  | BETA: splitting (29) gives:
% 176.00/27.31  | 
% 176.00/27.31  | Case 1:
% 176.00/27.31  | | 
% 176.00/27.31  | |   (94)  all_58_6 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | COMBINE_EQS: (62), (94) imply:
% 176.00/27.31  | |   (95)  all_52_17 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | SIMP: (95) implies:
% 176.00/27.31  | |   (96)  all_52_17 = e3
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (4), (96) imply:
% 176.00/27.31  | |   (97)   ~ (all_52_23 = e3)
% 176.00/27.31  | | 
% 176.00/27.31  | | SIMP: (97) implies:
% 176.00/27.31  | |   (98)   ~ (all_52_23 = e3)
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (26), (96) imply:
% 176.00/27.31  | |   (99)   ~ (all_52_25 = e3)
% 176.00/27.31  | | 
% 176.00/27.31  | | SIMP: (99) implies:
% 176.00/27.31  | |   (100)   ~ (all_52_25 = e3)
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (31), (96) imply:
% 176.00/27.31  | |   (101)   ~ (all_14_2 = e3)
% 176.00/27.31  | | 
% 176.00/27.31  | | REDUCE: (54), (96) imply:
% 176.00/27.31  | |   (102)  op(e3, e3) = all_52_16
% 176.00/27.31  | | 
% 176.00/27.31  | | GROUND_INST: instantiating (79) with all_4_2, all_52_16, e3, e3, simplifying
% 176.00/27.31  | |              with (77), (102) gives:
% 176.00/27.31  | |   (103)  all_52_16 = all_4_2
% 176.00/27.31  | | 
% 176.00/27.31  | | BETA: splitting (92) gives:
% 176.00/27.31  | | 
% 176.00/27.31  | | Case 1:
% 176.00/27.31  | | | 
% 176.00/27.31  | | |   (104)  all_58_4 = e3
% 176.00/27.31  | | | 
% 176.00/27.31  | | | COMBINE_EQS: (28), (104) imply:
% 176.00/27.31  | | |   (105)  all_52_5 = e3
% 176.00/27.31  | | | 
% 176.00/27.31  | | | SIMP: (105) implies:
% 176.00/27.31  | | |   (106)  all_52_5 = e3
% 176.00/27.31  | | | 
% 176.00/27.31  | | | REDUCE: (22), (106) imply:
% 176.00/27.31  | | |   (107)   ~ (all_52_7 = e3)
% 176.00/27.31  | | | 
% 176.00/27.31  | | | SIMP: (107) implies:
% 176.00/27.31  | | |   (108)   ~ (all_52_7 = e3)
% 176.00/27.31  | | | 
% 176.00/27.31  | | | REDUCE: (24), (106) imply:
% 176.00/27.31  | | |   (109)   ~ (all_4_2 = e3)
% 176.00/27.31  | | | 
% 176.00/27.31  | | | SIMP: (109) implies:
% 176.00/27.31  | | |   (110)   ~ (all_4_2 = e3)
% 176.00/27.31  | | | 
% 176.00/27.31  | | | BETA: splitting (84) gives:
% 176.00/27.31  | | | 
% 176.00/27.31  | | | Case 1:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | |   (111)  all_58_9 = e3
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | REF_CLOSE: (86), (108), (111) are inconsistent by sub-proof #972.
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | Case 2:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | |   (112)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | BETA: splitting (112) gives:
% 176.00/27.31  | | | | 
% 176.00/27.31  | | | | Case 1:
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | |   (113)  all_58_10 = e3
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | COMBINE_EQS: (23), (113) imply:
% 176.00/27.31  | | | | |   (114)  all_52_15 = e3
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | SIMP: (114) implies:
% 176.00/27.31  | | | | |   (115)  all_52_15 = e3
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (87), (115) imply:
% 176.00/27.31  | | | | |   (116)   ~ (all_52_26 = e3)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | SIMP: (116) implies:
% 176.00/27.31  | | | | |   (117)   ~ (all_52_26 = e3)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (14), (115) imply:
% 176.00/27.31  | | | | |   (118)  op(e0, e3) = e0
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | GROUND_INST: instantiating (79) with all_52_25, e0, e3, e0,
% 176.00/27.31  | | | | |              simplifying with (51), (118) gives:
% 176.00/27.31  | | | | |   (119)  all_52_25 = e0
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (82), (119) imply:
% 176.00/27.31  | | | | |   (120)   ~ (all_52_26 = e0)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | SIMP: (120) implies:
% 176.00/27.31  | | | | |   (121)   ~ (all_52_26 = e0)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (74), (119) imply:
% 176.00/27.31  | | | | |   (122)   ~ (all_4_2 = e0)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | SIMP: (122) implies:
% 176.00/27.31  | | | | |   (123)   ~ (all_4_2 = e0)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (7), (119) imply:
% 176.00/27.31  | | | | |   (124)  op(e3, e0) = all_52_24
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | GROUND_INST: instantiating (79) with all_52_7, all_52_24, e0, e3,
% 176.00/27.31  | | | | |              simplifying with (75), (124) gives:
% 176.00/27.31  | | | | |   (125)  all_52_7 = all_52_24
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | COMBINE_EQS: (86), (125) imply:
% 176.00/27.31  | | | | |   (126)  all_58_9 = all_52_24
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | REDUCE: (63), (125) imply:
% 176.00/27.31  | | | | |   (127)   ~ (all_52_3 = all_52_24)
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | BETA: splitting (65) gives:
% 176.00/27.31  | | | | | 
% 176.00/27.31  | | | | | Case 1:
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | |   (128)  all_56_4 = e3
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | | REF_CLOSE: (85), (117), (128) are inconsistent by sub-proof #818.
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | Case 2:
% 176.00/27.31  | | | | | | 
% 176.00/27.31  | | | | | |   (129)   ~ (all_56_4 = e3)
% 176.00/27.31  | | | | | |   (130)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.31  | | | | | | 
% 176.00/27.32  | | | | | | REF_CLOSE: (3), (6), (8), (10), (11), (12), (13), (16), (17), (18),
% 176.00/27.32  | | | | | |            (20), (25), (32), (34), (35), (36), (37), (46), (50),
% 176.00/27.32  | | | | | |            (57), (59), (60), (61), (64), (67), (68), (79), (85),
% 176.00/27.32  | | | | | |            (90), (93), (98), (110), (113), (117), (121), (123),
% 176.00/27.32  | | | | | |            (126), (127), (130) are inconsistent by sub-proof #757.
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | End of split
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | Case 2:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | |   (131)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | REF_CLOSE: (9), (19), (68), (98), (131) are inconsistent by sub-proof
% 176.00/27.32  | | | | |            #1016.
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | End of split
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | End of split
% 176.00/27.32  | | | 
% 176.00/27.32  | | Case 2:
% 176.00/27.32  | | | 
% 176.00/27.32  | | |   (132)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REF_CLOSE: (3), (5), (6), (12), (13), (15), (17), (20), (21), (25), (27),
% 176.00/27.32  | | |            (28), (30), (31), (32), (34), (35), (38), (39), (41), (42),
% 176.00/27.32  | | |            (43), (44), (45), (47), (48), (50), (52), (53), (54), (55),
% 176.00/27.32  | | |            (58), (62), (64), (65), (66), (69), (70), (71), (73), (76),
% 176.00/27.32  | | |            (77), (78), (79), (80), (82), (83), (85), (88), (89), (90),
% 176.00/27.32  | | |            (93), (100), (132) are inconsistent by sub-proof #215.
% 176.00/27.32  | | | 
% 176.00/27.32  | | End of split
% 176.00/27.32  | | 
% 176.00/27.32  | Case 2:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (133)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | BETA: splitting (133) gives:
% 176.00/27.32  | | 
% 176.00/27.32  | | Case 1:
% 176.00/27.32  | | | 
% 176.00/27.32  | | |   (134)  all_58_7 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | COMBINE_EQS: (25), (134) imply:
% 176.00/27.32  | | |   (135)  all_52_19 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (72), (135) imply:
% 176.00/27.32  | | |   (136)  $false
% 176.00/27.32  | | | 
% 176.00/27.32  | | | CLOSE: (136) is inconsistent.
% 176.00/27.32  | | | 
% 176.00/27.32  | | Case 2:
% 176.00/27.32  | | | 
% 176.00/27.32  | | |   (137)  all_58_8 = e3 | all_58_11 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | BETA: splitting (137) gives:
% 176.00/27.32  | | | 
% 176.00/27.32  | | | Case 1:
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | |   (138)  all_58_8 = e3
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | REF_CLOSE: (45), (78), (138) are inconsistent by sub-proof #901.
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | Case 2:
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | |   (139)  all_58_11 = e3
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | COMBINE_EQS: (68), (139) imply:
% 176.00/27.32  | | | |   (140)  all_52_23 = e3
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | SIMP: (140) implies:
% 176.00/27.32  | | | |   (141)  all_52_23 = e3
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | REDUCE: (81), (141) imply:
% 176.00/27.32  | | | |   (142)   ~ (all_52_7 = e3)
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | REDUCE: (1), (141) imply:
% 176.00/27.32  | | | |   (143)   ~ (all_14_2 = e3)
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | BETA: splitting (43) gives:
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | Case 1:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | |   (144)  all_58_0 = e3
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | COMBINE_EQS: (35), (144) imply:
% 176.00/27.32  | | | | |   (145)  all_4_2 = e3
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | REDUCE: (24), (145) imply:
% 176.00/27.32  | | | | |   (146)   ~ (all_52_5 = e3)
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | REDUCE: (74), (145) imply:
% 176.00/27.32  | | | | |   (147)   ~ (all_52_25 = e3)
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | BETA: splitting (92) gives:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | Case 1:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | |   (148)  all_58_4 = e3
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | REF_CLOSE: (28), (146), (148) are inconsistent by sub-proof #1025.
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | Case 2:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | |   (149)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | REF_CLOSE: (3), (5), (6), (12), (13), (15), (17), (20), (21), (25),
% 176.00/27.32  | | | | | |            (27), (28), (30), (31), (32), (34), (35), (38), (39),
% 176.00/27.32  | | | | | |            (41), (42), (43), (44), (45), (47), (48), (50), (52),
% 176.00/27.32  | | | | | |            (53), (54), (55), (58), (62), (64), (65), (66), (69),
% 176.00/27.32  | | | | | |            (70), (71), (73), (76), (77), (78), (79), (80), (82),
% 176.00/27.32  | | | | | |            (83), (85), (88), (89), (90), (93), (147), (149) are
% 176.00/27.32  | | | | | |            inconsistent by sub-proof #215.
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | End of split
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | Case 2:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | |   (150)   ~ (all_58_0 = e3)
% 176.00/27.32  | | | | |   (151)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | REDUCE: (35), (150) imply:
% 176.00/27.32  | | | | |   (152)   ~ (all_4_2 = e3)
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | BETA: splitting (91) gives:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | Case 1:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | |   (153)  all_58_0 = e3
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | COMBINE_EQS: (35), (153) imply:
% 176.00/27.32  | | | | | |   (154)  all_4_2 = e3
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | REDUCE: (152), (154) imply:
% 176.00/27.32  | | | | | |   (155)  $false
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | CLOSE: (155) is inconsistent.
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | Case 2:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | |   (156)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | BETA: splitting (151) gives:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | Case 1:
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | |   (157)  all_58_2 = e3
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | COMBINE_EQS: (64), (157) imply:
% 176.00/27.32  | | | | | | |   (158)  all_52_26 = e3
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | SIMP: (158) implies:
% 176.00/27.32  | | | | | | |   (159)  all_52_26 = e3
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | REF_CLOSE: (20), (77), (79), (90), (159) are inconsistent by
% 176.00/27.32  | | | | | | |            sub-proof #1005.
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | Case 2:
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | |   (160)   ~ (all_58_2 = e3)
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | REDUCE: (64), (160) imply:
% 176.00/27.32  | | | | | | |   (161)   ~ (all_52_26 = e3)
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | BETA: splitting (33) gives:
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | Case 1:
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | |   (162)  all_58_2 = e3
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | REF_CLOSE: (64), (161), (162) are inconsistent by sub-proof
% 176.00/27.32  | | | | | | | |            #1004.
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | Case 2:
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | |   (163)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | BETA: splitting (156) gives:
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | Case 1:
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | |   (164)  all_58_1 = e3
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | COMBINE_EQS: (34), (164) imply:
% 176.00/27.32  | | | | | | | | |   (165)  all_52_3 = e3
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | REDUCE: (60), (165) imply:
% 176.00/27.32  | | | | | | | | |   (166)  $false
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | CLOSE: (166) is inconsistent.
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | Case 2:
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | |   (167)  all_58_4 = e3 | all_58_9 = e3
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | BETA: splitting (167) gives:
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | Case 1:
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | |   (168)  all_58_4 = e3
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | | COMBINE_EQS: (28), (168) imply:
% 176.00/27.32  | | | | | | | | | |   (169)  all_52_5 = e3
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | | SIMP: (169) implies:
% 176.00/27.32  | | | | | | | | | |   (170)  all_52_5 = e3
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | | REDUCE: (2), (170) imply:
% 176.00/27.32  | | | | | | | | | |   (171)   ~ (all_52_13 = e3)
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | | SIMP: (171) implies:
% 176.00/27.32  | | | | | | | | | |   (172)   ~ (all_52_13 = e3)
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | | REF_CLOSE: (12), (17), (23), (25), (40), (45), (56), (68),
% 176.00/27.32  | | | | | | | | | |            (72), (78), (133), (163), (172) are inconsistent
% 176.00/27.32  | | | | | | | | | |            by sub-proof #966.
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | Case 2:
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | |   (173)  all_58_9 = e3
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | | REF_CLOSE: (86), (142), (173) are inconsistent by sub-proof
% 176.00/27.32  | | | | | | | | | |            #972.
% 176.00/27.32  | | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | End of split
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | End of split
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | End of split
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | End of split
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | End of split
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | End of split
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | End of split
% 176.00/27.32  | | | 
% 176.00/27.32  | | End of split
% 176.00/27.32  | | 
% 176.00/27.32  | End of split
% 176.00/27.32  | 
% 176.00/27.32  End of proof
% 176.00/27.32  
% 176.00/27.32  Sub-proof #215 shows that the following formulas are inconsistent:
% 176.00/27.32  ----------------------------------------------------------------
% 176.00/27.32    (1)   ~ (all_52_25 = e3)
% 176.00/27.32    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.32    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.32    (4)  op(e3, e2) = all_52_3
% 176.00/27.32    (5)  all_58_5 = all_52_13
% 176.00/27.32    (6)  op(e1, all_52_13) = e1
% 176.00/27.32    (7)  all_56_15 = all_6_2
% 176.00/27.32    (8)  all_58_3 = all_10_2
% 176.00/27.32    (9)   ~ (all_52_26 = all_4_2)
% 176.00/27.32    (10)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.32    (11)  all_58_7 = all_52_19
% 176.00/27.32    (12)   ~ (all_4_0 = e2)
% 176.00/27.32    (13)  all_58_4 = all_52_5
% 176.00/27.32    (14)   ~ (e3 = e1)
% 176.00/27.32    (15)   ~ (all_52_17 = all_14_2)
% 176.00/27.32    (16)  op(e3, all_4_2) = all_4_1
% 176.00/27.32    (17)  all_58_1 = all_52_3
% 176.00/27.32    (18)  all_58_0 = all_4_2
% 176.00/27.32    (19)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.32    (20)  all_58_14 = all_52_29
% 176.00/27.32    (21)   ~ (all_52_13 = all_52_26)
% 176.00/27.32    (22)   ~ (all_52_3 = all_52_5)
% 176.00/27.32    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.32    (24)  op(e2, e1) = all_52_13
% 176.00/27.32    (25)  all_58_8 = all_14_2
% 176.00/27.32    (26)  op(e0, e2) = all_52_27
% 176.00/27.32    (27)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.32    (28)   ~ (all_52_3 = all_4_2)
% 176.00/27.32    (29)  op(e0, all_6_2) = all_6_1
% 176.00/27.32    (30)  op(all_6_1, all_6_2) = e2
% 176.00/27.32    (31)  op(e3, all_52_17) = all_52_16
% 176.00/27.32    (32)   ~ (all_52_29 = e3)
% 176.00/27.32    (33)  all_58_13 = all_52_27
% 176.00/27.32    (34)  all_58_6 = all_52_17
% 176.00/27.32    (35)  all_58_2 = all_52_26
% 176.00/27.32    (36)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.32    (37)   ~ (e1 = e0)
% 176.00/27.32    (38)   ~ (all_4_0 = e1)
% 176.00/27.32    (39)   ~ (all_52_29 = all_6_2)
% 176.00/27.32    (40)  op(e3, e1) = all_52_5
% 176.00/27.32    (41)  op(e1, e3) = all_52_17
% 176.00/27.32    (42)  op(e2, all_10_2) = e2
% 176.00/27.32    (43)  op(e3, e3) = all_4_2
% 176.00/27.32    (44)   ~ (all_14_2 = e3)
% 176.00/27.32    (45)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.32    (46)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.32    (47)   ~ (all_52_27 = all_6_2)
% 176.00/27.32    (48)   ~ (all_52_25 = all_52_26)
% 176.00/27.32    (49)   ~ (all_52_17 = all_52_19)
% 176.00/27.32    (50)  all_56_4 = all_52_26
% 176.00/27.32    (51)  all_58_12 = all_52_25
% 176.00/27.32    (52)   ~ (all_52_17 = all_52_26)
% 176.00/27.32    (53)  op(e3, all_52_26) = e3
% 176.00/27.32    (54)  all_58_13 = e3
% 176.00/27.32  
% 176.00/27.32  Begin of proof
% 176.00/27.32  | 
% 176.00/27.32  | BETA: splitting (45) gives:
% 176.00/27.32  | 
% 176.00/27.32  | Case 1:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (55)  all_58_5 = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | COMBINE_EQS: (5), (55) imply:
% 176.00/27.32  | |   (56)  all_52_13 = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (56) implies:
% 176.00/27.32  | |   (57)  all_52_13 = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (21), (57) imply:
% 176.00/27.32  | |   (58)   ~ (all_52_26 = e3)
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (58) implies:
% 176.00/27.32  | |   (59)   ~ (all_52_26 = e3)
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (24), (57) imply:
% 176.00/27.32  | |   (60)  op(e2, e1) = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (6), (57) imply:
% 176.00/27.32  | |   (61)  op(e1, e3) = e1
% 176.00/27.32  | | 
% 176.00/27.32  | | GROUND_INST: instantiating (46) with all_52_17, e1, e3, e1, simplifying with
% 176.00/27.32  | |              (41), (61) gives:
% 176.00/27.32  | |   (62)  all_52_17 = e1
% 176.00/27.32  | | 
% 176.00/27.32  | | COMBINE_EQS: (34), (62) imply:
% 176.00/27.32  | |   (63)  all_58_6 = e1
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (49), (62) imply:
% 176.00/27.32  | |   (64)   ~ (all_52_19 = e1)
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (64) implies:
% 176.00/27.32  | |   (65)   ~ (all_52_19 = e1)
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (52), (62) imply:
% 176.00/27.32  | |   (66)   ~ (all_52_26 = e1)
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (66) implies:
% 176.00/27.32  | |   (67)   ~ (all_52_26 = e1)
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (15), (62) imply:
% 176.00/27.32  | |   (68)   ~ (all_14_2 = e1)
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (68) implies:
% 176.00/27.32  | |   (69)   ~ (all_14_2 = e1)
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (31), (62) imply:
% 176.00/27.32  | |   (70)  op(e3, e1) = all_52_16
% 176.00/27.32  | | 
% 176.00/27.32  | | BETA: splitting (23) gives:
% 176.00/27.32  | | 
% 176.00/27.32  | | Case 1:
% 176.00/27.32  | | | 
% 176.00/27.32  | | |   (71)  all_58_0 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | COMBINE_EQS: (18), (71) imply:
% 176.00/27.32  | | |   (72)  all_4_2 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (28), (72) imply:
% 176.00/27.32  | | |   (73)   ~ (all_52_3 = e3)
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (27), (72) imply:
% 176.00/27.32  | | |   (74)  op(all_4_1, e3) = all_4_0
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (16), (72) imply:
% 176.00/27.32  | | |   (75)  op(e3, e3) = all_4_1
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (43), (72) imply:
% 176.00/27.32  | | |   (76)  op(e3, e3) = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | GROUND_INST: instantiating (46) with all_52_5, all_52_16, e1, e3,
% 176.00/27.32  | | |              simplifying with (40), (70) gives:
% 176.00/27.32  | | |   (77)  all_52_5 = all_52_16
% 176.00/27.32  | | | 
% 176.00/27.32  | | | GROUND_INST: instantiating (46) with e3, all_4_1, e3, e3, simplifying with
% 176.00/27.32  | | |              (75), (76) gives:
% 176.00/27.32  | | |   (78)  all_4_1 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | COMBINE_EQS: (13), (77) imply:
% 176.00/27.32  | | |   (79)  all_58_4 = all_52_16
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (22), (77) imply:
% 176.00/27.32  | | |   (80)   ~ (all_52_3 = all_52_16)
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (74), (78) imply:
% 176.00/27.32  | | |   (81)  op(e3, e3) = all_4_0
% 176.00/27.32  | | | 
% 176.00/27.32  | | | GROUND_INST: instantiating (46) with e3, all_4_0, e3, e3, simplifying with
% 176.00/27.32  | | |              (76), (81) gives:
% 176.00/27.32  | | |   (82)  all_4_0 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REDUCE: (12), (82) imply:
% 176.00/27.32  | | |   (83)   ~ (e3 = e2)
% 176.00/27.32  | | | 
% 176.00/27.32  | | | BETA: splitting (36) gives:
% 176.00/27.32  | | | 
% 176.00/27.32  | | | Case 1:
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | |   (84)  all_56_4 = e3
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | REF_CLOSE: (50), (59), (84) are inconsistent by sub-proof #818.
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | Case 2:
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | |   (85)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | BETA: splitting (2) gives:
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | | Case 1:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | |   (86)  all_58_1 = e1
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | COMBINE_EQS: (17), (86) imply:
% 176.00/27.32  | | | | |   (87)  all_52_3 = e1
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | REDUCE: (80), (87) imply:
% 176.00/27.32  | | | | |   (88)   ~ (all_52_16 = e1)
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | SIMP: (88) implies:
% 176.00/27.32  | | | | |   (89)   ~ (all_52_16 = e1)
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | REDUCE: (73), (87) imply:
% 176.00/27.32  | | | | |   (90)   ~ (e3 = e1)
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | BETA: splitting (19) gives:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | Case 1:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | |   (91)  all_58_4 = e1
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | REF_CLOSE: (79), (89), (91) are inconsistent by sub-proof #260.
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | Case 2:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | |   (92)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | BETA: splitting (92) gives:
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | | Case 1:
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | |   (93)  all_58_5 = e1
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | REF_CLOSE: (14), (55), (93) are inconsistent by sub-proof #816.
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | Case 2:
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | |   (94)  all_58_8 = e1 | all_58_14 = e1
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | BETA: splitting (94) gives:
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | | Case 1:
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | |   (95)  all_58_8 = e1
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | REF_CLOSE: (25), (69), (95) are inconsistent by sub-proof #815.
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | Case 2:
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | |   (96)  all_58_14 = e1
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | COMBINE_EQS: (20), (96) imply:
% 176.00/27.32  | | | | | | | |   (97)  all_52_29 = e1
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | SIMP: (97) implies:
% 176.00/27.32  | | | | | | | |   (98)  all_52_29 = e1
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | REDUCE: (39), (98) imply:
% 176.00/27.32  | | | | | | | |   (99)   ~ (all_6_2 = e1)
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | SIMP: (99) implies:
% 176.00/27.32  | | | | | | | |   (100)   ~ (all_6_2 = e1)
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | BETA: splitting (3) gives:
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | | Case 1:
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | |   (101)  all_58_12 = e0
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | COMBINE_EQS: (51), (101) imply:
% 176.00/27.32  | | | | | | | | |   (102)  all_52_25 = e0
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | SIMP: (102) implies:
% 176.00/27.32  | | | | | | | | |   (103)  all_52_25 = e0
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | REDUCE: (48), (103) imply:
% 176.00/27.32  | | | | | | | | |   (104)   ~ (all_52_26 = e0)
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | SIMP: (104) implies:
% 176.00/27.32  | | | | | | | | |   (105)   ~ (all_52_26 = e0)
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | REF_CLOSE: (4), (46), (50), (53), (67), (73), (85), (105) are
% 176.00/27.32  | | | | | | | | |            inconsistent by sub-proof #766.
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | Case 2:
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | |   (106)  all_58_13 = e0 | all_58_14 = e0
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | | REF_CLOSE: (7), (10), (26), (29), (30), (33), (37), (46),
% 176.00/27.32  | | | | | | | | |            (47), (96), (100), (106) are inconsistent by
% 176.00/27.32  | | | | | | | | |            sub-proof #216.
% 176.00/27.32  | | | | | | | | | 
% 176.00/27.32  | | | | | | | | End of split
% 176.00/27.32  | | | | | | | | 
% 176.00/27.32  | | | | | | | End of split
% 176.00/27.32  | | | | | | | 
% 176.00/27.32  | | | | | | End of split
% 176.00/27.32  | | | | | | 
% 176.00/27.32  | | | | | End of split
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | Case 2:
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | |   (107)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | | REF_CLOSE: (8), (11), (14), (42), (46), (54), (60), (65), (83), (107)
% 176.00/27.32  | | | | |            are inconsistent by sub-proof #767.
% 176.00/27.32  | | | | | 
% 176.00/27.32  | | | | End of split
% 176.00/27.32  | | | | 
% 176.00/27.32  | | | End of split
% 176.00/27.32  | | | 
% 176.00/27.32  | | Case 2:
% 176.00/27.32  | | | 
% 176.00/27.32  | | |   (108)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.32  | | | 
% 176.00/27.32  | | | REF_CLOSE: (1), (14), (35), (51), (59), (63), (108) are inconsistent by
% 176.00/27.32  | | |            sub-proof #1001.
% 176.00/27.32  | | | 
% 176.00/27.32  | | End of split
% 176.00/27.32  | | 
% 176.00/27.32  | Case 2:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (109)  all_58_8 = e3 | all_58_14 = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | REF_CLOSE: (20), (25), (32), (44), (109) are inconsistent by sub-proof #999.
% 176.00/27.32  | | 
% 176.00/27.32  | End of split
% 176.00/27.32  | 
% 176.00/27.32  End of proof
% 176.00/27.32  
% 176.00/27.32  Sub-proof #216 shows that the following formulas are inconsistent:
% 176.00/27.32  ----------------------------------------------------------------
% 176.00/27.32    (1)  all_58_13 = e0 | all_58_14 = e0
% 176.00/27.32    (2)  all_56_15 = all_6_2
% 176.00/27.32    (3)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.32    (4)  op(e0, e2) = all_52_27
% 176.00/27.32    (5)  op(e0, all_6_2) = all_6_1
% 176.00/27.32    (6)  op(all_6_1, all_6_2) = e2
% 176.00/27.32    (7)   ~ (all_6_2 = e1)
% 176.00/27.32    (8)  all_58_13 = all_52_27
% 176.00/27.32    (9)  all_58_14 = e1
% 176.00/27.32    (10)   ~ (e1 = e0)
% 176.00/27.32    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.32    (12)   ~ (all_52_27 = all_6_2)
% 176.00/27.32  
% 176.00/27.32  Begin of proof
% 176.00/27.32  | 
% 176.00/27.32  | BETA: splitting (1) gives:
% 176.00/27.32  | 
% 176.00/27.32  | Case 1:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (13)  all_58_13 = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | COMBINE_EQS: (8), (13) imply:
% 176.00/27.32  | |   (14)  all_52_27 = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (14) implies:
% 176.00/27.32  | |   (15)  all_52_27 = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (12), (15) imply:
% 176.00/27.32  | |   (16)   ~ (all_6_2 = e0)
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (16) implies:
% 176.00/27.32  | |   (17)   ~ (all_6_2 = e0)
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (4), (15) imply:
% 176.00/27.32  | |   (18)  op(e0, e2) = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | REF_CLOSE: (2), (3), (5), (6), (7), (11), (17), (18) are inconsistent by
% 176.00/27.32  | |            sub-proof #218.
% 176.00/27.32  | | 
% 176.00/27.32  | Case 2:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (19)  all_58_14 = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | REF_CLOSE: (9), (10), (19) are inconsistent by sub-proof #217.
% 176.00/27.32  | | 
% 176.00/27.32  | End of split
% 176.00/27.32  | 
% 176.00/27.32  End of proof
% 176.00/27.32  
% 176.00/27.32  Sub-proof #217 shows that the following formulas are inconsistent:
% 176.00/27.32  ----------------------------------------------------------------
% 176.00/27.32    (1)  all_58_14 = e1
% 176.00/27.32    (2)  all_58_14 = e0
% 176.00/27.32    (3)   ~ (e1 = e0)
% 176.00/27.32  
% 176.00/27.32  Begin of proof
% 176.00/27.32  | 
% 176.00/27.32  | COMBINE_EQS: (1), (2) imply:
% 176.00/27.32  |   (4)  e1 = e0
% 176.00/27.32  | 
% 176.00/27.32  | SIMP: (4) implies:
% 176.00/27.32  |   (5)  e1 = e0
% 176.00/27.32  | 
% 176.00/27.32  | REDUCE: (3), (5) imply:
% 176.00/27.32  |   (6)  $false
% 176.00/27.32  | 
% 176.00/27.32  | CLOSE: (6) is inconsistent.
% 176.00/27.32  | 
% 176.00/27.32  End of proof
% 176.00/27.32  
% 176.00/27.32  Sub-proof #218 shows that the following formulas are inconsistent:
% 176.00/27.32  ----------------------------------------------------------------
% 176.00/27.32    (1)   ~ (all_6_2 = e0)
% 176.00/27.32    (2)  all_56_15 = all_6_2
% 176.00/27.32    (3)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.32    (4)  op(e0, e2) = e0
% 176.00/27.32    (5)  op(e0, all_6_2) = all_6_1
% 176.00/27.32    (6)  op(all_6_1, all_6_2) = e2
% 176.00/27.32    (7)   ~ (all_6_2 = e1)
% 176.00/27.32    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.32  
% 176.00/27.32  Begin of proof
% 176.00/27.32  | 
% 176.00/27.32  | BETA: splitting (3) gives:
% 176.00/27.32  | 
% 176.00/27.32  | Case 1:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (9)  all_56_15 = e2
% 176.00/27.32  | | 
% 176.00/27.32  | | COMBINE_EQS: (2), (9) imply:
% 176.00/27.32  | |   (10)  all_6_2 = e2
% 176.00/27.32  | | 
% 176.00/27.32  | | SIMP: (10) implies:
% 176.00/27.32  | |   (11)  all_6_2 = e2
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (1), (11) imply:
% 176.00/27.32  | |   (12)   ~ (e2 = e0)
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (6), (11) imply:
% 176.00/27.32  | |   (13)  op(all_6_1, e2) = e2
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (5), (11) imply:
% 176.00/27.32  | |   (14)  op(e0, e2) = all_6_1
% 176.00/27.32  | | 
% 176.00/27.32  | | GROUND_INST: instantiating (8) with e0, all_6_1, e2, e0, simplifying with
% 176.00/27.32  | |              (4), (14) gives:
% 176.00/27.32  | |   (15)  all_6_1 = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (13), (15) imply:
% 176.00/27.32  | |   (16)  op(e0, e2) = e2
% 176.00/27.32  | | 
% 176.00/27.32  | | GROUND_INST: instantiating (8) with e0, e2, e2, e0, simplifying with (4),
% 176.00/27.32  | |              (16) gives:
% 176.00/27.32  | |   (17)  e2 = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | REDUCE: (12), (17) imply:
% 176.00/27.32  | |   (18)  $false
% 176.00/27.32  | | 
% 176.00/27.32  | | CLOSE: (18) is inconsistent.
% 176.00/27.32  | | 
% 176.00/27.32  | Case 2:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (19)  all_56_15 = e1 | all_56_15 = e0
% 176.00/27.32  | | 
% 176.00/27.32  | | REF_CLOSE: (1), (2), (7), (19) are inconsistent by sub-proof #653.
% 176.00/27.32  | | 
% 176.00/27.32  | End of split
% 176.00/27.32  | 
% 176.00/27.32  End of proof
% 176.00/27.32  
% 176.00/27.32  Sub-proof #219 shows that the following formulas are inconsistent:
% 176.00/27.32  ----------------------------------------------------------------
% 176.00/27.32    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.32    (2)   ~ (all_52_13 = all_52_29)
% 176.00/27.32    (3)  op(e3, e2) = all_52_3
% 176.00/27.32    (4)   ~ (all_6_2 = e3)
% 176.00/27.32    (5)   ~ (all_14_1 = e2)
% 176.00/27.32    (6)  all_58_5 = all_52_13
% 176.00/27.32    (7)  op(e1, all_52_13) = e1
% 176.00/27.32    (8)  op(e0, all_52_15) = e0
% 176.00/27.32    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.32    (10)  all_58_3 = all_10_2
% 176.00/27.32    (11)  all_58_15 = all_6_2
% 176.00/27.32    (12)   ~ (all_52_26 = all_4_2)
% 176.00/27.32    (13)   ~ (all_52_5 = all_52_7)
% 176.00/27.32    (14)  all_58_10 = all_52_15
% 176.00/27.32    (15)  all_58_7 = all_52_19
% 176.00/27.32    (16)   ~ (all_52_17 = all_52_25)
% 176.00/27.32    (17)  all_58_4 = all_52_5
% 176.00/27.32    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.32    (19)   ~ (e3 = e1)
% 176.00/27.32    (20)   ~ (all_52_17 = all_14_2)
% 176.00/27.32    (21)  op(e3, all_4_2) = all_4_1
% 176.00/27.32    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.32    (23)   ~ (all_52_7 = all_4_2)
% 176.00/27.32    (24)  all_58_1 = all_52_3
% 176.00/27.32    (25)  all_58_0 = all_4_2
% 176.00/27.32    (26)   ~ (all_4_1 = e2)
% 176.00/27.32    (27)  all_58_14 = all_52_29
% 176.00/27.32    (28)   ~ (all_10_2 = e3)
% 176.00/27.32    (29)   ~ (all_52_13 = all_52_26)
% 176.00/27.32    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.32    (31)  all_58_8 = all_14_2
% 176.00/27.32    (32)   ~ (all_52_5 = all_14_2)
% 176.00/27.32    (33)   ~ (all_52_3 = all_4_2)
% 176.00/27.32    (34)  op(e0, e3) = all_52_25
% 176.00/27.32    (35)   ~ (all_52_13 = all_14_2)
% 176.00/27.32    (36)   ~ (all_52_3 = e3)
% 176.00/27.32    (37)  all_58_6 = all_52_17
% 176.00/27.32    (38)  all_58_2 = all_52_26
% 176.00/27.32    (39)  all_58_11 = all_52_23
% 176.00/27.32    (40)   ~ (all_52_7 = all_52_15)
% 176.00/27.32    (41)  op(e1, e3) = all_52_17
% 176.00/27.32    (42)  op(e3, e3) = all_4_2
% 176.00/27.32    (43)  all_14_2 = e3
% 176.00/27.32    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.00/27.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.00/27.32    (45)   ~ (all_52_7 = all_52_23)
% 176.00/27.32    (46)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.32    (47)  op(e1, all_14_2) = all_14_1
% 176.00/27.32    (48)  all_58_9 = all_52_7
% 176.00/27.32    (49)   ~ (e2 = e0)
% 176.00/27.32    (50)  all_58_12 = all_52_25
% 176.00/27.32    (51)  op(e3, all_52_26) = e3
% 176.00/27.32    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.32    (53)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.00/27.32    (54)   ~ (all_52_19 = all_14_2)
% 176.00/27.32  
% 176.00/27.32  Begin of proof
% 176.00/27.32  | 
% 176.00/27.32  | REDUCE: (32), (43) imply:
% 176.00/27.32  |   (55)   ~ (all_52_5 = e3)
% 176.00/27.32  | 
% 176.00/27.32  | REDUCE: (43), (54) imply:
% 176.00/27.32  |   (56)   ~ (all_52_19 = e3)
% 176.00/27.32  | 
% 176.00/27.32  | REDUCE: (1), (43) imply:
% 176.00/27.32  |   (57)   ~ (all_52_23 = e3)
% 176.00/27.32  | 
% 176.00/27.32  | REDUCE: (43), (47) imply:
% 176.00/27.32  |   (58)  op(e1, e3) = all_14_1
% 176.00/27.32  | 
% 176.00/27.32  | GROUND_INST: instantiating (44) with all_52_17, all_14_1, e3, e1, simplifying
% 176.00/27.32  |              with (41), (58) gives:
% 176.00/27.32  |   (59)  all_52_17 = all_14_1
% 176.00/27.32  | 
% 176.00/27.32  | COMBINE_EQS: (37), (59) imply:
% 176.00/27.32  |   (60)  all_58_6 = all_14_1
% 176.00/27.32  | 
% 176.00/27.32  | BETA: splitting (46) gives:
% 176.00/27.32  | 
% 176.00/27.32  | Case 1:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (61)  all_58_9 = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | COMBINE_EQS: (48), (61) imply:
% 176.00/27.32  | |   (62)  all_52_7 = e3
% 176.00/27.32  | | 
% 176.00/27.32  | | REF_CLOSE: (2), (6), (7), (10), (12), (13), (14), (15), (16), (17), (18),
% 176.00/27.32  | |            (19), (20), (22), (23), (25), (27), (28), (29), (30), (31), (35),
% 176.00/27.32  | |            (37), (38), (39), (40), (41), (42), (44), (45), (50), (51), (53),
% 176.00/27.32  | |            (56), (62) are inconsistent by sub-proof #983.
% 176.00/27.32  | | 
% 176.00/27.32  | Case 2:
% 176.00/27.32  | | 
% 176.00/27.32  | |   (63)   ~ (all_58_9 = e3)
% 176.00/27.33  | |   (64)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.00/27.33  | | 
% 176.00/27.33  | | REDUCE: (48), (63) imply:
% 176.00/27.33  | |   (65)   ~ (all_52_7 = e3)
% 176.00/27.33  | | 
% 176.00/27.33  | | BETA: splitting (52) gives:
% 176.00/27.33  | | 
% 176.00/27.33  | | Case 1:
% 176.00/27.33  | | | 
% 176.00/27.33  | | |   (66)  all_58_0 = e3
% 176.00/27.33  | | | 
% 176.00/27.33  | | | COMBINE_EQS: (25), (66) imply:
% 176.00/27.33  | | |   (67)  all_4_2 = e3
% 176.00/27.33  | | | 
% 176.00/27.33  | | | REDUCE: (21), (67) imply:
% 176.00/27.33  | | |   (68)  op(e3, e3) = all_4_1
% 176.00/27.33  | | | 
% 176.00/27.33  | | | REDUCE: (42), (67) imply:
% 176.00/27.33  | | |   (69)  op(e3, e3) = e3
% 176.00/27.33  | | | 
% 176.00/27.33  | | | BETA: splitting (64) gives:
% 176.00/27.33  | | | 
% 176.00/27.33  | | | Case 1:
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | |   (70)  all_58_10 = e3
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | COMBINE_EQS: (14), (70) imply:
% 176.00/27.33  | | | |   (71)  all_52_15 = e3
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | SIMP: (71) implies:
% 176.00/27.33  | | | |   (72)  all_52_15 = e3
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | REDUCE: (8), (72) imply:
% 176.00/27.33  | | | |   (73)  op(e0, e3) = e0
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | GROUND_INST: instantiating (44) with all_52_25, e0, e3, e0, simplifying
% 176.00/27.33  | | | |              with (34), (73) gives:
% 176.00/27.33  | | | |   (74)  all_52_25 = e0
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | GROUND_INST: instantiating (44) with e3, all_4_1, e3, e3, simplifying
% 176.00/27.33  | | | |              with (68), (69) gives:
% 176.00/27.33  | | | |   (75)  all_4_1 = e3
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | COMBINE_EQS: (50), (74) imply:
% 176.00/27.33  | | | |   (76)  all_58_12 = e0
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | REDUCE: (26), (75) imply:
% 176.00/27.33  | | | |   (77)   ~ (e3 = e2)
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | BETA: splitting (9) gives:
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | Case 1:
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | |   (78)  all_58_0 = e2
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | | COMBINE_EQS: (66), (78) imply:
% 176.00/27.33  | | | | |   (79)  e3 = e2
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | | REDUCE: (77), (79) imply:
% 176.00/27.33  | | | | |   (80)  $false
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | | CLOSE: (80) is inconsistent.
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | Case 2:
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | |   (81)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | | BETA: splitting (81) gives:
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | | Case 1:
% 176.00/27.33  | | | | | | 
% 176.00/27.33  | | | | | |   (82)  all_58_2 = e2
% 176.00/27.33  | | | | | | 
% 176.00/27.33  | | | | | | REF_CLOSE: (3), (36), (38), (44), (51), (82) are inconsistent by
% 176.00/27.33  | | | | | |            sub-proof #596.
% 176.00/27.33  | | | | | | 
% 176.00/27.33  | | | | | Case 2:
% 176.00/27.33  | | | | | | 
% 176.00/27.33  | | | | | |   (83)  all_58_6 = e2 | all_58_12 = e2
% 176.00/27.33  | | | | | | 
% 176.00/27.33  | | | | | | BETA: splitting (83) gives:
% 176.00/27.33  | | | | | | 
% 176.00/27.33  | | | | | | Case 1:
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | |   (84)  all_58_6 = e2
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | | REF_CLOSE: (5), (60), (84) are inconsistent by sub-proof #847.
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | Case 2:
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | |   (85)  all_58_12 = e2
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | | COMBINE_EQS: (76), (85) imply:
% 176.00/27.33  | | | | | | |   (86)  e2 = e0
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | | REDUCE: (49), (86) imply:
% 176.00/27.33  | | | | | | |   (87)  $false
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | | CLOSE: (87) is inconsistent.
% 176.00/27.33  | | | | | | | 
% 176.00/27.33  | | | | | | End of split
% 176.00/27.33  | | | | | | 
% 176.00/27.33  | | | | | End of split
% 176.00/27.33  | | | | | 
% 176.00/27.33  | | | | End of split
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | Case 2:
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | |   (88)  all_58_11 = e3 | all_58_15 = e3
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | | REF_CLOSE: (4), (11), (39), (57), (88) are inconsistent by sub-proof
% 176.00/27.33  | | | |            #1016.
% 176.00/27.33  | | | | 
% 176.00/27.33  | | | End of split
% 176.00/27.33  | | | 
% 176.00/27.33  | | Case 2:
% 176.00/27.33  | | | 
% 176.00/27.33  | | |   (89)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.00/27.33  | | | 
% 176.00/27.33  | | | REF_CLOSE: (17), (24), (36), (48), (55), (65), (89) are inconsistent by
% 176.00/27.33  | | |            sub-proof #728.
% 176.00/27.33  | | | 
% 176.00/27.33  | | End of split
% 176.00/27.33  | | 
% 176.00/27.33  | End of split
% 176.00/27.33  | 
% 176.00/27.33  End of proof
% 176.00/27.33  
% 176.00/27.33  Sub-proof #220 shows that the following formulas are inconsistent:
% 176.00/27.33  ----------------------------------------------------------------
% 176.00/27.33    (1)   ~ (all_52_23 = all_14_2)
% 176.00/27.33    (2)   ~ (all_52_5 = all_52_13)
% 176.00/27.33    (3)   ~ (all_52_27 = all_10_2)
% 176.00/27.33    (4)   ~ (all_52_17 = all_52_23)
% 176.00/27.33    (5)   ~ (all_52_13 = all_52_29)
% 176.00/27.33    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.00/27.33    (7)  op(e3, e2) = all_52_3
% 176.00/27.33    (8)   ~ (all_52_9 = all_52_25)
% 176.00/27.33    (9)   ~ (all_52_19 = all_52_23)
% 176.00/27.33    (10)  all_56_11 = all_52_23
% 176.00/27.33    (11)  op(e1, e2) = all_52_19
% 176.00/27.33    (12)  all_16_1 = all_6_1
% 176.00/27.33    (13)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.00/27.33    (14)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.00/27.33    (15)   ~ (all_52_3 = all_10_2)
% 176.00/27.33    (16)  all_58_5 = all_52_13
% 176.00/27.33    (17)   ~ (all_6_2 = e0)
% 176.00/27.33    (18)   ~ (all_52_25 = all_52_29)
% 176.00/27.33    (19)  all_16_2 = all_6_2
% 176.00/27.33    (20)  all_56_15 = all_6_2
% 176.00/27.33    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.00/27.33    (22)  op(e2, e0) = all_52_15
% 176.00/27.33    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.00/27.33    (24)  all_58_3 = all_10_2
% 176.00/27.33    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.00/27.33    (26)  all_58_15 = all_6_2
% 176.00/27.33    (27)   ~ (all_52_9 = all_4_2)
% 176.00/27.33    (28)   ~ (all_52_5 = all_52_7)
% 176.00/27.33    (29)  all_58_10 = all_52_15
% 176.00/27.33    (30)  all_8_2 = all_6_2
% 176.00/27.33    (31)   ~ (all_52_5 = all_4_2)
% 176.00/27.33    (32)  all_58_7 = all_52_19
% 176.00/27.33    (33)  all_56_4 = all_52_9
% 176.00/27.33    (34)   ~ (all_52_17 = all_52_25)
% 176.00/27.33    (35)  op(e0, e1) = all_52_29
% 176.00/27.33    (36)   ~ (all_4_0 = e2)
% 176.00/27.33    (37)  all_58_4 = all_52_5
% 176.00/27.33    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.00/27.33    (39)   ~ (all_52_27 = all_52_29)
% 176.00/27.33    (40)  op(e3, all_4_2) = all_4_1
% 176.00/27.33    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.00/27.33    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.00/27.33    (43)   ~ (all_52_7 = all_4_2)
% 176.00/27.33    (44)  all_58_1 = all_52_3
% 176.00/27.33    (45)   ~ (all_52_13 = all_52_15)
% 176.00/27.33    (46)  all_58_0 = all_4_2
% 176.00/27.33    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.00/27.33    (48)  op(e1, all_52_29) = all_52_28
% 176.00/27.33    (49)  op(e1, all_52_5) = all_52_4
% 176.00/27.33    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.00/27.33    (51)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.00/27.33    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.00/27.33    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.00/27.33    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.00/27.33    (55)  all_58_14 = all_52_29
% 176.00/27.33    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.00/27.33    (57)   ~ (all_52_3 = all_52_5)
% 176.00/27.33    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.00/27.33    (59)  op(e2, e1) = all_52_13
% 176.00/27.33    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.00/27.33    (61)  all_58_8 = all_14_2
% 176.00/27.33    (62)  all_56_1 = all_52_3
% 176.00/27.33    (63)  all_56_14 = all_52_29
% 176.00/27.33    (64)  op(all_4_1, all_4_2) = all_4_0
% 176.00/27.33    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.00/27.33    (66)   ~ (all_52_5 = all_14_2)
% 176.00/27.33    (67)   ~ (all_52_3 = all_52_27)
% 176.00/27.33    (68)   ~ (all_52_3 = all_4_2)
% 176.00/27.33    (69)  op(e0, e3) = all_52_25
% 176.00/27.33    (70)  op(e0, all_6_2) = all_6_1
% 176.00/27.33    (71)  all_52_0 = all_4_1
% 176.00/27.33    (72)   ~ (all_52_9 = all_10_2)
% 176.00/27.33    (73)  op(all_6_1, all_6_2) = e2
% 176.00/27.33    (74)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.26/27.33    (75)   ~ (all_52_13 = all_14_2)
% 176.26/27.33    (76)   ~ (e3 = e0)
% 176.26/27.33    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.26/27.33    (78)   ~ (all_52_9 = all_52_13)
% 176.26/27.33    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.26/27.33    (80)  op(e0, all_52_23) = all_52_22
% 176.26/27.33    (81)   ~ (all_52_15 = all_52_23)
% 176.26/27.33    (82)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.26/27.33    (83)   ~ (all_52_5 = all_52_29)
% 176.26/27.33    (84)  all_56_2 = all_52_5
% 176.26/27.33    (85)  op(e1, e0) = all_52_23
% 176.26/27.33    (86)  all_56_12 = all_52_25
% 176.26/27.33    (87)  all_58_13 = all_52_27
% 176.26/27.33    (88)  op(e2, all_52_3) = all_52_2
% 176.26/27.33    (89)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.26/27.33    (90)  all_56_5 = all_10_2
% 176.26/27.33    (91)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.26/27.33    (92)   ~ (all_52_9 = all_52_17)
% 176.26/27.33    (93)  all_58_6 = all_52_17
% 176.26/27.33    (94)   ~ (all_52_3 = all_52_7)
% 176.26/27.33    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.26/27.33    (96)   ~ (e1 = e0)
% 176.26/27.33    (97)  all_56_0 = all_4_2
% 176.26/27.33    (98)  all_58_11 = all_52_23
% 176.26/27.33    (99)   ~ (all_52_3 = all_52_19)
% 176.26/27.33    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.26/27.33    (101)   ~ (all_52_7 = all_52_15)
% 176.26/27.33    (102)   ~ (all_52_29 = all_14_2)
% 176.26/27.33    (103)   ~ (all_4_0 = e1)
% 176.26/27.33    (104)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.26/27.33    (105)   ~ (all_52_19 = all_10_2)
% 176.26/27.33    (106)   ~ (all_52_23 = all_6_2)
% 176.26/27.33    (107)   ~ (all_52_29 = all_6_2)
% 176.26/27.33    (108)  all_58_2 = all_52_9
% 176.26/27.33    (109)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.26/27.33    (110)  op(e3, e1) = all_52_5
% 176.26/27.33    (111)  all_56_10 = all_14_2
% 176.26/27.33    (112)   ~ (all_52_25 = all_6_2)
% 176.26/27.33    (113)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.26/27.33    (114)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.26/27.33    (115)  op(e1, e1) = all_14_2
% 176.26/27.33    (116)  op(e1, e3) = all_52_17
% 176.26/27.33    (117)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.26/27.33    (118)   ~ (all_52_25 = all_4_2)
% 176.26/27.33    (119)  op(e3, e0) = all_52_7
% 176.26/27.33    (120)   ~ (all_52_17 = all_4_2)
% 176.26/27.33    (121)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.33             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.33    (122)   ~ (all_52_25 = all_52_27)
% 176.26/27.33    (123)   ~ (all_52_27 = all_6_2)
% 176.26/27.33    (124)  all_8_1 = all_6_1
% 176.26/27.33    (125)   ~ (all_52_7 = all_6_2)
% 176.26/27.33    (126)   ~ (all_52_19 = all_52_27)
% 176.26/27.33    (127)  all_56_7 = all_52_15
% 176.26/27.33    (128)   ~ (all_52_7 = all_52_23)
% 176.26/27.33    (129)   ~ (all_52_13 = all_10_2)
% 176.26/27.33    (130)  op(e2, all_52_27) = all_52_26
% 176.26/27.33    (131)   ~ (all_52_17 = all_52_19)
% 176.26/27.33    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.26/27.33    (133)  all_58_9 = all_52_7
% 176.26/27.33    (134)  all_58_12 = all_52_25
% 176.26/27.33    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.26/27.33    (136)   ~ (all_52_9 = all_52_15)
% 176.26/27.33    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.26/27.33    (138)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.26/27.33    (139)   ~ (all_52_19 = all_14_2)
% 176.26/27.33    (140)  op(e0, all_52_7) = all_52_6
% 176.26/27.33    (141)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.26/27.33    (142)  op(e2, e3) = all_52_9
% 176.26/27.33    (143)  all_56_13 = all_52_27
% 176.26/27.33  
% 176.26/27.33  Begin of proof
% 176.26/27.33  | 
% 176.26/27.33  | ALPHA: (141) implies:
% 176.26/27.33  |   (144)  all_52_6 = e0
% 176.26/27.33  |   (145)  all_52_4 = e1
% 176.26/27.33  |   (146)  all_52_2 = e2
% 176.26/27.33  |   (147)  all_52_0 = e3
% 176.26/27.33  | 
% 176.26/27.33  | COMBINE_EQS: (71), (147) imply:
% 176.26/27.33  |   (148)  all_4_1 = e3
% 176.26/27.33  | 
% 176.26/27.33  | REDUCE: (64), (148) imply:
% 176.26/27.33  |   (149)  op(e3, all_4_2) = all_4_0
% 176.26/27.33  | 
% 176.26/27.33  | REDUCE: (40), (148) imply:
% 176.26/27.33  |   (150)  op(e3, all_4_2) = e3
% 176.26/27.33  | 
% 176.26/27.33  | REDUCE: (88), (146) imply:
% 176.26/27.33  |   (151)  op(e2, all_52_3) = e2
% 176.26/27.33  | 
% 176.26/27.33  | REDUCE: (49), (145) imply:
% 176.26/27.33  |   (152)  op(e1, all_52_5) = e1
% 176.26/27.33  | 
% 176.26/27.33  | REDUCE: (140), (144) imply:
% 176.26/27.33  |   (153)  op(e0, all_52_7) = e0
% 176.26/27.33  | 
% 176.26/27.33  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.26/27.33  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.26/27.33  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 176.26/27.33  |            (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 176.26/27.33  |            (47), (48), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 176.26/27.33  |            (59), (60), (61), (62), (63), (65), (66), (67), (68), (69), (70),
% 176.26/27.33  |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 176.26/27.33  |            (83), (84), (85), (86), (87), (89), (90), (91), (92), (93), (94),
% 176.26/27.33  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 176.26/27.33  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 176.26/27.33  |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 176.26/27.33  |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 176.26/27.33  |            (132), (133), (134), (135), (136), (137), (138), (139), (142),
% 176.26/27.33  |            (143), (149), (150), (151), (152), (153) are inconsistent by
% 176.26/27.33  |            sub-proof #221.
% 176.26/27.33  | 
% 176.26/27.33  End of proof
% 176.26/27.33  
% 176.26/27.33  Sub-proof #221 shows that the following formulas are inconsistent:
% 176.26/27.33  ----------------------------------------------------------------
% 176.26/27.33    (1)   ~ (all_52_23 = all_14_2)
% 176.26/27.33    (2)   ~ (all_52_5 = all_52_13)
% 176.26/27.33    (3)   ~ (all_52_27 = all_10_2)
% 176.26/27.33    (4)   ~ (all_52_17 = all_52_23)
% 176.26/27.33    (5)  op(e2, all_52_3) = e2
% 176.26/27.33    (6)   ~ (all_52_13 = all_52_29)
% 176.26/27.33    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.26/27.33    (8)  op(e3, e2) = all_52_3
% 176.26/27.33    (9)   ~ (all_52_9 = all_52_25)
% 176.26/27.33    (10)   ~ (all_52_19 = all_52_23)
% 176.26/27.33    (11)  all_56_11 = all_52_23
% 176.26/27.33    (12)  op(e1, e2) = all_52_19
% 176.26/27.33    (13)  all_16_1 = all_6_1
% 176.26/27.33    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.26/27.33    (15)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.26/27.33    (16)   ~ (all_52_3 = all_10_2)
% 176.26/27.33    (17)  all_58_5 = all_52_13
% 176.26/27.33    (18)   ~ (all_6_2 = e0)
% 176.26/27.33    (19)   ~ (all_52_25 = all_52_29)
% 176.26/27.33    (20)  all_16_2 = all_6_2
% 176.26/27.33    (21)  all_56_15 = all_6_2
% 176.26/27.33    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.26/27.33    (23)  op(e2, e0) = all_52_15
% 176.26/27.33    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.26/27.33    (25)  all_58_3 = all_10_2
% 176.26/27.33    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.26/27.33    (27)  all_58_15 = all_6_2
% 176.26/27.33    (28)   ~ (all_52_9 = all_4_2)
% 176.26/27.33    (29)   ~ (all_52_5 = all_52_7)
% 176.26/27.33    (30)  all_58_10 = all_52_15
% 176.26/27.33    (31)  all_8_2 = all_6_2
% 176.26/27.33    (32)   ~ (all_52_5 = all_4_2)
% 176.26/27.33    (33)  all_58_7 = all_52_19
% 176.26/27.33    (34)  all_56_4 = all_52_9
% 176.26/27.33    (35)   ~ (all_52_17 = all_52_25)
% 176.26/27.33    (36)  op(e0, e1) = all_52_29
% 176.26/27.33    (37)   ~ (all_4_0 = e2)
% 176.26/27.33    (38)  all_58_4 = all_52_5
% 176.26/27.33    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.26/27.33    (40)   ~ (all_52_27 = all_52_29)
% 176.26/27.33    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.33    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.26/27.33    (43)   ~ (all_52_7 = all_4_2)
% 176.26/27.33    (44)  all_58_1 = all_52_3
% 176.26/27.33    (45)   ~ (all_52_13 = all_52_15)
% 176.26/27.33    (46)  all_58_0 = all_4_2
% 176.26/27.33    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.26/27.33    (48)  op(e1, all_52_29) = all_52_28
% 176.26/27.33    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.26/27.33    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.26/27.33    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.26/27.33    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.26/27.33    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.26/27.33    (54)  all_58_14 = all_52_29
% 176.26/27.33    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.26/27.33    (56)   ~ (all_52_3 = all_52_5)
% 176.26/27.33    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.26/27.33    (58)  op(e2, e1) = all_52_13
% 176.26/27.33    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.26/27.33    (60)  all_58_8 = all_14_2
% 176.26/27.33    (61)  all_56_1 = all_52_3
% 176.26/27.33    (62)  all_56_14 = all_52_29
% 176.26/27.33    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.26/27.33    (64)   ~ (all_52_5 = all_14_2)
% 176.26/27.33    (65)   ~ (all_52_3 = all_52_27)
% 176.26/27.33    (66)   ~ (all_52_3 = all_4_2)
% 176.26/27.33    (67)  op(e3, all_4_2) = e3
% 176.26/27.33    (68)  op(e0, e3) = all_52_25
% 176.26/27.33    (69)  op(e0, all_6_2) = all_6_1
% 176.26/27.33    (70)   ~ (all_52_9 = all_10_2)
% 176.26/27.33    (71)  op(all_6_1, all_6_2) = e2
% 176.26/27.33    (72)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.26/27.33    (73)   ~ (all_52_13 = all_14_2)
% 176.26/27.33    (74)   ~ (e3 = e0)
% 176.26/27.33    (75)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.26/27.33    (76)   ~ (all_52_9 = all_52_13)
% 176.26/27.33    (77)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.26/27.33    (78)  op(e0, all_52_23) = all_52_22
% 176.26/27.33    (79)   ~ (all_52_15 = all_52_23)
% 176.26/27.33    (80)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.26/27.33    (81)   ~ (all_52_5 = all_52_29)
% 176.26/27.33    (82)  all_56_2 = all_52_5
% 176.26/27.33    (83)  op(e1, e0) = all_52_23
% 176.26/27.33    (84)  all_56_12 = all_52_25
% 176.26/27.33    (85)  all_58_13 = all_52_27
% 176.26/27.33    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.26/27.33    (87)  all_56_5 = all_10_2
% 176.26/27.33    (88)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.26/27.33    (89)   ~ (all_52_9 = all_52_17)
% 176.26/27.33    (90)  all_58_6 = all_52_17
% 176.26/27.33    (91)   ~ (all_52_3 = all_52_7)
% 176.26/27.33    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.26/27.33    (93)   ~ (e1 = e0)
% 176.26/27.33    (94)  all_56_0 = all_4_2
% 176.26/27.33    (95)  all_58_11 = all_52_23
% 176.26/27.33    (96)   ~ (all_52_3 = all_52_19)
% 176.26/27.33    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.26/27.33    (98)   ~ (all_52_7 = all_52_15)
% 176.26/27.33    (99)   ~ (all_52_29 = all_14_2)
% 176.26/27.33    (100)   ~ (all_4_0 = e1)
% 176.26/27.33    (101)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.26/27.33    (102)   ~ (all_52_19 = all_10_2)
% 176.26/27.33    (103)   ~ (all_52_23 = all_6_2)
% 176.26/27.33    (104)   ~ (all_52_29 = all_6_2)
% 176.26/27.33    (105)  all_58_2 = all_52_9
% 176.26/27.33    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.26/27.33    (107)  op(e3, e1) = all_52_5
% 176.26/27.33    (108)  all_56_10 = all_14_2
% 176.26/27.33    (109)   ~ (all_52_25 = all_6_2)
% 176.26/27.33    (110)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.26/27.33    (111)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.26/27.33    (112)  op(e1, e1) = all_14_2
% 176.26/27.33    (113)  op(e1, e3) = all_52_17
% 176.26/27.33    (114)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.26/27.33    (115)   ~ (all_52_25 = all_4_2)
% 176.26/27.33    (116)  op(e3, e0) = all_52_7
% 176.26/27.33    (117)   ~ (all_52_17 = all_4_2)
% 176.26/27.33    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.33             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.33    (119)   ~ (all_52_25 = all_52_27)
% 176.26/27.33    (120)   ~ (all_52_27 = all_6_2)
% 176.26/27.33    (121)  all_8_1 = all_6_1
% 176.26/27.33    (122)   ~ (all_52_7 = all_6_2)
% 176.26/27.33    (123)   ~ (all_52_19 = all_52_27)
% 176.26/27.33    (124)  all_56_7 = all_52_15
% 176.26/27.33    (125)  op(e1, all_52_5) = e1
% 176.26/27.33    (126)   ~ (all_52_7 = all_52_23)
% 176.26/27.33    (127)   ~ (all_52_13 = all_10_2)
% 176.26/27.33    (128)  op(e3, all_4_2) = all_4_0
% 176.26/27.33    (129)  op(e0, all_52_7) = e0
% 176.26/27.33    (130)  op(e2, all_52_27) = all_52_26
% 176.26/27.33    (131)   ~ (all_52_17 = all_52_19)
% 176.26/27.33    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.26/27.33    (133)  all_58_9 = all_52_7
% 176.26/27.33    (134)  all_58_12 = all_52_25
% 176.26/27.33    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.26/27.33    (136)   ~ (all_52_9 = all_52_15)
% 176.26/27.33    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.26/27.33    (138)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.26/27.33    (139)   ~ (all_52_19 = all_14_2)
% 176.26/27.33    (140)  op(e2, e3) = all_52_9
% 176.26/27.33    (141)  all_56_13 = all_52_27
% 176.26/27.33  
% 176.26/27.33  Begin of proof
% 176.26/27.33  | 
% 176.26/27.33  | GROUND_INST: instantiating (118) with e3, all_4_0, all_4_2, e3, simplifying
% 176.26/27.33  |              with (67), (128) gives:
% 176.26/27.33  |   (142)  all_4_0 = e3
% 176.26/27.33  | 
% 176.26/27.33  | REDUCE: (37), (142) imply:
% 176.26/27.33  |   (143)   ~ (e3 = e2)
% 176.26/27.33  | 
% 176.26/27.33  | REDUCE: (100), (142) imply:
% 176.26/27.33  |   (144)   ~ (e3 = e1)
% 176.26/27.33  | 
% 176.26/27.33  | BETA: splitting (41) gives:
% 176.26/27.33  | 
% 176.26/27.33  | Case 1:
% 176.26/27.33  | | 
% 176.26/27.33  | |   (145)  all_56_15 = e3
% 176.26/27.33  | | 
% 176.26/27.33  | | COMBINE_EQS: (21), (145) imply:
% 176.26/27.33  | |   (146)  all_6_2 = e3
% 176.26/27.33  | | 
% 176.26/27.33  | | SIMP: (146) implies:
% 176.26/27.33  | |   (147)  all_6_2 = e3
% 176.26/27.33  | | 
% 176.26/27.33  | | REF_CLOSE: (9), (13), (20), (68), (69), (71), (77), (84), (101), (109),
% 176.26/27.33  | |            (111), (118), (134), (140), (147) are inconsistent by sub-proof
% 176.26/27.33  | |            #226.
% 176.26/27.33  | | 
% 176.26/27.33  | Case 2:
% 176.26/27.33  | | 
% 176.26/27.33  | |   (148)   ~ (all_56_15 = e3)
% 176.26/27.33  | |   (149)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.33  | | 
% 176.26/27.33  | | REDUCE: (21), (148) imply:
% 176.26/27.33  | |   (150)   ~ (all_6_2 = e3)
% 176.26/27.33  | | 
% 176.26/27.33  | | BETA: splitting (55) gives:
% 176.26/27.33  | | 
% 176.26/27.33  | | Case 1:
% 176.26/27.33  | | | 
% 176.26/27.33  | | |   (151)  all_56_13 = e3
% 176.26/27.33  | | | 
% 176.26/27.33  | | | COMBINE_EQS: (141), (151) imply:
% 176.26/27.33  | | |   (152)  all_52_27 = e3
% 176.26/27.33  | | | 
% 176.26/27.33  | | | SIMP: (152) implies:
% 176.26/27.33  | | |   (153)  all_52_27 = e3
% 176.26/27.33  | | | 
% 176.26/27.33  | | | REDUCE: (65), (153) imply:
% 176.26/27.33  | | |   (154)   ~ (all_52_3 = e3)
% 176.26/27.33  | | | 
% 176.26/27.33  | | | REDUCE: (123), (153) imply:
% 176.26/27.33  | | |   (155)   ~ (all_52_19 = e3)
% 176.26/27.33  | | | 
% 176.26/27.33  | | | REDUCE: (119), (153) imply:
% 176.26/27.33  | | |   (156)   ~ (all_52_25 = e3)
% 176.26/27.33  | | | 
% 176.26/27.33  | | | REDUCE: (40), (153) imply:
% 176.26/27.33  | | |   (157)   ~ (all_52_29 = e3)
% 176.26/27.33  | | | 
% 176.26/27.33  | | | SIMP: (157) implies:
% 176.26/27.33  | | |   (158)   ~ (all_52_29 = e3)
% 176.26/27.33  | | | 
% 176.26/27.33  | | | REDUCE: (120), (153) imply:
% 176.26/27.33  | | |   (159)   ~ (all_6_2 = e3)
% 176.26/27.33  | | | 
% 176.26/27.33  | | | REDUCE: (130), (153) imply:
% 176.26/27.33  | | |   (160)  op(e2, e3) = all_52_26
% 176.26/27.33  | | | 
% 176.26/27.34  | | | REF_CLOSE: (1), (4), (5), (8), (9), (12), (14), (17), (18), (19), (21),
% 176.26/27.34  | | |            (22), (23), (26), (27), (28), (29), (30), (32), (33), (34),
% 176.26/27.34  | | |            (35), (36), (38), (39), (43), (44), (45), (46), (47), (49),
% 176.26/27.34  | | |            (50), (51), (53), (54), (56), (57), (60), (61), (62), (64),
% 176.26/27.34  | | |            (67), (68), (72), (73), (74), (75), (76), (77), (80), (81),
% 176.26/27.34  | | |            (82), (83), (84), (86), (88), (89), (90), (91), (92), (93),
% 176.26/27.34  | | |            (94), (95), (96), (97), (98), (99), (103), (104), (105), (107),
% 176.26/27.34  | | |            (108), (109), (112), (113), (115), (116), (117), (118), (122),
% 176.26/27.34  | | |            (125), (126), (129), (131), (132), (133), (134), (135), (136),
% 176.26/27.34  | | |            (137), (138), (139), (140), (143), (144), (149), (150), (154),
% 176.26/27.34  | | |            (155), (156), (158), (160) are inconsistent by sub-proof #799.
% 176.26/27.34  | | | 
% 176.26/27.34  | | Case 2:
% 176.26/27.34  | | | 
% 176.26/27.34  | | |   (161)   ~ (all_56_13 = e3)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (141), (161) imply:
% 176.26/27.34  | | |   (162)   ~ (all_52_27 = e3)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | BETA: splitting (59) gives:
% 176.26/27.34  | | | 
% 176.26/27.34  | | | Case 1:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (163)  all_58_12 = e3
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | REF_CLOSE: (1), (2), (5), (8), (10), (11), (17), (19), (25), (26), (27),
% 176.26/27.34  | | | |            (28), (29), (30), (33), (35), (38), (39), (43), (44), (45),
% 176.26/27.34  | | | |            (46), (52), (54), (56), (60), (64), (67), (68), (74), (75),
% 176.26/27.34  | | | |            (79), (85), (86), (90), (91), (94), (95), (96), (98), (106),
% 176.26/27.34  | | | |            (107), (109), (113), (115), (116), (117), (118), (119),
% 176.26/27.34  | | | |            (122), (125), (126), (127), (129), (132), (133), (134),
% 176.26/27.34  | | | |            (135), (137), (140), (163) are inconsistent by sub-proof
% 176.26/27.34  | | | |            #797.
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | Case 2:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (164)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (12), (14), (15), (16), (17),
% 176.26/27.34  | | | |            (18), (21), (24), (25), (26), (27), (28), (29), (30), (31),
% 176.26/27.34  | | | |            (32), (33), (36), (38), (39), (42), (43), (44), (46), (47),
% 176.26/27.34  | | | |            (48), (51), (52), (54), (56), (57), (58), (60), (63), (64),
% 176.26/27.34  | | | |            (66), (67), (68), (69), (70), (74), (78), (79), (81), (82),
% 176.26/27.34  | | | |            (83), (85), (86), (87), (90), (91), (94), (95), (97), (98),
% 176.26/27.34  | | | |            (99), (102), (104), (105), (107), (110), (112), (113), (114),
% 176.26/27.34  | | | |            (115), (117), (118), (121), (122), (124), (125), (126),
% 176.26/27.34  | | | |            (129), (132), (133), (134), (135), (138), (140), (143),
% 176.26/27.34  | | | |            (144), (149), (150), (162), (164) are inconsistent by
% 176.26/27.34  | | | |            sub-proof #222.
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | End of split
% 176.26/27.34  | | | 
% 176.26/27.34  | | End of split
% 176.26/27.34  | | 
% 176.26/27.34  | End of split
% 176.26/27.34  | 
% 176.26/27.34  End of proof
% 176.26/27.34  
% 176.26/27.34  Sub-proof #222 shows that the following formulas are inconsistent:
% 176.26/27.34  ----------------------------------------------------------------
% 176.26/27.34    (1)   ~ (all_52_5 = all_52_13)
% 176.26/27.34    (2)   ~ (all_52_27 = all_10_2)
% 176.26/27.34    (3)  op(e2, all_52_3) = e2
% 176.26/27.34    (4)   ~ (all_52_13 = all_52_29)
% 176.26/27.34    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.26/27.34    (6)  op(e3, e2) = all_52_3
% 176.26/27.34    (7)  op(e1, e2) = all_52_19
% 176.26/27.34    (8)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.26/27.34    (9)   ~ (all_52_27 = e3)
% 176.26/27.34    (10)   ~ (all_6_2 = e3)
% 176.26/27.34    (11)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.26/27.34    (12)   ~ (all_52_3 = all_10_2)
% 176.26/27.34    (13)  all_58_5 = all_52_13
% 176.26/27.34    (14)   ~ (all_6_2 = e0)
% 176.26/27.34    (15)  all_56_15 = all_6_2
% 176.26/27.34    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.26/27.34    (17)  all_58_3 = all_10_2
% 176.26/27.34    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.26/27.34    (19)  all_58_15 = all_6_2
% 176.26/27.34    (20)   ~ (all_52_9 = all_4_2)
% 176.26/27.34    (21)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.34    (22)   ~ (all_52_5 = all_52_7)
% 176.26/27.34    (23)  all_58_10 = all_52_15
% 176.26/27.34    (24)  all_8_2 = all_6_2
% 176.26/27.34    (25)   ~ (all_52_5 = all_4_2)
% 176.26/27.34    (26)  all_58_7 = all_52_19
% 176.26/27.34    (27)  op(e0, e1) = all_52_29
% 176.26/27.34    (28)  all_58_4 = all_52_5
% 176.26/27.34    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.26/27.34    (30)   ~ (e3 = e1)
% 176.26/27.34    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.26/27.34    (32)   ~ (all_52_7 = all_4_2)
% 176.26/27.34    (33)  all_58_1 = all_52_3
% 176.26/27.34    (34)  all_58_0 = all_4_2
% 176.26/27.34    (35)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.26/27.34    (36)  op(e1, all_52_29) = all_52_28
% 176.26/27.34    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.26/27.34    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.26/27.34    (39)  all_58_14 = all_52_29
% 176.26/27.34    (40)   ~ (all_52_3 = all_52_5)
% 176.26/27.34    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.26/27.34    (42)  op(e2, e1) = all_52_13
% 176.26/27.34    (43)  all_58_8 = all_14_2
% 176.26/27.34    (44)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.26/27.34    (45)   ~ (all_52_5 = all_14_2)
% 176.26/27.34    (46)   ~ (all_52_3 = all_4_2)
% 176.26/27.34    (47)  op(e3, all_4_2) = e3
% 176.26/27.34    (48)  op(e0, e3) = all_52_25
% 176.26/27.34    (49)  op(e0, all_6_2) = all_6_1
% 176.26/27.34    (50)   ~ (all_52_9 = all_10_2)
% 176.26/27.34    (51)   ~ (e3 = e0)
% 176.26/27.34    (52)  op(e0, all_52_23) = all_52_22
% 176.26/27.34    (53)   ~ (all_52_15 = all_52_23)
% 176.26/27.34    (54)   ~ (all_52_5 = all_52_29)
% 176.26/27.34    (55)  all_56_2 = all_52_5
% 176.26/27.34    (56)  op(e1, e0) = all_52_23
% 176.26/27.34    (57)  all_58_13 = all_52_27
% 176.26/27.34    (58)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.26/27.34    (59)  all_56_5 = all_10_2
% 176.26/27.34    (60)  all_58_6 = all_52_17
% 176.26/27.34    (61)   ~ (all_52_3 = all_52_7)
% 176.26/27.34    (62)  all_56_0 = all_4_2
% 176.26/27.34    (63)  all_58_11 = all_52_23
% 176.26/27.34    (64)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.26/27.34    (65)   ~ (all_52_7 = all_52_15)
% 176.26/27.34    (66)   ~ (all_52_29 = all_14_2)
% 176.26/27.34    (67)   ~ (all_52_19 = all_10_2)
% 176.26/27.34    (68)   ~ (all_52_29 = all_6_2)
% 176.26/27.34    (69)  all_58_2 = all_52_9
% 176.26/27.34    (70)  op(e3, e1) = all_52_5
% 176.26/27.34    (71)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.26/27.34    (72)  op(e1, e1) = all_14_2
% 176.26/27.34    (73)  op(e1, e3) = all_52_17
% 176.26/27.34    (74)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.26/27.34    (75)   ~ (all_52_25 = all_4_2)
% 176.26/27.34    (76)   ~ (all_52_17 = all_4_2)
% 176.26/27.34    (77)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.34    (78)  all_8_1 = all_6_1
% 176.26/27.34    (79)   ~ (all_52_7 = all_6_2)
% 176.26/27.34    (80)  all_56_7 = all_52_15
% 176.26/27.34    (81)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.26/27.34    (82)  op(e1, all_52_5) = e1
% 176.26/27.34    (83)   ~ (all_52_7 = all_52_23)
% 176.26/27.34    (84)  op(e0, all_52_7) = e0
% 176.26/27.34    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.26/27.34    (86)  all_58_9 = all_52_7
% 176.26/27.34    (87)  all_58_12 = all_52_25
% 176.26/27.34    (88)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.26/27.34    (89)   ~ (e3 = e2)
% 176.26/27.34    (90)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.26/27.34    (91)  op(e2, e3) = all_52_9
% 176.26/27.34  
% 176.26/27.34  Begin of proof
% 176.26/27.34  | 
% 176.26/27.34  | BETA: splitting (81) gives:
% 176.26/27.34  | 
% 176.26/27.34  | Case 1:
% 176.26/27.34  | | 
% 176.26/27.34  | |   (92)  all_58_13 = e3
% 176.26/27.34  | | 
% 176.26/27.34  | | REF_CLOSE: (9), (57), (92) are inconsistent by sub-proof #1026.
% 176.26/27.34  | | 
% 176.26/27.34  | Case 2:
% 176.26/27.34  | | 
% 176.26/27.34  | |   (93)  all_58_14 = e3 | all_58_15 = e3
% 176.26/27.34  | | 
% 176.26/27.34  | | BETA: splitting (93) gives:
% 176.26/27.34  | | 
% 176.26/27.34  | | Case 1:
% 176.26/27.34  | | | 
% 176.26/27.34  | | |   (94)  all_58_14 = e3
% 176.26/27.34  | | | 
% 176.26/27.34  | | | COMBINE_EQS: (39), (94) imply:
% 176.26/27.34  | | |   (95)  all_52_29 = e3
% 176.26/27.34  | | | 
% 176.26/27.34  | | | SIMP: (95) implies:
% 176.26/27.34  | | |   (96)  all_52_29 = e3
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (54), (96) imply:
% 176.26/27.34  | | |   (97)   ~ (all_52_5 = e3)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (4), (96) imply:
% 176.26/27.34  | | |   (98)   ~ (all_52_13 = e3)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (66), (96) imply:
% 176.26/27.34  | | |   (99)   ~ (all_14_2 = e3)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | SIMP: (99) implies:
% 176.26/27.34  | | |   (100)   ~ (all_14_2 = e3)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (68), (96) imply:
% 176.26/27.34  | | |   (101)   ~ (all_6_2 = e3)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (36), (96) imply:
% 176.26/27.34  | | |   (102)  op(e1, e3) = all_52_28
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (27), (96) imply:
% 176.26/27.34  | | |   (103)  op(e0, e1) = e3
% 176.26/27.34  | | | 
% 176.26/27.34  | | | GROUND_INST: instantiating (77) with all_52_17, all_52_28, e3, e1,
% 176.26/27.34  | | |              simplifying with (73), (102) gives:
% 176.26/27.34  | | |   (104)  all_52_17 = all_52_28
% 176.26/27.34  | | | 
% 176.26/27.34  | | | COMBINE_EQS: (60), (104) imply:
% 176.26/27.34  | | |   (105)  all_58_6 = all_52_28
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (76), (104) imply:
% 176.26/27.34  | | |   (106)   ~ (all_52_28 = all_4_2)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | BETA: splitting (90) gives:
% 176.26/27.34  | | | 
% 176.26/27.34  | | | Case 1:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (107)  all_56_2 = e3
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | REF_CLOSE: (55), (97), (107) are inconsistent by sub-proof #931.
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | Case 2:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (108)   ~ (all_56_2 = e3)
% 176.26/27.34  | | | |   (109)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | BETA: splitting (38) gives:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | Case 1:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | |   (110)  all_58_1 = e3
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | COMBINE_EQS: (33), (110) imply:
% 176.26/27.34  | | | | |   (111)  all_52_3 = e3
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (40), (111) imply:
% 176.26/27.34  | | | | |   (112)   ~ (all_52_5 = e3)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (12), (111) imply:
% 176.26/27.34  | | | | |   (113)   ~ (all_10_2 = e3)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | SIMP: (113) implies:
% 176.26/27.34  | | | | |   (114)   ~ (all_10_2 = e3)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (46), (111) imply:
% 176.26/27.34  | | | | |   (115)   ~ (all_4_2 = e3)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | SIMP: (115) implies:
% 176.26/27.34  | | | | |   (116)   ~ (all_4_2 = e3)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (3), (111) imply:
% 176.26/27.34  | | | | |   (117)  op(e2, e3) = e2
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | GROUND_INST: instantiating (77) with all_52_9, e2, e3, e2, simplifying
% 176.26/27.34  | | | | |              with (91), (117) gives:
% 176.26/27.34  | | | | |   (118)  all_52_9 = e2
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (50), (118) imply:
% 176.26/27.34  | | | | |   (119)   ~ (all_10_2 = e2)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | SIMP: (119) implies:
% 176.26/27.34  | | | | |   (120)   ~ (all_10_2 = e2)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (20), (118) imply:
% 176.26/27.34  | | | | |   (121)   ~ (all_4_2 = e2)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | SIMP: (121) implies:
% 176.26/27.34  | | | | |   (122)   ~ (all_4_2 = e2)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | BETA: splitting (71) gives:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | Case 1:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (123)  all_56_5 = e3
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REF_CLOSE: (59), (114), (123) are inconsistent by sub-proof #895.
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | Case 2:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (124)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REF_CLOSE: (2), (5), (7), (11), (14), (15), (18), (21), (24), (25),
% 176.26/27.34  | | | | | |            (28), (34), (44), (47), (49), (57), (58), (59), (62),
% 176.26/27.34  | | | | | |            (64), (67), (70), (75), (77), (78), (79), (82), (86),
% 176.26/27.34  | | | | | |            (87), (89), (94), (97), (103), (110), (114), (116),
% 176.26/27.34  | | | | | |            (120), (122), (124) are inconsistent by sub-proof #223.
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | End of split
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | Case 2:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | |   (125)   ~ (all_58_1 = e3)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (33), (125) imply:
% 176.26/27.34  | | | | |   (126)   ~ (all_52_3 = e3)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | BETA: splitting (88) gives:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | Case 1:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (127)  all_58_0 = e3
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | COMBINE_EQS: (34), (127) imply:
% 176.26/27.34  | | | | | |   (128)  all_4_2 = e3
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REDUCE: (106), (128) imply:
% 176.26/27.34  | | | | | |   (129)   ~ (all_52_28 = e3)
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (12), (13), (16), (17),
% 176.26/27.34  | | | | | |            (18), (19), (20), (22), (23), (26), (28), (29), (30),
% 176.26/27.34  | | | | | |            (31), (32), (33), (34), (35), (37), (38), (40), (41),
% 176.26/27.34  | | | | | |            (42), (43), (45), (46), (47), (48), (51), (52), (53),
% 176.26/27.34  | | | | | |            (55), (56), (58), (61), (62), (63), (64), (65), (69),
% 176.26/27.34  | | | | | |            (70), (72), (74), (75), (77), (79), (80), (82), (83),
% 176.26/27.34  | | | | | |            (84), (85), (86), (88), (89), (91), (97), (98), (100),
% 176.26/27.34  | | | | | |            (103), (105), (109), (129) are inconsistent by sub-proof
% 176.26/27.34  | | | | | |            #789.
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | Case 2:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (130)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REF_CLOSE: (6), (18), (19), (22), (23), (28), (32), (33), (34),
% 176.26/27.34  | | | | | |            (47), (48), (58), (61), (62), (63), (65), (70), (75),
% 176.26/27.34  | | | | | |            (77), (79), (83), (84), (85), (86), (97), (126), (130)
% 176.26/27.34  | | | | | |            are inconsistent by sub-proof #1013.
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | End of split
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | End of split
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | End of split
% 176.26/27.34  | | | 
% 176.26/27.34  | | Case 2:
% 176.26/27.34  | | | 
% 176.26/27.34  | | |   (131)  all_58_15 = e3
% 176.26/27.34  | | | 
% 176.26/27.34  | | | COMBINE_EQS: (19), (131) imply:
% 176.26/27.34  | | |   (132)  all_6_2 = e3
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (10), (132) imply:
% 176.26/27.34  | | |   (133)  $false
% 176.26/27.34  | | | 
% 176.26/27.34  | | | CLOSE: (133) is inconsistent.
% 176.26/27.34  | | | 
% 176.26/27.34  | | End of split
% 176.26/27.34  | | 
% 176.26/27.34  | End of split
% 176.26/27.34  | 
% 176.26/27.34  End of proof
% 176.26/27.34  
% 176.26/27.34  Sub-proof #223 shows that the following formulas are inconsistent:
% 176.26/27.34  ----------------------------------------------------------------
% 176.26/27.34    (1)   ~ (all_52_27 = all_10_2)
% 176.26/27.34    (2)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.26/27.34    (3)   ~ (all_4_2 = e2)
% 176.26/27.34    (4)  op(e1, e2) = all_52_19
% 176.26/27.34    (5)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.26/27.34    (6)   ~ (all_6_2 = e0)
% 176.26/27.34    (7)  all_56_15 = all_6_2
% 176.26/27.34    (8)   ~ (all_4_2 = e3)
% 176.26/27.34    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.26/27.34    (10)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.34    (11)  all_8_2 = all_6_2
% 176.26/27.34    (12)   ~ (all_52_5 = all_4_2)
% 176.26/27.34    (13)  all_58_4 = all_52_5
% 176.26/27.34    (14)  all_58_0 = all_4_2
% 176.26/27.34    (15)   ~ (all_10_2 = e3)
% 176.26/27.34    (16)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.26/27.34    (17)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.26/27.34    (18)  op(e3, all_4_2) = e3
% 176.26/27.34    (19)  op(e0, all_6_2) = all_6_1
% 176.26/27.34    (20)   ~ (all_52_5 = e3)
% 176.26/27.34    (21)  all_58_13 = all_52_27
% 176.26/27.34    (22)  all_58_1 = e3
% 176.26/27.34    (23)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.26/27.34    (24)  all_56_5 = all_10_2
% 176.26/27.34    (25)  all_56_0 = all_4_2
% 176.26/27.34    (26)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.26/27.34    (27)   ~ (all_52_19 = all_10_2)
% 176.26/27.34    (28)  op(e3, e1) = all_52_5
% 176.26/27.34    (29)   ~ (all_10_2 = e2)
% 176.26/27.34    (30)   ~ (all_52_25 = all_4_2)
% 176.26/27.34    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.34    (32)  op(e0, e1) = e3
% 176.26/27.34    (33)  all_8_1 = all_6_1
% 176.26/27.34    (34)   ~ (all_52_7 = all_6_2)
% 176.26/27.34    (35)  all_58_14 = e3
% 176.26/27.34    (36)  op(e1, all_52_5) = e1
% 176.26/27.34    (37)  all_58_9 = all_52_7
% 176.26/27.34    (38)  all_58_12 = all_52_25
% 176.26/27.34    (39)   ~ (e3 = e2)
% 176.26/27.34  
% 176.26/27.34  Begin of proof
% 176.26/27.34  | 
% 176.26/27.34  | BETA: splitting (9) gives:
% 176.26/27.34  | 
% 176.26/27.34  | Case 1:
% 176.26/27.34  | | 
% 176.26/27.34  | |   (40)  all_56_0 = e3
% 176.26/27.34  | | 
% 176.26/27.34  | | REF_CLOSE: (8), (25), (40) are inconsistent by sub-proof #1024.
% 176.26/27.34  | | 
% 176.26/27.34  | Case 2:
% 176.26/27.34  | | 
% 176.26/27.34  | |   (41)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.26/27.34  | | 
% 176.26/27.34  | | BETA: splitting (26) gives:
% 176.26/27.34  | | 
% 176.26/27.34  | | Case 1:
% 176.26/27.34  | | | 
% 176.26/27.34  | | |   (42)  all_58_4 = e2
% 176.26/27.34  | | | 
% 176.26/27.34  | | | COMBINE_EQS: (13), (42) imply:
% 176.26/27.34  | | |   (43)  all_52_5 = e2
% 176.26/27.34  | | | 
% 176.26/27.34  | | | SIMP: (43) implies:
% 176.26/27.34  | | |   (44)  all_52_5 = e2
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (12), (44) imply:
% 176.26/27.34  | | |   (45)   ~ (all_4_2 = e2)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (36), (44) imply:
% 176.26/27.34  | | |   (46)  op(e1, e2) = e1
% 176.26/27.34  | | | 
% 176.26/27.34  | | | GROUND_INST: instantiating (31) with all_52_19, e1, e2, e1, simplifying
% 176.26/27.34  | | |              with (4), (46) gives:
% 176.26/27.34  | | |   (47)  all_52_19 = e1
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (27), (47) imply:
% 176.26/27.34  | | |   (48)   ~ (all_10_2 = e1)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | SIMP: (48) implies:
% 176.26/27.34  | | |   (49)   ~ (all_10_2 = e1)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | BETA: splitting (16) gives:
% 176.26/27.34  | | | 
% 176.26/27.34  | | | Case 1:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (50)  all_56_5 = e2
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | REF_CLOSE: (24), (29), (50) are inconsistent by sub-proof #710.
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | Case 2:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (51)  all_56_5 = e1 | all_56_5 = e0
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | BETA: splitting (51) gives:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | Case 1:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | |   (52)  all_56_5 = e1
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REF_CLOSE: (24), (49), (52) are inconsistent by sub-proof #709.
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | Case 2:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | |   (53)  all_56_5 = e0
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | COMBINE_EQS: (24), (53) imply:
% 176.26/27.34  | | | | |   (54)  all_10_2 = e0
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | SIMP: (54) implies:
% 176.26/27.34  | | | | |   (55)  all_10_2 = e0
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (1), (55) imply:
% 176.26/27.34  | | | | |   (56)   ~ (all_52_27 = e0)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (15), (55) imply:
% 176.26/27.34  | | | | |   (57)   ~ (e3 = e0)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | SIMP: (57) implies:
% 176.26/27.34  | | | | |   (58)   ~ (e3 = e0)
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | BETA: splitting (2) gives:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | Case 1:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (59)  all_58_12 = e0
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | COMBINE_EQS: (38), (59) imply:
% 176.26/27.34  | | | | | |   (60)  all_52_25 = e0
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | SIMP: (60) implies:
% 176.26/27.34  | | | | | |   (61)  all_52_25 = e0
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REDUCE: (30), (61) imply:
% 176.26/27.34  | | | | | |   (62)   ~ (all_4_2 = e0)
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | SIMP: (62) implies:
% 176.26/27.34  | | | | | |   (63)   ~ (all_4_2 = e0)
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | BETA: splitting (23) gives:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | Case 1:
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | |   (64)  all_58_0 = e1
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | | COMBINE_EQS: (14), (64) imply:
% 176.26/27.34  | | | | | | |   (65)  all_4_2 = e1
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | | REDUCE: (18), (65) imply:
% 176.26/27.34  | | | | | | |   (66)  op(e3, e1) = e3
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | | REF_CLOSE: (20), (28), (31), (66) are inconsistent by sub-proof
% 176.26/27.34  | | | | | | |            #1023.
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | Case 2:
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | |   (67)   ~ (all_58_0 = e1)
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | | REDUCE: (14), (67) imply:
% 176.26/27.34  | | | | | | |   (68)   ~ (all_4_2 = e1)
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | | REF_CLOSE: (3), (25), (41), (63), (68) are inconsistent by
% 176.26/27.34  | | | | | | |            sub-proof #882.
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | End of split
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | Case 2:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (69)  all_58_13 = e0 | all_58_14 = e0
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | BETA: splitting (69) gives:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | Case 1:
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | |   (70)  all_58_13 = e0
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | | REF_CLOSE: (21), (56), (70) are inconsistent by sub-proof #731.
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | Case 2:
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | |   (71)  all_58_14 = e0
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | | REF_CLOSE: (35), (58), (71) are inconsistent by sub-proof #643.
% 176.26/27.34  | | | | | | | 
% 176.26/27.34  | | | | | | End of split
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | End of split
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | End of split
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | End of split
% 176.26/27.34  | | | 
% 176.26/27.34  | | Case 2:
% 176.26/27.34  | | | 
% 176.26/27.34  | | |   (72)   ~ (all_58_4 = e2)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (13), (72) imply:
% 176.26/27.34  | | |   (73)   ~ (all_52_5 = e2)
% 176.26/27.34  | | | 
% 176.26/27.34  | | | BETA: splitting (17) gives:
% 176.26/27.34  | | | 
% 176.26/27.34  | | | Case 1:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (74)  all_58_0 = e2
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | COMBINE_EQS: (14), (74) imply:
% 176.26/27.34  | | | |   (75)  all_4_2 = e2
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | REDUCE: (3), (75) imply:
% 176.26/27.34  | | | |   (76)  $false
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | CLOSE: (76) is inconsistent.
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | Case 2:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | |   (77)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | BETA: splitting (77) gives:
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | | Case 1:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | |   (78)  all_58_1 = e2
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | COMBINE_EQS: (22), (78) imply:
% 176.26/27.34  | | | | |   (79)  e3 = e2
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | REDUCE: (39), (79) imply:
% 176.26/27.34  | | | | |   (80)  $false
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | CLOSE: (80) is inconsistent.
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | Case 2:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | |   (81)  all_58_4 = e2 | all_58_9 = e2
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | BETA: splitting (81) gives:
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | | Case 1:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (82)  all_58_4 = e2
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REF_CLOSE: (13), (73), (82) are inconsistent by sub-proof #675.
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | Case 2:
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | |   (83)  all_58_9 = e2
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | COMBINE_EQS: (37), (83) imply:
% 176.26/27.34  | | | | | |   (84)  all_52_7 = e2
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | SIMP: (84) implies:
% 176.26/27.34  | | | | | |   (85)  all_52_7 = e2
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REDUCE: (34), (85) imply:
% 176.26/27.34  | | | | | |   (86)   ~ (all_6_2 = e2)
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | | REF_CLOSE: (5), (6), (7), (10), (11), (19), (31), (32), (33), (86)
% 176.26/27.34  | | | | | |            are inconsistent by sub-proof #224.
% 176.26/27.34  | | | | | | 
% 176.26/27.34  | | | | | End of split
% 176.26/27.34  | | | | | 
% 176.26/27.34  | | | | End of split
% 176.26/27.34  | | | | 
% 176.26/27.34  | | | End of split
% 176.26/27.34  | | | 
% 176.26/27.34  | | End of split
% 176.26/27.34  | | 
% 176.26/27.34  | End of split
% 176.26/27.34  | 
% 176.26/27.34  End of proof
% 176.26/27.34  
% 176.26/27.34  Sub-proof #224 shows that the following formulas are inconsistent:
% 176.26/27.34  ----------------------------------------------------------------
% 176.26/27.34    (1)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.26/27.34    (2)   ~ (all_6_2 = e0)
% 176.26/27.34    (3)  all_56_15 = all_6_2
% 176.26/27.34    (4)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.34    (5)  all_8_2 = all_6_2
% 176.26/27.34    (6)   ~ (all_6_2 = e2)
% 176.26/27.34    (7)  op(e0, all_6_2) = all_6_1
% 176.26/27.34    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.34    (9)  op(e0, e1) = e3
% 176.26/27.34    (10)  all_8_1 = all_6_1
% 176.26/27.34  
% 176.26/27.34  Begin of proof
% 176.26/27.34  | 
% 176.26/27.34  | SIMP: (6) implies:
% 176.26/27.34  |   (11)   ~ (all_6_2 = e2)
% 176.26/27.34  | 
% 176.26/27.34  | BETA: splitting (4) gives:
% 176.26/27.34  | 
% 176.26/27.34  | Case 1:
% 176.26/27.34  | | 
% 176.26/27.34  | |   (12)  all_56_15 = e2
% 176.26/27.34  | | 
% 176.26/27.34  | | COMBINE_EQS: (3), (12) imply:
% 176.26/27.34  | |   (13)  all_6_2 = e2
% 176.26/27.34  | | 
% 176.26/27.34  | | REDUCE: (11), (13) imply:
% 176.26/27.34  | |   (14)  $false
% 176.26/27.34  | | 
% 176.26/27.34  | | CLOSE: (14) is inconsistent.
% 176.26/27.34  | | 
% 176.26/27.34  | Case 2:
% 176.26/27.34  | | 
% 176.26/27.34  | |   (15)  all_56_15 = e1 | all_56_15 = e0
% 176.26/27.34  | | 
% 176.26/27.34  | | BETA: splitting (15) gives:
% 176.26/27.34  | | 
% 176.26/27.34  | | Case 1:
% 176.26/27.34  | | | 
% 176.26/27.34  | | |   (16)  all_56_15 = e1
% 176.26/27.34  | | | 
% 176.26/27.34  | | | COMBINE_EQS: (3), (16) imply:
% 176.26/27.34  | | |   (17)  all_6_2 = e1
% 176.26/27.34  | | | 
% 176.26/27.34  | | | COMBINE_EQS: (5), (17) imply:
% 176.26/27.34  | | |   (18)  all_8_2 = e1
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (7), (17) imply:
% 176.26/27.34  | | |   (19)  op(e0, e1) = all_6_1
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REF_CLOSE: (1), (8), (9), (10), (18), (19) are inconsistent by sub-proof
% 176.26/27.34  | | |            #225.
% 176.26/27.34  | | | 
% 176.26/27.34  | | Case 2:
% 176.26/27.34  | | | 
% 176.26/27.34  | | |   (20)  all_56_15 = e0
% 176.26/27.34  | | | 
% 176.26/27.34  | | | COMBINE_EQS: (3), (20) imply:
% 176.26/27.34  | | |   (21)  all_6_2 = e0
% 176.26/27.34  | | | 
% 176.26/27.34  | | | REDUCE: (2), (21) imply:
% 176.26/27.34  | | |   (22)  $false
% 176.26/27.34  | | | 
% 176.26/27.34  | | | CLOSE: (22) is inconsistent.
% 176.26/27.34  | | | 
% 176.26/27.34  | | End of split
% 176.26/27.34  | | 
% 176.26/27.34  | End of split
% 176.26/27.34  | 
% 176.26/27.34  End of proof
% 176.26/27.34  
% 176.26/27.34  Sub-proof #225 shows that the following formulas are inconsistent:
% 176.26/27.34  ----------------------------------------------------------------
% 176.26/27.34    (1)   ~ (all_8_1 = e3) |  ~ (all_8_2 = e1)
% 176.26/27.34    (2)  all_8_2 = e1
% 176.26/27.34    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.34    (4)  op(e0, e1) = e3
% 176.26/27.34    (5)  all_8_1 = all_6_1
% 176.26/27.34    (6)  op(e0, e1) = all_6_1
% 176.26/27.34  
% 176.26/27.34  Begin of proof
% 176.26/27.34  | 
% 176.26/27.34  | BETA: splitting (1) gives:
% 176.26/27.34  | 
% 176.26/27.34  | Case 1:
% 176.26/27.34  | | 
% 176.26/27.34  | |   (7)   ~ (all_8_1 = e3)
% 176.26/27.34  | | 
% 176.26/27.35  | | REDUCE: (5), (7) imply:
% 176.26/27.35  | |   (8)   ~ (all_6_1 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | GROUND_INST: instantiating (3) with e3, all_6_1, e1, e0, simplifying with
% 176.26/27.35  | |              (4), (6) gives:
% 176.26/27.35  | |   (9)  all_6_1 = e3
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (8), (9) imply:
% 176.26/27.35  | |   (10)  $false
% 176.26/27.35  | | 
% 176.26/27.35  | | CLOSE: (10) is inconsistent.
% 176.26/27.35  | | 
% 176.26/27.35  | Case 2:
% 176.26/27.35  | | 
% 176.26/27.35  | |   (11)   ~ (all_8_2 = e1)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (2), (11) imply:
% 176.26/27.35  | |   (12)  $false
% 176.26/27.35  | | 
% 176.26/27.35  | | CLOSE: (12) is inconsistent.
% 176.26/27.35  | | 
% 176.26/27.35  | End of split
% 176.26/27.35  | 
% 176.26/27.35  End of proof
% 176.26/27.35  
% 176.26/27.35  Sub-proof #226 shows that the following formulas are inconsistent:
% 176.26/27.35  ----------------------------------------------------------------
% 176.26/27.35    (1)   ~ (all_52_9 = all_52_25)
% 176.26/27.35    (2)  all_16_1 = all_6_1
% 176.26/27.35    (3)  all_6_2 = e3
% 176.26/27.35    (4)  all_16_2 = all_6_2
% 176.26/27.35    (5)  op(e0, e3) = all_52_25
% 176.26/27.35    (6)  op(e0, all_6_2) = all_6_1
% 176.26/27.35    (7)  op(all_6_1, all_6_2) = e2
% 176.26/27.35    (8)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.26/27.35    (9)  all_56_12 = all_52_25
% 176.26/27.35    (10)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.26/27.35    (11)   ~ (all_52_25 = all_6_2)
% 176.26/27.35    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.26/27.35    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.35    (14)  all_58_12 = all_52_25
% 176.26/27.35    (15)  op(e2, e3) = all_52_9
% 176.26/27.35  
% 176.26/27.35  Begin of proof
% 176.26/27.35  | 
% 176.26/27.35  | COMBINE_EQS: (3), (4) imply:
% 176.26/27.35  |   (16)  all_16_2 = e3
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (3), (11) imply:
% 176.26/27.35  |   (17)   ~ (all_52_25 = e3)
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (3), (7) imply:
% 176.26/27.35  |   (18)  op(all_6_1, e3) = e2
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (3), (6) imply:
% 176.26/27.35  |   (19)  op(e0, e3) = all_6_1
% 176.26/27.35  | 
% 176.26/27.35  | REF_CLOSE: (1), (2), (5), (8), (9), (10), (12), (13), (14), (15), (16), (17),
% 176.26/27.35  |            (18), (19) are inconsistent by sub-proof #227.
% 176.26/27.35  | 
% 176.26/27.35  End of proof
% 176.26/27.35  
% 176.26/27.35  Sub-proof #227 shows that the following formulas are inconsistent:
% 176.26/27.35  ----------------------------------------------------------------
% 176.26/27.35    (1)   ~ (all_52_25 = e3)
% 176.26/27.35    (2)   ~ (all_52_9 = all_52_25)
% 176.26/27.35    (3)  all_16_1 = all_6_1
% 176.26/27.35    (4)  all_16_2 = e3
% 176.26/27.35    (5)  op(all_6_1, e3) = e2
% 176.26/27.35    (6)  op(e0, e3) = all_52_25
% 176.26/27.35    (7)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.26/27.35    (8)  all_56_12 = all_52_25
% 176.26/27.35    (9)   ~ (all_16_1 = e1) |  ~ (all_16_2 = e3)
% 176.26/27.35    (10)  op(e0, e3) = all_6_1
% 176.26/27.35    (11)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.26/27.35    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.35    (13)  all_58_12 = all_52_25
% 176.26/27.35    (14)  op(e2, e3) = all_52_9
% 176.26/27.35  
% 176.26/27.35  Begin of proof
% 176.26/27.35  | 
% 176.26/27.35  | BETA: splitting (9) gives:
% 176.26/27.35  | 
% 176.26/27.35  | Case 1:
% 176.26/27.35  | | 
% 176.26/27.35  | |   (15)   ~ (all_16_1 = e1)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (3), (15) imply:
% 176.26/27.35  | |   (16)   ~ (all_6_1 = e1)
% 176.26/27.35  | | 
% 176.26/27.35  | | GROUND_INST: instantiating (12) with all_52_25, all_6_1, e3, e0, simplifying
% 176.26/27.35  | |              with (6), (10) gives:
% 176.26/27.35  | |   (17)  all_52_25 = all_6_1
% 176.26/27.35  | | 
% 176.26/27.35  | | COMBINE_EQS: (8), (17) imply:
% 176.26/27.35  | |   (18)  all_56_12 = all_6_1
% 176.26/27.35  | | 
% 176.26/27.35  | | COMBINE_EQS: (13), (17) imply:
% 176.26/27.35  | |   (19)  all_58_12 = all_6_1
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (2), (17) imply:
% 176.26/27.35  | |   (20)   ~ (all_52_9 = all_6_1)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (1), (17) imply:
% 176.26/27.35  | |   (21)   ~ (all_6_1 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | BETA: splitting (7) gives:
% 176.26/27.35  | | 
% 176.26/27.35  | | Case 1:
% 176.26/27.35  | | | 
% 176.26/27.35  | | |   (22)  all_56_12 = e3
% 176.26/27.35  | | | 
% 176.26/27.35  | | | REF_CLOSE: (18), (21), (22) are inconsistent by sub-proof #509.
% 176.26/27.35  | | | 
% 176.26/27.35  | | Case 2:
% 176.26/27.35  | | | 
% 176.26/27.35  | | |   (23)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.26/27.35  | | | 
% 176.26/27.35  | | | BETA: splitting (11) gives:
% 176.26/27.35  | | | 
% 176.26/27.35  | | | Case 1:
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | |   (24)  all_58_12 = e2
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | COMBINE_EQS: (19), (24) imply:
% 176.26/27.35  | | | |   (25)  all_6_1 = e2
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | SIMP: (25) implies:
% 176.26/27.35  | | | |   (26)  all_6_1 = e2
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | REDUCE: (20), (26) imply:
% 176.26/27.35  | | | |   (27)   ~ (all_52_9 = e2)
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | REDUCE: (5), (26) imply:
% 176.26/27.35  | | | |   (28)  op(e2, e3) = e2
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | GROUND_INST: instantiating (12) with all_52_9, e2, e3, e2, simplifying
% 176.26/27.35  | | | |              with (14), (28) gives:
% 176.26/27.35  | | | |   (29)  all_52_9 = e2
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | REDUCE: (27), (29) imply:
% 176.26/27.35  | | | |   (30)  $false
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | CLOSE: (30) is inconsistent.
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | Case 2:
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | |   (31)   ~ (all_58_12 = e2)
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | REDUCE: (19), (31) imply:
% 176.26/27.35  | | | |   (32)   ~ (all_6_1 = e2)
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | BETA: splitting (23) gives:
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | Case 1:
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | |   (33)  all_56_12 = e2
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | | REF_CLOSE: (18), (32), (33) are inconsistent by sub-proof #507.
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | Case 2:
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | |   (34)   ~ (all_56_12 = e2)
% 176.26/27.35  | | | | |   (35)  all_56_12 = e1 | all_56_12 = e0
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | | BETA: splitting (35) gives:
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | | Case 1:
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | |   (36)  all_56_12 = e1
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | REF_CLOSE: (16), (18), (36) are inconsistent by sub-proof #506.
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | Case 2:
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | |   (37)  all_56_12 = e0
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | COMBINE_EQS: (18), (37) imply:
% 176.26/27.35  | | | | | |   (38)  all_6_1 = e0
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | SIMP: (38) implies:
% 176.26/27.35  | | | | | |   (39)  all_6_1 = e0
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | REDUCE: (32), (39) imply:
% 176.26/27.35  | | | | | |   (40)   ~ (e2 = e0)
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | SIMP: (40) implies:
% 176.26/27.35  | | | | | |   (41)   ~ (e2 = e0)
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | REDUCE: (5), (39) imply:
% 176.26/27.35  | | | | | |   (42)  op(e0, e3) = e2
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | REDUCE: (10), (39) imply:
% 176.26/27.35  | | | | | |   (43)  op(e0, e3) = e0
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | GROUND_INST: instantiating (12) with e0, e2, e3, e0, simplifying
% 176.26/27.35  | | | | | |              with (42), (43) gives:
% 176.26/27.35  | | | | | |   (44)  e2 = e0
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | REDUCE: (41), (44) imply:
% 176.26/27.35  | | | | | |   (45)  $false
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | CLOSE: (45) is inconsistent.
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | End of split
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | End of split
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | End of split
% 176.26/27.35  | | | 
% 176.26/27.35  | | End of split
% 176.26/27.35  | | 
% 176.26/27.35  | Case 2:
% 176.26/27.35  | | 
% 176.26/27.35  | |   (46)   ~ (all_16_2 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (4), (46) imply:
% 176.26/27.35  | |   (47)  $false
% 176.26/27.35  | | 
% 176.26/27.35  | | CLOSE: (47) is inconsistent.
% 176.26/27.35  | | 
% 176.26/27.35  | End of split
% 176.26/27.35  | 
% 176.26/27.35  End of proof
% 176.26/27.35  
% 176.26/27.35  Sub-proof #228 shows that the following formulas are inconsistent:
% 176.26/27.35  ----------------------------------------------------------------
% 176.26/27.35    (1)  all_58_15 = all_6_2
% 176.26/27.35    (2)  op(e0, e0) = all_6_2
% 176.26/27.35    (3)  op(e0, all_6_2) = all_6_1
% 176.26/27.35    (4)  op(all_6_1, all_6_2) = e2
% 176.26/27.35    (5)  all_58_15 = e0
% 176.26/27.35    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.35    (7)   ~ (e2 = e0)
% 176.26/27.35  
% 176.26/27.35  Begin of proof
% 176.26/27.35  | 
% 176.26/27.35  | COMBINE_EQS: (1), (5) imply:
% 176.26/27.35  |   (8)  all_6_2 = e0
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (4), (8) imply:
% 176.26/27.35  |   (9)  op(all_6_1, e0) = e2
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (3), (8) imply:
% 176.26/27.35  |   (10)  op(e0, e0) = all_6_1
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (2), (8) imply:
% 176.26/27.35  |   (11)  op(e0, e0) = e0
% 176.26/27.35  | 
% 176.26/27.35  | REF_CLOSE: (6), (7), (9), (10), (11) are inconsistent by sub-proof #229.
% 176.26/27.35  | 
% 176.26/27.35  End of proof
% 176.26/27.35  
% 176.26/27.35  Sub-proof #229 shows that the following formulas are inconsistent:
% 176.26/27.35  ----------------------------------------------------------------
% 176.26/27.35    (1)  op(e0, e0) = all_6_1
% 176.26/27.35    (2)  op(e0, e0) = e0
% 176.26/27.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.35    (4)   ~ (e2 = e0)
% 176.26/27.35    (5)  op(all_6_1, e0) = e2
% 176.26/27.35  
% 176.26/27.35  Begin of proof
% 176.26/27.35  | 
% 176.26/27.35  | GROUND_INST: instantiating (3) with e0, all_6_1, e0, e0, simplifying with (1),
% 176.26/27.35  |              (2) gives:
% 176.26/27.35  |   (6)  all_6_1 = e0
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (5), (6) imply:
% 176.26/27.35  |   (7)  op(e0, e0) = e2
% 176.26/27.35  | 
% 176.26/27.35  | GROUND_INST: instantiating (3) with e0, e2, e0, e0, simplifying with (2), (7)
% 176.26/27.35  |              gives:
% 176.26/27.35  |   (8)  e2 = e0
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (4), (8) imply:
% 176.26/27.35  |   (9)  $false
% 176.26/27.35  | 
% 176.26/27.35  | CLOSE: (9) is inconsistent.
% 176.26/27.35  | 
% 176.26/27.35  End of proof
% 176.26/27.35  
% 176.26/27.35  Sub-proof #230 shows that the following formulas are inconsistent:
% 176.26/27.35  ----------------------------------------------------------------
% 176.26/27.35    (1)   ~ (all_52_23 = all_14_2)
% 176.26/27.35    (2)   ~ (all_52_5 = all_52_13)
% 176.26/27.35    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.26/27.35    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.26/27.35    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.26/27.35    (6)   ~ (all_52_27 = all_10_2)
% 176.26/27.35    (7)  op(e2, e2) = all_10_2
% 176.26/27.35    (8)   ~ (all_52_17 = all_52_23)
% 176.26/27.35    (9)  op(e2, all_52_3) = e2
% 176.26/27.35    (10)  op(e2, all_10_2) = all_10_1
% 176.26/27.35    (11)   ~ (all_52_13 = all_52_29)
% 176.26/27.35    (12)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.26/27.35    (13)  all_56_3 = all_52_7
% 176.26/27.35    (14)  op(e3, e2) = all_52_3
% 176.26/27.35    (15)   ~ (all_52_9 = all_52_25)
% 176.26/27.35    (16)  op(e3, all_52_25) = all_52_24
% 176.26/27.35    (17)   ~ (all_52_19 = all_52_23)
% 176.26/27.35    (18)  all_56_11 = all_52_23
% 176.26/27.35    (19)  op(e1, e2) = all_52_19
% 176.26/27.35    (20)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.26/27.35    (21)  op(e3, all_52_9) = all_52_8
% 176.26/27.35    (22)   ~ (all_52_3 = all_10_2)
% 176.26/27.35    (23)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.26/27.35    (24)  all_58_5 = all_52_13
% 176.26/27.35    (25)   ~ (all_6_2 = e0)
% 176.26/27.35    (26)   ~ (all_52_25 = all_52_29)
% 176.26/27.35    (27)  all_56_15 = all_6_2
% 176.26/27.35    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.26/27.35    (29)  op(e2, e0) = all_52_15
% 176.26/27.35    (30)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.26/27.35    (31)  all_58_3 = all_10_2
% 176.26/27.35    (32)  all_56_9 = all_52_19
% 176.26/27.35    (33)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.26/27.35    (34)  all_58_15 = all_6_2
% 176.26/27.35    (35)   ~ (all_52_9 = all_4_2)
% 176.26/27.35    (36)   ~ (all_52_5 = all_52_7)
% 176.26/27.35    (37)  all_58_10 = all_52_15
% 176.26/27.35    (38)   ~ (all_52_5 = all_4_2)
% 176.26/27.35    (39)  all_58_7 = all_52_19
% 176.26/27.35    (40)  all_56_4 = all_52_9
% 176.26/27.35    (41)   ~ (all_52_15 = all_6_2)
% 176.26/27.35    (42)   ~ (all_52_17 = all_52_25)
% 176.26/27.35    (43)  op(e0, e1) = all_52_29
% 176.26/27.35    (44)   ~ (all_4_0 = e2)
% 176.26/27.35    (45)  all_58_4 = all_52_5
% 176.26/27.35    (46)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.26/27.35    (47)   ~ (all_52_27 = all_52_29)
% 176.26/27.35    (48)   ~ (all_52_17 = all_14_2)
% 176.26/27.35    (49)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.35    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.26/27.35    (51)   ~ (all_52_7 = all_4_2)
% 176.26/27.35    (52)  all_58_1 = all_52_3
% 176.26/27.35    (53)   ~ (all_52_13 = all_52_15)
% 176.26/27.35    (54)  all_58_0 = all_4_2
% 176.26/27.35    (55)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.26/27.35    (56)  op(e1, all_52_29) = all_52_28
% 176.26/27.35    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.26/27.35    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.26/27.35    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.26/27.35    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.26/27.35    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.26/27.35    (62)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.26/27.35    (63)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.26/27.35    (64)  all_58_14 = all_52_29
% 176.26/27.35    (65)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.26/27.35    (66)   ~ (all_52_3 = all_52_5)
% 176.26/27.35    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.26/27.35    (68)  op(e2, e1) = all_52_13
% 176.26/27.35    (69)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.26/27.35    (70)  all_58_8 = all_14_2
% 176.26/27.35    (71)  all_56_1 = all_52_3
% 176.26/27.35    (72)  op(e0, e2) = all_52_27
% 176.26/27.35    (73)  all_56_14 = all_52_29
% 176.26/27.35    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.26/27.35    (75)   ~ (all_52_5 = all_14_2)
% 176.26/27.35    (76)   ~ (all_52_3 = all_52_27)
% 176.26/27.35    (77)   ~ (all_52_3 = all_4_2)
% 176.26/27.35    (78)  op(all_6_1, all_6_2) = all_6_0
% 176.26/27.35    (79)  op(e3, all_4_2) = e3
% 176.26/27.35    (80)  op(e0, e3) = all_52_25
% 176.26/27.35    (81)  op(e0, all_6_2) = all_6_1
% 176.26/27.35    (82)   ~ (all_52_9 = all_10_2)
% 176.26/27.35    (83)  op(e3, all_52_17) = all_52_16
% 176.26/27.35    (84)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.26/27.35    (85)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.26/27.35    (86)   ~ (all_52_13 = all_14_2)
% 176.26/27.35    (87)   ~ (e3 = e0)
% 176.26/27.35    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.26/27.35    (89)  op(all_14_1, all_14_2) = e2
% 176.26/27.35    (90)   ~ (all_52_9 = all_52_13)
% 176.26/27.35    (91)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.26/27.35    (92)  op(e0, all_52_23) = all_52_22
% 176.26/27.35    (93)   ~ (all_52_15 = all_52_23)
% 176.26/27.35    (94)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.26/27.35    (95)   ~ (all_52_5 = all_52_29)
% 176.26/27.35    (96)  all_56_2 = all_52_5
% 176.26/27.35    (97)  op(e1, e0) = all_52_23
% 176.26/27.35    (98)  all_56_12 = all_52_25
% 176.26/27.35    (99)  all_58_13 = all_52_27
% 176.26/27.35    (100)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.26/27.35    (101)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.26/27.35    (102)   ~ (all_52_9 = all_52_17)
% 176.26/27.35    (103)  all_58_6 = all_52_17
% 176.26/27.35    (104)   ~ (all_52_3 = all_52_7)
% 176.26/27.35    (105)  op(all_10_1, all_10_2) = e3
% 176.26/27.35    (106)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.26/27.35    (107)  op(e2, all_52_19) = all_52_18
% 176.26/27.35    (108)   ~ (e1 = e0)
% 176.26/27.35    (109)  all_56_0 = all_4_2
% 176.26/27.35    (110)  all_58_11 = all_52_23
% 176.26/27.35    (111)   ~ (all_52_3 = all_52_19)
% 176.26/27.35    (112)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.26/27.35    (113)   ~ (all_52_7 = all_52_15)
% 176.26/27.35    (114)  op(e0, all_52_15) = all_52_14
% 176.26/27.35    (115)   ~ (all_52_29 = all_14_2)
% 176.26/27.35    (116)   ~ (all_4_0 = e1)
% 176.26/27.35    (117)   ~ (all_52_19 = all_10_2)
% 176.26/27.35    (118)   ~ (all_52_23 = all_6_2)
% 176.26/27.35    (119)   ~ (all_6_0 = e2)
% 176.26/27.35    (120)   ~ (all_52_29 = all_6_2)
% 176.26/27.35    (121)  all_58_2 = all_52_9
% 176.26/27.35    (122)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.26/27.35    (123)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.26/27.35    (124)  op(e3, e1) = all_52_5
% 176.26/27.35    (125)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.26/27.35    (126)   ~ (e2 = e1)
% 176.26/27.35    (127)  all_56_10 = all_14_2
% 176.26/27.35    (128)   ~ (all_52_25 = all_6_2)
% 176.26/27.35    (129)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.26/27.35    (130)  op(e1, e1) = all_14_2
% 176.26/27.35    (131)  op(e1, e3) = all_52_17
% 176.26/27.35    (132)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.26/27.35    (133)   ~ (all_52_25 = all_4_2)
% 176.26/27.35    (134)  op(e3, e0) = all_52_7
% 176.26/27.35    (135)  all_56_8 = all_52_17
% 176.26/27.35    (136)   ~ (all_52_17 = all_4_2)
% 176.26/27.35    (137)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.26/27.35             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.26/27.35    (138)   ~ (all_52_25 = all_52_27)
% 176.26/27.35    (139)   ~ (all_52_27 = all_6_2)
% 176.26/27.35    (140)   ~ (all_52_7 = all_6_2)
% 176.26/27.35    (141)   ~ (all_52_19 = all_52_27)
% 176.26/27.35    (142)  all_56_7 = all_52_15
% 176.26/27.35    (143)   ~ (all_14_1 = e0) |  ~ (all_14_2 = e3)
% 176.26/27.35    (144)  op(e1, all_52_5) = e1
% 176.26/27.35    (145)   ~ (all_52_7 = all_52_23)
% 176.26/27.35    (146)   ~ (all_52_13 = all_10_2)
% 176.26/27.35    (147)   ~ (all_6_0 = e1)
% 176.26/27.35    (148)  op(e3, all_4_2) = all_4_0
% 176.26/27.35    (149)  op(e0, all_52_7) = e0
% 176.26/27.35    (150)  op(e2, all_52_27) = all_52_26
% 176.26/27.35    (151)   ~ (all_52_17 = all_52_19)
% 176.26/27.35    (152)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.26/27.35    (153)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.26/27.35    (154)  op(e1, all_14_2) = all_14_1
% 176.26/27.35    (155)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.26/27.35    (156)  all_58_9 = all_52_7
% 176.26/27.35    (157)  all_58_12 = all_52_25
% 176.26/27.35    (158)  all_56_6 = all_52_13
% 176.26/27.35    (159)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.26/27.35    (160)   ~ (all_52_9 = all_52_15)
% 176.26/27.35    (161)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.26/27.35    (162)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.26/27.35    (163)   ~ (all_52_19 = all_14_2)
% 176.26/27.35    (164)  op(e2, e3) = all_52_9
% 176.26/27.35    (165)  all_56_13 = all_52_27
% 176.26/27.35  
% 176.26/27.35  Begin of proof
% 176.26/27.35  | 
% 176.26/27.35  | GROUND_INST: instantiating (137) with e3, all_4_0, all_4_2, e3, simplifying
% 176.26/27.35  |              with (79), (148) gives:
% 176.26/27.35  |   (166)  all_4_0 = e3
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (44), (166) imply:
% 176.26/27.35  |   (167)   ~ (e3 = e2)
% 176.26/27.35  | 
% 176.26/27.35  | REDUCE: (116), (166) imply:
% 176.26/27.35  |   (168)   ~ (e3 = e1)
% 176.26/27.35  | 
% 176.26/27.35  | BETA: splitting (49) gives:
% 176.26/27.35  | 
% 176.26/27.35  | Case 1:
% 176.26/27.35  | | 
% 176.26/27.35  | |   (169)  all_56_15 = e3
% 176.26/27.35  | | 
% 176.26/27.35  | | COMBINE_EQS: (27), (169) imply:
% 176.26/27.35  | |   (170)  all_6_2 = e3
% 176.26/27.35  | | 
% 176.26/27.35  | | SIMP: (170) implies:
% 176.26/27.35  | |   (171)  all_6_2 = e3
% 176.26/27.35  | | 
% 176.26/27.35  | | COMBINE_EQS: (34), (171) imply:
% 176.26/27.35  | |   (172)  all_58_15 = e3
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (140), (171) imply:
% 176.26/27.35  | |   (173)   ~ (all_52_7 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (118), (171) imply:
% 176.26/27.35  | |   (174)   ~ (all_52_23 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (128), (171) imply:
% 176.26/27.35  | |   (175)   ~ (all_52_25 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (139), (171) imply:
% 176.26/27.35  | |   (176)   ~ (all_52_27 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (120), (171) imply:
% 176.26/27.35  | |   (177)   ~ (all_52_29 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (78), (171) imply:
% 176.26/27.35  | |   (178)  op(all_6_1, e3) = all_6_0
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (81), (171) imply:
% 176.26/27.35  | |   (179)  op(e0, e3) = all_6_1
% 176.26/27.35  | | 
% 176.26/27.35  | | GROUND_INST: instantiating (137) with all_52_25, all_6_1, e3, e0,
% 176.26/27.35  | |              simplifying with (80), (179) gives:
% 176.26/27.35  | |   (180)  all_52_25 = all_6_1
% 176.26/27.35  | | 
% 176.26/27.35  | | COMBINE_EQS: (98), (180) imply:
% 176.26/27.35  | |   (181)  all_56_12 = all_6_1
% 176.26/27.35  | | 
% 176.26/27.35  | | COMBINE_EQS: (157), (180) imply:
% 176.26/27.35  | |   (182)  all_58_12 = all_6_1
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (15), (180) imply:
% 176.26/27.35  | |   (183)   ~ (all_52_9 = all_6_1)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (42), (180) imply:
% 176.26/27.35  | |   (184)   ~ (all_52_17 = all_6_1)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (138), (180) imply:
% 176.26/27.35  | |   (185)   ~ (all_52_27 = all_6_1)
% 176.26/27.35  | | 
% 176.26/27.35  | | SIMP: (185) implies:
% 176.26/27.35  | |   (186)   ~ (all_52_27 = all_6_1)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (26), (180) imply:
% 176.26/27.35  | |   (187)   ~ (all_52_29 = all_6_1)
% 176.26/27.35  | | 
% 176.26/27.35  | | SIMP: (187) implies:
% 176.26/27.35  | |   (188)   ~ (all_52_29 = all_6_1)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (133), (180) imply:
% 176.26/27.35  | |   (189)   ~ (all_6_1 = all_4_2)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (175), (180) imply:
% 176.26/27.35  | |   (190)   ~ (all_6_1 = e3)
% 176.26/27.35  | | 
% 176.26/27.35  | | REDUCE: (16), (180) imply:
% 176.26/27.35  | |   (191)  op(e3, all_6_1) = all_52_24
% 176.26/27.35  | | 
% 176.26/27.35  | | BETA: splitting (65) gives:
% 176.26/27.35  | | 
% 176.26/27.35  | | Case 1:
% 176.26/27.35  | | | 
% 176.26/27.35  | | |   (192)  all_56_13 = e3
% 176.26/27.35  | | | 
% 176.26/27.35  | | | REF_CLOSE: (165), (176), (192) are inconsistent by sub-proof #876.
% 176.26/27.35  | | | 
% 176.26/27.35  | | Case 2:
% 176.26/27.35  | | | 
% 176.26/27.35  | | |   (193)   ~ (all_56_13 = e3)
% 176.26/27.35  | | |   (194)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.26/27.35  | | | 
% 176.26/27.35  | | | BETA: splitting (153) gives:
% 176.26/27.35  | | | 
% 176.26/27.35  | | | Case 1:
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | |   (195)  all_56_3 = e3
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | REF_CLOSE: (13), (173), (195) are inconsistent by sub-proof #1034.
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | Case 2:
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | |   (196)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | BETA: splitting (91) gives:
% 176.26/27.35  | | | | 
% 176.26/27.35  | | | | Case 1:
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | |   (197)  all_56_12 = e3
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | | REF_CLOSE: (181), (190), (197) are inconsistent by sub-proof #509.
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | Case 2:
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | |   (198)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | | BETA: splitting (59) gives:
% 176.26/27.35  | | | | | 
% 176.26/27.35  | | | | | Case 1:
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | |   (199)  all_56_14 = e3
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | REF_CLOSE: (73), (177), (199) are inconsistent by sub-proof #896.
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | Case 2:
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | |   (200)   ~ (all_56_14 = e3)
% 176.26/27.35  | | | | | |   (201)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | BETA: splitting (123) gives:
% 176.26/27.35  | | | | | | 
% 176.26/27.35  | | | | | | Case 1:
% 176.26/27.35  | | | | | | | 
% 176.26/27.35  | | | | | | |   (202)  all_56_11 = e3
% 176.26/27.35  | | | | | | | 
% 176.26/27.35  | | | | | | | REF_CLOSE: (18), (174), (202) are inconsistent by sub-proof #939.
% 176.26/27.35  | | | | | | | 
% 176.26/27.35  | | | | | | Case 2:
% 176.26/27.35  | | | | | | | 
% 176.26/27.35  | | | | | | |   (203)   ~ (all_56_11 = e3)
% 176.26/27.35  | | | | | | |   (204)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.26/27.35  | | | | | | | 
% 176.26/27.35  | | | | | | | BETA: splitting (67) gives:
% 176.26/27.35  | | | | | | | 
% 176.26/27.35  | | | | | | | Case 1:
% 176.26/27.35  | | | | | | | | 
% 176.26/27.35  | | | | | | | |   (205)  all_58_0 = e3
% 176.26/27.35  | | | | | | | | 
% 176.26/27.35  | | | | | | | | COMBINE_EQS: (54), (205) imply:
% 176.26/27.35  | | | | | | | |   (206)  all_4_2 = e3
% 176.26/27.35  | | | | | | | | 
% 176.26/27.35  | | | | | | | | REDUCE: (77), (206) imply:
% 176.26/27.35  | | | | | | | |   (207)   ~ (all_52_3 = e3)
% 176.26/27.35  | | | | | | | | 
% 176.26/27.35  | | | | | | | | REDUCE: (35), (206) imply:
% 176.26/27.35  | | | | | | | |   (208)   ~ (all_52_9 = e3)
% 176.26/27.35  | | | | | | | | 
% 176.26/27.35  | | | | | | | | REDUCE: (136), (206) imply:
% 176.26/27.35  | | | | | | | |   (209)   ~ (all_52_17 = e3)
% 176.26/27.35  | | | | | | | | 
% 176.26/27.35  | | | | | | | | BETA: splitting (61) gives:
% 176.26/27.35  | | | | | | | | 
% 176.26/27.35  | | | | | | | | Case 1:
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | |   (210)  all_58_1 = e3
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | COMBINE_EQS: (52), (210) imply:
% 176.26/27.35  | | | | | | | | |   (211)  all_52_3 = e3
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | REDUCE: (207), (211) imply:
% 176.26/27.35  | | | | | | | | |   (212)  $false
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | CLOSE: (212) is inconsistent.
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | Case 2:
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | |   (213)   ~ (all_58_1 = e3)
% 176.26/27.35  | | | | | | | | |   (214)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | BETA: splitting (46) gives:
% 176.26/27.35  | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | Case 1:
% 176.26/27.35  | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | |   (215)  all_58_6 = e3
% 176.26/27.35  | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | | REF_CLOSE: (103), (209), (215) are inconsistent by sub-proof
% 176.26/27.35  | | | | | | | | | |            #981.
% 176.26/27.35  | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | Case 2:
% 176.26/27.35  | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | |   (216)   ~ (all_58_6 = e3)
% 176.26/27.35  | | | | | | | | | |   (217)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.26/27.35  | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | | BETA: splitting (3) gives:
% 176.26/27.35  | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | | Case 1:
% 176.26/27.35  | | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | | |   (218)  all_56_8 = e3
% 176.26/27.35  | | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | | | REF_CLOSE: (135), (209), (218) are inconsistent by sub-proof
% 176.26/27.35  | | | | | | | | | | |            #461.
% 176.26/27.35  | | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | | Case 2:
% 176.26/27.35  | | | | | | | | | | | 
% 176.26/27.35  | | | | | | | | | | |   (219)   ~ (all_56_8 = e3)
% 176.26/27.36  | | | | | | | | | | |   (220)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.26/27.36  | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | BETA: splitting (57) gives:
% 176.26/27.36  | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | |   (221)  all_56_1 = e3
% 176.26/27.36  | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | REF_CLOSE: (71), (207), (221) are inconsistent by sub-proof
% 176.26/27.36  | | | | | | | | | | | |            #862.
% 176.26/27.36  | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | |   (222)   ~ (all_56_1 = e3)
% 176.26/27.36  | | | | | | | | | | | |   (223)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.26/27.36  | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | BETA: splitting (122) gives:
% 176.26/27.36  | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | |   (224)  all_58_12 = e1
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | COMBINE_EQS: (182), (224) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (225)  all_6_1 = e1
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | SIMP: (225) implies:
% 176.26/27.36  | | | | | | | | | | | | |   (226)  all_6_1 = e1
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (183), (226) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (227)   ~ (all_52_9 = e1)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (184), (226) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (228)   ~ (all_52_17 = e1)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (188), (226) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (229)   ~ (all_52_29 = e1)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (190), (226) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (230)   ~ (e3 = e1)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (178), (226) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (231)  op(e1, e3) = all_6_0
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | GROUND_INST: instantiating (137) with all_52_17, all_6_0, e3,
% 176.26/27.36  | | | | | | | | | | | | |              e1, simplifying with (131), (231) gives:
% 176.26/27.36  | | | | | | | | | | | | |   (232)  all_52_17 = all_6_0
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | COMBINE_EQS: (135), (232) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (233)  all_56_8 = all_6_0
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | COMBINE_EQS: (103), (232) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (234)  all_58_6 = all_6_0
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (102), (232) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (235)   ~ (all_52_9 = all_6_0)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (8), (232) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (236)   ~ (all_52_23 = all_6_0)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | SIMP: (236) implies:
% 176.26/27.36  | | | | | | | | | | | | |   (237)   ~ (all_52_23 = all_6_0)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (83), (232) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (238)  op(e3, all_6_0) = all_52_16
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | BETA: splitting (28) gives:
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | |   (239)  all_58_0 = e2
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | COMBINE_EQS: (205), (239) imply:
% 176.26/27.36  | | | | | | | | | | | | | |   (240)  e3 = e2
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | REDUCE: (167), (240) imply:
% 176.26/27.36  | | | | | | | | | | | | | |   (241)  $false
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | CLOSE: (241) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | |   (242)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | |   (243)  all_56_8 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | REF_CLOSE: (119), (233), (243) are inconsistent by sub-proof
% 176.26/27.36  | | | | | | | | | | | | | | |            #415.
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | |   (244)   ~ (all_56_8 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | |   (245)  all_56_8 = e1 | all_56_8 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | |   (246)  all_56_8 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REF_CLOSE: (147), (233), (246) are inconsistent by sub-proof
% 176.26/27.36  | | | | | | | | | | | | | | | |            #414.
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | |   (247)  all_56_8 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (247) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (248)  all_6_0 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | SIMP: (248) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (249)  all_6_0 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | COMBINE_EQS: (234), (249) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (250)  all_58_6 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (235), (249) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (251)   ~ (all_52_9 = e0)
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (237), (249) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (252)   ~ (all_52_23 = e0)
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (119), (249) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (253)   ~ (e2 = e0)
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | SIMP: (253) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (254)   ~ (e2 = e0)
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (147), (249) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (255)   ~ (e1 = e0)
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (238), (249) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (256)  op(e3, e0) = all_52_16
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (231), (249) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (257)  op(e1, e3) = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (258)  all_58_2 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (258) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (259)  all_52_9 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | SIMP: (259) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (260)  all_52_9 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (90), (260) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (261)   ~ (all_52_13 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | SIMP: (261) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (262)   ~ (all_52_13 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (160), (260) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (263)   ~ (all_52_15 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | SIMP: (263) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (264)   ~ (all_52_15 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (208), (260) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (265)   ~ (e3 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (21), (260) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (266)  op(e3, e2) = all_52_8
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (137) with all_52_7, all_52_16, e0,
% 176.26/27.36  | | | | | | | | | | | | | | | | |              e3, simplifying with (134), (256) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (267)  all_52_7 = all_52_16
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (137) with all_52_3, all_52_8, e2,
% 176.26/27.36  | | | | | | | | | | | | | | | | |              e3, simplifying with (14), (266) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (268)  all_52_3 = all_52_8
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (268) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (269)  all_56_1 = all_52_8
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (267) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (270)  all_58_9 = all_52_16
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (268) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (271)  all_58_1 = all_52_8
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (104), (267), (268) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (272)   ~ (all_52_8 = all_52_16)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (76), (268) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (273)   ~ (all_52_8 = all_52_27)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (145), (267) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (274)   ~ (all_52_16 = all_52_23)
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (9), (268) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (275)  op(e2, all_52_8) = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (149), (267) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (276)  op(e0, all_52_16) = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (277)  all_58_9 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (277) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (278)  all_52_16 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (272), (278) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (279)   ~ (all_52_8 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (274), (278) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (280)   ~ (all_52_23 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | SIMP: (280) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (281)   ~ (all_52_23 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (276), (278) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (282)  op(e0, e2) = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (283)  all_56_11 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (283) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (284)  all_52_23 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | SIMP: (284) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (285)  all_52_23 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | REDUCE: (281), (285) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (286)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | CLOSE: (286) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (287)  all_56_11 = e1 | all_56_11 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (288)  all_56_11 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (288) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (289)  all_52_23 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | SIMP: (289) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (290)  all_52_23 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (290) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (291)  all_58_11 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (290) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (292)   ~ (all_14_2 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (293)   ~ (all_14_2 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (294)  all_58_9 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (254), (277), (294) are inconsistent by sub-proof
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            #834.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (295)  all_58_10 = e0 | all_58_11 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (296)  all_58_10 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (296) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (297)  all_52_15 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | SIMP: (297) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (298)  all_52_15 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (298) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (299)   ~ (all_52_13 = e0)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (137) with all_52_27, e0, e2, e0,
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |              simplifying with (72), (282) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (300)  all_52_27 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (300) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (301)   ~ (all_52_8 = e0)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_56_6 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (302) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_52_13 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (303) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_52_13 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (304) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_58_5 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (60), (64), (70), (75), (130), (137), (144),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | |            (168), (229), (293), (305) are inconsistent by
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #813.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | |   (307)  all_58_1 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (307) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_52_8 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (308) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | |   (309)  op(e2, e1) = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_56_6 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (262), (310) are inconsistent by sub-proof
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |            #722.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (311)   ~ (all_56_6 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_56_6 = e1 | all_56_6 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_56_6 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (313) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_52_13 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (314) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_52_13 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (262), (315) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)   ~ (e2 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (315) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  op(e2, e1) = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (137) with e1, e2, e1, e2,
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (309), (317) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  e2 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (318) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (319) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_56_6 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (299), (320) are inconsistent by sub-proof
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            #720.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | |   (321)   ~ (all_58_1 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (321) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | |   (322)   ~ (all_52_8 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_56_1 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (323) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_52_8 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (324) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (325) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_56_1 = e1 | all_56_1 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_56_1 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (327) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_52_8 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (322), (328) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (329) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_56_1 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (330) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_52_8 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (301), (331) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (333)  all_58_11 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (291), (333) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (334)  e1 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (335)  e1 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (335) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | |   (336)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (337)  all_56_11 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (337) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (338)  all_52_23 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | SIMP: (338) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (339)  all_52_23 = e0
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | REDUCE: (252), (339) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (340)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | CLOSE: (340) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (341)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (342)  all_58_10 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (342) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (343)  all_52_15 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | REDUCE: (264), (343) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (344)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | CLOSE: (344) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (345)  all_58_11 = e2 | all_58_15 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (345) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (346)  all_58_11 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (346) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (347)  all_52_23 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (347) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (348)   ~ (all_52_19 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (349)  all_56_9 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (349) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (350)  all_52_19 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | SIMP: (350) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (351)  all_52_19 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (351) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (352)  all_58_7 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (351) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (353)   ~ (all_52_27 = e3)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (351) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (354)   ~ (all_14_2 = e3)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | SIMP: (354) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (355)   ~ (all_14_2 = e3)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (19), (20), (22), (23),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (24), (28), (30), (31), (33), (34), (35), (36),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (37), (38), (39), (40), (43), (45), (46), (47),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (48), (50), (51), (52), (53), (54), (57), (60),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (64), (66), (68), (70), (71), (74), (75), (76),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (77), (79), (80), (82), (83), (84), (85), (86),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (88), (90), (94), (95), (96), (97), (99), (100),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (107),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (111), (112), (113), (115),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (121), (122), (124), (125), (126), (127), (129),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (130), (131), (133), (134), (135), (136), (137),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (140), (144), (145), (146), (147), (149), (152),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (155), (156), (159), (161), (162), (164), (165),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (176), (177),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (178), (182), (183), (184), (190), (191), (194),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (196), (207), (209), (351), (352), (355) are
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #233.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (356)   ~ (all_56_9 = e3)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (356) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (357)   ~ (all_52_19 = e3)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (70), (94), (110), (127), (137), (143),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (154), (174), (217), (257), (357) are inconsistent
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #304.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (358)  all_58_15 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (172), (358) are inconsistent by sub-proof
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |            #286.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (359)  all_58_6 = e2 | all_58_12 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (224), (250), (254), (359) are inconsistent
% 176.26/27.36  | | | | | | | | | | | | | | | | |            by sub-proof #411.
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | End of split
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | |   (360)   ~ (all_58_12 = e1)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | REDUCE: (182), (360) imply:
% 176.26/27.36  | | | | | | | | | | | | |   (361)   ~ (all_6_1 = e1)
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | BETA: splitting (100) gives:
% 176.26/27.36  | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | |   (362)  all_58_0 = e1
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | COMBINE_EQS: (205), (362) imply:
% 176.26/27.36  | | | | | | | | | | | | | |   (363)  e3 = e1
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | REDUCE: (168), (363) imply:
% 176.26/27.36  | | | | | | | | | | | | | |   (364)  $false
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | CLOSE: (364) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | |   (365)   ~ (all_58_0 = e1)
% 176.26/27.36  | | | | | | | | | | | | | |   (366)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 176.26/27.36  | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | |   (367)  all_56_9 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10),
% 176.26/27.36  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (17), (19), (20), (22),
% 176.26/27.36  | | | | | | | | | | | | | | |            (23), (24), (28), (30), (31), (32), (33), (34),
% 176.26/27.36  | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (43), (45),
% 176.26/27.36  | | | | | | | | | | | | | | |            (46), (47), (48), (50), (51), (52), (53), (54),
% 176.26/27.36  | | | | | | | | | | | | | | |            (57), (60), (64), (66), (68), (70), (71), (74),
% 176.26/27.36  | | | | | | | | | | | | | | |            (75), (76), (77), (79), (80), (82), (83), (84),
% 176.26/27.36  | | | | | | | | | | | | | | |            (85), (86), (88), (90), (94), (95), (96), (97),
% 176.26/27.36  | | | | | | | | | | | | | | |            (99), (100), (101), (102), (103), (104), (105),
% 176.26/27.36  | | | | | | | | | | | | | | |            (106), (107), (108), (109), (110), (111), (112),
% 176.26/27.36  | | | | | | | | | | | | | | |            (113), (115), (121), (122), (124), (125), (126),
% 176.26/27.36  | | | | | | | | | | | | | | |            (127), (129), (130), (131), (133), (134), (135),
% 176.26/27.36  | | | | | | | | | | | | | | |            (136), (137), (140), (141), (144), (145), (146),
% 176.26/27.36  | | | | | | | | | | | | | | |            (147), (149), (151), (152), (155), (156), (159),
% 176.26/27.36  | | | | | | | | | | | | | | |            (161), (162), (163), (164), (165), (167), (168),
% 176.26/27.36  | | | | | | | | | | | | | | |            (172), (173), (177), (178), (182), (183), (184),
% 176.26/27.36  | | | | | | | | | | | | | | |            (190), (191), (194), (196), (367) are inconsistent
% 176.26/27.36  | | | | | | | | | | | | | | |            by sub-proof #232.
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | |   (368)   ~ (all_56_9 = e3)
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | REDUCE: (32), (368) imply:
% 176.26/27.36  | | | | | | | | | | | | | | |   (369)   ~ (all_52_19 = e3)
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | |   (370)  all_58_3 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (370) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (371)  all_10_2 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (105), (371) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (372)  op(all_10_1, e3) = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (10), (371) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (373)  op(e2, e3) = all_10_1
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | REDUCE: (7), (371) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | |   (374)  op(e2, e2) = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (375)  all_58_7 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (375) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (376)  all_52_19 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | REDUCE: (369), (376) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (377)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | CLOSE: (377) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | |   (378)  all_58_8 = e3 | all_58_11 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | BETA: splitting (378) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (379)  all_58_8 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (379) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (380)  all_14_2 = e3
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (89), (380) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (381)  op(all_14_1, e3) = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (154), (380) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (382)  op(e1, e3) = all_14_1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (137) with all_52_17, all_14_1, e3,
% 176.26/27.36  | | | | | | | | | | | | | | | | | |              e1, simplifying with (131), (382) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (383)  all_52_17 = all_14_1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (137) with all_52_9, all_10_1, e3,
% 176.26/27.36  | | | | | | | | | | | | | | | | | |              e2, simplifying with (164), (373) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (384)  all_52_9 = all_10_1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (383) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (385)  all_56_8 = all_14_1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (383) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (386)  all_58_6 = all_14_1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (384) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (387)  all_58_2 = all_10_1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (90), (384) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (388)   ~ (all_52_13 = all_10_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | SIMP: (388) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (389)   ~ (all_52_13 = all_10_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (160), (384) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (390)   ~ (all_52_15 = all_10_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | SIMP: (390) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (391)   ~ (all_52_15 = all_10_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (151), (383) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (392)   ~ (all_52_19 = all_14_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | SIMP: (392) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (393)   ~ (all_52_19 = all_14_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (8), (383) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (394)   ~ (all_52_23 = all_14_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | SIMP: (394) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (395)   ~ (all_52_23 = all_14_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | REDUCE: (184), (383) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | |   (396)   ~ (all_14_1 = all_6_1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (397)  all_58_6 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (397) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (398)  all_14_1 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | REDUCE: (396), (398) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (399)   ~ (all_6_1 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | REDUCE: (381), (398) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (400)  op(e1, e3) = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (121), (126), (131), (137), (164), (181),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |            (182), (184), (198), (209), (361), (366), (372),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |            (373), (400) are inconsistent by sub-proof #238.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (401)   ~ (all_58_6 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | REDUCE: (386), (401) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | |   (402)   ~ (all_14_1 = e1)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (403)  all_58_0 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (403) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (404)  e3 = e1
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (404) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | |   (405)  $false
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | CLOSE: (405) is inconsistent.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (406)  all_58_6 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (386), (406) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (407)  all_14_1 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | SIMP: (407) implies:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (408)  all_14_1 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (408) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (409)  op(e1, e3) = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (103), (121), (126), (131), (137), (164), (181),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (182), (184), (198), (209), (361), (366), (372),
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |            (373), (409) are inconsistent by sub-proof #238.
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (410)   ~ (all_58_6 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (411)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (410) imply:
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | |   (412)   ~ (all_14_1 = e2)
% 176.26/27.36  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (13), (17), (19), (20), (23), (28),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (29), (30), (36), (39), (43), (45), (47), (52),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (57), (63), (64), (66), (68), (71), (72), (73),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (74), (76), (87), (95), (97), (99), (100), (104),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (110), (111), (112), (122), (126), (129), (137),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (141), (144), (145), (147), (149), (156), (165),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (167), (168), (172), (173), (174), (176), (177),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (178), (182), (186), (188), (194), (196), (201),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (205), (207), (220), (373), (374), (379), (385),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (386), (387), (389), (391), (393), (395), (396),
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | |            (411), (412) are inconsistent by sub-proof #831.
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | Case 2:
% 176.26/27.37  | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | |   (413)  all_58_11 = e3
% 176.26/27.37  | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (174), (413) are inconsistent by sub-proof
% 176.26/27.37  | | | | | | | | | | | | | | | | | |            #1017.
% 176.26/27.37  | | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | Case 2:
% 176.26/27.37  | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | |   (414)  all_58_7 = e3 | all_58_13 = e3
% 176.26/27.37  | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (99), (176), (369), (414) are inconsistent
% 176.26/27.37  | | | | | | | | | | | | | | | |            by sub-proof #976.
% 176.26/27.37  | | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | | 
% 176.26/27.37  | | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | | 
% 176.26/27.37  | | | | | | | | End of split
% 176.26/27.37  | | | | | | | | 
% 176.26/27.37  | | | | | | | Case 2:
% 176.26/27.37  | | | | | | | | 
% 176.26/27.37  | | | | | | | |   (415)   ~ (all_58_0 = e3)
% 176.26/27.37  | | | | | | | | 
% 176.26/27.37  | | | | | | | | REDUCE: (54), (415) imply:
% 176.26/27.37  | | | | | | | |   (416)   ~ (all_4_2 = e3)
% 176.26/27.37  | | | | | | | | 
% 176.26/27.37  | | | | | | | | REF_CLOSE: (1), (2), (9), (14), (24), (33), (34), (35), (36),
% 176.26/27.37  | | | | | | | |            (37), (38), (39), (45), (46), (48), (51), (52), (54),
% 176.26/27.37  | | | | | | | |            (64), (66), (70), (75), (79), (80), (86), (88), (94),
% 176.26/27.37  | | | | | | | |            (95), (100), (103), (104), (109), (110), (111),
% 176.26/27.37  | | | | | | | |            (113), (115), (124), (127), (131), (133), (134),
% 176.26/27.37  | | | | | | | |            (136), (137), (140), (144), (145), (149), (152),
% 176.26/27.37  | | | | | | | |            (156), (159), (161), (164), (177), (416) are
% 176.26/27.37  | | | | | | | |            inconsistent by sub-proof #864.
% 176.26/27.37  | | | | | | | | 
% 176.26/27.37  | | | | | | | End of split
% 176.26/27.37  | | | | | | | 
% 176.26/27.37  | | | | | | End of split
% 176.26/27.37  | | | | | | 
% 176.26/27.37  | | | | | End of split
% 176.26/27.37  | | | | | 
% 176.26/27.37  | | | | End of split
% 176.26/27.37  | | | | 
% 176.26/27.37  | | | End of split
% 176.26/27.37  | | | 
% 176.26/27.37  | | End of split
% 176.26/27.37  | | 
% 176.26/27.37  | Case 2:
% 176.26/27.37  | | 
% 176.26/27.37  | |   (417)   ~ (all_56_15 = e3)
% 176.26/27.37  | |   (418)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.37  | | 
% 176.26/27.37  | | REF_CLOSE: (1), (2), (8), (9), (11), (14), (15), (17), (18), (19), (20),
% 176.26/27.37  | |            (22), (24), (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 176.26/27.37  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (45), (46),
% 176.26/27.37  | |            (47), (50), (51), (52), (53), (54), (55), (56), (57), (59), (60),
% 176.26/27.37  | |            (61), (63), (64), (65), (66), (67), (68), (69), (70), (71), (73),
% 176.26/27.37  | |            (75), (76), (77), (79), (80), (85), (86), (87), (88), (90), (91),
% 176.26/27.37  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 176.26/27.37  | |            (102), (103), (104), (106), (108), (109), (110), (111), (112),
% 176.26/27.37  | |            (113), (114), (115), (118), (120), (121), (123), (124), (127),
% 176.26/27.37  | |            (128), (130), (131), (132), (133), (134), (136), (137), (138),
% 176.26/27.37  | |            (139), (140), (141), (142), (144), (145), (146), (149), (150),
% 176.26/27.37  | |            (151), (152), (156), (157), (159), (160), (161), (162), (163),
% 176.26/27.37  | |            (164), (165), (167), (168), (417), (418) are inconsistent by
% 176.26/27.37  | |            sub-proof #785.
% 176.26/27.37  | | 
% 176.26/27.37  | End of split
% 176.26/27.37  | 
% 176.26/27.37  End of proof
% 176.26/27.37  
% 176.26/27.37  Sub-proof #231 shows that the following formulas are inconsistent:
% 176.26/27.37  ----------------------------------------------------------------
% 176.26/27.37    (1)   ~ (all_52_23 = all_14_2)
% 176.26/27.37    (2)   ~ (all_52_5 = all_52_13)
% 176.26/27.37    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.26/27.37    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.26/27.37    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.26/27.37    (6)   ~ (all_52_27 = all_10_2)
% 176.26/27.37    (7)  op(e2, e2) = all_10_2
% 176.26/27.37    (8)   ~ (all_52_17 = all_52_23)
% 176.26/27.37    (9)   ~ (all_6_0 = e3)
% 176.26/27.37    (10)  op(e2, all_10_2) = all_10_1
% 176.26/27.37    (11)   ~ (all_52_13 = all_52_29)
% 176.26/27.37    (12)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.26/27.37    (13)  all_56_3 = all_52_7
% 176.26/27.37    (14)  op(e3, e2) = all_52_3
% 176.26/27.37    (15)   ~ (all_52_9 = all_52_25)
% 176.26/27.37    (16)  op(e3, all_52_25) = all_52_24
% 176.26/27.37    (17)   ~ (all_52_19 = all_52_23)
% 176.26/27.37    (18)  all_56_11 = all_52_23
% 176.26/27.37    (19)  op(e1, e2) = all_52_19
% 176.26/27.37    (20)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.26/27.37    (21)  op(e3, all_52_9) = all_52_8
% 176.26/27.37    (22)   ~ (all_52_3 = all_10_2)
% 176.26/27.37    (23)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.26/27.37    (24)  all_58_5 = all_52_13
% 176.26/27.37    (25)   ~ (all_6_2 = e0)
% 176.26/27.37    (26)   ~ (all_52_25 = all_52_29)
% 176.26/27.37    (27)  all_56_15 = all_6_2
% 176.26/27.37    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.26/27.37    (29)  op(e2, e0) = all_52_15
% 176.26/27.37    (30)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.26/27.37    (31)  all_58_3 = all_10_2
% 176.26/27.37    (32)  all_56_9 = all_52_19
% 176.26/27.37    (33)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.26/27.37    (34)  all_58_15 = all_6_2
% 176.26/27.37    (35)   ~ (all_52_9 = all_4_2)
% 176.26/27.37    (36)   ~ (all_52_5 = all_52_7)
% 176.26/27.37    (37)  all_58_10 = all_52_15
% 176.26/27.37    (38)   ~ (all_52_5 = all_4_2)
% 176.26/27.37    (39)  all_58_7 = all_52_19
% 176.26/27.37    (40)  all_56_4 = all_52_9
% 176.26/27.37    (41)   ~ (all_52_15 = all_6_2)
% 176.26/27.37    (42)   ~ (all_52_17 = all_52_25)
% 176.26/27.37    (43)  op(e0, e1) = all_52_29
% 176.26/27.37    (44)   ~ (all_4_0 = e2)
% 176.26/27.37    (45)  all_58_4 = all_52_5
% 176.26/27.37    (46)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.26/27.37    (47)   ~ (e3 = e1)
% 176.26/27.37    (48)   ~ (all_52_27 = all_52_29)
% 176.26/27.37    (49)   ~ (all_52_17 = all_14_2)
% 176.26/27.37    (50)  op(e3, all_4_2) = all_4_1
% 176.26/27.37    (51)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.26/27.37    (52)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.26/27.37    (53)   ~ (all_52_7 = all_4_2)
% 176.26/27.37    (54)  all_58_1 = all_52_3
% 176.26/27.37    (55)   ~ (all_52_13 = all_52_15)
% 176.26/27.37    (56)  all_58_0 = all_4_2
% 176.26/27.37    (57)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.26/27.37    (58)  op(e1, all_52_29) = all_52_28
% 176.26/27.37    (59)  op(e1, all_52_5) = all_52_4
% 176.26/27.37    (60)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.26/27.37    (61)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.26/27.37    (62)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.26/27.37    (63)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.26/27.37    (64)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.38/27.37    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.38/27.37    (66)  all_58_14 = all_52_29
% 176.38/27.37    (67)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.37    (68)   ~ (all_52_3 = all_52_5)
% 176.38/27.37    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.38/27.37    (70)  op(e2, e1) = all_52_13
% 176.38/27.37    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.38/27.37    (72)  all_58_8 = all_14_2
% 176.38/27.37    (73)  all_56_1 = all_52_3
% 176.38/27.37    (74)  op(e0, e2) = all_52_27
% 176.38/27.37    (75)  all_56_14 = all_52_29
% 176.38/27.37    (76)  op(all_14_1, all_14_2) = e3
% 176.38/27.37    (77)  op(all_4_1, all_4_2) = all_4_0
% 176.38/27.37    (78)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.38/27.37    (79)   ~ (all_52_5 = all_14_2)
% 176.38/27.37    (80)   ~ (all_52_3 = all_52_27)
% 176.38/27.37    (81)   ~ (all_52_3 = all_4_2)
% 176.38/27.37    (82)  op(all_6_1, all_6_2) = all_6_0
% 176.38/27.37    (83)  op(e0, e3) = all_52_25
% 176.38/27.37    (84)  op(e0, all_6_2) = all_6_1
% 176.38/27.37    (85)  all_52_0 = all_4_1
% 176.38/27.37    (86)   ~ (all_52_9 = all_10_2)
% 176.38/27.37    (87)  op(e3, all_52_17) = all_52_16
% 176.38/27.37    (88)  all_52_10 = all_10_1
% 176.38/27.37    (89)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.38/27.37    (90)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.38/27.37    (91)   ~ (all_52_13 = all_14_2)
% 176.38/27.37    (92)   ~ (e3 = e0)
% 176.38/27.37    (93)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.38/27.37    (94)   ~ (all_52_9 = all_52_13)
% 176.38/27.37    (95)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.38/27.37    (96)  op(e0, all_52_23) = all_52_22
% 176.38/27.37    (97)   ~ (all_52_15 = all_52_23)
% 176.38/27.37    (98)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.38/27.37    (99)   ~ (all_52_5 = all_52_29)
% 176.38/27.37    (100)  all_56_2 = all_52_5
% 176.38/27.37    (101)  op(e1, e0) = all_52_23
% 176.38/27.37    (102)  all_56_12 = all_52_25
% 176.38/27.37    (103)  all_58_13 = all_52_27
% 176.38/27.37    (104)  op(e2, all_52_3) = all_52_2
% 176.38/27.37    (105)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.38/27.37    (106)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.38/27.37    (107)   ~ (all_52_9 = all_52_17)
% 176.38/27.37    (108)  all_58_6 = all_52_17
% 176.38/27.37    (109)   ~ (all_52_3 = all_52_7)
% 176.38/27.37    (110)  op(all_10_1, all_10_2) = e3
% 176.38/27.37    (111)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.38/27.37    (112)  op(e2, all_52_19) = all_52_18
% 176.38/27.37    (113)   ~ (e1 = e0)
% 176.38/27.37    (114)  all_56_0 = all_4_2
% 176.38/27.37    (115)  all_58_11 = all_52_23
% 176.38/27.37    (116)   ~ (all_52_3 = all_52_19)
% 176.38/27.37    (117)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.38/27.37    (118)   ~ (all_52_7 = all_52_15)
% 176.38/27.37    (119)  op(e0, all_52_15) = all_52_14
% 176.38/27.37    (120)   ~ (all_52_29 = all_14_2)
% 176.38/27.37    (121)   ~ (all_4_0 = e1)
% 176.38/27.37    (122)   ~ (all_52_19 = all_10_2)
% 176.38/27.37    (123)   ~ (all_52_23 = all_6_2)
% 176.38/27.37    (124)   ~ (all_6_0 = e2)
% 176.38/27.37    (125)   ~ (all_52_29 = all_6_2)
% 176.38/27.37    (126)  all_58_2 = all_52_9
% 176.38/27.37    (127)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.38/27.37    (128)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.38/27.37    (129)  op(e3, e1) = all_52_5
% 176.38/27.37    (130)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.38/27.37    (131)   ~ (e2 = e1)
% 176.38/27.37    (132)  all_56_10 = all_14_2
% 176.38/27.37    (133)   ~ (all_52_25 = all_6_2)
% 176.38/27.37    (134)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.38/27.37    (135)  op(e1, e1) = all_14_2
% 176.38/27.37    (136)  op(e1, e3) = all_52_17
% 176.38/27.37    (137)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.38/27.37    (138)   ~ (all_52_25 = all_4_2)
% 176.38/27.37    (139)  op(e3, e0) = all_52_7
% 176.38/27.37    (140)  op(e3, e3) = all_4_2
% 176.38/27.37    (141)  all_56_8 = all_52_17
% 176.38/27.37    (142)   ~ (all_52_17 = all_4_2)
% 176.38/27.37    (143)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.38/27.37             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.38/27.37    (144)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.38/27.37           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.38/27.37           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.38/27.37           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.38/27.37    (145)   ~ (all_52_25 = all_52_27)
% 176.38/27.37    (146)   ~ (all_52_27 = all_6_2)
% 176.38/27.37    (147)   ~ (all_52_7 = all_6_2)
% 176.38/27.37    (148)   ~ (all_52_15 = all_10_2)
% 176.38/27.37    (149)   ~ (all_52_19 = all_52_27)
% 176.38/27.37    (150)  all_56_7 = all_52_15
% 176.38/27.37    (151)   ~ (all_52_7 = all_52_23)
% 176.38/27.37    (152)   ~ (all_52_13 = all_10_2)
% 176.38/27.37    (153)   ~ (all_6_0 = e1)
% 176.38/27.37    (154)  op(e2, all_52_27) = all_52_26
% 176.38/27.37    (155)  all_52_20 = all_14_1
% 176.38/27.37    (156)   ~ (all_52_17 = all_52_19)
% 176.38/27.37    (157)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.38/27.37    (158)  all_52_30 = all_6_1
% 176.38/27.37    (159)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.38/27.37    (160)  op(e1, all_14_2) = all_14_1
% 176.38/27.37    (161)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.38/27.37    (162)  all_58_9 = all_52_7
% 176.38/27.37    (163)  all_58_12 = all_52_25
% 176.38/27.37    (164)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.38/27.37    (165)   ~ (all_52_9 = all_52_15)
% 176.38/27.37    (166)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.38/27.37    (167)   ~ (e3 = e2)
% 176.38/27.37    (168)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.38/27.37    (169)   ~ (all_52_19 = all_14_2)
% 176.38/27.37    (170)  op(e0, all_52_7) = all_52_6
% 176.38/27.37    (171)  op(e2, e3) = all_52_9
% 176.38/27.37    (172)  all_56_13 = all_52_27
% 176.38/27.37  
% 176.38/27.37  Begin of proof
% 176.38/27.37  | 
% 176.38/27.37  | BETA: splitting (144) gives:
% 176.38/27.37  | 
% 176.38/27.37  | Case 1:
% 176.38/27.37  | | 
% 176.38/27.37  | |   (173)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.38/27.37  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.38/27.37  | | 
% 176.38/27.37  | | BETA: splitting (173) gives:
% 176.38/27.37  | | 
% 176.38/27.37  | | Case 1:
% 176.38/27.37  | | | 
% 176.38/27.37  | | |   (174)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.38/27.37  | | | 
% 176.38/27.37  | | | ALPHA: (174) implies:
% 176.38/27.37  | | |   (175)  all_52_6 = e0
% 176.38/27.37  | | |   (176)  all_52_4 = e1
% 176.38/27.37  | | |   (177)  all_52_2 = e2
% 176.38/27.37  | | |   (178)  all_52_0 = e3
% 176.38/27.37  | | | 
% 176.38/27.37  | | | COMBINE_EQS: (85), (178) imply:
% 176.38/27.37  | | |   (179)  all_4_1 = e3
% 176.38/27.37  | | | 
% 176.38/27.37  | | | REDUCE: (77), (179) imply:
% 176.38/27.37  | | |   (180)  op(e3, all_4_2) = all_4_0
% 176.38/27.37  | | | 
% 176.38/27.37  | | | REDUCE: (50), (179) imply:
% 176.38/27.37  | | |   (181)  op(e3, all_4_2) = e3
% 176.38/27.37  | | | 
% 176.38/27.37  | | | REDUCE: (104), (177) imply:
% 176.38/27.37  | | |   (182)  op(e2, all_52_3) = e2
% 176.38/27.37  | | | 
% 176.38/27.37  | | | REDUCE: (59), (176) imply:
% 176.38/27.37  | | |   (183)  op(e1, all_52_5) = e1
% 176.38/27.37  | | | 
% 176.38/27.37  | | | REDUCE: (170), (175) imply:
% 176.38/27.37  | | |   (184)  op(e0, all_52_7) = e0
% 176.38/27.37  | | | 
% 176.38/27.37  | | | GROUND_INST: instantiating (143) with e3, all_4_0, all_4_2, e3,
% 176.38/27.37  | | |              simplifying with (180), (181) gives:
% 176.38/27.37  | | |   (185)  all_4_0 = e3
% 176.38/27.37  | | | 
% 176.38/27.37  | | | BETA: splitting (51) gives:
% 176.38/27.37  | | | 
% 176.38/27.37  | | | Case 1:
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | |   (186)  all_56_15 = e3
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | COMBINE_EQS: (27), (186) imply:
% 176.38/27.37  | | | |   (187)  all_6_2 = e3
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | SIMP: (187) implies:
% 176.38/27.37  | | | |   (188)  all_6_2 = e3
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | COMBINE_EQS: (34), (188) imply:
% 176.38/27.37  | | | |   (189)  all_58_15 = e3
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (147), (188) imply:
% 176.38/27.37  | | | |   (190)   ~ (all_52_7 = e3)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (123), (188) imply:
% 176.38/27.37  | | | |   (191)   ~ (all_52_23 = e3)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (133), (188) imply:
% 176.38/27.37  | | | |   (192)   ~ (all_52_25 = e3)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (146), (188) imply:
% 176.38/27.37  | | | |   (193)   ~ (all_52_27 = e3)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (125), (188) imply:
% 176.38/27.37  | | | |   (194)   ~ (all_52_29 = e3)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (82), (188) imply:
% 176.38/27.37  | | | |   (195)  op(all_6_1, e3) = all_6_0
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (84), (188) imply:
% 176.38/27.37  | | | |   (196)  op(e0, e3) = all_6_1
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | GROUND_INST: instantiating (143) with all_52_25, all_6_1, e3, e0,
% 176.38/27.37  | | | |              simplifying with (83), (196) gives:
% 176.38/27.37  | | | |   (197)  all_52_25 = all_6_1
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | COMBINE_EQS: (163), (197) imply:
% 176.38/27.37  | | | |   (198)  all_58_12 = all_6_1
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (15), (197) imply:
% 176.38/27.37  | | | |   (199)   ~ (all_52_9 = all_6_1)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (42), (197) imply:
% 176.38/27.37  | | | |   (200)   ~ (all_52_17 = all_6_1)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (145), (197) imply:
% 176.38/27.37  | | | |   (201)   ~ (all_52_27 = all_6_1)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | SIMP: (201) implies:
% 176.38/27.37  | | | |   (202)   ~ (all_52_27 = all_6_1)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (26), (197) imply:
% 176.38/27.37  | | | |   (203)   ~ (all_52_29 = all_6_1)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | SIMP: (203) implies:
% 176.38/27.37  | | | |   (204)   ~ (all_52_29 = all_6_1)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (192), (197) imply:
% 176.38/27.37  | | | |   (205)   ~ (all_6_1 = e3)
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REDUCE: (16), (197) imply:
% 176.38/27.37  | | | |   (206)  op(e3, all_6_1) = all_52_24
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | BETA: splitting (67) gives:
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | Case 1:
% 176.38/27.37  | | | | | 
% 176.38/27.37  | | | | |   (207)  all_56_13 = e3
% 176.38/27.37  | | | | | 
% 176.38/27.37  | | | | | REF_CLOSE: (172), (193), (207) are inconsistent by sub-proof #876.
% 176.38/27.37  | | | | | 
% 176.38/27.37  | | | | Case 2:
% 176.38/27.37  | | | | | 
% 176.38/27.37  | | | | |   (208)   ~ (all_56_13 = e3)
% 176.38/27.37  | | | | |   (209)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.37  | | | | | 
% 176.38/27.37  | | | | | BETA: splitting (62) gives:
% 176.38/27.37  | | | | | 
% 176.38/27.37  | | | | | Case 1:
% 176.38/27.37  | | | | | | 
% 176.38/27.37  | | | | | |   (210)  all_56_14 = e3
% 176.38/27.37  | | | | | | 
% 176.38/27.37  | | | | | | REF_CLOSE: (75), (194), (210) are inconsistent by sub-proof #896.
% 176.38/27.37  | | | | | | 
% 176.38/27.37  | | | | | Case 2:
% 176.38/27.37  | | | | | | 
% 176.38/27.37  | | | | | |   (211)   ~ (all_56_14 = e3)
% 176.38/27.37  | | | | | |   (212)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.38/27.37  | | | | | | 
% 176.38/27.37  | | | | | | BETA: splitting (159) gives:
% 176.38/27.37  | | | | | | 
% 176.38/27.37  | | | | | | Case 1:
% 176.38/27.37  | | | | | | | 
% 176.38/27.37  | | | | | | |   (213)  all_56_3 = e3
% 176.38/27.37  | | | | | | | 
% 176.38/27.37  | | | | | | | REF_CLOSE: (13), (190), (213) are inconsistent by sub-proof #1034.
% 176.38/27.37  | | | | | | | 
% 176.38/27.37  | | | | | | Case 2:
% 176.38/27.37  | | | | | | | 
% 176.38/27.37  | | | | | | |   (214)   ~ (all_56_3 = e3)
% 176.38/27.37  | | | | | | |   (215)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.38/27.37  | | | | | | | 
% 176.38/27.37  | | | | | | | BETA: splitting (61) gives:
% 176.38/27.37  | | | | | | | 
% 176.38/27.37  | | | | | | | Case 1:
% 176.38/27.37  | | | | | | | | 
% 176.38/27.37  | | | | | | | |   (216)  all_56_9 = e3
% 176.38/27.37  | | | | | | | | 
% 176.38/27.37  | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12),
% 176.38/27.37  | | | | | | | |            (13), (14), (17), (19), (20), (22), (23), (24), (28),
% 176.38/27.37  | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 176.38/27.37  | | | | | | | |            (39), (40), (43), (45), (46), (47), (48), (49), (52),
% 176.38/27.37  | | | | | | | |            (53), (54), (55), (56), (60), (63), (66), (68), (70),
% 176.38/27.37  | | | | | | | |            (72), (73), (78), (79), (80), (81), (83), (86), (87),
% 176.38/27.37  | | | | | | | |            (89), (90), (91), (93), (94), (98), (99), (100),
% 176.38/27.37  | | | | | | | |            (101), (103), (105), (106), (107), (108), (109),
% 176.38/27.37  | | | | | | | |            (110), (111), (112), (113), (114), (115), (116),
% 176.38/27.37  | | | | | | | |            (117), (118), (120), (126), (127), (129), (130),
% 176.38/27.37  | | | | | | | |            (131), (132), (134), (135), (136), (138), (139),
% 176.38/27.37  | | | | | | | |            (141), (142), (143), (147), (149), (151), (152),
% 176.38/27.37  | | | | | | | |            (153), (156), (157), (161), (162), (164), (166),
% 176.38/27.37  | | | | | | | |            (167), (168), (169), (171), (172), (181), (182),
% 176.38/27.37  | | | | | | | |            (183), (184), (189), (190), (194), (195), (198),
% 176.38/27.37  | | | | | | | |            (199), (200), (205), (206), (209), (215), (216) are
% 176.38/27.37  | | | | | | | |            inconsistent by sub-proof #232.
% 176.38/27.37  | | | | | | | | 
% 176.38/27.37  | | | | | | | Case 2:
% 176.38/27.37  | | | | | | | | 
% 176.38/27.37  | | | | | | | |   (217)   ~ (all_56_9 = e3)
% 176.38/27.37  | | | | | | | | 
% 176.38/27.37  | | | | | | | | REDUCE: (32), (217) imply:
% 176.38/27.37  | | | | | | | |   (218)   ~ (all_52_19 = e3)
% 176.38/27.37  | | | | | | | | 
% 176.38/27.37  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (13),
% 176.38/27.37  | | | | | | | |            (14), (17), (19), (20), (23), (24), (28), (29), (30),
% 176.38/27.37  | | | | | | | |            (31), (33), (34), (35), (36), (37), (38), (39), (43),
% 176.38/27.37  | | | | | | | |            (45), (46), (47), (48), (49), (53), (54), (56), (60),
% 176.38/27.37  | | | | | | | |            (64), (65), (66), (68), (70), (72), (73), (74), (75),
% 176.38/27.37  | | | | | | | |            (76), (78), (79), (80), (81), (83), (86), (91), (92),
% 176.38/27.37  | | | | | | | |            (93), (94), (98), (99), (101), (103), (105), (106),
% 176.38/27.37  | | | | | | | |            (108), (109), (114), (115), (116), (117), (118),
% 176.38/27.37  | | | | | | | |            (120), (122), (126), (127), (129), (131), (132),
% 176.38/27.37  | | | | | | | |            (134), (136), (138), (139), (141), (142), (143),
% 176.38/27.37  | | | | | | | |            (147), (149), (151), (153), (156), (157), (160),
% 176.38/27.37  | | | | | | | |            (162), (164), (165), (166), (167), (171), (172),
% 176.38/27.37  | | | | | | | |            (181), (182), (183), (184), (189), (191), (193),
% 176.38/27.37  | | | | | | | |            (194), (195), (198), (200), (202), (204), (209),
% 176.38/27.37  | | | | | | | |            (212), (215), (218) are inconsistent by sub-proof
% 176.38/27.37  | | | | | | | |            #342.
% 176.38/27.37  | | | | | | | | 
% 176.38/27.37  | | | | | | | End of split
% 176.38/27.37  | | | | | | | 
% 176.38/27.37  | | | | | | End of split
% 176.38/27.37  | | | | | | 
% 176.38/27.37  | | | | | End of split
% 176.38/27.37  | | | | | 
% 176.38/27.37  | | | | End of split
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | Case 2:
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | |   (219)   ~ (all_56_15 = e3)
% 176.38/27.37  | | | |   (220)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | | REF_CLOSE: (1), (2), (8), (11), (14), (15), (17), (18), (19), (20),
% 176.38/27.37  | | | |            (22), (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 176.38/27.37  | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 176.38/27.37  | | | |            (45), (46), (47), (48), (52), (53), (54), (55), (56), (57),
% 176.38/27.37  | | | |            (58), (60), (62), (63), (64), (65), (66), (67), (68), (69),
% 176.38/27.37  | | | |            (70), (71), (72), (73), (75), (79), (80), (81), (83), (90),
% 176.38/27.37  | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 176.38/27.37  | | | |            (101), (102), (103), (105), (106), (107), (108), (109),
% 176.38/27.37  | | | |            (111), (113), (114), (115), (116), (117), (118), (119),
% 176.38/27.37  | | | |            (120), (123), (125), (126), (128), (129), (132), (133),
% 176.38/27.37  | | | |            (135), (136), (137), (138), (139), (142), (143), (145),
% 176.38/27.37  | | | |            (146), (147), (149), (150), (151), (152), (154), (156),
% 176.38/27.37  | | | |            (157), (162), (163), (164), (165), (166), (167), (168),
% 176.38/27.37  | | | |            (169), (171), (172), (181), (182), (183), (184), (219), (220)
% 176.38/27.37  | | | |            are inconsistent by sub-proof #785.
% 176.38/27.37  | | | | 
% 176.38/27.37  | | | End of split
% 176.38/27.37  | | | 
% 176.38/27.37  | | Case 2:
% 176.38/27.37  | | | 
% 176.38/27.37  | | |   (221)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.38/27.37  | | | 
% 176.38/27.37  | | | ALPHA: (221) implies:
% 176.38/27.37  | | |   (222)  all_52_10 = e2
% 176.38/27.37  | | | 
% 176.38/27.37  | | | COMBINE_EQS: (88), (222) imply:
% 176.38/27.37  | | |   (223)  all_10_1 = e2
% 176.38/27.37  | | | 
% 176.38/27.37  | | | REF_CLOSE: (10), (110), (143), (167), (223) are inconsistent by sub-proof
% 176.38/27.37  | | |            #263.
% 176.38/27.37  | | | 
% 176.38/27.37  | | End of split
% 176.38/27.37  | | 
% 176.38/27.37  | Case 2:
% 176.38/27.37  | | 
% 176.38/27.38  | |   (224)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 176.38/27.38  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 176.38/27.38  | |            e0)
% 176.38/27.38  | | 
% 176.38/27.38  | | REF_CLOSE: (4), (5), (6), (8), (9), (11), (12), (14), (15), (16), (17),
% 176.38/27.38  | |            (18), (20), (21), (23), (24), (25), (26), (27), (28), (30), (31),
% 176.38/27.38  | |            (33), (34), (35), (36), (37), (38), (39), (42), (43), (44), (45),
% 176.38/27.38  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 176.38/27.38  | |            (57), (58), (62), (63), (64), (66), (67), (68), (69), (71), (72),
% 176.38/27.38  | |            (74), (75), (76), (77), (80), (81), (82), (83), (84), (86), (87),
% 176.38/27.38  | |            (89), (91), (93), (94), (95), (99), (100), (101), (102), (103),
% 176.38/27.38  | |            (105), (106), (107), (108), (109), (114), (115), (116), (118),
% 176.38/27.38  | |            (121), (122), (123), (124), (125), (126), (128), (129), (131),
% 176.38/27.38  | |            (133), (134), (136), (137), (138), (139), (140), (142), (143),
% 176.38/27.38  | |            (145), (146), (147), (148), (149), (150), (151), (153), (154),
% 176.38/27.38  | |            (155), (156), (157), (158), (160), (162), (163), (164), (165),
% 176.38/27.38  | |            (166), (167), (168), (171), (172), (224) are inconsistent by
% 176.38/27.38  | |            sub-proof #319.
% 176.38/27.38  | | 
% 176.38/27.38  | End of split
% 176.38/27.38  | 
% 176.38/27.38  End of proof
% 176.38/27.38  
% 176.38/27.38  Sub-proof #232 shows that the following formulas are inconsistent:
% 176.38/27.38  ----------------------------------------------------------------
% 176.38/27.38    (1)   ~ (all_52_23 = all_14_2)
% 176.38/27.38    (2)   ~ (all_52_5 = all_52_13)
% 176.38/27.38    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.38/27.38    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.38/27.38    (5)   ~ (all_52_27 = all_10_2)
% 176.38/27.38    (6)  op(e2, e2) = all_10_2
% 176.38/27.38    (7)   ~ (all_52_17 = all_52_23)
% 176.38/27.38    (8)  op(e2, all_52_3) = e2
% 176.38/27.38    (9)  all_58_15 = e3
% 176.38/27.38    (10)  op(e2, all_10_2) = all_10_1
% 176.38/27.38    (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.38/27.38    (12)   ~ (all_52_13 = all_52_29)
% 176.38/27.38    (13)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.38/27.38    (14)  all_56_3 = all_52_7
% 176.38/27.38    (15)  op(e3, e2) = all_52_3
% 176.38/27.38    (16)   ~ (all_52_19 = all_52_23)
% 176.38/27.38    (17)  op(e1, e2) = all_52_19
% 176.38/27.38    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.38/27.38    (19)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.38    (20)  all_58_12 = all_6_1
% 176.38/27.38    (21)  op(all_6_1, e3) = all_6_0
% 176.38/27.38    (22)   ~ (all_52_3 = all_10_2)
% 176.38/27.38    (23)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.38/27.38    (24)  all_58_5 = all_52_13
% 176.38/27.38    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.38/27.38    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.38/27.38    (27)  all_58_3 = all_10_2
% 176.38/27.38    (28)  all_56_9 = all_52_19
% 176.38/27.38    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.38/27.38    (30)  all_58_15 = all_6_2
% 176.38/27.38    (31)   ~ (all_52_9 = all_4_2)
% 176.38/27.38    (32)   ~ (all_52_5 = all_52_7)
% 176.38/27.38    (33)  all_58_10 = all_52_15
% 176.38/27.38    (34)   ~ (all_52_5 = all_4_2)
% 176.38/27.38    (35)  all_58_7 = all_52_19
% 176.38/27.38    (36)  all_56_4 = all_52_9
% 176.38/27.38    (37)  op(e3, all_6_1) = all_52_24
% 176.38/27.38    (38)  op(e0, e1) = all_52_29
% 176.38/27.38    (39)  all_58_4 = all_52_5
% 176.38/27.38    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.38/27.38    (41)   ~ (e3 = e1)
% 176.38/27.38    (42)   ~ (all_52_27 = all_52_29)
% 176.38/27.38    (43)   ~ (all_52_17 = all_14_2)
% 176.38/27.38    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.38/27.38    (45)   ~ (all_52_7 = all_4_2)
% 176.38/27.38    (46)  all_58_1 = all_52_3
% 176.38/27.38    (47)   ~ (all_52_13 = all_52_15)
% 176.38/27.38    (48)  all_58_0 = all_4_2
% 176.38/27.38    (49)   ~ (all_52_9 = all_6_1)
% 176.38/27.38    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.38/27.38    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.38/27.38    (52)  all_58_14 = all_52_29
% 176.38/27.38    (53)   ~ (all_52_3 = all_52_5)
% 176.38/27.38    (54)  op(e2, e1) = all_52_13
% 176.38/27.38    (55)   ~ (all_52_17 = all_6_1)
% 176.38/27.38    (56)  all_58_8 = all_14_2
% 176.38/27.38    (57)  all_56_1 = all_52_3
% 176.38/27.38    (58)   ~ (all_6_1 = e3)
% 176.38/27.38    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.38/27.38    (60)   ~ (all_52_5 = all_14_2)
% 176.38/27.38    (61)   ~ (all_52_3 = all_52_27)
% 176.38/27.38    (62)   ~ (all_52_3 = all_4_2)
% 176.38/27.38    (63)  op(e3, all_4_2) = e3
% 176.38/27.38    (64)  op(e0, e3) = all_52_25
% 176.38/27.38    (65)   ~ (all_52_9 = all_10_2)
% 176.38/27.38    (66)  op(e3, all_52_17) = all_52_16
% 176.38/27.38    (67)   ~ (all_52_29 = e3)
% 176.38/27.38    (68)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.38/27.38    (69)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.38/27.38    (70)   ~ (all_52_13 = all_14_2)
% 176.38/27.38    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.38/27.38    (72)   ~ (all_52_9 = all_52_13)
% 176.38/27.38    (73)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.38/27.38    (74)   ~ (all_52_5 = all_52_29)
% 176.38/27.38    (75)  all_56_2 = all_52_5
% 176.38/27.38    (76)  op(e1, e0) = all_52_23
% 176.38/27.38    (77)  all_58_13 = all_52_27
% 176.38/27.38    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.38/27.38    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.38/27.38    (80)   ~ (all_52_9 = all_52_17)
% 176.38/27.38    (81)  all_58_6 = all_52_17
% 176.38/27.38    (82)   ~ (all_52_3 = all_52_7)
% 176.38/27.38    (83)  op(all_10_1, all_10_2) = e3
% 176.38/27.38    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.38/27.38    (85)  op(e2, all_52_19) = all_52_18
% 176.38/27.38    (86)   ~ (e1 = e0)
% 176.38/27.38    (87)  all_56_0 = all_4_2
% 176.38/27.38    (88)  all_58_11 = all_52_23
% 176.38/27.38    (89)   ~ (all_52_3 = all_52_19)
% 176.38/27.38    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.38/27.38    (91)   ~ (all_52_7 = all_52_15)
% 176.38/27.38    (92)   ~ (all_52_29 = all_14_2)
% 176.38/27.38    (93)  all_58_2 = all_52_9
% 176.38/27.38    (94)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.38/27.38    (95)  op(e3, e1) = all_52_5
% 176.38/27.38    (96)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.38/27.38    (97)   ~ (e2 = e1)
% 176.38/27.38    (98)  all_56_10 = all_14_2
% 176.38/27.38    (99)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.38/27.38    (100)  op(e1, e1) = all_14_2
% 176.38/27.38    (101)  op(e1, e3) = all_52_17
% 176.38/27.38    (102)   ~ (all_52_25 = all_4_2)
% 176.38/27.38    (103)  op(e3, e0) = all_52_7
% 176.38/27.38    (104)  all_56_8 = all_52_17
% 176.38/27.38    (105)   ~ (all_52_17 = all_4_2)
% 176.38/27.38    (106)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.38/27.38             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.38/27.38    (107)   ~ (all_52_7 = all_6_2)
% 176.38/27.38    (108)   ~ (all_52_19 = all_52_27)
% 176.38/27.38    (109)  all_56_9 = e3
% 176.38/27.38    (110)   ~ (all_52_7 = e3)
% 176.38/27.38    (111)  op(e1, all_52_5) = e1
% 176.38/27.38    (112)   ~ (all_52_7 = all_52_23)
% 176.38/27.38    (113)   ~ (all_52_13 = all_10_2)
% 176.38/27.38    (114)   ~ (all_6_0 = e1)
% 176.38/27.38    (115)  op(e0, all_52_7) = e0
% 176.38/27.38    (116)   ~ (all_52_17 = all_52_19)
% 176.38/27.38    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.38/27.38    (118)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.38/27.38    (119)  all_58_9 = all_52_7
% 176.38/27.38    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.38/27.38    (121)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.38/27.38    (122)   ~ (e3 = e2)
% 176.38/27.38    (123)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.38/27.38    (124)   ~ (all_52_19 = all_14_2)
% 176.38/27.38    (125)  op(e2, e3) = all_52_9
% 176.38/27.38    (126)  all_56_13 = all_52_27
% 176.38/27.38  
% 176.38/27.38  Begin of proof
% 176.38/27.38  | 
% 176.38/27.38  | COMBINE_EQS: (28), (109) imply:
% 176.38/27.38  |   (127)  all_52_19 = e3
% 176.38/27.38  | 
% 176.38/27.38  | SIMP: (127) implies:
% 176.38/27.38  |   (128)  all_52_19 = e3
% 176.38/27.38  | 
% 176.38/27.38  | COMBINE_EQS: (35), (128) imply:
% 176.38/27.38  |   (129)  all_58_7 = e3
% 176.38/27.38  | 
% 176.38/27.38  | REDUCE: (89), (128) imply:
% 176.38/27.38  |   (130)   ~ (all_52_3 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | REDUCE: (116), (128) imply:
% 176.38/27.38  |   (131)   ~ (all_52_17 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | REDUCE: (16), (128) imply:
% 176.38/27.38  |   (132)   ~ (all_52_23 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | SIMP: (132) implies:
% 176.38/27.38  |   (133)   ~ (all_52_23 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | REDUCE: (108), (128) imply:
% 176.38/27.38  |   (134)   ~ (all_52_27 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | SIMP: (134) implies:
% 176.38/27.38  |   (135)   ~ (all_52_27 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | REDUCE: (124), (128) imply:
% 176.38/27.38  |   (136)   ~ (all_14_2 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | SIMP: (136) implies:
% 176.38/27.38  |   (137)   ~ (all_14_2 = e3)
% 176.38/27.38  | 
% 176.38/27.38  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.38/27.38  |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.38/27.38  |            (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), (36),
% 176.38/27.38  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 176.38/27.38  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 176.38/27.38  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 176.38/27.38  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 176.38/27.38  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 176.38/27.38  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 176.38/27.38  |            (102), (103), (104), (105), (106), (107), (110), (111), (112),
% 176.38/27.38  |            (113), (114), (115), (117), (118), (119), (120), (121), (122),
% 176.38/27.38  |            (123), (125), (126), (128), (129), (130), (131), (133), (135),
% 176.38/27.38  |            (137) are inconsistent by sub-proof #233.
% 176.38/27.38  | 
% 176.38/27.38  End of proof
% 176.38/27.38  
% 176.38/27.38  Sub-proof #233 shows that the following formulas are inconsistent:
% 176.38/27.38  ----------------------------------------------------------------
% 176.38/27.38    (1)   ~ (all_52_23 = all_14_2)
% 176.38/27.38    (2)   ~ (all_52_5 = all_52_13)
% 176.38/27.38    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.38/27.38    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.38/27.38    (5)   ~ (all_52_27 = all_10_2)
% 176.38/27.38    (6)  op(e2, e2) = all_10_2
% 176.38/27.38    (7)   ~ (all_52_17 = all_52_23)
% 176.38/27.38    (8)  op(e2, all_52_3) = e2
% 176.38/27.38    (9)  all_58_15 = e3
% 176.38/27.38    (10)  op(e2, all_10_2) = all_10_1
% 176.38/27.38    (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.38/27.38    (12)   ~ (all_52_13 = all_52_29)
% 176.38/27.38    (13)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.38/27.38    (14)  all_56_3 = all_52_7
% 176.38/27.38    (15)  op(e3, e2) = all_52_3
% 176.38/27.38    (16)  op(e1, e2) = all_52_19
% 176.38/27.38    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.38/27.38    (18)   ~ (all_52_27 = e3)
% 176.38/27.38    (19)   ~ (all_52_17 = e3)
% 176.38/27.38    (20)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.38    (21)  all_58_12 = all_6_1
% 176.38/27.38    (22)  op(all_6_1, e3) = all_6_0
% 176.38/27.38    (23)   ~ (all_52_3 = all_10_2)
% 176.38/27.38    (24)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.38/27.38    (25)  all_58_5 = all_52_13
% 176.38/27.38    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.38/27.38    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.38/27.38    (28)  all_58_3 = all_10_2
% 176.38/27.38    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.38/27.38    (30)  all_58_15 = all_6_2
% 176.38/27.38    (31)   ~ (all_52_9 = all_4_2)
% 176.38/27.38    (32)   ~ (all_52_5 = all_52_7)
% 176.38/27.38    (33)  all_58_10 = all_52_15
% 176.38/27.38    (34)   ~ (all_52_5 = all_4_2)
% 176.38/27.38    (35)  all_58_7 = all_52_19
% 176.38/27.38    (36)  all_56_4 = all_52_9
% 176.38/27.38    (37)  op(e3, all_6_1) = all_52_24
% 176.38/27.38    (38)  op(e0, e1) = all_52_29
% 176.38/27.38    (39)  all_58_4 = all_52_5
% 176.38/27.38    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.38/27.38    (41)   ~ (e3 = e1)
% 176.38/27.38    (42)   ~ (all_52_27 = all_52_29)
% 176.38/27.38    (43)   ~ (all_52_17 = all_14_2)
% 176.38/27.38    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.38/27.38    (45)   ~ (all_52_7 = all_4_2)
% 176.38/27.38    (46)  all_58_1 = all_52_3
% 176.38/27.38    (47)   ~ (all_52_13 = all_52_15)
% 176.38/27.38    (48)  all_58_0 = all_4_2
% 176.38/27.38    (49)   ~ (all_52_9 = all_6_1)
% 176.38/27.38    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.38/27.38    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.38/27.38    (52)  all_58_14 = all_52_29
% 176.38/27.38    (53)  all_58_7 = e3
% 176.38/27.38    (54)   ~ (all_52_3 = all_52_5)
% 176.38/27.38    (55)  op(e2, e1) = all_52_13
% 176.38/27.38    (56)   ~ (all_52_17 = all_6_1)
% 176.38/27.38    (57)  all_58_8 = all_14_2
% 176.38/27.38    (58)  all_56_1 = all_52_3
% 176.38/27.38    (59)   ~ (all_6_1 = e3)
% 176.38/27.38    (60)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.38/27.38    (61)   ~ (all_52_5 = all_14_2)
% 176.38/27.38    (62)   ~ (all_52_23 = e3)
% 176.38/27.38    (63)   ~ (all_52_3 = all_52_27)
% 176.38/27.38    (64)   ~ (all_52_3 = all_4_2)
% 176.38/27.38    (65)  op(e3, all_4_2) = e3
% 176.38/27.38    (66)  op(e0, e3) = all_52_25
% 176.38/27.38    (67)   ~ (all_52_9 = all_10_2)
% 176.38/27.38    (68)  op(e3, all_52_17) = all_52_16
% 176.38/27.38    (69)   ~ (all_52_29 = e3)
% 176.38/27.38    (70)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.38/27.38    (71)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.38/27.38    (72)   ~ (all_52_13 = all_14_2)
% 176.38/27.38    (73)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.38/27.38    (74)   ~ (all_52_9 = all_52_13)
% 176.38/27.38    (75)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.38/27.38    (76)   ~ (all_52_5 = all_52_29)
% 176.38/27.38    (77)  all_56_2 = all_52_5
% 176.38/27.38    (78)  op(e1, e0) = all_52_23
% 176.38/27.38    (79)  all_58_13 = all_52_27
% 176.38/27.38    (80)   ~ (all_52_3 = e3)
% 176.38/27.38    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.38/27.38    (82)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.38/27.38    (83)   ~ (all_52_9 = all_52_17)
% 176.38/27.38    (84)  all_58_6 = all_52_17
% 176.38/27.38    (85)   ~ (all_52_3 = all_52_7)
% 176.38/27.38    (86)  op(all_10_1, all_10_2) = e3
% 176.38/27.38    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.38/27.38    (88)  op(e2, all_52_19) = all_52_18
% 176.38/27.38    (89)   ~ (e1 = e0)
% 176.38/27.38    (90)  all_56_0 = all_4_2
% 176.38/27.38    (91)  all_58_11 = all_52_23
% 176.38/27.38    (92)   ~ (all_52_3 = all_52_19)
% 176.38/27.38    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.38/27.38    (94)   ~ (all_52_7 = all_52_15)
% 176.38/27.38    (95)   ~ (all_52_29 = all_14_2)
% 176.38/27.38    (96)  all_58_2 = all_52_9
% 176.38/27.38    (97)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.38/27.38    (98)  op(e3, e1) = all_52_5
% 176.38/27.38    (99)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.38/27.38    (100)   ~ (e2 = e1)
% 176.38/27.38    (101)  all_56_10 = all_14_2
% 176.38/27.38    (102)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.38/27.38    (103)  op(e1, e1) = all_14_2
% 176.38/27.38    (104)  all_52_19 = e3
% 176.38/27.38    (105)  op(e1, e3) = all_52_17
% 176.38/27.38    (106)   ~ (all_52_25 = all_4_2)
% 176.38/27.38    (107)  op(e3, e0) = all_52_7
% 176.38/27.38    (108)  all_56_8 = all_52_17
% 176.38/27.38    (109)   ~ (all_14_2 = e3)
% 176.38/27.38    (110)   ~ (all_52_17 = all_4_2)
% 176.38/27.38    (111)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.38/27.38             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.38/27.38    (112)   ~ (all_52_7 = all_6_2)
% 176.38/27.38    (113)   ~ (all_52_7 = e3)
% 176.38/27.38    (114)  op(e1, all_52_5) = e1
% 176.38/27.38    (115)   ~ (all_52_7 = all_52_23)
% 176.38/27.38    (116)   ~ (all_52_13 = all_10_2)
% 176.38/27.38    (117)   ~ (all_6_0 = e1)
% 176.38/27.38    (118)  op(e0, all_52_7) = e0
% 176.38/27.38    (119)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.38/27.38    (120)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.38/27.38    (121)  all_58_9 = all_52_7
% 176.38/27.38    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.38/27.38    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.38/27.38    (124)   ~ (e3 = e2)
% 176.38/27.38    (125)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.38/27.38    (126)  op(e2, e3) = all_52_9
% 176.38/27.38    (127)  all_56_13 = all_52_27
% 176.38/27.38  
% 176.38/27.38  Begin of proof
% 176.38/27.38  | 
% 176.38/27.38  | REDUCE: (88), (104) imply:
% 176.38/27.38  |   (128)  op(e2, e3) = all_52_18
% 176.38/27.38  | 
% 176.38/27.38  | REDUCE: (16), (104) imply:
% 176.38/27.38  |   (129)  op(e1, e2) = e3
% 176.38/27.38  | 
% 176.38/27.38  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.38/27.38  |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.38/27.38  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.38/27.38  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.38/27.38  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 176.38/27.38  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 176.38/27.38  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 176.38/27.38  |            (80), (81), (82), (83), (84), (85), (86), (87), (89), (90), (91),
% 176.38/27.38  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 176.38/27.38  |            (102), (103), (105), (106), (107), (108), (109), (110), (111),
% 176.38/27.38  |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 176.38/27.38  |            (121), (122), (123), (124), (125), (126), (127), (128), (129) are
% 176.38/27.38  |            inconsistent by sub-proof #255.
% 176.38/27.38  | 
% 176.38/27.38  End of proof
% 176.38/27.38  
% 176.38/27.38  Sub-proof #234 shows that the following formulas are inconsistent:
% 176.38/27.38  ----------------------------------------------------------------
% 176.38/27.38    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.38/27.38    (2)   ~ (all_52_27 = all_10_2)
% 176.38/27.38    (3)   ~ (all_6_0 = e3)
% 176.38/27.38    (4)  op(e2, all_10_2) = all_10_1
% 176.38/27.38    (5)  all_56_3 = all_52_7
% 176.38/27.38    (6)  op(e3, e2) = all_52_3
% 176.38/27.38    (7)   ~ (all_52_9 = all_52_25)
% 176.38/27.38    (8)  op(e3, all_52_25) = all_52_24
% 176.38/27.38    (9)   ~ (all_52_19 = all_52_23)
% 176.38/27.38    (10)  all_56_11 = all_52_23
% 176.38/27.38    (11)  op(e1, e2) = all_52_19
% 176.38/27.38    (12)   ~ (all_52_3 = all_10_2)
% 176.38/27.38    (13)  all_58_5 = all_52_13
% 176.38/27.38    (14)   ~ (all_52_25 = all_52_29)
% 176.38/27.38    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.38/27.38    (16)  all_56_9 = all_52_19
% 176.38/27.38    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.38/27.38    (18)  all_58_15 = all_6_2
% 176.38/27.38    (19)   ~ (all_52_5 = all_52_7)
% 176.38/27.38    (20)  all_58_10 = all_52_15
% 176.38/27.38    (21)   ~ (all_52_5 = all_4_2)
% 176.38/27.38    (22)  all_58_7 = all_52_19
% 176.38/27.38    (23)   ~ (all_52_17 = all_52_25)
% 176.38/27.38    (24)  op(e0, e1) = all_52_29
% 176.38/27.38    (25)  all_58_4 = all_52_5
% 176.38/27.38    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.38/27.38    (27)   ~ (e3 = e1)
% 176.38/27.38    (28)   ~ (all_52_27 = all_52_29)
% 176.38/27.38    (29)  op(e3, all_4_2) = all_4_1
% 176.38/27.38    (30)   ~ (all_52_7 = all_4_2)
% 176.38/27.38    (31)  all_58_1 = all_52_3
% 176.38/27.38    (32)  all_58_0 = all_4_2
% 176.38/27.38    (33)  op(e0, e0) = all_6_2
% 176.38/27.38    (34)  op(e1, all_52_29) = all_52_28
% 176.38/27.38    (35)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.38/27.38    (36)   ~ (all_4_1 = e2)
% 176.38/27.38    (37)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.38/27.38    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.38/27.38    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.38/27.38    (40)  all_58_14 = all_52_29
% 176.38/27.38    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.38    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.38/27.38    (43)  op(e2, e1) = all_52_13
% 176.38/27.38    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.38/27.38    (45)  all_58_8 = all_14_2
% 176.38/27.38    (46)  op(e0, e2) = all_52_27
% 176.38/27.38    (47)  all_56_14 = all_52_29
% 176.38/27.38    (48)  op(e1, all_14_2) = e3
% 176.38/27.38    (49)  op(all_4_1, all_4_2) = all_4_0
% 176.38/27.38    (50)   ~ (all_52_5 = all_14_2)
% 176.38/27.38    (51)   ~ (all_52_3 = all_52_27)
% 176.38/27.38    (52)   ~ (all_52_3 = all_4_2)
% 176.38/27.38    (53)  op(all_6_1, all_6_2) = all_6_0
% 176.38/27.38    (54)  op(e0, e3) = all_52_25
% 176.38/27.38    (55)  op(e0, all_6_2) = all_6_1
% 176.38/27.38    (56)  all_52_0 = all_4_1
% 176.38/27.38    (57)  op(e3, all_52_17) = all_52_16
% 176.38/27.38    (58)  all_52_10 = all_10_1
% 176.38/27.38    (59)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.38/27.38    (60)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.38/27.38    (61)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.38/27.38    (62)   ~ (all_52_5 = all_52_29)
% 176.38/27.38    (63)  op(e1, e0) = all_52_23
% 176.38/27.38    (64)  all_56_12 = all_52_25
% 176.38/27.38    (65)  all_58_13 = all_52_27
% 176.38/27.38    (66)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.38/27.38    (67)  all_56_5 = all_10_2
% 176.38/27.38    (68)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.38/27.38    (69)   ~ (all_52_9 = all_52_17)
% 176.38/27.38    (70)  all_58_6 = all_52_17
% 176.38/27.38    (71)   ~ (all_52_3 = all_52_7)
% 176.38/27.38    (72)  op(all_10_1, all_10_2) = e3
% 176.38/27.38    (73)  all_52_20 = e3
% 176.38/27.38    (74)  all_56_0 = all_4_2
% 176.38/27.38    (75)  all_58_11 = all_52_23
% 176.38/27.38    (76)   ~ (all_52_3 = all_52_19)
% 176.38/27.38    (77)   ~ (all_52_7 = all_52_15)
% 176.38/27.38    (78)   ~ (all_52_29 = all_14_2)
% 176.38/27.38    (79)   ~ (all_52_19 = all_10_2)
% 176.38/27.38    (80)  all_58_15 = e0
% 176.38/27.38    (81)   ~ (all_52_23 = all_6_2)
% 176.38/27.38    (82)   ~ (all_52_29 = all_6_2)
% 176.38/27.38    (83)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.38/27.38    (84)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.38/27.38    (85)  op(e3, e1) = all_52_5
% 176.38/27.38    (86)  all_56_10 = all_14_2
% 176.38/27.38    (87)   ~ (all_52_25 = all_6_2)
% 176.38/27.38    (88)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.38/27.38    (89)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.38/27.38    (90)  op(e1, e1) = all_14_2
% 176.38/27.38    (91)  op(e1, e3) = all_52_17
% 176.38/27.38    (92)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.38/27.38    (93)   ~ (all_52_25 = all_4_2)
% 176.38/27.38    (94)  op(e3, e0) = all_52_7
% 176.38/27.38    (95)  op(e3, e3) = all_4_2
% 176.38/27.38    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.38/27.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.38/27.38    (97)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.38/27.38          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.38/27.38          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.38/27.38          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.38/27.38    (98)   ~ (all_52_25 = all_52_27)
% 176.38/27.38    (99)   ~ (all_52_27 = all_6_2)
% 176.38/27.38    (100)   ~ (all_52_7 = all_6_2)
% 176.38/27.38    (101)   ~ (all_52_19 = all_52_27)
% 176.38/27.38    (102)   ~ (all_52_7 = all_52_23)
% 176.38/27.38    (103)   ~ (all_52_13 = all_10_2)
% 176.38/27.38    (104)   ~ (all_6_0 = e1)
% 176.38/27.38    (105)  op(e2, all_52_27) = all_52_26
% 176.38/27.38    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.38/27.39    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.38/27.39    (108)  op(e3, all_14_2) = all_14_0
% 176.38/27.39    (109)  all_58_9 = all_52_7
% 176.38/27.39    (110)  all_58_12 = all_52_25
% 176.38/27.39    (111)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.38/27.39    (112)   ~ (e3 = e2)
% 176.38/27.39    (113)   ~ (all_52_19 = all_14_2)
% 176.38/27.39    (114)  op(e0, all_52_7) = all_52_6
% 176.38/27.39    (115)  op(e2, e3) = all_52_9
% 176.38/27.39    (116)  all_56_13 = all_52_27
% 176.38/27.39  
% 176.38/27.39  Begin of proof
% 176.38/27.39  | 
% 176.38/27.39  | COMBINE_EQS: (18), (80) imply:
% 176.38/27.39  |   (117)  all_6_2 = e0
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (100), (117) imply:
% 176.38/27.39  |   (118)   ~ (all_52_7 = e0)
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (81), (117) imply:
% 176.38/27.39  |   (119)   ~ (all_52_23 = e0)
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (87), (117) imply:
% 176.38/27.39  |   (120)   ~ (all_52_25 = e0)
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (99), (117) imply:
% 176.38/27.39  |   (121)   ~ (all_52_27 = e0)
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (82), (117) imply:
% 176.38/27.39  |   (122)   ~ (all_52_29 = e0)
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (53), (117) imply:
% 176.38/27.39  |   (123)  op(all_6_1, e0) = all_6_0
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (55), (117) imply:
% 176.38/27.39  |   (124)  op(e0, e0) = all_6_1
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (33), (117) imply:
% 176.38/27.39  |   (125)  op(e0, e0) = e0
% 176.38/27.39  | 
% 176.38/27.39  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.38/27.39  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.38/27.39  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 176.38/27.39  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.38/27.39  |            (47), (48), (49), (50), (51), (52), (54), (56), (57), (58), (59),
% 176.38/27.39  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 176.38/27.39  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (83),
% 176.38/27.39  |            (84), (85), (86), (88), (89), (90), (91), (92), (93), (94), (95),
% 176.38/27.39  |            (96), (97), (98), (100), (101), (102), (103), (104), (105), (106),
% 176.38/27.39  |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 176.38/27.39  |            (116), (118), (119), (120), (121), (122), (123), (124), (125) are
% 176.38/27.39  |            inconsistent by sub-proof #236.
% 176.38/27.39  | 
% 176.38/27.39  End of proof
% 176.38/27.39  
% 176.38/27.39  Sub-proof #235 shows that the following formulas are inconsistent:
% 176.38/27.39  ----------------------------------------------------------------
% 176.38/27.39    (1)   ~ (all_52_23 = all_14_2)
% 176.38/27.39    (2)   ~ (all_52_5 = all_52_13)
% 176.38/27.39    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.38/27.39    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.38/27.39    (5)   ~ (all_52_27 = all_10_2)
% 176.38/27.39    (6)  op(e2, e2) = all_10_2
% 176.38/27.39    (7)   ~ (all_52_17 = all_52_23)
% 176.38/27.39    (8)  op(e2, all_52_3) = e2
% 176.38/27.39    (9)  op(e2, all_10_2) = all_10_1
% 176.38/27.39    (10)   ~ (all_52_13 = all_52_29)
% 176.38/27.39    (11)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.38/27.39    (12)  all_56_3 = all_52_7
% 176.38/27.39    (13)  op(e3, e2) = all_52_3
% 176.38/27.39    (14)   ~ (all_52_9 = all_52_25)
% 176.38/27.39    (15)  op(e3, all_52_25) = all_52_24
% 176.38/27.39    (16)   ~ (all_52_19 = all_52_23)
% 176.38/27.39    (17)  all_56_11 = all_52_23
% 176.38/27.39    (18)  op(e1, e2) = all_52_19
% 176.38/27.39    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.38/27.39    (20)   ~ (all_52_3 = all_10_2)
% 176.38/27.39    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.38/27.39    (22)  all_58_5 = all_52_13
% 176.38/27.39    (23)   ~ (all_6_2 = e0)
% 176.38/27.39    (24)   ~ (all_52_25 = all_52_29)
% 176.38/27.39    (25)  all_56_15 = all_6_2
% 176.38/27.39    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.38/27.39    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.38/27.39    (28)  all_58_3 = all_10_2
% 176.38/27.39    (29)  all_56_9 = all_52_19
% 176.38/27.39    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.38/27.39    (31)  all_58_15 = all_6_2
% 176.38/27.39    (32)   ~ (all_52_9 = all_4_2)
% 176.38/27.39    (33)   ~ (all_52_5 = all_52_7)
% 176.38/27.39    (34)  all_58_10 = all_52_15
% 176.38/27.39    (35)   ~ (all_52_5 = all_4_2)
% 176.38/27.39    (36)  all_58_7 = all_52_19
% 176.38/27.39    (37)  all_56_4 = all_52_9
% 176.38/27.39    (38)   ~ (all_52_15 = all_6_2)
% 176.38/27.39    (39)   ~ (all_52_17 = all_52_25)
% 176.38/27.39    (40)  op(e0, e1) = all_52_29
% 176.38/27.39    (41)   ~ (all_4_0 = e2)
% 176.38/27.39    (42)  all_58_4 = all_52_5
% 176.38/27.39    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.38/27.39    (44)   ~ (all_52_27 = all_52_29)
% 176.38/27.39    (45)   ~ (all_52_17 = all_14_2)
% 176.38/27.39    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.38/27.39    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.38/27.39    (48)   ~ (all_52_7 = all_4_2)
% 176.38/27.39    (49)  all_58_1 = all_52_3
% 176.38/27.39    (50)   ~ (all_52_13 = all_52_15)
% 176.38/27.39    (51)  all_58_0 = all_4_2
% 176.38/27.39    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.38/27.39    (53)  op(e1, all_52_29) = all_52_28
% 176.38/27.39    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.38/27.39    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.38/27.39    (56)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.38/27.39    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.38/27.39    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.38/27.39    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.38/27.39    (60)  all_58_14 = all_52_29
% 176.38/27.39    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.39    (62)   ~ (all_52_3 = all_52_5)
% 176.38/27.39    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.38/27.39    (64)  op(e2, e1) = all_52_13
% 176.38/27.39    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.38/27.39    (66)  all_58_8 = all_14_2
% 176.38/27.39    (67)  all_56_1 = all_52_3
% 176.38/27.39    (68)  all_56_14 = all_52_29
% 176.38/27.39    (69)  op(e1, all_14_2) = e3
% 176.38/27.39    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.38/27.39    (71)   ~ (all_52_5 = all_14_2)
% 176.38/27.39    (72)   ~ (all_52_3 = all_52_27)
% 176.38/27.39    (73)   ~ (all_52_3 = all_4_2)
% 176.38/27.39    (74)  op(all_6_1, all_6_2) = all_6_0
% 176.38/27.39    (75)  op(e3, all_4_2) = e3
% 176.38/27.39    (76)  op(e0, e3) = all_52_25
% 176.38/27.39    (77)  op(e0, all_6_2) = all_6_1
% 176.38/27.39    (78)   ~ (all_52_9 = all_10_2)
% 176.38/27.39    (79)  op(e3, all_52_17) = all_52_16
% 176.38/27.39    (80)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.38/27.39    (81)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.38/27.39    (82)   ~ (all_52_13 = all_14_2)
% 176.38/27.39    (83)   ~ (e3 = e0)
% 176.38/27.39    (84)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.38/27.39    (85)   ~ (all_52_9 = all_52_13)
% 176.38/27.39    (86)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.38/27.39    (87)  op(e0, all_52_23) = all_52_22
% 176.38/27.39    (88)   ~ (all_52_15 = all_52_23)
% 176.38/27.39    (89)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.38/27.39    (90)   ~ (all_52_5 = all_52_29)
% 176.38/27.39    (91)  all_56_2 = all_52_5
% 176.38/27.39    (92)  op(e1, e0) = all_52_23
% 176.38/27.39    (93)  all_56_12 = all_52_25
% 176.38/27.39    (94)  all_58_13 = all_52_27
% 176.38/27.39    (95)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.38/27.39    (96)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.38/27.39    (97)   ~ (all_52_9 = all_52_17)
% 176.38/27.39    (98)  all_58_6 = all_52_17
% 176.38/27.39    (99)   ~ (all_52_3 = all_52_7)
% 176.38/27.39    (100)  op(all_10_1, all_10_2) = e3
% 176.38/27.39    (101)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.38/27.39    (102)  op(e2, all_52_19) = all_52_18
% 176.38/27.39    (103)   ~ (e1 = e0)
% 176.38/27.39    (104)  all_56_0 = all_4_2
% 176.38/27.39    (105)  all_58_11 = all_52_23
% 176.38/27.39    (106)   ~ (all_52_3 = all_52_19)
% 176.38/27.39    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.38/27.39    (108)   ~ (all_52_7 = all_52_15)
% 176.38/27.39    (109)  op(e0, all_52_15) = all_52_14
% 176.38/27.39    (110)   ~ (all_52_29 = all_14_2)
% 176.38/27.39    (111)   ~ (all_4_0 = e1)
% 176.38/27.39    (112)   ~ (all_52_19 = all_10_2)
% 176.38/27.39    (113)   ~ (all_52_23 = all_6_2)
% 176.38/27.39    (114)   ~ (all_52_29 = all_6_2)
% 176.38/27.39    (115)  all_58_2 = all_52_9
% 176.38/27.39    (116)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.38/27.39    (117)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.38/27.39    (118)  op(e3, e1) = all_52_5
% 176.38/27.39    (119)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.38/27.39    (120)   ~ (e2 = e1)
% 176.38/27.39    (121)  all_56_10 = all_14_2
% 176.38/27.39    (122)   ~ (all_52_25 = all_6_2)
% 176.38/27.39    (123)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.38/27.39    (124)  op(e1, e1) = all_14_2
% 176.38/27.39    (125)  op(e1, e3) = all_52_17
% 176.38/27.39    (126)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.38/27.39    (127)   ~ (all_52_25 = all_4_2)
% 176.38/27.39    (128)  op(e3, e0) = all_52_7
% 176.38/27.39    (129)  all_56_8 = all_52_17
% 176.38/27.39    (130)   ~ (all_52_17 = all_4_2)
% 176.38/27.39    (131)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.38/27.39             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.38/27.39    (132)   ~ (all_52_25 = all_52_27)
% 176.38/27.39    (133)   ~ (all_52_27 = all_6_2)
% 176.38/27.39    (134)   ~ (all_52_7 = all_6_2)
% 176.38/27.39    (135)   ~ (all_52_19 = all_52_27)
% 176.38/27.39    (136)  all_56_7 = all_52_15
% 176.38/27.39    (137)  op(e1, all_52_5) = e1
% 176.38/27.39    (138)   ~ (all_52_7 = all_52_23)
% 176.38/27.39    (139)   ~ (all_52_13 = all_10_2)
% 176.38/27.39    (140)   ~ (all_6_0 = e1)
% 176.38/27.39    (141)  op(e3, all_4_2) = all_4_0
% 176.38/27.39    (142)  op(e0, all_52_7) = e0
% 176.38/27.39    (143)  op(e2, all_52_27) = all_52_26
% 176.38/27.39    (144)   ~ (all_52_17 = all_52_19)
% 176.38/27.39    (145)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.38/27.39    (146)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.38/27.39    (147)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.38/27.39    (148)  all_58_9 = all_52_7
% 176.38/27.39    (149)  all_58_12 = all_52_25
% 176.38/27.39    (150)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.38/27.39    (151)   ~ (all_52_9 = all_52_15)
% 176.38/27.39    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.38/27.39    (153)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.38/27.39    (154)   ~ (all_52_19 = all_14_2)
% 176.38/27.39    (155)  op(e2, e3) = all_52_9
% 176.38/27.39    (156)  all_56_13 = all_52_27
% 176.38/27.39  
% 176.38/27.39  Begin of proof
% 176.38/27.39  | 
% 176.38/27.39  | GROUND_INST: instantiating (131) with e3, all_4_0, all_4_2, e3, simplifying
% 176.38/27.39  |              with (75), (141) gives:
% 176.38/27.39  |   (157)  all_4_0 = e3
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (41), (157) imply:
% 176.38/27.39  |   (158)   ~ (e3 = e2)
% 176.38/27.39  | 
% 176.38/27.39  | REDUCE: (111), (157) imply:
% 176.38/27.39  |   (159)   ~ (e3 = e1)
% 176.38/27.39  | 
% 176.38/27.39  | BETA: splitting (46) gives:
% 176.38/27.39  | 
% 176.38/27.39  | Case 1:
% 176.38/27.39  | | 
% 176.38/27.39  | |   (160)  all_56_15 = e3
% 176.38/27.39  | | 
% 176.38/27.39  | | COMBINE_EQS: (25), (160) imply:
% 176.38/27.39  | |   (161)  all_6_2 = e3
% 176.38/27.39  | | 
% 176.38/27.39  | | SIMP: (161) implies:
% 176.38/27.39  | |   (162)  all_6_2 = e3
% 176.38/27.39  | | 
% 176.38/27.39  | | COMBINE_EQS: (31), (162) imply:
% 176.38/27.39  | |   (163)  all_58_15 = e3
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (134), (162) imply:
% 176.38/27.39  | |   (164)   ~ (all_52_7 = e3)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (38), (162) imply:
% 176.38/27.39  | |   (165)   ~ (all_52_15 = e3)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (122), (162) imply:
% 176.38/27.39  | |   (166)   ~ (all_52_25 = e3)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (133), (162) imply:
% 176.38/27.39  | |   (167)   ~ (all_52_27 = e3)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (114), (162) imply:
% 176.38/27.39  | |   (168)   ~ (all_52_29 = e3)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (74), (162) imply:
% 176.38/27.39  | |   (169)  op(all_6_1, e3) = all_6_0
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (77), (162) imply:
% 176.38/27.39  | |   (170)  op(e0, e3) = all_6_1
% 176.38/27.39  | | 
% 176.38/27.39  | | GROUND_INST: instantiating (131) with all_52_25, all_6_1, e3, e0,
% 176.38/27.39  | |              simplifying with (76), (170) gives:
% 176.38/27.39  | |   (171)  all_52_25 = all_6_1
% 176.38/27.39  | | 
% 176.38/27.39  | | COMBINE_EQS: (149), (171) imply:
% 176.38/27.39  | |   (172)  all_58_12 = all_6_1
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (14), (171) imply:
% 176.38/27.39  | |   (173)   ~ (all_52_9 = all_6_1)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (39), (171) imply:
% 176.38/27.39  | |   (174)   ~ (all_52_17 = all_6_1)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (127), (171) imply:
% 176.38/27.39  | |   (175)   ~ (all_6_1 = all_4_2)
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (15), (171) imply:
% 176.38/27.39  | |   (176)  op(e3, all_6_1) = all_52_24
% 176.38/27.39  | | 
% 176.38/27.39  | | BETA: splitting (61) gives:
% 176.38/27.39  | | 
% 176.38/27.39  | | Case 1:
% 176.38/27.39  | | | 
% 176.38/27.39  | | |   (177)  all_56_13 = e3
% 176.38/27.39  | | | 
% 176.38/27.39  | | | REF_CLOSE: (156), (167), (177) are inconsistent by sub-proof #876.
% 176.38/27.39  | | | 
% 176.38/27.39  | | Case 2:
% 176.38/27.39  | | | 
% 176.38/27.39  | | |   (178)   ~ (all_56_13 = e3)
% 176.38/27.39  | | |   (179)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.39  | | | 
% 176.38/27.39  | | | BETA: splitting (146) gives:
% 176.38/27.39  | | | 
% 176.38/27.39  | | | Case 1:
% 176.38/27.39  | | | | 
% 176.38/27.39  | | | |   (180)  all_56_3 = e3
% 176.38/27.39  | | | | 
% 176.38/27.39  | | | | REF_CLOSE: (12), (164), (180) are inconsistent by sub-proof #1034.
% 176.38/27.39  | | | | 
% 176.38/27.39  | | | Case 2:
% 176.38/27.39  | | | | 
% 176.38/27.39  | | | |   (181)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.38/27.39  | | | | 
% 176.38/27.39  | | | | BETA: splitting (55) gives:
% 176.38/27.39  | | | | 
% 176.38/27.39  | | | | Case 1:
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | |   (182)  all_56_9 = e3
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | COMBINE_EQS: (29), (182) imply:
% 176.38/27.39  | | | | |   (183)  all_52_19 = e3
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | SIMP: (183) implies:
% 176.38/27.39  | | | | |   (184)  all_52_19 = e3
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | COMBINE_EQS: (36), (184) imply:
% 176.38/27.39  | | | | |   (185)  all_58_7 = e3
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (144), (184) imply:
% 176.38/27.39  | | | | |   (186)   ~ (all_52_17 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (16), (184) imply:
% 176.38/27.39  | | | | |   (187)   ~ (all_52_23 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | SIMP: (187) implies:
% 176.38/27.39  | | | | |   (188)   ~ (all_52_23 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (135), (184) imply:
% 176.38/27.39  | | | | |   (189)   ~ (all_52_27 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (112), (184) imply:
% 176.38/27.39  | | | | |   (190)   ~ (all_10_2 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | SIMP: (190) implies:
% 176.38/27.39  | | | | |   (191)   ~ (all_10_2 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (102), (184) imply:
% 176.38/27.39  | | | | |   (192)  op(e2, e3) = all_52_18
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (18), (184) imply:
% 176.38/27.39  | | | | |   (193)  op(e1, e2) = e3
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | GROUND_INST: instantiating (131) with all_52_9, all_52_18, e3, e2,
% 176.38/27.39  | | | | |              simplifying with (155), (192) gives:
% 176.38/27.39  | | | | |   (194)  all_52_9 = all_52_18
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | COMBINE_EQS: (37), (194) imply:
% 176.38/27.39  | | | | |   (195)  all_56_4 = all_52_18
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | COMBINE_EQS: (115), (194) imply:
% 176.38/27.39  | | | | |   (196)  all_58_2 = all_52_18
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (85), (194) imply:
% 176.38/27.39  | | | | |   (197)   ~ (all_52_13 = all_52_18)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | SIMP: (197) implies:
% 176.38/27.39  | | | | |   (198)   ~ (all_52_13 = all_52_18)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (97), (194) imply:
% 176.38/27.39  | | | | |   (199)   ~ (all_52_17 = all_52_18)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | SIMP: (199) implies:
% 176.38/27.39  | | | | |   (200)   ~ (all_52_17 = all_52_18)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (78), (194) imply:
% 176.38/27.39  | | | | |   (201)   ~ (all_52_18 = all_10_2)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (173), (194) imply:
% 176.38/27.39  | | | | |   (202)   ~ (all_52_18 = all_6_1)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (32), (194) imply:
% 176.38/27.39  | | | | |   (203)   ~ (all_52_18 = all_4_2)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | BETA: splitting (63) gives:
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | Case 1:
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | |   (204)  all_58_0 = e3
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | | COMBINE_EQS: (51), (204) imply:
% 176.38/27.39  | | | | | |   (205)  all_4_2 = e3
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | | REDUCE: (73), (205) imply:
% 176.38/27.39  | | | | | |   (206)   ~ (all_52_3 = e3)
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | | REDUCE: (203), (205) imply:
% 176.38/27.39  | | | | | |   (207)   ~ (all_52_18 = e3)
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | | REDUCE: (175), (205) imply:
% 176.38/27.39  | | | | | |   (208)   ~ (all_6_1 = e3)
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.38/27.39  | | | | | |            (13), (19), (20), (21), (22), (26), (27), (28), (34),
% 176.38/27.39  | | | | | |            (40), (42), (44), (45), (47), (49), (54), (57), (60),
% 176.38/27.39  | | | | | |            (62), (64), (66), (67), (70), (71), (72), (79), (80),
% 176.38/27.39  | | | | | |            (81), (90), (91), (92), (94), (95), (96), (98), (99),
% 176.38/27.39  | | | | | |            (100), (101), (103), (107), (108), (116), (118), (119),
% 176.38/27.39  | | | | | |            (120), (123), (124), (128), (129), (131), (137), (138),
% 176.38/27.39  | | | | | |            (139), (140), (142), (147), (148), (153), (156), (158),
% 176.38/27.39  | | | | | |            (159), (163), (164), (165), (167), (169), (172), (174),
% 176.38/27.39  | | | | | |            (176), (179), (181), (185), (186), (188), (191), (192),
% 176.38/27.39  | | | | | |            (193), (195), (196), (198), (200), (201), (202), (204),
% 176.38/27.39  | | | | | |            (206), (207), (208) are inconsistent by sub-proof #256.
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | Case 2:
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | |   (209)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | | BETA: splitting (209) gives:
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | | Case 1:
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | |   (210)  all_58_2 = e3
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | | COMBINE_EQS: (196), (210) imply:
% 176.38/27.39  | | | | | | |   (211)  all_52_18 = e3
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | | SIMP: (211) implies:
% 176.38/27.39  | | | | | | |   (212)  all_52_18 = e3
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | | REDUCE: (198), (212) imply:
% 176.38/27.39  | | | | | | |   (213)   ~ (all_52_13 = e3)
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | | REF_CLOSE: (13), (22), (30), (33), (35), (42), (45), (51), (60),
% 176.38/27.39  | | | | | | |            (62), (66), (69), (75), (84), (104), (125), (128),
% 176.38/27.39  | | | | | | |            (130), (131), (137), (152), (168), (213) are
% 176.38/27.39  | | | | | | |            inconsistent by sub-proof #419.
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | Case 2:
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | |   (214)  all_58_6 = e3 | all_58_12 = e3
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | | REF_CLOSE: (98), (149), (166), (186), (214) are inconsistent by
% 176.38/27.39  | | | | | | |            sub-proof #483.
% 176.38/27.39  | | | | | | | 
% 176.38/27.39  | | | | | | End of split
% 176.38/27.39  | | | | | | 
% 176.38/27.39  | | | | | End of split
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | Case 2:
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | |   (215)   ~ (all_56_9 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REDUCE: (29), (215) imply:
% 176.38/27.39  | | | | |   (216)   ~ (all_52_19 = e3)
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | | REF_CLOSE: (8), (13), (22), (28), (30), (32), (33), (35), (36), (42),
% 176.38/27.39  | | | | |            (45), (49), (51), (58), (60), (62), (66), (69), (73), (75),
% 176.38/27.39  | | | | |            (84), (94), (95), (99), (104), (118), (125), (128), (130),
% 176.38/27.39  | | | | |            (131), (137), (139), (152), (155), (167), (168), (216) are
% 176.38/27.39  | | | | |            inconsistent by sub-proof #418.
% 176.38/27.39  | | | | | 
% 176.38/27.39  | | | | End of split
% 176.38/27.39  | | | | 
% 176.38/27.39  | | | End of split
% 176.38/27.39  | | | 
% 176.38/27.39  | | End of split
% 176.38/27.39  | | 
% 176.38/27.39  | Case 2:
% 176.38/27.39  | | 
% 176.38/27.39  | |   (217)   ~ (all_56_15 = e3)
% 176.38/27.39  | |   (218)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.38/27.39  | | 
% 176.38/27.39  | | REDUCE: (25), (217) imply:
% 176.38/27.39  | |   (219)   ~ (all_6_2 = e3)
% 176.38/27.39  | | 
% 176.38/27.39  | | REF_CLOSE: (1), (2), (7), (8), (10), (13), (14), (16), (17), (18), (19),
% 176.38/27.39  | |            (20), (22), (23), (24), (25), (26), (27), (28), (30), (31), (32),
% 176.38/27.39  | |            (33), (34), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 176.38/27.39  | |            (45), (47), (48), (49), (50), (51), (52), (53), (56), (57), (58),
% 176.38/27.39  | |            (59), (60), (61), (62), (63), (64), (65), (66), (68), (69), (71),
% 176.38/27.39  | |            (73), (75), (76), (81), (82), (83), (84), (85), (86), (87), (88),
% 176.38/27.39  | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 176.38/27.39  | |            (101), (103), (104), (105), (106), (107), (108), (109), (110),
% 176.38/27.39  | |            (113), (114), (115), (117), (118), (121), (122), (124), (125),
% 176.38/27.39  | |            (126), (127), (128), (130), (131), (132), (133), (134), (135),
% 176.38/27.39  | |            (136), (137), (138), (139), (142), (143), (144), (145), (148),
% 176.38/27.39  | |            (149), (150), (151), (152), (153), (154), (155), (156), (158),
% 176.38/27.39  | |            (159), (218), (219) are inconsistent by sub-proof #401.
% 176.38/27.39  | | 
% 176.38/27.39  | End of split
% 176.38/27.39  | 
% 176.38/27.39  End of proof
% 176.38/27.39  
% 176.38/27.39  Sub-proof #236 shows that the following formulas are inconsistent:
% 176.38/27.39  ----------------------------------------------------------------
% 176.38/27.39    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.38/27.39    (2)   ~ (all_52_27 = all_10_2)
% 176.38/27.39    (3)   ~ (all_6_0 = e3)
% 176.38/27.39    (4)  op(e2, all_10_2) = all_10_1
% 176.38/27.39    (5)  all_56_3 = all_52_7
% 176.38/27.39    (6)  op(e3, e2) = all_52_3
% 176.38/27.39    (7)   ~ (all_52_9 = all_52_25)
% 176.38/27.39    (8)  op(e3, all_52_25) = all_52_24
% 176.38/27.39    (9)   ~ (all_52_19 = all_52_23)
% 176.38/27.39    (10)  all_56_11 = all_52_23
% 176.38/27.39    (11)  op(e1, e2) = all_52_19
% 176.38/27.39    (12)   ~ (all_52_27 = e0)
% 176.38/27.39    (13)   ~ (all_52_23 = e0)
% 176.38/27.39    (14)   ~ (all_52_3 = all_10_2)
% 176.38/27.39    (15)  all_58_5 = all_52_13
% 176.38/27.39    (16)   ~ (all_52_25 = all_52_29)
% 176.38/27.39    (17)  op(e0, e0) = all_6_1
% 176.38/27.39    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.38/27.39    (19)  all_56_9 = all_52_19
% 176.38/27.39    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.38/27.39    (21)  all_58_15 = all_6_2
% 176.38/27.39    (22)   ~ (all_52_5 = all_52_7)
% 176.38/27.39    (23)  all_58_10 = all_52_15
% 176.38/27.39    (24)   ~ (all_52_5 = all_4_2)
% 176.38/27.39    (25)  all_58_7 = all_52_19
% 176.38/27.39    (26)   ~ (all_52_17 = all_52_25)
% 176.38/27.39    (27)  op(e0, e1) = all_52_29
% 176.38/27.39    (28)  all_58_4 = all_52_5
% 176.38/27.39    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.38/27.39    (30)   ~ (e3 = e1)
% 176.38/27.39    (31)   ~ (all_52_27 = all_52_29)
% 176.38/27.39    (32)  op(e3, all_4_2) = all_4_1
% 176.38/27.39    (33)   ~ (all_52_7 = all_4_2)
% 176.38/27.39    (34)  all_58_1 = all_52_3
% 176.38/27.39    (35)  all_58_0 = all_4_2
% 176.38/27.39    (36)  op(e1, all_52_29) = all_52_28
% 176.38/27.39    (37)   ~ (all_52_7 = e0)
% 176.38/27.39    (38)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.38/27.39    (39)   ~ (all_4_1 = e2)
% 176.38/27.39    (40)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.38/27.39    (41)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.38/27.39    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.38/27.39    (43)  all_58_14 = all_52_29
% 176.38/27.39    (44)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.38/27.39    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.38/27.39    (46)  op(e2, e1) = all_52_13
% 176.38/27.39    (47)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.38/27.39    (48)  all_58_8 = all_14_2
% 176.38/27.39    (49)  op(e0, e2) = all_52_27
% 176.38/27.39    (50)  all_56_14 = all_52_29
% 176.38/27.39    (51)  op(e1, all_14_2) = e3
% 176.38/27.39    (52)  op(all_4_1, all_4_2) = all_4_0
% 176.38/27.39    (53)   ~ (all_52_5 = all_14_2)
% 176.38/27.39    (54)   ~ (all_52_3 = all_52_27)
% 176.38/27.39    (55)   ~ (all_52_3 = all_4_2)
% 176.38/27.39    (56)  op(e0, e3) = all_52_25
% 176.38/27.39    (57)  all_52_0 = all_4_1
% 176.45/27.39    (58)  op(e3, all_52_17) = all_52_16
% 176.45/27.39    (59)  all_52_10 = all_10_1
% 176.45/27.39    (60)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.45/27.39    (61)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.45/27.39    (62)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.45/27.39    (63)   ~ (all_52_5 = all_52_29)
% 176.45/27.39    (64)  op(e1, e0) = all_52_23
% 176.45/27.39    (65)  all_56_12 = all_52_25
% 176.45/27.40    (66)  all_58_13 = all_52_27
% 176.45/27.40    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.40    (68)  all_56_5 = all_10_2
% 176.45/27.40    (69)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.45/27.40    (70)  op(e0, e0) = e0
% 176.45/27.40    (71)   ~ (all_52_25 = e0)
% 176.45/27.40    (72)   ~ (all_52_9 = all_52_17)
% 176.45/27.40    (73)  all_58_6 = all_52_17
% 176.45/27.40    (74)   ~ (all_52_3 = all_52_7)
% 176.45/27.40    (75)  op(all_10_1, all_10_2) = e3
% 176.45/27.40    (76)  all_52_20 = e3
% 176.45/27.40    (77)  all_56_0 = all_4_2
% 176.45/27.40    (78)  all_58_11 = all_52_23
% 176.45/27.40    (79)   ~ (all_52_3 = all_52_19)
% 176.45/27.40    (80)   ~ (all_52_7 = all_52_15)
% 176.45/27.40    (81)   ~ (all_52_29 = all_14_2)
% 176.45/27.40    (82)   ~ (all_52_19 = all_10_2)
% 176.45/27.40    (83)  all_58_15 = e0
% 176.45/27.40    (84)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.45/27.40    (85)   ~ (all_52_29 = e0)
% 176.45/27.40    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.45/27.40    (87)  op(e3, e1) = all_52_5
% 176.45/27.40    (88)  all_56_10 = all_14_2
% 176.45/27.40    (89)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.45/27.40    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.45/27.40    (91)  op(e1, e1) = all_14_2
% 176.45/27.40    (92)  op(e1, e3) = all_52_17
% 176.45/27.40    (93)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.45/27.40    (94)   ~ (all_52_25 = all_4_2)
% 176.45/27.40    (95)  op(e3, e0) = all_52_7
% 176.45/27.40    (96)  op(e3, e3) = all_4_2
% 176.45/27.40    (97)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.40    (98)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.45/27.40          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.45/27.40          (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.45/27.40          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.45/27.40    (99)   ~ (all_52_25 = all_52_27)
% 176.45/27.40    (100)   ~ (all_52_7 = all_6_2)
% 176.45/27.40    (101)   ~ (all_52_19 = all_52_27)
% 176.45/27.40    (102)  op(all_6_1, e0) = all_6_0
% 176.45/27.40    (103)   ~ (all_52_7 = all_52_23)
% 176.45/27.40    (104)   ~ (all_52_13 = all_10_2)
% 176.45/27.40    (105)   ~ (all_6_0 = e1)
% 176.45/27.40    (106)  op(e2, all_52_27) = all_52_26
% 176.45/27.40    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.45/27.40    (108)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.45/27.40    (109)  op(e3, all_14_2) = all_14_0
% 176.45/27.40    (110)  all_58_9 = all_52_7
% 176.45/27.40    (111)  all_58_12 = all_52_25
% 176.45/27.40    (112)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.45/27.40    (113)   ~ (e3 = e2)
% 176.45/27.40    (114)   ~ (all_52_19 = all_14_2)
% 176.45/27.40    (115)  op(e0, all_52_7) = all_52_6
% 176.45/27.40    (116)  op(e2, e3) = all_52_9
% 176.45/27.40    (117)  all_56_13 = all_52_27
% 176.45/27.40  
% 176.45/27.40  Begin of proof
% 176.45/27.40  | 
% 176.45/27.40  | GROUND_INST: instantiating (97) with e0, all_6_1, e0, e0, simplifying with
% 176.45/27.40  |              (17), (70) gives:
% 176.45/27.40  |   (118)  all_6_1 = e0
% 176.45/27.40  | 
% 176.45/27.40  | REDUCE: (102), (118) imply:
% 176.45/27.40  |   (119)  op(e0, e0) = all_6_0
% 176.45/27.40  | 
% 176.45/27.40  | GROUND_INST: instantiating (97) with e0, all_6_0, e0, e0, simplifying with
% 176.45/27.40  |              (70), (119) gives:
% 176.45/27.40  |   (120)  all_6_0 = e0
% 176.45/27.40  | 
% 176.45/27.40  | REDUCE: (3), (120) imply:
% 176.45/27.40  |   (121)   ~ (e3 = e0)
% 176.45/27.40  | 
% 176.45/27.40  | SIMP: (121) implies:
% 176.45/27.40  |   (122)   ~ (e3 = e0)
% 176.45/27.40  | 
% 176.45/27.40  | REDUCE: (105), (120) imply:
% 176.45/27.40  |   (123)   ~ (e1 = e0)
% 176.45/27.40  | 
% 176.45/27.40  | SIMP: (123) implies:
% 176.45/27.40  |   (124)   ~ (e1 = e0)
% 176.45/27.40  | 
% 176.45/27.40  | BETA: splitting (98) gives:
% 176.45/27.40  | 
% 176.45/27.40  | Case 1:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (125)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.45/27.40  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.45/27.40  | | 
% 176.45/27.40  | | BETA: splitting (125) gives:
% 176.45/27.40  | | 
% 176.45/27.40  | | Case 1:
% 176.45/27.40  | | | 
% 176.45/27.40  | | |   (126)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.45/27.40  | | | 
% 176.45/27.40  | | | ALPHA: (126) implies:
% 176.45/27.40  | | |   (127)  all_52_6 = e0
% 176.45/27.40  | | |   (128)  all_52_0 = e3
% 176.45/27.40  | | | 
% 176.45/27.40  | | | COMBINE_EQS: (57), (128) imply:
% 176.45/27.40  | | |   (129)  all_4_1 = e3
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REDUCE: (52), (129) imply:
% 176.45/27.40  | | |   (130)  op(e3, all_4_2) = all_4_0
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REDUCE: (32), (129) imply:
% 176.45/27.40  | | |   (131)  op(e3, all_4_2) = e3
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REDUCE: (115), (127) imply:
% 176.45/27.40  | | |   (132)  op(e0, all_52_7) = e0
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REF_CLOSE: (5), (6), (12), (18), (20), (21), (22), (23), (27), (28), (33),
% 176.45/27.40  | | |            (34), (35), (37), (42), (43), (44), (45), (47), (49), (56),
% 176.45/27.40  | | |            (60), (61), (63), (65), (66), (67), (71), (74), (77), (78),
% 176.45/27.40  | | |            (80), (83), (84), (85), (87), (90), (94), (97), (99), (100),
% 176.45/27.40  | | |            (103), (107), (108), (110), (111), (112), (117), (122), (130),
% 176.45/27.40  | | |            (131), (132) are inconsistent by sub-proof #1009.
% 176.45/27.40  | | | 
% 176.45/27.40  | | Case 2:
% 176.45/27.40  | | | 
% 176.45/27.40  | | |   (133)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.45/27.40  | | | 
% 176.45/27.40  | | | ALPHA: (133) implies:
% 176.45/27.40  | | |   (134)  all_52_10 = e2
% 176.45/27.40  | | | 
% 176.45/27.40  | | | COMBINE_EQS: (59), (134) imply:
% 176.45/27.40  | | |   (135)  all_10_1 = e2
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REF_CLOSE: (4), (75), (97), (113), (135) are inconsistent by sub-proof
% 176.45/27.40  | | |            #263.
% 176.45/27.40  | | | 
% 176.45/27.40  | | End of split
% 176.45/27.40  | | 
% 176.45/27.40  | Case 2:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (136)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 176.45/27.40  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 176.45/27.40  | |            e0)
% 176.45/27.40  | | 
% 176.45/27.40  | | BETA: splitting (136) gives:
% 176.45/27.40  | | 
% 176.45/27.40  | | Case 1:
% 176.45/27.40  | | | 
% 176.45/27.40  | | |   (137)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REF_CLOSE: (30), (76), (137) are inconsistent by sub-proof #427.
% 176.45/27.40  | | | 
% 176.45/27.40  | | Case 2:
% 176.45/27.40  | | | 
% 176.45/27.40  | | |   (138)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.45/27.40  | | | 
% 176.45/27.40  | | | ALPHA: (138) implies:
% 176.45/27.40  | | |   (139)  all_52_28 = e1
% 176.45/27.40  | | |   (140)  all_52_26 = e2
% 176.45/27.40  | | |   (141)  all_52_24 = e3
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REDUCE: (8), (141) imply:
% 176.45/27.40  | | |   (142)  op(e3, all_52_25) = e3
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REDUCE: (106), (140) imply:
% 176.45/27.40  | | |   (143)  op(e2, all_52_27) = e2
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REDUCE: (36), (139) imply:
% 176.45/27.40  | | |   (144)  op(e1, all_52_29) = e1
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (13), (14), (15),
% 176.45/27.40  | | |            (16), (19), (20), (22), (24), (25), (26), (28), (29), (30),
% 176.45/27.40  | | |            (31), (32), (33), (35), (38), (39), (40), (41), (43), (44),
% 176.45/27.40  | | |            (46), (47), (48), (50), (51), (53), (54), (55), (58), (61),
% 176.45/27.40  | | |            (62), (63), (64), (65), (66), (68), (69), (71), (72), (73),
% 176.45/27.40  | | |            (77), (78), (79), (81), (82), (83), (84), (85), (86), (87),
% 176.45/27.40  | | |            (88), (89), (91), (92), (93), (94), (95), (96), (97), (99),
% 176.45/27.40  | | |            (101), (103), (104), (108), (109), (111), (114), (116), (117),
% 176.45/27.40  | | |            (122), (124), (142), (143), (144) are inconsistent by sub-proof
% 176.45/27.40  | | |            #422.
% 176.45/27.40  | | | 
% 176.45/27.40  | | End of split
% 176.45/27.40  | | 
% 176.45/27.40  | End of split
% 176.45/27.40  | 
% 176.45/27.40  End of proof
% 176.45/27.40  
% 176.45/27.40  Sub-proof #237 shows that the following formulas are inconsistent:
% 176.45/27.40  ----------------------------------------------------------------
% 176.45/27.40    (1)  op(e2, all_10_2) = all_10_1
% 176.45/27.40    (2)  op(e3, all_4_2) = all_4_1
% 176.45/27.40    (3)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.45/27.40         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.45/27.40    (4)   ~ (all_4_1 = e2)
% 176.45/27.40    (5)  all_52_0 = all_4_1
% 176.45/27.40    (6)  op(all_4_1, all_4_2) = e2
% 176.45/27.40    (7)  all_52_10 = all_10_1
% 176.45/27.40    (8)  op(all_10_1, all_10_2) = e3
% 176.45/27.40    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.40    (10)   ~ (e3 = e2)
% 176.45/27.40  
% 176.45/27.40  Begin of proof
% 176.45/27.40  | 
% 176.45/27.40  | BETA: splitting (3) gives:
% 176.45/27.40  | 
% 176.45/27.40  | Case 1:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (11)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.45/27.40  | | 
% 176.45/27.40  | | REF_CLOSE: (2), (4), (5), (6), (9), (11) are inconsistent by sub-proof #494.
% 176.45/27.40  | | 
% 176.45/27.40  | Case 2:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (12)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.45/27.40  | | 
% 176.45/27.40  | | ALPHA: (12) implies:
% 176.45/27.40  | |   (13)  all_52_10 = e2
% 176.45/27.40  | | 
% 176.45/27.40  | | COMBINE_EQS: (7), (13) imply:
% 176.45/27.40  | |   (14)  all_10_1 = e2
% 176.45/27.40  | | 
% 176.45/27.40  | | REF_CLOSE: (1), (8), (9), (10), (14) are inconsistent by sub-proof #263.
% 176.45/27.40  | | 
% 176.45/27.40  | End of split
% 176.45/27.40  | 
% 176.45/27.40  End of proof
% 176.45/27.40  
% 176.45/27.40  Sub-proof #238 shows that the following formulas are inconsistent:
% 176.45/27.40  ----------------------------------------------------------------
% 176.45/27.40    (1)   ~ (all_52_17 = e3)
% 176.45/27.40    (2)  all_58_12 = all_6_1
% 176.45/27.40    (3)   ~ (all_6_1 = e1)
% 176.45/27.40    (4)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.40    (5)   ~ (all_52_17 = all_6_1)
% 176.45/27.40    (6)  op(all_10_1, e3) = e3
% 176.45/27.40    (7)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.45/27.40    (8)  op(e1, e3) = e2
% 176.45/27.40    (9)  all_58_6 = all_52_17
% 176.45/27.40    (10)  all_58_2 = all_52_9
% 176.45/27.40    (11)   ~ (e2 = e1)
% 176.45/27.40    (12)  op(e1, e3) = all_52_17
% 176.45/27.40    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.40    (14)  all_56_12 = all_6_1
% 176.45/27.40    (15)  op(e2, e3) = all_10_1
% 176.45/27.40    (16)  op(e2, e3) = all_52_9
% 176.45/27.40  
% 176.45/27.40  Begin of proof
% 176.45/27.40  | 
% 176.45/27.40  | GROUND_INST: instantiating (13) with all_52_17, e2, e3, e1, simplifying with
% 176.45/27.40  |              (8), (12) gives:
% 176.45/27.40  |   (17)  all_52_17 = e2
% 176.45/27.40  | 
% 176.45/27.40  | GROUND_INST: instantiating (13) with all_52_9, all_10_1, e3, e2, simplifying
% 176.45/27.40  |              with (15), (16) gives:
% 176.45/27.40  |   (18)  all_52_9 = all_10_1
% 176.45/27.40  | 
% 176.45/27.40  | COMBINE_EQS: (9), (17) imply:
% 176.45/27.40  |   (19)  all_58_6 = e2
% 176.45/27.40  | 
% 176.45/27.40  | COMBINE_EQS: (10), (18) imply:
% 176.45/27.40  |   (20)  all_58_2 = all_10_1
% 176.45/27.40  | 
% 176.45/27.40  | REDUCE: (5), (17) imply:
% 176.45/27.40  |   (21)   ~ (all_6_1 = e2)
% 176.45/27.40  | 
% 176.45/27.40  | SIMP: (21) implies:
% 176.45/27.40  |   (22)   ~ (all_6_1 = e2)
% 176.45/27.40  | 
% 176.45/27.40  | BETA: splitting (4) gives:
% 176.45/27.40  | 
% 176.45/27.40  | Case 1:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (23)  all_58_2 = e1
% 176.45/27.40  | | 
% 176.45/27.40  | | COMBINE_EQS: (20), (23) imply:
% 176.45/27.40  | |   (24)  all_10_1 = e1
% 176.45/27.40  | | 
% 176.45/27.40  | | SIMP: (24) implies:
% 176.45/27.40  | |   (25)  all_10_1 = e1
% 176.45/27.40  | | 
% 176.45/27.40  | | REDUCE: (6), (25) imply:
% 176.45/27.40  | |   (26)  op(e1, e3) = e3
% 176.45/27.40  | | 
% 176.45/27.40  | | REF_CLOSE: (1), (12), (13), (26) are inconsistent by sub-proof #508.
% 176.45/27.40  | | 
% 176.45/27.40  | Case 2:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (27)  all_58_6 = e1 | all_58_12 = e1
% 176.45/27.40  | | 
% 176.45/27.40  | | BETA: splitting (7) gives:
% 176.45/27.40  | | 
% 176.45/27.40  | | Case 1:
% 176.45/27.40  | | | 
% 176.45/27.40  | | |   (28)  all_56_12 = e2
% 176.45/27.40  | | | 
% 176.45/27.40  | | | REF_CLOSE: (14), (22), (28) are inconsistent by sub-proof #507.
% 176.45/27.40  | | | 
% 176.45/27.40  | | Case 2:
% 176.45/27.40  | | | 
% 176.45/27.40  | | |   (29)  all_56_12 = e1 | all_56_12 = e0
% 176.45/27.40  | | | 
% 176.45/27.40  | | | BETA: splitting (29) gives:
% 176.45/27.40  | | | 
% 176.45/27.40  | | | Case 1:
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | |   (30)  all_56_12 = e1
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | REF_CLOSE: (3), (14), (30) are inconsistent by sub-proof #506.
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | Case 2:
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | |   (31)  all_56_12 = e0
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | COMBINE_EQS: (14), (31) imply:
% 176.45/27.40  | | | |   (32)  all_6_1 = e0
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | SIMP: (32) implies:
% 176.45/27.40  | | | |   (33)  all_6_1 = e0
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | COMBINE_EQS: (2), (33) imply:
% 176.45/27.40  | | | |   (34)  all_58_12 = e0
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | REDUCE: (3), (33) imply:
% 176.45/27.40  | | | |   (35)   ~ (e1 = e0)
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | SIMP: (35) implies:
% 176.45/27.40  | | | |   (36)   ~ (e1 = e0)
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | BETA: splitting (27) gives:
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | | Case 1:
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | |   (37)  all_58_6 = e1
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | | REF_CLOSE: (11), (19), (37) are inconsistent by sub-proof #779.
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | Case 2:
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | |   (38)  all_58_12 = e1
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | | COMBINE_EQS: (34), (38) imply:
% 176.45/27.40  | | | | |   (39)  e1 = e0
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | | REDUCE: (36), (39) imply:
% 176.45/27.40  | | | | |   (40)  $false
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | | CLOSE: (40) is inconsistent.
% 176.45/27.40  | | | | | 
% 176.45/27.40  | | | | End of split
% 176.45/27.40  | | | | 
% 176.45/27.40  | | | End of split
% 176.45/27.40  | | | 
% 176.45/27.40  | | End of split
% 176.45/27.40  | | 
% 176.45/27.40  | End of split
% 176.45/27.40  | 
% 176.45/27.40  End of proof
% 176.45/27.40  
% 176.45/27.40  Sub-proof #239 shows that the following formulas are inconsistent:
% 176.45/27.40  ----------------------------------------------------------------
% 176.45/27.40    (1)  op(e1, e3) = e0
% 176.45/27.40    (2)  op(e1, all_14_2) = e2
% 176.45/27.40    (3)  all_56_10 = all_14_2
% 176.45/27.40    (4)  all_56_10 = e3
% 176.45/27.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.40    (6)   ~ (e2 = e0)
% 176.45/27.40  
% 176.45/27.40  Begin of proof
% 176.45/27.40  | 
% 176.45/27.40  | COMBINE_EQS: (3), (4) imply:
% 176.45/27.40  |   (7)  all_14_2 = e3
% 176.45/27.40  | 
% 176.45/27.40  | SIMP: (7) implies:
% 176.45/27.40  |   (8)  all_14_2 = e3
% 176.45/27.40  | 
% 176.45/27.40  | REDUCE: (2), (8) imply:
% 176.45/27.40  |   (9)  op(e1, e3) = e2
% 176.45/27.40  | 
% 176.45/27.40  | GROUND_INST: instantiating (5) with e0, e2, e3, e1, simplifying with (1), (9)
% 176.45/27.40  |              gives:
% 176.45/27.40  |   (10)  e2 = e0
% 176.45/27.40  | 
% 176.45/27.40  | REDUCE: (6), (10) imply:
% 176.45/27.40  |   (11)  $false
% 176.45/27.40  | 
% 176.45/27.40  | CLOSE: (11) is inconsistent.
% 176.45/27.40  | 
% 176.45/27.40  End of proof
% 176.45/27.40  
% 176.45/27.40  Sub-proof #240 shows that the following formulas are inconsistent:
% 176.45/27.40  ----------------------------------------------------------------
% 176.45/27.40    (1)  op(e2, all_10_2) = all_10_1
% 176.45/27.40    (2)  all_56_3 = all_52_7
% 176.45/27.40    (3)  op(e3, e2) = all_52_3
% 176.45/27.40    (4)   ~ (all_52_27 = e0)
% 176.45/27.40    (5)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.45/27.40    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.45/27.40    (7)  all_58_15 = all_6_2
% 176.45/27.40    (8)   ~ (all_52_5 = all_52_7)
% 176.45/27.40    (9)  all_58_10 = all_52_15
% 176.45/27.40    (10)  op(e0, e1) = all_52_29
% 176.45/27.40    (11)  all_58_4 = all_52_5
% 176.45/27.40    (12)  op(e3, all_4_2) = all_4_1
% 176.45/27.40    (13)   ~ (all_52_7 = all_4_2)
% 176.45/27.40    (14)  all_58_1 = all_52_3
% 176.45/27.40    (15)  all_58_0 = all_4_2
% 176.45/27.40    (16)   ~ (all_52_7 = e0)
% 176.45/27.40    (17)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.45/27.40          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.45/27.40    (18)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.45/27.40    (19)  all_58_14 = all_52_29
% 176.45/27.40    (20)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.45/27.40    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.45/27.40    (22)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.45/27.40    (23)  op(e0, e2) = all_52_27
% 176.45/27.40    (24)  op(all_4_1, all_4_2) = all_4_0
% 176.45/27.40    (25)  op(e0, e3) = all_52_25
% 176.45/27.40    (26)  all_52_0 = all_4_1
% 176.45/27.40    (27)  all_52_10 = all_10_1
% 176.45/27.40    (28)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.45/27.40    (29)   ~ (e3 = e0)
% 176.45/27.40    (30)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.45/27.40    (31)   ~ (all_52_5 = all_52_29)
% 176.45/27.40    (32)  all_56_12 = all_52_25
% 176.45/27.40    (33)  all_58_13 = all_52_27
% 176.45/27.40    (34)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.40    (35)   ~ (all_52_25 = e0)
% 176.45/27.40    (36)   ~ (all_52_3 = all_52_7)
% 176.45/27.40    (37)  op(all_10_1, all_10_2) = e3
% 176.45/27.40    (38)  all_56_0 = all_4_2
% 176.45/27.40    (39)  all_58_11 = all_52_23
% 176.45/27.40    (40)   ~ (all_52_7 = all_52_15)
% 176.45/27.40    (41)  all_58_15 = e0
% 176.45/27.40    (42)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.45/27.40    (43)   ~ (all_52_29 = e0)
% 176.45/27.40    (44)  op(e3, e1) = all_52_5
% 176.45/27.40    (45)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.45/27.40    (46)   ~ (all_52_25 = all_4_2)
% 176.45/27.40    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.40    (48)   ~ (all_52_25 = all_52_27)
% 176.45/27.40    (49)   ~ (all_52_7 = all_6_2)
% 176.45/27.40    (50)   ~ (all_52_7 = all_52_23)
% 176.45/27.40    (51)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.45/27.40    (52)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.45/27.40    (53)  all_58_9 = all_52_7
% 176.45/27.40    (54)  all_58_12 = all_52_25
% 176.45/27.40    (55)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.45/27.40    (56)   ~ (e3 = e2)
% 176.45/27.40    (57)  op(e0, all_52_7) = all_52_6
% 176.45/27.40    (58)  all_56_13 = all_52_27
% 176.45/27.40  
% 176.45/27.40  Begin of proof
% 176.45/27.40  | 
% 176.45/27.40  | BETA: splitting (17) gives:
% 176.45/27.40  | 
% 176.45/27.40  | Case 1:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (59)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.45/27.40  | | 
% 176.45/27.40  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 176.45/27.40  | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 176.45/27.40  | |            (26), (28), (29), (30), (31), (32), (33), (34), (35), (36), (38),
% 176.45/27.40  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 176.45/27.40  | |            (50), (51), (52), (53), (54), (55), (57), (58), (59) are
% 176.45/27.40  | |            inconsistent by sub-proof #1008.
% 176.45/27.40  | | 
% 176.45/27.40  | Case 2:
% 176.45/27.40  | | 
% 176.45/27.40  | |   (60)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.45/27.40  | | 
% 176.45/27.40  | | ALPHA: (60) implies:
% 176.45/27.40  | |   (61)  all_52_10 = e2
% 176.45/27.40  | | 
% 176.45/27.40  | | COMBINE_EQS: (27), (61) imply:
% 176.45/27.40  | |   (62)  all_10_1 = e2
% 176.45/27.40  | | 
% 176.45/27.40  | | REF_CLOSE: (1), (37), (47), (56), (62) are inconsistent by sub-proof #263.
% 176.45/27.40  | | 
% 176.45/27.40  | End of split
% 176.45/27.40  | 
% 176.45/27.40  End of proof
% 176.45/27.40  
% 176.45/27.40  Sub-proof #241 shows that the following formulas are inconsistent:
% 176.45/27.40  ----------------------------------------------------------------
% 176.45/27.40    (1)   ~ (all_52_23 = all_14_2)
% 176.45/27.40    (2)   ~ (all_52_5 = all_52_13)
% 176.45/27.40    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.45/27.40    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.45/27.40    (5)   ~ (all_52_17 = all_52_23)
% 176.45/27.40    (6)  op(e2, all_10_2) = all_10_1
% 176.45/27.40    (7)  all_52_16 = e3
% 176.45/27.40    (8)  op(e3, e2) = all_52_3
% 176.45/27.40    (9)   ~ (all_52_9 = all_52_25)
% 176.45/27.40    (10)  op(e3, all_52_25) = all_52_24
% 176.45/27.40    (11)   ~ (all_52_19 = all_52_23)
% 176.45/27.40    (12)  op(e1, e2) = all_52_19
% 176.45/27.40    (13)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.45/27.40    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.45/27.40    (15)  all_58_5 = all_52_13
% 176.45/27.40    (16)   ~ (all_52_25 = all_52_29)
% 176.45/27.40    (17)  all_56_15 = all_6_2
% 176.45/27.40    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.45/27.40    (19)  op(e2, e0) = all_52_15
% 176.45/27.40    (20)  op(all_14_1, all_14_2) = all_14_0
% 176.45/27.40    (21)  all_58_3 = all_10_2
% 176.45/27.40    (22)  all_56_9 = all_52_19
% 176.45/27.40    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.45/27.40    (24)  all_58_15 = all_6_2
% 176.45/27.40    (25)   ~ (all_52_9 = all_4_2)
% 176.45/27.40    (26)   ~ (all_52_5 = all_52_7)
% 176.45/27.40    (27)  all_58_10 = all_52_15
% 176.45/27.40    (28)   ~ (all_52_5 = all_4_2)
% 176.45/27.40    (29)  all_58_7 = all_52_19
% 176.45/27.40    (30)   ~ (all_52_17 = all_52_25)
% 176.45/27.40    (31)  all_58_4 = all_52_5
% 176.45/27.40    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.45/27.40    (33)  all_52_18 = e2
% 176.45/27.40    (34)  all_34_1 = all_4_1
% 176.45/27.40    (35)   ~ (all_52_27 = all_52_29)
% 176.45/27.40    (36)   ~ (all_52_17 = all_14_2)
% 176.45/27.40    (37)  op(e3, all_4_2) = all_4_1
% 176.45/27.40    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.45/27.40    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.45/27.40    (40)   ~ (all_52_7 = all_4_2)
% 176.45/27.40    (41)  all_58_1 = all_52_3
% 176.45/27.40    (42)  all_58_0 = all_4_2
% 176.45/27.40    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.45/27.40    (44)  op(all_4_1, all_4_2) = e1
% 176.45/27.40    (45)  op(e1, all_52_29) = all_52_28
% 176.45/27.40    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.45/27.40    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.45/27.40    (48)   ~ (all_4_1 = e2)
% 176.45/27.40    (49)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.45/27.40    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.45/27.40    (51)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.45/27.40    (52)  all_58_14 = all_52_29
% 176.45/27.40    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.45/27.40    (54)   ~ (all_52_3 = all_52_5)
% 176.45/27.40    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.45/27.40    (56)  op(e2, e1) = all_52_13
% 176.45/27.40    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.45/27.40    (58)  all_58_8 = all_14_2
% 176.45/27.40    (59)  all_56_1 = all_52_3
% 176.45/27.40    (60)   ~ (all_14_0 = e3)
% 176.45/27.40    (61)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.45/27.40    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.45/27.40    (63)   ~ (all_52_5 = all_14_2)
% 176.45/27.40    (64)   ~ (all_52_3 = all_52_27)
% 176.45/27.40    (65)   ~ (all_52_3 = all_4_2)
% 176.45/27.40    (66)  op(e0, e3) = all_52_25
% 176.45/27.40    (67)   ~ (all_52_9 = all_10_2)
% 176.45/27.40    (68)  op(e3, all_52_17) = all_52_16
% 176.45/27.40    (69)   ~ (e3 = e0)
% 176.45/27.40    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.45/27.40    (71)   ~ (all_52_9 = all_52_13)
% 176.45/27.40    (72)  op(e0, all_52_23) = all_52_22
% 176.45/27.40    (73)   ~ (all_52_15 = all_52_23)
% 176.45/27.40    (74)   ~ (all_52_5 = all_52_29)
% 176.45/27.40    (75)  all_56_2 = all_52_5
% 176.45/27.40    (76)  all_58_13 = all_52_27
% 176.45/27.40    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.40    (78)  all_56_5 = all_10_2
% 176.45/27.40    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.45/27.40    (80)   ~ (all_52_9 = all_52_17)
% 176.45/27.40    (81)   ~ (all_14_0 = e2)
% 176.45/27.40    (82)  all_58_6 = all_52_17
% 176.45/27.40    (83)   ~ (all_52_3 = all_52_7)
% 176.45/27.40    (84)  op(all_10_1, all_10_2) = e3
% 176.45/27.40    (85)  op(e2, all_52_19) = all_52_18
% 176.45/27.40    (86)   ~ (e1 = e0)
% 176.45/27.40    (87)  all_56_0 = all_4_2
% 176.45/27.40    (88)  all_58_11 = all_52_23
% 176.45/27.40    (89)   ~ (all_52_3 = all_52_19)
% 176.45/27.40    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.45/27.40    (91)   ~ (all_52_7 = all_52_15)
% 176.45/27.40    (92)   ~ (all_52_29 = all_14_2)
% 176.45/27.40    (93)   ~ (all_52_19 = all_10_2)
% 176.45/27.40    (94)   ~ (all_52_23 = all_6_2)
% 176.45/27.40    (95)  all_58_2 = all_52_9
% 176.45/27.40    (96)  op(e3, e1) = all_52_5
% 176.45/27.40    (97)   ~ (all_52_25 = all_6_2)
% 176.45/27.40    (98)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.45/27.40    (99)  op(e1, e3) = all_52_17
% 176.45/27.40    (100)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.45/27.40    (101)   ~ (all_52_25 = all_4_2)
% 176.45/27.40    (102)  op(e3, e0) = all_52_7
% 176.45/27.40    (103)  op(e3, e3) = all_4_2
% 176.45/27.41    (104)  all_56_8 = all_52_17
% 176.45/27.41    (105)   ~ (all_52_17 = all_4_2)
% 176.45/27.41    (106)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.41             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.41    (107)   ~ (all_52_25 = all_52_27)
% 176.45/27.41    (108)  all_34_2 = all_4_2
% 176.45/27.41    (109)   ~ (all_52_27 = all_6_2)
% 176.45/27.41    (110)   ~ (all_52_7 = all_6_2)
% 176.45/27.41    (111)   ~ (all_52_15 = all_10_2)
% 176.45/27.41    (112)   ~ (all_52_19 = all_52_27)
% 176.45/27.41    (113)  all_56_7 = all_52_15
% 176.45/27.41    (114)   ~ (all_52_7 = all_52_23)
% 176.45/27.41    (115)   ~ (all_52_13 = all_10_2)
% 176.45/27.41    (116)  op(e2, all_52_27) = all_52_26
% 176.45/27.41    (117)   ~ (all_52_17 = all_52_19)
% 176.45/27.41    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.45/27.41    (119)  all_52_22 = e0
% 176.45/27.41    (120)  op(e1, all_14_2) = all_14_1
% 176.45/27.41    (121)  all_58_9 = all_52_7
% 176.45/27.41    (122)   ~ (e2 = e0)
% 176.45/27.41    (123)  all_58_12 = all_52_25
% 176.45/27.41    (124)  all_14_1 = e1
% 176.45/27.41    (125)  all_56_6 = all_52_13
% 176.45/27.41    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.45/27.41    (127)   ~ (all_52_9 = all_52_15)
% 176.45/27.41    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.45/27.41    (129)   ~ (e3 = e2)
% 176.45/27.41    (130)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.45/27.41    (131)   ~ (all_52_19 = all_14_2)
% 176.45/27.41    (132)  op(e2, e3) = all_52_9
% 176.45/27.41    (133)  all_56_13 = all_52_27
% 176.45/27.41  
% 176.45/27.41  Begin of proof
% 176.45/27.41  | 
% 176.45/27.41  | REDUCE: (20), (124) imply:
% 176.45/27.41  |   (134)  op(e1, all_14_2) = all_14_0
% 176.45/27.41  | 
% 176.45/27.41  | REDUCE: (7), (68) imply:
% 176.45/27.41  |   (135)  op(e3, all_52_17) = e3
% 176.45/27.41  | 
% 176.45/27.41  | REDUCE: (33), (85) imply:
% 176.45/27.41  |   (136)  op(e2, all_52_19) = e2
% 176.45/27.41  | 
% 176.45/27.41  | REDUCE: (120), (124) imply:
% 176.45/27.41  |   (137)  op(e1, all_14_2) = e1
% 176.45/27.41  | 
% 176.45/27.41  | REDUCE: (72), (119) imply:
% 176.45/27.41  |   (138)  op(e0, all_52_23) = e0
% 176.45/27.41  | 
% 176.45/27.41  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 176.45/27.41  |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 176.45/27.41  |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37),
% 176.45/27.41  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 176.45/27.41  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 176.45/27.41  |            (60), (61), (62), (63), (64), (65), (66), (67), (69), (70), (71),
% 176.45/27.41  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 176.45/27.41  |            (84), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 176.45/27.41  |            (96), (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 176.45/27.41  |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 176.45/27.41  |            (115), (116), (117), (118), (121), (122), (123), (125), (126),
% 176.45/27.41  |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 176.45/27.41  |            (136), (137), (138) are inconsistent by sub-proof #242.
% 176.45/27.41  | 
% 176.45/27.41  End of proof
% 176.45/27.41  
% 176.45/27.41  Sub-proof #242 shows that the following formulas are inconsistent:
% 176.45/27.41  ----------------------------------------------------------------
% 176.45/27.41    (1)   ~ (all_52_23 = all_14_2)
% 176.45/27.41    (2)   ~ (all_52_5 = all_52_13)
% 176.45/27.41    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.45/27.41    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.45/27.41    (5)   ~ (all_52_17 = all_52_23)
% 176.45/27.41    (6)  op(e2, all_10_2) = all_10_1
% 176.45/27.41    (7)  op(e3, e2) = all_52_3
% 176.45/27.41    (8)   ~ (all_52_9 = all_52_25)
% 176.45/27.41    (9)  op(e3, all_52_25) = all_52_24
% 176.45/27.41    (10)   ~ (all_52_19 = all_52_23)
% 176.45/27.41    (11)  op(e1, e2) = all_52_19
% 176.45/27.41    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.45/27.41    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.45/27.41    (14)  all_58_5 = all_52_13
% 176.45/27.41    (15)   ~ (all_52_25 = all_52_29)
% 176.45/27.41    (16)  all_56_15 = all_6_2
% 176.45/27.41    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.45/27.41    (18)  op(e2, e0) = all_52_15
% 176.45/27.41    (19)  all_58_3 = all_10_2
% 176.45/27.41    (20)  all_56_9 = all_52_19
% 176.45/27.41    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.45/27.41    (22)  all_58_15 = all_6_2
% 176.45/27.41    (23)   ~ (all_52_9 = all_4_2)
% 176.45/27.41    (24)   ~ (all_52_5 = all_52_7)
% 176.45/27.41    (25)  all_58_10 = all_52_15
% 176.45/27.41    (26)   ~ (all_52_5 = all_4_2)
% 176.45/27.41    (27)  all_58_7 = all_52_19
% 176.45/27.41    (28)   ~ (all_52_17 = all_52_25)
% 176.45/27.41    (29)  all_58_4 = all_52_5
% 176.45/27.41    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.45/27.41    (31)  all_34_1 = all_4_1
% 176.45/27.41    (32)   ~ (all_52_27 = all_52_29)
% 176.45/27.41    (33)   ~ (all_52_17 = all_14_2)
% 176.45/27.41    (34)  op(e3, all_4_2) = all_4_1
% 176.45/27.41    (35)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.45/27.41    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.45/27.41    (37)   ~ (all_52_7 = all_4_2)
% 176.45/27.41    (38)  all_58_1 = all_52_3
% 176.45/27.41    (39)  all_58_0 = all_4_2
% 176.45/27.41    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.45/27.41    (41)  op(all_4_1, all_4_2) = e1
% 176.45/27.41    (42)  op(e1, all_52_29) = all_52_28
% 176.45/27.41    (43)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.45/27.41    (44)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.45/27.41    (45)   ~ (all_4_1 = e2)
% 176.45/27.41    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.45/27.41    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.45/27.41    (48)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.45/27.41    (49)  all_58_14 = all_52_29
% 176.45/27.41    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.45/27.41    (51)   ~ (all_52_3 = all_52_5)
% 176.45/27.41    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.45/27.41    (53)  op(e2, e1) = all_52_13
% 176.45/27.41    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.45/27.41    (55)  all_58_8 = all_14_2
% 176.45/27.41    (56)  all_56_1 = all_52_3
% 176.45/27.41    (57)   ~ (all_14_0 = e3)
% 176.45/27.41    (58)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.45/27.41    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.45/27.41    (60)   ~ (all_52_5 = all_14_2)
% 176.45/27.41    (61)   ~ (all_52_3 = all_52_27)
% 176.45/27.41    (62)   ~ (all_52_3 = all_4_2)
% 176.45/27.41    (63)  op(e0, e3) = all_52_25
% 176.45/27.41    (64)   ~ (all_52_9 = all_10_2)
% 176.45/27.41    (65)  op(e1, all_14_2) = all_14_0
% 176.45/27.41    (66)   ~ (e3 = e0)
% 176.45/27.41    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.45/27.41    (68)   ~ (all_52_9 = all_52_13)
% 176.45/27.41    (69)   ~ (all_52_15 = all_52_23)
% 176.45/27.41    (70)   ~ (all_52_5 = all_52_29)
% 176.45/27.41    (71)  all_56_2 = all_52_5
% 176.45/27.41    (72)  all_58_13 = all_52_27
% 176.45/27.41    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.41    (74)  all_56_5 = all_10_2
% 176.45/27.41    (75)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.45/27.41    (76)   ~ (all_52_9 = all_52_17)
% 176.45/27.41    (77)   ~ (all_14_0 = e2)
% 176.45/27.41    (78)  all_58_6 = all_52_17
% 176.45/27.41    (79)   ~ (all_52_3 = all_52_7)
% 176.45/27.41    (80)  op(e2, all_52_19) = e2
% 176.45/27.41    (81)  op(all_10_1, all_10_2) = e3
% 176.45/27.41    (82)  op(e3, all_52_17) = e3
% 176.45/27.41    (83)   ~ (e1 = e0)
% 176.45/27.41    (84)  all_56_0 = all_4_2
% 176.45/27.41    (85)  all_58_11 = all_52_23
% 176.45/27.41    (86)   ~ (all_52_3 = all_52_19)
% 176.45/27.41    (87)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.45/27.41    (88)   ~ (all_52_7 = all_52_15)
% 176.45/27.41    (89)   ~ (all_52_29 = all_14_2)
% 176.45/27.41    (90)   ~ (all_52_19 = all_10_2)
% 176.45/27.41    (91)   ~ (all_52_23 = all_6_2)
% 176.45/27.41    (92)  all_58_2 = all_52_9
% 176.45/27.41    (93)  op(e3, e1) = all_52_5
% 176.45/27.41    (94)   ~ (all_52_25 = all_6_2)
% 176.45/27.41    (95)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.45/27.41    (96)  op(e1, e3) = all_52_17
% 176.45/27.41    (97)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.45/27.41    (98)   ~ (all_52_25 = all_4_2)
% 176.45/27.41    (99)  op(e3, e0) = all_52_7
% 176.45/27.41    (100)  op(e3, e3) = all_4_2
% 176.45/27.41    (101)  all_56_8 = all_52_17
% 176.45/27.41    (102)   ~ (all_52_17 = all_4_2)
% 176.45/27.41    (103)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.41             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.41    (104)   ~ (all_52_25 = all_52_27)
% 176.45/27.41    (105)  all_34_2 = all_4_2
% 176.45/27.41    (106)   ~ (all_52_27 = all_6_2)
% 176.45/27.41    (107)   ~ (all_52_7 = all_6_2)
% 176.45/27.41    (108)  op(e0, all_52_23) = e0
% 176.45/27.41    (109)   ~ (all_52_15 = all_10_2)
% 176.45/27.41    (110)   ~ (all_52_19 = all_52_27)
% 176.45/27.41    (111)  all_56_7 = all_52_15
% 176.45/27.41    (112)  op(e1, all_14_2) = e1
% 176.45/27.41    (113)   ~ (all_52_7 = all_52_23)
% 176.45/27.41    (114)   ~ (all_52_13 = all_10_2)
% 176.45/27.41    (115)  op(e2, all_52_27) = all_52_26
% 176.45/27.41    (116)   ~ (all_52_17 = all_52_19)
% 176.45/27.41    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.45/27.41    (118)  all_58_9 = all_52_7
% 176.45/27.41    (119)   ~ (e2 = e0)
% 176.45/27.41    (120)  all_58_12 = all_52_25
% 176.45/27.41    (121)  all_56_6 = all_52_13
% 176.45/27.41    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.45/27.41    (123)   ~ (all_52_9 = all_52_15)
% 176.45/27.41    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.45/27.41    (125)   ~ (e3 = e2)
% 176.45/27.41    (126)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.45/27.41    (127)   ~ (all_52_19 = all_14_2)
% 176.45/27.41    (128)  op(e2, e3) = all_52_9
% 176.45/27.41    (129)  all_56_13 = all_52_27
% 176.45/27.41  
% 176.45/27.41  Begin of proof
% 176.45/27.41  | 
% 176.45/27.41  | GROUND_INST: instantiating (103) with e1, all_14_0, all_14_2, e1, simplifying
% 176.45/27.41  |              with (65), (112) gives:
% 176.45/27.41  |   (130)  all_14_0 = e1
% 176.45/27.41  | 
% 176.45/27.41  | REDUCE: (57), (130) imply:
% 176.45/27.41  |   (131)   ~ (e3 = e1)
% 176.45/27.41  | 
% 176.45/27.41  | SIMP: (131) implies:
% 176.45/27.41  |   (132)   ~ (e3 = e1)
% 176.45/27.41  | 
% 176.45/27.41  | REDUCE: (77), (130) imply:
% 176.45/27.41  |   (133)   ~ (e2 = e1)
% 176.45/27.41  | 
% 176.45/27.41  | SIMP: (133) implies:
% 176.45/27.41  |   (134)   ~ (e2 = e1)
% 176.45/27.41  | 
% 176.45/27.41  | BETA: splitting (35) gives:
% 176.45/27.41  | 
% 176.45/27.41  | Case 1:
% 176.45/27.41  | | 
% 176.45/27.41  | |   (135)  all_56_15 = e3
% 176.45/27.41  | | 
% 176.45/27.41  | | REF_CLOSE: (16), (20), (27), (30), (34), (36), (39), (41), (44), (52), (55),
% 176.45/27.41  | |            (60), (76), (78), (80), (82), (85), (91), (92), (93), (94), (96),
% 176.45/27.41  | |            (100), (102), (103), (112), (120), (122), (125), (128), (132),
% 176.45/27.41  | |            (135) are inconsistent by sub-proof #568.
% 176.45/27.41  | | 
% 176.45/27.41  | Case 2:
% 176.45/27.41  | | 
% 176.45/27.41  | |   (136)   ~ (all_56_15 = e3)
% 176.45/27.41  | |   (137)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.45/27.41  | | 
% 176.45/27.41  | | REDUCE: (16), (136) imply:
% 176.45/27.41  | |   (138)   ~ (all_6_2 = e3)
% 176.45/27.41  | | 
% 176.45/27.41  | | BETA: splitting (50) gives:
% 176.45/27.41  | | 
% 176.45/27.41  | | Case 1:
% 176.45/27.41  | | | 
% 176.45/27.41  | | |   (139)  all_56_13 = e3
% 176.45/27.41  | | | 
% 176.45/27.41  | | | COMBINE_EQS: (129), (139) imply:
% 176.45/27.41  | | |   (140)  all_52_27 = e3
% 176.45/27.41  | | | 
% 176.45/27.41  | | | SIMP: (140) implies:
% 176.45/27.41  | | |   (141)  all_52_27 = e3
% 176.45/27.41  | | | 
% 176.45/27.41  | | | REF_CLOSE: (1), (7), (11), (12), (14), (17), (22), (24), (25), (26), (27),
% 176.45/27.41  | | |            (29), (30), (31), (32), (33), (34), (36), (39), (41), (43),
% 176.45/27.41  | | |            (48), (49), (51), (52), (55), (56), (60), (62), (63), (68),
% 176.45/27.41  | | |            (78), (82), (85), (86), (92), (93), (96), (100), (102), (103),
% 176.45/27.41  | | |            (104), (105), (106), (108), (112), (115), (117), (118), (119),
% 176.45/27.41  | | |            (120), (121), (123), (124), (125), (127), (128), (132), (141)
% 176.45/27.41  | | |            are inconsistent by sub-proof #565.
% 176.45/27.41  | | | 
% 176.45/27.41  | | Case 2:
% 176.45/27.41  | | | 
% 176.45/27.41  | | |   (142)   ~ (all_56_13 = e3)
% 176.45/27.41  | | | 
% 176.45/27.41  | | | REDUCE: (129), (142) imply:
% 176.45/27.41  | | |   (143)   ~ (all_52_27 = e3)
% 176.45/27.41  | | | 
% 176.45/27.41  | | | BETA: splitting (54) gives:
% 176.45/27.41  | | | 
% 176.45/27.41  | | | Case 1:
% 176.45/27.41  | | | | 
% 176.45/27.41  | | | |   (144)  all_58_12 = e3
% 176.45/27.41  | | | | 
% 176.45/27.41  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (11), (14), (15), (19), (21),
% 176.45/27.41  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (33),
% 176.45/27.41  | | | |            (36), (37), (38), (39), (40), (47), (49), (53), (55), (60),
% 176.45/27.41  | | | |            (61), (62), (63), (64), (66), (67), (69), (70), (71), (72),
% 176.45/27.41  | | | |            (73), (74), (75), (76), (78), (79), (80), (81), (82), (83),
% 176.45/27.41  | | | |            (84), (85), (86), (88), (90), (92), (93), (94), (95), (96),
% 176.45/27.41  | | | |            (97), (98), (99), (101), (102), (103), (104), (108), (109),
% 176.45/27.41  | | | |            (111), (112), (114), (116), (117), (118), (119), (120),
% 176.45/27.41  | | | |            (122), (123), (124), (126), (127), (128), (132), (134), (144)
% 176.45/27.41  | | | |            are inconsistent by sub-proof #250.
% 176.45/27.41  | | | | 
% 176.45/27.41  | | | Case 2:
% 176.45/27.41  | | | | 
% 176.45/27.41  | | | |   (145)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.45/27.41  | | | | 
% 176.45/27.41  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (13), (14), (15),
% 176.45/27.41  | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 176.45/27.41  | | | |            (27), (28), (29), (30), (33), (34), (36), (37), (38), (39),
% 176.45/27.41  | | | |            (40), (41), (42), (44), (45), (46), (47), (49), (51), (52),
% 176.45/27.41  | | | |            (55), (58), (59), (60), (62), (63), (68), (70), (72), (76),
% 176.45/27.41  | | | |            (78), (80), (82), (84), (85), (86), (87), (89), (91), (92),
% 176.45/27.41  | | | |            (93), (94), (96), (98), (99), (100), (101), (102), (103),
% 176.45/27.41  | | | |            (104), (106), (107), (108), (110), (112), (113), (114),
% 176.45/27.41  | | | |            (116), (118), (120), (122), (125), (127), (128), (132),
% 176.45/27.41  | | | |            (137), (138), (143), (145) are inconsistent by sub-proof
% 176.45/27.41  | | | |            #562.
% 176.45/27.41  | | | | 
% 176.45/27.41  | | | End of split
% 176.45/27.41  | | | 
% 176.45/27.41  | | End of split
% 176.45/27.41  | | 
% 176.45/27.41  | End of split
% 176.45/27.41  | 
% 176.45/27.41  End of proof
% 176.45/27.41  
% 176.45/27.41  Sub-proof #243 shows that the following formulas are inconsistent:
% 176.45/27.41  ----------------------------------------------------------------
% 176.45/27.41    (1)  op(e2, all_10_2) = all_10_1
% 176.45/27.41    (2)   ~ (e3 = e1)
% 176.45/27.41    (3)  op(e3, all_4_2) = all_4_1
% 176.45/27.41    (4)  op(all_4_1, all_4_2) = e1
% 176.45/27.41    (5)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.45/27.41         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.45/27.41    (6)  all_52_0 = all_4_1
% 176.45/27.41    (7)  all_52_10 = all_10_1
% 176.45/27.41    (8)  op(all_10_1, all_10_2) = e3
% 176.45/27.41    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.41    (10)   ~ (e3 = e2)
% 176.45/27.41  
% 176.45/27.41  Begin of proof
% 176.45/27.41  | 
% 176.45/27.41  | BETA: splitting (5) gives:
% 176.45/27.41  | 
% 176.45/27.41  | Case 1:
% 176.45/27.41  | | 
% 176.45/27.41  | |   (11)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.45/27.41  | | 
% 176.45/27.41  | | REF_CLOSE: (2), (3), (4), (6), (9), (11) are inconsistent by sub-proof #600.
% 176.45/27.41  | | 
% 176.45/27.41  | Case 2:
% 176.45/27.41  | | 
% 176.45/27.41  | |   (12)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.45/27.41  | | 
% 176.45/27.41  | | ALPHA: (12) implies:
% 176.45/27.41  | |   (13)  all_52_10 = e2
% 176.45/27.41  | | 
% 176.45/27.41  | | COMBINE_EQS: (7), (13) imply:
% 176.45/27.41  | |   (14)  all_10_1 = e2
% 176.45/27.41  | | 
% 176.45/27.41  | | REF_CLOSE: (1), (8), (9), (10), (14) are inconsistent by sub-proof #263.
% 176.45/27.41  | | 
% 176.45/27.41  | End of split
% 176.45/27.41  | 
% 176.45/27.41  End of proof
% 176.45/27.41  
% 176.45/27.41  Sub-proof #244 shows that the following formulas are inconsistent:
% 176.45/27.41  ----------------------------------------------------------------
% 176.45/27.41    (1)   ~ (all_52_23 = all_14_2)
% 176.45/27.41    (2)   ~ (all_52_5 = all_52_13)
% 176.45/27.41    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.45/27.41    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.45/27.41    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.45/27.41    (6)   ~ (all_52_27 = all_10_2)
% 176.45/27.41    (7)   ~ (all_52_17 = all_52_23)
% 176.45/27.41    (8)  op(e2, all_10_2) = all_10_1
% 176.45/27.41    (9)  all_40_2 = all_4_2
% 176.45/27.41    (10)   ~ (all_52_13 = all_52_29)
% 176.45/27.41    (11)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.45/27.41    (12)  op(e3, e2) = all_52_3
% 176.45/27.41    (13)   ~ (all_52_9 = all_52_25)
% 176.45/27.41    (14)  op(e3, all_52_25) = all_52_24
% 176.45/27.41    (15)   ~ (all_52_19 = all_52_23)
% 176.45/27.41    (16)  op(e1, e2) = all_52_19
% 176.45/27.41    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.45/27.41    (18)  op(e3, all_52_9) = all_52_8
% 176.45/27.41    (19)   ~ (all_52_3 = all_10_2)
% 176.45/27.41    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.45/27.41    (21)  all_58_5 = all_52_13
% 176.45/27.41    (22)   ~ (all_6_2 = e0)
% 176.45/27.41    (23)   ~ (all_52_25 = all_52_29)
% 176.45/27.41    (24)  all_56_15 = all_6_2
% 176.45/27.41    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.45/27.41    (26)  op(e2, e0) = all_52_15
% 176.45/27.41    (27)  op(all_14_1, all_14_2) = all_14_0
% 176.45/27.41    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.45/27.41    (29)  all_58_3 = all_10_2
% 176.45/27.41    (30)  all_56_9 = all_52_19
% 176.45/27.41    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.45/27.41    (32)  all_58_15 = all_6_2
% 176.45/27.41    (33)   ~ (all_52_9 = all_4_2)
% 176.45/27.41    (34)   ~ (all_52_5 = all_52_7)
% 176.45/27.41    (35)  all_58_10 = all_52_15
% 176.45/27.41    (36)   ~ (all_52_5 = all_4_2)
% 176.45/27.41    (37)  all_58_7 = all_52_19
% 176.45/27.41    (38)   ~ (all_52_17 = all_52_25)
% 176.45/27.41    (39)  op(e0, e1) = all_52_29
% 176.45/27.41    (40)   ~ (all_4_0 = e2)
% 176.45/27.41    (41)  all_58_4 = all_52_5
% 176.45/27.41    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.45/27.41    (43)   ~ (e3 = e1)
% 176.45/27.41    (44)   ~ (all_52_27 = all_52_29)
% 176.45/27.41    (45)   ~ (all_52_17 = all_14_2)
% 176.45/27.41    (46)  op(e3, all_4_2) = all_4_1
% 176.45/27.41    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.45/27.41    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.45/27.41    (49)   ~ (all_52_7 = all_4_2)
% 176.45/27.41    (50)  all_58_1 = all_52_3
% 176.45/27.41    (51)   ~ (all_52_13 = all_52_15)
% 176.45/27.41    (52)  all_58_0 = all_4_2
% 176.45/27.41    (53)  all_52_0 = e1
% 176.45/27.41    (54)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.45/27.41    (55)  op(e1, all_52_29) = all_52_28
% 176.45/27.41    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.45/27.41    (57)   ~ (all_4_1 = e2)
% 176.45/27.41    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.45/27.41    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.45/27.41    (60)  all_58_14 = all_52_29
% 176.45/27.41    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.45/27.41    (62)   ~ (all_52_3 = all_52_5)
% 176.45/27.41    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.45/27.41    (64)  op(e2, e1) = all_52_13
% 176.45/27.41    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.45/27.41    (66)  all_58_8 = all_14_2
% 176.45/27.41    (67)  op(e0, e2) = all_52_27
% 176.45/27.41    (68)   ~ (all_14_0 = e3)
% 176.45/27.41    (69)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.45/27.41    (70)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.45/27.41    (71)  op(all_4_1, all_4_2) = all_4_0
% 176.45/27.41    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.45/27.41    (73)   ~ (all_52_5 = all_14_2)
% 176.45/27.41    (74)   ~ (all_52_3 = all_52_27)
% 176.45/27.41    (75)   ~ (all_52_3 = all_4_2)
% 176.45/27.41    (76)  op(e0, e3) = all_52_25
% 176.45/27.41    (77)  op(e0, all_6_2) = all_6_1
% 176.45/27.41    (78)   ~ (all_52_9 = all_10_2)
% 176.45/27.41    (79)  op(e3, all_52_17) = all_52_16
% 176.45/27.41    (80)  all_52_10 = all_10_1
% 176.45/27.41    (81)   ~ (e3 = e0)
% 176.45/27.41    (82)  all_40_0 = all_4_0
% 176.45/27.41    (83)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.45/27.41    (84)   ~ (all_52_9 = all_52_13)
% 176.45/27.41    (85)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.45/27.41    (86)  op(e0, all_52_23) = all_52_22
% 176.45/27.41    (87)   ~ (all_52_15 = all_52_23)
% 176.45/27.41    (88)   ~ (all_52_5 = all_52_29)
% 176.45/27.41    (89)  all_56_2 = all_52_5
% 176.45/27.41    (90)  op(e1, e0) = all_52_23
% 176.45/27.41    (91)  all_56_12 = all_52_25
% 176.45/27.41    (92)  all_58_13 = all_52_27
% 176.45/27.41    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.41    (94)  all_56_5 = all_10_2
% 176.45/27.41    (95)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.45/27.41    (96)   ~ (all_52_9 = all_52_17)
% 176.45/27.41    (97)   ~ (all_14_0 = e2)
% 176.45/27.41    (98)  all_58_6 = all_52_17
% 176.45/27.41    (99)   ~ (all_52_3 = all_52_7)
% 176.45/27.41    (100)  op(all_10_1, all_10_2) = e3
% 176.45/27.41    (101)  op(e2, all_52_19) = all_52_18
% 176.45/27.41    (102)   ~ (e1 = e0)
% 176.45/27.41    (103)  all_56_0 = all_4_2
% 176.45/27.41    (104)  all_58_11 = all_52_23
% 176.45/27.41    (105)   ~ (all_52_3 = all_52_19)
% 176.45/27.41    (106)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.45/27.41    (107)   ~ (all_52_7 = all_52_15)
% 176.45/27.41    (108)   ~ (all_52_29 = all_14_2)
% 176.45/27.41    (109)   ~ (all_4_0 = e1)
% 176.45/27.41    (110)   ~ (all_52_19 = all_10_2)
% 176.45/27.41    (111)   ~ (all_52_23 = all_6_2)
% 176.45/27.41    (112)  op(e1, all_4_2) = all_4_0
% 176.45/27.41    (113)   ~ (all_52_29 = all_6_2)
% 176.45/27.41    (114)  all_58_2 = all_52_9
% 176.45/27.41    (115)  op(e3, e1) = all_52_5
% 176.45/27.41    (116)   ~ (e2 = e1)
% 176.45/27.41    (117)   ~ (all_52_25 = all_6_2)
% 176.45/27.41    (118)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.45/27.41    (119)  op(e1, e3) = all_52_17
% 176.45/27.41    (120)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.45/27.41    (121)   ~ (all_52_25 = all_4_2)
% 176.45/27.41    (122)  op(e3, e0) = all_52_7
% 176.45/27.41    (123)  op(e3, e3) = all_4_2
% 176.45/27.41    (124)  all_56_8 = all_52_17
% 176.45/27.41    (125)   ~ (all_52_17 = all_4_2)
% 176.45/27.41    (126)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.41             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.41    (127)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.45/27.41           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.45/27.41           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.45/27.41           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.45/27.41    (128)   ~ (all_52_25 = all_52_27)
% 176.45/27.41    (129)   ~ (all_52_27 = all_6_2)
% 176.45/27.41    (130)   ~ (all_52_7 = all_6_2)
% 176.45/27.41    (131)   ~ (all_52_15 = all_10_2)
% 176.45/27.42    (132)   ~ (all_52_19 = all_52_27)
% 176.45/27.42    (133)  all_56_7 = all_52_15
% 176.45/27.42    (134)   ~ (all_52_7 = all_52_23)
% 176.45/27.42    (135)   ~ (all_52_13 = all_10_2)
% 176.45/27.42    (136)  op(e2, all_52_27) = all_52_26
% 176.45/27.42    (137)  all_52_20 = all_14_1
% 176.45/27.42    (138)   ~ (all_52_17 = all_52_19)
% 176.45/27.42    (139)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.45/27.42    (140)  all_52_30 = all_6_1
% 176.45/27.42    (141)  op(e1, all_14_2) = all_14_1
% 176.45/27.42    (142)  all_58_9 = all_52_7
% 176.45/27.42    (143)   ~ (e2 = e0)
% 176.45/27.42    (144)  all_58_12 = all_52_25
% 176.45/27.42    (145)  op(e3, all_4_2) = e1
% 176.45/27.42    (146)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.45/27.42    (147)   ~ (all_52_9 = all_52_15)
% 176.45/27.42    (148)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.45/27.42    (149)   ~ (e3 = e2)
% 176.45/27.42    (150)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.45/27.42    (151)   ~ (all_52_19 = all_14_2)
% 176.45/27.42    (152)  op(e2, e3) = all_52_9
% 176.45/27.42    (153)  all_56_13 = all_52_27
% 176.45/27.42  
% 176.45/27.42  Begin of proof
% 176.45/27.42  | 
% 176.45/27.42  | BETA: splitting (127) gives:
% 176.45/27.42  | 
% 176.45/27.42  | Case 1:
% 176.45/27.42  | | 
% 176.45/27.42  | |   (154)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.45/27.42  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.45/27.42  | | 
% 176.45/27.42  | | REF_CLOSE: (8), (43), (53), (80), (100), (126), (149), (154) are
% 176.45/27.42  | |            inconsistent by sub-proof #247.
% 176.45/27.42  | | 
% 176.45/27.42  | Case 2:
% 176.45/27.42  | | 
% 176.45/27.42  | |   (155)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 176.45/27.42  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 176.45/27.42  | |            e0)
% 176.45/27.42  | | 
% 176.45/27.42  | | BETA: splitting (155) gives:
% 176.45/27.42  | | 
% 176.45/27.42  | | Case 1:
% 176.45/27.42  | | | 
% 176.45/27.42  | | |   (156)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.45/27.42  | | | 
% 176.45/27.42  | | | ALPHA: (156) implies:
% 176.45/27.42  | | |   (157)  all_52_22 = e0
% 176.45/27.42  | | |   (158)  all_52_20 = e1
% 176.45/27.42  | | |   (159)  all_52_18 = e2
% 176.45/27.42  | | |   (160)  all_52_16 = e3
% 176.45/27.42  | | | 
% 176.45/27.42  | | | COMBINE_EQS: (137), (158) imply:
% 176.45/27.42  | | |   (161)  all_14_1 = e1
% 176.45/27.42  | | | 
% 176.45/27.42  | | | SIMP: (161) implies:
% 176.45/27.42  | | |   (162)  all_14_1 = e1
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REDUCE: (27), (162) imply:
% 176.45/27.42  | | |   (163)  op(e1, all_14_2) = all_14_0
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REDUCE: (79), (160) imply:
% 176.45/27.42  | | |   (164)  op(e3, all_52_17) = e3
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REDUCE: (101), (159) imply:
% 176.45/27.42  | | |   (165)  op(e2, all_52_19) = e2
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REDUCE: (141), (162) imply:
% 176.45/27.42  | | |   (166)  op(e1, all_14_2) = e1
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REDUCE: (86), (157) imply:
% 176.45/27.42  | | |   (167)  op(e0, all_52_23) = e0
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 176.45/27.42  | | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 176.45/27.42  | | |            (25), (26), (29), (30), (31), (32), (33), (34), (35), (36),
% 176.45/27.42  | | |            (37), (38), (40), (41), (42), (44), (45), (46), (47), (48),
% 176.45/27.42  | | |            (49), (50), (52), (54), (55), (56), (57), (58), (59), (60),
% 176.45/27.42  | | |            (61), (62), (63), (64), (65), (66), (68), (69), (70), (71),
% 176.45/27.42  | | |            (72), (73), (74), (75), (76), (78), (81), (82), (83), (84),
% 176.45/27.42  | | |            (85), (87), (88), (89), (91), (92), (93), (94), (95), (96),
% 176.45/27.42  | | |            (97), (98), (99), (100), (102), (103), (104), (105), (106),
% 176.45/27.42  | | |            (107), (108), (109), (110), (111), (112), (114), (115), (117),
% 176.45/27.42  | | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 176.45/27.42  | | |            (128), (129), (130), (131), (132), (133), (134), (135), (138),
% 176.45/27.42  | | |            (139), (142), (143), (144), (145), (146), (147), (148), (149),
% 176.45/27.42  | | |            (150), (151), (152), (153), (163), (164), (165), (166), (167)
% 176.45/27.42  | | |            are inconsistent by sub-proof #245.
% 176.45/27.42  | | | 
% 176.45/27.42  | | Case 2:
% 176.45/27.42  | | | 
% 176.45/27.42  | | |   (168)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 176.45/27.42  | | |            (17), (18), (21), (22), (23), (24), (25), (28), (29), (31),
% 176.45/27.42  | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 176.45/27.42  | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 176.45/27.42  | | |            (52), (54), (55), (58), (59), (60), (61), (62), (63), (65),
% 176.45/27.42  | | |            (66), (67), (71), (74), (76), (77), (78), (79), (81), (83),
% 176.45/27.42  | | |            (85), (88), (90), (91), (92), (93), (96), (98), (99), (102),
% 176.45/27.42  | | |            (103), (104), (109), (110), (113), (114), (115), (116), (117),
% 176.45/27.42  | | |            (119), (121), (122), (123), (125), (126), (128), (129), (130),
% 176.45/27.42  | | |            (131), (136), (138), (139), (140), (142), (144), (145), (146),
% 176.45/27.42  | | |            (147), (149), (152), (153), (168) are inconsistent by sub-proof
% 176.45/27.42  | | |            #444.
% 176.45/27.42  | | | 
% 176.45/27.42  | | End of split
% 176.45/27.42  | | 
% 176.45/27.42  | End of split
% 176.45/27.42  | 
% 176.45/27.42  End of proof
% 176.45/27.42  
% 176.45/27.42  Sub-proof #245 shows that the following formulas are inconsistent:
% 176.45/27.42  ----------------------------------------------------------------
% 176.45/27.42    (1)   ~ (all_52_23 = all_14_2)
% 176.45/27.42    (2)   ~ (all_52_5 = all_52_13)
% 176.45/27.42    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.45/27.42    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.45/27.42    (5)   ~ (all_52_17 = all_52_23)
% 176.45/27.42    (6)  op(e2, all_10_2) = all_10_1
% 176.45/27.42    (7)  all_40_2 = all_4_2
% 176.45/27.42    (8)   ~ (all_52_13 = all_52_29)
% 176.45/27.42    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.45/27.42    (10)  op(e3, e2) = all_52_3
% 176.45/27.42    (11)   ~ (all_52_9 = all_52_25)
% 176.45/27.42    (12)  op(e3, all_52_25) = all_52_24
% 176.45/27.42    (13)   ~ (all_52_19 = all_52_23)
% 176.45/27.42    (14)  op(e1, e2) = all_52_19
% 176.45/27.42    (15)  op(e3, all_52_9) = all_52_8
% 176.45/27.42    (16)   ~ (all_52_3 = all_10_2)
% 176.45/27.42    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.45/27.42    (18)  all_58_5 = all_52_13
% 176.45/27.42    (19)   ~ (all_6_2 = e0)
% 176.45/27.42    (20)   ~ (all_52_25 = all_52_29)
% 176.45/27.42    (21)  all_56_15 = all_6_2
% 176.45/27.42    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.45/27.42    (23)  op(e2, e0) = all_52_15
% 176.45/27.42    (24)  all_58_3 = all_10_2
% 176.45/27.42    (25)  all_56_9 = all_52_19
% 176.45/27.42    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.45/27.42    (27)  all_58_15 = all_6_2
% 176.45/27.42    (28)   ~ (all_52_9 = all_4_2)
% 176.45/27.42    (29)   ~ (all_52_5 = all_52_7)
% 176.45/27.42    (30)  all_58_10 = all_52_15
% 176.45/27.42    (31)   ~ (all_52_5 = all_4_2)
% 176.45/27.42    (32)  all_58_7 = all_52_19
% 176.45/27.42    (33)   ~ (all_52_17 = all_52_25)
% 176.45/27.42    (34)   ~ (all_4_0 = e2)
% 176.45/27.42    (35)  all_58_4 = all_52_5
% 176.45/27.42    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.45/27.42    (37)   ~ (all_52_27 = all_52_29)
% 176.45/27.42    (38)   ~ (all_52_17 = all_14_2)
% 176.45/27.42    (39)  op(e3, all_4_2) = all_4_1
% 176.45/27.42    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.45/27.42    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.45/27.42    (42)   ~ (all_52_7 = all_4_2)
% 176.45/27.42    (43)  all_58_1 = all_52_3
% 176.45/27.42    (44)  all_58_0 = all_4_2
% 176.45/27.42    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.45/27.42    (46)  op(e1, all_52_29) = all_52_28
% 176.45/27.42    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.45/27.42    (48)   ~ (all_4_1 = e2)
% 176.45/27.42    (49)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.45/27.42    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.45/27.42    (51)  all_58_14 = all_52_29
% 176.45/27.42    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.45/27.42    (53)   ~ (all_52_3 = all_52_5)
% 176.45/27.42    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.45/27.42    (55)  op(e2, e1) = all_52_13
% 176.45/27.42    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.45/27.42    (57)  all_58_8 = all_14_2
% 176.45/27.42    (58)   ~ (all_14_0 = e3)
% 176.45/27.42    (59)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.45/27.42    (60)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.45/27.42    (61)  op(all_4_1, all_4_2) = all_4_0
% 176.45/27.42    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.45/27.42    (63)   ~ (all_52_5 = all_14_2)
% 176.45/27.42    (64)   ~ (all_52_3 = all_52_27)
% 176.45/27.42    (65)   ~ (all_52_3 = all_4_2)
% 176.45/27.42    (66)  op(e0, e3) = all_52_25
% 176.45/27.42    (67)   ~ (all_52_9 = all_10_2)
% 176.45/27.42    (68)  op(e1, all_14_2) = all_14_0
% 176.45/27.42    (69)   ~ (e3 = e0)
% 176.45/27.42    (70)  all_40_0 = all_4_0
% 176.45/27.42    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.45/27.42    (72)   ~ (all_52_9 = all_52_13)
% 176.45/27.42    (73)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.45/27.42    (74)   ~ (all_52_15 = all_52_23)
% 176.45/27.42    (75)   ~ (all_52_5 = all_52_29)
% 176.45/27.42    (76)  all_56_2 = all_52_5
% 176.45/27.42    (77)  all_56_12 = all_52_25
% 176.45/27.42    (78)  all_58_13 = all_52_27
% 176.45/27.42    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.42    (80)  all_56_5 = all_10_2
% 176.45/27.42    (81)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.45/27.42    (82)   ~ (all_52_9 = all_52_17)
% 176.45/27.42    (83)   ~ (all_14_0 = e2)
% 176.45/27.42    (84)  all_58_6 = all_52_17
% 176.45/27.42    (85)   ~ (all_52_3 = all_52_7)
% 176.45/27.42    (86)  op(e2, all_52_19) = e2
% 176.45/27.42    (87)  op(all_10_1, all_10_2) = e3
% 176.45/27.42    (88)  op(e3, all_52_17) = e3
% 176.45/27.42    (89)   ~ (e1 = e0)
% 176.45/27.42    (90)  all_56_0 = all_4_2
% 176.45/27.42    (91)  all_58_11 = all_52_23
% 176.45/27.42    (92)   ~ (all_52_3 = all_52_19)
% 176.45/27.42    (93)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.45/27.42    (94)   ~ (all_52_7 = all_52_15)
% 176.45/27.42    (95)   ~ (all_52_29 = all_14_2)
% 176.45/27.42    (96)   ~ (all_4_0 = e1)
% 176.45/27.42    (97)   ~ (all_52_19 = all_10_2)
% 176.45/27.42    (98)   ~ (all_52_23 = all_6_2)
% 176.45/27.42    (99)  op(e1, all_4_2) = all_4_0
% 176.45/27.42    (100)  all_58_2 = all_52_9
% 176.45/27.42    (101)  op(e3, e1) = all_52_5
% 176.45/27.42    (102)   ~ (all_52_25 = all_6_2)
% 176.45/27.42    (103)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.45/27.42    (104)  op(e1, e3) = all_52_17
% 176.45/27.42    (105)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.45/27.42    (106)   ~ (all_52_25 = all_4_2)
% 176.45/27.42    (107)  op(e3, e0) = all_52_7
% 176.45/27.42    (108)  op(e3, e3) = all_4_2
% 176.45/27.42    (109)  all_56_8 = all_52_17
% 176.45/27.42    (110)   ~ (all_52_17 = all_4_2)
% 176.45/27.42    (111)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.42             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.42    (112)   ~ (all_52_25 = all_52_27)
% 176.45/27.42    (113)   ~ (all_52_27 = all_6_2)
% 176.45/27.42    (114)   ~ (all_52_7 = all_6_2)
% 176.45/27.42    (115)  op(e0, all_52_23) = e0
% 176.45/27.42    (116)   ~ (all_52_15 = all_10_2)
% 176.45/27.42    (117)   ~ (all_52_19 = all_52_27)
% 176.45/27.42    (118)  all_56_7 = all_52_15
% 176.45/27.42    (119)  op(e1, all_14_2) = e1
% 176.45/27.42    (120)   ~ (all_52_7 = all_52_23)
% 176.45/27.42    (121)   ~ (all_52_13 = all_10_2)
% 176.45/27.42    (122)   ~ (all_52_17 = all_52_19)
% 176.45/27.42    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.45/27.42    (124)  all_58_9 = all_52_7
% 176.45/27.42    (125)   ~ (e2 = e0)
% 176.45/27.42    (126)  all_58_12 = all_52_25
% 176.45/27.42    (127)  op(e3, all_4_2) = e1
% 176.45/27.42    (128)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.45/27.42    (129)   ~ (all_52_9 = all_52_15)
% 176.45/27.42    (130)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.45/27.42    (131)   ~ (e3 = e2)
% 176.45/27.42    (132)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.45/27.42    (133)   ~ (all_52_19 = all_14_2)
% 176.45/27.42    (134)  op(e2, e3) = all_52_9
% 176.45/27.42    (135)  all_56_13 = all_52_27
% 176.45/27.42  
% 176.45/27.42  Begin of proof
% 176.45/27.42  | 
% 176.45/27.42  | GROUND_INST: instantiating (111) with e1, all_14_0, all_14_2, e1, simplifying
% 176.45/27.42  |              with (68), (119) gives:
% 176.45/27.42  |   (136)  all_14_0 = e1
% 176.45/27.42  | 
% 176.45/27.42  | REDUCE: (58), (136) imply:
% 176.45/27.42  |   (137)   ~ (e3 = e1)
% 176.45/27.42  | 
% 176.45/27.42  | SIMP: (137) implies:
% 176.45/27.42  |   (138)   ~ (e3 = e1)
% 176.45/27.42  | 
% 176.45/27.42  | REDUCE: (83), (136) imply:
% 176.45/27.42  |   (139)   ~ (e2 = e1)
% 176.45/27.42  | 
% 176.45/27.42  | SIMP: (139) implies:
% 176.45/27.42  |   (140)   ~ (e2 = e1)
% 176.45/27.42  | 
% 176.45/27.42  | BETA: splitting (40) gives:
% 176.45/27.42  | 
% 176.45/27.42  | Case 1:
% 176.45/27.42  | | 
% 176.45/27.42  | |   (141)  all_56_15 = e3
% 176.45/27.42  | | 
% 176.45/27.42  | | COMBINE_EQS: (21), (141) imply:
% 176.45/27.42  | |   (142)  all_6_2 = e3
% 176.45/27.42  | | 
% 176.45/27.42  | | REF_CLOSE: (25), (32), (36), (41), (44), (47), (54), (57), (63), (82), (84),
% 176.45/27.42  | |            (86), (88), (91), (98), (100), (101), (102), (104), (108), (110),
% 176.45/27.42  | |            (111), (119), (126), (127), (131), (134), (138), (142) are
% 176.45/27.42  | |            inconsistent by sub-proof #608.
% 176.45/27.42  | | 
% 176.45/27.42  | Case 2:
% 176.45/27.42  | | 
% 176.45/27.42  | |   (143)   ~ (all_56_15 = e3)
% 176.45/27.42  | |   (144)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.45/27.42  | | 
% 176.45/27.42  | | REDUCE: (21), (143) imply:
% 176.45/27.42  | |   (145)   ~ (all_6_2 = e3)
% 176.45/27.42  | | 
% 176.45/27.42  | | BETA: splitting (52) gives:
% 176.45/27.42  | | 
% 176.45/27.42  | | Case 1:
% 176.45/27.42  | | | 
% 176.45/27.42  | | |   (146)  all_56_13 = e3
% 176.45/27.42  | | | 
% 176.45/27.42  | | | COMBINE_EQS: (135), (146) imply:
% 176.45/27.42  | | |   (147)  all_52_27 = e3
% 176.45/27.42  | | | 
% 176.45/27.42  | | | SIMP: (147) implies:
% 176.45/27.42  | | |   (148)  all_52_27 = e3
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REF_CLOSE: (7), (10), (14), (25), (26), (27), (30), (31), (32), (34),
% 176.45/27.42  | | |            (35), (36), (41), (42), (43), (44), (47), (54), (57), (59),
% 176.45/27.42  | | |            (63), (64), (66), (70), (74), (79), (82), (84), (86), (88),
% 176.45/27.42  | | |            (90), (91), (92), (99), (100), (101), (104), (105), (106),
% 176.45/27.42  | | |            (108), (110), (111), (112), (113), (115), (117), (118), (119),
% 176.45/27.42  | | |            (120), (123), (124), (126), (127), (128), (130), (131), (134),
% 176.45/27.42  | | |            (138), (148) are inconsistent by sub-proof #246.
% 176.45/27.42  | | | 
% 176.45/27.42  | | Case 2:
% 176.45/27.42  | | | 
% 176.45/27.42  | | |   (149)   ~ (all_56_13 = e3)
% 176.45/27.42  | | | 
% 176.45/27.42  | | | REDUCE: (135), (149) imply:
% 176.45/27.42  | | |   (150)   ~ (all_52_27 = e3)
% 176.45/27.42  | | | 
% 176.45/27.42  | | | BETA: splitting (56) gives:
% 176.45/27.42  | | | 
% 176.45/27.42  | | | Case 1:
% 176.45/27.42  | | | | 
% 176.45/27.42  | | | |   (151)  all_58_12 = e3
% 176.45/27.42  | | | | 
% 176.45/27.42  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (11), (14), (18), (20), (24), (26),
% 176.45/27.42  | | | |            (27), (28), (29), (30), (31), (32), (33), (35), (36), (38),
% 176.45/27.42  | | | |            (41), (42), (43), (44), (45), (50), (51), (55), (57), (63),
% 176.45/27.42  | | | |            (64), (65), (66), (67), (69), (71), (74), (75), (76), (78),
% 176.45/27.42  | | | |            (79), (80), (81), (82), (84), (85), (86), (87), (88), (89),
% 176.45/27.42  | | | |            (90), (91), (92), (94), (97), (100), (101), (102), (103),
% 176.45/27.42  | | | |            (104), (105), (106), (107), (109), (110), (111), (112),
% 176.45/27.42  | | | |            (115), (116), (118), (119), (121), (122), (123), (124),
% 176.45/27.42  | | | |            (125), (126), (128), (129), (130), (132), (133), (134),
% 176.45/27.42  | | | |            (138), (140), (151) are inconsistent by sub-proof #250.
% 176.45/27.42  | | | | 
% 176.45/27.42  | | | Case 2:
% 176.45/27.42  | | | | 
% 176.45/27.42  | | | |   (152)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.45/27.42  | | | | 
% 176.45/27.42  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13),
% 176.45/27.42  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.45/27.42  | | | |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 176.45/27.42  | | | |            (35), (36), (37), (38), (39), (41), (43), (44), (45), (46),
% 176.45/27.42  | | | |            (47), (48), (49), (50), (51), (53), (54), (57), (60), (61),
% 176.45/27.42  | | | |            (62), (63), (65), (66), (67), (72), (73), (75), (77), (78),
% 176.45/27.42  | | | |            (82), (84), (86), (88), (90), (91), (92), (93), (95), (96),
% 176.45/27.42  | | | |            (97), (98), (100), (101), (102), (104), (106), (107), (108),
% 176.45/27.42  | | | |            (109), (110), (111), (112), (113), (114), (115), (117),
% 176.45/27.42  | | | |            (119), (121), (122), (124), (126), (131), (133), (134),
% 176.45/27.42  | | | |            (144), (145), (150), (152) are inconsistent by sub-proof
% 176.45/27.42  | | | |            #670.
% 176.45/27.42  | | | | 
% 176.45/27.42  | | | End of split
% 176.45/27.42  | | | 
% 176.45/27.42  | | End of split
% 176.45/27.42  | | 
% 176.45/27.42  | End of split
% 176.45/27.42  | 
% 176.45/27.42  End of proof
% 176.45/27.42  
% 176.45/27.42  Sub-proof #246 shows that the following formulas are inconsistent:
% 176.45/27.42  ----------------------------------------------------------------
% 176.45/27.42    (1)  all_40_2 = all_4_2
% 176.45/27.42    (2)  op(e3, e2) = all_52_3
% 176.45/27.42    (3)  op(e1, e2) = all_52_19
% 176.45/27.42    (4)  all_52_27 = e3
% 176.45/27.42    (5)  all_56_9 = all_52_19
% 176.45/27.42    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.45/27.42    (7)  all_58_15 = all_6_2
% 176.45/27.42    (8)  all_58_10 = all_52_15
% 176.45/27.42    (9)   ~ (all_52_5 = all_4_2)
% 176.45/27.42    (10)  all_58_7 = all_52_19
% 176.45/27.42    (11)   ~ (all_4_0 = e2)
% 176.45/27.42    (12)  all_58_4 = all_52_5
% 176.45/27.42    (13)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.45/27.42    (14)   ~ (e3 = e1)
% 176.45/27.42    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.45/27.42    (16)   ~ (all_52_7 = all_4_2)
% 176.45/27.42    (17)  all_58_1 = all_52_3
% 176.45/27.42    (18)  all_58_0 = all_4_2
% 176.45/27.42    (19)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.45/27.42    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.45/27.42    (21)  all_58_8 = all_14_2
% 176.45/27.42    (22)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.45/27.42    (23)   ~ (all_52_5 = all_14_2)
% 176.45/27.42    (24)   ~ (all_52_3 = all_52_27)
% 176.45/27.42    (25)  op(e0, e3) = all_52_25
% 176.45/27.42    (26)  all_40_0 = all_4_0
% 176.45/27.42    (27)   ~ (all_52_15 = all_52_23)
% 176.45/27.42    (28)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.45/27.42    (29)   ~ (all_52_9 = all_52_17)
% 176.45/27.42    (30)  all_58_6 = all_52_17
% 176.45/27.42    (31)  op(e2, all_52_19) = e2
% 176.45/27.42    (32)  op(e3, all_52_17) = e3
% 176.45/27.42    (33)  all_56_0 = all_4_2
% 176.45/27.42    (34)  all_58_11 = all_52_23
% 176.45/27.42    (35)   ~ (all_52_3 = all_52_19)
% 176.45/27.42    (36)  op(e1, all_4_2) = all_4_0
% 176.45/27.42    (37)  all_58_2 = all_52_9
% 176.45/27.42    (38)  op(e3, e1) = all_52_5
% 176.45/27.42    (39)  op(e1, e3) = all_52_17
% 176.45/27.42    (40)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.45/27.42    (41)   ~ (all_52_25 = all_4_2)
% 176.45/27.42    (42)  op(e3, e3) = all_4_2
% 176.45/27.42    (43)   ~ (all_52_17 = all_4_2)
% 176.45/27.42    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.45/27.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.45/27.42    (45)   ~ (all_52_25 = all_52_27)
% 176.45/27.42    (46)   ~ (all_52_27 = all_6_2)
% 176.45/27.42    (47)  op(e0, all_52_23) = e0
% 176.45/27.42    (48)   ~ (all_52_19 = all_52_27)
% 176.45/27.42    (49)  all_56_7 = all_52_15
% 176.45/27.42    (50)  op(e1, all_14_2) = e1
% 176.45/27.42    (51)   ~ (all_52_7 = all_52_23)
% 176.45/27.42    (52)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.45/27.42    (53)  all_58_9 = all_52_7
% 176.45/27.42    (54)  all_58_12 = all_52_25
% 176.45/27.42    (55)  op(e3, all_4_2) = e1
% 176.45/27.42    (56)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.42    (57)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.42    (58)   ~ (e3 = e2)
% 176.56/27.42    (59)  op(e2, e3) = all_52_9
% 176.56/27.42  
% 176.56/27.42  Begin of proof
% 176.56/27.42  | 
% 176.56/27.42  | REDUCE: (4), (24) imply:
% 176.56/27.42  |   (60)   ~ (all_52_3 = e3)
% 176.56/27.42  | 
% 176.56/27.42  | REDUCE: (4), (48) imply:
% 176.56/27.42  |   (61)   ~ (all_52_19 = e3)
% 176.56/27.42  | 
% 176.56/27.42  | REDUCE: (4), (45) imply:
% 176.56/27.42  |   (62)   ~ (all_52_25 = e3)
% 176.56/27.42  | 
% 176.56/27.42  | REDUCE: (4), (46) imply:
% 176.56/27.42  |   (63)   ~ (all_6_2 = e3)
% 176.56/27.42  | 
% 176.56/27.42  | SIMP: (63) implies:
% 176.56/27.42  |   (64)   ~ (all_6_2 = e3)
% 176.56/27.42  | 
% 176.56/27.42  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 176.56/27.42  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 176.56/27.42  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 176.56/27.42  |            (37), (38), (39), (40), (41), (42), (43), (44), (47), (49), (50),
% 176.56/27.42  |            (51), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 176.56/27.42  |            (62), (64) are inconsistent by sub-proof #607.
% 176.56/27.42  | 
% 176.56/27.42  End of proof
% 176.56/27.42  
% 176.56/27.42  Sub-proof #247 shows that the following formulas are inconsistent:
% 176.56/27.42  ----------------------------------------------------------------
% 176.56/27.42    (1)  op(e2, all_10_2) = all_10_1
% 176.56/27.42    (2)   ~ (e3 = e1)
% 176.56/27.42    (3)  all_52_0 = e1
% 176.56/27.42    (4)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.56/27.42         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.56/27.42    (5)  all_52_10 = all_10_1
% 176.56/27.42    (6)  op(all_10_1, all_10_2) = e3
% 176.56/27.42    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.42    (8)   ~ (e3 = e2)
% 176.56/27.42  
% 176.56/27.42  Begin of proof
% 176.56/27.42  | 
% 176.56/27.42  | BETA: splitting (4) gives:
% 176.56/27.42  | 
% 176.56/27.42  | Case 1:
% 176.56/27.42  | | 
% 176.56/27.42  | |   (9)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.56/27.42  | | 
% 176.56/27.42  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #632.
% 176.56/27.42  | | 
% 176.56/27.42  | Case 2:
% 176.56/27.42  | | 
% 176.56/27.42  | |   (10)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.56/27.42  | | 
% 176.56/27.42  | | ALPHA: (10) implies:
% 176.56/27.42  | |   (11)  all_52_10 = e2
% 176.56/27.42  | | 
% 176.56/27.42  | | COMBINE_EQS: (5), (11) imply:
% 176.56/27.42  | |   (12)  all_10_1 = e2
% 176.56/27.42  | | 
% 176.56/27.42  | | REF_CLOSE: (1), (6), (7), (8), (12) are inconsistent by sub-proof #263.
% 176.56/27.42  | | 
% 176.56/27.42  | End of split
% 176.56/27.42  | 
% 176.56/27.42  End of proof
% 176.56/27.42  
% 176.56/27.42  Sub-proof #248 shows that the following formulas are inconsistent:
% 176.56/27.42  ----------------------------------------------------------------
% 176.56/27.42    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.42    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.42    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.42    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.42    (5)   ~ (all_52_27 = all_10_2)
% 176.56/27.42    (6)   ~ (all_52_17 = all_52_23)
% 176.56/27.42    (7)  op(e2, all_10_2) = all_10_1
% 176.56/27.42    (8)   ~ (all_52_13 = all_52_29)
% 176.56/27.42    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.56/27.42    (10)  op(e3, e2) = all_52_3
% 176.56/27.42    (11)   ~ (all_52_9 = all_52_25)
% 176.56/27.42    (12)  op(e3, all_52_25) = all_52_24
% 176.56/27.42    (13)   ~ (all_52_19 = all_52_23)
% 176.56/27.42    (14)  op(e1, e2) = all_52_19
% 176.56/27.42    (15)  op(e3, all_52_9) = all_52_8
% 176.56/27.42    (16)   ~ (all_52_3 = all_10_2)
% 176.56/27.42    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.42    (18)  all_58_5 = all_52_13
% 176.56/27.42    (19)   ~ (all_6_2 = e0)
% 176.56/27.42    (20)   ~ (all_52_25 = all_52_29)
% 176.56/27.42    (21)  all_56_15 = all_6_2
% 176.56/27.42    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.43    (23)  op(e2, e0) = all_52_15
% 176.56/27.43    (24)  all_58_3 = all_10_2
% 176.56/27.43    (25)  all_56_9 = all_52_19
% 176.56/27.43    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.43    (27)  all_58_15 = all_6_2
% 176.56/27.43    (28)   ~ (all_52_9 = all_4_2)
% 176.56/27.43    (29)   ~ (all_52_5 = all_52_7)
% 176.56/27.43    (30)  all_58_10 = all_52_15
% 176.56/27.43    (31)   ~ (all_52_5 = all_4_2)
% 176.56/27.43    (32)  all_58_7 = all_52_19
% 176.56/27.43    (33)   ~ (all_52_17 = all_52_25)
% 176.56/27.43    (34)   ~ (all_4_0 = e2)
% 176.56/27.43    (35)  all_58_4 = all_52_5
% 176.56/27.43    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.43    (37)   ~ (all_52_27 = all_52_29)
% 176.56/27.43    (38)   ~ (all_52_17 = all_14_2)
% 176.56/27.43    (39)  op(e3, all_4_2) = all_4_1
% 176.56/27.43    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.43    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.43    (42)   ~ (all_52_7 = all_4_2)
% 176.56/27.43    (43)  all_58_1 = all_52_3
% 176.56/27.43    (44)  all_58_0 = all_4_2
% 176.56/27.43    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.43    (46)  op(e1, all_52_29) = all_52_28
% 176.56/27.43    (47)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.43    (48)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.56/27.43    (49)   ~ (all_4_1 = e2)
% 176.56/27.43    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.43    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.43    (52)  all_58_14 = all_52_29
% 176.56/27.43    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.43    (54)   ~ (all_52_3 = all_52_5)
% 176.56/27.43    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.43    (56)  op(e2, e1) = all_52_13
% 176.56/27.43    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.43    (58)  all_58_8 = all_14_2
% 176.56/27.43    (59)  all_56_1 = all_52_3
% 176.56/27.43    (60)  op(e0, e2) = all_52_27
% 176.56/27.43    (61)   ~ (all_14_0 = e3)
% 176.56/27.43    (62)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.56/27.43    (63)  op(all_4_1, all_4_2) = all_4_0
% 176.56/27.43    (64)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.43    (65)   ~ (all_52_5 = all_14_2)
% 176.56/27.43    (66)   ~ (all_52_3 = all_52_27)
% 176.56/27.43    (67)   ~ (all_52_3 = all_4_2)
% 176.56/27.43    (68)  op(e0, e3) = all_52_25
% 176.56/27.43    (69)   ~ (all_52_9 = all_10_2)
% 176.56/27.43    (70)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.43    (71)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.43    (72)  op(e1, all_14_2) = all_14_0
% 176.56/27.43    (73)   ~ (e3 = e0)
% 176.56/27.43    (74)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.43    (75)   ~ (all_52_9 = all_52_13)
% 176.56/27.43    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.43    (77)   ~ (all_52_15 = all_52_23)
% 176.56/27.43    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.43    (79)   ~ (all_52_5 = all_52_29)
% 176.56/27.43    (80)  all_56_2 = all_52_5
% 176.56/27.43    (81)  op(e1, e0) = all_52_23
% 176.56/27.43    (82)  all_56_12 = all_52_25
% 176.56/27.43    (83)  all_58_13 = all_52_27
% 176.56/27.43    (84)   ~ (all_4_1 = e1)
% 176.56/27.43    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.43    (86)  all_56_5 = all_10_2
% 176.56/27.43    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.43    (88)   ~ (all_52_9 = all_52_17)
% 176.56/27.43    (89)   ~ (all_14_0 = e2)
% 176.56/27.43    (90)  all_58_6 = all_52_17
% 176.56/27.43    (91)   ~ (all_52_3 = all_52_7)
% 176.56/27.43    (92)  op(e2, all_52_19) = e2
% 176.56/27.43    (93)  op(all_10_1, all_10_2) = e3
% 176.56/27.43    (94)  op(e3, all_52_17) = e3
% 176.56/27.43    (95)   ~ (e1 = e0)
% 176.56/27.43    (96)  all_56_0 = all_4_2
% 176.56/27.43    (97)  all_58_11 = all_52_23
% 176.56/27.43    (98)   ~ (all_52_3 = all_52_19)
% 176.56/27.43    (99)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.43    (100)   ~ (all_52_7 = all_52_15)
% 176.56/27.43    (101)   ~ (all_52_29 = all_14_2)
% 176.56/27.43    (102)   ~ (all_4_0 = e1)
% 176.56/27.43    (103)   ~ (all_52_19 = all_10_2)
% 176.56/27.43    (104)   ~ (all_52_23 = all_6_2)
% 176.56/27.43    (105)   ~ (all_52_29 = all_6_2)
% 176.56/27.43    (106)  all_58_2 = all_52_9
% 176.56/27.43    (107)  op(e3, e1) = all_52_5
% 176.56/27.43    (108)  all_56_10 = all_14_2
% 176.56/27.43    (109)   ~ (all_52_25 = all_6_2)
% 176.56/27.43    (110)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.43    (111)  op(e1, e3) = all_52_17
% 176.56/27.43    (112)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.43    (113)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.56/27.43    (114)   ~ (all_52_25 = all_4_2)
% 176.56/27.43    (115)  op(e3, e0) = all_52_7
% 176.56/27.43    (116)  op(e3, e3) = all_4_2
% 176.56/27.43    (117)  all_56_8 = all_52_17
% 176.56/27.43    (118)   ~ (all_52_17 = all_4_2)
% 176.56/27.43    (119)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.43             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.43    (120)   ~ (all_52_25 = all_52_27)
% 176.56/27.43    (121)   ~ (all_52_27 = all_6_2)
% 176.56/27.43    (122)   ~ (all_52_7 = all_6_2)
% 176.56/27.43    (123)  op(e0, all_52_23) = e0
% 176.56/27.43    (124)   ~ (all_52_15 = all_10_2)
% 176.56/27.43    (125)   ~ (all_52_19 = all_52_27)
% 176.56/27.43    (126)  all_56_7 = all_52_15
% 176.56/27.43    (127)  op(e1, all_14_2) = e1
% 176.56/27.43    (128)   ~ (all_52_7 = all_52_23)
% 176.56/27.43    (129)   ~ (all_52_13 = all_10_2)
% 176.56/27.43    (130)  op(e2, all_52_27) = all_52_26
% 176.56/27.43    (131)   ~ (all_52_17 = all_52_19)
% 176.56/27.43    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.43    (133)  all_58_9 = all_52_7
% 176.56/27.43    (134)   ~ (e2 = e0)
% 176.56/27.43    (135)  all_58_12 = all_52_25
% 176.56/27.43    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.43    (137)   ~ (all_52_9 = all_52_15)
% 176.56/27.43    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.43    (139)   ~ (e3 = e2)
% 176.56/27.43    (140)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.43    (141)   ~ (all_52_19 = all_14_2)
% 176.56/27.43    (142)  op(e2, e3) = all_52_9
% 176.56/27.43    (143)  all_56_13 = all_52_27
% 176.56/27.43  
% 176.56/27.43  Begin of proof
% 176.56/27.43  | 
% 176.56/27.43  | GROUND_INST: instantiating (119) with e1, all_14_0, all_14_2, e1, simplifying
% 176.56/27.43  |              with (72), (127) gives:
% 176.56/27.43  |   (144)  all_14_0 = e1
% 176.56/27.43  | 
% 176.56/27.43  | REDUCE: (61), (144) imply:
% 176.56/27.43  |   (145)   ~ (e3 = e1)
% 176.56/27.43  | 
% 176.56/27.43  | SIMP: (145) implies:
% 176.56/27.43  |   (146)   ~ (e3 = e1)
% 176.56/27.43  | 
% 176.56/27.43  | REDUCE: (89), (144) imply:
% 176.56/27.43  |   (147)   ~ (e2 = e1)
% 176.56/27.43  | 
% 176.56/27.43  | SIMP: (147) implies:
% 176.56/27.43  |   (148)   ~ (e2 = e1)
% 176.56/27.43  | 
% 176.56/27.43  | BETA: splitting (40) gives:
% 176.56/27.43  | 
% 176.56/27.43  | Case 1:
% 176.56/27.43  | | 
% 176.56/27.43  | |   (149)  all_56_15 = e3
% 176.56/27.43  | | 
% 176.56/27.43  | | COMBINE_EQS: (21), (149) imply:
% 176.56/27.43  | |   (150)  all_6_2 = e3
% 176.56/27.43  | | 
% 176.56/27.43  | | SIMP: (150) implies:
% 176.56/27.43  | |   (151)  all_6_2 = e3
% 176.56/27.43  | | 
% 176.56/27.43  | | COMBINE_EQS: (27), (151) imply:
% 176.56/27.43  | |   (152)  all_58_15 = e3
% 176.56/27.43  | | 
% 176.56/27.43  | | REDUCE: (104), (151) imply:
% 176.56/27.43  | |   (153)   ~ (all_52_23 = e3)
% 176.56/27.43  | | 
% 176.56/27.43  | | REDUCE: (109), (151) imply:
% 176.56/27.43  | |   (154)   ~ (all_52_25 = e3)
% 176.56/27.43  | | 
% 176.56/27.43  | | REDUCE: (105), (151) imply:
% 176.56/27.43  | |   (155)   ~ (all_52_29 = e3)
% 176.56/27.43  | | 
% 176.56/27.43  | | BETA: splitting (48) gives:
% 176.56/27.43  | | 
% 176.56/27.43  | | Case 1:
% 176.56/27.43  | | | 
% 176.56/27.43  | | |   (156)  all_56_9 = e3
% 176.56/27.43  | | | 
% 176.56/27.43  | | | COMBINE_EQS: (25), (156) imply:
% 176.56/27.43  | | |   (157)  all_52_19 = e3
% 176.56/27.43  | | | 
% 176.56/27.43  | | | SIMP: (157) implies:
% 176.56/27.43  | | |   (158)  all_52_19 = e3
% 176.56/27.43  | | | 
% 176.56/27.43  | | | COMBINE_EQS: (32), (158) imply:
% 176.56/27.43  | | |   (159)  all_58_7 = e3
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REDUCE: (13), (158) imply:
% 176.56/27.43  | | |   (160)   ~ (all_52_23 = e3)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REDUCE: (92), (158) imply:
% 176.56/27.43  | | |   (161)  op(e2, e3) = e2
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REDUCE: (14), (158) imply:
% 176.56/27.43  | | |   (162)  op(e1, e2) = e3
% 176.56/27.43  | | | 
% 176.56/27.43  | | | GROUND_INST: instantiating (119) with all_52_9, e2, e3, e2, simplifying
% 176.56/27.43  | | |              with (142), (161) gives:
% 176.56/27.43  | | |   (163)  all_52_9 = e2
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REDUCE: (137), (163) imply:
% 176.56/27.43  | | |   (164)   ~ (all_52_15 = e2)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | SIMP: (164) implies:
% 176.56/27.43  | | |   (165)   ~ (all_52_15 = e2)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REDUCE: (88), (163) imply:
% 176.56/27.43  | | |   (166)   ~ (all_52_17 = e2)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | SIMP: (166) implies:
% 176.56/27.43  | | |   (167)   ~ (all_52_17 = e2)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REDUCE: (69), (163) imply:
% 176.56/27.43  | | |   (168)   ~ (all_10_2 = e2)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | SIMP: (168) implies:
% 176.56/27.43  | | |   (169)   ~ (all_10_2 = e2)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | BETA: splitting (55) gives:
% 176.56/27.43  | | | 
% 176.56/27.43  | | | Case 1:
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | |   (170)  all_58_0 = e3
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | COMBINE_EQS: (44), (170) imply:
% 176.56/27.43  | | | |   (171)  all_4_2 = e3
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | REDUCE: (31), (171) imply:
% 176.56/27.43  | | | |   (172)   ~ (all_52_5 = e3)
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | REDUCE: (42), (171) imply:
% 176.56/27.43  | | | |   (173)   ~ (all_52_7 = e3)
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | REDUCE: (63), (171) imply:
% 176.56/27.43  | | | |   (174)  op(all_4_1, e3) = all_4_0
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | REDUCE: (39), (171) imply:
% 176.56/27.43  | | | |   (175)  op(e3, e3) = all_4_1
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | REDUCE: (116), (171) imply:
% 176.56/27.43  | | | |   (176)  op(e3, e3) = e3
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | BETA: splitting (138) gives:
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | Case 1:
% 176.56/27.43  | | | | | 
% 176.56/27.43  | | | | |   (177)  all_58_4 = e3
% 176.56/27.43  | | | | | 
% 176.56/27.43  | | | | | REF_CLOSE: (35), (172), (177) are inconsistent by sub-proof #1025.
% 176.56/27.43  | | | | | 
% 176.56/27.43  | | | | Case 2:
% 176.56/27.43  | | | | | 
% 176.56/27.43  | | | | |   (178)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.43  | | | | | 
% 176.56/27.43  | | | | | BETA: splitting (178) gives:
% 176.56/27.43  | | | | | 
% 176.56/27.43  | | | | | Case 1:
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | |   (179)  all_58_5 = e3
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | COMBINE_EQS: (18), (179) imply:
% 176.56/27.43  | | | | | |   (180)  all_52_13 = e3
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | SIMP: (180) implies:
% 176.56/27.43  | | | | | |   (181)  all_52_13 = e3
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | REDUCE: (129), (181) imply:
% 176.56/27.43  | | | | | |   (182)   ~ (all_10_2 = e3)
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | SIMP: (182) implies:
% 176.56/27.43  | | | | | |   (183)   ~ (all_10_2 = e3)
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | REDUCE: (56), (181) imply:
% 176.56/27.43  | | | | | |   (184)  op(e2, e1) = e3
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | GROUND_INST: instantiating (119) with e3, all_4_1, e3, e3,
% 176.56/27.43  | | | | | |              simplifying with (175), (176) gives:
% 176.56/27.43  | | | | | |   (185)  all_4_1 = e3
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | REDUCE: (174), (185) imply:
% 176.56/27.43  | | | | | |   (186)  op(e3, e3) = all_4_0
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | GROUND_INST: instantiating (119) with e3, all_4_0, e3, e3,
% 176.56/27.43  | | | | | |              simplifying with (176), (186) gives:
% 176.56/27.43  | | | | | |   (187)  all_4_0 = e3
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | BETA: splitting (110) gives:
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | Case 1:
% 176.56/27.43  | | | | | | | 
% 176.56/27.43  | | | | | | |   (188)  all_56_5 = e3
% 176.56/27.43  | | | | | | | 
% 176.56/27.43  | | | | | | | REF_CLOSE: (86), (183), (188) are inconsistent by sub-proof #895.
% 176.56/27.43  | | | | | | | 
% 176.56/27.43  | | | | | | Case 2:
% 176.56/27.43  | | | | | | | 
% 176.56/27.43  | | | | | | |   (189)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.43  | | | | | | | 
% 176.56/27.43  | | | | | | | BETA: splitting (87) gives:
% 176.56/27.43  | | | | | | | 
% 176.56/27.43  | | | | | | | Case 1:
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | |   (190)  all_58_6 = e2
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | | COMBINE_EQS: (90), (190) imply:
% 176.56/27.43  | | | | | | | |   (191)  all_52_17 = e2
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | | REDUCE: (167), (191) imply:
% 176.56/27.43  | | | | | | | |   (192)  $false
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | | CLOSE: (192) is inconsistent.
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | Case 2:
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | |   (193)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | | BETA: splitting (70) gives:
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | | Case 1:
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | |   (194)  all_58_9 = e2
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | COMBINE_EQS: (133), (194) imply:
% 176.56/27.43  | | | | | | | | |   (195)  all_52_7 = e2
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | REDUCE: (128), (195) imply:
% 176.56/27.43  | | | | | | | | |   (196)   ~ (all_52_23 = e2)
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | SIMP: (196) implies:
% 176.56/27.43  | | | | | | | | |   (197)   ~ (all_52_23 = e2)
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | REDUCE: (173), (195) imply:
% 176.56/27.43  | | | | | | | | |   (198)   ~ (e3 = e2)
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | REF_CLOSE: (58), (97), (119), (127), (139), (146), (159),
% 176.56/27.43  | | | | | | | | |            (162), (193), (197) are inconsistent by sub-proof
% 176.56/27.43  | | | | | | | | |            #714.
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | Case 2:
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | |   (199)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | BETA: splitting (199) gives:
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | Case 1:
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | |   (200)  all_58_10 = e2
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | COMBINE_EQS: (30), (200) imply:
% 176.56/27.43  | | | | | | | | | |   (201)  all_52_15 = e2
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | REDUCE: (165), (201) imply:
% 176.56/27.43  | | | | | | | | | |   (202)  $false
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | CLOSE: (202) is inconsistent.
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | Case 2:
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | |   (203)  all_58_11 = e2 | all_58_15 = e2
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | BETA: splitting (203) gives:
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | Case 1:
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | |   (204)  all_58_11 = e2
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | | COMBINE_EQS: (97), (204) imply:
% 176.56/27.43  | | | | | | | | | | |   (205)  all_52_23 = e2
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | | REDUCE: (123), (205) imply:
% 176.56/27.43  | | | | | | | | | | |   (206)  op(e0, e2) = e0
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | | GROUND_INST: instantiating (119) with all_52_27, e0, e2, e0,
% 176.56/27.43  | | | | | | | | | | |              simplifying with (60), (206) gives:
% 176.56/27.43  | | | | | | | | | | |   (207)  all_52_27 = e0
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | | REDUCE: (5), (207) imply:
% 176.56/27.43  | | | | | | | | | | |   (208)   ~ (all_10_2 = e0)
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | | SIMP: (208) implies:
% 176.56/27.43  | | | | | | | | | | |   (209)   ~ (all_10_2 = e0)
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | | REF_CLOSE: (7), (86), (93), (107), (119), (169), (172),
% 176.56/27.43  | | | | | | | | | | |            (184), (189), (209) are inconsistent by sub-proof
% 176.56/27.43  | | | | | | | | | | |            #254.
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | Case 2:
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | |   (210)  all_58_15 = e2
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | | REF_CLOSE: (139), (152), (210) are inconsistent by sub-proof
% 176.56/27.43  | | | | | | | | | | |            #286.
% 176.56/27.43  | | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | | End of split
% 176.56/27.43  | | | | | | | | | | 
% 176.56/27.43  | | | | | | | | | End of split
% 176.56/27.43  | | | | | | | | | 
% 176.56/27.43  | | | | | | | | End of split
% 176.56/27.43  | | | | | | | | 
% 176.56/27.43  | | | | | | | End of split
% 176.56/27.43  | | | | | | | 
% 176.56/27.43  | | | | | | End of split
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | Case 2:
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | |   (211)  all_58_8 = e3 | all_58_14 = e3
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | | REF_CLOSE: (1), (32), (36), (38), (52), (58), (65), (90), (94),
% 176.56/27.43  | | | | | |            (97), (107), (111), (119), (127), (141), (155), (211) are
% 176.56/27.43  | | | | | |            inconsistent by sub-proof #703.
% 176.56/27.43  | | | | | | 
% 176.56/27.43  | | | | | End of split
% 176.56/27.43  | | | | | 
% 176.56/27.43  | | | | End of split
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | Case 2:
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | |   (212)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | | REF_CLOSE: (25), (32), (36), (41), (48), (58), (65), (88), (90), (92),
% 176.56/27.43  | | | |            (94), (97), (106), (107), (111), (116), (118), (119), (127),
% 176.56/27.43  | | | |            (135), (139), (142), (153), (154), (212) are inconsistent by
% 176.56/27.43  | | | |            sub-proof #945.
% 176.56/27.43  | | | | 
% 176.56/27.43  | | | End of split
% 176.56/27.43  | | | 
% 176.56/27.43  | | Case 2:
% 176.56/27.43  | | | 
% 176.56/27.43  | | |   (213)   ~ (all_56_9 = e3)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REDUCE: (25), (213) imply:
% 176.56/27.43  | | |   (214)   ~ (all_52_19 = e3)
% 176.56/27.43  | | | 
% 176.56/27.43  | | | REF_CLOSE: (32), (36), (58), (65), (90), (94), (97), (107), (111), (116),
% 176.56/27.43  | | |            (118), (119), (127), (153), (214) are inconsistent by sub-proof
% 176.56/27.43  | | |            #702.
% 176.56/27.43  | | | 
% 176.56/27.43  | | End of split
% 176.56/27.43  | | 
% 176.56/27.43  | Case 2:
% 176.56/27.43  | | 
% 176.56/27.43  | |   (215)   ~ (all_56_15 = e3)
% 176.56/27.43  | |   (216)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.43  | | 
% 176.56/27.43  | | REDUCE: (21), (215) imply:
% 176.56/27.43  | |   (217)   ~ (all_6_2 = e3)
% 176.56/27.43  | | 
% 176.56/27.43  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 176.56/27.43  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.56/27.43  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.56/27.43  | |            (36), (37), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 176.56/27.43  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 176.56/27.43  | |            (59), (62), (63), (64), (65), (66), (67), (68), (69), (71), (73),
% 176.56/27.43  | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 176.56/27.43  | |            (85), (86), (87), (88), (90), (91), (92), (93), (94), (95), (96),
% 176.56/27.43  | |            (97), (98), (99), (100), (101), (102), (103), (104), (106),
% 176.56/27.43  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 176.56/27.43  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 176.56/27.43  | |            (125), (126), (127), (129), (130), (131), (132), (133), (134),
% 176.56/27.43  | |            (135), (136), (137), (138), (139), (140), (141), (142), (143),
% 176.56/27.43  | |            (146), (148), (216), (217) are inconsistent by sub-proof #249.
% 176.56/27.43  | | 
% 176.56/27.43  | End of split
% 176.56/27.43  | 
% 176.56/27.43  End of proof
% 176.56/27.43  
% 176.56/27.43  Sub-proof #249 shows that the following formulas are inconsistent:
% 176.56/27.43  ----------------------------------------------------------------
% 176.56/27.43    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.43    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.43    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.43    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.43    (5)   ~ (all_52_17 = all_52_23)
% 176.56/27.43    (6)  op(e2, all_10_2) = all_10_1
% 176.56/27.43    (7)   ~ (all_52_13 = all_52_29)
% 176.56/27.43    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.56/27.43    (9)  op(e3, e2) = all_52_3
% 176.56/27.43    (10)   ~ (all_52_9 = all_52_25)
% 176.56/27.43    (11)  op(e3, all_52_25) = all_52_24
% 176.56/27.43    (12)   ~ (all_52_19 = all_52_23)
% 176.56/27.43    (13)  op(e1, e2) = all_52_19
% 176.56/27.43    (14)   ~ (all_6_2 = e3)
% 176.56/27.43    (15)  op(e3, all_52_9) = all_52_8
% 176.56/27.43    (16)   ~ (all_52_3 = all_10_2)
% 176.56/27.43    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.43    (18)  all_58_5 = all_52_13
% 176.56/27.43    (19)   ~ (all_6_2 = e0)
% 176.56/27.43    (20)   ~ (all_52_25 = all_52_29)
% 176.56/27.43    (21)  all_56_15 = all_6_2
% 176.56/27.43    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.43    (23)  op(e2, e0) = all_52_15
% 176.56/27.43    (24)  all_58_3 = all_10_2
% 176.56/27.43    (25)  all_56_9 = all_52_19
% 176.56/27.43    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.43    (27)  all_58_15 = all_6_2
% 176.56/27.43    (28)   ~ (all_52_9 = all_4_2)
% 176.56/27.43    (29)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.43    (30)   ~ (all_52_5 = all_52_7)
% 176.56/27.43    (31)  all_58_10 = all_52_15
% 176.56/27.43    (32)   ~ (all_52_5 = all_4_2)
% 176.56/27.43    (33)  all_58_7 = all_52_19
% 176.56/27.43    (34)   ~ (all_52_17 = all_52_25)
% 176.56/27.43    (35)   ~ (all_4_0 = e2)
% 176.56/27.43    (36)  all_58_4 = all_52_5
% 176.56/27.43    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.43    (38)   ~ (e3 = e1)
% 176.56/27.43    (39)   ~ (all_52_27 = all_52_29)
% 176.56/27.43    (40)   ~ (all_52_17 = all_14_2)
% 176.56/27.43    (41)  op(e3, all_4_2) = all_4_1
% 176.56/27.43    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.43    (43)   ~ (all_52_7 = all_4_2)
% 176.56/27.43    (44)  all_58_1 = all_52_3
% 176.56/27.43    (45)  all_58_0 = all_4_2
% 176.56/27.43    (46)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.43    (47)  op(e1, all_52_29) = all_52_28
% 176.56/27.43    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.43    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.56/27.43    (50)   ~ (all_4_1 = e2)
% 176.56/27.43    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.43    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.43    (53)  all_58_14 = all_52_29
% 176.56/27.43    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.43    (55)   ~ (all_52_3 = all_52_5)
% 176.56/27.43    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.43    (57)  op(e2, e1) = all_52_13
% 176.56/27.43    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.43    (59)  all_58_8 = all_14_2
% 176.56/27.43    (60)  all_56_1 = all_52_3
% 176.56/27.43    (61)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.56/27.43    (62)  op(all_4_1, all_4_2) = all_4_0
% 176.56/27.43    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.43    (64)   ~ (all_52_5 = all_14_2)
% 176.56/27.43    (65)   ~ (all_52_3 = all_52_27)
% 176.56/27.43    (66)   ~ (all_52_3 = all_4_2)
% 176.56/27.43    (67)  op(e0, e3) = all_52_25
% 176.56/27.43    (68)   ~ (all_52_9 = all_10_2)
% 176.56/27.43    (69)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.43    (70)   ~ (e3 = e0)
% 176.56/27.43    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.43    (72)   ~ (all_52_9 = all_52_13)
% 176.56/27.43    (73)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.43    (74)   ~ (all_52_15 = all_52_23)
% 176.56/27.43    (75)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.43    (76)   ~ (all_52_5 = all_52_29)
% 176.56/27.43    (77)  all_56_2 = all_52_5
% 176.56/27.43    (78)  op(e1, e0) = all_52_23
% 176.56/27.43    (79)  all_56_12 = all_52_25
% 176.56/27.43    (80)  all_58_13 = all_52_27
% 176.56/27.43    (81)   ~ (all_4_1 = e1)
% 176.56/27.43    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.43    (83)  all_56_5 = all_10_2
% 176.56/27.43    (84)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.43    (85)   ~ (all_52_9 = all_52_17)
% 176.56/27.43    (86)  all_58_6 = all_52_17
% 176.56/27.43    (87)   ~ (all_52_3 = all_52_7)
% 176.56/27.43    (88)  op(e2, all_52_19) = e2
% 176.56/27.43    (89)  op(all_10_1, all_10_2) = e3
% 176.56/27.43    (90)  op(e3, all_52_17) = e3
% 176.56/27.43    (91)   ~ (e1 = e0)
% 176.56/27.43    (92)  all_56_0 = all_4_2
% 176.56/27.43    (93)  all_58_11 = all_52_23
% 176.56/27.43    (94)   ~ (all_52_3 = all_52_19)
% 176.56/27.43    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.43    (96)   ~ (all_52_7 = all_52_15)
% 176.56/27.43    (97)   ~ (all_52_29 = all_14_2)
% 176.56/27.43    (98)   ~ (all_4_0 = e1)
% 176.56/27.43    (99)   ~ (all_52_19 = all_10_2)
% 176.56/27.43    (100)   ~ (all_52_23 = all_6_2)
% 176.56/27.43    (101)  all_58_2 = all_52_9
% 176.56/27.43    (102)  op(e3, e1) = all_52_5
% 176.56/27.43    (103)   ~ (e2 = e1)
% 176.56/27.43    (104)  all_56_10 = all_14_2
% 176.56/27.43    (105)   ~ (all_52_25 = all_6_2)
% 176.56/27.43    (106)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.43    (107)  op(e1, e3) = all_52_17
% 176.56/27.43    (108)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.43    (109)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.56/27.43    (110)   ~ (all_52_25 = all_4_2)
% 176.56/27.43    (111)  op(e3, e0) = all_52_7
% 176.56/27.43    (112)  op(e3, e3) = all_4_2
% 176.56/27.43    (113)  all_56_8 = all_52_17
% 176.56/27.43    (114)   ~ (all_52_17 = all_4_2)
% 176.56/27.44    (115)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.44             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.44    (116)   ~ (all_52_25 = all_52_27)
% 176.56/27.44    (117)   ~ (all_52_27 = all_6_2)
% 176.56/27.44    (118)   ~ (all_52_7 = all_6_2)
% 176.56/27.44    (119)  op(e0, all_52_23) = e0
% 176.56/27.44    (120)   ~ (all_52_15 = all_10_2)
% 176.56/27.44    (121)   ~ (all_52_19 = all_52_27)
% 176.56/27.44    (122)  all_56_7 = all_52_15
% 176.56/27.44    (123)  op(e1, all_14_2) = e1
% 176.56/27.44    (124)   ~ (all_52_13 = all_10_2)
% 176.56/27.44    (125)  op(e2, all_52_27) = all_52_26
% 176.56/27.44    (126)   ~ (all_52_17 = all_52_19)
% 176.56/27.44    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.44    (128)  all_58_9 = all_52_7
% 176.56/27.44    (129)   ~ (e2 = e0)
% 176.56/27.44    (130)  all_58_12 = all_52_25
% 176.56/27.44    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.44    (132)   ~ (all_52_9 = all_52_15)
% 176.56/27.44    (133)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.44    (134)   ~ (e3 = e2)
% 176.56/27.44    (135)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.44    (136)   ~ (all_52_19 = all_14_2)
% 176.56/27.44    (137)  op(e2, e3) = all_52_9
% 176.56/27.44    (138)  all_56_13 = all_52_27
% 176.56/27.44  
% 176.56/27.44  Begin of proof
% 176.56/27.44  | 
% 176.56/27.44  | BETA: splitting (54) gives:
% 176.56/27.44  | 
% 176.56/27.44  | Case 1:
% 176.56/27.44  | | 
% 176.56/27.44  | |   (139)  all_56_13 = e3
% 176.56/27.44  | | 
% 176.56/27.44  | | COMBINE_EQS: (138), (139) imply:
% 176.56/27.44  | |   (140)  all_52_27 = e3
% 176.56/27.44  | | 
% 176.56/27.44  | | REF_CLOSE: (1), (2), (9), (11), (12), (18), (20), (22), (23), (25), (30),
% 176.56/27.44  | |            (31), (32), (33), (34), (36), (37), (38), (39), (40), (41), (45),
% 176.56/27.44  | |            (46), (48), (49), (53), (56), (59), (60), (62), (64), (65), (66),
% 176.56/27.44  | |            (67), (69), (75), (78), (81), (82), (85), (86), (88), (90), (91),
% 176.56/27.44  | |            (93), (94), (98), (101), (102), (103), (104), (107), (109),
% 176.56/27.44  | |            (110), (111), (112), (114), (115), (116), (119), (121), (123),
% 176.56/27.44  | |            (125), (126), (128), (129), (130), (133), (134), (136), (137),
% 176.56/27.44  | |            (140) are inconsistent by sub-proof #686.
% 176.56/27.44  | | 
% 176.56/27.44  | Case 2:
% 176.56/27.44  | | 
% 176.56/27.44  | |   (141)   ~ (all_56_13 = e3)
% 176.56/27.44  | | 
% 176.56/27.44  | | REDUCE: (138), (141) imply:
% 176.56/27.44  | |   (142)   ~ (all_52_27 = e3)
% 176.56/27.44  | | 
% 176.56/27.44  | | BETA: splitting (58) gives:
% 176.56/27.44  | | 
% 176.56/27.44  | | Case 1:
% 176.56/27.44  | | | 
% 176.56/27.44  | | |   (143)  all_58_12 = e3
% 176.56/27.44  | | | 
% 176.56/27.44  | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (13), (18), (20), (24), (26),
% 176.56/27.44  | | |            (27), (28), (30), (31), (32), (33), (34), (36), (37), (38),
% 176.56/27.44  | | |            (40), (42), (43), (44), (45), (46), (52), (53), (57), (59),
% 176.56/27.44  | | |            (64), (65), (66), (67), (68), (70), (71), (74), (76), (77),
% 176.56/27.44  | | |            (80), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 176.56/27.44  | | |            (91), (92), (93), (94), (96), (99), (101), (102), (103), (105),
% 176.56/27.44  | | |            (106), (107), (108), (110), (111), (113), (114), (115), (116),
% 176.56/27.44  | | |            (119), (120), (122), (123), (124), (126), (127), (128), (129),
% 176.56/27.44  | | |            (130), (131), (132), (133), (135), (136), (137), (143) are
% 176.56/27.44  | | |            inconsistent by sub-proof #250.
% 176.56/27.44  | | | 
% 176.56/27.44  | | Case 2:
% 176.56/27.44  | | | 
% 176.56/27.44  | | |   (144)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.44  | | | 
% 176.56/27.44  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 176.56/27.44  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.56/27.44  | | |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34),
% 176.56/27.44  | | |            (35), (36), (37), (39), (40), (41), (42), (44), (45), (46),
% 176.56/27.44  | | |            (47), (49), (50), (51), (52), (53), (55), (56), (59), (61),
% 176.56/27.44  | | |            (62), (63), (64), (66), (67), (68), (72), (73), (76), (79),
% 176.56/27.44  | | |            (80), (85), (86), (88), (90), (92), (93), (94), (95), (97),
% 176.56/27.44  | | |            (98), (99), (100), (101), (102), (105), (107), (110), (111),
% 176.56/27.44  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (121),
% 176.56/27.44  | | |            (123), (124), (126), (128), (130), (134), (136), (137), (142),
% 176.56/27.44  | | |            (144) are inconsistent by sub-proof #670.
% 176.56/27.44  | | | 
% 176.56/27.44  | | End of split
% 176.56/27.44  | | 
% 176.56/27.44  | End of split
% 176.56/27.44  | 
% 176.56/27.44  End of proof
% 176.56/27.44  
% 176.56/27.44  Sub-proof #250 shows that the following formulas are inconsistent:
% 176.56/27.44  ----------------------------------------------------------------
% 176.56/27.44    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.44    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.44    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.44    (4)   ~ (all_52_17 = all_52_23)
% 176.56/27.44    (5)  op(e2, all_10_2) = all_10_1
% 176.56/27.44    (6)   ~ (all_52_9 = all_52_25)
% 176.56/27.44    (7)  op(e1, e2) = all_52_19
% 176.56/27.44    (8)  all_58_5 = all_52_13
% 176.56/27.44    (9)   ~ (all_52_25 = all_52_29)
% 176.56/27.44    (10)  all_58_3 = all_10_2
% 176.56/27.44    (11)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.44    (12)  all_58_15 = all_6_2
% 176.56/27.44    (13)   ~ (all_52_9 = all_4_2)
% 176.56/27.44    (14)   ~ (all_52_5 = all_52_7)
% 176.56/27.44    (15)  all_58_10 = all_52_15
% 176.56/27.44    (16)   ~ (all_52_5 = all_4_2)
% 176.56/27.44    (17)  all_58_7 = all_52_19
% 176.56/27.44    (18)   ~ (all_52_17 = all_52_25)
% 176.56/27.44    (19)  all_58_4 = all_52_5
% 176.56/27.44    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.44    (21)   ~ (e3 = e1)
% 176.56/27.44    (22)   ~ (all_52_17 = all_14_2)
% 176.56/27.44    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.44    (24)   ~ (all_52_7 = all_4_2)
% 176.56/27.44    (25)  all_58_1 = all_52_3
% 176.56/27.44    (26)  all_58_0 = all_4_2
% 176.56/27.44    (27)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.44    (28)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.44    (29)  all_58_14 = all_52_29
% 176.56/27.44    (30)  op(e2, e1) = all_52_13
% 176.56/27.44    (31)  all_58_8 = all_14_2
% 176.56/27.44    (32)   ~ (all_52_5 = all_14_2)
% 176.56/27.44    (33)   ~ (all_52_3 = all_52_27)
% 176.56/27.44    (34)   ~ (all_52_3 = all_4_2)
% 176.56/27.44    (35)  op(e0, e3) = all_52_25
% 176.56/27.44    (36)   ~ (all_52_9 = all_10_2)
% 176.56/27.44    (37)   ~ (e3 = e0)
% 176.56/27.44    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.44    (39)   ~ (all_52_15 = all_52_23)
% 176.56/27.44    (40)   ~ (all_52_5 = all_52_29)
% 176.56/27.44    (41)  all_56_2 = all_52_5
% 176.56/27.44    (42)  all_58_13 = all_52_27
% 176.56/27.44    (43)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.44    (44)  all_56_5 = all_10_2
% 176.56/27.44    (45)  all_58_12 = e3
% 176.56/27.44    (46)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.44    (47)   ~ (all_52_9 = all_52_17)
% 176.56/27.44    (48)  all_58_6 = all_52_17
% 176.56/27.44    (49)   ~ (all_52_3 = all_52_7)
% 176.56/27.44    (50)  op(e2, all_52_19) = e2
% 176.56/27.44    (51)  op(all_10_1, all_10_2) = e3
% 176.56/27.44    (52)  op(e3, all_52_17) = e3
% 176.56/27.44    (53)   ~ (e1 = e0)
% 176.56/27.44    (54)  all_56_0 = all_4_2
% 176.56/27.44    (55)  all_58_11 = all_52_23
% 176.56/27.44    (56)   ~ (all_52_3 = all_52_19)
% 176.56/27.44    (57)   ~ (all_52_7 = all_52_15)
% 176.56/27.44    (58)   ~ (all_52_19 = all_10_2)
% 176.56/27.44    (59)  all_58_2 = all_52_9
% 176.56/27.44    (60)  op(e3, e1) = all_52_5
% 176.56/27.44    (61)   ~ (e2 = e1)
% 176.56/27.44    (62)   ~ (all_52_25 = all_6_2)
% 176.56/27.44    (63)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.44    (64)  op(e1, e3) = all_52_17
% 176.56/27.44    (65)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.44    (66)   ~ (all_52_25 = all_4_2)
% 176.56/27.44    (67)  op(e3, e0) = all_52_7
% 176.56/27.44    (68)  all_56_8 = all_52_17
% 176.56/27.44    (69)   ~ (all_52_17 = all_4_2)
% 176.56/27.44    (70)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.44    (71)   ~ (all_52_25 = all_52_27)
% 176.56/27.44    (72)  op(e0, all_52_23) = e0
% 176.56/27.44    (73)   ~ (all_52_15 = all_10_2)
% 176.56/27.44    (74)  all_56_7 = all_52_15
% 176.56/27.44    (75)  op(e1, all_14_2) = e1
% 176.56/27.44    (76)   ~ (all_52_13 = all_10_2)
% 176.56/27.44    (77)   ~ (all_52_17 = all_52_19)
% 176.56/27.44    (78)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.44    (79)  all_58_9 = all_52_7
% 176.56/27.44    (80)   ~ (e2 = e0)
% 176.56/27.44    (81)  all_58_12 = all_52_25
% 176.56/27.44    (82)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.44    (83)   ~ (all_52_9 = all_52_15)
% 176.56/27.44    (84)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.44    (85)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.44    (86)   ~ (all_52_19 = all_14_2)
% 176.56/27.44    (87)  op(e2, e3) = all_52_9
% 176.56/27.44  
% 176.56/27.44  Begin of proof
% 176.56/27.44  | 
% 176.56/27.44  | COMBINE_EQS: (45), (81) imply:
% 176.56/27.44  |   (88)  all_52_25 = e3
% 176.56/27.44  | 
% 176.56/27.44  | SIMP: (88) implies:
% 176.56/27.44  |   (89)  all_52_25 = e3
% 176.56/27.44  | 
% 176.56/27.44  | REDUCE: (6), (89) imply:
% 176.56/27.44  |   (90)   ~ (all_52_9 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | REDUCE: (18), (89) imply:
% 176.56/27.44  |   (91)   ~ (all_52_17 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | REDUCE: (71), (89) imply:
% 176.56/27.44  |   (92)   ~ (all_52_27 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | SIMP: (92) implies:
% 176.56/27.44  |   (93)   ~ (all_52_27 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | REDUCE: (9), (89) imply:
% 176.56/27.44  |   (94)   ~ (all_52_29 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | SIMP: (94) implies:
% 176.56/27.44  |   (95)   ~ (all_52_29 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | REDUCE: (62), (89) imply:
% 176.56/27.44  |   (96)   ~ (all_6_2 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | SIMP: (96) implies:
% 176.56/27.44  |   (97)   ~ (all_6_2 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | REDUCE: (66), (89) imply:
% 176.56/27.44  |   (98)   ~ (all_4_2 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | SIMP: (98) implies:
% 176.56/27.44  |   (99)   ~ (all_4_2 = e3)
% 176.56/27.44  | 
% 176.56/27.44  | REDUCE: (35), (89) imply:
% 176.56/27.44  |   (100)  op(e0, e3) = e3
% 176.56/27.44  | 
% 176.56/27.44  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 176.56/27.44  |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 176.56/27.44  |            (27), (28), (29), (30), (31), (32), (33), (34), (36), (37), (38),
% 176.56/27.44  |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 176.56/27.44  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 176.56/27.44  |            (61), (63), (64), (65), (67), (68), (69), (70), (72), (73), (74),
% 176.56/27.44  |            (75), (76), (77), (78), (79), (80), (82), (83), (84), (85), (86),
% 176.56/27.44  |            (87), (90), (91), (93), (95), (97), (99), (100) are inconsistent by
% 176.56/27.44  |            sub-proof #251.
% 176.56/27.44  | 
% 176.56/27.44  End of proof
% 176.56/27.44  
% 176.56/27.44  Sub-proof #251 shows that the following formulas are inconsistent:
% 176.56/27.44  ----------------------------------------------------------------
% 176.56/27.44    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.44    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.44    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.44    (4)   ~ (all_52_17 = all_52_23)
% 176.56/27.44    (5)  op(e2, all_10_2) = all_10_1
% 176.56/27.44    (6)  op(e1, e2) = all_52_19
% 176.56/27.44    (7)   ~ (all_52_27 = e3)
% 176.56/27.44    (8)   ~ (all_52_17 = e3)
% 176.56/27.44    (9)   ~ (all_6_2 = e3)
% 176.56/27.44    (10)  all_58_5 = all_52_13
% 176.56/27.44    (11)   ~ (all_4_2 = e3)
% 176.56/27.44    (12)  all_58_3 = all_10_2
% 176.56/27.44    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.44    (14)  all_58_15 = all_6_2
% 176.56/27.44    (15)   ~ (all_52_9 = all_4_2)
% 176.56/27.44    (16)   ~ (all_52_5 = all_52_7)
% 176.56/27.44    (17)  all_58_10 = all_52_15
% 176.56/27.44    (18)   ~ (all_52_5 = all_4_2)
% 176.56/27.44    (19)  all_58_7 = all_52_19
% 176.56/27.44    (20)  all_58_4 = all_52_5
% 176.56/27.44    (21)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.44    (22)   ~ (e3 = e1)
% 176.56/27.44    (23)   ~ (all_52_17 = all_14_2)
% 176.56/27.44    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.44    (25)   ~ (all_52_7 = all_4_2)
% 176.56/27.44    (26)  all_58_1 = all_52_3
% 176.56/27.44    (27)  all_58_0 = all_4_2
% 176.56/27.44    (28)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.44    (29)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.44    (30)  all_58_14 = all_52_29
% 176.56/27.44    (31)  op(e0, e3) = e3
% 176.56/27.44    (32)  op(e2, e1) = all_52_13
% 176.56/27.44    (33)  all_58_8 = all_14_2
% 176.56/27.44    (34)   ~ (all_52_5 = all_14_2)
% 176.56/27.44    (35)   ~ (all_52_3 = all_52_27)
% 176.56/27.44    (36)   ~ (all_52_3 = all_4_2)
% 176.56/27.44    (37)   ~ (all_52_9 = all_10_2)
% 176.56/27.44    (38)   ~ (all_52_29 = e3)
% 176.56/27.44    (39)   ~ (e3 = e0)
% 176.56/27.44    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.44    (41)   ~ (all_52_15 = all_52_23)
% 176.56/27.44    (42)   ~ (all_52_5 = all_52_29)
% 176.56/27.44    (43)  all_56_2 = all_52_5
% 176.56/27.44    (44)  all_58_13 = all_52_27
% 176.56/27.44    (45)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.44    (46)  all_56_5 = all_10_2
% 176.56/27.44    (47)  all_58_12 = e3
% 176.56/27.44    (48)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.44    (49)   ~ (all_52_9 = all_52_17)
% 176.56/27.44    (50)  all_58_6 = all_52_17
% 176.56/27.44    (51)   ~ (all_52_3 = all_52_7)
% 176.56/27.44    (52)  op(e2, all_52_19) = e2
% 176.56/27.44    (53)  op(all_10_1, all_10_2) = e3
% 176.56/27.44    (54)  op(e3, all_52_17) = e3
% 176.56/27.44    (55)   ~ (e1 = e0)
% 176.56/27.44    (56)  all_56_0 = all_4_2
% 176.56/27.44    (57)  all_58_11 = all_52_23
% 176.56/27.44    (58)   ~ (all_52_3 = all_52_19)
% 176.56/27.44    (59)   ~ (all_52_7 = all_52_15)
% 176.56/27.44    (60)   ~ (all_52_19 = all_10_2)
% 176.56/27.44    (61)   ~ (all_52_9 = e3)
% 176.56/27.44    (62)  all_58_2 = all_52_9
% 176.56/27.44    (63)  op(e3, e1) = all_52_5
% 176.56/27.44    (64)   ~ (e2 = e1)
% 176.56/27.44    (65)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.44    (66)  op(e1, e3) = all_52_17
% 176.56/27.44    (67)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.44    (68)  op(e3, e0) = all_52_7
% 176.56/27.44    (69)  all_56_8 = all_52_17
% 176.56/27.44    (70)   ~ (all_52_17 = all_4_2)
% 176.56/27.44    (71)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.44            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.44    (72)  op(e0, all_52_23) = e0
% 176.56/27.44    (73)   ~ (all_52_15 = all_10_2)
% 176.56/27.44    (74)  all_56_7 = all_52_15
% 176.56/27.44    (75)  op(e1, all_14_2) = e1
% 176.56/27.44    (76)   ~ (all_52_13 = all_10_2)
% 176.56/27.44    (77)   ~ (all_52_17 = all_52_19)
% 176.56/27.44    (78)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.44    (79)  all_58_9 = all_52_7
% 176.56/27.44    (80)   ~ (e2 = e0)
% 176.56/27.44    (81)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.44    (82)   ~ (all_52_9 = all_52_15)
% 176.56/27.44    (83)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.44    (84)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.44    (85)   ~ (all_52_19 = all_14_2)
% 176.56/27.44    (86)  op(e2, e3) = all_52_9
% 176.56/27.44  
% 176.56/27.44  Begin of proof
% 176.56/27.44  | 
% 176.56/27.44  | BETA: splitting (3) gives:
% 176.56/27.44  | 
% 176.56/27.44  | Case 1:
% 176.56/27.44  | | 
% 176.56/27.44  | |   (87)  all_56_8 = e3
% 176.56/27.44  | | 
% 176.56/27.44  | | REF_CLOSE: (8), (69), (87) are inconsistent by sub-proof #461.
% 176.56/27.44  | | 
% 176.56/27.44  | Case 2:
% 176.56/27.44  | | 
% 176.56/27.44  | |   (88)   ~ (all_56_8 = e3)
% 176.56/27.44  | |   (89)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.44  | | 
% 176.56/27.44  | | BETA: splitting (84) gives:
% 176.56/27.44  | | 
% 176.56/27.44  | | Case 1:
% 176.56/27.44  | | | 
% 176.56/27.44  | | |   (90)  all_56_2 = e3
% 176.56/27.44  | | | 
% 176.56/27.44  | | | COMBINE_EQS: (43), (90) imply:
% 176.56/27.44  | | |   (91)  all_52_5 = e3
% 176.56/27.44  | | | 
% 176.56/27.44  | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 176.56/27.44  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 176.56/27.44  | | |            (27), (28), (29), (30), (31), (33), (34), (39), (40), (41),
% 176.56/27.44  | | |            (42), (44), (45), (47), (48), (49), (50), (52), (54), (55),
% 176.56/27.44  | | |            (56), (57), (58), (59), (62), (63), (64), (66), (67), (68),
% 176.56/27.44  | | |            (70), (71), (72), (73), (74), (75), (77), (78), (79), (80),
% 176.56/27.44  | | |            (81), (82), (83), (85), (86), (91) are inconsistent by
% 176.56/27.44  | | |            sub-proof #281.
% 176.56/27.44  | | | 
% 176.56/27.44  | | Case 2:
% 176.56/27.44  | | | 
% 176.56/27.44  | | |   (92)   ~ (all_56_2 = e3)
% 176.56/27.44  | | | 
% 176.56/27.44  | | | REDUCE: (43), (92) imply:
% 176.56/27.44  | | |   (93)   ~ (all_52_5 = e3)
% 176.56/27.44  | | | 
% 176.56/27.44  | | | BETA: splitting (83) gives:
% 176.56/27.44  | | | 
% 176.56/27.44  | | | Case 1:
% 176.56/27.44  | | | | 
% 176.56/27.44  | | | |   (94)  all_58_4 = e3
% 176.56/27.44  | | | | 
% 176.56/27.44  | | | | REF_CLOSE: (20), (93), (94) are inconsistent by sub-proof #1025.
% 176.56/27.44  | | | | 
% 176.56/27.44  | | | Case 2:
% 176.56/27.44  | | | | 
% 176.56/27.44  | | | |   (95)   ~ (all_58_4 = e3)
% 176.56/27.44  | | | |   (96)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.44  | | | | 
% 176.56/27.44  | | | | BETA: splitting (81) gives:
% 176.56/27.44  | | | | 
% 176.56/27.44  | | | | Case 1:
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | |   (97)  all_58_0 = e3
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | | COMBINE_EQS: (27), (97) imply:
% 176.56/27.44  | | | | |   (98)  all_4_2 = e3
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | | REDUCE: (11), (98) imply:
% 176.56/27.44  | | | | |   (99)  $false
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | | CLOSE: (99) is inconsistent.
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | Case 2:
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | |   (100)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | | BETA: splitting (65) gives:
% 176.56/27.44  | | | | | 
% 176.56/27.44  | | | | | Case 1:
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | |   (101)  all_56_5 = e3
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | | COMBINE_EQS: (46), (101) imply:
% 176.56/27.44  | | | | | |   (102)  all_10_2 = e3
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | | SIMP: (102) implies:
% 176.56/27.44  | | | | | |   (103)  all_10_2 = e3
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | | REDUCE: (76), (103) imply:
% 176.56/27.44  | | | | | |   (104)   ~ (all_52_13 = e3)
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | | REF_CLOSE: (1), (10), (19), (21), (23), (30), (33), (34), (38),
% 176.56/27.44  | | | | | |            (50), (54), (57), (63), (66), (71), (75), (85), (96),
% 176.56/27.44  | | | | | |            (104) are inconsistent by sub-proof #253.
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | Case 2:
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | |   (105)   ~ (all_56_5 = e3)
% 176.56/27.44  | | | | | |   (106)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | | REDUCE: (46), (105) imply:
% 176.56/27.44  | | | | | |   (107)   ~ (all_10_2 = e3)
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | | BETA: splitting (29) gives:
% 176.56/27.44  | | | | | | 
% 176.56/27.44  | | | | | | Case 1:
% 176.56/27.44  | | | | | | | 
% 176.56/27.44  | | | | | | |   (108)  all_58_1 = e3
% 176.56/27.44  | | | | | | | 
% 176.56/27.44  | | | | | | | REF_CLOSE: (6), (8), (9), (12), (13), (14), (15), (16), (17),
% 176.56/27.44  | | | | | | |            (18), (19), (20), (21), (22), (25), (26), (27), (28),
% 176.56/27.44  | | | | | | |            (29), (31), (33), (34), (35), (36), (39), (40), (41),
% 176.56/27.44  | | | | | | |            (44), (45), (47), (48), (49), (50), (51), (52), (54),
% 176.56/27.44  | | | | | | |            (55), (56), (57), (58), (59), (62), (63), (64), (66),
% 176.56/27.44  | | | | | | |            (67), (68), (70), (71), (72), (73), (74), (75), (77),
% 176.56/27.44  | | | | | | |            (78), (79), (80), (81), (82), (83), (86), (108) are
% 176.56/27.44  | | | | | | |            inconsistent by sub-proof #280.
% 176.56/27.44  | | | | | | | 
% 176.56/27.44  | | | | | | Case 2:
% 176.56/27.44  | | | | | | | 
% 176.56/27.44  | | | | | | |   (109)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.44  | | | | | | | 
% 176.56/27.44  | | | | | | | BETA: splitting (109) gives:
% 176.56/27.44  | | | | | | | 
% 176.56/27.44  | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | |   (110)  all_58_3 = e3
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | | COMBINE_EQS: (12), (110) imply:
% 176.56/27.44  | | | | | | | |   (111)  all_10_2 = e3
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | | REDUCE: (107), (111) imply:
% 176.56/27.44  | | | | | | | |   (112)  $false
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | | CLOSE: (112) is inconsistent.
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | |   (113)  all_58_7 = e3 | all_58_13 = e3
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | | BETA: splitting (113) gives:
% 176.56/27.44  | | | | | | | | 
% 176.56/27.44  | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | 
% 176.56/27.44  | | | | | | | | |   (114)  all_58_7 = e3
% 176.56/27.44  | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | COMBINE_EQS: (19), (114) imply:
% 176.56/27.44  | | | | | | | | |   (115)  all_52_19 = e3
% 176.56/27.44  | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | REDUCE: (58), (115) imply:
% 176.56/27.44  | | | | | | | | |   (116)   ~ (all_52_3 = e3)
% 176.56/27.44  | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | REDUCE: (60), (115) imply:
% 176.56/27.44  | | | | | | | | |   (117)   ~ (all_10_2 = e3)
% 176.56/27.44  | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | REDUCE: (52), (115) imply:
% 176.56/27.44  | | | | | | | | |   (118)  op(e2, e3) = e2
% 176.56/27.44  | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | BETA: splitting (100) gives:
% 176.56/27.44  | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | |   (119)  all_58_1 = e3
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | COMBINE_EQS: (26), (119) imply:
% 176.56/27.44  | | | | | | | | | |   (120)  all_52_3 = e3
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | REDUCE: (116), (120) imply:
% 176.56/27.44  | | | | | | | | | |   (121)  $false
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | CLOSE: (121) is inconsistent.
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | |   (122)  all_58_4 = e3 | all_58_9 = e3
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | BETA: splitting (122) gives:
% 176.56/27.44  | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | |   (123)  all_58_4 = e3
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | REF_CLOSE: (20), (93), (123) are inconsistent by sub-proof
% 176.56/27.44  | | | | | | | | | | |            #1025.
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | |   (124)  all_58_9 = e3
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | COMBINE_EQS: (79), (124) imply:
% 176.56/27.44  | | | | | | | | | | |   (125)  all_52_7 = e3
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | SIMP: (125) implies:
% 176.56/27.44  | | | | | | | | | | |   (126)  all_52_7 = e3
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | REDUCE: (59), (126) imply:
% 176.56/27.44  | | | | | | | | | | |   (127)   ~ (all_52_15 = e3)
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | SIMP: (127) implies:
% 176.56/27.44  | | | | | | | | | | |   (128)   ~ (all_52_15 = e3)
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | BETA: splitting (24) gives:
% 176.56/27.44  | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | |   (129)  all_58_2 = e3
% 176.56/27.44  | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | REF_CLOSE: (61), (62), (129) are inconsistent by sub-proof
% 176.56/27.44  | | | | | | | | | | | |            #980.
% 176.56/27.44  | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | |   (130)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.44  | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | BETA: splitting (130) gives:
% 176.56/27.44  | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | |   (131)  all_58_3 = e3
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | COMBINE_EQS: (12), (131) imply:
% 176.56/27.44  | | | | | | | | | | | | |   (132)  all_10_2 = e3
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | REDUCE: (107), (132) imply:
% 176.56/27.44  | | | | | | | | | | | | |   (133)  $false
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | CLOSE: (133) is inconsistent.
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | |   (134)  all_58_5 = e3 | all_58_10 = e3
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | BETA: splitting (134) gives:
% 176.56/27.44  | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | |   (135)  all_58_5 = e3
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | COMBINE_EQS: (10), (135) imply:
% 176.56/27.44  | | | | | | | | | | | | | |   (136)  all_52_13 = e3
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | SIMP: (136) implies:
% 176.56/27.44  | | | | | | | | | | | | | |   (137)  all_52_13 = e3
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | REDUCE: (32), (137) imply:
% 176.56/27.44  | | | | | | | | | | | | | |   (138)  op(e2, e1) = e3
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_52_9, e2, e3, e2,
% 176.56/27.44  | | | | | | | | | | | | | |              simplifying with (86), (118) gives:
% 176.56/27.44  | | | | | | | | | | | | | |   (139)  all_52_9 = e2
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | COMBINE_EQS: (62), (139) imply:
% 176.56/27.44  | | | | | | | | | | | | | |   (140)  all_58_2 = e2
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | REDUCE: (49), (139) imply:
% 176.56/27.44  | | | | | | | | | | | | | |   (141)   ~ (all_52_17 = e2)
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | SIMP: (141) implies:
% 176.56/27.44  | | | | | | | | | | | | | |   (142)   ~ (all_52_17 = e2)
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | REDUCE: (37), (139) imply:
% 176.56/27.44  | | | | | | | | | | | | | |   (143)   ~ (all_10_2 = e2)
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | SIMP: (143) implies:
% 176.56/27.44  | | | | | | | | | | | | | |   (144)   ~ (all_10_2 = e2)
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | |   (145)  all_58_0 = e1
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | COMBINE_EQS: (27), (145) imply:
% 176.56/27.44  | | | | | | | | | | | | | | |   (146)  all_4_2 = e1
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | REDUCE: (70), (146) imply:
% 176.56/27.44  | | | | | | | | | | | | | | |   (147)   ~ (all_52_17 = e1)
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | |   (148)  all_56_8 = e2
% 176.56/27.44  | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | REF_CLOSE: (69), (142), (148) are inconsistent by sub-proof
% 176.56/27.44  | | | | | | | | | | | | | | | |            #460.
% 176.56/27.44  | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | |   (149)  all_56_8 = e1 | all_56_8 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 176.56/27.44  | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | |   (150)  all_56_8 = e1
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (147), (150) are inconsistent by sub-proof
% 176.56/27.44  | | | | | | | | | | | | | | | | |            #287.
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | |   (151)  all_56_8 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (151) imply:
% 176.56/27.44  | | | | | | | | | | | | | | | | |   (152)  all_52_17 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | SIMP: (152) implies:
% 176.56/27.44  | | | | | | | | | | | | | | | | |   (153)  all_52_17 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | REDUCE: (4), (153) imply:
% 176.56/27.44  | | | | | | | | | | | | | | | | |   (154)   ~ (all_52_23 = e0)
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | SIMP: (154) implies:
% 176.56/27.44  | | | | | | | | | | | | | | | | |   (155)   ~ (all_52_23 = e0)
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | REDUCE: (8), (153) imply:
% 176.56/27.44  | | | | | | | | | | | | | | | | |   (156)   ~ (e3 = e0)
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | |   (157)  all_58_9 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (124), (157) are inconsistent by sub-proof
% 176.56/27.44  | | | | | | | | | | | | | | | | | |            #928.
% 176.56/27.44  | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | |   (158)  all_58_10 = e0 | all_58_11 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |   (159)  all_58_10 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (159) imply:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |   (160)  all_52_15 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | SIMP: (160) implies:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |   (161)  all_52_15 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | REDUCE: (73), (161) imply:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |   (162)   ~ (all_10_2 = e0)
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | SIMP: (162) implies:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |   (163)   ~ (all_10_2 = e0)
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (46), (53), (63), (71), (93), (106), (138),
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |            (144), (163) are inconsistent by sub-proof #254.
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |   (164)  all_58_11 = e0
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (155), (164) are inconsistent by sub-proof
% 176.56/27.44  | | | | | | | | | | | | | | | | | | |            #252.
% 176.56/27.44  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | | End of split
% 176.56/27.44  | | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | | End of split
% 176.56/27.44  | | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | | End of split
% 176.56/27.44  | | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | End of split
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | |   (165)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | | REF_CLOSE: (22), (47), (50), (54), (63), (64), (71), (93),
% 176.56/27.44  | | | | | | | | | | | | | | |            (140), (165) are inconsistent by sub-proof #919.
% 176.56/27.44  | | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | | End of split
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.44  | | | | | | | | | | | | | Case 2:
% 176.56/27.44  | | | | | | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | | | | | |   (166)  all_58_10 = e3
% 176.56/27.45  | | | | | | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | | | | | | REF_CLOSE: (17), (128), (166) are inconsistent by sub-proof
% 176.56/27.45  | | | | | | | | | | | | | |            #1018.
% 176.56/27.45  | | | | | | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | | | | | End of split
% 176.56/27.45  | | | | | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | | | | End of split
% 176.56/27.45  | | | | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | | | End of split
% 176.56/27.45  | | | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | | End of split
% 176.56/27.45  | | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | End of split
% 176.56/27.45  | | | | | | | | | 
% 176.56/27.45  | | | | | | | | Case 2:
% 176.56/27.45  | | | | | | | | | 
% 176.56/27.45  | | | | | | | | |   (167)  all_58_13 = e3
% 176.56/27.45  | | | | | | | | | 
% 176.56/27.45  | | | | | | | | | REF_CLOSE: (7), (44), (167) are inconsistent by sub-proof
% 176.56/27.45  | | | | | | | | |            #1026.
% 176.56/27.45  | | | | | | | | | 
% 176.56/27.45  | | | | | | | | End of split
% 176.56/27.45  | | | | | | | | 
% 176.56/27.45  | | | | | | | End of split
% 176.56/27.45  | | | | | | | 
% 176.56/27.45  | | | | | | End of split
% 176.56/27.45  | | | | | | 
% 176.56/27.45  | | | | | End of split
% 176.56/27.45  | | | | | 
% 176.56/27.45  | | | | End of split
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | End of split
% 176.56/27.45  | | | 
% 176.56/27.45  | | End of split
% 176.56/27.45  | | 
% 176.56/27.45  | End of split
% 176.56/27.45  | 
% 176.56/27.45  End of proof
% 176.56/27.45  
% 176.56/27.45  Sub-proof #252 shows that the following formulas are inconsistent:
% 176.56/27.45  ----------------------------------------------------------------
% 176.56/27.45    (1)  all_58_11 = all_52_23
% 176.56/27.45    (2)  all_58_11 = e0
% 176.56/27.45    (3)   ~ (all_52_23 = e0)
% 176.56/27.45  
% 176.56/27.45  Begin of proof
% 176.56/27.45  | 
% 176.56/27.45  | COMBINE_EQS: (1), (2) imply:
% 176.56/27.45  |   (4)  all_52_23 = e0
% 176.56/27.45  | 
% 176.56/27.45  | SIMP: (4) implies:
% 176.56/27.45  |   (5)  all_52_23 = e0
% 176.56/27.45  | 
% 176.56/27.45  | REDUCE: (3), (5) imply:
% 176.56/27.45  |   (6)  $false
% 176.56/27.45  | 
% 176.56/27.45  | CLOSE: (6) is inconsistent.
% 176.56/27.45  | 
% 176.56/27.45  End of proof
% 176.56/27.45  
% 176.56/27.45  Sub-proof #253 shows that the following formulas are inconsistent:
% 176.56/27.45  ----------------------------------------------------------------
% 176.56/27.45    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.45    (2)  all_58_5 = all_52_13
% 176.56/27.45    (3)  all_58_7 = all_52_19
% 176.56/27.45    (4)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.45    (5)   ~ (all_52_17 = all_14_2)
% 176.56/27.45    (6)  all_58_14 = all_52_29
% 176.56/27.45    (7)  all_58_8 = all_14_2
% 176.56/27.45    (8)   ~ (all_52_5 = all_14_2)
% 176.56/27.45    (9)   ~ (all_52_29 = e3)
% 176.56/27.45    (10)   ~ (all_52_13 = e3)
% 176.56/27.45    (11)  all_58_6 = all_52_17
% 176.56/27.45    (12)  op(e3, all_52_17) = e3
% 176.56/27.45    (13)  all_58_11 = all_52_23
% 176.56/27.45    (14)  op(e3, e1) = all_52_5
% 176.56/27.45    (15)  op(e1, e3) = all_52_17
% 176.56/27.45    (16)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.45    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.45    (18)  op(e1, all_14_2) = e1
% 176.56/27.45    (19)   ~ (all_52_19 = all_14_2)
% 176.56/27.45  
% 176.56/27.45  Begin of proof
% 176.56/27.45  | 
% 176.56/27.45  | BETA: splitting (16) gives:
% 176.56/27.45  | 
% 176.56/27.45  | Case 1:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (20)  all_58_5 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | REF_CLOSE: (2), (10), (20) are inconsistent by sub-proof #969.
% 176.56/27.45  | | 
% 176.56/27.45  | Case 2:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (21)  all_58_8 = e3 | all_58_14 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 176.56/27.45  | |            (15), (17), (18), (19), (21) are inconsistent by sub-proof #703.
% 176.56/27.45  | | 
% 176.56/27.45  | End of split
% 176.56/27.45  | 
% 176.56/27.45  End of proof
% 176.56/27.45  
% 176.56/27.45  Sub-proof #254 shows that the following formulas are inconsistent:
% 176.56/27.45  ----------------------------------------------------------------
% 176.56/27.45    (1)  op(e2, all_10_2) = all_10_1
% 176.56/27.45    (2)   ~ (all_10_2 = e0)
% 176.56/27.45    (3)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.45    (4)   ~ (all_52_5 = e3)
% 176.56/27.45    (5)  all_56_5 = all_10_2
% 176.56/27.45    (6)  op(all_10_1, all_10_2) = e3
% 176.56/27.45    (7)  op(e2, e1) = e3
% 176.56/27.45    (8)  op(e3, e1) = all_52_5
% 176.56/27.45    (9)   ~ (all_10_2 = e2)
% 176.56/27.45    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.45  
% 176.56/27.45  Begin of proof
% 176.56/27.45  | 
% 176.56/27.45  | BETA: splitting (3) gives:
% 176.56/27.45  | 
% 176.56/27.45  | Case 1:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (11)  all_56_5 = e2
% 176.56/27.45  | | 
% 176.56/27.45  | | REF_CLOSE: (5), (9), (11) are inconsistent by sub-proof #710.
% 176.56/27.45  | | 
% 176.56/27.45  | Case 2:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (12)  all_56_5 = e1 | all_56_5 = e0
% 176.56/27.45  | | 
% 176.56/27.45  | | BETA: splitting (12) gives:
% 176.56/27.45  | | 
% 176.56/27.45  | | Case 1:
% 176.56/27.45  | | | 
% 176.56/27.45  | | |   (13)  all_56_5 = e1
% 176.56/27.45  | | | 
% 176.56/27.45  | | | COMBINE_EQS: (5), (13) imply:
% 176.56/27.45  | | |   (14)  all_10_2 = e1
% 176.56/27.45  | | | 
% 176.56/27.45  | | | SIMP: (14) implies:
% 176.56/27.45  | | |   (15)  all_10_2 = e1
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (6), (15) imply:
% 176.56/27.45  | | |   (16)  op(all_10_1, e1) = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (1), (15) imply:
% 176.56/27.45  | | |   (17)  op(e2, e1) = all_10_1
% 176.56/27.45  | | | 
% 176.56/27.45  | | | GROUND_INST: instantiating (10) with e3, all_10_1, e1, e2, simplifying
% 176.56/27.45  | | |              with (7), (17) gives:
% 176.56/27.45  | | |   (18)  all_10_1 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (16), (18) imply:
% 176.56/27.45  | | |   (19)  op(e3, e1) = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REF_CLOSE: (4), (8), (10), (19) are inconsistent by sub-proof #1023.
% 176.56/27.45  | | | 
% 176.56/27.45  | | Case 2:
% 176.56/27.45  | | | 
% 176.56/27.45  | | |   (20)  all_56_5 = e0
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REF_CLOSE: (2), (5), (20) are inconsistent by sub-proof #708.
% 176.56/27.45  | | | 
% 176.56/27.45  | | End of split
% 176.56/27.45  | | 
% 176.56/27.45  | End of split
% 176.56/27.45  | 
% 176.56/27.45  End of proof
% 176.56/27.45  
% 176.56/27.45  Sub-proof #255 shows that the following formulas are inconsistent:
% 176.56/27.45  ----------------------------------------------------------------
% 176.56/27.45    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.45    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.45    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.45    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.45    (5)   ~ (all_52_27 = all_10_2)
% 176.56/27.45    (6)  op(e2, e2) = all_10_2
% 176.56/27.45    (7)   ~ (all_52_17 = all_52_23)
% 176.56/27.45    (8)  op(e2, all_52_3) = e2
% 176.56/27.45    (9)  all_58_15 = e3
% 176.56/27.45    (10)  op(e2, all_10_2) = all_10_1
% 176.56/27.45    (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.45    (12)   ~ (all_52_13 = all_52_29)
% 176.56/27.45    (13)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.56/27.45    (14)  all_56_3 = all_52_7
% 176.56/27.45    (15)  op(e3, e2) = all_52_3
% 176.56/27.45    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.45    (17)   ~ (all_52_27 = e3)
% 176.56/27.45    (18)   ~ (all_52_17 = e3)
% 176.56/27.45    (19)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.45    (20)  all_58_12 = all_6_1
% 176.56/27.45    (21)  op(all_6_1, e3) = all_6_0
% 176.56/27.45    (22)   ~ (all_52_3 = all_10_2)
% 176.56/27.45    (23)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.45    (24)  all_58_5 = all_52_13
% 176.56/27.45    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.45    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.45    (27)  all_58_3 = all_10_2
% 176.56/27.45    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.45    (29)  all_58_15 = all_6_2
% 176.56/27.45    (30)   ~ (all_52_9 = all_4_2)
% 176.56/27.45    (31)   ~ (all_52_5 = all_52_7)
% 176.56/27.45    (32)  all_58_10 = all_52_15
% 176.56/27.45    (33)   ~ (all_52_5 = all_4_2)
% 176.56/27.45    (34)  all_58_7 = all_52_19
% 176.56/27.45    (35)  all_56_4 = all_52_9
% 176.56/27.45    (36)  op(e3, all_6_1) = all_52_24
% 176.56/27.45    (37)  op(e0, e1) = all_52_29
% 176.56/27.45    (38)  all_58_4 = all_52_5
% 176.56/27.45    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.45    (40)   ~ (e3 = e1)
% 176.56/27.45    (41)   ~ (all_52_27 = all_52_29)
% 176.56/27.45    (42)   ~ (all_52_17 = all_14_2)
% 176.56/27.45    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.45    (44)   ~ (all_52_7 = all_4_2)
% 176.56/27.45    (45)  all_58_1 = all_52_3
% 176.56/27.45    (46)   ~ (all_52_13 = all_52_15)
% 176.56/27.45    (47)  all_58_0 = all_4_2
% 176.56/27.45    (48)   ~ (all_52_9 = all_6_1)
% 176.56/27.45    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.45    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.45    (51)  all_58_14 = all_52_29
% 176.56/27.45    (52)  all_58_7 = e3
% 176.56/27.45    (53)   ~ (all_52_3 = all_52_5)
% 176.56/27.45    (54)  op(e2, e1) = all_52_13
% 176.56/27.45    (55)   ~ (all_52_17 = all_6_1)
% 176.56/27.45    (56)  all_58_8 = all_14_2
% 176.56/27.45    (57)  all_56_1 = all_52_3
% 176.56/27.45    (58)   ~ (all_6_1 = e3)
% 176.56/27.45    (59)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.45    (60)   ~ (all_52_5 = all_14_2)
% 176.56/27.45    (61)   ~ (all_52_23 = e3)
% 176.56/27.45    (62)   ~ (all_52_3 = all_52_27)
% 176.56/27.45    (63)   ~ (all_52_3 = all_4_2)
% 176.56/27.45    (64)  op(e3, all_4_2) = e3
% 176.56/27.45    (65)  op(e0, e3) = all_52_25
% 176.56/27.45    (66)   ~ (all_52_9 = all_10_2)
% 176.56/27.45    (67)  op(e3, all_52_17) = all_52_16
% 176.56/27.45    (68)   ~ (all_52_29 = e3)
% 176.56/27.45    (69)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.45    (70)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.45    (71)   ~ (all_52_13 = all_14_2)
% 176.56/27.45    (72)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.45    (73)   ~ (all_52_9 = all_52_13)
% 176.56/27.45    (74)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.45    (75)   ~ (all_52_5 = all_52_29)
% 176.56/27.45    (76)  all_56_2 = all_52_5
% 176.56/27.45    (77)  op(e1, e0) = all_52_23
% 176.56/27.45    (78)  all_58_13 = all_52_27
% 176.56/27.45    (79)   ~ (all_52_3 = e3)
% 176.56/27.45    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.45    (81)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.45    (82)   ~ (all_52_9 = all_52_17)
% 176.56/27.45    (83)  all_58_6 = all_52_17
% 176.56/27.45    (84)   ~ (all_52_3 = all_52_7)
% 176.56/27.45    (85)  op(all_10_1, all_10_2) = e3
% 176.56/27.45    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.45    (87)   ~ (e1 = e0)
% 176.56/27.45    (88)  all_56_0 = all_4_2
% 176.56/27.45    (89)  all_58_11 = all_52_23
% 176.56/27.45    (90)   ~ (all_52_3 = all_52_19)
% 176.56/27.45    (91)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.45    (92)   ~ (all_52_7 = all_52_15)
% 176.56/27.45    (93)   ~ (all_52_29 = all_14_2)
% 176.56/27.45    (94)  all_58_2 = all_52_9
% 176.56/27.45    (95)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.56/27.45    (96)  op(e3, e1) = all_52_5
% 176.56/27.45    (97)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.56/27.45    (98)   ~ (e2 = e1)
% 176.56/27.45    (99)  all_56_10 = all_14_2
% 176.56/27.45    (100)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.56/27.45    (101)  op(e1, e1) = all_14_2
% 176.56/27.45    (102)  op(e1, e3) = all_52_17
% 176.56/27.45    (103)   ~ (all_52_25 = all_4_2)
% 176.56/27.45    (104)  op(e3, e0) = all_52_7
% 176.56/27.45    (105)  all_56_8 = all_52_17
% 176.56/27.45    (106)   ~ (all_14_2 = e3)
% 176.56/27.45    (107)   ~ (all_52_17 = all_4_2)
% 176.56/27.45    (108)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.45             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.45    (109)   ~ (all_52_7 = all_6_2)
% 176.56/27.45    (110)  op(e2, e3) = all_52_18
% 176.56/27.45    (111)   ~ (all_52_7 = e3)
% 176.56/27.45    (112)  op(e1, all_52_5) = e1
% 176.56/27.45    (113)   ~ (all_52_7 = all_52_23)
% 176.56/27.45    (114)   ~ (all_52_13 = all_10_2)
% 176.56/27.45    (115)   ~ (all_6_0 = e1)
% 176.56/27.45    (116)  op(e0, all_52_7) = e0
% 176.56/27.45    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.45    (118)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.56/27.45    (119)  all_58_9 = all_52_7
% 176.56/27.45    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.45    (121)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.45    (122)   ~ (e3 = e2)
% 176.56/27.45    (123)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.45    (124)  op(e1, e2) = e3
% 176.56/27.45    (125)  op(e2, e3) = all_52_9
% 176.56/27.45    (126)  all_56_13 = all_52_27
% 176.56/27.45  
% 176.56/27.45  Begin of proof
% 176.56/27.45  | 
% 176.56/27.45  | GROUND_INST: instantiating (108) with all_52_9, all_52_18, e3, e2, simplifying
% 176.56/27.45  |              with (110), (125) gives:
% 176.56/27.45  |   (127)  all_52_9 = all_52_18
% 176.56/27.45  | 
% 176.56/27.45  | COMBINE_EQS: (35), (127) imply:
% 176.56/27.45  |   (128)  all_56_4 = all_52_18
% 176.56/27.45  | 
% 176.56/27.45  | COMBINE_EQS: (94), (127) imply:
% 176.56/27.45  |   (129)  all_58_2 = all_52_18
% 176.56/27.45  | 
% 176.56/27.45  | REDUCE: (73), (127) imply:
% 176.56/27.45  |   (130)   ~ (all_52_13 = all_52_18)
% 176.56/27.45  | 
% 176.56/27.45  | SIMP: (130) implies:
% 176.56/27.45  |   (131)   ~ (all_52_13 = all_52_18)
% 176.56/27.45  | 
% 176.56/27.45  | REDUCE: (82), (127) imply:
% 176.56/27.45  |   (132)   ~ (all_52_17 = all_52_18)
% 176.56/27.45  | 
% 176.56/27.45  | SIMP: (132) implies:
% 176.56/27.45  |   (133)   ~ (all_52_17 = all_52_18)
% 176.56/27.45  | 
% 176.56/27.45  | REDUCE: (66), (127) imply:
% 176.56/27.45  |   (134)   ~ (all_52_18 = all_10_2)
% 176.56/27.45  | 
% 176.56/27.45  | REDUCE: (48), (127) imply:
% 176.56/27.45  |   (135)   ~ (all_52_18 = all_6_1)
% 176.56/27.45  | 
% 176.56/27.45  | BETA: splitting (121) gives:
% 176.56/27.45  | 
% 176.56/27.45  | Case 1:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (136)  all_58_4 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | COMBINE_EQS: (38), (136) imply:
% 176.56/27.45  | |   (137)  all_52_5 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | SIMP: (137) implies:
% 176.56/27.45  | |   (138)  all_52_5 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | REF_CLOSE: (1), (2), (8), (15), (24), (28), (29), (30), (31), (32), (33),
% 176.56/27.45  | |            (34), (38), (39), (42), (44), (45), (47), (51), (53), (56), (60),
% 176.56/27.45  | |            (64), (65), (71), (72), (74), (75), (80), (83), (84), (88), (89),
% 176.56/27.45  | |            (90), (92), (93), (96), (99), (102), (103), (104), (107), (108),
% 176.56/27.45  | |            (109), (112), (113), (116), (117), (119), (120), (121), (125),
% 176.56/27.45  | |            (138) are inconsistent by sub-proof #863.
% 176.56/27.45  | | 
% 176.56/27.45  | Case 2:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (139)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | BETA: splitting (139) gives:
% 176.56/27.45  | | 
% 176.56/27.45  | | Case 1:
% 176.56/27.45  | | | 
% 176.56/27.45  | | |   (140)  all_58_5 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | COMBINE_EQS: (24), (140) imply:
% 176.56/27.45  | | |   (141)  all_52_13 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | SIMP: (141) implies:
% 176.56/27.45  | | |   (142)  all_52_13 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (2), (142) imply:
% 176.56/27.45  | | |   (143)   ~ (all_52_5 = e3)
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (46), (142) imply:
% 176.56/27.45  | | |   (144)   ~ (all_52_15 = e3)
% 176.56/27.45  | | | 
% 176.56/27.45  | | | SIMP: (144) implies:
% 176.56/27.45  | | |   (145)   ~ (all_52_15 = e3)
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (131), (142) imply:
% 176.56/27.45  | | |   (146)   ~ (all_52_18 = e3)
% 176.56/27.45  | | | 
% 176.56/27.45  | | | SIMP: (146) implies:
% 176.56/27.45  | | |   (147)   ~ (all_52_18 = e3)
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (114), (142) imply:
% 176.56/27.45  | | |   (148)   ~ (all_10_2 = e3)
% 176.56/27.45  | | | 
% 176.56/27.45  | | | SIMP: (148) implies:
% 176.56/27.45  | | |   (149)   ~ (all_10_2 = e3)
% 176.56/27.45  | | | 
% 176.56/27.45  | | | BETA: splitting (120) gives:
% 176.56/27.45  | | | 
% 176.56/27.45  | | | Case 1:
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | |   (150)  all_58_0 = e3
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.56/27.45  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 176.56/27.45  | | | |            (23), (24), (25), (26), (27), (32), (36), (37), (38), (40),
% 176.56/27.45  | | | |            (41), (42), (43), (45), (49), (50), (51), (52), (53), (54),
% 176.56/27.45  | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (67), (69),
% 176.56/27.45  | | | |            (70), (75), (76), (77), (78), (79), (80), (81), (83), (84),
% 176.56/27.45  | | | |            (85), (86), (87), (91), (92), (95), (96), (97), (98), (100),
% 176.56/27.45  | | | |            (101), (104), (105), (108), (110), (111), (112), (113),
% 176.56/27.45  | | | |            (114), (115), (116), (118), (119), (122), (123), (124),
% 176.56/27.45  | | | |            (126), (128), (129), (131), (133), (134), (135), (145),
% 176.56/27.45  | | | |            (147), (149), (150) are inconsistent by sub-proof #256.
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | Case 2:
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | |   (151)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | REF_CLOSE: (8), (15), (28), (29), (30), (31), (32), (38), (44), (45),
% 176.56/27.45  | | | |            (47), (53), (63), (64), (65), (80), (84), (88), (89), (92),
% 176.56/27.45  | | | |            (96), (103), (104), (108), (109), (113), (116), (117), (119),
% 176.56/27.45  | | | |            (125), (143), (151) are inconsistent by sub-proof #787.
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | End of split
% 176.56/27.45  | | | 
% 176.56/27.45  | | Case 2:
% 176.56/27.45  | | | 
% 176.56/27.45  | | |   (152)  all_58_8 = e3 | all_58_14 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REF_CLOSE: (51), (56), (68), (106), (152) are inconsistent by sub-proof
% 176.56/27.45  | | |            #999.
% 176.56/27.45  | | | 
% 176.56/27.45  | | End of split
% 176.56/27.45  | | 
% 176.56/27.45  | End of split
% 176.56/27.45  | 
% 176.56/27.45  End of proof
% 176.56/27.45  
% 176.56/27.45  Sub-proof #256 shows that the following formulas are inconsistent:
% 176.56/27.45  ----------------------------------------------------------------
% 176.56/27.45    (1)   ~ (all_52_5 = all_52_13)
% 176.56/27.45    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.45    (3)  all_58_2 = all_52_18
% 176.56/27.45    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.45    (5)   ~ (all_52_27 = all_10_2)
% 176.56/27.45    (6)  op(e2, e2) = all_10_2
% 176.56/27.45    (7)   ~ (all_52_17 = all_52_23)
% 176.56/27.45    (8)  op(e2, all_52_3) = e2
% 176.56/27.45    (9)  all_58_15 = e3
% 176.56/27.45    (10)  op(e2, all_10_2) = all_10_1
% 176.56/27.45    (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.45    (12)   ~ (all_52_13 = all_52_29)
% 176.56/27.45    (13)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.56/27.45    (14)  all_56_3 = all_52_7
% 176.56/27.45    (15)  op(e3, e2) = all_52_3
% 176.56/27.45    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.45    (17)   ~ (all_52_27 = e3)
% 176.56/27.45    (18)   ~ (all_52_17 = e3)
% 176.56/27.45    (19)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.45    (20)  all_58_12 = all_6_1
% 176.56/27.45    (21)  op(all_6_1, e3) = all_6_0
% 176.56/27.45    (22)   ~ (all_52_3 = all_10_2)
% 176.56/27.45    (23)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.45    (24)  all_58_5 = all_52_13
% 176.56/27.45    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.45    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.45    (27)  all_58_3 = all_10_2
% 176.56/27.45    (28)  all_58_10 = all_52_15
% 176.56/27.45    (29)   ~ (all_52_17 = all_52_18)
% 176.56/27.45    (30)  op(e3, all_6_1) = all_52_24
% 176.56/27.45    (31)  op(e0, e1) = all_52_29
% 176.56/27.45    (32)  all_58_4 = all_52_5
% 176.56/27.45    (33)   ~ (e3 = e1)
% 176.56/27.45    (34)   ~ (all_52_27 = all_52_29)
% 176.56/27.45    (35)   ~ (all_52_17 = all_14_2)
% 176.56/27.45    (36)  all_56_4 = all_52_18
% 176.56/27.45    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.45    (38)  all_58_1 = all_52_3
% 176.56/27.45    (39)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.45    (40)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.45    (41)   ~ (all_52_18 = all_6_1)
% 176.56/27.45    (42)  all_58_14 = all_52_29
% 176.56/27.45    (43)  all_58_7 = e3
% 176.56/27.45    (44)   ~ (all_10_2 = e3)
% 176.56/27.45    (45)   ~ (all_52_3 = all_52_5)
% 176.56/27.45    (46)  op(e2, e1) = all_52_13
% 176.56/27.45    (47)   ~ (all_52_17 = all_6_1)
% 176.56/27.45    (48)  all_58_8 = all_14_2
% 176.56/27.45    (49)  all_56_1 = all_52_3
% 176.56/27.45    (50)   ~ (all_6_1 = e3)
% 176.56/27.45    (51)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.45    (52)   ~ (all_52_5 = all_14_2)
% 176.56/27.45    (53)   ~ (all_52_23 = e3)
% 176.56/27.45    (54)   ~ (all_52_3 = all_52_27)
% 176.56/27.45    (55)  op(e3, all_52_17) = all_52_16
% 176.56/27.45    (56)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.45    (57)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.45    (58)   ~ (all_52_15 = e3)
% 176.56/27.45    (59)   ~ (all_52_5 = all_52_29)
% 176.56/27.45    (60)  all_56_2 = all_52_5
% 176.56/27.45    (61)  op(e1, e0) = all_52_23
% 176.56/27.45    (62)  all_58_13 = all_52_27
% 176.56/27.45    (63)   ~ (all_52_3 = e3)
% 176.56/27.45    (64)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.45    (65)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.45    (66)  all_58_6 = all_52_17
% 176.56/27.45    (67)   ~ (all_52_3 = all_52_7)
% 176.56/27.45    (68)  op(all_10_1, all_10_2) = e3
% 176.56/27.45    (69)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.45    (70)   ~ (e1 = e0)
% 176.56/27.45    (71)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.45    (72)   ~ (all_52_7 = all_52_15)
% 176.56/27.45    (73)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.56/27.45    (74)  op(e3, e1) = all_52_5
% 176.56/27.45    (75)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.56/27.45    (76)   ~ (e2 = e1)
% 176.56/27.45    (77)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.56/27.45    (78)  op(e1, e1) = all_14_2
% 176.56/27.45    (79)  op(e3, e0) = all_52_7
% 176.56/27.45    (80)  all_56_8 = all_52_17
% 176.56/27.45    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.45    (82)  op(e2, e3) = all_52_18
% 176.56/27.45    (83)   ~ (all_52_18 = e3)
% 176.56/27.45    (84)   ~ (all_52_7 = e3)
% 176.56/27.45    (85)  op(e1, all_52_5) = e1
% 176.56/27.45    (86)   ~ (all_52_7 = all_52_23)
% 176.56/27.45    (87)   ~ (all_52_13 = all_10_2)
% 176.56/27.45    (88)   ~ (all_6_0 = e1)
% 176.56/27.45    (89)  op(e0, all_52_7) = e0
% 176.56/27.45    (90)   ~ (all_52_18 = all_10_2)
% 176.56/27.45    (91)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.56/27.45    (92)  all_58_9 = all_52_7
% 176.56/27.45    (93)   ~ (all_52_13 = all_52_18)
% 176.56/27.45    (94)   ~ (e3 = e2)
% 176.56/27.45    (95)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.45    (96)  all_58_0 = e3
% 176.56/27.45    (97)  op(e1, e2) = e3
% 176.56/27.45    (98)  all_56_13 = all_52_27
% 176.56/27.45  
% 176.56/27.45  Begin of proof
% 176.56/27.45  | 
% 176.56/27.45  | BETA: splitting (37) gives:
% 176.56/27.45  | 
% 176.56/27.45  | Case 1:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (99)  all_58_2 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | COMBINE_EQS: (3), (99) imply:
% 176.56/27.45  | |   (100)  all_52_18 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | SIMP: (100) implies:
% 176.56/27.45  | |   (101)  all_52_18 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | REDUCE: (83), (101) imply:
% 176.56/27.45  | |   (102)  $false
% 176.56/27.45  | | 
% 176.56/27.45  | | CLOSE: (102) is inconsistent.
% 176.56/27.45  | | 
% 176.56/27.45  | Case 2:
% 176.56/27.45  | | 
% 176.56/27.45  | |   (103)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.45  | | 
% 176.56/27.45  | | BETA: splitting (103) gives:
% 176.56/27.45  | | 
% 176.56/27.45  | | Case 1:
% 176.56/27.45  | | | 
% 176.56/27.45  | | |   (104)  all_58_3 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | COMBINE_EQS: (27), (104) imply:
% 176.56/27.45  | | |   (105)  all_10_2 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | REDUCE: (44), (105) imply:
% 176.56/27.45  | | |   (106)  $false
% 176.56/27.45  | | | 
% 176.56/27.45  | | | CLOSE: (106) is inconsistent.
% 176.56/27.45  | | | 
% 176.56/27.45  | | Case 2:
% 176.56/27.45  | | | 
% 176.56/27.45  | | |   (107)  all_58_5 = e3 | all_58_10 = e3
% 176.56/27.45  | | | 
% 176.56/27.45  | | | BETA: splitting (107) gives:
% 176.56/27.45  | | | 
% 176.56/27.45  | | | Case 1:
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | |   (108)  all_58_5 = e3
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | COMBINE_EQS: (24), (108) imply:
% 176.56/27.45  | | | |   (109)  all_52_13 = e3
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | SIMP: (109) implies:
% 176.56/27.45  | | | |   (110)  all_52_13 = e3
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | REDUCE: (1), (110) imply:
% 176.56/27.45  | | | |   (111)   ~ (all_52_5 = e3)
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | REDUCE: (93), (110) imply:
% 176.56/27.45  | | | |   (112)   ~ (all_52_18 = e3)
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | REDUCE: (12), (110) imply:
% 176.56/27.45  | | | |   (113)   ~ (all_52_29 = e3)
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | SIMP: (113) implies:
% 176.56/27.45  | | | |   (114)   ~ (all_52_29 = e3)
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | REDUCE: (87), (110) imply:
% 176.56/27.45  | | | |   (115)   ~ (all_10_2 = e3)
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | REDUCE: (46), (110) imply:
% 176.56/27.45  | | | |   (116)  op(e2, e1) = e3
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | BETA: splitting (95) gives:
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | | Case 1:
% 176.56/27.45  | | | | | 
% 176.56/27.45  | | | | |   (117)  all_56_2 = e3
% 176.56/27.45  | | | | | 
% 176.56/27.45  | | | | | REF_CLOSE: (60), (111), (117) are inconsistent by sub-proof #931.
% 176.56/27.45  | | | | | 
% 176.56/27.45  | | | | Case 2:
% 176.56/27.45  | | | | | 
% 176.56/27.45  | | | | |   (118)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.45  | | | | | 
% 176.56/27.45  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 176.56/27.45  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.56/27.45  | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 176.56/27.45  | | | | |            (35), (36), (38), (39), (40), (41), (42), (43), (44), (45),
% 176.56/27.45  | | | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 176.56/27.45  | | | | |            (57), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 176.56/27.45  | | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 176.56/27.45  | | | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (88),
% 176.56/27.45  | | | | |            (89), (90), (91), (92), (94), (96), (97), (98), (108),
% 176.56/27.45  | | | | |            (114), (116), (118) are inconsistent by sub-proof #257.
% 176.56/27.45  | | | | | 
% 176.56/27.45  | | | | End of split
% 176.56/27.45  | | | | 
% 176.56/27.45  | | | Case 2:
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | |   (119)  all_58_10 = e3
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | | REF_CLOSE: (28), (58), (119) are inconsistent by sub-proof #1018.
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | End of split
% 176.56/27.46  | | | 
% 176.56/27.46  | | End of split
% 176.56/27.46  | | 
% 176.56/27.46  | End of split
% 176.56/27.46  | 
% 176.56/27.46  End of proof
% 176.56/27.46  
% 176.56/27.46  Sub-proof #257 shows that the following formulas are inconsistent:
% 176.56/27.46  ----------------------------------------------------------------
% 176.56/27.46    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.46    (2)  all_58_2 = all_52_18
% 176.56/27.46    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.46    (4)   ~ (all_52_27 = all_10_2)
% 176.56/27.46    (5)  op(e2, e2) = all_10_2
% 176.56/27.46    (6)   ~ (all_52_17 = all_52_23)
% 176.56/27.46    (7)  op(e2, all_52_3) = e2
% 176.56/27.46    (8)  all_58_15 = e3
% 176.56/27.46    (9)  op(e2, all_10_2) = all_10_1
% 176.56/27.46    (10)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.46    (11)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.56/27.46    (12)  all_56_3 = all_52_7
% 176.56/27.46    (13)  op(e3, e2) = all_52_3
% 176.56/27.46    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.46    (15)   ~ (all_52_27 = e3)
% 176.56/27.46    (16)   ~ (all_52_17 = e3)
% 176.56/27.46    (17)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.46    (18)  all_58_12 = all_6_1
% 176.56/27.46    (19)  op(all_6_1, e3) = all_6_0
% 176.56/27.46    (20)   ~ (all_52_3 = all_10_2)
% 176.56/27.46    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.46    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.46    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.46    (24)  all_58_3 = all_10_2
% 176.56/27.46    (25)  all_58_10 = all_52_15
% 176.56/27.46    (26)   ~ (all_52_17 = all_52_18)
% 176.56/27.46    (27)  op(e3, all_6_1) = all_52_24
% 176.56/27.46    (28)  op(e0, e1) = all_52_29
% 176.56/27.46    (29)  all_58_4 = all_52_5
% 176.56/27.46    (30)   ~ (e3 = e1)
% 176.56/27.46    (31)  all_58_5 = e3
% 176.56/27.46    (32)   ~ (all_52_27 = all_52_29)
% 176.56/27.46    (33)   ~ (all_52_17 = all_14_2)
% 176.56/27.46    (34)  all_56_4 = all_52_18
% 176.56/27.46    (35)  all_58_1 = all_52_3
% 176.56/27.46    (36)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.46    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.46    (38)   ~ (all_52_18 = all_6_1)
% 176.56/27.46    (39)  all_58_14 = all_52_29
% 176.56/27.46    (40)  all_58_7 = e3
% 176.56/27.46    (41)   ~ (all_10_2 = e3)
% 176.56/27.46    (42)   ~ (all_52_3 = all_52_5)
% 176.56/27.46    (43)   ~ (all_52_17 = all_6_1)
% 176.56/27.46    (44)  all_58_8 = all_14_2
% 176.56/27.46    (45)  all_56_1 = all_52_3
% 176.56/27.46    (46)   ~ (all_6_1 = e3)
% 176.56/27.46    (47)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.46    (48)   ~ (all_52_5 = all_14_2)
% 176.56/27.46    (49)   ~ (all_52_23 = e3)
% 176.56/27.46    (50)   ~ (all_52_3 = all_52_27)
% 176.56/27.46    (51)  op(e3, all_52_17) = all_52_16
% 176.56/27.46    (52)   ~ (all_52_29 = e3)
% 176.56/27.46    (53)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.46    (54)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.46    (55)   ~ (all_52_5 = all_52_29)
% 176.56/27.46    (56)  all_56_2 = all_52_5
% 176.56/27.46    (57)  op(e1, e0) = all_52_23
% 176.56/27.46    (58)  all_58_13 = all_52_27
% 176.56/27.46    (59)   ~ (all_52_3 = e3)
% 176.56/27.46    (60)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.46    (61)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.46    (62)  all_58_6 = all_52_17
% 176.56/27.46    (63)   ~ (all_52_3 = all_52_7)
% 176.56/27.46    (64)  op(all_10_1, all_10_2) = e3
% 176.56/27.46    (65)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.46    (66)   ~ (e1 = e0)
% 176.56/27.46    (67)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.46    (68)   ~ (all_52_7 = all_52_15)
% 176.56/27.46    (69)  op(e2, e1) = e3
% 176.56/27.46    (70)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.56/27.46    (71)  op(e3, e1) = all_52_5
% 176.56/27.46    (72)  all_58_6 = e1 | all_58_7 = e1 | all_58_8 = e1 | all_58_11 = e1
% 176.56/27.46    (73)   ~ (e2 = e1)
% 176.56/27.46    (74)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.56/27.46    (75)  op(e1, e1) = all_14_2
% 176.56/27.46    (76)  op(e3, e0) = all_52_7
% 176.56/27.46    (77)  all_56_8 = all_52_17
% 176.56/27.46    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.46    (79)  op(e2, e3) = all_52_18
% 176.56/27.46    (80)   ~ (all_52_18 = e3)
% 176.56/27.46    (81)   ~ (all_52_7 = e3)
% 176.56/27.46    (82)  op(e1, all_52_5) = e1
% 176.56/27.46    (83)   ~ (all_52_7 = all_52_23)
% 176.56/27.46    (84)   ~ (all_6_0 = e1)
% 176.56/27.46    (85)  op(e0, all_52_7) = e0
% 176.56/27.46    (86)   ~ (all_52_18 = all_10_2)
% 176.56/27.46    (87)  all_58_2 = e2 | all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.56/27.46    (88)  all_58_9 = all_52_7
% 176.56/27.46    (89)   ~ (e3 = e2)
% 176.56/27.46    (90)  all_58_0 = e3
% 176.56/27.46    (91)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.46    (92)  op(e1, e2) = e3
% 176.56/27.46    (93)  all_56_13 = all_52_27
% 176.56/27.46  
% 176.56/27.46  Begin of proof
% 176.56/27.46  | 
% 176.56/27.46  | BETA: splitting (65) gives:
% 176.56/27.46  | 
% 176.56/27.46  | Case 1:
% 176.56/27.46  | | 
% 176.56/27.46  | |   (94)  all_56_4 = e3
% 176.56/27.46  | | 
% 176.56/27.46  | | REF_CLOSE: (34), (80), (94) are inconsistent by sub-proof #398.
% 176.56/27.46  | | 
% 176.56/27.46  | Case 2:
% 176.56/27.46  | | 
% 176.56/27.46  | |   (95)   ~ (all_56_4 = e3)
% 176.56/27.46  | |   (96)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.46  | | 
% 176.56/27.46  | | BETA: splitting (1) gives:
% 176.56/27.46  | | 
% 176.56/27.46  | | Case 1:
% 176.56/27.46  | | | 
% 176.56/27.46  | | |   (97)  all_56_8 = e3
% 176.56/27.46  | | | 
% 176.56/27.46  | | | REF_CLOSE: (16), (77), (97) are inconsistent by sub-proof #461.
% 176.56/27.46  | | | 
% 176.56/27.46  | | Case 2:
% 176.56/27.46  | | | 
% 176.56/27.46  | | |   (98)   ~ (all_56_8 = e3)
% 176.56/27.46  | | |   (99)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.46  | | | 
% 176.56/27.46  | | | BETA: splitting (36) gives:
% 176.56/27.46  | | | 
% 176.56/27.46  | | | Case 1:
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | |   (100)  all_56_1 = e3
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | | REF_CLOSE: (45), (59), (100) are inconsistent by sub-proof #862.
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | Case 2:
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | |   (101)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | | BETA: splitting (61) gives:
% 176.56/27.46  | | | | 
% 176.56/27.46  | | | | Case 1:
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | |   (102)  all_58_6 = e2
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | COMBINE_EQS: (62), (102) imply:
% 176.56/27.46  | | | | |   (103)  all_52_17 = e2
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | SIMP: (103) implies:
% 176.56/27.46  | | | | |   (104)  all_52_17 = e2
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | REDUCE: (26), (104) imply:
% 176.56/27.46  | | | | |   (105)   ~ (all_52_18 = e2)
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | SIMP: (105) implies:
% 176.56/27.46  | | | | |   (106)   ~ (all_52_18 = e2)
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | REDUCE: (16), (104) imply:
% 176.56/27.46  | | | | |   (107)   ~ (e3 = e2)
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | REDUCE: (51), (104) imply:
% 176.56/27.46  | | | | |   (108)  op(e3, e2) = all_52_16
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | GROUND_INST: instantiating (78) with all_52_3, all_52_16, e2, e3,
% 176.56/27.46  | | | | |              simplifying with (13), (108) gives:
% 176.56/27.46  | | | | |   (109)  all_52_3 = all_52_16
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | COMBINE_EQS: (35), (109) imply:
% 176.56/27.46  | | | | |   (110)  all_58_1 = all_52_16
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | REDUCE: (20), (109) imply:
% 176.56/27.46  | | | | |   (111)   ~ (all_52_16 = all_10_2)
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | REDUCE: (7), (109) imply:
% 176.56/27.46  | | | | |   (112)  op(e2, all_52_16) = e2
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | BETA: splitting (67) gives:
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | Case 1:
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | |   (113)  all_58_4 = e2
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | COMBINE_EQS: (29), (113) imply:
% 176.56/27.46  | | | | | |   (114)  all_52_5 = e2
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | REDUCE: (82), (114) imply:
% 176.56/27.46  | | | | | |   (115)  op(e1, e2) = e1
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | REF_CLOSE: (30), (78), (92), (115) are inconsistent by sub-proof
% 176.56/27.46  | | | | | |            #861.
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | Case 2:
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | |   (116)   ~ (all_58_4 = e2)
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | REDUCE: (29), (116) imply:
% 176.56/27.46  | | | | | |   (117)   ~ (all_52_5 = e2)
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | BETA: splitting (53) gives:
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | Case 1:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | |   (118)  all_58_9 = e2
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | COMBINE_EQS: (88), (118) imply:
% 176.56/27.46  | | | | | | |   (119)  all_52_7 = e2
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (68), (119) imply:
% 176.56/27.46  | | | | | | |   (120)   ~ (all_52_15 = e2)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | SIMP: (120) implies:
% 176.56/27.46  | | | | | | |   (121)   ~ (all_52_15 = e2)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | BETA: splitting (87) gives:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (122)  all_58_2 = e2
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | COMBINE_EQS: (2), (122) imply:
% 176.56/27.46  | | | | | | | |   (123)  all_52_18 = e2
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | REDUCE: (106), (123) imply:
% 176.56/27.46  | | | | | | | |   (124)  $false
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | CLOSE: (124) is inconsistent.
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (125)  all_58_3 = e2 | all_58_5 = e2 | all_58_10 = e2
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | BETA: splitting (125) gives:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (126)  all_58_3 = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | COMBINE_EQS: (24), (126) imply:
% 176.56/27.46  | | | | | | | | |   (127)  all_10_2 = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (64), (127) imply:
% 176.56/27.46  | | | | | | | | |   (128)  op(all_10_1, e2) = e3
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (9), (127) imply:
% 176.56/27.46  | | | | | | | | |   (129)  op(e2, e2) = all_10_1
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (5), (127) imply:
% 176.56/27.46  | | | | | | | | |   (130)  op(e2, e2) = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | GROUND_INST: instantiating (78) with e2, all_10_1, e2, e2,
% 176.56/27.46  | | | | | | | | |              simplifying with (129), (130) gives:
% 176.56/27.46  | | | | | | | | |   (131)  all_10_1 = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (128), (131) imply:
% 176.56/27.46  | | | | | | | | |   (132)  op(e2, e2) = e3
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REF_CLOSE: (78), (89), (130), (132) are inconsistent by
% 176.56/27.46  | | | | | | | | |            sub-proof #848.
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (133)  all_58_5 = e2 | all_58_10 = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REF_CLOSE: (25), (31), (89), (121), (133) are inconsistent by
% 176.56/27.46  | | | | | | | | |            sub-proof #261.
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | End of split
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | Case 2:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | |   (134)   ~ (all_58_9 = e2)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (88), (134) imply:
% 176.56/27.46  | | | | | | |   (135)   ~ (all_52_7 = e2)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | BETA: splitting (47) gives:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (136)  all_58_0 = e2
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | COMBINE_EQS: (90), (136) imply:
% 176.56/27.46  | | | | | | | |   (137)  e3 = e2
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | REDUCE: (89), (137) imply:
% 176.56/27.46  | | | | | | | |   (138)  $false
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | CLOSE: (138) is inconsistent.
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (139)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | BETA: splitting (139) gives:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (140)  all_58_1 = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | COMBINE_EQS: (110), (140) imply:
% 176.56/27.46  | | | | | | | | |   (141)  all_52_16 = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (111), (141) imply:
% 176.56/27.46  | | | | | | | | |   (142)   ~ (all_10_2 = e2)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (142) implies:
% 176.56/27.46  | | | | | | | | |   (143)   ~ (all_10_2 = e2)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (112), (141) imply:
% 176.56/27.46  | | | | | | | | |   (144)  op(e2, e2) = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REF_CLOSE: (5), (78), (143), (144) are inconsistent by
% 176.56/27.46  | | | | | | | | |            sub-proof #453.
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (145)  all_58_4 = e2 | all_58_9 = e2
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REF_CLOSE: (29), (88), (117), (135), (145) are inconsistent by
% 176.56/27.46  | | | | | | | | |            sub-proof #285.
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | End of split
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | End of split
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | End of split
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | Case 2:
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | |   (146)   ~ (all_58_6 = e2)
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | REDUCE: (62), (146) imply:
% 176.56/27.46  | | | | |   (147)   ~ (all_52_17 = e2)
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | BETA: splitting (22) gives:
% 176.56/27.46  | | | | | 
% 176.56/27.46  | | | | | Case 1:
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | |   (148)  all_58_0 = e2
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | COMBINE_EQS: (90), (148) imply:
% 176.56/27.46  | | | | | |   (149)  e3 = e2
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | REDUCE: (89), (149) imply:
% 176.56/27.46  | | | | | |   (150)  $false
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | CLOSE: (150) is inconsistent.
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | Case 2:
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | |   (151)   ~ (all_58_0 = e2)
% 176.56/27.46  | | | | | |   (152)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | BETA: splitting (72) gives:
% 176.56/27.46  | | | | | | 
% 176.56/27.46  | | | | | | Case 1:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | |   (153)  all_58_6 = e1
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | COMBINE_EQS: (62), (153) imply:
% 176.56/27.46  | | | | | | |   (154)  all_52_17 = e1
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | SIMP: (154) implies:
% 176.56/27.46  | | | | | | |   (155)  all_52_17 = e1
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (33), (155) imply:
% 176.56/27.46  | | | | | | |   (156)   ~ (all_14_2 = e1)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | SIMP: (156) implies:
% 176.56/27.46  | | | | | | |   (157)   ~ (all_14_2 = e1)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (16), (155) imply:
% 176.56/27.46  | | | | | | |   (158)   ~ (e3 = e1)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (51), (155) imply:
% 176.56/27.46  | | | | | | |   (159)  op(e3, e1) = all_52_16
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | GROUND_INST: instantiating (78) with all_52_5, all_52_16, e1, e3,
% 176.56/27.46  | | | | | | |              simplifying with (71), (159) gives:
% 176.56/27.46  | | | | | | |   (160)  all_52_5 = all_52_16
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | COMBINE_EQS: (29), (160) imply:
% 176.56/27.46  | | | | | | |   (161)  all_58_4 = all_52_16
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (55), (160) imply:
% 176.56/27.46  | | | | | | |   (162)   ~ (all_52_16 = all_52_29)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (48), (160) imply:
% 176.56/27.46  | | | | | | |   (163)   ~ (all_52_16 = all_14_2)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (82), (160) imply:
% 176.56/27.46  | | | | | | |   (164)  op(e1, all_52_16) = e1
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | BETA: splitting (37) gives:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (165)  all_58_4 = e1
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | COMBINE_EQS: (161), (165) imply:
% 176.56/27.46  | | | | | | | |   (166)  all_52_16 = e1
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | SIMP: (166) implies:
% 176.56/27.46  | | | | | | | |   (167)  all_52_16 = e1
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | REDUCE: (164), (167) imply:
% 176.56/27.46  | | | | | | | |   (168)  op(e1, e1) = e1
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | REF_CLOSE: (75), (78), (157), (168) are inconsistent by
% 176.56/27.46  | | | | | | | |            sub-proof #860.
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (169)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | BETA: splitting (169) gives:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (170)  all_58_5 = e1
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REF_CLOSE: (30), (31), (170) are inconsistent by sub-proof
% 176.56/27.46  | | | | | | | | |            #816.
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (171)  all_58_8 = e1 | all_58_14 = e1
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | BETA: splitting (171) gives:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | |   (172)  all_58_8 = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | REF_CLOSE: (44), (157), (172) are inconsistent by sub-proof
% 176.56/27.46  | | | | | | | | | |            #815.
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | |   (173)  all_58_14 = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | COMBINE_EQS: (39), (173) imply:
% 176.56/27.46  | | | | | | | | | |   (174)  all_52_29 = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | SIMP: (174) implies:
% 176.56/27.46  | | | | | | | | | |   (175)  all_52_29 = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | REDUCE: (162), (175) imply:
% 176.56/27.46  | | | | | | | | | |   (176)   ~ (all_52_16 = e1)
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | REDUCE: (28), (175) imply:
% 176.56/27.46  | | | | | | | | | |   (177)  op(e0, e1) = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | BETA: splitting (23) gives:
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | |   (178)  all_58_9 = e1
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | COMBINE_EQS: (88), (178) imply:
% 176.56/27.46  | | | | | | | | | | |   (179)  all_52_7 = e1
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | REDUCE: (85), (179) imply:
% 176.56/27.46  | | | | | | | | | | |   (180)  op(e0, e1) = e0
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | REF_CLOSE: (66), (78), (177), (180) are inconsistent by
% 176.56/27.46  | | | | | | | | | | |            sub-proof #771.
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | |   (181)   ~ (all_58_9 = e1)
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | REDUCE: (88), (181) imply:
% 176.56/27.46  | | | | | | | | | | |   (182)   ~ (all_52_7 = e1)
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | BETA: splitting (14) gives:
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | |   (183)  all_58_0 = e1
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | COMBINE_EQS: (90), (183) imply:
% 176.56/27.46  | | | | | | | | | | | |   (184)  e3 = e1
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | REDUCE: (30), (184) imply:
% 176.56/27.46  | | | | | | | | | | | |   (185)  $false
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | |   (186)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | BETA: splitting (3) gives:
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | |   (187)  all_58_1 = e1
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | COMBINE_EQS: (35), (187) imply:
% 176.56/27.46  | | | | | | | | | | | | |   (188)  all_52_3 = e1
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | REDUCE: (7), (188) imply:
% 176.56/27.46  | | | | | | | | | | | | |   (189)  op(e2, e1) = e2
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | REF_CLOSE: (69), (78), (89), (189) are inconsistent by
% 176.56/27.46  | | | | | | | | | | | | |            sub-proof #856.
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | |   (190)   ~ (all_58_1 = e1)
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | REDUCE: (35), (190) imply:
% 176.56/27.46  | | | | | | | | | | | | |   (191)   ~ (all_52_3 = e1)
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | BETA: splitting (186) gives:
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | |   (192)  all_58_1 = e1
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | COMBINE_EQS: (35), (192) imply:
% 176.56/27.46  | | | | | | | | | | | | | |   (193)  all_52_3 = e1
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | REDUCE: (191), (193) imply:
% 176.56/27.46  | | | | | | | | | | | | | |   (194)  $false
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | |   (195)  all_58_4 = e1 | all_58_9 = e1
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | |   (196)  all_58_4 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | REF_CLOSE: (161), (176), (196) are inconsistent by sub-proof
% 176.56/27.46  | | | | | | | | | | | | | | |            #260.
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | |   (197)  all_58_9 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | REF_CLOSE: (88), (182), (197) are inconsistent by sub-proof
% 176.56/27.46  | | | | | | | | | | | | | | |            #793.
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | End of split
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | End of split
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | Case 2:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | |   (198)   ~ (all_58_6 = e1)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | REDUCE: (62), (198) imply:
% 176.56/27.46  | | | | | | |   (199)   ~ (all_52_17 = e1)
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | BETA: splitting (99) gives:
% 176.56/27.46  | | | | | | | 
% 176.56/27.46  | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (200)  all_56_8 = e2
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | REF_CLOSE: (77), (147), (200) are inconsistent by sub-proof
% 176.56/27.46  | | | | | | | |            #460.
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | |   (201)   ~ (all_56_8 = e2)
% 176.56/27.46  | | | | | | | |   (202)  all_56_8 = e1 | all_56_8 = e0
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | BETA: splitting (202) gives:
% 176.56/27.46  | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (203)  all_56_8 = e1
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REF_CLOSE: (77), (199), (203) are inconsistent by sub-proof
% 176.56/27.46  | | | | | | | | |            #287.
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | |   (204)  all_56_8 = e0
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | COMBINE_EQS: (77), (204) imply:
% 176.56/27.46  | | | | | | | | |   (205)  all_52_17 = e0
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (205) implies:
% 176.56/27.46  | | | | | | | | |   (206)  all_52_17 = e0
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | COMBINE_EQS: (62), (206) imply:
% 176.56/27.46  | | | | | | | | |   (207)  all_58_6 = e0
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (26), (206) imply:
% 176.56/27.46  | | | | | | | | |   (208)   ~ (all_52_18 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (208) implies:
% 176.56/27.46  | | | | | | | | |   (209)   ~ (all_52_18 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (6), (206) imply:
% 176.56/27.46  | | | | | | | | |   (210)   ~ (all_52_23 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (210) implies:
% 176.56/27.46  | | | | | | | | |   (211)   ~ (all_52_23 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (33), (206) imply:
% 176.56/27.46  | | | | | | | | |   (212)   ~ (all_14_2 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (212) implies:
% 176.56/27.46  | | | | | | | | |   (213)   ~ (all_14_2 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (43), (206) imply:
% 176.56/27.46  | | | | | | | | |   (214)   ~ (all_6_1 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (214) implies:
% 176.56/27.46  | | | | | | | | |   (215)   ~ (all_6_1 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (16), (206) imply:
% 176.56/27.46  | | | | | | | | |   (216)   ~ (e3 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (216) implies:
% 176.56/27.46  | | | | | | | | |   (217)   ~ (e3 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (147), (206) imply:
% 176.56/27.46  | | | | | | | | |   (218)   ~ (e2 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | SIMP: (218) implies:
% 176.56/27.46  | | | | | | | | |   (219)   ~ (e2 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (199), (206) imply:
% 176.56/27.46  | | | | | | | | |   (220)   ~ (e1 = e0)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (51), (206) imply:
% 176.56/27.46  | | | | | | | | |   (221)  op(e3, e0) = all_52_16
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | GROUND_INST: instantiating (78) with all_52_7, all_52_16, e0,
% 176.56/27.46  | | | | | | | | |              e3, simplifying with (76), (221) gives:
% 176.56/27.46  | | | | | | | | |   (222)  all_52_7 = all_52_16
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | COMBINE_EQS: (12), (222) imply:
% 176.56/27.46  | | | | | | | | |   (223)  all_56_3 = all_52_16
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | COMBINE_EQS: (88), (222) imply:
% 176.56/27.46  | | | | | | | | |   (224)  all_58_9 = all_52_16
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (63), (222) imply:
% 176.56/27.46  | | | | | | | | |   (225)   ~ (all_52_3 = all_52_16)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | REDUCE: (83), (222) imply:
% 176.56/27.46  | | | | | | | | |   (226)   ~ (all_52_16 = all_52_23)
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | BETA: splitting (60) gives:
% 176.56/27.46  | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | |   (227)  all_58_0 = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | COMBINE_EQS: (90), (227) imply:
% 176.56/27.46  | | | | | | | | | |   (228)  e3 = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | REDUCE: (30), (228) imply:
% 176.56/27.46  | | | | | | | | | |   (229)  $false
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | CLOSE: (229) is inconsistent.
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | |   (230)   ~ (all_58_0 = e1)
% 176.56/27.46  | | | | | | | | | |   (231)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | BETA: splitting (54) gives:
% 176.56/27.46  | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | |   (232)  all_58_4 = e0
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | COMBINE_EQS: (29), (232) imply:
% 176.56/27.46  | | | | | | | | | | |   (233)  all_52_5 = e0
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | SIMP: (233) implies:
% 176.56/27.46  | | | | | | | | | | |   (234)  all_52_5 = e0
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | REDUCE: (55), (234) imply:
% 176.56/27.46  | | | | | | | | | | |   (235)   ~ (all_52_29 = e0)
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | SIMP: (235) implies:
% 176.56/27.46  | | | | | | | | | | |   (236)   ~ (all_52_29 = e0)
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | REDUCE: (82), (234) imply:
% 176.56/27.46  | | | | | | | | | | |   (237)  op(e1, e0) = e1
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | BETA: splitting (11) gives:
% 176.56/27.46  | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | |   (238)  all_58_12 = e0
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | COMBINE_EQS: (18), (238) imply:
% 176.56/27.46  | | | | | | | | | | | |   (239)  all_6_1 = e0
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | SIMP: (239) implies:
% 176.56/27.46  | | | | | | | | | | | |   (240)  all_6_1 = e0
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | REDUCE: (215), (240) imply:
% 176.56/27.46  | | | | | | | | | | | |   (241)  $false
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | CLOSE: (241) is inconsistent.
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | |   (242)  all_58_13 = e0 | all_58_14 = e0
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | BETA: splitting (242) gives:
% 176.56/27.46  | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | |   (243)  all_58_13 = e0
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | COMBINE_EQS: (58), (243) imply:
% 176.56/27.46  | | | | | | | | | | | | |   (244)  all_52_27 = e0
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | SIMP: (244) implies:
% 176.56/27.46  | | | | | | | | | | | | |   (245)  all_52_27 = e0
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | REDUCE: (50), (245) imply:
% 176.56/27.46  | | | | | | | | | | | | |   (246)   ~ (all_52_3 = e0)
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_23, e1, e0, e1,
% 176.56/27.46  | | | | | | | | | | | | |              simplifying with (57), (237) gives:
% 176.56/27.46  | | | | | | | | | | | | |   (247)  all_52_23 = e1
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | REDUCE: (226), (247) imply:
% 176.56/27.46  | | | | | | | | | | | | |   (248)   ~ (all_52_16 = e1)
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | REDUCE: (49), (247) imply:
% 176.56/27.46  | | | | | | | | | | | | |   (249)   ~ (e3 = e1)
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | BETA: splitting (14) gives:
% 176.56/27.46  | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | |   (250)  all_58_0 = e1
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | COMBINE_EQS: (90), (250) imply:
% 176.56/27.46  | | | | | | | | | | | | | |   (251)  e3 = e1
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | REDUCE: (30), (251) imply:
% 176.56/27.46  | | | | | | | | | | | | | |   (252)  $false
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | CLOSE: (252) is inconsistent.
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | |   (253)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 176.56/27.46  | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | |   (254)  all_58_1 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | COMBINE_EQS: (35), (254) imply:
% 176.56/27.46  | | | | | | | | | | | | | | |   (255)  all_52_3 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | REDUCE: (7), (255) imply:
% 176.56/27.46  | | | | | | | | | | | | | | |   (256)  op(e2, e1) = e2
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | REF_CLOSE: (69), (78), (89), (256) are inconsistent by
% 176.56/27.46  | | | | | | | | | | | | | | |            sub-proof #856.
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | |   (257)   ~ (all_58_1 = e1)
% 176.56/27.46  | | | | | | | | | | | | | | |   (258)  all_58_4 = e1 | all_58_9 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | REDUCE: (35), (257) imply:
% 176.56/27.46  | | | | | | | | | | | | | | |   (259)   ~ (all_52_3 = e1)
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 176.56/27.46  | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | |   (260)  all_56_3 = e2
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (260) imply:
% 176.56/27.46  | | | | | | | | | | | | | | | |   (261)  all_52_16 = e2
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | SIMP: (261) implies:
% 176.56/27.46  | | | | | | | | | | | | | | | |   (262)  all_52_16 = e2
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | REDUCE: (225), (262) imply:
% 176.56/27.46  | | | | | | | | | | | | | | | |   (263)   ~ (all_52_3 = e2)
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (101), (246), (259), (263) are inconsistent
% 176.56/27.46  | | | | | | | | | | | | | | | |            by sub-proof #833.
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | |   (264)  all_56_3 = e1 | all_56_3 = e0
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 176.56/27.46  | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (265)  all_56_3 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (265) imply:
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (266)  all_52_16 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (267)  all_52_16 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | REDUCE: (248), (267) imply:
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (268)  $false
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | CLOSE: (268) is inconsistent.
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (269)  all_56_3 = e0
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (269) imply:
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (270)  all_52_16 = e0
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | SIMP: (270) implies:
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (271)  all_52_16 = e0
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (224), (271) imply:
% 176.56/27.46  | | | | | | | | | | | | | | | | |   (272)  all_58_9 = e0
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 176.56/27.46  | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.46  | | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | |   (273)  all_58_4 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (273) imply:
% 176.56/27.46  | | | | | | | | | | | | | | | | | |   (274)  all_52_5 = e1
% 176.56/27.46  | | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (75), (78), (82), (274) are inconsistent by
% 176.56/27.46  | | | | | | | | | | | | | | | | | |            sub-proof #859.
% 176.56/27.46  | | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.46  | | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | |   (275)   ~ (all_58_4 = e1)
% 176.56/27.46  | | | | | | | | | | | | | | | | | | 
% 176.56/27.46  | | | | | | | | | | | | | | | | | | REDUCE: (29), (275) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (276)   ~ (all_52_5 = e1)
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (66), (258), (272), (276) are inconsistent
% 176.56/27.47  | | | | | | | | | | | | | | | | | |            by sub-proof #808.
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | |   (277)  all_58_14 = e0
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | REF_CLOSE: (39), (236), (277) are inconsistent by sub-proof
% 176.56/27.47  | | | | | | | | | | | | |            #696.
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | |   (278)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.47  | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | BETA: splitting (278) gives:
% 176.56/27.47  | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | |   (279)  all_58_5 = e0
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | REF_CLOSE: (31), (217), (279) are inconsistent by sub-proof
% 176.56/27.47  | | | | | | | | | | | |            #810.
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | |   (280)  all_58_8 = e0 | all_58_14 = e0
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | BETA: splitting (280) gives:
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | |   (281)  all_58_8 = e0
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | COMBINE_EQS: (44), (281) imply:
% 176.56/27.47  | | | | | | | | | | | | |   (282)  all_14_2 = e0
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | SIMP: (282) implies:
% 176.56/27.47  | | | | | | | | | | | | |   (283)  all_14_2 = e0
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | REDUCE: (213), (283) imply:
% 176.56/27.47  | | | | | | | | | | | | |   (284)  $false
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | CLOSE: (284) is inconsistent.
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | |   (285)  all_58_14 = e0
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | COMBINE_EQS: (39), (285) imply:
% 176.56/27.47  | | | | | | | | | | | | |   (286)  all_52_29 = e0
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | SIMP: (286) implies:
% 176.56/27.47  | | | | | | | | | | | | |   (287)  all_52_29 = e0
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | REDUCE: (55), (287) imply:
% 176.56/27.47  | | | | | | | | | | | | |   (288)   ~ (all_52_5 = e0)
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | REDUCE: (32), (287) imply:
% 176.56/27.47  | | | | | | | | | | | | |   (289)   ~ (all_52_27 = e0)
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | BETA: splitting (74) gives:
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | |   (290)  all_58_12 = e2
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | COMBINE_EQS: (18), (290) imply:
% 176.56/27.47  | | | | | | | | | | | | | |   (291)  all_6_1 = e2
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | REDUCE: (38), (291) imply:
% 176.56/27.47  | | | | | | | | | | | | | |   (292)   ~ (all_52_18 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | REDUCE: (19), (291) imply:
% 176.56/27.47  | | | | | | | | | | | | | |   (293)  op(e2, e3) = all_6_0
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | |   (294)  all_58_2 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | COMBINE_EQS: (2), (294) imply:
% 176.56/27.47  | | | | | | | | | | | | | | |   (295)  all_52_18 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | SIMP: (295) implies:
% 176.56/27.47  | | | | | | | | | | | | | | |   (296)  all_52_18 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | REDUCE: (79), (296) imply:
% 176.56/27.47  | | | | | | | | | | | | | | |   (297)  op(e2, e3) = e1
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | REF_CLOSE: (78), (84), (293), (297) are inconsistent by
% 176.56/27.47  | | | | | | | | | | | | | | |            sub-proof #838.
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | |   (298)   ~ (all_58_2 = e1)
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | REDUCE: (2), (298) imply:
% 176.56/27.47  | | | | | | | | | | | | | | |   (299)   ~ (all_52_18 = e1)
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | REF_CLOSE: (34), (96), (209), (292), (299) are inconsistent
% 176.56/27.47  | | | | | | | | | | | | | | |            by sub-proof #297.
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | |   (300)   ~ (all_58_12 = e2)
% 176.56/27.47  | | | | | | | | | | | | | |   (301)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | REDUCE: (18), (300) imply:
% 176.56/27.47  | | | | | | | | | | | | | |   (302)   ~ (all_6_1 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | |   (303)  all_58_13 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | COMBINE_EQS: (58), (303) imply:
% 176.56/27.47  | | | | | | | | | | | | | | |   (304)  all_52_27 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | REDUCE: (4), (304) imply:
% 176.56/27.47  | | | | | | | | | | | | | | |   (305)   ~ (all_10_2 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | SIMP: (305) implies:
% 176.56/27.47  | | | | | | | | | | | | | | |   (306)   ~ (all_10_2 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | REDUCE: (15), (304) imply:
% 176.56/27.47  | | | | | | | | | | | | | | |   (307)   ~ (e3 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | |   (308)  all_58_12 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (308) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (309)  all_6_1 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | SIMP: (309) implies:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (310)  all_6_1 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | REDUCE: (46), (310) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (311)   ~ (e3 = e1)
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | REDUCE: (27), (310) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (312)  op(e3, e1) = all_52_24
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (78) with all_52_5, all_52_24, e1,
% 176.56/27.47  | | | | | | | | | | | | | | | |              e3, simplifying with (71), (312) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (313)  all_52_5 = all_52_24
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (313) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (314)  all_56_2 = all_52_24
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (313) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (315)  all_58_4 = all_52_24
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | REDUCE: (82), (313) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | |   (316)  op(e1, all_52_24) = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (317)  all_58_4 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (317) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (318)  all_52_24 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | REDUCE: (316), (318) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (319)  op(e1, e2) = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (78), (92), (319) are inconsistent by
% 176.56/27.47  | | | | | | | | | | | | | | | | |            sub-proof #861.
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (320)   ~ (all_58_4 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | REDUCE: (315), (320) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (321)   ~ (all_52_24 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (322)  all_56_2 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (322) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (323)  all_52_24 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | SIMP: (323) implies:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (324)  all_52_24 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | REDUCE: (321), (324) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (325)  $false
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | CLOSE: (325) is inconsistent.
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (326)  all_56_2 = e1 | all_56_2 = e0
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (56), (75), (78), (82), (288), (326) are
% 176.56/27.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | |   (327)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (328)  all_58_13 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (35), (40), (42), (48), (56), (73),
% 176.56/27.47  | | | | | | | | | | | | | | | | |            (75), (78), (82), (89), (91), (288), (306), (328)
% 176.56/27.47  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #258.
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (329)  all_58_14 = e1 | all_58_15 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (30), (66), (285), (329) are inconsistent by
% 176.56/27.47  | | | | | | | | | | | | | | | | |            sub-proof #835.
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | |   (330)   ~ (all_58_13 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | REDUCE: (58), (330) imply:
% 176.56/27.47  | | | | | | | | | | | | | | |   (331)   ~ (all_52_27 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | |   (332)  all_56_13 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | REF_CLOSE: (93), (331), (332) are inconsistent by sub-proof
% 176.56/27.47  | | | | | | | | | | | | | | | |            #624.
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | |   (333)   ~ (all_56_13 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | |   (334)  all_56_13 = e1 | all_56_13 = e0
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (335)  all_56_13 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (335) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (336)  all_52_27 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | SIMP: (336) implies:
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (337)  all_52_27 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (337) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (338)  all_58_13 = e1
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | REDUCE: (331), (337) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (339)   ~ (e2 = e1)
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (340)  all_58_2 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (340) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (341)  all_52_18 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | SIMP: (341) implies:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (342)  all_52_18 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | REDUCE: (86), (342) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (343)   ~ (all_10_2 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | SIMP: (343) implies:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (344)   ~ (all_10_2 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | REDUCE: (80), (342) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (345)   ~ (e3 = e2)
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (35), (40), (42), (48), (56), (73),
% 176.56/27.47  | | | | | | | | | | | | | | | | | |            (75), (78), (82), (89), (91), (288), (338), (344)
% 176.56/27.47  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #258.
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | |   (346)  all_58_6 = e2 | all_58_12 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | Case 1:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | |   (347)  all_58_6 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (207), (347) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | |   (348)  e2 = e0
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | REDUCE: (219), (348) imply:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | |   (349)  $false
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | CLOSE: (349) is inconsistent.
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | |   (350)  all_58_12 = e2
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (302), (350) are inconsistent by sub-proof
% 176.56/27.47  | | | | | | | | | | | | | | | | | | |            #846.
% 176.56/27.47  | | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | Case 2:
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | |   (351)  all_56_13 = e0
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (93), (289), (351) are inconsistent by sub-proof
% 176.56/27.47  | | | | | | | | | | | | | | | | |            #844.
% 176.56/27.47  | | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | | 
% 176.56/27.47  | | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | | 
% 176.56/27.47  | | | | | | | | End of split
% 176.56/27.47  | | | | | | | | 
% 176.56/27.47  | | | | | | | End of split
% 176.56/27.47  | | | | | | | 
% 176.56/27.47  | | | | | | End of split
% 176.56/27.47  | | | | | | 
% 176.56/27.47  | | | | | End of split
% 176.56/27.47  | | | | | 
% 176.56/27.47  | | | | End of split
% 176.56/27.47  | | | | 
% 176.56/27.47  | | | End of split
% 176.56/27.47  | | | 
% 176.56/27.47  | | End of split
% 176.56/27.47  | | 
% 176.56/27.47  | End of split
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #258 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.47    (2)  all_58_3 = all_10_2
% 176.56/27.47    (3)   ~ (all_52_5 = e0)
% 176.56/27.47    (4)  all_58_1 = all_52_3
% 176.56/27.47    (5)  all_58_7 = e3
% 176.56/27.47    (6)   ~ (all_52_3 = all_52_5)
% 176.56/27.47    (7)   ~ (all_52_5 = all_14_2)
% 176.56/27.47    (8)  all_58_13 = e1
% 176.56/27.47    (9)  all_56_2 = all_52_5
% 176.56/27.47    (10)   ~ (all_10_2 = e2)
% 176.56/27.47    (11)   ~ (e2 = e1)
% 176.56/27.47    (12)  op(e1, e1) = all_14_2
% 176.56/27.47    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.47    (14)  op(e1, all_52_5) = e1
% 176.56/27.47    (15)   ~ (e3 = e2)
% 176.56/27.47    (16)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.47  
% 176.56/27.47  Begin of proof
% 176.56/27.47  | 
% 176.56/27.47  | BETA: splitting (1) gives:
% 176.56/27.47  | 
% 176.56/27.47  | Case 1:
% 176.56/27.47  | | 
% 176.56/27.47  | |   (17)  all_58_1 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | COMBINE_EQS: (4), (17) imply:
% 176.56/27.47  | |   (18)  all_52_3 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | REDUCE: (6), (18) imply:
% 176.56/27.47  | |   (19)   ~ (all_52_5 = e2)
% 176.56/27.47  | | 
% 176.56/27.47  | | SIMP: (19) implies:
% 176.56/27.47  | |   (20)   ~ (all_52_5 = e2)
% 176.56/27.47  | | 
% 176.56/27.47  | | BETA: splitting (16) gives:
% 176.56/27.47  | | 
% 176.56/27.47  | | Case 1:
% 176.56/27.47  | | | 
% 176.56/27.47  | | |   (21)  all_56_2 = e2
% 176.56/27.47  | | | 
% 176.56/27.47  | | | REF_CLOSE: (9), (20), (21) are inconsistent by sub-proof #827.
% 176.56/27.47  | | | 
% 176.56/27.47  | | Case 2:
% 176.56/27.47  | | | 
% 176.56/27.47  | | |   (22)  all_56_2 = e1 | all_56_2 = e0
% 176.56/27.47  | | | 
% 176.56/27.47  | | | REF_CLOSE: (3), (7), (9), (12), (13), (14), (22) are inconsistent by
% 176.56/27.47  | | |            sub-proof #858.
% 176.56/27.47  | | | 
% 176.56/27.47  | | End of split
% 176.56/27.47  | | 
% 176.56/27.47  | Case 2:
% 176.56/27.47  | | 
% 176.56/27.47  | |   (23)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | BETA: splitting (23) gives:
% 176.56/27.47  | | 
% 176.56/27.47  | | Case 1:
% 176.56/27.47  | | | 
% 176.56/27.47  | | |   (24)  all_58_3 = e2
% 176.56/27.47  | | | 
% 176.56/27.47  | | | COMBINE_EQS: (2), (24) imply:
% 176.56/27.47  | | |   (25)  all_10_2 = e2
% 176.56/27.47  | | | 
% 176.56/27.47  | | | REDUCE: (10), (25) imply:
% 176.56/27.47  | | |   (26)  $false
% 176.56/27.47  | | | 
% 176.56/27.47  | | | CLOSE: (26) is inconsistent.
% 176.56/27.47  | | | 
% 176.56/27.47  | | Case 2:
% 176.56/27.47  | | | 
% 176.56/27.47  | | |   (27)  all_58_7 = e2 | all_58_13 = e2
% 176.56/27.47  | | | 
% 176.56/27.47  | | | REF_CLOSE: (5), (8), (11), (15), (27) are inconsistent by sub-proof #259.
% 176.56/27.47  | | | 
% 176.56/27.47  | | End of split
% 176.56/27.47  | | 
% 176.56/27.47  | End of split
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #259 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)  all_58_7 = e3
% 176.56/27.47    (2)  all_58_13 = e1
% 176.56/27.47    (3)   ~ (e2 = e1)
% 176.56/27.47    (4)  all_58_7 = e2 | all_58_13 = e2
% 176.56/27.47    (5)   ~ (e3 = e2)
% 176.56/27.47  
% 176.56/27.47  Begin of proof
% 176.56/27.47  | 
% 176.56/27.47  | BETA: splitting (4) gives:
% 176.56/27.47  | 
% 176.56/27.47  | Case 1:
% 176.56/27.47  | | 
% 176.56/27.47  | |   (6)  all_58_7 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | COMBINE_EQS: (1), (6) imply:
% 176.56/27.47  | |   (7)  e3 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | REDUCE: (5), (7) imply:
% 176.56/27.47  | |   (8)  $false
% 176.56/27.47  | | 
% 176.56/27.47  | | CLOSE: (8) is inconsistent.
% 176.56/27.47  | | 
% 176.56/27.47  | Case 2:
% 176.56/27.47  | | 
% 176.56/27.47  | |   (9)  all_58_13 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | COMBINE_EQS: (2), (9) imply:
% 176.56/27.47  | |   (10)  e2 = e1
% 176.56/27.47  | | 
% 176.56/27.47  | | REDUCE: (3), (10) imply:
% 176.56/27.47  | |   (11)  $false
% 176.56/27.47  | | 
% 176.56/27.47  | | CLOSE: (11) is inconsistent.
% 176.56/27.47  | | 
% 176.56/27.47  | End of split
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #260 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)  all_58_4 = all_52_16
% 176.56/27.47    (2)  all_58_4 = e1
% 176.56/27.47    (3)   ~ (all_52_16 = e1)
% 176.56/27.47  
% 176.56/27.47  Begin of proof
% 176.56/27.47  | 
% 176.56/27.47  | COMBINE_EQS: (1), (2) imply:
% 176.56/27.47  |   (4)  all_52_16 = e1
% 176.56/27.47  | 
% 176.56/27.47  | SIMP: (4) implies:
% 176.56/27.47  |   (5)  all_52_16 = e1
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (3), (5) imply:
% 176.56/27.47  |   (6)  $false
% 176.56/27.47  | 
% 176.56/27.47  | CLOSE: (6) is inconsistent.
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #261 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)  all_58_5 = e2 | all_58_10 = e2
% 176.56/27.47    (2)  all_58_10 = all_52_15
% 176.56/27.47    (3)  all_58_5 = e3
% 176.56/27.47    (4)   ~ (all_52_15 = e2)
% 176.56/27.47    (5)   ~ (e3 = e2)
% 176.56/27.47  
% 176.56/27.47  Begin of proof
% 176.56/27.47  | 
% 176.56/27.47  | BETA: splitting (1) gives:
% 176.56/27.47  | 
% 176.56/27.47  | Case 1:
% 176.56/27.47  | | 
% 176.56/27.47  | |   (6)  all_58_5 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #262.
% 176.56/27.47  | | 
% 176.56/27.47  | Case 2:
% 176.56/27.47  | | 
% 176.56/27.47  | |   (7)  all_58_10 = e2
% 176.56/27.47  | | 
% 176.56/27.47  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #711.
% 176.56/27.47  | | 
% 176.56/27.47  | End of split
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #262 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)  all_58_5 = e3
% 176.56/27.47    (2)  all_58_5 = e2
% 176.56/27.47    (3)   ~ (e3 = e2)
% 176.56/27.47  
% 176.56/27.47  Begin of proof
% 176.56/27.47  | 
% 176.56/27.47  | COMBINE_EQS: (1), (2) imply:
% 176.56/27.47  |   (4)  e3 = e2
% 176.56/27.47  | 
% 176.56/27.47  | SIMP: (4) implies:
% 176.56/27.47  |   (5)  e3 = e2
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (3), (5) imply:
% 176.56/27.47  |   (6)  $false
% 176.56/27.47  | 
% 176.56/27.47  | CLOSE: (6) is inconsistent.
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #263 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)  op(e2, all_10_2) = all_10_1
% 176.56/27.47    (2)  op(all_10_1, all_10_2) = e3
% 176.56/27.47    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.47    (4)  all_10_1 = e2
% 176.56/27.47    (5)   ~ (e3 = e2)
% 176.56/27.47  
% 176.56/27.47  Begin of proof
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (2), (4) imply:
% 176.56/27.47  |   (6)  op(e2, all_10_2) = e3
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (1), (4) imply:
% 176.56/27.47  |   (7)  op(e2, all_10_2) = e2
% 176.56/27.47  | 
% 176.56/27.47  | GROUND_INST: instantiating (3) with e2, e3, all_10_2, e2, simplifying with
% 176.56/27.47  |              (6), (7) gives:
% 176.56/27.47  |   (8)  e3 = e2
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (5), (8) imply:
% 176.56/27.47  |   (9)  $false
% 176.56/27.47  | 
% 176.56/27.47  | CLOSE: (9) is inconsistent.
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #264 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.47    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.47    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.47    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.47    (5)   ~ (all_52_17 = all_52_23)
% 176.56/27.47    (6)  all_56_3 = all_52_7
% 176.56/27.47    (7)  all_52_16 = e3
% 176.56/27.47    (8)  op(e3, e2) = all_52_3
% 176.56/27.47    (9)   ~ (all_52_9 = all_52_25)
% 176.56/27.47    (10)  op(e3, all_52_25) = all_52_24
% 176.56/27.47    (11)   ~ (all_52_19 = all_52_23)
% 176.56/27.47    (12)  op(e1, e2) = all_52_19
% 176.56/27.47    (13)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.56/27.47    (14)  op(e3, all_52_9) = all_52_8
% 176.56/27.47    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.47    (16)  all_58_5 = all_52_13
% 176.56/27.47    (17)   ~ (all_6_2 = e0)
% 176.56/27.47    (18)   ~ (all_52_25 = all_52_29)
% 176.56/27.47    (19)  all_56_15 = all_6_2
% 176.56/27.47    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.47    (21)  op(e2, e0) = all_52_15
% 176.56/27.47    (22)  op(all_14_1, all_14_2) = all_14_0
% 176.56/27.47    (23)  all_58_3 = all_10_2
% 176.56/27.47    (24)  all_56_9 = all_52_19
% 176.56/27.47    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.47    (26)  all_58_15 = all_6_2
% 176.56/27.47    (27)   ~ (all_52_9 = all_4_2)
% 176.56/27.47    (28)   ~ (all_52_5 = all_52_7)
% 176.56/27.47    (29)  all_58_10 = all_52_15
% 176.56/27.47    (30)   ~ (all_52_5 = all_4_2)
% 176.56/27.47    (31)  all_58_7 = all_52_19
% 176.56/27.47    (32)   ~ (all_52_17 = all_52_25)
% 176.56/27.47    (33)  op(e0, e1) = all_52_29
% 176.56/27.47    (34)  all_58_4 = all_52_5
% 176.56/27.47    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.47    (36)  all_52_18 = e2
% 176.56/27.47    (37)  all_34_1 = all_4_1
% 176.56/27.47    (38)   ~ (all_52_17 = all_14_2)
% 176.56/27.47    (39)  op(e3, all_4_2) = all_4_1
% 176.56/27.47    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.47    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.47    (42)   ~ (all_52_7 = all_4_2)
% 176.56/27.47    (43)  all_58_1 = all_52_3
% 176.56/27.47    (44)  all_58_0 = all_4_2
% 176.56/27.47    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.47    (46)  op(all_4_1, all_4_2) = e1
% 176.56/27.47    (47)  op(e1, all_52_29) = all_52_28
% 176.56/27.47    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.47    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.56/27.47    (50)   ~ (all_4_1 = e2)
% 176.56/27.47    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.47    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.47    (53)  all_58_14 = all_52_29
% 176.56/27.47    (54)   ~ (all_52_3 = all_52_5)
% 176.56/27.47    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.47    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.47    (57)  all_58_8 = all_14_2
% 176.56/27.47    (58)  all_56_1 = all_52_3
% 176.56/27.47    (59)   ~ (all_14_0 = e3)
% 176.56/27.47    (60)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.56/27.47    (61)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.47    (62)   ~ (all_52_5 = all_14_2)
% 176.56/27.47    (63)   ~ (all_52_3 = all_52_27)
% 176.56/27.47    (64)   ~ (all_52_3 = all_4_2)
% 176.56/27.47    (65)  op(e0, e3) = all_52_25
% 176.56/27.47    (66)  op(e3, all_52_17) = all_52_16
% 176.56/27.47    (67)   ~ (all_52_9 = all_52_13)
% 176.56/27.47    (68)  op(e0, all_52_23) = all_52_22
% 176.56/27.47    (69)   ~ (all_52_5 = all_52_29)
% 176.56/27.47    (70)  all_56_2 = all_52_5
% 176.56/27.47    (71)  op(e1, e0) = all_52_23
% 176.56/27.47    (72)  all_58_13 = all_52_27
% 176.56/27.47    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.47    (74)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.47    (75)   ~ (all_52_9 = all_52_17)
% 176.56/27.47    (76)  all_58_6 = all_52_17
% 176.56/27.47    (77)  op(e2, all_52_19) = all_52_18
% 176.56/27.47    (78)  all_56_0 = all_4_2
% 176.56/27.47    (79)  all_58_11 = all_52_23
% 176.56/27.47    (80)   ~ (all_52_3 = all_52_19)
% 176.56/27.47    (81)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.47    (82)   ~ (all_52_29 = all_14_2)
% 176.56/27.47    (83)   ~ (all_52_23 = all_6_2)
% 176.56/27.47    (84)   ~ (all_52_29 = all_6_2)
% 176.56/27.47    (85)  all_58_2 = all_52_9
% 176.56/27.47    (86)  op(e3, e1) = all_52_5
% 176.56/27.47    (87)   ~ (all_52_25 = all_6_2)
% 176.56/27.47    (88)  op(e1, e3) = all_52_17
% 176.56/27.47    (89)   ~ (all_52_25 = all_4_2)
% 176.56/27.47    (90)  op(e3, e0) = all_52_7
% 176.56/27.47    (91)  op(e3, e3) = all_4_2
% 176.56/27.47    (92)  all_56_8 = all_52_17
% 176.56/27.47    (93)   ~ (all_52_17 = all_4_2)
% 176.56/27.47    (94)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.47    (95)   ~ (all_52_25 = all_52_27)
% 176.56/27.47    (96)  all_34_2 = all_4_2
% 176.56/27.47    (97)   ~ (all_52_27 = all_6_2)
% 176.56/27.47    (98)   ~ (all_52_7 = all_6_2)
% 176.56/27.47    (99)   ~ (all_52_19 = all_52_27)
% 176.56/27.47    (100)   ~ (all_52_7 = all_52_23)
% 176.56/27.47    (101)   ~ (all_52_13 = all_10_2)
% 176.56/27.47    (102)   ~ (all_52_17 = all_52_19)
% 176.56/27.47    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.47    (104)  all_52_22 = e0
% 176.56/27.47    (105)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.47    (106)  op(e1, all_14_2) = all_14_1
% 176.56/27.47    (107)  all_58_9 = all_52_7
% 176.56/27.47    (108)   ~ (e2 = e0)
% 176.56/27.47    (109)  all_58_12 = all_52_25
% 176.56/27.47    (110)  all_14_1 = e1
% 176.56/27.47    (111)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.47    (112)   ~ (all_52_9 = all_52_15)
% 176.56/27.47    (113)   ~ (e3 = e2)
% 176.56/27.47    (114)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.47    (115)   ~ (all_52_19 = all_14_2)
% 176.56/27.47    (116)  op(e2, e3) = all_52_9
% 176.56/27.47  
% 176.56/27.47  Begin of proof
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (22), (110) imply:
% 176.56/27.47  |   (117)  op(e1, all_14_2) = all_14_0
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (7), (66) imply:
% 176.56/27.47  |   (118)  op(e3, all_52_17) = e3
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (36), (77) imply:
% 176.56/27.47  |   (119)  op(e2, all_52_19) = e2
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (106), (110) imply:
% 176.56/27.47  |   (120)  op(e1, all_14_2) = e1
% 176.56/27.47  | 
% 176.56/27.47  | REDUCE: (68), (104) imply:
% 176.56/27.47  |   (121)  op(e0, all_52_23) = e0
% 176.56/27.47  | 
% 176.56/27.47  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 176.56/27.47  |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 176.56/27.47  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (37),
% 176.56/27.47  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 176.56/27.47  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 176.56/27.47  |            (60), (61), (62), (63), (64), (65), (67), (69), (70), (71), (72),
% 176.56/27.47  |            (73), (74), (75), (76), (78), (79), (80), (81), (82), (83), (84),
% 176.56/27.47  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 176.56/27.47  |            (96), (97), (98), (99), (100), (101), (102), (103), (105), (107),
% 176.56/27.47  |            (108), (109), (111), (112), (113), (114), (115), (116), (117),
% 176.56/27.47  |            (118), (119), (120), (121) are inconsistent by sub-proof #273.
% 176.56/27.47  | 
% 176.56/27.47  End of proof
% 176.56/27.47  
% 176.56/27.47  Sub-proof #265 shows that the following formulas are inconsistent:
% 176.56/27.47  ----------------------------------------------------------------
% 176.56/27.47    (1)  all_52_10 = e3
% 176.56/27.47    (2)   ~ (all_52_23 = all_14_2)
% 176.56/27.47    (3)   ~ (all_52_5 = all_52_13)
% 176.56/27.47    (4)   ~ (all_52_17 = all_52_23)
% 176.56/27.47    (5)   ~ (all_52_13 = all_52_29)
% 176.56/27.47    (6)  all_56_3 = all_52_7
% 176.56/27.47    (7)  op(e3, e2) = all_52_3
% 176.56/27.47    (8)   ~ (all_52_9 = all_52_25)
% 176.56/27.47    (9)   ~ (all_52_19 = all_52_23)
% 176.56/27.47    (10)  all_56_11 = all_52_23
% 176.56/27.47    (11)  op(e1, e2) = all_52_19
% 176.56/27.47    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.47    (13)   ~ (all_52_3 = all_10_2)
% 176.56/27.47    (14)  all_58_5 = all_52_13
% 176.56/27.47    (15)   ~ (all_6_2 = e0)
% 176.56/27.47    (16)   ~ (all_52_25 = all_52_29)
% 176.56/27.47    (17)  all_56_15 = all_6_2
% 176.56/27.47    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.47    (19)  op(e2, e0) = all_52_15
% 176.56/27.47    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.47    (21)  all_58_3 = all_10_2
% 176.56/27.47    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.47    (23)  all_58_15 = all_6_2
% 176.56/27.47    (24)   ~ (all_52_9 = all_4_2)
% 176.56/27.47    (25)   ~ (all_52_5 = all_52_7)
% 176.56/27.47    (26)  all_58_10 = all_52_15
% 176.56/27.47    (27)   ~ (all_52_5 = all_4_2)
% 176.56/27.47    (28)  all_58_7 = all_52_19
% 176.56/27.47    (29)  all_56_4 = all_52_9
% 176.56/27.47    (30)   ~ (all_52_15 = all_6_2)
% 176.56/27.47    (31)   ~ (all_52_17 = all_52_25)
% 176.56/27.47    (32)  op(e0, e1) = all_52_29
% 176.56/27.47    (33)  all_58_4 = all_52_5
% 176.56/27.47    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.47    (35)   ~ (e3 = e1)
% 176.56/27.47    (36)   ~ (all_52_27 = all_52_29)
% 176.56/27.47    (37)   ~ (all_52_17 = all_14_2)
% 176.56/27.47    (38)  op(e3, all_4_2) = all_4_1
% 176.56/27.47    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.47    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.47    (41)   ~ (all_52_7 = all_4_2)
% 176.56/27.47    (42)  all_58_1 = all_52_3
% 176.56/27.47    (43)   ~ (all_52_13 = all_52_15)
% 176.56/27.47    (44)  all_58_0 = all_4_2
% 176.56/27.48    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.48    (46)  op(e1, all_52_13) = all_52_12
% 176.56/27.48    (47)  op(e0, e0) = all_6_2
% 176.56/27.48    (48)  op(e1, all_52_29) = all_52_28
% 176.56/27.48    (49)  op(e1, all_52_5) = all_52_4
% 176.56/27.48    (50)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.56/27.48          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.56/27.48    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.48    (52)   ~ (all_4_1 = e2)
% 176.56/27.48    (53)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.56/27.48    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.48    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.48    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.56/27.48    (57)  all_58_14 = all_52_29
% 176.56/27.48    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.48    (59)   ~ (all_52_3 = all_52_5)
% 176.56/27.48    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.48    (61)  op(e2, e1) = all_52_13
% 176.56/27.48    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.48    (63)  all_58_8 = all_14_2
% 176.56/27.48    (64)  all_56_1 = all_52_3
% 176.56/27.48    (65)  op(e0, e2) = all_52_27
% 176.56/27.48    (66)  all_56_14 = all_52_29
% 176.56/27.48    (67)   ~ (all_52_5 = all_14_2)
% 176.56/27.48    (68)   ~ (all_52_3 = all_52_27)
% 176.56/27.48    (69)   ~ (all_52_3 = all_4_2)
% 176.56/27.48    (70)  op(e0, e3) = all_52_25
% 176.56/27.48    (71)  all_52_0 = all_4_1
% 176.56/27.48    (72)   ~ (all_52_9 = all_10_2)
% 176.56/27.48    (73)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.48    (74)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.48    (75)   ~ (all_52_13 = all_14_2)
% 176.56/27.48    (76)   ~ (e3 = e0)
% 176.56/27.48    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.48    (78)   ~ (all_52_9 = all_52_13)
% 176.56/27.48    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.48    (80)  op(e0, all_52_23) = all_52_22
% 176.56/27.48    (81)   ~ (all_52_15 = all_52_23)
% 176.56/27.48    (82)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.48    (83)   ~ (all_52_5 = all_52_29)
% 176.56/27.48    (84)  all_56_2 = all_52_5
% 176.56/27.48    (85)  op(e1, e0) = all_52_23
% 176.56/27.48    (86)  all_56_12 = all_52_25
% 176.56/27.48    (87)  all_58_13 = all_52_27
% 176.56/27.48    (88)  op(e2, all_52_3) = all_52_2
% 176.56/27.48    (89)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.48    (90)  all_56_5 = all_10_2
% 176.56/27.48    (91)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.48    (92)   ~ (all_52_9 = all_52_17)
% 176.56/27.48    (93)  all_58_6 = all_52_17
% 176.56/27.48    (94)   ~ (all_52_3 = all_52_7)
% 176.56/27.48    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.48    (96)   ~ (e1 = e0)
% 176.56/27.48    (97)  all_56_0 = all_4_2
% 176.56/27.48    (98)  all_58_11 = all_52_23
% 176.56/27.48    (99)   ~ (all_52_3 = all_52_19)
% 176.56/27.48    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.48    (101)   ~ (all_52_7 = all_52_15)
% 176.56/27.48    (102)  op(e0, all_52_15) = all_52_14
% 176.56/27.48    (103)   ~ (all_52_29 = all_14_2)
% 176.56/27.48    (104)   ~ (all_52_23 = all_6_2)
% 176.56/27.48    (105)   ~ (all_52_29 = all_6_2)
% 176.56/27.48    (106)  all_58_2 = all_52_9
% 176.56/27.48    (107)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.56/27.48    (108)  op(e3, e1) = all_52_5
% 176.56/27.48    (109)  all_56_10 = all_14_2
% 176.56/27.48    (110)   ~ (all_52_25 = all_6_2)
% 176.56/27.48    (111)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.48    (112)  op(e1, e1) = all_14_2
% 176.56/27.48    (113)  op(e1, e3) = all_52_17
% 176.56/27.48    (114)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.48    (115)   ~ (all_52_25 = all_4_2)
% 176.56/27.48    (116)  op(e3, e0) = all_52_7
% 176.56/27.48    (117)   ~ (all_52_17 = all_4_2)
% 176.56/27.48    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.48             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.48    (119)   ~ (all_52_25 = all_52_27)
% 176.56/27.48    (120)   ~ (all_52_27 = all_6_2)
% 176.56/27.48    (121)   ~ (all_52_7 = all_6_2)
% 176.56/27.48    (122)   ~ (all_52_19 = all_52_27)
% 176.56/27.48    (123)  all_56_7 = all_52_15
% 176.56/27.48    (124)   ~ (all_52_7 = all_52_23)
% 176.56/27.48    (125)   ~ (all_52_13 = all_10_2)
% 176.56/27.48    (126)  op(e2, all_52_27) = all_52_26
% 176.56/27.48    (127)   ~ (all_52_17 = all_52_19)
% 176.56/27.48    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.48    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.48    (130)  op(e2, all_10_2) = e3
% 176.56/27.48    (131)  all_58_9 = all_52_7
% 176.56/27.48    (132)  all_58_12 = all_52_25
% 176.56/27.48    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.48    (134)   ~ (all_52_9 = all_52_15)
% 176.56/27.48    (135)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.48    (136)   ~ (e3 = e2)
% 176.56/27.48    (137)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.48    (138)   ~ (all_52_19 = all_14_2)
% 176.56/27.48    (139)  op(e0, all_52_7) = all_52_6
% 176.56/27.48    (140)  op(e2, e3) = all_52_9
% 176.56/27.48    (141)  all_56_13 = all_52_27
% 176.56/27.48  
% 176.56/27.48  Begin of proof
% 176.56/27.48  | 
% 176.56/27.48  | BETA: splitting (50) gives:
% 176.56/27.48  | 
% 176.56/27.48  | Case 1:
% 176.56/27.48  | | 
% 176.56/27.48  | |   (142)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.56/27.48  | | 
% 176.56/27.48  | | ALPHA: (142) implies:
% 176.56/27.48  | |   (143)  all_52_6 = e0
% 176.56/27.48  | |   (144)  all_52_4 = e1
% 176.56/27.48  | |   (145)  all_52_2 = e2
% 176.56/27.48  | |   (146)  all_52_0 = e3
% 176.56/27.48  | | 
% 176.56/27.48  | | COMBINE_EQS: (71), (146) imply:
% 176.56/27.48  | |   (147)  all_4_1 = e3
% 176.56/27.48  | | 
% 176.56/27.48  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 176.56/27.48  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.56/27.48  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.56/27.48  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.56/27.48  | |            (47), (48), (49), (51), (53), (54), (55), (56), (57), (58), (59),
% 176.56/27.48  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 176.56/27.48  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 176.56/27.48  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 176.56/27.48  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 176.56/27.48  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 176.56/27.48  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 176.56/27.48  | |            (122), (123), (124), (125), (126), (127), (128), (129), (130),
% 176.56/27.48  | |            (131), (132), (133), (134), (135), (136), (137), (138), (139),
% 176.56/27.48  | |            (140), (141), (143), (144), (145), (147) are inconsistent by
% 176.56/27.48  | |            sub-proof #269.
% 176.56/27.48  | | 
% 176.56/27.48  | Case 2:
% 176.56/27.48  | | 
% 176.56/27.48  | |   (148)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.56/27.48  | | 
% 176.56/27.48  | | REF_CLOSE: (1), (136), (148) are inconsistent by sub-proof #289.
% 176.56/27.48  | | 
% 176.56/27.48  | End of split
% 176.56/27.48  | 
% 176.56/27.48  End of proof
% 176.56/27.48  
% 176.56/27.48  Sub-proof #266 shows that the following formulas are inconsistent:
% 176.56/27.48  ----------------------------------------------------------------
% 176.56/27.48    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.48    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.48    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.48    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.56/27.48    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.48    (6)   ~ (all_52_17 = all_52_23)
% 176.56/27.48    (7)  all_40_2 = all_4_2
% 176.56/27.48    (8)   ~ (all_52_13 = all_52_29)
% 176.56/27.48    (9)  op(e3, e2) = all_52_3
% 176.56/27.48    (10)   ~ (all_52_9 = all_52_25)
% 176.56/27.48    (11)  op(e3, all_52_25) = all_52_24
% 176.56/27.48    (12)   ~ (all_52_19 = all_52_23)
% 176.56/27.48    (13)  all_56_11 = all_52_23
% 176.56/27.48    (14)  op(e1, e2) = all_52_19
% 176.56/27.48    (15)  op(e3, all_52_9) = all_52_8
% 176.56/27.48    (16)   ~ (all_52_3 = all_10_2)
% 176.56/27.48    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.48    (18)  all_58_5 = all_52_13
% 176.56/27.48    (19)   ~ (all_52_25 = all_52_29)
% 176.56/27.48    (20)  all_56_15 = all_6_2
% 176.56/27.48    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.48    (22)  op(e2, e0) = all_52_15
% 176.56/27.48    (23)  op(all_14_1, all_14_2) = all_14_0
% 176.56/27.48    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.48    (25)  all_58_3 = all_10_2
% 176.56/27.48    (26)  all_56_9 = all_52_19
% 176.56/27.48    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.48    (28)  all_58_15 = all_6_2
% 176.56/27.48    (29)   ~ (all_52_9 = all_4_2)
% 176.56/27.48    (30)   ~ (all_52_5 = all_52_7)
% 176.56/27.48    (31)  all_58_10 = all_52_15
% 176.56/27.48    (32)   ~ (all_52_5 = all_4_2)
% 176.56/27.48    (33)  all_58_7 = all_52_19
% 176.56/27.48    (34)   ~ (all_52_17 = all_52_25)
% 176.56/27.48    (35)  op(e0, e1) = all_52_29
% 176.56/27.48    (36)   ~ (all_4_0 = e2)
% 176.56/27.48    (37)  all_58_4 = all_52_5
% 176.56/27.48    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.48    (39)   ~ (all_52_27 = all_52_29)
% 176.56/27.48    (40)   ~ (all_52_17 = all_14_2)
% 176.56/27.48    (41)  op(e3, all_4_2) = all_4_1
% 176.56/27.48    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.48    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.48    (44)   ~ (all_52_7 = all_4_2)
% 176.56/27.48    (45)  all_58_1 = all_52_3
% 176.56/27.48    (46)  all_58_0 = all_4_2
% 176.56/27.48    (47)  op(e1, all_52_29) = all_52_28
% 176.56/27.48    (48)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.56/27.48    (49)   ~ (all_4_1 = e2)
% 176.56/27.48    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.56/27.48    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.48    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.48    (53)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.56/27.48    (54)  all_58_14 = all_52_29
% 176.56/27.48    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.48    (56)   ~ (all_52_3 = all_52_5)
% 176.56/27.48    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.48    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.48    (59)  all_58_8 = all_14_2
% 176.56/27.48    (60)  op(e0, e2) = all_52_27
% 176.56/27.48    (61)  all_56_14 = all_52_29
% 176.56/27.48    (62)   ~ (all_14_0 = e3)
% 176.56/27.48    (63)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.56/27.48    (64)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.56/27.48    (65)  op(all_4_1, all_4_2) = all_4_0
% 176.56/27.48    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.48    (67)   ~ (all_52_5 = all_14_2)
% 176.56/27.48    (68)   ~ (all_52_3 = all_52_27)
% 176.56/27.48    (69)   ~ (all_52_3 = all_4_2)
% 176.56/27.48    (70)  op(e0, e3) = all_52_25
% 176.56/27.48    (71)   ~ (all_52_9 = all_10_2)
% 176.56/27.48    (72)  op(e3, all_52_17) = all_52_16
% 176.56/27.48    (73)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.48    (74)   ~ (all_52_13 = all_14_2)
% 176.56/27.48    (75)   ~ (e3 = e0)
% 176.56/27.48    (76)  all_40_0 = all_4_0
% 176.56/27.48    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.48    (78)   ~ (all_52_9 = all_52_13)
% 176.56/27.48    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.48    (80)  op(e0, all_52_23) = all_52_22
% 176.56/27.48    (81)   ~ (all_52_15 = all_52_23)
% 176.56/27.48    (82)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.48    (83)   ~ (all_52_5 = all_52_29)
% 176.56/27.48    (84)  all_56_2 = all_52_5
% 176.56/27.48    (85)  all_56_12 = all_52_25
% 176.56/27.48    (86)  all_58_13 = all_52_27
% 176.56/27.48    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.48    (88)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.48    (89)   ~ (all_52_9 = all_52_17)
% 176.56/27.48    (90)   ~ (all_14_0 = e2)
% 176.56/27.48    (91)  all_58_6 = all_52_17
% 176.56/27.48    (92)   ~ (all_52_3 = all_52_7)
% 176.56/27.48    (93)  op(e2, all_52_19) = all_52_18
% 176.56/27.48    (94)   ~ (e1 = e0)
% 176.56/27.48    (95)  all_56_0 = all_4_2
% 176.56/27.48    (96)  all_58_11 = all_52_23
% 176.56/27.48    (97)   ~ (all_52_3 = all_52_19)
% 176.56/27.48    (98)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.48    (99)   ~ (all_52_7 = all_52_15)
% 176.56/27.48    (100)   ~ (all_52_29 = all_14_2)
% 176.56/27.48    (101)   ~ (all_4_0 = e1)
% 176.56/27.48    (102)   ~ (all_52_19 = all_10_2)
% 176.56/27.48    (103)   ~ (all_52_23 = all_6_2)
% 176.56/27.48    (104)  op(e1, all_4_2) = all_4_0
% 176.56/27.48    (105)   ~ (all_52_29 = all_6_2)
% 176.56/27.48    (106)  all_58_2 = all_52_9
% 176.56/27.48    (107)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.56/27.48    (108)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.56/27.48    (109)  op(e3, e1) = all_52_5
% 176.56/27.48    (110)  all_56_10 = all_14_2
% 176.56/27.48    (111)   ~ (all_52_25 = all_6_2)
% 176.56/27.48    (112)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.56/27.48    (113)  op(e1, e3) = all_52_17
% 176.56/27.48    (114)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.48    (115)   ~ (all_52_25 = all_4_2)
% 176.56/27.48    (116)  op(e3, e0) = all_52_7
% 176.56/27.48    (117)  op(e3, e3) = all_4_2
% 176.56/27.48    (118)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 176.56/27.48             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 176.56/27.48    (119)  all_56_8 = all_52_17
% 176.56/27.48    (120)   ~ (all_52_17 = all_4_2)
% 176.56/27.48    (121)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.48             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.48    (122)   ~ (all_52_25 = all_52_27)
% 176.56/27.48    (123)   ~ (all_52_27 = all_6_2)
% 176.56/27.48    (124)   ~ (all_52_7 = all_6_2)
% 176.56/27.48    (125)   ~ (all_52_15 = all_10_2)
% 176.56/27.48    (126)   ~ (all_52_19 = all_52_27)
% 176.56/27.48    (127)  all_56_7 = all_52_15
% 176.56/27.48    (128)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.56/27.48    (129)   ~ (all_52_7 = all_52_23)
% 176.56/27.48    (130)   ~ (all_52_13 = all_10_2)
% 176.56/27.48    (131)  all_52_20 = all_14_1
% 176.56/27.48    (132)   ~ (all_52_17 = all_52_19)
% 176.56/27.48    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.48    (134)  op(e2, all_10_2) = e3
% 176.56/27.48    (135)  op(e1, all_14_2) = all_14_1
% 176.56/27.48    (136)  all_58_9 = all_52_7
% 176.56/27.48    (137)   ~ (e2 = e0)
% 176.56/27.48    (138)  all_58_12 = all_52_25
% 176.56/27.48    (139)  op(e3, all_4_2) = e1
% 176.56/27.48    (140)  all_56_6 = all_52_13
% 176.56/27.48    (141)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.48    (142)   ~ (all_52_9 = all_52_15)
% 176.56/27.48    (143)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.48    (144)   ~ (e3 = e2)
% 176.56/27.48    (145)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.48    (146)   ~ (all_52_19 = all_14_2)
% 176.56/27.48    (147)  op(e2, e3) = all_52_9
% 176.56/27.48    (148)  all_56_13 = all_52_27
% 176.56/27.48  
% 176.56/27.48  Begin of proof
% 176.56/27.48  | 
% 176.56/27.48  | ALPHA: (128) implies:
% 176.56/27.48  |   (149)  all_52_22 = e0
% 176.56/27.48  |   (150)  all_52_20 = e1
% 176.56/27.48  |   (151)  all_52_18 = e2
% 176.56/27.48  |   (152)  all_52_16 = e3
% 176.56/27.48  | 
% 176.56/27.48  | COMBINE_EQS: (131), (150) imply:
% 176.56/27.48  |   (153)  all_14_1 = e1
% 176.56/27.48  | 
% 176.56/27.48  | REDUCE: (23), (153) imply:
% 176.56/27.48  |   (154)  op(e1, all_14_2) = all_14_0
% 176.56/27.48  | 
% 176.56/27.48  | REDUCE: (72), (152) imply:
% 176.56/27.48  |   (155)  op(e3, all_52_17) = e3
% 176.56/27.48  | 
% 176.56/27.48  | REDUCE: (93), (151) imply:
% 176.56/27.48  |   (156)  op(e2, all_52_19) = e2
% 176.56/27.48  | 
% 176.56/27.48  | REDUCE: (135), (153) imply:
% 176.56/27.48  |   (157)  op(e1, all_14_2) = e1
% 176.56/27.48  | 
% 176.56/27.48  | REDUCE: (80), (149) imply:
% 176.56/27.48  |   (158)  op(e0, all_52_23) = e0
% 176.56/27.48  | 
% 176.56/27.48  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.56/27.48  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 176.56/27.48  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.56/27.48  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.56/27.48  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 176.56/27.48  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 176.56/27.48  |            (69), (70), (71), (73), (74), (75), (76), (77), (78), (79), (81),
% 176.56/27.48  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 176.56/27.48  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 176.56/27.48  |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 176.56/27.48  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 176.56/27.48  |            (122), (123), (124), (125), (126), (127), (129), (130), (132),
% 176.56/27.48  |            (133), (134), (136), (137), (138), (139), (140), (141), (142),
% 176.56/27.48  |            (143), (144), (145), (146), (147), (148), (154), (155), (156),
% 176.56/27.48  |            (157), (158) are inconsistent by sub-proof #277.
% 176.56/27.48  | 
% 176.56/27.48  End of proof
% 176.56/27.48  
% 176.56/27.48  Sub-proof #267 shows that the following formulas are inconsistent:
% 176.56/27.48  ----------------------------------------------------------------
% 176.56/27.48    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.48    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.48    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.56/27.48    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.56/27.48    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.56/27.48    (6)   ~ (all_52_17 = all_52_23)
% 176.56/27.48    (7)   ~ (all_52_13 = all_52_29)
% 176.56/27.48    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.56/27.48    (9)  all_52_16 = e3
% 176.56/27.48    (10)  op(e3, e2) = all_52_3
% 176.56/27.48    (11)   ~ (all_52_9 = all_52_25)
% 176.56/27.48    (12)  op(e3, all_52_25) = all_52_24
% 176.56/27.48    (13)   ~ (all_52_19 = all_52_23)
% 176.56/27.48    (14)  op(e1, e2) = all_52_19
% 176.56/27.48    (15)  op(e3, all_52_9) = all_52_8
% 176.56/27.48    (16)   ~ (all_52_3 = all_10_2)
% 176.56/27.48    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.56/27.48    (18)  all_58_5 = all_52_13
% 176.56/27.48    (19)   ~ (all_6_2 = e0)
% 176.56/27.48    (20)   ~ (all_52_25 = all_52_29)
% 176.56/27.48    (21)  all_56_15 = all_6_2
% 176.56/27.48    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.48    (23)  op(e2, e0) = all_52_15
% 176.56/27.48    (24)  op(all_14_1, all_14_2) = all_14_0
% 176.56/27.48    (25)  all_58_3 = all_10_2
% 176.56/27.48    (26)  all_56_9 = all_52_19
% 176.56/27.48    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.48    (28)  all_58_15 = all_6_2
% 176.56/27.48    (29)   ~ (all_52_9 = all_4_2)
% 176.56/27.48    (30)   ~ (all_52_5 = all_52_7)
% 176.56/27.48    (31)  all_58_10 = all_52_15
% 176.56/27.48    (32)   ~ (all_52_5 = all_4_2)
% 176.56/27.48    (33)  all_58_7 = all_52_19
% 176.56/27.48    (34)   ~ (all_52_15 = all_6_2)
% 176.56/27.48    (35)   ~ (all_52_17 = all_52_25)
% 176.56/27.48    (36)  op(e0, e1) = all_52_29
% 176.56/27.48    (37)   ~ (all_4_0 = e2)
% 176.56/27.48    (38)  all_58_4 = all_52_5
% 176.56/27.48    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.48    (40)  all_52_18 = e2
% 176.56/27.48    (41)   ~ (all_52_27 = all_52_29)
% 176.56/27.48    (42)   ~ (all_52_17 = all_14_2)
% 176.56/27.48    (43)  op(e3, all_4_2) = all_4_1
% 176.56/27.48    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.48    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.48    (46)   ~ (all_52_7 = all_4_2)
% 176.56/27.48    (47)  all_58_1 = all_52_3
% 176.56/27.48    (48)  all_58_0 = all_4_2
% 176.56/27.48    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.48    (50)  op(e1, all_52_29) = all_52_28
% 176.56/27.48    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.48    (52)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.56/27.48    (53)   ~ (all_4_1 = e2)
% 176.56/27.48    (54)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.56/27.48    (55)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.48    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.48    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.56/27.48    (58)  all_58_14 = all_52_29
% 176.56/27.48    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.48    (60)   ~ (all_52_3 = all_52_5)
% 176.56/27.48    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.48    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.48    (63)  all_58_8 = all_14_2
% 176.56/27.48    (64)  all_56_1 = all_52_3
% 176.56/27.48    (65)  op(e0, e2) = all_52_27
% 176.56/27.48    (66)  all_56_14 = all_52_29
% 176.56/27.48    (67)   ~ (all_14_0 = e3)
% 176.56/27.48    (68)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.56/27.48    (69)  op(all_4_1, all_4_2) = all_4_0
% 176.56/27.48    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.56/27.48    (71)   ~ (all_52_5 = all_14_2)
% 176.56/27.48    (72)   ~ (all_52_3 = all_52_27)
% 176.56/27.48    (73)   ~ (all_52_3 = all_4_2)
% 176.56/27.48    (74)  op(e0, e3) = all_52_25
% 176.56/27.48    (75)  op(e0, all_6_2) = all_6_1
% 176.56/27.48    (76)   ~ (all_52_9 = all_10_2)
% 176.56/27.48    (77)  op(e3, all_52_17) = all_52_16
% 176.56/27.48    (78)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.48    (79)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.48    (80)   ~ (all_52_13 = all_14_2)
% 176.56/27.48    (81)   ~ (e3 = e0)
% 176.56/27.48    (82)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.48    (83)   ~ (all_52_9 = all_52_13)
% 176.56/27.48    (84)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.48    (85)  op(e0, all_52_23) = all_52_22
% 176.56/27.48    (86)   ~ (all_52_15 = all_52_23)
% 176.56/27.48    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.48    (88)   ~ (all_52_5 = all_52_29)
% 176.56/27.48    (89)  all_56_2 = all_52_5
% 176.56/27.48    (90)  op(e1, e0) = all_52_23
% 176.56/27.48    (91)  all_56_12 = all_52_25
% 176.56/27.48    (92)  all_58_13 = all_52_27
% 176.56/27.48    (93)   ~ (all_4_1 = e1)
% 176.56/27.48    (94)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.48    (95)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.48    (96)   ~ (all_52_9 = all_52_17)
% 176.56/27.48    (97)   ~ (all_14_0 = e2)
% 176.56/27.48    (98)  all_58_6 = all_52_17
% 176.56/27.48    (99)   ~ (all_52_3 = all_52_7)
% 176.56/27.48    (100)  op(e2, all_52_19) = all_52_18
% 176.56/27.48    (101)   ~ (e1 = e0)
% 176.56/27.48    (102)  all_56_0 = all_4_2
% 176.56/27.48    (103)  all_58_11 = all_52_23
% 176.56/27.48    (104)   ~ (all_52_3 = all_52_19)
% 176.56/27.48    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.48    (106)   ~ (all_52_7 = all_52_15)
% 176.56/27.48    (107)   ~ (all_52_29 = all_14_2)
% 176.56/27.48    (108)   ~ (all_4_0 = e1)
% 176.56/27.48    (109)   ~ (all_52_19 = all_10_2)
% 176.56/27.48    (110)   ~ (all_52_23 = all_6_2)
% 176.56/27.48    (111)  all_58_2 = all_52_9
% 176.56/27.48    (112)  op(e3, e1) = all_52_5
% 176.56/27.48    (113)  all_56_10 = all_14_2
% 176.56/27.48    (114)   ~ (all_52_25 = all_6_2)
% 176.56/27.48    (115)  op(e1, e3) = all_52_17
% 176.56/27.48    (116)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.48    (117)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.56/27.48    (118)   ~ (all_52_25 = all_4_2)
% 176.56/27.48    (119)  op(e3, e0) = all_52_7
% 176.56/27.48    (120)  op(e3, e3) = all_4_2
% 176.56/27.48    (121)  all_56_8 = all_52_17
% 176.56/27.48    (122)   ~ (all_52_17 = all_4_2)
% 176.56/27.48    (123)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.49             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.49    (124)   ~ (all_52_25 = all_52_27)
% 176.56/27.49    (125)   ~ (all_52_27 = all_6_2)
% 176.56/27.49    (126)   ~ (all_52_7 = all_6_2)
% 176.56/27.49    (127)   ~ (all_52_15 = all_10_2)
% 176.56/27.49    (128)   ~ (all_52_19 = all_52_27)
% 176.56/27.49    (129)  all_56_7 = all_52_15
% 176.56/27.49    (130)   ~ (all_52_7 = all_52_23)
% 176.56/27.49    (131)   ~ (all_52_13 = all_10_2)
% 176.56/27.49    (132)  op(e2, all_52_27) = all_52_26
% 176.56/27.49    (133)   ~ (all_52_17 = all_52_19)
% 176.56/27.49    (134)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.49    (135)  all_52_22 = e0
% 176.56/27.49    (136)  op(e2, all_10_2) = e3
% 176.56/27.49    (137)  op(e1, all_14_2) = all_14_1
% 176.56/27.49    (138)  all_58_9 = all_52_7
% 176.56/27.49    (139)   ~ (e2 = e0)
% 176.56/27.49    (140)  all_58_12 = all_52_25
% 176.56/27.49    (141)  all_14_1 = e1
% 176.56/27.49    (142)  all_56_6 = all_52_13
% 176.56/27.49    (143)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.49    (144)   ~ (all_52_9 = all_52_15)
% 176.56/27.49    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.49    (146)   ~ (e3 = e2)
% 176.56/27.49    (147)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.49    (148)   ~ (all_52_19 = all_14_2)
% 176.56/27.49    (149)  op(e2, e3) = all_52_9
% 176.56/27.49    (150)  all_56_13 = all_52_27
% 176.56/27.49  
% 176.56/27.49  Begin of proof
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (24), (141) imply:
% 176.56/27.49  |   (151)  op(e1, all_14_2) = all_14_0
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (9), (77) imply:
% 176.56/27.49  |   (152)  op(e3, all_52_17) = e3
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (40), (100) imply:
% 176.56/27.49  |   (153)  op(e2, all_52_19) = e2
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (137), (141) imply:
% 176.56/27.49  |   (154)  op(e1, all_14_2) = e1
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (85), (135) imply:
% 176.56/27.49  |   (155)  op(e0, all_52_23) = e0
% 176.56/27.49  | 
% 176.56/27.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 176.56/27.49  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 176.56/27.49  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 176.56/27.49  |            (37), (38), (39), (41), (42), (43), (44), (45), (46), (47), (48),
% 176.56/27.49  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 176.56/27.49  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 176.56/27.49  |            (71), (72), (73), (74), (75), (76), (78), (79), (80), (81), (82),
% 176.56/27.49  |            (83), (84), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 176.56/27.49  |            (95), (96), (97), (98), (99), (101), (102), (103), (104), (105),
% 176.56/27.49  |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 176.56/27.49  |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 176.56/27.49  |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 176.56/27.49  |            (133), (134), (136), (138), (139), (140), (142), (143), (144),
% 176.56/27.49  |            (145), (146), (147), (148), (149), (150), (151), (152), (153),
% 176.56/27.49  |            (154), (155) are inconsistent by sub-proof #278.
% 176.56/27.49  | 
% 176.56/27.49  End of proof
% 176.56/27.49  
% 176.56/27.49  Sub-proof #268 shows that the following formulas are inconsistent:
% 176.56/27.49  ----------------------------------------------------------------
% 176.56/27.49    (1)  all_52_10 = e3
% 176.56/27.49    (2)   ~ (all_52_23 = all_14_2)
% 176.56/27.49    (3)   ~ (all_52_5 = all_52_13)
% 176.56/27.49    (4)   ~ (all_52_17 = all_52_23)
% 176.56/27.49    (5)   ~ (all_52_13 = all_52_29)
% 176.56/27.49    (6)  all_56_3 = all_52_7
% 176.56/27.49    (7)  op(e3, e2) = all_52_3
% 176.56/27.49    (8)   ~ (all_52_9 = all_52_25)
% 176.56/27.49    (9)   ~ (all_52_19 = all_52_23)
% 176.56/27.49    (10)  all_56_11 = all_52_23
% 176.56/27.49    (11)  op(e1, e2) = all_52_19
% 176.56/27.49    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.49    (13)   ~ (all_52_3 = all_10_2)
% 176.56/27.49    (14)  all_58_5 = all_52_13
% 176.56/27.49    (15)   ~ (all_6_2 = e0)
% 176.56/27.49    (16)   ~ (all_52_25 = all_52_29)
% 176.56/27.49    (17)  all_56_15 = all_6_2
% 176.56/27.49    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.49    (19)  op(e2, e0) = all_52_15
% 176.56/27.49    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.49    (21)  all_58_3 = all_10_2
% 176.56/27.49    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.49    (23)  all_58_15 = all_6_2
% 176.56/27.49    (24)   ~ (all_52_9 = all_4_2)
% 176.56/27.49    (25)   ~ (all_52_5 = all_52_7)
% 176.56/27.49    (26)  all_58_10 = all_52_15
% 176.56/27.49    (27)   ~ (all_52_5 = all_4_2)
% 176.56/27.49    (28)  all_58_7 = all_52_19
% 176.56/27.49    (29)  all_56_4 = all_52_9
% 176.56/27.49    (30)   ~ (all_52_15 = all_6_2)
% 176.56/27.49    (31)   ~ (all_52_17 = all_52_25)
% 176.56/27.49    (32)  op(e0, e1) = all_52_29
% 176.56/27.49    (33)  all_58_4 = all_52_5
% 176.56/27.49    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.49    (35)   ~ (all_52_27 = all_52_29)
% 176.56/27.49    (36)   ~ (all_52_17 = all_14_2)
% 176.56/27.49    (37)  op(e3, all_4_2) = all_4_1
% 176.56/27.49    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.49    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.49    (40)   ~ (all_52_7 = all_4_2)
% 176.56/27.49    (41)  all_58_1 = all_52_3
% 176.56/27.49    (42)   ~ (all_52_13 = all_52_15)
% 176.56/27.49    (43)  all_58_0 = all_4_2
% 176.56/27.49    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.49    (45)  op(e1, all_52_13) = all_52_12
% 176.56/27.49    (46)  op(e0, e0) = all_6_2
% 176.56/27.49    (47)  op(e1, all_52_29) = all_52_28
% 176.56/27.49    (48)  op(e1, all_52_5) = all_52_4
% 176.56/27.49    (49)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.56/27.49          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.56/27.49    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.49    (51)   ~ (all_4_1 = e2)
% 176.56/27.49    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.56/27.49    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.49    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.49    (55)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.56/27.49    (56)  all_58_14 = all_52_29
% 176.56/27.49    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.49    (58)   ~ (all_52_3 = all_52_5)
% 176.56/27.49    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.49    (60)  op(e2, e1) = all_52_13
% 176.56/27.49    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.49    (62)  all_58_8 = all_14_2
% 176.56/27.49    (63)  all_56_1 = all_52_3
% 176.56/27.49    (64)  op(e0, e2) = all_52_27
% 176.56/27.49    (65)  all_56_14 = all_52_29
% 176.56/27.49    (66)   ~ (all_52_5 = all_14_2)
% 176.56/27.49    (67)   ~ (all_52_3 = all_52_27)
% 176.56/27.49    (68)   ~ (all_52_3 = all_4_2)
% 176.56/27.49    (69)  op(e0, e3) = all_52_25
% 176.56/27.49    (70)  all_52_0 = all_4_1
% 176.56/27.49    (71)   ~ (all_52_9 = all_10_2)
% 176.56/27.49    (72)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.49    (73)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.49    (74)   ~ (all_52_13 = all_14_2)
% 176.56/27.49    (75)   ~ (e3 = e0)
% 176.56/27.49    (76)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.49    (77)   ~ (all_52_9 = all_52_13)
% 176.56/27.49    (78)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.49    (79)  op(e0, all_52_23) = all_52_22
% 176.56/27.49    (80)   ~ (all_52_15 = all_52_23)
% 176.56/27.49    (81)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.49    (82)   ~ (all_52_5 = all_52_29)
% 176.56/27.49    (83)  all_56_2 = all_52_5
% 176.56/27.49    (84)  op(e1, e0) = all_52_23
% 176.56/27.49    (85)  all_56_12 = all_52_25
% 176.56/27.49    (86)  all_58_13 = all_52_27
% 176.56/27.49    (87)   ~ (all_4_1 = e1)
% 176.56/27.49    (88)  op(e2, all_52_3) = all_52_2
% 176.56/27.49    (89)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.49    (90)  all_56_5 = all_10_2
% 176.56/27.49    (91)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.49    (92)   ~ (all_52_9 = all_52_17)
% 176.56/27.49    (93)  all_58_6 = all_52_17
% 176.56/27.49    (94)   ~ (all_52_3 = all_52_7)
% 176.56/27.49    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.49    (96)   ~ (e1 = e0)
% 176.56/27.49    (97)  all_56_0 = all_4_2
% 176.56/27.49    (98)  all_58_11 = all_52_23
% 176.56/27.49    (99)   ~ (all_52_3 = all_52_19)
% 176.56/27.49    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.49    (101)   ~ (all_52_7 = all_52_15)
% 176.56/27.49    (102)  op(e0, all_52_15) = all_52_14
% 176.56/27.49    (103)   ~ (all_52_29 = all_14_2)
% 176.56/27.49    (104)   ~ (all_52_23 = all_6_2)
% 176.56/27.49    (105)   ~ (all_52_29 = all_6_2)
% 176.56/27.49    (106)  all_58_2 = all_52_9
% 176.56/27.49    (107)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.56/27.49    (108)  op(e3, e1) = all_52_5
% 176.56/27.49    (109)  all_56_10 = all_14_2
% 176.56/27.49    (110)   ~ (all_52_25 = all_6_2)
% 176.56/27.49    (111)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.49    (112)  op(e1, e1) = all_14_2
% 176.56/27.49    (113)  op(e1, e3) = all_52_17
% 176.56/27.49    (114)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.49    (115)   ~ (all_52_25 = all_4_2)
% 176.56/27.49    (116)  op(e3, e0) = all_52_7
% 176.56/27.49    (117)   ~ (all_52_17 = all_4_2)
% 176.56/27.49    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.49             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.49    (119)   ~ (all_52_25 = all_52_27)
% 176.56/27.49    (120)   ~ (all_52_27 = all_6_2)
% 176.56/27.49    (121)   ~ (all_52_7 = all_6_2)
% 176.56/27.49    (122)   ~ (all_52_19 = all_52_27)
% 176.56/27.49    (123)  all_56_7 = all_52_15
% 176.56/27.49    (124)   ~ (all_52_7 = all_52_23)
% 176.56/27.49    (125)   ~ (all_52_13 = all_10_2)
% 176.56/27.49    (126)  op(e2, all_52_27) = all_52_26
% 176.56/27.49    (127)   ~ (all_52_17 = all_52_19)
% 176.56/27.49    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.49    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.49    (130)  op(e2, all_10_2) = e3
% 176.56/27.49    (131)  all_58_9 = all_52_7
% 176.56/27.49    (132)  all_58_12 = all_52_25
% 176.56/27.49    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.49    (134)   ~ (all_52_9 = all_52_15)
% 176.56/27.49    (135)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.49    (136)   ~ (e3 = e2)
% 176.56/27.49    (137)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.49    (138)   ~ (all_52_19 = all_14_2)
% 176.56/27.49    (139)  op(e0, all_52_7) = all_52_6
% 176.56/27.49    (140)  op(e2, e3) = all_52_9
% 176.56/27.49    (141)  all_56_13 = all_52_27
% 176.56/27.49  
% 176.56/27.49  Begin of proof
% 176.56/27.49  | 
% 176.56/27.49  | BETA: splitting (49) gives:
% 176.56/27.49  | 
% 176.56/27.49  | Case 1:
% 176.56/27.49  | | 
% 176.56/27.49  | |   (142)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.56/27.49  | | 
% 176.56/27.49  | | ALPHA: (142) implies:
% 176.56/27.49  | |   (143)  all_52_6 = e0
% 176.56/27.49  | |   (144)  all_52_4 = e1
% 176.56/27.49  | |   (145)  all_52_2 = e2
% 176.56/27.49  | |   (146)  all_52_0 = e3
% 176.56/27.49  | | 
% 176.56/27.49  | | COMBINE_EQS: (70), (146) imply:
% 176.56/27.49  | |   (147)  all_4_1 = e3
% 176.56/27.49  | | 
% 176.56/27.49  | | REDUCE: (87), (147) imply:
% 176.56/27.49  | |   (148)   ~ (e3 = e1)
% 176.56/27.49  | | 
% 176.56/27.49  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 176.56/27.49  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.56/27.49  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 176.56/27.49  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.56/27.49  | |            (47), (48), (50), (52), (53), (54), (55), (56), (57), (58), (59),
% 176.56/27.49  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 176.56/27.49  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 176.56/27.49  | |            (83), (84), (85), (86), (88), (89), (90), (91), (92), (93), (94),
% 176.56/27.49  | |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 176.56/27.49  | |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 176.56/27.49  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 176.56/27.49  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 176.56/27.49  | |            (132), (133), (134), (135), (136), (137), (138), (139), (140),
% 176.56/27.49  | |            (141), (143), (144), (145), (147), (148) are inconsistent by
% 176.56/27.49  | |            sub-proof #269.
% 176.56/27.49  | | 
% 176.56/27.49  | Case 2:
% 176.56/27.49  | | 
% 176.56/27.49  | |   (149)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.56/27.49  | | 
% 176.56/27.49  | | REF_CLOSE: (1), (136), (149) are inconsistent by sub-proof #289.
% 176.56/27.49  | | 
% 176.56/27.49  | End of split
% 176.56/27.49  | 
% 176.56/27.49  End of proof
% 176.56/27.49  
% 176.56/27.49  Sub-proof #269 shows that the following formulas are inconsistent:
% 176.56/27.49  ----------------------------------------------------------------
% 176.56/27.49    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.49    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.49    (3)   ~ (all_52_17 = all_52_23)
% 176.56/27.49    (4)   ~ (all_52_13 = all_52_29)
% 176.56/27.49    (5)  all_56_3 = all_52_7
% 176.56/27.49    (6)  op(e3, e2) = all_52_3
% 176.56/27.49    (7)   ~ (all_52_9 = all_52_25)
% 176.56/27.49    (8)   ~ (all_52_19 = all_52_23)
% 176.56/27.49    (9)  all_56_11 = all_52_23
% 176.56/27.49    (10)  op(e1, e2) = all_52_19
% 176.56/27.49    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.49    (12)   ~ (all_52_3 = all_10_2)
% 176.56/27.49    (13)  all_58_5 = all_52_13
% 176.56/27.49    (14)   ~ (all_6_2 = e0)
% 176.56/27.49    (15)   ~ (all_52_25 = all_52_29)
% 176.56/27.49    (16)  all_56_15 = all_6_2
% 176.56/27.49    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.49    (18)  op(e2, e0) = all_52_15
% 176.56/27.49    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.49    (20)  all_58_3 = all_10_2
% 176.56/27.49    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.49    (22)  all_58_15 = all_6_2
% 176.56/27.49    (23)   ~ (all_52_9 = all_4_2)
% 176.56/27.49    (24)   ~ (all_52_5 = all_52_7)
% 176.56/27.49    (25)  all_58_10 = all_52_15
% 176.56/27.49    (26)   ~ (all_52_5 = all_4_2)
% 176.56/27.49    (27)  all_58_7 = all_52_19
% 176.56/27.49    (28)  all_56_4 = all_52_9
% 176.56/27.49    (29)   ~ (all_52_15 = all_6_2)
% 176.56/27.49    (30)   ~ (all_52_17 = all_52_25)
% 176.56/27.49    (31)  op(e0, e1) = all_52_29
% 176.56/27.49    (32)  all_58_4 = all_52_5
% 176.56/27.49    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.49    (34)   ~ (e3 = e1)
% 176.56/27.49    (35)   ~ (all_52_27 = all_52_29)
% 176.56/27.49    (36)   ~ (all_52_17 = all_14_2)
% 176.56/27.49    (37)  op(e3, all_4_2) = all_4_1
% 176.56/27.49    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.49    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.49    (40)   ~ (all_52_7 = all_4_2)
% 176.56/27.49    (41)  all_58_1 = all_52_3
% 176.56/27.49    (42)   ~ (all_52_13 = all_52_15)
% 176.56/27.49    (43)  all_58_0 = all_4_2
% 176.56/27.49    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.49    (45)  op(e1, all_52_13) = all_52_12
% 176.56/27.49    (46)  op(e0, e0) = all_6_2
% 176.56/27.49    (47)  op(e1, all_52_29) = all_52_28
% 176.56/27.49    (48)  op(e1, all_52_5) = all_52_4
% 176.56/27.49    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.49    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.56/27.49    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.49    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.49    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.56/27.49    (54)  all_58_14 = all_52_29
% 176.56/27.49    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.49    (56)   ~ (all_52_3 = all_52_5)
% 176.56/27.49    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.49    (58)  op(e2, e1) = all_52_13
% 176.56/27.49    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.49    (60)  all_58_8 = all_14_2
% 176.56/27.49    (61)  all_56_1 = all_52_3
% 176.56/27.49    (62)  op(e0, e2) = all_52_27
% 176.56/27.49    (63)  all_56_14 = all_52_29
% 176.56/27.49    (64)   ~ (all_52_5 = all_14_2)
% 176.56/27.49    (65)   ~ (all_52_3 = all_52_27)
% 176.56/27.49    (66)   ~ (all_52_3 = all_4_2)
% 176.56/27.49    (67)  op(e0, e3) = all_52_25
% 176.56/27.49    (68)   ~ (all_52_9 = all_10_2)
% 176.56/27.49    (69)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.49    (70)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.49    (71)   ~ (all_52_13 = all_14_2)
% 176.56/27.49    (72)   ~ (e3 = e0)
% 176.56/27.49    (73)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.49    (74)   ~ (all_52_9 = all_52_13)
% 176.56/27.49    (75)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.49    (76)  op(e0, all_52_23) = all_52_22
% 176.56/27.49    (77)   ~ (all_52_15 = all_52_23)
% 176.56/27.49    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.49    (79)   ~ (all_52_5 = all_52_29)
% 176.56/27.49    (80)  all_56_2 = all_52_5
% 176.56/27.49    (81)  op(e1, e0) = all_52_23
% 176.56/27.49    (82)  all_56_12 = all_52_25
% 176.56/27.49    (83)  all_58_13 = all_52_27
% 176.56/27.49    (84)  op(e2, all_52_3) = all_52_2
% 176.56/27.49    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.49    (86)  all_56_5 = all_10_2
% 176.56/27.49    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.49    (88)   ~ (all_52_9 = all_52_17)
% 176.56/27.49    (89)  all_58_6 = all_52_17
% 176.56/27.49    (90)   ~ (all_52_3 = all_52_7)
% 176.56/27.49    (91)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.49    (92)   ~ (e1 = e0)
% 176.56/27.49    (93)  all_56_0 = all_4_2
% 176.56/27.49    (94)  all_58_11 = all_52_23
% 176.56/27.49    (95)   ~ (all_52_3 = all_52_19)
% 176.56/27.49    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.49    (97)   ~ (all_52_7 = all_52_15)
% 176.56/27.49    (98)  op(e0, all_52_15) = all_52_14
% 176.56/27.49    (99)  all_52_4 = e1
% 176.56/27.49    (100)   ~ (all_52_29 = all_14_2)
% 176.56/27.49    (101)   ~ (all_52_23 = all_6_2)
% 176.56/27.49    (102)   ~ (all_52_29 = all_6_2)
% 176.56/27.49    (103)  all_58_2 = all_52_9
% 176.56/27.49    (104)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.56/27.49    (105)  op(e3, e1) = all_52_5
% 176.56/27.49    (106)  all_56_10 = all_14_2
% 176.56/27.49    (107)   ~ (all_52_25 = all_6_2)
% 176.56/27.49    (108)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.49    (109)  op(e1, e1) = all_14_2
% 176.56/27.49    (110)  op(e1, e3) = all_52_17
% 176.56/27.49    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.49    (112)   ~ (all_52_25 = all_4_2)
% 176.56/27.49    (113)  op(e3, e0) = all_52_7
% 176.56/27.49    (114)   ~ (all_52_17 = all_4_2)
% 176.56/27.49    (115)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.49             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.49    (116)   ~ (all_52_25 = all_52_27)
% 176.56/27.49    (117)   ~ (all_52_27 = all_6_2)
% 176.56/27.49    (118)   ~ (all_52_7 = all_6_2)
% 176.56/27.49    (119)   ~ (all_52_19 = all_52_27)
% 176.56/27.49    (120)  all_56_7 = all_52_15
% 176.56/27.49    (121)   ~ (all_52_7 = all_52_23)
% 176.56/27.49    (122)   ~ (all_52_13 = all_10_2)
% 176.56/27.49    (123)  op(e2, all_52_27) = all_52_26
% 176.56/27.49    (124)  all_52_6 = e0
% 176.56/27.49    (125)   ~ (all_52_17 = all_52_19)
% 176.56/27.49    (126)  all_52_2 = e2
% 176.56/27.49    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.49    (128)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.49    (129)  all_4_1 = e3
% 176.56/27.49    (130)  op(e2, all_10_2) = e3
% 176.56/27.49    (131)  all_58_9 = all_52_7
% 176.56/27.49    (132)  all_58_12 = all_52_25
% 176.56/27.49    (133)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.49    (134)   ~ (all_52_9 = all_52_15)
% 176.56/27.49    (135)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.49    (136)   ~ (e3 = e2)
% 176.56/27.49    (137)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.49    (138)   ~ (all_52_19 = all_14_2)
% 176.56/27.49    (139)  op(e0, all_52_7) = all_52_6
% 176.56/27.49    (140)  op(e2, e3) = all_52_9
% 176.56/27.49    (141)  all_56_13 = all_52_27
% 176.56/27.49  
% 176.56/27.49  Begin of proof
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (37), (129) imply:
% 176.56/27.49  |   (142)  op(e3, all_4_2) = e3
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (84), (126) imply:
% 176.56/27.49  |   (143)  op(e2, all_52_3) = e2
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (48), (99) imply:
% 176.56/27.49  |   (144)  op(e1, all_52_5) = e1
% 176.56/27.49  | 
% 176.56/27.49  | REDUCE: (124), (139) imply:
% 176.56/27.49  |   (145)  op(e0, all_52_7) = e0
% 176.56/27.49  | 
% 176.56/27.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.56/27.49  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.56/27.49  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 176.56/27.49  |            (35), (36), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 176.56/27.49  |            (47), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 176.56/27.49  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 176.56/27.49  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 176.56/27.49  |            (81), (82), (83), (85), (86), (87), (88), (89), (90), (91), (92),
% 176.56/27.49  |            (93), (94), (95), (96), (97), (98), (100), (101), (102), (103),
% 176.56/27.49  |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 176.56/27.49  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 176.56/27.49  |            (122), (123), (125), (127), (128), (130), (131), (132), (133),
% 176.56/27.49  |            (134), (135), (136), (137), (138), (140), (141), (142), (143),
% 176.56/27.49  |            (144), (145) are inconsistent by sub-proof #270.
% 176.56/27.49  | 
% 176.56/27.49  End of proof
% 176.56/27.49  
% 176.56/27.49  Sub-proof #270 shows that the following formulas are inconsistent:
% 176.56/27.49  ----------------------------------------------------------------
% 176.56/27.49    (1)   ~ (all_52_23 = all_14_2)
% 176.56/27.49    (2)   ~ (all_52_5 = all_52_13)
% 176.56/27.49    (3)   ~ (all_52_17 = all_52_23)
% 176.56/27.49    (4)  op(e2, all_52_3) = e2
% 176.56/27.49    (5)   ~ (all_52_13 = all_52_29)
% 176.56/27.49    (6)  all_56_3 = all_52_7
% 176.56/27.49    (7)  op(e3, e2) = all_52_3
% 176.56/27.49    (8)   ~ (all_52_9 = all_52_25)
% 176.56/27.49    (9)   ~ (all_52_19 = all_52_23)
% 176.56/27.49    (10)  all_56_11 = all_52_23
% 176.56/27.49    (11)  op(e1, e2) = all_52_19
% 176.56/27.49    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.56/27.49    (13)   ~ (all_52_3 = all_10_2)
% 176.56/27.49    (14)  all_58_5 = all_52_13
% 176.56/27.49    (15)   ~ (all_6_2 = e0)
% 176.56/27.49    (16)   ~ (all_52_25 = all_52_29)
% 176.56/27.49    (17)  all_56_15 = all_6_2
% 176.56/27.49    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.56/27.49    (19)  op(e2, e0) = all_52_15
% 176.56/27.50    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.56/27.50    (21)  all_58_3 = all_10_2
% 176.56/27.50    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.56/27.50    (23)  all_58_15 = all_6_2
% 176.56/27.50    (24)   ~ (all_52_9 = all_4_2)
% 176.56/27.50    (25)   ~ (all_52_5 = all_52_7)
% 176.56/27.50    (26)  all_58_10 = all_52_15
% 176.56/27.50    (27)   ~ (all_52_5 = all_4_2)
% 176.56/27.50    (28)  all_58_7 = all_52_19
% 176.56/27.50    (29)  all_56_4 = all_52_9
% 176.56/27.50    (30)   ~ (all_52_15 = all_6_2)
% 176.56/27.50    (31)   ~ (all_52_17 = all_52_25)
% 176.56/27.50    (32)  op(e0, e1) = all_52_29
% 176.56/27.50    (33)  all_58_4 = all_52_5
% 176.56/27.50    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.50    (35)   ~ (e3 = e1)
% 176.56/27.50    (36)   ~ (all_52_27 = all_52_29)
% 176.56/27.50    (37)   ~ (all_52_17 = all_14_2)
% 176.56/27.50    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.50    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.50    (40)   ~ (all_52_7 = all_4_2)
% 176.56/27.50    (41)  all_58_1 = all_52_3
% 176.56/27.50    (42)   ~ (all_52_13 = all_52_15)
% 176.56/27.50    (43)  all_58_0 = all_4_2
% 176.56/27.50    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.56/27.50    (45)  op(e1, all_52_13) = all_52_12
% 176.56/27.50    (46)  op(e0, e0) = all_6_2
% 176.56/27.50    (47)  op(e1, all_52_29) = all_52_28
% 176.56/27.50    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.56/27.50    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.56/27.50    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.56/27.50    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.56/27.50    (52)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 176.56/27.50    (53)  all_58_14 = all_52_29
% 176.56/27.50    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.56/27.50    (55)   ~ (all_52_3 = all_52_5)
% 176.56/27.50    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.56/27.50    (57)  op(e2, e1) = all_52_13
% 176.56/27.50    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.56/27.50    (59)  all_58_8 = all_14_2
% 176.56/27.50    (60)  all_56_1 = all_52_3
% 176.56/27.50    (61)  op(e0, e2) = all_52_27
% 176.56/27.50    (62)  all_56_14 = all_52_29
% 176.56/27.50    (63)   ~ (all_52_5 = all_14_2)
% 176.56/27.50    (64)   ~ (all_52_3 = all_52_27)
% 176.56/27.50    (65)   ~ (all_52_3 = all_4_2)
% 176.56/27.50    (66)  op(e3, all_4_2) = e3
% 176.56/27.50    (67)  op(e0, e3) = all_52_25
% 176.56/27.50    (68)   ~ (all_52_9 = all_10_2)
% 176.56/27.50    (69)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.56/27.50    (70)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.56/27.50    (71)   ~ (all_52_13 = all_14_2)
% 176.56/27.50    (72)   ~ (e3 = e0)
% 176.56/27.50    (73)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.56/27.50    (74)   ~ (all_52_9 = all_52_13)
% 176.56/27.50    (75)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.56/27.50    (76)  op(e0, all_52_23) = all_52_22
% 176.56/27.50    (77)   ~ (all_52_15 = all_52_23)
% 176.56/27.50    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.56/27.50    (79)   ~ (all_52_5 = all_52_29)
% 176.56/27.50    (80)  all_56_2 = all_52_5
% 176.56/27.50    (81)  op(e1, e0) = all_52_23
% 176.56/27.50    (82)  all_56_12 = all_52_25
% 176.56/27.50    (83)  all_58_13 = all_52_27
% 176.56/27.50    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.56/27.50    (85)  all_56_5 = all_10_2
% 176.56/27.50    (86)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.56/27.50    (87)   ~ (all_52_9 = all_52_17)
% 176.56/27.50    (88)  all_58_6 = all_52_17
% 176.56/27.50    (89)   ~ (all_52_3 = all_52_7)
% 176.56/27.50    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 176.56/27.50    (91)   ~ (e1 = e0)
% 176.56/27.50    (92)  all_56_0 = all_4_2
% 176.56/27.50    (93)  all_58_11 = all_52_23
% 176.56/27.50    (94)   ~ (all_52_3 = all_52_19)
% 176.56/27.50    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.56/27.50    (96)   ~ (all_52_7 = all_52_15)
% 176.56/27.50    (97)  op(e0, all_52_15) = all_52_14
% 176.56/27.50    (98)   ~ (all_52_29 = all_14_2)
% 176.56/27.50    (99)   ~ (all_52_23 = all_6_2)
% 176.56/27.50    (100)   ~ (all_52_29 = all_6_2)
% 176.56/27.50    (101)  all_58_2 = all_52_9
% 176.56/27.50    (102)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.56/27.50    (103)  op(e3, e1) = all_52_5
% 176.56/27.50    (104)  all_56_10 = all_14_2
% 176.56/27.50    (105)   ~ (all_52_25 = all_6_2)
% 176.56/27.50    (106)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.56/27.50    (107)  op(e1, e1) = all_14_2
% 176.56/27.50    (108)  op(e1, e3) = all_52_17
% 176.56/27.50    (109)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.56/27.50    (110)   ~ (all_52_25 = all_4_2)
% 176.56/27.50    (111)  op(e3, e0) = all_52_7
% 176.56/27.50    (112)   ~ (all_52_17 = all_4_2)
% 176.56/27.50    (113)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.56/27.50             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.56/27.50    (114)   ~ (all_52_25 = all_52_27)
% 176.56/27.50    (115)   ~ (all_52_27 = all_6_2)
% 176.56/27.50    (116)   ~ (all_52_7 = all_6_2)
% 176.56/27.50    (117)   ~ (all_52_19 = all_52_27)
% 176.56/27.50    (118)  all_56_7 = all_52_15
% 176.56/27.50    (119)  op(e1, all_52_5) = e1
% 176.56/27.50    (120)   ~ (all_52_7 = all_52_23)
% 176.56/27.50    (121)   ~ (all_52_13 = all_10_2)
% 176.56/27.50    (122)  op(e0, all_52_7) = e0
% 176.56/27.50    (123)  op(e2, all_52_27) = all_52_26
% 176.56/27.50    (124)   ~ (all_52_17 = all_52_19)
% 176.56/27.50    (125)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.56/27.50    (126)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.50    (127)  op(e2, all_10_2) = e3
% 176.56/27.50    (128)  all_58_9 = all_52_7
% 176.56/27.50    (129)  all_58_12 = all_52_25
% 176.56/27.50    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.56/27.50    (131)   ~ (all_52_9 = all_52_15)
% 176.56/27.50    (132)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.56/27.50    (133)   ~ (e3 = e2)
% 176.56/27.50    (134)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.56/27.50    (135)   ~ (all_52_19 = all_14_2)
% 176.56/27.50    (136)  op(e2, e3) = all_52_9
% 176.56/27.50    (137)  all_56_13 = all_52_27
% 176.56/27.50  
% 176.56/27.50  Begin of proof
% 176.56/27.50  | 
% 176.56/27.50  | BETA: splitting (106) gives:
% 176.56/27.50  | 
% 176.56/27.50  | Case 1:
% 176.56/27.50  | | 
% 176.56/27.50  | |   (138)  all_56_5 = e3
% 176.56/27.50  | | 
% 176.56/27.50  | | REF_CLOSE: (68), (85), (113), (127), (136), (138) are inconsistent by
% 176.56/27.50  | |            sub-proof #271.
% 176.56/27.50  | | 
% 176.56/27.50  | Case 2:
% 176.56/27.50  | | 
% 176.56/27.50  | |   (139)   ~ (all_56_5 = e3)
% 176.56/27.50  | | 
% 176.56/27.50  | | REDUCE: (85), (139) imply:
% 176.56/27.50  | |   (140)   ~ (all_10_2 = e3)
% 176.56/27.50  | | 
% 176.56/27.50  | | BETA: splitting (38) gives:
% 176.56/27.50  | | 
% 176.56/27.50  | | Case 1:
% 176.56/27.50  | | | 
% 176.56/27.50  | | |   (141)  all_56_15 = e3
% 176.56/27.50  | | | 
% 176.56/27.50  | | | COMBINE_EQS: (17), (141) imply:
% 176.56/27.50  | | |   (142)  all_6_2 = e3
% 176.56/27.50  | | | 
% 176.56/27.50  | | | SIMP: (142) implies:
% 176.56/27.50  | | |   (143)  all_6_2 = e3
% 176.56/27.50  | | | 
% 176.56/27.50  | | | REDUCE: (30), (143) imply:
% 176.56/27.50  | | |   (144)   ~ (all_52_15 = e3)
% 176.56/27.50  | | | 
% 176.56/27.50  | | | REDUCE: (99), (143) imply:
% 176.56/27.50  | | |   (145)   ~ (all_52_23 = e3)
% 176.56/27.50  | | | 
% 176.56/27.50  | | | REDUCE: (100), (143) imply:
% 176.56/27.50  | | |   (146)   ~ (all_52_29 = e3)
% 176.56/27.50  | | | 
% 176.56/27.50  | | | REDUCE: (46), (143) imply:
% 176.56/27.50  | | |   (147)  op(e0, e0) = e3
% 176.56/27.50  | | | 
% 176.56/27.50  | | | BETA: splitting (39) gives:
% 176.56/27.50  | | | 
% 176.56/27.50  | | | Case 1:
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | |   (148)  all_58_2 = e3
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | | COMBINE_EQS: (101), (148) imply:
% 176.56/27.50  | | | |   (149)  all_52_9 = e3
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | | REF_CLOSE: (1), (2), (4), (7), (14), (22), (23), (24), (25), (26), (27),
% 176.56/27.50  | | | |            (28), (33), (34), (37), (40), (41), (43), (53), (55), (59),
% 176.56/27.50  | | | |            (63), (66), (67), (71), (73), (78), (79), (84), (88), (89),
% 176.56/27.50  | | | |            (92), (93), (94), (96), (98), (103), (104), (108), (110),
% 176.56/27.50  | | | |            (111), (112), (113), (116), (119), (120), (122), (125),
% 176.56/27.50  | | | |            (128), (130), (132), (136), (146), (149) are inconsistent by
% 176.56/27.50  | | | |            sub-proof #413.
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | Case 2:
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | |   (150)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | | BETA: splitting (150) gives:
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | | Case 1:
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | |   (151)  all_58_3 = e3
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | | COMBINE_EQS: (21), (151) imply:
% 176.56/27.50  | | | | |   (152)  all_10_2 = e3
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | | REDUCE: (140), (152) imply:
% 176.56/27.50  | | | | |   (153)  $false
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | | CLOSE: (153) is inconsistent.
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | Case 2:
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | |   (154)  all_58_5 = e3 | all_58_10 = e3
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | | BETA: splitting (154) gives:
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | | Case 1:
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | |   (155)  all_58_5 = e3
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | COMBINE_EQS: (14), (155) imply:
% 176.56/27.50  | | | | | |   (156)  all_52_13 = e3
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | SIMP: (156) implies:
% 176.56/27.50  | | | | | |   (157)  all_52_13 = e3
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | REDUCE: (5), (157) imply:
% 176.56/27.50  | | | | | |   (158)   ~ (all_52_29 = e3)
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | REDUCE: (71), (157) imply:
% 176.56/27.50  | | | | | |   (159)   ~ (all_14_2 = e3)
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | SIMP: (159) implies:
% 176.56/27.50  | | | | | |   (160)   ~ (all_14_2 = e3)
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | REDUCE: (57), (157) imply:
% 176.56/27.50  | | | | | |   (161)  op(e2, e1) = e3
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | REDUCE: (45), (157) imply:
% 176.56/27.50  | | | | | |   (162)  op(e1, e3) = all_52_12
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | GROUND_INST: instantiating (113) with all_52_17, all_52_12, e3, e1,
% 176.56/27.50  | | | | | |              simplifying with (108), (162) gives:
% 176.56/27.50  | | | | | |   (163)  all_52_12 = all_52_17
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | BETA: splitting (56) gives:
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | Case 1:
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | |   (164)  all_58_0 = e3
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | COMBINE_EQS: (43), (164) imply:
% 176.56/27.50  | | | | | | |   (165)  all_4_2 = e3
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | REDUCE: (27), (165) imply:
% 176.56/27.50  | | | | | | |   (166)   ~ (all_52_5 = e3)
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | REDUCE: (40), (165) imply:
% 176.56/27.50  | | | | | | |   (167)   ~ (all_52_7 = e3)
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | REDUCE: (112), (165) imply:
% 176.56/27.50  | | | | | | |   (168)   ~ (all_52_17 = e3)
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | BETA: splitting (34) gives:
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | Case 1:
% 176.56/27.50  | | | | | | | | 
% 176.56/27.50  | | | | | | | |   (169)  all_58_6 = e3
% 176.56/27.50  | | | | | | | | 
% 176.56/27.50  | | | | | | | | REF_CLOSE: (88), (168), (169) are inconsistent by sub-proof
% 176.56/27.50  | | | | | | | |            #981.
% 176.56/27.50  | | | | | | | | 
% 176.56/27.50  | | | | | | | Case 2:
% 176.56/27.50  | | | | | | | | 
% 176.56/27.50  | | | | | | | |   (170)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.56/27.50  | | | | | | | | 
% 176.56/27.50  | | | | | | | | BETA: splitting (170) gives:
% 176.56/27.50  | | | | | | | | 
% 176.56/27.50  | | | | | | | | Case 1:
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | |   (171)  all_58_7 = e3
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | COMBINE_EQS: (28), (171) imply:
% 176.56/27.50  | | | | | | | | |   (172)  all_52_19 = e3
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | REDUCE: (94), (172) imply:
% 176.56/27.50  | | | | | | | | |   (173)   ~ (all_52_3 = e3)
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | REDUCE: (11), (172) imply:
% 176.56/27.50  | | | | | | | | |   (174)  op(e1, e2) = e3
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | BETA: splitting (126) gives:
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | Case 1:
% 176.56/27.50  | | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | |   (175)  all_56_3 = e3
% 176.56/27.50  | | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | | REF_CLOSE: (6), (167), (175) are inconsistent by sub-proof
% 176.56/27.50  | | | | | | | | | |            #1034.
% 176.56/27.50  | | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | Case 2:
% 176.56/27.50  | | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | |   (176)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.56/27.50  | | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | | REF_CLOSE: (4), (6), (20), (32), (48), (60), (61), (63),
% 176.56/27.50  | | | | | | | | | |            (64), (69), (79), (80), (89), (107), (113), (119),
% 176.56/27.50  | | | | | | | | | |            (122), (128), (134), (147), (161), (166), (167),
% 176.56/27.50  | | | | | | | | | |            (173), (174), (176) are inconsistent by sub-proof
% 176.56/27.50  | | | | | | | | | |            #852.
% 176.56/27.50  | | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | End of split
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | Case 2:
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | |   (177)  all_58_8 = e3 | all_58_11 = e3
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | | REF_CLOSE: (59), (93), (145), (160), (177) are inconsistent by
% 176.56/27.50  | | | | | | | | |            sub-proof #997.
% 176.56/27.50  | | | | | | | | | 
% 176.56/27.50  | | | | | | | | End of split
% 176.56/27.50  | | | | | | | | 
% 176.56/27.50  | | | | | | | End of split
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | Case 2:
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | |   (178)   ~ (all_58_0 = e3)
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | REDUCE: (43), (178) imply:
% 176.56/27.50  | | | | | | |   (179)   ~ (all_4_2 = e3)
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | | REF_CLOSE: (1), (2), (4), (7), (14), (22), (23), (24), (25), (26),
% 176.56/27.50  | | | | | | |            (27), (28), (33), (34), (37), (40), (41), (43), (53),
% 176.56/27.50  | | | | | | |            (55), (59), (63), (66), (67), (71), (73), (78), (79),
% 176.56/27.50  | | | | | | |            (84), (88), (89), (92), (93), (94), (96), (98), (103),
% 176.56/27.50  | | | | | | |            (104), (108), (110), (111), (112), (113), (116), (119),
% 176.56/27.50  | | | | | | |            (120), (122), (125), (128), (130), (132), (136), (146),
% 176.56/27.50  | | | | | | |            (179) are inconsistent by sub-proof #864.
% 176.56/27.50  | | | | | | | 
% 176.56/27.50  | | | | | | End of split
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | Case 2:
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | |   (180)  all_58_10 = e3
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | | REF_CLOSE: (26), (144), (180) are inconsistent by sub-proof #1018.
% 176.56/27.50  | | | | | | 
% 176.56/27.50  | | | | | End of split
% 176.56/27.50  | | | | | 
% 176.56/27.50  | | | | End of split
% 176.56/27.50  | | | | 
% 176.56/27.50  | | | End of split
% 176.56/27.50  | | | 
% 176.56/27.50  | | Case 2:
% 176.56/27.50  | | | 
% 176.56/27.50  | | |   (181)   ~ (all_56_15 = e3)
% 176.56/27.50  | | |   (182)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.56/27.50  | | | 
% 176.84/27.50  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 176.84/27.50  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.84/27.50  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 176.84/27.50  | | |            (34), (35), (36), (39), (40), (41), (42), (43), (44), (47),
% 176.84/27.50  | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 176.84/27.50  | | |            (58), (59), (60), (62), (63), (64), (65), (66), (67), (70),
% 176.84/27.50  | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 176.84/27.50  | | |            (81), (82), (83), (84), (86), (87), (88), (89), (90), (91),
% 176.84/27.50  | | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 176.84/27.50  | | |            (102), (103), (104), (105), (107), (108), (109), (110), (111),
% 176.84/27.50  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 176.84/27.50  | | |            (121), (122), (123), (124), (125), (128), (129), (130), (131),
% 176.84/27.50  | | |            (132), (133), (134), (135), (136), (137), (181), (182) are
% 176.84/27.50  | | |            inconsistent by sub-proof #785.
% 176.84/27.50  | | | 
% 176.84/27.50  | | End of split
% 176.84/27.50  | | 
% 176.84/27.50  | End of split
% 176.84/27.50  | 
% 176.84/27.50  End of proof
% 176.84/27.50  
% 176.84/27.50  Sub-proof #271 shows that the following formulas are inconsistent:
% 176.84/27.50  ----------------------------------------------------------------
% 176.84/27.50    (1)   ~ (all_52_9 = all_10_2)
% 176.84/27.50    (2)  all_56_5 = e3
% 176.84/27.50    (3)  all_56_5 = all_10_2
% 176.84/27.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.50    (5)  op(e2, all_10_2) = e3
% 176.84/27.50    (6)  op(e2, e3) = all_52_9
% 176.84/27.50  
% 176.84/27.50  Begin of proof
% 176.84/27.50  | 
% 176.84/27.50  | COMBINE_EQS: (2), (3) imply:
% 176.84/27.50  |   (7)  all_10_2 = e3
% 176.84/27.50  | 
% 176.84/27.50  | SIMP: (7) implies:
% 176.84/27.50  |   (8)  all_10_2 = e3
% 176.84/27.50  | 
% 176.84/27.50  | REDUCE: (1), (8) imply:
% 176.84/27.50  |   (9)   ~ (all_52_9 = e3)
% 176.84/27.50  | 
% 176.84/27.50  | REDUCE: (5), (8) imply:
% 176.84/27.50  |   (10)  op(e2, e3) = e3
% 176.84/27.50  | 
% 176.84/27.50  | REF_CLOSE: (4), (6), (9), (10) are inconsistent by sub-proof #498.
% 176.84/27.50  | 
% 176.84/27.50  End of proof
% 176.84/27.50  
% 176.84/27.50  Sub-proof #272 shows that the following formulas are inconsistent:
% 176.84/27.50  ----------------------------------------------------------------
% 176.84/27.50    (1)  all_52_10 = e3
% 176.84/27.50    (2)   ~ (all_52_23 = all_14_2)
% 176.84/27.50    (3)   ~ (all_52_5 = all_52_13)
% 176.84/27.50    (4)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.50    (5)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.50    (6)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.84/27.50    (7)   ~ (all_52_17 = all_52_23)
% 176.84/27.50    (8)   ~ (all_6_0 = e3)
% 176.84/27.50    (9)   ~ (all_52_13 = all_52_29)
% 176.84/27.50    (10)  all_56_3 = all_52_7
% 176.84/27.50    (11)  op(e3, e2) = all_52_3
% 176.84/27.50    (12)   ~ (all_52_9 = all_52_25)
% 176.84/27.50    (13)  op(e3, all_52_25) = all_52_24
% 176.84/27.50    (14)   ~ (all_52_19 = all_52_23)
% 176.84/27.50    (15)  all_56_11 = all_52_23
% 176.84/27.50    (16)  op(e1, e2) = all_52_19
% 176.84/27.50    (17)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.84/27.50    (18)  op(e3, all_52_9) = all_52_8
% 176.84/27.50    (19)   ~ (all_52_3 = all_10_2)
% 176.84/27.50    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.50    (21)  all_58_5 = all_52_13
% 176.84/27.50    (22)   ~ (all_52_25 = all_52_29)
% 176.84/27.50    (23)  all_56_15 = all_6_2
% 176.84/27.50    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.50    (25)  op(e2, e0) = all_52_15
% 176.84/27.50    (26)  op(all_14_1, all_14_2) = all_14_0
% 176.84/27.50    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.84/27.50    (28)  all_58_3 = all_10_2
% 176.84/27.50    (29)  all_56_9 = all_52_19
% 176.84/27.50    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.50    (31)  all_58_15 = all_6_2
% 176.84/27.50    (32)   ~ (all_52_9 = all_4_2)
% 176.84/27.50    (33)   ~ (all_52_5 = all_52_7)
% 176.84/27.50    (34)  all_58_10 = all_52_15
% 176.84/27.50    (35)   ~ (all_52_5 = all_4_2)
% 176.84/27.50    (36)  all_58_7 = all_52_19
% 176.84/27.50    (37)   ~ (all_52_17 = all_52_25)
% 176.84/27.50    (38)  op(e0, e1) = all_52_29
% 176.84/27.50    (39)  all_58_4 = all_52_5
% 176.84/27.50    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.50    (41)   ~ (e3 = e1)
% 176.84/27.50    (42)  all_34_1 = all_4_1
% 176.84/27.50    (43)   ~ (all_52_27 = all_52_29)
% 176.84/27.50    (44)   ~ (all_52_17 = all_14_2)
% 176.84/27.50    (45)  op(e3, all_4_2) = all_4_1
% 176.84/27.50    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.50    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.50    (48)   ~ (all_52_7 = all_4_2)
% 176.84/27.50    (49)  all_58_1 = all_52_3
% 176.84/27.50    (50)  all_58_0 = all_4_2
% 176.84/27.50    (51)  op(e0, e0) = all_6_2
% 176.84/27.50    (52)  op(e1, all_52_29) = all_52_28
% 176.84/27.50    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.84/27.50    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.50    (55)   ~ (all_4_1 = e2)
% 176.84/27.50    (56)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.50    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.50    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.50    (59)  all_58_14 = all_52_29
% 176.84/27.50    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.50    (61)   ~ (all_52_3 = all_52_5)
% 176.84/27.50    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.50    (63)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.50    (64)  all_58_8 = all_14_2
% 176.84/27.50    (65)  all_56_1 = all_52_3
% 176.84/27.50    (66)  op(e0, e2) = all_52_27
% 176.84/27.50    (67)  all_56_14 = all_52_29
% 176.84/27.50    (68)   ~ (all_14_0 = e3)
% 176.84/27.50    (69)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.84/27.50    (70)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.50    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.50    (72)   ~ (all_52_5 = all_14_2)
% 176.84/27.50    (73)   ~ (all_52_3 = all_52_27)
% 176.84/27.50    (74)   ~ (all_52_3 = all_4_2)
% 176.84/27.50    (75)  op(all_6_1, all_6_2) = all_6_0
% 176.84/27.50    (76)  op(e0, e3) = all_52_25
% 176.84/27.50    (77)  op(e0, all_6_2) = all_6_1
% 176.84/27.50    (78)  all_52_0 = all_4_1
% 176.84/27.50    (79)   ~ (all_52_9 = all_10_2)
% 176.84/27.50    (80)  op(e3, all_52_17) = all_52_16
% 176.84/27.50    (81)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.50    (82)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.50    (83)   ~ (all_52_9 = all_52_13)
% 176.84/27.50    (84)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.50    (85)  op(e0, all_52_23) = all_52_22
% 176.84/27.50    (86)   ~ (all_52_15 = all_52_23)
% 176.84/27.50    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.84/27.50    (88)   ~ (all_52_5 = all_52_29)
% 176.84/27.50    (89)  all_56_2 = all_52_5
% 176.84/27.50    (90)  op(e1, e0) = all_52_23
% 176.84/27.50    (91)  all_56_12 = all_52_25
% 176.84/27.50    (92)  all_58_13 = all_52_27
% 176.84/27.50    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.50    (94)  all_56_5 = all_10_2
% 176.84/27.50    (95)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.50    (96)   ~ (all_52_9 = all_52_17)
% 176.84/27.50    (97)   ~ (all_14_0 = e2)
% 176.84/27.50    (98)  all_58_6 = all_52_17
% 176.84/27.50    (99)   ~ (all_52_3 = all_52_7)
% 176.84/27.50    (100)  op(e2, all_52_19) = all_52_18
% 176.84/27.50    (101)  all_56_0 = all_4_2
% 176.84/27.50    (102)  all_58_11 = all_52_23
% 176.84/27.50    (103)   ~ (all_52_3 = all_52_19)
% 176.84/27.50    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.84/27.50    (105)   ~ (all_52_7 = all_52_15)
% 176.84/27.50    (106)   ~ (all_52_29 = all_14_2)
% 176.84/27.50    (107)  all_4_0 = e1
% 176.84/27.50    (108)   ~ (all_52_19 = all_10_2)
% 176.84/27.50    (109)   ~ (all_52_23 = all_6_2)
% 176.84/27.50    (110)   ~ (all_6_0 = e2)
% 176.84/27.50    (111)   ~ (all_52_29 = all_6_2)
% 176.84/27.50    (112)  all_58_2 = all_52_9
% 176.84/27.50    (113)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.84/27.50    (114)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.84/27.50    (115)  op(e3, e1) = all_52_5
% 176.84/27.50    (116)  all_56_10 = all_14_2
% 176.84/27.50    (117)   ~ (all_52_25 = all_6_2)
% 176.84/27.50    (118)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.84/27.50    (119)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.84/27.50    (120)  op(e1, e1) = all_14_2
% 176.84/27.50    (121)  op(e1, e3) = all_52_17
% 176.84/27.50    (122)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.50    (123)   ~ (all_52_25 = all_4_2)
% 176.84/27.50    (124)  op(e3, e0) = all_52_7
% 176.84/27.50    (125)  op(e3, e3) = all_4_2
% 176.84/27.50    (126)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 176.84/27.50             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 176.84/27.50    (127)  all_56_8 = all_52_17
% 176.84/27.50    (128)   ~ (all_52_17 = all_4_2)
% 176.84/27.50    (129)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.50             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.50    (130)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.84/27.50           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.84/27.50           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.84/27.50           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.84/27.50    (131)   ~ (all_52_25 = all_52_27)
% 176.84/27.50    (132)  all_34_2 = all_4_2
% 176.84/27.50    (133)   ~ (all_52_27 = all_6_2)
% 176.84/27.50    (134)   ~ (all_52_7 = all_6_2)
% 176.84/27.50    (135)   ~ (all_52_19 = all_52_27)
% 176.84/27.51    (136)  all_56_7 = all_52_15
% 176.84/27.51    (137)   ~ (all_52_7 = all_52_23)
% 176.84/27.51    (138)   ~ (all_52_13 = all_10_2)
% 176.84/27.51    (139)   ~ (all_6_0 = e1)
% 176.84/27.51    (140)  op(e2, all_52_27) = all_52_26
% 176.84/27.51    (141)  all_52_20 = all_14_1
% 176.84/27.51    (142)   ~ (all_52_17 = all_52_19)
% 176.84/27.51    (143)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.51    (144)  all_52_30 = all_6_1
% 176.84/27.51    (145)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.51    (146)  op(e1, all_14_2) = all_14_1
% 176.84/27.51    (147)  all_58_9 = all_52_7
% 176.84/27.51    (148)   ~ (e2 = e0)
% 176.84/27.51    (149)  all_58_12 = all_52_25
% 176.84/27.51    (150)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.51    (151)   ~ (all_52_9 = all_52_15)
% 176.84/27.51    (152)   ~ (e3 = e2)
% 176.84/27.51    (153)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.51    (154)   ~ (all_52_19 = all_14_2)
% 176.84/27.51    (155)  op(e2, e3) = all_52_9
% 176.84/27.51    (156)  all_56_13 = all_52_27
% 176.84/27.51  
% 176.84/27.51  Begin of proof
% 176.84/27.51  | 
% 176.84/27.51  | REDUCE: (70), (107) imply:
% 176.84/27.51  |   (157)  op(all_4_1, all_4_2) = e1
% 176.84/27.51  | 
% 176.84/27.51  | BETA: splitting (126) gives:
% 176.84/27.51  | 
% 176.84/27.51  | Case 1:
% 176.84/27.51  | | 
% 176.84/27.51  | |   (158)  all_58_15 = e0
% 176.84/27.51  | | 
% 176.84/27.51  | | COMBINE_EQS: (31), (158) imply:
% 176.84/27.51  | |   (159)  all_6_2 = e0
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (134), (159) imply:
% 176.84/27.51  | |   (160)   ~ (all_52_7 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (109), (159) imply:
% 176.84/27.51  | |   (161)   ~ (all_52_23 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (117), (159) imply:
% 176.84/27.51  | |   (162)   ~ (all_52_25 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (133), (159) imply:
% 176.84/27.51  | |   (163)   ~ (all_52_27 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (111), (159) imply:
% 176.84/27.51  | |   (164)   ~ (all_52_29 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (75), (159) imply:
% 176.84/27.51  | |   (165)  op(all_6_1, e0) = all_6_0
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (77), (159) imply:
% 176.84/27.51  | |   (166)  op(e0, e0) = all_6_1
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (51), (159) imply:
% 176.84/27.51  | |   (167)  op(e0, e0) = e0
% 176.84/27.51  | | 
% 176.84/27.51  | | GROUND_INST: instantiating (129) with e0, all_6_1, e0, e0, simplifying with
% 176.84/27.51  | |              (166), (167) gives:
% 176.84/27.51  | |   (168)  all_6_1 = e0
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (165), (168) imply:
% 176.84/27.51  | |   (169)  op(e0, e0) = all_6_0
% 176.84/27.51  | | 
% 176.84/27.51  | | GROUND_INST: instantiating (129) with e0, all_6_0, e0, e0, simplifying with
% 176.84/27.51  | |              (167), (169) gives:
% 176.84/27.51  | |   (170)  all_6_0 = e0
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (8), (170) imply:
% 176.84/27.51  | |   (171)   ~ (e3 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | SIMP: (171) implies:
% 176.84/27.51  | |   (172)   ~ (e3 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (110), (170) imply:
% 176.84/27.51  | |   (173)   ~ (e2 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (139), (170) imply:
% 176.84/27.51  | |   (174)   ~ (e1 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | SIMP: (174) implies:
% 176.84/27.51  | |   (175)   ~ (e1 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | BETA: splitting (130) gives:
% 176.84/27.51  | | 
% 176.84/27.51  | | Case 1:
% 176.84/27.51  | | | 
% 176.84/27.51  | | |   (176)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.84/27.51  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.84/27.51  | | |            e0)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | BETA: splitting (176) gives:
% 176.84/27.51  | | | 
% 176.84/27.51  | | | Case 1:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (177)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REF_CLOSE: (41), (45), (78), (129), (157), (177) are inconsistent by
% 176.84/27.51  | | | |            sub-proof #600.
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | Case 2:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (178)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.84/27.51  | | | |          e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REF_CLOSE: (1), (152), (178) are inconsistent by sub-proof #274.
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | End of split
% 176.84/27.51  | | | 
% 176.84/27.51  | | Case 2:
% 176.84/27.51  | | | 
% 176.84/27.51  | | |   (179)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 176.84/27.51  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 176.84/27.51  | | |            all_52_30 = e0)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | REF_CLOSE: (2), (4), (5), (7), (9), (10), (11), (12), (13), (14), (15),
% 176.84/27.51  | | |            (16), (17), (19), (21), (22), (24), (26), (27), (28), (29),
% 176.84/27.51  | | |            (30), (32), (33), (34), (36), (37), (38), (39), (40), (41),
% 176.84/27.51  | | |            (42), (43), (45), (47), (48), (49), (50), (52), (53), (54),
% 176.84/27.51  | | |            (55), (56), (58), (59), (60), (62), (63), (64), (65), (66),
% 176.84/27.51  | | |            (67), (68), (71), (72), (73), (74), (76), (79), (80), (81),
% 176.84/27.51  | | |            (82), (84), (85), (86), (87), (88), (90), (91), (92), (93),
% 176.84/27.51  | | |            (94), (96), (97), (98), (99), (100), (101), (102), (103),
% 176.84/27.51  | | |            (106), (108), (112), (113), (114), (115), (116), (118), (119),
% 176.84/27.51  | | |            (121), (122), (123), (124), (125), (127), (128), (129), (131),
% 176.84/27.51  | | |            (132), (135), (136), (137), (140), (141), (143), (145), (146),
% 176.84/27.51  | | |            (147), (148), (149), (150), (151), (152), (154), (155), (156),
% 176.84/27.51  | | |            (157), (158), (160), (161), (162), (163), (164), (172), (175),
% 176.84/27.51  | | |            (179) are inconsistent by sub-proof #575.
% 176.84/27.51  | | | 
% 176.84/27.51  | | End of split
% 176.84/27.51  | | 
% 176.84/27.51  | Case 2:
% 176.84/27.51  | | 
% 176.84/27.51  | |   (180)   ~ (all_58_15 = e0)
% 176.84/27.51  | |   (181)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 176.84/27.51  | |            | all_58_13 = e0 | all_58_14 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | ALPHA: (181) implies:
% 176.84/27.51  | |   (182)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.84/27.51  | |   (183)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (31), (180) imply:
% 176.84/27.51  | |   (184)   ~ (all_6_2 = e0)
% 176.84/27.51  | | 
% 176.84/27.51  | | BETA: splitting (130) gives:
% 176.84/27.51  | | 
% 176.84/27.51  | | Case 1:
% 176.84/27.51  | | | 
% 176.84/27.51  | | |   (185)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.84/27.51  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.84/27.51  | | |            e0)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | BETA: splitting (185) gives:
% 176.84/27.51  | | | 
% 176.84/27.51  | | | Case 1:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (186)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REF_CLOSE: (41), (45), (78), (129), (157), (186) are inconsistent by
% 176.84/27.51  | | | |            sub-proof #600.
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | Case 2:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (187)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 176.84/27.51  | | | |          e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REF_CLOSE: (1), (152), (187) are inconsistent by sub-proof #289.
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | End of split
% 176.84/27.51  | | | 
% 176.84/27.51  | | Case 2:
% 176.84/27.51  | | | 
% 176.84/27.51  | | |   (188)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 176.84/27.51  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 176.84/27.51  | | |            all_52_30 = e0)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | BETA: splitting (188) gives:
% 176.84/27.51  | | | 
% 176.84/27.51  | | | Case 1:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (189)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 176.84/27.51  | | | |          e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | ALPHA: (189) implies:
% 176.84/27.51  | | | |   (190)  all_52_22 = e0
% 176.84/27.51  | | | |   (191)  all_52_20 = e1
% 176.84/27.51  | | | |   (192)  all_52_18 = e2
% 176.84/27.51  | | | |   (193)  all_52_16 = e3
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | COMBINE_EQS: (141), (191) imply:
% 176.84/27.51  | | | |   (194)  all_14_1 = e1
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | SIMP: (194) implies:
% 176.84/27.51  | | | |   (195)  all_14_1 = e1
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REDUCE: (26), (195) imply:
% 176.84/27.51  | | | |   (196)  op(e1, all_14_2) = all_14_0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REDUCE: (80), (193) imply:
% 176.84/27.51  | | | |   (197)  op(e3, all_52_17) = e3
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REDUCE: (100), (192) imply:
% 176.84/27.51  | | | |   (198)  op(e2, all_52_19) = e2
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REDUCE: (146), (195) imply:
% 176.84/27.51  | | | |   (199)  op(e1, all_14_2) = e1
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REDUCE: (85), (190) imply:
% 176.84/27.51  | | | |   (200)  op(e0, all_52_23) = e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (11), (12), (13), (14), (16),
% 176.84/27.51  | | | |            (17), (18), (20), (21), (22), (23), (24), (25), (28), (29),
% 176.84/27.51  | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 176.84/27.51  | | | |            (40), (42), (44), (45), (46), (47), (48), (49), (50), (52),
% 176.84/27.51  | | | |            (53), (54), (55), (57), (58), (59), (61), (62), (63), (64),
% 176.84/27.51  | | | |            (65), (68), (69), (71), (72), (73), (74), (76), (83), (88),
% 176.84/27.51  | | | |            (89), (90), (92), (93), (95), (96), (98), (101), (102),
% 176.84/27.51  | | | |            (103), (104), (106), (109), (111), (112), (115), (117),
% 176.84/27.51  | | | |            (121), (123), (124), (125), (127), (128), (129), (131),
% 176.84/27.51  | | | |            (132), (133), (134), (135), (137), (138), (142), (143),
% 176.84/27.51  | | | |            (145), (147), (148), (149), (150), (151), (152), (153),
% 176.84/27.51  | | | |            (154), (155), (157), (183), (184), (196), (197), (198),
% 176.84/27.51  | | | |            (199), (200) are inconsistent by sub-proof #273.
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | Case 2:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (201)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 176.84/27.51  | | | |          e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REF_CLOSE: (5), (8), (10), (11), (12), (13), (14), (16), (17), (18),
% 176.84/27.51  | | | |            (19), (20), (23), (24), (28), (30), (31), (33), (34), (36),
% 176.84/27.51  | | | |            (37), (38), (39), (41), (42), (43), (45), (46), (48), (49),
% 176.84/27.51  | | | |            (50), (52), (53), (55), (59), (60), (61), (62), (63), (65),
% 176.84/27.51  | | | |            (66), (73), (74), (75), (76), (77), (79), (81), (82), (89),
% 176.84/27.51  | | | |            (90), (92), (93), (98), (99), (101), (102), (103), (105),
% 176.84/27.51  | | | |            (106), (110), (112), (115), (119), (120), (121), (123),
% 176.84/27.51  | | | |            (124), (125), (128), (129), (131), (132), (134), (135),
% 176.84/27.51  | | | |            (137), (139), (140), (142), (143), (144), (145), (147),
% 176.84/27.51  | | | |            (149), (151), (152), (153), (155), (156), (157), (182), (201)
% 176.84/27.51  | | | |            are inconsistent by sub-proof #534.
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | End of split
% 176.84/27.51  | | | 
% 176.84/27.51  | | End of split
% 176.84/27.51  | | 
% 176.84/27.51  | End of split
% 176.84/27.51  | 
% 176.84/27.51  End of proof
% 176.84/27.51  
% 176.84/27.51  Sub-proof #273 shows that the following formulas are inconsistent:
% 176.84/27.51  ----------------------------------------------------------------
% 176.84/27.51    (1)   ~ (all_52_23 = all_14_2)
% 176.84/27.51    (2)   ~ (all_52_5 = all_52_13)
% 176.84/27.51    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.51    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.84/27.51    (5)   ~ (all_52_17 = all_52_23)
% 176.84/27.51    (6)  all_56_3 = all_52_7
% 176.84/27.51    (7)  op(e3, e2) = all_52_3
% 176.84/27.51    (8)   ~ (all_52_9 = all_52_25)
% 176.84/27.51    (9)  op(e3, all_52_25) = all_52_24
% 176.84/27.51    (10)   ~ (all_52_19 = all_52_23)
% 176.84/27.51    (11)  op(e1, e2) = all_52_19
% 176.84/27.51    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.84/27.51    (13)  op(e3, all_52_9) = all_52_8
% 176.84/27.51    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.51    (15)  all_58_5 = all_52_13
% 176.84/27.51    (16)   ~ (all_6_2 = e0)
% 176.84/27.51    (17)   ~ (all_52_25 = all_52_29)
% 176.84/27.51    (18)  all_56_15 = all_6_2
% 176.84/27.51    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.51    (20)  op(e2, e0) = all_52_15
% 176.84/27.51    (21)  all_58_3 = all_10_2
% 176.84/27.51    (22)  all_56_9 = all_52_19
% 176.84/27.51    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.51    (24)  all_58_15 = all_6_2
% 176.84/27.51    (25)   ~ (all_52_9 = all_4_2)
% 176.84/27.51    (26)   ~ (all_52_5 = all_52_7)
% 176.84/27.51    (27)  all_58_10 = all_52_15
% 176.84/27.51    (28)   ~ (all_52_5 = all_4_2)
% 176.84/27.51    (29)  all_58_7 = all_52_19
% 176.84/27.51    (30)   ~ (all_52_17 = all_52_25)
% 176.84/27.51    (31)  op(e0, e1) = all_52_29
% 176.84/27.51    (32)  all_58_4 = all_52_5
% 176.84/27.51    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.51    (34)  all_34_1 = all_4_1
% 176.84/27.51    (35)   ~ (all_52_17 = all_14_2)
% 176.84/27.51    (36)  op(e3, all_4_2) = all_4_1
% 176.84/27.51    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.51    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.51    (39)   ~ (all_52_7 = all_4_2)
% 176.84/27.51    (40)  all_58_1 = all_52_3
% 176.84/27.51    (41)  all_58_0 = all_4_2
% 176.84/27.51    (42)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.51    (43)  op(all_4_1, all_4_2) = e1
% 176.84/27.51    (44)  op(e1, all_52_29) = all_52_28
% 176.84/27.51    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.84/27.51    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.51    (47)   ~ (all_4_1 = e2)
% 176.84/27.51    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.51    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.51    (50)  all_58_14 = all_52_29
% 176.84/27.51    (51)   ~ (all_52_3 = all_52_5)
% 176.84/27.51    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.51    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.51    (54)  all_58_8 = all_14_2
% 176.84/27.51    (55)  all_56_1 = all_52_3
% 176.84/27.51    (56)   ~ (all_14_0 = e3)
% 176.84/27.51    (57)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.84/27.51    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.51    (59)   ~ (all_52_5 = all_14_2)
% 176.84/27.51    (60)   ~ (all_52_3 = all_52_27)
% 176.84/27.51    (61)   ~ (all_52_3 = all_4_2)
% 176.84/27.51    (62)  op(e0, e3) = all_52_25
% 176.84/27.51    (63)  op(e1, all_14_2) = all_14_0
% 176.84/27.51    (64)   ~ (all_52_9 = all_52_13)
% 176.84/27.51    (65)   ~ (all_52_5 = all_52_29)
% 176.84/27.51    (66)  all_56_2 = all_52_5
% 176.84/27.51    (67)  op(e1, e0) = all_52_23
% 176.84/27.51    (68)  all_58_13 = all_52_27
% 176.84/27.51    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.51    (70)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.51    (71)   ~ (all_52_9 = all_52_17)
% 176.84/27.51    (72)  all_58_6 = all_52_17
% 176.84/27.51    (73)  op(e2, all_52_19) = e2
% 176.84/27.51    (74)  op(e3, all_52_17) = e3
% 176.84/27.51    (75)  all_56_0 = all_4_2
% 176.84/27.51    (76)  all_58_11 = all_52_23
% 176.84/27.51    (77)   ~ (all_52_3 = all_52_19)
% 176.84/27.51    (78)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.84/27.51    (79)   ~ (all_52_29 = all_14_2)
% 176.84/27.51    (80)   ~ (all_52_23 = all_6_2)
% 176.84/27.51    (81)   ~ (all_52_29 = all_6_2)
% 176.84/27.51    (82)  all_58_2 = all_52_9
% 176.84/27.51    (83)  op(e3, e1) = all_52_5
% 176.84/27.51    (84)   ~ (all_52_25 = all_6_2)
% 176.84/27.51    (85)  op(e1, e3) = all_52_17
% 176.84/27.51    (86)   ~ (all_52_25 = all_4_2)
% 176.84/27.51    (87)  op(e3, e0) = all_52_7
% 176.84/27.51    (88)  op(e3, e3) = all_4_2
% 176.84/27.51    (89)  all_56_8 = all_52_17
% 176.84/27.51    (90)   ~ (all_52_17 = all_4_2)
% 176.84/27.51    (91)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.51    (92)   ~ (all_52_25 = all_52_27)
% 176.84/27.51    (93)  all_34_2 = all_4_2
% 176.84/27.51    (94)   ~ (all_52_27 = all_6_2)
% 176.84/27.51    (95)   ~ (all_52_7 = all_6_2)
% 176.84/27.51    (96)  op(e0, all_52_23) = e0
% 176.84/27.51    (97)   ~ (all_52_19 = all_52_27)
% 176.84/27.51    (98)  op(e1, all_14_2) = e1
% 176.84/27.51    (99)   ~ (all_52_7 = all_52_23)
% 176.84/27.51    (100)   ~ (all_52_13 = all_10_2)
% 176.84/27.51    (101)   ~ (all_52_17 = all_52_19)
% 176.84/27.51    (102)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.51    (103)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.51    (104)  all_58_9 = all_52_7
% 176.84/27.51    (105)   ~ (e2 = e0)
% 176.84/27.51    (106)  all_58_12 = all_52_25
% 176.84/27.51    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.51    (108)   ~ (all_52_9 = all_52_15)
% 176.84/27.51    (109)   ~ (e3 = e2)
% 176.84/27.51    (110)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.51    (111)   ~ (all_52_19 = all_14_2)
% 176.84/27.51    (112)  op(e2, e3) = all_52_9
% 176.84/27.51  
% 176.84/27.51  Begin of proof
% 176.84/27.51  | 
% 176.84/27.51  | GROUND_INST: instantiating (91) with e1, all_14_0, all_14_2, e1, simplifying
% 176.84/27.51  |              with (63), (98) gives:
% 176.84/27.51  |   (113)  all_14_0 = e1
% 176.84/27.51  | 
% 176.84/27.51  | REDUCE: (56), (113) imply:
% 176.84/27.51  |   (114)   ~ (e3 = e1)
% 176.84/27.51  | 
% 176.84/27.51  | SIMP: (114) implies:
% 176.84/27.51  |   (115)   ~ (e3 = e1)
% 176.84/27.51  | 
% 176.84/27.51  | BETA: splitting (37) gives:
% 176.84/27.51  | 
% 176.84/27.51  | Case 1:
% 176.84/27.51  | | 
% 176.84/27.51  | |   (116)  all_56_15 = e3
% 176.84/27.51  | | 
% 176.84/27.51  | | COMBINE_EQS: (18), (116) imply:
% 176.84/27.51  | |   (117)  all_6_2 = e3
% 176.84/27.51  | | 
% 176.84/27.51  | | SIMP: (117) implies:
% 176.84/27.51  | |   (118)  all_6_2 = e3
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (80), (118) imply:
% 176.84/27.51  | |   (119)   ~ (all_52_23 = e3)
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (84), (118) imply:
% 176.84/27.51  | |   (120)   ~ (all_52_25 = e3)
% 176.84/27.51  | | 
% 176.84/27.51  | | REF_CLOSE: (22), (29), (33), (36), (38), (41), (43), (46), (52), (54), (59),
% 176.84/27.51  | |            (71), (72), (73), (74), (76), (82), (83), (85), (88), (90), (91),
% 176.84/27.51  | |            (98), (106), (107), (109), (112), (115), (119), (120) are
% 176.84/27.51  | |            inconsistent by sub-proof #569.
% 176.84/27.51  | | 
% 176.84/27.51  | Case 2:
% 176.84/27.51  | | 
% 176.84/27.51  | |   (121)   ~ (all_56_15 = e3)
% 176.84/27.51  | |   (122)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.51  | | 
% 176.84/27.51  | | REDUCE: (18), (121) imply:
% 176.84/27.51  | |   (123)   ~ (all_6_2 = e3)
% 176.84/27.51  | | 
% 176.84/27.51  | | BETA: splitting (53) gives:
% 176.84/27.51  | | 
% 176.84/27.51  | | Case 1:
% 176.84/27.51  | | | 
% 176.84/27.51  | | |   (124)  all_58_12 = e3
% 176.84/27.51  | | | 
% 176.84/27.51  | | | COMBINE_EQS: (106), (124) imply:
% 176.84/27.51  | | |   (125)  all_52_25 = e3
% 176.84/27.51  | | | 
% 176.84/27.51  | | | SIMP: (125) implies:
% 176.84/27.51  | | |   (126)  all_52_25 = e3
% 176.84/27.51  | | | 
% 176.84/27.51  | | | REDUCE: (8), (126) imply:
% 176.84/27.51  | | |   (127)   ~ (all_52_9 = e3)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | REDUCE: (30), (126) imply:
% 176.84/27.51  | | |   (128)   ~ (all_52_17 = e3)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | REDUCE: (86), (126) imply:
% 176.84/27.51  | | |   (129)   ~ (all_4_2 = e3)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | SIMP: (129) implies:
% 176.84/27.51  | | |   (130)   ~ (all_4_2 = e3)
% 176.84/27.51  | | | 
% 176.84/27.51  | | | BETA: splitting (23) gives:
% 176.84/27.51  | | | 
% 176.84/27.51  | | | Case 1:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (131)  all_56_0 = e3
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | COMBINE_EQS: (75), (131) imply:
% 176.84/27.51  | | | |   (132)  all_4_2 = e3
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | REDUCE: (130), (132) imply:
% 176.84/27.51  | | | |   (133)  $false
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | CLOSE: (133) is inconsistent.
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | Case 2:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | |   (134)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | BETA: splitting (69) gives:
% 176.84/27.51  | | | | 
% 176.84/27.51  | | | | Case 1:
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | |   (135)  all_58_0 = e1
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | COMBINE_EQS: (41), (135) imply:
% 176.84/27.51  | | | | |   (136)  all_4_2 = e1
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | REDUCE: (28), (136) imply:
% 176.84/27.51  | | | | |   (137)   ~ (all_52_5 = e1)
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | REDUCE: (39), (136) imply:
% 176.84/27.51  | | | | |   (138)   ~ (all_52_7 = e1)
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | REDUCE: (43), (136) imply:
% 176.84/27.51  | | | | |   (139)  op(all_4_1, e1) = e1
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | REDUCE: (36), (136) imply:
% 176.84/27.51  | | | | |   (140)  op(e3, e1) = all_4_1
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | GROUND_INST: instantiating (91) with all_52_5, all_4_1, e1, e3,
% 176.84/27.51  | | | | |              simplifying with (83), (140) gives:
% 176.84/27.51  | | | | |   (141)  all_52_5 = all_4_1
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | COMBINE_EQS: (66), (141) imply:
% 176.84/27.51  | | | | |   (142)  all_56_2 = all_4_1
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | REDUCE: (26), (141) imply:
% 176.84/27.51  | | | | |   (143)   ~ (all_52_7 = all_4_1)
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | SIMP: (143) implies:
% 176.84/27.51  | | | | |   (144)   ~ (all_52_7 = all_4_1)
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | REDUCE: (137), (141) imply:
% 176.84/27.51  | | | | |   (145)   ~ (all_4_1 = e1)
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | BETA: splitting (110) gives:
% 176.84/27.51  | | | | | 
% 176.84/27.51  | | | | | Case 1:
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | |   (146)  all_56_2 = e3
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | | COMBINE_EQS: (142), (146) imply:
% 176.84/27.51  | | | | | |   (147)  all_4_1 = e3
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | | SIMP: (147) implies:
% 176.84/27.51  | | | | | |   (148)  all_4_1 = e3
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | | REDUCE: (139), (148) imply:
% 176.84/27.51  | | | | | |   (149)  op(e3, e1) = e1
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | | REF_CLOSE: (83), (91), (137), (149) are inconsistent by sub-proof
% 176.84/27.51  | | | | | |            #627.
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | Case 2:
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | |   (150)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | | BETA: splitting (150) gives:
% 176.84/27.51  | | | | | | 
% 176.84/27.51  | | | | | | Case 1:
% 176.84/27.51  | | | | | | | 
% 176.84/27.51  | | | | | | |   (151)  all_56_2 = e2
% 176.84/27.51  | | | | | | | 
% 176.84/27.51  | | | | | | | REF_CLOSE: (47), (142), (151) are inconsistent by sub-proof #929.
% 176.84/27.51  | | | | | | | 
% 176.84/27.51  | | | | | | Case 2:
% 176.84/27.51  | | | | | | | 
% 176.84/27.51  | | | | | | |   (152)  all_56_2 = e1 | all_56_2 = e0
% 176.84/27.51  | | | | | | | 
% 176.84/27.51  | | | | | | | BETA: splitting (152) gives:
% 176.84/27.51  | | | | | | | 
% 176.84/27.51  | | | | | | | Case 1:
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | |   (153)  all_56_2 = e1
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | REF_CLOSE: (142), (145), (153) are inconsistent by sub-proof
% 176.84/27.51  | | | | | | | |            #723.
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | Case 2:
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | |   (154)  all_56_2 = e0
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | COMBINE_EQS: (142), (154) imply:
% 176.84/27.51  | | | | | | | |   (155)  all_4_1 = e0
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | SIMP: (155) implies:
% 176.84/27.51  | | | | | | | |   (156)  all_4_1 = e0
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | REDUCE: (144), (156) imply:
% 176.84/27.51  | | | | | | | |   (157)   ~ (all_52_7 = e0)
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | REDUCE: (139), (156) imply:
% 176.84/27.51  | | | | | | | |   (158)  op(e0, e1) = e1
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | GROUND_INST: instantiating (91) with all_52_29, e1, e1, e0,
% 176.84/27.51  | | | | | | | |              simplifying with (31), (158) gives:
% 176.84/27.51  | | | | | | | |   (159)  all_52_29 = e1
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | REDUCE: (81), (159) imply:
% 176.84/27.51  | | | | | | | |   (160)   ~ (all_6_2 = e1)
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | SIMP: (160) implies:
% 176.84/27.51  | | | | | | | |   (161)   ~ (all_6_2 = e1)
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | BETA: splitting (122) gives:
% 176.84/27.51  | | | | | | | | 
% 176.84/27.51  | | | | | | | | Case 1:
% 176.84/27.51  | | | | | | | | | 
% 176.84/27.51  | | | | | | | | |   (162)  all_56_15 = e2
% 176.84/27.51  | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | COMBINE_EQS: (18), (162) imply:
% 176.84/27.51  | | | | | | | | |   (163)  all_6_2 = e2
% 176.84/27.51  | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | SIMP: (163) implies:
% 176.84/27.51  | | | | | | | | |   (164)  all_6_2 = e2
% 176.84/27.51  | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | REDUCE: (95), (164) imply:
% 176.84/27.51  | | | | | | | | |   (165)   ~ (all_52_7 = e2)
% 176.84/27.51  | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | REDUCE: (80), (164) imply:
% 176.84/27.51  | | | | | | | | |   (166)   ~ (all_52_23 = e2)
% 176.84/27.51  | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | BETA: splitting (103) gives:
% 176.84/27.51  | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | Case 1:
% 176.84/27.51  | | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | |   (167)  all_56_3 = e3
% 176.84/27.51  | | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | | COMBINE_EQS: (6), (167) imply:
% 176.84/27.51  | | | | | | | | | |   (168)  all_52_7 = e3
% 176.84/27.51  | | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | | SIMP: (168) implies:
% 176.84/27.51  | | | | | | | | | |   (169)  all_52_7 = e3
% 176.84/27.51  | | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | | REDUCE: (99), (169) imply:
% 176.84/27.51  | | | | | | | | | |   (170)   ~ (all_52_23 = e3)
% 176.84/27.51  | | | | | | | | | | 
% 176.84/27.51  | | | | | | | | | | SIMP: (170) implies:
% 176.84/27.51  | | | | | | | | | |   (171)   ~ (all_52_23 = e3)
% 176.84/27.51  | | | | | | | | | | 
% 176.84/27.52  | | | | | | | | | | REF_CLOSE: (11), (22), (29), (33), (46), (54), (59), (70),
% 176.84/27.52  | | | | | | | | | |            (71), (72), (73), (74), (76), (83), (85), (91),
% 176.84/27.52  | | | | | | | | | |            (98), (112), (115), (127), (128), (166), (171) are
% 176.84/27.52  | | | | | | | | | |            inconsistent by sub-proof #712.
% 176.84/27.52  | | | | | | | | | | 
% 176.84/27.52  | | | | | | | | | Case 2:
% 176.84/27.52  | | | | | | | | | | 
% 176.84/27.52  | | | | | | | | | |   (172)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.52  | | | | | | | | | | 
% 176.84/27.52  | | | | | | | | | | REF_CLOSE: (6), (138), (157), (165), (172) are inconsistent
% 176.84/27.52  | | | | | | | | | |            by sub-proof #893.
% 176.84/27.52  | | | | | | | | | | 
% 176.84/27.52  | | | | | | | | | End of split
% 176.84/27.52  | | | | | | | | | 
% 176.84/27.52  | | | | | | | | Case 2:
% 176.84/27.52  | | | | | | | | | 
% 176.84/27.52  | | | | | | | | |   (173)  all_56_15 = e1 | all_56_15 = e0
% 176.84/27.52  | | | | | | | | | 
% 176.84/27.52  | | | | | | | | | REF_CLOSE: (16), (18), (161), (173) are inconsistent by
% 176.84/27.52  | | | | | | | | |            sub-proof #653.
% 176.84/27.52  | | | | | | | | | 
% 176.84/27.52  | | | | | | | | End of split
% 176.84/27.52  | | | | | | | | 
% 176.84/27.52  | | | | | | | End of split
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | End of split
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | End of split
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | Case 2:
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | |   (174)   ~ (all_58_0 = e1)
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | | REDUCE: (41), (174) imply:
% 176.84/27.52  | | | | |   (175)   ~ (all_4_2 = e1)
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | | REF_CLOSE: (6), (7), (11), (12), (19), (34), (36), (39), (41), (43),
% 176.84/27.52  | | | | |            (45), (47), (55), (61), (67), (75), (77), (87), (91), (93),
% 176.84/27.52  | | | | |            (99), (103), (115), (134), (175) are inconsistent by
% 176.84/27.52  | | | | |            sub-proof #587.
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | End of split
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | End of split
% 176.84/27.52  | | | 
% 176.84/27.52  | | Case 2:
% 176.84/27.52  | | | 
% 176.84/27.52  | | |   (176)   ~ (all_58_12 = e3)
% 176.84/27.52  | | |   (177)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REDUCE: (106), (176) imply:
% 176.84/27.52  | | |   (178)   ~ (all_52_25 = e3)
% 176.84/27.52  | | | 
% 176.84/27.52  | | | BETA: splitting (102) gives:
% 176.84/27.52  | | | 
% 176.84/27.52  | | | Case 1:
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | |   (179)  all_58_9 = e3
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | | COMBINE_EQS: (104), (179) imply:
% 176.84/27.52  | | | |   (180)  all_52_7 = e3
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | | SIMP: (180) implies:
% 176.84/27.52  | | | |   (181)  all_52_7 = e3
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | | REDUCE: (99), (181) imply:
% 176.84/27.52  | | | |   (182)   ~ (all_52_23 = e3)
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | | SIMP: (182) implies:
% 176.84/27.52  | | | |   (183)   ~ (all_52_23 = e3)
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | | REF_CLOSE: (22), (29), (33), (36), (38), (41), (43), (46), (52), (54),
% 176.84/27.52  | | | |            (59), (71), (72), (73), (74), (76), (82), (83), (85), (88),
% 176.84/27.52  | | | |            (90), (91), (98), (106), (107), (109), (112), (115), (178),
% 176.84/27.52  | | | |            (183) are inconsistent by sub-proof #569.
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | Case 2:
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | |   (184)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | | BETA: splitting (52) gives:
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | | Case 1:
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | |   (185)  all_58_0 = e3
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | | COMBINE_EQS: (41), (185) imply:
% 176.84/27.52  | | | | |   (186)  all_4_2 = e3
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | | REF_CLOSE: (36), (43), (88), (91), (115), (186) are inconsistent by
% 176.84/27.52  | | | | |            sub-proof #599.
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | Case 2:
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | |   (187)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | | BETA: splitting (187) gives:
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | | Case 1:
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | |   (188)  all_58_2 = e3
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | COMBINE_EQS: (82), (188) imply:
% 176.84/27.52  | | | | | |   (189)  all_52_9 = e3
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | SIMP: (189) implies:
% 176.84/27.52  | | | | | |   (190)  all_52_9 = e3
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | REDUCE: (108), (190) imply:
% 176.84/27.52  | | | | | |   (191)   ~ (all_52_15 = e3)
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | SIMP: (191) implies:
% 176.84/27.52  | | | | | |   (192)   ~ (all_52_15 = e3)
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | REDUCE: (13), (190) imply:
% 176.84/27.52  | | | | | |   (193)  op(e3, e3) = all_52_8
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | GROUND_INST: instantiating (91) with all_4_2, all_52_8, e3, e3,
% 176.84/27.52  | | | | | |              simplifying with (88), (193) gives:
% 176.84/27.52  | | | | | |   (194)  all_52_8 = all_4_2
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | BETA: splitting (49) gives:
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | Case 1:
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | |   (195)  all_58_1 = e3
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | | COMBINE_EQS: (40), (195) imply:
% 176.84/27.52  | | | | | | |   (196)  all_52_3 = e3
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | | REDUCE: (60), (196) imply:
% 176.84/27.52  | | | | | | |   (197)   ~ (all_52_27 = e3)
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | | SIMP: (197) implies:
% 176.84/27.52  | | | | | | |   (198)   ~ (all_52_27 = e3)
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (14), (15),
% 176.84/27.52  | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 176.84/27.52  | | | | | | |            (27), (28), (29), (30), (32), (33), (35), (36), (38),
% 176.84/27.52  | | | | | | |            (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 176.84/27.52  | | | | | | |            (49), (50), (51), (52), (54), (57), (58), (59), (61),
% 176.84/27.52  | | | | | | |            (62), (64), (65), (68), (71), (72), (73), (74), (75),
% 176.84/27.52  | | | | | | |            (76), (77), (78), (79), (80), (82), (83), (84), (85),
% 176.84/27.52  | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94), (95),
% 176.84/27.52  | | | | | | |            (96), (97), (98), (99), (100), (101), (104), (106),
% 176.84/27.52  | | | | | | |            (107), (109), (111), (112), (115), (122), (123), (177),
% 176.84/27.52  | | | | | | |            (198) are inconsistent by sub-proof #562.
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | Case 2:
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | |   (199)   ~ (all_58_1 = e3)
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | | REDUCE: (40), (199) imply:
% 176.84/27.52  | | | | | | |   (200)   ~ (all_52_3 = e3)
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | | REF_CLOSE: (7), (11), (12), (19), (24), (27), (34), (36), (41),
% 176.84/27.52  | | | | | | |            (43), (45), (55), (61), (62), (72), (74), (76), (77),
% 176.84/27.52  | | | | | | |            (91), (93), (96), (105), (106), (109), (115), (123),
% 176.84/27.52  | | | | | | |            (184), (188), (192), (200) are inconsistent by
% 176.84/27.52  | | | | | | |            sub-proof #566.
% 176.84/27.52  | | | | | | | 
% 176.84/27.52  | | | | | | End of split
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | Case 2:
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | |   (201)  all_58_6 = e3 | all_58_12 = e3
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | | REF_CLOSE: (72), (74), (88), (90), (91), (106), (178), (201) are
% 176.84/27.52  | | | | | |            inconsistent by sub-proof #947.
% 176.84/27.52  | | | | | | 
% 176.84/27.52  | | | | | End of split
% 176.84/27.52  | | | | | 
% 176.84/27.52  | | | | End of split
% 176.84/27.52  | | | | 
% 176.84/27.52  | | | End of split
% 176.84/27.52  | | | 
% 176.84/27.52  | | End of split
% 176.84/27.52  | | 
% 176.84/27.52  | End of split
% 176.84/27.52  | 
% 176.84/27.52  End of proof
% 176.84/27.52  
% 176.84/27.52  Sub-proof #274 shows that the following formulas are inconsistent:
% 176.84/27.52  ----------------------------------------------------------------
% 176.84/27.52    (1)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.84/27.52    (2)  all_52_10 = e3
% 176.84/27.52    (3)   ~ (e3 = e2)
% 176.84/27.52  
% 176.84/27.52  Begin of proof
% 176.84/27.52  | 
% 176.84/27.52  | ALPHA: (1) implies:
% 176.84/27.52  |   (4)  all_52_10 = e2
% 176.84/27.52  | 
% 176.84/27.52  | COMBINE_EQS: (2), (4) imply:
% 176.84/27.52  |   (5)  e3 = e2
% 176.84/27.52  | 
% 176.84/27.52  | SIMP: (5) implies:
% 176.84/27.52  |   (6)  e3 = e2
% 176.84/27.52  | 
% 176.84/27.52  | REDUCE: (3), (6) imply:
% 176.84/27.52  |   (7)  $false
% 176.84/27.52  | 
% 176.84/27.52  | CLOSE: (7) is inconsistent.
% 176.84/27.52  | 
% 176.84/27.52  End of proof
% 176.84/27.52  
% 176.84/27.52  Sub-proof #275 shows that the following formulas are inconsistent:
% 176.84/27.52  ----------------------------------------------------------------
% 176.84/27.52    (1)  all_52_10 = e3
% 176.84/27.52    (2)   ~ (all_52_23 = all_14_2)
% 176.84/27.52    (3)   ~ (all_52_5 = all_52_13)
% 176.84/27.52    (4)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.52    (5)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.52    (6)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.84/27.52    (7)   ~ (all_52_27 = all_10_2)
% 176.84/27.52    (8)   ~ (all_52_17 = all_52_23)
% 176.84/27.52    (9)   ~ (all_6_0 = e3)
% 176.84/27.52    (10)  all_40_2 = all_4_2
% 176.84/27.52    (11)   ~ (all_52_13 = all_52_29)
% 176.84/27.52    (12)  all_56_3 = all_52_7
% 176.84/27.52    (13)  op(e3, e2) = all_52_3
% 176.84/27.52    (14)   ~ (all_52_9 = all_52_25)
% 176.84/27.52    (15)  op(e3, all_52_25) = all_52_24
% 176.84/27.52    (16)   ~ (all_52_19 = all_52_23)
% 176.84/27.52    (17)  all_56_11 = all_52_23
% 176.84/27.52    (18)  op(e1, e2) = all_52_19
% 176.84/27.52    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.84/27.52    (20)  op(e3, all_52_9) = all_52_8
% 176.84/27.52    (21)   ~ (all_52_3 = all_10_2)
% 176.84/27.52    (22)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.52    (23)  all_58_5 = all_52_13
% 176.84/27.52    (24)   ~ (all_52_25 = all_52_29)
% 176.84/27.52    (25)  all_56_15 = all_6_2
% 176.84/27.52    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.52    (27)  op(e2, e0) = all_52_15
% 176.84/27.52    (28)  op(all_14_1, all_14_2) = all_14_0
% 176.84/27.52    (29)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.84/27.52    (30)  all_58_3 = all_10_2
% 176.84/27.52    (31)  all_56_9 = all_52_19
% 176.84/27.52    (32)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.52    (33)  all_58_15 = all_6_2
% 176.84/27.52    (34)   ~ (all_52_9 = all_4_2)
% 176.84/27.52    (35)   ~ (all_52_5 = all_52_7)
% 176.84/27.52    (36)  all_58_10 = all_52_15
% 176.84/27.52    (37)   ~ (all_52_5 = all_4_2)
% 176.84/27.52    (38)  all_58_7 = all_52_19
% 176.84/27.52    (39)   ~ (all_52_17 = all_52_25)
% 176.84/27.52    (40)  op(e0, e1) = all_52_29
% 176.84/27.52    (41)   ~ (all_4_0 = e2)
% 176.84/27.52    (42)  all_58_4 = all_52_5
% 176.84/27.52    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.52    (44)   ~ (e3 = e1)
% 176.84/27.52    (45)   ~ (all_52_27 = all_52_29)
% 176.84/27.52    (46)   ~ (all_52_17 = all_14_2)
% 176.84/27.52    (47)  op(e3, all_4_2) = all_4_1
% 176.84/27.52    (48)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.52    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.52    (50)   ~ (all_52_7 = all_4_2)
% 176.84/27.52    (51)  all_58_1 = all_52_3
% 176.84/27.52    (52)   ~ (all_52_13 = all_52_15)
% 176.84/27.52    (53)  all_58_0 = all_4_2
% 176.84/27.52    (54)  op(e1, all_52_29) = all_52_28
% 176.84/27.52    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.52    (56)   ~ (all_4_1 = e2)
% 176.84/27.52    (57)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.52    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.52    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.52    (60)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.84/27.52    (61)  all_58_14 = all_52_29
% 176.84/27.52    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.52    (63)   ~ (all_52_3 = all_52_5)
% 176.84/27.52    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.52    (65)  op(e2, e1) = all_52_13
% 176.84/27.52    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.52    (67)  all_58_8 = all_14_2
% 176.84/27.52    (68)  op(e0, e2) = all_52_27
% 176.84/27.52    (69)  all_56_14 = all_52_29
% 176.84/27.52    (70)   ~ (all_14_0 = e3)
% 176.84/27.52    (71)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.84/27.52    (72)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.84/27.52    (73)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.52    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.52    (75)   ~ (all_52_5 = all_14_2)
% 176.84/27.52    (76)   ~ (all_52_3 = all_52_27)
% 176.84/27.52    (77)   ~ (all_52_3 = all_4_2)
% 176.84/27.52    (78)  op(all_6_1, all_6_2) = all_6_0
% 176.84/27.52    (79)  op(e0, e3) = all_52_25
% 176.84/27.52    (80)  op(e0, all_6_2) = all_6_1
% 176.84/27.52    (81)  all_52_0 = all_4_1
% 176.84/27.52    (82)   ~ (all_52_9 = all_10_2)
% 176.84/27.52    (83)  op(e3, all_52_17) = all_52_16
% 176.84/27.52    (84)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.52    (85)   ~ (all_52_13 = all_14_2)
% 176.84/27.52    (86)   ~ (e3 = e0)
% 176.84/27.52    (87)  all_40_0 = all_4_0
% 176.84/27.52    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.52    (89)   ~ (all_52_9 = all_52_13)
% 176.84/27.52    (90)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.52    (91)  op(e0, all_52_23) = all_52_22
% 176.84/27.52    (92)   ~ (all_52_15 = all_52_23)
% 176.84/27.52    (93)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.84/27.52    (94)   ~ (all_52_5 = all_52_29)
% 176.84/27.52    (95)  all_56_2 = all_52_5
% 176.84/27.52    (96)  op(e1, e0) = all_52_23
% 176.84/27.52    (97)  all_56_12 = all_52_25
% 176.84/27.52    (98)  all_58_13 = all_52_27
% 176.84/27.52    (99)  all_4_1 = e1
% 176.84/27.52    (100)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.52    (101)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.52    (102)   ~ (all_52_9 = all_52_17)
% 176.84/27.52    (103)   ~ (all_14_0 = e2)
% 176.84/27.52    (104)  all_58_6 = all_52_17
% 176.84/27.52    (105)   ~ (all_52_3 = all_52_7)
% 176.84/27.52    (106)  op(e2, all_52_19) = all_52_18
% 176.84/27.52    (107)   ~ (e1 = e0)
% 176.84/27.52    (108)  all_56_0 = all_4_2
% 176.84/27.52    (109)  all_58_11 = all_52_23
% 176.84/27.52    (110)   ~ (all_52_3 = all_52_19)
% 176.84/27.52    (111)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.84/27.52    (112)   ~ (all_52_7 = all_52_15)
% 176.84/27.52    (113)   ~ (all_52_29 = all_14_2)
% 176.84/27.52    (114)   ~ (all_4_0 = e1)
% 176.84/27.52    (115)   ~ (all_52_19 = all_10_2)
% 176.84/27.52    (116)   ~ (all_52_23 = all_6_2)
% 176.84/27.52    (117)   ~ (all_6_0 = e2)
% 176.84/27.52    (118)   ~ (all_52_29 = all_6_2)
% 176.84/27.52    (119)  all_58_2 = all_52_9
% 176.84/27.52    (120)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.84/27.52    (121)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.84/27.52    (122)  op(e3, e1) = all_52_5
% 176.84/27.52    (123)  all_56_10 = all_14_2
% 176.84/27.52    (124)   ~ (all_52_25 = all_6_2)
% 176.84/27.52    (125)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.84/27.52    (126)  op(e1, e3) = all_52_17
% 176.84/27.52    (127)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.52    (128)   ~ (all_52_25 = all_4_2)
% 176.84/27.52    (129)  op(e3, e0) = all_52_7
% 176.84/27.52    (130)  op(e3, e3) = all_4_2
% 176.84/27.52    (131)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 176.84/27.52             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 176.84/27.52    (132)  all_56_8 = all_52_17
% 176.84/27.52    (133)   ~ (all_52_17 = all_4_2)
% 176.84/27.52    (134)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.52             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.52    (135)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.84/27.52           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.84/27.52           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.84/27.52           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.84/27.52    (136)   ~ (all_52_25 = all_52_27)
% 176.84/27.52    (137)   ~ (all_52_27 = all_6_2)
% 176.84/27.52    (138)   ~ (all_52_7 = all_6_2)
% 176.84/27.52    (139)   ~ (all_52_15 = all_10_2)
% 176.84/27.52    (140)   ~ (all_52_19 = all_52_27)
% 176.84/27.52    (141)  all_56_7 = all_52_15
% 176.84/27.52    (142)   ~ (all_52_7 = all_52_23)
% 176.84/27.52    (143)   ~ (all_52_13 = all_10_2)
% 176.84/27.52    (144)   ~ (all_6_0 = e1)
% 176.84/27.52    (145)  op(e2, all_52_27) = all_52_26
% 176.84/27.52    (146)  all_52_20 = all_14_1
% 176.84/27.52    (147)   ~ (all_52_17 = all_52_19)
% 176.84/27.52    (148)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.52    (149)  all_52_30 = all_6_1
% 176.84/27.52    (150)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.52    (151)  op(e2, all_10_2) = e3
% 176.84/27.52    (152)  op(e1, all_14_2) = all_14_1
% 176.84/27.52    (153)  all_58_9 = all_52_7
% 176.84/27.52    (154)   ~ (e2 = e0)
% 176.84/27.52    (155)  all_58_12 = all_52_25
% 176.84/27.52    (156)  all_56_6 = all_52_13
% 176.84/27.52    (157)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.52    (158)   ~ (all_52_9 = all_52_15)
% 176.84/27.52    (159)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.52    (160)   ~ (e3 = e2)
% 176.84/27.52    (161)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.52    (162)   ~ (all_52_19 = all_14_2)
% 176.84/27.52    (163)  op(e2, e3) = all_52_9
% 176.84/27.52    (164)  all_56_13 = all_52_27
% 176.84/27.52  
% 176.84/27.52  Begin of proof
% 176.84/27.52  | 
% 176.84/27.52  | COMBINE_EQS: (81), (99) imply:
% 176.84/27.52  |   (165)  all_52_0 = e1
% 176.84/27.52  | 
% 176.84/27.52  | REDUCE: (56), (99) imply:
% 176.84/27.52  |   (166)   ~ (e2 = e1)
% 176.84/27.52  | 
% 176.84/27.52  | SIMP: (166) implies:
% 176.84/27.52  |   (167)   ~ (e2 = e1)
% 176.84/27.52  | 
% 176.84/27.52  | REDUCE: (73), (99) imply:
% 176.84/27.52  |   (168)  op(e1, all_4_2) = all_4_0
% 176.84/27.52  | 
% 176.84/27.52  | REDUCE: (47), (99) imply:
% 176.84/27.52  |   (169)  op(e3, all_4_2) = e1
% 176.84/27.52  | 
% 176.84/27.52  | BETA: splitting (135) gives:
% 176.84/27.52  | 
% 176.84/27.52  | Case 1:
% 176.84/27.52  | | 
% 176.84/27.52  | |   (170)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.84/27.52  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.84/27.52  | | 
% 176.84/27.52  | | BETA: splitting (170) gives:
% 176.84/27.52  | | 
% 176.84/27.52  | | Case 1:
% 176.84/27.52  | | | 
% 176.84/27.52  | | |   (171)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REF_CLOSE: (44), (165), (171) are inconsistent by sub-proof #632.
% 176.84/27.52  | | | 
% 176.84/27.52  | | Case 2:
% 176.84/27.52  | | | 
% 176.84/27.52  | | |   (172)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REF_CLOSE: (1), (160), (172) are inconsistent by sub-proof #289.
% 176.84/27.52  | | | 
% 176.84/27.52  | | End of split
% 176.84/27.52  | | 
% 176.84/27.52  | Case 2:
% 176.84/27.52  | | 
% 176.84/27.52  | |   (173)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 176.84/27.52  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 176.84/27.52  | |            e0)
% 176.84/27.52  | | 
% 176.84/27.52  | | BETA: splitting (173) gives:
% 176.84/27.52  | | 
% 176.84/27.52  | | Case 1:
% 176.84/27.52  | | | 
% 176.84/27.52  | | |   (174)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.84/27.52  | | | 
% 176.84/27.52  | | | ALPHA: (174) implies:
% 176.84/27.52  | | |   (175)  all_52_22 = e0
% 176.84/27.52  | | |   (176)  all_52_20 = e1
% 176.84/27.52  | | |   (177)  all_52_18 = e2
% 176.84/27.52  | | |   (178)  all_52_16 = e3
% 176.84/27.52  | | | 
% 176.84/27.52  | | | COMBINE_EQS: (146), (176) imply:
% 176.84/27.52  | | |   (179)  all_14_1 = e1
% 176.84/27.52  | | | 
% 176.84/27.52  | | | SIMP: (179) implies:
% 176.84/27.52  | | |   (180)  all_14_1 = e1
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REDUCE: (28), (180) imply:
% 176.84/27.52  | | |   (181)  op(e1, all_14_2) = all_14_0
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REDUCE: (83), (178) imply:
% 176.84/27.52  | | |   (182)  op(e3, all_52_17) = e3
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REDUCE: (106), (177) imply:
% 176.84/27.52  | | |   (183)  op(e2, all_52_19) = e2
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REDUCE: (152), (180) imply:
% 176.84/27.52  | | |   (184)  op(e1, all_14_2) = e1
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REDUCE: (91), (175) imply:
% 176.84/27.52  | | |   (185)  op(e0, all_52_23) = e0
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (13), (14), (15),
% 176.84/27.52  | | |            (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 176.84/27.52  | | |            (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 176.84/27.52  | | |            (38), (39), (40), (41), (42), (43), (45), (46), (47), (48),
% 176.84/27.52  | | |            (49), (50), (51), (53), (54), (55), (56), (57), (58), (59),
% 176.84/27.52  | | |            (60), (61), (62), (63), (64), (66), (67), (68), (69), (70),
% 176.84/27.52  | | |            (71), (72), (73), (74), (75), (76), (77), (79), (82), (84),
% 176.84/27.52  | | |            (85), (86), (87), (88), (89), (90), (92), (93), (94), (95),
% 176.84/27.52  | | |            (97), (98), (100), (101), (102), (103), (104), (105), (107),
% 176.84/27.52  | | |            (108), (109), (110), (111), (112), (113), (114), (115), (116),
% 176.84/27.52  | | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 176.84/27.52  | | |            (127), (128), (129), (130), (131), (132), (133), (134), (136),
% 176.84/27.52  | | |            (137), (138), (139), (140), (141), (142), (143), (147), (148),
% 176.84/27.52  | | |            (151), (153), (154), (155), (156), (157), (158), (159), (160),
% 176.84/27.52  | | |            (161), (162), (163), (164), (168), (169), (181), (182), (183),
% 176.84/27.52  | | |            (184), (185) are inconsistent by sub-proof #277.
% 176.84/27.52  | | | 
% 176.84/27.52  | | Case 2:
% 176.84/27.52  | | | 
% 176.84/27.52  | | |   (186)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.84/27.52  | | | 
% 176.84/27.52  | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 176.84/27.52  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 176.84/27.52  | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 176.84/27.52  | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 176.84/27.52  | | |            (49), (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 176.84/27.52  | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 176.84/27.52  | | |            (73), (76), (77), (78), (79), (80), (82), (83), (84), (85),
% 176.84/27.52  | | |            (87), (88), (89), (90), (94), (95), (96), (97), (98), (100),
% 176.84/27.52  | | |            (101), (102), (104), (105), (108), (109), (110), (112), (113),
% 176.84/27.52  | | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 176.84/27.52  | | |            (124), (125), (126), (127), (128), (129), (130), (131), (133),
% 176.84/27.52  | | |            (134), (136), (137), (138), (139), (140), (141), (142), (144),
% 176.84/27.52  | | |            (145), (147), (148), (149), (150), (153), (155), (157), (158),
% 176.84/27.52  | | |            (159), (160), (161), (163), (164), (167), (168), (169), (186)
% 176.84/27.52  | | |            are inconsistent by sub-proof #276.
% 176.84/27.52  | | | 
% 176.84/27.52  | | End of split
% 176.84/27.52  | | 
% 176.84/27.52  | End of split
% 176.84/27.52  | 
% 176.84/27.52  End of proof
% 176.84/27.52  
% 176.84/27.52  Sub-proof #276 shows that the following formulas are inconsistent:
% 176.84/27.52  ----------------------------------------------------------------
% 176.84/27.52    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.52    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.84/27.52    (3)   ~ (all_52_27 = all_10_2)
% 176.84/27.52    (4)   ~ (all_52_17 = all_52_23)
% 176.84/27.52    (5)   ~ (all_6_0 = e3)
% 176.84/27.52    (6)  all_40_2 = all_4_2
% 176.84/27.52    (7)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.84/27.52    (8)   ~ (all_52_13 = all_52_29)
% 176.84/27.52    (9)  all_56_3 = all_52_7
% 176.84/27.52    (10)  op(e3, e2) = all_52_3
% 176.84/27.52    (11)   ~ (all_52_9 = all_52_25)
% 176.84/27.52    (12)  op(e3, all_52_25) = all_52_24
% 176.84/27.52    (13)   ~ (all_52_19 = all_52_23)
% 176.84/27.52    (14)  all_56_11 = all_52_23
% 176.84/27.52    (15)  op(e1, e2) = all_52_19
% 176.84/27.52    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 176.84/27.52    (17)  op(e3, all_52_9) = all_52_8
% 176.84/27.52    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.52    (19)  all_58_5 = all_52_13
% 176.84/27.52    (20)   ~ (all_52_25 = all_52_29)
% 176.84/27.52    (21)  all_56_15 = all_6_2
% 176.84/27.52    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.52    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.84/27.52    (24)  all_58_3 = all_10_2
% 176.84/27.52    (25)  all_56_9 = all_52_19
% 176.84/27.52    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.52    (27)  all_58_15 = all_6_2
% 176.84/27.52    (28)   ~ (all_52_9 = all_4_2)
% 176.84/27.52    (29)   ~ (all_52_5 = all_52_7)
% 176.84/27.52    (30)  all_58_10 = all_52_15
% 176.84/27.52    (31)   ~ (all_52_5 = all_4_2)
% 176.84/27.52    (32)  all_58_7 = all_52_19
% 176.84/27.52    (33)   ~ (all_52_17 = all_52_25)
% 176.84/27.52    (34)  op(e0, e1) = all_52_29
% 176.84/27.52    (35)   ~ (all_4_0 = e2)
% 176.84/27.52    (36)  all_58_4 = all_52_5
% 176.84/27.52    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.52    (38)   ~ (e3 = e1)
% 176.84/27.52    (39)   ~ (all_52_27 = all_52_29)
% 176.84/27.52    (40)   ~ (all_52_17 = all_14_2)
% 176.84/27.52    (41)  op(e3, all_4_2) = all_4_1
% 176.84/27.52    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.52    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.52    (44)   ~ (all_52_7 = all_4_2)
% 176.84/27.52    (45)  all_58_1 = all_52_3
% 176.84/27.52    (46)   ~ (all_52_13 = all_52_15)
% 176.84/27.53    (47)  all_58_0 = all_4_2
% 176.84/27.53    (48)  op(e1, all_52_29) = all_52_28
% 176.84/27.53    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.53    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.53    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.53    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.53    (53)  all_58_14 = all_52_29
% 176.84/27.53    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.53    (55)   ~ (all_52_3 = all_52_5)
% 176.84/27.53    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.53    (57)  op(e2, e1) = all_52_13
% 176.84/27.53    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.53    (59)  all_58_8 = all_14_2
% 176.84/27.53    (60)  op(e0, e2) = all_52_27
% 176.84/27.53    (61)  all_56_14 = all_52_29
% 176.84/27.53    (62)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.84/27.53    (63)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.53    (64)   ~ (all_52_3 = all_52_27)
% 176.84/27.53    (65)   ~ (all_52_3 = all_4_2)
% 176.84/27.53    (66)  op(all_6_1, all_6_2) = all_6_0
% 176.84/27.53    (67)  op(e0, e3) = all_52_25
% 176.84/27.53    (68)  op(e0, all_6_2) = all_6_1
% 176.84/27.53    (69)   ~ (all_52_9 = all_10_2)
% 176.84/27.53    (70)  op(e3, all_52_17) = all_52_16
% 176.84/27.53    (71)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.53    (72)   ~ (all_52_13 = all_14_2)
% 176.84/27.53    (73)  all_40_0 = all_4_0
% 176.84/27.53    (74)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.53    (75)   ~ (all_52_9 = all_52_13)
% 176.84/27.53    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.53    (77)   ~ (all_52_5 = all_52_29)
% 176.84/27.53    (78)  all_56_2 = all_52_5
% 176.84/27.53    (79)  op(e1, e0) = all_52_23
% 176.84/27.53    (80)  all_56_12 = all_52_25
% 176.84/27.53    (81)  all_58_13 = all_52_27
% 176.84/27.53    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.53    (83)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.53    (84)   ~ (all_52_9 = all_52_17)
% 176.84/27.53    (85)  all_58_6 = all_52_17
% 176.84/27.53    (86)   ~ (all_52_3 = all_52_7)
% 176.84/27.53    (87)  all_56_0 = all_4_2
% 176.84/27.53    (88)  all_58_11 = all_52_23
% 176.84/27.53    (89)   ~ (all_52_3 = all_52_19)
% 176.84/27.53    (90)   ~ (all_52_7 = all_52_15)
% 176.84/27.53    (91)   ~ (all_52_29 = all_14_2)
% 176.84/27.53    (92)   ~ (all_4_0 = e1)
% 176.84/27.53    (93)   ~ (all_52_19 = all_10_2)
% 176.84/27.53    (94)   ~ (all_52_23 = all_6_2)
% 176.84/27.53    (95)  op(e1, all_4_2) = all_4_0
% 176.84/27.53    (96)   ~ (all_6_0 = e2)
% 176.84/27.53    (97)   ~ (all_52_29 = all_6_2)
% 176.84/27.53    (98)  all_58_2 = all_52_9
% 176.84/27.53    (99)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.84/27.53    (100)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.84/27.53    (101)  op(e3, e1) = all_52_5
% 176.84/27.53    (102)   ~ (e2 = e1)
% 176.84/27.53    (103)   ~ (all_52_25 = all_6_2)
% 176.84/27.53    (104)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.84/27.53    (105)  op(e1, e3) = all_52_17
% 176.84/27.53    (106)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.53    (107)   ~ (all_52_25 = all_4_2)
% 176.84/27.53    (108)  op(e3, e0) = all_52_7
% 176.84/27.53    (109)  op(e3, e3) = all_4_2
% 176.84/27.53    (110)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 176.84/27.53             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 176.84/27.53    (111)   ~ (all_52_17 = all_4_2)
% 176.84/27.53    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.53             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.53    (113)   ~ (all_52_25 = all_52_27)
% 176.84/27.53    (114)   ~ (all_52_27 = all_6_2)
% 176.84/27.53    (115)   ~ (all_52_7 = all_6_2)
% 176.84/27.53    (116)   ~ (all_52_15 = all_10_2)
% 176.84/27.53    (117)   ~ (all_52_19 = all_52_27)
% 176.84/27.53    (118)  all_56_7 = all_52_15
% 176.84/27.53    (119)   ~ (all_52_7 = all_52_23)
% 176.84/27.53    (120)   ~ (all_6_0 = e1)
% 176.84/27.53    (121)  op(e2, all_52_27) = all_52_26
% 176.84/27.53    (122)   ~ (all_52_17 = all_52_19)
% 176.84/27.53    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.53    (124)  all_52_30 = all_6_1
% 176.84/27.53    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.53    (126)  all_58_9 = all_52_7
% 176.84/27.53    (127)  all_58_12 = all_52_25
% 176.84/27.53    (128)  op(e3, all_4_2) = e1
% 176.84/27.53    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.53    (130)   ~ (all_52_9 = all_52_15)
% 176.84/27.53    (131)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.53    (132)   ~ (e3 = e2)
% 176.84/27.53    (133)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.53    (134)  op(e2, e3) = all_52_9
% 176.84/27.53    (135)  all_56_13 = all_52_27
% 176.84/27.53  
% 176.84/27.53  Begin of proof
% 176.84/27.53  | 
% 176.84/27.53  | ALPHA: (7) implies:
% 176.84/27.53  |   (136)  all_52_30 = e0
% 176.84/27.53  |   (137)  all_52_28 = e1
% 176.84/27.53  |   (138)  all_52_26 = e2
% 176.84/27.53  |   (139)  all_52_24 = e3
% 176.84/27.53  | 
% 176.84/27.53  | COMBINE_EQS: (124), (136) imply:
% 176.84/27.53  |   (140)  all_6_1 = e0
% 176.84/27.53  | 
% 176.84/27.53  | SIMP: (140) implies:
% 176.84/27.53  |   (141)  all_6_1 = e0
% 176.84/27.53  | 
% 176.84/27.53  | REDUCE: (66), (141) imply:
% 176.84/27.53  |   (142)  op(e0, all_6_2) = all_6_0
% 176.84/27.53  | 
% 176.84/27.53  | REDUCE: (12), (139) imply:
% 176.84/27.53  |   (143)  op(e3, all_52_25) = e3
% 176.84/27.53  | 
% 176.84/27.53  | REDUCE: (121), (138) imply:
% 176.84/27.53  |   (144)  op(e2, all_52_27) = e2
% 176.84/27.53  | 
% 176.84/27.53  | REDUCE: (48), (137) imply:
% 176.84/27.53  |   (145)  op(e1, all_52_29) = e1
% 176.84/27.53  | 
% 176.84/27.53  | REDUCE: (68), (141) imply:
% 176.84/27.53  |   (146)  op(e0, all_6_2) = e0
% 176.84/27.53  | 
% 176.84/27.53  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 176.84/27.53  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 176.84/27.53  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 176.84/27.53  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 176.84/27.53  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 176.84/27.53  |            (60), (61), (62), (63), (64), (65), (67), (69), (70), (71), (72),
% 176.84/27.53  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 176.84/27.53  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 176.84/27.53  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 176.84/27.53  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 176.84/27.53  |            (114), (115), (116), (117), (118), (119), (120), (122), (123),
% 176.84/27.53  |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 176.84/27.53  |            (134), (135), (142), (143), (144), (145), (146) are inconsistent by
% 176.84/27.53  |            sub-proof #529.
% 176.84/27.53  | 
% 176.84/27.53  End of proof
% 176.84/27.53  
% 176.84/27.53  Sub-proof #277 shows that the following formulas are inconsistent:
% 176.84/27.53  ----------------------------------------------------------------
% 176.84/27.53    (1)   ~ (all_52_23 = all_14_2)
% 176.84/27.53    (2)   ~ (all_52_5 = all_52_13)
% 176.84/27.53    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.53    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.53    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.84/27.53    (6)   ~ (all_52_17 = all_52_23)
% 176.84/27.53    (7)  all_40_2 = all_4_2
% 176.84/27.53    (8)   ~ (all_52_13 = all_52_29)
% 176.84/27.53    (9)  op(e3, e2) = all_52_3
% 176.84/27.53    (10)   ~ (all_52_9 = all_52_25)
% 176.84/27.53    (11)  op(e3, all_52_25) = all_52_24
% 176.84/27.53    (12)   ~ (all_52_19 = all_52_23)
% 176.84/27.53    (13)  all_56_11 = all_52_23
% 176.84/27.53    (14)  op(e1, e2) = all_52_19
% 176.84/27.53    (15)  op(e3, all_52_9) = all_52_8
% 176.84/27.53    (16)   ~ (all_52_3 = all_10_2)
% 176.84/27.53    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.53    (18)  all_58_5 = all_52_13
% 176.84/27.53    (19)   ~ (all_52_25 = all_52_29)
% 176.84/27.53    (20)  all_56_15 = all_6_2
% 176.84/27.53    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.53    (22)  op(e2, e0) = all_52_15
% 176.84/27.53    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.84/27.53    (24)  all_58_3 = all_10_2
% 176.84/27.53    (25)  all_56_9 = all_52_19
% 176.84/27.53    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.53    (27)  all_58_15 = all_6_2
% 176.84/27.53    (28)   ~ (all_52_9 = all_4_2)
% 176.84/27.53    (29)   ~ (all_52_5 = all_52_7)
% 176.84/27.53    (30)  all_58_10 = all_52_15
% 176.84/27.53    (31)   ~ (all_52_5 = all_4_2)
% 176.84/27.53    (32)  all_58_7 = all_52_19
% 176.84/27.53    (33)   ~ (all_52_17 = all_52_25)
% 176.84/27.53    (34)  op(e0, e1) = all_52_29
% 176.84/27.53    (35)   ~ (all_4_0 = e2)
% 176.84/27.53    (36)  all_58_4 = all_52_5
% 176.84/27.53    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.53    (38)   ~ (all_52_27 = all_52_29)
% 176.84/27.53    (39)   ~ (all_52_17 = all_14_2)
% 176.84/27.53    (40)  op(e3, all_4_2) = all_4_1
% 176.84/27.53    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.53    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.53    (43)   ~ (all_52_7 = all_4_2)
% 176.84/27.53    (44)  all_58_1 = all_52_3
% 176.84/27.53    (45)  all_58_0 = all_4_2
% 176.84/27.53    (46)  op(e1, all_52_29) = all_52_28
% 176.84/27.53    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.53    (48)   ~ (all_4_1 = e2)
% 176.84/27.53    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.53    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.53    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.53    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.84/27.53    (53)  all_58_14 = all_52_29
% 176.84/27.53    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.53    (55)   ~ (all_52_3 = all_52_5)
% 176.84/27.53    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.53    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.53    (58)  all_58_8 = all_14_2
% 176.84/27.53    (59)  op(e0, e2) = all_52_27
% 176.84/27.53    (60)  all_56_14 = all_52_29
% 176.84/27.53    (61)   ~ (all_14_0 = e3)
% 176.84/27.53    (62)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.84/27.53    (63)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.84/27.53    (64)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.53    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.53    (66)   ~ (all_52_5 = all_14_2)
% 176.84/27.53    (67)   ~ (all_52_3 = all_52_27)
% 176.84/27.53    (68)   ~ (all_52_3 = all_4_2)
% 176.84/27.53    (69)  op(e0, e3) = all_52_25
% 176.84/27.53    (70)   ~ (all_52_9 = all_10_2)
% 176.84/27.53    (71)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.53    (72)   ~ (all_52_13 = all_14_2)
% 176.84/27.53    (73)  op(e1, all_14_2) = all_14_0
% 176.84/27.53    (74)   ~ (e3 = e0)
% 176.84/27.53    (75)  all_40_0 = all_4_0
% 176.84/27.53    (76)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.53    (77)   ~ (all_52_9 = all_52_13)
% 176.84/27.53    (78)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.53    (79)   ~ (all_52_15 = all_52_23)
% 176.84/27.53    (80)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.84/27.53    (81)   ~ (all_52_5 = all_52_29)
% 176.84/27.53    (82)  all_56_2 = all_52_5
% 176.84/27.53    (83)  all_56_12 = all_52_25
% 176.84/27.53    (84)  all_58_13 = all_52_27
% 176.84/27.53    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.53    (86)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.53    (87)   ~ (all_52_9 = all_52_17)
% 176.84/27.53    (88)   ~ (all_14_0 = e2)
% 176.84/27.53    (89)  all_58_6 = all_52_17
% 176.84/27.53    (90)   ~ (all_52_3 = all_52_7)
% 176.84/27.53    (91)  op(e2, all_52_19) = e2
% 176.84/27.53    (92)  op(e3, all_52_17) = e3
% 176.84/27.53    (93)   ~ (e1 = e0)
% 176.84/27.53    (94)  all_56_0 = all_4_2
% 176.84/27.53    (95)  all_58_11 = all_52_23
% 176.84/27.53    (96)   ~ (all_52_3 = all_52_19)
% 176.84/27.53    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.84/27.53    (98)   ~ (all_52_7 = all_52_15)
% 176.84/27.53    (99)   ~ (all_52_29 = all_14_2)
% 176.84/27.53    (100)   ~ (all_4_0 = e1)
% 176.84/27.53    (101)   ~ (all_52_19 = all_10_2)
% 176.84/27.53    (102)   ~ (all_52_23 = all_6_2)
% 176.84/27.53    (103)  op(e1, all_4_2) = all_4_0
% 176.84/27.53    (104)   ~ (all_52_29 = all_6_2)
% 176.84/27.53    (105)  all_58_2 = all_52_9
% 176.84/27.53    (106)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.84/27.53    (107)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.84/27.53    (108)  op(e3, e1) = all_52_5
% 176.84/27.53    (109)  all_56_10 = all_14_2
% 176.84/27.53    (110)   ~ (all_52_25 = all_6_2)
% 176.84/27.53    (111)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.84/27.53    (112)  op(e1, e3) = all_52_17
% 176.84/27.53    (113)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.53    (114)   ~ (all_52_25 = all_4_2)
% 176.84/27.53    (115)  op(e3, e0) = all_52_7
% 176.84/27.53    (116)  op(e3, e3) = all_4_2
% 176.84/27.53    (117)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 176.84/27.53             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 176.84/27.53    (118)  all_56_8 = all_52_17
% 176.84/27.53    (119)   ~ (all_52_17 = all_4_2)
% 176.84/27.53    (120)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.53             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.53    (121)   ~ (all_52_25 = all_52_27)
% 176.84/27.53    (122)   ~ (all_52_27 = all_6_2)
% 176.84/27.53    (123)   ~ (all_52_7 = all_6_2)
% 176.84/27.53    (124)  op(e0, all_52_23) = e0
% 176.84/27.53    (125)   ~ (all_52_15 = all_10_2)
% 176.84/27.53    (126)   ~ (all_52_19 = all_52_27)
% 176.84/27.53    (127)  all_56_7 = all_52_15
% 176.84/27.53    (128)  op(e1, all_14_2) = e1
% 176.84/27.53    (129)   ~ (all_52_7 = all_52_23)
% 176.84/27.53    (130)   ~ (all_52_13 = all_10_2)
% 176.84/27.53    (131)   ~ (all_52_17 = all_52_19)
% 176.84/27.53    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.53    (133)  op(e2, all_10_2) = e3
% 176.84/27.53    (134)  all_58_9 = all_52_7
% 176.84/27.53    (135)   ~ (e2 = e0)
% 176.84/27.53    (136)  all_58_12 = all_52_25
% 176.84/27.53    (137)  op(e3, all_4_2) = e1
% 176.84/27.53    (138)  all_56_6 = all_52_13
% 176.84/27.53    (139)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.53    (140)   ~ (all_52_9 = all_52_15)
% 176.84/27.53    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.53    (142)   ~ (e3 = e2)
% 176.84/27.53    (143)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.53    (144)   ~ (all_52_19 = all_14_2)
% 176.84/27.53    (145)  op(e2, e3) = all_52_9
% 176.84/27.53    (146)  all_56_13 = all_52_27
% 176.84/27.53  
% 176.84/27.53  Begin of proof
% 176.84/27.53  | 
% 176.84/27.53  | GROUND_INST: instantiating (120) with e1, all_14_0, all_14_2, e1, simplifying
% 176.84/27.53  |              with (73), (128) gives:
% 176.84/27.53  |   (147)  all_14_0 = e1
% 176.84/27.53  | 
% 176.84/27.53  | REDUCE: (61), (147) imply:
% 176.84/27.53  |   (148)   ~ (e3 = e1)
% 176.84/27.53  | 
% 176.84/27.53  | SIMP: (148) implies:
% 176.84/27.53  |   (149)   ~ (e3 = e1)
% 176.84/27.53  | 
% 176.84/27.53  | REDUCE: (88), (147) imply:
% 176.84/27.53  |   (150)   ~ (e2 = e1)
% 176.84/27.53  | 
% 176.84/27.53  | SIMP: (150) implies:
% 176.84/27.53  |   (151)   ~ (e2 = e1)
% 176.84/27.53  | 
% 176.84/27.53  | BETA: splitting (117) gives:
% 176.84/27.53  | 
% 176.84/27.53  | Case 1:
% 176.84/27.53  | | 
% 176.84/27.53  | |   (152)  all_58_15 = e0
% 176.84/27.53  | | 
% 176.84/27.53  | | REF_CLOSE: (2), (9), (10), (11), (13), (18), (19), (23), (24), (25), (27),
% 176.84/27.53  | |            (30), (31), (32), (33), (34), (36), (37), (38), (42), (43), (44),
% 176.84/27.53  | |            (45), (46), (47), (52), (53), (54), (56), (57), (58), (59), (61),
% 176.84/27.53  | |            (66), (69), (71), (72), (73), (74), (78), (81), (83), (84), (85),
% 176.84/27.53  | |            (87), (88), (89), (91), (92), (93), (95), (96), (98), (99),
% 176.84/27.53  | |            (101), (102), (104), (105), (106), (107), (108), (110), (111),
% 176.84/27.53  | |            (112), (116), (119), (120), (121), (122), (124), (128), (129),
% 176.84/27.53  | |            (132), (134), (135), (136), (137), (138), (139), (142), (145),
% 176.84/27.53  | |            (146), (152) are inconsistent by sub-proof #532.
% 176.84/27.53  | | 
% 176.84/27.53  | Case 2:
% 176.84/27.53  | | 
% 176.84/27.53  | |   (153)   ~ (all_58_15 = e0)
% 176.84/27.53  | |   (154)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 176.84/27.53  | |            | all_58_13 = e0 | all_58_14 = e0)
% 176.84/27.53  | | 
% 176.84/27.53  | | ALPHA: (154) implies:
% 176.84/27.53  | |   (155)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.84/27.53  | |   (156)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.53  | | 
% 176.84/27.53  | | REDUCE: (27), (153) imply:
% 176.84/27.53  | |   (157)   ~ (all_6_2 = e0)
% 176.84/27.53  | | 
% 176.84/27.53  | | BETA: splitting (41) gives:
% 176.84/27.53  | | 
% 176.84/27.53  | | Case 1:
% 176.84/27.53  | | | 
% 176.84/27.53  | | |   (158)  all_56_15 = e3
% 176.84/27.53  | | | 
% 176.84/27.53  | | | COMBINE_EQS: (20), (158) imply:
% 176.84/27.53  | | |   (159)  all_6_2 = e3
% 176.84/27.53  | | | 
% 176.84/27.53  | | | SIMP: (159) implies:
% 176.84/27.53  | | |   (160)  all_6_2 = e3
% 176.84/27.53  | | | 
% 176.84/27.53  | | | REF_CLOSE: (25), (32), (37), (42), (45), (47), (56), (58), (66), (87),
% 176.84/27.53  | | |            (89), (91), (92), (95), (102), (105), (108), (110), (112),
% 176.84/27.53  | | |            (116), (119), (120), (128), (136), (137), (142), (145), (149),
% 176.84/27.53  | | |            (160) are inconsistent by sub-proof #608.
% 176.84/27.53  | | | 
% 176.84/27.53  | | Case 2:
% 176.84/27.53  | | | 
% 176.84/27.53  | | |   (161)   ~ (all_56_15 = e3)
% 176.84/27.53  | | |   (162)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.53  | | | 
% 176.84/27.53  | | | REDUCE: (20), (161) imply:
% 176.84/27.53  | | |   (163)   ~ (all_6_2 = e3)
% 176.84/27.53  | | | 
% 176.84/27.53  | | | BETA: splitting (57) gives:
% 176.84/27.53  | | | 
% 176.84/27.53  | | | Case 1:
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | |   (164)  all_58_12 = e3
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | | COMBINE_EQS: (136), (164) imply:
% 176.84/27.53  | | | |   (165)  all_52_25 = e3
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | | SIMP: (165) implies:
% 176.84/27.53  | | | |   (166)  all_52_25 = e3
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | | REDUCE: (121), (166) imply:
% 176.84/27.53  | | | |   (167)   ~ (all_52_27 = e3)
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | | SIMP: (167) implies:
% 176.84/27.53  | | | |   (168)   ~ (all_52_27 = e3)
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | | REDUCE: (110), (166) imply:
% 176.84/27.53  | | | |   (169)   ~ (all_6_2 = e3)
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 176.84/27.53  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 176.84/27.53  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 176.84/27.53  | | | |            (35), (36), (37), (38), (39), (40), (42), (43), (44), (45),
% 176.84/27.53  | | | |            (46), (47), (48), (49), (50), (51), (53), (55), (56), (57),
% 176.84/27.53  | | | |            (58), (60), (63), (64), (65), (66), (67), (68), (69), (70),
% 176.84/27.53  | | | |            (74), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 176.84/27.53  | | | |            (85), (86), (87), (89), (90), (91), (92), (93), (94), (95),
% 176.84/27.53  | | | |            (96), (97), (98), (99), (100), (101), (102), (105), (108),
% 176.84/27.53  | | | |            (109), (110), (112), (113), (114), (115), (116), (118),
% 176.84/27.53  | | | |            (119), (120), (121), (122), (123), (124), (125), (126),
% 176.84/27.53  | | | |            (127), (128), (130), (131), (132), (133), (134), (135),
% 176.84/27.53  | | | |            (136), (139), (140), (141), (142), (143), (144), (145),
% 176.84/27.53  | | | |            (149), (151), (155), (156), (157), (162), (163), (168) are
% 176.84/27.53  | | | |            inconsistent by sub-proof #279.
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | Case 2:
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | |   (170)   ~ (all_58_12 = e3)
% 176.84/27.53  | | | |   (171)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.84/27.53  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 176.84/27.53  | | | |            (25), (26), (27), (28), (30), (31), (32), (33), (35), (36),
% 176.84/27.53  | | | |            (37), (38), (39), (40), (42), (43), (44), (45), (46), (47),
% 176.84/27.53  | | | |            (48), (50), (51), (53), (55), (56), (58), (62), (63), (64),
% 176.84/27.53  | | | |            (65), (66), (67), (68), (69), (70), (75), (77), (78), (79),
% 176.84/27.53  | | | |            (81), (83), (84), (85), (87), (89), (91), (92), (94), (95),
% 176.84/27.53  | | | |            (96), (97), (99), (100), (101), (102), (103), (105), (108),
% 176.84/27.53  | | | |            (110), (112), (113), (114), (115), (116), (118), (119),
% 176.84/27.53  | | | |            (120), (121), (122), (123), (124), (126), (127), (128),
% 176.84/27.53  | | | |            (129), (130), (131), (132), (134), (136), (137), (139),
% 176.84/27.53  | | | |            (141), (142), (144), (145), (149), (155), (156), (162),
% 176.84/27.53  | | | |            (163), (170), (171) are inconsistent by sub-proof #606.
% 176.84/27.53  | | | | 
% 176.84/27.53  | | | End of split
% 176.84/27.53  | | | 
% 176.84/27.53  | | End of split
% 176.84/27.53  | | 
% 176.84/27.53  | End of split
% 176.84/27.53  | 
% 176.84/27.53  End of proof
% 176.84/27.53  
% 176.84/27.53  Sub-proof #278 shows that the following formulas are inconsistent:
% 176.84/27.53  ----------------------------------------------------------------
% 176.84/27.53    (1)   ~ (all_52_23 = all_14_2)
% 176.84/27.53    (2)   ~ (all_52_5 = all_52_13)
% 176.84/27.53    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.53    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.53    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.84/27.53    (6)   ~ (all_52_17 = all_52_23)
% 176.84/27.53    (7)   ~ (all_52_13 = all_52_29)
% 176.84/27.53    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.84/27.53    (9)  op(e3, e2) = all_52_3
% 176.84/27.53    (10)   ~ (all_52_9 = all_52_25)
% 176.84/27.53    (11)  op(e3, all_52_25) = all_52_24
% 176.84/27.53    (12)   ~ (all_52_19 = all_52_23)
% 176.84/27.53    (13)  op(e1, e2) = all_52_19
% 176.84/27.53    (14)  op(e3, all_52_9) = all_52_8
% 176.84/27.53    (15)   ~ (all_52_3 = all_10_2)
% 176.84/27.53    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.53    (17)  all_58_5 = all_52_13
% 176.84/27.53    (18)   ~ (all_6_2 = e0)
% 176.84/27.53    (19)   ~ (all_52_25 = all_52_29)
% 176.84/27.53    (20)  all_56_15 = all_6_2
% 176.84/27.54    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.54    (22)  op(e2, e0) = all_52_15
% 176.84/27.54    (23)  all_58_3 = all_10_2
% 176.84/27.54    (24)  all_56_9 = all_52_19
% 176.84/27.54    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.54    (26)  all_58_15 = all_6_2
% 176.84/27.54    (27)   ~ (all_52_9 = all_4_2)
% 176.84/27.54    (28)   ~ (all_52_5 = all_52_7)
% 176.84/27.54    (29)  all_58_10 = all_52_15
% 176.84/27.54    (30)   ~ (all_52_5 = all_4_2)
% 176.84/27.54    (31)  all_58_7 = all_52_19
% 176.84/27.54    (32)   ~ (all_52_15 = all_6_2)
% 176.84/27.54    (33)   ~ (all_52_17 = all_52_25)
% 176.84/27.54    (34)  op(e0, e1) = all_52_29
% 176.84/27.54    (35)   ~ (all_4_0 = e2)
% 176.84/27.54    (36)  all_58_4 = all_52_5
% 176.84/27.54    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.54    (38)   ~ (all_52_27 = all_52_29)
% 176.84/27.54    (39)   ~ (all_52_17 = all_14_2)
% 176.84/27.54    (40)  op(e3, all_4_2) = all_4_1
% 176.84/27.54    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.54    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.54    (43)   ~ (all_52_7 = all_4_2)
% 176.84/27.54    (44)  all_58_1 = all_52_3
% 176.84/27.54    (45)  all_58_0 = all_4_2
% 176.84/27.54    (46)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.54    (47)  op(e1, all_52_29) = all_52_28
% 176.84/27.54    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.84/27.54    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.54    (50)   ~ (all_4_1 = e2)
% 176.84/27.54    (51)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.54    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.54    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.54    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.84/27.54    (55)  all_58_14 = all_52_29
% 176.84/27.54    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.54    (57)   ~ (all_52_3 = all_52_5)
% 176.84/27.54    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.54    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.54    (60)  all_58_8 = all_14_2
% 176.84/27.54    (61)  all_56_1 = all_52_3
% 176.84/27.54    (62)  op(e0, e2) = all_52_27
% 176.84/27.54    (63)  all_56_14 = all_52_29
% 176.84/27.54    (64)   ~ (all_14_0 = e3)
% 176.84/27.54    (65)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.84/27.54    (66)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.54    (67)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.54    (68)   ~ (all_52_5 = all_14_2)
% 176.84/27.54    (69)   ~ (all_52_3 = all_52_27)
% 176.84/27.54    (70)   ~ (all_52_3 = all_4_2)
% 176.84/27.54    (71)  op(e0, e3) = all_52_25
% 176.84/27.54    (72)  op(e0, all_6_2) = all_6_1
% 176.84/27.54    (73)   ~ (all_52_9 = all_10_2)
% 176.84/27.54    (74)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.54    (75)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 176.84/27.54    (76)   ~ (all_52_13 = all_14_2)
% 176.84/27.54    (77)  op(e1, all_14_2) = all_14_0
% 176.84/27.54    (78)   ~ (e3 = e0)
% 176.84/27.54    (79)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.54    (80)   ~ (all_52_9 = all_52_13)
% 176.84/27.54    (81)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.54    (82)   ~ (all_52_15 = all_52_23)
% 176.84/27.54    (83)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.84/27.54    (84)   ~ (all_52_5 = all_52_29)
% 176.84/27.54    (85)  all_56_2 = all_52_5
% 176.84/27.54    (86)  op(e1, e0) = all_52_23
% 176.84/27.54    (87)  all_56_12 = all_52_25
% 176.84/27.54    (88)  all_58_13 = all_52_27
% 176.84/27.54    (89)   ~ (all_4_1 = e1)
% 176.84/27.54    (90)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.54    (91)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.54    (92)   ~ (all_52_9 = all_52_17)
% 176.84/27.54    (93)   ~ (all_14_0 = e2)
% 176.84/27.54    (94)  all_58_6 = all_52_17
% 176.84/27.54    (95)   ~ (all_52_3 = all_52_7)
% 176.84/27.54    (96)  op(e2, all_52_19) = e2
% 176.84/27.54    (97)  op(e3, all_52_17) = e3
% 176.84/27.54    (98)   ~ (e1 = e0)
% 176.84/27.54    (99)  all_56_0 = all_4_2
% 176.84/27.54    (100)  all_58_11 = all_52_23
% 176.84/27.54    (101)   ~ (all_52_3 = all_52_19)
% 176.84/27.54    (102)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.84/27.54    (103)   ~ (all_52_7 = all_52_15)
% 176.84/27.54    (104)   ~ (all_52_29 = all_14_2)
% 176.84/27.54    (105)   ~ (all_4_0 = e1)
% 176.84/27.54    (106)   ~ (all_52_19 = all_10_2)
% 176.84/27.54    (107)   ~ (all_52_23 = all_6_2)
% 176.84/27.54    (108)  all_58_2 = all_52_9
% 176.84/27.54    (109)  op(e3, e1) = all_52_5
% 176.84/27.54    (110)  all_56_10 = all_14_2
% 176.84/27.54    (111)   ~ (all_52_25 = all_6_2)
% 176.84/27.54    (112)  op(e1, e3) = all_52_17
% 176.84/27.54    (113)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.54    (114)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 176.84/27.54    (115)   ~ (all_52_25 = all_4_2)
% 176.84/27.54    (116)  op(e3, e0) = all_52_7
% 176.84/27.54    (117)  op(e3, e3) = all_4_2
% 176.84/27.54    (118)  all_56_8 = all_52_17
% 176.84/27.54    (119)   ~ (all_52_17 = all_4_2)
% 176.84/27.54    (120)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.54             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.54    (121)   ~ (all_52_25 = all_52_27)
% 176.84/27.54    (122)   ~ (all_52_27 = all_6_2)
% 176.84/27.54    (123)   ~ (all_52_7 = all_6_2)
% 176.84/27.54    (124)  op(e0, all_52_23) = e0
% 176.84/27.54    (125)   ~ (all_52_15 = all_10_2)
% 176.84/27.54    (126)   ~ (all_52_19 = all_52_27)
% 176.84/27.54    (127)  all_56_7 = all_52_15
% 176.84/27.54    (128)  op(e1, all_14_2) = e1
% 176.84/27.54    (129)   ~ (all_52_7 = all_52_23)
% 176.84/27.54    (130)   ~ (all_52_13 = all_10_2)
% 176.84/27.54    (131)  op(e2, all_52_27) = all_52_26
% 176.84/27.54    (132)   ~ (all_52_17 = all_52_19)
% 176.84/27.54    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.54    (134)  op(e2, all_10_2) = e3
% 176.84/27.54    (135)  all_58_9 = all_52_7
% 176.84/27.54    (136)   ~ (e2 = e0)
% 176.84/27.54    (137)  all_58_12 = all_52_25
% 176.84/27.54    (138)  all_56_6 = all_52_13
% 176.84/27.54    (139)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.54    (140)   ~ (all_52_9 = all_52_15)
% 176.84/27.54    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.54    (142)   ~ (e3 = e2)
% 176.84/27.54    (143)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.54    (144)   ~ (all_52_19 = all_14_2)
% 176.84/27.54    (145)  op(e2, e3) = all_52_9
% 176.84/27.54    (146)  all_56_13 = all_52_27
% 176.84/27.54  
% 176.84/27.54  Begin of proof
% 176.84/27.54  | 
% 176.84/27.54  | GROUND_INST: instantiating (120) with e1, all_14_0, all_14_2, e1, simplifying
% 176.84/27.54  |              with (77), (128) gives:
% 176.84/27.54  |   (147)  all_14_0 = e1
% 176.84/27.54  | 
% 176.84/27.54  | REDUCE: (64), (147) imply:
% 176.84/27.54  |   (148)   ~ (e3 = e1)
% 176.84/27.54  | 
% 176.84/27.54  | SIMP: (148) implies:
% 176.84/27.54  |   (149)   ~ (e3 = e1)
% 176.84/27.54  | 
% 176.84/27.54  | REDUCE: (93), (147) imply:
% 176.84/27.54  |   (150)   ~ (e2 = e1)
% 176.84/27.54  | 
% 176.84/27.54  | SIMP: (150) implies:
% 176.84/27.54  |   (151)   ~ (e2 = e1)
% 176.84/27.54  | 
% 176.84/27.54  | BETA: splitting (41) gives:
% 176.84/27.54  | 
% 176.84/27.54  | Case 1:
% 176.84/27.54  | | 
% 176.84/27.54  | |   (152)  all_56_15 = e3
% 176.84/27.54  | | 
% 176.84/27.54  | | REF_CLOSE: (2), (3), (6), (9), (10), (13), (14), (16), (17), (20), (23),
% 176.84/27.54  | |            (24), (26), (27), (29), (31), (32), (33), (36), (37), (40), (42),
% 176.84/27.54  | |            (43), (44), (45), (49), (54), (58), (60), (62), (66), (67), (68),
% 176.84/27.54  | |            (69), (71), (72), (73), (74), (76), (80), (81), (87), (88), (91),
% 176.84/27.54  | |            (92), (94), (95), (96), (97), (100), (101), (102), (105), (106),
% 176.84/27.54  | |            (107), (108), (109), (111), (112), (116), (117), (118), (119),
% 176.84/27.54  | |            (120), (121), (124), (126), (128), (129), (135), (136), (137),
% 176.84/27.54  | |            (138), (140), (142), (145), (152) are inconsistent by sub-proof
% 176.84/27.54  | |            #284.
% 176.84/27.54  | | 
% 176.84/27.54  | Case 2:
% 176.84/27.54  | | 
% 176.84/27.54  | |   (153)   ~ (all_56_15 = e3)
% 176.84/27.54  | |   (154)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (20), (153) imply:
% 176.84/27.54  | |   (155)   ~ (all_6_2 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | BETA: splitting (56) gives:
% 176.84/27.54  | | 
% 176.84/27.54  | | Case 1:
% 176.84/27.54  | | | 
% 176.84/27.54  | | |   (156)  all_56_13 = e3
% 176.84/27.54  | | | 
% 176.84/27.54  | | | COMBINE_EQS: (146), (156) imply:
% 176.84/27.54  | | |   (157)  all_52_27 = e3
% 176.84/27.54  | | | 
% 176.84/27.54  | | | SIMP: (157) implies:
% 176.84/27.54  | | |   (158)  all_52_27 = e3
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REF_CLOSE: (1), (2), (9), (11), (12), (17), (19), (21), (22), (24), (28),
% 176.84/27.54  | | |            (29), (30), (31), (33), (36), (37), (38), (39), (40), (45),
% 176.84/27.54  | | |            (46), (48), (49), (55), (58), (60), (61), (66), (68), (69),
% 176.84/27.54  | | |            (70), (71), (75), (83), (86), (89), (90), (92), (94), (96),
% 176.84/27.54  | | |            (97), (98), (100), (101), (105), (108), (109), (110), (112),
% 176.84/27.54  | | |            (114), (115), (116), (117), (119), (120), (121), (124), (126),
% 176.84/27.54  | | |            (128), (131), (132), (135), (136), (137), (141), (142), (144),
% 176.84/27.54  | | |            (145), (149), (151), (158) are inconsistent by sub-proof #686.
% 176.84/27.54  | | | 
% 176.84/27.54  | | Case 2:
% 176.84/27.54  | | | 
% 176.84/27.54  | | |   (159)   ~ (all_56_13 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (146), (159) imply:
% 176.84/27.54  | | |   (160)   ~ (all_52_27 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.84/27.54  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 176.84/27.54  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 176.84/27.54  | | |            (34), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 176.84/27.54  | | |            (45), (46), (47), (49), (50), (51), (52), (53), (55), (57),
% 176.84/27.54  | | |            (58), (59), (60), (63), (65), (66), (67), (68), (69), (70),
% 176.84/27.54  | | |            (71), (73), (78), (79), (80), (81), (82), (83), (84), (85),
% 176.84/27.54  | | |            (87), (88), (90), (91), (92), (94), (95), (96), (97), (98),
% 176.84/27.54  | | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 176.84/27.54  | | |            (108), (109), (110), (111), (112), (113), (115), (116), (117),
% 176.84/27.54  | | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 176.84/27.54  | | |            (127), (128), (130), (132), (133), (134), (135), (136), (137),
% 176.84/27.54  | | |            (139), (140), (141), (142), (143), (144), (145), (149), (151),
% 176.84/27.54  | | |            (154), (155), (160) are inconsistent by sub-proof #279.
% 176.84/27.54  | | | 
% 176.84/27.54  | | End of split
% 176.84/27.54  | | 
% 176.84/27.54  | End of split
% 176.84/27.54  | 
% 176.84/27.54  End of proof
% 176.84/27.54  
% 176.84/27.54  Sub-proof #279 shows that the following formulas are inconsistent:
% 176.84/27.54  ----------------------------------------------------------------
% 176.84/27.54    (1)   ~ (all_52_23 = all_14_2)
% 176.84/27.54    (2)   ~ (all_52_5 = all_52_13)
% 176.84/27.54    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.54    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.54    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 176.84/27.54    (6)   ~ (all_52_17 = all_52_23)
% 176.84/27.54    (7)   ~ (all_52_13 = all_52_29)
% 176.84/27.54    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.84/27.54    (9)  op(e3, e2) = all_52_3
% 176.84/27.54    (10)   ~ (all_52_9 = all_52_25)
% 176.84/27.54    (11)  op(e3, all_52_25) = all_52_24
% 176.84/27.54    (12)   ~ (all_52_19 = all_52_23)
% 176.84/27.54    (13)  op(e1, e2) = all_52_19
% 176.84/27.54    (14)   ~ (all_52_27 = e3)
% 176.84/27.54    (15)   ~ (all_6_2 = e3)
% 176.84/27.54    (16)  op(e3, all_52_9) = all_52_8
% 176.84/27.54    (17)   ~ (all_52_3 = all_10_2)
% 176.84/27.54    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.54    (19)  all_58_5 = all_52_13
% 176.84/27.54    (20)   ~ (all_6_2 = e0)
% 176.84/27.54    (21)   ~ (all_52_25 = all_52_29)
% 176.84/27.54    (22)  all_56_15 = all_6_2
% 176.84/27.54    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.54    (24)  op(e2, e0) = all_52_15
% 176.84/27.54    (25)  all_58_3 = all_10_2
% 176.84/27.54    (26)  all_56_9 = all_52_19
% 176.84/27.54    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.54    (28)  all_58_15 = all_6_2
% 176.84/27.54    (29)   ~ (all_52_9 = all_4_2)
% 176.84/27.54    (30)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.54    (31)   ~ (all_52_5 = all_52_7)
% 176.84/27.54    (32)  all_58_10 = all_52_15
% 176.84/27.54    (33)   ~ (all_52_5 = all_4_2)
% 176.84/27.54    (34)  all_58_7 = all_52_19
% 176.84/27.54    (35)   ~ (all_52_17 = all_52_25)
% 176.84/27.54    (36)  op(e0, e1) = all_52_29
% 176.84/27.54    (37)   ~ (all_4_0 = e2)
% 176.84/27.54    (38)  all_58_4 = all_52_5
% 176.84/27.54    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.54    (40)   ~ (e3 = e1)
% 176.84/27.54    (41)   ~ (all_52_27 = all_52_29)
% 176.84/27.54    (42)   ~ (all_52_17 = all_14_2)
% 176.84/27.54    (43)  op(e3, all_4_2) = all_4_1
% 176.84/27.54    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.54    (45)   ~ (all_52_7 = all_4_2)
% 176.84/27.54    (46)  all_58_1 = all_52_3
% 176.84/27.54    (47)  all_58_0 = all_4_2
% 176.84/27.54    (48)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.54    (49)  op(e1, all_52_29) = all_52_28
% 176.84/27.54    (50)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.54    (51)   ~ (all_4_1 = e2)
% 176.84/27.54    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.54    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.54    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.54    (55)  all_58_14 = all_52_29
% 176.84/27.54    (56)   ~ (all_52_3 = all_52_5)
% 176.84/27.54    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.54    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.54    (59)  all_58_8 = all_14_2
% 176.84/27.54    (60)  all_56_14 = all_52_29
% 176.84/27.54    (61)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 176.84/27.54    (62)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.54    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.54    (64)   ~ (all_52_5 = all_14_2)
% 176.84/27.54    (65)   ~ (all_52_3 = all_52_27)
% 176.84/27.54    (66)   ~ (all_52_3 = all_4_2)
% 176.84/27.54    (67)  op(e0, e3) = all_52_25
% 176.84/27.54    (68)   ~ (all_52_9 = all_10_2)
% 176.84/27.54    (69)   ~ (e3 = e0)
% 176.84/27.54    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.54    (71)   ~ (all_52_9 = all_52_13)
% 176.84/27.54    (72)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.54    (73)   ~ (all_52_15 = all_52_23)
% 176.84/27.54    (74)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.84/27.54    (75)   ~ (all_52_5 = all_52_29)
% 176.84/27.54    (76)  all_56_2 = all_52_5
% 176.84/27.54    (77)  all_56_12 = all_52_25
% 176.84/27.54    (78)  all_58_13 = all_52_27
% 176.84/27.54    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.54    (80)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.54    (81)   ~ (all_52_9 = all_52_17)
% 176.84/27.54    (82)  all_58_6 = all_52_17
% 176.84/27.54    (83)   ~ (all_52_3 = all_52_7)
% 176.84/27.54    (84)  op(e2, all_52_19) = e2
% 176.84/27.54    (85)  op(e3, all_52_17) = e3
% 176.84/27.54    (86)   ~ (e1 = e0)
% 176.84/27.54    (87)  all_56_0 = all_4_2
% 176.84/27.54    (88)  all_58_11 = all_52_23
% 176.84/27.54    (89)   ~ (all_52_3 = all_52_19)
% 176.84/27.54    (90)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.84/27.54    (91)   ~ (all_52_7 = all_52_15)
% 176.84/27.54    (92)   ~ (all_52_29 = all_14_2)
% 176.84/27.54    (93)   ~ (all_4_0 = e1)
% 176.84/27.54    (94)   ~ (all_52_19 = all_10_2)
% 176.84/27.54    (95)   ~ (all_52_23 = all_6_2)
% 176.84/27.54    (96)  all_58_2 = all_52_9
% 176.84/27.54    (97)  op(e3, e1) = all_52_5
% 176.84/27.54    (98)   ~ (e2 = e1)
% 176.84/27.54    (99)  all_56_10 = all_14_2
% 176.84/27.54    (100)   ~ (all_52_25 = all_6_2)
% 176.84/27.54    (101)  op(e1, e3) = all_52_17
% 176.84/27.54    (102)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.54    (103)   ~ (all_52_25 = all_4_2)
% 176.84/27.54    (104)  op(e3, e0) = all_52_7
% 176.84/27.54    (105)  op(e3, e3) = all_4_2
% 176.84/27.54    (106)  all_56_8 = all_52_17
% 176.84/27.54    (107)   ~ (all_52_17 = all_4_2)
% 176.84/27.54    (108)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.54             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.54    (109)   ~ (all_52_25 = all_52_27)
% 176.84/27.54    (110)   ~ (all_52_27 = all_6_2)
% 176.84/27.54    (111)   ~ (all_52_7 = all_6_2)
% 176.84/27.54    (112)  op(e0, all_52_23) = e0
% 176.84/27.54    (113)   ~ (all_52_15 = all_10_2)
% 176.84/27.54    (114)   ~ (all_52_19 = all_52_27)
% 176.84/27.54    (115)  all_56_7 = all_52_15
% 176.84/27.54    (116)  op(e1, all_14_2) = e1
% 176.84/27.54    (117)   ~ (all_52_13 = all_10_2)
% 176.84/27.54    (118)   ~ (all_52_17 = all_52_19)
% 176.84/27.54    (119)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.54    (120)  op(e2, all_10_2) = e3
% 176.84/27.54    (121)  all_58_9 = all_52_7
% 176.84/27.54    (122)   ~ (e2 = e0)
% 176.84/27.54    (123)  all_58_12 = all_52_25
% 176.84/27.54    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.54    (125)   ~ (all_52_9 = all_52_15)
% 176.84/27.54    (126)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.54    (127)   ~ (e3 = e2)
% 176.84/27.54    (128)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.54    (129)   ~ (all_52_19 = all_14_2)
% 176.84/27.54    (130)  op(e2, e3) = all_52_9
% 176.84/27.54  
% 176.84/27.54  Begin of proof
% 176.84/27.54  | 
% 176.84/27.54  | BETA: splitting (58) gives:
% 176.84/27.54  | 
% 176.84/27.54  | Case 1:
% 176.84/27.54  | | 
% 176.84/27.54  | |   (131)  all_58_12 = e3
% 176.84/27.54  | | 
% 176.84/27.54  | | COMBINE_EQS: (123), (131) imply:
% 176.84/27.54  | |   (132)  all_52_25 = e3
% 176.84/27.54  | | 
% 176.84/27.54  | | SIMP: (132) implies:
% 176.84/27.54  | |   (133)  all_52_25 = e3
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (10), (133) imply:
% 176.84/27.54  | |   (134)   ~ (all_52_9 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (35), (133) imply:
% 176.84/27.54  | |   (135)   ~ (all_52_17 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (109), (133) imply:
% 176.84/27.54  | |   (136)   ~ (all_52_27 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (21), (133) imply:
% 176.84/27.54  | |   (137)   ~ (all_52_29 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | SIMP: (137) implies:
% 176.84/27.54  | |   (138)   ~ (all_52_29 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (100), (133) imply:
% 176.84/27.54  | |   (139)   ~ (all_6_2 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (103), (133) imply:
% 176.84/27.54  | |   (140)   ~ (all_4_2 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | SIMP: (140) implies:
% 176.84/27.54  | |   (141)   ~ (all_4_2 = e3)
% 176.84/27.54  | | 
% 176.84/27.54  | | REDUCE: (67), (133) imply:
% 176.84/27.54  | |   (142)  op(e0, e3) = e3
% 176.84/27.54  | | 
% 176.84/27.54  | | BETA: splitting (50) gives:
% 176.84/27.54  | | 
% 176.84/27.54  | | Case 1:
% 176.84/27.54  | | | 
% 176.84/27.54  | | |   (143)  all_56_9 = e3
% 176.84/27.54  | | | 
% 176.84/27.54  | | | COMBINE_EQS: (26), (143) imply:
% 176.84/27.54  | | |   (144)  all_52_19 = e3
% 176.84/27.54  | | | 
% 176.84/27.54  | | | SIMP: (144) implies:
% 176.84/27.54  | | |   (145)  all_52_19 = e3
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (89), (145) imply:
% 176.84/27.54  | | |   (146)   ~ (all_52_3 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (12), (145) imply:
% 176.84/27.54  | | |   (147)   ~ (all_52_23 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | SIMP: (147) implies:
% 176.84/27.54  | | |   (148)   ~ (all_52_23 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (84), (145) imply:
% 176.84/27.54  | | |   (149)  op(e2, e3) = e2
% 176.84/27.54  | | | 
% 176.84/27.54  | | | GROUND_INST: instantiating (108) with all_52_9, e2, e3, e2, simplifying
% 176.84/27.54  | | |              with (130), (149) gives:
% 176.84/27.54  | | |   (150)  all_52_9 = e2
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (134), (150) imply:
% 176.84/27.54  | | |   (151)   ~ (e3 = e2)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (16), (150) imply:
% 176.84/27.54  | | |   (152)  op(e3, e2) = all_52_8
% 176.84/27.54  | | | 
% 176.84/27.54  | | | GROUND_INST: instantiating (108) with all_52_3, all_52_8, e2, e3,
% 176.84/27.54  | | |              simplifying with (9), (152) gives:
% 176.84/27.54  | | |   (153)  all_52_3 = all_52_8
% 176.84/27.54  | | | 
% 176.84/27.54  | | | COMBINE_EQS: (46), (153) imply:
% 176.84/27.54  | | |   (154)  all_58_1 = all_52_8
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (146), (153) imply:
% 176.84/27.54  | | |   (155)   ~ (all_52_8 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | BETA: splitting (126) gives:
% 176.84/27.54  | | | 
% 176.84/27.54  | | | Case 1:
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | |   (156)  all_58_4 = e3
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | | COMBINE_EQS: (38), (156) imply:
% 176.84/27.54  | | | |   (157)  all_52_5 = e3
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | | REF_CLOSE: (1), (2), (13), (14), (15), (19), (25), (27), (28), (29),
% 176.84/27.54  | | | |            (31), (32), (33), (34), (38), (39), (40), (42), (45), (46),
% 176.84/27.54  | | | |            (47), (48), (54), (55), (59), (64), (69), (70), (73), (75),
% 176.84/27.54  | | | |            (78), (79), (80), (81), (82), (84), (85), (86), (87), (88),
% 176.84/27.54  | | | |            (89), (91), (96), (97), (98), (101), (102), (104), (107),
% 176.84/27.54  | | | |            (108), (112), (113), (115), (116), (118), (119), (121),
% 176.84/27.54  | | | |            (122), (124), (125), (126), (129), (130), (131), (135),
% 176.84/27.54  | | | |            (142), (157) are inconsistent by sub-proof #281.
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | Case 2:
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | |   (158)   ~ (all_58_4 = e3)
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | | REDUCE: (38), (158) imply:
% 176.84/27.54  | | | |   (159)   ~ (all_52_5 = e3)
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | | BETA: splitting (124) gives:
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | | Case 1:
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | |   (160)  all_58_0 = e3
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | | COMBINE_EQS: (47), (160) imply:
% 176.84/27.54  | | | | |   (161)  all_4_2 = e3
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | | REDUCE: (141), (161) imply:
% 176.84/27.54  | | | | |   (162)  $false
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | | CLOSE: (162) is inconsistent.
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | Case 2:
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | |   (163)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | | BETA: splitting (163) gives:
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | | Case 1:
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | |   (164)  all_58_1 = e3
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | | COMBINE_EQS: (154), (164) imply:
% 176.84/27.54  | | | | | |   (165)  all_52_8 = e3
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | | REDUCE: (155), (165) imply:
% 176.84/27.54  | | | | | |   (166)  $false
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | | CLOSE: (166) is inconsistent.
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | Case 2:
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | |   (167)  all_58_4 = e3 | all_58_9 = e3
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | | BETA: splitting (167) gives:
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | | Case 1:
% 176.84/27.54  | | | | | | | 
% 176.84/27.54  | | | | | | |   (168)  all_58_4 = e3
% 176.84/27.54  | | | | | | | 
% 176.84/27.54  | | | | | | | REF_CLOSE: (38), (159), (168) are inconsistent by sub-proof #1025.
% 176.84/27.54  | | | | | | | 
% 176.84/27.54  | | | | | | Case 2:
% 176.84/27.54  | | | | | | | 
% 176.84/27.54  | | | | | | |   (169)  all_58_9 = e3
% 176.84/27.54  | | | | | | | 
% 176.84/27.54  | | | | | | | REF_CLOSE: (1), (4), (34), (36), (37), (38), (39), (40), (43),
% 176.84/27.54  | | | | | | |            (46), (47), (51), (52), (56), (59), (60), (62), (63),
% 176.84/27.54  | | | | | | |            (64), (69), (74), (75), (76), (79), (82), (84), (85),
% 176.84/27.54  | | | | | | |            (86), (88), (93), (96), (97), (98), (99), (101), (108),
% 176.84/27.54  | | | | | | |            (116), (122), (127), (128), (129), (130), (131), (135),
% 176.84/27.54  | | | | | | |            (138), (148), (159), (169) are inconsistent by
% 176.84/27.54  | | | | | | |            sub-proof #917.
% 176.84/27.54  | | | | | | | 
% 176.84/27.54  | | | | | | End of split
% 176.84/27.54  | | | | | | 
% 176.84/27.54  | | | | | End of split
% 176.84/27.54  | | | | | 
% 176.84/27.54  | | | | End of split
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | End of split
% 176.84/27.54  | | | 
% 176.84/27.54  | | Case 2:
% 176.84/27.54  | | | 
% 176.84/27.54  | | |   (170)   ~ (all_56_9 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | REDUCE: (26), (170) imply:
% 176.84/27.54  | | |   (171)   ~ (all_52_19 = e3)
% 176.84/27.54  | | | 
% 176.84/27.54  | | | BETA: splitting (54) gives:
% 176.84/27.54  | | | 
% 176.84/27.54  | | | Case 1:
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | |   (172)  all_58_1 = e3
% 176.84/27.54  | | | | 
% 176.84/27.54  | | | | REF_CLOSE: (13), (15), (25), (27), (28), (29), (31), (32), (33), (34),
% 176.84/27.54  | | | |            (38), (39), (40), (45), (46), (47), (48), (54), (59), (64),
% 176.84/27.54  | | | |            (65), (66), (69), (70), (73), (78), (79), (80), (81), (82),
% 176.84/27.54  | | | |            (83), (84), (85), (86), (87), (88), (89), (91), (96), (97),
% 176.84/27.54  | | | |            (98), (101), (102), (104), (107), (108), (112), (113), (115),
% 176.84/27.54  | | | |            (116), (118), (119), (121), (122), (124), (125), (126),
% 176.84/27.54  | | | |            (130), (131), (135), (142), (172) are inconsistent by
% 176.84/27.54  | | | |            sub-proof #280.
% 176.84/27.55  | | | | 
% 176.84/27.55  | | | Case 2:
% 176.84/27.55  | | | | 
% 176.84/27.55  | | | |   (173)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.55  | | | | 
% 176.84/27.55  | | | | BETA: splitting (173) gives:
% 176.84/27.55  | | | | 
% 176.84/27.55  | | | | Case 1:
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | |   (174)  all_58_3 = e3
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | | COMBINE_EQS: (25), (174) imply:
% 176.84/27.55  | | | | |   (175)  all_10_2 = e3
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | | REDUCE: (120), (175) imply:
% 176.84/27.55  | | | | |   (176)  op(e2, e3) = e3
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | | REF_CLOSE: (108), (130), (134), (176) are inconsistent by sub-proof
% 176.84/27.55  | | | | |            #498.
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | Case 2:
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | |   (177)  all_58_7 = e3 | all_58_13 = e3
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | | REF_CLOSE: (14), (34), (78), (171), (177) are inconsistent by
% 176.84/27.55  | | | | |            sub-proof #976.
% 176.84/27.55  | | | | | 
% 176.84/27.55  | | | | End of split
% 176.84/27.55  | | | | 
% 176.84/27.55  | | | End of split
% 176.84/27.55  | | | 
% 176.84/27.55  | | End of split
% 176.84/27.55  | | 
% 176.84/27.55  | Case 2:
% 176.84/27.55  | | 
% 176.84/27.55  | |   (178)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.55  | | 
% 176.84/27.55  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 176.84/27.55  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.84/27.55  | |            (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (37),
% 176.84/27.55  | |            (38), (39), (41), (42), (43), (44), (46), (47), (48), (49), (50),
% 176.84/27.55  | |            (51), (53), (54), (55), (56), (57), (59), (61), (62), (63), (64),
% 176.84/27.55  | |            (66), (67), (68), (71), (72), (75), (77), (78), (81), (82), (84),
% 176.84/27.55  | |            (85), (87), (88), (89), (90), (92), (93), (94), (95), (96), (97),
% 176.84/27.55  | |            (100), (101), (103), (104), (105), (106), (107), (108), (109),
% 176.84/27.55  | |            (110), (111), (112), (114), (116), (117), (118), (121), (123),
% 176.84/27.55  | |            (127), (129), (130), (178) are inconsistent by sub-proof #670.
% 176.84/27.55  | | 
% 176.84/27.55  | End of split
% 176.84/27.55  | 
% 176.84/27.55  End of proof
% 176.84/27.55  
% 176.84/27.55  Sub-proof #280 shows that the following formulas are inconsistent:
% 176.84/27.55  ----------------------------------------------------------------
% 176.84/27.55    (1)  op(e1, e2) = all_52_19
% 176.84/27.55    (2)   ~ (all_52_17 = e3)
% 176.84/27.55    (3)   ~ (all_6_2 = e3)
% 176.84/27.55    (4)  all_58_3 = all_10_2
% 176.84/27.55    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.55    (6)  all_58_15 = all_6_2
% 176.84/27.55    (7)   ~ (all_52_9 = all_4_2)
% 176.84/27.55    (8)   ~ (all_52_5 = all_52_7)
% 176.84/27.55    (9)  all_58_10 = all_52_15
% 176.84/27.55    (10)   ~ (all_52_5 = all_4_2)
% 176.84/27.55    (11)  all_58_7 = all_52_19
% 176.84/27.55    (12)  all_58_4 = all_52_5
% 176.84/27.55    (13)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.55    (14)   ~ (e3 = e1)
% 176.84/27.55    (15)   ~ (all_52_7 = all_4_2)
% 176.84/27.55    (16)  all_58_1 = all_52_3
% 176.84/27.55    (17)  all_58_0 = all_4_2
% 176.84/27.55    (18)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.55    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.55    (20)  op(e0, e3) = e3
% 176.84/27.55    (21)  all_58_8 = all_14_2
% 176.84/27.55    (22)   ~ (all_52_5 = all_14_2)
% 176.84/27.55    (23)   ~ (all_52_3 = all_52_27)
% 176.84/27.55    (24)   ~ (all_52_3 = all_4_2)
% 176.84/27.55    (25)   ~ (e3 = e0)
% 176.84/27.55    (26)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.55    (27)   ~ (all_52_15 = all_52_23)
% 176.84/27.55    (28)  all_58_13 = all_52_27
% 176.84/27.55    (29)  all_58_1 = e3
% 176.84/27.55    (30)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.55    (31)  all_58_12 = e3
% 176.84/27.55    (32)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.55    (33)   ~ (all_52_9 = all_52_17)
% 176.84/27.55    (34)  all_58_6 = all_52_17
% 176.84/27.55    (35)   ~ (all_52_3 = all_52_7)
% 176.84/27.55    (36)  op(e2, all_52_19) = e2
% 176.84/27.55    (37)  op(e3, all_52_17) = e3
% 176.84/27.55    (38)   ~ (e1 = e0)
% 176.84/27.55    (39)  all_56_0 = all_4_2
% 176.84/27.55    (40)  all_58_11 = all_52_23
% 176.84/27.55    (41)   ~ (all_52_3 = all_52_19)
% 176.84/27.55    (42)   ~ (all_52_7 = all_52_15)
% 176.84/27.55    (43)  all_58_2 = all_52_9
% 176.84/27.55    (44)  op(e3, e1) = all_52_5
% 176.84/27.55    (45)   ~ (e2 = e1)
% 176.84/27.55    (46)  op(e1, e3) = all_52_17
% 176.84/27.55    (47)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.55    (48)  op(e3, e0) = all_52_7
% 176.84/27.55    (49)   ~ (all_52_17 = all_4_2)
% 176.84/27.55    (50)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.55    (51)  op(e0, all_52_23) = e0
% 176.84/27.55    (52)   ~ (all_52_15 = all_10_2)
% 176.84/27.55    (53)  all_56_7 = all_52_15
% 176.84/27.55    (54)  op(e1, all_14_2) = e1
% 176.84/27.55    (55)   ~ (all_52_17 = all_52_19)
% 176.84/27.55    (56)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.55    (57)  all_58_9 = all_52_7
% 176.84/27.55    (58)   ~ (e2 = e0)
% 176.84/27.55    (59)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.55    (60)   ~ (all_52_9 = all_52_15)
% 176.84/27.55    (61)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.55    (62)  op(e2, e3) = all_52_9
% 176.84/27.55  
% 176.84/27.55  Begin of proof
% 176.84/27.55  | 
% 176.84/27.55  | COMBINE_EQS: (16), (29) imply:
% 176.84/27.55  |   (63)  all_52_3 = e3
% 176.84/27.55  | 
% 176.84/27.55  | REDUCE: (35), (63) imply:
% 176.84/27.55  |   (64)   ~ (all_52_7 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | SIMP: (64) implies:
% 176.84/27.55  |   (65)   ~ (all_52_7 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | REDUCE: (23), (63) imply:
% 176.84/27.55  |   (66)   ~ (all_52_27 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | SIMP: (66) implies:
% 176.84/27.55  |   (67)   ~ (all_52_27 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | REDUCE: (24), (63) imply:
% 176.84/27.55  |   (68)   ~ (all_4_2 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | SIMP: (68) implies:
% 176.84/27.55  |   (69)   ~ (all_4_2 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.84/27.55  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (25),
% 176.84/27.55  |            (26), (27), (28), (30), (31), (32), (33), (34), (36), (37), (38),
% 176.84/27.55  |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 176.84/27.55  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 176.84/27.55  |            (61), (62), (65), (67), (69) are inconsistent by sub-proof #283.
% 176.84/27.55  | 
% 176.84/27.55  End of proof
% 176.84/27.55  
% 176.84/27.55  Sub-proof #281 shows that the following formulas are inconsistent:
% 176.84/27.55  ----------------------------------------------------------------
% 176.84/27.55    (1)   ~ (all_52_23 = all_14_2)
% 176.84/27.55    (2)   ~ (all_52_5 = all_52_13)
% 176.84/27.55    (3)  op(e1, e2) = all_52_19
% 176.84/27.55    (4)   ~ (all_52_27 = e3)
% 176.84/27.55    (5)   ~ (all_52_17 = e3)
% 176.84/27.55    (6)   ~ (all_6_2 = e3)
% 176.84/27.55    (7)  all_58_5 = all_52_13
% 176.84/27.55    (8)  all_58_3 = all_10_2
% 176.84/27.55    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.55    (10)  all_58_15 = all_6_2
% 176.84/27.55    (11)   ~ (all_52_9 = all_4_2)
% 176.84/27.55    (12)   ~ (all_52_5 = all_52_7)
% 176.84/27.55    (13)  all_58_10 = all_52_15
% 176.84/27.55    (14)   ~ (all_52_5 = all_4_2)
% 176.84/27.55    (15)  all_58_7 = all_52_19
% 176.84/27.55    (16)  all_58_4 = all_52_5
% 176.84/27.55    (17)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.55    (18)   ~ (e3 = e1)
% 176.84/27.55    (19)   ~ (all_52_17 = all_14_2)
% 176.84/27.55    (20)   ~ (all_52_7 = all_4_2)
% 176.84/27.55    (21)  all_58_1 = all_52_3
% 176.84/27.55    (22)  all_58_0 = all_4_2
% 176.84/27.55    (23)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.55    (24)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.55    (25)  all_58_14 = all_52_29
% 176.84/27.55    (26)  op(e0, e3) = e3
% 176.84/27.55    (27)  all_58_8 = all_14_2
% 176.84/27.55    (28)   ~ (all_52_5 = all_14_2)
% 176.84/27.55    (29)   ~ (e3 = e0)
% 176.84/27.55    (30)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.55    (31)   ~ (all_52_15 = all_52_23)
% 176.84/27.55    (32)   ~ (all_52_5 = all_52_29)
% 176.84/27.55    (33)  all_58_13 = all_52_27
% 176.84/27.55    (34)  all_52_5 = e3
% 176.84/27.55    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.55    (36)  all_58_12 = e3
% 176.84/27.55    (37)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.55    (38)   ~ (all_52_9 = all_52_17)
% 176.84/27.55    (39)  all_58_6 = all_52_17
% 176.84/27.55    (40)  op(e2, all_52_19) = e2
% 176.84/27.55    (41)  op(e3, all_52_17) = e3
% 176.84/27.55    (42)   ~ (e1 = e0)
% 176.84/27.55    (43)  all_56_0 = all_4_2
% 176.84/27.55    (44)  all_58_11 = all_52_23
% 176.84/27.55    (45)   ~ (all_52_3 = all_52_19)
% 176.84/27.55    (46)   ~ (all_52_7 = all_52_15)
% 176.84/27.55    (47)  all_58_2 = all_52_9
% 176.84/27.55    (48)  op(e3, e1) = all_52_5
% 176.84/27.55    (49)   ~ (e2 = e1)
% 176.84/27.55    (50)  op(e1, e3) = all_52_17
% 176.84/27.55    (51)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.55    (52)  op(e3, e0) = all_52_7
% 176.84/27.55    (53)   ~ (all_52_17 = all_4_2)
% 176.84/27.55    (54)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.55    (55)  op(e0, all_52_23) = e0
% 176.84/27.55    (56)   ~ (all_52_15 = all_10_2)
% 176.84/27.55    (57)  all_56_7 = all_52_15
% 176.84/27.55    (58)  op(e1, all_14_2) = e1
% 176.84/27.55    (59)   ~ (all_52_17 = all_52_19)
% 176.84/27.55    (60)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.55    (61)  all_58_9 = all_52_7
% 176.84/27.55    (62)   ~ (e2 = e0)
% 176.84/27.55    (63)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.55    (64)   ~ (all_52_9 = all_52_15)
% 176.84/27.55    (65)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.55    (66)   ~ (all_52_19 = all_14_2)
% 176.84/27.55    (67)  op(e2, e3) = all_52_9
% 176.84/27.55  
% 176.84/27.55  Begin of proof
% 176.84/27.55  | 
% 176.84/27.55  | SIMP: (34) implies:
% 176.84/27.55  |   (68)  all_52_5 = e3
% 176.84/27.55  | 
% 176.84/27.55  | REDUCE: (2), (68) imply:
% 176.84/27.55  |   (69)   ~ (all_52_13 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | SIMP: (69) implies:
% 176.84/27.55  |   (70)   ~ (all_52_13 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | REDUCE: (32), (68) imply:
% 176.84/27.55  |   (71)   ~ (all_52_29 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | SIMP: (71) implies:
% 176.84/27.55  |   (72)   ~ (all_52_29 = e3)
% 176.84/27.55  | 
% 176.84/27.55  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 176.84/27.55  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 176.84/27.55  |            (25), (26), (27), (28), (29), (30), (31), (33), (35), (36), (37),
% 176.84/27.55  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 176.84/27.55  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 176.84/27.55  |            (60), (61), (62), (63), (64), (65), (66), (67), (70), (72) are
% 176.84/27.55  |            inconsistent by sub-proof #282.
% 176.84/27.55  | 
% 176.84/27.55  End of proof
% 176.84/27.55  
% 176.84/27.55  Sub-proof #282 shows that the following formulas are inconsistent:
% 176.84/27.55  ----------------------------------------------------------------
% 176.84/27.55    (1)   ~ (all_52_23 = all_14_2)
% 176.84/27.55    (2)  op(e1, e2) = all_52_19
% 176.84/27.55    (3)   ~ (all_52_27 = e3)
% 176.84/27.55    (4)   ~ (all_52_17 = e3)
% 176.84/27.55    (5)   ~ (all_6_2 = e3)
% 176.84/27.55    (6)  all_58_5 = all_52_13
% 176.84/27.55    (7)  all_58_3 = all_10_2
% 176.84/27.55    (8)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.55    (9)  all_58_15 = all_6_2
% 176.84/27.55    (10)   ~ (all_52_9 = all_4_2)
% 176.84/27.55    (11)   ~ (all_52_5 = all_52_7)
% 176.84/27.55    (12)  all_58_10 = all_52_15
% 176.84/27.55    (13)   ~ (all_52_5 = all_4_2)
% 176.84/27.55    (14)  all_58_7 = all_52_19
% 176.84/27.55    (15)  all_58_4 = all_52_5
% 176.84/27.55    (16)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.55    (17)   ~ (e3 = e1)
% 176.84/27.55    (18)   ~ (all_52_17 = all_14_2)
% 176.84/27.55    (19)   ~ (all_52_7 = all_4_2)
% 176.84/27.55    (20)  all_58_1 = all_52_3
% 176.84/27.55    (21)  all_58_0 = all_4_2
% 176.84/27.55    (22)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.55    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.55    (24)  all_58_14 = all_52_29
% 176.84/27.55    (25)  op(e0, e3) = e3
% 176.84/27.55    (26)  all_58_8 = all_14_2
% 176.84/27.55    (27)   ~ (all_52_5 = all_14_2)
% 176.84/27.55    (28)   ~ (all_52_29 = e3)
% 176.84/27.55    (29)   ~ (e3 = e0)
% 176.84/27.55    (30)   ~ (all_52_13 = e3)
% 176.84/27.55    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.55    (32)   ~ (all_52_15 = all_52_23)
% 176.84/27.55    (33)  all_58_13 = all_52_27
% 176.84/27.55    (34)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.55    (35)  all_58_12 = e3
% 176.84/27.55    (36)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.55    (37)   ~ (all_52_9 = all_52_17)
% 176.84/27.55    (38)  all_58_6 = all_52_17
% 176.84/27.55    (39)  op(e2, all_52_19) = e2
% 176.84/27.55    (40)  op(e3, all_52_17) = e3
% 176.84/27.55    (41)   ~ (e1 = e0)
% 176.84/27.55    (42)  all_56_0 = all_4_2
% 176.84/27.55    (43)  all_58_11 = all_52_23
% 176.84/27.55    (44)   ~ (all_52_3 = all_52_19)
% 176.84/27.55    (45)   ~ (all_52_7 = all_52_15)
% 176.84/27.55    (46)  all_58_2 = all_52_9
% 176.84/27.55    (47)  op(e3, e1) = all_52_5
% 176.84/27.55    (48)   ~ (e2 = e1)
% 176.84/27.55    (49)  op(e1, e3) = all_52_17
% 176.84/27.55    (50)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.55    (51)  op(e3, e0) = all_52_7
% 176.84/27.55    (52)   ~ (all_52_17 = all_4_2)
% 176.84/27.55    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.55    (54)  op(e0, all_52_23) = e0
% 176.84/27.55    (55)   ~ (all_52_15 = all_10_2)
% 176.84/27.55    (56)  all_56_7 = all_52_15
% 176.84/27.55    (57)  op(e1, all_14_2) = e1
% 176.84/27.55    (58)   ~ (all_52_17 = all_52_19)
% 176.84/27.55    (59)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.55    (60)  all_58_9 = all_52_7
% 176.84/27.55    (61)   ~ (e2 = e0)
% 176.84/27.55    (62)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.55    (63)   ~ (all_52_9 = all_52_15)
% 176.84/27.55    (64)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.55    (65)   ~ (all_52_19 = all_14_2)
% 176.84/27.55    (66)  op(e2, e3) = all_52_9
% 176.84/27.55  
% 176.84/27.55  Begin of proof
% 176.84/27.55  | 
% 176.84/27.55  | BETA: splitting (64) gives:
% 176.84/27.55  | 
% 176.84/27.55  | Case 1:
% 176.84/27.55  | | 
% 176.84/27.55  | |   (67)  all_58_4 = e3
% 176.84/27.55  | | 
% 176.84/27.55  | | COMBINE_EQS: (15), (67) imply:
% 176.84/27.55  | |   (68)  all_52_5 = e3
% 176.84/27.55  | | 
% 176.84/27.55  | | SIMP: (68) implies:
% 176.84/27.55  | |   (69)  all_52_5 = e3
% 176.84/27.55  | | 
% 176.84/27.55  | | REDUCE: (11), (69) imply:
% 176.84/27.55  | |   (70)   ~ (all_52_7 = e3)
% 176.84/27.55  | | 
% 176.84/27.55  | | SIMP: (70) implies:
% 176.84/27.55  | |   (71)   ~ (all_52_7 = e3)
% 176.84/27.55  | | 
% 176.84/27.55  | | REDUCE: (13), (69) imply:
% 176.84/27.55  | |   (72)   ~ (all_4_2 = e3)
% 176.84/27.55  | | 
% 176.84/27.55  | | SIMP: (72) implies:
% 176.84/27.55  | |   (73)   ~ (all_4_2 = e3)
% 176.84/27.55  | | 
% 176.84/27.55  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 176.84/27.55  | |            (15), (16), (17), (19), (20), (21), (22), (23), (25), (26), (27),
% 176.84/27.55  | |            (29), (31), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 176.84/27.55  | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 176.84/27.55  | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 176.84/27.55  | |            (63), (64), (66), (71), (73) are inconsistent by sub-proof #283.
% 176.84/27.55  | | 
% 176.84/27.55  | Case 2:
% 176.84/27.55  | | 
% 176.84/27.55  | |   (74)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.55  | | 
% 176.84/27.55  | | REF_CLOSE: (1), (6), (14), (16), (18), (24), (26), (27), (28), (30), (38),
% 176.84/27.55  | |            (40), (43), (47), (49), (53), (57), (65), (74) are inconsistent
% 176.84/27.55  | |            by sub-proof #484.
% 176.84/27.55  | | 
% 176.84/27.55  | End of split
% 176.84/27.55  | 
% 176.84/27.55  End of proof
% 176.84/27.55  
% 176.84/27.55  Sub-proof #283 shows that the following formulas are inconsistent:
% 176.84/27.55  ----------------------------------------------------------------
% 176.84/27.55    (1)  op(e1, e2) = all_52_19
% 176.84/27.55    (2)   ~ (all_52_27 = e3)
% 176.84/27.55    (3)   ~ (all_52_17 = e3)
% 176.84/27.55    (4)   ~ (all_6_2 = e3)
% 176.84/27.55    (5)   ~ (all_4_2 = e3)
% 176.84/27.55    (6)  all_58_3 = all_10_2
% 176.84/27.55    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.55    (8)  all_58_15 = all_6_2
% 176.84/27.55    (9)   ~ (all_52_9 = all_4_2)
% 176.84/27.55    (10)   ~ (all_52_5 = all_52_7)
% 176.84/27.55    (11)  all_58_10 = all_52_15
% 176.84/27.55    (12)   ~ (all_52_5 = all_4_2)
% 176.84/27.55    (13)  all_58_7 = all_52_19
% 176.84/27.55    (14)  all_58_4 = all_52_5
% 176.84/27.55    (15)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.55    (16)   ~ (e3 = e1)
% 176.84/27.55    (17)   ~ (all_52_7 = all_4_2)
% 176.84/27.55    (18)  all_58_1 = all_52_3
% 176.84/27.55    (19)  all_58_0 = all_4_2
% 176.84/27.55    (20)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 176.84/27.55    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.55    (22)  op(e0, e3) = e3
% 176.84/27.55    (23)  all_58_8 = all_14_2
% 176.84/27.55    (24)   ~ (all_52_5 = all_14_2)
% 176.84/27.55    (25)   ~ (e3 = e0)
% 176.84/27.55    (26)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.55    (27)   ~ (all_52_15 = all_52_23)
% 176.84/27.55    (28)  all_58_13 = all_52_27
% 176.84/27.55    (29)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.55    (30)  all_58_12 = e3
% 176.84/27.55    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.55    (32)   ~ (all_52_9 = all_52_17)
% 176.84/27.55    (33)  all_58_6 = all_52_17
% 176.84/27.55    (34)  op(e2, all_52_19) = e2
% 176.84/27.55    (35)  op(e3, all_52_17) = e3
% 176.84/27.55    (36)   ~ (e1 = e0)
% 176.84/27.55    (37)  all_56_0 = all_4_2
% 176.84/27.55    (38)  all_58_11 = all_52_23
% 176.84/27.55    (39)   ~ (all_52_3 = all_52_19)
% 176.84/27.55    (40)   ~ (all_52_7 = all_52_15)
% 176.84/27.55    (41)  all_58_2 = all_52_9
% 176.84/27.55    (42)  op(e3, e1) = all_52_5
% 176.84/27.55    (43)   ~ (e2 = e1)
% 176.84/27.55    (44)  op(e1, e3) = all_52_17
% 176.84/27.55    (45)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.55    (46)  op(e3, e0) = all_52_7
% 176.84/27.55    (47)   ~ (all_52_17 = all_4_2)
% 176.84/27.55    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.55    (49)  op(e0, all_52_23) = e0
% 176.84/27.55    (50)   ~ (all_52_15 = all_10_2)
% 176.84/27.55    (51)  all_56_7 = all_52_15
% 176.84/27.55    (52)  op(e1, all_14_2) = e1
% 176.84/27.55    (53)   ~ (all_52_7 = e3)
% 176.84/27.55    (54)   ~ (all_52_17 = all_52_19)
% 176.84/27.55    (55)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.55    (56)  all_58_9 = all_52_7
% 176.84/27.55    (57)   ~ (e2 = e0)
% 176.84/27.55    (58)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.55    (59)   ~ (all_52_9 = all_52_15)
% 176.84/27.55    (60)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 176.84/27.55    (61)  op(e2, e3) = all_52_9
% 176.84/27.55  
% 176.84/27.55  Begin of proof
% 176.84/27.55  | 
% 176.84/27.55  | BETA: splitting (55) gives:
% 176.84/27.55  | 
% 176.84/27.55  | Case 1:
% 176.84/27.55  | | 
% 176.84/27.55  | |   (62)  all_58_9 = e3
% 176.84/27.55  | | 
% 176.84/27.55  | | REF_CLOSE: (53), (56), (62) are inconsistent by sub-proof #972.
% 176.84/27.55  | | 
% 176.84/27.55  | Case 2:
% 176.84/27.55  | | 
% 176.84/27.55  | |   (63)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.55  | | 
% 176.84/27.55  | | BETA: splitting (7) gives:
% 176.84/27.55  | | 
% 176.84/27.55  | | Case 1:
% 176.84/27.55  | | | 
% 176.84/27.55  | | |   (64)  all_56_0 = e3
% 176.84/27.55  | | | 
% 176.84/27.55  | | | REF_CLOSE: (5), (37), (64) are inconsistent by sub-proof #1024.
% 176.84/27.55  | | | 
% 176.84/27.55  | | Case 2:
% 176.84/27.55  | | | 
% 176.84/27.55  | | |   (65)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.55  | | | 
% 176.84/27.55  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 176.84/27.55  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.84/27.55  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 176.84/27.55  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 176.84/27.55  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (54),
% 176.84/27.55  | | |            (56), (57), (58), (59), (60), (61), (63), (65) are inconsistent
% 176.84/27.55  | | |            by sub-proof #678.
% 176.84/27.55  | | | 
% 176.84/27.55  | | End of split
% 176.84/27.55  | | 
% 176.84/27.55  | End of split
% 176.84/27.55  | 
% 176.84/27.55  End of proof
% 176.84/27.55  
% 176.84/27.55  Sub-proof #284 shows that the following formulas are inconsistent:
% 176.84/27.55  ----------------------------------------------------------------
% 176.84/27.55    (1)   ~ (all_52_5 = all_52_13)
% 176.84/27.55    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.55    (3)   ~ (all_52_17 = all_52_23)
% 176.84/27.55    (4)  op(e3, e2) = all_52_3
% 176.84/27.55    (5)   ~ (all_52_9 = all_52_25)
% 176.84/27.55    (6)  op(e1, e2) = all_52_19
% 176.84/27.55    (7)  op(e3, all_52_9) = all_52_8
% 176.84/27.55    (8)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.55    (9)  all_56_15 = e3
% 176.84/27.55    (10)  all_58_5 = all_52_13
% 176.84/27.55    (11)  all_56_15 = all_6_2
% 176.84/27.55    (12)  all_58_3 = all_10_2
% 176.84/27.55    (13)  all_56_9 = all_52_19
% 176.84/27.55    (14)  all_58_15 = all_6_2
% 176.84/27.55    (15)   ~ (all_52_9 = all_4_2)
% 176.84/27.55    (16)  all_58_10 = all_52_15
% 176.84/27.55    (17)  all_58_7 = all_52_19
% 176.84/27.55    (18)   ~ (all_52_15 = all_6_2)
% 176.84/27.55    (19)   ~ (all_52_17 = all_52_25)
% 176.84/27.55    (20)  all_58_4 = all_52_5
% 176.84/27.55    (21)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.55    (22)  op(e3, all_4_2) = all_4_1
% 176.84/27.55    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.55    (24)   ~ (all_52_7 = all_4_2)
% 176.84/27.55    (25)  all_58_1 = all_52_3
% 176.84/27.55    (26)  all_58_0 = all_4_2
% 176.84/27.55    (27)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.55    (28)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 176.84/27.55    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.55    (30)  all_58_8 = all_14_2
% 176.84/27.55    (31)  op(e0, e2) = all_52_27
% 176.84/27.55    (32)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.55    (33)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.55    (34)   ~ (all_52_5 = all_14_2)
% 176.84/27.55    (35)   ~ (all_52_3 = all_52_27)
% 176.84/27.55    (36)  op(e0, e3) = all_52_25
% 176.84/27.55    (37)  op(e0, all_6_2) = all_6_1
% 176.84/27.55    (38)   ~ (all_52_9 = all_10_2)
% 176.84/27.55    (39)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.55    (40)   ~ (all_52_13 = all_14_2)
% 176.84/27.55    (41)   ~ (all_52_9 = all_52_13)
% 176.84/27.55    (42)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.55    (43)  all_56_12 = all_52_25
% 176.84/27.55    (44)  all_58_13 = all_52_27
% 176.84/27.55    (45)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.55    (46)   ~ (all_52_9 = all_52_17)
% 176.84/27.55    (47)  all_58_6 = all_52_17
% 176.84/27.55    (48)   ~ (all_52_3 = all_52_7)
% 176.84/27.55    (49)  op(e2, all_52_19) = e2
% 176.84/27.55    (50)  op(e3, all_52_17) = e3
% 176.84/27.55    (51)  all_58_11 = all_52_23
% 176.84/27.55    (52)   ~ (all_52_3 = all_52_19)
% 176.84/27.55    (53)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 176.84/27.55    (54)   ~ (all_4_0 = e1)
% 176.84/27.55    (55)   ~ (all_52_19 = all_10_2)
% 176.84/27.55    (56)   ~ (all_52_23 = all_6_2)
% 176.84/27.55    (57)  all_58_2 = all_52_9
% 176.84/27.55    (58)  op(e3, e1) = all_52_5
% 176.84/27.55    (59)   ~ (all_52_25 = all_6_2)
% 176.84/27.55    (60)  op(e1, e3) = all_52_17
% 176.84/27.55    (61)  op(e3, e0) = all_52_7
% 176.84/27.55    (62)  op(e3, e3) = all_4_2
% 176.84/27.55    (63)  all_56_8 = all_52_17
% 176.84/27.55    (64)   ~ (all_52_17 = all_4_2)
% 176.84/27.55    (65)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.55    (66)   ~ (all_52_25 = all_52_27)
% 176.84/27.55    (67)  op(e0, all_52_23) = e0
% 176.84/27.55    (68)   ~ (all_52_19 = all_52_27)
% 176.84/27.55    (69)  op(e1, all_14_2) = e1
% 176.84/27.55    (70)   ~ (all_52_7 = all_52_23)
% 176.84/27.55    (71)  all_58_9 = all_52_7
% 176.84/27.55    (72)   ~ (e2 = e0)
% 176.84/27.55    (73)  all_58_12 = all_52_25
% 176.84/27.55    (74)  all_56_6 = all_52_13
% 176.84/27.55    (75)   ~ (all_52_9 = all_52_15)
% 176.84/27.55    (76)   ~ (e3 = e2)
% 176.84/27.55    (77)  op(e2, e3) = all_52_9
% 176.84/27.55  
% 176.84/27.55  Begin of proof
% 176.84/27.55  | 
% 176.84/27.55  | COMBINE_EQS: (9), (11) imply:
% 176.84/27.55  |   (78)  all_6_2 = e3
% 176.84/27.55  | 
% 176.84/27.55  | SIMP: (78) implies:
% 176.84/27.55  |   (79)  all_6_2 = e3
% 176.84/27.55  | 
% 176.84/27.55  | COMBINE_EQS: (14), (79) imply:
% 176.84/27.55  |   (80)  all_58_15 = e3
% 176.84/27.55  | 
% 176.84/27.55  | REDUCE: (18), (79) imply:
% 176.84/27.56  |   (81)   ~ (all_52_15 = e3)
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (56), (79) imply:
% 176.84/27.56  |   (82)   ~ (all_52_23 = e3)
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (59), (79) imply:
% 176.84/27.56  |   (83)   ~ (all_52_25 = e3)
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (37), (79) imply:
% 176.84/27.56  |   (84)  op(e0, e3) = all_6_1
% 176.84/27.56  | 
% 176.84/27.56  | GROUND_INST: instantiating (65) with all_52_25, all_6_1, e3, e0, simplifying
% 176.84/27.56  |              with (36), (84) gives:
% 176.84/27.56  |   (85)  all_52_25 = all_6_1
% 176.84/27.56  | 
% 176.84/27.56  | COMBINE_EQS: (43), (85) imply:
% 176.84/27.56  |   (86)  all_56_12 = all_6_1
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (5), (85) imply:
% 176.84/27.56  |   (87)   ~ (all_52_9 = all_6_1)
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (19), (85) imply:
% 176.84/27.56  |   (88)   ~ (all_52_17 = all_6_1)
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (66), (85) imply:
% 176.84/27.56  |   (89)   ~ (all_52_27 = all_6_1)
% 176.84/27.56  | 
% 176.84/27.56  | SIMP: (89) implies:
% 176.84/27.56  |   (90)   ~ (all_52_27 = all_6_1)
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (83), (85) imply:
% 176.84/27.56  |   (91)   ~ (all_6_1 = e3)
% 176.84/27.56  | 
% 176.84/27.56  | BETA: splitting (42) gives:
% 176.84/27.56  | 
% 176.84/27.56  | Case 1:
% 176.84/27.56  | | 
% 176.84/27.56  | |   (92)  all_56_12 = e3
% 176.84/27.56  | | 
% 176.84/27.56  | | REF_CLOSE: (86), (91), (92) are inconsistent by sub-proof #509.
% 176.84/27.56  | | 
% 176.84/27.56  | Case 2:
% 176.84/27.56  | | 
% 176.84/27.56  | |   (93)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.56  | | 
% 176.84/27.56  | | BETA: splitting (29) gives:
% 176.84/27.56  | | 
% 176.84/27.56  | | Case 1:
% 176.84/27.56  | | | 
% 176.84/27.56  | | |   (94)  all_58_0 = e3
% 176.84/27.56  | | | 
% 176.84/27.56  | | | COMBINE_EQS: (26), (94) imply:
% 176.84/27.56  | | |   (95)  all_4_2 = e3
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (24), (95) imply:
% 176.84/27.56  | | |   (96)   ~ (all_52_7 = e3)
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (15), (95) imply:
% 176.84/27.56  | | |   (97)   ~ (all_52_9 = e3)
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (64), (95) imply:
% 176.84/27.56  | | |   (98)   ~ (all_52_17 = e3)
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (32), (95) imply:
% 176.84/27.56  | | |   (99)  op(all_4_1, e3) = all_4_0
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (22), (95) imply:
% 176.84/27.56  | | |   (100)  op(e3, e3) = all_4_1
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (62), (95) imply:
% 176.84/27.56  | | |   (101)  op(e3, e3) = e3
% 176.84/27.56  | | | 
% 176.84/27.56  | | | GROUND_INST: instantiating (65) with e3, all_4_1, e3, e3, simplifying with
% 176.84/27.56  | | |              (100), (101) gives:
% 176.84/27.56  | | |   (102)  all_4_1 = e3
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (99), (102) imply:
% 176.84/27.56  | | |   (103)  op(e3, e3) = all_4_0
% 176.84/27.56  | | | 
% 176.84/27.56  | | | GROUND_INST: instantiating (65) with e3, all_4_0, e3, e3, simplifying with
% 176.84/27.56  | | |              (101), (103) gives:
% 176.84/27.56  | | |   (104)  all_4_0 = e3
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REDUCE: (54), (104) imply:
% 176.84/27.56  | | |   (105)   ~ (e3 = e1)
% 176.84/27.56  | | | 
% 176.84/27.56  | | | BETA: splitting (21) gives:
% 176.84/27.56  | | | 
% 176.84/27.56  | | | Case 1:
% 176.84/27.56  | | | | 
% 176.84/27.56  | | | |   (106)  all_58_6 = e3
% 176.84/27.56  | | | | 
% 176.84/27.56  | | | | REF_CLOSE: (47), (98), (106) are inconsistent by sub-proof #981.
% 176.84/27.56  | | | | 
% 176.84/27.56  | | | Case 2:
% 176.84/27.56  | | | | 
% 176.84/27.56  | | | |   (107)   ~ (all_58_6 = e3)
% 176.84/27.56  | | | |   (108)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.56  | | | | 
% 176.84/27.56  | | | | BETA: splitting (23) gives:
% 176.84/27.56  | | | | 
% 176.84/27.56  | | | | Case 1:
% 176.84/27.56  | | | | | 
% 176.84/27.56  | | | | |   (109)  all_58_2 = e3
% 176.84/27.56  | | | | | 
% 176.84/27.56  | | | | | REF_CLOSE: (57), (97), (109) are inconsistent by sub-proof #980.
% 176.84/27.56  | | | | | 
% 176.84/27.56  | | | | Case 2:
% 176.84/27.56  | | | | | 
% 176.84/27.56  | | | | |   (110)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.56  | | | | | 
% 176.84/27.56  | | | | | BETA: splitting (2) gives:
% 176.84/27.56  | | | | | 
% 176.84/27.56  | | | | | Case 1:
% 176.84/27.56  | | | | | | 
% 176.84/27.56  | | | | | |   (111)  all_56_8 = e3
% 176.84/27.56  | | | | | | 
% 176.84/27.56  | | | | | | REF_CLOSE: (63), (98), (111) are inconsistent by sub-proof #461.
% 176.84/27.56  | | | | | | 
% 176.84/27.56  | | | | | Case 2:
% 176.84/27.56  | | | | | | 
% 176.84/27.56  | | | | | |   (112)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.56  | | | | | | 
% 176.84/27.56  | | | | | | BETA: splitting (28) gives:
% 176.84/27.56  | | | | | | 
% 176.84/27.56  | | | | | | Case 1:
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | |   (113)  all_56_6 = e3
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | COMBINE_EQS: (74), (113) imply:
% 176.84/27.56  | | | | | | |   (114)  all_52_13 = e3
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | SIMP: (114) implies:
% 176.84/27.56  | | | | | | |   (115)  all_52_13 = e3
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | REDUCE: (1), (115) imply:
% 176.84/27.56  | | | | | | |   (116)   ~ (all_52_5 = e3)
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | REDUCE: (40), (115) imply:
% 176.84/27.56  | | | | | | |   (117)   ~ (all_14_2 = e3)
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | SIMP: (117) implies:
% 176.84/27.56  | | | | | | |   (118)   ~ (all_14_2 = e3)
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | BETA: splitting (108) gives:
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | |   (119)  all_58_7 = e3
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | COMBINE_EQS: (17), (119) imply:
% 176.84/27.56  | | | | | | | |   (120)  all_52_19 = e3
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (52), (120) imply:
% 176.84/27.56  | | | | | | | |   (121)   ~ (all_52_3 = e3)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (68), (120) imply:
% 176.84/27.56  | | | | | | | |   (122)   ~ (all_52_27 = e3)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | SIMP: (122) implies:
% 176.84/27.56  | | | | | | | |   (123)   ~ (all_52_27 = e3)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (49), (120) imply:
% 176.84/27.56  | | | | | | | |   (124)  op(e2, e3) = e2
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (6), (120) imply:
% 176.84/27.56  | | | | | | | |   (125)  op(e1, e2) = e3
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | GROUND_INST: instantiating (65) with all_52_9, e2, e3, e2,
% 176.84/27.56  | | | | | | | |              simplifying with (77), (124) gives:
% 176.84/27.56  | | | | | | | |   (126)  all_52_9 = e2
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (75), (126) imply:
% 176.84/27.56  | | | | | | | |   (127)   ~ (all_52_15 = e2)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | SIMP: (127) implies:
% 176.84/27.56  | | | | | | | |   (128)   ~ (all_52_15 = e2)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (38), (126) imply:
% 176.84/27.56  | | | | | | | |   (129)   ~ (all_10_2 = e2)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | SIMP: (129) implies:
% 176.84/27.56  | | | | | | | |   (130)   ~ (all_10_2 = e2)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (87), (126) imply:
% 176.84/27.56  | | | | | | | |   (131)   ~ (all_6_1 = e2)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | SIMP: (131) implies:
% 176.84/27.56  | | | | | | | |   (132)   ~ (all_6_1 = e2)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (97), (126) imply:
% 176.84/27.56  | | | | | | | |   (133)   ~ (e3 = e2)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (7), (126) imply:
% 176.84/27.56  | | | | | | | |   (134)  op(e3, e2) = all_52_8
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | GROUND_INST: instantiating (65) with all_52_3, all_52_8, e2, e3,
% 176.84/27.56  | | | | | | | |              simplifying with (4), (134) gives:
% 176.84/27.56  | | | | | | | |   (135)  all_52_3 = all_52_8
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | COMBINE_EQS: (25), (135) imply:
% 176.84/27.56  | | | | | | | |   (136)  all_58_1 = all_52_8
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (48), (135) imply:
% 176.84/27.56  | | | | | | | |   (137)   ~ (all_52_7 = all_52_8)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | SIMP: (137) implies:
% 176.84/27.56  | | | | | | | |   (138)   ~ (all_52_7 = all_52_8)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (35), (135) imply:
% 176.84/27.56  | | | | | | | |   (139)   ~ (all_52_8 = all_52_27)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REDUCE: (121), (135) imply:
% 176.84/27.56  | | | | | | | |   (140)   ~ (all_52_8 = e3)
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | BETA: splitting (8) gives:
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | |   (141)  all_58_1 = e2
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | COMBINE_EQS: (136), (141) imply:
% 176.84/27.56  | | | | | | | | |   (142)  all_52_8 = e2
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | REDUCE: (138), (142) imply:
% 176.84/27.56  | | | | | | | | |   (143)   ~ (all_52_7 = e2)
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | BETA: splitting (39) gives:
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | |   (144)  all_58_9 = e2
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | COMBINE_EQS: (71), (144) imply:
% 176.84/27.56  | | | | | | | | | |   (145)  all_52_7 = e2
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | REDUCE: (143), (145) imply:
% 176.84/27.56  | | | | | | | | | |   (146)  $false
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | CLOSE: (146) is inconsistent.
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | |   (147)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | BETA: splitting (147) gives:
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | |   (148)  all_58_10 = e2
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | REF_CLOSE: (16), (128), (148) are inconsistent by sub-proof
% 176.84/27.56  | | | | | | | | | | |            #711.
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | |   (149)  all_58_11 = e2 | all_58_15 = e2
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | BETA: splitting (149) gives:
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | |   (150)  all_58_11 = e2
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | COMBINE_EQS: (51), (150) imply:
% 176.84/27.56  | | | | | | | | | | | |   (151)  all_52_23 = e2
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | SIMP: (151) implies:
% 176.84/27.56  | | | | | | | | | | | |   (152)  all_52_23 = e2
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | REDUCE: (3), (152) imply:
% 176.84/27.56  | | | | | | | | | | | |   (153)   ~ (all_52_17 = e2)
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | REDUCE: (67), (152) imply:
% 176.84/27.56  | | | | | | | | | | | |   (154)  op(e0, e2) = e0
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | GROUND_INST: instantiating (65) with all_52_27, e0, e2, e0,
% 176.84/27.56  | | | | | | | | | | | |              simplifying with (31), (154) gives:
% 176.84/27.56  | | | | | | | | | | | |   (155)  all_52_27 = e0
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | REDUCE: (90), (155) imply:
% 176.84/27.56  | | | | | | | | | | | |   (156)   ~ (all_6_1 = e0)
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | SIMP: (156) implies:
% 176.84/27.56  | | | | | | | | | | | |   (157)   ~ (all_6_1 = e0)
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | BETA: splitting (93) gives:
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | |   (158)  all_56_12 = e2
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | REF_CLOSE: (86), (132), (158) are inconsistent by sub-proof
% 176.84/27.56  | | | | | | | | | | | | |            #507.
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | |   (159)  all_56_12 = e1 | all_56_12 = e0
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | BETA: splitting (159) gives:
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | |   (160)  all_56_12 = e1
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | COMBINE_EQS: (86), (160) imply:
% 176.84/27.56  | | | | | | | | | | | | | |   (161)  all_6_1 = e1
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | SIMP: (161) implies:
% 176.84/27.56  | | | | | | | | | | | | | |   (162)  all_6_1 = e1
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | REDUCE: (88), (162) imply:
% 176.84/27.56  | | | | | | | | | | | | | |   (163)   ~ (all_52_17 = e1)
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | |   (164)  all_56_8 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | REF_CLOSE: (63), (153), (164) are inconsistent by sub-proof
% 176.84/27.56  | | | | | | | | | | | | | | |            #460.
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | |   (165)  all_56_8 = e1 | all_56_8 = e0
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | |   (166)  all_56_8 = e1
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | REF_CLOSE: (63), (163), (166) are inconsistent by sub-proof
% 176.84/27.56  | | | | | | | | | | | | | | | |            #287.
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | |   (167)  all_56_8 = e0
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (167) imply:
% 176.84/27.56  | | | | | | | | | | | | | | | |   (168)  all_52_17 = e0
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | SIMP: (168) implies:
% 176.84/27.56  | | | | | | | | | | | | | | | |   (169)  all_52_17 = e0
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | REDUCE: (50), (169) imply:
% 176.84/27.56  | | | | | | | | | | | | | | | |   (170)  op(e3, e0) = e3
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | REF_CLOSE: (61), (65), (96), (170) are inconsistent by
% 176.84/27.56  | | | | | | | | | | | | | | | |            sub-proof #908.
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | |   (171)  all_56_12 = e0
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | COMBINE_EQS: (86), (171) imply:
% 176.84/27.56  | | | | | | | | | | | | | |   (172)  all_6_1 = e0
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | SIMP: (172) implies:
% 176.84/27.56  | | | | | | | | | | | | | |   (173)  all_6_1 = e0
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | REDUCE: (157), (173) imply:
% 176.84/27.56  | | | | | | | | | | | | | |   (174)  $false
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | CLOSE: (174) is inconsistent.
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | |   (175)  all_58_15 = e2
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | REF_CLOSE: (76), (80), (175) are inconsistent by sub-proof
% 176.84/27.56  | | | | | | | | | | | |            #286.
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | |   (176)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | BETA: splitting (176) gives:
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | |   (177)  all_58_3 = e2
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | COMBINE_EQS: (12), (177) imply:
% 176.84/27.56  | | | | | | | | | |   (178)  all_10_2 = e2
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | REDUCE: (130), (178) imply:
% 176.84/27.56  | | | | | | | | | |   (179)  $false
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | CLOSE: (179) is inconsistent.
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | |   (180)  all_58_7 = e2 | all_58_13 = e2
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | BETA: splitting (180) gives:
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | |   (181)  all_58_7 = e2
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | COMBINE_EQS: (119), (181) imply:
% 176.84/27.56  | | | | | | | | | | |   (182)  e3 = e2
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | REDUCE: (76), (182) imply:
% 176.84/27.56  | | | | | | | | | | |   (183)  $false
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | |   (184)  all_58_13 = e2
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | COMBINE_EQS: (44), (184) imply:
% 176.84/27.56  | | | | | | | | | | |   (185)  all_52_27 = e2
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | REDUCE: (139), (185) imply:
% 176.84/27.56  | | | | | | | | | | |   (186)   ~ (all_52_8 = e2)
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | REDUCE: (31), (185) imply:
% 176.84/27.56  | | | | | | | | | | |   (187)  op(e0, e2) = e2
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | BETA: splitting (39) gives:
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | |   (188)  all_58_9 = e2
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | COMBINE_EQS: (71), (188) imply:
% 176.84/27.56  | | | | | | | | | | | |   (189)  all_52_7 = e2
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | REDUCE: (70), (189) imply:
% 176.84/27.56  | | | | | | | | | | | |   (190)   ~ (all_52_23 = e2)
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | SIMP: (190) implies:
% 176.84/27.56  | | | | | | | | | | | |   (191)   ~ (all_52_23 = e2)
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | REF_CLOSE: (30), (45), (46), (47), (51), (65), (69), (77),
% 176.84/27.56  | | | | | | | | | | | |            (97), (105), (119), (124), (125), (191) are
% 176.84/27.56  | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | |   (192)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | BETA: splitting (192) gives:
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | |   (193)  all_58_10 = e2
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | COMBINE_EQS: (16), (193) imply:
% 176.84/27.56  | | | | | | | | | | | | |   (194)  all_52_15 = e2
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | REDUCE: (128), (194) imply:
% 176.84/27.56  | | | | | | | | | | | | |   (195)  $false
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | |   (196)  all_58_11 = e2 | all_58_15 = e2
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | |   (197)  all_58_0 = e2
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | COMBINE_EQS: (94), (197) imply:
% 176.84/27.56  | | | | | | | | | | | | | |   (198)  e3 = e2
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | REDUCE: (76), (198) imply:
% 176.84/27.56  | | | | | | | | | | | | | |   (199)  $false
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | CLOSE: (199) is inconsistent.
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | |   (200)   ~ (all_58_0 = e2)
% 176.84/27.56  | | | | | | | | | | | | | |   (201)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | |   (202)  all_58_11 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | COMBINE_EQS: (51), (202) imply:
% 176.84/27.56  | | | | | | | | | | | | | | |   (203)  all_52_23 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | REDUCE: (70), (203) imply:
% 176.84/27.56  | | | | | | | | | | | | | | |   (204)   ~ (all_52_7 = e2)
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | REDUCE: (67), (203) imply:
% 176.84/27.56  | | | | | | | | | | | | | | |   (205)  op(e0, e2) = e0
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | |   (206)  all_58_4 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (206) imply:
% 176.84/27.56  | | | | | | | | | | | | | | | |   (207)  all_52_5 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (65) with e2, e0, e2, e0,
% 176.84/27.56  | | | | | | | | | | | | | | | |              simplifying with (187), (205) gives:
% 176.84/27.56  | | | | | | | | | | | | | | | |   (208)  e2 = e0
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (208) imply:
% 176.84/27.56  | | | | | | | | | | | | | | | |   (209)  all_58_11 = e0
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | REF_CLOSE: (72), (76), (80), (196), (209) are inconsistent by
% 176.84/27.56  | | | | | | | | | | | | | | | |            sub-proof #303.
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | |   (210)   ~ (all_58_4 = e2)
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | REDUCE: (20), (210) imply:
% 176.84/27.56  | | | | | | | | | | | | | | | |   (211)   ~ (all_52_5 = e2)
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | Case 1:
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | |   (212)  all_58_1 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (212) imply:
% 176.84/27.56  | | | | | | | | | | | | | | | | |   (213)  all_52_8 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | | REDUCE: (186), (213) imply:
% 176.84/27.56  | | | | | | | | | | | | | | | | |   (214)  $false
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent.
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | |   (215)  all_58_4 = e2 | all_58_9 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (71), (204), (211), (215) are inconsistent
% 176.84/27.56  | | | | | | | | | | | | | | | | |            by sub-proof #285.
% 176.84/27.56  | | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | |   (216)  all_58_15 = e2
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | | REF_CLOSE: (76), (80), (216) are inconsistent by sub-proof
% 176.84/27.56  | | | | | | | | | | | | | | |            #286.
% 176.84/27.56  | | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | | 
% 176.84/27.56  | | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | | 
% 176.84/27.56  | | | | | | | | End of split
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | Case 2:
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | |   (217)  all_58_8 = e3 | all_58_11 = e3
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | | REF_CLOSE: (30), (51), (82), (118), (217) are inconsistent by
% 176.84/27.56  | | | | | | | |            sub-proof #997.
% 176.84/27.56  | | | | | | | | 
% 176.84/27.56  | | | | | | | End of split
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | Case 2:
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | |   (218)   ~ (all_56_6 = e3)
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | REDUCE: (74), (218) imply:
% 176.84/27.56  | | | | | | |   (219)   ~ (all_52_13 = e3)
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | | REF_CLOSE: (10), (12), (16), (17), (30), (34), (50), (51), (55),
% 176.84/27.56  | | | | | | |            (58), (60), (65), (69), (81), (82), (108), (110), (219)
% 176.84/27.56  | | | | | | |            are inconsistent by sub-proof #683.
% 176.84/27.56  | | | | | | | 
% 176.84/27.56  | | | | | | End of split
% 176.84/27.56  | | | | | | 
% 176.84/27.56  | | | | | End of split
% 176.84/27.56  | | | | | 
% 176.84/27.56  | | | | End of split
% 176.84/27.56  | | | | 
% 176.84/27.56  | | | End of split
% 176.84/27.56  | | | 
% 176.84/27.56  | | Case 2:
% 176.84/27.56  | | | 
% 176.84/27.56  | | |   (220)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.56  | | | 
% 176.84/27.56  | | | REF_CLOSE: (13), (17), (21), (23), (27), (30), (34), (46), (47), (49),
% 176.84/27.56  | | |            (50), (51), (57), (58), (60), (62), (64), (65), (69), (73),
% 176.84/27.56  | | |            (76), (77), (82), (83), (220) are inconsistent by sub-proof
% 176.84/27.56  | | |            #945.
% 176.84/27.56  | | | 
% 176.84/27.56  | | End of split
% 176.84/27.56  | | 
% 176.84/27.56  | End of split
% 176.84/27.56  | 
% 176.84/27.56  End of proof
% 176.84/27.56  
% 176.84/27.56  Sub-proof #285 shows that the following formulas are inconsistent:
% 176.84/27.56  ----------------------------------------------------------------
% 176.84/27.56    (1)   ~ (all_52_5 = e2)
% 176.84/27.56    (2)  all_58_4 = all_52_5
% 176.84/27.56    (3)  all_58_4 = e2 | all_58_9 = e2
% 176.84/27.56    (4)   ~ (all_52_7 = e2)
% 176.84/27.56    (5)  all_58_9 = all_52_7
% 176.84/27.56  
% 176.84/27.56  Begin of proof
% 176.84/27.56  | 
% 176.84/27.56  | BETA: splitting (3) gives:
% 176.84/27.56  | 
% 176.84/27.56  | Case 1:
% 176.84/27.56  | | 
% 176.84/27.56  | |   (6)  all_58_4 = e2
% 176.84/27.56  | | 
% 176.84/27.56  | | COMBINE_EQS: (2), (6) imply:
% 176.84/27.56  | |   (7)  all_52_5 = e2
% 176.84/27.56  | | 
% 176.84/27.56  | | REDUCE: (1), (7) imply:
% 176.84/27.56  | |   (8)  $false
% 176.84/27.56  | | 
% 176.84/27.56  | | CLOSE: (8) is inconsistent.
% 176.84/27.56  | | 
% 176.84/27.56  | Case 2:
% 176.84/27.56  | | 
% 176.84/27.56  | |   (9)  all_58_9 = e2
% 176.84/27.56  | | 
% 176.84/27.56  | | COMBINE_EQS: (5), (9) imply:
% 176.84/27.56  | |   (10)  all_52_7 = e2
% 176.84/27.56  | | 
% 176.84/27.56  | | REDUCE: (4), (10) imply:
% 176.84/27.56  | |   (11)  $false
% 176.84/27.56  | | 
% 176.84/27.56  | | CLOSE: (11) is inconsistent.
% 176.84/27.56  | | 
% 176.84/27.56  | End of split
% 176.84/27.56  | 
% 176.84/27.56  End of proof
% 176.84/27.56  
% 176.84/27.56  Sub-proof #286 shows that the following formulas are inconsistent:
% 176.84/27.56  ----------------------------------------------------------------
% 176.84/27.56    (1)  all_58_15 = e3
% 176.84/27.56    (2)  all_58_15 = e2
% 176.84/27.56    (3)   ~ (e3 = e2)
% 176.84/27.56  
% 176.84/27.56  Begin of proof
% 176.84/27.56  | 
% 176.84/27.56  | COMBINE_EQS: (1), (2) imply:
% 176.84/27.56  |   (4)  e3 = e2
% 176.84/27.56  | 
% 176.84/27.56  | SIMP: (4) implies:
% 176.84/27.56  |   (5)  e3 = e2
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (3), (5) imply:
% 176.84/27.56  |   (6)  $false
% 176.84/27.56  | 
% 176.84/27.56  | CLOSE: (6) is inconsistent.
% 176.84/27.56  | 
% 176.84/27.56  End of proof
% 176.84/27.56  
% 176.84/27.56  Sub-proof #287 shows that the following formulas are inconsistent:
% 176.84/27.56  ----------------------------------------------------------------
% 176.84/27.56    (1)  all_56_8 = all_52_17
% 176.84/27.56    (2)  all_56_8 = e1
% 176.84/27.56    (3)   ~ (all_52_17 = e1)
% 176.84/27.56  
% 176.84/27.56  Begin of proof
% 176.84/27.56  | 
% 176.84/27.56  | COMBINE_EQS: (1), (2) imply:
% 176.84/27.56  |   (4)  all_52_17 = e1
% 176.84/27.56  | 
% 176.84/27.56  | SIMP: (4) implies:
% 176.84/27.56  |   (5)  all_52_17 = e1
% 176.84/27.56  | 
% 176.84/27.56  | REDUCE: (3), (5) imply:
% 176.84/27.56  |   (6)  $false
% 176.84/27.56  | 
% 176.84/27.56  | CLOSE: (6) is inconsistent.
% 176.84/27.56  | 
% 176.84/27.56  End of proof
% 176.84/27.56  
% 176.84/27.56  Sub-proof #288 shows that the following formulas are inconsistent:
% 176.84/27.56  ----------------------------------------------------------------
% 176.84/27.56    (1)  all_52_10 = e3
% 176.84/27.56    (2)   ~ (all_52_23 = all_14_2)
% 176.84/27.56    (3)   ~ (all_52_5 = all_52_13)
% 176.84/27.56    (4)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 176.84/27.56    (5)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.56    (6)   ~ (all_52_27 = all_10_2)
% 176.84/27.56    (7)   ~ (all_52_17 = all_52_23)
% 176.84/27.56    (8)   ~ (all_6_0 = e3)
% 176.84/27.56    (9)   ~ (all_52_13 = all_52_29)
% 176.84/27.56    (10)  all_56_3 = all_52_7
% 176.84/27.56    (11)  op(e3, e2) = all_52_3
% 176.84/27.56    (12)   ~ (all_52_9 = all_52_25)
% 176.84/27.56    (13)  op(e3, all_52_25) = all_52_24
% 176.84/27.56    (14)   ~ (all_52_19 = all_52_23)
% 176.84/27.56    (15)  all_56_11 = all_52_23
% 176.84/27.56    (16)  op(e1, e2) = all_52_19
% 176.84/27.56    (17)   ~ (all_52_27 = e0)
% 176.84/27.56    (18)  op(e3, all_52_9) = all_52_8
% 176.84/27.56    (19)   ~ (all_52_23 = e0)
% 176.84/27.56    (20)   ~ (all_52_3 = all_10_2)
% 176.84/27.56    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.56    (22)  all_58_5 = all_52_13
% 176.84/27.56    (23)   ~ (all_52_25 = all_52_29)
% 176.84/27.56    (24)  op(e0, e0) = all_6_1
% 176.84/27.56    (25)  op(all_14_1, all_14_2) = all_14_0
% 176.84/27.56    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 176.84/27.56    (27)  all_58_3 = all_10_2
% 176.84/27.56    (28)  all_56_9 = all_52_19
% 176.84/27.56    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.56    (30)  all_58_15 = all_6_2
% 176.84/27.56    (31)   ~ (all_52_9 = all_4_2)
% 176.84/27.56    (32)   ~ (all_52_5 = all_52_7)
% 176.84/27.56    (33)  all_58_10 = all_52_15
% 176.84/27.56    (34)   ~ (all_52_5 = all_4_2)
% 176.84/27.56    (35)  all_58_7 = all_52_19
% 176.84/27.56    (36)   ~ (all_52_17 = all_52_25)
% 176.84/27.56    (37)  op(e0, e1) = all_52_29
% 176.84/27.56    (38)   ~ (all_4_0 = e2)
% 176.84/27.56    (39)  all_58_4 = all_52_5
% 176.84/27.56    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 176.84/27.56    (41)   ~ (e3 = e1)
% 176.84/27.56    (42)   ~ (all_52_27 = all_52_29)
% 176.84/27.56    (43)  op(e3, all_4_2) = all_4_1
% 176.84/27.56    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 176.84/27.56    (45)   ~ (all_52_7 = all_4_2)
% 176.84/27.56    (46)  all_58_1 = all_52_3
% 176.84/27.56    (47)  all_58_0 = all_4_2
% 176.84/27.56    (48)  op(e1, all_52_29) = all_52_28
% 176.84/27.56    (49)   ~ (all_52_7 = e0)
% 176.84/27.56    (50)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.56    (51)   ~ (all_4_1 = e2)
% 176.84/27.56    (52)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.56    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 176.84/27.56    (54)  all_58_14 = all_52_29
% 176.84/27.56    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.56    (56)   ~ (all_52_3 = all_52_5)
% 176.84/27.56    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.56    (58)  op(e2, e1) = all_52_13
% 176.84/27.56    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.56    (60)  all_58_8 = all_14_2
% 176.84/27.56    (61)  op(e0, e2) = all_52_27
% 176.84/27.56    (62)  all_56_14 = all_52_29
% 176.84/27.56    (63)   ~ (all_14_0 = e3)
% 176.84/27.56    (64)  op(all_4_1, all_4_2) = all_4_0
% 176.84/27.56    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 176.84/27.56    (66)   ~ (all_52_5 = all_14_2)
% 176.84/27.56    (67)   ~ (all_52_3 = all_4_2)
% 176.84/27.56    (68)  op(e0, e3) = all_52_25
% 176.84/27.56    (69)  all_52_0 = all_4_1
% 176.84/27.56    (70)   ~ (all_52_9 = all_10_2)
% 176.84/27.56    (71)  op(e3, all_52_17) = all_52_16
% 176.84/27.56    (72)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.56    (73)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.56    (74)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.56    (75)  op(e0, all_52_23) = all_52_22
% 176.84/27.56    (76)   ~ (all_52_15 = all_52_23)
% 176.84/27.56    (77)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 176.84/27.56    (78)   ~ (all_52_5 = all_52_29)
% 176.84/27.56    (79)  all_56_2 = all_52_5
% 176.84/27.56    (80)  all_56_12 = all_52_25
% 176.84/27.56    (81)  all_58_13 = all_52_27
% 176.84/27.56    (82)   ~ (all_4_1 = e1)
% 176.84/27.56    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.56    (84)  all_56_5 = all_10_2
% 176.84/27.56    (85)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.56    (86)  op(e0, e0) = e0
% 176.84/27.56    (87)   ~ (all_52_25 = e0)
% 176.84/27.56    (88)   ~ (all_52_9 = all_52_17)
% 176.84/27.56    (89)   ~ (all_14_0 = e2)
% 176.84/27.56    (90)  all_58_6 = all_52_17
% 176.84/27.56    (91)   ~ (all_52_3 = all_52_7)
% 176.84/27.56    (92)  op(e2, all_52_19) = all_52_18
% 176.84/27.56    (93)  all_56_0 = all_4_2
% 176.84/27.56    (94)  all_58_11 = all_52_23
% 176.84/27.56    (95)   ~ (all_52_7 = all_52_15)
% 176.84/27.56    (96)   ~ (all_52_29 = all_14_2)
% 176.84/27.56    (97)   ~ (all_4_0 = e1)
% 176.84/27.56    (98)   ~ (all_52_19 = all_10_2)
% 176.84/27.56    (99)  all_58_15 = e0
% 176.84/27.56    (100)   ~ (all_6_0 = e2)
% 176.84/27.56    (101)  all_58_2 = all_52_9
% 176.84/27.56    (102)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.84/27.56    (103)   ~ (all_52_29 = e0)
% 176.84/27.56    (104)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 176.84/27.56    (105)  op(e3, e1) = all_52_5
% 176.84/27.56    (106)  all_56_10 = all_14_2
% 176.84/27.56    (107)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 176.84/27.56    (108)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.84/27.56    (109)  op(e1, e3) = all_52_17
% 176.84/27.56    (110)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 176.84/27.56    (111)   ~ (all_52_25 = all_4_2)
% 176.84/27.56    (112)  op(e3, e0) = all_52_7
% 176.84/27.56    (113)  op(e3, e3) = all_4_2
% 176.84/27.56    (114)  all_56_8 = all_52_17
% 176.84/27.56    (115)   ~ (all_52_17 = all_4_2)
% 176.84/27.56    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.56             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.56    (117)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.84/27.56           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 176.84/27.56           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.84/27.56           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.84/27.56    (118)   ~ (all_52_25 = all_52_27)
% 176.84/27.56    (119)   ~ (all_52_7 = all_6_2)
% 176.84/27.56    (120)   ~ (all_52_19 = all_52_27)
% 176.84/27.56    (121)  all_56_7 = all_52_15
% 176.84/27.56    (122)  op(all_6_1, e0) = all_6_0
% 176.84/27.56    (123)   ~ (all_52_7 = all_52_23)
% 176.84/27.56    (124)   ~ (all_6_0 = e1)
% 176.84/27.56    (125)  op(e2, all_52_27) = all_52_26
% 176.84/27.56    (126)  all_52_20 = all_14_1
% 176.84/27.57    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.57    (128)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.57    (129)  op(e1, all_14_2) = all_14_1
% 176.84/27.57    (130)  all_58_9 = all_52_7
% 176.84/27.57    (131)  all_58_12 = all_52_25
% 176.84/27.57    (132)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 176.84/27.57    (133)   ~ (all_52_9 = all_52_15)
% 176.84/27.57    (134)   ~ (e3 = e2)
% 176.84/27.57    (135)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.57    (136)   ~ (all_52_19 = all_14_2)
% 176.84/27.57    (137)  op(e0, all_52_7) = all_52_6
% 176.84/27.57    (138)  op(e2, e3) = all_52_9
% 176.84/27.57    (139)  all_56_13 = all_52_27
% 176.84/27.57  
% 176.84/27.57  Begin of proof
% 176.84/27.57  | 
% 176.84/27.57  | GROUND_INST: instantiating (116) with e0, all_6_1, e0, e0, simplifying with
% 176.84/27.57  |              (24), (86) gives:
% 176.84/27.57  |   (140)  all_6_1 = e0
% 176.84/27.57  | 
% 176.84/27.57  | REDUCE: (122), (140) imply:
% 176.84/27.57  |   (141)  op(e0, e0) = all_6_0
% 176.84/27.57  | 
% 176.84/27.57  | GROUND_INST: instantiating (116) with e0, all_6_0, e0, e0, simplifying with
% 176.84/27.57  |              (86), (141) gives:
% 176.84/27.57  |   (142)  all_6_0 = e0
% 176.84/27.57  | 
% 176.84/27.57  | REDUCE: (8), (142) imply:
% 176.84/27.57  |   (143)   ~ (e3 = e0)
% 176.84/27.57  | 
% 176.84/27.57  | SIMP: (143) implies:
% 176.84/27.57  |   (144)   ~ (e3 = e0)
% 176.84/27.57  | 
% 176.84/27.57  | REDUCE: (100), (142) imply:
% 176.84/27.57  |   (145)   ~ (e2 = e0)
% 176.84/27.57  | 
% 176.84/27.57  | SIMP: (145) implies:
% 176.84/27.57  |   (146)   ~ (e2 = e0)
% 176.84/27.57  | 
% 176.84/27.57  | REDUCE: (124), (142) imply:
% 176.84/27.57  |   (147)   ~ (e1 = e0)
% 176.84/27.57  | 
% 176.84/27.57  | SIMP: (147) implies:
% 176.84/27.57  |   (148)   ~ (e1 = e0)
% 176.84/27.57  | 
% 176.84/27.57  | BETA: splitting (117) gives:
% 176.84/27.57  | 
% 176.84/27.57  | Case 1:
% 176.84/27.57  | | 
% 176.84/27.57  | |   (149)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 176.84/27.57  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 176.84/27.57  | | 
% 176.84/27.57  | | BETA: splitting (149) gives:
% 176.84/27.57  | | 
% 176.84/27.57  | | Case 1:
% 176.84/27.57  | | | 
% 176.84/27.57  | | |   (150)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 176.84/27.57  | | | 
% 176.84/27.57  | | | REF_CLOSE: (10), (11), (17), (26), (29), (30), (32), (33), (37), (39),
% 176.84/27.57  | | |            (43), (45), (46), (47), (49), (53), (54), (55), (57), (59),
% 176.84/27.57  | | |            (61), (64), (68), (69), (72), (74), (78), (80), (81), (83),
% 176.84/27.57  | | |            (87), (91), (93), (94), (95), (99), (102), (103), (105), (108),
% 176.84/27.57  | | |            (111), (116), (118), (119), (123), (127), (128), (130), (131),
% 176.84/27.57  | | |            (132), (137), (139), (144), (150) are inconsistent by sub-proof
% 176.84/27.57  | | |            #1008.
% 176.84/27.57  | | | 
% 176.84/27.57  | | Case 2:
% 176.84/27.57  | | | 
% 176.84/27.57  | | |   (151)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.84/27.57  | | | 
% 176.84/27.57  | | | REF_CLOSE: (1), (134), (151) are inconsistent by sub-proof #289.
% 176.84/27.57  | | | 
% 176.84/27.57  | | End of split
% 176.84/27.57  | | 
% 176.84/27.57  | Case 2:
% 176.84/27.57  | | 
% 176.84/27.57  | |   (152)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 176.84/27.57  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 176.84/27.57  | |            e0)
% 176.84/27.57  | | 
% 176.84/27.57  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 176.84/27.57  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 176.84/27.57  | |            (27), (28), (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 176.84/27.57  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 176.84/27.57  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 176.84/27.57  | |            (61), (62), (63), (64), (65), (66), (67), (68), (70), (71), (72),
% 176.84/27.57  | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 176.84/27.57  | |            (84), (85), (87), (88), (89), (90), (91), (92), (93), (94), (96),
% 176.84/27.57  | |            (97), (98), (99), (101), (102), (103), (104), (105), (106),
% 176.84/27.57  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 176.84/27.57  | |            (116), (118), (120), (121), (123), (125), (126), (127), (128),
% 176.84/27.57  | |            (129), (130), (131), (132), (133), (134), (135), (136), (138),
% 176.84/27.57  | |            (139), (144), (146), (148), (152) are inconsistent by sub-proof
% 176.84/27.57  | |            #877.
% 176.84/27.57  | | 
% 176.84/27.57  | End of split
% 176.84/27.57  | 
% 176.84/27.57  End of proof
% 176.84/27.57  
% 176.84/27.57  Sub-proof #289 shows that the following formulas are inconsistent:
% 176.84/27.57  ----------------------------------------------------------------
% 176.84/27.57    (1)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 176.84/27.57    (2)  all_52_10 = e3
% 176.84/27.57    (3)   ~ (e3 = e2)
% 176.84/27.57  
% 176.84/27.57  Begin of proof
% 176.84/27.57  | 
% 176.84/27.57  | ALPHA: (1) implies:
% 176.84/27.57  |   (4)  all_52_10 = e2
% 176.84/27.57  | 
% 176.84/27.57  | COMBINE_EQS: (2), (4) imply:
% 176.84/27.57  |   (5)  e3 = e2
% 176.84/27.57  | 
% 176.84/27.57  | REDUCE: (3), (5) imply:
% 176.84/27.57  |   (6)  $false
% 176.84/27.57  | 
% 176.84/27.57  | CLOSE: (6) is inconsistent.
% 176.84/27.57  | 
% 176.84/27.57  End of proof
% 176.84/27.57  
% 176.84/27.57  Sub-proof #290 shows that the following formulas are inconsistent:
% 176.84/27.57  ----------------------------------------------------------------
% 176.84/27.57    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.57    (2)   ~ (all_6_0 = e3)
% 176.84/27.57    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 176.84/27.57    (4)  all_56_3 = all_52_7
% 176.84/27.57    (5)  op(e3, e2) = all_52_3
% 176.84/27.57    (6)   ~ (all_52_9 = all_52_25)
% 176.84/27.57    (7)  op(e3, all_52_25) = all_52_24
% 176.84/27.57    (8)   ~ (all_52_19 = all_52_23)
% 176.84/27.57    (9)  op(e1, e2) = all_52_19
% 176.84/27.57    (10)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.84/27.57    (11)  op(e3, all_52_9) = all_52_8
% 176.84/27.57    (12)   ~ (all_52_3 = all_10_2)
% 176.84/27.57    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 176.84/27.57    (14)  all_56_15 = all_6_2
% 176.84/27.57    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.57    (16)  all_58_3 = all_10_2
% 176.84/27.57    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.57    (18)  all_58_15 = all_6_2
% 176.84/27.57    (19)   ~ (all_52_5 = all_52_7)
% 176.84/27.57    (20)  all_58_10 = all_52_15
% 176.84/27.57    (21)  all_58_7 = all_52_19
% 176.84/27.57    (22)   ~ (all_52_17 = all_52_25)
% 176.84/27.57    (23)  op(e0, e1) = all_52_29
% 176.84/27.57    (24)  all_58_4 = all_52_5
% 176.84/27.57    (25)   ~ (e3 = e1)
% 176.84/27.57    (26)  all_34_1 = all_4_1
% 176.84/27.57    (27)   ~ (all_52_27 = all_52_29)
% 176.84/27.57    (28)  op(e3, all_4_2) = all_4_1
% 176.84/27.57    (29)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 176.84/27.57    (30)   ~ (all_52_7 = all_4_2)
% 176.84/27.57    (31)  all_58_1 = all_52_3
% 176.84/27.57    (32)  all_58_0 = all_4_2
% 176.84/27.57    (33)  op(all_4_1, all_4_2) = e1
% 176.84/27.57    (34)  op(e1, all_52_29) = all_52_28
% 176.84/27.57    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.84/27.57    (36)   ~ (all_4_1 = e2)
% 176.84/27.57    (37)  all_58_14 = all_52_29
% 176.84/27.57    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.57    (39)   ~ (all_52_3 = all_52_5)
% 176.84/27.57    (40)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.57    (41)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.57    (42)  all_56_1 = all_52_3
% 176.84/27.57    (43)  op(e0, e2) = all_52_27
% 176.84/27.57    (44)   ~ (all_52_3 = all_52_27)
% 176.84/27.57    (45)   ~ (all_52_3 = all_4_2)
% 176.84/27.57    (46)  op(all_6_1, all_6_2) = all_6_0
% 176.84/27.57    (47)  op(e0, e3) = all_52_25
% 176.84/27.57    (48)  op(e0, all_6_2) = all_6_1
% 176.84/27.57    (49)   ~ (all_52_9 = all_10_2)
% 176.84/27.57    (50)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.57    (51)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 176.84/27.57    (52)  op(all_14_1, all_14_2) = e2
% 176.84/27.57    (53)  all_56_2 = all_52_5
% 176.84/27.57    (54)  op(e1, e0) = all_52_23
% 176.84/27.57    (55)  all_58_13 = all_52_27
% 176.84/27.57    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 176.84/27.57    (57)  all_58_6 = all_52_17
% 176.84/27.57    (58)   ~ (all_52_3 = all_52_7)
% 176.84/27.57    (59)  all_56_0 = all_4_2
% 176.84/27.57    (60)  all_58_11 = all_52_23
% 176.84/27.57    (61)   ~ (all_52_3 = all_52_19)
% 176.84/27.57    (62)   ~ (all_52_7 = all_52_15)
% 176.84/27.57    (63)   ~ (all_52_29 = all_14_2)
% 176.84/27.57    (64)   ~ (all_6_0 = e2)
% 176.84/27.57    (65)  all_58_2 = all_52_9
% 176.84/27.57    (66)  op(e3, e1) = all_52_5
% 176.84/27.57    (67)   ~ (e2 = e1)
% 176.84/27.57    (68)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.84/27.57    (69)  op(e1, e1) = all_14_2
% 176.84/27.57    (70)  op(e1, e3) = all_52_17
% 176.84/27.57    (71)   ~ (all_52_25 = all_4_2)
% 176.84/27.57    (72)  op(e3, e0) = all_52_7
% 176.84/27.57    (73)  op(e3, e3) = all_4_2
% 176.84/27.57    (74)   ~ (all_52_17 = all_4_2)
% 176.84/27.57    (75)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.57    (76)   ~ (all_52_25 = all_52_27)
% 176.84/27.57    (77)  all_34_2 = all_4_2
% 176.84/27.57    (78)   ~ (all_52_7 = all_6_2)
% 176.84/27.57    (79)   ~ (all_52_19 = all_52_27)
% 176.84/27.57    (80)   ~ (all_52_7 = all_52_23)
% 176.84/27.57    (81)   ~ (all_6_0 = e1)
% 176.84/27.57    (82)  op(e2, all_52_27) = all_52_26
% 176.84/27.57    (83)  all_52_20 = all_14_1
% 176.84/27.57    (84)   ~ (all_52_17 = all_52_19)
% 176.84/27.57    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 176.84/27.57    (86)  all_52_30 = all_6_1
% 176.84/27.57    (87)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.57    (88)  op(e1, all_14_2) = all_14_1
% 176.84/27.57    (89)  all_58_9 = all_52_7
% 176.84/27.57    (90)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.84/27.57          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.84/27.57    (91)  all_58_12 = all_52_25
% 176.84/27.57    (92)   ~ (all_52_9 = all_52_15)
% 176.84/27.57    (93)   ~ (e3 = e2)
% 176.84/27.57    (94)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 176.84/27.57    (95)  op(e2, e3) = all_52_9
% 176.84/27.57    (96)  all_56_13 = all_52_27
% 176.84/27.57  
% 176.84/27.57  Begin of proof
% 176.84/27.57  | 
% 176.84/27.57  | BETA: splitting (90) gives:
% 176.84/27.57  | 
% 176.84/27.57  | Case 1:
% 176.84/27.57  | | 
% 176.84/27.57  | |   (97)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.84/27.57  | | 
% 176.84/27.57  | | ALPHA: (97) implies:
% 176.84/27.57  | |   (98)  all_52_20 = e1
% 176.84/27.57  | | 
% 176.84/27.57  | | COMBINE_EQS: (83), (98) imply:
% 176.84/27.57  | |   (99)  all_14_1 = e1
% 176.84/27.57  | | 
% 176.84/27.57  | | REF_CLOSE: (52), (67), (75), (88), (99) are inconsistent by sub-proof #315.
% 176.84/27.57  | | 
% 176.84/27.57  | Case 2:
% 176.84/27.57  | | 
% 176.84/27.57  | |   (100)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.84/27.57  | | 
% 176.84/27.57  | | ALPHA: (100) implies:
% 176.84/27.57  | |   (101)  all_52_30 = e0
% 176.84/27.57  | |   (102)  all_52_28 = e1
% 176.84/27.57  | |   (103)  all_52_26 = e2
% 176.84/27.57  | |   (104)  all_52_24 = e3
% 176.84/27.57  | | 
% 176.84/27.57  | | COMBINE_EQS: (86), (101) imply:
% 176.84/27.57  | |   (105)  all_6_1 = e0
% 176.84/27.57  | | 
% 176.84/27.57  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.84/27.57  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.84/27.57  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 176.84/27.57  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 176.84/27.57  | |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 176.84/27.57  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (68), (69),
% 176.84/27.57  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 176.84/27.57  | |            (81), (82), (84), (85), (87), (89), (91), (92), (93), (94), (95),
% 176.84/27.57  | |            (96), (102), (103), (104), (105) are inconsistent by sub-proof
% 176.84/27.57  | |            #555.
% 176.84/27.57  | | 
% 176.84/27.57  | End of split
% 176.84/27.57  | 
% 176.84/27.57  End of proof
% 176.84/27.57  
% 176.84/27.57  Sub-proof #291 shows that the following formulas are inconsistent:
% 176.84/27.57  ----------------------------------------------------------------
% 176.84/27.57    (1)  all_56_3 = all_52_7
% 176.84/27.57    (2)  op(e3, e2) = all_52_3
% 176.84/27.57    (3)   ~ (all_52_9 = all_52_25)
% 176.84/27.57    (4)  op(e3, all_52_25) = all_52_24
% 176.84/27.57    (5)  op(e1, e2) = all_52_19
% 176.84/27.57    (6)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 176.84/27.57    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 176.84/27.57    (8)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.57    (9)   ~ (e3 = e1)
% 176.84/27.57    (10)  all_34_1 = all_4_1
% 176.84/27.57    (11)  op(e3, all_4_2) = all_4_1
% 176.84/27.57    (12)   ~ (all_52_7 = all_4_2)
% 176.84/27.57    (13)  all_58_0 = all_4_2
% 176.84/27.57    (14)  op(all_4_1, all_4_2) = e1
% 176.84/27.57    (15)  op(e1, all_52_29) = all_52_28
% 176.84/27.57    (16)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 176.84/27.57    (17)   ~ (all_4_1 = e2)
% 176.84/27.57    (18)  all_58_14 = all_52_29
% 176.84/27.57    (19)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.57    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 176.84/27.57    (21)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.57    (22)  all_56_1 = all_52_3
% 176.84/27.57    (23)   ~ (all_52_3 = all_4_2)
% 176.84/27.57    (24)   ~ (e3 = e0)
% 176.84/27.57    (25)  op(all_14_1, all_14_2) = e2
% 176.84/27.57    (26)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.57    (27)  op(e1, e0) = all_52_23
% 176.84/27.57    (28)  all_56_12 = all_52_25
% 176.84/27.57    (29)  all_58_13 = all_52_27
% 176.84/27.57    (30)   ~ (all_52_25 = e0)
% 176.84/27.57    (31)  all_56_0 = all_4_2
% 176.84/27.57    (32)   ~ (all_52_3 = all_52_19)
% 176.84/27.57    (33)  all_58_15 = e0
% 176.84/27.57    (34)   ~ (e2 = e1)
% 176.84/27.57    (35)  op(e1, e3) = all_52_17
% 176.84/27.57    (36)   ~ (all_52_25 = all_4_2)
% 176.84/27.57    (37)  op(e3, e0) = all_52_7
% 176.84/27.57    (38)  op(e3, e3) = all_4_2
% 176.84/27.57    (39)   ~ (all_52_17 = all_4_2)
% 176.84/27.57    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.57    (41)   ~ (all_52_25 = all_52_27)
% 176.84/27.57    (42)  all_34_2 = all_4_2
% 176.84/27.57    (43)   ~ (all_52_7 = all_52_23)
% 176.84/27.57    (44)  op(e2, all_52_27) = all_52_26
% 176.84/27.57    (45)  all_52_20 = all_14_1
% 176.84/27.57    (46)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.57    (47)  op(e1, all_14_2) = all_14_1
% 176.84/27.57    (48)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.84/27.57          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.84/27.57    (49)  all_58_12 = all_52_25
% 176.84/27.57    (50)  op(e2, e3) = all_52_9
% 176.84/27.57    (51)  all_56_13 = all_52_27
% 176.84/27.57  
% 176.84/27.57  Begin of proof
% 176.84/27.57  | 
% 176.84/27.57  | BETA: splitting (48) gives:
% 176.84/27.57  | 
% 176.84/27.57  | Case 1:
% 176.84/27.57  | | 
% 176.84/27.57  | |   (52)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.84/27.57  | | 
% 176.84/27.57  | | ALPHA: (52) implies:
% 176.84/27.57  | |   (53)  all_52_20 = e1
% 176.84/27.57  | | 
% 176.84/27.57  | | COMBINE_EQS: (45), (53) imply:
% 176.84/27.57  | |   (54)  all_14_1 = e1
% 176.84/27.57  | | 
% 176.84/27.57  | | REF_CLOSE: (25), (34), (40), (47), (54) are inconsistent by sub-proof #315.
% 176.84/27.57  | | 
% 176.84/27.57  | Case 2:
% 176.84/27.57  | | 
% 176.84/27.57  | |   (55)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 176.84/27.57  | | 
% 176.84/27.57  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 176.84/27.57  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 176.84/27.57  | |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36),
% 176.84/27.57  | |            (37), (38), (39), (40), (41), (42), (43), (44), (46), (49), (50),
% 176.84/27.57  | |            (51), (55) are inconsistent by sub-proof #576.
% 176.84/27.57  | | 
% 176.84/27.57  | End of split
% 176.84/27.57  | 
% 176.84/27.57  End of proof
% 176.84/27.57  
% 176.84/27.57  Sub-proof #292 shows that the following formulas are inconsistent:
% 176.84/27.57  ----------------------------------------------------------------
% 176.84/27.57    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 176.84/27.57    (2)  all_40_2 = all_4_2
% 176.84/27.57    (3)  all_56_3 = all_52_7
% 176.84/27.57    (4)  op(e3, e2) = all_52_3
% 176.84/27.57    (5)   ~ (all_52_9 = all_52_25)
% 176.84/27.57    (6)  op(e3, all_52_25) = all_52_24
% 176.84/27.57    (7)  op(e1, e2) = all_52_19
% 176.84/27.57    (8)  all_58_5 = all_52_13
% 176.84/27.57    (9)   ~ (all_52_25 = all_52_29)
% 176.84/27.57    (10)  all_56_9 = all_52_19
% 176.84/27.57    (11)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 176.84/27.57    (12)   ~ (all_52_9 = all_4_2)
% 176.84/27.57    (13)   ~ (all_52_5 = all_52_7)
% 176.84/27.57    (14)   ~ (all_52_5 = all_4_2)
% 176.84/27.57    (15)  all_58_7 = all_52_19
% 176.84/27.57    (16)   ~ (all_52_17 = all_52_25)
% 176.84/27.57    (17)   ~ (all_4_0 = e2)
% 176.84/27.57    (18)  all_58_4 = all_52_5
% 176.84/27.57    (19)   ~ (e3 = e1)
% 176.84/27.57    (20)   ~ (all_52_27 = all_52_29)
% 176.84/27.57    (21)   ~ (all_52_17 = all_14_2)
% 176.84/27.57    (22)  all_58_0 = all_4_2
% 176.84/27.57    (23)  op(e1, all_52_29) = all_52_28
% 176.84/27.57    (24)   ~ (all_52_7 = e0)
% 176.84/27.57    (25)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 176.84/27.57    (26)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 176.84/27.57    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 176.84/27.57    (28)  all_58_14 = all_52_29
% 176.84/27.57    (29)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 176.84/27.57    (30)  op(e2, e1) = all_52_13
% 176.84/27.57    (31)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 176.84/27.57    (32)  all_58_8 = all_14_2
% 176.84/27.57    (33)  all_56_14 = all_52_29
% 176.84/27.57    (34)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 176.84/27.57    (35)   ~ (all_52_3 = all_52_27)
% 176.84/27.57    (36)   ~ (all_52_3 = all_4_2)
% 176.84/27.57    (37)  op(e3, all_52_17) = all_52_16
% 176.84/27.57    (38)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 176.84/27.57    (39)   ~ (e3 = e0)
% 176.84/27.57    (40)  all_40_0 = all_4_0
% 176.84/27.57    (41)  op(all_14_1, all_14_2) = e2
% 176.84/27.57    (42)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 176.84/27.57    (43)  op(e1, e0) = all_52_23
% 176.84/27.57    (44)  all_56_12 = all_52_25
% 176.84/27.57    (45)  all_58_13 = all_52_27
% 176.84/27.57    (46)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 176.84/27.57    (47)   ~ (all_52_25 = e0)
% 176.84/27.57    (48)   ~ (all_52_9 = all_52_17)
% 176.84/27.57    (49)  all_58_6 = all_52_17
% 176.84/27.57    (50)   ~ (all_52_3 = all_52_7)
% 176.84/27.57    (51)   ~ (e1 = e0)
% 176.84/27.57    (52)  all_56_0 = all_4_2
% 176.84/27.57    (53)  all_58_11 = all_52_23
% 176.84/27.57    (54)   ~ (all_52_3 = all_52_19)
% 176.84/27.57    (55)   ~ (all_52_29 = all_14_2)
% 176.84/27.57    (56)  all_58_15 = e0
% 176.84/27.57    (57)  op(e1, all_4_2) = all_4_0
% 176.84/27.57    (58)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 176.84/27.57    (59)   ~ (all_52_29 = e0)
% 176.84/27.57    (60)  op(e3, e1) = all_52_5
% 176.84/27.57    (61)   ~ (e2 = e1)
% 176.84/27.57    (62)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 176.84/27.57    (63)  op(e1, e3) = all_52_17
% 176.84/27.57    (64)   ~ (all_52_25 = all_4_2)
% 176.84/27.57    (65)  op(e3, e0) = all_52_7
% 176.84/27.57    (66)  op(e3, e3) = all_4_2
% 176.84/27.57    (67)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 176.84/27.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 176.84/27.57    (68)   ~ (all_52_25 = all_52_27)
% 176.84/27.57    (69)  op(e2, all_52_27) = all_52_26
% 176.84/27.57    (70)  all_52_20 = all_14_1
% 176.84/27.57    (71)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 176.84/27.57    (72)  op(e1, all_14_2) = all_14_1
% 176.84/27.57    (73)  all_58_9 = all_52_7
% 176.84/27.57    (74)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 176.84/27.57          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 176.84/27.57    (75)  all_58_12 = all_52_25
% 176.84/27.57    (76)  op(e3, all_4_2) = e1
% 176.84/27.57    (77)  op(e2, e3) = all_52_9
% 176.84/27.57    (78)  all_56_13 = all_52_27
% 176.84/27.57  
% 176.84/27.57  Begin of proof
% 176.84/27.57  | 
% 176.84/27.57  | BETA: splitting (74) gives:
% 176.84/27.57  | 
% 176.84/27.57  | Case 1:
% 176.84/27.57  | | 
% 176.84/27.57  | |   (79)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 176.84/27.57  | | 
% 176.84/27.57  | | ALPHA: (79) implies:
% 176.84/27.57  | |   (80)  all_52_20 = e1
% 176.84/27.57  | | 
% 176.84/27.57  | | COMBINE_EQS: (70), (80) imply:
% 176.84/27.57  | |   (81)  all_14_1 = e1
% 176.84/27.57  | | 
% 176.84/27.57  | | REF_CLOSE: (41), (61), (67), (72), (81) are inconsistent by sub-proof #315.
% 177.04/27.57  | | 
% 177.04/27.57  | Case 2:
% 177.04/27.57  | | 
% 177.04/27.57  | |   (82)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.04/27.57  | | 
% 177.04/27.57  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.04/27.57  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.04/27.57  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.04/27.57  | |            (35), (36), (37), (38), (39), (40), (42), (43), (44), (45), (46),
% 177.04/27.57  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.04/27.57  | |            (58), (59), (60), (62), (63), (64), (65), (66), (67), (68), (69),
% 177.04/27.57  | |            (71), (73), (75), (76), (77), (78), (82) are inconsistent by
% 177.04/27.57  | |            sub-proof #615.
% 177.04/27.57  | | 
% 177.04/27.57  | End of split
% 177.04/27.57  | 
% 177.04/27.57  End of proof
% 177.04/27.57  
% 177.04/27.57  Sub-proof #293 shows that the following formulas are inconsistent:
% 177.04/27.57  ----------------------------------------------------------------
% 177.04/27.57    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.57    (2)   ~ (all_52_27 = all_10_2)
% 177.04/27.57    (3)  op(e2, e2) = all_10_2
% 177.04/27.57    (4)   ~ (all_52_17 = all_52_23)
% 177.04/27.57    (5)  all_52_26 = e2
% 177.04/27.57    (6)   ~ (all_6_0 = e3)
% 177.04/27.57    (7)   ~ (all_52_13 = all_52_29)
% 177.04/27.57    (8)  all_56_3 = all_52_7
% 177.04/27.57    (9)  op(e3, e2) = all_52_3
% 177.04/27.57    (10)   ~ (all_52_9 = all_52_25)
% 177.04/27.57    (11)  op(e3, all_52_25) = all_52_24
% 177.04/27.57    (12)   ~ (all_52_19 = all_52_23)
% 177.04/27.57    (13)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.04/27.57    (14)  op(e3, all_52_9) = all_52_8
% 177.04/27.57    (15)  all_50_1 = all_4_1
% 177.04/27.57    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.57    (17)  all_58_5 = all_52_13
% 177.04/27.57    (18)   ~ (all_52_25 = all_52_29)
% 177.04/27.57    (19)  all_56_15 = all_6_2
% 177.04/27.57    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.57    (21)  all_6_1 = e0
% 177.04/27.57    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.57    (23)  all_58_3 = all_10_2
% 177.04/27.57    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.57    (25)  all_58_15 = all_6_2
% 177.04/27.57    (26)   ~ (all_52_9 = all_4_2)
% 177.04/27.57    (27)   ~ (all_52_5 = all_52_7)
% 177.04/27.57    (28)  all_58_10 = all_52_15
% 177.04/27.57    (29)   ~ (all_52_5 = all_4_2)
% 177.04/27.57    (30)  all_58_7 = all_52_19
% 177.04/27.57    (31)   ~ (all_52_17 = all_52_25)
% 177.04/27.57    (32)  op(e0, e1) = all_52_29
% 177.04/27.57    (33)  all_58_4 = all_52_5
% 177.04/27.57    (34)   ~ (e3 = e1)
% 177.04/27.57    (35)   ~ (all_52_27 = all_52_29)
% 177.04/27.57    (36)   ~ (all_52_17 = all_14_2)
% 177.04/27.57    (37)  op(e3, all_4_2) = all_4_1
% 177.04/27.57    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.57    (39)   ~ (all_52_7 = all_4_2)
% 177.04/27.57    (40)  all_58_1 = all_52_3
% 177.04/27.57    (41)   ~ (all_52_13 = all_52_15)
% 177.04/27.57    (42)  all_58_0 = all_4_2
% 177.04/27.57    (43)  op(e1, all_52_29) = all_52_28
% 177.04/27.57    (44)  all_50_2 = all_4_2
% 177.04/27.57    (45)   ~ (all_4_1 = e2)
% 177.04/27.57    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.57    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.57    (48)  all_58_14 = all_52_29
% 177.04/27.57    (49)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.57    (50)  all_26_2 = all_4_2
% 177.04/27.57    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.57    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.57    (53)  all_58_8 = all_14_2
% 177.04/27.57    (54)  op(e0, e2) = all_52_27
% 177.04/27.57    (55)   ~ (all_52_3 = all_4_2)
% 177.04/27.57    (56)  op(all_6_1, all_6_2) = all_6_0
% 177.04/27.57    (57)  op(e0, e3) = all_52_25
% 177.04/27.57    (58)  op(e0, all_6_2) = all_6_1
% 177.04/27.57    (59)   ~ (all_52_9 = all_10_2)
% 177.04/27.57    (60)  op(all_4_1, all_4_2) = e2
% 177.04/27.57    (61)  op(e3, all_52_17) = all_52_16
% 177.04/27.57    (62)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.04/27.57    (63)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.57    (64)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.57    (65)  all_56_12 = all_52_25
% 177.04/27.57    (66)  all_58_13 = all_52_27
% 177.04/27.57    (67)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.04/27.57    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.57    (69)   ~ (all_52_9 = all_52_17)
% 177.04/27.58    (70)  all_58_6 = all_52_17
% 177.04/27.58    (71)   ~ (all_52_3 = all_52_7)
% 177.04/27.58    (72)  all_56_0 = all_4_2
% 177.04/27.58    (73)  all_58_11 = all_52_23
% 177.04/27.58    (74)  all_26_1 = all_4_1
% 177.04/27.58    (75)   ~ (all_6_0 = e2)
% 177.04/27.58    (76)   ~ (all_52_29 = all_6_2)
% 177.04/27.58    (77)  all_58_2 = all_52_9
% 177.04/27.58    (78)  op(e3, e1) = all_52_5
% 177.04/27.58    (79)   ~ (all_52_25 = all_6_2)
% 177.04/27.58    (80)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.58    (81)  op(e1, e3) = all_52_17
% 177.04/27.58    (82)   ~ (all_52_25 = all_4_2)
% 177.04/27.58    (83)  op(e3, e0) = all_52_7
% 177.04/27.58    (84)  all_52_28 = e1
% 177.04/27.58    (85)  op(e3, e3) = all_4_2
% 177.04/27.58    (86)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.04/27.58            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.04/27.58    (87)   ~ (all_52_17 = all_4_2)
% 177.04/27.58    (88)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.58    (89)   ~ (all_52_25 = all_52_27)
% 177.04/27.58    (90)   ~ (all_52_7 = all_6_2)
% 177.04/27.58    (91)   ~ (all_6_0 = e1)
% 177.04/27.58    (92)  op(e2, all_52_27) = all_52_26
% 177.04/27.58    (93)   ~ (all_52_17 = all_52_19)
% 177.04/27.58    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.58    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.58    (96)  all_58_9 = all_52_7
% 177.04/27.58    (97)  all_52_24 = e3
% 177.04/27.58    (98)  all_58_12 = all_52_25
% 177.04/27.58    (99)   ~ (all_52_9 = all_52_15)
% 177.04/27.58    (100)   ~ (e3 = e2)
% 177.04/27.58    (101)  op(e2, e3) = all_52_9
% 177.04/27.58    (102)  all_56_13 = all_52_27
% 177.04/27.58  
% 177.04/27.58  Begin of proof
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (21), (56) imply:
% 177.04/27.58  |   (103)  op(e0, all_6_2) = all_6_0
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (11), (97) imply:
% 177.04/27.58  |   (104)  op(e3, all_52_25) = e3
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (5), (92) imply:
% 177.04/27.58  |   (105)  op(e2, all_52_27) = e2
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (43), (84) imply:
% 177.04/27.58  |   (106)  op(e1, all_52_29) = e1
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (21), (58) imply:
% 177.04/27.58  |   (107)  op(e0, all_6_2) = e0
% 177.04/27.58  | 
% 177.04/27.58  | GROUND_INST: instantiating (88) with e0, all_6_0, all_6_2, e0, simplifying
% 177.04/27.58  |              with (103), (107) gives:
% 177.04/27.58  |   (108)  all_6_0 = e0
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (6), (108) imply:
% 177.04/27.58  |   (109)   ~ (e3 = e0)
% 177.04/27.58  | 
% 177.04/27.58  | SIMP: (109) implies:
% 177.04/27.58  |   (110)   ~ (e3 = e0)
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (75), (108) imply:
% 177.04/27.58  |   (111)   ~ (e2 = e0)
% 177.04/27.58  | 
% 177.04/27.58  | SIMP: (111) implies:
% 177.04/27.58  |   (112)   ~ (e2 = e0)
% 177.04/27.58  | 
% 177.04/27.58  | BETA: splitting (86) gives:
% 177.04/27.58  | 
% 177.04/27.58  | Case 1:
% 177.04/27.58  | | 
% 177.04/27.58  | |   (113)  all_58_15 = e0
% 177.04/27.58  | | 
% 177.04/27.58  | | COMBINE_EQS: (25), (113) imply:
% 177.04/27.58  | |   (114)  all_6_2 = e0
% 177.04/27.58  | | 
% 177.04/27.58  | | REDUCE: (79), (114) imply:
% 177.04/27.58  | |   (115)   ~ (all_52_25 = e0)
% 177.04/27.58  | | 
% 177.04/27.58  | | REF_CLOSE: (8), (9), (10), (18), (24), (26), (27), (29), (31), (37), (39),
% 177.04/27.58  | |            (42), (45), (48), (49), (50), (52), (55), (60), (64), (65), (66),
% 177.04/27.58  | |            (67), (68), (72), (74), (78), (80), (81), (82), (83), (85), (87),
% 177.04/27.58  | |            (88), (89), (95), (98), (100), (101), (102), (104), (105), (106),
% 177.04/27.58  | |            (110), (112), (113), (115) are inconsistent by sub-proof #471.
% 177.04/27.58  | | 
% 177.04/27.58  | Case 2:
% 177.04/27.58  | | 
% 177.04/27.58  | |   (116)   ~ (all_58_15 = e0)
% 177.04/27.58  | |   (117)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.04/27.58  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.04/27.58  | | 
% 177.04/27.58  | | ALPHA: (117) implies:
% 177.04/27.58  | |   (118)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.58  | | 
% 177.04/27.58  | | REDUCE: (25), (116) imply:
% 177.04/27.58  | |   (119)   ~ (all_6_2 = e0)
% 177.04/27.58  | | 
% 177.04/27.58  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 177.04/27.58  | |            (15), (16), (17), (18), (19), (20), (22), (23), (24), (25), (28),
% 177.04/27.58  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 177.04/27.58  | |            (40), (41), (42), (44), (45), (46), (47), (48), (49), (50), (51),
% 177.04/27.58  | |            (52), (53), (54), (55), (57), (59), (60), (61), (62), (63), (64),
% 177.04/27.58  | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 177.04/27.58  | |            (76), (77), (78), (79), (80), (81), (82), (83), (85), (87), (88),
% 177.04/27.58  | |            (89), (90), (91), (93), (94), (95), (96), (98), (99), (100),
% 177.04/27.58  | |            (101), (102), (103), (104), (105), (106), (107), (118), (119) are
% 177.04/27.58  | |            inconsistent by sub-proof #451.
% 177.04/27.58  | | 
% 177.04/27.58  | End of split
% 177.04/27.58  | 
% 177.04/27.58  End of proof
% 177.04/27.58  
% 177.04/27.58  Sub-proof #294 shows that the following formulas are inconsistent:
% 177.04/27.58  ----------------------------------------------------------------
% 177.04/27.58    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.58    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.58    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.04/27.58    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.58    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.58    (6)   ~ (all_52_27 = all_10_2)
% 177.04/27.58    (7)   ~ (all_52_17 = all_52_23)
% 177.04/27.58    (8)  op(e2, all_10_2) = all_10_1
% 177.04/27.58    (9)   ~ (all_52_13 = all_52_29)
% 177.04/27.58    (10)  all_56_3 = all_52_7
% 177.04/27.58    (11)  op(e3, e2) = all_52_3
% 177.04/27.58    (12)   ~ (all_52_9 = all_52_25)
% 177.04/27.58    (13)  op(e3, all_52_25) = all_52_24
% 177.04/27.58    (14)   ~ (all_52_19 = all_52_23)
% 177.04/27.58    (15)  all_56_11 = all_52_23
% 177.04/27.58    (16)  op(e1, e2) = all_52_19
% 177.04/27.58    (17)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.04/27.58    (18)  op(e3, all_52_9) = all_52_8
% 177.04/27.58    (19)  all_50_1 = all_4_1
% 177.04/27.58    (20)   ~ (all_52_3 = all_10_2)
% 177.04/27.58    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.04/27.58    (22)  all_58_5 = all_52_13
% 177.04/27.58    (23)   ~ (all_6_2 = e0)
% 177.04/27.58    (24)   ~ (all_52_25 = all_52_29)
% 177.04/27.58    (25)  all_56_15 = all_6_2
% 177.04/27.58    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.58    (27)  op(e2, e0) = all_52_15
% 177.04/27.58    (28)  all_58_3 = all_10_2
% 177.04/27.58    (29)  all_56_9 = all_52_19
% 177.04/27.58    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.58    (31)  all_58_15 = all_6_2
% 177.04/27.58    (32)   ~ (all_52_9 = all_4_2)
% 177.04/27.58    (33)   ~ (all_52_5 = all_52_7)
% 177.04/27.58    (34)  all_58_10 = all_52_15
% 177.04/27.58    (35)   ~ (all_52_5 = all_4_2)
% 177.04/27.58    (36)  all_58_7 = all_52_19
% 177.04/27.58    (37)  all_56_4 = all_52_9
% 177.04/27.58    (38)   ~ (all_52_15 = all_6_2)
% 177.04/27.58    (39)   ~ (all_52_17 = all_52_25)
% 177.04/27.58    (40)  all_58_4 = all_52_5
% 177.04/27.58    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.58    (42)   ~ (e3 = e1)
% 177.04/27.58    (43)   ~ (all_52_27 = all_52_29)
% 177.04/27.58    (44)   ~ (all_52_17 = all_14_2)
% 177.04/27.58    (45)  op(e3, all_4_2) = all_4_1
% 177.04/27.58    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.58    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.58    (48)   ~ (all_52_7 = all_4_2)
% 177.04/27.58    (49)  all_58_1 = all_52_3
% 177.04/27.58    (50)   ~ (all_52_13 = all_52_15)
% 177.04/27.58    (51)  all_58_0 = all_4_2
% 177.04/27.58    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.58    (53)  op(e1, all_52_13) = all_52_12
% 177.04/27.58    (54)  op(e1, all_52_29) = all_52_28
% 177.04/27.58    (55)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.58          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.04/27.58    (56)  all_50_2 = all_4_2
% 177.04/27.58    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.58    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.58    (59)   ~ (all_4_1 = e2)
% 177.04/27.58    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.58    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.58    (62)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.58    (63)  all_58_14 = all_52_29
% 177.04/27.58    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.58    (65)  all_26_2 = all_4_2
% 177.04/27.58    (66)   ~ (all_52_3 = all_52_5)
% 177.04/27.58    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.58    (68)  op(e2, e1) = all_52_13
% 177.04/27.58    (69)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.58    (70)  all_58_8 = all_14_2
% 177.04/27.58    (71)  all_56_1 = all_52_3
% 177.04/27.58    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.58    (73)   ~ (all_52_3 = all_52_27)
% 177.04/27.58    (74)   ~ (all_52_3 = all_4_2)
% 177.04/27.58    (75)  op(e0, e3) = all_52_25
% 177.04/27.58    (76)  all_52_0 = all_4_1
% 177.04/27.58    (77)   ~ (all_52_9 = all_10_2)
% 177.04/27.58    (78)  op(all_4_1, all_4_2) = e2
% 177.04/27.58    (79)  op(e3, all_52_17) = all_52_16
% 177.04/27.58    (80)  all_52_10 = all_10_1
% 177.04/27.58    (81)   ~ (all_52_13 = all_14_2)
% 177.04/27.58    (82)   ~ (e3 = e0)
% 177.04/27.58    (83)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.58    (84)  op(all_14_1, all_14_2) = e2
% 177.04/27.58    (85)   ~ (all_52_9 = all_52_13)
% 177.04/27.58    (86)  op(e0, all_52_23) = all_52_22
% 177.04/27.58    (87)   ~ (all_52_15 = all_52_23)
% 177.04/27.58    (88)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.58    (89)  op(all_10_1, all_10_2) = all_10_0
% 177.04/27.58    (90)   ~ (all_52_5 = all_52_29)
% 177.04/27.58    (91)  all_56_2 = all_52_5
% 177.04/27.58    (92)  op(e1, e0) = all_52_23
% 177.04/27.58    (93)  all_58_13 = all_52_27
% 177.04/27.58    (94)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.04/27.58    (95)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.58    (96)  all_56_5 = all_10_2
% 177.04/27.58    (97)   ~ (all_52_9 = all_52_17)
% 177.04/27.58    (98)  all_58_6 = all_52_17
% 177.04/27.58    (99)   ~ (all_52_3 = all_52_7)
% 177.04/27.58    (100)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.58    (101)  op(e2, all_52_19) = all_52_18
% 177.04/27.58    (102)   ~ (e1 = e0)
% 177.04/27.58    (103)  all_56_0 = all_4_2
% 177.04/27.58    (104)  all_58_11 = all_52_23
% 177.04/27.58    (105)   ~ (all_52_3 = all_52_19)
% 177.04/27.58    (106)   ~ (all_52_7 = all_52_15)
% 177.04/27.58    (107)  all_26_1 = all_4_1
% 177.04/27.58    (108)  op(e0, all_52_15) = all_52_14
% 177.04/27.58    (109)   ~ (all_52_29 = all_14_2)
% 177.04/27.58    (110)   ~ (all_52_19 = all_10_2)
% 177.04/27.58    (111)   ~ (all_52_23 = all_6_2)
% 177.04/27.58    (112)   ~ (all_52_29 = all_6_2)
% 177.04/27.58    (113)  all_58_2 = all_52_9
% 177.04/27.58    (114)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.58    (115)  op(e3, e1) = all_52_5
% 177.04/27.58    (116)  all_56_10 = all_14_2
% 177.04/27.58    (117)   ~ (all_52_25 = all_6_2)
% 177.04/27.58    (118)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.58    (119)  op(e1, e3) = all_52_17
% 177.04/27.58    (120)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.58    (121)   ~ (all_52_25 = all_4_2)
% 177.04/27.58    (122)  op(e3, e0) = all_52_7
% 177.04/27.58    (123)  op(e3, e3) = all_4_2
% 177.04/27.58    (124)  all_56_8 = all_52_17
% 177.04/27.58    (125)   ~ (all_52_17 = all_4_2)
% 177.04/27.58    (126)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.58             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.58    (127)   ~ (all_52_25 = all_52_27)
% 177.04/27.58    (128)   ~ (all_52_27 = all_6_2)
% 177.04/27.58    (129)   ~ (all_52_7 = all_6_2)
% 177.04/27.58    (130)  all_56_7 = all_52_15
% 177.04/27.58    (131)   ~ (all_52_7 = all_52_23)
% 177.04/27.58    (132)   ~ (all_52_13 = all_10_2)
% 177.04/27.58    (133)  op(e2, all_52_27) = all_52_26
% 177.04/27.58    (134)   ~ (all_52_17 = all_52_19)
% 177.04/27.58    (135)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.58    (136)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.58    (137)  op(e1, all_14_2) = all_14_1
% 177.04/27.58    (138)  all_58_9 = all_52_7
% 177.04/27.58    (139)   ~ (e2 = e0)
% 177.04/27.58    (140)  all_58_12 = all_52_25
% 177.04/27.58    (141)   ~ (all_10_0 = e1)
% 177.04/27.58    (142)  all_56_6 = all_52_13
% 177.04/27.58    (143)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.58    (144)   ~ (all_52_9 = all_52_15)
% 177.04/27.58    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.58    (146)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.58    (147)   ~ (all_52_19 = all_14_2)
% 177.04/27.58    (148)  op(e2, e3) = all_52_9
% 177.04/27.58    (149)  all_56_13 = all_52_27
% 177.04/27.58  
% 177.04/27.58  Begin of proof
% 177.04/27.58  | 
% 177.04/27.58  | BETA: splitting (55) gives:
% 177.04/27.58  | 
% 177.04/27.58  | Case 1:
% 177.04/27.58  | | 
% 177.04/27.58  | |   (150)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.04/27.58  | | 
% 177.04/27.58  | | REF_CLOSE: (45), (59), (76), (78), (126), (150) are inconsistent by
% 177.04/27.58  | |            sub-proof #494.
% 177.04/27.58  | | 
% 177.04/27.58  | Case 2:
% 177.04/27.58  | | 
% 177.04/27.58  | |   (151)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.04/27.58  | | 
% 177.04/27.58  | | ALPHA: (151) implies:
% 177.04/27.58  | |   (152)  all_52_14 = e0
% 177.04/27.58  | |   (153)  all_52_12 = e1
% 177.04/27.58  | |   (154)  all_52_10 = e2
% 177.04/27.58  | |   (155)  all_52_8 = e3
% 177.04/27.58  | | 
% 177.04/27.58  | | COMBINE_EQS: (80), (154) imply:
% 177.04/27.58  | |   (156)  all_10_1 = e2
% 177.04/27.58  | | 
% 177.04/27.58  | | REDUCE: (89), (156) imply:
% 177.04/27.58  | |   (157)  op(e2, all_10_2) = all_10_0
% 177.04/27.58  | | 
% 177.04/27.58  | | REDUCE: (18), (155) imply:
% 177.04/27.58  | |   (158)  op(e3, all_52_9) = e3
% 177.04/27.58  | | 
% 177.04/27.58  | | REDUCE: (8), (156) imply:
% 177.04/27.58  | |   (159)  op(e2, all_10_2) = e2
% 177.04/27.58  | | 
% 177.04/27.58  | | REDUCE: (53), (153) imply:
% 177.04/27.58  | |   (160)  op(e1, all_52_13) = e1
% 177.04/27.58  | | 
% 177.04/27.58  | | REDUCE: (108), (152) imply:
% 177.04/27.58  | |   (161)  op(e0, all_52_15) = e0
% 177.04/27.58  | | 
% 177.04/27.58  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 177.04/27.58  | |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 177.04/27.58  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.04/27.58  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.04/27.58  | |            (48), (49), (50), (51), (52), (54), (56), (57), (58), (59), (60),
% 177.04/27.58  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 177.04/27.58  | |            (72), (73), (74), (75), (77), (78), (79), (81), (82), (83), (84),
% 177.04/27.58  | |            (85), (86), (87), (88), (90), (91), (92), (93), (94), (95), (96),
% 177.04/27.58  | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 177.04/27.58  | |            (106), (107), (109), (110), (111), (112), (113), (114), (115),
% 177.04/27.58  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.04/27.58  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 177.04/27.58  | |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 177.04/27.58  | |            (143), (144), (145), (146), (147), (148), (149), (157), (158),
% 177.04/27.58  | |            (159), (160), (161) are inconsistent by sub-proof #295.
% 177.04/27.58  | | 
% 177.04/27.58  | End of split
% 177.04/27.58  | 
% 177.04/27.58  End of proof
% 177.04/27.58  
% 177.04/27.58  Sub-proof #295 shows that the following formulas are inconsistent:
% 177.04/27.58  ----------------------------------------------------------------
% 177.04/27.58    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.58    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.58    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.04/27.58    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.58    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.58    (6)   ~ (all_52_27 = all_10_2)
% 177.04/27.58    (7)   ~ (all_52_17 = all_52_23)
% 177.04/27.58    (8)   ~ (all_52_13 = all_52_29)
% 177.04/27.58    (9)  op(e2, all_10_2) = all_10_0
% 177.04/27.58    (10)  all_56_3 = all_52_7
% 177.04/27.58    (11)  op(e3, e2) = all_52_3
% 177.04/27.58    (12)   ~ (all_52_9 = all_52_25)
% 177.04/27.58    (13)  op(e3, all_52_25) = all_52_24
% 177.04/27.58    (14)   ~ (all_52_19 = all_52_23)
% 177.04/27.58    (15)  all_56_11 = all_52_23
% 177.04/27.58    (16)  op(e1, e2) = all_52_19
% 177.04/27.58    (17)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.04/27.58    (18)  all_50_1 = all_4_1
% 177.04/27.58    (19)   ~ (all_52_3 = all_10_2)
% 177.04/27.58    (20)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.04/27.58    (21)  all_58_5 = all_52_13
% 177.04/27.58    (22)   ~ (all_6_2 = e0)
% 177.04/27.58    (23)   ~ (all_52_25 = all_52_29)
% 177.04/27.58    (24)  op(e1, all_52_13) = e1
% 177.04/27.58    (25)  op(e0, all_52_15) = e0
% 177.04/27.58    (26)  all_56_15 = all_6_2
% 177.04/27.58    (27)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.58    (28)  op(e2, e0) = all_52_15
% 177.04/27.58    (29)  all_58_3 = all_10_2
% 177.04/27.58    (30)  all_56_9 = all_52_19
% 177.04/27.58    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.58    (32)  all_58_15 = all_6_2
% 177.04/27.58    (33)   ~ (all_52_9 = all_4_2)
% 177.04/27.58    (34)   ~ (all_52_5 = all_52_7)
% 177.04/27.58    (35)  all_58_10 = all_52_15
% 177.04/27.58    (36)   ~ (all_52_5 = all_4_2)
% 177.04/27.58    (37)  all_58_7 = all_52_19
% 177.04/27.58    (38)  all_56_4 = all_52_9
% 177.04/27.58    (39)   ~ (all_52_15 = all_6_2)
% 177.04/27.58    (40)   ~ (all_52_17 = all_52_25)
% 177.04/27.58    (41)  all_58_4 = all_52_5
% 177.04/27.58    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.58    (43)   ~ (e3 = e1)
% 177.04/27.58    (44)   ~ (all_52_27 = all_52_29)
% 177.04/27.58    (45)   ~ (all_52_17 = all_14_2)
% 177.04/27.58    (46)  op(e3, all_4_2) = all_4_1
% 177.04/27.58    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.58    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.58    (49)   ~ (all_52_7 = all_4_2)
% 177.04/27.58    (50)  all_58_1 = all_52_3
% 177.04/27.58    (51)   ~ (all_52_13 = all_52_15)
% 177.04/27.58    (52)  all_58_0 = all_4_2
% 177.04/27.58    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.58    (54)  op(e1, all_52_29) = all_52_28
% 177.04/27.58    (55)  all_50_2 = all_4_2
% 177.04/27.58    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.58    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.58    (58)   ~ (all_4_1 = e2)
% 177.04/27.58    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.58    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.58    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.58    (62)  all_58_14 = all_52_29
% 177.04/27.58    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.58    (64)  all_26_2 = all_4_2
% 177.04/27.58    (65)   ~ (all_52_3 = all_52_5)
% 177.04/27.58    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.58    (67)  op(e2, e1) = all_52_13
% 177.04/27.58    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.58    (69)  all_58_8 = all_14_2
% 177.04/27.58    (70)  all_56_1 = all_52_3
% 177.04/27.58    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.58    (72)   ~ (all_52_3 = all_52_27)
% 177.04/27.58    (73)   ~ (all_52_3 = all_4_2)
% 177.04/27.58    (74)  op(e0, e3) = all_52_25
% 177.04/27.58    (75)   ~ (all_52_9 = all_10_2)
% 177.04/27.58    (76)  op(all_4_1, all_4_2) = e2
% 177.04/27.58    (77)  op(e3, all_52_17) = all_52_16
% 177.04/27.58    (78)   ~ (all_52_13 = all_14_2)
% 177.04/27.58    (79)  op(e3, all_52_9) = e3
% 177.04/27.58    (80)   ~ (e3 = e0)
% 177.04/27.58    (81)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.58    (82)  op(all_14_1, all_14_2) = e2
% 177.04/27.58    (83)   ~ (all_52_9 = all_52_13)
% 177.04/27.58    (84)  op(e0, all_52_23) = all_52_22
% 177.04/27.58    (85)   ~ (all_52_15 = all_52_23)
% 177.04/27.58    (86)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.58    (87)   ~ (all_52_5 = all_52_29)
% 177.04/27.58    (88)  all_56_2 = all_52_5
% 177.04/27.58    (89)  op(e1, e0) = all_52_23
% 177.04/27.58    (90)  all_58_13 = all_52_27
% 177.04/27.58    (91)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.04/27.58    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.58    (93)  all_56_5 = all_10_2
% 177.04/27.58    (94)   ~ (all_52_9 = all_52_17)
% 177.04/27.58    (95)  all_58_6 = all_52_17
% 177.04/27.58    (96)   ~ (all_52_3 = all_52_7)
% 177.04/27.58    (97)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.58    (98)  op(e2, all_52_19) = all_52_18
% 177.04/27.58    (99)   ~ (e1 = e0)
% 177.04/27.58    (100)  all_56_0 = all_4_2
% 177.04/27.58    (101)  all_58_11 = all_52_23
% 177.04/27.58    (102)   ~ (all_52_3 = all_52_19)
% 177.04/27.58    (103)   ~ (all_52_7 = all_52_15)
% 177.04/27.58    (104)  all_26_1 = all_4_1
% 177.04/27.58    (105)   ~ (all_52_29 = all_14_2)
% 177.04/27.58    (106)   ~ (all_52_19 = all_10_2)
% 177.04/27.58    (107)   ~ (all_52_23 = all_6_2)
% 177.04/27.58    (108)   ~ (all_52_29 = all_6_2)
% 177.04/27.58    (109)  all_58_2 = all_52_9
% 177.04/27.58    (110)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.58    (111)  op(e3, e1) = all_52_5
% 177.04/27.58    (112)  all_56_10 = all_14_2
% 177.04/27.58    (113)   ~ (all_52_25 = all_6_2)
% 177.04/27.58    (114)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.58    (115)  op(e1, e3) = all_52_17
% 177.04/27.58    (116)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.58    (117)   ~ (all_52_25 = all_4_2)
% 177.04/27.58    (118)  op(e3, e0) = all_52_7
% 177.04/27.58    (119)  op(e2, all_10_2) = e2
% 177.04/27.58    (120)  op(e3, e3) = all_4_2
% 177.04/27.58    (121)  all_56_8 = all_52_17
% 177.04/27.58    (122)   ~ (all_52_17 = all_4_2)
% 177.04/27.58    (123)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.58             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.58    (124)   ~ (all_52_25 = all_52_27)
% 177.04/27.58    (125)   ~ (all_52_27 = all_6_2)
% 177.04/27.58    (126)   ~ (all_52_7 = all_6_2)
% 177.04/27.58    (127)  all_56_7 = all_52_15
% 177.04/27.58    (128)   ~ (all_52_7 = all_52_23)
% 177.04/27.58    (129)   ~ (all_52_13 = all_10_2)
% 177.04/27.58    (130)  op(e2, all_52_27) = all_52_26
% 177.04/27.58    (131)   ~ (all_52_17 = all_52_19)
% 177.04/27.58    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.58    (133)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.58    (134)  op(e1, all_14_2) = all_14_1
% 177.04/27.58    (135)  all_58_9 = all_52_7
% 177.04/27.58    (136)   ~ (e2 = e0)
% 177.04/27.58    (137)  all_58_12 = all_52_25
% 177.04/27.58    (138)   ~ (all_10_0 = e1)
% 177.04/27.58    (139)  all_56_6 = all_52_13
% 177.04/27.58    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.58    (141)   ~ (all_52_9 = all_52_15)
% 177.04/27.58    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.58    (143)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.58    (144)   ~ (all_52_19 = all_14_2)
% 177.04/27.58    (145)  op(e2, e3) = all_52_9
% 177.04/27.58    (146)  all_56_13 = all_52_27
% 177.04/27.58  
% 177.04/27.58  Begin of proof
% 177.04/27.58  | 
% 177.04/27.58  | GROUND_INST: instantiating (123) with e2, all_10_0, all_10_2, e2, simplifying
% 177.04/27.58  |              with (9), (119) gives:
% 177.04/27.58  |   (147)  all_10_0 = e2
% 177.04/27.58  | 
% 177.04/27.58  | REDUCE: (138), (147) imply:
% 177.04/27.58  |   (148)   ~ (e2 = e1)
% 177.04/27.58  | 
% 177.04/27.58  | BETA: splitting (47) gives:
% 177.04/27.58  | 
% 177.04/27.58  | Case 1:
% 177.04/27.58  | | 
% 177.04/27.58  | |   (149)  all_56_15 = e3
% 177.04/27.58  | | 
% 177.04/27.58  | | COMBINE_EQS: (26), (149) imply:
% 177.04/27.59  | |   (150)  all_6_2 = e3
% 177.04/27.59  | | 
% 177.04/27.59  | | SIMP: (150) implies:
% 177.04/27.59  | |   (151)  all_6_2 = e3
% 177.04/27.59  | | 
% 177.04/27.59  | | REF_CLOSE: (10), (11), (19), (21), (24), (27), (29), (31), (33), (35), (38),
% 177.04/27.59  | |            (39), (46), (48), (49), (52), (58), (61), (64), (66), (76), (79),
% 177.04/27.59  | |            (83), (91), (94), (97), (100), (104), (109), (115), (118), (119),
% 177.04/27.59  | |            (120), (122), (123), (126), (133), (139), (145), (151) are
% 177.04/27.59  | |            inconsistent by sub-proof #467.
% 177.04/27.59  | | 
% 177.04/27.59  | Case 2:
% 177.04/27.59  | | 
% 177.04/27.59  | |   (152)   ~ (all_56_15 = e3)
% 177.04/27.59  | |   (153)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.59  | | 
% 177.04/27.59  | | REDUCE: (26), (152) imply:
% 177.04/27.59  | |   (154)   ~ (all_6_2 = e3)
% 177.04/27.59  | | 
% 177.04/27.59  | | BETA: splitting (63) gives:
% 177.04/27.59  | | 
% 177.04/27.59  | | Case 1:
% 177.04/27.59  | | | 
% 177.04/27.59  | | |   (155)  all_56_13 = e3
% 177.04/27.59  | | | 
% 177.04/27.59  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 177.04/27.59  | | |            (16), (19), (20), (21), (24), (25), (27), (28), (29), (31),
% 177.04/27.59  | | |            (32), (33), (34), (35), (36), (37), (38), (40), (41), (42),
% 177.04/27.59  | | |            (43), (44), (45), (46), (48), (50), (51), (52), (53), (56),
% 177.04/27.59  | | |            (58), (62), (65), (66), (69), (70), (72), (73), (74), (75),
% 177.04/27.59  | | |            (76), (77), (78), (79), (83), (85), (89), (90), (92), (93),
% 177.04/27.59  | | |            (95), (96), (97), (99), (100), (101), (106), (109), (114),
% 177.04/27.59  | | |            (115), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.04/27.59  | | |            (125), (129), (130), (131), (132), (135), (137), (141), (142),
% 177.04/27.59  | | |            (145), (146), (148), (155) are inconsistent by sub-proof #464.
% 177.04/27.59  | | | 
% 177.04/27.59  | | Case 2:
% 177.04/27.59  | | | 
% 177.04/27.59  | | |   (156)   ~ (all_56_13 = e3)
% 177.04/27.59  | | | 
% 177.04/27.59  | | | REDUCE: (146), (156) imply:
% 177.04/27.59  | | |   (157)   ~ (all_52_27 = e3)
% 177.04/27.59  | | | 
% 177.04/27.59  | | | BETA: splitting (68) gives:
% 177.04/27.59  | | | 
% 177.04/27.59  | | | Case 1:
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | |   (158)  all_58_12 = e3
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (14), (15),
% 177.04/27.59  | | | |            (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 177.04/27.59  | | | |            (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.04/27.59  | | | |            (38), (40), (41), (42), (44), (45), (46), (48), (49), (50),
% 177.04/27.59  | | | |            (52), (53), (55), (57), (58), (59), (60), (61), (62), (64),
% 177.04/27.59  | | | |            (65), (67), (69), (71), (73), (74), (76), (77), (78), (79),
% 177.04/27.59  | | | |            (80), (81), (82), (83), (84), (86), (87), (88), (90), (91),
% 177.04/27.59  | | | |            (92), (94), (95), (96), (97), (98), (100), (101), (102),
% 177.04/27.59  | | | |            (103), (104), (105), (106), (107), (109), (110), (111),
% 177.04/27.59  | | | |            (112), (113), (115), (116), (117), (118), (119), (123),
% 177.04/27.59  | | | |            (124), (125), (126), (127), (128), (131), (132), (133),
% 177.04/27.59  | | | |            (134), (135), (136), (137), (139), (140), (141), (142),
% 177.04/27.59  | | | |            (143), (144), (145), (148), (153), (158) are inconsistent by
% 177.04/27.59  | | | |            sub-proof #296.
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | Case 2:
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | |   (159)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | REF_CLOSE: (3), (7), (11), (17), (18), (19), (23), (25), (27), (29),
% 177.04/27.59  | | | |            (31), (32), (33), (35), (36), (37), (40), (43), (44), (46),
% 177.04/27.59  | | | |            (48), (49), (50), (52), (54), (55), (58), (60), (62), (66),
% 177.04/27.59  | | | |            (74), (76), (77), (79), (87), (88), (90), (92), (95), (96),
% 177.04/27.59  | | | |            (99), (100), (101), (108), (109), (111), (115), (117), (119),
% 177.04/27.59  | | | |            (120), (121), (122), (123), (131), (132), (135), (137),
% 177.04/27.59  | | | |            (143), (145), (148), (154), (157), (159) are inconsistent by
% 177.04/27.59  | | | |            sub-proof #463.
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | End of split
% 177.04/27.59  | | | 
% 177.04/27.59  | | End of split
% 177.04/27.59  | | 
% 177.04/27.59  | End of split
% 177.04/27.59  | 
% 177.04/27.59  End of proof
% 177.04/27.59  
% 177.04/27.59  Sub-proof #296 shows that the following formulas are inconsistent:
% 177.04/27.59  ----------------------------------------------------------------
% 177.04/27.59    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.59    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.59    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.59    (4)   ~ (all_52_27 = all_10_2)
% 177.04/27.59    (5)   ~ (all_52_17 = all_52_23)
% 177.04/27.59    (6)   ~ (all_52_13 = all_52_29)
% 177.04/27.59    (7)  all_56_3 = all_52_7
% 177.04/27.59    (8)  op(e3, e2) = all_52_3
% 177.04/27.59    (9)   ~ (all_52_9 = all_52_25)
% 177.04/27.59    (10)   ~ (all_52_19 = all_52_23)
% 177.04/27.59    (11)  all_56_11 = all_52_23
% 177.04/27.59    (12)  op(e1, e2) = all_52_19
% 177.04/27.59    (13)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.04/27.59    (14)  all_50_1 = all_4_1
% 177.04/27.59    (15)   ~ (all_52_3 = all_10_2)
% 177.04/27.59    (16)  all_58_5 = all_52_13
% 177.04/27.59    (17)   ~ (all_6_2 = e0)
% 177.04/27.59    (18)   ~ (all_52_25 = all_52_29)
% 177.04/27.59    (19)  op(e1, all_52_13) = e1
% 177.04/27.59    (20)  op(e0, all_52_15) = e0
% 177.04/27.59    (21)  all_56_15 = all_6_2
% 177.04/27.59    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.59    (23)  all_58_3 = all_10_2
% 177.04/27.59    (24)  all_56_9 = all_52_19
% 177.04/27.59    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.59    (26)  all_58_15 = all_6_2
% 177.04/27.59    (27)   ~ (all_52_9 = all_4_2)
% 177.04/27.59    (28)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.59    (29)   ~ (all_52_5 = all_52_7)
% 177.04/27.59    (30)  all_58_10 = all_52_15
% 177.04/27.59    (31)   ~ (all_52_5 = all_4_2)
% 177.04/27.59    (32)  all_58_7 = all_52_19
% 177.04/27.59    (33)  all_56_4 = all_52_9
% 177.04/27.59    (34)   ~ (all_52_17 = all_52_25)
% 177.04/27.59    (35)  all_58_4 = all_52_5
% 177.04/27.59    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.59    (37)   ~ (all_52_27 = all_52_29)
% 177.04/27.59    (38)   ~ (all_52_17 = all_14_2)
% 177.04/27.59    (39)  op(e3, all_4_2) = all_4_1
% 177.04/27.59    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.59    (41)   ~ (all_52_7 = all_4_2)
% 177.04/27.59    (42)  all_58_1 = all_52_3
% 177.04/27.59    (43)  all_58_0 = all_4_2
% 177.04/27.59    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.59    (45)  all_50_2 = all_4_2
% 177.04/27.59    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.59    (47)   ~ (all_4_1 = e2)
% 177.04/27.59    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.59    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.59    (50)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.59    (51)  all_58_14 = all_52_29
% 177.04/27.59    (52)  all_26_2 = all_4_2
% 177.04/27.59    (53)   ~ (all_52_3 = all_52_5)
% 177.04/27.59    (54)  op(e2, e1) = all_52_13
% 177.04/27.59    (55)  all_58_8 = all_14_2
% 177.04/27.59    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.59    (57)   ~ (all_52_3 = all_4_2)
% 177.04/27.59    (58)  op(e0, e3) = all_52_25
% 177.04/27.59    (59)  op(all_4_1, all_4_2) = e2
% 177.04/27.59    (60)  op(e3, all_52_17) = all_52_16
% 177.04/27.59    (61)   ~ (all_52_13 = all_14_2)
% 177.04/27.59    (62)  op(e3, all_52_9) = e3
% 177.04/27.59    (63)   ~ (e3 = e0)
% 177.04/27.59    (64)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.59    (65)  op(all_14_1, all_14_2) = e2
% 177.04/27.59    (66)   ~ (all_52_9 = all_52_13)
% 177.04/27.59    (67)  op(e0, all_52_23) = all_52_22
% 177.04/27.59    (68)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.59    (69)   ~ (all_52_5 = all_52_29)
% 177.04/27.59    (70)  all_56_2 = all_52_5
% 177.04/27.59    (71)  all_58_13 = all_52_27
% 177.04/27.59    (72)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.04/27.59    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.59    (74)  all_58_12 = e3
% 177.04/27.59    (75)   ~ (all_52_9 = all_52_17)
% 177.04/27.59    (76)  all_58_6 = all_52_17
% 177.04/27.59    (77)   ~ (all_52_3 = all_52_7)
% 177.04/27.59    (78)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.59    (79)  op(e2, all_52_19) = all_52_18
% 177.04/27.59    (80)  all_56_0 = all_4_2
% 177.04/27.59    (81)  all_58_11 = all_52_23
% 177.04/27.59    (82)   ~ (all_52_3 = all_52_19)
% 177.04/27.59    (83)   ~ (all_52_7 = all_52_15)
% 177.04/27.59    (84)  all_26_1 = all_4_1
% 177.04/27.59    (85)   ~ (all_52_29 = all_14_2)
% 177.04/27.59    (86)   ~ (all_52_19 = all_10_2)
% 177.04/27.59    (87)   ~ (all_52_23 = all_6_2)
% 177.04/27.59    (88)  all_58_2 = all_52_9
% 177.04/27.59    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.59    (90)  op(e3, e1) = all_52_5
% 177.04/27.59    (91)   ~ (e2 = e1)
% 177.04/27.59    (92)  all_56_10 = all_14_2
% 177.04/27.59    (93)   ~ (all_52_25 = all_6_2)
% 177.04/27.59    (94)  op(e1, e3) = all_52_17
% 177.04/27.59    (95)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.59    (96)   ~ (all_52_25 = all_4_2)
% 177.04/27.59    (97)  op(e3, e0) = all_52_7
% 177.04/27.59    (98)  op(e2, all_10_2) = e2
% 177.04/27.59    (99)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.59    (100)   ~ (all_52_25 = all_52_27)
% 177.04/27.59    (101)   ~ (all_52_27 = all_6_2)
% 177.04/27.59    (102)   ~ (all_52_7 = all_6_2)
% 177.04/27.59    (103)  all_56_7 = all_52_15
% 177.04/27.59    (104)   ~ (all_52_7 = all_52_23)
% 177.04/27.59    (105)   ~ (all_52_17 = all_52_19)
% 177.04/27.59    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.59    (107)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.59    (108)  op(e1, all_14_2) = all_14_1
% 177.04/27.59    (109)  all_58_9 = all_52_7
% 177.04/27.59    (110)   ~ (e2 = e0)
% 177.04/27.59    (111)  all_58_12 = all_52_25
% 177.04/27.59    (112)  all_56_6 = all_52_13
% 177.04/27.59    (113)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.59    (114)   ~ (all_52_9 = all_52_15)
% 177.04/27.59    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.59    (116)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.59    (117)   ~ (all_52_19 = all_14_2)
% 177.04/27.59    (118)  op(e2, e3) = all_52_9
% 177.04/27.59  
% 177.04/27.59  Begin of proof
% 177.04/27.59  | 
% 177.04/27.59  | COMBINE_EQS: (74), (111) imply:
% 177.04/27.59  |   (119)  all_52_25 = e3
% 177.04/27.59  | 
% 177.04/27.59  | SIMP: (119) implies:
% 177.04/27.59  |   (120)  all_52_25 = e3
% 177.04/27.59  | 
% 177.04/27.59  | REDUCE: (9), (120) imply:
% 177.04/27.59  |   (121)   ~ (all_52_9 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | REDUCE: (34), (120) imply:
% 177.04/27.59  |   (122)   ~ (all_52_17 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | REDUCE: (100), (120) imply:
% 177.04/27.59  |   (123)   ~ (all_52_27 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | SIMP: (123) implies:
% 177.04/27.59  |   (124)   ~ (all_52_27 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | REDUCE: (18), (120) imply:
% 177.04/27.59  |   (125)   ~ (all_52_29 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | SIMP: (125) implies:
% 177.04/27.59  |   (126)   ~ (all_52_29 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | REDUCE: (93), (120) imply:
% 177.04/27.59  |   (127)   ~ (all_6_2 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | SIMP: (127) implies:
% 177.04/27.59  |   (128)   ~ (all_6_2 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | REDUCE: (96), (120) imply:
% 177.04/27.59  |   (129)   ~ (all_4_2 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | SIMP: (129) implies:
% 177.04/27.59  |   (130)   ~ (all_4_2 = e3)
% 177.04/27.59  | 
% 177.04/27.59  | REDUCE: (58), (120) imply:
% 177.04/27.59  |   (131)  op(e0, e3) = e3
% 177.04/27.59  | 
% 177.04/27.59  | BETA: splitting (78) gives:
% 177.04/27.59  | 
% 177.04/27.59  | Case 1:
% 177.04/27.59  | | 
% 177.04/27.59  | |   (132)  all_56_4 = e3
% 177.04/27.59  | | 
% 177.04/27.59  | | REF_CLOSE: (33), (121), (132) are inconsistent by sub-proof #782.
% 177.04/27.59  | | 
% 177.04/27.59  | Case 2:
% 177.04/27.59  | | 
% 177.04/27.59  | |   (133)   ~ (all_56_4 = e3)
% 177.04/27.59  | |   (134)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.59  | | 
% 177.04/27.59  | | BETA: splitting (25) gives:
% 177.04/27.59  | | 
% 177.04/27.59  | | Case 1:
% 177.04/27.59  | | | 
% 177.04/27.59  | | |   (135)  all_56_0 = e3
% 177.04/27.59  | | | 
% 177.04/27.59  | | | COMBINE_EQS: (80), (135) imply:
% 177.04/27.59  | | |   (136)  all_4_2 = e3
% 177.04/27.59  | | | 
% 177.04/27.59  | | | REDUCE: (130), (136) imply:
% 177.04/27.59  | | |   (137)  $false
% 177.04/27.59  | | | 
% 177.04/27.59  | | | CLOSE: (137) is inconsistent.
% 177.04/27.59  | | | 
% 177.04/27.59  | | Case 2:
% 177.04/27.59  | | | 
% 177.04/27.59  | | |   (138)   ~ (all_56_0 = e3)
% 177.04/27.59  | | |   (139)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.59  | | | 
% 177.04/27.59  | | | BETA: splitting (73) gives:
% 177.04/27.59  | | | 
% 177.04/27.59  | | | Case 1:
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | |   (140)  all_58_0 = e1
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | COMBINE_EQS: (43), (140) imply:
% 177.04/27.59  | | | |   (141)  all_4_2 = e1
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | COMBINE_EQS: (45), (141) imply:
% 177.04/27.59  | | | |   (142)  all_50_2 = e1
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | REDUCE: (31), (141) imply:
% 177.04/27.59  | | | |   (143)   ~ (all_52_5 = e1)
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | REDUCE: (39), (141) imply:
% 177.04/27.59  | | | |   (144)  op(e3, e1) = all_4_1
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | BETA: splitting (13) gives:
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | Case 1:
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | |   (145)   ~ (all_50_2 = e1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (142), (145) imply:
% 177.04/27.59  | | | | |   (146)  $false
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | CLOSE: (146) is inconsistent.
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | Case 2:
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | |   (147)   ~ (all_50_1 = e0)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (14), (147) imply:
% 177.04/27.59  | | | | |   (148)   ~ (all_4_1 = e0)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | GROUND_INST: instantiating (99) with all_52_5, all_4_1, e1, e3,
% 177.04/27.59  | | | | |              simplifying with (90), (144) gives:
% 177.04/27.59  | | | | |   (149)  all_52_5 = all_4_1
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | COMBINE_EQS: (70), (149) imply:
% 177.04/27.59  | | | | |   (150)  all_56_2 = all_4_1
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (2), (149) imply:
% 177.04/27.59  | | | | |   (151)   ~ (all_52_13 = all_4_1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | SIMP: (151) implies:
% 177.04/27.59  | | | | |   (152)   ~ (all_52_13 = all_4_1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (69), (149) imply:
% 177.04/27.59  | | | | |   (153)   ~ (all_52_29 = all_4_1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | SIMP: (153) implies:
% 177.04/27.59  | | | | |   (154)   ~ (all_52_29 = all_4_1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (143), (149) imply:
% 177.04/27.59  | | | | |   (155)   ~ (all_4_1 = e1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | BETA: splitting (116) gives:
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | Case 1:
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | |   (156)  all_56_2 = e3
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | COMBINE_EQS: (150), (156) imply:
% 177.04/27.59  | | | | | |   (157)  all_4_1 = e3
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | REDUCE: (152), (157) imply:
% 177.04/27.59  | | | | | |   (158)   ~ (all_52_13 = e3)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | REDUCE: (47), (157) imply:
% 177.04/27.59  | | | | | |   (159)   ~ (e3 = e2)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 177.04/27.59  | | | | | |            (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 177.04/27.59  | | | | | |            (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 177.04/27.59  | | | | | |            (36), (37), (38), (40), (41), (42), (43), (44), (46),
% 177.04/27.59  | | | | | |            (48), (49), (50), (51), (53), (54), (55), (56), (60),
% 177.04/27.59  | | | | | |            (61), (62), (63), (66), (67), (68), (71), (74), (75),
% 177.04/27.59  | | | | | |            (76), (77), (78), (79), (80), (81), (82), (83), (85),
% 177.04/27.59  | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94), (97),
% 177.04/27.59  | | | | | |            (98), (99), (101), (102), (104), (105), (106), (107),
% 177.04/27.59  | | | | | |            (108), (109), (112), (114), (115), (117), (118), (121),
% 177.04/27.59  | | | | | |            (124), (126), (128), (131), (139), (158), (159) are
% 177.04/27.59  | | | | | |            inconsistent by sub-proof #382.
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | Case 2:
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | |   (160)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | REF_CLOSE: (47), (148), (150), (155), (160) are inconsistent by
% 177.04/27.59  | | | | | |            sub-proof #478.
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | End of split
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | End of split
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | Case 2:
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | |   (161)   ~ (all_58_0 = e1)
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | REDUCE: (43), (161) imply:
% 177.04/27.59  | | | |   (162)   ~ (all_4_2 = e1)
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | BETA: splitting (22) gives:
% 177.04/27.59  | | | | 
% 177.04/27.59  | | | | Case 1:
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | |   (163)  all_58_0 = e2
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | COMBINE_EQS: (43), (163) imply:
% 177.04/27.59  | | | | |   (164)  all_4_2 = e2
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (57), (164) imply:
% 177.04/27.59  | | | | |   (165)   ~ (all_52_3 = e2)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (31), (164) imply:
% 177.04/27.59  | | | | |   (166)   ~ (all_52_5 = e2)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (27), (164) imply:
% 177.04/27.59  | | | | |   (167)   ~ (all_52_9 = e2)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (130), (164) imply:
% 177.04/27.59  | | | | |   (168)   ~ (e3 = e2)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | SIMP: (168) implies:
% 177.04/27.59  | | | | |   (169)   ~ (e3 = e2)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (39), (164) imply:
% 177.04/27.59  | | | | |   (170)  op(e3, e2) = all_4_1
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | GROUND_INST: instantiating (99) with all_52_3, all_4_1, e2, e3,
% 177.04/27.59  | | | | |              simplifying with (8), (170) gives:
% 177.04/27.59  | | | | |   (171)  all_52_3 = all_4_1
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | COMBINE_EQS: (42), (171) imply:
% 177.04/27.59  | | | | |   (172)  all_58_1 = all_4_1
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | REDUCE: (77), (171) imply:
% 177.04/27.59  | | | | |   (173)   ~ (all_52_7 = all_4_1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | SIMP: (173) implies:
% 177.04/27.59  | | | | |   (174)   ~ (all_52_7 = all_4_1)
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | BETA: splitting (107) gives:
% 177.04/27.59  | | | | | 
% 177.04/27.59  | | | | | Case 1:
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | |   (175)  all_56_3 = e3
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | COMBINE_EQS: (7), (175) imply:
% 177.04/27.59  | | | | | |   (176)  all_52_7 = e3
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | SIMP: (176) implies:
% 177.04/27.59  | | | | | |   (177)  all_52_7 = e3
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | COMBINE_EQS: (109), (177) imply:
% 177.04/27.59  | | | | | |   (178)  all_58_9 = e3
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | REDUCE: (83), (177) imply:
% 177.04/27.59  | | | | | |   (179)   ~ (all_52_15 = e3)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | SIMP: (179) implies:
% 177.04/27.59  | | | | | |   (180)   ~ (all_52_15 = e3)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | REDUCE: (104), (177) imply:
% 177.04/27.59  | | | | | |   (181)   ~ (all_52_23 = e3)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | SIMP: (181) implies:
% 177.04/27.59  | | | | | |   (182)   ~ (all_52_23 = e3)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | REDUCE: (174), (177) imply:
% 177.04/27.59  | | | | | |   (183)   ~ (all_4_1 = e3)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | SIMP: (183) implies:
% 177.04/27.59  | | | | | |   (184)   ~ (all_4_1 = e3)
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | BETA: splitting (40) gives:
% 177.04/27.59  | | | | | | 
% 177.04/27.59  | | | | | | Case 1:
% 177.04/27.59  | | | | | | | 
% 177.04/27.59  | | | | | | |   (185)  all_58_2 = e3
% 177.04/27.59  | | | | | | | 
% 177.04/27.59  | | | | | | | REF_CLOSE: (88), (121), (185) are inconsistent by sub-proof #980.
% 177.04/27.59  | | | | | | | 
% 177.04/27.59  | | | | | | Case 2:
% 177.04/27.59  | | | | | | | 
% 177.04/27.59  | | | | | | |   (186)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.59  | | | | | | | 
% 177.04/27.59  | | | | | | | BETA: splitting (49) gives:
% 177.04/27.59  | | | | | | | 
% 177.04/27.59  | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | |   (187)  all_58_1 = e3
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | | COMBINE_EQS: (172), (187) imply:
% 177.04/27.59  | | | | | | | |   (188)  all_4_1 = e3
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | | REDUCE: (184), (188) imply:
% 177.04/27.59  | | | | | | | |   (189)  $false
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | | CLOSE: (189) is inconsistent.
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | |   (190)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | | BETA: splitting (36) gives:
% 177.04/27.59  | | | | | | | | 
% 177.04/27.59  | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | 
% 177.04/27.59  | | | | | | | | |   (191)  all_58_6 = e3
% 177.04/27.59  | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | REF_CLOSE: (76), (122), (191) are inconsistent by sub-proof
% 177.04/27.59  | | | | | | | | |            #981.
% 177.04/27.59  | | | | | | | | | 
% 177.04/27.59  | | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | | 
% 177.04/27.59  | | | | | | | | |   (192)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.59  | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | BETA: splitting (64) gives:
% 177.04/27.59  | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | |   (193)  all_58_0 = e0
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | COMBINE_EQS: (163), (193) imply:
% 177.04/27.59  | | | | | | | | | |   (194)  e2 = e0
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | REDUCE: (110), (194) imply:
% 177.04/27.59  | | | | | | | | | |   (195)  $false
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | CLOSE: (195) is inconsistent.
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | |   (196)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | BETA: splitting (50) gives:
% 177.04/27.59  | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | |   (197)  all_56_6 = e3
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | COMBINE_EQS: (112), (197) imply:
% 177.04/27.59  | | | | | | | | | | |   (198)  all_52_13 = e3
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | SIMP: (198) implies:
% 177.04/27.59  | | | | | | | | | | |   (199)  all_52_13 = e3
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | REDUCE: (61), (199) imply:
% 177.04/27.59  | | | | | | | | | | |   (200)   ~ (all_14_2 = e3)
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | SIMP: (200) implies:
% 177.04/27.59  | | | | | | | | | | |   (201)   ~ (all_14_2 = e3)
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | REDUCE: (19), (199) imply:
% 177.04/27.59  | | | | | | | | | | |   (202)  op(e1, e3) = e1
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | BETA: splitting (192) gives:
% 177.04/27.59  | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | |   (203)  all_58_7 = e3
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | COMBINE_EQS: (32), (203) imply:
% 177.04/27.59  | | | | | | | | | | | |   (204)  all_52_19 = e3
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | SIMP: (204) implies:
% 177.04/27.59  | | | | | | | | | | | |   (205)  all_52_19 = e3
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | REDUCE: (79), (205) imply:
% 177.04/27.59  | | | | | | | | | | | |   (206)  op(e2, e3) = all_52_18
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | REDUCE: (12), (205) imply:
% 177.04/27.59  | | | | | | | | | | | |   (207)  op(e1, e2) = e3
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | GROUND_INST: instantiating (99) with all_52_17, e1, e3, e1,
% 177.04/27.59  | | | | | | | | | | | |              simplifying with (94), (202) gives:
% 177.04/27.59  | | | | | | | | | | | |   (208)  all_52_17 = e1
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | GROUND_INST: instantiating (99) with all_52_9, all_52_18, e3,
% 177.04/27.59  | | | | | | | | | | | |              e2, simplifying with (118), (206) gives:
% 177.04/27.59  | | | | | | | | | | | |   (209)  all_52_9 = all_52_18
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | COMBINE_EQS: (33), (209) imply:
% 177.04/27.59  | | | | | | | | | | | |   (210)  all_56_4 = all_52_18
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | COMBINE_EQS: (88), (209) imply:
% 177.04/27.59  | | | | | | | | | | | |   (211)  all_58_2 = all_52_18
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | REDUCE: (114), (209) imply:
% 177.04/27.59  | | | | | | | | | | | |   (212)   ~ (all_52_15 = all_52_18)
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | SIMP: (212) implies:
% 177.04/27.59  | | | | | | | | | | | |   (213)   ~ (all_52_15 = all_52_18)
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | REDUCE: (75), (208), (209) imply:
% 177.04/27.59  | | | | | | | | | | | |   (214)   ~ (all_52_18 = e1)
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | REDUCE: (121), (209) imply:
% 177.04/27.59  | | | | | | | | | | | |   (215)   ~ (all_52_18 = e3)
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | REDUCE: (167), (209) imply:
% 177.04/27.59  | | | | | | | | | | | |   (216)   ~ (all_52_18 = e2)
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | REDUCE: (38), (208) imply:
% 177.04/27.59  | | | | | | | | | | | |   (217)   ~ (all_14_2 = e1)
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | SIMP: (217) implies:
% 177.04/27.59  | | | | | | | | | | | |   (218)   ~ (all_14_2 = e1)
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | BETA: splitting (196) gives:
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | |   (219)  all_58_2 = e0
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | COMBINE_EQS: (211), (219) imply:
% 177.04/27.59  | | | | | | | | | | | | |   (220)  all_52_18 = e0
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | REDUCE: (213), (220) imply:
% 177.04/27.59  | | | | | | | | | | | | |   (221)   ~ (all_52_15 = e0)
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | REDUCE: (215), (220) imply:
% 177.04/27.59  | | | | | | | | | | | | |   (222)   ~ (e3 = e0)
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | BETA: splitting (44) gives:
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | |   (223)  all_58_9 = e0
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | COMBINE_EQS: (178), (223) imply:
% 177.04/27.59  | | | | | | | | | | | | | |   (224)  e3 = e0
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | REDUCE: (63), (224) imply:
% 177.04/27.59  | | | | | | | | | | | | | |   (225)  $false
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | |   (226)  all_58_10 = e0 | all_58_11 = e0
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | |   (227)  all_58_10 = e0
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | REF_CLOSE: (30), (221), (227) are inconsistent by sub-proof
% 177.04/27.59  | | | | | | | | | | | | | | |            #741.
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | |   (228)  all_58_11 = e0
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | COMBINE_EQS: (81), (228) imply:
% 177.04/27.59  | | | | | | | | | | | | | | |   (229)  all_52_23 = e0
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | SIMP: (229) implies:
% 177.04/27.59  | | | | | | | | | | | | | | |   (230)  all_52_23 = e0
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | REDUCE: (1), (230) imply:
% 177.04/27.59  | | | | | | | | | | | | | | |   (231)   ~ (all_14_2 = e0)
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | SIMP: (231) implies:
% 177.04/27.59  | | | | | | | | | | | | | | |   (232)   ~ (all_14_2 = e0)
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | |   (233)  all_56_10 = e3
% 177.04/27.59  | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | REF_CLOSE: (92), (201), (233) are inconsistent by sub-proof
% 177.04/27.59  | | | | | | | | | | | | | | | |            #552.
% 177.04/27.59  | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | |   (234)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.59  | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 177.04/27.59  | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | Case 1:
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (235)  all_56_10 = e2
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (235) imply:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (236)  all_14_2 = e2
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | SIMP: (236) implies:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (237)  all_14_2 = e2
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | REDUCE: (65), (237) imply:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (238)  op(all_14_1, e2) = e2
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | REDUCE: (108), (237) imply:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (239)  op(e1, e2) = all_14_1
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (99) with e3, all_14_1, e2, e1,
% 177.04/27.59  | | | | | | | | | | | | | | | | |              simplifying with (207), (239) gives:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (240)  all_14_1 = e3
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | REDUCE: (238), (240) imply:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (241)  op(e3, e2) = e2
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (99) with all_4_1, e2, e2, e3,
% 177.04/27.59  | | | | | | | | | | | | | | | | |              simplifying with (170), (241) gives:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (242)  all_4_1 = e2
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | REDUCE: (47), (242) imply:
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (243)  $false
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | CLOSE: (243) is inconsistent.
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | |   (244)  all_56_10 = e1 | all_56_10 = e0
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (218), (232), (244) are inconsistent by
% 177.04/27.59  | | | | | | | | | | | | | | | | |            sub-proof #738.
% 177.04/27.59  | | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | | End of split
% 177.04/27.59  | | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | | End of split
% 177.04/27.59  | | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | | End of split
% 177.04/27.59  | | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | End of split
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | Case 2:
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | |   (245)   ~ (all_58_2 = e0)
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | REDUCE: (211), (245) imply:
% 177.04/27.59  | | | | | | | | | | | | |   (246)   ~ (all_52_18 = e0)
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | | REF_CLOSE: (134), (210), (214), (216), (246) are inconsistent
% 177.04/27.59  | | | | | | | | | | | | |            by sub-proof #297.
% 177.04/27.59  | | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | | End of split
% 177.04/27.59  | | | | | | | | | | | | 
% 177.04/27.59  | | | | | | | | | | | Case 2:
% 177.04/27.60  | | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | | |   (247)  all_58_8 = e3 | all_58_11 = e3
% 177.04/27.60  | | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | | | REF_CLOSE: (55), (81), (182), (201), (247) are inconsistent
% 177.04/27.60  | | | | | | | | | | | |            by sub-proof #997.
% 177.04/27.60  | | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | | End of split
% 177.04/27.60  | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | Case 2:
% 177.04/27.60  | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | |   (248)   ~ (all_56_6 = e3)
% 177.04/27.60  | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | | REDUCE: (112), (248) imply:
% 177.04/27.60  | | | | | | | | | | |   (249)   ~ (all_52_13 = e3)
% 177.04/27.60  | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | | REF_CLOSE: (4), (8), (15), (16), (23), (30), (32), (62),
% 177.04/27.60  | | | | | | | | | | |            (71), (86), (98), (99), (118), (180), (186),
% 177.04/27.60  | | | | | | | | | | |            (190), (249) are inconsistent by sub-proof #736.
% 177.04/27.60  | | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | End of split
% 177.04/27.60  | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | End of split
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | End of split
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | End of split
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | End of split
% 177.04/27.60  | | | | | | 
% 177.04/27.60  | | | | | Case 2:
% 177.04/27.60  | | | | | | 
% 177.04/27.60  | | | | | |   (250)   ~ (all_56_3 = e3)
% 177.04/27.60  | | | | | | 
% 177.04/27.60  | | | | | | REDUCE: (7), (250) imply:
% 177.04/27.60  | | | | | |   (251)   ~ (all_52_7 = e3)
% 177.04/27.60  | | | | | | 
% 177.04/27.60  | | | | | | BETA: splitting (106) gives:
% 177.04/27.60  | | | | | | 
% 177.04/27.60  | | | | | | Case 1:
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | |   (252)  all_58_9 = e3
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | | REF_CLOSE: (109), (251), (252) are inconsistent by sub-proof #972.
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | Case 2:
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | |   (253)   ~ (all_58_9 = e3)
% 177.04/27.60  | | | | | | |   (254)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | | BETA: splitting (113) gives:
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | | Case 1:
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | |   (255)  all_58_0 = e3
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | | COMBINE_EQS: (163), (255) imply:
% 177.04/27.60  | | | | | | | |   (256)  e3 = e2
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | | SIMP: (256) implies:
% 177.04/27.60  | | | | | | | |   (257)  e3 = e2
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | | REDUCE: (169), (257) imply:
% 177.04/27.60  | | | | | | | |   (258)  $false
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | | CLOSE: (258) is inconsistent.
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | Case 2:
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | |   (259)   ~ (all_58_0 = e3)
% 177.04/27.60  | | | | | | | |   (260)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | | BETA: splitting (116) gives:
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | | Case 1:
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | |   (261)  all_56_2 = e3
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | COMBINE_EQS: (70), (261) imply:
% 177.04/27.60  | | | | | | | | |   (262)  all_52_5 = e3
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | SIMP: (262) implies:
% 177.04/27.60  | | | | | | | | |   (263)  all_52_5 = e3
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | REDUCE: (2), (263) imply:
% 177.04/27.60  | | | | | | | | |   (264)   ~ (all_52_13 = e3)
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | SIMP: (264) implies:
% 177.04/27.60  | | | | | | | | |   (265)   ~ (all_52_13 = e3)
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11),
% 177.04/27.60  | | | | | | | | |            (12), (15), (16), (17), (19), (20), (21), (22),
% 177.04/27.60  | | | | | | | | |            (23), (24), (26), (27), (28), (29), (30), (31),
% 177.04/27.60  | | | | | | | | |            (32), (33), (35), (36), (37), (38), (40), (41),
% 177.04/27.60  | | | | | | | | |            (42), (43), (44), (46), (48), (49), (50), (51),
% 177.04/27.60  | | | | | | | | |            (53), (54), (55), (56), (60), (61), (62), (63),
% 177.04/27.60  | | | | | | | | |            (66), (67), (68), (71), (74), (75), (76), (77),
% 177.04/27.60  | | | | | | | | |            (78), (79), (80), (81), (82), (83), (85), (86),
% 177.04/27.60  | | | | | | | | |            (87), (88), (89), (90), (91), (92), (94), (97),
% 177.04/27.60  | | | | | | | | |            (98), (99), (101), (102), (104), (105), (106),
% 177.04/27.60  | | | | | | | | |            (107), (108), (109), (112), (114), (115), (117),
% 177.04/27.60  | | | | | | | | |            (118), (121), (124), (126), (128), (131), (139),
% 177.04/27.60  | | | | | | | | |            (169), (265) are inconsistent by sub-proof #382.
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | Case 2:
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | |   (266)   ~ (all_56_2 = e3)
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | REDUCE: (70), (266) imply:
% 177.04/27.60  | | | | | | | | |   (267)   ~ (all_52_5 = e3)
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | BETA: splitting (260) gives:
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | Case 1:
% 177.04/27.60  | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | |   (268)  all_58_1 = e3
% 177.04/27.60  | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (16), (17), (19), (20),
% 177.04/27.60  | | | | | | | | | |            (21), (23), (26), (27), (28), (29), (30), (31),
% 177.04/27.60  | | | | | | | | | |            (32), (33), (35), (37), (38), (41), (43), (48),
% 177.04/27.60  | | | | | | | | | |            (51), (54), (55), (56), (60), (62), (63), (71),
% 177.04/27.60  | | | | | | | | | |            (75), (80), (81), (90), (94), (95), (97), (98),
% 177.04/27.60  | | | | | | | | | |            (99), (101), (102), (103), (104), (105), (107),
% 177.04/27.60  | | | | | | | | | |            (115), (126), (128), (131), (134), (139), (169),
% 177.04/27.60  | | | | | | | | | |            (254), (267), (268) are inconsistent by sub-proof
% 177.04/27.60  | | | | | | | | | |            #387.
% 177.04/27.60  | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | Case 2:
% 177.04/27.60  | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | |   (269)  all_58_4 = e3 | all_58_9 = e3
% 177.04/27.60  | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | | REF_CLOSE: (35), (109), (251), (267), (269) are inconsistent
% 177.04/27.60  | | | | | | | | | |            by sub-proof #729.
% 177.04/27.60  | | | | | | | | | | 
% 177.04/27.60  | | | | | | | | | End of split
% 177.04/27.60  | | | | | | | | | 
% 177.04/27.60  | | | | | | | | End of split
% 177.04/27.60  | | | | | | | | 
% 177.04/27.60  | | | | | | | End of split
% 177.04/27.60  | | | | | | | 
% 177.04/27.60  | | | | | | End of split
% 177.04/27.60  | | | | | | 
% 177.04/27.60  | | | | | End of split
% 177.04/27.60  | | | | | 
% 177.04/27.60  | | | | Case 2:
% 177.04/27.60  | | | | | 
% 177.04/27.60  | | | | |   (270)   ~ (all_58_0 = e2)
% 177.04/27.60  | | | | | 
% 177.04/27.60  | | | | | REDUCE: (43), (270) imply:
% 177.04/27.60  | | | | |   (271)   ~ (all_4_2 = e2)
% 177.04/27.60  | | | | | 
% 177.04/27.60  | | | | | REF_CLOSE: (7), (39), (41), (47), (52), (59), (72), (80), (84), (97),
% 177.04/27.60  | | | | |            (99), (107), (139), (162), (271) are inconsistent by
% 177.04/27.60  | | | | |            sub-proof #482.
% 177.04/27.60  | | | | | 
% 177.04/27.60  | | | | End of split
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | End of split
% 177.04/27.60  | | | 
% 177.04/27.60  | | End of split
% 177.04/27.60  | | 
% 177.04/27.60  | End of split
% 177.04/27.60  | 
% 177.04/27.60  End of proof
% 177.04/27.60  
% 177.04/27.60  Sub-proof #297 shows that the following formulas are inconsistent:
% 177.04/27.60  ----------------------------------------------------------------
% 177.04/27.60    (1)   ~ (all_52_18 = e1)
% 177.04/27.60    (2)   ~ (all_52_18 = e2)
% 177.04/27.60    (3)  all_56_4 = all_52_18
% 177.04/27.60    (4)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.60    (5)   ~ (all_52_18 = e0)
% 177.04/27.60  
% 177.04/27.60  Begin of proof
% 177.04/27.60  | 
% 177.04/27.60  | BETA: splitting (4) gives:
% 177.04/27.60  | 
% 177.04/27.60  | Case 1:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (6)  all_56_4 = e2
% 177.04/27.60  | | 
% 177.04/27.60  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #781.
% 177.04/27.60  | | 
% 177.04/27.60  | Case 2:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (7)  all_56_4 = e1 | all_56_4 = e0
% 177.04/27.60  | | 
% 177.04/27.60  | | BETA: splitting (7) gives:
% 177.04/27.60  | | 
% 177.04/27.60  | | Case 1:
% 177.04/27.60  | | | 
% 177.04/27.60  | | |   (8)  all_56_4 = e1
% 177.04/27.60  | | | 
% 177.04/27.60  | | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #780.
% 177.04/27.60  | | | 
% 177.04/27.60  | | Case 2:
% 177.04/27.60  | | | 
% 177.04/27.60  | | |   (9)  all_56_4 = e0
% 177.04/27.60  | | | 
% 177.04/27.60  | | | COMBINE_EQS: (3), (9) imply:
% 177.04/27.60  | | |   (10)  all_52_18 = e0
% 177.04/27.60  | | | 
% 177.04/27.60  | | | SIMP: (10) implies:
% 177.04/27.60  | | |   (11)  all_52_18 = e0
% 177.04/27.60  | | | 
% 177.04/27.60  | | | REDUCE: (5), (11) imply:
% 177.04/27.60  | | |   (12)  $false
% 177.04/27.60  | | | 
% 177.04/27.60  | | | CLOSE: (12) is inconsistent.
% 177.04/27.60  | | | 
% 177.04/27.60  | | End of split
% 177.04/27.60  | | 
% 177.04/27.60  | End of split
% 177.04/27.60  | 
% 177.04/27.60  End of proof
% 177.04/27.60  
% 177.04/27.60  Sub-proof #298 shows that the following formulas are inconsistent:
% 177.04/27.60  ----------------------------------------------------------------
% 177.04/27.60    (1)  all_56_3 = all_52_7
% 177.04/27.60    (2)  op(e3, e2) = all_52_3
% 177.04/27.60    (3)   ~ (all_52_9 = all_52_25)
% 177.04/27.60    (4)  op(e3, all_52_25) = all_52_24
% 177.04/27.60    (5)   ~ (all_52_25 = all_52_29)
% 177.04/27.60    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.60    (7)   ~ (all_52_9 = all_4_2)
% 177.04/27.60    (8)   ~ (all_52_5 = all_52_7)
% 177.04/27.60    (9)   ~ (all_52_5 = all_4_2)
% 177.04/27.60    (10)   ~ (all_52_17 = all_52_25)
% 177.04/27.60    (11)  op(e3, all_4_2) = all_4_1
% 177.04/27.60    (12)   ~ (all_52_7 = all_4_2)
% 177.04/27.60    (13)  all_58_0 = all_4_2
% 177.04/27.60    (14)  op(e1, all_52_29) = all_52_28
% 177.04/27.60    (15)   ~ (all_4_1 = e2)
% 177.04/27.60    (16)  all_58_14 = all_52_29
% 177.04/27.60    (17)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.60    (18)  all_26_2 = all_4_2
% 177.04/27.60    (19)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.60    (20)   ~ (all_52_3 = all_4_2)
% 177.04/27.60    (21)  op(all_4_1, all_4_2) = e2
% 177.04/27.60    (22)   ~ (e3 = e0)
% 177.04/27.60    (23)  op(all_14_1, all_14_2) = e2
% 177.04/27.60    (24)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.60    (25)  all_56_12 = all_52_25
% 177.04/27.60    (26)  all_58_13 = all_52_27
% 177.04/27.60    (27)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.04/27.60    (28)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.60    (29)   ~ (all_52_25 = e0)
% 177.04/27.60    (30)  all_56_0 = all_4_2
% 177.04/27.60    (31)  all_26_1 = all_4_1
% 177.04/27.60    (32)  all_58_15 = e0
% 177.04/27.60    (33)  op(e3, e1) = all_52_5
% 177.04/27.60    (34)   ~ (e2 = e1)
% 177.04/27.60    (35)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.60    (36)  op(e1, e3) = all_52_17
% 177.04/27.60    (37)   ~ (all_52_25 = all_4_2)
% 177.04/27.60    (38)  op(e3, e0) = all_52_7
% 177.04/27.60    (39)  op(e3, e3) = all_4_2
% 177.04/27.60    (40)   ~ (all_52_17 = all_4_2)
% 177.04/27.60    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.60    (42)   ~ (all_52_25 = all_52_27)
% 177.04/27.60    (43)  op(e2, all_52_27) = all_52_26
% 177.04/27.60    (44)  all_52_20 = all_14_1
% 177.04/27.60    (45)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.60    (46)  op(e1, all_14_2) = all_14_1
% 177.04/27.60    (47)   ~ (e2 = e0)
% 177.04/27.60    (48)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.60          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.60    (49)  all_58_12 = all_52_25
% 177.04/27.60    (50)   ~ (e3 = e2)
% 177.04/27.60    (51)  op(e2, e3) = all_52_9
% 177.04/27.60    (52)  all_56_13 = all_52_27
% 177.04/27.60  
% 177.04/27.60  Begin of proof
% 177.04/27.60  | 
% 177.04/27.60  | BETA: splitting (48) gives:
% 177.04/27.60  | 
% 177.04/27.60  | Case 1:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (53)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.04/27.60  | | 
% 177.04/27.60  | | ALPHA: (53) implies:
% 177.04/27.60  | |   (54)  all_52_20 = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | COMBINE_EQS: (44), (54) imply:
% 177.04/27.60  | |   (55)  all_14_1 = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | REF_CLOSE: (23), (34), (41), (46), (55) are inconsistent by sub-proof #315.
% 177.04/27.60  | | 
% 177.04/27.60  | Case 2:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (56)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.04/27.60  | | 
% 177.04/27.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.04/27.60  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 177.04/27.60  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36),
% 177.04/27.60  | |            (37), (38), (39), (40), (41), (42), (43), (45), (47), (49), (50),
% 177.04/27.60  | |            (51), (52), (56) are inconsistent by sub-proof #470.
% 177.04/27.60  | | 
% 177.04/27.60  | End of split
% 177.04/27.60  | 
% 177.04/27.60  End of proof
% 177.04/27.60  
% 177.04/27.60  Sub-proof #299 shows that the following formulas are inconsistent:
% 177.04/27.60  ----------------------------------------------------------------
% 177.04/27.60    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.60    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.60    (3)   ~ (all_52_17 = all_52_23)
% 177.04/27.60    (4)   ~ (all_52_13 = all_52_29)
% 177.04/27.60    (5)  op(e3, e2) = all_52_3
% 177.04/27.60    (6)   ~ (all_52_9 = all_52_25)
% 177.04/27.60    (7)   ~ (all_52_19 = all_52_23)
% 177.04/27.60    (8)  all_56_11 = all_52_23
% 177.04/27.60    (9)  op(e1, e2) = all_52_19
% 177.04/27.60    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.04/27.60    (11)   ~ (all_52_3 = all_10_2)
% 177.04/27.60    (12)  all_58_5 = all_52_13
% 177.04/27.60    (13)   ~ (all_52_25 = all_52_29)
% 177.04/27.60    (14)  all_56_15 = all_6_2
% 177.04/27.60    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.60    (16)  op(e2, e0) = all_52_15
% 177.04/27.60    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.60    (18)  all_58_3 = all_10_2
% 177.04/27.60    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.60    (20)  all_58_15 = all_6_2
% 177.04/27.60    (21)   ~ (all_52_9 = all_4_2)
% 177.04/27.60    (22)   ~ (all_52_5 = all_52_7)
% 177.04/27.60    (23)  all_58_10 = all_52_15
% 177.04/27.60    (24)   ~ (all_52_5 = all_4_2)
% 177.04/27.60    (25)  all_58_7 = all_52_19
% 177.04/27.60    (26)  all_56_4 = all_52_9
% 177.04/27.60    (27)   ~ (all_52_15 = all_6_2)
% 177.04/27.60    (28)   ~ (all_52_17 = all_52_25)
% 177.04/27.60    (29)  op(e0, e1) = all_52_29
% 177.04/27.60    (30)   ~ (all_4_0 = e2)
% 177.04/27.60    (31)  all_58_4 = all_52_5
% 177.04/27.60    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.60    (33)   ~ (e3 = e1)
% 177.04/27.60    (34)   ~ (all_52_27 = all_52_29)
% 177.04/27.60    (35)   ~ (all_52_17 = all_14_2)
% 177.04/27.60    (36)  op(e3, all_4_2) = all_4_1
% 177.04/27.60    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.60    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.60    (39)   ~ (all_52_7 = all_4_2)
% 177.04/27.60    (40)  all_58_1 = all_52_3
% 177.04/27.60    (41)   ~ (all_52_13 = all_52_15)
% 177.04/27.60    (42)  all_58_0 = all_4_2
% 177.04/27.60    (43)  op(e0, e0) = all_6_2
% 177.04/27.60    (44)  op(e1, all_52_29) = all_52_28
% 177.04/27.60    (45)  op(e1, all_52_5) = all_52_4
% 177.04/27.60    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.60    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.04/27.60    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.60    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.60    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.04/27.60    (51)  all_58_14 = all_52_29
% 177.04/27.60    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.60    (53)   ~ (all_52_3 = all_52_5)
% 177.04/27.60    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.60    (55)  op(e2, e1) = all_52_13
% 177.04/27.60    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.60    (57)  all_58_8 = all_14_2
% 177.04/27.60    (58)  all_56_1 = all_52_3
% 177.04/27.60    (59)  all_56_14 = all_52_29
% 177.04/27.60    (60)  all_52_10 = e1
% 177.04/27.60    (61)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.60    (62)   ~ (all_52_5 = all_14_2)
% 177.04/27.60    (63)   ~ (all_52_3 = all_52_27)
% 177.04/27.60    (64)   ~ (all_52_3 = all_4_2)
% 177.04/27.60    (65)  op(e0, e3) = all_52_25
% 177.04/27.60    (66)  op(e0, all_6_2) = all_6_1
% 177.04/27.60    (67)  all_52_0 = all_4_1
% 177.04/27.60    (68)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.04/27.60    (69)   ~ (all_52_13 = all_14_2)
% 177.04/27.60    (70)   ~ (e3 = e0)
% 177.04/27.60    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.60    (72)  op(all_14_1, all_14_2) = e2
% 177.04/27.60    (73)   ~ (all_52_9 = all_52_13)
% 177.04/27.60    (74)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.60    (75)  op(e0, all_52_23) = all_52_22
% 177.04/27.60    (76)   ~ (all_52_15 = all_52_23)
% 177.04/27.60    (77)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.60    (78)   ~ (all_52_5 = all_52_29)
% 177.04/27.60    (79)  all_56_2 = all_52_5
% 177.04/27.60    (80)  op(e1, e0) = all_52_23
% 177.04/27.60    (81)  all_56_12 = all_52_25
% 177.04/27.60    (82)  all_58_13 = all_52_27
% 177.04/27.60    (83)  op(e2, all_52_3) = all_52_2
% 177.04/27.60    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.60    (85)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.04/27.60    (86)   ~ (all_52_9 = all_52_17)
% 177.04/27.60    (87)  all_58_6 = all_52_17
% 177.04/27.60    (88)   ~ (all_52_3 = all_52_7)
% 177.04/27.60    (89)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.60    (90)   ~ (e1 = e0)
% 177.04/27.60    (91)  all_56_0 = all_4_2
% 177.04/27.60    (92)  all_58_11 = all_52_23
% 177.04/27.60    (93)   ~ (all_52_3 = all_52_19)
% 177.04/27.60    (94)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.04/27.60    (95)   ~ (all_52_7 = all_52_15)
% 177.04/27.60    (96)  op(e0, all_52_15) = all_52_14
% 177.04/27.60    (97)   ~ (all_52_29 = all_14_2)
% 177.04/27.60    (98)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.04/27.60    (99)   ~ (all_52_23 = all_6_2)
% 177.04/27.60    (100)   ~ (all_52_29 = all_6_2)
% 177.04/27.60    (101)  all_58_2 = all_52_9
% 177.04/27.60    (102)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.04/27.60    (103)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.60    (104)  op(e3, e1) = all_52_5
% 177.04/27.60    (105)   ~ (e2 = e1)
% 177.04/27.60    (106)  all_56_10 = all_14_2
% 177.04/27.60    (107)   ~ (all_52_25 = all_6_2)
% 177.04/27.60    (108)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.60    (109)  op(e1, e1) = all_14_2
% 177.04/27.60    (110)  op(e1, e3) = all_52_17
% 177.04/27.60    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.60    (112)   ~ (all_52_25 = all_4_2)
% 177.04/27.60    (113)  op(e3, e0) = all_52_7
% 177.04/27.60    (114)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.04/27.60             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.04/27.60    (115)   ~ (all_52_17 = all_4_2)
% 177.04/27.60    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.60             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.60    (117)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.60           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.04/27.60           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.60           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.60    (118)   ~ (all_52_25 = all_52_27)
% 177.04/27.60    (119)   ~ (all_52_27 = all_6_2)
% 177.04/27.60    (120)   ~ (all_52_7 = all_6_2)
% 177.04/27.60    (121)   ~ (all_52_19 = all_52_27)
% 177.04/27.60    (122)  all_56_7 = all_52_15
% 177.04/27.60    (123)   ~ (all_52_7 = all_52_23)
% 177.04/27.60    (124)   ~ (all_52_13 = all_10_2)
% 177.04/27.60    (125)  op(e2, all_52_27) = all_52_26
% 177.04/27.60    (126)  all_52_20 = all_14_1
% 177.04/27.60    (127)   ~ (all_52_17 = all_52_19)
% 177.04/27.60    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.60    (129)  all_52_30 = all_6_1
% 177.04/27.60    (130)  op(e1, all_14_2) = all_14_1
% 177.04/27.60    (131)  all_58_9 = all_52_7
% 177.04/27.60    (132)  all_58_12 = all_52_25
% 177.04/27.60    (133)  all_34_0 = all_4_0
% 177.04/27.60    (134)  op(all_6_1, all_6_2) = e3
% 177.04/27.60    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.60    (136)   ~ (all_52_9 = all_52_15)
% 177.04/27.60    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.60    (138)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.60    (139)   ~ (all_52_19 = all_14_2)
% 177.04/27.60    (140)  op(e0, all_52_7) = all_52_6
% 177.04/27.60    (141)  op(e2, e3) = all_52_9
% 177.04/27.60    (142)  all_56_13 = all_52_27
% 177.04/27.60  
% 177.04/27.60  Begin of proof
% 177.04/27.60  | 
% 177.04/27.60  | BETA: splitting (98) gives:
% 177.04/27.60  | 
% 177.04/27.60  | Case 1:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (143)   ~ (all_34_0 = e1)
% 177.04/27.60  | | 
% 177.04/27.60  | | REDUCE: (133), (143) imply:
% 177.04/27.60  | |   (144)   ~ (all_4_0 = e1)
% 177.04/27.60  | | 
% 177.04/27.60  | | BETA: splitting (117) gives:
% 177.04/27.60  | | 
% 177.04/27.60  | | Case 1:
% 177.04/27.60  | | | 
% 177.04/27.60  | | |   (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.60  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.04/27.60  | | |            e0)
% 177.04/27.60  | | | 
% 177.04/27.60  | | | BETA: splitting (145) gives:
% 177.04/27.60  | | | 
% 177.04/27.60  | | | Case 1:
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | |   (146)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 177.04/27.60  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 177.04/27.60  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 177.04/27.60  | | | |            (32), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 177.04/27.60  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 177.04/27.60  | | | |            (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 177.04/27.60  | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (73), (74),
% 177.04/27.60  | | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 177.04/27.60  | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 177.04/27.60  | | | |            (95), (96), (97), (99), (100), (101), (102), (103), (104),
% 177.04/27.60  | | | |            (106), (107), (108), (109), (110), (111), (112), (113),
% 177.04/27.60  | | | |            (114), (115), (116), (118), (119), (120), (121), (122),
% 177.04/27.60  | | | |            (123), (124), (125), (127), (128), (131), (132), (134),
% 177.04/27.60  | | | |            (135), (136), (137), (138), (139), (140), (141), (142),
% 177.04/27.60  | | | |            (144), (146) are inconsistent by sub-proof #317.
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | Case 2:
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | |   (147)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.04/27.60  | | | |          e0
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | | REF_CLOSE: (60), (105), (147) are inconsistent by sub-proof #533.
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | End of split
% 177.04/27.60  | | | 
% 177.04/27.60  | | Case 2:
% 177.04/27.60  | | | 
% 177.04/27.60  | | |   (148)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.60  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.04/27.60  | | |            all_52_30 = e0)
% 177.04/27.60  | | | 
% 177.04/27.60  | | | REF_CLOSE: (66), (70), (72), (105), (116), (126), (129), (130), (134),
% 177.04/27.60  | | |            (148) are inconsistent by sub-proof #300.
% 177.04/27.60  | | | 
% 177.04/27.60  | | End of split
% 177.04/27.60  | | 
% 177.04/27.60  | Case 2:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (149)  all_34_0 = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | COMBINE_EQS: (133), (149) imply:
% 177.04/27.60  | |   (150)  all_4_0 = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | SIMP: (150) implies:
% 177.04/27.60  | |   (151)  all_4_0 = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | REDUCE: (30), (151) imply:
% 177.04/27.60  | |   (152)   ~ (e2 = e1)
% 177.04/27.60  | | 
% 177.04/27.60  | | REDUCE: (61), (151) imply:
% 177.04/27.60  | |   (153)  op(all_4_1, all_4_2) = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | BETA: splitting (117) gives:
% 177.04/27.60  | | 
% 177.04/27.60  | | Case 1:
% 177.04/27.60  | | | 
% 177.04/27.60  | | |   (154)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.60  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.04/27.60  | | |            e0)
% 177.04/27.60  | | | 
% 177.04/27.60  | | | BETA: splitting (154) gives:
% 177.04/27.60  | | | 
% 177.04/27.60  | | | Case 1:
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | |   (155)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | | REF_CLOSE: (33), (36), (67), (116), (153), (155) are inconsistent by
% 177.04/27.60  | | | |            sub-proof #600.
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | Case 2:
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | |   (156)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.04/27.60  | | | |          e0
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | | REF_CLOSE: (60), (105), (156) are inconsistent by sub-proof #533.
% 177.04/27.60  | | | | 
% 177.04/27.60  | | | End of split
% 177.04/27.60  | | | 
% 177.04/27.60  | | Case 2:
% 177.04/27.60  | | | 
% 177.04/27.60  | | |   (157)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.60  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.04/27.60  | | |            all_52_30 = e0)
% 177.04/27.60  | | | 
% 177.04/27.60  | | | REF_CLOSE: (66), (70), (72), (105), (116), (126), (129), (130), (134),
% 177.04/27.60  | | |            (157) are inconsistent by sub-proof #300.
% 177.04/27.60  | | | 
% 177.04/27.60  | | End of split
% 177.04/27.60  | | 
% 177.04/27.60  | End of split
% 177.04/27.60  | 
% 177.04/27.60  End of proof
% 177.04/27.60  
% 177.04/27.60  Sub-proof #300 shows that the following formulas are inconsistent:
% 177.04/27.60  ----------------------------------------------------------------
% 177.04/27.60    (1)  op(e0, all_6_2) = all_6_1
% 177.04/27.60    (2)   ~ (e3 = e0)
% 177.04/27.60    (3)  op(all_14_1, all_14_2) = e2
% 177.04/27.60    (4)   ~ (e2 = e1)
% 177.04/27.60    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.60    (6)  all_52_20 = all_14_1
% 177.04/27.60    (7)  all_52_30 = all_6_1
% 177.04/27.60    (8)  op(e1, all_14_2) = all_14_1
% 177.04/27.60    (9)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.60         (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.60    (10)  op(all_6_1, all_6_2) = e3
% 177.04/27.60  
% 177.04/27.60  Begin of proof
% 177.04/27.60  | 
% 177.04/27.60  | BETA: splitting (9) gives:
% 177.04/27.60  | 
% 177.04/27.60  | Case 1:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.04/27.60  | | 
% 177.04/27.60  | | ALPHA: (11) implies:
% 177.04/27.60  | |   (12)  all_52_20 = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | COMBINE_EQS: (6), (12) imply:
% 177.04/27.60  | |   (13)  all_14_1 = e1
% 177.04/27.60  | | 
% 177.04/27.60  | | REF_CLOSE: (3), (4), (5), (8), (13) are inconsistent by sub-proof #315.
% 177.04/27.60  | | 
% 177.04/27.60  | Case 2:
% 177.04/27.60  | | 
% 177.04/27.60  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.04/27.60  | | 
% 177.04/27.60  | | REF_CLOSE: (1), (2), (5), (7), (10), (14) are inconsistent by sub-proof
% 177.04/27.60  | |            #501.
% 177.04/27.60  | | 
% 177.04/27.60  | End of split
% 177.04/27.60  | 
% 177.04/27.60  End of proof
% 177.04/27.60  
% 177.04/27.60  Sub-proof #301 shows that the following formulas are inconsistent:
% 177.04/27.60  ----------------------------------------------------------------
% 177.04/27.60    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.60    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.60    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.60    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.60    (5)   ~ (all_52_27 = all_10_2)
% 177.04/27.60    (6)   ~ (all_52_17 = all_52_23)
% 177.04/27.60    (7)  op(e2, all_10_2) = all_10_1
% 177.04/27.60    (8)  all_40_2 = all_4_2
% 177.04/27.60    (9)   ~ (all_52_13 = all_52_29)
% 177.04/27.60    (10)  all_56_3 = all_52_7
% 177.04/27.60    (11)  op(e3, e2) = all_52_3
% 177.04/27.60    (12)   ~ (all_52_9 = all_52_25)
% 177.04/27.60    (13)  op(e3, all_52_25) = all_52_24
% 177.04/27.60    (14)   ~ (all_52_19 = all_52_23)
% 177.04/27.60    (15)  all_56_11 = all_52_23
% 177.04/27.60    (16)  op(e1, e2) = all_52_19
% 177.04/27.60    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.04/27.60    (18)  op(e3, all_52_9) = all_52_8
% 177.04/27.60    (19)   ~ (all_52_3 = all_10_2)
% 177.04/27.60    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.60    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.04/27.60    (22)  all_58_5 = all_52_13
% 177.04/27.60    (23)   ~ (all_52_25 = all_52_29)
% 177.04/27.60    (24)  all_56_15 = all_6_2
% 177.04/27.61    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.61    (26)  op(e2, e0) = all_52_15
% 177.04/27.61    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.61    (28)  all_58_3 = all_10_2
% 177.04/27.61    (29)  all_56_9 = all_52_19
% 177.04/27.61    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.61    (31)  all_58_15 = all_6_2
% 177.04/27.61    (32)   ~ (all_52_9 = all_4_2)
% 177.04/27.61    (33)   ~ (all_52_5 = all_52_7)
% 177.04/27.61    (34)  all_58_10 = all_52_15
% 177.04/27.61    (35)   ~ (all_52_5 = all_4_2)
% 177.04/27.61    (36)  all_58_7 = all_52_19
% 177.04/27.61    (37)  all_56_4 = all_52_9
% 177.04/27.61    (38)   ~ (all_52_15 = all_6_2)
% 177.04/27.61    (39)   ~ (all_52_17 = all_52_25)
% 177.04/27.61    (40)  op(e0, e1) = all_52_29
% 177.04/27.61    (41)   ~ (all_4_0 = e2)
% 177.04/27.61    (42)  all_58_4 = all_52_5
% 177.04/27.61    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.61    (44)   ~ (e3 = e1)
% 177.04/27.61    (45)   ~ (all_52_27 = all_52_29)
% 177.04/27.61    (46)   ~ (all_52_17 = all_14_2)
% 177.04/27.61    (47)  op(e3, all_4_2) = all_4_1
% 177.04/27.61    (48)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.61    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.61    (50)   ~ (all_52_7 = all_4_2)
% 177.04/27.61    (51)  all_58_1 = all_52_3
% 177.04/27.61    (52)   ~ (all_52_13 = all_52_15)
% 177.04/27.61    (53)  all_58_0 = all_4_2
% 177.04/27.61    (54)  all_52_0 = e1
% 177.04/27.61    (55)  op(e1, all_52_13) = all_52_12
% 177.04/27.61    (56)  op(e1, all_52_29) = all_52_28
% 177.04/27.61    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.61    (58)   ~ (all_4_1 = e2)
% 177.04/27.61    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.61    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.61    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.61    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.04/27.61    (63)  all_58_14 = all_52_29
% 177.04/27.61    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.61    (65)   ~ (all_52_3 = all_52_5)
% 177.04/27.61    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.61    (67)  op(e2, e1) = all_52_13
% 177.04/27.61    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.61    (69)  all_58_8 = all_14_2
% 177.04/27.61    (70)  op(e0, e2) = all_52_27
% 177.04/27.61    (71)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.04/27.61    (72)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.04/27.61    (73)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.61    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.61    (75)   ~ (all_52_5 = all_14_2)
% 177.04/27.61    (76)   ~ (all_52_3 = all_52_27)
% 177.04/27.61    (77)   ~ (all_52_3 = all_4_2)
% 177.04/27.61    (78)  op(e0, e3) = all_52_25
% 177.04/27.61    (79)  op(e0, all_6_2) = all_6_1
% 177.04/27.61    (80)   ~ (all_52_9 = all_10_2)
% 177.04/27.61    (81)  op(e3, all_52_17) = all_52_16
% 177.04/27.61    (82)  all_52_10 = all_10_1
% 177.04/27.61    (83)   ~ (all_52_13 = all_14_2)
% 177.04/27.61    (84)   ~ (e3 = e0)
% 177.04/27.61    (85)  all_40_0 = all_4_0
% 177.04/27.61    (86)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.61    (87)  op(all_14_1, all_14_2) = e2
% 177.04/27.61    (88)   ~ (all_52_9 = all_52_13)
% 177.04/27.61    (89)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.61    (90)  op(e0, all_52_23) = all_52_22
% 177.04/27.61    (91)   ~ (all_52_15 = all_52_23)
% 177.04/27.61    (92)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.61    (93)  op(all_10_1, all_10_2) = all_10_0
% 177.04/27.61    (94)   ~ (all_52_5 = all_52_29)
% 177.04/27.61    (95)  all_56_2 = all_52_5
% 177.04/27.61    (96)  op(e1, e0) = all_52_23
% 177.04/27.61    (97)  all_56_12 = all_52_25
% 177.04/27.61    (98)  all_58_13 = all_52_27
% 177.04/27.61    (99)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.61    (100)  all_56_5 = all_10_2
% 177.04/27.61    (101)   ~ (all_52_9 = all_52_17)
% 177.04/27.61    (102)  all_58_6 = all_52_17
% 177.04/27.61    (103)   ~ (all_52_3 = all_52_7)
% 177.04/27.61    (104)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.61    (105)  op(e2, all_52_19) = all_52_18
% 177.04/27.61    (106)   ~ (e1 = e0)
% 177.04/27.61    (107)  all_56_0 = all_4_2
% 177.04/27.61    (108)  all_58_11 = all_52_23
% 177.04/27.61    (109)   ~ (all_52_3 = all_52_19)
% 177.04/27.61    (110)   ~ (all_52_7 = all_52_15)
% 177.04/27.61    (111)  op(e0, all_52_15) = all_52_14
% 177.04/27.61    (112)   ~ (all_52_29 = all_14_2)
% 177.04/27.61    (113)   ~ (all_4_0 = e1)
% 177.04/27.61    (114)   ~ (all_52_19 = all_10_2)
% 177.04/27.61    (115)   ~ (all_58_15 = e0)
% 177.04/27.61    (116)   ~ (all_52_23 = all_6_2)
% 177.04/27.61    (117)  op(e1, all_4_2) = all_4_0
% 177.04/27.61    (118)   ~ (all_52_29 = all_6_2)
% 177.04/27.61    (119)  all_58_2 = all_52_9
% 177.04/27.61    (120)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.61    (121)  op(e3, e1) = all_52_5
% 177.04/27.61    (122)   ~ (e2 = e1)
% 177.04/27.61    (123)  all_56_10 = all_14_2
% 177.04/27.61    (124)   ~ (all_52_25 = all_6_2)
% 177.04/27.61    (125)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.61    (126)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.61    (127)  op(e1, e1) = all_14_2
% 177.04/27.61    (128)  op(e1, e3) = all_52_17
% 177.04/27.61    (129)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.61    (130)   ~ (all_52_25 = all_4_2)
% 177.04/27.61    (131)  op(e3, e0) = all_52_7
% 177.04/27.61    (132)  op(e3, e3) = all_4_2
% 177.04/27.61    (133)   ~ (all_52_17 = all_4_2)
% 177.04/27.61    (134)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.61             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.61    (135)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.61           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.04/27.61           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.61           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.61    (136)   ~ (all_52_25 = all_52_27)
% 177.04/27.61    (137)   ~ (all_52_27 = all_6_2)
% 177.04/27.61    (138)   ~ (all_52_7 = all_6_2)
% 177.04/27.61    (139)   ~ (all_10_0 = e3)
% 177.04/27.61    (140)   ~ (all_52_15 = all_10_2)
% 177.04/27.61    (141)   ~ (all_52_19 = all_52_27)
% 177.04/27.61    (142)  all_56_7 = all_52_15
% 177.04/27.61    (143)   ~ (all_52_7 = all_52_23)
% 177.04/27.61    (144)   ~ (all_52_13 = all_10_2)
% 177.04/27.61    (145)  op(e2, all_52_27) = all_52_26
% 177.04/27.61    (146)  all_52_20 = all_14_1
% 177.04/27.61    (147)   ~ (all_52_17 = all_52_19)
% 177.04/27.61    (148)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.61    (149)  all_52_30 = all_6_1
% 177.04/27.61    (150)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.61    (151)  op(e1, all_14_2) = all_14_1
% 177.04/27.61    (152)  all_58_9 = all_52_7
% 177.04/27.61    (153)   ~ (e2 = e0)
% 177.04/27.61    (154)  all_58_12 = all_52_25
% 177.04/27.61    (155)  op(e3, all_4_2) = e1
% 177.04/27.61    (156)   ~ (all_10_0 = e1)
% 177.04/27.61    (157)  all_56_6 = all_52_13
% 177.04/27.61    (158)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 177.04/27.61             all_58_13 = e0 | all_58_14 = e0)
% 177.04/27.61    (159)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.61    (160)   ~ (all_52_9 = all_52_15)
% 177.04/27.61    (161)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.61    (162)   ~ (e3 = e2)
% 177.04/27.61    (163)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.61    (164)   ~ (all_52_19 = all_14_2)
% 177.04/27.61    (165)  op(e0, all_52_7) = all_52_6
% 177.04/27.61    (166)  op(e2, e3) = all_52_9
% 177.04/27.61    (167)  all_56_13 = all_52_27
% 177.04/27.61  
% 177.04/27.61  Begin of proof
% 177.04/27.61  | 
% 177.04/27.61  | ALPHA: (158) implies:
% 177.04/27.61  |   (168)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.61  |   (169)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.61  | 
% 177.04/27.61  | REDUCE: (31), (115) imply:
% 177.04/27.61  |   (170)   ~ (all_6_2 = e0)
% 177.04/27.61  | 
% 177.04/27.61  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.04/27.61  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.04/27.61  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.04/27.61  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.04/27.61  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.04/27.61  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.04/27.61  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 177.04/27.61  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 177.04/27.61  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.04/27.61  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 177.04/27.61  |            (110), (111), (112), (113), (114), (116), (117), (118), (119),
% 177.04/27.61  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 177.04/27.61  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 177.04/27.61  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 177.04/27.61  |            (147), (148), (149), (150), (151), (152), (153), (154), (155),
% 177.04/27.61  |            (156), (157), (159), (160), (161), (162), (163), (164), (165),
% 177.04/27.61  |            (166), (167), (168), (169), (170) are inconsistent by sub-proof
% 177.04/27.61  |            #307.
% 177.04/27.61  | 
% 177.04/27.61  End of proof
% 177.04/27.61  
% 177.04/27.61  Sub-proof #302 shows that the following formulas are inconsistent:
% 177.04/27.61  ----------------------------------------------------------------
% 177.04/27.61    (1)  all_56_8 = e1 | all_56_8 = e0
% 177.04/27.61    (2)  all_56_8 = all_10_0
% 177.04/27.61    (3)   ~ (all_10_0 = e1)
% 177.04/27.61    (4)   ~ (all_10_0 = e0)
% 177.04/27.61  
% 177.04/27.61  Begin of proof
% 177.04/27.61  | 
% 177.04/27.61  | BETA: splitting (1) gives:
% 177.04/27.61  | 
% 177.04/27.61  | Case 1:
% 177.04/27.61  | | 
% 177.04/27.61  | |   (5)  all_56_8 = e1
% 177.04/27.61  | | 
% 177.04/27.61  | | COMBINE_EQS: (2), (5) imply:
% 177.04/27.61  | |   (6)  all_10_0 = e1
% 177.04/27.61  | | 
% 177.04/27.61  | | SIMP: (6) implies:
% 177.04/27.61  | |   (7)  all_10_0 = e1
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (3), (7) imply:
% 177.04/27.61  | |   (8)  $false
% 177.04/27.61  | | 
% 177.04/27.61  | | CLOSE: (8) is inconsistent.
% 177.04/27.61  | | 
% 177.04/27.61  | Case 2:
% 177.04/27.61  | | 
% 177.04/27.61  | |   (9)  all_56_8 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | COMBINE_EQS: (2), (9) imply:
% 177.04/27.61  | |   (10)  all_10_0 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | SIMP: (10) implies:
% 177.04/27.61  | |   (11)  all_10_0 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (4), (11) imply:
% 177.04/27.61  | |   (12)  $false
% 177.04/27.61  | | 
% 177.04/27.61  | | CLOSE: (12) is inconsistent.
% 177.04/27.61  | | 
% 177.04/27.61  | End of split
% 177.04/27.61  | 
% 177.04/27.61  End of proof
% 177.04/27.61  
% 177.04/27.61  Sub-proof #303 shows that the following formulas are inconsistent:
% 177.04/27.61  ----------------------------------------------------------------
% 177.04/27.61    (1)  all_58_15 = e3
% 177.04/27.61    (2)  all_58_11 = e0
% 177.04/27.61    (3)  all_58_11 = e2 | all_58_15 = e2
% 177.04/27.61    (4)   ~ (e2 = e0)
% 177.04/27.61    (5)   ~ (e3 = e2)
% 177.04/27.61  
% 177.04/27.61  Begin of proof
% 177.04/27.61  | 
% 177.04/27.61  | BETA: splitting (3) gives:
% 177.04/27.61  | 
% 177.04/27.61  | Case 1:
% 177.04/27.61  | | 
% 177.04/27.61  | |   (6)  all_58_11 = e2
% 177.04/27.61  | | 
% 177.04/27.61  | | COMBINE_EQS: (2), (6) imply:
% 177.04/27.61  | |   (7)  e2 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (4), (7) imply:
% 177.04/27.61  | |   (8)  $false
% 177.04/27.61  | | 
% 177.04/27.61  | | CLOSE: (8) is inconsistent.
% 177.04/27.61  | | 
% 177.04/27.61  | Case 2:
% 177.04/27.61  | | 
% 177.04/27.61  | |   (9)  all_58_15 = e2
% 177.04/27.61  | | 
% 177.04/27.61  | | COMBINE_EQS: (1), (9) imply:
% 177.04/27.61  | |   (10)  e3 = e2
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (5), (10) imply:
% 177.04/27.61  | |   (11)  $false
% 177.04/27.61  | | 
% 177.04/27.61  | | CLOSE: (11) is inconsistent.
% 177.04/27.61  | | 
% 177.04/27.61  | End of split
% 177.04/27.61  | 
% 177.04/27.61  End of proof
% 177.04/27.61  
% 177.04/27.61  Sub-proof #304 shows that the following formulas are inconsistent:
% 177.04/27.61  ----------------------------------------------------------------
% 177.04/27.61    (1)  op(e1, e3) = e0
% 177.04/27.61    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.61    (3)  all_58_7 = all_52_19
% 177.04/27.61    (4)  all_58_8 = all_14_2
% 177.04/27.61    (5)   ~ (all_52_23 = e3)
% 177.04/27.61    (6)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.61    (7)  all_58_11 = all_52_23
% 177.04/27.61    (8)  all_56_10 = all_14_2
% 177.04/27.61    (9)   ~ (all_52_19 = e3)
% 177.04/27.61    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.61    (11)   ~ (all_14_1 = e0) |  ~ (all_14_2 = e3)
% 177.04/27.61    (12)  op(e1, all_14_2) = all_14_1
% 177.04/27.61  
% 177.04/27.61  Begin of proof
% 177.04/27.61  | 
% 177.04/27.61  | BETA: splitting (6) gives:
% 177.04/27.61  | 
% 177.04/27.61  | Case 1:
% 177.04/27.61  | | 
% 177.04/27.61  | |   (13)  all_56_10 = e3
% 177.04/27.61  | | 
% 177.04/27.61  | | COMBINE_EQS: (8), (13) imply:
% 177.04/27.61  | |   (14)  all_14_2 = e3
% 177.04/27.61  | | 
% 177.04/27.61  | | SIMP: (14) implies:
% 177.04/27.61  | |   (15)  all_14_2 = e3
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (12), (15) imply:
% 177.04/27.61  | |   (16)  op(e1, e3) = all_14_1
% 177.04/27.61  | | 
% 177.04/27.61  | | BETA: splitting (11) gives:
% 177.04/27.61  | | 
% 177.04/27.61  | | Case 1:
% 177.04/27.61  | | | 
% 177.04/27.61  | | |   (17)   ~ (all_14_2 = e3)
% 177.04/27.61  | | | 
% 177.04/27.61  | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (17) are inconsistent by
% 177.04/27.61  | | |            sub-proof #996.
% 177.04/27.61  | | | 
% 177.04/27.61  | | Case 2:
% 177.04/27.61  | | | 
% 177.04/27.61  | | |   (18)   ~ (all_14_1 = e0)
% 177.04/27.61  | | | 
% 177.04/27.61  | | | GROUND_INST: instantiating (10) with e0, all_14_1, e3, e1, simplifying
% 177.04/27.61  | | |              with (1), (16) gives:
% 177.04/27.61  | | |   (19)  all_14_1 = e0
% 177.04/27.61  | | | 
% 177.04/27.61  | | | REDUCE: (18), (19) imply:
% 177.04/27.61  | | |   (20)  $false
% 177.04/27.61  | | | 
% 177.04/27.61  | | | CLOSE: (20) is inconsistent.
% 177.04/27.61  | | | 
% 177.04/27.61  | | End of split
% 177.04/27.61  | | 
% 177.04/27.61  | Case 2:
% 177.04/27.61  | | 
% 177.04/27.61  | |   (21)   ~ (all_56_10 = e3)
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (8), (21) imply:
% 177.04/27.61  | |   (22)   ~ (all_14_2 = e3)
% 177.04/27.61  | | 
% 177.04/27.61  | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (22) are inconsistent by sub-proof
% 177.04/27.61  | |            #996.
% 177.04/27.61  | | 
% 177.04/27.61  | End of split
% 177.04/27.61  | 
% 177.04/27.61  End of proof
% 177.04/27.61  
% 177.04/27.61  Sub-proof #305 shows that the following formulas are inconsistent:
% 177.04/27.61  ----------------------------------------------------------------
% 177.04/27.61    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.61    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.61    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.61    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.61    (5)   ~ (all_52_27 = all_10_2)
% 177.04/27.61    (6)   ~ (all_52_17 = all_52_23)
% 177.04/27.61    (7)   ~ (all_6_0 = e3)
% 177.04/27.61    (8)  op(e2, all_10_2) = all_10_1
% 177.04/27.61    (9)   ~ (all_52_13 = all_52_29)
% 177.04/27.61    (10)  all_56_3 = all_52_7
% 177.04/27.61    (11)  op(e3, e2) = all_52_3
% 177.04/27.61    (12)   ~ (all_52_9 = all_52_25)
% 177.04/27.61    (13)  op(e3, all_52_25) = all_52_24
% 177.04/27.61    (14)   ~ (all_52_19 = all_52_23)
% 177.04/27.61    (15)  all_56_11 = all_52_23
% 177.04/27.61    (16)  op(e1, e2) = all_52_19
% 177.04/27.61    (17)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.04/27.61    (18)  op(e3, all_52_9) = all_52_8
% 177.04/27.61    (19)   ~ (all_52_3 = all_10_2)
% 177.04/27.61    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.61    (21)  all_58_5 = all_52_13
% 177.04/27.61    (22)   ~ (all_52_25 = all_52_29)
% 177.04/27.61    (23)  all_56_15 = all_6_2
% 177.04/27.61    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.61    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.61    (26)  all_58_3 = all_10_2
% 177.04/27.61    (27)  all_56_9 = all_52_19
% 177.04/27.61    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.61    (29)  all_58_15 = all_6_2
% 177.04/27.61    (30)   ~ (all_52_9 = all_4_2)
% 177.04/27.61    (31)   ~ (all_52_5 = all_52_7)
% 177.04/27.61    (32)  all_58_10 = all_52_15
% 177.04/27.61    (33)   ~ (all_52_5 = all_4_2)
% 177.04/27.61    (34)  all_58_7 = all_52_19
% 177.04/27.61    (35)  all_56_4 = all_52_9
% 177.04/27.61    (36)   ~ (all_52_15 = all_6_2)
% 177.04/27.61    (37)   ~ (all_52_17 = all_52_25)
% 177.04/27.61    (38)  op(e0, e1) = all_52_29
% 177.04/27.61    (39)   ~ (all_4_0 = e2)
% 177.04/27.61    (40)  all_58_4 = all_52_5
% 177.04/27.61    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.61    (42)   ~ (e3 = e1)
% 177.04/27.61    (43)  all_34_1 = all_4_1
% 177.04/27.61    (44)   ~ (all_52_27 = all_52_29)
% 177.04/27.61    (45)   ~ (all_52_17 = all_14_2)
% 177.04/27.61    (46)  op(e3, all_4_2) = all_4_1
% 177.04/27.61    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.61    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.61    (49)   ~ (all_52_7 = all_4_2)
% 177.04/27.61    (50)  all_58_1 = all_52_3
% 177.04/27.61    (51)  all_58_0 = all_4_2
% 177.04/27.61    (52)  op(e1, all_52_13) = all_52_12
% 177.04/27.61    (53)  op(e0, e0) = all_6_2
% 177.04/27.61    (54)  op(e1, all_52_29) = all_52_28
% 177.04/27.61    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.61    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.61    (57)   ~ (all_4_1 = e2)
% 177.04/27.61    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.61    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.61    (60)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.61    (61)  all_58_14 = all_52_29
% 177.04/27.61    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.61    (63)   ~ (all_52_3 = all_52_5)
% 177.04/27.61    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.61    (65)  op(e2, e1) = all_52_13
% 177.04/27.61    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.61    (67)  all_58_8 = all_14_2
% 177.04/27.61    (68)  all_56_1 = all_52_3
% 177.04/27.61    (69)  op(e0, e2) = all_52_27
% 177.04/27.61    (70)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.61    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.61    (72)   ~ (all_52_3 = all_52_27)
% 177.04/27.61    (73)   ~ (all_52_3 = all_4_2)
% 177.04/27.61    (74)  op(all_6_1, all_6_2) = all_6_0
% 177.04/27.61    (75)  op(e0, e3) = all_52_25
% 177.04/27.61    (76)  op(e0, all_6_2) = all_6_1
% 177.04/27.61    (77)  all_52_0 = all_4_1
% 177.04/27.61    (78)   ~ (all_52_9 = all_10_2)
% 177.04/27.61    (79)  op(e3, all_52_17) = all_52_16
% 177.04/27.61    (80)  all_52_10 = all_10_1
% 177.04/27.61    (81)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.04/27.61    (82)   ~ (all_52_13 = all_14_2)
% 177.04/27.61    (83)   ~ (e3 = e0)
% 177.04/27.61    (84)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.61    (85)  op(all_14_1, all_14_2) = e2
% 177.04/27.61    (86)   ~ (all_52_9 = all_52_13)
% 177.04/27.61    (87)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.61    (88)  op(e0, all_52_23) = all_52_22
% 177.04/27.61    (89)   ~ (all_52_15 = all_52_23)
% 177.04/27.61    (90)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.61    (91)  op(all_10_1, all_10_2) = all_10_0
% 177.04/27.61    (92)   ~ (all_52_5 = all_52_29)
% 177.04/27.61    (93)  all_56_2 = all_52_5
% 177.04/27.61    (94)  op(e1, e0) = all_52_23
% 177.04/27.61    (95)  all_56_12 = all_52_25
% 177.04/27.61    (96)  all_58_13 = all_52_27
% 177.04/27.61    (97)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.61    (98)   ~ (all_52_9 = all_52_17)
% 177.04/27.61    (99)  all_58_6 = all_52_17
% 177.04/27.61    (100)   ~ (all_52_3 = all_52_7)
% 177.04/27.61    (101)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.61    (102)  op(e2, all_52_19) = all_52_18
% 177.04/27.61    (103)   ~ (e1 = e0)
% 177.04/27.61    (104)  all_56_0 = all_4_2
% 177.04/27.61    (105)  all_58_11 = all_52_23
% 177.04/27.61    (106)   ~ (all_52_3 = all_52_19)
% 177.04/27.61    (107)   ~ (all_52_7 = all_52_15)
% 177.04/27.61    (108)  op(e0, all_52_15) = all_52_14
% 177.04/27.61    (109)   ~ (all_52_29 = all_14_2)
% 177.04/27.61    (110)  all_4_0 = e1
% 177.04/27.61    (111)   ~ (all_52_19 = all_10_2)
% 177.04/27.61    (112)   ~ (all_52_23 = all_6_2)
% 177.04/27.61    (113)   ~ (all_6_0 = e2)
% 177.04/27.61    (114)   ~ (all_52_29 = all_6_2)
% 177.04/27.61    (115)  all_58_2 = all_52_9
% 177.04/27.61    (116)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.04/27.61    (117)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.61    (118)  op(e3, e1) = all_52_5
% 177.04/27.61    (119)  all_56_10 = all_14_2
% 177.04/27.61    (120)   ~ (all_52_25 = all_6_2)
% 177.04/27.61    (121)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.61    (122)  op(e1, e1) = all_14_2
% 177.04/27.61    (123)  op(e1, e3) = all_52_17
% 177.04/27.61    (124)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.61    (125)   ~ (all_52_25 = all_4_2)
% 177.04/27.61    (126)  op(e3, e0) = all_52_7
% 177.04/27.61    (127)  op(e3, e3) = all_4_2
% 177.04/27.61    (128)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.04/27.61             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.04/27.61    (129)   ~ (all_52_17 = all_4_2)
% 177.04/27.61    (130)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.61             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.61    (131)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.61           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.04/27.61           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.61           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.61    (132)   ~ (all_52_25 = all_52_27)
% 177.04/27.61    (133)  all_34_2 = all_4_2
% 177.04/27.61    (134)   ~ (all_52_27 = all_6_2)
% 177.04/27.61    (135)   ~ (all_52_7 = all_6_2)
% 177.04/27.61    (136)   ~ (all_10_0 = e3)
% 177.04/27.61    (137)   ~ (all_52_19 = all_52_27)
% 177.04/27.61    (138)  all_56_7 = all_52_15
% 177.04/27.61    (139)   ~ (all_52_7 = all_52_23)
% 177.04/27.61    (140)   ~ (all_6_0 = e1)
% 177.04/27.61    (141)  op(e2, all_52_27) = all_52_26
% 177.04/27.61    (142)  all_52_20 = all_14_1
% 177.04/27.61    (143)   ~ (all_52_17 = all_52_19)
% 177.04/27.61    (144)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.61    (145)  all_52_30 = all_6_1
% 177.04/27.61    (146)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.61    (147)  op(e1, all_14_2) = all_14_1
% 177.04/27.61    (148)  all_58_9 = all_52_7
% 177.04/27.61    (149)  all_58_12 = all_52_25
% 177.04/27.61    (150)   ~ (all_10_0 = e1)
% 177.04/27.61    (151)  all_56_6 = all_52_13
% 177.04/27.61    (152)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.61    (153)   ~ (all_52_9 = all_52_15)
% 177.04/27.61    (154)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.61    (155)   ~ (e3 = e2)
% 177.04/27.61    (156)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.61    (157)   ~ (all_52_19 = all_14_2)
% 177.04/27.61    (158)  op(e2, e3) = all_52_9
% 177.04/27.61    (159)  all_56_13 = all_52_27
% 177.04/27.61  
% 177.04/27.61  Begin of proof
% 177.04/27.61  | 
% 177.04/27.61  | REDUCE: (39), (110) imply:
% 177.04/27.61  |   (160)   ~ (e2 = e1)
% 177.04/27.61  | 
% 177.04/27.61  | SIMP: (160) implies:
% 177.04/27.61  |   (161)   ~ (e2 = e1)
% 177.04/27.61  | 
% 177.04/27.61  | REDUCE: (70), (110) imply:
% 177.04/27.61  |   (162)  op(all_4_1, all_4_2) = e1
% 177.04/27.61  | 
% 177.04/27.61  | BETA: splitting (128) gives:
% 177.04/27.61  | 
% 177.04/27.61  | Case 1:
% 177.04/27.61  | | 
% 177.04/27.61  | |   (163)  all_58_15 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | COMBINE_EQS: (29), (163) imply:
% 177.04/27.61  | |   (164)  all_6_2 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (36), (164) imply:
% 177.04/27.61  | |   (165)   ~ (all_52_15 = e0)
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (120), (164) imply:
% 177.04/27.61  | |   (166)   ~ (all_52_25 = e0)
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (134), (164) imply:
% 177.04/27.61  | |   (167)   ~ (all_52_27 = e0)
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (114), (164) imply:
% 177.04/27.61  | |   (168)   ~ (all_52_29 = e0)
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (74), (164) imply:
% 177.04/27.61  | |   (169)  op(all_6_1, e0) = all_6_0
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (76), (164) imply:
% 177.04/27.61  | |   (170)  op(e0, e0) = all_6_1
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (53), (164) imply:
% 177.04/27.61  | |   (171)  op(e0, e0) = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | GROUND_INST: instantiating (130) with e0, all_6_1, e0, e0, simplifying with
% 177.04/27.61  | |              (170), (171) gives:
% 177.04/27.61  | |   (172)  all_6_1 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (169), (172) imply:
% 177.04/27.61  | |   (173)  op(e0, e0) = all_6_0
% 177.04/27.61  | | 
% 177.04/27.61  | | GROUND_INST: instantiating (130) with e0, all_6_0, e0, e0, simplifying with
% 177.04/27.61  | |              (171), (173) gives:
% 177.04/27.61  | |   (174)  all_6_0 = e0
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (7), (174) imply:
% 177.04/27.61  | |   (175)   ~ (e3 = e0)
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (113), (174) imply:
% 177.04/27.61  | |   (176)   ~ (e2 = e0)
% 177.04/27.61  | | 
% 177.04/27.61  | | SIMP: (176) implies:
% 177.04/27.61  | |   (177)   ~ (e2 = e0)
% 177.04/27.61  | | 
% 177.04/27.61  | | REDUCE: (140), (174) imply:
% 177.04/27.62  | |   (178)   ~ (e1 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | BETA: splitting (131) gives:
% 177.04/27.62  | | 
% 177.04/27.62  | | Case 1:
% 177.04/27.62  | | | 
% 177.04/27.62  | | |   (179)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.62  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.04/27.62  | | |            e0)
% 177.04/27.62  | | | 
% 177.04/27.62  | | | REF_CLOSE: (5), (6), (8), (9), (10), (11), (12), (16), (17), (18), (19),
% 177.04/27.62  | | |            (21), (22), (24), (25), (26), (28), (30), (32), (34), (35),
% 177.04/27.62  | | |            (37), (38), (41), (42), (43), (46), (48), (49), (50), (51),
% 177.04/27.62  | | |            (52), (55), (57), (59), (60), (61), (62), (64), (66), (67),
% 177.04/27.62  | | |            (68), (69), (72), (73), (75), (77), (80), (81), (83), (86),
% 177.04/27.62  | | |            (87), (90), (91), (94), (95), (96), (99), (100), (101), (103),
% 177.04/27.62  | | |            (104), (105), (106), (107), (108), (111), (115), (116), (119),
% 177.04/27.62  | | |            (123), (124), (125), (126), (127), (129), (130), (132), (133),
% 177.04/27.62  | | |            (136), (138), (139), (141), (144), (146), (148), (149), (150),
% 177.04/27.62  | | |            (151), (152), (153), (157), (158), (159), (162), (163), (165),
% 177.04/27.62  | | |            (166), (167), (168), (177), (179) are inconsistent by sub-proof
% 177.04/27.62  | | |            #330.
% 177.04/27.62  | | | 
% 177.04/27.62  | | Case 2:
% 177.04/27.62  | | | 
% 177.04/27.62  | | |   (180)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.62  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.04/27.62  | | |            all_52_30 = e0)
% 177.04/27.62  | | | 
% 177.04/27.62  | | | BETA: splitting (180) gives:
% 177.04/27.62  | | | 
% 177.04/27.62  | | | Case 1:
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | |   (181)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.62  | | | |          e0
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | | REF_CLOSE: (85), (130), (142), (147), (161), (181) are inconsistent by
% 177.04/27.62  | | | |            sub-proof #314.
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | Case 2:
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | |   (182)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.04/27.62  | | | |          e0
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | | REF_CLOSE: (10), (11), (12), (13), (16), (17), (24), (28), (42), (43),
% 177.04/27.62  | | | |            (46), (49), (51), (54), (55), (57), (61), (62), (64), (66),
% 177.04/27.62  | | | |            (68), (73), (83), (87), (94), (95), (96), (104), (106),
% 177.04/27.62  | | | |            (123), (125), (126), (127), (129), (130), (132), (133),
% 177.04/27.62  | | | |            (139), (141), (146), (149), (158), (159), (162), (163),
% 177.04/27.62  | | | |            (166), (182) are inconsistent by sub-proof #576.
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | End of split
% 177.04/27.62  | | | 
% 177.04/27.62  | | End of split
% 177.04/27.62  | | 
% 177.04/27.62  | Case 2:
% 177.04/27.62  | | 
% 177.04/27.62  | |   (183)   ~ (all_58_15 = e0)
% 177.04/27.62  | |   (184)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.04/27.62  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | ALPHA: (184) implies:
% 177.04/27.62  | |   (185)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.62  | |   (186)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (29), (183) imply:
% 177.04/27.62  | |   (187)   ~ (all_6_2 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | BETA: splitting (131) gives:
% 177.04/27.62  | | 
% 177.04/27.62  | | Case 1:
% 177.04/27.62  | | | 
% 177.04/27.62  | | |   (188)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.62  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.04/27.62  | | |            e0)
% 177.04/27.62  | | | 
% 177.04/27.62  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 177.04/27.62  | | |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (26),
% 177.04/27.62  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.04/27.62  | | |            (37), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.04/27.62  | | |            (49), (50), (51), (52), (54), (55), (56), (57), (58), (59),
% 177.04/27.62  | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (71),
% 177.04/27.62  | | |            (72), (73), (75), (76), (77), (79), (80), (82), (83), (86),
% 177.04/27.62  | | |            (88), (89), (90), (91), (92), (93), (94), (96), (97), (98),
% 177.04/27.62  | | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 177.04/27.62  | | |            (108), (109), (111), (112), (114), (115), (117), (118), (119),
% 177.04/27.62  | | |            (120), (122), (123), (125), (126), (127), (129), (130), (132),
% 177.04/27.62  | | |            (133), (134), (135), (136), (139), (141), (143), (144), (146),
% 177.04/27.62  | | |            (147), (148), (149), (150), (151), (152), (153), (154), (156),
% 177.04/27.62  | | |            (157), (158), (159), (162), (186), (187), (188) are
% 177.04/27.62  | | |            inconsistent by sub-proof #327.
% 177.04/27.62  | | | 
% 177.04/27.62  | | Case 2:
% 177.04/27.62  | | | 
% 177.04/27.62  | | |   (189)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.62  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.04/27.62  | | |            all_52_30 = e0)
% 177.04/27.62  | | | 
% 177.04/27.62  | | | BETA: splitting (189) gives:
% 177.04/27.62  | | | 
% 177.04/27.62  | | | Case 1:
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | |   (190)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.62  | | | |          e0
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | | REF_CLOSE: (85), (130), (142), (147), (161), (190) are inconsistent by
% 177.04/27.62  | | | |            sub-proof #314.
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | Case 2:
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | |   (191)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.04/27.62  | | | |          e0
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | | REF_CLOSE: (3), (7), (10), (11), (12), (13), (14), (16), (17), (18),
% 177.04/27.62  | | | |            (19), (20), (23), (24), (26), (28), (29), (31), (32), (34),
% 177.04/27.62  | | | |            (37), (38), (40), (42), (43), (44), (46), (47), (49), (50),
% 177.04/27.62  | | | |            (51), (54), (55), (57), (61), (62), (63), (64), (66), (68),
% 177.04/27.62  | | | |            (69), (72), (73), (74), (75), (76), (78), (81), (84), (93),
% 177.04/27.62  | | | |            (94), (96), (97), (99), (100), (104), (105), (106), (107),
% 177.04/27.62  | | | |            (109), (113), (115), (118), (121), (122), (123), (125),
% 177.04/27.62  | | | |            (126), (127), (129), (130), (132), (133), (135), (137),
% 177.04/27.62  | | | |            (139), (140), (141), (143), (144), (145), (146), (148),
% 177.04/27.62  | | | |            (149), (153), (155), (156), (158), (159), (162), (185), (191)
% 177.04/27.62  | | | |            are inconsistent by sub-proof #534.
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | End of split
% 177.04/27.62  | | | 
% 177.04/27.62  | | End of split
% 177.04/27.62  | | 
% 177.04/27.62  | End of split
% 177.04/27.62  | 
% 177.04/27.62  End of proof
% 177.04/27.62  
% 177.04/27.62  Sub-proof #306 shows that the following formulas are inconsistent:
% 177.04/27.62  ----------------------------------------------------------------
% 177.04/27.62    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.62    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.62    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.62    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.62    (5)   ~ (all_52_27 = all_10_2)
% 177.04/27.62    (6)   ~ (all_52_17 = all_52_23)
% 177.04/27.62    (7)   ~ (all_6_0 = e3)
% 177.04/27.62    (8)  op(e2, all_10_2) = all_10_1
% 177.04/27.62    (9)  all_40_2 = all_4_2
% 177.04/27.62    (10)   ~ (all_52_13 = all_52_29)
% 177.04/27.62    (11)  all_56_3 = all_52_7
% 177.04/27.62    (12)  op(e3, e2) = all_52_3
% 177.04/27.62    (13)   ~ (all_52_9 = all_52_25)
% 177.04/27.62    (14)  op(e3, all_52_25) = all_52_24
% 177.04/27.62    (15)   ~ (all_52_19 = all_52_23)
% 177.04/27.62    (16)  all_56_11 = all_52_23
% 177.04/27.62    (17)  op(e1, e2) = all_52_19
% 177.04/27.62    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.04/27.62    (19)  op(e3, all_52_9) = all_52_8
% 177.04/27.62    (20)   ~ (all_52_3 = all_10_2)
% 177.04/27.62    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.62    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.04/27.62    (23)  all_58_5 = all_52_13
% 177.04/27.62    (24)   ~ (all_52_25 = all_52_29)
% 177.04/27.62    (25)  all_56_15 = all_6_2
% 177.04/27.62    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.62    (27)  op(e2, e0) = all_52_15
% 177.04/27.62    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.62    (29)  all_58_3 = all_10_2
% 177.04/27.62    (30)  all_56_9 = all_52_19
% 177.04/27.62    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.62    (32)  all_58_15 = all_6_2
% 177.04/27.62    (33)   ~ (all_52_9 = all_4_2)
% 177.04/27.62    (34)   ~ (all_52_5 = all_52_7)
% 177.04/27.62    (35)  all_58_10 = all_52_15
% 177.04/27.62    (36)   ~ (all_52_5 = all_4_2)
% 177.04/27.62    (37)  all_58_7 = all_52_19
% 177.04/27.62    (38)  all_56_4 = all_52_9
% 177.04/27.62    (39)   ~ (all_52_15 = all_6_2)
% 177.04/27.62    (40)   ~ (all_52_17 = all_52_25)
% 177.04/27.62    (41)  op(e0, e1) = all_52_29
% 177.04/27.62    (42)   ~ (all_4_0 = e2)
% 177.04/27.62    (43)  all_58_4 = all_52_5
% 177.04/27.62    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.62    (45)   ~ (e3 = e1)
% 177.04/27.62    (46)   ~ (all_52_27 = all_52_29)
% 177.04/27.62    (47)   ~ (all_52_17 = all_14_2)
% 177.04/27.62    (48)  op(e3, all_4_2) = all_4_1
% 177.04/27.62    (49)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.62    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.62    (51)   ~ (all_52_7 = all_4_2)
% 177.04/27.62    (52)  all_58_1 = all_52_3
% 177.04/27.62    (53)   ~ (all_52_13 = all_52_15)
% 177.04/27.62    (54)  all_58_0 = all_4_2
% 177.04/27.62    (55)  op(e1, all_52_13) = all_52_12
% 177.04/27.62    (56)  op(e0, e0) = all_6_2
% 177.04/27.62    (57)  op(e1, all_52_29) = all_52_28
% 177.04/27.62    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.62    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.62    (60)   ~ (all_4_1 = e2)
% 177.04/27.62    (61)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.04/27.62    (62)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.62    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.62    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.62    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.04/27.62    (66)  all_58_14 = all_52_29
% 177.04/27.62    (67)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.62    (68)   ~ (all_52_3 = all_52_5)
% 177.04/27.62    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.62    (70)  op(e2, e1) = all_52_13
% 177.04/27.62    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.62    (72)  all_58_8 = all_14_2
% 177.04/27.62    (73)  all_56_1 = all_52_3
% 177.04/27.62    (74)  op(e0, e2) = all_52_27
% 177.04/27.62    (75)  all_56_14 = all_52_29
% 177.04/27.62    (76)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.04/27.62    (77)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.04/27.62    (78)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.62    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.62    (80)   ~ (all_52_5 = all_14_2)
% 177.04/27.62    (81)   ~ (all_52_3 = all_52_27)
% 177.04/27.62    (82)   ~ (all_52_3 = all_4_2)
% 177.04/27.62    (83)  op(all_6_1, all_6_2) = all_6_0
% 177.04/27.62    (84)  op(e0, e3) = all_52_25
% 177.04/27.62    (85)  op(e0, all_6_2) = all_6_1
% 177.04/27.62    (86)  all_52_0 = all_4_1
% 177.04/27.62    (87)   ~ (all_52_9 = all_10_2)
% 177.04/27.62    (88)  op(e3, all_52_17) = all_52_16
% 177.04/27.62    (89)  all_52_10 = all_10_1
% 177.04/27.62    (90)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.04/27.62    (91)   ~ (all_52_13 = all_14_2)
% 177.04/27.62    (92)   ~ (e3 = e0)
% 177.04/27.62    (93)  all_40_0 = all_4_0
% 177.04/27.62    (94)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.62    (95)  op(all_14_1, all_14_2) = e2
% 177.04/27.62    (96)   ~ (all_52_9 = all_52_13)
% 177.04/27.62    (97)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.62    (98)  op(e0, all_52_23) = all_52_22
% 177.04/27.62    (99)   ~ (all_52_15 = all_52_23)
% 177.04/27.62    (100)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.62    (101)  op(all_10_1, all_10_2) = all_10_0
% 177.04/27.62    (102)   ~ (all_52_5 = all_52_29)
% 177.04/27.62    (103)  all_56_2 = all_52_5
% 177.04/27.62    (104)  op(e1, e0) = all_52_23
% 177.04/27.62    (105)  all_56_12 = all_52_25
% 177.04/27.62    (106)  all_58_13 = all_52_27
% 177.04/27.62    (107)  all_4_1 = e1
% 177.04/27.62    (108)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.62    (109)  all_56_5 = all_10_2
% 177.04/27.62    (110)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.04/27.62    (111)   ~ (all_52_9 = all_52_17)
% 177.04/27.62    (112)  all_58_6 = all_52_17
% 177.04/27.62    (113)   ~ (all_52_3 = all_52_7)
% 177.04/27.62    (114)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.62    (115)  op(e2, all_52_19) = all_52_18
% 177.04/27.62    (116)   ~ (e1 = e0)
% 177.04/27.62    (117)  all_56_0 = all_4_2
% 177.04/27.62    (118)  all_58_11 = all_52_23
% 177.04/27.62    (119)   ~ (all_52_3 = all_52_19)
% 177.04/27.62    (120)   ~ (all_52_7 = all_52_15)
% 177.04/27.62    (121)  op(e0, all_52_15) = all_52_14
% 177.04/27.62    (122)   ~ (all_52_29 = all_14_2)
% 177.04/27.62    (123)   ~ (all_4_0 = e1)
% 177.04/27.62    (124)   ~ (all_52_19 = all_10_2)
% 177.04/27.62    (125)   ~ (all_52_23 = all_6_2)
% 177.04/27.62    (126)   ~ (all_6_0 = e2)
% 177.04/27.62    (127)   ~ (all_52_29 = all_6_2)
% 177.04/27.62    (128)  all_58_2 = all_52_9
% 177.04/27.62    (129)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.04/27.62    (130)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.62    (131)  op(e3, e1) = all_52_5
% 177.04/27.62    (132)  all_56_10 = all_14_2
% 177.04/27.62    (133)   ~ (all_52_25 = all_6_2)
% 177.04/27.62    (134)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.62    (135)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.62    (136)  op(e1, e1) = all_14_2
% 177.04/27.62    (137)  op(e1, e3) = all_52_17
% 177.04/27.62    (138)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.62    (139)   ~ (all_52_25 = all_4_2)
% 177.04/27.62    (140)  op(e3, e0) = all_52_7
% 177.04/27.62    (141)  op(e3, e3) = all_4_2
% 177.04/27.62    (142)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.04/27.62             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.04/27.62    (143)   ~ (all_52_17 = all_4_2)
% 177.04/27.62    (144)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.62             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.62    (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.62           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.04/27.62           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.62           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.62    (146)   ~ (all_52_25 = all_52_27)
% 177.04/27.62    (147)   ~ (all_52_27 = all_6_2)
% 177.04/27.62    (148)   ~ (all_52_7 = all_6_2)
% 177.04/27.62    (149)   ~ (all_10_0 = e3)
% 177.04/27.62    (150)   ~ (all_52_15 = all_10_2)
% 177.04/27.62    (151)   ~ (all_52_19 = all_52_27)
% 177.04/27.62    (152)  all_56_7 = all_52_15
% 177.04/27.62    (153)   ~ (all_52_7 = all_52_23)
% 177.04/27.62    (154)   ~ (all_52_13 = all_10_2)
% 177.04/27.62    (155)   ~ (all_6_0 = e1)
% 177.04/27.62    (156)  op(e2, all_52_27) = all_52_26
% 177.04/27.62    (157)  all_52_20 = all_14_1
% 177.04/27.62    (158)   ~ (all_52_17 = all_52_19)
% 177.04/27.62    (159)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.62    (160)  all_52_30 = all_6_1
% 177.04/27.62    (161)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.62    (162)  op(e1, all_14_2) = all_14_1
% 177.04/27.62    (163)  all_58_9 = all_52_7
% 177.04/27.62    (164)   ~ (e2 = e0)
% 177.04/27.62    (165)  all_58_12 = all_52_25
% 177.04/27.62    (166)   ~ (all_10_0 = e1)
% 177.04/27.62    (167)  all_56_6 = all_52_13
% 177.04/27.62    (168)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.62    (169)   ~ (all_52_9 = all_52_15)
% 177.04/27.62    (170)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.62    (171)   ~ (e3 = e2)
% 177.04/27.62    (172)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.62    (173)   ~ (all_52_19 = all_14_2)
% 177.04/27.62    (174)  op(e0, all_52_7) = all_52_6
% 177.04/27.62    (175)  op(e2, e3) = all_52_9
% 177.04/27.62    (176)  all_56_13 = all_52_27
% 177.04/27.62  
% 177.04/27.62  Begin of proof
% 177.04/27.62  | 
% 177.04/27.62  | COMBINE_EQS: (86), (107) imply:
% 177.04/27.62  |   (177)  all_52_0 = e1
% 177.04/27.62  | 
% 177.04/27.62  | REDUCE: (60), (107) imply:
% 177.04/27.62  |   (178)   ~ (e2 = e1)
% 177.04/27.62  | 
% 177.04/27.62  | SIMP: (178) implies:
% 177.04/27.62  |   (179)   ~ (e2 = e1)
% 177.04/27.62  | 
% 177.04/27.62  | REDUCE: (78), (107) imply:
% 177.04/27.62  |   (180)  op(e1, all_4_2) = all_4_0
% 177.04/27.62  | 
% 177.04/27.62  | REDUCE: (48), (107) imply:
% 177.04/27.62  |   (181)  op(e3, all_4_2) = e1
% 177.04/27.62  | 
% 177.04/27.62  | BETA: splitting (142) gives:
% 177.04/27.62  | 
% 177.04/27.62  | Case 1:
% 177.04/27.62  | | 
% 177.04/27.62  | |   (182)  all_58_15 = e0
% 177.04/27.62  | | 
% 177.04/27.62  | | COMBINE_EQS: (32), (182) imply:
% 177.04/27.62  | |   (183)  all_6_2 = e0
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (148), (183) imply:
% 177.04/27.62  | |   (184)   ~ (all_52_7 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (39), (183) imply:
% 177.04/27.62  | |   (185)   ~ (all_52_15 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (133), (183) imply:
% 177.04/27.62  | |   (186)   ~ (all_52_25 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (147), (183) imply:
% 177.04/27.62  | |   (187)   ~ (all_52_27 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (127), (183) imply:
% 177.04/27.62  | |   (188)   ~ (all_52_29 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (83), (183) imply:
% 177.04/27.62  | |   (189)  op(all_6_1, e0) = all_6_0
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (85), (183) imply:
% 177.04/27.62  | |   (190)  op(e0, e0) = all_6_1
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (56), (183) imply:
% 177.04/27.62  | |   (191)  op(e0, e0) = e0
% 177.04/27.62  | | 
% 177.04/27.62  | | GROUND_INST: instantiating (144) with e0, all_6_1, e0, e0, simplifying with
% 177.04/27.62  | |              (190), (191) gives:
% 177.04/27.62  | |   (192)  all_6_1 = e0
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (189), (192) imply:
% 177.04/27.62  | |   (193)  op(e0, e0) = all_6_0
% 177.04/27.62  | | 
% 177.04/27.62  | | GROUND_INST: instantiating (144) with e0, all_6_0, e0, e0, simplifying with
% 177.04/27.62  | |              (191), (193) gives:
% 177.04/27.62  | |   (194)  all_6_0 = e0
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (7), (194) imply:
% 177.04/27.62  | |   (195)   ~ (e3 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (126), (194) imply:
% 177.04/27.62  | |   (196)   ~ (e2 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (155), (194) imply:
% 177.04/27.62  | |   (197)   ~ (e1 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | BETA: splitting (145) gives:
% 177.04/27.62  | | 
% 177.04/27.62  | | Case 1:
% 177.04/27.62  | | | 
% 177.04/27.62  | | |   (198)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.62  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.04/27.62  | | |            e0)
% 177.04/27.62  | | | 
% 177.04/27.62  | | | REF_CLOSE: (5), (6), (8), (10), (11), (12), (13), (14), (19), (20), (23),
% 177.04/27.62  | | |            (24), (28), (29), (33), (34), (35), (37), (40), (41), (42),
% 177.04/27.62  | | |            (43), (44), (45), (46), (47), (48), (50), (51), (52), (54),
% 177.04/27.62  | | |            (55), (57), (58), (63), (66), (67), (69), (71), (72), (73),
% 177.04/27.62  | | |            (74), (78), (82), (84), (89), (90), (91), (92), (96), (97),
% 177.04/27.62  | | |            (99), (100), (101), (105), (106), (111), (112), (113), (116),
% 177.04/27.62  | | |            (118), (119), (120), (121), (122), (123), (124), (128), (129),
% 177.04/27.62  | | |            (131), (132), (135), (137), (138), (141), (144), (146), (149),
% 177.04/27.62  | | |            (151), (152), (153), (156), (158), (159), (161), (163), (164),
% 177.04/27.62  | | |            (165), (166), (168), (170), (173), (175), (176), (177), (182),
% 177.04/27.62  | | |            (185), (186), (187), (188), (198) are inconsistent by sub-proof
% 177.04/27.62  | | |            #337.
% 177.04/27.62  | | | 
% 177.04/27.62  | | Case 2:
% 177.04/27.62  | | | 
% 177.04/27.62  | | |   (199)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.62  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.04/27.62  | | |            all_52_30 = e0)
% 177.04/27.62  | | | 
% 177.04/27.62  | | | BETA: splitting (199) gives:
% 177.04/27.62  | | | 
% 177.04/27.62  | | | Case 1:
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | |   (200)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.04/27.62  | | | |          e0
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | | REF_CLOSE: (95), (144), (157), (162), (179), (200) are inconsistent by
% 177.04/27.62  | | | |            sub-proof #314.
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | Case 2:
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | |   (201)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.04/27.62  | | | |          e0
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | | REF_CLOSE: (3), (9), (11), (12), (13), (14), (17), (23), (24), (30),
% 177.04/27.62  | | | |            (31), (33), (34), (36), (37), (40), (42), (43), (45), (46),
% 177.04/27.62  | | | |            (47), (54), (57), (59), (61), (62), (66), (67), (70), (71),
% 177.04/27.62  | | | |            (72), (75), (76), (81), (82), (88), (90), (92), (93), (97),
% 177.04/27.62  | | | |            (104), (105), (106), (110), (111), (112), (113), (116),
% 177.04/27.62  | | | |            (117), (118), (119), (122), (129), (131), (135), (137),
% 177.04/27.62  | | | |            (139), (140), (141), (144), (146), (156), (161), (163),
% 177.04/27.62  | | | |            (165), (175), (176), (180), (181), (182), (184), (186),
% 177.04/27.62  | | | |            (188), (201) are inconsistent by sub-proof #615.
% 177.04/27.62  | | | | 
% 177.04/27.62  | | | End of split
% 177.04/27.62  | | | 
% 177.04/27.62  | | End of split
% 177.04/27.62  | | 
% 177.04/27.62  | Case 2:
% 177.04/27.62  | | 
% 177.04/27.62  | |   (202)   ~ (all_58_15 = e0)
% 177.04/27.62  | |   (203)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.04/27.62  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | ALPHA: (203) implies:
% 177.04/27.62  | |   (204)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.62  | |   (205)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.62  | | 
% 177.04/27.62  | | REDUCE: (32), (202) imply:
% 177.04/27.62  | |   (206)   ~ (all_6_2 = e0)
% 177.04/27.62  | | 
% 177.04/27.62  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 177.04/27.62  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.04/27.62  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.04/27.62  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.04/27.62  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (57), (59),
% 177.04/27.62  | |            (60), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 177.04/27.62  | |            (72), (74), (76), (77), (78), (79), (80), (81), (82), (84), (85),
% 177.04/27.62  | |            (87), (88), (89), (91), (92), (93), (94), (95), (96), (97), (98),
% 177.04/27.62  | |            (99), (100), (101), (102), (103), (104), (105), (106), (108),
% 177.04/27.62  | |            (109), (111), (112), (113), (114), (115), (116), (117), (118),
% 177.04/27.62  | |            (119), (120), (121), (122), (123), (124), (125), (127), (128),
% 177.04/27.62  | |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 177.04/27.62  | |            (139), (140), (141), (143), (144), (145), (146), (147), (148),
% 177.04/27.62  | |            (149), (150), (151), (152), (153), (154), (156), (157), (158),
% 177.04/27.62  | |            (159), (160), (161), (162), (163), (164), (165), (166), (167),
% 177.04/27.62  | |            (168), (169), (170), (171), (172), (173), (174), (175), (176),
% 177.04/27.62  | |            (177), (179), (180), (181), (204), (205), (206) are inconsistent
% 177.04/27.62  | |            by sub-proof #307.
% 177.04/27.62  | | 
% 177.04/27.62  | End of split
% 177.04/27.62  | 
% 177.04/27.62  End of proof
% 177.04/27.62  
% 177.04/27.62  Sub-proof #307 shows that the following formulas are inconsistent:
% 177.04/27.62  ----------------------------------------------------------------
% 177.04/27.62    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.62    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.62    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.62    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.62    (5)   ~ (all_52_27 = all_10_2)
% 177.04/27.62    (6)   ~ (all_52_17 = all_52_23)
% 177.04/27.62    (7)  op(e2, all_10_2) = all_10_1
% 177.04/27.62    (8)  all_40_2 = all_4_2
% 177.04/27.62    (9)   ~ (all_52_13 = all_52_29)
% 177.04/27.62    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.62    (11)  all_56_3 = all_52_7
% 177.04/27.62    (12)  op(e3, e2) = all_52_3
% 177.04/27.62    (13)   ~ (all_52_9 = all_52_25)
% 177.04/27.62    (14)  op(e3, all_52_25) = all_52_24
% 177.04/27.62    (15)   ~ (all_52_19 = all_52_23)
% 177.04/27.62    (16)  all_56_11 = all_52_23
% 177.04/27.62    (17)  op(e1, e2) = all_52_19
% 177.04/27.62    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.04/27.62    (19)  op(e3, all_52_9) = all_52_8
% 177.04/27.62    (20)   ~ (all_52_3 = all_10_2)
% 177.04/27.62    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.62    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.04/27.62    (23)  all_58_5 = all_52_13
% 177.04/27.62    (24)   ~ (all_6_2 = e0)
% 177.04/27.62    (25)   ~ (all_52_25 = all_52_29)
% 177.04/27.62    (26)  all_56_15 = all_6_2
% 177.04/27.62    (27)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.62    (28)  op(e2, e0) = all_52_15
% 177.04/27.63    (29)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.63    (30)  all_58_3 = all_10_2
% 177.04/27.63    (31)  all_56_9 = all_52_19
% 177.04/27.63    (32)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.63    (33)  all_58_15 = all_6_2
% 177.04/27.63    (34)   ~ (all_52_9 = all_4_2)
% 177.04/27.63    (35)   ~ (all_52_5 = all_52_7)
% 177.04/27.63    (36)  all_58_10 = all_52_15
% 177.04/27.63    (37)   ~ (all_52_5 = all_4_2)
% 177.04/27.63    (38)  all_58_7 = all_52_19
% 177.04/27.63    (39)  all_56_4 = all_52_9
% 177.04/27.63    (40)   ~ (all_52_15 = all_6_2)
% 177.04/27.63    (41)   ~ (all_52_17 = all_52_25)
% 177.04/27.63    (42)  op(e0, e1) = all_52_29
% 177.04/27.63    (43)   ~ (all_4_0 = e2)
% 177.04/27.63    (44)  all_58_4 = all_52_5
% 177.04/27.63    (45)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.63    (46)   ~ (e3 = e1)
% 177.04/27.63    (47)   ~ (all_52_27 = all_52_29)
% 177.04/27.63    (48)   ~ (all_52_17 = all_14_2)
% 177.04/27.63    (49)  op(e3, all_4_2) = all_4_1
% 177.04/27.63    (50)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.63    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.63    (52)   ~ (all_52_7 = all_4_2)
% 177.04/27.63    (53)  all_58_1 = all_52_3
% 177.04/27.63    (54)   ~ (all_52_13 = all_52_15)
% 177.04/27.63    (55)  all_58_0 = all_4_2
% 177.04/27.63    (56)  all_52_0 = e1
% 177.04/27.63    (57)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.63    (58)  op(e1, all_52_13) = all_52_12
% 177.04/27.63    (59)  op(e1, all_52_29) = all_52_28
% 177.04/27.63    (60)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.63    (61)   ~ (all_4_1 = e2)
% 177.04/27.63    (62)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.63    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.63    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.63    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.04/27.63    (66)  all_58_14 = all_52_29
% 177.04/27.63    (67)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.63    (68)   ~ (all_52_3 = all_52_5)
% 177.04/27.63    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.63    (70)  op(e2, e1) = all_52_13
% 177.04/27.63    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.63    (72)  all_58_8 = all_14_2
% 177.04/27.63    (73)  op(e0, e2) = all_52_27
% 177.04/27.63    (74)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.04/27.63    (75)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.04/27.63    (76)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.63    (77)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.63    (78)   ~ (all_52_5 = all_14_2)
% 177.04/27.63    (79)   ~ (all_52_3 = all_52_27)
% 177.04/27.63    (80)   ~ (all_52_3 = all_4_2)
% 177.04/27.63    (81)  op(e0, e3) = all_52_25
% 177.04/27.63    (82)  op(e0, all_6_2) = all_6_1
% 177.04/27.63    (83)   ~ (all_52_9 = all_10_2)
% 177.04/27.63    (84)  op(e3, all_52_17) = all_52_16
% 177.04/27.63    (85)  all_52_10 = all_10_1
% 177.04/27.63    (86)   ~ (all_52_13 = all_14_2)
% 177.04/27.63    (87)   ~ (e3 = e0)
% 177.04/27.63    (88)  all_40_0 = all_4_0
% 177.04/27.63    (89)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.63    (90)  op(all_14_1, all_14_2) = e2
% 177.04/27.63    (91)   ~ (all_52_9 = all_52_13)
% 177.04/27.63    (92)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.63    (93)  op(e0, all_52_23) = all_52_22
% 177.04/27.63    (94)   ~ (all_52_15 = all_52_23)
% 177.04/27.63    (95)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.63    (96)  op(all_10_1, all_10_2) = all_10_0
% 177.04/27.63    (97)   ~ (all_52_5 = all_52_29)
% 177.04/27.63    (98)  all_56_2 = all_52_5
% 177.04/27.63    (99)  op(e1, e0) = all_52_23
% 177.04/27.63    (100)  all_56_12 = all_52_25
% 177.04/27.63    (101)  all_58_13 = all_52_27
% 177.04/27.63    (102)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.63    (103)  all_56_5 = all_10_2
% 177.04/27.63    (104)   ~ (all_52_9 = all_52_17)
% 177.04/27.63    (105)  all_58_6 = all_52_17
% 177.04/27.63    (106)   ~ (all_52_3 = all_52_7)
% 177.04/27.63    (107)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.63    (108)  op(e2, all_52_19) = all_52_18
% 177.04/27.63    (109)   ~ (e1 = e0)
% 177.04/27.63    (110)  all_56_0 = all_4_2
% 177.04/27.63    (111)  all_58_11 = all_52_23
% 177.04/27.63    (112)   ~ (all_52_3 = all_52_19)
% 177.04/27.63    (113)   ~ (all_52_7 = all_52_15)
% 177.04/27.63    (114)  op(e0, all_52_15) = all_52_14
% 177.04/27.63    (115)   ~ (all_52_29 = all_14_2)
% 177.04/27.63    (116)   ~ (all_4_0 = e1)
% 177.04/27.63    (117)   ~ (all_52_19 = all_10_2)
% 177.04/27.63    (118)   ~ (all_52_23 = all_6_2)
% 177.04/27.63    (119)  op(e1, all_4_2) = all_4_0
% 177.04/27.63    (120)   ~ (all_52_29 = all_6_2)
% 177.04/27.63    (121)  all_58_2 = all_52_9
% 177.04/27.63    (122)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.63    (123)  op(e3, e1) = all_52_5
% 177.04/27.63    (124)   ~ (e2 = e1)
% 177.04/27.63    (125)  all_56_10 = all_14_2
% 177.04/27.63    (126)   ~ (all_52_25 = all_6_2)
% 177.04/27.63    (127)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.63    (128)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.63    (129)  op(e1, e1) = all_14_2
% 177.04/27.63    (130)  op(e1, e3) = all_52_17
% 177.04/27.63    (131)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.63    (132)   ~ (all_52_25 = all_4_2)
% 177.04/27.63    (133)  op(e3, e0) = all_52_7
% 177.04/27.63    (134)  op(e3, e3) = all_4_2
% 177.04/27.63    (135)   ~ (all_52_17 = all_4_2)
% 177.04/27.63    (136)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.63             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.63    (137)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.63           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.04/27.63           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.63           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.63    (138)   ~ (all_52_25 = all_52_27)
% 177.04/27.63    (139)   ~ (all_52_27 = all_6_2)
% 177.04/27.63    (140)   ~ (all_52_7 = all_6_2)
% 177.04/27.63    (141)   ~ (all_10_0 = e3)
% 177.04/27.63    (142)   ~ (all_52_15 = all_10_2)
% 177.04/27.63    (143)   ~ (all_52_19 = all_52_27)
% 177.04/27.63    (144)  all_56_7 = all_52_15
% 177.04/27.63    (145)   ~ (all_52_7 = all_52_23)
% 177.04/27.63    (146)   ~ (all_52_13 = all_10_2)
% 177.04/27.63    (147)  op(e2, all_52_27) = all_52_26
% 177.04/27.63    (148)  all_52_20 = all_14_1
% 177.04/27.63    (149)   ~ (all_52_17 = all_52_19)
% 177.04/27.63    (150)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.63    (151)  all_52_30 = all_6_1
% 177.04/27.63    (152)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.63    (153)  op(e1, all_14_2) = all_14_1
% 177.04/27.63    (154)  all_58_9 = all_52_7
% 177.04/27.63    (155)   ~ (e2 = e0)
% 177.04/27.63    (156)  all_58_12 = all_52_25
% 177.04/27.63    (157)  op(e3, all_4_2) = e1
% 177.04/27.63    (158)   ~ (all_10_0 = e1)
% 177.04/27.63    (159)  all_56_6 = all_52_13
% 177.04/27.63    (160)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.63    (161)   ~ (all_52_9 = all_52_15)
% 177.04/27.63    (162)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.63    (163)   ~ (e3 = e2)
% 177.04/27.63    (164)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.63    (165)   ~ (all_52_19 = all_14_2)
% 177.04/27.63    (166)  op(e0, all_52_7) = all_52_6
% 177.04/27.63    (167)  op(e2, e3) = all_52_9
% 177.04/27.63    (168)  all_56_13 = all_52_27
% 177.04/27.63  
% 177.04/27.63  Begin of proof
% 177.04/27.63  | 
% 177.04/27.63  | BETA: splitting (137) gives:
% 177.04/27.63  | 
% 177.04/27.63  | Case 1:
% 177.04/27.63  | | 
% 177.04/27.63  | |   (169)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.63  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.04/27.63  | | 
% 177.04/27.63  | | BETA: splitting (169) gives:
% 177.04/27.63  | | 
% 177.04/27.63  | | Case 1:
% 177.04/27.63  | | | 
% 177.04/27.63  | | |   (170)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REF_CLOSE: (46), (56), (170) are inconsistent by sub-proof #632.
% 177.04/27.63  | | | 
% 177.04/27.63  | | Case 2:
% 177.04/27.63  | | | 
% 177.04/27.63  | | |   (171)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.04/27.63  | | | 
% 177.04/27.63  | | | ALPHA: (171) implies:
% 177.04/27.63  | | |   (172)  all_52_14 = e0
% 177.04/27.63  | | |   (173)  all_52_12 = e1
% 177.04/27.63  | | |   (174)  all_52_10 = e2
% 177.04/27.63  | | |   (175)  all_52_8 = e3
% 177.04/27.63  | | | 
% 177.04/27.63  | | | COMBINE_EQS: (85), (174) imply:
% 177.04/27.63  | | |   (176)  all_10_1 = e2
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REDUCE: (96), (176) imply:
% 177.04/27.63  | | |   (177)  op(e2, all_10_2) = all_10_0
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REDUCE: (19), (175) imply:
% 177.04/27.63  | | |   (178)  op(e3, all_52_9) = e3
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REDUCE: (7), (176) imply:
% 177.04/27.63  | | |   (179)  op(e2, all_10_2) = e2
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REDUCE: (58), (173) imply:
% 177.04/27.63  | | |   (180)  op(e1, all_52_13) = e1
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REDUCE: (114), (172) imply:
% 177.04/27.63  | | |   (181)  op(e0, all_52_15) = e0
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 177.04/27.63  | | |            (14), (15), (16), (17), (20), (21), (22), (23), (24), (25),
% 177.04/27.63  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.04/27.63  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.04/27.63  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (55), (57),
% 177.04/27.63  | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.04/27.63  | | |            (69), (70), (71), (72), (74), (75), (76), (77), (78), (79),
% 177.04/27.63  | | |            (80), (81), (82), (84), (86), (87), (88), (91), (93), (94),
% 177.04/27.63  | | |            (95), (97), (98), (99), (101), (102), (103), (104), (105),
% 177.04/27.63  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (115),
% 177.04/27.63  | | |            (117), (118), (119), (120), (121), (122), (123), (125), (126),
% 177.04/27.63  | | |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 177.04/27.63  | | |            (136), (138), (139), (140), (141), (143), (144), (145), (146),
% 177.04/27.63  | | |            (147), (149), (150), (152), (153), (154), (155), (156), (157),
% 177.04/27.63  | | |            (158), (159), (160), (161), (162), (164), (165), (166), (167),
% 177.04/27.63  | | |            (168), (177), (178), (179), (180), (181) are inconsistent by
% 177.04/27.63  | | |            sub-proof #308.
% 177.04/27.63  | | | 
% 177.04/27.63  | | End of split
% 177.04/27.63  | | 
% 177.04/27.63  | Case 2:
% 177.04/27.63  | | 
% 177.04/27.63  | |   (182)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 177.04/27.63  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.04/27.63  | |            e0)
% 177.04/27.63  | | 
% 177.04/27.63  | | BETA: splitting (182) gives:
% 177.04/27.63  | | 
% 177.04/27.63  | | Case 1:
% 177.04/27.63  | | | 
% 177.04/27.63  | | |   (183)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REF_CLOSE: (90), (124), (136), (148), (153), (183) are inconsistent by
% 177.04/27.63  | | |            sub-proof #314.
% 177.04/27.63  | | | 
% 177.04/27.63  | | Case 2:
% 177.04/27.63  | | | 
% 177.04/27.63  | | |   (184)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.04/27.63  | | | 
% 177.04/27.63  | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (12), (13), (14), (15),
% 177.04/27.63  | | |            (18), (19), (23), (24), (25), (26), (27), (29), (30), (32),
% 177.04/27.63  | | |            (33), (34), (35), (36), (37), (38), (41), (42), (43), (44),
% 177.04/27.63  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 177.04/27.63  | | |            (55), (57), (59), (62), (63), (66), (67), (68), (69), (71),
% 177.04/27.63  | | |            (72), (73), (76), (79), (81), (82), (83), (84), (87), (89),
% 177.04/27.63  | | |            (92), (97), (99), (100), (101), (102), (104), (105), (106),
% 177.04/27.63  | | |            (109), (110), (111), (116), (117), (120), (121), (123), (124),
% 177.04/27.63  | | |            (126), (130), (132), (133), (134), (135), (136), (138), (139),
% 177.04/27.63  | | |            (140), (142), (147), (149), (150), (151), (154), (156), (157),
% 177.04/27.63  | | |            (160), (161), (163), (167), (168), (184) are inconsistent by
% 177.04/27.63  | | |            sub-proof #444.
% 177.04/27.63  | | | 
% 177.04/27.63  | | End of split
% 177.04/27.63  | | 
% 177.04/27.63  | End of split
% 177.04/27.63  | 
% 177.04/27.63  End of proof
% 177.04/27.63  
% 177.04/27.63  Sub-proof #308 shows that the following formulas are inconsistent:
% 177.04/27.63  ----------------------------------------------------------------
% 177.04/27.63    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.63    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.63    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.63    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.63    (5)   ~ (all_52_27 = all_10_2)
% 177.04/27.63    (6)   ~ (all_52_17 = all_52_23)
% 177.04/27.63    (7)  all_40_2 = all_4_2
% 177.04/27.63    (8)   ~ (all_52_13 = all_52_29)
% 177.04/27.63    (9)  op(e2, all_10_2) = all_10_0
% 177.04/27.63    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.63    (11)  all_56_3 = all_52_7
% 177.04/27.63    (12)  op(e3, e2) = all_52_3
% 177.04/27.63    (13)   ~ (all_52_9 = all_52_25)
% 177.04/27.63    (14)  op(e3, all_52_25) = all_52_24
% 177.04/27.63    (15)   ~ (all_52_19 = all_52_23)
% 177.04/27.63    (16)  all_56_11 = all_52_23
% 177.04/27.63    (17)  op(e1, e2) = all_52_19
% 177.04/27.63    (18)   ~ (all_52_3 = all_10_2)
% 177.04/27.63    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.63    (20)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.04/27.63    (21)  all_58_5 = all_52_13
% 177.04/27.63    (22)   ~ (all_6_2 = e0)
% 177.04/27.63    (23)   ~ (all_52_25 = all_52_29)
% 177.04/27.63    (24)  op(e1, all_52_13) = e1
% 177.04/27.63    (25)  op(e0, all_52_15) = e0
% 177.04/27.63    (26)  all_56_15 = all_6_2
% 177.04/27.63    (27)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.63    (28)  op(e2, e0) = all_52_15
% 177.04/27.63    (29)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.63    (30)  all_58_3 = all_10_2
% 177.04/27.63    (31)  all_56_9 = all_52_19
% 177.04/27.63    (32)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.63    (33)  all_58_15 = all_6_2
% 177.04/27.63    (34)   ~ (all_52_9 = all_4_2)
% 177.04/27.63    (35)   ~ (all_52_5 = all_52_7)
% 177.04/27.63    (36)  all_58_10 = all_52_15
% 177.04/27.63    (37)   ~ (all_52_5 = all_4_2)
% 177.04/27.63    (38)  all_58_7 = all_52_19
% 177.04/27.63    (39)  all_56_4 = all_52_9
% 177.04/27.63    (40)   ~ (all_52_15 = all_6_2)
% 177.04/27.63    (41)   ~ (all_52_17 = all_52_25)
% 177.04/27.63    (42)  op(e0, e1) = all_52_29
% 177.04/27.63    (43)   ~ (all_4_0 = e2)
% 177.04/27.63    (44)  all_58_4 = all_52_5
% 177.04/27.63    (45)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.63    (46)   ~ (e3 = e1)
% 177.04/27.63    (47)   ~ (all_52_27 = all_52_29)
% 177.04/27.63    (48)   ~ (all_52_17 = all_14_2)
% 177.04/27.63    (49)  op(e3, all_4_2) = all_4_1
% 177.04/27.63    (50)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.63    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.63    (52)   ~ (all_52_7 = all_4_2)
% 177.04/27.63    (53)  all_58_1 = all_52_3
% 177.04/27.63    (54)  all_58_0 = all_4_2
% 177.04/27.63    (55)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.63    (56)  op(e1, all_52_29) = all_52_28
% 177.04/27.63    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.63    (58)   ~ (all_4_1 = e2)
% 177.04/27.63    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.63    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.63    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.63    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.04/27.63    (63)  all_58_14 = all_52_29
% 177.04/27.63    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.63    (65)   ~ (all_52_3 = all_52_5)
% 177.04/27.63    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.63    (67)  op(e2, e1) = all_52_13
% 177.04/27.63    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.63    (69)  all_58_8 = all_14_2
% 177.04/27.63    (70)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.04/27.63    (71)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.04/27.63    (72)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.63    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.63    (74)   ~ (all_52_5 = all_14_2)
% 177.04/27.63    (75)   ~ (all_52_3 = all_52_27)
% 177.04/27.63    (76)   ~ (all_52_3 = all_4_2)
% 177.04/27.63    (77)  op(e0, e3) = all_52_25
% 177.04/27.63    (78)  op(e0, all_6_2) = all_6_1
% 177.04/27.63    (79)  op(e3, all_52_17) = all_52_16
% 177.04/27.63    (80)   ~ (all_52_13 = all_14_2)
% 177.04/27.63    (81)  op(e3, all_52_9) = e3
% 177.04/27.63    (82)   ~ (e3 = e0)
% 177.04/27.63    (83)  all_40_0 = all_4_0
% 177.04/27.63    (84)   ~ (all_52_9 = all_52_13)
% 177.04/27.63    (85)  op(e0, all_52_23) = all_52_22
% 177.04/27.63    (86)   ~ (all_52_15 = all_52_23)
% 177.04/27.63    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.63    (88)   ~ (all_52_5 = all_52_29)
% 177.04/27.63    (89)  all_56_2 = all_52_5
% 177.04/27.63    (90)  op(e1, e0) = all_52_23
% 177.04/27.63    (91)  all_58_13 = all_52_27
% 177.04/27.63    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.63    (93)  all_56_5 = all_10_2
% 177.04/27.63    (94)   ~ (all_52_9 = all_52_17)
% 177.04/27.63    (95)  all_58_6 = all_52_17
% 177.04/27.63    (96)   ~ (all_52_3 = all_52_7)
% 177.04/27.63    (97)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.63    (98)  op(e2, all_52_19) = all_52_18
% 177.04/27.63    (99)   ~ (e1 = e0)
% 177.04/27.63    (100)  all_56_0 = all_4_2
% 177.04/27.63    (101)  all_58_11 = all_52_23
% 177.04/27.63    (102)   ~ (all_52_3 = all_52_19)
% 177.04/27.63    (103)   ~ (all_52_7 = all_52_15)
% 177.04/27.63    (104)   ~ (all_52_29 = all_14_2)
% 177.04/27.63    (105)   ~ (all_52_19 = all_10_2)
% 177.04/27.63    (106)   ~ (all_52_23 = all_6_2)
% 177.04/27.63    (107)  op(e1, all_4_2) = all_4_0
% 177.04/27.63    (108)   ~ (all_52_29 = all_6_2)
% 177.04/27.63    (109)  all_58_2 = all_52_9
% 177.04/27.63    (110)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.63    (111)  op(e3, e1) = all_52_5
% 177.04/27.63    (112)  all_56_10 = all_14_2
% 177.04/27.63    (113)   ~ (all_52_25 = all_6_2)
% 177.04/27.63    (114)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.63    (115)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.63    (116)  op(e1, e1) = all_14_2
% 177.04/27.63    (117)  op(e1, e3) = all_52_17
% 177.04/27.63    (118)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.63    (119)   ~ (all_52_25 = all_4_2)
% 177.04/27.63    (120)  op(e3, e0) = all_52_7
% 177.04/27.63    (121)  op(e2, all_10_2) = e2
% 177.04/27.63    (122)  op(e3, e3) = all_4_2
% 177.04/27.63    (123)   ~ (all_52_17 = all_4_2)
% 177.04/27.63    (124)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.63             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.63    (125)   ~ (all_52_25 = all_52_27)
% 177.04/27.63    (126)   ~ (all_52_27 = all_6_2)
% 177.04/27.63    (127)   ~ (all_52_7 = all_6_2)
% 177.04/27.63    (128)   ~ (all_10_0 = e3)
% 177.04/27.63    (129)   ~ (all_52_19 = all_52_27)
% 177.04/27.63    (130)  all_56_7 = all_52_15
% 177.04/27.63    (131)   ~ (all_52_7 = all_52_23)
% 177.04/27.63    (132)   ~ (all_52_13 = all_10_2)
% 177.04/27.63    (133)  op(e2, all_52_27) = all_52_26
% 177.04/27.63    (134)   ~ (all_52_17 = all_52_19)
% 177.04/27.63    (135)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.63    (136)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.63    (137)  op(e1, all_14_2) = all_14_1
% 177.04/27.63    (138)  all_58_9 = all_52_7
% 177.04/27.63    (139)   ~ (e2 = e0)
% 177.04/27.63    (140)  all_58_12 = all_52_25
% 177.04/27.63    (141)  op(e3, all_4_2) = e1
% 177.04/27.63    (142)   ~ (all_10_0 = e1)
% 177.04/27.63    (143)  all_56_6 = all_52_13
% 177.04/27.63    (144)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.63    (145)   ~ (all_52_9 = all_52_15)
% 177.04/27.63    (146)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.63    (147)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.63    (148)   ~ (all_52_19 = all_14_2)
% 177.04/27.63    (149)  op(e0, all_52_7) = all_52_6
% 177.04/27.63    (150)  op(e2, e3) = all_52_9
% 177.04/27.63    (151)  all_56_13 = all_52_27
% 177.04/27.63  
% 177.04/27.63  Begin of proof
% 177.04/27.63  | 
% 177.04/27.63  | GROUND_INST: instantiating (124) with e2, all_10_0, all_10_2, e2, simplifying
% 177.04/27.63  |              with (9), (121) gives:
% 177.04/27.63  |   (152)  all_10_0 = e2
% 177.04/27.63  | 
% 177.04/27.63  | REDUCE: (128), (152) imply:
% 177.04/27.63  |   (153)   ~ (e3 = e2)
% 177.04/27.63  | 
% 177.04/27.63  | SIMP: (153) implies:
% 177.04/27.64  |   (154)   ~ (e3 = e2)
% 177.04/27.64  | 
% 177.04/27.64  | REDUCE: (142), (152) imply:
% 177.04/27.64  |   (155)   ~ (e2 = e1)
% 177.04/27.64  | 
% 177.04/27.64  | BETA: splitting (50) gives:
% 177.04/27.64  | 
% 177.04/27.64  | Case 1:
% 177.04/27.64  | | 
% 177.04/27.64  | |   (156)  all_56_15 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | COMBINE_EQS: (26), (156) imply:
% 177.04/27.64  | |   (157)  all_6_2 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | SIMP: (157) implies:
% 177.04/27.64  | |   (158)  all_6_2 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | REF_CLOSE: (12), (13), (18), (21), (24), (27), (30), (34), (36), (38), (39),
% 177.04/27.64  | |            (40), (43), (45), (46), (49), (51), (52), (53), (54), (60), (61),
% 177.04/27.64  | |            (66), (69), (72), (77), (78), (80), (81), (91), (94), (95), (97),
% 177.04/27.64  | |            (98), (101), (102), (106), (109), (113), (115), (117), (120),
% 177.04/27.64  | |            (121), (122), (123), (124), (126), (134), (140), (143), (150),
% 177.04/27.64  | |            (155), (158) are inconsistent by sub-proof #773.
% 177.04/27.64  | | 
% 177.04/27.64  | Case 2:
% 177.04/27.64  | | 
% 177.04/27.64  | |   (159)   ~ (all_56_15 = e3)
% 177.04/27.64  | |   (160)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (26), (159) imply:
% 177.04/27.64  | |   (161)   ~ (all_6_2 = e3)
% 177.04/27.64  | | 
% 177.04/27.64  | | BETA: splitting (64) gives:
% 177.04/27.64  | | 
% 177.04/27.64  | | Case 1:
% 177.04/27.64  | | | 
% 177.04/27.64  | | |   (162)  all_56_13 = e3
% 177.04/27.64  | | | 
% 177.04/27.64  | | | COMBINE_EQS: (151), (162) imply:
% 177.04/27.64  | | |   (163)  all_52_27 = e3
% 177.04/27.64  | | | 
% 177.04/27.64  | | | SIMP: (163) implies:
% 177.04/27.64  | | |   (164)  all_52_27 = e3
% 177.04/27.64  | | | 
% 177.04/27.64  | | | REF_CLOSE: (2), (5), (6), (7), (8), (11), (12), (17), (21), (24), (25),
% 177.04/27.64  | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (41),
% 177.04/27.64  | | |            (43), (44), (45), (46), (48), (51), (52), (53), (54), (57),
% 177.04/27.64  | | |            (63), (66), (69), (70), (74), (75), (77), (80), (81), (83),
% 177.04/27.64  | | |            (84), (86), (92), (95), (100), (101), (102), (103), (107),
% 177.04/27.64  | | |            (109), (111), (117), (119), (122), (123), (124), (126), (129),
% 177.04/27.64  | | |            (131), (133), (135), (136), (138), (140), (141), (144), (146),
% 177.04/27.64  | | |            (150), (164) are inconsistent by sub-proof #610.
% 177.04/27.64  | | | 
% 177.04/27.64  | | Case 2:
% 177.04/27.64  | | | 
% 177.04/27.64  | | |   (165)   ~ (all_56_13 = e3)
% 177.04/27.64  | | | 
% 177.04/27.64  | | | REDUCE: (151), (165) imply:
% 177.04/27.64  | | |   (166)   ~ (all_52_27 = e3)
% 177.04/27.64  | | | 
% 177.04/27.64  | | | BETA: splitting (68) gives:
% 177.04/27.64  | | | 
% 177.04/27.64  | | | Case 1:
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | |   (167)  all_58_12 = e3
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 177.04/27.64  | | | |            (13), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 177.04/27.64  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.04/27.64  | | | |            (35), (36), (37), (38), (39), (42), (43), (44), (45), (46),
% 177.04/27.64  | | | |            (47), (48), (51), (52), (53), (54), (55), (57), (59), (60),
% 177.04/27.64  | | | |            (61), (62), (63), (65), (67), (69), (70), (73), (74), (75),
% 177.04/27.64  | | | |            (76), (77), (79), (80), (81), (82), (83), (84), (85), (87),
% 177.04/27.64  | | | |            (88), (89), (91), (92), (93), (94), (95), (96), (97), (98),
% 177.04/27.64  | | | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 177.04/27.64  | | | |            (109), (110), (111), (112), (113), (114), (117), (118),
% 177.04/27.64  | | | |            (119), (120), (121), (124), (125), (126), (127), (129),
% 177.04/27.64  | | | |            (130), (131), (132), (133), (134), (135), (136), (137),
% 177.04/27.64  | | | |            (138), (139), (140), (141), (143), (145), (146), (147),
% 177.04/27.64  | | | |            (148), (149), (150), (154), (160), (167) are inconsistent by
% 177.04/27.64  | | | |            sub-proof #365.
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | Case 2:
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | |   (168)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | | REF_CLOSE: (2), (6), (8), (12), (13), (14), (15), (16), (18), (20),
% 177.04/27.64  | | | |            (21), (24), (25), (27), (28), (30), (33), (34), (36), (37),
% 177.04/27.64  | | | |            (38), (39), (43), (44), (45), (46), (47), (49), (51), (52),
% 177.04/27.64  | | | |            (53), (54), (55), (56), (58), (60), (61), (63), (65), (66),
% 177.04/27.64  | | | |            (69), (71), (72), (76), (77), (80), (81), (84), (86), (88),
% 177.04/27.64  | | | |            (89), (90), (91), (92), (95), (96), (97), (98), (99), (101),
% 177.04/27.64  | | | |            (102), (103), (104), (108), (109), (110), (111), (116),
% 177.04/27.64  | | | |            (117), (119), (120), (121), (122), (123), (124), (125),
% 177.04/27.64  | | | |            (129), (134), (135), (138), (140), (143), (144), (145),
% 177.04/27.64  | | | |            (147), (150), (155), (161), (166), (168) are inconsistent by
% 177.04/27.64  | | | |            sub-proof #340.
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | End of split
% 177.04/27.64  | | | 
% 177.04/27.64  | | End of split
% 177.04/27.64  | | 
% 177.04/27.64  | End of split
% 177.04/27.64  | 
% 177.04/27.64  End of proof
% 177.04/27.64  
% 177.04/27.64  Sub-proof #309 shows that the following formulas are inconsistent:
% 177.04/27.64  ----------------------------------------------------------------
% 177.04/27.64    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.64    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.64    (3)   ~ (all_52_27 = all_10_2)
% 177.04/27.64    (4)   ~ (all_52_17 = all_52_23)
% 177.04/27.64    (5)   ~ (all_6_0 = e3)
% 177.04/27.64    (6)   ~ (all_52_13 = all_52_29)
% 177.04/27.64    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.64    (8)  op(e3, e2) = all_52_3
% 177.04/27.64    (9)   ~ (all_52_9 = all_52_25)
% 177.04/27.64    (10)  op(e3, all_52_25) = all_52_24
% 177.04/27.64    (11)   ~ (all_52_19 = all_52_23)
% 177.04/27.64    (12)  all_56_11 = all_52_23
% 177.04/27.64    (13)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.04/27.64    (14)  op(e3, all_52_9) = all_52_8
% 177.04/27.64    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.64    (16)  all_58_5 = all_52_13
% 177.04/27.64    (17)   ~ (all_6_2 = e0)
% 177.04/27.64    (18)   ~ (all_52_25 = all_52_29)
% 177.04/27.64    (19)  all_56_15 = all_6_2
% 177.04/27.64    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.64    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.64    (22)  all_58_3 = all_10_2
% 177.04/27.64    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.64    (24)  all_58_15 = all_6_2
% 177.04/27.64    (25)   ~ (all_52_9 = all_4_2)
% 177.04/27.64    (26)   ~ (all_52_5 = all_52_7)
% 177.04/27.64    (27)  all_58_10 = all_52_15
% 177.04/27.64    (28)   ~ (all_52_5 = all_4_2)
% 177.04/27.64    (29)  all_58_7 = all_52_19
% 177.04/27.64    (30)   ~ (all_52_17 = all_52_25)
% 177.04/27.64    (31)  op(e0, e1) = all_52_29
% 177.04/27.64    (32)   ~ (all_4_0 = e2)
% 177.04/27.64    (33)  all_58_4 = all_52_5
% 177.04/27.64    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.64    (35)   ~ (e3 = e1)
% 177.04/27.64    (36)   ~ (all_52_27 = all_52_29)
% 177.04/27.64    (37)   ~ (all_52_17 = all_14_2)
% 177.04/27.64    (38)  op(e3, all_4_2) = all_4_1
% 177.04/27.64    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.64    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.64    (41)   ~ (all_52_7 = all_4_2)
% 177.04/27.64    (42)  all_58_1 = all_52_3
% 177.04/27.64    (43)   ~ (all_52_13 = all_52_15)
% 177.04/27.64    (44)  all_58_0 = all_4_2
% 177.04/27.64    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.64    (46)  op(e1, all_52_29) = all_52_28
% 177.04/27.64    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.04/27.64    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.64    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.64    (50)  all_58_14 = all_52_29
% 177.04/27.64    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.64    (52)   ~ (all_52_3 = all_52_5)
% 177.04/27.64    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.64    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.64    (55)  all_58_8 = all_14_2
% 177.04/27.64    (56)  op(e0, e2) = all_52_27
% 177.04/27.64    (57)  all_56_14 = all_52_29
% 177.04/27.64    (58)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.64    (59)   ~ (all_52_3 = all_52_27)
% 177.04/27.64    (60)   ~ (all_52_3 = all_4_2)
% 177.04/27.64    (61)  op(all_6_1, all_6_2) = all_6_0
% 177.04/27.64    (62)  op(e0, e3) = all_52_25
% 177.04/27.64    (63)  op(e0, all_6_2) = all_6_1
% 177.04/27.64    (64)   ~ (all_52_9 = all_10_2)
% 177.04/27.64    (65)  op(e3, all_52_17) = all_52_16
% 177.04/27.64    (66)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.04/27.64    (67)   ~ (all_52_13 = all_14_2)
% 177.04/27.64    (68)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.64    (69)  op(all_14_1, all_14_2) = e2
% 177.04/27.64    (70)   ~ (all_52_9 = all_52_13)
% 177.04/27.64    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.64    (72)   ~ (all_52_5 = all_52_29)
% 177.04/27.64    (73)  all_56_2 = all_52_5
% 177.04/27.64    (74)  op(e1, e0) = all_52_23
% 177.04/27.64    (75)  all_56_12 = all_52_25
% 177.04/27.64    (76)  all_58_13 = all_52_27
% 177.04/27.64    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.64    (78)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.04/27.64    (79)   ~ (all_52_9 = all_52_17)
% 177.04/27.64    (80)  all_58_6 = all_52_17
% 177.04/27.64    (81)   ~ (all_52_3 = all_52_7)
% 177.04/27.64    (82)  all_56_0 = all_4_2
% 177.04/27.64    (83)  all_58_11 = all_52_23
% 177.04/27.64    (84)   ~ (all_52_3 = all_52_19)
% 177.04/27.64    (85)   ~ (all_52_7 = all_52_15)
% 177.04/27.64    (86)   ~ (all_4_0 = e1)
% 177.04/27.64    (87)   ~ (all_52_19 = all_10_2)
% 177.04/27.64    (88)   ~ (all_52_23 = all_6_2)
% 177.04/27.64    (89)   ~ (all_6_0 = e2)
% 177.04/27.64    (90)   ~ (all_52_29 = all_6_2)
% 177.04/27.64    (91)  all_58_2 = all_52_9
% 177.04/27.64    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.64    (93)  op(e3, e1) = all_52_5
% 177.04/27.64    (94)   ~ (e2 = e1)
% 177.04/27.64    (95)   ~ (all_52_25 = all_6_2)
% 177.04/27.64    (96)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.64    (97)  op(e1, e3) = all_52_17
% 177.04/27.64    (98)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.64    (99)   ~ (all_52_25 = all_4_2)
% 177.04/27.64    (100)  op(e3, e0) = all_52_7
% 177.04/27.64    (101)  op(e3, e3) = all_4_2
% 177.04/27.64    (102)   ~ (all_52_17 = all_4_2)
% 177.04/27.64    (103)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.64             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.64    (104)   ~ (all_52_25 = all_52_27)
% 177.04/27.64    (105)   ~ (all_52_27 = all_6_2)
% 177.04/27.64    (106)   ~ (all_52_7 = all_6_2)
% 177.04/27.64    (107)   ~ (all_52_15 = all_10_2)
% 177.04/27.64    (108)   ~ (all_52_19 = all_52_27)
% 177.04/27.64    (109)  all_56_7 = all_52_15
% 177.04/27.64    (110)   ~ (all_52_7 = all_52_23)
% 177.04/27.64    (111)   ~ (all_6_0 = e1)
% 177.04/27.64    (112)  op(e2, all_52_27) = all_52_26
% 177.04/27.64    (113)  all_52_20 = all_14_1
% 177.04/27.64    (114)   ~ (all_52_17 = all_52_19)
% 177.04/27.64    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.64    (116)  all_52_30 = all_6_1
% 177.04/27.64    (117)  op(e1, all_14_2) = all_14_1
% 177.04/27.64    (118)  all_58_9 = all_52_7
% 177.04/27.64    (119)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.64           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.64    (120)  all_58_12 = all_52_25
% 177.04/27.64    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.64    (122)   ~ (all_52_9 = all_52_15)
% 177.04/27.64    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.64    (124)   ~ (e3 = e2)
% 177.04/27.64    (125)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.64    (126)  op(e2, e3) = all_52_9
% 177.04/27.64    (127)  all_56_13 = all_52_27
% 177.04/27.64  
% 177.04/27.64  Begin of proof
% 177.04/27.64  | 
% 177.04/27.64  | BETA: splitting (119) gives:
% 177.04/27.64  | 
% 177.04/27.64  | Case 1:
% 177.04/27.64  | | 
% 177.04/27.64  | |   (128)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.04/27.64  | | 
% 177.04/27.64  | | ALPHA: (128) implies:
% 177.04/27.64  | |   (129)  all_52_20 = e1
% 177.04/27.64  | | 
% 177.04/27.64  | | COMBINE_EQS: (113), (129) imply:
% 177.04/27.64  | |   (130)  all_14_1 = e1
% 177.04/27.64  | | 
% 177.04/27.64  | | REF_CLOSE: (69), (94), (103), (117), (130) are inconsistent by sub-proof
% 177.04/27.64  | |            #315.
% 177.04/27.64  | | 
% 177.04/27.64  | Case 2:
% 177.04/27.64  | | 
% 177.04/27.64  | |   (131)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.04/27.64  | | 
% 177.04/27.64  | | ALPHA: (131) implies:
% 177.04/27.64  | |   (132)  all_52_30 = e0
% 177.04/27.64  | |   (133)  all_52_28 = e1
% 177.04/27.64  | |   (134)  all_52_26 = e2
% 177.04/27.64  | |   (135)  all_52_24 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | COMBINE_EQS: (116), (132) imply:
% 177.04/27.64  | |   (136)  all_6_1 = e0
% 177.04/27.64  | | 
% 177.04/27.64  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.04/27.64  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.04/27.64  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.04/27.64  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.04/27.64  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.04/27.64  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.04/27.64  | |            (68), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.04/27.64  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 177.04/27.64  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.04/27.64  | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 177.04/27.64  | |            (110), (111), (112), (114), (115), (118), (120), (121), (122),
% 177.04/27.64  | |            (123), (124), (125), (126), (127), (133), (134), (135), (136) are
% 177.04/27.64  | |            inconsistent by sub-proof #635.
% 177.04/27.64  | | 
% 177.04/27.64  | End of split
% 177.04/27.64  | 
% 177.04/27.64  End of proof
% 177.04/27.64  
% 177.04/27.64  Sub-proof #310 shows that the following formulas are inconsistent:
% 177.04/27.64  ----------------------------------------------------------------
% 177.04/27.64    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.64    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.64    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.04/27.64    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.64    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.64    (6)   ~ (all_52_27 = all_10_2)
% 177.04/27.64    (7)  op(e2, e2) = all_10_2
% 177.04/27.64    (8)   ~ (all_52_17 = all_52_23)
% 177.04/27.64    (9)  op(e2, all_52_3) = e2
% 177.04/27.64    (10)  op(e2, all_10_2) = all_10_1
% 177.04/27.64    (11)   ~ (all_52_13 = all_52_29)
% 177.04/27.64    (12)  all_56_3 = all_52_7
% 177.04/27.64    (13)  op(e3, e2) = all_52_3
% 177.04/27.64    (14)   ~ (all_52_9 = all_52_25)
% 177.04/27.64    (15)   ~ (all_52_19 = all_52_23)
% 177.04/27.64    (16)  all_56_11 = all_52_23
% 177.04/27.64    (17)  op(e1, e2) = all_52_19
% 177.04/27.64    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.04/27.64    (19)   ~ (all_52_3 = all_10_2)
% 177.04/27.64    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.64    (21)  all_58_5 = all_52_13
% 177.04/27.64    (22)   ~ (all_6_2 = e0)
% 177.04/27.64    (23)   ~ (all_52_25 = all_52_29)
% 177.04/27.64    (24)  all_56_15 = all_6_2
% 177.04/27.64    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.64    (26)  op(e2, e0) = all_52_15
% 177.04/27.64    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.64    (28)  all_58_3 = all_10_2
% 177.04/27.64    (29)  all_56_9 = all_52_19
% 177.04/27.64    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.64    (31)  all_58_15 = all_6_2
% 177.04/27.64    (32)   ~ (all_52_9 = all_4_2)
% 177.04/27.64    (33)   ~ (all_52_5 = all_52_7)
% 177.04/27.64    (34)  all_58_10 = all_52_15
% 177.04/27.64    (35)   ~ (all_52_5 = all_4_2)
% 177.04/27.64    (36)  all_58_7 = all_52_19
% 177.04/27.64    (37)  all_56_4 = all_52_9
% 177.04/27.64    (38)   ~ (all_52_15 = all_6_2)
% 177.04/27.64    (39)   ~ (all_52_17 = all_52_25)
% 177.04/27.64    (40)  op(e0, e1) = all_52_29
% 177.04/27.64    (41)   ~ (all_4_0 = e2)
% 177.04/27.64    (42)  all_58_4 = all_52_5
% 177.04/27.64    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.64    (44)   ~ (all_52_27 = all_52_29)
% 177.04/27.64    (45)   ~ (all_52_17 = all_14_2)
% 177.04/27.64    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.64    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.64    (48)   ~ (all_52_7 = all_4_2)
% 177.04/27.64    (49)  all_58_1 = all_52_3
% 177.04/27.64    (50)   ~ (all_52_13 = all_52_15)
% 177.04/27.64    (51)  all_58_0 = all_4_2
% 177.04/27.64    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.64    (53)  op(e0, e0) = all_6_2
% 177.04/27.64    (54)  op(e1, all_52_29) = all_52_28
% 177.04/27.64    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.64    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.64    (57)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.04/27.64    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.64    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.64    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.04/27.64    (61)  all_58_14 = all_52_29
% 177.04/27.64    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.64    (63)   ~ (all_52_3 = all_52_5)
% 177.04/27.64    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.64    (65)  op(e2, e1) = all_52_13
% 177.04/27.64    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.64    (67)  all_58_8 = all_14_2
% 177.04/27.64    (68)  all_56_1 = all_52_3
% 177.04/27.64    (69)  op(e0, e2) = all_52_27
% 177.04/27.64    (70)  all_56_14 = all_52_29
% 177.04/27.64    (71)   ~ (all_10_1 = e1)
% 177.04/27.64    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.64    (73)   ~ (all_52_5 = all_14_2)
% 177.04/27.64    (74)   ~ (all_52_3 = all_52_27)
% 177.04/27.64    (75)   ~ (all_52_3 = all_4_2)
% 177.04/27.64    (76)  op(all_6_1, all_6_2) = all_6_0
% 177.04/27.64    (77)  op(e3, all_4_2) = e3
% 177.04/27.64    (78)  op(e0, e3) = all_52_25
% 177.04/27.64    (79)  op(e0, all_6_2) = all_6_1
% 177.04/27.64    (80)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.04/27.64    (81)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.04/27.64    (82)   ~ (all_52_13 = all_14_2)
% 177.04/27.64    (83)   ~ (e3 = e0)
% 177.04/27.64    (84)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.64    (85)  op(all_14_1, all_14_2) = e2
% 177.04/27.64    (86)   ~ (all_52_9 = all_52_13)
% 177.04/27.64    (87)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.64    (88)  op(e0, all_52_23) = all_52_22
% 177.04/27.64    (89)   ~ (all_52_15 = all_52_23)
% 177.04/27.64    (90)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.64    (91)   ~ (all_52_5 = all_52_29)
% 177.04/27.64    (92)  all_56_2 = all_52_5
% 177.04/27.64    (93)  op(e1, e0) = all_52_23
% 177.04/27.64    (94)  all_56_12 = all_52_25
% 177.04/27.64    (95)  all_58_13 = all_52_27
% 177.04/27.64    (96)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.64    (97)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.04/27.64    (98)   ~ (all_52_9 = all_52_17)
% 177.04/27.64    (99)  all_58_6 = all_52_17
% 177.04/27.64    (100)   ~ (all_52_3 = all_52_7)
% 177.04/27.64    (101)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.64    (102)   ~ (e1 = e0)
% 177.04/27.64    (103)  all_56_0 = all_4_2
% 177.04/27.64    (104)  all_58_11 = all_52_23
% 177.04/27.64    (105)   ~ (all_52_3 = all_52_19)
% 177.04/27.64    (106)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.04/27.64    (107)   ~ (all_52_7 = all_52_15)
% 177.04/27.64    (108)  op(e0, all_52_15) = all_52_14
% 177.04/27.64    (109)   ~ (all_52_29 = all_14_2)
% 177.04/27.64    (110)   ~ (all_4_0 = e1)
% 177.04/27.64    (111)   ~ (all_52_19 = all_10_2)
% 177.04/27.64    (112)   ~ (all_52_23 = all_6_2)
% 177.04/27.64    (113)   ~ (all_52_29 = all_6_2)
% 177.04/27.64    (114)  all_58_2 = all_52_9
% 177.04/27.64    (115)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.04/27.64    (116)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.64    (117)  op(e3, e1) = all_52_5
% 177.04/27.64    (118)   ~ (e2 = e1)
% 177.04/27.64    (119)  all_56_10 = all_14_2
% 177.04/27.64    (120)   ~ (all_52_25 = all_6_2)
% 177.04/27.64    (121)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.64    (122)  op(e1, e1) = all_14_2
% 177.04/27.64    (123)  op(e1, e3) = all_52_17
% 177.04/27.64    (124)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.64    (125)   ~ (all_52_25 = all_4_2)
% 177.04/27.64    (126)  op(e3, e0) = all_52_7
% 177.04/27.64    (127)  all_56_8 = all_52_17
% 177.04/27.64    (128)   ~ (all_52_17 = all_4_2)
% 177.04/27.64    (129)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.64             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.64    (130)   ~ (all_52_25 = all_52_27)
% 177.04/27.64    (131)   ~ (all_52_27 = all_6_2)
% 177.04/27.64    (132)   ~ (all_52_7 = all_6_2)
% 177.04/27.64    (133)   ~ (all_52_19 = all_52_27)
% 177.04/27.64    (134)  all_56_7 = all_52_15
% 177.04/27.64    (135)  op(e1, all_52_5) = e1
% 177.04/27.64    (136)   ~ (all_52_7 = all_52_23)
% 177.04/27.64    (137)   ~ (all_52_13 = all_10_2)
% 177.04/27.64    (138)   ~ (all_6_0 = e1)
% 177.04/27.64    (139)  op(e3, all_4_2) = all_4_0
% 177.04/27.64    (140)  op(e0, all_52_7) = e0
% 177.04/27.64    (141)  op(e2, all_52_27) = all_52_26
% 177.04/27.64    (142)   ~ (all_52_17 = all_52_19)
% 177.04/27.64    (143)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.64    (144)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.64    (145)  op(e1, all_14_2) = all_14_1
% 177.04/27.64    (146)  all_58_9 = all_52_7
% 177.04/27.64    (147)  all_58_12 = all_52_25
% 177.04/27.64    (148)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.64    (149)   ~ (all_52_9 = all_52_15)
% 177.04/27.64    (150)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.64    (151)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.64    (152)   ~ (all_52_19 = all_14_2)
% 177.04/27.64    (153)  op(e2, e3) = all_52_9
% 177.04/27.64    (154)  all_56_13 = all_52_27
% 177.04/27.64  
% 177.04/27.64  Begin of proof
% 177.04/27.64  | 
% 177.04/27.64  | GROUND_INST: instantiating (129) with e3, all_4_0, all_4_2, e3, simplifying
% 177.04/27.64  |              with (77), (139) gives:
% 177.04/27.64  |   (155)  all_4_0 = e3
% 177.04/27.64  | 
% 177.04/27.64  | REDUCE: (41), (155) imply:
% 177.04/27.64  |   (156)   ~ (e3 = e2)
% 177.04/27.64  | 
% 177.04/27.64  | REDUCE: (110), (155) imply:
% 177.04/27.64  |   (157)   ~ (e3 = e1)
% 177.04/27.64  | 
% 177.04/27.64  | BETA: splitting (46) gives:
% 177.04/27.64  | 
% 177.04/27.64  | Case 1:
% 177.04/27.64  | | 
% 177.04/27.64  | |   (158)  all_56_15 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | COMBINE_EQS: (24), (158) imply:
% 177.04/27.64  | |   (159)  all_6_2 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | SIMP: (159) implies:
% 177.04/27.64  | |   (160)  all_6_2 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | COMBINE_EQS: (31), (160) imply:
% 177.04/27.64  | |   (161)  all_58_15 = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (132), (160) imply:
% 177.04/27.64  | |   (162)   ~ (all_52_7 = e3)
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (38), (160) imply:
% 177.04/27.64  | |   (163)   ~ (all_52_15 = e3)
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (112), (160) imply:
% 177.04/27.64  | |   (164)   ~ (all_52_23 = e3)
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (131), (160) imply:
% 177.04/27.64  | |   (165)   ~ (all_52_27 = e3)
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (113), (160) imply:
% 177.04/27.64  | |   (166)   ~ (all_52_29 = e3)
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (76), (160) imply:
% 177.04/27.64  | |   (167)  op(all_6_1, e3) = all_6_0
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (79), (160) imply:
% 177.04/27.64  | |   (168)  op(e0, e3) = all_6_1
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (53), (160) imply:
% 177.04/27.64  | |   (169)  op(e0, e0) = e3
% 177.04/27.64  | | 
% 177.04/27.64  | | GROUND_INST: instantiating (129) with all_52_25, all_6_1, e3, e0,
% 177.04/27.64  | |              simplifying with (78), (168) gives:
% 177.04/27.64  | |   (170)  all_52_25 = all_6_1
% 177.04/27.64  | | 
% 177.04/27.64  | | COMBINE_EQS: (147), (170) imply:
% 177.04/27.64  | |   (171)  all_58_12 = all_6_1
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (39), (170) imply:
% 177.04/27.64  | |   (172)   ~ (all_52_17 = all_6_1)
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (130), (170) imply:
% 177.04/27.64  | |   (173)   ~ (all_52_27 = all_6_1)
% 177.04/27.64  | | 
% 177.04/27.64  | | SIMP: (173) implies:
% 177.04/27.64  | |   (174)   ~ (all_52_27 = all_6_1)
% 177.04/27.64  | | 
% 177.04/27.64  | | REDUCE: (23), (170) imply:
% 177.04/27.64  | |   (175)   ~ (all_52_29 = all_6_1)
% 177.04/27.64  | | 
% 177.04/27.64  | | SIMP: (175) implies:
% 177.04/27.64  | |   (176)   ~ (all_52_29 = all_6_1)
% 177.04/27.64  | | 
% 177.04/27.64  | | BETA: splitting (62) gives:
% 177.04/27.64  | | 
% 177.04/27.64  | | Case 1:
% 177.04/27.64  | | | 
% 177.04/27.64  | | |   (177)  all_56_13 = e3
% 177.04/27.64  | | | 
% 177.04/27.64  | | | REF_CLOSE: (154), (165), (177) are inconsistent by sub-proof #876.
% 177.04/27.64  | | | 
% 177.04/27.64  | | Case 2:
% 177.04/27.64  | | | 
% 177.04/27.64  | | |   (178)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.64  | | | 
% 177.04/27.64  | | | BETA: splitting (144) gives:
% 177.04/27.64  | | | 
% 177.04/27.64  | | | Case 1:
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | |   (179)  all_56_3 = e3
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | | REF_CLOSE: (12), (162), (179) are inconsistent by sub-proof #1034.
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | Case 2:
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | |   (180)   ~ (all_56_3 = e3)
% 177.04/27.64  | | | |   (181)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | | BETA: splitting (57) gives:
% 177.04/27.64  | | | | 
% 177.04/27.64  | | | | Case 1:
% 177.04/27.64  | | | | | 
% 177.04/27.64  | | | | |   (182)  all_56_14 = e3
% 177.04/27.64  | | | | | 
% 177.04/27.64  | | | | | REF_CLOSE: (70), (166), (182) are inconsistent by sub-proof #896.
% 177.04/27.64  | | | | | 
% 177.04/27.64  | | | | Case 2:
% 177.04/27.64  | | | | | 
% 177.04/27.64  | | | | |   (183)   ~ (all_56_14 = e3)
% 177.04/27.65  | | | | |   (184)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.04/27.65  | | | | | 
% 177.04/27.65  | | | | | BETA: splitting (56) gives:
% 177.04/27.65  | | | | | 
% 177.04/27.65  | | | | | Case 1:
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | |   (185)  all_56_9 = e3
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | | REF_CLOSE: (1), (2), (9), (12), (13), (17), (21), (27), (29), (30),
% 177.04/27.65  | | | | | |            (31), (32), (33), (34), (35), (36), (40), (42), (43),
% 177.04/27.65  | | | | | |            (45), (48), (49), (51), (55), (61), (63), (65), (67),
% 177.04/27.65  | | | | | |            (68), (69), (73), (74), (77), (78), (80), (82), (84),
% 177.04/27.65  | | | | | |            (90), (91), (92), (96), (99), (100), (103), (104), (105),
% 177.04/27.65  | | | | | |            (107), (109), (117), (119), (122), (123), (125), (126),
% 177.04/27.65  | | | | | |            (128), (129), (132), (135), (136), (140), (143), (146),
% 177.04/27.65  | | | | | |            (148), (150), (151), (152), (153), (162), (166), (169),
% 177.04/27.65  | | | | | |            (181), (185) are inconsistent by sub-proof #521.
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | Case 2:
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | |   (186)   ~ (all_56_9 = e3)
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | | REDUCE: (29), (186) imply:
% 177.04/27.65  | | | | | |   (187)   ~ (all_52_19 = e3)
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | | BETA: splitting (43) gives:
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | | Case 1:
% 177.04/27.65  | | | | | | | 
% 177.04/27.65  | | | | | | |   (188)  all_58_6 = e3
% 177.04/27.65  | | | | | | | 
% 177.04/27.65  | | | | | | | REF_CLOSE: (1), (2), (9), (13), (21), (30), (31), (32), (33),
% 177.04/27.65  | | | | | | |            (34), (35), (36), (42), (43), (45), (48), (49), (51),
% 177.04/27.65  | | | | | | |            (61), (63), (67), (73), (77), (78), (82), (84), (90),
% 177.04/27.65  | | | | | | |            (91), (96), (99), (100), (103), (104), (105), (107),
% 177.04/27.65  | | | | | | |            (109), (117), (119), (123), (125), (126), (128), (129),
% 177.04/27.65  | | | | | | |            (132), (135), (136), (140), (143), (146), (148), (150),
% 177.04/27.65  | | | | | | |            (153), (166), (188) are inconsistent by sub-proof #850.
% 177.04/27.65  | | | | | | | 
% 177.04/27.65  | | | | | | Case 2:
% 177.04/27.65  | | | | | | | 
% 177.04/27.65  | | | | | | |   (189)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.65  | | | | | | | 
% 177.04/27.65  | | | | | | | BETA: splitting (189) gives:
% 177.04/27.65  | | | | | | | 
% 177.04/27.65  | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | |   (190)  all_58_7 = e3
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | | COMBINE_EQS: (36), (190) imply:
% 177.04/27.65  | | | | | | | |   (191)  all_52_19 = e3
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | | REDUCE: (187), (191) imply:
% 177.04/27.65  | | | | | | | |   (192)  $false
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | | CLOSE: (192) is inconsistent.
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | |   (193)  all_58_8 = e3 | all_58_11 = e3
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | | BETA: splitting (193) gives:
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | |   (194)  all_58_8 = e3
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | COMBINE_EQS: (67), (194) imply:
% 177.04/27.65  | | | | | | | | |   (195)  all_14_2 = e3
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | SIMP: (195) implies:
% 177.04/27.65  | | | | | | | | |   (196)  all_14_2 = e3
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (73), (196) imply:
% 177.04/27.65  | | | | | | | | |   (197)   ~ (all_52_5 = e3)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (82), (196) imply:
% 177.04/27.65  | | | | | | | | |   (198)   ~ (all_52_13 = e3)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (45), (196) imply:
% 177.04/27.65  | | | | | | | | |   (199)   ~ (all_52_17 = e3)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (85), (196) imply:
% 177.04/27.65  | | | | | | | | |   (200)  op(all_14_1, e3) = e2
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (145), (196) imply:
% 177.04/27.65  | | | | | | | | |   (201)  op(e1, e3) = all_14_1
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | GROUND_INST: instantiating (129) with all_52_17, all_14_1, e3,
% 177.04/27.65  | | | | | | | | |              e1, simplifying with (123), (201) gives:
% 177.04/27.65  | | | | | | | | |   (202)  all_52_17 = all_14_1
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | COMBINE_EQS: (127), (202) imply:
% 177.04/27.65  | | | | | | | | |   (203)  all_56_8 = all_14_1
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | COMBINE_EQS: (99), (202) imply:
% 177.04/27.65  | | | | | | | | |   (204)  all_58_6 = all_14_1
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (98), (202) imply:
% 177.04/27.65  | | | | | | | | |   (205)   ~ (all_52_9 = all_14_1)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (142), (202) imply:
% 177.04/27.65  | | | | | | | | |   (206)   ~ (all_52_19 = all_14_1)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | SIMP: (206) implies:
% 177.04/27.65  | | | | | | | | |   (207)   ~ (all_52_19 = all_14_1)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (8), (202) imply:
% 177.04/27.65  | | | | | | | | |   (208)   ~ (all_52_23 = all_14_1)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | SIMP: (208) implies:
% 177.04/27.65  | | | | | | | | |   (209)   ~ (all_52_23 = all_14_1)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (172), (202) imply:
% 177.04/27.65  | | | | | | | | |   (210)   ~ (all_14_1 = all_6_1)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REDUCE: (199), (202) imply:
% 177.04/27.65  | | | | | | | | |   (211)   ~ (all_14_1 = e3)
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | BETA: splitting (3) gives:
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | |   (212)  all_56_8 = e3
% 177.04/27.65  | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | REF_CLOSE: (203), (211), (212) are inconsistent by sub-proof
% 177.04/27.65  | | | | | | | | | |            #849.
% 177.04/27.65  | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | |   (213)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.04/27.65  | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | BETA: splitting (47) gives:
% 177.04/27.65  | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | |   (214)  all_58_2 = e3
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | COMBINE_EQS: (114), (214) imply:
% 177.04/27.65  | | | | | | | | | | |   (215)  all_52_9 = e3
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | REF_CLOSE: (9), (13), (30), (31), (32), (33), (34), (42),
% 177.04/27.65  | | | | | | | | | | |            (48), (49), (51), (59), (77), (78), (96), (100),
% 177.04/27.65  | | | | | | | | | | |            (103), (104), (107), (117), (125), (129), (132),
% 177.04/27.65  | | | | | | | | | | |            (136), (140), (143), (146), (148), (153), (156),
% 177.04/27.65  | | | | | | | | | | |            (197), (215) are inconsistent by sub-proof #312.
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | |   (216)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | BETA: splitting (216) gives:
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | |   (217)  all_58_3 = e3
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | COMBINE_EQS: (28), (217) imply:
% 177.04/27.65  | | | | | | | | | | | |   (218)  all_10_2 = e3
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | REDUCE: (10), (218) imply:
% 177.04/27.65  | | | | | | | | | | | |   (219)  op(e2, e3) = all_10_1
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | BETA: splitting (148) gives:
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | |   (220)  all_58_0 = e3
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | COMBINE_EQS: (51), (220) imply:
% 177.04/27.65  | | | | | | | | | | | | |   (221)  all_4_2 = e3
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | REDUCE: (75), (221) imply:
% 177.04/27.65  | | | | | | | | | | | | |   (222)   ~ (all_52_3 = e3)
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | REDUCE: (32), (221) imply:
% 177.04/27.65  | | | | | | | | | | | | |   (223)   ~ (all_52_9 = e3)
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | GROUND_INST: instantiating (129) with all_52_9, all_10_1, e3,
% 177.04/27.65  | | | | | | | | | | | | |              e2, simplifying with (153), (219) gives:
% 177.04/27.65  | | | | | | | | | | | | |   (224)  all_52_9 = all_10_1
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | COMBINE_EQS: (37), (224) imply:
% 177.04/27.65  | | | | | | | | | | | | |   (225)  all_56_4 = all_10_1
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | REDUCE: (205), (224) imply:
% 177.04/27.65  | | | | | | | | | | | | |   (226)   ~ (all_14_1 = all_10_1)
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | SIMP: (226) implies:
% 177.04/27.65  | | | | | | | | | | | | |   (227)   ~ (all_14_1 = all_10_1)
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | REDUCE: (223), (224) imply:
% 177.04/27.65  | | | | | | | | | | | | |   (228)   ~ (all_10_1 = e3)
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | BETA: splitting (101) gives:
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | |   (229)  all_56_4 = e3
% 177.04/27.65  | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | REF_CLOSE: (225), (228), (229) are inconsistent by sub-proof
% 177.04/27.65  | | | | | | | | | | | | | |            #311.
% 177.04/27.65  | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | |   (230)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.65  | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 177.04/27.65  | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | |   (231)  all_56_8 = e2
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | COMBINE_EQS: (203), (231) imply:
% 177.04/27.65  | | | | | | | | | | | | | | |   (232)  all_14_1 = e2
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | REDUCE: (227), (232) imply:
% 177.04/27.65  | | | | | | | | | | | | | | |   (233)   ~ (all_10_1 = e2)
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | SIMP: (233) implies:
% 177.04/27.65  | | | | | | | | | | | | | | |   (234)   ~ (all_10_1 = e2)
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | REDUCE: (200), (232) imply:
% 177.04/27.65  | | | | | | | | | | | | | | |   (235)  op(e2, e3) = e2
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | |   (236)  all_56_4 = e2
% 177.04/27.65  | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | REF_CLOSE: (225), (234), (236) are inconsistent by sub-proof
% 177.04/27.65  | | | | | | | | | | | | | | | |            #544.
% 177.04/27.65  | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | |   (237)   ~ (all_56_4 = e2)
% 177.04/27.65  | | | | | | | | | | | | | | | |   (238)  all_56_4 = e1 | all_56_4 = e0
% 177.04/27.65  | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 177.04/27.65  | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | Case 1:
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (239)  all_56_4 = e1
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (225), (239) are inconsistent by sub-proof
% 177.04/27.65  | | | | | | | | | | | | | | | | |            #543.
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (240)  all_56_4 = e0
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | COMBINE_EQS: (225), (240) imply:
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (241)  all_10_1 = e0
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | SIMP: (241) implies:
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (242)  all_10_1 = e0
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | REDUCE: (234), (242) imply:
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (243)   ~ (e2 = e0)
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | SIMP: (243) implies:
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (244)   ~ (e2 = e0)
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | REDUCE: (219), (242) imply:
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (245)  op(e2, e3) = e0
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (129) with e0, e2, e3, e2,
% 177.04/27.65  | | | | | | | | | | | | | | | | |              simplifying with (235), (245) gives:
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (246)  e2 = e0
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | REDUCE: (244), (246) imply:
% 177.04/27.65  | | | | | | | | | | | | | | | | |   (247)  $false
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 177.04/27.65  | | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | |   (248)   ~ (all_56_8 = e2)
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | REDUCE: (203), (248) imply:
% 177.04/27.65  | | | | | | | | | | | | | | |   (249)   ~ (all_14_1 = e2)
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (10), (12), (15), (17),
% 177.04/27.65  | | | | | | | | | | | | | | |            (18), (19), (20), (25), (26), (27), (28), (33),
% 177.04/27.65  | | | | | | | | | | | | | | |            (36), (40), (42), (44), (49), (55), (59), (60),
% 177.04/27.65  | | | | | | | | | | | | | | |            (61), (63), (65), (68), (69), (70), (72), (74),
% 177.04/27.65  | | | | | | | | | | | | | | |            (83), (86), (91), (93), (95), (96), (97), (100),
% 177.04/27.65  | | | | | | | | | | | | | | |            (104), (105), (106), (114), (115), (118), (121),
% 177.04/27.65  | | | | | | | | | | | | | | |            (129), (133), (135), (136), (138), (140), (146),
% 177.04/27.65  | | | | | | | | | | | | | | |            (149), (153), (154), (156), (157), (161), (162),
% 177.04/27.65  | | | | | | | | | | | | | | |            (164), (165), (166), (167), (171), (174), (176),
% 177.04/27.65  | | | | | | | | | | | | | | |            (178), (181), (184), (187), (194), (203), (204),
% 177.04/27.65  | | | | | | | | | | | | | | |            (207), (209), (210), (213), (220), (222), (249)
% 177.04/27.65  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #830.
% 177.04/27.65  | | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | |   (250)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | | REF_CLOSE: (9), (13), (30), (31), (32), (33), (34), (42),
% 177.04/27.65  | | | | | | | | | | | | |            (48), (49), (51), (63), (75), (77), (78), (96),
% 177.04/27.65  | | | | | | | | | | | | |            (100), (103), (104), (107), (117), (125), (126),
% 177.04/27.65  | | | | | | | | | | | | |            (129), (132), (136), (140), (143), (146), (153),
% 177.04/27.65  | | | | | | | | | | | | |            (197), (250) are inconsistent by sub-proof #787.
% 177.04/27.65  | | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | |   (251)  all_58_5 = e3 | all_58_10 = e3
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | | REF_CLOSE: (21), (34), (163), (198), (251) are inconsistent
% 177.04/27.65  | | | | | | | | | | | |            by sub-proof #958.
% 177.04/27.65  | | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | Case 2:
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | |   (252)  all_58_11 = e3
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | | REF_CLOSE: (104), (164), (252) are inconsistent by sub-proof
% 177.04/27.65  | | | | | | | | |            #1017.
% 177.04/27.65  | | | | | | | | | 
% 177.04/27.65  | | | | | | | | End of split
% 177.04/27.65  | | | | | | | | 
% 177.04/27.65  | | | | | | | End of split
% 177.04/27.65  | | | | | | | 
% 177.04/27.65  | | | | | | End of split
% 177.04/27.65  | | | | | | 
% 177.04/27.65  | | | | | End of split
% 177.04/27.65  | | | | | 
% 177.04/27.65  | | | | End of split
% 177.04/27.65  | | | | 
% 177.04/27.65  | | | End of split
% 177.04/27.65  | | | 
% 177.04/27.65  | | End of split
% 177.04/27.65  | | 
% 177.04/27.65  | Case 2:
% 177.04/27.65  | | 
% 177.04/27.65  | |   (253)   ~ (all_56_15 = e3)
% 177.04/27.65  | |   (254)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.65  | | 
% 177.04/27.65  | | REF_CLOSE: (1), (2), (8), (9), (11), (13), (14), (15), (16), (17), (18),
% 177.04/27.65  | |            (19), (21), (22), (23), (24), (25), (26), (27), (28), (30), (31),
% 177.04/27.65  | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (42), (43),
% 177.04/27.65  | |            (44), (47), (48), (49), (50), (51), (52), (54), (55), (57), (58),
% 177.04/27.65  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (70),
% 177.04/27.65  | |            (73), (74), (75), (77), (78), (81), (82), (83), (84), (86), (87),
% 177.04/27.65  | |            (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 177.04/27.65  | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 177.04/27.65  | |            (108), (109), (112), (113), (114), (116), (117), (119), (120),
% 177.04/27.65  | |            (122), (123), (124), (125), (126), (128), (129), (130), (131),
% 177.04/27.65  | |            (132), (133), (134), (135), (136), (137), (140), (141), (142),
% 177.04/27.65  | |            (143), (146), (147), (148), (149), (150), (151), (152), (153),
% 177.04/27.65  | |            (154), (156), (157), (253), (254) are inconsistent by sub-proof
% 177.04/27.65  | |            #785.
% 177.04/27.65  | | 
% 177.04/27.65  | End of split
% 177.04/27.65  | 
% 177.04/27.65  End of proof
% 177.04/27.65  
% 177.04/27.65  Sub-proof #311 shows that the following formulas are inconsistent:
% 177.04/27.65  ----------------------------------------------------------------
% 177.04/27.65    (1)  all_56_4 = all_10_1
% 177.04/27.65    (2)  all_56_4 = e3
% 177.04/27.65    (3)   ~ (all_10_1 = e3)
% 177.04/27.65  
% 177.04/27.65  Begin of proof
% 177.04/27.65  | 
% 177.04/27.65  | COMBINE_EQS: (1), (2) imply:
% 177.04/27.65  |   (4)  all_10_1 = e3
% 177.04/27.65  | 
% 177.04/27.65  | SIMP: (4) implies:
% 177.04/27.65  |   (5)  all_10_1 = e3
% 177.04/27.65  | 
% 177.04/27.65  | REDUCE: (3), (5) imply:
% 177.04/27.65  |   (6)  $false
% 177.04/27.65  | 
% 177.04/27.65  | CLOSE: (6) is inconsistent.
% 177.04/27.65  | 
% 177.04/27.65  End of proof
% 177.04/27.65  
% 177.04/27.65  Sub-proof #312 shows that the following formulas are inconsistent:
% 177.04/27.65  ----------------------------------------------------------------
% 177.04/27.65    (1)  op(e2, all_52_3) = e2
% 177.04/27.65    (2)  op(e3, e2) = all_52_3
% 177.04/27.65    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.65    (4)  all_58_15 = all_6_2
% 177.04/27.65    (5)   ~ (all_52_9 = all_4_2)
% 177.04/27.65    (6)   ~ (all_52_5 = all_52_7)
% 177.04/27.65    (7)  all_58_10 = all_52_15
% 177.04/27.65    (8)  all_58_4 = all_52_5
% 177.04/27.65    (9)   ~ (all_52_7 = all_4_2)
% 177.04/27.65    (10)  all_58_1 = all_52_3
% 177.04/27.65    (11)  all_58_0 = all_4_2
% 177.04/27.65    (12)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.65    (13)  op(e3, all_4_2) = e3
% 177.04/27.65    (14)  op(e0, e3) = all_52_25
% 177.04/27.65    (15)   ~ (all_52_5 = e3)
% 177.04/27.65    (16)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.65    (17)   ~ (all_52_3 = all_52_7)
% 177.04/27.65    (18)  all_56_0 = all_4_2
% 177.04/27.65    (19)  all_58_11 = all_52_23
% 177.04/27.65    (20)   ~ (all_52_7 = all_52_15)
% 177.04/27.65    (21)  all_52_9 = e3
% 177.04/27.65    (22)  op(e3, e1) = all_52_5
% 177.04/27.65    (23)   ~ (all_52_25 = all_4_2)
% 177.04/27.65    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.65    (25)   ~ (all_52_7 = all_6_2)
% 177.04/27.65    (26)   ~ (all_52_7 = all_52_23)
% 177.04/27.65    (27)  op(e0, all_52_7) = e0
% 177.04/27.65    (28)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.65    (29)  all_58_9 = all_52_7
% 177.04/27.65    (30)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.65    (31)   ~ (e3 = e2)
% 177.04/27.65    (32)  op(e2, e3) = all_52_9
% 177.04/27.65  
% 177.04/27.65  Begin of proof
% 177.04/27.65  | 
% 177.04/27.65  | REDUCE: (5), (21) imply:
% 177.04/27.65  |   (33)   ~ (all_4_2 = e3)
% 177.04/27.65  | 
% 177.04/27.65  | SIMP: (33) implies:
% 177.04/27.65  |   (34)   ~ (all_4_2 = e3)
% 177.04/27.65  | 
% 177.04/27.65  | REDUCE: (21), (32) imply:
% 177.04/27.65  |   (35)  op(e2, e3) = e3
% 177.04/27.65  | 
% 177.04/27.65  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 177.04/27.65  |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 177.04/27.65  |            (26), (27), (28), (29), (30), (31), (34), (35) are inconsistent by
% 177.04/27.65  |            sub-proof #796.
% 177.04/27.65  | 
% 177.04/27.65  End of proof
% 177.04/27.65  
% 177.04/27.65  Sub-proof #313 shows that the following formulas are inconsistent:
% 177.04/27.65  ----------------------------------------------------------------
% 177.04/27.65    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.65    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.65    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.04/27.65    (4)   ~ (all_52_27 = all_10_2)
% 177.04/27.65    (5)   ~ (all_52_17 = all_52_23)
% 177.04/27.65    (6)   ~ (all_6_0 = e3)
% 177.04/27.65    (7)  op(e2, all_10_2) = all_10_1
% 177.04/27.65    (8)   ~ (all_52_13 = all_52_29)
% 177.04/27.65    (9)  all_56_3 = all_52_7
% 177.04/27.65    (10)  op(e3, e2) = all_52_3
% 177.04/27.65    (11)   ~ (all_52_9 = all_52_25)
% 177.04/27.65    (12)  op(e3, all_52_25) = all_52_24
% 177.04/27.65    (13)   ~ (all_52_19 = all_52_23)
% 177.04/27.65    (14)  op(e1, e2) = all_52_19
% 177.04/27.65    (15)   ~ (all_52_27 = e0)
% 177.04/27.65    (16)  op(e3, all_52_9) = all_52_8
% 177.04/27.65    (17)   ~ (all_52_23 = e0)
% 177.04/27.65    (18)   ~ (all_52_3 = all_10_2)
% 177.04/27.65    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.65    (20)  all_58_5 = all_52_13
% 177.04/27.65    (21)   ~ (all_52_25 = all_52_29)
% 177.04/27.65    (22)  op(e0, e0) = all_6_1
% 177.04/27.65    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.65    (24)  all_58_3 = all_10_2
% 177.04/27.65    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.65    (26)  all_58_15 = all_6_2
% 177.04/27.65    (27)   ~ (all_52_9 = all_4_2)
% 177.04/27.65    (28)   ~ (all_52_5 = all_52_7)
% 177.04/27.65    (29)  all_58_10 = all_52_15
% 177.04/27.65    (30)   ~ (all_52_5 = all_4_2)
% 177.04/27.65    (31)  all_58_7 = all_52_19
% 177.04/27.65    (32)   ~ (all_52_17 = all_52_25)
% 177.04/27.65    (33)  op(e0, e1) = all_52_29
% 177.04/27.65    (34)   ~ (all_4_0 = e2)
% 177.04/27.65    (35)  all_58_4 = all_52_5
% 177.04/27.65    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.65    (37)   ~ (e3 = e1)
% 177.04/27.65    (38)   ~ (all_52_27 = all_52_29)
% 177.04/27.65    (39)   ~ (all_52_17 = all_14_2)
% 177.04/27.65    (40)  op(e3, all_4_2) = all_4_1
% 177.04/27.65    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.65    (42)   ~ (all_52_7 = all_4_2)
% 177.04/27.65    (43)  all_58_1 = all_52_3
% 177.04/27.65    (44)  all_58_0 = all_4_2
% 177.04/27.65    (45)  op(e1, all_52_13) = all_52_12
% 177.04/27.65    (46)  op(e1, all_52_29) = all_52_28
% 177.04/27.65    (47)   ~ (all_52_7 = e0)
% 177.04/27.65    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.65    (49)   ~ (all_4_1 = e2)
% 177.04/27.65    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.04/27.65    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.65    (52)  all_58_14 = all_52_29
% 177.04/27.65    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.65    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.65    (55)  op(e2, e1) = all_52_13
% 177.04/27.65    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.65    (57)  all_58_8 = all_14_2
% 177.04/27.65    (58)  all_56_1 = all_52_3
% 177.04/27.65    (59)  op(e0, e2) = all_52_27
% 177.04/27.65    (60)  all_56_14 = all_52_29
% 177.04/27.65    (61)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.65    (62)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.65    (63)   ~ (all_52_3 = all_4_2)
% 177.04/27.65    (64)  op(e0, e3) = all_52_25
% 177.04/27.65    (65)  all_52_0 = all_4_1
% 177.04/27.65    (66)   ~ (all_52_9 = all_10_2)
% 177.04/27.65    (67)  op(e3, all_52_17) = all_52_16
% 177.04/27.65    (68)  all_52_10 = all_10_1
% 177.04/27.65    (69)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.04/27.65    (70)   ~ (all_52_13 = all_14_2)
% 177.04/27.65    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.65    (72)  op(all_14_1, all_14_2) = e2
% 177.04/27.65    (73)   ~ (all_52_9 = all_52_13)
% 177.04/27.65    (74)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.65    (75)   ~ (all_52_15 = all_52_23)
% 177.04/27.65    (76)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.65    (77)  op(all_10_1, all_10_2) = all_10_0
% 177.04/27.65    (78)   ~ (all_52_5 = all_52_29)
% 177.04/27.65    (79)  all_56_12 = all_52_25
% 177.04/27.65    (80)  all_58_13 = all_52_27
% 177.04/27.65    (81)   ~ (all_4_1 = e1)
% 177.04/27.65    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.65    (83)  all_56_5 = all_10_2
% 177.04/27.65    (84)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.04/27.65    (85)  op(e0, e0) = e0
% 177.04/27.65    (86)   ~ (all_52_25 = e0)
% 177.04/27.65    (87)   ~ (all_52_9 = all_52_17)
% 177.04/27.65    (88)  all_58_6 = all_52_17
% 177.04/27.65    (89)   ~ (all_52_3 = all_52_7)
% 177.04/27.65    (90)  all_56_0 = all_4_2
% 177.04/27.65    (91)  all_58_11 = all_52_23
% 177.04/27.65    (92)   ~ (all_52_3 = all_52_19)
% 177.04/27.65    (93)   ~ (all_52_7 = all_52_15)
% 177.04/27.65    (94)  op(e0, all_52_15) = all_52_14
% 177.04/27.65    (95)   ~ (all_52_29 = all_14_2)
% 177.04/27.65    (96)   ~ (all_4_0 = e1)
% 177.04/27.65    (97)   ~ (all_52_19 = all_10_2)
% 177.04/27.65    (98)  all_58_15 = e0
% 177.04/27.65    (99)   ~ (all_6_0 = e2)
% 177.04/27.65    (100)  all_58_2 = all_52_9
% 177.04/27.65    (101)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.04/27.65    (102)   ~ (all_52_29 = e0)
% 177.04/27.65    (103)  op(e3, e1) = all_52_5
% 177.04/27.65    (104)   ~ (e2 = e1)
% 177.04/27.65    (105)  all_56_10 = all_14_2
% 177.04/27.65    (106)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.65    (107)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.65    (108)  op(e1, e3) = all_52_17
% 177.04/27.65    (109)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.65    (110)   ~ (all_52_25 = all_4_2)
% 177.04/27.65    (111)  op(e3, e0) = all_52_7
% 177.04/27.65    (112)  op(e3, e3) = all_4_2
% 177.04/27.65    (113)  all_56_8 = all_52_17
% 177.04/27.65    (114)   ~ (all_52_17 = all_4_2)
% 177.04/27.65    (115)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.65             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.65    (116)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.65           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.04/27.65           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.65           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.65    (117)   ~ (all_52_25 = all_52_27)
% 177.04/27.65    (118)   ~ (all_52_7 = all_6_2)
% 177.04/27.65    (119)   ~ (all_10_0 = e3)
% 177.04/27.65    (120)   ~ (all_52_19 = all_52_27)
% 177.04/27.65    (121)  all_56_7 = all_52_15
% 177.04/27.65    (122)   ~ (all_52_15 = e0)
% 177.04/27.65    (123)  op(all_6_1, e0) = all_6_0
% 177.04/27.65    (124)   ~ (all_52_7 = all_52_23)
% 177.04/27.65    (125)   ~ (all_6_0 = e1)
% 177.04/27.65    (126)  op(e2, all_52_27) = all_52_26
% 177.04/27.65    (127)  all_52_20 = all_14_1
% 177.04/27.65    (128)   ~ (all_52_17 = all_52_19)
% 177.04/27.65    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.65    (130)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.65    (131)  op(e1, all_14_2) = all_14_1
% 177.04/27.65    (132)  all_58_9 = all_52_7
% 177.04/27.65    (133)  all_58_12 = all_52_25
% 177.04/27.65    (134)   ~ (all_10_0 = e1)
% 177.04/27.65    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.65    (136)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.65    (137)   ~ (all_52_19 = all_14_2)
% 177.04/27.65    (138)  op(e0, all_52_7) = all_52_6
% 177.04/27.65    (139)  op(e2, e3) = all_52_9
% 177.04/27.65    (140)  all_56_13 = all_52_27
% 177.04/27.65  
% 177.04/27.65  Begin of proof
% 177.04/27.65  | 
% 177.04/27.65  | GROUND_INST: instantiating (115) with e0, all_6_1, e0, e0, simplifying with
% 177.04/27.65  |              (22), (85) gives:
% 177.04/27.65  |   (141)  all_6_1 = e0
% 177.04/27.65  | 
% 177.04/27.65  | REDUCE: (123), (141) imply:
% 177.04/27.65  |   (142)  op(e0, e0) = all_6_0
% 177.04/27.65  | 
% 177.04/27.65  | GROUND_INST: instantiating (115) with e0, all_6_0, e0, e0, simplifying with
% 177.04/27.65  |              (85), (142) gives:
% 177.04/27.65  |   (143)  all_6_0 = e0
% 177.04/27.65  | 
% 177.04/27.65  | REDUCE: (6), (143) imply:
% 177.04/27.65  |   (144)   ~ (e3 = e0)
% 177.04/27.65  | 
% 177.04/27.65  | SIMP: (144) implies:
% 177.04/27.65  |   (145)   ~ (e3 = e0)
% 177.04/27.65  | 
% 177.04/27.65  | REDUCE: (99), (143) imply:
% 177.04/27.65  |   (146)   ~ (e2 = e0)
% 177.04/27.65  | 
% 177.04/27.65  | SIMP: (146) implies:
% 177.04/27.65  |   (147)   ~ (e2 = e0)
% 177.04/27.65  | 
% 177.04/27.65  | REDUCE: (125), (143) imply:
% 177.04/27.65  |   (148)   ~ (e1 = e0)
% 177.04/27.65  | 
% 177.04/27.65  | SIMP: (148) implies:
% 177.04/27.65  |   (149)   ~ (e1 = e0)
% 177.04/27.65  | 
% 177.04/27.65  | BETA: splitting (116) gives:
% 177.04/27.65  | 
% 177.04/27.65  | Case 1:
% 177.04/27.65  | | 
% 177.04/27.65  | |   (150)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.65  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.04/27.65  | | 
% 177.04/27.65  | | BETA: splitting (150) gives:
% 177.04/27.65  | | 
% 177.04/27.65  | | Case 1:
% 177.04/27.65  | | | 
% 177.04/27.65  | | |   (151)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.04/27.65  | | | 
% 177.04/27.65  | | | REF_CLOSE: (9), (10), (15), (23), (25), (26), (28), (29), (33), (35),
% 177.04/27.65  | | |            (40), (42), (43), (44), (47), (51), (52), (53), (54), (56),
% 177.04/27.65  | | |            (59), (61), (64), (65), (69), (74), (78), (79), (80), (82),
% 177.04/27.65  | | |            (86), (89), (90), (91), (93), (98), (101), (102), (103), (107),
% 177.04/27.65  | | |            (110), (115), (117), (118), (124), (129), (130), (132), (133),
% 177.04/27.65  | | |            (135), (138), (140), (145), (151) are inconsistent by sub-proof
% 177.04/27.65  | | |            #1008.
% 177.04/27.65  | | | 
% 177.04/27.65  | | Case 2:
% 177.04/27.65  | | | 
% 177.04/27.65  | | |   (152)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.04/27.65  | | | 
% 177.04/27.66  | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (12), (15), (16), (18),
% 177.04/27.66  | | |            (20), (21), (23), (24), (27), (28), (29), (31), (32), (33),
% 177.04/27.66  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 177.04/27.66  | | |            (44), (45), (46), (48), (51), (52), (53), (54), (56), (57),
% 177.04/27.66  | | |            (58), (59), (61), (63), (64), (68), (69), (70), (73), (74),
% 177.04/27.66  | | |            (75), (76), (77), (79), (80), (86), (87), (88), (89), (91),
% 177.04/27.66  | | |            (92), (93), (94), (95), (96), (97), (98), (100), (101), (102),
% 177.04/27.66  | | |            (103), (105), (107), (108), (109), (112), (115), (117), (119),
% 177.04/27.66  | | |            (120), (121), (122), (124), (126), (128), (129), (130), (132),
% 177.04/27.66  | | |            (133), (134), (135), (136), (137), (139), (140), (145), (147),
% 177.04/27.66  | | |            (149), (152) are inconsistent by sub-proof #631.
% 177.04/27.66  | | | 
% 177.04/27.66  | | End of split
% 177.04/27.66  | | 
% 177.04/27.66  | Case 2:
% 177.04/27.66  | | 
% 177.04/27.66  | |   (153)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 177.04/27.66  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.04/27.66  | |            e0)
% 177.04/27.66  | | 
% 177.04/27.66  | | BETA: splitting (153) gives:
% 177.04/27.66  | | 
% 177.04/27.66  | | Case 1:
% 177.04/27.66  | | | 
% 177.04/27.66  | | |   (154)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.04/27.66  | | | 
% 177.04/27.66  | | | REF_CLOSE: (72), (104), (115), (127), (131), (154) are inconsistent by
% 177.04/27.66  | | |            sub-proof #314.
% 177.04/27.66  | | | 
% 177.04/27.66  | | Case 2:
% 177.04/27.66  | | | 
% 177.04/27.66  | | |   (155)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.04/27.66  | | | 
% 177.04/27.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13),
% 177.04/27.66  | | |            (14), (16), (17), (19), (21), (23), (24), (25), (27), (28),
% 177.04/27.66  | | |            (30), (31), (32), (35), (37), (38), (40), (42), (43), (44),
% 177.04/27.66  | | |            (46), (49), (50), (52), (53), (54), (55), (56), (57), (60),
% 177.04/27.66  | | |            (62), (63), (66), (67), (69), (71), (74), (78), (79), (80),
% 177.04/27.66  | | |            (81), (83), (84), (86), (87), (88), (89), (90), (91), (95),
% 177.04/27.66  | | |            (97), (98), (100), (101), (102), (103), (106), (108), (110),
% 177.04/27.66  | | |            (111), (112), (113), (114), (115), (117), (126), (130), (132),
% 177.04/27.66  | | |            (133), (139), (140), (145), (149), (155) are inconsistent by
% 177.04/27.66  | | |            sub-proof #878.
% 177.04/27.66  | | | 
% 177.04/27.66  | | End of split
% 177.04/27.66  | | 
% 177.04/27.66  | End of split
% 177.04/27.66  | 
% 177.04/27.66  End of proof
% 177.04/27.66  
% 177.04/27.66  Sub-proof #314 shows that the following formulas are inconsistent:
% 177.04/27.66  ----------------------------------------------------------------
% 177.04/27.66    (1)  op(all_14_1, all_14_2) = e2
% 177.04/27.66    (2)   ~ (e2 = e1)
% 177.04/27.66    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.66    (4)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.04/27.66    (5)  all_52_20 = all_14_1
% 177.04/27.66    (6)  op(e1, all_14_2) = all_14_1
% 177.04/27.66  
% 177.04/27.66  Begin of proof
% 177.04/27.66  | 
% 177.04/27.66  | ALPHA: (4) implies:
% 177.04/27.66  |   (7)  all_52_20 = e1
% 177.04/27.66  | 
% 177.04/27.66  | COMBINE_EQS: (5), (7) imply:
% 177.04/27.66  |   (8)  all_14_1 = e1
% 177.04/27.66  | 
% 177.04/27.66  | SIMP: (8) implies:
% 177.04/27.66  |   (9)  all_14_1 = e1
% 177.04/27.66  | 
% 177.04/27.66  | REF_CLOSE: (1), (2), (3), (6), (9) are inconsistent by sub-proof #315.
% 177.04/27.66  | 
% 177.04/27.66  End of proof
% 177.04/27.66  
% 177.04/27.66  Sub-proof #315 shows that the following formulas are inconsistent:
% 177.04/27.66  ----------------------------------------------------------------
% 177.04/27.66    (1)  op(all_14_1, all_14_2) = e2
% 177.04/27.66    (2)   ~ (e2 = e1)
% 177.04/27.66    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.66    (4)  op(e1, all_14_2) = all_14_1
% 177.04/27.66    (5)  all_14_1 = e1
% 177.04/27.66  
% 177.04/27.66  Begin of proof
% 177.04/27.66  | 
% 177.04/27.66  | REDUCE: (1), (5) imply:
% 177.04/27.66  |   (6)  op(e1, all_14_2) = e2
% 177.04/27.66  | 
% 177.04/27.66  | REDUCE: (4), (5) imply:
% 177.04/27.66  |   (7)  op(e1, all_14_2) = e1
% 177.04/27.66  | 
% 177.04/27.66  | GROUND_INST: instantiating (3) with e1, e2, all_14_2, e1, simplifying with
% 177.04/27.66  |              (6), (7) gives:
% 177.04/27.66  |   (8)  e2 = e1
% 177.04/27.66  | 
% 177.04/27.66  | REDUCE: (2), (8) imply:
% 177.04/27.66  |   (9)  $false
% 177.04/27.66  | 
% 177.04/27.66  | CLOSE: (9) is inconsistent.
% 177.04/27.66  | 
% 177.04/27.66  End of proof
% 177.04/27.66  
% 177.04/27.66  Sub-proof #316 shows that the following formulas are inconsistent:
% 177.04/27.66  ----------------------------------------------------------------
% 177.04/27.66    (1)   ~ (all_52_23 = all_14_2)
% 177.04/27.66    (2)   ~ (all_52_5 = all_52_13)
% 177.04/27.66    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.04/27.66    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.04/27.66    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.04/27.66    (6)   ~ (all_52_27 = all_10_2)
% 177.04/27.66    (7)  op(e2, e2) = all_10_2
% 177.04/27.66    (8)   ~ (all_52_17 = all_52_23)
% 177.04/27.66    (9)  op(e2, all_10_2) = all_10_1
% 177.04/27.66    (10)  all_40_2 = all_4_2
% 177.04/27.66    (11)   ~ (all_52_13 = all_52_29)
% 177.04/27.66    (12)  all_56_3 = all_52_7
% 177.04/27.66    (13)  op(e3, e2) = all_52_3
% 177.04/27.66    (14)   ~ (all_52_9 = all_52_25)
% 177.04/27.66    (15)  op(e3, all_52_25) = all_52_24
% 177.04/27.66    (16)   ~ (all_52_19 = all_52_23)
% 177.04/27.66    (17)  all_56_11 = all_52_23
% 177.04/27.66    (18)  op(e1, e2) = all_52_19
% 177.04/27.66    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.04/27.66    (20)  op(e3, all_52_9) = all_52_8
% 177.04/27.66    (21)  all_50_1 = all_4_1
% 177.04/27.66    (22)  all_18_0 = all_14_0
% 177.04/27.66    (23)   ~ (all_52_3 = all_10_2)
% 177.04/27.66    (24)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.04/27.66    (25)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.04/27.66    (26)  all_58_5 = all_52_13
% 177.04/27.66    (27)   ~ (all_52_25 = all_52_29)
% 177.04/27.66    (28)  all_56_15 = all_6_2
% 177.04/27.66    (29)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.04/27.66    (30)  op(e2, e0) = all_52_15
% 177.04/27.66    (31)  op(all_14_1, all_14_2) = all_14_0
% 177.04/27.66    (32)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.04/27.66    (33)  all_58_3 = all_10_2
% 177.04/27.66    (34)  all_56_9 = all_52_19
% 177.04/27.66    (35)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.04/27.66    (36)  all_58_15 = all_6_2
% 177.04/27.66    (37)   ~ (all_52_9 = all_4_2)
% 177.04/27.66    (38)   ~ (all_52_5 = all_52_7)
% 177.04/27.66    (39)  all_58_10 = all_52_15
% 177.04/27.66    (40)   ~ (all_52_5 = all_4_2)
% 177.04/27.66    (41)  all_58_7 = all_52_19
% 177.04/27.66    (42)  all_56_4 = all_52_9
% 177.04/27.66    (43)   ~ (all_52_15 = all_6_2)
% 177.04/27.66    (44)   ~ (all_52_17 = all_52_25)
% 177.04/27.66    (45)  op(e0, e1) = all_52_29
% 177.04/27.66    (46)  all_58_4 = all_52_5
% 177.04/27.66    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.04/27.66    (48)   ~ (e3 = e1)
% 177.04/27.66    (49)  all_34_1 = all_4_1
% 177.04/27.66    (50)   ~ (all_52_27 = all_52_29)
% 177.04/27.66    (51)   ~ (all_52_17 = all_14_2)
% 177.04/27.66    (52)  op(e3, all_4_2) = all_4_1
% 177.04/27.66    (53)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.04/27.66    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.04/27.66    (55)   ~ (all_52_7 = all_4_2)
% 177.04/27.66    (56)  all_58_1 = all_52_3
% 177.04/27.66    (57)   ~ (all_52_13 = all_52_15)
% 177.04/27.66    (58)  all_58_0 = all_4_2
% 177.04/27.66    (59)  op(e1, all_52_13) = all_52_12
% 177.04/27.66    (60)  op(e0, e0) = all_6_2
% 177.04/27.66    (61)  op(e1, all_52_29) = all_52_28
% 177.04/27.66    (62)  all_50_0 = all_4_0
% 177.04/27.66    (63)  op(e1, all_52_5) = all_52_4
% 177.04/27.66    (64)  all_50_2 = all_4_2
% 177.04/27.66    (65)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.04/27.66    (66)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.04/27.66    (67)   ~ (all_4_1 = e2)
% 177.04/27.66    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.04/27.66    (69)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.04/27.66    (70)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.04/27.66    (71)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.04/27.66    (72)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.04/27.66    (73)  all_58_14 = all_52_29
% 177.04/27.66    (74)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.04/27.66    (75)  all_24_0 = all_10_0
% 177.04/27.66    (76)  all_40_1 = all_4_1
% 177.04/27.66    (77)  all_26_2 = all_4_2
% 177.04/27.66    (78)   ~ (all_52_3 = all_52_5)
% 177.04/27.66    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.04/27.66    (80)  op(e2, e1) = all_52_13
% 177.04/27.66    (81)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.04/27.66    (82)  all_58_8 = all_14_2
% 177.04/27.66    (83)  all_56_1 = all_52_3
% 177.04/27.66    (84)  op(e0, e2) = all_52_27
% 177.04/27.66    (85)  all_56_14 = all_52_29
% 177.04/27.66    (86)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.04/27.66    (87)  op(all_4_1, all_4_2) = all_4_0
% 177.04/27.66    (88)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.04/27.66    (89)   ~ (all_52_5 = all_14_2)
% 177.04/27.66    (90)   ~ (all_52_3 = all_52_27)
% 177.04/27.66    (91)   ~ (all_52_3 = all_4_2)
% 177.04/27.66    (92)  op(all_6_1, all_6_2) = all_6_0
% 177.04/27.66    (93)  op(e0, e3) = all_52_25
% 177.04/27.66    (94)  op(e0, all_6_2) = all_6_1
% 177.04/27.66    (95)  all_52_0 = all_4_1
% 177.04/27.66    (96)   ~ (all_52_9 = all_10_2)
% 177.04/27.66    (97)  op(e3, all_52_17) = all_52_16
% 177.04/27.66    (98)  all_52_10 = all_10_1
% 177.04/27.66    (99)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.04/27.66    (100)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.04/27.66    (101)   ~ (all_52_13 = all_14_2)
% 177.04/27.66    (102)   ~ (e3 = e0)
% 177.04/27.66    (103)  all_40_0 = all_4_0
% 177.04/27.66    (104)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.04/27.66    (105)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 177.04/27.66    (106)   ~ (all_52_9 = all_52_13)
% 177.04/27.66    (107)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.04/27.66    (108)  op(e0, all_52_23) = all_52_22
% 177.04/27.66    (109)   ~ (all_52_15 = all_52_23)
% 177.04/27.66    (110)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.04/27.66    (111)  op(all_10_1, all_10_2) = all_10_0
% 177.04/27.66    (112)   ~ (all_52_5 = all_52_29)
% 177.04/27.66    (113)  all_56_2 = all_52_5
% 177.04/27.66    (114)  op(e1, e0) = all_52_23
% 177.04/27.66    (115)  all_56_12 = all_52_25
% 177.04/27.66    (116)  all_58_13 = all_52_27
% 177.04/27.66    (117)  op(e2, all_52_3) = all_52_2
% 177.04/27.66    (118)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 177.04/27.66    (119)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.04/27.66    (120)  all_56_5 = all_10_2
% 177.04/27.66    (121)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.04/27.66    (122)   ~ (all_52_9 = all_52_17)
% 177.04/27.66    (123)   ~ (all_14_0 = e2)
% 177.04/27.66    (124)  all_58_6 = all_52_17
% 177.04/27.66    (125)   ~ (all_52_3 = all_52_7)
% 177.04/27.66    (126)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.04/27.66    (127)  op(e2, all_52_19) = all_52_18
% 177.04/27.66    (128)   ~ (e1 = e0)
% 177.04/27.66    (129)  all_56_0 = all_4_2
% 177.04/27.66    (130)  all_58_11 = all_52_23
% 177.04/27.66    (131)   ~ (all_52_3 = all_52_19)
% 177.04/27.66    (132)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.04/27.66    (133)   ~ (all_52_7 = all_52_15)
% 177.04/27.66    (134)  all_26_1 = all_4_1
% 177.04/27.66    (135)  op(e0, all_52_15) = all_52_14
% 177.04/27.66    (136)   ~ (all_52_29 = all_14_2)
% 177.04/27.66    (137)   ~ (all_52_19 = all_10_2)
% 177.04/27.66    (138)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.04/27.66    (139)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.04/27.66    (140)   ~ (all_52_23 = all_6_2)
% 177.04/27.66    (141)   ~ (all_6_0 = e2)
% 177.04/27.66    (142)   ~ (all_52_29 = all_6_2)
% 177.04/27.66    (143)  all_58_2 = all_52_9
% 177.04/27.66    (144)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.04/27.66    (145)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.04/27.66    (146)  op(e3, e1) = all_52_5
% 177.04/27.66    (147)   ~ (e2 = e1)
% 177.04/27.66    (148)  all_56_10 = all_14_2
% 177.04/27.66    (149)   ~ (all_52_25 = all_6_2)
% 177.04/27.66    (150)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.04/27.66    (151)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.04/27.66    (152)  op(e1, e1) = all_14_2
% 177.04/27.66    (153)  op(e1, e3) = all_52_17
% 177.04/27.66    (154)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.04/27.66    (155)  all_26_0 = all_4_0
% 177.04/27.66    (156)   ~ (all_52_25 = all_4_2)
% 177.04/27.66    (157)  op(e3, e0) = all_52_7
% 177.04/27.66    (158)  op(e3, e3) = all_4_2
% 177.04/27.66    (159)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.04/27.66             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.04/27.66    (160)  all_56_8 = all_52_17
% 177.04/27.66    (161)   ~ (all_52_17 = all_4_2)
% 177.04/27.66    (162)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.04/27.66             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.04/27.66    (163)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.04/27.66           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.04/27.66           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.04/27.66           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.66    (164)   ~ (all_52_25 = all_52_27)
% 177.04/27.66    (165)  all_34_2 = all_4_2
% 177.04/27.66    (166)   ~ (all_52_27 = all_6_2)
% 177.04/27.66    (167)   ~ (all_52_7 = all_6_2)
% 177.04/27.66    (168)   ~ (all_10_0 = e3)
% 177.04/27.66    (169)   ~ (all_52_15 = all_10_2)
% 177.04/27.66    (170)   ~ (all_52_19 = all_52_27)
% 177.04/27.66    (171)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2)
% 177.04/27.66    (172)  all_56_7 = all_52_15
% 177.04/27.66    (173)  all_18_2 = all_14_2
% 177.04/27.66    (174)  all_18_0 = e3
% 177.04/27.66    (175)   ~ (all_52_7 = all_52_23)
% 177.04/27.66    (176)   ~ (all_52_13 = all_10_2)
% 177.04/27.66    (177)   ~ (all_6_0 = e1)
% 177.04/27.66    (178)  op(e2, all_52_27) = all_52_26
% 177.04/27.66    (179)  all_52_20 = all_14_1
% 177.04/27.66    (180)   ~ (all_52_17 = all_52_19)
% 177.04/27.66    (181)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.04/27.66    (182)  all_52_30 = all_6_1
% 177.04/27.66    (183)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.04/27.66    (184)  op(e1, all_14_2) = all_14_1
% 177.04/27.66    (185)  all_58_9 = all_52_7
% 177.04/27.66    (186)   ~ (all_28_0 = e3) |  ~ (all_28_1 = e2) |  ~ (all_28_2 = e1)
% 177.04/27.66    (187)  all_58_12 = all_52_25
% 177.04/27.66    (188)  all_34_0 = all_4_0
% 177.04/27.66    (189)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.04/27.66    (190)  all_56_6 = all_52_13
% 177.04/27.66    (191)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.04/27.66    (192)   ~ (all_52_9 = all_52_15)
% 177.04/27.66    (193)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.04/27.66    (194)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.04/27.66    (195)   ~ (all_52_19 = all_14_2)
% 177.04/27.66    (196)  op(e0, all_52_7) = all_52_6
% 177.04/27.66    (197)  all_28_0 = all_6_0
% 177.04/27.66    (198)  op(e2, e3) = all_52_9
% 177.04/27.66    (199)  all_56_13 = all_52_27
% 177.04/27.66  
% 177.04/27.66  Begin of proof
% 177.04/27.66  | 
% 177.04/27.66  | COMBINE_EQS: (22), (174) imply:
% 177.04/27.66  |   (200)  all_14_0 = e3
% 177.04/27.66  | 
% 177.04/27.66  | REDUCE: (123), (200) imply:
% 177.04/27.66  |   (201)   ~ (e3 = e2)
% 177.04/27.66  | 
% 177.04/27.66  | REDUCE: (31), (200) imply:
% 177.04/27.66  |   (202)  op(all_14_1, all_14_2) = e3
% 177.04/27.66  | 
% 177.04/27.66  | BETA: splitting (105) gives:
% 177.04/27.66  | 
% 177.04/27.66  | Case 1:
% 177.04/27.66  | | 
% 177.04/27.66  | |   (203)   ~ (all_24_0 = e1)
% 177.04/27.66  | | 
% 177.04/27.66  | | REDUCE: (75), (203) imply:
% 177.04/27.66  | |   (204)   ~ (all_10_0 = e1)
% 177.04/27.66  | | 
% 177.04/27.66  | | BETA: splitting (189) gives:
% 177.04/27.66  | | 
% 177.04/27.66  | | Case 1:
% 177.04/27.66  | | | 
% 177.04/27.66  | | |   (205)   ~ (all_26_0 = e2)
% 177.04/27.66  | | | 
% 177.04/27.66  | | | REDUCE: (155), (205) imply:
% 177.04/27.66  | | |   (206)   ~ (all_4_0 = e2)
% 177.04/27.66  | | | 
% 177.04/27.66  | | | BETA: splitting (186) gives:
% 177.04/27.66  | | | 
% 177.04/27.66  | | | Case 1:
% 177.04/27.66  | | | | 
% 177.04/27.66  | | | |   (207)   ~ (all_28_0 = e3)
% 177.04/27.66  | | | | 
% 177.04/27.66  | | | | REDUCE: (197), (207) imply:
% 177.04/27.66  | | | |   (208)   ~ (all_6_0 = e3)
% 177.04/27.66  | | | | 
% 177.04/27.66  | | | | BETA: splitting (138) gives:
% 177.04/27.66  | | | | 
% 177.04/27.66  | | | | Case 1:
% 177.04/27.66  | | | | | 
% 177.04/27.66  | | | | |   (209)   ~ (all_34_0 = e1)
% 177.04/27.66  | | | | | 
% 177.04/27.66  | | | | | REDUCE: (188), (209) imply:
% 177.04/27.66  | | | | |   (210)   ~ (all_4_0 = e1)
% 177.04/27.66  | | | | | 
% 177.04/27.66  | | | | | BETA: splitting (171) gives:
% 177.04/27.66  | | | | | 
% 177.04/27.66  | | | | | Case 1:
% 177.04/27.66  | | | | | | 
% 177.04/27.66  | | | | | |   (211)   ~ (all_40_1 = e1)
% 177.04/27.66  | | | | | | 
% 177.04/27.66  | | | | | | REDUCE: (76), (211) imply:
% 177.04/27.66  | | | | | |   (212)   ~ (all_4_1 = e1)
% 177.04/27.66  | | | | | | 
% 177.04/27.66  | | | | | | BETA: splitting (159) gives:
% 177.04/27.66  | | | | | | 
% 177.04/27.66  | | | | | | Case 1:
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | |   (213)  all_58_15 = e0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | COMBINE_EQS: (36), (213) imply:
% 177.04/27.66  | | | | | | |   (214)  all_6_2 = e0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (167), (214) imply:
% 177.04/27.66  | | | | | | |   (215)   ~ (all_52_7 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (43), (214) imply:
% 177.04/27.66  | | | | | | |   (216)   ~ (all_52_15 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (140), (214) imply:
% 177.04/27.66  | | | | | | |   (217)   ~ (all_52_23 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (149), (214) imply:
% 177.04/27.66  | | | | | | |   (218)   ~ (all_52_25 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (166), (214) imply:
% 177.04/27.66  | | | | | | |   (219)   ~ (all_52_27 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (142), (214) imply:
% 177.04/27.66  | | | | | | |   (220)   ~ (all_52_29 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (92), (214) imply:
% 177.04/27.66  | | | | | | |   (221)  op(all_6_1, e0) = all_6_0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (94), (214) imply:
% 177.04/27.66  | | | | | | |   (222)  op(e0, e0) = all_6_1
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (60), (214) imply:
% 177.04/27.66  | | | | | | |   (223)  op(e0, e0) = e0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.04/27.66  | | | | | | |              simplifying with (222), (223) gives:
% 177.04/27.66  | | | | | | |   (224)  all_6_1 = e0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (221), (224) imply:
% 177.04/27.66  | | | | | | |   (225)  op(e0, e0) = all_6_0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.04/27.66  | | | | | | |              simplifying with (223), (225) gives:
% 177.04/27.66  | | | | | | |   (226)  all_6_0 = e0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (208), (226) imply:
% 177.04/27.66  | | | | | | |   (227)   ~ (e3 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (141), (226) imply:
% 177.04/27.66  | | | | | | |   (228)   ~ (e2 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | SIMP: (228) implies:
% 177.04/27.66  | | | | | | |   (229)   ~ (e2 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (177), (226) imply:
% 177.04/27.66  | | | | | | |   (230)   ~ (e1 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | BETA: splitting (163) gives:
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | Case 1:
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | |   (231)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.04/27.66  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.04/27.66  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (12), (13), (14), (15), (20),
% 177.04/27.66  | | | | | | | |            (23), (26), (27), (32), (33), (35), (36), (37), (38),
% 177.04/27.66  | | | | | | | |            (39), (41), (44), (45), (46), (47), (48), (50), (51),
% 177.04/27.66  | | | | | | | |            (52), (54), (55), (56), (58), (59), (61), (65), (70),
% 177.04/27.66  | | | | | | | |            (73), (74), (79), (81), (82), (83), (84), (87), (91),
% 177.04/27.66  | | | | | | | |            (93), (95), (98), (99), (101), (102), (106), (107),
% 177.04/27.66  | | | | | | | |            (109), (110), (111), (112), (115), (116), (119),
% 177.04/27.66  | | | | | | | |            (122), (124), (125), (128), (129), (130), (131),
% 177.04/27.66  | | | | | | | |            (133), (135), (136), (137), (143), (144), (146),
% 177.04/27.66  | | | | | | | |            (148), (151), (153), (154), (156), (158), (162),
% 177.04/27.66  | | | | | | | |            (164), (167), (168), (170), (172), (175), (178),
% 177.04/27.66  | | | | | | | |            (180), (181), (183), (185), (187), (191), (193),
% 177.04/27.66  | | | | | | | |            (195), (196), (198), (199), (204), (206), (210),
% 177.04/27.66  | | | | | | | |            (213), (215), (216), (218), (219), (220), (229),
% 177.04/27.66  | | | | | | | |            (231) are inconsistent by sub-proof #952.
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | Case 2:
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | |   (232)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.04/27.66  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.04/27.66  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | | BETA: splitting (232) gives:
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | | Case 1:
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | |   (233)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.04/27.66  | | | | | | | | |          all_52_22 = e0
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REF_CLOSE: (48), (162), (179), (184), (202), (233) are
% 177.04/27.66  | | | | | | | | |            inconsistent by sub-proof #343.
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | Case 2:
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | |   (234)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.04/27.66  | | | | | | | | |          all_52_30 = e0
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (11), (12), (13), (14),
% 177.04/27.66  | | | | | | | | |            (15), (16), (18), (20), (24), (27), (32), (33),
% 177.04/27.66  | | | | | | | | |            (35), (37), (38), (40), (41), (44), (46), (48),
% 177.04/27.66  | | | | | | | | |            (50), (52), (55), (56), (58), (61), (67), (68),
% 177.04/27.66  | | | | | | | | |            (73), (74), (79), (80), (81), (82), (85), (88),
% 177.04/27.66  | | | | | | | | |            (91), (96), (97), (99), (102), (104), (107), (112),
% 177.04/27.66  | | | | | | | | |            (115), (116), (120), (121), (122), (124), (125),
% 177.04/27.66  | | | | | | | | |            (128), (129), (130), (136), (137), (143), (144),
% 177.04/27.66  | | | | | | | | |            (146), (150), (153), (156), (157), (158), (160),
% 177.04/27.66  | | | | | | | | |            (161), (162), (164), (178), (183), (185), (187),
% 177.04/27.66  | | | | | | | | |            (198), (199), (212), (213), (217), (218), (220),
% 177.04/27.66  | | | | | | | | |            (234) are inconsistent by sub-proof #878.
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | End of split
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | End of split
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | Case 2:
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | |   (235)   ~ (all_58_15 = e0)
% 177.04/27.66  | | | | | | |   (236)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.04/27.66  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | ALPHA: (236) implies:
% 177.04/27.66  | | | | | | |   (237)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.04/27.66  | | | | | | |   (238)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | REDUCE: (36), (235) imply:
% 177.04/27.66  | | | | | | |   (239)   ~ (all_6_2 = e0)
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | BETA: splitting (163) gives:
% 177.04/27.66  | | | | | | | 
% 177.04/27.66  | | | | | | | Case 1:
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | |   (240)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.04/27.66  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.04/27.66  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | | BETA: splitting (240) gives:
% 177.04/27.66  | | | | | | | | 
% 177.04/27.66  | | | | | | | | Case 1:
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | |   (241)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.04/27.66  | | | | | | | | |          all_52_6 = e0
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | ALPHA: (241) implies:
% 177.04/27.66  | | | | | | | | |   (242)  all_52_6 = e0
% 177.04/27.66  | | | | | | | | |   (243)  all_52_4 = e1
% 177.04/27.66  | | | | | | | | |   (244)  all_52_2 = e2
% 177.04/27.66  | | | | | | | | |   (245)  all_52_0 = e3
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | COMBINE_EQS: (95), (245) imply:
% 177.04/27.66  | | | | | | | | |   (246)  all_4_1 = e3
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REDUCE: (87), (246) imply:
% 177.04/27.66  | | | | | | | | |   (247)  op(e3, all_4_2) = all_4_0
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REDUCE: (52), (246) imply:
% 177.04/27.66  | | | | | | | | |   (248)  op(e3, all_4_2) = e3
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REDUCE: (117), (244) imply:
% 177.04/27.66  | | | | | | | | |   (249)  op(e2, all_52_3) = e2
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REDUCE: (63), (243) imply:
% 177.04/27.66  | | | | | | | | |   (250)  op(e1, all_52_5) = e1
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REDUCE: (196), (242) imply:
% 177.04/27.66  | | | | | | | | |   (251)  op(e0, all_52_7) = e0
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 177.04/27.66  | | | | | | | | |            (12), (13), (14), (16), (17), (18), (19), (23),
% 177.04/27.66  | | | | | | | | |            (24), (26), (27), (28), (29), (30), (32), (33),
% 177.04/27.66  | | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41),
% 177.04/27.66  | | | | | | | | |            (42), (43), (44), (45), (46), (47), (50), (51),
% 177.04/27.66  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (60), (61),
% 177.04/27.66  | | | | | | | | |            (65), (66), (68), (69), (70), (72), (73), (74),
% 177.04/27.66  | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 177.04/27.66  | | | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (96),
% 177.04/27.66  | | | | | | | | |            (99), (100), (101), (102), (104), (106), (107),
% 177.04/27.66  | | | | | | | | |            (108), (109), (110), (112), (113), (114), (115),
% 177.04/27.66  | | | | | | | | |            (116), (119), (121), (122), (124), (125), (126),
% 177.04/27.66  | | | | | | | | |            (128), (129), (130), (131), (132), (133), (135),
% 177.04/27.66  | | | | | | | | |            (136), (137), (140), (142), (143), (144), (145),
% 177.04/27.66  | | | | | | | | |            (146), (147), (148), (149), (151), (152), (153),
% 177.04/27.66  | | | | | | | | |            (154), (156), (157), (160), (161), (162), (164),
% 177.04/27.66  | | | | | | | | |            (166), (167), (170), (172), (175), (176), (177),
% 177.04/27.66  | | | | | | | | |            (178), (180), (181), (183), (184), (185), (187),
% 177.04/27.66  | | | | | | | | |            (191), (192), (193), (194), (195), (198), (199),
% 177.04/27.66  | | | | | | | | |            (202), (206), (210), (238), (239), (247), (248),
% 177.04/27.66  | | | | | | | | |            (249), (250), (251) are inconsistent by sub-proof
% 177.04/27.66  | | | | | | | | |            #341.
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | Case 2:
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.66  | | | | | | | | |   (252)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.04/27.66  | | | | | | | | |          all_52_14 = e0
% 177.04/27.66  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (11), (12), (13),
% 177.04/27.67  | | | | | | | | |            (14), (15), (16), (17), (18), (20), (23), (25),
% 177.04/27.67  | | | | | | | | |            (26), (27), (28), (29), (30), (33), (34), (35),
% 177.04/27.67  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 177.04/27.67  | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 177.04/27.67  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (61),
% 177.04/27.67  | | | | | | | | |            (65), (66), (67), (69), (70), (71), (72), (73),
% 177.04/27.67  | | | | | | | | |            (74), (78), (79), (80), (81), (82), (83), (84),
% 177.04/27.67  | | | | | | | | |            (86), (87), (88), (90), (91), (93), (94), (96),
% 177.04/27.67  | | | | | | | | |            (97), (98), (101), (102), (106), (108), (109),
% 177.04/27.67  | | | | | | | | |            (110), (111), (112), (113), (114), (116), (119),
% 177.04/27.67  | | | | | | | | |            (122), (124), (125), (126), (127), (128), (129),
% 177.04/27.67  | | | | | | | | |            (130), (131), (133), (135), (136), (137), (140),
% 177.04/27.67  | | | | | | | | |            (142), (143), (145), (146), (148), (149), (151),
% 177.04/27.67  | | | | | | | | |            (152), (153), (154), (156), (157), (158), (161),
% 177.04/27.67  | | | | | | | | |            (162), (164), (166), (167), (168), (170), (172),
% 177.04/27.67  | | | | | | | | |            (175), (178), (180), (181), (183), (184), (185),
% 177.04/27.67  | | | | | | | | |            (187), (190), (191), (192), (193), (194), (195),
% 177.04/27.67  | | | | | | | | |            (198), (199), (204), (206), (210), (212), (237),
% 177.04/27.67  | | | | | | | | |            (238), (239), (252) are inconsistent by sub-proof
% 177.04/27.67  | | | | | | | | |            #338.
% 177.04/27.67  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | End of split
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | Case 2:
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | |   (253)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.04/27.67  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.04/27.67  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | | BETA: splitting (253) gives:
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | | Case 1:
% 177.04/27.67  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | |   (254)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.04/27.67  | | | | | | | | |          all_52_22 = e0
% 177.04/27.67  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | | REF_CLOSE: (48), (162), (179), (184), (202), (254) are
% 177.04/27.67  | | | | | | | | |            inconsistent by sub-proof #343.
% 177.04/27.67  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | Case 2:
% 177.04/27.67  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | |   (255)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.04/27.67  | | | | | | | | |          all_52_30 = e0
% 177.04/27.67  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (13), (14), (15), (16),
% 177.04/27.67  | | | | | | | | |            (17), (19), (20), (24), (26), (27), (28), (29),
% 177.04/27.67  | | | | | | | | |            (32), (33), (35), (36), (37), (38), (39), (40),
% 177.04/27.67  | | | | | | | | |            (41), (44), (45), (46), (47), (48), (50), (51),
% 177.04/27.67  | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (61),
% 177.04/27.67  | | | | | | | | |            (68), (69), (70), (73), (74), (78), (79), (81),
% 177.04/27.67  | | | | | | | | |            (82), (84), (85), (87), (90), (91), (92), (93),
% 177.04/27.67  | | | | | | | | |            (94), (96), (97), (99), (101), (104), (106), (107),
% 177.04/27.67  | | | | | | | | |            (112), (113), (114), (115), (116), (119), (121),
% 177.04/27.67  | | | | | | | | |            (122), (124), (125), (129), (130), (131), (133),
% 177.04/27.67  | | | | | | | | |            (137), (140), (141), (142), (143), (145), (146),
% 177.04/27.67  | | | | | | | | |            (147), (149), (151), (153), (154), (156), (157),
% 177.04/27.67  | | | | | | | | |            (158), (161), (162), (164), (166), (167), (169),
% 177.04/27.67  | | | | | | | | |            (170), (172), (175), (177), (178), (180), (181),
% 177.04/27.67  | | | | | | | | |            (182), (185), (187), (191), (192), (193), (194),
% 177.04/27.67  | | | | | | | | |            (198), (199), (201), (206), (208), (210), (237),
% 177.04/27.67  | | | | | | | | |            (238), (239), (255) are inconsistent by sub-proof
% 177.04/27.67  | | | | | | | | |            #634.
% 177.04/27.67  | | | | | | | | | 
% 177.04/27.67  | | | | | | | | End of split
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | End of split
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | End of split
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | Case 2:
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | |   (256)  all_40_1 = e1
% 177.04/27.67  | | | | | |   (257)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | COMBINE_EQS: (76), (256) imply:
% 177.04/27.67  | | | | | |   (258)  all_4_1 = e1
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | COMBINE_EQS: (95), (258) imply:
% 177.04/27.67  | | | | | |   (259)  all_52_0 = e1
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (67), (258) imply:
% 177.04/27.67  | | | | | |   (260)   ~ (e2 = e1)
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (87), (258) imply:
% 177.04/27.67  | | | | | |   (261)  op(e1, all_4_2) = all_4_0
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (52), (258) imply:
% 177.04/27.67  | | | | | |   (262)  op(e3, all_4_2) = e1
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | BETA: splitting (159) gives:
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | Case 1:
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | |   (263)  all_58_15 = e0
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | COMBINE_EQS: (36), (263) imply:
% 177.04/27.67  | | | | | | |   (264)  all_6_2 = e0
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (167), (264) imply:
% 177.04/27.67  | | | | | | |   (265)   ~ (all_52_7 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (43), (264) imply:
% 177.04/27.67  | | | | | | |   (266)   ~ (all_52_15 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (149), (264) imply:
% 177.04/27.67  | | | | | | |   (267)   ~ (all_52_25 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (166), (264) imply:
% 177.04/27.67  | | | | | | |   (268)   ~ (all_52_27 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (142), (264) imply:
% 177.04/27.67  | | | | | | |   (269)   ~ (all_52_29 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (92), (264) imply:
% 177.04/27.67  | | | | | | |   (270)  op(all_6_1, e0) = all_6_0
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (94), (264) imply:
% 177.04/27.67  | | | | | | |   (271)  op(e0, e0) = all_6_1
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (60), (264) imply:
% 177.04/27.67  | | | | | | |   (272)  op(e0, e0) = e0
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.04/27.67  | | | | | | |              simplifying with (271), (272) gives:
% 177.04/27.67  | | | | | | |   (273)  all_6_1 = e0
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (270), (273) imply:
% 177.04/27.67  | | | | | | |   (274)  op(e0, e0) = all_6_0
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.04/27.67  | | | | | | |              simplifying with (272), (274) gives:
% 177.04/27.67  | | | | | | |   (275)  all_6_0 = e0
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (208), (275) imply:
% 177.04/27.67  | | | | | | |   (276)   ~ (e3 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (141), (275) imply:
% 177.04/27.67  | | | | | | |   (277)   ~ (e2 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | SIMP: (277) implies:
% 177.04/27.67  | | | | | | |   (278)   ~ (e2 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REDUCE: (177), (275) imply:
% 177.04/27.67  | | | | | | |   (279)   ~ (e1 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | BETA: splitting (163) gives:
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | Case 1:
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | |   (280)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.04/27.67  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.04/27.67  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (12), (13), (14), (15), (20),
% 177.04/27.67  | | | | | | | |            (23), (26), (27), (32), (33), (37), (38), (39), (41),
% 177.04/27.67  | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52), (54),
% 177.04/27.67  | | | | | | | |            (55), (56), (58), (59), (61), (65), (70), (73), (74),
% 177.04/27.67  | | | | | | | |            (79), (81), (82), (83), (84), (87), (91), (93), (98),
% 177.04/27.67  | | | | | | | |            (99), (101), (102), (106), (107), (109), (110),
% 177.04/27.67  | | | | | | | |            (111), (115), (116), (122), (124), (125), (128),
% 177.04/27.67  | | | | | | | |            (130), (131), (133), (135), (136), (137), (143),
% 177.04/27.67  | | | | | | | |            (144), (146), (148), (151), (153), (154), (158),
% 177.04/27.67  | | | | | | | |            (162), (164), (168), (170), (172), (175), (178),
% 177.04/27.67  | | | | | | | |            (180), (181), (183), (185), (187), (191), (193),
% 177.04/27.67  | | | | | | | |            (195), (198), (199), (204), (206), (210), (259),
% 177.04/27.67  | | | | | | | |            (263), (266), (267), (268), (269), (278), (280) are
% 177.04/27.67  | | | | | | | |            inconsistent by sub-proof #337.
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | Case 2:
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | |   (281)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.04/27.67  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.04/27.67  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | | REF_CLOSE: (4), (10), (12), (13), (14), (15), (18), (26), (27),
% 177.04/27.67  | | | | | | | |            (34), (35), (37), (38), (40), (41), (44), (46), (48),
% 177.04/27.67  | | | | | | | |            (50), (51), (58), (61), (66), (68), (69), (73), (74),
% 177.04/27.67  | | | | | | | |            (80), (81), (82), (85), (90), (91), (97), (99),
% 177.04/27.67  | | | | | | | |            (102), (103), (107), (114), (115), (116), (121),
% 177.04/27.67  | | | | | | | |            (122), (124), (125), (128), (129), (130), (131),
% 177.04/27.67  | | | | | | | |            (136), (144), (146), (151), (153), (156), (157),
% 177.04/27.67  | | | | | | | |            (158), (162), (164), (178), (179), (183), (184),
% 177.04/27.67  | | | | | | | |            (185), (187), (198), (199), (202), (206), (257),
% 177.04/27.67  | | | | | | | |            (261), (262), (263), (265), (267), (269), (281) are
% 177.04/27.67  | | | | | | | |            inconsistent by sub-proof #336.
% 177.04/27.67  | | | | | | | | 
% 177.04/27.67  | | | | | | | End of split
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | Case 2:
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | |   (282)   ~ (all_58_15 = e0)
% 177.04/27.67  | | | | | | |   (283)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.04/27.67  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12),
% 177.04/27.67  | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (23),
% 177.04/27.67  | | | | | | |            (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 177.04/27.67  | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 177.04/27.67  | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 177.04/27.67  | | | | | | |            (54), (55), (56), (57), (58), (59), (61), (66), (67),
% 177.04/27.67  | | | | | | |            (69), (70), (71), (73), (74), (78), (79), (80), (81),
% 177.04/27.67  | | | | | | |            (82), (84), (86), (87), (88), (89), (90), (91), (93),
% 177.04/27.67  | | | | | | |            (94), (96), (97), (98), (101), (102), (103), (104),
% 177.04/27.67  | | | | | | |            (106), (107), (108), (109), (110), (111), (112), (113),
% 177.04/27.67  | | | | | | |            (114), (115), (116), (118), (119), (121), (122), (124),
% 177.04/27.67  | | | | | | |            (125), (126), (127), (128), (129), (130), (131), (133),
% 177.04/27.67  | | | | | | |            (135), (136), (137), (140), (142), (143), (145), (146),
% 177.04/27.67  | | | | | | |            (147), (148), (149), (151), (152), (153), (156), (157),
% 177.04/27.67  | | | | | | |            (158), (161), (162), (163), (164), (166), (167), (168),
% 177.04/27.67  | | | | | | |            (169), (170), (173), (175), (178), (179), (180), (181),
% 177.04/27.67  | | | | | | |            (182), (183), (184), (185), (187), (190), (191), (192),
% 177.04/27.67  | | | | | | |            (193), (194), (195), (198), (199), (201), (202), (204),
% 177.04/27.67  | | | | | | |            (206), (210), (257), (259), (261), (262), (282), (283)
% 177.04/27.67  | | | | | | |            are inconsistent by sub-proof #331.
% 177.04/27.67  | | | | | | | 
% 177.04/27.67  | | | | | | End of split
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | End of split
% 177.04/27.67  | | | | | 
% 177.04/27.67  | | | | Case 2:
% 177.04/27.67  | | | | | 
% 177.04/27.67  | | | | |   (284)  all_34_0 = e1
% 177.04/27.67  | | | | |   (285)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.04/27.67  | | | | | 
% 177.04/27.67  | | | | | COMBINE_EQS: (188), (284) imply:
% 177.04/27.67  | | | | |   (286)  all_4_0 = e1
% 177.04/27.67  | | | | | 
% 177.04/27.67  | | | | | SIMP: (286) implies:
% 177.04/27.67  | | | | |   (287)  all_4_0 = e1
% 177.04/27.67  | | | | | 
% 177.04/27.67  | | | | | REDUCE: (87), (287) imply:
% 177.04/27.67  | | | | |   (288)  op(all_4_1, all_4_2) = e1
% 177.04/27.67  | | | | | 
% 177.04/27.67  | | | | | BETA: splitting (159) gives:
% 177.04/27.67  | | | | | 
% 177.04/27.67  | | | | | Case 1:
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | |   (289)  all_58_15 = e0
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | COMBINE_EQS: (36), (289) imply:
% 177.04/27.67  | | | | | |   (290)  all_6_2 = e0
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (43), (290) imply:
% 177.04/27.67  | | | | | |   (291)   ~ (all_52_15 = e0)
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (149), (290) imply:
% 177.04/27.67  | | | | | |   (292)   ~ (all_52_25 = e0)
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (166), (290) imply:
% 177.04/27.67  | | | | | |   (293)   ~ (all_52_27 = e0)
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (142), (290) imply:
% 177.04/27.67  | | | | | |   (294)   ~ (all_52_29 = e0)
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (92), (290) imply:
% 177.04/27.67  | | | | | |   (295)  op(all_6_1, e0) = all_6_0
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (94), (290) imply:
% 177.04/27.67  | | | | | |   (296)  op(e0, e0) = all_6_1
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (60), (290) imply:
% 177.04/27.67  | | | | | |   (297)  op(e0, e0) = e0
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.04/27.67  | | | | | |              simplifying with (296), (297) gives:
% 177.04/27.67  | | | | | |   (298)  all_6_1 = e0
% 177.04/27.67  | | | | | | 
% 177.04/27.67  | | | | | | REDUCE: (295), (298) imply:
% 177.04/27.67  | | | | | |   (299)  op(e0, e0) = all_6_0
% 177.04/27.67  | | | | | | 
% 177.16/27.67  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.16/27.67  | | | | | |              simplifying with (297), (299) gives:
% 177.16/27.67  | | | | | |   (300)  all_6_0 = e0
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | REDUCE: (208), (300) imply:
% 177.16/27.67  | | | | | |   (301)   ~ (e3 = e0)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | REDUCE: (141), (300) imply:
% 177.16/27.67  | | | | | |   (302)   ~ (e2 = e0)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | SIMP: (302) implies:
% 177.16/27.67  | | | | | |   (303)   ~ (e2 = e0)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | REDUCE: (177), (300) imply:
% 177.16/27.67  | | | | | |   (304)   ~ (e1 = e0)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | BETA: splitting (163) gives:
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | Case 1:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | |   (305)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.67  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.67  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | REF_CLOSE: (6), (8), (9), (11), (12), (13), (14), (18), (20),
% 177.16/27.67  | | | | | | |            (23), (26), (27), (29), (32), (33), (35), (37), (39),
% 177.16/27.67  | | | | | | |            (41), (42), (44), (45), (47), (48), (49), (52), (54),
% 177.16/27.67  | | | | | | |            (55), (56), (58), (59), (65), (67), (70), (71), (73),
% 177.16/27.67  | | | | | | |            (74), (79), (81), (82), (83), (84), (90), (91), (93),
% 177.16/27.67  | | | | | | |            (95), (98), (99), (102), (106), (107), (110), (111),
% 177.16/27.67  | | | | | | |            (114), (115), (116), (124), (125), (126), (128), (129),
% 177.16/27.67  | | | | | | |            (130), (131), (133), (135), (137), (143), (144), (148),
% 177.16/27.67  | | | | | | |            (153), (154), (156), (157), (158), (161), (162), (164),
% 177.16/27.67  | | | | | | |            (165), (168), (172), (175), (178), (181), (183), (185),
% 177.16/27.67  | | | | | | |            (187), (190), (191), (192), (195), (198), (199), (204),
% 177.16/27.67  | | | | | | |            (285), (288), (289), (291), (292), (293), (294), (303),
% 177.16/27.67  | | | | | | |            (305) are inconsistent by sub-proof #330.
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | Case 2:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | |   (306)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.67  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.67  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | REF_CLOSE: (12), (13), (14), (15), (18), (29), (35), (48), (49),
% 177.16/27.67  | | | | | | |            (52), (55), (58), (61), (65), (67), (73), (74), (79),
% 177.16/27.67  | | | | | | |            (81), (83), (91), (102), (107), (114), (115), (116),
% 177.16/27.67  | | | | | | |            (129), (131), (153), (156), (157), (158), (161), (162),
% 177.16/27.67  | | | | | | |            (164), (165), (175), (178), (179), (183), (184), (187),
% 177.16/27.67  | | | | | | |            (198), (199), (202), (285), (288), (289), (292), (306)
% 177.16/27.67  | | | | | | |            are inconsistent by sub-proof #329.
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | End of split
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | Case 2:
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | |   (307)   ~ (all_58_15 = e0)
% 177.16/27.67  | | | | | |   (308)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.67  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | ALPHA: (308) implies:
% 177.16/27.67  | | | | | |   (309)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.16/27.67  | | | | | |   (310)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | REDUCE: (36), (307) imply:
% 177.16/27.67  | | | | | |   (311)   ~ (all_6_2 = e0)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | BETA: splitting (163) gives:
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | Case 1:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | |   (312)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.67  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.67  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (11), (12), (13), (14),
% 177.16/27.67  | | | | | | |            (16), (17), (18), (20), (23), (26), (27), (28), (29),
% 177.16/27.67  | | | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 177.16/27.67  | | | | | | |            (42), (43), (44), (46), (47), (48), (49), (50), (51),
% 177.16/27.67  | | | | | | |            (52), (53), (54), (55), (56), (58), (59), (61), (65),
% 177.16/27.67  | | | | | | |            (66), (67), (69), (70), (71), (73), (74), (78), (79),
% 177.16/27.67  | | | | | | |            (80), (81), (82), (83), (88), (90), (91), (93), (94),
% 177.16/27.67  | | | | | | |            (95), (97), (98), (101), (102), (106), (108), (109),
% 177.16/27.67  | | | | | | |            (110), (111), (112), (113), (114), (116), (119), (122),
% 177.16/27.67  | | | | | | |            (124), (125), (126), (127), (128), (129), (130), (131),
% 177.16/27.67  | | | | | | |            (133), (135), (136), (137), (140), (142), (143), (145),
% 177.16/27.67  | | | | | | |            (146), (148), (149), (152), (153), (156), (157), (158),
% 177.16/27.67  | | | | | | |            (161), (162), (164), (165), (166), (167), (168), (175),
% 177.16/27.67  | | | | | | |            (178), (180), (181), (183), (184), (185), (187), (190),
% 177.16/27.67  | | | | | | |            (191), (192), (193), (194), (195), (198), (199), (204),
% 177.16/27.67  | | | | | | |            (285), (288), (310), (311), (312) are inconsistent by
% 177.16/27.67  | | | | | | |            sub-proof #327.
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | Case 2:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | |   (313)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.67  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.67  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | BETA: splitting (313) gives:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | Case 1:
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | |   (314)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.67  | | | | | | | |          all_52_22 = e0
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | ALPHA: (314) implies:
% 177.16/27.67  | | | | | | | |   (315)  all_52_20 = e1
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | COMBINE_EQS: (179), (315) imply:
% 177.16/27.67  | | | | | | | |   (316)  all_14_1 = e1
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | REF_CLOSE: (48), (162), (184), (202), (316) are inconsistent by
% 177.16/27.67  | | | | | | | |            sub-proof #344.
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | Case 2:
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | |   (317)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.16/27.67  | | | | | | | |          all_52_30 = e0
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | ALPHA: (317) implies:
% 177.16/27.67  | | | | | | | |   (318)  all_52_30 = e0
% 177.16/27.67  | | | | | | | |   (319)  all_52_28 = e1
% 177.16/27.67  | | | | | | | |   (320)  all_52_26 = e2
% 177.16/27.67  | | | | | | | |   (321)  all_52_24 = e3
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | COMBINE_EQS: (182), (318) imply:
% 177.16/27.67  | | | | | | | |   (322)  all_6_1 = e0
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | REF_CLOSE: (4), (12), (13), (14), (15), (16), (18), (20), (23),
% 177.16/27.67  | | | | | | | |            (24), (28), (29), (33), (35), (36), (38), (39), (41),
% 177.16/27.67  | | | | | | | |            (44), (45), (46), (48), (49), (50), (52), (53), (55),
% 177.16/27.67  | | | | | | | |            (56), (58), (61), (65), (67), (73), (74), (78), (79),
% 177.16/27.67  | | | | | | | |            (81), (83), (84), (90), (91), (92), (93), (94), (96),
% 177.16/27.67  | | | | | | | |            (99), (104), (113), (114), (116), (119), (124),
% 177.16/27.67  | | | | | | | |            (125), (129), (130), (131), (133), (136), (141),
% 177.16/27.67  | | | | | | | |            (143), (146), (151), (152), (153), (156), (157),
% 177.16/27.67  | | | | | | | |            (158), (161), (162), (164), (165), (167), (170),
% 177.16/27.67  | | | | | | | |            (175), (177), (178), (180), (181), (183), (185),
% 177.16/27.67  | | | | | | | |            (187), (192), (194), (198), (199), (201), (208),
% 177.16/27.67  | | | | | | | |            (285), (288), (309), (319), (320), (321), (322) are
% 177.16/27.67  | | | | | | | |            inconsistent by sub-proof #555.
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | End of split
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | End of split
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | End of split
% 177.16/27.67  | | | | | 
% 177.16/27.67  | | | | End of split
% 177.16/27.67  | | | | 
% 177.16/27.67  | | | Case 2:
% 177.16/27.67  | | | | 
% 177.16/27.67  | | | |   (323)  all_28_0 = e3
% 177.16/27.67  | | | | 
% 177.16/27.67  | | | | COMBINE_EQS: (197), (323) imply:
% 177.16/27.67  | | | |   (324)  all_6_0 = e3
% 177.16/27.67  | | | | 
% 177.16/27.67  | | | | SIMP: (324) implies:
% 177.16/27.67  | | | |   (325)  all_6_0 = e3
% 177.16/27.67  | | | | 
% 177.16/27.67  | | | | REDUCE: (92), (325) imply:
% 177.16/27.67  | | | |   (326)  op(all_6_1, all_6_2) = e3
% 177.16/27.67  | | | | 
% 177.16/27.67  | | | | BETA: splitting (138) gives:
% 177.16/27.67  | | | | 
% 177.16/27.67  | | | | Case 1:
% 177.16/27.67  | | | | | 
% 177.16/27.67  | | | | |   (327)   ~ (all_34_0 = e1)
% 177.16/27.67  | | | | | 
% 177.16/27.67  | | | | | REDUCE: (188), (327) imply:
% 177.16/27.67  | | | | |   (328)   ~ (all_4_0 = e1)
% 177.16/27.67  | | | | | 
% 177.16/27.67  | | | | | BETA: splitting (171) gives:
% 177.16/27.67  | | | | | 
% 177.16/27.67  | | | | | Case 1:
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | |   (329)   ~ (all_40_1 = e1)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | REDUCE: (76), (329) imply:
% 177.16/27.67  | | | | | |   (330)   ~ (all_4_1 = e1)
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | BETA: splitting (159) gives:
% 177.16/27.67  | | | | | | 
% 177.16/27.67  | | | | | | Case 1:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | |   (331)  all_58_15 = e0
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | REF_CLOSE: (36), (60), (94), (102), (162), (326), (331) are
% 177.16/27.67  | | | | | | |            inconsistent by sub-proof #510.
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | Case 2:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | |   (332)   ~ (all_58_15 = e0)
% 177.16/27.67  | | | | | | |   (333)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.67  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | ALPHA: (333) implies:
% 177.16/27.67  | | | | | | |   (334)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.16/27.67  | | | | | | |   (335)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | REDUCE: (36), (332) imply:
% 177.16/27.67  | | | | | | |   (336)   ~ (all_6_2 = e0)
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | BETA: splitting (163) gives:
% 177.16/27.67  | | | | | | | 
% 177.16/27.67  | | | | | | | Case 1:
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | |   (337)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.67  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.16/27.67  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | BETA: splitting (337) gives:
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | | Case 1:
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | |   (338)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.67  | | | | | | | | |          all_52_6 = e0
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | REF_CLOSE: (1), (2), (8), (11), (13), (14), (16), (17), (18),
% 177.16/27.67  | | | | | | | | |            (19), (23), (26), (27), (28), (29), (30), (32),
% 177.16/27.67  | | | | | | | | |            (33), (35), (36), (37), (38), (39), (40), (41),
% 177.16/27.67  | | | | | | | | |            (42), (43), (44), (45), (46), (47), (50), (51),
% 177.16/27.67  | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (61),
% 177.16/27.67  | | | | | | | | |            (63), (65), (68), (69), (70), (72), (73), (74),
% 177.16/27.67  | | | | | | | | |            (78), (79), (80), (81), (82), (83), (85), (87),
% 177.16/27.67  | | | | | | | | |            (89), (90), (91), (93), (94), (95), (100), (101),
% 177.16/27.67  | | | | | | | | |            (102), (104), (106), (107), (108), (109), (110),
% 177.16/27.67  | | | | | | | | |            (112), (113), (114), (115), (116), (117), (119),
% 177.16/27.67  | | | | | | | | |            (121), (122), (124), (125), (126), (128), (129),
% 177.16/27.67  | | | | | | | | |            (130), (131), (132), (133), (135), (136), (140),
% 177.16/27.67  | | | | | | | | |            (142), (143), (144), (145), (146), (148), (149),
% 177.16/27.67  | | | | | | | | |            (151), (152), (153), (154), (156), (157), (161),
% 177.16/27.67  | | | | | | | | |            (162), (164), (166), (167), (170), (172), (175),
% 177.16/27.67  | | | | | | | | |            (176), (178), (180), (181), (185), (187), (191),
% 177.16/27.67  | | | | | | | | |            (192), (193), (194), (195), (196), (198), (199),
% 177.16/27.67  | | | | | | | | |            (206), (326), (328), (335), (336), (338) are
% 177.16/27.67  | | | | | | | | |            inconsistent by sub-proof #436.
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | Case 2:
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | |   (339)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.16/27.67  | | | | | | | | |          all_52_14 = e0
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | ALPHA: (339) implies:
% 177.16/27.67  | | | | | | | | |   (340)  all_52_14 = e0
% 177.16/27.67  | | | | | | | | |   (341)  all_52_12 = e1
% 177.16/27.67  | | | | | | | | |   (342)  all_52_10 = e2
% 177.16/27.67  | | | | | | | | |   (343)  all_52_8 = e3
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | COMBINE_EQS: (98), (342) imply:
% 177.16/27.67  | | | | | | | | |   (344)  all_10_1 = e2
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | REDUCE: (111), (344) imply:
% 177.16/27.67  | | | | | | | | |   (345)  op(e2, all_10_2) = all_10_0
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | REDUCE: (20), (343) imply:
% 177.16/27.67  | | | | | | | | |   (346)  op(e3, all_52_9) = e3
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | REDUCE: (9), (344) imply:
% 177.16/27.67  | | | | | | | | |   (347)  op(e2, all_10_2) = e2
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | REDUCE: (59), (341) imply:
% 177.16/27.67  | | | | | | | | |   (348)  op(e1, all_52_13) = e1
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | REDUCE: (135), (340) imply:
% 177.16/27.67  | | | | | | | | |   (349)  op(e0, all_52_15) = e0
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (11), (12), (13), (14),
% 177.16/27.67  | | | | | | | | |            (15), (16), (17), (18), (23), (25), (26), (27),
% 177.16/27.67  | | | | | | | | |            (28), (29), (30), (33), (34), (35), (36), (37),
% 177.16/27.67  | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 177.16/27.67  | | | | | | | | |            (46), (47), (48), (50), (51), (52), (53), (54),
% 177.16/27.67  | | | | | | | | |            (55), (56), (57), (58), (61), (65), (66), (67),
% 177.16/27.67  | | | | | | | | |            (69), (70), (71), (72), (73), (74), (78), (79),
% 177.16/27.67  | | | | | | | | |            (80), (81), (82), (83), (84), (86), (87), (88),
% 177.16/27.67  | | | | | | | | |            (90), (91), (93), (94), (96), (97), (101), (102),
% 177.16/27.67  | | | | | | | | |            (106), (108), (109), (110), (112), (113), (114),
% 177.16/27.67  | | | | | | | | |            (116), (119), (122), (124), (125), (126), (127),
% 177.16/27.67  | | | | | | | | |            (128), (129), (130), (131), (133), (136), (137),
% 177.16/27.67  | | | | | | | | |            (140), (142), (143), (145), (146), (148), (149),
% 177.16/27.67  | | | | | | | | |            (151), (152), (153), (154), (156), (157), (158),
% 177.16/27.67  | | | | | | | | |            (161), (162), (164), (166), (167), (168), (170),
% 177.16/27.67  | | | | | | | | |            (172), (175), (178), (180), (181), (183), (184),
% 177.16/27.67  | | | | | | | | |            (185), (187), (190), (191), (192), (193), (194),
% 177.16/27.67  | | | | | | | | |            (195), (198), (199), (204), (206), (328), (330),
% 177.16/27.67  | | | | | | | | |            (334), (335), (336), (345), (346), (347), (348),
% 177.16/27.67  | | | | | | | | |            (349) are inconsistent by sub-proof #339.
% 177.16/27.67  | | | | | | | | | 
% 177.16/27.67  | | | | | | | | End of split
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | Case 2:
% 177.16/27.67  | | | | | | | | 
% 177.16/27.67  | | | | | | | |   (350)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.68  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.68  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REF_CLOSE: (48), (94), (102), (162), (179), (182), (184), (202),
% 177.16/27.68  | | | | | | | |            (326), (350) are inconsistent by sub-proof #326.
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | End of split
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | End of split
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | Case 2:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (351)  all_40_1 = e1
% 177.16/27.68  | | | | | |   (352)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | COMBINE_EQS: (76), (351) imply:
% 177.16/27.68  | | | | | |   (353)  all_4_1 = e1
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | SIMP: (353) implies:
% 177.16/27.68  | | | | | |   (354)  all_4_1 = e1
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | COMBINE_EQS: (95), (354) imply:
% 177.16/27.68  | | | | | |   (355)  all_52_0 = e1
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (67), (354) imply:
% 177.16/27.68  | | | | | |   (356)   ~ (e2 = e1)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (87), (354) imply:
% 177.16/27.68  | | | | | |   (357)  op(e1, all_4_2) = all_4_0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (52), (354) imply:
% 177.16/27.68  | | | | | |   (358)  op(e3, all_4_2) = e1
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | BETA: splitting (159) gives:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | Case 1:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (359)  all_58_15 = e0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REF_CLOSE: (36), (60), (94), (102), (162), (326), (359) are
% 177.16/27.68  | | | | | | |            inconsistent by sub-proof #510.
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | Case 2:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (360)   ~ (all_58_15 = e0)
% 177.16/27.68  | | | | | | |   (361)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.68  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | ALPHA: (361) implies:
% 177.16/27.68  | | | | | | |   (362)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.16/27.68  | | | | | | |   (363)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (36), (360) imply:
% 177.16/27.68  | | | | | | |   (364)   ~ (all_6_2 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12),
% 177.16/27.68  | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (23),
% 177.16/27.68  | | | | | | |            (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 177.16/27.68  | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 177.16/27.68  | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 177.16/27.68  | | | | | | |            (54), (55), (56), (57), (58), (59), (61), (66), (67),
% 177.16/27.68  | | | | | | |            (69), (70), (71), (73), (74), (78), (79), (80), (81),
% 177.16/27.68  | | | | | | |            (82), (84), (86), (87), (88), (89), (90), (91), (93),
% 177.16/27.68  | | | | | | |            (94), (96), (97), (98), (101), (102), (103), (104),
% 177.16/27.68  | | | | | | |            (106), (107), (108), (109), (110), (111), (112), (113),
% 177.16/27.68  | | | | | | |            (114), (115), (116), (118), (119), (121), (122), (124),
% 177.16/27.68  | | | | | | |            (125), (126), (127), (128), (129), (130), (131), (133),
% 177.16/27.68  | | | | | | |            (135), (136), (137), (140), (142), (143), (145), (146),
% 177.16/27.68  | | | | | | |            (147), (148), (149), (151), (152), (153), (156), (157),
% 177.16/27.68  | | | | | | |            (158), (161), (162), (163), (164), (166), (167), (168),
% 177.16/27.68  | | | | | | |            (169), (170), (173), (175), (178), (179), (180), (181),
% 177.16/27.68  | | | | | | |            (182), (183), (184), (185), (187), (190), (191), (192),
% 177.16/27.68  | | | | | | |            (193), (194), (195), (198), (199), (201), (202), (204),
% 177.16/27.68  | | | | | | |            (206), (328), (352), (355), (357), (358), (362), (363),
% 177.16/27.68  | | | | | | |            (364) are inconsistent by sub-proof #332.
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | End of split
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | End of split
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | Case 2:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | |   (365)  all_34_0 = e1
% 177.16/27.68  | | | | |   (366)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | COMBINE_EQS: (188), (365) imply:
% 177.16/27.68  | | | | |   (367)  all_4_0 = e1
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | SIMP: (367) implies:
% 177.16/27.68  | | | | |   (368)  all_4_0 = e1
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | REDUCE: (87), (368) imply:
% 177.16/27.68  | | | | |   (369)  op(all_4_1, all_4_2) = e1
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | BETA: splitting (159) gives:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | Case 1:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (370)  all_58_15 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REF_CLOSE: (36), (60), (94), (102), (162), (326), (370) are
% 177.16/27.68  | | | | | |            inconsistent by sub-proof #510.
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | Case 2:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (371)   ~ (all_58_15 = e0)
% 177.16/27.68  | | | | | |   (372)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.68  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | ALPHA: (372) implies:
% 177.16/27.68  | | | | | |   (373)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (36), (371) imply:
% 177.16/27.68  | | | | | |   (374)   ~ (all_6_2 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | BETA: splitting (163) gives:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | Case 1:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (375)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.68  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.68  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | BETA: splitting (375) gives:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | Case 1:
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | |   (376)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.68  | | | | | | | |          all_52_6 = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REF_CLOSE: (48), (52), (95), (162), (369), (376) are
% 177.16/27.68  | | | | | | | |            inconsistent by sub-proof #600.
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | Case 2:
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | |   (377)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.16/27.68  | | | | | | | |          all_52_14 = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | ALPHA: (377) implies:
% 177.16/27.68  | | | | | | | |   (378)  all_52_14 = e0
% 177.16/27.68  | | | | | | | |   (379)  all_52_12 = e1
% 177.16/27.68  | | | | | | | |   (380)  all_52_10 = e2
% 177.16/27.68  | | | | | | | |   (381)  all_52_8 = e3
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | COMBINE_EQS: (98), (380) imply:
% 177.16/27.68  | | | | | | | |   (382)  all_10_1 = e2
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (111), (382) imply:
% 177.16/27.68  | | | | | | | |   (383)  op(e2, all_10_2) = all_10_0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (20), (381) imply:
% 177.16/27.68  | | | | | | | |   (384)  op(e3, all_52_9) = e3
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (9), (382) imply:
% 177.16/27.68  | | | | | | | |   (385)  op(e2, all_10_2) = e2
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (59), (379) imply:
% 177.16/27.68  | | | | | | | |   (386)  op(e1, all_52_13) = e1
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (135), (378) imply:
% 177.16/27.68  | | | | | | | |   (387)  op(e0, all_52_15) = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (11), (12), (13), (14),
% 177.16/27.68  | | | | | | | |            (16), (17), (18), (23), (26), (27), (28), (29), (33),
% 177.16/27.68  | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 177.16/27.68  | | | | | | | |            (43), (44), (46), (47), (48), (49), (50), (51), (52),
% 177.16/27.68  | | | | | | | |            (53), (54), (55), (56), (58), (61), (65), (66), (67),
% 177.16/27.68  | | | | | | | |            (69), (70), (71), (73), (74), (78), (79), (80), (81),
% 177.16/27.68  | | | | | | | |            (82), (83), (88), (90), (91), (93), (94), (97),
% 177.16/27.68  | | | | | | | |            (101), (102), (106), (108), (109), (110), (112),
% 177.16/27.68  | | | | | | | |            (113), (114), (116), (119), (122), (124), (125),
% 177.16/27.68  | | | | | | | |            (126), (127), (128), (129), (130), (131), (133),
% 177.16/27.68  | | | | | | | |            (136), (137), (140), (142), (143), (145), (146),
% 177.16/27.68  | | | | | | | |            (148), (149), (152), (153), (156), (157), (158),
% 177.16/27.68  | | | | | | | |            (161), (162), (164), (165), (166), (167), (168),
% 177.16/27.68  | | | | | | | |            (175), (178), (180), (181), (183), (184), (185),
% 177.16/27.68  | | | | | | | |            (187), (190), (191), (192), (193), (194), (195),
% 177.16/27.68  | | | | | | | |            (198), (199), (204), (366), (369), (373), (374),
% 177.16/27.68  | | | | | | | |            (383), (384), (385), (386), (387) are inconsistent by
% 177.16/27.68  | | | | | | | |            sub-proof #328.
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | End of split
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | Case 2:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (388)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.68  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.68  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REF_CLOSE: (48), (94), (102), (162), (179), (182), (184), (202),
% 177.16/27.68  | | | | | | |            (326), (388) are inconsistent by sub-proof #326.
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | End of split
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | End of split
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | End of split
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | End of split
% 177.16/27.68  | | | 
% 177.16/27.68  | | Case 2:
% 177.16/27.68  | | | 
% 177.16/27.68  | | |   (389)  all_26_0 = e2
% 177.16/27.68  | | |   (390)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.16/27.68  | | | 
% 177.16/27.68  | | | COMBINE_EQS: (155), (389) imply:
% 177.16/27.68  | | |   (391)  all_4_0 = e2
% 177.16/27.68  | | | 
% 177.16/27.68  | | | SIMP: (391) implies:
% 177.16/27.68  | | |   (392)  all_4_0 = e2
% 177.16/27.68  | | | 
% 177.16/27.68  | | | COMBINE_EQS: (62), (392) imply:
% 177.16/27.68  | | |   (393)  all_50_0 = e2
% 177.16/27.68  | | | 
% 177.16/27.68  | | | REDUCE: (87), (392) imply:
% 177.16/27.68  | | |   (394)  op(all_4_1, all_4_2) = e2
% 177.16/27.68  | | | 
% 177.16/27.68  | | | BETA: splitting (186) gives:
% 177.16/27.68  | | | 
% 177.16/27.68  | | | Case 1:
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | |   (395)   ~ (all_28_0 = e3)
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | REDUCE: (197), (395) imply:
% 177.16/27.68  | | | |   (396)   ~ (all_6_0 = e3)
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | BETA: splitting (139) gives:
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | Case 1:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | |   (397)   ~ (all_50_0 = e2)
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | REDUCE: (393), (397) imply:
% 177.16/27.68  | | | | |   (398)  $false
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | CLOSE: (398) is inconsistent.
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | Case 2:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | |   (399)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | BETA: splitting (159) gives:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | Case 1:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (400)  all_58_15 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | COMBINE_EQS: (36), (400) imply:
% 177.16/27.68  | | | | | |   (401)  all_6_2 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (43), (401) imply:
% 177.16/27.68  | | | | | |   (402)   ~ (all_52_15 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (149), (401) imply:
% 177.16/27.68  | | | | | |   (403)   ~ (all_52_25 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (166), (401) imply:
% 177.16/27.68  | | | | | |   (404)   ~ (all_52_27 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (142), (401) imply:
% 177.16/27.68  | | | | | |   (405)   ~ (all_52_29 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (92), (401) imply:
% 177.16/27.68  | | | | | |   (406)  op(all_6_1, e0) = all_6_0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (94), (401) imply:
% 177.16/27.68  | | | | | |   (407)  op(e0, e0) = all_6_1
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (60), (401) imply:
% 177.16/27.68  | | | | | |   (408)  op(e0, e0) = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.16/27.68  | | | | | |              simplifying with (407), (408) gives:
% 177.16/27.68  | | | | | |   (409)  all_6_1 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (406), (409) imply:
% 177.16/27.68  | | | | | |   (410)  op(e0, e0) = all_6_0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.16/27.68  | | | | | |              simplifying with (408), (410) gives:
% 177.16/27.68  | | | | | |   (411)  all_6_0 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (396), (411) imply:
% 177.16/27.68  | | | | | |   (412)   ~ (e3 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (141), (411) imply:
% 177.16/27.68  | | | | | |   (413)   ~ (e2 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | SIMP: (413) implies:
% 177.16/27.68  | | | | | |   (414)   ~ (e2 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (177), (411) imply:
% 177.16/27.68  | | | | | |   (415)   ~ (e1 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | BETA: splitting (163) gives:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | Case 1:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (416)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.68  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.68  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REF_CLOSE: (2), (6), (8), (9), (11), (12), (13), (14), (15), (20),
% 177.16/27.68  | | | | | | |            (23), (26), (27), (32), (33), (37), (38), (39), (41),
% 177.16/27.68  | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52), (54),
% 177.16/27.68  | | | | | | |            (55), (56), (57), (58), (59), (61), (67), (68), (70),
% 177.16/27.68  | | | | | | |            (73), (74), (79), (81), (82), (84), (85), (91), (93),
% 177.16/27.68  | | | | | | |            (95), (98), (99), (101), (102), (106), (107), (109),
% 177.16/27.68  | | | | | | |            (110), (111), (115), (116), (122), (124), (125), (128),
% 177.16/27.68  | | | | | | |            (130), (131), (133), (135), (136), (137), (143), (144),
% 177.16/27.68  | | | | | | |            (146), (148), (151), (153), (154), (158), (161), (162),
% 177.16/27.68  | | | | | | |            (164), (168), (170), (172), (175), (176), (178), (180),
% 177.16/27.68  | | | | | | |            (181), (183), (185), (187), (191), (193), (195), (198),
% 177.16/27.68  | | | | | | |            (199), (204), (394), (400), (402), (403), (404), (405),
% 177.16/27.68  | | | | | | |            (414), (416) are inconsistent by sub-proof #325.
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | Case 2:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (417)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.68  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.68  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REF_CLOSE: (12), (13), (14), (15), (27), (35), (37), (38), (40),
% 177.16/27.68  | | | | | | |            (44), (48), (52), (55), (58), (61), (67), (73), (74),
% 177.16/27.68  | | | | | | |            (77), (81), (91), (102), (107), (115), (116), (119),
% 177.16/27.68  | | | | | | |            (129), (134), (146), (151), (153), (156), (157), (158),
% 177.16/27.68  | | | | | | |            (161), (162), (164), (178), (179), (183), (184), (187),
% 177.16/27.68  | | | | | | |            (198), (199), (201), (202), (390), (394), (400), (403),
% 177.16/27.68  | | | | | | |            (414), (417) are inconsistent by sub-proof #324.
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | End of split
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | Case 2:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (418)   ~ (all_58_15 = e0)
% 177.16/27.68  | | | | | |   (419)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.68  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | ALPHA: (419) implies:
% 177.16/27.68  | | | | | |   (420)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.16/27.68  | | | | | |   (421)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (36), (418) imply:
% 177.16/27.68  | | | | | |   (422)   ~ (all_6_2 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | BETA: splitting (163) gives:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | Case 1:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (423)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.68  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.68  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | BETA: splitting (423) gives:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | Case 1:
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | |   (424)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.68  | | | | | | | |          all_52_6 = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REF_CLOSE: (52), (67), (95), (162), (394), (424) are
% 177.16/27.68  | | | | | | | |            inconsistent by sub-proof #494.
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | Case 2:
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | |   (425)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.16/27.68  | | | | | | | |          all_52_14 = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | ALPHA: (425) implies:
% 177.16/27.68  | | | | | | | |   (426)  all_52_14 = e0
% 177.16/27.68  | | | | | | | |   (427)  all_52_12 = e1
% 177.16/27.68  | | | | | | | |   (428)  all_52_10 = e2
% 177.16/27.68  | | | | | | | |   (429)  all_52_8 = e3
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | COMBINE_EQS: (98), (428) imply:
% 177.16/27.68  | | | | | | | |   (430)  all_10_1 = e2
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (111), (430) imply:
% 177.16/27.68  | | | | | | | |   (431)  op(e2, all_10_2) = all_10_0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (20), (429) imply:
% 177.16/27.68  | | | | | | | |   (432)  op(e3, all_52_9) = e3
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (9), (430) imply:
% 177.16/27.68  | | | | | | | |   (433)  op(e2, all_10_2) = e2
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (59), (427) imply:
% 177.16/27.68  | | | | | | | |   (434)  op(e1, all_52_13) = e1
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REDUCE: (135), (426) imply:
% 177.16/27.68  | | | | | | | |   (435)  op(e0, all_52_15) = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (12), (13),
% 177.16/27.68  | | | | | | | |            (14), (15), (16), (17), (18), (21), (23), (25), (26),
% 177.16/27.68  | | | | | | | |            (27), (28), (29), (30), (33), (34), (35), (36), (37),
% 177.16/27.68  | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 177.16/27.68  | | | | | | | |            (48), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.16/27.68  | | | | | | | |            (58), (61), (64), (65), (66), (67), (69), (70), (71),
% 177.16/27.68  | | | | | | | |            (73), (74), (77), (78), (79), (80), (81), (82), (83),
% 177.16/27.68  | | | | | | | |            (88), (90), (91), (93), (96), (97), (101), (102),
% 177.16/27.68  | | | | | | | |            (106), (108), (109), (110), (112), (113), (114),
% 177.16/27.68  | | | | | | | |            (116), (118), (119), (120), (121), (122), (124),
% 177.16/27.68  | | | | | | | |            (125), (126), (127), (128), (129), (130), (131),
% 177.16/27.68  | | | | | | | |            (133), (134), (136), (137), (140), (142), (143),
% 177.16/27.68  | | | | | | | |            (145), (146), (148), (149), (150), (153), (156),
% 177.16/27.68  | | | | | | | |            (157), (158), (160), (161), (162), (164), (166),
% 177.16/27.68  | | | | | | | |            (167), (168), (173), (175), (176), (178), (180),
% 177.16/27.68  | | | | | | | |            (181), (183), (184), (185), (187), (190), (191),
% 177.16/27.68  | | | | | | | |            (192), (193), (194), (195), (198), (199), (202),
% 177.16/27.68  | | | | | | | |            (204), (390), (394), (399), (421), (422), (431),
% 177.16/27.68  | | | | | | | |            (432), (433), (434), (435) are inconsistent by
% 177.16/27.68  | | | | | | | |            sub-proof #323.
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | End of split
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | Case 2:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (436)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.68  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.68  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REF_CLOSE: (4), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 177.16/27.68  | | | | | | |            (20), (21), (24), (26), (27), (28), (29), (32), (33),
% 177.16/27.68  | | | | | | |            (35), (36), (39), (40), (41), (44), (45), (46), (48),
% 177.16/27.68  | | | | | | |            (50), (51), (52), (53), (55), (56), (57), (58), (61),
% 177.16/27.68  | | | | | | |            (64), (67), (69), (70), (73), (74), (77), (79), (81),
% 177.16/27.68  | | | | | | |            (82), (84), (91), (92), (93), (94), (96), (97), (99),
% 177.16/27.68  | | | | | | |            (104), (107), (115), (116), (119), (122), (124), (125),
% 177.16/27.68  | | | | | | |            (129), (130), (134), (141), (142), (143), (146), (149),
% 177.16/27.68  | | | | | | |            (151), (153), (156), (157), (158), (161), (162), (164),
% 177.16/27.68  | | | | | | |            (167), (177), (178), (179), (180), (181), (182), (183),
% 177.16/27.68  | | | | | | |            (184), (185), (187), (192), (198), (199), (201), (202),
% 177.16/27.68  | | | | | | |            (390), (394), (396), (399), (420), (422), (436) are
% 177.16/27.68  | | | | | | |            inconsistent by sub-proof #322.
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | End of split
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | End of split
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | End of split
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | Case 2:
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | |   (437)  all_28_0 = e3
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | COMBINE_EQS: (197), (437) imply:
% 177.16/27.68  | | | |   (438)  all_6_0 = e3
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | SIMP: (438) implies:
% 177.16/27.68  | | | |   (439)  all_6_0 = e3
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | REDUCE: (92), (439) imply:
% 177.16/27.68  | | | |   (440)  op(all_6_1, all_6_2) = e3
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | BETA: splitting (139) gives:
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | Case 1:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | |   (441)   ~ (all_50_0 = e2)
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | REDUCE: (393), (441) imply:
% 177.16/27.68  | | | | |   (442)  $false
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | CLOSE: (442) is inconsistent.
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | Case 2:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | |   (443)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | BETA: splitting (159) gives:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | Case 1:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (444)  all_58_15 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REF_CLOSE: (36), (60), (94), (102), (162), (440), (444) are
% 177.16/27.68  | | | | | |            inconsistent by sub-proof #510.
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | Case 2:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (445)   ~ (all_58_15 = e0)
% 177.16/27.68  | | | | | |   (446)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.68  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | ALPHA: (446) implies:
% 177.16/27.68  | | | | | |   (447)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (36), (445) imply:
% 177.16/27.68  | | | | | |   (448)   ~ (all_6_2 = e0)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | BETA: splitting (163) gives:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | Case 1:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (449)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.68  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.68  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12),
% 177.16/27.68  | | | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (23),
% 177.16/27.68  | | | | | | |            (25), (26), (27), (28), (29), (30), (33), (34), (35),
% 177.16/27.68  | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 177.16/27.68  | | | | | | |            (46), (47), (48), (50), (51), (52), (53), (54), (55),
% 177.16/27.68  | | | | | | |            (56), (57), (58), (59), (61), (64), (65), (66), (67),
% 177.16/27.68  | | | | | | |            (69), (70), (71), (73), (74), (77), (78), (79), (80),
% 177.16/27.68  | | | | | | |            (81), (82), (83), (88), (90), (91), (93), (95), (96),
% 177.16/27.68  | | | | | | |            (97), (98), (101), (102), (106), (108), (109), (110),
% 177.16/27.68  | | | | | | |            (111), (112), (113), (114), (116), (118), (119), (120),
% 177.16/27.68  | | | | | | |            (121), (122), (124), (125), (126), (127), (128), (129),
% 177.16/27.68  | | | | | | |            (130), (131), (133), (134), (135), (136), (137), (140),
% 177.16/27.68  | | | | | | |            (142), (143), (145), (146), (148), (149), (150), (153),
% 177.16/27.68  | | | | | | |            (156), (157), (158), (160), (161), (162), (164), (166),
% 177.16/27.68  | | | | | | |            (167), (168), (173), (175), (176), (178), (180), (181),
% 177.16/27.68  | | | | | | |            (183), (184), (185), (187), (190), (191), (192), (193),
% 177.16/27.68  | | | | | | |            (194), (195), (198), (199), (202), (204), (390), (394),
% 177.16/27.68  | | | | | | |            (443), (447), (448), (449) are inconsistent by
% 177.16/27.68  | | | | | | |            sub-proof #321.
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | Case 2:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (450)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.68  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.68  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | BETA: splitting (450) gives:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | Case 1:
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | |   (451)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.68  | | | | | | | |          all_52_22 = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REF_CLOSE: (48), (162), (179), (184), (202), (451) are
% 177.16/27.68  | | | | | | | |            inconsistent by sub-proof #343.
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | Case 2:
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | |   (452)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.16/27.68  | | | | | | | |          all_52_30 = e0
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | | REF_CLOSE: (94), (102), (162), (182), (440), (452) are
% 177.16/27.68  | | | | | | | |            inconsistent by sub-proof #501.
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | End of split
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | End of split
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | End of split
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | End of split
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | End of split
% 177.16/27.68  | | | 
% 177.16/27.68  | | End of split
% 177.16/27.68  | | 
% 177.16/27.68  | Case 2:
% 177.16/27.68  | | 
% 177.16/27.68  | |   (453)  all_24_0 = e1
% 177.16/27.68  | | 
% 177.16/27.68  | | COMBINE_EQS: (75), (453) imply:
% 177.16/27.68  | |   (454)  all_10_0 = e1
% 177.16/27.68  | | 
% 177.16/27.68  | | REDUCE: (168), (454) imply:
% 177.16/27.68  | |   (455)   ~ (e3 = e1)
% 177.16/27.68  | | 
% 177.16/27.68  | | REDUCE: (111), (454) imply:
% 177.16/27.68  | |   (456)  op(all_10_1, all_10_2) = e1
% 177.16/27.68  | | 
% 177.16/27.68  | | BETA: splitting (189) gives:
% 177.16/27.68  | | 
% 177.16/27.68  | | Case 1:
% 177.16/27.68  | | | 
% 177.16/27.68  | | |   (457)   ~ (all_26_0 = e2)
% 177.16/27.68  | | | 
% 177.16/27.68  | | | REDUCE: (155), (457) imply:
% 177.16/27.68  | | |   (458)   ~ (all_4_0 = e2)
% 177.16/27.68  | | | 
% 177.16/27.68  | | | BETA: splitting (186) gives:
% 177.16/27.68  | | | 
% 177.16/27.68  | | | Case 1:
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | |   (459)   ~ (all_28_0 = e3)
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | REDUCE: (197), (459) imply:
% 177.16/27.68  | | | |   (460)   ~ (all_6_0 = e3)
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | BETA: splitting (138) gives:
% 177.16/27.68  | | | | 
% 177.16/27.68  | | | | Case 1:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | |   (461)   ~ (all_34_0 = e1)
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | REDUCE: (188), (461) imply:
% 177.16/27.68  | | | | |   (462)   ~ (all_4_0 = e1)
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | BETA: splitting (171) gives:
% 177.16/27.68  | | | | | 
% 177.16/27.68  | | | | | Case 1:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | |   (463)   ~ (all_40_1 = e1)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | REDUCE: (76), (463) imply:
% 177.16/27.68  | | | | | |   (464)   ~ (all_4_1 = e1)
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | BETA: splitting (159) gives:
% 177.16/27.68  | | | | | | 
% 177.16/27.68  | | | | | | Case 1:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | |   (465)  all_58_15 = e0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | COMBINE_EQS: (36), (465) imply:
% 177.16/27.68  | | | | | | |   (466)  all_6_2 = e0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (167), (466) imply:
% 177.16/27.68  | | | | | | |   (467)   ~ (all_52_7 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (140), (466) imply:
% 177.16/27.68  | | | | | | |   (468)   ~ (all_52_23 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (149), (466) imply:
% 177.16/27.68  | | | | | | |   (469)   ~ (all_52_25 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (166), (466) imply:
% 177.16/27.68  | | | | | | |   (470)   ~ (all_52_27 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (142), (466) imply:
% 177.16/27.68  | | | | | | |   (471)   ~ (all_52_29 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (92), (466) imply:
% 177.16/27.68  | | | | | | |   (472)  op(all_6_1, e0) = all_6_0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (94), (466) imply:
% 177.16/27.68  | | | | | | |   (473)  op(e0, e0) = all_6_1
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (60), (466) imply:
% 177.16/27.68  | | | | | | |   (474)  op(e0, e0) = e0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.16/27.68  | | | | | | |              simplifying with (473), (474) gives:
% 177.16/27.68  | | | | | | |   (475)  all_6_1 = e0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (472), (475) imply:
% 177.16/27.68  | | | | | | |   (476)  op(e0, e0) = all_6_0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.16/27.68  | | | | | | |              simplifying with (474), (476) gives:
% 177.16/27.68  | | | | | | |   (477)  all_6_0 = e0
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (460), (477) imply:
% 177.16/27.68  | | | | | | |   (478)   ~ (e3 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | REDUCE: (177), (477) imply:
% 177.16/27.68  | | | | | | |   (479)   ~ (e1 = e0)
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | BETA: splitting (163) gives:
% 177.16/27.68  | | | | | | | 
% 177.16/27.68  | | | | | | | Case 1:
% 177.16/27.68  | | | | | | | | 
% 177.16/27.68  | | | | | | | |   (480)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.68  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.16/27.68  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.16/27.68  | | | | | | | | 
% 177.16/27.69  | | | | | | | | REF_CLOSE: (9), (12), (13), (32), (35), (36), (38), (39), (45),
% 177.16/27.69  | | | | | | | |            (46), (52), (55), (56), (58), (70), (73), (74), (79),
% 177.16/27.69  | | | | | | | |            (81), (84), (87), (93), (95), (98), (99), (102),
% 177.16/27.69  | | | | | | | |            (107), (112), (115), (116), (119), (125), (129),
% 177.16/27.69  | | | | | | | |            (130), (133), (144), (146), (147), (151), (156),
% 177.16/27.69  | | | | | | | |            (162), (164), (167), (175), (181), (183), (185),
% 177.16/27.69  | | | | | | | |            (187), (191), (196), (199), (456), (465), (467),
% 177.16/27.69  | | | | | | | |            (469), (470), (471), (480) are inconsistent by
% 177.16/27.69  | | | | | | | |            sub-proof #439.
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | Case 2:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | |   (481)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (11), (12), (13), (14),
% 177.16/27.69  | | | | | | | |            (15), (16), (18), (20), (24), (27), (32), (33), (35),
% 177.16/27.69  | | | | | | | |            (37), (38), (40), (41), (44), (46), (48), (50), (52),
% 177.16/27.69  | | | | | | | |            (55), (56), (58), (61), (67), (68), (73), (74), (79),
% 177.16/27.69  | | | | | | | |            (80), (81), (82), (85), (88), (91), (96), (97), (99),
% 177.16/27.69  | | | | | | | |            (102), (104), (107), (112), (115), (116), (120),
% 177.16/27.69  | | | | | | | |            (121), (122), (124), (125), (128), (129), (130),
% 177.16/27.69  | | | | | | | |            (136), (137), (143), (144), (146), (150), (153),
% 177.16/27.69  | | | | | | | |            (156), (157), (158), (160), (161), (162), (164),
% 177.16/27.69  | | | | | | | |            (178), (179), (183), (184), (185), (187), (198),
% 177.16/27.69  | | | | | | | |            (199), (202), (464), (465), (468), (469), (471),
% 177.16/27.69  | | | | | | | |            (481) are inconsistent by sub-proof #320.
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | End of split
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | Case 2:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (482)   ~ (all_58_15 = e0)
% 177.16/27.69  | | | | | | |   (483)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.69  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | ALPHA: (483) implies:
% 177.16/27.69  | | | | | | |   (484)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.16/27.69  | | | | | | |   (485)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (36), (482) imply:
% 177.16/27.69  | | | | | | |   (486)   ~ (all_6_2 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | BETA: splitting (163) gives:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | Case 1:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | |   (487)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.69  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.16/27.69  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | BETA: splitting (487) gives:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | Case 1:
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | |   (488)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.69  | | | | | | | | |          all_52_6 = e0
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | ALPHA: (488) implies:
% 177.16/27.69  | | | | | | | | |   (489)  all_52_6 = e0
% 177.16/27.69  | | | | | | | | |   (490)  all_52_4 = e1
% 177.16/27.69  | | | | | | | | |   (491)  all_52_2 = e2
% 177.16/27.69  | | | | | | | | |   (492)  all_52_0 = e3
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | COMBINE_EQS: (95), (492) imply:
% 177.16/27.69  | | | | | | | | |   (493)  all_4_1 = e3
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REDUCE: (87), (493) imply:
% 177.16/27.69  | | | | | | | | |   (494)  op(e3, all_4_2) = all_4_0
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REDUCE: (52), (493) imply:
% 177.16/27.69  | | | | | | | | |   (495)  op(e3, all_4_2) = e3
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REDUCE: (117), (491) imply:
% 177.16/27.69  | | | | | | | | |   (496)  op(e2, all_52_3) = e2
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REDUCE: (63), (490) imply:
% 177.16/27.69  | | | | | | | | |   (497)  op(e1, all_52_5) = e1
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REDUCE: (196), (489) imply:
% 177.16/27.69  | | | | | | | | |   (498)  op(e0, all_52_7) = e0
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 177.16/27.69  | | | | | | | | |            (12), (13), (14), (16), (17), (18), (19), (23),
% 177.16/27.69  | | | | | | | | |            (24), (26), (27), (28), (29), (30), (32), (33),
% 177.16/27.69  | | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41),
% 177.16/27.69  | | | | | | | | |            (42), (43), (44), (45), (46), (47), (50), (51),
% 177.16/27.69  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (60), (61),
% 177.16/27.69  | | | | | | | | |            (65), (66), (68), (69), (70), (72), (73), (74),
% 177.16/27.69  | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 177.16/27.69  | | | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (96),
% 177.16/27.69  | | | | | | | | |            (99), (100), (101), (102), (104), (106), (107),
% 177.16/27.69  | | | | | | | | |            (108), (109), (110), (112), (113), (114), (115),
% 177.16/27.69  | | | | | | | | |            (116), (119), (121), (122), (124), (125), (126),
% 177.16/27.69  | | | | | | | | |            (128), (129), (130), (131), (132), (133), (135),
% 177.16/27.69  | | | | | | | | |            (136), (137), (140), (142), (143), (144), (145),
% 177.16/27.69  | | | | | | | | |            (146), (147), (148), (149), (151), (152), (153),
% 177.16/27.69  | | | | | | | | |            (154), (156), (157), (160), (161), (162), (164),
% 177.16/27.69  | | | | | | | | |            (166), (167), (170), (172), (175), (176), (177),
% 177.16/27.69  | | | | | | | | |            (178), (180), (181), (183), (184), (185), (187),
% 177.16/27.69  | | | | | | | | |            (191), (192), (193), (194), (195), (198), (199),
% 177.16/27.69  | | | | | | | | |            (202), (458), (462), (485), (486), (494), (495),
% 177.16/27.69  | | | | | | | | |            (496), (497), (498) are inconsistent by sub-proof
% 177.16/27.69  | | | | | | | | |            #341.
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | Case 2:
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | |   (499)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.16/27.69  | | | | | | | | |          all_52_14 = e0
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | ALPHA: (499) implies:
% 177.16/27.69  | | | | | | | | |   (500)  all_52_10 = e2
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | COMBINE_EQS: (98), (500) imply:
% 177.16/27.69  | | | | | | | | |   (501)  all_10_1 = e2
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REF_CLOSE: (9), (147), (162), (456), (501) are inconsistent by
% 177.16/27.69  | | | | | | | | |            sub-proof #446.
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | End of split
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | Case 2:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | |   (502)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (11), (13), (14), (15), (16),
% 177.16/27.69  | | | | | | | |            (17), (19), (20), (24), (26), (27), (28), (29), (32),
% 177.16/27.69  | | | | | | | |            (33), (35), (36), (37), (38), (39), (40), (41), (44),
% 177.16/27.69  | | | | | | | |            (45), (46), (47), (48), (50), (51), (52), (53), (54),
% 177.16/27.69  | | | | | | | |            (55), (56), (57), (58), (61), (68), (69), (70), (73),
% 177.16/27.69  | | | | | | | |            (74), (78), (79), (81), (82), (84), (85), (87), (90),
% 177.16/27.69  | | | | | | | |            (91), (92), (93), (94), (96), (97), (99), (101),
% 177.16/27.69  | | | | | | | |            (104), (106), (107), (112), (113), (114), (115),
% 177.16/27.69  | | | | | | | |            (116), (119), (121), (122), (124), (125), (129),
% 177.16/27.69  | | | | | | | |            (130), (131), (133), (137), (140), (141), (142),
% 177.16/27.69  | | | | | | | |            (143), (145), (146), (147), (149), (151), (153),
% 177.16/27.69  | | | | | | | |            (154), (156), (157), (158), (161), (162), (164),
% 177.16/27.69  | | | | | | | |            (166), (167), (169), (170), (172), (175), (177),
% 177.16/27.69  | | | | | | | |            (178), (179), (180), (181), (182), (184), (185),
% 177.16/27.69  | | | | | | | |            (187), (191), (192), (193), (194), (198), (199),
% 177.16/27.69  | | | | | | | |            (201), (202), (458), (460), (462), (484), (485),
% 177.16/27.69  | | | | | | | |            (486), (502) are inconsistent by sub-proof #319.
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | End of split
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | End of split
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | Case 2:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | |   (503)  all_40_1 = e1
% 177.16/27.69  | | | | | |   (504)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | COMBINE_EQS: (76), (503) imply:
% 177.16/27.69  | | | | | |   (505)  all_4_1 = e1
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | COMBINE_EQS: (95), (505) imply:
% 177.16/27.69  | | | | | |   (506)  all_52_0 = e1
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (67), (505) imply:
% 177.16/27.69  | | | | | |   (507)   ~ (e2 = e1)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (87), (505) imply:
% 177.16/27.69  | | | | | |   (508)  op(e1, all_4_2) = all_4_0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (52), (505) imply:
% 177.16/27.69  | | | | | |   (509)  op(e3, all_4_2) = e1
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | BETA: splitting (159) gives:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | Case 1:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (510)  all_58_15 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | COMBINE_EQS: (36), (510) imply:
% 177.16/27.69  | | | | | | |   (511)  all_6_2 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (167), (511) imply:
% 177.16/27.69  | | | | | | |   (512)   ~ (all_52_7 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (149), (511) imply:
% 177.16/27.69  | | | | | | |   (513)   ~ (all_52_25 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (142), (511) imply:
% 177.16/27.69  | | | | | | |   (514)   ~ (all_52_29 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (92), (511) imply:
% 177.16/27.69  | | | | | | |   (515)  op(all_6_1, e0) = all_6_0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (94), (511) imply:
% 177.16/27.69  | | | | | | |   (516)  op(e0, e0) = all_6_1
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (60), (511) imply:
% 177.16/27.69  | | | | | | |   (517)  op(e0, e0) = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.16/27.69  | | | | | | |              simplifying with (516), (517) gives:
% 177.16/27.69  | | | | | | |   (518)  all_6_1 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (515), (518) imply:
% 177.16/27.69  | | | | | | |   (519)  op(e0, e0) = all_6_0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.16/27.69  | | | | | | |              simplifying with (517), (519) gives:
% 177.16/27.69  | | | | | | |   (520)  all_6_0 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (460), (520) imply:
% 177.16/27.69  | | | | | | |   (521)   ~ (e3 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (177), (520) imply:
% 177.16/27.69  | | | | | | |   (522)   ~ (e1 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | BETA: splitting (163) gives:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | Case 1:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | |   (523)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.69  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.16/27.69  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | REF_CLOSE: (9), (48), (98), (147), (162), (456), (506), (523)
% 177.16/27.69  | | | | | | | |            are inconsistent by sub-proof #445.
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | Case 2:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | |   (524)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | REF_CLOSE: (4), (10), (12), (13), (14), (15), (18), (26), (27),
% 177.16/27.69  | | | | | | | |            (34), (35), (37), (38), (40), (41), (44), (46), (48),
% 177.16/27.69  | | | | | | | |            (50), (51), (58), (61), (66), (68), (69), (73), (74),
% 177.16/27.69  | | | | | | | |            (80), (81), (82), (85), (90), (91), (97), (99),
% 177.16/27.69  | | | | | | | |            (102), (103), (107), (114), (115), (116), (121),
% 177.16/27.69  | | | | | | | |            (122), (124), (125), (128), (129), (130), (131),
% 177.16/27.69  | | | | | | | |            (136), (144), (146), (151), (153), (156), (157),
% 177.16/27.69  | | | | | | | |            (158), (162), (164), (178), (179), (183), (184),
% 177.16/27.69  | | | | | | | |            (185), (187), (198), (199), (202), (458), (504),
% 177.16/27.69  | | | | | | | |            (508), (509), (510), (512), (513), (514), (524) are
% 177.16/27.69  | | | | | | | |            inconsistent by sub-proof #336.
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | End of split
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | Case 2:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (525)   ~ (all_58_15 = e0)
% 177.16/27.69  | | | | | | |   (526)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.69  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | ALPHA: (526) implies:
% 177.16/27.69  | | | | | | |   (527)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.16/27.69  | | | | | | |   (528)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REDUCE: (36), (525) imply:
% 177.16/27.69  | | | | | | |   (529)   ~ (all_6_2 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | BETA: splitting (163) gives:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | Case 1:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | |   (530)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.16/27.69  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.16/27.69  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | REF_CLOSE: (9), (48), (98), (147), (162), (456), (506), (530)
% 177.16/27.69  | | | | | | | |            are inconsistent by sub-proof #445.
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | Case 2:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | |   (531)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | BETA: splitting (531) gives:
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | | Case 1:
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | |   (532)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | | | |          all_52_22 = e0
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REF_CLOSE: (48), (162), (179), (184), (202), (532) are
% 177.16/27.69  | | | | | | | | |            inconsistent by sub-proof #343.
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | Case 2:
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | |   (533)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.16/27.69  | | | | | | | | |          all_52_30 = e0
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (11), (13), (14), (15),
% 177.16/27.69  | | | | | | | | |            (16), (19), (20), (26), (27), (28), (29), (32),
% 177.16/27.69  | | | | | | | | |            (33), (35), (36), (37), (38), (39), (40), (41),
% 177.16/27.69  | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 177.16/27.69  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (61), (69),
% 177.16/27.69  | | | | | | | | |            (70), (73), (74), (78), (79), (81), (82), (84),
% 177.16/27.69  | | | | | | | | |            (87), (90), (93), (94), (96), (97), (102), (104),
% 177.16/27.69  | | | | | | | | |            (107), (112), (114), (115), (116), (119), (122),
% 177.16/27.69  | | | | | | | | |            (124), (125), (128), (129), (130), (137), (142),
% 177.16/27.69  | | | | | | | | |            (143), (146), (147), (149), (153), (156), (157),
% 177.16/27.69  | | | | | | | | |            (158), (161), (162), (164), (166), (167), (169),
% 177.16/27.69  | | | | | | | | |            (178), (180), (181), (182), (185), (187), (191),
% 177.16/27.69  | | | | | | | | |            (192), (198), (199), (201), (458), (462), (509),
% 177.16/27.69  | | | | | | | | |            (527), (528), (529), (533) are inconsistent by
% 177.16/27.69  | | | | | | | | |            sub-proof #444.
% 177.16/27.69  | | | | | | | | | 
% 177.16/27.69  | | | | | | | | End of split
% 177.16/27.69  | | | | | | | | 
% 177.16/27.69  | | | | | | | End of split
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | End of split
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | End of split
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | Case 2:
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | |   (534)  all_34_0 = e1
% 177.16/27.69  | | | | |   (535)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | COMBINE_EQS: (188), (534) imply:
% 177.16/27.69  | | | | |   (536)  all_4_0 = e1
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | SIMP: (536) implies:
% 177.16/27.69  | | | | |   (537)  all_4_0 = e1
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | REDUCE: (458), (537) imply:
% 177.16/27.69  | | | | |   (538)   ~ (e2 = e1)
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | REDUCE: (87), (537) imply:
% 177.16/27.69  | | | | |   (539)  op(all_4_1, all_4_2) = e1
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | BETA: splitting (159) gives:
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | Case 1:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | |   (540)  all_58_15 = e0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | COMBINE_EQS: (36), (540) imply:
% 177.16/27.69  | | | | | |   (541)  all_6_2 = e0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (149), (541) imply:
% 177.16/27.69  | | | | | |   (542)   ~ (all_52_25 = e0)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (92), (541) imply:
% 177.16/27.69  | | | | | |   (543)  op(all_6_1, e0) = all_6_0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (94), (541) imply:
% 177.16/27.69  | | | | | |   (544)  op(e0, e0) = all_6_1
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (60), (541) imply:
% 177.16/27.69  | | | | | |   (545)  op(e0, e0) = e0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.16/27.69  | | | | | |              simplifying with (544), (545) gives:
% 177.16/27.69  | | | | | |   (546)  all_6_1 = e0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (543), (546) imply:
% 177.16/27.69  | | | | | |   (547)  op(e0, e0) = all_6_0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.16/27.69  | | | | | |              simplifying with (545), (547) gives:
% 177.16/27.69  | | | | | |   (548)  all_6_0 = e0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REDUCE: (460), (548) imply:
% 177.16/27.69  | | | | | |   (549)   ~ (e3 = e0)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | BETA: splitting (163) gives:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | Case 1:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (550)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.69  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.69  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (9), (48), (52), (95), (98), (147), (162), (456),
% 177.16/27.69  | | | | | | |            (539), (550) are inconsistent by sub-proof #441.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | Case 2:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (551)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (12), (13), (14), (15), (18), (29), (35), (48), (49),
% 177.16/27.69  | | | | | | |            (52), (55), (58), (61), (65), (67), (73), (74), (79),
% 177.16/27.69  | | | | | | |            (81), (83), (91), (102), (107), (114), (115), (116),
% 177.16/27.69  | | | | | | |            (129), (131), (153), (156), (157), (158), (161), (162),
% 177.16/27.69  | | | | | | |            (164), (165), (175), (178), (179), (183), (184), (187),
% 177.16/27.69  | | | | | | |            (198), (199), (202), (535), (539), (540), (542), (551)
% 177.16/27.69  | | | | | | |            are inconsistent by sub-proof #329.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | End of split
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | Case 2:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | |   (552)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.16/27.69  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | ALPHA: (552) implies:
% 177.16/27.69  | | | | | |   (553)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | BETA: splitting (163) gives:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | Case 1:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (554)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.69  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.16/27.69  | | | | | | |            e1 & all_52_14 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (9), (48), (52), (95), (98), (147), (162), (456),
% 177.16/27.69  | | | | | | |            (539), (554) are inconsistent by sub-proof #441.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | Case 2:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (555)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (4), (12), (13), (14), (15), (16), (18), (20), (23),
% 177.16/27.69  | | | | | | |            (24), (28), (29), (33), (35), (36), (38), (39), (41),
% 177.16/27.69  | | | | | | |            (44), (45), (46), (48), (49), (50), (52), (53), (55),
% 177.16/27.69  | | | | | | |            (56), (58), (61), (65), (67), (73), (74), (78), (79),
% 177.16/27.69  | | | | | | |            (81), (83), (84), (90), (91), (92), (93), (94), (96),
% 177.16/27.69  | | | | | | |            (99), (104), (113), (114), (116), (119), (124), (125),
% 177.16/27.69  | | | | | | |            (129), (130), (131), (133), (136), (141), (143), (146),
% 177.16/27.69  | | | | | | |            (151), (152), (153), (156), (157), (158), (161), (162),
% 177.16/27.69  | | | | | | |            (164), (165), (167), (170), (175), (177), (178), (179),
% 177.16/27.69  | | | | | | |            (180), (181), (182), (183), (184), (185), (187), (192),
% 177.16/27.69  | | | | | | |            (194), (198), (199), (201), (202), (460), (535), (539),
% 177.16/27.69  | | | | | | |            (553), (555) are inconsistent by sub-proof #318.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | End of split
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | End of split
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | End of split
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | Case 2:
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | |   (556)  all_28_0 = e3
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | | COMBINE_EQS: (197), (556) imply:
% 177.16/27.69  | | | |   (557)  all_6_0 = e3
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | | SIMP: (557) implies:
% 177.16/27.69  | | | |   (558)  all_6_0 = e3
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | | REDUCE: (92), (558) imply:
% 177.16/27.69  | | | |   (559)  op(all_6_1, all_6_2) = e3
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | | BETA: splitting (138) gives:
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | | Case 1:
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | |   (560)   ~ (all_34_0 = e1)
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | REDUCE: (188), (560) imply:
% 177.16/27.69  | | | | |   (561)   ~ (all_4_0 = e1)
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | BETA: splitting (163) gives:
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | Case 1:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | |   (562)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 177.16/27.69  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.16/27.69  | | | | | |            all_52_14 = e0)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | BETA: splitting (562) gives:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | Case 1:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (563)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.16/27.69  | | | | | | |          = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (1), (2), (8), (11), (13), (14), (16), (17), (18),
% 177.16/27.69  | | | | | | |            (19), (23), (26), (27), (28), (29), (30), (32), (33),
% 177.16/27.69  | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 177.16/27.69  | | | | | | |            (44), (45), (46), (47), (50), (51), (52), (53), (54),
% 177.16/27.69  | | | | | | |            (55), (56), (57), (58), (60), (61), (63), (65), (68),
% 177.16/27.69  | | | | | | |            (69), (70), (72), (73), (74), (78), (79), (80), (81),
% 177.16/27.69  | | | | | | |            (82), (83), (85), (87), (89), (90), (91), (93), (94),
% 177.16/27.69  | | | | | | |            (95), (100), (101), (102), (104), (106), (107), (108),
% 177.16/27.69  | | | | | | |            (109), (110), (112), (113), (114), (115), (116), (117),
% 177.16/27.69  | | | | | | |            (119), (121), (122), (124), (125), (126), (128), (129),
% 177.16/27.69  | | | | | | |            (130), (131), (132), (133), (135), (136), (140), (142),
% 177.16/27.69  | | | | | | |            (143), (144), (145), (146), (148), (149), (151), (152),
% 177.16/27.69  | | | | | | |            (153), (154), (156), (157), (159), (161), (162), (164),
% 177.16/27.69  | | | | | | |            (166), (167), (170), (172), (175), (176), (178), (180),
% 177.16/27.69  | | | | | | |            (181), (185), (187), (191), (192), (193), (194), (195),
% 177.16/27.69  | | | | | | |            (196), (198), (199), (458), (559), (561), (563) are
% 177.16/27.69  | | | | | | |            inconsistent by sub-proof #317.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | Case 2:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (564)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.16/27.69  | | | | | | |          all_52_14 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | ALPHA: (564) implies:
% 177.16/27.69  | | | | | | |   (565)  all_52_10 = e2
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | COMBINE_EQS: (98), (565) imply:
% 177.16/27.69  | | | | | | |   (566)  all_10_1 = e2
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (9), (147), (162), (456), (566) are inconsistent by
% 177.16/27.69  | | | | | | |            sub-proof #446.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | End of split
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | Case 2:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | |   (567)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REF_CLOSE: (48), (94), (102), (162), (179), (182), (184), (202),
% 177.16/27.69  | | | | | |            (559), (567) are inconsistent by sub-proof #326.
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | End of split
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | Case 2:
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | |   (568)  all_34_0 = e1
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | COMBINE_EQS: (188), (568) imply:
% 177.16/27.69  | | | | |   (569)  all_4_0 = e1
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | SIMP: (569) implies:
% 177.16/27.69  | | | | |   (570)  all_4_0 = e1
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | REDUCE: (458), (570) imply:
% 177.16/27.69  | | | | |   (571)   ~ (e2 = e1)
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | REDUCE: (87), (570) imply:
% 177.16/27.69  | | | | |   (572)  op(all_4_1, all_4_2) = e1
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | BETA: splitting (163) gives:
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | | Case 1:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | |   (573)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 177.16/27.69  | | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.16/27.69  | | | | | |            all_52_14 = e0)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | REF_CLOSE: (9), (48), (52), (95), (98), (147), (162), (456), (572),
% 177.16/27.69  | | | | | |            (573) are inconsistent by sub-proof #441.
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | Case 2:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | |   (574)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.16/27.69  | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | BETA: splitting (574) gives:
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | | Case 1:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (575)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.16/27.69  | | | | | | |          all_52_22 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (48), (162), (179), (184), (202), (575) are
% 177.16/27.69  | | | | | | |            inconsistent by sub-proof #343.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | Case 2:
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | |   (576)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.16/27.69  | | | | | | |          all_52_30 = e0
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | | REF_CLOSE: (94), (102), (162), (182), (559), (576) are
% 177.16/27.69  | | | | | | |            inconsistent by sub-proof #501.
% 177.16/27.69  | | | | | | | 
% 177.16/27.69  | | | | | | End of split
% 177.16/27.69  | | | | | | 
% 177.16/27.69  | | | | | End of split
% 177.16/27.69  | | | | | 
% 177.16/27.69  | | | | End of split
% 177.16/27.69  | | | | 
% 177.16/27.69  | | | End of split
% 177.16/27.69  | | | 
% 177.19/27.69  | | Case 2:
% 177.19/27.69  | | | 
% 177.19/27.69  | | |   (577)  all_26_0 = e2
% 177.19/27.69  | | |   (578)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.19/27.69  | | | 
% 177.19/27.69  | | | COMBINE_EQS: (155), (577) imply:
% 177.19/27.69  | | |   (579)  all_4_0 = e2
% 177.19/27.69  | | | 
% 177.19/27.69  | | | COMBINE_EQS: (62), (579) imply:
% 177.19/27.69  | | |   (580)  all_50_0 = e2
% 177.19/27.69  | | | 
% 177.19/27.69  | | | REDUCE: (87), (579) imply:
% 177.19/27.69  | | |   (581)  op(all_4_1, all_4_2) = e2
% 177.19/27.69  | | | 
% 177.19/27.69  | | | BETA: splitting (186) gives:
% 177.19/27.69  | | | 
% 177.19/27.69  | | | Case 1:
% 177.19/27.69  | | | | 
% 177.19/27.69  | | | |   (582)   ~ (all_28_0 = e3)
% 177.19/27.69  | | | | 
% 177.19/27.69  | | | | REDUCE: (197), (582) imply:
% 177.19/27.69  | | | |   (583)   ~ (all_6_0 = e3)
% 177.19/27.69  | | | | 
% 177.19/27.69  | | | | BETA: splitting (139) gives:
% 177.19/27.69  | | | | 
% 177.19/27.69  | | | | Case 1:
% 177.19/27.69  | | | | | 
% 177.19/27.69  | | | | |   (584)   ~ (all_50_0 = e2)
% 177.19/27.69  | | | | | 
% 177.19/27.69  | | | | | REDUCE: (580), (584) imply:
% 177.19/27.69  | | | | |   (585)  $false
% 177.19/27.69  | | | | | 
% 177.19/27.69  | | | | | CLOSE: (585) is inconsistent.
% 177.19/27.69  | | | | | 
% 177.19/27.69  | | | | Case 2:
% 177.19/27.69  | | | | | 
% 177.19/27.69  | | | | |   (586)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.19/27.69  | | | | | 
% 177.19/27.69  | | | | | BETA: splitting (159) gives:
% 177.19/27.69  | | | | | 
% 177.19/27.69  | | | | | Case 1:
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | |   (587)  all_58_15 = e0
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | COMBINE_EQS: (36), (587) imply:
% 177.19/27.69  | | | | | |   (588)  all_6_2 = e0
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | REDUCE: (149), (588) imply:
% 177.19/27.69  | | | | | |   (589)   ~ (all_52_25 = e0)
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | REDUCE: (92), (588) imply:
% 177.19/27.69  | | | | | |   (590)  op(all_6_1, e0) = all_6_0
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | REDUCE: (94), (588) imply:
% 177.19/27.69  | | | | | |   (591)  op(e0, e0) = all_6_1
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | REDUCE: (60), (588) imply:
% 177.19/27.69  | | | | | |   (592)  op(e0, e0) = e0
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_1, e0, e0,
% 177.19/27.69  | | | | | |              simplifying with (591), (592) gives:
% 177.19/27.69  | | | | | |   (593)  all_6_1 = e0
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | REDUCE: (590), (593) imply:
% 177.19/27.69  | | | | | |   (594)  op(e0, e0) = all_6_0
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | GROUND_INST: instantiating (162) with e0, all_6_0, e0, e0,
% 177.19/27.69  | | | | | |              simplifying with (592), (594) gives:
% 177.19/27.69  | | | | | |   (595)  all_6_0 = e0
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | REDUCE: (583), (595) imply:
% 177.19/27.69  | | | | | |   (596)   ~ (e3 = e0)
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | REDUCE: (141), (595) imply:
% 177.19/27.69  | | | | | |   (597)   ~ (e2 = e0)
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | SIMP: (597) implies:
% 177.19/27.69  | | | | | |   (598)   ~ (e2 = e0)
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | BETA: splitting (163) gives:
% 177.19/27.69  | | | | | | 
% 177.19/27.69  | | | | | | Case 1:
% 177.19/27.69  | | | | | | | 
% 177.19/27.69  | | | | | | |   (599)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.19/27.69  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.19/27.69  | | | | | | |            e1 & all_52_14 = e0)
% 177.19/27.69  | | | | | | | 
% 177.19/27.69  | | | | | | | REF_CLOSE: (9), (52), (67), (95), (98), (147), (162), (456),
% 177.19/27.69  | | | | | | |            (581), (599) are inconsistent by sub-proof #434.
% 177.19/27.69  | | | | | | | 
% 177.19/27.69  | | | | | | Case 2:
% 177.19/27.69  | | | | | | | 
% 177.19/27.69  | | | | | | |   (600)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.19/27.69  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.19/27.69  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.19/27.69  | | | | | | | 
% 177.19/27.69  | | | | | | | REF_CLOSE: (12), (13), (14), (15), (27), (35), (37), (38), (40),
% 177.19/27.69  | | | | | | |            (44), (48), (52), (55), (58), (61), (67), (73), (74),
% 177.19/27.69  | | | | | | |            (77), (81), (91), (102), (107), (115), (116), (119),
% 177.19/27.70  | | | | | | |            (129), (134), (146), (151), (153), (156), (157), (158),
% 177.19/27.70  | | | | | | |            (161), (162), (164), (178), (179), (183), (184), (187),
% 177.19/27.70  | | | | | | |            (198), (199), (201), (202), (578), (581), (587), (589),
% 177.19/27.70  | | | | | | |            (598), (600) are inconsistent by sub-proof #324.
% 177.19/27.70  | | | | | | | 
% 177.19/27.70  | | | | | | End of split
% 177.19/27.70  | | | | | | 
% 177.19/27.70  | | | | | Case 2:
% 177.19/27.70  | | | | | | 
% 177.19/27.70  | | | | | |   (601)   ~ (all_58_15 = e0)
% 177.19/27.70  | | | | | |   (602)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.19/27.70  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.19/27.70  | | | | | | 
% 177.19/27.70  | | | | | | ALPHA: (602) implies:
% 177.19/27.70  | | | | | |   (603)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.19/27.70  | | | | | | 
% 177.19/27.70  | | | | | | REDUCE: (36), (601) imply:
% 177.19/27.70  | | | | | |   (604)   ~ (all_6_2 = e0)
% 177.19/27.70  | | | | | | 
% 177.19/27.70  | | | | | | BETA: splitting (163) gives:
% 177.19/27.70  | | | | | | 
% 177.19/27.70  | | | | | | Case 1:
% 177.19/27.70  | | | | | | | 
% 177.19/27.70  | | | | | | |   (605)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.19/27.70  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.19/27.70  | | | | | | |            e1 & all_52_14 = e0)
% 177.19/27.70  | | | | | | | 
% 177.19/27.70  | | | | | | | REF_CLOSE: (9), (52), (67), (95), (98), (147), (162), (456),
% 177.19/27.70  | | | | | | |            (581), (605) are inconsistent by sub-proof #434.
% 177.19/27.70  | | | | | | | 
% 177.19/27.70  | | | | | | Case 2:
% 177.19/27.70  | | | | | | | 
% 177.19/27.70  | | | | | | |   (606)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.19/27.70  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.19/27.70  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.19/27.70  | | | | | | | 
% 177.19/27.70  | | | | | | | REF_CLOSE: (4), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 177.19/27.70  | | | | | | |            (20), (21), (24), (26), (27), (28), (29), (32), (33),
% 177.19/27.70  | | | | | | |            (35), (36), (39), (40), (41), (44), (45), (46), (48),
% 177.19/27.70  | | | | | | |            (50), (51), (52), (53), (55), (56), (57), (58), (61),
% 177.19/27.70  | | | | | | |            (64), (67), (69), (70), (73), (74), (77), (79), (81),
% 177.19/27.70  | | | | | | |            (82), (84), (91), (92), (93), (94), (96), (97), (99),
% 177.19/27.70  | | | | | | |            (104), (107), (115), (116), (119), (122), (124), (125),
% 177.19/27.70  | | | | | | |            (129), (130), (134), (141), (142), (143), (146), (149),
% 177.19/27.70  | | | | | | |            (151), (153), (156), (157), (158), (161), (162), (164),
% 177.19/27.70  | | | | | | |            (167), (177), (178), (179), (180), (181), (182), (183),
% 177.19/27.70  | | | | | | |            (184), (185), (187), (192), (198), (199), (201), (202),
% 177.19/27.70  | | | | | | |            (578), (581), (583), (586), (603), (604), (606) are
% 177.19/27.70  | | | | | | |            inconsistent by sub-proof #322.
% 177.19/27.70  | | | | | | | 
% 177.19/27.70  | | | | | | End of split
% 177.19/27.70  | | | | | | 
% 177.19/27.70  | | | | | End of split
% 177.19/27.70  | | | | | 
% 177.19/27.70  | | | | End of split
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | Case 2:
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | |   (607)  all_28_0 = e3
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | | COMBINE_EQS: (197), (607) imply:
% 177.19/27.70  | | | |   (608)  all_6_0 = e3
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | | SIMP: (608) implies:
% 177.19/27.70  | | | |   (609)  all_6_0 = e3
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | | REDUCE: (92), (609) imply:
% 177.19/27.70  | | | |   (610)  op(all_6_1, all_6_2) = e3
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | | BETA: splitting (163) gives:
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | | Case 1:
% 177.19/27.70  | | | | | 
% 177.19/27.70  | | | | |   (611)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 177.19/27.70  | | | | |            e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.19/27.70  | | | | |            all_52_14 = e0)
% 177.19/27.70  | | | | | 
% 177.19/27.70  | | | | | REF_CLOSE: (9), (52), (67), (95), (98), (147), (162), (456), (581),
% 177.19/27.70  | | | | |            (611) are inconsistent by sub-proof #434.
% 177.19/27.70  | | | | | 
% 177.19/27.70  | | | | Case 2:
% 177.19/27.70  | | | | | 
% 177.19/27.70  | | | | |   (612)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 177.19/27.70  | | | | |            = e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.19/27.70  | | | | |            all_52_30 = e0)
% 177.19/27.70  | | | | | 
% 177.19/27.70  | | | | | REF_CLOSE: (48), (94), (102), (162), (179), (182), (184), (202),
% 177.19/27.70  | | | | |            (610), (612) are inconsistent by sub-proof #326.
% 177.19/27.70  | | | | | 
% 177.19/27.70  | | | | End of split
% 177.19/27.70  | | | | 
% 177.19/27.70  | | | End of split
% 177.19/27.70  | | | 
% 177.19/27.70  | | End of split
% 177.19/27.70  | | 
% 177.19/27.70  | End of split
% 177.19/27.70  | 
% 177.19/27.70  End of proof
% 177.19/27.70  
% 177.19/27.70  Sub-proof #317 shows that the following formulas are inconsistent:
% 177.19/27.70  ----------------------------------------------------------------
% 177.19/27.70    (1)   ~ (all_52_23 = all_14_2)
% 177.19/27.70    (2)   ~ (all_52_5 = all_52_13)
% 177.19/27.70    (3)   ~ (all_52_17 = all_52_23)
% 177.19/27.70    (4)   ~ (all_52_13 = all_52_29)
% 177.19/27.70    (5)  op(e3, e2) = all_52_3
% 177.19/27.70    (6)   ~ (all_52_9 = all_52_25)
% 177.19/27.70    (7)   ~ (all_52_19 = all_52_23)
% 177.19/27.70    (8)  all_56_11 = all_52_23
% 177.19/27.70    (9)  op(e1, e2) = all_52_19
% 177.19/27.70    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.19/27.70    (11)   ~ (all_52_3 = all_10_2)
% 177.19/27.70    (12)  all_58_5 = all_52_13
% 177.19/27.70    (13)   ~ (all_52_25 = all_52_29)
% 177.19/27.70    (14)  all_56_15 = all_6_2
% 177.19/27.70    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.19/27.70    (16)  op(e2, e0) = all_52_15
% 177.19/27.70    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.19/27.70    (18)  all_58_3 = all_10_2
% 177.19/27.70    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.70    (20)  all_58_15 = all_6_2
% 177.19/27.70    (21)   ~ (all_52_9 = all_4_2)
% 177.19/27.70    (22)   ~ (all_52_5 = all_52_7)
% 177.19/27.70    (23)  all_58_10 = all_52_15
% 177.19/27.70    (24)   ~ (all_52_5 = all_4_2)
% 177.19/27.70    (25)  all_58_7 = all_52_19
% 177.19/27.70    (26)  all_56_4 = all_52_9
% 177.19/27.70    (27)   ~ (all_52_15 = all_6_2)
% 177.19/27.70    (28)   ~ (all_52_17 = all_52_25)
% 177.19/27.70    (29)  op(e0, e1) = all_52_29
% 177.19/27.70    (30)   ~ (all_4_0 = e2)
% 177.19/27.70    (31)  all_58_4 = all_52_5
% 177.19/27.70    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.19/27.70    (33)   ~ (all_52_27 = all_52_29)
% 177.19/27.70    (34)   ~ (all_52_17 = all_14_2)
% 177.19/27.70    (35)  op(e3, all_4_2) = all_4_1
% 177.19/27.70    (36)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.19/27.70    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.19/27.70    (38)   ~ (all_52_7 = all_4_2)
% 177.19/27.70    (39)  all_58_1 = all_52_3
% 177.19/27.70    (40)   ~ (all_52_13 = all_52_15)
% 177.19/27.70    (41)  all_58_0 = all_4_2
% 177.19/27.70    (42)  op(e0, e0) = all_6_2
% 177.19/27.70    (43)  op(e1, all_52_29) = all_52_28
% 177.19/27.70    (44)  op(e1, all_52_5) = all_52_4
% 177.19/27.70    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.19/27.70    (46)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.19/27.70    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.19/27.70    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.19/27.70    (49)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.19/27.70    (50)  all_58_14 = all_52_29
% 177.19/27.70    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.70    (52)   ~ (all_52_3 = all_52_5)
% 177.19/27.70    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.19/27.70    (54)  op(e2, e1) = all_52_13
% 177.19/27.70    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.70    (56)  all_58_8 = all_14_2
% 177.19/27.70    (57)  all_56_1 = all_52_3
% 177.19/27.70    (58)  all_56_14 = all_52_29
% 177.19/27.70    (59)  op(all_4_1, all_4_2) = all_4_0
% 177.19/27.70    (60)   ~ (all_52_5 = all_14_2)
% 177.19/27.70    (61)   ~ (all_52_3 = all_52_27)
% 177.19/27.70    (62)   ~ (all_52_3 = all_4_2)
% 177.19/27.70    (63)  op(e0, e3) = all_52_25
% 177.19/27.70    (64)  op(e0, all_6_2) = all_6_1
% 177.19/27.70    (65)  all_52_0 = all_4_1
% 177.19/27.70    (66)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.19/27.70    (67)   ~ (all_52_13 = all_14_2)
% 177.19/27.70    (68)   ~ (e3 = e0)
% 177.19/27.70    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.19/27.70    (70)   ~ (all_52_9 = all_52_13)
% 177.19/27.70    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.19/27.70    (72)  op(e0, all_52_23) = all_52_22
% 177.19/27.70    (73)   ~ (all_52_15 = all_52_23)
% 177.19/27.70    (74)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.19/27.70    (75)   ~ (all_52_5 = all_52_29)
% 177.19/27.70    (76)  all_56_2 = all_52_5
% 177.19/27.70    (77)  op(e1, e0) = all_52_23
% 177.19/27.70    (78)  all_56_12 = all_52_25
% 177.19/27.70    (79)  all_58_13 = all_52_27
% 177.19/27.70    (80)  op(e2, all_52_3) = all_52_2
% 177.19/27.70    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.19/27.70    (82)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.19/27.70    (83)   ~ (all_52_9 = all_52_17)
% 177.19/27.70    (84)  all_58_6 = all_52_17
% 177.19/27.70    (85)   ~ (all_52_3 = all_52_7)
% 177.19/27.70    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.19/27.70    (87)   ~ (e1 = e0)
% 177.19/27.70    (88)  all_56_0 = all_4_2
% 177.19/27.70    (89)  all_58_11 = all_52_23
% 177.19/27.70    (90)   ~ (all_52_3 = all_52_19)
% 177.19/27.70    (91)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.19/27.70    (92)   ~ (all_52_7 = all_52_15)
% 177.19/27.70    (93)  op(e0, all_52_15) = all_52_14
% 177.19/27.70    (94)   ~ (all_52_29 = all_14_2)
% 177.19/27.70    (95)   ~ (all_4_0 = e1)
% 177.19/27.70    (96)   ~ (all_52_23 = all_6_2)
% 177.19/27.70    (97)   ~ (all_52_29 = all_6_2)
% 177.19/27.70    (98)  all_58_2 = all_52_9
% 177.19/27.70    (99)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.19/27.70    (100)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.19/27.70    (101)  op(e3, e1) = all_52_5
% 177.19/27.70    (102)  all_56_10 = all_14_2
% 177.19/27.70    (103)   ~ (all_52_25 = all_6_2)
% 177.19/27.70    (104)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.19/27.70    (105)  op(e1, e1) = all_14_2
% 177.19/27.70    (106)  op(e1, e3) = all_52_17
% 177.19/27.70    (107)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.19/27.70    (108)   ~ (all_52_25 = all_4_2)
% 177.19/27.70    (109)  op(e3, e0) = all_52_7
% 177.19/27.70    (110)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.19/27.70             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.19/27.70    (111)   ~ (all_52_17 = all_4_2)
% 177.19/27.70    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.19/27.70             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.19/27.70    (113)   ~ (all_52_25 = all_52_27)
% 177.19/27.70    (114)   ~ (all_52_27 = all_6_2)
% 177.19/27.70    (115)   ~ (all_52_7 = all_6_2)
% 177.19/27.70    (116)   ~ (all_52_19 = all_52_27)
% 177.19/27.70    (117)  all_56_7 = all_52_15
% 177.19/27.70    (118)   ~ (all_52_7 = all_52_23)
% 177.19/27.70    (119)   ~ (all_52_13 = all_10_2)
% 177.19/27.70    (120)  op(e2, all_52_27) = all_52_26
% 177.19/27.70    (121)   ~ (all_52_17 = all_52_19)
% 177.19/27.70    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.19/27.70    (123)  all_58_9 = all_52_7
% 177.19/27.70    (124)  all_58_12 = all_52_25
% 177.19/27.70    (125)  op(all_6_1, all_6_2) = e3
% 177.19/27.70    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.19/27.70    (127)   ~ (all_52_9 = all_52_15)
% 177.19/27.70    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.19/27.70    (129)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.19/27.70    (130)   ~ (all_52_19 = all_14_2)
% 177.19/27.70    (131)  op(e0, all_52_7) = all_52_6
% 177.19/27.70    (132)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.19/27.70    (133)  op(e2, e3) = all_52_9
% 177.19/27.70    (134)  all_56_13 = all_52_27
% 177.19/27.70  
% 177.19/27.70  Begin of proof
% 177.19/27.70  | 
% 177.19/27.70  | ALPHA: (132) implies:
% 177.19/27.70  |   (135)  all_52_6 = e0
% 177.19/27.70  |   (136)  all_52_4 = e1
% 177.19/27.70  |   (137)  all_52_2 = e2
% 177.19/27.70  |   (138)  all_52_0 = e3
% 177.19/27.70  | 
% 177.19/27.70  | COMBINE_EQS: (65), (138) imply:
% 177.19/27.70  |   (139)  all_4_1 = e3
% 177.19/27.70  | 
% 177.19/27.70  | REDUCE: (59), (139) imply:
% 177.19/27.70  |   (140)  op(e3, all_4_2) = all_4_0
% 177.19/27.70  | 
% 177.19/27.70  | REDUCE: (35), (139) imply:
% 177.19/27.70  |   (141)  op(e3, all_4_2) = e3
% 177.19/27.70  | 
% 177.19/27.70  | REDUCE: (80), (137) imply:
% 177.19/27.70  |   (142)  op(e2, all_52_3) = e2
% 177.19/27.70  | 
% 177.19/27.70  | REDUCE: (44), (136) imply:
% 177.19/27.70  |   (143)  op(e1, all_52_5) = e1
% 177.19/27.70  | 
% 177.19/27.70  | REDUCE: (131), (135) imply:
% 177.19/27.70  |   (144)  op(e0, all_52_7) = e0
% 177.19/27.70  | 
% 177.19/27.70  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.19/27.70  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.19/27.70  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.19/27.70  |            (36), (37), (38), (39), (40), (41), (42), (43), (45), (46), (47),
% 177.19/27.70  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 177.19/27.70  |            (60), (61), (62), (63), (64), (66), (67), (68), (69), (70), (71),
% 177.19/27.70  |            (72), (73), (74), (75), (76), (77), (78), (79), (81), (82), (83),
% 177.19/27.70  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 177.19/27.70  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 177.19/27.70  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 177.19/27.70  |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 177.19/27.70  |            (123), (124), (125), (126), (127), (128), (129), (130), (133),
% 177.19/27.70  |            (134), (140), (141), (142), (143), (144) are inconsistent by
% 177.19/27.70  |            sub-proof #495.
% 177.19/27.70  | 
% 177.19/27.70  End of proof
% 177.19/27.70  
% 177.19/27.70  Sub-proof #318 shows that the following formulas are inconsistent:
% 177.19/27.70  ----------------------------------------------------------------
% 177.19/27.70    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.19/27.70    (2)   ~ (all_6_0 = e3)
% 177.19/27.70    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.19/27.70    (4)  all_56_3 = all_52_7
% 177.19/27.70    (5)  op(e3, e2) = all_52_3
% 177.19/27.70    (6)   ~ (all_52_9 = all_52_25)
% 177.19/27.70    (7)  op(e3, all_52_25) = all_52_24
% 177.19/27.70    (8)   ~ (all_52_19 = all_52_23)
% 177.19/27.70    (9)  op(e1, e2) = all_52_19
% 177.19/27.70    (10)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.19/27.70    (11)  op(e3, all_52_9) = all_52_8
% 177.19/27.70    (12)   ~ (all_52_3 = all_10_2)
% 177.19/27.70    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.19/27.70    (14)  all_56_15 = all_6_2
% 177.19/27.70    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.19/27.70    (16)  all_58_3 = all_10_2
% 177.19/27.70    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.70    (18)  all_58_15 = all_6_2
% 177.19/27.70    (19)   ~ (all_52_5 = all_52_7)
% 177.19/27.70    (20)  all_58_10 = all_52_15
% 177.19/27.70    (21)  all_58_7 = all_52_19
% 177.19/27.70    (22)   ~ (all_52_17 = all_52_25)
% 177.19/27.70    (23)  op(e0, e1) = all_52_29
% 177.19/27.70    (24)  all_58_4 = all_52_5
% 177.19/27.70    (25)   ~ (e3 = e1)
% 177.19/27.70    (26)  all_34_1 = all_4_1
% 177.19/27.70    (27)   ~ (all_52_27 = all_52_29)
% 177.19/27.70    (28)  op(e3, all_4_2) = all_4_1
% 177.19/27.70    (29)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.19/27.70    (30)   ~ (all_52_7 = all_4_2)
% 177.19/27.70    (31)  all_58_1 = all_52_3
% 177.19/27.70    (32)  all_58_0 = all_4_2
% 177.19/27.70    (33)  op(all_4_1, all_4_2) = e1
% 177.19/27.70    (34)  op(e1, all_52_29) = all_52_28
% 177.19/27.70    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.19/27.70    (36)   ~ (all_4_1 = e2)
% 177.19/27.70    (37)  all_58_14 = all_52_29
% 177.19/27.70    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.70    (39)   ~ (all_52_3 = all_52_5)
% 177.19/27.70    (40)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.19/27.70    (41)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.70    (42)  all_56_1 = all_52_3
% 177.19/27.70    (43)  op(e0, e2) = all_52_27
% 177.19/27.70    (44)  op(all_14_1, all_14_2) = e3
% 177.19/27.70    (45)   ~ (all_52_3 = all_52_27)
% 177.19/27.70    (46)   ~ (all_52_3 = all_4_2)
% 177.19/27.70    (47)  op(all_6_1, all_6_2) = all_6_0
% 177.19/27.70    (48)  op(e0, e3) = all_52_25
% 177.19/27.70    (49)  op(e0, all_6_2) = all_6_1
% 177.19/27.70    (50)   ~ (all_52_9 = all_10_2)
% 177.19/27.70    (51)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.19/27.70    (52)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.19/27.70    (53)  all_56_2 = all_52_5
% 177.19/27.70    (54)  op(e1, e0) = all_52_23
% 177.19/27.70    (55)  all_58_13 = all_52_27
% 177.19/27.70    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.19/27.70    (57)  all_58_6 = all_52_17
% 177.19/27.70    (58)   ~ (all_52_3 = all_52_7)
% 177.19/27.70    (59)  all_56_0 = all_4_2
% 177.19/27.70    (60)  all_58_11 = all_52_23
% 177.19/27.70    (61)   ~ (all_52_3 = all_52_19)
% 177.19/27.70    (62)   ~ (all_52_7 = all_52_15)
% 177.19/27.70    (63)   ~ (all_52_29 = all_14_2)
% 177.19/27.70    (64)   ~ (all_6_0 = e2)
% 177.19/27.70    (65)  all_58_2 = all_52_9
% 177.19/27.70    (66)  op(e3, e1) = all_52_5
% 177.19/27.70    (67)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.19/27.70    (68)  op(e1, e1) = all_14_2
% 177.19/27.70    (69)  op(e1, e3) = all_52_17
% 177.19/27.70    (70)   ~ (all_52_25 = all_4_2)
% 177.19/27.70    (71)  op(e3, e0) = all_52_7
% 177.19/27.70    (72)  op(e3, e3) = all_4_2
% 177.19/27.70    (73)   ~ (all_52_17 = all_4_2)
% 177.19/27.70    (74)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.19/27.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.19/27.70    (75)   ~ (all_52_25 = all_52_27)
% 177.19/27.70    (76)  all_34_2 = all_4_2
% 177.19/27.70    (77)   ~ (all_52_7 = all_6_2)
% 177.19/27.70    (78)   ~ (all_52_19 = all_52_27)
% 177.19/27.70    (79)   ~ (all_52_7 = all_52_23)
% 177.19/27.70    (80)   ~ (all_6_0 = e1)
% 177.19/27.70    (81)  op(e2, all_52_27) = all_52_26
% 177.19/27.70    (82)  all_52_20 = all_14_1
% 177.19/27.70    (83)   ~ (all_52_17 = all_52_19)
% 177.19/27.70    (84)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.19/27.70    (85)  all_52_30 = all_6_1
% 177.19/27.70    (86)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.19/27.70    (87)  op(e1, all_14_2) = all_14_1
% 177.19/27.70    (88)  all_58_9 = all_52_7
% 177.19/27.70    (89)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.19/27.70          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.19/27.70    (90)  all_58_12 = all_52_25
% 177.19/27.70    (91)   ~ (all_52_9 = all_52_15)
% 177.19/27.70    (92)   ~ (e3 = e2)
% 177.19/27.70    (93)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.19/27.70    (94)  op(e2, e3) = all_52_9
% 177.19/27.70    (95)  all_56_13 = all_52_27
% 177.19/27.70  
% 177.19/27.70  Begin of proof
% 177.19/27.70  | 
% 177.19/27.70  | BETA: splitting (89) gives:
% 177.19/27.70  | 
% 177.19/27.70  | Case 1:
% 177.19/27.70  | | 
% 177.19/27.70  | |   (96)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.19/27.70  | | 
% 177.19/27.70  | | ALPHA: (96) implies:
% 177.19/27.70  | |   (97)  all_52_20 = e1
% 177.19/27.70  | | 
% 177.19/27.70  | | COMBINE_EQS: (82), (97) imply:
% 177.19/27.70  | |   (98)  all_14_1 = e1
% 177.19/27.70  | | 
% 177.19/27.70  | | REF_CLOSE: (25), (44), (74), (87), (98) are inconsistent by sub-proof #344.
% 177.19/27.70  | | 
% 177.19/27.70  | Case 2:
% 177.19/27.70  | | 
% 177.19/27.70  | |   (99)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.19/27.70  | | 
% 177.19/27.70  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.19/27.70  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.19/27.70  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.19/27.70  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (45), (46),
% 177.19/27.70  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.19/27.70  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.19/27.70  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.19/27.70  | |            (80), (81), (83), (84), (85), (86), (88), (90), (91), (92), (93),
% 177.19/27.70  | |            (94), (95), (99) are inconsistent by sub-proof #534.
% 177.19/27.70  | | 
% 177.19/27.70  | End of split
% 177.19/27.70  | 
% 177.19/27.70  End of proof
% 177.19/27.70  
% 177.19/27.70  Sub-proof #319 shows that the following formulas are inconsistent:
% 177.19/27.70  ----------------------------------------------------------------
% 177.19/27.70    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.19/27.70    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.19/27.70    (3)   ~ (all_52_27 = all_10_2)
% 177.19/27.70    (4)   ~ (all_52_17 = all_52_23)
% 177.19/27.70    (5)   ~ (all_6_0 = e3)
% 177.19/27.70    (6)   ~ (all_52_13 = all_52_29)
% 177.19/27.70    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.19/27.70    (8)  op(e3, e2) = all_52_3
% 177.19/27.70    (9)   ~ (all_52_9 = all_52_25)
% 177.19/27.70    (10)  op(e3, all_52_25) = all_52_24
% 177.19/27.70    (11)   ~ (all_52_19 = all_52_23)
% 177.19/27.70    (12)  all_56_11 = all_52_23
% 177.19/27.70    (13)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.19/27.70    (14)  op(e3, all_52_9) = all_52_8
% 177.19/27.70    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.19/27.70    (16)  all_58_5 = all_52_13
% 177.19/27.70    (17)   ~ (all_6_2 = e0)
% 177.19/27.70    (18)   ~ (all_52_25 = all_52_29)
% 177.19/27.70    (19)  all_56_15 = all_6_2
% 177.19/27.70    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.19/27.70    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.19/27.70    (22)  all_58_3 = all_10_2
% 177.19/27.70    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.70    (24)  all_58_15 = all_6_2
% 177.19/27.70    (25)   ~ (all_52_9 = all_4_2)
% 177.19/27.70    (26)   ~ (all_52_5 = all_52_7)
% 177.19/27.70    (27)  all_58_10 = all_52_15
% 177.19/27.70    (28)   ~ (all_52_5 = all_4_2)
% 177.19/27.70    (29)  all_58_7 = all_52_19
% 177.19/27.70    (30)   ~ (all_52_17 = all_52_25)
% 177.19/27.70    (31)  op(e0, e1) = all_52_29
% 177.19/27.70    (32)   ~ (all_4_0 = e2)
% 177.19/27.70    (33)  all_58_4 = all_52_5
% 177.19/27.70    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.19/27.70    (35)   ~ (e3 = e1)
% 177.19/27.70    (36)   ~ (all_52_27 = all_52_29)
% 177.19/27.70    (37)   ~ (all_52_17 = all_14_2)
% 177.19/27.70    (38)  op(e3, all_4_2) = all_4_1
% 177.19/27.70    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.19/27.70    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.19/27.70    (41)   ~ (all_52_7 = all_4_2)
% 177.19/27.70    (42)  all_58_1 = all_52_3
% 177.19/27.70    (43)   ~ (all_52_13 = all_52_15)
% 177.19/27.70    (44)  all_58_0 = all_4_2
% 177.19/27.70    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.19/27.70    (46)  op(e1, all_52_29) = all_52_28
% 177.19/27.70    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.19/27.70    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.19/27.70    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.19/27.70    (50)  all_58_14 = all_52_29
% 177.19/27.70    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.70    (52)   ~ (all_52_3 = all_52_5)
% 177.19/27.70    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.19/27.70    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.70    (55)  all_58_8 = all_14_2
% 177.19/27.70    (56)  op(e0, e2) = all_52_27
% 177.19/27.70    (57)  all_56_14 = all_52_29
% 177.19/27.70    (58)  op(all_14_1, all_14_2) = e3
% 177.19/27.70    (59)  op(all_4_1, all_4_2) = all_4_0
% 177.19/27.70    (60)   ~ (all_52_3 = all_52_27)
% 177.19/27.70    (61)   ~ (all_52_3 = all_4_2)
% 177.19/27.70    (62)  op(all_6_1, all_6_2) = all_6_0
% 177.19/27.70    (63)  op(e0, e3) = all_52_25
% 177.19/27.70    (64)  op(e0, all_6_2) = all_6_1
% 177.19/27.70    (65)   ~ (all_52_9 = all_10_2)
% 177.19/27.70    (66)  op(e3, all_52_17) = all_52_16
% 177.19/27.70    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.19/27.70    (68)   ~ (all_52_13 = all_14_2)
% 177.19/27.70    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.19/27.70    (70)   ~ (all_52_9 = all_52_13)
% 177.19/27.70    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.19/27.70    (72)   ~ (all_52_5 = all_52_29)
% 177.19/27.70    (73)  all_56_2 = all_52_5
% 177.19/27.70    (74)  op(e1, e0) = all_52_23
% 177.19/27.70    (75)  all_56_12 = all_52_25
% 177.19/27.70    (76)  all_58_13 = all_52_27
% 177.19/27.70    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.19/27.70    (78)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.19/27.70    (79)   ~ (all_52_9 = all_52_17)
% 177.19/27.70    (80)  all_58_6 = all_52_17
% 177.19/27.70    (81)   ~ (all_52_3 = all_52_7)
% 177.19/27.70    (82)  all_56_0 = all_4_2
% 177.19/27.70    (83)  all_58_11 = all_52_23
% 177.19/27.70    (84)   ~ (all_52_3 = all_52_19)
% 177.19/27.70    (85)   ~ (all_52_7 = all_52_15)
% 177.19/27.70    (86)   ~ (all_4_0 = e1)
% 177.19/27.70    (87)   ~ (all_52_19 = all_10_2)
% 177.19/27.70    (88)   ~ (all_52_23 = all_6_2)
% 177.19/27.70    (89)   ~ (all_6_0 = e2)
% 177.19/27.70    (90)   ~ (all_52_29 = all_6_2)
% 177.19/27.70    (91)  all_58_2 = all_52_9
% 177.19/27.70    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.19/27.70    (93)  op(e3, e1) = all_52_5
% 177.19/27.70    (94)   ~ (e2 = e1)
% 177.19/27.70    (95)   ~ (all_52_25 = all_6_2)
% 177.19/27.70    (96)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.19/27.70    (97)  op(e1, e3) = all_52_17
% 177.19/27.70    (98)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.19/27.70    (99)   ~ (all_52_25 = all_4_2)
% 177.19/27.70    (100)  op(e3, e0) = all_52_7
% 177.19/27.70    (101)  op(e3, e3) = all_4_2
% 177.19/27.70    (102)   ~ (all_52_17 = all_4_2)
% 177.19/27.70    (103)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.19/27.70             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.19/27.70    (104)   ~ (all_52_25 = all_52_27)
% 177.19/27.70    (105)   ~ (all_52_27 = all_6_2)
% 177.19/27.70    (106)   ~ (all_52_7 = all_6_2)
% 177.19/27.70    (107)   ~ (all_52_15 = all_10_2)
% 177.19/27.70    (108)   ~ (all_52_19 = all_52_27)
% 177.19/27.70    (109)  all_56_7 = all_52_15
% 177.19/27.70    (110)   ~ (all_52_7 = all_52_23)
% 177.19/27.71    (111)   ~ (all_6_0 = e1)
% 177.19/27.71    (112)  op(e2, all_52_27) = all_52_26
% 177.19/27.71    (113)  all_52_20 = all_14_1
% 177.19/27.71    (114)   ~ (all_52_17 = all_52_19)
% 177.19/27.71    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.19/27.71    (116)  all_52_30 = all_6_1
% 177.19/27.71    (117)  op(e1, all_14_2) = all_14_1
% 177.19/27.71    (118)  all_58_9 = all_52_7
% 177.19/27.71    (119)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.19/27.71           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.19/27.71    (120)  all_58_12 = all_52_25
% 177.19/27.71    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.19/27.71    (122)   ~ (all_52_9 = all_52_15)
% 177.19/27.71    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.19/27.71    (124)   ~ (e3 = e2)
% 177.19/27.71    (125)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.19/27.71    (126)  op(e2, e3) = all_52_9
% 177.19/27.71    (127)  all_56_13 = all_52_27
% 177.19/27.71  
% 177.19/27.71  Begin of proof
% 177.19/27.71  | 
% 177.19/27.71  | BETA: splitting (119) gives:
% 177.19/27.71  | 
% 177.19/27.71  | Case 1:
% 177.19/27.71  | | 
% 177.19/27.71  | |   (128)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | ALPHA: (128) implies:
% 177.19/27.71  | |   (129)  all_52_20 = e1
% 177.19/27.71  | | 
% 177.19/27.71  | | COMBINE_EQS: (113), (129) imply:
% 177.19/27.71  | |   (130)  all_14_1 = e1
% 177.19/27.71  | | 
% 177.19/27.71  | | REF_CLOSE: (35), (58), (103), (117), (130) are inconsistent by sub-proof
% 177.19/27.71  | |            #344.
% 177.19/27.71  | | 
% 177.19/27.71  | Case 2:
% 177.19/27.71  | | 
% 177.19/27.71  | |   (131)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | ALPHA: (131) implies:
% 177.19/27.71  | |   (132)  all_52_30 = e0
% 177.19/27.71  | |   (133)  all_52_28 = e1
% 177.19/27.71  | |   (134)  all_52_26 = e2
% 177.19/27.71  | |   (135)  all_52_24 = e3
% 177.19/27.71  | | 
% 177.19/27.71  | | COMBINE_EQS: (116), (132) imply:
% 177.19/27.71  | |   (136)  all_6_1 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.19/27.71  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.19/27.71  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.19/27.71  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.19/27.71  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.19/27.71  | |            (57), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.19/27.71  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.19/27.71  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 177.19/27.71  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.19/27.71  | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 177.19/27.71  | |            (110), (111), (112), (114), (115), (118), (120), (121), (122),
% 177.19/27.71  | |            (123), (124), (125), (126), (127), (133), (134), (135), (136) are
% 177.19/27.71  | |            inconsistent by sub-proof #635.
% 177.19/27.71  | | 
% 177.19/27.71  | End of split
% 177.19/27.71  | 
% 177.19/27.71  End of proof
% 177.19/27.71  
% 177.19/27.71  Sub-proof #320 shows that the following formulas are inconsistent:
% 177.19/27.71  ----------------------------------------------------------------
% 177.19/27.71    (1)   ~ (all_52_23 = all_14_2)
% 177.19/27.71    (2)   ~ (all_52_5 = all_52_13)
% 177.19/27.71    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.19/27.71    (4)   ~ (all_52_27 = all_10_2)
% 177.19/27.71    (5)   ~ (all_52_17 = all_52_23)
% 177.19/27.71    (6)   ~ (all_52_13 = all_52_29)
% 177.19/27.71    (7)  all_56_3 = all_52_7
% 177.19/27.71    (8)  op(e3, e2) = all_52_3
% 177.19/27.71    (9)   ~ (all_52_9 = all_52_25)
% 177.19/27.71    (10)  op(e3, all_52_25) = all_52_24
% 177.19/27.71    (11)   ~ (all_52_19 = all_52_23)
% 177.19/27.71    (12)  op(e1, e2) = all_52_19
% 177.19/27.71    (13)  op(e3, all_52_9) = all_52_8
% 177.19/27.71    (14)   ~ (all_52_23 = e0)
% 177.19/27.71    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.19/27.71    (16)   ~ (all_52_25 = all_52_29)
% 177.19/27.71    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.19/27.71    (18)  all_58_3 = all_10_2
% 177.19/27.71    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.71    (20)   ~ (all_52_9 = all_4_2)
% 177.19/27.71    (21)   ~ (all_52_5 = all_52_7)
% 177.19/27.71    (22)   ~ (all_52_5 = all_4_2)
% 177.19/27.71    (23)  all_58_7 = all_52_19
% 177.19/27.71    (24)   ~ (all_52_17 = all_52_25)
% 177.19/27.71    (25)  all_58_4 = all_52_5
% 177.19/27.71    (26)   ~ (e3 = e1)
% 177.19/27.71    (27)   ~ (all_52_27 = all_52_29)
% 177.19/27.71    (28)  op(e3, all_4_2) = all_4_1
% 177.19/27.71    (29)   ~ (all_52_7 = all_4_2)
% 177.19/27.71    (30)  all_58_1 = all_52_3
% 177.19/27.71    (31)  all_58_0 = all_4_2
% 177.19/27.71    (32)  op(e1, all_52_29) = all_52_28
% 177.19/27.71    (33)   ~ (all_4_1 = e2)
% 177.19/27.71    (34)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.19/27.71    (35)  all_58_14 = all_52_29
% 177.19/27.71    (36)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.71    (37)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.19/27.71    (38)  op(e2, e1) = all_52_13
% 177.19/27.71    (39)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.71    (40)  all_58_8 = all_14_2
% 177.19/27.71    (41)  all_56_14 = all_52_29
% 177.19/27.71    (42)  op(all_14_1, all_14_2) = e3
% 177.19/27.71    (43)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.19/27.71    (44)   ~ (all_52_3 = all_4_2)
% 177.19/27.71    (45)   ~ (all_52_9 = all_10_2)
% 177.19/27.71    (46)  op(e3, all_52_17) = all_52_16
% 177.19/27.71    (47)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.19/27.71    (48)   ~ (e3 = e0)
% 177.19/27.71    (49)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.19/27.71    (50)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.19/27.71    (51)   ~ (all_52_5 = all_52_29)
% 177.19/27.71    (52)  all_56_12 = all_52_25
% 177.19/27.71    (53)  all_58_13 = all_52_27
% 177.19/27.71    (54)   ~ (all_4_1 = e1)
% 177.19/27.71    (55)  all_56_5 = all_10_2
% 177.19/27.71    (56)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.19/27.71    (57)   ~ (all_52_25 = e0)
% 177.19/27.71    (58)   ~ (all_52_9 = all_52_17)
% 177.19/27.71    (59)  all_58_6 = all_52_17
% 177.19/27.71    (60)   ~ (all_52_3 = all_52_7)
% 177.19/27.71    (61)   ~ (e1 = e0)
% 177.19/27.71    (62)  all_56_0 = all_4_2
% 177.19/27.71    (63)  all_58_11 = all_52_23
% 177.19/27.71    (64)   ~ (all_52_29 = all_14_2)
% 177.19/27.71    (65)   ~ (all_52_19 = all_10_2)
% 177.19/27.71    (66)  all_58_15 = e0
% 177.19/27.71    (67)  all_58_2 = all_52_9
% 177.19/27.71    (68)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.19/27.71    (69)   ~ (all_52_29 = e0)
% 177.19/27.71    (70)  op(e3, e1) = all_52_5
% 177.19/27.71    (71)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.19/27.71    (72)  op(e1, e3) = all_52_17
% 177.19/27.71    (73)   ~ (all_52_25 = all_4_2)
% 177.19/27.71    (74)  op(e3, e0) = all_52_7
% 177.19/27.71    (75)  op(e3, e3) = all_4_2
% 177.19/27.71    (76)  all_56_8 = all_52_17
% 177.19/27.71    (77)   ~ (all_52_17 = all_4_2)
% 177.19/27.71    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.19/27.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.19/27.71    (79)   ~ (all_52_25 = all_52_27)
% 177.19/27.71    (80)  op(e2, all_52_27) = all_52_26
% 177.19/27.71    (81)  all_52_20 = all_14_1
% 177.19/27.71    (82)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.19/27.71    (83)  op(e1, all_14_2) = all_14_1
% 177.19/27.71    (84)  all_58_9 = all_52_7
% 177.19/27.71    (85)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.19/27.71          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.19/27.71    (86)  all_58_12 = all_52_25
% 177.19/27.71    (87)  op(e2, e3) = all_52_9
% 177.19/27.71    (88)  all_56_13 = all_52_27
% 177.19/27.71  
% 177.19/27.71  Begin of proof
% 177.19/27.71  | 
% 177.19/27.71  | BETA: splitting (85) gives:
% 177.19/27.71  | 
% 177.19/27.71  | Case 1:
% 177.19/27.71  | | 
% 177.19/27.71  | |   (89)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | ALPHA: (89) implies:
% 177.19/27.71  | |   (90)  all_52_20 = e1
% 177.19/27.71  | | 
% 177.19/27.71  | | COMBINE_EQS: (81), (90) imply:
% 177.19/27.71  | |   (91)  all_14_1 = e1
% 177.19/27.71  | | 
% 177.19/27.71  | | REF_CLOSE: (26), (42), (78), (83), (91) are inconsistent by sub-proof #344.
% 177.19/27.71  | | 
% 177.19/27.71  | Case 2:
% 177.19/27.71  | | 
% 177.19/27.71  | |   (92)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.19/27.71  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.19/27.71  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.19/27.71  | |            (35), (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 177.19/27.71  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.19/27.71  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.19/27.71  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.19/27.71  | |            (80), (82), (84), (86), (87), (88), (92) are inconsistent by
% 177.19/27.71  | |            sub-proof #878.
% 177.19/27.71  | | 
% 177.19/27.71  | End of split
% 177.19/27.71  | 
% 177.19/27.71  End of proof
% 177.19/27.71  
% 177.19/27.71  Sub-proof #321 shows that the following formulas are inconsistent:
% 177.19/27.71  ----------------------------------------------------------------
% 177.19/27.71    (1)   ~ (all_52_23 = all_14_2)
% 177.19/27.71    (2)   ~ (all_52_5 = all_52_13)
% 177.19/27.71    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.19/27.71    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.19/27.71    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.19/27.71    (6)   ~ (all_52_27 = all_10_2)
% 177.19/27.71    (7)   ~ (all_52_17 = all_52_23)
% 177.19/27.71    (8)  op(e2, all_10_2) = all_10_1
% 177.19/27.71    (9)   ~ (all_52_13 = all_52_29)
% 177.19/27.71    (10)  all_56_3 = all_52_7
% 177.19/27.71    (11)  op(e3, e2) = all_52_3
% 177.19/27.71    (12)   ~ (all_52_9 = all_52_25)
% 177.19/27.71    (13)  op(e3, all_52_25) = all_52_24
% 177.19/27.71    (14)   ~ (all_52_19 = all_52_23)
% 177.19/27.71    (15)  all_56_11 = all_52_23
% 177.19/27.71    (16)  op(e1, e2) = all_52_19
% 177.19/27.71    (17)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.19/27.71    (18)  op(e3, all_52_9) = all_52_8
% 177.19/27.71    (19)  all_50_1 = all_4_1
% 177.19/27.71    (20)   ~ (all_52_3 = all_10_2)
% 177.19/27.71    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.19/27.71    (22)  all_58_5 = all_52_13
% 177.19/27.71    (23)   ~ (all_6_2 = e0)
% 177.19/27.71    (24)   ~ (all_52_25 = all_52_29)
% 177.19/27.71    (25)  all_56_15 = all_6_2
% 177.19/27.71    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.19/27.71    (27)  op(e2, e0) = all_52_15
% 177.19/27.71    (28)  all_58_3 = all_10_2
% 177.19/27.71    (29)  all_56_9 = all_52_19
% 177.19/27.71    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.71    (31)  all_58_15 = all_6_2
% 177.19/27.71    (32)   ~ (all_52_9 = all_4_2)
% 177.19/27.71    (33)   ~ (all_52_5 = all_52_7)
% 177.19/27.71    (34)  all_58_10 = all_52_15
% 177.19/27.71    (35)   ~ (all_52_5 = all_4_2)
% 177.19/27.71    (36)  all_58_7 = all_52_19
% 177.19/27.71    (37)  all_56_4 = all_52_9
% 177.19/27.71    (38)   ~ (all_52_15 = all_6_2)
% 177.19/27.71    (39)   ~ (all_52_17 = all_52_25)
% 177.19/27.71    (40)  all_58_4 = all_52_5
% 177.19/27.71    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.19/27.71    (42)   ~ (e3 = e1)
% 177.19/27.71    (43)   ~ (all_52_27 = all_52_29)
% 177.19/27.71    (44)   ~ (all_52_17 = all_14_2)
% 177.19/27.71    (45)  op(e3, all_4_2) = all_4_1
% 177.19/27.71    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.19/27.71    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.19/27.71    (48)   ~ (all_52_7 = all_4_2)
% 177.19/27.71    (49)  all_58_1 = all_52_3
% 177.19/27.71    (50)   ~ (all_52_13 = all_52_15)
% 177.19/27.71    (51)  all_58_0 = all_4_2
% 177.19/27.71    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.19/27.71    (53)  op(e1, all_52_13) = all_52_12
% 177.19/27.71    (54)  op(e1, all_52_29) = all_52_28
% 177.19/27.71    (55)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.19/27.71          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.19/27.71    (56)  all_50_2 = all_4_2
% 177.19/27.71    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.19/27.71    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.19/27.71    (59)   ~ (all_4_1 = e2)
% 177.19/27.71    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.19/27.71    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.19/27.71    (62)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.19/27.71    (63)  all_58_14 = all_52_29
% 177.19/27.71    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.71    (65)  all_26_2 = all_4_2
% 177.19/27.71    (66)   ~ (all_52_3 = all_52_5)
% 177.19/27.71    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.19/27.71    (68)  op(e2, e1) = all_52_13
% 177.19/27.71    (69)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.71    (70)  all_58_8 = all_14_2
% 177.19/27.71    (71)  all_56_1 = all_52_3
% 177.19/27.71    (72)  op(all_14_1, all_14_2) = e3
% 177.19/27.71    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.19/27.71    (74)   ~ (all_52_3 = all_52_27)
% 177.19/27.71    (75)   ~ (all_52_3 = all_4_2)
% 177.19/27.71    (76)  op(e0, e3) = all_52_25
% 177.19/27.71    (77)  all_52_0 = all_4_1
% 177.19/27.71    (78)   ~ (all_52_9 = all_10_2)
% 177.19/27.71    (79)  op(all_4_1, all_4_2) = e2
% 177.19/27.71    (80)  op(e3, all_52_17) = all_52_16
% 177.19/27.71    (81)  all_52_10 = all_10_1
% 177.19/27.71    (82)   ~ (all_52_13 = all_14_2)
% 177.19/27.71    (83)   ~ (e3 = e0)
% 177.19/27.71    (84)   ~ (all_52_9 = all_52_13)
% 177.19/27.71    (85)  op(e0, all_52_23) = all_52_22
% 177.19/27.71    (86)   ~ (all_52_15 = all_52_23)
% 177.19/27.71    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.19/27.71    (88)  op(all_10_1, all_10_2) = all_10_0
% 177.19/27.71    (89)   ~ (all_52_5 = all_52_29)
% 177.19/27.71    (90)  all_56_2 = all_52_5
% 177.19/27.71    (91)  op(e1, e0) = all_52_23
% 177.19/27.71    (92)  all_58_13 = all_52_27
% 177.19/27.71    (93)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.19/27.71    (94)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 177.19/27.71    (95)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.19/27.71    (96)  all_56_5 = all_10_2
% 177.19/27.71    (97)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.19/27.71    (98)   ~ (all_52_9 = all_52_17)
% 177.19/27.71    (99)  all_58_6 = all_52_17
% 177.19/27.71    (100)   ~ (all_52_3 = all_52_7)
% 177.19/27.71    (101)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.19/27.71    (102)  op(e2, all_52_19) = all_52_18
% 177.19/27.71    (103)   ~ (e1 = e0)
% 177.19/27.71    (104)  all_56_0 = all_4_2
% 177.19/27.71    (105)  all_58_11 = all_52_23
% 177.19/27.71    (106)   ~ (all_52_3 = all_52_19)
% 177.19/27.71    (107)   ~ (all_52_7 = all_52_15)
% 177.19/27.71    (108)  all_26_1 = all_4_1
% 177.19/27.71    (109)  op(e0, all_52_15) = all_52_14
% 177.19/27.71    (110)   ~ (all_52_29 = all_14_2)
% 177.19/27.71    (111)   ~ (all_52_19 = all_10_2)
% 177.19/27.71    (112)   ~ (all_52_23 = all_6_2)
% 177.19/27.71    (113)   ~ (all_52_29 = all_6_2)
% 177.19/27.71    (114)  all_58_2 = all_52_9
% 177.19/27.71    (115)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.19/27.71    (116)  op(e3, e1) = all_52_5
% 177.19/27.71    (117)  all_56_10 = all_14_2
% 177.19/27.71    (118)   ~ (all_52_25 = all_6_2)
% 177.19/27.71    (119)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.19/27.71    (120)  op(e1, e3) = all_52_17
% 177.19/27.71    (121)   ~ (all_52_25 = all_4_2)
% 177.19/27.71    (122)  op(e3, e0) = all_52_7
% 177.19/27.71    (123)  op(e3, e3) = all_4_2
% 177.19/27.71    (124)  all_56_8 = all_52_17
% 177.19/27.71    (125)   ~ (all_52_17 = all_4_2)
% 177.19/27.71    (126)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.19/27.71             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.19/27.71    (127)   ~ (all_52_25 = all_52_27)
% 177.19/27.71    (128)   ~ (all_52_27 = all_6_2)
% 177.19/27.71    (129)   ~ (all_52_7 = all_6_2)
% 177.19/27.71    (130)   ~ (all_10_0 = e3)
% 177.19/27.71    (131)  all_18_2 = all_14_2
% 177.19/27.71    (132)   ~ (all_52_7 = all_52_23)
% 177.19/27.71    (133)   ~ (all_52_13 = all_10_2)
% 177.19/27.71    (134)  op(e2, all_52_27) = all_52_26
% 177.19/27.71    (135)   ~ (all_52_17 = all_52_19)
% 177.19/27.71    (136)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.19/27.71    (137)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.19/27.71    (138)  op(e1, all_14_2) = all_14_1
% 177.19/27.71    (139)  all_58_9 = all_52_7
% 177.19/27.71    (140)  all_58_12 = all_52_25
% 177.19/27.71    (141)   ~ (all_10_0 = e1)
% 177.19/27.71    (142)  all_56_6 = all_52_13
% 177.19/27.71    (143)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.19/27.71    (144)   ~ (all_52_9 = all_52_15)
% 177.19/27.71    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.19/27.71    (146)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.19/27.71    (147)   ~ (all_52_19 = all_14_2)
% 177.19/27.71    (148)  op(e2, e3) = all_52_9
% 177.19/27.71    (149)  all_56_13 = all_52_27
% 177.19/27.71  
% 177.19/27.71  Begin of proof
% 177.19/27.71  | 
% 177.19/27.71  | BETA: splitting (55) gives:
% 177.19/27.71  | 
% 177.19/27.71  | Case 1:
% 177.19/27.71  | | 
% 177.19/27.71  | |   (150)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | REF_CLOSE: (45), (59), (77), (79), (126), (150) are inconsistent by
% 177.19/27.71  | |            sub-proof #494.
% 177.19/27.71  | | 
% 177.19/27.71  | Case 2:
% 177.19/27.71  | | 
% 177.19/27.71  | |   (151)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | ALPHA: (151) implies:
% 177.19/27.71  | |   (152)  all_52_14 = e0
% 177.19/27.71  | |   (153)  all_52_12 = e1
% 177.19/27.71  | |   (154)  all_52_10 = e2
% 177.19/27.71  | |   (155)  all_52_8 = e3
% 177.19/27.71  | | 
% 177.19/27.71  | | COMBINE_EQS: (81), (154) imply:
% 177.19/27.71  | |   (156)  all_10_1 = e2
% 177.19/27.71  | | 
% 177.19/27.71  | | REDUCE: (88), (156) imply:
% 177.19/27.71  | |   (157)  op(e2, all_10_2) = all_10_0
% 177.19/27.71  | | 
% 177.19/27.71  | | REDUCE: (18), (155) imply:
% 177.19/27.71  | |   (158)  op(e3, all_52_9) = e3
% 177.19/27.71  | | 
% 177.19/27.71  | | REDUCE: (8), (156) imply:
% 177.19/27.71  | |   (159)  op(e2, all_10_2) = e2
% 177.19/27.71  | | 
% 177.19/27.71  | | REDUCE: (53), (153) imply:
% 177.19/27.71  | |   (160)  op(e1, all_52_13) = e1
% 177.19/27.71  | | 
% 177.19/27.71  | | REDUCE: (109), (152) imply:
% 177.19/27.71  | |   (161)  op(e0, all_52_15) = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 177.19/27.71  | |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 177.19/27.71  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.19/27.71  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.19/27.71  | |            (48), (49), (50), (51), (52), (54), (56), (57), (58), (59), (60),
% 177.19/27.71  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 177.19/27.71  | |            (72), (73), (74), (75), (76), (78), (79), (80), (82), (83), (84),
% 177.19/27.71  | |            (85), (86), (87), (89), (90), (91), (92), (93), (94), (95), (96),
% 177.19/27.71  | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 177.19/27.71  | |            (106), (107), (108), (110), (111), (112), (113), (114), (115),
% 177.19/27.71  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.19/27.71  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 177.19/27.71  | |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 177.19/27.71  | |            (143), (144), (145), (146), (147), (148), (149), (157), (158),
% 177.19/27.71  | |            (159), (160), (161) are inconsistent by sub-proof #323.
% 177.19/27.71  | | 
% 177.19/27.71  | End of split
% 177.19/27.71  | 
% 177.19/27.71  End of proof
% 177.19/27.71  
% 177.19/27.71  Sub-proof #322 shows that the following formulas are inconsistent:
% 177.19/27.71  ----------------------------------------------------------------
% 177.19/27.71    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.19/27.71    (2)   ~ (all_52_27 = all_10_2)
% 177.19/27.71    (3)  op(e2, e2) = all_10_2
% 177.19/27.71    (4)   ~ (all_52_17 = all_52_23)
% 177.19/27.71    (5)   ~ (all_6_0 = e3)
% 177.19/27.71    (6)   ~ (all_52_13 = all_52_29)
% 177.19/27.71    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.19/27.71    (8)  all_56_3 = all_52_7
% 177.19/27.71    (9)  op(e3, e2) = all_52_3
% 177.19/27.71    (10)   ~ (all_52_9 = all_52_25)
% 177.19/27.71    (11)  op(e3, all_52_25) = all_52_24
% 177.19/27.71    (12)   ~ (all_52_19 = all_52_23)
% 177.19/27.71    (13)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.19/27.71    (14)  op(e3, all_52_9) = all_52_8
% 177.19/27.71    (15)  all_50_1 = all_4_1
% 177.19/27.71    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.19/27.71    (17)  all_58_5 = all_52_13
% 177.19/27.71    (18)   ~ (all_6_2 = e0)
% 177.19/27.71    (19)   ~ (all_52_25 = all_52_29)
% 177.19/27.71    (20)  all_56_15 = all_6_2
% 177.19/27.71    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.19/27.71    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.19/27.71    (23)  all_58_3 = all_10_2
% 177.19/27.71    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.71    (25)  all_58_15 = all_6_2
% 177.19/27.71    (26)  all_58_10 = all_52_15
% 177.19/27.71    (27)   ~ (all_52_5 = all_4_2)
% 177.19/27.71    (28)  all_58_7 = all_52_19
% 177.19/27.71    (29)   ~ (all_52_17 = all_52_25)
% 177.19/27.71    (30)  op(e0, e1) = all_52_29
% 177.19/27.71    (31)  all_58_4 = all_52_5
% 177.19/27.71    (32)   ~ (e3 = e1)
% 177.19/27.71    (33)   ~ (all_52_27 = all_52_29)
% 177.19/27.71    (34)   ~ (all_52_17 = all_14_2)
% 177.19/27.71    (35)  op(e3, all_4_2) = all_4_1
% 177.19/27.71    (36)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.19/27.71    (37)   ~ (all_52_7 = all_4_2)
% 177.19/27.71    (38)  all_58_1 = all_52_3
% 177.19/27.71    (39)   ~ (all_52_13 = all_52_15)
% 177.19/27.71    (40)  all_58_0 = all_4_2
% 177.19/27.71    (41)  op(e1, all_52_29) = all_52_28
% 177.19/27.71    (42)  all_50_2 = all_4_2
% 177.19/27.71    (43)   ~ (all_4_1 = e2)
% 177.19/27.71    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.19/27.71    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.19/27.71    (46)  all_58_14 = all_52_29
% 177.19/27.71    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.71    (48)  all_26_2 = all_4_2
% 177.19/27.71    (49)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.19/27.71    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.71    (51)  all_58_8 = all_14_2
% 177.19/27.71    (52)  op(e0, e2) = all_52_27
% 177.19/27.71    (53)  op(all_14_1, all_14_2) = e3
% 177.19/27.71    (54)   ~ (all_52_3 = all_4_2)
% 177.19/27.71    (55)  op(all_6_1, all_6_2) = all_6_0
% 177.19/27.71    (56)  op(e0, e3) = all_52_25
% 177.19/27.71    (57)  op(e0, all_6_2) = all_6_1
% 177.19/27.71    (58)   ~ (all_52_9 = all_10_2)
% 177.19/27.71    (59)  op(all_4_1, all_4_2) = e2
% 177.19/27.71    (60)  op(e3, all_52_17) = all_52_16
% 177.19/27.71    (61)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.19/27.71    (62)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.19/27.71    (63)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.19/27.71    (64)  all_56_12 = all_52_25
% 177.19/27.71    (65)  all_58_13 = all_52_27
% 177.19/27.71    (66)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.19/27.71    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.19/27.71    (68)   ~ (all_52_9 = all_52_17)
% 177.19/27.71    (69)  all_58_6 = all_52_17
% 177.19/27.71    (70)   ~ (all_52_3 = all_52_7)
% 177.19/27.71    (71)  all_56_0 = all_4_2
% 177.19/27.71    (72)  all_58_11 = all_52_23
% 177.19/27.71    (73)  all_26_1 = all_4_1
% 177.19/27.71    (74)   ~ (all_6_0 = e2)
% 177.19/27.71    (75)   ~ (all_52_29 = all_6_2)
% 177.19/27.71    (76)  all_58_2 = all_52_9
% 177.19/27.71    (77)  op(e3, e1) = all_52_5
% 177.19/27.71    (78)   ~ (all_52_25 = all_6_2)
% 177.19/27.71    (79)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.19/27.71    (80)  op(e1, e3) = all_52_17
% 177.19/27.71    (81)   ~ (all_52_25 = all_4_2)
% 177.19/27.71    (82)  op(e3, e0) = all_52_7
% 177.19/27.71    (83)  op(e3, e3) = all_4_2
% 177.19/27.71    (84)   ~ (all_52_17 = all_4_2)
% 177.19/27.71    (85)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.19/27.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.19/27.71    (86)   ~ (all_52_25 = all_52_27)
% 177.19/27.71    (87)   ~ (all_52_7 = all_6_2)
% 177.19/27.71    (88)   ~ (all_6_0 = e1)
% 177.19/27.71    (89)  op(e2, all_52_27) = all_52_26
% 177.19/27.71    (90)  all_52_20 = all_14_1
% 177.19/27.71    (91)   ~ (all_52_17 = all_52_19)
% 177.19/27.71    (92)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.19/27.71    (93)  all_52_30 = all_6_1
% 177.19/27.71    (94)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.19/27.71    (95)  op(e1, all_14_2) = all_14_1
% 177.19/27.71    (96)  all_58_9 = all_52_7
% 177.19/27.71    (97)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.19/27.71          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.19/27.71    (98)  all_58_12 = all_52_25
% 177.19/27.71    (99)   ~ (all_52_9 = all_52_15)
% 177.19/27.71    (100)   ~ (e3 = e2)
% 177.19/27.71    (101)  op(e2, e3) = all_52_9
% 177.19/27.71    (102)  all_56_13 = all_52_27
% 177.19/27.71  
% 177.19/27.71  Begin of proof
% 177.19/27.71  | 
% 177.19/27.71  | BETA: splitting (97) gives:
% 177.19/27.71  | 
% 177.19/27.71  | Case 1:
% 177.19/27.71  | | 
% 177.19/27.71  | |   (103)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.19/27.71  | | 
% 177.19/27.71  | | ALPHA: (103) implies:
% 177.19/27.71  | |   (104)  all_52_20 = e1
% 177.19/27.71  | | 
% 177.19/27.71  | | COMBINE_EQS: (90), (104) imply:
% 177.19/27.71  | |   (105)  all_14_1 = e1
% 177.19/27.71  | | 
% 177.19/27.72  | | REF_CLOSE: (32), (53), (85), (95), (105) are inconsistent by sub-proof #344.
% 177.19/27.72  | | 
% 177.19/27.72  | Case 2:
% 177.19/27.72  | | 
% 177.19/27.72  | |   (106)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.19/27.72  | | 
% 177.19/27.72  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.19/27.72  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.19/27.72  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.19/27.72  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.19/27.72  | |            (46), (47), (48), (49), (50), (51), (52), (54), (55), (56), (57),
% 177.19/27.72  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.19/27.72  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.19/27.72  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (91),
% 177.19/27.72  | |            (92), (93), (94), (96), (98), (99), (100), (101), (102), (106)
% 177.19/27.72  | |            are inconsistent by sub-proof #449.
% 177.19/27.72  | | 
% 177.19/27.72  | End of split
% 177.19/27.72  | 
% 177.19/27.72  End of proof
% 177.19/27.72  
% 177.19/27.72  Sub-proof #323 shows that the following formulas are inconsistent:
% 177.19/27.72  ----------------------------------------------------------------
% 177.19/27.72    (1)   ~ (all_52_23 = all_14_2)
% 177.19/27.72    (2)   ~ (all_52_5 = all_52_13)
% 177.19/27.72    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.19/27.72    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.19/27.72    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.19/27.72    (6)   ~ (all_52_27 = all_10_2)
% 177.19/27.72    (7)   ~ (all_52_17 = all_52_23)
% 177.19/27.72    (8)   ~ (all_52_13 = all_52_29)
% 177.19/27.72    (9)  op(e2, all_10_2) = all_10_0
% 177.19/27.72    (10)  all_56_3 = all_52_7
% 177.19/27.72    (11)  op(e3, e2) = all_52_3
% 177.19/27.72    (12)   ~ (all_52_9 = all_52_25)
% 177.19/27.72    (13)  op(e3, all_52_25) = all_52_24
% 177.19/27.72    (14)   ~ (all_52_19 = all_52_23)
% 177.19/27.72    (15)  all_56_11 = all_52_23
% 177.19/27.72    (16)  op(e1, e2) = all_52_19
% 177.19/27.72    (17)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.19/27.72    (18)  all_50_1 = all_4_1
% 177.19/27.72    (19)   ~ (all_52_3 = all_10_2)
% 177.19/27.72    (20)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.19/27.72    (21)  all_58_5 = all_52_13
% 177.19/27.72    (22)   ~ (all_6_2 = e0)
% 177.19/27.72    (23)   ~ (all_52_25 = all_52_29)
% 177.19/27.72    (24)  op(e1, all_52_13) = e1
% 177.19/27.72    (25)  op(e0, all_52_15) = e0
% 177.19/27.72    (26)  all_56_15 = all_6_2
% 177.19/27.72    (27)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.19/27.72    (28)  op(e2, e0) = all_52_15
% 177.19/27.72    (29)  all_58_3 = all_10_2
% 177.19/27.72    (30)  all_56_9 = all_52_19
% 177.19/27.72    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.72    (32)  all_58_15 = all_6_2
% 177.19/27.72    (33)   ~ (all_52_9 = all_4_2)
% 177.19/27.72    (34)   ~ (all_52_5 = all_52_7)
% 177.19/27.72    (35)  all_58_10 = all_52_15
% 177.19/27.72    (36)   ~ (all_52_5 = all_4_2)
% 177.19/27.72    (37)  all_58_7 = all_52_19
% 177.19/27.72    (38)  all_56_4 = all_52_9
% 177.19/27.72    (39)   ~ (all_52_15 = all_6_2)
% 177.19/27.72    (40)   ~ (all_52_17 = all_52_25)
% 177.19/27.72    (41)  all_58_4 = all_52_5
% 177.19/27.72    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.19/27.72    (43)   ~ (e3 = e1)
% 177.19/27.72    (44)   ~ (all_52_27 = all_52_29)
% 177.19/27.72    (45)   ~ (all_52_17 = all_14_2)
% 177.19/27.72    (46)  op(e3, all_4_2) = all_4_1
% 177.19/27.72    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.19/27.72    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.19/27.72    (49)   ~ (all_52_7 = all_4_2)
% 177.19/27.72    (50)  all_58_1 = all_52_3
% 177.19/27.72    (51)   ~ (all_52_13 = all_52_15)
% 177.19/27.72    (52)  all_58_0 = all_4_2
% 177.19/27.72    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.19/27.72    (54)  op(e1, all_52_29) = all_52_28
% 177.19/27.72    (55)  all_50_2 = all_4_2
% 177.19/27.72    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.19/27.72    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.19/27.72    (58)   ~ (all_4_1 = e2)
% 177.19/27.72    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.19/27.72    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.19/27.72    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.19/27.72    (62)  all_58_14 = all_52_29
% 177.19/27.72    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.72    (64)  all_26_2 = all_4_2
% 177.19/27.72    (65)   ~ (all_52_3 = all_52_5)
% 177.19/27.72    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.19/27.72    (67)  op(e2, e1) = all_52_13
% 177.19/27.72    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.72    (69)  all_58_8 = all_14_2
% 177.19/27.72    (70)  all_56_1 = all_52_3
% 177.19/27.72    (71)  op(all_14_1, all_14_2) = e3
% 177.19/27.72    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.19/27.72    (73)   ~ (all_52_3 = all_52_27)
% 177.19/27.72    (74)   ~ (all_52_3 = all_4_2)
% 177.19/27.72    (75)  op(e0, e3) = all_52_25
% 177.19/27.72    (76)   ~ (all_52_9 = all_10_2)
% 177.19/27.72    (77)  op(all_4_1, all_4_2) = e2
% 177.19/27.72    (78)  op(e3, all_52_17) = all_52_16
% 177.19/27.72    (79)   ~ (all_52_13 = all_14_2)
% 177.19/27.72    (80)  op(e3, all_52_9) = e3
% 177.19/27.72    (81)   ~ (e3 = e0)
% 177.19/27.72    (82)   ~ (all_52_9 = all_52_13)
% 177.19/27.72    (83)  op(e0, all_52_23) = all_52_22
% 177.19/27.72    (84)   ~ (all_52_15 = all_52_23)
% 177.19/27.72    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.19/27.72    (86)   ~ (all_52_5 = all_52_29)
% 177.19/27.72    (87)  all_56_2 = all_52_5
% 177.19/27.72    (88)  op(e1, e0) = all_52_23
% 177.19/27.72    (89)  all_58_13 = all_52_27
% 177.19/27.72    (90)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.19/27.72    (91)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 177.19/27.72    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.19/27.72    (93)  all_56_5 = all_10_2
% 177.19/27.72    (94)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.19/27.72    (95)   ~ (all_52_9 = all_52_17)
% 177.19/27.72    (96)  all_58_6 = all_52_17
% 177.19/27.72    (97)   ~ (all_52_3 = all_52_7)
% 177.19/27.72    (98)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.19/27.72    (99)  op(e2, all_52_19) = all_52_18
% 177.19/27.72    (100)   ~ (e1 = e0)
% 177.19/27.72    (101)  all_56_0 = all_4_2
% 177.19/27.72    (102)  all_58_11 = all_52_23
% 177.19/27.72    (103)   ~ (all_52_3 = all_52_19)
% 177.19/27.72    (104)   ~ (all_52_7 = all_52_15)
% 177.19/27.72    (105)  all_26_1 = all_4_1
% 177.19/27.72    (106)   ~ (all_52_29 = all_14_2)
% 177.19/27.72    (107)   ~ (all_52_19 = all_10_2)
% 177.19/27.72    (108)   ~ (all_52_23 = all_6_2)
% 177.19/27.72    (109)   ~ (all_52_29 = all_6_2)
% 177.19/27.72    (110)  all_58_2 = all_52_9
% 177.19/27.72    (111)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.19/27.72    (112)  op(e3, e1) = all_52_5
% 177.19/27.72    (113)  all_56_10 = all_14_2
% 177.19/27.72    (114)   ~ (all_52_25 = all_6_2)
% 177.19/27.72    (115)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.19/27.72    (116)  op(e1, e3) = all_52_17
% 177.19/27.72    (117)   ~ (all_52_25 = all_4_2)
% 177.19/27.72    (118)  op(e3, e0) = all_52_7
% 177.19/27.72    (119)  op(e2, all_10_2) = e2
% 177.19/27.72    (120)  op(e3, e3) = all_4_2
% 177.19/27.72    (121)  all_56_8 = all_52_17
% 177.19/27.72    (122)   ~ (all_52_17 = all_4_2)
% 177.19/27.72    (123)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.19/27.72             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.19/27.72    (124)   ~ (all_52_25 = all_52_27)
% 177.19/27.72    (125)   ~ (all_52_27 = all_6_2)
% 177.19/27.72    (126)   ~ (all_52_7 = all_6_2)
% 177.19/27.72    (127)   ~ (all_10_0 = e3)
% 177.19/27.72    (128)  all_18_2 = all_14_2
% 177.19/27.72    (129)   ~ (all_52_7 = all_52_23)
% 177.19/27.72    (130)   ~ (all_52_13 = all_10_2)
% 177.19/27.72    (131)  op(e2, all_52_27) = all_52_26
% 177.19/27.72    (132)   ~ (all_52_17 = all_52_19)
% 177.19/27.72    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.19/27.72    (134)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.19/27.72    (135)  op(e1, all_14_2) = all_14_1
% 177.19/27.72    (136)  all_58_9 = all_52_7
% 177.19/27.72    (137)  all_58_12 = all_52_25
% 177.19/27.72    (138)   ~ (all_10_0 = e1)
% 177.19/27.72    (139)  all_56_6 = all_52_13
% 177.19/27.72    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.19/27.72    (141)   ~ (all_52_9 = all_52_15)
% 177.19/27.72    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.19/27.72    (143)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.19/27.72    (144)   ~ (all_52_19 = all_14_2)
% 177.19/27.72    (145)  op(e2, e3) = all_52_9
% 177.19/27.72    (146)  all_56_13 = all_52_27
% 177.19/27.72  
% 177.19/27.72  Begin of proof
% 177.19/27.72  | 
% 177.19/27.72  | GROUND_INST: instantiating (123) with e2, all_10_0, all_10_2, e2, simplifying
% 177.19/27.72  |              with (9), (119) gives:
% 177.19/27.72  |   (147)  all_10_0 = e2
% 177.19/27.72  | 
% 177.19/27.72  | REDUCE: (127), (147) imply:
% 177.19/27.72  |   (148)   ~ (e3 = e2)
% 177.19/27.72  | 
% 177.19/27.72  | SIMP: (148) implies:
% 177.19/27.72  |   (149)   ~ (e3 = e2)
% 177.19/27.72  | 
% 177.19/27.72  | REDUCE: (138), (147) imply:
% 177.19/27.72  |   (150)   ~ (e2 = e1)
% 177.19/27.72  | 
% 177.19/27.72  | BETA: splitting (47) gives:
% 177.19/27.72  | 
% 177.19/27.72  | Case 1:
% 177.19/27.72  | | 
% 177.19/27.72  | |   (151)  all_56_15 = e3
% 177.19/27.72  | | 
% 177.19/27.72  | | COMBINE_EQS: (26), (151) imply:
% 177.19/27.72  | |   (152)  all_6_2 = e3
% 177.19/27.72  | | 
% 177.19/27.72  | | REF_CLOSE: (10), (11), (19), (21), (24), (27), (29), (31), (33), (35), (38),
% 177.19/27.72  | |            (39), (46), (48), (49), (52), (58), (61), (64), (66), (77), (80),
% 177.19/27.72  | |            (82), (90), (95), (98), (101), (105), (110), (116), (118), (119),
% 177.19/27.72  | |            (120), (122), (123), (126), (134), (139), (145), (152) are
% 177.19/27.72  | |            inconsistent by sub-proof #467.
% 177.19/27.72  | | 
% 177.19/27.72  | Case 2:
% 177.19/27.72  | | 
% 177.19/27.72  | |   (153)   ~ (all_56_15 = e3)
% 177.19/27.72  | |   (154)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.19/27.72  | | 
% 177.19/27.72  | | REDUCE: (26), (153) imply:
% 177.19/27.72  | |   (155)   ~ (all_6_2 = e3)
% 177.19/27.72  | | 
% 177.19/27.72  | | BETA: splitting (63) gives:
% 177.19/27.72  | | 
% 177.19/27.72  | | Case 1:
% 177.19/27.72  | | | 
% 177.19/27.72  | | |   (156)  all_56_13 = e3
% 177.19/27.72  | | | 
% 177.19/27.72  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 177.19/27.72  | | |            (16), (19), (20), (21), (24), (25), (27), (28), (29), (31),
% 177.19/27.72  | | |            (32), (33), (34), (35), (36), (37), (38), (40), (41), (42),
% 177.19/27.72  | | |            (43), (44), (45), (46), (48), (50), (51), (52), (53), (56),
% 177.19/27.72  | | |            (58), (62), (65), (66), (69), (70), (73), (74), (75), (76),
% 177.19/27.72  | | |            (77), (78), (79), (80), (82), (84), (88), (89), (92), (93),
% 177.19/27.72  | | |            (96), (97), (98), (100), (101), (102), (107), (110), (115),
% 177.19/27.72  | | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.19/27.72  | | |            (125), (130), (131), (132), (133), (136), (137), (141), (142),
% 177.19/27.72  | | |            (145), (146), (150), (156) are inconsistent by sub-proof #464.
% 177.19/27.72  | | | 
% 177.19/27.72  | | Case 2:
% 177.19/27.72  | | | 
% 177.19/27.72  | | |   (157)   ~ (all_56_13 = e3)
% 177.19/27.72  | | | 
% 177.19/27.72  | | | REDUCE: (146), (157) imply:
% 177.19/27.72  | | |   (158)   ~ (all_52_27 = e3)
% 177.19/27.72  | | | 
% 177.19/27.72  | | | BETA: splitting (68) gives:
% 177.19/27.72  | | | 
% 177.19/27.72  | | | Case 1:
% 177.19/27.72  | | | | 
% 177.19/27.72  | | | |   (159)  all_58_12 = e3
% 177.19/27.72  | | | | 
% 177.19/27.72  | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (14), (15),
% 177.19/27.72  | | | |            (16), (19), (21), (22), (23), (24), (25), (26), (27), (29),
% 177.19/27.72  | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (40),
% 177.19/27.72  | | | |            (41), (42), (44), (45), (48), (49), (50), (52), (53), (57),
% 177.19/27.72  | | | |            (59), (60), (61), (62), (65), (67), (69), (71), (72), (75),
% 177.19/27.72  | | | |            (78), (79), (80), (81), (82), (83), (85), (89), (91), (94),
% 177.19/27.72  | | | |            (95), (96), (97), (98), (99), (101), (102), (103), (104),
% 177.19/27.72  | | | |            (106), (107), (108), (110), (111), (112), (113), (114),
% 177.19/27.72  | | | |            (116), (117), (118), (119), (122), (123), (124), (125),
% 177.19/27.72  | | | |            (126), (128), (129), (132), (133), (134), (135), (136),
% 177.19/27.72  | | | |            (137), (139), (140), (141), (142), (144), (145), (149),
% 177.19/27.72  | | | |            (150), (154), (159) are inconsistent by sub-proof #333.
% 177.19/27.72  | | | | 
% 177.19/27.72  | | | Case 2:
% 177.19/27.72  | | | | 
% 177.19/27.72  | | | |   (160)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.72  | | | | 
% 177.19/27.72  | | | | REF_CLOSE: (3), (7), (11), (17), (18), (19), (23), (25), (27), (29),
% 177.19/27.72  | | | |            (31), (32), (33), (35), (36), (37), (40), (43), (44), (46),
% 177.19/27.72  | | | |            (48), (49), (50), (52), (54), (55), (58), (60), (62), (66),
% 177.19/27.72  | | | |            (75), (77), (78), (80), (86), (87), (89), (92), (96), (97),
% 177.19/27.72  | | | |            (100), (101), (102), (109), (110), (112), (116), (117),
% 177.19/27.72  | | | |            (119), (120), (121), (122), (123), (132), (133), (136),
% 177.19/27.72  | | | |            (137), (143), (145), (150), (155), (158), (160) are
% 177.19/27.72  | | | |            inconsistent by sub-proof #463.
% 177.19/27.72  | | | | 
% 177.19/27.72  | | | End of split
% 177.19/27.72  | | | 
% 177.19/27.72  | | End of split
% 177.19/27.72  | | 
% 177.19/27.72  | End of split
% 177.19/27.72  | 
% 177.19/27.72  End of proof
% 177.19/27.72  
% 177.19/27.72  Sub-proof #324 shows that the following formulas are inconsistent:
% 177.19/27.72  ----------------------------------------------------------------
% 177.19/27.72    (1)  all_56_3 = all_52_7
% 177.19/27.72    (2)  op(e3, e2) = all_52_3
% 177.19/27.72    (3)   ~ (all_52_9 = all_52_25)
% 177.19/27.72    (4)  op(e3, all_52_25) = all_52_24
% 177.19/27.72    (5)   ~ (all_52_25 = all_52_29)
% 177.19/27.72    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.19/27.72    (7)   ~ (all_52_9 = all_4_2)
% 177.19/27.72    (8)   ~ (all_52_5 = all_52_7)
% 177.19/27.72    (9)   ~ (all_52_5 = all_4_2)
% 177.19/27.72    (10)   ~ (all_52_17 = all_52_25)
% 177.19/27.72    (11)   ~ (e3 = e1)
% 177.19/27.72    (12)  op(e3, all_4_2) = all_4_1
% 177.19/27.72    (13)   ~ (all_52_7 = all_4_2)
% 177.19/27.72    (14)  all_58_0 = all_4_2
% 177.19/27.72    (15)  op(e1, all_52_29) = all_52_28
% 177.19/27.72    (16)   ~ (all_4_1 = e2)
% 177.19/27.72    (17)  all_58_14 = all_52_29
% 177.19/27.72    (18)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.19/27.72    (19)  all_26_2 = all_4_2
% 177.19/27.72    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.19/27.72    (21)  op(all_14_1, all_14_2) = e3
% 177.19/27.72    (22)   ~ (all_52_3 = all_4_2)
% 177.19/27.72    (23)  op(all_4_1, all_4_2) = e2
% 177.19/27.72    (24)   ~ (e3 = e0)
% 177.19/27.72    (25)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.19/27.72    (26)  all_56_12 = all_52_25
% 177.19/27.72    (27)  all_58_13 = all_52_27
% 177.19/27.72    (28)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.19/27.72    (29)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.19/27.72    (30)   ~ (all_52_25 = e0)
% 177.19/27.72    (31)  all_56_0 = all_4_2
% 177.22/27.72    (32)  all_26_1 = all_4_1
% 177.22/27.72    (33)  all_58_15 = e0
% 177.22/27.72    (34)  op(e3, e1) = all_52_5
% 177.22/27.72    (35)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.72    (36)  op(e1, e3) = all_52_17
% 177.22/27.72    (37)   ~ (all_52_25 = all_4_2)
% 177.22/27.72    (38)  op(e3, e0) = all_52_7
% 177.22/27.72    (39)  op(e3, e3) = all_4_2
% 177.22/27.72    (40)   ~ (all_52_17 = all_4_2)
% 177.22/27.72    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.72    (42)   ~ (all_52_25 = all_52_27)
% 177.22/27.72    (43)  op(e2, all_52_27) = all_52_26
% 177.22/27.72    (44)  all_52_20 = all_14_1
% 177.22/27.72    (45)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.72    (46)  op(e1, all_14_2) = all_14_1
% 177.22/27.72    (47)   ~ (e2 = e0)
% 177.22/27.72    (48)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.22/27.72          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.72    (49)  all_58_12 = all_52_25
% 177.22/27.72    (50)   ~ (e3 = e2)
% 177.22/27.72    (51)  op(e2, e3) = all_52_9
% 177.22/27.72    (52)  all_56_13 = all_52_27
% 177.22/27.72  
% 177.22/27.72  Begin of proof
% 177.22/27.72  | 
% 177.22/27.72  | BETA: splitting (48) gives:
% 177.22/27.72  | 
% 177.22/27.72  | Case 1:
% 177.22/27.72  | | 
% 177.22/27.72  | |   (53)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.22/27.72  | | 
% 177.22/27.72  | | ALPHA: (53) implies:
% 177.22/27.72  | |   (54)  all_52_20 = e1
% 177.22/27.72  | | 
% 177.22/27.72  | | COMBINE_EQS: (44), (54) imply:
% 177.22/27.72  | |   (55)  all_14_1 = e1
% 177.22/27.72  | | 
% 177.22/27.72  | | REF_CLOSE: (11), (21), (41), (46), (55) are inconsistent by sub-proof #344.
% 177.22/27.72  | | 
% 177.22/27.72  | Case 2:
% 177.22/27.72  | | 
% 177.22/27.72  | |   (56)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.22/27.72  | | 
% 177.22/27.72  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 177.22/27.72  | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 177.22/27.72  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.22/27.72  | |            (37), (38), (39), (40), (41), (42), (43), (45), (47), (49), (50),
% 177.22/27.72  | |            (51), (52), (56) are inconsistent by sub-proof #470.
% 177.22/27.72  | | 
% 177.22/27.72  | End of split
% 177.22/27.72  | 
% 177.22/27.72  End of proof
% 177.22/27.72  
% 177.22/27.72  Sub-proof #325 shows that the following formulas are inconsistent:
% 177.22/27.72  ----------------------------------------------------------------
% 177.22/27.72    (1)   ~ (all_52_5 = all_52_13)
% 177.22/27.72    (2)   ~ (all_52_27 = all_10_2)
% 177.22/27.72    (3)   ~ (all_52_17 = all_52_23)
% 177.22/27.72    (4)  op(e2, all_10_2) = all_10_1
% 177.22/27.72    (5)   ~ (all_52_13 = all_52_29)
% 177.22/27.72    (6)  all_56_3 = all_52_7
% 177.22/27.72    (7)  op(e3, e2) = all_52_3
% 177.22/27.72    (8)   ~ (all_52_9 = all_52_25)
% 177.22/27.72    (9)  op(e3, all_52_25) = all_52_24
% 177.22/27.72    (10)   ~ (all_52_27 = e0)
% 177.22/27.72    (11)  op(e3, all_52_9) = all_52_8
% 177.22/27.72    (12)   ~ (all_52_3 = all_10_2)
% 177.22/27.72    (13)  all_58_5 = all_52_13
% 177.22/27.72    (14)   ~ (all_52_25 = all_52_29)
% 177.22/27.72    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.72    (16)  all_58_3 = all_10_2
% 177.22/27.72    (17)   ~ (all_52_9 = all_4_2)
% 177.22/27.72    (18)   ~ (all_52_5 = all_52_7)
% 177.22/27.72    (19)  all_58_10 = all_52_15
% 177.22/27.72    (20)  all_58_7 = all_52_19
% 177.22/27.72    (21)   ~ (all_52_17 = all_52_25)
% 177.22/27.72    (22)  op(e0, e1) = all_52_29
% 177.22/27.72    (23)  all_58_4 = all_52_5
% 177.22/27.72    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.72    (25)   ~ (e3 = e1)
% 177.22/27.72    (26)   ~ (all_52_27 = all_52_29)
% 177.22/27.72    (27)   ~ (all_52_17 = all_14_2)
% 177.22/27.72    (28)  op(e3, all_4_2) = all_4_1
% 177.22/27.72    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.72    (30)   ~ (all_52_7 = all_4_2)
% 177.22/27.72    (31)  all_58_1 = all_52_3
% 177.22/27.72    (32)   ~ (all_52_13 = all_52_15)
% 177.22/27.72    (33)  all_58_0 = all_4_2
% 177.22/27.72    (34)  op(e1, all_52_13) = all_52_12
% 177.22/27.72    (35)  op(e1, all_52_29) = all_52_28
% 177.22/27.72    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.72          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.72    (37)   ~ (all_4_1 = e2)
% 177.22/27.72    (38)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.72    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.72    (40)  all_58_14 = all_52_29
% 177.22/27.72    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.72    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.72    (43)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.72    (44)  all_58_8 = all_14_2
% 177.22/27.72    (45)  op(e0, e2) = all_52_27
% 177.22/27.72    (46)  all_56_14 = all_52_29
% 177.22/27.72    (47)   ~ (all_52_3 = all_4_2)
% 177.22/27.72    (48)  op(e0, e3) = all_52_25
% 177.22/27.72    (49)  all_52_0 = all_4_1
% 177.22/27.72    (50)  op(all_4_1, all_4_2) = e2
% 177.22/27.72    (51)  all_52_10 = all_10_1
% 177.22/27.72    (52)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.72    (53)   ~ (all_52_13 = all_14_2)
% 177.22/27.72    (54)   ~ (e3 = e0)
% 177.22/27.72    (55)   ~ (all_52_9 = all_52_13)
% 177.22/27.72    (56)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.72    (57)   ~ (all_52_15 = all_52_23)
% 177.22/27.72    (58)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.72    (59)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.72    (60)  all_56_12 = all_52_25
% 177.22/27.72    (61)  all_58_13 = all_52_27
% 177.22/27.72    (62)   ~ (all_52_25 = e0)
% 177.22/27.72    (63)   ~ (all_52_9 = all_52_17)
% 177.22/27.72    (64)  all_58_6 = all_52_17
% 177.22/27.72    (65)   ~ (all_52_3 = all_52_7)
% 177.22/27.72    (66)   ~ (e1 = e0)
% 177.22/27.72    (67)  all_58_11 = all_52_23
% 177.22/27.72    (68)   ~ (all_52_3 = all_52_19)
% 177.22/27.72    (69)   ~ (all_52_7 = all_52_15)
% 177.22/27.72    (70)  op(e0, all_52_15) = all_52_14
% 177.22/27.72    (71)   ~ (all_52_29 = all_14_2)
% 177.22/27.72    (72)   ~ (all_52_19 = all_10_2)
% 177.22/27.72    (73)  all_58_15 = e0
% 177.22/27.72    (74)  all_58_2 = all_52_9
% 177.22/27.72    (75)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.22/27.72    (76)   ~ (all_52_29 = e0)
% 177.22/27.72    (77)  op(e3, e1) = all_52_5
% 177.22/27.72    (78)  all_56_10 = all_14_2
% 177.22/27.72    (79)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.72    (80)  op(e1, e3) = all_52_17
% 177.22/27.72    (81)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.72    (82)  op(e3, e3) = all_4_2
% 177.22/27.72    (83)   ~ (all_52_17 = all_4_2)
% 177.22/27.72    (84)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.72    (85)   ~ (all_52_25 = all_52_27)
% 177.22/27.72    (86)   ~ (all_10_0 = e3)
% 177.22/27.72    (87)   ~ (all_52_19 = all_52_27)
% 177.22/27.72    (88)  all_56_7 = all_52_15
% 177.22/27.72    (89)   ~ (all_52_15 = e0)
% 177.22/27.72    (90)   ~ (all_52_7 = all_52_23)
% 177.22/27.72    (91)   ~ (all_52_13 = all_10_2)
% 177.22/27.72    (92)  op(e2, all_52_27) = all_52_26
% 177.22/27.72    (93)   ~ (all_52_17 = all_52_19)
% 177.22/27.72    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.72    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.72    (96)  all_58_9 = all_52_7
% 177.22/27.72    (97)   ~ (e2 = e0)
% 177.22/27.72    (98)  all_58_12 = all_52_25
% 177.22/27.72    (99)   ~ (all_10_0 = e1)
% 177.22/27.72    (100)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.72    (101)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.72    (102)   ~ (all_52_19 = all_14_2)
% 177.22/27.72    (103)  op(e2, e3) = all_52_9
% 177.22/27.72    (104)  all_56_13 = all_52_27
% 177.22/27.72  
% 177.22/27.72  Begin of proof
% 177.22/27.72  | 
% 177.22/27.72  | BETA: splitting (36) gives:
% 177.22/27.72  | 
% 177.22/27.72  | Case 1:
% 177.22/27.72  | | 
% 177.22/27.72  | |   (105)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.22/27.72  | | 
% 177.22/27.72  | | REF_CLOSE: (28), (37), (49), (50), (84), (105) are inconsistent by sub-proof
% 177.22/27.72  | |            #494.
% 177.22/27.72  | | 
% 177.22/27.72  | Case 2:
% 177.22/27.72  | | 
% 177.22/27.72  | |   (106)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.72  | | 
% 177.22/27.72  | | ALPHA: (106) implies:
% 177.22/27.72  | |   (107)  all_52_14 = e0
% 177.22/27.72  | |   (108)  all_52_12 = e1
% 177.22/27.72  | |   (109)  all_52_10 = e2
% 177.22/27.72  | |   (110)  all_52_8 = e3
% 177.22/27.72  | | 
% 177.22/27.72  | | COMBINE_EQS: (51), (109) imply:
% 177.22/27.72  | |   (111)  all_10_1 = e2
% 177.22/27.72  | | 
% 177.22/27.72  | | REDUCE: (59), (111) imply:
% 177.22/27.72  | |   (112)  op(e2, all_10_2) = all_10_0
% 177.22/27.72  | | 
% 177.22/27.72  | | REDUCE: (11), (110) imply:
% 177.22/27.72  | |   (113)  op(e3, all_52_9) = e3
% 177.22/27.72  | | 
% 177.22/27.72  | | REDUCE: (4), (111) imply:
% 177.22/27.72  | |   (114)  op(e2, all_10_2) = e2
% 177.22/27.72  | | 
% 177.22/27.72  | | REDUCE: (34), (108) imply:
% 177.22/27.72  | |   (115)  op(e1, all_52_13) = e1
% 177.22/27.72  | | 
% 177.22/27.72  | | REDUCE: (70), (107) imply:
% 177.22/27.72  | |   (116)  op(e0, all_52_15) = e0
% 177.22/27.72  | | 
% 177.22/27.72  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 177.22/27.72  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.22/27.72  | |            (26), (27), (28), (29), (30), (31), (32), (33), (35), (37), (38),
% 177.22/27.72  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (50),
% 177.22/27.72  | |            (52), (53), (54), (55), (56), (57), (58), (60), (61), (62), (63),
% 177.22/27.72  | |            (64), (65), (66), (67), (68), (69), (71), (72), (73), (74), (75),
% 177.22/27.72  | |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 177.22/27.72  | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 177.22/27.72  | |            (98), (99), (100), (101), (102), (103), (104), (112), (113),
% 177.22/27.72  | |            (114), (115), (116) are inconsistent by sub-proof #485.
% 177.22/27.72  | | 
% 177.22/27.72  | End of split
% 177.22/27.72  | 
% 177.22/27.72  End of proof
% 177.22/27.72  
% 177.22/27.72  Sub-proof #326 shows that the following formulas are inconsistent:
% 177.22/27.72  ----------------------------------------------------------------
% 177.22/27.72    (1)   ~ (e3 = e1)
% 177.22/27.72    (2)  op(all_14_1, all_14_2) = e3
% 177.22/27.72    (3)  op(e0, all_6_2) = all_6_1
% 177.22/27.72    (4)   ~ (e3 = e0)
% 177.22/27.72    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.72    (6)  all_52_20 = all_14_1
% 177.22/27.72    (7)  all_52_30 = all_6_1
% 177.22/27.72    (8)  op(e1, all_14_2) = all_14_1
% 177.22/27.72    (9)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.22/27.72         (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.72    (10)  op(all_6_1, all_6_2) = e3
% 177.22/27.72  
% 177.22/27.72  Begin of proof
% 177.22/27.72  | 
% 177.22/27.72  | BETA: splitting (9) gives:
% 177.22/27.72  | 
% 177.22/27.72  | Case 1:
% 177.22/27.72  | | 
% 177.22/27.72  | |   (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.22/27.72  | | 
% 177.22/27.72  | | ALPHA: (11) implies:
% 177.22/27.72  | |   (12)  all_52_20 = e1
% 177.22/27.72  | | 
% 177.22/27.72  | | COMBINE_EQS: (6), (12) imply:
% 177.22/27.72  | |   (13)  all_14_1 = e1
% 177.22/27.72  | | 
% 177.22/27.72  | | REF_CLOSE: (1), (2), (5), (8), (13) are inconsistent by sub-proof #344.
% 177.22/27.72  | | 
% 177.22/27.72  | Case 2:
% 177.22/27.72  | | 
% 177.22/27.72  | |   (14)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.22/27.72  | | 
% 177.22/27.72  | | REF_CLOSE: (3), (4), (5), (7), (10), (14) are inconsistent by sub-proof
% 177.22/27.72  | |            #501.
% 177.22/27.72  | | 
% 177.22/27.73  | End of split
% 177.22/27.73  | 
% 177.22/27.73  End of proof
% 177.22/27.73  
% 177.22/27.73  Sub-proof #327 shows that the following formulas are inconsistent:
% 177.22/27.73  ----------------------------------------------------------------
% 177.22/27.73    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.73    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.73    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.73    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.73    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.73    (6)  op(e2, all_10_2) = all_10_1
% 177.22/27.73    (7)   ~ (all_52_13 = all_52_29)
% 177.22/27.73    (8)  all_56_3 = all_52_7
% 177.22/27.73    (9)  op(e3, e2) = all_52_3
% 177.22/27.73    (10)   ~ (all_52_9 = all_52_25)
% 177.22/27.73    (11)   ~ (all_52_19 = all_52_23)
% 177.22/27.73    (12)  all_56_11 = all_52_23
% 177.22/27.73    (13)  op(e1, e2) = all_52_19
% 177.22/27.73    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.73    (15)  op(e3, all_52_9) = all_52_8
% 177.22/27.73    (16)   ~ (all_52_3 = all_10_2)
% 177.22/27.73    (17)  all_58_5 = all_52_13
% 177.22/27.73    (18)   ~ (all_6_2 = e0)
% 177.22/27.73    (19)   ~ (all_52_25 = all_52_29)
% 177.22/27.73    (20)  all_56_15 = all_6_2
% 177.22/27.73    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.73    (22)  all_58_3 = all_10_2
% 177.22/27.73    (23)  all_56_9 = all_52_19
% 177.22/27.73    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.73    (25)  all_58_15 = all_6_2
% 177.22/27.73    (26)   ~ (all_52_9 = all_4_2)
% 177.22/27.73    (27)   ~ (all_52_5 = all_52_7)
% 177.22/27.73    (28)  all_58_10 = all_52_15
% 177.22/27.73    (29)   ~ (all_52_5 = all_4_2)
% 177.22/27.73    (30)  all_58_7 = all_52_19
% 177.22/27.73    (31)  all_56_4 = all_52_9
% 177.22/27.73    (32)   ~ (all_52_15 = all_6_2)
% 177.22/27.73    (33)   ~ (all_52_17 = all_52_25)
% 177.22/27.73    (34)  all_58_4 = all_52_5
% 177.22/27.73    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.73    (36)   ~ (e3 = e1)
% 177.22/27.73    (37)  all_34_1 = all_4_1
% 177.22/27.73    (38)   ~ (all_52_27 = all_52_29)
% 177.22/27.73    (39)   ~ (all_52_17 = all_14_2)
% 177.22/27.73    (40)  op(e3, all_4_2) = all_4_1
% 177.22/27.73    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.73    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.73    (43)   ~ (all_52_7 = all_4_2)
% 177.22/27.73    (44)  all_58_1 = all_52_3
% 177.22/27.73    (45)  all_58_0 = all_4_2
% 177.22/27.73    (46)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.73    (47)  op(e1, all_52_13) = all_52_12
% 177.22/27.73    (48)  op(all_4_1, all_4_2) = e1
% 177.22/27.73    (49)  op(e1, all_52_29) = all_52_28
% 177.22/27.73    (50)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.73          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.73    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.73    (52)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.73    (53)   ~ (all_4_1 = e2)
% 177.22/27.73    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.73    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.73    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.73    (57)  all_58_14 = all_52_29
% 177.22/27.73    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.73    (59)   ~ (all_52_3 = all_52_5)
% 177.22/27.73    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.73    (61)  op(e2, e1) = all_52_13
% 177.22/27.73    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.73    (63)  all_58_8 = all_14_2
% 177.22/27.73    (64)  all_56_1 = all_52_3
% 177.22/27.73    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.73    (66)   ~ (all_52_3 = all_52_27)
% 177.22/27.73    (67)   ~ (all_52_3 = all_4_2)
% 177.22/27.73    (68)  op(e0, e3) = all_52_25
% 177.22/27.73    (69)  op(e0, all_6_2) = all_6_1
% 177.22/27.73    (70)  all_52_0 = all_4_1
% 177.22/27.73    (71)  op(e3, all_52_17) = all_52_16
% 177.22/27.73    (72)  all_52_10 = all_10_1
% 177.22/27.73    (73)   ~ (all_52_13 = all_14_2)
% 177.22/27.73    (74)   ~ (e3 = e0)
% 177.22/27.73    (75)   ~ (all_52_9 = all_52_13)
% 177.22/27.73    (76)  op(e0, all_52_23) = all_52_22
% 177.22/27.73    (77)   ~ (all_52_15 = all_52_23)
% 177.22/27.73    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.73    (79)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.73    (80)   ~ (all_52_5 = all_52_29)
% 177.22/27.73    (81)  all_56_2 = all_52_5
% 177.22/27.73    (82)  op(e1, e0) = all_52_23
% 177.22/27.73    (83)  all_58_13 = all_52_27
% 177.22/27.73    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.73    (85)   ~ (all_52_9 = all_52_17)
% 177.22/27.73    (86)  all_58_6 = all_52_17
% 177.22/27.73    (87)   ~ (all_52_3 = all_52_7)
% 177.22/27.73    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.73    (89)  op(e2, all_52_19) = all_52_18
% 177.22/27.73    (90)   ~ (e1 = e0)
% 177.22/27.73    (91)  all_56_0 = all_4_2
% 177.22/27.73    (92)  all_58_11 = all_52_23
% 177.22/27.73    (93)   ~ (all_52_3 = all_52_19)
% 177.22/27.73    (94)   ~ (all_52_7 = all_52_15)
% 177.22/27.73    (95)  op(e0, all_52_15) = all_52_14
% 177.22/27.73    (96)   ~ (all_52_29 = all_14_2)
% 177.22/27.73    (97)   ~ (all_52_19 = all_10_2)
% 177.22/27.73    (98)   ~ (all_52_23 = all_6_2)
% 177.22/27.73    (99)   ~ (all_52_29 = all_6_2)
% 177.22/27.73    (100)  all_58_2 = all_52_9
% 177.22/27.73    (101)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.73    (102)  op(e3, e1) = all_52_5
% 177.22/27.73    (103)  all_56_10 = all_14_2
% 177.22/27.73    (104)   ~ (all_52_25 = all_6_2)
% 177.22/27.73    (105)  op(e1, e1) = all_14_2
% 177.22/27.73    (106)  op(e1, e3) = all_52_17
% 177.22/27.73    (107)   ~ (all_52_25 = all_4_2)
% 177.22/27.73    (108)  op(e3, e0) = all_52_7
% 177.22/27.73    (109)  op(e3, e3) = all_4_2
% 177.22/27.73    (110)   ~ (all_52_17 = all_4_2)
% 177.22/27.73    (111)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.73             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.73    (112)   ~ (all_52_25 = all_52_27)
% 177.22/27.73    (113)  all_34_2 = all_4_2
% 177.22/27.73    (114)   ~ (all_52_27 = all_6_2)
% 177.22/27.73    (115)   ~ (all_52_7 = all_6_2)
% 177.22/27.73    (116)   ~ (all_10_0 = e3)
% 177.22/27.73    (117)   ~ (all_52_7 = all_52_23)
% 177.22/27.73    (118)  op(e2, all_52_27) = all_52_26
% 177.22/27.73    (119)   ~ (all_52_17 = all_52_19)
% 177.22/27.73    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.73    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.73    (122)  op(e1, all_14_2) = all_14_1
% 177.22/27.73    (123)  all_58_9 = all_52_7
% 177.22/27.73    (124)  all_58_12 = all_52_25
% 177.22/27.73    (125)   ~ (all_10_0 = e1)
% 177.22/27.73    (126)  all_56_6 = all_52_13
% 177.22/27.73    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.73    (128)   ~ (all_52_9 = all_52_15)
% 177.22/27.73    (129)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.73    (130)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.73    (131)   ~ (all_52_19 = all_14_2)
% 177.22/27.73    (132)  op(e2, e3) = all_52_9
% 177.22/27.73    (133)  all_56_13 = all_52_27
% 177.22/27.73  
% 177.22/27.73  Begin of proof
% 177.22/27.73  | 
% 177.22/27.73  | BETA: splitting (50) gives:
% 177.22/27.73  | 
% 177.22/27.73  | Case 1:
% 177.22/27.73  | | 
% 177.22/27.73  | |   (134)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.22/27.73  | | 
% 177.22/27.73  | | REF_CLOSE: (36), (40), (48), (70), (111), (134) are inconsistent by
% 177.22/27.73  | |            sub-proof #600.
% 177.22/27.73  | | 
% 177.22/27.73  | Case 2:
% 177.22/27.73  | | 
% 177.22/27.73  | |   (135)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.73  | | 
% 177.22/27.73  | | ALPHA: (135) implies:
% 177.22/27.73  | |   (136)  all_52_14 = e0
% 177.22/27.73  | |   (137)  all_52_12 = e1
% 177.22/27.73  | |   (138)  all_52_10 = e2
% 177.22/27.73  | |   (139)  all_52_8 = e3
% 177.22/27.73  | | 
% 177.22/27.73  | | COMBINE_EQS: (72), (138) imply:
% 177.22/27.73  | |   (140)  all_10_1 = e2
% 177.22/27.73  | | 
% 177.22/27.73  | | REDUCE: (79), (140) imply:
% 177.22/27.73  | |   (141)  op(e2, all_10_2) = all_10_0
% 177.22/27.73  | | 
% 177.22/27.73  | | REDUCE: (15), (139) imply:
% 177.22/27.73  | |   (142)  op(e3, all_52_9) = e3
% 177.22/27.73  | | 
% 177.22/27.73  | | REDUCE: (6), (140) imply:
% 177.22/27.73  | |   (143)  op(e2, all_10_2) = e2
% 177.22/27.73  | | 
% 177.22/27.73  | | REDUCE: (47), (137) imply:
% 177.22/27.73  | |   (144)  op(e1, all_52_13) = e1
% 177.22/27.73  | | 
% 177.22/27.73  | | REDUCE: (95), (136) imply:
% 177.22/27.73  | |   (145)  op(e0, all_52_15) = e0
% 177.22/27.73  | | 
% 177.22/27.73  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.22/27.73  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.22/27.73  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.22/27.73  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (48),
% 177.22/27.73  | |            (49), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 177.22/27.73  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (71), (73),
% 177.22/27.73  | |            (74), (75), (76), (77), (78), (80), (81), (82), (83), (84), (85),
% 177.22/27.73  | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (96), (97),
% 177.22/27.73  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 177.22/27.73  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 177.22/27.73  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.22/27.73  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 177.22/27.73  | |            (141), (142), (143), (144), (145) are inconsistent by sub-proof
% 177.22/27.73  | |            #328.
% 177.22/27.73  | | 
% 177.22/27.73  | End of split
% 177.22/27.73  | 
% 177.22/27.73  End of proof
% 177.22/27.73  
% 177.22/27.73  Sub-proof #328 shows that the following formulas are inconsistent:
% 177.22/27.73  ----------------------------------------------------------------
% 177.22/27.73    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.73    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.73    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.73    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.73    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.73    (6)   ~ (all_52_13 = all_52_29)
% 177.22/27.73    (7)  op(e2, all_10_2) = all_10_0
% 177.22/27.73    (8)  all_56_3 = all_52_7
% 177.22/27.73    (9)  op(e3, e2) = all_52_3
% 177.22/27.73    (10)   ~ (all_52_9 = all_52_25)
% 177.22/27.73    (11)   ~ (all_52_19 = all_52_23)
% 177.22/27.73    (12)  all_56_11 = all_52_23
% 177.22/27.73    (13)  op(e1, e2) = all_52_19
% 177.22/27.73    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.73    (15)   ~ (all_52_3 = all_10_2)
% 177.22/27.73    (16)  all_58_5 = all_52_13
% 177.22/27.73    (17)   ~ (all_6_2 = e0)
% 177.22/27.73    (18)   ~ (all_52_25 = all_52_29)
% 177.22/27.73    (19)  op(e1, all_52_13) = e1
% 177.22/27.73    (20)  op(e0, all_52_15) = e0
% 177.22/27.73    (21)  all_56_15 = all_6_2
% 177.22/27.73    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.73    (23)  all_58_3 = all_10_2
% 177.22/27.73    (24)  all_56_9 = all_52_19
% 177.22/27.73    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.73    (26)  all_58_15 = all_6_2
% 177.22/27.73    (27)   ~ (all_52_9 = all_4_2)
% 177.22/27.73    (28)   ~ (all_52_5 = all_52_7)
% 177.22/27.73    (29)  all_58_10 = all_52_15
% 177.22/27.73    (30)   ~ (all_52_5 = all_4_2)
% 177.22/27.73    (31)  all_58_7 = all_52_19
% 177.22/27.73    (32)  all_56_4 = all_52_9
% 177.22/27.73    (33)   ~ (all_52_15 = all_6_2)
% 177.22/27.73    (34)   ~ (all_52_17 = all_52_25)
% 177.22/27.73    (35)  all_58_4 = all_52_5
% 177.22/27.73    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.73    (37)   ~ (e3 = e1)
% 177.22/27.73    (38)  all_34_1 = all_4_1
% 177.22/27.73    (39)   ~ (all_52_27 = all_52_29)
% 177.22/27.73    (40)   ~ (all_52_17 = all_14_2)
% 177.22/27.73    (41)  op(e3, all_4_2) = all_4_1
% 177.22/27.73    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.73    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.73    (44)   ~ (all_52_7 = all_4_2)
% 177.22/27.73    (45)  all_58_1 = all_52_3
% 177.22/27.73    (46)  all_58_0 = all_4_2
% 177.22/27.73    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.73    (48)  op(all_4_1, all_4_2) = e1
% 177.22/27.73    (49)  op(e1, all_52_29) = all_52_28
% 177.22/27.73    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.73    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.73    (52)   ~ (all_4_1 = e2)
% 177.22/27.73    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.73    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.73    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.73    (56)  all_58_14 = all_52_29
% 177.22/27.73    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.73    (58)   ~ (all_52_3 = all_52_5)
% 177.22/27.73    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.73    (60)  op(e2, e1) = all_52_13
% 177.22/27.73    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.73    (62)  all_58_8 = all_14_2
% 177.22/27.73    (63)  all_56_1 = all_52_3
% 177.22/27.73    (64)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.73    (65)   ~ (all_52_3 = all_52_27)
% 177.22/27.73    (66)   ~ (all_52_3 = all_4_2)
% 177.22/27.73    (67)  op(e0, e3) = all_52_25
% 177.22/27.73    (68)  op(e0, all_6_2) = all_6_1
% 177.22/27.73    (69)  op(e3, all_52_17) = all_52_16
% 177.22/27.73    (70)   ~ (all_52_13 = all_14_2)
% 177.22/27.73    (71)  op(e3, all_52_9) = e3
% 177.22/27.73    (72)   ~ (e3 = e0)
% 177.22/27.73    (73)   ~ (all_52_9 = all_52_13)
% 177.22/27.73    (74)  op(e0, all_52_23) = all_52_22
% 177.22/27.73    (75)   ~ (all_52_15 = all_52_23)
% 177.22/27.73    (76)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.73    (77)   ~ (all_52_5 = all_52_29)
% 177.22/27.73    (78)  all_56_2 = all_52_5
% 177.22/27.73    (79)  op(e1, e0) = all_52_23
% 177.22/27.73    (80)  all_58_13 = all_52_27
% 177.22/27.73    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.73    (82)   ~ (all_52_9 = all_52_17)
% 177.22/27.73    (83)  all_58_6 = all_52_17
% 177.22/27.73    (84)   ~ (all_52_3 = all_52_7)
% 177.22/27.73    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.73    (86)  op(e2, all_52_19) = all_52_18
% 177.22/27.73    (87)   ~ (e1 = e0)
% 177.22/27.73    (88)  all_56_0 = all_4_2
% 177.22/27.73    (89)  all_58_11 = all_52_23
% 177.22/27.73    (90)   ~ (all_52_3 = all_52_19)
% 177.22/27.73    (91)   ~ (all_52_7 = all_52_15)
% 177.22/27.73    (92)   ~ (all_52_29 = all_14_2)
% 177.22/27.73    (93)   ~ (all_52_19 = all_10_2)
% 177.22/27.73    (94)   ~ (all_52_23 = all_6_2)
% 177.22/27.73    (95)   ~ (all_52_29 = all_6_2)
% 177.22/27.73    (96)  all_58_2 = all_52_9
% 177.22/27.73    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.73    (98)  op(e3, e1) = all_52_5
% 177.22/27.73    (99)  all_56_10 = all_14_2
% 177.22/27.73    (100)   ~ (all_52_25 = all_6_2)
% 177.22/27.73    (101)  op(e1, e1) = all_14_2
% 177.22/27.73    (102)  op(e1, e3) = all_52_17
% 177.22/27.73    (103)   ~ (all_52_25 = all_4_2)
% 177.22/27.73    (104)  op(e3, e0) = all_52_7
% 177.22/27.73    (105)  op(e2, all_10_2) = e2
% 177.22/27.73    (106)  op(e3, e3) = all_4_2
% 177.22/27.73    (107)   ~ (all_52_17 = all_4_2)
% 177.22/27.73    (108)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.73             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.73    (109)   ~ (all_52_25 = all_52_27)
% 177.22/27.73    (110)  all_34_2 = all_4_2
% 177.22/27.73    (111)   ~ (all_52_27 = all_6_2)
% 177.22/27.73    (112)   ~ (all_52_7 = all_6_2)
% 177.22/27.73    (113)   ~ (all_10_0 = e3)
% 177.22/27.73    (114)   ~ (all_52_7 = all_52_23)
% 177.22/27.73    (115)  op(e2, all_52_27) = all_52_26
% 177.22/27.73    (116)   ~ (all_52_17 = all_52_19)
% 177.22/27.73    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.73    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.73    (119)  op(e1, all_14_2) = all_14_1
% 177.22/27.73    (120)  all_58_9 = all_52_7
% 177.22/27.73    (121)  all_58_12 = all_52_25
% 177.22/27.73    (122)   ~ (all_10_0 = e1)
% 177.22/27.73    (123)  all_56_6 = all_52_13
% 177.22/27.73    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.73    (125)   ~ (all_52_9 = all_52_15)
% 177.22/27.73    (126)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.73    (127)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.73    (128)   ~ (all_52_19 = all_14_2)
% 177.22/27.73    (129)  op(e2, e3) = all_52_9
% 177.22/27.73    (130)  all_56_13 = all_52_27
% 177.22/27.73  
% 177.22/27.73  Begin of proof
% 177.22/27.73  | 
% 177.22/27.73  | GROUND_INST: instantiating (108) with e2, all_10_0, all_10_2, e2, simplifying
% 177.22/27.73  |              with (7), (105) gives:
% 177.22/27.73  |   (131)  all_10_0 = e2
% 177.22/27.73  | 
% 177.22/27.73  | REDUCE: (113), (131) imply:
% 177.22/27.73  |   (132)   ~ (e3 = e2)
% 177.22/27.73  | 
% 177.22/27.73  | SIMP: (132) implies:
% 177.22/27.73  |   (133)   ~ (e3 = e2)
% 177.22/27.73  | 
% 177.22/27.73  | REDUCE: (122), (131) imply:
% 177.22/27.73  |   (134)   ~ (e2 = e1)
% 177.22/27.73  | 
% 177.22/27.73  | BETA: splitting (42) gives:
% 177.22/27.73  | 
% 177.22/27.73  | Case 1:
% 177.22/27.73  | | 
% 177.22/27.73  | |   (135)  all_56_15 = e3
% 177.22/27.73  | | 
% 177.22/27.73  | | REF_CLOSE: (9), (15), (16), (19), (21), (23), (27), (29), (31), (33), (37),
% 177.22/27.73  | |            (41), (43), (45), (46), (48), (54), (59), (67), (68), (71), (80),
% 177.22/27.73  | |            (83), (96), (100), (102), (105), (106), (108), (111), (116),
% 177.22/27.73  | |            (121), (129), (135) are inconsistent by sub-proof #574.
% 177.22/27.73  | | 
% 177.22/27.73  | Case 2:
% 177.22/27.73  | | 
% 177.22/27.73  | |   (136)   ~ (all_56_15 = e3)
% 177.22/27.73  | |   (137)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.73  | | 
% 177.22/27.73  | | REDUCE: (21), (136) imply:
% 177.22/27.73  | |   (138)   ~ (all_6_2 = e3)
% 177.22/27.73  | | 
% 177.22/27.73  | | BETA: splitting (57) gives:
% 177.22/27.73  | | 
% 177.22/27.73  | | Case 1:
% 177.22/27.73  | | | 
% 177.22/27.73  | | |   (139)  all_56_13 = e3
% 177.22/27.73  | | | 
% 177.22/27.73  | | | REF_CLOSE: (4), (9), (10), (13), (14), (16), (19), (20), (22), (23), (25),
% 177.22/27.73  | | |            (27), (29), (32), (37), (38), (41), (43), (46), (48), (50),
% 177.22/27.73  | | |            (55), (59), (63), (65), (66), (67), (71), (73), (83), (85),
% 177.22/27.73  | | |            (88), (90), (96), (102), (103), (106), (107), (108), (109),
% 177.22/27.73  | | |            (110), (115), (121), (123), (124), (125), (129), (130), (139)
% 177.22/27.73  | | |            are inconsistent by sub-proof #593.
% 177.22/27.73  | | | 
% 177.22/27.73  | | Case 2:
% 177.22/27.73  | | | 
% 177.22/27.73  | | |   (140)   ~ (all_56_13 = e3)
% 177.22/27.73  | | | 
% 177.22/27.73  | | | REDUCE: (130), (140) imply:
% 177.22/27.73  | | |   (141)   ~ (all_52_27 = e3)
% 177.22/27.73  | | | 
% 177.22/27.73  | | | BETA: splitting (61) gives:
% 177.22/27.73  | | | 
% 177.22/27.73  | | | Case 1:
% 177.22/27.73  | | | | 
% 177.22/27.73  | | | |   (142)  all_58_12 = e3
% 177.22/27.73  | | | | 
% 177.22/27.73  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 177.22/27.73  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.22/27.73  | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 177.22/27.73  | | | |            (35), (36), (38), (39), (40), (41), (43), (44), (45), (46),
% 177.22/27.73  | | | |            (47), (48), (50), (51), (52), (53), (54), (55), (56), (58),
% 177.22/27.73  | | | |            (60), (62), (63), (64), (66), (67), (69), (70), (71), (72),
% 177.22/27.73  | | | |            (73), (74), (76), (79), (80), (82), (83), (84), (85), (86),
% 177.22/27.73  | | | |            (88), (89), (90), (91), (92), (93), (94), (96), (97), (98),
% 177.22/27.73  | | | |            (99), (100), (102), (103), (104), (105), (107), (108), (109),
% 177.22/27.73  | | | |            (110), (111), (112), (114), (116), (117), (118), (119),
% 177.22/27.73  | | | |            (120), (121), (123), (125), (126), (128), (129), (133),
% 177.22/27.73  | | | |            (134), (137), (142) are inconsistent by sub-proof #359.
% 177.22/27.73  | | | | 
% 177.22/27.73  | | | Case 2:
% 177.22/27.73  | | | | 
% 177.22/27.73  | | | |   (143)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.73  | | | | 
% 177.22/27.73  | | | | REF_CLOSE: (2), (5), (6), (9), (15), (16), (19), (20), (22), (23), (26),
% 177.22/27.73  | | | |            (27), (29), (30), (31), (32), (35), (36), (37), (41), (43),
% 177.22/27.73  | | | |            (45), (46), (48), (49), (52), (55), (56), (58), (59), (62),
% 177.22/27.73  | | | |            (66), (67), (70), (71), (73), (75), (77), (78), (80), (81),
% 177.22/27.73  | | | |            (83), (85), (87), (89), (90), (91), (92), (95), (96), (98),
% 177.22/27.73  | | | |            (101), (102), (103), (104), (105), (106), (107), (108),
% 177.22/27.73  | | | |            (117), (120), (121), (123), (124), (125), (127), (129),
% 177.22/27.73  | | | |            (134), (138), (141), (143) are inconsistent by sub-proof
% 177.22/27.73  | | | |            #572.
% 177.22/27.73  | | | | 
% 177.22/27.73  | | | End of split
% 177.22/27.73  | | | 
% 177.22/27.73  | | End of split
% 177.22/27.73  | | 
% 177.22/27.73  | End of split
% 177.22/27.73  | 
% 177.22/27.73  End of proof
% 177.22/27.73  
% 177.22/27.73  Sub-proof #329 shows that the following formulas are inconsistent:
% 177.22/27.73  ----------------------------------------------------------------
% 177.22/27.73    (1)  all_56_3 = all_52_7
% 177.22/27.73    (2)  op(e3, e2) = all_52_3
% 177.22/27.73    (3)   ~ (all_52_9 = all_52_25)
% 177.22/27.73    (4)  op(e3, all_52_25) = all_52_24
% 177.22/27.73    (5)  op(e1, e2) = all_52_19
% 177.22/27.73    (6)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.73    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.73    (8)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.73    (9)   ~ (e3 = e1)
% 177.22/27.73    (10)  all_34_1 = all_4_1
% 177.22/27.73    (11)  op(e3, all_4_2) = all_4_1
% 177.22/27.73    (12)   ~ (all_52_7 = all_4_2)
% 177.22/27.73    (13)  all_58_0 = all_4_2
% 177.22/27.73    (14)  op(all_4_1, all_4_2) = e1
% 177.22/27.73    (15)  op(e1, all_52_29) = all_52_28
% 177.22/27.73    (16)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.73    (17)   ~ (all_4_1 = e2)
% 177.22/27.73    (18)  all_58_14 = all_52_29
% 177.22/27.73    (19)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.73    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.73    (21)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.73    (22)  all_56_1 = all_52_3
% 177.22/27.73    (23)  op(all_14_1, all_14_2) = e3
% 177.22/27.73    (24)   ~ (all_52_3 = all_4_2)
% 177.22/27.73    (25)   ~ (e3 = e0)
% 177.22/27.73    (26)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.73    (27)  op(e1, e0) = all_52_23
% 177.22/27.73    (28)  all_56_12 = all_52_25
% 177.22/27.73    (29)  all_58_13 = all_52_27
% 177.22/27.73    (30)   ~ (all_52_25 = e0)
% 177.22/27.73    (31)  all_56_0 = all_4_2
% 177.22/27.73    (32)   ~ (all_52_3 = all_52_19)
% 177.22/27.73    (33)  all_58_15 = e0
% 177.22/27.73    (34)  op(e1, e3) = all_52_17
% 177.22/27.73    (35)   ~ (all_52_25 = all_4_2)
% 177.22/27.73    (36)  op(e3, e0) = all_52_7
% 177.22/27.73    (37)  op(e3, e3) = all_4_2
% 177.22/27.73    (38)   ~ (all_52_17 = all_4_2)
% 177.22/27.73    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.73    (40)   ~ (all_52_25 = all_52_27)
% 177.22/27.73    (41)  all_34_2 = all_4_2
% 177.22/27.73    (42)   ~ (all_52_7 = all_52_23)
% 177.22/27.73    (43)  op(e2, all_52_27) = all_52_26
% 177.22/27.73    (44)  all_52_20 = all_14_1
% 177.22/27.73    (45)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.73    (46)  op(e1, all_14_2) = all_14_1
% 177.22/27.73    (47)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.22/27.73          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.73    (48)  all_58_12 = all_52_25
% 177.22/27.73    (49)  op(e2, e3) = all_52_9
% 177.22/27.73    (50)  all_56_13 = all_52_27
% 177.22/27.73  
% 177.22/27.73  Begin of proof
% 177.22/27.73  | 
% 177.22/27.73  | BETA: splitting (47) gives:
% 177.22/27.73  | 
% 177.22/27.73  | Case 1:
% 177.22/27.73  | | 
% 177.22/27.73  | |   (51)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.22/27.73  | | 
% 177.22/27.73  | | ALPHA: (51) implies:
% 177.22/27.73  | |   (52)  all_52_20 = e1
% 177.22/27.73  | | 
% 177.22/27.73  | | COMBINE_EQS: (44), (52) imply:
% 177.22/27.73  | |   (53)  all_14_1 = e1
% 177.22/27.73  | | 
% 177.22/27.73  | | REF_CLOSE: (9), (23), (39), (46), (53) are inconsistent by sub-proof #344.
% 177.22/27.73  | | 
% 177.22/27.73  | Case 2:
% 177.22/27.73  | | 
% 177.22/27.73  | |   (54)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.22/27.73  | | 
% 177.22/27.73  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.73  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 177.22/27.73  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.22/27.73  | |            (36), (37), (38), (39), (40), (41), (42), (43), (45), (48), (49),
% 177.22/27.73  | |            (50), (54) are inconsistent by sub-proof #576.
% 177.22/27.73  | | 
% 177.22/27.73  | End of split
% 177.22/27.73  | 
% 177.22/27.73  End of proof
% 177.22/27.73  
% 177.22/27.73  Sub-proof #330 shows that the following formulas are inconsistent:
% 177.22/27.73  ----------------------------------------------------------------
% 177.22/27.73    (1)   ~ (all_52_27 = all_10_2)
% 177.22/27.73    (2)   ~ (all_52_17 = all_52_23)
% 177.22/27.73    (3)  op(e2, all_10_2) = all_10_1
% 177.22/27.73    (4)   ~ (all_52_13 = all_52_29)
% 177.22/27.73    (5)  all_56_3 = all_52_7
% 177.22/27.73    (6)  op(e3, e2) = all_52_3
% 177.22/27.73    (7)   ~ (all_52_9 = all_52_25)
% 177.22/27.73    (8)  op(e1, e2) = all_52_19
% 177.22/27.73    (9)   ~ (all_52_27 = e0)
% 177.22/27.73    (10)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.73    (11)  op(e3, all_52_9) = all_52_8
% 177.22/27.73    (12)   ~ (all_52_3 = all_10_2)
% 177.22/27.73    (13)  all_58_5 = all_52_13
% 177.22/27.73    (14)   ~ (all_52_25 = all_52_29)
% 177.22/27.73    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.73    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.73    (17)  all_58_3 = all_10_2
% 177.22/27.73    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.73    (19)   ~ (all_52_9 = all_4_2)
% 177.22/27.73    (20)  all_58_10 = all_52_15
% 177.22/27.73    (21)  all_58_7 = all_52_19
% 177.22/27.73    (22)  all_56_4 = all_52_9
% 177.22/27.73    (23)   ~ (all_52_17 = all_52_25)
% 177.22/27.74    (24)  op(e0, e1) = all_52_29
% 177.22/27.74    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.74    (26)   ~ (e3 = e1)
% 177.22/27.74    (27)  all_34_1 = all_4_1
% 177.22/27.74    (28)  op(e3, all_4_2) = all_4_1
% 177.22/27.74    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.74    (30)   ~ (all_52_7 = all_4_2)
% 177.22/27.74    (31)  all_58_1 = all_52_3
% 177.22/27.74    (32)  all_58_0 = all_4_2
% 177.22/27.74    (33)  op(e1, all_52_13) = all_52_12
% 177.22/27.74    (34)  op(all_4_1, all_4_2) = e1
% 177.22/27.74    (35)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.74          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.74    (36)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.74    (37)   ~ (all_4_1 = e2)
% 177.22/27.74    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.74    (39)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.74    (40)  all_58_14 = all_52_29
% 177.22/27.74    (41)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.74    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.74    (43)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.74    (44)  all_58_8 = all_14_2
% 177.22/27.74    (45)  all_56_1 = all_52_3
% 177.22/27.74    (46)  op(e0, e2) = all_52_27
% 177.22/27.74    (47)   ~ (all_52_3 = all_52_27)
% 177.22/27.74    (48)   ~ (all_52_3 = all_4_2)
% 177.22/27.74    (49)  op(e0, e3) = all_52_25
% 177.22/27.74    (50)  all_52_0 = all_4_1
% 177.22/27.74    (51)  all_52_10 = all_10_1
% 177.22/27.74    (52)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.74    (53)   ~ (e3 = e0)
% 177.22/27.74    (54)   ~ (all_52_9 = all_52_13)
% 177.22/27.74    (55)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.74    (56)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.74    (57)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.74    (58)  op(e1, e0) = all_52_23
% 177.22/27.74    (59)  all_56_12 = all_52_25
% 177.22/27.74    (60)  all_58_13 = all_52_27
% 177.22/27.74    (61)   ~ (all_52_25 = e0)
% 177.22/27.74    (62)  all_58_6 = all_52_17
% 177.22/27.74    (63)   ~ (all_52_3 = all_52_7)
% 177.22/27.74    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.74    (65)   ~ (e1 = e0)
% 177.22/27.74    (66)  all_56_0 = all_4_2
% 177.22/27.74    (67)  all_58_11 = all_52_23
% 177.22/27.74    (68)   ~ (all_52_3 = all_52_19)
% 177.22/27.74    (69)   ~ (all_52_7 = all_52_15)
% 177.22/27.74    (70)  op(e0, all_52_15) = all_52_14
% 177.22/27.74    (71)   ~ (all_52_19 = all_10_2)
% 177.22/27.74    (72)  all_58_15 = e0
% 177.22/27.74    (73)  all_58_2 = all_52_9
% 177.22/27.74    (74)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.22/27.74    (75)   ~ (all_52_29 = e0)
% 177.22/27.74    (76)  all_56_10 = all_14_2
% 177.22/27.74    (77)  op(e1, e3) = all_52_17
% 177.22/27.74    (78)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.74    (79)   ~ (all_52_25 = all_4_2)
% 177.22/27.74    (80)  op(e3, e0) = all_52_7
% 177.22/27.74    (81)  op(e3, e3) = all_4_2
% 177.22/27.74    (82)   ~ (all_52_17 = all_4_2)
% 177.22/27.74    (83)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.74    (84)   ~ (all_52_25 = all_52_27)
% 177.22/27.74    (85)  all_34_2 = all_4_2
% 177.22/27.74    (86)   ~ (all_10_0 = e3)
% 177.22/27.74    (87)  all_56_7 = all_52_15
% 177.22/27.74    (88)   ~ (all_52_15 = e0)
% 177.22/27.74    (89)   ~ (all_52_7 = all_52_23)
% 177.22/27.74    (90)  op(e2, all_52_27) = all_52_26
% 177.22/27.74    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.74    (92)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.74    (93)  all_58_9 = all_52_7
% 177.22/27.74    (94)   ~ (e2 = e0)
% 177.22/27.74    (95)  all_58_12 = all_52_25
% 177.22/27.74    (96)   ~ (all_10_0 = e1)
% 177.22/27.74    (97)  all_56_6 = all_52_13
% 177.22/27.74    (98)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.74    (99)   ~ (all_52_9 = all_52_15)
% 177.22/27.74    (100)   ~ (all_52_19 = all_14_2)
% 177.22/27.74    (101)  op(e2, e3) = all_52_9
% 177.22/27.74    (102)  all_56_13 = all_52_27
% 177.22/27.74  
% 177.22/27.74  Begin of proof
% 177.22/27.74  | 
% 177.22/27.74  | BETA: splitting (35) gives:
% 177.22/27.74  | 
% 177.22/27.74  | Case 1:
% 177.22/27.74  | | 
% 177.22/27.74  | |   (103)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.22/27.74  | | 
% 177.22/27.74  | | REF_CLOSE: (26), (28), (34), (50), (83), (103) are inconsistent by sub-proof
% 177.22/27.74  | |            #600.
% 177.22/27.74  | | 
% 177.22/27.74  | Case 2:
% 177.22/27.74  | | 
% 177.22/27.74  | |   (104)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.74  | | 
% 177.22/27.74  | | ALPHA: (104) implies:
% 177.22/27.74  | |   (105)  all_52_14 = e0
% 177.22/27.74  | |   (106)  all_52_12 = e1
% 177.22/27.74  | |   (107)  all_52_10 = e2
% 177.22/27.74  | |   (108)  all_52_8 = e3
% 177.22/27.74  | | 
% 177.22/27.74  | | COMBINE_EQS: (51), (107) imply:
% 177.22/27.74  | |   (109)  all_10_1 = e2
% 177.22/27.74  | | 
% 177.22/27.74  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.74  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.22/27.74  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.22/27.74  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.22/27.74  | |            (47), (48), (49), (52), (53), (54), (55), (56), (57), (58), (59),
% 177.22/27.74  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 177.22/27.74  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 177.22/27.74  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 177.22/27.74  | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 177.22/27.74  | |            (105), (106), (108), (109) are inconsistent by sub-proof #581.
% 177.22/27.74  | | 
% 177.22/27.74  | End of split
% 177.22/27.74  | 
% 177.22/27.74  End of proof
% 177.22/27.74  
% 177.22/27.74  Sub-proof #331 shows that the following formulas are inconsistent:
% 177.22/27.74  ----------------------------------------------------------------
% 177.22/27.74    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.74    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.74    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.74    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.74    (5)   ~ (all_52_27 = all_10_2)
% 177.22/27.74    (6)   ~ (all_52_17 = all_52_23)
% 177.22/27.74    (7)  op(e2, all_10_2) = all_10_1
% 177.22/27.74    (8)  all_40_2 = all_4_2
% 177.22/27.74    (9)   ~ (all_52_13 = all_52_29)
% 177.22/27.74    (10)  all_56_3 = all_52_7
% 177.22/27.74    (11)  op(e3, e2) = all_52_3
% 177.22/27.74    (12)   ~ (all_52_9 = all_52_25)
% 177.22/27.74    (13)  op(e3, all_52_25) = all_52_24
% 177.22/27.74    (14)   ~ (all_52_19 = all_52_23)
% 177.22/27.74    (15)  all_56_11 = all_52_23
% 177.22/27.74    (16)  op(e1, e2) = all_52_19
% 177.22/27.74    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.74    (18)  op(e3, all_52_9) = all_52_8
% 177.22/27.74    (19)   ~ (all_52_3 = all_10_2)
% 177.22/27.74    (20)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.22/27.74    (21)  all_58_5 = all_52_13
% 177.22/27.74    (22)   ~ (all_52_25 = all_52_29)
% 177.22/27.74    (23)  all_56_15 = all_6_2
% 177.22/27.74    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.74    (25)  op(e2, e0) = all_52_15
% 177.22/27.74    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.74    (27)  all_58_3 = all_10_2
% 177.22/27.74    (28)  all_56_9 = all_52_19
% 177.22/27.74    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.74    (30)  all_58_15 = all_6_2
% 177.22/27.74    (31)   ~ (all_52_9 = all_4_2)
% 177.22/27.74    (32)   ~ (all_52_5 = all_52_7)
% 177.22/27.74    (33)  all_58_10 = all_52_15
% 177.22/27.74    (34)   ~ (all_52_5 = all_4_2)
% 177.22/27.74    (35)  all_58_7 = all_52_19
% 177.22/27.74    (36)  all_56_4 = all_52_9
% 177.22/27.74    (37)   ~ (all_52_15 = all_6_2)
% 177.22/27.74    (38)   ~ (all_52_17 = all_52_25)
% 177.22/27.74    (39)  op(e0, e1) = all_52_29
% 177.22/27.74    (40)   ~ (all_4_0 = e2)
% 177.22/27.74    (41)  all_58_4 = all_52_5
% 177.22/27.74    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.74    (43)   ~ (e3 = e1)
% 177.22/27.74    (44)   ~ (all_52_27 = all_52_29)
% 177.22/27.74    (45)   ~ (all_52_17 = all_14_2)
% 177.22/27.74    (46)  op(e3, all_4_2) = all_4_1
% 177.22/27.74    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.74    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.74    (49)   ~ (all_52_7 = all_4_2)
% 177.22/27.74    (50)  all_58_1 = all_52_3
% 177.22/27.74    (51)   ~ (all_52_13 = all_52_15)
% 177.22/27.74    (52)  all_58_0 = all_4_2
% 177.22/27.74    (53)  all_52_0 = e1
% 177.22/27.74    (54)  op(e1, all_52_13) = all_52_12
% 177.22/27.74    (55)  op(e1, all_52_29) = all_52_28
% 177.22/27.74    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.74    (57)   ~ (all_4_1 = e2)
% 177.22/27.74    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.74    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.74    (60)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.74    (61)  all_58_14 = all_52_29
% 177.22/27.74    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.74    (63)   ~ (all_52_3 = all_52_5)
% 177.22/27.74    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.74    (65)  op(e2, e1) = all_52_13
% 177.22/27.74    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.74    (67)  all_58_8 = all_14_2
% 177.22/27.74    (68)  op(e0, e2) = all_52_27
% 177.22/27.74    (69)  op(all_14_1, all_14_2) = e3
% 177.22/27.74    (70)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.74    (71)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.22/27.74    (72)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.74    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.74    (74)   ~ (all_52_5 = all_14_2)
% 177.22/27.74    (75)   ~ (all_52_3 = all_52_27)
% 177.22/27.74    (76)   ~ (all_52_3 = all_4_2)
% 177.22/27.74    (77)  op(e0, e3) = all_52_25
% 177.22/27.74    (78)  op(e0, all_6_2) = all_6_1
% 177.22/27.74    (79)   ~ (all_52_9 = all_10_2)
% 177.22/27.74    (80)  op(e3, all_52_17) = all_52_16
% 177.22/27.74    (81)  all_52_10 = all_10_1
% 177.22/27.74    (82)   ~ (all_52_13 = all_14_2)
% 177.22/27.74    (83)   ~ (e3 = e0)
% 177.22/27.74    (84)  all_40_0 = all_4_0
% 177.22/27.74    (85)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.74    (86)   ~ (all_52_9 = all_52_13)
% 177.22/27.74    (87)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.74    (88)  op(e0, all_52_23) = all_52_22
% 177.22/27.74    (89)   ~ (all_52_15 = all_52_23)
% 177.22/27.74    (90)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.74    (91)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.74    (92)   ~ (all_52_5 = all_52_29)
% 177.22/27.74    (93)  all_56_2 = all_52_5
% 177.22/27.74    (94)  op(e1, e0) = all_52_23
% 177.22/27.74    (95)  all_56_12 = all_52_25
% 177.22/27.74    (96)  all_58_13 = all_52_27
% 177.22/27.74    (97)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 177.22/27.74    (98)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.74    (99)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.74    (100)   ~ (all_52_9 = all_52_17)
% 177.22/27.74    (101)  all_58_6 = all_52_17
% 177.22/27.74    (102)   ~ (all_52_3 = all_52_7)
% 177.22/27.74    (103)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.74    (104)  op(e2, all_52_19) = all_52_18
% 177.22/27.74    (105)   ~ (e1 = e0)
% 177.22/27.74    (106)  all_56_0 = all_4_2
% 177.22/27.74    (107)  all_58_11 = all_52_23
% 177.22/27.74    (108)   ~ (all_52_3 = all_52_19)
% 177.22/27.74    (109)   ~ (all_52_7 = all_52_15)
% 177.22/27.74    (110)  op(e0, all_52_15) = all_52_14
% 177.22/27.74    (111)   ~ (all_52_29 = all_14_2)
% 177.22/27.74    (112)   ~ (all_4_0 = e1)
% 177.22/27.74    (113)   ~ (all_52_19 = all_10_2)
% 177.22/27.74    (114)   ~ (all_58_15 = e0)
% 177.22/27.74    (115)   ~ (all_52_23 = all_6_2)
% 177.22/27.74    (116)  op(e1, all_4_2) = all_4_0
% 177.22/27.74    (117)   ~ (all_52_29 = all_6_2)
% 177.22/27.74    (118)  all_58_2 = all_52_9
% 177.22/27.74    (119)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.74    (120)  op(e3, e1) = all_52_5
% 177.22/27.74    (121)   ~ (e2 = e1)
% 177.22/27.74    (122)  all_56_10 = all_14_2
% 177.22/27.74    (123)   ~ (all_52_25 = all_6_2)
% 177.22/27.74    (124)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.74    (125)  op(e1, e1) = all_14_2
% 177.22/27.74    (126)  op(e1, e3) = all_52_17
% 177.22/27.74    (127)   ~ (all_52_25 = all_4_2)
% 177.22/27.74    (128)  op(e3, e0) = all_52_7
% 177.22/27.74    (129)  op(e3, e3) = all_4_2
% 177.22/27.74    (130)   ~ (all_52_17 = all_4_2)
% 177.22/27.74    (131)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.74             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.74    (132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.22/27.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.22/27.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.74    (133)   ~ (all_52_25 = all_52_27)
% 177.22/27.74    (134)   ~ (all_52_27 = all_6_2)
% 177.22/27.74    (135)   ~ (all_52_7 = all_6_2)
% 177.22/27.74    (136)   ~ (all_10_0 = e3)
% 177.22/27.74    (137)   ~ (all_52_15 = all_10_2)
% 177.22/27.74    (138)   ~ (all_52_19 = all_52_27)
% 177.22/27.74    (139)  all_18_2 = all_14_2
% 177.22/27.74    (140)   ~ (all_52_7 = all_52_23)
% 177.22/27.74    (141)  op(e2, all_52_27) = all_52_26
% 177.22/27.74    (142)  all_52_20 = all_14_1
% 177.22/27.74    (143)   ~ (all_52_17 = all_52_19)
% 177.22/27.74    (144)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.74    (145)  all_52_30 = all_6_1
% 177.22/27.74    (146)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.74    (147)  op(e1, all_14_2) = all_14_1
% 177.22/27.74    (148)  all_58_9 = all_52_7
% 177.22/27.74    (149)  all_58_12 = all_52_25
% 177.22/27.74    (150)  op(e3, all_4_2) = e1
% 177.22/27.74    (151)   ~ (all_10_0 = e1)
% 177.22/27.74    (152)  all_56_6 = all_52_13
% 177.22/27.74    (153)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 177.22/27.74             all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.74    (154)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.74    (155)   ~ (all_52_9 = all_52_15)
% 177.22/27.74    (156)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.74    (157)   ~ (e3 = e2)
% 177.22/27.74    (158)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.74    (159)   ~ (all_52_19 = all_14_2)
% 177.22/27.74    (160)  op(e2, e3) = all_52_9
% 177.22/27.74    (161)  all_56_13 = all_52_27
% 177.22/27.74  
% 177.22/27.74  Begin of proof
% 177.22/27.74  | 
% 177.22/27.74  | ALPHA: (153) implies:
% 177.22/27.74  |   (162)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.74  |   (163)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.74  | 
% 177.22/27.74  | REDUCE: (30), (114) imply:
% 177.22/27.74  |   (164)   ~ (all_6_2 = e0)
% 177.22/27.74  | 
% 177.22/27.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.74  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.22/27.74  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.22/27.74  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.22/27.74  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.22/27.74  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.22/27.74  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 177.22/27.74  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 177.22/27.74  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.22/27.74  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 177.22/27.74  |            (110), (111), (112), (113), (115), (116), (117), (118), (119),
% 177.22/27.74  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 177.22/27.74  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 177.22/27.74  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 177.22/27.74  |            (147), (148), (149), (150), (151), (152), (154), (155), (156),
% 177.22/27.74  |            (157), (158), (159), (160), (161), (162), (163), (164) are
% 177.22/27.74  |            inconsistent by sub-proof #332.
% 177.22/27.74  | 
% 177.22/27.74  End of proof
% 177.22/27.74  
% 177.22/27.74  Sub-proof #332 shows that the following formulas are inconsistent:
% 177.22/27.74  ----------------------------------------------------------------
% 177.22/27.74    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.74    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.74    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.74    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.74    (5)   ~ (all_52_27 = all_10_2)
% 177.22/27.74    (6)   ~ (all_52_17 = all_52_23)
% 177.22/27.74    (7)  op(e2, all_10_2) = all_10_1
% 177.22/27.74    (8)  all_40_2 = all_4_2
% 177.22/27.74    (9)   ~ (all_52_13 = all_52_29)
% 177.22/27.74    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.74    (11)  all_56_3 = all_52_7
% 177.22/27.74    (12)  op(e3, e2) = all_52_3
% 177.22/27.74    (13)   ~ (all_52_9 = all_52_25)
% 177.22/27.74    (14)  op(e3, all_52_25) = all_52_24
% 177.22/27.74    (15)   ~ (all_52_19 = all_52_23)
% 177.22/27.74    (16)  all_56_11 = all_52_23
% 177.22/27.74    (17)  op(e1, e2) = all_52_19
% 177.22/27.74    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.74    (19)  op(e3, all_52_9) = all_52_8
% 177.22/27.74    (20)   ~ (all_52_3 = all_10_2)
% 177.22/27.74    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.22/27.74    (22)  all_58_5 = all_52_13
% 177.22/27.74    (23)   ~ (all_6_2 = e0)
% 177.22/27.74    (24)   ~ (all_52_25 = all_52_29)
% 177.22/27.74    (25)  all_56_15 = all_6_2
% 177.22/27.74    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.74    (27)  op(e2, e0) = all_52_15
% 177.22/27.74    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.74    (29)  all_58_3 = all_10_2
% 177.22/27.74    (30)  all_56_9 = all_52_19
% 177.22/27.74    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.74    (32)  all_58_15 = all_6_2
% 177.22/27.74    (33)   ~ (all_52_9 = all_4_2)
% 177.22/27.74    (34)   ~ (all_52_5 = all_52_7)
% 177.22/27.74    (35)  all_58_10 = all_52_15
% 177.22/27.74    (36)   ~ (all_52_5 = all_4_2)
% 177.22/27.74    (37)  all_58_7 = all_52_19
% 177.22/27.74    (38)  all_56_4 = all_52_9
% 177.22/27.74    (39)   ~ (all_52_15 = all_6_2)
% 177.22/27.74    (40)   ~ (all_52_17 = all_52_25)
% 177.22/27.74    (41)  op(e0, e1) = all_52_29
% 177.22/27.74    (42)   ~ (all_4_0 = e2)
% 177.22/27.74    (43)  all_58_4 = all_52_5
% 177.22/27.74    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.74    (45)   ~ (e3 = e1)
% 177.22/27.74    (46)   ~ (all_52_27 = all_52_29)
% 177.22/27.74    (47)   ~ (all_52_17 = all_14_2)
% 177.22/27.74    (48)  op(e3, all_4_2) = all_4_1
% 177.22/27.74    (49)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.74    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.74    (51)   ~ (all_52_7 = all_4_2)
% 177.22/27.74    (52)  all_58_1 = all_52_3
% 177.22/27.74    (53)   ~ (all_52_13 = all_52_15)
% 177.22/27.74    (54)  all_58_0 = all_4_2
% 177.22/27.74    (55)  all_52_0 = e1
% 177.22/27.74    (56)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.74    (57)  op(e1, all_52_13) = all_52_12
% 177.22/27.74    (58)  op(e1, all_52_29) = all_52_28
% 177.22/27.74    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.74    (60)   ~ (all_4_1 = e2)
% 177.22/27.74    (61)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.74    (62)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.74    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.74    (64)  all_58_14 = all_52_29
% 177.22/27.74    (65)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.74    (66)   ~ (all_52_3 = all_52_5)
% 177.22/27.74    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.74    (68)  op(e2, e1) = all_52_13
% 177.22/27.74    (69)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.74    (70)  all_58_8 = all_14_2
% 177.22/27.74    (71)  op(e0, e2) = all_52_27
% 177.22/27.74    (72)  op(all_14_1, all_14_2) = e3
% 177.22/27.74    (73)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.74    (74)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.22/27.74    (75)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.74    (76)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.74    (77)   ~ (all_52_5 = all_14_2)
% 177.22/27.74    (78)   ~ (all_52_3 = all_52_27)
% 177.22/27.74    (79)   ~ (all_52_3 = all_4_2)
% 177.22/27.74    (80)  op(e0, e3) = all_52_25
% 177.22/27.74    (81)  op(e0, all_6_2) = all_6_1
% 177.22/27.74    (82)   ~ (all_52_9 = all_10_2)
% 177.22/27.74    (83)  op(e3, all_52_17) = all_52_16
% 177.22/27.74    (84)  all_52_10 = all_10_1
% 177.22/27.74    (85)   ~ (all_52_13 = all_14_2)
% 177.22/27.74    (86)   ~ (e3 = e0)
% 177.22/27.74    (87)  all_40_0 = all_4_0
% 177.22/27.74    (88)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.74    (89)   ~ (all_52_9 = all_52_13)
% 177.22/27.74    (90)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.74    (91)  op(e0, all_52_23) = all_52_22
% 177.22/27.74    (92)   ~ (all_52_15 = all_52_23)
% 177.22/27.74    (93)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.74    (94)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.74    (95)   ~ (all_52_5 = all_52_29)
% 177.22/27.74    (96)  all_56_2 = all_52_5
% 177.22/27.74    (97)  op(e1, e0) = all_52_23
% 177.22/27.74    (98)  all_56_12 = all_52_25
% 177.22/27.74    (99)  all_58_13 = all_52_27
% 177.22/27.74    (100)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 177.22/27.74    (101)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.74    (102)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.74    (103)   ~ (all_52_9 = all_52_17)
% 177.22/27.74    (104)  all_58_6 = all_52_17
% 177.22/27.74    (105)   ~ (all_52_3 = all_52_7)
% 177.22/27.74    (106)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.74    (107)  op(e2, all_52_19) = all_52_18
% 177.22/27.74    (108)   ~ (e1 = e0)
% 177.22/27.74    (109)  all_56_0 = all_4_2
% 177.22/27.74    (110)  all_58_11 = all_52_23
% 177.22/27.74    (111)   ~ (all_52_3 = all_52_19)
% 177.22/27.74    (112)   ~ (all_52_7 = all_52_15)
% 177.22/27.74    (113)  op(e0, all_52_15) = all_52_14
% 177.22/27.74    (114)   ~ (all_52_29 = all_14_2)
% 177.22/27.74    (115)   ~ (all_4_0 = e1)
% 177.22/27.74    (116)   ~ (all_52_19 = all_10_2)
% 177.22/27.74    (117)   ~ (all_52_23 = all_6_2)
% 177.22/27.74    (118)  op(e1, all_4_2) = all_4_0
% 177.22/27.74    (119)   ~ (all_52_29 = all_6_2)
% 177.22/27.74    (120)  all_58_2 = all_52_9
% 177.22/27.74    (121)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.74    (122)  op(e3, e1) = all_52_5
% 177.22/27.74    (123)   ~ (e2 = e1)
% 177.22/27.74    (124)  all_56_10 = all_14_2
% 177.22/27.74    (125)   ~ (all_52_25 = all_6_2)
% 177.22/27.74    (126)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.74    (127)  op(e1, e1) = all_14_2
% 177.22/27.74    (128)  op(e1, e3) = all_52_17
% 177.22/27.74    (129)   ~ (all_52_25 = all_4_2)
% 177.22/27.74    (130)  op(e3, e0) = all_52_7
% 177.22/27.74    (131)  op(e3, e3) = all_4_2
% 177.22/27.74    (132)   ~ (all_52_17 = all_4_2)
% 177.22/27.74    (133)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.74             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.74    (134)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.74           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.22/27.74           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.22/27.74           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.74    (135)   ~ (all_52_25 = all_52_27)
% 177.22/27.74    (136)   ~ (all_52_27 = all_6_2)
% 177.22/27.74    (137)   ~ (all_52_7 = all_6_2)
% 177.22/27.74    (138)   ~ (all_10_0 = e3)
% 177.22/27.74    (139)   ~ (all_52_15 = all_10_2)
% 177.22/27.74    (140)   ~ (all_52_19 = all_52_27)
% 177.22/27.74    (141)  all_18_2 = all_14_2
% 177.22/27.74    (142)   ~ (all_52_7 = all_52_23)
% 177.22/27.74    (143)  op(e2, all_52_27) = all_52_26
% 177.22/27.74    (144)  all_52_20 = all_14_1
% 177.22/27.74    (145)   ~ (all_52_17 = all_52_19)
% 177.22/27.74    (146)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.74    (147)  all_52_30 = all_6_1
% 177.22/27.74    (148)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.74    (149)  op(e1, all_14_2) = all_14_1
% 177.22/27.74    (150)  all_58_9 = all_52_7
% 177.22/27.74    (151)  all_58_12 = all_52_25
% 177.22/27.74    (152)  op(e3, all_4_2) = e1
% 177.22/27.74    (153)   ~ (all_10_0 = e1)
% 177.22/27.74    (154)  all_56_6 = all_52_13
% 177.22/27.75    (155)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.75    (156)   ~ (all_52_9 = all_52_15)
% 177.22/27.75    (157)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.75    (158)   ~ (e3 = e2)
% 177.22/27.75    (159)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.75    (160)   ~ (all_52_19 = all_14_2)
% 177.22/27.75    (161)  op(e2, e3) = all_52_9
% 177.22/27.75    (162)  all_56_13 = all_52_27
% 177.22/27.75  
% 177.22/27.75  Begin of proof
% 177.22/27.75  | 
% 177.22/27.75  | BETA: splitting (134) gives:
% 177.22/27.75  | 
% 177.22/27.75  | Case 1:
% 177.22/27.75  | | 
% 177.22/27.75  | |   (163)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.75  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.75  | | 
% 177.22/27.75  | | BETA: splitting (163) gives:
% 177.22/27.75  | | 
% 177.22/27.75  | | Case 1:
% 177.22/27.75  | | | 
% 177.22/27.75  | | |   (164)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REF_CLOSE: (45), (55), (164) are inconsistent by sub-proof #632.
% 177.22/27.75  | | | 
% 177.22/27.75  | | Case 2:
% 177.22/27.75  | | | 
% 177.22/27.75  | | |   (165)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.75  | | | 
% 177.22/27.75  | | | ALPHA: (165) implies:
% 177.22/27.75  | | |   (166)  all_52_14 = e0
% 177.22/27.75  | | |   (167)  all_52_12 = e1
% 177.22/27.75  | | |   (168)  all_52_10 = e2
% 177.22/27.75  | | |   (169)  all_52_8 = e3
% 177.22/27.75  | | | 
% 177.22/27.75  | | | COMBINE_EQS: (84), (168) imply:
% 177.22/27.75  | | |   (170)  all_10_1 = e2
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REDUCE: (94), (170) imply:
% 177.22/27.75  | | |   (171)  op(e2, all_10_2) = all_10_0
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REDUCE: (19), (169) imply:
% 177.22/27.75  | | |   (172)  op(e3, all_52_9) = e3
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REDUCE: (7), (170) imply:
% 177.22/27.75  | | |   (173)  op(e2, all_10_2) = e2
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REDUCE: (57), (167) imply:
% 177.22/27.75  | | |   (174)  op(e1, all_52_13) = e1
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REDUCE: (113), (166) imply:
% 177.22/27.75  | | |   (175)  op(e0, all_52_15) = e0
% 177.22/27.75  | | | 
% 177.22/27.75  | | | GROUND_INST: instantiating (133) with e2, all_10_0, all_10_2, e2,
% 177.22/27.75  | | |              simplifying with (171), (173) gives:
% 177.22/27.75  | | |   (176)  all_10_0 = e2
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REDUCE: (138), (176) imply:
% 177.22/27.75  | | |   (177)   ~ (e3 = e2)
% 177.22/27.75  | | | 
% 177.22/27.75  | | | BETA: splitting (49) gives:
% 177.22/27.75  | | | 
% 177.22/27.75  | | | Case 1:
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | |   (178)  all_56_15 = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | COMBINE_EQS: (25), (178) imply:
% 177.22/27.75  | | | |   (179)  all_6_2 = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (179) implies:
% 177.22/27.75  | | | |   (180)  all_6_2 = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REF_CLOSE: (12), (13), (20), (22), (26), (29), (33), (35), (37), (38),
% 177.22/27.75  | | | |            (39), (42), (44), (45), (48), (50), (51), (52), (54), (62),
% 177.22/27.75  | | | |            (63), (67), (70), (75), (80), (81), (85), (99), (103), (104),
% 177.22/27.75  | | | |            (106), (107), (110), (111), (117), (120), (123), (125),
% 177.22/27.75  | | | |            (126), (128), (130), (131), (132), (133), (136), (145),
% 177.22/27.75  | | | |            (151), (154), (161), (172), (173), (174), (180) are
% 177.22/27.75  | | | |            inconsistent by sub-proof #773.
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | Case 2:
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | |   (181)   ~ (all_56_15 = e3)
% 177.22/27.75  | | | |   (182)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (25), (181) imply:
% 177.22/27.75  | | | |   (183)   ~ (all_6_2 = e3)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | BETA: splitting (69) gives:
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | Case 1:
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | |   (184)  all_58_12 = e3
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (11), (12), (13), (15), (16),
% 177.22/27.75  | | | | |            (17), (20), (22), (23), (24), (25), (26), (29), (30), (31),
% 177.22/27.75  | | | | |            (32), (33), (34), (35), (36), (37), (38), (40), (43), (44),
% 177.22/27.75  | | | | |            (46), (47), (50), (51), (52), (54), (56), (59), (61), (62),
% 177.22/27.75  | | | | |            (63), (64), (66), (68), (70), (72), (76), (80), (83), (85),
% 177.22/27.75  | | | | |            (86), (89), (91), (93), (99), (100), (102), (103), (104),
% 177.22/27.75  | | | | |            (105), (106), (107), (109), (110), (111), (112), (114),
% 177.22/27.75  | | | | |            (116), (117), (120), (121), (122), (123), (124), (125),
% 177.22/27.75  | | | | |            (128), (129), (130), (132), (133), (135), (136), (137),
% 177.22/27.75  | | | | |            (141), (142), (145), (146), (148), (149), (150), (151),
% 177.22/27.75  | | | | |            (154), (155), (156), (157), (158), (160), (161), (172),
% 177.22/27.75  | | | | |            (173), (174), (175), (182), (184) are inconsistent by
% 177.22/27.75  | | | | |            sub-proof #333.
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | Case 2:
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | |   (185)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | BETA: splitting (185) gives:
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | Case 1:
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | |   (186)  all_58_13 = e3
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | COMBINE_EQS: (99), (186) imply:
% 177.22/27.75  | | | | | |   (187)  all_52_27 = e3
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | SIMP: (187) implies:
% 177.22/27.75  | | | | | |   (188)  all_52_27 = e3
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (12), (17), (22), (29),
% 177.22/27.75  | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (40),
% 177.22/27.75  | | | | | |            (42), (43), (44), (45), (47), (50), (51), (52), (54),
% 177.22/27.75  | | | | | |            (59), (64), (67), (70), (73), (77), (78), (80), (85),
% 177.22/27.75  | | | | | |            (87), (89), (92), (101), (104), (109), (110), (111),
% 177.22/27.75  | | | | | |            (112), (118), (120), (122), (128), (129), (131), (132),
% 177.22/27.75  | | | | | |            (133), (136), (140), (142), (143), (146), (148), (150),
% 177.22/27.75  | | | | | |            (151), (152), (155), (157), (161), (172), (174), (175),
% 177.22/27.75  | | | | | |            (188) are inconsistent by sub-proof #610.
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | Case 2:
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | |   (189)  all_58_14 = e3 | all_58_15 = e3
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | REF_CLOSE: (2), (6), (9), (12), (13), (14), (15), (16), (20), (21),
% 177.22/27.75  | | | | | |            (22), (26), (27), (29), (32), (33), (35), (36), (37),
% 177.22/27.75  | | | | | |            (38), (42), (43), (44), (45), (46), (48), (50), (51),
% 177.22/27.75  | | | | | |            (52), (54), (56), (58), (60), (62), (63), (64), (66),
% 177.22/27.75  | | | | | |            (67), (70), (74), (75), (79), (80), (85), (89), (92),
% 177.22/27.75  | | | | | |            (95), (96), (97), (99), (101), (104), (105), (106),
% 177.22/27.75  | | | | | |            (107), (108), (110), (111), (112), (114), (119), (120),
% 177.22/27.75  | | | | | |            (121), (122), (123), (127), (128), (129), (130), (131),
% 177.22/27.75  | | | | | |            (132), (133), (135), (140), (145), (146), (150), (151),
% 177.22/27.75  | | | | | |            (154), (155), (156), (159), (161), (172), (173), (174),
% 177.22/27.75  | | | | | |            (175), (183), (189) are inconsistent by sub-proof #718.
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | End of split
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | End of split
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | End of split
% 177.22/27.75  | | | 
% 177.22/27.75  | | End of split
% 177.22/27.75  | | 
% 177.22/27.75  | Case 2:
% 177.22/27.75  | | 
% 177.22/27.75  | |   (190)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 177.22/27.75  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.22/27.75  | |            e0)
% 177.22/27.75  | | 
% 177.22/27.75  | | BETA: splitting (190) gives:
% 177.22/27.75  | | 
% 177.22/27.75  | | Case 1:
% 177.22/27.75  | | | 
% 177.22/27.75  | | |   (191)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.22/27.75  | | | 
% 177.22/27.75  | | | ALPHA: (191) implies:
% 177.22/27.75  | | |   (192)  all_52_20 = e1
% 177.22/27.75  | | | 
% 177.22/27.75  | | | COMBINE_EQS: (144), (192) imply:
% 177.22/27.75  | | |   (193)  all_14_1 = e1
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REF_CLOSE: (45), (72), (133), (149), (193) are inconsistent by sub-proof
% 177.22/27.75  | | |            #344.
% 177.22/27.75  | | | 
% 177.22/27.75  | | Case 2:
% 177.22/27.75  | | | 
% 177.22/27.75  | | |   (194)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (12), (13), (14), (15),
% 177.22/27.75  | | |            (18), (19), (22), (23), (24), (25), (26), (28), (29), (31),
% 177.22/27.75  | | |            (32), (33), (34), (35), (36), (37), (40), (41), (42), (43),
% 177.22/27.75  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 177.22/27.75  | | |            (54), (56), (58), (61), (62), (64), (65), (66), (67), (69),
% 177.22/27.75  | | |            (70), (71), (75), (78), (80), (81), (82), (83), (86), (88),
% 177.22/27.75  | | |            (90), (95), (97), (98), (99), (101), (103), (104), (105),
% 177.22/27.75  | | |            (108), (109), (110), (115), (116), (119), (120), (122), (123),
% 177.22/27.75  | | |            (125), (128), (129), (130), (131), (132), (133), (135), (136),
% 177.22/27.75  | | |            (137), (139), (143), (145), (146), (147), (150), (151), (152),
% 177.22/27.75  | | |            (155), (156), (158), (161), (162), (194) are inconsistent by
% 177.22/27.75  | | |            sub-proof #444.
% 177.22/27.75  | | | 
% 177.22/27.75  | | End of split
% 177.22/27.75  | | 
% 177.22/27.75  | End of split
% 177.22/27.75  | 
% 177.22/27.75  End of proof
% 177.22/27.75  
% 177.22/27.75  Sub-proof #333 shows that the following formulas are inconsistent:
% 177.22/27.75  ----------------------------------------------------------------
% 177.22/27.75    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.75    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.75    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.75    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.75    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.75    (6)   ~ (all_52_13 = all_52_29)
% 177.22/27.75    (7)  all_56_3 = all_52_7
% 177.22/27.75    (8)  op(e3, e2) = all_52_3
% 177.22/27.75    (9)   ~ (all_52_9 = all_52_25)
% 177.22/27.75    (10)   ~ (all_52_19 = all_52_23)
% 177.22/27.75    (11)  all_56_11 = all_52_23
% 177.22/27.75    (12)  op(e1, e2) = all_52_19
% 177.22/27.75    (13)   ~ (all_52_3 = all_10_2)
% 177.22/27.75    (14)  all_58_5 = all_52_13
% 177.22/27.75    (15)   ~ (all_6_2 = e0)
% 177.22/27.75    (16)   ~ (all_52_25 = all_52_29)
% 177.22/27.75    (17)  op(e1, all_52_13) = e1
% 177.22/27.75    (18)  op(e0, all_52_15) = e0
% 177.22/27.75    (19)  all_56_15 = all_6_2
% 177.22/27.75    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.75    (21)  all_58_3 = all_10_2
% 177.22/27.75    (22)  all_56_9 = all_52_19
% 177.22/27.75    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.75    (24)  all_58_15 = all_6_2
% 177.22/27.75    (25)   ~ (all_52_9 = all_4_2)
% 177.22/27.75    (26)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.75    (27)   ~ (all_52_5 = all_52_7)
% 177.22/27.75    (28)  all_58_10 = all_52_15
% 177.22/27.75    (29)   ~ (all_52_5 = all_4_2)
% 177.22/27.75    (30)  all_58_7 = all_52_19
% 177.22/27.75    (31)  all_56_4 = all_52_9
% 177.22/27.75    (32)   ~ (all_52_17 = all_52_25)
% 177.22/27.75    (33)  all_58_4 = all_52_5
% 177.22/27.75    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.75    (35)   ~ (all_52_27 = all_52_29)
% 177.22/27.75    (36)   ~ (all_52_17 = all_14_2)
% 177.22/27.75    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.75    (38)   ~ (all_52_7 = all_4_2)
% 177.22/27.75    (39)  all_58_1 = all_52_3
% 177.22/27.75    (40)  all_58_0 = all_4_2
% 177.22/27.75    (41)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.75    (42)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.75    (43)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.75    (44)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.75    (45)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.75    (46)  all_58_14 = all_52_29
% 177.22/27.75    (47)   ~ (all_52_3 = all_52_5)
% 177.22/27.75    (48)  op(e2, e1) = all_52_13
% 177.22/27.75    (49)  all_58_8 = all_14_2
% 177.22/27.75    (50)  op(all_14_1, all_14_2) = e3
% 177.22/27.75    (51)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.75    (52)  op(e0, e3) = all_52_25
% 177.22/27.75    (53)  op(e3, all_52_17) = all_52_16
% 177.22/27.75    (54)   ~ (all_52_13 = all_14_2)
% 177.22/27.75    (55)  op(e3, all_52_9) = e3
% 177.22/27.75    (56)   ~ (e3 = e0)
% 177.22/27.75    (57)   ~ (all_52_9 = all_52_13)
% 177.22/27.75    (58)  op(e0, all_52_23) = all_52_22
% 177.22/27.75    (59)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.75    (60)  all_58_13 = all_52_27
% 177.22/27.75    (61)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 177.22/27.75    (62)  all_58_12 = e3
% 177.22/27.75    (63)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.75    (64)   ~ (all_52_9 = all_52_17)
% 177.22/27.75    (65)  all_58_6 = all_52_17
% 177.22/27.75    (66)   ~ (all_52_3 = all_52_7)
% 177.22/27.75    (67)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.75    (68)  op(e2, all_52_19) = all_52_18
% 177.22/27.75    (69)  all_56_0 = all_4_2
% 177.22/27.75    (70)  all_58_11 = all_52_23
% 177.22/27.75    (71)   ~ (all_52_3 = all_52_19)
% 177.22/27.75    (72)   ~ (all_52_7 = all_52_15)
% 177.22/27.75    (73)   ~ (all_52_29 = all_14_2)
% 177.22/27.75    (74)   ~ (all_52_19 = all_10_2)
% 177.22/27.75    (75)   ~ (all_52_23 = all_6_2)
% 177.22/27.75    (76)  all_58_2 = all_52_9
% 177.22/27.75    (77)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.75    (78)  op(e3, e1) = all_52_5
% 177.22/27.75    (79)   ~ (e2 = e1)
% 177.22/27.75    (80)  all_56_10 = all_14_2
% 177.22/27.75    (81)   ~ (all_52_25 = all_6_2)
% 177.22/27.75    (82)  op(e1, e3) = all_52_17
% 177.22/27.75    (83)   ~ (all_52_25 = all_4_2)
% 177.22/27.75    (84)  op(e3, e0) = all_52_7
% 177.22/27.75    (85)  op(e2, all_10_2) = e2
% 177.22/27.75    (86)   ~ (all_52_17 = all_4_2)
% 177.22/27.75    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.75    (88)   ~ (all_52_25 = all_52_27)
% 177.22/27.75    (89)   ~ (all_52_27 = all_6_2)
% 177.22/27.75    (90)   ~ (all_52_7 = all_6_2)
% 177.22/27.75    (91)  all_18_2 = all_14_2
% 177.22/27.75    (92)   ~ (all_52_7 = all_52_23)
% 177.22/27.75    (93)   ~ (all_52_17 = all_52_19)
% 177.22/27.75    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.75    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.75    (96)  op(e1, all_14_2) = all_14_1
% 177.22/27.75    (97)  all_58_9 = all_52_7
% 177.22/27.75    (98)  all_58_12 = all_52_25
% 177.22/27.75    (99)  all_56_6 = all_52_13
% 177.22/27.75    (100)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.75    (101)   ~ (all_52_9 = all_52_15)
% 177.22/27.75    (102)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.75    (103)   ~ (e3 = e2)
% 177.22/27.75    (104)   ~ (all_52_19 = all_14_2)
% 177.22/27.75    (105)  op(e2, e3) = all_52_9
% 177.22/27.75  
% 177.22/27.75  Begin of proof
% 177.22/27.75  | 
% 177.22/27.75  | COMBINE_EQS: (62), (98) imply:
% 177.22/27.75  |   (106)  all_52_25 = e3
% 177.22/27.75  | 
% 177.22/27.75  | SIMP: (106) implies:
% 177.22/27.75  |   (107)  all_52_25 = e3
% 177.22/27.75  | 
% 177.22/27.75  | REDUCE: (9), (107) imply:
% 177.22/27.75  |   (108)   ~ (all_52_9 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | REDUCE: (32), (107) imply:
% 177.22/27.75  |   (109)   ~ (all_52_17 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | REDUCE: (88), (107) imply:
% 177.22/27.75  |   (110)   ~ (all_52_27 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | SIMP: (110) implies:
% 177.22/27.75  |   (111)   ~ (all_52_27 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | REDUCE: (16), (107) imply:
% 177.22/27.75  |   (112)   ~ (all_52_29 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | SIMP: (112) implies:
% 177.22/27.75  |   (113)   ~ (all_52_29 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | REDUCE: (81), (107) imply:
% 177.22/27.75  |   (114)   ~ (all_6_2 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | SIMP: (114) implies:
% 177.22/27.75  |   (115)   ~ (all_6_2 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | REDUCE: (83), (107) imply:
% 177.22/27.75  |   (116)   ~ (all_4_2 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | SIMP: (116) implies:
% 177.22/27.75  |   (117)   ~ (all_4_2 = e3)
% 177.22/27.75  | 
% 177.22/27.75  | REDUCE: (52), (107) imply:
% 177.22/27.75  |   (118)  op(e0, e3) = e3
% 177.22/27.75  | 
% 177.22/27.75  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 177.22/27.75  |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.22/27.75  |            (26), (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 177.22/27.75  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.22/27.75  |            (49), (50), (51), (53), (54), (55), (56), (57), (58), (59), (60),
% 177.22/27.75  |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 177.22/27.75  |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (82), (84),
% 177.22/27.75  |            (85), (86), (87), (89), (90), (91), (92), (93), (94), (95), (96),
% 177.22/27.75  |            (97), (99), (100), (101), (102), (103), (104), (105), (108), (109),
% 177.22/27.75  |            (111), (113), (115), (117), (118) are inconsistent by sub-proof
% 177.22/27.75  |            #334.
% 177.22/27.75  | 
% 177.22/27.75  End of proof
% 177.22/27.75  
% 177.22/27.75  Sub-proof #334 shows that the following formulas are inconsistent:
% 177.22/27.75  ----------------------------------------------------------------
% 177.22/27.75    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.75    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.75    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.75    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.75    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.75    (6)   ~ (all_52_13 = all_52_29)
% 177.22/27.75    (7)  all_56_3 = all_52_7
% 177.22/27.75    (8)  op(e3, e2) = all_52_3
% 177.22/27.75    (9)   ~ (all_52_19 = all_52_23)
% 177.22/27.75    (10)  all_56_11 = all_52_23
% 177.22/27.75    (11)  op(e1, e2) = all_52_19
% 177.22/27.75    (12)   ~ (all_52_27 = e3)
% 177.22/27.75    (13)   ~ (all_52_17 = e3)
% 177.22/27.75    (14)   ~ (all_6_2 = e3)
% 177.22/27.75    (15)   ~ (all_52_3 = all_10_2)
% 177.22/27.75    (16)  all_58_5 = all_52_13
% 177.22/27.75    (17)   ~ (all_6_2 = e0)
% 177.22/27.75    (18)  op(e1, all_52_13) = e1
% 177.22/27.75    (19)  op(e0, all_52_15) = e0
% 177.22/27.75    (20)  all_56_15 = all_6_2
% 177.22/27.75    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.75    (22)   ~ (all_4_2 = e3)
% 177.22/27.75    (23)  all_58_3 = all_10_2
% 177.22/27.75    (24)  all_56_9 = all_52_19
% 177.22/27.75    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.75    (26)  all_58_15 = all_6_2
% 177.22/27.75    (27)   ~ (all_52_9 = all_4_2)
% 177.22/27.75    (28)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.75    (29)   ~ (all_52_5 = all_52_7)
% 177.22/27.75    (30)  all_58_10 = all_52_15
% 177.22/27.75    (31)   ~ (all_52_5 = all_4_2)
% 177.22/27.75    (32)  all_58_7 = all_52_19
% 177.22/27.75    (33)  all_56_4 = all_52_9
% 177.22/27.75    (34)  all_58_4 = all_52_5
% 177.22/27.75    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.75    (36)   ~ (all_52_27 = all_52_29)
% 177.22/27.75    (37)   ~ (all_52_17 = all_14_2)
% 177.22/27.75    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.75    (39)   ~ (all_52_7 = all_4_2)
% 177.22/27.75    (40)  all_58_1 = all_52_3
% 177.22/27.75    (41)  all_58_0 = all_4_2
% 177.22/27.75    (42)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.75    (43)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.75    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.75    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.75    (46)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.75    (47)  all_58_14 = all_52_29
% 177.22/27.75    (48)  op(e0, e3) = e3
% 177.22/27.75    (49)   ~ (all_52_3 = all_52_5)
% 177.22/27.75    (50)  op(e2, e1) = all_52_13
% 177.22/27.75    (51)  all_58_8 = all_14_2
% 177.22/27.75    (52)  op(all_14_1, all_14_2) = e3
% 177.22/27.75    (53)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.75    (54)  op(e3, all_52_17) = all_52_16
% 177.22/27.75    (55)   ~ (all_52_29 = e3)
% 177.22/27.75    (56)   ~ (all_52_13 = all_14_2)
% 177.22/27.75    (57)  op(e3, all_52_9) = e3
% 177.22/27.75    (58)   ~ (e3 = e0)
% 177.22/27.75    (59)   ~ (all_52_9 = all_52_13)
% 177.22/27.75    (60)  op(e0, all_52_23) = all_52_22
% 177.22/27.75    (61)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.75    (62)  all_58_13 = all_52_27
% 177.22/27.75    (63)   ~ (all_18_1 = e0) |  ~ (all_18_2 = e2)
% 177.22/27.75    (64)  all_58_12 = e3
% 177.22/27.75    (65)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.75    (66)   ~ (all_52_9 = all_52_17)
% 177.22/27.75    (67)  all_58_6 = all_52_17
% 177.22/27.75    (68)   ~ (all_52_3 = all_52_7)
% 177.22/27.75    (69)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.75    (70)  op(e2, all_52_19) = all_52_18
% 177.22/27.75    (71)  all_56_0 = all_4_2
% 177.22/27.75    (72)  all_58_11 = all_52_23
% 177.22/27.75    (73)   ~ (all_52_3 = all_52_19)
% 177.22/27.75    (74)   ~ (all_52_7 = all_52_15)
% 177.22/27.75    (75)   ~ (all_52_29 = all_14_2)
% 177.22/27.75    (76)   ~ (all_52_19 = all_10_2)
% 177.22/27.75    (77)   ~ (all_52_9 = e3)
% 177.22/27.75    (78)   ~ (all_52_23 = all_6_2)
% 177.22/27.75    (79)  all_58_2 = all_52_9
% 177.22/27.75    (80)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.75    (81)  op(e3, e1) = all_52_5
% 177.22/27.75    (82)   ~ (e2 = e1)
% 177.22/27.75    (83)  all_56_10 = all_14_2
% 177.22/27.75    (84)  op(e1, e3) = all_52_17
% 177.22/27.75    (85)  op(e3, e0) = all_52_7
% 177.22/27.75    (86)  op(e2, all_10_2) = e2
% 177.22/27.75    (87)   ~ (all_52_17 = all_4_2)
% 177.22/27.75    (88)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.75    (89)   ~ (all_52_27 = all_6_2)
% 177.22/27.75    (90)   ~ (all_52_7 = all_6_2)
% 177.22/27.75    (91)  all_18_2 = all_14_2
% 177.22/27.75    (92)   ~ (all_52_7 = all_52_23)
% 177.22/27.75    (93)   ~ (all_52_17 = all_52_19)
% 177.22/27.75    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.75    (95)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.75    (96)  op(e1, all_14_2) = all_14_1
% 177.22/27.75    (97)  all_58_9 = all_52_7
% 177.22/27.75    (98)  all_56_6 = all_52_13
% 177.22/27.75    (99)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.75    (100)   ~ (all_52_9 = all_52_15)
% 177.22/27.75    (101)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.75    (102)   ~ (e3 = e2)
% 177.22/27.75    (103)   ~ (all_52_19 = all_14_2)
% 177.22/27.75    (104)  op(e2, e3) = all_52_9
% 177.22/27.75  
% 177.22/27.75  Begin of proof
% 177.22/27.75  | 
% 177.22/27.75  | BETA: splitting (69) gives:
% 177.22/27.75  | 
% 177.22/27.75  | Case 1:
% 177.22/27.75  | | 
% 177.22/27.75  | |   (105)  all_56_4 = e3
% 177.22/27.75  | | 
% 177.22/27.75  | | REF_CLOSE: (33), (77), (105) are inconsistent by sub-proof #782.
% 177.22/27.75  | | 
% 177.22/27.75  | Case 2:
% 177.22/27.75  | | 
% 177.22/27.75  | |   (106)   ~ (all_56_4 = e3)
% 177.22/27.75  | |   (107)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.75  | | 
% 177.22/27.75  | | BETA: splitting (25) gives:
% 177.22/27.75  | | 
% 177.22/27.75  | | Case 1:
% 177.22/27.75  | | | 
% 177.22/27.75  | | |   (108)  all_56_0 = e3
% 177.22/27.75  | | | 
% 177.22/27.75  | | | COMBINE_EQS: (71), (108) imply:
% 177.22/27.75  | | |   (109)  all_4_2 = e3
% 177.22/27.75  | | | 
% 177.22/27.75  | | | REDUCE: (22), (109) imply:
% 177.22/27.75  | | |   (110)  $false
% 177.22/27.75  | | | 
% 177.22/27.75  | | | CLOSE: (110) is inconsistent.
% 177.22/27.75  | | | 
% 177.22/27.75  | | Case 2:
% 177.22/27.75  | | | 
% 177.22/27.75  | | |   (111)   ~ (all_56_0 = e3)
% 177.22/27.75  | | |   (112)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.75  | | | 
% 177.22/27.75  | | | BETA: splitting (46) gives:
% 177.22/27.75  | | | 
% 177.22/27.75  | | | Case 1:
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | |   (113)  all_56_6 = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | COMBINE_EQS: (98), (113) imply:
% 177.22/27.75  | | | |   (114)  all_52_13 = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (114) implies:
% 177.22/27.75  | | | |   (115)  all_52_13 = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | COMBINE_EQS: (16), (115) imply:
% 177.22/27.75  | | | |   (116)  all_58_5 = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (2), (115) imply:
% 177.22/27.75  | | | |   (117)   ~ (all_52_5 = e3)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (6), (115) imply:
% 177.22/27.75  | | | |   (118)   ~ (all_52_29 = e3)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (56), (115) imply:
% 177.22/27.75  | | | |   (119)   ~ (all_14_2 = e3)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (119) implies:
% 177.22/27.75  | | | |   (120)   ~ (all_14_2 = e3)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (50), (115) imply:
% 177.22/27.75  | | | |   (121)  op(e2, e1) = e3
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (18), (115) imply:
% 177.22/27.75  | | | |   (122)  op(e1, e3) = e1
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | GROUND_INST: instantiating (88) with all_52_17, e1, e3, e1, simplifying
% 177.22/27.75  | | | |              with (84), (122) gives:
% 177.22/27.75  | | | |   (123)  all_52_17 = e1
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | COMBINE_EQS: (67), (123) imply:
% 177.22/27.75  | | | |   (124)  all_58_6 = e1
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (66), (123) imply:
% 177.22/27.75  | | | |   (125)   ~ (all_52_9 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (93), (123) imply:
% 177.22/27.75  | | | |   (126)   ~ (all_52_19 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (126) implies:
% 177.22/27.75  | | | |   (127)   ~ (all_52_19 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (37), (123) imply:
% 177.22/27.75  | | | |   (128)   ~ (all_14_2 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (128) implies:
% 177.22/27.75  | | | |   (129)   ~ (all_14_2 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (87), (123) imply:
% 177.22/27.75  | | | |   (130)   ~ (all_4_2 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (130) implies:
% 177.22/27.75  | | | |   (131)   ~ (all_4_2 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (13), (123) imply:
% 177.22/27.75  | | | |   (132)   ~ (e3 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (132) implies:
% 177.22/27.75  | | | |   (133)   ~ (e3 = e1)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (54), (123) imply:
% 177.22/27.75  | | | |   (134)  op(e3, e1) = all_52_16
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | GROUND_INST: instantiating (88) with all_52_5, all_52_16, e1, e3,
% 177.22/27.75  | | | |              simplifying with (81), (134) gives:
% 177.22/27.75  | | | |   (135)  all_52_5 = all_52_16
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | COMBINE_EQS: (34), (135) imply:
% 177.22/27.75  | | | |   (136)  all_58_4 = all_52_16
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (29), (135) imply:
% 177.22/27.75  | | | |   (137)   ~ (all_52_7 = all_52_16)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | SIMP: (137) implies:
% 177.22/27.75  | | | |   (138)   ~ (all_52_7 = all_52_16)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | REDUCE: (31), (135) imply:
% 177.22/27.75  | | | |   (139)   ~ (all_52_16 = all_4_2)
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | BETA: splitting (94) gives:
% 177.22/27.75  | | | | 
% 177.22/27.75  | | | | Case 1:
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | |   (140)  all_58_9 = e3
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | COMBINE_EQS: (97), (140) imply:
% 177.22/27.75  | | | | |   (141)  all_52_7 = e3
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | SIMP: (141) implies:
% 177.22/27.75  | | | | |   (142)  all_52_7 = e3
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | REDUCE: (92), (142) imply:
% 177.22/27.75  | | | | |   (143)   ~ (all_52_23 = e3)
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | SIMP: (143) implies:
% 177.22/27.75  | | | | |   (144)   ~ (all_52_23 = e3)
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | REDUCE: (39), (142) imply:
% 177.22/27.75  | | | | |   (145)   ~ (all_4_2 = e3)
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | BETA: splitting (35) gives:
% 177.22/27.75  | | | | | 
% 177.22/27.75  | | | | | Case 1:
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | |   (146)  all_58_6 = e3
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | COMBINE_EQS: (124), (146) imply:
% 177.22/27.75  | | | | | |   (147)  e3 = e1
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | REDUCE: (133), (147) imply:
% 177.22/27.75  | | | | | |   (148)  $false
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | CLOSE: (148) is inconsistent.
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | Case 2:
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | |   (149)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | BETA: splitting (149) gives:
% 177.22/27.75  | | | | | | 
% 177.22/27.75  | | | | | | Case 1:
% 177.22/27.75  | | | | | | | 
% 177.22/27.75  | | | | | | |   (150)  all_58_7 = e3
% 177.22/27.75  | | | | | | | 
% 177.22/27.75  | | | | | | | COMBINE_EQS: (32), (150) imply:
% 177.22/27.76  | | | | | | |   (151)  all_52_19 = e3
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (73), (151) imply:
% 177.22/27.76  | | | | | | |   (152)   ~ (all_52_3 = e3)
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (70), (151) imply:
% 177.22/27.76  | | | | | | |   (153)  op(e2, e3) = all_52_18
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (11), (151) imply:
% 177.22/27.76  | | | | | | |   (154)  op(e1, e2) = e3
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | GROUND_INST: instantiating (88) with all_52_9, all_52_18, e3, e2,
% 177.22/27.76  | | | | | | |              simplifying with (104), (153) gives:
% 177.22/27.76  | | | | | | |   (155)  all_52_9 = all_52_18
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | COMBINE_EQS: (33), (155) imply:
% 177.22/27.76  | | | | | | |   (156)  all_56_4 = all_52_18
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | COMBINE_EQS: (79), (155) imply:
% 177.22/27.76  | | | | | | |   (157)  all_58_2 = all_52_18
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (100), (155) imply:
% 177.22/27.76  | | | | | | |   (158)   ~ (all_52_15 = all_52_18)
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | SIMP: (158) implies:
% 177.22/27.76  | | | | | | |   (159)   ~ (all_52_15 = all_52_18)
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (27), (155) imply:
% 177.22/27.76  | | | | | | |   (160)   ~ (all_52_18 = all_4_2)
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (77), (155) imply:
% 177.22/27.76  | | | | | | |   (161)   ~ (all_52_18 = e3)
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (125), (155) imply:
% 177.22/27.76  | | | | | | |   (162)   ~ (all_52_18 = e1)
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REDUCE: (57), (155) imply:
% 177.22/27.76  | | | | | | |   (163)  op(e3, all_52_18) = e3
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | BETA: splitting (21) gives:
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | |   (164)  all_58_0 = e2
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | | COMBINE_EQS: (41), (164) imply:
% 177.22/27.76  | | | | | | | |   (165)  all_4_2 = e2
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | | REDUCE: (160), (165) imply:
% 177.22/27.76  | | | | | | | |   (166)   ~ (all_52_18 = e2)
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | | REDUCE: (22), (165) imply:
% 177.22/27.76  | | | | | | | |   (167)   ~ (e3 = e2)
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | | BETA: splitting (107) gives:
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | 
% 177.22/27.76  | | | | | | | | |   (168)  all_56_4 = e2
% 177.22/27.76  | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | REF_CLOSE: (156), (166), (168) are inconsistent by sub-proof
% 177.22/27.76  | | | | | | | | |            #781.
% 177.22/27.76  | | | | | | | | | 
% 177.22/27.76  | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | 
% 177.22/27.76  | | | | | | | | |   (169)   ~ (all_56_4 = e2)
% 177.22/27.76  | | | | | | | | |   (170)  all_56_4 = e1 | all_56_4 = e0
% 177.22/27.76  | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | BETA: splitting (170) gives:
% 177.22/27.76  | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | |   (171)  all_56_4 = e1
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | REF_CLOSE: (156), (162), (171) are inconsistent by sub-proof
% 177.22/27.76  | | | | | | | | | |            #780.
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | |   (172)  all_56_4 = e0
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | COMBINE_EQS: (156), (172) imply:
% 177.22/27.76  | | | | | | | | | |   (173)  all_52_18 = e0
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | SIMP: (173) implies:
% 177.22/27.76  | | | | | | | | | |   (174)  all_52_18 = e0
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | REDUCE: (159), (174) imply:
% 177.22/27.76  | | | | | | | | | |   (175)   ~ (all_52_15 = e0)
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | REDUCE: (161), (174) imply:
% 177.22/27.76  | | | | | | | | | |   (176)   ~ (e3 = e0)
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | REDUCE: (166), (174) imply:
% 177.22/27.76  | | | | | | | | | |   (177)   ~ (e2 = e0)
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | SIMP: (177) implies:
% 177.22/27.76  | | | | | | | | | |   (178)   ~ (e2 = e0)
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | BETA: splitting (42) gives:
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | |   (179)  all_58_9 = e0
% 177.22/27.76  | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | REF_CLOSE: (58), (140), (179) are inconsistent by sub-proof
% 177.22/27.76  | | | | | | | | | | |            #928.
% 177.22/27.76  | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | |   (180)  all_58_10 = e0 | all_58_11 = e0
% 177.22/27.76  | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | BETA: splitting (180) gives:
% 177.22/27.76  | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | |   (181)  all_58_10 = e0
% 177.22/27.76  | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | REF_CLOSE: (30), (175), (181) are inconsistent by sub-proof
% 177.22/27.76  | | | | | | | | | | | |            #741.
% 177.22/27.76  | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | |   (182)  all_58_11 = e0
% 177.22/27.76  | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | BETA: splitting (65) gives:
% 177.22/27.76  | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | |   (183)  all_58_6 = e2
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | COMBINE_EQS: (124), (183) imply:
% 177.22/27.76  | | | | | | | | | | | | |   (184)  e2 = e1
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | REDUCE: (82), (184) imply:
% 177.22/27.76  | | | | | | | | | | | | |   (185)  $false
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | CLOSE: (185) is inconsistent.
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | |   (186)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | BETA: splitting (186) gives:
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | |   (187)  all_58_7 = e2
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | COMBINE_EQS: (150), (187) imply:
% 177.22/27.76  | | | | | | | | | | | | | |   (188)  e3 = e2
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | REDUCE: (102), (188) imply:
% 177.22/27.76  | | | | | | | | | | | | | |   (189)  $false
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | |   (190)  all_58_8 = e2 | all_58_11 = e2
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | |   (191)  all_58_8 = e2
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | COMBINE_EQS: (51), (191) imply:
% 177.22/27.76  | | | | | | | | | | | | | | |   (192)  all_14_2 = e2
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | COMBINE_EQS: (91), (192) imply:
% 177.22/27.76  | | | | | | | | | | | | | | |   (193)  all_18_2 = e2
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | REDUCE: (52), (192) imply:
% 177.22/27.76  | | | | | | | | | | | | | | |   (194)  op(all_14_1, e2) = e3
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | REDUCE: (96), (192) imply:
% 177.22/27.76  | | | | | | | | | | | | | | |   (195)  op(e1, e2) = all_14_1
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | |   (196)   ~ (all_18_2 = e2)
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | | REDUCE: (193), (196) imply:
% 177.22/27.76  | | | | | | | | | | | | | | | |   (197)  $false
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent.
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (88) with e3, all_14_1, e2, e1,
% 177.22/27.76  | | | | | | | | | | | | | | | |              simplifying with (154), (195) gives:
% 177.22/27.76  | | | | | | | | | | | | | | | |   (198)  all_14_1 = e3
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | | REDUCE: (194), (198) imply:
% 177.22/27.76  | | | | | | | | | | | | | | | |   (199)  op(e3, e2) = e3
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (88), (152), (199) are inconsistent by
% 177.22/27.76  | | | | | | | | | | | | | | | |            sub-proof #978.
% 177.22/27.76  | | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | |   (200)  all_58_11 = e2
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | COMBINE_EQS: (182), (200) imply:
% 177.22/27.76  | | | | | | | | | | | | | | |   (201)  e2 = e0
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | REDUCE: (178), (201) imply:
% 177.22/27.76  | | | | | | | | | | | | | | |   (202)  $false
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | | CLOSE: (202) is inconsistent.
% 177.22/27.76  | | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | | | 
% 177.22/27.76  | | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | | 
% 177.22/27.76  | | | | | | | | End of split
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | Case 2:
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | |   (203)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | | REF_CLOSE: (8), (64), (82), (88), (102), (124), (152), (157),
% 177.22/27.76  | | | | | | | |            (163), (203) are inconsistent by sub-proof #737.
% 177.22/27.76  | | | | | | | | 
% 177.22/27.76  | | | | | | | End of split
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | Case 2:
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | |   (204)  all_58_8 = e3 | all_58_11 = e3
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | | REF_CLOSE: (51), (72), (120), (144), (204) are inconsistent by
% 177.22/27.76  | | | | | | |            sub-proof #997.
% 177.22/27.76  | | | | | | | 
% 177.22/27.76  | | | | | | End of split
% 177.22/27.76  | | | | | | 
% 177.22/27.76  | | | | | End of split
% 177.22/27.76  | | | | | 
% 177.22/27.76  | | | | Case 2:
% 177.22/27.76  | | | | | 
% 177.22/27.76  | | | | |   (205)   ~ (all_58_9 = e3)
% 177.22/27.76  | | | | | 
% 177.22/27.76  | | | | | REDUCE: (97), (205) imply:
% 177.22/27.76  | | | | |   (206)   ~ (all_52_7 = e3)
% 177.22/27.76  | | | | | 
% 177.22/27.76  | | | | | REF_CLOSE: (3), (7), (17), (20), (22), (23), (27), (28), (32), (33),
% 177.22/27.76  | | | | |            (34), (36), (39), (41), (44), (47), (51), (53), (55), (57),
% 177.22/27.76  | | | | |            (62), (71), (85), (86), (88), (89), (90), (95), (97), (99),
% 177.22/27.76  | | | | |            (102), (107), (112), (116), (117), (121), (125), (127),
% 177.22/27.76  | | | | |            (129), (133), (136), (138), (139), (206) are inconsistent
% 177.22/27.76  | | | | |            by sub-proof #335.
% 177.22/27.76  | | | | | 
% 177.22/27.76  | | | | End of split
% 177.22/27.76  | | | | 
% 177.22/27.76  | | | Case 2:
% 177.22/27.76  | | | | 
% 177.22/27.76  | | | |   (207)   ~ (all_56_6 = e3)
% 177.22/27.76  | | | | 
% 177.22/27.76  | | | | REDUCE: (98), (207) imply:
% 177.22/27.76  | | | |   (208)   ~ (all_52_13 = e3)
% 177.22/27.76  | | | | 
% 177.22/27.76  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.76  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 177.22/27.76  | | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.22/27.76  | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.22/27.76  | | | |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 177.22/27.76  | | | |            (57), (58), (59), (60), (61), (62), (64), (66), (67), (68),
% 177.22/27.76  | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 177.22/27.76  | | | |            (79), (80), (81), (82), (83), (84), (85), (86), (88), (89),
% 177.22/27.76  | | | |            (90), (92), (93), (94), (95), (96), (97), (98), (100), (101),
% 177.22/27.76  | | | |            (102), (103), (104), (112), (208) are inconsistent by
% 177.22/27.76  | | | |            sub-proof #382.
% 177.22/27.76  | | | | 
% 177.22/27.76  | | | End of split
% 177.22/27.76  | | | 
% 177.22/27.76  | | End of split
% 177.22/27.76  | | 
% 177.22/27.76  | End of split
% 177.22/27.76  | 
% 177.22/27.76  End of proof
% 177.22/27.76  
% 177.22/27.76  Sub-proof #335 shows that the following formulas are inconsistent:
% 177.22/27.76  ----------------------------------------------------------------
% 177.22/27.76    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.76    (2)  all_56_3 = all_52_7
% 177.22/27.76    (3)   ~ (all_6_2 = e0)
% 177.22/27.76    (4)  all_56_15 = all_6_2
% 177.22/27.76    (5)   ~ (all_4_2 = e3)
% 177.22/27.76    (6)  all_58_3 = all_10_2
% 177.22/27.76    (7)   ~ (all_52_9 = all_4_2)
% 177.22/27.76    (8)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.76    (9)  all_58_7 = all_52_19
% 177.22/27.76    (10)  all_56_4 = all_52_9
% 177.22/27.76    (11)  all_58_4 = all_52_5
% 177.22/27.76    (12)   ~ (e3 = e1)
% 177.22/27.76    (13)  all_58_5 = e3
% 177.22/27.76    (14)   ~ (all_52_27 = all_52_29)
% 177.22/27.76    (15)   ~ (all_52_7 = all_4_2)
% 177.22/27.76    (16)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.76    (17)  all_58_0 = all_4_2
% 177.22/27.76    (18)  all_58_4 = all_52_16
% 177.22/27.76    (19)   ~ (all_52_16 = all_4_2)
% 177.22/27.76    (20)   ~ (all_14_2 = e1)
% 177.22/27.76    (21)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.76    (22)  all_58_14 = all_52_29
% 177.22/27.76    (23)   ~ (all_52_9 = e1)
% 177.22/27.76    (24)  all_58_8 = all_14_2
% 177.22/27.76    (25)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.76    (26)   ~ (all_52_29 = e3)
% 177.22/27.76    (27)   ~ (all_52_5 = e3)
% 177.22/27.76    (28)  op(e3, all_52_9) = e3
% 177.22/27.76    (29)  all_58_13 = all_52_27
% 177.22/27.76    (30)  all_56_0 = all_4_2
% 177.22/27.76    (31)  op(e2, e1) = e3
% 177.22/27.76    (32)  op(e3, e0) = all_52_7
% 177.22/27.76    (33)  op(e2, all_10_2) = e2
% 177.22/27.76    (34)   ~ (all_52_19 = e1)
% 177.22/27.76    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.76    (36)   ~ (all_52_27 = all_6_2)
% 177.22/27.76    (37)   ~ (all_52_7 = all_6_2)
% 177.22/27.76    (38)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.76    (39)   ~ (all_52_7 = all_52_16)
% 177.22/27.76    (40)   ~ (all_52_7 = e3)
% 177.22/27.76    (41)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.76    (42)  all_58_9 = all_52_7
% 177.22/27.76    (43)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.76    (44)   ~ (e3 = e2)
% 177.22/27.76  
% 177.22/27.76  Begin of proof
% 177.22/27.76  | 
% 177.22/27.76  | BETA: splitting (43) gives:
% 177.22/27.76  | 
% 177.22/27.76  | Case 1:
% 177.22/27.76  | | 
% 177.22/27.76  | |   (45)  all_58_0 = e3
% 177.22/27.76  | | 
% 177.22/27.76  | | COMBINE_EQS: (17), (45) imply:
% 177.22/27.76  | |   (46)  all_4_2 = e3
% 177.22/27.76  | | 
% 177.22/27.76  | | REDUCE: (5), (46) imply:
% 177.22/27.76  | |   (47)  $false
% 177.22/27.76  | | 
% 177.22/27.76  | | CLOSE: (47) is inconsistent.
% 177.22/27.76  | | 
% 177.22/27.76  | Case 2:
% 177.22/27.76  | | 
% 177.22/27.76  | |   (48)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.76  | | 
% 177.22/27.76  | | BETA: splitting (48) gives:
% 177.22/27.76  | | 
% 177.22/27.76  | | Case 1:
% 177.22/27.76  | | | 
% 177.22/27.76  | | |   (49)  all_58_1 = e3
% 177.22/27.76  | | | 
% 177.22/27.76  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 177.22/27.76  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.22/27.76  | | |            (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.22/27.76  | | |            (36), (37), (38), (39), (40), (41), (44), (49) are inconsistent
% 177.22/27.76  | | |            by sub-proof #747.
% 177.22/27.76  | | | 
% 177.22/27.76  | | Case 2:
% 177.22/27.76  | | | 
% 177.22/27.76  | | |   (50)  all_58_4 = e3 | all_58_9 = e3
% 177.22/27.76  | | | 
% 177.22/27.76  | | | REF_CLOSE: (11), (27), (40), (42), (50) are inconsistent by sub-proof
% 177.22/27.76  | | |            #729.
% 177.22/27.76  | | | 
% 177.22/27.76  | | End of split
% 177.22/27.76  | | 
% 177.22/27.76  | End of split
% 177.22/27.76  | 
% 177.22/27.76  End of proof
% 177.22/27.76  
% 177.22/27.76  Sub-proof #336 shows that the following formulas are inconsistent:
% 177.22/27.76  ----------------------------------------------------------------
% 177.22/27.76    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.76    (2)  all_40_2 = all_4_2
% 177.22/27.76    (3)  all_56_3 = all_52_7
% 177.22/27.76    (4)  op(e3, e2) = all_52_3
% 177.22/27.76    (5)   ~ (all_52_9 = all_52_25)
% 177.22/27.76    (6)  op(e3, all_52_25) = all_52_24
% 177.22/27.76    (7)  op(e1, e2) = all_52_19
% 177.22/27.76    (8)  all_58_5 = all_52_13
% 177.22/27.76    (9)   ~ (all_52_25 = all_52_29)
% 177.22/27.76    (10)  all_56_9 = all_52_19
% 177.22/27.76    (11)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.76    (12)   ~ (all_52_9 = all_4_2)
% 177.22/27.76    (13)   ~ (all_52_5 = all_52_7)
% 177.22/27.76    (14)   ~ (all_52_5 = all_4_2)
% 177.22/27.76    (15)  all_58_7 = all_52_19
% 177.22/27.76    (16)   ~ (all_52_17 = all_52_25)
% 177.22/27.76    (17)   ~ (all_4_0 = e2)
% 177.22/27.76    (18)  all_58_4 = all_52_5
% 177.22/27.76    (19)   ~ (e3 = e1)
% 177.22/27.76    (20)   ~ (all_52_27 = all_52_29)
% 177.22/27.76    (21)   ~ (all_52_17 = all_14_2)
% 177.22/27.76    (22)  all_58_0 = all_4_2
% 177.22/27.76    (23)  op(e1, all_52_29) = all_52_28
% 177.22/27.76    (24)   ~ (all_52_7 = e0)
% 177.22/27.76    (25)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.76    (26)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.76    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.76    (28)  all_58_14 = all_52_29
% 177.22/27.76    (29)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.76    (30)  op(e2, e1) = all_52_13
% 177.22/27.76    (31)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.76    (32)  all_58_8 = all_14_2
% 177.22/27.76    (33)  all_56_14 = all_52_29
% 177.22/27.76    (34)  op(all_14_1, all_14_2) = e3
% 177.22/27.76    (35)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.76    (36)   ~ (all_52_3 = all_52_27)
% 177.22/27.76    (37)   ~ (all_52_3 = all_4_2)
% 177.22/27.76    (38)  op(e3, all_52_17) = all_52_16
% 177.22/27.76    (39)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.76    (40)   ~ (e3 = e0)
% 177.22/27.76    (41)  all_40_0 = all_4_0
% 177.22/27.76    (42)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.76    (43)  op(e1, e0) = all_52_23
% 177.22/27.76    (44)  all_56_12 = all_52_25
% 177.22/27.76    (45)  all_58_13 = all_52_27
% 177.22/27.76    (46)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.76    (47)   ~ (all_52_25 = e0)
% 177.22/27.76    (48)   ~ (all_52_9 = all_52_17)
% 177.22/27.76    (49)  all_58_6 = all_52_17
% 177.22/27.76    (50)   ~ (all_52_3 = all_52_7)
% 177.22/27.76    (51)   ~ (e1 = e0)
% 177.22/27.76    (52)  all_56_0 = all_4_2
% 177.22/27.76    (53)  all_58_11 = all_52_23
% 177.22/27.76    (54)   ~ (all_52_3 = all_52_19)
% 177.22/27.76    (55)   ~ (all_52_29 = all_14_2)
% 177.22/27.76    (56)  all_58_15 = e0
% 177.22/27.76    (57)  op(e1, all_4_2) = all_4_0
% 177.22/27.76    (58)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.22/27.76    (59)   ~ (all_52_29 = e0)
% 177.22/27.76    (60)  op(e3, e1) = all_52_5
% 177.22/27.76    (61)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.76    (62)  op(e1, e3) = all_52_17
% 177.22/27.76    (63)   ~ (all_52_25 = all_4_2)
% 177.22/27.76    (64)  op(e3, e0) = all_52_7
% 177.22/27.76    (65)  op(e3, e3) = all_4_2
% 177.22/27.76    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.76    (67)   ~ (all_52_25 = all_52_27)
% 177.22/27.76    (68)  op(e2, all_52_27) = all_52_26
% 177.22/27.76    (69)  all_52_20 = all_14_1
% 177.22/27.76    (70)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.76    (71)  op(e1, all_14_2) = all_14_1
% 177.22/27.76    (72)  all_58_9 = all_52_7
% 177.22/27.76    (73)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.22/27.76          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.76    (74)  all_58_12 = all_52_25
% 177.22/27.76    (75)  op(e3, all_4_2) = e1
% 177.22/27.76    (76)  op(e2, e3) = all_52_9
% 177.22/27.76    (77)  all_56_13 = all_52_27
% 177.22/27.76  
% 177.22/27.76  Begin of proof
% 177.22/27.76  | 
% 177.22/27.76  | BETA: splitting (73) gives:
% 177.22/27.76  | 
% 177.22/27.76  | Case 1:
% 177.22/27.76  | | 
% 177.22/27.76  | |   (78)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.22/27.76  | | 
% 177.22/27.76  | | ALPHA: (78) implies:
% 177.22/27.76  | |   (79)  all_52_20 = e1
% 177.22/27.76  | | 
% 177.22/27.76  | | COMBINE_EQS: (69), (79) imply:
% 177.22/27.76  | |   (80)  all_14_1 = e1
% 177.22/27.76  | | 
% 177.22/27.76  | | REF_CLOSE: (19), (34), (66), (71), (80) are inconsistent by sub-proof #344.
% 177.22/27.76  | | 
% 177.22/27.76  | Case 2:
% 177.22/27.76  | | 
% 177.22/27.76  | |   (81)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.22/27.76  | | 
% 177.22/27.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.76  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.22/27.76  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 177.22/27.76  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.22/27.76  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.22/27.76  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.22/27.76  | |            (70), (72), (74), (75), (76), (77), (81) are inconsistent by
% 177.22/27.76  | |            sub-proof #615.
% 177.22/27.76  | | 
% 177.22/27.76  | End of split
% 177.22/27.76  | 
% 177.22/27.76  End of proof
% 177.22/27.76  
% 177.22/27.76  Sub-proof #337 shows that the following formulas are inconsistent:
% 177.22/27.76  ----------------------------------------------------------------
% 177.22/27.76    (1)   ~ (all_52_27 = all_10_2)
% 177.22/27.76    (2)   ~ (all_52_17 = all_52_23)
% 177.22/27.76    (3)  op(e2, all_10_2) = all_10_1
% 177.22/27.76    (4)   ~ (all_52_13 = all_52_29)
% 177.22/27.76    (5)  all_56_3 = all_52_7
% 177.22/27.76    (6)  op(e3, e2) = all_52_3
% 177.22/27.76    (7)   ~ (all_52_9 = all_52_25)
% 177.22/27.76    (8)  op(e3, all_52_25) = all_52_24
% 177.22/27.76    (9)   ~ (all_52_27 = e0)
% 177.22/27.76    (10)  op(e3, all_52_9) = all_52_8
% 177.22/27.76    (11)   ~ (all_52_3 = all_10_2)
% 177.22/27.76    (12)  all_58_5 = all_52_13
% 177.22/27.76    (13)   ~ (all_52_25 = all_52_29)
% 177.22/27.76    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.76    (15)  all_58_3 = all_10_2
% 177.22/27.76    (16)   ~ (all_52_9 = all_4_2)
% 177.22/27.76    (17)   ~ (all_52_5 = all_52_7)
% 177.22/27.76    (18)  all_58_10 = all_52_15
% 177.22/27.76    (19)  all_58_7 = all_52_19
% 177.22/27.76    (20)   ~ (all_52_17 = all_52_25)
% 177.22/27.76    (21)  op(e0, e1) = all_52_29
% 177.22/27.76    (22)   ~ (all_4_0 = e2)
% 177.22/27.76    (23)  all_58_4 = all_52_5
% 177.22/27.76    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.76    (25)   ~ (e3 = e1)
% 177.22/27.76    (26)   ~ (all_52_27 = all_52_29)
% 177.22/27.76    (27)   ~ (all_52_17 = all_14_2)
% 177.22/27.76    (28)  op(e3, all_4_2) = all_4_1
% 177.22/27.76    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.76    (30)   ~ (all_52_7 = all_4_2)
% 177.22/27.76    (31)  all_58_1 = all_52_3
% 177.22/27.76    (32)  all_58_0 = all_4_2
% 177.22/27.76    (33)  all_52_0 = e1
% 177.22/27.76    (34)  op(e1, all_52_13) = all_52_12
% 177.22/27.76    (35)  op(e1, all_52_29) = all_52_28
% 177.22/27.76    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.76          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.76    (37)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.76    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.76    (39)  all_58_14 = all_52_29
% 177.22/27.76    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.76    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.76    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.76    (43)  all_58_8 = all_14_2
% 177.22/27.76    (44)  all_56_1 = all_52_3
% 177.22/27.76    (45)  op(e0, e2) = all_52_27
% 177.22/27.76    (46)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.76    (47)   ~ (all_52_3 = all_4_2)
% 177.22/27.76    (48)  op(e0, e3) = all_52_25
% 177.22/27.76    (49)  all_52_10 = all_10_1
% 177.22/27.76    (50)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.76    (51)   ~ (all_52_13 = all_14_2)
% 177.22/27.76    (52)   ~ (e3 = e0)
% 177.22/27.76    (53)   ~ (all_52_9 = all_52_13)
% 177.22/27.76    (54)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.76    (55)   ~ (all_52_15 = all_52_23)
% 177.22/27.76    (56)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.76    (57)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.76    (58)  all_56_12 = all_52_25
% 177.22/27.76    (59)  all_58_13 = all_52_27
% 177.22/27.76    (60)   ~ (all_52_25 = e0)
% 177.22/27.76    (61)   ~ (all_52_9 = all_52_17)
% 177.22/27.76    (62)  all_58_6 = all_52_17
% 177.22/27.76    (63)   ~ (all_52_3 = all_52_7)
% 177.22/27.76    (64)   ~ (e1 = e0)
% 177.22/27.76    (65)  all_58_11 = all_52_23
% 177.22/27.76    (66)   ~ (all_52_3 = all_52_19)
% 177.22/27.76    (67)   ~ (all_52_7 = all_52_15)
% 177.22/27.76    (68)  op(e0, all_52_15) = all_52_14
% 177.22/27.76    (69)   ~ (all_52_29 = all_14_2)
% 177.22/27.76    (70)   ~ (all_4_0 = e1)
% 177.22/27.76    (71)   ~ (all_52_19 = all_10_2)
% 177.22/27.76    (72)  all_58_15 = e0
% 177.22/27.76    (73)  all_58_2 = all_52_9
% 177.22/27.76    (74)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.22/27.76    (75)   ~ (all_52_29 = e0)
% 177.22/27.76    (76)  op(e3, e1) = all_52_5
% 177.22/27.76    (77)  all_56_10 = all_14_2
% 177.22/27.76    (78)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.76    (79)  op(e1, e3) = all_52_17
% 177.22/27.76    (80)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.76    (81)  op(e3, e3) = all_4_2
% 177.22/27.76    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.76    (83)   ~ (all_52_25 = all_52_27)
% 177.22/27.76    (84)   ~ (all_10_0 = e3)
% 177.22/27.76    (85)   ~ (all_52_19 = all_52_27)
% 177.22/27.76    (86)  all_56_7 = all_52_15
% 177.22/27.76    (87)   ~ (all_52_15 = e0)
% 177.22/27.76    (88)   ~ (all_52_7 = all_52_23)
% 177.22/27.76    (89)  op(e2, all_52_27) = all_52_26
% 177.22/27.76    (90)   ~ (all_52_17 = all_52_19)
% 177.22/27.76    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.76    (92)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.76    (93)  all_58_9 = all_52_7
% 177.22/27.76    (94)   ~ (e2 = e0)
% 177.22/27.76    (95)  all_58_12 = all_52_25
% 177.22/27.76    (96)   ~ (all_10_0 = e1)
% 177.22/27.76    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.76    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.76    (99)   ~ (all_52_19 = all_14_2)
% 177.22/27.76    (100)  op(e2, e3) = all_52_9
% 177.22/27.76    (101)  all_56_13 = all_52_27
% 177.22/27.76  
% 177.22/27.76  Begin of proof
% 177.22/27.76  | 
% 177.22/27.76  | BETA: splitting (36) gives:
% 177.22/27.76  | 
% 177.22/27.76  | Case 1:
% 177.22/27.76  | | 
% 177.22/27.76  | |   (102)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.22/27.76  | | 
% 177.22/27.76  | | REF_CLOSE: (25), (33), (102) are inconsistent by sub-proof #632.
% 177.22/27.76  | | 
% 177.22/27.76  | Case 2:
% 177.22/27.76  | | 
% 177.22/27.76  | |   (103)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.76  | | 
% 177.22/27.76  | | ALPHA: (103) implies:
% 177.22/27.76  | |   (104)  all_52_14 = e0
% 177.22/27.76  | |   (105)  all_52_12 = e1
% 177.22/27.76  | |   (106)  all_52_10 = e2
% 177.22/27.76  | |   (107)  all_52_8 = e3
% 177.22/27.76  | | 
% 177.22/27.76  | | COMBINE_EQS: (49), (106) imply:
% 177.22/27.76  | |   (108)  all_10_1 = e2
% 177.22/27.76  | | 
% 177.22/27.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.76  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.22/27.76  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 177.22/27.76  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.22/27.76  | |            (48), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 177.22/27.76  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 177.22/27.76  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 177.22/27.76  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 177.22/27.76  | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (104),
% 177.22/27.76  | |            (105), (107), (108) are inconsistent by sub-proof #953.
% 177.22/27.76  | | 
% 177.22/27.76  | End of split
% 177.22/27.76  | 
% 177.22/27.76  End of proof
% 177.22/27.76  
% 177.22/27.76  Sub-proof #338 shows that the following formulas are inconsistent:
% 177.22/27.76  ----------------------------------------------------------------
% 177.22/27.76    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.76    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.76    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.76    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.76    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.76    (6)  op(e2, all_10_2) = all_10_1
% 177.22/27.76    (7)   ~ (all_52_13 = all_52_29)
% 177.22/27.76    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.76    (9)  all_56_3 = all_52_7
% 177.22/27.76    (10)  op(e3, e2) = all_52_3
% 177.22/27.76    (11)   ~ (all_52_9 = all_52_25)
% 177.22/27.76    (12)  op(e3, all_52_25) = all_52_24
% 177.22/27.76    (13)   ~ (all_52_19 = all_52_23)
% 177.22/27.76    (14)  all_56_11 = all_52_23
% 177.22/27.76    (15)  op(e1, e2) = all_52_19
% 177.22/27.76    (16)  op(e3, all_52_9) = all_52_8
% 177.22/27.76    (17)   ~ (all_52_3 = all_10_2)
% 177.22/27.76    (18)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.22/27.76    (19)  all_58_5 = all_52_13
% 177.22/27.76    (20)   ~ (all_6_2 = e0)
% 177.22/27.76    (21)   ~ (all_52_25 = all_52_29)
% 177.22/27.76    (22)  all_56_15 = all_6_2
% 177.22/27.76    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.76    (24)  op(e2, e0) = all_52_15
% 177.22/27.76    (25)  all_58_3 = all_10_2
% 177.22/27.76    (26)  all_56_9 = all_52_19
% 177.22/27.76    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.76    (28)  all_58_15 = all_6_2
% 177.22/27.76    (29)   ~ (all_52_9 = all_4_2)
% 177.22/27.76    (30)   ~ (all_52_5 = all_52_7)
% 177.22/27.76    (31)  all_58_10 = all_52_15
% 177.22/27.76    (32)   ~ (all_52_5 = all_4_2)
% 177.22/27.76    (33)  all_58_7 = all_52_19
% 177.22/27.76    (34)  all_56_4 = all_52_9
% 177.22/27.76    (35)   ~ (all_52_15 = all_6_2)
% 177.22/27.76    (36)   ~ (all_52_17 = all_52_25)
% 177.22/27.76    (37)  op(e0, e1) = all_52_29
% 177.22/27.76    (38)   ~ (all_4_0 = e2)
% 177.22/27.76    (39)  all_58_4 = all_52_5
% 177.22/27.76    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.76    (41)   ~ (e3 = e1)
% 177.22/27.76    (42)   ~ (all_52_27 = all_52_29)
% 177.22/27.76    (43)   ~ (all_52_17 = all_14_2)
% 177.22/27.76    (44)  op(e3, all_4_2) = all_4_1
% 177.22/27.76    (45)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.76    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.76    (47)   ~ (all_52_7 = all_4_2)
% 177.22/27.76    (48)  all_58_1 = all_52_3
% 177.22/27.76    (49)   ~ (all_52_13 = all_52_15)
% 177.22/27.76    (50)  all_58_0 = all_4_2
% 177.22/27.76    (51)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.76    (52)  op(e1, all_52_13) = all_52_12
% 177.22/27.77    (53)  op(e1, all_52_29) = all_52_28
% 177.22/27.77    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.77    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.77    (56)   ~ (all_4_1 = e2)
% 177.22/27.77    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.77    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.77    (59)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.77    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.77    (61)  all_58_14 = all_52_29
% 177.22/27.77    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.77    (63)   ~ (all_52_3 = all_52_5)
% 177.22/27.77    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.77    (65)  op(e2, e1) = all_52_13
% 177.22/27.77    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.77    (67)  all_58_8 = all_14_2
% 177.22/27.77    (68)  all_56_1 = all_52_3
% 177.22/27.77    (69)  op(e0, e2) = all_52_27
% 177.22/27.77    (70)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.22/27.77    (71)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.77    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.77    (73)   ~ (all_52_3 = all_52_27)
% 177.22/27.77    (74)   ~ (all_52_3 = all_4_2)
% 177.22/27.77    (75)  op(e0, e3) = all_52_25
% 177.22/27.77    (76)  op(e0, all_6_2) = all_6_1
% 177.22/27.77    (77)   ~ (all_52_9 = all_10_2)
% 177.22/27.77    (78)  op(e3, all_52_17) = all_52_16
% 177.22/27.77    (79)  all_52_10 = all_10_1
% 177.22/27.77    (80)   ~ (all_52_13 = all_14_2)
% 177.22/27.77    (81)   ~ (e3 = e0)
% 177.22/27.77    (82)   ~ (all_52_9 = all_52_13)
% 177.22/27.77    (83)  op(e0, all_52_23) = all_52_22
% 177.22/27.77    (84)   ~ (all_52_15 = all_52_23)
% 177.22/27.77    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.77    (86)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.77    (87)   ~ (all_52_5 = all_52_29)
% 177.22/27.77    (88)  all_56_2 = all_52_5
% 177.22/27.77    (89)  op(e1, e0) = all_52_23
% 177.22/27.77    (90)  all_58_13 = all_52_27
% 177.22/27.77    (91)   ~ (all_4_1 = e1)
% 177.22/27.77    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.77    (93)   ~ (all_52_9 = all_52_17)
% 177.22/27.77    (94)  all_58_6 = all_52_17
% 177.22/27.77    (95)   ~ (all_52_3 = all_52_7)
% 177.22/27.77    (96)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.77    (97)  op(e2, all_52_19) = all_52_18
% 177.22/27.77    (98)   ~ (e1 = e0)
% 177.22/27.77    (99)  all_56_0 = all_4_2
% 177.22/27.77    (100)  all_58_11 = all_52_23
% 177.22/27.77    (101)   ~ (all_52_3 = all_52_19)
% 177.22/27.77    (102)   ~ (all_52_7 = all_52_15)
% 177.22/27.77    (103)  op(e0, all_52_15) = all_52_14
% 177.22/27.77    (104)   ~ (all_52_29 = all_14_2)
% 177.22/27.77    (105)   ~ (all_4_0 = e1)
% 177.22/27.77    (106)   ~ (all_52_19 = all_10_2)
% 177.22/27.77    (107)   ~ (all_52_23 = all_6_2)
% 177.22/27.77    (108)   ~ (all_52_29 = all_6_2)
% 177.22/27.77    (109)  all_58_2 = all_52_9
% 177.22/27.77    (110)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.77    (111)  op(e3, e1) = all_52_5
% 177.22/27.77    (112)  all_56_10 = all_14_2
% 177.22/27.77    (113)   ~ (all_52_25 = all_6_2)
% 177.22/27.77    (114)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.77    (115)  op(e1, e1) = all_14_2
% 177.22/27.77    (116)  op(e1, e3) = all_52_17
% 177.22/27.77    (117)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.77    (118)   ~ (all_52_25 = all_4_2)
% 177.22/27.77    (119)  op(e3, e0) = all_52_7
% 177.22/27.77    (120)  op(e3, e3) = all_4_2
% 177.22/27.77    (121)   ~ (all_52_17 = all_4_2)
% 177.22/27.77    (122)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.77             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.77    (123)   ~ (all_52_25 = all_52_27)
% 177.22/27.77    (124)   ~ (all_52_27 = all_6_2)
% 177.22/27.77    (125)   ~ (all_52_7 = all_6_2)
% 177.22/27.77    (126)   ~ (all_10_0 = e3)
% 177.22/27.77    (127)   ~ (all_52_19 = all_52_27)
% 177.22/27.77    (128)  all_56_7 = all_52_15
% 177.22/27.77    (129)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.77    (130)   ~ (all_52_7 = all_52_23)
% 177.22/27.77    (131)  op(e2, all_52_27) = all_52_26
% 177.22/27.77    (132)   ~ (all_52_17 = all_52_19)
% 177.22/27.77    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.77    (134)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.77    (135)  op(e1, all_14_2) = all_14_1
% 177.22/27.77    (136)  all_58_9 = all_52_7
% 177.22/27.77    (137)  all_58_12 = all_52_25
% 177.22/27.77    (138)   ~ (all_10_0 = e1)
% 177.22/27.77    (139)  all_56_6 = all_52_13
% 177.22/27.77    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.77    (141)   ~ (all_52_9 = all_52_15)
% 177.22/27.77    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.77    (143)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.77    (144)   ~ (all_52_19 = all_14_2)
% 177.22/27.77    (145)  op(e2, e3) = all_52_9
% 177.22/27.77    (146)  all_56_13 = all_52_27
% 177.22/27.77  
% 177.22/27.77  Begin of proof
% 177.22/27.77  | 
% 177.22/27.77  | ALPHA: (129) implies:
% 177.22/27.77  |   (147)  all_52_14 = e0
% 177.22/27.77  |   (148)  all_52_12 = e1
% 177.22/27.77  |   (149)  all_52_10 = e2
% 177.22/27.77  |   (150)  all_52_8 = e3
% 177.22/27.77  | 
% 177.22/27.77  | COMBINE_EQS: (79), (149) imply:
% 177.22/27.77  |   (151)  all_10_1 = e2
% 177.22/27.77  | 
% 177.22/27.77  | REDUCE: (86), (151) imply:
% 177.22/27.77  |   (152)  op(e2, all_10_2) = all_10_0
% 177.22/27.77  | 
% 177.22/27.77  | REDUCE: (16), (150) imply:
% 177.22/27.77  |   (153)  op(e3, all_52_9) = e3
% 177.22/27.77  | 
% 177.22/27.77  | REDUCE: (6), (151) imply:
% 177.22/27.77  |   (154)  op(e2, all_10_2) = e2
% 177.22/27.77  | 
% 177.22/27.77  | REDUCE: (52), (148) imply:
% 177.22/27.77  |   (155)  op(e1, all_52_13) = e1
% 177.22/27.77  | 
% 177.22/27.77  | REDUCE: (103), (147) imply:
% 177.22/27.77  |   (156)  op(e0, all_52_15) = e0
% 177.22/27.77  | 
% 177.22/27.77  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.22/27.77  |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.22/27.77  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.22/27.77  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.22/27.77  |            (48), (49), (50), (51), (53), (54), (55), (56), (57), (58), (59),
% 177.22/27.77  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 177.22/27.77  |            (71), (72), (73), (74), (75), (76), (77), (78), (80), (81), (82),
% 177.22/27.77  |            (83), (84), (85), (87), (88), (89), (90), (91), (92), (93), (94),
% 177.22/27.77  |            (95), (96), (97), (98), (99), (100), (101), (102), (104), (105),
% 177.22/27.77  |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 177.22/27.77  |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 177.22/27.77  |            (124), (125), (126), (127), (128), (130), (131), (132), (133),
% 177.22/27.77  |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 177.22/27.77  |            (143), (144), (145), (146), (152), (153), (154), (155), (156) are
% 177.22/27.77  |            inconsistent by sub-proof #339.
% 177.22/27.77  | 
% 177.22/27.77  End of proof
% 177.22/27.77  
% 177.22/27.77  Sub-proof #339 shows that the following formulas are inconsistent:
% 177.22/27.77  ----------------------------------------------------------------
% 177.22/27.77    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.77    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.77    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.77    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.77    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.77    (6)   ~ (all_52_13 = all_52_29)
% 177.22/27.77    (7)  op(e2, all_10_2) = all_10_0
% 177.22/27.77    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.77    (9)  all_56_3 = all_52_7
% 177.22/27.77    (10)  op(e3, e2) = all_52_3
% 177.22/27.77    (11)   ~ (all_52_9 = all_52_25)
% 177.22/27.77    (12)  op(e3, all_52_25) = all_52_24
% 177.22/27.77    (13)   ~ (all_52_19 = all_52_23)
% 177.22/27.77    (14)  all_56_11 = all_52_23
% 177.22/27.77    (15)  op(e1, e2) = all_52_19
% 177.22/27.77    (16)   ~ (all_52_3 = all_10_2)
% 177.22/27.77    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.22/27.77    (18)  all_58_5 = all_52_13
% 177.22/27.77    (19)   ~ (all_6_2 = e0)
% 177.22/27.77    (20)   ~ (all_52_25 = all_52_29)
% 177.22/27.77    (21)  op(e1, all_52_13) = e1
% 177.22/27.77    (22)  op(e0, all_52_15) = e0
% 177.22/27.77    (23)  all_56_15 = all_6_2
% 177.22/27.77    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.77    (25)  op(e2, e0) = all_52_15
% 177.22/27.77    (26)  all_58_3 = all_10_2
% 177.22/27.77    (27)  all_56_9 = all_52_19
% 177.22/27.77    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.77    (29)  all_58_15 = all_6_2
% 177.22/27.77    (30)   ~ (all_52_9 = all_4_2)
% 177.22/27.77    (31)   ~ (all_52_5 = all_52_7)
% 177.22/27.77    (32)  all_58_10 = all_52_15
% 177.22/27.77    (33)   ~ (all_52_5 = all_4_2)
% 177.22/27.77    (34)  all_58_7 = all_52_19
% 177.22/27.77    (35)  all_56_4 = all_52_9
% 177.22/27.77    (36)   ~ (all_52_15 = all_6_2)
% 177.22/27.77    (37)   ~ (all_52_17 = all_52_25)
% 177.22/27.77    (38)  op(e0, e1) = all_52_29
% 177.22/27.77    (39)   ~ (all_4_0 = e2)
% 177.22/27.77    (40)  all_58_4 = all_52_5
% 177.22/27.77    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.77    (42)   ~ (e3 = e1)
% 177.22/27.77    (43)   ~ (all_52_27 = all_52_29)
% 177.22/27.77    (44)   ~ (all_52_17 = all_14_2)
% 177.22/27.77    (45)  op(e3, all_4_2) = all_4_1
% 177.22/27.77    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.77    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.77    (48)   ~ (all_52_7 = all_4_2)
% 177.22/27.77    (49)  all_58_1 = all_52_3
% 177.22/27.77    (50)   ~ (all_52_13 = all_52_15)
% 177.22/27.77    (51)  all_58_0 = all_4_2
% 177.22/27.77    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.77    (53)  op(e1, all_52_29) = all_52_28
% 177.22/27.77    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.77    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.77    (56)   ~ (all_4_1 = e2)
% 177.22/27.77    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.77    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.77    (59)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.77    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.77    (61)  all_58_14 = all_52_29
% 177.22/27.77    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.77    (63)   ~ (all_52_3 = all_52_5)
% 177.22/27.77    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.77    (65)  op(e2, e1) = all_52_13
% 177.22/27.77    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.77    (67)  all_58_8 = all_14_2
% 177.22/27.77    (68)  all_56_1 = all_52_3
% 177.22/27.77    (69)  op(e0, e2) = all_52_27
% 177.22/27.77    (70)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.22/27.77    (71)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.77    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.77    (73)   ~ (all_52_3 = all_52_27)
% 177.22/27.77    (74)   ~ (all_52_3 = all_4_2)
% 177.22/27.77    (75)  op(e0, e3) = all_52_25
% 177.22/27.77    (76)  op(e0, all_6_2) = all_6_1
% 177.22/27.77    (77)   ~ (all_52_9 = all_10_2)
% 177.22/27.77    (78)  op(e3, all_52_17) = all_52_16
% 177.22/27.77    (79)   ~ (all_52_13 = all_14_2)
% 177.22/27.77    (80)  op(e3, all_52_9) = e3
% 177.22/27.77    (81)   ~ (e3 = e0)
% 177.22/27.77    (82)   ~ (all_52_9 = all_52_13)
% 177.22/27.77    (83)  op(e0, all_52_23) = all_52_22
% 177.22/27.77    (84)   ~ (all_52_15 = all_52_23)
% 177.22/27.77    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.77    (86)   ~ (all_52_5 = all_52_29)
% 177.22/27.77    (87)  all_56_2 = all_52_5
% 177.22/27.77    (88)  op(e1, e0) = all_52_23
% 177.22/27.77    (89)  all_58_13 = all_52_27
% 177.22/27.77    (90)   ~ (all_4_1 = e1)
% 177.22/27.77    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.77    (92)   ~ (all_52_9 = all_52_17)
% 177.22/27.77    (93)  all_58_6 = all_52_17
% 177.22/27.77    (94)   ~ (all_52_3 = all_52_7)
% 177.22/27.77    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.77    (96)  op(e2, all_52_19) = all_52_18
% 177.22/27.77    (97)   ~ (e1 = e0)
% 177.22/27.77    (98)  all_56_0 = all_4_2
% 177.22/27.77    (99)  all_58_11 = all_52_23
% 177.22/27.77    (100)   ~ (all_52_3 = all_52_19)
% 177.22/27.77    (101)   ~ (all_52_7 = all_52_15)
% 177.22/27.77    (102)   ~ (all_52_29 = all_14_2)
% 177.22/27.77    (103)   ~ (all_4_0 = e1)
% 177.22/27.77    (104)   ~ (all_52_19 = all_10_2)
% 177.22/27.77    (105)   ~ (all_52_23 = all_6_2)
% 177.22/27.77    (106)   ~ (all_52_29 = all_6_2)
% 177.22/27.77    (107)  all_58_2 = all_52_9
% 177.22/27.77    (108)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.77    (109)  op(e3, e1) = all_52_5
% 177.22/27.77    (110)  all_56_10 = all_14_2
% 177.22/27.77    (111)   ~ (all_52_25 = all_6_2)
% 177.22/27.77    (112)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.77    (113)  op(e1, e1) = all_14_2
% 177.22/27.77    (114)  op(e1, e3) = all_52_17
% 177.22/27.77    (115)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.77    (116)   ~ (all_52_25 = all_4_2)
% 177.22/27.77    (117)  op(e3, e0) = all_52_7
% 177.22/27.77    (118)  op(e2, all_10_2) = e2
% 177.22/27.77    (119)  op(e3, e3) = all_4_2
% 177.22/27.77    (120)   ~ (all_52_17 = all_4_2)
% 177.22/27.77    (121)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.77             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.77    (122)   ~ (all_52_25 = all_52_27)
% 177.22/27.77    (123)   ~ (all_52_27 = all_6_2)
% 177.22/27.77    (124)   ~ (all_52_7 = all_6_2)
% 177.22/27.77    (125)   ~ (all_10_0 = e3)
% 177.22/27.77    (126)   ~ (all_52_19 = all_52_27)
% 177.22/27.77    (127)  all_56_7 = all_52_15
% 177.22/27.77    (128)   ~ (all_52_7 = all_52_23)
% 177.22/27.77    (129)  op(e2, all_52_27) = all_52_26
% 177.22/27.77    (130)   ~ (all_52_17 = all_52_19)
% 177.22/27.77    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.77    (132)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.77    (133)  op(e1, all_14_2) = all_14_1
% 177.22/27.77    (134)  all_58_9 = all_52_7
% 177.22/27.77    (135)  all_58_12 = all_52_25
% 177.22/27.77    (136)   ~ (all_10_0 = e1)
% 177.22/27.77    (137)  all_56_6 = all_52_13
% 177.22/27.77    (138)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.77    (139)   ~ (all_52_9 = all_52_15)
% 177.22/27.77    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.77    (141)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.77    (142)   ~ (all_52_19 = all_14_2)
% 177.22/27.77    (143)  op(e2, e3) = all_52_9
% 177.22/27.77    (144)  all_56_13 = all_52_27
% 177.22/27.77  
% 177.22/27.77  Begin of proof
% 177.22/27.77  | 
% 177.22/27.77  | GROUND_INST: instantiating (121) with e2, all_10_0, all_10_2, e2, simplifying
% 177.22/27.77  |              with (7), (118) gives:
% 177.22/27.77  |   (145)  all_10_0 = e2
% 177.22/27.77  | 
% 177.22/27.77  | REDUCE: (125), (145) imply:
% 177.22/27.77  |   (146)   ~ (e3 = e2)
% 177.22/27.77  | 
% 177.22/27.77  | SIMP: (146) implies:
% 177.22/27.77  |   (147)   ~ (e3 = e2)
% 177.22/27.77  | 
% 177.22/27.77  | REDUCE: (136), (145) imply:
% 177.22/27.77  |   (148)   ~ (e2 = e1)
% 177.22/27.77  | 
% 177.22/27.77  | BETA: splitting (46) gives:
% 177.22/27.77  | 
% 177.22/27.77  | Case 1:
% 177.22/27.77  | | 
% 177.22/27.77  | |   (149)  all_56_15 = e3
% 177.22/27.77  | | 
% 177.22/27.77  | | COMBINE_EQS: (23), (149) imply:
% 177.22/27.77  | |   (150)  all_6_2 = e3
% 177.22/27.77  | | 
% 177.22/27.77  | | REF_CLOSE: (10), (11), (16), (18), (21), (24), (26), (30), (32), (34), (35),
% 177.22/27.77  | |            (36), (39), (41), (42), (45), (47), (48), (49), (51), (58), (59),
% 177.22/27.77  | |            (64), (67), (71), (75), (76), (79), (80), (89), (92), (93), (95),
% 177.22/27.77  | |            (96), (99), (100), (105), (107), (111), (112), (114), (117),
% 177.22/27.77  | |            (118), (119), (120), (121), (123), (130), (135), (137), (143),
% 177.22/27.77  | |            (148), (150) are inconsistent by sub-proof #773.
% 177.22/27.77  | | 
% 177.22/27.77  | Case 2:
% 177.22/27.77  | | 
% 177.22/27.77  | |   (151)   ~ (all_56_15 = e3)
% 177.22/27.77  | |   (152)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.77  | | 
% 177.22/27.77  | | REDUCE: (23), (151) imply:
% 177.22/27.77  | |   (153)   ~ (all_6_2 = e3)
% 177.22/27.77  | | 
% 177.22/27.77  | | BETA: splitting (62) gives:
% 177.22/27.77  | | 
% 177.22/27.77  | | Case 1:
% 177.22/27.77  | | | 
% 177.22/27.77  | | |   (154)  all_56_13 = e3
% 177.22/27.77  | | | 
% 177.22/27.77  | | | REF_CLOSE: (1), (2), (3), (4), (6), (10), (11), (12), (13), (14), (16),
% 177.22/27.77  | | |            (17), (18), (21), (22), (26), (28), (29), (30), (31), (32),
% 177.22/27.77  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 177.22/27.77  | | |            (43), (44), (45), (47), (48), (49), (50), (51), (52), (54),
% 177.22/27.77  | | |            (57), (60), (61), (63), (64), (65), (67), (68), (71), (73),
% 177.22/27.77  | | |            (74), (75), (77), (78), (79), (80), (82), (83), (84), (88),
% 177.22/27.77  | | |            (89), (90), (91), (92), (93), (94), (95), (97), (98), (99),
% 177.22/27.77  | | |            (101), (103), (105), (107), (108), (109), (114), (116), (117),
% 177.22/27.77  | | |            (118), (119), (121), (122), (123), (126), (128), (129), (130),
% 177.22/27.77  | | |            (131), (134), (135), (139), (140), (143), (144), (154) are
% 177.22/27.77  | | |            inconsistent by sub-proof #755.
% 177.22/27.77  | | | 
% 177.22/27.77  | | Case 2:
% 177.22/27.77  | | | 
% 177.22/27.77  | | |   (155)   ~ (all_56_13 = e3)
% 177.22/27.77  | | |   (156)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.77  | | | 
% 177.22/27.77  | | | REDUCE: (144), (155) imply:
% 177.22/27.77  | | |   (157)   ~ (all_52_27 = e3)
% 177.22/27.77  | | | 
% 177.22/27.77  | | | BETA: splitting (66) gives:
% 177.22/27.77  | | | 
% 177.22/27.77  | | | Case 1:
% 177.22/27.77  | | | | 
% 177.22/27.77  | | | |   (158)  all_58_12 = e3
% 177.22/27.77  | | | | 
% 177.22/27.77  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13),
% 177.22/27.77  | | | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 177.22/27.77  | | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.22/27.77  | | | |            (37), (39), (40), (41), (43), (44), (45), (47), (48), (49),
% 177.22/27.77  | | | |            (51), (52), (54), (55), (57), (58), (59), (61), (63), (65),
% 177.22/27.77  | | | |            (67), (68), (69), (71), (72), (73), (74), (75), (78), (79),
% 177.22/27.77  | | | |            (80), (81), (82), (83), (85), (86), (87), (89), (90), (92),
% 177.22/27.77  | | | |            (93), (94), (95), (96), (98), (99), (100), (101), (102),
% 177.22/27.77  | | | |            (103), (104), (105), (107), (108), (109), (110), (111),
% 177.22/27.77  | | | |            (114), (115), (116), (117), (118), (121), (122), (123),
% 177.22/27.77  | | | |            (124), (127), (128), (130), (131), (132), (133), (134),
% 177.22/27.77  | | | |            (135), (137), (138), (139), (140), (141), (142), (143),
% 177.22/27.77  | | | |            (144), (147), (148), (152), (156), (158) are inconsistent by
% 177.22/27.77  | | | |            sub-proof #380.
% 177.22/27.77  | | | | 
% 177.22/27.77  | | | Case 2:
% 177.22/27.77  | | | | 
% 177.22/27.77  | | | |   (159)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.77  | | | | 
% 177.22/27.77  | | | | REF_CLOSE: (2), (5), (6), (10), (11), (12), (13), (14), (16), (17),
% 177.22/27.77  | | | |            (18), (21), (22), (24), (25), (26), (29), (30), (32), (33),
% 177.22/27.77  | | | |            (34), (35), (39), (40), (41), (42), (43), (45), (47), (48),
% 177.22/27.77  | | | |            (49), (51), (52), (53), (56), (58), (59), (61), (63), (64),
% 177.22/27.77  | | | |            (67), (70), (71), (74), (75), (79), (80), (82), (84), (86),
% 177.22/27.77  | | | |            (87), (88), (89), (91), (93), (94), (95), (96), (97), (99),
% 177.22/27.77  | | | |            (100), (101), (102), (106), (107), (108), (109), (113),
% 177.22/27.77  | | | |            (114), (116), (117), (118), (119), (120), (121), (122),
% 177.22/27.77  | | | |            (126), (130), (131), (134), (135), (137), (138), (139),
% 177.22/27.77  | | | |            (141), (143), (148), (153), (157), (159) are inconsistent by
% 177.22/27.77  | | | |            sub-proof #340.
% 177.22/27.77  | | | | 
% 177.22/27.77  | | | End of split
% 177.22/27.77  | | | 
% 177.22/27.77  | | End of split
% 177.22/27.77  | | 
% 177.22/27.77  | End of split
% 177.22/27.77  | 
% 177.22/27.77  End of proof
% 177.22/27.77  
% 177.22/27.77  Sub-proof #340 shows that the following formulas are inconsistent:
% 177.22/27.77  ----------------------------------------------------------------
% 177.22/27.77    (1)   ~ (all_52_5 = all_52_13)
% 177.22/27.77    (2)   ~ (all_52_17 = all_52_23)
% 177.22/27.77    (3)   ~ (all_52_13 = all_52_29)
% 177.22/27.77    (4)  op(e3, e2) = all_52_3
% 177.22/27.77    (5)   ~ (all_52_9 = all_52_25)
% 177.22/27.77    (6)  op(e3, all_52_25) = all_52_24
% 177.22/27.77    (7)   ~ (all_52_19 = all_52_23)
% 177.22/27.77    (8)  all_56_11 = all_52_23
% 177.22/27.77    (9)   ~ (all_52_27 = e3)
% 177.22/27.77    (10)   ~ (all_6_2 = e3)
% 177.22/27.77    (11)   ~ (all_52_3 = all_10_2)
% 177.22/27.77    (12)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.22/27.77    (13)  all_58_5 = all_52_13
% 177.22/27.77    (14)  op(e1, all_52_13) = e1
% 177.22/27.77    (15)  op(e0, all_52_15) = e0
% 177.22/27.77    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.77    (17)  op(e2, e0) = all_52_15
% 177.22/27.77    (18)  all_58_3 = all_10_2
% 177.22/27.77    (19)  all_58_15 = all_6_2
% 177.22/27.77    (20)   ~ (all_52_9 = all_4_2)
% 177.22/27.77    (21)  all_58_10 = all_52_15
% 177.22/27.77    (22)   ~ (all_52_5 = all_4_2)
% 177.22/27.77    (23)  all_58_7 = all_52_19
% 177.22/27.77    (24)  all_56_4 = all_52_9
% 177.22/27.77    (25)   ~ (all_4_0 = e2)
% 177.22/27.77    (26)  all_58_4 = all_52_5
% 177.22/27.77    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.77    (28)   ~ (e3 = e1)
% 177.22/27.77    (29)   ~ (all_52_27 = all_52_29)
% 177.22/27.77    (30)  op(e3, all_4_2) = all_4_1
% 177.22/27.77    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.77    (32)   ~ (all_52_7 = all_4_2)
% 177.22/27.77    (33)  all_58_1 = all_52_3
% 177.22/27.77    (34)  all_58_0 = all_4_2
% 177.22/27.77    (35)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.77    (36)  op(e1, all_52_29) = all_52_28
% 177.22/27.77    (37)   ~ (all_4_1 = e2)
% 177.22/27.77    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.77    (39)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.77    (40)  all_58_14 = all_52_29
% 177.22/27.77    (41)   ~ (all_52_3 = all_52_5)
% 177.22/27.77    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.77    (43)  all_58_8 = all_14_2
% 177.22/27.77    (44)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.22/27.77    (45)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.77    (46)   ~ (all_52_3 = all_4_2)
% 177.22/27.77    (47)  op(e0, e3) = all_52_25
% 177.22/27.77    (48)   ~ (all_52_13 = all_14_2)
% 177.22/27.77    (49)  op(e3, all_52_9) = e3
% 177.22/27.77    (50)   ~ (all_52_9 = all_52_13)
% 177.22/27.77    (51)   ~ (all_52_15 = all_52_23)
% 177.22/27.77    (52)   ~ (all_52_5 = all_52_29)
% 177.22/27.77    (53)  all_56_2 = all_52_5
% 177.22/27.77    (54)  op(e1, e0) = all_52_23
% 177.22/27.77    (55)  all_58_13 = all_52_27
% 177.22/27.77    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.77    (57)  all_58_6 = all_52_17
% 177.22/27.77    (58)   ~ (all_52_3 = all_52_7)
% 177.22/27.77    (59)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.77    (60)  op(e2, all_52_19) = all_52_18
% 177.22/27.77    (61)   ~ (e1 = e0)
% 177.22/27.77    (62)  all_58_11 = all_52_23
% 177.22/27.77    (63)   ~ (all_52_3 = all_52_19)
% 177.22/27.77    (64)   ~ (all_52_7 = all_52_15)
% 177.22/27.77    (65)   ~ (all_52_29 = all_14_2)
% 177.22/27.77    (66)   ~ (all_52_29 = all_6_2)
% 177.22/27.77    (67)  all_58_2 = all_52_9
% 177.22/27.77    (68)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.77    (69)  op(e3, e1) = all_52_5
% 177.22/27.77    (70)   ~ (e2 = e1)
% 177.22/27.77    (71)  op(e1, e1) = all_14_2
% 177.22/27.77    (72)  op(e1, e3) = all_52_17
% 177.22/27.77    (73)   ~ (all_52_25 = all_4_2)
% 177.22/27.77    (74)  op(e3, e0) = all_52_7
% 177.22/27.77    (75)  op(e2, all_10_2) = e2
% 177.22/27.77    (76)  op(e3, e3) = all_4_2
% 177.22/27.77    (77)   ~ (all_52_17 = all_4_2)
% 177.22/27.77    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.77    (79)   ~ (all_52_25 = all_52_27)
% 177.22/27.77    (80)   ~ (all_52_19 = all_52_27)
% 177.22/27.77    (81)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.77    (82)   ~ (all_52_17 = all_52_19)
% 177.22/27.77    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.77    (84)  all_58_9 = all_52_7
% 177.22/27.77    (85)  all_58_12 = all_52_25
% 177.22/27.77    (86)  all_56_6 = all_52_13
% 177.22/27.77    (87)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.77    (88)   ~ (all_52_9 = all_52_15)
% 177.22/27.77    (89)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.77    (90)  op(e2, e3) = all_52_9
% 177.22/27.77  
% 177.22/27.77  Begin of proof
% 177.22/27.77  | 
% 177.22/27.77  | BETA: splitting (81) gives:
% 177.22/27.77  | 
% 177.22/27.77  | Case 1:
% 177.22/27.77  | | 
% 177.22/27.77  | |   (91)  all_58_13 = e3
% 177.22/27.77  | | 
% 177.22/27.77  | | REF_CLOSE: (9), (55), (91) are inconsistent by sub-proof #1026.
% 177.22/27.77  | | 
% 177.22/27.77  | Case 2:
% 177.22/27.77  | | 
% 177.22/27.77  | |   (92)  all_58_14 = e3 | all_58_15 = e3
% 177.22/27.77  | | 
% 177.22/27.77  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 177.22/27.77  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.22/27.77  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.22/27.77  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.22/27.77  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.22/27.77  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.22/27.77  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.22/27.77  | |            (80), (82), (83), (84), (85), (86), (87), (88), (89), (90), (92)
% 177.22/27.77  | |            are inconsistent by sub-proof #718.
% 177.22/27.77  | | 
% 177.22/27.77  | End of split
% 177.22/27.77  | 
% 177.22/27.77  End of proof
% 177.22/27.77  
% 177.22/27.77  Sub-proof #341 shows that the following formulas are inconsistent:
% 177.22/27.77  ----------------------------------------------------------------
% 177.22/27.77    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.77    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.77    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.22/27.77    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.77    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.77    (6)   ~ (all_52_27 = all_10_2)
% 177.22/27.77    (7)  op(e2, e2) = all_10_2
% 177.22/27.77    (8)   ~ (all_52_17 = all_52_23)
% 177.22/27.77    (9)  op(e2, all_52_3) = e2
% 177.22/27.77    (10)  op(e2, all_10_2) = all_10_1
% 177.22/27.77    (11)   ~ (all_52_13 = all_52_29)
% 177.22/27.77    (12)  all_56_3 = all_52_7
% 177.22/27.77    (13)  op(e3, e2) = all_52_3
% 177.22/27.77    (14)   ~ (all_52_9 = all_52_25)
% 177.22/27.77    (15)   ~ (all_52_19 = all_52_23)
% 177.22/27.77    (16)  all_56_11 = all_52_23
% 177.22/27.77    (17)  op(e1, e2) = all_52_19
% 177.22/27.77    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.77    (19)   ~ (all_52_3 = all_10_2)
% 177.22/27.77    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.77    (21)  all_58_5 = all_52_13
% 177.22/27.77    (22)   ~ (all_6_2 = e0)
% 177.22/27.77    (23)   ~ (all_52_25 = all_52_29)
% 177.22/27.77    (24)  all_56_15 = all_6_2
% 177.22/27.78    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.78    (26)  op(e2, e0) = all_52_15
% 177.22/27.78    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.78    (28)  all_58_3 = all_10_2
% 177.22/27.78    (29)  all_56_9 = all_52_19
% 177.22/27.78    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.78    (31)  all_58_15 = all_6_2
% 177.22/27.78    (32)   ~ (all_52_9 = all_4_2)
% 177.22/27.78    (33)   ~ (all_52_5 = all_52_7)
% 177.22/27.78    (34)  all_58_10 = all_52_15
% 177.22/27.78    (35)   ~ (all_52_5 = all_4_2)
% 177.22/27.78    (36)  all_58_7 = all_52_19
% 177.22/27.78    (37)  all_56_4 = all_52_9
% 177.22/27.78    (38)   ~ (all_52_15 = all_6_2)
% 177.22/27.78    (39)   ~ (all_52_17 = all_52_25)
% 177.22/27.78    (40)  op(e0, e1) = all_52_29
% 177.22/27.78    (41)   ~ (all_4_0 = e2)
% 177.22/27.78    (42)  all_58_4 = all_52_5
% 177.22/27.78    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.78    (44)   ~ (all_52_27 = all_52_29)
% 177.22/27.78    (45)   ~ (all_52_17 = all_14_2)
% 177.22/27.78    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.78    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.78    (48)   ~ (all_52_7 = all_4_2)
% 177.22/27.78    (49)  all_58_1 = all_52_3
% 177.22/27.78    (50)   ~ (all_52_13 = all_52_15)
% 177.22/27.78    (51)  all_58_0 = all_4_2
% 177.22/27.78    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.78    (53)  op(e0, e0) = all_6_2
% 177.22/27.78    (54)  op(e1, all_52_29) = all_52_28
% 177.22/27.78    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.78    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.78    (57)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.78    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.78    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.78    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.78    (61)  all_58_14 = all_52_29
% 177.22/27.78    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.78    (63)   ~ (all_52_3 = all_52_5)
% 177.22/27.78    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.78    (65)  op(e2, e1) = all_52_13
% 177.22/27.78    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.78    (67)  all_58_8 = all_14_2
% 177.22/27.78    (68)  all_56_1 = all_52_3
% 177.22/27.78    (69)  op(e0, e2) = all_52_27
% 177.22/27.78    (70)  all_56_14 = all_52_29
% 177.22/27.78    (71)  op(all_14_1, all_14_2) = e3
% 177.22/27.78    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.78    (73)   ~ (all_52_5 = all_14_2)
% 177.22/27.78    (74)   ~ (all_52_3 = all_52_27)
% 177.22/27.78    (75)   ~ (all_52_3 = all_4_2)
% 177.22/27.78    (76)  op(all_6_1, all_6_2) = all_6_0
% 177.22/27.78    (77)  op(e3, all_4_2) = e3
% 177.22/27.78    (78)  op(e0, e3) = all_52_25
% 177.22/27.78    (79)  op(e0, all_6_2) = all_6_1
% 177.22/27.78    (80)   ~ (all_52_9 = all_10_2)
% 177.22/27.78    (81)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.78    (82)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.22/27.78    (83)   ~ (all_52_13 = all_14_2)
% 177.22/27.78    (84)   ~ (e3 = e0)
% 177.22/27.78    (85)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.78    (86)   ~ (all_52_9 = all_52_13)
% 177.22/27.78    (87)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.78    (88)  op(e0, all_52_23) = all_52_22
% 177.22/27.78    (89)   ~ (all_52_15 = all_52_23)
% 177.22/27.78    (90)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.78    (91)   ~ (all_52_5 = all_52_29)
% 177.22/27.78    (92)  all_56_2 = all_52_5
% 177.22/27.78    (93)  op(e1, e0) = all_52_23
% 177.22/27.78    (94)  all_56_12 = all_52_25
% 177.22/27.78    (95)  all_58_13 = all_52_27
% 177.22/27.78    (96)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.78    (97)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.78    (98)   ~ (all_52_9 = all_52_17)
% 177.22/27.78    (99)  all_58_6 = all_52_17
% 177.22/27.78    (100)   ~ (all_52_3 = all_52_7)
% 177.22/27.78    (101)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.78    (102)   ~ (e1 = e0)
% 177.22/27.78    (103)  all_56_0 = all_4_2
% 177.22/27.78    (104)  all_58_11 = all_52_23
% 177.22/27.78    (105)   ~ (all_52_3 = all_52_19)
% 177.22/27.78    (106)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.78    (107)   ~ (all_52_7 = all_52_15)
% 177.22/27.78    (108)  op(e0, all_52_15) = all_52_14
% 177.22/27.78    (109)   ~ (all_52_29 = all_14_2)
% 177.22/27.78    (110)   ~ (all_4_0 = e1)
% 177.22/27.78    (111)   ~ (all_52_19 = all_10_2)
% 177.22/27.78    (112)   ~ (all_52_23 = all_6_2)
% 177.22/27.78    (113)   ~ (all_52_29 = all_6_2)
% 177.22/27.78    (114)  all_58_2 = all_52_9
% 177.22/27.78    (115)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.22/27.78    (116)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.78    (117)  op(e3, e1) = all_52_5
% 177.22/27.78    (118)   ~ (e2 = e1)
% 177.22/27.78    (119)  all_56_10 = all_14_2
% 177.22/27.78    (120)   ~ (all_52_25 = all_6_2)
% 177.22/27.78    (121)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.78    (122)  op(e1, e1) = all_14_2
% 177.22/27.78    (123)  op(e1, e3) = all_52_17
% 177.22/27.78    (124)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.78    (125)   ~ (all_52_25 = all_4_2)
% 177.22/27.78    (126)  op(e3, e0) = all_52_7
% 177.22/27.78    (127)  all_56_8 = all_52_17
% 177.22/27.78    (128)   ~ (all_52_17 = all_4_2)
% 177.22/27.78    (129)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.78             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.78    (130)   ~ (all_52_25 = all_52_27)
% 177.22/27.78    (131)   ~ (all_52_27 = all_6_2)
% 177.22/27.78    (132)   ~ (all_52_7 = all_6_2)
% 177.22/27.78    (133)   ~ (all_52_19 = all_52_27)
% 177.22/27.78    (134)  all_56_7 = all_52_15
% 177.22/27.78    (135)  op(e1, all_52_5) = e1
% 177.22/27.78    (136)   ~ (all_52_7 = all_52_23)
% 177.22/27.78    (137)   ~ (all_52_13 = all_10_2)
% 177.22/27.78    (138)   ~ (all_6_0 = e1)
% 177.22/27.78    (139)  op(e3, all_4_2) = all_4_0
% 177.22/27.78    (140)  op(e0, all_52_7) = e0
% 177.22/27.78    (141)  op(e2, all_52_27) = all_52_26
% 177.22/27.78    (142)   ~ (all_52_17 = all_52_19)
% 177.22/27.78    (143)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.78    (144)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.78    (145)  op(e1, all_14_2) = all_14_1
% 177.22/27.78    (146)  all_58_9 = all_52_7
% 177.22/27.78    (147)  all_58_12 = all_52_25
% 177.22/27.78    (148)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.78    (149)   ~ (all_52_9 = all_52_15)
% 177.22/27.78    (150)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.78    (151)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.78    (152)   ~ (all_52_19 = all_14_2)
% 177.22/27.78    (153)  op(e2, e3) = all_52_9
% 177.22/27.78    (154)  all_56_13 = all_52_27
% 177.22/27.78  
% 177.22/27.78  Begin of proof
% 177.22/27.78  | 
% 177.22/27.78  | GROUND_INST: instantiating (129) with e3, all_4_0, all_4_2, e3, simplifying
% 177.22/27.78  |              with (77), (139) gives:
% 177.22/27.78  |   (155)  all_4_0 = e3
% 177.22/27.78  | 
% 177.22/27.78  | REDUCE: (41), (155) imply:
% 177.22/27.78  |   (156)   ~ (e3 = e2)
% 177.22/27.78  | 
% 177.22/27.78  | REDUCE: (110), (155) imply:
% 177.22/27.78  |   (157)   ~ (e3 = e1)
% 177.22/27.78  | 
% 177.22/27.78  | BETA: splitting (46) gives:
% 177.22/27.78  | 
% 177.22/27.78  | Case 1:
% 177.22/27.78  | | 
% 177.22/27.78  | |   (158)  all_56_15 = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | COMBINE_EQS: (24), (158) imply:
% 177.22/27.78  | |   (159)  all_6_2 = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | SIMP: (159) implies:
% 177.22/27.78  | |   (160)  all_6_2 = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | COMBINE_EQS: (31), (160) imply:
% 177.22/27.78  | |   (161)  all_58_15 = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (132), (160) imply:
% 177.22/27.78  | |   (162)   ~ (all_52_7 = e3)
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (112), (160) imply:
% 177.22/27.78  | |   (163)   ~ (all_52_23 = e3)
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (131), (160) imply:
% 177.22/27.78  | |   (164)   ~ (all_52_27 = e3)
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (113), (160) imply:
% 177.22/27.78  | |   (165)   ~ (all_52_29 = e3)
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (76), (160) imply:
% 177.22/27.78  | |   (166)  op(all_6_1, e3) = all_6_0
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (79), (160) imply:
% 177.22/27.78  | |   (167)  op(e0, e3) = all_6_1
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (53), (160) imply:
% 177.22/27.78  | |   (168)  op(e0, e0) = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | GROUND_INST: instantiating (129) with all_52_25, all_6_1, e3, e0,
% 177.22/27.78  | |              simplifying with (78), (167) gives:
% 177.22/27.78  | |   (169)  all_52_25 = all_6_1
% 177.22/27.78  | | 
% 177.22/27.78  | | COMBINE_EQS: (147), (169) imply:
% 177.22/27.78  | |   (170)  all_58_12 = all_6_1
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (39), (169) imply:
% 177.22/27.78  | |   (171)   ~ (all_52_17 = all_6_1)
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (130), (169) imply:
% 177.22/27.78  | |   (172)   ~ (all_52_27 = all_6_1)
% 177.22/27.78  | | 
% 177.22/27.78  | | SIMP: (172) implies:
% 177.22/27.78  | |   (173)   ~ (all_52_27 = all_6_1)
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (23), (169) imply:
% 177.22/27.78  | |   (174)   ~ (all_52_29 = all_6_1)
% 177.22/27.78  | | 
% 177.22/27.78  | | SIMP: (174) implies:
% 177.22/27.78  | |   (175)   ~ (all_52_29 = all_6_1)
% 177.22/27.78  | | 
% 177.22/27.78  | | BETA: splitting (62) gives:
% 177.22/27.78  | | 
% 177.22/27.78  | | Case 1:
% 177.22/27.78  | | | 
% 177.22/27.78  | | |   (176)  all_56_13 = e3
% 177.22/27.78  | | | 
% 177.22/27.78  | | | REF_CLOSE: (154), (164), (176) are inconsistent by sub-proof #876.
% 177.22/27.78  | | | 
% 177.22/27.78  | | Case 2:
% 177.22/27.78  | | | 
% 177.22/27.78  | | |   (177)   ~ (all_56_13 = e3)
% 177.22/27.78  | | |   (178)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.78  | | | 
% 177.22/27.78  | | | BETA: splitting (144) gives:
% 177.22/27.78  | | | 
% 177.22/27.78  | | | Case 1:
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | |   (179)  all_56_3 = e3
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | REF_CLOSE: (12), (162), (179) are inconsistent by sub-proof #1034.
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | Case 2:
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | |   (180)   ~ (all_56_3 = e3)
% 177.22/27.78  | | | |   (181)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | BETA: splitting (57) gives:
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | Case 1:
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | |   (182)  all_56_14 = e3
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | | REF_CLOSE: (70), (165), (182) are inconsistent by sub-proof #896.
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | Case 2:
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | |   (183)   ~ (all_56_14 = e3)
% 177.22/27.78  | | | | |   (184)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | | BETA: splitting (56) gives:
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | | Case 1:
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | |   (185)  all_56_9 = e3
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | REF_CLOSE: (1), (2), (9), (12), (13), (17), (21), (27), (29), (30),
% 177.22/27.78  | | | | | |            (31), (32), (33), (34), (35), (36), (40), (42), (43),
% 177.22/27.78  | | | | | |            (45), (48), (49), (51), (55), (61), (63), (65), (67),
% 177.22/27.78  | | | | | |            (68), (69), (73), (74), (77), (78), (81), (83), (85),
% 177.22/27.78  | | | | | |            (90), (91), (92), (96), (99), (100), (103), (104), (105),
% 177.22/27.78  | | | | | |            (107), (109), (117), (119), (122), (123), (125), (126),
% 177.22/27.78  | | | | | |            (128), (129), (132), (135), (136), (140), (143), (146),
% 177.22/27.78  | | | | | |            (148), (150), (151), (152), (153), (162), (165), (168),
% 177.22/27.78  | | | | | |            (181), (185) are inconsistent by sub-proof #521.
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | Case 2:
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | |   (186)   ~ (all_56_9 = e3)
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | REDUCE: (29), (186) imply:
% 177.22/27.78  | | | | | |   (187)   ~ (all_52_19 = e3)
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 177.22/27.78  | | | | | |            (13), (15), (17), (18), (20), (21), (25), (26), (27),
% 177.22/27.78  | | | | | |            (28), (30), (31), (32), (33), (34), (35), (36), (40),
% 177.22/27.78  | | | | | |            (42), (43), (44), (45), (48), (49), (51), (55), (59),
% 177.22/27.78  | | | | | |            (60), (61), (63), (65), (67), (68), (69), (70), (71),
% 177.22/27.78  | | | | | |            (72), (73), (74), (75), (77), (78), (80), (83), (84),
% 177.22/27.78  | | | | | |            (85), (86), (90), (91), (93), (95), (96), (97), (99),
% 177.22/27.78  | | | | | |            (100), (103), (104), (105), (106), (107), (109), (111),
% 177.22/27.78  | | | | | |            (114), (115), (117), (118), (119), (121), (123), (125),
% 177.22/27.78  | | | | | |            (126), (127), (128), (129), (132), (133), (135), (136),
% 177.22/27.78  | | | | | |            (138), (140), (142), (143), (145), (146), (148), (149),
% 177.22/27.78  | | | | | |            (150), (153), (154), (156), (157), (161), (163), (164),
% 177.22/27.78  | | | | | |            (165), (166), (170), (171), (173), (175), (178), (181),
% 177.22/27.78  | | | | | |            (184), (187) are inconsistent by sub-proof #342.
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | End of split
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | End of split
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | End of split
% 177.22/27.78  | | | 
% 177.22/27.78  | | End of split
% 177.22/27.78  | | 
% 177.22/27.78  | Case 2:
% 177.22/27.78  | | 
% 177.22/27.78  | |   (188)   ~ (all_56_15 = e3)
% 177.22/27.78  | |   (189)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.78  | | 
% 177.22/27.78  | | REF_CLOSE: (1), (2), (8), (9), (11), (13), (14), (15), (16), (17), (18),
% 177.22/27.78  | |            (19), (21), (22), (23), (24), (25), (26), (27), (28), (30), (31),
% 177.22/27.78  | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (42), (43),
% 177.22/27.78  | |            (44), (47), (48), (49), (50), (51), (52), (54), (55), (57), (58),
% 177.22/27.78  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (70),
% 177.22/27.78  | |            (73), (74), (75), (77), (78), (82), (83), (84), (85), (86), (87),
% 177.22/27.78  | |            (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 177.22/27.78  | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 177.22/27.78  | |            (108), (109), (112), (113), (114), (116), (117), (119), (120),
% 177.22/27.78  | |            (122), (123), (124), (125), (126), (128), (129), (130), (131),
% 177.22/27.78  | |            (132), (133), (134), (135), (136), (137), (140), (141), (142),
% 177.22/27.78  | |            (143), (146), (147), (148), (149), (150), (151), (152), (153),
% 177.22/27.78  | |            (154), (156), (157), (188), (189) are inconsistent by sub-proof
% 177.22/27.78  | |            #785.
% 177.22/27.78  | | 
% 177.22/27.78  | End of split
% 177.22/27.78  | 
% 177.22/27.78  End of proof
% 177.22/27.78  
% 177.22/27.78  Sub-proof #342 shows that the following formulas are inconsistent:
% 177.22/27.78  ----------------------------------------------------------------
% 177.22/27.78    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.78    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.78    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.22/27.78    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.78    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.78    (6)   ~ (all_52_27 = all_10_2)
% 177.22/27.78    (7)  op(e2, e2) = all_10_2
% 177.22/27.78    (8)   ~ (all_52_17 = all_52_23)
% 177.22/27.78    (9)  op(e2, all_52_3) = e2
% 177.22/27.78    (10)  all_58_15 = e3
% 177.22/27.78    (11)  op(e2, all_10_2) = all_10_1
% 177.22/27.78    (12)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.78    (13)  all_56_3 = all_52_7
% 177.22/27.78    (14)  op(e3, e2) = all_52_3
% 177.22/27.78    (15)   ~ (all_52_19 = all_52_23)
% 177.22/27.78    (16)  op(e1, e2) = all_52_19
% 177.22/27.78    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.78    (18)   ~ (all_52_27 = e3)
% 177.22/27.78    (19)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.78    (20)  all_58_12 = all_6_1
% 177.22/27.78    (21)  op(all_6_1, e3) = all_6_0
% 177.22/27.78    (22)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.78    (23)  all_58_5 = all_52_13
% 177.22/27.78    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.78    (25)  op(e2, e0) = all_52_15
% 177.22/27.78    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.78    (27)  all_58_3 = all_10_2
% 177.22/27.78    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.78    (29)  all_58_15 = all_6_2
% 177.22/27.78    (30)   ~ (all_52_9 = all_4_2)
% 177.22/27.78    (31)   ~ (all_52_5 = all_52_7)
% 177.22/27.78    (32)  all_58_10 = all_52_15
% 177.22/27.78    (33)   ~ (all_52_5 = all_4_2)
% 177.22/27.78    (34)  all_58_7 = all_52_19
% 177.22/27.78    (35)  op(e0, e1) = all_52_29
% 177.22/27.78    (36)  all_58_4 = all_52_5
% 177.22/27.78    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.78    (38)   ~ (e3 = e1)
% 177.22/27.78    (39)   ~ (all_52_27 = all_52_29)
% 177.22/27.78    (40)   ~ (all_52_17 = all_14_2)
% 177.22/27.78    (41)   ~ (all_52_7 = all_4_2)
% 177.22/27.78    (42)  all_58_1 = all_52_3
% 177.22/27.78    (43)  all_58_0 = all_4_2
% 177.22/27.78    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.78    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.78    (46)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.78    (47)  all_58_14 = all_52_29
% 177.22/27.78    (48)   ~ (all_52_3 = all_52_5)
% 177.22/27.78    (49)  op(e2, e1) = all_52_13
% 177.22/27.78    (50)   ~ (all_52_17 = all_6_1)
% 177.22/27.78    (51)  all_58_8 = all_14_2
% 177.22/27.78    (52)  all_56_1 = all_52_3
% 177.22/27.78    (53)  op(e0, e2) = all_52_27
% 177.22/27.78    (54)  all_56_14 = all_52_29
% 177.22/27.78    (55)  op(all_14_1, all_14_2) = e3
% 177.22/27.78    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.78    (57)   ~ (all_52_5 = all_14_2)
% 177.22/27.78    (58)   ~ (all_52_23 = e3)
% 177.22/27.78    (59)   ~ (all_52_3 = all_52_27)
% 177.22/27.78    (60)   ~ (all_52_3 = all_4_2)
% 177.22/27.78    (61)  op(e3, all_4_2) = e3
% 177.22/27.78    (62)  op(e0, e3) = all_52_25
% 177.22/27.78    (63)   ~ (all_52_9 = all_10_2)
% 177.22/27.78    (64)   ~ (all_52_29 = e3)
% 177.22/27.78    (65)   ~ (all_52_13 = all_14_2)
% 177.22/27.78    (66)   ~ (e3 = e0)
% 177.22/27.78    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.78    (68)   ~ (all_52_9 = all_52_13)
% 177.22/27.78    (69)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.78    (70)   ~ (all_52_5 = all_52_29)
% 177.22/27.78    (71)  op(e1, e0) = all_52_23
% 177.22/27.78    (72)  all_58_13 = all_52_27
% 177.22/27.78    (73)   ~ (all_52_27 = all_6_1)
% 177.22/27.78    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.78    (75)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.78    (76)  all_58_6 = all_52_17
% 177.22/27.78    (77)   ~ (all_52_3 = all_52_7)
% 177.22/27.78    (78)  all_56_0 = all_4_2
% 177.22/27.78    (79)  all_58_11 = all_52_23
% 177.22/27.78    (80)   ~ (all_52_3 = all_52_19)
% 177.22/27.78    (81)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.78    (82)   ~ (all_52_7 = all_52_15)
% 177.22/27.78    (83)   ~ (all_52_29 = all_14_2)
% 177.22/27.78    (84)   ~ (all_52_19 = all_10_2)
% 177.22/27.78    (85)  all_58_2 = all_52_9
% 177.22/27.78    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.22/27.78    (87)  op(e3, e1) = all_52_5
% 177.22/27.78    (88)   ~ (e2 = e1)
% 177.22/27.78    (89)  all_56_10 = all_14_2
% 177.22/27.78    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.78    (91)   ~ (all_52_19 = e3)
% 177.22/27.78    (92)  op(e1, e3) = all_52_17
% 177.22/27.78    (93)   ~ (all_52_25 = all_4_2)
% 177.22/27.78    (94)  op(e3, e0) = all_52_7
% 177.22/27.78    (95)  all_56_8 = all_52_17
% 177.22/27.78    (96)   ~ (all_52_17 = all_4_2)
% 177.22/27.78    (97)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.78    (98)   ~ (all_52_7 = all_6_2)
% 177.22/27.78    (99)   ~ (all_52_19 = all_52_27)
% 177.22/27.78    (100)  op(e1, all_52_5) = e1
% 177.22/27.78    (101)   ~ (all_52_7 = all_52_23)
% 177.22/27.78    (102)   ~ (all_6_0 = e1)
% 177.22/27.78    (103)  op(e0, all_52_7) = e0
% 177.22/27.78    (104)   ~ (all_52_29 = all_6_1)
% 177.22/27.78    (105)   ~ (all_52_17 = all_52_19)
% 177.22/27.78    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.78    (107)  op(e1, all_14_2) = all_14_1
% 177.22/27.78    (108)  all_58_9 = all_52_7
% 177.22/27.78    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.78    (110)   ~ (all_52_9 = all_52_15)
% 177.22/27.78    (111)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.78    (112)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.78    (113)   ~ (e3 = e2)
% 177.22/27.78    (114)  op(e2, e3) = all_52_9
% 177.22/27.78    (115)  all_56_13 = all_52_27
% 177.22/27.78  
% 177.22/27.78  Begin of proof
% 177.22/27.78  | 
% 177.22/27.78  | BETA: splitting (45) gives:
% 177.22/27.78  | 
% 177.22/27.78  | Case 1:
% 177.22/27.78  | | 
% 177.22/27.78  | |   (116)  all_58_1 = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | COMBINE_EQS: (42), (116) imply:
% 177.22/27.78  | |   (117)  all_52_3 = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | REDUCE: (60), (117) imply:
% 177.22/27.78  | |   (118)   ~ (all_4_2 = e3)
% 177.22/27.78  | | 
% 177.22/27.78  | | SIMP: (118) implies:
% 177.22/27.78  | |   (119)   ~ (all_4_2 = e3)
% 177.22/27.78  | | 
% 177.22/27.78  | | REF_CLOSE: (1), (2), (9), (14), (23), (28), (29), (30), (31), (32), (33),
% 177.22/27.78  | |            (34), (36), (37), (40), (41), (42), (43), (47), (48), (51), (57),
% 177.22/27.78  | |            (61), (62), (64), (65), (67), (69), (70), (74), (76), (77), (78),
% 177.22/27.78  | |            (79), (80), (82), (83), (87), (89), (92), (93), (94), (96), (97),
% 177.22/27.78  | |            (98), (100), (101), (103), (106), (108), (109), (111), (114),
% 177.22/27.78  | |            (119) are inconsistent by sub-proof #864.
% 177.22/27.78  | | 
% 177.22/27.78  | Case 2:
% 177.22/27.78  | | 
% 177.22/27.78  | |   (120)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.78  | | 
% 177.22/27.78  | | BETA: splitting (120) gives:
% 177.22/27.78  | | 
% 177.22/27.78  | | Case 1:
% 177.22/27.78  | | | 
% 177.22/27.78  | | |   (121)  all_58_3 = e3
% 177.22/27.78  | | | 
% 177.22/27.78  | | | COMBINE_EQS: (27), (121) imply:
% 177.22/27.78  | | |   (122)  all_10_2 = e3
% 177.22/27.78  | | | 
% 177.22/27.78  | | | REDUCE: (63), (122) imply:
% 177.22/27.78  | | |   (123)   ~ (all_52_9 = e3)
% 177.22/27.78  | | | 
% 177.22/27.78  | | | REDUCE: (11), (122) imply:
% 177.22/27.78  | | |   (124)  op(e2, e3) = all_10_1
% 177.22/27.78  | | | 
% 177.22/27.78  | | | REDUCE: (7), (122) imply:
% 177.22/27.78  | | |   (125)  op(e2, e2) = e3
% 177.22/27.78  | | | 
% 177.22/27.78  | | | GROUND_INST: instantiating (97) with all_52_9, all_10_1, e3, e2,
% 177.22/27.78  | | |              simplifying with (114), (124) gives:
% 177.22/27.78  | | |   (126)  all_52_9 = all_10_1
% 177.22/27.78  | | | 
% 177.22/27.78  | | | COMBINE_EQS: (85), (126) imply:
% 177.22/27.78  | | |   (127)  all_58_2 = all_10_1
% 177.22/27.78  | | | 
% 177.22/27.78  | | | REDUCE: (68), (126) imply:
% 177.22/27.78  | | |   (128)   ~ (all_52_13 = all_10_1)
% 177.22/27.78  | | | 
% 177.22/27.78  | | | SIMP: (128) implies:
% 177.22/27.78  | | |   (129)   ~ (all_52_13 = all_10_1)
% 177.22/27.78  | | | 
% 177.22/27.78  | | | REDUCE: (110), (126) imply:
% 177.22/27.78  | | |   (130)   ~ (all_52_15 = all_10_1)
% 177.22/27.78  | | | 
% 177.22/27.78  | | | SIMP: (130) implies:
% 177.22/27.78  | | |   (131)   ~ (all_52_15 = all_10_1)
% 177.22/27.78  | | | 
% 177.22/27.78  | | | BETA: splitting (109) gives:
% 177.22/27.78  | | | 
% 177.22/27.78  | | | Case 1:
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | |   (132)  all_58_0 = e3
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | COMBINE_EQS: (43), (132) imply:
% 177.22/27.78  | | | |   (133)  all_4_2 = e3
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | REDUCE: (60), (133) imply:
% 177.22/27.78  | | | |   (134)   ~ (all_52_3 = e3)
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | REDUCE: (41), (133) imply:
% 177.22/27.78  | | | |   (135)   ~ (all_52_7 = e3)
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | REDUCE: (96), (133) imply:
% 177.22/27.78  | | | |   (136)   ~ (all_52_17 = e3)
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | BETA: splitting (37) gives:
% 177.22/27.78  | | | | 
% 177.22/27.78  | | | | Case 1:
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | |   (137)  all_58_6 = e3
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | | REF_CLOSE: (76), (136), (137) are inconsistent by sub-proof #981.
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | Case 2:
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | |   (138)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | | BETA: splitting (138) gives:
% 177.22/27.78  | | | | | 
% 177.22/27.78  | | | | | Case 1:
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | |   (139)  all_58_7 = e3
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | COMBINE_EQS: (34), (139) imply:
% 177.22/27.78  | | | | | |   (140)  all_52_19 = e3
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | REDUCE: (91), (140) imply:
% 177.22/27.78  | | | | | |   (141)  $false
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | CLOSE: (141) is inconsistent.
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | Case 2:
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | |   (142)  all_58_8 = e3 | all_58_11 = e3
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | BETA: splitting (142) gives:
% 177.22/27.78  | | | | | | 
% 177.22/27.78  | | | | | | Case 1:
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | |   (143)  all_58_8 = e3
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | COMBINE_EQS: (51), (143) imply:
% 177.22/27.78  | | | | | | |   (144)  all_14_2 = e3
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | REDUCE: (55), (144) imply:
% 177.22/27.78  | | | | | | |   (145)  op(all_14_1, e3) = e3
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | REDUCE: (107), (144) imply:
% 177.22/27.78  | | | | | | |   (146)  op(e1, e3) = all_14_1
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | GROUND_INST: instantiating (97) with all_52_17, all_14_1, e3, e1,
% 177.22/27.78  | | | | | | |              simplifying with (92), (146) gives:
% 177.22/27.78  | | | | | | |   (147)  all_52_17 = all_14_1
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | COMBINE_EQS: (95), (147) imply:
% 177.22/27.78  | | | | | | |   (148)  all_56_8 = all_14_1
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | COMBINE_EQS: (76), (147) imply:
% 177.22/27.78  | | | | | | |   (149)  all_58_6 = all_14_1
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | REDUCE: (105), (147) imply:
% 177.22/27.78  | | | | | | |   (150)   ~ (all_52_19 = all_14_1)
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | SIMP: (150) implies:
% 177.22/27.78  | | | | | | |   (151)   ~ (all_52_19 = all_14_1)
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | REDUCE: (8), (147) imply:
% 177.22/27.78  | | | | | | |   (152)   ~ (all_52_23 = all_14_1)
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | SIMP: (152) implies:
% 177.22/27.78  | | | | | | |   (153)   ~ (all_52_23 = all_14_1)
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | REDUCE: (50), (147) imply:
% 177.22/27.78  | | | | | | |   (154)   ~ (all_14_1 = all_6_1)
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | REDUCE: (136), (147) imply:
% 177.22/27.78  | | | | | | |   (155)   ~ (all_14_1 = e3)
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | BETA: splitting (3) gives:
% 177.22/27.78  | | | | | | | 
% 177.22/27.78  | | | | | | | Case 1:
% 177.22/27.78  | | | | | | | | 
% 177.22/27.78  | | | | | | | |   (156)  all_56_8 = e3
% 177.22/27.78  | | | | | | | | 
% 177.22/27.78  | | | | | | | | REF_CLOSE: (148), (155), (156) are inconsistent by sub-proof
% 177.22/27.78  | | | | | | | |            #849.
% 177.22/27.78  | | | | | | | | 
% 177.22/27.78  | | | | | | | Case 2:
% 177.22/27.78  | | | | | | | | 
% 177.22/27.78  | | | | | | | |   (157)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.22/27.78  | | | | | | | | 
% 177.22/27.78  | | | | | | | | BETA: splitting (75) gives:
% 177.22/27.78  | | | | | | | | 
% 177.22/27.78  | | | | | | | | Case 1:
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | |   (158)  all_58_6 = e2
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | | COMBINE_EQS: (149), (158) imply:
% 177.22/27.78  | | | | | | | | |   (159)  all_14_1 = e2
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | | SIMP: (159) implies:
% 177.22/27.78  | | | | | | | | |   (160)  all_14_1 = e2
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | | REDUCE: (145), (160) imply:
% 177.22/27.78  | | | | | | | | |   (161)  op(e2, e3) = e3
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | | REF_CLOSE: (97), (114), (123), (161) are inconsistent by
% 177.22/27.78  | | | | | | | | |            sub-proof #498.
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | Case 2:
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | |   (162)   ~ (all_58_6 = e2)
% 177.22/27.78  | | | | | | | | |   (163)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.78  | | | | | | | | | REDUCE: (149), (162) imply:
% 177.22/27.78  | | | | | | | | |   (164)   ~ (all_14_1 = e2)
% 177.22/27.78  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REF_CLOSE: (4), (5), (9), (10), (12), (13), (15), (16), (17),
% 177.22/27.79  | | | | | | | | |            (18), (19), (20), (21), (22), (24), (25), (26),
% 177.22/27.79  | | | | | | | | |            (31), (34), (35), (36), (38), (39), (42), (44),
% 177.22/27.79  | | | | | | | | |            (46), (47), (48), (49), (52), (53), (54), (56),
% 177.22/27.79  | | | | | | | | |            (58), (59), (64), (66), (70), (71), (72), (73),
% 177.22/27.79  | | | | | | | | |            (74), (77), (79), (80), (81), (86), (88), (90),
% 177.22/27.79  | | | | | | | | |            (97), (99), (100), (101), (102), (103), (104),
% 177.22/27.79  | | | | | | | | |            (108), (112), (113), (115), (124), (125), (127),
% 177.22/27.79  | | | | | | | | |            (129), (131), (132), (134), (135), (143), (148),
% 177.22/27.79  | | | | | | | | |            (149), (151), (153), (154), (157), (163), (164) are
% 177.22/27.79  | | | | | | | | |            inconsistent by sub-proof #831.
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | End of split
% 177.22/27.79  | | | | | | | | 
% 177.22/27.79  | | | | | | | End of split
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | Case 2:
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | |   (165)  all_58_11 = e3
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REF_CLOSE: (58), (79), (165) are inconsistent by sub-proof #1017.
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | End of split
% 177.22/27.79  | | | | | | 
% 177.22/27.79  | | | | | End of split
% 177.22/27.79  | | | | | 
% 177.22/27.79  | | | | End of split
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | Case 2:
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | |   (166)   ~ (all_58_0 = e3)
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | | REDUCE: (43), (166) imply:
% 177.22/27.79  | | | |   (167)   ~ (all_4_2 = e3)
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | | REF_CLOSE: (1), (2), (9), (14), (23), (28), (29), (30), (31), (32),
% 177.22/27.79  | | | |            (33), (34), (36), (37), (40), (41), (42), (43), (47), (48),
% 177.22/27.79  | | | |            (51), (57), (61), (62), (64), (65), (67), (69), (70), (74),
% 177.22/27.79  | | | |            (76), (77), (78), (79), (80), (82), (83), (87), (89), (92),
% 177.22/27.79  | | | |            (93), (94), (96), (97), (98), (100), (101), (103), (106),
% 177.22/27.79  | | | |            (108), (109), (111), (114), (167) are inconsistent by
% 177.22/27.79  | | | |            sub-proof #864.
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | End of split
% 177.22/27.79  | | | 
% 177.22/27.79  | | Case 2:
% 177.22/27.79  | | | 
% 177.22/27.79  | | |   (168)  all_58_7 = e3 | all_58_13 = e3
% 177.22/27.79  | | | 
% 177.22/27.79  | | | REF_CLOSE: (18), (34), (72), (91), (168) are inconsistent by sub-proof
% 177.22/27.79  | | |            #976.
% 177.22/27.79  | | | 
% 177.22/27.79  | | End of split
% 177.22/27.79  | | 
% 177.22/27.79  | End of split
% 177.22/27.79  | 
% 177.22/27.79  End of proof
% 177.22/27.79  
% 177.22/27.79  Sub-proof #343 shows that the following formulas are inconsistent:
% 177.22/27.79  ----------------------------------------------------------------
% 177.22/27.79    (1)   ~ (e3 = e1)
% 177.22/27.79    (2)  op(all_14_1, all_14_2) = e3
% 177.22/27.79    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.79    (4)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.22/27.79    (5)  all_52_20 = all_14_1
% 177.22/27.79    (6)  op(e1, all_14_2) = all_14_1
% 177.22/27.79  
% 177.22/27.79  Begin of proof
% 177.22/27.79  | 
% 177.22/27.79  | ALPHA: (4) implies:
% 177.22/27.79  |   (7)  all_52_20 = e1
% 177.22/27.79  | 
% 177.22/27.79  | COMBINE_EQS: (5), (7) imply:
% 177.22/27.79  |   (8)  all_14_1 = e1
% 177.22/27.79  | 
% 177.22/27.79  | SIMP: (8) implies:
% 177.22/27.79  |   (9)  all_14_1 = e1
% 177.22/27.79  | 
% 177.22/27.79  | REF_CLOSE: (1), (2), (3), (6), (9) are inconsistent by sub-proof #344.
% 177.22/27.79  | 
% 177.22/27.79  End of proof
% 177.22/27.79  
% 177.22/27.79  Sub-proof #344 shows that the following formulas are inconsistent:
% 177.22/27.79  ----------------------------------------------------------------
% 177.22/27.79    (1)   ~ (e3 = e1)
% 177.22/27.79    (2)  op(all_14_1, all_14_2) = e3
% 177.22/27.79    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.79    (4)  op(e1, all_14_2) = all_14_1
% 177.22/27.79    (5)  all_14_1 = e1
% 177.22/27.79  
% 177.22/27.79  Begin of proof
% 177.22/27.79  | 
% 177.22/27.79  | REDUCE: (2), (5) imply:
% 177.22/27.79  |   (6)  op(e1, all_14_2) = e3
% 177.22/27.79  | 
% 177.22/27.79  | REDUCE: (4), (5) imply:
% 177.22/27.79  |   (7)  op(e1, all_14_2) = e1
% 177.22/27.79  | 
% 177.22/27.79  | GROUND_INST: instantiating (3) with e1, e3, all_14_2, e1, simplifying with
% 177.22/27.79  |              (6), (7) gives:
% 177.22/27.79  |   (8)  e3 = e1
% 177.22/27.79  | 
% 177.22/27.79  | REDUCE: (1), (8) imply:
% 177.22/27.79  |   (9)  $false
% 177.22/27.79  | 
% 177.22/27.79  | CLOSE: (9) is inconsistent.
% 177.22/27.79  | 
% 177.22/27.79  End of proof
% 177.22/27.79  
% 177.22/27.79  Sub-proof #345 shows that the following formulas are inconsistent:
% 177.22/27.79  ----------------------------------------------------------------
% 177.22/27.79    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.79    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.79    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.22/27.79    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.79    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.79    (6)   ~ (all_52_27 = all_10_2)
% 177.22/27.79    (7)  op(e2, e2) = all_10_2
% 177.22/27.79    (8)   ~ (all_52_17 = all_52_23)
% 177.22/27.79    (9)  op(e2, all_10_2) = all_10_1
% 177.22/27.79    (10)  all_40_2 = all_4_2
% 177.22/27.79    (11)  all_36_0 = all_6_0
% 177.22/27.79    (12)  all_22_2 = all_14_2
% 177.22/27.79    (13)   ~ (all_52_13 = all_52_29)
% 177.22/27.79    (14)  all_56_3 = all_52_7
% 177.22/27.79    (15)  op(e3, e2) = all_52_3
% 177.22/27.79    (16)   ~ (all_52_9 = all_52_25)
% 177.22/27.79    (17)  op(e3, all_52_25) = all_52_24
% 177.22/27.79    (18)   ~ (all_52_19 = all_52_23)
% 177.22/27.79    (19)  all_56_11 = all_52_23
% 177.22/27.79    (20)  op(e1, e2) = all_52_19
% 177.22/27.79    (21)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.79    (22)  op(e3, all_52_9) = all_52_8
% 177.22/27.79    (23)  all_50_1 = all_4_1
% 177.22/27.79    (24)   ~ (all_52_3 = all_10_2)
% 177.22/27.79    (25)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.79    (26)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.22/27.79    (27)  all_58_5 = all_52_13
% 177.22/27.79    (28)   ~ (all_52_25 = all_52_29)
% 177.22/27.79    (29)  all_56_15 = all_6_2
% 177.22/27.79    (30)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.79    (31)  op(e2, e0) = all_52_15
% 177.22/27.79    (32)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.79    (33)  all_58_3 = all_10_2
% 177.22/27.79    (34)  all_56_9 = all_52_19
% 177.22/27.79    (35)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.79    (36)  all_58_15 = all_6_2
% 177.22/27.79    (37)   ~ (all_52_9 = all_4_2)
% 177.22/27.79    (38)   ~ (all_52_5 = all_52_7)
% 177.22/27.79    (39)  all_58_10 = all_52_15
% 177.22/27.79    (40)   ~ (all_52_5 = all_4_2)
% 177.22/27.79    (41)  all_58_7 = all_52_19
% 177.22/27.79    (42)  all_56_4 = all_52_9
% 177.22/27.79    (43)   ~ (all_52_15 = all_6_2)
% 177.22/27.79    (44)   ~ (all_52_17 = all_52_25)
% 177.22/27.79    (45)  op(e0, e1) = all_52_29
% 177.22/27.79    (46)  all_58_4 = all_52_5
% 177.22/27.79    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.79    (48)   ~ (e3 = e1)
% 177.22/27.79    (49)  all_34_1 = all_4_1
% 177.22/27.79    (50)   ~ (all_52_27 = all_52_29)
% 177.22/27.79    (51)   ~ (all_52_17 = all_14_2)
% 177.22/27.79    (52)  op(e3, all_4_2) = all_4_1
% 177.22/27.79    (53)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.79    (54)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.79    (55)   ~ (all_52_7 = all_4_2)
% 177.22/27.79    (56)  all_58_1 = all_52_3
% 177.22/27.79    (57)   ~ (all_52_13 = all_52_15)
% 177.22/27.79    (58)  all_58_0 = all_4_2
% 177.22/27.79    (59)  op(e1, all_52_13) = all_52_12
% 177.22/27.79    (60)  op(e0, e0) = all_6_2
% 177.22/27.79    (61)  op(e1, all_52_29) = all_52_28
% 177.22/27.79    (62)  all_50_0 = all_4_0
% 177.22/27.79    (63)  op(e1, all_52_5) = all_52_4
% 177.22/27.79    (64)  all_50_2 = all_4_2
% 177.22/27.79    (65)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.79    (66)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.79    (67)   ~ (all_4_1 = e2)
% 177.22/27.79    (68)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.79    (69)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.79    (70)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.79    (71)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.79    (72)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.79    (73)  all_58_14 = all_52_29
% 177.22/27.79    (74)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.79    (75)  all_24_0 = all_10_0
% 177.22/27.79    (76)  all_40_1 = all_4_1
% 177.22/27.79    (77)  all_26_2 = all_4_2
% 177.22/27.79    (78)   ~ (all_52_3 = all_52_5)
% 177.22/27.79    (79)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.79    (80)  op(e2, e1) = all_52_13
% 177.22/27.79    (81)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.79    (82)  all_58_8 = all_14_2
% 177.22/27.79    (83)  all_56_1 = all_52_3
% 177.22/27.79    (84)  op(e0, e2) = all_52_27
% 177.22/27.79    (85)  all_56_14 = all_52_29
% 177.22/27.79    (86)  op(e1, all_14_2) = e3
% 177.22/27.79    (87)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.22/27.79    (88)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.79    (89)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.79    (90)   ~ (all_52_5 = all_14_2)
% 177.22/27.79    (91)   ~ (all_52_3 = all_52_27)
% 177.22/27.79    (92)   ~ (all_52_3 = all_4_2)
% 177.22/27.79    (93)  op(all_6_1, all_6_2) = all_6_0
% 177.22/27.79    (94)   ~ (all_36_0 = e3) |  ~ (all_36_1 = e1) |  ~ (all_36_2 = e2)
% 177.22/27.79    (95)  op(e0, e3) = all_52_25
% 177.22/27.79    (96)  op(e0, all_6_2) = all_6_1
% 177.22/27.79    (97)  all_52_0 = all_4_1
% 177.22/27.79    (98)   ~ (all_52_9 = all_10_2)
% 177.22/27.79    (99)  op(e3, all_52_17) = all_52_16
% 177.22/27.79    (100)  all_52_10 = all_10_1
% 177.22/27.79    (101)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.79    (102)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.22/27.79    (103)   ~ (all_52_13 = all_14_2)
% 177.22/27.79    (104)   ~ (e3 = e0)
% 177.22/27.79    (105)  all_40_0 = all_4_0
% 177.22/27.79    (106)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.79    (107)  all_22_0 = all_14_0
% 177.22/27.79    (108)   ~ (all_24_0 = e1) |  ~ (all_24_1 = e0) |  ~ (all_24_2 = e3)
% 177.22/27.79    (109)   ~ (all_52_9 = all_52_13)
% 177.22/27.79    (110)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.79    (111)  op(e0, all_52_23) = all_52_22
% 177.22/27.79    (112)   ~ (all_52_15 = all_52_23)
% 177.22/27.79    (113)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.79    (114)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.79    (115)   ~ (all_52_5 = all_52_29)
% 177.22/27.79    (116)  all_56_2 = all_52_5
% 177.22/27.79    (117)  op(e1, e0) = all_52_23
% 177.22/27.79    (118)  all_56_12 = all_52_25
% 177.22/27.79    (119)  all_58_13 = all_52_27
% 177.22/27.79    (120)  op(e2, all_52_3) = all_52_2
% 177.22/27.79    (121)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.79    (122)  all_56_5 = all_10_2
% 177.22/27.79    (123)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.22/27.79    (124)   ~ (all_52_9 = all_52_17)
% 177.22/27.79    (125)   ~ (all_14_0 = e2)
% 177.22/27.79    (126)  all_58_6 = all_52_17
% 177.22/27.79    (127)   ~ (all_52_3 = all_52_7)
% 177.22/27.79    (128)  all_52_20 = e3
% 177.22/27.79    (129)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.79    (130)  op(e2, all_52_19) = all_52_18
% 177.22/27.79    (131)   ~ (e1 = e0)
% 177.22/27.79    (132)  all_56_0 = all_4_2
% 177.22/27.79    (133)  all_58_11 = all_52_23
% 177.22/27.79    (134)   ~ (all_52_3 = all_52_19)
% 177.22/27.79    (135)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.79    (136)   ~ (all_52_7 = all_52_15)
% 177.22/27.79    (137)  all_26_1 = all_4_1
% 177.22/27.79    (138)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 177.22/27.79    (139)  op(e0, all_52_15) = all_52_14
% 177.22/27.79    (140)   ~ (all_52_29 = all_14_2)
% 177.22/27.79    (141)   ~ (all_52_19 = all_10_2)
% 177.22/27.79    (142)   ~ (all_34_0 = e1) |  ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.79    (143)   ~ (all_50_0 = e2) |  ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.79    (144)   ~ (all_52_23 = all_6_2)
% 177.22/27.79    (145)   ~ (all_6_0 = e2)
% 177.22/27.79    (146)   ~ (all_52_29 = all_6_2)
% 177.22/27.79    (147)  all_58_2 = all_52_9
% 177.22/27.79    (148)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.22/27.79    (149)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.79    (150)  op(e3, e1) = all_52_5
% 177.22/27.79    (151)   ~ (e2 = e1)
% 177.22/27.79    (152)  all_56_10 = all_14_2
% 177.22/27.79    (153)   ~ (all_52_25 = all_6_2)
% 177.22/27.79    (154)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.79    (155)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.79    (156)  op(e1, e1) = all_14_2
% 177.22/27.79    (157)  op(e1, e3) = all_52_17
% 177.22/27.79    (158)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.79    (159)  all_26_0 = all_4_0
% 177.22/27.79    (160)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 177.22/27.79    (161)   ~ (all_52_25 = all_4_2)
% 177.22/27.79    (162)  op(e3, e0) = all_52_7
% 177.22/27.79    (163)  op(e3, e3) = all_4_2
% 177.22/27.79    (164)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.79             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.22/27.79    (165)  all_56_8 = all_52_17
% 177.22/27.79    (166)   ~ (all_52_17 = all_4_2)
% 177.22/27.79    (167)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.79             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.79    (168)  all_36_2 = all_6_2
% 177.22/27.79    (169)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.79           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.22/27.79           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.22/27.79           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.79    (170)   ~ (all_52_25 = all_52_27)
% 177.22/27.79    (171)  all_34_2 = all_4_2
% 177.22/27.79    (172)   ~ (all_52_27 = all_6_2)
% 177.22/27.79    (173)   ~ (all_52_7 = all_6_2)
% 177.22/27.79    (174)   ~ (all_10_0 = e3)
% 177.22/27.79    (175)   ~ (all_52_15 = all_10_2)
% 177.22/27.79    (176)   ~ (all_52_19 = all_52_27)
% 177.22/27.79    (177)   ~ (all_40_0 = e0) |  ~ (all_40_1 = e1) |  ~ (all_40_2 = e2)
% 177.22/27.79    (178)  all_56_7 = all_52_15
% 177.22/27.79    (179)   ~ (all_52_7 = all_52_23)
% 177.22/27.79    (180)   ~ (all_52_13 = all_10_2)
% 177.22/27.79    (181)   ~ (all_6_0 = e1)
% 177.22/27.79    (182)  op(e2, all_52_27) = all_52_26
% 177.22/27.79    (183)   ~ (all_52_17 = all_52_19)
% 177.22/27.79    (184)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.79    (185)  all_52_30 = all_6_1
% 177.22/27.79    (186)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.79    (187)  op(e1, all_14_2) = all_14_1
% 177.22/27.79    (188)  op(e3, all_14_2) = all_14_0
% 177.22/27.79    (189)  all_58_9 = all_52_7
% 177.22/27.79    (190)   ~ (all_28_0 = e3) |  ~ (all_28_1 = e2) |  ~ (all_28_2 = e1)
% 177.22/27.79    (191)   ~ (e2 = e0)
% 177.22/27.79    (192)  all_58_12 = all_52_25
% 177.22/27.79    (193)  all_34_0 = all_4_0
% 177.22/27.79    (194)   ~ (all_26_0 = e2) |  ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.79    (195)  all_56_6 = all_52_13
% 177.22/27.79    (196)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.79    (197)   ~ (all_52_9 = all_52_15)
% 177.22/27.79    (198)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.79    (199)   ~ (e3 = e2)
% 177.22/27.79    (200)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.79    (201)   ~ (all_52_19 = all_14_2)
% 177.22/27.79    (202)  op(e0, all_52_7) = all_52_6
% 177.22/27.79    (203)  all_28_0 = all_6_0
% 177.22/27.79    (204)  op(e2, e3) = all_52_9
% 177.22/27.79    (205)  all_56_13 = all_52_27
% 177.22/27.79  
% 177.22/27.79  Begin of proof
% 177.22/27.79  | 
% 177.22/27.79  | BETA: splitting (108) gives:
% 177.22/27.79  | 
% 177.22/27.79  | Case 1:
% 177.22/27.79  | | 
% 177.22/27.79  | |   (206)   ~ (all_24_0 = e1)
% 177.22/27.79  | | 
% 177.22/27.79  | | REDUCE: (75), (206) imply:
% 177.22/27.79  | |   (207)   ~ (all_10_0 = e1)
% 177.22/27.79  | | 
% 177.22/27.79  | | BETA: splitting (194) gives:
% 177.22/27.79  | | 
% 177.22/27.79  | | Case 1:
% 177.22/27.79  | | | 
% 177.22/27.79  | | |   (208)   ~ (all_26_0 = e2)
% 177.22/27.79  | | | 
% 177.22/27.79  | | | REDUCE: (159), (208) imply:
% 177.22/27.79  | | |   (209)   ~ (all_4_0 = e2)
% 177.22/27.79  | | | 
% 177.22/27.79  | | | BETA: splitting (190) gives:
% 177.22/27.79  | | | 
% 177.22/27.79  | | | Case 1:
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | |   (210)   ~ (all_28_0 = e3)
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | | REDUCE: (203), (210) imply:
% 177.22/27.79  | | | |   (211)   ~ (all_6_0 = e3)
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | | BETA: splitting (142) gives:
% 177.22/27.79  | | | | 
% 177.22/27.79  | | | | Case 1:
% 177.22/27.79  | | | | | 
% 177.22/27.79  | | | | |   (212)   ~ (all_34_0 = e1)
% 177.22/27.79  | | | | | 
% 177.22/27.79  | | | | | REDUCE: (193), (212) imply:
% 177.22/27.79  | | | | |   (213)   ~ (all_4_0 = e1)
% 177.22/27.79  | | | | | 
% 177.22/27.79  | | | | | BETA: splitting (177) gives:
% 177.22/27.79  | | | | | 
% 177.22/27.79  | | | | | Case 1:
% 177.22/27.79  | | | | | | 
% 177.22/27.79  | | | | | |   (214)   ~ (all_40_1 = e1)
% 177.22/27.79  | | | | | | 
% 177.22/27.79  | | | | | | REDUCE: (76), (214) imply:
% 177.22/27.79  | | | | | |   (215)   ~ (all_4_1 = e1)
% 177.22/27.79  | | | | | | 
% 177.22/27.79  | | | | | | BETA: splitting (164) gives:
% 177.22/27.79  | | | | | | 
% 177.22/27.79  | | | | | | Case 1:
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | |   (216)  all_58_15 = e0
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | COMBINE_EQS: (36), (216) imply:
% 177.22/27.79  | | | | | | |   (217)  all_6_2 = e0
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (173), (217) imply:
% 177.22/27.79  | | | | | | |   (218)   ~ (all_52_7 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (43), (217) imply:
% 177.22/27.79  | | | | | | |   (219)   ~ (all_52_15 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (144), (217) imply:
% 177.22/27.79  | | | | | | |   (220)   ~ (all_52_23 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (153), (217) imply:
% 177.22/27.79  | | | | | | |   (221)   ~ (all_52_25 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (172), (217) imply:
% 177.22/27.79  | | | | | | |   (222)   ~ (all_52_27 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (146), (217) imply:
% 177.22/27.79  | | | | | | |   (223)   ~ (all_52_29 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (93), (217) imply:
% 177.22/27.79  | | | | | | |   (224)  op(all_6_1, e0) = all_6_0
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (96), (217) imply:
% 177.22/27.79  | | | | | | |   (225)  op(e0, e0) = all_6_1
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (60), (217) imply:
% 177.22/27.79  | | | | | | |   (226)  op(e0, e0) = e0
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | GROUND_INST: instantiating (167) with e0, all_6_1, e0, e0,
% 177.22/27.79  | | | | | | |              simplifying with (225), (226) gives:
% 177.22/27.79  | | | | | | |   (227)  all_6_1 = e0
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (224), (227) imply:
% 177.22/27.79  | | | | | | |   (228)  op(e0, e0) = all_6_0
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, e0, e0,
% 177.22/27.79  | | | | | | |              simplifying with (226), (228) gives:
% 177.22/27.79  | | | | | | |   (229)  all_6_0 = e0
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (211), (229) imply:
% 177.22/27.79  | | | | | | |   (230)   ~ (e3 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (145), (229) imply:
% 177.22/27.79  | | | | | | |   (231)   ~ (e2 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | REDUCE: (181), (229) imply:
% 177.22/27.79  | | | | | | |   (232)   ~ (e1 = e0)
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | BETA: splitting (169) gives:
% 177.22/27.79  | | | | | | | 
% 177.22/27.79  | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | 
% 177.22/27.79  | | | | | | | |   (233)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.79  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.79  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.79  | | | | | | | | 
% 177.22/27.79  | | | | | | | | BETA: splitting (233) gives:
% 177.22/27.79  | | | | | | | | 
% 177.22/27.79  | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | |   (234)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.79  | | | | | | | | |          all_52_6 = e0
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REF_CLOSE: (14), (15), (32), (35), (36), (38), (39), (45),
% 177.22/27.79  | | | | | | | | |            (46), (52), (55), (56), (58), (70), (73), (74),
% 177.22/27.79  | | | | | | | | |            (79), (81), (84), (88), (95), (97), (101), (104),
% 177.22/27.79  | | | | | | | | |            (110), (115), (118), (119), (121), (127), (132),
% 177.22/27.79  | | | | | | | | |            (133), (136), (148), (150), (155), (161), (167),
% 177.22/27.79  | | | | | | | | |            (170), (173), (179), (184), (186), (189), (192),
% 177.22/27.79  | | | | | | | | |            (196), (202), (205), (216), (218), (221), (222),
% 177.22/27.79  | | | | | | | | |            (223), (234) are inconsistent by sub-proof #1008.
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | Case 2:
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | |   (235)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.79  | | | | | | | | |          all_52_14 = e0
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | ALPHA: (235) implies:
% 177.22/27.79  | | | | | | | | |   (236)  all_52_14 = e0
% 177.22/27.79  | | | | | | | | |   (237)  all_52_12 = e1
% 177.22/27.79  | | | | | | | | |   (238)  all_52_10 = e2
% 177.22/27.79  | | | | | | | | |   (239)  all_52_8 = e3
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | COMBINE_EQS: (100), (238) imply:
% 177.22/27.79  | | | | | | | | |   (240)  all_10_1 = e2
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | SIMP: (240) implies:
% 177.22/27.79  | | | | | | | | |   (241)  all_10_1 = e2
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REDUCE: (114), (241) imply:
% 177.22/27.79  | | | | | | | | |   (242)  op(e2, all_10_2) = all_10_0
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REDUCE: (22), (239) imply:
% 177.22/27.79  | | | | | | | | |   (243)  op(e3, all_52_9) = e3
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REDUCE: (9), (241) imply:
% 177.22/27.79  | | | | | | | | |   (244)  op(e2, all_10_2) = e2
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REDUCE: (59), (237) imply:
% 177.22/27.79  | | | | | | | | |   (245)  op(e1, all_52_13) = e1
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REDUCE: (139), (236) imply:
% 177.22/27.79  | | | | | | | | |   (246)  op(e0, all_52_15) = e0
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | GROUND_INST: instantiating (167) with e2, all_10_0, all_10_2,
% 177.22/27.79  | | | | | | | | |              e2, simplifying with (242), (244) gives:
% 177.22/27.79  | | | | | | | | |   (247)  all_10_0 = e2
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | REDUCE: (174), (247) imply:
% 177.22/27.79  | | | | | | | | |   (248)   ~ (e3 = e2)
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | BETA: splitting (74) gives:
% 177.22/27.79  | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | |   (249)  all_56_13 = e3
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | COMBINE_EQS: (205), (249) imply:
% 177.22/27.79  | | | | | | | | | |   (250)  all_52_27 = e3
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | SIMP: (250) implies:
% 177.22/27.79  | | | | | | | | | |   (251)  all_52_27 = e3
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | COMBINE_EQS: (119), (251) imply:
% 177.22/27.79  | | | | | | | | | |   (252)  all_58_13 = e3
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (176), (251) imply:
% 177.22/27.79  | | | | | | | | | |   (253)   ~ (all_52_19 = e3)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (170), (251) imply:
% 177.22/27.79  | | | | | | | | | |   (254)   ~ (all_52_25 = e3)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (50), (251) imply:
% 177.22/27.79  | | | | | | | | | |   (255)   ~ (all_52_29 = e3)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | SIMP: (255) implies:
% 177.22/27.79  | | | | | | | | | |   (256)   ~ (all_52_29 = e3)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (6), (251) imply:
% 177.22/27.79  | | | | | | | | | |   (257)   ~ (all_10_2 = e3)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | SIMP: (257) implies:
% 177.22/27.79  | | | | | | | | | |   (258)   ~ (all_10_2 = e3)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (182), (251) imply:
% 177.22/27.79  | | | | | | | | | |   (259)  op(e2, e3) = all_52_26
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_9, all_52_26, e3,
% 177.22/27.79  | | | | | | | | | |              e2, simplifying with (204), (259) gives:
% 177.22/27.79  | | | | | | | | | |   (260)  all_52_9 = all_52_26
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | COMBINE_EQS: (147), (260) imply:
% 177.22/27.79  | | | | | | | | | |   (261)  all_58_2 = all_52_26
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (109), (260) imply:
% 177.22/27.79  | | | | | | | | | |   (262)   ~ (all_52_13 = all_52_26)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | SIMP: (262) implies:
% 177.22/27.79  | | | | | | | | | |   (263)   ~ (all_52_13 = all_52_26)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (37), (260) imply:
% 177.22/27.79  | | | | | | | | | |   (264)   ~ (all_52_26 = all_4_2)
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | REDUCE: (243), (260) imply:
% 177.22/27.79  | | | | | | | | | |   (265)  op(e3, all_52_26) = e3
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | BETA: splitting (110) gives:
% 177.22/27.79  | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | |   (266)  all_56_12 = e3
% 177.22/27.79  | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | REF_CLOSE: (118), (254), (266) are inconsistent by sub-proof
% 177.22/27.79  | | | | | | | | | | |            #1040.
% 177.22/27.79  | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | Case 2:
% 177.22/27.79  | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | |   (267)   ~ (all_56_12 = e3)
% 177.22/27.79  | | | | | | | | | | |   (268)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.79  | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | BETA: splitting (148) gives:
% 177.22/27.79  | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | |   (269)  all_58_12 = e1
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | COMBINE_EQS: (192), (269) imply:
% 177.22/27.79  | | | | | | | | | | | |   (270)  all_52_25 = e1
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | SIMP: (270) implies:
% 177.22/27.79  | | | | | | | | | | | |   (271)  all_52_25 = e1
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | REDUCE: (44), (271) imply:
% 177.22/27.79  | | | | | | | | | | | |   (272)   ~ (all_52_17 = e1)
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | REDUCE: (28), (271) imply:
% 177.22/27.79  | | | | | | | | | | | |   (273)   ~ (all_52_29 = e1)
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | SIMP: (273) implies:
% 177.22/27.79  | | | | | | | | | | | |   (274)   ~ (all_52_29 = e1)
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | REDUCE: (254), (271) imply:
% 177.22/27.79  | | | | | | | | | | | |   (275)   ~ (e3 = e1)
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | REDUCE: (17), (271) imply:
% 177.22/27.79  | | | | | | | | | | | |   (276)  op(e3, e1) = all_52_24
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | REDUCE: (95), (271) imply:
% 177.22/27.79  | | | | | | | | | | | |   (277)  op(e0, e3) = e1
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | BETA: splitting (155) gives:
% 177.22/27.79  | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | |   (278)  all_58_12 = e2
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | COMBINE_EQS: (269), (278) imply:
% 177.22/27.79  | | | | | | | | | | | | |   (279)  e2 = e1
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | REDUCE: (151), (279) imply:
% 177.22/27.79  | | | | | | | | | | | | |   (280)  $false
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | CLOSE: (280) is inconsistent.
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | Case 2:
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | |   (281)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | BETA: splitting (281) gives:
% 177.22/27.79  | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | |   (282)  all_58_13 = e2
% 177.22/27.79  | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | REF_CLOSE: (199), (252), (282) are inconsistent by sub-proof
% 177.22/27.79  | | | | | | | | | | | | | |            #906.
% 177.22/27.79  | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | Case 2:
% 177.22/27.79  | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | |   (283)  all_58_14 = e2 | all_58_15 = e2
% 177.22/27.79  | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 177.22/27.79  | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | |   (284)  all_58_14 = e2
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | COMBINE_EQS: (73), (284) imply:
% 177.22/27.79  | | | | | | | | | | | | | | |   (285)  all_52_29 = e2
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | SIMP: (285) implies:
% 177.22/27.79  | | | | | | | | | | | | | | |   (286)  all_52_29 = e2
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | REDUCE: (61), (286) imply:
% 177.22/27.79  | | | | | | | | | | | | | | |   (287)  op(e1, e2) = all_52_28
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_19, all_52_28, e2,
% 177.22/27.79  | | | | | | | | | | | | | | |              e1, simplifying with (20), (287) gives:
% 177.22/27.79  | | | | | | | | | | | | | | |   (288)  all_52_19 = all_52_28
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_5, all_52_24, e1,
% 177.22/27.79  | | | | | | | | | | | | | | |              e3, simplifying with (150), (276) gives:
% 177.22/27.79  | | | | | | | | | | | | | | |   (289)  all_52_5 = all_52_24
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | COMBINE_EQS: (41), (288) imply:
% 177.22/27.79  | | | | | | | | | | | | | | |   (290)  all_58_7 = all_52_28
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | COMBINE_EQS: (46), (289) imply:
% 177.22/27.79  | | | | | | | | | | | | | | |   (291)  all_58_4 = all_52_24
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | REDUCE: (2), (289) imply:
% 177.22/27.79  | | | | | | | | | | | | | | |   (292)   ~ (all_52_13 = all_52_24)
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | SIMP: (292) implies:
% 177.22/27.79  | | | | | | | | | | | | | | |   (293)   ~ (all_52_13 = all_52_24)
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | REDUCE: (253), (288) imply:
% 177.22/27.79  | | | | | | | | | | | | | | |   (294)   ~ (all_52_28 = e3)
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 177.22/27.79  | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | |   (295)  all_58_6 = e3
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | COMBINE_EQS: (126), (295) imply:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (296)  all_52_17 = e3
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | REDUCE: (8), (296) imply:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (297)   ~ (all_52_23 = e3)
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | SIMP: (297) implies:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (298)   ~ (all_52_23 = e3)
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | REDUCE: (51), (296) imply:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (299)   ~ (all_14_2 = e3)
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | SIMP: (299) implies:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (300)   ~ (all_14_2 = e3)
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | REDUCE: (166), (296) imply:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (301)   ~ (all_4_2 = e3)
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | SIMP: (301) implies:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (302)   ~ (all_4_2 = e3)
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | REDUCE: (99), (296) imply:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (303)  op(e3, e3) = all_52_16
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_4_2, all_52_16, e3,
% 177.22/27.79  | | | | | | | | | | | | | | | |              e3, simplifying with (163), (303) gives:
% 177.22/27.79  | | | | | | | | | | | | | | | |   (304)  all_52_16 = all_4_2
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.79  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (13), (27), (33), (39), (41), (44), (46),
% 177.22/27.79  | | | | | | | | | | | | | | | |            (47), (48), (51), (54), (57), (58), (73), (79),
% 177.22/27.79  | | | | | | | | | | | | | | | |            (82), (103), (126), (131), (133), (157), (163),
% 177.22/27.79  | | | | | | | | | | | | | | | |            (167), (180), (192), (198), (245), (246), (253),
% 177.22/27.79  | | | | | | | | | | | | | | | |            (256), (258), (261), (263), (264), (265), (277),
% 177.22/27.79  | | | | | | | | | | | | | | | |            (291), (293), (298), (300), (302) are inconsistent
% 177.22/27.79  | | | | | | | | | | | | | | | |            by sub-proof #491.
% 177.22/27.79  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | |   (305)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | |   (306)  all_58_7 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (306) imply:
% 177.22/27.80  | | | | | | | | | | | | | | | | |   (307)  all_52_28 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | REDUCE: (294), (307) imply:
% 177.22/27.80  | | | | | | | | | | | | | | | | |   (308)  $false
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | CLOSE: (308) is inconsistent.
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | |   (309)  all_58_8 = e3 | all_58_11 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | BETA: splitting (309) gives:
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | |   (310)  all_58_8 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (82), (86), (157), (167), (310) are
% 177.22/27.80  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #432.
% 177.22/27.80  | | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | |   (311)  all_58_11 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (39), (45), (48), (84), (101), (131), (151),
% 177.22/27.80  | | | | | | | | | | | | | | | | | |            (167), (191), (199), (216), (222), (223), (246),
% 177.22/27.80  | | | | | | | | | | | | | | | | | |            (311) are inconsistent by sub-proof #986.
% 177.22/27.80  | | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | |   (312)  all_58_15 = e2
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | REF_CLOSE: (191), (216), (312) are inconsistent by sub-proof
% 177.22/27.80  | | | | | | | | | | | | | | |            #991.
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | |   (313)   ~ (all_58_12 = e1)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | REF_CLOSE: (13), (14), (27), (32), (33), (38), (39), (41),
% 177.22/27.80  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (51), (54), (55),
% 177.22/27.80  | | | | | | | | | | | |            (58), (73), (79), (82), (84), (95), (101), (103),
% 177.22/27.80  | | | | | | | | | | | |            (104), (118), (126), (131), (133), (136), (155),
% 177.22/27.80  | | | | | | | | | | | |            (157), (158), (163), (167), (178), (179), (184),
% 177.22/27.80  | | | | | | | | | | | |            (186), (189), (192), (198), (216), (221), (222),
% 177.22/27.80  | | | | | | | | | | | |            (223), (245), (246), (253), (254), (258), (261),
% 177.22/27.80  | | | | | | | | | | | |            (263), (264), (265), (268), (313) are inconsistent
% 177.22/27.80  | | | | | | | | | | | |            by sub-proof #982.
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | |   (314)   ~ (all_56_13 = e3)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (205), (314) imply:
% 177.22/27.80  | | | | | | | | | |   (315)   ~ (all_52_27 = e3)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | BETA: splitting (81) gives:
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | |   (316)  all_58_12 = e3
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | COMBINE_EQS: (192), (316) imply:
% 177.22/27.80  | | | | | | | | | | |   (317)  all_52_25 = e3
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | SIMP: (317) implies:
% 177.22/27.80  | | | | | | | | | | |   (318)  all_52_25 = e3
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | REDUCE: (16), (318) imply:
% 177.22/27.80  | | | | | | | | | | |   (319)   ~ (all_52_9 = e3)
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | REDUCE: (44), (318) imply:
% 177.22/27.80  | | | | | | | | | | |   (320)   ~ (all_52_17 = e3)
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | REDUCE: (95), (318) imply:
% 177.22/27.80  | | | | | | | | | | |   (321)  op(e0, e3) = e3
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | REF_CLOSE: (1), (6), (8), (15), (19), (24), (27), (30), (32),
% 177.22/27.80  | | | | | | | | | | |            (33), (37), (39), (41), (45), (47), (48), (51),
% 177.22/27.80  | | | | | | | | | | |            (54), (56), (58), (70), (71), (82), (84), (86),
% 177.22/27.80  | | | | | | | | | | |            (89), (101), (103), (104), (113), (117), (119),
% 177.22/27.80  | | | | | | | | | | |            (126), (127), (130), (131), (133), (134), (136),
% 177.22/27.80  | | | | | | | | | | |            (141), (147), (149), (151), (152), (157), (158),
% 177.22/27.80  | | | | | | | | | | |            (163), (167), (178), (179), (184), (189), (191),
% 177.22/27.80  | | | | | | | | | | |            (195), (199), (204), (216), (219), (220), (222),
% 177.22/27.80  | | | | | | | | | | |            (223), (243), (244), (245), (246), (316), (319),
% 177.22/27.80  | | | | | | | | | | |            (320), (321) are inconsistent by sub-proof #428.
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | |   (322)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | REF_CLOSE: (13), (15), (16), (24), (27), (28), (32), (33),
% 177.22/27.80  | | | | | | | | | | |            (37), (39), (41), (45), (47), (50), (52), (54),
% 177.22/27.80  | | | | | | | | | | |            (55), (56), (58), (61), (65), (70), (73), (79),
% 177.22/27.80  | | | | | | | | | | |            (82), (83), (84), (88), (92), (95), (101), (104),
% 177.22/27.80  | | | | | | | | | | |            (110), (112), (118), (119), (124), (126), (133),
% 177.22/27.80  | | | | | | | | | | |            (134), (140), (147), (148), (151), (157), (158),
% 177.22/27.80  | | | | | | | | | | |            (163), (167), (178), (183), (184), (189), (191),
% 177.22/27.80  | | | | | | | | | | |            (192), (196), (204), (209), (213), (216), (221),
% 177.22/27.80  | | | | | | | | | | |            (222), (223), (243), (244), (246), (315), (322)
% 177.22/27.80  | | | | | | | | | | |            are inconsistent by sub-proof #955.
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | |   (323)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.80  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.80  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | BETA: splitting (323) gives:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | |   (324)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.80  | | | | | | | | |          all_52_22 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REF_CLOSE: (48), (128), (324) are inconsistent by sub-proof
% 177.22/27.80  | | | | | | | | |            #427.
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | |   (325)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.80  | | | | | | | | |          all_52_30 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REF_CLOSE: (4), (6), (14), (15), (16), (17), (18), (19), (20),
% 177.22/27.80  | | | | | | | | |            (24), (27), (28), (34), (35), (38), (40), (41),
% 177.22/27.80  | | | | | | | | |            (44), (46), (47), (48), (50), (52), (55), (58),
% 177.22/27.80  | | | | | | | | |            (61), (66), (67), (68), (69), (73), (74), (80),
% 177.22/27.80  | | | | | | | | |            (81), (82), (85), (86), (90), (91), (92), (99),
% 177.22/27.80  | | | | | | | | |            (104), (110), (113), (115), (117), (118), (119),
% 177.22/27.80  | | | | | | | | |            (122), (123), (124), (126), (131), (132), (133),
% 177.22/27.80  | | | | | | | | |            (134), (140), (141), (148), (149), (150), (152),
% 177.22/27.80  | | | | | | | | |            (154), (156), (157), (160), (161), (162), (163),
% 177.22/27.80  | | | | | | | | |            (167), (170), (176), (179), (180), (182), (186),
% 177.22/27.80  | | | | | | | | |            (188), (192), (201), (204), (205), (216), (220),
% 177.22/27.80  | | | | | | | | |            (221), (223), (325) are inconsistent by sub-proof
% 177.22/27.80  | | | | | | | | |            #421.
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | End of split
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | Case 2:
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | |   (326)   ~ (all_58_15 = e0)
% 177.22/27.80  | | | | | | |   (327)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.80  | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | | ALPHA: (327) implies:
% 177.22/27.80  | | | | | | |   (328)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.80  | | | | | | |   (329)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | | REDUCE: (36), (326) imply:
% 177.22/27.80  | | | | | | |   (330)   ~ (all_6_2 = e0)
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | | BETA: splitting (169) gives:
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | |   (331)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.80  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.80  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | BETA: splitting (331) gives:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | |   (332)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.80  | | | | | | | | |          all_52_6 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | ALPHA: (332) implies:
% 177.22/27.80  | | | | | | | | |   (333)  all_52_6 = e0
% 177.22/27.80  | | | | | | | | |   (334)  all_52_4 = e1
% 177.22/27.80  | | | | | | | | |   (335)  all_52_2 = e2
% 177.22/27.80  | | | | | | | | |   (336)  all_52_0 = e3
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | COMBINE_EQS: (97), (336) imply:
% 177.22/27.80  | | | | | | | | |   (337)  all_4_1 = e3
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (88), (337) imply:
% 177.22/27.80  | | | | | | | | |   (338)  op(e3, all_4_2) = all_4_0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (52), (337) imply:
% 177.22/27.80  | | | | | | | | |   (339)  op(e3, all_4_2) = e3
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (120), (335) imply:
% 177.22/27.80  | | | | | | | | |   (340)  op(e2, all_52_3) = e2
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (63), (334) imply:
% 177.22/27.80  | | | | | | | | |   (341)  op(e1, all_52_5) = e1
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (202), (333) imply:
% 177.22/27.80  | | | | | | | | |   (342)  op(e0, all_52_7) = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (13), (14), (15), (16),
% 177.22/27.80  | | | | | | | | |            (17), (18), (19), (20), (21), (22), (24), (27),
% 177.22/27.80  | | | | | | | | |            (28), (29), (30), (32), (33), (34), (35), (36),
% 177.22/27.80  | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 177.22/27.80  | | | | | | | | |            (45), (46), (47), (50), (51), (53), (54), (55),
% 177.22/27.80  | | | | | | | | |            (56), (57), (58), (60), (61), (65), (66), (68),
% 177.22/27.80  | | | | | | | | |            (69), (70), (71), (72), (73), (74), (78), (79),
% 177.22/27.80  | | | | | | | | |            (80), (81), (82), (83), (84), (85), (86), (90),
% 177.22/27.80  | | | | | | | | |            (91), (92), (93), (95), (96), (98), (101), (102),
% 177.22/27.80  | | | | | | | | |            (103), (104), (106), (109), (110), (111), (112),
% 177.22/27.80  | | | | | | | | |            (113), (115), (116), (117), (118), (119), (121),
% 177.22/27.80  | | | | | | | | |            (122), (123), (124), (126), (127), (129), (131),
% 177.22/27.80  | | | | | | | | |            (132), (133), (134), (135), (136), (139), (140),
% 177.22/27.80  | | | | | | | | |            (141), (144), (145), (146), (147), (148), (149),
% 177.22/27.80  | | | | | | | | |            (150), (151), (152), (153), (154), (155), (156),
% 177.22/27.80  | | | | | | | | |            (157), (158), (161), (162), (165), (166), (167),
% 177.22/27.80  | | | | | | | | |            (170), (172), (173), (175), (176), (178), (179),
% 177.22/27.80  | | | | | | | | |            (180), (181), (182), (183), (184), (186), (189),
% 177.22/27.80  | | | | | | | | |            (192), (195), (196), (197), (198), (200), (201),
% 177.22/27.80  | | | | | | | | |            (204), (205), (209), (211), (213), (329), (330),
% 177.22/27.80  | | | | | | | | |            (338), (339), (340), (341), (342) are inconsistent
% 177.22/27.80  | | | | | | | | |            by sub-proof #400.
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | |   (343)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.80  | | | | | | | | |          all_52_14 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | ALPHA: (343) implies:
% 177.22/27.80  | | | | | | | | |   (344)  all_52_14 = e0
% 177.22/27.80  | | | | | | | | |   (345)  all_52_12 = e1
% 177.22/27.80  | | | | | | | | |   (346)  all_52_10 = e2
% 177.22/27.80  | | | | | | | | |   (347)  all_52_8 = e3
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | COMBINE_EQS: (100), (346) imply:
% 177.22/27.80  | | | | | | | | |   (348)  all_10_1 = e2
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (114), (348) imply:
% 177.22/27.80  | | | | | | | | |   (349)  op(e2, all_10_2) = all_10_0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (22), (347) imply:
% 177.22/27.80  | | | | | | | | |   (350)  op(e3, all_52_9) = e3
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (9), (348) imply:
% 177.22/27.80  | | | | | | | | |   (351)  op(e2, all_10_2) = e2
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (59), (345) imply:
% 177.22/27.80  | | | | | | | | |   (352)  op(e1, all_52_13) = e1
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (139), (344) imply:
% 177.22/27.80  | | | | | | | | |   (353)  op(e0, all_52_15) = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (13), (14), (15), (16),
% 177.22/27.80  | | | | | | | | |            (17), (18), (19), (20), (21), (24), (26), (27),
% 177.22/27.80  | | | | | | | | |            (28), (29), (30), (31), (33), (34), (35), (36),
% 177.22/27.80  | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 177.22/27.80  | | | | | | | | |            (45), (46), (47), (48), (50), (51), (52), (53),
% 177.22/27.80  | | | | | | | | |            (54), (55), (56), (58), (61), (65), (66), (67),
% 177.22/27.80  | | | | | | | | |            (69), (70), (71), (72), (73), (74), (78), (79),
% 177.22/27.80  | | | | | | | | |            (80), (81), (82), (83), (84), (86), (87), (88),
% 177.22/27.80  | | | | | | | | |            (89), (90), (91), (92), (95), (96), (98), (99),
% 177.22/27.80  | | | | | | | | |            (103), (104), (109), (111), (112), (113), (115),
% 177.22/27.80  | | | | | | | | |            (116), (117), (119), (121), (122), (124), (126),
% 177.22/27.80  | | | | | | | | |            (127), (129), (130), (131), (132), (133), (134),
% 177.22/27.80  | | | | | | | | |            (135), (136), (140), (141), (144), (146), (147),
% 177.22/27.80  | | | | | | | | |            (149), (150), (152), (153), (154), (155), (157),
% 177.22/27.80  | | | | | | | | |            (158), (161), (162), (163), (166), (167), (170),
% 177.22/27.80  | | | | | | | | |            (172), (173), (174), (176), (178), (179), (180),
% 177.22/27.80  | | | | | | | | |            (182), (183), (184), (186), (187), (189), (192),
% 177.22/27.80  | | | | | | | | |            (195), (196), (197), (198), (200), (201), (204),
% 177.22/27.80  | | | | | | | | |            (205), (207), (209), (213), (215), (328), (329),
% 177.22/27.80  | | | | | | | | |            (330), (349), (350), (351), (352), (353) are
% 177.22/27.80  | | | | | | | | |            inconsistent by sub-proof #374.
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | |   (354)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.80  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.80  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | BETA: splitting (354) gives:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | |   (355)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.80  | | | | | | | | |          all_52_22 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REF_CLOSE: (48), (128), (355) are inconsistent by sub-proof
% 177.22/27.80  | | | | | | | | |            #373.
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | |   (356)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.80  | | | | | | | | |          all_52_30 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | ALPHA: (356) implies:
% 177.22/27.80  | | | | | | | | |   (357)  all_52_30 = e0
% 177.22/27.80  | | | | | | | | |   (358)  all_52_28 = e1
% 177.22/27.80  | | | | | | | | |   (359)  all_52_26 = e2
% 177.22/27.80  | | | | | | | | |   (360)  all_52_24 = e3
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | COMBINE_EQS: (185), (357) imply:
% 177.22/27.80  | | | | | | | | |   (361)  all_6_1 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REF_CLOSE: (4), (5), (8), (15), (16), (17), (18), (19), (20),
% 177.22/27.80  | | | | | | | | |            (22), (25), (27), (28), (29), (30), (32), (33),
% 177.22/27.80  | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (44),
% 177.22/27.80  | | | | | | | | |            (45), (46), (47), (48), (50), (51), (52), (53),
% 177.22/27.80  | | | | | | | | |            (55), (56), (57), (58), (61), (68), (69), (70),
% 177.22/27.80  | | | | | | | | |            (71), (73), (74), (78), (79), (81), (82), (84),
% 177.22/27.80  | | | | | | | | |            (85), (86), (88), (91), (92), (93), (95), (96),
% 177.22/27.80  | | | | | | | | |            (98), (99), (101), (103), (106), (109), (110),
% 177.22/27.80  | | | | | | | | |            (115), (116), (118), (119), (121), (124), (126),
% 177.22/27.80  | | | | | | | | |            (127), (132), (133), (135), (140), (141), (145),
% 177.22/27.80  | | | | | | | | |            (146), (147), (149), (150), (153), (155), (156),
% 177.22/27.80  | | | | | | | | |            (157), (161), (162), (163), (166), (167), (170),
% 177.22/27.80  | | | | | | | | |            (172), (173), (175), (176), (179), (181), (182),
% 177.22/27.80  | | | | | | | | |            (183), (184), (189), (192), (195), (197), (198),
% 177.22/27.80  | | | | | | | | |            (199), (200), (204), (205), (209), (211), (213),
% 177.22/27.80  | | | | | | | | |            (328), (330), (358), (359), (360), (361) are
% 177.22/27.80  | | | | | | | | |            inconsistent by sub-proof #369.
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | End of split
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | End of split
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | End of split
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | Case 2:
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | |   (362)  all_40_1 = e1
% 177.22/27.80  | | | | | |   (363)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | COMBINE_EQS: (76), (362) imply:
% 177.22/27.80  | | | | | |   (364)  all_4_1 = e1
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | SIMP: (364) implies:
% 177.22/27.80  | | | | | |   (365)  all_4_1 = e1
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | COMBINE_EQS: (97), (365) imply:
% 177.22/27.80  | | | | | |   (366)  all_52_0 = e1
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | REDUCE: (67), (365) imply:
% 177.22/27.80  | | | | | |   (367)   ~ (e2 = e1)
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | REDUCE: (88), (365) imply:
% 177.22/27.80  | | | | | |   (368)  op(e1, all_4_2) = all_4_0
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | REDUCE: (52), (365) imply:
% 177.22/27.80  | | | | | |   (369)  op(e3, all_4_2) = e1
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | BETA: splitting (169) gives:
% 177.22/27.80  | | | | | | 
% 177.22/27.80  | | | | | | Case 1:
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | |   (370)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.22/27.80  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.22/27.80  | | | | | | |            e1 & all_52_14 = e0)
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | | BETA: splitting (370) gives:
% 177.22/27.80  | | | | | | | 
% 177.22/27.80  | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | |   (371)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.80  | | | | | | | |          all_52_6 = e0
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | REF_CLOSE: (48), (366), (371) are inconsistent by sub-proof
% 177.22/27.80  | | | | | | | |            #632.
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | |   (372)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.80  | | | | | | | |          all_52_14 = e0
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | ALPHA: (372) implies:
% 177.22/27.80  | | | | | | | |   (373)  all_52_14 = e0
% 177.22/27.80  | | | | | | | |   (374)  all_52_12 = e1
% 177.22/27.80  | | | | | | | |   (375)  all_52_10 = e2
% 177.22/27.80  | | | | | | | |   (376)  all_52_8 = e3
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | COMBINE_EQS: (100), (375) imply:
% 177.22/27.80  | | | | | | | |   (377)  all_10_1 = e2
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | REDUCE: (114), (377) imply:
% 177.22/27.80  | | | | | | | |   (378)  op(e2, all_10_2) = all_10_0
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | REDUCE: (22), (376) imply:
% 177.22/27.80  | | | | | | | |   (379)  op(e3, all_52_9) = e3
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | REDUCE: (9), (377) imply:
% 177.22/27.80  | | | | | | | |   (380)  op(e2, all_10_2) = e2
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | REDUCE: (59), (374) imply:
% 177.22/27.80  | | | | | | | |   (381)  op(e1, all_52_13) = e1
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | REDUCE: (139), (373) imply:
% 177.22/27.80  | | | | | | | |   (382)  op(e0, all_52_15) = e0
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | GROUND_INST: instantiating (167) with e2, all_10_0, all_10_2,
% 177.22/27.80  | | | | | | | |              e2, simplifying with (378), (380) gives:
% 177.22/27.80  | | | | | | | |   (383)  all_10_0 = e2
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | REDUCE: (174), (383) imply:
% 177.22/27.80  | | | | | | | |   (384)   ~ (e3 = e2)
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | BETA: splitting (164) gives:
% 177.22/27.80  | | | | | | | | 
% 177.22/27.80  | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | |   (385)  all_58_15 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | COMBINE_EQS: (36), (385) imply:
% 177.22/27.80  | | | | | | | | |   (386)  all_6_2 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (43), (386) imply:
% 177.22/27.80  | | | | | | | | |   (387)   ~ (all_52_15 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (144), (386) imply:
% 177.22/27.80  | | | | | | | | |   (388)   ~ (all_52_23 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (153), (386) imply:
% 177.22/27.80  | | | | | | | | |   (389)   ~ (all_52_25 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (172), (386) imply:
% 177.22/27.80  | | | | | | | | |   (390)   ~ (all_52_27 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (146), (386) imply:
% 177.22/27.80  | | | | | | | | |   (391)   ~ (all_52_29 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (93), (386) imply:
% 177.22/27.80  | | | | | | | | |   (392)  op(all_6_1, e0) = all_6_0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (96), (386) imply:
% 177.22/27.80  | | | | | | | | |   (393)  op(e0, e0) = all_6_1
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (60), (386) imply:
% 177.22/27.80  | | | | | | | | |   (394)  op(e0, e0) = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | GROUND_INST: instantiating (167) with e0, all_6_1, e0, e0,
% 177.22/27.80  | | | | | | | | |              simplifying with (393), (394) gives:
% 177.22/27.80  | | | | | | | | |   (395)  all_6_1 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (392), (395) imply:
% 177.22/27.80  | | | | | | | | |   (396)  op(e0, e0) = all_6_0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, e0, e0,
% 177.22/27.80  | | | | | | | | |              simplifying with (394), (396) gives:
% 177.22/27.80  | | | | | | | | |   (397)  all_6_0 = e0
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (211), (397) imply:
% 177.22/27.80  | | | | | | | | |   (398)   ~ (e3 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (145), (397) imply:
% 177.22/27.80  | | | | | | | | |   (399)   ~ (e2 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | REDUCE: (181), (397) imply:
% 177.22/27.80  | | | | | | | | |   (400)   ~ (e1 = e0)
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | BETA: splitting (74) gives:
% 177.22/27.80  | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | |   (401)  all_56_13 = e3
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | COMBINE_EQS: (205), (401) imply:
% 177.22/27.80  | | | | | | | | | |   (402)  all_52_27 = e3
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | SIMP: (402) implies:
% 177.22/27.80  | | | | | | | | | |   (403)  all_52_27 = e3
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (91), (403) imply:
% 177.22/27.80  | | | | | | | | | |   (404)   ~ (all_52_3 = e3)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (176), (403) imply:
% 177.22/27.80  | | | | | | | | | |   (405)   ~ (all_52_19 = e3)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (170), (403) imply:
% 177.22/27.80  | | | | | | | | | |   (406)   ~ (all_52_25 = e3)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (6), (403) imply:
% 177.22/27.80  | | | | | | | | | |   (407)   ~ (all_10_2 = e3)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | SIMP: (407) implies:
% 177.22/27.80  | | | | | | | | | |   (408)   ~ (all_10_2 = e3)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (182), (403) imply:
% 177.22/27.80  | | | | | | | | | |   (409)  op(e2, e3) = all_52_26
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_9, all_52_26, e3,
% 177.22/27.80  | | | | | | | | | |              e2, simplifying with (204), (409) gives:
% 177.22/27.80  | | | | | | | | | |   (410)  all_52_9 = all_52_26
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | COMBINE_EQS: (147), (410) imply:
% 177.22/27.80  | | | | | | | | | |   (411)  all_58_2 = all_52_26
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (109), (410) imply:
% 177.22/27.80  | | | | | | | | | |   (412)   ~ (all_52_13 = all_52_26)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | SIMP: (412) implies:
% 177.22/27.80  | | | | | | | | | |   (413)   ~ (all_52_13 = all_52_26)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (37), (410) imply:
% 177.22/27.80  | | | | | | | | | |   (414)   ~ (all_52_26 = all_4_2)
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | REDUCE: (379), (410) imply:
% 177.22/27.80  | | | | | | | | | |   (415)  op(e3, all_52_26) = e3
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | BETA: splitting (110) gives:
% 177.22/27.80  | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | |   (416)  all_56_12 = e3
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | REF_CLOSE: (118), (406), (416) are inconsistent by sub-proof
% 177.22/27.80  | | | | | | | | | | |            #1040.
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | |   (417)   ~ (all_56_12 = e3)
% 177.22/27.80  | | | | | | | | | | |   (418)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | BETA: splitting (148) gives:
% 177.22/27.80  | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | |   (419)  all_58_12 = e1
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | COMBINE_EQS: (192), (419) imply:
% 177.22/27.80  | | | | | | | | | | | |   (420)  all_52_25 = e1
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | SIMP: (420) implies:
% 177.22/27.80  | | | | | | | | | | | |   (421)  all_52_25 = e1
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | REDUCE: (161), (421) imply:
% 177.22/27.80  | | | | | | | | | | | |   (422)   ~ (all_4_2 = e1)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | SIMP: (422) implies:
% 177.22/27.80  | | | | | | | | | | | |   (423)   ~ (all_4_2 = e1)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | REDUCE: (406), (421) imply:
% 177.22/27.80  | | | | | | | | | | | |   (424)   ~ (e3 = e1)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | REDUCE: (17), (421) imply:
% 177.22/27.80  | | | | | | | | | | | |   (425)  op(e3, e1) = all_52_24
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | REDUCE: (95), (421) imply:
% 177.22/27.80  | | | | | | | | | | | |   (426)  op(e0, e3) = e1
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_5, all_52_24, e1,
% 177.22/27.80  | | | | | | | | | | | |              e3, simplifying with (150), (425) gives:
% 177.22/27.80  | | | | | | | | | | | |   (427)  all_52_5 = all_52_24
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | COMBINE_EQS: (46), (427) imply:
% 177.22/27.80  | | | | | | | | | | | |   (428)  all_58_4 = all_52_24
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | REDUCE: (38), (427) imply:
% 177.22/27.80  | | | | | | | | | | | |   (429)   ~ (all_52_7 = all_52_24)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | SIMP: (429) implies:
% 177.22/27.80  | | | | | | | | | | | |   (430)   ~ (all_52_7 = all_52_24)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | REDUCE: (2), (427) imply:
% 177.22/27.80  | | | | | | | | | | | |   (431)   ~ (all_52_13 = all_52_24)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | SIMP: (431) implies:
% 177.22/27.80  | | | | | | | | | | | |   (432)   ~ (all_52_13 = all_52_24)
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | BETA: splitting (186) gives:
% 177.22/27.80  | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | |   (433)  all_56_3 = e3
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | COMBINE_EQS: (14), (433) imply:
% 177.22/27.80  | | | | | | | | | | | | |   (434)  all_52_7 = e3
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | SIMP: (434) implies:
% 177.22/27.80  | | | | | | | | | | | | |   (435)  all_52_7 = e3
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | REF_CLOSE: (13), (27), (33), (39), (41), (44), (47), (48),
% 177.22/27.80  | | | | | | | | | | | | |            (51), (54), (55), (58), (73), (79), (82), (103),
% 177.22/27.80  | | | | | | | | | | | | |            (126), (133), (136), (157), (163), (167), (179),
% 177.22/27.80  | | | | | | | | | | | | |            (192), (198), (381), (405), (408), (411), (413),
% 177.22/27.80  | | | | | | | | | | | | |            (414), (415), (428), (430), (435) are inconsistent
% 177.22/27.80  | | | | | | | | | | | | |            by sub-proof #993.
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | |   (436)   ~ (all_56_3 = e3)
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | REDUCE: (14), (436) imply:
% 177.22/27.80  | | | | | | | | | | | | |   (437)   ~ (all_52_7 = e3)
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | BETA: splitting (196) gives:
% 177.22/27.80  | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | |   (438)  all_58_0 = e3
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | COMBINE_EQS: (58), (438) imply:
% 177.22/27.80  | | | | | | | | | | | | | |   (439)  all_4_2 = e3
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | REF_CLOSE: (48), (163), (167), (369), (439) are inconsistent
% 177.22/27.80  | | | | | | | | | | | | | |            by sub-proof #630.
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | |   (440)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | BETA: splitting (440) gives:
% 177.22/27.80  | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | |   (441)  all_58_1 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | COMBINE_EQS: (56), (441) imply:
% 177.22/27.80  | | | | | | | | | | | | | | |   (442)  all_52_3 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | REDUCE: (404), (442) imply:
% 177.22/27.80  | | | | | | | | | | | | | | |   (443)  $false
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | CLOSE: (443) is inconsistent.
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | |   (444)  all_58_4 = e3 | all_58_9 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | BETA: splitting (444) gives:
% 177.22/27.80  | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | |   (445)  all_58_4 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | REF_CLOSE: (27), (33), (39), (54), (131), (163), (167),
% 177.22/27.80  | | | | | | | | | | | | | | | |            (382), (408), (411), (414), (415), (426), (428),
% 177.22/27.80  | | | | | | | | | | | | | | | |            (432), (445) are inconsistent by sub-proof #493.
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | |   (446)  all_58_9 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (446) imply:
% 177.22/27.80  | | | | | | | | | | | | | | | |   (447)  all_52_7 = e3
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | REDUCE: (437), (447) imply:
% 177.22/27.80  | | | | | | | | | | | | | | | |   (448)  $false
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.80  | | | | | | | | | | | | | | | | CLOSE: (448) is inconsistent.
% 177.22/27.80  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | |   (449)   ~ (all_58_12 = e1)
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | REDUCE: (192), (449) imply:
% 177.22/27.81  | | | | | | | | | | | |   (450)   ~ (all_52_25 = e1)
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | BETA: splitting (418) gives:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | |   (451)  all_56_12 = e2
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | COMBINE_EQS: (118), (451) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (452)  all_52_25 = e2
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | SIMP: (452) implies:
% 177.22/27.81  | | | | | | | | | | | | |   (453)  all_52_25 = e2
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REDUCE: (95), (453) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (454)  op(e0, e3) = e2
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | BETA: splitting (158) gives:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | |   (455)  all_56_7 = e3
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | REF_CLOSE: (167), (178), (191), (382), (454), (455) are
% 177.22/27.81  | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | |   (456)   ~ (all_56_7 = e3)
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | REDUCE: (178), (456) imply:
% 177.22/27.81  | | | | | | | | | | | | | |   (457)   ~ (all_52_15 = e3)
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | REF_CLOSE: (2), (13), (15), (24), (27), (33), (37), (39),
% 177.22/27.81  | | | | | | | | | | | | | |            (46), (47), (48), (51), (54), (58), (71), (73),
% 177.22/27.81  | | | | | | | | | | | | | |            (79), (82), (86), (126), (147), (157), (163),
% 177.22/27.81  | | | | | | | | | | | | | |            (166), (167), (192), (195), (198), (204), (369),
% 177.22/27.81  | | | | | | | | | | | | | |            (379), (380), (381), (406), (457) are inconsistent
% 177.22/27.81  | | | | | | | | | | | | | |            by sub-proof #368.
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | |   (458)  all_56_12 = e1 | all_56_12 = e0
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REF_CLOSE: (118), (389), (450), (458) are inconsistent by
% 177.22/27.81  | | | | | | | | | | | | |            sub-proof #1029.
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | |   (459)   ~ (all_56_13 = e3)
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | REDUCE: (205), (459) imply:
% 177.22/27.81  | | | | | | | | | |   (460)   ~ (all_52_27 = e3)
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | BETA: splitting (81) gives:
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | |   (461)  all_58_12 = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | COMBINE_EQS: (192), (461) imply:
% 177.22/27.81  | | | | | | | | | | |   (462)  all_52_25 = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | SIMP: (462) implies:
% 177.22/27.81  | | | | | | | | | | |   (463)  all_52_25 = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | REDUCE: (16), (463) imply:
% 177.22/27.81  | | | | | | | | | | |   (464)   ~ (all_52_9 = e3)
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | REDUCE: (44), (463) imply:
% 177.22/27.81  | | | | | | | | | | |   (465)   ~ (all_52_17 = e3)
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | REDUCE: (17), (463) imply:
% 177.22/27.81  | | | | | | | | | | |   (466)  op(e3, e3) = all_52_24
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | REDUCE: (95), (463) imply:
% 177.22/27.81  | | | | | | | | | | |   (467)  op(e0, e3) = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | GROUND_INST: instantiating (167) with all_4_2, all_52_24, e3,
% 177.22/27.81  | | | | | | | | | | |              e3, simplifying with (163), (466) gives:
% 177.22/27.81  | | | | | | | | | | |   (468)  all_52_24 = all_4_2
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | REF_CLOSE: (1), (6), (8), (15), (19), (24), (27), (30), (32),
% 177.22/27.81  | | | | | | | | | | |            (33), (37), (39), (41), (45), (47), (48), (51),
% 177.22/27.81  | | | | | | | | | | |            (54), (56), (58), (70), (71), (82), (84), (86),
% 177.22/27.81  | | | | | | | | | | |            (89), (101), (103), (104), (113), (117), (119),
% 177.22/27.81  | | | | | | | | | | |            (126), (127), (130), (131), (133), (134), (136),
% 177.22/27.81  | | | | | | | | | | |            (141), (147), (149), (151), (152), (157), (158),
% 177.22/27.81  | | | | | | | | | | |            (163), (167), (178), (179), (184), (189), (191),
% 177.22/27.81  | | | | | | | | | | |            (195), (199), (204), (379), (380), (381), (382),
% 177.22/27.81  | | | | | | | | | | |            (385), (387), (388), (390), (391), (461), (464),
% 177.22/27.81  | | | | | | | | | | |            (465), (467) are inconsistent by sub-proof #428.
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | |   (469)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | BETA: splitting (469) gives:
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | |   (470)  all_58_13 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | REF_CLOSE: (119), (460), (470) are inconsistent by sub-proof
% 177.22/27.81  | | | | | | | | | | | |            #1026.
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | |   (471)  all_58_14 = e3 | all_58_15 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | BETA: splitting (471) gives:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | |   (472)  all_58_14 = e3
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | COMBINE_EQS: (73), (472) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (473)  all_52_29 = e3
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | SIMP: (473) implies:
% 177.22/27.81  | | | | | | | | | | | | |   (474)  all_52_29 = e3
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REDUCE: (115), (474) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (475)   ~ (all_52_5 = e3)
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REDUCE: (13), (474) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (476)   ~ (all_52_13 = e3)
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REDUCE: (28), (474) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (477)   ~ (all_52_25 = e3)
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REDUCE: (140), (474) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (478)   ~ (all_14_2 = e3)
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | SIMP: (478) implies:
% 177.22/27.81  | | | | | | | | | | | | |   (479)   ~ (all_14_2 = e3)
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REDUCE: (61), (474) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (480)  op(e1, e3) = all_52_28
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_17, all_52_28, e3,
% 177.22/27.81  | | | | | | | | | | | | |              e1, simplifying with (157), (480) gives:
% 177.22/27.81  | | | | | | | | | | | | |   (481)  all_52_17 = all_52_28
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | COMBINE_EQS: (126), (481) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (482)  all_58_6 = all_52_28
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REDUCE: (124), (481) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (483)   ~ (all_52_9 = all_52_28)
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | BETA: splitting (110) gives:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | |   (484)  all_56_12 = e3
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | REF_CLOSE: (118), (477), (484) are inconsistent by sub-proof
% 177.22/27.81  | | | | | | | | | | | | | |            #1040.
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | |   (485)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | |   (486)  all_58_12 = e1
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | COMBINE_EQS: (192), (486) imply:
% 177.22/27.81  | | | | | | | | | | | | | | |   (487)  all_52_25 = e1
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | SIMP: (487) implies:
% 177.22/27.81  | | | | | | | | | | | | | | |   (488)  all_52_25 = e1
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | REDUCE: (161), (488) imply:
% 177.22/27.81  | | | | | | | | | | | | | | |   (489)   ~ (all_4_2 = e1)
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | SIMP: (489) implies:
% 177.22/27.81  | | | | | | | | | | | | | | |   (490)   ~ (all_4_2 = e1)
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | REDUCE: (95), (488) imply:
% 177.22/27.81  | | | | | | | | | | | | | | |   (491)  op(e0, e3) = e1
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | |   (492)  all_56_3 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (492) imply:
% 177.22/27.81  | | | | | | | | | | | | | | | |   (493)  all_52_7 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (24), (27), (33), (37), (39), (54), (136),
% 177.22/27.81  | | | | | | | | | | | | | | | |            (147), (163), (167), (204), (379), (380), (476),
% 177.22/27.81  | | | | | | | | | | | | | | | |            (493) are inconsistent by sub-proof #733.
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | |   (494)   ~ (all_56_3 = e3)
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | REDUCE: (14), (494) imply:
% 177.22/27.81  | | | | | | | | | | | | | | | |   (495)   ~ (all_52_7 = e3)
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | |   (496)  all_58_0 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (496) imply:
% 177.22/27.81  | | | | | | | | | | | | | | | | |   (497)  all_4_2 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (163), (167), (369), (497) are inconsistent
% 177.22/27.81  | | | | | | | | | | | | | | | | |            by sub-proof #630.
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | |   (498)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | BETA: splitting (498) gives:
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | |   (499)  all_58_1 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (499) imply:
% 177.22/27.81  | | | | | | | | | | | | | | | | | |   (500)  all_52_3 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (33), (37), (39), (41), (47), (54),
% 177.22/27.81  | | | | | | | | | | | | | | | | | |            (58), (79), (82), (92), (112), (131), (133),
% 177.22/27.81  | | | | | | | | | | | | | | | | | |            (134), (147), (163), (167), (379), (382), (476),
% 177.22/27.81  | | | | | | | | | | | | | | | | | |            (479), (482), (483), (491), (500) are inconsistent
% 177.22/27.81  | | | | | | | | | | | | | | | | | |            by sub-proof #963.
% 177.22/27.81  | | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | |   (501)  all_58_4 = e3 | all_58_9 = e3
% 177.22/27.81  | | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (189), (475), (495), (501) are inconsistent
% 177.22/27.81  | | | | | | | | | | | | | | | | | |            by sub-proof #729.
% 177.22/27.81  | | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | |   (502)   ~ (all_58_12 = e1)
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | REDUCE: (192), (502) imply:
% 177.22/27.81  | | | | | | | | | | | | | | |   (503)   ~ (all_52_25 = e1)
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | | REF_CLOSE: (16), (27), (33), (37), (39), (54), (95), (118),
% 177.22/27.81  | | | | | | | | | | | | | | |            (147), (158), (163), (167), (178), (204), (379),
% 177.22/27.81  | | | | | | | | | | | | | | |            (380), (382), (389), (476), (485), (503) are
% 177.22/27.81  | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 177.22/27.81  | | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | |   (504)  all_58_15 = e3
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REF_CLOSE: (104), (385), (504) are inconsistent by sub-proof
% 177.22/27.81  | | | | | | | | | | | | |            #1010.
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | |   (505)   ~ (all_58_15 = e0)
% 177.22/27.81  | | | | | | | | |   (506)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.81  | | | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | ALPHA: (506) implies:
% 177.22/27.81  | | | | | | | | |   (507)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.81  | | | | | | | | |   (508)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REDUCE: (36), (505) imply:
% 177.22/27.81  | | | | | | | | |   (509)   ~ (all_6_2 = e0)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (13), (14),
% 177.22/27.81  | | | | | | | | |            (15), (16), (18), (19), (20), (24), (25), (27),
% 177.22/27.81  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 177.22/27.81  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 177.22/27.81  | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 177.22/27.81  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (61), (66),
% 177.22/27.81  | | | | | | | | |            (67), (69), (70), (71), (72), (73), (74), (78),
% 177.22/27.81  | | | | | | | | |            (79), (80), (81), (82), (86), (89), (90), (91),
% 177.22/27.81  | | | | | | | | |            (92), (95), (99), (103), (104), (105), (109),
% 177.22/27.81  | | | | | | | | |            (111), (112), (113), (115), (116), (119), (121),
% 177.22/27.81  | | | | | | | | |            (122), (124), (126), (127), (129), (130), (131),
% 177.22/27.81  | | | | | | | | |            (132), (133), (134), (135), (136), (140), (141),
% 177.22/27.81  | | | | | | | | |            (144), (146), (147), (149), (150), (152), (153),
% 177.22/27.81  | | | | | | | | |            (154), (157), (158), (161), (162), (163), (166),
% 177.22/27.81  | | | | | | | | |            (167), (170), (172), (173), (176), (178), (179),
% 177.22/27.81  | | | | | | | | |            (180), (182), (183), (184), (186), (187), (189),
% 177.22/27.81  | | | | | | | | |            (191), (192), (195), (196), (197), (198), (199),
% 177.22/27.81  | | | | | | | | |            (200), (201), (202), (204), (205), (209), (363),
% 177.22/27.81  | | | | | | | | |            (368), (369), (379), (380), (381), (382), (507),
% 177.22/27.81  | | | | | | | | |            (508), (509) are inconsistent by sub-proof #363.
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | End of split
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | Case 2:
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | |   (510)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.81  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.81  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | | BETA: splitting (510) gives:
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | |   (511)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.81  | | | | | | | |          all_52_22 = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REF_CLOSE: (48), (128), (511) are inconsistent by sub-proof
% 177.22/27.81  | | | | | | | |            #427.
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | |   (512)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.81  | | | | | | | |          all_52_30 = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | ALPHA: (512) implies:
% 177.22/27.81  | | | | | | | |   (513)  all_52_30 = e0
% 177.22/27.81  | | | | | | | |   (514)  all_52_28 = e1
% 177.22/27.81  | | | | | | | |   (515)  all_52_26 = e2
% 177.22/27.81  | | | | | | | |   (516)  all_52_24 = e3
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | COMBINE_EQS: (185), (513) imply:
% 177.22/27.81  | | | | | | | |   (517)  all_6_1 = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | SIMP: (517) implies:
% 177.22/27.81  | | | | | | | |   (518)  all_6_1 = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (93), (518) imply:
% 177.22/27.81  | | | | | | | |   (519)  op(e0, all_6_2) = all_6_0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (17), (516) imply:
% 177.22/27.81  | | | | | | | |   (520)  op(e3, all_52_25) = e3
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (182), (515) imply:
% 177.22/27.81  | | | | | | | |   (521)  op(e2, all_52_27) = e2
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (61), (514) imply:
% 177.22/27.81  | | | | | | | |   (522)  op(e1, all_52_29) = e1
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (96), (518) imply:
% 177.22/27.81  | | | | | | | |   (523)  op(e0, all_6_2) = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, all_6_2, e0,
% 177.22/27.81  | | | | | | | |              simplifying with (519), (523) gives:
% 177.22/27.81  | | | | | | | |   (524)  all_6_0 = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (211), (524) imply:
% 177.22/27.81  | | | | | | | |   (525)   ~ (e3 = e0)
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (181), (524) imply:
% 177.22/27.81  | | | | | | | |   (526)   ~ (e1 = e0)
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | BETA: splitting (164) gives:
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | |   (527)  all_58_15 = e0
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | COMBINE_EQS: (36), (527) imply:
% 177.22/27.81  | | | | | | | | |   (528)  all_6_2 = e0
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REDUCE: (144), (528) imply:
% 177.22/27.81  | | | | | | | | |   (529)   ~ (all_52_23 = e0)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REDUCE: (153), (528) imply:
% 177.22/27.81  | | | | | | | | |   (530)   ~ (all_52_25 = e0)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REDUCE: (146), (528) imply:
% 177.22/27.81  | | | | | | | | |   (531)   ~ (all_52_29 = e0)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REF_CLOSE: (4), (6), (14), (15), (16), (18), (19), (20), (24),
% 177.22/27.81  | | | | | | | | |            (27), (28), (34), (35), (38), (40), (41), (44),
% 177.22/27.81  | | | | | | | | |            (46), (47), (48), (50), (52), (55), (58), (66),
% 177.22/27.81  | | | | | | | | |            (67), (68), (69), (73), (74), (80), (81), (82),
% 177.22/27.81  | | | | | | | | |            (85), (86), (90), (91), (92), (99), (104), (110),
% 177.22/27.81  | | | | | | | | |            (113), (115), (117), (118), (119), (122), (123),
% 177.22/27.81  | | | | | | | | |            (124), (126), (131), (132), (133), (134), (140),
% 177.22/27.81  | | | | | | | | |            (141), (148), (149), (150), (152), (154), (156),
% 177.22/27.81  | | | | | | | | |            (157), (160), (161), (162), (163), (167), (170),
% 177.22/27.81  | | | | | | | | |            (176), (179), (180), (186), (188), (192), (201),
% 177.22/27.81  | | | | | | | | |            (204), (205), (520), (521), (522), (527), (529),
% 177.22/27.81  | | | | | | | | |            (530), (531) are inconsistent by sub-proof #422.
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | |   (532)   ~ (all_58_15 = e0)
% 177.22/27.81  | | | | | | | | |   (533)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.81  | | | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (13), (15), (16), (18), (19),
% 177.22/27.81  | | | | | | | | |            (21), (22), (25), (27), (28), (29), (30), (32),
% 177.22/27.81  | | | | | | | | |            (33), (35), (36), (37), (38), (39), (40), (41),
% 177.22/27.81  | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 177.22/27.81  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (68), (69),
% 177.22/27.81  | | | | | | | | |            (70), (73), (74), (78), (79), (81), (82), (84),
% 177.22/27.81  | | | | | | | | |            (85), (88), (91), (92), (95), (98), (99), (101),
% 177.22/27.81  | | | | | | | | |            (103), (106), (109), (110), (115), (116), (117),
% 177.22/27.81  | | | | | | | | |            (118), (119), (121), (123), (124), (126), (127),
% 177.22/27.81  | | | | | | | | |            (132), (133), (134), (136), (141), (144), (145),
% 177.22/27.81  | | | | | | | | |            (146), (147), (149), (150), (151), (153), (155),
% 177.22/27.81  | | | | | | | | |            (157), (158), (161), (162), (163), (166), (167),
% 177.22/27.81  | | | | | | | | |            (170), (172), (173), (175), (176), (178), (179),
% 177.22/27.81  | | | | | | | | |            (181), (183), (184), (189), (192), (196), (197),
% 177.22/27.81  | | | | | | | | |            (198), (199), (200), (204), (205), (209), (211),
% 177.22/27.81  | | | | | | | | |            (213), (519), (520), (521), (522), (523), (532),
% 177.22/27.81  | | | | | | | | |            (533) are inconsistent by sub-proof #530.
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | End of split
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | End of split
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | End of split
% 177.22/27.81  | | | | | 
% 177.22/27.81  | | | | Case 2:
% 177.22/27.81  | | | | | 
% 177.22/27.81  | | | | |   (534)  all_34_0 = e1
% 177.22/27.81  | | | | |   (535)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.81  | | | | | 
% 177.22/27.81  | | | | | COMBINE_EQS: (193), (534) imply:
% 177.22/27.81  | | | | |   (536)  all_4_0 = e1
% 177.22/27.81  | | | | | 
% 177.22/27.81  | | | | | REDUCE: (88), (536) imply:
% 177.22/27.81  | | | | |   (537)  op(all_4_1, all_4_2) = e1
% 177.22/27.81  | | | | | 
% 177.22/27.81  | | | | | BETA: splitting (164) gives:
% 177.22/27.81  | | | | | 
% 177.22/27.81  | | | | | Case 1:
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | |   (538)  all_58_15 = e0
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | COMBINE_EQS: (36), (538) imply:
% 177.22/27.81  | | | | | |   (539)  all_6_2 = e0
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (43), (539) imply:
% 177.22/27.81  | | | | | |   (540)   ~ (all_52_15 = e0)
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (144), (539) imply:
% 177.22/27.81  | | | | | |   (541)   ~ (all_52_23 = e0)
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (153), (539) imply:
% 177.22/27.81  | | | | | |   (542)   ~ (all_52_25 = e0)
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (146), (539) imply:
% 177.22/27.81  | | | | | |   (543)   ~ (all_52_29 = e0)
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (93), (539) imply:
% 177.22/27.81  | | | | | |   (544)  op(all_6_1, e0) = all_6_0
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (96), (539) imply:
% 177.22/27.81  | | | | | |   (545)  op(e0, e0) = all_6_1
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (60), (539) imply:
% 177.22/27.81  | | | | | |   (546)  op(e0, e0) = e0
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_1, e0, e0,
% 177.22/27.81  | | | | | |              simplifying with (545), (546) gives:
% 177.22/27.81  | | | | | |   (547)  all_6_1 = e0
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (544), (547) imply:
% 177.22/27.81  | | | | | |   (548)  op(e0, e0) = all_6_0
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, e0, e0,
% 177.22/27.81  | | | | | |              simplifying with (546), (548) gives:
% 177.22/27.81  | | | | | |   (549)  all_6_0 = e0
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (211), (549) imply:
% 177.22/27.81  | | | | | |   (550)   ~ (e3 = e0)
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | REDUCE: (181), (549) imply:
% 177.22/27.81  | | | | | |   (551)   ~ (e1 = e0)
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | BETA: splitting (169) gives:
% 177.22/27.81  | | | | | | 
% 177.22/27.81  | | | | | | Case 1:
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | |   (552)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.22/27.81  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.22/27.81  | | | | | | |            e1 & all_52_14 = e0)
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | | BETA: splitting (552) gives:
% 177.22/27.81  | | | | | | | 
% 177.22/27.81  | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | |   (553)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.81  | | | | | | | |          all_52_6 = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REF_CLOSE: (48), (52), (97), (167), (537), (553) are
% 177.22/27.81  | | | | | | | |            inconsistent by sub-proof #600.
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | |   (554)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.81  | | | | | | | |          all_52_14 = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | ALPHA: (554) implies:
% 177.22/27.81  | | | | | | | |   (555)  all_52_14 = e0
% 177.22/27.81  | | | | | | | |   (556)  all_52_12 = e1
% 177.22/27.81  | | | | | | | |   (557)  all_52_10 = e2
% 177.22/27.81  | | | | | | | |   (558)  all_52_8 = e3
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | COMBINE_EQS: (100), (557) imply:
% 177.22/27.81  | | | | | | | |   (559)  all_10_1 = e2
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (114), (559) imply:
% 177.22/27.81  | | | | | | | |   (560)  op(e2, all_10_2) = all_10_0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (22), (558) imply:
% 177.22/27.81  | | | | | | | |   (561)  op(e3, all_52_9) = e3
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (9), (559) imply:
% 177.22/27.81  | | | | | | | |   (562)  op(e2, all_10_2) = e2
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (59), (556) imply:
% 177.22/27.81  | | | | | | | |   (563)  op(e1, all_52_13) = e1
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | REDUCE: (139), (555) imply:
% 177.22/27.81  | | | | | | | |   (564)  op(e0, all_52_15) = e0
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | GROUND_INST: instantiating (167) with e2, all_10_0, all_10_2,
% 177.22/27.81  | | | | | | | |              e2, simplifying with (560), (562) gives:
% 177.22/27.81  | | | | | | | |   (565)  all_10_0 = e2
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | BETA: splitting (74) gives:
% 177.22/27.81  | | | | | | | | 
% 177.22/27.81  | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | |   (566)  all_56_13 = e3
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | COMBINE_EQS: (205), (566) imply:
% 177.22/27.81  | | | | | | | | |   (567)  all_52_27 = e3
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | SIMP: (567) implies:
% 177.22/27.81  | | | | | | | | |   (568)  all_52_27 = e3
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REF_CLOSE: (2), (6), (15), (16), (20), (27), (30), (33), (35),
% 177.22/27.81  | | | | | | | | |            (37), (39), (40), (42), (46), (48), (49), (50),
% 177.22/27.81  | | | | | | | | |            (51), (52), (54), (58), (65), (71), (73), (78),
% 177.22/27.81  | | | | | | | | |            (79), (82), (83), (86), (91), (92), (95), (109),
% 177.22/27.81  | | | | | | | | |            (126), (129), (132), (134), (147), (157), (161),
% 177.22/27.81  | | | | | | | | |            (163), (166), (167), (170), (171), (182), (192),
% 177.22/27.81  | | | | | | | | |            (195), (197), (198), (204), (535), (537), (561),
% 177.22/27.81  | | | | | | | | |            (563), (564), (568) are inconsistent by sub-proof
% 177.22/27.81  | | | | | | | | |            #362.
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | |   (569)   ~ (all_56_13 = e3)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | REDUCE: (205), (569) imply:
% 177.22/27.81  | | | | | | | | |   (570)   ~ (all_52_27 = e3)
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | BETA: splitting (81) gives:
% 177.22/27.81  | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | |   (571)  all_58_12 = e3
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | COMBINE_EQS: (192), (571) imply:
% 177.22/27.81  | | | | | | | | | |   (572)  all_52_25 = e3
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | SIMP: (572) implies:
% 177.22/27.81  | | | | | | | | | |   (573)  all_52_25 = e3
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | REDUCE: (44), (573) imply:
% 177.22/27.81  | | | | | | | | | |   (574)   ~ (all_52_17 = e3)
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | REDUCE: (170), (573) imply:
% 177.22/27.81  | | | | | | | | | |   (575)   ~ (all_52_27 = e3)
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | REDUCE: (28), (573) imply:
% 177.22/27.81  | | | | | | | | | |   (576)   ~ (all_52_29 = e3)
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | SIMP: (576) implies:
% 177.22/27.81  | | | | | | | | | |   (577)   ~ (all_52_29 = e3)
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | REDUCE: (17), (573) imply:
% 177.22/27.81  | | | | | | | | | |   (578)  op(e3, e3) = all_52_24
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | REDUCE: (95), (573) imply:
% 177.22/27.81  | | | | | | | | | |   (579)  op(e0, e3) = e3
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | GROUND_INST: instantiating (167) with all_4_2, all_52_24, e3,
% 177.22/27.81  | | | | | | | | | |              e3, simplifying with (163), (578) gives:
% 177.22/27.81  | | | | | | | | | |   (580)  all_52_24 = all_4_2
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | BETA: splitting (149) gives:
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | |   (581)  all_56_11 = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | COMBINE_EQS: (19), (581) imply:
% 177.22/27.81  | | | | | | | | | | |   (582)  all_52_23 = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | SIMP: (582) implies:
% 177.22/27.81  | | | | | | | | | | |   (583)  all_52_23 = e3
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | REDUCE: (18), (583) imply:
% 177.22/27.81  | | | | | | | | | | |   (584)   ~ (all_52_19 = e3)
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | BETA: splitting (70) gives:
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | |   (585)  all_58_1 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | COMBINE_EQS: (56), (585) imply:
% 177.22/27.81  | | | | | | | | | | | |   (586)  all_52_3 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | REDUCE: (78), (586) imply:
% 177.22/27.81  | | | | | | | | | | | |   (587)   ~ (all_52_5 = e3)
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | SIMP: (587) implies:
% 177.22/27.81  | | | | | | | | | | | |   (588)   ~ (all_52_5 = e3)
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | REF_CLOSE: (14), (15), (20), (27), (30), (35), (46), (49),
% 177.22/27.81  | | | | | | | | | | | |            (51), (52), (55), (58), (65), (67), (73), (79),
% 177.22/27.81  | | | | | | | | | | | |            (82), (83), (86), (92), (117), (132), (134),
% 177.22/27.81  | | | | | | | | | | | |            (157), (162), (163), (166), (167), (171), (179),
% 177.22/27.81  | | | | | | | | | | | |            (186), (198), (535), (537), (563), (574), (577),
% 177.22/27.81  | | | | | | | | | | | |            (588) are inconsistent by sub-proof #361.
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | |   (589)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | REF_CLOSE: (15), (24), (33), (41), (119), (167), (204),
% 177.22/27.81  | | | | | | | | | | | |            (561), (562), (570), (584), (589) are inconsistent
% 177.22/27.81  | | | | | | | | | | | |            by sub-proof #975.
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | |   (590)   ~ (all_56_11 = e3)
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | REDUCE: (19), (590) imply:
% 177.22/27.81  | | | | | | | | | | |   (591)   ~ (all_52_23 = e3)
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | BETA: splitting (184) gives:
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | |   (592)  all_58_9 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | COMBINE_EQS: (189), (592) imply:
% 177.22/27.81  | | | | | | | | | | | |   (593)  all_52_7 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | SIMP: (593) implies:
% 177.22/27.81  | | | | | | | | | | | |   (594)  all_52_7 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | REDUCE: (38), (594) imply:
% 177.22/27.81  | | | | | | | | | | | |   (595)   ~ (all_52_5 = e3)
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | REF_CLOSE: (14), (15), (20), (27), (30), (35), (46), (49),
% 177.22/27.81  | | | | | | | | | | | |            (51), (52), (55), (58), (65), (67), (73), (79),
% 177.22/27.81  | | | | | | | | | | | |            (82), (83), (86), (92), (117), (132), (134),
% 177.22/27.81  | | | | | | | | | | | |            (157), (162), (163), (166), (167), (171), (179),
% 177.22/27.81  | | | | | | | | | | | |            (186), (198), (535), (537), (563), (574), (577),
% 177.22/27.81  | | | | | | | | | | | |            (595) are inconsistent by sub-proof #361.
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | |   (596)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | BETA: splitting (596) gives:
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | |   (597)  all_58_10 = e3
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | COMBINE_EQS: (39), (597) imply:
% 177.22/27.81  | | | | | | | | | | | | |   (598)  all_52_15 = e3
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | REF_CLOSE: (167), (540), (564), (579), (598) are inconsistent
% 177.22/27.81  | | | | | | | | | | | | |            by sub-proof #971.
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | |   (599)  all_58_11 = e3 | all_58_15 = e3
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | BETA: splitting (599) gives:
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | Case 1:
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | |   (600)  all_58_11 = e3
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | REF_CLOSE: (133), (591), (600) are inconsistent by sub-proof
% 177.22/27.81  | | | | | | | | | | | | | |            #1017.
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | Case 2:
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | |   (601)  all_58_15 = e3
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | | REF_CLOSE: (104), (538), (601) are inconsistent by sub-proof
% 177.22/27.81  | | | | | | | | | | | | | |            #1010.
% 177.22/27.81  | | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | | 
% 177.22/27.81  | | | | | | | | | | End of split
% 177.22/27.81  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | |   (602)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (20), (27), (28), (30),
% 177.22/27.82  | | | | | | | | | |            (33), (35), (37), (39), (49), (52), (54), (55),
% 177.22/27.82  | | | | | | | | | |            (58), (65), (67), (73), (79), (83), (92), (95),
% 177.22/27.82  | | | | | | | | | |            (104), (110), (117), (118), (119), (132), (134),
% 177.22/27.82  | | | | | | | | | |            (147), (148), (158), (161), (162), (163), (167),
% 177.22/27.82  | | | | | | | | | |            (171), (178), (179), (186), (192), (204), (535),
% 177.22/27.82  | | | | | | | | | |            (537), (538), (542), (561), (562), (564), (570),
% 177.22/27.82  | | | | | | | | | |            (602) are inconsistent by sub-proof #583.
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | End of split
% 177.22/27.82  | | | | | | | | | 
% 177.22/27.82  | | | | | | | | End of split
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | End of split
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | Case 2:
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | |   (603)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.82  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.82  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | BETA: splitting (603) gives:
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | |   (604)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.82  | | | | | | | |          all_52_22 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | REF_CLOSE: (48), (128), (604) are inconsistent by sub-proof
% 177.22/27.82  | | | | | | | |            #427.
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | |   (605)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.82  | | | | | | | |          all_52_30 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | REF_CLOSE: (4), (6), (14), (15), (16), (17), (18), (19), (20),
% 177.22/27.82  | | | | | | | |            (24), (27), (28), (34), (35), (38), (40), (41), (44),
% 177.22/27.82  | | | | | | | |            (46), (47), (48), (50), (52), (55), (58), (61), (66),
% 177.22/27.82  | | | | | | | |            (67), (68), (69), (73), (74), (80), (81), (82), (85),
% 177.22/27.82  | | | | | | | |            (86), (90), (91), (92), (99), (104), (110), (113),
% 177.22/27.82  | | | | | | | |            (115), (117), (118), (119), (122), (123), (124),
% 177.22/27.82  | | | | | | | |            (126), (131), (132), (133), (134), (140), (141),
% 177.22/27.82  | | | | | | | |            (148), (149), (150), (152), (154), (156), (157),
% 177.22/27.82  | | | | | | | |            (160), (161), (162), (163), (167), (170), (176),
% 177.22/27.82  | | | | | | | |            (179), (180), (182), (186), (188), (192), (201),
% 177.22/27.82  | | | | | | | |            (204), (205), (538), (541), (542), (543), (605) are
% 177.22/27.82  | | | | | | | |            inconsistent by sub-proof #421.
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | End of split
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | End of split
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | Case 2:
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | |   (606)   ~ (all_58_15 = e0)
% 177.22/27.82  | | | | | |   (607)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.82  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | ALPHA: (607) implies:
% 177.22/27.82  | | | | | |   (608)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.82  | | | | | |   (609)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | REDUCE: (36), (606) imply:
% 177.22/27.82  | | | | | |   (610)   ~ (all_6_2 = e0)
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | BETA: splitting (169) gives:
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | Case 1:
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | |   (611)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.22/27.82  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.22/27.82  | | | | | | |            e1 & all_52_14 = e0)
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (13), (14), (15), (16),
% 177.22/27.82  | | | | | | |            (18), (19), (20), (22), (24), (27), (28), (29), (30),
% 177.22/27.82  | | | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 177.22/27.82  | | | | | | |            (42), (43), (44), (46), (47), (48), (49), (50), (51),
% 177.22/27.82  | | | | | | |            (52), (53), (54), (55), (56), (58), (59), (61), (65),
% 177.22/27.82  | | | | | | |            (66), (67), (69), (70), (71), (73), (74), (78), (79),
% 177.22/27.82  | | | | | | |            (80), (81), (82), (83), (86), (89), (91), (92), (95),
% 177.22/27.82  | | | | | | |            (97), (99), (100), (103), (104), (109), (111), (112),
% 177.22/27.82  | | | | | | |            (113), (114), (117), (119), (121), (124), (126), (127),
% 177.22/27.82  | | | | | | |            (129), (130), (131), (132), (133), (134), (135), (136),
% 177.22/27.82  | | | | | | |            (139), (140), (141), (144), (146), (147), (149), (150),
% 177.22/27.82  | | | | | | |            (152), (153), (157), (161), (162), (163), (166), (167),
% 177.22/27.82  | | | | | | |            (170), (171), (172), (173), (174), (179), (182), (183),
% 177.22/27.82  | | | | | | |            (184), (186), (187), (189), (192), (195), (196), (197),
% 177.22/27.82  | | | | | | |            (198), (201), (204), (205), (207), (535), (537), (609),
% 177.22/27.82  | | | | | | |            (610), (611) are inconsistent by sub-proof #356.
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | Case 2:
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | |   (612)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.82  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.82  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | BETA: splitting (612) gives:
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | |   (613)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.82  | | | | | | | |          all_52_22 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | REF_CLOSE: (48), (128), (613) are inconsistent by sub-proof
% 177.22/27.82  | | | | | | | |            #427.
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | |   (614)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.82  | | | | | | | |          all_52_30 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | ALPHA: (614) implies:
% 177.22/27.82  | | | | | | | |   (615)  all_52_30 = e0
% 177.22/27.82  | | | | | | | |   (616)  all_52_28 = e1
% 177.22/27.82  | | | | | | | |   (617)  all_52_26 = e2
% 177.22/27.82  | | | | | | | |   (618)  all_52_24 = e3
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | COMBINE_EQS: (185), (615) imply:
% 177.22/27.82  | | | | | | | |   (619)  all_6_1 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | SIMP: (619) implies:
% 177.22/27.82  | | | | | | | |   (620)  all_6_1 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | REF_CLOSE: (4), (8), (13), (14), (15), (16), (17), (18), (20),
% 177.22/27.82  | | | | | | | |            (21), (22), (25), (27), (29), (30), (33), (35), (36),
% 177.22/27.82  | | | | | | | |            (37), (38), (39), (41), (45), (46), (48), (49), (50),
% 177.22/27.82  | | | | | | | |            (51), (52), (53), (55), (56), (57), (58), (61), (65),
% 177.22/27.82  | | | | | | | |            (67), (73), (74), (78), (79), (81), (82), (83), (84),
% 177.22/27.82  | | | | | | | |            (86), (92), (93), (95), (96), (98), (101), (109),
% 177.22/27.82  | | | | | | | |            (110), (116), (117), (118), (119), (121), (126),
% 177.22/27.82  | | | | | | | |            (132), (133), (134), (140), (145), (147), (150),
% 177.22/27.82  | | | | | | | |            (155), (156), (157), (161), (162), (163), (166),
% 177.22/27.82  | | | | | | | |            (167), (170), (171), (172), (173), (179), (181),
% 177.22/27.82  | | | | | | | |            (182), (183), (184), (186), (189), (192), (197),
% 177.22/27.82  | | | | | | | |            (198), (199), (200), (204), (205), (211), (535),
% 177.22/27.82  | | | | | | | |            (537), (608), (616), (617), (618), (620) are
% 177.22/27.82  | | | | | | | |            inconsistent by sub-proof #354.
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | End of split
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | End of split
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | End of split
% 177.22/27.82  | | | | | 
% 177.22/27.82  | | | | End of split
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | Case 2:
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | |   (621)  all_28_0 = e3
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | | COMBINE_EQS: (203), (621) imply:
% 177.22/27.82  | | | |   (622)  all_6_0 = e3
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | | SIMP: (622) implies:
% 177.22/27.82  | | | |   (623)  all_6_0 = e3
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | | COMBINE_EQS: (11), (623) imply:
% 177.22/27.82  | | | |   (624)  all_36_0 = e3
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | | REDUCE: (93), (623) imply:
% 177.22/27.82  | | | |   (625)  op(all_6_1, all_6_2) = e3
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | | BETA: splitting (142) gives:
% 177.22/27.82  | | | | 
% 177.22/27.82  | | | | Case 1:
% 177.22/27.82  | | | | | 
% 177.22/27.82  | | | | |   (626)   ~ (all_34_0 = e1)
% 177.22/27.82  | | | | | 
% 177.22/27.82  | | | | | REDUCE: (193), (626) imply:
% 177.22/27.82  | | | | |   (627)   ~ (all_4_0 = e1)
% 177.22/27.82  | | | | | 
% 177.22/27.82  | | | | | BETA: splitting (94) gives:
% 177.22/27.82  | | | | | 
% 177.22/27.82  | | | | | Case 1:
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | |   (628)   ~ (all_36_0 = e3)
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | REDUCE: (624), (628) imply:
% 177.22/27.82  | | | | | |   (629)  $false
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | CLOSE: (629) is inconsistent.
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | Case 2:
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | |   (630)   ~ (all_36_1 = e1) |  ~ (all_36_2 = e2)
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | BETA: splitting (177) gives:
% 177.22/27.82  | | | | | | 
% 177.22/27.82  | | | | | | Case 1:
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | |   (631)   ~ (all_40_1 = e1)
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | REDUCE: (76), (631) imply:
% 177.22/27.82  | | | | | | |   (632)   ~ (all_4_1 = e1)
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | BETA: splitting (164) gives:
% 177.22/27.82  | | | | | | | 
% 177.22/27.82  | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | |   (633)  all_58_15 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | REF_CLOSE: (36), (60), (96), (104), (167), (625), (633) are
% 177.22/27.82  | | | | | | | |            inconsistent by sub-proof #510.
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | |   (634)   ~ (all_58_15 = e0)
% 177.22/27.82  | | | | | | | |   (635)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.82  | | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | ALPHA: (635) implies:
% 177.22/27.82  | | | | | | | |   (636)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.82  | | | | | | | |   (637)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | REDUCE: (36), (634) imply:
% 177.22/27.82  | | | | | | | |   (638)   ~ (all_6_2 = e0)
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | BETA: splitting (169) gives:
% 177.22/27.82  | | | | | | | | 
% 177.22/27.82  | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | 
% 177.22/27.82  | | | | | | | | |   (639)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.82  | | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.82  | | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.82  | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | BETA: splitting (639) gives:
% 177.22/27.82  | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | |   (640)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.82  | | | | | | | | | |          all_52_6 = e0
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REF_CLOSE: (1), (2), (8), (13), (15), (16), (18), (19), (20),
% 177.22/27.82  | | | | | | | | | |            (21), (24), (27), (28), (29), (30), (31), (32),
% 177.22/27.82  | | | | | | | | | |            (33), (35), (36), (37), (38), (39), (40), (41),
% 177.22/27.82  | | | | | | | | | |            (42), (43), (44), (45), (46), (47), (50), (51),
% 177.22/27.82  | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (61),
% 177.22/27.82  | | | | | | | | | |            (63), (65), (68), (69), (70), (72), (73), (74),
% 177.22/27.82  | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (85), (88),
% 177.22/27.82  | | | | | | | | | |            (90), (91), (92), (95), (96), (97), (102), (103),
% 177.22/27.82  | | | | | | | | | |            (104), (106), (109), (110), (111), (112), (113),
% 177.22/27.82  | | | | | | | | | |            (115), (116), (117), (118), (119), (120), (121),
% 177.22/27.82  | | | | | | | | | |            (123), (124), (126), (127), (129), (131), (132),
% 177.22/27.82  | | | | | | | | | |            (133), (134), (135), (136), (139), (140), (144),
% 177.22/27.82  | | | | | | | | | |            (146), (147), (148), (149), (150), (152), (153),
% 177.22/27.82  | | | | | | | | | |            (155), (156), (157), (158), (161), (162), (166),
% 177.22/27.82  | | | | | | | | | |            (167), (170), (172), (173), (176), (178), (179),
% 177.22/27.82  | | | | | | | | | |            (180), (182), (183), (184), (189), (192), (196),
% 177.22/27.82  | | | | | | | | | |            (197), (198), (200), (201), (202), (204), (205),
% 177.22/27.82  | | | | | | | | | |            (209), (625), (627), (637), (638), (640) are
% 177.22/27.82  | | | | | | | | | |            inconsistent by sub-proof #436.
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | |   (641)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.82  | | | | | | | | | |          all_52_14 = e0
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | ALPHA: (641) implies:
% 177.22/27.82  | | | | | | | | | |   (642)  all_52_14 = e0
% 177.22/27.82  | | | | | | | | | |   (643)  all_52_12 = e1
% 177.22/27.82  | | | | | | | | | |   (644)  all_52_10 = e2
% 177.22/27.82  | | | | | | | | | |   (645)  all_52_8 = e3
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | COMBINE_EQS: (100), (644) imply:
% 177.22/27.82  | | | | | | | | | |   (646)  all_10_1 = e2
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REDUCE: (114), (646) imply:
% 177.22/27.82  | | | | | | | | | |   (647)  op(e2, all_10_2) = all_10_0
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REDUCE: (22), (645) imply:
% 177.22/27.82  | | | | | | | | | |   (648)  op(e3, all_52_9) = e3
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REDUCE: (9), (646) imply:
% 177.22/27.82  | | | | | | | | | |   (649)  op(e2, all_10_2) = e2
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REDUCE: (59), (643) imply:
% 177.22/27.82  | | | | | | | | | |   (650)  op(e1, all_52_13) = e1
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REDUCE: (139), (642) imply:
% 177.22/27.82  | | | | | | | | | |   (651)  op(e0, all_52_15) = e0
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | GROUND_INST: instantiating (167) with e2, all_10_0, all_10_2,
% 177.22/27.82  | | | | | | | | | |              e2, simplifying with (647), (649) gives:
% 177.22/27.82  | | | | | | | | | |   (652)  all_10_0 = e2
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | REDUCE: (174), (652) imply:
% 177.22/27.82  | | | | | | | | | |   (653)   ~ (e3 = e2)
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | BETA: splitting (53) gives:
% 177.22/27.82  | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | |   (654)  all_56_15 = e3
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | COMBINE_EQS: (29), (654) imply:
% 177.22/27.82  | | | | | | | | | | |   (655)  all_6_2 = e3
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | SIMP: (655) implies:
% 177.22/27.82  | | | | | | | | | | |   (656)  all_6_2 = e3
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (173), (656) imply:
% 177.22/27.82  | | | | | | | | | | |   (657)   ~ (all_52_7 = e3)
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (43), (656) imply:
% 177.22/27.82  | | | | | | | | | | |   (658)   ~ (all_52_15 = e3)
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (153), (656) imply:
% 177.22/27.82  | | | | | | | | | | |   (659)   ~ (all_52_25 = e3)
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (146), (656) imply:
% 177.22/27.82  | | | | | | | | | | |   (660)   ~ (all_52_29 = e3)
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (625), (656) imply:
% 177.22/27.82  | | | | | | | | | | |   (661)  op(all_6_1, e3) = e3
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (96), (656) imply:
% 177.22/27.82  | | | | | | | | | | |   (662)  op(e0, e3) = all_6_1
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_25, all_6_1, e3,
% 177.22/27.82  | | | | | | | | | | |              e0, simplifying with (95), (662) gives:
% 177.22/27.82  | | | | | | | | | | |   (663)  all_52_25 = all_6_1
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | COMBINE_EQS: (118), (663) imply:
% 177.22/27.82  | | | | | | | | | | |   (664)  all_56_12 = all_6_1
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | COMBINE_EQS: (192), (663) imply:
% 177.22/27.82  | | | | | | | | | | |   (665)  all_58_12 = all_6_1
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (161), (663) imply:
% 177.22/27.82  | | | | | | | | | | |   (666)   ~ (all_6_1 = all_4_2)
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (659), (663) imply:
% 177.22/27.82  | | | | | | | | | | |   (667)   ~ (all_6_1 = e3)
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | BETA: splitting (110) gives:
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | |   (668)  all_56_12 = e3
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REF_CLOSE: (664), (667), (668) are inconsistent by sub-proof
% 177.22/27.82  | | | | | | | | | | | |            #509.
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | |   (669)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | BETA: splitting (70) gives:
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | |   (670)  all_58_1 = e3
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | REF_CLOSE: (27), (37), (46), (47), (48), (51), (56), (58),
% 177.22/27.82  | | | | | | | | | | | | |            (73), (78), (79), (82), (86), (92), (126), (147),
% 177.22/27.82  | | | | | | | | | | | | |            (157), (163), (167), (192), (198), (648), (650),
% 177.22/27.82  | | | | | | | | | | | | |            (659), (660), (670) are inconsistent by sub-proof
% 177.22/27.82  | | | | | | | | | | | | |            #393.
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | |   (671)   ~ (all_58_1 = e3)
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | REDUCE: (56), (671) imply:
% 177.22/27.82  | | | | | | | | | | | | |   (672)   ~ (all_52_3 = e3)
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | BETA: splitting (196) gives:
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | |   (673)  all_58_0 = e3
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REF_CLOSE: (37), (58), (148), (155), (157), (166), (167),
% 177.22/27.82  | | | | | | | | | | | | | |            (204), (661), (662), (664), (665), (666), (669),
% 177.22/27.82  | | | | | | | | | | | | | |            (673) are inconsistent by sub-proof #497.
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | |   (674)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (24), (27), (33), (37), (39), (46),
% 177.22/27.82  | | | | | | | | | | | | | |            (54), (56), (147), (163), (167), (189), (204),
% 177.22/27.82  | | | | | | | | | | | | | |            (648), (649), (657), (658), (672), (674) are
% 177.22/27.82  | | | | | | | | | | | | | |            inconsistent by sub-proof #360.
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | End of split
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | End of split
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | End of split
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | |   (675)   ~ (all_56_15 = e3)
% 177.22/27.82  | | | | | | | | | | |   (676)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | REDUCE: (29), (675) imply:
% 177.22/27.82  | | | | | | | | | | |   (677)   ~ (all_6_2 = e3)
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | BETA: splitting (74) gives:
% 177.22/27.82  | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | |   (678)  all_56_13 = e3
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | COMBINE_EQS: (205), (678) imply:
% 177.22/27.82  | | | | | | | | | | | |   (679)  all_52_27 = e3
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | COMBINE_EQS: (119), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (680)  all_58_13 = e3
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (91), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (681)   ~ (all_52_3 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (176), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (682)   ~ (all_52_19 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (170), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (683)   ~ (all_52_25 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (50), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (684)   ~ (all_52_29 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | SIMP: (684) implies:
% 177.22/27.82  | | | | | | | | | | | |   (685)   ~ (all_52_29 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (6), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (686)   ~ (all_10_2 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | SIMP: (686) implies:
% 177.22/27.82  | | | | | | | | | | | |   (687)   ~ (all_10_2 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (172), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (688)   ~ (all_6_2 = e3)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (182), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (689)  op(e2, e3) = all_52_26
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (84), (679) imply:
% 177.22/27.82  | | | | | | | | | | | |   (690)  op(e0, e2) = e3
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_9, all_52_26, e3,
% 177.22/27.82  | | | | | | | | | | | |              e2, simplifying with (204), (689) gives:
% 177.22/27.82  | | | | | | | | | | | |   (691)  all_52_9 = all_52_26
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | COMBINE_EQS: (42), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (692)  all_56_4 = all_52_26
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | COMBINE_EQS: (147), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (693)  all_58_2 = all_52_26
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (109), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (694)   ~ (all_52_13 = all_52_26)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | SIMP: (694) implies:
% 177.22/27.82  | | | | | | | | | | | |   (695)   ~ (all_52_13 = all_52_26)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (197), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (696)   ~ (all_52_15 = all_52_26)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | SIMP: (696) implies:
% 177.22/27.82  | | | | | | | | | | | |   (697)   ~ (all_52_15 = all_52_26)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (16), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (698)   ~ (all_52_25 = all_52_26)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | SIMP: (698) implies:
% 177.22/27.82  | | | | | | | | | | | |   (699)   ~ (all_52_25 = all_52_26)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (98), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (700)   ~ (all_52_26 = all_10_2)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (37), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (701)   ~ (all_52_26 = all_4_2)
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | REDUCE: (648), (691) imply:
% 177.22/27.82  | | | | | | | | | | | |   (702)  op(e3, all_52_26) = e3
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | BETA: splitting (65) gives:
% 177.22/27.82  | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | |   (703)  all_56_1 = e3
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | COMBINE_EQS: (83), (703) imply:
% 177.22/27.82  | | | | | | | | | | | | |   (704)  all_52_3 = e3
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | REDUCE: (681), (704) imply:
% 177.22/27.82  | | | | | | | | | | | | |   (705)  $false
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | CLOSE: (705) is inconsistent.
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | |   (706)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | BETA: splitting (158) gives:
% 177.22/27.82  | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | |   (707)  all_56_7 = e3
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | COMBINE_EQS: (178), (707) imply:
% 177.22/27.82  | | | | | | | | | | | | | |   (708)  all_52_15 = e3
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | SIMP: (708) implies:
% 177.22/27.82  | | | | | | | | | | | | | |   (709)  all_52_15 = e3
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | COMBINE_EQS: (39), (709) imply:
% 177.22/27.82  | | | | | | | | | | | | | |   (710)  all_58_10 = e3
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REDUCE: (57), (709) imply:
% 177.22/27.82  | | | | | | | | | | | | | |   (711)   ~ (all_52_13 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REDUCE: (112), (709) imply:
% 177.22/27.82  | | | | | | | | | | | | | |   (712)   ~ (all_52_23 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | SIMP: (712) implies:
% 177.22/27.82  | | | | | | | | | | | | | |   (713)   ~ (all_52_23 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REDUCE: (697), (709) imply:
% 177.22/27.82  | | | | | | | | | | | | | |   (714)   ~ (all_52_26 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | SIMP: (714) implies:
% 177.22/27.82  | | | | | | | | | | | | | |   (715)   ~ (all_52_26 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REDUCE: (651), (709) imply:
% 177.22/27.82  | | | | | | | | | | | | | |   (716)  op(e0, e3) = e0
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (15), (17), (18), (24), (26), (27),
% 177.22/27.82  | | | | | | | | | | | | | |            (33), (35), (36), (39), (40), (41), (46), (51),
% 177.22/27.82  | | | | | | | | | | | | | |            (52), (55), (56), (58), (73), (78), (79), (82),
% 177.22/27.82  | | | | | | | | | | | | | |            (83), (88), (92), (95), (117), (121), (126),
% 177.22/27.82  | | | | | | | | | | | | | |            (127), (129), (132), (133), (150), (161), (162),
% 177.22/27.82  | | | | | | | | | | | | | |            (163), (167), (184), (189), (192), (198), (627),
% 177.22/27.82  | | | | | | | | | | | | | |            (632), (637), (650), (651), (677), (680), (683),
% 177.22/27.82  | | | | | | | | | | | | | |            (685), (692), (693), (697), (699), (700), (701),
% 177.22/27.82  | | | | | | | | | | | | | |            (702), (706), (710), (711), (713), (715), (716)
% 177.22/27.82  | | | | | | | | | | | | | |            are inconsistent by sub-proof #756.
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | |   (717)   ~ (all_56_7 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | REDUCE: (178), (717) imply:
% 177.22/27.82  | | | | | | | | | | | | | |   (718)   ~ (all_52_15 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 177.22/27.82  | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | |   (719)  all_58_9 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | COMBINE_EQS: (189), (719) imply:
% 177.22/27.82  | | | | | | | | | | | | | | |   (720)  all_52_7 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | REF_CLOSE: (13), (27), (33), (38), (39), (41), (44), (46),
% 177.22/27.82  | | | | | | | | | | | | | | |            (47), (48), (51), (54), (55), (58), (73), (79),
% 177.22/27.82  | | | | | | | | | | | | | | |            (82), (103), (126), (133), (136), (157), (163),
% 177.22/27.82  | | | | | | | | | | | | | | |            (167), (179), (192), (198), (650), (682), (687),
% 177.22/27.82  | | | | | | | | | | | | | | |            (693), (695), (701), (702), (720) are inconsistent
% 177.22/27.82  | | | | | | | | | | | | | | |            by sub-proof #983.
% 177.22/27.82  | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | |   (721)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | BETA: splitting (721) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | |   (722)  all_58_10 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (718), (722) are inconsistent by sub-proof
% 177.22/27.82  | | | | | | | | | | | | | | | |            #1018.
% 177.22/27.82  | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | |   (723)  all_58_11 = e3 | all_58_15 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | BETA: splitting (723) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | |   (724)  all_58_11 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (724) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | |   (725)  all_52_23 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | SIMP: (725) implies:
% 177.22/27.82  | | | | | | | | | | | | | | | | |   (726)  all_52_23 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | REDUCE: (8), (726) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | |   (727)   ~ (all_52_17 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | |   (728)  all_58_2 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (693), (728) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | |   (729)  all_52_26 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | SIMP: (729) implies:
% 177.22/27.82  | | | | | | | | | | | | | | | | | |   (730)  all_52_26 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (701), (702), (730) are inconsistent
% 177.22/27.82  | | | | | | | | | | | | | | | | | |            by sub-proof #1005.
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | |   (731)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | |   (732)  all_58_0 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (732) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | |   (733)  all_4_2 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | REDUCE: (88), (733) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | |   (734)  op(all_4_1, e3) = all_4_0
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | REDUCE: (52), (733) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | |   (735)  op(e3, e3) = all_4_1
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | REDUCE: (163), (733) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | |   (736)  op(e3, e3) = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (731) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | |   (737)  all_58_3 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (737) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | |   (738)  all_10_2 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (687), (738) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | |   (739)  $false
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | CLOSE: (739) is inconsistent.
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | |   (740)  all_58_5 = e3 | all_58_10 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (740) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (741)  all_58_5 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (741) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (742)  all_52_13 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | SIMP: (742) implies:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (743)  all_52_13 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (743) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (744)   ~ (all_52_5 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (743) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (745)  op(e2, e1) = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (650), (743) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (746)  op(e1, e3) = e1
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_17, e1, e3, e1,
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |              simplifying with (157), (746) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (747)  all_52_17 = e1
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with e3, all_4_1, e3, e3,
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |              simplifying with (735), (736) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (748)  all_4_1 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (747) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (749)   ~ (all_52_19 = e1)
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | SIMP: (749) implies:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (750)   ~ (all_52_19 = e1)
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (747) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (751)   ~ (all_14_2 = e1)
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | SIMP: (751) implies:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (752)   ~ (all_14_2 = e1)
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (734), (748) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (753)  op(e3, e3) = all_4_0
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (747) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (754)  op(e3, e1) = all_52_16
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_5, all_52_16, e1,
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (150), (754) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (755)  all_52_5 = all_52_16
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with e3, all_4_0, e3, e3,
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |              simplifying with (736), (753) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (756)  all_4_0 = e3
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (755) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (757)  all_58_4 = all_52_16
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (755) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (758)   ~ (all_52_3 = all_52_16)
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (744), (755) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | |   (759)   ~ (all_52_16 = e3)
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | |   (760)  all_58_4 = e1
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (757), (760) imply:
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | |   (761)  all_52_16 = e1
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.82  | | | | | | | | | | | | | | | | | | | | | | SIMP: (761) implies:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | |   (762)  all_52_16 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (758), (762) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | |   (763)   ~ (all_52_3 = e1)
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (759), (762) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | |   (764)   ~ (e3 = e1)
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |   (765)  all_58_1 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (765) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |   (766)  all_52_3 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (763), (766) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |   (767)  $false
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (767) is inconsistent.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |   (768)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (41), (48), (167), (199), (649), (680),
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |            (745), (750), (768) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |            #767.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | |   (769)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |   (770)  all_58_5 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (741), (770) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |            #816.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | |   (771)  all_58_8 = e1 | all_58_14 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (771) gives:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | |   (772)  all_58_8 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (752), (772) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | |            #815.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | |   (773)  all_58_14 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (773) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | |   (774)  all_52_29 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (774) implies:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | |   (775)  all_52_29 = e1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (775) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | |   (776)   ~ (all_6_2 = e1)
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (776) implies:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | |   (777)   ~ (all_6_2 = e1)
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (676) gives:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (778)  all_56_15 = e2
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (778) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (779)  all_6_2 = e2
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (779) implies:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (780)  all_6_2 = e2
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (780) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (781)  all_36_2 = e2
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (625), (780) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (782)  op(all_6_1, e2) = e3
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (96), (780) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (783)  op(e0, e2) = all_6_1
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (630) gives:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with e3, all_6_1, e2, e0,
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (690), (783) gives:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (784)  all_6_1 = e3
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (782), (784) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (785)  op(e3, e2) = e3
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (167), (681), (785) are inconsistent by
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #978.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (786)   ~ (all_36_2 = e2)
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (781), (786) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  $false
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (787) is inconsistent.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  all_56_15 = e1 | all_56_15 = e0
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (638), (777), (788) are inconsistent by
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | |   (789)  all_58_10 = e3
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (718), (789) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | |            #1018.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | |   (790)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (126), (147), (163), (167), (192), (648),
% 177.22/27.83  | | | | | | | | | | | | | | | | | | |            (683), (727), (790) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | | | | | | | | | | | |            #396.
% 177.22/27.83  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | |   (791)  all_58_15 = e3
% 177.22/27.83  | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (791) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | |   (792)  all_6_2 = e3
% 177.22/27.83  | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | REDUCE: (677), (792) imply:
% 177.22/27.83  | | | | | | | | | | | | | | | | |   (793)  $false
% 177.22/27.83  | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | | CLOSE: (793) is inconsistent.
% 177.22/27.83  | | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | |   (794)   ~ (all_56_13 = e3)
% 177.22/27.83  | | | | | | | | | | | |   (795)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | REDUCE: (205), (794) imply:
% 177.22/27.83  | | | | | | | | | | | |   (796)   ~ (all_52_27 = e3)
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (13), (14), (15), (16),
% 177.22/27.83  | | | | | | | | | | | |            (17), (18), (19), (20), (24), (26), (27), (28),
% 177.22/27.83  | | | | | | | | | | | |            (29), (30), (31), (33), (34), (35), (36), (37),
% 177.22/27.83  | | | | | | | | | | | |            (38), (39), (40), (41), (42), (44), (46), (47),
% 177.22/27.83  | | | | | | | | | | | |            (48), (50), (51), (52), (54), (55), (56), (58),
% 177.22/27.83  | | | | | | | | | | | |            (61), (65), (66), (67), (69), (70), (71), (73),
% 177.22/27.83  | | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (86),
% 177.22/27.83  | | | | | | | | | | | |            (87), (88), (89), (91), (92), (95), (99), (103),
% 177.22/27.83  | | | | | | | | | | | |            (104), (109), (111), (112), (113), (115), (116),
% 177.22/27.83  | | | | | | | | | | | |            (117), (119), (121), (124), (126), (127), (129),
% 177.22/27.83  | | | | | | | | | | | |            (130), (131), (132), (133), (134), (135), (136),
% 177.22/27.83  | | | | | | | | | | | |            (140), (141), (144), (146), (147), (149), (150),
% 177.22/27.83  | | | | | | | | | | | |            (151), (152), (153), (157), (158), (161), (162),
% 177.22/27.83  | | | | | | | | | | | |            (163), (167), (170), (172), (173), (176), (178),
% 177.22/27.83  | | | | | | | | | | | |            (179), (183), (184), (186), (187), (189), (192),
% 177.22/27.83  | | | | | | | | | | | |            (195), (196), (197), (198), (199), (200), (201),
% 177.22/27.83  | | | | | | | | | | | |            (204), (205), (209), (627), (632), (636), (637),
% 177.22/27.83  | | | | | | | | | | | |            (638), (648), (649), (650), (651), (676), (677),
% 177.22/27.83  | | | | | | | | | | | |            (795), (796) are inconsistent by sub-proof #375.
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | |   (797)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.83  | | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2
% 177.22/27.83  | | | | | | | | |            & all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | BETA: splitting (797) gives:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | |   (798)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.83  | | | | | | | | | |          all_52_22 = e0
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | REF_CLOSE: (48), (128), (798) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | | |            #373.
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | |   (799)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.83  | | | | | | | | | |          all_52_30 = e0
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | ALPHA: (799) implies:
% 177.22/27.83  | | | | | | | | | |   (800)  all_52_30 = e0
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | COMBINE_EQS: (185), (800) imply:
% 177.22/27.83  | | | | | | | | | |   (801)  all_6_1 = e0
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | REF_CLOSE: (96), (104), (167), (625), (801) are inconsistent
% 177.22/27.83  | | | | | | | | | |            by sub-proof #502.
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | End of split
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | Case 2:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | |   (802)  all_40_1 = e1
% 177.22/27.83  | | | | | | |   (803)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | COMBINE_EQS: (76), (802) imply:
% 177.22/27.83  | | | | | | |   (804)  all_4_1 = e1
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | COMBINE_EQS: (97), (804) imply:
% 177.22/27.83  | | | | | | |   (805)  all_52_0 = e1
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | REDUCE: (88), (804) imply:
% 177.22/27.83  | | | | | | |   (806)  op(e1, all_4_2) = all_4_0
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | REDUCE: (52), (804) imply:
% 177.22/27.83  | | | | | | |   (807)  op(e3, all_4_2) = e1
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | BETA: splitting (169) gives:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (808)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.83  | | | | | | | |            all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.83  | | | | | | | |            all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | BETA: splitting (808) gives:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | |   (809)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.83  | | | | | | | | |          all_52_6 = e0
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REF_CLOSE: (48), (805), (809) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | |            #632.
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | |   (810)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.83  | | | | | | | | |          all_52_14 = e0
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | ALPHA: (810) implies:
% 177.22/27.83  | | | | | | | | |   (811)  all_52_14 = e0
% 177.22/27.83  | | | | | | | | |   (812)  all_52_12 = e1
% 177.22/27.83  | | | | | | | | |   (813)  all_52_10 = e2
% 177.22/27.83  | | | | | | | | |   (814)  all_52_8 = e3
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | COMBINE_EQS: (100), (813) imply:
% 177.22/27.83  | | | | | | | | |   (815)  all_10_1 = e2
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (114), (815) imply:
% 177.22/27.83  | | | | | | | | |   (816)  op(e2, all_10_2) = all_10_0
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (22), (814) imply:
% 177.22/27.83  | | | | | | | | |   (817)  op(e3, all_52_9) = e3
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (9), (815) imply:
% 177.22/27.83  | | | | | | | | |   (818)  op(e2, all_10_2) = e2
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (59), (812) imply:
% 177.22/27.83  | | | | | | | | |   (819)  op(e1, all_52_13) = e1
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (139), (811) imply:
% 177.22/27.83  | | | | | | | | |   (820)  op(e0, all_52_15) = e0
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | GROUND_INST: instantiating (167) with e2, all_10_0, all_10_2,
% 177.22/27.83  | | | | | | | | |              e2, simplifying with (816), (818) gives:
% 177.22/27.83  | | | | | | | | |   (821)  all_10_0 = e2
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (174), (821) imply:
% 177.22/27.83  | | | | | | | | |   (822)   ~ (e3 = e2)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | BETA: splitting (164) gives:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | |   (823)  all_58_15 = e0
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | REF_CLOSE: (36), (60), (96), (104), (167), (625), (823) are
% 177.22/27.83  | | | | | | | | | |            inconsistent by sub-proof #510.
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | |   (824)   ~ (all_58_15 = e0)
% 177.22/27.83  | | | | | | | | | |   (825)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.83  | | | | | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | ALPHA: (825) implies:
% 177.22/27.83  | | | | | | | | | |   (826)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.83  | | | | | | | | | |   (827)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | REDUCE: (36), (824) imply:
% 177.22/27.83  | | | | | | | | | |   (828)   ~ (all_6_2 = e0)
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (13), (14),
% 177.22/27.83  | | | | | | | | | |            (15), (16), (18), (19), (20), (24), (25), (27),
% 177.22/27.83  | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 177.22/27.83  | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 177.22/27.83  | | | | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52),
% 177.22/27.83  | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (61), (66),
% 177.22/27.83  | | | | | | | | | |            (67), (69), (70), (71), (72), (73), (74), (78),
% 177.22/27.83  | | | | | | | | | |            (79), (80), (81), (82), (86), (89), (90), (91),
% 177.22/27.83  | | | | | | | | | |            (92), (95), (99), (103), (104), (105), (109),
% 177.22/27.83  | | | | | | | | | |            (111), (112), (113), (115), (116), (119), (121),
% 177.22/27.83  | | | | | | | | | |            (122), (124), (126), (127), (129), (130), (131),
% 177.22/27.83  | | | | | | | | | |            (132), (133), (134), (135), (136), (140), (141),
% 177.22/27.83  | | | | | | | | | |            (144), (146), (147), (149), (150), (152), (153),
% 177.22/27.83  | | | | | | | | | |            (154), (157), (158), (161), (162), (163), (166),
% 177.22/27.83  | | | | | | | | | |            (167), (170), (172), (173), (176), (178), (179),
% 177.22/27.83  | | | | | | | | | |            (180), (182), (183), (184), (186), (187), (189),
% 177.22/27.83  | | | | | | | | | |            (191), (192), (195), (196), (197), (198), (199),
% 177.22/27.83  | | | | | | | | | |            (200), (201), (202), (204), (205), (209), (803),
% 177.22/27.83  | | | | | | | | | |            (806), (807), (817), (818), (819), (820), (826),
% 177.22/27.83  | | | | | | | | | |            (827), (828) are inconsistent by sub-proof #363.
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (829)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.83  | | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.83  | | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | BETA: splitting (829) gives:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | |   (830)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.83  | | | | | | | | |          all_52_22 = e0
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REF_CLOSE: (48), (128), (830) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | |            #373.
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | |   (831)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.83  | | | | | | | | |          all_52_30 = e0
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REF_CLOSE: (96), (104), (167), (185), (625), (831) are
% 177.22/27.83  | | | | | | | | |            inconsistent by sub-proof #501.
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | End of split
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | End of split
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | End of split
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | End of split
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | Case 2:
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | |   (832)  all_34_0 = e1
% 177.22/27.83  | | | | |   (833)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | COMBINE_EQS: (193), (832) imply:
% 177.22/27.83  | | | | |   (834)  all_4_0 = e1
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | REDUCE: (88), (834) imply:
% 177.22/27.83  | | | | |   (835)  op(all_4_1, all_4_2) = e1
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | BETA: splitting (164) gives:
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | Case 1:
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | |   (836)  all_58_15 = e0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REF_CLOSE: (36), (60), (96), (104), (167), (625), (836) are
% 177.22/27.83  | | | | | |            inconsistent by sub-proof #510.
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | Case 2:
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | |   (837)   ~ (all_58_15 = e0)
% 177.22/27.83  | | | | | |   (838)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.83  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | ALPHA: (838) implies:
% 177.22/27.83  | | | | | |   (839)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (36), (837) imply:
% 177.22/27.83  | | | | | |   (840)   ~ (all_6_2 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | BETA: splitting (169) gives:
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | Case 1:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | |   (841)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.22/27.83  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.22/27.83  | | | | | | |            e1 & all_52_14 = e0)
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | BETA: splitting (841) gives:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (842)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.83  | | | | | | | |          all_52_6 = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REF_CLOSE: (48), (52), (97), (167), (835), (842) are
% 177.22/27.83  | | | | | | | |            inconsistent by sub-proof #600.
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (843)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.83  | | | | | | | |          all_52_14 = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | ALPHA: (843) implies:
% 177.22/27.83  | | | | | | | |   (844)  all_52_14 = e0
% 177.22/27.83  | | | | | | | |   (845)  all_52_12 = e1
% 177.22/27.83  | | | | | | | |   (846)  all_52_10 = e2
% 177.22/27.83  | | | | | | | |   (847)  all_52_8 = e3
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | COMBINE_EQS: (100), (846) imply:
% 177.22/27.83  | | | | | | | |   (848)  all_10_1 = e2
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (114), (848) imply:
% 177.22/27.83  | | | | | | | |   (849)  op(e2, all_10_2) = all_10_0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (22), (847) imply:
% 177.22/27.83  | | | | | | | |   (850)  op(e3, all_52_9) = e3
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (9), (848) imply:
% 177.22/27.83  | | | | | | | |   (851)  op(e2, all_10_2) = e2
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (59), (845) imply:
% 177.22/27.83  | | | | | | | |   (852)  op(e1, all_52_13) = e1
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (139), (844) imply:
% 177.22/27.83  | | | | | | | |   (853)  op(e0, all_52_15) = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (13), (14), (15), (16),
% 177.22/27.83  | | | | | | | |            (18), (19), (20), (24), (27), (28), (29), (30), (33),
% 177.22/27.83  | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 177.22/27.83  | | | | | | | |            (43), (44), (46), (47), (48), (49), (50), (51), (52),
% 177.22/27.83  | | | | | | | |            (53), (54), (55), (56), (58), (61), (65), (66), (67),
% 177.22/27.83  | | | | | | | |            (69), (70), (71), (73), (74), (78), (79), (80), (81),
% 177.22/27.83  | | | | | | | |            (82), (83), (86), (89), (91), (92), (95), (99),
% 177.22/27.83  | | | | | | | |            (103), (104), (109), (111), (112), (113), (117),
% 177.22/27.83  | | | | | | | |            (119), (121), (124), (126), (127), (129), (130),
% 177.22/27.83  | | | | | | | |            (131), (132), (133), (134), (135), (136), (140),
% 177.22/27.83  | | | | | | | |            (141), (144), (146), (147), (149), (150), (152),
% 177.22/27.83  | | | | | | | |            (153), (157), (161), (162), (163), (166), (167),
% 177.22/27.83  | | | | | | | |            (170), (171), (172), (173), (174), (179), (182),
% 177.22/27.83  | | | | | | | |            (183), (184), (186), (187), (189), (192), (195),
% 177.22/27.83  | | | | | | | |            (196), (197), (198), (201), (204), (205), (207),
% 177.22/27.83  | | | | | | | |            (833), (835), (839), (840), (849), (850), (851),
% 177.22/27.83  | | | | | | | |            (852), (853) are inconsistent by sub-proof #357.
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | End of split
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | Case 2:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | |   (854)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.83  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.83  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | BETA: splitting (854) gives:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (855)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.83  | | | | | | | |          all_52_22 = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REF_CLOSE: (48), (128), (855) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | |            #373.
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (856)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.83  | | | | | | | |          all_52_30 = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REF_CLOSE: (96), (104), (167), (185), (625), (856) are
% 177.22/27.83  | | | | | | | |            inconsistent by sub-proof #501.
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | End of split
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | End of split
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | End of split
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | End of split
% 177.22/27.83  | | | | 
% 177.22/27.83  | | | End of split
% 177.22/27.83  | | | 
% 177.22/27.83  | | Case 2:
% 177.22/27.83  | | | 
% 177.22/27.83  | | |   (857)  all_26_0 = e2
% 177.22/27.83  | | |   (858)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.83  | | | 
% 177.22/27.83  | | | COMBINE_EQS: (159), (857) imply:
% 177.22/27.83  | | |   (859)  all_4_0 = e2
% 177.22/27.83  | | | 
% 177.22/27.83  | | | SIMP: (859) implies:
% 177.22/27.83  | | |   (860)  all_4_0 = e2
% 177.22/27.83  | | | 
% 177.22/27.83  | | | COMBINE_EQS: (62), (860) imply:
% 177.22/27.83  | | |   (861)  all_50_0 = e2
% 177.22/27.83  | | | 
% 177.22/27.83  | | | REDUCE: (88), (860) imply:
% 177.22/27.83  | | |   (862)  op(all_4_1, all_4_2) = e2
% 177.22/27.83  | | | 
% 177.22/27.83  | | | BETA: splitting (190) gives:
% 177.22/27.83  | | | 
% 177.22/27.83  | | | Case 1:
% 177.22/27.83  | | | | 
% 177.22/27.83  | | | |   (863)   ~ (all_28_0 = e3)
% 177.22/27.83  | | | | 
% 177.22/27.83  | | | | REDUCE: (203), (863) imply:
% 177.22/27.83  | | | |   (864)   ~ (all_6_0 = e3)
% 177.22/27.83  | | | | 
% 177.22/27.83  | | | | BETA: splitting (143) gives:
% 177.22/27.83  | | | | 
% 177.22/27.83  | | | | Case 1:
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | |   (865)   ~ (all_50_0 = e2)
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | REDUCE: (861), (865) imply:
% 177.22/27.83  | | | | |   (866)  $false
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | CLOSE: (866) is inconsistent.
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | Case 2:
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | |   (867)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | BETA: splitting (164) gives:
% 177.22/27.83  | | | | | 
% 177.22/27.83  | | | | | Case 1:
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | |   (868)  all_58_15 = e0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | COMBINE_EQS: (36), (868) imply:
% 177.22/27.83  | | | | | |   (869)  all_6_2 = e0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (43), (869) imply:
% 177.22/27.83  | | | | | |   (870)   ~ (all_52_15 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (144), (869) imply:
% 177.22/27.83  | | | | | |   (871)   ~ (all_52_23 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (153), (869) imply:
% 177.22/27.83  | | | | | |   (872)   ~ (all_52_25 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (172), (869) imply:
% 177.22/27.83  | | | | | |   (873)   ~ (all_52_27 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (93), (869) imply:
% 177.22/27.83  | | | | | |   (874)  op(all_6_1, e0) = all_6_0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (96), (869) imply:
% 177.22/27.83  | | | | | |   (875)  op(e0, e0) = all_6_1
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (60), (869) imply:
% 177.22/27.83  | | | | | |   (876)  op(e0, e0) = e0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_1, e0, e0,
% 177.22/27.83  | | | | | |              simplifying with (875), (876) gives:
% 177.22/27.83  | | | | | |   (877)  all_6_1 = e0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (874), (877) imply:
% 177.22/27.83  | | | | | |   (878)  op(e0, e0) = all_6_0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, e0, e0,
% 177.22/27.83  | | | | | |              simplifying with (876), (878) gives:
% 177.22/27.83  | | | | | |   (879)  all_6_0 = e0
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (864), (879) imply:
% 177.22/27.83  | | | | | |   (880)   ~ (e3 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | REDUCE: (145), (879) imply:
% 177.22/27.83  | | | | | |   (881)   ~ (e2 = e0)
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | BETA: splitting (169) gives:
% 177.22/27.83  | | | | | | 
% 177.22/27.83  | | | | | | Case 1:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | |   (882)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.22/27.83  | | | | | | |            = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 =
% 177.22/27.83  | | | | | | |            e1 & all_52_14 = e0)
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | BETA: splitting (882) gives:
% 177.22/27.83  | | | | | | | 
% 177.22/27.83  | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (883)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.83  | | | | | | | |          all_52_6 = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REF_CLOSE: (52), (67), (97), (167), (862), (883) are
% 177.22/27.83  | | | | | | | |            inconsistent by sub-proof #494.
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | |   (884)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.83  | | | | | | | |          all_52_14 = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | ALPHA: (884) implies:
% 177.22/27.83  | | | | | | | |   (885)  all_52_14 = e0
% 177.22/27.83  | | | | | | | |   (886)  all_52_12 = e1
% 177.22/27.83  | | | | | | | |   (887)  all_52_10 = e2
% 177.22/27.83  | | | | | | | |   (888)  all_52_8 = e3
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | COMBINE_EQS: (100), (887) imply:
% 177.22/27.83  | | | | | | | |   (889)  all_10_1 = e2
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (114), (889) imply:
% 177.22/27.83  | | | | | | | |   (890)  op(e2, all_10_2) = all_10_0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (22), (888) imply:
% 177.22/27.83  | | | | | | | |   (891)  op(e3, all_52_9) = e3
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (9), (889) imply:
% 177.22/27.83  | | | | | | | |   (892)  op(e2, all_10_2) = e2
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (59), (886) imply:
% 177.22/27.83  | | | | | | | |   (893)  op(e1, all_52_13) = e1
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (139), (885) imply:
% 177.22/27.83  | | | | | | | |   (894)  op(e0, all_52_15) = e0
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | GROUND_INST: instantiating (167) with e2, all_10_0, all_10_2,
% 177.22/27.83  | | | | | | | |              e2, simplifying with (890), (892) gives:
% 177.22/27.83  | | | | | | | |   (895)  all_10_0 = e2
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | REDUCE: (174), (895) imply:
% 177.22/27.83  | | | | | | | |   (896)   ~ (e3 = e2)
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | BETA: splitting (74) gives:
% 177.22/27.83  | | | | | | | | 
% 177.22/27.83  | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | |   (897)  all_56_13 = e3
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | COMBINE_EQS: (205), (897) imply:
% 177.22/27.83  | | | | | | | | |   (898)  all_52_27 = e3
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | SIMP: (898) implies:
% 177.22/27.83  | | | | | | | | |   (899)  all_52_27 = e3
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | COMBINE_EQS: (119), (899) imply:
% 177.22/27.83  | | | | | | | | |   (900)  all_58_13 = e3
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (176), (899) imply:
% 177.22/27.83  | | | | | | | | |   (901)   ~ (all_52_19 = e3)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (170), (899) imply:
% 177.22/27.83  | | | | | | | | |   (902)   ~ (all_52_25 = e3)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (50), (899) imply:
% 177.22/27.83  | | | | | | | | |   (903)   ~ (all_52_29 = e3)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | SIMP: (903) implies:
% 177.22/27.83  | | | | | | | | |   (904)   ~ (all_52_29 = e3)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (6), (899) imply:
% 177.22/27.83  | | | | | | | | |   (905)   ~ (all_10_2 = e3)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | SIMP: (905) implies:
% 177.22/27.83  | | | | | | | | |   (906)   ~ (all_10_2 = e3)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (182), (899) imply:
% 177.22/27.83  | | | | | | | | |   (907)  op(e2, e3) = all_52_26
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | GROUND_INST: instantiating (167) with all_52_9, all_52_26, e3,
% 177.22/27.83  | | | | | | | | |              e2, simplifying with (204), (907) gives:
% 177.22/27.83  | | | | | | | | |   (908)  all_52_9 = all_52_26
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | COMBINE_EQS: (147), (908) imply:
% 177.22/27.83  | | | | | | | | |   (909)  all_58_2 = all_52_26
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (109), (908) imply:
% 177.22/27.83  | | | | | | | | |   (910)   ~ (all_52_13 = all_52_26)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | SIMP: (910) implies:
% 177.22/27.83  | | | | | | | | |   (911)   ~ (all_52_13 = all_52_26)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (124), (908) imply:
% 177.22/27.83  | | | | | | | | |   (912)   ~ (all_52_17 = all_52_26)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | SIMP: (912) implies:
% 177.22/27.83  | | | | | | | | |   (913)   ~ (all_52_17 = all_52_26)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (37), (908) imply:
% 177.22/27.83  | | | | | | | | |   (914)   ~ (all_52_26 = all_4_2)
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | REDUCE: (891), (908) imply:
% 177.22/27.83  | | | | | | | | |   (915)  op(e3, all_52_26) = e3
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | BETA: splitting (110) gives:
% 177.22/27.83  | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | |   (916)  all_56_12 = e3
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | REF_CLOSE: (118), (902), (916) are inconsistent by sub-proof
% 177.22/27.83  | | | | | | | | | |            #1040.
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | Case 2:
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | |   (917)   ~ (all_56_12 = e3)
% 177.22/27.83  | | | | | | | | | |   (918)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | BETA: splitting (148) gives:
% 177.22/27.83  | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | |   (919)  all_58_12 = e1
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | COMBINE_EQS: (192), (919) imply:
% 177.22/27.83  | | | | | | | | | | |   (920)  all_52_25 = e1
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | SIMP: (920) implies:
% 177.22/27.83  | | | | | | | | | | |   (921)  all_52_25 = e1
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | REDUCE: (44), (921) imply:
% 177.22/27.83  | | | | | | | | | | |   (922)   ~ (all_52_17 = e1)
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | REDUCE: (17), (921) imply:
% 177.22/27.83  | | | | | | | | | | |   (923)  op(e3, e1) = all_52_24
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | REDUCE: (95), (921) imply:
% 177.22/27.83  | | | | | | | | | | |   (924)  op(e0, e3) = e1
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | BETA: splitting (155) gives:
% 177.22/27.83  | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | Case 1:
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | |   (925)  all_58_12 = e2
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | COMBINE_EQS: (919), (925) imply:
% 177.22/27.83  | | | | | | | | | | | |   (926)  e2 = e1
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.83  | | | | | | | | | | | | REDUCE: (151), (926) imply:
% 177.22/27.83  | | | | | | | | | | | |   (927)  $false
% 177.22/27.83  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | CLOSE: (927) is inconsistent.
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | |   (928)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | BETA: splitting (928) gives:
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | |   (929)  all_58_13 = e2
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | REF_CLOSE: (199), (900), (929) are inconsistent by sub-proof
% 177.22/27.84  | | | | | | | | | | | | |            #906.
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_52_5, all_52_24, e1,
% 177.22/27.84  | | | | | | | | | | | | |              e3, simplifying with (150), (923) gives:
% 177.22/27.84  | | | | | | | | | | | | |   (930)  all_52_5 = all_52_24
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | COMBINE_EQS: (46), (930) imply:
% 177.22/27.84  | | | | | | | | | | | | |   (931)  all_58_4 = all_52_24
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | REDUCE: (38), (930) imply:
% 177.22/27.84  | | | | | | | | | | | | |   (932)   ~ (all_52_7 = all_52_24)
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | SIMP: (932) implies:
% 177.22/27.84  | | | | | | | | | | | | |   (933)   ~ (all_52_7 = all_52_24)
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | BETA: splitting (47) gives:
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | |   (934)  all_58_6 = e3
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | COMBINE_EQS: (126), (934) imply:
% 177.22/27.84  | | | | | | | | | | | | | |   (935)  all_52_17 = e3
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | REDUCE: (913), (935) imply:
% 177.22/27.84  | | | | | | | | | | | | | |   (936)   ~ (all_52_26 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | SIMP: (936) implies:
% 177.22/27.84  | | | | | | | | | | | | | |   (937)   ~ (all_52_26 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | REDUCE: (166), (935) imply:
% 177.22/27.84  | | | | | | | | | | | | | |   (938)   ~ (all_4_2 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | SIMP: (938) implies:
% 177.22/27.84  | | | | | | | | | | | | | |   (939)   ~ (all_4_2 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | REDUCE: (99), (935) imply:
% 177.22/27.84  | | | | | | | | | | | | | |   (940)  op(e3, e3) = all_52_16
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | GROUND_INST: instantiating (167) with all_4_2, all_52_16, e3,
% 177.22/27.84  | | | | | | | | | | | | | |              e3, simplifying with (163), (940) gives:
% 177.22/27.84  | | | | | | | | | | | | | |   (941)  all_52_16 = all_4_2
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | |   (942)  all_58_2 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | COMBINE_EQS: (909), (942) imply:
% 177.22/27.84  | | | | | | | | | | | | | | |   (943)  all_52_26 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | REDUCE: (937), (943) imply:
% 177.22/27.84  | | | | | | | | | | | | | | |   (944)  $false
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | CLOSE: (944) is inconsistent.
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | |   (945)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | |   (946)  all_58_9 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (946) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (947)  all_52_7 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | REDUCE: (136), (947) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (948)   ~ (all_52_15 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | SIMP: (948) implies:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (949)   ~ (all_52_15 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | REDUCE: (179), (947) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (950)   ~ (all_52_23 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | SIMP: (950) implies:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (951)   ~ (all_52_23 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | REDUCE: (933), (947) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (952)   ~ (all_52_24 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | SIMP: (952) implies:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (953)   ~ (all_52_24 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (27), (33), (39), (41), (44), (47), (48),
% 177.22/27.84  | | | | | | | | | | | | | | | |            (51), (54), (58), (73), (79), (82), (103), (126),
% 177.22/27.84  | | | | | | | | | | | | | | | |            (133), (157), (163), (167), (192), (198), (893),
% 177.22/27.84  | | | | | | | | | | | | | | | |            (901), (906), (909), (911), (914), (915), (931),
% 177.22/27.84  | | | | | | | | | | | | | | | |            (939), (949), (951), (953) are inconsistent by
% 177.22/27.84  | | | | | | | | | | | | | | | |            sub-proof #994.
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | |   (954)   ~ (all_58_9 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | |   (955)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | REDUCE: (189), (954) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | |   (956)   ~ (all_52_7 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | BETA: splitting (955) gives:
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | |   (957)  all_58_10 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (957) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | | |   (958)  all_52_15 = e3
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | | REDUCE: (894), (958) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | | |   (959)  op(e0, e3) = e0
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (131), (167), (924), (959) are inconsistent by
% 177.22/27.84  | | | | | | | | | | | | | | | | |            sub-proof #1007.
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | |   (960)   ~ (all_58_10 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | | REDUCE: (39), (960) imply:
% 177.22/27.84  | | | | | | | | | | | | | | | | |   (961)   ~ (all_52_15 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (15), (24), (27), (30), (33), (35),
% 177.22/27.84  | | | | | | | | | | | | | | | | |            (37), (39), (42), (46), (51), (52), (55), (58),
% 177.22/27.84  | | | | | | | | | | | | | | | | |            (67), (73), (77), (82), (86), (109), (124), (129),
% 177.22/27.84  | | | | | | | | | | | | | | | | |            (132), (137), (157), (162), (166), (167), (186),
% 177.22/27.84  | | | | | | | | | | | | | | | | |            (198), (204), (858), (862), (891), (892), (893),
% 177.22/27.84  | | | | | | | | | | | | | | | | |            (904), (939), (945), (956), (961) are inconsistent
% 177.22/27.84  | | | | | | | | | | | | | | | | |            by sub-proof #352.
% 177.22/27.84  | | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | |   (962)   ~ (all_58_6 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | REDUCE: (126), (962) imply:
% 177.22/27.84  | | | | | | | | | | | | | |   (963)   ~ (all_52_17 = e3)
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | | REF_CLOSE: (52), (58), (67), (79), (126), (163), (167),
% 177.22/27.84  | | | | | | | | | | | | | |            (192), (862), (902), (909), (914), (915), (963)
% 177.22/27.84  | | | | | | | | | | | | | |            are inconsistent by sub-proof #488.
% 177.22/27.84  | | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | |   (964)   ~ (all_58_12 = e1)
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | REF_CLOSE: (8), (13), (27), (33), (38), (39), (41), (44),
% 177.22/27.84  | | | | | | | | | | |            (46), (47), (48), (51), (52), (54), (55), (58),
% 177.22/27.84  | | | | | | | | | | |            (67), (73), (79), (82), (95), (103), (104), (118),
% 177.22/27.84  | | | | | | | | | | |            (126), (133), (136), (155), (157), (158), (163),
% 177.22/27.84  | | | | | | | | | | |            (167), (178), (179), (184), (189), (192), (198),
% 177.22/27.84  | | | | | | | | | | |            (862), (868), (872), (893), (894), (901), (902),
% 177.22/27.84  | | | | | | | | | | |            (906), (909), (911), (914), (915), (918), (964)
% 177.22/27.84  | | | | | | | | | | |            are inconsistent by sub-proof #487.
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | 
% 177.22/27.84  | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | 
% 177.22/27.84  | | | | | | | | |   (965)   ~ (all_56_13 = e3)
% 177.22/27.84  | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | REDUCE: (205), (965) imply:
% 177.22/27.84  | | | | | | | | |   (966)   ~ (all_52_27 = e3)
% 177.22/27.84  | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | BETA: splitting (81) gives:
% 177.22/27.84  | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | |   (967)  all_58_12 = e3
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | COMBINE_EQS: (192), (967) imply:
% 177.22/27.84  | | | | | | | | | |   (968)  all_52_25 = e3
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | SIMP: (968) implies:
% 177.22/27.84  | | | | | | | | | |   (969)  all_52_25 = e3
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | REDUCE: (16), (969) imply:
% 177.22/27.84  | | | | | | | | | |   (970)   ~ (all_52_9 = e3)
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | REDUCE: (44), (969) imply:
% 177.22/27.84  | | | | | | | | | |   (971)   ~ (all_52_17 = e3)
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | REDUCE: (28), (969) imply:
% 177.22/27.84  | | | | | | | | | |   (972)   ~ (all_52_29 = e3)
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | SIMP: (972) implies:
% 177.22/27.84  | | | | | | | | | |   (973)   ~ (all_52_29 = e3)
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | REDUCE: (161), (969) imply:
% 177.22/27.84  | | | | | | | | | |   (974)   ~ (all_4_2 = e3)
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | SIMP: (974) implies:
% 177.22/27.84  | | | | | | | | | |   (975)   ~ (all_4_2 = e3)
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | REDUCE: (17), (969) imply:
% 177.22/27.84  | | | | | | | | | |   (976)  op(e3, e3) = all_52_24
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | REDUCE: (95), (969) imply:
% 177.22/27.84  | | | | | | | | | |   (977)  op(e0, e3) = e3
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | GROUND_INST: instantiating (167) with all_4_2, all_52_24, e3,
% 177.22/27.84  | | | | | | | | | |              e3, simplifying with (163), (976) gives:
% 177.22/27.84  | | | | | | | | | |   (978)  all_52_24 = all_4_2
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | BETA: splitting (158) gives:
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | |   (979)  all_56_7 = e3
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | COMBINE_EQS: (178), (979) imply:
% 177.22/27.84  | | | | | | | | | | |   (980)  all_52_15 = e3
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | REF_CLOSE: (167), (870), (894), (977), (980) are inconsistent
% 177.22/27.84  | | | | | | | | | | |            by sub-proof #971.
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | |   (981)   ~ (all_56_7 = e3)
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | REDUCE: (178), (981) imply:
% 177.22/27.84  | | | | | | | | | | |   (982)   ~ (all_52_15 = e3)
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | BETA: splitting (184) gives:
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | |   (983)  all_58_9 = e3
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | COMBINE_EQS: (189), (983) imply:
% 177.22/27.84  | | | | | | | | | | | |   (984)  all_52_7 = e3
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | SIMP: (984) implies:
% 177.22/27.84  | | | | | | | | | | | |   (985)  all_52_7 = e3
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | REDUCE: (127), (985) imply:
% 177.22/27.84  | | | | | | | | | | | |   (986)   ~ (all_52_3 = e3)
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | REDUCE: (136), (985) imply:
% 177.22/27.84  | | | | | | | | | | | |   (987)   ~ (all_52_15 = e3)
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | REDUCE: (179), (985) imply:
% 177.22/27.84  | | | | | | | | | | | |   (988)   ~ (all_52_23 = e3)
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | SIMP: (988) implies:
% 177.22/27.84  | | | | | | | | | | | |   (989)   ~ (all_52_23 = e3)
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | REF_CLOSE: (1), (6), (8), (15), (19), (24), (27), (30), (33),
% 177.22/27.84  | | | | | | | | | | | |            (37), (39), (41), (47), (51), (54), (56), (58),
% 177.22/27.84  | | | | | | | | | | | |            (70), (71), (82), (86), (89), (103), (113), (117),
% 177.22/27.84  | | | | | | | | | | | |            (119), (126), (130), (133), (134), (141), (147),
% 177.22/27.84  | | | | | | | | | | | |            (149), (151), (152), (157), (163), (167), (195),
% 177.22/27.84  | | | | | | | | | | | |            (199), (204), (871), (891), (892), (893), (967),
% 177.22/27.84  | | | | | | | | | | | |            (970), (971), (982), (986), (989) are inconsistent
% 177.22/27.84  | | | | | | | | | | | |            by sub-proof #429.
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | |   (990)   ~ (all_58_9 = e3)
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | REDUCE: (189), (990) imply:
% 177.22/27.84  | | | | | | | | | | | |   (991)   ~ (all_52_7 = e3)
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | | REF_CLOSE: (2), (14), (15), (24), (27), (30), (33), (35),
% 177.22/27.84  | | | | | | | | | | | |            (37), (39), (42), (46), (51), (52), (54), (55),
% 177.22/27.84  | | | | | | | | | | | |            (58), (67), (73), (77), (82), (86), (109), (124),
% 177.22/27.84  | | | | | | | | | | | |            (129), (132), (137), (147), (157), (162), (166),
% 177.22/27.84  | | | | | | | | | | | |            (167), (186), (198), (204), (858), (862), (891),
% 177.22/27.84  | | | | | | | | | | | |            (892), (893), (970), (973), (975), (982), (991)
% 177.22/27.84  | | | | | | | | | | | |            are inconsistent by sub-proof #351.
% 177.22/27.84  | | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | |   (992)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | | REF_CLOSE: (13), (15), (16), (24), (27), (28), (33), (37),
% 177.22/27.84  | | | | | | | | | |            (39), (41), (47), (50), (52), (54), (56), (58),
% 177.22/27.84  | | | | | | | | | |            (61), (67), (70), (73), (79), (82), (92), (95),
% 177.22/27.84  | | | | | | | | | |            (104), (110), (112), (118), (119), (124), (126),
% 177.22/27.84  | | | | | | | | | |            (133), (134), (140), (147), (148), (157), (158),
% 177.22/27.84  | | | | | | | | | |            (163), (167), (178), (183), (192), (196), (204),
% 177.22/27.84  | | | | | | | | | |            (862), (868), (872), (891), (892), (894), (966),
% 177.22/27.84  | | | | | | | | | |            (992) are inconsistent by sub-proof #486.
% 177.22/27.84  | | | | | | | | | | 
% 177.22/27.84  | | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | | 
% 177.22/27.84  | | | | | | | | End of split
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | End of split
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | Case 2:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | |   (993)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | |            all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.84  | | | | | | |            all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | BETA: splitting (993) gives:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (994)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | | |          all_52_22 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (48), (128), (994) are inconsistent by sub-proof
% 177.22/27.84  | | | | | | | |            #373.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (995)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.84  | | | | | | | |          all_52_30 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (14), (15), (16), (17), (28), (35), (37), (38), (40),
% 177.22/27.84  | | | | | | | |            (44), (52), (55), (58), (61), (67), (73), (74), (77),
% 177.22/27.84  | | | | | | | |            (81), (92), (104), (110), (118), (119), (121), (132),
% 177.22/27.84  | | | | | | | |            (137), (150), (155), (157), (161), (162), (163),
% 177.22/27.84  | | | | | | | |            (166), (167), (170), (182), (186), (191), (192),
% 177.22/27.84  | | | | | | | |            (199), (204), (205), (858), (862), (868), (872),
% 177.22/27.84  | | | | | | | |            (995) are inconsistent by sub-proof #470.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | End of split
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | End of split
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | Case 2:
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | |   (996)   ~ (all_58_15 = e0)
% 177.22/27.84  | | | | | |   (997)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.84  | | | | | |          (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | ALPHA: (997) implies:
% 177.22/27.84  | | | | | |   (998)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.84  | | | | | |   (999)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (36), (996) imply:
% 177.22/27.84  | | | | | |   (1000)   ~ (all_6_2 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | BETA: splitting (169) gives:
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | Case 1:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | |   (1001)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.84  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.84  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | BETA: splitting (1001) gives:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (1002)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.84  | | | | | | | |           all_52_6 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (52), (67), (97), (167), (862), (1002) are
% 177.22/27.84  | | | | | | | |            inconsistent by sub-proof #494.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (1003)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.84  | | | | | | | |           all_52_14 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | ALPHA: (1003) implies:
% 177.22/27.84  | | | | | | | |   (1004)  all_52_14 = e0
% 177.22/27.84  | | | | | | | |   (1005)  all_52_12 = e1
% 177.22/27.84  | | | | | | | |   (1006)  all_52_10 = e2
% 177.22/27.84  | | | | | | | |   (1007)  all_52_8 = e3
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | COMBINE_EQS: (100), (1006) imply:
% 177.22/27.84  | | | | | | | |   (1008)  all_10_1 = e2
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REDUCE: (114), (1008) imply:
% 177.22/27.84  | | | | | | | |   (1009)  op(e2, all_10_2) = all_10_0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REDUCE: (22), (1007) imply:
% 177.22/27.84  | | | | | | | |   (1010)  op(e3, all_52_9) = e3
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REDUCE: (9), (1008) imply:
% 177.22/27.84  | | | | | | | |   (1011)  op(e2, all_10_2) = e2
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REDUCE: (59), (1005) imply:
% 177.22/27.84  | | | | | | | |   (1012)  op(e1, all_52_13) = e1
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REDUCE: (139), (1004) imply:
% 177.22/27.84  | | | | | | | |   (1013)  op(e0, all_52_15) = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (12), (13), (14),
% 177.22/27.84  | | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 177.22/27.84  | | | | | | | |            (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 177.22/27.84  | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44), (46),
% 177.22/27.84  | | | | | | | |            (47), (48), (50), (51), (52), (53), (54), (55), (56),
% 177.22/27.84  | | | | | | | |            (58), (61), (64), (65), (66), (67), (69), (70), (71),
% 177.22/27.84  | | | | | | | |            (73), (74), (77), (78), (79), (80), (81), (82), (83),
% 177.22/27.84  | | | | | | | |            (86), (89), (90), (91), (92), (95), (98), (99),
% 177.22/27.84  | | | | | | | |            (103), (104), (107), (109), (111), (112), (113),
% 177.22/27.84  | | | | | | | |            (115), (116), (119), (121), (122), (124), (125),
% 177.22/27.84  | | | | | | | |            (126), (127), (129), (130), (131), (132), (133),
% 177.22/27.84  | | | | | | | |            (134), (135), (136), (137), (138), (140), (141),
% 177.22/27.84  | | | | | | | |            (144), (146), (147), (149), (150), (152), (153),
% 177.22/27.84  | | | | | | | |            (154), (157), (161), (162), (163), (165), (166),
% 177.22/27.84  | | | | | | | |            (167), (170), (172), (173), (174), (176), (179),
% 177.22/27.84  | | | | | | | |            (180), (182), (183), (184), (186), (187), (188),
% 177.22/27.84  | | | | | | | |            (189), (192), (195), (196), (197), (198), (200),
% 177.22/27.84  | | | | | | | |            (201), (204), (205), (207), (858), (862), (867),
% 177.22/27.84  | | | | | | | |            (999), (1000), (1009), (1010), (1011), (1012), (1013)
% 177.22/27.84  | | | | | | | |            are inconsistent by sub-proof #349.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | End of split
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | Case 2:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | |   (1014)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.84  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | BETA: splitting (1014) gives:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (1015)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | | |           all_52_22 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (48), (128), (1015) are inconsistent by sub-proof
% 177.22/27.84  | | | | | | | |            #373.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (1016)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.84  | | | | | | | |           all_52_30 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | ALPHA: (1016) implies:
% 177.22/27.84  | | | | | | | |   (1017)  all_52_30 = e0
% 177.22/27.84  | | | | | | | |   (1018)  all_52_28 = e1
% 177.22/27.84  | | | | | | | |   (1019)  all_52_26 = e2
% 177.22/27.84  | | | | | | | |   (1020)  all_52_24 = e3
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | COMBINE_EQS: (185), (1017) imply:
% 177.22/27.84  | | | | | | | |   (1021)  all_6_1 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (14), (15), (16), (17), (18),
% 177.22/27.84  | | | | | | | |            (20), (21), (22), (23), (25), (27), (28), (29), (30),
% 177.22/27.84  | | | | | | | |            (32), (33), (35), (36), (37), (39), (40), (41), (44),
% 177.22/27.84  | | | | | | | |            (45), (46), (48), (50), (52), (53), (55), (56), (57),
% 177.22/27.84  | | | | | | | |            (58), (61), (64), (67), (69), (70), (73), (74), (77),
% 177.22/27.84  | | | | | | | |            (78), (79), (81), (82), (84), (86), (89), (92), (93),
% 177.22/27.84  | | | | | | | |            (95), (96), (98), (99), (101), (109), (110), (118),
% 177.22/27.84  | | | | | | | |            (119), (121), (124), (126), (127), (132), (133),
% 177.22/27.84  | | | | | | | |            (135), (137), (140), (145), (146), (147), (150),
% 177.22/27.84  | | | | | | | |            (153), (155), (156), (157), (161), (162), (163),
% 177.22/27.84  | | | | | | | |            (167), (170), (173), (176), (181), (182), (183),
% 177.22/27.84  | | | | | | | |            (184), (186), (189), (192), (197), (199), (204),
% 177.22/27.84  | | | | | | | |            (205), (858), (862), (864), (867), (998), (1000),
% 177.22/27.84  | | | | | | | |            (1018), (1019), (1020), (1021) are inconsistent by
% 177.22/27.84  | | | | | | | |            sub-proof #347.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | End of split
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | End of split
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | End of split
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | End of split
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | Case 2:
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | |   (1022)  all_28_0 = e3
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | COMBINE_EQS: (203), (1022) imply:
% 177.22/27.84  | | | |   (1023)  all_6_0 = e3
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | SIMP: (1023) implies:
% 177.22/27.84  | | | |   (1024)  all_6_0 = e3
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | REDUCE: (93), (1024) imply:
% 177.22/27.84  | | | |   (1025)  op(all_6_1, all_6_2) = e3
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | BETA: splitting (143) gives:
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | Case 1:
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | |   (1026)   ~ (all_50_0 = e2)
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | | REDUCE: (861), (1026) imply:
% 177.22/27.84  | | | | |   (1027)  $false
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | | CLOSE: (1027) is inconsistent.
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | Case 2:
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | |   (1028)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | | BETA: splitting (164) gives:
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | | Case 1:
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | |   (1029)  all_58_15 = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REF_CLOSE: (36), (60), (96), (104), (167), (1025), (1029) are
% 177.22/27.84  | | | | | |            inconsistent by sub-proof #510.
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | Case 2:
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | |   (1030)   ~ (all_58_15 = e0)
% 177.22/27.84  | | | | | |   (1031)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.84  | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | ALPHA: (1031) implies:
% 177.22/27.84  | | | | | |   (1032)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (36), (1030) imply:
% 177.22/27.84  | | | | | |   (1033)   ~ (all_6_2 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | BETA: splitting (169) gives:
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | Case 1:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | |   (1034)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.84  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.84  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (12), (13),
% 177.22/27.84  | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 177.22/27.84  | | | | | | |            (23), (24), (27), (28), (29), (30), (31), (33), (34),
% 177.22/27.84  | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 177.22/27.84  | | | | | | |            (44), (46), (47), (48), (50), (51), (52), (53), (54),
% 177.22/27.84  | | | | | | |            (55), (56), (58), (59), (61), (64), (65), (66), (67),
% 177.22/27.84  | | | | | | |            (69), (70), (71), (73), (74), (77), (78), (79), (80),
% 177.22/27.84  | | | | | | |            (81), (82), (83), (86), (89), (90), (91), (92), (95),
% 177.22/27.84  | | | | | | |            (97), (98), (99), (100), (103), (104), (107), (109),
% 177.22/27.84  | | | | | | |            (111), (112), (113), (114), (115), (116), (119), (121),
% 177.22/27.84  | | | | | | |            (122), (124), (125), (126), (127), (129), (130), (131),
% 177.22/27.84  | | | | | | |            (132), (133), (134), (135), (136), (137), (138), (139),
% 177.22/27.84  | | | | | | |            (140), (141), (144), (146), (147), (149), (150), (152),
% 177.22/27.84  | | | | | | |            (153), (154), (157), (161), (162), (163), (165), (166),
% 177.22/27.84  | | | | | | |            (167), (170), (172), (173), (174), (176), (179), (180),
% 177.22/27.84  | | | | | | |            (182), (183), (184), (186), (187), (188), (189), (192),
% 177.22/27.84  | | | | | | |            (195), (196), (197), (198), (200), (201), (204), (205),
% 177.22/27.84  | | | | | | |            (207), (858), (862), (1028), (1032), (1033), (1034) are
% 177.22/27.84  | | | | | | |            inconsistent by sub-proof #346.
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | Case 2:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | |   (1035)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.84  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | BETA: splitting (1035) gives:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (1036)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | | |           all_52_22 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (48), (128), (1036) are inconsistent by sub-proof
% 177.22/27.84  | | | | | | | |            #373.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | Case 2:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (1037)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.84  | | | | | | | |           all_52_30 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | | REF_CLOSE: (96), (104), (167), (185), (1025), (1037) are
% 177.22/27.84  | | | | | | | |            inconsistent by sub-proof #501.
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | End of split
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | End of split
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | End of split
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | End of split
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | End of split
% 177.22/27.84  | | | 
% 177.22/27.84  | | End of split
% 177.22/27.84  | | 
% 177.22/27.84  | Case 2:
% 177.22/27.84  | | 
% 177.22/27.84  | |   (1038)  all_24_0 = e1
% 177.22/27.84  | | 
% 177.22/27.84  | | COMBINE_EQS: (75), (1038) imply:
% 177.22/27.84  | |   (1039)  all_10_0 = e1
% 177.22/27.84  | | 
% 177.22/27.84  | | REDUCE: (174), (1039) imply:
% 177.22/27.84  | |   (1040)   ~ (e3 = e1)
% 177.22/27.84  | | 
% 177.22/27.84  | | REDUCE: (114), (1039) imply:
% 177.22/27.84  | |   (1041)  op(all_10_1, all_10_2) = e1
% 177.22/27.84  | | 
% 177.22/27.84  | | BETA: splitting (194) gives:
% 177.22/27.84  | | 
% 177.22/27.84  | | Case 1:
% 177.22/27.84  | | | 
% 177.22/27.84  | | |   (1042)   ~ (all_26_0 = e2)
% 177.22/27.84  | | | 
% 177.22/27.84  | | | REDUCE: (159), (1042) imply:
% 177.22/27.84  | | |   (1043)   ~ (all_4_0 = e2)
% 177.22/27.84  | | | 
% 177.22/27.84  | | | BETA: splitting (190) gives:
% 177.22/27.84  | | | 
% 177.22/27.84  | | | Case 1:
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | |   (1044)   ~ (all_28_0 = e3)
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | REDUCE: (203), (1044) imply:
% 177.22/27.84  | | | |   (1045)   ~ (all_6_0 = e3)
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | BETA: splitting (142) gives:
% 177.22/27.84  | | | | 
% 177.22/27.84  | | | | Case 1:
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | |   (1046)   ~ (all_34_0 = e1)
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | | REDUCE: (193), (1046) imply:
% 177.22/27.84  | | | | |   (1047)   ~ (all_4_0 = e1)
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | | BETA: splitting (164) gives:
% 177.22/27.84  | | | | | 
% 177.22/27.84  | | | | | Case 1:
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | |   (1048)  all_58_15 = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | COMBINE_EQS: (36), (1048) imply:
% 177.22/27.84  | | | | | |   (1049)  all_6_2 = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (173), (1049) imply:
% 177.22/27.84  | | | | | |   (1050)   ~ (all_52_7 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (144), (1049) imply:
% 177.22/27.84  | | | | | |   (1051)   ~ (all_52_23 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (153), (1049) imply:
% 177.22/27.84  | | | | | |   (1052)   ~ (all_52_25 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (172), (1049) imply:
% 177.22/27.84  | | | | | |   (1053)   ~ (all_52_27 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (146), (1049) imply:
% 177.22/27.84  | | | | | |   (1054)   ~ (all_52_29 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (93), (1049) imply:
% 177.22/27.84  | | | | | |   (1055)  op(all_6_1, e0) = all_6_0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (96), (1049) imply:
% 177.22/27.84  | | | | | |   (1056)  op(e0, e0) = all_6_1
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (60), (1049) imply:
% 177.22/27.84  | | | | | |   (1057)  op(e0, e0) = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_1, e0, e0,
% 177.22/27.84  | | | | | |              simplifying with (1056), (1057) gives:
% 177.22/27.84  | | | | | |   (1058)  all_6_1 = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (1055), (1058) imply:
% 177.22/27.84  | | | | | |   (1059)  op(e0, e0) = all_6_0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, e0, e0,
% 177.22/27.84  | | | | | |              simplifying with (1057), (1059) gives:
% 177.22/27.84  | | | | | |   (1060)  all_6_0 = e0
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (1045), (1060) imply:
% 177.22/27.84  | | | | | |   (1061)   ~ (e3 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | REDUCE: (181), (1060) imply:
% 177.22/27.84  | | | | | |   (1062)   ~ (e1 = e0)
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | BETA: splitting (169) gives:
% 177.22/27.84  | | | | | | 
% 177.22/27.84  | | | | | | Case 1:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | |   (1063)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.84  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.84  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | REF_CLOSE: (9), (14), (15), (32), (35), (36), (38), (39), (45),
% 177.22/27.84  | | | | | | |            (46), (52), (55), (56), (58), (70), (73), (74), (79),
% 177.22/27.84  | | | | | | |            (81), (84), (88), (95), (97), (100), (101), (104),
% 177.22/27.84  | | | | | | |            (110), (115), (118), (119), (121), (127), (132), (133),
% 177.22/27.84  | | | | | | |            (136), (148), (150), (151), (155), (161), (167), (170),
% 177.22/27.84  | | | | | | |            (173), (179), (184), (186), (189), (192), (196), (202),
% 177.22/27.84  | | | | | | |            (205), (1041), (1048), (1050), (1052), (1053), (1054),
% 177.22/27.84  | | | | | | |            (1063) are inconsistent by sub-proof #439.
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | Case 2:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | |   (1064)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.84  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | BETA: splitting (1064) gives:
% 177.22/27.84  | | | | | | | 
% 177.22/27.84  | | | | | | | Case 1:
% 177.22/27.84  | | | | | | | | 
% 177.22/27.84  | | | | | | | |   (1065)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.84  | | | | | | | |           all_52_22 = e0
% 177.22/27.84  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (48), (128), (1065) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | | |            #427.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1066)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (4), (6), (14), (15), (16), (17), (18), (19), (20),
% 177.22/27.85  | | | | | | | |            (24), (27), (28), (34), (35), (38), (40), (41), (44),
% 177.22/27.85  | | | | | | | |            (46), (47), (48), (50), (52), (55), (58), (61), (66),
% 177.22/27.85  | | | | | | | |            (67), (68), (69), (73), (74), (80), (81), (82), (85),
% 177.22/27.85  | | | | | | | |            (86), (90), (91), (92), (99), (104), (110), (113),
% 177.22/27.85  | | | | | | | |            (115), (117), (118), (119), (122), (123), (124),
% 177.22/27.85  | | | | | | | |            (126), (131), (132), (133), (134), (140), (141),
% 177.22/27.85  | | | | | | | |            (148), (149), (150), (152), (154), (156), (157),
% 177.22/27.85  | | | | | | | |            (160), (161), (162), (163), (167), (170), (176),
% 177.22/27.85  | | | | | | | |            (179), (180), (182), (186), (188), (192), (201),
% 177.22/27.85  | | | | | | | |            (204), (205), (1048), (1051), (1052), (1054), (1066)
% 177.22/27.85  | | | | | | | |            are inconsistent by sub-proof #421.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | End of split
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | End of split
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | Case 2:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1067)   ~ (all_58_15 = e0)
% 177.22/27.85  | | | | | |   (1068)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.85  | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | ALPHA: (1068) implies:
% 177.22/27.85  | | | | | |   (1069)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.85  | | | | | |   (1070)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (36), (1067) imply:
% 177.22/27.85  | | | | | |   (1071)   ~ (all_6_2 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | BETA: splitting (169) gives:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | Case 1:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1072)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.85  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.85  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | BETA: splitting (1072) gives:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | Case 1:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1073)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_6 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | ALPHA: (1073) implies:
% 177.22/27.85  | | | | | | | |   (1074)  all_52_6 = e0
% 177.22/27.85  | | | | | | | |   (1075)  all_52_4 = e1
% 177.22/27.85  | | | | | | | |   (1076)  all_52_2 = e2
% 177.22/27.85  | | | | | | | |   (1077)  all_52_0 = e3
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | COMBINE_EQS: (97), (1077) imply:
% 177.22/27.85  | | | | | | | |   (1078)  all_4_1 = e3
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REDUCE: (88), (1078) imply:
% 177.22/27.85  | | | | | | | |   (1079)  op(e3, all_4_2) = all_4_0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REDUCE: (52), (1078) imply:
% 177.22/27.85  | | | | | | | |   (1080)  op(e3, all_4_2) = e3
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REDUCE: (120), (1076) imply:
% 177.22/27.85  | | | | | | | |   (1081)  op(e2, all_52_3) = e2
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REDUCE: (63), (1075) imply:
% 177.22/27.85  | | | | | | | |   (1082)  op(e1, all_52_5) = e1
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REDUCE: (202), (1074) imply:
% 177.22/27.85  | | | | | | | |   (1083)  op(e0, all_52_7) = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (8), (13), (14), (15), (16),
% 177.22/27.85  | | | | | | | |            (17), (18), (19), (20), (21), (22), (24), (27), (28),
% 177.22/27.85  | | | | | | | |            (29), (30), (32), (33), (34), (35), (36), (37), (38),
% 177.22/27.85  | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.22/27.85  | | | | | | | |            (50), (51), (53), (54), (55), (56), (57), (58), (60),
% 177.22/27.85  | | | | | | | |            (61), (65), (66), (68), (69), (70), (71), (72), (73),
% 177.22/27.85  | | | | | | | |            (74), (78), (79), (80), (81), (82), (83), (84), (85),
% 177.22/27.85  | | | | | | | |            (86), (90), (91), (92), (93), (95), (96), (98),
% 177.22/27.85  | | | | | | | |            (101), (102), (103), (104), (106), (109), (110),
% 177.22/27.85  | | | | | | | |            (111), (112), (113), (115), (116), (117), (118),
% 177.22/27.85  | | | | | | | |            (119), (121), (122), (123), (124), (126), (127),
% 177.22/27.85  | | | | | | | |            (129), (131), (132), (133), (134), (135), (136),
% 177.22/27.85  | | | | | | | |            (139), (140), (141), (144), (145), (146), (147),
% 177.22/27.85  | | | | | | | |            (148), (149), (150), (151), (152), (153), (154),
% 177.22/27.85  | | | | | | | |            (155), (156), (157), (158), (161), (162), (165),
% 177.22/27.85  | | | | | | | |            (166), (167), (170), (172), (173), (175), (176),
% 177.22/27.85  | | | | | | | |            (178), (179), (180), (181), (182), (183), (184),
% 177.22/27.85  | | | | | | | |            (186), (189), (192), (195), (196), (197), (198),
% 177.22/27.85  | | | | | | | |            (200), (201), (204), (205), (1043), (1045), (1047),
% 177.22/27.85  | | | | | | | |            (1070), (1071), (1079), (1080), (1081), (1082),
% 177.22/27.85  | | | | | | | |            (1083) are inconsistent by sub-proof #400.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1084)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_14 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | ALPHA: (1084) implies:
% 177.22/27.85  | | | | | | | |   (1085)  all_52_10 = e2
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | COMBINE_EQS: (100), (1085) imply:
% 177.22/27.85  | | | | | | | |   (1086)  all_10_1 = e2
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (9), (151), (167), (1041), (1086) are inconsistent by
% 177.22/27.85  | | | | | | | |            sub-proof #446.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | End of split
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | Case 2:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1087)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.85  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | BETA: splitting (1087) gives:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | Case 1:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1088)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_22 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (48), (128), (1088) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | | |            #427.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1089)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | ALPHA: (1089) implies:
% 177.22/27.85  | | | | | | | |   (1090)  all_52_30 = e0
% 177.22/27.85  | | | | | | | |   (1091)  all_52_28 = e1
% 177.22/27.85  | | | | | | | |   (1092)  all_52_26 = e2
% 177.22/27.85  | | | | | | | |   (1093)  all_52_24 = e3
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | COMBINE_EQS: (185), (1090) imply:
% 177.22/27.85  | | | | | | | |   (1094)  all_6_1 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | SIMP: (1094) implies:
% 177.22/27.85  | | | | | | | |   (1095)  all_6_1 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (4), (5), (8), (15), (16), (17), (18), (19), (20),
% 177.22/27.85  | | | | | | | |            (22), (25), (27), (28), (29), (30), (32), (33), (35),
% 177.22/27.85  | | | | | | | |            (36), (37), (38), (39), (40), (41), (44), (45), (46),
% 177.22/27.85  | | | | | | | |            (47), (48), (50), (51), (52), (53), (55), (56), (57),
% 177.22/27.85  | | | | | | | |            (58), (61), (68), (69), (70), (71), (73), (74), (78),
% 177.22/27.85  | | | | | | | |            (79), (81), (82), (84), (85), (86), (88), (91), (92),
% 177.22/27.85  | | | | | | | |            (93), (95), (96), (98), (99), (101), (103), (106),
% 177.22/27.85  | | | | | | | |            (109), (110), (115), (116), (118), (119), (121),
% 177.22/27.85  | | | | | | | |            (124), (126), (127), (132), (133), (135), (140),
% 177.22/27.85  | | | | | | | |            (141), (145), (146), (147), (149), (150), (153),
% 177.22/27.85  | | | | | | | |            (155), (156), (157), (161), (162), (163), (166),
% 177.22/27.85  | | | | | | | |            (167), (170), (172), (173), (175), (176), (179),
% 177.22/27.85  | | | | | | | |            (181), (182), (183), (184), (189), (192), (195),
% 177.22/27.85  | | | | | | | |            (197), (198), (199), (200), (204), (205), (1043),
% 177.22/27.85  | | | | | | | |            (1045), (1047), (1069), (1071), (1091), (1092),
% 177.22/27.85  | | | | | | | |            (1093), (1095) are inconsistent by sub-proof #369.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | End of split
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | End of split
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | End of split
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | Case 2:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | |   (1096)  all_34_0 = e1
% 177.22/27.85  | | | | |   (1097)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | COMBINE_EQS: (193), (1096) imply:
% 177.22/27.85  | | | | |   (1098)  all_4_0 = e1
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | SIMP: (1098) implies:
% 177.22/27.85  | | | | |   (1099)  all_4_0 = e1
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | REDUCE: (1043), (1099) imply:
% 177.22/27.85  | | | | |   (1100)   ~ (e2 = e1)
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | REDUCE: (88), (1099) imply:
% 177.22/27.85  | | | | |   (1101)  op(all_4_1, all_4_2) = e1
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | BETA: splitting (164) gives:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | Case 1:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1102)  all_58_15 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | COMBINE_EQS: (36), (1102) imply:
% 177.22/27.85  | | | | | |   (1103)  all_6_2 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (144), (1103) imply:
% 177.22/27.85  | | | | | |   (1104)   ~ (all_52_23 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (153), (1103) imply:
% 177.22/27.85  | | | | | |   (1105)   ~ (all_52_25 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (146), (1103) imply:
% 177.22/27.85  | | | | | |   (1106)   ~ (all_52_29 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (93), (1103) imply:
% 177.22/27.85  | | | | | |   (1107)  op(all_6_1, e0) = all_6_0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (96), (1103) imply:
% 177.22/27.85  | | | | | |   (1108)  op(e0, e0) = all_6_1
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (60), (1103) imply:
% 177.22/27.85  | | | | | |   (1109)  op(e0, e0) = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_1, e0, e0,
% 177.22/27.85  | | | | | |              simplifying with (1108), (1109) gives:
% 177.22/27.85  | | | | | |   (1110)  all_6_1 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (1107), (1110) imply:
% 177.22/27.85  | | | | | |   (1111)  op(e0, e0) = all_6_0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, e0, e0,
% 177.22/27.85  | | | | | |              simplifying with (1109), (1111) gives:
% 177.22/27.85  | | | | | |   (1112)  all_6_0 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (1045), (1112) imply:
% 177.22/27.85  | | | | | |   (1113)   ~ (e3 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (181), (1112) imply:
% 177.22/27.85  | | | | | |   (1114)   ~ (e1 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | BETA: splitting (169) gives:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | Case 1:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1115)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.85  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.85  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | REF_CLOSE: (9), (48), (52), (97), (100), (151), (167), (1041),
% 177.22/27.85  | | | | | | |            (1101), (1115) are inconsistent by sub-proof #441.
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | Case 2:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1116)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.85  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | BETA: splitting (1116) gives:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | Case 1:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1117)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_22 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (48), (128), (1117) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | | |            #373.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1118)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (4), (6), (14), (15), (16), (17), (18), (19), (20),
% 177.22/27.85  | | | | | | | |            (24), (27), (28), (34), (35), (38), (40), (41), (44),
% 177.22/27.85  | | | | | | | |            (46), (47), (48), (50), (52), (55), (58), (61), (66),
% 177.22/27.85  | | | | | | | |            (67), (68), (69), (73), (74), (80), (81), (82), (85),
% 177.22/27.85  | | | | | | | |            (86), (90), (91), (92), (99), (104), (110), (113),
% 177.22/27.85  | | | | | | | |            (115), (117), (118), (119), (122), (123), (124),
% 177.22/27.85  | | | | | | | |            (126), (131), (132), (133), (134), (140), (141),
% 177.22/27.85  | | | | | | | |            (148), (149), (150), (152), (154), (156), (157),
% 177.22/27.85  | | | | | | | |            (160), (161), (162), (163), (167), (170), (176),
% 177.22/27.85  | | | | | | | |            (179), (180), (182), (186), (188), (192), (201),
% 177.22/27.85  | | | | | | | |            (204), (205), (1102), (1104), (1105), (1106), (1118)
% 177.22/27.85  | | | | | | | |            are inconsistent by sub-proof #421.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | End of split
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | End of split
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | Case 2:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1119)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.85  | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | ALPHA: (1119) implies:
% 177.22/27.85  | | | | | |   (1120)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | BETA: splitting (169) gives:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | Case 1:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1121)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.85  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.85  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | REF_CLOSE: (9), (48), (52), (97), (100), (151), (167), (1041),
% 177.22/27.85  | | | | | | |            (1101), (1121) are inconsistent by sub-proof #441.
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | Case 2:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1122)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.85  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | BETA: splitting (1122) gives:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | Case 1:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1123)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_22 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (48), (128), (1123) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | | |            #373.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1124)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | ALPHA: (1124) implies:
% 177.22/27.85  | | | | | | | |   (1125)  all_52_30 = e0
% 177.22/27.85  | | | | | | | |   (1126)  all_52_28 = e1
% 177.22/27.85  | | | | | | | |   (1127)  all_52_26 = e2
% 177.22/27.85  | | | | | | | |   (1128)  all_52_24 = e3
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | COMBINE_EQS: (185), (1125) imply:
% 177.22/27.85  | | | | | | | |   (1129)  all_6_1 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (4), (8), (13), (14), (15), (16), (17), (18), (20),
% 177.22/27.85  | | | | | | | |            (21), (22), (25), (27), (29), (30), (33), (35), (36),
% 177.22/27.85  | | | | | | | |            (37), (38), (39), (41), (45), (46), (48), (49), (50),
% 177.22/27.85  | | | | | | | |            (51), (52), (53), (55), (56), (57), (58), (61), (65),
% 177.22/27.85  | | | | | | | |            (67), (73), (74), (78), (79), (81), (82), (83), (84),
% 177.22/27.85  | | | | | | | |            (86), (92), (93), (95), (96), (98), (101), (109),
% 177.22/27.85  | | | | | | | |            (110), (116), (117), (118), (119), (121), (126),
% 177.22/27.85  | | | | | | | |            (132), (133), (134), (140), (145), (147), (150),
% 177.22/27.85  | | | | | | | |            (155), (156), (157), (161), (162), (163), (166),
% 177.22/27.85  | | | | | | | |            (167), (170), (171), (172), (173), (179), (181),
% 177.22/27.85  | | | | | | | |            (182), (183), (184), (186), (189), (192), (197),
% 177.22/27.85  | | | | | | | |            (198), (199), (200), (204), (205), (1045), (1097),
% 177.22/27.85  | | | | | | | |            (1101), (1120), (1126), (1127), (1128), (1129) are
% 177.22/27.85  | | | | | | | |            inconsistent by sub-proof #354.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | End of split
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | End of split
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | End of split
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | End of split
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | Case 2:
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | |   (1130)  all_28_0 = e3
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | COMBINE_EQS: (203), (1130) imply:
% 177.22/27.85  | | | |   (1131)  all_6_0 = e3
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | SIMP: (1131) implies:
% 177.22/27.85  | | | |   (1132)  all_6_0 = e3
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | REDUCE: (93), (1132) imply:
% 177.22/27.85  | | | |   (1133)  op(all_6_1, all_6_2) = e3
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | BETA: splitting (142) gives:
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | Case 1:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | |   (1134)   ~ (all_34_0 = e1)
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | REDUCE: (193), (1134) imply:
% 177.22/27.85  | | | | |   (1135)   ~ (all_4_0 = e1)
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | BETA: splitting (164) gives:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | Case 1:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1136)  all_58_15 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REF_CLOSE: (36), (60), (96), (104), (167), (1133), (1136) are
% 177.22/27.85  | | | | | |            inconsistent by sub-proof #510.
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | Case 2:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1137)   ~ (all_58_15 = e0)
% 177.22/27.85  | | | | | |   (1138)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.85  | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | ALPHA: (1138) implies:
% 177.22/27.85  | | | | | |   (1139)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (36), (1137) imply:
% 177.22/27.85  | | | | | |   (1140)   ~ (all_6_2 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | BETA: splitting (169) gives:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | Case 1:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1141)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.85  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.85  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | REF_CLOSE: (1), (2), (8), (9), (13), (15), (16), (18), (19), (20),
% 177.22/27.85  | | | | | | |            (21), (24), (27), (28), (29), (30), (31), (32), (33),
% 177.22/27.85  | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 177.22/27.85  | | | | | | |            (44), (45), (46), (47), (50), (51), (52), (53), (54),
% 177.22/27.85  | | | | | | |            (55), (56), (57), (58), (61), (63), (65), (68), (69),
% 177.22/27.85  | | | | | | |            (70), (72), (73), (74), (78), (79), (80), (81), (82),
% 177.22/27.85  | | | | | | |            (83), (85), (88), (90), (91), (92), (95), (96), (97),
% 177.22/27.85  | | | | | | |            (100), (102), (103), (104), (106), (109), (110), (111),
% 177.22/27.85  | | | | | | |            (112), (113), (115), (116), (117), (118), (119), (120),
% 177.22/27.85  | | | | | | |            (121), (123), (124), (126), (127), (129), (131), (132),
% 177.22/27.85  | | | | | | |            (133), (134), (135), (136), (139), (140), (144), (146),
% 177.22/27.85  | | | | | | |            (147), (148), (149), (150), (151), (152), (153), (155),
% 177.22/27.85  | | | | | | |            (156), (157), (158), (161), (162), (166), (167), (170),
% 177.22/27.85  | | | | | | |            (172), (173), (176), (178), (179), (180), (182), (183),
% 177.22/27.85  | | | | | | |            (184), (189), (192), (196), (197), (198), (200), (201),
% 177.22/27.85  | | | | | | |            (202), (204), (205), (1041), (1043), (1133), (1135),
% 177.22/27.85  | | | | | | |            (1139), (1140), (1141) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | |            #435.
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | Case 2:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1142)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.85  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | BETA: splitting (1142) gives:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | Case 1:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1143)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_22 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (48), (128), (1143) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | | |            #373.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1144)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (96), (104), (167), (185), (1133), (1144) are
% 177.22/27.85  | | | | | | | |            inconsistent by sub-proof #501.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | End of split
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | End of split
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | End of split
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | Case 2:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | |   (1145)  all_34_0 = e1
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | COMBINE_EQS: (193), (1145) imply:
% 177.22/27.85  | | | | |   (1146)  all_4_0 = e1
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | SIMP: (1146) implies:
% 177.22/27.85  | | | | |   (1147)  all_4_0 = e1
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | REDUCE: (1043), (1147) imply:
% 177.22/27.85  | | | | |   (1148)   ~ (e2 = e1)
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | REDUCE: (88), (1147) imply:
% 177.22/27.85  | | | | |   (1149)  op(all_4_1, all_4_2) = e1
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | BETA: splitting (169) gives:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | Case 1:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1150)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 177.22/27.85  | | | | | |             = e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 177.22/27.85  | | | | | |             & all_52_14 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REF_CLOSE: (9), (48), (52), (97), (100), (151), (167), (1041),
% 177.22/27.85  | | | | | |            (1149), (1150) are inconsistent by sub-proof #441.
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | Case 2:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1151)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.85  | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | BETA: splitting (1151) gives:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | Case 1:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1152)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | |           all_52_22 = e0
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | REF_CLOSE: (48), (128), (1152) are inconsistent by sub-proof #373.
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | Case 2:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1153)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | REF_CLOSE: (96), (104), (167), (185), (1133), (1153) are
% 177.22/27.85  | | | | | | |            inconsistent by sub-proof #501.
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | End of split
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | End of split
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | End of split
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | End of split
% 177.22/27.85  | | | 
% 177.22/27.85  | | Case 2:
% 177.22/27.85  | | | 
% 177.22/27.85  | | |   (1154)  all_26_0 = e2
% 177.22/27.85  | | |   (1155)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.85  | | | 
% 177.22/27.85  | | | COMBINE_EQS: (159), (1154) imply:
% 177.22/27.85  | | |   (1156)  all_4_0 = e2
% 177.22/27.85  | | | 
% 177.22/27.85  | | | SIMP: (1156) implies:
% 177.22/27.85  | | |   (1157)  all_4_0 = e2
% 177.22/27.85  | | | 
% 177.22/27.85  | | | COMBINE_EQS: (62), (1157) imply:
% 177.22/27.85  | | |   (1158)  all_50_0 = e2
% 177.22/27.85  | | | 
% 177.22/27.85  | | | REDUCE: (88), (1157) imply:
% 177.22/27.85  | | |   (1159)  op(all_4_1, all_4_2) = e2
% 177.22/27.85  | | | 
% 177.22/27.85  | | | BETA: splitting (190) gives:
% 177.22/27.85  | | | 
% 177.22/27.85  | | | Case 1:
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | |   (1160)   ~ (all_28_0 = e3)
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | REDUCE: (203), (1160) imply:
% 177.22/27.85  | | | |   (1161)   ~ (all_6_0 = e3)
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | BETA: splitting (143) gives:
% 177.22/27.85  | | | | 
% 177.22/27.85  | | | | Case 1:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | |   (1162)   ~ (all_50_0 = e2)
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | REDUCE: (1158), (1162) imply:
% 177.22/27.85  | | | | |   (1163)  $false
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | CLOSE: (1163) is inconsistent.
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | Case 2:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | |   (1164)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | BETA: splitting (164) gives:
% 177.22/27.85  | | | | | 
% 177.22/27.85  | | | | | Case 1:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1165)  all_58_15 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | COMBINE_EQS: (36), (1165) imply:
% 177.22/27.85  | | | | | |   (1166)  all_6_2 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (144), (1166) imply:
% 177.22/27.85  | | | | | |   (1167)   ~ (all_52_23 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (153), (1166) imply:
% 177.22/27.85  | | | | | |   (1168)   ~ (all_52_25 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (146), (1166) imply:
% 177.22/27.85  | | | | | |   (1169)   ~ (all_52_29 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (93), (1166) imply:
% 177.22/27.85  | | | | | |   (1170)  op(all_6_1, e0) = all_6_0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (96), (1166) imply:
% 177.22/27.85  | | | | | |   (1171)  op(e0, e0) = all_6_1
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (60), (1166) imply:
% 177.22/27.85  | | | | | |   (1172)  op(e0, e0) = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_1, e0, e0,
% 177.22/27.85  | | | | | |              simplifying with (1171), (1172) gives:
% 177.22/27.85  | | | | | |   (1173)  all_6_1 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (1170), (1173) imply:
% 177.22/27.85  | | | | | |   (1174)  op(e0, e0) = all_6_0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | GROUND_INST: instantiating (167) with e0, all_6_0, e0, e0,
% 177.22/27.85  | | | | | |              simplifying with (1172), (1174) gives:
% 177.22/27.85  | | | | | |   (1175)  all_6_0 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (1161), (1175) imply:
% 177.22/27.85  | | | | | |   (1176)   ~ (e3 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (181), (1175) imply:
% 177.22/27.85  | | | | | |   (1177)   ~ (e1 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | BETA: splitting (169) gives:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | Case 1:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1178)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.85  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.85  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | REF_CLOSE: (9), (52), (67), (97), (100), (151), (167), (1041),
% 177.22/27.85  | | | | | | |            (1159), (1178) are inconsistent by sub-proof #434.
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | Case 2:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1179)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.85  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | BETA: splitting (1179) gives:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | Case 1:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1180)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_22 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (48), (128), (1180) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | | |            #373.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1181)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (4), (6), (14), (15), (16), (17), (18), (19), (20),
% 177.22/27.85  | | | | | | | |            (24), (27), (28), (34), (35), (38), (40), (41), (44),
% 177.22/27.85  | | | | | | | |            (46), (47), (48), (50), (52), (55), (58), (61), (66),
% 177.22/27.85  | | | | | | | |            (67), (68), (69), (73), (74), (80), (81), (82), (85),
% 177.22/27.85  | | | | | | | |            (86), (90), (91), (92), (99), (104), (110), (113),
% 177.22/27.85  | | | | | | | |            (115), (117), (118), (119), (122), (123), (124),
% 177.22/27.85  | | | | | | | |            (126), (131), (132), (133), (134), (140), (141),
% 177.22/27.85  | | | | | | | |            (148), (149), (150), (152), (154), (156), (157),
% 177.22/27.85  | | | | | | | |            (160), (161), (162), (163), (167), (170), (176),
% 177.22/27.85  | | | | | | | |            (179), (180), (182), (186), (188), (192), (201),
% 177.22/27.85  | | | | | | | |            (204), (205), (1165), (1167), (1168), (1169), (1181)
% 177.22/27.85  | | | | | | | |            are inconsistent by sub-proof #421.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | End of split
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | End of split
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | Case 2:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | |   (1182)   ~ (all_58_15 = e0)
% 177.22/27.85  | | | | | |   (1183)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.22/27.85  | | | | | |           (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | ALPHA: (1183) implies:
% 177.22/27.85  | | | | | |   (1184)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | REDUCE: (36), (1182) imply:
% 177.22/27.85  | | | | | |   (1185)   ~ (all_6_2 = e0)
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | BETA: splitting (169) gives:
% 177.22/27.85  | | | | | | 
% 177.22/27.85  | | | | | | Case 1:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1186)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 177.22/27.85  | | | | | | |             all_52_6 = e0) | (all_52_8 = e3 & all_52_10 = e2 &
% 177.22/27.85  | | | | | | |             all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | REF_CLOSE: (9), (52), (67), (97), (100), (151), (167), (1041),
% 177.22/27.85  | | | | | | |            (1159), (1186) are inconsistent by sub-proof #434.
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | Case 2:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | |   (1187)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.85  | | | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | BETA: splitting (1187) gives:
% 177.22/27.85  | | | | | | | 
% 177.22/27.85  | | | | | | | Case 1:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1188)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_22 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | REF_CLOSE: (48), (128), (1188) are inconsistent by sub-proof
% 177.22/27.85  | | | | | | | |            #373.
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | Case 2:
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | |   (1189)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.85  | | | | | | | |           all_52_30 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | ALPHA: (1189) implies:
% 177.22/27.85  | | | | | | | |   (1190)  all_52_30 = e0
% 177.22/27.85  | | | | | | | |   (1191)  all_52_28 = e1
% 177.22/27.85  | | | | | | | |   (1192)  all_52_26 = e2
% 177.22/27.85  | | | | | | | |   (1193)  all_52_24 = e3
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | COMBINE_EQS: (185), (1190) imply:
% 177.22/27.85  | | | | | | | |   (1194)  all_6_1 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.85  | | | | | | | | SIMP: (1194) implies:
% 177.22/27.85  | | | | | | | |   (1195)  all_6_1 = e0
% 177.22/27.85  | | | | | | | | 
% 177.22/27.86  | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (14), (15), (16), (17), (18),
% 177.22/27.86  | | | | | | | |            (20), (21), (22), (23), (25), (27), (28), (29), (30),
% 177.22/27.86  | | | | | | | |            (32), (33), (35), (36), (37), (39), (40), (41), (44),
% 177.22/27.86  | | | | | | | |            (45), (46), (48), (50), (52), (53), (55), (56), (57),
% 177.22/27.86  | | | | | | | |            (58), (61), (64), (67), (69), (70), (73), (74), (77),
% 177.22/27.86  | | | | | | | |            (78), (79), (81), (82), (84), (86), (89), (92), (93),
% 177.22/27.86  | | | | | | | |            (95), (96), (98), (99), (101), (109), (110), (118),
% 177.22/27.86  | | | | | | | |            (119), (121), (124), (126), (127), (132), (133),
% 177.22/27.86  | | | | | | | |            (135), (137), (140), (145), (146), (147), (150),
% 177.22/27.86  | | | | | | | |            (153), (155), (156), (157), (161), (162), (163),
% 177.22/27.86  | | | | | | | |            (167), (170), (173), (176), (181), (182), (183),
% 177.22/27.86  | | | | | | | |            (184), (186), (189), (192), (197), (199), (204),
% 177.22/27.86  | | | | | | | |            (205), (1155), (1159), (1161), (1164), (1184),
% 177.22/27.86  | | | | | | | |            (1185), (1191), (1192), (1193), (1195) are
% 177.22/27.86  | | | | | | | |            inconsistent by sub-proof #347.
% 177.22/27.86  | | | | | | | | 
% 177.22/27.86  | | | | | | | End of split
% 177.22/27.86  | | | | | | | 
% 177.22/27.86  | | | | | | End of split
% 177.22/27.86  | | | | | | 
% 177.22/27.86  | | | | | End of split
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | End of split
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | Case 2:
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | |   (1196)  all_28_0 = e3
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | | COMBINE_EQS: (203), (1196) imply:
% 177.22/27.86  | | | |   (1197)  all_6_0 = e3
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | | SIMP: (1197) implies:
% 177.22/27.86  | | | |   (1198)  all_6_0 = e3
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | | REDUCE: (93), (1198) imply:
% 177.22/27.86  | | | |   (1199)  op(all_6_1, all_6_2) = e3
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | | BETA: splitting (169) gives:
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | | Case 1:
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | |   (1200)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 177.22/27.86  | | | | |             e0) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 177.22/27.86  | | | | |             all_52_14 = e0)
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | | REF_CLOSE: (9), (52), (67), (97), (100), (151), (167), (1041), (1159),
% 177.22/27.86  | | | | |            (1200) are inconsistent by sub-proof #434.
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | Case 2:
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | |   (1201)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.86  | | | | |             all_52_22 = e0) | (all_52_24 = e3 & all_52_26 = e2 &
% 177.22/27.86  | | | | |             all_52_28 = e1 & all_52_30 = e0)
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | | BETA: splitting (1201) gives:
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | | Case 1:
% 177.22/27.86  | | | | | | 
% 177.22/27.86  | | | | | |   (1202)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 177.22/27.86  | | | | | |           all_52_22 = e0
% 177.22/27.86  | | | | | | 
% 177.22/27.86  | | | | | | REF_CLOSE: (48), (128), (1202) are inconsistent by sub-proof #427.
% 177.22/27.86  | | | | | | 
% 177.22/27.86  | | | | | Case 2:
% 177.22/27.86  | | | | | | 
% 177.22/27.86  | | | | | |   (1203)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.22/27.86  | | | | | |           all_52_30 = e0
% 177.22/27.86  | | | | | | 
% 177.22/27.86  | | | | | | REF_CLOSE: (96), (104), (167), (185), (1199), (1203) are
% 177.22/27.86  | | | | | |            inconsistent by sub-proof #501.
% 177.22/27.86  | | | | | | 
% 177.22/27.86  | | | | | End of split
% 177.22/27.86  | | | | | 
% 177.22/27.86  | | | | End of split
% 177.22/27.86  | | | | 
% 177.22/27.86  | | | End of split
% 177.22/27.86  | | | 
% 177.22/27.86  | | End of split
% 177.22/27.86  | | 
% 177.22/27.86  | End of split
% 177.22/27.86  | 
% 177.22/27.86  End of proof
% 177.22/27.86  
% 177.22/27.86  Sub-proof #346 shows that the following formulas are inconsistent:
% 177.22/27.86  ----------------------------------------------------------------
% 177.22/27.86    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.86    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.86    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.22/27.86    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.86    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.86    (6)   ~ (all_52_27 = all_10_2)
% 177.22/27.86    (7)   ~ (all_52_17 = all_52_23)
% 177.22/27.86    (8)  op(e2, all_10_2) = all_10_1
% 177.22/27.86    (9)  all_22_2 = all_14_2
% 177.22/27.86    (10)   ~ (all_52_13 = all_52_29)
% 177.22/27.86    (11)  all_56_3 = all_52_7
% 177.22/27.86    (12)  op(e3, e2) = all_52_3
% 177.22/27.86    (13)   ~ (all_52_9 = all_52_25)
% 177.22/27.86    (14)  op(e3, all_52_25) = all_52_24
% 177.22/27.86    (15)   ~ (all_52_19 = all_52_23)
% 177.22/27.86    (16)  all_56_11 = all_52_23
% 177.22/27.86    (17)  op(e1, e2) = all_52_19
% 177.22/27.86    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.86    (19)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.86    (20)  op(e3, all_52_9) = all_52_8
% 177.22/27.86    (21)  all_50_1 = all_4_1
% 177.22/27.86    (22)   ~ (all_52_3 = all_10_2)
% 177.22/27.86    (23)  all_58_5 = all_52_13
% 177.22/27.86    (24)   ~ (all_6_2 = e0)
% 177.22/27.86    (25)   ~ (all_52_25 = all_52_29)
% 177.22/27.86    (26)  all_56_15 = all_6_2
% 177.22/27.86    (27)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.86    (28)  op(e2, e0) = all_52_15
% 177.22/27.86    (29)  all_58_3 = all_10_2
% 177.22/27.86    (30)  all_56_9 = all_52_19
% 177.22/27.86    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.86    (32)  all_58_15 = all_6_2
% 177.22/27.86    (33)   ~ (all_52_9 = all_4_2)
% 177.22/27.86    (34)   ~ (all_52_5 = all_52_7)
% 177.22/27.86    (35)  all_58_10 = all_52_15
% 177.22/27.86    (36)   ~ (all_52_5 = all_4_2)
% 177.22/27.86    (37)  all_58_7 = all_52_19
% 177.22/27.86    (38)  all_56_4 = all_52_9
% 177.22/27.86    (39)   ~ (all_52_15 = all_6_2)
% 177.22/27.86    (40)   ~ (all_52_17 = all_52_25)
% 177.22/27.86    (41)  all_58_4 = all_52_5
% 177.22/27.86    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.86    (43)   ~ (e3 = e1)
% 177.22/27.86    (44)   ~ (all_52_27 = all_52_29)
% 177.22/27.86    (45)   ~ (all_52_17 = all_14_2)
% 177.22/27.86    (46)  op(e3, all_4_2) = all_4_1
% 177.22/27.86    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.86    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.86    (49)   ~ (all_52_7 = all_4_2)
% 177.22/27.86    (50)  all_58_1 = all_52_3
% 177.22/27.86    (51)  all_58_0 = all_4_2
% 177.22/27.86    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.86    (53)  op(e1, all_52_13) = all_52_12
% 177.22/27.86    (54)  op(e1, all_52_29) = all_52_28
% 177.22/27.86    (55)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.86          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.86    (56)  all_50_2 = all_4_2
% 177.22/27.86    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.86    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.86    (59)   ~ (all_4_1 = e2)
% 177.22/27.86    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.86    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.86    (62)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.86    (63)  all_58_14 = all_52_29
% 177.22/27.86    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.86    (65)  all_26_2 = all_4_2
% 177.22/27.86    (66)   ~ (all_52_3 = all_52_5)
% 177.22/27.86    (67)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.86    (68)  op(e2, e1) = all_52_13
% 177.22/27.86    (69)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.86    (70)  all_58_8 = all_14_2
% 177.22/27.86    (71)  all_56_1 = all_52_3
% 177.22/27.86    (72)  op(e1, all_14_2) = e3
% 177.22/27.86    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.86    (74)   ~ (all_52_5 = all_14_2)
% 177.22/27.86    (75)   ~ (all_52_3 = all_52_27)
% 177.22/27.86    (76)   ~ (all_52_3 = all_4_2)
% 177.22/27.86    (77)  op(e0, e3) = all_52_25
% 177.22/27.86    (78)  all_52_0 = all_4_1
% 177.22/27.86    (79)   ~ (all_52_9 = all_10_2)
% 177.22/27.86    (80)  op(all_4_1, all_4_2) = e2
% 177.22/27.86    (81)  op(e3, all_52_17) = all_52_16
% 177.22/27.86    (82)  all_52_10 = all_10_1
% 177.22/27.86    (83)   ~ (all_52_13 = all_14_2)
% 177.22/27.86    (84)   ~ (e3 = e0)
% 177.22/27.86    (85)  all_22_0 = all_14_0
% 177.22/27.86    (86)   ~ (all_52_9 = all_52_13)
% 177.22/27.86    (87)  op(e0, all_52_23) = all_52_22
% 177.22/27.86    (88)   ~ (all_52_15 = all_52_23)
% 177.22/27.86    (89)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.86    (90)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.86    (91)   ~ (all_52_5 = all_52_29)
% 177.22/27.86    (92)  all_56_2 = all_52_5
% 177.22/27.86    (93)  all_58_13 = all_52_27
% 177.22/27.86    (94)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.86    (95)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.86    (96)  all_56_5 = all_10_2
% 177.22/27.86    (97)   ~ (all_52_9 = all_52_17)
% 177.22/27.86    (98)   ~ (all_14_0 = e2)
% 177.22/27.86    (99)  all_58_6 = all_52_17
% 177.22/27.86    (100)   ~ (all_52_3 = all_52_7)
% 177.22/27.86    (101)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.86    (102)  op(e2, all_52_19) = all_52_18
% 177.22/27.86    (103)   ~ (e1 = e0)
% 177.22/27.86    (104)  all_56_0 = all_4_2
% 177.22/27.86    (105)  all_58_11 = all_52_23
% 177.22/27.86    (106)   ~ (all_52_3 = all_52_19)
% 177.22/27.86    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.86    (108)   ~ (all_52_7 = all_52_15)
% 177.22/27.86    (109)  all_26_1 = all_4_1
% 177.22/27.86    (110)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 177.22/27.86    (111)  op(e0, all_52_15) = all_52_14
% 177.22/27.86    (112)   ~ (all_52_29 = all_14_2)
% 177.22/27.86    (113)   ~ (all_52_19 = all_10_2)
% 177.22/27.86    (114)   ~ (all_52_23 = all_6_2)
% 177.22/27.86    (115)   ~ (all_52_29 = all_6_2)
% 177.22/27.86    (116)  all_58_2 = all_52_9
% 177.22/27.86    (117)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.86    (118)  op(e3, e1) = all_52_5
% 177.22/27.86    (119)  all_56_10 = all_14_2
% 177.22/27.86    (120)   ~ (all_52_25 = all_6_2)
% 177.22/27.86    (121)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.86    (122)  op(e1, e3) = all_52_17
% 177.22/27.86    (123)   ~ (all_52_25 = all_4_2)
% 177.22/27.86    (124)  op(e3, e0) = all_52_7
% 177.22/27.86    (125)  op(e3, e3) = all_4_2
% 177.22/27.86    (126)  all_56_8 = all_52_17
% 177.22/27.86    (127)   ~ (all_52_17 = all_4_2)
% 177.22/27.86    (128)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.86             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.86    (129)   ~ (all_52_25 = all_52_27)
% 177.22/27.86    (130)   ~ (all_52_27 = all_6_2)
% 177.22/27.86    (131)   ~ (all_52_7 = all_6_2)
% 177.22/27.86    (132)   ~ (all_10_0 = e3)
% 177.22/27.86    (133)   ~ (all_52_19 = all_52_27)
% 177.22/27.86    (134)   ~ (all_52_7 = all_52_23)
% 177.22/27.86    (135)   ~ (all_52_13 = all_10_2)
% 177.22/27.86    (136)  op(e2, all_52_27) = all_52_26
% 177.22/27.86    (137)   ~ (all_52_17 = all_52_19)
% 177.22/27.86    (138)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.86    (139)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.86    (140)  op(e1, all_14_2) = all_14_1
% 177.22/27.86    (141)  op(e3, all_14_2) = all_14_0
% 177.22/27.86    (142)  all_58_9 = all_52_7
% 177.22/27.86    (143)  all_58_12 = all_52_25
% 177.22/27.86    (144)   ~ (all_10_0 = e1)
% 177.22/27.86    (145)  all_56_6 = all_52_13
% 177.22/27.86    (146)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.86    (147)   ~ (all_52_9 = all_52_15)
% 177.22/27.86    (148)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.86    (149)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.86    (150)   ~ (all_52_19 = all_14_2)
% 177.22/27.86    (151)  op(e2, e3) = all_52_9
% 177.22/27.86    (152)  all_56_13 = all_52_27
% 177.22/27.86  
% 177.22/27.86  Begin of proof
% 177.22/27.86  | 
% 177.22/27.86  | BETA: splitting (55) gives:
% 177.22/27.86  | 
% 177.22/27.86  | Case 1:
% 177.22/27.86  | | 
% 177.22/27.86  | |   (153)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.22/27.86  | | 
% 177.22/27.86  | | REF_CLOSE: (46), (59), (78), (80), (128), (153) are inconsistent by
% 177.22/27.86  | |            sub-proof #494.
% 177.22/27.86  | | 
% 177.22/27.86  | Case 2:
% 177.22/27.86  | | 
% 177.22/27.86  | |   (154)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.86  | | 
% 177.22/27.86  | | ALPHA: (154) implies:
% 177.22/27.86  | |   (155)  all_52_14 = e0
% 177.22/27.86  | |   (156)  all_52_12 = e1
% 177.22/27.86  | |   (157)  all_52_10 = e2
% 177.22/27.86  | |   (158)  all_52_8 = e3
% 177.22/27.86  | | 
% 177.22/27.86  | | COMBINE_EQS: (82), (157) imply:
% 177.22/27.86  | |   (159)  all_10_1 = e2
% 177.22/27.86  | | 
% 177.22/27.86  | | REDUCE: (90), (159) imply:
% 177.22/27.86  | |   (160)  op(e2, all_10_2) = all_10_0
% 177.22/27.86  | | 
% 177.22/27.86  | | REDUCE: (20), (158) imply:
% 177.22/27.86  | |   (161)  op(e3, all_52_9) = e3
% 177.22/27.86  | | 
% 177.22/27.86  | | REDUCE: (8), (159) imply:
% 177.22/27.86  | |   (162)  op(e2, all_10_2) = e2
% 177.22/27.86  | | 
% 177.22/27.86  | | REDUCE: (53), (156) imply:
% 177.22/27.86  | |   (163)  op(e1, all_52_13) = e1
% 177.22/27.86  | | 
% 177.22/27.86  | | REDUCE: (111), (155) imply:
% 177.22/27.86  | |   (164)  op(e0, all_52_15) = e0
% 177.22/27.86  | | 
% 177.22/27.86  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 177.22/27.86  | |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 177.22/27.86  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.22/27.86  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.22/27.86  | |            (48), (49), (50), (51), (52), (54), (56), (57), (58), (59), (60),
% 177.22/27.86  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 177.22/27.86  | |            (72), (73), (74), (75), (76), (77), (79), (80), (81), (83), (84),
% 177.22/27.86  | |            (85), (86), (87), (88), (89), (91), (92), (93), (94), (95), (96),
% 177.22/27.86  | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 177.22/27.86  | |            (106), (107), (108), (109), (110), (112), (113), (114), (115),
% 177.22/27.86  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.22/27.86  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 177.22/27.86  | |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 177.22/27.86  | |            (143), (144), (145), (146), (147), (148), (149), (150), (151),
% 177.22/27.86  | |            (152), (160), (161), (162), (163), (164) are inconsistent by
% 177.22/27.86  | |            sub-proof #349.
% 177.22/27.86  | | 
% 177.22/27.86  | End of split
% 177.22/27.86  | 
% 177.22/27.86  End of proof
% 177.22/27.86  
% 177.22/27.86  Sub-proof #347 shows that the following formulas are inconsistent:
% 177.22/27.86  ----------------------------------------------------------------
% 177.22/27.86    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.86    (2)   ~ (all_52_27 = all_10_2)
% 177.22/27.86    (3)  op(e2, e2) = all_10_2
% 177.22/27.86    (4)   ~ (all_52_17 = all_52_23)
% 177.22/27.86    (5)  all_52_26 = e2
% 177.22/27.86    (6)   ~ (all_6_0 = e3)
% 177.22/27.86    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.86    (8)  all_56_3 = all_52_7
% 177.22/27.86    (9)  op(e3, e2) = all_52_3
% 177.22/27.86    (10)   ~ (all_52_9 = all_52_25)
% 177.22/27.86    (11)  op(e3, all_52_25) = all_52_24
% 177.22/27.86    (12)   ~ (all_52_19 = all_52_23)
% 177.22/27.86    (13)  op(e1, e2) = all_52_19
% 177.22/27.86    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.86    (15)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.86    (16)  op(e3, all_52_9) = all_52_8
% 177.22/27.86    (17)  all_50_1 = all_4_1
% 177.22/27.86    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.86    (19)  all_58_5 = all_52_13
% 177.22/27.86    (20)   ~ (all_6_2 = e0)
% 177.22/27.86    (21)   ~ (all_52_25 = all_52_29)
% 177.22/27.86    (22)  all_56_15 = all_6_2
% 177.22/27.86    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.86    (24)  all_6_1 = e0
% 177.22/27.86    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.86    (26)  all_58_3 = all_10_2
% 177.22/27.86    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.86    (28)  all_58_15 = all_6_2
% 177.22/27.86    (29)   ~ (all_52_9 = all_4_2)
% 177.22/27.86    (30)  all_58_10 = all_52_15
% 177.22/27.86    (31)   ~ (all_52_5 = all_4_2)
% 177.22/27.86    (32)  all_58_7 = all_52_19
% 177.22/27.86    (33)   ~ (all_52_17 = all_52_25)
% 177.22/27.86    (34)  op(e0, e1) = all_52_29
% 177.22/27.86    (35)  all_58_4 = all_52_5
% 177.22/27.86    (36)   ~ (e3 = e1)
% 177.22/27.86    (37)   ~ (all_52_27 = all_52_29)
% 177.22/27.86    (38)  op(e3, all_4_2) = all_4_1
% 177.22/27.86    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.86    (40)   ~ (all_52_7 = all_4_2)
% 177.22/27.86    (41)  all_58_1 = all_52_3
% 177.22/27.86    (42)   ~ (all_52_13 = all_52_15)
% 177.22/27.86    (43)  all_58_0 = all_4_2
% 177.22/27.86    (44)  op(e1, all_52_29) = all_52_28
% 177.22/27.86    (45)  all_50_2 = all_4_2
% 177.22/27.86    (46)   ~ (all_4_1 = e2)
% 177.22/27.86    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.86    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.86    (49)  all_58_14 = all_52_29
% 177.22/27.86    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.86    (51)  all_26_2 = all_4_2
% 177.22/27.86    (52)   ~ (all_52_3 = all_52_5)
% 177.22/27.86    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.86    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.86    (55)  all_58_8 = all_14_2
% 177.22/27.86    (56)  op(e0, e2) = all_52_27
% 177.22/27.86    (57)  op(e1, all_14_2) = e3
% 177.22/27.86    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.86    (59)   ~ (all_52_3 = all_4_2)
% 177.22/27.86    (60)  op(all_6_1, all_6_2) = all_6_0
% 177.22/27.86    (61)  op(e0, e3) = all_52_25
% 177.22/27.86    (62)  op(e0, all_6_2) = all_6_1
% 177.22/27.86    (63)   ~ (all_52_9 = all_10_2)
% 177.22/27.86    (64)  op(all_4_1, all_4_2) = e2
% 177.22/27.86    (65)  op(e3, all_52_17) = all_52_16
% 177.22/27.86    (66)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.86    (67)   ~ (all_52_9 = all_52_13)
% 177.22/27.86    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.86    (69)  all_56_12 = all_52_25
% 177.22/27.86    (70)  all_58_13 = all_52_27
% 177.22/27.86    (71)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.86    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.86    (73)   ~ (all_52_9 = all_52_17)
% 177.22/27.86    (74)  all_58_6 = all_52_17
% 177.22/27.86    (75)   ~ (all_52_3 = all_52_7)
% 177.22/27.86    (76)  all_56_0 = all_4_2
% 177.22/27.86    (77)  all_58_11 = all_52_23
% 177.22/27.86    (78)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.86    (79)  all_26_1 = all_4_1
% 177.22/27.86    (80)   ~ (all_52_29 = all_14_2)
% 177.22/27.86    (81)   ~ (all_6_0 = e2)
% 177.22/27.86    (82)   ~ (all_52_29 = all_6_2)
% 177.22/27.86    (83)  all_58_2 = all_52_9
% 177.22/27.86    (84)  op(e3, e1) = all_52_5
% 177.22/27.86    (85)   ~ (all_52_25 = all_6_2)
% 177.22/27.86    (86)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.86    (87)  op(e1, e1) = all_14_2
% 177.22/27.86    (88)  op(e1, e3) = all_52_17
% 177.22/27.86    (89)   ~ (all_52_25 = all_4_2)
% 177.22/27.86    (90)  op(e3, e0) = all_52_7
% 177.22/27.86    (91)  all_52_28 = e1
% 177.22/27.86    (92)  op(e3, e3) = all_4_2
% 177.22/27.86    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.86    (94)   ~ (all_52_25 = all_52_27)
% 177.22/27.86    (95)   ~ (all_52_7 = all_6_2)
% 177.22/27.86    (96)   ~ (all_52_19 = all_52_27)
% 177.22/27.86    (97)   ~ (all_6_0 = e1)
% 177.22/27.86    (98)  op(e2, all_52_27) = all_52_26
% 177.22/27.86    (99)   ~ (all_52_17 = all_52_19)
% 177.22/27.86    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.86    (101)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.86    (102)  all_58_9 = all_52_7
% 177.22/27.86    (103)  all_52_24 = e3
% 177.22/27.86    (104)  all_58_12 = all_52_25
% 177.22/27.86    (105)   ~ (all_52_9 = all_52_15)
% 177.22/27.86    (106)   ~ (e3 = e2)
% 177.22/27.86    (107)  op(e2, e3) = all_52_9
% 177.22/27.86    (108)  all_56_13 = all_52_27
% 177.22/27.86  
% 177.22/27.86  Begin of proof
% 177.22/27.86  | 
% 177.22/27.86  | REDUCE: (24), (60) imply:
% 177.22/27.86  |   (109)  op(e0, all_6_2) = all_6_0
% 177.22/27.86  | 
% 177.22/27.86  | REDUCE: (11), (103) imply:
% 177.22/27.86  |   (110)  op(e3, all_52_25) = e3
% 177.22/27.86  | 
% 177.22/27.86  | REDUCE: (5), (98) imply:
% 177.22/27.86  |   (111)  op(e2, all_52_27) = e2
% 177.22/27.86  | 
% 177.22/27.86  | REDUCE: (44), (91) imply:
% 177.22/27.86  |   (112)  op(e1, all_52_29) = e1
% 177.22/27.86  | 
% 177.22/27.86  | REDUCE: (24), (62) imply:
% 177.22/27.86  |   (113)  op(e0, all_6_2) = e0
% 177.22/27.86  | 
% 177.22/27.86  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 177.22/27.86  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 177.22/27.86  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.22/27.86  |            (38), (39), (40), (41), (42), (43), (45), (46), (47), (48), (49),
% 177.22/27.86  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (61),
% 177.22/27.86  |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 177.22/27.86  |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 177.22/27.86  |            (85), (86), (87), (88), (89), (90), (92), (93), (94), (95), (96),
% 177.22/27.86  |            (97), (99), (100), (101), (102), (104), (105), (106), (107), (108),
% 177.22/27.86  |            (109), (110), (111), (112), (113) are inconsistent by sub-proof
% 177.22/27.86  |            #348.
% 177.22/27.86  | 
% 177.22/27.86  End of proof
% 177.22/27.86  
% 177.22/27.86  Sub-proof #348 shows that the following formulas are inconsistent:
% 177.22/27.86  ----------------------------------------------------------------
% 177.22/27.86    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.86    (2)   ~ (all_52_27 = all_10_2)
% 177.22/27.86    (3)  op(e2, e2) = all_10_2
% 177.22/27.86    (4)   ~ (all_52_17 = all_52_23)
% 177.22/27.86    (5)   ~ (all_6_0 = e3)
% 177.22/27.86    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.86    (7)  all_56_3 = all_52_7
% 177.22/27.86    (8)  op(e3, e2) = all_52_3
% 177.22/27.86    (9)   ~ (all_52_9 = all_52_25)
% 177.22/27.86    (10)   ~ (all_52_19 = all_52_23)
% 177.22/27.86    (11)  op(e1, e2) = all_52_19
% 177.22/27.86    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.86    (13)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.86    (14)  op(e3, all_52_9) = all_52_8
% 177.22/27.86    (15)  all_50_1 = all_4_1
% 177.22/27.86    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.86    (17)  all_58_5 = all_52_13
% 177.22/27.86    (18)   ~ (all_6_2 = e0)
% 177.22/27.86    (19)   ~ (all_52_25 = all_52_29)
% 177.22/27.86    (20)  all_56_15 = all_6_2
% 177.22/27.86    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.86    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.86    (23)  all_58_3 = all_10_2
% 177.22/27.86    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.86    (25)  all_58_15 = all_6_2
% 177.22/27.86    (26)  op(e0, all_6_2) = e0
% 177.22/27.86    (27)   ~ (all_52_9 = all_4_2)
% 177.22/27.86    (28)  all_58_10 = all_52_15
% 177.22/27.86    (29)   ~ (all_52_5 = all_4_2)
% 177.22/27.86    (30)  all_58_7 = all_52_19
% 177.22/27.86    (31)   ~ (all_52_17 = all_52_25)
% 177.22/27.86    (32)  op(e0, e1) = all_52_29
% 177.22/27.86    (33)  all_58_4 = all_52_5
% 177.22/27.86    (34)   ~ (e3 = e1)
% 177.22/27.86    (35)   ~ (all_52_27 = all_52_29)
% 177.22/27.86    (36)  op(e3, all_4_2) = all_4_1
% 177.22/27.86    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.86    (38)   ~ (all_52_7 = all_4_2)
% 177.22/27.86    (39)  all_58_1 = all_52_3
% 177.22/27.86    (40)   ~ (all_52_13 = all_52_15)
% 177.22/27.86    (41)  all_58_0 = all_4_2
% 177.22/27.86    (42)  op(e2, all_52_27) = e2
% 177.22/27.86    (43)  all_50_2 = all_4_2
% 177.22/27.86    (44)   ~ (all_4_1 = e2)
% 177.22/27.86    (45)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.86    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.86    (47)  all_58_14 = all_52_29
% 177.22/27.86    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.86    (49)  all_26_2 = all_4_2
% 177.22/27.86    (50)   ~ (all_52_3 = all_52_5)
% 177.22/27.86    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.86    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.86    (53)  all_58_8 = all_14_2
% 177.22/27.86    (54)  op(e0, e2) = all_52_27
% 177.22/27.86    (55)  op(e1, all_14_2) = e3
% 177.22/27.86    (56)  op(e1, all_52_29) = e1
% 177.22/27.86    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.86    (58)   ~ (all_52_3 = all_4_2)
% 177.22/27.86    (59)  op(e0, e3) = all_52_25
% 177.22/27.86    (60)   ~ (all_52_9 = all_10_2)
% 177.22/27.86    (61)  op(all_4_1, all_4_2) = e2
% 177.22/27.86    (62)  op(e3, all_52_17) = all_52_16
% 177.22/27.86    (63)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.86    (64)   ~ (all_52_9 = all_52_13)
% 177.22/27.86    (65)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.86    (66)  all_56_12 = all_52_25
% 177.22/27.86    (67)  all_58_13 = all_52_27
% 177.22/27.86    (68)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.86    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.86    (70)   ~ (all_52_9 = all_52_17)
% 177.22/27.86    (71)  all_58_6 = all_52_17
% 177.22/27.86    (72)   ~ (all_52_3 = all_52_7)
% 177.22/27.86    (73)  all_56_0 = all_4_2
% 177.22/27.86    (74)  all_58_11 = all_52_23
% 177.22/27.86    (75)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.86    (76)  all_26_1 = all_4_1
% 177.22/27.86    (77)   ~ (all_52_29 = all_14_2)
% 177.22/27.86    (78)  op(e3, all_52_25) = e3
% 177.22/27.86    (79)   ~ (all_6_0 = e2)
% 177.22/27.86    (80)   ~ (all_52_29 = all_6_2)
% 177.22/27.86    (81)  all_58_2 = all_52_9
% 177.22/27.86    (82)  op(e3, e1) = all_52_5
% 177.22/27.86    (83)   ~ (all_52_25 = all_6_2)
% 177.22/27.86    (84)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.86    (85)  op(e1, e1) = all_14_2
% 177.22/27.86    (86)  op(e1, e3) = all_52_17
% 177.22/27.86    (87)   ~ (all_52_25 = all_4_2)
% 177.22/27.86    (88)  op(e3, e0) = all_52_7
% 177.22/27.86    (89)  op(e3, e3) = all_4_2
% 177.22/27.86    (90)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.86    (91)   ~ (all_52_25 = all_52_27)
% 177.22/27.86    (92)  op(e0, all_6_2) = all_6_0
% 177.22/27.86    (93)   ~ (all_52_7 = all_6_2)
% 177.22/27.86    (94)   ~ (all_52_19 = all_52_27)
% 177.22/27.86    (95)   ~ (all_6_0 = e1)
% 177.22/27.86    (96)   ~ (all_52_17 = all_52_19)
% 177.22/27.87    (97)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.87    (98)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.87    (99)  all_58_9 = all_52_7
% 177.22/27.87    (100)  all_58_12 = all_52_25
% 177.22/27.87    (101)   ~ (all_52_9 = all_52_15)
% 177.22/27.87    (102)   ~ (e3 = e2)
% 177.22/27.87    (103)  op(e2, e3) = all_52_9
% 177.22/27.87    (104)  all_56_13 = all_52_27
% 177.22/27.87  
% 177.22/27.87  Begin of proof
% 177.22/27.87  | 
% 177.22/27.87  | GROUND_INST: instantiating (90) with e0, all_6_0, all_6_2, e0, simplifying
% 177.22/27.87  |              with (26), (92) gives:
% 177.22/27.87  |   (105)  all_6_0 = e0
% 177.22/27.87  | 
% 177.22/27.87  | REDUCE: (5), (105) imply:
% 177.22/27.87  |   (106)   ~ (e3 = e0)
% 177.22/27.87  | 
% 177.22/27.87  | SIMP: (106) implies:
% 177.22/27.87  |   (107)   ~ (e3 = e0)
% 177.22/27.87  | 
% 177.22/27.87  | REDUCE: (79), (105) imply:
% 177.22/27.87  |   (108)   ~ (e2 = e0)
% 177.22/27.87  | 
% 177.22/27.87  | SIMP: (108) implies:
% 177.22/27.87  |   (109)   ~ (e2 = e0)
% 177.22/27.87  | 
% 177.22/27.87  | REDUCE: (95), (105) imply:
% 177.22/27.87  |   (110)   ~ (e1 = e0)
% 177.22/27.87  | 
% 177.22/27.87  | SIMP: (110) implies:
% 177.22/27.87  |   (111)   ~ (e1 = e0)
% 177.22/27.87  | 
% 177.22/27.87  | BETA: splitting (37) gives:
% 177.22/27.87  | 
% 177.22/27.87  | Case 1:
% 177.22/27.87  | | 
% 177.22/27.87  | |   (112)  all_56_15 = e3
% 177.22/27.87  | | 
% 177.22/27.87  | | COMBINE_EQS: (20), (112) imply:
% 177.22/27.87  | |   (113)  all_6_2 = e3
% 177.22/27.87  | | 
% 177.22/27.87  | | REF_CLOSE: (26), (59), (78), (88), (90), (93), (113) are inconsistent by
% 177.22/27.87  | |            sub-proof #665.
% 177.22/27.87  | | 
% 177.22/27.87  | Case 2:
% 177.22/27.87  | | 
% 177.22/27.87  | |   (114)   ~ (all_56_15 = e3)
% 177.22/27.87  | |   (115)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.87  | | 
% 177.22/27.87  | | REDUCE: (20), (114) imply:
% 177.22/27.87  | |   (116)   ~ (all_6_2 = e3)
% 177.22/27.87  | | 
% 177.22/27.87  | | BETA: splitting (48) gives:
% 177.22/27.87  | | 
% 177.22/27.87  | | Case 1:
% 177.22/27.87  | | | 
% 177.22/27.87  | | |   (117)  all_56_13 = e3
% 177.22/27.87  | | | 
% 177.22/27.87  | | | COMBINE_EQS: (104), (117) imply:
% 177.22/27.87  | | |   (118)  all_52_27 = e3
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (118) implies:
% 177.22/27.87  | | |   (119)  all_52_27 = e3
% 177.22/27.87  | | | 
% 177.22/27.87  | | | COMBINE_EQS: (67), (119) imply:
% 177.22/27.87  | | |   (120)  all_58_13 = e3
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (94), (119) imply:
% 177.22/27.87  | | |   (121)   ~ (all_52_19 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (91), (119) imply:
% 177.22/27.87  | | |   (122)   ~ (all_52_25 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (35), (119) imply:
% 177.22/27.87  | | |   (123)   ~ (all_52_29 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (123) implies:
% 177.22/27.87  | | |   (124)   ~ (all_52_29 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (42), (119) imply:
% 177.22/27.87  | | |   (125)  op(e2, e3) = e2
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (54), (119) imply:
% 177.22/27.87  | | |   (126)  op(e0, e2) = e3
% 177.22/27.87  | | | 
% 177.22/27.87  | | | GROUND_INST: instantiating (90) with all_52_9, e2, e3, e2, simplifying
% 177.22/27.87  | | |              with (103), (125) gives:
% 177.22/27.87  | | |   (127)  all_52_9 = e2
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (64), (127) imply:
% 177.22/27.87  | | |   (128)   ~ (all_52_13 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (128) implies:
% 177.22/27.87  | | |   (129)   ~ (all_52_13 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (101), (127) imply:
% 177.22/27.87  | | |   (130)   ~ (all_52_15 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (130) implies:
% 177.22/27.87  | | |   (131)   ~ (all_52_15 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (9), (127) imply:
% 177.22/27.87  | | |   (132)   ~ (all_52_25 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (132) implies:
% 177.22/27.87  | | |   (133)   ~ (all_52_25 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (60), (127) imply:
% 177.22/27.87  | | |   (134)   ~ (all_10_2 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (134) implies:
% 177.22/27.87  | | |   (135)   ~ (all_10_2 = e2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (14), (127) imply:
% 177.22/27.87  | | |   (136)  op(e3, e2) = all_52_8
% 177.22/27.87  | | | 
% 177.22/27.87  | | | GROUND_INST: instantiating (90) with all_52_3, all_52_8, e2, e3,
% 177.22/27.87  | | |              simplifying with (8), (136) gives:
% 177.22/27.87  | | |   (137)  all_52_3 = all_52_8
% 177.22/27.87  | | | 
% 177.22/27.87  | | | COMBINE_EQS: (39), (137) imply:
% 177.22/27.87  | | |   (138)  all_58_1 = all_52_8
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (50), (137) imply:
% 177.22/27.87  | | |   (139)   ~ (all_52_5 = all_52_8)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (139) implies:
% 177.22/27.87  | | |   (140)   ~ (all_52_5 = all_52_8)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (72), (137) imply:
% 177.22/27.87  | | |   (141)   ~ (all_52_7 = all_52_8)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | SIMP: (141) implies:
% 177.22/27.87  | | |   (142)   ~ (all_52_7 = all_52_8)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (58), (137) imply:
% 177.22/27.87  | | |   (143)   ~ (all_52_8 = all_4_2)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | BETA: splitting (65) gives:
% 177.22/27.87  | | | 
% 177.22/27.87  | | | Case 1:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | |   (144)  all_56_12 = e3
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | | REF_CLOSE: (66), (122), (144) are inconsistent by sub-proof #1040.
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | Case 2:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | |   (145)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | | BETA: splitting (51) gives:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | | Case 1:
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | |   (146)  all_58_0 = e3
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | | REF_CLOSE: (36), (41), (44), (61), (89), (90), (146) are inconsistent
% 177.22/27.87  | | | | |            by sub-proof #489.
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | Case 2:
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | |   (147)   ~ (all_58_0 = e3)
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | | REDUCE: (41), (147) imply:
% 177.22/27.87  | | | | |   (148)   ~ (all_4_2 = e3)
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | | BETA: splitting (24) gives:
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | | Case 1:
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | |   (149)  all_56_0 = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | COMBINE_EQS: (73), (149) imply:
% 177.22/27.87  | | | | | |   (150)  all_4_2 = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (148), (150) imply:
% 177.22/27.87  | | | | | |   (151)  $false
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | CLOSE: (151) is inconsistent.
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | Case 2:
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | |   (152)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | BETA: splitting (16) gives:
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | Case 1:
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | |   (153)  all_58_1 = e2
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | COMBINE_EQS: (138), (153) imply:
% 177.22/27.87  | | | | | | |   (154)  all_52_8 = e2
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | REDUCE: (140), (154) imply:
% 177.22/27.87  | | | | | | |   (155)   ~ (all_52_5 = e2)
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | REDUCE: (142), (154) imply:
% 177.22/27.87  | | | | | | |   (156)   ~ (all_52_7 = e2)
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | REDUCE: (143), (154) imply:
% 177.22/27.87  | | | | | | |   (157)   ~ (all_4_2 = e2)
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | SIMP: (157) implies:
% 177.22/27.87  | | | | | | |   (158)   ~ (all_4_2 = e2)
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | BETA: splitting (97) gives:
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | Case 1:
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | |   (159)  all_58_9 = e3
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | COMBINE_EQS: (99), (159) imply:
% 177.22/27.87  | | | | | | | |   (160)  all_52_7 = e3
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | SIMP: (160) implies:
% 177.22/27.87  | | | | | | | |   (161)  all_52_7 = e3
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | REDUCE: (38), (161) imply:
% 177.22/27.87  | | | | | | | |   (162)   ~ (all_4_2 = e3)
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | BETA: splitting (75) gives:
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | Case 1:
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | |   (163)  all_58_4 = e2
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | REF_CLOSE: (33), (155), (163) are inconsistent by sub-proof
% 177.22/27.87  | | | | | | | | |            #675.
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | Case 2:
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | |   (164)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | BETA: splitting (12) gives:
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | Case 1:
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | |   (165)  all_58_0 = e1
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | COMBINE_EQS: (41), (165) imply:
% 177.22/27.87  | | | | | | | | | |   (166)  all_4_2 = e1
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | COMBINE_EQS: (43), (166) imply:
% 177.22/27.87  | | | | | | | | | |   (167)  all_50_2 = e1
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | REDUCE: (158), (166) imply:
% 177.22/27.87  | | | | | | | | | |   (168)   ~ (e2 = e1)
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | SIMP: (168) implies:
% 177.22/27.87  | | | | | | | | | |   (169)   ~ (e2 = e1)
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | REDUCE: (36), (166) imply:
% 177.22/27.87  | | | | | | | | | |   (170)  op(e3, e1) = all_4_1
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | REF_CLOSE: (1), (13), (15), (33), (39), (44), (57), (82),
% 177.22/27.87  | | | | | | | | | |            (90), (102), (107), (109), (111), (159), (165),
% 177.22/27.87  | | | | | | | | | |            (167), (169), (170) are inconsistent by sub-proof
% 177.22/27.87  | | | | | | | | | |            #480.
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | Case 2:
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | |   (171)   ~ (all_58_0 = e1)
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | REDUCE: (41), (171) imply:
% 177.22/27.87  | | | | | | | | | |   (172)   ~ (all_4_2 = e1)
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | REF_CLOSE: (6), (11), (17), (53), (55), (73), (87), (90),
% 177.22/27.87  | | | | | | | | | |            (100), (120), (121), (129), (148), (152), (158),
% 177.22/27.87  | | | | | | | | | |            (164), (172) are inconsistent by sub-proof #372.
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | End of split
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | End of split
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | Case 2:
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | |   (173)   ~ (all_58_9 = e3)
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | REDUCE: (99), (173) imply:
% 177.22/27.87  | | | | | | | |   (174)   ~ (all_52_7 = e3)
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | REF_CLOSE: (7), (36), (38), (41), (44), (49), (61), (66), (68),
% 177.22/27.87  | | | | | | | |            (69), (73), (76), (78), (87), (88), (90), (98),
% 177.22/27.87  | | | | | | | |            (133), (145), (152), (158), (174) are inconsistent by
% 177.22/27.87  | | | | | | | |            sub-proof #472.
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | End of split
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | Case 2:
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | |   (175)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | REF_CLOSE: (6), (10), (23), (25), (26), (28), (30), (47), (63),
% 177.22/27.87  | | | | | | |            (74), (78), (84), (88), (90), (93), (99), (100), (102),
% 177.22/27.87  | | | | | | |            (107), (109), (120), (121), (124), (126), (131), (133),
% 177.22/27.87  | | | | | | |            (135), (175) are inconsistent by sub-proof #657.
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | End of split
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | End of split
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | End of split
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | End of split
% 177.22/27.87  | | | 
% 177.22/27.87  | | Case 2:
% 177.22/27.87  | | | 
% 177.22/27.87  | | |   (176)   ~ (all_56_13 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (104), (176) imply:
% 177.22/27.87  | | |   (177)   ~ (all_52_27 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | BETA: splitting (52) gives:
% 177.22/27.87  | | | 
% 177.22/27.87  | | | Case 1:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | |   (178)  all_58_12 = e3
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | | REF_CLOSE: (78), (87), (89), (90), (100), (178) are inconsistent by
% 177.22/27.87  | | | |            sub-proof #884.
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | Case 2:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | |   (179)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | | BETA: splitting (179) gives:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | | Case 1:
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | |   (180)  all_58_13 = e3
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | | REF_CLOSE: (67), (177), (180) are inconsistent by sub-proof #1026.
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | Case 2:
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | |   (181)  all_58_14 = e3 | all_58_15 = e3
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | | BETA: splitting (181) gives:
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | | Case 1:
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | |   (182)  all_58_14 = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | COMBINE_EQS: (47), (182) imply:
% 177.22/27.87  | | | | | |   (183)  all_52_29 = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | SIMP: (183) implies:
% 177.22/27.87  | | | | | |   (184)  all_52_29 = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (19), (184) imply:
% 177.22/27.87  | | | | | |   (185)   ~ (all_52_25 = e3)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (77), (184) imply:
% 177.22/27.87  | | | | | |   (186)   ~ (all_14_2 = e3)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | SIMP: (186) implies:
% 177.22/27.87  | | | | | |   (187)   ~ (all_14_2 = e3)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (80), (184) imply:
% 177.22/27.87  | | | | | |   (188)   ~ (all_6_2 = e3)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (56), (184) imply:
% 177.22/27.87  | | | | | |   (189)  op(e1, e3) = e1
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (32), (184) imply:
% 177.22/27.87  | | | | | |   (190)  op(e0, e1) = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | GROUND_INST: instantiating (90) with all_52_17, e1, e3, e1,
% 177.22/27.87  | | | | | |              simplifying with (86), (189) gives:
% 177.22/27.87  | | | | | |   (191)  all_52_17 = e1
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | COMBINE_EQS: (71), (191) imply:
% 177.22/27.87  | | | | | |   (192)  all_58_6 = e1
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (70), (191) imply:
% 177.22/27.87  | | | | | |   (193)   ~ (all_52_9 = e1)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (96), (191) imply:
% 177.22/27.87  | | | | | |   (194)   ~ (all_52_19 = e1)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | SIMP: (194) implies:
% 177.22/27.87  | | | | | |   (195)   ~ (all_52_19 = e1)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (4), (191) imply:
% 177.22/27.87  | | | | | |   (196)   ~ (all_52_23 = e1)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | SIMP: (196) implies:
% 177.22/27.87  | | | | | |   (197)   ~ (all_52_23 = e1)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (31), (191) imply:
% 177.22/27.87  | | | | | |   (198)   ~ (all_52_25 = e1)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | SIMP: (198) implies:
% 177.22/27.87  | | | | | |   (199)   ~ (all_52_25 = e1)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (62), (191) imply:
% 177.22/27.87  | | | | | |   (200)  op(e3, e1) = all_52_16
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | GROUND_INST: instantiating (90) with all_52_5, all_52_16, e1, e3,
% 177.22/27.87  | | | | | |              simplifying with (82), (200) gives:
% 177.22/27.87  | | | | | |   (201)  all_52_5 = all_52_16
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | COMBINE_EQS: (33), (201) imply:
% 177.22/27.87  | | | | | |   (202)  all_58_4 = all_52_16
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (29), (201) imply:
% 177.22/27.87  | | | | | |   (203)   ~ (all_52_16 = all_4_2)
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | BETA: splitting (65) gives:
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | Case 1:
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | |   (204)  all_56_12 = e3
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | REF_CLOSE: (66), (185), (204) are inconsistent by sub-proof #1040.
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | Case 2:
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | |   (205)   ~ (all_56_12 = e3)
% 177.22/27.87  | | | | | | |   (206)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | BETA: splitting (51) gives:
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | | Case 1:
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | |   (207)  all_58_0 = e3
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | REF_CLOSE: (36), (41), (44), (61), (89), (90), (207) are
% 177.22/27.87  | | | | | | | |            inconsistent by sub-proof #489.
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | Case 2:
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | |   (208)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | BETA: splitting (208) gives:
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | | Case 1:
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | |   (209)  all_58_2 = e3
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | COMBINE_EQS: (81), (209) imply:
% 177.22/27.87  | | | | | | | | |   (210)  all_52_9 = e3
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | SIMP: (210) implies:
% 177.22/27.87  | | | | | | | | |   (211)  all_52_9 = e3
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | REDUCE: (101), (211) imply:
% 177.22/27.87  | | | | | | | | |   (212)   ~ (all_52_15 = e3)
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | SIMP: (212) implies:
% 177.22/27.87  | | | | | | | | |   (213)   ~ (all_52_15 = e3)
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | REDUCE: (9), (211) imply:
% 177.22/27.87  | | | | | | | | |   (214)   ~ (all_52_25 = e3)
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | REDUCE: (60), (211) imply:
% 177.22/27.87  | | | | | | | | |   (215)   ~ (all_10_2 = e3)
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | SIMP: (215) implies:
% 177.22/27.87  | | | | | | | | |   (216)   ~ (all_10_2 = e3)
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | REDUCE: (27), (211) imply:
% 177.22/27.87  | | | | | | | | |   (217)   ~ (all_4_2 = e3)
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | SIMP: (217) implies:
% 177.22/27.87  | | | | | | | | |   (218)   ~ (all_4_2 = e3)
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | BETA: splitting (24) gives:
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | Case 1:
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | |   (219)  all_56_0 = e3
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | COMBINE_EQS: (73), (219) imply:
% 177.22/27.87  | | | | | | | | | |   (220)  all_4_2 = e3
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | REDUCE: (218), (220) imply:
% 177.22/27.87  | | | | | | | | | |   (221)  $false
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | CLOSE: (221) is inconsistent.
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | Case 2:
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | |   (222)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | BETA: splitting (45) gives:
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | Case 1:
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | |   (223)  all_58_4 = e1
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | | COMBINE_EQS: (202), (223) imply:
% 177.22/27.87  | | | | | | | | | | |   (224)  all_52_16 = e1
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | | SIMP: (224) implies:
% 177.22/27.87  | | | | | | | | | | |   (225)  all_52_16 = e1
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | | REDUCE: (203), (225) imply:
% 177.22/27.87  | | | | | | | | | | |   (226)   ~ (all_4_2 = e1)
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | | SIMP: (226) implies:
% 177.22/27.87  | | | | | | | | | | |   (227)   ~ (all_4_2 = e1)
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (7), (8), (21), (36), (38), (39),
% 177.22/27.87  | | | | | | | | | | |            (41), (42), (44), (49), (54), (61), (66), (68),
% 177.22/27.87  | | | | | | | | | | |            (73), (76), (78), (87), (88), (90), (98), (99),
% 177.22/27.87  | | | | | | | | | | |            (185), (199), (206), (222), (223), (227) are
% 177.22/27.87  | | | | | | | | | | |            inconsistent by sub-proof #452.
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | Case 2:
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | |   (228)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | | REF_CLOSE: (10), (17), (18), (20), (22), (23), (25), (26),
% 177.22/27.87  | | | | | | | | | | |            (28), (30), (34), (39), (40), (46), (53), (55),
% 177.22/27.87  | | | | | | | | | | |            (66), (67), (72), (74), (78), (83), (85), (88),
% 177.22/27.87  | | | | | | | | | | |            (90), (93), (97), (99), (107), (115), (116),
% 177.22/27.87  | | | | | | | | | | |            (177), (182), (187), (190), (195), (197), (199),
% 177.22/27.87  | | | | | | | | | | |            (206), (213), (216), (228) are inconsistent by
% 177.22/27.87  | | | | | | | | | | |            sub-proof #371.
% 177.22/27.87  | | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | | End of split
% 177.22/27.87  | | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | End of split
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | Case 2:
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | |   (229)  all_58_6 = e3 | all_58_12 = e3
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | | REF_CLOSE: (34), (100), (185), (192), (229) are inconsistent
% 177.22/27.87  | | | | | | | | |            by sub-proof #1002.
% 177.22/27.87  | | | | | | | | | 
% 177.22/27.87  | | | | | | | | End of split
% 177.22/27.87  | | | | | | | | 
% 177.22/27.87  | | | | | | | End of split
% 177.22/27.87  | | | | | | | 
% 177.22/27.87  | | | | | | End of split
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | Case 2:
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | |   (230)  all_58_15 = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | COMBINE_EQS: (25), (230) imply:
% 177.22/27.87  | | | | | |   (231)  all_6_2 = e3
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | REDUCE: (116), (231) imply:
% 177.22/27.87  | | | | | |   (232)  $false
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | | CLOSE: (232) is inconsistent.
% 177.22/27.87  | | | | | | 
% 177.22/27.87  | | | | | End of split
% 177.22/27.87  | | | | | 
% 177.22/27.87  | | | | End of split
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | End of split
% 177.22/27.87  | | | 
% 177.22/27.87  | | End of split
% 177.22/27.87  | | 
% 177.22/27.87  | End of split
% 177.22/27.87  | 
% 177.22/27.87  End of proof
% 177.22/27.87  
% 177.22/27.87  Sub-proof #349 shows that the following formulas are inconsistent:
% 177.22/27.87  ----------------------------------------------------------------
% 177.22/27.87    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.87    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.87    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.22/27.87    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.87    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.87    (6)   ~ (all_52_27 = all_10_2)
% 177.22/27.87    (7)   ~ (all_52_17 = all_52_23)
% 177.22/27.87    (8)  all_22_2 = all_14_2
% 177.22/27.87    (9)   ~ (all_52_13 = all_52_29)
% 177.22/27.87    (10)  op(e2, all_10_2) = all_10_0
% 177.22/27.87    (11)  all_56_3 = all_52_7
% 177.22/27.87    (12)  op(e3, e2) = all_52_3
% 177.22/27.87    (13)   ~ (all_52_9 = all_52_25)
% 177.22/27.87    (14)  op(e3, all_52_25) = all_52_24
% 177.22/27.87    (15)   ~ (all_52_19 = all_52_23)
% 177.22/27.87    (16)  all_56_11 = all_52_23
% 177.22/27.87    (17)  op(e1, e2) = all_52_19
% 177.22/27.87    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.87    (19)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.22/27.87    (20)  all_50_1 = all_4_1
% 177.22/27.87    (21)   ~ (all_52_3 = all_10_2)
% 177.22/27.87    (22)  all_58_5 = all_52_13
% 177.22/27.87    (23)   ~ (all_6_2 = e0)
% 177.22/27.87    (24)   ~ (all_52_25 = all_52_29)
% 177.22/27.87    (25)  op(e1, all_52_13) = e1
% 177.22/27.87    (26)  op(e0, all_52_15) = e0
% 177.22/27.87    (27)  all_56_15 = all_6_2
% 177.22/27.87    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.87    (29)  op(e2, e0) = all_52_15
% 177.22/27.87    (30)  all_58_3 = all_10_2
% 177.22/27.87    (31)  all_56_9 = all_52_19
% 177.22/27.87    (32)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.87    (33)  all_58_15 = all_6_2
% 177.22/27.87    (34)   ~ (all_52_9 = all_4_2)
% 177.22/27.87    (35)   ~ (all_52_5 = all_52_7)
% 177.22/27.87    (36)  all_58_10 = all_52_15
% 177.22/27.87    (37)   ~ (all_52_5 = all_4_2)
% 177.22/27.87    (38)  all_58_7 = all_52_19
% 177.22/27.87    (39)  all_56_4 = all_52_9
% 177.22/27.87    (40)   ~ (all_52_15 = all_6_2)
% 177.22/27.87    (41)   ~ (all_52_17 = all_52_25)
% 177.22/27.87    (42)  all_58_4 = all_52_5
% 177.22/27.87    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.87    (44)   ~ (e3 = e1)
% 177.22/27.87    (45)   ~ (all_52_27 = all_52_29)
% 177.22/27.87    (46)   ~ (all_52_17 = all_14_2)
% 177.22/27.87    (47)  op(e3, all_4_2) = all_4_1
% 177.22/27.87    (48)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.87    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.87    (50)   ~ (all_52_7 = all_4_2)
% 177.22/27.87    (51)  all_58_1 = all_52_3
% 177.22/27.87    (52)  all_58_0 = all_4_2
% 177.22/27.87    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.87    (54)  op(e1, all_52_29) = all_52_28
% 177.22/27.87    (55)  all_50_2 = all_4_2
% 177.22/27.87    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.87    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.87    (58)   ~ (all_4_1 = e2)
% 177.22/27.87    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.87    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.87    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.87    (62)  all_58_14 = all_52_29
% 177.22/27.87    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.87    (64)  all_26_2 = all_4_2
% 177.22/27.87    (65)   ~ (all_52_3 = all_52_5)
% 177.22/27.87    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.87    (67)  op(e2, e1) = all_52_13
% 177.22/27.87    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.87    (69)  all_58_8 = all_14_2
% 177.22/27.87    (70)  all_56_1 = all_52_3
% 177.22/27.87    (71)  op(e1, all_14_2) = e3
% 177.22/27.87    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.87    (73)   ~ (all_52_5 = all_14_2)
% 177.22/27.87    (74)   ~ (all_52_3 = all_52_27)
% 177.22/27.87    (75)   ~ (all_52_3 = all_4_2)
% 177.22/27.87    (76)  op(e0, e3) = all_52_25
% 177.22/27.87    (77)   ~ (all_52_9 = all_10_2)
% 177.22/27.87    (78)  op(all_4_1, all_4_2) = e2
% 177.22/27.87    (79)  op(e3, all_52_17) = all_52_16
% 177.22/27.87    (80)   ~ (all_52_13 = all_14_2)
% 177.22/27.87    (81)  op(e3, all_52_9) = e3
% 177.22/27.87    (82)   ~ (e3 = e0)
% 177.22/27.87    (83)  all_22_0 = all_14_0
% 177.22/27.87    (84)   ~ (all_52_9 = all_52_13)
% 177.22/27.87    (85)  op(e0, all_52_23) = all_52_22
% 177.22/27.87    (86)   ~ (all_52_15 = all_52_23)
% 177.22/27.87    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.87    (88)   ~ (all_52_5 = all_52_29)
% 177.22/27.87    (89)  all_56_2 = all_52_5
% 177.22/27.87    (90)  all_58_13 = all_52_27
% 177.22/27.87    (91)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.87    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.87    (93)  all_56_5 = all_10_2
% 177.22/27.87    (94)   ~ (all_52_9 = all_52_17)
% 177.22/27.87    (95)   ~ (all_14_0 = e2)
% 177.22/27.87    (96)  all_58_6 = all_52_17
% 177.22/27.87    (97)   ~ (all_52_3 = all_52_7)
% 177.22/27.87    (98)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.87    (99)  op(e2, all_52_19) = all_52_18
% 177.22/27.87    (100)   ~ (e1 = e0)
% 177.22/27.87    (101)  all_56_0 = all_4_2
% 177.22/27.87    (102)  all_58_11 = all_52_23
% 177.22/27.87    (103)   ~ (all_52_3 = all_52_19)
% 177.22/27.87    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.87    (105)   ~ (all_52_7 = all_52_15)
% 177.22/27.87    (106)  all_26_1 = all_4_1
% 177.22/27.87    (107)   ~ (all_22_0 = e0) |  ~ (all_22_2 = e2)
% 177.22/27.87    (108)   ~ (all_52_29 = all_14_2)
% 177.22/27.87    (109)   ~ (all_52_19 = all_10_2)
% 177.22/27.87    (110)   ~ (all_52_23 = all_6_2)
% 177.22/27.87    (111)   ~ (all_52_29 = all_6_2)
% 177.22/27.87    (112)  all_58_2 = all_52_9
% 177.22/27.87    (113)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.87    (114)  op(e3, e1) = all_52_5
% 177.22/27.87    (115)  all_56_10 = all_14_2
% 177.22/27.87    (116)   ~ (all_52_25 = all_6_2)
% 177.22/27.87    (117)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.87    (118)  op(e1, e3) = all_52_17
% 177.22/27.87    (119)   ~ (all_52_25 = all_4_2)
% 177.22/27.87    (120)  op(e3, e0) = all_52_7
% 177.22/27.87    (121)  op(e2, all_10_2) = e2
% 177.22/27.87    (122)  op(e3, e3) = all_4_2
% 177.22/27.87    (123)  all_56_8 = all_52_17
% 177.22/27.87    (124)   ~ (all_52_17 = all_4_2)
% 177.22/27.87    (125)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.87             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.87    (126)   ~ (all_52_25 = all_52_27)
% 177.22/27.87    (127)   ~ (all_52_27 = all_6_2)
% 177.22/27.87    (128)   ~ (all_52_7 = all_6_2)
% 177.22/27.87    (129)   ~ (all_10_0 = e3)
% 177.22/27.87    (130)   ~ (all_52_19 = all_52_27)
% 177.22/27.87    (131)   ~ (all_52_7 = all_52_23)
% 177.22/27.87    (132)   ~ (all_52_13 = all_10_2)
% 177.22/27.87    (133)  op(e2, all_52_27) = all_52_26
% 177.22/27.87    (134)   ~ (all_52_17 = all_52_19)
% 177.22/27.87    (135)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.87    (136)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.87    (137)  op(e1, all_14_2) = all_14_1
% 177.22/27.87    (138)  op(e3, all_14_2) = all_14_0
% 177.22/27.87    (139)  all_58_9 = all_52_7
% 177.22/27.87    (140)  all_58_12 = all_52_25
% 177.22/27.87    (141)   ~ (all_10_0 = e1)
% 177.22/27.87    (142)  all_56_6 = all_52_13
% 177.22/27.87    (143)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.87    (144)   ~ (all_52_9 = all_52_15)
% 177.22/27.87    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.87    (146)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.87    (147)   ~ (all_52_19 = all_14_2)
% 177.22/27.87    (148)  op(e2, e3) = all_52_9
% 177.22/27.87    (149)  all_56_13 = all_52_27
% 177.22/27.87  
% 177.22/27.87  Begin of proof
% 177.22/27.87  | 
% 177.22/27.87  | GROUND_INST: instantiating (125) with e2, all_10_0, all_10_2, e2, simplifying
% 177.22/27.87  |              with (10), (121) gives:
% 177.22/27.87  |   (150)  all_10_0 = e2
% 177.22/27.87  | 
% 177.22/27.87  | REDUCE: (129), (150) imply:
% 177.22/27.87  |   (151)   ~ (e3 = e2)
% 177.22/27.87  | 
% 177.22/27.87  | SIMP: (151) implies:
% 177.22/27.87  |   (152)   ~ (e3 = e2)
% 177.22/27.87  | 
% 177.22/27.87  | REDUCE: (141), (150) imply:
% 177.22/27.87  |   (153)   ~ (e2 = e1)
% 177.22/27.87  | 
% 177.22/27.87  | BETA: splitting (48) gives:
% 177.22/27.87  | 
% 177.22/27.87  | Case 1:
% 177.22/27.87  | | 
% 177.22/27.87  | |   (154)  all_56_15 = e3
% 177.22/27.87  | | 
% 177.22/27.87  | | COMBINE_EQS: (27), (154) imply:
% 177.22/27.87  | |   (155)  all_6_2 = e3
% 177.22/27.87  | | 
% 177.22/27.87  | | SIMP: (155) implies:
% 177.22/27.87  | |   (156)  all_6_2 = e3
% 177.22/27.87  | | 
% 177.22/27.87  | | REDUCE: (128), (156) imply:
% 177.22/27.87  | |   (157)   ~ (all_52_7 = e3)
% 177.22/27.87  | | 
% 177.22/27.87  | | REDUCE: (40), (156) imply:
% 177.22/27.87  | |   (158)   ~ (all_52_15 = e3)
% 177.22/27.87  | | 
% 177.22/27.87  | | REDUCE: (111), (156) imply:
% 177.22/27.87  | |   (159)   ~ (all_52_29 = e3)
% 177.22/27.87  | | 
% 177.22/27.87  | | BETA: splitting (98) gives:
% 177.22/27.87  | | 
% 177.22/27.87  | | Case 1:
% 177.22/27.87  | | | 
% 177.22/27.87  | | |   (160)  all_56_4 = e3
% 177.22/27.87  | | | 
% 177.22/27.87  | | | COMBINE_EQS: (39), (160) imply:
% 177.22/27.87  | | |   (161)  all_52_9 = e3
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REF_CLOSE: (34), (81), (122), (125), (161) are inconsistent by sub-proof
% 177.22/27.87  | | |            #967.
% 177.22/27.87  | | | 
% 177.22/27.87  | | Case 2:
% 177.22/27.87  | | | 
% 177.22/27.87  | | |   (162)   ~ (all_56_4 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | REDUCE: (39), (162) imply:
% 177.22/27.87  | | |   (163)   ~ (all_52_9 = e3)
% 177.22/27.87  | | | 
% 177.22/27.87  | | | BETA: splitting (66) gives:
% 177.22/27.87  | | | 
% 177.22/27.87  | | | Case 1:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | |   (164)  all_58_0 = e3
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | | REF_CLOSE: (47), (52), (58), (78), (122), (125), (164) are inconsistent
% 177.22/27.87  | | | |            by sub-proof #489.
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | Case 2:
% 177.22/27.87  | | | | 
% 177.22/27.87  | | | |   (165)   ~ (all_58_0 = e3)
% 177.22/27.87  | | | | 
% 177.22/27.88  | | | | REDUCE: (52), (165) imply:
% 177.22/27.88  | | | |   (166)   ~ (all_4_2 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REF_CLOSE: (2), (11), (12), (21), (22), (25), (28), (30), (32), (34),
% 177.22/27.88  | | | |            (36), (39), (42), (46), (47), (49), (50), (52), (58), (62),
% 177.22/27.88  | | | |            (64), (69), (71), (78), (81), (84), (91), (94), (98), (101),
% 177.22/27.88  | | | |            (106), (112), (118), (120), (121), (124), (125), (136),
% 177.22/27.88  | | | |            (145), (148), (157), (158), (159), (163), (166) are
% 177.22/27.88  | | | |            inconsistent by sub-proof #351.
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | End of split
% 177.22/27.88  | | | 
% 177.22/27.88  | | End of split
% 177.22/27.88  | | 
% 177.22/27.88  | Case 2:
% 177.22/27.88  | | 
% 177.22/27.88  | |   (167)   ~ (all_56_15 = e3)
% 177.22/27.88  | |   (168)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.88  | | 
% 177.22/27.88  | | REDUCE: (27), (167) imply:
% 177.22/27.88  | |   (169)   ~ (all_6_2 = e3)
% 177.22/27.88  | | 
% 177.22/27.88  | | BETA: splitting (63) gives:
% 177.22/27.88  | | 
% 177.22/27.88  | | Case 1:
% 177.22/27.88  | | | 
% 177.22/27.88  | | |   (170)  all_56_13 = e3
% 177.22/27.88  | | | 
% 177.22/27.88  | | | COMBINE_EQS: (149), (170) imply:
% 177.22/27.88  | | |   (171)  all_52_27 = e3
% 177.22/27.88  | | | 
% 177.22/27.88  | | | COMBINE_EQS: (90), (171) imply:
% 177.22/27.88  | | |   (172)  all_58_13 = e3
% 177.22/27.88  | | | 
% 177.22/27.88  | | | REDUCE: (74), (171) imply:
% 177.22/27.88  | | |   (173)   ~ (all_52_3 = e3)
% 177.22/27.88  | | | 
% 177.22/27.88  | | | REDUCE: (130), (171) imply:
% 177.22/27.88  | | |   (174)   ~ (all_52_19 = e3)
% 177.22/27.88  | | | 
% 177.22/27.88  | | | REDUCE: (6), (171) imply:
% 177.22/27.88  | | |   (175)   ~ (all_10_2 = e3)
% 177.22/27.88  | | | 
% 177.22/27.88  | | | SIMP: (175) implies:
% 177.22/27.88  | | |   (176)   ~ (all_10_2 = e3)
% 177.22/27.88  | | | 
% 177.22/27.88  | | | REDUCE: (127), (171) imply:
% 177.22/27.88  | | |   (177)   ~ (all_6_2 = e3)
% 177.22/27.88  | | | 
% 177.22/27.88  | | | REDUCE: (133), (171) imply:
% 177.22/27.88  | | |   (178)  op(e2, e3) = all_52_26
% 177.22/27.88  | | | 
% 177.22/27.88  | | | REF_CLOSE: (2), (4), (5), (7), (9), (12), (13), (14), (17), (18), (21),
% 177.22/27.88  | | |            (22), (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 177.22/27.88  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 177.22/27.88  | | |            (46), (47), (49), (50), (51), (52), (56), (58), (62), (65),
% 177.22/27.88  | | |            (66), (69), (70), (71), (73), (75), (76), (77), (78), (80),
% 177.22/27.88  | | |            (81), (84), (86), (93), (96), (98), (101), (102), (103), (104),
% 177.22/27.88  | | |            (105), (109), (111), (112), (116), (117), (118), (119), (120),
% 177.22/27.88  | | |            (121), (122), (124), (125), (128), (131), (132), (134), (135),
% 177.22/27.88  | | |            (139), (140), (143), (144), (145), (148), (168), (169), (172),
% 177.22/27.88  | | |            (173), (174), (176), (178) are inconsistent by sub-proof #350.
% 177.22/27.88  | | | 
% 177.22/27.88  | | Case 2:
% 177.22/27.88  | | | 
% 177.22/27.88  | | |   (179)   ~ (all_56_13 = e3)
% 177.22/27.88  | | | 
% 177.22/27.88  | | | REDUCE: (149), (179) imply:
% 177.22/27.88  | | |   (180)   ~ (all_52_27 = e3)
% 177.22/27.88  | | | 
% 177.22/27.88  | | | BETA: splitting (68) gives:
% 177.22/27.88  | | | 
% 177.22/27.88  | | | Case 1:
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | |   (181)  all_58_12 = e3
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | COMBINE_EQS: (140), (181) imply:
% 177.22/27.88  | | | |   (182)  all_52_25 = e3
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | SIMP: (182) implies:
% 177.22/27.88  | | | |   (183)  all_52_25 = e3
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REDUCE: (13), (183) imply:
% 177.22/27.88  | | | |   (184)   ~ (all_52_9 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REDUCE: (126), (183) imply:
% 177.22/27.88  | | | |   (185)   ~ (all_52_27 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REDUCE: (24), (183) imply:
% 177.22/27.88  | | | |   (186)   ~ (all_52_29 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | SIMP: (186) implies:
% 177.22/27.88  | | | |   (187)   ~ (all_52_29 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REDUCE: (116), (183) imply:
% 177.22/27.88  | | | |   (188)   ~ (all_6_2 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REDUCE: (119), (183) imply:
% 177.22/27.88  | | | |   (189)   ~ (all_4_2 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | SIMP: (189) implies:
% 177.22/27.88  | | | |   (190)   ~ (all_4_2 = e3)
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REDUCE: (76), (183) imply:
% 177.22/27.88  | | | |   (191)  op(e0, e3) = e3
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | BETA: splitting (98) gives:
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | Case 1:
% 177.22/27.88  | | | | | 
% 177.22/27.88  | | | | |   (192)  all_56_4 = e3
% 177.22/27.88  | | | | | 
% 177.22/27.88  | | | | | REF_CLOSE: (39), (184), (192) are inconsistent by sub-proof #782.
% 177.22/27.88  | | | | | 
% 177.22/27.88  | | | | Case 2:
% 177.22/27.88  | | | | | 
% 177.22/27.88  | | | | |   (193)   ~ (all_56_4 = e3)
% 177.22/27.88  | | | | |   (194)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.88  | | | | | 
% 177.22/27.88  | | | | | BETA: splitting (32) gives:
% 177.22/27.88  | | | | | 
% 177.22/27.88  | | | | | Case 1:
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | |   (195)  all_56_0 = e3
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | | COMBINE_EQS: (101), (195) imply:
% 177.22/27.88  | | | | | |   (196)  all_4_2 = e3
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | | REDUCE: (190), (196) imply:
% 177.22/27.88  | | | | | |   (197)  $false
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | | CLOSE: (197) is inconsistent.
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | Case 2:
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | |   (198)   ~ (all_56_0 = e3)
% 177.22/27.88  | | | | | |   (199)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | | BETA: splitting (136) gives:
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | | Case 1:
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | |   (200)  all_56_3 = e3
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | COMBINE_EQS: (11), (200) imply:
% 177.22/27.88  | | | | | | |   (201)  all_52_7 = e3
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | SIMP: (201) implies:
% 177.22/27.88  | | | | | | |   (202)  all_52_7 = e3
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | COMBINE_EQS: (139), (202) imply:
% 177.22/27.88  | | | | | | |   (203)  all_58_9 = e3
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | REDUCE: (97), (202) imply:
% 177.22/27.88  | | | | | | |   (204)   ~ (all_52_3 = e3)
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | REDUCE: (105), (202) imply:
% 177.22/27.88  | | | | | | |   (205)   ~ (all_52_15 = e3)
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | SIMP: (205) implies:
% 177.22/27.88  | | | | | | |   (206)   ~ (all_52_15 = e3)
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | BETA: splitting (60) gives:
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | |   (207)  all_58_1 = e3
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | COMBINE_EQS: (51), (207) imply:
% 177.22/27.88  | | | | | | | |   (208)  all_52_3 = e3
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | REDUCE: (204), (208) imply:
% 177.22/27.88  | | | | | | | |   (209)  $false
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | CLOSE: (209) is inconsistent.
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | |   (210)   ~ (all_58_1 = e3)
% 177.22/27.88  | | | | | | | |   (211)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | BETA: splitting (49) gives:
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | 
% 177.22/27.88  | | | | | | | | |   (212)  all_58_2 = e3
% 177.22/27.88  | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | REF_CLOSE: (112), (184), (212) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | |            #980.
% 177.22/27.88  | | | | | | | | | 
% 177.22/27.88  | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | 
% 177.22/27.88  | | | | | | | | |   (213)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.88  | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | BETA: splitting (56) gives:
% 177.22/27.88  | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | |   (214)  all_56_1 = e3
% 177.22/27.88  | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | REF_CLOSE: (70), (204), (214) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | | |            #862.
% 177.22/27.88  | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | |   (215)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.88  | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | BETA: splitting (61) gives:
% 177.22/27.88  | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | |   (216)  all_56_6 = e3
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | COMBINE_EQS: (142), (216) imply:
% 177.22/27.88  | | | | | | | | | | |   (217)  all_52_13 = e3
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | SIMP: (217) implies:
% 177.22/27.88  | | | | | | | | | | |   (218)  all_52_13 = e3
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | REDUCE: (132), (218) imply:
% 177.22/27.88  | | | | | | | | | | |   (219)   ~ (all_10_2 = e3)
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | SIMP: (219) implies:
% 177.22/27.88  | | | | | | | | | | |   (220)   ~ (all_10_2 = e3)
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | REDUCE: (25), (218) imply:
% 177.22/27.88  | | | | | | | | | | |   (221)  op(e1, e3) = e1
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | BETA: splitting (211) gives:
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | |   (222)  all_58_3 = e3
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | COMBINE_EQS: (30), (222) imply:
% 177.22/27.88  | | | | | | | | | | | |   (223)  all_10_2 = e3
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | REDUCE: (220), (223) imply:
% 177.22/27.88  | | | | | | | | | | | |   (224)  $false
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | |   (225)  all_58_7 = e3 | all_58_13 = e3
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | BETA: splitting (225) gives:
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | |   (226)  all_58_7 = e3
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | COMBINE_EQS: (38), (226) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (227)  all_52_19 = e3
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (147), (227) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (228)   ~ (all_14_2 = e3)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | SIMP: (228) implies:
% 177.22/27.88  | | | | | | | | | | | | |   (229)   ~ (all_14_2 = e3)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (99), (227) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (230)  op(e2, e3) = all_52_18
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | GROUND_INST: instantiating (125) with all_52_17, e1, e3, e1,
% 177.22/27.88  | | | | | | | | | | | | |              simplifying with (118), (221) gives:
% 177.22/27.88  | | | | | | | | | | | | |   (231)  all_52_17 = e1
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | GROUND_INST: instantiating (125) with all_52_9, all_52_18, e3,
% 177.22/27.88  | | | | | | | | | | | | |              e2, simplifying with (148), (230) gives:
% 177.22/27.88  | | | | | | | | | | | | |   (232)  all_52_9 = all_52_18
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | COMBINE_EQS: (39), (232) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (233)  all_56_4 = all_52_18
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | COMBINE_EQS: (96), (231) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (234)  all_58_6 = e1
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | COMBINE_EQS: (112), (232) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (235)  all_58_2 = all_52_18
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (144), (232) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (236)   ~ (all_52_15 = all_52_18)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | SIMP: (236) implies:
% 177.22/27.88  | | | | | | | | | | | | |   (237)   ~ (all_52_15 = all_52_18)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (94), (231), (232) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (238)   ~ (all_52_18 = e1)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (34), (232) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (239)   ~ (all_52_18 = all_4_2)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (184), (232) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (240)   ~ (all_52_18 = e3)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (46), (231) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (241)   ~ (all_14_2 = e1)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | SIMP: (241) implies:
% 177.22/27.88  | | | | | | | | | | | | |   (242)   ~ (all_14_2 = e1)
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REDUCE: (81), (232) imply:
% 177.22/27.88  | | | | | | | | | | | | |   (243)  op(e3, all_52_18) = e3
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | BETA: splitting (87) gives:
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | |   (244)  all_56_10 = e3
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | COMBINE_EQS: (115), (244) imply:
% 177.22/27.88  | | | | | | | | | | | | | |   (245)  all_14_2 = e3
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | REDUCE: (229), (245) imply:
% 177.22/27.88  | | | | | | | | | | | | | |   (246)  $false
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | CLOSE: (246) is inconsistent.
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | |   (247)   ~ (all_56_10 = e3)
% 177.22/27.88  | | | | | | | | | | | | | |   (248)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | |   (249)  all_58_0 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | COMBINE_EQS: (52), (249) imply:
% 177.22/27.88  | | | | | | | | | | | | | | |   (250)  all_4_2 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | REDUCE: (239), (250) imply:
% 177.22/27.88  | | | | | | | | | | | | | | |   (251)   ~ (all_52_18 = e2)
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | REDUCE: (78), (250) imply:
% 177.22/27.88  | | | | | | | | | | | | | | |   (252)  op(all_4_1, e2) = e2
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | REDUCE: (47), (250) imply:
% 177.22/27.88  | | | | | | | | | | | | | | |   (253)  op(e3, e2) = all_4_1
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | |   (254)  all_56_4 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | REF_CLOSE: (233), (251), (254) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | | | | | | | | |            #781.
% 177.22/27.88  | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | |   (255)  all_56_4 = e1 | all_56_4 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | |   (256)  all_56_4 = e1
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (233), (238), (256) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | | | | | | | | | |            #780.
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | |   (257)  all_56_4 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (257) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | |   (258)  all_52_18 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | SIMP: (258) implies:
% 177.22/27.88  | | | | | | | | | | | | | | | | |   (259)  all_52_18 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | REDUCE: (237), (259) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | |   (260)   ~ (all_52_15 = e0)
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | REDUCE: (240), (259) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | |   (261)   ~ (e3 = e0)
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | |   (262)  all_58_9 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (203), (262) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | | | | | | | | | | |            #928.
% 177.22/27.88  | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | |   (263)  all_58_10 = e0 | all_58_11 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | |   (264)  all_58_10 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (260), (264) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | | | | | | | | | | | |            #741.
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | |   (265)  all_58_11 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (265) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | |   (266)  all_52_23 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | |   (267)  all_52_23 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | REDUCE: (1), (267) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | |   (268)   ~ (all_14_2 = e0)
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | SIMP: (268) implies:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | |   (269)   ~ (all_14_2 = e0)
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |   (270)  all_56_10 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (270) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |   (271)  all_14_2 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |   (272)  all_14_2 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (272) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |   (273)  all_22_2 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (272) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |   (274)  op(e3, e2) = all_14_0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (71), (272) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |   (275)  op(e1, e2) = e3
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (276)   ~ (all_22_2 = e2)
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | REDUCE: (273), (276) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (277)  $false
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent.
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (278)   ~ (all_22_0 = e0)
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | REDUCE: (83), (278) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (279)   ~ (all_14_0 = e0)
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (125) with all_52_3, all_4_1, e2,
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (12), (253) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (280)  all_52_3 = all_4_1
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (125) with all_52_3, all_14_0, e2,
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (12), (274) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (281)  all_52_3 = all_14_0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (281) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (282)  all_14_0 = all_4_1
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (280) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (283)  all_56_1 = all_4_1
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | REDUCE: (279), (282) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | |   (284)   ~ (all_4_1 = e0)
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | |   (285)  all_56_1 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (285) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | |   (286)  all_4_1 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (58), (286) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | |   (287)  $false
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (287) is inconsistent.
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | |   (288)  all_56_1 = e1 | all_56_1 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_56_1 = e1
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (289) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_4_1 = e1
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (252), (290) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (291)  op(e1, e2) = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (125) with e3, e2, e2, e1,
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (275), (291) gives:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (292)  e3 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (152), (292) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (293)  $false
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent.
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_56_1 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (294) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_4_1 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (284), (295) imply:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | |   (296)  $false
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (296) is inconsistent.
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |   (297)  all_56_10 = e1 | all_56_10 = e0
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (115), (242), (269), (297) are inconsistent by
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | |            sub-proof #738.
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | |   (298)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | | REF_CLOSE: (12), (125), (152), (153), (181), (204), (234),
% 177.22/27.88  | | | | | | | | | | | | | | |            (235), (243), (298) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | | | | | | | |            #737.
% 177.22/27.88  | | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | |   (299)  all_58_13 = e3
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | | REF_CLOSE: (90), (180), (299) are inconsistent by sub-proof
% 177.22/27.88  | | | | | | | | | | | | |            #1026.
% 177.22/27.88  | | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | |   (300)   ~ (all_56_6 = e3)
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | REDUCE: (142), (300) imply:
% 177.22/27.88  | | | | | | | | | | |   (301)   ~ (all_52_13 = e3)
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | | REF_CLOSE: (12), (21), (22), (30), (36), (81), (121), (125),
% 177.22/27.88  | | | | | | | | | | |            (148), (206), (213), (301) are inconsistent by
% 177.22/27.88  | | | | | | | | | | |            sub-proof #777.
% 177.22/27.88  | | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | | 
% 177.22/27.88  | | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | | 
% 177.22/27.88  | | | | | | | | End of split
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | End of split
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | Case 2:
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | |   (302)   ~ (all_56_3 = e3)
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | REDUCE: (11), (302) imply:
% 177.22/27.88  | | | | | | |   (303)   ~ (all_52_7 = e3)
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | BETA: splitting (145) gives:
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | | Case 1:
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | |   (304)  all_58_4 = e3
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | COMBINE_EQS: (42), (304) imply:
% 177.22/27.88  | | | | | | | |   (305)  all_52_5 = e3
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (11), (12), (15), (16),
% 177.22/27.88  | | | | | | | |            (17), (21), (22), (23), (25), (26), (27), (28), (30),
% 177.22/27.88  | | | | | | | |            (31), (33), (34), (35), (36), (37), (38), (39), (42),
% 177.22/27.88  | | | | | | | |            (43), (45), (46), (49), (50), (51), (52), (53), (57),
% 177.22/27.88  | | | | | | | |            (59), (60), (61), (62), (65), (67), (69), (72), (79),
% 177.22/27.88  | | | | | | | |            (80), (81), (82), (84), (85), (87), (88), (90), (94),
% 177.22/27.88  | | | | | | | |            (96), (97), (98), (99), (101), (102), (103), (105),
% 177.22/27.88  | | | | | | | |            (108), (109), (110), (112), (113), (114), (115),
% 177.22/27.88  | | | | | | | |            (118), (120), (121), (125), (127), (128), (131),
% 177.22/27.88  | | | | | | | |            (134), (135), (136), (137), (139), (142), (144),
% 177.22/27.88  | | | | | | | |            (145), (147), (148), (152), (153), (168), (169),
% 177.22/27.88  | | | | | | | |            (180), (181), (184), (191), (199), (305) are
% 177.22/27.88  | | | | | | | |            inconsistent by sub-proof #381.
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | Case 2:
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | |   (306)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | | REF_CLOSE: (11), (22), (25), (28), (32), (34), (39), (46), (47),
% 177.22/27.88  | | | | | | | |            (50), (52), (58), (62), (64), (69), (71), (78), (81),
% 177.22/27.88  | | | | | | | |            (84), (91), (94), (98), (101), (106), (118), (120),
% 177.22/27.88  | | | | | | | |            (124), (125), (136), (187), (190), (303), (306) are
% 177.22/27.88  | | | | | | | |            inconsistent by sub-proof #353.
% 177.22/27.88  | | | | | | | | 
% 177.22/27.88  | | | | | | | End of split
% 177.22/27.88  | | | | | | | 
% 177.22/27.88  | | | | | | End of split
% 177.22/27.88  | | | | | | 
% 177.22/27.88  | | | | | End of split
% 177.22/27.88  | | | | | 
% 177.22/27.88  | | | | End of split
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | Case 2:
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | |   (307)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | | REF_CLOSE: (3), (7), (12), (19), (20), (21), (24), (26), (28), (30),
% 177.22/27.88  | | | |            (32), (33), (34), (36), (37), (38), (41), (44), (45), (47),
% 177.22/27.88  | | | |            (49), (50), (51), (52), (54), (55), (58), (60), (62), (66),
% 177.22/27.88  | | | |            (76), (78), (79), (81), (88), (89), (90), (92), (96), (97),
% 177.22/27.88  | | | |            (100), (101), (102), (111), (112), (114), (118), (119),
% 177.22/27.88  | | | |            (121), (122), (123), (124), (125), (134), (135), (139),
% 177.22/27.88  | | | |            (140), (146), (148), (153), (169), (180), (307) are
% 177.22/27.88  | | | |            inconsistent by sub-proof #463.
% 177.22/27.88  | | | | 
% 177.22/27.88  | | | End of split
% 177.22/27.88  | | | 
% 177.22/27.88  | | End of split
% 177.22/27.88  | | 
% 177.22/27.88  | End of split
% 177.22/27.88  | 
% 177.22/27.88  End of proof
% 177.22/27.88  
% 177.22/27.88  Sub-proof #350 shows that the following formulas are inconsistent:
% 177.22/27.88  ----------------------------------------------------------------
% 177.22/27.88    (1)   ~ (all_52_5 = all_52_13)
% 177.22/27.88    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.88    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.88    (4)   ~ (all_52_17 = all_52_23)
% 177.22/27.88    (5)   ~ (all_52_13 = all_52_29)
% 177.22/27.88    (6)  op(e3, e2) = all_52_3
% 177.22/27.88    (7)   ~ (all_52_9 = all_52_25)
% 177.22/27.88    (8)  op(e3, all_52_25) = all_52_24
% 177.22/27.88    (9)  op(e1, e2) = all_52_19
% 177.22/27.88    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.88    (11)   ~ (all_6_2 = e3)
% 177.22/27.88    (12)   ~ (all_52_3 = all_10_2)
% 177.22/27.88    (13)  all_58_5 = all_52_13
% 177.22/27.88    (14)  op(e1, all_52_13) = e1
% 177.22/27.88    (15)  op(e0, all_52_15) = e0
% 177.22/27.88    (16)  all_56_15 = all_6_2
% 177.22/27.88    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.88    (18)  op(e2, e0) = all_52_15
% 177.22/27.88    (19)  all_58_3 = all_10_2
% 177.22/27.88    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.88    (21)  all_58_15 = all_6_2
% 177.22/27.88    (22)   ~ (all_52_9 = all_4_2)
% 177.22/27.88    (23)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.88    (24)   ~ (all_52_5 = all_52_7)
% 177.22/27.88    (25)  all_58_10 = all_52_15
% 177.22/27.88    (26)   ~ (all_52_5 = all_4_2)
% 177.22/27.88    (27)  all_58_7 = all_52_19
% 177.22/27.88    (28)  all_56_4 = all_52_9
% 177.22/27.88    (29)   ~ (all_52_15 = all_6_2)
% 177.22/27.88    (30)   ~ (all_52_17 = all_52_25)
% 177.22/27.88    (31)  all_58_4 = all_52_5
% 177.22/27.88    (32)  op(e2, e3) = all_52_26
% 177.22/27.88    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.88    (34)   ~ (e3 = e1)
% 177.22/27.88    (35)   ~ (all_52_17 = all_14_2)
% 177.22/27.88    (36)  op(e3, all_4_2) = all_4_1
% 177.22/27.88    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.88    (38)   ~ (all_52_7 = all_4_2)
% 177.22/27.88    (39)  all_58_1 = all_52_3
% 177.22/27.88    (40)  all_58_0 = all_4_2
% 177.22/27.88    (41)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.88    (42)   ~ (all_4_1 = e2)
% 177.22/27.88    (43)  all_58_14 = all_52_29
% 177.22/27.88    (44)   ~ (all_10_2 = e3)
% 177.22/27.88    (45)   ~ (all_52_3 = all_52_5)
% 177.22/27.88    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.88    (47)  all_58_8 = all_14_2
% 177.22/27.88    (48)  all_56_1 = all_52_3
% 177.22/27.88    (49)  op(e1, all_14_2) = e3
% 177.22/27.88    (50)   ~ (all_52_5 = all_14_2)
% 177.22/27.88    (51)   ~ (all_52_3 = all_4_2)
% 177.22/27.88    (52)  op(e0, e3) = all_52_25
% 177.22/27.88    (53)   ~ (all_52_9 = all_10_2)
% 177.22/27.88    (54)  op(all_4_1, all_4_2) = e2
% 177.22/27.88    (55)   ~ (all_52_13 = all_14_2)
% 177.22/27.88    (56)  op(e3, all_52_9) = e3
% 177.22/27.88    (57)   ~ (all_52_9 = all_52_13)
% 177.22/27.88    (58)   ~ (all_52_15 = all_52_23)
% 177.22/27.88    (59)   ~ (all_52_3 = e3)
% 177.22/27.88    (60)  all_56_5 = all_10_2
% 177.22/27.88    (61)  all_58_6 = all_52_17
% 177.22/27.88    (62)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.88    (63)  all_56_0 = all_4_2
% 177.22/27.88    (64)  all_58_11 = all_52_23
% 177.22/27.88    (65)   ~ (all_52_3 = all_52_19)
% 177.22/27.88    (66)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.88    (67)   ~ (all_52_7 = all_52_15)
% 177.22/27.88    (68)   ~ (all_52_19 = all_10_2)
% 177.22/27.88    (69)   ~ (all_52_29 = all_6_2)
% 177.22/27.88    (70)  all_58_2 = all_52_9
% 177.22/27.88    (71)   ~ (all_52_25 = all_6_2)
% 177.22/27.88    (72)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.88    (73)   ~ (all_52_19 = e3)
% 177.22/27.88    (74)  op(e1, e3) = all_52_17
% 177.22/27.88    (75)   ~ (all_52_25 = all_4_2)
% 177.22/27.88    (76)  op(e3, e0) = all_52_7
% 177.22/27.88    (77)  op(e2, all_10_2) = e2
% 177.22/27.88    (78)  op(e3, e3) = all_4_2
% 177.22/27.88    (79)   ~ (all_52_17 = all_4_2)
% 177.22/27.88    (80)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.88    (81)   ~ (all_52_7 = all_6_2)
% 177.22/27.88    (82)   ~ (all_52_7 = all_52_23)
% 177.22/27.88    (83)   ~ (all_52_13 = all_10_2)
% 177.22/27.88    (84)   ~ (all_52_17 = all_52_19)
% 177.22/27.88    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.88    (86)  all_58_9 = all_52_7
% 177.22/27.88    (87)  all_58_12 = all_52_25
% 177.22/27.88    (88)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.88    (89)   ~ (all_52_9 = all_52_15)
% 177.22/27.88    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.88    (91)  all_58_13 = e3
% 177.22/27.88    (92)  op(e2, e3) = all_52_9
% 177.22/27.88  
% 177.22/27.88  Begin of proof
% 177.22/27.88  | 
% 177.22/27.88  | GROUND_INST: instantiating (80) with all_52_9, all_52_26, e3, e2, simplifying
% 177.22/27.88  |              with (32), (92) gives:
% 177.22/27.88  |   (93)  all_52_9 = all_52_26
% 177.22/27.88  | 
% 177.22/27.88  | COMBINE_EQS: (28), (93) imply:
% 177.22/27.88  |   (94)  all_56_4 = all_52_26
% 177.22/27.88  | 
% 177.22/27.88  | COMBINE_EQS: (70), (93) imply:
% 177.22/27.88  |   (95)  all_58_2 = all_52_26
% 177.22/27.88  | 
% 177.22/27.88  | REDUCE: (57), (93) imply:
% 177.22/27.88  |   (96)   ~ (all_52_13 = all_52_26)
% 177.22/27.88  | 
% 177.22/27.88  | SIMP: (96) implies:
% 177.22/27.88  |   (97)   ~ (all_52_13 = all_52_26)
% 177.22/27.88  | 
% 177.22/27.88  | REDUCE: (89), (93) imply:
% 177.22/27.88  |   (98)   ~ (all_52_15 = all_52_26)
% 177.22/27.88  | 
% 177.22/27.88  | SIMP: (98) implies:
% 177.22/27.88  |   (99)   ~ (all_52_15 = all_52_26)
% 177.22/27.88  | 
% 177.22/27.88  | REDUCE: (7), (93) imply:
% 177.22/27.88  |   (100)   ~ (all_52_25 = all_52_26)
% 177.22/27.88  | 
% 177.22/27.88  | SIMP: (100) implies:
% 177.22/27.88  |   (101)   ~ (all_52_25 = all_52_26)
% 177.22/27.88  | 
% 177.22/27.88  | REDUCE: (53), (93) imply:
% 177.22/27.88  |   (102)   ~ (all_52_26 = all_10_2)
% 177.22/27.88  | 
% 177.22/27.88  | REDUCE: (22), (93) imply:
% 177.22/27.88  |   (103)   ~ (all_52_26 = all_4_2)
% 177.22/27.88  | 
% 177.22/27.89  | REDUCE: (56), (93) imply:
% 177.22/27.89  |   (104)  op(e3, all_52_26) = e3
% 177.22/27.89  | 
% 177.22/27.89  | BETA: splitting (72) gives:
% 177.22/27.89  | 
% 177.22/27.89  | Case 1:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (105)  all_56_5 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | REF_CLOSE: (44), (60), (105) are inconsistent by sub-proof #895.
% 177.22/27.89  | | 
% 177.22/27.89  | Case 2:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (106)   ~ (all_56_5 = e3)
% 177.22/27.89  | |   (107)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.89  | | 
% 177.22/27.89  | | BETA: splitting (41) gives:
% 177.22/27.89  | | 
% 177.22/27.89  | | Case 1:
% 177.22/27.89  | | | 
% 177.22/27.89  | | |   (108)  all_56_1 = e3
% 177.22/27.89  | | | 
% 177.22/27.89  | | | COMBINE_EQS: (48), (108) imply:
% 177.22/27.89  | | |   (109)  all_52_3 = e3
% 177.22/27.89  | | | 
% 177.22/27.89  | | | REDUCE: (59), (109) imply:
% 177.22/27.89  | | |   (110)  $false
% 177.22/27.89  | | | 
% 177.22/27.89  | | | CLOSE: (110) is inconsistent.
% 177.22/27.89  | | | 
% 177.22/27.89  | | Case 2:
% 177.22/27.89  | | | 
% 177.22/27.89  | | |   (111)   ~ (all_56_1 = e3)
% 177.22/27.89  | | |   (112)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.89  | | | 
% 177.22/27.89  | | | BETA: splitting (85) gives:
% 177.22/27.89  | | | 
% 177.22/27.89  | | | Case 1:
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | |   (113)  all_58_9 = e3
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | COMBINE_EQS: (86), (113) imply:
% 177.22/27.89  | | | |   (114)  all_52_7 = e3
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | REDUCE: (24), (114) imply:
% 177.22/27.89  | | | |   (115)   ~ (all_52_5 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | REDUCE: (67), (114) imply:
% 177.22/27.89  | | | |   (116)   ~ (all_52_15 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | SIMP: (116) implies:
% 177.22/27.89  | | | |   (117)   ~ (all_52_15 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | REDUCE: (82), (114) imply:
% 177.22/27.89  | | | |   (118)   ~ (all_52_23 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | SIMP: (118) implies:
% 177.22/27.89  | | | |   (119)   ~ (all_52_23 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | REDUCE: (38), (114) imply:
% 177.22/27.89  | | | |   (120)   ~ (all_4_2 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | SIMP: (120) implies:
% 177.22/27.89  | | | |   (121)   ~ (all_4_2 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | BETA: splitting (90) gives:
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | Case 1:
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | |   (122)  all_58_4 = e3
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | | REF_CLOSE: (31), (115), (122) are inconsistent by sub-proof #1025.
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | Case 2:
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | |   (123)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | | REF_CLOSE: (5), (13), (14), (19), (25), (27), (30), (33), (34), (35),
% 177.22/27.89  | | | | |            (37), (40), (43), (44), (46), (47), (55), (61), (64), (73),
% 177.22/27.89  | | | | |            (74), (78), (80), (87), (95), (97), (103), (104), (117),
% 177.22/27.89  | | | | |            (119), (121), (123) are inconsistent by sub-proof #995.
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | End of split
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | Case 2:
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | |   (124)   ~ (all_58_9 = e3)
% 177.22/27.89  | | | |   (125)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | REDUCE: (86), (124) imply:
% 177.22/27.89  | | | |   (126)   ~ (all_52_7 = e3)
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | BETA: splitting (88) gives:
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | | Case 1:
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | |   (127)  all_58_0 = e3
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | | REF_CLOSE: (36), (40), (42), (54), (78), (80), (127) are inconsistent
% 177.22/27.89  | | | | |            by sub-proof #489.
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | Case 2:
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | |   (128)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | | BETA: splitting (128) gives:
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | | Case 1:
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | |   (129)  all_58_1 = e3
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | | COMBINE_EQS: (39), (129) imply:
% 177.22/27.89  | | | | | |   (130)  all_52_3 = e3
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | | REDUCE: (59), (130) imply:
% 177.22/27.89  | | | | | |   (131)  $false
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | | CLOSE: (131) is inconsistent.
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | Case 2:
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | |   (132)  all_58_4 = e3 | all_58_9 = e3
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | | BETA: splitting (132) gives:
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | | Case 1:
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | |   (133)  all_58_4 = e3
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | COMBINE_EQS: (31), (133) imply:
% 177.22/27.89  | | | | | | |   (134)  all_52_5 = e3
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | REDUCE: (1), (134) imply:
% 177.22/27.89  | | | | | | |   (135)   ~ (all_52_13 = e3)
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | SIMP: (135) implies:
% 177.22/27.89  | | | | | | |   (136)   ~ (all_52_13 = e3)
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | REDUCE: (50), (134) imply:
% 177.22/27.89  | | | | | | |   (137)   ~ (all_14_2 = e3)
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | SIMP: (137) implies:
% 177.22/27.89  | | | | | | |   (138)   ~ (all_14_2 = e3)
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | REDUCE: (26), (134) imply:
% 177.22/27.89  | | | | | | |   (139)   ~ (all_4_2 = e3)
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | SIMP: (139) implies:
% 177.22/27.89  | | | | | | |   (140)   ~ (all_4_2 = e3)
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | BETA: splitting (46) gives:
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | |   (141)  all_58_0 = e3
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | | COMBINE_EQS: (40), (141) imply:
% 177.22/27.89  | | | | | | | |   (142)  all_4_2 = e3
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | | REDUCE: (140), (142) imply:
% 177.22/27.89  | | | | | | | |   (143)  $false
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | | CLOSE: (143) is inconsistent.
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | |   (144)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | | BETA: splitting (33) gives:
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | |   (145)  all_58_6 = e3
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | COMBINE_EQS: (61), (145) imply:
% 177.22/27.89  | | | | | | | | |   (146)  all_52_17 = e3
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | SIMP: (146) implies:
% 177.22/27.89  | | | | | | | | |   (147)  all_52_17 = e3
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | REDUCE: (84), (147) imply:
% 177.22/27.89  | | | | | | | | |   (148)   ~ (all_52_19 = e3)
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | REDUCE: (4), (147) imply:
% 177.22/27.89  | | | | | | | | |   (149)   ~ (all_52_23 = e3)
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | SIMP: (149) implies:
% 177.22/27.89  | | | | | | | | |   (150)   ~ (all_52_23 = e3)
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | BETA: splitting (125) gives:
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | |   (151)  all_58_10 = e3
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | COMBINE_EQS: (25), (151) imply:
% 177.22/27.89  | | | | | | | | | |   (152)  all_52_15 = e3
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | SIMP: (152) implies:
% 177.22/27.89  | | | | | | | | | |   (153)  all_52_15 = e3
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (99), (153) imply:
% 177.22/27.89  | | | | | | | | | |   (154)   ~ (all_52_26 = e3)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | SIMP: (154) implies:
% 177.22/27.89  | | | | | | | | | |   (155)   ~ (all_52_26 = e3)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (29), (153) imply:
% 177.22/27.89  | | | | | | | | | |   (156)   ~ (all_6_2 = e3)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (18), (153) imply:
% 177.22/27.89  | | | | | | | | | |   (157)  op(e2, e0) = e3
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (15), (153) imply:
% 177.22/27.89  | | | | | | | | | |   (158)  op(e0, e3) = e0
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | GROUND_INST: instantiating (80) with all_52_25, e0, e3, e0,
% 177.22/27.89  | | | | | | | | | |              simplifying with (52), (158) gives:
% 177.22/27.89  | | | | | | | | | |   (159)  all_52_25 = e0
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (101), (159) imply:
% 177.22/27.89  | | | | | | | | | |   (160)   ~ (all_52_26 = e0)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | SIMP: (160) implies:
% 177.22/27.89  | | | | | | | | | |   (161)   ~ (all_52_26 = e0)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (71), (159) imply:
% 177.22/27.89  | | | | | | | | | |   (162)   ~ (all_6_2 = e0)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | SIMP: (162) implies:
% 177.22/27.89  | | | | | | | | | |   (163)   ~ (all_6_2 = e0)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (75), (159) imply:
% 177.22/27.89  | | | | | | | | | |   (164)   ~ (all_4_2 = e0)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | SIMP: (164) implies:
% 177.22/27.89  | | | | | | | | | |   (165)   ~ (all_4_2 = e0)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (8), (159) imply:
% 177.22/27.89  | | | | | | | | | |   (166)  op(e3, e0) = all_52_24
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | GROUND_INST: instantiating (80) with all_52_7, all_52_24, e0,
% 177.22/27.89  | | | | | | | | | |              e3, simplifying with (76), (166) gives:
% 177.22/27.89  | | | | | | | | | |   (167)  all_52_7 = all_52_24
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | COMBINE_EQS: (86), (167) imply:
% 177.22/27.89  | | | | | | | | | |   (168)  all_58_9 = all_52_24
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (81), (167) imply:
% 177.22/27.89  | | | | | | | | | |   (169)   ~ (all_52_24 = all_6_2)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REDUCE: (126), (167) imply:
% 177.22/27.89  | | | | | | | | | |   (170)   ~ (all_52_24 = e3)
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | BETA: splitting (20) gives:
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | |   (171)  all_56_0 = e3
% 177.22/27.89  | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | REF_CLOSE: (63), (140), (171) are inconsistent by sub-proof
% 177.22/27.89  | | | | | | | | | | |            #1024.
% 177.22/27.89  | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | |   (172)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.89  | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | BETA: splitting (62) gives:
% 177.22/27.89  | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | |   (173)  all_56_4 = e3
% 177.22/27.89  | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | REF_CLOSE: (94), (155), (173) are inconsistent by sub-proof
% 177.22/27.89  | | | | | | | | | | | |            #818.
% 177.22/27.89  | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | |   (174)   ~ (all_56_4 = e3)
% 177.22/27.89  | | | | | | | | | | | |   (175)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.89  | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | BETA: splitting (17) gives:
% 177.22/27.89  | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | |   (176)  all_58_0 = e2
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | COMBINE_EQS: (40), (176) imply:
% 177.22/27.89  | | | | | | | | | | | | |   (177)  all_4_2 = e2
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | REDUCE: (51), (177) imply:
% 177.22/27.89  | | | | | | | | | | | | |   (178)   ~ (all_52_3 = e2)
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | REDUCE: (103), (177) imply:
% 177.22/27.89  | | | | | | | | | | | | |   (179)   ~ (all_52_26 = e2)
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | REDUCE: (165), (177) imply:
% 177.22/27.89  | | | | | | | | | | | | |   (180)   ~ (e2 = e0)
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | REDUCE: (54), (177) imply:
% 177.22/27.89  | | | | | | | | | | | | |   (181)  op(all_4_1, e2) = e2
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | REDUCE: (36), (177) imply:
% 177.22/27.89  | | | | | | | | | | | | |   (182)  op(e3, e2) = all_4_1
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | BETA: splitting (175) gives:
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | |   (183)  all_56_4 = e2
% 177.22/27.89  | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | REF_CLOSE: (94), (179), (183) are inconsistent by sub-proof
% 177.22/27.89  | | | | | | | | | | | | | |            #807.
% 177.22/27.89  | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | |   (184)   ~ (all_56_4 = e2)
% 177.22/27.89  | | | | | | | | | | | | | |   (185)  all_56_4 = e1 | all_56_4 = e0
% 177.22/27.89  | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 177.22/27.89  | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | |   (186)  all_56_4 = e1
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | COMBINE_EQS: (94), (186) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (187)  all_52_26 = e1
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | SIMP: (187) implies:
% 177.22/27.89  | | | | | | | | | | | | | | |   (188)  all_52_26 = e1
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | REDUCE: (102), (188) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (189)   ~ (all_10_2 = e1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | SIMP: (189) implies:
% 177.22/27.89  | | | | | | | | | | | | | | |   (190)   ~ (all_10_2 = e1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | REDUCE: (155), (188) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (191)   ~ (e3 = e1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | REDUCE: (179), (188) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (192)   ~ (e2 = e1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | SIMP: (192) implies:
% 177.22/27.89  | | | | | | | | | | | | | | |   (193)   ~ (e2 = e1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | GROUND_INST: instantiating (80) with all_52_3, all_4_1, e2, e3,
% 177.22/27.89  | | | | | | | | | | | | | | |              simplifying with (6), (182) gives:
% 177.22/27.89  | | | | | | | | | | | | | | |   (194)  all_52_3 = all_4_1
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | COMBINE_EQS: (48), (194) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (195)  all_56_1 = all_4_1
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | COMBINE_EQS: (39), (194) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (196)  all_58_1 = all_4_1
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | REDUCE: (65), (194) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (197)   ~ (all_52_19 = all_4_1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | SIMP: (197) implies:
% 177.22/27.89  | | | | | | | | | | | | | | |   (198)   ~ (all_52_19 = all_4_1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | REDUCE: (12), (194) imply:
% 177.22/27.89  | | | | | | | | | | | | | | |   (199)   ~ (all_10_2 = all_4_1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | SIMP: (199) implies:
% 177.22/27.89  | | | | | | | | | | | | | | |   (200)   ~ (all_10_2 = all_4_1)
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | |   (201)  all_58_1 = e1
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (201) imply:
% 177.22/27.89  | | | | | | | | | | | | | | | |   (202)  all_4_1 = e1
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | | REDUCE: (181), (202) imply:
% 177.22/27.89  | | | | | | | | | | | | | | | |   (203)  op(e1, e2) = e2
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (60), (68), (73), (77), (80), (107),
% 177.22/27.89  | | | | | | | | | | | | | | | |            (157), (176), (180), (190), (203) are inconsistent
% 177.22/27.89  | | | | | | | | | | | | | | | |            by sub-proof #466.
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | |   (204)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (11), (13), (16), (19), (23), (27),
% 177.22/27.89  | | | | | | | | | | | | | | | |            (34), (42), (43), (47), (49), (60), (66), (68),
% 177.22/27.89  | | | | | | | | | | | | | | | |            (69), (73), (80), (83), (91), (107), (112), (133),
% 177.22/27.89  | | | | | | | | | | | | | | | |            (163), (168), (169), (170), (176), (190), (193),
% 177.22/27.89  | | | | | | | | | | | | | | | |            (195), (196), (198), (200), (204) are inconsistent
% 177.22/27.89  | | | | | | | | | | | | | | | |            by sub-proof #390.
% 177.22/27.89  | | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | |   (205)  all_56_4 = e0
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | | REF_CLOSE: (94), (161), (205) are inconsistent by sub-proof
% 177.22/27.89  | | | | | | | | | | | | | | |            #806.
% 177.22/27.89  | | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | |   (206)   ~ (all_58_0 = e2)
% 177.22/27.89  | | | | | | | | | | | | |   (207)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | REDUCE: (40), (206) imply:
% 177.22/27.89  | | | | | | | | | | | | |   (208)   ~ (all_4_2 = e2)
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | | REF_CLOSE: (6), (59), (63), (80), (94), (95), (103), (104),
% 177.22/27.89  | | | | | | | | | | | | |            (161), (165), (172), (175), (207), (208) are
% 177.22/27.89  | | | | | | | | | | | | |            inconsistent by sub-proof #595.
% 177.22/27.89  | | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | |   (209)  all_58_11 = e3 | all_58_15 = e3
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | | REF_CLOSE: (11), (21), (64), (150), (209) are inconsistent by
% 177.22/27.89  | | | | | | | | | |            sub-proof #1016.
% 177.22/27.89  | | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | Case 2:
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | |   (210)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | | REF_CLOSE: (13), (19), (22), (25), (27), (37), (44), (47),
% 177.22/27.89  | | | | | | | | |            (56), (58), (64), (70), (73), (78), (80), (136),
% 177.22/27.89  | | | | | | | | |            (138), (144), (210) are inconsistent by sub-proof
% 177.22/27.89  | | | | | | | | |            #965.
% 177.22/27.89  | | | | | | | | | 
% 177.22/27.89  | | | | | | | | End of split
% 177.22/27.89  | | | | | | | | 
% 177.22/27.89  | | | | | | | End of split
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | Case 2:
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | |   (211)  all_58_9 = e3
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | COMBINE_EQS: (86), (211) imply:
% 177.22/27.89  | | | | | | |   (212)  all_52_7 = e3
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | REDUCE: (126), (212) imply:
% 177.22/27.89  | | | | | | |   (213)  $false
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | | CLOSE: (213) is inconsistent.
% 177.22/27.89  | | | | | | | 
% 177.22/27.89  | | | | | | End of split
% 177.22/27.89  | | | | | | 
% 177.22/27.89  | | | | | End of split
% 177.22/27.89  | | | | | 
% 177.22/27.89  | | | | End of split
% 177.22/27.89  | | | | 
% 177.22/27.89  | | | End of split
% 177.22/27.89  | | | 
% 177.22/27.89  | | End of split
% 177.22/27.89  | | 
% 177.22/27.89  | End of split
% 177.22/27.89  | 
% 177.22/27.89  End of proof
% 177.22/27.89  
% 177.22/27.89  Sub-proof #351 shows that the following formulas are inconsistent:
% 177.22/27.89  ----------------------------------------------------------------
% 177.22/27.89    (1)   ~ (all_52_5 = all_52_13)
% 177.22/27.89    (2)  all_56_3 = all_52_7
% 177.22/27.89    (3)  op(e3, e2) = all_52_3
% 177.22/27.89    (4)   ~ (all_52_3 = all_10_2)
% 177.22/27.89    (5)  all_58_5 = all_52_13
% 177.22/27.89    (6)  op(e1, all_52_13) = e1
% 177.22/27.89    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.89    (8)   ~ (all_4_2 = e3)
% 177.22/27.89    (9)  all_58_3 = all_10_2
% 177.22/27.89    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.89    (11)   ~ (all_52_9 = all_4_2)
% 177.22/27.89    (12)  all_58_10 = all_52_15
% 177.22/27.89    (13)  all_56_4 = all_52_9
% 177.22/27.89    (14)  all_58_4 = all_52_5
% 177.22/27.89    (15)   ~ (all_52_17 = all_14_2)
% 177.22/27.89    (16)  op(e3, all_4_2) = all_4_1
% 177.22/27.89    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.89    (18)   ~ (all_52_7 = all_4_2)
% 177.22/27.89    (19)  all_58_0 = all_4_2
% 177.22/27.89    (20)   ~ (all_4_1 = e2)
% 177.22/27.89    (21)  all_58_14 = all_52_29
% 177.22/27.89    (22)  all_26_2 = all_4_2
% 177.22/27.89    (23)  all_58_8 = all_14_2
% 177.22/27.89    (24)  op(e1, all_14_2) = e3
% 177.22/27.89    (25)  op(all_4_1, all_4_2) = e2
% 177.22/27.89    (26)   ~ (all_52_29 = e3)
% 177.22/27.89    (27)  op(e3, all_52_9) = e3
% 177.22/27.89    (28)   ~ (all_52_9 = all_52_13)
% 177.22/27.89    (29)   ~ (all_52_15 = e3)
% 177.22/27.89    (30)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.89    (31)   ~ (all_52_9 = all_52_17)
% 177.22/27.89    (32)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.89    (33)  all_56_0 = all_4_2
% 177.22/27.89    (34)  all_26_1 = all_4_1
% 177.22/27.89    (35)   ~ (all_52_9 = e3)
% 177.22/27.89    (36)  all_58_2 = all_52_9
% 177.22/27.89    (37)  op(e1, e3) = all_52_17
% 177.22/27.89    (38)  op(e3, e0) = all_52_7
% 177.22/27.89    (39)  op(e2, all_10_2) = e2
% 177.22/27.89    (40)   ~ (all_52_17 = all_4_2)
% 177.22/27.89    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.89    (42)   ~ (all_52_7 = e3)
% 177.22/27.89    (43)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.89    (44)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.89    (45)  op(e2, e3) = all_52_9
% 177.22/27.89  
% 177.22/27.89  Begin of proof
% 177.22/27.89  | 
% 177.22/27.89  | BETA: splitting (17) gives:
% 177.22/27.89  | 
% 177.22/27.89  | Case 1:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (46)  all_58_2 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | REF_CLOSE: (35), (36), (46) are inconsistent by sub-proof #980.
% 177.22/27.89  | | 
% 177.22/27.89  | Case 2:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (47)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.89  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 177.22/27.89  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (37),
% 177.22/27.89  | |            (38), (39), (40), (41), (42), (43), (44), (45), (47) are
% 177.22/27.89  | |            inconsistent by sub-proof #352.
% 177.22/27.89  | | 
% 177.22/27.89  | End of split
% 177.22/27.89  | 
% 177.22/27.89  End of proof
% 177.22/27.89  
% 177.22/27.89  Sub-proof #352 shows that the following formulas are inconsistent:
% 177.22/27.89  ----------------------------------------------------------------
% 177.22/27.89    (1)   ~ (all_52_5 = all_52_13)
% 177.22/27.89    (2)  all_56_3 = all_52_7
% 177.22/27.89    (3)  op(e3, e2) = all_52_3
% 177.22/27.89    (4)   ~ (all_52_3 = all_10_2)
% 177.22/27.89    (5)  all_58_5 = all_52_13
% 177.22/27.89    (6)  op(e1, all_52_13) = e1
% 177.22/27.89    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.89    (8)   ~ (all_4_2 = e3)
% 177.22/27.89    (9)  all_58_3 = all_10_2
% 177.22/27.89    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.89    (11)   ~ (all_52_9 = all_4_2)
% 177.22/27.89    (12)  all_58_10 = all_52_15
% 177.22/27.89    (13)  all_56_4 = all_52_9
% 177.22/27.89    (14)  all_58_4 = all_52_5
% 177.22/27.89    (15)   ~ (all_52_17 = all_14_2)
% 177.22/27.89    (16)  op(e3, all_4_2) = all_4_1
% 177.22/27.89    (17)   ~ (all_52_7 = all_4_2)
% 177.22/27.89    (18)  all_58_0 = all_4_2
% 177.22/27.89    (19)   ~ (all_4_1 = e2)
% 177.22/27.89    (20)  all_58_14 = all_52_29
% 177.22/27.89    (21)  all_26_2 = all_4_2
% 177.22/27.89    (22)  all_58_8 = all_14_2
% 177.22/27.89    (23)  op(e1, all_14_2) = e3
% 177.22/27.89    (24)  op(all_4_1, all_4_2) = e2
% 177.22/27.89    (25)   ~ (all_52_29 = e3)
% 177.22/27.89    (26)  op(e3, all_52_9) = e3
% 177.22/27.89    (27)   ~ (all_52_9 = all_52_13)
% 177.22/27.89    (28)   ~ (all_52_15 = e3)
% 177.22/27.89    (29)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.89    (30)   ~ (all_52_9 = all_52_17)
% 177.22/27.89    (31)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.89    (32)  all_56_0 = all_4_2
% 177.22/27.89    (33)  all_26_1 = all_4_1
% 177.22/27.89    (34)  op(e1, e3) = all_52_17
% 177.22/27.89    (35)  op(e3, e0) = all_52_7
% 177.22/27.89    (36)  op(e2, all_10_2) = e2
% 177.22/27.89    (37)   ~ (all_52_17 = all_4_2)
% 177.22/27.89    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.89    (39)   ~ (all_52_7 = e3)
% 177.22/27.89    (40)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.89    (41)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.89    (42)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.89    (43)  op(e2, e3) = all_52_9
% 177.22/27.89  
% 177.22/27.89  Begin of proof
% 177.22/27.89  | 
% 177.22/27.89  | BETA: splitting (42) gives:
% 177.22/27.89  | 
% 177.22/27.89  | Case 1:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (44)  all_58_4 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | COMBINE_EQS: (14), (44) imply:
% 177.22/27.89  | |   (45)  all_52_5 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | SIMP: (45) implies:
% 177.22/27.89  | |   (46)  all_52_5 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | REDUCE: (1), (46) imply:
% 177.22/27.89  | |   (47)   ~ (all_52_13 = e3)
% 177.22/27.89  | | 
% 177.22/27.89  | | SIMP: (47) implies:
% 177.22/27.89  | |   (48)   ~ (all_52_13 = e3)
% 177.22/27.89  | | 
% 177.22/27.89  | | REF_CLOSE: (3), (4), (5), (9), (12), (26), (28), (36), (38), (40), (43),
% 177.22/27.89  | |            (48) are inconsistent by sub-proof #777.
% 177.22/27.89  | | 
% 177.22/27.89  | Case 2:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (49)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (11), (13), (15), (16), (17),
% 177.22/27.89  | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (29),
% 177.22/27.89  | |            (30), (31), (32), (33), (34), (35), (37), (38), (39), (41), (49)
% 177.22/27.89  | |            are inconsistent by sub-proof #353.
% 177.22/27.89  | | 
% 177.22/27.89  | End of split
% 177.22/27.89  | 
% 177.22/27.89  End of proof
% 177.22/27.89  
% 177.22/27.89  Sub-proof #353 shows that the following formulas are inconsistent:
% 177.22/27.89  ----------------------------------------------------------------
% 177.22/27.89    (1)  all_56_3 = all_52_7
% 177.22/27.89    (2)  all_58_5 = all_52_13
% 177.22/27.89    (3)  op(e1, all_52_13) = e1
% 177.22/27.89    (4)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.89    (5)   ~ (all_4_2 = e3)
% 177.22/27.89    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.89    (7)   ~ (all_52_9 = all_4_2)
% 177.22/27.89    (8)  all_56_4 = all_52_9
% 177.22/27.89    (9)   ~ (all_52_17 = all_14_2)
% 177.22/27.89    (10)  op(e3, all_4_2) = all_4_1
% 177.22/27.89    (11)   ~ (all_52_7 = all_4_2)
% 177.22/27.89    (12)  all_58_0 = all_4_2
% 177.22/27.89    (13)   ~ (all_4_1 = e2)
% 177.22/27.89    (14)  all_58_14 = all_52_29
% 177.22/27.89    (15)  all_26_2 = all_4_2
% 177.22/27.89    (16)  all_58_8 = all_14_2
% 177.22/27.89    (17)  op(e1, all_14_2) = e3
% 177.22/27.89    (18)  op(all_4_1, all_4_2) = e2
% 177.22/27.89    (19)   ~ (all_52_29 = e3)
% 177.22/27.89    (20)  op(e3, all_52_9) = e3
% 177.22/27.89    (21)   ~ (all_52_9 = all_52_13)
% 177.22/27.89    (22)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.22/27.89    (23)   ~ (all_52_9 = all_52_17)
% 177.22/27.89    (24)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.89    (25)  all_56_0 = all_4_2
% 177.22/27.89    (26)  all_26_1 = all_4_1
% 177.22/27.89    (27)  op(e1, e3) = all_52_17
% 177.22/27.89    (28)  op(e3, e0) = all_52_7
% 177.22/27.89    (29)   ~ (all_52_17 = all_4_2)
% 177.22/27.89    (30)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.89    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.89    (32)   ~ (all_52_7 = e3)
% 177.22/27.89    (33)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.89  
% 177.22/27.89  Begin of proof
% 177.22/27.89  | 
% 177.22/27.89  | BETA: splitting (30) gives:
% 177.22/27.89  | 
% 177.22/27.89  | Case 1:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (34)  all_58_5 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | COMBINE_EQS: (2), (34) imply:
% 177.22/27.89  | |   (35)  all_52_13 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (15),
% 177.22/27.89  | |            (18), (20), (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 177.22/27.89  | |            (31), (32), (33), (35) are inconsistent by sub-proof #468.
% 177.22/27.89  | | 
% 177.22/27.89  | Case 2:
% 177.22/27.89  | | 
% 177.22/27.89  | |   (36)  all_58_8 = e3 | all_58_14 = e3
% 177.22/27.89  | | 
% 177.22/27.89  | | REF_CLOSE: (9), (14), (16), (17), (19), (27), (31), (36) are inconsistent by
% 177.22/27.89  | |            sub-proof #397.
% 177.22/27.89  | | 
% 177.22/27.89  | End of split
% 177.22/27.89  | 
% 177.22/27.89  End of proof
% 177.22/27.89  
% 177.22/27.89  Sub-proof #354 shows that the following formulas are inconsistent:
% 177.22/27.89  ----------------------------------------------------------------
% 177.22/27.89    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.89    (2)   ~ (all_52_17 = all_52_23)
% 177.22/27.89    (3)  all_52_26 = e2
% 177.22/27.89    (4)   ~ (all_6_0 = e3)
% 177.22/27.89    (5)   ~ (all_52_13 = all_52_29)
% 177.22/27.89    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.89    (7)  all_56_3 = all_52_7
% 177.22/27.89    (8)  op(e3, e2) = all_52_3
% 177.22/27.89    (9)   ~ (all_52_9 = all_52_25)
% 177.22/27.89    (10)  op(e3, all_52_25) = all_52_24
% 177.22/27.89    (11)   ~ (all_52_19 = all_52_23)
% 177.22/27.89    (12)  op(e1, e2) = all_52_19
% 177.22/27.89    (13)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.89    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.89    (15)  op(e3, all_52_9) = all_52_8
% 177.22/27.89    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.89    (17)  all_58_5 = all_52_13
% 177.22/27.89    (18)  all_56_15 = all_6_2
% 177.22/27.89    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.89    (20)  all_6_1 = e0
% 177.22/27.89    (21)  all_58_3 = all_10_2
% 177.22/27.89    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.89    (23)  all_58_15 = all_6_2
% 177.22/27.89    (24)   ~ (all_52_9 = all_4_2)
% 177.22/27.89    (25)   ~ (all_52_5 = all_52_7)
% 177.22/27.89    (26)  all_58_10 = all_52_15
% 177.22/27.89    (27)  all_58_7 = all_52_19
% 177.22/27.89    (28)  op(e0, e1) = all_52_29
% 177.22/27.89    (29)  all_58_4 = all_52_5
% 177.22/27.89    (30)   ~ (e3 = e1)
% 177.22/27.89    (31)  all_34_1 = all_4_1
% 177.22/27.89    (32)   ~ (all_52_27 = all_52_29)
% 177.22/27.89    (33)   ~ (all_52_17 = all_14_2)
% 177.22/27.89    (34)  op(e3, all_4_2) = all_4_1
% 177.22/27.89    (35)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.89    (36)   ~ (all_52_7 = all_4_2)
% 177.22/27.89    (37)  all_58_1 = all_52_3
% 177.22/27.89    (38)   ~ (all_52_13 = all_52_15)
% 177.22/27.89    (39)  all_58_0 = all_4_2
% 177.22/27.89    (40)  op(all_4_1, all_4_2) = e1
% 177.22/27.89    (41)  op(e1, all_52_29) = all_52_28
% 177.22/27.89    (42)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.89    (43)   ~ (all_4_1 = e2)
% 177.22/27.89    (44)  all_58_14 = all_52_29
% 177.22/27.89    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.89    (46)   ~ (all_52_3 = all_52_5)
% 177.22/27.89    (47)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.89    (48)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.89    (49)  all_58_8 = all_14_2
% 177.22/27.89    (50)  all_56_1 = all_52_3
% 177.22/27.89    (51)  op(e0, e2) = all_52_27
% 177.22/27.89    (52)  op(e1, all_14_2) = e3
% 177.22/27.89    (53)   ~ (all_52_3 = all_4_2)
% 177.22/27.89    (54)  op(all_6_1, all_6_2) = all_6_0
% 177.22/27.89    (55)  op(e0, e3) = all_52_25
% 177.22/27.89    (56)  op(e0, all_6_2) = all_6_1
% 177.22/27.89    (57)   ~ (all_52_9 = all_10_2)
% 177.22/27.89    (58)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.89    (59)   ~ (all_52_9 = all_52_13)
% 177.22/27.89    (60)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.89    (61)  all_56_2 = all_52_5
% 177.22/27.89    (62)  op(e1, e0) = all_52_23
% 177.22/27.89    (63)  all_56_12 = all_52_25
% 177.22/27.89    (64)  all_58_13 = all_52_27
% 177.22/27.89    (65)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.89    (66)  all_58_6 = all_52_17
% 177.22/27.89    (67)  all_56_0 = all_4_2
% 177.22/27.89    (68)  all_58_11 = all_52_23
% 177.22/27.89    (69)   ~ (all_52_3 = all_52_19)
% 177.22/27.90    (70)   ~ (all_52_29 = all_14_2)
% 177.22/27.90    (71)   ~ (all_6_0 = e2)
% 177.22/27.90    (72)  all_58_2 = all_52_9
% 177.22/27.90    (73)  op(e3, e1) = all_52_5
% 177.22/27.90    (74)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.90    (75)  op(e1, e1) = all_14_2
% 177.22/27.90    (76)  op(e1, e3) = all_52_17
% 177.22/27.90    (77)   ~ (all_52_25 = all_4_2)
% 177.22/27.90    (78)  op(e3, e0) = all_52_7
% 177.22/27.90    (79)  all_52_28 = e1
% 177.22/27.90    (80)  op(e3, e3) = all_4_2
% 177.22/27.90    (81)   ~ (all_52_17 = all_4_2)
% 177.22/27.90    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.90    (83)   ~ (all_52_25 = all_52_27)
% 177.22/27.90    (84)  all_34_2 = all_4_2
% 177.22/27.90    (85)   ~ (all_52_27 = all_6_2)
% 177.22/27.90    (86)   ~ (all_52_7 = all_6_2)
% 177.22/27.90    (87)   ~ (all_52_7 = all_52_23)
% 177.22/27.90    (88)   ~ (all_6_0 = e1)
% 177.22/27.90    (89)  op(e2, all_52_27) = all_52_26
% 177.22/27.90    (90)   ~ (all_52_17 = all_52_19)
% 177.22/27.90    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.90    (92)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.90    (93)  all_58_9 = all_52_7
% 177.22/27.90    (94)  all_52_24 = e3
% 177.22/27.90    (95)  all_58_12 = all_52_25
% 177.22/27.90    (96)   ~ (all_52_9 = all_52_15)
% 177.22/27.90    (97)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.90    (98)   ~ (e3 = e2)
% 177.22/27.90    (99)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.90    (100)  op(e2, e3) = all_52_9
% 177.22/27.90    (101)  all_56_13 = all_52_27
% 177.22/27.90  
% 177.22/27.90  Begin of proof
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (20), (54) imply:
% 177.22/27.90  |   (102)  op(e0, all_6_2) = all_6_0
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (10), (94) imply:
% 177.22/27.90  |   (103)  op(e3, all_52_25) = e3
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (3), (89) imply:
% 177.22/27.90  |   (104)  op(e2, all_52_27) = e2
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (41), (79) imply:
% 177.22/27.90  |   (105)  op(e1, all_52_29) = e1
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (20), (56) imply:
% 177.22/27.90  |   (106)  op(e0, all_6_2) = e0
% 177.22/27.90  | 
% 177.22/27.90  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 177.22/27.90  |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 177.22/27.90  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.22/27.90  |            (38), (39), (40), (42), (43), (44), (45), (46), (47), (48), (49),
% 177.22/27.90  |            (50), (51), (52), (53), (55), (57), (58), (59), (60), (61), (62),
% 177.22/27.90  |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 177.22/27.90  |            (74), (75), (76), (77), (78), (80), (81), (82), (83), (84), (85),
% 177.22/27.90  |            (86), (87), (88), (90), (91), (92), (93), (95), (96), (97), (98),
% 177.22/27.90  |            (99), (100), (101), (102), (103), (104), (105), (106) are
% 177.22/27.90  |            inconsistent by sub-proof #355.
% 177.22/27.90  | 
% 177.22/27.90  End of proof
% 177.22/27.90  
% 177.22/27.90  Sub-proof #355 shows that the following formulas are inconsistent:
% 177.22/27.90  ----------------------------------------------------------------
% 177.22/27.90    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.90    (2)   ~ (all_52_17 = all_52_23)
% 177.22/27.90    (3)   ~ (all_6_0 = e3)
% 177.22/27.90    (4)   ~ (all_52_13 = all_52_29)
% 177.22/27.90    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.90    (6)  all_56_3 = all_52_7
% 177.22/27.90    (7)  op(e3, e2) = all_52_3
% 177.22/27.90    (8)   ~ (all_52_9 = all_52_25)
% 177.22/27.90    (9)   ~ (all_52_19 = all_52_23)
% 177.22/27.90    (10)  op(e1, e2) = all_52_19
% 177.22/27.90    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.22/27.90    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.90    (13)  op(e3, all_52_9) = all_52_8
% 177.22/27.90    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.90    (15)  all_58_5 = all_52_13
% 177.22/27.90    (16)  all_56_15 = all_6_2
% 177.22/27.90    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.90    (18)  all_58_3 = all_10_2
% 177.22/27.90    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.90    (20)  all_58_15 = all_6_2
% 177.22/27.90    (21)  op(e0, all_6_2) = e0
% 177.22/27.90    (22)   ~ (all_52_9 = all_4_2)
% 177.22/27.90    (23)   ~ (all_52_5 = all_52_7)
% 177.22/27.90    (24)  all_58_10 = all_52_15
% 177.22/27.90    (25)  all_58_7 = all_52_19
% 177.22/27.90    (26)  op(e0, e1) = all_52_29
% 177.22/27.90    (27)  all_58_4 = all_52_5
% 177.22/27.90    (28)   ~ (e3 = e1)
% 177.22/27.90    (29)  all_34_1 = all_4_1
% 177.22/27.90    (30)   ~ (all_52_27 = all_52_29)
% 177.22/27.90    (31)   ~ (all_52_17 = all_14_2)
% 177.22/27.90    (32)  op(e3, all_4_2) = all_4_1
% 177.22/27.90    (33)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.90    (34)   ~ (all_52_7 = all_4_2)
% 177.22/27.90    (35)  all_58_1 = all_52_3
% 177.22/27.90    (36)   ~ (all_52_13 = all_52_15)
% 177.22/27.90    (37)  all_58_0 = all_4_2
% 177.22/27.90    (38)  op(all_4_1, all_4_2) = e1
% 177.22/27.90    (39)  op(e2, all_52_27) = e2
% 177.22/27.90    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.90    (41)   ~ (all_4_1 = e2)
% 177.22/27.90    (42)  all_58_14 = all_52_29
% 177.22/27.90    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.90    (44)   ~ (all_52_3 = all_52_5)
% 177.22/27.90    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.90    (46)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.90    (47)  all_58_8 = all_14_2
% 177.22/27.90    (48)  all_56_1 = all_52_3
% 177.22/27.90    (49)  op(e0, e2) = all_52_27
% 177.22/27.90    (50)  op(e1, all_14_2) = e3
% 177.22/27.90    (51)  op(e1, all_52_29) = e1
% 177.22/27.90    (52)   ~ (all_52_3 = all_4_2)
% 177.22/27.90    (53)  op(e0, e3) = all_52_25
% 177.22/27.90    (54)   ~ (all_52_9 = all_10_2)
% 177.22/27.90    (55)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.90    (56)   ~ (all_52_9 = all_52_13)
% 177.22/27.90    (57)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.90    (58)  all_56_2 = all_52_5
% 177.22/27.90    (59)  op(e1, e0) = all_52_23
% 177.22/27.90    (60)  all_56_12 = all_52_25
% 177.22/27.90    (61)  all_58_13 = all_52_27
% 177.22/27.90    (62)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.90    (63)  all_58_6 = all_52_17
% 177.22/27.90    (64)  all_56_0 = all_4_2
% 177.22/27.90    (65)  all_58_11 = all_52_23
% 177.22/27.90    (66)   ~ (all_52_3 = all_52_19)
% 177.22/27.90    (67)   ~ (all_52_29 = all_14_2)
% 177.22/27.90    (68)  op(e3, all_52_25) = e3
% 177.22/27.90    (69)   ~ (all_6_0 = e2)
% 177.22/27.90    (70)  all_58_2 = all_52_9
% 177.22/27.90    (71)  op(e3, e1) = all_52_5
% 177.22/27.90    (72)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.90    (73)  op(e1, e1) = all_14_2
% 177.22/27.90    (74)  op(e1, e3) = all_52_17
% 177.22/27.90    (75)   ~ (all_52_25 = all_4_2)
% 177.22/27.90    (76)  op(e3, e0) = all_52_7
% 177.22/27.90    (77)  op(e3, e3) = all_4_2
% 177.22/27.90    (78)   ~ (all_52_17 = all_4_2)
% 177.22/27.90    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.90    (80)   ~ (all_52_25 = all_52_27)
% 177.22/27.90    (81)  all_34_2 = all_4_2
% 177.22/27.90    (82)  op(e0, all_6_2) = all_6_0
% 177.22/27.90    (83)   ~ (all_52_27 = all_6_2)
% 177.22/27.90    (84)   ~ (all_52_7 = all_6_2)
% 177.22/27.90    (85)   ~ (all_52_7 = all_52_23)
% 177.22/27.90    (86)   ~ (all_6_0 = e1)
% 177.22/27.90    (87)   ~ (all_52_17 = all_52_19)
% 177.22/27.90    (88)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.90    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.90    (90)  all_58_9 = all_52_7
% 177.22/27.90    (91)  all_58_12 = all_52_25
% 177.22/27.90    (92)   ~ (all_52_9 = all_52_15)
% 177.22/27.90    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.90    (94)   ~ (e3 = e2)
% 177.22/27.90    (95)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.90    (96)  op(e2, e3) = all_52_9
% 177.22/27.90    (97)  all_56_13 = all_52_27
% 177.22/27.90  
% 177.22/27.90  Begin of proof
% 177.22/27.90  | 
% 177.22/27.90  | GROUND_INST: instantiating (79) with e0, all_6_0, all_6_2, e0, simplifying
% 177.22/27.90  |              with (21), (82) gives:
% 177.22/27.90  |   (98)  all_6_0 = e0
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (3), (98) imply:
% 177.22/27.90  |   (99)   ~ (e3 = e0)
% 177.22/27.90  | 
% 177.22/27.90  | SIMP: (99) implies:
% 177.22/27.90  |   (100)   ~ (e3 = e0)
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (69), (98) imply:
% 177.22/27.90  |   (101)   ~ (e2 = e0)
% 177.22/27.90  | 
% 177.22/27.90  | SIMP: (101) implies:
% 177.22/27.90  |   (102)   ~ (e2 = e0)
% 177.22/27.90  | 
% 177.22/27.90  | REDUCE: (86), (98) imply:
% 177.22/27.90  |   (103)   ~ (e1 = e0)
% 177.22/27.90  | 
% 177.22/27.90  | SIMP: (103) implies:
% 177.22/27.90  |   (104)   ~ (e1 = e0)
% 177.22/27.90  | 
% 177.22/27.90  | BETA: splitting (33) gives:
% 177.22/27.90  | 
% 177.22/27.90  | Case 1:
% 177.22/27.90  | | 
% 177.22/27.90  | |   (105)  all_56_15 = e3
% 177.22/27.90  | | 
% 177.22/27.90  | | COMBINE_EQS: (16), (105) imply:
% 177.22/27.90  | |   (106)  all_6_2 = e3
% 177.22/27.90  | | 
% 177.22/27.90  | | SIMP: (106) implies:
% 177.22/27.90  | |   (107)  all_6_2 = e3
% 177.22/27.90  | | 
% 177.22/27.90  | | REF_CLOSE: (21), (53), (68), (76), (79), (84), (107) are inconsistent by
% 177.22/27.90  | |            sub-proof #665.
% 177.22/27.90  | | 
% 177.22/27.90  | Case 2:
% 177.22/27.90  | | 
% 177.22/27.90  | |   (108)   ~ (all_56_15 = e3)
% 177.22/27.90  | | 
% 177.22/27.90  | | REDUCE: (16), (108) imply:
% 177.22/27.90  | |   (109)   ~ (all_6_2 = e3)
% 177.22/27.90  | | 
% 177.22/27.90  | | BETA: splitting (43) gives:
% 177.22/27.90  | | 
% 177.22/27.90  | | Case 1:
% 177.22/27.90  | | | 
% 177.22/27.90  | | |   (110)  all_56_13 = e3
% 177.22/27.90  | | | 
% 177.22/27.90  | | | COMBINE_EQS: (97), (110) imply:
% 177.22/27.90  | | |   (111)  all_52_27 = e3
% 177.22/27.90  | | | 
% 177.22/27.90  | | | COMBINE_EQS: (61), (111) imply:
% 177.22/27.90  | | |   (112)  all_58_13 = e3
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (80), (111) imply:
% 177.22/27.90  | | |   (113)   ~ (all_52_25 = e3)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (30), (111) imply:
% 177.22/27.90  | | |   (114)   ~ (all_52_29 = e3)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | SIMP: (114) implies:
% 177.22/27.90  | | |   (115)   ~ (all_52_29 = e3)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (83), (111) imply:
% 177.22/27.90  | | |   (116)   ~ (all_6_2 = e3)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (39), (111) imply:
% 177.22/27.90  | | |   (117)  op(e2, e3) = e2
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (49), (111) imply:
% 177.22/27.90  | | |   (118)  op(e0, e2) = e3
% 177.22/27.90  | | | 
% 177.22/27.90  | | | GROUND_INST: instantiating (79) with all_52_9, e2, e3, e2, simplifying
% 177.22/27.90  | | |              with (96), (117) gives:
% 177.22/27.90  | | |   (119)  all_52_9 = e2
% 177.22/27.90  | | | 
% 177.22/27.90  | | | COMBINE_EQS: (70), (119) imply:
% 177.22/27.90  | | |   (120)  all_58_2 = e2
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (56), (119) imply:
% 177.22/27.90  | | |   (121)   ~ (all_52_13 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | SIMP: (121) implies:
% 177.22/27.90  | | |   (122)   ~ (all_52_13 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (92), (119) imply:
% 177.22/27.90  | | |   (123)   ~ (all_52_15 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | SIMP: (123) implies:
% 177.22/27.90  | | |   (124)   ~ (all_52_15 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (8), (119) imply:
% 177.22/27.90  | | |   (125)   ~ (all_52_25 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | SIMP: (125) implies:
% 177.22/27.90  | | |   (126)   ~ (all_52_25 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (54), (119) imply:
% 177.22/27.90  | | |   (127)   ~ (all_10_2 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | SIMP: (127) implies:
% 177.22/27.90  | | |   (128)   ~ (all_10_2 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (22), (119) imply:
% 177.22/27.90  | | |   (129)   ~ (all_4_2 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | SIMP: (129) implies:
% 177.22/27.90  | | |   (130)   ~ (all_4_2 = e2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (13), (119) imply:
% 177.22/27.90  | | |   (131)  op(e3, e2) = all_52_8
% 177.22/27.90  | | | 
% 177.22/27.90  | | | GROUND_INST: instantiating (79) with all_52_3, all_52_8, e2, e3,
% 177.22/27.90  | | |              simplifying with (7), (131) gives:
% 177.22/27.90  | | |   (132)  all_52_3 = all_52_8
% 177.22/27.90  | | | 
% 177.22/27.90  | | | COMBINE_EQS: (35), (132) imply:
% 177.22/27.90  | | |   (133)  all_58_1 = all_52_8
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (44), (132) imply:
% 177.22/27.90  | | |   (134)   ~ (all_52_5 = all_52_8)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | SIMP: (134) implies:
% 177.22/27.90  | | |   (135)   ~ (all_52_5 = all_52_8)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (52), (132) imply:
% 177.22/27.90  | | |   (136)   ~ (all_52_8 = all_4_2)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | BETA: splitting (57) gives:
% 177.22/27.90  | | | 
% 177.22/27.90  | | | Case 1:
% 177.22/27.90  | | | | 
% 177.22/27.90  | | | |   (137)  all_56_12 = e3
% 177.22/27.90  | | | | 
% 177.22/27.90  | | | | REF_CLOSE: (60), (113), (137) are inconsistent by sub-proof #1040.
% 177.22/27.90  | | | | 
% 177.22/27.90  | | | Case 2:
% 177.22/27.90  | | | | 
% 177.22/27.90  | | | |   (138)   ~ (all_56_12 = e3)
% 177.22/27.90  | | | |   (139)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.90  | | | | 
% 177.22/27.90  | | | | BETA: splitting (45) gives:
% 177.22/27.90  | | | | 
% 177.22/27.90  | | | | Case 1:
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | |   (140)  all_58_0 = e3
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | | COMBINE_EQS: (37), (140) imply:
% 177.22/27.90  | | | | |   (141)  all_4_2 = e3
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | | REF_CLOSE: (28), (32), (38), (77), (79), (141) are inconsistent by
% 177.22/27.90  | | | | |            sub-proof #599.
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | Case 2:
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | |   (142)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | | BETA: splitting (142) gives:
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | | Case 1:
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | |   (143)  all_58_2 = e3
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | | COMBINE_EQS: (120), (143) imply:
% 177.22/27.90  | | | | | |   (144)  e3 = e2
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | | REDUCE: (94), (144) imply:
% 177.22/27.90  | | | | | |   (145)  $false
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | | CLOSE: (145) is inconsistent.
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | Case 2:
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | |   (146)  all_58_6 = e3 | all_58_12 = e3
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | | BETA: splitting (146) gives:
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | | Case 1:
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | |   (147)  all_58_6 = e3
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | COMBINE_EQS: (63), (147) imply:
% 177.22/27.90  | | | | | | |   (148)  all_52_17 = e3
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | SIMP: (148) implies:
% 177.22/27.90  | | | | | | |   (149)  all_52_17 = e3
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | REDUCE: (87), (149) imply:
% 177.22/27.90  | | | | | | |   (150)   ~ (all_52_19 = e3)
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | SIMP: (150) implies:
% 177.22/27.90  | | | | | | |   (151)   ~ (all_52_19 = e3)
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | REDUCE: (2), (149) imply:
% 177.22/27.90  | | | | | | |   (152)   ~ (all_52_23 = e3)
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | SIMP: (152) implies:
% 177.22/27.90  | | | | | | |   (153)   ~ (all_52_23 = e3)
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | REDUCE: (78), (149) imply:
% 177.22/27.90  | | | | | | |   (154)   ~ (all_4_2 = e3)
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | SIMP: (154) implies:
% 177.22/27.90  | | | | | | |   (155)   ~ (all_4_2 = e3)
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | BETA: splitting (19) gives:
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | Case 1:
% 177.22/27.90  | | | | | | | | 
% 177.22/27.90  | | | | | | | |   (156)  all_56_0 = e3
% 177.22/27.90  | | | | | | | | 
% 177.22/27.90  | | | | | | | | REF_CLOSE: (64), (155), (156) are inconsistent by sub-proof
% 177.22/27.90  | | | | | | | |            #1024.
% 177.22/27.90  | | | | | | | | 
% 177.22/27.90  | | | | | | | Case 2:
% 177.22/27.90  | | | | | | | | 
% 177.22/27.90  | | | | | | | |   (157)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.90  | | | | | | | | 
% 177.22/27.90  | | | | | | | | BETA: splitting (93) gives:
% 177.22/27.90  | | | | | | | | 
% 177.22/27.90  | | | | | | | | Case 1:
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | |   (158)  all_58_4 = e3
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | COMBINE_EQS: (27), (158) imply:
% 177.22/27.90  | | | | | | | | |   (159)  all_52_5 = e3
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | SIMP: (159) implies:
% 177.22/27.90  | | | | | | | | |   (160)  all_52_5 = e3
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | REDUCE: (23), (160) imply:
% 177.22/27.90  | | | | | | | | |   (161)   ~ (all_52_7 = e3)
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | SIMP: (161) implies:
% 177.22/27.90  | | | | | | | | |   (162)   ~ (all_52_7 = e3)
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | BETA: splitting (11) gives:
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | Case 1:
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | |   (163)  all_58_0 = e1
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | COMBINE_EQS: (37), (163) imply:
% 177.22/27.90  | | | | | | | | | |   (164)  all_4_2 = e1
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | REDUCE: (75), (164) imply:
% 177.22/27.90  | | | | | | | | | |   (165)   ~ (all_52_25 = e1)
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | REF_CLOSE: (60), (68), (76), (79), (126), (139), (162), (165)
% 177.22/27.90  | | | | | | | | | |            are inconsistent by sub-proof #663.
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | Case 2:
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | |   (166)   ~ (all_58_0 = e1)
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | REDUCE: (37), (166) imply:
% 177.22/27.90  | | | | | | | | | |   (167)   ~ (all_4_2 = e1)
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | REF_CLOSE: (6), (28), (32), (34), (38), (41), (59), (64),
% 177.22/27.90  | | | | | | | | | |            (76), (79), (85), (89), (130), (157), (167) are
% 177.22/27.90  | | | | | | | | | |            inconsistent by sub-proof #588.
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | End of split
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | Case 2:
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | |   (168)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | BETA: splitting (168) gives:
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | Case 1:
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | |   (169)  all_58_5 = e3
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | COMBINE_EQS: (15), (169) imply:
% 177.22/27.90  | | | | | | | | | |   (170)  all_52_13 = e3
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | SIMP: (170) implies:
% 177.22/27.90  | | | | | | | | | |   (171)  all_52_13 = e3
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | REDUCE: (36), (171) imply:
% 177.22/27.90  | | | | | | | | | |   (172)   ~ (all_52_15 = e3)
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | SIMP: (172) implies:
% 177.22/27.90  | | | | | | | | | |   (173)   ~ (all_52_15 = e3)
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | REF_CLOSE: (1), (5), (6), (9), (14), (18), (20), (21), (23),
% 177.22/27.90  | | | | | | | | | |            (24), (25), (26), (27), (28), (32), (34), (37),
% 177.22/27.90  | | | | | | | | | |            (38), (41), (42), (51), (55), (58), (59), (62),
% 177.22/27.90  | | | | | | | | | |            (64), (65), (67), (68), (71), (72), (73), (76),
% 177.22/27.90  | | | | | | | | | |            (79), (84), (85), (88), (89), (90), (91), (94),
% 177.22/27.90  | | | | | | | | | |            (95), (100), (102), (104), (109), (112), (115),
% 177.22/27.90  | | | | | | | | | |            (118), (124), (126), (128), (133), (135), (136),
% 177.22/27.90  | | | | | | | | | |            (151), (153), (157), (173) are inconsistent by
% 177.22/27.90  | | | | | | | | | |            sub-proof #558.
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | Case 2:
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | |   (174)  all_58_8 = e3 | all_58_14 = e3
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | | REF_CLOSE: (31), (42), (47), (50), (74), (79), (115), (174)
% 177.22/27.90  | | | | | | | | | |            are inconsistent by sub-proof #397.
% 177.22/27.90  | | | | | | | | | | 
% 177.22/27.90  | | | | | | | | | End of split
% 177.22/27.90  | | | | | | | | | 
% 177.22/27.90  | | | | | | | | End of split
% 177.22/27.90  | | | | | | | | 
% 177.22/27.90  | | | | | | | End of split
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | Case 2:
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | |   (175)  all_58_12 = e3
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | | REF_CLOSE: (91), (113), (175) are inconsistent by sub-proof #1003.
% 177.22/27.90  | | | | | | | 
% 177.22/27.90  | | | | | | End of split
% 177.22/27.90  | | | | | | 
% 177.22/27.90  | | | | | End of split
% 177.22/27.90  | | | | | 
% 177.22/27.90  | | | | End of split
% 177.22/27.90  | | | | 
% 177.22/27.90  | | | End of split
% 177.22/27.90  | | | 
% 177.22/27.90  | | Case 2:
% 177.22/27.90  | | | 
% 177.22/27.90  | | |   (176)   ~ (all_56_13 = e3)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REDUCE: (97), (176) imply:
% 177.22/27.90  | | |   (177)   ~ (all_52_27 = e3)
% 177.22/27.90  | | | 
% 177.22/27.90  | | | REF_CLOSE: (6), (7), (10), (12), (17), (19), (20), (28), (29), (32), (34),
% 177.22/27.90  | | |            (37), (38), (40), (41), (42), (45), (46), (48), (51), (52),
% 177.22/27.90  | | |            (59), (61), (64), (66), (68), (74), (75), (76), (77), (78),
% 177.22/27.90  | | |            (79), (81), (85), (89), (91), (109), (177) are inconsistent by
% 177.22/27.90  | | |            sub-proof #557.
% 177.22/27.90  | | | 
% 177.22/27.90  | | End of split
% 177.22/27.90  | | 
% 177.22/27.90  | End of split
% 177.22/27.90  | 
% 177.22/27.90  End of proof
% 177.22/27.90  
% 177.22/27.90  Sub-proof #356 shows that the following formulas are inconsistent:
% 177.22/27.90  ----------------------------------------------------------------
% 177.22/27.90    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.90    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.90    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.90    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.90    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.90    (6)  op(e2, all_10_2) = all_10_1
% 177.22/27.90    (7)   ~ (all_52_13 = all_52_29)
% 177.22/27.90    (8)  all_56_3 = all_52_7
% 177.22/27.90    (9)  op(e3, e2) = all_52_3
% 177.22/27.90    (10)   ~ (all_52_9 = all_52_25)
% 177.22/27.90    (11)   ~ (all_52_19 = all_52_23)
% 177.22/27.90    (12)  all_56_11 = all_52_23
% 177.22/27.90    (13)  op(e1, e2) = all_52_19
% 177.22/27.90    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.90    (15)  op(e3, all_52_9) = all_52_8
% 177.22/27.90    (16)   ~ (all_52_3 = all_10_2)
% 177.22/27.90    (17)  all_58_5 = all_52_13
% 177.22/27.90    (18)   ~ (all_6_2 = e0)
% 177.22/27.90    (19)   ~ (all_52_25 = all_52_29)
% 177.22/27.90    (20)  all_56_15 = all_6_2
% 177.22/27.90    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.90    (22)  all_58_3 = all_10_2
% 177.22/27.90    (23)  all_56_9 = all_52_19
% 177.22/27.90    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.90    (25)  all_58_15 = all_6_2
% 177.22/27.90    (26)   ~ (all_52_9 = all_4_2)
% 177.22/27.90    (27)   ~ (all_52_5 = all_52_7)
% 177.22/27.90    (28)  all_58_10 = all_52_15
% 177.22/27.90    (29)   ~ (all_52_5 = all_4_2)
% 177.22/27.90    (30)  all_58_7 = all_52_19
% 177.22/27.90    (31)  all_56_4 = all_52_9
% 177.22/27.90    (32)   ~ (all_52_15 = all_6_2)
% 177.22/27.90    (33)   ~ (all_52_17 = all_52_25)
% 177.22/27.90    (34)  all_58_4 = all_52_5
% 177.22/27.90    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.90    (36)   ~ (e3 = e1)
% 177.22/27.90    (37)  all_34_1 = all_4_1
% 177.22/27.90    (38)   ~ (all_52_27 = all_52_29)
% 177.22/27.90    (39)   ~ (all_52_17 = all_14_2)
% 177.22/27.90    (40)  op(e3, all_4_2) = all_4_1
% 177.22/27.90    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.90    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.90    (43)   ~ (all_52_7 = all_4_2)
% 177.22/27.90    (44)  all_58_1 = all_52_3
% 177.22/27.90    (45)  all_58_0 = all_4_2
% 177.22/27.90    (46)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.90    (47)  op(e1, all_52_13) = all_52_12
% 177.22/27.90    (48)  op(all_4_1, all_4_2) = e1
% 177.22/27.90    (49)  op(e1, all_52_29) = all_52_28
% 177.22/27.90    (50)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.22/27.90          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.22/27.90    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.90    (52)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.90    (53)   ~ (all_4_1 = e2)
% 177.22/27.90    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.90    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.90    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.90    (57)  all_58_14 = all_52_29
% 177.22/27.90    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.90    (59)   ~ (all_52_3 = all_52_5)
% 177.22/27.90    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.90    (61)  op(e2, e1) = all_52_13
% 177.22/27.90    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.90    (63)  all_58_8 = all_14_2
% 177.22/27.90    (64)  all_56_1 = all_52_3
% 177.22/27.90    (65)  op(e1, all_14_2) = e3
% 177.22/27.90    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.90    (67)   ~ (all_52_3 = all_52_27)
% 177.22/27.90    (68)   ~ (all_52_3 = all_4_2)
% 177.22/27.90    (69)  op(e0, e3) = all_52_25
% 177.22/27.90    (70)  all_52_0 = all_4_1
% 177.22/27.90    (71)  op(e3, all_52_17) = all_52_16
% 177.22/27.90    (72)  all_52_10 = all_10_1
% 177.22/27.90    (73)   ~ (all_52_13 = all_14_2)
% 177.22/27.90    (74)   ~ (e3 = e0)
% 177.22/27.90    (75)   ~ (all_52_9 = all_52_13)
% 177.22/27.90    (76)  op(e0, all_52_23) = all_52_22
% 177.22/27.90    (77)   ~ (all_52_15 = all_52_23)
% 177.22/27.90    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.90    (79)  op(all_10_1, all_10_2) = all_10_0
% 177.22/27.90    (80)  op(e1, e0) = all_52_23
% 177.22/27.90    (81)  all_58_13 = all_52_27
% 177.22/27.90    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.90    (83)   ~ (all_52_9 = all_52_17)
% 177.22/27.90    (84)  all_58_6 = all_52_17
% 177.22/27.90    (85)   ~ (all_52_3 = all_52_7)
% 177.22/27.90    (86)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.90    (87)  op(e2, all_52_19) = all_52_18
% 177.22/27.90    (88)   ~ (e1 = e0)
% 177.22/27.90    (89)  all_56_0 = all_4_2
% 177.22/27.90    (90)  all_58_11 = all_52_23
% 177.22/27.90    (91)   ~ (all_52_3 = all_52_19)
% 177.22/27.90    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.90    (93)   ~ (all_52_7 = all_52_15)
% 177.22/27.90    (94)  op(e0, all_52_15) = all_52_14
% 177.22/27.90    (95)   ~ (all_52_29 = all_14_2)
% 177.22/27.90    (96)   ~ (all_52_19 = all_10_2)
% 177.22/27.90    (97)   ~ (all_52_23 = all_6_2)
% 177.22/27.90    (98)   ~ (all_52_29 = all_6_2)
% 177.22/27.90    (99)  all_58_2 = all_52_9
% 177.22/27.90    (100)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.90    (101)  op(e3, e1) = all_52_5
% 177.22/27.90    (102)  all_56_10 = all_14_2
% 177.22/27.90    (103)   ~ (all_52_25 = all_6_2)
% 177.22/27.90    (104)  op(e1, e3) = all_52_17
% 177.22/27.90    (105)   ~ (all_52_25 = all_4_2)
% 177.22/27.90    (106)  op(e3, e0) = all_52_7
% 177.22/27.90    (107)  op(e3, e3) = all_4_2
% 177.22/27.90    (108)   ~ (all_52_17 = all_4_2)
% 177.22/27.90    (109)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.90             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.90    (110)   ~ (all_52_25 = all_52_27)
% 177.22/27.90    (111)  all_34_2 = all_4_2
% 177.22/27.90    (112)   ~ (all_52_27 = all_6_2)
% 177.22/27.90    (113)   ~ (all_52_7 = all_6_2)
% 177.22/27.90    (114)   ~ (all_10_0 = e3)
% 177.22/27.90    (115)   ~ (all_52_7 = all_52_23)
% 177.22/27.90    (116)  op(e2, all_52_27) = all_52_26
% 177.22/27.90    (117)   ~ (all_52_17 = all_52_19)
% 177.22/27.90    (118)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.90    (119)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.90    (120)  op(e1, all_14_2) = all_14_1
% 177.22/27.90    (121)  all_58_9 = all_52_7
% 177.22/27.90    (122)  all_58_12 = all_52_25
% 177.22/27.90    (123)   ~ (all_10_0 = e1)
% 177.22/27.90    (124)  all_56_6 = all_52_13
% 177.22/27.90    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.90    (126)   ~ (all_52_9 = all_52_15)
% 177.22/27.90    (127)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.90    (128)   ~ (all_52_19 = all_14_2)
% 177.22/27.90    (129)  op(e2, e3) = all_52_9
% 177.22/27.90    (130)  all_56_13 = all_52_27
% 177.22/27.90  
% 177.22/27.90  Begin of proof
% 177.22/27.90  | 
% 177.22/27.90  | BETA: splitting (50) gives:
% 177.22/27.90  | 
% 177.22/27.90  | Case 1:
% 177.22/27.90  | | 
% 177.22/27.91  | |   (131)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.22/27.91  | | 
% 177.22/27.91  | | REF_CLOSE: (36), (40), (48), (70), (109), (131) are inconsistent by
% 177.22/27.91  | |            sub-proof #600.
% 177.22/27.91  | | 
% 177.22/27.91  | Case 2:
% 177.22/27.91  | | 
% 177.22/27.91  | |   (132)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.22/27.91  | | 
% 177.22/27.91  | | ALPHA: (132) implies:
% 177.22/27.91  | |   (133)  all_52_14 = e0
% 177.22/27.91  | |   (134)  all_52_12 = e1
% 177.22/27.91  | |   (135)  all_52_10 = e2
% 177.22/27.91  | |   (136)  all_52_8 = e3
% 177.22/27.91  | | 
% 177.22/27.91  | | COMBINE_EQS: (72), (135) imply:
% 177.22/27.91  | |   (137)  all_10_1 = e2
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (79), (137) imply:
% 177.22/27.91  | |   (138)  op(e2, all_10_2) = all_10_0
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (15), (136) imply:
% 177.22/27.91  | |   (139)  op(e3, all_52_9) = e3
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (6), (137) imply:
% 177.22/27.91  | |   (140)  op(e2, all_10_2) = e2
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (47), (134) imply:
% 177.22/27.91  | |   (141)  op(e1, all_52_13) = e1
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (94), (133) imply:
% 177.22/27.91  | |   (142)  op(e0, all_52_15) = e0
% 177.22/27.91  | | 
% 177.22/27.91  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.22/27.91  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.22/27.91  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.22/27.91  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (48),
% 177.22/27.91  | |            (49), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 177.22/27.91  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (71), (73),
% 177.22/27.91  | |            (74), (75), (76), (77), (78), (80), (81), (82), (83), (84), (85),
% 177.22/27.91  | |            (86), (87), (88), (89), (90), (91), (92), (93), (95), (96), (97),
% 177.22/27.91  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 177.22/27.91  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 177.22/27.91  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.22/27.91  | |            (125), (126), (127), (128), (129), (130), (138), (139), (140),
% 177.22/27.91  | |            (141), (142) are inconsistent by sub-proof #357.
% 177.22/27.91  | | 
% 177.22/27.91  | End of split
% 177.22/27.91  | 
% 177.22/27.91  End of proof
% 177.22/27.91  
% 177.22/27.91  Sub-proof #357 shows that the following formulas are inconsistent:
% 177.22/27.91  ----------------------------------------------------------------
% 177.22/27.91    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.91    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.91    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.91    (4)   ~ (all_52_27 = all_10_2)
% 177.22/27.91    (5)   ~ (all_52_17 = all_52_23)
% 177.22/27.91    (6)   ~ (all_52_13 = all_52_29)
% 177.22/27.91    (7)  op(e2, all_10_2) = all_10_0
% 177.22/27.91    (8)  all_56_3 = all_52_7
% 177.22/27.91    (9)  op(e3, e2) = all_52_3
% 177.22/27.91    (10)   ~ (all_52_9 = all_52_25)
% 177.22/27.91    (11)   ~ (all_52_19 = all_52_23)
% 177.22/27.91    (12)  all_56_11 = all_52_23
% 177.22/27.91    (13)  op(e1, e2) = all_52_19
% 177.22/27.91    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.91    (15)   ~ (all_52_3 = all_10_2)
% 177.22/27.91    (16)  all_58_5 = all_52_13
% 177.22/27.91    (17)   ~ (all_6_2 = e0)
% 177.22/27.91    (18)   ~ (all_52_25 = all_52_29)
% 177.22/27.91    (19)  op(e1, all_52_13) = e1
% 177.22/27.91    (20)  op(e0, all_52_15) = e0
% 177.22/27.91    (21)  all_56_15 = all_6_2
% 177.22/27.91    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.91    (23)  all_58_3 = all_10_2
% 177.22/27.91    (24)  all_56_9 = all_52_19
% 177.22/27.91    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.91    (26)  all_58_15 = all_6_2
% 177.22/27.91    (27)   ~ (all_52_9 = all_4_2)
% 177.22/27.91    (28)   ~ (all_52_5 = all_52_7)
% 177.22/27.91    (29)  all_58_10 = all_52_15
% 177.22/27.91    (30)   ~ (all_52_5 = all_4_2)
% 177.22/27.91    (31)  all_58_7 = all_52_19
% 177.22/27.91    (32)  all_56_4 = all_52_9
% 177.22/27.91    (33)   ~ (all_52_15 = all_6_2)
% 177.22/27.91    (34)   ~ (all_52_17 = all_52_25)
% 177.22/27.91    (35)  all_58_4 = all_52_5
% 177.22/27.91    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.91    (37)   ~ (e3 = e1)
% 177.22/27.91    (38)  all_34_1 = all_4_1
% 177.22/27.91    (39)   ~ (all_52_27 = all_52_29)
% 177.22/27.91    (40)   ~ (all_52_17 = all_14_2)
% 177.22/27.91    (41)  op(e3, all_4_2) = all_4_1
% 177.22/27.91    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.91    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.91    (44)   ~ (all_52_7 = all_4_2)
% 177.22/27.91    (45)  all_58_1 = all_52_3
% 177.22/27.91    (46)  all_58_0 = all_4_2
% 177.22/27.91    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.91    (48)  op(all_4_1, all_4_2) = e1
% 177.22/27.91    (49)  op(e1, all_52_29) = all_52_28
% 177.22/27.91    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.91    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.91    (52)   ~ (all_4_1 = e2)
% 177.22/27.91    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.91    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.91    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.91    (56)  all_58_14 = all_52_29
% 177.22/27.91    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.91    (58)   ~ (all_52_3 = all_52_5)
% 177.22/27.91    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.91    (60)  op(e2, e1) = all_52_13
% 177.22/27.91    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.91    (62)  all_58_8 = all_14_2
% 177.22/27.91    (63)  all_56_1 = all_52_3
% 177.22/27.91    (64)  op(e1, all_14_2) = e3
% 177.22/27.91    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.91    (66)   ~ (all_52_3 = all_52_27)
% 177.22/27.91    (67)   ~ (all_52_3 = all_4_2)
% 177.22/27.91    (68)  op(e0, e3) = all_52_25
% 177.22/27.91    (69)  op(e3, all_52_17) = all_52_16
% 177.22/27.91    (70)   ~ (all_52_13 = all_14_2)
% 177.22/27.91    (71)  op(e3, all_52_9) = e3
% 177.22/27.91    (72)   ~ (e3 = e0)
% 177.22/27.91    (73)   ~ (all_52_9 = all_52_13)
% 177.22/27.91    (74)  op(e0, all_52_23) = all_52_22
% 177.22/27.91    (75)   ~ (all_52_15 = all_52_23)
% 177.22/27.91    (76)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.91    (77)  op(e1, e0) = all_52_23
% 177.22/27.91    (78)  all_58_13 = all_52_27
% 177.22/27.91    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.91    (80)   ~ (all_52_9 = all_52_17)
% 177.22/27.91    (81)  all_58_6 = all_52_17
% 177.22/27.91    (82)   ~ (all_52_3 = all_52_7)
% 177.22/27.91    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.91    (84)  op(e2, all_52_19) = all_52_18
% 177.22/27.91    (85)   ~ (e1 = e0)
% 177.22/27.91    (86)  all_56_0 = all_4_2
% 177.22/27.91    (87)  all_58_11 = all_52_23
% 177.22/27.91    (88)   ~ (all_52_3 = all_52_19)
% 177.22/27.91    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.91    (90)   ~ (all_52_7 = all_52_15)
% 177.22/27.91    (91)   ~ (all_52_29 = all_14_2)
% 177.22/27.91    (92)   ~ (all_52_19 = all_10_2)
% 177.22/27.91    (93)   ~ (all_52_23 = all_6_2)
% 177.22/27.91    (94)   ~ (all_52_29 = all_6_2)
% 177.22/27.91    (95)  all_58_2 = all_52_9
% 177.22/27.91    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.91    (97)  op(e3, e1) = all_52_5
% 177.22/27.91    (98)  all_56_10 = all_14_2
% 177.22/27.91    (99)   ~ (all_52_25 = all_6_2)
% 177.22/27.91    (100)  op(e1, e3) = all_52_17
% 177.22/27.91    (101)   ~ (all_52_25 = all_4_2)
% 177.22/27.91    (102)  op(e3, e0) = all_52_7
% 177.22/27.91    (103)  op(e2, all_10_2) = e2
% 177.22/27.91    (104)  op(e3, e3) = all_4_2
% 177.22/27.91    (105)   ~ (all_52_17 = all_4_2)
% 177.22/27.91    (106)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.91             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.91    (107)   ~ (all_52_25 = all_52_27)
% 177.22/27.91    (108)  all_34_2 = all_4_2
% 177.22/27.91    (109)   ~ (all_52_27 = all_6_2)
% 177.22/27.91    (110)   ~ (all_52_7 = all_6_2)
% 177.22/27.91    (111)   ~ (all_10_0 = e3)
% 177.22/27.91    (112)   ~ (all_52_7 = all_52_23)
% 177.22/27.91    (113)  op(e2, all_52_27) = all_52_26
% 177.22/27.91    (114)   ~ (all_52_17 = all_52_19)
% 177.22/27.91    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.91    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.91    (117)  op(e1, all_14_2) = all_14_1
% 177.22/27.91    (118)  all_58_9 = all_52_7
% 177.22/27.91    (119)  all_58_12 = all_52_25
% 177.22/27.91    (120)   ~ (all_10_0 = e1)
% 177.22/27.91    (121)  all_56_6 = all_52_13
% 177.22/27.91    (122)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.91    (123)   ~ (all_52_9 = all_52_15)
% 177.22/27.91    (124)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.91    (125)   ~ (all_52_19 = all_14_2)
% 177.22/27.91    (126)  op(e2, e3) = all_52_9
% 177.22/27.91    (127)  all_56_13 = all_52_27
% 177.22/27.91  
% 177.22/27.91  Begin of proof
% 177.22/27.91  | 
% 177.22/27.91  | GROUND_INST: instantiating (106) with e2, all_10_0, all_10_2, e2, simplifying
% 177.22/27.91  |              with (7), (103) gives:
% 177.22/27.91  |   (128)  all_10_0 = e2
% 177.22/27.91  | 
% 177.22/27.91  | REDUCE: (111), (128) imply:
% 177.22/27.91  |   (129)   ~ (e3 = e2)
% 177.22/27.91  | 
% 177.22/27.91  | SIMP: (129) implies:
% 177.22/27.91  |   (130)   ~ (e3 = e2)
% 177.22/27.91  | 
% 177.22/27.91  | REDUCE: (120), (128) imply:
% 177.22/27.91  |   (131)   ~ (e2 = e1)
% 177.22/27.91  | 
% 177.22/27.91  | BETA: splitting (42) gives:
% 177.22/27.91  | 
% 177.22/27.91  | Case 1:
% 177.22/27.91  | | 
% 177.22/27.91  | |   (132)  all_56_15 = e3
% 177.22/27.91  | | 
% 177.22/27.91  | | COMBINE_EQS: (21), (132) imply:
% 177.22/27.91  | |   (133)  all_6_2 = e3
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (110), (133) imply:
% 177.22/27.91  | |   (134)   ~ (all_52_7 = e3)
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (33), (133) imply:
% 177.22/27.91  | |   (135)   ~ (all_52_15 = e3)
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (99), (133) imply:
% 177.22/27.91  | |   (136)   ~ (all_52_25 = e3)
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (94), (133) imply:
% 177.22/27.91  | |   (137)   ~ (all_52_29 = e3)
% 177.22/27.91  | | 
% 177.22/27.91  | | BETA: splitting (54) gives:
% 177.22/27.91  | | 
% 177.22/27.91  | | Case 1:
% 177.22/27.91  | | | 
% 177.22/27.91  | | |   (138)  all_58_1 = e3
% 177.22/27.91  | | | 
% 177.22/27.91  | | | COMBINE_EQS: (45), (138) imply:
% 177.22/27.91  | | |   (139)  all_52_3 = e3
% 177.22/27.91  | | | 
% 177.22/27.91  | | | REDUCE: (58), (139) imply:
% 177.22/27.91  | | |   (140)   ~ (all_52_5 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | SIMP: (140) implies:
% 177.22/27.91  | | |   (141)   ~ (all_52_5 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | REDUCE: (67), (139) imply:
% 177.22/27.91  | | |   (142)   ~ (all_4_2 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | SIMP: (142) implies:
% 177.22/27.91  | | |   (143)   ~ (all_4_2 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | REF_CLOSE: (16), (19), (27), (35), (36), (37), (40), (46), (56), (59),
% 177.22/27.91  | | |            (62), (64), (71), (81), (95), (100), (104), (106), (119),
% 177.22/27.91  | | |            (124), (136), (137), (141), (143) are inconsistent by sub-proof
% 177.22/27.91  | | |            #394.
% 177.22/27.91  | | | 
% 177.22/27.91  | | Case 2:
% 177.22/27.91  | | | 
% 177.22/27.91  | | |   (144)   ~ (all_58_1 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | REDUCE: (45), (144) imply:
% 177.22/27.91  | | |   (145)   ~ (all_52_3 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | BETA: splitting (122) gives:
% 177.22/27.91  | | | 
% 177.22/27.91  | | | Case 1:
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | |   (146)  all_58_0 = e3
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | | COMBINE_EQS: (46), (146) imply:
% 177.22/27.91  | | | |   (147)  all_4_2 = e3
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | | REF_CLOSE: (37), (41), (48), (104), (106), (147) are inconsistent by
% 177.22/27.91  | | | |            sub-proof #599.
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | Case 2:
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | |   (148)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | | REF_CLOSE: (2), (9), (15), (16), (23), (27), (29), (35), (43), (45),
% 177.22/27.91  | | | |            (71), (95), (103), (104), (106), (118), (126), (134), (135),
% 177.22/27.91  | | | |            (145), (148) are inconsistent by sub-proof #360.
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | End of split
% 177.22/27.91  | | | 
% 177.22/27.91  | | End of split
% 177.22/27.91  | | 
% 177.22/27.91  | Case 2:
% 177.22/27.91  | | 
% 177.22/27.91  | |   (149)   ~ (all_56_15 = e3)
% 177.22/27.91  | |   (150)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (21), (149) imply:
% 177.22/27.91  | |   (151)   ~ (all_6_2 = e3)
% 177.22/27.91  | | 
% 177.22/27.91  | | BETA: splitting (57) gives:
% 177.22/27.91  | | 
% 177.22/27.91  | | Case 1:
% 177.22/27.91  | | | 
% 177.22/27.91  | | |   (152)  all_56_13 = e3
% 177.22/27.91  | | | 
% 177.22/27.91  | | | COMBINE_EQS: (127), (152) imply:
% 177.22/27.91  | | |   (153)  all_52_27 = e3
% 177.22/27.91  | | | 
% 177.22/27.91  | | | SIMP: (153) implies:
% 177.22/27.91  | | |   (154)  all_52_27 = e3
% 177.22/27.91  | | | 
% 177.22/27.91  | | | REF_CLOSE: (2), (4), (9), (10), (13), (14), (16), (19), (20), (22), (23),
% 177.22/27.91  | | |            (25), (27), (29), (30), (32), (35), (37), (38), (39), (40),
% 177.22/27.91  | | |            (41), (43), (46), (48), (50), (55), (56), (58), (59), (62),
% 177.22/27.91  | | |            (63), (64), (66), (67), (68), (71), (73), (81), (83), (86),
% 177.22/27.91  | | |            (88), (95), (100), (101), (104), (105), (106), (107), (108),
% 177.22/27.91  | | |            (113), (119), (121), (123), (124), (126), (154) are
% 177.22/27.91  | | |            inconsistent by sub-proof #362.
% 177.22/27.91  | | | 
% 177.22/27.91  | | Case 2:
% 177.22/27.91  | | | 
% 177.22/27.91  | | |   (155)   ~ (all_56_13 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | REDUCE: (127), (155) imply:
% 177.22/27.91  | | |   (156)   ~ (all_52_27 = e3)
% 177.22/27.91  | | | 
% 177.22/27.91  | | | BETA: splitting (61) gives:
% 177.22/27.91  | | | 
% 177.22/27.91  | | | Case 1:
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | |   (157)  all_58_12 = e3
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 177.22/27.91  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.22/27.91  | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 177.22/27.91  | | | |            (35), (36), (38), (39), (40), (41), (43), (44), (45), (46),
% 177.22/27.91  | | | |            (47), (48), (50), (51), (52), (53), (54), (55), (56), (58),
% 177.22/27.91  | | | |            (60), (62), (63), (65), (67), (68), (69), (70), (71), (72),
% 177.22/27.91  | | | |            (73), (74), (76), (77), (78), (80), (81), (82), (83), (84),
% 177.22/27.91  | | | |            (86), (87), (88), (90), (91), (92), (93), (95), (96), (97),
% 177.22/27.91  | | | |            (98), (99), (100), (101), (102), (103), (105), (106), (107),
% 177.22/27.91  | | | |            (108), (109), (110), (112), (114), (115), (116), (117),
% 177.22/27.91  | | | |            (118), (119), (121), (123), (124), (125), (126), (130),
% 177.22/27.91  | | | |            (131), (150), (157) are inconsistent by sub-proof #359.
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | Case 2:
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | |   (158)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | | BETA: splitting (158) gives:
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | | Case 1:
% 177.22/27.91  | | | | | 
% 177.22/27.91  | | | | |   (159)  all_58_13 = e3
% 177.22/27.91  | | | | | 
% 177.22/27.91  | | | | | REF_CLOSE: (78), (156), (159) are inconsistent by sub-proof #1026.
% 177.22/27.91  | | | | | 
% 177.22/27.91  | | | | Case 2:
% 177.22/27.91  | | | | | 
% 177.22/27.91  | | | | |   (160)  all_58_14 = e3 | all_58_15 = e3
% 177.22/27.91  | | | | | 
% 177.22/27.91  | | | | | BETA: splitting (160) gives:
% 177.22/27.91  | | | | | 
% 177.22/27.91  | | | | | Case 1:
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | |   (161)  all_58_14 = e3
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | COMBINE_EQS: (56), (161) imply:
% 177.22/27.91  | | | | | |   (162)  all_52_29 = e3
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | SIMP: (162) implies:
% 177.22/27.91  | | | | | |   (163)  all_52_29 = e3
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (6), (163) imply:
% 177.22/27.91  | | | | | |   (164)   ~ (all_52_13 = e3)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (18), (163) imply:
% 177.22/27.91  | | | | | |   (165)   ~ (all_52_25 = e3)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (91), (163) imply:
% 177.22/27.91  | | | | | |   (166)   ~ (all_14_2 = e3)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | SIMP: (166) implies:
% 177.22/27.91  | | | | | |   (167)   ~ (all_14_2 = e3)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (94), (163) imply:
% 177.22/27.91  | | | | | |   (168)   ~ (all_6_2 = e3)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (49), (163) imply:
% 177.22/27.91  | | | | | |   (169)  op(e1, e3) = all_52_28
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | GROUND_INST: instantiating (106) with all_52_17, all_52_28, e3, e1,
% 177.22/27.91  | | | | | |              simplifying with (100), (169) gives:
% 177.22/27.91  | | | | | |   (170)  all_52_17 = all_52_28
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | COMBINE_EQS: (81), (170) imply:
% 177.22/27.91  | | | | | |   (171)  all_58_6 = all_52_28
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (114), (170) imply:
% 177.22/27.91  | | | | | |   (172)   ~ (all_52_19 = all_52_28)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | SIMP: (172) implies:
% 177.22/27.91  | | | | | |   (173)   ~ (all_52_19 = all_52_28)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (5), (170) imply:
% 177.22/27.91  | | | | | |   (174)   ~ (all_52_23 = all_52_28)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | SIMP: (174) implies:
% 177.22/27.91  | | | | | |   (175)   ~ (all_52_23 = all_52_28)
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | BETA: splitting (54) gives:
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | Case 1:
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | |   (176)  all_58_1 = e3
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | COMBINE_EQS: (45), (176) imply:
% 177.22/27.91  | | | | | | |   (177)  all_52_3 = e3
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REDUCE: (58), (177) imply:
% 177.22/27.91  | | | | | | |   (178)   ~ (all_52_5 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | SIMP: (178) implies:
% 177.22/27.91  | | | | | | |   (179)   ~ (all_52_5 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REDUCE: (82), (177) imply:
% 177.22/27.91  | | | | | | |   (180)   ~ (all_52_7 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | SIMP: (180) implies:
% 177.22/27.91  | | | | | | |   (181)   ~ (all_52_7 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REDUCE: (88), (177) imply:
% 177.22/27.91  | | | | | | |   (182)   ~ (all_52_19 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | SIMP: (182) implies:
% 177.22/27.91  | | | | | | |   (183)   ~ (all_52_19 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REDUCE: (15), (177) imply:
% 177.22/27.91  | | | | | | |   (184)   ~ (all_10_2 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | SIMP: (184) implies:
% 177.22/27.91  | | | | | | |   (185)   ~ (all_10_2 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REDUCE: (67), (177) imply:
% 177.22/27.91  | | | | | | |   (186)   ~ (all_4_2 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | SIMP: (186) implies:
% 177.22/27.91  | | | | | | |   (187)   ~ (all_4_2 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REF_CLOSE: (13), (16), (20), (23), (26), (27), (29), (31), (32),
% 177.22/27.91  | | | | | | |            (35), (36), (37), (41), (43), (46), (52), (59), (62),
% 177.22/27.91  | | | | | | |            (64), (68), (71), (73), (75), (79), (83), (85), (87),
% 177.22/27.91  | | | | | | |            (89), (90), (95), (97), (102), (104), (106), (115),
% 177.22/27.91  | | | | | | |            (118), (119), (123), (151), (161), (164), (167), (171),
% 177.22/27.91  | | | | | | |            (173), (175), (179), (181), (183), (185), (187) are
% 177.22/27.91  | | | | | | |            inconsistent by sub-proof #377.
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | Case 2:
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | |   (188)   ~ (all_58_1 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REDUCE: (45), (188) imply:
% 177.22/27.91  | | | | | | |   (189)   ~ (all_52_3 = e3)
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | | REF_CLOSE: (9), (15), (23), (27), (31), (37), (41), (43), (45),
% 177.22/27.91  | | | | | | |            (46), (48), (54), (59), (71), (78), (95), (103), (104),
% 177.22/27.91  | | | | | | |            (106), (119), (122), (126), (156), (165), (171), (173),
% 177.22/27.91  | | | | | | |            (189) are inconsistent by sub-proof #358.
% 177.22/27.91  | | | | | | | 
% 177.22/27.91  | | | | | | End of split
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | Case 2:
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | |   (190)  all_58_15 = e3
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | COMBINE_EQS: (26), (190) imply:
% 177.22/27.91  | | | | | |   (191)  all_6_2 = e3
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | REDUCE: (151), (191) imply:
% 177.22/27.91  | | | | | |   (192)  $false
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | | CLOSE: (192) is inconsistent.
% 177.22/27.91  | | | | | | 
% 177.22/27.91  | | | | | End of split
% 177.22/27.91  | | | | | 
% 177.22/27.91  | | | | End of split
% 177.22/27.91  | | | | 
% 177.22/27.91  | | | End of split
% 177.22/27.91  | | | 
% 177.22/27.91  | | End of split
% 177.22/27.91  | | 
% 177.22/27.91  | End of split
% 177.22/27.91  | 
% 177.22/27.91  End of proof
% 177.22/27.91  
% 177.22/27.91  Sub-proof #358 shows that the following formulas are inconsistent:
% 177.22/27.91  ----------------------------------------------------------------
% 177.22/27.91    (1)   ~ (all_52_25 = e3)
% 177.22/27.91    (2)  all_58_6 = all_52_28
% 177.22/27.91    (3)  op(e3, e2) = all_52_3
% 177.22/27.91    (4)   ~ (all_52_27 = e3)
% 177.22/27.91    (5)   ~ (all_52_3 = all_10_2)
% 177.22/27.91    (6)  all_58_3 = all_10_2
% 177.22/27.91    (7)   ~ (all_52_9 = all_4_2)
% 177.22/27.91    (8)  all_58_7 = all_52_19
% 177.22/27.91    (9)   ~ (e3 = e1)
% 177.22/27.91    (10)  op(e3, all_4_2) = all_4_1
% 177.22/27.91    (11)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.91    (12)  all_58_1 = all_52_3
% 177.22/27.91    (13)  all_58_0 = all_4_2
% 177.22/27.91    (14)  op(all_4_1, all_4_2) = e1
% 177.22/27.91    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.91    (16)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.91    (17)  op(e3, all_52_9) = e3
% 177.22/27.91    (18)   ~ (all_52_19 = all_52_28)
% 177.22/27.91    (19)  all_58_13 = all_52_27
% 177.22/27.91    (20)   ~ (all_52_3 = e3)
% 177.22/27.91    (21)  all_58_2 = all_52_9
% 177.22/27.91    (22)  op(e2, all_10_2) = e2
% 177.22/27.91    (23)  op(e3, e3) = all_4_2
% 177.22/27.91    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.91    (25)  all_58_12 = all_52_25
% 177.22/27.91    (26)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.91    (27)  op(e2, e3) = all_52_9
% 177.22/27.91  
% 177.22/27.91  Begin of proof
% 177.22/27.91  | 
% 177.22/27.91  | BETA: splitting (26) gives:
% 177.22/27.91  | 
% 177.22/27.91  | Case 1:
% 177.22/27.91  | | 
% 177.22/27.91  | |   (28)  all_58_0 = e3
% 177.22/27.91  | | 
% 177.22/27.91  | | COMBINE_EQS: (13), (28) imply:
% 177.22/27.91  | |   (29)  all_4_2 = e3
% 177.22/27.91  | | 
% 177.22/27.91  | | REF_CLOSE: (9), (10), (14), (23), (24), (29) are inconsistent by sub-proof
% 177.22/27.91  | |            #599.
% 177.22/27.91  | | 
% 177.22/27.91  | Case 2:
% 177.22/27.91  | | 
% 177.22/27.91  | |   (30)   ~ (all_58_0 = e3)
% 177.22/27.91  | | 
% 177.22/27.91  | | REDUCE: (13), (30) imply:
% 177.22/27.91  | |   (31)   ~ (all_4_2 = e3)
% 177.22/27.91  | | 
% 177.22/27.91  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (15),
% 177.22/27.91  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 177.22/27.91  | |            (31) are inconsistent by sub-proof #960.
% 177.22/27.91  | | 
% 177.22/27.91  | End of split
% 177.22/27.91  | 
% 177.22/27.91  End of proof
% 177.22/27.91  
% 177.22/27.91  Sub-proof #359 shows that the following formulas are inconsistent:
% 177.22/27.91  ----------------------------------------------------------------
% 177.22/27.91    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.91    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.91    (3)   ~ (all_52_27 = all_10_2)
% 177.22/27.91    (4)   ~ (all_52_17 = all_52_23)
% 177.22/27.91    (5)   ~ (all_52_13 = all_52_29)
% 177.22/27.91    (6)  all_56_3 = all_52_7
% 177.22/27.91    (7)  op(e3, e2) = all_52_3
% 177.22/27.91    (8)   ~ (all_52_9 = all_52_25)
% 177.22/27.91    (9)   ~ (all_52_19 = all_52_23)
% 177.22/27.91    (10)  all_56_11 = all_52_23
% 177.22/27.91    (11)  op(e1, e2) = all_52_19
% 177.22/27.91    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.91    (13)   ~ (all_52_3 = all_10_2)
% 177.22/27.91    (14)  all_58_5 = all_52_13
% 177.22/27.91    (15)   ~ (all_6_2 = e0)
% 177.22/27.91    (16)   ~ (all_52_25 = all_52_29)
% 177.22/27.91    (17)  op(e1, all_52_13) = e1
% 177.22/27.91    (18)  op(e0, all_52_15) = e0
% 177.22/27.91    (19)  all_56_15 = all_6_2
% 177.22/27.91    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.91    (21)  all_58_3 = all_10_2
% 177.22/27.91    (22)  all_56_9 = all_52_19
% 177.22/27.91    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.91    (24)  all_58_15 = all_6_2
% 177.22/27.91    (25)   ~ (all_52_9 = all_4_2)
% 177.22/27.91    (26)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.91    (27)   ~ (all_52_5 = all_52_7)
% 177.22/27.91    (28)  all_58_10 = all_52_15
% 177.22/27.91    (29)   ~ (all_52_5 = all_4_2)
% 177.22/27.91    (30)  all_58_7 = all_52_19
% 177.22/27.91    (31)  all_56_4 = all_52_9
% 177.22/27.91    (32)   ~ (all_52_17 = all_52_25)
% 177.22/27.91    (33)  all_58_4 = all_52_5
% 177.22/27.91    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.91    (35)  all_34_1 = all_4_1
% 177.22/27.91    (36)   ~ (all_52_27 = all_52_29)
% 177.22/27.91    (37)   ~ (all_52_17 = all_14_2)
% 177.22/27.91    (38)  op(e3, all_4_2) = all_4_1
% 177.22/27.91    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.91    (40)   ~ (all_52_7 = all_4_2)
% 177.22/27.91    (41)  all_58_1 = all_52_3
% 177.22/27.91    (42)  all_58_0 = all_4_2
% 177.22/27.91    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.91    (44)  op(all_4_1, all_4_2) = e1
% 177.22/27.91    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.91    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.91    (47)   ~ (all_4_1 = e2)
% 177.22/27.91    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.91    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.91    (50)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.91    (51)  all_58_14 = all_52_29
% 177.22/27.91    (52)   ~ (all_52_3 = all_52_5)
% 177.22/27.91    (53)  op(e2, e1) = all_52_13
% 177.22/27.91    (54)  all_58_8 = all_14_2
% 177.22/27.91    (55)  all_56_1 = all_52_3
% 177.22/27.91    (56)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.91    (57)   ~ (all_52_3 = all_4_2)
% 177.22/27.91    (58)  op(e0, e3) = all_52_25
% 177.22/27.91    (59)  op(e3, all_52_17) = all_52_16
% 177.22/27.91    (60)   ~ (all_52_13 = all_14_2)
% 177.22/27.91    (61)  op(e3, all_52_9) = e3
% 177.22/27.91    (62)   ~ (e3 = e0)
% 177.22/27.91    (63)   ~ (all_52_9 = all_52_13)
% 177.22/27.91    (64)  op(e0, all_52_23) = all_52_22
% 177.22/27.91    (65)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.91    (66)  op(e1, e0) = all_52_23
% 177.22/27.91    (67)  all_58_13 = all_52_27
% 177.22/27.91    (68)  all_58_12 = e3
% 177.22/27.91    (69)   ~ (all_52_9 = all_52_17)
% 177.22/27.91    (70)  all_58_6 = all_52_17
% 177.22/27.91    (71)   ~ (all_52_3 = all_52_7)
% 177.22/27.91    (72)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.91    (73)  op(e2, all_52_19) = all_52_18
% 177.22/27.91    (74)  all_56_0 = all_4_2
% 177.22/27.91    (75)  all_58_11 = all_52_23
% 177.22/27.91    (76)   ~ (all_52_3 = all_52_19)
% 177.22/27.91    (77)   ~ (all_52_7 = all_52_15)
% 177.22/27.91    (78)   ~ (all_52_29 = all_14_2)
% 177.22/27.91    (79)   ~ (all_52_19 = all_10_2)
% 177.22/27.91    (80)   ~ (all_52_23 = all_6_2)
% 177.22/27.91    (81)  all_58_2 = all_52_9
% 177.22/27.91    (82)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.91    (83)  op(e3, e1) = all_52_5
% 177.22/27.91    (84)   ~ (e2 = e1)
% 177.22/27.91    (85)  all_56_10 = all_14_2
% 177.22/27.91    (86)   ~ (all_52_25 = all_6_2)
% 177.22/27.91    (87)  op(e1, e3) = all_52_17
% 177.22/27.91    (88)   ~ (all_52_25 = all_4_2)
% 177.22/27.91    (89)  op(e3, e0) = all_52_7
% 177.22/27.91    (90)  op(e2, all_10_2) = e2
% 177.22/27.91    (91)   ~ (all_52_17 = all_4_2)
% 177.22/27.92    (92)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.92    (93)   ~ (all_52_25 = all_52_27)
% 177.22/27.92    (94)  all_34_2 = all_4_2
% 177.22/27.92    (95)   ~ (all_52_27 = all_6_2)
% 177.22/27.92    (96)   ~ (all_52_7 = all_6_2)
% 177.22/27.92    (97)   ~ (all_52_7 = all_52_23)
% 177.22/27.92    (98)   ~ (all_52_17 = all_52_19)
% 177.22/27.92    (99)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.92    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.92    (101)  op(e1, all_14_2) = all_14_1
% 177.22/27.92    (102)  all_58_9 = all_52_7
% 177.22/27.92    (103)  all_58_12 = all_52_25
% 177.22/27.92    (104)  all_56_6 = all_52_13
% 177.22/27.92    (105)   ~ (all_52_9 = all_52_15)
% 177.22/27.92    (106)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.92    (107)   ~ (e3 = e2)
% 177.22/27.92    (108)   ~ (all_52_19 = all_14_2)
% 177.22/27.92    (109)  op(e2, e3) = all_52_9
% 177.22/27.92  
% 177.22/27.92  Begin of proof
% 177.22/27.92  | 
% 177.22/27.92  | COMBINE_EQS: (68), (103) imply:
% 177.22/27.92  |   (110)  all_52_25 = e3
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (110) implies:
% 177.22/27.92  |   (111)  all_52_25 = e3
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (8), (111) imply:
% 177.22/27.92  |   (112)   ~ (all_52_9 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (32), (111) imply:
% 177.22/27.92  |   (113)   ~ (all_52_17 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (93), (111) imply:
% 177.22/27.92  |   (114)   ~ (all_52_27 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (114) implies:
% 177.22/27.92  |   (115)   ~ (all_52_27 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (16), (111) imply:
% 177.22/27.92  |   (116)   ~ (all_52_29 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (116) implies:
% 177.22/27.92  |   (117)   ~ (all_52_29 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (86), (111) imply:
% 177.22/27.92  |   (118)   ~ (all_6_2 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (118) implies:
% 177.22/27.92  |   (119)   ~ (all_6_2 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (88), (111) imply:
% 177.22/27.92  |   (120)   ~ (all_4_2 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (120) implies:
% 177.22/27.92  |   (121)   ~ (all_4_2 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (58), (111) imply:
% 177.22/27.92  |   (122)  op(e0, e3) = e3
% 177.22/27.92  | 
% 177.22/27.92  | BETA: splitting (23) gives:
% 177.22/27.92  | 
% 177.22/27.92  | Case 1:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (123)  all_56_0 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | COMBINE_EQS: (74), (123) imply:
% 177.22/27.92  | |   (124)  all_4_2 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | REDUCE: (121), (124) imply:
% 177.22/27.92  | |   (125)  $false
% 177.22/27.92  | | 
% 177.22/27.92  | | CLOSE: (125) is inconsistent.
% 177.22/27.92  | | 
% 177.22/27.92  | Case 2:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (126)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.92  | | 
% 177.22/27.92  | | BETA: splitting (50) gives:
% 177.22/27.92  | | 
% 177.22/27.92  | | Case 1:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (127)  all_56_6 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | COMBINE_EQS: (104), (127) imply:
% 177.22/27.92  | | |   (128)  all_52_13 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | SIMP: (128) implies:
% 177.22/27.92  | | |   (129)  all_52_13 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (17), (129) imply:
% 177.22/27.92  | | |   (130)  op(e1, e3) = e1
% 177.22/27.92  | | | 
% 177.22/27.92  | | | GROUND_INST: instantiating (92) with all_52_17, e1, e3, e1, simplifying
% 177.22/27.92  | | |              with (87), (130) gives:
% 177.22/27.92  | | |   (131)  all_52_17 = e1
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (91), (131) imply:
% 177.22/27.92  | | |   (132)   ~ (all_4_2 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | SIMP: (132) implies:
% 177.22/27.92  | | |   (133)   ~ (all_4_2 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (113), (131) imply:
% 177.22/27.92  | | |   (134)   ~ (e3 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | SIMP: (134) implies:
% 177.22/27.92  | | |   (135)   ~ (e3 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REF_CLOSE: (6), (7), (11), (12), (20), (35), (38), (40), (42), (44), (45),
% 177.22/27.92  | | |            (47), (55), (57), (66), (74), (76), (89), (92), (94), (97),
% 177.22/27.92  | | |            (100), (126), (133), (135) are inconsistent by sub-proof #587.
% 177.22/27.92  | | | 
% 177.22/27.92  | | Case 2:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (136)   ~ (all_56_6 = e3)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (104), (136) imply:
% 177.22/27.92  | | |   (137)   ~ (all_52_13 = e3)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 177.22/27.92  | | |            (15), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 177.22/27.92  | | |            (27), (28), (29), (30), (31), (33), (34), (36), (37), (39),
% 177.22/27.92  | | |            (40), (41), (42), (43), (46), (48), (49), (50), (51), (52),
% 177.22/27.92  | | |            (53), (54), (56), (59), (60), (61), (62), (63), (64), (65),
% 177.22/27.92  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 177.22/27.92  | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (87),
% 177.22/27.92  | | |            (89), (90), (92), (95), (96), (97), (98), (99), (100), (101),
% 177.22/27.92  | | |            (102), (104), (105), (106), (107), (108), (109), (112), (115),
% 177.22/27.92  | | |            (117), (119), (122), (126), (137) are inconsistent by sub-proof
% 177.22/27.92  | | |            #382.
% 177.22/27.92  | | | 
% 177.22/27.92  | | End of split
% 177.22/27.92  | | 
% 177.22/27.92  | End of split
% 177.22/27.92  | 
% 177.22/27.92  End of proof
% 177.22/27.92  
% 177.22/27.92  Sub-proof #360 shows that the following formulas are inconsistent:
% 177.22/27.92  ----------------------------------------------------------------
% 177.22/27.92    (1)   ~ (all_52_5 = all_52_13)
% 177.22/27.92    (2)  op(e3, e2) = all_52_3
% 177.22/27.92    (3)   ~ (all_52_3 = all_10_2)
% 177.22/27.92    (4)  all_58_5 = all_52_13
% 177.22/27.92    (5)  all_58_3 = all_10_2
% 177.22/27.92    (6)   ~ (all_52_9 = all_4_2)
% 177.22/27.92    (7)  all_58_10 = all_52_15
% 177.22/27.92    (8)  all_58_4 = all_52_5
% 177.22/27.92    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.92    (10)  all_58_1 = all_52_3
% 177.22/27.92    (11)  op(e3, all_52_9) = e3
% 177.22/27.92    (12)   ~ (all_52_15 = e3)
% 177.22/27.92    (13)   ~ (all_52_3 = e3)
% 177.22/27.92    (14)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.92    (15)  all_58_2 = all_52_9
% 177.22/27.92    (16)  op(e2, all_10_2) = e2
% 177.22/27.92    (17)  op(e3, e3) = all_4_2
% 177.22/27.92    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.92    (19)   ~ (all_52_7 = e3)
% 177.22/27.92    (20)  all_58_9 = all_52_7
% 177.22/27.92    (21)  op(e2, e3) = all_52_9
% 177.22/27.92  
% 177.22/27.92  Begin of proof
% 177.22/27.92  | 
% 177.22/27.92  | BETA: splitting (14) gives:
% 177.22/27.92  | 
% 177.22/27.92  | Case 1:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (22)  all_58_1 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | COMBINE_EQS: (10), (22) imply:
% 177.22/27.92  | |   (23)  all_52_3 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | REDUCE: (13), (23) imply:
% 177.22/27.92  | |   (24)  $false
% 177.22/27.92  | | 
% 177.22/27.92  | | CLOSE: (24) is inconsistent.
% 177.22/27.92  | | 
% 177.22/27.92  | Case 2:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (25)  all_58_4 = e3 | all_58_9 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | BETA: splitting (25) gives:
% 177.22/27.92  | | 
% 177.22/27.92  | | Case 1:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (26)  all_58_4 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (15),
% 177.22/27.92  | | |            (16), (17), (18), (21), (26) are inconsistent by sub-proof
% 177.22/27.92  | | |            #399.
% 177.22/27.92  | | | 
% 177.22/27.92  | | Case 2:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (27)  all_58_9 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REF_CLOSE: (19), (20), (27) are inconsistent by sub-proof #972.
% 177.22/27.92  | | | 
% 177.22/27.92  | | End of split
% 177.22/27.92  | | 
% 177.22/27.92  | End of split
% 177.22/27.92  | 
% 177.22/27.92  End of proof
% 177.22/27.92  
% 177.22/27.92  Sub-proof #361 shows that the following formulas are inconsistent:
% 177.22/27.92  ----------------------------------------------------------------
% 177.22/27.92    (1)  all_56_3 = all_52_7
% 177.22/27.92    (2)  op(e3, e2) = all_52_3
% 177.22/27.92    (3)  op(e1, e2) = all_52_19
% 177.22/27.92    (4)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.92    (5)   ~ (all_52_17 = e3)
% 177.22/27.92    (6)  all_58_5 = all_52_13
% 177.22/27.92    (7)  op(e1, all_52_13) = e1
% 177.22/27.92    (8)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.92    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.92    (10)  all_58_4 = all_52_5
% 177.22/27.92    (11)  all_34_1 = all_4_1
% 177.22/27.92    (12)   ~ (all_52_17 = all_14_2)
% 177.22/27.92    (13)  op(e3, all_4_2) = all_4_1
% 177.22/27.92    (14)   ~ (all_52_7 = all_4_2)
% 177.22/27.92    (15)  all_58_0 = all_4_2
% 177.22/27.92    (16)  op(all_4_1, all_4_2) = e1
% 177.22/27.92    (17)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.92    (18)   ~ (all_4_1 = e2)
% 177.22/27.92    (19)  all_58_14 = all_52_29
% 177.22/27.92    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.92    (21)  all_58_8 = all_14_2
% 177.22/27.92    (22)  all_56_1 = all_52_3
% 177.22/27.92    (23)  op(e1, all_14_2) = e3
% 177.22/27.92    (24)   ~ (all_52_3 = all_4_2)
% 177.22/27.92    (25)   ~ (all_52_29 = e3)
% 177.22/27.92    (26)   ~ (all_52_5 = e3)
% 177.22/27.92    (27)  op(e1, e0) = all_52_23
% 177.22/27.92    (28)  all_56_0 = all_4_2
% 177.22/27.92    (29)   ~ (all_52_3 = all_52_19)
% 177.22/27.92    (30)  op(e1, e3) = all_52_17
% 177.22/27.92    (31)  op(e3, e0) = all_52_7
% 177.22/27.92    (32)  op(e3, e3) = all_4_2
% 177.22/27.92    (33)   ~ (all_52_17 = all_4_2)
% 177.22/27.92    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.92    (35)  all_34_2 = all_4_2
% 177.22/27.92    (36)   ~ (all_52_7 = all_52_23)
% 177.22/27.92    (37)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.92    (38)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.92  
% 177.22/27.92  Begin of proof
% 177.22/27.92  | 
% 177.22/27.92  | BETA: splitting (38) gives:
% 177.22/27.92  | 
% 177.22/27.92  | Case 1:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (39)  all_58_4 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | REF_CLOSE: (10), (26), (39) are inconsistent by sub-proof #1025.
% 177.22/27.92  | | 
% 177.22/27.92  | Case 2:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (40)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | BETA: splitting (40) gives:
% 177.22/27.92  | | 
% 177.22/27.92  | | Case 1:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (41)  all_58_5 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | COMBINE_EQS: (6), (41) imply:
% 177.22/27.92  | | |   (42)  all_52_13 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | SIMP: (42) implies:
% 177.22/27.92  | | |   (43)  all_52_13 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (7), (43) imply:
% 177.22/27.92  | | |   (44)  op(e1, e3) = e1
% 177.22/27.92  | | | 
% 177.22/27.92  | | | GROUND_INST: instantiating (34) with all_52_17, e1, e3, e1, simplifying
% 177.22/27.92  | | |              with (30), (44) gives:
% 177.22/27.92  | | |   (45)  all_52_17 = e1
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (33), (45) imply:
% 177.22/27.92  | | |   (46)   ~ (all_4_2 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | SIMP: (46) implies:
% 177.22/27.92  | | |   (47)   ~ (all_4_2 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (5), (45) imply:
% 177.22/27.92  | | |   (48)   ~ (e3 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | SIMP: (48) implies:
% 177.22/27.92  | | |   (49)   ~ (e3 = e1)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (11), (13), (14), (15), (16),
% 177.22/27.92  | | |            (17), (18), (20), (22), (24), (27), (28), (29), (31), (32),
% 177.22/27.92  | | |            (34), (35), (36), (37), (47), (49) are inconsistent by
% 177.22/27.92  | | |            sub-proof #585.
% 177.22/27.92  | | | 
% 177.22/27.92  | | Case 2:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (50)  all_58_8 = e3 | all_58_14 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REF_CLOSE: (12), (19), (21), (23), (25), (30), (34), (50) are inconsistent
% 177.22/27.92  | | |            by sub-proof #397.
% 177.22/27.92  | | | 
% 177.22/27.92  | | End of split
% 177.22/27.92  | | 
% 177.22/27.92  | End of split
% 177.22/27.92  | 
% 177.22/27.92  End of proof
% 177.22/27.92  
% 177.22/27.92  Sub-proof #362 shows that the following formulas are inconsistent:
% 177.22/27.92  ----------------------------------------------------------------
% 177.22/27.92    (1)   ~ (all_52_5 = all_52_13)
% 177.22/27.92    (2)   ~ (all_52_27 = all_10_2)
% 177.22/27.92    (3)  op(e3, e2) = all_52_3
% 177.22/27.92    (4)   ~ (all_52_9 = all_52_25)
% 177.22/27.92    (5)  op(e1, e2) = all_52_19
% 177.22/27.92    (6)  all_52_27 = e3
% 177.22/27.92    (7)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.22/27.92    (8)  all_58_5 = all_52_13
% 177.22/27.92    (9)  op(e1, all_52_13) = e1
% 177.22/27.92    (10)  op(e0, all_52_15) = e0
% 177.22/27.92    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.92    (12)  all_58_3 = all_10_2
% 177.22/27.92    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.92    (14)   ~ (all_52_9 = all_4_2)
% 177.22/27.92    (15)  all_58_10 = all_52_15
% 177.22/27.92    (16)   ~ (all_52_5 = all_4_2)
% 177.22/27.92    (17)  all_56_4 = all_52_9
% 177.22/27.92    (18)  all_58_4 = all_52_5
% 177.22/27.92    (19)   ~ (e3 = e1)
% 177.22/27.92    (20)  all_34_1 = all_4_1
% 177.22/27.92    (21)   ~ (all_52_27 = all_52_29)
% 177.22/27.92    (22)   ~ (all_52_17 = all_14_2)
% 177.22/27.92    (23)  op(e3, all_4_2) = all_4_1
% 177.22/27.92    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.92    (25)  all_58_0 = all_4_2
% 177.22/27.92    (26)  op(all_4_1, all_4_2) = e1
% 177.22/27.92    (27)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.92    (28)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.92    (29)  all_58_14 = all_52_29
% 177.22/27.92    (30)   ~ (all_52_3 = all_52_5)
% 177.22/27.92    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.92    (32)  all_58_8 = all_14_2
% 177.22/27.92    (33)  all_56_1 = all_52_3
% 177.22/27.92    (34)  op(e1, all_14_2) = e3
% 177.22/27.92    (35)   ~ (all_52_3 = all_52_27)
% 177.22/27.92    (36)   ~ (all_52_3 = all_4_2)
% 177.22/27.92    (37)  op(e0, e3) = all_52_25
% 177.22/27.92    (38)  op(e3, all_52_9) = e3
% 177.22/27.92    (39)   ~ (all_52_9 = all_52_13)
% 177.22/27.92    (40)  all_58_6 = all_52_17
% 177.22/27.92    (41)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.92    (42)  all_56_0 = all_4_2
% 177.22/27.92    (43)   ~ (all_52_3 = all_52_19)
% 177.22/27.92    (44)  all_58_2 = all_52_9
% 177.22/27.92    (45)  op(e1, e3) = all_52_17
% 177.22/27.92    (46)   ~ (all_52_25 = all_4_2)
% 177.22/27.92    (47)  op(e3, e3) = all_4_2
% 177.22/27.92    (48)   ~ (all_52_17 = all_4_2)
% 177.22/27.92    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.92    (50)   ~ (all_52_25 = all_52_27)
% 177.22/27.92    (51)  all_34_2 = all_4_2
% 177.22/27.92    (52)  op(e2, all_52_27) = all_52_26
% 177.22/27.92    (53)  all_58_12 = all_52_25
% 177.22/27.92    (54)  all_56_6 = all_52_13
% 177.22/27.92    (55)   ~ (all_52_9 = all_52_15)
% 177.22/27.92    (56)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.92    (57)  op(e2, e3) = all_52_9
% 177.22/27.92  
% 177.22/27.92  Begin of proof
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (6), (35) imply:
% 177.22/27.92  |   (58)   ~ (all_52_3 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (6), (50) imply:
% 177.22/27.92  |   (59)   ~ (all_52_25 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (6), (21) imply:
% 177.22/27.92  |   (60)   ~ (all_52_29 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (60) implies:
% 177.22/27.92  |   (61)   ~ (all_52_29 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (2), (6) imply:
% 177.22/27.92  |   (62)   ~ (all_10_2 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (62) implies:
% 177.22/27.92  |   (63)   ~ (all_10_2 = e3)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (6), (52) imply:
% 177.22/27.92  |   (64)  op(e2, e3) = all_52_26
% 177.22/27.92  | 
% 177.22/27.92  | GROUND_INST: instantiating (49) with all_52_9, all_52_26, e3, e2, simplifying
% 177.22/27.92  |              with (57), (64) gives:
% 177.22/27.92  |   (65)  all_52_9 = all_52_26
% 177.22/27.92  | 
% 177.22/27.92  | COMBINE_EQS: (17), (65) imply:
% 177.22/27.92  |   (66)  all_56_4 = all_52_26
% 177.22/27.92  | 
% 177.22/27.92  | COMBINE_EQS: (44), (65) imply:
% 177.22/27.92  |   (67)  all_58_2 = all_52_26
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (39), (65) imply:
% 177.22/27.92  |   (68)   ~ (all_52_13 = all_52_26)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (68) implies:
% 177.22/27.92  |   (69)   ~ (all_52_13 = all_52_26)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (55), (65) imply:
% 177.22/27.92  |   (70)   ~ (all_52_15 = all_52_26)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (70) implies:
% 177.22/27.92  |   (71)   ~ (all_52_15 = all_52_26)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (4), (65) imply:
% 177.22/27.92  |   (72)   ~ (all_52_25 = all_52_26)
% 177.22/27.92  | 
% 177.22/27.92  | SIMP: (72) implies:
% 177.22/27.92  |   (73)   ~ (all_52_25 = all_52_26)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (14), (65) imply:
% 177.22/27.92  |   (74)   ~ (all_52_26 = all_4_2)
% 177.22/27.92  | 
% 177.22/27.92  | REDUCE: (38), (65) imply:
% 177.22/27.92  |   (75)  op(e3, all_52_26) = e3
% 177.22/27.92  | 
% 177.22/27.92  | BETA: splitting (27) gives:
% 177.22/27.92  | 
% 177.22/27.92  | Case 1:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (76)  all_56_1 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | COMBINE_EQS: (33), (76) imply:
% 177.22/27.92  | |   (77)  all_52_3 = e3
% 177.22/27.92  | | 
% 177.22/27.92  | | REDUCE: (58), (77) imply:
% 177.22/27.92  | |   (78)  $false
% 177.22/27.92  | | 
% 177.22/27.92  | | CLOSE: (78) is inconsistent.
% 177.22/27.92  | | 
% 177.22/27.92  | Case 2:
% 177.22/27.92  | | 
% 177.22/27.92  | |   (79)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.22/27.92  | | 
% 177.22/27.92  | | BETA: splitting (28) gives:
% 177.22/27.92  | | 
% 177.22/27.92  | | Case 1:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (80)  all_56_6 = e3
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REF_CLOSE: (9), (19), (23), (25), (26), (31), (40), (45), (47), (48),
% 177.22/27.92  | | |            (49), (53), (54), (59), (67), (69), (80) are inconsistent by
% 177.22/27.92  | | |            sub-proof #598.
% 177.22/27.92  | | | 
% 177.22/27.92  | | Case 2:
% 177.22/27.92  | | | 
% 177.22/27.92  | | |   (81)   ~ (all_56_6 = e3)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | REDUCE: (54), (81) imply:
% 177.22/27.92  | | |   (82)   ~ (all_52_13 = e3)
% 177.22/27.92  | | | 
% 177.22/27.92  | | | BETA: splitting (56) gives:
% 177.22/27.92  | | | 
% 177.22/27.92  | | | Case 1:
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | |   (83)  all_58_4 = e3
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | | COMBINE_EQS: (18), (83) imply:
% 177.22/27.92  | | | |   (84)  all_52_5 = e3
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | | SIMP: (84) implies:
% 177.22/27.92  | | | |   (85)  all_52_5 = e3
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | | REDUCE: (1), (85) imply:
% 177.22/27.92  | | | |   (86)   ~ (all_52_13 = e3)
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | | REDUCE: (16), (85) imply:
% 177.22/27.92  | | | |   (87)   ~ (all_4_2 = e3)
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | | SIMP: (87) implies:
% 177.22/27.92  | | | |   (88)   ~ (all_4_2 = e3)
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | | REF_CLOSE: (3), (5), (7), (8), (10), (11), (12), (13), (15), (20), (23),
% 177.22/27.92  | | | |            (24), (25), (26), (33), (36), (37), (41), (42), (43), (46),
% 177.22/27.92  | | | |            (47), (49), (51), (58), (63), (66), (67), (71), (73), (74),
% 177.22/27.92  | | | |            (75), (79), (82), (88) are inconsistent by sub-proof #594.
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | Case 2:
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | |   (89)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | | REF_CLOSE: (8), (22), (29), (32), (34), (45), (49), (61), (82), (89) are
% 177.22/27.92  | | | |            inconsistent by sub-proof #420.
% 177.22/27.92  | | | | 
% 177.22/27.92  | | | End of split
% 177.22/27.92  | | | 
% 177.22/27.92  | | End of split
% 177.22/27.92  | | 
% 177.22/27.92  | End of split
% 177.22/27.92  | 
% 177.22/27.92  End of proof
% 177.22/27.92  
% 177.22/27.92  Sub-proof #363 shows that the following formulas are inconsistent:
% 177.22/27.92  ----------------------------------------------------------------
% 177.22/27.92    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.92    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.92    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.92    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.92    (5)   ~ (all_52_27 = all_10_2)
% 177.22/27.92    (6)   ~ (all_52_17 = all_52_23)
% 177.22/27.92    (7)  all_40_2 = all_4_2
% 177.22/27.92    (8)   ~ (all_52_13 = all_52_29)
% 177.22/27.92    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.92    (10)  all_56_3 = all_52_7
% 177.22/27.92    (11)  op(e3, e2) = all_52_3
% 177.22/27.92    (12)   ~ (all_52_9 = all_52_25)
% 177.22/27.92    (13)   ~ (all_52_19 = all_52_23)
% 177.22/27.92    (14)  all_56_11 = all_52_23
% 177.22/27.92    (15)  op(e1, e2) = all_52_19
% 177.22/27.92    (16)   ~ (all_52_3 = all_10_2)
% 177.22/27.92    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.92    (18)  all_58_5 = all_52_13
% 177.22/27.92    (19)   ~ (all_6_2 = e0)
% 177.22/27.92    (20)   ~ (all_52_25 = all_52_29)
% 177.22/27.92    (21)  op(e1, all_52_13) = e1
% 177.22/27.92    (22)  op(e0, all_52_15) = e0
% 177.22/27.92    (23)  all_56_15 = all_6_2
% 177.22/27.92    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.92    (25)  op(e2, e0) = all_52_15
% 177.22/27.92    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.92    (27)  all_58_3 = all_10_2
% 177.22/27.92    (28)  all_56_9 = all_52_19
% 177.22/27.92    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.92    (30)  all_58_15 = all_6_2
% 177.22/27.92    (31)   ~ (all_52_9 = all_4_2)
% 177.22/27.92    (32)   ~ (all_52_5 = all_52_7)
% 177.22/27.92    (33)  all_58_10 = all_52_15
% 177.22/27.92    (34)   ~ (all_52_5 = all_4_2)
% 177.22/27.92    (35)  all_58_7 = all_52_19
% 177.22/27.92    (36)  all_56_4 = all_52_9
% 177.22/27.92    (37)   ~ (all_52_15 = all_6_2)
% 177.22/27.92    (38)   ~ (all_52_17 = all_52_25)
% 177.22/27.92    (39)  op(e0, e1) = all_52_29
% 177.22/27.92    (40)   ~ (all_4_0 = e2)
% 177.22/27.92    (41)  all_58_4 = all_52_5
% 177.22/27.92    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.92    (43)   ~ (e3 = e1)
% 177.22/27.92    (44)   ~ (all_52_27 = all_52_29)
% 177.22/27.92    (45)   ~ (all_52_17 = all_14_2)
% 177.22/27.92    (46)  op(e3, all_4_2) = all_4_1
% 177.22/27.92    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.92    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.92    (49)   ~ (all_52_7 = all_4_2)
% 177.22/27.92    (50)  all_58_1 = all_52_3
% 177.22/27.92    (51)   ~ (all_52_13 = all_52_15)
% 177.22/27.92    (52)  all_58_0 = all_4_2
% 177.22/27.92    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.92    (54)  op(e1, all_52_29) = all_52_28
% 177.22/27.92    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.92    (56)   ~ (all_4_1 = e2)
% 177.22/27.92    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.92    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.92    (59)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.92    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.92    (61)  all_58_14 = all_52_29
% 177.22/27.92    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.92    (63)   ~ (all_52_3 = all_52_5)
% 177.22/27.92    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.92    (65)  op(e2, e1) = all_52_13
% 177.22/27.92    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.92    (67)  all_58_8 = all_14_2
% 177.22/27.92    (68)  op(e1, all_14_2) = e3
% 177.22/27.92    (69)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.92    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.92    (71)   ~ (all_52_5 = all_14_2)
% 177.22/27.92    (72)   ~ (all_52_3 = all_52_27)
% 177.22/27.92    (73)   ~ (all_52_3 = all_4_2)
% 177.22/27.92    (74)  op(e0, e3) = all_52_25
% 177.22/27.92    (75)  op(e3, all_52_17) = all_52_16
% 177.22/27.92    (76)   ~ (all_52_13 = all_14_2)
% 177.22/27.92    (77)  op(e3, all_52_9) = e3
% 177.22/27.92    (78)   ~ (e3 = e0)
% 177.22/27.92    (79)  all_40_0 = all_4_0
% 177.22/27.92    (80)   ~ (all_52_9 = all_52_13)
% 177.22/27.92    (81)  op(e0, all_52_23) = all_52_22
% 177.22/27.92    (82)   ~ (all_52_15 = all_52_23)
% 177.22/27.92    (83)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.92    (84)   ~ (all_52_5 = all_52_29)
% 177.22/27.92    (85)  all_56_2 = all_52_5
% 177.22/27.92    (86)  all_58_13 = all_52_27
% 177.22/27.92    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.92    (88)  all_56_5 = all_10_2
% 177.22/27.92    (89)   ~ (all_52_9 = all_52_17)
% 177.22/27.92    (90)  all_58_6 = all_52_17
% 177.22/27.92    (91)   ~ (all_52_3 = all_52_7)
% 177.22/27.92    (92)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.92    (93)  op(e2, all_52_19) = all_52_18
% 177.22/27.92    (94)   ~ (e1 = e0)
% 177.22/27.92    (95)  all_56_0 = all_4_2
% 177.22/27.92    (96)  all_58_11 = all_52_23
% 177.22/27.92    (97)   ~ (all_52_3 = all_52_19)
% 177.22/27.92    (98)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.92    (99)   ~ (all_52_7 = all_52_15)
% 177.22/27.92    (100)   ~ (all_52_29 = all_14_2)
% 177.22/27.92    (101)   ~ (all_52_19 = all_10_2)
% 177.22/27.92    (102)   ~ (all_52_23 = all_6_2)
% 177.22/27.92    (103)  op(e1, all_4_2) = all_4_0
% 177.22/27.92    (104)   ~ (all_52_29 = all_6_2)
% 177.22/27.92    (105)  all_58_2 = all_52_9
% 177.22/27.92    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.92    (107)  op(e3, e1) = all_52_5
% 177.22/27.92    (108)  all_56_10 = all_14_2
% 177.22/27.92    (109)   ~ (all_52_25 = all_6_2)
% 177.22/27.92    (110)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.92    (111)  op(e1, e3) = all_52_17
% 177.22/27.92    (112)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.92    (113)   ~ (all_52_25 = all_4_2)
% 177.22/27.92    (114)  op(e3, e0) = all_52_7
% 177.22/27.92    (115)  op(e2, all_10_2) = e2
% 177.22/27.92    (116)  op(e3, e3) = all_4_2
% 177.22/27.92    (117)   ~ (all_52_17 = all_4_2)
% 177.22/27.92    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.92             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.92    (119)   ~ (all_52_25 = all_52_27)
% 177.22/27.92    (120)   ~ (all_52_27 = all_6_2)
% 177.22/27.92    (121)   ~ (all_52_7 = all_6_2)
% 177.22/27.92    (122)   ~ (all_52_19 = all_52_27)
% 177.22/27.92    (123)  all_56_7 = all_52_15
% 177.22/27.92    (124)   ~ (all_52_7 = all_52_23)
% 177.22/27.92    (125)   ~ (all_52_13 = all_10_2)
% 177.22/27.92    (126)  op(e2, all_52_27) = all_52_26
% 177.22/27.92    (127)   ~ (all_52_17 = all_52_19)
% 177.22/27.92    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.92    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.92    (130)  op(e1, all_14_2) = all_14_1
% 177.22/27.92    (131)  all_58_9 = all_52_7
% 177.22/27.92    (132)   ~ (e2 = e0)
% 177.22/27.92    (133)  all_58_12 = all_52_25
% 177.22/27.92    (134)  op(e3, all_4_2) = e1
% 177.22/27.92    (135)  all_56_6 = all_52_13
% 177.22/27.92    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.92    (137)   ~ (all_52_9 = all_52_15)
% 177.22/27.93    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.93    (139)   ~ (e3 = e2)
% 177.22/27.93    (140)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.93    (141)   ~ (all_52_19 = all_14_2)
% 177.22/27.93    (142)  op(e0, all_52_7) = all_52_6
% 177.22/27.93    (143)  op(e2, e3) = all_52_9
% 177.22/27.93    (144)  all_56_13 = all_52_27
% 177.22/27.93  
% 177.22/27.93  Begin of proof
% 177.22/27.93  | 
% 177.22/27.93  | BETA: splitting (47) gives:
% 177.22/27.93  | 
% 177.22/27.93  | Case 1:
% 177.22/27.93  | | 
% 177.22/27.93  | |   (145)  all_56_15 = e3
% 177.22/27.93  | | 
% 177.22/27.93  | | COMBINE_EQS: (23), (145) imply:
% 177.22/27.93  | |   (146)  all_6_2 = e3
% 177.22/27.93  | | 
% 177.22/27.93  | | REDUCE: (37), (146) imply:
% 177.22/27.93  | |   (147)   ~ (all_52_15 = e3)
% 177.22/27.93  | | 
% 177.22/27.93  | | REDUCE: (109), (146) imply:
% 177.22/27.93  | |   (148)   ~ (all_52_25 = e3)
% 177.22/27.93  | | 
% 177.22/27.93  | | REF_CLOSE: (2), (8), (11), (16), (18), (21), (27), (31), (33), (41), (42),
% 177.22/27.93  | |            (43), (45), (48), (52), (59), (61), (64), (67), (68), (77), (90),
% 177.22/27.93  | |            (105), (111), (115), (116), (117), (118), (133), (134), (135),
% 177.22/27.93  | |            (138), (143), (147), (148) are inconsistent by sub-proof #368.
% 177.22/27.93  | | 
% 177.22/27.93  | Case 2:
% 177.22/27.93  | | 
% 177.22/27.93  | |   (149)   ~ (all_56_15 = e3)
% 177.22/27.93  | |   (150)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.93  | | 
% 177.22/27.93  | | REDUCE: (23), (149) imply:
% 177.22/27.93  | |   (151)   ~ (all_6_2 = e3)
% 177.22/27.93  | | 
% 177.22/27.93  | | BETA: splitting (66) gives:
% 177.22/27.93  | | 
% 177.22/27.93  | | Case 1:
% 177.22/27.93  | | | 
% 177.22/27.93  | | |   (152)  all_58_12 = e3
% 177.22/27.93  | | | 
% 177.22/27.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.22/27.93  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 177.22/27.93  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 177.22/27.93  | | |            (33), (34), (35), (36), (39), (40), (41), (42), (43), (44),
% 177.22/27.93  | | |            (45), (48), (49), (50), (52), (53), (55), (57), (58), (59),
% 177.22/27.93  | | |            (60), (61), (63), (65), (67), (69), (70), (71), (72), (73),
% 177.22/27.93  | | |            (74), (75), (76), (77), (78), (79), (80), (81), (83), (84),
% 177.22/27.93  | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 177.22/27.93  | | |            (95), (96), (97), (99), (100), (101), (102), (103), (105),
% 177.22/27.93  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 177.22/27.93  | | |            (115), (118), (119), (120), (121), (122), (123), (124), (125),
% 177.22/27.93  | | |            (126), (127), (128), (129), (130), (131), (132), (133), (134),
% 177.22/27.93  | | |            (135), (137), (138), (139), (140), (141), (142), (143), (150),
% 177.22/27.93  | | |            (152) are inconsistent by sub-proof #365.
% 177.22/27.93  | | | 
% 177.22/27.93  | | Case 2:
% 177.22/27.93  | | | 
% 177.22/27.93  | | |   (153)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.93  | | | 
% 177.22/27.93  | | | BETA: splitting (62) gives:
% 177.22/27.93  | | | 
% 177.22/27.93  | | | Case 1:
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | |   (154)  all_56_13 = e3
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | COMBINE_EQS: (144), (154) imply:
% 177.22/27.93  | | | |   (155)  all_52_27 = e3
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | SIMP: (155) implies:
% 177.22/27.93  | | | |   (156)  all_52_27 = e3
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | REF_CLOSE: (6), (7), (11), (15), (18), (21), (22), (28), (29), (30),
% 177.22/27.93  | | | |            (31), (32), (33), (34), (36), (38), (40), (41), (43), (44),
% 177.22/27.93  | | | |            (45), (51), (52), (55), (61), (64), (67), (68), (69), (74),
% 177.22/27.93  | | | |            (77), (79), (80), (87), (90), (92), (95), (96), (97), (103),
% 177.22/27.93  | | | |            (105), (107), (111), (113), (116), (118), (119), (120),
% 177.22/27.93  | | | |            (122), (126), (128), (131), (133), (134), (138), (143), (156)
% 177.22/27.93  | | | |            are inconsistent by sub-proof #364.
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | Case 2:
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | |   (157)   ~ (all_56_13 = e3)
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | REDUCE: (144), (157) imply:
% 177.22/27.93  | | | |   (158)   ~ (all_52_27 = e3)
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | BETA: splitting (153) gives:
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | Case 1:
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | |   (159)  all_58_13 = e3
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | | REF_CLOSE: (86), (158), (159) are inconsistent by sub-proof #1026.
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | Case 2:
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | |   (160)  all_58_14 = e3 | all_58_15 = e3
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | | BETA: splitting (160) gives:
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | | Case 1:
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | |   (161)  all_58_14 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | COMBINE_EQS: (61), (161) imply:
% 177.22/27.93  | | | | | |   (162)  all_52_29 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | SIMP: (162) implies:
% 177.22/27.93  | | | | | |   (163)  all_52_29 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (84), (163) imply:
% 177.22/27.93  | | | | | |   (164)   ~ (all_52_5 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (8), (163) imply:
% 177.22/27.93  | | | | | |   (165)   ~ (all_52_13 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (100), (163) imply:
% 177.22/27.93  | | | | | |   (166)   ~ (all_14_2 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | SIMP: (166) implies:
% 177.22/27.93  | | | | | |   (167)   ~ (all_14_2 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (104), (163) imply:
% 177.22/27.93  | | | | | |   (168)   ~ (all_6_2 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (54), (163) imply:
% 177.22/27.93  | | | | | |   (169)  op(e1, e3) = all_52_28
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | GROUND_INST: instantiating (118) with all_52_17, all_52_28, e3, e1,
% 177.22/27.93  | | | | | |              simplifying with (111), (169) gives:
% 177.22/27.93  | | | | | |   (170)  all_52_17 = all_52_28
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | COMBINE_EQS: (90), (170) imply:
% 177.22/27.93  | | | | | |   (171)  all_58_6 = all_52_28
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (127), (170) imply:
% 177.22/27.93  | | | | | |   (172)   ~ (all_52_19 = all_52_28)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | SIMP: (172) implies:
% 177.22/27.93  | | | | | |   (173)   ~ (all_52_19 = all_52_28)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (6), (170) imply:
% 177.22/27.93  | | | | | |   (174)   ~ (all_52_23 = all_52_28)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | SIMP: (174) implies:
% 177.22/27.93  | | | | | |   (175)   ~ (all_52_23 = all_52_28)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | BETA: splitting (129) gives:
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | Case 1:
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | |   (176)  all_56_3 = e3
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | COMBINE_EQS: (10), (176) imply:
% 177.22/27.93  | | | | | | |   (177)  all_52_7 = e3
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | REF_CLOSE: (11), (16), (18), (27), (31), (33), (48), (77), (99),
% 177.22/27.93  | | | | | | |            (105), (115), (116), (118), (143), (165), (177) are
% 177.22/27.93  | | | | | | |            inconsistent by sub-proof #733.
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | Case 2:
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | |   (178)   ~ (all_56_3 = e3)
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | REDUCE: (10), (178) imply:
% 177.22/27.93  | | | | | | |   (179)   ~ (all_52_7 = e3)
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | BETA: splitting (136) gives:
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | Case 1:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | |   (180)  all_58_0 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | COMBINE_EQS: (52), (180) imply:
% 177.22/27.93  | | | | | | | |   (181)  all_4_2 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | REF_CLOSE: (43), (116), (118), (134), (181) are inconsistent by
% 177.22/27.93  | | | | | | | |            sub-proof #630.
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | Case 2:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | |   (182)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | BETA: splitting (182) gives:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | Case 1:
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | |   (183)  all_58_1 = e3
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | REF_CLOSE: (15), (16), (18), (22), (27), (30), (31), (33),
% 177.22/27.93  | | | | | | | | |            (35), (36), (41), (42), (43), (46), (48), (50),
% 177.22/27.93  | | | | | | | | |            (52), (56), (63), (64), (67), (68), (73), (74),
% 177.22/27.93  | | | | | | | | |            (77), (80), (82), (87), (91), (92), (94), (96),
% 177.22/27.93  | | | | | | | | |            (97), (98), (99), (105), (107), (114), (116),
% 177.22/27.93  | | | | | | | | |            (118), (128), (131), (133), (137), (151), (161),
% 177.22/27.93  | | | | | | | | |            (165), (167), (171), (173), (175), (183) are
% 177.22/27.93  | | | | | | | | |            inconsistent by sub-proof #376.
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | Case 2:
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | |   (184)  all_58_4 = e3 | all_58_9 = e3
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | REF_CLOSE: (41), (131), (164), (179), (184) are inconsistent
% 177.22/27.93  | | | | | | | | |            by sub-proof #729.
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | End of split
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | End of split
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | End of split
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | Case 2:
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | |   (185)  all_58_15 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | COMBINE_EQS: (30), (185) imply:
% 177.22/27.93  | | | | | |   (186)  all_6_2 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (151), (186) imply:
% 177.22/27.93  | | | | | |   (187)  $false
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | CLOSE: (187) is inconsistent.
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | End of split
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | End of split
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | End of split
% 177.22/27.93  | | | 
% 177.22/27.93  | | End of split
% 177.22/27.93  | | 
% 177.22/27.93  | End of split
% 177.22/27.93  | 
% 177.22/27.93  End of proof
% 177.22/27.93  
% 177.22/27.93  Sub-proof #364 shows that the following formulas are inconsistent:
% 177.22/27.93  ----------------------------------------------------------------
% 177.22/27.93    (1)   ~ (all_52_17 = all_52_23)
% 177.22/27.93    (2)  all_40_2 = all_4_2
% 177.22/27.93    (3)  op(e3, e2) = all_52_3
% 177.22/27.93    (4)  op(e1, e2) = all_52_19
% 177.22/27.93    (5)  all_52_27 = e3
% 177.22/27.93    (6)  all_58_5 = all_52_13
% 177.22/27.93    (7)  op(e1, all_52_13) = e1
% 177.22/27.93    (8)  op(e0, all_52_15) = e0
% 177.22/27.93    (9)  all_56_9 = all_52_19
% 177.22/27.93    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.93    (11)  all_58_15 = all_6_2
% 177.22/27.93    (12)   ~ (all_52_9 = all_4_2)
% 177.22/27.93    (13)   ~ (all_52_5 = all_52_7)
% 177.22/27.93    (14)  all_58_10 = all_52_15
% 177.22/27.93    (15)   ~ (all_52_5 = all_4_2)
% 177.22/27.93    (16)  all_56_4 = all_52_9
% 177.22/27.93    (17)   ~ (all_52_17 = all_52_25)
% 177.22/27.93    (18)   ~ (all_4_0 = e2)
% 177.22/27.93    (19)  all_58_4 = all_52_5
% 177.22/27.93    (20)   ~ (e3 = e1)
% 177.22/27.93    (21)   ~ (all_52_27 = all_52_29)
% 177.22/27.93    (22)   ~ (all_52_17 = all_14_2)
% 177.22/27.93    (23)   ~ (all_52_13 = all_52_15)
% 177.22/27.93    (24)  all_58_0 = all_4_2
% 177.22/27.93    (25)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.93    (26)  all_58_14 = all_52_29
% 177.22/27.93    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.93    (28)  all_58_8 = all_14_2
% 177.22/27.93    (29)  op(e1, all_14_2) = e3
% 177.22/27.93    (30)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.93    (31)  op(e0, e3) = all_52_25
% 177.22/27.93    (32)  op(e3, all_52_9) = e3
% 177.22/27.93    (33)  all_40_0 = all_4_0
% 177.22/27.93    (34)   ~ (all_52_9 = all_52_13)
% 177.22/27.93    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.93    (36)  all_58_6 = all_52_17
% 177.22/27.93    (37)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.93    (38)  all_56_0 = all_4_2
% 177.22/27.93    (39)  all_58_11 = all_52_23
% 177.22/27.93    (40)   ~ (all_52_3 = all_52_19)
% 177.22/27.93    (41)  op(e1, all_4_2) = all_4_0
% 177.22/27.93    (42)  all_58_2 = all_52_9
% 177.22/27.93    (43)  op(e3, e1) = all_52_5
% 177.22/27.93    (44)  op(e1, e3) = all_52_17
% 177.22/27.93    (45)   ~ (all_52_25 = all_4_2)
% 177.22/27.93    (46)  op(e3, e3) = all_4_2
% 177.22/27.93    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.93    (48)   ~ (all_52_25 = all_52_27)
% 177.22/27.93    (49)   ~ (all_52_27 = all_6_2)
% 177.22/27.93    (50)   ~ (all_52_19 = all_52_27)
% 177.22/27.93    (51)  op(e2, all_52_27) = all_52_26
% 177.22/27.93    (52)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.93    (53)  all_58_9 = all_52_7
% 177.22/27.93    (54)  all_58_12 = all_52_25
% 177.22/27.93    (55)  op(e3, all_4_2) = e1
% 177.22/27.93    (56)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.93    (57)  op(e2, e3) = all_52_9
% 177.22/27.93  
% 177.22/27.93  Begin of proof
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (5), (50) imply:
% 177.22/27.93  |   (58)   ~ (all_52_19 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (5), (48) imply:
% 177.22/27.93  |   (59)   ~ (all_52_25 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (5), (21) imply:
% 177.22/27.93  |   (60)   ~ (all_52_29 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (60) implies:
% 177.22/27.93  |   (61)   ~ (all_52_29 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (5), (49) imply:
% 177.22/27.93  |   (62)   ~ (all_6_2 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (62) implies:
% 177.22/27.93  |   (63)   ~ (all_6_2 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (5), (51) imply:
% 177.22/27.93  |   (64)  op(e2, e3) = all_52_26
% 177.22/27.93  | 
% 177.22/27.93  | GROUND_INST: instantiating (47) with all_52_9, all_52_26, e3, e2, simplifying
% 177.22/27.93  |              with (57), (64) gives:
% 177.22/27.93  |   (65)  all_52_9 = all_52_26
% 177.22/27.93  | 
% 177.22/27.93  | COMBINE_EQS: (16), (65) imply:
% 177.22/27.93  |   (66)  all_56_4 = all_52_26
% 177.22/27.93  | 
% 177.22/27.93  | COMBINE_EQS: (42), (65) imply:
% 177.22/27.93  |   (67)  all_58_2 = all_52_26
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (34), (65) imply:
% 177.22/27.93  |   (68)   ~ (all_52_13 = all_52_26)
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (68) implies:
% 177.22/27.93  |   (69)   ~ (all_52_13 = all_52_26)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (12), (65) imply:
% 177.22/27.93  |   (70)   ~ (all_52_26 = all_4_2)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (32), (65) imply:
% 177.22/27.93  |   (71)  op(e3, all_52_26) = e3
% 177.22/27.93  | 
% 177.22/27.93  | BETA: splitting (25) gives:
% 177.22/27.93  | 
% 177.22/27.93  | Case 1:
% 177.22/27.93  | | 
% 177.22/27.93  | |   (72)  all_56_9 = e3
% 177.22/27.93  | | 
% 177.22/27.93  | | REF_CLOSE: (9), (58), (72) are inconsistent by sub-proof #700.
% 177.22/27.93  | | 
% 177.22/27.93  | Case 2:
% 177.22/27.93  | | 
% 177.22/27.93  | |   (73)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.93  | | 
% 177.22/27.93  | | BETA: splitting (37) gives:
% 177.22/27.93  | | 
% 177.22/27.93  | | Case 1:
% 177.22/27.93  | | | 
% 177.22/27.93  | | |   (74)  all_56_4 = e3
% 177.22/27.93  | | | 
% 177.22/27.93  | | | COMBINE_EQS: (66), (74) imply:
% 177.22/27.93  | | |   (75)  all_52_26 = e3
% 177.22/27.93  | | | 
% 177.22/27.93  | | | SIMP: (75) implies:
% 177.22/27.93  | | |   (76)  all_52_26 = e3
% 177.22/27.93  | | | 
% 177.22/27.93  | | | REF_CLOSE: (46), (47), (70), (71), (76) are inconsistent by sub-proof
% 177.22/27.93  | | |            #1005.
% 177.22/27.93  | | | 
% 177.22/27.93  | | Case 2:
% 177.22/27.93  | | | 
% 177.22/27.93  | | |   (77)   ~ (all_56_4 = e3)
% 177.22/27.93  | | | 
% 177.22/27.93  | | | REDUCE: (66), (77) imply:
% 177.22/27.93  | | |   (78)   ~ (all_52_26 = e3)
% 177.22/27.93  | | | 
% 177.22/27.93  | | | BETA: splitting (27) gives:
% 177.22/27.93  | | | 
% 177.22/27.93  | | | Case 1:
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | |   (79)  all_58_0 = e3
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | COMBINE_EQS: (24), (79) imply:
% 177.22/27.93  | | | |   (80)  all_4_2 = e3
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | REDUCE: (55), (80) imply:
% 177.22/27.93  | | | |   (81)  op(e3, e3) = e1
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | REDUCE: (46), (80) imply:
% 177.22/27.93  | | | |   (82)  op(e3, e3) = e3
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | GROUND_INST: instantiating (47) with e1, e3, e3, e3, simplifying with
% 177.22/27.93  | | | |              (81), (82) gives:
% 177.22/27.93  | | | |   (83)  e3 = e1
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | REDUCE: (20), (83) imply:
% 177.22/27.93  | | | |   (84)  $false
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | CLOSE: (84) is inconsistent.
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | Case 2:
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | |   (85)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | BETA: splitting (85) gives:
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | | Case 1:
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | |   (86)  all_58_2 = e3
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | | REF_CLOSE: (67), (78), (86) are inconsistent by sub-proof #1004.
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | Case 2:
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | |   (87)  all_58_6 = e3 | all_58_12 = e3
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | | BETA: splitting (87) gives:
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | | Case 1:
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | |   (88)  all_58_6 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | COMBINE_EQS: (36), (88) imply:
% 177.22/27.93  | | | | | |   (89)  all_52_17 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | SIMP: (89) implies:
% 177.22/27.93  | | | | | |   (90)  all_52_17 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (1), (90) imply:
% 177.22/27.93  | | | | | |   (91)   ~ (all_52_23 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | SIMP: (91) implies:
% 177.22/27.93  | | | | | |   (92)   ~ (all_52_23 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (17), (90) imply:
% 177.22/27.93  | | | | | |   (93)   ~ (all_52_25 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (22), (90) imply:
% 177.22/27.93  | | | | | |   (94)   ~ (all_14_2 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | SIMP: (94) implies:
% 177.22/27.93  | | | | | |   (95)   ~ (all_14_2 = e3)
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REDUCE: (44), (90) imply:
% 177.22/27.93  | | | | | |   (96)  op(e1, e3) = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | BETA: splitting (52) gives:
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | Case 1:
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | |   (97)  all_58_9 = e3
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | COMBINE_EQS: (53), (97) imply:
% 177.22/27.93  | | | | | | |   (98)  all_52_7 = e3
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | SIMP: (98) implies:
% 177.22/27.93  | | | | | | |   (99)  all_52_7 = e3
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | REDUCE: (13), (99) imply:
% 177.22/27.93  | | | | | | |   (100)   ~ (all_52_5 = e3)
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | BETA: splitting (56) gives:
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | Case 1:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | |   (101)  all_58_4 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | REF_CLOSE: (19), (100), (101) are inconsistent by sub-proof
% 177.22/27.93  | | | | | | | |            #1025.
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | Case 2:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | |   (102)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | REF_CLOSE: (6), (7), (20), (26), (28), (47), (54), (59), (61),
% 177.22/27.93  | | | | | | | |            (67), (69), (85), (88), (95), (96), (102) are
% 177.22/27.93  | | | | | | | |            inconsistent by sub-proof #998.
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | End of split
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | Case 2:
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | |   (103)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | BETA: splitting (103) gives:
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | | Case 1:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | |   (104)  all_58_10 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | COMBINE_EQS: (14), (104) imply:
% 177.22/27.93  | | | | | | | |   (105)  all_52_15 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | SIMP: (105) implies:
% 177.22/27.93  | | | | | | | |   (106)  all_52_15 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | REDUCE: (23), (106) imply:
% 177.22/27.93  | | | | | | | |   (107)   ~ (all_52_13 = e3)
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | REDUCE: (8), (106) imply:
% 177.22/27.93  | | | | | | | |   (108)  op(e0, e3) = e0
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | BETA: splitting (56) gives:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | Case 1:
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | |   (109)  all_58_4 = e3
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | COMBINE_EQS: (19), (109) imply:
% 177.22/27.93  | | | | | | | | |   (110)  all_52_5 = e3
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | SIMP: (110) implies:
% 177.22/27.93  | | | | | | | | |   (111)  all_52_5 = e3
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | REDUCE: (15), (111) imply:
% 177.22/27.93  | | | | | | | | |   (112)   ~ (all_4_2 = e3)
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | SIMP: (112) implies:
% 177.22/27.93  | | | | | | | | |   (113)   ~ (all_4_2 = e3)
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | REDUCE: (43), (111) imply:
% 177.22/27.93  | | | | | | | | |   (114)  op(e3, e1) = e3
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | REF_CLOSE: (2), (3), (4), (9), (10), (18), (24), (30), (31),
% 177.22/27.93  | | | | | | | | |            (33), (35), (38), (40), (41), (45), (47), (55),
% 177.22/27.93  | | | | | | | | |            (73), (108), (113), (114) are inconsistent by
% 177.22/27.93  | | | | | | | | |            sub-proof #611.
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | Case 2:
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | |   (115)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | | REF_CLOSE: (6), (22), (26), (28), (29), (44), (47), (61),
% 177.22/27.93  | | | | | | | | |            (107), (115) are inconsistent by sub-proof #420.
% 177.22/27.93  | | | | | | | | | 
% 177.22/27.93  | | | | | | | | End of split
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | Case 2:
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | |   (116)  all_58_11 = e3 | all_58_15 = e3
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | | REF_CLOSE: (11), (39), (63), (92), (116) are inconsistent by
% 177.22/27.93  | | | | | | | |            sub-proof #1016.
% 177.22/27.93  | | | | | | | | 
% 177.22/27.93  | | | | | | | End of split
% 177.22/27.93  | | | | | | | 
% 177.22/27.93  | | | | | | End of split
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | Case 2:
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | |   (117)  all_58_12 = e3
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | | REF_CLOSE: (54), (59), (117) are inconsistent by sub-proof #1003.
% 177.22/27.93  | | | | | | 
% 177.22/27.93  | | | | | End of split
% 177.22/27.93  | | | | | 
% 177.22/27.93  | | | | End of split
% 177.22/27.93  | | | | 
% 177.22/27.93  | | | End of split
% 177.22/27.93  | | | 
% 177.22/27.93  | | End of split
% 177.22/27.93  | | 
% 177.22/27.93  | End of split
% 177.22/27.93  | 
% 177.22/27.93  End of proof
% 177.22/27.93  
% 177.22/27.93  Sub-proof #365 shows that the following formulas are inconsistent:
% 177.22/27.93  ----------------------------------------------------------------
% 177.22/27.93    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.93    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.93    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.93    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.93    (5)   ~ (all_52_27 = all_10_2)
% 177.22/27.93    (6)   ~ (all_52_17 = all_52_23)
% 177.22/27.93    (7)  all_40_2 = all_4_2
% 177.22/27.93    (8)   ~ (all_52_13 = all_52_29)
% 177.22/27.93    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.93    (10)  all_56_3 = all_52_7
% 177.22/27.93    (11)  op(e3, e2) = all_52_3
% 177.22/27.93    (12)   ~ (all_52_9 = all_52_25)
% 177.22/27.93    (13)   ~ (all_52_19 = all_52_23)
% 177.22/27.93    (14)  all_56_11 = all_52_23
% 177.22/27.93    (15)  op(e1, e2) = all_52_19
% 177.22/27.93    (16)   ~ (all_52_3 = all_10_2)
% 177.22/27.93    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.93    (18)  all_58_5 = all_52_13
% 177.22/27.93    (19)   ~ (all_6_2 = e0)
% 177.22/27.93    (20)   ~ (all_52_25 = all_52_29)
% 177.22/27.93    (21)  op(e1, all_52_13) = e1
% 177.22/27.93    (22)  op(e0, all_52_15) = e0
% 177.22/27.93    (23)  all_56_15 = all_6_2
% 177.22/27.93    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.93    (25)  op(e2, e0) = all_52_15
% 177.22/27.93    (26)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.93    (27)  all_58_3 = all_10_2
% 177.22/27.93    (28)  all_56_9 = all_52_19
% 177.22/27.93    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.93    (30)  all_58_15 = all_6_2
% 177.22/27.93    (31)   ~ (all_52_9 = all_4_2)
% 177.22/27.93    (32)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.93    (33)   ~ (all_52_5 = all_52_7)
% 177.22/27.93    (34)  all_58_10 = all_52_15
% 177.22/27.93    (35)   ~ (all_52_5 = all_4_2)
% 177.22/27.93    (36)  all_58_7 = all_52_19
% 177.22/27.93    (37)  all_56_4 = all_52_9
% 177.22/27.93    (38)  op(e0, e1) = all_52_29
% 177.22/27.93    (39)   ~ (all_4_0 = e2)
% 177.22/27.93    (40)  all_58_4 = all_52_5
% 177.22/27.93    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.93    (42)   ~ (e3 = e1)
% 177.22/27.93    (43)   ~ (all_52_27 = all_52_29)
% 177.22/27.93    (44)   ~ (all_52_17 = all_14_2)
% 177.22/27.93    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.93    (46)   ~ (all_52_7 = all_4_2)
% 177.22/27.93    (47)  all_58_1 = all_52_3
% 177.22/27.93    (48)  all_58_0 = all_4_2
% 177.22/27.93    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.22/27.93    (50)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.93    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.93    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.93    (53)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.93    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.93    (55)  all_58_14 = all_52_29
% 177.22/27.93    (56)   ~ (all_52_3 = all_52_5)
% 177.22/27.93    (57)  op(e2, e1) = all_52_13
% 177.22/27.93    (58)  all_58_8 = all_14_2
% 177.22/27.93    (59)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.22/27.93    (60)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.93    (61)   ~ (all_52_5 = all_14_2)
% 177.22/27.93    (62)   ~ (all_52_3 = all_52_27)
% 177.22/27.93    (63)   ~ (all_52_3 = all_4_2)
% 177.22/27.93    (64)  op(e0, e3) = all_52_25
% 177.22/27.93    (65)  op(e3, all_52_17) = all_52_16
% 177.22/27.93    (66)   ~ (all_52_13 = all_14_2)
% 177.22/27.93    (67)  op(e3, all_52_9) = e3
% 177.22/27.93    (68)   ~ (e3 = e0)
% 177.22/27.93    (69)  all_40_0 = all_4_0
% 177.22/27.93    (70)   ~ (all_52_9 = all_52_13)
% 177.22/27.93    (71)  op(e0, all_52_23) = all_52_22
% 177.22/27.93    (72)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.93    (73)   ~ (all_52_5 = all_52_29)
% 177.22/27.93    (74)  all_56_2 = all_52_5
% 177.22/27.93    (75)  all_58_13 = all_52_27
% 177.22/27.93    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.93    (77)  all_56_5 = all_10_2
% 177.22/27.93    (78)  all_58_12 = e3
% 177.22/27.93    (79)   ~ (all_52_9 = all_52_17)
% 177.22/27.93    (80)  all_58_6 = all_52_17
% 177.22/27.93    (81)   ~ (all_52_3 = all_52_7)
% 177.22/27.93    (82)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.93    (83)  op(e2, all_52_19) = all_52_18
% 177.22/27.93    (84)   ~ (e1 = e0)
% 177.22/27.93    (85)  all_56_0 = all_4_2
% 177.22/27.93    (86)  all_58_11 = all_52_23
% 177.22/27.93    (87)   ~ (all_52_3 = all_52_19)
% 177.22/27.93    (88)   ~ (all_52_7 = all_52_15)
% 177.22/27.93    (89)   ~ (all_52_29 = all_14_2)
% 177.22/27.93    (90)   ~ (all_52_19 = all_10_2)
% 177.22/27.93    (91)   ~ (all_52_23 = all_6_2)
% 177.22/27.93    (92)  op(e1, all_4_2) = all_4_0
% 177.22/27.93    (93)  all_58_2 = all_52_9
% 177.22/27.93    (94)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.93    (95)  op(e3, e1) = all_52_5
% 177.22/27.93    (96)  all_56_10 = all_14_2
% 177.22/27.93    (97)   ~ (all_52_25 = all_6_2)
% 177.22/27.93    (98)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.93    (99)  op(e1, e3) = all_52_17
% 177.22/27.93    (100)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.22/27.93    (101)   ~ (all_52_25 = all_4_2)
% 177.22/27.93    (102)  op(e3, e0) = all_52_7
% 177.22/27.93    (103)  op(e2, all_10_2) = e2
% 177.22/27.93    (104)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.93             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.93    (105)   ~ (all_52_25 = all_52_27)
% 177.22/27.93    (106)   ~ (all_52_27 = all_6_2)
% 177.22/27.93    (107)   ~ (all_52_7 = all_6_2)
% 177.22/27.93    (108)   ~ (all_52_19 = all_52_27)
% 177.22/27.93    (109)  all_56_7 = all_52_15
% 177.22/27.93    (110)   ~ (all_52_7 = all_52_23)
% 177.22/27.93    (111)   ~ (all_52_13 = all_10_2)
% 177.22/27.93    (112)  op(e2, all_52_27) = all_52_26
% 177.22/27.93    (113)   ~ (all_52_17 = all_52_19)
% 177.22/27.93    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.93    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.93    (116)  op(e1, all_14_2) = all_14_1
% 177.22/27.93    (117)  all_58_9 = all_52_7
% 177.22/27.93    (118)   ~ (e2 = e0)
% 177.22/27.93    (119)  all_58_12 = all_52_25
% 177.22/27.93    (120)  op(e3, all_4_2) = e1
% 177.22/27.93    (121)  all_56_6 = all_52_13
% 177.22/27.93    (122)   ~ (all_52_9 = all_52_15)
% 177.22/27.93    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.93    (124)   ~ (e3 = e2)
% 177.22/27.93    (125)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.93    (126)   ~ (all_52_19 = all_14_2)
% 177.22/27.93    (127)  op(e0, all_52_7) = all_52_6
% 177.22/27.93    (128)  op(e2, e3) = all_52_9
% 177.22/27.93  
% 177.22/27.93  Begin of proof
% 177.22/27.93  | 
% 177.22/27.93  | COMBINE_EQS: (78), (119) imply:
% 177.22/27.93  |   (129)  all_52_25 = e3
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (129) implies:
% 177.22/27.93  |   (130)  all_52_25 = e3
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (12), (130) imply:
% 177.22/27.93  |   (131)   ~ (all_52_9 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (105), (130) imply:
% 177.22/27.93  |   (132)   ~ (all_52_27 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (132) implies:
% 177.22/27.93  |   (133)   ~ (all_52_27 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (20), (130) imply:
% 177.22/27.93  |   (134)   ~ (all_52_29 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (134) implies:
% 177.22/27.93  |   (135)   ~ (all_52_29 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (97), (130) imply:
% 177.22/27.93  |   (136)   ~ (all_6_2 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (136) implies:
% 177.22/27.93  |   (137)   ~ (all_6_2 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (101), (130) imply:
% 177.22/27.93  |   (138)   ~ (all_4_2 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | SIMP: (138) implies:
% 177.22/27.93  |   (139)   ~ (all_4_2 = e3)
% 177.22/27.93  | 
% 177.22/27.93  | REDUCE: (64), (130) imply:
% 177.22/27.93  |   (140)  op(e0, e3) = e3
% 177.22/27.93  | 
% 177.22/27.93  | BETA: splitting (82) gives:
% 177.22/27.93  | 
% 177.22/27.93  | Case 1:
% 177.22/27.94  | | 
% 177.22/27.94  | |   (141)  all_56_4 = e3
% 177.22/27.94  | | 
% 177.22/27.94  | | REF_CLOSE: (37), (131), (141) are inconsistent by sub-proof #782.
% 177.22/27.94  | | 
% 177.22/27.94  | Case 2:
% 177.22/27.94  | | 
% 177.22/27.94  | |   (142)   ~ (all_56_4 = e3)
% 177.22/27.94  | |   (143)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.94  | | 
% 177.22/27.94  | | BETA: splitting (29) gives:
% 177.22/27.94  | | 
% 177.22/27.94  | | Case 1:
% 177.22/27.94  | | | 
% 177.22/27.94  | | |   (144)  all_56_0 = e3
% 177.22/27.94  | | | 
% 177.22/27.94  | | | COMBINE_EQS: (85), (144) imply:
% 177.22/27.94  | | |   (145)  all_4_2 = e3
% 177.22/27.94  | | | 
% 177.22/27.94  | | | REDUCE: (139), (145) imply:
% 177.22/27.94  | | |   (146)  $false
% 177.22/27.94  | | | 
% 177.22/27.94  | | | CLOSE: (146) is inconsistent.
% 177.22/27.94  | | | 
% 177.22/27.94  | | Case 2:
% 177.22/27.94  | | | 
% 177.22/27.94  | | |   (147)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.94  | | | 
% 177.22/27.94  | | | BETA: splitting (100) gives:
% 177.22/27.94  | | | 
% 177.22/27.94  | | | Case 1:
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | |   (148)  all_56_7 = e3
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | | REF_CLOSE: (22), (68), (104), (109), (140), (148) are inconsistent by
% 177.22/27.94  | | | |            sub-proof #388.
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | Case 2:
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | |   (149)   ~ (all_56_7 = e3)
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | | REDUCE: (109), (149) imply:
% 177.22/27.94  | | | |   (150)   ~ (all_52_15 = e3)
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | | BETA: splitting (114) gives:
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | | Case 1:
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | |   (151)  all_58_9 = e3
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | COMBINE_EQS: (117), (151) imply:
% 177.22/27.94  | | | | |   (152)  all_52_7 = e3
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | REDUCE: (33), (152) imply:
% 177.22/27.94  | | | | |   (153)   ~ (all_52_5 = e3)
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | REDUCE: (102), (152) imply:
% 177.22/27.94  | | | | |   (154)  op(e3, e0) = e3
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | REDUCE: (127), (152) imply:
% 177.22/27.94  | | | | |   (155)  op(e0, e3) = all_52_6
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | GROUND_INST: instantiating (104) with e3, all_52_6, e3, e0,
% 177.22/27.94  | | | | |              simplifying with (140), (155) gives:
% 177.22/27.94  | | | | |   (156)  all_52_6 = e3
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | BETA: splitting (123) gives:
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | Case 1:
% 177.22/27.94  | | | | | | 
% 177.22/27.94  | | | | | |   (157)  all_58_4 = e3
% 177.22/27.94  | | | | | | 
% 177.22/27.94  | | | | | | REF_CLOSE: (40), (153), (157) are inconsistent by sub-proof #1025.
% 177.22/27.94  | | | | | | 
% 177.22/27.94  | | | | | Case 2:
% 177.22/27.94  | | | | | | 
% 177.22/27.94  | | | | | |   (158)   ~ (all_58_4 = e3)
% 177.22/27.94  | | | | | |   (159)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.94  | | | | | | 
% 177.22/27.94  | | | | | | BETA: splitting (125) gives:
% 177.22/27.94  | | | | | | 
% 177.22/27.94  | | | | | | Case 1:
% 177.22/27.94  | | | | | | | 
% 177.22/27.94  | | | | | | |   (160)  all_56_2 = e3
% 177.22/27.94  | | | | | | | 
% 177.22/27.94  | | | | | | | REF_CLOSE: (74), (153), (160) are inconsistent by sub-proof #931.
% 177.22/27.94  | | | | | | | 
% 177.22/27.94  | | | | | | Case 2:
% 177.22/27.94  | | | | | | | 
% 177.22/27.94  | | | | | | |   (161)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.94  | | | | | | | 
% 177.22/27.94  | | | | | | | BETA: splitting (76) gives:
% 177.22/27.94  | | | | | | | 
% 177.22/27.94  | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | |   (162)  all_58_0 = e1
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | | REF_CLOSE: (35), (48), (95), (104), (120), (162) are
% 177.22/27.94  | | | | | | | |            inconsistent by sub-proof #626.
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | |   (163)   ~ (all_58_0 = e1)
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | | REDUCE: (48), (163) imply:
% 177.22/27.94  | | | | | | | |   (164)   ~ (all_4_2 = e1)
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | | BETA: splitting (60) gives:
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | |   (165)  all_58_0 = e2
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | COMBINE_EQS: (48), (165) imply:
% 177.22/27.94  | | | | | | | | |   (166)  all_4_2 = e2
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | COMBINE_EQS: (7), (166) imply:
% 177.22/27.94  | | | | | | | | |   (167)  all_40_2 = e2
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | REDUCE: (63), (166) imply:
% 177.22/27.94  | | | | | | | | |   (168)   ~ (all_52_3 = e2)
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | REDUCE: (35), (166) imply:
% 177.22/27.94  | | | | | | | | |   (169)   ~ (all_52_5 = e2)
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | REDUCE: (120), (166) imply:
% 177.22/27.94  | | | | | | | | |   (170)  op(e3, e2) = e1
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | REDUCE: (92), (166) imply:
% 177.22/27.94  | | | | | | | | |   (171)  op(e1, e2) = all_4_0
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | BETA: splitting (59) gives:
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | |   (172)   ~ (all_40_2 = e2)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (167), (172) imply:
% 177.22/27.94  | | | | | | | | | |   (173)  $false
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | CLOSE: (173) is inconsistent.
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | |   (174)   ~ (all_40_0 = e0)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (69), (174) imply:
% 177.22/27.94  | | | | | | | | | |   (175)   ~ (all_4_0 = e0)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | GROUND_INST: instantiating (104) with all_52_19, all_4_0, e2,
% 177.22/27.94  | | | | | | | | | |              e1, simplifying with (15), (171) gives:
% 177.22/27.94  | | | | | | | | | |   (176)  all_52_19 = all_4_0
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | GROUND_INST: instantiating (104) with all_52_3, e1, e2, e3,
% 177.22/27.94  | | | | | | | | | |              simplifying with (11), (170) gives:
% 177.22/27.94  | | | | | | | | | |   (177)  all_52_3 = e1
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | COMBINE_EQS: (28), (176) imply:
% 177.22/27.94  | | | | | | | | | |   (178)  all_56_9 = all_4_0
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | COMBINE_EQS: (47), (177) imply:
% 177.22/27.94  | | | | | | | | | |   (179)  all_58_1 = e1
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (87), (176), (177) imply:
% 177.22/27.94  | | | | | | | | | |   (180)   ~ (all_4_0 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | SIMP: (180) implies:
% 177.22/27.94  | | | | | | | | | |   (181)   ~ (all_4_0 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (62), (177) imply:
% 177.22/27.94  | | | | | | | | | |   (182)   ~ (all_52_27 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | SIMP: (182) implies:
% 177.22/27.94  | | | | | | | | | |   (183)   ~ (all_52_27 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (16), (177) imply:
% 177.22/27.94  | | | | | | | | | |   (184)   ~ (all_10_2 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | SIMP: (184) implies:
% 177.22/27.94  | | | | | | | | | |   (185)   ~ (all_10_2 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (168), (177) imply:
% 177.22/27.94  | | | | | | | | | |   (186)   ~ (e2 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | SIMP: (186) implies:
% 177.22/27.94  | | | | | | | | | |   (187)   ~ (e2 = e1)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (113), (176) imply:
% 177.22/27.94  | | | | | | | | | |   (188)   ~ (all_52_17 = all_4_0)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (108), (176) imply:
% 177.22/27.94  | | | | | | | | | |   (189)   ~ (all_52_27 = all_4_0)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | SIMP: (189) implies:
% 177.22/27.94  | | | | | | | | | |   (190)   ~ (all_52_27 = all_4_0)
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | REDUCE: (83), (176) imply:
% 177.22/27.94  | | | | | | | | | |   (191)  op(e2, all_4_0) = all_52_18
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | BETA: splitting (3) gives:
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | |   (192)  all_58_0 = e0
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | COMBINE_EQS: (165), (192) imply:
% 177.22/27.94  | | | | | | | | | | |   (193)  e2 = e0
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | REDUCE: (118), (193) imply:
% 177.22/27.94  | | | | | | | | | | |   (194)  $false
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | |   (195)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | BETA: splitting (50) gives:
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | |   (196)  all_56_9 = e3
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | COMBINE_EQS: (178), (196) imply:
% 177.22/27.94  | | | | | | | | | | | |   (197)  all_4_0 = e3
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | SIMP: (197) implies:
% 177.22/27.94  | | | | | | | | | | | |   (198)  all_4_0 = e3
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | REDUCE: (188), (198) imply:
% 177.22/27.94  | | | | | | | | | | | |   (199)   ~ (all_52_17 = e3)
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | REDUCE: (191), (198) imply:
% 177.22/27.94  | | | | | | | | | | | |   (200)  op(e2, e3) = all_52_18
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | BETA: splitting (195) gives:
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | |   (201)  all_58_1 = e0
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | COMBINE_EQS: (179), (201) imply:
% 177.22/27.94  | | | | | | | | | | | | |   (202)  e1 = e0
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | REDUCE: (84), (202) imply:
% 177.22/27.94  | | | | | | | | | | | | |   (203)  $false
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | |   (204)   ~ (all_58_1 = e0)
% 177.22/27.94  | | | | | | | | | | | | |   (205)  all_58_4 = e0 | all_58_9 = e0
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | BETA: splitting (161) gives:
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | |   (206)  all_56_2 = e2
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | COMBINE_EQS: (74), (206) imply:
% 177.22/27.94  | | | | | | | | | | | | | |   (207)  all_52_5 = e2
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | REDUCE: (169), (207) imply:
% 177.22/27.94  | | | | | | | | | | | | | |   (208)  $false
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | CLOSE: (208) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | |   (209)  all_56_2 = e1 | all_56_2 = e0
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | |   (210)  all_58_5 = e3
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | COMBINE_EQS: (18), (210) imply:
% 177.22/27.94  | | | | | | | | | | | | | | |   (211)  all_52_13 = e3
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | SIMP: (211) implies:
% 177.22/27.94  | | | | | | | | | | | | | | |   (212)  all_52_13 = e3
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | REDUCE: (66), (212) imply:
% 177.22/27.94  | | | | | | | | | | | | | | |   (213)   ~ (all_14_2 = e3)
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | SIMP: (213) implies:
% 177.22/27.94  | | | | | | | | | | | | | | |   (214)   ~ (all_14_2 = e3)
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | REDUCE: (111), (212) imply:
% 177.22/27.94  | | | | | | | | | | | | | | |   (215)   ~ (all_10_2 = e3)
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | SIMP: (215) implies:
% 177.22/27.94  | | | | | | | | | | | | | | |   (216)   ~ (all_10_2 = e3)
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | REDUCE: (21), (212) imply:
% 177.22/27.94  | | | | | | | | | | | | | | |   (217)  op(e1, e3) = e1
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | |   (218)  all_56_2 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (218) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (219)  all_52_5 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (219) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (220)  all_58_4 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | REF_CLOSE: (68), (84), (151), (205), (220) are inconsistent
% 177.22/27.94  | | | | | | | | | | | | | | | |            by sub-proof #927.
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | |   (221)  all_56_2 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (221) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (222)  all_52_5 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | REDUCE: (73), (222) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (223)   ~ (all_52_29 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | SIMP: (223) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (224)   ~ (all_52_29 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | REDUCE: (61), (222) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (225)   ~ (all_14_2 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | SIMP: (225) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (226)   ~ (all_14_2 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | REDUCE: (153), (222) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | |   (227)   ~ (e3 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | |   (228)  all_58_12 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (78), (228) are inconsistent by sub-proof
% 177.22/27.94  | | | | | | | | | | | | | | | | |            #682.
% 177.22/27.94  | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | |   (229)  all_58_13 = e0 | all_58_14 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (230)  all_58_13 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (230) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (231)  all_52_27 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | SIMP: (231) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (232)  all_52_27 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | REDUCE: (5), (232) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (233)   ~ (all_10_2 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | SIMP: (233) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (234)   ~ (all_10_2 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | REDUCE: (183), (232) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (235)   ~ (e1 = e0)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | REDUCE: (112), (232) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (236)  op(e2, e0) = all_52_26
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | |   (237)  all_56_5 = e3
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (237) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | |   (238)  all_10_2 = e3
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | REDUCE: (216), (238) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | |   (239)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | CLOSE: (239) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | |   (240)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | |   (241)  all_58_1 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (241) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | |   (242)  e2 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | |   (243)  e2 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (243) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | |   (244)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | CLOSE: (244) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | |   (245)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (246)  all_58_3 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (246) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (247)  all_10_2 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (104) with all_52_17, e1, e3, e1,
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |              simplifying with (99), (217) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (248)  all_52_17 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (104) with all_52_15, all_52_26, e0,
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (25), (236) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (249)  all_52_15 = all_52_26
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (104) with all_52_9, all_52_18, e3,
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (128), (200) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (250)  all_52_9 = all_52_18
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (249) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (251)  all_58_10 = all_52_26
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (250) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (252)  all_58_2 = all_52_18
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (248), (250) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (253)   ~ (all_52_18 = e1)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (248) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (254)   ~ (all_14_2 = e1)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (255)   ~ (all_14_2 = e1)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (199), (248) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (256)   ~ (e3 = e1)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (249) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (257)  op(e0, all_52_26) = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | |   (258)  all_56_10 = e3
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (214), (258) are inconsistent by sub-proof
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | |            #552.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | |   (259)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_58_2 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (260) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_52_18 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (253), (261) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | |   (262)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_58_4 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (84), (151), (205), (264) are inconsistent
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #927.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_56_10 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (266) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_14_2 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (267) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_14_2 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (268) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_58_8 = e2
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (89), (268) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (270)   ~ (all_52_29 = e2)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_58_5 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (271) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  e3 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (272) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_58_8 = e1 | all_58_14 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_58_8 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (275) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  e2 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (276) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (277) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_58_14 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (278) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_52_29 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (279) implies:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_52_29 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (280) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  op(e0, e1) = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_58_9 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (282) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  e3 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (283) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (284) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)   ~ (all_58_9 = e1)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_58_10 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (287) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_52_26 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (257), (288) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  op(e0, e1) = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (104), (281), (289) are inconsistent by
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #771.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)   ~ (all_58_10 = e1)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (251), (290) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)   ~ (all_52_26 = e1)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_58_3 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (292) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  e2 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (293) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_58_5 = e1 | all_58_10 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_58_5 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (296) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  e3 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (297) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (298) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_58_10 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (299) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_52_26 = e1
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (300) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  $false
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_56_10 = e1 | all_56_10 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (226), (255), (302) are inconsistent by
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #738.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (303)   ~ (all_58_3 = e2)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | REDUCE: (27), (303) imply:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |   (304)   ~ (all_10_2 = e2)
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (77), (185), (234), (240), (304) are inconsistent
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #367.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | |   (305)  all_58_14 = e0
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (224), (305) are inconsistent by sub-proof
% 177.22/27.94  | | | | | | | | | | | | | | | | | |            #696.
% 177.22/27.94  | | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | |   (306)  all_58_8 = e3 | all_58_14 = e3
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (10), (11), (13), (14),
% 177.22/27.94  | | | | | | | | | | | | | | |            (15), (16), (18), (19), (21), (22), (23), (24),
% 177.22/27.94  | | | | | | | | | | | | | | |            (27), (28), (30), (31), (32), (33), (34), (35),
% 177.22/27.94  | | | | | | | | | | | | | | |            (36), (37), (40), (41), (43), (44), (45), (46),
% 177.22/27.94  | | | | | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (55),
% 177.22/27.94  | | | | | | | | | | | | | | |            (56), (57), (58), (60), (65), (66), (67), (68),
% 177.22/27.94  | | | | | | | | | | | | | | |            (70), (71), (72), (75), (78), (79), (80), (81),
% 177.22/27.94  | | | | | | | | | | | | | | |            (82), (83), (85), (86), (87), (88), (89), (90),
% 177.22/27.94  | | | | | | | | | | | | | | |            (91), (93), (94), (95), (96), (99), (102), (103),
% 177.22/27.94  | | | | | | | | | | | | | | |            (104), (106), (107), (110), (113), (114), (115),
% 177.22/27.94  | | | | | | | | | | | | | | |            (116), (117), (121), (122), (123), (124), (126),
% 177.22/27.94  | | | | | | | | | | | | | | |            (128), (131), (133), (135), (137), (140), (147),
% 177.22/27.94  | | | | | | | | | | | | | | |            (187), (306) are inconsistent by sub-proof #383.
% 177.22/27.94  | | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | |   (307)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | | REF_CLOSE: (39), (175), (178), (181), (307) are inconsistent
% 177.22/27.94  | | | | | | | | | | | |            by sub-proof #619.
% 177.22/27.94  | | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | Case 2:
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | |   (308)   ~ (all_58_0 = e2)
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | REDUCE: (48), (308) imply:
% 177.22/27.94  | | | | | | | | |   (309)   ~ (all_4_2 = e2)
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | | REF_CLOSE: (42), (85), (104), (120), (147), (154), (164),
% 177.22/27.94  | | | | | | | | |            (309) are inconsistent by sub-proof #604.
% 177.22/27.94  | | | | | | | | | 
% 177.22/27.94  | | | | | | | | End of split
% 177.22/27.94  | | | | | | | | 
% 177.22/27.94  | | | | | | | End of split
% 177.22/27.94  | | | | | | | 
% 177.22/27.94  | | | | | | End of split
% 177.22/27.94  | | | | | | 
% 177.22/27.94  | | | | | End of split
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | Case 2:
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | |   (310)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | | REF_CLOSE: (1), (4), (6), (8), (10), (11), (13), (16), (18), (19),
% 177.22/27.94  | | | | |            (21), (22), (23), (27), (28), (30), (31), (32), (33), (34),
% 177.22/27.94  | | | | |            (35), (36), (37), (40), (43), (44), (46), (47), (48), (50),
% 177.22/27.94  | | | | |            (51), (52), (55), (56), (57), (58), (60), (65), (67), (68),
% 177.22/27.94  | | | | |            (71), (75), (79), (81), (85), (86), (91), (95), (99),
% 177.22/27.94  | | | | |            (102), (103), (104), (106), (107), (110), (113), (114),
% 177.22/27.94  | | | | |            (115), (117), (123), (124), (128), (133), (135), (137),
% 177.22/27.94  | | | | |            (140), (143), (147), (150), (310) are inconsistent by
% 177.22/27.94  | | | | |            sub-proof #366.
% 177.22/27.94  | | | | | 
% 177.22/27.94  | | | | End of split
% 177.22/27.94  | | | | 
% 177.22/27.94  | | | End of split
% 177.22/27.94  | | | 
% 177.22/27.94  | | End of split
% 177.22/27.94  | | 
% 177.22/27.94  | End of split
% 177.22/27.94  | 
% 177.22/27.94  End of proof
% 177.22/27.94  
% 177.22/27.94  Sub-proof #366 shows that the following formulas are inconsistent:
% 177.22/27.94  ----------------------------------------------------------------
% 177.22/27.94    (1)   ~ (all_52_23 = all_14_2)
% 177.22/27.94    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.94    (3)   ~ (all_52_17 = all_52_23)
% 177.22/27.94    (4)   ~ (all_52_13 = all_52_29)
% 177.22/27.94    (5)  all_56_3 = all_52_7
% 177.22/27.94    (6)  op(e3, e2) = all_52_3
% 177.22/27.94    (7)   ~ (all_52_19 = all_52_23)
% 177.22/27.94    (8)   ~ (all_52_27 = e3)
% 177.22/27.94    (9)   ~ (all_6_2 = e3)
% 177.22/27.94    (10)   ~ (all_52_3 = all_10_2)
% 177.22/27.94    (11)  all_58_5 = all_52_13
% 177.22/27.94    (12)   ~ (all_6_2 = e0)
% 177.22/27.94    (13)  op(e1, all_52_13) = e1
% 177.22/27.94    (14)  op(e0, all_52_15) = e0
% 177.22/27.94    (15)  all_56_15 = all_6_2
% 177.22/27.94    (16)  all_58_3 = all_10_2
% 177.22/27.94    (17)  all_56_9 = all_52_19
% 177.22/27.94    (18)  all_58_15 = all_6_2
% 177.22/27.94    (19)   ~ (all_52_9 = all_4_2)
% 177.22/27.94    (20)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.94    (21)   ~ (all_52_5 = all_52_7)
% 177.22/27.94    (22)  all_58_10 = all_52_15
% 177.22/27.94    (23)   ~ (all_52_5 = all_4_2)
% 177.22/27.94    (24)  all_58_7 = all_52_19
% 177.22/27.94    (25)  all_56_4 = all_52_9
% 177.22/27.94    (26)  all_58_4 = all_52_5
% 177.22/27.94    (27)   ~ (all_52_27 = all_52_29)
% 177.22/27.94    (28)   ~ (all_52_17 = all_14_2)
% 177.22/27.94    (29)   ~ (all_52_7 = all_4_2)
% 177.22/27.94    (30)  all_58_1 = all_52_3
% 177.22/27.94    (31)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.22/27.94    (32)  all_58_0 = all_4_2
% 177.22/27.94    (33)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.22/27.94    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.94    (35)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.94    (36)  all_58_14 = all_52_29
% 177.22/27.94    (37)  op(e0, e3) = e3
% 177.22/27.94    (38)   ~ (all_52_3 = all_52_5)
% 177.22/27.94    (39)  op(e2, e1) = all_52_13
% 177.22/27.94    (40)  all_58_8 = all_14_2
% 177.22/27.94    (41)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.22/27.94    (42)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.94    (43)  op(e3, all_52_17) = all_52_16
% 177.22/27.94    (44)   ~ (all_52_29 = e3)
% 177.22/27.94    (45)  op(e3, all_52_9) = e3
% 177.22/27.94    (46)   ~ (e3 = e0)
% 177.22/27.94    (47)  op(e0, all_52_23) = all_52_22
% 177.22/27.94    (48)   ~ (all_52_15 = e3)
% 177.22/27.94    (49)  all_58_13 = all_52_27
% 177.22/27.94    (50)   ~ (all_52_9 = all_52_17)
% 177.22/27.94    (51)   ~ (all_52_3 = all_52_7)
% 177.22/27.94    (52)  all_56_0 = all_4_2
% 177.22/27.94    (53)  all_58_11 = all_52_23
% 177.22/27.94    (54)   ~ (all_52_23 = all_6_2)
% 177.22/27.94    (55)  op(e3, e1) = all_52_5
% 177.22/27.94    (56)  op(e1, e3) = all_52_17
% 177.22/27.94    (57)  op(e3, e0) = all_52_7
% 177.22/27.94    (58)  op(e2, all_10_2) = e2
% 177.22/27.94    (59)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.94    (60)   ~ (all_52_27 = all_6_2)
% 177.22/27.94    (61)   ~ (all_52_7 = all_6_2)
% 177.22/27.94    (62)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.94    (63)   ~ (all_52_7 = all_52_23)
% 177.22/27.94    (64)   ~ (all_52_17 = all_52_19)
% 177.22/27.94    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.94    (66)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.22/27.94    (67)  all_58_9 = all_52_7
% 177.22/27.94    (68)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.94    (69)   ~ (e3 = e2)
% 177.22/27.94    (70)  op(e2, e3) = all_52_9
% 177.22/27.94  
% 177.22/27.94  Begin of proof
% 177.22/27.94  | 
% 177.22/27.94  | BETA: splitting (42) gives:
% 177.22/27.94  | 
% 177.22/27.94  | Case 1:
% 177.22/27.94  | | 
% 177.22/27.94  | |   (71)  all_58_10 = e3
% 177.22/27.94  | | 
% 177.22/27.94  | | REF_CLOSE: (22), (48), (71) are inconsistent by sub-proof #1018.
% 177.22/27.94  | | 
% 177.22/27.94  | Case 2:
% 177.22/27.94  | | 
% 177.22/27.94  | |   (72)  all_58_11 = e3 | all_58_15 = e3
% 177.22/27.94  | | 
% 177.22/27.94  | | BETA: splitting (72) gives:
% 177.22/27.94  | | 
% 177.22/27.94  | | Case 1:
% 177.22/27.94  | | | 
% 177.22/27.94  | | |   (73)  all_58_11 = e3
% 177.22/27.94  | | | 
% 177.22/27.94  | | | COMBINE_EQS: (53), (73) imply:
% 177.22/27.94  | | |   (74)  all_52_23 = e3
% 177.22/27.94  | | | 
% 177.22/27.94  | | | SIMP: (74) implies:
% 177.22/27.94  | | |   (75)  all_52_23 = e3
% 177.22/27.94  | | | 
% 177.22/27.94  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 177.22/27.94  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.22/27.94  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 177.22/27.94  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (43), (44),
% 177.22/27.94  | | |            (45), (46), (47), (49), (50), (51), (52), (53), (54), (55),
% 177.22/27.94  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 177.22/27.94  | | |            (66), (67), (68), (69), (70), (75) are inconsistent by
% 177.22/27.94  | | |            sub-proof #742.
% 177.22/27.94  | | | 
% 177.22/27.94  | | Case 2:
% 177.22/27.94  | | | 
% 177.22/27.94  | | |   (76)  all_58_15 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | COMBINE_EQS: (18), (76) imply:
% 177.22/27.95  | | |   (77)  all_6_2 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (9), (77) imply:
% 177.22/27.95  | | |   (78)  $false
% 177.22/27.95  | | | 
% 177.22/27.95  | | | CLOSE: (78) is inconsistent.
% 177.22/27.95  | | | 
% 177.22/27.95  | | End of split
% 177.22/27.95  | | 
% 177.22/27.95  | End of split
% 177.22/27.95  | 
% 177.22/27.95  End of proof
% 177.22/27.95  
% 177.22/27.95  Sub-proof #367 shows that the following formulas are inconsistent:
% 177.22/27.95  ----------------------------------------------------------------
% 177.22/27.95    (1)   ~ (all_10_2 = e0)
% 177.22/27.95    (2)   ~ (all_10_2 = e1)
% 177.22/27.95    (3)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.22/27.95    (4)  all_56_5 = all_10_2
% 177.22/27.95    (5)   ~ (all_10_2 = e2)
% 177.22/27.95  
% 177.22/27.95  Begin of proof
% 177.22/27.95  | 
% 177.22/27.95  | BETA: splitting (3) gives:
% 177.22/27.95  | 
% 177.22/27.95  | Case 1:
% 177.22/27.95  | | 
% 177.22/27.95  | |   (6)  all_56_5 = e2
% 177.22/27.95  | | 
% 177.22/27.95  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #710.
% 177.22/27.95  | | 
% 177.22/27.95  | Case 2:
% 177.22/27.95  | | 
% 177.22/27.95  | |   (7)  all_56_5 = e1 | all_56_5 = e0
% 177.22/27.95  | | 
% 177.22/27.95  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #527.
% 177.22/27.95  | | 
% 177.22/27.95  | End of split
% 177.22/27.95  | 
% 177.22/27.95  End of proof
% 177.22/27.95  
% 177.22/27.95  Sub-proof #368 shows that the following formulas are inconsistent:
% 177.22/27.95  ----------------------------------------------------------------
% 177.22/27.95    (1)   ~ (all_52_25 = e3)
% 177.22/27.95    (2)   ~ (all_52_5 = all_52_13)
% 177.22/27.95    (3)   ~ (all_52_13 = all_52_29)
% 177.22/27.95    (4)  op(e3, e2) = all_52_3
% 177.22/27.95    (5)   ~ (all_52_3 = all_10_2)
% 177.22/27.95    (6)  all_58_5 = all_52_13
% 177.22/27.95    (7)  op(e1, all_52_13) = e1
% 177.22/27.95    (8)  all_58_3 = all_10_2
% 177.22/27.95    (9)   ~ (all_52_9 = all_4_2)
% 177.22/27.95    (10)  all_58_10 = all_52_15
% 177.22/27.95    (11)  all_58_4 = all_52_5
% 177.22/27.95    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.95    (13)   ~ (e3 = e1)
% 177.22/27.95    (14)   ~ (all_52_17 = all_14_2)
% 177.22/27.95    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.22/27.95    (16)  all_58_0 = all_4_2
% 177.22/27.95    (17)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.95    (18)  all_58_14 = all_52_29
% 177.22/27.95    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.95    (20)  all_58_8 = all_14_2
% 177.22/27.95    (21)  op(e1, all_14_2) = e3
% 177.22/27.95    (22)  op(e3, all_52_9) = e3
% 177.22/27.95    (23)   ~ (all_52_15 = e3)
% 177.22/27.95    (24)  all_58_6 = all_52_17
% 177.22/27.95    (25)  all_58_2 = all_52_9
% 177.22/27.95    (26)  op(e1, e3) = all_52_17
% 177.22/27.95    (27)  op(e2, all_10_2) = e2
% 177.22/27.95    (28)  op(e3, e3) = all_4_2
% 177.22/27.95    (29)   ~ (all_52_17 = all_4_2)
% 177.22/27.95    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.95    (31)  all_58_12 = all_52_25
% 177.22/27.95    (32)  op(e3, all_4_2) = e1
% 177.22/27.95    (33)  all_56_6 = all_52_13
% 177.22/27.95    (34)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.95    (35)  op(e2, e3) = all_52_9
% 177.22/27.95  
% 177.22/27.95  Begin of proof
% 177.22/27.95  | 
% 177.22/27.95  | BETA: splitting (17) gives:
% 177.22/27.95  | 
% 177.22/27.95  | Case 1:
% 177.22/27.95  | | 
% 177.22/27.95  | |   (36)  all_56_6 = e3
% 177.22/27.95  | | 
% 177.22/27.95  | | COMBINE_EQS: (33), (36) imply:
% 177.22/27.95  | |   (37)  all_52_13 = e3
% 177.22/27.95  | | 
% 177.22/27.95  | | SIMP: (37) implies:
% 177.22/27.95  | |   (38)  all_52_13 = e3
% 177.22/27.95  | | 
% 177.22/27.95  | | REDUCE: (2), (38) imply:
% 177.22/27.95  | |   (39)   ~ (all_52_5 = e3)
% 177.22/27.95  | | 
% 177.22/27.95  | | REDUCE: (3), (38) imply:
% 177.22/27.95  | |   (40)   ~ (all_52_29 = e3)
% 177.22/27.95  | | 
% 177.22/27.95  | | SIMP: (40) implies:
% 177.22/27.95  | |   (41)   ~ (all_52_29 = e3)
% 177.22/27.95  | | 
% 177.22/27.95  | | REDUCE: (7), (38) imply:
% 177.22/27.95  | |   (42)  op(e1, e3) = e1
% 177.22/27.95  | | 
% 177.22/27.95  | | GROUND_INST: instantiating (30) with all_52_17, e1, e3, e1, simplifying with
% 177.22/27.95  | |              (26), (42) gives:
% 177.22/27.95  | |   (43)  all_52_17 = e1
% 177.22/27.95  | | 
% 177.22/27.95  | | REDUCE: (29), (43) imply:
% 177.22/27.95  | |   (44)   ~ (all_4_2 = e1)
% 177.22/27.95  | | 
% 177.22/27.95  | | SIMP: (44) implies:
% 177.22/27.95  | |   (45)   ~ (all_4_2 = e1)
% 177.22/27.95  | | 
% 177.22/27.95  | | BETA: splitting (19) gives:
% 177.22/27.95  | | 
% 177.22/27.95  | | Case 1:
% 177.22/27.95  | | | 
% 177.22/27.95  | | |   (46)  all_58_0 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | COMBINE_EQS: (16), (46) imply:
% 177.22/27.95  | | |   (47)  all_4_2 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REF_CLOSE: (13), (28), (30), (32), (47) are inconsistent by sub-proof
% 177.22/27.95  | | |            #630.
% 177.22/27.95  | | | 
% 177.22/27.95  | | Case 2:
% 177.22/27.95  | | | 
% 177.22/27.95  | | |   (48)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | BETA: splitting (34) gives:
% 177.22/27.95  | | | 
% 177.22/27.95  | | | Case 1:
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | |   (49)  all_58_4 = e3
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | REF_CLOSE: (11), (39), (49) are inconsistent by sub-proof #1025.
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | Case 2:
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | |   (50)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | REF_CLOSE: (1), (6), (7), (9), (12), (13), (14), (18), (20), (21), (22),
% 177.22/27.95  | | | |            (24), (25), (26), (28), (30), (31), (41), (48), (50) are
% 177.22/27.95  | | | |            inconsistent by sub-proof #395.
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | End of split
% 177.22/27.95  | | | 
% 177.22/27.95  | | End of split
% 177.22/27.95  | | 
% 177.22/27.95  | Case 2:
% 177.22/27.95  | | 
% 177.22/27.95  | |   (51)   ~ (all_56_6 = e3)
% 177.22/27.95  | | 
% 177.22/27.95  | | REDUCE: (33), (51) imply:
% 177.22/27.95  | |   (52)   ~ (all_52_13 = e3)
% 177.22/27.95  | | 
% 177.22/27.95  | | REF_CLOSE: (4), (5), (6), (8), (9), (10), (15), (22), (23), (25), (27),
% 177.22/27.95  | |            (28), (30), (35), (52) are inconsistent by sub-proof #772.
% 177.22/27.95  | | 
% 177.22/27.95  | End of split
% 177.22/27.95  | 
% 177.22/27.95  End of proof
% 177.22/27.95  
% 177.22/27.95  Sub-proof #369 shows that the following formulas are inconsistent:
% 177.22/27.95  ----------------------------------------------------------------
% 177.22/27.95    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.95    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.95    (3)   ~ (all_52_17 = all_52_23)
% 177.22/27.95    (4)  all_52_26 = e2
% 177.22/27.95    (5)   ~ (all_6_0 = e3)
% 177.22/27.95    (6)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.95    (7)  op(e3, e2) = all_52_3
% 177.22/27.95    (8)   ~ (all_52_9 = all_52_25)
% 177.22/27.95    (9)  op(e3, all_52_25) = all_52_24
% 177.22/27.95    (10)   ~ (all_52_19 = all_52_23)
% 177.22/27.95    (11)  all_56_11 = all_52_23
% 177.22/27.95    (12)  op(e1, e2) = all_52_19
% 177.22/27.95    (13)  op(e3, all_52_9) = all_52_8
% 177.22/27.95    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.95    (15)  all_58_5 = all_52_13
% 177.22/27.95    (16)   ~ (all_6_2 = e0)
% 177.22/27.95    (17)   ~ (all_52_25 = all_52_29)
% 177.22/27.95    (18)  all_56_15 = all_6_2
% 177.22/27.95    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.95    (20)  all_6_1 = e0
% 177.22/27.95    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.95    (22)  all_58_3 = all_10_2
% 177.22/27.95    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.95    (24)  all_58_15 = all_6_2
% 177.22/27.95    (25)   ~ (all_52_9 = all_4_2)
% 177.22/27.95    (26)   ~ (all_52_5 = all_52_7)
% 177.22/27.95    (27)  all_58_10 = all_52_15
% 177.22/27.95    (28)   ~ (all_52_5 = all_4_2)
% 177.22/27.95    (29)  all_58_7 = all_52_19
% 177.22/27.95    (30)   ~ (all_52_17 = all_52_25)
% 177.22/27.95    (31)  op(e0, e1) = all_52_29
% 177.22/27.95    (32)   ~ (all_4_0 = e2)
% 177.22/27.95    (33)  all_58_4 = all_52_5
% 177.22/27.95    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.95    (35)   ~ (e3 = e1)
% 177.22/27.95    (36)   ~ (all_52_27 = all_52_29)
% 177.22/27.95    (37)   ~ (all_52_17 = all_14_2)
% 177.22/27.95    (38)  op(e3, all_4_2) = all_4_1
% 177.22/27.95    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.95    (40)   ~ (all_52_7 = all_4_2)
% 177.22/27.95    (41)  all_58_1 = all_52_3
% 177.22/27.95    (42)   ~ (all_52_13 = all_52_15)
% 177.22/27.95    (43)  all_58_0 = all_4_2
% 177.22/27.95    (44)  op(e1, all_52_29) = all_52_28
% 177.22/27.95    (45)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.95    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.95    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.95    (48)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.95    (49)  all_58_14 = all_52_29
% 177.22/27.95    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.95    (51)   ~ (all_52_3 = all_52_5)
% 177.22/27.95    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.95    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.95    (54)  all_58_8 = all_14_2
% 177.22/27.95    (55)  op(e0, e2) = all_52_27
% 177.22/27.95    (56)  all_56_14 = all_52_29
% 177.22/27.95    (57)  op(e1, all_14_2) = e3
% 177.22/27.95    (58)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.95    (59)   ~ (all_52_3 = all_52_27)
% 177.22/27.95    (60)   ~ (all_52_3 = all_4_2)
% 177.22/27.95    (61)  op(all_6_1, all_6_2) = all_6_0
% 177.22/27.95    (62)  op(e0, e3) = all_52_25
% 177.22/27.95    (63)  op(e0, all_6_2) = all_6_1
% 177.22/27.95    (64)   ~ (all_52_9 = all_10_2)
% 177.22/27.95    (65)  op(e3, all_52_17) = all_52_16
% 177.22/27.95    (66)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.95    (67)   ~ (all_52_13 = all_14_2)
% 177.22/27.95    (68)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.95    (69)   ~ (all_52_9 = all_52_13)
% 177.22/27.95    (70)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.95    (71)   ~ (all_52_5 = all_52_29)
% 177.22/27.95    (72)  all_56_2 = all_52_5
% 177.22/27.95    (73)  all_56_12 = all_52_25
% 177.22/27.95    (74)  all_58_13 = all_52_27
% 177.22/27.95    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.95    (76)   ~ (all_52_9 = all_52_17)
% 177.22/27.95    (77)  all_58_6 = all_52_17
% 177.22/27.95    (78)   ~ (all_52_3 = all_52_7)
% 177.22/27.95    (79)  all_56_0 = all_4_2
% 177.22/27.95    (80)  all_58_11 = all_52_23
% 177.22/27.95    (81)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.95    (82)   ~ (all_52_29 = all_14_2)
% 177.22/27.95    (83)   ~ (all_4_0 = e1)
% 177.22/27.95    (84)   ~ (all_52_19 = all_10_2)
% 177.22/27.95    (85)   ~ (all_6_0 = e2)
% 177.22/27.95    (86)   ~ (all_52_29 = all_6_2)
% 177.22/27.95    (87)  all_58_2 = all_52_9
% 177.22/27.95    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.95    (89)  op(e3, e1) = all_52_5
% 177.22/27.95    (90)   ~ (all_52_25 = all_6_2)
% 177.22/27.95    (91)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.95    (92)  op(e1, e1) = all_14_2
% 177.22/27.95    (93)  op(e1, e3) = all_52_17
% 177.22/27.95    (94)   ~ (all_52_25 = all_4_2)
% 177.22/27.95    (95)  op(e3, e0) = all_52_7
% 177.22/27.95    (96)  all_52_28 = e1
% 177.22/27.95    (97)  op(e3, e3) = all_4_2
% 177.22/27.95    (98)   ~ (all_52_17 = all_4_2)
% 177.22/27.95    (99)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.95    (100)   ~ (all_52_25 = all_52_27)
% 177.22/27.95    (101)   ~ (all_52_27 = all_6_2)
% 177.22/27.95    (102)   ~ (all_52_7 = all_6_2)
% 177.22/27.95    (103)   ~ (all_52_15 = all_10_2)
% 177.22/27.95    (104)   ~ (all_52_19 = all_52_27)
% 177.22/27.95    (105)   ~ (all_52_7 = all_52_23)
% 177.22/27.95    (106)   ~ (all_6_0 = e1)
% 177.22/27.95    (107)  op(e2, all_52_27) = all_52_26
% 177.22/27.95    (108)   ~ (all_52_17 = all_52_19)
% 177.22/27.95    (109)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.95    (110)  all_58_9 = all_52_7
% 177.22/27.95    (111)  all_52_24 = e3
% 177.22/27.95    (112)  all_58_12 = all_52_25
% 177.22/27.95    (113)  all_56_6 = all_52_13
% 177.22/27.95    (114)   ~ (all_52_9 = all_52_15)
% 177.22/27.95    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.95    (116)   ~ (e3 = e2)
% 177.22/27.95    (117)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.95    (118)  op(e2, e3) = all_52_9
% 177.22/27.95    (119)  all_56_13 = all_52_27
% 177.22/27.95  
% 177.22/27.95  Begin of proof
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (20), (61) imply:
% 177.22/27.95  |   (120)  op(e0, all_6_2) = all_6_0
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (9), (111) imply:
% 177.22/27.95  |   (121)  op(e3, all_52_25) = e3
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (4), (107) imply:
% 177.22/27.95  |   (122)  op(e2, all_52_27) = e2
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (44), (96) imply:
% 177.22/27.95  |   (123)  op(e1, all_52_29) = e1
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (20), (63) imply:
% 177.22/27.95  |   (124)  op(e0, all_6_2) = e0
% 177.22/27.95  | 
% 177.22/27.95  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 177.22/27.95  |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 177.22/27.95  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.22/27.95  |            (38), (39), (40), (41), (42), (43), (45), (46), (47), (48), (49),
% 177.22/27.95  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 177.22/27.95  |            (62), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 177.22/27.95  |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 177.22/27.95  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 177.22/27.95  |            (97), (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 177.22/27.95  |            (108), (109), (110), (112), (113), (114), (115), (116), (117),
% 177.22/27.95  |            (118), (119), (120), (121), (122), (123), (124) are inconsistent by
% 177.22/27.95  |            sub-proof #370.
% 177.22/27.95  | 
% 177.22/27.95  End of proof
% 177.22/27.95  
% 177.22/27.95  Sub-proof #370 shows that the following formulas are inconsistent:
% 177.22/27.95  ----------------------------------------------------------------
% 177.22/27.95    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.22/27.95    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.22/27.95    (3)   ~ (all_52_17 = all_52_23)
% 177.22/27.95    (4)   ~ (all_6_0 = e3)
% 177.22/27.95    (5)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.95    (6)  op(e3, e2) = all_52_3
% 177.22/27.95    (7)   ~ (all_52_9 = all_52_25)
% 177.22/27.95    (8)   ~ (all_52_19 = all_52_23)
% 177.22/27.95    (9)  all_56_11 = all_52_23
% 177.22/27.95    (10)  op(e1, e2) = all_52_19
% 177.22/27.95    (11)  op(e3, all_52_9) = all_52_8
% 177.22/27.95    (12)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.95    (13)  all_58_5 = all_52_13
% 177.22/27.95    (14)   ~ (all_6_2 = e0)
% 177.22/27.95    (15)   ~ (all_52_25 = all_52_29)
% 177.22/27.95    (16)  all_56_15 = all_6_2
% 177.22/27.95    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.22/27.95    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.95    (19)  all_58_3 = all_10_2
% 177.22/27.95    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.95    (21)  all_58_15 = all_6_2
% 177.22/27.95    (22)  op(e0, all_6_2) = e0
% 177.22/27.95    (23)   ~ (all_52_9 = all_4_2)
% 177.22/27.95    (24)   ~ (all_52_5 = all_52_7)
% 177.22/27.95    (25)  all_58_10 = all_52_15
% 177.22/27.95    (26)   ~ (all_52_5 = all_4_2)
% 177.22/27.95    (27)  all_58_7 = all_52_19
% 177.22/27.95    (28)   ~ (all_52_17 = all_52_25)
% 177.22/27.95    (29)  op(e0, e1) = all_52_29
% 177.22/27.95    (30)   ~ (all_4_0 = e2)
% 177.22/27.95    (31)  all_58_4 = all_52_5
% 177.22/27.95    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.95    (33)   ~ (e3 = e1)
% 177.22/27.95    (34)   ~ (all_52_27 = all_52_29)
% 177.22/27.95    (35)   ~ (all_52_17 = all_14_2)
% 177.22/27.95    (36)  op(e3, all_4_2) = all_4_1
% 177.22/27.95    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.95    (38)   ~ (all_52_7 = all_4_2)
% 177.22/27.95    (39)  all_58_1 = all_52_3
% 177.22/27.95    (40)   ~ (all_52_13 = all_52_15)
% 177.22/27.95    (41)  all_58_0 = all_4_2
% 177.22/27.95    (42)  op(e2, all_52_27) = e2
% 177.22/27.95    (43)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.95    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.95    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.95    (46)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.22/27.95    (47)  all_58_14 = all_52_29
% 177.22/27.95    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.95    (49)   ~ (all_52_3 = all_52_5)
% 177.22/27.95    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.95    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.95    (52)  all_58_8 = all_14_2
% 177.22/27.95    (53)  op(e0, e2) = all_52_27
% 177.22/27.95    (54)  all_56_14 = all_52_29
% 177.22/27.95    (55)  op(e1, all_14_2) = e3
% 177.22/27.95    (56)  op(e1, all_52_29) = e1
% 177.22/27.95    (57)  op(all_4_1, all_4_2) = all_4_0
% 177.22/27.95    (58)   ~ (all_52_3 = all_52_27)
% 177.22/27.95    (59)   ~ (all_52_3 = all_4_2)
% 177.22/27.95    (60)  op(e0, e3) = all_52_25
% 177.22/27.95    (61)   ~ (all_52_9 = all_10_2)
% 177.22/27.95    (62)  op(e3, all_52_17) = all_52_16
% 177.22/27.95    (63)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.95    (64)   ~ (all_52_13 = all_14_2)
% 177.22/27.95    (65)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.95    (66)   ~ (all_52_9 = all_52_13)
% 177.22/27.95    (67)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.95    (68)   ~ (all_52_5 = all_52_29)
% 177.22/27.95    (69)  all_56_2 = all_52_5
% 177.22/27.95    (70)  all_56_12 = all_52_25
% 177.22/27.95    (71)  all_58_13 = all_52_27
% 177.22/27.95    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.22/27.95    (73)   ~ (all_52_9 = all_52_17)
% 177.22/27.95    (74)  all_58_6 = all_52_17
% 177.22/27.95    (75)   ~ (all_52_3 = all_52_7)
% 177.22/27.95    (76)  all_56_0 = all_4_2
% 177.22/27.95    (77)  all_58_11 = all_52_23
% 177.22/27.95    (78)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.95    (79)   ~ (all_52_29 = all_14_2)
% 177.22/27.95    (80)  op(e3, all_52_25) = e3
% 177.22/27.95    (81)   ~ (all_4_0 = e1)
% 177.22/27.95    (82)   ~ (all_52_19 = all_10_2)
% 177.22/27.95    (83)   ~ (all_6_0 = e2)
% 177.22/27.95    (84)   ~ (all_52_29 = all_6_2)
% 177.22/27.95    (85)  all_58_2 = all_52_9
% 177.22/27.95    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.22/27.95    (87)  op(e3, e1) = all_52_5
% 177.22/27.95    (88)   ~ (all_52_25 = all_6_2)
% 177.22/27.95    (89)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.22/27.95    (90)  op(e1, e1) = all_14_2
% 177.22/27.95    (91)  op(e1, e3) = all_52_17
% 177.22/27.95    (92)   ~ (all_52_25 = all_4_2)
% 177.22/27.95    (93)  op(e3, e0) = all_52_7
% 177.22/27.95    (94)  op(e3, e3) = all_4_2
% 177.22/27.95    (95)   ~ (all_52_17 = all_4_2)
% 177.22/27.95    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.95    (97)   ~ (all_52_25 = all_52_27)
% 177.22/27.95    (98)  op(e0, all_6_2) = all_6_0
% 177.22/27.95    (99)   ~ (all_52_27 = all_6_2)
% 177.22/27.95    (100)   ~ (all_52_7 = all_6_2)
% 177.22/27.95    (101)   ~ (all_52_15 = all_10_2)
% 177.22/27.95    (102)   ~ (all_52_19 = all_52_27)
% 177.22/27.95    (103)   ~ (all_52_7 = all_52_23)
% 177.22/27.95    (104)   ~ (all_6_0 = e1)
% 177.22/27.95    (105)   ~ (all_52_17 = all_52_19)
% 177.22/27.95    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.95    (107)  all_58_9 = all_52_7
% 177.22/27.95    (108)  all_58_12 = all_52_25
% 177.22/27.95    (109)  all_56_6 = all_52_13
% 177.22/27.95    (110)   ~ (all_52_9 = all_52_15)
% 177.22/27.95    (111)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.95    (112)   ~ (e3 = e2)
% 177.22/27.95    (113)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.95    (114)  op(e2, e3) = all_52_9
% 177.22/27.95    (115)  all_56_13 = all_52_27
% 177.22/27.95  
% 177.22/27.95  Begin of proof
% 177.22/27.95  | 
% 177.22/27.95  | GROUND_INST: instantiating (96) with e0, all_6_0, all_6_2, e0, simplifying
% 177.22/27.95  |              with (22), (98) gives:
% 177.22/27.95  |   (116)  all_6_0 = e0
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (4), (116) imply:
% 177.22/27.95  |   (117)   ~ (e3 = e0)
% 177.22/27.95  | 
% 177.22/27.95  | SIMP: (117) implies:
% 177.22/27.95  |   (118)   ~ (e3 = e0)
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (83), (116) imply:
% 177.22/27.95  |   (119)   ~ (e2 = e0)
% 177.22/27.95  | 
% 177.22/27.95  | SIMP: (119) implies:
% 177.22/27.95  |   (120)   ~ (e2 = e0)
% 177.22/27.95  | 
% 177.22/27.95  | REDUCE: (104), (116) imply:
% 177.22/27.95  |   (121)   ~ (e1 = e0)
% 177.22/27.95  | 
% 177.22/27.95  | SIMP: (121) implies:
% 177.22/27.95  |   (122)   ~ (e1 = e0)
% 177.22/27.95  | 
% 177.22/27.95  | BETA: splitting (37) gives:
% 177.22/27.95  | 
% 177.22/27.95  | Case 1:
% 177.22/27.95  | | 
% 177.22/27.95  | |   (123)  all_56_15 = e3
% 177.22/27.95  | | 
% 177.22/27.95  | | COMBINE_EQS: (16), (123) imply:
% 177.22/27.95  | |   (124)  all_6_2 = e3
% 177.22/27.95  | | 
% 177.22/27.95  | | SIMP: (124) implies:
% 177.22/27.95  | |   (125)  all_6_2 = e3
% 177.22/27.95  | | 
% 177.22/27.95  | | REF_CLOSE: (22), (60), (80), (93), (96), (100), (125) are inconsistent by
% 177.22/27.95  | |            sub-proof #665.
% 177.22/27.95  | | 
% 177.22/27.95  | Case 2:
% 177.22/27.95  | | 
% 177.22/27.95  | |   (126)   ~ (all_56_15 = e3)
% 177.22/27.95  | |   (127)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.95  | | 
% 177.22/27.95  | | REDUCE: (16), (126) imply:
% 177.22/27.95  | |   (128)   ~ (all_6_2 = e3)
% 177.22/27.95  | | 
% 177.22/27.95  | | BETA: splitting (48) gives:
% 177.22/27.95  | | 
% 177.22/27.95  | | Case 1:
% 177.22/27.95  | | | 
% 177.22/27.95  | | |   (129)  all_56_13 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | COMBINE_EQS: (115), (129) imply:
% 177.22/27.95  | | |   (130)  all_52_27 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (130) implies:
% 177.22/27.95  | | |   (131)  all_52_27 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | COMBINE_EQS: (71), (131) imply:
% 177.22/27.95  | | |   (132)  all_58_13 = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (58), (131) imply:
% 177.22/27.95  | | |   (133)   ~ (all_52_3 = e3)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (102), (131) imply:
% 177.22/27.95  | | |   (134)   ~ (all_52_19 = e3)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (97), (131) imply:
% 177.22/27.95  | | |   (135)   ~ (all_52_25 = e3)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (34), (131) imply:
% 177.22/27.95  | | |   (136)   ~ (all_52_29 = e3)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (136) implies:
% 177.22/27.95  | | |   (137)   ~ (all_52_29 = e3)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (42), (131) imply:
% 177.22/27.95  | | |   (138)  op(e2, e3) = e2
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (53), (131) imply:
% 177.22/27.95  | | |   (139)  op(e0, e2) = e3
% 177.22/27.95  | | | 
% 177.22/27.95  | | | GROUND_INST: instantiating (96) with all_52_9, e2, e3, e2, simplifying
% 177.22/27.95  | | |              with (114), (138) gives:
% 177.22/27.95  | | |   (140)  all_52_9 = e2
% 177.22/27.95  | | | 
% 177.22/27.95  | | | COMBINE_EQS: (85), (140) imply:
% 177.22/27.95  | | |   (141)  all_58_2 = e2
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (66), (140) imply:
% 177.22/27.95  | | |   (142)   ~ (all_52_13 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (142) implies:
% 177.22/27.95  | | |   (143)   ~ (all_52_13 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (110), (140) imply:
% 177.22/27.95  | | |   (144)   ~ (all_52_15 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (144) implies:
% 177.22/27.95  | | |   (145)   ~ (all_52_15 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (7), (140) imply:
% 177.22/27.95  | | |   (146)   ~ (all_52_25 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (146) implies:
% 177.22/27.95  | | |   (147)   ~ (all_52_25 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (61), (140) imply:
% 177.22/27.95  | | |   (148)   ~ (all_10_2 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (148) implies:
% 177.22/27.95  | | |   (149)   ~ (all_10_2 = e2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (11), (140) imply:
% 177.22/27.95  | | |   (150)  op(e3, e2) = all_52_8
% 177.22/27.95  | | | 
% 177.22/27.95  | | | GROUND_INST: instantiating (96) with all_52_3, all_52_8, e2, e3,
% 177.22/27.95  | | |              simplifying with (6), (150) gives:
% 177.22/27.95  | | |   (151)  all_52_3 = all_52_8
% 177.22/27.95  | | | 
% 177.22/27.95  | | | COMBINE_EQS: (39), (151) imply:
% 177.22/27.95  | | |   (152)  all_58_1 = all_52_8
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (49), (151) imply:
% 177.22/27.95  | | |   (153)   ~ (all_52_5 = all_52_8)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (153) implies:
% 177.22/27.95  | | |   (154)   ~ (all_52_5 = all_52_8)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (75), (151) imply:
% 177.22/27.95  | | |   (155)   ~ (all_52_7 = all_52_8)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | SIMP: (155) implies:
% 177.22/27.95  | | |   (156)   ~ (all_52_7 = all_52_8)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (59), (151) imply:
% 177.22/27.95  | | |   (157)   ~ (all_52_8 = all_4_2)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | REDUCE: (133), (151) imply:
% 177.22/27.95  | | |   (158)   ~ (all_52_8 = e3)
% 177.22/27.95  | | | 
% 177.22/27.95  | | | BETA: splitting (12) gives:
% 177.22/27.95  | | | 
% 177.22/27.95  | | | Case 1:
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | |   (159)  all_58_1 = e2
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | COMBINE_EQS: (152), (159) imply:
% 177.22/27.95  | | | |   (160)  all_52_8 = e2
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | REDUCE: (154), (160) imply:
% 177.22/27.95  | | | |   (161)   ~ (all_52_5 = e2)
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | REDUCE: (156), (160) imply:
% 177.22/27.95  | | | |   (162)   ~ (all_52_7 = e2)
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | REDUCE: (157), (160) imply:
% 177.22/27.95  | | | |   (163)   ~ (all_4_2 = e2)
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | SIMP: (163) implies:
% 177.22/27.95  | | | |   (164)   ~ (all_4_2 = e2)
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | REDUCE: (158), (160) imply:
% 177.22/27.95  | | | |   (165)   ~ (e3 = e2)
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | BETA: splitting (50) gives:
% 177.22/27.95  | | | | 
% 177.22/27.95  | | | | Case 1:
% 177.22/27.95  | | | | | 
% 177.22/27.95  | | | | |   (166)  all_58_0 = e3
% 177.22/27.95  | | | | | 
% 177.22/27.95  | | | | | COMBINE_EQS: (41), (166) imply:
% 177.22/27.95  | | | | |   (167)  all_4_2 = e3
% 177.22/27.95  | | | | | 
% 177.22/27.95  | | | | | REDUCE: (26), (167) imply:
% 177.22/27.95  | | | | |   (168)   ~ (all_52_5 = e3)
% 177.22/27.95  | | | | | 
% 177.22/27.95  | | | | | REDUCE: (95), (167) imply:
% 177.22/27.95  | | | | |   (169)   ~ (all_52_17 = e3)
% 177.22/27.95  | | | | | 
% 177.22/27.95  | | | | | BETA: splitting (63) gives:
% 177.22/27.95  | | | | | 
% 177.22/27.95  | | | | | Case 1:
% 177.22/27.95  | | | | | | 
% 177.22/27.95  | | | | | |   (170)  all_58_9 = e2
% 177.22/27.95  | | | | | | 
% 177.22/27.95  | | | | | | REF_CLOSE: (107), (162), (170) are inconsistent by sub-proof #664.
% 177.22/27.95  | | | | | | 
% 177.22/27.95  | | | | | Case 2:
% 177.22/27.95  | | | | | | 
% 177.22/27.95  | | | | | |   (171)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.22/27.95  | | | | | | 
% 177.22/27.95  | | | | | | BETA: splitting (32) gives:
% 177.22/27.95  | | | | | | 
% 177.22/27.95  | | | | | | Case 1:
% 177.22/27.95  | | | | | | | 
% 177.22/27.95  | | | | | | |   (172)  all_58_6 = e3
% 177.22/27.95  | | | | | | | 
% 177.22/27.95  | | | | | | | REF_CLOSE: (74), (169), (172) are inconsistent by sub-proof #981.
% 177.22/27.95  | | | | | | | 
% 177.22/27.95  | | | | | | Case 2:
% 177.22/27.95  | | | | | | | 
% 177.22/27.95  | | | | | | |   (173)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.22/27.95  | | | | | | | 
% 177.22/27.95  | | | | | | | BETA: splitting (111) gives:
% 177.22/27.95  | | | | | | | 
% 177.22/27.95  | | | | | | | Case 1:
% 177.22/27.95  | | | | | | | | 
% 177.22/27.95  | | | | | | | |   (174)  all_58_4 = e3
% 177.22/27.95  | | | | | | | | 
% 177.22/27.95  | | | | | | | | REF_CLOSE: (31), (168), (174) are inconsistent by sub-proof
% 177.22/27.95  | | | | | | | |            #1025.
% 177.22/27.95  | | | | | | | | 
% 177.22/27.95  | | | | | | | Case 2:
% 177.22/27.95  | | | | | | | | 
% 177.22/27.95  | | | | | | | |   (175)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.22/27.95  | | | | | | | | 
% 177.22/27.95  | | | | | | | | BETA: splitting (46) gives:
% 177.22/27.95  | | | | | | | | 
% 177.22/27.95  | | | | | | | | Case 1:
% 177.22/27.95  | | | | | | | | | 
% 177.22/27.95  | | | | | | | | |   (176)  all_56_6 = e3
% 177.22/27.95  | | | | | | | | | 
% 177.22/27.95  | | | | | | | | | COMBINE_EQS: (109), (176) imply:
% 177.22/27.95  | | | | | | | | |   (177)  all_52_13 = e3
% 177.22/27.95  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REF_CLOSE: (21), (22), (25), (27), (52), (64), (96), (118),
% 177.22/27.96  | | | | | | | | |            (134), (139), (143), (145), (171), (173), (177) are
% 177.22/27.96  | | | | | | | | |            inconsistent by sub-proof #661.
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | |   (178)   ~ (all_56_6 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (109), (178) imply:
% 177.22/27.96  | | | | | | | | |   (179)   ~ (all_52_13 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REF_CLOSE: (13), (35), (47), (52), (55), (91), (96), (137),
% 177.22/27.96  | | | | | | | | |            (175), (179) are inconsistent by sub-proof #420.
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | End of split
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | End of split
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | End of split
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | Case 2:
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | |   (180)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | | BETA: splitting (180) gives:
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | | Case 1:
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | |   (181)  all_58_2 = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | COMBINE_EQS: (141), (181) imply:
% 177.22/27.96  | | | | | |   (182)  e3 = e2
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (112), (182) imply:
% 177.22/27.96  | | | | | |   (183)  $false
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | CLOSE: (183) is inconsistent.
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | Case 2:
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | |   (184)  all_58_6 = e3 | all_58_12 = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | BETA: splitting (184) gives:
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | Case 1:
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | |   (185)  all_58_6 = e3
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | COMBINE_EQS: (74), (185) imply:
% 177.22/27.96  | | | | | | |   (186)  all_52_17 = e3
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | SIMP: (186) implies:
% 177.22/27.96  | | | | | | |   (187)  all_52_17 = e3
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | REDUCE: (105), (187) imply:
% 177.22/27.96  | | | | | | |   (188)   ~ (all_52_19 = e3)
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | REDUCE: (95), (187) imply:
% 177.22/27.96  | | | | | | |   (189)   ~ (all_4_2 = e3)
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | SIMP: (189) implies:
% 177.22/27.96  | | | | | | |   (190)   ~ (all_4_2 = e3)
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | BETA: splitting (20) gives:
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | |   (191)  all_56_0 = e3
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REF_CLOSE: (76), (190), (191) are inconsistent by sub-proof
% 177.22/27.96  | | | | | | | |            #1024.
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | |   (192)   ~ (all_56_0 = e3)
% 177.22/27.96  | | | | | | | |   (193)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | BETA: splitting (78) gives:
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | |   (194)  all_58_4 = e2
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REF_CLOSE: (31), (161), (194) are inconsistent by sub-proof
% 177.22/27.96  | | | | | | | | |            #675.
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | |   (195)   ~ (all_58_4 = e2)
% 177.22/27.96  | | | | | | | | |   (196)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | BETA: splitting (72) gives:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | |   (197)  all_58_0 = e1
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | COMBINE_EQS: (41), (197) imply:
% 177.22/27.96  | | | | | | | | | |   (198)  all_4_2 = e1
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REDUCE: (26), (198) imply:
% 177.22/27.96  | | | | | | | | | |   (199)   ~ (all_52_5 = e1)
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REDUCE: (57), (198) imply:
% 177.22/27.96  | | | | | | | | | |   (200)  op(all_4_1, e1) = all_4_0
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REDUCE: (36), (198) imply:
% 177.22/27.96  | | | | | | | | | |   (201)  op(e3, e1) = all_4_1
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | BETA: splitting (65) gives:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | |   (202)  all_58_0 = e0
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | COMBINE_EQS: (197), (202) imply:
% 177.22/27.96  | | | | | | | | | | |   (203)  e1 = e0
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | REDUCE: (122), (203) imply:
% 177.22/27.96  | | | | | | | | | | |   (204)  $false
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | |   (205)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | BETA: splitting (205) gives:
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | |   (206)  all_58_2 = e0
% 177.22/27.96  | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | REF_CLOSE: (120), (141), (206) are inconsistent by sub-proof
% 177.22/27.96  | | | | | | | | | | | |            #909.
% 177.22/27.96  | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | |   (207)  all_58_6 = e0 | all_58_12 = e0
% 177.22/27.96  | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | BETA: splitting (207) gives:
% 177.22/27.96  | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | |   (208)  all_58_6 = e0
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | REF_CLOSE: (118), (185), (208) are inconsistent by sub-proof
% 177.22/27.96  | | | | | | | | | | | | |            #559.
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | |   (209)  all_58_12 = e0
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | COMBINE_EQS: (108), (209) imply:
% 177.22/27.96  | | | | | | | | | | | | |   (210)  all_52_25 = e0
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | SIMP: (210) implies:
% 177.22/27.96  | | | | | | | | | | | | |   (211)  all_52_25 = e0
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | REDUCE: (80), (211) imply:
% 177.22/27.96  | | | | | | | | | | | | |   (212)  op(e3, e0) = e3
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | GROUND_INST: instantiating (96) with all_52_7, e3, e0, e3,
% 177.22/27.96  | | | | | | | | | | | | |              simplifying with (93), (212) gives:
% 177.22/27.96  | | | | | | | | | | | | |   (213)  all_52_7 = e3
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | GROUND_INST: instantiating (96) with all_52_5, all_4_1, e1, e3,
% 177.22/27.96  | | | | | | | | | | | | |              simplifying with (87), (201) gives:
% 177.22/27.96  | | | | | | | | | | | | |   (214)  all_52_5 = all_4_1
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | COMBINE_EQS: (69), (214) imply:
% 177.22/27.96  | | | | | | | | | | | | |   (215)  all_56_2 = all_4_1
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | REDUCE: (24), (213), (214) imply:
% 177.22/27.96  | | | | | | | | | | | | |   (216)   ~ (all_4_1 = e3)
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | REDUCE: (68), (214) imply:
% 177.22/27.96  | | | | | | | | | | | | |   (217)   ~ (all_52_29 = all_4_1)
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | SIMP: (217) implies:
% 177.22/27.96  | | | | | | | | | | | | |   (218)   ~ (all_52_29 = all_4_1)
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | REDUCE: (161), (214) imply:
% 177.22/27.96  | | | | | | | | | | | | |   (219)   ~ (all_4_1 = e2)
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | REDUCE: (199), (214) imply:
% 177.22/27.96  | | | | | | | | | | | | |   (220)   ~ (all_4_1 = e1)
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | |   (221)  all_56_2 = e3
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | COMBINE_EQS: (215), (221) imply:
% 177.22/27.96  | | | | | | | | | | | | | |   (222)  all_4_1 = e3
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | SIMP: (222) implies:
% 177.22/27.96  | | | | | | | | | | | | | |   (223)  all_4_1 = e3
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | REDUCE: (216), (223) imply:
% 177.22/27.96  | | | | | | | | | | | | | |   (224)  $false
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | |   (225)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | |   (226)  all_56_2 = e2
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | COMBINE_EQS: (215), (226) imply:
% 177.22/27.96  | | | | | | | | | | | | | | |   (227)  all_4_1 = e2
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | REDUCE: (219), (227) imply:
% 177.22/27.96  | | | | | | | | | | | | | | |   (228)  $false
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | |   (229)  all_56_2 = e1 | all_56_2 = e0
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | |   (230)  all_56_2 = e1
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (230) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (231)  all_4_1 = e1
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | REDUCE: (220), (231) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (232)  $false
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | |   (233)  all_56_2 = e0
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (233) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (234)  all_4_1 = e0
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | REDUCE: (218), (234) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (235)   ~ (all_52_29 = e0)
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | REDUCE: (200), (234) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (236)  op(e0, e1) = all_4_0
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (96) with all_52_29, all_4_0, e1,
% 177.22/27.96  | | | | | | | | | | | | | | | |              e0, simplifying with (29), (236) gives:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (237)  all_52_29 = all_4_0
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (237) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (238)  all_56_14 = all_4_0
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (237) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (239)  all_58_14 = all_4_0
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | REDUCE: (235), (237) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | |   (240)   ~ (all_4_0 = e0)
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | |   (241)  all_56_14 = e3
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (241) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | | |   (242)  all_4_0 = e3
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (242) imply:
% 177.22/27.96  | | | | | | | | | | | | | | | | |   (243)  all_58_14 = e3
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (52), (55), (96), (112), (134), (143),
% 177.22/27.96  | | | | | | | | | | | | | | | | |            (196), (243) are inconsistent by sub-proof #378.
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | |   (244)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (81), (238), (240), (244) are inconsistent
% 177.22/27.96  | | | | | | | | | | | | | | | | |            by sub-proof #925.
% 177.22/27.96  | | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | |   (245)   ~ (all_58_0 = e1)
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REDUCE: (41), (245) imply:
% 177.22/27.96  | | | | | | | | | |   (246)   ~ (all_4_2 = e1)
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REF_CLOSE: (5), (10), (13), (52), (55), (76), (92), (96),
% 177.22/27.96  | | | | | | | | | |            (108), (132), (134), (143), (164), (190), (193),
% 177.22/27.96  | | | | | | | | | |            (196), (246) are inconsistent by sub-proof #372.
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | End of split
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | Case 2:
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | |   (247)  all_58_12 = e3
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | REF_CLOSE: (108), (135), (247) are inconsistent by sub-proof
% 177.22/27.96  | | | | | | |            #1003.
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | End of split
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | End of split
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | End of split
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | Case 2:
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | |   (248)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | | REF_CLOSE: (5), (8), (19), (21), (22), (25), (27), (47), (63), (77),
% 177.22/27.96  | | | |            (80), (89), (93), (96), (100), (107), (108), (112), (118),
% 177.22/27.96  | | | |            (120), (132), (134), (137), (139), (145), (147), (149), (248)
% 177.22/27.96  | | | |            are inconsistent by sub-proof #657.
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | End of split
% 177.22/27.96  | | | 
% 177.22/27.96  | | Case 2:
% 177.22/27.96  | | | 
% 177.22/27.96  | | |   (249)   ~ (all_56_13 = e3)
% 177.22/27.96  | | |   (250)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.22/27.96  | | | 
% 177.22/27.96  | | | REDUCE: (115), (249) imply:
% 177.22/27.96  | | |   (251)   ~ (all_52_27 = e3)
% 177.22/27.96  | | | 
% 177.22/27.96  | | | BETA: splitting (51) gives:
% 177.22/27.96  | | | 
% 177.22/27.96  | | | Case 1:
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | |   (252)  all_58_12 = e3
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | | REF_CLOSE: (80), (92), (94), (96), (108), (252) are inconsistent by
% 177.22/27.96  | | | |            sub-proof #884.
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | Case 2:
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | |   (253)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | | BETA: splitting (253) gives:
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | | Case 1:
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | |   (254)  all_58_13 = e3
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | | REF_CLOSE: (71), (251), (254) are inconsistent by sub-proof #1026.
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | Case 2:
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | |   (255)  all_58_14 = e3 | all_58_15 = e3
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | | BETA: splitting (255) gives:
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | | Case 1:
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | |   (256)  all_58_14 = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | COMBINE_EQS: (47), (256) imply:
% 177.22/27.96  | | | | | |   (257)  all_52_29 = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | SIMP: (257) implies:
% 177.22/27.96  | | | | | |   (258)  all_52_29 = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (15), (258) imply:
% 177.22/27.96  | | | | | |   (259)   ~ (all_52_25 = e3)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (79), (258) imply:
% 177.22/27.96  | | | | | |   (260)   ~ (all_14_2 = e3)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | SIMP: (260) implies:
% 177.22/27.96  | | | | | |   (261)   ~ (all_14_2 = e3)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (84), (258) imply:
% 177.22/27.96  | | | | | |   (262)   ~ (all_6_2 = e3)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (56), (258) imply:
% 177.22/27.96  | | | | | |   (263)  op(e1, e3) = e1
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (29), (258) imply:
% 177.22/27.96  | | | | | |   (264)  op(e0, e1) = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | GROUND_INST: instantiating (96) with all_52_17, e1, e3, e1,
% 177.22/27.96  | | | | | |              simplifying with (91), (263) gives:
% 177.22/27.96  | | | | | |   (265)  all_52_17 = e1
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | COMBINE_EQS: (74), (265) imply:
% 177.22/27.96  | | | | | |   (266)  all_58_6 = e1
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (73), (265) imply:
% 177.22/27.96  | | | | | |   (267)   ~ (all_52_9 = e1)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (105), (265) imply:
% 177.22/27.96  | | | | | |   (268)   ~ (all_52_19 = e1)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | SIMP: (268) implies:
% 177.22/27.96  | | | | | |   (269)   ~ (all_52_19 = e1)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (3), (265) imply:
% 177.22/27.96  | | | | | |   (270)   ~ (all_52_23 = e1)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | SIMP: (270) implies:
% 177.22/27.96  | | | | | |   (271)   ~ (all_52_23 = e1)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (28), (265) imply:
% 177.22/27.96  | | | | | |   (272)   ~ (all_52_25 = e1)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | SIMP: (272) implies:
% 177.22/27.96  | | | | | |   (273)   ~ (all_52_25 = e1)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (62), (265) imply:
% 177.22/27.96  | | | | | |   (274)  op(e3, e1) = all_52_16
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | GROUND_INST: instantiating (96) with all_52_5, all_52_16, e1, e3,
% 177.22/27.96  | | | | | |              simplifying with (87), (274) gives:
% 177.22/27.96  | | | | | |   (275)  all_52_5 = all_52_16
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | COMBINE_EQS: (31), (275) imply:
% 177.22/27.96  | | | | | |   (276)  all_58_4 = all_52_16
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (49), (275) imply:
% 177.22/27.96  | | | | | |   (277)   ~ (all_52_3 = all_52_16)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (24), (275) imply:
% 177.22/27.96  | | | | | |   (278)   ~ (all_52_7 = all_52_16)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | SIMP: (278) implies:
% 177.22/27.96  | | | | | |   (279)   ~ (all_52_7 = all_52_16)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (26), (275) imply:
% 177.22/27.96  | | | | | |   (280)   ~ (all_52_16 = all_4_2)
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | BETA: splitting (67) gives:
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | Case 1:
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | |   (281)  all_56_12 = e3
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | REF_CLOSE: (70), (259), (281) are inconsistent by sub-proof #1040.
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | Case 2:
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | |   (282)   ~ (all_56_12 = e3)
% 177.22/27.96  | | | | | | |   (283)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | BETA: splitting (50) gives:
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | |   (284)  all_58_0 = e3
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | COMBINE_EQS: (41), (284) imply:
% 177.22/27.96  | | | | | | | |   (285)  all_4_2 = e3
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REDUCE: (59), (285) imply:
% 177.22/27.96  | | | | | | | |   (286)   ~ (all_52_3 = e3)
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REDUCE: (38), (285) imply:
% 177.22/27.96  | | | | | | | |   (287)   ~ (all_52_7 = e3)
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REDUCE: (280), (285) imply:
% 177.22/27.96  | | | | | | | |   (288)   ~ (all_52_16 = e3)
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REDUCE: (57), (285) imply:
% 177.22/27.96  | | | | | | | |   (289)  op(all_4_1, e3) = all_4_0
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REDUCE: (36), (285) imply:
% 177.22/27.96  | | | | | | | |   (290)  op(e3, e3) = all_4_1
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REDUCE: (94), (285) imply:
% 177.22/27.96  | | | | | | | |   (291)  op(e3, e3) = e3
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | GROUND_INST: instantiating (96) with e3, all_4_1, e3, e3,
% 177.22/27.96  | | | | | | | |              simplifying with (290), (291) gives:
% 177.22/27.96  | | | | | | | |   (292)  all_4_1 = e3
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | REDUCE: (289), (292) imply:
% 177.22/27.96  | | | | | | | |   (293)  op(e3, e3) = all_4_0
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | GROUND_INST: instantiating (96) with e3, all_4_0, e3, e3,
% 177.22/27.96  | | | | | | | |              simplifying with (291), (293) gives:
% 177.22/27.96  | | | | | | | |   (294)  all_4_0 = e3
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | BETA: splitting (44) gives:
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | |   (295)  all_58_4 = e1
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | COMBINE_EQS: (276), (295) imply:
% 177.22/27.96  | | | | | | | | |   (296)  all_52_16 = e1
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | SIMP: (296) implies:
% 177.22/27.96  | | | | | | | | |   (297)  all_52_16 = e1
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (277), (297) imply:
% 177.22/27.96  | | | | | | | | |   (298)   ~ (all_52_3 = e1)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (279), (297) imply:
% 177.22/27.96  | | | | | | | | |   (299)   ~ (all_52_7 = e1)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (288), (297) imply:
% 177.22/27.96  | | | | | | | | |   (300)   ~ (e3 = e1)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REF_CLOSE: (2), (5), (8), (9), (14), (16), (18), (21), (22),
% 177.22/27.96  | | | | | | | | |            (27), (33), (39), (45), (70), (71), (77), (80),
% 177.22/27.96  | | | | | | | | |            (86), (88), (93), (96), (97), (99), (103), (106),
% 177.22/27.96  | | | | | | | | |            (107), (108), (118), (127), (128), (251), (264),
% 177.22/27.96  | | | | | | | | |            (269), (271), (283), (286), (287), (298), (299) are
% 177.22/27.96  | | | | | | | | |            inconsistent by sub-proof #651.
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | |   (301)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | BETA: splitting (301) gives:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | |   (302)  all_58_5 = e1
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | COMBINE_EQS: (13), (302) imply:
% 177.22/27.96  | | | | | | | | | |   (303)  all_52_13 = e1
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | SIMP: (303) implies:
% 177.22/27.96  | | | | | | | | | |   (304)  all_52_13 = e1
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REDUCE: (40), (304) imply:
% 177.22/27.96  | | | | | | | | | |   (305)   ~ (all_52_15 = e1)
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | SIMP: (305) implies:
% 177.22/27.96  | | | | | | | | | |   (306)   ~ (all_52_15 = e1)
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REF_CLOSE: (14), (16), (18), (21), (22), (25), (70), (77),
% 177.22/27.96  | | | | | | | | | |            (80), (88), (93), (96), (100), (107), (118),
% 177.22/27.96  | | | | | | | | | |            (127), (264), (271), (273), (283), (287), (306)
% 177.22/27.96  | | | | | | | | | |            are inconsistent by sub-proof #646.
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | |   (307)  all_58_8 = e1 | all_58_14 = e1
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REF_CLOSE: (33), (52), (55), (90), (96), (256), (261), (307)
% 177.22/27.96  | | | | | | | | | |            are inconsistent by sub-proof #423.
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | |   (308)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | BETA: splitting (308) gives:
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | |   (309)  all_58_2 = e3
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | COMBINE_EQS: (85), (309) imply:
% 177.22/27.96  | | | | | | | | |   (310)  all_52_9 = e3
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | SIMP: (310) implies:
% 177.22/27.96  | | | | | | | | |   (311)  all_52_9 = e3
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (110), (311) imply:
% 177.22/27.96  | | | | | | | | |   (312)   ~ (all_52_15 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | SIMP: (312) implies:
% 177.22/27.96  | | | | | | | | |   (313)   ~ (all_52_15 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (7), (311) imply:
% 177.22/27.96  | | | | | | | | |   (314)   ~ (all_52_25 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (61), (311) imply:
% 177.22/27.96  | | | | | | | | |   (315)   ~ (all_10_2 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | SIMP: (315) implies:
% 177.22/27.96  | | | | | | | | |   (316)   ~ (all_10_2 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REDUCE: (23), (311) imply:
% 177.22/27.96  | | | | | | | | |   (317)   ~ (all_4_2 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | SIMP: (317) implies:
% 177.22/27.96  | | | | | | | | |   (318)   ~ (all_4_2 = e3)
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | BETA: splitting (20) gives:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | |   (319)  all_56_0 = e3
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | REF_CLOSE: (76), (318), (319) are inconsistent by sub-proof
% 177.22/27.96  | | | | | | | | | |            #1024.
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | |   (320)   ~ (all_56_0 = e3)
% 177.22/27.96  | | | | | | | | | |   (321)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | BETA: splitting (44) gives:
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | Case 1:
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | |   (322)  all_58_4 = e1
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | COMBINE_EQS: (276), (322) imply:
% 177.22/27.96  | | | | | | | | | | |   (323)  all_52_16 = e1
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | SIMP: (323) implies:
% 177.22/27.96  | | | | | | | | | | |   (324)  all_52_16 = e1
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | REDUCE: (277), (324) imply:
% 177.22/27.96  | | | | | | | | | | |   (325)   ~ (all_52_3 = e1)
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | REDUCE: (279), (324) imply:
% 177.22/27.96  | | | | | | | | | | |   (326)   ~ (all_52_7 = e1)
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | REDUCE: (280), (324) imply:
% 177.22/27.96  | | | | | | | | | | |   (327)   ~ (all_4_2 = e1)
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | SIMP: (327) implies:
% 177.22/27.96  | | | | | | | | | | |   (328)   ~ (all_4_2 = e1)
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (8), (16), (17), (18), (19),
% 177.22/27.96  | | | | | | | | | | |            (21), (22), (25), (27), (30), (32), (36), (39),
% 177.22/27.96  | | | | | | | | | | |            (41), (45), (53), (57), (58), (70), (71), (75),
% 177.22/27.96  | | | | | | | | | | |            (76), (77), (80), (81), (82), (88), (92), (93),
% 177.22/27.96  | | | | | | | | | | |            (96), (99), (100), (101), (106), (107), (108),
% 177.22/27.96  | | | | | | | | | | |            (115), (127), (128), (250), (251), (256), (259),
% 177.22/27.96  | | | | | | | | | | |            (264), (266), (269), (271), (273), (283), (313),
% 177.22/27.96  | | | | | | | | | | |            (316), (318), (321), (322), (325), (326), (328)
% 177.22/27.96  | | | | | | | | | | |            are inconsistent by sub-proof #641.
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | |   (329)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | | REF_CLOSE: (8), (13), (14), (16), (18), (19), (21), (22),
% 177.22/27.96  | | | | | | | | | | |            (25), (27), (33), (39), (40), (45), (52), (55),
% 177.22/27.96  | | | | | | | | | | |            (70), (71), (75), (77), (80), (88), (90), (93),
% 177.22/27.96  | | | | | | | | | | |            (96), (100), (106), (107), (118), (127), (128),
% 177.22/27.96  | | | | | | | | | | |            (251), (256), (261), (264), (269), (271), (273),
% 177.22/27.96  | | | | | | | | | | |            (283), (313), (316), (329) are inconsistent by
% 177.22/27.96  | | | | | | | | | | |            sub-proof #371.
% 177.22/27.96  | | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | Case 2:
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | |   (330)  all_58_6 = e3 | all_58_12 = e3
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | | REF_CLOSE: (33), (108), (259), (266), (330) are inconsistent
% 177.22/27.96  | | | | | | | | |            by sub-proof #1002.
% 177.22/27.96  | | | | | | | | | 
% 177.22/27.96  | | | | | | | | End of split
% 177.22/27.96  | | | | | | | | 
% 177.22/27.96  | | | | | | | End of split
% 177.22/27.96  | | | | | | | 
% 177.22/27.96  | | | | | | End of split
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | Case 2:
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | |   (331)  all_58_15 = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | COMBINE_EQS: (21), (331) imply:
% 177.22/27.96  | | | | | |   (332)  all_6_2 = e3
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | REDUCE: (128), (332) imply:
% 177.22/27.96  | | | | | |   (333)  $false
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | | CLOSE: (333) is inconsistent.
% 177.22/27.96  | | | | | | 
% 177.22/27.96  | | | | | End of split
% 177.22/27.96  | | | | | 
% 177.22/27.96  | | | | End of split
% 177.22/27.96  | | | | 
% 177.22/27.96  | | | End of split
% 177.22/27.96  | | | 
% 177.22/27.96  | | End of split
% 177.22/27.96  | | 
% 177.22/27.96  | End of split
% 177.22/27.96  | 
% 177.22/27.96  End of proof
% 177.22/27.96  
% 177.22/27.96  Sub-proof #371 shows that the following formulas are inconsistent:
% 177.22/27.96  ----------------------------------------------------------------
% 177.22/27.96    (1)   ~ (all_52_19 = all_52_23)
% 177.22/27.96    (2)   ~ (all_52_27 = e3)
% 177.22/27.96    (3)   ~ (all_6_2 = e3)
% 177.22/27.96    (4)  all_58_5 = all_52_13
% 177.22/27.96    (5)   ~ (all_6_2 = e0)
% 177.22/27.96    (6)  all_56_15 = all_6_2
% 177.22/27.96    (7)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.22/27.96    (8)  all_58_3 = all_10_2
% 177.22/27.96    (9)  all_58_15 = all_6_2
% 177.22/27.96    (10)  op(e0, all_6_2) = e0
% 177.22/27.96    (11)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.22/27.96    (12)  all_58_10 = all_52_15
% 177.22/27.96    (13)  all_58_7 = all_52_19
% 177.22/27.96    (14)   ~ (e3 = e1)
% 177.22/27.96    (15)  all_58_1 = all_52_3
% 177.22/27.96    (16)   ~ (all_52_13 = all_52_15)
% 177.22/27.96    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.22/27.96    (18)   ~ (all_10_2 = e3)
% 177.22/27.96    (19)  all_58_8 = all_14_2
% 177.22/27.96    (20)  op(e1, all_14_2) = e3
% 177.22/27.96    (21)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.22/27.96    (22)   ~ (all_52_23 = e1)
% 177.22/27.96    (23)   ~ (e3 = e0)
% 177.22/27.96    (24)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.22/27.96    (25)   ~ (all_52_15 = e3)
% 177.22/27.96    (26)  all_56_12 = all_52_25
% 177.22/27.96    (27)  all_58_13 = all_52_27
% 177.22/27.96    (28)   ~ (all_52_25 = e1)
% 177.22/27.96    (29)   ~ (all_52_3 = all_52_7)
% 177.22/27.96    (30)  all_58_11 = all_52_23
% 177.22/27.96    (31)  op(e3, all_52_25) = e3
% 177.22/27.96    (32)   ~ (all_52_25 = all_6_2)
% 177.22/27.96    (33)  op(e1, e1) = all_14_2
% 177.22/27.96    (34)  op(e3, e0) = all_52_7
% 177.22/27.96    (35)   ~ (all_52_19 = e1)
% 177.22/27.96    (36)   ~ (all_14_2 = e3)
% 177.22/27.96    (37)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.96    (38)  op(e0, e1) = e3
% 177.22/27.96    (39)   ~ (all_52_7 = all_6_2)
% 177.22/27.96    (40)  all_58_14 = e3
% 177.22/27.96    (41)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.22/27.96    (42)  all_58_9 = all_52_7
% 177.22/27.96  
% 177.22/27.96  Begin of proof
% 177.22/27.96  | 
% 177.22/27.96  | BETA: splitting (21) gives:
% 177.22/27.96  | 
% 177.22/27.96  | Case 1:
% 177.22/27.96  | | 
% 177.22/27.96  | |   (43)  all_58_5 = e1
% 177.22/27.96  | | 
% 177.22/27.96  | | COMBINE_EQS: (4), (43) imply:
% 177.22/27.96  | |   (44)  all_52_13 = e1
% 177.22/27.96  | | 
% 177.22/27.96  | | SIMP: (44) implies:
% 177.22/27.96  | |   (45)  all_52_13 = e1
% 177.22/27.96  | | 
% 177.22/27.96  | | REDUCE: (16), (45) imply:
% 177.22/27.96  | |   (46)   ~ (all_52_15 = e1)
% 177.22/27.96  | | 
% 177.22/27.96  | | SIMP: (46) implies:
% 177.22/27.96  | |   (47)   ~ (all_52_15 = e1)
% 177.22/27.96  | | 
% 177.22/27.96  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 177.22/27.96  | |            (15), (17), (18), (22), (23), (24), (25), (26), (27), (28), (29),
% 177.22/27.96  | |            (30), (31), (32), (34), (35), (37), (38), (39), (41), (42), (47)
% 177.22/27.96  | |            are inconsistent by sub-proof #644.
% 177.22/27.96  | | 
% 177.22/27.96  | Case 2:
% 177.22/27.96  | | 
% 177.22/27.96  | |   (48)  all_58_8 = e1 | all_58_14 = e1
% 177.22/27.96  | | 
% 177.22/27.96  | | REF_CLOSE: (14), (19), (20), (33), (36), (37), (40), (48) are inconsistent
% 177.22/27.96  | |            by sub-proof #423.
% 177.22/27.96  | | 
% 177.22/27.96  | End of split
% 177.22/27.96  | 
% 177.22/27.96  End of proof
% 177.22/27.96  
% 177.22/27.96  Sub-proof #372 shows that the following formulas are inconsistent:
% 177.22/27.96  ----------------------------------------------------------------
% 177.22/27.96    (1)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.22/27.96    (2)   ~ (all_4_2 = e2)
% 177.22/27.96    (3)  op(e1, e2) = all_52_19
% 177.22/27.96    (4)  all_58_5 = all_52_13
% 177.22/27.96    (5)   ~ (all_4_2 = e3)
% 177.22/27.96    (6)  all_58_8 = all_14_2
% 177.22/27.96    (7)  op(e1, all_14_2) = e3
% 177.22/27.96    (8)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.22/27.96    (9)  all_56_0 = all_4_2
% 177.22/27.96    (10)   ~ (all_52_19 = e3)
% 177.22/27.96    (11)   ~ (all_52_25 = all_4_2)
% 177.22/27.96    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.22/27.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.22/27.96    (13)   ~ (all_52_13 = e2)
% 177.22/27.96    (14)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.22/27.96    (15)   ~ (all_4_2 = e1)
% 177.22/27.96    (16)  all_58_12 = all_52_25
% 177.22/27.96    (17)  all_58_13 = e3
% 177.22/27.96  
% 177.22/27.96  Begin of proof
% 177.22/27.96  | 
% 177.22/27.96  | BETA: splitting (14) gives:
% 177.22/27.96  | 
% 177.22/27.96  | Case 1:
% 177.22/27.96  | | 
% 177.22/27.96  | |   (18)  all_56_0 = e2
% 177.22/27.96  | | 
% 177.22/27.96  | | REF_CLOSE: (2), (9), (18) are inconsistent by sub-proof #904.
% 177.22/27.96  | | 
% 177.22/27.96  | Case 2:
% 177.22/27.96  | | 
% 177.22/27.96  | |   (19)   ~ (all_56_0 = e2)
% 177.22/27.96  | |   (20)  all_56_0 = e1 | all_56_0 = e0
% 177.22/27.96  | | 
% 177.22/27.96  | | BETA: splitting (20) gives:
% 177.22/27.96  | | 
% 177.22/27.96  | | Case 1:
% 177.22/27.96  | | | 
% 177.22/27.96  | | |   (21)  all_56_0 = e1
% 177.22/27.96  | | | 
% 177.22/27.96  | | | REF_CLOSE: (9), (15), (21) are inconsistent by sub-proof #1022.
% 177.22/27.96  | | | 
% 177.22/27.96  | | Case 2:
% 177.22/27.96  | | | 
% 177.22/27.96  | | |   (22)  all_56_0 = e0
% 177.22/27.96  | | | 
% 177.22/27.96  | | | COMBINE_EQS: (9), (22) imply:
% 177.22/27.96  | | |   (23)  all_4_2 = e0
% 177.22/27.96  | | | 
% 177.22/27.96  | | | SIMP: (23) implies:
% 177.22/27.96  | | |   (24)  all_4_2 = e0
% 177.22/27.96  | | | 
% 177.22/27.96  | | | REDUCE: (11), (24) imply:
% 177.22/27.96  | | |   (25)   ~ (all_52_25 = e0)
% 177.22/27.96  | | | 
% 177.22/27.96  | | | REDUCE: (5), (24) imply:
% 177.22/27.96  | | |   (26)   ~ (e3 = e0)
% 177.22/27.96  | | | 
% 177.22/27.96  | | | SIMP: (26) implies:
% 177.22/27.96  | | |   (27)   ~ (e3 = e0)
% 177.22/27.96  | | | 
% 177.22/27.96  | | | REDUCE: (2), (24) imply:
% 177.22/27.97  | | |   (28)   ~ (e2 = e0)
% 177.22/27.97  | | | 
% 177.22/27.97  | | | SIMP: (28) implies:
% 177.22/27.97  | | |   (29)   ~ (e2 = e0)
% 177.22/27.97  | | | 
% 177.22/27.97  | | | BETA: splitting (1) gives:
% 177.22/27.97  | | | 
% 177.22/27.97  | | | Case 1:
% 177.22/27.97  | | | | 
% 177.22/27.97  | | | |   (30)  all_58_12 = e0
% 177.22/27.97  | | | | 
% 177.22/27.97  | | | | REF_CLOSE: (16), (25), (30) are inconsistent by sub-proof #649.
% 177.22/27.97  | | | | 
% 177.22/27.97  | | | Case 2:
% 177.22/27.97  | | | | 
% 177.22/27.97  | | | |   (31)  all_58_13 = e0 | all_58_14 = e0
% 177.22/27.97  | | | | 
% 177.22/27.97  | | | | BETA: splitting (8) gives:
% 177.22/27.97  | | | | 
% 177.22/27.97  | | | | Case 1:
% 177.22/27.97  | | | | | 
% 177.22/27.97  | | | | |   (32)  all_58_5 = e2
% 177.22/27.97  | | | | | 
% 177.22/27.97  | | | | | REF_CLOSE: (4), (13), (32) are inconsistent by sub-proof #391.
% 177.22/27.97  | | | | | 
% 177.22/27.97  | | | | Case 2:
% 177.22/27.97  | | | | | 
% 177.22/27.97  | | | | |   (33)  all_58_8 = e2 | all_58_14 = e2
% 177.22/27.97  | | | | | 
% 177.22/27.97  | | | | | BETA: splitting (33) gives:
% 177.22/27.97  | | | | | 
% 177.22/27.97  | | | | | Case 1:
% 177.22/27.97  | | | | | | 
% 177.22/27.97  | | | | | |   (34)  all_58_8 = e2
% 177.22/27.97  | | | | | | 
% 177.22/27.97  | | | | | | COMBINE_EQS: (6), (34) imply:
% 177.46/27.97  | | | | | |   (35)  all_14_2 = e2
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REF_CLOSE: (3), (7), (10), (12), (35) are inconsistent by sub-proof
% 177.46/27.97  | | | | | |            #379.
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | Case 2:
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | |   (36)  all_58_14 = e2
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REF_CLOSE: (17), (27), (29), (31), (36) are inconsistent by
% 177.46/27.97  | | | | | |            sub-proof #658.
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | End of split
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | End of split
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | End of split
% 177.46/27.97  | | | 
% 177.46/27.97  | | End of split
% 177.46/27.97  | | 
% 177.46/27.97  | End of split
% 177.46/27.97  | 
% 177.46/27.97  End of proof
% 177.46/27.97  
% 177.46/27.97  Sub-proof #373 shows that the following formulas are inconsistent:
% 177.46/27.97  ----------------------------------------------------------------
% 177.46/27.97    (1)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.46/27.97    (2)  all_52_20 = e3
% 177.46/27.97    (3)   ~ (e3 = e1)
% 177.46/27.97  
% 177.46/27.97  Begin of proof
% 177.46/27.97  | 
% 177.46/27.97  | ALPHA: (1) implies:
% 177.46/27.97  |   (4)  all_52_20 = e1
% 177.46/27.97  | 
% 177.46/27.97  | COMBINE_EQS: (2), (4) imply:
% 177.46/27.97  |   (5)  e3 = e1
% 177.46/27.97  | 
% 177.46/27.97  | REDUCE: (3), (5) imply:
% 177.46/27.97  |   (6)  $false
% 177.46/27.97  | 
% 177.46/27.97  | CLOSE: (6) is inconsistent.
% 177.46/27.97  | 
% 177.46/27.97  End of proof
% 177.46/27.97  
% 177.46/27.97  Sub-proof #374 shows that the following formulas are inconsistent:
% 177.46/27.97  ----------------------------------------------------------------
% 177.46/27.97    (1)   ~ (all_52_23 = all_14_2)
% 177.46/27.97    (2)   ~ (all_52_5 = all_52_13)
% 177.46/27.97    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/27.97    (4)   ~ (all_52_27 = all_10_2)
% 177.46/27.97    (5)   ~ (all_52_17 = all_52_23)
% 177.46/27.97    (6)   ~ (all_52_13 = all_52_29)
% 177.46/27.97    (7)  op(e2, all_10_2) = all_10_0
% 177.46/27.97    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.46/27.97    (9)  all_56_3 = all_52_7
% 177.46/27.97    (10)  op(e3, e2) = all_52_3
% 177.46/27.97    (11)   ~ (all_52_9 = all_52_25)
% 177.46/27.97    (12)  op(e3, all_52_25) = all_52_24
% 177.46/27.97    (13)   ~ (all_52_19 = all_52_23)
% 177.46/27.97    (14)  all_56_11 = all_52_23
% 177.46/27.97    (15)  op(e1, e2) = all_52_19
% 177.46/27.97    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.46/27.97    (17)   ~ (all_52_3 = all_10_2)
% 177.46/27.97    (18)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.46/27.97    (19)  all_58_5 = all_52_13
% 177.46/27.97    (20)   ~ (all_6_2 = e0)
% 177.46/27.97    (21)   ~ (all_52_25 = all_52_29)
% 177.46/27.97    (22)  op(e1, all_52_13) = e1
% 177.46/27.97    (23)  op(e0, all_52_15) = e0
% 177.46/27.97    (24)  all_56_15 = all_6_2
% 177.46/27.97    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/27.97    (26)  op(e2, e0) = all_52_15
% 177.46/27.97    (27)  all_58_3 = all_10_2
% 177.46/27.97    (28)  all_56_9 = all_52_19
% 177.46/27.97    (29)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/27.97    (30)  all_58_15 = all_6_2
% 177.46/27.97    (31)   ~ (all_52_9 = all_4_2)
% 177.46/27.97    (32)   ~ (all_52_5 = all_52_7)
% 177.46/27.97    (33)  all_58_10 = all_52_15
% 177.46/27.97    (34)   ~ (all_52_5 = all_4_2)
% 177.46/27.97    (35)  all_58_7 = all_52_19
% 177.46/27.97    (36)  all_56_4 = all_52_9
% 177.46/27.97    (37)   ~ (all_52_15 = all_6_2)
% 177.46/27.97    (38)   ~ (all_52_17 = all_52_25)
% 177.46/27.97    (39)  op(e0, e1) = all_52_29
% 177.46/27.97    (40)   ~ (all_4_0 = e2)
% 177.46/27.97    (41)  all_58_4 = all_52_5
% 177.46/27.97    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.97    (43)   ~ (e3 = e1)
% 177.46/27.97    (44)   ~ (all_52_27 = all_52_29)
% 177.46/27.97    (45)   ~ (all_52_17 = all_14_2)
% 177.46/27.97    (46)  op(e3, all_4_2) = all_4_1
% 177.46/27.97    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/27.97    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.97    (49)   ~ (all_52_7 = all_4_2)
% 177.46/27.97    (50)  all_58_1 = all_52_3
% 177.46/27.97    (51)  all_58_0 = all_4_2
% 177.46/27.97    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/27.97    (53)  op(e1, all_52_29) = all_52_28
% 177.46/27.97    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/27.97    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/27.97    (56)   ~ (all_4_1 = e2)
% 177.46/27.97    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/27.97    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.97    (59)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.46/27.97    (60)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.46/27.97    (61)  all_58_14 = all_52_29
% 177.46/27.97    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.46/27.97    (63)   ~ (all_52_3 = all_52_5)
% 177.46/27.97    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/27.97    (65)  op(e2, e1) = all_52_13
% 177.46/27.97    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.46/27.97    (67)  all_58_8 = all_14_2
% 177.46/27.97    (68)  all_56_1 = all_52_3
% 177.46/27.97    (69)  op(e0, e2) = all_52_27
% 177.46/27.97    (70)  op(e1, all_14_2) = e3
% 177.46/27.97    (71)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.46/27.97    (72)  op(all_4_1, all_4_2) = all_4_0
% 177.46/27.97    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/27.97    (74)   ~ (all_52_5 = all_14_2)
% 177.46/27.97    (75)   ~ (all_52_3 = all_52_27)
% 177.46/27.97    (76)   ~ (all_52_3 = all_4_2)
% 177.46/27.97    (77)  op(e0, e3) = all_52_25
% 177.46/27.97    (78)  op(e0, all_6_2) = all_6_1
% 177.46/27.97    (79)   ~ (all_52_9 = all_10_2)
% 177.46/27.97    (80)  op(e3, all_52_17) = all_52_16
% 177.46/27.97    (81)   ~ (all_52_13 = all_14_2)
% 177.46/27.97    (82)  op(e3, all_52_9) = e3
% 177.46/27.97    (83)   ~ (e3 = e0)
% 177.46/27.97    (84)   ~ (all_52_9 = all_52_13)
% 177.46/27.97    (85)  op(e0, all_52_23) = all_52_22
% 177.46/27.97    (86)   ~ (all_52_15 = all_52_23)
% 177.46/27.97    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/27.97    (88)   ~ (all_52_5 = all_52_29)
% 177.46/27.97    (89)  all_56_2 = all_52_5
% 177.46/27.97    (90)  op(e1, e0) = all_52_23
% 177.46/27.97    (91)  all_58_13 = all_52_27
% 177.46/27.97    (92)   ~ (all_4_1 = e1)
% 177.46/27.97    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/27.97    (94)  all_56_5 = all_10_2
% 177.46/27.97    (95)   ~ (all_52_9 = all_52_17)
% 177.46/27.97    (96)  all_58_6 = all_52_17
% 177.46/27.97    (97)   ~ (all_52_3 = all_52_7)
% 177.46/27.97    (98)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.97    (99)  op(e2, all_52_19) = all_52_18
% 177.46/27.97    (100)   ~ (e1 = e0)
% 177.46/27.97    (101)  all_56_0 = all_4_2
% 177.46/27.97    (102)  all_58_11 = all_52_23
% 177.46/27.97    (103)   ~ (all_52_3 = all_52_19)
% 177.46/27.97    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/27.97    (105)   ~ (all_52_7 = all_52_15)
% 177.46/27.97    (106)   ~ (all_52_29 = all_14_2)
% 177.46/27.97    (107)   ~ (all_4_0 = e1)
% 177.46/27.97    (108)   ~ (all_52_19 = all_10_2)
% 177.46/27.97    (109)   ~ (all_52_23 = all_6_2)
% 177.46/27.97    (110)   ~ (all_52_29 = all_6_2)
% 177.46/27.97    (111)  all_58_2 = all_52_9
% 177.46/27.97    (112)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/27.97    (113)  op(e3, e1) = all_52_5
% 177.46/27.97    (114)  all_56_10 = all_14_2
% 177.46/27.97    (115)   ~ (all_52_25 = all_6_2)
% 177.46/27.97    (116)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.46/27.97    (117)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.46/27.97    (118)  op(e1, e3) = all_52_17
% 177.46/27.97    (119)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.46/27.97    (120)   ~ (all_52_25 = all_4_2)
% 177.46/27.97    (121)  op(e3, e0) = all_52_7
% 177.46/27.97    (122)  op(e2, all_10_2) = e2
% 177.46/27.97    (123)  op(e3, e3) = all_4_2
% 177.46/27.97    (124)   ~ (all_52_17 = all_4_2)
% 177.46/27.97    (125)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.97             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.97    (126)   ~ (all_52_25 = all_52_27)
% 177.46/27.97    (127)   ~ (all_52_27 = all_6_2)
% 177.46/27.97    (128)   ~ (all_52_7 = all_6_2)
% 177.46/27.97    (129)   ~ (all_10_0 = e3)
% 177.46/27.97    (130)   ~ (all_52_19 = all_52_27)
% 177.46/27.97    (131)  all_56_7 = all_52_15
% 177.46/27.97    (132)   ~ (all_52_7 = all_52_23)
% 177.46/27.97    (133)   ~ (all_52_13 = all_10_2)
% 177.46/27.97    (134)  op(e2, all_52_27) = all_52_26
% 177.46/27.97    (135)   ~ (all_52_17 = all_52_19)
% 177.46/27.97    (136)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/27.97    (137)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/27.97    (138)  op(e1, all_14_2) = all_14_1
% 177.46/27.97    (139)  all_58_9 = all_52_7
% 177.46/27.97    (140)  all_58_12 = all_52_25
% 177.46/27.97    (141)   ~ (all_10_0 = e1)
% 177.46/27.97    (142)  all_56_6 = all_52_13
% 177.46/27.97    (143)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.46/27.97    (144)   ~ (all_52_9 = all_52_15)
% 177.46/27.97    (145)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/27.97    (146)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.46/27.97    (147)   ~ (all_52_19 = all_14_2)
% 177.46/27.97    (148)  op(e2, e3) = all_52_9
% 177.46/27.97    (149)  all_56_13 = all_52_27
% 177.46/27.97  
% 177.46/27.97  Begin of proof
% 177.46/27.97  | 
% 177.46/27.97  | GROUND_INST: instantiating (125) with e2, all_10_0, all_10_2, e2, simplifying
% 177.46/27.97  |              with (7), (122) gives:
% 177.46/27.97  |   (150)  all_10_0 = e2
% 177.46/27.97  | 
% 177.46/27.97  | REDUCE: (129), (150) imply:
% 177.46/27.97  |   (151)   ~ (e3 = e2)
% 177.46/27.97  | 
% 177.46/27.97  | SIMP: (151) implies:
% 177.46/27.97  |   (152)   ~ (e3 = e2)
% 177.46/27.97  | 
% 177.46/27.97  | REDUCE: (141), (150) imply:
% 177.46/27.97  |   (153)   ~ (e2 = e1)
% 177.46/27.97  | 
% 177.46/27.97  | BETA: splitting (47) gives:
% 177.46/27.97  | 
% 177.46/27.97  | Case 1:
% 177.46/27.97  | | 
% 177.46/27.97  | |   (154)  all_56_15 = e3
% 177.46/27.97  | | 
% 177.46/27.97  | | COMBINE_EQS: (24), (154) imply:
% 177.46/27.97  | |   (155)  all_6_2 = e3
% 177.46/27.97  | | 
% 177.46/27.97  | | SIMP: (155) implies:
% 177.46/27.97  | |   (156)  all_6_2 = e3
% 177.46/27.97  | | 
% 177.46/27.97  | | REDUCE: (37), (156) imply:
% 177.46/27.97  | |   (157)   ~ (all_52_15 = e3)
% 177.46/27.97  | | 
% 177.46/27.97  | | REDUCE: (115), (156) imply:
% 177.46/27.97  | |   (158)   ~ (all_52_25 = e3)
% 177.46/27.97  | | 
% 177.46/27.97  | | REDUCE: (127), (156) imply:
% 177.46/27.97  | |   (159)   ~ (all_52_27 = e3)
% 177.46/27.97  | | 
% 177.46/27.97  | | REDUCE: (110), (156) imply:
% 177.46/27.97  | |   (160)   ~ (all_52_29 = e3)
% 177.46/27.97  | | 
% 177.46/27.97  | | REDUCE: (78), (156) imply:
% 177.46/27.97  | |   (161)  op(e0, e3) = all_6_1
% 177.46/27.97  | | 
% 177.46/27.97  | | GROUND_INST: instantiating (125) with all_52_25, all_6_1, e3, e0,
% 177.46/27.97  | |              simplifying with (77), (161) gives:
% 177.46/27.97  | |   (162)  all_52_25 = all_6_1
% 177.46/27.97  | | 
% 177.46/27.97  | | COMBINE_EQS: (140), (162) imply:
% 177.46/27.97  | |   (163)  all_58_12 = all_6_1
% 177.46/27.97  | | 
% 177.46/27.97  | | REDUCE: (11), (162) imply:
% 177.46/27.97  | |   (164)   ~ (all_52_9 = all_6_1)
% 177.46/27.97  | | 
% 177.46/27.97  | | BETA: splitting (55) gives:
% 177.46/27.97  | | 
% 177.46/27.97  | | Case 1:
% 177.46/27.97  | | | 
% 177.46/27.97  | | |   (165)  all_56_9 = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | COMBINE_EQS: (28), (165) imply:
% 177.46/27.97  | | |   (166)  all_52_19 = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (166) implies:
% 177.46/27.97  | | |   (167)  all_52_19 = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (99), (167) imply:
% 177.46/27.97  | | |   (168)  op(e2, e3) = all_52_18
% 177.46/27.97  | | | 
% 177.46/27.97  | | | GROUND_INST: instantiating (125) with all_52_9, all_52_18, e3, e2,
% 177.46/27.97  | | |              simplifying with (148), (168) gives:
% 177.46/27.97  | | |   (169)  all_52_9 = all_52_18
% 177.46/27.97  | | | 
% 177.46/27.97  | | | COMBINE_EQS: (36), (169) imply:
% 177.46/27.97  | | |   (170)  all_56_4 = all_52_18
% 177.46/27.97  | | | 
% 177.46/27.97  | | | COMBINE_EQS: (111), (169) imply:
% 177.46/27.97  | | |   (171)  all_58_2 = all_52_18
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (95), (169) imply:
% 177.46/27.97  | | |   (172)   ~ (all_52_17 = all_52_18)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (172) implies:
% 177.46/27.97  | | |   (173)   ~ (all_52_17 = all_52_18)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (164), (169) imply:
% 177.46/27.97  | | |   (174)   ~ (all_52_18 = all_6_1)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (31), (169) imply:
% 177.46/27.97  | | |   (175)   ~ (all_52_18 = all_4_2)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (82), (169) imply:
% 177.46/27.97  | | |   (176)  op(e3, all_52_18) = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | BETA: splitting (145) gives:
% 177.46/27.97  | | | 
% 177.46/27.97  | | | Case 1:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | |   (177)  all_58_4 = e3
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | REF_CLOSE: (2), (10), (17), (19), (27), (31), (33), (41), (48), (82),
% 177.46/27.97  | | | |            (111), (122), (123), (125), (148), (157), (177) are
% 177.46/27.97  | | | |            inconsistent by sub-proof #399.
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | Case 2:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | |   (178)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | BETA: splitting (178) gives:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | Case 1:
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | |   (179)  all_58_5 = e3
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | COMBINE_EQS: (19), (179) imply:
% 177.46/27.97  | | | | |   (180)  all_52_13 = e3
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | SIMP: (180) implies:
% 177.46/27.97  | | | | |   (181)  all_52_13 = e3
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | REDUCE: (6), (181) imply:
% 177.46/27.97  | | | | |   (182)   ~ (all_52_29 = e3)
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | REDUCE: (22), (181) imply:
% 177.46/27.97  | | | | |   (183)  op(e1, e3) = e1
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | BETA: splitting (64) gives:
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | Case 1:
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | |   (184)  all_58_0 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | COMBINE_EQS: (51), (184) imply:
% 177.46/27.97  | | | | | |   (185)  all_4_2 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (76), (185) imply:
% 177.46/27.97  | | | | | |   (186)   ~ (all_52_3 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (49), (185) imply:
% 177.46/27.97  | | | | | |   (187)   ~ (all_52_7 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (175), (185) imply:
% 177.46/27.97  | | | | | |   (188)   ~ (all_52_18 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (72), (185) imply:
% 177.46/27.97  | | | | | |   (189)  op(all_4_1, e3) = all_4_0
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (46), (185) imply:
% 177.46/27.97  | | | | | |   (190)  op(e3, e3) = all_4_1
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (123), (185) imply:
% 177.46/27.97  | | | | | |   (191)  op(e3, e3) = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | GROUND_INST: instantiating (125) with all_52_17, e1, e3, e1,
% 177.46/27.97  | | | | | |              simplifying with (118), (183) gives:
% 177.46/27.97  | | | | | |   (192)  all_52_17 = e1
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | GROUND_INST: instantiating (125) with e3, all_4_1, e3, e3,
% 177.46/27.97  | | | | | |              simplifying with (190), (191) gives:
% 177.46/27.97  | | | | | |   (193)  all_4_1 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | COMBINE_EQS: (96), (192) imply:
% 177.46/27.97  | | | | | |   (194)  all_58_6 = e1
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (173), (192) imply:
% 177.46/27.97  | | | | | |   (195)   ~ (all_52_18 = e1)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | SIMP: (195) implies:
% 177.46/27.97  | | | | | |   (196)   ~ (all_52_18 = e1)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (189), (193) imply:
% 177.46/27.97  | | | | | |   (197)  op(e3, e3) = all_4_0
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | GROUND_INST: instantiating (125) with e3, all_4_0, e3, e3,
% 177.46/27.97  | | | | | |              simplifying with (191), (197) gives:
% 177.46/27.97  | | | | | |   (198)  all_4_0 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | BETA: splitting (98) gives:
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | Case 1:
% 177.46/27.97  | | | | | | | 
% 177.46/27.97  | | | | | | |   (199)  all_56_4 = e3
% 177.46/27.97  | | | | | | | 
% 177.46/27.97  | | | | | | | REF_CLOSE: (170), (188), (199) are inconsistent by sub-proof #398.
% 177.46/27.97  | | | | | | | 
% 177.46/27.97  | | | | | | Case 2:
% 177.46/27.97  | | | | | | | 
% 177.46/27.97  | | | | | | |   (200)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.97  | | | | | | | 
% 177.46/27.97  | | | | | | | REF_CLOSE: (10), (25), (117), (121), (125), (152), (153), (163),
% 177.46/27.97  | | | | | | |            (170), (171), (174), (176), (184), (186), (187), (194),
% 177.46/27.97  | | | | | | |            (196), (200) are inconsistent by sub-proof #778.
% 177.46/27.97  | | | | | | | 
% 177.46/27.97  | | | | | | End of split
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | Case 2:
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | |   (201)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REF_CLOSE: (19), (22), (31), (42), (43), (45), (61), (67), (70),
% 177.46/27.97  | | | | | |            (82), (96), (111), (118), (123), (125), (140), (158),
% 177.46/27.97  | | | | | |            (160), (178), (201) are inconsistent by sub-proof #395.
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | End of split
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | Case 2:
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | |   (202)  all_58_8 = e3 | all_58_14 = e3
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | REF_CLOSE: (45), (61), (67), (70), (118), (125), (160), (202) are
% 177.46/27.97  | | | | |            inconsistent by sub-proof #397.
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | End of split
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | End of split
% 177.46/27.97  | | | 
% 177.46/27.97  | | Case 2:
% 177.46/27.97  | | | 
% 177.46/27.97  | | |   (203)   ~ (all_56_9 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (28), (203) imply:
% 177.46/27.97  | | |   (204)   ~ (all_52_19 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | BETA: splitting (58) gives:
% 177.46/27.97  | | | 
% 177.46/27.97  | | | Case 1:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | |   (205)  all_58_1 = e3
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | REF_CLOSE: (19), (22), (31), (41), (42), (43), (45), (50), (51), (61),
% 177.46/27.97  | | | |            (63), (64), (67), (70), (76), (82), (96), (111), (118),
% 177.46/27.97  | | | |            (123), (125), (140), (145), (158), (160), (205) are
% 177.46/27.97  | | | |            inconsistent by sub-proof #393.
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | Case 2:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | |   (206)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | REF_CLOSE: (10), (17), (27), (35), (82), (91), (122), (125), (148),
% 177.46/27.97  | | | |            (159), (204), (206) are inconsistent by sub-proof #975.
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | End of split
% 177.46/27.97  | | | 
% 177.46/27.97  | | End of split
% 177.46/27.97  | | 
% 177.46/27.97  | Case 2:
% 177.46/27.97  | | 
% 177.46/27.97  | |   (207)   ~ (all_56_15 = e3)
% 177.46/27.97  | |   (208)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/27.97  | | 
% 177.46/27.97  | | REDUCE: (24), (207) imply:
% 177.46/27.97  | |   (209)   ~ (all_6_2 = e3)
% 177.46/27.97  | | 
% 177.46/27.97  | | BETA: splitting (62) gives:
% 177.46/27.97  | | 
% 177.46/27.97  | | Case 1:
% 177.46/27.97  | | | 
% 177.46/27.97  | | |   (210)  all_56_13 = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | COMBINE_EQS: (149), (210) imply:
% 177.46/27.97  | | |   (211)  all_52_27 = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (211) implies:
% 177.46/27.97  | | |   (212)  all_52_27 = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | COMBINE_EQS: (91), (212) imply:
% 177.46/27.97  | | |   (213)  all_58_13 = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (75), (212) imply:
% 177.46/27.97  | | |   (214)   ~ (all_52_3 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (130), (212) imply:
% 177.46/27.97  | | |   (215)   ~ (all_52_19 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (126), (212) imply:
% 177.46/27.97  | | |   (216)   ~ (all_52_25 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (44), (212) imply:
% 177.46/27.97  | | |   (217)   ~ (all_52_29 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (217) implies:
% 177.46/27.97  | | |   (218)   ~ (all_52_29 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (4), (212) imply:
% 177.46/27.97  | | |   (219)   ~ (all_10_2 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (219) implies:
% 177.46/27.97  | | |   (220)   ~ (all_10_2 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (127), (212) imply:
% 177.46/27.97  | | |   (221)   ~ (all_6_2 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (134), (212) imply:
% 177.46/27.97  | | |   (222)  op(e2, e3) = all_52_26
% 177.46/27.97  | | | 
% 177.46/27.97  | | | GROUND_INST: instantiating (125) with all_52_9, all_52_26, e3, e2,
% 177.46/27.97  | | |              simplifying with (148), (222) gives:
% 177.46/27.97  | | |   (223)  all_52_9 = all_52_26
% 177.46/27.97  | | | 
% 177.46/27.97  | | | COMBINE_EQS: (36), (223) imply:
% 177.46/27.97  | | |   (224)  all_56_4 = all_52_26
% 177.46/27.97  | | | 
% 177.46/27.97  | | | COMBINE_EQS: (111), (223) imply:
% 177.46/27.97  | | |   (225)  all_58_2 = all_52_26
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (84), (223) imply:
% 177.46/27.97  | | |   (226)   ~ (all_52_13 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (226) implies:
% 177.46/27.97  | | |   (227)   ~ (all_52_13 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (144), (223) imply:
% 177.46/27.97  | | |   (228)   ~ (all_52_15 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (228) implies:
% 177.46/27.97  | | |   (229)   ~ (all_52_15 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (95), (223) imply:
% 177.46/27.97  | | |   (230)   ~ (all_52_17 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (230) implies:
% 177.46/27.97  | | |   (231)   ~ (all_52_17 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (11), (223) imply:
% 177.46/27.97  | | |   (232)   ~ (all_52_25 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | SIMP: (232) implies:
% 177.46/27.97  | | |   (233)   ~ (all_52_25 = all_52_26)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (79), (223) imply:
% 177.46/27.97  | | |   (234)   ~ (all_52_26 = all_10_2)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (31), (223) imply:
% 177.46/27.97  | | |   (235)   ~ (all_52_26 = all_4_2)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (82), (223) imply:
% 177.46/27.97  | | |   (236)  op(e3, all_52_26) = e3
% 177.46/27.97  | | | 
% 177.46/27.97  | | | BETA: splitting (54) gives:
% 177.46/27.97  | | | 
% 177.46/27.97  | | | Case 1:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | |   (237)  all_56_1 = e3
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | REF_CLOSE: (68), (214), (237) are inconsistent by sub-proof #862.
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | Case 2:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | |   (238)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | BETA: splitting (116) gives:
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | | Case 1:
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | |   (239)  all_56_5 = e3
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | REF_CLOSE: (94), (220), (239) are inconsistent by sub-proof #895.
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | Case 2:
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | |   (240)   ~ (all_56_5 = e3)
% 177.46/27.97  | | | | |   (241)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | BETA: splitting (145) gives:
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | | Case 1:
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | |   (242)  all_58_4 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | COMBINE_EQS: (41), (242) imply:
% 177.46/27.97  | | | | | |   (243)  all_52_5 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | SIMP: (243) implies:
% 177.46/27.97  | | | | | |   (244)  all_52_5 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (2), (244) imply:
% 177.46/27.97  | | | | | |   (245)   ~ (all_52_13 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | SIMP: (245) implies:
% 177.46/27.97  | | | | | |   (246)   ~ (all_52_13 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (74), (244) imply:
% 177.46/27.97  | | | | | |   (247)   ~ (all_14_2 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | SIMP: (247) implies:
% 177.46/27.97  | | | | | |   (248)   ~ (all_14_2 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REDUCE: (34), (244) imply:
% 177.46/27.97  | | | | | |   (249)   ~ (all_4_2 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | SIMP: (249) implies:
% 177.46/27.97  | | | | | |   (250)   ~ (all_4_2 = e3)
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REF_CLOSE: (3), (10), (12), (15), (16), (17), (19), (23), (24),
% 177.46/27.97  | | | | | |            (27), (29), (31), (33), (35), (37), (42), (43), (46),
% 177.46/27.97  | | | | | |            (48), (50), (51), (61), (64), (67), (68), (70), (76),
% 177.46/27.97  | | | | | |            (77), (82), (86), (92), (93), (94), (96), (98), (100),
% 177.46/27.97  | | | | | |            (101), (102), (103), (104), (105), (108), (110), (111),
% 177.46/27.97  | | | | | |            (115), (120), (121), (123), (124), (125), (128), (133),
% 177.46/27.97  | | | | | |            (135), (139), (140), (208), (213), (214), (215), (220),
% 177.46/27.97  | | | | | |            (224), (225), (229), (231), (233), (234), (235), (236),
% 177.46/27.97  | | | | | |            (238), (241), (242), (246), (248), (250) are inconsistent
% 177.46/27.97  | | | | | |            by sub-proof #389.
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | Case 2:
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | |   (251)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | | REF_CLOSE: (1), (3), (10), (17), (19), (22), (23), (27), (30), (33),
% 177.46/27.97  | | | | | |            (34), (35), (39), (40), (41), (43), (45), (46), (49),
% 177.46/27.97  | | | | | |            (50), (51), (57), (60), (61), (63), (64), (65), (67),
% 177.46/27.97  | | | | | |            (72), (76), (77), (80), (93), (96), (98), (100), (102),
% 177.46/27.97  | | | | | |            (107), (113), (118), (122), (123), (125), (135), (136),
% 177.46/27.97  | | | | | |            (139), (140), (209), (213), (216), (218), (224), (225),
% 177.46/27.97  | | | | | |            (227), (229), (231), (233), (235), (236), (251) are
% 177.46/27.97  | | | | | |            inconsistent by sub-proof #763.
% 177.46/27.97  | | | | | | 
% 177.46/27.97  | | | | | End of split
% 177.46/27.97  | | | | | 
% 177.46/27.97  | | | | End of split
% 177.46/27.97  | | | | 
% 177.46/27.97  | | | End of split
% 177.46/27.97  | | | 
% 177.46/27.97  | | Case 2:
% 177.46/27.97  | | | 
% 177.46/27.97  | | |   (252)   ~ (all_56_13 = e3)
% 177.46/27.97  | | |   (253)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REDUCE: (149), (252) imply:
% 177.46/27.97  | | |   (254)   ~ (all_52_27 = e3)
% 177.46/27.97  | | | 
% 177.46/27.97  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 177.46/27.97  | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.46/27.97  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.46/27.97  | | |            (35), (36), (38), (40), (41), (42), (43), (44), (45), (46),
% 177.46/27.97  | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.46/27.97  | | |            (58), (59), (61), (63), (64), (65), (66), (67), (68), (69),
% 177.46/27.97  | | |            (70), (71), (72), (73), (75), (76), (77), (80), (81), (82),
% 177.46/27.97  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 177.46/27.97  | | |            (93), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 177.46/27.97  | | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 177.46/27.97  | | |            (113), (114), (115), (118), (119), (120), (121), (122), (123),
% 177.46/27.97  | | |            (125), (126), (127), (128), (130), (131), (132), (135), (136),
% 177.46/27.97  | | |            (137), (138), (139), (140), (142), (143), (144), (145), (146),
% 177.46/27.97  | | |            (147), (148), (149), (152), (153), (208), (209), (253), (254)
% 177.46/27.97  | | |            are inconsistent by sub-proof #375.
% 177.46/27.97  | | | 
% 177.46/27.97  | | End of split
% 177.46/27.97  | | 
% 177.46/27.97  | End of split
% 177.46/27.97  | 
% 177.46/27.97  End of proof
% 177.46/27.97  
% 177.46/27.97  Sub-proof #375 shows that the following formulas are inconsistent:
% 177.46/27.97  ----------------------------------------------------------------
% 177.46/27.97    (1)   ~ (all_52_23 = all_14_2)
% 177.46/27.97    (2)   ~ (all_52_5 = all_52_13)
% 177.46/27.97    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/27.97    (4)   ~ (all_52_27 = all_10_2)
% 177.46/27.97    (5)   ~ (all_52_17 = all_52_23)
% 177.46/27.97    (6)   ~ (all_52_13 = all_52_29)
% 177.46/27.97    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.46/27.97    (8)  all_56_3 = all_52_7
% 177.46/27.97    (9)  op(e3, e2) = all_52_3
% 177.46/27.97    (10)   ~ (all_52_9 = all_52_25)
% 177.46/27.97    (11)  op(e3, all_52_25) = all_52_24
% 177.46/27.97    (12)   ~ (all_52_19 = all_52_23)
% 177.46/27.97    (13)  all_56_11 = all_52_23
% 177.46/27.97    (14)  op(e1, e2) = all_52_19
% 177.46/27.97    (15)   ~ (all_52_27 = e3)
% 177.46/27.97    (16)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.46/27.97    (17)   ~ (all_6_2 = e3)
% 177.46/27.97    (18)   ~ (all_52_3 = all_10_2)
% 177.46/27.98    (19)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.46/27.98    (20)  all_58_5 = all_52_13
% 177.46/27.98    (21)   ~ (all_6_2 = e0)
% 177.46/27.98    (22)   ~ (all_52_25 = all_52_29)
% 177.46/27.98    (23)  op(e1, all_52_13) = e1
% 177.46/27.98    (24)  op(e0, all_52_15) = e0
% 177.46/27.98    (25)  all_56_15 = all_6_2
% 177.46/27.98    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/27.98    (27)  op(e2, e0) = all_52_15
% 177.46/27.98    (28)  all_58_3 = all_10_2
% 177.46/27.98    (29)  all_56_9 = all_52_19
% 177.46/27.98    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/27.98    (31)  all_58_15 = all_6_2
% 177.46/27.98    (32)   ~ (all_52_9 = all_4_2)
% 177.46/27.98    (33)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/27.98    (34)   ~ (all_52_5 = all_52_7)
% 177.46/27.98    (35)  all_58_10 = all_52_15
% 177.46/27.98    (36)   ~ (all_52_5 = all_4_2)
% 177.46/27.98    (37)  all_58_7 = all_52_19
% 177.46/27.98    (38)  all_56_4 = all_52_9
% 177.46/27.98    (39)   ~ (all_52_17 = all_52_25)
% 177.46/27.98    (40)   ~ (all_4_0 = e2)
% 177.46/27.98    (41)  all_58_4 = all_52_5
% 177.46/27.98    (42)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.98    (43)   ~ (e3 = e1)
% 177.46/27.98    (44)   ~ (all_52_27 = all_52_29)
% 177.46/27.98    (45)   ~ (all_52_17 = all_14_2)
% 177.46/27.98    (46)  op(e3, all_4_2) = all_4_1
% 177.46/27.98    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.98    (48)   ~ (all_52_7 = all_4_2)
% 177.46/27.98    (49)  all_58_1 = all_52_3
% 177.46/27.98    (50)  all_58_0 = all_4_2
% 177.46/27.98    (51)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/27.98    (52)  op(e1, all_52_29) = all_52_28
% 177.46/27.98    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/27.98    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/27.98    (55)   ~ (all_4_1 = e2)
% 177.46/27.98    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/27.98    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.98    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.46/27.98    (59)  all_58_14 = all_52_29
% 177.46/27.98    (60)   ~ (all_52_3 = all_52_5)
% 177.46/27.98    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/27.98    (62)  op(e2, e1) = all_52_13
% 177.46/27.98    (63)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.46/27.98    (64)  all_58_8 = all_14_2
% 177.46/27.98    (65)  all_56_1 = all_52_3
% 177.46/27.98    (66)  op(e0, e2) = all_52_27
% 177.46/27.98    (67)  op(e1, all_14_2) = e3
% 177.46/27.98    (68)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.46/27.98    (69)  op(all_4_1, all_4_2) = all_4_0
% 177.46/27.98    (70)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/27.98    (71)   ~ (all_52_3 = all_52_27)
% 177.46/27.98    (72)   ~ (all_52_3 = all_4_2)
% 177.46/27.98    (73)  op(e0, e3) = all_52_25
% 177.46/27.98    (74)  op(e3, all_52_17) = all_52_16
% 177.46/27.98    (75)   ~ (all_52_13 = all_14_2)
% 177.46/27.98    (76)  op(e3, all_52_9) = e3
% 177.46/27.98    (77)   ~ (e3 = e0)
% 177.46/27.98    (78)   ~ (all_52_9 = all_52_13)
% 177.46/27.98    (79)  op(e0, all_52_23) = all_52_22
% 177.46/27.98    (80)   ~ (all_52_15 = all_52_23)
% 177.46/27.98    (81)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/27.98    (82)   ~ (all_52_5 = all_52_29)
% 177.46/27.98    (83)  all_56_2 = all_52_5
% 177.46/27.98    (84)  op(e1, e0) = all_52_23
% 177.46/27.98    (85)  all_58_13 = all_52_27
% 177.46/27.98    (86)   ~ (all_4_1 = e1)
% 177.46/27.98    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/27.98    (88)   ~ (all_52_9 = all_52_17)
% 177.46/27.98    (89)  all_58_6 = all_52_17
% 177.46/27.98    (90)   ~ (all_52_3 = all_52_7)
% 177.46/27.98    (91)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.98    (92)  op(e2, all_52_19) = all_52_18
% 177.46/27.98    (93)   ~ (e1 = e0)
% 177.46/27.98    (94)  all_56_0 = all_4_2
% 177.46/27.98    (95)  all_58_11 = all_52_23
% 177.46/27.98    (96)   ~ (all_52_3 = all_52_19)
% 177.46/27.98    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/27.98    (98)   ~ (all_52_7 = all_52_15)
% 177.46/27.98    (99)   ~ (all_52_29 = all_14_2)
% 177.46/27.98    (100)   ~ (all_4_0 = e1)
% 177.46/27.98    (101)   ~ (all_52_19 = all_10_2)
% 177.46/27.98    (102)   ~ (all_52_23 = all_6_2)
% 177.46/27.98    (103)   ~ (all_52_29 = all_6_2)
% 177.46/27.98    (104)  all_58_2 = all_52_9
% 177.46/27.98    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/27.98    (106)  op(e3, e1) = all_52_5
% 177.46/27.98    (107)   ~ (e2 = e1)
% 177.46/27.98    (108)  all_56_10 = all_14_2
% 177.46/27.98    (109)   ~ (all_52_25 = all_6_2)
% 177.46/27.98    (110)  op(e1, e3) = all_52_17
% 177.46/27.98    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.46/27.98    (112)   ~ (all_52_25 = all_4_2)
% 177.46/27.98    (113)  op(e3, e0) = all_52_7
% 177.46/27.98    (114)  op(e2, all_10_2) = e2
% 177.46/27.98    (115)  op(e3, e3) = all_4_2
% 177.46/27.98    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.98             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.98    (117)   ~ (all_52_25 = all_52_27)
% 177.46/27.98    (118)   ~ (all_52_27 = all_6_2)
% 177.46/27.98    (119)   ~ (all_52_7 = all_6_2)
% 177.46/27.98    (120)   ~ (all_52_19 = all_52_27)
% 177.46/27.98    (121)  all_56_7 = all_52_15
% 177.46/27.98    (122)   ~ (all_52_7 = all_52_23)
% 177.46/27.98    (123)   ~ (all_52_17 = all_52_19)
% 177.46/27.98    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/27.98    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/27.98    (126)  op(e1, all_14_2) = all_14_1
% 177.46/27.98    (127)  all_58_9 = all_52_7
% 177.46/27.98    (128)  all_58_12 = all_52_25
% 177.46/27.98    (129)  all_56_6 = all_52_13
% 177.46/27.98    (130)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.46/27.98    (131)   ~ (all_52_9 = all_52_15)
% 177.46/27.98    (132)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/27.98    (133)   ~ (e3 = e2)
% 177.46/27.98    (134)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.46/27.98    (135)   ~ (all_52_19 = all_14_2)
% 177.46/27.98    (136)  op(e2, e3) = all_52_9
% 177.46/27.98    (137)  all_56_13 = all_52_27
% 177.46/27.98  
% 177.46/27.98  Begin of proof
% 177.46/27.98  | 
% 177.46/27.98  | BETA: splitting (63) gives:
% 177.46/27.98  | 
% 177.46/27.98  | Case 1:
% 177.46/27.98  | | 
% 177.46/27.98  | |   (138)  all_58_12 = e3
% 177.46/27.98  | | 
% 177.46/27.98  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 177.46/27.98  | |            (14), (16), (18), (20), (21), (22), (23), (24), (25), (26), (28),
% 177.46/27.98  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 177.46/27.98  | |            (40), (41), (42), (44), (45), (46), (47), (48), (49), (50), (51),
% 177.46/27.98  | |            (53), (54), (56), (57), (58), (59), (60), (62), (64), (65), (66),
% 177.46/27.98  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.46/27.98  | |            (81), (82), (83), (85), (86), (88), (89), (90), (91), (92), (94),
% 177.46/27.98  | |            (95), (96), (98), (99), (100), (101), (102), (104), (105), (106),
% 177.46/27.98  | |            (107), (108), (109), (110), (111), (112), (113), (114), (116),
% 177.46/27.98  | |            (117), (118), (119), (121), (122), (123), (124), (125), (126),
% 177.46/27.98  | |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 177.46/27.98  | |            (136), (137), (138) are inconsistent by sub-proof #380.
% 177.46/27.98  | | 
% 177.46/27.98  | Case 2:
% 177.46/27.98  | | 
% 177.46/27.98  | |   (139)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.46/27.98  | | 
% 177.46/27.98  | | BETA: splitting (139) gives:
% 177.46/27.98  | | 
% 177.46/27.98  | | Case 1:
% 177.46/27.98  | | | 
% 177.46/27.98  | | |   (140)  all_58_13 = e3
% 177.46/27.98  | | | 
% 177.46/27.98  | | | REF_CLOSE: (15), (85), (140) are inconsistent by sub-proof #1026.
% 177.46/27.98  | | | 
% 177.46/27.98  | | Case 2:
% 177.46/27.98  | | | 
% 177.46/27.98  | | |   (141)  all_58_14 = e3 | all_58_15 = e3
% 177.46/27.98  | | | 
% 177.46/27.98  | | | BETA: splitting (141) gives:
% 177.46/27.98  | | | 
% 177.46/27.98  | | | Case 1:
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | |   (142)  all_58_14 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | COMBINE_EQS: (59), (142) imply:
% 177.46/27.98  | | | |   (143)  all_52_29 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | SIMP: (143) implies:
% 177.46/27.98  | | | |   (144)  all_52_29 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (82), (144) imply:
% 177.46/27.98  | | | |   (145)   ~ (all_52_5 = e3)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (6), (144) imply:
% 177.46/27.98  | | | |   (146)   ~ (all_52_13 = e3)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (22), (144) imply:
% 177.46/27.98  | | | |   (147)   ~ (all_52_25 = e3)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (99), (144) imply:
% 177.46/27.98  | | | |   (148)   ~ (all_14_2 = e3)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | SIMP: (148) implies:
% 177.46/27.98  | | | |   (149)   ~ (all_14_2 = e3)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (103), (144) imply:
% 177.46/27.98  | | | |   (150)   ~ (all_6_2 = e3)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (52), (144) imply:
% 177.46/27.98  | | | |   (151)  op(e1, e3) = all_52_28
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | GROUND_INST: instantiating (116) with all_52_17, all_52_28, e3, e1,
% 177.46/27.98  | | | |              simplifying with (110), (151) gives:
% 177.46/27.98  | | | |   (152)  all_52_17 = all_52_28
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | COMBINE_EQS: (89), (152) imply:
% 177.46/27.98  | | | |   (153)  all_58_6 = all_52_28
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (123), (152) imply:
% 177.46/27.98  | | | |   (154)   ~ (all_52_19 = all_52_28)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | SIMP: (154) implies:
% 177.46/27.98  | | | |   (155)   ~ (all_52_19 = all_52_28)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (5), (152) imply:
% 177.46/27.98  | | | |   (156)   ~ (all_52_23 = all_52_28)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | SIMP: (156) implies:
% 177.46/27.98  | | | |   (157)   ~ (all_52_23 = all_52_28)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | BETA: splitting (54) gives:
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | Case 1:
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | |   (158)  all_56_9 = e3
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | COMBINE_EQS: (29), (158) imply:
% 177.46/27.98  | | | | |   (159)  all_52_19 = e3
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | SIMP: (159) implies:
% 177.46/27.98  | | | | |   (160)  all_52_19 = e3
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | COMBINE_EQS: (37), (160) imply:
% 177.46/27.98  | | | | |   (161)  all_58_7 = e3
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | REDUCE: (96), (160) imply:
% 177.46/27.98  | | | | |   (162)   ~ (all_52_3 = e3)
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | REDUCE: (12), (160) imply:
% 177.46/27.98  | | | | |   (163)   ~ (all_52_23 = e3)
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | SIMP: (163) implies:
% 177.46/27.98  | | | | |   (164)   ~ (all_52_23 = e3)
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | REDUCE: (120), (160) imply:
% 177.46/27.98  | | | | |   (165)   ~ (all_52_27 = e3)
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | REDUCE: (92), (160) imply:
% 177.46/27.98  | | | | |   (166)  op(e2, e3) = all_52_18
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | REF_CLOSE: (9), (10), (11), (15), (17), (18), (19), (20), (23), (24),
% 177.46/27.98  | | | | |            (27), (28), (31), (32), (35), (37), (40), (41), (46), (47),
% 177.46/27.98  | | | | |            (48), (49), (50), (51), (57), (61), (68), (69), (72), (73),
% 177.46/27.98  | | | | |            (76), (80), (84), (85), (90), (93), (95), (98), (104),
% 177.46/27.98  | | | | |            (112), (113), (114), (115), (116), (117), (124), (127),
% 177.46/27.98  | | | | |            (128), (130), (136), (145), (147), (153), (155), (161),
% 177.46/27.98  | | | | |            (162), (164), (166) are inconsistent by sub-proof #727.
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | Case 2:
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | |   (167)   ~ (all_56_9 = e3)
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | REDUCE: (29), (167) imply:
% 177.46/27.98  | | | | |   (168)   ~ (all_52_19 = e3)
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | BETA: splitting (57) gives:
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | Case 1:
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | |   (169)  all_58_1 = e3
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | REF_CLOSE: (14), (17), (18), (20), (24), (28), (31), (32), (35),
% 177.46/27.98  | | | | | |            (37), (38), (41), (42), (43), (46), (47), (49), (50),
% 177.46/27.98  | | | | | |            (55), (60), (61), (64), (67), (72), (73), (76), (78),
% 177.46/27.98  | | | | | |            (80), (87), (90), (91), (93), (95), (96), (97), (98),
% 177.46/27.98  | | | | | |            (104), (106), (113), (115), (116), (124), (127), (128),
% 177.46/27.98  | | | | | |            (131), (142), (146), (149), (153), (155), (157), (169)
% 177.46/27.98  | | | | | |            are inconsistent by sub-proof #376.
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | Case 2:
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | |   (170)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | REF_CLOSE: (9), (15), (18), (28), (37), (76), (85), (114), (116),
% 177.46/27.98  | | | | | |            (136), (168), (170) are inconsistent by sub-proof #975.
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | End of split
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | End of split
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | Case 2:
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | |   (171)  all_58_15 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | COMBINE_EQS: (31), (171) imply:
% 177.46/27.98  | | | |   (172)  all_6_2 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (17), (172) imply:
% 177.46/27.98  | | | |   (173)  $false
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | CLOSE: (173) is inconsistent.
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | End of split
% 177.46/27.98  | | | 
% 177.46/27.98  | | End of split
% 177.46/27.98  | | 
% 177.46/27.98  | End of split
% 177.46/27.98  | 
% 177.46/27.98  End of proof
% 177.46/27.98  
% 177.46/27.98  Sub-proof #376 shows that the following formulas are inconsistent:
% 177.46/27.98  ----------------------------------------------------------------
% 177.46/27.98    (1)   ~ (all_52_23 = all_52_28)
% 177.46/27.98    (2)  all_58_6 = all_52_28
% 177.46/27.98    (3)  op(e1, e2) = all_52_19
% 177.46/27.98    (4)   ~ (all_6_2 = e3)
% 177.46/27.98    (5)   ~ (all_52_3 = all_10_2)
% 177.46/27.98    (6)  all_58_5 = all_52_13
% 177.46/27.98    (7)  op(e0, all_52_15) = e0
% 177.46/27.98    (8)  all_58_3 = all_10_2
% 177.46/27.98    (9)  all_58_15 = all_6_2
% 177.46/27.98    (10)   ~ (all_52_9 = all_4_2)
% 177.46/27.98    (11)  all_58_10 = all_52_15
% 177.46/27.98    (12)  all_58_7 = all_52_19
% 177.46/27.98    (13)  all_56_4 = all_52_9
% 177.46/27.98    (14)  all_58_4 = all_52_5
% 177.46/27.98    (15)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.98    (16)   ~ (e3 = e1)
% 177.46/27.98    (17)  op(e3, all_4_2) = all_4_1
% 177.46/27.98    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.98    (19)  all_58_1 = all_52_3
% 177.46/27.98    (20)  all_58_0 = all_4_2
% 177.46/27.98    (21)   ~ (all_4_1 = e2)
% 177.46/27.98    (22)   ~ (all_52_3 = all_52_5)
% 177.46/27.98    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/27.98    (24)  all_58_8 = all_14_2
% 177.46/27.98    (25)  op(e1, all_14_2) = e3
% 177.46/27.98    (26)   ~ (all_52_3 = all_4_2)
% 177.46/27.98    (27)  op(e0, e3) = all_52_25
% 177.46/27.98    (28)  op(e3, all_52_9) = e3
% 177.46/27.98    (29)   ~ (all_52_13 = e3)
% 177.46/27.98    (30)   ~ (all_52_9 = all_52_13)
% 177.46/27.98    (31)   ~ (all_52_19 = all_52_28)
% 177.46/27.98    (32)   ~ (all_52_15 = all_52_23)
% 177.46/27.98    (33)  all_58_1 = e3
% 177.46/27.98    (34)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/27.98    (35)   ~ (all_52_3 = all_52_7)
% 177.46/27.98    (36)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.98    (37)   ~ (e1 = e0)
% 177.46/27.98    (38)  all_58_11 = all_52_23
% 177.46/27.98    (39)   ~ (all_52_3 = all_52_19)
% 177.46/27.98    (40)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/27.98    (41)   ~ (all_52_7 = all_52_15)
% 177.46/27.98    (42)  all_58_2 = all_52_9
% 177.46/27.98    (43)  op(e3, e1) = all_52_5
% 177.46/27.98    (44)  op(e3, e0) = all_52_7
% 177.46/27.98    (45)  op(e3, e3) = all_4_2
% 177.46/27.98    (46)   ~ (all_14_2 = e3)
% 177.46/27.98    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.98    (48)  all_58_14 = e3
% 177.46/27.98    (49)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/27.98    (50)  all_58_9 = all_52_7
% 177.46/27.98    (51)  all_58_12 = all_52_25
% 177.46/27.98    (52)   ~ (all_52_9 = all_52_15)
% 177.46/27.98  
% 177.46/27.98  Begin of proof
% 177.46/27.98  | 
% 177.46/27.98  | COMBINE_EQS: (19), (33) imply:
% 177.46/27.98  |   (53)  all_52_3 = e3
% 177.46/27.98  | 
% 177.46/27.98  | REDUCE: (22), (53) imply:
% 177.46/27.98  |   (54)   ~ (all_52_5 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | SIMP: (54) implies:
% 177.46/27.98  |   (55)   ~ (all_52_5 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | REDUCE: (35), (53) imply:
% 177.46/27.98  |   (56)   ~ (all_52_7 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | SIMP: (56) implies:
% 177.46/27.98  |   (57)   ~ (all_52_7 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | REDUCE: (39), (53) imply:
% 177.46/27.98  |   (58)   ~ (all_52_19 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | SIMP: (58) implies:
% 177.46/27.98  |   (59)   ~ (all_52_19 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | REDUCE: (5), (53) imply:
% 177.46/27.98  |   (60)   ~ (all_10_2 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | SIMP: (60) implies:
% 177.46/27.98  |   (61)   ~ (all_10_2 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | REDUCE: (26), (53) imply:
% 177.46/27.98  |   (62)   ~ (all_4_2 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | SIMP: (62) implies:
% 177.46/27.98  |   (63)   ~ (all_4_2 = e3)
% 177.46/27.98  | 
% 177.46/27.98  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 177.46/27.98  |            (14), (15), (16), (17), (18), (20), (21), (23), (24), (25), (27),
% 177.46/27.98  |            (28), (29), (30), (31), (32), (34), (36), (37), (38), (40), (41),
% 177.46/27.98  |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 177.46/27.98  |            (55), (57), (59), (61), (63) are inconsistent by sub-proof #377.
% 177.46/27.98  | 
% 177.46/27.98  End of proof
% 177.46/27.98  
% 177.46/27.98  Sub-proof #377 shows that the following formulas are inconsistent:
% 177.46/27.98  ----------------------------------------------------------------
% 177.46/27.98    (1)   ~ (all_52_23 = all_52_28)
% 177.46/27.98    (2)  all_58_6 = all_52_28
% 177.46/27.98    (3)  op(e1, e2) = all_52_19
% 177.46/27.98    (4)   ~ (all_6_2 = e3)
% 177.46/27.98    (5)  all_58_5 = all_52_13
% 177.46/27.98    (6)  op(e0, all_52_15) = e0
% 177.46/27.98    (7)   ~ (all_4_2 = e3)
% 177.46/27.98    (8)  all_58_3 = all_10_2
% 177.46/27.98    (9)  all_58_15 = all_6_2
% 177.46/27.98    (10)   ~ (all_52_9 = all_4_2)
% 177.46/27.98    (11)  all_58_10 = all_52_15
% 177.46/27.98    (12)  all_58_7 = all_52_19
% 177.46/27.98    (13)  all_56_4 = all_52_9
% 177.46/27.98    (14)  all_58_4 = all_52_5
% 177.46/27.98    (15)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.98    (16)   ~ (e3 = e1)
% 177.46/27.98    (17)  op(e3, all_4_2) = all_4_1
% 177.46/27.98    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.98    (19)  all_58_0 = all_4_2
% 177.46/27.98    (20)   ~ (all_4_1 = e2)
% 177.46/27.98    (21)   ~ (all_10_2 = e3)
% 177.46/27.98    (22)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/27.98    (23)  all_58_8 = all_14_2
% 177.46/27.98    (24)  op(e1, all_14_2) = e3
% 177.46/27.98    (25)  op(e0, e3) = all_52_25
% 177.46/27.98    (26)   ~ (all_52_5 = e3)
% 177.46/27.98    (27)  op(e3, all_52_9) = e3
% 177.46/27.98    (28)   ~ (all_52_13 = e3)
% 177.46/27.98    (29)   ~ (all_52_9 = all_52_13)
% 177.46/27.98    (30)   ~ (all_52_19 = all_52_28)
% 177.46/27.98    (31)   ~ (all_52_15 = all_52_23)
% 177.46/27.98    (32)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/27.98    (33)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.98    (34)   ~ (e1 = e0)
% 177.46/27.98    (35)  all_58_11 = all_52_23
% 177.46/27.98    (36)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/27.98    (37)   ~ (all_52_7 = all_52_15)
% 177.46/27.98    (38)  all_58_2 = all_52_9
% 177.46/27.98    (39)  op(e3, e1) = all_52_5
% 177.46/27.98    (40)   ~ (all_52_19 = e3)
% 177.46/27.98    (41)  op(e3, e0) = all_52_7
% 177.46/27.98    (42)  op(e3, e3) = all_4_2
% 177.46/27.98    (43)   ~ (all_14_2 = e3)
% 177.46/27.98    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.98            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.98    (45)  all_58_14 = e3
% 177.46/27.98    (46)   ~ (all_52_7 = e3)
% 177.46/27.98    (47)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/27.98    (48)  all_58_9 = all_52_7
% 177.46/27.98    (49)  all_58_12 = all_52_25
% 177.46/27.98    (50)   ~ (all_52_9 = all_52_15)
% 177.46/27.98  
% 177.46/27.98  Begin of proof
% 177.46/27.98  | 
% 177.46/27.98  | BETA: splitting (15) gives:
% 177.46/27.98  | 
% 177.46/27.98  | Case 1:
% 177.46/27.98  | | 
% 177.46/27.98  | |   (51)  all_58_6 = e3
% 177.46/27.98  | | 
% 177.46/27.98  | | COMBINE_EQS: (2), (51) imply:
% 177.46/27.98  | |   (52)  all_52_28 = e3
% 177.46/27.98  | | 
% 177.46/27.98  | | SIMP: (52) implies:
% 177.46/27.98  | |   (53)  all_52_28 = e3
% 177.46/27.98  | | 
% 177.46/27.98  | | REDUCE: (1), (53) imply:
% 177.46/27.98  | |   (54)   ~ (all_52_23 = e3)
% 177.46/27.98  | | 
% 177.46/27.98  | | BETA: splitting (47) gives:
% 177.46/27.98  | | 
% 177.46/27.98  | | Case 1:
% 177.46/27.98  | | | 
% 177.46/27.98  | | |   (55)  all_58_9 = e3
% 177.46/27.98  | | | 
% 177.46/27.98  | | | COMBINE_EQS: (48), (55) imply:
% 177.46/27.98  | | |   (56)  all_52_7 = e3
% 177.46/27.98  | | | 
% 177.46/27.98  | | | REDUCE: (46), (56) imply:
% 177.46/27.98  | | |   (57)  $false
% 177.46/27.98  | | | 
% 177.46/27.98  | | | CLOSE: (57) is inconsistent.
% 177.46/27.98  | | | 
% 177.46/27.98  | | Case 2:
% 177.46/27.98  | | | 
% 177.46/27.98  | | |   (58)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/27.98  | | | 
% 177.46/27.98  | | | BETA: splitting (58) gives:
% 177.46/27.98  | | | 
% 177.46/27.98  | | | Case 1:
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | |   (59)  all_58_10 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | COMBINE_EQS: (11), (59) imply:
% 177.46/27.98  | | | |   (60)  all_52_15 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | SIMP: (60) implies:
% 177.46/27.98  | | | |   (61)  all_52_15 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (50), (61) imply:
% 177.46/27.98  | | | |   (62)   ~ (all_52_9 = e3)
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REDUCE: (6), (61) imply:
% 177.46/27.98  | | | |   (63)  op(e0, e3) = e0
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | GROUND_INST: instantiating (44) with all_52_25, e0, e3, e0, simplifying
% 177.46/27.98  | | | |              with (25), (63) gives:
% 177.46/27.98  | | | |   (64)  all_52_25 = e0
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | COMBINE_EQS: (49), (64) imply:
% 177.46/27.98  | | | |   (65)  all_58_12 = e0
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | BETA: splitting (33) gives:
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | Case 1:
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | |   (66)  all_56_4 = e3
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | REF_CLOSE: (13), (62), (66) are inconsistent by sub-proof #782.
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | Case 2:
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | |   (67)   ~ (all_56_4 = e3)
% 177.46/27.98  | | | | |   (68)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | BETA: splitting (32) gives:
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | | Case 1:
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | |   (69)  all_58_0 = e1
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | COMBINE_EQS: (19), (69) imply:
% 177.46/27.98  | | | | | |   (70)  all_4_2 = e1
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | REDUCE: (10), (70) imply:
% 177.46/27.98  | | | | | |   (71)   ~ (all_52_9 = e1)
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | REDUCE: (17), (70) imply:
% 177.46/27.98  | | | | | |   (72)  op(e3, e1) = all_4_1
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | BETA: splitting (68) gives:
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | Case 1:
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | |   (73)  all_56_4 = e2
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | COMBINE_EQS: (13), (73) imply:
% 177.46/27.98  | | | | | | |   (74)  all_52_9 = e2
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | SIMP: (74) implies:
% 177.46/27.98  | | | | | | |   (75)  all_52_9 = e2
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | REDUCE: (29), (75) imply:
% 177.46/27.98  | | | | | | |   (76)   ~ (all_52_13 = e2)
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | SIMP: (76) implies:
% 177.46/27.98  | | | | | | |   (77)   ~ (all_52_13 = e2)
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | REDUCE: (62), (75) imply:
% 177.46/27.98  | | | | | | |   (78)   ~ (e3 = e2)
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | SIMP: (78) implies:
% 177.46/27.98  | | | | | | |   (79)   ~ (e3 = e2)
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | GROUND_INST: instantiating (44) with all_52_5, all_4_1, e1, e3,
% 177.46/27.98  | | | | | | |              simplifying with (39), (72) gives:
% 177.46/27.98  | | | | | | |   (80)  all_52_5 = all_4_1
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | COMBINE_EQS: (14), (80) imply:
% 177.46/27.98  | | | | | | |   (81)  all_58_4 = all_4_1
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | BETA: splitting (36) gives:
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | Case 1:
% 177.46/27.98  | | | | | | | | 
% 177.46/27.98  | | | | | | | |   (82)  all_58_4 = e2
% 177.46/27.98  | | | | | | | | 
% 177.46/27.98  | | | | | | | | REF_CLOSE: (20), (81), (82) are inconsistent by sub-proof #673.
% 177.46/27.98  | | | | | | | | 
% 177.46/27.98  | | | | | | | Case 2:
% 177.46/27.98  | | | | | | | | 
% 177.46/27.98  | | | | | | | |   (83)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/27.98  | | | | | | | | 
% 177.46/27.98  | | | | | | | | REF_CLOSE: (3), (5), (23), (24), (40), (44), (45), (77), (79),
% 177.46/27.98  | | | | | | | |            (83) are inconsistent by sub-proof #378.
% 177.46/27.98  | | | | | | | | 
% 177.46/27.98  | | | | | | | End of split
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | Case 2:
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | |   (84)  all_56_4 = e1 | all_56_4 = e0
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | | REF_CLOSE: (13), (27), (41), (44), (46), (71), (84) are
% 177.46/27.98  | | | | | | |            inconsistent by sub-proof #754.
% 177.46/27.98  | | | | | | | 
% 177.46/27.98  | | | | | | End of split
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | Case 2:
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | |   (85)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | | REF_CLOSE: (16), (26), (27), (34), (38), (39), (44), (51), (65),
% 177.46/27.98  | | | | | |            (85) are inconsistent by sub-proof #725.
% 177.46/27.98  | | | | | | 
% 177.46/27.98  | | | | | End of split
% 177.46/27.98  | | | | | 
% 177.46/27.98  | | | | End of split
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | Case 2:
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | |   (86)  all_58_11 = e3 | all_58_15 = e3
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | | REF_CLOSE: (4), (9), (35), (54), (86) are inconsistent by sub-proof
% 177.46/27.98  | | | |            #1016.
% 177.46/27.98  | | | | 
% 177.46/27.98  | | | End of split
% 177.46/27.98  | | | 
% 177.46/27.98  | | End of split
% 177.46/27.98  | | 
% 177.46/27.98  | Case 2:
% 177.46/27.98  | | 
% 177.46/27.98  | |   (87)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.98  | | 
% 177.46/27.98  | | REF_CLOSE: (5), (7), (8), (10), (11), (12), (18), (19), (21), (22), (23),
% 177.46/27.98  | |            (27), (28), (31), (35), (38), (40), (42), (43), (44), (87) are
% 177.46/27.98  | |            inconsistent by sub-proof #964.
% 177.46/27.98  | | 
% 177.46/27.98  | End of split
% 177.46/27.98  | 
% 177.46/27.98  End of proof
% 177.46/27.98  
% 177.46/27.98  Sub-proof #378 shows that the following formulas are inconsistent:
% 177.46/27.98  ----------------------------------------------------------------
% 177.46/27.98    (1)  op(e1, e2) = all_52_19
% 177.46/27.98    (2)  all_58_5 = all_52_13
% 177.46/27.98    (3)  all_58_8 = all_14_2
% 177.46/27.98    (4)  op(e1, all_14_2) = e3
% 177.46/27.98    (5)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/27.98    (6)   ~ (all_52_19 = e3)
% 177.46/27.98    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.98    (8)   ~ (all_52_13 = e2)
% 177.46/27.98    (9)  all_58_14 = e3
% 177.46/27.98    (10)   ~ (e3 = e2)
% 177.46/27.98  
% 177.46/27.98  Begin of proof
% 177.46/27.98  | 
% 177.46/27.98  | BETA: splitting (5) gives:
% 177.46/27.98  | 
% 177.46/27.98  | Case 1:
% 177.46/27.98  | | 
% 177.46/27.98  | |   (11)  all_58_5 = e2
% 177.46/27.98  | | 
% 177.46/27.98  | | REF_CLOSE: (2), (8), (11) are inconsistent by sub-proof #391.
% 177.46/27.98  | | 
% 177.46/27.98  | Case 2:
% 177.46/27.98  | | 
% 177.46/27.98  | |   (12)  all_58_8 = e2 | all_58_14 = e2
% 177.46/27.98  | | 
% 177.46/27.98  | | BETA: splitting (12) gives:
% 177.46/27.98  | | 
% 177.46/27.98  | | Case 1:
% 177.46/27.98  | | | 
% 177.46/27.98  | | |   (13)  all_58_8 = e2
% 177.46/27.98  | | | 
% 177.46/27.98  | | | COMBINE_EQS: (3), (13) imply:
% 177.46/27.98  | | |   (14)  all_14_2 = e2
% 177.46/27.98  | | | 
% 177.46/27.98  | | | SIMP: (14) implies:
% 177.46/27.98  | | |   (15)  all_14_2 = e2
% 177.46/27.98  | | | 
% 177.46/27.98  | | | REF_CLOSE: (1), (4), (6), (7), (15) are inconsistent by sub-proof #379.
% 177.46/27.98  | | | 
% 177.46/27.98  | | Case 2:
% 177.46/27.98  | | | 
% 177.46/27.98  | | |   (16)  all_58_14 = e2
% 177.46/27.98  | | | 
% 177.46/27.98  | | | REF_CLOSE: (9), (10), (16) are inconsistent by sub-proof #905.
% 177.46/27.98  | | | 
% 177.46/27.98  | | End of split
% 177.46/27.98  | | 
% 177.46/27.98  | End of split
% 177.46/27.98  | 
% 177.46/27.98  End of proof
% 177.46/27.98  
% 177.46/27.98  Sub-proof #379 shows that the following formulas are inconsistent:
% 177.46/27.98  ----------------------------------------------------------------
% 177.46/27.98    (1)  op(e1, e2) = all_52_19
% 177.46/27.98    (2)  op(e1, all_14_2) = e3
% 177.46/27.98    (3)   ~ (all_52_19 = e3)
% 177.46/27.98    (4)  all_14_2 = e2
% 177.46/27.98    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.98  
% 177.46/27.98  Begin of proof
% 177.46/27.98  | 
% 177.46/27.98  | REDUCE: (2), (4) imply:
% 177.46/27.98  |   (6)  op(e1, e2) = e3
% 177.46/27.98  | 
% 177.46/27.98  | GROUND_INST: instantiating (5) with all_52_19, e3, e2, e1, simplifying with
% 177.46/27.98  |              (1), (6) gives:
% 177.46/27.98  |   (7)  all_52_19 = e3
% 177.46/27.98  | 
% 177.46/27.98  | REDUCE: (3), (7) imply:
% 177.46/27.98  |   (8)  $false
% 177.46/27.98  | 
% 177.46/27.98  | CLOSE: (8) is inconsistent.
% 177.46/27.98  | 
% 177.46/27.98  End of proof
% 177.46/27.98  
% 177.46/27.98  Sub-proof #380 shows that the following formulas are inconsistent:
% 177.46/27.98  ----------------------------------------------------------------
% 177.46/27.98    (1)   ~ (all_52_23 = all_14_2)
% 177.46/27.98    (2)   ~ (all_52_5 = all_52_13)
% 177.46/27.98    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/27.98    (4)   ~ (all_52_27 = all_10_2)
% 177.46/27.98    (5)   ~ (all_52_17 = all_52_23)
% 177.46/27.98    (6)   ~ (all_52_13 = all_52_29)
% 177.46/27.98    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.46/27.99    (8)  all_56_3 = all_52_7
% 177.46/27.99    (9)  op(e3, e2) = all_52_3
% 177.46/27.99    (10)   ~ (all_52_9 = all_52_25)
% 177.46/27.99    (11)   ~ (all_52_19 = all_52_23)
% 177.46/27.99    (12)  all_56_11 = all_52_23
% 177.46/27.99    (13)  op(e1, e2) = all_52_19
% 177.46/27.99    (14)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.46/27.99    (15)   ~ (all_52_3 = all_10_2)
% 177.46/27.99    (16)  all_58_5 = all_52_13
% 177.46/27.99    (17)   ~ (all_6_2 = e0)
% 177.46/27.99    (18)   ~ (all_52_25 = all_52_29)
% 177.46/27.99    (19)  op(e1, all_52_13) = e1
% 177.46/27.99    (20)  op(e0, all_52_15) = e0
% 177.46/27.99    (21)  all_56_15 = all_6_2
% 177.46/27.99    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/27.99    (23)  all_58_3 = all_10_2
% 177.46/27.99    (24)  all_56_9 = all_52_19
% 177.46/27.99    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/27.99    (26)  all_58_15 = all_6_2
% 177.46/27.99    (27)   ~ (all_52_9 = all_4_2)
% 177.46/27.99    (28)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/27.99    (29)   ~ (all_52_5 = all_52_7)
% 177.46/27.99    (30)  all_58_10 = all_52_15
% 177.46/27.99    (31)   ~ (all_52_5 = all_4_2)
% 177.46/27.99    (32)  all_58_7 = all_52_19
% 177.46/27.99    (33)  all_56_4 = all_52_9
% 177.46/27.99    (34)   ~ (all_52_17 = all_52_25)
% 177.46/27.99    (35)   ~ (all_4_0 = e2)
% 177.46/27.99    (36)  all_58_4 = all_52_5
% 177.46/27.99    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.99    (38)   ~ (all_52_27 = all_52_29)
% 177.46/27.99    (39)   ~ (all_52_17 = all_14_2)
% 177.46/27.99    (40)  op(e3, all_4_2) = all_4_1
% 177.46/27.99    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.99    (42)   ~ (all_52_7 = all_4_2)
% 177.46/27.99    (43)  all_58_1 = all_52_3
% 177.46/27.99    (44)  all_58_0 = all_4_2
% 177.46/27.99    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/27.99    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/27.99    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/27.99    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/27.99    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.99    (50)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.46/27.99    (51)  all_58_14 = all_52_29
% 177.46/27.99    (52)   ~ (all_52_3 = all_52_5)
% 177.46/27.99    (53)  op(e2, e1) = all_52_13
% 177.46/27.99    (54)  all_58_8 = all_14_2
% 177.46/27.99    (55)  all_56_1 = all_52_3
% 177.46/27.99    (56)  op(e0, e2) = all_52_27
% 177.46/27.99    (57)  op(all_4_1, all_4_2) = all_4_0
% 177.46/27.99    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/27.99    (59)   ~ (all_52_3 = all_52_27)
% 177.46/27.99    (60)   ~ (all_52_3 = all_4_2)
% 177.46/27.99    (61)  op(e0, e3) = all_52_25
% 177.46/27.99    (62)  op(e3, all_52_17) = all_52_16
% 177.46/27.99    (63)   ~ (all_52_13 = all_14_2)
% 177.46/27.99    (64)  op(e3, all_52_9) = e3
% 177.46/27.99    (65)   ~ (e3 = e0)
% 177.46/27.99    (66)   ~ (all_52_9 = all_52_13)
% 177.46/27.99    (67)  op(e0, all_52_23) = all_52_22
% 177.46/27.99    (68)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/27.99    (69)   ~ (all_52_5 = all_52_29)
% 177.46/27.99    (70)  all_56_2 = all_52_5
% 177.46/27.99    (71)  all_58_13 = all_52_27
% 177.46/27.99    (72)   ~ (all_4_1 = e1)
% 177.46/27.99    (73)  all_58_12 = e3
% 177.46/27.99    (74)   ~ (all_52_9 = all_52_17)
% 177.46/27.99    (75)  all_58_6 = all_52_17
% 177.46/27.99    (76)   ~ (all_52_3 = all_52_7)
% 177.46/27.99    (77)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.99    (78)  op(e2, all_52_19) = all_52_18
% 177.46/27.99    (79)  all_56_0 = all_4_2
% 177.46/27.99    (80)  all_58_11 = all_52_23
% 177.46/27.99    (81)   ~ (all_52_3 = all_52_19)
% 177.46/27.99    (82)   ~ (all_52_7 = all_52_15)
% 177.46/27.99    (83)   ~ (all_52_29 = all_14_2)
% 177.46/27.99    (84)   ~ (all_4_0 = e1)
% 177.46/27.99    (85)   ~ (all_52_19 = all_10_2)
% 177.46/27.99    (86)   ~ (all_52_23 = all_6_2)
% 177.46/27.99    (87)  all_58_2 = all_52_9
% 177.46/27.99    (88)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/27.99    (89)  op(e3, e1) = all_52_5
% 177.46/27.99    (90)   ~ (e2 = e1)
% 177.46/27.99    (91)  all_56_10 = all_14_2
% 177.46/27.99    (92)   ~ (all_52_25 = all_6_2)
% 177.46/27.99    (93)  op(e1, e3) = all_52_17
% 177.46/27.99    (94)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.46/27.99    (95)   ~ (all_52_25 = all_4_2)
% 177.46/27.99    (96)  op(e3, e0) = all_52_7
% 177.46/27.99    (97)  op(e2, all_10_2) = e2
% 177.46/27.99    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.99    (99)   ~ (all_52_25 = all_52_27)
% 177.46/27.99    (100)   ~ (all_52_27 = all_6_2)
% 177.46/27.99    (101)   ~ (all_52_7 = all_6_2)
% 177.46/27.99    (102)  all_56_7 = all_52_15
% 177.46/27.99    (103)   ~ (all_52_7 = all_52_23)
% 177.46/27.99    (104)   ~ (all_52_17 = all_52_19)
% 177.46/27.99    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/27.99    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/27.99    (107)  op(e1, all_14_2) = all_14_1
% 177.46/27.99    (108)  all_58_9 = all_52_7
% 177.46/27.99    (109)  all_58_12 = all_52_25
% 177.46/27.99    (110)  all_56_6 = all_52_13
% 177.46/27.99    (111)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.46/27.99    (112)   ~ (all_52_9 = all_52_15)
% 177.46/27.99    (113)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/27.99    (114)   ~ (e3 = e2)
% 177.46/27.99    (115)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.46/27.99    (116)   ~ (all_52_19 = all_14_2)
% 177.46/27.99    (117)  op(e2, e3) = all_52_9
% 177.46/27.99    (118)  all_56_13 = all_52_27
% 177.46/27.99  
% 177.46/27.99  Begin of proof
% 177.46/27.99  | 
% 177.46/27.99  | COMBINE_EQS: (73), (109) imply:
% 177.46/27.99  |   (119)  all_52_25 = e3
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (119) implies:
% 177.46/27.99  |   (120)  all_52_25 = e3
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (10), (120) imply:
% 177.46/27.99  |   (121)   ~ (all_52_9 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (34), (120) imply:
% 177.46/27.99  |   (122)   ~ (all_52_17 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (99), (120) imply:
% 177.46/27.99  |   (123)   ~ (all_52_27 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (123) implies:
% 177.46/27.99  |   (124)   ~ (all_52_27 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (18), (120) imply:
% 177.46/27.99  |   (125)   ~ (all_52_29 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (125) implies:
% 177.46/27.99  |   (126)   ~ (all_52_29 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (92), (120) imply:
% 177.46/27.99  |   (127)   ~ (all_6_2 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (127) implies:
% 177.46/27.99  |   (128)   ~ (all_6_2 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (95), (120) imply:
% 177.46/27.99  |   (129)   ~ (all_4_2 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (129) implies:
% 177.46/27.99  |   (130)   ~ (all_4_2 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (61), (120) imply:
% 177.46/27.99  |   (131)  op(e0, e3) = e3
% 177.46/27.99  | 
% 177.46/27.99  | BETA: splitting (77) gives:
% 177.46/27.99  | 
% 177.46/27.99  | Case 1:
% 177.46/27.99  | | 
% 177.46/27.99  | |   (132)  all_56_4 = e3
% 177.46/27.99  | | 
% 177.46/27.99  | | REF_CLOSE: (33), (121), (132) are inconsistent by sub-proof #782.
% 177.46/27.99  | | 
% 177.46/27.99  | Case 2:
% 177.46/27.99  | | 
% 177.46/27.99  | |   (133)   ~ (all_56_4 = e3)
% 177.46/27.99  | |   (134)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.99  | | 
% 177.46/27.99  | | BETA: splitting (25) gives:
% 177.46/27.99  | | 
% 177.46/27.99  | | Case 1:
% 177.46/27.99  | | | 
% 177.46/27.99  | | |   (135)  all_56_0 = e3
% 177.46/27.99  | | | 
% 177.46/27.99  | | | COMBINE_EQS: (79), (135) imply:
% 177.46/27.99  | | |   (136)  all_4_2 = e3
% 177.46/27.99  | | | 
% 177.46/27.99  | | | REDUCE: (130), (136) imply:
% 177.46/27.99  | | |   (137)  $false
% 177.46/27.99  | | | 
% 177.46/27.99  | | | CLOSE: (137) is inconsistent.
% 177.46/27.99  | | | 
% 177.46/27.99  | | Case 2:
% 177.46/27.99  | | | 
% 177.46/27.99  | | |   (138)   ~ (all_56_0 = e3)
% 177.46/27.99  | | |   (139)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/27.99  | | | 
% 177.46/27.99  | | | BETA: splitting (46) gives:
% 177.46/27.99  | | | 
% 177.46/27.99  | | | Case 1:
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | |   (140)  all_56_1 = e3
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | | COMBINE_EQS: (55), (140) imply:
% 177.46/27.99  | | | |   (141)  all_52_3 = e3
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | | SIMP: (141) implies:
% 177.46/27.99  | | | |   (142)  all_52_3 = e3
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | | REF_CLOSE: (1), (3), (5), (6), (8), (16), (17), (19), (20), (21), (23),
% 177.46/27.99  | | | |            (26), (27), (28), (29), (30), (31), (32), (33), (36), (38),
% 177.46/27.99  | | | |            (39), (42), (43), (44), (48), (51), (52), (53), (54), (58),
% 177.46/27.99  | | | |            (62), (64), (65), (71), (74), (76), (79), (80), (89), (93),
% 177.46/27.99  | | | |            (94), (96), (97), (98), (100), (101), (102), (103), (104),
% 177.46/27.99  | | | |            (105), (106), (108), (113), (114), (126), (128), (131),
% 177.46/27.99  | | | |            (134), (139), (142) are inconsistent by sub-proof #386.
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | Case 2:
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | |   (143)   ~ (all_56_1 = e3)
% 177.46/27.99  | | | |   (144)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | | REDUCE: (55), (143) imply:
% 177.46/27.99  | | | |   (145)   ~ (all_52_3 = e3)
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | | BETA: splitting (49) gives:
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | | Case 1:
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | |   (146)  all_58_1 = e3
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | | COMBINE_EQS: (43), (146) imply:
% 177.46/27.99  | | | | |   (147)  all_52_3 = e3
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | | REDUCE: (145), (147) imply:
% 177.46/27.99  | | | | |   (148)  $false
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | | CLOSE: (148) is inconsistent.
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | Case 2:
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | |   (149)   ~ (all_58_1 = e3)
% 177.46/27.99  | | | | |   (150)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | | BETA: splitting (111) gives:
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | | Case 1:
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | |   (151)  all_58_0 = e3
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | | COMBINE_EQS: (44), (151) imply:
% 177.46/27.99  | | | | | |   (152)  all_4_2 = e3
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | | REDUCE: (130), (152) imply:
% 177.46/27.99  | | | | | |   (153)  $false
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | | CLOSE: (153) is inconsistent.
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | Case 2:
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | |   (154)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | | BETA: splitting (22) gives:
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | | Case 1:
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | |   (155)  all_58_0 = e2
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | COMBINE_EQS: (44), (155) imply:
% 177.46/27.99  | | | | | | |   (156)  all_4_2 = e2
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | REDUCE: (60), (156) imply:
% 177.46/27.99  | | | | | | |   (157)   ~ (all_52_3 = e2)
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | REDUCE: (57), (156) imply:
% 177.46/27.99  | | | | | | |   (158)  op(all_4_1, e2) = all_4_0
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | REDUCE: (40), (156) imply:
% 177.46/27.99  | | | | | | |   (159)  op(e3, e2) = all_4_1
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | GROUND_INST: instantiating (98) with all_52_3, all_4_1, e2, e3,
% 177.46/27.99  | | | | | | |              simplifying with (9), (159) gives:
% 177.46/27.99  | | | | | | |   (160)  all_52_3 = all_4_1
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | COMBINE_EQS: (55), (160) imply:
% 177.46/27.99  | | | | | | |   (161)  all_56_1 = all_4_1
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | REDUCE: (59), (160) imply:
% 177.46/27.99  | | | | | | |   (162)   ~ (all_52_27 = all_4_1)
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | SIMP: (162) implies:
% 177.46/27.99  | | | | | | |   (163)   ~ (all_52_27 = all_4_1)
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | REDUCE: (145), (160) imply:
% 177.46/27.99  | | | | | | |   (164)   ~ (all_4_1 = e3)
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | REDUCE: (157), (160) imply:
% 177.46/27.99  | | | | | | |   (165)   ~ (all_4_1 = e2)
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | BETA: splitting (144) gives:
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | |   (166)  all_56_1 = e2
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | COMBINE_EQS: (161), (166) imply:
% 177.46/27.99  | | | | | | | |   (167)  all_4_1 = e2
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | REDUCE: (165), (167) imply:
% 177.46/27.99  | | | | | | | |   (168)  $false
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | CLOSE: (168) is inconsistent.
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | |   (169)  all_56_1 = e1 | all_56_1 = e0
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | BETA: splitting (169) gives:
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | |   (170)  all_56_1 = e1
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | COMBINE_EQS: (161), (170) imply:
% 177.46/27.99  | | | | | | | | |   (171)  all_4_1 = e1
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | REDUCE: (72), (171) imply:
% 177.46/27.99  | | | | | | | | |   (172)  $false
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | CLOSE: (172) is inconsistent.
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | |   (173)  all_56_1 = e0
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | COMBINE_EQS: (161), (173) imply:
% 177.46/27.99  | | | | | | | | |   (174)  all_4_1 = e0
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | REDUCE: (163), (174) imply:
% 177.46/27.99  | | | | | | | | |   (175)   ~ (all_52_27 = e0)
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | REDUCE: (164), (174) imply:
% 177.46/27.99  | | | | | | | | |   (176)   ~ (e3 = e0)
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | REDUCE: (158), (174) imply:
% 177.46/27.99  | | | | | | | | |   (177)  op(e0, e2) = all_4_0
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | BETA: splitting (7) gives:
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | |   (178)  all_58_12 = e0
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | REF_CLOSE: (65), (73), (178) are inconsistent by sub-proof
% 177.46/27.99  | | | | | | | | | |            #682.
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | |   (179)  all_58_13 = e0 | all_58_14 = e0
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | BETA: splitting (179) gives:
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | |   (180)  all_58_13 = e0
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | REF_CLOSE: (71), (175), (180) are inconsistent by sub-proof
% 177.46/27.99  | | | | | | | | | | |            #731.
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | |   (181)  all_58_14 = e0
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | COMBINE_EQS: (51), (181) imply:
% 177.46/27.99  | | | | | | | | | | |   (182)  all_52_29 = e0
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | SIMP: (182) implies:
% 177.46/27.99  | | | | | | | | | | |   (183)  all_52_29 = e0
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | GROUND_INST: instantiating (98) with all_52_27, all_4_0, e2,
% 177.46/27.99  | | | | | | | | | | |              e0, simplifying with (56), (177) gives:
% 177.46/27.99  | | | | | | | | | | |   (184)  all_52_27 = all_4_0
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | REF_CLOSE: (14), (35), (84), (118), (175), (184) are
% 177.46/27.99  | | | | | | | | | | |            inconsistent by sub-proof #650.
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | End of split
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | End of split
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | End of split
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | End of split
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | Case 2:
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | |   (185)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | BETA: splitting (115) gives:
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | |   (186)  all_56_2 = e3
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | COMBINE_EQS: (70), (186) imply:
% 177.46/27.99  | | | | | | | |   (187)  all_52_5 = e3
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12),
% 177.46/27.99  | | | | | | | |            (13), (15), (16), (17), (19), (20), (21), (22), (23),
% 177.46/27.99  | | | | | | | |            (24), (26), (27), (28), (29), (30), (31), (32), (33),
% 177.46/27.99  | | | | | | | |            (36), (37), (38), (39), (41), (42), (43), (44), (45),
% 177.46/27.99  | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54), (58),
% 177.46/27.99  | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 177.46/27.99  | | | | | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 177.46/27.99  | | | | | | | |            (82), (83), (85), (86), (87), (88), (89), (90), (91),
% 177.46/27.99  | | | | | | | |            (93), (96), (97), (98), (100), (101), (103), (104),
% 177.46/27.99  | | | | | | | |            (105), (106), (107), (108), (110), (112), (113),
% 177.46/27.99  | | | | | | | |            (114), (116), (117), (121), (124), (128), (131),
% 177.46/27.99  | | | | | | | |            (139), (187) are inconsistent by sub-proof #381.
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | |   (188)   ~ (all_56_2 = e3)
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | REDUCE: (70), (188) imply:
% 177.46/27.99  | | | | | | | |   (189)   ~ (all_52_5 = e3)
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | BETA: splitting (154) gives:
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | |   (190)  all_58_1 = e3
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | COMBINE_EQS: (43), (190) imply:
% 177.46/27.99  | | | | | | | | |   (191)  all_52_3 = e3
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | REDUCE: (145), (191) imply:
% 177.46/27.99  | | | | | | | | |   (192)  $false
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | CLOSE: (192) is inconsistent.
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | |   (193)  all_58_4 = e3 | all_58_9 = e3
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | BETA: splitting (193) gives:
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | |   (194)  all_58_4 = e3
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | REF_CLOSE: (36), (189), (194) are inconsistent by sub-proof
% 177.46/27.99  | | | | | | | | | |            #1025.
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | |   (195)  all_58_9 = e3
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | COMBINE_EQS: (108), (195) imply:
% 177.46/27.99  | | | | | | | | | |   (196)  all_52_7 = e3
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | SIMP: (196) implies:
% 177.46/27.99  | | | | | | | | | |   (197)  all_52_7 = e3
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | REDUCE: (82), (197) imply:
% 177.46/27.99  | | | | | | | | | |   (198)   ~ (all_52_15 = e3)
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | SIMP: (198) implies:
% 177.46/27.99  | | | | | | | | | |   (199)   ~ (all_52_15 = e3)
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | REDUCE: (103), (197) imply:
% 177.46/27.99  | | | | | | | | | |   (200)   ~ (all_52_23 = e3)
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | SIMP: (200) implies:
% 177.46/27.99  | | | | | | | | | |   (201)   ~ (all_52_23 = e3)
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | BETA: splitting (41) gives:
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | |   (202)  all_58_2 = e3
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | REF_CLOSE: (87), (121), (202) are inconsistent by sub-proof
% 177.46/27.99  | | | | | | | | | | |            #980.
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | |   (203)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | BETA: splitting (37) gives:
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | Case 1:
% 177.46/27.99  | | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | |   (204)  all_58_6 = e3
% 177.46/27.99  | | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | | REF_CLOSE: (75), (122), (204) are inconsistent by sub-proof
% 177.46/27.99  | | | | | | | | | | | |            #981.
% 177.46/27.99  | | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | Case 2:
% 177.46/27.99  | | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | |   (205)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.99  | | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | | REF_CLOSE: (4), (9), (15), (16), (19), (23), (30), (32),
% 177.46/27.99  | | | | | | | | | | | |            (50), (54), (63), (64), (71), (73), (75), (78),
% 177.46/27.99  | | | | | | | | | | | |            (80), (81), (85), (87), (90), (93), (97), (98),
% 177.46/27.99  | | | | | | | | | | | |            (110), (114), (117), (150), (185), (199), (201),
% 177.46/27.99  | | | | | | | | | | | |            (203), (205) are inconsistent by sub-proof #430.
% 177.46/27.99  | | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | | End of split
% 177.46/27.99  | | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | | End of split
% 177.46/27.99  | | | | | | | | | | 
% 177.46/27.99  | | | | | | | | | End of split
% 177.46/27.99  | | | | | | | | | 
% 177.46/27.99  | | | | | | | | End of split
% 177.46/27.99  | | | | | | | | 
% 177.46/27.99  | | | | | | | End of split
% 177.46/27.99  | | | | | | | 
% 177.46/27.99  | | | | | | End of split
% 177.46/27.99  | | | | | | 
% 177.46/27.99  | | | | | End of split
% 177.46/27.99  | | | | | 
% 177.46/27.99  | | | | End of split
% 177.46/27.99  | | | | 
% 177.46/27.99  | | | End of split
% 177.46/27.99  | | | 
% 177.46/27.99  | | End of split
% 177.46/27.99  | | 
% 177.46/27.99  | End of split
% 177.46/27.99  | 
% 177.46/27.99  End of proof
% 177.46/27.99  
% 177.46/27.99  Sub-proof #381 shows that the following formulas are inconsistent:
% 177.46/27.99  ----------------------------------------------------------------
% 177.46/27.99    (1)   ~ (all_52_23 = all_14_2)
% 177.46/27.99    (2)   ~ (all_52_5 = all_52_13)
% 177.46/27.99    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/27.99    (4)   ~ (all_52_27 = all_10_2)
% 177.46/27.99    (5)   ~ (all_52_17 = all_52_23)
% 177.46/27.99    (6)   ~ (all_52_13 = all_52_29)
% 177.46/27.99    (7)  all_56_3 = all_52_7
% 177.46/27.99    (8)  op(e3, e2) = all_52_3
% 177.46/27.99    (9)   ~ (all_52_19 = all_52_23)
% 177.46/27.99    (10)  all_56_11 = all_52_23
% 177.46/27.99    (11)  op(e1, e2) = all_52_19
% 177.46/27.99    (12)   ~ (all_52_27 = e3)
% 177.46/27.99    (13)   ~ (all_6_2 = e3)
% 177.46/27.99    (14)   ~ (all_52_3 = all_10_2)
% 177.46/27.99    (15)  all_58_5 = all_52_13
% 177.46/27.99    (16)   ~ (all_6_2 = e0)
% 177.46/27.99    (17)  op(e1, all_52_13) = e1
% 177.46/27.99    (18)  op(e0, all_52_15) = e0
% 177.46/27.99    (19)  all_56_15 = all_6_2
% 177.46/27.99    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/27.99    (21)  all_58_3 = all_10_2
% 177.46/27.99    (22)  all_56_9 = all_52_19
% 177.46/27.99    (23)  all_58_15 = all_6_2
% 177.46/27.99    (24)   ~ (all_52_9 = all_4_2)
% 177.46/27.99    (25)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/27.99    (26)   ~ (all_52_5 = all_52_7)
% 177.46/27.99    (27)  all_58_10 = all_52_15
% 177.46/27.99    (28)   ~ (all_52_5 = all_4_2)
% 177.46/27.99    (29)  all_58_7 = all_52_19
% 177.46/27.99    (30)  all_56_4 = all_52_9
% 177.46/27.99    (31)  all_58_4 = all_52_5
% 177.46/27.99    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.99    (33)   ~ (all_52_27 = all_52_29)
% 177.46/27.99    (34)   ~ (all_52_17 = all_14_2)
% 177.46/27.99    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.99    (36)   ~ (all_52_7 = all_4_2)
% 177.46/27.99    (37)  all_58_1 = all_52_3
% 177.46/27.99    (38)  all_58_0 = all_4_2
% 177.46/27.99    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/27.99    (40)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/27.99    (41)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/27.99    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.99    (43)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.46/27.99    (44)  all_58_14 = all_52_29
% 177.46/27.99    (45)  op(e0, e3) = e3
% 177.46/27.99    (46)   ~ (all_52_3 = all_52_5)
% 177.46/27.99    (47)  op(e2, e1) = all_52_13
% 177.46/27.99    (48)  all_58_8 = all_14_2
% 177.46/27.99    (49)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/27.99    (50)  op(e3, all_52_17) = all_52_16
% 177.46/27.99    (51)   ~ (all_52_13 = all_14_2)
% 177.46/27.99    (52)  op(e3, all_52_9) = e3
% 177.46/27.99    (53)   ~ (e3 = e0)
% 177.46/27.99    (54)   ~ (all_52_9 = all_52_13)
% 177.46/27.99    (55)  op(e0, all_52_23) = all_52_22
% 177.46/27.99    (56)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/27.99    (57)   ~ (all_52_5 = all_52_29)
% 177.46/27.99    (58)  all_58_13 = all_52_27
% 177.46/27.99    (59)  all_52_5 = e3
% 177.46/27.99    (60)  all_58_12 = e3
% 177.46/27.99    (61)   ~ (all_52_9 = all_52_17)
% 177.46/27.99    (62)  all_58_6 = all_52_17
% 177.46/27.99    (63)   ~ (all_52_3 = all_52_7)
% 177.46/27.99    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/27.99    (65)  op(e2, all_52_19) = all_52_18
% 177.46/27.99    (66)  all_56_0 = all_4_2
% 177.46/27.99    (67)  all_58_11 = all_52_23
% 177.46/27.99    (68)   ~ (all_52_3 = all_52_19)
% 177.46/27.99    (69)   ~ (all_52_7 = all_52_15)
% 177.46/27.99    (70)   ~ (all_52_29 = all_14_2)
% 177.46/27.99    (71)   ~ (all_52_19 = all_10_2)
% 177.46/27.99    (72)   ~ (all_52_9 = e3)
% 177.46/27.99    (73)   ~ (all_52_23 = all_6_2)
% 177.46/27.99    (74)  all_58_2 = all_52_9
% 177.46/27.99    (75)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/27.99    (76)  op(e3, e1) = all_52_5
% 177.46/27.99    (77)   ~ (e2 = e1)
% 177.46/27.99    (78)  all_56_10 = all_14_2
% 177.46/27.99    (79)  op(e1, e3) = all_52_17
% 177.46/27.99    (80)  op(e3, e0) = all_52_7
% 177.46/27.99    (81)  op(e2, all_10_2) = e2
% 177.46/27.99    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/27.99            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/27.99    (83)   ~ (all_52_27 = all_6_2)
% 177.46/27.99    (84)   ~ (all_52_7 = all_6_2)
% 177.46/27.99    (85)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/27.99    (86)   ~ (all_52_7 = all_52_23)
% 177.46/27.99    (87)   ~ (all_52_17 = all_52_19)
% 177.46/27.99    (88)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/27.99    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/27.99    (90)  op(e1, all_14_2) = all_14_1
% 177.46/27.99    (91)  all_58_9 = all_52_7
% 177.46/27.99    (92)  all_56_6 = all_52_13
% 177.46/27.99    (93)   ~ (all_52_9 = all_52_15)
% 177.46/27.99    (94)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/27.99    (95)   ~ (e3 = e2)
% 177.46/27.99    (96)   ~ (all_52_19 = all_14_2)
% 177.46/27.99    (97)  op(e2, e3) = all_52_9
% 177.46/27.99  
% 177.46/27.99  Begin of proof
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (59) implies:
% 177.46/27.99  |   (98)  all_52_5 = e3
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (2), (98) imply:
% 177.46/27.99  |   (99)   ~ (all_52_13 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (99) implies:
% 177.46/27.99  |   (100)   ~ (all_52_13 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REDUCE: (57), (98) imply:
% 177.46/27.99  |   (101)   ~ (all_52_29 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | SIMP: (101) implies:
% 177.46/27.99  |   (102)   ~ (all_52_29 = e3)
% 177.46/27.99  | 
% 177.46/27.99  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 177.46/27.99  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.46/27.99  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.46/27.99  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.46/27.99  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (58),
% 177.46/27.99  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 177.46/27.99  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 177.46/27.99  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 177.46/27.99  |            (93), (94), (95), (96), (97), (100), (102) are inconsistent by
% 177.46/27.99  |            sub-proof #382.
% 177.46/27.99  | 
% 177.46/27.99  End of proof
% 177.46/27.99  
% 177.46/27.99  Sub-proof #382 shows that the following formulas are inconsistent:
% 177.46/27.99  ----------------------------------------------------------------
% 177.46/27.99    (1)   ~ (all_52_23 = all_14_2)
% 177.46/27.99    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/27.99    (3)   ~ (all_52_27 = all_10_2)
% 177.46/27.99    (4)   ~ (all_52_17 = all_52_23)
% 177.46/27.99    (5)   ~ (all_52_13 = all_52_29)
% 177.46/27.99    (6)  all_56_3 = all_52_7
% 177.46/27.99    (7)  op(e3, e2) = all_52_3
% 177.46/27.99    (8)   ~ (all_52_19 = all_52_23)
% 177.46/27.99    (9)  all_56_11 = all_52_23
% 177.46/27.99    (10)  op(e1, e2) = all_52_19
% 177.46/27.99    (11)   ~ (all_52_27 = e3)
% 177.46/27.99    (12)   ~ (all_6_2 = e3)
% 177.46/27.99    (13)   ~ (all_52_3 = all_10_2)
% 177.46/27.99    (14)  all_58_5 = all_52_13
% 177.46/27.99    (15)   ~ (all_6_2 = e0)
% 177.46/27.99    (16)  op(e1, all_52_13) = e1
% 177.46/27.99    (17)  op(e0, all_52_15) = e0
% 177.46/27.99    (18)  all_56_15 = all_6_2
% 177.46/27.99    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/27.99    (20)  all_58_3 = all_10_2
% 177.46/27.99    (21)  all_56_9 = all_52_19
% 177.46/27.99    (22)  all_58_15 = all_6_2
% 177.46/27.99    (23)   ~ (all_52_9 = all_4_2)
% 177.46/27.99    (24)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/27.99    (25)   ~ (all_52_5 = all_52_7)
% 177.46/27.99    (26)  all_58_10 = all_52_15
% 177.46/27.99    (27)   ~ (all_52_5 = all_4_2)
% 177.46/27.99    (28)  all_58_7 = all_52_19
% 177.46/27.99    (29)  all_56_4 = all_52_9
% 177.46/27.99    (30)  all_58_4 = all_52_5
% 177.46/27.99    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/27.99    (32)   ~ (all_52_27 = all_52_29)
% 177.46/27.99    (33)   ~ (all_52_17 = all_14_2)
% 177.46/27.99    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/27.99    (35)   ~ (all_52_7 = all_4_2)
% 177.46/27.99    (36)  all_58_1 = all_52_3
% 177.46/27.99    (37)  all_58_0 = all_4_2
% 177.46/27.99    (38)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/27.99    (39)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/27.99    (40)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/27.99    (41)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/27.99    (42)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.46/27.99    (43)  all_58_14 = all_52_29
% 177.46/28.00    (44)  op(e0, e3) = e3
% 177.46/28.00    (45)   ~ (all_52_3 = all_52_5)
% 177.46/28.00    (46)  op(e2, e1) = all_52_13
% 177.46/28.00    (47)  all_58_8 = all_14_2
% 177.46/28.00    (48)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/28.00    (49)  op(e3, all_52_17) = all_52_16
% 177.46/28.00    (50)   ~ (all_52_29 = e3)
% 177.46/28.00    (51)   ~ (all_52_13 = all_14_2)
% 177.46/28.00    (52)  op(e3, all_52_9) = e3
% 177.46/28.00    (53)   ~ (e3 = e0)
% 177.46/28.00    (54)   ~ (all_52_13 = e3)
% 177.46/28.00    (55)   ~ (all_52_9 = all_52_13)
% 177.46/28.00    (56)  op(e0, all_52_23) = all_52_22
% 177.46/28.00    (57)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/28.00    (58)  all_58_13 = all_52_27
% 177.46/28.00    (59)  all_58_12 = e3
% 177.46/28.00    (60)   ~ (all_52_9 = all_52_17)
% 177.46/28.00    (61)  all_58_6 = all_52_17
% 177.46/28.00    (62)   ~ (all_52_3 = all_52_7)
% 177.46/28.00    (63)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.00    (64)  op(e2, all_52_19) = all_52_18
% 177.46/28.00    (65)  all_56_0 = all_4_2
% 177.46/28.00    (66)  all_58_11 = all_52_23
% 177.46/28.00    (67)   ~ (all_52_3 = all_52_19)
% 177.46/28.00    (68)   ~ (all_52_7 = all_52_15)
% 177.46/28.00    (69)   ~ (all_52_29 = all_14_2)
% 177.46/28.00    (70)   ~ (all_52_19 = all_10_2)
% 177.46/28.00    (71)   ~ (all_52_9 = e3)
% 177.46/28.00    (72)   ~ (all_52_23 = all_6_2)
% 177.46/28.00    (73)  all_58_2 = all_52_9
% 177.46/28.00    (74)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/28.00    (75)  op(e3, e1) = all_52_5
% 177.46/28.00    (76)   ~ (e2 = e1)
% 177.46/28.00    (77)  all_56_10 = all_14_2
% 177.46/28.00    (78)  op(e1, e3) = all_52_17
% 177.46/28.00    (79)  op(e3, e0) = all_52_7
% 177.46/28.00    (80)  op(e2, all_10_2) = e2
% 177.46/28.00    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.00    (82)   ~ (all_52_27 = all_6_2)
% 177.46/28.00    (83)   ~ (all_52_7 = all_6_2)
% 177.46/28.00    (84)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.00    (85)   ~ (all_52_7 = all_52_23)
% 177.46/28.00    (86)   ~ (all_52_17 = all_52_19)
% 177.46/28.00    (87)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/28.00    (89)  op(e1, all_14_2) = all_14_1
% 177.46/28.00    (90)  all_58_9 = all_52_7
% 177.46/28.00    (91)  all_56_6 = all_52_13
% 177.46/28.00    (92)   ~ (all_52_9 = all_52_15)
% 177.46/28.00    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00    (94)   ~ (e3 = e2)
% 177.46/28.00    (95)   ~ (all_52_19 = all_14_2)
% 177.46/28.00    (96)  op(e2, e3) = all_52_9
% 177.46/28.00  
% 177.46/28.00  Begin of proof
% 177.46/28.00  | 
% 177.46/28.00  | BETA: splitting (93) gives:
% 177.46/28.00  | 
% 177.46/28.00  | Case 1:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (97)  all_58_4 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | COMBINE_EQS: (30), (97) imply:
% 177.46/28.00  | |   (98)  all_52_5 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REF_CLOSE: (7), (8), (11), (12), (13), (17), (20), (21), (22), (25), (26),
% 177.46/28.00  | |            (28), (36), (39), (41), (44), (45), (52), (53), (58), (66), (80),
% 177.46/28.00  | |            (81), (87), (90), (96), (98) are inconsistent by sub-proof #384.
% 177.46/28.00  | | 
% 177.46/28.00  | Case 2:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (99)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | BETA: splitting (99) gives:
% 177.46/28.00  | | 
% 177.46/28.00  | | Case 1:
% 177.46/28.00  | | | 
% 177.46/28.00  | | |   (100)  all_58_5 = e3
% 177.46/28.00  | | | 
% 177.46/28.00  | | | REF_CLOSE: (14), (54), (100) are inconsistent by sub-proof #969.
% 177.46/28.00  | | | 
% 177.46/28.00  | | Case 2:
% 177.46/28.00  | | | 
% 177.46/28.00  | | |   (101)  all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00  | | | 
% 177.46/28.00  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.46/28.00  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 177.46/28.00  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 177.46/28.00  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 177.46/28.00  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 177.46/28.00  | | |            (53), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 177.46/28.00  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 177.46/28.00  | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 177.46/28.00  | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 177.46/28.00  | | |            (94), (95), (96), (101) are inconsistent by sub-proof #383.
% 177.46/28.00  | | | 
% 177.46/28.00  | | End of split
% 177.46/28.00  | | 
% 177.46/28.00  | End of split
% 177.46/28.00  | 
% 177.46/28.00  End of proof
% 177.46/28.00  
% 177.46/28.00  Sub-proof #383 shows that the following formulas are inconsistent:
% 177.46/28.00  ----------------------------------------------------------------
% 177.46/28.00    (1)   ~ (all_52_23 = all_14_2)
% 177.46/28.00    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/28.00    (3)   ~ (all_52_27 = all_10_2)
% 177.46/28.00    (4)   ~ (all_52_17 = all_52_23)
% 177.46/28.00    (5)   ~ (all_52_13 = all_52_29)
% 177.46/28.00    (6)  all_56_3 = all_52_7
% 177.46/28.00    (7)  op(e3, e2) = all_52_3
% 177.46/28.00    (8)   ~ (all_52_19 = all_52_23)
% 177.46/28.00    (9)  all_56_11 = all_52_23
% 177.46/28.00    (10)  op(e1, e2) = all_52_19
% 177.46/28.00    (11)   ~ (all_52_27 = e3)
% 177.46/28.00    (12)   ~ (all_6_2 = e3)
% 177.46/28.00    (13)   ~ (all_52_3 = all_10_2)
% 177.46/28.00    (14)  all_58_5 = all_52_13
% 177.46/28.00    (15)   ~ (all_6_2 = e0)
% 177.46/28.00    (16)  op(e1, all_52_13) = e1
% 177.46/28.00    (17)  op(e0, all_52_15) = e0
% 177.46/28.00    (18)  all_56_15 = all_6_2
% 177.46/28.00    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/28.00    (20)  all_58_3 = all_10_2
% 177.46/28.00    (21)  all_56_9 = all_52_19
% 177.46/28.00    (22)  all_58_15 = all_6_2
% 177.46/28.00    (23)   ~ (all_52_9 = all_4_2)
% 177.46/28.00    (24)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.00    (25)   ~ (all_52_5 = all_52_7)
% 177.46/28.00    (26)  all_58_10 = all_52_15
% 177.46/28.00    (27)   ~ (all_52_5 = all_4_2)
% 177.46/28.00    (28)  all_58_7 = all_52_19
% 177.46/28.00    (29)  all_56_4 = all_52_9
% 177.46/28.00    (30)  all_58_4 = all_52_5
% 177.46/28.00    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.00    (32)   ~ (all_52_27 = all_52_29)
% 177.46/28.00    (33)   ~ (all_52_17 = all_14_2)
% 177.46/28.00    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/28.00    (35)   ~ (all_52_7 = all_4_2)
% 177.46/28.00    (36)  all_58_1 = all_52_3
% 177.46/28.00    (37)  all_58_0 = all_4_2
% 177.46/28.00    (38)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/28.00    (39)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/28.00    (40)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/28.00    (41)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/28.00    (42)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.46/28.00    (43)  all_58_14 = all_52_29
% 177.46/28.00    (44)  op(e0, e3) = e3
% 177.46/28.00    (45)   ~ (all_52_3 = all_52_5)
% 177.46/28.00    (46)  op(e2, e1) = all_52_13
% 177.46/28.00    (47)  all_58_8 = all_14_2
% 177.46/28.00    (48)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/28.00    (49)  op(e3, all_52_17) = all_52_16
% 177.46/28.00    (50)   ~ (all_52_29 = e3)
% 177.46/28.00    (51)   ~ (all_52_13 = all_14_2)
% 177.46/28.00    (52)  op(e3, all_52_9) = e3
% 177.46/28.00    (53)   ~ (e3 = e0)
% 177.46/28.00    (54)   ~ (all_52_9 = all_52_13)
% 177.46/28.00    (55)  op(e0, all_52_23) = all_52_22
% 177.46/28.00    (56)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/28.00    (57)  all_58_13 = all_52_27
% 177.46/28.00    (58)  all_58_12 = e3
% 177.46/28.00    (59)   ~ (all_52_9 = all_52_17)
% 177.46/28.00    (60)  all_58_6 = all_52_17
% 177.46/28.00    (61)   ~ (all_52_3 = all_52_7)
% 177.46/28.00    (62)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.00    (63)  op(e2, all_52_19) = all_52_18
% 177.46/28.00    (64)  all_56_0 = all_4_2
% 177.46/28.00    (65)  all_58_11 = all_52_23
% 177.46/28.00    (66)   ~ (all_52_3 = all_52_19)
% 177.46/28.00    (67)   ~ (all_52_7 = all_52_15)
% 177.46/28.00    (68)   ~ (all_52_29 = all_14_2)
% 177.46/28.00    (69)   ~ (all_52_19 = all_10_2)
% 177.46/28.00    (70)   ~ (all_52_9 = e3)
% 177.46/28.00    (71)   ~ (all_52_23 = all_6_2)
% 177.46/28.00    (72)  all_58_2 = all_52_9
% 177.46/28.00    (73)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/28.00    (74)  op(e3, e1) = all_52_5
% 177.46/28.00    (75)   ~ (e2 = e1)
% 177.46/28.00    (76)  all_56_10 = all_14_2
% 177.46/28.00    (77)  all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00    (78)  op(e1, e3) = all_52_17
% 177.46/28.00    (79)  op(e3, e0) = all_52_7
% 177.46/28.00    (80)  op(e2, all_10_2) = e2
% 177.46/28.00    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.00    (82)   ~ (all_52_27 = all_6_2)
% 177.46/28.00    (83)   ~ (all_52_7 = all_6_2)
% 177.46/28.00    (84)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.00    (85)   ~ (all_52_7 = all_52_23)
% 177.46/28.00    (86)   ~ (all_52_17 = all_52_19)
% 177.46/28.00    (87)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/28.00    (89)  op(e1, all_14_2) = all_14_1
% 177.46/28.00    (90)  all_58_9 = all_52_7
% 177.46/28.00    (91)  all_56_6 = all_52_13
% 177.46/28.00    (92)   ~ (all_52_9 = all_52_15)
% 177.46/28.00    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00    (94)   ~ (e3 = e2)
% 177.46/28.00    (95)   ~ (all_52_19 = all_14_2)
% 177.46/28.00    (96)  op(e2, e3) = all_52_9
% 177.46/28.00  
% 177.46/28.00  Begin of proof
% 177.46/28.00  | 
% 177.46/28.00  | BETA: splitting (77) gives:
% 177.46/28.00  | 
% 177.46/28.00  | Case 1:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (97)  all_58_8 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | COMBINE_EQS: (47), (97) imply:
% 177.46/28.00  | |   (98)  all_14_2 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REDUCE: (33), (98) imply:
% 177.46/28.00  | |   (99)   ~ (all_52_17 = e3)
% 177.46/28.00  | | 
% 177.46/28.00  | | REDUCE: (89), (98) imply:
% 177.46/28.00  | |   (100)  op(e1, e3) = all_14_1
% 177.46/28.00  | | 
% 177.46/28.00  | | GROUND_INST: instantiating (81) with all_52_17, all_14_1, e3, e1,
% 177.46/28.00  | |              simplifying with (78), (100) gives:
% 177.46/28.00  | |   (101)  all_52_17 = all_14_1
% 177.46/28.00  | | 
% 177.46/28.00  | | REDUCE: (99), (101) imply:
% 177.46/28.00  | |   (102)   ~ (all_14_1 = e3)
% 177.46/28.00  | | 
% 177.46/28.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.46/28.00  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.46/28.00  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.46/28.00  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.46/28.00  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.46/28.00  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.46/28.00  | |            (69), (70), (71), (72), (73), (74), (75), (76), (78), (79), (80),
% 177.46/28.00  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 177.46/28.00  | |            (92), (93), (94), (95), (96), (99), (102) are inconsistent by
% 177.46/28.00  | |            sub-proof #735.
% 177.46/28.00  | | 
% 177.46/28.00  | Case 2:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (103)  all_58_14 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REF_CLOSE: (43), (50), (103) are inconsistent by sub-proof #1000.
% 177.46/28.00  | | 
% 177.46/28.00  | End of split
% 177.46/28.00  | 
% 177.46/28.00  End of proof
% 177.46/28.00  
% 177.46/28.00  Sub-proof #384 shows that the following formulas are inconsistent:
% 177.46/28.00  ----------------------------------------------------------------
% 177.46/28.00    (1)  op(e3, e2) = all_52_3
% 177.46/28.00    (2)   ~ (all_52_19 = all_52_23)
% 177.46/28.00    (3)   ~ (all_52_27 = e3)
% 177.46/28.00    (4)   ~ (all_6_2 = e3)
% 177.46/28.00    (5)   ~ (all_52_3 = all_10_2)
% 177.46/28.00    (6)  op(e0, all_52_15) = e0
% 177.46/28.00    (7)  all_58_3 = all_10_2
% 177.46/28.00    (8)  all_56_9 = all_52_19
% 177.46/28.00    (9)  all_58_15 = all_6_2
% 177.46/28.00    (10)   ~ (all_52_5 = all_52_7)
% 177.46/28.00    (11)  all_58_10 = all_52_15
% 177.46/28.00    (12)  all_58_7 = all_52_19
% 177.46/28.00    (13)  all_58_1 = all_52_3
% 177.46/28.00    (14)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/28.00    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/28.00    (16)  op(e0, e3) = e3
% 177.46/28.00    (17)   ~ (all_52_3 = all_52_5)
% 177.46/28.00    (18)  all_52_5 = e3
% 177.46/28.00    (19)  op(e3, all_52_9) = e3
% 177.46/28.00    (20)   ~ (e3 = e0)
% 177.46/28.00    (21)  all_58_13 = all_52_27
% 177.46/28.00    (22)  all_58_11 = all_52_23
% 177.46/28.00    (23)  op(e2, all_10_2) = e2
% 177.46/28.00    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.00    (25)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00    (26)  all_58_9 = all_52_7
% 177.46/28.00    (27)  op(e2, e3) = all_52_9
% 177.46/28.00  
% 177.46/28.00  Begin of proof
% 177.46/28.00  | 
% 177.46/28.00  | REDUCE: (17), (18) imply:
% 177.46/28.00  |   (28)   ~ (all_52_3 = e3)
% 177.46/28.00  | 
% 177.46/28.00  | REDUCE: (10), (18) imply:
% 177.46/28.00  |   (29)   ~ (all_52_7 = e3)
% 177.46/28.00  | 
% 177.46/28.00  | SIMP: (29) implies:
% 177.46/28.00  |   (30)   ~ (all_52_7 = e3)
% 177.46/28.00  | 
% 177.46/28.00  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 177.46/28.00  |            (14), (15), (16), (19), (20), (21), (22), (23), (24), (25), (26),
% 177.46/28.00  |            (27), (28), (30) are inconsistent by sub-proof #385.
% 177.46/28.00  | 
% 177.46/28.00  End of proof
% 177.46/28.00  
% 177.46/28.00  Sub-proof #385 shows that the following formulas are inconsistent:
% 177.46/28.00  ----------------------------------------------------------------
% 177.46/28.00    (1)  op(e3, e2) = all_52_3
% 177.46/28.00    (2)   ~ (all_52_19 = all_52_23)
% 177.46/28.00    (3)   ~ (all_52_27 = e3)
% 177.46/28.00    (4)   ~ (all_6_2 = e3)
% 177.46/28.00    (5)   ~ (all_52_3 = all_10_2)
% 177.46/28.00    (6)  op(e0, all_52_15) = e0
% 177.46/28.00    (7)  all_58_3 = all_10_2
% 177.46/28.00    (8)  all_56_9 = all_52_19
% 177.46/28.00    (9)  all_58_15 = all_6_2
% 177.46/28.00    (10)  all_58_10 = all_52_15
% 177.46/28.00    (11)  all_58_7 = all_52_19
% 177.46/28.00    (12)  all_58_1 = all_52_3
% 177.46/28.00    (13)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/28.00    (14)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/28.00    (15)  op(e0, e3) = e3
% 177.46/28.00    (16)  op(e3, all_52_9) = e3
% 177.46/28.00    (17)   ~ (e3 = e0)
% 177.46/28.00    (18)  all_58_13 = all_52_27
% 177.46/28.00    (19)   ~ (all_52_3 = e3)
% 177.46/28.00    (20)  all_58_11 = all_52_23
% 177.46/28.00    (21)  op(e2, all_10_2) = e2
% 177.46/28.00    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.00    (23)   ~ (all_52_7 = e3)
% 177.46/28.00    (24)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00    (25)  all_58_9 = all_52_7
% 177.46/28.00    (26)  op(e2, e3) = all_52_9
% 177.46/28.00  
% 177.46/28.00  Begin of proof
% 177.46/28.00  | 
% 177.46/28.00  | BETA: splitting (14) gives:
% 177.46/28.00  | 
% 177.46/28.00  | Case 1:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (27)  all_58_1 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | COMBINE_EQS: (12), (27) imply:
% 177.46/28.00  | |   (28)  all_52_3 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REDUCE: (19), (28) imply:
% 177.46/28.00  | |   (29)  $false
% 177.46/28.00  | | 
% 177.46/28.00  | | CLOSE: (29) is inconsistent.
% 177.46/28.00  | | 
% 177.46/28.00  | Case 2:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (30)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 177.46/28.00  | |            (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 177.46/28.00  | |            (30) are inconsistent by sub-proof #744.
% 177.46/28.00  | | 
% 177.46/28.00  | End of split
% 177.46/28.00  | 
% 177.46/28.00  End of proof
% 177.46/28.00  
% 177.46/28.00  Sub-proof #386 shows that the following formulas are inconsistent:
% 177.46/28.00  ----------------------------------------------------------------
% 177.46/28.00    (1)   ~ (all_52_23 = all_14_2)
% 177.46/28.00    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/28.00    (3)   ~ (all_52_17 = all_52_23)
% 177.46/28.00    (4)   ~ (all_52_13 = all_52_29)
% 177.46/28.00    (5)  all_56_3 = all_52_7
% 177.46/28.00    (6)   ~ (all_6_2 = e3)
% 177.46/28.00    (7)  all_58_5 = all_52_13
% 177.46/28.00    (8)   ~ (all_6_2 = e0)
% 177.46/28.00    (9)  op(e1, all_52_13) = e1
% 177.46/28.00    (10)  op(e0, all_52_15) = e0
% 177.46/28.00    (11)  all_56_15 = all_6_2
% 177.46/28.00    (12)  all_58_3 = all_10_2
% 177.46/28.00    (13)  all_58_15 = all_6_2
% 177.46/28.00    (14)   ~ (all_52_9 = all_4_2)
% 177.46/28.00    (15)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.00    (16)   ~ (all_52_5 = all_52_7)
% 177.46/28.00    (17)  all_58_10 = all_52_15
% 177.46/28.00    (18)   ~ (all_52_5 = all_4_2)
% 177.46/28.00    (19)  all_58_7 = all_52_19
% 177.46/28.00    (20)  all_56_4 = all_52_9
% 177.46/28.00    (21)  all_58_4 = all_52_5
% 177.46/28.00    (22)   ~ (all_52_27 = all_52_29)
% 177.46/28.00    (23)   ~ (all_52_17 = all_14_2)
% 177.46/28.00    (24)   ~ (all_52_7 = all_4_2)
% 177.46/28.00    (25)  all_58_1 = all_52_3
% 177.46/28.00    (26)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.00    (27)  all_58_0 = all_4_2
% 177.46/28.00    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/28.00    (29)  all_58_14 = all_52_29
% 177.46/28.00    (30)  op(e0, e3) = e3
% 177.46/28.00    (31)   ~ (all_52_3 = all_52_5)
% 177.46/28.00    (32)  op(e2, e1) = all_52_13
% 177.46/28.00    (33)  all_58_8 = all_14_2
% 177.46/28.00    (34)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/28.00    (35)  op(e3, all_52_17) = all_52_16
% 177.46/28.00    (36)   ~ (all_52_29 = e3)
% 177.46/28.00    (37)  op(e3, all_52_9) = e3
% 177.46/28.00    (38)   ~ (e3 = e0)
% 177.46/28.00    (39)  all_58_13 = all_52_27
% 177.46/28.00    (40)  all_52_3 = e3
% 177.46/28.00    (41)   ~ (all_52_9 = all_52_17)
% 177.46/28.00    (42)   ~ (all_52_3 = all_52_7)
% 177.46/28.00    (43)  all_56_0 = all_4_2
% 177.46/28.00    (44)  all_58_11 = all_52_23
% 177.46/28.00    (45)  op(e3, e1) = all_52_5
% 177.46/28.00    (46)  op(e1, e3) = all_52_17
% 177.46/28.00    (47)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.46/28.00    (48)  op(e3, e0) = all_52_7
% 177.46/28.00    (49)  op(e2, all_10_2) = e2
% 177.46/28.00    (50)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.00    (51)   ~ (all_52_27 = all_6_2)
% 177.46/28.00    (52)   ~ (all_52_7 = all_6_2)
% 177.46/28.00    (53)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.00    (54)  all_56_7 = all_52_15
% 177.46/28.00    (55)   ~ (all_52_7 = all_52_23)
% 177.46/28.00    (56)   ~ (all_52_17 = all_52_19)
% 177.46/28.00    (57)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00    (58)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/28.00    (59)  all_58_9 = all_52_7
% 177.46/28.00    (60)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00    (61)   ~ (e3 = e2)
% 177.46/28.00  
% 177.46/28.00  Begin of proof
% 177.46/28.00  | 
% 177.46/28.00  | COMBINE_EQS: (25), (40) imply:
% 177.46/28.00  |   (62)  all_58_1 = e3
% 177.46/28.00  | 
% 177.46/28.00  | REDUCE: (31), (40) imply:
% 177.46/28.00  |   (63)   ~ (all_52_5 = e3)
% 177.46/28.00  | 
% 177.46/28.00  | SIMP: (63) implies:
% 177.46/28.00  |   (64)   ~ (all_52_5 = e3)
% 177.46/28.00  | 
% 177.46/28.00  | REDUCE: (40), (42) imply:
% 177.46/28.00  |   (65)   ~ (all_52_7 = e3)
% 177.46/28.00  | 
% 177.46/28.00  | SIMP: (65) implies:
% 177.46/28.00  |   (66)   ~ (all_52_7 = e3)
% 177.46/28.00  | 
% 177.46/28.00  | BETA: splitting (57) gives:
% 177.46/28.00  | 
% 177.46/28.00  | Case 1:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (67)  all_58_9 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REF_CLOSE: (59), (66), (67) are inconsistent by sub-proof #972.
% 177.46/28.00  | | 
% 177.46/28.00  | Case 2:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (68)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.46/28.00  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.46/28.00  | |            (24), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 177.46/28.00  | |            (37), (38), (39), (41), (43), (44), (45), (46), (47), (48), (49),
% 177.46/28.00  | |            (50), (51), (52), (53), (54), (55), (56), (58), (60), (61), (62),
% 177.46/28.00  | |            (64), (68) are inconsistent by sub-proof #387.
% 177.46/28.00  | | 
% 177.46/28.00  | End of split
% 177.46/28.00  | 
% 177.46/28.00  End of proof
% 177.46/28.00  
% 177.46/28.00  Sub-proof #387 shows that the following formulas are inconsistent:
% 177.46/28.00  ----------------------------------------------------------------
% 177.46/28.00    (1)   ~ (all_52_23 = all_14_2)
% 177.46/28.00    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/28.00    (3)   ~ (all_52_17 = all_52_23)
% 177.46/28.00    (4)   ~ (all_52_13 = all_52_29)
% 177.46/28.00    (5)  all_56_3 = all_52_7
% 177.46/28.00    (6)   ~ (all_6_2 = e3)
% 177.46/28.00    (7)  all_58_5 = all_52_13
% 177.46/28.00    (8)   ~ (all_6_2 = e0)
% 177.46/28.00    (9)  op(e1, all_52_13) = e1
% 177.46/28.00    (10)  op(e0, all_52_15) = e0
% 177.46/28.00    (11)  all_56_15 = all_6_2
% 177.46/28.00    (12)  all_58_3 = all_10_2
% 177.46/28.00    (13)  all_58_15 = all_6_2
% 177.46/28.00    (14)   ~ (all_52_9 = all_4_2)
% 177.46/28.00    (15)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.00    (16)   ~ (all_52_5 = all_52_7)
% 177.46/28.00    (17)  all_58_10 = all_52_15
% 177.46/28.00    (18)   ~ (all_52_5 = all_4_2)
% 177.46/28.00    (19)  all_58_7 = all_52_19
% 177.46/28.00    (20)  all_56_4 = all_52_9
% 177.46/28.00    (21)  all_58_4 = all_52_5
% 177.46/28.00    (22)   ~ (all_52_27 = all_52_29)
% 177.46/28.00    (23)   ~ (all_52_17 = all_14_2)
% 177.46/28.00    (24)   ~ (all_52_7 = all_4_2)
% 177.46/28.00    (25)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.00    (26)  all_58_0 = all_4_2
% 177.46/28.00    (27)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/28.00    (28)  all_58_14 = all_52_29
% 177.46/28.00    (29)  op(e0, e3) = e3
% 177.46/28.00    (30)  op(e2, e1) = all_52_13
% 177.46/28.00    (31)  all_58_8 = all_14_2
% 177.46/28.00    (32)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.46/28.00    (33)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00    (34)  op(e3, all_52_17) = all_52_16
% 177.46/28.00    (35)   ~ (all_52_29 = e3)
% 177.46/28.00    (36)   ~ (all_52_5 = e3)
% 177.46/28.00    (37)  op(e3, all_52_9) = e3
% 177.46/28.00    (38)   ~ (e3 = e0)
% 177.46/28.00    (39)  all_58_13 = all_52_27
% 177.46/28.00    (40)  all_58_1 = e3
% 177.46/28.00    (41)   ~ (all_52_9 = all_52_17)
% 177.46/28.00    (42)  all_56_0 = all_4_2
% 177.46/28.00    (43)  all_58_11 = all_52_23
% 177.46/28.00    (44)  op(e3, e1) = all_52_5
% 177.46/28.00    (45)  op(e1, e3) = all_52_17
% 177.46/28.00    (46)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.46/28.00    (47)  op(e3, e0) = all_52_7
% 177.46/28.00    (48)  op(e2, all_10_2) = e2
% 177.46/28.00    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.00    (50)   ~ (all_52_27 = all_6_2)
% 177.46/28.00    (51)   ~ (all_52_7 = all_6_2)
% 177.46/28.00    (52)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.00    (53)  all_56_7 = all_52_15
% 177.46/28.00    (54)   ~ (all_52_7 = all_52_23)
% 177.46/28.00    (55)   ~ (all_52_17 = all_52_19)
% 177.46/28.00    (56)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/28.00    (57)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00    (58)   ~ (e3 = e2)
% 177.46/28.00  
% 177.46/28.00  Begin of proof
% 177.46/28.00  | 
% 177.46/28.00  | BETA: splitting (57) gives:
% 177.46/28.00  | 
% 177.46/28.00  | Case 1:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (59)  all_58_4 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | REF_CLOSE: (21), (36), (59) are inconsistent by sub-proof #1025.
% 177.46/28.00  | | 
% 177.46/28.00  | Case 2:
% 177.46/28.00  | | 
% 177.46/28.00  | |   (60)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.00  | | 
% 177.46/28.00  | | BETA: splitting (46) gives:
% 177.46/28.00  | | 
% 177.46/28.00  | | Case 1:
% 177.46/28.00  | | | 
% 177.46/28.00  | | |   (61)  all_56_7 = e3
% 177.46/28.00  | | | 
% 177.46/28.00  | | | REF_CLOSE: (10), (29), (38), (49), (53), (61) are inconsistent by
% 177.46/28.00  | | |            sub-proof #388.
% 177.46/28.00  | | | 
% 177.46/28.00  | | Case 2:
% 177.46/28.00  | | | 
% 177.46/28.00  | | |   (62)   ~ (all_56_7 = e3)
% 177.46/28.00  | | | 
% 177.46/28.00  | | | REDUCE: (53), (62) imply:
% 177.46/28.00  | | |   (63)   ~ (all_52_15 = e3)
% 177.46/28.00  | | | 
% 177.46/28.00  | | | BETA: splitting (33) gives:
% 177.46/28.00  | | | 
% 177.46/28.00  | | | Case 1:
% 177.46/28.00  | | | | 
% 177.46/28.00  | | | |   (64)  all_58_10 = e3
% 177.46/28.00  | | | | 
% 177.46/28.00  | | | | REF_CLOSE: (17), (63), (64) are inconsistent by sub-proof #1018.
% 177.46/28.00  | | | | 
% 177.46/28.00  | | | Case 2:
% 177.46/28.00  | | | | 
% 177.46/28.00  | | | |   (65)  all_58_11 = e3 | all_58_15 = e3
% 177.46/28.00  | | | | 
% 177.46/28.00  | | | | BETA: splitting (65) gives:
% 177.46/28.00  | | | | 
% 177.46/28.00  | | | | Case 1:
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | |   (66)  all_58_11 = e3
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | COMBINE_EQS: (43), (66) imply:
% 177.46/28.00  | | | | |   (67)  all_52_23 = e3
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | SIMP: (67) implies:
% 177.46/28.00  | | | | |   (68)  all_52_23 = e3
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | REDUCE: (54), (68) imply:
% 177.46/28.00  | | | | |   (69)   ~ (all_52_7 = e3)
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | REDUCE: (3), (68) imply:
% 177.46/28.00  | | | | |   (70)   ~ (all_52_17 = e3)
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | REDUCE: (1), (68) imply:
% 177.46/28.00  | | | | |   (71)   ~ (all_14_2 = e3)
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | SIMP: (71) implies:
% 177.46/28.00  | | | | |   (72)   ~ (all_14_2 = e3)
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (11), (12), (14), (15), (16),
% 177.46/28.00  | | | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 177.46/28.00  | | | | |            (28), (30), (31), (32), (34), (35), (37), (39), (40), (41),
% 177.46/28.00  | | | | |            (42), (44), (45), (47), (48), (49), (50), (51), (52), (55),
% 177.46/28.00  | | | | |            (56), (58), (60), (69), (70), (72) are inconsistent by
% 177.46/28.00  | | | | |            sub-proof #746.
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | Case 2:
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | |   (73)  all_58_15 = e3
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | COMBINE_EQS: (13), (73) imply:
% 177.46/28.00  | | | | |   (74)  all_6_2 = e3
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | REDUCE: (6), (74) imply:
% 177.46/28.00  | | | | |   (75)  $false
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | | CLOSE: (75) is inconsistent.
% 177.46/28.00  | | | | | 
% 177.46/28.00  | | | | End of split
% 177.46/28.00  | | | | 
% 177.46/28.00  | | | End of split
% 177.46/28.00  | | | 
% 177.46/28.00  | | End of split
% 177.46/28.00  | | 
% 177.46/28.00  | End of split
% 177.46/28.00  | 
% 177.46/28.00  End of proof
% 177.46/28.00  
% 177.46/28.00  Sub-proof #388 shows that the following formulas are inconsistent:
% 177.46/28.00  ----------------------------------------------------------------
% 177.46/28.00    (1)  op(e0, all_52_15) = e0
% 177.46/28.00    (2)  all_56_7 = e3
% 177.46/28.00    (3)  op(e0, e3) = e3
% 177.46/28.00    (4)   ~ (e3 = e0)
% 177.46/28.01    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.01    (6)  all_56_7 = all_52_15
% 177.46/28.01  
% 177.46/28.01  Begin of proof
% 177.46/28.01  | 
% 177.46/28.01  | COMBINE_EQS: (2), (6) imply:
% 177.46/28.01  |   (7)  all_52_15 = e3
% 177.46/28.01  | 
% 177.46/28.01  | SIMP: (7) implies:
% 177.46/28.01  |   (8)  all_52_15 = e3
% 177.46/28.01  | 
% 177.46/28.01  | REDUCE: (1), (8) imply:
% 177.46/28.01  |   (9)  op(e0, e3) = e0
% 177.46/28.01  | 
% 177.46/28.01  | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1027.
% 177.46/28.01  | 
% 177.46/28.01  End of proof
% 177.46/28.01  
% 177.46/28.01  Sub-proof #389 shows that the following formulas are inconsistent:
% 177.46/28.01  ----------------------------------------------------------------
% 177.46/28.01    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/28.01    (2)  op(e3, e2) = all_52_3
% 177.46/28.01    (3)  op(e3, all_52_25) = all_52_24
% 177.46/28.01    (4)  op(e1, e2) = all_52_19
% 177.46/28.01    (5)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.46/28.01    (6)   ~ (all_52_3 = all_10_2)
% 177.46/28.01    (7)  all_58_5 = all_52_13
% 177.46/28.01    (8)  all_58_4 = e3
% 177.46/28.01    (9)  op(e0, all_52_15) = e0
% 177.46/28.01    (10)  all_56_15 = all_6_2
% 177.46/28.01    (11)   ~ (all_4_2 = e3)
% 177.46/28.01    (12)   ~ (all_52_26 = all_10_2)
% 177.46/28.01    (13)  all_58_3 = all_10_2
% 177.46/28.01    (14)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.01    (15)   ~ (all_52_9 = all_4_2)
% 177.46/28.01    (16)   ~ (all_52_26 = all_4_2)
% 177.46/28.01    (17)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.01    (18)  all_58_10 = all_52_15
% 177.46/28.01    (19)  all_58_7 = all_52_19
% 177.46/28.01    (20)   ~ (all_52_15 = all_6_2)
% 177.46/28.01    (21)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.01    (22)   ~ (e3 = e1)
% 177.46/28.01    (23)  op(e3, all_4_2) = all_4_1
% 177.46/28.01    (24)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/28.01    (25)  all_58_1 = all_52_3
% 177.46/28.01    (26)  all_58_0 = all_4_2
% 177.46/28.01    (27)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/28.01    (28)  all_58_14 = all_52_29
% 177.46/28.01    (29)   ~ (all_10_2 = e3)
% 177.46/28.01    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.01    (31)  all_58_8 = all_14_2
% 177.46/28.01    (32)  all_56_1 = all_52_3
% 177.46/28.01    (33)  op(e1, all_14_2) = e3
% 177.46/28.01    (34)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.46/28.01    (35)   ~ (all_52_3 = all_4_2)
% 177.46/28.01    (36)  op(e0, e3) = all_52_25
% 177.46/28.01    (37)  op(e3, all_52_9) = e3
% 177.46/28.01    (38)   ~ (all_52_13 = e3)
% 177.46/28.01    (39)   ~ (all_52_15 = all_52_23)
% 177.46/28.01    (40)   ~ (all_4_1 = e1)
% 177.46/28.01    (41)   ~ (all_52_3 = e3)
% 177.46/28.01    (42)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/28.01    (43)  all_56_5 = all_10_2
% 177.46/28.01    (44)  all_58_6 = all_52_17
% 177.46/28.01    (45)  all_58_2 = all_52_26
% 177.46/28.01    (46)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.01    (47)   ~ (e1 = e0)
% 177.46/28.01    (48)  all_56_0 = all_4_2
% 177.46/28.01    (49)  all_58_11 = all_52_23
% 177.46/28.01    (50)   ~ (all_52_3 = all_52_19)
% 177.46/28.01    (51)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/28.01    (52)   ~ (all_52_7 = all_52_15)
% 177.46/28.01    (53)   ~ (all_52_19 = all_10_2)
% 177.46/28.01    (54)   ~ (all_52_29 = all_6_2)
% 177.46/28.01    (55)  all_58_2 = all_52_9
% 177.46/28.01    (56)   ~ (all_52_25 = all_6_2)
% 177.46/28.01    (57)   ~ (all_52_19 = e3)
% 177.46/28.01    (58)   ~ (all_52_25 = all_4_2)
% 177.46/28.01    (59)  op(e3, e0) = all_52_7
% 177.46/28.01    (60)  op(e3, e3) = all_4_2
% 177.46/28.01    (61)   ~ (all_14_2 = e3)
% 177.46/28.01    (62)   ~ (all_52_17 = all_4_2)
% 177.46/28.01    (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.01    (64)   ~ (all_52_7 = all_6_2)
% 177.46/28.01    (65)   ~ (all_52_13 = all_10_2)
% 177.46/28.01    (66)   ~ (all_52_25 = all_52_26)
% 177.46/28.01    (67)   ~ (all_52_17 = all_52_19)
% 177.46/28.01    (68)  all_56_4 = all_52_26
% 177.46/28.01    (69)  all_58_9 = all_52_7
% 177.46/28.01    (70)   ~ (all_52_15 = all_52_26)
% 177.46/28.01    (71)  all_58_12 = all_52_25
% 177.46/28.01    (72)   ~ (all_52_17 = all_52_26)
% 177.46/28.01    (73)  op(e3, all_52_26) = e3
% 177.46/28.01    (74)  all_58_13 = e3
% 177.46/28.01  
% 177.46/28.01  Begin of proof
% 177.46/28.01  | 
% 177.46/28.01  | BETA: splitting (21) gives:
% 177.46/28.01  | 
% 177.46/28.01  | Case 1:
% 177.46/28.01  | | 
% 177.46/28.01  | |   (75)  all_58_6 = e3
% 177.46/28.01  | | 
% 177.46/28.01  | | COMBINE_EQS: (44), (75) imply:
% 177.46/28.01  | |   (76)  all_52_17 = e3
% 177.46/28.01  | | 
% 177.46/28.01  | | SIMP: (76) implies:
% 177.46/28.01  | |   (77)  all_52_17 = e3
% 177.46/28.01  | | 
% 177.46/28.01  | | REDUCE: (67), (77) imply:
% 177.46/28.01  | |   (78)   ~ (all_52_19 = e3)
% 177.46/28.01  | | 
% 177.46/28.01  | | REDUCE: (72), (77) imply:
% 177.46/28.01  | |   (79)   ~ (all_52_26 = e3)
% 177.46/28.01  | | 
% 177.46/28.01  | | SIMP: (79) implies:
% 177.46/28.01  | |   (80)   ~ (all_52_26 = e3)
% 177.46/28.01  | | 
% 177.46/28.01  | | REDUCE: (62), (77) imply:
% 177.46/28.01  | |   (81)   ~ (all_4_2 = e3)
% 177.46/28.01  | | 
% 177.46/28.01  | | BETA: splitting (24) gives:
% 177.46/28.01  | | 
% 177.46/28.01  | | Case 1:
% 177.46/28.01  | | | 
% 177.46/28.01  | | |   (82)  all_58_2 = e3
% 177.46/28.01  | | | 
% 177.46/28.01  | | | REF_CLOSE: (45), (80), (82) are inconsistent by sub-proof #1004.
% 177.46/28.01  | | | 
% 177.46/28.01  | | Case 2:
% 177.46/28.01  | | | 
% 177.46/28.01  | | |   (83)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/28.01  | | | 
% 177.46/28.01  | | | BETA: splitting (83) gives:
% 177.46/28.01  | | | 
% 177.46/28.01  | | | Case 1:
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | |   (84)  all_58_3 = e3
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | COMBINE_EQS: (13), (84) imply:
% 177.46/28.01  | | | |   (85)  all_10_2 = e3
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | REDUCE: (29), (85) imply:
% 177.46/28.01  | | | |   (86)  $false
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | CLOSE: (86) is inconsistent.
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | Case 2:
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | |   (87)  all_58_5 = e3 | all_58_10 = e3
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | BETA: splitting (87) gives:
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | Case 1:
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | |   (88)  all_58_5 = e3
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REF_CLOSE: (7), (38), (88) are inconsistent by sub-proof #969.
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | Case 2:
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | |   (89)  all_58_10 = e3
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | COMBINE_EQS: (18), (89) imply:
% 177.46/28.01  | | | | |   (90)  all_52_15 = e3
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | SIMP: (90) implies:
% 177.46/28.01  | | | | |   (91)  all_52_15 = e3
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (52), (91) imply:
% 177.46/28.01  | | | | |   (92)   ~ (all_52_7 = e3)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (20), (91) imply:
% 177.46/28.01  | | | | |   (93)   ~ (all_6_2 = e3)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | SIMP: (93) implies:
% 177.46/28.01  | | | | |   (94)   ~ (all_6_2 = e3)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (9), (91) imply:
% 177.46/28.01  | | | | |   (95)  op(e0, e3) = e0
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | GROUND_INST: instantiating (63) with all_52_25, e0, e3, e0,
% 177.46/28.01  | | | | |              simplifying with (36), (95) gives:
% 177.46/28.01  | | | | |   (96)  all_52_25 = e0
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | COMBINE_EQS: (71), (96) imply:
% 177.46/28.01  | | | | |   (97)  all_58_12 = e0
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (66), (96) imply:
% 177.46/28.01  | | | | |   (98)   ~ (all_52_26 = e0)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | SIMP: (98) implies:
% 177.46/28.01  | | | | |   (99)   ~ (all_52_26 = e0)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (56), (96) imply:
% 177.46/28.01  | | | | |   (100)   ~ (all_6_2 = e0)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | SIMP: (100) implies:
% 177.46/28.01  | | | | |   (101)   ~ (all_6_2 = e0)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (58), (96) imply:
% 177.46/28.01  | | | | |   (102)   ~ (all_4_2 = e0)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | SIMP: (102) implies:
% 177.46/28.01  | | | | |   (103)   ~ (all_4_2 = e0)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (3), (96) imply:
% 177.46/28.01  | | | | |   (104)  op(e3, e0) = all_52_24
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | GROUND_INST: instantiating (63) with all_52_7, all_52_24, e0, e3,
% 177.46/28.01  | | | | |              simplifying with (59), (104) gives:
% 177.46/28.01  | | | | |   (105)  all_52_7 = all_52_24
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | COMBINE_EQS: (69), (105) imply:
% 177.46/28.01  | | | | |   (106)  all_58_9 = all_52_24
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (64), (105) imply:
% 177.46/28.01  | | | | |   (107)   ~ (all_52_24 = all_6_2)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (92), (105) imply:
% 177.46/28.01  | | | | |   (108)   ~ (all_52_24 = e3)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | BETA: splitting (14) gives:
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | Case 1:
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | |   (109)  all_56_0 = e3
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | REF_CLOSE: (11), (48), (109) are inconsistent by sub-proof #1024.
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | Case 2:
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | |   (110)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | BETA: splitting (46) gives:
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | Case 1:
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | |   (111)  all_56_4 = e3
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | REF_CLOSE: (68), (80), (111) are inconsistent by sub-proof #818.
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | Case 2:
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | |   (112)   ~ (all_56_4 = e3)
% 177.46/28.01  | | | | | | |   (113)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | BETA: splitting (42) gives:
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | |   (114)  all_58_0 = e1
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | COMBINE_EQS: (26), (114) imply:
% 177.46/28.01  | | | | | | | |   (115)  all_4_2 = e1
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | REDUCE: (16), (115) imply:
% 177.46/28.01  | | | | | | | |   (116)   ~ (all_52_26 = e1)
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | REF_CLOSE: (2), (41), (63), (68), (73), (99), (113), (116) are
% 177.46/28.01  | | | | | | | |            inconsistent by sub-proof #766.
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | |   (117)   ~ (all_58_0 = e1)
% 177.46/28.01  | | | | | | | |   (118)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | REDUCE: (26), (117) imply:
% 177.46/28.01  | | | | | | | |   (119)   ~ (all_4_2 = e1)
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | BETA: splitting (110) gives:
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | |   (120)  all_56_0 = e2
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | COMBINE_EQS: (48), (120) imply:
% 177.46/28.01  | | | | | | | | |   (121)  all_4_2 = e2
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | SIMP: (121) implies:
% 177.46/28.01  | | | | | | | | |   (122)  all_4_2 = e2
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | COMBINE_EQS: (26), (122) imply:
% 177.46/28.01  | | | | | | | | |   (123)  all_58_0 = e2
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REDUCE: (35), (122) imply:
% 177.46/28.01  | | | | | | | | |   (124)   ~ (all_52_3 = e2)
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REDUCE: (16), (122) imply:
% 177.46/28.01  | | | | | | | | |   (125)   ~ (all_52_26 = e2)
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REDUCE: (23), (122) imply:
% 177.46/28.01  | | | | | | | | |   (126)  op(e3, e2) = all_4_1
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | BETA: splitting (118) gives:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | |   (127)  all_58_2 = e1
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | COMBINE_EQS: (45), (127) imply:
% 177.46/28.01  | | | | | | | | | |   (128)  all_52_26 = e1
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | SIMP: (128) implies:
% 177.46/28.01  | | | | | | | | | |   (129)  all_52_26 = e1
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (12), (129) imply:
% 177.46/28.01  | | | | | | | | | |   (130)   ~ (all_10_2 = e1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | SIMP: (130) implies:
% 177.46/28.01  | | | | | | | | | |   (131)   ~ (all_10_2 = e1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (80), (129) imply:
% 177.46/28.01  | | | | | | | | | |   (132)   ~ (e3 = e1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (125), (129) imply:
% 177.46/28.01  | | | | | | | | | |   (133)   ~ (e2 = e1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | SIMP: (133) implies:
% 177.46/28.01  | | | | | | | | | |   (134)   ~ (e2 = e1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | GROUND_INST: instantiating (63) with all_52_3, all_4_1, e2, e3,
% 177.46/28.01  | | | | | | | | | |              simplifying with (2), (126) gives:
% 177.46/28.01  | | | | | | | | | |   (135)  all_52_3 = all_4_1
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | COMBINE_EQS: (32), (135) imply:
% 177.46/28.01  | | | | | | | | | |   (136)  all_56_1 = all_4_1
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | COMBINE_EQS: (25), (135) imply:
% 177.46/28.01  | | | | | | | | | |   (137)  all_58_1 = all_4_1
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (50), (135) imply:
% 177.46/28.01  | | | | | | | | | |   (138)   ~ (all_52_19 = all_4_1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | SIMP: (138) implies:
% 177.46/28.01  | | | | | | | | | |   (139)   ~ (all_52_19 = all_4_1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (6), (135) imply:
% 177.46/28.01  | | | | | | | | | |   (140)   ~ (all_10_2 = all_4_1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | SIMP: (140) implies:
% 177.46/28.01  | | | | | | | | | |   (141)   ~ (all_10_2 = all_4_1)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (124), (135) imply:
% 177.46/28.01  | | | | | | | | | |   (142)   ~ (all_4_1 = e2)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | BETA: splitting (1) gives:
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | |   (143)  all_58_1 = e1
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | COMBINE_EQS: (137), (143) imply:
% 177.46/28.01  | | | | | | | | | | |   (144)  all_4_1 = e1
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | REDUCE: (40), (144) imply:
% 177.46/28.01  | | | | | | | | | | |   (145)  $false
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | CLOSE: (145) is inconsistent.
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | |   (146)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (10), (13), (17), (19), (22),
% 177.46/28.01  | | | | | | | | | | |            (27), (28), (31), (33), (34), (43), (51), (53),
% 177.46/28.01  | | | | | | | | | | |            (54), (57), (63), (65), (74), (94), (101), (106),
% 177.46/28.01  | | | | | | | | | | |            (107), (108), (123), (131), (134), (136), (137),
% 177.46/28.01  | | | | | | | | | | |            (139), (141), (142), (146) are inconsistent by
% 177.46/28.01  | | | | | | | | | | |            sub-proof #390.
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | |   (147)  all_58_6 = e1 | all_58_12 = e1
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REF_CLOSE: (22), (47), (75), (97), (147) are inconsistent by
% 177.46/28.01  | | | | | | | | | |            sub-proof #726.
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | |   (148)  all_56_0 = e1 | all_56_0 = e0
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REF_CLOSE: (48), (103), (119), (148) are inconsistent by
% 177.46/28.01  | | | | | | | | |            sub-proof #1020.
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | End of split
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | End of split
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | End of split
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | End of split
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | End of split
% 177.46/28.01  | | | 
% 177.46/28.01  | | End of split
% 177.46/28.01  | | 
% 177.46/28.01  | Case 2:
% 177.46/28.01  | | 
% 177.46/28.01  | |   (149)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.01  | | 
% 177.46/28.01  | | REF_CLOSE: (7), (11), (13), (15), (18), (19), (24), (26), (29), (30), (31),
% 177.46/28.01  | |            (37), (38), (39), (49), (55), (57), (60), (61), (63), (149) are
% 177.46/28.01  | |            inconsistent by sub-proof #964.
% 177.46/28.01  | | 
% 177.46/28.01  | End of split
% 177.46/28.01  | 
% 177.46/28.01  End of proof
% 177.46/28.01  
% 177.46/28.01  Sub-proof #390 shows that the following formulas are inconsistent:
% 177.46/28.01  ----------------------------------------------------------------
% 177.46/28.01    (1)  op(e1, e2) = all_52_19
% 177.46/28.01    (2)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.46/28.01    (3)   ~ (all_10_2 = e1)
% 177.46/28.01    (4)   ~ (all_6_2 = e3)
% 177.46/28.01    (5)  all_58_5 = all_52_13
% 177.46/28.01    (6)   ~ (all_6_2 = e0)
% 177.46/28.01    (7)  all_58_4 = e3
% 177.46/28.01    (8)  all_56_15 = all_6_2
% 177.46/28.01    (9)  all_58_3 = all_10_2
% 177.46/28.01    (10)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.01    (11)  all_58_7 = all_52_19
% 177.46/28.01    (12)   ~ (e3 = e1)
% 177.46/28.01    (13)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/28.01    (14)   ~ (all_4_1 = e2)
% 177.46/28.01    (15)  all_58_14 = all_52_29
% 177.46/28.01    (16)   ~ (all_52_24 = all_6_2)
% 177.46/28.01    (17)  all_58_8 = all_14_2
% 177.46/28.01    (18)  op(e1, all_14_2) = e3
% 177.46/28.01    (19)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.46/28.01    (20)   ~ (all_52_19 = all_4_1)
% 177.46/28.01    (21)   ~ (all_10_2 = all_4_1)
% 177.46/28.01    (22)  all_58_1 = all_4_1
% 177.46/28.01    (23)  all_56_5 = all_10_2
% 177.46/28.01    (24)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/28.01    (25)   ~ (all_52_19 = all_10_2)
% 177.46/28.01    (26)   ~ (all_52_29 = all_6_2)
% 177.46/28.01    (27)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.46/28.01    (28)   ~ (e2 = e1)
% 177.46/28.01    (29)   ~ (all_52_19 = e3)
% 177.46/28.01    (30)  all_56_1 = all_4_1
% 177.46/28.01    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.01    (32)  all_58_9 = all_52_24
% 177.46/28.01    (33)   ~ (all_52_13 = all_10_2)
% 177.46/28.01    (34)  all_58_0 = e2
% 177.46/28.01    (35)   ~ (all_52_24 = e3)
% 177.46/28.01    (36)  all_58_13 = e3
% 177.46/28.01  
% 177.46/28.01  Begin of proof
% 177.46/28.01  | 
% 177.46/28.01  | BETA: splitting (27) gives:
% 177.46/28.01  | 
% 177.46/28.01  | Case 1:
% 177.46/28.01  | | 
% 177.46/28.01  | |   (37)  all_58_3 = e1
% 177.46/28.01  | | 
% 177.46/28.01  | | COMBINE_EQS: (9), (37) imply:
% 177.46/28.01  | |   (38)  all_10_2 = e1
% 177.46/28.01  | | 
% 177.46/28.01  | | REDUCE: (3), (38) imply:
% 177.46/28.01  | |   (39)  $false
% 177.46/28.01  | | 
% 177.46/28.01  | | CLOSE: (39) is inconsistent.
% 177.46/28.01  | | 
% 177.46/28.01  | Case 2:
% 177.46/28.01  | | 
% 177.46/28.01  | |   (40)  all_58_7 = e1 | all_58_13 = e1
% 177.46/28.01  | | 
% 177.46/28.01  | | BETA: splitting (2) gives:
% 177.46/28.01  | | 
% 177.46/28.01  | | Case 1:
% 177.46/28.01  | | | 
% 177.46/28.01  | | |   (41)  all_58_0 = e1
% 177.46/28.01  | | | 
% 177.46/28.01  | | | COMBINE_EQS: (34), (41) imply:
% 177.46/28.01  | | |   (42)  e2 = e1
% 177.46/28.01  | | | 
% 177.46/28.01  | | | REDUCE: (28), (42) imply:
% 177.46/28.01  | | |   (43)  $false
% 177.46/28.01  | | | 
% 177.46/28.01  | | | CLOSE: (43) is inconsistent.
% 177.46/28.01  | | | 
% 177.46/28.01  | | Case 2:
% 177.46/28.01  | | | 
% 177.46/28.01  | | |   (44)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.46/28.01  | | | 
% 177.46/28.01  | | | BETA: splitting (13) gives:
% 177.46/28.01  | | | 
% 177.46/28.01  | | | Case 1:
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | |   (45)  all_56_1 = e2
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | REF_CLOSE: (14), (30), (45) are inconsistent by sub-proof #762.
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | Case 2:
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | |   (46)  all_56_1 = e1 | all_56_1 = e0
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | BETA: splitting (40) gives:
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | | Case 1:
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | |   (47)  all_58_7 = e1
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | COMBINE_EQS: (11), (47) imply:
% 177.46/28.01  | | | | |   (48)  all_52_19 = e1
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (25), (48) imply:
% 177.46/28.01  | | | | |   (49)   ~ (all_10_2 = e1)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (20), (48) imply:
% 177.46/28.01  | | | | |   (50)   ~ (all_4_1 = e1)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | SIMP: (50) implies:
% 177.46/28.01  | | | | |   (51)   ~ (all_4_1 = e1)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (29), (48) imply:
% 177.46/28.01  | | | | |   (52)   ~ (e3 = e1)
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REDUCE: (1), (48) imply:
% 177.46/28.01  | | | | |   (53)  op(e1, e2) = e1
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | BETA: splitting (46) gives:
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | Case 1:
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | |   (54)  all_56_1 = e1
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | REF_CLOSE: (30), (51), (54) are inconsistent by sub-proof #761.
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | Case 2:
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | |   (55)  all_56_1 = e0
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | COMBINE_EQS: (30), (55) imply:
% 177.46/28.01  | | | | | |   (56)  all_4_1 = e0
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | SIMP: (56) implies:
% 177.46/28.01  | | | | | |   (57)  all_4_1 = e0
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | COMBINE_EQS: (22), (57) imply:
% 177.46/28.01  | | | | | |   (58)  all_58_1 = e0
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | REDUCE: (21), (57) imply:
% 177.46/28.01  | | | | | |   (59)   ~ (all_10_2 = e0)
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | REDUCE: (51), (57) imply:
% 177.46/28.01  | | | | | |   (60)   ~ (e1 = e0)
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | SIMP: (60) implies:
% 177.46/28.01  | | | | | |   (61)   ~ (e1 = e0)
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | BETA: splitting (44) gives:
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | | Case 1:
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | |   (62)  all_58_1 = e1
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | COMBINE_EQS: (58), (62) imply:
% 177.46/28.01  | | | | | | |   (63)  e1 = e0
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | SIMP: (63) implies:
% 177.46/28.01  | | | | | | |   (64)  e1 = e0
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | REDUCE: (61), (64) imply:
% 177.46/28.01  | | | | | | |   (65)  $false
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | CLOSE: (65) is inconsistent.
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | Case 2:
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | |   (66)  all_58_4 = e1 | all_58_9 = e1
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | BETA: splitting (19) gives:
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | |   (67)  all_56_5 = e2
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | COMBINE_EQS: (23), (67) imply:
% 177.46/28.01  | | | | | | | |   (68)  all_10_2 = e2
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | SIMP: (68) implies:
% 177.46/28.01  | | | | | | | |   (69)  all_10_2 = e2
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | REDUCE: (33), (69) imply:
% 177.46/28.01  | | | | | | | |   (70)   ~ (all_52_13 = e2)
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | BETA: splitting (66) gives:
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | |   (71)  all_58_4 = e1
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REF_CLOSE: (7), (12), (71) are inconsistent by sub-proof #392.
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | |   (72)  all_58_9 = e1
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | COMBINE_EQS: (32), (72) imply:
% 177.46/28.01  | | | | | | | | |   (73)  all_52_24 = e1
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | SIMP: (73) implies:
% 177.46/28.01  | | | | | | | | |   (74)  all_52_24 = e1
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REDUCE: (16), (74) imply:
% 177.46/28.01  | | | | | | | | |   (75)   ~ (all_6_2 = e1)
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | SIMP: (75) implies:
% 177.46/28.01  | | | | | | | | |   (76)   ~ (all_6_2 = e1)
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | BETA: splitting (10) gives:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | |   (77)  all_56_15 = e2
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | COMBINE_EQS: (8), (77) imply:
% 177.46/28.01  | | | | | | | | | |   (78)  all_6_2 = e2
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | SIMP: (78) implies:
% 177.46/28.01  | | | | | | | | | |   (79)  all_6_2 = e2
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (26), (79) imply:
% 177.46/28.01  | | | | | | | | | |   (80)   ~ (all_52_29 = e2)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REDUCE: (4), (79) imply:
% 177.46/28.01  | | | | | | | | | |   (81)   ~ (e3 = e2)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | SIMP: (81) implies:
% 177.46/28.01  | | | | | | | | | |   (82)   ~ (e3 = e2)
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | BETA: splitting (24) gives:
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | |   (83)  all_58_4 = e2
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | COMBINE_EQS: (7), (83) imply:
% 177.46/28.01  | | | | | | | | | | |   (84)  e3 = e2
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | REDUCE: (82), (84) imply:
% 177.46/28.01  | | | | | | | | | | |   (85)  $false
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | CLOSE: (85) is inconsistent.
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | |   (86)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | BETA: splitting (86) gives:
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | |   (87)  all_58_5 = e2
% 177.46/28.01  | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | REF_CLOSE: (5), (70), (87) are inconsistent by sub-proof
% 177.46/28.01  | | | | | | | | | | | |            #391.
% 177.46/28.01  | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | |   (88)  all_58_8 = e2 | all_58_14 = e2
% 177.46/28.01  | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | BETA: splitting (88) gives:
% 177.46/28.01  | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | |   (89)  all_58_8 = e2
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | | COMBINE_EQS: (17), (89) imply:
% 177.46/28.01  | | | | | | | | | | | | |   (90)  all_14_2 = e2
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | | REDUCE: (18), (90) imply:
% 177.46/28.01  | | | | | | | | | | | | |   (91)  op(e1, e2) = e3
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | | REF_CLOSE: (12), (31), (53), (91) are inconsistent by
% 177.46/28.01  | | | | | | | | | | | | |            sub-proof #861.
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | |   (92)  all_58_14 = e2
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | | REF_CLOSE: (15), (80), (92) are inconsistent by sub-proof
% 177.46/28.01  | | | | | | | | | | | | |            #524.
% 177.46/28.01  | | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | |   (93)  all_56_15 = e1 | all_56_15 = e0
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | | REF_CLOSE: (6), (8), (76), (93) are inconsistent by sub-proof
% 177.46/28.01  | | | | | | | | | |            #653.
% 177.46/28.01  | | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | |   (94)  all_56_5 = e1 | all_56_5 = e0
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | BETA: splitting (94) gives:
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | | Case 1:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | |   (95)  all_56_5 = e1
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REF_CLOSE: (3), (23), (95) are inconsistent by sub-proof #709.
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | Case 2:
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | |   (96)  all_56_5 = e0
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | | REF_CLOSE: (23), (59), (96) are inconsistent by sub-proof
% 177.46/28.01  | | | | | | | | |            #708.
% 177.46/28.01  | | | | | | | | | 
% 177.46/28.01  | | | | | | | | End of split
% 177.46/28.01  | | | | | | | | 
% 177.46/28.01  | | | | | | | End of split
% 177.46/28.01  | | | | | | | 
% 177.46/28.01  | | | | | | End of split
% 177.46/28.01  | | | | | | 
% 177.46/28.01  | | | | | End of split
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | Case 2:
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | |   (97)  all_58_13 = e1
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | | REF_CLOSE: (12), (36), (97) are inconsistent by sub-proof #769.
% 177.46/28.01  | | | | | 
% 177.46/28.01  | | | | End of split
% 177.46/28.01  | | | | 
% 177.46/28.01  | | | End of split
% 177.46/28.01  | | | 
% 177.46/28.01  | | End of split
% 177.46/28.01  | | 
% 177.46/28.01  | End of split
% 177.46/28.01  | 
% 177.46/28.01  End of proof
% 177.46/28.01  
% 177.46/28.01  Sub-proof #391 shows that the following formulas are inconsistent:
% 177.46/28.01  ----------------------------------------------------------------
% 177.46/28.01    (1)  all_58_5 = all_52_13
% 177.46/28.01    (2)  all_58_5 = e2
% 177.46/28.01    (3)   ~ (all_52_13 = e2)
% 177.46/28.01  
% 177.46/28.01  Begin of proof
% 177.46/28.01  | 
% 177.46/28.01  | COMBINE_EQS: (1), (2) imply:
% 177.46/28.01  |   (4)  all_52_13 = e2
% 177.46/28.01  | 
% 177.46/28.01  | SIMP: (4) implies:
% 177.46/28.01  |   (5)  all_52_13 = e2
% 177.46/28.01  | 
% 177.46/28.01  | REDUCE: (3), (5) imply:
% 177.46/28.01  |   (6)  $false
% 177.46/28.01  | 
% 177.46/28.01  | CLOSE: (6) is inconsistent.
% 177.46/28.01  | 
% 177.46/28.01  End of proof
% 177.46/28.01  
% 177.46/28.01  Sub-proof #392 shows that the following formulas are inconsistent:
% 177.46/28.01  ----------------------------------------------------------------
% 177.46/28.01    (1)  all_58_4 = e3
% 177.46/28.01    (2)  all_58_4 = e1
% 177.46/28.01    (3)   ~ (e3 = e1)
% 177.46/28.01  
% 177.46/28.01  Begin of proof
% 177.46/28.01  | 
% 177.46/28.01  | COMBINE_EQS: (1), (2) imply:
% 177.46/28.01  |   (4)  e3 = e1
% 177.46/28.01  | 
% 177.46/28.01  | SIMP: (4) implies:
% 177.46/28.01  |   (5)  e3 = e1
% 177.46/28.01  | 
% 177.46/28.01  | REDUCE: (3), (5) imply:
% 177.46/28.01  |   (6)  $false
% 177.46/28.01  | 
% 177.46/28.01  | CLOSE: (6) is inconsistent.
% 177.46/28.01  | 
% 177.46/28.01  End of proof
% 177.46/28.01  
% 177.46/28.01  Sub-proof #393 shows that the following formulas are inconsistent:
% 177.46/28.01  ----------------------------------------------------------------
% 177.46/28.01    (1)   ~ (all_52_25 = e3)
% 177.46/28.01    (2)  all_58_5 = all_52_13
% 177.46/28.01    (3)  op(e1, all_52_13) = e1
% 177.46/28.01    (4)   ~ (all_52_9 = all_4_2)
% 177.46/28.01    (5)  all_58_4 = all_52_5
% 177.46/28.01    (6)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.01    (7)   ~ (e3 = e1)
% 177.46/28.01    (8)   ~ (all_52_17 = all_14_2)
% 177.46/28.01    (9)  all_58_1 = all_52_3
% 177.46/28.01    (10)  all_58_0 = all_4_2
% 177.46/28.01    (11)  all_58_14 = all_52_29
% 177.46/28.01    (12)   ~ (all_52_3 = all_52_5)
% 177.46/28.01    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.01    (14)  all_58_8 = all_14_2
% 177.46/28.01    (15)  op(e1, all_14_2) = e3
% 177.46/28.01    (16)   ~ (all_52_3 = all_4_2)
% 177.46/28.01    (17)   ~ (all_52_29 = e3)
% 177.46/28.01    (18)  op(e3, all_52_9) = e3
% 177.46/28.01    (19)  all_58_1 = e3
% 177.46/28.01    (20)  all_58_6 = all_52_17
% 177.46/28.01    (21)  all_58_2 = all_52_9
% 177.46/28.01    (22)  op(e1, e3) = all_52_17
% 177.46/28.01    (23)  op(e3, e3) = all_4_2
% 177.46/28.01    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.01    (25)  all_58_12 = all_52_25
% 177.46/28.01    (26)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.01  
% 177.46/28.01  Begin of proof
% 177.46/28.01  | 
% 177.46/28.01  | COMBINE_EQS: (9), (19) imply:
% 177.46/28.01  |   (27)  all_52_3 = e3
% 177.46/28.01  | 
% 177.46/28.01  | REDUCE: (12), (27) imply:
% 177.46/28.01  |   (28)   ~ (all_52_5 = e3)
% 177.46/28.01  | 
% 177.46/28.01  | SIMP: (28) implies:
% 177.46/28.01  |   (29)   ~ (all_52_5 = e3)
% 177.46/28.01  | 
% 177.46/28.01  | REDUCE: (16), (27) imply:
% 177.46/28.01  |   (30)   ~ (all_4_2 = e3)
% 177.46/28.01  | 
% 177.46/28.01  | SIMP: (30) implies:
% 177.46/28.01  |   (31)   ~ (all_4_2 = e3)
% 177.46/28.01  | 
% 177.46/28.01  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14),
% 177.46/28.01  |            (15), (17), (18), (20), (21), (22), (23), (24), (25), (26), (29),
% 177.46/28.01  |            (31) are inconsistent by sub-proof #394.
% 177.46/28.01  | 
% 177.46/28.01  End of proof
% 177.46/28.01  
% 177.46/28.01  Sub-proof #394 shows that the following formulas are inconsistent:
% 177.46/28.01  ----------------------------------------------------------------
% 177.46/28.01    (1)   ~ (all_52_25 = e3)
% 177.46/28.01    (2)  all_58_5 = all_52_13
% 177.46/28.01    (3)  op(e1, all_52_13) = e1
% 177.46/28.01    (4)   ~ (all_4_2 = e3)
% 177.46/28.01    (5)   ~ (all_52_9 = all_4_2)
% 177.46/28.01    (6)  all_58_4 = all_52_5
% 177.46/28.01    (7)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.01    (8)   ~ (e3 = e1)
% 177.46/28.01    (9)   ~ (all_52_17 = all_14_2)
% 177.46/28.01    (10)  all_58_0 = all_4_2
% 177.46/28.01    (11)  all_58_14 = all_52_29
% 177.46/28.01    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.01    (13)  all_58_8 = all_14_2
% 177.46/28.01    (14)  op(e1, all_14_2) = e3
% 177.46/28.01    (15)   ~ (all_52_29 = e3)
% 177.46/28.01    (16)   ~ (all_52_5 = e3)
% 177.46/28.01    (17)  op(e3, all_52_9) = e3
% 177.46/28.01    (18)  all_58_6 = all_52_17
% 177.46/28.01    (19)  all_58_2 = all_52_9
% 177.46/28.01    (20)  op(e1, e3) = all_52_17
% 177.46/28.01    (21)  op(e3, e3) = all_4_2
% 177.46/28.01    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.01    (23)  all_58_12 = all_52_25
% 177.46/28.01    (24)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.01  
% 177.46/28.01  Begin of proof
% 177.46/28.01  | 
% 177.46/28.01  | BETA: splitting (12) gives:
% 177.46/28.01  | 
% 177.46/28.01  | Case 1:
% 177.46/28.01  | | 
% 177.46/28.02  | |   (25)  all_58_0 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | COMBINE_EQS: (10), (25) imply:
% 177.46/28.02  | |   (26)  all_4_2 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (4), (26) imply:
% 177.46/28.02  | |   (27)  $false
% 177.46/28.02  | | 
% 177.46/28.02  | | CLOSE: (27) is inconsistent.
% 177.46/28.02  | | 
% 177.46/28.02  | Case 2:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (28)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | BETA: splitting (24) gives:
% 177.46/28.02  | | 
% 177.46/28.02  | | Case 1:
% 177.46/28.02  | | | 
% 177.46/28.02  | | |   (29)  all_58_4 = e3
% 177.46/28.02  | | | 
% 177.46/28.02  | | | REF_CLOSE: (6), (16), (29) are inconsistent by sub-proof #1025.
% 177.46/28.02  | | | 
% 177.46/28.02  | | Case 2:
% 177.46/28.02  | | | 
% 177.46/28.02  | | |   (30)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.02  | | | 
% 177.46/28.02  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (13), (14), (15),
% 177.46/28.02  | | |            (17), (18), (19), (20), (21), (22), (23), (28), (30) are
% 177.46/28.02  | | |            inconsistent by sub-proof #395.
% 177.46/28.02  | | | 
% 177.46/28.02  | | End of split
% 177.46/28.02  | | 
% 177.46/28.02  | End of split
% 177.46/28.02  | 
% 177.46/28.02  End of proof
% 177.46/28.02  
% 177.46/28.02  Sub-proof #395 shows that the following formulas are inconsistent:
% 177.46/28.02  ----------------------------------------------------------------
% 177.46/28.02    (1)   ~ (all_52_25 = e3)
% 177.46/28.02    (2)  all_58_5 = all_52_13
% 177.46/28.02    (3)  op(e1, all_52_13) = e1
% 177.46/28.02    (4)   ~ (all_52_9 = all_4_2)
% 177.46/28.02    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.02    (6)   ~ (e3 = e1)
% 177.46/28.02    (7)   ~ (all_52_17 = all_14_2)
% 177.46/28.02    (8)  all_58_14 = all_52_29
% 177.46/28.02    (9)  all_58_8 = all_14_2
% 177.46/28.02    (10)  op(e1, all_14_2) = e3
% 177.46/28.02    (11)   ~ (all_52_29 = e3)
% 177.46/28.02    (12)  op(e3, all_52_9) = e3
% 177.46/28.02    (13)  all_58_6 = all_52_17
% 177.46/28.02    (14)  all_58_2 = all_52_9
% 177.46/28.02    (15)  op(e1, e3) = all_52_17
% 177.46/28.02    (16)  op(e3, e3) = all_4_2
% 177.46/28.02    (17)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.02    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.02    (19)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.02    (20)  all_58_12 = all_52_25
% 177.46/28.02  
% 177.46/28.02  Begin of proof
% 177.46/28.02  | 
% 177.46/28.02  | BETA: splitting (5) gives:
% 177.46/28.02  | 
% 177.46/28.02  | Case 1:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (21)  all_58_6 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | COMBINE_EQS: (13), (21) imply:
% 177.46/28.02  | |   (22)  all_52_17 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | SIMP: (22) implies:
% 177.46/28.02  | |   (23)  all_52_17 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (15), (23) imply:
% 177.46/28.02  | |   (24)  op(e1, e3) = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | BETA: splitting (17) gives:
% 177.46/28.02  | | 
% 177.46/28.02  | | Case 1:
% 177.46/28.02  | | | 
% 177.46/28.02  | | |   (25)  all_58_5 = e3
% 177.46/28.02  | | | 
% 177.46/28.02  | | | COMBINE_EQS: (2), (25) imply:
% 177.46/28.02  | | |   (26)  all_52_13 = e3
% 177.46/28.02  | | | 
% 177.46/28.02  | | | SIMP: (26) implies:
% 177.46/28.02  | | |   (27)  all_52_13 = e3
% 177.46/28.02  | | | 
% 177.46/28.02  | | | REDUCE: (3), (27) imply:
% 177.46/28.02  | | |   (28)  op(e1, e3) = e1
% 177.46/28.02  | | | 
% 177.46/28.02  | | | GROUND_INST: instantiating (18) with e1, e3, e3, e1, simplifying with
% 177.46/28.02  | | |              (24), (28) gives:
% 177.46/28.02  | | |   (29)  e3 = e1
% 177.46/28.02  | | | 
% 177.46/28.02  | | | REDUCE: (6), (29) imply:
% 177.46/28.02  | | |   (30)  $false
% 177.46/28.02  | | | 
% 177.46/28.02  | | | CLOSE: (30) is inconsistent.
% 177.46/28.02  | | | 
% 177.46/28.02  | | Case 2:
% 177.46/28.02  | | | 
% 177.46/28.02  | | |   (31)  all_58_8 = e3 | all_58_14 = e3
% 177.46/28.02  | | | 
% 177.46/28.02  | | | REF_CLOSE: (7), (8), (9), (10), (11), (15), (18), (31) are inconsistent by
% 177.46/28.02  | | |            sub-proof #397.
% 177.46/28.02  | | | 
% 177.46/28.02  | | End of split
% 177.46/28.02  | | 
% 177.46/28.02  | Case 2:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (32)   ~ (all_58_6 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (13), (32) imply:
% 177.46/28.02  | |   (33)   ~ (all_52_17 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REF_CLOSE: (1), (4), (12), (13), (14), (16), (18), (19), (20), (33) are
% 177.46/28.02  | |            inconsistent by sub-proof #396.
% 177.46/28.02  | | 
% 177.46/28.02  | End of split
% 177.46/28.02  | 
% 177.46/28.02  End of proof
% 177.46/28.02  
% 177.46/28.02  Sub-proof #396 shows that the following formulas are inconsistent:
% 177.46/28.02  ----------------------------------------------------------------
% 177.46/28.02    (1)   ~ (all_52_25 = e3)
% 177.46/28.02    (2)   ~ (all_52_17 = e3)
% 177.46/28.02    (3)   ~ (all_52_9 = all_4_2)
% 177.46/28.02    (4)  op(e3, all_52_9) = e3
% 177.46/28.02    (5)  all_58_6 = all_52_17
% 177.46/28.02    (6)  all_58_2 = all_52_9
% 177.46/28.02    (7)  op(e3, e3) = all_4_2
% 177.46/28.02    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.02    (9)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.02    (10)  all_58_12 = all_52_25
% 177.46/28.02  
% 177.46/28.02  Begin of proof
% 177.46/28.02  | 
% 177.46/28.02  | BETA: splitting (9) gives:
% 177.46/28.02  | 
% 177.46/28.02  | Case 1:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (11)  all_58_2 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | COMBINE_EQS: (6), (11) imply:
% 177.46/28.02  | |   (12)  all_52_9 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | REF_CLOSE: (3), (4), (7), (8), (12) are inconsistent by sub-proof #967.
% 177.46/28.02  | | 
% 177.46/28.02  | Case 2:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (13)  all_58_6 = e3 | all_58_12 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | REF_CLOSE: (1), (2), (5), (10), (13) are inconsistent by sub-proof #483.
% 177.46/28.02  | | 
% 177.46/28.02  | End of split
% 177.46/28.02  | 
% 177.46/28.02  End of proof
% 177.46/28.02  
% 177.46/28.02  Sub-proof #397 shows that the following formulas are inconsistent:
% 177.46/28.02  ----------------------------------------------------------------
% 177.46/28.02    (1)   ~ (all_52_17 = all_14_2)
% 177.46/28.02    (2)  all_58_14 = all_52_29
% 177.46/28.02    (3)  all_58_8 = all_14_2
% 177.46/28.02    (4)  op(e1, all_14_2) = e3
% 177.46/28.02    (5)   ~ (all_52_29 = e3)
% 177.46/28.02    (6)  all_58_8 = e3 | all_58_14 = e3
% 177.46/28.02    (7)  op(e1, e3) = all_52_17
% 177.46/28.02    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.02  
% 177.46/28.02  Begin of proof
% 177.46/28.02  | 
% 177.46/28.02  | BETA: splitting (6) gives:
% 177.46/28.02  | 
% 177.46/28.02  | Case 1:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (9)  all_58_8 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | REF_CLOSE: (1), (3), (4), (7), (8), (9) are inconsistent by sub-proof #432.
% 177.46/28.02  | | 
% 177.46/28.02  | Case 2:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (10)  all_58_14 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #1000.
% 177.46/28.02  | | 
% 177.46/28.02  | End of split
% 177.46/28.02  | 
% 177.46/28.02  End of proof
% 177.46/28.02  
% 177.46/28.02  Sub-proof #398 shows that the following formulas are inconsistent:
% 177.46/28.02  ----------------------------------------------------------------
% 177.46/28.02    (1)  all_56_4 = all_52_18
% 177.46/28.02    (2)  all_56_4 = e3
% 177.46/28.02    (3)   ~ (all_52_18 = e3)
% 177.46/28.02  
% 177.46/28.02  Begin of proof
% 177.46/28.02  | 
% 177.46/28.02  | COMBINE_EQS: (1), (2) imply:
% 177.46/28.02  |   (4)  all_52_18 = e3
% 177.46/28.02  | 
% 177.46/28.02  | SIMP: (4) implies:
% 177.46/28.02  |   (5)  all_52_18 = e3
% 177.46/28.02  | 
% 177.46/28.02  | REDUCE: (3), (5) imply:
% 177.46/28.02  |   (6)  $false
% 177.46/28.02  | 
% 177.46/28.02  | CLOSE: (6) is inconsistent.
% 177.46/28.02  | 
% 177.46/28.02  End of proof
% 177.46/28.02  
% 177.46/28.02  Sub-proof #399 shows that the following formulas are inconsistent:
% 177.46/28.02  ----------------------------------------------------------------
% 177.46/28.02    (1)   ~ (all_52_5 = all_52_13)
% 177.46/28.02    (2)  op(e3, e2) = all_52_3
% 177.46/28.02    (3)   ~ (all_52_3 = all_10_2)
% 177.46/28.02    (4)  all_58_5 = all_52_13
% 177.46/28.02    (5)  all_58_4 = e3
% 177.46/28.02    (6)  all_58_3 = all_10_2
% 177.46/28.02    (7)   ~ (all_52_9 = all_4_2)
% 177.46/28.02    (8)  all_58_10 = all_52_15
% 177.46/28.02    (9)  all_58_4 = all_52_5
% 177.46/28.02    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/28.02    (11)  op(e3, all_52_9) = e3
% 177.46/28.02    (12)   ~ (all_52_15 = e3)
% 177.46/28.02    (13)  all_58_2 = all_52_9
% 177.46/28.02    (14)  op(e2, all_10_2) = e2
% 177.46/28.02    (15)  op(e3, e3) = all_4_2
% 177.46/28.02    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.02            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.02    (17)  op(e2, e3) = all_52_9
% 177.46/28.02  
% 177.46/28.02  Begin of proof
% 177.46/28.02  | 
% 177.46/28.02  | COMBINE_EQS: (5), (9) imply:
% 177.46/28.02  |   (18)  all_52_5 = e3
% 177.46/28.02  | 
% 177.46/28.02  | SIMP: (18) implies:
% 177.46/28.02  |   (19)  all_52_5 = e3
% 177.46/28.02  | 
% 177.46/28.02  | REDUCE: (1), (19) imply:
% 177.46/28.02  |   (20)   ~ (all_52_13 = e3)
% 177.46/28.02  | 
% 177.46/28.02  | SIMP: (20) implies:
% 177.46/28.02  |   (21)   ~ (all_52_13 = e3)
% 177.46/28.02  | 
% 177.46/28.02  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 177.46/28.02  |            (16), (17), (21) are inconsistent by sub-proof #772.
% 177.46/28.02  | 
% 177.46/28.02  End of proof
% 177.46/28.02  
% 177.46/28.02  Sub-proof #400 shows that the following formulas are inconsistent:
% 177.46/28.02  ----------------------------------------------------------------
% 177.46/28.02    (1)   ~ (all_52_23 = all_14_2)
% 177.46/28.02    (2)   ~ (all_52_5 = all_52_13)
% 177.46/28.02    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.46/28.02    (4)   ~ (all_52_27 = all_10_2)
% 177.46/28.02    (5)   ~ (all_52_17 = all_52_23)
% 177.46/28.02    (6)   ~ (all_6_0 = e3)
% 177.46/28.02    (7)  op(e2, all_52_3) = e2
% 177.46/28.02    (8)   ~ (all_52_13 = all_52_29)
% 177.46/28.02    (9)  all_56_3 = all_52_7
% 177.46/28.02    (10)  op(e3, e2) = all_52_3
% 177.46/28.02    (11)   ~ (all_52_9 = all_52_25)
% 177.46/28.02    (12)  op(e3, all_52_25) = all_52_24
% 177.46/28.02    (13)   ~ (all_52_19 = all_52_23)
% 177.46/28.02    (14)  all_56_11 = all_52_23
% 177.46/28.02    (15)  op(e1, e2) = all_52_19
% 177.46/28.02    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.46/28.02    (17)  op(e3, all_52_9) = all_52_8
% 177.46/28.02    (18)   ~ (all_52_3 = all_10_2)
% 177.46/28.02    (19)  all_58_5 = all_52_13
% 177.46/28.02    (20)   ~ (all_6_2 = e0)
% 177.46/28.02    (21)   ~ (all_52_25 = all_52_29)
% 177.46/28.02    (22)  all_56_15 = all_6_2
% 177.46/28.02    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/28.02    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.46/28.02    (25)  all_58_3 = all_10_2
% 177.46/28.02    (26)  all_56_9 = all_52_19
% 177.46/28.02    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.02    (28)  all_58_15 = all_6_2
% 177.46/28.02    (29)   ~ (all_52_9 = all_4_2)
% 177.46/28.02    (30)   ~ (all_52_5 = all_52_7)
% 177.46/28.02    (31)  all_58_10 = all_52_15
% 177.46/28.02    (32)   ~ (all_52_5 = all_4_2)
% 177.46/28.02    (33)  all_58_7 = all_52_19
% 177.46/28.02    (34)  all_56_4 = all_52_9
% 177.46/28.02    (35)   ~ (all_52_15 = all_6_2)
% 177.46/28.02    (36)   ~ (all_52_17 = all_52_25)
% 177.46/28.02    (37)  op(e0, e1) = all_52_29
% 177.46/28.02    (38)   ~ (all_4_0 = e2)
% 177.46/28.02    (39)  all_58_4 = all_52_5
% 177.46/28.02    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.02    (41)   ~ (all_52_27 = all_52_29)
% 177.46/28.02    (42)   ~ (all_52_17 = all_14_2)
% 177.46/28.02    (43)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.02    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/28.02    (45)   ~ (all_52_7 = all_4_2)
% 177.46/28.02    (46)  all_58_1 = all_52_3
% 177.46/28.02    (47)   ~ (all_52_13 = all_52_15)
% 177.46/28.02    (48)  all_58_0 = all_4_2
% 177.46/28.02    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/28.02    (50)  op(e0, e0) = all_6_2
% 177.46/28.02    (51)  op(e1, all_52_29) = all_52_28
% 177.46/28.02    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/28.02    (53)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.46/28.02    (54)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.46/28.02    (55)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/28.02    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/28.02    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.46/28.02    (58)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.46/28.02    (59)  all_58_14 = all_52_29
% 177.46/28.02    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.46/28.02    (61)   ~ (all_52_3 = all_52_5)
% 177.46/28.02    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.02    (63)  op(e2, e1) = all_52_13
% 177.46/28.02    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.46/28.02    (65)  all_58_8 = all_14_2
% 177.46/28.02    (66)  all_56_1 = all_52_3
% 177.46/28.02    (67)  op(e0, e2) = all_52_27
% 177.46/28.02    (68)  all_56_14 = all_52_29
% 177.46/28.02    (69)  op(e1, all_14_2) = e3
% 177.46/28.02    (70)   ~ (all_52_5 = all_14_2)
% 177.46/28.02    (71)   ~ (all_52_3 = all_52_27)
% 177.46/28.02    (72)   ~ (all_52_3 = all_4_2)
% 177.46/28.02    (73)  op(all_6_1, all_6_2) = all_6_0
% 177.46/28.02    (74)  op(e3, all_4_2) = e3
% 177.46/28.02    (75)  op(e0, e3) = all_52_25
% 177.46/28.02    (76)  op(e0, all_6_2) = all_6_1
% 177.46/28.02    (77)   ~ (all_52_9 = all_10_2)
% 177.46/28.02    (78)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.46/28.02    (79)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.46/28.02    (80)   ~ (all_52_13 = all_14_2)
% 177.46/28.02    (81)   ~ (e3 = e0)
% 177.46/28.02    (82)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.46/28.02    (83)   ~ (all_52_9 = all_52_13)
% 177.46/28.02    (84)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.46/28.02    (85)  op(e0, all_52_23) = all_52_22
% 177.46/28.02    (86)   ~ (all_52_15 = all_52_23)
% 177.46/28.02    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/28.02    (88)   ~ (all_52_5 = all_52_29)
% 177.46/28.02    (89)  all_56_2 = all_52_5
% 177.46/28.02    (90)  op(e1, e0) = all_52_23
% 177.46/28.02    (91)  all_56_12 = all_52_25
% 177.46/28.02    (92)  all_58_13 = all_52_27
% 177.46/28.02    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/28.02    (94)  all_56_5 = all_10_2
% 177.46/28.02    (95)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.46/28.02    (96)   ~ (all_52_9 = all_52_17)
% 177.46/28.02    (97)  all_58_6 = all_52_17
% 177.46/28.02    (98)   ~ (all_52_3 = all_52_7)
% 177.46/28.02    (99)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.02    (100)   ~ (e1 = e0)
% 177.46/28.02    (101)  all_56_0 = all_4_2
% 177.46/28.02    (102)  all_58_11 = all_52_23
% 177.46/28.02    (103)   ~ (all_52_3 = all_52_19)
% 177.46/28.02    (104)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/28.02    (105)   ~ (all_52_7 = all_52_15)
% 177.46/28.02    (106)  op(e0, all_52_15) = all_52_14
% 177.46/28.02    (107)   ~ (all_52_29 = all_14_2)
% 177.46/28.02    (108)   ~ (all_4_0 = e1)
% 177.46/28.02    (109)   ~ (all_52_19 = all_10_2)
% 177.46/28.02    (110)   ~ (all_52_23 = all_6_2)
% 177.46/28.02    (111)   ~ (all_6_0 = e2)
% 177.46/28.02    (112)   ~ (all_52_29 = all_6_2)
% 177.46/28.02    (113)  all_58_2 = all_52_9
% 177.46/28.02    (114)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.46/28.02    (115)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/28.02    (116)  op(e3, e1) = all_52_5
% 177.46/28.02    (117)   ~ (e2 = e1)
% 177.46/28.02    (118)  all_56_10 = all_14_2
% 177.46/28.02    (119)   ~ (all_52_25 = all_6_2)
% 177.46/28.02    (120)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.46/28.02    (121)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.46/28.02    (122)  op(e1, e1) = all_14_2
% 177.46/28.02    (123)  op(e1, e3) = all_52_17
% 177.46/28.02    (124)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.46/28.02    (125)   ~ (all_52_25 = all_4_2)
% 177.46/28.02    (126)  op(e3, e0) = all_52_7
% 177.46/28.02    (127)  all_56_8 = all_52_17
% 177.46/28.02    (128)   ~ (all_52_17 = all_4_2)
% 177.46/28.02    (129)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.02             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.02    (130)   ~ (all_52_25 = all_52_27)
% 177.46/28.02    (131)   ~ (all_52_27 = all_6_2)
% 177.46/28.02    (132)   ~ (all_52_7 = all_6_2)
% 177.46/28.02    (133)   ~ (all_52_15 = all_10_2)
% 177.46/28.02    (134)   ~ (all_52_19 = all_52_27)
% 177.46/28.02    (135)  all_56_7 = all_52_15
% 177.46/28.02    (136)  op(e1, all_52_5) = e1
% 177.46/28.02    (137)   ~ (all_52_7 = all_52_23)
% 177.46/28.02    (138)   ~ (all_52_13 = all_10_2)
% 177.46/28.02    (139)   ~ (all_6_0 = e1)
% 177.46/28.02    (140)  op(e3, all_4_2) = all_4_0
% 177.46/28.02    (141)  op(e0, all_52_7) = e0
% 177.46/28.02    (142)  op(e2, all_52_27) = all_52_26
% 177.46/28.02    (143)   ~ (all_52_17 = all_52_19)
% 177.46/28.02    (144)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.02    (145)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/28.02    (146)  all_58_9 = all_52_7
% 177.46/28.02    (147)  all_58_12 = all_52_25
% 177.46/28.02    (148)  all_56_6 = all_52_13
% 177.46/28.02    (149)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.46/28.02    (150)   ~ (all_52_9 = all_52_15)
% 177.46/28.02    (151)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.02    (152)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.46/28.02    (153)   ~ (all_52_19 = all_14_2)
% 177.46/28.02    (154)  op(e2, e3) = all_52_9
% 177.46/28.02    (155)  all_56_13 = all_52_27
% 177.46/28.02  
% 177.46/28.02  Begin of proof
% 177.46/28.02  | 
% 177.46/28.02  | GROUND_INST: instantiating (129) with e3, all_4_0, all_4_2, e3, simplifying
% 177.46/28.02  |              with (74), (140) gives:
% 177.46/28.02  |   (156)  all_4_0 = e3
% 177.46/28.02  | 
% 177.46/28.02  | REDUCE: (38), (156) imply:
% 177.46/28.02  |   (157)   ~ (e3 = e2)
% 177.46/28.02  | 
% 177.46/28.02  | REDUCE: (108), (156) imply:
% 177.46/28.02  |   (158)   ~ (e3 = e1)
% 177.46/28.02  | 
% 177.46/28.02  | BETA: splitting (43) gives:
% 177.46/28.02  | 
% 177.46/28.02  | Case 1:
% 177.46/28.02  | | 
% 177.46/28.02  | |   (159)  all_56_15 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | COMBINE_EQS: (22), (159) imply:
% 177.46/28.02  | |   (160)  all_6_2 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | SIMP: (160) implies:
% 177.46/28.02  | |   (161)  all_6_2 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | COMBINE_EQS: (28), (161) imply:
% 177.46/28.02  | |   (162)  all_58_15 = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (132), (161) imply:
% 177.46/28.02  | |   (163)   ~ (all_52_7 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (110), (161) imply:
% 177.46/28.02  | |   (164)   ~ (all_52_23 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (119), (161) imply:
% 177.46/28.02  | |   (165)   ~ (all_52_25 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (131), (161) imply:
% 177.46/28.02  | |   (166)   ~ (all_52_27 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (112), (161) imply:
% 177.46/28.02  | |   (167)   ~ (all_52_29 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (73), (161) imply:
% 177.46/28.02  | |   (168)  op(all_6_1, e3) = all_6_0
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (76), (161) imply:
% 177.46/28.02  | |   (169)  op(e0, e3) = all_6_1
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (50), (161) imply:
% 177.46/28.02  | |   (170)  op(e0, e0) = e3
% 177.46/28.02  | | 
% 177.46/28.02  | | GROUND_INST: instantiating (129) with all_52_25, all_6_1, e3, e0,
% 177.46/28.02  | |              simplifying with (75), (169) gives:
% 177.46/28.02  | |   (171)  all_52_25 = all_6_1
% 177.46/28.02  | | 
% 177.46/28.02  | | COMBINE_EQS: (91), (171) imply:
% 177.46/28.02  | |   (172)  all_56_12 = all_6_1
% 177.46/28.02  | | 
% 177.46/28.02  | | COMBINE_EQS: (147), (171) imply:
% 177.46/28.02  | |   (173)  all_58_12 = all_6_1
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (11), (171) imply:
% 177.46/28.02  | |   (174)   ~ (all_52_9 = all_6_1)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (36), (171) imply:
% 177.46/28.02  | |   (175)   ~ (all_52_17 = all_6_1)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (21), (171) imply:
% 177.46/28.02  | |   (176)   ~ (all_52_29 = all_6_1)
% 177.46/28.02  | | 
% 177.46/28.02  | | SIMP: (176) implies:
% 177.46/28.02  | |   (177)   ~ (all_52_29 = all_6_1)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (125), (171) imply:
% 177.46/28.02  | |   (178)   ~ (all_6_1 = all_4_2)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (165), (171) imply:
% 177.46/28.02  | |   (179)   ~ (all_6_1 = e3)
% 177.46/28.02  | | 
% 177.46/28.02  | | REDUCE: (12), (171) imply:
% 177.46/28.02  | |   (180)  op(e3, all_6_1) = all_52_24
% 177.46/28.02  | | 
% 177.46/28.02  | | BETA: splitting (145) gives:
% 177.46/28.02  | | 
% 177.46/28.02  | | Case 1:
% 177.46/28.02  | | | 
% 177.46/28.02  | | |   (181)  all_56_3 = e3
% 177.46/28.02  | | | 
% 177.46/28.02  | | | REF_CLOSE: (9), (163), (181) are inconsistent by sub-proof #1034.
% 177.46/28.02  | | | 
% 177.46/28.02  | | Case 2:
% 177.46/28.02  | | | 
% 177.46/28.02  | | |   (182)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.46/28.02  | | | 
% 177.46/28.02  | | | BETA: splitting (84) gives:
% 177.46/28.02  | | | 
% 177.46/28.02  | | | Case 1:
% 177.46/28.02  | | | | 
% 177.46/28.02  | | | |   (183)  all_56_12 = e3
% 177.46/28.02  | | | | 
% 177.46/28.02  | | | | REF_CLOSE: (172), (179), (183) are inconsistent by sub-proof #509.
% 177.46/28.02  | | | | 
% 177.46/28.02  | | | Case 2:
% 177.46/28.02  | | | | 
% 177.46/28.02  | | | |   (184)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.46/28.02  | | | | 
% 177.46/28.02  | | | | BETA: splitting (78) gives:
% 177.46/28.02  | | | | 
% 177.46/28.02  | | | | Case 1:
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | |   (185)  all_58_9 = e2
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | COMBINE_EQS: (146), (185) imply:
% 177.46/28.02  | | | | |   (186)  all_52_7 = e2
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | SIMP: (186) implies:
% 177.46/28.02  | | | | |   (187)  all_52_7 = e2
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | REDUCE: (98), (187) imply:
% 177.46/28.02  | | | | |   (188)   ~ (all_52_3 = e2)
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | REDUCE: (141), (187) imply:
% 177.46/28.02  | | | | |   (189)  op(e0, e2) = e0
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | GROUND_INST: instantiating (129) with all_52_27, e0, e2, e0,
% 177.46/28.02  | | | | |              simplifying with (67), (189) gives:
% 177.46/28.02  | | | | |   (190)  all_52_27 = e0
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | REDUCE: (71), (190) imply:
% 177.46/28.02  | | | | |   (191)   ~ (all_52_3 = e0)
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | REDUCE: (4), (190) imply:
% 177.46/28.02  | | | | |   (192)   ~ (all_10_2 = e0)
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | SIMP: (192) implies:
% 177.46/28.02  | | | | |   (193)   ~ (all_10_2 = e0)
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | BETA: splitting (52) gives:
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | Case 1:
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | |   (194)  all_56_1 = e3
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | REF_CLOSE: (1), (2), (7), (10), (19), (27), (28), (29), (30), (31),
% 177.46/28.02  | | | | | |            (32), (33), (39), (40), (42), (45), (46), (48), (59),
% 177.46/28.02  | | | | | |            (61), (65), (66), (70), (72), (74), (75), (80), (82),
% 177.46/28.02  | | | | | |            (87), (88), (93), (97), (98), (101), (102), (103), (105),
% 177.46/28.02  | | | | | |            (107), (116), (118), (123), (125), (126), (128), (129),
% 177.46/28.02  | | | | | |            (132), (136), (137), (141), (144), (146), (149), (151),
% 177.46/28.02  | | | | | |            (154), (167), (194) are inconsistent by sub-proof #528.
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | Case 2:
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | |   (195)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | BETA: splitting (195) gives:
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | Case 1:
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | |   (196)  all_56_1 = e2
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | | REF_CLOSE: (66), (188), (196) are inconsistent by sub-proof #857.
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | Case 2:
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | |   (197)  all_56_1 = e1 | all_56_1 = e0
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | | BETA: splitting (197) gives:
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | | Case 1:
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | |   (198)  all_56_1 = e1
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | COMBINE_EQS: (66), (198) imply:
% 177.46/28.02  | | | | | | | |   (199)  all_52_3 = e1
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | SIMP: (199) implies:
% 177.46/28.02  | | | | | | | |   (200)  all_52_3 = e1
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | REDUCE: (18), (200) imply:
% 177.46/28.02  | | | | | | | |   (201)   ~ (all_10_2 = e1)
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | SIMP: (201) implies:
% 177.46/28.02  | | | | | | | |   (202)   ~ (all_10_2 = e1)
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | REDUCE: (7), (200) imply:
% 177.46/28.02  | | | | | | | |   (203)  op(e2, e1) = e2
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | GROUND_INST: instantiating (129) with all_52_13, e2, e1, e2,
% 177.46/28.02  | | | | | | | |              simplifying with (63), (203) gives:
% 177.46/28.02  | | | | | | | |   (204)  all_52_13 = e2
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | REDUCE: (138), (204) imply:
% 177.46/28.02  | | | | | | | |   (205)   ~ (all_10_2 = e2)
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | SIMP: (205) implies:
% 177.46/28.02  | | | | | | | |   (206)   ~ (all_10_2 = e2)
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | REF_CLOSE: (7), (10), (19), (25), (27), (29), (30), (32), (33),
% 177.46/28.02  | | | | | | | |            (39), (42), (46), (48), (56), (59), (61), (65), (69),
% 177.46/28.02  | | | | | | | |            (72), (74), (82), (92), (93), (94), (98), (101),
% 177.46/28.02  | | | | | | | |            (109), (116), (120), (123), (126), (128), (129),
% 177.46/28.02  | | | | | | | |            (136), (138), (151), (154), (166), (167), (193),
% 177.46/28.02  | | | | | | | |            (202), (206) are inconsistent by sub-proof #417.
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | Case 2:
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | |   (207)  all_56_1 = e0
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | REF_CLOSE: (66), (191), (207) are inconsistent by sub-proof
% 177.46/28.02  | | | | | | | |            #855.
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | End of split
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | End of split
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | End of split
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | Case 2:
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | |   (208)   ~ (all_58_9 = e2)
% 177.46/28.02  | | | | |   (209)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | REDUCE: (146), (208) imply:
% 177.46/28.02  | | | | |   (210)   ~ (all_52_7 = e2)
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | BETA: splitting (114) gives:
% 177.46/28.02  | | | | | 
% 177.46/28.02  | | | | | Case 1:
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | |   (211)  all_58_12 = e1
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | COMBINE_EQS: (173), (211) imply:
% 177.46/28.02  | | | | | |   (212)  all_6_1 = e1
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | SIMP: (212) implies:
% 177.46/28.02  | | | | | |   (213)  all_6_1 = e1
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | REDUCE: (175), (213) imply:
% 177.46/28.02  | | | | | |   (214)   ~ (all_52_17 = e1)
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | REDUCE: (168), (213) imply:
% 177.46/28.02  | | | | | |   (215)  op(e1, e3) = all_6_0
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | GROUND_INST: instantiating (129) with all_52_17, all_6_0, e3, e1,
% 177.46/28.02  | | | | | |              simplifying with (123), (215) gives:
% 177.46/28.02  | | | | | |   (216)  all_52_17 = all_6_0
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | COMBINE_EQS: (127), (216) imply:
% 177.46/28.02  | | | | | |   (217)  all_56_8 = all_6_0
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | COMBINE_EQS: (97), (216) imply:
% 177.46/28.02  | | | | | |   (218)  all_58_6 = all_6_0
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | REDUCE: (42), (216) imply:
% 177.46/28.02  | | | | | |   (219)   ~ (all_14_2 = all_6_0)
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | SIMP: (219) implies:
% 177.46/28.02  | | | | | |   (220)   ~ (all_14_2 = all_6_0)
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | BETA: splitting (3) gives:
% 177.46/28.02  | | | | | | 
% 177.46/28.02  | | | | | | Case 1:
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | |   (221)  all_56_8 = e3
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | | REF_CLOSE: (6), (217), (221) are inconsistent by sub-proof #416.
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | Case 2:
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | |   (222)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | | BETA: splitting (222) gives:
% 177.46/28.02  | | | | | | | 
% 177.46/28.02  | | | | | | | Case 1:
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | |   (223)  all_56_8 = e2
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | REF_CLOSE: (111), (217), (223) are inconsistent by sub-proof
% 177.46/28.02  | | | | | | | |            #415.
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | Case 2:
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | |   (224)   ~ (all_56_8 = e2)
% 177.46/28.02  | | | | | | | |   (225)  all_56_8 = e1 | all_56_8 = e0
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | BETA: splitting (225) gives:
% 177.46/28.02  | | | | | | | | 
% 177.46/28.02  | | | | | | | | Case 1:
% 177.46/28.02  | | | | | | | | | 
% 177.46/28.02  | | | | | | | | |   (226)  all_56_8 = e1
% 177.46/28.02  | | | | | | | | | 
% 177.46/28.02  | | | | | | | | | REF_CLOSE: (139), (217), (226) are inconsistent by sub-proof
% 177.46/28.02  | | | | | | | | |            #414.
% 177.46/28.02  | | | | | | | | | 
% 177.46/28.02  | | | | | | | | Case 2:
% 177.46/28.02  | | | | | | | | | 
% 177.46/28.02  | | | | | | | | |   (227)  all_56_8 = e0
% 177.46/28.02  | | | | | | | | | 
% 177.46/28.02  | | | | | | | | | COMBINE_EQS: (217), (227) imply:
% 177.46/28.02  | | | | | | | | |   (228)  all_6_0 = e0
% 177.46/28.02  | | | | | | | | | 
% 177.46/28.02  | | | | | | | | | SIMP: (228) implies:
% 177.46/28.02  | | | | | | | | |   (229)  all_6_0 = e0
% 177.46/28.02  | | | | | | | | | 
% 177.46/28.02  | | | | | | | | | COMBINE_EQS: (218), (229) imply:
% 177.46/28.03  | | | | | | | | |   (230)  all_58_6 = e0
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | REDUCE: (220), (229) imply:
% 177.46/28.03  | | | | | | | | |   (231)   ~ (all_14_2 = e0)
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | REDUCE: (111), (229) imply:
% 177.46/28.03  | | | | | | | | |   (232)   ~ (e2 = e0)
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | SIMP: (232) implies:
% 177.46/28.03  | | | | | | | | |   (233)   ~ (e2 = e0)
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | BETA: splitting (99) gives:
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | |   (234)  all_56_4 = e3
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | COMBINE_EQS: (34), (234) imply:
% 177.46/28.03  | | | | | | | | | |   (235)  all_52_9 = e3
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REF_CLOSE: (1), (2), (7), (10), (19), (27), (28), (29), (30),
% 177.46/28.03  | | | | | | | | | |            (31), (32), (33), (39), (40), (42), (45), (46),
% 177.46/28.03  | | | | | | | | | |            (48), (59), (61), (65), (70), (74), (75), (80),
% 177.46/28.03  | | | | | | | | | |            (82), (87), (88), (93), (97), (98), (101), (102),
% 177.46/28.03  | | | | | | | | | |            (103), (105), (107), (116), (118), (123), (125),
% 177.46/28.03  | | | | | | | | | |            (126), (128), (129), (132), (136), (137), (141),
% 177.46/28.03  | | | | | | | | | |            (144), (146), (149), (151), (154), (167), (235)
% 177.46/28.03  | | | | | | | | | |            are inconsistent by sub-proof #413.
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | |   (236)   ~ (all_56_4 = e3)
% 177.46/28.03  | | | | | | | | | |   (237)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (34), (236) imply:
% 177.46/28.03  | | | | | | | | | |   (238)   ~ (all_52_9 = e3)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | BETA: splitting (237) gives:
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | |   (239)  all_56_4 = e2
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | COMBINE_EQS: (34), (239) imply:
% 177.46/28.03  | | | | | | | | | | |   (240)  all_52_9 = e2
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | SIMP: (240) implies:
% 177.46/28.03  | | | | | | | | | | |   (241)  all_52_9 = e2
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | REDUCE: (150), (241) imply:
% 177.46/28.03  | | | | | | | | | | |   (242)   ~ (all_52_15 = e2)
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | SIMP: (242) implies:
% 177.46/28.03  | | | | | | | | | | |   (243)   ~ (all_52_15 = e2)
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | REDUCE: (238), (241) imply:
% 177.46/28.03  | | | | | | | | | | |   (244)   ~ (e3 = e2)
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | BETA: splitting (209) gives:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | |   (245)  all_58_10 = e2
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REF_CLOSE: (31), (243), (245) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | | |            #711.
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | |   (246)  all_58_11 = e2 | all_58_15 = e2
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REF_CLOSE: (1), (7), (10), (19), (25), (26), (27), (29),
% 177.46/28.03  | | | | | | | | | | | |            (30), (32), (33), (39), (42), (46), (48), (53),
% 177.46/28.03  | | | | | | | | | | | |            (56), (59), (61), (65), (69), (72), (74), (82),
% 177.46/28.03  | | | | | | | | | | | |            (87), (92), (93), (98), (101), (102), (116),
% 177.46/28.03  | | | | | | | | | | | |            (118), (122), (123), (126), (128), (129), (136),
% 177.46/28.03  | | | | | | | | | | | |            (138), (151), (153), (154), (157), (162), (166),
% 177.46/28.03  | | | | | | | | | | | |            (167), (231), (246) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | | |            #412.
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | |   (247)   ~ (all_56_4 = e2)
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | REDUCE: (34), (247) imply:
% 177.46/28.03  | | | | | | | | | | |   (248)   ~ (all_52_9 = e2)
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | REF_CLOSE: (1), (2), (7), (10), (19), (23), (27), (28), (29),
% 177.46/28.03  | | | | | | | | | | |            (30), (31), (32), (33), (39), (40), (42), (45),
% 177.46/28.03  | | | | | | | | | | |            (46), (48), (59), (61), (62), (65), (70), (74),
% 177.46/28.03  | | | | | | | | | | |            (75), (80), (82), (87), (88), (93), (97), (98),
% 177.46/28.03  | | | | | | | | | | |            (101), (102), (103), (105), (107), (113), (116),
% 177.46/28.03  | | | | | | | | | | |            (117), (118), (123), (125), (126), (128), (129),
% 177.46/28.03  | | | | | | | | | | |            (132), (136), (137), (141), (144), (146), (149),
% 177.46/28.03  | | | | | | | | | | |            (151), (154), (157), (167), (211), (230), (233),
% 177.46/28.03  | | | | | | | | | | |            (248) are inconsistent by sub-proof #410.
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | End of split
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | End of split
% 177.46/28.03  | | | | | | 
% 177.46/28.03  | | | | | Case 2:
% 177.46/28.03  | | | | | | 
% 177.46/28.03  | | | | | |   (249)   ~ (all_58_12 = e1)
% 177.46/28.03  | | | | | |   (250)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.46/28.03  | | | | | | 
% 177.46/28.03  | | | | | | REDUCE: (173), (249) imply:
% 177.46/28.03  | | | | | |   (251)   ~ (all_6_1 = e1)
% 177.46/28.03  | | | | | | 
% 177.46/28.03  | | | | | | BETA: splitting (151) gives:
% 177.46/28.03  | | | | | | 
% 177.46/28.03  | | | | | | Case 1:
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | |   (252)  all_58_4 = e3
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | | COMBINE_EQS: (39), (252) imply:
% 177.46/28.03  | | | | | | |   (253)  all_52_5 = e3
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | | SIMP: (253) implies:
% 177.46/28.03  | | | | | | |   (254)  all_52_5 = e3
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | | REF_CLOSE: (1), (2), (7), (10), (19), (27), (28), (29), (30),
% 177.46/28.03  | | | | | | |            (31), (32), (33), (39), (40), (42), (45), (46), (48),
% 177.46/28.03  | | | | | | |            (59), (61), (65), (70), (74), (75), (80), (82), (87),
% 177.46/28.03  | | | | | | |            (88), (93), (97), (98), (101), (102), (103), (105),
% 177.46/28.03  | | | | | | |            (107), (116), (118), (123), (125), (126), (128), (129),
% 177.46/28.03  | | | | | | |            (132), (136), (137), (141), (144), (146), (149), (151),
% 177.46/28.03  | | | | | | |            (154), (254) are inconsistent by sub-proof #863.
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | Case 2:
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | |   (255)   ~ (all_58_4 = e3)
% 177.46/28.03  | | | | | | |   (256)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | | REDUCE: (39), (255) imply:
% 177.46/28.03  | | | | | | |   (257)   ~ (all_52_5 = e3)
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | | BETA: splitting (149) gives:
% 177.46/28.03  | | | | | | | 
% 177.46/28.03  | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | |   (258)  all_58_0 = e3
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | | COMBINE_EQS: (48), (258) imply:
% 177.46/28.03  | | | | | | | |   (259)  all_4_2 = e3
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | | REDUCE: (29), (259) imply:
% 177.46/28.03  | | | | | | | |   (260)   ~ (all_52_9 = e3)
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | | BETA: splitting (99) gives:
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | |   (261)  all_56_4 = e3
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | REF_CLOSE: (34), (260), (261) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | |            #782.
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | |   (262)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | BETA: splitting (121) gives:
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | |   (263)  all_58_12 = e2
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | COMBINE_EQS: (173), (263) imply:
% 177.46/28.03  | | | | | | | | | |   (264)  all_6_1 = e2
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | SIMP: (264) implies:
% 177.46/28.03  | | | | | | | | | |   (265)  all_6_1 = e2
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (174), (265) imply:
% 177.46/28.03  | | | | | | | | | |   (266)   ~ (all_52_9 = e2)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (179), (265) imply:
% 177.46/28.03  | | | | | | | | | |   (267)   ~ (e3 = e2)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (168), (265) imply:
% 177.46/28.03  | | | | | | | | | |   (268)  op(e2, e3) = all_6_0
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | GROUND_INST: instantiating (129) with all_52_9, all_6_0, e3,
% 177.46/28.03  | | | | | | | | | |              e2, simplifying with (154), (268) gives:
% 177.46/28.03  | | | | | | | | | |   (269)  all_52_9 = all_6_0
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | COMBINE_EQS: (34), (269) imply:
% 177.46/28.03  | | | | | | | | | |   (270)  all_56_4 = all_6_0
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | COMBINE_EQS: (113), (269) imply:
% 177.46/28.03  | | | | | | | | | |   (271)  all_58_2 = all_6_0
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (150), (269) imply:
% 177.46/28.03  | | | | | | | | | |   (272)   ~ (all_52_15 = all_6_0)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | SIMP: (272) implies:
% 177.46/28.03  | | | | | | | | | |   (273)   ~ (all_52_15 = all_6_0)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (77), (269) imply:
% 177.46/28.03  | | | | | | | | | |   (274)   ~ (all_10_2 = all_6_0)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | SIMP: (274) implies:
% 177.46/28.03  | | | | | | | | | |   (275)   ~ (all_10_2 = all_6_0)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (17), (269) imply:
% 177.46/28.03  | | | | | | | | | |   (276)  op(e3, all_6_0) = all_52_8
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | BETA: splitting (82) gives:
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | |   (277)  all_58_0 = e0
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | COMBINE_EQS: (258), (277) imply:
% 177.46/28.03  | | | | | | | | | | |   (278)  e3 = e0
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | REDUCE: (81), (278) imply:
% 177.46/28.03  | | | | | | | | | | |   (279)  $false
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | CLOSE: (279) is inconsistent.
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | |   (280)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | BETA: splitting (280) gives:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | |   (281)  all_58_2 = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | COMBINE_EQS: (271), (281) imply:
% 177.46/28.03  | | | | | | | | | | | |   (282)  all_6_0 = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | SIMP: (282) implies:
% 177.46/28.03  | | | | | | | | | | | |   (283)  all_6_0 = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (273), (283) imply:
% 177.46/28.03  | | | | | | | | | | | |   (284)   ~ (all_52_15 = e0)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (275), (283) imply:
% 177.46/28.03  | | | | | | | | | | | |   (285)   ~ (all_10_2 = e0)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (139), (283) imply:
% 177.46/28.03  | | | | | | | | | | | |   (286)   ~ (e1 = e0)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (276), (283) imply:
% 177.46/28.03  | | | | | | | | | | | |   (287)  op(e3, e0) = all_52_8
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | GROUND_INST: instantiating (129) with all_52_7, all_52_8, e0,
% 177.46/28.03  | | | | | | | | | | | |              e3, simplifying with (126), (287) gives:
% 177.46/28.03  | | | | | | | | | | | |   (288)  all_52_7 = all_52_8
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | COMBINE_EQS: (9), (288) imply:
% 177.46/28.03  | | | | | | | | | | | |   (289)  all_56_3 = all_52_8
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | COMBINE_EQS: (146), (288) imply:
% 177.46/28.03  | | | | | | | | | | | |   (290)  all_58_9 = all_52_8
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (137), (288) imply:
% 177.46/28.03  | | | | | | | | | | | |   (291)   ~ (all_52_8 = all_52_23)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (163), (288) imply:
% 177.46/28.03  | | | | | | | | | | | |   (292)   ~ (all_52_8 = e3)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (210), (288) imply:
% 177.46/28.03  | | | | | | | | | | | |   (293)   ~ (all_52_8 = e2)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (141), (288) imply:
% 177.46/28.03  | | | | | | | | | | | |   (294)  op(e0, all_52_8) = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | BETA: splitting (24) gives:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | |   (295)  all_58_9 = e1
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | COMBINE_EQS: (290), (295) imply:
% 177.46/28.03  | | | | | | | | | | | | |   (296)  all_52_8 = e1
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | SIMP: (296) implies:
% 177.46/28.03  | | | | | | | | | | | | |   (297)  all_52_8 = e1
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | REDUCE: (291), (297) imply:
% 177.46/28.03  | | | | | | | | | | | | |   (298)   ~ (all_52_23 = e1)
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | SIMP: (298) implies:
% 177.46/28.03  | | | | | | | | | | | | |   (299)   ~ (all_52_23 = e1)
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | REDUCE: (292), (297) imply:
% 177.46/28.03  | | | | | | | | | | | | |   (300)   ~ (e3 = e1)
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | REDUCE: (294), (297) imply:
% 177.46/28.03  | | | | | | | | | | | | |   (301)  op(e0, e1) = e0
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | BETA: splitting (49) gives:
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | |   (302)  all_58_9 = e0
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | REF_CLOSE: (100), (295), (302) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | | | | |            #809.
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | |   (303)  all_58_10 = e0 | all_58_11 = e0
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | |   (304)  all_58_10 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | REF_CLOSE: (31), (284), (304) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | | | | | |            #741.
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | |   (305)  all_58_11 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | COMBINE_EQS: (102), (305) imply:
% 177.46/28.03  | | | | | | | | | | | | | | |   (306)  all_52_23 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | SIMP: (306) implies:
% 177.46/28.03  | | | | | | | | | | | | | | |   (307)  all_52_23 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | REDUCE: (1), (307) imply:
% 177.46/28.03  | | | | | | | | | | | | | | |   (308)   ~ (all_14_2 = e0)
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | SIMP: (308) implies:
% 177.46/28.03  | | | | | | | | | | | | | | |   (309)   ~ (all_14_2 = e0)
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | |   (310)  all_58_10 = e2
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (310) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (311)  all_52_15 = e2
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | SIMP: (311) implies:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (312)  all_52_15 = e2
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | REDUCE: (133), (312) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (313)   ~ (all_10_2 = e2)
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | SIMP: (313) implies:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (314)   ~ (all_10_2 = e2)
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (129) with all_52_29, e0, e1, e0,
% 177.46/28.03  | | | | | | | | | | | | | | | |              simplifying with (37), (301) gives:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (315)  all_52_29 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (315) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (316)  all_58_14 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | |   (317)  all_58_13 = e1
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (317) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | | |   (318)  all_52_27 = e1
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | | SIMP: (318) implies:
% 177.46/28.03  | | | | | | | | | | | | | | | | |   (319)  all_52_27 = e1
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | | REDUCE: (4), (319) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | | |   (320)   ~ (all_10_2 = e1)
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | | SIMP: (320) implies:
% 177.46/28.03  | | | | | | | | | | | | | | | | |   (321)   ~ (all_10_2 = e1)
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (19), (25), (27), (29), (30), (32),
% 177.46/28.03  | | | | | | | | | | | | | | | | |            (33), (39), (42), (46), (48), (56), (59), (61),
% 177.46/28.03  | | | | | | | | | | | | | | | | |            (65), (69), (72), (74), (82), (92), (93), (94),
% 177.46/28.03  | | | | | | | | | | | | | | | | |            (98), (101), (109), (116), (120), (123), (126),
% 177.46/28.03  | | | | | | | | | | | | | | | | |            (128), (129), (136), (138), (151), (154), (166),
% 177.46/28.03  | | | | | | | | | | | | | | | | |            (167), (285), (314), (321) are inconsistent by
% 177.46/28.03  | | | | | | | | | | | | | | | | |            sub-proof #417.
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | |   (322)  all_58_14 = e1 | all_58_15 = e1
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (158), (162), (316), (322) are inconsistent
% 177.46/28.03  | | | | | | | | | | | | | | | | |            by sub-proof #835.
% 177.46/28.03  | | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | |   (323)  all_58_11 = e2 | all_58_15 = e2
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (10), (19), (25), (26), (27), (29),
% 177.46/28.03  | | | | | | | | | | | | | | | |            (30), (32), (33), (39), (42), (46), (48), (53),
% 177.46/28.03  | | | | | | | | | | | | | | | |            (56), (59), (61), (65), (69), (72), (74), (82),
% 177.46/28.03  | | | | | | | | | | | | | | | |            (87), (92), (93), (98), (101), (102), (116),
% 177.46/28.03  | | | | | | | | | | | | | | | |            (118), (122), (123), (126), (128), (129), (136),
% 177.46/28.03  | | | | | | | | | | | | | | | |            (138), (151), (153), (154), (157), (162), (166),
% 177.46/28.03  | | | | | | | | | | | | | | | |            (167), (309), (323) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | | | | | | |            #412.
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | |   (324)   ~ (all_58_9 = e1)
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | REF_CLOSE: (129), (170), (182), (289), (290), (292), (293),
% 177.46/28.03  | | | | | | | | | | | | |            (294), (324) are inconsistent by sub-proof #409.
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | |   (325)   ~ (all_58_2 = e0)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (271), (325) imply:
% 177.46/28.03  | | | | | | | | | | | |   (326)   ~ (all_6_0 = e0)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REF_CLOSE: (111), (139), (262), (270), (326) are inconsistent
% 177.46/28.03  | | | | | | | | | | | |            by sub-proof #408.
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | |   (327)   ~ (all_58_12 = e2)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | REDUCE: (173), (327) imply:
% 177.46/28.03  | | | | | | | | | |   (328)   ~ (all_6_1 = e2)
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | BETA: splitting (184) gives:
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | |   (329)  all_56_12 = e2
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | REF_CLOSE: (172), (328), (329) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | |            #507.
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | |   (330)  all_56_12 = e1 | all_56_12 = e0
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | BETA: splitting (330) gives:
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | |   (331)  all_56_12 = e1
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REF_CLOSE: (172), (251), (331) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | | |            #506.
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | |   (332)  all_56_12 = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | COMBINE_EQS: (172), (332) imply:
% 177.46/28.03  | | | | | | | | | | | |   (333)  all_6_1 = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | SIMP: (333) implies:
% 177.46/28.03  | | | | | | | | | | | |   (334)  all_6_1 = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (177), (334) imply:
% 177.46/28.03  | | | | | | | | | | | |   (335)   ~ (all_52_29 = e0)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (168), (334) imply:
% 177.46/28.03  | | | | | | | | | | | |   (336)  op(e0, e3) = all_6_0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (180), (334) imply:
% 177.46/28.03  | | | | | | | | | | | |   (337)  op(e3, e0) = all_52_24
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (169), (334) imply:
% 177.46/28.03  | | | | | | | | | | | |   (338)  op(e0, e3) = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | GROUND_INST: instantiating (129) with e0, all_6_0, e3, e0,
% 177.46/28.03  | | | | | | | | | | | |              simplifying with (336), (338) gives:
% 177.46/28.03  | | | | | | | | | | | |   (339)  all_6_0 = e0
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | GROUND_INST: instantiating (129) with all_52_7, all_52_24, e0,
% 177.46/28.03  | | | | | | | | | | | |              e3, simplifying with (126), (337) gives:
% 177.46/28.03  | | | | | | | | | | | |   (340)  all_52_7 = all_52_24
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | COMBINE_EQS: (9), (340) imply:
% 177.46/28.03  | | | | | | | | | | | |   (341)  all_56_3 = all_52_24
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (30), (340) imply:
% 177.46/28.03  | | | | | | | | | | | |   (342)   ~ (all_52_5 = all_52_24)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (137), (340) imply:
% 177.46/28.03  | | | | | | | | | | | |   (343)   ~ (all_52_23 = all_52_24)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | SIMP: (343) implies:
% 177.46/28.03  | | | | | | | | | | | |   (344)   ~ (all_52_23 = all_52_24)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (163), (340) imply:
% 177.46/28.03  | | | | | | | | | | | |   (345)   ~ (all_52_24 = e3)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (210), (340) imply:
% 177.46/28.03  | | | | | | | | | | | |   (346)   ~ (all_52_24 = e2)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | REDUCE: (6), (339) imply:
% 177.46/28.03  | | | | | | | | | | | |   (347)   ~ (e3 = e0)
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | BETA: splitting (57) gives:
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | |   (348)  all_56_6 = e3
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | COMBINE_EQS: (148), (348) imply:
% 177.46/28.03  | | | | | | | | | | | | |   (349)  all_52_13 = e3
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | SIMP: (349) implies:
% 177.46/28.03  | | | | | | | | | | | | |   (350)  all_52_13 = e3
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | COMBINE_EQS: (19), (350) imply:
% 177.46/28.03  | | | | | | | | | | | | |   (351)  all_58_5 = e3
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | |   (352)  all_58_4 = e0
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | COMBINE_EQS: (39), (352) imply:
% 177.46/28.03  | | | | | | | | | | | | | |   (353)  all_52_5 = e0
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | REDUCE: (342), (353) imply:
% 177.46/28.03  | | | | | | | | | | | | | |   (354)   ~ (all_52_24 = e0)
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | SIMP: (354) implies:
% 177.46/28.03  | | | | | | | | | | | | | |   (355)   ~ (all_52_24 = e0)
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | REDUCE: (136), (353) imply:
% 177.46/28.03  | | | | | | | | | | | | | |   (356)  op(e1, e0) = e1
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | REF_CLOSE: (90), (129), (145), (341), (344), (345), (346),
% 177.46/28.03  | | | | | | | | | | | | | |            (355), (356) are inconsistent by sub-proof #407.
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | |   (357)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | BETA: splitting (357) gives:
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | |   (358)  all_58_5 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | COMBINE_EQS: (351), (358) imply:
% 177.46/28.03  | | | | | | | | | | | | | | |   (359)  e3 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | REDUCE: (81), (359) imply:
% 177.46/28.03  | | | | | | | | | | | | | | |   (360)  $false
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | CLOSE: (360) is inconsistent.
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | |   (361)  all_58_8 = e0 | all_58_14 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | BETA: splitting (361) gives:
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | Case 1:
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | |   (362)  all_58_8 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (362) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (363)  all_14_2 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | REDUCE: (69), (363) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (364)  op(e1, e0) = e3
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (129) with all_52_23, e3, e0, e1,
% 177.46/28.03  | | | | | | | | | | | | | | | |              simplifying with (90), (364) gives:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (365)  all_52_23 = e3
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | REDUCE: (164), (365) imply:
% 177.46/28.03  | | | | | | | | | | | | | | | |   (366)  $false
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | CLOSE: (366) is inconsistent.
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | |   (367)  all_58_14 = e0
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | | REF_CLOSE: (59), (335), (367) are inconsistent by sub-proof
% 177.46/28.03  | | | | | | | | | | | | | | | |            #696.
% 177.46/28.03  | | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | |   (368)   ~ (all_56_6 = e3)
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | REDUCE: (148), (368) imply:
% 177.46/28.03  | | | | | | | | | | | | |   (369)   ~ (all_52_13 = e3)
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | | REF_CLOSE: (19), (42), (59), (65), (69), (123), (129), (167),
% 177.46/28.03  | | | | | | | | | | | | |            (256), (369) are inconsistent by sub-proof #420.
% 177.46/28.03  | | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | | 
% 177.46/28.03  | | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | | 
% 177.46/28.03  | | | | | | | | End of split
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | Case 2:
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | |   (370)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.46/28.03  | | | | | | | | 
% 177.46/28.03  | | | | | | | | REF_CLOSE: (7), (10), (27), (28), (29), (30), (31), (39), (45),
% 177.46/28.03  | | | | | | | |            (46), (48), (61), (72), (74), (75), (93), (98),
% 177.46/28.03  | | | | | | | |            (101), (102), (105), (116), (125), (126), (129),
% 177.46/28.03  | | | | | | | |            (132), (137), (141), (144), (146), (154), (257),
% 177.46/28.04  | | | | | | | |            (370) are inconsistent by sub-proof #787.
% 177.46/28.04  | | | | | | | | 
% 177.46/28.04  | | | | | | | End of split
% 177.46/28.04  | | | | | | | 
% 177.46/28.04  | | | | | | End of split
% 177.46/28.04  | | | | | | 
% 177.46/28.04  | | | | | End of split
% 177.46/28.04  | | | | | 
% 177.46/28.04  | | | | End of split
% 177.46/28.04  | | | | 
% 177.46/28.04  | | | End of split
% 177.46/28.04  | | | 
% 177.46/28.04  | | End of split
% 177.46/28.04  | | 
% 177.46/28.04  | Case 2:
% 177.46/28.04  | | 
% 177.46/28.04  | |   (371)   ~ (all_56_15 = e3)
% 177.46/28.04  | |   (372)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.04  | | 
% 177.46/28.04  | | REDUCE: (22), (371) imply:
% 177.46/28.04  | |   (373)   ~ (all_6_2 = e3)
% 177.46/28.04  | | 
% 177.46/28.04  | | REF_CLOSE: (1), (2), (5), (7), (8), (10), (11), (13), (14), (15), (16),
% 177.46/28.04  | |            (18), (19), (20), (21), (22), (23), (24), (25), (27), (28), (29),
% 177.46/28.04  | |            (30), (31), (32), (33), (34), (35), (36), (37), (39), (40), (41),
% 177.46/28.04  | |            (42), (44), (45), (46), (47), (48), (49), (51), (54), (55), (56),
% 177.46/28.04  | |            (58), (59), (60), (61), (62), (63), (64), (65), (68), (69), (70),
% 177.46/28.04  | |            (72), (74), (75), (79), (80), (81), (82), (83), (84), (85), (86),
% 177.46/28.04  | |            (87), (88), (89), (90), (91), (92), (93), (95), (96), (97), (98),
% 177.46/28.04  | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 177.46/28.04  | |            (110), (112), (113), (115), (116), (118), (119), (122), (123),
% 177.46/28.04  | |            (124), (125), (126), (128), (129), (130), (131), (132), (134),
% 177.46/28.04  | |            (135), (136), (137), (138), (141), (142), (143), (144), (146),
% 177.46/28.04  | |            (147), (149), (150), (151), (152), (153), (154), (155), (157),
% 177.46/28.04  | |            (158), (372), (373) are inconsistent by sub-proof #401.
% 177.46/28.04  | | 
% 177.46/28.04  | End of split
% 177.46/28.04  | 
% 177.46/28.04  End of proof
% 177.46/28.04  
% 177.46/28.04  Sub-proof #401 shows that the following formulas are inconsistent:
% 177.46/28.04  ----------------------------------------------------------------
% 177.46/28.04    (1)   ~ (all_52_23 = all_14_2)
% 177.46/28.04    (2)   ~ (all_52_5 = all_52_13)
% 177.46/28.04    (3)   ~ (all_52_17 = all_52_23)
% 177.46/28.04    (4)  op(e2, all_52_3) = e2
% 177.46/28.04    (5)   ~ (all_52_13 = all_52_29)
% 177.46/28.04    (6)  op(e3, e2) = all_52_3
% 177.46/28.04    (7)   ~ (all_52_9 = all_52_25)
% 177.46/28.04    (8)   ~ (all_52_19 = all_52_23)
% 177.46/28.04    (9)  all_56_11 = all_52_23
% 177.46/28.04    (10)  op(e1, e2) = all_52_19
% 177.46/28.04    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.46/28.04    (12)   ~ (all_6_2 = e3)
% 177.46/28.04    (13)   ~ (all_52_3 = all_10_2)
% 177.46/28.04    (14)  all_58_5 = all_52_13
% 177.46/28.04    (15)   ~ (all_6_2 = e0)
% 177.46/28.04    (16)   ~ (all_52_25 = all_52_29)
% 177.46/28.04    (17)  all_56_15 = all_6_2
% 177.46/28.04    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.46/28.04    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.46/28.04    (20)  all_58_3 = all_10_2
% 177.46/28.04    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.04    (22)  all_58_15 = all_6_2
% 177.46/28.04    (23)   ~ (all_52_9 = all_4_2)
% 177.46/28.04    (24)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.46/28.04    (25)   ~ (all_52_5 = all_52_7)
% 177.46/28.04    (26)  all_58_10 = all_52_15
% 177.46/28.04    (27)   ~ (all_52_5 = all_4_2)
% 177.46/28.04    (28)  all_58_7 = all_52_19
% 177.46/28.04    (29)  all_56_4 = all_52_9
% 177.46/28.04    (30)   ~ (all_52_15 = all_6_2)
% 177.46/28.04    (31)   ~ (all_52_17 = all_52_25)
% 177.46/28.04    (32)  op(e0, e1) = all_52_29
% 177.46/28.04    (33)  all_58_4 = all_52_5
% 177.46/28.04    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.46/28.04    (35)   ~ (e3 = e1)
% 177.46/28.04    (36)   ~ (all_52_27 = all_52_29)
% 177.46/28.04    (37)   ~ (all_52_17 = all_14_2)
% 177.46/28.04    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.46/28.04    (39)   ~ (all_52_7 = all_4_2)
% 177.46/28.04    (40)  all_58_1 = all_52_3
% 177.46/28.04    (41)   ~ (all_52_13 = all_52_15)
% 177.46/28.04    (42)  all_58_0 = all_4_2
% 177.46/28.04    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.46/28.04    (44)  op(e1, all_52_29) = all_52_28
% 177.46/28.04    (45)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.46/28.04    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.46/28.04    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/28.04    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.46/28.04    (49)  all_58_14 = all_52_29
% 177.46/28.04    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.46/28.04    (51)   ~ (all_52_3 = all_52_5)
% 177.46/28.04    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.46/28.04    (53)  op(e2, e1) = all_52_13
% 177.46/28.04    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.46/28.04    (55)  all_58_8 = all_14_2
% 177.46/28.04    (56)  all_56_14 = all_52_29
% 177.46/28.04    (57)  op(e1, all_14_2) = e3
% 177.46/28.04    (58)   ~ (all_52_5 = all_14_2)
% 177.46/28.04    (59)   ~ (all_52_3 = all_4_2)
% 177.46/28.04    (60)  op(e3, all_4_2) = e3
% 177.46/28.04    (61)  op(e0, e3) = all_52_25
% 177.46/28.04    (62)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.46/28.04    (63)   ~ (all_52_13 = all_14_2)
% 177.46/28.04    (64)   ~ (e3 = e0)
% 177.46/28.04    (65)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.46/28.04    (66)   ~ (all_52_9 = all_52_13)
% 177.46/28.04    (67)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.46/28.04    (68)  op(e0, all_52_23) = all_52_22
% 177.46/28.04    (69)   ~ (all_52_15 = all_52_23)
% 177.46/28.04    (70)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.46/28.04    (71)   ~ (all_52_5 = all_52_29)
% 177.46/28.04    (72)  all_56_2 = all_52_5
% 177.46/28.04    (73)  op(e1, e0) = all_52_23
% 177.46/28.04    (74)  all_56_12 = all_52_25
% 177.46/28.04    (75)  all_58_13 = all_52_27
% 177.46/28.04    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.46/28.04    (77)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.46/28.04    (78)   ~ (all_52_9 = all_52_17)
% 177.46/28.04    (79)  all_58_6 = all_52_17
% 177.46/28.04    (80)   ~ (all_52_3 = all_52_7)
% 177.46/28.04    (81)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.46/28.04    (82)   ~ (e1 = e0)
% 177.46/28.04    (83)  all_56_0 = all_4_2
% 177.46/28.04    (84)  all_58_11 = all_52_23
% 177.46/28.04    (85)   ~ (all_52_3 = all_52_19)
% 177.46/28.04    (86)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.46/28.04    (87)   ~ (all_52_7 = all_52_15)
% 177.46/28.04    (88)  op(e0, all_52_15) = all_52_14
% 177.46/28.04    (89)   ~ (all_52_29 = all_14_2)
% 177.46/28.04    (90)   ~ (all_52_23 = all_6_2)
% 177.46/28.04    (91)   ~ (all_52_29 = all_6_2)
% 177.46/28.04    (92)  all_58_2 = all_52_9
% 177.46/28.04    (93)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.46/28.04    (94)  op(e3, e1) = all_52_5
% 177.46/28.04    (95)  all_56_10 = all_14_2
% 177.46/28.04    (96)   ~ (all_52_25 = all_6_2)
% 177.46/28.04    (97)  op(e1, e1) = all_14_2
% 177.46/28.04    (98)  op(e1, e3) = all_52_17
% 177.46/28.04    (99)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.46/28.04    (100)   ~ (all_52_25 = all_4_2)
% 177.46/28.04    (101)  op(e3, e0) = all_52_7
% 177.46/28.04    (102)   ~ (all_52_17 = all_4_2)
% 177.46/28.04    (103)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.46/28.04             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.46/28.04    (104)   ~ (all_52_25 = all_52_27)
% 177.46/28.04    (105)   ~ (all_52_27 = all_6_2)
% 177.46/28.04    (106)   ~ (all_52_7 = all_6_2)
% 177.46/28.04    (107)   ~ (all_52_19 = all_52_27)
% 177.46/28.04    (108)  all_56_7 = all_52_15
% 177.46/28.04    (109)  op(e1, all_52_5) = e1
% 177.46/28.04    (110)   ~ (all_52_7 = all_52_23)
% 177.46/28.04    (111)   ~ (all_52_13 = all_10_2)
% 177.46/28.04    (112)  op(e0, all_52_7) = e0
% 177.46/28.04    (113)  op(e2, all_52_27) = all_52_26
% 177.46/28.04    (114)   ~ (all_52_17 = all_52_19)
% 177.46/28.04    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.46/28.04    (116)  all_58_9 = all_52_7
% 177.46/28.04    (117)  all_58_12 = all_52_25
% 177.46/28.04    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.46/28.04    (119)   ~ (all_52_9 = all_52_15)
% 177.46/28.04    (120)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.46/28.04    (121)   ~ (e3 = e2)
% 177.46/28.04    (122)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.46/28.04    (123)   ~ (all_52_19 = all_14_2)
% 177.46/28.04    (124)  op(e2, e3) = all_52_9
% 177.46/28.04    (125)  all_56_13 = all_52_27
% 177.46/28.04  
% 177.46/28.04  Begin of proof
% 177.46/28.04  | 
% 177.46/28.04  | BETA: splitting (50) gives:
% 177.46/28.04  | 
% 177.46/28.04  | Case 1:
% 177.46/28.04  | | 
% 177.46/28.04  | |   (126)  all_56_13 = e3
% 177.46/28.04  | | 
% 177.46/28.04  | | COMBINE_EQS: (125), (126) imply:
% 177.46/28.04  | |   (127)  all_52_27 = e3
% 177.46/28.04  | | 
% 177.46/28.04  | | SIMP: (127) implies:
% 177.46/28.04  | |   (128)  all_52_27 = e3
% 177.46/28.04  | | 
% 177.46/28.04  | | REF_CLOSE: (3), (6), (7), (10), (11), (14), (15), (16), (17), (18), (21),
% 177.46/28.04  | |            (22), (23), (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 177.46/28.04  | |            (34), (35), (36), (37), (39), (40), (41), (42), (43), (45), (46),
% 177.46/28.04  | |            (48), (49), (51), (52), (55), (56), (57), (58), (60), (61), (62),
% 177.46/28.04  | |            (63), (64), (65), (66), (67), (70), (71), (72), (73), (74), (76),
% 177.46/28.04  | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86), (89),
% 177.46/28.04  | |            (90), (91), (92), (94), (95), (96), (97), (98), (100), (101),
% 177.46/28.04  | |            (102), (103), (104), (105), (107), (109), (112), (113), (114),
% 177.46/28.04  | |            (115), (116), (117), (119), (120), (121), (122), (123), (124),
% 177.46/28.04  | |            (128) are inconsistent by sub-proof #404.
% 177.46/28.04  | | 
% 177.46/28.04  | Case 2:
% 177.46/28.04  | | 
% 177.46/28.04  | |   (129)   ~ (all_56_13 = e3)
% 177.46/28.04  | | 
% 177.46/28.04  | | REDUCE: (125), (129) imply:
% 177.46/28.04  | |   (130)   ~ (all_52_27 = e3)
% 177.46/28.04  | | 
% 177.46/28.04  | | BETA: splitting (54) gives:
% 177.46/28.04  | | 
% 177.46/28.04  | | Case 1:
% 177.46/28.04  | | | 
% 177.46/28.04  | | |   (131)  all_58_12 = e3
% 177.46/28.04  | | | 
% 177.46/28.04  | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (14), (16), (20), (21), (22),
% 177.46/28.04  | | |            (23), (25), (26), (28), (33), (37), (40), (41), (42), (47),
% 177.46/28.04  | | |            (49), (51), (55), (57), (60), (61), (64), (65), (75), (76),
% 177.46/28.04  | | |            (80), (83), (84), (93), (94), (96), (98), (100), (101), (102),
% 177.46/28.04  | | |            (103), (104), (109), (111), (112), (115), (116), (117), (120),
% 177.46/28.04  | | |            (124), (131) are inconsistent by sub-proof #402.
% 177.46/28.04  | | | 
% 177.46/28.04  | | Case 2:
% 177.46/28.04  | | | 
% 177.46/28.04  | | |   (132)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.46/28.04  | | | 
% 177.46/28.04  | | | REF_CLOSE: (2), (4), (5), (6), (10), (11), (12), (13), (14), (19), (20),
% 177.46/28.04  | | |            (21), (22), (23), (25), (26), (27), (28), (30), (32), (33),
% 177.46/28.04  | | |            (34), (35), (38), (39), (40), (41), (42), (43), (44), (46),
% 177.46/28.04  | | |            (47), (49), (51), (52), (53), (55), (58), (59), (60), (61),
% 177.46/28.04  | | |            (64), (68), (69), (71), (72), (73), (75), (76), (79), (80),
% 177.46/28.04  | | |            (83), (84), (86), (87), (88), (89), (91), (92), (94), (97),
% 177.46/28.04  | | |            (98), (99), (100), (101), (102), (103), (106), (108), (109),
% 177.46/28.04  | | |            (110), (112), (115), (116), (118), (121), (122), (124), (130),
% 177.46/28.04  | | |            (132) are inconsistent by sub-proof #786.
% 177.46/28.04  | | | 
% 177.46/28.04  | | End of split
% 177.46/28.04  | | 
% 177.46/28.04  | End of split
% 177.46/28.04  | 
% 177.46/28.04  End of proof
% 177.46/28.04  
% 177.46/28.04  Sub-proof #402 shows that the following formulas are inconsistent:
% 177.46/28.04  ----------------------------------------------------------------
% 177.46/28.04    (1)   ~ (all_52_23 = all_14_2)
% 177.46/28.04    (2)   ~ (all_52_5 = all_52_13)
% 177.46/28.04    (3)  op(e2, all_52_3) = e2
% 177.46/28.04    (4)  op(e3, e2) = all_52_3
% 177.46/28.04    (5)   ~ (all_52_19 = all_52_23)
% 177.46/28.04    (6)  all_56_11 = all_52_23
% 177.46/28.04    (7)  all_58_5 = all_52_13
% 177.46/28.04    (8)   ~ (all_52_25 = all_52_29)
% 177.46/28.04    (9)  all_58_3 = all_10_2
% 177.46/28.04    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.46/28.04    (11)  all_58_15 = all_6_2
% 177.46/28.04    (12)   ~ (all_52_9 = all_4_2)
% 177.46/28.04    (13)   ~ (all_52_5 = all_52_7)
% 177.46/28.04    (14)  all_58_10 = all_52_15
% 177.46/28.04    (15)  all_58_7 = all_52_19
% 177.46/28.04    (16)  all_58_4 = all_52_5
% 177.46/28.04    (17)   ~ (all_52_17 = all_14_2)
% 177.46/28.04    (18)  all_58_1 = all_52_3
% 177.46/28.04    (19)   ~ (all_52_13 = all_52_15)
% 177.46/28.04    (20)  all_58_0 = all_4_2
% 177.46/28.04    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.46/28.04    (22)  all_58_14 = all_52_29
% 177.46/28.04    (23)   ~ (all_52_3 = all_52_5)
% 177.46/28.04    (24)  all_58_8 = all_14_2
% 177.46/28.04    (25)  op(e1, all_14_2) = e3
% 177.46/28.04    (26)  op(e3, all_4_2) = e3
% 177.46/28.04    (27)  op(e0, e3) = all_52_25
% 177.46/28.04    (28)   ~ (e3 = e0)
% 177.46/28.04    (29)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.46/28.04    (30)  all_58_13 = all_52_27
% 177.58/28.04    (31)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.04    (32)  all_58_12 = e3
% 177.58/28.04    (33)   ~ (all_52_3 = all_52_7)
% 177.58/28.04    (34)  all_56_0 = all_4_2
% 177.58/28.04    (35)  all_58_11 = all_52_23
% 177.58/28.04    (36)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.04    (37)  op(e3, e1) = all_52_5
% 177.58/28.04    (38)   ~ (all_52_25 = all_6_2)
% 177.58/28.04    (39)  op(e1, e3) = all_52_17
% 177.58/28.04    (40)   ~ (all_52_25 = all_4_2)
% 177.58/28.04    (41)  op(e3, e0) = all_52_7
% 177.58/28.04    (42)   ~ (all_52_17 = all_4_2)
% 177.58/28.04    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.04    (44)   ~ (all_52_25 = all_52_27)
% 177.58/28.04    (45)  op(e1, all_52_5) = e1
% 177.58/28.04    (46)   ~ (all_52_13 = all_10_2)
% 177.58/28.04    (47)  op(e0, all_52_7) = e0
% 177.58/28.04    (48)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.04    (49)  all_58_9 = all_52_7
% 177.58/28.04    (50)  all_58_12 = all_52_25
% 177.58/28.04    (51)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.04    (52)  op(e2, e3) = all_52_9
% 177.58/28.04  
% 177.58/28.04  Begin of proof
% 177.58/28.04  | 
% 177.58/28.04  | COMBINE_EQS: (32), (50) imply:
% 177.58/28.04  |   (53)  all_52_25 = e3
% 177.58/28.04  | 
% 177.58/28.04  | SIMP: (53) implies:
% 177.58/28.04  |   (54)  all_52_25 = e3
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (44), (54) imply:
% 177.58/28.04  |   (55)   ~ (all_52_27 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | SIMP: (55) implies:
% 177.58/28.04  |   (56)   ~ (all_52_27 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (8), (54) imply:
% 177.58/28.04  |   (57)   ~ (all_52_29 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | SIMP: (57) implies:
% 177.58/28.04  |   (58)   ~ (all_52_29 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (38), (54) imply:
% 177.58/28.04  |   (59)   ~ (all_6_2 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | SIMP: (59) implies:
% 177.58/28.04  |   (60)   ~ (all_6_2 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (40), (54) imply:
% 177.58/28.04  |   (61)   ~ (all_4_2 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | SIMP: (61) implies:
% 177.58/28.04  |   (62)   ~ (all_4_2 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (27), (54) imply:
% 177.58/28.04  |   (63)  op(e0, e3) = e3
% 177.58/28.04  | 
% 177.58/28.04  | BETA: splitting (10) gives:
% 177.58/28.04  | 
% 177.58/28.04  | Case 1:
% 177.58/28.04  | | 
% 177.58/28.04  | |   (64)  all_56_0 = e3
% 177.58/28.04  | | 
% 177.58/28.04  | | COMBINE_EQS: (34), (64) imply:
% 177.58/28.04  | |   (65)  all_4_2 = e3
% 177.58/28.04  | | 
% 177.58/28.04  | | REDUCE: (62), (65) imply:
% 177.58/28.04  | |   (66)  $false
% 177.58/28.04  | | 
% 177.58/28.04  | | CLOSE: (66) is inconsistent.
% 177.58/28.04  | | 
% 177.58/28.04  | Case 2:
% 177.58/28.04  | | 
% 177.58/28.04  | |   (67)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.04  | | 
% 177.58/28.04  | | BETA: splitting (36) gives:
% 177.58/28.04  | | 
% 177.58/28.04  | | Case 1:
% 177.58/28.04  | | | 
% 177.58/28.04  | | |   (68)  all_56_11 = e3
% 177.58/28.04  | | | 
% 177.58/28.04  | | | COMBINE_EQS: (6), (68) imply:
% 177.58/28.04  | | |   (69)  all_52_23 = e3
% 177.58/28.04  | | | 
% 177.58/28.04  | | | SIMP: (69) implies:
% 177.58/28.04  | | |   (70)  all_52_23 = e3
% 177.58/28.04  | | | 
% 177.58/28.04  | | | REDUCE: (5), (70) imply:
% 177.58/28.04  | | |   (71)   ~ (all_52_19 = e3)
% 177.58/28.04  | | | 
% 177.58/28.04  | | | REDUCE: (1), (70) imply:
% 177.58/28.04  | | |   (72)   ~ (all_14_2 = e3)
% 177.58/28.04  | | | 
% 177.58/28.04  | | | SIMP: (72) implies:
% 177.58/28.04  | | |   (73)   ~ (all_14_2 = e3)
% 177.58/28.04  | | | 
% 177.58/28.04  | | | BETA: splitting (21) gives:
% 177.58/28.04  | | | 
% 177.58/28.04  | | | Case 1:
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | |   (74)  all_58_1 = e3
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | | REF_CLOSE: (2), (3), (7), (12), (16), (18), (20), (22), (23), (24),
% 177.58/28.04  | | | |            (26), (31), (33), (34), (37), (41), (43), (51), (52), (58),
% 177.58/28.04  | | | |            (67), (73), (74) are inconsistent by sub-proof #866.
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | Case 2:
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | |   (75)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | | BETA: splitting (75) gives:
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | | Case 1:
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | |   (76)  all_58_3 = e3
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | COMBINE_EQS: (9), (76) imply:
% 177.58/28.04  | | | | |   (77)  all_10_2 = e3
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | REDUCE: (46), (77) imply:
% 177.58/28.04  | | | | |   (78)   ~ (all_52_13 = e3)
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | REF_CLOSE: (4), (7), (13), (16), (17), (20), (22), (23), (24), (25),
% 177.58/28.04  | | | | |            (26), (29), (34), (39), (41), (42), (43), (45), (51), (58),
% 177.58/28.04  | | | | |            (67), (78) are inconsistent by sub-proof #403.
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | Case 2:
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | |   (79)  all_58_7 = e3 | all_58_13 = e3
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | REF_CLOSE: (15), (30), (56), (71), (79) are inconsistent by sub-proof
% 177.58/28.04  | | | | |            #976.
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | End of split
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | End of split
% 177.58/28.04  | | | 
% 177.58/28.04  | | Case 2:
% 177.58/28.04  | | | 
% 177.58/28.04  | | |   (80)   ~ (all_56_11 = e3)
% 177.58/28.04  | | | 
% 177.58/28.04  | | | REDUCE: (6), (80) imply:
% 177.58/28.04  | | |   (81)   ~ (all_52_23 = e3)
% 177.58/28.04  | | | 
% 177.58/28.04  | | | BETA: splitting (48) gives:
% 177.58/28.04  | | | 
% 177.58/28.04  | | | Case 1:
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | |   (82)  all_58_9 = e3
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | | REF_CLOSE: (28), (43), (47), (49), (63), (82) are inconsistent by
% 177.58/28.04  | | | |            sub-proof #798.
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | Case 2:
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | |   (83)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | | BETA: splitting (83) gives:
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | | Case 1:
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | |   (84)  all_58_10 = e3
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | COMBINE_EQS: (14), (84) imply:
% 177.58/28.04  | | | | |   (85)  all_52_15 = e3
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | SIMP: (85) implies:
% 177.58/28.04  | | | | |   (86)  all_52_15 = e3
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | REDUCE: (19), (86) imply:
% 177.58/28.04  | | | | |   (87)   ~ (all_52_13 = e3)
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | REF_CLOSE: (4), (7), (13), (16), (17), (20), (22), (23), (24), (25),
% 177.58/28.04  | | | | |            (26), (29), (34), (39), (41), (42), (43), (45), (51), (58),
% 177.58/28.04  | | | | |            (67), (87) are inconsistent by sub-proof #403.
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | Case 2:
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | |   (88)  all_58_11 = e3 | all_58_15 = e3
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | | REF_CLOSE: (11), (35), (60), (81), (88) are inconsistent by sub-proof
% 177.58/28.04  | | | | |            #1016.
% 177.58/28.04  | | | | | 
% 177.58/28.04  | | | | End of split
% 177.58/28.04  | | | | 
% 177.58/28.04  | | | End of split
% 177.58/28.04  | | | 
% 177.58/28.04  | | End of split
% 177.58/28.04  | | 
% 177.58/28.04  | End of split
% 177.58/28.04  | 
% 177.58/28.04  End of proof
% 177.58/28.04  
% 177.58/28.04  Sub-proof #403 shows that the following formulas are inconsistent:
% 177.58/28.04  ----------------------------------------------------------------
% 177.58/28.04    (1)  op(e3, e2) = all_52_3
% 177.58/28.04    (2)  all_58_5 = all_52_13
% 177.58/28.04    (3)   ~ (all_52_5 = all_52_7)
% 177.58/28.04    (4)  all_58_4 = all_52_5
% 177.58/28.04    (5)   ~ (all_52_17 = all_14_2)
% 177.58/28.04    (6)  all_58_0 = all_4_2
% 177.58/28.04    (7)  all_58_14 = all_52_29
% 177.58/28.04    (8)   ~ (all_52_3 = all_52_5)
% 177.58/28.04    (9)  all_58_8 = all_14_2
% 177.58/28.04    (10)  op(e1, all_14_2) = e3
% 177.58/28.04    (11)  op(e3, all_4_2) = e3
% 177.58/28.04    (12)   ~ (all_52_29 = e3)
% 177.58/28.04    (13)   ~ (all_52_13 = e3)
% 177.58/28.04    (14)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.04    (15)  all_56_0 = all_4_2
% 177.58/28.04    (16)  op(e1, e3) = all_52_17
% 177.58/28.04    (17)  op(e3, e0) = all_52_7
% 177.58/28.04    (18)   ~ (all_52_17 = all_4_2)
% 177.58/28.04    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.04    (20)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.04    (21)  op(e1, all_52_5) = e1
% 177.58/28.04    (22)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.04  
% 177.58/28.04  Begin of proof
% 177.58/28.04  | 
% 177.58/28.04  | BETA: splitting (22) gives:
% 177.58/28.04  | 
% 177.58/28.04  | Case 1:
% 177.58/28.04  | | 
% 177.58/28.04  | |   (23)  all_58_4 = e3
% 177.58/28.04  | | 
% 177.58/28.04  | | REF_CLOSE: (1), (3), (4), (6), (8), (11), (14), (15), (16), (17), (18),
% 177.58/28.04  | |            (19), (20), (21), (23) are inconsistent by sub-proof #868.
% 177.58/28.04  | | 
% 177.58/28.04  | Case 2:
% 177.58/28.04  | | 
% 177.58/28.04  | |   (24)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.04  | | 
% 177.58/28.04  | | REF_CLOSE: (2), (5), (7), (9), (10), (12), (13), (16), (19), (24) are
% 177.58/28.04  | |            inconsistent by sub-proof #420.
% 177.58/28.04  | | 
% 177.58/28.04  | End of split
% 177.58/28.04  | 
% 177.58/28.04  End of proof
% 177.58/28.04  
% 177.58/28.04  Sub-proof #404 shows that the following formulas are inconsistent:
% 177.58/28.04  ----------------------------------------------------------------
% 177.58/28.04    (1)   ~ (all_52_17 = all_52_23)
% 177.58/28.04    (2)  op(e3, e2) = all_52_3
% 177.58/28.04    (3)   ~ (all_52_9 = all_52_25)
% 177.58/28.04    (4)  op(e1, e2) = all_52_19
% 177.58/28.04    (5)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.58/28.04    (6)  all_52_27 = e3
% 177.58/28.04    (7)  all_58_5 = all_52_13
% 177.58/28.04    (8)   ~ (all_6_2 = e0)
% 177.58/28.04    (9)   ~ (all_52_25 = all_52_29)
% 177.58/28.04    (10)  all_56_15 = all_6_2
% 177.58/28.04    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.04    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.04    (13)  all_58_15 = all_6_2
% 177.58/28.04    (14)   ~ (all_52_9 = all_4_2)
% 177.58/28.04    (15)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.04    (16)   ~ (all_52_5 = all_52_7)
% 177.58/28.04    (17)  all_58_10 = all_52_15
% 177.58/28.04    (18)   ~ (all_52_5 = all_4_2)
% 177.58/28.04    (19)  all_58_7 = all_52_19
% 177.58/28.04    (20)  all_56_4 = all_52_9
% 177.58/28.04    (21)   ~ (all_52_17 = all_52_25)
% 177.58/28.04    (22)  op(e0, e1) = all_52_29
% 177.58/28.04    (23)  all_58_4 = all_52_5
% 177.58/28.04    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.04    (25)   ~ (e3 = e1)
% 177.58/28.04    (26)   ~ (all_52_27 = all_52_29)
% 177.58/28.04    (27)   ~ (all_52_17 = all_14_2)
% 177.58/28.04    (28)   ~ (all_52_7 = all_4_2)
% 177.58/28.04    (29)  all_58_1 = all_52_3
% 177.58/28.04    (30)   ~ (all_52_13 = all_52_15)
% 177.58/28.04    (31)  all_58_0 = all_4_2
% 177.58/28.04    (32)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.04    (33)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.04    (34)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.04    (35)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.58/28.04    (36)  all_58_14 = all_52_29
% 177.58/28.04    (37)   ~ (all_52_3 = all_52_5)
% 177.58/28.04    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.04    (39)  all_58_8 = all_14_2
% 177.58/28.04    (40)  all_56_14 = all_52_29
% 177.58/28.04    (41)  op(e1, all_14_2) = e3
% 177.58/28.04    (42)   ~ (all_52_5 = all_14_2)
% 177.58/28.04    (43)  op(e3, all_4_2) = e3
% 177.58/28.04    (44)  op(e0, e3) = all_52_25
% 177.58/28.04    (45)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.58/28.04    (46)   ~ (all_52_13 = all_14_2)
% 177.58/28.04    (47)   ~ (e3 = e0)
% 177.58/28.04    (48)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.04    (49)   ~ (all_52_9 = all_52_13)
% 177.58/28.04    (50)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.04    (51)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.04    (52)   ~ (all_52_5 = all_52_29)
% 177.58/28.04    (53)  all_56_2 = all_52_5
% 177.58/28.04    (54)  op(e1, e0) = all_52_23
% 177.58/28.04    (55)  all_56_12 = all_52_25
% 177.58/28.04    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.04    (57)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.04    (58)   ~ (all_52_9 = all_52_17)
% 177.58/28.04    (59)  all_58_6 = all_52_17
% 177.58/28.04    (60)   ~ (all_52_3 = all_52_7)
% 177.58/28.04    (61)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.58/28.04    (62)   ~ (e1 = e0)
% 177.58/28.04    (63)  all_56_0 = all_4_2
% 177.58/28.04    (64)  all_58_11 = all_52_23
% 177.58/28.04    (65)   ~ (all_52_3 = all_52_19)
% 177.58/28.04    (66)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.58/28.04    (67)   ~ (all_52_29 = all_14_2)
% 177.58/28.04    (68)   ~ (all_52_23 = all_6_2)
% 177.58/28.04    (69)   ~ (all_52_29 = all_6_2)
% 177.58/28.04    (70)  all_58_2 = all_52_9
% 177.58/28.04    (71)  op(e3, e1) = all_52_5
% 177.58/28.04    (72)  all_56_10 = all_14_2
% 177.58/28.04    (73)   ~ (all_52_25 = all_6_2)
% 177.58/28.04    (74)  op(e1, e1) = all_14_2
% 177.58/28.04    (75)  op(e1, e3) = all_52_17
% 177.58/28.04    (76)   ~ (all_52_25 = all_4_2)
% 177.58/28.04    (77)  op(e3, e0) = all_52_7
% 177.58/28.04    (78)   ~ (all_52_17 = all_4_2)
% 177.58/28.04    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.04    (80)   ~ (all_52_25 = all_52_27)
% 177.58/28.04    (81)   ~ (all_52_27 = all_6_2)
% 177.58/28.04    (82)   ~ (all_52_19 = all_52_27)
% 177.58/28.04    (83)  op(e1, all_52_5) = e1
% 177.58/28.04    (84)  op(e0, all_52_7) = e0
% 177.58/28.04    (85)  op(e2, all_52_27) = all_52_26
% 177.58/28.04    (86)   ~ (all_52_17 = all_52_19)
% 177.58/28.04    (87)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.04    (88)  all_58_9 = all_52_7
% 177.58/28.04    (89)  all_58_12 = all_52_25
% 177.58/28.04    (90)   ~ (all_52_9 = all_52_15)
% 177.58/28.04    (91)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.04    (92)   ~ (e3 = e2)
% 177.58/28.04    (93)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.58/28.04    (94)   ~ (all_52_19 = all_14_2)
% 177.58/28.04    (95)  op(e2, e3) = all_52_9
% 177.58/28.04  
% 177.58/28.04  Begin of proof
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (6), (82) imply:
% 177.58/28.04  |   (96)   ~ (all_52_19 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (6), (80) imply:
% 177.58/28.04  |   (97)   ~ (all_52_25 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (6), (26) imply:
% 177.58/28.04  |   (98)   ~ (all_52_29 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | SIMP: (98) implies:
% 177.58/28.04  |   (99)   ~ (all_52_29 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | REDUCE: (6), (81) imply:
% 177.58/28.04  |   (100)   ~ (all_6_2 = e3)
% 177.58/28.04  | 
% 177.58/28.04  | SIMP: (100) implies:
% 177.58/28.05  |   (101)   ~ (all_6_2 = e3)
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (6), (85) imply:
% 177.58/28.05  |   (102)  op(e2, e3) = all_52_26
% 177.58/28.05  | 
% 177.58/28.05  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.58/28.05  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.58/28.05  |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.58/28.05  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.58/28.05  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 177.58/28.05  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 177.58/28.05  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (83),
% 177.58/28.05  |            (84), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 177.58/28.05  |            (96), (97), (99), (101), (102) are inconsistent by sub-proof #405.
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #405 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)   ~ (all_52_25 = e3)
% 177.58/28.05    (2)   ~ (all_52_17 = all_52_23)
% 177.58/28.05    (3)  op(e3, e2) = all_52_3
% 177.58/28.05    (4)   ~ (all_52_9 = all_52_25)
% 177.58/28.05    (5)  op(e1, e2) = all_52_19
% 177.58/28.05    (6)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.58/28.05    (7)   ~ (all_6_2 = e3)
% 177.58/28.05    (8)  all_58_5 = all_52_13
% 177.58/28.05    (9)   ~ (all_6_2 = e0)
% 177.58/28.05    (10)   ~ (all_52_25 = all_52_29)
% 177.58/28.05    (11)  all_56_15 = all_6_2
% 177.58/28.05    (12)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.05    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.05    (14)  all_58_15 = all_6_2
% 177.58/28.05    (15)   ~ (all_52_9 = all_4_2)
% 177.58/28.05    (16)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.05    (17)   ~ (all_52_5 = all_52_7)
% 177.58/28.05    (18)  all_58_10 = all_52_15
% 177.58/28.05    (19)   ~ (all_52_5 = all_4_2)
% 177.58/28.05    (20)  all_58_7 = all_52_19
% 177.58/28.05    (21)  all_56_4 = all_52_9
% 177.58/28.05    (22)   ~ (all_52_17 = all_52_25)
% 177.58/28.05    (23)  op(e0, e1) = all_52_29
% 177.58/28.05    (24)  all_58_4 = all_52_5
% 177.58/28.05    (25)  op(e2, e3) = all_52_26
% 177.58/28.05    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.05    (27)   ~ (e3 = e1)
% 177.58/28.05    (28)   ~ (all_52_17 = all_14_2)
% 177.58/28.05    (29)   ~ (all_52_7 = all_4_2)
% 177.58/28.05    (30)  all_58_1 = all_52_3
% 177.58/28.05    (31)   ~ (all_52_13 = all_52_15)
% 177.58/28.05    (32)  all_58_0 = all_4_2
% 177.58/28.05    (33)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.05    (34)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.05    (35)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.05    (36)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.58/28.05    (37)  all_58_14 = all_52_29
% 177.58/28.05    (38)   ~ (all_52_3 = all_52_5)
% 177.58/28.05    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.05    (40)  all_58_8 = all_14_2
% 177.58/28.05    (41)  all_56_14 = all_52_29
% 177.58/28.05    (42)  op(e1, all_14_2) = e3
% 177.58/28.05    (43)   ~ (all_52_5 = all_14_2)
% 177.58/28.05    (44)  op(e3, all_4_2) = e3
% 177.58/28.05    (45)  op(e0, e3) = all_52_25
% 177.58/28.05    (46)   ~ (all_52_29 = e3)
% 177.58/28.05    (47)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.58/28.05    (48)   ~ (all_52_13 = all_14_2)
% 177.58/28.05    (49)   ~ (e3 = e0)
% 177.58/28.05    (50)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.05    (51)   ~ (all_52_9 = all_52_13)
% 177.58/28.05    (52)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.05    (53)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.05    (54)   ~ (all_52_5 = all_52_29)
% 177.58/28.05    (55)  all_56_2 = all_52_5
% 177.58/28.05    (56)  op(e1, e0) = all_52_23
% 177.58/28.05    (57)  all_56_12 = all_52_25
% 177.58/28.05    (58)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.05    (59)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.05    (60)   ~ (all_52_9 = all_52_17)
% 177.58/28.05    (61)  all_58_6 = all_52_17
% 177.58/28.05    (62)   ~ (all_52_3 = all_52_7)
% 177.58/28.05    (63)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.58/28.05    (64)   ~ (e1 = e0)
% 177.58/28.05    (65)  all_56_0 = all_4_2
% 177.58/28.05    (66)  all_58_11 = all_52_23
% 177.58/28.05    (67)   ~ (all_52_3 = all_52_19)
% 177.58/28.05    (68)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.58/28.05    (69)   ~ (all_52_29 = all_14_2)
% 177.58/28.05    (70)   ~ (all_52_23 = all_6_2)
% 177.58/28.05    (71)   ~ (all_52_29 = all_6_2)
% 177.58/28.05    (72)  all_58_2 = all_52_9
% 177.58/28.05    (73)  op(e3, e1) = all_52_5
% 177.58/28.05    (74)  all_56_10 = all_14_2
% 177.58/28.05    (75)   ~ (all_52_25 = all_6_2)
% 177.58/28.05    (76)  op(e1, e1) = all_14_2
% 177.58/28.05    (77)   ~ (all_52_19 = e3)
% 177.58/28.05    (78)  op(e1, e3) = all_52_17
% 177.58/28.05    (79)   ~ (all_52_25 = all_4_2)
% 177.58/28.05    (80)  op(e3, e0) = all_52_7
% 177.58/28.05    (81)   ~ (all_52_17 = all_4_2)
% 177.58/28.05    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.05    (83)  op(e1, all_52_5) = e1
% 177.58/28.05    (84)  op(e0, all_52_7) = e0
% 177.58/28.05    (85)   ~ (all_52_17 = all_52_19)
% 177.58/28.05    (86)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.05    (87)  all_58_9 = all_52_7
% 177.58/28.05    (88)  all_58_12 = all_52_25
% 177.58/28.05    (89)   ~ (all_52_9 = all_52_15)
% 177.58/28.05    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.05    (91)   ~ (e3 = e2)
% 177.58/28.05    (92)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.58/28.05    (93)   ~ (all_52_19 = all_14_2)
% 177.58/28.05    (94)  op(e2, e3) = all_52_9
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | GROUND_INST: instantiating (82) with all_52_9, all_52_26, e3, e2, simplifying
% 177.58/28.05  |              with (25), (94) gives:
% 177.58/28.05  |   (95)  all_52_9 = all_52_26
% 177.58/28.05  | 
% 177.58/28.05  | COMBINE_EQS: (21), (95) imply:
% 177.58/28.05  |   (96)  all_56_4 = all_52_26
% 177.58/28.05  | 
% 177.58/28.05  | COMBINE_EQS: (72), (95) imply:
% 177.58/28.05  |   (97)  all_58_2 = all_52_26
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (51), (95) imply:
% 177.58/28.05  |   (98)   ~ (all_52_13 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | SIMP: (98) implies:
% 177.58/28.05  |   (99)   ~ (all_52_13 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (89), (95) imply:
% 177.58/28.05  |   (100)   ~ (all_52_15 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | SIMP: (100) implies:
% 177.58/28.05  |   (101)   ~ (all_52_15 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (60), (95) imply:
% 177.58/28.05  |   (102)   ~ (all_52_17 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | SIMP: (102) implies:
% 177.58/28.05  |   (103)   ~ (all_52_17 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (4), (95) imply:
% 177.58/28.05  |   (104)   ~ (all_52_25 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | SIMP: (104) implies:
% 177.58/28.05  |   (105)   ~ (all_52_25 = all_52_26)
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (15), (95) imply:
% 177.58/28.05  |   (106)   ~ (all_52_26 = all_4_2)
% 177.58/28.05  | 
% 177.58/28.05  | BETA: splitting (34) gives:
% 177.58/28.05  | 
% 177.58/28.05  | Case 1:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (107)  all_56_14 = e3
% 177.58/28.05  | | 
% 177.58/28.05  | | REF_CLOSE: (41), (46), (107) are inconsistent by sub-proof #896.
% 177.58/28.05  | | 
% 177.58/28.05  | Case 2:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (108)   ~ (all_56_14 = e3)
% 177.58/28.05  | |   (109)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.05  | | 
% 177.58/28.05  | | BETA: splitting (52) gives:
% 177.58/28.05  | | 
% 177.58/28.05  | | Case 1:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (110)  all_56_12 = e3
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REF_CLOSE: (1), (57), (110) are inconsistent by sub-proof #1040.
% 177.58/28.05  | | | 
% 177.58/28.05  | | Case 2:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (111)   ~ (all_56_12 = e3)
% 177.58/28.05  | | |   (112)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | BETA: splitting (53) gives:
% 177.58/28.05  | | | 
% 177.58/28.05  | | | Case 1:
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | |   (113)  all_56_10 = e3
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REF_CLOSE: (28), (42), (74), (78), (82), (113) are inconsistent by
% 177.58/28.05  | | | |            sub-proof #406.
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | Case 2:
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | |   (114)   ~ (all_56_10 = e3)
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REDUCE: (74), (114) imply:
% 177.58/28.05  | | | |   (115)   ~ (all_14_2 = e3)
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.58/28.05  | | | |            (13), (14), (16), (17), (18), (19), (20), (22), (23), (24),
% 177.58/28.05  | | | |            (26), (27), (29), (30), (31), (32), (33), (35), (36), (37),
% 177.58/28.05  | | | |            (38), (39), (40), (41), (43), (44), (45), (46), (47), (48),
% 177.58/28.05  | | | |            (49), (50), (54), (55), (56), (57), (58), (59), (61), (62),
% 177.58/28.05  | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (73),
% 177.58/28.05  | | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 177.58/28.05  | | | |            (85), (86), (87), (88), (90), (91), (92), (93), (96), (97),
% 177.58/28.05  | | | |            (99), (101), (103), (105), (106), (109), (112), (115) are
% 177.58/28.05  | | | |            inconsistent by sub-proof #800.
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | End of split
% 177.58/28.05  | | | 
% 177.58/28.05  | | End of split
% 177.58/28.05  | | 
% 177.58/28.05  | End of split
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #406 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)   ~ (all_52_17 = all_14_2)
% 177.58/28.05    (2)  op(e1, all_14_2) = e3
% 177.58/28.05    (3)  all_56_10 = all_14_2
% 177.58/28.05    (4)  op(e1, e3) = all_52_17
% 177.58/28.05    (5)  all_56_10 = e3
% 177.58/28.05    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | COMBINE_EQS: (3), (5) imply:
% 177.58/28.05  |   (7)  all_14_2 = e3
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (1), (7) imply:
% 177.58/28.05  |   (8)   ~ (all_52_17 = e3)
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (2), (7) imply:
% 177.58/28.05  |   (9)  op(e1, e3) = e3
% 177.58/28.05  | 
% 177.58/28.05  | REF_CLOSE: (4), (6), (8), (9) are inconsistent by sub-proof #508.
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #407 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)   ~ (all_52_23 = all_52_24)
% 177.58/28.05    (2)   ~ (all_52_24 = e0)
% 177.58/28.05    (3)   ~ (all_52_24 = e2)
% 177.58/28.05    (4)  op(e1, e0) = e1
% 177.58/28.05    (5)  op(e1, e0) = all_52_23
% 177.58/28.05    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.05    (7)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.05    (8)   ~ (all_52_24 = e3)
% 177.58/28.05    (9)  all_56_3 = all_52_24
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | BETA: splitting (7) gives:
% 177.58/28.05  | 
% 177.58/28.05  | Case 1:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (10)  all_56_3 = e3
% 177.58/28.05  | | 
% 177.58/28.05  | | REF_CLOSE: (8), (9), (10) are inconsistent by sub-proof #458.
% 177.58/28.05  | | 
% 177.58/28.05  | Case 2:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (11)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.05  | | 
% 177.58/28.05  | | BETA: splitting (11) gives:
% 177.58/28.05  | | 
% 177.58/28.05  | | Case 1:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (12)  all_56_3 = e2
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #516.
% 177.58/28.05  | | | 
% 177.58/28.05  | | Case 2:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (13)  all_56_3 = e1 | all_56_3 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | BETA: splitting (13) gives:
% 177.58/28.05  | | | 
% 177.58/28.05  | | | Case 1:
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | |   (14)  all_56_3 = e1
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | COMBINE_EQS: (9), (14) imply:
% 177.58/28.05  | | | |   (15)  all_52_24 = e1
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | SIMP: (15) implies:
% 177.58/28.05  | | | |   (16)  all_52_24 = e1
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REDUCE: (1), (16) imply:
% 177.58/28.05  | | | |   (17)   ~ (all_52_23 = e1)
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REF_CLOSE: (4), (5), (6), (17) are inconsistent by sub-proof #590.
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | Case 2:
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | |   (18)  all_56_3 = e0
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | COMBINE_EQS: (9), (18) imply:
% 177.58/28.05  | | | |   (19)  all_52_24 = e0
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | SIMP: (19) implies:
% 177.58/28.05  | | | |   (20)  all_52_24 = e0
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REDUCE: (2), (20) imply:
% 177.58/28.05  | | | |   (21)  $false
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | CLOSE: (21) is inconsistent.
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | End of split
% 177.58/28.05  | | | 
% 177.58/28.05  | | End of split
% 177.58/28.05  | | 
% 177.58/28.05  | End of split
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #408 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)   ~ (all_6_0 = e0)
% 177.58/28.05    (2)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.58/28.05    (3)   ~ (all_6_0 = e2)
% 177.58/28.05    (4)  all_56_4 = all_6_0
% 177.58/28.05    (5)   ~ (all_6_0 = e1)
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | BETA: splitting (2) gives:
% 177.58/28.05  | 
% 177.58/28.05  | Case 1:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (6)  all_56_4 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | COMBINE_EQS: (4), (6) imply:
% 177.58/28.05  | |   (7)  all_6_0 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | SIMP: (7) implies:
% 177.58/28.05  | |   (8)  all_6_0 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | REDUCE: (3), (8) imply:
% 177.58/28.05  | |   (9)  $false
% 177.58/28.05  | | 
% 177.58/28.05  | | CLOSE: (9) is inconsistent.
% 177.58/28.05  | | 
% 177.58/28.05  | Case 2:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (10)  all_56_4 = e1 | all_56_4 = e0
% 177.58/28.05  | | 
% 177.58/28.05  | | BETA: splitting (10) gives:
% 177.58/28.05  | | 
% 177.58/28.05  | | Case 1:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (11)  all_56_4 = e1
% 177.58/28.05  | | | 
% 177.58/28.05  | | | COMBINE_EQS: (4), (11) imply:
% 177.58/28.05  | | |   (12)  all_6_0 = e1
% 177.58/28.05  | | | 
% 177.58/28.05  | | | SIMP: (12) implies:
% 177.58/28.05  | | |   (13)  all_6_0 = e1
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REDUCE: (5), (13) imply:
% 177.58/28.05  | | |   (14)  $false
% 177.58/28.05  | | | 
% 177.58/28.05  | | | CLOSE: (14) is inconsistent.
% 177.58/28.05  | | | 
% 177.58/28.05  | | Case 2:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (15)  all_56_4 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | COMBINE_EQS: (4), (15) imply:
% 177.58/28.05  | | |   (16)  all_6_0 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | SIMP: (16) implies:
% 177.58/28.05  | | |   (17)  all_6_0 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REDUCE: (1), (17) imply:
% 177.58/28.05  | | |   (18)  $false
% 177.58/28.05  | | | 
% 177.58/28.05  | | | CLOSE: (18) is inconsistent.
% 177.58/28.05  | | | 
% 177.58/28.05  | | End of split
% 177.58/28.05  | | 
% 177.58/28.05  | End of split
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #409 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)  op(e0, all_52_8) = e0
% 177.58/28.05    (2)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.05    (3)   ~ (all_52_8 = e2)
% 177.58/28.05    (4)   ~ (all_58_9 = e1)
% 177.58/28.05    (5)  all_56_3 = all_52_8
% 177.58/28.05    (6)  all_58_9 = all_52_8
% 177.58/28.05    (7)   ~ (all_52_8 = e3)
% 177.58/28.05    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.05    (9)  op(e0, e0) = e3
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | REDUCE: (4), (6) imply:
% 177.58/28.05  |   (10)   ~ (all_52_8 = e1)
% 177.58/28.05  | 
% 177.58/28.05  | BETA: splitting (2) gives:
% 177.58/28.05  | 
% 177.58/28.05  | Case 1:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (11)  all_56_3 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | COMBINE_EQS: (5), (11) imply:
% 177.58/28.05  | |   (12)  all_52_8 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | SIMP: (12) implies:
% 177.58/28.05  | |   (13)  all_52_8 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | REDUCE: (3), (13) imply:
% 177.58/28.05  | |   (14)  $false
% 177.58/28.05  | | 
% 177.58/28.05  | | CLOSE: (14) is inconsistent.
% 177.58/28.05  | | 
% 177.58/28.05  | Case 2:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (15)  all_56_3 = e1 | all_56_3 = e0
% 177.58/28.05  | | 
% 177.58/28.05  | | BETA: splitting (15) gives:
% 177.58/28.05  | | 
% 177.58/28.05  | | Case 1:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (16)  all_56_3 = e1
% 177.58/28.05  | | | 
% 177.58/28.05  | | | COMBINE_EQS: (5), (16) imply:
% 177.58/28.05  | | |   (17)  all_52_8 = e1
% 177.58/28.05  | | | 
% 177.58/28.05  | | | SIMP: (17) implies:
% 177.58/28.05  | | |   (18)  all_52_8 = e1
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REDUCE: (10), (18) imply:
% 177.58/28.05  | | |   (19)  $false
% 177.58/28.05  | | | 
% 177.58/28.05  | | | CLOSE: (19) is inconsistent.
% 177.58/28.05  | | | 
% 177.58/28.05  | | Case 2:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (20)  all_56_3 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | COMBINE_EQS: (5), (20) imply:
% 177.58/28.05  | | |   (21)  all_52_8 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | SIMP: (21) implies:
% 177.58/28.05  | | |   (22)  all_52_8 = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REDUCE: (7), (22) imply:
% 177.58/28.05  | | |   (23)   ~ (e3 = e0)
% 177.58/28.05  | | | 
% 177.58/28.05  | | | SIMP: (23) implies:
% 177.58/28.05  | | |   (24)   ~ (e3 = e0)
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REDUCE: (1), (22) imply:
% 177.58/28.05  | | |   (25)  op(e0, e0) = e0
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REF_CLOSE: (8), (9), (24), (25) are inconsistent by sub-proof #854.
% 177.58/28.05  | | | 
% 177.58/28.05  | | End of split
% 177.58/28.05  | | 
% 177.58/28.05  | End of split
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #410 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.05    (2)   ~ (all_52_5 = all_52_13)
% 177.58/28.05    (3)  op(e2, all_52_3) = e2
% 177.58/28.05    (4)  all_58_6 = e0
% 177.58/28.05    (5)  op(e3, e2) = all_52_3
% 177.58/28.05    (6)  all_58_5 = all_52_13
% 177.58/28.05    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.05    (8)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.05    (9)  all_58_15 = all_6_2
% 177.58/28.05    (10)   ~ (all_52_9 = all_4_2)
% 177.58/28.05    (11)   ~ (all_52_5 = all_52_7)
% 177.58/28.05    (12)  all_58_10 = all_52_15
% 177.58/28.05    (13)   ~ (all_52_5 = all_4_2)
% 177.58/28.05    (14)  all_58_7 = all_52_19
% 177.58/28.05    (15)  all_58_4 = all_52_5
% 177.58/28.05    (16)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.05    (17)   ~ (all_52_17 = all_14_2)
% 177.58/28.05    (18)   ~ (all_52_7 = all_4_2)
% 177.58/28.05    (19)  all_58_1 = all_52_3
% 177.58/28.05    (20)  all_58_0 = all_4_2
% 177.58/28.05    (21)  all_58_14 = all_52_29
% 177.58/28.05    (22)   ~ (all_52_3 = all_52_5)
% 177.58/28.05    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.05    (24)  all_58_8 = all_14_2
% 177.58/28.05    (25)   ~ (all_52_5 = all_14_2)
% 177.58/28.05    (26)  op(e3, all_4_2) = e3
% 177.58/28.05    (27)  op(e0, e3) = all_52_25
% 177.58/28.05    (28)   ~ (all_52_29 = e3)
% 177.58/28.05    (29)   ~ (all_52_13 = all_14_2)
% 177.58/28.05    (30)   ~ (all_52_9 = e2)
% 177.58/28.05    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.05    (32)  all_58_12 = e1
% 177.58/28.05    (33)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.05    (34)   ~ (all_52_5 = all_52_29)
% 177.58/28.05    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.05    (36)  all_58_6 = all_52_17
% 177.58/28.05    (37)   ~ (all_52_3 = all_52_7)
% 177.58/28.05    (38)  all_56_0 = all_4_2
% 177.58/28.05    (39)  all_58_11 = all_52_23
% 177.58/28.05    (40)   ~ (all_52_3 = all_52_19)
% 177.58/28.05    (41)   ~ (all_52_7 = all_52_15)
% 177.58/28.05    (42)   ~ (all_52_29 = all_14_2)
% 177.58/28.05    (43)  all_58_2 = all_52_9
% 177.58/28.05    (44)  op(e3, e1) = all_52_5
% 177.58/28.05    (45)   ~ (e2 = e1)
% 177.58/28.05    (46)  all_56_10 = all_14_2
% 177.58/28.05    (47)  op(e1, e3) = all_52_17
% 177.58/28.05    (48)   ~ (all_52_25 = all_4_2)
% 177.58/28.05    (49)  op(e3, e0) = all_52_7
% 177.58/28.05    (50)   ~ (all_52_17 = all_4_2)
% 177.58/28.05    (51)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.05    (52)   ~ (all_52_7 = all_6_2)
% 177.58/28.05    (53)  op(e1, all_52_5) = e1
% 177.58/28.05    (54)   ~ (all_52_7 = all_52_23)
% 177.58/28.05    (55)  op(e0, all_52_7) = e0
% 177.58/28.05    (56)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.05    (57)  all_58_9 = all_52_7
% 177.58/28.05    (58)   ~ (e2 = e0)
% 177.58/28.05    (59)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.05    (60)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.05    (61)   ~ (e3 = e2)
% 177.58/28.05    (62)  op(e2, e3) = all_52_9
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | BETA: splitting (23) gives:
% 177.58/28.05  | 
% 177.58/28.05  | Case 1:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (63)  all_58_0 = e3
% 177.58/28.05  | | 
% 177.58/28.05  | | COMBINE_EQS: (20), (63) imply:
% 177.58/28.05  | |   (64)  all_4_2 = e3
% 177.58/28.05  | | 
% 177.58/28.05  | | BETA: splitting (7) gives:
% 177.58/28.05  | | 
% 177.58/28.05  | | Case 1:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (65)  all_58_0 = e2
% 177.58/28.05  | | | 
% 177.58/28.05  | | | COMBINE_EQS: (63), (65) imply:
% 177.58/28.05  | | |   (66)  e3 = e2
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REDUCE: (61), (66) imply:
% 177.58/28.05  | | |   (67)  $false
% 177.58/28.05  | | | 
% 177.58/28.05  | | | CLOSE: (67) is inconsistent.
% 177.58/28.05  | | | 
% 177.58/28.05  | | Case 2:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (68)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.05  | | | 
% 177.58/28.05  | | | BETA: splitting (68) gives:
% 177.58/28.05  | | | 
% 177.58/28.05  | | | Case 1:
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | |   (69)  all_58_2 = e2
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | COMBINE_EQS: (43), (69) imply:
% 177.58/28.05  | | | |   (70)  all_52_9 = e2
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | SIMP: (70) implies:
% 177.58/28.05  | | | |   (71)  all_52_9 = e2
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REDUCE: (30), (71) imply:
% 177.58/28.05  | | | |   (72)  $false
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | CLOSE: (72) is inconsistent.
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | Case 2:
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | |   (73)  all_58_6 = e2 | all_58_12 = e2
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | | REF_CLOSE: (4), (32), (45), (58), (73) are inconsistent by sub-proof
% 177.58/28.05  | | | |            #411.
% 177.58/28.05  | | | | 
% 177.58/28.05  | | | End of split
% 177.58/28.05  | | | 
% 177.58/28.05  | | End of split
% 177.58/28.05  | | 
% 177.58/28.05  | Case 2:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (74)   ~ (all_58_0 = e3)
% 177.58/28.05  | | 
% 177.58/28.05  | | REDUCE: (20), (74) imply:
% 177.58/28.05  | |   (75)   ~ (all_4_2 = e3)
% 177.58/28.05  | | 
% 177.58/28.05  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 177.58/28.05  | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 177.58/28.05  | |            (27), (28), (29), (31), (33), (34), (35), (36), (37), (38), (39),
% 177.58/28.05  | |            (40), (41), (42), (44), (46), (47), (48), (49), (50), (51), (52),
% 177.58/28.05  | |            (53), (54), (55), (56), (57), (59), (60), (62), (75) are
% 177.58/28.05  | |            inconsistent by sub-proof #864.
% 177.58/28.05  | | 
% 177.58/28.05  | End of split
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #411 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)  all_58_6 = e0
% 177.58/28.05    (2)  all_58_12 = e1
% 177.58/28.05    (3)   ~ (e2 = e1)
% 177.58/28.05    (4)   ~ (e2 = e0)
% 177.58/28.05    (5)  all_58_6 = e2 | all_58_12 = e2
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | BETA: splitting (5) gives:
% 177.58/28.05  | 
% 177.58/28.05  | Case 1:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (6)  all_58_6 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | COMBINE_EQS: (1), (6) imply:
% 177.58/28.05  | |   (7)  e2 = e0
% 177.58/28.05  | | 
% 177.58/28.05  | | REDUCE: (4), (7) imply:
% 177.58/28.05  | |   (8)  $false
% 177.58/28.05  | | 
% 177.58/28.05  | | CLOSE: (8) is inconsistent.
% 177.58/28.05  | | 
% 177.58/28.05  | Case 2:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (9)  all_58_12 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | COMBINE_EQS: (2), (9) imply:
% 177.58/28.05  | |   (10)  e2 = e1
% 177.58/28.05  | | 
% 177.58/28.05  | | REDUCE: (3), (10) imply:
% 177.58/28.05  | |   (11)  $false
% 177.58/28.05  | | 
% 177.58/28.05  | | CLOSE: (11) is inconsistent.
% 177.58/28.05  | | 
% 177.58/28.05  | End of split
% 177.58/28.05  | 
% 177.58/28.05  End of proof
% 177.58/28.05  
% 177.58/28.05  Sub-proof #412 shows that the following formulas are inconsistent:
% 177.58/28.05  ----------------------------------------------------------------
% 177.58/28.05    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.05    (2)  op(e2, all_52_3) = e2
% 177.58/28.05    (3)  all_58_15 = e3
% 177.58/28.05    (4)  op(e3, e2) = all_52_3
% 177.58/28.05    (5)   ~ (all_52_27 = e3)
% 177.58/28.05    (6)  all_58_5 = all_52_13
% 177.58/28.05    (7)  all_58_3 = all_10_2
% 177.58/28.05    (8)  all_56_9 = all_52_19
% 177.58/28.05    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.05    (10)   ~ (all_52_9 = all_4_2)
% 177.58/28.05    (11)   ~ (all_52_5 = all_52_7)
% 177.58/28.05    (12)   ~ (all_52_5 = all_4_2)
% 177.58/28.05    (13)  all_58_7 = all_52_19
% 177.58/28.05    (14)   ~ (all_14_2 = e0)
% 177.58/28.05    (15)  all_58_4 = all_52_5
% 177.58/28.05    (16)   ~ (all_52_17 = all_14_2)
% 177.58/28.05    (17)  all_58_1 = all_52_3
% 177.58/28.05    (18)  all_58_0 = all_4_2
% 177.58/28.05    (19)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.05    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.05    (21)  all_58_14 = all_52_29
% 177.58/28.05    (22)   ~ (all_52_3 = all_52_5)
% 177.58/28.05    (23)  all_58_8 = all_14_2
% 177.58/28.05    (24)  op(e1, all_14_2) = e3
% 177.58/28.05    (25)   ~ (all_52_3 = all_4_2)
% 177.58/28.05    (26)  op(e3, all_4_2) = e3
% 177.58/28.05    (27)   ~ (all_52_29 = e3)
% 177.58/28.05    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.05    (29)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.05    (30)  all_58_13 = all_52_27
% 177.58/28.05    (31)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.05    (32)   ~ (all_52_3 = all_52_7)
% 177.58/28.05    (33)  all_56_0 = all_4_2
% 177.58/28.05    (34)  all_58_11 = all_52_23
% 177.58/28.05    (35)  all_58_11 = e2 | all_58_15 = e2
% 177.58/28.05    (36)  op(e3, e1) = all_52_5
% 177.58/28.05    (37)  all_56_10 = all_14_2
% 177.58/28.05    (38)  op(e1, e1) = all_14_2
% 177.58/28.05    (39)  op(e1, e3) = all_52_17
% 177.58/28.05    (40)  op(e3, e0) = all_52_7
% 177.58/28.05    (41)   ~ (all_52_17 = all_4_2)
% 177.58/28.05    (42)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.05    (43)  op(e1, all_52_5) = e1
% 177.58/28.05    (44)   ~ (all_52_13 = all_10_2)
% 177.58/28.05    (45)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.05    (46)   ~ (e3 = e2)
% 177.58/28.05    (47)   ~ (all_52_19 = all_14_2)
% 177.58/28.05    (48)  op(e2, e3) = all_52_9
% 177.58/28.05  
% 177.58/28.05  Begin of proof
% 177.58/28.05  | 
% 177.58/28.05  | BETA: splitting (35) gives:
% 177.58/28.05  | 
% 177.58/28.05  | Case 1:
% 177.58/28.05  | | 
% 177.58/28.05  | |   (49)  all_58_11 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | COMBINE_EQS: (34), (49) imply:
% 177.58/28.05  | |   (50)  all_52_23 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | SIMP: (50) implies:
% 177.58/28.05  | |   (51)  all_52_23 = e2
% 177.58/28.05  | | 
% 177.58/28.05  | | REDUCE: (1), (51) imply:
% 177.58/28.05  | |   (52)   ~ (all_14_2 = e2)
% 177.58/28.05  | | 
% 177.58/28.05  | | SIMP: (52) implies:
% 177.58/28.05  | |   (53)   ~ (all_14_2 = e2)
% 177.58/28.05  | | 
% 177.58/28.05  | | BETA: splitting (19) gives:
% 177.58/28.05  | | 
% 177.58/28.05  | | Case 1:
% 177.58/28.05  | | | 
% 177.58/28.05  | | |   (54)  all_56_9 = e3
% 177.58/28.05  | | | 
% 177.58/28.05  | | | COMBINE_EQS: (8), (54) imply:
% 177.58/28.05  | | |   (55)  all_52_19 = e3
% 177.58/28.05  | | | 
% 177.58/28.05  | | | SIMP: (55) implies:
% 177.58/28.05  | | |   (56)  all_52_19 = e3
% 177.58/28.05  | | | 
% 177.58/28.05  | | | REDUCE: (47), (56) imply:
% 177.58/28.05  | | |   (57)   ~ (all_14_2 = e3)
% 177.58/28.05  | | | 
% 177.58/28.05  | | | SIMP: (57) implies:
% 177.58/28.05  | | |   (58)   ~ (all_14_2 = e3)
% 177.58/28.05  | | | 
% 177.58/28.05  | | | BETA: splitting (29) gives:
% 177.58/28.05  | | | 
% 177.58/28.05  | | | Case 1:
% 177.58/28.05  | | | | 
% 177.58/28.06  | | | |   (59)  all_56_10 = e3
% 177.58/28.06  | | | | 
% 177.58/28.06  | | | | REF_CLOSE: (37), (58), (59) are inconsistent by sub-proof #552.
% 177.58/28.06  | | | | 
% 177.58/28.06  | | | Case 2:
% 177.58/28.06  | | | | 
% 177.58/28.06  | | | |   (60)   ~ (all_56_10 = e3)
% 177.58/28.06  | | | |   (61)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.06  | | | | 
% 177.58/28.06  | | | | BETA: splitting (61) gives:
% 177.58/28.06  | | | | 
% 177.58/28.06  | | | | Case 1:
% 177.58/28.06  | | | | | 
% 177.58/28.06  | | | | |   (62)  all_56_10 = e2
% 177.58/28.06  | | | | | 
% 177.58/28.06  | | | | | REF_CLOSE: (37), (53), (62) are inconsistent by sub-proof #691.
% 177.58/28.06  | | | | | 
% 177.58/28.06  | | | | Case 2:
% 177.58/28.06  | | | | | 
% 177.58/28.06  | | | | |   (63)  all_56_10 = e1 | all_56_10 = e0
% 177.58/28.06  | | | | | 
% 177.58/28.06  | | | | | BETA: splitting (63) gives:
% 177.58/28.06  | | | | | 
% 177.58/28.06  | | | | | Case 1:
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | |   (64)  all_56_10 = e1
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | | COMBINE_EQS: (37), (64) imply:
% 177.58/28.06  | | | | | |   (65)  all_14_2 = e1
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | | SIMP: (65) implies:
% 177.58/28.06  | | | | | |   (66)  all_14_2 = e1
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | | REF_CLOSE: (24), (38), (42), (58), (66) are inconsistent by
% 177.58/28.06  | | | | | |            sub-proof #424.
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | Case 2:
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | |   (67)  all_56_10 = e0
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | | REF_CLOSE: (14), (37), (67) are inconsistent by sub-proof #739.
% 177.58/28.06  | | | | | | 
% 177.58/28.06  | | | | | End of split
% 177.58/28.06  | | | | | 
% 177.58/28.06  | | | | End of split
% 177.58/28.06  | | | | 
% 177.58/28.06  | | | End of split
% 177.58/28.06  | | | 
% 177.58/28.06  | | Case 2:
% 177.58/28.06  | | | 
% 177.58/28.06  | | |   (68)   ~ (all_56_9 = e3)
% 177.58/28.06  | | | 
% 177.58/28.06  | | | REDUCE: (8), (68) imply:
% 177.58/28.06  | | |   (69)   ~ (all_52_19 = e3)
% 177.58/28.06  | | | 
% 177.58/28.06  | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (15),
% 177.58/28.06  | | |            (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 177.58/28.06  | | |            (27), (28), (30), (31), (32), (33), (36), (39), (40), (41),
% 177.58/28.06  | | |            (42), (43), (44), (45), (48), (69) are inconsistent by
% 177.58/28.06  | | |            sub-proof #418.
% 177.58/28.06  | | | 
% 177.58/28.06  | | End of split
% 177.58/28.06  | | 
% 177.58/28.06  | Case 2:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (70)  all_58_15 = e2
% 177.58/28.06  | | 
% 177.58/28.06  | | COMBINE_EQS: (3), (70) imply:
% 177.58/28.06  | |   (71)  e3 = e2
% 177.58/28.06  | | 
% 177.58/28.06  | | REDUCE: (46), (71) imply:
% 177.58/28.06  | |   (72)  $false
% 177.58/28.06  | | 
% 177.58/28.06  | | CLOSE: (72) is inconsistent.
% 177.58/28.06  | | 
% 177.58/28.06  | End of split
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #413 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.06    (2)   ~ (all_52_5 = all_52_13)
% 177.58/28.06    (3)  op(e2, all_52_3) = e2
% 177.58/28.06    (4)  op(e3, e2) = all_52_3
% 177.58/28.06    (5)  all_58_5 = all_52_13
% 177.58/28.06    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.06    (7)  all_58_15 = all_6_2
% 177.58/28.06    (8)   ~ (all_52_9 = all_4_2)
% 177.58/28.06    (9)   ~ (all_52_5 = all_52_7)
% 177.58/28.06    (10)  all_58_10 = all_52_15
% 177.58/28.06    (11)   ~ (all_52_5 = all_4_2)
% 177.58/28.06    (12)  all_58_7 = all_52_19
% 177.58/28.06    (13)  all_58_4 = all_52_5
% 177.58/28.06    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.06    (15)   ~ (all_52_17 = all_14_2)
% 177.58/28.06    (16)   ~ (all_52_7 = all_4_2)
% 177.58/28.06    (17)  all_58_1 = all_52_3
% 177.58/28.06    (18)  all_58_0 = all_4_2
% 177.58/28.06    (19)  all_58_14 = all_52_29
% 177.58/28.06    (20)   ~ (all_52_3 = all_52_5)
% 177.58/28.06    (21)  all_58_8 = all_14_2
% 177.58/28.06    (22)   ~ (all_52_5 = all_14_2)
% 177.58/28.06    (23)  op(e3, all_4_2) = e3
% 177.58/28.06    (24)  op(e0, e3) = all_52_25
% 177.58/28.06    (25)   ~ (all_52_29 = e3)
% 177.58/28.06    (26)   ~ (all_52_13 = all_14_2)
% 177.58/28.06    (27)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.06    (28)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.06    (29)   ~ (all_52_5 = all_52_29)
% 177.58/28.06    (30)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.06    (31)  all_58_6 = all_52_17
% 177.58/28.06    (32)   ~ (all_52_3 = all_52_7)
% 177.58/28.06    (33)  all_56_0 = all_4_2
% 177.58/28.06    (34)  all_58_11 = all_52_23
% 177.58/28.06    (35)   ~ (all_52_3 = all_52_19)
% 177.58/28.06    (36)   ~ (all_52_7 = all_52_15)
% 177.58/28.06    (37)   ~ (all_52_29 = all_14_2)
% 177.58/28.06    (38)  all_52_9 = e3
% 177.58/28.06    (39)  op(e3, e1) = all_52_5
% 177.58/28.06    (40)  all_56_10 = all_14_2
% 177.58/28.06    (41)  op(e1, e3) = all_52_17
% 177.58/28.06    (42)   ~ (all_52_25 = all_4_2)
% 177.58/28.06    (43)  op(e3, e0) = all_52_7
% 177.58/28.06    (44)   ~ (all_52_17 = all_4_2)
% 177.58/28.06    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.06    (46)   ~ (all_52_7 = all_6_2)
% 177.58/28.06    (47)  op(e1, all_52_5) = e1
% 177.58/28.06    (48)   ~ (all_52_7 = all_52_23)
% 177.58/28.06    (49)  op(e0, all_52_7) = e0
% 177.58/28.06    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.06    (51)  all_58_9 = all_52_7
% 177.58/28.06    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.06    (53)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.06    (54)  op(e2, e3) = all_52_9
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | SIMP: (38) implies:
% 177.58/28.06  |   (55)  all_52_9 = e3
% 177.58/28.06  | 
% 177.58/28.06  | REDUCE: (8), (55) imply:
% 177.58/28.06  |   (56)   ~ (all_4_2 = e3)
% 177.58/28.06  | 
% 177.58/28.06  | SIMP: (56) implies:
% 177.58/28.06  |   (57)   ~ (all_4_2 = e3)
% 177.58/28.06  | 
% 177.58/28.06  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.58/28.06  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.58/28.06  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.58/28.06  |            (35), (36), (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.58/28.06  |            (47), (48), (49), (50), (51), (52), (53), (54), (57) are
% 177.58/28.06  |            inconsistent by sub-proof #864.
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #414 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  all_56_8 = all_6_0
% 177.58/28.06    (2)  all_56_8 = e1
% 177.58/28.06    (3)   ~ (all_6_0 = e1)
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | COMBINE_EQS: (1), (2) imply:
% 177.58/28.06  |   (4)  all_6_0 = e1
% 177.58/28.06  | 
% 177.58/28.06  | SIMP: (4) implies:
% 177.58/28.06  |   (5)  all_6_0 = e1
% 177.58/28.06  | 
% 177.58/28.06  | REDUCE: (3), (5) imply:
% 177.58/28.06  |   (6)  $false
% 177.58/28.06  | 
% 177.58/28.06  | CLOSE: (6) is inconsistent.
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #415 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  all_56_8 = all_6_0
% 177.58/28.06    (2)  all_56_8 = e2
% 177.58/28.06    (3)   ~ (all_6_0 = e2)
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | COMBINE_EQS: (1), (2) imply:
% 177.58/28.06  |   (4)  all_6_0 = e2
% 177.58/28.06  | 
% 177.58/28.06  | SIMP: (4) implies:
% 177.58/28.06  |   (5)  all_6_0 = e2
% 177.58/28.06  | 
% 177.58/28.06  | REDUCE: (3), (5) imply:
% 177.58/28.06  |   (6)  $false
% 177.58/28.06  | 
% 177.58/28.06  | CLOSE: (6) is inconsistent.
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #416 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  all_56_8 = all_6_0
% 177.58/28.06    (2)  all_56_8 = e3
% 177.58/28.06    (3)   ~ (all_6_0 = e3)
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | COMBINE_EQS: (1), (2) imply:
% 177.58/28.06  |   (4)  all_6_0 = e3
% 177.58/28.06  | 
% 177.58/28.06  | SIMP: (4) implies:
% 177.58/28.06  |   (5)  all_6_0 = e3
% 177.58/28.06  | 
% 177.58/28.06  | REDUCE: (3), (5) imply:
% 177.58/28.06  |   (6)  $false
% 177.58/28.06  | 
% 177.58/28.06  | CLOSE: (6) is inconsistent.
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #417 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  op(e2, all_52_3) = e2
% 177.58/28.06    (2)   ~ (all_10_2 = e0)
% 177.58/28.06    (3)  op(e3, e2) = all_52_3
% 177.58/28.06    (4)   ~ (all_10_2 = e1)
% 177.58/28.06    (5)   ~ (all_52_27 = e3)
% 177.58/28.06    (6)  all_58_5 = all_52_13
% 177.58/28.06    (7)  all_58_3 = all_10_2
% 177.58/28.06    (8)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.06    (9)   ~ (all_52_9 = all_4_2)
% 177.58/28.06    (10)   ~ (all_52_5 = all_52_7)
% 177.58/28.06    (11)   ~ (all_52_5 = all_4_2)
% 177.58/28.06    (12)  all_58_7 = all_52_19
% 177.58/28.06    (13)  all_58_4 = all_52_5
% 177.58/28.06    (14)   ~ (all_52_17 = all_14_2)
% 177.58/28.06    (15)  all_58_1 = all_52_3
% 177.58/28.06    (16)  all_58_0 = all_4_2
% 177.58/28.06    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.06    (18)  all_58_14 = all_52_29
% 177.58/28.06    (19)   ~ (all_52_3 = all_52_5)
% 177.58/28.06    (20)  all_58_8 = all_14_2
% 177.58/28.06    (21)  op(e1, all_14_2) = e3
% 177.58/28.06    (22)   ~ (all_52_3 = all_4_2)
% 177.58/28.06    (23)  op(e3, all_4_2) = e3
% 177.58/28.06    (24)   ~ (all_52_29 = e3)
% 177.58/28.06    (25)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.06    (26)  all_58_13 = all_52_27
% 177.58/28.06    (27)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.06    (28)  all_56_5 = all_10_2
% 177.58/28.06    (29)   ~ (all_52_3 = all_52_7)
% 177.58/28.06    (30)  all_56_0 = all_4_2
% 177.58/28.06    (31)   ~ (all_52_19 = all_10_2)
% 177.58/28.06    (32)  op(e3, e1) = all_52_5
% 177.58/28.06    (33)   ~ (all_10_2 = e2)
% 177.58/28.06    (34)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.06    (35)  op(e1, e3) = all_52_17
% 177.58/28.06    (36)  op(e3, e0) = all_52_7
% 177.58/28.06    (37)   ~ (all_52_17 = all_4_2)
% 177.58/28.06    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.06    (39)  op(e1, all_52_5) = e1
% 177.58/28.06    (40)   ~ (all_52_13 = all_10_2)
% 177.58/28.06    (41)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.06    (42)  op(e2, e3) = all_52_9
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | BETA: splitting (34) gives:
% 177.58/28.06  | 
% 177.58/28.06  | Case 1:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (43)  all_56_5 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | COMBINE_EQS: (28), (43) imply:
% 177.58/28.06  | |   (44)  all_10_2 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | SIMP: (44) implies:
% 177.58/28.06  | |   (45)  all_10_2 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | REDUCE: (31), (45) imply:
% 177.58/28.06  | |   (46)   ~ (all_52_19 = e3)
% 177.58/28.06  | | 
% 177.58/28.06  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 177.58/28.06  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.58/28.06  | |            (26), (27), (29), (30), (32), (35), (36), (37), (38), (39), (40),
% 177.58/28.06  | |            (41), (42), (46) are inconsistent by sub-proof #418.
% 177.58/28.06  | | 
% 177.58/28.06  | Case 2:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (47)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.06  | | 
% 177.58/28.06  | | REF_CLOSE: (2), (4), (28), (33), (47) are inconsistent by sub-proof #526.
% 177.58/28.06  | | 
% 177.58/28.06  | End of split
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #418 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  op(e2, all_52_3) = e2
% 177.58/28.06    (2)  op(e3, e2) = all_52_3
% 177.58/28.06    (3)   ~ (all_52_27 = e3)
% 177.58/28.06    (4)  all_58_5 = all_52_13
% 177.58/28.06    (5)  all_58_3 = all_10_2
% 177.58/28.06    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.06    (7)   ~ (all_52_9 = all_4_2)
% 177.58/28.06    (8)   ~ (all_52_5 = all_52_7)
% 177.58/28.06    (9)   ~ (all_52_5 = all_4_2)
% 177.58/28.06    (10)  all_58_7 = all_52_19
% 177.58/28.06    (11)  all_58_4 = all_52_5
% 177.58/28.06    (12)   ~ (all_52_17 = all_14_2)
% 177.58/28.06    (13)  all_58_1 = all_52_3
% 177.58/28.06    (14)  all_58_0 = all_4_2
% 177.58/28.06    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.06    (16)  all_58_14 = all_52_29
% 177.58/28.06    (17)   ~ (all_52_3 = all_52_5)
% 177.58/28.06    (18)  all_58_8 = all_14_2
% 177.58/28.06    (19)  op(e1, all_14_2) = e3
% 177.58/28.06    (20)   ~ (all_52_3 = all_4_2)
% 177.58/28.06    (21)  op(e3, all_4_2) = e3
% 177.58/28.06    (22)   ~ (all_52_29 = e3)
% 177.58/28.06    (23)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.06    (24)  all_58_13 = all_52_27
% 177.58/28.06    (25)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.06    (26)   ~ (all_52_3 = all_52_7)
% 177.58/28.06    (27)  all_56_0 = all_4_2
% 177.58/28.06    (28)  op(e3, e1) = all_52_5
% 177.58/28.06    (29)   ~ (all_52_19 = e3)
% 177.58/28.06    (30)  op(e1, e3) = all_52_17
% 177.58/28.06    (31)  op(e3, e0) = all_52_7
% 177.58/28.06    (32)   ~ (all_52_17 = all_4_2)
% 177.58/28.06    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.06    (34)  op(e1, all_52_5) = e1
% 177.58/28.06    (35)   ~ (all_52_13 = all_10_2)
% 177.58/28.06    (36)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.06    (37)  op(e2, e3) = all_52_9
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | BETA: splitting (15) gives:
% 177.58/28.06  | 
% 177.58/28.06  | Case 1:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (38)  all_58_1 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | REF_CLOSE: (1), (6), (7), (13), (14), (17), (20), (21), (25), (26), (27),
% 177.58/28.06  | |            (28), (31), (33), (37), (38) are inconsistent by sub-proof #788.
% 177.58/28.06  | | 
% 177.58/28.06  | Case 2:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (39)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | BETA: splitting (39) gives:
% 177.58/28.06  | | 
% 177.58/28.06  | | Case 1:
% 177.58/28.06  | | | 
% 177.58/28.06  | | |   (40)  all_58_3 = e3
% 177.58/28.06  | | | 
% 177.58/28.06  | | | COMBINE_EQS: (5), (40) imply:
% 177.58/28.06  | | |   (41)  all_10_2 = e3
% 177.58/28.06  | | | 
% 177.58/28.06  | | | REDUCE: (35), (41) imply:
% 177.58/28.06  | | |   (42)   ~ (all_52_13 = e3)
% 177.58/28.06  | | | 
% 177.58/28.06  | | | REF_CLOSE: (2), (4), (6), (8), (9), (11), (12), (14), (16), (17), (18),
% 177.58/28.06  | | |            (19), (21), (22), (23), (27), (30), (31), (32), (33), (34),
% 177.58/28.06  | | |            (36), (42) are inconsistent by sub-proof #419.
% 177.58/28.06  | | | 
% 177.58/28.06  | | Case 2:
% 177.58/28.06  | | | 
% 177.58/28.06  | | |   (43)  all_58_7 = e3 | all_58_13 = e3
% 177.58/28.06  | | | 
% 177.58/28.06  | | | REF_CLOSE: (3), (10), (24), (29), (43) are inconsistent by sub-proof #976.
% 177.58/28.06  | | | 
% 177.58/28.06  | | End of split
% 177.58/28.06  | | 
% 177.58/28.06  | End of split
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #419 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  op(e3, e2) = all_52_3
% 177.58/28.06    (2)  all_58_5 = all_52_13
% 177.58/28.06    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.06    (4)   ~ (all_52_5 = all_52_7)
% 177.58/28.06    (5)   ~ (all_52_5 = all_4_2)
% 177.58/28.06    (6)  all_58_4 = all_52_5
% 177.58/28.06    (7)   ~ (all_52_17 = all_14_2)
% 177.58/28.06    (8)  all_58_0 = all_4_2
% 177.58/28.06    (9)  all_58_14 = all_52_29
% 177.58/28.06    (10)   ~ (all_52_3 = all_52_5)
% 177.58/28.06    (11)  all_58_8 = all_14_2
% 177.58/28.06    (12)  op(e1, all_14_2) = e3
% 177.58/28.06    (13)  op(e3, all_4_2) = e3
% 177.58/28.06    (14)   ~ (all_52_29 = e3)
% 177.58/28.06    (15)   ~ (all_52_13 = e3)
% 177.58/28.06    (16)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.06    (17)  all_56_0 = all_4_2
% 177.58/28.06    (18)  op(e1, e3) = all_52_17
% 177.58/28.06    (19)  op(e3, e0) = all_52_7
% 177.58/28.06    (20)   ~ (all_52_17 = all_4_2)
% 177.58/28.06    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.06    (22)  op(e1, all_52_5) = e1
% 177.58/28.06    (23)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | BETA: splitting (23) gives:
% 177.58/28.06  | 
% 177.58/28.06  | Case 1:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (24)  all_58_4 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (13), (16), (17), (18), (19),
% 177.58/28.06  | |            (20), (21), (22), (24) are inconsistent by sub-proof #821.
% 177.58/28.06  | | 
% 177.58/28.06  | Case 2:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (25)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | REF_CLOSE: (2), (7), (9), (11), (12), (14), (15), (18), (21), (25) are
% 177.58/28.06  | |            inconsistent by sub-proof #420.
% 177.58/28.06  | | 
% 177.58/28.06  | End of split
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #420 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  all_58_5 = all_52_13
% 177.58/28.06    (2)   ~ (all_52_17 = all_14_2)
% 177.58/28.06    (3)  all_58_14 = all_52_29
% 177.58/28.06    (4)  all_58_8 = all_14_2
% 177.58/28.06    (5)  op(e1, all_14_2) = e3
% 177.58/28.06    (6)   ~ (all_52_29 = e3)
% 177.58/28.06    (7)   ~ (all_52_13 = e3)
% 177.58/28.06    (8)  op(e1, e3) = all_52_17
% 177.58/28.06    (9)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.06    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | BETA: splitting (9) gives:
% 177.58/28.06  | 
% 177.58/28.06  | Case 1:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (11)  all_58_5 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #969.
% 177.58/28.06  | | 
% 177.58/28.06  | Case 2:
% 177.58/28.06  | | 
% 177.58/28.06  | |   (12)  all_58_8 = e3 | all_58_14 = e3
% 177.58/28.06  | | 
% 177.58/28.06  | | BETA: splitting (12) gives:
% 177.58/28.06  | | 
% 177.58/28.06  | | Case 1:
% 177.58/28.06  | | | 
% 177.58/28.06  | | |   (13)  all_58_8 = e3
% 177.58/28.06  | | | 
% 177.58/28.06  | | | REF_CLOSE: (2), (4), (5), (8), (10), (13) are inconsistent by sub-proof
% 177.58/28.06  | | |            #432.
% 177.58/28.06  | | | 
% 177.58/28.06  | | Case 2:
% 177.58/28.06  | | | 
% 177.58/28.06  | | |   (14)  all_58_14 = e3
% 177.58/28.06  | | | 
% 177.58/28.06  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #1000.
% 177.58/28.06  | | | 
% 177.58/28.06  | | End of split
% 177.58/28.06  | | 
% 177.58/28.06  | End of split
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #421 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.06    (2)   ~ (all_52_27 = all_10_2)
% 177.58/28.06    (3)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.58/28.06    (4)  all_56_3 = all_52_7
% 177.58/28.06    (5)  op(e3, e2) = all_52_3
% 177.58/28.06    (6)   ~ (all_52_9 = all_52_25)
% 177.58/28.06    (7)  op(e3, all_52_25) = all_52_24
% 177.58/28.06    (8)   ~ (all_52_19 = all_52_23)
% 177.58/28.06    (9)  all_56_11 = all_52_23
% 177.58/28.06    (10)  op(e1, e2) = all_52_19
% 177.58/28.06    (11)   ~ (all_52_23 = e0)
% 177.58/28.06    (12)   ~ (all_52_3 = all_10_2)
% 177.58/28.06    (13)  all_58_5 = all_52_13
% 177.58/28.06    (14)   ~ (all_52_25 = all_52_29)
% 177.58/28.06    (15)  all_56_9 = all_52_19
% 177.58/28.06    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.06    (17)   ~ (all_52_5 = all_52_7)
% 177.58/28.06    (18)   ~ (all_52_5 = all_4_2)
% 177.58/28.06    (19)  all_58_7 = all_52_19
% 177.58/28.06    (20)   ~ (all_52_17 = all_52_25)
% 177.58/28.06    (21)  all_58_4 = all_52_5
% 177.58/28.06    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.06    (23)   ~ (e3 = e1)
% 177.58/28.06    (24)   ~ (all_52_27 = all_52_29)
% 177.58/28.06    (25)  op(e3, all_4_2) = all_4_1
% 177.58/28.06    (26)   ~ (all_52_7 = all_4_2)
% 177.58/28.06    (27)  all_58_0 = all_4_2
% 177.58/28.06    (28)  op(e1, all_52_29) = all_52_28
% 177.58/28.06    (29)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.06    (30)   ~ (all_4_1 = e2)
% 177.58/28.06    (31)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.06    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.06    (33)  all_58_14 = all_52_29
% 177.58/28.06    (34)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.06    (35)  op(e2, e1) = all_52_13
% 177.58/28.06    (36)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.06    (37)  all_58_8 = all_14_2
% 177.58/28.06    (38)  all_56_14 = all_52_29
% 177.58/28.06    (39)  op(e1, all_14_2) = e3
% 177.58/28.06    (40)   ~ (all_52_5 = all_14_2)
% 177.58/28.06    (41)   ~ (all_52_3 = all_52_27)
% 177.58/28.06    (42)   ~ (all_52_3 = all_4_2)
% 177.58/28.06    (43)  op(e3, all_52_17) = all_52_16
% 177.58/28.06    (44)   ~ (e3 = e0)
% 177.58/28.06    (45)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.06    (46)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.06    (47)   ~ (all_52_5 = all_52_29)
% 177.58/28.06    (48)  op(e1, e0) = all_52_23
% 177.58/28.06    (49)  all_56_12 = all_52_25
% 177.58/28.06    (50)  all_58_13 = all_52_27
% 177.58/28.06    (51)  all_56_5 = all_10_2
% 177.58/28.06    (52)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.06    (53)   ~ (all_52_25 = e0)
% 177.58/28.06    (54)   ~ (all_52_9 = all_52_17)
% 177.58/28.06    (55)  all_58_6 = all_52_17
% 177.58/28.06    (56)   ~ (e1 = e0)
% 177.58/28.06    (57)  all_56_0 = all_4_2
% 177.58/28.06    (58)  all_58_11 = all_52_23
% 177.58/28.06    (59)   ~ (all_52_3 = all_52_19)
% 177.58/28.06    (60)   ~ (all_52_29 = all_14_2)
% 177.58/28.06    (61)   ~ (all_52_19 = all_10_2)
% 177.58/28.06    (62)  all_58_15 = e0
% 177.58/28.06    (63)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.58/28.06    (64)   ~ (all_52_29 = e0)
% 177.58/28.06    (65)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.06    (66)  op(e3, e1) = all_52_5
% 177.58/28.06    (67)  all_56_10 = all_14_2
% 177.58/28.06    (68)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.06    (69)  op(e1, e1) = all_14_2
% 177.58/28.06    (70)  op(e1, e3) = all_52_17
% 177.58/28.06    (71)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 177.58/28.06    (72)   ~ (all_52_25 = all_4_2)
% 177.58/28.06    (73)  op(e3, e0) = all_52_7
% 177.58/28.06    (74)  op(e3, e3) = all_4_2
% 177.58/28.06    (75)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.06    (76)   ~ (all_52_25 = all_52_27)
% 177.58/28.06    (77)   ~ (all_52_19 = all_52_27)
% 177.58/28.06    (78)   ~ (all_52_7 = all_52_23)
% 177.58/28.06    (79)   ~ (all_52_13 = all_10_2)
% 177.58/28.06    (80)  op(e2, all_52_27) = all_52_26
% 177.58/28.06    (81)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.06    (82)  op(e3, all_14_2) = all_14_0
% 177.58/28.06    (83)  all_58_12 = all_52_25
% 177.58/28.06    (84)   ~ (all_52_19 = all_14_2)
% 177.58/28.06    (85)  op(e2, e3) = all_52_9
% 177.58/28.06    (86)  all_56_13 = all_52_27
% 177.58/28.06  
% 177.58/28.06  Begin of proof
% 177.58/28.06  | 
% 177.58/28.06  | ALPHA: (3) implies:
% 177.58/28.06  |   (87)  all_52_28 = e1
% 177.58/28.06  |   (88)  all_52_26 = e2
% 177.58/28.06  |   (89)  all_52_24 = e3
% 177.58/28.06  | 
% 177.58/28.06  | REDUCE: (7), (89) imply:
% 177.58/28.06  |   (90)  op(e3, all_52_25) = e3
% 177.58/28.06  | 
% 177.58/28.06  | REDUCE: (80), (88) imply:
% 177.58/28.06  |   (91)  op(e2, all_52_27) = e2
% 177.58/28.06  | 
% 177.58/28.06  | REDUCE: (28), (87) imply:
% 177.58/28.06  |   (92)  op(e1, all_52_29) = e1
% 177.58/28.06  | 
% 177.58/28.06  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 177.58/28.06  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.58/28.06  |            (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.58/28.06  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.58/28.06  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 177.58/28.06  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 177.58/28.06  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (81), (82),
% 177.58/28.06  |            (83), (84), (85), (86), (90), (91), (92) are inconsistent by
% 177.58/28.06  |            sub-proof #422.
% 177.58/28.06  | 
% 177.58/28.06  End of proof
% 177.58/28.06  
% 177.58/28.06  Sub-proof #422 shows that the following formulas are inconsistent:
% 177.58/28.06  ----------------------------------------------------------------
% 177.58/28.06    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.06    (2)   ~ (all_52_27 = all_10_2)
% 177.58/28.06    (3)  all_56_3 = all_52_7
% 177.58/28.06    (4)  op(e3, e2) = all_52_3
% 177.58/28.06    (5)   ~ (all_52_9 = all_52_25)
% 177.58/28.06    (6)   ~ (all_52_19 = all_52_23)
% 177.58/28.06    (7)  all_56_11 = all_52_23
% 177.58/28.06    (8)  op(e1, e2) = all_52_19
% 177.58/28.06    (9)   ~ (all_52_23 = e0)
% 177.58/28.06    (10)   ~ (all_52_3 = all_10_2)
% 177.58/28.06    (11)  all_58_5 = all_52_13
% 177.58/28.06    (12)   ~ (all_52_25 = all_52_29)
% 177.58/28.06    (13)  all_56_9 = all_52_19
% 177.58/28.06    (14)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.06    (15)   ~ (all_52_5 = all_52_7)
% 177.58/28.06    (16)   ~ (all_52_5 = all_4_2)
% 177.58/28.06    (17)  all_58_7 = all_52_19
% 177.58/28.06    (18)   ~ (all_52_17 = all_52_25)
% 177.58/28.06    (19)  all_58_4 = all_52_5
% 177.58/28.06    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.06    (21)   ~ (e3 = e1)
% 177.58/28.06    (22)   ~ (all_52_27 = all_52_29)
% 177.58/28.06    (23)  op(e3, all_4_2) = all_4_1
% 177.58/28.06    (24)   ~ (all_52_7 = all_4_2)
% 177.58/28.06    (25)  all_58_0 = all_4_2
% 177.58/28.06    (26)  op(e2, all_52_27) = e2
% 177.58/28.06    (27)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.06    (28)   ~ (all_4_1 = e2)
% 177.58/28.06    (29)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.06    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.06    (31)  all_58_14 = all_52_29
% 177.58/28.06    (32)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.06    (33)  op(e2, e1) = all_52_13
% 177.58/28.06    (34)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.06    (35)  all_58_8 = all_14_2
% 177.58/28.06    (36)  all_56_14 = all_52_29
% 177.58/28.06    (37)  op(e1, all_14_2) = e3
% 177.58/28.06    (38)  op(e1, all_52_29) = e1
% 177.58/28.06    (39)   ~ (all_52_5 = all_14_2)
% 177.58/28.06    (40)   ~ (all_52_3 = all_52_27)
% 177.58/28.06    (41)   ~ (all_52_3 = all_4_2)
% 177.58/28.06    (42)  op(e3, all_52_17) = all_52_16
% 177.58/28.06    (43)   ~ (e3 = e0)
% 177.58/28.06    (44)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.06    (45)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.06    (46)   ~ (all_52_5 = all_52_29)
% 177.58/28.06    (47)  op(e1, e0) = all_52_23
% 177.58/28.06    (48)  all_56_12 = all_52_25
% 177.58/28.06    (49)  all_58_13 = all_52_27
% 177.58/28.06    (50)  all_56_5 = all_10_2
% 177.58/28.07    (51)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.07    (52)   ~ (all_52_25 = e0)
% 177.58/28.07    (53)   ~ (all_52_9 = all_52_17)
% 177.58/28.07    (54)  all_58_6 = all_52_17
% 177.58/28.07    (55)   ~ (e1 = e0)
% 177.58/28.07    (56)  all_56_0 = all_4_2
% 177.58/28.07    (57)  all_58_11 = all_52_23
% 177.58/28.07    (58)   ~ (all_52_3 = all_52_19)
% 177.58/28.07    (59)   ~ (all_52_29 = all_14_2)
% 177.58/28.07    (60)  op(e3, all_52_25) = e3
% 177.58/28.07    (61)   ~ (all_52_19 = all_10_2)
% 177.58/28.07    (62)  all_58_15 = e0
% 177.58/28.07    (63)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.58/28.07    (64)   ~ (all_52_29 = e0)
% 177.58/28.07    (65)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.07    (66)  op(e3, e1) = all_52_5
% 177.58/28.07    (67)  all_56_10 = all_14_2
% 177.58/28.07    (68)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.07    (69)  op(e1, e1) = all_14_2
% 177.58/28.07    (70)  op(e1, e3) = all_52_17
% 177.58/28.07    (71)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 177.58/28.07    (72)   ~ (all_52_25 = all_4_2)
% 177.58/28.07    (73)  op(e3, e0) = all_52_7
% 177.58/28.07    (74)  op(e3, e3) = all_4_2
% 177.58/28.07    (75)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.07    (76)   ~ (all_52_25 = all_52_27)
% 177.58/28.07    (77)   ~ (all_52_19 = all_52_27)
% 177.58/28.07    (78)   ~ (all_52_7 = all_52_23)
% 177.58/28.07    (79)   ~ (all_52_13 = all_10_2)
% 177.58/28.07    (80)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.07    (81)  op(e3, all_14_2) = all_14_0
% 177.58/28.07    (82)  all_58_12 = all_52_25
% 177.58/28.07    (83)   ~ (all_52_19 = all_14_2)
% 177.58/28.07    (84)  op(e2, e3) = all_52_9
% 177.58/28.07    (85)  all_56_13 = all_52_27
% 177.58/28.07  
% 177.58/28.07  Begin of proof
% 177.58/28.07  | 
% 177.58/28.07  | BETA: splitting (32) gives:
% 177.58/28.07  | 
% 177.58/28.07  | Case 1:
% 177.58/28.07  | | 
% 177.58/28.07  | |   (86)  all_56_13 = e3
% 177.58/28.07  | | 
% 177.58/28.07  | | COMBINE_EQS: (85), (86) imply:
% 177.58/28.07  | |   (87)  all_52_27 = e3
% 177.58/28.07  | | 
% 177.58/28.07  | | SIMP: (87) implies:
% 177.58/28.07  | |   (88)  all_52_27 = e3
% 177.58/28.07  | | 
% 177.58/28.07  | | REDUCE: (76), (88) imply:
% 177.58/28.07  | |   (89)   ~ (all_52_25 = e3)
% 177.58/28.07  | | 
% 177.58/28.07  | | REDUCE: (22), (88) imply:
% 177.58/28.07  | |   (90)   ~ (all_52_29 = e3)
% 177.58/28.07  | | 
% 177.58/28.07  | | SIMP: (90) implies:
% 177.58/28.07  | |   (91)   ~ (all_52_29 = e3)
% 177.58/28.07  | | 
% 177.58/28.07  | | REDUCE: (26), (88) imply:
% 177.58/28.07  | |   (92)  op(e2, e3) = e2
% 177.58/28.07  | | 
% 177.58/28.07  | | GROUND_INST: instantiating (75) with all_52_9, e2, e3, e2, simplifying with
% 177.58/28.07  | |              (84), (92) gives:
% 177.58/28.07  | |   (93)  all_52_9 = e2
% 177.58/28.07  | | 
% 177.58/28.07  | | REDUCE: (53), (93) imply:
% 177.58/28.07  | |   (94)   ~ (all_52_17 = e2)
% 177.58/28.07  | | 
% 177.58/28.07  | | SIMP: (94) implies:
% 177.58/28.07  | |   (95)   ~ (all_52_17 = e2)
% 177.58/28.07  | | 
% 177.58/28.07  | | REDUCE: (5), (93) imply:
% 177.58/28.07  | |   (96)   ~ (all_52_25 = e2)
% 177.58/28.07  | | 
% 177.58/28.07  | | SIMP: (96) implies:
% 177.58/28.07  | |   (97)   ~ (all_52_25 = e2)
% 177.58/28.07  | | 
% 177.58/28.07  | | BETA: splitting (44) gives:
% 177.58/28.07  | | 
% 177.58/28.07  | | Case 1:
% 177.58/28.07  | | | 
% 177.58/28.07  | | |   (98)  all_56_12 = e3
% 177.58/28.07  | | | 
% 177.58/28.07  | | | COMBINE_EQS: (48), (98) imply:
% 177.58/28.07  | | |   (99)  all_52_25 = e3
% 177.58/28.07  | | | 
% 177.58/28.07  | | | REDUCE: (89), (99) imply:
% 177.58/28.07  | | |   (100)  $false
% 177.58/28.07  | | | 
% 177.58/28.07  | | | CLOSE: (100) is inconsistent.
% 177.58/28.07  | | | 
% 177.58/28.07  | | Case 2:
% 177.58/28.07  | | | 
% 177.58/28.07  | | |   (101)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.07  | | | 
% 177.58/28.07  | | | BETA: splitting (101) gives:
% 177.58/28.07  | | | 
% 177.58/28.07  | | | Case 1:
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | |   (102)  all_56_12 = e2
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | COMBINE_EQS: (48), (102) imply:
% 177.58/28.07  | | | |   (103)  all_52_25 = e2
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | REDUCE: (97), (103) imply:
% 177.58/28.07  | | | |   (104)  $false
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | CLOSE: (104) is inconsistent.
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | Case 2:
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | |   (105)  all_56_12 = e1 | all_56_12 = e0
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | BETA: splitting (105) gives:
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | Case 1:
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | |   (106)  all_56_12 = e1
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | COMBINE_EQS: (48), (106) imply:
% 177.58/28.07  | | | | |   (107)  all_52_25 = e1
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (12), (107) imply:
% 177.58/28.07  | | | | |   (108)   ~ (all_52_29 = e1)
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | SIMP: (108) implies:
% 177.58/28.07  | | | | |   (109)   ~ (all_52_29 = e1)
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (60), (107) imply:
% 177.58/28.07  | | | | |   (110)  op(e3, e1) = e3
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | BETA: splitting (29) gives:
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | Case 1:
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | |   (111)  all_56_14 = e3
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | REF_CLOSE: (36), (91), (111) are inconsistent by sub-proof #896.
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | Case 2:
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | |   (112)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | BETA: splitting (112) gives:
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | Case 1:
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | |   (113)  all_56_14 = e2
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | COMBINE_EQS: (36), (113) imply:
% 177.58/28.07  | | | | | | |   (114)  all_52_29 = e2
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | SIMP: (114) implies:
% 177.58/28.07  | | | | | | |   (115)  all_52_29 = e2
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (46), (115) imply:
% 177.58/28.07  | | | | | | |   (116)   ~ (all_52_5 = e2)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (59), (115) imply:
% 177.58/28.07  | | | | | | |   (117)   ~ (all_14_2 = e2)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | SIMP: (117) implies:
% 177.58/28.07  | | | | | | |   (118)   ~ (all_14_2 = e2)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (109), (115) imply:
% 177.58/28.07  | | | | | | |   (119)   ~ (e2 = e1)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (38), (115) imply:
% 177.58/28.07  | | | | | | |   (120)  op(e1, e2) = e1
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | GROUND_INST: instantiating (75) with all_52_19, e1, e2, e1,
% 177.58/28.07  | | | | | | |              simplifying with (8), (120) gives:
% 177.58/28.07  | | | | | | |   (121)  all_52_19 = e1
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | GROUND_INST: instantiating (75) with all_52_5, e3, e1, e3,
% 177.58/28.07  | | | | | | |              simplifying with (66), (110) gives:
% 177.58/28.07  | | | | | | |   (122)  all_52_5 = e3
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | COMBINE_EQS: (17), (121) imply:
% 177.58/28.07  | | | | | | |   (123)  all_58_7 = e1
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (39), (122) imply:
% 177.58/28.07  | | | | | | |   (124)   ~ (all_14_2 = e3)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | SIMP: (124) implies:
% 177.58/28.07  | | | | | | |   (125)   ~ (all_14_2 = e3)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (116), (122) imply:
% 177.58/28.07  | | | | | | |   (126)   ~ (e3 = e2)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (6), (121) imply:
% 177.58/28.07  | | | | | | |   (127)   ~ (all_52_23 = e1)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | SIMP: (127) implies:
% 177.58/28.07  | | | | | | |   (128)   ~ (all_52_23 = e1)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REDUCE: (83), (121) imply:
% 177.58/28.07  | | | | | | |   (129)   ~ (all_14_2 = e1)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | SIMP: (129) implies:
% 177.58/28.07  | | | | | | |   (130)   ~ (all_14_2 = e1)
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | BETA: splitting (51) gives:
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | |   (131)  all_58_6 = e2
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | REF_CLOSE: (54), (95), (131) are inconsistent by sub-proof #894.
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | |   (132)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | BETA: splitting (45) gives:
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | |   (133)  all_56_10 = e3
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REF_CLOSE: (67), (125), (133) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | |            #552.
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | |   (134)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | BETA: splitting (65) gives:
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | |   (135)  all_56_11 = e3
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | COMBINE_EQS: (7), (135) imply:
% 177.58/28.07  | | | | | | | | | |   (136)  all_52_23 = e3
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | SIMP: (136) implies:
% 177.58/28.07  | | | | | | | | | |   (137)  all_52_23 = e3
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | COMBINE_EQS: (57), (137) imply:
% 177.58/28.07  | | | | | | | | | |   (138)  all_58_11 = e3
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | REF_CLOSE: (35), (118), (119), (123), (126), (132), (138) are
% 177.58/28.07  | | | | | | | | | |            inconsistent by sub-proof #803.
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | |   (139)   ~ (all_56_11 = e3)
% 177.58/28.07  | | | | | | | | | |   (140)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | REDUCE: (7), (139) imply:
% 177.58/28.07  | | | | | | | | | |   (141)   ~ (all_52_23 = e3)
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | BETA: splitting (134) gives:
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | |   (142)  all_56_10 = e2
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | COMBINE_EQS: (67), (142) imply:
% 177.58/28.07  | | | | | | | | | | |   (143)  all_14_2 = e2
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | REDUCE: (118), (143) imply:
% 177.58/28.07  | | | | | | | | | | |   (144)  $false
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | |   (145)   ~ (all_56_10 = e2)
% 177.58/28.07  | | | | | | | | | | |   (146)  all_56_10 = e1 | all_56_10 = e0
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | BETA: splitting (132) gives:
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | |   (147)  all_58_7 = e2
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | REF_CLOSE: (119), (123), (147) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | | | | |            #891.
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | |   (148)  all_58_8 = e2 | all_58_11 = e2
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | BETA: splitting (146) gives:
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | |   (149)  all_56_10 = e1
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | REF_CLOSE: (67), (130), (149) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | | | | | |            #740.
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | |   (150)  all_56_10 = e0
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | COMBINE_EQS: (67), (150) imply:
% 177.58/28.07  | | | | | | | | | | | | |   (151)  all_14_2 = e0
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | SIMP: (151) implies:
% 177.58/28.07  | | | | | | | | | | | | |   (152)  all_14_2 = e0
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | REDUCE: (118), (152) imply:
% 177.58/28.07  | | | | | | | | | | | | |   (153)   ~ (e2 = e0)
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | SIMP: (153) implies:
% 177.58/28.07  | | | | | | | | | | | | |   (154)   ~ (e2 = e0)
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | REDUCE: (37), (152) imply:
% 177.58/28.07  | | | | | | | | | | | | |   (155)  op(e1, e0) = e3
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | BETA: splitting (140) gives:
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | |   (156)  all_56_11 = e2
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | COMBINE_EQS: (7), (156) imply:
% 177.58/28.07  | | | | | | | | | | | | | |   (157)  all_52_23 = e2
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | SIMP: (157) implies:
% 177.58/28.07  | | | | | | | | | | | | | |   (158)  all_52_23 = e2
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | REDUCE: (141), (158) imply:
% 177.58/28.07  | | | | | | | | | | | | | |   (159)   ~ (e3 = e2)
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | REDUCE: (47), (158) imply:
% 177.58/28.07  | | | | | | | | | | | | | |   (160)  op(e1, e0) = e2
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | REF_CLOSE: (75), (126), (155), (160) are inconsistent by
% 177.58/28.07  | | | | | | | | | | | | | |            sub-proof #551.
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | |   (161)  all_56_11 = e1 | all_56_11 = e0
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | |   (162)  all_56_11 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | COMBINE_EQS: (7), (162) imply:
% 177.58/28.07  | | | | | | | | | | | | | | |   (163)  all_52_23 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | SIMP: (163) implies:
% 177.58/28.07  | | | | | | | | | | | | | | |   (164)  all_52_23 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | REDUCE: (128), (164) imply:
% 177.58/28.07  | | | | | | | | | | | | | | |   (165)  $false
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | |   (166)  all_56_11 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | COMBINE_EQS: (7), (166) imply:
% 177.58/28.07  | | | | | | | | | | | | | | |   (167)  all_52_23 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | SIMP: (167) implies:
% 177.58/28.07  | | | | | | | | | | | | | | |   (168)  all_52_23 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | COMBINE_EQS: (57), (168) imply:
% 177.58/28.07  | | | | | | | | | | | | | | |   (169)  all_58_11 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | REF_CLOSE: (35), (118), (148), (154), (169) are inconsistent
% 177.58/28.07  | | | | | | | | | | | | | | |            by sub-proof #890.
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | End of split
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | Case 2:
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | |   (170)  all_56_14 = e1 | all_56_14 = e0
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REF_CLOSE: (36), (64), (109), (170) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | |            #886.
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | End of split
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | End of split
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | Case 2:
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | |   (171)  all_56_12 = e0
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | COMBINE_EQS: (48), (171) imply:
% 177.58/28.07  | | | | |   (172)  all_52_25 = e0
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (52), (172) imply:
% 177.58/28.07  | | | | |   (173)  $false
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | CLOSE: (173) is inconsistent.
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | End of split
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | End of split
% 177.58/28.07  | | | 
% 177.58/28.07  | | End of split
% 177.58/28.07  | | 
% 177.58/28.07  | Case 2:
% 177.58/28.07  | | 
% 177.58/28.07  | |   (174)   ~ (all_56_13 = e3)
% 177.58/28.07  | | 
% 177.58/28.07  | | REDUCE: (85), (174) imply:
% 177.58/28.07  | |   (175)   ~ (all_52_27 = e3)
% 177.58/28.07  | | 
% 177.58/28.07  | | BETA: splitting (34) gives:
% 177.58/28.07  | | 
% 177.58/28.07  | | Case 1:
% 177.58/28.07  | | | 
% 177.58/28.07  | | |   (176)  all_58_12 = e3
% 177.58/28.07  | | | 
% 177.58/28.07  | | | REF_CLOSE: (60), (72), (74), (75), (82), (176) are inconsistent by
% 177.58/28.07  | | |            sub-proof #884.
% 177.58/28.07  | | | 
% 177.58/28.07  | | Case 2:
% 177.58/28.07  | | | 
% 177.58/28.07  | | |   (177)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.07  | | | 
% 177.58/28.07  | | | BETA: splitting (177) gives:
% 177.58/28.07  | | | 
% 177.58/28.07  | | | Case 1:
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | |   (178)  all_58_13 = e3
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | REF_CLOSE: (49), (175), (178) are inconsistent by sub-proof #1026.
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | Case 2:
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | |   (179)  all_58_14 = e3 | all_58_15 = e3
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | BETA: splitting (179) gives:
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | | Case 1:
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | |   (180)  all_58_14 = e3
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | COMBINE_EQS: (31), (180) imply:
% 177.58/28.07  | | | | |   (181)  all_52_29 = e3
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | SIMP: (181) implies:
% 177.58/28.07  | | | | |   (182)  all_52_29 = e3
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (12), (182) imply:
% 177.58/28.07  | | | | |   (183)   ~ (all_52_25 = e3)
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (59), (182) imply:
% 177.58/28.07  | | | | |   (184)   ~ (all_14_2 = e3)
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | SIMP: (184) implies:
% 177.58/28.07  | | | | |   (185)   ~ (all_14_2 = e3)
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (38), (182) imply:
% 177.58/28.07  | | | | |   (186)  op(e1, e3) = e1
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | GROUND_INST: instantiating (75) with all_52_17, e1, e3, e1,
% 177.58/28.07  | | | | |              simplifying with (70), (186) gives:
% 177.58/28.07  | | | | |   (187)  all_52_17 = e1
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | COMBINE_EQS: (54), (187) imply:
% 177.58/28.07  | | | | |   (188)  all_58_6 = e1
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (18), (187) imply:
% 177.58/28.07  | | | | |   (189)   ~ (all_52_25 = e1)
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | SIMP: (189) implies:
% 177.58/28.07  | | | | |   (190)   ~ (all_52_25 = e1)
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REDUCE: (42), (187) imply:
% 177.58/28.07  | | | | |   (191)  op(e3, e1) = all_52_16
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | BETA: splitting (44) gives:
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | Case 1:
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | |   (192)  all_56_12 = e3
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | COMBINE_EQS: (48), (192) imply:
% 177.58/28.07  | | | | | |   (193)  all_52_25 = e3
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | REDUCE: (183), (193) imply:
% 177.58/28.07  | | | | | |   (194)  $false
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | CLOSE: (194) is inconsistent.
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | Case 2:
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | |   (195)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | BETA: splitting (63) gives:
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | | Case 1:
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | |   (196)  all_58_12 = e1
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | REF_CLOSE: (82), (190), (196) are inconsistent by sub-proof #883.
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | Case 2:
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | |   (197)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | BETA: splitting (197) gives:
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | |   (198)  all_58_13 = e1
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | COMBINE_EQS: (49), (198) imply:
% 177.58/28.07  | | | | | | | |   (199)  all_52_27 = e1
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | SIMP: (199) implies:
% 177.58/28.07  | | | | | | | |   (200)  all_52_27 = e1
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | REDUCE: (40), (200) imply:
% 177.58/28.07  | | | | | | | |   (201)   ~ (all_52_3 = e1)
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | REDUCE: (77), (200) imply:
% 177.58/28.07  | | | | | | | |   (202)   ~ (all_52_19 = e1)
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | REDUCE: (2), (200) imply:
% 177.58/28.07  | | | | | | | |   (203)   ~ (all_10_2 = e1)
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | SIMP: (203) implies:
% 177.58/28.07  | | | | | | | |   (204)   ~ (all_10_2 = e1)
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | REDUCE: (26), (200) imply:
% 177.58/28.07  | | | | | | | |   (205)  op(e2, e1) = e2
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | BETA: splitting (195) gives:
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | |   (206)  all_56_12 = e2
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | COMBINE_EQS: (48), (206) imply:
% 177.58/28.07  | | | | | | | | |   (207)  all_52_25 = e2
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | SIMP: (207) implies:
% 177.58/28.07  | | | | | | | | |   (208)  all_52_25 = e2
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (72), (208) imply:
% 177.58/28.07  | | | | | | | | |   (209)   ~ (all_4_2 = e2)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | SIMP: (209) implies:
% 177.58/28.07  | | | | | | | | |   (210)   ~ (all_4_2 = e2)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (190), (208) imply:
% 177.58/28.07  | | | | | | | | |   (211)   ~ (e2 = e1)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (60), (208) imply:
% 177.58/28.07  | | | | | | | | |   (212)  op(e3, e2) = e3
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | GROUND_INST: instantiating (75) with all_52_13, e2, e1, e2,
% 177.58/28.07  | | | | | | | | |              simplifying with (33), (205) gives:
% 177.58/28.07  | | | | | | | | |   (213)  all_52_13 = e2
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | GROUND_INST: instantiating (75) with all_52_5, all_52_16, e1,
% 177.58/28.07  | | | | | | | | |              e3, simplifying with (66), (191) gives:
% 177.58/28.07  | | | | | | | | |   (214)  all_52_5 = all_52_16
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | GROUND_INST: instantiating (75) with all_52_3, e3, e2, e3,
% 177.58/28.07  | | | | | | | | |              simplifying with (4), (212) gives:
% 177.58/28.07  | | | | | | | | |   (215)  all_52_3 = e3
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | COMBINE_EQS: (11), (213) imply:
% 177.58/28.07  | | | | | | | | |   (216)  all_58_5 = e2
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | COMBINE_EQS: (19), (214) imply:
% 177.58/28.07  | | | | | | | | |   (217)  all_58_4 = all_52_16
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (58), (215) imply:
% 177.58/28.07  | | | | | | | | |   (218)   ~ (all_52_19 = e3)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | SIMP: (218) implies:
% 177.58/28.07  | | | | | | | | |   (219)   ~ (all_52_19 = e3)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (10), (215) imply:
% 177.58/28.07  | | | | | | | | |   (220)   ~ (all_10_2 = e3)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | SIMP: (220) implies:
% 177.58/28.07  | | | | | | | | |   (221)   ~ (all_10_2 = e3)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (41), (215) imply:
% 177.58/28.07  | | | | | | | | |   (222)   ~ (all_4_2 = e3)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | SIMP: (222) implies:
% 177.58/28.07  | | | | | | | | |   (223)   ~ (all_4_2 = e3)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (15), (214) imply:
% 177.58/28.07  | | | | | | | | |   (224)   ~ (all_52_7 = all_52_16)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | SIMP: (224) implies:
% 177.58/28.07  | | | | | | | | |   (225)   ~ (all_52_7 = all_52_16)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (16), (214) imply:
% 177.58/28.07  | | | | | | | | |   (226)   ~ (all_52_16 = all_4_2)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REDUCE: (79), (213) imply:
% 177.58/28.07  | | | | | | | | |   (227)   ~ (all_10_2 = e2)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | SIMP: (227) implies:
% 177.58/28.07  | | | | | | | | |   (228)   ~ (all_10_2 = e2)
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | BETA: splitting (14) gives:
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | |   (229)  all_56_0 = e3
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | COMBINE_EQS: (56), (229) imply:
% 177.58/28.07  | | | | | | | | | |   (230)  all_4_2 = e3
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | REDUCE: (223), (230) imply:
% 177.58/28.07  | | | | | | | | | |   (231)  $false
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | CLOSE: (231) is inconsistent.
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | |   (232)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | BETA: splitting (20) gives:
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | |   (233)  all_58_6 = e3
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | COMBINE_EQS: (188), (233) imply:
% 177.58/28.07  | | | | | | | | | | |   (234)  e3 = e1
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | REDUCE: (21), (234) imply:
% 177.58/28.07  | | | | | | | | | | |   (235)  $false
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | |   (236)   ~ (all_58_6 = e3)
% 177.58/28.07  | | | | | | | | | | |   (237)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | REDUCE: (188), (236) imply:
% 177.58/28.07  | | | | | | | | | | |   (238)   ~ (e3 = e1)
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | BETA: splitting (68) gives:
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | |   (239)  all_56_5 = e3
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | REF_CLOSE: (50), (221), (239) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | | | | |            #895.
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | |   (240)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | BETA: splitting (240) gives:
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | |   (241)  all_56_5 = e2
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | REF_CLOSE: (50), (228), (241) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | | | | | |            #710.
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | |   (242)  all_56_5 = e1 | all_56_5 = e0
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | BETA: splitting (242) gives:
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | |   (243)  all_56_5 = e1
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | REF_CLOSE: (50), (204), (243) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | | | | | | |            #709.
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | |   (244)  all_56_5 = e0
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | COMBINE_EQS: (50), (244) imply:
% 177.58/28.07  | | | | | | | | | | | | | |   (245)  all_10_2 = e0
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | SIMP: (245) implies:
% 177.58/28.07  | | | | | | | | | | | | | |   (246)  all_10_2 = e0
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | REDUCE: (61), (246) imply:
% 177.58/28.07  | | | | | | | | | | | | | |   (247)   ~ (all_52_19 = e0)
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | |   (248)  all_56_9 = e3
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | REF_CLOSE: (13), (219), (248) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | | | | | | | |            #700.
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | |   (249)   ~ (all_56_9 = e3)
% 177.58/28.07  | | | | | | | | | | | | | | |   (250)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | |   (251)  all_58_4 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | COMBINE_EQS: (217), (251) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | |   (252)  all_52_16 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | REDUCE: (225), (252) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | |   (253)   ~ (all_52_7 = e1)
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | REDUCE: (226), (252) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | |   (254)   ~ (all_4_2 = e1)
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | SIMP: (254) implies:
% 177.58/28.07  | | | | | | | | | | | | | | | |   (255)   ~ (all_4_2 = e1)
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (256)  all_58_0 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (256) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (257)  all_4_2 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | REDUCE: (24), (257) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (258)   ~ (all_52_7 = e0)
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | REDUCE: (255), (257) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (259)   ~ (e1 = e0)
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | REDUCE: (23), (257) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (260)  op(e3, e0) = all_4_1
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | |   (261)  all_56_9 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (261) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | |   (262)  all_52_19 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | SIMP: (262) implies:
% 177.58/28.07  | | | | | | | | | | | | | | | | | |   (263)  all_52_19 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (263) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | |   (264)  all_58_7 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |   (265)  all_56_11 = e3
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7), (265) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |   (266)  all_52_23 = e3
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | SIMP: (266) implies:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |   (267)  all_52_23 = e3
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (267) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |   (268)  all_58_11 = e3
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | REDUCE: (78), (267) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |   (269)   ~ (all_52_7 = e3)
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | |   (270)  all_58_6 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (188), (270) are inconsistent by sub-proof
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | |            #426.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | |   (271)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | |   (272)  all_56_3 = e3
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (272) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | |   (273)  all_52_7 = e3
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (273) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | |   (274)  $false
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | CLOSE: (274) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | |   (275)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | |   (276)  all_56_3 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (276) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | |   (277)  all_52_7 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (277) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | |   (278)   ~ (e2 = e0)
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (277) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | |   (279)  op(e3, e0) = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_58_7 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (280) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | |   (281)  e2 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (278), (281) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | |   (282)  $false
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (282) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_58_8 = e0 | all_58_11 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_58_8 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (284) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_14_2 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (285) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (286)  op(e3, e0) = all_14_0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with all_4_1, all_14_0, e0, e3,
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (260), (286) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_14_0 = all_4_1
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (75) with e2, all_14_0, e0, e3,
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (279), (286) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_14_0 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (288) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_4_1 = e2
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (289) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (290)  $false
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (290) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_58_11 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (291) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (292)  e3 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (292) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | |   (293)  $false
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (293) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | |   (294)  all_56_3 = e1 | all_56_3 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (253), (258), (294) are inconsistent by
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1037.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |   (295)   ~ (all_56_11 = e3)
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | REDUCE: (7), (295) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |   (296)   ~ (all_52_23 = e3)
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (35), (57), (185), (219), (237), (296) are
% 177.58/28.07  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #996.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | |   (297)  all_56_9 = e1 | all_56_9 = e0
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (202), (247), (297) are inconsistent by
% 177.58/28.07  | | | | | | | | | | | | | | | | | |            sub-proof #688.
% 177.58/28.07  | | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (298)   ~ (all_58_0 = e0)
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | REDUCE: (25), (298) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (299)   ~ (all_4_2 = e0)
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (210), (232), (255), (299) are inconsistent
% 177.58/28.07  | | | | | | | | | | | | | | | | |            by sub-proof #882.
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | |   (300)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | Case 1:
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (301)  all_58_5 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | COMBINE_EQS: (216), (301) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (302)  e2 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | REDUCE: (211), (302) imply:
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (303)  $false
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent.
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | |   (304)  all_58_8 = e1 | all_58_14 = e1
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (35), (37), (69), (75), (180), (185), (304)
% 177.58/28.07  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #423.
% 177.58/28.07  | | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | |   (305)  all_56_12 = e1 | all_56_12 = e0
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | | REF_CLOSE: (48), (52), (190), (305) are inconsistent by
% 177.58/28.07  | | | | | | | | |            sub-proof #1029.
% 177.58/28.07  | | | | | | | | | 
% 177.58/28.07  | | | | | | | | End of split
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | Case 2:
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | |   (306)  all_58_14 = e1 | all_58_15 = e1
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | | REF_CLOSE: (21), (55), (62), (180), (306) are inconsistent by
% 177.58/28.07  | | | | | | | |            sub-proof #880.
% 177.58/28.07  | | | | | | | | 
% 177.58/28.07  | | | | | | | End of split
% 177.58/28.07  | | | | | | | 
% 177.58/28.07  | | | | | | End of split
% 177.58/28.07  | | | | | | 
% 177.58/28.07  | | | | | End of split
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | Case 2:
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | |   (307)  all_58_15 = e3
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | | REF_CLOSE: (43), (62), (307) are inconsistent by sub-proof #1010.
% 177.58/28.07  | | | | | 
% 177.58/28.07  | | | | End of split
% 177.58/28.07  | | | | 
% 177.58/28.07  | | | End of split
% 177.58/28.07  | | | 
% 177.58/28.07  | | End of split
% 177.58/28.07  | | 
% 177.58/28.07  | End of split
% 177.58/28.07  | 
% 177.58/28.07  End of proof
% 177.58/28.07  
% 177.58/28.07  Sub-proof #423 shows that the following formulas are inconsistent:
% 177.58/28.07  ----------------------------------------------------------------
% 177.58/28.07    (1)   ~ (e3 = e1)
% 177.58/28.07    (2)  all_58_8 = all_14_2
% 177.58/28.07    (3)  op(e1, all_14_2) = e3
% 177.58/28.07    (4)  all_58_8 = e1 | all_58_14 = e1
% 177.58/28.07    (5)  op(e1, e1) = all_14_2
% 177.58/28.07    (6)   ~ (all_14_2 = e3)
% 177.58/28.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.07    (8)  all_58_14 = e3
% 177.58/28.07  
% 177.58/28.07  Begin of proof
% 177.58/28.07  | 
% 177.58/28.07  | BETA: splitting (4) gives:
% 177.58/28.07  | 
% 177.58/28.07  | Case 1:
% 177.58/28.07  | | 
% 177.58/28.07  | |   (9)  all_58_8 = e1
% 177.58/28.08  | | 
% 177.58/28.08  | | COMBINE_EQS: (2), (9) imply:
% 177.58/28.08  | |   (10)  all_14_2 = e1
% 177.58/28.08  | | 
% 177.58/28.08  | | REF_CLOSE: (3), (5), (6), (7), (10) are inconsistent by sub-proof #424.
% 177.58/28.08  | | 
% 177.58/28.08  | Case 2:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (11)  all_58_14 = e1
% 177.58/28.08  | | 
% 177.58/28.08  | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #881.
% 177.58/28.08  | | 
% 177.58/28.08  | End of split
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #424 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)  all_14_2 = e1
% 177.58/28.08    (2)  op(e1, all_14_2) = e3
% 177.58/28.08    (3)  op(e1, e1) = all_14_2
% 177.58/28.08    (4)   ~ (all_14_2 = e3)
% 177.58/28.08    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (1), (4) imply:
% 177.58/28.08  |   (6)   ~ (e3 = e1)
% 177.58/28.08  | 
% 177.58/28.08  | SIMP: (6) implies:
% 177.58/28.08  |   (7)   ~ (e3 = e1)
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (1), (2) imply:
% 177.58/28.08  |   (8)  op(e1, e1) = e3
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (1), (3) imply:
% 177.58/28.08  |   (9)  op(e1, e1) = e1
% 177.58/28.08  | 
% 177.58/28.08  | REF_CLOSE: (5), (7), (8), (9) are inconsistent by sub-proof #425.
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #425 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.08    (2)  op(e1, e1) = e3
% 177.58/28.08    (3)  op(e1, e1) = e1
% 177.58/28.08    (4)   ~ (e3 = e1)
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | GROUND_INST: instantiating (1) with e1, e3, e1, e1, simplifying with (2), (3)
% 177.58/28.08  |              gives:
% 177.58/28.08  |   (5)  e3 = e1
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (4), (5) imply:
% 177.58/28.08  |   (6)  $false
% 177.58/28.08  | 
% 177.58/28.08  | CLOSE: (6) is inconsistent.
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #426 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)  all_58_6 = e1
% 177.58/28.08    (2)  all_58_6 = e0
% 177.58/28.08    (3)   ~ (e1 = e0)
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | COMBINE_EQS: (1), (2) imply:
% 177.58/28.08  |   (4)  e1 = e0
% 177.58/28.08  | 
% 177.58/28.08  | SIMP: (4) implies:
% 177.58/28.08  |   (5)  e1 = e0
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (3), (5) imply:
% 177.58/28.08  |   (6)  $false
% 177.58/28.08  | 
% 177.58/28.08  | CLOSE: (6) is inconsistent.
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #427 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.58/28.08    (2)  all_52_20 = e3
% 177.58/28.08    (3)   ~ (e3 = e1)
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | ALPHA: (1) implies:
% 177.58/28.08  |   (4)  all_52_20 = e1
% 177.58/28.08  | 
% 177.58/28.08  | COMBINE_EQS: (2), (4) imply:
% 177.58/28.08  |   (5)  e3 = e1
% 177.58/28.08  | 
% 177.58/28.08  | SIMP: (5) implies:
% 177.58/28.08  |   (6)  e3 = e1
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (3), (6) imply:
% 177.58/28.08  |   (7)  $false
% 177.58/28.08  | 
% 177.58/28.08  | CLOSE: (7) is inconsistent.
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #428 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.08    (2)   ~ (all_52_27 = all_10_2)
% 177.58/28.08    (3)   ~ (all_52_17 = all_52_23)
% 177.58/28.08    (4)  op(e3, e2) = all_52_3
% 177.58/28.08    (5)  all_56_11 = all_52_23
% 177.58/28.08    (6)   ~ (all_52_27 = e0)
% 177.58/28.08    (7)   ~ (all_52_17 = e3)
% 177.58/28.08    (8)   ~ (all_52_23 = e0)
% 177.58/28.08    (9)   ~ (all_52_3 = all_10_2)
% 177.58/28.08    (10)  all_58_5 = all_52_13
% 177.58/28.08    (11)  op(e1, all_52_13) = e1
% 177.58/28.08    (12)  op(e0, all_52_15) = e0
% 177.58/28.08    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.08    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.08    (15)  all_58_3 = all_10_2
% 177.58/28.08    (16)   ~ (all_52_9 = all_4_2)
% 177.58/28.08    (17)  all_58_10 = all_52_15
% 177.58/28.08    (18)  all_58_7 = all_52_19
% 177.58/28.08    (19)  op(e0, e1) = all_52_29
% 177.58/28.08    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.08    (21)   ~ (e3 = e1)
% 177.58/28.08    (22)   ~ (all_52_17 = all_14_2)
% 177.58/28.08    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.08    (24)  all_58_1 = all_52_3
% 177.58/28.08    (25)  all_58_0 = all_4_2
% 177.58/28.08    (26)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.08    (27)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.58/28.08    (28)  op(e0, e3) = e3
% 177.58/28.08    (29)  all_58_8 = all_14_2
% 177.58/28.08    (30)  op(e0, e2) = all_52_27
% 177.58/28.08    (31)  op(e1, all_14_2) = e3
% 177.58/28.08    (32)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.08    (33)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.58/28.08    (34)   ~ (all_52_13 = all_14_2)
% 177.58/28.08    (35)  op(e3, all_52_9) = e3
% 177.58/28.08    (36)   ~ (e3 = e0)
% 177.58/28.08    (37)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.08    (38)  op(e1, e0) = all_52_23
% 177.58/28.08    (39)  all_58_13 = all_52_27
% 177.58/28.08    (40)  all_58_12 = e3
% 177.58/28.08    (41)  all_58_6 = all_52_17
% 177.58/28.08    (42)   ~ (all_52_3 = all_52_7)
% 177.58/28.08    (43)  op(e2, all_52_19) = all_52_18
% 177.58/28.08    (44)   ~ (e1 = e0)
% 177.58/28.08    (45)  all_58_11 = all_52_23
% 177.58/28.08    (46)   ~ (all_52_3 = all_52_19)
% 177.58/28.08    (47)   ~ (all_52_7 = all_52_15)
% 177.58/28.08    (48)   ~ (all_52_19 = all_10_2)
% 177.58/28.08    (49)  all_58_15 = e0
% 177.58/28.08    (50)   ~ (all_52_9 = e3)
% 177.58/28.08    (51)  all_58_2 = all_52_9
% 177.58/28.08    (52)   ~ (all_52_29 = e0)
% 177.58/28.08    (53)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.08    (54)   ~ (e2 = e1)
% 177.58/28.08    (55)  all_56_10 = all_14_2
% 177.58/28.08    (56)  op(e1, e3) = all_52_17
% 177.58/28.08    (57)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.08    (58)  op(e2, all_10_2) = e2
% 177.58/28.08    (59)  op(e3, e3) = all_4_2
% 177.58/28.08    (60)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.08            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.08    (61)  all_56_7 = all_52_15
% 177.58/28.08    (62)   ~ (all_52_15 = e0)
% 177.58/28.08    (63)   ~ (all_52_7 = all_52_23)
% 177.58/28.08    (64)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.08    (65)  all_58_9 = all_52_7
% 177.58/28.08    (66)   ~ (e2 = e0)
% 177.58/28.08    (67)  all_56_6 = all_52_13
% 177.58/28.08    (68)   ~ (e3 = e2)
% 177.58/28.08    (69)  op(e2, e3) = all_52_9
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | BETA: splitting (57) gives:
% 177.58/28.08  | 
% 177.58/28.08  | Case 1:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (70)  all_56_7 = e3
% 177.58/28.08  | | 
% 177.58/28.08  | | COMBINE_EQS: (61), (70) imply:
% 177.58/28.08  | |   (71)  all_52_15 = e3
% 177.58/28.08  | | 
% 177.58/28.08  | | REF_CLOSE: (12), (28), (60), (62), (71) are inconsistent by sub-proof #971.
% 177.58/28.08  | | 
% 177.58/28.08  | Case 2:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (72)   ~ (all_56_7 = e3)
% 177.58/28.08  | | 
% 177.58/28.08  | | REDUCE: (61), (72) imply:
% 177.58/28.08  | |   (73)   ~ (all_52_15 = e3)
% 177.58/28.08  | | 
% 177.58/28.08  | | BETA: splitting (64) gives:
% 177.58/28.08  | | 
% 177.58/28.08  | | Case 1:
% 177.58/28.08  | | | 
% 177.58/28.08  | | |   (74)  all_58_9 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | COMBINE_EQS: (65), (74) imply:
% 177.58/28.08  | | |   (75)  all_52_7 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | SIMP: (75) implies:
% 177.58/28.08  | | |   (76)  all_52_7 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REDUCE: (42), (76) imply:
% 177.58/28.08  | | |   (77)   ~ (all_52_3 = e3)
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REDUCE: (47), (76) imply:
% 177.58/28.08  | | |   (78)   ~ (all_52_15 = e3)
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REDUCE: (63), (76) imply:
% 177.58/28.08  | | |   (79)   ~ (all_52_23 = e3)
% 177.58/28.08  | | | 
% 177.58/28.08  | | | SIMP: (79) implies:
% 177.58/28.08  | | |   (80)   ~ (all_52_23 = e3)
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (15),
% 177.58/28.08  | | |            (16), (17), (18), (20), (22), (23), (24), (25), (26), (27),
% 177.58/28.08  | | |            (29), (31), (32), (34), (35), (37), (38), (39), (40), (41),
% 177.58/28.08  | | |            (43), (45), (46), (48), (50), (51), (53), (54), (55), (56),
% 177.58/28.08  | | |            (58), (59), (60), (67), (68), (69), (73), (77), (80) are
% 177.58/28.08  | | |            inconsistent by sub-proof #429.
% 177.58/28.08  | | | 
% 177.58/28.08  | | Case 2:
% 177.58/28.08  | | | 
% 177.58/28.08  | | |   (81)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REF_CLOSE: (6), (12), (14), (17), (19), (21), (30), (33), (36), (44),
% 177.58/28.08  | | |            (49), (52), (54), (60), (66), (68), (73), (81) are inconsistent
% 177.58/28.08  | | |            by sub-proof #985.
% 177.58/28.08  | | | 
% 177.58/28.08  | | End of split
% 177.58/28.08  | | 
% 177.58/28.08  | End of split
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #429 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.08    (2)   ~ (all_52_27 = all_10_2)
% 177.58/28.08    (3)   ~ (all_52_17 = all_52_23)
% 177.58/28.08    (4)  op(e3, e2) = all_52_3
% 177.58/28.08    (5)  all_56_11 = all_52_23
% 177.58/28.08    (6)   ~ (all_52_17 = e3)
% 177.58/28.08    (7)   ~ (all_52_23 = e0)
% 177.58/28.08    (8)   ~ (all_52_3 = all_10_2)
% 177.58/28.08    (9)  all_58_5 = all_52_13
% 177.58/28.08    (10)  op(e1, all_52_13) = e1
% 177.58/28.08    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.08    (12)  all_58_3 = all_10_2
% 177.58/28.08    (13)   ~ (all_52_9 = all_4_2)
% 177.58/28.08    (14)  all_58_10 = all_52_15
% 177.58/28.08    (15)  all_58_7 = all_52_19
% 177.58/28.08    (16)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.08    (17)   ~ (all_52_17 = all_14_2)
% 177.58/28.08    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.08    (19)  all_58_1 = all_52_3
% 177.58/28.08    (20)  all_58_0 = all_4_2
% 177.58/28.08    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.08    (22)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.58/28.08    (23)  all_58_8 = all_14_2
% 177.58/28.08    (24)  op(e1, all_14_2) = e3
% 177.58/28.08    (25)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.08    (26)   ~ (all_52_23 = e3)
% 177.58/28.08    (27)   ~ (all_52_13 = all_14_2)
% 177.58/28.08    (28)  op(e3, all_52_9) = e3
% 177.58/28.08    (29)   ~ (all_52_15 = e3)
% 177.58/28.08    (30)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.08    (31)  op(e1, e0) = all_52_23
% 177.58/28.08    (32)  all_58_13 = all_52_27
% 177.58/28.08    (33)   ~ (all_52_3 = e3)
% 177.58/28.08    (34)  all_58_12 = e3
% 177.58/28.08    (35)  all_58_6 = all_52_17
% 177.58/28.08    (36)  op(e2, all_52_19) = all_52_18
% 177.58/28.08    (37)  all_58_11 = all_52_23
% 177.58/28.08    (38)   ~ (all_52_3 = all_52_19)
% 177.58/28.08    (39)   ~ (all_52_19 = all_10_2)
% 177.58/28.08    (40)   ~ (all_52_9 = e3)
% 177.58/28.08    (41)  all_58_2 = all_52_9
% 177.58/28.08    (42)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.08    (43)   ~ (e2 = e1)
% 177.58/28.08    (44)  all_56_10 = all_14_2
% 177.58/28.08    (45)  op(e1, e3) = all_52_17
% 177.58/28.08    (46)  op(e2, all_10_2) = e2
% 177.58/28.08    (47)  op(e3, e3) = all_4_2
% 177.58/28.08    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.08            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.08    (49)  all_56_6 = all_52_13
% 177.58/28.08    (50)   ~ (e3 = e2)
% 177.58/28.08    (51)  op(e2, e3) = all_52_9
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | BETA: splitting (42) gives:
% 177.58/28.08  | 
% 177.58/28.08  | Case 1:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (52)  all_56_11 = e3
% 177.58/28.08  | | 
% 177.58/28.08  | | COMBINE_EQS: (5), (52) imply:
% 177.58/28.08  | |   (53)  all_52_23 = e3
% 177.58/28.08  | | 
% 177.58/28.08  | | REDUCE: (26), (53) imply:
% 177.58/28.08  | |   (54)  $false
% 177.58/28.08  | | 
% 177.58/28.08  | | CLOSE: (54) is inconsistent.
% 177.58/28.08  | | 
% 177.58/28.08  | Case 2:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (55)   ~ (all_56_11 = e3)
% 177.58/28.08  | |   (56)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.08  | | 
% 177.58/28.08  | | BETA: splitting (21) gives:
% 177.58/28.08  | | 
% 177.58/28.08  | | Case 1:
% 177.58/28.08  | | | 
% 177.58/28.08  | | |   (57)  all_58_1 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | COMBINE_EQS: (19), (57) imply:
% 177.58/28.08  | | |   (58)  all_52_3 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REDUCE: (33), (58) imply:
% 177.58/28.08  | | |   (59)  $false
% 177.58/28.08  | | | 
% 177.58/28.08  | | | CLOSE: (59) is inconsistent.
% 177.58/28.08  | | | 
% 177.58/28.08  | | Case 2:
% 177.58/28.08  | | | 
% 177.58/28.08  | | |   (60)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | BETA: splitting (18) gives:
% 177.58/28.08  | | | 
% 177.58/28.08  | | | Case 1:
% 177.58/28.08  | | | | 
% 177.58/28.08  | | | |   (61)  all_58_2 = e3
% 177.58/28.08  | | | | 
% 177.58/28.08  | | | | REF_CLOSE: (40), (41), (61) are inconsistent by sub-proof #980.
% 177.58/28.08  | | | | 
% 177.58/28.08  | | | Case 2:
% 177.58/28.08  | | | | 
% 177.58/28.08  | | | |   (62)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.08  | | | | 
% 177.58/28.08  | | | | BETA: splitting (16) gives:
% 177.58/28.08  | | | | 
% 177.58/28.08  | | | | Case 1:
% 177.58/28.08  | | | | | 
% 177.58/28.08  | | | | |   (63)  all_58_6 = e3
% 177.58/28.08  | | | | | 
% 177.58/28.08  | | | | | REF_CLOSE: (6), (35), (63) are inconsistent by sub-proof #981.
% 177.58/28.08  | | | | | 
% 177.58/28.08  | | | | Case 2:
% 177.58/28.08  | | | | | 
% 177.58/28.08  | | | | |   (64)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.08  | | | | | 
% 177.58/28.08  | | | | | BETA: splitting (25) gives:
% 177.58/28.08  | | | | | 
% 177.58/28.08  | | | | | Case 1:
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | |   (65)  all_58_0 = e2
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | | COMBINE_EQS: (20), (65) imply:
% 177.58/28.08  | | | | | |   (66)  all_4_2 = e2
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | | REDUCE: (13), (66) imply:
% 177.58/28.08  | | | | | |   (67)   ~ (all_52_9 = e2)
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | | BETA: splitting (22) gives:
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | | Case 1:
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | |   (68)  all_56_6 = e3
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | COMBINE_EQS: (49), (68) imply:
% 177.58/28.08  | | | | | | |   (69)  all_52_13 = e3
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | SIMP: (69) implies:
% 177.58/28.08  | | | | | | |   (70)  all_52_13 = e3
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REDUCE: (27), (70) imply:
% 177.58/28.08  | | | | | | |   (71)   ~ (all_14_2 = e3)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | SIMP: (71) implies:
% 177.58/28.08  | | | | | | |   (72)   ~ (all_14_2 = e3)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REDUCE: (10), (70) imply:
% 177.58/28.08  | | | | | | |   (73)  op(e1, e3) = e1
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | GROUND_INST: instantiating (48) with all_52_17, e1, e3, e1,
% 177.58/28.08  | | | | | | |              simplifying with (45), (73) gives:
% 177.58/28.08  | | | | | | |   (74)  all_52_17 = e1
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REDUCE: (3), (74) imply:
% 177.58/28.08  | | | | | | |   (75)   ~ (all_52_23 = e1)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | SIMP: (75) implies:
% 177.58/28.08  | | | | | | |   (76)   ~ (all_52_23 = e1)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REDUCE: (17), (74) imply:
% 177.58/28.08  | | | | | | |   (77)   ~ (all_14_2 = e1)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | SIMP: (77) implies:
% 177.58/28.08  | | | | | | |   (78)   ~ (all_14_2 = e1)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | BETA: splitting (56) gives:
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | Case 1:
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | |   (79)  all_56_11 = e2
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | COMBINE_EQS: (5), (79) imply:
% 177.58/28.08  | | | | | | | |   (80)  all_52_23 = e2
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | REDUCE: (1), (80) imply:
% 177.58/28.08  | | | | | | | |   (81)   ~ (all_14_2 = e2)
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | SIMP: (81) implies:
% 177.58/28.08  | | | | | | | |   (82)   ~ (all_14_2 = e2)
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | REDUCE: (26), (80) imply:
% 177.58/28.08  | | | | | | | |   (83)   ~ (e3 = e2)
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | REDUCE: (31), (80) imply:
% 177.58/28.08  | | | | | | | |   (84)  op(e1, e0) = e2
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | BETA: splitting (30) gives:
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | Case 1:
% 177.58/28.08  | | | | | | | | | 
% 177.58/28.08  | | | | | | | | |   (85)  all_56_10 = e3
% 177.58/28.08  | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | REF_CLOSE: (44), (72), (85) are inconsistent by sub-proof
% 177.58/28.08  | | | | | | | | |            #552.
% 177.58/28.08  | | | | | | | | | 
% 177.58/28.08  | | | | | | | | Case 2:
% 177.58/28.08  | | | | | | | | | 
% 177.58/28.08  | | | | | | | | |   (86)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.08  | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | BETA: splitting (86) gives:
% 177.58/28.08  | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | Case 1:
% 177.58/28.08  | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | |   (87)  all_56_10 = e2
% 177.58/28.08  | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | REF_CLOSE: (44), (82), (87) are inconsistent by sub-proof
% 177.58/28.08  | | | | | | | | | |            #691.
% 177.58/28.08  | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | Case 2:
% 177.58/28.08  | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | |   (88)  all_56_10 = e1 | all_56_10 = e0
% 177.58/28.08  | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | BETA: splitting (88) gives:
% 177.58/28.08  | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | Case 1:
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | |   (89)  all_56_10 = e1
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | | REF_CLOSE: (44), (78), (89) are inconsistent by sub-proof
% 177.58/28.08  | | | | | | | | | | |            #740.
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | Case 2:
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | |   (90)  all_56_10 = e0
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | | COMBINE_EQS: (44), (90) imply:
% 177.58/28.08  | | | | | | | | | | |   (91)  all_14_2 = e0
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | | SIMP: (91) implies:
% 177.58/28.08  | | | | | | | | | | |   (92)  all_14_2 = e0
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | | REDUCE: (24), (92) imply:
% 177.58/28.08  | | | | | | | | | | |   (93)  op(e1, e0) = e3
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | | REF_CLOSE: (48), (50), (84), (93) are inconsistent by
% 177.58/28.08  | | | | | | | | | | |            sub-proof #551.
% 177.58/28.08  | | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | | End of split
% 177.58/28.08  | | | | | | | | | | 
% 177.58/28.08  | | | | | | | | | End of split
% 177.58/28.08  | | | | | | | | | 
% 177.58/28.08  | | | | | | | | End of split
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | Case 2:
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | |   (94)  all_56_11 = e1 | all_56_11 = e0
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | | REF_CLOSE: (5), (7), (76), (94) are inconsistent by sub-proof
% 177.58/28.08  | | | | | | | |            #431.
% 177.58/28.08  | | | | | | | | 
% 177.58/28.08  | | | | | | | End of split
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | Case 2:
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | |   (95)   ~ (all_56_6 = e3)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REDUCE: (49), (95) imply:
% 177.58/28.08  | | | | | | |   (96)   ~ (all_52_13 = e3)
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REF_CLOSE: (9), (12), (13), (14), (18), (28), (29), (41), (46),
% 177.58/28.08  | | | | | | |            (47), (48), (51), (67), (96) are inconsistent by
% 177.58/28.08  | | | | | | |            sub-proof #957.
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | End of split
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | Case 2:
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | |   (97)   ~ (all_58_0 = e2)
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | | REDUCE: (20), (97) imply:
% 177.58/28.08  | | | | | |   (98)   ~ (all_4_2 = e2)
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | | BETA: splitting (11) gives:
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | | Case 1:
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | |   (99)  all_58_0 = e2
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | COMBINE_EQS: (20), (99) imply:
% 177.58/28.08  | | | | | | |   (100)  all_4_2 = e2
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REDUCE: (98), (100) imply:
% 177.58/28.08  | | | | | | |   (101)  $false
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | CLOSE: (101) is inconsistent.
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | Case 2:
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | |   (102)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | | REF_CLOSE: (2), (4), (8), (9), (10), (12), (14), (15), (22), (23),
% 177.58/28.08  | | | | | | |            (26), (27), (28), (29), (32), (34), (35), (36), (37),
% 177.58/28.08  | | | | | | |            (38), (39), (41), (43), (45), (46), (48), (49), (50),
% 177.58/28.08  | | | | | | |            (51), (60), (62), (64), (102) are inconsistent by
% 177.58/28.08  | | | | | | |            sub-proof #430.
% 177.58/28.08  | | | | | | | 
% 177.58/28.08  | | | | | | End of split
% 177.58/28.08  | | | | | | 
% 177.58/28.08  | | | | | End of split
% 177.58/28.08  | | | | | 
% 177.58/28.08  | | | | End of split
% 177.58/28.08  | | | | 
% 177.58/28.08  | | | End of split
% 177.58/28.08  | | | 
% 177.58/28.08  | | End of split
% 177.58/28.08  | | 
% 177.58/28.08  | End of split
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #430 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)   ~ (all_52_27 = all_10_2)
% 177.58/28.08    (2)  op(e3, e2) = all_52_3
% 177.58/28.08    (3)   ~ (all_52_3 = all_10_2)
% 177.58/28.08    (4)  all_58_5 = all_52_13
% 177.58/28.08    (5)  op(e1, all_52_13) = e1
% 177.58/28.08    (6)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.08    (7)  all_58_3 = all_10_2
% 177.58/28.08    (8)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.08    (9)  all_58_10 = all_52_15
% 177.58/28.08    (10)  all_58_7 = all_52_19
% 177.58/28.08    (11)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.58/28.08    (12)  all_58_8 = all_14_2
% 177.58/28.08    (13)   ~ (all_52_23 = e3)
% 177.58/28.08    (14)   ~ (all_52_13 = all_14_2)
% 177.58/28.08    (15)  op(e3, all_52_9) = e3
% 177.58/28.08    (16)   ~ (all_52_15 = e3)
% 177.58/28.08    (17)  all_58_13 = all_52_27
% 177.58/28.08    (18)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.08    (19)  all_58_12 = e3
% 177.58/28.08    (20)  all_58_6 = all_52_17
% 177.58/28.08    (21)  op(e2, all_52_19) = all_52_18
% 177.58/28.08    (22)  all_58_11 = all_52_23
% 177.58/28.08    (23)   ~ (all_52_3 = all_52_19)
% 177.58/28.08    (24)   ~ (all_52_19 = all_10_2)
% 177.58/28.08    (25)  all_58_2 = all_52_9
% 177.58/28.08    (26)   ~ (e2 = e1)
% 177.58/28.08    (27)  op(e1, e3) = all_52_17
% 177.58/28.08    (28)  op(e2, all_10_2) = e2
% 177.58/28.08    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.08            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.08    (30)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.08    (31)  all_56_6 = all_52_13
% 177.58/28.08    (32)   ~ (e3 = e2)
% 177.58/28.08    (33)  op(e2, e3) = all_52_9
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | BETA: splitting (11) gives:
% 177.58/28.08  | 
% 177.58/28.08  | Case 1:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (34)  all_56_6 = e3
% 177.58/28.08  | | 
% 177.58/28.08  | | COMBINE_EQS: (31), (34) imply:
% 177.58/28.08  | |   (35)  all_52_13 = e3
% 177.58/28.08  | | 
% 177.58/28.08  | | SIMP: (35) implies:
% 177.58/28.08  | |   (36)  all_52_13 = e3
% 177.58/28.08  | | 
% 177.58/28.08  | | REDUCE: (14), (36) imply:
% 177.58/28.08  | |   (37)   ~ (all_14_2 = e3)
% 177.58/28.08  | | 
% 177.58/28.08  | | SIMP: (37) implies:
% 177.58/28.08  | |   (38)   ~ (all_14_2 = e3)
% 177.58/28.08  | | 
% 177.58/28.08  | | REDUCE: (5), (36) imply:
% 177.58/28.08  | |   (39)  op(e1, e3) = e1
% 177.58/28.08  | | 
% 177.58/28.08  | | BETA: splitting (6) gives:
% 177.58/28.08  | | 
% 177.58/28.08  | | Case 1:
% 177.58/28.08  | | | 
% 177.58/28.08  | | |   (40)  all_58_7 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | COMBINE_EQS: (10), (40) imply:
% 177.58/28.08  | | |   (41)  all_52_19 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | SIMP: (41) implies:
% 177.58/28.08  | | |   (42)  all_52_19 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REDUCE: (23), (42) imply:
% 177.58/28.08  | | |   (43)   ~ (all_52_3 = e3)
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REDUCE: (21), (42) imply:
% 177.58/28.08  | | |   (44)  op(e2, e3) = all_52_18
% 177.58/28.08  | | | 
% 177.58/28.08  | | | GROUND_INST: instantiating (29) with all_52_17, e1, e3, e1, simplifying
% 177.58/28.08  | | |              with (27), (39) gives:
% 177.58/28.08  | | |   (45)  all_52_17 = e1
% 177.58/28.08  | | | 
% 177.58/28.08  | | | GROUND_INST: instantiating (29) with all_52_9, all_52_18, e3, e2,
% 177.58/28.08  | | |              simplifying with (33), (44) gives:
% 177.58/28.08  | | |   (46)  all_52_9 = all_52_18
% 177.58/28.08  | | | 
% 177.58/28.08  | | | COMBINE_EQS: (20), (45) imply:
% 177.58/28.08  | | |   (47)  all_58_6 = e1
% 177.58/28.08  | | | 
% 177.58/28.08  | | | COMBINE_EQS: (25), (46) imply:
% 177.58/28.08  | | |   (48)  all_58_2 = all_52_18
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REDUCE: (15), (46) imply:
% 177.58/28.08  | | |   (49)  op(e3, all_52_18) = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REF_CLOSE: (2), (18), (19), (26), (29), (32), (43), (47), (48), (49) are
% 177.58/28.08  | | |            inconsistent by sub-proof #737.
% 177.58/28.08  | | | 
% 177.58/28.08  | | Case 2:
% 177.58/28.08  | | | 
% 177.58/28.08  | | |   (50)  all_58_8 = e3 | all_58_11 = e3
% 177.58/28.08  | | | 
% 177.58/28.08  | | | REF_CLOSE: (12), (13), (22), (38), (50) are inconsistent by sub-proof
% 177.58/28.08  | | |            #997.
% 177.58/28.08  | | | 
% 177.58/28.08  | | End of split
% 177.58/28.08  | | 
% 177.58/28.08  | Case 2:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (51)   ~ (all_56_6 = e3)
% 177.58/28.08  | | 
% 177.58/28.08  | | REDUCE: (31), (51) imply:
% 177.58/28.08  | |   (52)   ~ (all_52_13 = e3)
% 177.58/28.08  | | 
% 177.58/28.08  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (15), (16), (17), (24),
% 177.58/28.08  | |            (28), (29), (30), (33), (52) are inconsistent by sub-proof #736.
% 177.58/28.08  | | 
% 177.58/28.08  | End of split
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #431 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)  all_56_11 = e1 | all_56_11 = e0
% 177.58/28.08    (2)  all_56_11 = all_52_23
% 177.58/28.08    (3)   ~ (all_52_23 = e1)
% 177.58/28.08    (4)   ~ (all_52_23 = e0)
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | BETA: splitting (1) gives:
% 177.58/28.08  | 
% 177.58/28.08  | Case 1:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (5)  all_56_11 = e1
% 177.58/28.08  | | 
% 177.58/28.08  | | COMBINE_EQS: (2), (5) imply:
% 177.58/28.08  | |   (6)  all_52_23 = e1
% 177.58/28.08  | | 
% 177.58/28.08  | | REDUCE: (3), (6) imply:
% 177.58/28.08  | |   (7)  $false
% 177.58/28.08  | | 
% 177.58/28.08  | | CLOSE: (7) is inconsistent.
% 177.58/28.08  | | 
% 177.58/28.08  | Case 2:
% 177.58/28.08  | | 
% 177.58/28.08  | |   (8)  all_56_11 = e0
% 177.58/28.08  | | 
% 177.58/28.08  | | COMBINE_EQS: (2), (8) imply:
% 177.58/28.08  | |   (9)  all_52_23 = e0
% 177.58/28.08  | | 
% 177.58/28.08  | | REDUCE: (4), (9) imply:
% 177.58/28.08  | |   (10)  $false
% 177.58/28.08  | | 
% 177.58/28.08  | | CLOSE: (10) is inconsistent.
% 177.58/28.08  | | 
% 177.58/28.08  | End of split
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #432 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)   ~ (all_52_17 = all_14_2)
% 177.58/28.08    (2)  all_58_8 = all_14_2
% 177.58/28.08    (3)  op(e1, all_14_2) = e3
% 177.58/28.08    (4)  op(e1, e3) = all_52_17
% 177.58/28.08    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.08    (6)  all_58_8 = e3
% 177.58/28.08  
% 177.58/28.08  Begin of proof
% 177.58/28.08  | 
% 177.58/28.08  | COMBINE_EQS: (2), (6) imply:
% 177.58/28.08  |   (7)  all_14_2 = e3
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (1), (7) imply:
% 177.58/28.08  |   (8)   ~ (all_52_17 = e3)
% 177.58/28.08  | 
% 177.58/28.08  | REDUCE: (3), (7) imply:
% 177.58/28.08  |   (9)  op(e1, e3) = e3
% 177.58/28.08  | 
% 177.58/28.08  | REF_CLOSE: (4), (5), (8), (9) are inconsistent by sub-proof #508.
% 177.58/28.08  | 
% 177.58/28.08  End of proof
% 177.58/28.08  
% 177.58/28.08  Sub-proof #433 shows that the following formulas are inconsistent:
% 177.58/28.08  ----------------------------------------------------------------
% 177.58/28.08    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.08    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.58/28.08    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.08    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.08    (5)   ~ (all_52_27 = all_10_2)
% 177.58/28.08    (6)  op(e2, e2) = all_10_2
% 177.58/28.08    (7)   ~ (all_52_17 = all_52_23)
% 177.58/28.08    (8)   ~ (all_6_0 = e3)
% 177.58/28.08    (9)   ~ (all_52_13 = all_52_29)
% 177.58/28.08    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.08    (11)  all_56_3 = all_52_7
% 177.58/28.08    (12)  op(e3, e2) = all_52_3
% 177.58/28.08    (13)   ~ (all_52_9 = all_52_25)
% 177.58/28.08    (14)  op(e3, all_52_25) = all_52_24
% 177.58/28.08    (15)   ~ (all_52_19 = all_52_23)
% 177.58/28.08    (16)  op(e1, e2) = all_52_19
% 177.58/28.08    (17)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.58/28.08    (18)  op(e3, all_52_9) = all_52_8
% 177.58/28.08    (19)  all_50_1 = all_4_1
% 177.58/28.08    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.08    (21)  all_58_5 = all_52_13
% 177.58/28.08    (22)   ~ (all_6_2 = e0)
% 177.58/28.08    (23)   ~ (all_52_25 = all_52_29)
% 177.58/28.08    (24)  all_56_15 = all_6_2
% 177.58/28.08    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.08    (26)  op(all_14_1, all_14_2) = all_14_0
% 177.58/28.08    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.08    (28)  all_58_3 = all_10_2
% 177.58/28.08    (29)  all_56_9 = all_52_19
% 177.58/28.08    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.08    (31)  all_58_15 = all_6_2
% 177.58/28.08    (32)   ~ (all_52_9 = all_4_2)
% 177.58/28.08    (33)   ~ (all_52_5 = all_52_7)
% 177.58/28.08    (34)  all_58_10 = all_52_15
% 177.58/28.08    (35)   ~ (all_52_5 = all_4_2)
% 177.58/28.08    (36)  all_58_7 = all_52_19
% 177.58/28.08    (37)   ~ (all_52_17 = all_52_25)
% 177.58/28.08    (38)  op(e0, e1) = all_52_29
% 177.58/28.08    (39)  all_58_4 = all_52_5
% 177.58/28.08    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.08    (41)   ~ (e3 = e1)
% 177.58/28.08    (42)   ~ (all_52_27 = all_52_29)
% 177.58/28.08    (43)   ~ (all_52_17 = all_14_2)
% 177.58/28.08    (44)  op(e3, all_4_2) = all_4_1
% 177.58/28.08    (45)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.08    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.08    (47)   ~ (all_52_7 = all_4_2)
% 177.58/28.08    (48)  all_58_1 = all_52_3
% 177.58/28.08    (49)   ~ (all_52_13 = all_52_15)
% 177.58/28.08    (50)  all_58_0 = all_4_2
% 177.58/28.08    (51)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.08    (52)  op(e1, all_52_29) = all_52_28
% 177.58/28.08    (53)  all_50_2 = all_4_2
% 177.58/28.08    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.58/28.08    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.09    (56)   ~ (all_4_1 = e2)
% 177.58/28.09    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.09    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.09    (59)  all_58_14 = all_52_29
% 177.58/28.09    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.09    (61)  all_26_2 = all_4_2
% 177.58/28.09    (62)   ~ (all_52_3 = all_52_5)
% 177.58/28.09    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.09    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.09    (65)  all_58_8 = all_14_2
% 177.58/28.09    (66)  all_56_1 = all_52_3
% 177.58/28.09    (67)  op(e0, e2) = all_52_27
% 177.58/28.09    (68)   ~ (all_14_0 = e3)
% 177.58/28.09    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.09    (70)   ~ (all_52_5 = all_14_2)
% 177.58/28.09    (71)   ~ (all_52_3 = all_52_27)
% 177.58/28.09    (72)   ~ (all_52_3 = all_4_2)
% 177.58/28.09    (73)  op(all_6_1, all_6_2) = all_6_0
% 177.58/28.09    (74)  op(e0, e3) = all_52_25
% 177.58/28.09    (75)  op(e0, all_6_2) = all_6_1
% 177.58/28.09    (76)   ~ (all_52_9 = all_10_2)
% 177.58/28.09    (77)  op(all_4_1, all_4_2) = e2
% 177.58/28.09    (78)  op(e3, all_52_17) = all_52_16
% 177.58/28.09    (79)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.58/28.09    (80)   ~ (e3 = e0)
% 177.58/28.09    (81)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.09    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.09    (83)  op(e0, all_52_23) = all_52_22
% 177.58/28.09    (84)   ~ (all_52_15 = all_52_23)
% 177.58/28.09    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.09    (86)   ~ (all_52_5 = all_52_29)
% 177.58/28.09    (87)  all_56_2 = all_52_5
% 177.58/28.09    (88)  op(e1, e0) = all_52_23
% 177.58/28.09    (89)  all_56_12 = all_52_25
% 177.58/28.09    (90)  all_58_13 = all_52_27
% 177.58/28.09    (91)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.58/28.09    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.09    (93)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.09    (94)   ~ (all_52_9 = all_52_17)
% 177.58/28.09    (95)   ~ (all_14_0 = e2)
% 177.58/28.09    (96)  all_58_6 = all_52_17
% 177.58/28.09    (97)   ~ (all_52_3 = all_52_7)
% 177.58/28.09    (98)  op(e2, all_52_19) = all_52_18
% 177.58/28.09    (99)   ~ (e1 = e0)
% 177.58/28.09    (100)  all_56_0 = all_4_2
% 177.58/28.09    (101)  all_58_11 = all_52_23
% 177.58/28.09    (102)   ~ (all_52_3 = all_52_19)
% 177.58/28.09    (103)   ~ (all_52_7 = all_52_15)
% 177.58/28.09    (104)  all_26_1 = all_4_1
% 177.58/28.09    (105)   ~ (all_52_29 = all_14_2)
% 177.58/28.09    (106)   ~ (all_52_23 = all_6_2)
% 177.58/28.09    (107)   ~ (all_6_0 = e2)
% 177.58/28.09    (108)   ~ (all_52_29 = all_6_2)
% 177.58/28.09    (109)  all_58_2 = all_52_9
% 177.58/28.09    (110)  op(e3, e1) = all_52_5
% 177.58/28.09    (111)  all_56_10 = all_14_2
% 177.58/28.09    (112)   ~ (all_52_25 = all_6_2)
% 177.58/28.09    (113)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.09    (114)  op(e1, e3) = all_52_17
% 177.58/28.09    (115)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.09    (116)   ~ (all_52_25 = all_4_2)
% 177.58/28.09    (117)  op(e3, e0) = all_52_7
% 177.58/28.09    (118)  op(e3, e3) = all_4_2
% 177.58/28.09    (119)  all_56_8 = all_52_17
% 177.58/28.09    (120)   ~ (all_52_17 = all_4_2)
% 177.58/28.09    (121)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.09             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.09    (122)   ~ (all_52_25 = all_52_27)
% 177.58/28.09    (123)   ~ (all_52_27 = all_6_2)
% 177.58/28.09    (124)   ~ (all_52_7 = all_6_2)
% 177.58/28.09    (125)   ~ (all_52_15 = all_10_2)
% 177.58/28.09    (126)  all_56_7 = all_52_15
% 177.58/28.09    (127)   ~ (all_52_7 = all_52_23)
% 177.58/28.09    (128)   ~ (all_6_0 = e1)
% 177.58/28.09    (129)  op(e2, all_52_27) = all_52_26
% 177.58/28.09    (130)  all_52_20 = all_14_1
% 177.58/28.09    (131)   ~ (all_52_17 = all_52_19)
% 177.58/28.09    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.09    (133)  all_52_30 = all_6_1
% 177.58/28.09    (134)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.09    (135)  op(e1, all_14_2) = all_14_1
% 177.58/28.09    (136)  all_58_9 = all_52_7
% 177.58/28.09    (137)   ~ (e2 = e0)
% 177.58/28.09    (138)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.58/28.09           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.58/28.09    (139)  all_58_12 = all_52_25
% 177.58/28.09    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.09    (141)   ~ (all_52_9 = all_52_15)
% 177.58/28.09    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.09    (143)   ~ (e3 = e2)
% 177.58/28.09    (144)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.58/28.09    (145)   ~ (all_52_19 = all_14_2)
% 177.58/28.09    (146)  op(e2, e3) = all_52_9
% 177.58/28.09    (147)  all_56_13 = all_52_27
% 177.58/28.09  
% 177.58/28.09  Begin of proof
% 177.58/28.09  | 
% 177.58/28.09  | BETA: splitting (138) gives:
% 177.58/28.09  | 
% 177.58/28.09  | Case 1:
% 177.58/28.09  | | 
% 177.58/28.09  | |   (148)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.58/28.09  | | 
% 177.58/28.09  | | ALPHA: (148) implies:
% 177.58/28.09  | |   (149)  all_52_22 = e0
% 177.58/28.09  | |   (150)  all_52_20 = e1
% 177.58/28.09  | |   (151)  all_52_18 = e2
% 177.58/28.09  | |   (152)  all_52_16 = e3
% 177.58/28.09  | | 
% 177.58/28.09  | | COMBINE_EQS: (130), (150) imply:
% 177.58/28.09  | |   (153)  all_14_1 = e1
% 177.58/28.09  | | 
% 177.58/28.09  | | REF_CLOSE: (1), (2), (3), (4), (7), (11), (12), (13), (14), (15), (16),
% 177.58/28.09  | |            (17), (18), (19), (23), (24), (25), (26), (28), (29), (30), (31),
% 177.58/28.09  | |            (32), (33), (34), (35), (36), (37), (39), (40), (43), (44), (45),
% 177.58/28.09  | |            (46), (47), (48), (50), (51), (52), (53), (54), (55), (56), (58),
% 177.58/28.09  | |            (59), (60), (62), (63), (64), (65), (66), (68), (69), (70), (71),
% 177.58/28.09  | |            (72), (74), (77), (78), (80), (81), (83), (84), (85), (86), (87),
% 177.58/28.09  | |            (88), (90), (92), (93), (94), (95), (96), (97), (98), (99),
% 177.58/28.09  | |            (100), (101), (102), (103), (105), (106), (109), (110), (111),
% 177.58/28.09  | |            (112), (114), (115), (116), (117), (118), (119), (120), (121),
% 177.58/28.09  | |            (122), (123), (125), (126), (127), (129), (131), (132), (134),
% 177.58/28.09  | |            (135), (136), (137), (139), (140), (141), (142), (143), (144),
% 177.58/28.09  | |            (145), (146), (147), (149), (151), (152), (153) are inconsistent
% 177.58/28.09  | |            by sub-proof #454.
% 177.58/28.09  | | 
% 177.58/28.09  | Case 2:
% 177.58/28.09  | | 
% 177.58/28.09  | |   (154)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.58/28.09  | | 
% 177.58/28.09  | | ALPHA: (154) implies:
% 177.58/28.09  | |   (155)  all_52_30 = e0
% 177.58/28.09  | |   (156)  all_52_28 = e1
% 177.58/28.09  | |   (157)  all_52_26 = e2
% 177.58/28.09  | |   (158)  all_52_24 = e3
% 177.58/28.09  | | 
% 177.58/28.09  | | COMBINE_EQS: (133), (155) imply:
% 177.58/28.09  | |   (159)  all_6_1 = e0
% 177.58/28.09  | | 
% 177.58/28.09  | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 177.58/28.09  | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (27), (28),
% 177.58/28.09  | |            (30), (31), (34), (35), (36), (37), (38), (39), (41), (42), (43),
% 177.58/28.09  | |            (44), (45), (47), (48), (49), (50), (52), (53), (56), (57), (58),
% 177.58/28.09  | |            (59), (60), (61), (63), (64), (65), (67), (72), (73), (74), (75),
% 177.58/28.09  | |            (76), (77), (78), (79), (81), (82), (89), (90), (91), (92), (94),
% 177.58/28.09  | |            (96), (97), (100), (101), (104), (107), (108), (109), (110),
% 177.58/28.09  | |            (112), (113), (114), (116), (117), (118), (120), (121), (122),
% 177.58/28.09  | |            (124), (128), (129), (131), (132), (134), (136), (139), (141),
% 177.58/28.09  | |            (143), (146), (147), (156), (157), (158), (159) are inconsistent
% 177.58/28.09  | |            by sub-proof #450.
% 177.58/28.09  | | 
% 177.58/28.09  | End of split
% 177.58/28.09  | 
% 177.58/28.09  End of proof
% 177.58/28.09  
% 177.58/28.09  Sub-proof #434 shows that the following formulas are inconsistent:
% 177.58/28.09  ----------------------------------------------------------------
% 177.58/28.09    (1)  op(e2, all_10_2) = all_10_1
% 177.58/28.09    (2)  op(all_10_1, all_10_2) = e1
% 177.58/28.09    (3)  op(e3, all_4_2) = all_4_1
% 177.58/28.09    (4)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.09         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.58/28.09    (5)   ~ (all_4_1 = e2)
% 177.58/28.09    (6)  all_52_0 = all_4_1
% 177.58/28.09    (7)  op(all_4_1, all_4_2) = e2
% 177.58/28.09    (8)  all_52_10 = all_10_1
% 177.58/28.09    (9)   ~ (e2 = e1)
% 177.58/28.09    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.09            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.09  
% 177.58/28.09  Begin of proof
% 177.58/28.09  | 
% 177.58/28.09  | BETA: splitting (4) gives:
% 177.58/28.09  | 
% 177.58/28.09  | Case 1:
% 177.58/28.09  | | 
% 177.58/28.09  | |   (11)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.58/28.09  | | 
% 177.58/28.09  | | REF_CLOSE: (3), (5), (6), (7), (10), (11) are inconsistent by sub-proof
% 177.58/28.09  | |            #494.
% 177.58/28.09  | | 
% 177.58/28.09  | Case 2:
% 177.58/28.09  | | 
% 177.58/28.09  | |   (12)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.58/28.09  | | 
% 177.58/28.09  | | ALPHA: (12) implies:
% 177.58/28.09  | |   (13)  all_52_10 = e2
% 177.58/28.09  | | 
% 177.58/28.09  | | COMBINE_EQS: (8), (13) imply:
% 177.58/28.09  | |   (14)  all_10_1 = e2
% 177.58/28.09  | | 
% 177.58/28.09  | | REF_CLOSE: (1), (2), (9), (10), (14) are inconsistent by sub-proof #446.
% 177.58/28.09  | | 
% 177.58/28.09  | End of split
% 177.58/28.09  | 
% 177.58/28.09  End of proof
% 177.58/28.09  
% 177.58/28.09  Sub-proof #435 shows that the following formulas are inconsistent:
% 177.58/28.09  ----------------------------------------------------------------
% 177.58/28.09    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.09    (2)   ~ (all_52_5 = all_52_13)
% 177.58/28.09    (3)   ~ (all_52_17 = all_52_23)
% 177.58/28.09    (4)  op(e2, all_10_2) = all_10_1
% 177.58/28.09    (5)   ~ (all_52_13 = all_52_29)
% 177.58/28.09    (6)  op(all_10_1, all_10_2) = e1
% 177.58/28.09    (7)  op(e3, e2) = all_52_3
% 177.58/28.09    (8)   ~ (all_52_9 = all_52_25)
% 177.58/28.09    (9)   ~ (all_52_19 = all_52_23)
% 177.58/28.09    (10)  all_56_11 = all_52_23
% 177.58/28.09    (11)  op(e1, e2) = all_52_19
% 177.58/28.09    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.58/28.09    (13)   ~ (all_52_3 = all_10_2)
% 177.58/28.09    (14)  all_58_5 = all_52_13
% 177.58/28.09    (15)   ~ (all_6_2 = e0)
% 177.58/28.09    (16)   ~ (all_52_25 = all_52_29)
% 177.58/28.09    (17)  all_56_15 = all_6_2
% 177.58/28.09    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.09    (19)  op(e2, e0) = all_52_15
% 177.58/28.09    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.09    (21)  all_58_3 = all_10_2
% 177.58/28.09    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.09    (23)  all_58_15 = all_6_2
% 177.58/28.09    (24)   ~ (all_52_9 = all_4_2)
% 177.58/28.09    (25)   ~ (all_52_5 = all_52_7)
% 177.58/28.09    (26)  all_58_10 = all_52_15
% 177.58/28.09    (27)   ~ (all_52_5 = all_4_2)
% 177.58/28.09    (28)  all_58_7 = all_52_19
% 177.58/28.09    (29)  all_56_4 = all_52_9
% 177.58/28.09    (30)   ~ (all_52_15 = all_6_2)
% 177.58/28.09    (31)   ~ (all_52_17 = all_52_25)
% 177.58/28.09    (32)  op(e0, e1) = all_52_29
% 177.58/28.09    (33)   ~ (all_4_0 = e2)
% 177.58/28.09    (34)  all_58_4 = all_52_5
% 177.58/28.09    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.09    (36)   ~ (all_52_27 = all_52_29)
% 177.58/28.09    (37)   ~ (all_52_17 = all_14_2)
% 177.58/28.09    (38)  op(e3, all_4_2) = all_4_1
% 177.58/28.09    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.09    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.09    (41)   ~ (all_52_7 = all_4_2)
% 177.58/28.09    (42)  all_58_1 = all_52_3
% 177.58/28.09    (43)   ~ (all_52_13 = all_52_15)
% 177.58/28.09    (44)  all_58_0 = all_4_2
% 177.58/28.09    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.09    (46)  op(e1, all_52_29) = all_52_28
% 177.58/28.09    (47)  op(e1, all_52_5) = all_52_4
% 177.58/28.09    (48)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.09          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.58/28.09    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.58/28.09    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.09    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.09    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.09    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.58/28.09    (54)  all_58_14 = all_52_29
% 177.58/28.09    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.09    (56)   ~ (all_52_3 = all_52_5)
% 177.58/28.09    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.09    (58)  op(e2, e1) = all_52_13
% 177.58/28.09    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.09    (60)  all_58_8 = all_14_2
% 177.58/28.09    (61)  all_56_1 = all_52_3
% 177.58/28.09    (62)  all_56_14 = all_52_29
% 177.58/28.09    (63)  op(all_4_1, all_4_2) = all_4_0
% 177.58/28.09    (64)   ~ (all_52_5 = all_14_2)
% 177.58/28.09    (65)   ~ (all_52_3 = all_52_27)
% 177.58/28.09    (66)   ~ (all_52_3 = all_4_2)
% 177.58/28.09    (67)  op(e0, e3) = all_52_25
% 177.58/28.09    (68)  op(e0, all_6_2) = all_6_1
% 177.58/28.09    (69)  all_52_0 = all_4_1
% 177.58/28.09    (70)  all_52_10 = all_10_1
% 177.58/28.09    (71)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.58/28.09    (72)   ~ (all_52_13 = all_14_2)
% 177.58/28.09    (73)   ~ (e3 = e0)
% 177.58/28.09    (74)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.09    (75)   ~ (all_52_9 = all_52_13)
% 177.58/28.09    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.09    (77)  op(e0, all_52_23) = all_52_22
% 177.58/28.09    (78)   ~ (all_52_15 = all_52_23)
% 177.58/28.09    (79)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.09    (80)   ~ (all_52_5 = all_52_29)
% 177.58/28.09    (81)  all_56_2 = all_52_5
% 177.58/28.09    (82)  op(e1, e0) = all_52_23
% 177.58/28.09    (83)  all_56_12 = all_52_25
% 177.58/28.09    (84)  all_58_13 = all_52_27
% 177.58/28.09    (85)  op(e2, all_52_3) = all_52_2
% 177.58/28.09    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.09    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.09    (88)   ~ (all_52_9 = all_52_17)
% 177.58/28.09    (89)  all_58_6 = all_52_17
% 177.58/28.09    (90)   ~ (all_52_3 = all_52_7)
% 177.58/28.09    (91)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.58/28.09    (92)   ~ (e1 = e0)
% 177.58/28.09    (93)  all_56_0 = all_4_2
% 177.58/28.09    (94)  all_58_11 = all_52_23
% 177.58/28.09    (95)   ~ (all_52_3 = all_52_19)
% 177.58/28.09    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.58/28.09    (97)   ~ (all_52_7 = all_52_15)
% 177.58/28.09    (98)  op(e0, all_52_15) = all_52_14
% 177.58/28.09    (99)   ~ (all_52_29 = all_14_2)
% 177.58/28.09    (100)   ~ (all_4_0 = e1)
% 177.58/28.09    (101)   ~ (all_52_23 = all_6_2)
% 177.58/28.09    (102)   ~ (all_52_29 = all_6_2)
% 177.58/28.09    (103)  all_58_2 = all_52_9
% 177.58/28.09    (104)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.58/28.09    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.09    (106)  op(e3, e1) = all_52_5
% 177.58/28.09    (107)   ~ (e2 = e1)
% 177.58/28.09    (108)  all_56_10 = all_14_2
% 177.58/28.09    (109)   ~ (all_52_25 = all_6_2)
% 177.58/28.09    (110)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.09    (111)  op(e1, e1) = all_14_2
% 177.58/28.09    (112)  op(e1, e3) = all_52_17
% 177.58/28.09    (113)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.09    (114)   ~ (all_52_25 = all_4_2)
% 177.58/28.09    (115)  op(e3, e0) = all_52_7
% 177.58/28.09    (116)   ~ (all_52_17 = all_4_2)
% 177.58/28.09    (117)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.09             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.09    (118)   ~ (all_52_25 = all_52_27)
% 177.58/28.09    (119)   ~ (all_52_27 = all_6_2)
% 177.58/28.09    (120)   ~ (all_52_7 = all_6_2)
% 177.58/28.09    (121)   ~ (all_52_19 = all_52_27)
% 177.58/28.09    (122)  all_56_7 = all_52_15
% 177.58/28.09    (123)   ~ (all_52_7 = all_52_23)
% 177.58/28.09    (124)   ~ (all_52_13 = all_10_2)
% 177.58/28.09    (125)  op(e2, all_52_27) = all_52_26
% 177.58/28.09    (126)   ~ (all_52_17 = all_52_19)
% 177.58/28.09    (127)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.09    (128)  all_58_9 = all_52_7
% 177.58/28.09    (129)  all_58_12 = all_52_25
% 177.58/28.09    (130)  op(all_6_1, all_6_2) = e3
% 177.58/28.09    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.09    (132)   ~ (all_52_9 = all_52_15)
% 177.58/28.09    (133)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.09    (134)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.58/28.09    (135)   ~ (all_52_19 = all_14_2)
% 177.58/28.09    (136)  op(e0, all_52_7) = all_52_6
% 177.58/28.09    (137)  op(e2, e3) = all_52_9
% 177.58/28.09    (138)  all_56_13 = all_52_27
% 177.58/28.09  
% 177.58/28.09  Begin of proof
% 177.58/28.09  | 
% 177.58/28.09  | BETA: splitting (48) gives:
% 177.58/28.09  | 
% 177.58/28.09  | Case 1:
% 177.58/28.09  | | 
% 177.58/28.09  | |   (139)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.58/28.09  | | 
% 177.58/28.09  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 177.58/28.09  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.58/28.09  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.58/28.09  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.58/28.09  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 177.58/28.09  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 177.58/28.09  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 177.58/28.09  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 177.58/28.09  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 177.58/28.09  | |            (104), (105), (106), (108), (109), (110), (111), (112), (113),
% 177.58/28.09  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 177.58/28.09  | |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 177.58/28.09  | |            (132), (133), (134), (135), (136), (137), (138), (139) are
% 177.58/28.09  | |            inconsistent by sub-proof #436.
% 177.58/28.09  | | 
% 177.58/28.09  | Case 2:
% 177.58/28.09  | | 
% 177.58/28.09  | |   (140)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.58/28.09  | | 
% 177.58/28.09  | | ALPHA: (140) implies:
% 177.58/28.09  | |   (141)  all_52_10 = e2
% 177.58/28.09  | | 
% 177.58/28.09  | | COMBINE_EQS: (70), (141) imply:
% 177.58/28.09  | |   (142)  all_10_1 = e2
% 177.58/28.09  | | 
% 177.58/28.09  | | REF_CLOSE: (4), (6), (107), (117), (142) are inconsistent by sub-proof #446.
% 177.58/28.09  | | 
% 177.58/28.09  | End of split
% 177.58/28.09  | 
% 177.58/28.09  End of proof
% 177.58/28.09  
% 177.58/28.09  Sub-proof #436 shows that the following formulas are inconsistent:
% 177.58/28.09  ----------------------------------------------------------------
% 177.58/28.09    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.09    (2)   ~ (all_52_5 = all_52_13)
% 177.58/28.09    (3)   ~ (all_52_17 = all_52_23)
% 177.58/28.09    (4)   ~ (all_52_13 = all_52_29)
% 177.58/28.09    (5)  op(e3, e2) = all_52_3
% 177.58/28.09    (6)   ~ (all_52_9 = all_52_25)
% 177.58/28.09    (7)   ~ (all_52_19 = all_52_23)
% 177.58/28.09    (8)  all_56_11 = all_52_23
% 177.58/28.09    (9)  op(e1, e2) = all_52_19
% 177.58/28.09    (10)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.58/28.09    (11)   ~ (all_52_3 = all_10_2)
% 177.58/28.09    (12)  all_58_5 = all_52_13
% 177.58/28.09    (13)   ~ (all_6_2 = e0)
% 177.58/28.09    (14)   ~ (all_52_25 = all_52_29)
% 177.58/28.09    (15)  all_56_15 = all_6_2
% 177.58/28.09    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.09    (17)  op(e2, e0) = all_52_15
% 177.58/28.09    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.09    (19)  all_58_3 = all_10_2
% 177.58/28.09    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.09    (21)  all_58_15 = all_6_2
% 177.58/28.09    (22)   ~ (all_52_9 = all_4_2)
% 177.58/28.09    (23)   ~ (all_52_5 = all_52_7)
% 177.58/28.09    (24)  all_58_10 = all_52_15
% 177.58/28.09    (25)   ~ (all_52_5 = all_4_2)
% 177.58/28.09    (26)  all_58_7 = all_52_19
% 177.58/28.09    (27)  all_56_4 = all_52_9
% 177.58/28.09    (28)   ~ (all_52_15 = all_6_2)
% 177.58/28.09    (29)   ~ (all_52_17 = all_52_25)
% 177.58/28.09    (30)  op(e0, e1) = all_52_29
% 177.58/28.09    (31)   ~ (all_4_0 = e2)
% 177.58/28.09    (32)  all_58_4 = all_52_5
% 177.58/28.09    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.09    (34)   ~ (all_52_27 = all_52_29)
% 177.58/28.09    (35)   ~ (all_52_17 = all_14_2)
% 177.58/28.09    (36)  op(e3, all_4_2) = all_4_1
% 177.58/28.09    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.09    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.09    (39)   ~ (all_52_7 = all_4_2)
% 177.58/28.09    (40)  all_58_1 = all_52_3
% 177.58/28.09    (41)   ~ (all_52_13 = all_52_15)
% 177.58/28.09    (42)  all_58_0 = all_4_2
% 177.58/28.09    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.09    (44)  op(e1, all_52_29) = all_52_28
% 177.58/28.09    (45)  op(e1, all_52_5) = all_52_4
% 177.58/28.09    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.58/28.09    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.58/28.09    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.09    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.09    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.58/28.09    (51)  all_58_14 = all_52_29
% 177.58/28.09    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.09    (53)   ~ (all_52_3 = all_52_5)
% 177.58/28.09    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.09    (55)  op(e2, e1) = all_52_13
% 177.58/28.09    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.09    (57)  all_58_8 = all_14_2
% 177.58/28.09    (58)  all_56_1 = all_52_3
% 177.58/28.09    (59)  all_56_14 = all_52_29
% 177.58/28.09    (60)  op(all_4_1, all_4_2) = all_4_0
% 177.58/28.09    (61)   ~ (all_52_5 = all_14_2)
% 177.58/28.09    (62)   ~ (all_52_3 = all_52_27)
% 177.58/28.09    (63)   ~ (all_52_3 = all_4_2)
% 177.58/28.09    (64)  op(e0, e3) = all_52_25
% 177.58/28.09    (65)  op(e0, all_6_2) = all_6_1
% 177.58/28.09    (66)  all_52_0 = all_4_1
% 177.58/28.09    (67)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.58/28.09    (68)   ~ (all_52_13 = all_14_2)
% 177.58/28.09    (69)   ~ (e3 = e0)
% 177.58/28.09    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.09    (71)   ~ (all_52_9 = all_52_13)
% 177.58/28.09    (72)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.09    (73)  op(e0, all_52_23) = all_52_22
% 177.58/28.09    (74)   ~ (all_52_15 = all_52_23)
% 177.58/28.09    (75)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.09    (76)   ~ (all_52_5 = all_52_29)
% 177.58/28.09    (77)  all_56_2 = all_52_5
% 177.58/28.09    (78)  op(e1, e0) = all_52_23
% 177.58/28.09    (79)  all_56_12 = all_52_25
% 177.58/28.09    (80)  all_58_13 = all_52_27
% 177.58/28.09    (81)  op(e2, all_52_3) = all_52_2
% 177.58/28.09    (82)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.09    (83)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.09    (84)   ~ (all_52_9 = all_52_17)
% 177.58/28.09    (85)  all_58_6 = all_52_17
% 177.58/28.09    (86)   ~ (all_52_3 = all_52_7)
% 177.58/28.09    (87)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.58/28.09    (88)   ~ (e1 = e0)
% 177.58/28.09    (89)  all_56_0 = all_4_2
% 177.58/28.09    (90)  all_58_11 = all_52_23
% 177.58/28.09    (91)   ~ (all_52_3 = all_52_19)
% 177.58/28.09    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.58/28.09    (93)   ~ (all_52_7 = all_52_15)
% 177.58/28.09    (94)  op(e0, all_52_15) = all_52_14
% 177.58/28.09    (95)   ~ (all_52_29 = all_14_2)
% 177.58/28.09    (96)   ~ (all_4_0 = e1)
% 177.58/28.09    (97)   ~ (all_52_23 = all_6_2)
% 177.58/28.09    (98)   ~ (all_52_29 = all_6_2)
% 177.58/28.09    (99)  all_58_2 = all_52_9
% 177.58/28.09    (100)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.58/28.09    (101)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.58/28.09    (102)  op(e3, e1) = all_52_5
% 177.58/28.09    (103)  all_56_10 = all_14_2
% 177.58/28.09    (104)   ~ (all_52_25 = all_6_2)
% 177.58/28.09    (105)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.09    (106)  op(e1, e1) = all_14_2
% 177.58/28.09    (107)  op(e1, e3) = all_52_17
% 177.58/28.09    (108)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.09    (109)   ~ (all_52_25 = all_4_2)
% 177.58/28.09    (110)  op(e3, e0) = all_52_7
% 177.58/28.09    (111)   ~ (all_52_17 = all_4_2)
% 177.58/28.09    (112)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.09             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.09    (113)   ~ (all_52_25 = all_52_27)
% 177.58/28.09    (114)   ~ (all_52_27 = all_6_2)
% 177.58/28.09    (115)   ~ (all_52_7 = all_6_2)
% 177.58/28.09    (116)   ~ (all_52_19 = all_52_27)
% 177.58/28.09    (117)  all_56_7 = all_52_15
% 177.58/28.09    (118)   ~ (all_52_7 = all_52_23)
% 177.58/28.09    (119)   ~ (all_52_13 = all_10_2)
% 177.58/28.09    (120)  op(e2, all_52_27) = all_52_26
% 177.58/28.09    (121)   ~ (all_52_17 = all_52_19)
% 177.58/28.09    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.09    (123)  all_58_9 = all_52_7
% 177.58/28.09    (124)  all_58_12 = all_52_25
% 177.58/28.09    (125)  op(all_6_1, all_6_2) = e3
% 177.58/28.09    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.09    (127)   ~ (all_52_9 = all_52_15)
% 177.58/28.09    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.09    (129)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.58/28.09    (130)   ~ (all_52_19 = all_14_2)
% 177.58/28.09    (131)  op(e0, all_52_7) = all_52_6
% 177.58/28.09    (132)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.58/28.09    (133)  op(e2, e3) = all_52_9
% 177.58/28.09    (134)  all_56_13 = all_52_27
% 177.58/28.09  
% 177.58/28.09  Begin of proof
% 177.58/28.09  | 
% 177.58/28.09  | ALPHA: (132) implies:
% 177.58/28.09  |   (135)  all_52_6 = e0
% 177.58/28.09  |   (136)  all_52_4 = e1
% 177.58/28.09  |   (137)  all_52_2 = e2
% 177.58/28.09  |   (138)  all_52_0 = e3
% 177.58/28.09  | 
% 177.58/28.09  | COMBINE_EQS: (66), (138) imply:
% 177.58/28.09  |   (139)  all_4_1 = e3
% 177.58/28.09  | 
% 177.58/28.09  | REDUCE: (60), (139) imply:
% 177.58/28.10  |   (140)  op(e3, all_4_2) = all_4_0
% 177.58/28.10  | 
% 177.58/28.10  | REDUCE: (36), (139) imply:
% 177.58/28.10  |   (141)  op(e3, all_4_2) = e3
% 177.58/28.10  | 
% 177.58/28.10  | REDUCE: (81), (137) imply:
% 177.58/28.10  |   (142)  op(e2, all_52_3) = e2
% 177.58/28.10  | 
% 177.58/28.10  | REDUCE: (45), (136) imply:
% 177.58/28.10  |   (143)  op(e1, all_52_5) = e1
% 177.58/28.10  | 
% 177.58/28.10  | REDUCE: (131), (135) imply:
% 177.58/28.10  |   (144)  op(e0, all_52_7) = e0
% 177.58/28.10  | 
% 177.58/28.10  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.58/28.10  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.58/28.10  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.58/28.10  |            (35), (37), (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 177.58/28.10  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 177.58/28.10  |            (59), (61), (62), (63), (64), (65), (67), (68), (69), (70), (71),
% 177.58/28.10  |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (82), (83),
% 177.58/28.10  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 177.58/28.10  |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 177.58/28.10  |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 177.58/28.10  |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 177.58/28.10  |            (123), (124), (125), (126), (127), (128), (129), (130), (133),
% 177.58/28.10  |            (134), (140), (141), (142), (143), (144) are inconsistent by
% 177.58/28.10  |            sub-proof #496.
% 177.58/28.10  | 
% 177.58/28.10  End of proof
% 177.58/28.10  
% 177.58/28.10  Sub-proof #437 shows that the following formulas are inconsistent:
% 177.58/28.10  ----------------------------------------------------------------
% 177.58/28.10    (1)   ~ (all_10_1 = e0)
% 177.58/28.10    (2)  op(all_10_1, e3) = e1
% 177.58/28.10    (3)  all_56_4 = all_10_1
% 177.58/28.10    (4)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.58/28.10    (5)  op(e1, e3) = e2
% 177.58/28.10    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.10    (7)   ~ (all_10_1 = e2)
% 177.58/28.10  
% 177.58/28.10  Begin of proof
% 177.58/28.10  | 
% 177.58/28.10  | BETA: splitting (4) gives:
% 177.58/28.10  | 
% 177.58/28.10  | Case 1:
% 177.58/28.10  | | 
% 177.58/28.10  | |   (8)  all_56_4 = e2
% 177.58/28.10  | | 
% 177.58/28.10  | | REF_CLOSE: (3), (7), (8) are inconsistent by sub-proof #544.
% 177.58/28.10  | | 
% 177.58/28.10  | Case 2:
% 177.58/28.10  | | 
% 177.58/28.10  | |   (9)   ~ (all_56_4 = e2)
% 177.58/28.10  | |   (10)  all_56_4 = e1 | all_56_4 = e0
% 177.58/28.10  | | 
% 177.58/28.10  | | BETA: splitting (10) gives:
% 177.58/28.10  | | 
% 177.58/28.10  | | Case 1:
% 177.58/28.10  | | | 
% 177.58/28.10  | | |   (11)  all_56_4 = e1
% 177.58/28.10  | | | 
% 177.58/28.10  | | | COMBINE_EQS: (3), (11) imply:
% 177.58/28.10  | | |   (12)  all_10_1 = e1
% 177.58/28.10  | | | 
% 177.58/28.10  | | | SIMP: (12) implies:
% 177.58/28.10  | | |   (13)  all_10_1 = e1
% 177.58/28.10  | | | 
% 177.58/28.10  | | | REDUCE: (7), (13) imply:
% 177.58/28.10  | | |   (14)   ~ (e2 = e1)
% 177.58/28.10  | | | 
% 177.58/28.10  | | | SIMP: (14) implies:
% 177.58/28.10  | | |   (15)   ~ (e2 = e1)
% 177.58/28.10  | | | 
% 177.58/28.10  | | | REDUCE: (2), (13) imply:
% 177.58/28.10  | | |   (16)  op(e1, e3) = e1
% 177.58/28.10  | | | 
% 177.58/28.10  | | | REF_CLOSE: (5), (6), (15), (16) are inconsistent by sub-proof #438.
% 177.58/28.10  | | | 
% 177.58/28.10  | | Case 2:
% 177.58/28.10  | | | 
% 177.58/28.10  | | |   (17)  all_56_4 = e0
% 177.58/28.10  | | | 
% 177.58/28.10  | | | REF_CLOSE: (1), (3), (17) are inconsistent by sub-proof #542.
% 177.58/28.10  | | | 
% 177.58/28.10  | | End of split
% 177.58/28.10  | | 
% 177.58/28.10  | End of split
% 177.58/28.10  | 
% 177.58/28.10  End of proof
% 177.58/28.10  
% 177.58/28.10  Sub-proof #438 shows that the following formulas are inconsistent:
% 177.58/28.10  ----------------------------------------------------------------
% 177.58/28.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.10    (2)  op(e1, e3) = e2
% 177.58/28.10    (3)  op(e1, e3) = e1
% 177.58/28.10    (4)   ~ (e2 = e1)
% 177.58/28.10  
% 177.58/28.10  Begin of proof
% 177.58/28.10  | 
% 177.58/28.10  | GROUND_INST: instantiating (1) with e2, e1, e3, e1, simplifying with (2), (3)
% 177.58/28.10  |              gives:
% 177.58/28.10  |   (5)  e2 = e1
% 177.58/28.10  | 
% 177.58/28.10  | REDUCE: (4), (5) imply:
% 177.58/28.10  |   (6)  $false
% 177.58/28.10  | 
% 177.58/28.10  | CLOSE: (6) is inconsistent.
% 177.58/28.10  | 
% 177.58/28.10  End of proof
% 177.58/28.10  
% 177.58/28.10  Sub-proof #439 shows that the following formulas are inconsistent:
% 177.58/28.10  ----------------------------------------------------------------
% 177.58/28.10    (1)  op(e2, all_10_2) = all_10_1
% 177.58/28.10    (2)  all_56_3 = all_52_7
% 177.58/28.10    (3)  op(all_10_1, all_10_2) = e1
% 177.58/28.10    (4)  op(e3, e2) = all_52_3
% 177.58/28.10    (5)   ~ (all_52_27 = e0)
% 177.58/28.10    (6)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.10    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.10    (8)  all_58_15 = all_6_2
% 177.58/28.10    (9)   ~ (all_52_5 = all_52_7)
% 177.58/28.10    (10)  all_58_10 = all_52_15
% 177.58/28.10    (11)  op(e0, e1) = all_52_29
% 177.58/28.10    (12)  all_58_4 = all_52_5
% 177.58/28.10    (13)  op(e3, all_4_2) = all_4_1
% 177.58/28.10    (14)   ~ (all_52_7 = all_4_2)
% 177.58/28.10    (15)  all_58_1 = all_52_3
% 177.58/28.10    (16)  all_58_0 = all_4_2
% 177.58/28.10    (17)   ~ (all_52_7 = e0)
% 177.58/28.10    (18)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.10          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.58/28.10    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.10    (20)  all_58_14 = all_52_29
% 177.58/28.10    (21)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.10    (22)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.10    (23)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.10    (24)  op(e0, e2) = all_52_27
% 177.58/28.10    (25)  op(all_4_1, all_4_2) = all_4_0
% 177.58/28.10    (26)  op(e0, e3) = all_52_25
% 177.58/28.10    (27)  all_52_0 = all_4_1
% 177.58/28.10    (28)  all_52_10 = all_10_1
% 177.58/28.10    (29)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.58/28.10    (30)   ~ (e3 = e0)
% 177.58/28.10    (31)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.10    (32)   ~ (all_52_5 = all_52_29)
% 177.58/28.10    (33)  all_56_12 = all_52_25
% 177.58/28.10    (34)  all_58_13 = all_52_27
% 177.58/28.10    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.10    (36)   ~ (all_52_25 = e0)
% 177.58/28.10    (37)   ~ (all_52_3 = all_52_7)
% 177.58/28.10    (38)  all_56_0 = all_4_2
% 177.58/28.10    (39)  all_58_11 = all_52_23
% 177.58/28.10    (40)   ~ (all_52_7 = all_52_15)
% 177.58/28.10    (41)  all_58_15 = e0
% 177.58/28.10    (42)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.58/28.10    (43)   ~ (all_52_29 = e0)
% 177.58/28.10    (44)  op(e3, e1) = all_52_5
% 177.58/28.10    (45)   ~ (e2 = e1)
% 177.58/28.10    (46)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.10    (47)   ~ (all_52_25 = all_4_2)
% 177.58/28.10    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.10            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.10    (49)   ~ (all_52_25 = all_52_27)
% 177.58/28.10    (50)   ~ (all_52_7 = all_6_2)
% 177.58/28.10    (51)   ~ (all_52_7 = all_52_23)
% 177.58/28.10    (52)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.10    (53)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.10    (54)  all_58_9 = all_52_7
% 177.58/28.10    (55)  all_58_12 = all_52_25
% 177.58/28.10    (56)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.10    (57)  op(e0, all_52_7) = all_52_6
% 177.58/28.10    (58)  all_56_13 = all_52_27
% 177.58/28.10  
% 177.58/28.10  Begin of proof
% 177.58/28.10  | 
% 177.58/28.10  | BETA: splitting (18) gives:
% 177.58/28.10  | 
% 177.58/28.10  | Case 1:
% 177.58/28.10  | | 
% 177.58/28.10  | |   (59)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.58/28.10  | | 
% 177.58/28.10  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 177.58/28.10  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), (26),
% 177.58/28.10  | |            (27), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 177.58/28.10  | |            (39), (40), (41), (42), (43), (44), (46), (47), (48), (49), (50),
% 177.58/28.10  | |            (51), (52), (53), (54), (55), (56), (57), (58), (59) are
% 177.58/28.10  | |            inconsistent by sub-proof #1008.
% 177.58/28.10  | | 
% 177.58/28.10  | Case 2:
% 177.58/28.10  | | 
% 177.58/28.10  | |   (60)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.58/28.10  | | 
% 177.58/28.10  | | ALPHA: (60) implies:
% 177.58/28.10  | |   (61)  all_52_10 = e2
% 177.58/28.10  | | 
% 177.58/28.10  | | COMBINE_EQS: (28), (61) imply:
% 177.58/28.10  | |   (62)  all_10_1 = e2
% 177.58/28.10  | | 
% 177.58/28.10  | | REF_CLOSE: (1), (3), (45), (48), (62) are inconsistent by sub-proof #446.
% 177.58/28.10  | | 
% 177.58/28.10  | End of split
% 177.58/28.10  | 
% 177.58/28.10  End of proof
% 177.58/28.10  
% 177.58/28.10  Sub-proof #440 shows that the following formulas are inconsistent:
% 177.58/28.10  ----------------------------------------------------------------
% 177.58/28.10    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.10    (2)   ~ (all_52_5 = all_52_13)
% 177.58/28.10    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.58/28.10    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.10    (5)   ~ (all_52_17 = all_52_23)
% 177.58/28.10    (6)  op(e2, all_10_2) = all_10_1
% 177.58/28.10    (7)  op(e3, e2) = all_52_3
% 177.58/28.10    (8)   ~ (all_52_9 = all_52_25)
% 177.58/28.10    (9)  op(e3, all_52_25) = all_52_24
% 177.58/28.10    (10)   ~ (all_52_19 = all_52_23)
% 177.58/28.10    (11)  op(e1, e2) = all_52_19
% 177.58/28.10    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.58/28.10    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.10    (14)  all_58_5 = all_52_13
% 177.58/28.10    (15)   ~ (all_52_25 = all_52_29)
% 177.58/28.10    (16)  all_56_15 = all_6_2
% 177.58/28.10    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.10    (18)  op(e2, e0) = all_52_15
% 177.58/28.10    (19)  op(all_14_1, all_14_2) = all_14_0
% 177.58/28.10    (20)  all_58_3 = all_10_2
% 177.58/28.10    (21)  all_56_9 = all_52_19
% 177.58/28.10    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.10    (23)  all_58_15 = all_6_2
% 177.58/28.10    (24)   ~ (all_52_9 = all_4_2)
% 177.58/28.10    (25)   ~ (all_52_5 = all_52_7)
% 177.58/28.10    (26)  all_58_10 = all_52_15
% 177.58/28.10    (27)   ~ (all_52_5 = all_4_2)
% 177.58/28.10    (28)  all_58_7 = all_52_19
% 177.58/28.10    (29)   ~ (all_52_17 = all_52_25)
% 177.58/28.10    (30)  all_58_4 = all_52_5
% 177.58/28.10    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.10    (32)  all_34_1 = all_4_1
% 177.58/28.10    (33)   ~ (all_52_27 = all_52_29)
% 177.58/28.10    (34)   ~ (all_52_17 = all_14_2)
% 177.58/28.10    (35)  op(e3, all_4_2) = all_4_1
% 177.58/28.10    (36)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.10    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.10    (38)   ~ (all_52_7 = all_4_2)
% 177.58/28.10    (39)  all_58_1 = all_52_3
% 177.58/28.10    (40)  all_58_0 = all_4_2
% 177.58/28.10    (41)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.10    (42)  op(all_4_1, all_4_2) = e1
% 177.58/28.10    (43)  op(e1, all_52_29) = all_52_28
% 177.58/28.10    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.58/28.10    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.10    (46)   ~ (all_4_1 = e2)
% 177.58/28.10    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.10    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.10    (49)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.58/28.10    (50)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.58/28.10    (51)  all_58_14 = all_52_29
% 177.58/28.10    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.10    (53)   ~ (all_52_3 = all_52_5)
% 177.58/28.10    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.10    (55)  op(e2, e1) = all_52_13
% 177.58/28.10    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.10    (57)  all_58_8 = all_14_2
% 177.58/28.10    (58)  all_56_1 = all_52_3
% 177.58/28.10    (59)   ~ (all_14_0 = e3)
% 177.58/28.10    (60)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.58/28.10    (61)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.10    (62)   ~ (all_52_5 = all_14_2)
% 177.58/28.10    (63)   ~ (all_52_3 = all_4_2)
% 177.58/28.10    (64)  op(e0, e3) = all_52_25
% 177.58/28.10    (65)   ~ (all_52_9 = all_10_2)
% 177.58/28.10    (66)  op(e3, all_52_17) = all_52_16
% 177.58/28.10    (67)   ~ (all_52_13 = all_14_2)
% 177.58/28.10    (68)   ~ (e3 = e0)
% 177.58/28.10    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.10    (70)   ~ (all_52_9 = all_52_13)
% 177.58/28.10    (71)  op(e0, all_52_23) = all_52_22
% 177.58/28.10    (72)   ~ (all_52_15 = all_52_23)
% 177.58/28.10    (73)   ~ (all_52_5 = all_52_29)
% 177.58/28.10    (74)  all_58_13 = all_52_27
% 177.58/28.10    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.10    (76)  all_56_5 = all_10_2
% 177.58/28.10    (77)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.10    (78)   ~ (all_52_9 = all_52_17)
% 177.58/28.10    (79)   ~ (all_14_0 = e2)
% 177.58/28.10    (80)  all_58_6 = all_52_17
% 177.58/28.10    (81)  op(e2, all_52_19) = all_52_18
% 177.58/28.10    (82)   ~ (e1 = e0)
% 177.58/28.10    (83)  all_56_0 = all_4_2
% 177.58/28.10    (84)  all_58_11 = all_52_23
% 177.58/28.10    (85)   ~ (all_52_3 = all_52_19)
% 177.58/28.10    (86)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.58/28.10    (87)   ~ (all_52_7 = all_52_15)
% 177.58/28.10    (88)   ~ (all_52_29 = all_14_2)
% 177.58/28.10    (89)   ~ (all_52_19 = all_10_2)
% 177.58/28.10    (90)   ~ (all_52_23 = all_6_2)
% 177.58/28.10    (91)  all_58_2 = all_52_9
% 177.58/28.10    (92)  op(e3, e1) = all_52_5
% 177.58/28.10    (93)   ~ (all_52_25 = all_6_2)
% 177.58/28.10    (94)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.10    (95)  op(e1, e3) = all_52_17
% 177.58/28.10    (96)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.10    (97)   ~ (all_52_25 = all_4_2)
% 177.58/28.10    (98)  op(e3, e0) = all_52_7
% 177.58/28.10    (99)  op(e3, e3) = all_4_2
% 177.58/28.10    (100)   ~ (all_10_1 = e3)
% 177.58/28.10    (101)  all_56_8 = all_52_17
% 177.58/28.10    (102)   ~ (all_52_17 = all_4_2)
% 177.58/28.10    (103)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.10             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.10    (104)   ~ (all_52_25 = all_52_27)
% 177.58/28.10    (105)  all_34_2 = all_4_2
% 177.58/28.10    (106)   ~ (all_52_27 = all_6_2)
% 177.58/28.10    (107)   ~ (all_52_7 = all_6_2)
% 177.58/28.10    (108)   ~ (all_52_15 = all_10_2)
% 177.58/28.10    (109)   ~ (all_52_19 = all_52_27)
% 177.58/28.10    (110)  all_56_7 = all_52_15
% 177.58/28.10    (111)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.58/28.10    (112)   ~ (all_52_7 = all_52_23)
% 177.58/28.10    (113)   ~ (all_52_13 = all_10_2)
% 177.58/28.10    (114)  op(e2, all_52_27) = all_52_26
% 177.58/28.10    (115)  all_52_20 = all_14_1
% 177.58/28.10    (116)   ~ (all_52_17 = all_52_19)
% 177.58/28.10    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.10    (118)  op(e1, all_14_2) = all_14_1
% 177.58/28.10    (119)  all_58_9 = all_52_7
% 177.58/28.10    (120)   ~ (e2 = e0)
% 177.58/28.10    (121)  all_58_12 = all_52_25
% 177.58/28.10    (122)  all_56_6 = all_52_13
% 177.58/28.10    (123)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.10    (124)   ~ (all_52_9 = all_52_15)
% 177.58/28.10    (125)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.10    (126)   ~ (e3 = e2)
% 177.58/28.10    (127)   ~ (all_52_19 = all_14_2)
% 177.58/28.10    (128)  op(e2, e3) = all_52_9
% 177.58/28.10    (129)  all_56_13 = all_52_27
% 177.58/28.10  
% 177.58/28.10  Begin of proof
% 177.58/28.10  | 
% 177.58/28.10  | ALPHA: (111) implies:
% 177.58/28.10  |   (130)  all_52_22 = e0
% 177.58/28.10  |   (131)  all_52_20 = e1
% 177.58/28.10  |   (132)  all_52_18 = e2
% 177.58/28.10  |   (133)  all_52_16 = e3
% 177.58/28.10  | 
% 177.58/28.10  | COMBINE_EQS: (115), (131) imply:
% 177.58/28.10  |   (134)  all_14_1 = e1
% 177.58/28.10  | 
% 177.58/28.10  | SIMP: (134) implies:
% 177.58/28.10  |   (135)  all_14_1 = e1
% 177.58/28.10  | 
% 177.58/28.10  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.58/28.10  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.58/28.10  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.58/28.10  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.58/28.10  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.58/28.10  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.58/28.10  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 177.58/28.10  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 177.58/28.10  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.58/28.10  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 177.58/28.10  |            (110), (112), (113), (114), (116), (117), (118), (119), (120),
% 177.58/28.10  |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 177.58/28.10  |            (130), (132), (133), (135) are inconsistent by sub-proof #560.
% 177.58/28.10  | 
% 177.58/28.10  End of proof
% 177.58/28.10  
% 177.58/28.10  Sub-proof #441 shows that the following formulas are inconsistent:
% 177.58/28.10  ----------------------------------------------------------------
% 177.58/28.10    (1)  op(e2, all_10_2) = all_10_1
% 177.58/28.10    (2)  op(all_10_1, all_10_2) = e1
% 177.58/28.10    (3)   ~ (e3 = e1)
% 177.58/28.10    (4)  op(e3, all_4_2) = all_4_1
% 177.58/28.10    (5)  op(all_4_1, all_4_2) = e1
% 177.58/28.10    (6)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.10         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.58/28.10    (7)  all_52_0 = all_4_1
% 177.58/28.10    (8)  all_52_10 = all_10_1
% 177.58/28.10    (9)   ~ (e2 = e1)
% 177.58/28.10    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.10            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.10  
% 177.58/28.10  Begin of proof
% 177.58/28.10  | 
% 177.58/28.10  | BETA: splitting (6) gives:
% 177.58/28.10  | 
% 177.58/28.10  | Case 1:
% 177.58/28.10  | | 
% 177.58/28.10  | |   (11)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.58/28.10  | | 
% 177.58/28.10  | | REF_CLOSE: (3), (4), (5), (7), (10), (11) are inconsistent by sub-proof
% 177.58/28.10  | |            #600.
% 177.58/28.10  | | 
% 177.58/28.10  | Case 2:
% 177.58/28.10  | | 
% 177.58/28.10  | |   (12)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.58/28.10  | | 
% 177.58/28.10  | | ALPHA: (12) implies:
% 177.58/28.10  | |   (13)  all_52_10 = e2
% 177.58/28.10  | | 
% 177.58/28.10  | | COMBINE_EQS: (8), (13) imply:
% 177.58/28.10  | |   (14)  all_10_1 = e2
% 177.58/28.10  | | 
% 177.58/28.10  | | REF_CLOSE: (1), (2), (9), (10), (14) are inconsistent by sub-proof #446.
% 177.58/28.10  | | 
% 177.58/28.10  | End of split
% 177.58/28.10  | 
% 177.58/28.10  End of proof
% 177.58/28.10  
% 177.58/28.10  Sub-proof #442 shows that the following formulas are inconsistent:
% 177.58/28.10  ----------------------------------------------------------------
% 177.58/28.10    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.10    (2)   ~ (all_52_5 = all_52_13)
% 177.58/28.10    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.58/28.10    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.10    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.10    (6)   ~ (all_52_27 = all_10_2)
% 177.58/28.10    (7)   ~ (all_52_17 = all_52_23)
% 177.58/28.10    (8)  op(e2, all_10_2) = all_10_1
% 177.58/28.10    (9)  all_40_2 = all_4_2
% 177.58/28.10    (10)   ~ (all_52_13 = all_52_29)
% 177.58/28.10    (11)  op(all_10_1, all_10_2) = e1
% 177.58/28.10    (12)  op(e3, e2) = all_52_3
% 177.58/28.10    (13)   ~ (all_52_9 = all_52_25)
% 177.58/28.10    (14)  op(e3, all_52_25) = all_52_24
% 177.58/28.10    (15)   ~ (all_52_19 = all_52_23)
% 177.58/28.10    (16)  op(e1, e2) = all_52_19
% 177.58/28.10    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.58/28.10    (18)  op(e3, all_52_9) = all_52_8
% 177.58/28.10    (19)   ~ (all_52_3 = all_10_2)
% 177.58/28.10    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.10    (21)  all_58_5 = all_52_13
% 177.58/28.10    (22)   ~ (all_52_25 = all_52_29)
% 177.58/28.10    (23)  all_56_15 = all_6_2
% 177.58/28.10    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.10    (25)  op(e2, e0) = all_52_15
% 177.58/28.10    (26)  op(all_14_1, all_14_2) = all_14_0
% 177.58/28.10    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.10    (28)  all_58_3 = all_10_2
% 177.58/28.10    (29)  all_56_9 = all_52_19
% 177.58/28.10    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.10    (31)  all_58_15 = all_6_2
% 177.58/28.10    (32)   ~ (all_52_9 = all_4_2)
% 177.58/28.10    (33)   ~ (all_52_5 = all_52_7)
% 177.58/28.10    (34)  all_58_10 = all_52_15
% 177.58/28.10    (35)   ~ (all_52_5 = all_4_2)
% 177.58/28.10    (36)  all_58_7 = all_52_19
% 177.58/28.10    (37)   ~ (all_52_17 = all_52_25)
% 177.58/28.10    (38)  op(e0, e1) = all_52_29
% 177.58/28.10    (39)   ~ (all_4_0 = e2)
% 177.58/28.10    (40)  all_58_4 = all_52_5
% 177.58/28.10    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.10    (42)   ~ (e3 = e1)
% 177.58/28.10    (43)   ~ (all_52_27 = all_52_29)
% 177.58/28.10    (44)   ~ (all_52_17 = all_14_2)
% 177.58/28.10    (45)  op(e3, all_4_2) = all_4_1
% 177.58/28.10    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.10    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.10    (48)   ~ (all_52_7 = all_4_2)
% 177.58/28.10    (49)  all_58_1 = all_52_3
% 177.58/28.10    (50)   ~ (all_52_13 = all_52_15)
% 177.58/28.10    (51)  all_58_0 = all_4_2
% 177.58/28.10    (52)  all_52_0 = e1
% 177.58/28.10    (53)  op(e1, all_52_29) = all_52_28
% 177.58/28.10    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.10    (55)   ~ (all_4_1 = e2)
% 177.58/28.10    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.10    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.10    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.58/28.10    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.58/28.10    (60)  all_58_14 = all_52_29
% 177.58/28.10    (61)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.10    (62)   ~ (all_52_3 = all_52_5)
% 177.58/28.10    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.10    (64)  op(e2, e1) = all_52_13
% 177.58/28.10    (65)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.10    (66)  all_58_8 = all_14_2
% 177.58/28.10    (67)  op(e0, e2) = all_52_27
% 177.58/28.10    (68)   ~ (all_14_0 = e3)
% 177.58/28.10    (69)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.58/28.10    (70)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.58/28.10    (71)  op(all_4_1, all_4_2) = all_4_0
% 177.58/28.10    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.10    (73)   ~ (all_52_5 = all_14_2)
% 177.58/28.10    (74)   ~ (all_52_3 = all_52_27)
% 177.58/28.10    (75)   ~ (all_52_3 = all_4_2)
% 177.58/28.10    (76)  op(e0, e3) = all_52_25
% 177.58/28.10    (77)  op(e0, all_6_2) = all_6_1
% 177.58/28.10    (78)   ~ (all_52_9 = all_10_2)
% 177.58/28.10    (79)  op(e3, all_52_17) = all_52_16
% 177.58/28.10    (80)  all_52_10 = all_10_1
% 177.58/28.10    (81)   ~ (all_52_13 = all_14_2)
% 177.58/28.10    (82)   ~ (e3 = e0)
% 177.58/28.10    (83)  all_40_0 = all_4_0
% 177.58/28.10    (84)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.10    (85)   ~ (all_52_9 = all_52_13)
% 177.58/28.10    (86)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.10    (87)  op(e0, all_52_23) = all_52_22
% 177.58/28.10    (88)   ~ (all_52_15 = all_52_23)
% 177.58/28.10    (89)   ~ (all_52_5 = all_52_29)
% 177.58/28.10    (90)  op(e1, e0) = all_52_23
% 177.58/28.10    (91)  all_56_12 = all_52_25
% 177.58/28.10    (92)  all_58_13 = all_52_27
% 177.58/28.10    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.10    (94)  all_56_5 = all_10_2
% 177.58/28.10    (95)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.10    (96)   ~ (all_52_9 = all_52_17)
% 177.58/28.10    (97)   ~ (all_14_0 = e2)
% 177.58/28.10    (98)  all_58_6 = all_52_17
% 177.58/28.10    (99)   ~ (all_52_3 = all_52_7)
% 177.58/28.10    (100)  op(e2, all_52_19) = all_52_18
% 177.58/28.10    (101)   ~ (e1 = e0)
% 177.58/28.10    (102)  all_56_0 = all_4_2
% 177.58/28.10    (103)  all_58_11 = all_52_23
% 177.58/28.10    (104)   ~ (all_52_3 = all_52_19)
% 177.58/28.10    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.58/28.10    (106)   ~ (all_52_7 = all_52_15)
% 177.58/28.10    (107)   ~ (all_52_29 = all_14_2)
% 177.58/28.10    (108)   ~ (all_4_0 = e1)
% 177.58/28.10    (109)   ~ (all_52_19 = all_10_2)
% 177.58/28.10    (110)   ~ (all_58_15 = e0)
% 177.58/28.10    (111)   ~ (all_52_23 = all_6_2)
% 177.58/28.10    (112)  op(e1, all_4_2) = all_4_0
% 177.58/28.10    (113)   ~ (all_52_29 = all_6_2)
% 177.58/28.10    (114)  all_58_2 = all_52_9
% 177.58/28.10    (115)  op(e3, e1) = all_52_5
% 177.58/28.10    (116)   ~ (e2 = e1)
% 177.58/28.10    (117)   ~ (all_52_25 = all_6_2)
% 177.58/28.10    (118)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.10    (119)  op(e1, e3) = all_52_17
% 177.58/28.10    (120)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.10    (121)   ~ (all_52_25 = all_4_2)
% 177.58/28.10    (122)  op(e3, e0) = all_52_7
% 177.58/28.10    (123)  op(e3, e3) = all_4_2
% 177.58/28.10    (124)   ~ (all_10_1 = e3)
% 177.58/28.10    (125)  all_56_8 = all_52_17
% 177.58/28.10    (126)   ~ (all_52_17 = all_4_2)
% 177.58/28.10    (127)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.10             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.10    (128)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.10           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.58/28.10           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.58/28.10           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.58/28.10    (129)   ~ (all_52_25 = all_52_27)
% 177.58/28.10    (130)   ~ (all_52_27 = all_6_2)
% 177.58/28.10    (131)   ~ (all_52_7 = all_6_2)
% 177.58/28.10    (132)   ~ (all_52_15 = all_10_2)
% 177.58/28.10    (133)   ~ (all_52_19 = all_52_27)
% 177.58/28.10    (134)  all_56_7 = all_52_15
% 177.58/28.10    (135)   ~ (all_52_7 = all_52_23)
% 177.58/28.10    (136)   ~ (all_52_13 = all_10_2)
% 177.58/28.10    (137)  op(e2, all_52_27) = all_52_26
% 177.58/28.10    (138)  all_52_20 = all_14_1
% 177.58/28.10    (139)   ~ (all_52_17 = all_52_19)
% 177.58/28.10    (140)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.10    (141)  all_52_30 = all_6_1
% 177.58/28.10    (142)  op(e1, all_14_2) = all_14_1
% 177.58/28.10    (143)  all_58_9 = all_52_7
% 177.58/28.10    (144)   ~ (e2 = e0)
% 177.58/28.10    (145)  all_58_12 = all_52_25
% 177.58/28.10    (146)  op(e3, all_4_2) = e1
% 177.58/28.10    (147)  all_56_6 = all_52_13
% 177.58/28.10    (148)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 177.58/28.10             all_58_13 = e0 | all_58_14 = e0)
% 177.58/28.10    (149)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.10    (150)   ~ (all_52_9 = all_52_15)
% 177.58/28.10    (151)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.10    (152)   ~ (e3 = e2)
% 177.58/28.10    (153)   ~ (all_52_19 = all_14_2)
% 177.58/28.10    (154)  op(e2, e3) = all_52_9
% 177.58/28.10    (155)  all_56_13 = all_52_27
% 177.58/28.10  
% 177.58/28.10  Begin of proof
% 177.58/28.10  | 
% 177.58/28.10  | ALPHA: (148) implies:
% 177.58/28.11  |   (156)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.11  |   (157)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.11  | 
% 177.58/28.11  | REDUCE: (31), (110) imply:
% 177.58/28.11  |   (158)   ~ (all_6_2 = e0)
% 177.58/28.11  | 
% 177.58/28.11  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.58/28.11  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.58/28.11  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.58/28.11  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.58/28.11  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.58/28.11  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.58/28.11  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 177.58/28.11  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 177.58/28.11  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.58/28.11  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 177.58/28.11  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 177.58/28.11  |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 177.58/28.11  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 177.58/28.11  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 177.58/28.11  |            (147), (149), (150), (151), (152), (153), (154), (155), (156),
% 177.58/28.11  |            (157), (158) are inconsistent by sub-proof #443.
% 177.58/28.11  | 
% 177.58/28.11  End of proof
% 177.58/28.11  
% 177.58/28.11  Sub-proof #443 shows that the following formulas are inconsistent:
% 177.58/28.11  ----------------------------------------------------------------
% 177.58/28.11    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.11    (2)   ~ (all_52_5 = all_52_13)
% 177.58/28.11    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.58/28.11    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.11    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.11    (6)   ~ (all_52_27 = all_10_2)
% 177.58/28.11    (7)   ~ (all_52_17 = all_52_23)
% 177.58/28.11    (8)  op(e2, all_10_2) = all_10_1
% 177.58/28.11    (9)  all_40_2 = all_4_2
% 177.58/28.11    (10)   ~ (all_52_13 = all_52_29)
% 177.58/28.11    (11)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.11    (12)  op(all_10_1, all_10_2) = e1
% 177.58/28.11    (13)  op(e3, e2) = all_52_3
% 177.58/28.11    (14)   ~ (all_52_9 = all_52_25)
% 177.58/28.11    (15)  op(e3, all_52_25) = all_52_24
% 177.58/28.11    (16)   ~ (all_52_19 = all_52_23)
% 177.58/28.11    (17)  op(e1, e2) = all_52_19
% 177.58/28.11    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.58/28.11    (19)  op(e3, all_52_9) = all_52_8
% 177.58/28.11    (20)   ~ (all_52_3 = all_10_2)
% 177.58/28.11    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.11    (22)  all_58_5 = all_52_13
% 177.58/28.11    (23)   ~ (all_6_2 = e0)
% 177.58/28.11    (24)   ~ (all_52_25 = all_52_29)
% 177.58/28.11    (25)  all_56_15 = all_6_2
% 177.58/28.11    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.11    (27)  op(e2, e0) = all_52_15
% 177.58/28.11    (28)  op(all_14_1, all_14_2) = all_14_0
% 177.58/28.11    (29)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.11    (30)  all_58_3 = all_10_2
% 177.58/28.11    (31)  all_56_9 = all_52_19
% 177.58/28.11    (32)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.11    (33)  all_58_15 = all_6_2
% 177.58/28.11    (34)   ~ (all_52_9 = all_4_2)
% 177.58/28.11    (35)   ~ (all_52_5 = all_52_7)
% 177.58/28.11    (36)  all_58_10 = all_52_15
% 177.58/28.11    (37)   ~ (all_52_5 = all_4_2)
% 177.58/28.11    (38)  all_58_7 = all_52_19
% 177.58/28.11    (39)   ~ (all_52_17 = all_52_25)
% 177.58/28.11    (40)  op(e0, e1) = all_52_29
% 177.58/28.11    (41)   ~ (all_4_0 = e2)
% 177.58/28.11    (42)  all_58_4 = all_52_5
% 177.58/28.11    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.11    (44)   ~ (e3 = e1)
% 177.58/28.11    (45)   ~ (all_52_27 = all_52_29)
% 177.58/28.11    (46)   ~ (all_52_17 = all_14_2)
% 177.58/28.11    (47)  op(e3, all_4_2) = all_4_1
% 177.58/28.11    (48)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.11    (49)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.11    (50)   ~ (all_52_7 = all_4_2)
% 177.58/28.11    (51)  all_58_1 = all_52_3
% 177.58/28.11    (52)   ~ (all_52_13 = all_52_15)
% 177.58/28.11    (53)  all_58_0 = all_4_2
% 177.58/28.11    (54)  all_52_0 = e1
% 177.58/28.11    (55)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.11    (56)  op(e1, all_52_29) = all_52_28
% 177.58/28.11    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.11    (58)   ~ (all_4_1 = e2)
% 177.58/28.11    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.11    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.11    (61)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.58/28.11    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.58/28.11    (63)  all_58_14 = all_52_29
% 177.58/28.11    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.11    (65)   ~ (all_52_3 = all_52_5)
% 177.58/28.11    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.11    (67)  op(e2, e1) = all_52_13
% 177.58/28.11    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.11    (69)  all_58_8 = all_14_2
% 177.58/28.11    (70)  op(e0, e2) = all_52_27
% 177.58/28.11    (71)   ~ (all_14_0 = e3)
% 177.58/28.11    (72)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.58/28.11    (73)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.58/28.11    (74)  op(all_4_1, all_4_2) = all_4_0
% 177.58/28.11    (75)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.11    (76)   ~ (all_52_5 = all_14_2)
% 177.58/28.11    (77)   ~ (all_52_3 = all_52_27)
% 177.58/28.11    (78)   ~ (all_52_3 = all_4_2)
% 177.58/28.11    (79)  op(e0, e3) = all_52_25
% 177.58/28.11    (80)  op(e0, all_6_2) = all_6_1
% 177.58/28.11    (81)   ~ (all_52_9 = all_10_2)
% 177.58/28.11    (82)  op(e3, all_52_17) = all_52_16
% 177.58/28.11    (83)  all_52_10 = all_10_1
% 177.58/28.11    (84)   ~ (all_52_13 = all_14_2)
% 177.58/28.11    (85)   ~ (e3 = e0)
% 177.58/28.11    (86)  all_40_0 = all_4_0
% 177.58/28.11    (87)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.11    (88)   ~ (all_52_9 = all_52_13)
% 177.58/28.11    (89)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.11    (90)  op(e0, all_52_23) = all_52_22
% 177.58/28.11    (91)   ~ (all_52_15 = all_52_23)
% 177.58/28.11    (92)   ~ (all_52_5 = all_52_29)
% 177.58/28.11    (93)  op(e1, e0) = all_52_23
% 177.58/28.11    (94)  all_56_12 = all_52_25
% 177.58/28.11    (95)  all_58_13 = all_52_27
% 177.58/28.11    (96)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.11    (97)  all_56_5 = all_10_2
% 177.58/28.11    (98)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.11    (99)   ~ (all_52_9 = all_52_17)
% 177.58/28.11    (100)   ~ (all_14_0 = e2)
% 177.58/28.11    (101)  all_58_6 = all_52_17
% 177.58/28.11    (102)   ~ (all_52_3 = all_52_7)
% 177.58/28.11    (103)  op(e2, all_52_19) = all_52_18
% 177.58/28.11    (104)   ~ (e1 = e0)
% 177.58/28.11    (105)  all_56_0 = all_4_2
% 177.58/28.11    (106)  all_58_11 = all_52_23
% 177.58/28.11    (107)   ~ (all_52_3 = all_52_19)
% 177.58/28.11    (108)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.58/28.11    (109)   ~ (all_52_7 = all_52_15)
% 177.58/28.11    (110)   ~ (all_52_29 = all_14_2)
% 177.58/28.11    (111)   ~ (all_4_0 = e1)
% 177.58/28.11    (112)   ~ (all_52_19 = all_10_2)
% 177.58/28.11    (113)   ~ (all_52_23 = all_6_2)
% 177.58/28.11    (114)  op(e1, all_4_2) = all_4_0
% 177.58/28.11    (115)   ~ (all_52_29 = all_6_2)
% 177.58/28.11    (116)  all_58_2 = all_52_9
% 177.58/28.11    (117)  op(e3, e1) = all_52_5
% 177.58/28.11    (118)   ~ (e2 = e1)
% 177.58/28.11    (119)   ~ (all_52_25 = all_6_2)
% 177.58/28.11    (120)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.58/28.11    (121)  op(e1, e3) = all_52_17
% 177.58/28.11    (122)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.11    (123)   ~ (all_52_25 = all_4_2)
% 177.58/28.11    (124)  op(e3, e0) = all_52_7
% 177.58/28.11    (125)  op(e3, e3) = all_4_2
% 177.58/28.11    (126)   ~ (all_10_1 = e3)
% 177.58/28.11    (127)  all_56_8 = all_52_17
% 177.58/28.11    (128)   ~ (all_52_17 = all_4_2)
% 177.58/28.11    (129)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.11             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.11    (130)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.11           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.58/28.11           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.58/28.11           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.58/28.11    (131)   ~ (all_52_25 = all_52_27)
% 177.58/28.11    (132)   ~ (all_52_27 = all_6_2)
% 177.58/28.11    (133)   ~ (all_52_7 = all_6_2)
% 177.58/28.11    (134)   ~ (all_52_15 = all_10_2)
% 177.58/28.11    (135)   ~ (all_52_19 = all_52_27)
% 177.58/28.11    (136)  all_56_7 = all_52_15
% 177.58/28.11    (137)   ~ (all_52_7 = all_52_23)
% 177.58/28.11    (138)   ~ (all_52_13 = all_10_2)
% 177.58/28.11    (139)  op(e2, all_52_27) = all_52_26
% 177.58/28.11    (140)  all_52_20 = all_14_1
% 177.58/28.11    (141)   ~ (all_52_17 = all_52_19)
% 177.58/28.11    (142)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.11    (143)  all_52_30 = all_6_1
% 177.58/28.11    (144)  op(e1, all_14_2) = all_14_1
% 177.58/28.11    (145)  all_58_9 = all_52_7
% 177.58/28.11    (146)   ~ (e2 = e0)
% 177.58/28.11    (147)  all_58_12 = all_52_25
% 177.58/28.11    (148)  op(e3, all_4_2) = e1
% 177.58/28.11    (149)  all_56_6 = all_52_13
% 177.58/28.11    (150)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.11    (151)   ~ (all_52_9 = all_52_15)
% 177.58/28.11    (152)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.11    (153)   ~ (e3 = e2)
% 177.58/28.11    (154)   ~ (all_52_19 = all_14_2)
% 177.58/28.11    (155)  op(e2, e3) = all_52_9
% 177.58/28.11    (156)  all_56_13 = all_52_27
% 177.58/28.11  
% 177.58/28.11  Begin of proof
% 177.58/28.11  | 
% 177.58/28.11  | BETA: splitting (130) gives:
% 177.58/28.11  | 
% 177.58/28.11  | Case 1:
% 177.58/28.11  | | 
% 177.58/28.11  | |   (157)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.11  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.58/28.11  | | 
% 177.58/28.11  | | REF_CLOSE: (8), (12), (44), (54), (83), (118), (129), (157) are inconsistent
% 177.58/28.11  | |            by sub-proof #445.
% 177.58/28.11  | | 
% 177.58/28.11  | Case 2:
% 177.58/28.11  | | 
% 177.58/28.11  | |   (158)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 177.58/28.11  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.58/28.11  | |            e0)
% 177.58/28.11  | | 
% 177.58/28.11  | | BETA: splitting (158) gives:
% 177.58/28.11  | | 
% 177.58/28.11  | | Case 1:
% 177.58/28.11  | | | 
% 177.58/28.11  | | |   (159)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.58/28.11  | | | 
% 177.58/28.11  | | | ALPHA: (159) implies:
% 177.58/28.11  | | |   (160)  all_52_22 = e0
% 177.58/28.11  | | |   (161)  all_52_20 = e1
% 177.58/28.11  | | |   (162)  all_52_18 = e2
% 177.58/28.11  | | |   (163)  all_52_16 = e3
% 177.58/28.11  | | | 
% 177.58/28.11  | | | COMBINE_EQS: (140), (161) imply:
% 177.58/28.11  | | |   (164)  all_14_1 = e1
% 177.58/28.11  | | | 
% 177.58/28.11  | | | REDUCE: (28), (164) imply:
% 177.58/28.11  | | |   (165)  op(e1, all_14_2) = all_14_0
% 177.58/28.11  | | | 
% 177.58/28.11  | | | REDUCE: (82), (163) imply:
% 177.58/28.11  | | |   (166)  op(e3, all_52_17) = e3
% 177.58/28.11  | | | 
% 177.58/28.11  | | | REDUCE: (103), (162) imply:
% 177.58/28.11  | | |   (167)  op(e2, all_52_19) = e2
% 177.58/28.11  | | | 
% 177.58/28.11  | | | REDUCE: (144), (164) imply:
% 177.58/28.11  | | |   (168)  op(e1, all_14_2) = e1
% 177.58/28.11  | | | 
% 177.58/28.11  | | | REDUCE: (90), (160) imply:
% 177.58/28.11  | | |   (169)  op(e0, all_52_23) = e0
% 177.58/28.11  | | | 
% 177.58/28.11  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (13), (14),
% 177.58/28.11  | | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 177.58/28.11  | | |            (26), (27), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.58/28.11  | | |            (38), (39), (41), (42), (43), (45), (46), (47), (48), (49),
% 177.58/28.11  | | |            (50), (51), (53), (55), (56), (57), (58), (59), (60), (61),
% 177.58/28.11  | | |            (62), (63), (65), (66), (67), (68), (69), (71), (72), (73),
% 177.58/28.11  | | |            (74), (75), (76), (77), (78), (79), (81), (84), (85), (86),
% 177.58/28.11  | | |            (87), (88), (89), (91), (92), (94), (95), (96), (97), (98),
% 177.58/28.11  | | |            (99), (100), (101), (104), (105), (106), (107), (108), (109),
% 177.58/28.11  | | |            (110), (111), (112), (113), (114), (116), (117), (119), (120),
% 177.58/28.11  | | |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 177.58/28.11  | | |            (131), (132), (133), (134), (135), (136), (137), (138), (141),
% 177.58/28.11  | | |            (142), (145), (146), (147), (148), (149), (150), (151), (152),
% 177.58/28.11  | | |            (153), (154), (155), (165), (166), (167), (168), (169) are
% 177.58/28.11  | | |            inconsistent by sub-proof #605.
% 177.58/28.11  | | | 
% 177.58/28.11  | | Case 2:
% 177.58/28.11  | | | 
% 177.58/28.11  | | |   (170)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.58/28.11  | | | 
% 177.58/28.11  | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (13), (14), (15), (16),
% 177.58/28.11  | | |            (18), (19), (22), (23), (24), (25), (26), (29), (30), (32),
% 177.58/28.11  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 177.58/28.11  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 177.58/28.11  | | |            (53), (55), (56), (59), (60), (63), (64), (65), (66), (68),
% 177.58/28.11  | | |            (69), (70), (74), (77), (79), (80), (81), (82), (85), (87),
% 177.58/28.11  | | |            (89), (92), (93), (94), (95), (96), (99), (101), (102), (104),
% 177.58/28.11  | | |            (105), (106), (111), (112), (115), (116), (117), (118), (119),
% 177.58/28.11  | | |            (121), (123), (124), (125), (128), (129), (131), (132), (133),
% 177.58/28.11  | | |            (134), (139), (141), (142), (143), (145), (147), (148), (150),
% 177.58/28.11  | | |            (151), (153), (155), (156), (170) are inconsistent by sub-proof
% 177.58/28.11  | | |            #444.
% 177.58/28.11  | | | 
% 177.58/28.11  | | End of split
% 177.58/28.11  | | 
% 177.58/28.11  | End of split
% 177.58/28.11  | 
% 177.58/28.11  End of proof
% 177.58/28.11  
% 177.58/28.11  Sub-proof #444 shows that the following formulas are inconsistent:
% 177.58/28.11  ----------------------------------------------------------------
% 177.58/28.11    (1)   ~ (all_52_5 = all_52_13)
% 177.58/28.11    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.11    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.11    (4)   ~ (all_52_27 = all_10_2)
% 177.58/28.11    (5)   ~ (all_52_17 = all_52_23)
% 177.58/28.11    (6)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.58/28.11    (7)   ~ (all_52_13 = all_52_29)
% 177.58/28.11    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.11    (9)  op(e3, e2) = all_52_3
% 177.58/28.11    (10)   ~ (all_52_9 = all_52_25)
% 177.58/28.11    (11)  op(e3, all_52_25) = all_52_24
% 177.58/28.11    (12)   ~ (all_52_19 = all_52_23)
% 177.58/28.11    (13)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.58/28.11    (14)  op(e3, all_52_9) = all_52_8
% 177.58/28.11    (15)  all_58_5 = all_52_13
% 177.58/28.11    (16)   ~ (all_6_2 = e0)
% 177.58/28.11    (17)   ~ (all_52_25 = all_52_29)
% 177.58/28.11    (18)  all_56_15 = all_6_2
% 177.58/28.11    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.11    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.11    (21)  all_58_3 = all_10_2
% 177.58/28.11    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.11    (23)  all_58_15 = all_6_2
% 177.58/28.11    (24)   ~ (all_52_9 = all_4_2)
% 177.58/28.11    (25)   ~ (all_52_5 = all_52_7)
% 177.58/28.11    (26)  all_58_10 = all_52_15
% 177.58/28.11    (27)   ~ (all_52_5 = all_4_2)
% 177.58/28.11    (28)  all_58_7 = all_52_19
% 177.58/28.11    (29)   ~ (all_52_17 = all_52_25)
% 177.58/28.11    (30)  op(e0, e1) = all_52_29
% 177.58/28.11    (31)   ~ (all_4_0 = e2)
% 177.58/28.11    (32)  all_58_4 = all_52_5
% 177.58/28.11    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.11    (34)   ~ (e3 = e1)
% 177.58/28.11    (35)   ~ (all_52_27 = all_52_29)
% 177.58/28.11    (36)   ~ (all_52_17 = all_14_2)
% 177.58/28.11    (37)  op(e3, all_4_2) = all_4_1
% 177.58/28.11    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.11    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.11    (40)   ~ (all_52_7 = all_4_2)
% 177.58/28.11    (41)  all_58_1 = all_52_3
% 177.58/28.11    (42)   ~ (all_52_13 = all_52_15)
% 177.58/28.11    (43)  all_58_0 = all_4_2
% 177.58/28.11    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.11    (45)  op(e1, all_52_29) = all_52_28
% 177.58/28.11    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.11    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.11    (48)  all_58_14 = all_52_29
% 177.58/28.11    (49)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.11    (50)   ~ (all_52_3 = all_52_5)
% 177.58/28.11    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.11    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.11    (53)  all_58_8 = all_14_2
% 177.58/28.11    (54)  op(e0, e2) = all_52_27
% 177.58/28.11    (55)  op(all_4_1, all_4_2) = all_4_0
% 177.58/28.11    (56)   ~ (all_52_3 = all_52_27)
% 177.58/28.11    (57)  op(e0, e3) = all_52_25
% 177.58/28.11    (58)  op(e0, all_6_2) = all_6_1
% 177.58/28.11    (59)   ~ (all_52_9 = all_10_2)
% 177.58/28.11    (60)  op(e3, all_52_17) = all_52_16
% 177.58/28.11    (61)   ~ (e3 = e0)
% 177.58/28.11    (62)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.11    (63)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.11    (64)   ~ (all_52_5 = all_52_29)
% 177.58/28.11    (65)  op(e1, e0) = all_52_23
% 177.58/28.11    (66)  all_56_12 = all_52_25
% 177.58/28.11    (67)  all_58_13 = all_52_27
% 177.58/28.11    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.11    (69)   ~ (all_52_9 = all_52_17)
% 177.58/28.11    (70)  all_58_6 = all_52_17
% 177.58/28.11    (71)   ~ (all_52_3 = all_52_7)
% 177.58/28.11    (72)   ~ (e1 = e0)
% 177.58/28.11    (73)  all_56_0 = all_4_2
% 177.58/28.11    (74)  all_58_11 = all_52_23
% 177.58/28.11    (75)   ~ (all_4_0 = e1)
% 177.58/28.11    (76)   ~ (all_52_19 = all_10_2)
% 177.58/28.11    (77)   ~ (all_52_29 = all_6_2)
% 177.58/28.11    (78)  all_58_2 = all_52_9
% 177.58/28.11    (79)  op(e3, e1) = all_52_5
% 177.58/28.11    (80)   ~ (e2 = e1)
% 177.58/28.11    (81)   ~ (all_52_25 = all_6_2)
% 177.58/28.11    (82)  op(e1, e3) = all_52_17
% 177.58/28.11    (83)   ~ (all_52_25 = all_4_2)
% 177.58/28.11    (84)  op(e3, e0) = all_52_7
% 177.58/28.11    (85)  op(e3, e3) = all_4_2
% 177.58/28.11    (86)   ~ (all_52_17 = all_4_2)
% 177.58/28.11    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.11    (88)   ~ (all_52_25 = all_52_27)
% 177.58/28.11    (89)   ~ (all_52_27 = all_6_2)
% 177.58/28.11    (90)   ~ (all_52_7 = all_6_2)
% 177.58/28.11    (91)   ~ (all_52_15 = all_10_2)
% 177.58/28.11    (92)  op(e2, all_52_27) = all_52_26
% 177.58/28.11    (93)   ~ (all_52_17 = all_52_19)
% 177.58/28.11    (94)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.11    (95)  all_52_30 = all_6_1
% 177.58/28.11    (96)  all_58_9 = all_52_7
% 177.58/28.11    (97)  all_58_12 = all_52_25
% 177.58/28.11    (98)  op(e3, all_4_2) = e1
% 177.58/28.11    (99)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.11    (100)   ~ (all_52_9 = all_52_15)
% 177.58/28.11    (101)   ~ (e3 = e2)
% 177.58/28.11    (102)  op(e2, e3) = all_52_9
% 177.58/28.11    (103)  all_56_13 = all_52_27
% 177.58/28.11  
% 177.58/28.11  Begin of proof
% 177.58/28.11  | 
% 177.58/28.11  | ALPHA: (6) implies:
% 177.58/28.11  |   (104)  all_52_30 = e0
% 177.58/28.11  |   (105)  all_52_28 = e1
% 177.58/28.11  |   (106)  all_52_26 = e2
% 177.58/28.11  |   (107)  all_52_24 = e3
% 177.58/28.11  | 
% 177.58/28.11  | COMBINE_EQS: (95), (104) imply:
% 177.58/28.11  |   (108)  all_6_1 = e0
% 177.58/28.11  | 
% 177.58/28.11  | SIMP: (108) implies:
% 177.58/28.11  |   (109)  all_6_1 = e0
% 177.58/28.11  | 
% 177.58/28.11  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.58/28.11  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.58/28.11  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.58/28.11  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.58/28.11  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.58/28.11  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.58/28.11  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.58/28.11  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 177.58/28.11  |            (91), (92), (93), (94), (96), (97), (98), (99), (100), (101),
% 177.58/28.11  |            (102), (103), (105), (106), (107), (109) are inconsistent by
% 177.58/28.11  |            sub-proof #602.
% 177.58/28.11  | 
% 177.58/28.11  End of proof
% 177.58/28.11  
% 177.58/28.11  Sub-proof #445 shows that the following formulas are inconsistent:
% 177.58/28.11  ----------------------------------------------------------------
% 177.58/28.11    (1)  op(e2, all_10_2) = all_10_1
% 177.58/28.11    (2)  op(all_10_1, all_10_2) = e1
% 177.58/28.11    (3)   ~ (e3 = e1)
% 177.58/28.11    (4)  all_52_0 = e1
% 177.58/28.11    (5)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.58/28.11         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.58/28.11    (6)  all_52_10 = all_10_1
% 177.58/28.11    (7)   ~ (e2 = e1)
% 177.58/28.11    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.11  
% 177.58/28.11  Begin of proof
% 177.58/28.11  | 
% 177.58/28.11  | BETA: splitting (5) gives:
% 177.58/28.11  | 
% 177.58/28.11  | Case 1:
% 177.58/28.11  | | 
% 177.58/28.11  | |   (9)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.58/28.11  | | 
% 177.58/28.11  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #632.
% 177.58/28.11  | | 
% 177.58/28.11  | Case 2:
% 177.58/28.11  | | 
% 177.58/28.11  | |   (10)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.58/28.11  | | 
% 177.58/28.11  | | ALPHA: (10) implies:
% 177.58/28.11  | |   (11)  all_52_10 = e2
% 177.58/28.11  | | 
% 177.58/28.11  | | COMBINE_EQS: (6), (11) imply:
% 177.58/28.11  | |   (12)  all_10_1 = e2
% 177.58/28.11  | | 
% 177.58/28.11  | | REF_CLOSE: (1), (2), (7), (8), (12) are inconsistent by sub-proof #446.
% 177.58/28.11  | | 
% 177.58/28.11  | End of split
% 177.58/28.11  | 
% 177.58/28.11  End of proof
% 177.58/28.11  
% 177.58/28.11  Sub-proof #446 shows that the following formulas are inconsistent:
% 177.58/28.11  ----------------------------------------------------------------
% 177.58/28.11    (1)  op(e2, all_10_2) = all_10_1
% 177.58/28.11    (2)  op(all_10_1, all_10_2) = e1
% 177.58/28.11    (3)   ~ (e2 = e1)
% 177.58/28.11    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.11    (5)  all_10_1 = e2
% 177.58/28.11  
% 177.58/28.11  Begin of proof
% 177.58/28.11  | 
% 177.58/28.11  | REDUCE: (2), (5) imply:
% 177.58/28.11  |   (6)  op(e2, all_10_2) = e1
% 177.58/28.11  | 
% 177.58/28.11  | REDUCE: (1), (5) imply:
% 177.58/28.11  |   (7)  op(e2, all_10_2) = e2
% 177.58/28.11  | 
% 177.58/28.11  | GROUND_INST: instantiating (4) with e1, e2, all_10_2, e2, simplifying with
% 177.58/28.11  |              (6), (7) gives:
% 177.58/28.11  |   (8)  e2 = e1
% 177.58/28.11  | 
% 177.58/28.11  | REDUCE: (3), (8) imply:
% 177.58/28.11  |   (9)  $false
% 177.58/28.11  | 
% 177.58/28.11  | CLOSE: (9) is inconsistent.
% 177.58/28.11  | 
% 177.58/28.11  End of proof
% 177.58/28.11  
% 177.58/28.11  Sub-proof #447 shows that the following formulas are inconsistent:
% 177.58/28.11  ----------------------------------------------------------------
% 177.58/28.11    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.11    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.58/28.11    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.11    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.11    (5)   ~ (all_52_17 = all_52_23)
% 177.58/28.11    (6)  all_56_3 = all_52_7
% 177.58/28.11    (7)  op(e3, e2) = all_52_3
% 177.58/28.11    (8)   ~ (all_52_9 = all_52_25)
% 177.58/28.11    (9)  op(e3, all_52_25) = all_52_24
% 177.58/28.11    (10)   ~ (all_52_19 = all_52_23)
% 177.58/28.11    (11)  op(e1, e2) = all_52_19
% 177.58/28.11    (12)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.58/28.11    (13)  op(e3, all_52_9) = all_52_8
% 177.58/28.11    (14)  all_50_1 = all_4_1
% 177.58/28.11    (15)   ~ (all_52_25 = all_52_29)
% 177.58/28.11    (16)  all_56_15 = all_6_2
% 177.58/28.11    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.11    (18)  op(all_14_1, all_14_2) = all_14_0
% 177.58/28.11    (19)  all_58_3 = all_10_2
% 177.58/28.11    (20)  all_56_9 = all_52_19
% 177.58/28.11    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.11    (22)  all_58_15 = all_6_2
% 177.58/28.11    (23)   ~ (all_52_9 = all_4_2)
% 177.58/28.11    (24)   ~ (all_52_5 = all_52_7)
% 177.58/28.11    (25)  all_58_10 = all_52_15
% 177.58/28.11    (26)   ~ (all_52_5 = all_4_2)
% 177.58/28.11    (27)  all_58_7 = all_52_19
% 177.58/28.11    (28)   ~ (all_52_17 = all_52_25)
% 177.58/28.11    (29)  all_58_4 = all_52_5
% 177.58/28.11    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.11    (31)   ~ (all_52_17 = all_14_2)
% 177.58/28.11    (32)  op(e3, all_4_2) = all_4_1
% 177.58/28.11    (33)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.11    (34)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.11    (35)   ~ (all_52_7 = all_4_2)
% 177.58/28.11    (36)  all_58_1 = all_52_3
% 177.58/28.11    (37)  all_58_0 = all_4_2
% 177.58/28.11    (38)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.11    (39)  op(e1, all_52_29) = all_52_28
% 177.58/28.11    (40)  all_50_2 = all_4_2
% 177.58/28.11    (41)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.58/28.11    (42)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.11    (43)   ~ (all_4_1 = e2)
% 177.58/28.11    (44)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.11    (45)  all_58_14 = all_52_29
% 177.58/28.11    (46)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.11    (47)   ~ (all_52_3 = all_52_5)
% 177.58/28.11    (48)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.11    (49)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.11    (50)  all_58_8 = all_14_2
% 177.58/28.11    (51)  all_56_1 = all_52_3
% 177.58/28.11    (52)   ~ (all_14_0 = e3)
% 177.58/28.11    (53)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.11    (54)   ~ (all_52_5 = all_14_2)
% 177.58/28.11    (55)   ~ (all_52_3 = all_52_27)
% 177.58/28.11    (56)   ~ (all_52_3 = all_4_2)
% 177.58/28.11    (57)  op(e0, e3) = all_52_25
% 177.58/28.11    (58)  op(e0, all_6_2) = all_6_1
% 177.58/28.11    (59)  op(all_4_1, all_4_2) = e2
% 177.58/28.12    (60)  op(e3, all_52_17) = all_52_16
% 177.58/28.12    (61)   ~ (e3 = e0)
% 177.58/28.12    (62)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.12    (63)  op(e0, all_52_23) = all_52_22
% 177.58/28.12    (64)   ~ (all_52_15 = all_52_23)
% 177.58/28.12    (65)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.12    (66)   ~ (all_52_5 = all_52_29)
% 177.58/28.12    (67)  all_56_2 = all_52_5
% 177.58/28.12    (68)  op(e1, e0) = all_52_23
% 177.58/28.12    (69)  all_58_13 = all_52_27
% 177.58/28.12    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.12    (71)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.12    (72)   ~ (all_52_9 = all_52_17)
% 177.58/28.12    (73)   ~ (all_14_0 = e2)
% 177.58/28.12    (74)  all_58_6 = all_52_17
% 177.58/28.12    (75)   ~ (all_52_3 = all_52_7)
% 177.58/28.12    (76)  op(e2, all_52_19) = all_52_18
% 177.58/28.12    (77)   ~ (e1 = e0)
% 177.58/28.12    (78)  all_56_0 = all_4_2
% 177.58/28.12    (79)  all_58_11 = all_52_23
% 177.58/28.12    (80)   ~ (all_52_3 = all_52_19)
% 177.58/28.12    (81)   ~ (all_52_7 = all_52_15)
% 177.58/28.12    (82)   ~ (all_52_29 = all_14_2)
% 177.58/28.12    (83)   ~ (all_52_23 = all_6_2)
% 177.58/28.12    (84)  all_58_2 = all_52_9
% 177.58/28.12    (85)  op(e3, e1) = all_52_5
% 177.58/28.12    (86)  all_56_10 = all_14_2
% 177.58/28.12    (87)   ~ (all_52_25 = all_6_2)
% 177.58/28.12    (88)  op(e1, e3) = all_52_17
% 177.58/28.12    (89)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.12    (90)   ~ (all_52_25 = all_4_2)
% 177.58/28.12    (91)  op(e3, e0) = all_52_7
% 177.58/28.12    (92)  op(e3, e3) = all_4_2
% 177.58/28.12    (93)  all_56_8 = all_52_17
% 177.58/28.12    (94)   ~ (all_52_17 = all_4_2)
% 177.58/28.12    (95)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.12    (96)   ~ (all_52_25 = all_52_27)
% 177.58/28.12    (97)   ~ (all_52_27 = all_6_2)
% 177.58/28.12    (98)   ~ (all_52_15 = all_10_2)
% 177.58/28.12    (99)  all_56_7 = all_52_15
% 177.58/28.12    (100)   ~ (all_52_7 = all_52_23)
% 177.58/28.12    (101)  op(e2, all_52_27) = all_52_26
% 177.58/28.12    (102)  all_52_20 = all_14_1
% 177.58/28.12    (103)   ~ (all_52_17 = all_52_19)
% 177.58/28.12    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.12    (105)  all_52_30 = all_6_1
% 177.58/28.12    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.12    (107)  op(e1, all_14_2) = all_14_1
% 177.58/28.12    (108)  all_58_9 = all_52_7
% 177.58/28.12    (109)   ~ (e2 = e0)
% 177.58/28.12    (110)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.58/28.12           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.58/28.12    (111)  all_58_12 = all_52_25
% 177.58/28.12    (112)  op(all_6_1, all_6_2) = e3
% 177.58/28.12    (113)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.12    (114)   ~ (all_52_9 = all_52_15)
% 177.58/28.12    (115)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.12    (116)   ~ (e3 = e2)
% 177.58/28.12    (117)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.58/28.12    (118)   ~ (all_52_19 = all_14_2)
% 177.58/28.12    (119)  op(e2, e3) = all_52_9
% 177.58/28.12    (120)  all_56_13 = all_52_27
% 177.58/28.12  
% 177.58/28.12  Begin of proof
% 177.58/28.12  | 
% 177.58/28.12  | BETA: splitting (110) gives:
% 177.58/28.12  | 
% 177.58/28.12  | Case 1:
% 177.58/28.12  | | 
% 177.58/28.12  | |   (121)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.58/28.12  | | 
% 177.58/28.12  | | ALPHA: (121) implies:
% 177.58/28.12  | |   (122)  all_52_22 = e0
% 177.58/28.12  | |   (123)  all_52_20 = e1
% 177.58/28.12  | |   (124)  all_52_18 = e2
% 177.58/28.12  | |   (125)  all_52_16 = e3
% 177.58/28.12  | | 
% 177.58/28.12  | | COMBINE_EQS: (102), (123) imply:
% 177.58/28.12  | |   (126)  all_14_1 = e1
% 177.58/28.12  | | 
% 177.58/28.12  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.58/28.12  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.58/28.12  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.58/28.12  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.58/28.12  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.58/28.12  | |            (57), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.58/28.12  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.58/28.12  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 177.58/28.12  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.58/28.12  | |            (101), (103), (104), (106), (107), (108), (109), (111), (113),
% 177.58/28.12  | |            (114), (115), (116), (117), (118), (119), (120), (122), (124),
% 177.58/28.12  | |            (125), (126) are inconsistent by sub-proof #454.
% 177.58/28.12  | | 
% 177.58/28.12  | Case 2:
% 177.58/28.12  | | 
% 177.58/28.12  | |   (127)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.58/28.12  | | 
% 177.58/28.12  | | REF_CLOSE: (58), (61), (95), (105), (112), (127) are inconsistent by
% 177.58/28.12  | |            sub-proof #501.
% 177.58/28.12  | | 
% 177.58/28.12  | End of split
% 177.58/28.12  | 
% 177.58/28.12  End of proof
% 177.58/28.12  
% 177.58/28.12  Sub-proof #448 shows that the following formulas are inconsistent:
% 177.58/28.12  ----------------------------------------------------------------
% 177.58/28.12    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.12    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.58/28.12    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.12    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.12    (5)   ~ (all_52_27 = all_10_2)
% 177.58/28.12    (6)  op(e2, e2) = all_10_2
% 177.58/28.12    (7)   ~ (all_52_17 = all_52_23)
% 177.58/28.12    (8)   ~ (all_6_0 = e3)
% 177.58/28.12    (9)   ~ (all_52_13 = all_52_29)
% 177.58/28.12    (10)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.12    (11)  all_56_3 = all_52_7
% 177.58/28.12    (12)  op(e3, e2) = all_52_3
% 177.58/28.12    (13)   ~ (all_52_9 = all_52_25)
% 177.58/28.12    (14)  op(e3, all_52_25) = all_52_24
% 177.58/28.12    (15)   ~ (all_52_19 = all_52_23)
% 177.58/28.12    (16)  op(e1, e2) = all_52_19
% 177.58/28.12    (17)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.58/28.12    (18)  op(e3, all_52_9) = all_52_8
% 177.58/28.12    (19)  all_50_1 = all_4_1
% 177.58/28.12    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.12    (21)  all_58_5 = all_52_13
% 177.58/28.12    (22)   ~ (all_6_2 = e0)
% 177.58/28.12    (23)   ~ (all_52_25 = all_52_29)
% 177.58/28.12    (24)  all_56_15 = all_6_2
% 177.58/28.12    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.12    (26)  op(all_14_1, all_14_2) = all_14_0
% 177.58/28.12    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.12    (28)  all_58_3 = all_10_2
% 177.58/28.12    (29)  all_56_9 = all_52_19
% 177.58/28.12    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.12    (31)  all_58_15 = all_6_2
% 177.58/28.12    (32)   ~ (all_52_9 = all_4_2)
% 177.58/28.12    (33)   ~ (all_52_5 = all_52_7)
% 177.58/28.12    (34)  all_58_10 = all_52_15
% 177.58/28.12    (35)   ~ (all_52_5 = all_4_2)
% 177.58/28.12    (36)  all_58_7 = all_52_19
% 177.58/28.12    (37)   ~ (all_52_17 = all_52_25)
% 177.58/28.12    (38)  op(e0, e1) = all_52_29
% 177.58/28.12    (39)  all_58_4 = all_52_5
% 177.58/28.12    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.58/28.12    (41)   ~ (e3 = e1)
% 177.58/28.12    (42)   ~ (all_52_27 = all_52_29)
% 177.58/28.12    (43)   ~ (all_52_17 = all_14_2)
% 177.58/28.12    (44)  op(e3, all_4_2) = all_4_1
% 177.58/28.12    (45)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.12    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.58/28.12    (47)   ~ (all_52_7 = all_4_2)
% 177.58/28.12    (48)  all_58_1 = all_52_3
% 177.58/28.12    (49)   ~ (all_52_13 = all_52_15)
% 177.58/28.12    (50)  all_58_0 = all_4_2
% 177.58/28.12    (51)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.58/28.12    (52)  op(e1, all_52_29) = all_52_28
% 177.58/28.12    (53)  all_50_2 = all_4_2
% 177.58/28.12    (54)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.58/28.12    (55)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.58/28.12    (56)   ~ (all_4_1 = e2)
% 177.58/28.12    (57)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.12    (58)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.12    (59)  all_58_14 = all_52_29
% 177.58/28.12    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.12    (61)  all_26_2 = all_4_2
% 177.58/28.12    (62)   ~ (all_52_3 = all_52_5)
% 177.58/28.12    (63)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.12    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.12    (65)  all_58_8 = all_14_2
% 177.58/28.12    (66)  all_56_1 = all_52_3
% 177.58/28.12    (67)  op(e0, e2) = all_52_27
% 177.58/28.12    (68)   ~ (all_14_0 = e3)
% 177.58/28.12    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.58/28.12    (70)   ~ (all_52_5 = all_14_2)
% 177.58/28.12    (71)   ~ (all_52_3 = all_52_27)
% 177.58/28.12    (72)   ~ (all_52_3 = all_4_2)
% 177.58/28.12    (73)  op(all_6_1, all_6_2) = all_6_0
% 177.58/28.12    (74)  op(e0, e3) = all_52_25
% 177.58/28.12    (75)  op(e0, all_6_2) = all_6_1
% 177.58/28.12    (76)   ~ (all_52_9 = all_10_2)
% 177.58/28.12    (77)  op(all_4_1, all_4_2) = e2
% 177.58/28.12    (78)  op(e3, all_52_17) = all_52_16
% 177.58/28.12    (79)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.58/28.12    (80)   ~ (e3 = e0)
% 177.58/28.12    (81)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.12    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.12    (83)  op(e0, all_52_23) = all_52_22
% 177.58/28.12    (84)   ~ (all_52_15 = all_52_23)
% 177.58/28.12    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.58/28.12    (86)   ~ (all_52_5 = all_52_29)
% 177.58/28.12    (87)  all_56_2 = all_52_5
% 177.58/28.12    (88)  op(e1, e0) = all_52_23
% 177.58/28.12    (89)  all_56_12 = all_52_25
% 177.58/28.12    (90)  all_58_13 = all_52_27
% 177.58/28.12    (91)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.58/28.12    (92)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.12    (93)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.58/28.12    (94)   ~ (all_52_9 = all_52_17)
% 177.58/28.12    (95)   ~ (all_14_0 = e2)
% 177.58/28.12    (96)  all_58_6 = all_52_17
% 177.58/28.12    (97)   ~ (all_52_3 = all_52_7)
% 177.58/28.12    (98)  op(e2, all_52_19) = all_52_18
% 177.58/28.12    (99)   ~ (e1 = e0)
% 177.58/28.12    (100)  all_56_0 = all_4_2
% 177.58/28.12    (101)  all_58_11 = all_52_23
% 177.58/28.12    (102)   ~ (all_52_3 = all_52_19)
% 177.58/28.12    (103)   ~ (all_52_7 = all_52_15)
% 177.58/28.12    (104)  all_26_1 = all_4_1
% 177.58/28.12    (105)   ~ (all_52_29 = all_14_2)
% 177.58/28.12    (106)   ~ (all_52_23 = all_6_2)
% 177.58/28.12    (107)   ~ (all_6_0 = e2)
% 177.58/28.12    (108)   ~ (all_52_29 = all_6_2)
% 177.58/28.12    (109)  all_58_2 = all_52_9
% 177.58/28.12    (110)  op(e3, e1) = all_52_5
% 177.58/28.12    (111)  all_56_10 = all_14_2
% 177.58/28.12    (112)   ~ (all_52_25 = all_6_2)
% 177.58/28.12    (113)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.12    (114)  op(e1, e3) = all_52_17
% 177.58/28.12    (115)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.58/28.12    (116)   ~ (all_52_25 = all_4_2)
% 177.58/28.12    (117)  op(e3, e0) = all_52_7
% 177.58/28.12    (118)  op(e3, e3) = all_4_2
% 177.58/28.12    (119)  all_56_8 = all_52_17
% 177.58/28.12    (120)   ~ (all_52_17 = all_4_2)
% 177.58/28.12    (121)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.12             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.12    (122)   ~ (all_52_25 = all_52_27)
% 177.58/28.12    (123)   ~ (all_52_27 = all_6_2)
% 177.58/28.12    (124)   ~ (all_52_7 = all_6_2)
% 177.58/28.12    (125)   ~ (all_52_15 = all_10_2)
% 177.58/28.12    (126)  all_56_7 = all_52_15
% 177.58/28.12    (127)   ~ (all_52_7 = all_52_23)
% 177.58/28.12    (128)   ~ (all_6_0 = e1)
% 177.58/28.12    (129)  op(e2, all_52_27) = all_52_26
% 177.58/28.12    (130)  all_52_20 = all_14_1
% 177.58/28.12    (131)   ~ (all_52_17 = all_52_19)
% 177.58/28.12    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.12    (133)  all_52_30 = all_6_1
% 177.58/28.12    (134)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.12    (135)  op(e1, all_14_2) = all_14_1
% 177.58/28.12    (136)  all_58_9 = all_52_7
% 177.58/28.12    (137)   ~ (e2 = e0)
% 177.58/28.12    (138)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.58/28.12           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.58/28.12    (139)  all_58_12 = all_52_25
% 177.58/28.12    (140)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.58/28.12    (141)   ~ (all_52_9 = all_52_15)
% 177.58/28.12    (142)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.58/28.12    (143)   ~ (e3 = e2)
% 177.58/28.12    (144)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.58/28.12    (145)   ~ (all_52_19 = all_14_2)
% 177.58/28.12    (146)  op(e2, e3) = all_52_9
% 177.58/28.12    (147)  all_56_13 = all_52_27
% 177.58/28.12  
% 177.58/28.12  Begin of proof
% 177.58/28.12  | 
% 177.58/28.12  | BETA: splitting (138) gives:
% 177.58/28.12  | 
% 177.58/28.12  | Case 1:
% 177.58/28.12  | | 
% 177.58/28.12  | |   (148)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.58/28.12  | | 
% 177.58/28.12  | | ALPHA: (148) implies:
% 177.58/28.12  | |   (149)  all_52_22 = e0
% 177.58/28.12  | |   (150)  all_52_20 = e1
% 177.58/28.12  | |   (151)  all_52_18 = e2
% 177.58/28.12  | |   (152)  all_52_16 = e3
% 177.58/28.12  | | 
% 177.58/28.12  | | COMBINE_EQS: (130), (150) imply:
% 177.58/28.12  | |   (153)  all_14_1 = e1
% 177.58/28.12  | | 
% 177.58/28.12  | | SIMP: (153) implies:
% 177.58/28.12  | |   (154)  all_14_1 = e1
% 177.58/28.12  | | 
% 177.58/28.12  | | REF_CLOSE: (1), (2), (3), (4), (7), (11), (12), (13), (14), (15), (16),
% 177.58/28.12  | |            (17), (18), (19), (23), (24), (25), (26), (28), (29), (30), (31),
% 177.58/28.12  | |            (32), (33), (34), (35), (36), (37), (39), (40), (43), (44), (45),
% 177.58/28.12  | |            (46), (47), (48), (50), (51), (52), (53), (54), (55), (56), (58),
% 177.58/28.12  | |            (59), (60), (62), (63), (64), (65), (66), (68), (69), (70), (71),
% 177.58/28.12  | |            (72), (74), (77), (78), (80), (81), (83), (84), (85), (86), (87),
% 177.58/28.12  | |            (88), (90), (92), (93), (94), (95), (96), (97), (98), (99),
% 177.58/28.12  | |            (100), (101), (102), (103), (105), (106), (109), (110), (111),
% 177.58/28.12  | |            (112), (114), (115), (116), (117), (118), (119), (120), (121),
% 177.58/28.12  | |            (122), (123), (125), (126), (127), (129), (131), (132), (134),
% 177.58/28.12  | |            (135), (136), (137), (139), (140), (141), (142), (143), (144),
% 177.58/28.12  | |            (145), (146), (147), (149), (151), (152), (154) are inconsistent
% 177.58/28.12  | |            by sub-proof #454.
% 177.58/28.12  | | 
% 177.58/28.12  | Case 2:
% 177.58/28.12  | | 
% 177.58/28.12  | |   (155)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.58/28.12  | | 
% 177.58/28.12  | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 177.58/28.12  | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (27), (28),
% 177.58/28.12  | |            (30), (31), (34), (35), (36), (37), (38), (39), (41), (42), (43),
% 177.58/28.12  | |            (44), (45), (47), (48), (49), (50), (52), (53), (56), (57), (58),
% 177.58/28.12  | |            (59), (60), (61), (63), (64), (65), (67), (72), (73), (74), (75),
% 177.58/28.12  | |            (76), (77), (78), (79), (81), (82), (89), (90), (91), (92), (94),
% 177.58/28.12  | |            (96), (97), (100), (101), (104), (107), (108), (109), (110),
% 177.58/28.12  | |            (112), (113), (114), (116), (117), (118), (120), (121), (122),
% 177.58/28.12  | |            (124), (128), (129), (131), (132), (133), (134), (136), (139),
% 177.58/28.12  | |            (141), (143), (146), (147), (155) are inconsistent by sub-proof
% 177.58/28.12  | |            #449.
% 177.58/28.12  | | 
% 177.58/28.12  | End of split
% 177.58/28.12  | 
% 177.58/28.12  End of proof
% 177.58/28.12  
% 177.58/28.12  Sub-proof #449 shows that the following formulas are inconsistent:
% 177.58/28.12  ----------------------------------------------------------------
% 177.58/28.12    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.12    (2)   ~ (all_52_27 = all_10_2)
% 177.58/28.12    (3)  op(e2, e2) = all_10_2
% 177.58/28.12    (4)   ~ (all_52_17 = all_52_23)
% 177.58/28.12    (5)   ~ (all_6_0 = e3)
% 177.58/28.12    (6)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.58/28.12    (7)   ~ (all_52_13 = all_52_29)
% 177.58/28.12    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.12    (9)  all_56_3 = all_52_7
% 177.58/28.12    (10)  op(e3, e2) = all_52_3
% 177.58/28.12    (11)   ~ (all_52_9 = all_52_25)
% 177.58/28.12    (12)  op(e3, all_52_25) = all_52_24
% 177.58/28.12    (13)   ~ (all_52_19 = all_52_23)
% 177.58/28.12    (14)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.58/28.12    (15)  op(e3, all_52_9) = all_52_8
% 177.58/28.12    (16)  all_50_1 = all_4_1
% 177.58/28.12    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.12    (18)  all_58_5 = all_52_13
% 177.58/28.12    (19)   ~ (all_6_2 = e0)
% 177.58/28.12    (20)   ~ (all_52_25 = all_52_29)
% 177.58/28.12    (21)  all_56_15 = all_6_2
% 177.58/28.12    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.12    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.12    (24)  all_58_3 = all_10_2
% 177.58/28.12    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.12    (26)  all_58_15 = all_6_2
% 177.58/28.12    (27)  all_58_10 = all_52_15
% 177.58/28.12    (28)   ~ (all_52_5 = all_4_2)
% 177.58/28.12    (29)  all_58_7 = all_52_19
% 177.58/28.12    (30)   ~ (all_52_17 = all_52_25)
% 177.58/28.12    (31)  op(e0, e1) = all_52_29
% 177.58/28.12    (32)  all_58_4 = all_52_5
% 177.58/28.12    (33)   ~ (e3 = e1)
% 177.58/28.12    (34)   ~ (all_52_27 = all_52_29)
% 177.58/28.12    (35)   ~ (all_52_17 = all_14_2)
% 177.58/28.12    (36)  op(e3, all_4_2) = all_4_1
% 177.58/28.12    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.12    (38)   ~ (all_52_7 = all_4_2)
% 177.58/28.12    (39)  all_58_1 = all_52_3
% 177.58/28.12    (40)   ~ (all_52_13 = all_52_15)
% 177.58/28.12    (41)  all_58_0 = all_4_2
% 177.58/28.12    (42)  op(e1, all_52_29) = all_52_28
% 177.58/28.12    (43)  all_50_2 = all_4_2
% 177.58/28.12    (44)   ~ (all_4_1 = e2)
% 177.58/28.12    (45)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.12    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.12    (47)  all_58_14 = all_52_29
% 177.58/28.12    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.12    (49)  all_26_2 = all_4_2
% 177.58/28.12    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.12    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.12    (52)  all_58_8 = all_14_2
% 177.58/28.12    (53)  op(e0, e2) = all_52_27
% 177.58/28.12    (54)   ~ (all_52_3 = all_4_2)
% 177.58/28.12    (55)  op(all_6_1, all_6_2) = all_6_0
% 177.58/28.12    (56)  op(e0, e3) = all_52_25
% 177.58/28.12    (57)  op(e0, all_6_2) = all_6_1
% 177.58/28.12    (58)   ~ (all_52_9 = all_10_2)
% 177.58/28.12    (59)  op(all_4_1, all_4_2) = e2
% 177.58/28.12    (60)  op(e3, all_52_17) = all_52_16
% 177.58/28.12    (61)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.58/28.12    (62)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.12    (63)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.12    (64)  all_56_12 = all_52_25
% 177.58/28.12    (65)  all_58_13 = all_52_27
% 177.58/28.12    (66)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.58/28.12    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.12    (68)   ~ (all_52_9 = all_52_17)
% 177.58/28.12    (69)  all_58_6 = all_52_17
% 177.58/28.12    (70)   ~ (all_52_3 = all_52_7)
% 177.58/28.12    (71)  all_56_0 = all_4_2
% 177.58/28.12    (72)  all_58_11 = all_52_23
% 177.58/28.12    (73)  all_26_1 = all_4_1
% 177.58/28.12    (74)   ~ (all_6_0 = e2)
% 177.58/28.12    (75)   ~ (all_52_29 = all_6_2)
% 177.58/28.12    (76)  all_58_2 = all_52_9
% 177.58/28.12    (77)  op(e3, e1) = all_52_5
% 177.58/28.12    (78)   ~ (all_52_25 = all_6_2)
% 177.58/28.12    (79)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.12    (80)  op(e1, e3) = all_52_17
% 177.58/28.12    (81)   ~ (all_52_25 = all_4_2)
% 177.58/28.12    (82)  op(e3, e0) = all_52_7
% 177.58/28.12    (83)  op(e3, e3) = all_4_2
% 177.58/28.12    (84)   ~ (all_52_17 = all_4_2)
% 177.58/28.12    (85)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.12    (86)   ~ (all_52_25 = all_52_27)
% 177.58/28.12    (87)   ~ (all_52_7 = all_6_2)
% 177.58/28.12    (88)   ~ (all_6_0 = e1)
% 177.58/28.12    (89)  op(e2, all_52_27) = all_52_26
% 177.58/28.12    (90)   ~ (all_52_17 = all_52_19)
% 177.58/28.12    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.12    (92)  all_52_30 = all_6_1
% 177.58/28.12    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.12    (94)  all_58_9 = all_52_7
% 177.58/28.12    (95)  all_58_12 = all_52_25
% 177.58/28.12    (96)   ~ (all_52_9 = all_52_15)
% 177.58/28.12    (97)   ~ (e3 = e2)
% 177.58/28.12    (98)  op(e2, e3) = all_52_9
% 177.58/28.12    (99)  all_56_13 = all_52_27
% 177.58/28.12  
% 177.58/28.12  Begin of proof
% 177.58/28.12  | 
% 177.58/28.12  | ALPHA: (6) implies:
% 177.58/28.12  |   (100)  all_52_30 = e0
% 177.58/28.12  |   (101)  all_52_28 = e1
% 177.58/28.12  |   (102)  all_52_26 = e2
% 177.58/28.12  |   (103)  all_52_24 = e3
% 177.58/28.12  | 
% 177.58/28.12  | COMBINE_EQS: (92), (100) imply:
% 177.58/28.12  |   (104)  all_6_1 = e0
% 177.58/28.12  | 
% 177.58/28.12  | SIMP: (104) implies:
% 177.58/28.12  |   (105)  all_6_1 = e0
% 177.58/28.12  | 
% 177.58/28.12  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.58/28.12  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.58/28.12  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.58/28.12  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.58/28.12  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.58/28.12  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.58/28.12  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.58/28.12  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 177.58/28.12  |            (91), (93), (94), (95), (96), (97), (98), (99), (101), (102),
% 177.58/28.12  |            (103), (105) are inconsistent by sub-proof #450.
% 177.58/28.12  | 
% 177.58/28.12  End of proof
% 177.58/28.12  
% 177.58/28.12  Sub-proof #450 shows that the following formulas are inconsistent:
% 177.58/28.12  ----------------------------------------------------------------
% 177.58/28.12    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.12    (2)   ~ (all_52_27 = all_10_2)
% 177.58/28.12    (3)  op(e2, e2) = all_10_2
% 177.58/28.12    (4)   ~ (all_52_17 = all_52_23)
% 177.58/28.12    (5)  all_52_26 = e2
% 177.58/28.12    (6)   ~ (all_6_0 = e3)
% 177.58/28.12    (7)   ~ (all_52_13 = all_52_29)
% 177.58/28.12    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.12    (9)  all_56_3 = all_52_7
% 177.58/28.12    (10)  op(e3, e2) = all_52_3
% 177.58/28.12    (11)   ~ (all_52_9 = all_52_25)
% 177.58/28.12    (12)  op(e3, all_52_25) = all_52_24
% 177.58/28.12    (13)   ~ (all_52_19 = all_52_23)
% 177.58/28.12    (14)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.58/28.12    (15)  op(e3, all_52_9) = all_52_8
% 177.58/28.12    (16)  all_50_1 = all_4_1
% 177.58/28.12    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.12    (18)  all_58_5 = all_52_13
% 177.58/28.12    (19)   ~ (all_6_2 = e0)
% 177.58/28.12    (20)   ~ (all_52_25 = all_52_29)
% 177.58/28.12    (21)  all_56_15 = all_6_2
% 177.58/28.12    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.12    (23)  all_6_1 = e0
% 177.58/28.12    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.12    (25)  all_58_3 = all_10_2
% 177.58/28.12    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.12    (27)  all_58_15 = all_6_2
% 177.58/28.12    (28)  all_58_10 = all_52_15
% 177.58/28.12    (29)   ~ (all_52_5 = all_4_2)
% 177.58/28.12    (30)  all_58_7 = all_52_19
% 177.58/28.12    (31)   ~ (all_52_17 = all_52_25)
% 177.58/28.12    (32)  op(e0, e1) = all_52_29
% 177.58/28.12    (33)  all_58_4 = all_52_5
% 177.58/28.12    (34)   ~ (e3 = e1)
% 177.58/28.12    (35)   ~ (all_52_27 = all_52_29)
% 177.58/28.12    (36)   ~ (all_52_17 = all_14_2)
% 177.58/28.12    (37)  op(e3, all_4_2) = all_4_1
% 177.58/28.12    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.12    (39)   ~ (all_52_7 = all_4_2)
% 177.58/28.12    (40)  all_58_1 = all_52_3
% 177.58/28.12    (41)   ~ (all_52_13 = all_52_15)
% 177.58/28.12    (42)  all_58_0 = all_4_2
% 177.58/28.12    (43)  op(e1, all_52_29) = all_52_28
% 177.58/28.12    (44)  all_50_2 = all_4_2
% 177.58/28.12    (45)   ~ (all_4_1 = e2)
% 177.58/28.12    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.12    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.12    (48)  all_58_14 = all_52_29
% 177.58/28.12    (49)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.12    (50)  all_26_2 = all_4_2
% 177.58/28.12    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.12    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.12    (53)  all_58_8 = all_14_2
% 177.58/28.12    (54)  op(e0, e2) = all_52_27
% 177.58/28.12    (55)   ~ (all_52_3 = all_4_2)
% 177.58/28.12    (56)  op(all_6_1, all_6_2) = all_6_0
% 177.58/28.12    (57)  op(e0, e3) = all_52_25
% 177.58/28.13    (58)  op(e0, all_6_2) = all_6_1
% 177.58/28.13    (59)   ~ (all_52_9 = all_10_2)
% 177.58/28.13    (60)  op(all_4_1, all_4_2) = e2
% 177.58/28.13    (61)  op(e3, all_52_17) = all_52_16
% 177.58/28.13    (62)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.58/28.13    (63)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.13    (64)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.13    (65)  all_56_12 = all_52_25
% 177.58/28.13    (66)  all_58_13 = all_52_27
% 177.58/28.13    (67)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.58/28.13    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.13    (69)   ~ (all_52_9 = all_52_17)
% 177.58/28.13    (70)  all_58_6 = all_52_17
% 177.58/28.13    (71)   ~ (all_52_3 = all_52_7)
% 177.58/28.13    (72)  all_56_0 = all_4_2
% 177.58/28.13    (73)  all_58_11 = all_52_23
% 177.58/28.13    (74)  all_26_1 = all_4_1
% 177.58/28.13    (75)   ~ (all_6_0 = e2)
% 177.58/28.13    (76)   ~ (all_52_29 = all_6_2)
% 177.58/28.13    (77)  all_58_2 = all_52_9
% 177.58/28.13    (78)  op(e3, e1) = all_52_5
% 177.58/28.13    (79)   ~ (all_52_25 = all_6_2)
% 177.58/28.13    (80)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.13    (81)  op(e1, e3) = all_52_17
% 177.58/28.13    (82)   ~ (all_52_25 = all_4_2)
% 177.58/28.13    (83)  op(e3, e0) = all_52_7
% 177.58/28.13    (84)  all_52_28 = e1
% 177.58/28.13    (85)  op(e3, e3) = all_4_2
% 177.58/28.13    (86)   ~ (all_52_17 = all_4_2)
% 177.58/28.13    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.13    (88)   ~ (all_52_25 = all_52_27)
% 177.58/28.13    (89)   ~ (all_52_7 = all_6_2)
% 177.58/28.13    (90)   ~ (all_6_0 = e1)
% 177.58/28.13    (91)  op(e2, all_52_27) = all_52_26
% 177.58/28.13    (92)   ~ (all_52_17 = all_52_19)
% 177.58/28.13    (93)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.13    (94)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.13    (95)  all_58_9 = all_52_7
% 177.58/28.13    (96)  all_52_24 = e3
% 177.58/28.13    (97)  all_58_12 = all_52_25
% 177.58/28.13    (98)   ~ (all_52_9 = all_52_15)
% 177.58/28.13    (99)   ~ (e3 = e2)
% 177.58/28.13    (100)  op(e2, e3) = all_52_9
% 177.58/28.13    (101)  all_56_13 = all_52_27
% 177.58/28.13  
% 177.58/28.13  Begin of proof
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (23), (56) imply:
% 177.58/28.13  |   (102)  op(e0, all_6_2) = all_6_0
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (12), (96) imply:
% 177.58/28.13  |   (103)  op(e3, all_52_25) = e3
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (5), (91) imply:
% 177.58/28.13  |   (104)  op(e2, all_52_27) = e2
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (43), (84) imply:
% 177.58/28.13  |   (105)  op(e1, all_52_29) = e1
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (23), (58) imply:
% 177.58/28.13  |   (106)  op(e0, all_6_2) = e0
% 177.58/28.13  | 
% 177.58/28.13  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 177.58/28.13  |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 177.58/28.13  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.58/28.13  |            (38), (39), (40), (41), (42), (44), (45), (46), (47), (48), (49),
% 177.58/28.13  |            (50), (51), (52), (53), (54), (55), (57), (59), (60), (61), (62),
% 177.58/28.13  |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 177.58/28.13  |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (85),
% 177.58/28.13  |            (86), (87), (88), (89), (90), (92), (93), (94), (95), (97), (98),
% 177.58/28.13  |            (99), (100), (101), (102), (103), (104), (105), (106) are
% 177.58/28.13  |            inconsistent by sub-proof #451.
% 177.58/28.13  | 
% 177.58/28.13  End of proof
% 177.58/28.13  
% 177.58/28.13  Sub-proof #451 shows that the following formulas are inconsistent:
% 177.58/28.13  ----------------------------------------------------------------
% 177.58/28.13    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.13    (2)   ~ (all_52_27 = all_10_2)
% 177.58/28.13    (3)  op(e2, e2) = all_10_2
% 177.58/28.13    (4)   ~ (all_52_17 = all_52_23)
% 177.58/28.13    (5)   ~ (all_6_0 = e3)
% 177.58/28.13    (6)   ~ (all_52_13 = all_52_29)
% 177.58/28.13    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.58/28.13    (8)  all_56_3 = all_52_7
% 177.58/28.13    (9)  op(e3, e2) = all_52_3
% 177.58/28.13    (10)   ~ (all_52_9 = all_52_25)
% 177.58/28.13    (11)   ~ (all_52_19 = all_52_23)
% 177.58/28.13    (12)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.58/28.13    (13)  op(e3, all_52_9) = all_52_8
% 177.58/28.13    (14)  all_50_1 = all_4_1
% 177.58/28.13    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.13    (16)  all_58_5 = all_52_13
% 177.58/28.13    (17)   ~ (all_6_2 = e0)
% 177.58/28.13    (18)   ~ (all_52_25 = all_52_29)
% 177.58/28.13    (19)  all_56_15 = all_6_2
% 177.58/28.13    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.13    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.58/28.13    (22)  all_58_3 = all_10_2
% 177.58/28.13    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.13    (24)  all_58_15 = all_6_2
% 177.58/28.13    (25)  op(e0, all_6_2) = e0
% 177.58/28.13    (26)  all_58_10 = all_52_15
% 177.58/28.13    (27)   ~ (all_52_5 = all_4_2)
% 177.58/28.13    (28)  all_58_7 = all_52_19
% 177.58/28.13    (29)   ~ (all_52_17 = all_52_25)
% 177.58/28.13    (30)  op(e0, e1) = all_52_29
% 177.58/28.13    (31)  all_58_4 = all_52_5
% 177.58/28.13    (32)   ~ (e3 = e1)
% 177.58/28.13    (33)   ~ (all_52_27 = all_52_29)
% 177.58/28.13    (34)   ~ (all_52_17 = all_14_2)
% 177.58/28.13    (35)  op(e3, all_4_2) = all_4_1
% 177.58/28.13    (36)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.13    (37)   ~ (all_52_7 = all_4_2)
% 177.58/28.13    (38)  all_58_1 = all_52_3
% 177.58/28.13    (39)   ~ (all_52_13 = all_52_15)
% 177.58/28.13    (40)  all_58_0 = all_4_2
% 177.58/28.13    (41)  op(e2, all_52_27) = e2
% 177.58/28.13    (42)  all_50_2 = all_4_2
% 177.58/28.13    (43)   ~ (all_4_1 = e2)
% 177.58/28.13    (44)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.13    (45)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.58/28.13    (46)  all_58_14 = all_52_29
% 177.58/28.13    (47)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.58/28.13    (48)  all_26_2 = all_4_2
% 177.58/28.13    (49)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.13    (50)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.13    (51)  all_58_8 = all_14_2
% 177.58/28.13    (52)  op(e0, e2) = all_52_27
% 177.58/28.13    (53)  op(e1, all_52_29) = e1
% 177.58/28.13    (54)   ~ (all_52_3 = all_4_2)
% 177.58/28.13    (55)  op(e0, e3) = all_52_25
% 177.58/28.13    (56)   ~ (all_52_9 = all_10_2)
% 177.58/28.13    (57)  op(all_4_1, all_4_2) = e2
% 177.58/28.13    (58)  op(e3, all_52_17) = all_52_16
% 177.58/28.13    (59)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.58/28.13    (60)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.13    (61)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.13    (62)  all_56_12 = all_52_25
% 177.58/28.13    (63)  all_58_13 = all_52_27
% 177.58/28.13    (64)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.58/28.13    (65)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.58/28.13    (66)   ~ (all_52_9 = all_52_17)
% 177.58/28.13    (67)  all_58_6 = all_52_17
% 177.58/28.13    (68)   ~ (all_52_3 = all_52_7)
% 177.58/28.13    (69)  all_56_0 = all_4_2
% 177.58/28.13    (70)  all_58_11 = all_52_23
% 177.58/28.13    (71)  all_26_1 = all_4_1
% 177.58/28.13    (72)  op(e3, all_52_25) = e3
% 177.58/28.13    (73)   ~ (all_6_0 = e2)
% 177.58/28.13    (74)   ~ (all_52_29 = all_6_2)
% 177.58/28.13    (75)  all_58_2 = all_52_9
% 177.58/28.13    (76)  op(e3, e1) = all_52_5
% 177.58/28.13    (77)   ~ (all_52_25 = all_6_2)
% 177.58/28.13    (78)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.58/28.13    (79)  op(e1, e3) = all_52_17
% 177.58/28.13    (80)   ~ (all_52_25 = all_4_2)
% 177.58/28.13    (81)  op(e3, e0) = all_52_7
% 177.58/28.13    (82)  op(e3, e3) = all_4_2
% 177.58/28.13    (83)   ~ (all_52_17 = all_4_2)
% 177.58/28.13    (84)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.13    (85)   ~ (all_52_25 = all_52_27)
% 177.58/28.13    (86)  op(e0, all_6_2) = all_6_0
% 177.58/28.13    (87)   ~ (all_52_7 = all_6_2)
% 177.58/28.13    (88)   ~ (all_6_0 = e1)
% 177.58/28.13    (89)   ~ (all_52_17 = all_52_19)
% 177.58/28.13    (90)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.58/28.13    (91)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.13    (92)  all_58_9 = all_52_7
% 177.58/28.13    (93)  all_58_12 = all_52_25
% 177.58/28.13    (94)   ~ (all_52_9 = all_52_15)
% 177.58/28.13    (95)   ~ (e3 = e2)
% 177.58/28.13    (96)  op(e2, e3) = all_52_9
% 177.58/28.13    (97)  all_56_13 = all_52_27
% 177.58/28.13  
% 177.58/28.13  Begin of proof
% 177.58/28.13  | 
% 177.58/28.13  | GROUND_INST: instantiating (84) with e0, all_6_0, all_6_2, e0, simplifying
% 177.58/28.13  |              with (25), (86) gives:
% 177.58/28.13  |   (98)  all_6_0 = e0
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (5), (98) imply:
% 177.58/28.13  |   (99)   ~ (e3 = e0)
% 177.58/28.13  | 
% 177.58/28.13  | SIMP: (99) implies:
% 177.58/28.13  |   (100)   ~ (e3 = e0)
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (73), (98) imply:
% 177.58/28.13  |   (101)   ~ (e2 = e0)
% 177.58/28.13  | 
% 177.58/28.13  | SIMP: (101) implies:
% 177.58/28.13  |   (102)   ~ (e2 = e0)
% 177.58/28.13  | 
% 177.58/28.13  | REDUCE: (88), (98) imply:
% 177.58/28.13  |   (103)   ~ (e1 = e0)
% 177.58/28.13  | 
% 177.58/28.13  | SIMP: (103) implies:
% 177.58/28.13  |   (104)   ~ (e1 = e0)
% 177.58/28.13  | 
% 177.58/28.13  | BETA: splitting (36) gives:
% 177.58/28.13  | 
% 177.58/28.13  | Case 1:
% 177.58/28.13  | | 
% 177.58/28.13  | |   (105)  all_56_15 = e3
% 177.58/28.13  | | 
% 177.58/28.13  | | COMBINE_EQS: (19), (105) imply:
% 177.58/28.13  | |   (106)  all_6_2 = e3
% 177.58/28.13  | | 
% 177.58/28.13  | | REF_CLOSE: (25), (55), (72), (81), (84), (87), (106) are inconsistent by
% 177.58/28.13  | |            sub-proof #665.
% 177.58/28.13  | | 
% 177.58/28.13  | Case 2:
% 177.58/28.13  | | 
% 177.58/28.13  | |   (107)   ~ (all_56_15 = e3)
% 177.58/28.13  | |   (108)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.58/28.13  | | 
% 177.58/28.13  | | REDUCE: (19), (107) imply:
% 177.58/28.13  | |   (109)   ~ (all_6_2 = e3)
% 177.58/28.13  | | 
% 177.58/28.13  | | BETA: splitting (47) gives:
% 177.58/28.13  | | 
% 177.58/28.13  | | Case 1:
% 177.58/28.13  | | | 
% 177.58/28.13  | | |   (110)  all_56_13 = e3
% 177.58/28.13  | | | 
% 177.58/28.13  | | | COMBINE_EQS: (97), (110) imply:
% 177.58/28.13  | | |   (111)  all_52_27 = e3
% 177.58/28.13  | | | 
% 177.58/28.13  | | | SIMP: (111) implies:
% 177.58/28.13  | | |   (112)  all_52_27 = e3
% 177.58/28.13  | | | 
% 177.58/28.13  | | | COMBINE_EQS: (63), (112) imply:
% 177.58/28.13  | | |   (113)  all_58_13 = e3
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (85), (112) imply:
% 177.58/28.13  | | |   (114)   ~ (all_52_25 = e3)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (33), (112) imply:
% 177.58/28.13  | | |   (115)   ~ (all_52_29 = e3)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | SIMP: (115) implies:
% 177.58/28.13  | | |   (116)   ~ (all_52_29 = e3)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (41), (112) imply:
% 177.58/28.13  | | |   (117)  op(e2, e3) = e2
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (52), (112) imply:
% 177.58/28.13  | | |   (118)  op(e0, e2) = e3
% 177.58/28.13  | | | 
% 177.58/28.13  | | | GROUND_INST: instantiating (84) with all_52_9, e2, e3, e2, simplifying
% 177.58/28.13  | | |              with (96), (117) gives:
% 177.58/28.13  | | |   (119)  all_52_9 = e2
% 177.58/28.13  | | | 
% 177.58/28.13  | | | COMBINE_EQS: (75), (119) imply:
% 177.58/28.13  | | |   (120)  all_58_2 = e2
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (94), (119) imply:
% 177.58/28.13  | | |   (121)   ~ (all_52_15 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | SIMP: (121) implies:
% 177.58/28.13  | | |   (122)   ~ (all_52_15 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (66), (119) imply:
% 177.58/28.13  | | |   (123)   ~ (all_52_17 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | SIMP: (123) implies:
% 177.58/28.13  | | |   (124)   ~ (all_52_17 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (10), (119) imply:
% 177.58/28.13  | | |   (125)   ~ (all_52_25 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | SIMP: (125) implies:
% 177.58/28.13  | | |   (126)   ~ (all_52_25 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (56), (119) imply:
% 177.58/28.13  | | |   (127)   ~ (all_10_2 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | SIMP: (127) implies:
% 177.58/28.13  | | |   (128)   ~ (all_10_2 = e2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (13), (119) imply:
% 177.58/28.13  | | |   (129)  op(e3, e2) = all_52_8
% 177.58/28.13  | | | 
% 177.58/28.13  | | | GROUND_INST: instantiating (84) with all_52_3, all_52_8, e2, e3,
% 177.58/28.13  | | |              simplifying with (9), (129) gives:
% 177.58/28.13  | | |   (130)  all_52_3 = all_52_8
% 177.58/28.13  | | | 
% 177.58/28.13  | | | COMBINE_EQS: (38), (130) imply:
% 177.58/28.13  | | |   (131)  all_58_1 = all_52_8
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (54), (130) imply:
% 177.58/28.13  | | |   (132)   ~ (all_52_8 = all_4_2)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | BETA: splitting (49) gives:
% 177.58/28.13  | | | 
% 177.58/28.13  | | | Case 1:
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | |   (133)  all_58_0 = e3
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | | REF_CLOSE: (35), (40), (43), (57), (82), (84), (133) are inconsistent by
% 177.58/28.13  | | | |            sub-proof #489.
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | Case 2:
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | |   (134)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | | BETA: splitting (134) gives:
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | | Case 1:
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | |   (135)  all_58_2 = e3
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | COMBINE_EQS: (120), (135) imply:
% 177.58/28.13  | | | | |   (136)  e3 = e2
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | REDUCE: (95), (136) imply:
% 177.58/28.13  | | | | |   (137)  $false
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | CLOSE: (137) is inconsistent.
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | Case 2:
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | |   (138)  all_58_6 = e3 | all_58_12 = e3
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | BETA: splitting (138) gives:
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | Case 1:
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | |   (139)  all_58_6 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | COMBINE_EQS: (67), (139) imply:
% 177.58/28.13  | | | | | |   (140)  all_52_17 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (140) implies:
% 177.58/28.13  | | | | | |   (141)  all_52_17 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (89), (141) imply:
% 177.58/28.13  | | | | | |   (142)   ~ (all_52_19 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (142) implies:
% 177.58/28.13  | | | | | |   (143)   ~ (all_52_19 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (29), (141) imply:
% 177.58/28.13  | | | | | |   (144)   ~ (all_52_25 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (83), (141) imply:
% 177.58/28.13  | | | | | |   (145)   ~ (all_4_2 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (145) implies:
% 177.58/28.13  | | | | | |   (146)   ~ (all_4_2 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | BETA: splitting (23) gives:
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | Case 1:
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | |   (147)  all_56_0 = e3
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | COMBINE_EQS: (69), (147) imply:
% 177.58/28.13  | | | | | | |   (148)  all_4_2 = e3
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | REDUCE: (146), (148) imply:
% 177.58/28.13  | | | | | | |   (149)  $false
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | CLOSE: (149) is inconsistent.
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | Case 2:
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | |   (150)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | BETA: splitting (15) gives:
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | |   (151)  all_58_1 = e2
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | COMBINE_EQS: (131), (151) imply:
% 177.58/28.13  | | | | | | | |   (152)  all_52_8 = e2
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | REDUCE: (132), (152) imply:
% 177.58/28.13  | | | | | | | |   (153)   ~ (all_4_2 = e2)
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | SIMP: (153) implies:
% 177.58/28.13  | | | | | | | |   (154)   ~ (all_4_2 = e2)
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | BETA: splitting (65) gives:
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | |   (155)  all_58_0 = e1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | COMBINE_EQS: (40), (155) imply:
% 177.58/28.13  | | | | | | | | |   (156)  all_4_2 = e1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | COMBINE_EQS: (42), (156) imply:
% 177.58/28.13  | | | | | | | | |   (157)  all_50_2 = e1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REDUCE: (80), (156) imply:
% 177.58/28.13  | | | | | | | | |   (158)   ~ (all_52_25 = e1)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REDUCE: (35), (156) imply:
% 177.58/28.13  | | | | | | | | |   (159)  op(e3, e1) = all_4_1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | BETA: splitting (12) gives:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (160)   ~ (all_50_2 = e1)
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REDUCE: (157), (160) imply:
% 177.58/28.13  | | | | | | | | | |   (161)  $false
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | CLOSE: (161) is inconsistent.
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (162)   ~ (all_50_1 = e0)
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REDUCE: (14), (162) imply:
% 177.58/28.13  | | | | | | | | | |   (163)   ~ (all_4_1 = e0)
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | BETA: splitting (60) gives:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | |   (164)  all_58_0 = e0
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | COMBINE_EQS: (155), (164) imply:
% 177.58/28.13  | | | | | | | | | | |   (165)  e1 = e0
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | REDUCE: (104), (165) imply:
% 177.58/28.13  | | | | | | | | | | |   (166)  $false
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | |   (167)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | BETA: splitting (167) gives:
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | |   (168)  all_58_2 = e0
% 177.58/28.13  | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | REF_CLOSE: (102), (120), (168) are inconsistent by sub-proof
% 177.58/28.13  | | | | | | | | | | | |            #909.
% 177.58/28.13  | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | |   (169)  all_58_6 = e0 | all_58_12 = e0
% 177.58/28.13  | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | BETA: splitting (169) gives:
% 177.58/28.13  | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | |   (170)  all_58_6 = e0
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | REF_CLOSE: (100), (139), (170) are inconsistent by sub-proof
% 177.58/28.13  | | | | | | | | | | | | |            #559.
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | |   (171)  all_58_12 = e0
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | COMBINE_EQS: (93), (171) imply:
% 177.58/28.13  | | | | | | | | | | | | |   (172)  all_52_25 = e0
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | SIMP: (172) implies:
% 177.58/28.13  | | | | | | | | | | | | |   (173)  all_52_25 = e0
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | REDUCE: (72), (173) imply:
% 177.58/28.13  | | | | | | | | | | | | |   (174)  op(e3, e0) = e3
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | GROUND_INST: instantiating (84) with all_52_7, e3, e0, e3,
% 177.58/28.13  | | | | | | | | | | | | |              simplifying with (81), (174) gives:
% 177.58/28.13  | | | | | | | | | | | | |   (175)  all_52_7 = e3
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | GROUND_INST: instantiating (84) with all_52_5, all_4_1, e1, e3,
% 177.58/28.13  | | | | | | | | | | | | |              simplifying with (76), (159) gives:
% 177.58/28.13  | | | | | | | | | | | | |   (176)  all_52_5 = all_4_1
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | COMBINE_EQS: (92), (175) imply:
% 177.58/28.13  | | | | | | | | | | | | |   (177)  all_58_9 = e3
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | COMBINE_EQS: (31), (176) imply:
% 177.58/28.13  | | | | | | | | | | | | |   (178)  all_58_4 = all_4_1
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | | REF_CLOSE: (1), (100), (102), (104), (151), (155), (163),
% 177.58/28.13  | | | | | | | | | | | | |            (177), (178) are inconsistent by sub-proof #481.
% 177.58/28.13  | | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | |   (179)   ~ (all_58_0 = e1)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REDUCE: (40), (179) imply:
% 177.58/28.13  | | | | | | | | |   (180)   ~ (all_4_2 = e1)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REF_CLOSE: (8), (35), (37), (43), (48), (57), (64), (69),
% 177.58/28.13  | | | | | | | | |            (71), (81), (84), (91), (150), (154), (180) are
% 177.58/28.13  | | | | | | | | |            inconsistent by sub-proof #482.
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | |   (181)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | REF_CLOSE: (7), (11), (22), (24), (25), (26), (28), (46), (59),
% 177.58/28.13  | | | | | | | |            (70), (72), (78), (81), (84), (87), (92), (93), (95),
% 177.58/28.13  | | | | | | | |            (100), (102), (113), (116), (118), (122), (126),
% 177.58/28.13  | | | | | | | |            (128), (143), (181) are inconsistent by sub-proof
% 177.58/28.13  | | | | | | | |            #657.
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | End of split
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | End of split
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | Case 2:
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | |   (182)  all_58_12 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REF_CLOSE: (93), (114), (182) are inconsistent by sub-proof #1003.
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | End of split
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | End of split
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | End of split
% 177.58/28.13  | | | 
% 177.58/28.13  | | Case 2:
% 177.58/28.13  | | | 
% 177.58/28.13  | | |   (183)   ~ (all_56_13 = e3)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | REDUCE: (97), (183) imply:
% 177.58/28.13  | | |   (184)   ~ (all_52_27 = e3)
% 177.58/28.13  | | | 
% 177.58/28.13  | | | BETA: splitting (50) gives:
% 177.58/28.13  | | | 
% 177.58/28.13  | | | Case 1:
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | |   (185)  all_58_12 = e3
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | | REF_CLOSE: (72), (80), (82), (84), (93), (185) are inconsistent by
% 177.58/28.13  | | | |            sub-proof #884.
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | Case 2:
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | |   (186)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | | BETA: splitting (186) gives:
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | | Case 1:
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | |   (187)  all_58_13 = e3
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | REF_CLOSE: (63), (184), (187) are inconsistent by sub-proof #1026.
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | Case 2:
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | |   (188)  all_58_14 = e3 | all_58_15 = e3
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | BETA: splitting (188) gives:
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | | Case 1:
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | |   (189)  all_58_14 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | COMBINE_EQS: (46), (189) imply:
% 177.58/28.13  | | | | | |   (190)  all_52_29 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (190) implies:
% 177.58/28.13  | | | | | |   (191)  all_52_29 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (6), (191) imply:
% 177.58/28.13  | | | | | |   (192)   ~ (all_52_13 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (18), (191) imply:
% 177.58/28.13  | | | | | |   (193)   ~ (all_52_25 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (74), (191) imply:
% 177.58/28.13  | | | | | |   (194)   ~ (all_6_2 = e3)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (53), (191) imply:
% 177.58/28.13  | | | | | |   (195)  op(e1, e3) = e1
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (30), (191) imply:
% 177.58/28.13  | | | | | |   (196)  op(e0, e1) = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | GROUND_INST: instantiating (84) with all_52_17, e1, e3, e1,
% 177.58/28.13  | | | | | |              simplifying with (79), (195) gives:
% 177.58/28.13  | | | | | |   (197)  all_52_17 = e1
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | COMBINE_EQS: (67), (197) imply:
% 177.58/28.13  | | | | | |   (198)  all_58_6 = e1
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (89), (197) imply:
% 177.58/28.13  | | | | | |   (199)   ~ (all_52_19 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (199) implies:
% 177.58/28.13  | | | | | |   (200)   ~ (all_52_19 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (4), (197) imply:
% 177.58/28.13  | | | | | |   (201)   ~ (all_52_23 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (201) implies:
% 177.58/28.13  | | | | | |   (202)   ~ (all_52_23 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (29), (197) imply:
% 177.58/28.13  | | | | | |   (203)   ~ (all_52_25 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (203) implies:
% 177.58/28.13  | | | | | |   (204)   ~ (all_52_25 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (34), (197) imply:
% 177.58/28.13  | | | | | |   (205)   ~ (all_14_2 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | SIMP: (205) implies:
% 177.58/28.13  | | | | | |   (206)   ~ (all_14_2 = e1)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (58), (197) imply:
% 177.58/28.13  | | | | | |   (207)  op(e3, e1) = all_52_16
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | GROUND_INST: instantiating (84) with all_52_5, all_52_16, e1, e3,
% 177.58/28.13  | | | | | |              simplifying with (76), (207) gives:
% 177.58/28.13  | | | | | |   (208)  all_52_5 = all_52_16
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | COMBINE_EQS: (31), (208) imply:
% 177.58/28.13  | | | | | |   (209)  all_58_4 = all_52_16
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (27), (208) imply:
% 177.58/28.13  | | | | | |   (210)   ~ (all_52_16 = all_4_2)
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | BETA: splitting (61) gives:
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | Case 1:
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | |   (211)  all_56_12 = e3
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | REF_CLOSE: (62), (193), (211) are inconsistent by sub-proof #1040.
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | Case 2:
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | |   (212)   ~ (all_56_12 = e3)
% 177.58/28.13  | | | | | | |   (213)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | BETA: splitting (44) gives:
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | |   (214)  all_58_4 = e1
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | COMBINE_EQS: (209), (214) imply:
% 177.58/28.13  | | | | | | | |   (215)  all_52_16 = e1
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | SIMP: (215) implies:
% 177.58/28.13  | | | | | | | |   (216)  all_52_16 = e1
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | REDUCE: (210), (216) imply:
% 177.58/28.13  | | | | | | | |   (217)   ~ (all_4_2 = e1)
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | SIMP: (217) implies:
% 177.58/28.13  | | | | | | | |   (218)   ~ (all_4_2 = e1)
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | BETA: splitting (49) gives:
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | |   (219)  all_58_0 = e3
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REF_CLOSE: (35), (40), (43), (57), (82), (84), (219) are
% 177.58/28.13  | | | | | | | | |            inconsistent by sub-proof #489.
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | |   (220)   ~ (all_58_0 = e3)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REDUCE: (40), (220) imply:
% 177.58/28.13  | | | | | | | | |   (221)   ~ (all_4_2 = e3)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | BETA: splitting (23) gives:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (222)  all_56_0 = e3
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REF_CLOSE: (69), (221), (222) are inconsistent by sub-proof
% 177.58/28.13  | | | | | | | | | |            #1024.
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (223)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (8), (9), (20), (35), (37), (38),
% 177.58/28.13  | | | | | | | | | |            (40), (41), (43), (48), (52), (57), (62), (64),
% 177.58/28.13  | | | | | | | | | |            (69), (71), (72), (80), (81), (84), (91), (92),
% 177.58/28.13  | | | | | | | | | |            (193), (204), (213), (214), (218), (223) are
% 177.58/28.13  | | | | | | | | | |            inconsistent by sub-proof #452.
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | |   (224)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | BETA: splitting (224) gives:
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | |   (225)  all_58_5 = e1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | COMBINE_EQS: (16), (225) imply:
% 177.58/28.13  | | | | | | | | |   (226)  all_52_13 = e1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | SIMP: (226) implies:
% 177.58/28.13  | | | | | | | | |   (227)  all_52_13 = e1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REDUCE: (39), (227) imply:
% 177.58/28.13  | | | | | | | | |   (228)   ~ (all_52_15 = e1)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | SIMP: (228) implies:
% 177.58/28.13  | | | | | | | | |   (229)   ~ (all_52_15 = e1)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | REDUCE: (192), (227) imply:
% 177.58/28.13  | | | | | | | | |   (230)   ~ (e3 = e1)
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | BETA: splitting (49) gives:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (231)  all_58_0 = e3
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REF_CLOSE: (35), (40), (43), (57), (82), (84), (231) are
% 177.58/28.13  | | | | | | | | | |            inconsistent by sub-proof #489.
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (232)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REF_CLOSE: (11), (17), (19), (21), (22), (24), (25), (26),
% 177.58/28.13  | | | | | | | | | |            (28), (32), (38), (45), (56), (62), (63), (68),
% 177.58/28.13  | | | | | | | | | |            (70), (72), (75), (77), (81), (84), (87), (90),
% 177.58/28.13  | | | | | | | | | |            (92), (93), (94), (100), (108), (109), (184),
% 177.58/28.13  | | | | | | | | | |            (193), (196), (198), (200), (202), (204), (213),
% 177.58/28.13  | | | | | | | | | |            (229), (232) are inconsistent by sub-proof #639.
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | |   (233)  all_58_8 = e1 | all_58_14 = e1
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | BETA: splitting (233) gives:
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 1:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (234)  all_58_8 = e1
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REF_CLOSE: (51), (206), (234) are inconsistent by sub-proof
% 177.58/28.13  | | | | | | | | | |            #815.
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | Case 2:
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | |   (235)  all_58_14 = e1
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | | REF_CLOSE: (32), (189), (235) are inconsistent by sub-proof
% 177.58/28.13  | | | | | | | | | |            #881.
% 177.58/28.13  | | | | | | | | | | 
% 177.58/28.13  | | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | | 
% 177.58/28.13  | | | | | | | | End of split
% 177.58/28.13  | | | | | | | | 
% 177.58/28.13  | | | | | | | End of split
% 177.58/28.13  | | | | | | | 
% 177.58/28.13  | | | | | | End of split
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | Case 2:
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | |   (236)  all_58_15 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | COMBINE_EQS: (24), (236) imply:
% 177.58/28.13  | | | | | |   (237)  all_6_2 = e3
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | REDUCE: (109), (237) imply:
% 177.58/28.13  | | | | | |   (238)  $false
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | | CLOSE: (238) is inconsistent.
% 177.58/28.13  | | | | | | 
% 177.58/28.13  | | | | | End of split
% 177.58/28.13  | | | | | 
% 177.58/28.13  | | | | End of split
% 177.58/28.13  | | | | 
% 177.58/28.13  | | | End of split
% 177.58/28.13  | | | 
% 177.58/28.13  | | End of split
% 177.58/28.13  | | 
% 177.58/28.13  | End of split
% 177.58/28.13  | 
% 177.58/28.13  End of proof
% 177.58/28.13  
% 177.58/28.13  Sub-proof #452 shows that the following formulas are inconsistent:
% 177.58/28.13  ----------------------------------------------------------------
% 177.58/28.13    (1)   ~ (all_52_25 = e3)
% 177.58/28.13    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.13    (3)   ~ (all_52_27 = all_10_2)
% 177.58/28.13    (4)  op(e2, e2) = all_10_2
% 177.58/28.13    (5)  all_56_3 = all_52_7
% 177.58/28.13    (6)  all_58_4 = e1
% 177.58/28.13    (7)  op(e3, e2) = all_52_3
% 177.58/28.13    (8)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.58/28.13    (9)  op(e3, all_4_2) = all_4_1
% 177.58/28.13    (10)   ~ (all_52_7 = all_4_2)
% 177.58/28.13    (11)  all_58_1 = all_52_3
% 177.58/28.13    (12)  all_58_0 = all_4_2
% 177.58/28.13    (13)  op(e2, all_52_27) = e2
% 177.58/28.13    (14)   ~ (all_4_1 = e2)
% 177.58/28.14    (15)  all_26_2 = all_4_2
% 177.58/28.14    (16)  op(e0, e2) = all_52_27
% 177.58/28.14    (17)  op(all_4_1, all_4_2) = e2
% 177.58/28.14    (18)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.58/28.14    (19)  all_56_12 = all_52_25
% 177.58/28.14    (20)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.58/28.14    (21)   ~ (all_52_25 = e1)
% 177.58/28.14    (22)  all_56_0 = all_4_2
% 177.58/28.14    (23)  all_26_1 = all_4_1
% 177.58/28.14    (24)  op(e3, all_52_25) = e3
% 177.58/28.14    (25)   ~ (all_52_25 = all_4_2)
% 177.58/28.14    (26)  op(e3, e0) = all_52_7
% 177.58/28.14    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.14    (28)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.58/28.14    (29)   ~ (all_4_2 = e1)
% 177.58/28.14    (30)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.58/28.14    (31)  all_58_9 = all_52_7
% 177.58/28.14  
% 177.58/28.14  Begin of proof
% 177.58/28.14  | 
% 177.58/28.14  | BETA: splitting (8) gives:
% 177.58/28.14  | 
% 177.58/28.14  | Case 1:
% 177.58/28.14  | | 
% 177.58/28.14  | |   (32)  all_58_0 = e2
% 177.58/28.14  | | 
% 177.58/28.14  | | COMBINE_EQS: (12), (32) imply:
% 177.58/28.14  | |   (33)  all_4_2 = e2
% 177.58/28.14  | | 
% 177.58/28.14  | | REDUCE: (25), (33) imply:
% 177.58/28.14  | |   (34)   ~ (all_52_25 = e2)
% 177.58/28.14  | | 
% 177.58/28.14  | | REDUCE: (17), (33) imply:
% 177.58/28.14  | |   (35)  op(all_4_1, e2) = e2
% 177.58/28.14  | | 
% 177.58/28.14  | | REDUCE: (9), (33) imply:
% 177.58/28.14  | |   (36)  op(e3, e2) = all_4_1
% 177.58/28.14  | | 
% 177.58/28.14  | | BETA: splitting (18) gives:
% 177.58/28.14  | | 
% 177.58/28.14  | | Case 1:
% 177.58/28.14  | | | 
% 177.58/28.14  | | |   (37)  all_56_12 = e2
% 177.58/28.14  | | | 
% 177.58/28.14  | | | REF_CLOSE: (19), (34), (37) are inconsistent by sub-proof #1032.
% 177.58/28.14  | | | 
% 177.58/28.14  | | Case 2:
% 177.58/28.14  | | | 
% 177.58/28.14  | | |   (38)   ~ (all_56_12 = e2)
% 177.58/28.14  | | |   (39)  all_56_12 = e1 | all_56_12 = e0
% 177.58/28.14  | | | 
% 177.58/28.14  | | | BETA: splitting (39) gives:
% 177.58/28.14  | | | 
% 177.58/28.14  | | | Case 1:
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | |   (40)  all_56_12 = e1
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | REF_CLOSE: (19), (21), (40) are inconsistent by sub-proof #1031.
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | Case 2:
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | |   (41)  all_56_12 = e0
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | COMBINE_EQS: (19), (41) imply:
% 177.58/28.14  | | | |   (42)  all_52_25 = e0
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | SIMP: (42) implies:
% 177.58/28.14  | | | |   (43)  all_52_25 = e0
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | REDUCE: (1), (43) imply:
% 177.58/28.14  | | | |   (44)   ~ (e3 = e0)
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | SIMP: (44) implies:
% 177.58/28.14  | | | |   (45)   ~ (e3 = e0)
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | REDUCE: (34), (43) imply:
% 177.58/28.14  | | | |   (46)   ~ (e2 = e0)
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | SIMP: (46) implies:
% 177.58/28.14  | | | |   (47)   ~ (e2 = e0)
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | REDUCE: (21), (43) imply:
% 177.58/28.14  | | | |   (48)   ~ (e1 = e0)
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | SIMP: (48) implies:
% 177.58/28.14  | | | |   (49)   ~ (e1 = e0)
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | REDUCE: (24), (43) imply:
% 177.58/28.14  | | | |   (50)  op(e3, e0) = e3
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | GROUND_INST: instantiating (27) with all_52_7, e3, e0, e3, simplifying
% 177.58/28.14  | | | |              with (26), (50) gives:
% 177.58/28.14  | | | |   (51)  all_52_7 = e3
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | GROUND_INST: instantiating (27) with all_52_3, all_4_1, e2, e3,
% 177.58/28.14  | | | |              simplifying with (7), (36) gives:
% 177.58/28.14  | | | |   (52)  all_52_3 = all_4_1
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | COMBINE_EQS: (31), (51) imply:
% 177.58/28.14  | | | |   (53)  all_58_9 = e3
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | COMBINE_EQS: (11), (52) imply:
% 177.58/28.14  | | | |   (54)  all_58_1 = all_4_1
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | BETA: splitting (2) gives:
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | | Case 1:
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | |   (55)  all_58_0 = e0
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | | COMBINE_EQS: (32), (55) imply:
% 177.58/28.14  | | | | |   (56)  e2 = e0
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | | REDUCE: (47), (56) imply:
% 177.58/28.14  | | | | |   (57)  $false
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | | CLOSE: (57) is inconsistent.
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | Case 2:
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | |   (58)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | | BETA: splitting (58) gives:
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | | Case 1:
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | |   (59)  all_58_1 = e0
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | COMBINE_EQS: (54), (59) imply:
% 177.58/28.14  | | | | | |   (60)  all_4_1 = e0
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | REDUCE: (35), (60) imply:
% 177.58/28.14  | | | | | |   (61)  op(e0, e2) = e2
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | GROUND_INST: instantiating (27) with all_52_27, e2, e2, e0,
% 177.58/28.14  | | | | | |              simplifying with (16), (61) gives:
% 177.58/28.14  | | | | | |   (62)  all_52_27 = e2
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | REDUCE: (3), (62) imply:
% 177.58/28.14  | | | | | |   (63)   ~ (all_10_2 = e2)
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | SIMP: (63) implies:
% 177.58/28.14  | | | | | |   (64)   ~ (all_10_2 = e2)
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | REDUCE: (13), (62) imply:
% 177.58/28.14  | | | | | |   (65)  op(e2, e2) = e2
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | REF_CLOSE: (4), (27), (64), (65) are inconsistent by sub-proof #453.
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | Case 2:
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | |   (66)  all_58_4 = e0 | all_58_9 = e0
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | | REF_CLOSE: (6), (45), (49), (53), (66) are inconsistent by sub-proof
% 177.58/28.14  | | | | | |            #927.
% 177.58/28.14  | | | | | | 
% 177.58/28.14  | | | | | End of split
% 177.58/28.14  | | | | | 
% 177.58/28.14  | | | | End of split
% 177.58/28.14  | | | | 
% 177.58/28.14  | | | End of split
% 177.58/28.14  | | | 
% 177.58/28.14  | | End of split
% 177.58/28.14  | | 
% 177.58/28.14  | Case 2:
% 177.58/28.14  | | 
% 177.58/28.14  | |   (67)   ~ (all_58_0 = e2)
% 177.58/28.14  | | 
% 177.58/28.14  | | REDUCE: (12), (67) imply:
% 177.58/28.14  | |   (68)   ~ (all_4_2 = e2)
% 177.58/28.14  | | 
% 177.58/28.14  | | REF_CLOSE: (5), (9), (10), (14), (15), (17), (20), (22), (23), (26), (27),
% 177.58/28.14  | |            (28), (29), (30), (68) are inconsistent by sub-proof #482.
% 177.58/28.14  | | 
% 177.58/28.14  | End of split
% 177.58/28.14  | 
% 177.58/28.14  End of proof
% 177.58/28.14  
% 177.58/28.14  Sub-proof #453 shows that the following formulas are inconsistent:
% 177.58/28.14  ----------------------------------------------------------------
% 177.58/28.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.58/28.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.58/28.14    (2)  op(e2, e2) = all_10_2
% 177.58/28.14    (3)  op(e2, e2) = e2
% 177.58/28.14    (4)   ~ (all_10_2 = e2)
% 177.58/28.14  
% 177.58/28.14  Begin of proof
% 177.58/28.14  | 
% 177.58/28.14  | GROUND_INST: instantiating (1) with all_10_2, e2, e2, e2, simplifying with
% 177.58/28.14  |              (2), (3) gives:
% 177.58/28.14  |   (5)  all_10_2 = e2
% 177.58/28.14  | 
% 177.58/28.14  | REDUCE: (4), (5) imply:
% 177.58/28.14  |   (6)  $false
% 177.58/28.14  | 
% 177.58/28.14  | CLOSE: (6) is inconsistent.
% 177.58/28.14  | 
% 177.58/28.14  End of proof
% 177.58/28.14  
% 177.58/28.14  Sub-proof #454 shows that the following formulas are inconsistent:
% 177.58/28.14  ----------------------------------------------------------------
% 177.58/28.14    (1)   ~ (all_52_23 = all_14_2)
% 177.58/28.14    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.58/28.14    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.58/28.14    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.58/28.14    (5)   ~ (all_52_17 = all_52_23)
% 177.58/28.14    (6)  all_56_3 = all_52_7
% 177.58/28.14    (7)  all_52_16 = e3
% 177.58/28.14    (8)  op(e3, e2) = all_52_3
% 177.58/28.14    (9)   ~ (all_52_9 = all_52_25)
% 177.68/28.14    (10)  op(e3, all_52_25) = all_52_24
% 177.68/28.14    (11)   ~ (all_52_19 = all_52_23)
% 177.68/28.14    (12)  op(e1, e2) = all_52_19
% 177.68/28.14    (13)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.14    (14)  op(e3, all_52_9) = all_52_8
% 177.68/28.14    (15)  all_50_1 = all_4_1
% 177.68/28.14    (16)   ~ (all_52_25 = all_52_29)
% 177.68/28.14    (17)  all_56_15 = all_6_2
% 177.68/28.14    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.14    (19)  op(all_14_1, all_14_2) = all_14_0
% 177.68/28.14    (20)  all_58_3 = all_10_2
% 177.68/28.14    (21)  all_56_9 = all_52_19
% 177.68/28.14    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.14    (23)  all_58_15 = all_6_2
% 177.68/28.14    (24)   ~ (all_52_9 = all_4_2)
% 177.68/28.14    (25)   ~ (all_52_5 = all_52_7)
% 177.68/28.14    (26)  all_58_10 = all_52_15
% 177.68/28.14    (27)   ~ (all_52_5 = all_4_2)
% 177.68/28.14    (28)  all_58_7 = all_52_19
% 177.68/28.14    (29)   ~ (all_52_17 = all_52_25)
% 177.68/28.14    (30)  all_58_4 = all_52_5
% 177.68/28.14    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.14    (32)  all_52_18 = e2
% 177.68/28.14    (33)   ~ (all_52_17 = all_14_2)
% 177.68/28.14    (34)  op(e3, all_4_2) = all_4_1
% 177.68/28.14    (35)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.68/28.14    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.14    (37)   ~ (all_52_7 = all_4_2)
% 177.68/28.14    (38)  all_58_1 = all_52_3
% 177.68/28.14    (39)  all_58_0 = all_4_2
% 177.68/28.14    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.68/28.14    (41)  op(e1, all_52_29) = all_52_28
% 177.68/28.14    (42)  all_50_2 = all_4_2
% 177.68/28.14    (43)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.14    (44)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.14    (45)   ~ (all_4_1 = e2)
% 177.68/28.14    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.68/28.14    (47)  all_58_14 = all_52_29
% 177.68/28.14    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.14    (49)   ~ (all_52_3 = all_52_5)
% 177.68/28.14    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.14    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.14    (52)  all_58_8 = all_14_2
% 177.68/28.14    (53)  all_56_1 = all_52_3
% 177.68/28.14    (54)   ~ (all_14_0 = e3)
% 177.68/28.14    (55)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.68/28.14    (56)   ~ (all_52_5 = all_14_2)
% 177.68/28.14    (57)   ~ (all_52_3 = all_52_27)
% 177.68/28.14    (58)   ~ (all_52_3 = all_4_2)
% 177.68/28.14    (59)  op(e0, e3) = all_52_25
% 177.68/28.14    (60)  op(all_4_1, all_4_2) = e2
% 177.68/28.14    (61)  op(e3, all_52_17) = all_52_16
% 177.68/28.14    (62)   ~ (e3 = e0)
% 177.68/28.14    (63)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.68/28.14    (64)  op(e0, all_52_23) = all_52_22
% 177.68/28.14    (65)   ~ (all_52_15 = all_52_23)
% 177.68/28.14    (66)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.14    (67)   ~ (all_52_5 = all_52_29)
% 177.68/28.14    (68)  all_56_2 = all_52_5
% 177.68/28.14    (69)  op(e1, e0) = all_52_23
% 177.68/28.14    (70)  all_58_13 = all_52_27
% 177.68/28.14    (71)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.14    (72)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.68/28.14    (73)   ~ (all_52_9 = all_52_17)
% 177.68/28.14    (74)   ~ (all_14_0 = e2)
% 177.68/28.14    (75)  all_58_6 = all_52_17
% 177.68/28.14    (76)   ~ (all_52_3 = all_52_7)
% 177.68/28.14    (77)  op(e2, all_52_19) = all_52_18
% 177.68/28.14    (78)   ~ (e1 = e0)
% 177.68/28.14    (79)  all_56_0 = all_4_2
% 177.68/28.14    (80)  all_58_11 = all_52_23
% 177.68/28.14    (81)   ~ (all_52_3 = all_52_19)
% 177.68/28.14    (82)   ~ (all_52_7 = all_52_15)
% 177.68/28.14    (83)   ~ (all_52_29 = all_14_2)
% 177.68/28.14    (84)   ~ (all_52_23 = all_6_2)
% 177.68/28.14    (85)  all_58_2 = all_52_9
% 177.68/28.14    (86)  op(e3, e1) = all_52_5
% 177.68/28.14    (87)  all_56_10 = all_14_2
% 177.68/28.14    (88)   ~ (all_52_25 = all_6_2)
% 177.68/28.14    (89)  op(e1, e3) = all_52_17
% 177.68/28.14    (90)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.68/28.14    (91)   ~ (all_52_25 = all_4_2)
% 177.68/28.14    (92)  op(e3, e0) = all_52_7
% 177.68/28.14    (93)  op(e3, e3) = all_4_2
% 177.68/28.14    (94)  all_56_8 = all_52_17
% 177.68/28.14    (95)   ~ (all_52_17 = all_4_2)
% 177.68/28.14    (96)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.14    (97)   ~ (all_52_25 = all_52_27)
% 177.68/28.14    (98)   ~ (all_52_27 = all_6_2)
% 177.68/28.14    (99)   ~ (all_52_15 = all_10_2)
% 177.68/28.14    (100)  all_56_7 = all_52_15
% 177.68/28.14    (101)   ~ (all_52_7 = all_52_23)
% 177.68/28.14    (102)  op(e2, all_52_27) = all_52_26
% 177.68/28.14    (103)   ~ (all_52_17 = all_52_19)
% 177.68/28.14    (104)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.14    (105)  all_52_22 = e0
% 177.68/28.14    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.14    (107)  op(e1, all_14_2) = all_14_1
% 177.68/28.14    (108)  all_58_9 = all_52_7
% 177.68/28.14    (109)   ~ (e2 = e0)
% 177.68/28.14    (110)  all_58_12 = all_52_25
% 177.68/28.14    (111)  all_14_1 = e1
% 177.68/28.14    (112)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.68/28.14    (113)   ~ (all_52_9 = all_52_15)
% 177.68/28.14    (114)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.14    (115)   ~ (e3 = e2)
% 177.68/28.14    (116)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.14    (117)   ~ (all_52_19 = all_14_2)
% 177.68/28.14    (118)  op(e2, e3) = all_52_9
% 177.68/28.14    (119)  all_56_13 = all_52_27
% 177.68/28.14  
% 177.68/28.14  Begin of proof
% 177.68/28.14  | 
% 177.68/28.14  | REDUCE: (19), (111) imply:
% 177.68/28.14  |   (120)  op(e1, all_14_2) = all_14_0
% 177.68/28.14  | 
% 177.68/28.14  | REDUCE: (7), (61) imply:
% 177.68/28.14  |   (121)  op(e3, all_52_17) = e3
% 177.68/28.14  | 
% 177.68/28.14  | REDUCE: (32), (77) imply:
% 177.68/28.14  |   (122)  op(e2, all_52_19) = e2
% 177.68/28.14  | 
% 177.68/28.14  | REDUCE: (107), (111) imply:
% 177.68/28.14  |   (123)  op(e1, all_14_2) = e1
% 177.68/28.14  | 
% 177.68/28.14  | REDUCE: (64), (105) imply:
% 177.68/28.14  |   (124)  op(e0, all_52_23) = e0
% 177.68/28.14  | 
% 177.68/28.14  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 177.68/28.14  |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 177.68/28.14  |            (26), (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 177.68/28.14  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.68/28.14  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 177.68/28.14  |            (60), (62), (63), (65), (66), (67), (68), (69), (70), (71), (72),
% 177.68/28.14  |            (73), (74), (75), (76), (78), (79), (80), (81), (82), (83), (84),
% 177.68/28.14  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 177.68/28.14  |            (96), (97), (98), (99), (100), (101), (102), (103), (104), (106),
% 177.68/28.14  |            (108), (109), (110), (112), (113), (114), (115), (116), (117),
% 177.68/28.14  |            (118), (119), (120), (121), (122), (123), (124) are inconsistent by
% 177.68/28.14  |            sub-proof #455.
% 177.68/28.14  | 
% 177.68/28.14  End of proof
% 177.68/28.14  
% 177.68/28.14  Sub-proof #455 shows that the following formulas are inconsistent:
% 177.68/28.14  ----------------------------------------------------------------
% 177.68/28.14    (1)   ~ (all_52_23 = all_14_2)
% 177.68/28.14    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.14    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.14    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.68/28.14    (5)   ~ (all_52_17 = all_52_23)
% 177.68/28.14    (6)  all_56_3 = all_52_7
% 177.68/28.14    (7)  op(e3, e2) = all_52_3
% 177.68/28.14    (8)   ~ (all_52_9 = all_52_25)
% 177.68/28.14    (9)  op(e3, all_52_25) = all_52_24
% 177.68/28.14    (10)   ~ (all_52_19 = all_52_23)
% 177.68/28.14    (11)  op(e1, e2) = all_52_19
% 177.68/28.14    (12)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.14    (13)  op(e3, all_52_9) = all_52_8
% 177.68/28.14    (14)  all_50_1 = all_4_1
% 177.68/28.14    (15)   ~ (all_52_25 = all_52_29)
% 177.68/28.14    (16)  all_56_15 = all_6_2
% 177.68/28.14    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.14    (18)  all_58_3 = all_10_2
% 177.68/28.14    (19)  all_56_9 = all_52_19
% 177.68/28.14    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.14    (21)  all_58_15 = all_6_2
% 177.68/28.14    (22)   ~ (all_52_9 = all_4_2)
% 177.68/28.14    (23)   ~ (all_52_5 = all_52_7)
% 177.68/28.14    (24)  all_58_10 = all_52_15
% 177.68/28.14    (25)   ~ (all_52_5 = all_4_2)
% 177.68/28.14    (26)  all_58_7 = all_52_19
% 177.68/28.14    (27)   ~ (all_52_17 = all_52_25)
% 177.68/28.14    (28)  all_58_4 = all_52_5
% 177.68/28.14    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.14    (30)   ~ (all_52_17 = all_14_2)
% 177.68/28.14    (31)  op(e3, all_4_2) = all_4_1
% 177.68/28.14    (32)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.68/28.14    (33)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.14    (34)   ~ (all_52_7 = all_4_2)
% 177.68/28.14    (35)  all_58_1 = all_52_3
% 177.68/28.14    (36)  all_58_0 = all_4_2
% 177.68/28.14    (37)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.68/28.14    (38)  op(e1, all_52_29) = all_52_28
% 177.68/28.14    (39)  all_50_2 = all_4_2
% 177.68/28.14    (40)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.14    (41)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.14    (42)   ~ (all_4_1 = e2)
% 177.68/28.14    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.68/28.14    (44)  all_58_14 = all_52_29
% 177.68/28.14    (45)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.14    (46)   ~ (all_52_3 = all_52_5)
% 177.68/28.14    (47)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.14    (48)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.14    (49)  all_58_8 = all_14_2
% 177.68/28.14    (50)  all_56_1 = all_52_3
% 177.68/28.14    (51)   ~ (all_14_0 = e3)
% 177.68/28.14    (52)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.68/28.14    (53)   ~ (all_52_5 = all_14_2)
% 177.68/28.14    (54)   ~ (all_52_3 = all_52_27)
% 177.68/28.14    (55)   ~ (all_52_3 = all_4_2)
% 177.68/28.14    (56)  op(e0, e3) = all_52_25
% 177.68/28.14    (57)  op(all_4_1, all_4_2) = e2
% 177.68/28.14    (58)  op(e1, all_14_2) = all_14_0
% 177.68/28.14    (59)   ~ (e3 = e0)
% 177.68/28.14    (60)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.68/28.14    (61)   ~ (all_52_15 = all_52_23)
% 177.68/28.14    (62)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.14    (63)   ~ (all_52_5 = all_52_29)
% 177.68/28.14    (64)  all_56_2 = all_52_5
% 177.68/28.14    (65)  op(e1, e0) = all_52_23
% 177.68/28.14    (66)  all_58_13 = all_52_27
% 177.68/28.14    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.14    (68)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.68/28.14    (69)   ~ (all_52_9 = all_52_17)
% 177.68/28.14    (70)   ~ (all_14_0 = e2)
% 177.68/28.14    (71)  all_58_6 = all_52_17
% 177.68/28.14    (72)   ~ (all_52_3 = all_52_7)
% 177.68/28.14    (73)  op(e2, all_52_19) = e2
% 177.68/28.14    (74)  op(e3, all_52_17) = e3
% 177.68/28.14    (75)   ~ (e1 = e0)
% 177.68/28.14    (76)  all_56_0 = all_4_2
% 177.68/28.14    (77)  all_58_11 = all_52_23
% 177.68/28.14    (78)   ~ (all_52_3 = all_52_19)
% 177.68/28.14    (79)   ~ (all_52_7 = all_52_15)
% 177.68/28.14    (80)   ~ (all_52_29 = all_14_2)
% 177.68/28.14    (81)   ~ (all_52_23 = all_6_2)
% 177.68/28.14    (82)  all_58_2 = all_52_9
% 177.68/28.14    (83)  op(e3, e1) = all_52_5
% 177.68/28.14    (84)  all_56_10 = all_14_2
% 177.68/28.14    (85)   ~ (all_52_25 = all_6_2)
% 177.68/28.14    (86)  op(e1, e3) = all_52_17
% 177.68/28.14    (87)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.68/28.14    (88)   ~ (all_52_25 = all_4_2)
% 177.68/28.14    (89)  op(e3, e0) = all_52_7
% 177.68/28.14    (90)  op(e3, e3) = all_4_2
% 177.68/28.14    (91)  all_56_8 = all_52_17
% 177.68/28.14    (92)   ~ (all_52_17 = all_4_2)
% 177.68/28.14    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.14    (94)   ~ (all_52_25 = all_52_27)
% 177.68/28.14    (95)   ~ (all_52_27 = all_6_2)
% 177.68/28.14    (96)  op(e0, all_52_23) = e0
% 177.68/28.14    (97)   ~ (all_52_15 = all_10_2)
% 177.68/28.14    (98)  all_56_7 = all_52_15
% 177.68/28.14    (99)  op(e1, all_14_2) = e1
% 177.68/28.14    (100)   ~ (all_52_7 = all_52_23)
% 177.68/28.14    (101)  op(e2, all_52_27) = all_52_26
% 177.68/28.14    (102)   ~ (all_52_17 = all_52_19)
% 177.68/28.14    (103)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.14    (104)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.14    (105)  all_58_9 = all_52_7
% 177.68/28.14    (106)   ~ (e2 = e0)
% 177.68/28.14    (107)  all_58_12 = all_52_25
% 177.68/28.14    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.68/28.14    (109)   ~ (all_52_9 = all_52_15)
% 177.68/28.14    (110)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.14    (111)   ~ (e3 = e2)
% 177.68/28.14    (112)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.14    (113)   ~ (all_52_19 = all_14_2)
% 177.68/28.14    (114)  op(e2, e3) = all_52_9
% 177.68/28.14    (115)  all_56_13 = all_52_27
% 177.68/28.14  
% 177.68/28.14  Begin of proof
% 177.68/28.14  | 
% 177.68/28.14  | GROUND_INST: instantiating (93) with e1, all_14_0, all_14_2, e1, simplifying
% 177.68/28.14  |              with (58), (99) gives:
% 177.68/28.14  |   (116)  all_14_0 = e1
% 177.68/28.14  | 
% 177.68/28.14  | REDUCE: (51), (116) imply:
% 177.68/28.14  |   (117)   ~ (e3 = e1)
% 177.68/28.14  | 
% 177.68/28.14  | SIMP: (117) implies:
% 177.68/28.14  |   (118)   ~ (e3 = e1)
% 177.68/28.14  | 
% 177.68/28.14  | REDUCE: (70), (116) imply:
% 177.68/28.14  |   (119)   ~ (e2 = e1)
% 177.68/28.14  | 
% 177.68/28.14  | SIMP: (119) implies:
% 177.68/28.14  |   (120)   ~ (e2 = e1)
% 177.68/28.14  | 
% 177.68/28.14  | BETA: splitting (32) gives:
% 177.68/28.14  | 
% 177.68/28.14  | Case 1:
% 177.68/28.14  | | 
% 177.68/28.14  | |   (121)  all_56_15 = e3
% 177.68/28.14  | | 
% 177.68/28.14  | | COMBINE_EQS: (16), (121) imply:
% 177.68/28.14  | |   (122)  all_6_2 = e3
% 177.68/28.14  | | 
% 177.68/28.14  | | SIMP: (122) implies:
% 177.68/28.14  | |   (123)  all_6_2 = e3
% 177.68/28.14  | | 
% 177.68/28.14  | | REDUCE: (81), (123) imply:
% 177.68/28.14  | |   (124)   ~ (all_52_23 = e3)
% 177.68/28.14  | | 
% 177.68/28.14  | | REDUCE: (85), (123) imply:
% 177.68/28.14  | |   (125)   ~ (all_52_25 = e3)
% 177.68/28.14  | | 
% 177.68/28.14  | | BETA: splitting (47) gives:
% 177.68/28.14  | | 
% 177.68/28.14  | | Case 1:
% 177.68/28.14  | | | 
% 177.68/28.14  | | |   (126)  all_58_0 = e3
% 177.68/28.14  | | | 
% 177.68/28.14  | | | REF_CLOSE: (31), (36), (42), (57), (90), (93), (126) are inconsistent by
% 177.68/28.14  | | |            sub-proof #489.
% 177.68/28.14  | | | 
% 177.68/28.14  | | Case 2:
% 177.68/28.14  | | | 
% 177.68/28.14  | | |   (127)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.14  | | | 
% 177.68/28.14  | | | REF_CLOSE: (19), (26), (29), (33), (41), (49), (53), (69), (71), (73),
% 177.68/28.14  | | |            (74), (77), (82), (83), (86), (90), (92), (93), (99), (107),
% 177.68/28.14  | | |            (111), (114), (124), (125), (127) are inconsistent by sub-proof
% 177.68/28.14  | | |            #945.
% 177.68/28.14  | | | 
% 177.68/28.14  | | End of split
% 177.68/28.14  | | 
% 177.68/28.14  | Case 2:
% 177.68/28.14  | | 
% 177.68/28.14  | |   (128)   ~ (all_56_15 = e3)
% 177.68/28.14  | | 
% 177.68/28.14  | | REDUCE: (16), (128) imply:
% 177.68/28.14  | |   (129)   ~ (all_6_2 = e3)
% 177.68/28.14  | | 
% 177.68/28.14  | | BETA: splitting (45) gives:
% 177.68/28.14  | | 
% 177.68/28.14  | | Case 1:
% 177.68/28.14  | | | 
% 177.68/28.14  | | |   (130)  all_56_13 = e3
% 177.68/28.14  | | | 
% 177.68/28.14  | | | COMBINE_EQS: (115), (130) imply:
% 177.68/28.14  | | |   (131)  all_52_27 = e3
% 177.68/28.14  | | | 
% 177.68/28.14  | | | SIMP: (131) implies:
% 177.68/28.14  | | |   (132)  all_52_27 = e3
% 177.68/28.14  | | | 
% 177.68/28.14  | | | REDUCE: (54), (132) imply:
% 177.68/28.14  | | |   (133)   ~ (all_52_3 = e3)
% 177.68/28.14  | | | 
% 177.68/28.14  | | | REDUCE: (94), (132) imply:
% 177.68/28.14  | | |   (134)   ~ (all_52_25 = e3)
% 177.68/28.14  | | | 
% 177.68/28.14  | | | REDUCE: (95), (132) imply:
% 177.68/28.14  | | |   (135)   ~ (all_6_2 = e3)
% 177.68/28.14  | | | 
% 177.68/28.14  | | | REDUCE: (101), (132) imply:
% 177.68/28.14  | | |   (136)  op(e2, e3) = all_52_26
% 177.68/28.14  | | | 
% 177.68/28.14  | | | GROUND_INST: instantiating (93) with all_52_9, all_52_26, e3, e2,
% 177.68/28.14  | | |              simplifying with (114), (136) gives:
% 177.68/28.14  | | |   (137)  all_52_9 = all_52_26
% 177.68/28.14  | | | 
% 177.68/28.14  | | | COMBINE_EQS: (82), (137) imply:
% 177.68/28.14  | | |   (138)  all_58_2 = all_52_26
% 177.68/28.14  | | | 
% 177.68/28.14  | | | REDUCE: (109), (137) imply:
% 177.68/28.14  | | |   (139)   ~ (all_52_15 = all_52_26)
% 177.68/28.14  | | | 
% 177.68/28.14  | | | SIMP: (139) implies:
% 177.68/28.14  | | |   (140)   ~ (all_52_15 = all_52_26)
% 177.68/28.14  | | | 
% 177.68/28.14  | | | BETA: splitting (103) gives:
% 177.68/28.14  | | | 
% 177.68/28.14  | | | Case 1:
% 177.68/28.14  | | | | 
% 177.68/28.14  | | | |   (141)  all_58_9 = e3
% 177.68/28.14  | | | | 
% 177.68/28.14  | | | | COMBINE_EQS: (105), (141) imply:
% 177.68/28.14  | | | |   (142)  all_52_7 = e3
% 177.68/28.14  | | | | 
% 177.68/28.14  | | | | REF_CLOSE: (19), (26), (29), (33), (34), (36), (41), (47), (49), (53),
% 177.68/28.14  | | | |            (69), (71), (73), (74), (77), (82), (83), (86), (90), (92),
% 177.68/28.14  | | | |            (93), (99), (100), (107), (111), (114), (134), (142) are
% 177.68/28.14  | | | |            inconsistent by sub-proof #943.
% 177.68/28.14  | | | | 
% 177.68/28.14  | | | Case 2:
% 177.68/28.14  | | | | 
% 177.68/28.14  | | | |   (143)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.14  | | | | 
% 177.68/28.14  | | | | BETA: splitting (108) gives:
% 177.68/28.14  | | | | 
% 177.68/28.14  | | | | Case 1:
% 177.68/28.14  | | | | | 
% 177.68/28.14  | | | | |   (144)  all_58_0 = e3
% 177.68/28.14  | | | | | 
% 177.68/28.14  | | | | | REF_CLOSE: (31), (36), (42), (57), (90), (93), (144) are inconsistent
% 177.68/28.14  | | | | |            by sub-proof #489.
% 177.68/28.14  | | | | | 
% 177.68/28.14  | | | | Case 2:
% 177.68/28.14  | | | | | 
% 177.68/28.14  | | | | |   (145)   ~ (all_58_0 = e3)
% 177.68/28.14  | | | | | 
% 177.68/28.14  | | | | | REDUCE: (36), (145) imply:
% 177.68/28.14  | | | | |   (146)   ~ (all_4_2 = e3)
% 177.68/28.14  | | | | | 
% 177.68/28.14  | | | | | BETA: splitting (29) gives:
% 177.68/28.14  | | | | | 
% 177.68/28.14  | | | | | Case 1:
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | |   (147)  all_58_6 = e3
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | | COMBINE_EQS: (71), (147) imply:
% 177.68/28.14  | | | | | |   (148)  all_52_17 = e3
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | | REF_CLOSE: (74), (90), (92), (93), (148) are inconsistent by
% 177.68/28.14  | | | | | |            sub-proof #948.
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | Case 2:
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | |   (149)   ~ (all_58_6 = e3)
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | | REDUCE: (71), (149) imply:
% 177.68/28.14  | | | | | |   (150)   ~ (all_52_17 = e3)
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | | BETA: splitting (47) gives:
% 177.68/28.14  | | | | | | 
% 177.68/28.14  | | | | | | Case 1:
% 177.68/28.14  | | | | | | | 
% 177.68/28.14  | | | | | | |   (151)  all_58_0 = e3
% 177.68/28.14  | | | | | | | 
% 177.68/28.14  | | | | | | | COMBINE_EQS: (36), (151) imply:
% 177.68/28.14  | | | | | | |   (152)  all_4_2 = e3
% 177.68/28.14  | | | | | | | 
% 177.68/28.14  | | | | | | | REDUCE: (146), (152) imply:
% 177.68/28.15  | | | | | | |   (153)  $false
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | | CLOSE: (153) is inconsistent.
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | Case 2:
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | |   (154)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | | BETA: splitting (154) gives:
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | |   (155)  all_58_2 = e3
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | COMBINE_EQS: (138), (155) imply:
% 177.68/28.15  | | | | | | | |   (156)  all_52_26 = e3
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | SIMP: (156) implies:
% 177.68/28.15  | | | | | | | |   (157)  all_52_26 = e3
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | REDUCE: (140), (157) imply:
% 177.68/28.15  | | | | | | | |   (158)   ~ (all_52_15 = e3)
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | BETA: splitting (143) gives:
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | |   (159)  all_58_10 = e3
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | REF_CLOSE: (24), (158), (159) are inconsistent by sub-proof
% 177.68/28.15  | | | | | | | | |            #1018.
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | |   (160)  all_58_11 = e3 | all_58_15 = e3
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | BETA: splitting (160) gives:
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | |   (161)  all_58_11 = e3
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | COMBINE_EQS: (77), (161) imply:
% 177.68/28.15  | | | | | | | | | |   (162)  all_52_23 = e3
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | SIMP: (162) implies:
% 177.68/28.15  | | | | | | | | | |   (163)  all_52_23 = e3
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (100), (163) imply:
% 177.68/28.15  | | | | | | | | | |   (164)   ~ (all_52_7 = e3)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (10), (163) imply:
% 177.68/28.15  | | | | | | | | | |   (165)   ~ (all_52_19 = e3)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (1), (163) imply:
% 177.68/28.15  | | | | | | | | | |   (166)   ~ (all_14_2 = e3)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | SIMP: (166) implies:
% 177.68/28.15  | | | | | | | | | |   (167)   ~ (all_14_2 = e3)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (65), (163) imply:
% 177.68/28.15  | | | | | | | | | |   (168)  op(e1, e0) = e3
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (96), (163) imply:
% 177.68/28.15  | | | | | | | | | |   (169)  op(e0, e3) = e0
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | GROUND_INST: instantiating (93) with all_52_25, e0, e3, e0,
% 177.68/28.15  | | | | | | | | | |              simplifying with (56), (169) gives:
% 177.68/28.15  | | | | | | | | | |   (170)  all_52_25 = e0
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | COMBINE_EQS: (107), (170) imply:
% 177.68/28.15  | | | | | | | | | |   (171)  all_58_12 = e0
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (27), (170) imply:
% 177.68/28.15  | | | | | | | | | |   (172)   ~ (all_52_17 = e0)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (9), (170) imply:
% 177.68/28.15  | | | | | | | | | |   (173)  op(e3, e0) = all_52_24
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | GROUND_INST: instantiating (93) with all_52_7, all_52_24, e0,
% 177.68/28.15  | | | | | | | | | |              e3, simplifying with (89), (173) gives:
% 177.68/28.15  | | | | | | | | | |   (174)  all_52_7 = all_52_24
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | COMBINE_EQS: (6), (174) imply:
% 177.68/28.15  | | | | | | | | | |   (175)  all_56_3 = all_52_24
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (72), (174) imply:
% 177.68/28.15  | | | | | | | | | |   (176)   ~ (all_52_3 = all_52_24)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (34), (174) imply:
% 177.68/28.15  | | | | | | | | | |   (177)   ~ (all_52_24 = all_4_2)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (164), (174) imply:
% 177.68/28.15  | | | | | | | | | |   (178)   ~ (all_52_24 = e3)
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | BETA: splitting (2) gives:
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | |   (179)  all_56_8 = e3
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | | REF_CLOSE: (91), (150), (179) are inconsistent by sub-proof
% 177.68/28.15  | | | | | | | | | | |            #461.
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | |   (180)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | | REF_CLOSE: (4), (7), (11), (17), (19), (30), (31), (35),
% 177.68/28.15  | | | | | | | | | | |            (36), (40), (41), (50), (55), (57), (62), (71),
% 177.68/28.15  | | | | | | | | | | |            (74), (78), (84), (91), (92), (93), (99), (102),
% 177.68/28.15  | | | | | | | | | | |            (104), (106), (111), (113), (133), (150), (155),
% 177.68/28.15  | | | | | | | | | | |            (165), (167), (168), (171), (172), (175), (176),
% 177.68/28.15  | | | | | | | | | | |            (177), (178), (180) are inconsistent by sub-proof
% 177.68/28.15  | | | | | | | | | | |            #457.
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | End of split
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | |   (181)  all_58_15 = e3
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | COMBINE_EQS: (21), (181) imply:
% 177.68/28.15  | | | | | | | | | |   (182)  all_6_2 = e3
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REDUCE: (129), (182) imply:
% 177.68/28.15  | | | | | | | | | |   (183)  $false
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | CLOSE: (183) is inconsistent.
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | End of split
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | End of split
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | |   (184)  all_58_6 = e3 | all_58_12 = e3
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | REF_CLOSE: (71), (107), (134), (150), (184) are inconsistent by
% 177.68/28.15  | | | | | | | |            sub-proof #483.
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | End of split
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | End of split
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | End of split
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | End of split
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | End of split
% 177.68/28.15  | | | 
% 177.68/28.15  | | Case 2:
% 177.68/28.15  | | | 
% 177.68/28.15  | | |   (185)   ~ (all_56_13 = e3)
% 177.68/28.15  | | | 
% 177.68/28.15  | | | REDUCE: (115), (185) imply:
% 177.68/28.15  | | |   (186)   ~ (all_52_27 = e3)
% 177.68/28.15  | | | 
% 177.68/28.15  | | | BETA: splitting (48) gives:
% 177.68/28.15  | | | 
% 177.68/28.15  | | | Case 1:
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | |   (187)  all_58_12 = e3
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REF_CLOSE: (1), (3), (11), (12), (14), (18), (20), (21), (22), (23),
% 177.68/28.15  | | | |            (24), (25), (26), (27), (28), (29), (31), (34), (35), (36),
% 177.68/28.15  | | | |            (37), (39), (42), (43), (49), (52), (53), (56), (59), (60),
% 177.68/28.15  | | | |            (61), (62), (66), (67), (68), (69), (71), (73), (74), (75),
% 177.68/28.15  | | | |            (76), (77), (78), (79), (82), (83), (84), (85), (86), (87),
% 177.68/28.15  | | | |            (88), (89), (92), (93), (94), (96), (97), (98), (99), (100),
% 177.68/28.15  | | | |            (102), (103), (105), (106), (107), (108), (109), (110),
% 177.68/28.15  | | | |            (111), (113), (114), (118), (120), (187) are inconsistent by
% 177.68/28.15  | | | |            sub-proof #456.
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | Case 2:
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | |   (188)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | BETA: splitting (188) gives:
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | Case 1:
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | |   (189)  all_58_13 = e3
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | | REF_CLOSE: (66), (186), (189) are inconsistent by sub-proof #1026.
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | Case 2:
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | |   (190)  all_58_14 = e3 | all_58_15 = e3
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | | BETA: splitting (190) gives:
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | | Case 1:
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | |   (191)  all_58_14 = e3
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | | REF_CLOSE: (2), (5), (8), (12), (13), (14), (15), (17), (19), (20),
% 177.68/28.15  | | | | | |            (22), (25), (26), (27), (28), (29), (31), (33), (34),
% 177.68/28.15  | | | | | |            (35), (36), (38), (39), (41), (42), (44), (46), (47),
% 177.68/28.15  | | | | | |            (49), (53), (55), (56), (57), (63), (64), (67), (69),
% 177.68/28.15  | | | | | |            (71), (73), (74), (76), (77), (78), (80), (82), (83),
% 177.68/28.15  | | | | | |            (86), (88), (90), (91), (92), (93), (96), (99), (100),
% 177.68/28.15  | | | | | |            (105), (107), (108), (111), (112), (114), (191) are
% 177.68/28.15  | | | | | |            inconsistent by sub-proof #475.
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | Case 2:
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | |   (192)  all_58_15 = e3
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | | COMBINE_EQS: (21), (192) imply:
% 177.68/28.15  | | | | | |   (193)  all_6_2 = e3
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | | REDUCE: (129), (193) imply:
% 177.68/28.15  | | | | | |   (194)  $false
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | | CLOSE: (194) is inconsistent.
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | End of split
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | End of split
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | End of split
% 177.68/28.15  | | | 
% 177.68/28.15  | | End of split
% 177.68/28.15  | | 
% 177.68/28.15  | End of split
% 177.68/28.15  | 
% 177.68/28.15  End of proof
% 177.68/28.15  
% 177.68/28.15  Sub-proof #456 shows that the following formulas are inconsistent:
% 177.68/28.15  ----------------------------------------------------------------
% 177.68/28.15    (1)   ~ (all_52_23 = all_14_2)
% 177.68/28.15    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.15    (3)  op(e1, e2) = all_52_19
% 177.68/28.15    (4)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.15    (5)  all_50_1 = all_4_1
% 177.68/28.15    (6)  all_58_3 = all_10_2
% 177.68/28.15    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.15    (8)  all_58_15 = all_6_2
% 177.68/28.15    (9)   ~ (all_52_9 = all_4_2)
% 177.68/28.15    (10)   ~ (all_52_5 = all_52_7)
% 177.68/28.15    (11)  all_58_10 = all_52_15
% 177.68/28.15    (12)   ~ (all_52_5 = all_4_2)
% 177.68/28.15    (13)  all_58_7 = all_52_19
% 177.68/28.15    (14)   ~ (all_52_17 = all_52_25)
% 177.68/28.15    (15)  all_58_4 = all_52_5
% 177.68/28.15    (16)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.15    (17)   ~ (e3 = e1)
% 177.68/28.15    (18)  op(e3, all_4_2) = all_4_1
% 177.68/28.15    (19)   ~ (all_52_7 = all_4_2)
% 177.68/28.15    (20)  all_58_1 = all_52_3
% 177.68/28.15    (21)  all_58_0 = all_4_2
% 177.68/28.15    (22)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.68/28.15    (23)  all_50_2 = all_4_2
% 177.68/28.15    (24)   ~ (all_4_1 = e2)
% 177.68/28.15    (25)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.68/28.15    (26)  all_58_8 = all_14_2
% 177.68/28.15    (27)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.68/28.15    (28)   ~ (all_52_5 = all_14_2)
% 177.68/28.15    (29)  op(e0, e3) = all_52_25
% 177.68/28.15    (30)   ~ (e3 = e0)
% 177.68/28.15    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.68/28.15    (32)   ~ (all_52_15 = all_52_23)
% 177.68/28.15    (33)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.15    (34)  all_58_13 = all_52_27
% 177.68/28.15    (35)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.15    (36)  all_58_12 = e3
% 177.68/28.15    (37)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.68/28.15    (38)   ~ (all_52_9 = all_52_17)
% 177.68/28.15    (39)  all_58_6 = all_52_17
% 177.68/28.15    (40)  op(e2, all_52_19) = e2
% 177.68/28.15    (41)  op(e3, all_52_17) = e3
% 177.68/28.15    (42)   ~ (e1 = e0)
% 177.68/28.15    (43)  all_56_0 = all_4_2
% 177.68/28.15    (44)  all_58_11 = all_52_23
% 177.68/28.15    (45)   ~ (all_52_3 = all_52_19)
% 177.68/28.15    (46)   ~ (all_52_7 = all_52_15)
% 177.68/28.15    (47)  all_58_2 = all_52_9
% 177.68/28.15    (48)  op(e3, e1) = all_52_5
% 177.68/28.15    (49)   ~ (e2 = e1)
% 177.68/28.15    (50)  all_56_10 = all_14_2
% 177.68/28.15    (51)   ~ (all_52_25 = all_6_2)
% 177.68/28.15    (52)  op(e1, e3) = all_52_17
% 177.68/28.15    (53)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.68/28.15    (54)   ~ (all_52_25 = all_4_2)
% 177.68/28.15    (55)  op(e3, e0) = all_52_7
% 177.68/28.15    (56)   ~ (all_52_17 = all_4_2)
% 177.68/28.15    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.15    (58)   ~ (all_52_25 = all_52_27)
% 177.68/28.15    (59)  op(e0, all_52_23) = e0
% 177.68/28.15    (60)   ~ (all_52_15 = all_10_2)
% 177.68/28.15    (61)  all_56_7 = all_52_15
% 177.68/28.15    (62)  op(e1, all_14_2) = e1
% 177.68/28.15    (63)   ~ (all_52_7 = all_52_23)
% 177.68/28.15    (64)   ~ (all_52_17 = all_52_19)
% 177.68/28.15    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.15    (66)  all_58_9 = all_52_7
% 177.68/28.15    (67)   ~ (e2 = e0)
% 177.68/28.15    (68)  all_58_12 = all_52_25
% 177.68/28.15    (69)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.68/28.15    (70)   ~ (all_52_9 = all_52_15)
% 177.68/28.15    (71)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.15    (72)   ~ (e3 = e2)
% 177.68/28.15    (73)   ~ (all_52_19 = all_14_2)
% 177.68/28.15    (74)  op(e2, e3) = all_52_9
% 177.68/28.15  
% 177.68/28.15  Begin of proof
% 177.68/28.15  | 
% 177.68/28.15  | COMBINE_EQS: (36), (68) imply:
% 177.68/28.15  |   (75)  all_52_25 = e3
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (75) implies:
% 177.68/28.15  |   (76)  all_52_25 = e3
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (14), (76) imply:
% 177.68/28.15  |   (77)   ~ (all_52_17 = e3)
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (58), (76) imply:
% 177.68/28.15  |   (78)   ~ (all_52_27 = e3)
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (78) implies:
% 177.68/28.15  |   (79)   ~ (all_52_27 = e3)
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (51), (76) imply:
% 177.68/28.15  |   (80)   ~ (all_6_2 = e3)
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (80) implies:
% 177.68/28.15  |   (81)   ~ (all_6_2 = e3)
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (54), (76) imply:
% 177.68/28.15  |   (82)   ~ (all_4_2 = e3)
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (82) implies:
% 177.68/28.15  |   (83)   ~ (all_4_2 = e3)
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (29), (76) imply:
% 177.68/28.15  |   (84)  op(e0, e3) = e3
% 177.68/28.15  | 
% 177.68/28.15  | BETA: splitting (7) gives:
% 177.68/28.15  | 
% 177.68/28.15  | Case 1:
% 177.68/28.15  | | 
% 177.68/28.15  | |   (85)  all_56_0 = e3
% 177.68/28.15  | | 
% 177.68/28.15  | | COMBINE_EQS: (43), (85) imply:
% 177.68/28.15  | |   (86)  all_4_2 = e3
% 177.68/28.15  | | 
% 177.68/28.15  | | REDUCE: (83), (86) imply:
% 177.68/28.15  | |   (87)  $false
% 177.68/28.15  | | 
% 177.68/28.15  | | CLOSE: (87) is inconsistent.
% 177.68/28.15  | | 
% 177.68/28.15  | Case 2:
% 177.68/28.15  | | 
% 177.68/28.15  | |   (88)   ~ (all_56_0 = e3)
% 177.68/28.15  | |   (89)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.15  | | 
% 177.68/28.15  | | BETA: splitting (65) gives:
% 177.68/28.15  | | 
% 177.68/28.15  | | Case 1:
% 177.68/28.15  | | | 
% 177.68/28.15  | | |   (90)  all_58_9 = e3
% 177.68/28.15  | | | 
% 177.68/28.15  | | | COMBINE_EQS: (66), (90) imply:
% 177.68/28.15  | | |   (91)  all_52_7 = e3
% 177.68/28.15  | | | 
% 177.68/28.15  | | | REDUCE: (10), (91) imply:
% 177.68/28.15  | | |   (92)   ~ (all_52_5 = e3)
% 177.68/28.15  | | | 
% 177.68/28.15  | | | REDUCE: (63), (91) imply:
% 177.68/28.15  | | |   (93)   ~ (all_52_23 = e3)
% 177.68/28.15  | | | 
% 177.68/28.15  | | | SIMP: (93) implies:
% 177.68/28.15  | | |   (94)   ~ (all_52_23 = e3)
% 177.68/28.15  | | | 
% 177.68/28.15  | | | REF_CLOSE: (1), (2), (4), (5), (13), (15), (16), (17), (18), (20), (21),
% 177.68/28.15  | | |            (23), (24), (26), (27), (28), (30), (33), (35), (36), (39),
% 177.68/28.15  | | |            (40), (41), (42), (44), (47), (48), (49), (50), (52), (57),
% 177.68/28.15  | | |            (62), (67), (72), (73), (74), (77), (90), (92), (94) are
% 177.68/28.15  | | |            inconsistent by sub-proof #479.
% 177.68/28.15  | | | 
% 177.68/28.15  | | Case 2:
% 177.68/28.15  | | | 
% 177.68/28.15  | | |   (95)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.15  | | | 
% 177.68/28.15  | | | REF_CLOSE: (3), (6), (8), (9), (10), (11), (12), (13), (15), (16), (17),
% 177.68/28.15  | | |            (19), (20), (21), (22), (25), (26), (28), (30), (31), (32),
% 177.68/28.15  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 177.68/28.15  | | |            (44), (45), (46), (47), (48), (49), (52), (53), (55), (56),
% 177.68/28.15  | | |            (57), (59), (60), (61), (62), (64), (66), (67), (69), (70),
% 177.68/28.15  | | |            (71), (74), (77), (79), (81), (83), (84), (89), (95) are
% 177.68/28.15  | | |            inconsistent by sub-proof #678.
% 177.68/28.15  | | | 
% 177.68/28.15  | | End of split
% 177.68/28.15  | | 
% 177.68/28.15  | End of split
% 177.68/28.15  | 
% 177.68/28.15  End of proof
% 177.68/28.15  
% 177.68/28.15  Sub-proof #457 shows that the following formulas are inconsistent:
% 177.68/28.15  ----------------------------------------------------------------
% 177.68/28.15    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.68/28.15    (2)  op(e3, e2) = all_52_3
% 177.68/28.15    (3)  op(e1, e2) = all_52_19
% 177.68/28.15    (4)   ~ (all_52_17 = e3)
% 177.68/28.15    (5)   ~ (all_52_17 = e0)
% 177.68/28.15    (6)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.15    (7)  all_56_9 = all_52_19
% 177.68/28.15    (8)  all_58_2 = e3
% 177.68/28.15    (9)   ~ (all_52_17 = all_14_2)
% 177.68/28.15    (10)  op(e3, all_4_2) = all_4_1
% 177.68/28.15    (11)  all_58_1 = all_52_3
% 177.68/28.15    (12)  all_58_0 = all_4_2
% 177.68/28.15    (13)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.15    (14)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.15    (15)  all_56_1 = all_52_3
% 177.68/28.15    (16)  all_58_12 = e0
% 177.68/28.15    (17)  op(e1, e0) = e3
% 177.68/28.15    (18)   ~ (all_52_3 = all_52_24)
% 177.68/28.15    (19)   ~ (all_52_3 = all_4_2)
% 177.68/28.15    (20)  op(all_4_1, all_4_2) = e2
% 177.68/28.15    (21)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.15    (22)   ~ (all_52_3 = e3)
% 177.68/28.15    (23)  all_58_6 = all_52_17
% 177.68/28.15    (24)  op(e3, all_52_17) = e3
% 177.68/28.15    (25)   ~ (all_52_3 = all_52_19)
% 177.68/28.15    (26)  all_56_10 = all_14_2
% 177.68/28.15    (27)   ~ (all_52_19 = e3)
% 177.68/28.15    (28)  all_56_8 = all_52_17
% 177.68/28.15    (29)   ~ (all_14_2 = e3)
% 177.68/28.15    (30)   ~ (all_52_17 = all_4_2)
% 177.68/28.15    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.15    (32)  op(e1, all_14_2) = e1
% 177.68/28.15    (33)   ~ (all_52_17 = all_52_19)
% 177.68/28.15    (34)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.15    (35)   ~ (all_52_24 = all_4_2)
% 177.68/28.15    (36)   ~ (e2 = e0)
% 177.68/28.15    (37)   ~ (all_52_24 = e3)
% 177.68/28.15    (38)   ~ (e3 = e2)
% 177.68/28.15    (39)  all_56_3 = all_52_24
% 177.68/28.15    (40)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.15    (41)   ~ (all_52_19 = all_14_2)
% 177.68/28.15  
% 177.68/28.15  Begin of proof
% 177.68/28.15  | 
% 177.68/28.15  | BETA: splitting (6) gives:
% 177.68/28.15  | 
% 177.68/28.15  | Case 1:
% 177.68/28.15  | | 
% 177.68/28.15  | |   (42)  all_58_0 = e2
% 177.68/28.15  | | 
% 177.68/28.15  | | COMBINE_EQS: (12), (42) imply:
% 177.68/28.15  | |   (43)  all_4_2 = e2
% 177.68/28.15  | | 
% 177.68/28.15  | | REDUCE: (19), (43) imply:
% 177.68/28.15  | |   (44)   ~ (all_52_3 = e2)
% 177.68/28.15  | | 
% 177.68/28.15  | | REDUCE: (30), (43) imply:
% 177.68/28.15  | |   (45)   ~ (all_52_17 = e2)
% 177.68/28.15  | | 
% 177.68/28.15  | | REDUCE: (35), (43) imply:
% 177.68/28.15  | |   (46)   ~ (all_52_24 = e2)
% 177.68/28.15  | | 
% 177.68/28.15  | | REDUCE: (20), (43) imply:
% 177.68/28.15  | |   (47)  op(all_4_1, e2) = e2
% 177.68/28.15  | | 
% 177.68/28.15  | | REDUCE: (10), (43) imply:
% 177.68/28.15  | |   (48)  op(e3, e2) = all_4_1
% 177.68/28.15  | | 
% 177.68/28.15  | | BETA: splitting (40) gives:
% 177.68/28.15  | | 
% 177.68/28.15  | | Case 1:
% 177.68/28.15  | | | 
% 177.68/28.15  | | |   (49)  all_56_8 = e2
% 177.68/28.15  | | | 
% 177.68/28.15  | | | REF_CLOSE: (28), (45), (49) are inconsistent by sub-proof #460.
% 177.68/28.15  | | | 
% 177.68/28.15  | | Case 2:
% 177.68/28.15  | | | 
% 177.68/28.15  | | |   (50)  all_56_8 = e1 | all_56_8 = e0
% 177.68/28.15  | | | 
% 177.68/28.15  | | | BETA: splitting (50) gives:
% 177.68/28.15  | | | 
% 177.68/28.15  | | | Case 1:
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | |   (51)  all_56_8 = e1
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | COMBINE_EQS: (28), (51) imply:
% 177.68/28.15  | | | |   (52)  all_52_17 = e1
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | SIMP: (52) implies:
% 177.68/28.15  | | | |   (53)  all_52_17 = e1
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (33), (53) imply:
% 177.68/28.15  | | | |   (54)   ~ (all_52_19 = e1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | SIMP: (54) implies:
% 177.68/28.15  | | | |   (55)   ~ (all_52_19 = e1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (9), (53) imply:
% 177.68/28.15  | | | |   (56)   ~ (all_14_2 = e1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | SIMP: (56) implies:
% 177.68/28.15  | | | |   (57)   ~ (all_14_2 = e1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (4), (53) imply:
% 177.68/28.15  | | | |   (58)   ~ (e3 = e1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | SIMP: (58) implies:
% 177.68/28.15  | | | |   (59)   ~ (e3 = e1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | GROUND_INST: instantiating (31) with all_52_3, all_4_1, e2, e3,
% 177.68/28.15  | | | |              simplifying with (2), (48) gives:
% 177.68/28.15  | | | |   (60)  all_52_3 = all_4_1
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | COMBINE_EQS: (15), (60) imply:
% 177.68/28.15  | | | |   (61)  all_56_1 = all_4_1
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | COMBINE_EQS: (11), (60) imply:
% 177.68/28.15  | | | |   (62)  all_58_1 = all_4_1
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (25), (60) imply:
% 177.68/28.15  | | | |   (63)   ~ (all_52_19 = all_4_1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | SIMP: (63) implies:
% 177.68/28.15  | | | |   (64)   ~ (all_52_19 = all_4_1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (18), (60) imply:
% 177.68/28.15  | | | |   (65)   ~ (all_52_24 = all_4_1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | SIMP: (65) implies:
% 177.68/28.15  | | | |   (66)   ~ (all_52_24 = all_4_1)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (22), (60) imply:
% 177.68/28.15  | | | |   (67)   ~ (all_4_1 = e3)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (44), (60) imply:
% 177.68/28.15  | | | |   (68)   ~ (all_4_1 = e2)
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | BETA: splitting (13) gives:
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | Case 1:
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | |   (69)  all_56_1 = e3
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | | REF_CLOSE: (61), (67), (69) are inconsistent by sub-proof #459.
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | Case 2:
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | |   (70)   ~ (all_56_1 = e3)
% 177.68/28.15  | | | | |   (71)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | | BETA: splitting (21) gives:
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | | Case 1:
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | |   (72)  all_56_10 = e3
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | | REF_CLOSE: (26), (29), (72) are inconsistent by sub-proof #552.
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | Case 2:
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | |   (73)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | | BETA: splitting (34) gives:
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | | Case 1:
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | |   (74)  all_56_3 = e3
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | | REF_CLOSE: (37), (39), (74) are inconsistent by sub-proof #458.
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | Case 2:
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | |   (75)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | | BETA: splitting (14) gives:
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | |   (76)  all_56_9 = e3
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | COMBINE_EQS: (7), (76) imply:
% 177.68/28.15  | | | | | | | |   (77)  all_52_19 = e3
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | REDUCE: (27), (77) imply:
% 177.68/28.15  | | | | | | | |   (78)  $false
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | CLOSE: (78) is inconsistent.
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | |   (79)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | BETA: splitting (1) gives:
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | |   (80)  all_58_1 = e1
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | COMBINE_EQS: (62), (80) imply:
% 177.68/28.15  | | | | | | | | |   (81)  all_4_1 = e1
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | REDUCE: (66), (81) imply:
% 177.68/28.15  | | | | | | | | |   (82)   ~ (all_52_24 = e1)
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | REDUCE: (47), (81) imply:
% 177.68/28.15  | | | | | | | | |   (83)  op(e1, e2) = e2
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | BETA: splitting (75) gives:
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | |   (84)  all_56_3 = e2
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | REF_CLOSE: (39), (46), (84) are inconsistent by sub-proof
% 177.68/28.15  | | | | | | | | | |            #516.
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | |   (85)  all_56_3 = e1 | all_56_3 = e0
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | BETA: splitting (85) gives:
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | Case 1:
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | |   (86)  all_56_3 = e1
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | | REF_CLOSE: (39), (82), (86) are inconsistent by sub-proof
% 177.68/28.15  | | | | | | | | | | |            #515.
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | | GROUND_INST: instantiating (31) with all_52_19, e2, e2, e1,
% 177.68/28.15  | | | | | | | | | | |              simplifying with (3), (83) gives:
% 177.68/28.15  | | | | | | | | | | |   (87)  all_52_19 = e2
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | | REF_CLOSE: (17), (26), (31), (32), (41), (57), (59), (73),
% 177.68/28.15  | | | | | | | | | | |            (87) are inconsistent by sub-proof #689.
% 177.68/28.15  | | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | | End of split
% 177.68/28.15  | | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | End of split
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | Case 2:
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | |   (88)   ~ (all_58_1 = e1)
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | REDUCE: (62), (88) imply:
% 177.68/28.15  | | | | | | | | |   (89)   ~ (all_4_1 = e1)
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | | REF_CLOSE: (7), (17), (26), (31), (32), (41), (55), (57),
% 177.68/28.15  | | | | | | | | |            (59), (61), (64), (68), (71), (73), (79), (89) are
% 177.68/28.15  | | | | | | | | |            inconsistent by sub-proof #687.
% 177.68/28.15  | | | | | | | | | 
% 177.68/28.15  | | | | | | | | End of split
% 177.68/28.15  | | | | | | | | 
% 177.68/28.15  | | | | | | | End of split
% 177.68/28.15  | | | | | | | 
% 177.68/28.15  | | | | | | End of split
% 177.68/28.15  | | | | | | 
% 177.68/28.15  | | | | | End of split
% 177.68/28.15  | | | | | 
% 177.68/28.15  | | | | End of split
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | Case 2:
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | |   (90)  all_56_8 = e0
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | COMBINE_EQS: (28), (90) imply:
% 177.68/28.15  | | | |   (91)  all_52_17 = e0
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | SIMP: (91) implies:
% 177.68/28.15  | | | |   (92)  all_52_17 = e0
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | REDUCE: (5), (92) imply:
% 177.68/28.15  | | | |   (93)  $false
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | | CLOSE: (93) is inconsistent.
% 177.68/28.15  | | | | 
% 177.68/28.15  | | | End of split
% 177.68/28.15  | | | 
% 177.68/28.15  | | End of split
% 177.68/28.15  | | 
% 177.68/28.15  | Case 2:
% 177.68/28.15  | | 
% 177.68/28.15  | |   (94)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.15  | | 
% 177.68/28.15  | | REF_CLOSE: (2), (8), (16), (22), (23), (24), (31), (36), (38), (94) are
% 177.68/28.15  | |            inconsistent by sub-proof #693.
% 177.68/28.15  | | 
% 177.68/28.15  | End of split
% 177.68/28.15  | 
% 177.68/28.15  End of proof
% 177.68/28.15  
% 177.68/28.15  Sub-proof #458 shows that the following formulas are inconsistent:
% 177.68/28.15  ----------------------------------------------------------------
% 177.68/28.15    (1)  all_56_3 = all_52_24
% 177.68/28.15    (2)  all_56_3 = e3
% 177.68/28.15    (3)   ~ (all_52_24 = e3)
% 177.68/28.15  
% 177.68/28.15  Begin of proof
% 177.68/28.15  | 
% 177.68/28.15  | COMBINE_EQS: (1), (2) imply:
% 177.68/28.15  |   (4)  all_52_24 = e3
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (4) implies:
% 177.68/28.15  |   (5)  all_52_24 = e3
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (3), (5) imply:
% 177.68/28.15  |   (6)  $false
% 177.68/28.15  | 
% 177.68/28.15  | CLOSE: (6) is inconsistent.
% 177.68/28.15  | 
% 177.68/28.15  End of proof
% 177.68/28.15  
% 177.68/28.15  Sub-proof #459 shows that the following formulas are inconsistent:
% 177.68/28.15  ----------------------------------------------------------------
% 177.68/28.15    (1)  all_56_1 = all_4_1
% 177.68/28.15    (2)  all_56_1 = e3
% 177.68/28.15    (3)   ~ (all_4_1 = e3)
% 177.68/28.15  
% 177.68/28.15  Begin of proof
% 177.68/28.15  | 
% 177.68/28.15  | COMBINE_EQS: (1), (2) imply:
% 177.68/28.15  |   (4)  all_4_1 = e3
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (4) implies:
% 177.68/28.15  |   (5)  all_4_1 = e3
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (3), (5) imply:
% 177.68/28.15  |   (6)  $false
% 177.68/28.15  | 
% 177.68/28.15  | CLOSE: (6) is inconsistent.
% 177.68/28.15  | 
% 177.68/28.15  End of proof
% 177.68/28.15  
% 177.68/28.15  Sub-proof #460 shows that the following formulas are inconsistent:
% 177.68/28.15  ----------------------------------------------------------------
% 177.68/28.15    (1)  all_56_8 = all_52_17
% 177.68/28.15    (2)  all_56_8 = e2
% 177.68/28.15    (3)   ~ (all_52_17 = e2)
% 177.68/28.15  
% 177.68/28.15  Begin of proof
% 177.68/28.15  | 
% 177.68/28.15  | COMBINE_EQS: (1), (2) imply:
% 177.68/28.15  |   (4)  all_52_17 = e2
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (4) implies:
% 177.68/28.15  |   (5)  all_52_17 = e2
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (3), (5) imply:
% 177.68/28.15  |   (6)  $false
% 177.68/28.15  | 
% 177.68/28.15  | CLOSE: (6) is inconsistent.
% 177.68/28.15  | 
% 177.68/28.15  End of proof
% 177.68/28.15  
% 177.68/28.15  Sub-proof #461 shows that the following formulas are inconsistent:
% 177.68/28.15  ----------------------------------------------------------------
% 177.68/28.15    (1)  all_56_8 = all_52_17
% 177.68/28.15    (2)  all_56_8 = e3
% 177.68/28.15    (3)   ~ (all_52_17 = e3)
% 177.68/28.15  
% 177.68/28.15  Begin of proof
% 177.68/28.15  | 
% 177.68/28.15  | COMBINE_EQS: (1), (2) imply:
% 177.68/28.15  |   (4)  all_52_17 = e3
% 177.68/28.15  | 
% 177.68/28.15  | SIMP: (4) implies:
% 177.68/28.15  |   (5)  all_52_17 = e3
% 177.68/28.15  | 
% 177.68/28.15  | REDUCE: (3), (5) imply:
% 177.68/28.15  |   (6)  $false
% 177.68/28.15  | 
% 177.68/28.15  | CLOSE: (6) is inconsistent.
% 177.68/28.15  | 
% 177.68/28.15  End of proof
% 177.68/28.15  
% 177.68/28.15  Sub-proof #462 shows that the following formulas are inconsistent:
% 177.68/28.15  ----------------------------------------------------------------
% 177.68/28.15    (1)   ~ (all_52_23 = all_14_2)
% 177.68/28.15    (2)   ~ (all_52_5 = all_52_13)
% 177.68/28.15    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.15    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.15    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.68/28.15    (6)   ~ (all_52_27 = all_10_2)
% 177.68/28.15    (7)   ~ (all_52_17 = all_52_23)
% 177.68/28.15    (8)  op(e2, all_10_2) = all_10_1
% 177.68/28.15    (9)   ~ (all_52_13 = all_52_29)
% 177.68/28.15    (10)  all_56_3 = all_52_7
% 177.68/28.15    (11)  op(e3, e2) = all_52_3
% 177.68/28.15    (12)   ~ (all_52_9 = all_52_25)
% 177.68/28.15    (13)  op(e3, all_52_25) = all_52_24
% 177.68/28.15    (14)   ~ (all_52_19 = all_52_23)
% 177.68/28.15    (15)  all_56_11 = all_52_23
% 177.68/28.15    (16)  op(e1, e2) = all_52_19
% 177.68/28.15    (17)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.15    (18)  op(e3, all_52_9) = all_52_8
% 177.68/28.15    (19)  all_50_1 = all_4_1
% 177.68/28.15    (20)   ~ (all_52_3 = all_10_2)
% 177.68/28.15    (21)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.68/28.15    (22)  all_58_5 = all_52_13
% 177.68/28.15    (23)   ~ (all_6_2 = e0)
% 177.68/28.15    (24)   ~ (all_52_25 = all_52_29)
% 177.68/28.15    (25)  all_56_15 = all_6_2
% 177.68/28.15    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.15    (27)  op(e2, e0) = all_52_15
% 177.68/28.15    (28)  all_58_3 = all_10_2
% 177.68/28.15    (29)  all_56_9 = all_52_19
% 177.68/28.15    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.15    (31)  all_58_15 = all_6_2
% 177.68/28.15    (32)   ~ (all_52_9 = all_4_2)
% 177.68/28.15    (33)   ~ (all_52_5 = all_52_7)
% 177.68/28.15    (34)  all_58_10 = all_52_15
% 177.68/28.15    (35)   ~ (all_52_5 = all_4_2)
% 177.68/28.15    (36)  all_58_7 = all_52_19
% 177.68/28.15    (37)  all_56_4 = all_52_9
% 177.68/28.15    (38)   ~ (all_52_15 = all_6_2)
% 177.68/28.15    (39)   ~ (all_52_17 = all_52_25)
% 177.68/28.15    (40)  all_58_4 = all_52_5
% 177.68/28.15    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.15    (42)   ~ (e3 = e1)
% 177.68/28.15    (43)   ~ (all_52_27 = all_52_29)
% 177.68/28.15    (44)   ~ (all_52_17 = all_14_2)
% 177.68/28.15    (45)  op(e3, all_4_2) = all_4_1
% 177.68/28.15    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.68/28.15    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.15    (48)   ~ (all_52_7 = all_4_2)
% 177.68/28.15    (49)  all_58_1 = all_52_3
% 177.68/28.15    (50)   ~ (all_52_13 = all_52_15)
% 177.68/28.15    (51)  all_58_0 = all_4_2
% 177.68/28.15    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.68/28.15    (53)  op(e1, all_52_13) = all_52_12
% 177.68/28.15    (54)  op(e1, all_52_29) = all_52_28
% 177.68/28.15    (55)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.68/28.15          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.68/28.15    (56)  all_50_2 = all_4_2
% 177.68/28.15    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.15    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.15    (59)   ~ (all_4_1 = e2)
% 177.68/28.15    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.68/28.16    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.68/28.16    (62)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.68/28.16    (63)   ~ (all_14_1 = e3)
% 177.68/28.16    (64)  all_58_14 = all_52_29
% 177.68/28.16    (65)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.16    (66)  all_26_2 = all_4_2
% 177.68/28.16    (67)   ~ (all_52_3 = all_52_5)
% 177.68/28.16    (68)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.16    (69)  op(e2, e1) = all_52_13
% 177.68/28.16    (70)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.16    (71)  all_58_8 = all_14_2
% 177.68/28.16    (72)  all_56_1 = all_52_3
% 177.68/28.16    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.68/28.16    (74)   ~ (all_52_3 = all_52_27)
% 177.68/28.16    (75)   ~ (all_52_3 = all_4_2)
% 177.68/28.16    (76)  op(e0, e3) = all_52_25
% 177.68/28.16    (77)  all_52_0 = all_4_1
% 177.68/28.16    (78)   ~ (all_52_9 = all_10_2)
% 177.68/28.16    (79)  op(all_4_1, all_4_2) = e2
% 177.68/28.16    (80)  op(e3, all_52_17) = all_52_16
% 177.68/28.16    (81)  all_52_10 = all_10_1
% 177.68/28.16    (82)   ~ (all_52_13 = all_14_2)
% 177.68/28.16    (83)   ~ (e3 = e0)
% 177.68/28.16    (84)   ~ (all_52_9 = all_52_13)
% 177.68/28.16    (85)  op(e0, all_52_23) = all_52_22
% 177.68/28.16    (86)   ~ (all_52_15 = all_52_23)
% 177.68/28.16    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.16    (88)  op(all_10_1, all_10_2) = all_10_0
% 177.68/28.16    (89)   ~ (all_52_5 = all_52_29)
% 177.68/28.16    (90)  all_56_2 = all_52_5
% 177.68/28.16    (91)  op(e1, e0) = all_52_23
% 177.68/28.16    (92)  all_58_13 = all_52_27
% 177.68/28.16    (93)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.16    (94)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.16    (95)  all_56_5 = all_10_2
% 177.68/28.16    (96)   ~ (all_52_9 = all_52_17)
% 177.68/28.16    (97)  all_58_6 = all_52_17
% 177.68/28.16    (98)   ~ (all_52_3 = all_52_7)
% 177.68/28.16    (99)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.68/28.16    (100)  op(e2, all_52_19) = all_52_18
% 177.68/28.16    (101)   ~ (e1 = e0)
% 177.68/28.16    (102)  all_56_0 = all_4_2
% 177.68/28.16    (103)  all_58_11 = all_52_23
% 177.68/28.16    (104)   ~ (all_52_3 = all_52_19)
% 177.68/28.16    (105)   ~ (all_52_7 = all_52_15)
% 177.68/28.16    (106)  all_26_1 = all_4_1
% 177.68/28.16    (107)  op(e0, all_52_15) = all_52_14
% 177.68/28.16    (108)   ~ (all_52_19 = all_10_2)
% 177.68/28.16    (109)   ~ (all_52_23 = all_6_2)
% 177.68/28.16    (110)   ~ (all_52_29 = all_6_2)
% 177.68/28.16    (111)  all_58_2 = all_52_9
% 177.68/28.16    (112)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.68/28.16    (113)  op(e3, e1) = all_52_5
% 177.68/28.16    (114)  all_56_10 = all_14_2
% 177.68/28.16    (115)   ~ (all_52_25 = all_6_2)
% 177.68/28.16    (116)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.68/28.16    (117)  op(e1, e3) = all_52_17
% 177.68/28.16    (118)   ~ (all_52_25 = all_4_2)
% 177.68/28.16    (119)  op(e3, e0) = all_52_7
% 177.68/28.16    (120)  op(e3, e3) = all_4_2
% 177.68/28.16    (121)  all_56_8 = all_52_17
% 177.68/28.16    (122)   ~ (all_52_17 = all_4_2)
% 177.68/28.16    (123)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.16             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.16    (124)   ~ (all_52_25 = all_52_27)
% 177.68/28.16    (125)   ~ (all_52_27 = all_6_2)
% 177.68/28.16    (126)   ~ (all_52_7 = all_6_2)
% 177.68/28.16    (127)   ~ (all_10_0 = e3)
% 177.68/28.16    (128)   ~ (all_52_7 = all_52_23)
% 177.68/28.16    (129)   ~ (all_52_13 = all_10_2)
% 177.68/28.16    (130)  op(e2, all_52_27) = all_52_26
% 177.68/28.16    (131)   ~ (all_52_17 = all_52_19)
% 177.68/28.16    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.16    (133)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.16    (134)  op(e1, all_14_2) = all_14_1
% 177.68/28.16    (135)  all_58_9 = all_52_7
% 177.68/28.16    (136)  all_58_12 = all_52_25
% 177.68/28.16    (137)   ~ (all_10_0 = e1)
% 177.68/28.16    (138)  all_56_6 = all_52_13
% 177.68/28.16    (139)   ~ (all_52_9 = all_52_15)
% 177.68/28.16    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.16    (141)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.16    (142)   ~ (all_52_19 = all_14_2)
% 177.68/28.16    (143)  op(e2, e3) = all_52_9
% 177.68/28.16    (144)  all_56_13 = all_52_27
% 177.68/28.16  
% 177.68/28.16  Begin of proof
% 177.68/28.16  | 
% 177.68/28.16  | BETA: splitting (55) gives:
% 177.68/28.16  | 
% 177.68/28.16  | Case 1:
% 177.68/28.16  | | 
% 177.68/28.16  | |   (145)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.68/28.16  | | 
% 177.68/28.16  | | REF_CLOSE: (45), (59), (77), (79), (123), (145) are inconsistent by
% 177.68/28.16  | |            sub-proof #494.
% 177.68/28.16  | | 
% 177.68/28.16  | Case 2:
% 177.68/28.16  | | 
% 177.68/28.16  | |   (146)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.68/28.16  | | 
% 177.68/28.16  | | ALPHA: (146) implies:
% 177.68/28.16  | |   (147)  all_52_14 = e0
% 177.68/28.16  | |   (148)  all_52_12 = e1
% 177.68/28.16  | |   (149)  all_52_10 = e2
% 177.68/28.16  | |   (150)  all_52_8 = e3
% 177.68/28.16  | | 
% 177.68/28.16  | | COMBINE_EQS: (81), (149) imply:
% 177.68/28.16  | |   (151)  all_10_1 = e2
% 177.68/28.16  | | 
% 177.68/28.16  | | REDUCE: (88), (151) imply:
% 177.68/28.16  | |   (152)  op(e2, all_10_2) = all_10_0
% 177.68/28.16  | | 
% 177.68/28.16  | | REDUCE: (18), (150) imply:
% 177.68/28.16  | |   (153)  op(e3, all_52_9) = e3
% 177.68/28.16  | | 
% 177.68/28.16  | | REDUCE: (8), (151) imply:
% 177.68/28.16  | |   (154)  op(e2, all_10_2) = e2
% 177.68/28.16  | | 
% 177.68/28.16  | | REDUCE: (53), (148) imply:
% 177.68/28.16  | |   (155)  op(e1, all_52_13) = e1
% 177.68/28.16  | | 
% 177.68/28.16  | | REDUCE: (107), (147) imply:
% 177.68/28.16  | |   (156)  op(e0, all_52_15) = e0
% 177.68/28.16  | | 
% 177.68/28.16  | | GROUND_INST: instantiating (123) with e2, all_10_0, all_10_2, e2,
% 177.68/28.16  | |              simplifying with (152), (154) gives:
% 177.68/28.16  | |   (157)  all_10_0 = e2
% 177.68/28.16  | | 
% 177.68/28.16  | | REDUCE: (127), (157) imply:
% 177.68/28.16  | |   (158)   ~ (e3 = e2)
% 177.68/28.16  | | 
% 177.68/28.16  | | SIMP: (158) implies:
% 177.68/28.16  | |   (159)   ~ (e3 = e2)
% 177.68/28.16  | | 
% 177.68/28.16  | | REDUCE: (137), (157) imply:
% 177.68/28.16  | |   (160)   ~ (e2 = e1)
% 177.68/28.16  | | 
% 177.68/28.16  | | BETA: splitting (46) gives:
% 177.68/28.16  | | 
% 177.68/28.16  | | Case 1:
% 177.68/28.16  | | | 
% 177.68/28.16  | | |   (161)  all_56_15 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | COMBINE_EQS: (25), (161) imply:
% 177.68/28.16  | | |   (162)  all_6_2 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | SIMP: (162) implies:
% 177.68/28.16  | | |   (163)  all_6_2 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REF_CLOSE: (10), (11), (20), (22), (26), (28), (30), (32), (34), (37),
% 177.68/28.16  | | |            (38), (45), (47), (48), (51), (59), (62), (66), (68), (79),
% 177.68/28.16  | | |            (84), (93), (96), (99), (102), (106), (111), (117), (119),
% 177.68/28.16  | | |            (120), (122), (123), (126), (133), (138), (143), (153), (154),
% 177.68/28.16  | | |            (155), (163) are inconsistent by sub-proof #467.
% 177.68/28.16  | | | 
% 177.68/28.16  | | Case 2:
% 177.68/28.16  | | | 
% 177.68/28.16  | | |   (164)   ~ (all_56_15 = e3)
% 177.68/28.16  | | |   (165)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (25), (164) imply:
% 177.68/28.16  | | |   (166)   ~ (all_6_2 = e3)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | BETA: splitting (65) gives:
% 177.68/28.16  | | | 
% 177.68/28.16  | | | Case 1:
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | |   (167)  all_56_13 = e3
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (11), (12), (13), (14),
% 177.68/28.16  | | | |            (16), (20), (21), (22), (26), (27), (28), (30), (31), (32),
% 177.68/28.16  | | | |            (33), (34), (35), (36), (37), (39), (40), (41), (42), (43),
% 177.68/28.16  | | | |            (44), (45), (47), (49), (50), (51), (52), (57), (59), (64),
% 177.68/28.16  | | | |            (67), (68), (71), (72), (74), (75), (76), (78), (79), (80),
% 177.68/28.16  | | | |            (82), (84), (86), (91), (92), (94), (95), (97), (98), (99),
% 177.68/28.16  | | | |            (101), (102), (103), (108), (111), (116), (117), (118),
% 177.68/28.16  | | | |            (119), (120), (121), (122), (123), (124), (125), (129),
% 177.68/28.16  | | | |            (130), (131), (132), (135), (136), (139), (140), (143),
% 177.68/28.16  | | | |            (144), (153), (154), (155), (156), (160), (167) are
% 177.68/28.16  | | | |            inconsistent by sub-proof #464.
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | Case 2:
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | |   (168)   ~ (all_56_13 = e3)
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | | REDUCE: (144), (168) imply:
% 177.68/28.16  | | | |   (169)   ~ (all_52_27 = e3)
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | | BETA: splitting (70) gives:
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | | Case 1:
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | |   (170)  all_58_12 = e3
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | REF_CLOSE: (1), (5), (6), (7), (9), (10), (11), (12), (14), (15),
% 177.68/28.16  | | | | |            (16), (20), (22), (23), (24), (25), (26), (28), (29), (30),
% 177.68/28.16  | | | | |            (31), (32), (33), (34), (35), (36), (37), (39), (40), (41),
% 177.68/28.16  | | | | |            (43), (44), (47), (48), (49), (51), (52), (58), (60), (61),
% 177.68/28.16  | | | | |            (62), (63), (64), (67), (69), (71), (73), (76), (80), (82),
% 177.68/28.16  | | | | |            (83), (84), (85), (87), (92), (96), (97), (98), (99),
% 177.68/28.16  | | | | |            (100), (102), (103), (104), (105), (108), (109), (111),
% 177.68/28.16  | | | | |            (112), (113), (114), (115), (117), (118), (119), (123),
% 177.68/28.16  | | | | |            (124), (125), (126), (128), (131), (132), (133), (134),
% 177.68/28.16  | | | | |            (135), (136), (138), (139), (140), (142), (143), (153),
% 177.68/28.16  | | | | |            (154), (155), (156), (159), (160), (165), (170) are
% 177.68/28.16  | | | | |            inconsistent by sub-proof #734.
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | Case 2:
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | |   (171)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | REF_CLOSE: (3), (7), (11), (17), (19), (20), (24), (26), (28), (30),
% 177.68/28.16  | | | | |            (31), (32), (34), (35), (36), (39), (42), (43), (45), (47),
% 177.68/28.16  | | | | |            (48), (49), (51), (54), (56), (59), (61), (64), (68), (76),
% 177.68/28.16  | | | | |            (79), (80), (89), (90), (92), (94), (97), (98), (101),
% 177.68/28.16  | | | | |            (102), (103), (110), (111), (113), (117), (118), (120),
% 177.68/28.16  | | | | |            (121), (122), (123), (131), (132), (135), (136), (141),
% 177.68/28.16  | | | | |            (143), (153), (154), (156), (160), (166), (169), (171) are
% 177.68/28.16  | | | | |            inconsistent by sub-proof #463.
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | End of split
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | End of split
% 177.68/28.16  | | | 
% 177.68/28.16  | | End of split
% 177.68/28.16  | | 
% 177.68/28.16  | End of split
% 177.68/28.16  | 
% 177.68/28.16  End of proof
% 177.68/28.16  
% 177.68/28.16  Sub-proof #463 shows that the following formulas are inconsistent:
% 177.68/28.16  ----------------------------------------------------------------
% 177.68/28.16    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.16    (2)   ~ (all_52_17 = all_52_23)
% 177.68/28.16    (3)  op(e3, e2) = all_52_3
% 177.68/28.16    (4)   ~ (all_52_27 = e3)
% 177.68/28.16    (5)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.16    (6)   ~ (all_6_2 = e3)
% 177.68/28.16    (7)  all_50_1 = all_4_1
% 177.68/28.16    (8)   ~ (all_52_3 = all_10_2)
% 177.68/28.16    (9)   ~ (all_52_25 = all_52_29)
% 177.68/28.16    (10)  op(e0, all_52_15) = e0
% 177.68/28.16    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.16    (12)  all_58_3 = all_10_2
% 177.68/28.16    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.16    (14)  all_58_15 = all_6_2
% 177.68/28.16    (15)   ~ (all_52_9 = all_4_2)
% 177.68/28.16    (16)  all_58_10 = all_52_15
% 177.68/28.16    (17)   ~ (all_52_5 = all_4_2)
% 177.68/28.16    (18)  all_58_7 = all_52_19
% 177.68/28.16    (19)   ~ (all_52_17 = all_52_25)
% 177.68/28.16    (20)   ~ (e3 = e1)
% 177.68/28.16    (21)   ~ (all_52_27 = all_52_29)
% 177.68/28.16    (22)  op(e3, all_4_2) = all_4_1
% 177.68/28.16    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.16    (24)   ~ (all_52_7 = all_4_2)
% 177.68/28.16    (25)  all_58_1 = all_52_3
% 177.68/28.16    (26)  all_58_0 = all_4_2
% 177.68/28.16    (27)  op(e1, all_52_29) = all_52_28
% 177.68/28.16    (28)  all_50_2 = all_4_2
% 177.68/28.16    (29)   ~ (all_4_1 = e2)
% 177.68/28.16    (30)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.68/28.16    (31)  all_58_14 = all_52_29
% 177.68/28.16    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.16    (33)  op(e0, e3) = all_52_25
% 177.68/28.16    (34)  op(all_4_1, all_4_2) = e2
% 177.68/28.16    (35)  op(e3, all_52_17) = all_52_16
% 177.68/28.16    (36)  op(e3, all_52_9) = e3
% 177.68/28.16    (37)   ~ (all_52_5 = all_52_29)
% 177.68/28.16    (38)  all_56_2 = all_52_5
% 177.68/28.16    (39)  all_58_13 = all_52_27
% 177.68/28.16    (40)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.16    (41)  all_58_6 = all_52_17
% 177.68/28.16    (42)   ~ (all_52_3 = all_52_7)
% 177.68/28.16    (43)   ~ (e1 = e0)
% 177.68/28.16    (44)  all_56_0 = all_4_2
% 177.68/28.16    (45)  all_58_11 = all_52_23
% 177.68/28.16    (46)   ~ (all_52_29 = all_6_2)
% 177.68/28.16    (47)  all_58_2 = all_52_9
% 177.68/28.16    (48)  op(e3, e1) = all_52_5
% 177.68/28.16    (49)   ~ (e2 = e1)
% 177.68/28.16    (50)  op(e1, e3) = all_52_17
% 177.68/28.16    (51)   ~ (all_52_25 = all_4_2)
% 177.68/28.16    (52)  op(e2, all_10_2) = e2
% 177.68/28.16    (53)  op(e3, e3) = all_4_2
% 177.68/28.16    (54)  all_56_8 = all_52_17
% 177.68/28.16    (55)   ~ (all_52_17 = all_4_2)
% 177.68/28.16    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.16    (57)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.16    (58)   ~ (all_52_17 = all_52_19)
% 177.68/28.16    (59)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.16    (60)  all_58_9 = all_52_7
% 177.68/28.16    (61)  all_58_12 = all_52_25
% 177.68/28.16    (62)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.16    (63)  op(e2, e3) = all_52_9
% 177.68/28.16  
% 177.68/28.16  Begin of proof
% 177.68/28.16  | 
% 177.68/28.16  | BETA: splitting (57) gives:
% 177.68/28.16  | 
% 177.68/28.16  | Case 1:
% 177.68/28.16  | | 
% 177.68/28.16  | |   (64)  all_58_13 = e3
% 177.68/28.16  | | 
% 177.68/28.16  | | REF_CLOSE: (4), (39), (64) are inconsistent by sub-proof #1026.
% 177.68/28.16  | | 
% 177.68/28.16  | Case 2:
% 177.68/28.16  | | 
% 177.68/28.16  | |   (65)  all_58_14 = e3 | all_58_15 = e3
% 177.68/28.16  | | 
% 177.68/28.16  | | BETA: splitting (65) gives:
% 177.68/28.16  | | 
% 177.68/28.16  | | Case 1:
% 177.68/28.16  | | | 
% 177.68/28.16  | | |   (66)  all_58_14 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | COMBINE_EQS: (31), (66) imply:
% 177.68/28.16  | | |   (67)  all_52_29 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | SIMP: (67) implies:
% 177.68/28.16  | | |   (68)  all_52_29 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (37), (68) imply:
% 177.68/28.16  | | |   (69)   ~ (all_52_5 = e3)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (9), (68) imply:
% 177.68/28.16  | | |   (70)   ~ (all_52_25 = e3)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (46), (68) imply:
% 177.68/28.16  | | |   (71)   ~ (all_6_2 = e3)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (27), (68) imply:
% 177.68/28.16  | | |   (72)  op(e1, e3) = all_52_28
% 177.68/28.16  | | | 
% 177.68/28.16  | | | GROUND_INST: instantiating (56) with all_52_17, all_52_28, e3, e1,
% 177.68/28.16  | | |              simplifying with (50), (72) gives:
% 177.68/28.16  | | |   (73)  all_52_17 = all_52_28
% 177.68/28.16  | | | 
% 177.68/28.16  | | | COMBINE_EQS: (54), (73) imply:
% 177.68/28.16  | | |   (74)  all_56_8 = all_52_28
% 177.68/28.16  | | | 
% 177.68/28.16  | | | COMBINE_EQS: (41), (73) imply:
% 177.68/28.16  | | |   (75)  all_58_6 = all_52_28
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (58), (73) imply:
% 177.68/28.16  | | |   (76)   ~ (all_52_19 = all_52_28)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | SIMP: (76) implies:
% 177.68/28.16  | | |   (77)   ~ (all_52_19 = all_52_28)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (2), (73) imply:
% 177.68/28.16  | | |   (78)   ~ (all_52_23 = all_52_28)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | SIMP: (78) implies:
% 177.68/28.16  | | |   (79)   ~ (all_52_23 = all_52_28)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (19), (73) imply:
% 177.68/28.16  | | |   (80)   ~ (all_52_25 = all_52_28)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | SIMP: (80) implies:
% 177.68/28.16  | | |   (81)   ~ (all_52_25 = all_52_28)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (55), (73) imply:
% 177.68/28.16  | | |   (82)   ~ (all_52_28 = all_4_2)
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (35), (73) imply:
% 177.68/28.16  | | |   (83)  op(e3, all_52_28) = all_52_16
% 177.68/28.16  | | | 
% 177.68/28.16  | | | BETA: splitting (62) gives:
% 177.68/28.16  | | | 
% 177.68/28.16  | | | Case 1:
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | |   (84)  all_56_2 = e3
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | | REF_CLOSE: (38), (69), (84) are inconsistent by sub-proof #931.
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | Case 2:
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | |   (85)   ~ (all_56_2 = e3)
% 177.68/28.16  | | | |   (86)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | | BETA: splitting (1) gives:
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | | Case 1:
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | |   (87)  all_56_8 = e3
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | COMBINE_EQS: (74), (87) imply:
% 177.68/28.16  | | | | |   (88)  all_52_28 = e3
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | SIMP: (88) implies:
% 177.68/28.16  | | | | |   (89)  all_52_28 = e3
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | COMBINE_EQS: (75), (89) imply:
% 177.68/28.16  | | | | |   (90)  all_58_6 = e3
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | REDUCE: (79), (89) imply:
% 177.68/28.16  | | | | |   (91)   ~ (all_52_23 = e3)
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | REDUCE: (82), (89) imply:
% 177.68/28.16  | | | | |   (92)   ~ (all_4_2 = e3)
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | SIMP: (92) implies:
% 177.68/28.16  | | | | |   (93)   ~ (all_4_2 = e3)
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | REDUCE: (83), (89) imply:
% 177.68/28.16  | | | | |   (94)  op(e3, e3) = all_52_16
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | GROUND_INST: instantiating (56) with all_4_2, all_52_16, e3, e3,
% 177.68/28.16  | | | | |              simplifying with (53), (94) gives:
% 177.68/28.16  | | | | |   (95)  all_52_16 = all_4_2
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | BETA: splitting (59) gives:
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | Case 1:
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | |   (96)  all_58_9 = e3
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | | REF_CLOSE: (3), (4), (8), (12), (15), (18), (23), (24), (25), (26),
% 177.68/28.16  | | | | | |            (30), (32), (36), (39), (42), (47), (52), (53), (56),
% 177.68/28.16  | | | | | |            (60), (61), (63), (70), (75), (77), (96) are inconsistent
% 177.68/28.16  | | | | | |            by sub-proof #732.
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | Case 2:
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | |   (97)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | | BETA: splitting (97) gives:
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | | Case 1:
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | |   (98)  all_58_10 = e3
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | COMBINE_EQS: (16), (98) imply:
% 177.68/28.16  | | | | | | |   (99)  all_52_15 = e3
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | SIMP: (99) implies:
% 177.68/28.16  | | | | | | |   (100)  all_52_15 = e3
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | REDUCE: (10), (100) imply:
% 177.68/28.16  | | | | | | |   (101)  op(e0, e3) = e0
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | GROUND_INST: instantiating (56) with all_52_25, e0, e3, e0,
% 177.68/28.16  | | | | | | |              simplifying with (33), (101) gives:
% 177.68/28.16  | | | | | | |   (102)  all_52_25 = e0
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | COMBINE_EQS: (61), (102) imply:
% 177.68/28.16  | | | | | | |   (103)  all_58_12 = e0
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | REDUCE: (51), (102) imply:
% 177.68/28.16  | | | | | | |   (104)   ~ (all_4_2 = e0)
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | SIMP: (104) implies:
% 177.68/28.16  | | | | | | |   (105)   ~ (all_4_2 = e0)
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | BETA: splitting (13) gives:
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | Case 1:
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | |   (106)  all_56_0 = e3
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | | REF_CLOSE: (44), (93), (106) are inconsistent by sub-proof
% 177.68/28.16  | | | | | | | |            #1024.
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | Case 2:
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | |   (107)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | | BETA: splitting (11) gives:
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | | Case 1:
% 177.68/28.16  | | | | | | | | | 
% 177.68/28.16  | | | | | | | | |   (108)  all_58_0 = e2
% 177.68/28.16  | | | | | | | | | 
% 177.68/28.16  | | | | | | | | | COMBINE_EQS: (26), (108) imply:
% 177.68/28.16  | | | | | | | | |   (109)  all_4_2 = e2
% 177.68/28.16  | | | | | | | | | 
% 177.68/28.16  | | | | | | | | | REF_CLOSE: (20), (36), (40), (43), (47), (48), (49), (56),
% 177.68/28.16  | | | | | | | | |            (69), (90), (103), (108) are inconsistent by
% 177.68/28.16  | | | | | | | | |            sub-proof #724.
% 177.68/28.16  | | | | | | | | | 
% 177.68/28.16  | | | | | | | | Case 2:
% 177.68/28.16  | | | | | | | | | 
% 177.68/28.16  | | | | | | | | |   (110)   ~ (all_58_0 = e2)
% 177.68/28.16  | | | | | | | | | 
% 177.68/28.16  | | | | | | | | | REF_CLOSE: (5), (7), (17), (22), (26), (28), (29), (38), (40),
% 177.68/28.16  | | | | | | | | |            (44), (48), (56), (86), (105), (107), (110) are
% 177.68/28.16  | | | | | | | | |            inconsistent by sub-proof #477.
% 177.68/28.16  | | | | | | | | | 
% 177.68/28.16  | | | | | | | | End of split
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | End of split
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | Case 2:
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | |   (111)  all_58_11 = e3 | all_58_15 = e3
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | REF_CLOSE: (6), (14), (45), (91), (111) are inconsistent by
% 177.68/28.16  | | | | | | |            sub-proof #1016.
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | End of split
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | End of split
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | Case 2:
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | |   (112)   ~ (all_56_8 = e3)
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | REDUCE: (74), (112) imply:
% 177.68/28.16  | | | | |   (113)   ~ (all_52_28 = e3)
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | BETA: splitting (32) gives:
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | | Case 1:
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | |   (114)  all_58_0 = e3
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | | REF_CLOSE: (22), (26), (29), (34), (53), (56), (114) are
% 177.68/28.16  | | | | | |            inconsistent by sub-proof #489.
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | Case 2:
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | |   (115)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | | BETA: splitting (115) gives:
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | | Case 1:
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | |   (116)  all_58_2 = e3
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | COMBINE_EQS: (47), (116) imply:
% 177.68/28.16  | | | | | | |   (117)  all_52_9 = e3
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | REF_CLOSE: (15), (36), (53), (56), (117) are inconsistent by
% 177.68/28.16  | | | | | | |            sub-proof #967.
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | Case 2:
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | |   (118)  all_58_6 = e3 | all_58_12 = e3
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | BETA: splitting (118) gives:
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | | Case 1:
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | |   (119)  all_58_6 = e3
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | | REF_CLOSE: (75), (113), (119) are inconsistent by sub-proof
% 177.68/28.16  | | | | | | | |            #790.
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | Case 2:
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | |   (120)  all_58_12 = e3
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | | REF_CLOSE: (61), (70), (120) are inconsistent by sub-proof
% 177.68/28.16  | | | | | | | |            #1003.
% 177.68/28.16  | | | | | | | | 
% 177.68/28.16  | | | | | | | End of split
% 177.68/28.16  | | | | | | | 
% 177.68/28.16  | | | | | | End of split
% 177.68/28.16  | | | | | | 
% 177.68/28.16  | | | | | End of split
% 177.68/28.16  | | | | | 
% 177.68/28.16  | | | | End of split
% 177.68/28.16  | | | | 
% 177.68/28.16  | | | End of split
% 177.68/28.16  | | | 
% 177.68/28.16  | | Case 2:
% 177.68/28.16  | | | 
% 177.68/28.16  | | |   (121)  all_58_15 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | COMBINE_EQS: (14), (121) imply:
% 177.68/28.16  | | |   (122)  all_6_2 = e3
% 177.68/28.16  | | | 
% 177.68/28.16  | | | REDUCE: (6), (122) imply:
% 177.68/28.16  | | |   (123)  $false
% 177.68/28.16  | | | 
% 177.68/28.16  | | | CLOSE: (123) is inconsistent.
% 177.68/28.16  | | | 
% 177.68/28.16  | | End of split
% 177.68/28.16  | | 
% 177.68/28.16  | End of split
% 177.68/28.16  | 
% 177.68/28.16  End of proof
% 177.68/28.16  
% 177.68/28.16  Sub-proof #464 shows that the following formulas are inconsistent:
% 177.68/28.16  ----------------------------------------------------------------
% 177.68/28.16    (1)   ~ (all_52_5 = all_52_13)
% 177.68/28.16    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.16    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.16    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.68/28.16    (5)   ~ (all_52_27 = all_10_2)
% 177.68/28.16    (6)   ~ (all_52_17 = all_52_23)
% 177.68/28.16    (7)   ~ (all_52_13 = all_52_29)
% 177.68/28.16    (8)  op(e3, e2) = all_52_3
% 177.68/28.16    (9)   ~ (all_52_9 = all_52_25)
% 177.68/28.16    (10)  op(e3, all_52_25) = all_52_24
% 177.68/28.16    (11)   ~ (all_52_19 = all_52_23)
% 177.68/28.16    (12)  op(e1, e2) = all_52_19
% 177.68/28.16    (13)   ~ (all_52_3 = all_10_2)
% 177.68/28.16    (14)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.68/28.16    (15)  all_58_5 = all_52_13
% 177.68/28.16    (16)  op(e1, all_52_13) = e1
% 177.68/28.16    (17)  op(e0, all_52_15) = e0
% 177.68/28.16    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.16    (19)  op(e2, e0) = all_52_15
% 177.68/28.16    (20)  all_58_3 = all_10_2
% 177.68/28.16    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.16    (22)  all_58_15 = all_6_2
% 177.68/28.16    (23)   ~ (all_52_9 = all_4_2)
% 177.68/28.16    (24)   ~ (all_52_5 = all_52_7)
% 177.68/28.16    (25)  all_58_10 = all_52_15
% 177.68/28.16    (26)   ~ (all_52_5 = all_4_2)
% 177.68/28.16    (27)  all_58_7 = all_52_19
% 177.68/28.16    (28)  all_56_4 = all_52_9
% 177.68/28.16    (29)   ~ (all_52_17 = all_52_25)
% 177.68/28.16    (30)  all_58_4 = all_52_5
% 177.68/28.16    (31)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.16    (32)   ~ (e3 = e1)
% 177.68/28.16    (33)   ~ (all_52_27 = all_52_29)
% 177.68/28.16    (34)   ~ (all_52_17 = all_14_2)
% 177.68/28.16    (35)  op(e3, all_4_2) = all_4_1
% 177.68/28.16    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.16    (37)  all_58_1 = all_52_3
% 177.68/28.16    (38)   ~ (all_52_13 = all_52_15)
% 177.68/28.16    (39)  all_58_0 = all_4_2
% 177.68/28.16    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.68/28.16    (41)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.16    (42)   ~ (all_4_1 = e2)
% 177.68/28.16    (43)  all_58_14 = all_52_29
% 177.68/28.16    (44)   ~ (all_52_3 = all_52_5)
% 177.68/28.16    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.16    (46)  all_58_8 = all_14_2
% 177.68/28.16    (47)  all_56_1 = all_52_3
% 177.68/28.16    (48)   ~ (all_52_3 = all_52_27)
% 177.68/28.16    (49)   ~ (all_52_3 = all_4_2)
% 177.68/28.16    (50)  op(e0, e3) = all_52_25
% 177.68/28.16    (51)   ~ (all_52_9 = all_10_2)
% 177.68/28.16    (52)  op(all_4_1, all_4_2) = e2
% 177.68/28.16    (53)  op(e3, all_52_17) = all_52_16
% 177.68/28.16    (54)   ~ (all_52_13 = all_14_2)
% 177.68/28.16    (55)  op(e3, all_52_9) = e3
% 177.68/28.16    (56)   ~ (all_52_9 = all_52_13)
% 177.68/28.16    (57)   ~ (all_52_15 = all_52_23)
% 177.68/28.16    (58)  op(e1, e0) = all_52_23
% 177.68/28.16    (59)  all_58_13 = all_52_27
% 177.68/28.16    (60)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.16    (61)  all_56_5 = all_10_2
% 177.68/28.16    (62)  all_58_6 = all_52_17
% 177.68/28.16    (63)   ~ (all_52_3 = all_52_7)
% 177.68/28.16    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.68/28.16    (65)   ~ (e1 = e0)
% 177.68/28.16    (66)  all_56_0 = all_4_2
% 177.68/28.16    (67)  all_58_11 = all_52_23
% 177.68/28.16    (68)   ~ (all_52_19 = all_10_2)
% 177.68/28.16    (69)  all_58_2 = all_52_9
% 177.68/28.16    (70)   ~ (e2 = e1)
% 177.68/28.16    (71)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.68/28.16    (72)  op(e1, e3) = all_52_17
% 177.68/28.16    (73)   ~ (all_52_25 = all_4_2)
% 177.68/28.16    (74)  op(e3, e0) = all_52_7
% 177.68/28.16    (75)  op(e2, all_10_2) = e2
% 177.68/28.16    (76)  op(e3, e3) = all_4_2
% 177.68/28.16    (77)  all_56_8 = all_52_17
% 177.68/28.16    (78)   ~ (all_52_17 = all_4_2)
% 177.68/28.16    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.16    (80)   ~ (all_52_25 = all_52_27)
% 177.68/28.16    (81)  all_56_13 = e3
% 177.68/28.16    (82)   ~ (all_52_27 = all_6_2)
% 177.68/28.16    (83)   ~ (all_52_13 = all_10_2)
% 177.68/28.16    (84)  op(e2, all_52_27) = all_52_26
% 177.68/28.16    (85)   ~ (all_52_17 = all_52_19)
% 177.68/28.16    (86)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.16    (87)  all_58_9 = all_52_7
% 177.68/28.16    (88)  all_58_12 = all_52_25
% 177.68/28.16    (89)   ~ (all_52_9 = all_52_15)
% 177.68/28.17    (90)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.17    (91)  op(e2, e3) = all_52_9
% 177.68/28.17    (92)  all_56_13 = all_52_27
% 177.68/28.17  
% 177.68/28.17  Begin of proof
% 177.68/28.17  | 
% 177.68/28.17  | COMBINE_EQS: (81), (92) imply:
% 177.68/28.17  |   (93)  all_52_27 = e3
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (93) implies:
% 177.68/28.17  |   (94)  all_52_27 = e3
% 177.68/28.17  | 
% 177.68/28.17  | COMBINE_EQS: (59), (94) imply:
% 177.68/28.17  |   (95)  all_58_13 = e3
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (48), (94) imply:
% 177.68/28.17  |   (96)   ~ (all_52_3 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (80), (94) imply:
% 177.68/28.17  |   (97)   ~ (all_52_25 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (33), (94) imply:
% 177.68/28.17  |   (98)   ~ (all_52_29 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (98) implies:
% 177.68/28.17  |   (99)   ~ (all_52_29 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (5), (94) imply:
% 177.68/28.17  |   (100)   ~ (all_10_2 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (100) implies:
% 177.68/28.17  |   (101)   ~ (all_10_2 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (82), (94) imply:
% 177.68/28.17  |   (102)   ~ (all_6_2 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (102) implies:
% 177.68/28.17  |   (103)   ~ (all_6_2 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (84), (94) imply:
% 177.68/28.17  |   (104)  op(e2, e3) = all_52_26
% 177.68/28.17  | 
% 177.68/28.17  | GROUND_INST: instantiating (79) with all_52_9, all_52_26, e3, e2, simplifying
% 177.68/28.17  |              with (91), (104) gives:
% 177.68/28.17  |   (105)  all_52_9 = all_52_26
% 177.68/28.17  | 
% 177.68/28.17  | COMBINE_EQS: (28), (105) imply:
% 177.68/28.17  |   (106)  all_56_4 = all_52_26
% 177.68/28.17  | 
% 177.68/28.17  | COMBINE_EQS: (69), (105) imply:
% 177.68/28.17  |   (107)  all_58_2 = all_52_26
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (56), (105) imply:
% 177.68/28.17  |   (108)   ~ (all_52_13 = all_52_26)
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (108) implies:
% 177.68/28.17  |   (109)   ~ (all_52_13 = all_52_26)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (89), (105) imply:
% 177.68/28.17  |   (110)   ~ (all_52_15 = all_52_26)
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (110) implies:
% 177.68/28.17  |   (111)   ~ (all_52_15 = all_52_26)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (9), (105) imply:
% 177.68/28.17  |   (112)   ~ (all_52_25 = all_52_26)
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (112) implies:
% 177.68/28.17  |   (113)   ~ (all_52_25 = all_52_26)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (51), (105) imply:
% 177.68/28.17  |   (114)   ~ (all_52_26 = all_10_2)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (23), (105) imply:
% 177.68/28.17  |   (115)   ~ (all_52_26 = all_4_2)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (55), (105) imply:
% 177.68/28.17  |   (116)  op(e3, all_52_26) = e3
% 177.68/28.17  | 
% 177.68/28.17  | BETA: splitting (71) gives:
% 177.68/28.17  | 
% 177.68/28.17  | Case 1:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (117)  all_56_5 = e3
% 177.68/28.17  | | 
% 177.68/28.17  | | REF_CLOSE: (61), (101), (117) are inconsistent by sub-proof #895.
% 177.68/28.17  | | 
% 177.68/28.17  | Case 2:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (118)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.68/28.17  | | 
% 177.68/28.17  | | BETA: splitting (41) gives:
% 177.68/28.17  | | 
% 177.68/28.17  | | Case 1:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (119)  all_56_1 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | COMBINE_EQS: (47), (119) imply:
% 177.68/28.17  | | |   (120)  all_52_3 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (96), (120) imply:
% 177.68/28.17  | | |   (121)  $false
% 177.68/28.17  | | | 
% 177.68/28.17  | | | CLOSE: (121) is inconsistent.
% 177.68/28.17  | | | 
% 177.68/28.17  | | Case 2:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (122)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.17  | | | 
% 177.68/28.17  | | | BETA: splitting (2) gives:
% 177.68/28.17  | | | 
% 177.68/28.17  | | | Case 1:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | |   (123)  all_56_8 = e3
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | COMBINE_EQS: (77), (123) imply:
% 177.68/28.17  | | | |   (124)  all_52_17 = e3
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | SIMP: (124) implies:
% 177.68/28.17  | | | |   (125)  all_52_17 = e3
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | COMBINE_EQS: (62), (125) imply:
% 177.68/28.17  | | | |   (126)  all_58_6 = e3
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REDUCE: (85), (125) imply:
% 177.68/28.17  | | | |   (127)   ~ (all_52_19 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | SIMP: (127) implies:
% 177.68/28.17  | | | |   (128)   ~ (all_52_19 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REDUCE: (6), (125) imply:
% 177.68/28.17  | | | |   (129)   ~ (all_52_23 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | SIMP: (129) implies:
% 177.68/28.17  | | | |   (130)   ~ (all_52_23 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REDUCE: (34), (125) imply:
% 177.68/28.17  | | | |   (131)   ~ (all_14_2 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | SIMP: (131) implies:
% 177.68/28.17  | | | |   (132)   ~ (all_14_2 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REDUCE: (78), (125) imply:
% 177.68/28.17  | | | |   (133)   ~ (all_4_2 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | SIMP: (133) implies:
% 177.68/28.17  | | | |   (134)   ~ (all_4_2 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REDUCE: (53), (125) imply:
% 177.68/28.17  | | | |   (135)  op(e3, e3) = all_52_16
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | GROUND_INST: instantiating (79) with all_4_2, all_52_16, e3, e3,
% 177.68/28.17  | | | |              simplifying with (76), (135) gives:
% 177.68/28.17  | | | |   (136)  all_52_16 = all_4_2
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | BETA: splitting (90) gives:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | Case 1:
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | |   (137)  all_58_4 = e3
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | COMBINE_EQS: (30), (137) imply:
% 177.68/28.17  | | | | |   (138)  all_52_5 = e3
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | SIMP: (138) implies:
% 177.68/28.17  | | | | |   (139)  all_52_5 = e3
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | REDUCE: (24), (139) imply:
% 177.68/28.17  | | | | |   (140)   ~ (all_52_7 = e3)
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | SIMP: (140) implies:
% 177.68/28.17  | | | | |   (141)   ~ (all_52_7 = e3)
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | REF_CLOSE: (3), (4), (8), (10), (11), (12), (13), (14), (15), (16),
% 177.68/28.17  | | | | |            (17), (18), (19), (20), (21), (22), (25), (27), (32), (35),
% 177.68/28.17  | | | | |            (37), (39), (40), (47), (49), (50), (52), (57), (58), (60),
% 177.68/28.17  | | | | |            (61), (63), (64), (65), (66), (67), (68), (70), (73), (74),
% 177.68/28.17  | | | | |            (75), (79), (86), (87), (88), (95), (96), (103), (106),
% 177.68/28.17  | | | | |            (107), (111), (113), (114), (115), (116), (118), (122),
% 177.68/28.17  | | | | |            (126), (128), (130), (134), (141) are inconsistent by
% 177.68/28.17  | | | | |            sub-proof #465.
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | Case 2:
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | |   (142)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | REF_CLOSE: (1), (7), (15), (16), (20), (25), (27), (29), (30), (31),
% 177.68/28.17  | | | | |            (32), (34), (36), (38), (39), (43), (45), (46), (54), (62),
% 177.68/28.17  | | | | |            (67), (72), (76), (79), (83), (88), (90), (99), (107),
% 177.68/28.17  | | | | |            (109), (115), (116), (128), (130), (132), (134), (142) are
% 177.68/28.17  | | | | |            inconsistent by sub-proof #492.
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | End of split
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | Case 2:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | |   (143)   ~ (all_56_8 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REDUCE: (77), (143) imply:
% 177.68/28.17  | | | |   (144)   ~ (all_52_17 = e3)
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REF_CLOSE: (35), (39), (42), (45), (52), (62), (76), (79), (88), (97),
% 177.68/28.17  | | | |            (107), (115), (116), (144) are inconsistent by sub-proof
% 177.68/28.17  | | | |            #488.
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | End of split
% 177.68/28.17  | | | 
% 177.68/28.17  | | End of split
% 177.68/28.17  | | 
% 177.68/28.17  | End of split
% 177.68/28.17  | 
% 177.68/28.17  End of proof
% 177.68/28.17  
% 177.68/28.17  Sub-proof #465 shows that the following formulas are inconsistent:
% 177.68/28.17  ----------------------------------------------------------------
% 177.68/28.17    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.17    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.68/28.17    (3)  op(e3, e2) = all_52_3
% 177.68/28.17    (4)  op(e3, all_52_25) = all_52_24
% 177.68/28.17    (5)   ~ (all_52_19 = all_52_23)
% 177.68/28.17    (6)  op(e1, e2) = all_52_19
% 177.68/28.17    (7)   ~ (all_6_2 = e3)
% 177.68/28.17    (8)   ~ (all_52_3 = all_10_2)
% 177.68/28.17    (9)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.68/28.17    (10)  all_58_5 = all_52_13
% 177.68/28.17    (11)  op(e1, all_52_13) = e1
% 177.68/28.17    (12)  op(e0, all_52_15) = e0
% 177.68/28.17    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.17    (14)  op(e2, e0) = all_52_15
% 177.68/28.17    (15)   ~ (all_4_2 = e3)
% 177.68/28.17    (16)   ~ (all_52_26 = all_10_2)
% 177.68/28.17    (17)  all_58_3 = all_10_2
% 177.68/28.17    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.17    (19)  all_58_15 = all_6_2
% 177.68/28.17    (20)   ~ (all_52_26 = all_4_2)
% 177.68/28.17    (21)  all_58_10 = all_52_15
% 177.68/28.17    (22)  all_58_7 = all_52_19
% 177.68/28.17    (23)   ~ (e3 = e1)
% 177.68/28.17    (24)  op(e3, all_4_2) = all_4_1
% 177.68/28.17    (25)  all_58_1 = all_52_3
% 177.68/28.17    (26)  all_58_0 = all_4_2
% 177.68/28.17    (27)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.68/28.17    (28)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.68/28.17    (29)  all_58_6 = e3
% 177.68/28.17    (30)  all_56_1 = all_52_3
% 177.68/28.17    (31)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.68/28.17    (32)   ~ (all_52_23 = e3)
% 177.68/28.17    (33)   ~ (all_52_3 = all_4_2)
% 177.68/28.17    (34)  op(e0, e3) = all_52_25
% 177.68/28.17    (35)  op(all_4_1, all_4_2) = e2
% 177.68/28.17    (36)   ~ (all_52_15 = all_52_23)
% 177.68/28.17    (37)  op(e1, e0) = all_52_23
% 177.68/28.17    (38)   ~ (all_52_3 = e3)
% 177.68/28.17    (39)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.17    (40)  all_56_5 = all_10_2
% 177.68/28.17    (41)   ~ (all_52_3 = all_52_7)
% 177.68/28.17    (42)  all_58_2 = all_52_26
% 177.68/28.17    (43)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.68/28.17    (44)   ~ (e1 = e0)
% 177.68/28.17    (45)  all_56_0 = all_4_2
% 177.68/28.17    (46)  all_58_11 = all_52_23
% 177.68/28.17    (47)   ~ (all_52_19 = all_10_2)
% 177.68/28.17    (48)   ~ (e2 = e1)
% 177.68/28.17    (49)   ~ (all_52_19 = e3)
% 177.68/28.17    (50)   ~ (all_52_25 = all_4_2)
% 177.68/28.17    (51)  op(e3, e0) = all_52_7
% 177.68/28.17    (52)  op(e2, all_10_2) = e2
% 177.68/28.17    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.17    (54)   ~ (all_52_7 = e3)
% 177.68/28.17    (55)   ~ (all_52_25 = all_52_26)
% 177.68/28.17    (56)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.17    (57)  all_56_4 = all_52_26
% 177.68/28.17    (58)  all_58_9 = all_52_7
% 177.68/28.17    (59)   ~ (all_52_15 = all_52_26)
% 177.68/28.17    (60)  all_58_12 = all_52_25
% 177.68/28.17    (61)  op(e3, all_52_26) = e3
% 177.68/28.17    (62)  all_58_13 = e3
% 177.68/28.17  
% 177.68/28.17  Begin of proof
% 177.68/28.17  | 
% 177.68/28.17  | BETA: splitting (56) gives:
% 177.68/28.17  | 
% 177.68/28.17  | Case 1:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (63)  all_58_9 = e3
% 177.68/28.17  | | 
% 177.68/28.17  | | REF_CLOSE: (54), (58), (63) are inconsistent by sub-proof #972.
% 177.68/28.17  | | 
% 177.68/28.17  | Case 2:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (64)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.17  | | 
% 177.68/28.17  | | BETA: splitting (64) gives:
% 177.68/28.17  | | 
% 177.68/28.17  | | Case 1:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (65)  all_58_10 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | COMBINE_EQS: (21), (65) imply:
% 177.68/28.17  | | |   (66)  all_52_15 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | SIMP: (66) implies:
% 177.68/28.17  | | |   (67)  all_52_15 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (36), (67) imply:
% 177.68/28.17  | | |   (68)   ~ (all_52_23 = e3)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (59), (67) imply:
% 177.68/28.17  | | |   (69)   ~ (all_52_26 = e3)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | SIMP: (69) implies:
% 177.68/28.17  | | |   (70)   ~ (all_52_26 = e3)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (14), (67) imply:
% 177.68/28.17  | | |   (71)  op(e2, e0) = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (12), (67) imply:
% 177.68/28.17  | | |   (72)  op(e0, e3) = e0
% 177.68/28.17  | | | 
% 177.68/28.17  | | | GROUND_INST: instantiating (53) with all_52_25, e0, e3, e0, simplifying
% 177.68/28.17  | | |              with (34), (72) gives:
% 177.68/28.17  | | |   (73)  all_52_25 = e0
% 177.68/28.17  | | | 
% 177.68/28.17  | | | COMBINE_EQS: (60), (73) imply:
% 177.68/28.17  | | |   (74)  all_58_12 = e0
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (55), (73) imply:
% 177.68/28.17  | | |   (75)   ~ (all_52_26 = e0)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | SIMP: (75) implies:
% 177.68/28.17  | | |   (76)   ~ (all_52_26 = e0)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (50), (73) imply:
% 177.68/28.17  | | |   (77)   ~ (all_4_2 = e0)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | SIMP: (77) implies:
% 177.68/28.17  | | |   (78)   ~ (all_4_2 = e0)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (4), (73) imply:
% 177.68/28.17  | | |   (79)  op(e3, e0) = all_52_24
% 177.68/28.17  | | | 
% 177.68/28.17  | | | GROUND_INST: instantiating (53) with all_52_7, all_52_24, e0, e3,
% 177.68/28.17  | | |              simplifying with (51), (79) gives:
% 177.68/28.17  | | |   (80)  all_52_7 = all_52_24
% 177.68/28.17  | | | 
% 177.68/28.17  | | | COMBINE_EQS: (58), (80) imply:
% 177.68/28.17  | | |   (81)  all_58_9 = all_52_24
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (41), (80) imply:
% 177.68/28.17  | | |   (82)   ~ (all_52_3 = all_52_24)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | BETA: splitting (43) gives:
% 177.68/28.17  | | | 
% 177.68/28.17  | | | Case 1:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | |   (83)  all_56_4 = e3
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REF_CLOSE: (57), (70), (83) are inconsistent by sub-proof #818.
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | Case 2:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | |   (84)   ~ (all_56_4 = e3)
% 177.68/28.17  | | | |   (85)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | BETA: splitting (18) gives:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | Case 1:
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | |   (86)  all_56_0 = e3
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | REF_CLOSE: (15), (45), (86) are inconsistent by sub-proof #1024.
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | Case 2:
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | |   (87)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | BETA: splitting (13) gives:
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | | Case 1:
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | |   (88)  all_58_0 = e2
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | COMBINE_EQS: (26), (88) imply:
% 177.68/28.17  | | | | | |   (89)  all_4_2 = e2
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | REDUCE: (33), (89) imply:
% 177.68/28.17  | | | | | |   (90)   ~ (all_52_3 = e2)
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | REDUCE: (78), (89) imply:
% 177.68/28.17  | | | | | |   (91)   ~ (e2 = e0)
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | REDUCE: (35), (89) imply:
% 177.68/28.17  | | | | | |   (92)  op(all_4_1, e2) = e2
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | REDUCE: (24), (89) imply:
% 177.68/28.17  | | | | | |   (93)  op(e3, e2) = all_4_1
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | BETA: splitting (39) gives:
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | Case 1:
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | |   (94)  all_58_0 = e1
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | | COMBINE_EQS: (88), (94) imply:
% 177.68/28.17  | | | | | | |   (95)  e2 = e1
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | | REDUCE: (48), (95) imply:
% 177.68/28.17  | | | | | | |   (96)  $false
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | | CLOSE: (96) is inconsistent.
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | Case 2:
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | |   (97)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | | BETA: splitting (97) gives:
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | | Case 1:
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | |   (98)  all_58_2 = e1
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | COMBINE_EQS: (42), (98) imply:
% 177.68/28.17  | | | | | | | |   (99)  all_52_26 = e1
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | SIMP: (99) implies:
% 177.68/28.17  | | | | | | | |   (100)  all_52_26 = e1
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | REDUCE: (16), (100) imply:
% 177.68/28.17  | | | | | | | |   (101)   ~ (all_10_2 = e1)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | SIMP: (101) implies:
% 177.68/28.17  | | | | | | | |   (102)   ~ (all_10_2 = e1)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | REDUCE: (70), (100) imply:
% 177.68/28.17  | | | | | | | |   (103)   ~ (e3 = e1)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | GROUND_INST: instantiating (53) with all_52_3, all_4_1, e2, e3,
% 177.68/28.17  | | | | | | | |              simplifying with (3), (93) gives:
% 177.68/28.17  | | | | | | | |   (104)  all_52_3 = all_4_1
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | COMBINE_EQS: (30), (104) imply:
% 177.68/28.17  | | | | | | | |   (105)  all_56_1 = all_4_1
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | COMBINE_EQS: (25), (104) imply:
% 177.68/28.17  | | | | | | | |   (106)  all_58_1 = all_4_1
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | REDUCE: (82), (104) imply:
% 177.68/28.17  | | | | | | | |   (107)   ~ (all_52_24 = all_4_1)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | SIMP: (107) implies:
% 177.68/28.17  | | | | | | | |   (108)   ~ (all_52_24 = all_4_1)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | REDUCE: (8), (104) imply:
% 177.68/28.17  | | | | | | | |   (109)   ~ (all_10_2 = all_4_1)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | SIMP: (109) implies:
% 177.68/28.17  | | | | | | | |   (110)   ~ (all_10_2 = all_4_1)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | REDUCE: (38), (104) imply:
% 177.68/28.17  | | | | | | | |   (111)   ~ (all_4_1 = e3)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | REDUCE: (90), (104) imply:
% 177.68/28.17  | | | | | | | |   (112)   ~ (all_4_1 = e2)
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | BETA: splitting (2) gives:
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | Case 1:
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | |   (113)  all_58_1 = e1
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | | COMBINE_EQS: (106), (113) imply:
% 177.68/28.17  | | | | | | | | |   (114)  all_4_1 = e1
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | | REDUCE: (92), (114) imply:
% 177.68/28.17  | | | | | | | | |   (115)  op(e1, e2) = e2
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | | REF_CLOSE: (1), (6), (31), (40), (47), (49), (52), (53), (71),
% 177.68/28.17  | | | | | | | | |            (88), (91), (102), (115) are inconsistent by
% 177.68/28.17  | | | | | | | | |            sub-proof #466.
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | Case 2:
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | |   (116)   ~ (all_58_1 = e1)
% 177.68/28.17  | | | | | | | | |   (117)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | | REDUCE: (106), (116) imply:
% 177.68/28.17  | | | | | | | | |   (118)   ~ (all_4_1 = e1)
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | | REF_CLOSE: (5), (9), (10), (11), (17), (22), (23), (27), (28),
% 177.68/28.17  | | | | | | | | |            (32), (37), (46), (53), (62), (65), (81), (98),
% 177.68/28.17  | | | | | | | | |            (102), (105), (108), (110), (111), (112), (117),
% 177.68/28.17  | | | | | | | | |            (118) are inconsistent by sub-proof #758.
% 177.68/28.17  | | | | | | | | | 
% 177.68/28.17  | | | | | | | | End of split
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | Case 2:
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | |   (119)  all_58_6 = e1 | all_58_12 = e1
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | | REF_CLOSE: (23), (29), (44), (74), (119) are inconsistent by
% 177.68/28.17  | | | | | | | |            sub-proof #726.
% 177.68/28.17  | | | | | | | | 
% 177.68/28.17  | | | | | | | End of split
% 177.68/28.17  | | | | | | | 
% 177.68/28.17  | | | | | | End of split
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | Case 2:
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | |   (120)   ~ (all_58_0 = e2)
% 177.68/28.17  | | | | | |   (121)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | REDUCE: (26), (120) imply:
% 177.68/28.17  | | | | | |   (122)   ~ (all_4_2 = e2)
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | | REF_CLOSE: (3), (20), (38), (42), (45), (53), (57), (61), (76),
% 177.68/28.17  | | | | | |            (78), (85), (87), (121), (122) are inconsistent by
% 177.68/28.17  | | | | | |            sub-proof #595.
% 177.68/28.17  | | | | | | 
% 177.68/28.17  | | | | | End of split
% 177.68/28.17  | | | | | 
% 177.68/28.17  | | | | End of split
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | End of split
% 177.68/28.17  | | | 
% 177.68/28.17  | | Case 2:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (123)  all_58_11 = e3 | all_58_15 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REF_CLOSE: (7), (19), (32), (46), (123) are inconsistent by sub-proof
% 177.68/28.17  | | |            #1016.
% 177.68/28.17  | | | 
% 177.68/28.17  | | End of split
% 177.68/28.17  | | 
% 177.68/28.17  | End of split
% 177.68/28.17  | 
% 177.68/28.17  End of proof
% 177.68/28.17  
% 177.68/28.17  Sub-proof #466 shows that the following formulas are inconsistent:
% 177.68/28.17  ----------------------------------------------------------------
% 177.68/28.17    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.17    (2)  op(e1, e2) = all_52_19
% 177.68/28.17    (3)   ~ (all_10_2 = e1)
% 177.68/28.17    (4)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.68/28.17    (5)  all_56_5 = all_10_2
% 177.68/28.17    (6)   ~ (all_52_19 = all_10_2)
% 177.68/28.17    (7)  op(e2, e0) = e3
% 177.68/28.17    (8)  op(e1, e2) = e2
% 177.68/28.17    (9)   ~ (all_52_19 = e3)
% 177.68/28.17    (10)  op(e2, all_10_2) = e2
% 177.68/28.17    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.17    (12)  all_58_0 = e2
% 177.68/28.17    (13)   ~ (e2 = e0)
% 177.68/28.17  
% 177.68/28.17  Begin of proof
% 177.68/28.17  | 
% 177.68/28.17  | BETA: splitting (1) gives:
% 177.68/28.17  | 
% 177.68/28.17  | Case 1:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (14)  all_58_0 = e0
% 177.68/28.17  | | 
% 177.68/28.17  | | COMBINE_EQS: (12), (14) imply:
% 177.68/28.17  | |   (15)  e2 = e0
% 177.68/28.17  | | 
% 177.68/28.17  | | REDUCE: (13), (15) imply:
% 177.68/28.17  | |   (16)  $false
% 177.68/28.17  | | 
% 177.68/28.17  | | CLOSE: (16) is inconsistent.
% 177.68/28.17  | | 
% 177.68/28.17  | Case 2:
% 177.68/28.17  | | 
% 177.68/28.17  | | 
% 177.68/28.17  | | GROUND_INST: instantiating (11) with all_52_19, e2, e2, e1, simplifying with
% 177.68/28.17  | |              (2), (8) gives:
% 177.68/28.17  | |   (17)  all_52_19 = e2
% 177.68/28.17  | | 
% 177.68/28.17  | | REDUCE: (6), (17) imply:
% 177.68/28.17  | |   (18)   ~ (all_10_2 = e2)
% 177.68/28.17  | | 
% 177.68/28.17  | | SIMP: (18) implies:
% 177.68/28.17  | |   (19)   ~ (all_10_2 = e2)
% 177.68/28.17  | | 
% 177.68/28.17  | | REDUCE: (9), (17) imply:
% 177.68/28.17  | |   (20)   ~ (e3 = e2)
% 177.68/28.17  | | 
% 177.68/28.17  | | SIMP: (20) implies:
% 177.68/28.17  | |   (21)   ~ (e3 = e2)
% 177.68/28.17  | | 
% 177.68/28.17  | | BETA: splitting (4) gives:
% 177.68/28.17  | | 
% 177.68/28.17  | | Case 1:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (22)  all_56_5 = e2
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REF_CLOSE: (5), (19), (22) are inconsistent by sub-proof #710.
% 177.68/28.17  | | | 
% 177.68/28.17  | | Case 2:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (23)  all_56_5 = e1 | all_56_5 = e0
% 177.68/28.17  | | | 
% 177.68/28.17  | | | BETA: splitting (23) gives:
% 177.68/28.17  | | | 
% 177.68/28.17  | | | Case 1:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | |   (24)  all_56_5 = e1
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REF_CLOSE: (3), (5), (24) are inconsistent by sub-proof #709.
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | Case 2:
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | |   (25)  all_56_5 = e0
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | COMBINE_EQS: (5), (25) imply:
% 177.68/28.17  | | | |   (26)  all_10_2 = e0
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | SIMP: (26) implies:
% 177.68/28.17  | | | |   (27)  all_10_2 = e0
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REDUCE: (10), (27) imply:
% 177.68/28.17  | | | |   (28)  op(e2, e0) = e2
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | | REF_CLOSE: (7), (11), (21), (28) are inconsistent by sub-proof #828.
% 177.68/28.17  | | | | 
% 177.68/28.17  | | | End of split
% 177.68/28.17  | | | 
% 177.68/28.17  | | End of split
% 177.68/28.17  | | 
% 177.68/28.17  | End of split
% 177.68/28.17  | 
% 177.68/28.17  End of proof
% 177.68/28.17  
% 177.68/28.17  Sub-proof #467 shows that the following formulas are inconsistent:
% 177.68/28.17  ----------------------------------------------------------------
% 177.68/28.17    (1)  all_56_3 = all_52_7
% 177.68/28.17    (2)  op(e3, e2) = all_52_3
% 177.68/28.17    (3)  all_6_2 = e3
% 177.68/28.17    (4)   ~ (all_52_3 = all_10_2)
% 177.68/28.17    (5)  all_58_5 = all_52_13
% 177.68/28.17    (6)  op(e1, all_52_13) = e1
% 177.68/28.17    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.17    (8)  all_58_3 = all_10_2
% 177.68/28.17    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.17    (10)   ~ (all_52_9 = all_4_2)
% 177.68/28.17    (11)  all_58_10 = all_52_15
% 177.68/28.17    (12)  all_56_4 = all_52_9
% 177.68/28.17    (13)   ~ (all_52_15 = all_6_2)
% 177.68/28.17    (14)  op(e3, all_4_2) = all_4_1
% 177.68/28.17    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.17    (16)   ~ (all_52_7 = all_4_2)
% 177.68/28.17    (17)  all_58_0 = all_4_2
% 177.68/28.17    (18)   ~ (all_4_1 = e2)
% 177.68/28.17    (19)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.68/28.17    (20)  all_26_2 = all_4_2
% 177.68/28.17    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.17    (22)  op(all_4_1, all_4_2) = e2
% 177.68/28.17    (23)  op(e3, all_52_9) = e3
% 177.68/28.17    (24)   ~ (all_52_9 = all_52_13)
% 177.68/28.17    (25)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.17    (26)   ~ (all_52_9 = all_52_17)
% 177.68/28.17    (27)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.68/28.17    (28)  all_56_0 = all_4_2
% 177.68/28.17    (29)  all_26_1 = all_4_1
% 177.68/28.17    (30)  all_58_2 = all_52_9
% 177.68/28.17    (31)  op(e1, e3) = all_52_17
% 177.68/28.17    (32)  op(e3, e0) = all_52_7
% 177.68/28.17    (33)  op(e2, all_10_2) = e2
% 177.68/28.17    (34)  op(e3, e3) = all_4_2
% 177.68/28.17    (35)   ~ (all_52_17 = all_4_2)
% 177.68/28.17    (36)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.17    (37)   ~ (all_52_7 = all_6_2)
% 177.68/28.17    (38)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.17    (39)  all_56_6 = all_52_13
% 177.68/28.17    (40)  op(e2, e3) = all_52_9
% 177.68/28.17  
% 177.68/28.17  Begin of proof
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (3), (37) imply:
% 177.68/28.17  |   (41)   ~ (all_52_7 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (3), (13) imply:
% 177.68/28.17  |   (42)   ~ (all_52_15 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | BETA: splitting (21) gives:
% 177.68/28.17  | 
% 177.68/28.17  | Case 1:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (43)  all_58_0 = e3
% 177.68/28.17  | | 
% 177.68/28.17  | | REF_CLOSE: (14), (17), (18), (22), (34), (36), (43) are inconsistent by
% 177.68/28.17  | |            sub-proof #489.
% 177.68/28.17  | | 
% 177.68/28.17  | Case 2:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (44)   ~ (all_58_0 = e3)
% 177.68/28.17  | | 
% 177.68/28.17  | | REDUCE: (17), (44) imply:
% 177.68/28.17  | |   (45)   ~ (all_4_2 = e3)
% 177.68/28.17  | | 
% 177.68/28.17  | | BETA: splitting (19) gives:
% 177.68/28.17  | | 
% 177.68/28.17  | | Case 1:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (46)  all_56_6 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | COMBINE_EQS: (39), (46) imply:
% 177.68/28.17  | | |   (47)  all_52_13 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REF_CLOSE: (1), (6), (7), (9), (10), (12), (14), (16), (17), (18), (20),
% 177.68/28.17  | | |            (22), (23), (24), (25), (26), (27), (28), (29), (31), (32),
% 177.68/28.17  | | |            (35), (36), (38), (41), (45), (47) are inconsistent by
% 177.68/28.17  | | |            sub-proof #468.
% 177.68/28.17  | | | 
% 177.68/28.17  | | Case 2:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (48)   ~ (all_56_6 = e3)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REDUCE: (39), (48) imply:
% 177.68/28.17  | | |   (49)   ~ (all_52_13 = e3)
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REF_CLOSE: (2), (4), (5), (8), (10), (11), (15), (23), (30), (33), (34),
% 177.68/28.17  | | |            (36), (40), (42), (49) are inconsistent by sub-proof #772.
% 177.68/28.17  | | | 
% 177.68/28.17  | | End of split
% 177.68/28.17  | | 
% 177.68/28.17  | End of split
% 177.68/28.17  | 
% 177.68/28.17  End of proof
% 177.68/28.17  
% 177.68/28.17  Sub-proof #468 shows that the following formulas are inconsistent:
% 177.68/28.17  ----------------------------------------------------------------
% 177.68/28.17    (1)  all_56_3 = all_52_7
% 177.68/28.17    (2)  op(e1, all_52_13) = e1
% 177.68/28.17    (3)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.17    (4)   ~ (all_4_2 = e3)
% 177.68/28.17    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.17    (6)   ~ (all_52_9 = all_4_2)
% 177.68/28.17    (7)  all_56_4 = all_52_9
% 177.68/28.17    (8)  op(e3, all_4_2) = all_4_1
% 177.68/28.17    (9)   ~ (all_52_7 = all_4_2)
% 177.68/28.17    (10)  all_58_0 = all_4_2
% 177.68/28.17    (11)   ~ (all_4_1 = e2)
% 177.68/28.17    (12)  all_26_2 = all_4_2
% 177.68/28.17    (13)  op(all_4_1, all_4_2) = e2
% 177.68/28.17    (14)  op(e3, all_52_9) = e3
% 177.68/28.17    (15)   ~ (all_52_9 = all_52_13)
% 177.68/28.17    (16)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.17    (17)   ~ (all_52_9 = all_52_17)
% 177.68/28.17    (18)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.68/28.17    (19)  all_56_0 = all_4_2
% 177.68/28.17    (20)  all_26_1 = all_4_1
% 177.68/28.17    (21)  op(e1, e3) = all_52_17
% 177.68/28.17    (22)  op(e3, e0) = all_52_7
% 177.68/28.17    (23)   ~ (all_52_17 = all_4_2)
% 177.68/28.17    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.17    (25)   ~ (all_52_7 = e3)
% 177.68/28.17    (26)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.17    (27)  all_52_13 = e3
% 177.68/28.17  
% 177.68/28.17  Begin of proof
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (27) implies:
% 177.68/28.17  |   (28)  all_52_13 = e3
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (15), (28) imply:
% 177.68/28.17  |   (29)   ~ (all_52_9 = e3)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (2), (28) imply:
% 177.68/28.17  |   (30)  op(e1, e3) = e1
% 177.68/28.17  | 
% 177.68/28.17  | GROUND_INST: instantiating (24) with all_52_17, e1, e3, e1, simplifying with
% 177.68/28.17  |              (21), (30) gives:
% 177.68/28.17  |   (31)  all_52_17 = e1
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (17), (31) imply:
% 177.68/28.17  |   (32)   ~ (all_52_9 = e1)
% 177.68/28.17  | 
% 177.68/28.17  | REDUCE: (23), (31) imply:
% 177.68/28.17  |   (33)   ~ (all_4_2 = e1)
% 177.68/28.17  | 
% 177.68/28.17  | SIMP: (33) implies:
% 177.68/28.17  |   (34)   ~ (all_4_2 = e1)
% 177.68/28.17  | 
% 177.68/28.17  | BETA: splitting (5) gives:
% 177.68/28.17  | 
% 177.68/28.17  | Case 1:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (35)  all_56_0 = e3
% 177.68/28.17  | | 
% 177.68/28.17  | | REF_CLOSE: (4), (19), (35) are inconsistent by sub-proof #1024.
% 177.68/28.17  | | 
% 177.68/28.17  | Case 2:
% 177.68/28.17  | | 
% 177.68/28.17  | |   (36)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.17  | | 
% 177.68/28.17  | | BETA: splitting (18) gives:
% 177.68/28.17  | | 
% 177.68/28.17  | | Case 1:
% 177.68/28.17  | | | 
% 177.68/28.17  | | |   (37)  all_56_4 = e3
% 177.68/28.17  | | | 
% 177.68/28.17  | | | REF_CLOSE: (7), (29), (37) are inconsistent by sub-proof #782.
% 177.68/28.17  | | | 
% 177.68/28.17  | | Case 2:
% 177.68/28.17  | | | 
% 177.68/28.18  | | |   (38)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.68/28.18  | | | 
% 177.68/28.18  | | | BETA: splitting (3) gives:
% 177.68/28.18  | | | 
% 177.68/28.18  | | | Case 1:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | |   (39)  all_58_0 = e2
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | COMBINE_EQS: (10), (39) imply:
% 177.68/28.18  | | | |   (40)  all_4_2 = e2
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | REDUCE: (6), (40) imply:
% 177.68/28.18  | | | |   (41)   ~ (all_52_9 = e2)
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | REF_CLOSE: (7), (14), (22), (24), (25), (32), (38), (41) are
% 177.68/28.18  | | | |            inconsistent by sub-proof #753.
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | Case 2:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | |   (42)   ~ (all_58_0 = e2)
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | REDUCE: (10), (42) imply:
% 177.68/28.18  | | | |   (43)   ~ (all_4_2 = e2)
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | REF_CLOSE: (1), (8), (9), (11), (12), (13), (16), (19), (20), (22),
% 177.68/28.18  | | | |            (24), (26), (34), (36), (43) are inconsistent by sub-proof
% 177.68/28.18  | | | |            #482.
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | End of split
% 177.68/28.18  | | | 
% 177.68/28.18  | | End of split
% 177.68/28.18  | | 
% 177.68/28.18  | End of split
% 177.68/28.18  | 
% 177.68/28.18  End of proof
% 177.68/28.18  
% 177.68/28.18  Sub-proof #469 shows that the following formulas are inconsistent:
% 177.68/28.18  ----------------------------------------------------------------
% 177.68/28.18    (1)   ~ (all_52_23 = all_14_2)
% 177.68/28.18    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.18    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.18    (4)   ~ (all_52_17 = all_52_23)
% 177.68/28.18    (5)  all_56_3 = all_52_7
% 177.68/28.18    (6)  op(e3, e2) = all_52_3
% 177.68/28.18    (7)   ~ (all_52_9 = all_52_25)
% 177.68/28.18    (8)  op(e3, all_52_25) = all_52_24
% 177.68/28.18    (9)   ~ (all_52_27 = e0)
% 177.68/28.18    (10)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.18    (11)  op(e3, all_52_9) = all_52_8
% 177.68/28.18    (12)   ~ (all_52_23 = e0)
% 177.68/28.18    (13)  all_50_1 = all_4_1
% 177.68/28.18    (14)  all_58_5 = all_52_13
% 177.68/28.18    (15)   ~ (all_52_25 = all_52_29)
% 177.68/28.18    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.18    (17)  op(all_14_1, all_14_2) = all_14_0
% 177.68/28.18    (18)  all_56_9 = all_52_19
% 177.68/28.18    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.18    (20)   ~ (all_52_9 = all_4_2)
% 177.68/28.18    (21)   ~ (all_52_5 = all_52_7)
% 177.68/28.18    (22)  all_58_10 = all_52_15
% 177.68/28.18    (23)   ~ (all_52_5 = all_4_2)
% 177.68/28.18    (24)  all_58_7 = all_52_19
% 177.68/28.18    (25)   ~ (all_52_17 = all_52_25)
% 177.68/28.18    (26)  all_58_4 = all_52_5
% 177.68/28.18    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.18    (28)   ~ (all_52_27 = all_52_29)
% 177.68/28.18    (29)   ~ (all_52_17 = all_14_2)
% 177.68/28.18    (30)  op(e3, all_4_2) = all_4_1
% 177.68/28.18    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.18    (32)   ~ (all_52_7 = all_4_2)
% 177.68/28.18    (33)  all_58_1 = all_52_3
% 177.68/28.18    (34)   ~ (all_52_13 = all_52_15)
% 177.68/28.18    (35)  all_58_0 = all_4_2
% 177.68/28.18    (36)  op(e1, all_52_29) = all_52_28
% 177.68/28.18    (37)   ~ (all_52_7 = e0)
% 177.68/28.18    (38)  all_50_2 = all_4_2
% 177.68/28.18    (39)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.18    (40)   ~ (all_4_1 = e2)
% 177.68/28.18    (41)  all_58_14 = all_52_29
% 177.68/28.18    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.18    (43)  all_26_2 = all_4_2
% 177.68/28.18    (44)   ~ (all_52_3 = all_52_5)
% 177.68/28.18    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.18    (46)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.18    (47)  all_58_8 = all_14_2
% 177.68/28.18    (48)   ~ (all_14_0 = e3)
% 177.68/28.18    (49)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.68/28.18    (50)   ~ (all_52_5 = all_14_2)
% 177.68/28.18    (51)   ~ (all_52_3 = all_52_27)
% 177.68/28.18    (52)   ~ (all_52_3 = all_4_2)
% 177.68/28.18    (53)  op(e0, e3) = all_52_25
% 177.68/28.18    (54)  op(all_4_1, all_4_2) = e2
% 177.68/28.18    (55)  op(e3, all_52_17) = all_52_16
% 177.68/28.18    (56)   ~ (e3 = e0)
% 177.68/28.18    (57)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.68/28.18    (58)   ~ (all_52_9 = all_52_13)
% 177.68/28.18    (59)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.18    (60)  op(e0, all_52_23) = all_52_22
% 177.68/28.18    (61)   ~ (all_52_15 = all_52_23)
% 177.68/28.18    (62)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.18    (63)   ~ (all_52_5 = all_52_29)
% 177.68/28.18    (64)  all_56_2 = all_52_5
% 177.68/28.18    (65)  all_56_12 = all_52_25
% 177.68/28.18    (66)  all_58_13 = all_52_27
% 177.68/28.18    (67)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.18    (68)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.18    (69)   ~ (all_52_25 = e0)
% 177.68/28.18    (70)   ~ (all_52_9 = all_52_17)
% 177.68/28.18    (71)   ~ (all_14_0 = e2)
% 177.68/28.18    (72)  all_58_6 = all_52_17
% 177.68/28.18    (73)  op(e2, all_52_19) = all_52_18
% 177.68/28.18    (74)   ~ (e1 = e0)
% 177.68/28.18    (75)  all_56_0 = all_4_2
% 177.68/28.18    (76)  all_58_11 = all_52_23
% 177.68/28.18    (77)   ~ (all_52_3 = all_52_19)
% 177.68/28.18    (78)  all_26_1 = all_4_1
% 177.68/28.18    (79)   ~ (all_52_29 = all_14_2)
% 177.68/28.18    (80)  all_58_15 = e0
% 177.68/28.18    (81)  all_58_2 = all_52_9
% 177.68/28.18    (82)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.68/28.18    (83)  op(e3, e1) = all_52_5
% 177.68/28.18    (84)  all_56_10 = all_14_2
% 177.68/28.18    (85)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.68/28.18    (86)  op(e1, e3) = all_52_17
% 177.68/28.18    (87)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.68/28.18    (88)   ~ (all_52_25 = all_4_2)
% 177.68/28.18    (89)  op(e3, e0) = all_52_7
% 177.68/28.18    (90)  op(e3, e3) = all_4_2
% 177.68/28.18    (91)  all_56_8 = all_52_17
% 177.68/28.18    (92)   ~ (all_52_17 = all_4_2)
% 177.68/28.18    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.18    (94)   ~ (all_52_25 = all_52_27)
% 177.68/28.18    (95)   ~ (all_52_19 = all_52_27)
% 177.68/28.18    (96)  all_56_7 = all_52_15
% 177.68/28.18    (97)   ~ (all_52_15 = e0)
% 177.68/28.18    (98)   ~ (all_52_7 = all_52_23)
% 177.68/28.18    (99)  op(e2, all_52_27) = all_52_26
% 177.68/28.18    (100)  all_52_20 = all_14_1
% 177.68/28.18    (101)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.18    (102)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.18    (103)  op(e1, all_14_2) = all_14_1
% 177.68/28.18    (104)  all_58_9 = all_52_7
% 177.68/28.18    (105)   ~ (e2 = e0)
% 177.68/28.18    (106)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.68/28.18           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.68/28.18    (107)  all_58_12 = all_52_25
% 177.68/28.18    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.68/28.18    (109)   ~ (all_52_9 = all_52_15)
% 177.68/28.18    (110)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.18    (111)   ~ (e3 = e2)
% 177.68/28.18    (112)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.18    (113)   ~ (all_52_19 = all_14_2)
% 177.68/28.18    (114)  op(e2, e3) = all_52_9
% 177.68/28.18    (115)  all_56_13 = all_52_27
% 177.68/28.18  
% 177.68/28.18  Begin of proof
% 177.68/28.18  | 
% 177.68/28.18  | BETA: splitting (106) gives:
% 177.68/28.18  | 
% 177.68/28.18  | Case 1:
% 177.68/28.18  | | 
% 177.68/28.18  | |   (116)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.68/28.18  | | 
% 177.68/28.18  | | ALPHA: (116) implies:
% 177.68/28.18  | |   (117)  all_52_22 = e0
% 177.68/28.18  | |   (118)  all_52_20 = e1
% 177.68/28.18  | |   (119)  all_52_18 = e2
% 177.68/28.18  | |   (120)  all_52_16 = e3
% 177.68/28.18  | | 
% 177.68/28.18  | | COMBINE_EQS: (100), (118) imply:
% 177.68/28.18  | |   (121)  all_14_1 = e1
% 177.68/28.18  | | 
% 177.68/28.18  | | SIMP: (121) implies:
% 177.68/28.18  | |   (122)  all_14_1 = e1
% 177.68/28.18  | | 
% 177.68/28.18  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.68/28.18  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.68/28.18  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.68/28.18  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.68/28.18  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.68/28.18  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.68/28.18  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.68/28.18  | |            (80), (81), (82), (83), (84), (86), (87), (88), (89), (90), (91),
% 177.68/28.18  | |            (92), (93), (94), (95), (96), (97), (98), (99), (101), (102),
% 177.68/28.18  | |            (103), (104), (105), (107), (108), (109), (110), (111), (112),
% 177.68/28.18  | |            (113), (114), (115), (117), (119), (120), (122) are inconsistent
% 177.68/28.18  | |            by sub-proof #473.
% 177.68/28.18  | | 
% 177.68/28.18  | Case 2:
% 177.68/28.18  | | 
% 177.68/28.18  | |   (123)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.68/28.18  | | 
% 177.68/28.18  | | REF_CLOSE: (5), (6), (7), (8), (15), (19), (20), (21), (23), (25), (30),
% 177.68/28.18  | |            (32), (35), (36), (40), (41), (42), (43), (46), (52), (54), (56),
% 177.68/28.18  | |            (59), (65), (66), (67), (68), (69), (75), (78), (80), (83), (85),
% 177.68/28.18  | |            (86), (88), (89), (90), (92), (93), (94), (99), (102), (105),
% 177.68/28.18  | |            (107), (111), (114), (115), (123) are inconsistent by sub-proof
% 177.68/28.18  | |            #470.
% 177.68/28.18  | | 
% 177.68/28.18  | End of split
% 177.68/28.18  | 
% 177.68/28.18  End of proof
% 177.68/28.18  
% 177.68/28.18  Sub-proof #470 shows that the following formulas are inconsistent:
% 177.68/28.18  ----------------------------------------------------------------
% 177.68/28.18    (1)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.68/28.18    (2)  all_56_3 = all_52_7
% 177.68/28.18    (3)  op(e3, e2) = all_52_3
% 177.68/28.18    (4)   ~ (all_52_9 = all_52_25)
% 177.68/28.18    (5)  op(e3, all_52_25) = all_52_24
% 177.68/28.18    (6)   ~ (all_52_25 = all_52_29)
% 177.68/28.18    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.18    (8)   ~ (all_52_9 = all_4_2)
% 177.68/28.18    (9)   ~ (all_52_5 = all_52_7)
% 177.68/28.18    (10)   ~ (all_52_5 = all_4_2)
% 177.68/28.18    (11)   ~ (all_52_17 = all_52_25)
% 177.68/28.18    (12)  op(e3, all_4_2) = all_4_1
% 177.68/28.18    (13)   ~ (all_52_7 = all_4_2)
% 177.68/28.18    (14)  all_58_0 = all_4_2
% 177.68/28.18    (15)  op(e1, all_52_29) = all_52_28
% 177.68/28.18    (16)   ~ (all_4_1 = e2)
% 177.68/28.18    (17)  all_58_14 = all_52_29
% 177.68/28.18    (18)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.18    (19)  all_26_2 = all_4_2
% 177.68/28.18    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.18    (21)   ~ (all_52_3 = all_4_2)
% 177.68/28.18    (22)  op(all_4_1, all_4_2) = e2
% 177.68/28.18    (23)   ~ (e3 = e0)
% 177.68/28.18    (24)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.18    (25)  all_56_12 = all_52_25
% 177.68/28.18    (26)  all_58_13 = all_52_27
% 177.68/28.18    (27)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.18    (28)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.18    (29)   ~ (all_52_25 = e0)
% 177.68/28.18    (30)  all_56_0 = all_4_2
% 177.68/28.18    (31)  all_26_1 = all_4_1
% 177.68/28.18    (32)  all_58_15 = e0
% 177.68/28.18    (33)  op(e3, e1) = all_52_5
% 177.68/28.18    (34)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.68/28.18    (35)  op(e1, e3) = all_52_17
% 177.68/28.18    (36)   ~ (all_52_25 = all_4_2)
% 177.68/28.18    (37)  op(e3, e0) = all_52_7
% 177.68/28.18    (38)  op(e3, e3) = all_4_2
% 177.68/28.18    (39)   ~ (all_52_17 = all_4_2)
% 177.68/28.18    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.18    (41)   ~ (all_52_25 = all_52_27)
% 177.68/28.18    (42)  op(e2, all_52_27) = all_52_26
% 177.68/28.18    (43)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.18    (44)   ~ (e2 = e0)
% 177.68/28.18    (45)  all_58_12 = all_52_25
% 177.68/28.18    (46)   ~ (e3 = e2)
% 177.68/28.18    (47)  op(e2, e3) = all_52_9
% 177.68/28.18    (48)  all_56_13 = all_52_27
% 177.68/28.18  
% 177.68/28.18  Begin of proof
% 177.68/28.18  | 
% 177.68/28.18  | ALPHA: (1) implies:
% 177.68/28.18  |   (49)  all_52_28 = e1
% 177.68/28.18  |   (50)  all_52_26 = e2
% 177.68/28.18  |   (51)  all_52_24 = e3
% 177.68/28.18  | 
% 177.68/28.18  | REDUCE: (5), (51) imply:
% 177.68/28.18  |   (52)  op(e3, all_52_25) = e3
% 177.68/28.18  | 
% 177.68/28.18  | REDUCE: (42), (50) imply:
% 177.68/28.18  |   (53)  op(e2, all_52_27) = e2
% 177.68/28.18  | 
% 177.68/28.18  | REDUCE: (15), (49) imply:
% 177.68/28.18  |   (54)  op(e1, all_52_29) = e1
% 177.68/28.18  | 
% 177.68/28.18  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 177.68/28.18  |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 177.68/28.18  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.68/28.18  |            (38), (39), (40), (41), (43), (44), (45), (46), (47), (48), (52),
% 177.68/28.18  |            (53), (54) are inconsistent by sub-proof #471.
% 177.68/28.18  | 
% 177.68/28.18  End of proof
% 177.68/28.18  
% 177.68/28.18  Sub-proof #471 shows that the following formulas are inconsistent:
% 177.68/28.18  ----------------------------------------------------------------
% 177.68/28.18    (1)  all_56_3 = all_52_7
% 177.68/28.18    (2)  op(e3, e2) = all_52_3
% 177.68/28.18    (3)   ~ (all_52_9 = all_52_25)
% 177.68/28.18    (4)   ~ (all_52_25 = all_52_29)
% 177.68/28.18    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.18    (6)   ~ (all_52_9 = all_4_2)
% 177.68/28.18    (7)   ~ (all_52_5 = all_52_7)
% 177.68/28.18    (8)   ~ (all_52_5 = all_4_2)
% 177.68/28.18    (9)   ~ (all_52_17 = all_52_25)
% 177.68/28.18    (10)  op(e3, all_4_2) = all_4_1
% 177.68/28.18    (11)   ~ (all_52_7 = all_4_2)
% 177.68/28.18    (12)  all_58_0 = all_4_2
% 177.68/28.18    (13)  op(e2, all_52_27) = e2
% 177.68/28.18    (14)   ~ (all_4_1 = e2)
% 177.68/28.18    (15)  all_58_14 = all_52_29
% 177.68/28.18    (16)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.18    (17)  all_26_2 = all_4_2
% 177.68/28.18    (18)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.18    (19)  op(e1, all_52_29) = e1
% 177.68/28.18    (20)   ~ (all_52_3 = all_4_2)
% 177.68/28.18    (21)  op(all_4_1, all_4_2) = e2
% 177.68/28.18    (22)   ~ (e3 = e0)
% 177.68/28.18    (23)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.18    (24)  all_56_12 = all_52_25
% 177.68/28.18    (25)  all_58_13 = all_52_27
% 177.68/28.18    (26)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.18    (27)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.18    (28)   ~ (all_52_25 = e0)
% 177.68/28.18    (29)  all_56_0 = all_4_2
% 177.68/28.18    (30)  all_26_1 = all_4_1
% 177.68/28.18    (31)  op(e3, all_52_25) = e3
% 177.68/28.18    (32)  all_58_15 = e0
% 177.68/28.18    (33)  op(e3, e1) = all_52_5
% 177.68/28.18    (34)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.68/28.18    (35)  op(e1, e3) = all_52_17
% 177.68/28.18    (36)   ~ (all_52_25 = all_4_2)
% 177.68/28.18    (37)  op(e3, e0) = all_52_7
% 177.68/28.18    (38)  op(e3, e3) = all_4_2
% 177.68/28.18    (39)   ~ (all_52_17 = all_4_2)
% 177.68/28.18    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.18    (41)   ~ (all_52_25 = all_52_27)
% 177.68/28.18    (42)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.18    (43)   ~ (e2 = e0)
% 177.68/28.18    (44)  all_58_12 = all_52_25
% 177.68/28.18    (45)   ~ (e3 = e2)
% 177.68/28.18    (46)  op(e2, e3) = all_52_9
% 177.68/28.18    (47)  all_56_13 = all_52_27
% 177.68/28.18  
% 177.68/28.18  Begin of proof
% 177.68/28.18  | 
% 177.68/28.18  | BETA: splitting (16) gives:
% 177.68/28.18  | 
% 177.68/28.18  | Case 1:
% 177.68/28.18  | | 
% 177.68/28.18  | |   (48)  all_56_13 = e3
% 177.68/28.18  | | 
% 177.68/28.18  | | COMBINE_EQS: (47), (48) imply:
% 177.68/28.18  | |   (49)  all_52_27 = e3
% 177.68/28.18  | | 
% 177.68/28.18  | | SIMP: (49) implies:
% 177.68/28.18  | |   (50)  all_52_27 = e3
% 177.68/28.18  | | 
% 177.68/28.18  | | COMBINE_EQS: (25), (50) imply:
% 177.68/28.18  | |   (51)  all_58_13 = e3
% 177.68/28.18  | | 
% 177.68/28.18  | | REDUCE: (41), (50) imply:
% 177.68/28.18  | |   (52)   ~ (all_52_25 = e3)
% 177.68/28.18  | | 
% 177.68/28.18  | | REDUCE: (13), (50) imply:
% 177.68/28.18  | |   (53)  op(e2, e3) = e2
% 177.68/28.18  | | 
% 177.68/28.18  | | GROUND_INST: instantiating (40) with all_52_9, e2, e3, e2, simplifying with
% 177.68/28.18  | |              (46), (53) gives:
% 177.68/28.18  | |   (54)  all_52_9 = e2
% 177.68/28.18  | | 
% 177.68/28.18  | | REDUCE: (3), (54) imply:
% 177.68/28.18  | |   (55)   ~ (all_52_25 = e2)
% 177.68/28.18  | | 
% 177.68/28.18  | | SIMP: (55) implies:
% 177.68/28.18  | |   (56)   ~ (all_52_25 = e2)
% 177.68/28.18  | | 
% 177.68/28.18  | | REDUCE: (6), (54) imply:
% 177.68/28.18  | |   (57)   ~ (all_4_2 = e2)
% 177.68/28.18  | | 
% 177.68/28.18  | | SIMP: (57) implies:
% 177.68/28.18  | |   (58)   ~ (all_4_2 = e2)
% 177.68/28.18  | | 
% 177.68/28.18  | | BETA: splitting (23) gives:
% 177.68/28.18  | | 
% 177.68/28.18  | | Case 1:
% 177.68/28.18  | | | 
% 177.68/28.18  | | |   (59)  all_56_12 = e3
% 177.68/28.18  | | | 
% 177.68/28.18  | | | REF_CLOSE: (24), (52), (59) are inconsistent by sub-proof #1040.
% 177.68/28.18  | | | 
% 177.68/28.18  | | Case 2:
% 177.68/28.18  | | | 
% 177.68/28.18  | | |   (60)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.18  | | | 
% 177.68/28.18  | | | BETA: splitting (34) gives:
% 177.68/28.18  | | | 
% 177.68/28.18  | | | Case 1:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | |   (61)  all_58_12 = e2
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | REF_CLOSE: (44), (56), (61) are inconsistent by sub-proof #660.
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | Case 2:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | |   (62)   ~ (all_58_12 = e2)
% 177.68/28.18  | | | |   (63)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | BETA: splitting (63) gives:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | Case 1:
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | |   (64)  all_58_13 = e2
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | REF_CLOSE: (45), (51), (64) are inconsistent by sub-proof #906.
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | Case 2:
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | |   (65)  all_58_14 = e2 | all_58_15 = e2
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | BETA: splitting (60) gives:
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | Case 1:
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | |   (66)  all_56_12 = e2
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | | REF_CLOSE: (24), (56), (66) are inconsistent by sub-proof #1032.
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | Case 2:
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | |   (67)   ~ (all_56_12 = e2)
% 177.68/28.18  | | | | | |   (68)  all_56_12 = e1 | all_56_12 = e0
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | | BETA: splitting (68) gives:
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | | Case 1:
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | |   (69)  all_56_12 = e1
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | COMBINE_EQS: (24), (69) imply:
% 177.68/28.18  | | | | | | |   (70)  all_52_25 = e1
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | SIMP: (70) implies:
% 177.68/28.18  | | | | | | |   (71)  all_52_25 = e1
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | REDUCE: (31), (71) imply:
% 177.68/28.18  | | | | | | |   (72)  op(e3, e1) = e3
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | BETA: splitting (65) gives:
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | Case 1:
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | GROUND_INST: instantiating (40) with all_52_5, e3, e1, e3,
% 177.68/28.18  | | | | | | | |              simplifying with (33), (72) gives:
% 177.68/28.18  | | | | | | | |   (73)  all_52_5 = e3
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | REDUCE: (7), (73) imply:
% 177.68/28.18  | | | | | | | |   (74)   ~ (all_52_7 = e3)
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | SIMP: (74) implies:
% 177.68/28.18  | | | | | | | |   (75)   ~ (all_52_7 = e3)
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | REDUCE: (8), (73) imply:
% 177.68/28.18  | | | | | | | |   (76)   ~ (all_4_2 = e3)
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | SIMP: (76) implies:
% 177.68/28.18  | | | | | | | |   (77)   ~ (all_4_2 = e3)
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | BETA: splitting (5) gives:
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | Case 1:
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | |   (78)  all_56_0 = e3
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | | COMBINE_EQS: (29), (78) imply:
% 177.68/28.18  | | | | | | | | |   (79)  all_4_2 = e3
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | | REDUCE: (77), (79) imply:
% 177.68/28.18  | | | | | | | | |   (80)  $false
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | | CLOSE: (80) is inconsistent.
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | Case 2:
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | |   (81)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | | REF_CLOSE: (1), (10), (11), (12), (14), (17), (21), (24),
% 177.68/28.18  | | | | | | | | |            (26), (27), (29), (30), (31), (36), (37), (40),
% 177.68/28.18  | | | | | | | | |            (42), (56), (58), (60), (75), (81) are inconsistent
% 177.68/28.18  | | | | | | | | |            by sub-proof #472.
% 177.68/28.18  | | | | | | | | | 
% 177.68/28.18  | | | | | | | | End of split
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | Case 2:
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | |   (82)  all_58_15 = e2
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | REF_CLOSE: (32), (43), (82) are inconsistent by sub-proof #991.
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | End of split
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | Case 2:
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | |   (83)  all_56_12 = e0
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | REF_CLOSE: (24), (28), (83) are inconsistent by sub-proof #1030.
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | End of split
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | End of split
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | End of split
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | End of split
% 177.68/28.18  | | | 
% 177.68/28.18  | | End of split
% 177.68/28.18  | | 
% 177.68/28.18  | Case 2:
% 177.68/28.18  | | 
% 177.68/28.18  | |   (84)   ~ (all_56_13 = e3)
% 177.68/28.18  | | 
% 177.68/28.18  | | REDUCE: (47), (84) imply:
% 177.68/28.18  | |   (85)   ~ (all_52_27 = e3)
% 177.68/28.18  | | 
% 177.68/28.18  | | BETA: splitting (18) gives:
% 177.68/28.18  | | 
% 177.68/28.18  | | Case 1:
% 177.68/28.18  | | | 
% 177.68/28.18  | | |   (86)  all_58_12 = e3
% 177.68/28.18  | | | 
% 177.68/28.18  | | | REF_CLOSE: (31), (36), (38), (40), (44), (86) are inconsistent by
% 177.68/28.18  | | |            sub-proof #884.
% 177.68/28.18  | | | 
% 177.68/28.18  | | Case 2:
% 177.68/28.18  | | | 
% 177.68/28.18  | | |   (87)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.18  | | | 
% 177.68/28.18  | | | BETA: splitting (87) gives:
% 177.68/28.18  | | | 
% 177.68/28.18  | | | Case 1:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | |   (88)  all_58_13 = e3
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | REF_CLOSE: (25), (85), (88) are inconsistent by sub-proof #1026.
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | Case 2:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | |   (89)  all_58_14 = e3 | all_58_15 = e3
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | BETA: splitting (89) gives:
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | | Case 1:
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | |   (90)  all_58_14 = e3
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | COMBINE_EQS: (15), (90) imply:
% 177.68/28.18  | | | | |   (91)  all_52_29 = e3
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | SIMP: (91) implies:
% 177.68/28.18  | | | | |   (92)  all_52_29 = e3
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | REDUCE: (4), (92) imply:
% 177.68/28.18  | | | | |   (93)   ~ (all_52_25 = e3)
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | REDUCE: (19), (92) imply:
% 177.68/28.18  | | | | |   (94)  op(e1, e3) = e1
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | GROUND_INST: instantiating (40) with all_52_17, e1, e3, e1,
% 177.68/28.18  | | | | |              simplifying with (35), (94) gives:
% 177.68/28.18  | | | | |   (95)  all_52_17 = e1
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | REDUCE: (9), (95) imply:
% 177.68/28.18  | | | | |   (96)   ~ (all_52_25 = e1)
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | SIMP: (96) implies:
% 177.68/28.18  | | | | |   (97)   ~ (all_52_25 = e1)
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | REDUCE: (39), (95) imply:
% 177.68/28.18  | | | | |   (98)   ~ (all_4_2 = e1)
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | SIMP: (98) implies:
% 177.68/28.18  | | | | |   (99)   ~ (all_4_2 = e1)
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | BETA: splitting (23) gives:
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | Case 1:
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | |   (100)  all_56_12 = e3
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | | REF_CLOSE: (24), (93), (100) are inconsistent by sub-proof #1040.
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | Case 2:
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | |   (101)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | | BETA: splitting (34) gives:
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | | Case 1:
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | |   (102)  all_58_12 = e2
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | COMBINE_EQS: (44), (102) imply:
% 177.68/28.18  | | | | | | |   (103)  all_52_25 = e2
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | SIMP: (103) implies:
% 177.68/28.18  | | | | | | |   (104)  all_52_25 = e2
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | REDUCE: (36), (104) imply:
% 177.68/28.18  | | | | | | |   (105)   ~ (all_4_2 = e2)
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | SIMP: (105) implies:
% 177.68/28.18  | | | | | | |   (106)   ~ (all_4_2 = e2)
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | REDUCE: (31), (104) imply:
% 177.68/28.18  | | | | | | |   (107)  op(e3, e2) = e3
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | GROUND_INST: instantiating (40) with all_52_3, e3, e2, e3,
% 177.68/28.18  | | | | | | |              simplifying with (2), (107) gives:
% 177.68/28.18  | | | | | | |   (108)  all_52_3 = e3
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | REDUCE: (20), (108) imply:
% 177.68/28.18  | | | | | | |   (109)   ~ (all_4_2 = e3)
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | SIMP: (109) implies:
% 177.68/28.18  | | | | | | |   (110)   ~ (all_4_2 = e3)
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | BETA: splitting (5) gives:
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | Case 1:
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | |   (111)  all_56_0 = e3
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | COMBINE_EQS: (29), (111) imply:
% 177.68/28.18  | | | | | | | |   (112)  all_4_2 = e3
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | REDUCE: (110), (112) imply:
% 177.68/28.18  | | | | | | | |   (113)  $false
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | CLOSE: (113) is inconsistent.
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | Case 2:
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | |   (114)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | | REF_CLOSE: (1), (10), (11), (14), (17), (21), (26), (29), (30),
% 177.68/28.18  | | | | | | | |            (37), (40), (42), (99), (106), (114) are inconsistent
% 177.68/28.18  | | | | | | | |            by sub-proof #482.
% 177.68/28.18  | | | | | | | | 
% 177.68/28.18  | | | | | | | End of split
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | Case 2:
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | |   (115)   ~ (all_58_12 = e2)
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | REDUCE: (44), (115) imply:
% 177.68/28.18  | | | | | | |   (116)   ~ (all_52_25 = e2)
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | | REF_CLOSE: (24), (28), (97), (101), (116) are inconsistent by
% 177.68/28.18  | | | | | | |            sub-proof #1028.
% 177.68/28.18  | | | | | | | 
% 177.68/28.18  | | | | | | End of split
% 177.68/28.18  | | | | | | 
% 177.68/28.18  | | | | | End of split
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | Case 2:
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | |   (117)  all_58_15 = e3
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | | REF_CLOSE: (22), (32), (117) are inconsistent by sub-proof #1010.
% 177.68/28.18  | | | | | 
% 177.68/28.18  | | | | End of split
% 177.68/28.18  | | | | 
% 177.68/28.18  | | | End of split
% 177.68/28.18  | | | 
% 177.68/28.18  | | End of split
% 177.68/28.18  | | 
% 177.68/28.18  | End of split
% 177.68/28.18  | 
% 177.68/28.18  End of proof
% 177.68/28.18  
% 177.68/28.18  Sub-proof #472 shows that the following formulas are inconsistent:
% 177.68/28.18  ----------------------------------------------------------------
% 177.68/28.18    (1)  all_56_3 = all_52_7
% 177.68/28.18    (2)   ~ (all_4_2 = e2)
% 177.68/28.18    (3)  op(e3, all_4_2) = all_4_1
% 177.68/28.18    (4)   ~ (all_52_7 = all_4_2)
% 177.68/28.18    (5)  all_58_0 = all_4_2
% 177.68/28.18    (6)   ~ (all_4_1 = e2)
% 177.68/28.18    (7)  all_26_2 = all_4_2
% 177.68/28.18    (8)   ~ (all_52_25 = e2)
% 177.68/28.18    (9)  op(all_4_1, all_4_2) = e2
% 177.68/28.18    (10)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.18    (11)  all_56_12 = all_52_25
% 177.68/28.18    (12)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.18    (13)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.18    (14)  all_56_0 = all_4_2
% 177.68/28.18    (15)  all_26_1 = all_4_1
% 177.68/28.18    (16)  op(e3, all_52_25) = e3
% 177.68/28.18    (17)   ~ (all_52_25 = all_4_2)
% 177.68/28.18    (18)  op(e3, e0) = all_52_7
% 177.68/28.18    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.18    (20)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.18    (21)   ~ (all_52_7 = e3)
% 177.68/28.18    (22)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.18  
% 177.68/28.18  Begin of proof
% 177.68/28.18  | 
% 177.68/28.18  | BETA: splitting (13) gives:
% 177.68/28.18  | 
% 177.68/28.18  | Case 1:
% 177.68/28.18  | | 
% 177.68/28.18  | |   (23)  all_58_0 = e1
% 177.68/28.18  | | 
% 177.68/28.18  | | COMBINE_EQS: (5), (23) imply:
% 177.68/28.18  | |   (24)  all_4_2 = e1
% 177.68/28.18  | | 
% 177.68/28.18  | | REDUCE: (17), (24) imply:
% 177.68/28.18  | |   (25)   ~ (all_52_25 = e1)
% 177.68/28.18  | | 
% 177.68/28.18  | | REF_CLOSE: (8), (10), (11), (16), (18), (19), (21), (25) are inconsistent by
% 177.68/28.18  | |            sub-proof #663.
% 177.68/28.18  | | 
% 177.68/28.18  | Case 2:
% 177.68/28.18  | | 
% 177.68/28.18  | |   (26)   ~ (all_58_0 = e1)
% 177.68/28.18  | | 
% 177.68/28.18  | | REDUCE: (5), (26) imply:
% 177.68/28.18  | |   (27)   ~ (all_4_2 = e1)
% 177.68/28.18  | | 
% 177.68/28.18  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (12), (14), (15), (18), (19),
% 177.68/28.18  | |            (20), (22), (27) are inconsistent by sub-proof #482.
% 177.68/28.18  | | 
% 177.68/28.18  | End of split
% 177.68/28.18  | 
% 177.68/28.18  End of proof
% 177.68/28.18  
% 177.68/28.18  Sub-proof #473 shows that the following formulas are inconsistent:
% 177.68/28.18  ----------------------------------------------------------------
% 177.68/28.18    (1)   ~ (all_52_23 = all_14_2)
% 177.68/28.18    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.18    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.18    (4)   ~ (all_52_17 = all_52_23)
% 177.68/28.18    (5)  all_56_3 = all_52_7
% 177.68/28.18    (6)  all_52_16 = e3
% 177.68/28.18    (7)   ~ (all_52_9 = all_52_25)
% 177.68/28.18    (8)  op(e3, all_52_25) = all_52_24
% 177.68/28.18    (9)   ~ (all_52_27 = e0)
% 177.68/28.19    (10)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.19    (11)  op(e3, all_52_9) = all_52_8
% 177.68/28.19    (12)   ~ (all_52_23 = e0)
% 177.68/28.19    (13)  all_50_1 = all_4_1
% 177.68/28.19    (14)  all_58_5 = all_52_13
% 177.68/28.19    (15)   ~ (all_52_25 = all_52_29)
% 177.68/28.19    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.19    (17)  op(all_14_1, all_14_2) = all_14_0
% 177.68/28.19    (18)  all_56_9 = all_52_19
% 177.68/28.19    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.19    (20)   ~ (all_52_9 = all_4_2)
% 177.68/28.19    (21)   ~ (all_52_5 = all_52_7)
% 177.68/28.19    (22)  all_58_10 = all_52_15
% 177.68/28.19    (23)   ~ (all_52_5 = all_4_2)
% 177.68/28.19    (24)  all_58_7 = all_52_19
% 177.68/28.19    (25)   ~ (all_52_17 = all_52_25)
% 177.68/28.19    (26)  all_58_4 = all_52_5
% 177.68/28.19    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.19    (28)  all_52_18 = e2
% 177.68/28.19    (29)   ~ (all_52_27 = all_52_29)
% 177.68/28.19    (30)   ~ (all_52_17 = all_14_2)
% 177.68/28.19    (31)  op(e3, all_4_2) = all_4_1
% 177.68/28.19    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.19    (33)   ~ (all_52_7 = all_4_2)
% 177.68/28.19    (34)  all_58_1 = all_52_3
% 177.68/28.19    (35)   ~ (all_52_13 = all_52_15)
% 177.68/28.19    (36)  all_58_0 = all_4_2
% 177.68/28.19    (37)  op(e1, all_52_29) = all_52_28
% 177.68/28.19    (38)   ~ (all_52_7 = e0)
% 177.68/28.19    (39)  all_50_2 = all_4_2
% 177.68/28.19    (40)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.19    (41)   ~ (all_4_1 = e2)
% 177.68/28.19    (42)  all_58_14 = all_52_29
% 177.68/28.19    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.19    (44)  all_26_2 = all_4_2
% 177.68/28.19    (45)   ~ (all_52_3 = all_52_5)
% 177.68/28.19    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.19    (47)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.19    (48)  all_58_8 = all_14_2
% 177.68/28.19    (49)   ~ (all_14_0 = e3)
% 177.68/28.19    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.68/28.19    (51)   ~ (all_52_5 = all_14_2)
% 177.68/28.19    (52)   ~ (all_52_3 = all_52_27)
% 177.68/28.19    (53)   ~ (all_52_3 = all_4_2)
% 177.68/28.19    (54)  op(e0, e3) = all_52_25
% 177.68/28.19    (55)  op(all_4_1, all_4_2) = e2
% 177.68/28.19    (56)  op(e3, all_52_17) = all_52_16
% 177.68/28.19    (57)   ~ (e3 = e0)
% 177.68/28.19    (58)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.68/28.19    (59)   ~ (all_52_9 = all_52_13)
% 177.68/28.19    (60)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.19    (61)  op(e0, all_52_23) = all_52_22
% 177.68/28.19    (62)   ~ (all_52_15 = all_52_23)
% 177.68/28.19    (63)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.19    (64)   ~ (all_52_5 = all_52_29)
% 177.68/28.19    (65)  all_56_2 = all_52_5
% 177.68/28.19    (66)  all_56_12 = all_52_25
% 177.68/28.19    (67)  all_58_13 = all_52_27
% 177.68/28.19    (68)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.19    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.19    (70)   ~ (all_52_25 = e0)
% 177.68/28.19    (71)   ~ (all_52_9 = all_52_17)
% 177.68/28.19    (72)   ~ (all_14_0 = e2)
% 177.68/28.19    (73)  all_58_6 = all_52_17
% 177.68/28.19    (74)  op(e2, all_52_19) = all_52_18
% 177.68/28.19    (75)   ~ (e1 = e0)
% 177.68/28.19    (76)  all_56_0 = all_4_2
% 177.68/28.19    (77)  all_58_11 = all_52_23
% 177.68/28.19    (78)   ~ (all_52_3 = all_52_19)
% 177.68/28.19    (79)  all_26_1 = all_4_1
% 177.68/28.19    (80)   ~ (all_52_29 = all_14_2)
% 177.68/28.19    (81)  all_58_15 = e0
% 177.68/28.19    (82)  all_58_2 = all_52_9
% 177.68/28.19    (83)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.68/28.19    (84)  op(e3, e1) = all_52_5
% 177.68/28.19    (85)  all_56_10 = all_14_2
% 177.68/28.19    (86)  op(e1, e3) = all_52_17
% 177.68/28.19    (87)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.68/28.19    (88)   ~ (all_52_25 = all_4_2)
% 177.68/28.19    (89)  op(e3, e0) = all_52_7
% 177.68/28.19    (90)  op(e3, e3) = all_4_2
% 177.68/28.19    (91)  all_56_8 = all_52_17
% 177.68/28.19    (92)   ~ (all_52_17 = all_4_2)
% 177.68/28.19    (93)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.19    (94)   ~ (all_52_25 = all_52_27)
% 177.68/28.19    (95)   ~ (all_52_19 = all_52_27)
% 177.68/28.19    (96)  all_56_7 = all_52_15
% 177.68/28.19    (97)   ~ (all_52_15 = e0)
% 177.68/28.19    (98)   ~ (all_52_7 = all_52_23)
% 177.68/28.19    (99)  op(e2, all_52_27) = all_52_26
% 177.68/28.19    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.19    (101)  all_52_22 = e0
% 177.68/28.19    (102)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.19    (103)  op(e1, all_14_2) = all_14_1
% 177.68/28.19    (104)  all_58_9 = all_52_7
% 177.68/28.19    (105)   ~ (e2 = e0)
% 177.68/28.19    (106)  all_58_12 = all_52_25
% 177.68/28.19    (107)  all_14_1 = e1
% 177.68/28.19    (108)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.68/28.19    (109)   ~ (all_52_9 = all_52_15)
% 177.68/28.19    (110)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.19    (111)   ~ (e3 = e2)
% 177.68/28.19    (112)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.19    (113)   ~ (all_52_19 = all_14_2)
% 177.68/28.19    (114)  op(e2, e3) = all_52_9
% 177.68/28.19    (115)  all_56_13 = all_52_27
% 177.68/28.19  
% 177.68/28.19  Begin of proof
% 177.68/28.19  | 
% 177.68/28.19  | REDUCE: (17), (107) imply:
% 177.68/28.19  |   (116)  op(e1, all_14_2) = all_14_0
% 177.68/28.19  | 
% 177.68/28.19  | REDUCE: (6), (56) imply:
% 177.68/28.19  |   (117)  op(e3, all_52_17) = e3
% 177.68/28.19  | 
% 177.68/28.19  | REDUCE: (28), (74) imply:
% 177.68/28.19  |   (118)  op(e2, all_52_19) = e2
% 177.68/28.19  | 
% 177.68/28.19  | REDUCE: (103), (107) imply:
% 177.68/28.19  |   (119)  op(e1, all_14_2) = e1
% 177.68/28.19  | 
% 177.68/28.19  | REDUCE: (61), (101) imply:
% 177.68/28.19  |   (120)  op(e0, all_52_23) = e0
% 177.68/28.19  | 
% 177.68/28.19  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 177.68/28.19  |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 177.68/28.19  |            (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.68/28.19  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.68/28.19  |            (49), (50), (51), (52), (53), (54), (55), (57), (58), (59), (60),
% 177.68/28.19  |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 177.68/28.19  |            (73), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 177.68/28.19  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 177.68/28.19  |            (96), (97), (98), (99), (100), (102), (104), (105), (106), (108),
% 177.68/28.19  |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 177.68/28.19  |            (118), (119), (120) are inconsistent by sub-proof #474.
% 177.68/28.19  | 
% 177.68/28.19  End of proof
% 177.68/28.19  
% 177.68/28.19  Sub-proof #474 shows that the following formulas are inconsistent:
% 177.68/28.19  ----------------------------------------------------------------
% 177.68/28.19    (1)   ~ (all_52_23 = all_14_2)
% 177.68/28.19    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.68/28.19    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.68/28.19    (4)   ~ (all_52_17 = all_52_23)
% 177.68/28.19    (5)  all_56_3 = all_52_7
% 177.68/28.19    (6)   ~ (all_52_9 = all_52_25)
% 177.68/28.19    (7)  op(e3, all_52_25) = all_52_24
% 177.68/28.19    (8)   ~ (all_52_27 = e0)
% 177.68/28.19    (9)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.68/28.19    (10)  op(e3, all_52_9) = all_52_8
% 177.68/28.19    (11)   ~ (all_52_23 = e0)
% 177.68/28.19    (12)  all_50_1 = all_4_1
% 177.68/28.19    (13)  all_58_5 = all_52_13
% 177.68/28.19    (14)   ~ (all_52_25 = all_52_29)
% 177.68/28.19    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.68/28.19    (16)  all_56_9 = all_52_19
% 177.68/28.19    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.19    (18)   ~ (all_52_9 = all_4_2)
% 177.68/28.19    (19)   ~ (all_52_5 = all_52_7)
% 177.68/28.19    (20)  all_58_10 = all_52_15
% 177.68/28.19    (21)   ~ (all_52_5 = all_4_2)
% 177.68/28.19    (22)  all_58_7 = all_52_19
% 177.68/28.19    (23)   ~ (all_52_17 = all_52_25)
% 177.68/28.19    (24)  all_58_4 = all_52_5
% 177.68/28.19    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.19    (26)   ~ (all_52_27 = all_52_29)
% 177.68/28.19    (27)   ~ (all_52_17 = all_14_2)
% 177.68/28.19    (28)  op(e3, all_4_2) = all_4_1
% 177.68/28.19    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.68/28.19    (30)   ~ (all_52_7 = all_4_2)
% 177.68/28.19    (31)  all_58_1 = all_52_3
% 177.68/28.19    (32)   ~ (all_52_13 = all_52_15)
% 177.68/28.19    (33)  all_58_0 = all_4_2
% 177.68/28.19    (34)  op(e1, all_52_29) = all_52_28
% 177.68/28.19    (35)   ~ (all_52_7 = e0)
% 177.68/28.19    (36)  all_50_2 = all_4_2
% 177.68/28.19    (37)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.68/28.19    (38)   ~ (all_4_1 = e2)
% 177.68/28.19    (39)  all_58_14 = all_52_29
% 177.68/28.19    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.68/28.19    (41)  all_26_2 = all_4_2
% 177.68/28.19    (42)   ~ (all_52_3 = all_52_5)
% 177.68/28.19    (43)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.19    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.68/28.19    (45)  all_58_8 = all_14_2
% 177.68/28.19    (46)   ~ (all_14_0 = e3)
% 177.68/28.19    (47)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.68/28.19    (48)   ~ (all_52_5 = all_14_2)
% 177.68/28.19    (49)   ~ (all_52_3 = all_52_27)
% 177.68/28.19    (50)   ~ (all_52_3 = all_4_2)
% 177.68/28.19    (51)  op(e0, e3) = all_52_25
% 177.68/28.19    (52)  op(all_4_1, all_4_2) = e2
% 177.68/28.19    (53)  op(e1, all_14_2) = all_14_0
% 177.68/28.19    (54)   ~ (e3 = e0)
% 177.68/28.19    (55)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.68/28.19    (56)   ~ (all_52_9 = all_52_13)
% 177.68/28.19    (57)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.19    (58)   ~ (all_52_15 = all_52_23)
% 177.68/28.19    (59)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.68/28.19    (60)   ~ (all_52_5 = all_52_29)
% 177.68/28.19    (61)  all_56_2 = all_52_5
% 177.68/28.19    (62)  all_56_12 = all_52_25
% 177.68/28.19    (63)  all_58_13 = all_52_27
% 177.68/28.19    (64)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.68/28.19    (65)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.68/28.19    (66)   ~ (all_52_25 = e0)
% 177.68/28.19    (67)   ~ (all_52_9 = all_52_17)
% 177.68/28.19    (68)   ~ (all_14_0 = e2)
% 177.68/28.19    (69)  all_58_6 = all_52_17
% 177.68/28.19    (70)  op(e2, all_52_19) = e2
% 177.68/28.19    (71)  op(e3, all_52_17) = e3
% 177.68/28.19    (72)   ~ (e1 = e0)
% 177.68/28.19    (73)  all_56_0 = all_4_2
% 177.68/28.19    (74)  all_58_11 = all_52_23
% 177.68/28.19    (75)   ~ (all_52_3 = all_52_19)
% 177.68/28.19    (76)  all_26_1 = all_4_1
% 177.68/28.19    (77)   ~ (all_52_29 = all_14_2)
% 177.68/28.19    (78)  all_58_15 = e0
% 177.68/28.19    (79)  all_58_2 = all_52_9
% 177.68/28.19    (80)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.68/28.19    (81)  op(e3, e1) = all_52_5
% 177.68/28.19    (82)  all_56_10 = all_14_2
% 177.68/28.19    (83)  op(e1, e3) = all_52_17
% 177.68/28.19    (84)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.68/28.19    (85)   ~ (all_52_25 = all_4_2)
% 177.68/28.19    (86)  op(e3, e0) = all_52_7
% 177.68/28.19    (87)  op(e3, e3) = all_4_2
% 177.68/28.19    (88)  all_56_8 = all_52_17
% 177.68/28.19    (89)   ~ (all_52_17 = all_4_2)
% 177.68/28.19    (90)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.68/28.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.68/28.19    (91)   ~ (all_52_25 = all_52_27)
% 177.68/28.19    (92)  op(e0, all_52_23) = e0
% 177.68/28.19    (93)   ~ (all_52_19 = all_52_27)
% 177.68/28.19    (94)  all_56_7 = all_52_15
% 177.68/28.19    (95)  op(e1, all_14_2) = e1
% 177.68/28.19    (96)   ~ (all_52_15 = e0)
% 177.68/28.19    (97)   ~ (all_52_7 = all_52_23)
% 177.68/28.19    (98)  op(e2, all_52_27) = all_52_26
% 177.68/28.19    (99)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.19    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.68/28.19    (101)  all_58_9 = all_52_7
% 177.68/28.19    (102)   ~ (e2 = e0)
% 177.68/28.19    (103)  all_58_12 = all_52_25
% 177.68/28.19    (104)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.68/28.19    (105)   ~ (all_52_9 = all_52_15)
% 177.68/28.19    (106)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.19    (107)   ~ (e3 = e2)
% 177.68/28.19    (108)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.68/28.19    (109)   ~ (all_52_19 = all_14_2)
% 177.68/28.19    (110)  op(e2, e3) = all_52_9
% 177.68/28.19    (111)  all_56_13 = all_52_27
% 177.68/28.19  
% 177.68/28.19  Begin of proof
% 177.68/28.19  | 
% 177.68/28.19  | GROUND_INST: instantiating (90) with e1, all_14_0, all_14_2, e1, simplifying
% 177.68/28.19  |              with (53), (95) gives:
% 177.68/28.19  |   (112)  all_14_0 = e1
% 177.68/28.19  | 
% 177.68/28.19  | REDUCE: (46), (112) imply:
% 177.68/28.19  |   (113)   ~ (e3 = e1)
% 177.68/28.19  | 
% 177.68/28.19  | SIMP: (113) implies:
% 177.68/28.19  |   (114)   ~ (e3 = e1)
% 177.68/28.19  | 
% 177.68/28.19  | REDUCE: (68), (112) imply:
% 177.68/28.19  |   (115)   ~ (e2 = e1)
% 177.68/28.19  | 
% 177.68/28.19  | SIMP: (115) implies:
% 177.68/28.19  |   (116)   ~ (e2 = e1)
% 177.68/28.19  | 
% 177.68/28.19  | BETA: splitting (40) gives:
% 177.68/28.19  | 
% 177.68/28.19  | Case 1:
% 177.68/28.19  | | 
% 177.68/28.19  | |   (117)  all_56_13 = e3
% 177.68/28.19  | | 
% 177.68/28.19  | | COMBINE_EQS: (111), (117) imply:
% 177.68/28.19  | |   (118)  all_52_27 = e3
% 177.68/28.19  | | 
% 177.68/28.19  | | SIMP: (118) implies:
% 177.68/28.19  | |   (119)  all_52_27 = e3
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (49), (119) imply:
% 177.68/28.19  | |   (120)   ~ (all_52_3 = e3)
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (93), (119) imply:
% 177.68/28.19  | |   (121)   ~ (all_52_19 = e3)
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (91), (119) imply:
% 177.68/28.19  | |   (122)   ~ (all_52_25 = e3)
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (26), (119) imply:
% 177.68/28.19  | |   (123)   ~ (all_52_29 = e3)
% 177.68/28.19  | | 
% 177.68/28.19  | | SIMP: (123) implies:
% 177.68/28.19  | |   (124)   ~ (all_52_29 = e3)
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (98), (119) imply:
% 177.68/28.19  | |   (125)  op(e2, e3) = all_52_26
% 177.68/28.19  | | 
% 177.68/28.19  | | GROUND_INST: instantiating (90) with all_52_9, all_52_26, e3, e2,
% 177.68/28.19  | |              simplifying with (110), (125) gives:
% 177.68/28.19  | |   (126)  all_52_9 = all_52_26
% 177.68/28.19  | | 
% 177.68/28.19  | | COMBINE_EQS: (79), (126) imply:
% 177.68/28.19  | |   (127)  all_58_2 = all_52_26
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (56), (126) imply:
% 177.68/28.19  | |   (128)   ~ (all_52_13 = all_52_26)
% 177.68/28.19  | | 
% 177.68/28.19  | | SIMP: (128) implies:
% 177.68/28.19  | |   (129)   ~ (all_52_13 = all_52_26)
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (105), (126) imply:
% 177.68/28.19  | |   (130)   ~ (all_52_15 = all_52_26)
% 177.68/28.19  | | 
% 177.68/28.19  | | SIMP: (130) implies:
% 177.68/28.19  | |   (131)   ~ (all_52_15 = all_52_26)
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (67), (126) imply:
% 177.68/28.19  | |   (132)   ~ (all_52_17 = all_52_26)
% 177.68/28.19  | | 
% 177.68/28.19  | | SIMP: (132) implies:
% 177.68/28.19  | |   (133)   ~ (all_52_17 = all_52_26)
% 177.68/28.19  | | 
% 177.68/28.19  | | BETA: splitting (57) gives:
% 177.68/28.19  | | 
% 177.68/28.19  | | Case 1:
% 177.68/28.19  | | | 
% 177.68/28.19  | | |   (134)  all_56_12 = e3
% 177.68/28.19  | | | 
% 177.68/28.19  | | | REF_CLOSE: (62), (122), (134) are inconsistent by sub-proof #1040.
% 177.68/28.19  | | | 
% 177.68/28.19  | | Case 2:
% 177.68/28.19  | | | 
% 177.68/28.19  | | |   (135)   ~ (all_56_12 = e3)
% 177.68/28.19  | | |   (136)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.68/28.19  | | | 
% 177.68/28.19  | | | BETA: splitting (80) gives:
% 177.68/28.19  | | | 
% 177.68/28.19  | | | Case 1:
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | |   (137)  all_58_12 = e1
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | COMBINE_EQS: (103), (137) imply:
% 177.68/28.19  | | | |   (138)  all_52_25 = e1
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | SIMP: (138) implies:
% 177.68/28.19  | | | |   (139)  all_52_25 = e1
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | REDUCE: (7), (139) imply:
% 177.68/28.19  | | | |   (140)  op(e3, e1) = all_52_24
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | REDUCE: (51), (139) imply:
% 177.68/28.19  | | | |   (141)  op(e0, e3) = e1
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | GROUND_INST: instantiating (90) with all_52_5, all_52_24, e1, e3,
% 177.68/28.19  | | | |              simplifying with (81), (140) gives:
% 177.68/28.19  | | | |   (142)  all_52_5 = all_52_24
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | COMBINE_EQS: (24), (142) imply:
% 177.68/28.19  | | | |   (143)  all_58_4 = all_52_24
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | REDUCE: (19), (142) imply:
% 177.68/28.19  | | | |   (144)   ~ (all_52_7 = all_52_24)
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | SIMP: (144) implies:
% 177.68/28.19  | | | |   (145)   ~ (all_52_7 = all_52_24)
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | BETA: splitting (2) gives:
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | Case 1:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | |   (146)  all_56_8 = e3
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | COMBINE_EQS: (88), (146) imply:
% 177.68/28.19  | | | | |   (147)  all_52_17 = e3
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REF_CLOSE: (71), (87), (89), (90), (147) are inconsistent by sub-proof
% 177.68/28.19  | | | | |            #948.
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | Case 2:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | |   (148)   ~ (all_56_8 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REDUCE: (88), (148) imply:
% 177.68/28.19  | | | | |   (149)   ~ (all_52_17 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | BETA: splitting (43) gives:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | Case 1:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | |   (150)  all_58_0 = e3
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | REF_CLOSE: (28), (33), (38), (52), (87), (90), (150) are
% 177.68/28.19  | | | | | |            inconsistent by sub-proof #489.
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | Case 2:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | |   (151)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | BETA: splitting (151) gives:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | Case 1:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | |   (152)  all_58_2 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | COMBINE_EQS: (127), (152) imply:
% 177.68/28.19  | | | | | | |   (153)  all_52_26 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | SIMP: (153) implies:
% 177.68/28.19  | | | | | | |   (154)  all_52_26 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REDUCE: (129), (154) imply:
% 177.68/28.19  | | | | | | |   (155)   ~ (all_52_13 = e3)
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REDUCE: (131), (154) imply:
% 177.68/28.19  | | | | | | |   (156)   ~ (all_52_15 = e3)
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | BETA: splitting (106) gives:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | Case 1:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | |   (157)  all_58_4 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | COMBINE_EQS: (143), (157) imply:
% 177.68/28.19  | | | | | | | |   (158)  all_52_24 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | SIMP: (158) implies:
% 177.68/28.19  | | | | | | | |   (159)  all_52_24 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | REDUCE: (145), (159) imply:
% 177.68/28.19  | | | | | | | |   (160)   ~ (all_52_7 = e3)
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | REF_CLOSE: (20), (54), (72), (74), (78), (90), (92), (99),
% 177.68/28.19  | | | | | | | |            (101), (141), (156), (160) are inconsistent by
% 177.68/28.19  | | | | | | | |            sub-proof #941.
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | Case 2:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | |   (161)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | REF_CLOSE: (1), (13), (22), (25), (27), (39), (45), (48), (69),
% 177.68/28.19  | | | | | | | |            (71), (74), (81), (83), (90), (95), (109), (124),
% 177.68/28.19  | | | | | | | |            (155), (161) are inconsistent by sub-proof #484.
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | End of split
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | Case 2:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | |   (162)  all_58_6 = e3 | all_58_12 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REF_CLOSE: (69), (103), (122), (149), (162) are inconsistent by
% 177.68/28.19  | | | | | | |            sub-proof #483.
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | End of split
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | End of split
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | End of split
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | Case 2:
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | |   (163)   ~ (all_58_12 = e1)
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | REDUCE: (103), (163) imply:
% 177.68/28.19  | | | |   (164)   ~ (all_52_25 = e1)
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | BETA: splitting (136) gives:
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | Case 1:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | |   (165)  all_56_12 = e2
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | COMBINE_EQS: (62), (165) imply:
% 177.68/28.19  | | | | |   (166)  all_52_25 = e2
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | SIMP: (166) implies:
% 177.68/28.19  | | | | |   (167)  all_52_25 = e2
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REDUCE: (122), (167) imply:
% 177.68/28.19  | | | | |   (168)   ~ (e3 = e2)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REDUCE: (51), (167) imply:
% 177.68/28.19  | | | | |   (169)  op(e0, e3) = e2
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | BETA: splitting (108) gives:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | Case 1:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | |   (170)  all_56_2 = e3
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | COMBINE_EQS: (61), (170) imply:
% 177.68/28.19  | | | | | |   (171)  all_52_5 = e3
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | SIMP: (171) implies:
% 177.68/28.19  | | | | | |   (172)  all_52_5 = e3
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | REDUCE: (48), (172) imply:
% 177.68/28.19  | | | | | |   (173)   ~ (all_14_2 = e3)
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | SIMP: (173) implies:
% 177.68/28.19  | | | | | |   (174)   ~ (all_14_2 = e3)
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | REDUCE: (21), (172) imply:
% 177.68/28.19  | | | | | |   (175)   ~ (all_4_2 = e3)
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | SIMP: (175) implies:
% 177.68/28.19  | | | | | |   (176)   ~ (all_4_2 = e3)
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | BETA: splitting (43) gives:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | Case 1:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | |   (177)  all_58_0 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | COMBINE_EQS: (33), (177) imply:
% 177.68/28.19  | | | | | | |   (178)  all_4_2 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REDUCE: (176), (178) imply:
% 177.68/28.19  | | | | | | |   (179)  $false
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | CLOSE: (179) is inconsistent.
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | Case 2:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | |   (180)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | BETA: splitting (29) gives:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | Case 1:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | |   (181)  all_58_2 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | COMBINE_EQS: (127), (181) imply:
% 177.68/28.19  | | | | | | | |   (182)  all_52_26 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | SIMP: (182) implies:
% 177.68/28.19  | | | | | | | |   (183)  all_52_26 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | REDUCE: (133), (183) imply:
% 177.68/28.19  | | | | | | | |   (184)   ~ (all_52_17 = e3)
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | BETA: splitting (25) gives:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | Case 1:
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | |   (185)  all_58_6 = e3
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | | REF_CLOSE: (69), (184), (185) are inconsistent by sub-proof
% 177.68/28.19  | | | | | | | | |            #981.
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | Case 2:
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | |   (186)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | | REF_CLOSE: (22), (45), (74), (90), (92), (102), (121), (169),
% 177.68/28.19  | | | | | | | | |            (174), (186) are inconsistent by sub-proof #900.
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | End of split
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | Case 2:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | |   (187)   ~ (all_58_2 = e3)
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | REDUCE: (127), (187) imply:
% 177.68/28.19  | | | | | | | |   (188)   ~ (all_52_26 = e3)
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | REF_CLOSE: (69), (71), (87), (89), (90), (103), (122), (127),
% 177.68/28.19  | | | | | | | |            (180), (188) are inconsistent by sub-proof #567.
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | End of split
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | End of split
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | Case 2:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | |   (189)   ~ (all_56_2 = e3)
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | REDUCE: (61), (189) imply:
% 177.68/28.19  | | | | | |   (190)   ~ (all_52_5 = e3)
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | BETA: splitting (104) gives:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | Case 1:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | |   (191)  all_58_0 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REF_CLOSE: (28), (33), (38), (52), (87), (90), (191) are
% 177.68/28.19  | | | | | | |            inconsistent by sub-proof #489.
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | Case 2:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | |   (192)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REF_CLOSE: (16), (22), (24), (25), (29), (30), (31), (33), (37),
% 177.68/28.19  | | | | | | |            (43), (45), (48), (67), (69), (70), (71), (74), (79),
% 177.68/28.19  | | | | | | |            (81), (83), (87), (89), (90), (95), (97), (101), (103),
% 177.68/28.19  | | | | | | |            (107), (110), (120), (122), (190), (192) are
% 177.68/28.19  | | | | | | |            inconsistent by sub-proof #564.
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | End of split
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | End of split
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | Case 2:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | |   (193)  all_56_12 = e1 | all_56_12 = e0
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REF_CLOSE: (62), (66), (164), (193) are inconsistent by sub-proof
% 177.68/28.19  | | | | |            #1029.
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | End of split
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | End of split
% 177.68/28.19  | | | 
% 177.68/28.19  | | End of split
% 177.68/28.19  | | 
% 177.68/28.19  | Case 2:
% 177.68/28.19  | | 
% 177.68/28.19  | |   (194)   ~ (all_56_13 = e3)
% 177.68/28.19  | | 
% 177.68/28.19  | | REDUCE: (111), (194) imply:
% 177.68/28.19  | |   (195)   ~ (all_52_27 = e3)
% 177.68/28.19  | | 
% 177.68/28.19  | | BETA: splitting (44) gives:
% 177.68/28.19  | | 
% 177.68/28.19  | | Case 1:
% 177.68/28.19  | | | 
% 177.68/28.19  | | |   (196)  all_58_12 = e3
% 177.68/28.19  | | | 
% 177.68/28.19  | | | COMBINE_EQS: (103), (196) imply:
% 177.68/28.19  | | |   (197)  all_52_25 = e3
% 177.68/28.19  | | | 
% 177.68/28.19  | | | SIMP: (197) implies:
% 177.68/28.19  | | |   (198)  all_52_25 = e3
% 177.68/28.19  | | | 
% 177.68/28.19  | | | REDUCE: (23), (198) imply:
% 177.68/28.19  | | |   (199)   ~ (all_52_17 = e3)
% 177.68/28.19  | | | 
% 177.68/28.19  | | | REDUCE: (14), (198) imply:
% 177.68/28.19  | | |   (200)   ~ (all_52_29 = e3)
% 177.68/28.19  | | | 
% 177.68/28.19  | | | SIMP: (200) implies:
% 177.68/28.19  | | |   (201)   ~ (all_52_29 = e3)
% 177.68/28.19  | | | 
% 177.68/28.19  | | | REDUCE: (51), (198) imply:
% 177.68/28.19  | | |   (202)  op(e0, e3) = e3
% 177.68/28.19  | | | 
% 177.68/28.19  | | | BETA: splitting (84) gives:
% 177.68/28.19  | | | 
% 177.68/28.19  | | | Case 1:
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | |   (203)  all_56_7 = e3
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | COMBINE_EQS: (94), (203) imply:
% 177.68/28.19  | | | |   (204)  all_52_15 = e3
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | SIMP: (204) implies:
% 177.68/28.19  | | | |   (205)  all_52_15 = e3
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | REDUCE: (32), (205) imply:
% 177.68/28.19  | | | |   (206)   ~ (all_52_13 = e3)
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | REDUCE: (58), (205) imply:
% 177.68/28.19  | | | |   (207)   ~ (all_52_23 = e3)
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | SIMP: (207) implies:
% 177.68/28.19  | | | |   (208)   ~ (all_52_23 = e3)
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | BETA: splitting (106) gives:
% 177.68/28.19  | | | | 
% 177.68/28.19  | | | | Case 1:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | |   (209)  all_58_4 = e3
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | COMBINE_EQS: (24), (209) imply:
% 177.68/28.19  | | | | |   (210)  all_52_5 = e3
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | SIMP: (210) implies:
% 177.68/28.19  | | | | |   (211)  all_52_5 = e3
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REDUCE: (19), (211) imply:
% 177.68/28.19  | | | | |   (212)   ~ (all_52_7 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | SIMP: (212) implies:
% 177.68/28.19  | | | | |   (213)   ~ (all_52_7 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REDUCE: (48), (211) imply:
% 177.68/28.19  | | | | |   (214)   ~ (all_14_2 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | SIMP: (214) implies:
% 177.68/28.19  | | | | |   (215)   ~ (all_14_2 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | REDUCE: (21), (211) imply:
% 177.68/28.19  | | | | |   (216)   ~ (all_4_2 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | SIMP: (216) implies:
% 177.68/28.19  | | | | |   (217)   ~ (all_4_2 = e3)
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | BETA: splitting (25) gives:
% 177.68/28.19  | | | | | 
% 177.68/28.19  | | | | | Case 1:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | |   (218)  all_58_6 = e3
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | REF_CLOSE: (69), (199), (218) are inconsistent by sub-proof #981.
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | Case 2:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | |   (219)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | BETA: splitting (219) gives:
% 177.68/28.19  | | | | | | 
% 177.68/28.19  | | | | | | Case 1:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | |   (220)  all_58_7 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | COMBINE_EQS: (22), (220) imply:
% 177.68/28.19  | | | | | | |   (221)  all_52_19 = e3
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REDUCE: (70), (221) imply:
% 177.68/28.19  | | | | | | |   (222)  op(e2, e3) = e2
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | GROUND_INST: instantiating (90) with all_52_9, e2, e3, e2,
% 177.68/28.19  | | | | | | |              simplifying with (110), (222) gives:
% 177.68/28.19  | | | | | | |   (223)  all_52_9 = e2
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | COMBINE_EQS: (79), (223) imply:
% 177.68/28.19  | | | | | | |   (224)  all_58_2 = e2
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | REDUCE: (18), (223) imply:
% 177.68/28.19  | | | | | | |   (225)   ~ (all_4_2 = e2)
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | SIMP: (225) implies:
% 177.68/28.19  | | | | | | |   (226)   ~ (all_4_2 = e2)
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | BETA: splitting (17) gives:
% 177.68/28.19  | | | | | | | 
% 177.68/28.19  | | | | | | | Case 1:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | |   (227)  all_56_0 = e3
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | REF_CLOSE: (73), (217), (227) are inconsistent by sub-proof
% 177.68/28.19  | | | | | | | |            #1024.
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | Case 2:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | |   (228)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | BETA: splitting (65) gives:
% 177.68/28.19  | | | | | | | | 
% 177.68/28.19  | | | | | | | | Case 1:
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | |   (229)  all_58_0 = e1
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | | REF_CLOSE: (54), (55), (69), (71), (72), (86), (90), (102),
% 177.68/28.19  | | | | | | | | |            (196), (213), (224), (229) are inconsistent by
% 177.68/28.19  | | | | | | | | |            sub-proof #681.
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | Case 2:
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | |   (230)   ~ (all_58_0 = e1)
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.19  | | | | | | | | | REDUCE: (33), (230) imply:
% 177.68/28.19  | | | | | | | | |   (231)   ~ (all_4_2 = e1)
% 177.68/28.19  | | | | | | | | | 
% 177.68/28.20  | | | | | | | | | REF_CLOSE: (5), (28), (30), (38), (41), (52), (64), (73),
% 177.68/28.20  | | | | | | | | |            (76), (86), (90), (100), (226), (228), (231) are
% 177.68/28.20  | | | | | | | | |            inconsistent by sub-proof #482.
% 177.68/28.20  | | | | | | | | | 
% 177.68/28.20  | | | | | | | | End of split
% 177.68/28.20  | | | | | | | | 
% 177.68/28.20  | | | | | | | End of split
% 177.68/28.20  | | | | | | | 
% 177.68/28.20  | | | | | | Case 2:
% 177.68/28.20  | | | | | | | 
% 177.68/28.20  | | | | | | |   (232)  all_58_8 = e3 | all_58_11 = e3
% 177.68/28.20  | | | | | | | 
% 177.68/28.20  | | | | | | | REF_CLOSE: (45), (74), (208), (215), (232) are inconsistent by
% 177.68/28.20  | | | | | | |            sub-proof #997.
% 177.68/28.20  | | | | | | | 
% 177.68/28.20  | | | | | | End of split
% 177.68/28.20  | | | | | | 
% 177.68/28.20  | | | | | End of split
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | Case 2:
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | |   (233)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | REF_CLOSE: (1), (13), (22), (25), (27), (39), (45), (48), (69), (71),
% 177.68/28.20  | | | | |            (74), (81), (83), (90), (95), (109), (201), (206), (233)
% 177.68/28.20  | | | | |            are inconsistent by sub-proof #484.
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | End of split
% 177.68/28.20  | | | | 
% 177.68/28.20  | | | Case 2:
% 177.68/28.20  | | | | 
% 177.68/28.20  | | | |   (234)   ~ (all_56_7 = e3)
% 177.68/28.20  | | | | 
% 177.68/28.20  | | | | REDUCE: (94), (234) imply:
% 177.68/28.20  | | | |   (235)   ~ (all_52_15 = e3)
% 177.68/28.20  | | | | 
% 177.68/28.20  | | | | BETA: splitting (99) gives:
% 177.68/28.20  | | | | 
% 177.68/28.20  | | | | Case 1:
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | |   (236)  all_58_9 = e3
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | COMBINE_EQS: (101), (236) imply:
% 177.68/28.20  | | | | |   (237)  all_52_7 = e3
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | SIMP: (237) implies:
% 177.68/28.20  | | | | |   (238)  all_52_7 = e3
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | REDUCE: (19), (238) imply:
% 177.68/28.20  | | | | |   (239)   ~ (all_52_5 = e3)
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | REDUCE: (97), (238) imply:
% 177.68/28.20  | | | | |   (240)   ~ (all_52_23 = e3)
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | SIMP: (240) implies:
% 177.68/28.20  | | | | |   (241)   ~ (all_52_23 = e3)
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | REF_CLOSE: (1), (3), (9), (12), (22), (24), (25), (28), (31), (33),
% 177.68/28.20  | | | | |            (36), (38), (45), (47), (48), (54), (59), (65), (69), (70),
% 177.68/28.20  | | | | |            (71), (72), (74), (79), (81), (82), (83), (90), (95),
% 177.68/28.20  | | | | |            (102), (107), (109), (110), (114), (116), (196), (199),
% 177.68/28.20  | | | | |            (236), (239), (241) are inconsistent by sub-proof #479.
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | Case 2:
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | |   (242)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | BETA: splitting (242) gives:
% 177.68/28.20  | | | | | 
% 177.68/28.20  | | | | | Case 1:
% 177.68/28.20  | | | | | | 
% 177.68/28.20  | | | | | |   (243)  all_58_10 = e3
% 177.68/28.20  | | | | | | 
% 177.68/28.20  | | | | | | REF_CLOSE: (20), (235), (243) are inconsistent by sub-proof #1018.
% 177.68/28.20  | | | | | | 
% 177.68/28.20  | | | | | Case 2:
% 177.68/28.20  | | | | | | 
% 177.74/28.20  | | | | | |   (244)  all_58_11 = e3 | all_58_15 = e3
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | | REF_CLOSE: (11), (54), (74), (78), (90), (92), (202), (244) are
% 177.74/28.20  | | | | | |            inconsistent by sub-proof #915.
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | End of split
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | End of split
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | End of split
% 177.74/28.20  | | | 
% 177.74/28.20  | | Case 2:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (245)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.20  | | | 
% 177.74/28.20  | | | BETA: splitting (245) gives:
% 177.74/28.20  | | | 
% 177.74/28.20  | | | Case 1:
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | |   (246)  all_58_13 = e3
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | REF_CLOSE: (63), (195), (246) are inconsistent by sub-proof #1026.
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | Case 2:
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | |   (247)  all_58_14 = e3 | all_58_15 = e3
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | BETA: splitting (247) gives:
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | Case 1:
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | |   (248)  all_58_14 = e3
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | REF_CLOSE: (2), (4), (6), (9), (10), (12), (14), (15), (16), (17),
% 177.74/28.20  | | | | |            (18), (21), (22), (23), (24), (25), (28), (29), (30), (31),
% 177.74/28.20  | | | | |            (33), (34), (36), (37), (38), (39), (42), (43), (45), (48),
% 177.74/28.20  | | | | |            (50), (51), (52), (60), (61), (65), (67), (69), (70), (71),
% 177.74/28.20  | | | | |            (73), (74), (75), (77), (79), (81), (83), (85), (87), (88),
% 177.74/28.20  | | | | |            (89), (90), (92), (95), (97), (101), (103), (104), (107),
% 177.74/28.20  | | | | |            (108), (110), (248) are inconsistent by sub-proof #475.
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | Case 2:
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | |   (249)  all_58_15 = e3
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | REF_CLOSE: (54), (78), (249) are inconsistent by sub-proof #1010.
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | End of split
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | End of split
% 177.74/28.20  | | | 
% 177.74/28.20  | | End of split
% 177.74/28.20  | | 
% 177.74/28.20  | End of split
% 177.74/28.20  | 
% 177.74/28.20  End of proof
% 177.74/28.20  
% 177.74/28.20  Sub-proof #475 shows that the following formulas are inconsistent:
% 177.74/28.20  ----------------------------------------------------------------
% 177.74/28.20    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.74/28.20    (2)   ~ (all_52_17 = all_52_23)
% 177.74/28.20    (3)   ~ (all_52_9 = all_52_25)
% 177.74/28.20    (4)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.74/28.20    (5)  op(e3, all_52_9) = all_52_8
% 177.74/28.20    (6)  all_50_1 = all_4_1
% 177.74/28.20    (7)   ~ (all_52_25 = all_52_29)
% 177.74/28.20    (8)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.74/28.20    (9)  all_56_9 = all_52_19
% 177.74/28.20    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.20    (11)   ~ (all_52_9 = all_4_2)
% 177.74/28.20    (12)   ~ (all_52_5 = all_4_2)
% 177.74/28.20    (13)  all_58_7 = all_52_19
% 177.74/28.20    (14)   ~ (all_52_17 = all_52_25)
% 177.74/28.20    (15)  all_58_4 = all_52_5
% 177.74/28.20    (16)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.20    (17)  op(e3, all_4_2) = all_4_1
% 177.74/28.20    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.20    (19)   ~ (all_52_7 = all_4_2)
% 177.74/28.20    (20)  all_58_1 = all_52_3
% 177.74/28.20    (21)  all_58_0 = all_4_2
% 177.74/28.20    (22)  op(e1, all_52_29) = all_52_28
% 177.74/28.20    (23)  all_50_2 = all_4_2
% 177.74/28.20    (24)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.74/28.20    (25)   ~ (all_4_1 = e2)
% 177.74/28.20    (26)  all_58_14 = all_52_29
% 177.74/28.20    (27)   ~ (all_52_3 = all_52_5)
% 177.74/28.20    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.20    (29)  all_58_8 = all_14_2
% 177.74/28.20    (30)   ~ (all_52_5 = all_14_2)
% 177.74/28.20    (31)   ~ (all_52_3 = all_4_2)
% 177.74/28.20    (32)  op(e0, e3) = all_52_25
% 177.74/28.20    (33)  op(all_4_1, all_4_2) = e2
% 177.74/28.20    (34)   ~ (all_52_5 = all_52_29)
% 177.74/28.20    (35)  all_56_2 = all_52_5
% 177.74/28.20    (36)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.20    (37)   ~ (all_52_9 = all_52_17)
% 177.74/28.20    (38)  all_58_6 = all_52_17
% 177.74/28.20    (39)  op(e2, all_52_19) = e2
% 177.74/28.20    (40)  op(e3, all_52_17) = e3
% 177.74/28.20    (41)  all_56_0 = all_4_2
% 177.74/28.20    (42)  all_58_11 = all_52_23
% 177.74/28.20    (43)   ~ (all_52_3 = all_52_19)
% 177.74/28.20    (44)   ~ (all_52_29 = all_14_2)
% 177.74/28.20    (45)  all_58_2 = all_52_9
% 177.74/28.20    (46)  op(e3, e1) = all_52_5
% 177.74/28.20    (47)  op(e1, e3) = all_52_17
% 177.74/28.20    (48)   ~ (all_52_25 = all_4_2)
% 177.74/28.20    (49)  op(e3, e3) = all_4_2
% 177.74/28.20    (50)  all_56_8 = all_52_17
% 177.74/28.20    (51)   ~ (all_52_17 = all_4_2)
% 177.74/28.20    (52)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.20    (53)  op(e0, all_52_23) = e0
% 177.74/28.20    (54)  all_58_14 = e3
% 177.74/28.20    (55)  op(e1, all_14_2) = e1
% 177.74/28.20    (56)   ~ (all_52_7 = all_52_23)
% 177.74/28.20    (57)  all_58_9 = all_52_7
% 177.74/28.20    (58)  all_58_12 = all_52_25
% 177.74/28.20    (59)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.20    (60)   ~ (e3 = e2)
% 177.74/28.20    (61)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.20    (62)  op(e2, e3) = all_52_9
% 177.74/28.20  
% 177.74/28.20  Begin of proof
% 177.74/28.20  | 
% 177.74/28.20  | COMBINE_EQS: (26), (54) imply:
% 177.74/28.20  |   (63)  all_52_29 = e3
% 177.74/28.20  | 
% 177.74/28.20  | SIMP: (63) implies:
% 177.74/28.20  |   (64)  all_52_29 = e3
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (34), (64) imply:
% 177.74/28.20  |   (65)   ~ (all_52_5 = e3)
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (7), (64) imply:
% 177.74/28.20  |   (66)   ~ (all_52_25 = e3)
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (44), (64) imply:
% 177.74/28.20  |   (67)   ~ (all_14_2 = e3)
% 177.74/28.20  | 
% 177.74/28.20  | SIMP: (67) implies:
% 177.74/28.20  |   (68)   ~ (all_14_2 = e3)
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (22), (64) imply:
% 177.74/28.20  |   (69)  op(e1, e3) = all_52_28
% 177.74/28.20  | 
% 177.74/28.20  | GROUND_INST: instantiating (52) with all_52_17, all_52_28, e3, e1, simplifying
% 177.74/28.20  |              with (47), (69) gives:
% 177.74/28.20  |   (70)  all_52_17 = all_52_28
% 177.74/28.20  | 
% 177.74/28.20  | COMBINE_EQS: (50), (70) imply:
% 177.74/28.20  |   (71)  all_56_8 = all_52_28
% 177.74/28.20  | 
% 177.74/28.20  | COMBINE_EQS: (38), (70) imply:
% 177.74/28.20  |   (72)  all_58_6 = all_52_28
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (37), (70) imply:
% 177.74/28.20  |   (73)   ~ (all_52_9 = all_52_28)
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (2), (70) imply:
% 177.74/28.20  |   (74)   ~ (all_52_23 = all_52_28)
% 177.74/28.20  | 
% 177.74/28.20  | SIMP: (74) implies:
% 177.74/28.20  |   (75)   ~ (all_52_23 = all_52_28)
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (14), (70) imply:
% 177.74/28.20  |   (76)   ~ (all_52_25 = all_52_28)
% 177.74/28.20  | 
% 177.74/28.20  | SIMP: (76) implies:
% 177.74/28.20  |   (77)   ~ (all_52_25 = all_52_28)
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (51), (70) imply:
% 177.74/28.20  |   (78)   ~ (all_52_28 = all_4_2)
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (40), (70) imply:
% 177.74/28.20  |   (79)  op(e3, all_52_28) = e3
% 177.74/28.20  | 
% 177.74/28.20  | BETA: splitting (61) gives:
% 177.74/28.20  | 
% 177.74/28.20  | Case 1:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (80)  all_56_2 = e3
% 177.74/28.20  | | 
% 177.74/28.20  | | COMBINE_EQS: (35), (80) imply:
% 177.74/28.20  | |   (81)  all_52_5 = e3
% 177.74/28.20  | | 
% 177.74/28.20  | | REDUCE: (65), (81) imply:
% 177.74/28.20  | |   (82)  $false
% 177.74/28.20  | | 
% 177.74/28.20  | | CLOSE: (82) is inconsistent.
% 177.74/28.20  | | 
% 177.74/28.20  | Case 2:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (83)   ~ (all_56_2 = e3)
% 177.74/28.20  | |   (84)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.20  | | 
% 177.74/28.20  | | BETA: splitting (18) gives:
% 177.74/28.20  | | 
% 177.74/28.20  | | Case 1:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (85)  all_58_2 = e3
% 177.74/28.20  | | | 
% 177.74/28.20  | | | COMBINE_EQS: (45), (85) imply:
% 177.74/28.20  | | |   (86)  all_52_9 = e3
% 177.74/28.20  | | | 
% 177.74/28.20  | | | SIMP: (86) implies:
% 177.74/28.20  | | |   (87)  all_52_9 = e3
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (3), (87) imply:
% 177.74/28.20  | | |   (88)   ~ (all_52_25 = e3)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (73), (87) imply:
% 177.74/28.20  | | |   (89)   ~ (all_52_28 = e3)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | SIMP: (89) implies:
% 177.74/28.20  | | |   (90)   ~ (all_52_28 = e3)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (11), (87) imply:
% 177.74/28.20  | | |   (91)   ~ (all_4_2 = e3)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | SIMP: (91) implies:
% 177.74/28.20  | | |   (92)   ~ (all_4_2 = e3)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (5), (87) imply:
% 177.74/28.20  | | |   (93)  op(e3, e3) = all_52_8
% 177.74/28.20  | | | 
% 177.74/28.20  | | | GROUND_INST: instantiating (52) with all_4_2, all_52_8, e3, e3,
% 177.74/28.20  | | |              simplifying with (49), (93) gives:
% 177.74/28.20  | | |   (94)  all_52_8 = all_4_2
% 177.74/28.20  | | | 
% 177.74/28.20  | | | BETA: splitting (59) gives:
% 177.74/28.20  | | | 
% 177.74/28.20  | | | Case 1:
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | |   (95)  all_58_0 = e3
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | COMBINE_EQS: (21), (95) imply:
% 177.74/28.20  | | | |   (96)  all_4_2 = e3
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | REDUCE: (92), (96) imply:
% 177.74/28.20  | | | |   (97)  $false
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | CLOSE: (97) is inconsistent.
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | Case 2:
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | |   (98)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | BETA: splitting (98) gives:
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | | Case 1:
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | |   (99)  all_58_1 = e3
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | COMBINE_EQS: (20), (99) imply:
% 177.74/28.20  | | | | |   (100)  all_52_3 = e3
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | REDUCE: (27), (100) imply:
% 177.74/28.20  | | | | |   (101)   ~ (all_52_5 = e3)
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | REDUCE: (43), (100) imply:
% 177.74/28.20  | | | | |   (102)   ~ (all_52_19 = e3)
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | SIMP: (102) implies:
% 177.74/28.20  | | | | |   (103)   ~ (all_52_19 = e3)
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | BETA: splitting (16) gives:
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | Case 1:
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | |   (104)  all_58_6 = e3
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | | REF_CLOSE: (72), (90), (104) are inconsistent by sub-proof #790.
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | Case 2:
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | |   (105)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | | BETA: splitting (105) gives:
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | | Case 1:
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | |   (106)  all_58_7 = e3
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | | COMBINE_EQS: (13), (106) imply:
% 177.74/28.20  | | | | | | |   (107)  all_52_19 = e3
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | | REDUCE: (103), (107) imply:
% 177.74/28.20  | | | | | | |   (108)  $false
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | | CLOSE: (108) is inconsistent.
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | Case 2:
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | |   (109)  all_58_8 = e3 | all_58_11 = e3
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | | BETA: splitting (109) gives:
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | | Case 1:
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | |   (110)  all_58_8 = e3
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | COMBINE_EQS: (29), (110) imply:
% 177.74/28.20  | | | | | | | |   (111)  all_14_2 = e3
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | REDUCE: (68), (111) imply:
% 177.74/28.20  | | | | | | | |   (112)  $false
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | CLOSE: (112) is inconsistent.
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | Case 2:
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | |   (113)  all_58_11 = e3
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | COMBINE_EQS: (42), (113) imply:
% 177.74/28.20  | | | | | | | |   (114)  all_52_23 = e3
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | SIMP: (114) implies:
% 177.74/28.20  | | | | | | | |   (115)  all_52_23 = e3
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | REDUCE: (53), (115) imply:
% 177.74/28.20  | | | | | | | |   (116)  op(e0, e3) = e0
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | GROUND_INST: instantiating (52) with all_52_25, e0, e3, e0,
% 177.74/28.20  | | | | | | | |              simplifying with (32), (116) gives:
% 177.74/28.20  | | | | | | | |   (117)  all_52_25 = e0
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | REDUCE: (77), (117) imply:
% 177.74/28.20  | | | | | | | |   (118)   ~ (all_52_28 = e0)
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | SIMP: (118) implies:
% 177.74/28.20  | | | | | | | |   (119)   ~ (all_52_28 = e0)
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | REDUCE: (48), (117) imply:
% 177.74/28.20  | | | | | | | |   (120)   ~ (all_4_2 = e0)
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | SIMP: (120) implies:
% 177.74/28.20  | | | | | | | |   (121)   ~ (all_4_2 = e0)
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | BETA: splitting (10) gives:
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | | Case 1:
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | |   (122)  all_56_0 = e3
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | COMBINE_EQS: (41), (122) imply:
% 177.74/28.20  | | | | | | | | |   (123)  all_4_2 = e3
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | REDUCE: (92), (123) imply:
% 177.74/28.20  | | | | | | | | |   (124)  $false
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | CLOSE: (124) is inconsistent.
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | Case 2:
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | |   (125)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | BETA: splitting (1) gives:
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | Case 1:
% 177.74/28.20  | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | |   (126)  all_56_8 = e3
% 177.74/28.20  | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | REF_CLOSE: (71), (90), (126) are inconsistent by sub-proof
% 177.74/28.20  | | | | | | | | | |            #676.
% 177.74/28.20  | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | Case 2:
% 177.74/28.20  | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | |   (127)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.74/28.20  | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | BETA: splitting (8) gives:
% 177.74/28.20  | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | Case 1:
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | |   (128)  all_58_0 = e2
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | | COMBINE_EQS: (21), (128) imply:
% 177.74/28.20  | | | | | | | | | | |   (129)  all_4_2 = e2
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | | REDUCE: (78), (129) imply:
% 177.74/28.20  | | | | | | | | | | |   (130)   ~ (all_52_28 = e2)
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | | REF_CLOSE: (46), (52), (65), (71), (79), (119), (127), (130)
% 177.74/28.20  | | | | | | | | | | |            are inconsistent by sub-proof #903.
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | Case 2:
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | |   (131)   ~ (all_58_0 = e2)
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | | REF_CLOSE: (4), (6), (12), (17), (21), (23), (25), (35),
% 177.74/28.20  | | | | | | | | | | |            (36), (41), (46), (52), (84), (121), (125), (131)
% 177.74/28.20  | | | | | | | | | | |            are inconsistent by sub-proof #477.
% 177.74/28.20  | | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | | End of split
% 177.74/28.20  | | | | | | | | | | 
% 177.74/28.20  | | | | | | | | | End of split
% 177.74/28.20  | | | | | | | | | 
% 177.74/28.20  | | | | | | | | End of split
% 177.74/28.20  | | | | | | | | 
% 177.74/28.20  | | | | | | | End of split
% 177.74/28.20  | | | | | | | 
% 177.74/28.20  | | | | | | End of split
% 177.74/28.20  | | | | | | 
% 177.74/28.20  | | | | | End of split
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | Case 2:
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | |   (132)  all_58_4 = e3 | all_58_9 = e3
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | | REF_CLOSE: (9), (13), (15), (16), (18), (19), (21), (24), (28), (29),
% 177.74/28.20  | | | | |            (30), (37), (38), (39), (40), (42), (45), (46), (47), (49),
% 177.74/28.20  | | | | |            (51), (52), (55), (56), (57), (58), (60), (62), (65), (66),
% 177.74/28.20  | | | | |            (132) are inconsistent by sub-proof #623.
% 177.74/28.20  | | | | | 
% 177.74/28.20  | | | | End of split
% 177.74/28.20  | | | | 
% 177.74/28.20  | | | End of split
% 177.74/28.20  | | | 
% 177.74/28.20  | | Case 2:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (133)   ~ (all_58_2 = e3)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (45), (133) imply:
% 177.74/28.20  | | |   (134)   ~ (all_52_9 = e3)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REF_CLOSE: (17), (21), (25), (28), (33), (38), (40), (45), (49), (51),
% 177.74/28.20  | | |            (52), (58), (66), (134) are inconsistent by sub-proof #476.
% 177.74/28.20  | | | 
% 177.74/28.20  | | End of split
% 177.74/28.20  | | 
% 177.74/28.20  | End of split
% 177.74/28.20  | 
% 177.74/28.20  End of proof
% 177.74/28.20  
% 177.74/28.20  Sub-proof #476 shows that the following formulas are inconsistent:
% 177.74/28.20  ----------------------------------------------------------------
% 177.74/28.20    (1)   ~ (all_52_25 = e3)
% 177.74/28.20    (2)  op(e3, all_4_2) = all_4_1
% 177.74/28.20    (3)  all_58_0 = all_4_2
% 177.74/28.20    (4)   ~ (all_4_1 = e2)
% 177.74/28.20    (5)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.20    (6)  op(all_4_1, all_4_2) = e2
% 177.74/28.20    (7)  all_58_6 = all_52_17
% 177.74/28.20    (8)  op(e3, all_52_17) = e3
% 177.74/28.20    (9)   ~ (all_52_9 = e3)
% 177.74/28.20    (10)  all_58_2 = all_52_9
% 177.74/28.20    (11)  op(e3, e3) = all_4_2
% 177.74/28.20    (12)   ~ (all_52_17 = all_4_2)
% 177.74/28.20    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.20    (14)  all_58_12 = all_52_25
% 177.74/28.20  
% 177.74/28.20  Begin of proof
% 177.74/28.20  | 
% 177.74/28.20  | BETA: splitting (5) gives:
% 177.74/28.20  | 
% 177.74/28.20  | Case 1:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (15)  all_58_0 = e3
% 177.74/28.20  | | 
% 177.74/28.20  | | REF_CLOSE: (2), (3), (4), (6), (11), (13), (15) are inconsistent by
% 177.74/28.20  | |            sub-proof #489.
% 177.74/28.20  | | 
% 177.74/28.20  | Case 2:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (16)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.20  | | 
% 177.74/28.20  | | BETA: splitting (16) gives:
% 177.74/28.20  | | 
% 177.74/28.20  | | Case 1:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (17)  all_58_2 = e3
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REF_CLOSE: (9), (10), (17) are inconsistent by sub-proof #980.
% 177.74/28.20  | | | 
% 177.74/28.20  | | Case 2:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (18)  all_58_6 = e3 | all_58_12 = e3
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REF_CLOSE: (1), (7), (8), (11), (12), (13), (14), (18) are inconsistent by
% 177.74/28.20  | | |            sub-proof #947.
% 177.74/28.20  | | | 
% 177.74/28.20  | | End of split
% 177.74/28.20  | | 
% 177.74/28.20  | End of split
% 177.74/28.20  | 
% 177.74/28.20  End of proof
% 177.74/28.20  
% 177.74/28.20  Sub-proof #477 shows that the following formulas are inconsistent:
% 177.74/28.20  ----------------------------------------------------------------
% 177.74/28.20    (1)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.74/28.20    (2)  all_50_1 = all_4_1
% 177.74/28.20    (3)   ~ (all_52_5 = all_4_2)
% 177.74/28.20    (4)  op(e3, all_4_2) = all_4_1
% 177.74/28.20    (5)  all_58_0 = all_4_2
% 177.74/28.20    (6)  all_50_2 = all_4_2
% 177.74/28.20    (7)   ~ (all_4_1 = e2)
% 177.74/28.20    (8)  all_56_2 = all_52_5
% 177.74/28.20    (9)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.20    (10)  all_56_0 = all_4_2
% 177.74/28.20    (11)  op(e3, e1) = all_52_5
% 177.74/28.20    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.20    (13)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.20    (14)   ~ (all_4_2 = e0)
% 177.74/28.20    (15)   ~ (all_58_0 = e2)
% 177.74/28.20    (16)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.20  
% 177.74/28.20  Begin of proof
% 177.74/28.20  | 
% 177.74/28.20  | REDUCE: (5), (15) imply:
% 177.74/28.20  |   (17)   ~ (all_4_2 = e2)
% 177.74/28.20  | 
% 177.74/28.20  | BETA: splitting (9) gives:
% 177.74/28.20  | 
% 177.74/28.20  | Case 1:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (18)  all_58_0 = e1
% 177.74/28.20  | | 
% 177.74/28.20  | | COMBINE_EQS: (5), (18) imply:
% 177.74/28.20  | |   (19)  all_4_2 = e1
% 177.74/28.20  | | 
% 177.74/28.20  | | COMBINE_EQS: (6), (19) imply:
% 177.74/28.20  | |   (20)  all_50_2 = e1
% 177.74/28.20  | | 
% 177.74/28.20  | | REDUCE: (3), (19) imply:
% 177.74/28.20  | |   (21)   ~ (all_52_5 = e1)
% 177.74/28.20  | | 
% 177.74/28.20  | | REDUCE: (4), (19) imply:
% 177.74/28.20  | |   (22)  op(e3, e1) = all_4_1
% 177.74/28.20  | | 
% 177.74/28.20  | | BETA: splitting (1) gives:
% 177.74/28.20  | | 
% 177.74/28.20  | | Case 1:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (23)   ~ (all_50_2 = e1)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (20), (23) imply:
% 177.74/28.20  | | |   (24)  $false
% 177.74/28.20  | | | 
% 177.74/28.20  | | | CLOSE: (24) is inconsistent.
% 177.74/28.20  | | | 
% 177.74/28.20  | | Case 2:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (25)   ~ (all_50_1 = e0)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (2), (25) imply:
% 177.74/28.20  | | |   (26)   ~ (all_4_1 = e0)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | GROUND_INST: instantiating (12) with all_52_5, all_4_1, e1, e3,
% 177.74/28.20  | | |              simplifying with (11), (22) gives:
% 177.74/28.20  | | |   (27)  all_52_5 = all_4_1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | COMBINE_EQS: (8), (27) imply:
% 177.74/28.20  | | |   (28)  all_56_2 = all_4_1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (21), (27) imply:
% 177.74/28.20  | | |   (29)   ~ (all_4_1 = e1)
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REF_CLOSE: (7), (16), (26), (28), (29) are inconsistent by sub-proof #478.
% 177.74/28.20  | | | 
% 177.74/28.20  | | End of split
% 177.74/28.20  | | 
% 177.74/28.20  | Case 2:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (30)   ~ (all_58_0 = e1)
% 177.74/28.20  | | 
% 177.74/28.20  | | REDUCE: (5), (30) imply:
% 177.74/28.20  | |   (31)   ~ (all_4_2 = e1)
% 177.74/28.20  | | 
% 177.74/28.20  | | REF_CLOSE: (10), (13), (14), (17), (31) are inconsistent by sub-proof #882.
% 177.74/28.20  | | 
% 177.74/28.20  | End of split
% 177.74/28.20  | 
% 177.74/28.20  End of proof
% 177.74/28.20  
% 177.74/28.20  Sub-proof #478 shows that the following formulas are inconsistent:
% 177.74/28.20  ----------------------------------------------------------------
% 177.74/28.20    (1)   ~ (all_4_1 = e2)
% 177.74/28.20    (2)   ~ (all_4_1 = e1)
% 177.74/28.20    (3)  all_56_2 = all_4_1
% 177.74/28.20    (4)   ~ (all_4_1 = e0)
% 177.74/28.20    (5)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.20  
% 177.74/28.20  Begin of proof
% 177.74/28.20  | 
% 177.74/28.20  | BETA: splitting (5) gives:
% 177.74/28.20  | 
% 177.74/28.20  | Case 1:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (6)  all_56_2 = e2
% 177.74/28.20  | | 
% 177.74/28.20  | | COMBINE_EQS: (3), (6) imply:
% 177.74/28.20  | |   (7)  all_4_1 = e2
% 177.74/28.20  | | 
% 177.74/28.20  | | REDUCE: (1), (7) imply:
% 177.74/28.20  | |   (8)  $false
% 177.74/28.20  | | 
% 177.74/28.20  | | CLOSE: (8) is inconsistent.
% 177.74/28.20  | | 
% 177.74/28.20  | Case 2:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (9)  all_56_2 = e1 | all_56_2 = e0
% 177.74/28.20  | | 
% 177.74/28.20  | | BETA: splitting (9) gives:
% 177.74/28.20  | | 
% 177.74/28.20  | | Case 1:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (10)  all_56_2 = e1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | COMBINE_EQS: (3), (10) imply:
% 177.74/28.20  | | |   (11)  all_4_1 = e1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (2), (11) imply:
% 177.74/28.20  | | |   (12)  $false
% 177.74/28.20  | | | 
% 177.74/28.20  | | | CLOSE: (12) is inconsistent.
% 177.74/28.20  | | | 
% 177.74/28.20  | | Case 2:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (13)  all_56_2 = e0
% 177.74/28.20  | | | 
% 177.74/28.20  | | | COMBINE_EQS: (3), (13) imply:
% 177.74/28.20  | | |   (14)  all_4_1 = e0
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (4), (14) imply:
% 177.74/28.20  | | |   (15)  $false
% 177.74/28.20  | | | 
% 177.74/28.20  | | | CLOSE: (15) is inconsistent.
% 177.74/28.20  | | | 
% 177.74/28.20  | | End of split
% 177.74/28.20  | | 
% 177.74/28.20  | End of split
% 177.74/28.20  | 
% 177.74/28.20  End of proof
% 177.74/28.20  
% 177.74/28.20  Sub-proof #479 shows that the following formulas are inconsistent:
% 177.74/28.20  ----------------------------------------------------------------
% 177.74/28.20    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.20    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.74/28.20    (3)   ~ (all_52_17 = e3)
% 177.74/28.20    (4)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.74/28.20    (5)  all_50_1 = all_4_1
% 177.74/28.20    (6)  all_58_7 = all_52_19
% 177.74/28.20    (7)  all_58_4 = all_52_5
% 177.74/28.20    (8)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.20    (9)   ~ (e3 = e1)
% 177.74/28.20    (10)  op(e3, all_4_2) = all_4_1
% 177.74/28.20    (11)  all_58_9 = e3
% 177.74/28.20    (12)  all_58_1 = all_52_3
% 177.74/28.20    (13)  all_58_0 = all_4_2
% 177.74/28.20    (14)  all_50_2 = all_4_2
% 177.74/28.20    (15)   ~ (all_4_1 = e2)
% 177.74/28.20    (16)  all_58_8 = all_14_2
% 177.74/28.20    (17)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.74/28.20    (18)   ~ (all_52_5 = all_14_2)
% 177.74/28.20    (19)   ~ (all_52_23 = e3)
% 177.74/28.20    (20)   ~ (all_52_5 = e3)
% 177.74/28.20    (21)   ~ (e3 = e0)
% 177.74/28.20    (22)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.74/28.20    (23)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.20    (24)  all_58_12 = e3
% 177.74/28.20    (25)  all_58_6 = all_52_17
% 177.74/28.20    (26)  op(e2, all_52_19) = e2
% 177.74/28.20    (27)  op(e3, all_52_17) = e3
% 177.74/28.20    (28)   ~ (e1 = e0)
% 177.74/28.20    (29)  all_58_11 = all_52_23
% 177.74/28.20    (30)  all_58_2 = all_52_9
% 177.74/28.20    (31)  op(e3, e1) = all_52_5
% 177.74/28.20    (32)   ~ (e2 = e1)
% 177.74/28.20    (33)  all_56_10 = all_14_2
% 177.74/28.20    (34)  op(e1, e3) = all_52_17
% 177.74/28.20    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.20    (36)  op(e1, all_14_2) = e1
% 177.74/28.20    (37)   ~ (e2 = e0)
% 177.74/28.20    (38)   ~ (e3 = e2)
% 177.74/28.20    (39)   ~ (all_52_19 = all_14_2)
% 177.74/28.20    (40)  op(e2, e3) = all_52_9
% 177.74/28.20  
% 177.74/28.20  Begin of proof
% 177.74/28.20  | 
% 177.74/28.20  | BETA: splitting (8) gives:
% 177.74/28.20  | 
% 177.74/28.20  | Case 1:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (41)  all_58_6 = e3
% 177.74/28.20  | | 
% 177.74/28.20  | | REF_CLOSE: (3), (25), (41) are inconsistent by sub-proof #981.
% 177.74/28.20  | | 
% 177.74/28.20  | Case 2:
% 177.74/28.20  | | 
% 177.74/28.20  | |   (42)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.20  | | 
% 177.74/28.20  | | BETA: splitting (23) gives:
% 177.74/28.20  | | 
% 177.74/28.20  | | Case 1:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (43)  all_58_0 = e1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | COMBINE_EQS: (13), (43) imply:
% 177.74/28.20  | | |   (44)  all_4_2 = e1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | COMBINE_EQS: (14), (44) imply:
% 177.74/28.20  | | |   (45)  all_50_2 = e1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REDUCE: (10), (44) imply:
% 177.74/28.20  | | |   (46)  op(e3, e1) = all_4_1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REF_CLOSE: (2), (4), (5), (7), (11), (12), (15), (17), (21), (28), (31),
% 177.74/28.20  | | |            (32), (35), (37), (38), (43), (45), (46) are inconsistent by
% 177.74/28.20  | | |            sub-proof #480.
% 177.74/28.20  | | | 
% 177.74/28.20  | | Case 2:
% 177.74/28.20  | | | 
% 177.74/28.20  | | |   (47)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.20  | | | 
% 177.74/28.20  | | | REF_CLOSE: (1), (6), (9), (16), (18), (19), (20), (22), (24), (25), (26),
% 177.74/28.20  | | |            (27), (29), (30), (31), (32), (33), (34), (35), (36), (39),
% 177.74/28.20  | | |            (40), (42), (47) are inconsistent by sub-proof #918.
% 177.74/28.20  | | | 
% 177.74/28.20  | | End of split
% 177.74/28.20  | | 
% 177.74/28.20  | End of split
% 177.74/28.20  | 
% 177.74/28.20  End of proof
% 177.74/28.20  
% 177.74/28.20  Sub-proof #480 shows that the following formulas are inconsistent:
% 177.74/28.20  ----------------------------------------------------------------
% 177.74/28.20    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.74/28.20    (2)   ~ (all_50_1 = e0) |  ~ (all_50_2 = e1)
% 177.74/28.20    (3)  all_50_2 = e1
% 177.74/28.20    (4)  all_50_1 = all_4_1
% 177.74/28.20    (5)  all_58_4 = all_52_5
% 177.74/28.20    (6)  all_58_9 = e3
% 177.74/28.20    (7)  all_58_1 = all_52_3
% 177.74/28.20    (8)   ~ (all_4_1 = e2)
% 177.74/28.20    (9)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.74/28.20    (10)   ~ (e3 = e0)
% 177.74/28.20    (11)  op(e3, e1) = all_4_1
% 177.74/28.20    (12)  all_58_0 = e1
% 177.74/28.20    (13)   ~ (e1 = e0)
% 177.74/28.20    (14)  op(e3, e1) = all_52_5
% 177.74/28.20    (15)   ~ (e2 = e1)
% 177.74/28.20    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.20    (17)   ~ (e2 = e0)
% 177.74/28.20    (18)   ~ (e3 = e2)
% 177.74/28.20  
% 177.74/28.20  Begin of proof
% 177.74/28.20  | 
% 177.74/28.20  | BETA: splitting (2) gives:
% 177.74/28.20  | 
% 177.74/28.21  | Case 1:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (19)   ~ (all_50_2 = e1)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (3), (19) imply:
% 177.74/28.21  | |   (20)  $false
% 177.74/28.21  | | 
% 177.74/28.21  | | CLOSE: (20) is inconsistent.
% 177.74/28.21  | | 
% 177.74/28.21  | Case 2:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (21)   ~ (all_50_1 = e0)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (4), (21) imply:
% 177.74/28.21  | |   (22)   ~ (all_4_1 = e0)
% 177.74/28.21  | | 
% 177.74/28.21  | | GROUND_INST: instantiating (16) with all_52_5, all_4_1, e1, e3, simplifying
% 177.74/28.21  | |              with (11), (14) gives:
% 177.74/28.21  | |   (23)  all_52_5 = all_4_1
% 177.74/28.21  | | 
% 177.74/28.21  | | COMBINE_EQS: (5), (23) imply:
% 177.74/28.21  | |   (24)  all_58_4 = all_4_1
% 177.74/28.21  | | 
% 177.74/28.21  | | BETA: splitting (9) gives:
% 177.74/28.21  | | 
% 177.74/28.21  | | Case 1:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (25)  all_58_0 = e2
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REF_CLOSE: (12), (15), (25) are inconsistent by sub-proof #930.
% 177.74/28.21  | | | 
% 177.74/28.21  | | Case 2:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (26)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.74/28.21  | | | 
% 177.74/28.21  | | | BETA: splitting (26) gives:
% 177.74/28.21  | | | 
% 177.74/28.21  | | | Case 1:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (27)  all_58_1 = e2
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | COMBINE_EQS: (7), (27) imply:
% 177.74/28.21  | | | |   (28)  all_52_3 = e2
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REF_CLOSE: (1), (6), (10), (12), (13), (17), (22), (24), (27) are
% 177.74/28.21  | | | |            inconsistent by sub-proof #481.
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | Case 2:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (29)  all_58_4 = e2 | all_58_9 = e2
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REF_CLOSE: (6), (8), (18), (24), (29) are inconsistent by sub-proof
% 177.74/28.21  | | | |            #923.
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | End of split
% 177.74/28.21  | | | 
% 177.74/28.21  | | End of split
% 177.74/28.21  | | 
% 177.74/28.21  | End of split
% 177.74/28.21  | 
% 177.74/28.21  End of proof
% 177.74/28.21  
% 177.74/28.21  Sub-proof #481 shows that the following formulas are inconsistent:
% 177.74/28.21  ----------------------------------------------------------------
% 177.74/28.21    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.74/28.21    (2)  all_58_9 = e3
% 177.74/28.21    (3)   ~ (e3 = e0)
% 177.74/28.21    (4)  all_58_0 = e1
% 177.74/28.21    (5)   ~ (e1 = e0)
% 177.74/28.21    (6)   ~ (all_4_1 = e0)
% 177.74/28.21    (7)  all_58_4 = all_4_1
% 177.74/28.21    (8)   ~ (e2 = e0)
% 177.74/28.21    (9)  all_58_1 = e2
% 177.74/28.21  
% 177.74/28.21  Begin of proof
% 177.74/28.21  | 
% 177.74/28.21  | BETA: splitting (1) gives:
% 177.74/28.21  | 
% 177.74/28.21  | Case 1:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (10)  all_58_0 = e0
% 177.74/28.21  | | 
% 177.74/28.21  | | COMBINE_EQS: (4), (10) imply:
% 177.74/28.21  | |   (11)  e1 = e0
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (5), (11) imply:
% 177.74/28.21  | |   (12)  $false
% 177.74/28.21  | | 
% 177.74/28.21  | | CLOSE: (12) is inconsistent.
% 177.74/28.21  | | 
% 177.74/28.21  | Case 2:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (13)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.74/28.21  | | 
% 177.74/28.21  | | BETA: splitting (13) gives:
% 177.74/28.21  | | 
% 177.74/28.21  | | Case 1:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (14)  all_58_1 = e0
% 177.74/28.21  | | | 
% 177.74/28.21  | | | COMBINE_EQS: (9), (14) imply:
% 177.74/28.21  | | |   (15)  e2 = e0
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REDUCE: (8), (15) imply:
% 177.74/28.21  | | |   (16)  $false
% 177.74/28.21  | | | 
% 177.74/28.21  | | | CLOSE: (16) is inconsistent.
% 177.74/28.21  | | | 
% 177.74/28.21  | | Case 2:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (17)  all_58_4 = e0 | all_58_9 = e0
% 177.74/28.21  | | | 
% 177.74/28.21  | | | BETA: splitting (17) gives:
% 177.74/28.21  | | | 
% 177.74/28.21  | | | Case 1:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (18)  all_58_4 = e0
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | COMBINE_EQS: (7), (18) imply:
% 177.74/28.21  | | | |   (19)  all_4_1 = e0
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REDUCE: (6), (19) imply:
% 177.74/28.21  | | | |   (20)  $false
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | CLOSE: (20) is inconsistent.
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | Case 2:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (21)  all_58_9 = e0
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | COMBINE_EQS: (2), (21) imply:
% 177.74/28.21  | | | |   (22)  e3 = e0
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REDUCE: (3), (22) imply:
% 177.74/28.21  | | | |   (23)  $false
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | CLOSE: (23) is inconsistent.
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | End of split
% 177.74/28.21  | | | 
% 177.74/28.21  | | End of split
% 177.74/28.21  | | 
% 177.74/28.21  | End of split
% 177.74/28.21  | 
% 177.74/28.21  End of proof
% 177.74/28.21  
% 177.74/28.21  Sub-proof #482 shows that the following formulas are inconsistent:
% 177.74/28.21  ----------------------------------------------------------------
% 177.74/28.21    (1)  all_56_3 = all_52_7
% 177.74/28.21    (2)   ~ (all_4_2 = e2)
% 177.74/28.21    (3)  op(e3, all_4_2) = all_4_1
% 177.74/28.21    (4)   ~ (all_52_7 = all_4_2)
% 177.74/28.21    (5)   ~ (all_4_1 = e2)
% 177.74/28.21    (6)  all_26_2 = all_4_2
% 177.74/28.21    (7)  op(all_4_1, all_4_2) = e2
% 177.74/28.21    (8)   ~ (all_26_1 = e1) |  ~ (all_26_2 = e0)
% 177.74/28.21    (9)  all_56_0 = all_4_2
% 177.74/28.21    (10)  all_26_1 = all_4_1
% 177.74/28.21    (11)  op(e3, e0) = all_52_7
% 177.74/28.21    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.21    (13)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.21    (14)   ~ (all_4_2 = e1)
% 177.74/28.21    (15)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.74/28.21  
% 177.74/28.21  Begin of proof
% 177.74/28.21  | 
% 177.74/28.21  | BETA: splitting (13) gives:
% 177.74/28.21  | 
% 177.74/28.21  | Case 1:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (16)  all_56_0 = e2
% 177.74/28.21  | | 
% 177.74/28.21  | | COMBINE_EQS: (9), (16) imply:
% 177.74/28.21  | |   (17)  all_4_2 = e2
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (2), (17) imply:
% 177.74/28.21  | |   (18)  $false
% 177.74/28.21  | | 
% 177.74/28.21  | | CLOSE: (18) is inconsistent.
% 177.74/28.21  | | 
% 177.74/28.21  | Case 2:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (19)  all_56_0 = e1 | all_56_0 = e0
% 177.74/28.21  | | 
% 177.74/28.21  | | BETA: splitting (19) gives:
% 177.74/28.21  | | 
% 177.74/28.21  | | Case 1:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (20)  all_56_0 = e1
% 177.74/28.21  | | | 
% 177.74/28.21  | | | COMBINE_EQS: (9), (20) imply:
% 177.74/28.21  | | |   (21)  all_4_2 = e1
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REDUCE: (14), (21) imply:
% 177.74/28.21  | | |   (22)  $false
% 177.74/28.21  | | | 
% 177.74/28.21  | | | CLOSE: (22) is inconsistent.
% 177.74/28.21  | | | 
% 177.74/28.21  | | Case 2:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (23)  all_56_0 = e0
% 177.74/28.21  | | | 
% 177.74/28.21  | | | COMBINE_EQS: (9), (23) imply:
% 177.74/28.21  | | |   (24)  all_4_2 = e0
% 177.74/28.21  | | | 
% 177.74/28.21  | | | COMBINE_EQS: (6), (24) imply:
% 177.74/28.21  | | |   (25)  all_26_2 = e0
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REDUCE: (4), (24) imply:
% 177.74/28.21  | | |   (26)   ~ (all_52_7 = e0)
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REDUCE: (7), (24) imply:
% 177.74/28.21  | | |   (27)  op(all_4_1, e0) = e2
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REDUCE: (3), (24) imply:
% 177.74/28.21  | | |   (28)  op(e3, e0) = all_4_1
% 177.74/28.21  | | | 
% 177.74/28.21  | | | BETA: splitting (8) gives:
% 177.74/28.21  | | | 
% 177.74/28.21  | | | Case 1:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (29)   ~ (all_26_1 = e1)
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REDUCE: (10), (29) imply:
% 177.74/28.21  | | | |   (30)   ~ (all_4_1 = e1)
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | GROUND_INST: instantiating (12) with all_52_7, all_4_1, e0, e3,
% 177.74/28.21  | | | |              simplifying with (11), (28) gives:
% 177.74/28.21  | | | |   (31)  all_52_7 = all_4_1
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | COMBINE_EQS: (1), (31) imply:
% 177.74/28.21  | | | |   (32)  all_56_3 = all_4_1
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REDUCE: (26), (31) imply:
% 177.74/28.21  | | | |   (33)   ~ (all_4_1 = e0)
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | BETA: splitting (15) gives:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | Case 1:
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | |   (34)  all_56_3 = e3
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | COMBINE_EQS: (32), (34) imply:
% 177.74/28.21  | | | | |   (35)  all_4_1 = e3
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | SIMP: (35) implies:
% 177.74/28.21  | | | | |   (36)  all_4_1 = e3
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (5), (36) imply:
% 177.74/28.21  | | | | |   (37)   ~ (e3 = e2)
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (27), (36) imply:
% 177.74/28.21  | | | | |   (38)  op(e3, e0) = e2
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (28), (36) imply:
% 177.74/28.21  | | | | |   (39)  op(e3, e0) = e3
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | GROUND_INST: instantiating (12) with e2, e3, e0, e3, simplifying with
% 177.74/28.21  | | | | |              (38), (39) gives:
% 177.74/28.21  | | | | |   (40)  e3 = e2
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (37), (40) imply:
% 177.74/28.21  | | | | |   (41)  $false
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | CLOSE: (41) is inconsistent.
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | Case 2:
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | |   (42)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | BETA: splitting (42) gives:
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | Case 1:
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | |   (43)  all_56_3 = e2
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | REF_CLOSE: (5), (32), (43) are inconsistent by sub-proof #591.
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | Case 2:
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | |   (44)  all_56_3 = e1 | all_56_3 = e0
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | BETA: splitting (44) gives:
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | Case 1:
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | |   (45)  all_56_3 = e1
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | COMBINE_EQS: (32), (45) imply:
% 177.74/28.21  | | | | | | |   (46)  all_4_1 = e1
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | SIMP: (46) implies:
% 177.74/28.21  | | | | | | |   (47)  all_4_1 = e1
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REDUCE: (30), (47) imply:
% 177.74/28.21  | | | | | | |   (48)  $false
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | CLOSE: (48) is inconsistent.
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | Case 2:
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | |   (49)  all_56_3 = e0
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REF_CLOSE: (32), (33), (49) are inconsistent by sub-proof #589.
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | End of split
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | End of split
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | End of split
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | Case 2:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (50)   ~ (all_26_2 = e0)
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REDUCE: (25), (50) imply:
% 177.74/28.21  | | | |   (51)  $false
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | CLOSE: (51) is inconsistent.
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | End of split
% 177.74/28.21  | | | 
% 177.74/28.21  | | End of split
% 177.74/28.21  | | 
% 177.74/28.21  | End of split
% 177.74/28.21  | 
% 177.74/28.21  End of proof
% 177.74/28.21  
% 177.74/28.21  Sub-proof #483 shows that the following formulas are inconsistent:
% 177.74/28.21  ----------------------------------------------------------------
% 177.74/28.21    (1)   ~ (all_52_25 = e3)
% 177.74/28.21    (2)   ~ (all_52_17 = e3)
% 177.74/28.21    (3)  all_58_6 = all_52_17
% 177.74/28.21    (4)  all_58_6 = e3 | all_58_12 = e3
% 177.74/28.21    (5)  all_58_12 = all_52_25
% 177.74/28.21  
% 177.74/28.21  Begin of proof
% 177.74/28.21  | 
% 177.74/28.21  | BETA: splitting (4) gives:
% 177.74/28.21  | 
% 177.74/28.21  | Case 1:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (6)  all_58_6 = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #981.
% 177.74/28.21  | | 
% 177.74/28.21  | Case 2:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (7)  all_58_12 = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1003.
% 177.74/28.21  | | 
% 177.74/28.21  | End of split
% 177.74/28.21  | 
% 177.74/28.21  End of proof
% 177.74/28.21  
% 177.74/28.21  Sub-proof #484 shows that the following formulas are inconsistent:
% 177.74/28.21  ----------------------------------------------------------------
% 177.74/28.21    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.21    (2)  all_58_5 = all_52_13
% 177.74/28.21    (3)  all_58_7 = all_52_19
% 177.74/28.21    (4)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.21    (5)   ~ (all_52_17 = all_14_2)
% 177.74/28.21    (6)  all_58_14 = all_52_29
% 177.74/28.21    (7)  all_58_8 = all_14_2
% 177.74/28.21    (8)   ~ (all_52_5 = all_14_2)
% 177.74/28.21    (9)   ~ (all_52_29 = e3)
% 177.74/28.21    (10)   ~ (all_52_13 = e3)
% 177.74/28.21    (11)  all_58_6 = all_52_17
% 177.74/28.21    (12)  op(e3, all_52_17) = e3
% 177.74/28.21    (13)  all_58_11 = all_52_23
% 177.74/28.21    (14)  op(e3, e1) = all_52_5
% 177.74/28.21    (15)  op(e1, e3) = all_52_17
% 177.74/28.21    (16)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.21    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.21    (18)  op(e1, all_14_2) = e1
% 177.74/28.21    (19)   ~ (all_52_19 = all_14_2)
% 177.74/28.21  
% 177.74/28.21  Begin of proof
% 177.74/28.21  | 
% 177.74/28.21  | BETA: splitting (16) gives:
% 177.74/28.21  | 
% 177.74/28.21  | Case 1:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (20)  all_58_5 = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | REF_CLOSE: (2), (10), (20) are inconsistent by sub-proof #969.
% 177.74/28.21  | | 
% 177.74/28.21  | Case 2:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (21)  all_58_8 = e3 | all_58_14 = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 177.74/28.21  | |            (15), (17), (18), (19), (21) are inconsistent by sub-proof #703.
% 177.74/28.21  | | 
% 177.74/28.21  | End of split
% 177.74/28.21  | 
% 177.74/28.21  End of proof
% 177.74/28.21  
% 177.74/28.21  Sub-proof #485 shows that the following formulas are inconsistent:
% 177.74/28.21  ----------------------------------------------------------------
% 177.74/28.21    (1)   ~ (all_52_5 = all_52_13)
% 177.74/28.21    (2)   ~ (all_52_27 = all_10_2)
% 177.74/28.21    (3)   ~ (all_52_17 = all_52_23)
% 177.74/28.21    (4)   ~ (all_52_13 = all_52_29)
% 177.74/28.21    (5)  op(e2, all_10_2) = all_10_0
% 177.74/28.21    (6)  all_56_3 = all_52_7
% 177.74/28.21    (7)  op(e3, e2) = all_52_3
% 177.74/28.21    (8)   ~ (all_52_9 = all_52_25)
% 177.74/28.21    (9)  op(e3, all_52_25) = all_52_24
% 177.74/28.21    (10)   ~ (all_52_27 = e0)
% 177.74/28.21    (11)   ~ (all_52_3 = all_10_2)
% 177.74/28.21    (12)  all_58_5 = all_52_13
% 177.74/28.21    (13)   ~ (all_52_25 = all_52_29)
% 177.74/28.21    (14)  op(e1, all_52_13) = e1
% 177.74/28.21    (15)  op(e0, all_52_15) = e0
% 177.74/28.21    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.74/28.21    (17)  all_58_3 = all_10_2
% 177.74/28.21    (18)   ~ (all_52_9 = all_4_2)
% 177.74/28.21    (19)   ~ (all_52_5 = all_52_7)
% 177.74/28.21    (20)  all_58_10 = all_52_15
% 177.74/28.21    (21)  all_58_7 = all_52_19
% 177.74/28.21    (22)   ~ (all_52_17 = all_52_25)
% 177.74/28.21    (23)  op(e0, e1) = all_52_29
% 177.74/28.21    (24)  all_58_4 = all_52_5
% 177.74/28.21    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.21    (26)   ~ (e3 = e1)
% 177.74/28.21    (27)   ~ (all_52_27 = all_52_29)
% 177.74/28.21    (28)   ~ (all_52_17 = all_14_2)
% 177.74/28.21    (29)  op(e3, all_4_2) = all_4_1
% 177.74/28.21    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.21    (31)   ~ (all_52_7 = all_4_2)
% 177.74/28.21    (32)  all_58_1 = all_52_3
% 177.74/28.21    (33)   ~ (all_52_13 = all_52_15)
% 177.74/28.21    (34)  all_58_0 = all_4_2
% 177.74/28.21    (35)  op(e1, all_52_29) = all_52_28
% 177.74/28.21    (36)   ~ (all_4_1 = e2)
% 177.74/28.21    (37)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.74/28.21    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.21    (39)  all_58_14 = all_52_29
% 177.74/28.21    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.74/28.21    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.21    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.21    (43)  all_58_8 = all_14_2
% 177.74/28.21    (44)  op(e0, e2) = all_52_27
% 177.74/28.21    (45)  all_56_14 = all_52_29
% 177.74/28.21    (46)   ~ (all_52_3 = all_4_2)
% 177.74/28.21    (47)  op(e0, e3) = all_52_25
% 177.74/28.21    (48)  op(all_4_1, all_4_2) = e2
% 177.74/28.21    (49)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.74/28.21    (50)   ~ (all_52_13 = all_14_2)
% 177.74/28.21    (51)  op(e3, all_52_9) = e3
% 177.74/28.21    (52)   ~ (e3 = e0)
% 177.74/28.21    (53)   ~ (all_52_9 = all_52_13)
% 177.74/28.21    (54)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.21    (55)   ~ (all_52_15 = all_52_23)
% 177.74/28.21    (56)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.74/28.21    (57)  all_56_12 = all_52_25
% 177.74/28.21    (58)  all_58_13 = all_52_27
% 177.74/28.21    (59)   ~ (all_52_25 = e0)
% 177.74/28.21    (60)   ~ (all_52_9 = all_52_17)
% 177.74/28.21    (61)  all_58_6 = all_52_17
% 177.74/28.21    (62)   ~ (all_52_3 = all_52_7)
% 177.74/28.21    (63)   ~ (e1 = e0)
% 177.74/28.21    (64)  all_58_11 = all_52_23
% 177.74/28.21    (65)   ~ (all_52_3 = all_52_19)
% 177.74/28.21    (66)   ~ (all_52_7 = all_52_15)
% 177.74/28.21    (67)   ~ (all_52_29 = all_14_2)
% 177.74/28.21    (68)   ~ (all_52_19 = all_10_2)
% 177.74/28.21    (69)  all_58_15 = e0
% 177.74/28.21    (70)  all_58_2 = all_52_9
% 177.74/28.21    (71)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.21    (72)   ~ (all_52_29 = e0)
% 177.74/28.21    (73)  op(e3, e1) = all_52_5
% 177.74/28.21    (74)  all_56_10 = all_14_2
% 177.74/28.21    (75)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.21    (76)  op(e1, e3) = all_52_17
% 177.74/28.21    (77)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.21    (78)  op(e2, all_10_2) = e2
% 177.74/28.21    (79)  op(e3, e3) = all_4_2
% 177.74/28.21    (80)   ~ (all_52_17 = all_4_2)
% 177.74/28.21    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.21    (82)   ~ (all_52_25 = all_52_27)
% 177.74/28.21    (83)   ~ (all_10_0 = e3)
% 177.74/28.21    (84)   ~ (all_52_19 = all_52_27)
% 177.74/28.21    (85)  all_56_7 = all_52_15
% 177.74/28.21    (86)   ~ (all_52_15 = e0)
% 177.74/28.21    (87)   ~ (all_52_7 = all_52_23)
% 177.74/28.21    (88)   ~ (all_52_13 = all_10_2)
% 177.74/28.21    (89)  op(e2, all_52_27) = all_52_26
% 177.74/28.21    (90)   ~ (all_52_17 = all_52_19)
% 177.74/28.21    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.21    (92)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.74/28.21    (93)  all_58_9 = all_52_7
% 177.74/28.21    (94)   ~ (e2 = e0)
% 177.74/28.21    (95)  all_58_12 = all_52_25
% 177.74/28.21    (96)   ~ (all_10_0 = e1)
% 177.74/28.21    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.21    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.21    (99)   ~ (all_52_19 = all_14_2)
% 177.74/28.21    (100)  op(e2, e3) = all_52_9
% 177.74/28.21    (101)  all_56_13 = all_52_27
% 177.74/28.21  
% 177.74/28.21  Begin of proof
% 177.74/28.21  | 
% 177.74/28.21  | GROUND_INST: instantiating (81) with e2, all_10_0, all_10_2, e2, simplifying
% 177.74/28.21  |              with (5), (78) gives:
% 177.74/28.21  |   (102)  all_10_0 = e2
% 177.74/28.21  | 
% 177.74/28.21  | REDUCE: (83), (102) imply:
% 177.74/28.21  |   (103)   ~ (e3 = e2)
% 177.74/28.21  | 
% 177.74/28.21  | SIMP: (103) implies:
% 177.74/28.21  |   (104)   ~ (e3 = e2)
% 177.74/28.21  | 
% 177.74/28.21  | REDUCE: (96), (102) imply:
% 177.74/28.21  |   (105)   ~ (e2 = e1)
% 177.74/28.21  | 
% 177.74/28.21  | BETA: splitting (40) gives:
% 177.74/28.21  | 
% 177.74/28.21  | Case 1:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (106)  all_56_13 = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | COMBINE_EQS: (101), (106) imply:
% 177.74/28.21  | |   (107)  all_52_27 = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | SIMP: (107) implies:
% 177.74/28.21  | |   (108)  all_52_27 = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (84), (108) imply:
% 177.74/28.21  | |   (109)   ~ (all_52_19 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (82), (108) imply:
% 177.74/28.21  | |   (110)   ~ (all_52_25 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (27), (108) imply:
% 177.74/28.21  | |   (111)   ~ (all_52_29 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | SIMP: (111) implies:
% 177.74/28.21  | |   (112)   ~ (all_52_29 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (2), (108) imply:
% 177.74/28.21  | |   (113)   ~ (all_10_2 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | SIMP: (113) implies:
% 177.74/28.21  | |   (114)   ~ (all_10_2 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (89), (108) imply:
% 177.74/28.21  | |   (115)  op(e2, e3) = all_52_26
% 177.74/28.21  | | 
% 177.74/28.21  | | GROUND_INST: instantiating (81) with all_52_9, all_52_26, e3, e2,
% 177.74/28.21  | |              simplifying with (100), (115) gives:
% 177.74/28.21  | |   (116)  all_52_9 = all_52_26
% 177.74/28.21  | | 
% 177.74/28.21  | | COMBINE_EQS: (70), (116) imply:
% 177.74/28.21  | |   (117)  all_58_2 = all_52_26
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (53), (116) imply:
% 177.74/28.21  | |   (118)   ~ (all_52_13 = all_52_26)
% 177.74/28.21  | | 
% 177.74/28.21  | | SIMP: (118) implies:
% 177.74/28.21  | |   (119)   ~ (all_52_13 = all_52_26)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (18), (116) imply:
% 177.74/28.21  | |   (120)   ~ (all_52_26 = all_4_2)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (51), (116) imply:
% 177.74/28.21  | |   (121)  op(e3, all_52_26) = e3
% 177.74/28.21  | | 
% 177.74/28.21  | | BETA: splitting (54) gives:
% 177.74/28.21  | | 
% 177.74/28.21  | | Case 1:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (122)  all_56_12 = e3
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REF_CLOSE: (57), (110), (122) are inconsistent by sub-proof #1040.
% 177.74/28.21  | | | 
% 177.74/28.21  | | Case 2:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (123)   ~ (all_56_12 = e3)
% 177.74/28.21  | | |   (124)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.21  | | | 
% 177.74/28.21  | | | BETA: splitting (37) gives:
% 177.74/28.21  | | | 
% 177.74/28.21  | | | Case 1:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (125)  all_56_14 = e3
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | REF_CLOSE: (45), (112), (125) are inconsistent by sub-proof #896.
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | Case 2:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | |   (126)   ~ (all_56_14 = e3)
% 177.74/28.21  | | | |   (127)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | BETA: splitting (71) gives:
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | | Case 1:
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | |   (128)  all_58_12 = e1
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | COMBINE_EQS: (95), (128) imply:
% 177.74/28.21  | | | | |   (129)  all_52_25 = e1
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | SIMP: (129) implies:
% 177.74/28.21  | | | | |   (130)  all_52_25 = e1
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (22), (130) imply:
% 177.74/28.21  | | | | |   (131)   ~ (all_52_17 = e1)
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (13), (130) imply:
% 177.74/28.21  | | | | |   (132)   ~ (all_52_29 = e1)
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | SIMP: (132) implies:
% 177.74/28.21  | | | | |   (133)   ~ (all_52_29 = e1)
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (9), (130) imply:
% 177.74/28.21  | | | | |   (134)  op(e3, e1) = all_52_24
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REDUCE: (47), (130) imply:
% 177.74/28.21  | | | | |   (135)  op(e0, e3) = e1
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | BETA: splitting (127) gives:
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | Case 1:
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | GROUND_INST: instantiating (81) with all_52_5, all_52_24, e1, e3,
% 177.74/28.21  | | | | | |              simplifying with (73), (134) gives:
% 177.74/28.21  | | | | | |   (136)  all_52_5 = all_52_24
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | COMBINE_EQS: (24), (136) imply:
% 177.74/28.21  | | | | | |   (137)  all_58_4 = all_52_24
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | REDUCE: (1), (136) imply:
% 177.74/28.21  | | | | | |   (138)   ~ (all_52_13 = all_52_24)
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | SIMP: (138) implies:
% 177.74/28.21  | | | | | |   (139)   ~ (all_52_13 = all_52_24)
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | BETA: splitting (25) gives:
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | Case 1:
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | |   (140)  all_58_6 = e3
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | COMBINE_EQS: (61), (140) imply:
% 177.74/28.21  | | | | | | |   (141)  all_52_17 = e3
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REDUCE: (3), (141) imply:
% 177.74/28.21  | | | | | | |   (142)   ~ (all_52_23 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | SIMP: (142) implies:
% 177.74/28.21  | | | | | | |   (143)   ~ (all_52_23 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REDUCE: (28), (141) imply:
% 177.74/28.21  | | | | | | |   (144)   ~ (all_14_2 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | SIMP: (144) implies:
% 177.74/28.21  | | | | | | |   (145)   ~ (all_14_2 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REDUCE: (80), (141) imply:
% 177.74/28.21  | | | | | | |   (146)   ~ (all_4_2 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | SIMP: (146) implies:
% 177.74/28.21  | | | | | | |   (147)   ~ (all_4_2 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REF_CLOSE: (1), (4), (12), (14), (15), (17), (20), (21), (22),
% 177.74/28.21  | | | | | | |            (24), (25), (26), (28), (30), (33), (34), (39), (41),
% 177.74/28.21  | | | | | | |            (43), (50), (61), (63), (64), (76), (79), (81), (88),
% 177.74/28.21  | | | | | | |            (95), (98), (109), (112), (114), (117), (119), (120),
% 177.74/28.21  | | | | | | |            (121), (135), (137), (139), (143), (145), (147) are
% 177.74/28.21  | | | | | | |            inconsistent by sub-proof #491.
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | Case 2:
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | |   (148)   ~ (all_58_6 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REDUCE: (61), (148) imply:
% 177.74/28.21  | | | | | | |   (149)   ~ (all_52_17 = e3)
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | | REF_CLOSE: (29), (34), (36), (41), (48), (61), (79), (81), (95),
% 177.74/28.21  | | | | | | |            (110), (117), (120), (121), (149) are inconsistent by
% 177.74/28.21  | | | | | | |            sub-proof #488.
% 177.74/28.21  | | | | | | | 
% 177.74/28.21  | | | | | | End of split
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | Case 2:
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | |   (150)  all_56_14 = e1 | all_56_14 = e0
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | | REF_CLOSE: (45), (72), (133), (150) are inconsistent by sub-proof
% 177.74/28.21  | | | | | |            #886.
% 177.74/28.21  | | | | | | 
% 177.74/28.21  | | | | | End of split
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | Case 2:
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | |   (151)   ~ (all_58_12 = e1)
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | | REF_CLOSE: (3), (4), (12), (14), (15), (17), (19), (20), (21), (22),
% 177.74/28.21  | | | | |            (24), (25), (26), (28), (29), (30), (31), (34), (36), (39),
% 177.74/28.21  | | | | |            (41), (43), (47), (48), (50), (52), (57), (59), (61), (64),
% 177.74/28.21  | | | | |            (66), (69), (75), (76), (77), (79), (81), (85), (87), (91),
% 177.74/28.21  | | | | |            (93), (95), (98), (109), (110), (114), (117), (119), (120),
% 177.74/28.21  | | | | |            (121), (124), (151) are inconsistent by sub-proof #487.
% 177.74/28.21  | | | | | 
% 177.74/28.21  | | | | End of split
% 177.74/28.21  | | | | 
% 177.74/28.21  | | | End of split
% 177.74/28.21  | | | 
% 177.74/28.21  | | End of split
% 177.74/28.21  | | 
% 177.74/28.21  | Case 2:
% 177.74/28.21  | | 
% 177.74/28.21  | |   (152)   ~ (all_56_13 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | REDUCE: (101), (152) imply:
% 177.74/28.21  | |   (153)   ~ (all_52_27 = e3)
% 177.74/28.21  | | 
% 177.74/28.21  | | BETA: splitting (42) gives:
% 177.74/28.21  | | 
% 177.74/28.21  | | Case 1:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (154)  all_58_12 = e3
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REF_CLOSE: (3), (6), (7), (8), (10), (11), (12), (14), (15), (16), (17),
% 177.74/28.21  | | |            (20), (21), (22), (23), (25), (26), (30), (32), (38), (43),
% 177.74/28.21  | | |            (44), (47), (49), (51), (56), (58), (59), (61), (62), (63),
% 177.74/28.21  | | |            (64), (66), (68), (69), (70), (72), (74), (76), (77), (78),
% 177.74/28.21  | | |            (81), (82), (85), (86), (87), (91), (92), (93), (94), (95),
% 177.74/28.21  | | |            (99), (100), (104), (105), (154) are inconsistent by sub-proof
% 177.74/28.21  | | |            #970.
% 177.74/28.21  | | | 
% 177.74/28.21  | | Case 2:
% 177.74/28.21  | | | 
% 177.74/28.21  | | |   (155)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.21  | | | 
% 177.74/28.21  | | | REF_CLOSE: (4), (7), (8), (11), (12), (13), (15), (17), (18), (20), (21),
% 177.74/28.21  | | |            (25), (27), (29), (30), (32), (34), (35), (36), (38), (39),
% 177.74/28.21  | | |            (41), (43), (46), (47), (48), (51), (52), (54), (55), (57),
% 177.74/28.21  | | |            (58), (59), (60), (61), (64), (65), (67), (69), (70), (71),
% 177.74/28.21  | | |            (76), (77), (78), (79), (81), (85), (90), (95), (97), (100),
% 177.74/28.21  | | |            (153), (155) are inconsistent by sub-proof #486.
% 177.74/28.21  | | | 
% 177.74/28.21  | | End of split
% 177.74/28.21  | | 
% 177.74/28.21  | End of split
% 177.74/28.21  | 
% 177.74/28.21  End of proof
% 177.74/28.21  
% 177.74/28.21  Sub-proof #486 shows that the following formulas are inconsistent:
% 177.74/28.21  ----------------------------------------------------------------
% 177.74/28.21    (1)   ~ (all_52_13 = all_52_29)
% 177.74/28.21    (2)  op(e3, e2) = all_52_3
% 177.74/28.21    (3)   ~ (all_52_9 = all_52_25)
% 177.74/28.21    (4)   ~ (all_52_27 = e3)
% 177.74/28.21    (5)   ~ (all_52_3 = all_10_2)
% 177.74/28.21    (6)  all_58_5 = all_52_13
% 177.74/28.21    (7)   ~ (all_52_25 = all_52_29)
% 177.74/28.21    (8)  op(e0, all_52_15) = e0
% 177.74/28.21    (9)  all_58_3 = all_10_2
% 177.74/28.21    (10)   ~ (all_52_9 = all_4_2)
% 177.74/28.21    (11)  all_58_10 = all_52_15
% 177.74/28.21    (12)  all_58_7 = all_52_19
% 177.74/28.21    (13)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.21    (14)   ~ (all_52_27 = all_52_29)
% 177.74/28.21    (15)  op(e3, all_4_2) = all_4_1
% 177.74/28.21    (16)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.21    (17)  all_58_1 = all_52_3
% 177.74/28.21    (18)  all_58_0 = all_4_2
% 177.74/28.21    (19)  op(e1, all_52_29) = all_52_28
% 177.74/28.21    (20)   ~ (all_4_1 = e2)
% 177.74/28.21    (21)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.21    (22)  all_58_14 = all_52_29
% 177.74/28.21    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.21    (24)  all_58_8 = all_14_2
% 177.74/28.21    (25)   ~ (all_52_3 = all_4_2)
% 177.74/28.21    (26)  op(e0, e3) = all_52_25
% 177.74/28.21    (27)  op(all_4_1, all_4_2) = e2
% 177.74/28.21    (28)  op(e3, all_52_9) = e3
% 177.74/28.21    (29)   ~ (e3 = e0)
% 177.74/28.21    (30)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.21    (31)   ~ (all_52_15 = all_52_23)
% 177.74/28.21    (32)  all_56_12 = all_52_25
% 177.74/28.21    (33)  all_58_13 = all_52_27
% 177.74/28.21    (34)   ~ (all_52_25 = e0)
% 177.74/28.21    (35)   ~ (all_52_9 = all_52_17)
% 177.74/28.21    (36)  all_58_6 = all_52_17
% 177.74/28.21    (37)  all_58_11 = all_52_23
% 177.74/28.21    (38)   ~ (all_52_3 = all_52_19)
% 177.74/28.21    (39)   ~ (all_52_29 = all_14_2)
% 177.74/28.21    (40)  all_58_15 = e0
% 177.74/28.22    (41)  all_58_2 = all_52_9
% 177.74/28.22    (42)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.22    (43)  op(e1, e3) = all_52_17
% 177.74/28.22    (44)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.22    (45)  op(e2, all_10_2) = e2
% 177.74/28.22    (46)  op(e3, e3) = all_4_2
% 177.74/28.22    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (48)  all_56_7 = all_52_15
% 177.74/28.22    (49)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.22    (50)   ~ (all_52_17 = all_52_19)
% 177.74/28.22    (51)  all_58_12 = all_52_25
% 177.74/28.22    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.22    (53)  op(e2, e3) = all_52_9
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | BETA: splitting (49) gives:
% 177.74/28.22  | 
% 177.74/28.22  | Case 1:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (54)  all_58_13 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (4), (33), (54) are inconsistent by sub-proof #1026.
% 177.74/28.22  | | 
% 177.74/28.22  | Case 2:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (55)  all_58_14 = e3 | all_58_15 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | BETA: splitting (55) gives:
% 177.74/28.22  | | 
% 177.74/28.22  | | Case 1:
% 177.74/28.22  | | | 
% 177.74/28.22  | | |   (56)  all_58_14 = e3
% 177.74/28.22  | | | 
% 177.74/28.22  | | | COMBINE_EQS: (22), (56) imply:
% 177.74/28.22  | | |   (57)  all_52_29 = e3
% 177.74/28.22  | | | 
% 177.74/28.22  | | | SIMP: (57) implies:
% 177.74/28.22  | | |   (58)  all_52_29 = e3
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REDUCE: (1), (58) imply:
% 177.74/28.22  | | |   (59)   ~ (all_52_13 = e3)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REDUCE: (7), (58) imply:
% 177.74/28.22  | | |   (60)   ~ (all_52_25 = e3)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REDUCE: (39), (58) imply:
% 177.74/28.22  | | |   (61)   ~ (all_14_2 = e3)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | SIMP: (61) implies:
% 177.74/28.22  | | |   (62)   ~ (all_14_2 = e3)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REDUCE: (19), (58) imply:
% 177.74/28.22  | | |   (63)  op(e1, e3) = all_52_28
% 177.74/28.22  | | | 
% 177.74/28.22  | | | GROUND_INST: instantiating (47) with all_52_17, all_52_28, e3, e1,
% 177.74/28.22  | | |              simplifying with (43), (63) gives:
% 177.74/28.22  | | |   (64)  all_52_17 = all_52_28
% 177.74/28.22  | | | 
% 177.74/28.22  | | | COMBINE_EQS: (36), (64) imply:
% 177.74/28.22  | | |   (65)  all_58_6 = all_52_28
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REDUCE: (35), (64) imply:
% 177.74/28.22  | | |   (66)   ~ (all_52_9 = all_52_28)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REDUCE: (50), (64) imply:
% 177.74/28.22  | | |   (67)   ~ (all_52_19 = all_52_28)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | SIMP: (67) implies:
% 177.74/28.22  | | |   (68)   ~ (all_52_19 = all_52_28)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | BETA: splitting (30) gives:
% 177.74/28.22  | | | 
% 177.74/28.22  | | | Case 1:
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | |   (69)  all_56_12 = e3
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | | REF_CLOSE: (32), (60), (69) are inconsistent by sub-proof #1040.
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | Case 2:
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | |   (70)   ~ (all_56_12 = e3)
% 177.74/28.22  | | | |   (71)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | | BETA: splitting (42) gives:
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | | Case 1:
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | |   (72)  all_58_12 = e1
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | COMBINE_EQS: (51), (72) imply:
% 177.74/28.22  | | | | |   (73)  all_52_25 = e1
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | SIMP: (73) implies:
% 177.74/28.22  | | | | |   (74)  all_52_25 = e1
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | REDUCE: (34), (74) imply:
% 177.74/28.22  | | | | |   (75)   ~ (e1 = e0)
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | REDUCE: (26), (74) imply:
% 177.74/28.22  | | | | |   (76)  op(e0, e3) = e1
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | BETA: splitting (21) gives:
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | Case 1:
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | |   (77)  all_58_1 = e3
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | COMBINE_EQS: (17), (77) imply:
% 177.74/28.22  | | | | | |   (78)  all_52_3 = e3
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | REF_CLOSE: (5), (6), (8), (9), (10), (11), (12), (13), (16), (18),
% 177.74/28.22  | | | | | |            (23), (24), (25), (28), (31), (37), (38), (41), (46),
% 177.74/28.22  | | | | | |            (47), (59), (62), (65), (66), (75), (76), (78) are
% 177.74/28.22  | | | | | |            inconsistent by sub-proof #963.
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | Case 2:
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | |   (79)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | BETA: splitting (52) gives:
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | Case 1:
% 177.74/28.22  | | | | | | | 
% 177.74/28.22  | | | | | | |   (80)  all_58_0 = e3
% 177.74/28.22  | | | | | | | 
% 177.74/28.22  | | | | | | | REF_CLOSE: (15), (18), (20), (27), (46), (47), (80) are
% 177.74/28.22  | | | | | | |            inconsistent by sub-proof #489.
% 177.74/28.22  | | | | | | | 
% 177.74/28.22  | | | | | | Case 2:
% 177.74/28.22  | | | | | | | 
% 177.74/28.22  | | | | | | |   (81)   ~ (all_58_0 = e3)
% 177.74/28.22  | | | | | | | 
% 177.74/28.22  | | | | | | | REDUCE: (18), (81) imply:
% 177.74/28.22  | | | | | | |   (82)   ~ (all_4_2 = e3)
% 177.74/28.22  | | | | | | | 
% 177.74/28.22  | | | | | | | REF_CLOSE: (2), (4), (5), (9), (10), (12), (16), (18), (23), (28),
% 177.74/28.22  | | | | | | |            (33), (41), (45), (46), (47), (51), (53), (60), (65),
% 177.74/28.22  | | | | | | |            (68), (79), (82) are inconsistent by sub-proof #961.
% 177.74/28.22  | | | | | | | 
% 177.74/28.22  | | | | | | End of split
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | End of split
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | Case 2:
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | |   (83)   ~ (all_58_12 = e1)
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | REDUCE: (51), (83) imply:
% 177.74/28.22  | | | | |   (84)   ~ (all_52_25 = e1)
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | REF_CLOSE: (3), (6), (8), (9), (10), (11), (16), (26), (28), (32),
% 177.74/28.22  | | | | |            (34), (41), (44), (45), (46), (47), (48), (53), (59), (71),
% 177.74/28.22  | | | | |            (84) are inconsistent by sub-proof #956.
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | End of split
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | End of split
% 177.74/28.22  | | | 
% 177.74/28.22  | | Case 2:
% 177.74/28.22  | | | 
% 177.74/28.22  | | |   (85)  all_58_15 = e3
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REF_CLOSE: (29), (40), (85) are inconsistent by sub-proof #1010.
% 177.74/28.22  | | | 
% 177.74/28.22  | | End of split
% 177.74/28.22  | | 
% 177.74/28.22  | End of split
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #487 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)   ~ (all_52_25 = e3)
% 177.74/28.22    (2)   ~ (all_52_17 = all_52_23)
% 177.74/28.22    (3)   ~ (all_52_13 = all_52_29)
% 177.74/28.22    (4)  all_58_5 = all_52_13
% 177.74/28.22    (5)  op(e1, all_52_13) = e1
% 177.74/28.22    (6)  op(e0, all_52_15) = e0
% 177.74/28.22    (7)  all_58_3 = all_10_2
% 177.74/28.22    (8)   ~ (all_52_26 = all_4_2)
% 177.74/28.22    (9)   ~ (all_52_5 = all_52_7)
% 177.74/28.22    (10)  all_58_10 = all_52_15
% 177.74/28.22    (11)  all_58_7 = all_52_19
% 177.74/28.22    (12)   ~ (all_52_17 = all_52_25)
% 177.74/28.22    (13)  all_58_4 = all_52_5
% 177.74/28.22    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.22    (15)   ~ (e3 = e1)
% 177.74/28.22    (16)   ~ (all_52_17 = all_14_2)
% 177.74/28.22    (17)  op(e3, all_4_2) = all_4_1
% 177.74/28.22    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.22    (19)   ~ (all_52_7 = all_4_2)
% 177.74/28.22    (20)  all_58_0 = all_4_2
% 177.74/28.22    (21)   ~ (all_4_1 = e2)
% 177.74/28.22    (22)  all_58_14 = all_52_29
% 177.74/28.22    (23)   ~ (all_10_2 = e3)
% 177.74/28.22    (24)   ~ (all_52_13 = all_52_26)
% 177.74/28.22    (25)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.22    (26)  all_58_8 = all_14_2
% 177.74/28.22    (27)  op(e0, e3) = all_52_25
% 177.74/28.22    (28)  op(all_4_1, all_4_2) = e2
% 177.74/28.22    (29)   ~ (all_52_13 = all_14_2)
% 177.74/28.22    (30)   ~ (e3 = e0)
% 177.74/28.22    (31)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.22    (32)   ~ (all_58_12 = e1)
% 177.74/28.22    (33)  all_56_12 = all_52_25
% 177.74/28.22    (34)   ~ (all_52_25 = e0)
% 177.74/28.22    (35)  all_58_6 = all_52_17
% 177.74/28.22    (36)  all_58_2 = all_52_26
% 177.74/28.22    (37)  all_58_11 = all_52_23
% 177.74/28.22    (38)   ~ (all_52_7 = all_52_15)
% 177.74/28.22    (39)  all_58_15 = e0
% 177.74/28.22    (40)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.22    (41)   ~ (all_52_19 = e3)
% 177.74/28.22    (42)  op(e1, e3) = all_52_17
% 177.74/28.22    (43)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.22    (44)  op(e3, e3) = all_4_2
% 177.74/28.22    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (46)  all_56_7 = all_52_15
% 177.74/28.22    (47)   ~ (all_52_7 = all_52_23)
% 177.74/28.22    (48)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.22    (49)  all_58_9 = all_52_7
% 177.74/28.22    (50)  all_58_12 = all_52_25
% 177.74/28.22    (51)  op(e3, all_52_26) = e3
% 177.74/28.22    (52)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (32), (50) imply:
% 177.74/28.22  |   (53)   ~ (all_52_25 = e1)
% 177.74/28.22  | 
% 177.74/28.22  | BETA: splitting (40) gives:
% 177.74/28.22  | 
% 177.74/28.22  | Case 1:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (54)  all_58_12 = e2
% 177.74/28.22  | | 
% 177.74/28.22  | | COMBINE_EQS: (50), (54) imply:
% 177.74/28.22  | |   (55)  all_52_25 = e2
% 177.74/28.22  | | 
% 177.74/28.22  | | SIMP: (55) implies:
% 177.74/28.22  | |   (56)  all_52_25 = e2
% 177.74/28.22  | | 
% 177.74/28.22  | | REDUCE: (34), (56) imply:
% 177.74/28.22  | |   (57)   ~ (e2 = e0)
% 177.74/28.22  | | 
% 177.74/28.22  | | REDUCE: (27), (56) imply:
% 177.74/28.22  | |   (58)  op(e0, e3) = e2
% 177.74/28.22  | | 
% 177.74/28.22  | | BETA: splitting (43) gives:
% 177.74/28.22  | | 
% 177.74/28.22  | | Case 1:
% 177.74/28.22  | | | 
% 177.74/28.22  | | |   (59)  all_56_7 = e3
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REF_CLOSE: (6), (45), (46), (57), (58), (59) are inconsistent by sub-proof
% 177.74/28.22  | | |            #959.
% 177.74/28.22  | | | 
% 177.74/28.22  | | Case 2:
% 177.74/28.22  | | | 
% 177.74/28.22  | | |   (60)   ~ (all_56_7 = e3)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | REDUCE: (46), (60) imply:
% 177.74/28.22  | | |   (61)   ~ (all_52_15 = e3)
% 177.74/28.22  | | | 
% 177.74/28.22  | | | BETA: splitting (48) gives:
% 177.74/28.22  | | | 
% 177.74/28.22  | | | Case 1:
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | |   (62)  all_58_9 = e3
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | | COMBINE_EQS: (49), (62) imply:
% 177.74/28.22  | | | |   (63)  all_52_7 = e3
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 177.74/28.22  | | | |            (15), (16), (18), (19), (20), (22), (23), (24), (25), (26),
% 177.74/28.22  | | | |            (29), (35), (36), (37), (38), (41), (42), (44), (45), (47),
% 177.74/28.22  | | | |            (50), (51), (52), (63) are inconsistent by sub-proof #983.
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | Case 2:
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | |   (64)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | | BETA: splitting (64) gives:
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | | Case 1:
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | |   (65)  all_58_10 = e3
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | REF_CLOSE: (10), (61), (65) are inconsistent by sub-proof #1018.
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | Case 2:
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | |   (66)  all_58_11 = e3 | all_58_15 = e3
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | BETA: splitting (66) gives:
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | | Case 1:
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | |   (67)  all_58_11 = e3
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | COMBINE_EQS: (37), (67) imply:
% 177.74/28.22  | | | | | |   (68)  all_52_23 = e3
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | SIMP: (68) implies:
% 177.74/28.22  | | | | | |   (69)  all_52_23 = e3
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | REDUCE: (2), (69) imply:
% 177.74/28.22  | | | | | |   (70)   ~ (all_52_17 = e3)
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | REF_CLOSE: (1), (8), (17), (20), (21), (25), (28), (35), (36), (44),
% 177.74/28.22  | | | | | |            (45), (50), (51), (70) are inconsistent by sub-proof
% 177.74/28.22  | | | | | |            #488.
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | Case 2:
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | |   (71)  all_58_15 = e3
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | | REF_CLOSE: (30), (39), (71) are inconsistent by sub-proof #1010.
% 177.74/28.22  | | | | | | 
% 177.74/28.22  | | | | | End of split
% 177.74/28.22  | | | | | 
% 177.74/28.22  | | | | End of split
% 177.74/28.22  | | | | 
% 177.74/28.22  | | | End of split
% 177.74/28.22  | | | 
% 177.74/28.22  | | End of split
% 177.74/28.22  | | 
% 177.74/28.22  | Case 2:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (72)   ~ (all_58_12 = e2)
% 177.74/28.22  | | 
% 177.74/28.22  | | REDUCE: (50), (72) imply:
% 177.74/28.22  | |   (73)   ~ (all_52_25 = e2)
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (31), (33), (34), (53), (73) are inconsistent by sub-proof #1028.
% 177.74/28.22  | | 
% 177.74/28.22  | End of split
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #488 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)   ~ (all_52_25 = e3)
% 177.74/28.22    (2)   ~ (all_52_17 = e3)
% 177.74/28.22    (3)   ~ (all_52_26 = all_4_2)
% 177.74/28.22    (4)  op(e3, all_4_2) = all_4_1
% 177.74/28.22    (5)  all_58_0 = all_4_2
% 177.74/28.22    (6)   ~ (all_4_1 = e2)
% 177.74/28.22    (7)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.22    (8)  op(all_4_1, all_4_2) = e2
% 177.74/28.22    (9)  all_58_6 = all_52_17
% 177.74/28.22    (10)  all_58_2 = all_52_26
% 177.74/28.22    (11)  op(e3, e3) = all_4_2
% 177.74/28.22    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (13)  all_58_12 = all_52_25
% 177.74/28.22    (14)  op(e3, all_52_26) = e3
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | BETA: splitting (7) gives:
% 177.74/28.22  | 
% 177.74/28.22  | Case 1:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (15)  all_58_0 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (4), (5), (6), (8), (11), (12), (15) are inconsistent by
% 177.74/28.22  | |            sub-proof #489.
% 177.74/28.22  | | 
% 177.74/28.22  | Case 2:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (16)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (1), (2), (3), (9), (10), (11), (12), (13), (14), (16) are
% 177.74/28.22  | |            inconsistent by sub-proof #765.
% 177.74/28.22  | | 
% 177.74/28.22  | End of split
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #489 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)  op(e3, all_4_2) = all_4_1
% 177.74/28.22    (2)  all_58_0 = all_4_2
% 177.74/28.22    (3)   ~ (all_4_1 = e2)
% 177.74/28.22    (4)  op(all_4_1, all_4_2) = e2
% 177.74/28.22    (5)  op(e3, e3) = all_4_2
% 177.74/28.22    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (7)  all_58_0 = e3
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | COMBINE_EQS: (2), (7) imply:
% 177.74/28.22  |   (8)  all_4_2 = e3
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (4), (8) imply:
% 177.74/28.22  |   (9)  op(all_4_1, e3) = e2
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (1), (8) imply:
% 177.74/28.22  |   (10)  op(e3, e3) = all_4_1
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (5), (8) imply:
% 177.74/28.22  |   (11)  op(e3, e3) = e3
% 177.74/28.22  | 
% 177.74/28.22  | REF_CLOSE: (3), (6), (9), (10), (11) are inconsistent by sub-proof #490.
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #490 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)  op(e3, e3) = e3
% 177.74/28.22    (2)   ~ (all_4_1 = e2)
% 177.74/28.22    (3)  op(e3, e3) = all_4_1
% 177.74/28.22    (4)  op(all_4_1, e3) = e2
% 177.74/28.22    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | GROUND_INST: instantiating (5) with e3, all_4_1, e3, e3, simplifying with (1),
% 177.74/28.22  |              (3) gives:
% 177.74/28.22  |   (6)  all_4_1 = e3
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (2), (6) imply:
% 177.74/28.22  |   (7)   ~ (e3 = e2)
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (4), (6) imply:
% 177.74/28.22  |   (8)  op(e3, e3) = e2
% 177.74/28.22  | 
% 177.74/28.22  | GROUND_INST: instantiating (5) with e3, e2, e3, e3, simplifying with (1), (8)
% 177.74/28.22  |              gives:
% 177.74/28.22  |   (9)  e3 = e2
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (7), (9) imply:
% 177.74/28.22  |   (10)  $false
% 177.74/28.22  | 
% 177.74/28.22  | CLOSE: (10) is inconsistent.
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #491 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)   ~ (all_52_5 = all_52_13)
% 177.74/28.22    (2)   ~ (all_52_13 = all_52_29)
% 177.74/28.22    (3)  op(e0, e3) = e1
% 177.74/28.22    (4)  all_58_5 = all_52_13
% 177.74/28.22    (5)  op(e1, all_52_13) = e1
% 177.74/28.22    (6)  op(e0, all_52_15) = e0
% 177.74/28.22    (7)   ~ (all_4_2 = e3)
% 177.74/28.22    (8)  all_58_3 = all_10_2
% 177.74/28.22    (9)   ~ (all_52_26 = all_4_2)
% 177.74/28.22    (10)  all_58_10 = all_52_15
% 177.74/28.22    (11)  all_58_7 = all_52_19
% 177.74/28.22    (12)   ~ (all_52_17 = all_52_25)
% 177.74/28.22    (13)  all_58_4 = all_52_5
% 177.74/28.22    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.22    (15)   ~ (e3 = e1)
% 177.74/28.22    (16)   ~ (all_52_17 = all_14_2)
% 177.74/28.22    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.22    (18)   ~ (all_52_13 = all_52_15)
% 177.74/28.22    (19)  all_58_0 = all_4_2
% 177.74/28.22    (20)  all_58_14 = all_52_29
% 177.74/28.22    (21)   ~ (all_10_2 = e3)
% 177.74/28.22    (22)   ~ (all_52_13 = all_52_26)
% 177.74/28.22    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.22    (24)  all_58_8 = all_14_2
% 177.74/28.22    (25)   ~ (all_52_23 = e3)
% 177.74/28.22    (26)   ~ (all_52_29 = e3)
% 177.74/28.22    (27)   ~ (all_52_13 = all_14_2)
% 177.74/28.22    (28)   ~ (all_52_13 = all_52_24)
% 177.74/28.22    (29)  all_58_6 = all_52_17
% 177.74/28.22    (30)  all_58_2 = all_52_26
% 177.74/28.22    (31)   ~ (e1 = e0)
% 177.74/28.22    (32)  all_58_11 = all_52_23
% 177.74/28.22    (33)   ~ (all_52_19 = e3)
% 177.74/28.22    (34)  op(e1, e3) = all_52_17
% 177.74/28.22    (35)  op(e3, e3) = all_4_2
% 177.74/28.22    (36)   ~ (all_14_2 = e3)
% 177.74/28.22    (37)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (38)  all_58_4 = all_52_24
% 177.74/28.22    (39)   ~ (all_52_13 = all_10_2)
% 177.74/28.22    (40)  all_58_12 = all_52_25
% 177.74/28.22    (41)  op(e3, all_52_26) = e3
% 177.74/28.22    (42)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | BETA: splitting (42) gives:
% 177.74/28.22  | 
% 177.74/28.22  | Case 1:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (43)  all_58_4 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (3), (4), (6), (8), (9), (10), (17), (21), (28), (30), (31),
% 177.74/28.22  | |            (35), (37), (38), (41), (43) are inconsistent by sub-proof #493.
% 177.74/28.22  | | 
% 177.74/28.22  | Case 2:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (44)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 177.74/28.22  | |            (15), (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 177.74/28.22  | |            (27), (29), (30), (32), (33), (34), (35), (36), (37), (39), (40),
% 177.74/28.22  | |            (41), (42), (44) are inconsistent by sub-proof #492.
% 177.74/28.22  | | 
% 177.74/28.22  | End of split
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #492 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)   ~ (all_52_5 = all_52_13)
% 177.74/28.22    (2)   ~ (all_52_13 = all_52_29)
% 177.74/28.22    (3)  all_58_5 = all_52_13
% 177.74/28.22    (4)  op(e1, all_52_13) = e1
% 177.74/28.22    (5)   ~ (all_4_2 = e3)
% 177.74/28.22    (6)  all_58_3 = all_10_2
% 177.74/28.22    (7)   ~ (all_52_26 = all_4_2)
% 177.74/28.22    (8)  all_58_10 = all_52_15
% 177.74/28.22    (9)  all_58_7 = all_52_19
% 177.74/28.22    (10)   ~ (all_52_17 = all_52_25)
% 177.74/28.22    (11)  all_58_4 = all_52_5
% 177.74/28.22    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.22    (13)   ~ (e3 = e1)
% 177.74/28.22    (14)   ~ (all_52_17 = all_14_2)
% 177.74/28.22    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.22    (16)   ~ (all_52_13 = all_52_15)
% 177.74/28.22    (17)  all_58_0 = all_4_2
% 177.74/28.22    (18)  all_58_14 = all_52_29
% 177.74/28.22    (19)   ~ (all_52_13 = all_52_26)
% 177.74/28.22    (20)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.22    (21)  all_58_8 = all_14_2
% 177.74/28.22    (22)   ~ (all_52_23 = e3)
% 177.74/28.22    (23)   ~ (all_52_29 = e3)
% 177.74/28.22    (24)   ~ (all_52_13 = all_14_2)
% 177.74/28.22    (25)  all_58_6 = all_52_17
% 177.74/28.22    (26)  all_58_2 = all_52_26
% 177.74/28.22    (27)  all_58_11 = all_52_23
% 177.74/28.22    (28)   ~ (all_52_19 = e3)
% 177.74/28.22    (29)  op(e1, e3) = all_52_17
% 177.74/28.22    (30)  op(e3, e3) = all_4_2
% 177.74/28.22    (31)   ~ (all_14_2 = e3)
% 177.74/28.22    (32)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.22    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (34)   ~ (all_52_13 = all_10_2)
% 177.74/28.22    (35)  all_58_12 = all_52_25
% 177.74/28.22    (36)  op(e3, all_52_26) = e3
% 177.74/28.22    (37)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | BETA: splitting (32) gives:
% 177.74/28.22  | 
% 177.74/28.22  | Case 1:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (38)  all_58_5 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | COMBINE_EQS: (3), (38) imply:
% 177.74/28.22  | |   (39)  all_52_13 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | SIMP: (39) implies:
% 177.74/28.22  | |   (40)  all_52_13 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REDUCE: (1), (40) imply:
% 177.74/28.22  | |   (41)   ~ (all_52_5 = e3)
% 177.74/28.22  | | 
% 177.74/28.22  | | REDUCE: (16), (40) imply:
% 177.74/28.22  | |   (42)   ~ (all_52_15 = e3)
% 177.74/28.22  | | 
% 177.74/28.22  | | SIMP: (42) implies:
% 177.74/28.22  | |   (43)   ~ (all_52_15 = e3)
% 177.74/28.22  | | 
% 177.74/28.22  | | REDUCE: (34), (40) imply:
% 177.74/28.22  | |   (44)   ~ (all_10_2 = e3)
% 177.74/28.22  | | 
% 177.74/28.22  | | SIMP: (44) implies:
% 177.74/28.22  | |   (45)   ~ (all_10_2 = e3)
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 177.74/28.22  | |            (14), (15), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 177.74/28.22  | |            (27), (28), (29), (30), (33), (35), (36), (37), (41), (43), (45)
% 177.74/28.22  | |            are inconsistent by sub-proof #984.
% 177.74/28.22  | | 
% 177.74/28.22  | Case 2:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (46)  all_58_8 = e3 | all_58_14 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (18), (21), (23), (31), (46) are inconsistent by sub-proof #999.
% 177.74/28.22  | | 
% 177.74/28.22  | End of split
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #493 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)  op(e0, e3) = e1
% 177.74/28.22    (2)  all_58_5 = all_52_13
% 177.74/28.22    (3)  all_58_4 = e3
% 177.74/28.22    (4)  op(e0, all_52_15) = e0
% 177.74/28.22    (5)  all_58_3 = all_10_2
% 177.74/28.22    (6)   ~ (all_52_26 = all_4_2)
% 177.74/28.22    (7)  all_58_10 = all_52_15
% 177.74/28.22    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.22    (9)   ~ (all_10_2 = e3)
% 177.74/28.22    (10)   ~ (all_52_13 = all_52_24)
% 177.74/28.22    (11)  all_58_2 = all_52_26
% 177.74/28.22    (12)   ~ (e1 = e0)
% 177.74/28.22    (13)  op(e3, e3) = all_4_2
% 177.74/28.22    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (15)  all_58_4 = all_52_24
% 177.74/28.22    (16)  op(e3, all_52_26) = e3
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | COMBINE_EQS: (3), (15) imply:
% 177.74/28.22  |   (17)  all_52_24 = e3
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (10), (17) imply:
% 177.74/28.22  |   (18)   ~ (all_52_13 = e3)
% 177.74/28.22  | 
% 177.74/28.22  | BETA: splitting (8) gives:
% 177.74/28.22  | 
% 177.74/28.22  | Case 1:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (19)  all_58_2 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | COMBINE_EQS: (11), (19) imply:
% 177.74/28.22  | |   (20)  all_52_26 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (6), (13), (14), (16), (20) are inconsistent by sub-proof #1005.
% 177.74/28.22  | | 
% 177.74/28.22  | Case 2:
% 177.74/28.22  | | 
% 177.74/28.22  | |   (21)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.22  | | 
% 177.74/28.22  | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (12), (14), (18), (21) are
% 177.74/28.22  | |            inconsistent by sub-proof #968.
% 177.74/28.22  | | 
% 177.74/28.22  | End of split
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #494 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)  op(e3, all_4_2) = all_4_1
% 177.74/28.22    (2)   ~ (all_4_1 = e2)
% 177.74/28.22    (3)  all_52_0 = all_4_1
% 177.74/28.22    (4)  op(all_4_1, all_4_2) = e2
% 177.74/28.22    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.22    (6)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.74/28.22  
% 177.74/28.22  Begin of proof
% 177.74/28.22  | 
% 177.74/28.22  | ALPHA: (6) implies:
% 177.74/28.22  |   (7)  all_52_0 = e3
% 177.74/28.22  | 
% 177.74/28.22  | COMBINE_EQS: (3), (7) imply:
% 177.74/28.22  |   (8)  all_4_1 = e3
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (2), (8) imply:
% 177.74/28.22  |   (9)   ~ (e3 = e2)
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (4), (8) imply:
% 177.74/28.22  |   (10)  op(e3, all_4_2) = e2
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (1), (8) imply:
% 177.74/28.22  |   (11)  op(e3, all_4_2) = e3
% 177.74/28.22  | 
% 177.74/28.22  | GROUND_INST: instantiating (5) with e2, e3, all_4_2, e3, simplifying with
% 177.74/28.22  |              (10), (11) gives:
% 177.74/28.22  |   (12)  e3 = e2
% 177.74/28.22  | 
% 177.74/28.22  | REDUCE: (9), (12) imply:
% 177.74/28.22  |   (13)  $false
% 177.74/28.22  | 
% 177.74/28.22  | CLOSE: (13) is inconsistent.
% 177.74/28.22  | 
% 177.74/28.22  End of proof
% 177.74/28.22  
% 177.74/28.22  Sub-proof #495 shows that the following formulas are inconsistent:
% 177.74/28.22  ----------------------------------------------------------------
% 177.74/28.22    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.22    (2)   ~ (all_52_5 = all_52_13)
% 177.74/28.22    (3)   ~ (all_52_17 = all_52_23)
% 177.74/28.22    (4)  op(e2, all_52_3) = e2
% 177.74/28.22    (5)   ~ (all_52_13 = all_52_29)
% 177.74/28.22    (6)  op(e3, e2) = all_52_3
% 177.74/28.22    (7)   ~ (all_52_9 = all_52_25)
% 177.74/28.22    (8)   ~ (all_52_19 = all_52_23)
% 177.74/28.22    (9)  all_56_11 = all_52_23
% 177.74/28.22    (10)  op(e1, e2) = all_52_19
% 177.74/28.22    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.74/28.22    (12)   ~ (all_52_3 = all_10_2)
% 177.74/28.22    (13)  all_58_5 = all_52_13
% 177.74/28.22    (14)   ~ (all_52_25 = all_52_29)
% 177.74/28.22    (15)  all_56_15 = all_6_2
% 177.74/28.22    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.74/28.22    (17)  op(e2, e0) = all_52_15
% 177.74/28.22    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.74/28.22    (19)  all_58_3 = all_10_2
% 177.74/28.22    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.22    (21)  all_58_15 = all_6_2
% 177.74/28.22    (22)   ~ (all_52_9 = all_4_2)
% 177.74/28.22    (23)   ~ (all_52_5 = all_52_7)
% 177.74/28.22    (24)  all_58_10 = all_52_15
% 177.74/28.22    (25)   ~ (all_52_5 = all_4_2)
% 177.74/28.22    (26)  all_58_7 = all_52_19
% 177.74/28.22    (27)  all_56_4 = all_52_9
% 177.74/28.22    (28)   ~ (all_52_15 = all_6_2)
% 177.74/28.22    (29)   ~ (all_52_17 = all_52_25)
% 177.74/28.22    (30)  op(e0, e1) = all_52_29
% 177.74/28.22    (31)   ~ (all_4_0 = e2)
% 177.74/28.22    (32)  all_58_4 = all_52_5
% 177.74/28.22    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.22    (34)   ~ (all_52_27 = all_52_29)
% 177.74/28.22    (35)   ~ (all_52_17 = all_14_2)
% 177.74/28.22    (36)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.22    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.22    (38)   ~ (all_52_7 = all_4_2)
% 177.74/28.22    (39)  all_58_1 = all_52_3
% 177.74/28.22    (40)   ~ (all_52_13 = all_52_15)
% 177.74/28.22    (41)  all_58_0 = all_4_2
% 177.74/28.22    (42)  op(e0, e0) = all_6_2
% 177.74/28.22    (43)  op(e1, all_52_29) = all_52_28
% 177.74/28.22    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.74/28.22    (45)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.74/28.22    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.74/28.22    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.22    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.74/28.22    (49)  all_58_14 = all_52_29
% 177.74/28.22    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.74/28.22    (51)   ~ (all_52_3 = all_52_5)
% 177.74/28.22    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.22    (53)  op(e2, e1) = all_52_13
% 177.74/28.22    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.23    (55)  all_58_8 = all_14_2
% 177.74/28.23    (56)  all_56_1 = all_52_3
% 177.74/28.23    (57)  all_56_14 = all_52_29
% 177.74/28.23    (58)   ~ (all_52_5 = all_14_2)
% 177.74/28.23    (59)   ~ (all_52_3 = all_52_27)
% 177.74/28.23    (60)   ~ (all_52_3 = all_4_2)
% 177.74/28.23    (61)  op(e3, all_4_2) = e3
% 177.74/28.23    (62)  op(e0, e3) = all_52_25
% 177.74/28.23    (63)  op(e0, all_6_2) = all_6_1
% 177.74/28.23    (64)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.74/28.23    (65)   ~ (all_52_13 = all_14_2)
% 177.74/28.23    (66)   ~ (e3 = e0)
% 177.74/28.23    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.74/28.23    (68)   ~ (all_52_9 = all_52_13)
% 177.74/28.23    (69)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.23    (70)  op(e0, all_52_23) = all_52_22
% 177.74/28.23    (71)   ~ (all_52_15 = all_52_23)
% 177.74/28.23    (72)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.74/28.23    (73)   ~ (all_52_5 = all_52_29)
% 177.74/28.23    (74)  all_56_2 = all_52_5
% 177.74/28.23    (75)  op(e1, e0) = all_52_23
% 177.74/28.23    (76)  all_56_12 = all_52_25
% 177.74/28.23    (77)  all_58_13 = all_52_27
% 177.74/28.23    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.23    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.74/28.23    (80)   ~ (all_52_9 = all_52_17)
% 177.74/28.23    (81)  all_58_6 = all_52_17
% 177.74/28.23    (82)   ~ (all_52_3 = all_52_7)
% 177.74/28.23    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.74/28.23    (84)   ~ (e1 = e0)
% 177.74/28.23    (85)  all_56_0 = all_4_2
% 177.74/28.23    (86)  all_58_11 = all_52_23
% 177.74/28.23    (87)   ~ (all_52_3 = all_52_19)
% 177.74/28.23    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.74/28.23    (89)   ~ (all_52_7 = all_52_15)
% 177.74/28.23    (90)  op(e0, all_52_15) = all_52_14
% 177.74/28.23    (91)   ~ (all_52_29 = all_14_2)
% 177.74/28.23    (92)   ~ (all_4_0 = e1)
% 177.74/28.23    (93)   ~ (all_52_23 = all_6_2)
% 177.74/28.23    (94)   ~ (all_52_29 = all_6_2)
% 177.74/28.23    (95)  all_58_2 = all_52_9
% 177.74/28.23    (96)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.23    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.74/28.23    (98)  op(e3, e1) = all_52_5
% 177.74/28.23    (99)  all_56_10 = all_14_2
% 177.74/28.23    (100)   ~ (all_52_25 = all_6_2)
% 177.74/28.23    (101)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.23    (102)  op(e1, e1) = all_14_2
% 177.74/28.23    (103)  op(e1, e3) = all_52_17
% 177.74/28.23    (104)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.23    (105)   ~ (all_52_25 = all_4_2)
% 177.74/28.23    (106)  op(e3, e0) = all_52_7
% 177.74/28.23    (107)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.74/28.23             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.74/28.23    (108)   ~ (all_52_17 = all_4_2)
% 177.74/28.23    (109)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.23             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.23    (110)   ~ (all_52_25 = all_52_27)
% 177.74/28.23    (111)   ~ (all_52_27 = all_6_2)
% 177.74/28.23    (112)   ~ (all_52_7 = all_6_2)
% 177.74/28.23    (113)   ~ (all_52_19 = all_52_27)
% 177.74/28.23    (114)  all_56_7 = all_52_15
% 177.74/28.23    (115)  op(e1, all_52_5) = e1
% 177.74/28.23    (116)   ~ (all_52_7 = all_52_23)
% 177.74/28.23    (117)   ~ (all_52_13 = all_10_2)
% 177.74/28.23    (118)  op(e3, all_4_2) = all_4_0
% 177.74/28.23    (119)  op(e0, all_52_7) = e0
% 177.74/28.23    (120)  op(e2, all_52_27) = all_52_26
% 177.74/28.23    (121)   ~ (all_52_17 = all_52_19)
% 177.74/28.23    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.23    (123)  all_58_9 = all_52_7
% 177.74/28.23    (124)  all_58_12 = all_52_25
% 177.74/28.23    (125)  op(all_6_1, all_6_2) = e3
% 177.74/28.23    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.23    (127)   ~ (all_52_9 = all_52_15)
% 177.74/28.23    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.23    (129)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.23    (130)   ~ (all_52_19 = all_14_2)
% 177.74/28.23    (131)  op(e2, e3) = all_52_9
% 177.74/28.23    (132)  all_56_13 = all_52_27
% 177.74/28.23  
% 177.74/28.23  Begin of proof
% 177.74/28.23  | 
% 177.74/28.23  | GROUND_INST: instantiating (109) with e3, all_4_0, all_4_2, e3, simplifying
% 177.74/28.23  |              with (61), (118) gives:
% 177.74/28.23  |   (133)  all_4_0 = e3
% 177.74/28.23  | 
% 177.74/28.23  | BETA: splitting (107) gives:
% 177.74/28.23  | 
% 177.74/28.23  | Case 1:
% 177.74/28.23  | | 
% 177.74/28.23  | |   (134)  all_58_15 = e0
% 177.74/28.23  | | 
% 177.74/28.23  | | REF_CLOSE: (21), (42), (63), (66), (109), (125), (134) are inconsistent by
% 177.74/28.23  | |            sub-proof #510.
% 177.74/28.23  | | 
% 177.74/28.23  | Case 2:
% 177.74/28.23  | | 
% 177.74/28.23  | |   (135)   ~ (all_58_15 = e0)
% 177.74/28.23  | |   (136)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.74/28.23  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.74/28.23  | | 
% 177.74/28.23  | | ALPHA: (136) implies:
% 177.74/28.23  | |   (137)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (21), (135) imply:
% 177.74/28.23  | |   (138)   ~ (all_6_2 = e0)
% 177.74/28.23  | | 
% 177.74/28.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.74/28.23  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.74/28.23  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.74/28.23  | |            (35), (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 177.74/28.23  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.74/28.23  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.74/28.23  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.74/28.23  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 177.74/28.23  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.74/28.23  | |            (101), (102), (103), (104), (105), (106), (108), (109), (110),
% 177.74/28.23  | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 177.74/28.23  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 177.74/28.23  | |            (129), (130), (131), (132), (137), (138) are inconsistent by
% 177.74/28.23  | |            sub-proof #496.
% 177.74/28.23  | | 
% 177.74/28.23  | End of split
% 177.74/28.23  | 
% 177.74/28.23  End of proof
% 177.74/28.23  
% 177.74/28.23  Sub-proof #496 shows that the following formulas are inconsistent:
% 177.74/28.23  ----------------------------------------------------------------
% 177.74/28.23    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.23    (2)   ~ (all_52_5 = all_52_13)
% 177.74/28.23    (3)   ~ (all_52_17 = all_52_23)
% 177.74/28.23    (4)  op(e2, all_52_3) = e2
% 177.74/28.23    (5)   ~ (all_52_13 = all_52_29)
% 177.74/28.23    (6)  op(e3, e2) = all_52_3
% 177.74/28.23    (7)   ~ (all_52_9 = all_52_25)
% 177.74/28.23    (8)   ~ (all_52_19 = all_52_23)
% 177.74/28.23    (9)  all_56_11 = all_52_23
% 177.74/28.23    (10)  op(e1, e2) = all_52_19
% 177.74/28.23    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.74/28.23    (12)   ~ (all_52_3 = all_10_2)
% 177.74/28.23    (13)  all_58_5 = all_52_13
% 177.74/28.23    (14)   ~ (all_6_2 = e0)
% 177.74/28.23    (15)   ~ (all_52_25 = all_52_29)
% 177.74/28.23    (16)  all_56_15 = all_6_2
% 177.74/28.23    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.74/28.23    (18)  op(e2, e0) = all_52_15
% 177.74/28.23    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.74/28.23    (20)  all_58_3 = all_10_2
% 177.74/28.23    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.23    (22)  all_58_15 = all_6_2
% 177.74/28.23    (23)   ~ (all_52_9 = all_4_2)
% 177.74/28.23    (24)   ~ (all_52_5 = all_52_7)
% 177.74/28.23    (25)  all_58_10 = all_52_15
% 177.74/28.23    (26)   ~ (all_52_5 = all_4_2)
% 177.74/28.23    (27)  all_58_7 = all_52_19
% 177.74/28.23    (28)  all_56_4 = all_52_9
% 177.74/28.23    (29)   ~ (all_52_15 = all_6_2)
% 177.74/28.23    (30)   ~ (all_52_17 = all_52_25)
% 177.74/28.23    (31)  op(e0, e1) = all_52_29
% 177.74/28.23    (32)   ~ (all_4_0 = e2)
% 177.74/28.23    (33)  all_58_4 = all_52_5
% 177.74/28.23    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.23    (35)   ~ (all_52_27 = all_52_29)
% 177.74/28.23    (36)   ~ (all_52_17 = all_14_2)
% 177.74/28.23    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.23    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.23    (39)   ~ (all_52_7 = all_4_2)
% 177.74/28.23    (40)  all_58_1 = all_52_3
% 177.74/28.23    (41)   ~ (all_52_13 = all_52_15)
% 177.74/28.23    (42)  all_58_0 = all_4_2
% 177.74/28.23    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.74/28.23    (44)  op(e1, all_52_29) = all_52_28
% 177.74/28.23    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.74/28.23    (46)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.74/28.23    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.74/28.23    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.23    (49)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.74/28.23    (50)  all_58_14 = all_52_29
% 177.74/28.23    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.74/28.23    (52)   ~ (all_52_3 = all_52_5)
% 177.74/28.23    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.23    (54)  op(e2, e1) = all_52_13
% 177.74/28.23    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.23    (56)  all_58_8 = all_14_2
% 177.74/28.23    (57)  all_56_1 = all_52_3
% 177.74/28.23    (58)  all_56_14 = all_52_29
% 177.74/28.23    (59)   ~ (all_52_5 = all_14_2)
% 177.74/28.23    (60)   ~ (all_52_3 = all_52_27)
% 177.74/28.23    (61)   ~ (all_52_3 = all_4_2)
% 177.74/28.23    (62)  op(e3, all_4_2) = e3
% 177.74/28.23    (63)  op(e0, e3) = all_52_25
% 177.74/28.23    (64)  op(e0, all_6_2) = all_6_1
% 177.74/28.23    (65)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.74/28.23    (66)   ~ (all_52_13 = all_14_2)
% 177.74/28.23    (67)   ~ (e3 = e0)
% 177.74/28.23    (68)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.74/28.23    (69)   ~ (all_52_9 = all_52_13)
% 177.74/28.23    (70)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.23    (71)  op(e0, all_52_23) = all_52_22
% 177.74/28.23    (72)   ~ (all_52_15 = all_52_23)
% 177.74/28.23    (73)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.74/28.23    (74)   ~ (all_52_5 = all_52_29)
% 177.74/28.23    (75)  all_56_2 = all_52_5
% 177.74/28.23    (76)  op(e1, e0) = all_52_23
% 177.74/28.23    (77)  all_56_12 = all_52_25
% 177.74/28.23    (78)  all_58_13 = all_52_27
% 177.74/28.23    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.23    (80)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.74/28.23    (81)   ~ (all_52_9 = all_52_17)
% 177.74/28.23    (82)  all_58_6 = all_52_17
% 177.74/28.23    (83)   ~ (all_52_3 = all_52_7)
% 177.74/28.23    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.74/28.23    (85)   ~ (e1 = e0)
% 177.74/28.23    (86)  all_56_0 = all_4_2
% 177.74/28.23    (87)  all_58_11 = all_52_23
% 177.74/28.23    (88)   ~ (all_52_3 = all_52_19)
% 177.74/28.23    (89)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.74/28.23    (90)   ~ (all_52_7 = all_52_15)
% 177.74/28.23    (91)  op(e0, all_52_15) = all_52_14
% 177.74/28.23    (92)   ~ (all_52_29 = all_14_2)
% 177.74/28.23    (93)   ~ (all_4_0 = e1)
% 177.74/28.23    (94)   ~ (all_52_23 = all_6_2)
% 177.74/28.23    (95)   ~ (all_52_29 = all_6_2)
% 177.74/28.23    (96)  all_58_2 = all_52_9
% 177.74/28.23    (97)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.23    (98)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.74/28.23    (99)  op(e3, e1) = all_52_5
% 177.74/28.23    (100)  all_56_10 = all_14_2
% 177.74/28.23    (101)   ~ (all_52_25 = all_6_2)
% 177.74/28.23    (102)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.23    (103)  op(e1, e1) = all_14_2
% 177.74/28.23    (104)  op(e1, e3) = all_52_17
% 177.74/28.23    (105)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.23    (106)   ~ (all_52_25 = all_4_2)
% 177.74/28.23    (107)  op(e3, e0) = all_52_7
% 177.74/28.23    (108)   ~ (all_52_17 = all_4_2)
% 177.74/28.23    (109)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.23             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.23    (110)   ~ (all_52_25 = all_52_27)
% 177.74/28.23    (111)   ~ (all_52_27 = all_6_2)
% 177.74/28.23    (112)   ~ (all_52_7 = all_6_2)
% 177.74/28.23    (113)   ~ (all_52_19 = all_52_27)
% 177.74/28.23    (114)  all_56_7 = all_52_15
% 177.74/28.23    (115)  op(e1, all_52_5) = e1
% 177.74/28.23    (116)   ~ (all_52_7 = all_52_23)
% 177.74/28.23    (117)   ~ (all_52_13 = all_10_2)
% 177.74/28.23    (118)  op(e3, all_4_2) = all_4_0
% 177.74/28.23    (119)  op(e0, all_52_7) = e0
% 177.74/28.23    (120)  op(e2, all_52_27) = all_52_26
% 177.74/28.23    (121)   ~ (all_52_17 = all_52_19)
% 177.74/28.23    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.23    (123)  all_58_9 = all_52_7
% 177.74/28.23    (124)  all_58_12 = all_52_25
% 177.74/28.23    (125)  op(all_6_1, all_6_2) = e3
% 177.74/28.23    (126)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.23    (127)   ~ (all_52_9 = all_52_15)
% 177.74/28.23    (128)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.23    (129)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.23    (130)   ~ (all_52_19 = all_14_2)
% 177.74/28.23    (131)  op(e2, e3) = all_52_9
% 177.74/28.23    (132)  all_56_13 = all_52_27
% 177.74/28.23  
% 177.74/28.23  Begin of proof
% 177.74/28.23  | 
% 177.74/28.23  | GROUND_INST: instantiating (109) with e3, all_4_0, all_4_2, e3, simplifying
% 177.74/28.23  |              with (62), (118) gives:
% 177.74/28.23  |   (133)  all_4_0 = e3
% 177.74/28.23  | 
% 177.74/28.23  | REDUCE: (32), (133) imply:
% 177.74/28.23  |   (134)   ~ (e3 = e2)
% 177.74/28.23  | 
% 177.74/28.23  | REDUCE: (93), (133) imply:
% 177.74/28.23  |   (135)   ~ (e3 = e1)
% 177.74/28.23  | 
% 177.74/28.23  | BETA: splitting (37) gives:
% 177.74/28.23  | 
% 177.74/28.23  | Case 1:
% 177.74/28.23  | | 
% 177.74/28.23  | |   (136)  all_56_15 = e3
% 177.74/28.23  | | 
% 177.74/28.23  | | COMBINE_EQS: (16), (136) imply:
% 177.74/28.23  | |   (137)  all_6_2 = e3
% 177.74/28.23  | | 
% 177.74/28.23  | | SIMP: (137) implies:
% 177.74/28.23  | |   (138)  all_6_2 = e3
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (101), (138) imply:
% 177.74/28.23  | |   (139)   ~ (all_52_25 = e3)
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (95), (138) imply:
% 177.74/28.23  | |   (140)   ~ (all_52_29 = e3)
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (125), (138) imply:
% 177.74/28.23  | |   (141)  op(all_6_1, e3) = e3
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (64), (138) imply:
% 177.74/28.23  | |   (142)  op(e0, e3) = all_6_1
% 177.74/28.23  | | 
% 177.74/28.23  | | GROUND_INST: instantiating (109) with all_52_25, all_6_1, e3, e0,
% 177.74/28.23  | |              simplifying with (63), (142) gives:
% 177.74/28.23  | |   (143)  all_52_25 = all_6_1
% 177.74/28.23  | | 
% 177.74/28.23  | | COMBINE_EQS: (77), (143) imply:
% 177.74/28.23  | |   (144)  all_56_12 = all_6_1
% 177.74/28.23  | | 
% 177.74/28.23  | | COMBINE_EQS: (124), (143) imply:
% 177.74/28.23  | |   (145)  all_58_12 = all_6_1
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (106), (143) imply:
% 177.74/28.23  | |   (146)   ~ (all_6_1 = all_4_2)
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (139), (143) imply:
% 177.74/28.23  | |   (147)   ~ (all_6_1 = e3)
% 177.74/28.23  | | 
% 177.74/28.23  | | BETA: splitting (70) gives:
% 177.74/28.23  | | 
% 177.74/28.23  | | Case 1:
% 177.74/28.23  | | | 
% 177.74/28.23  | | |   (148)  all_56_12 = e3
% 177.74/28.23  | | | 
% 177.74/28.23  | | | REF_CLOSE: (144), (147), (148) are inconsistent by sub-proof #509.
% 177.74/28.23  | | | 
% 177.74/28.23  | | Case 2:
% 177.74/28.23  | | | 
% 177.74/28.23  | | |   (149)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.23  | | | 
% 177.74/28.23  | | | BETA: splitting (53) gives:
% 177.74/28.23  | | | 
% 177.74/28.23  | | | Case 1:
% 177.74/28.23  | | | | 
% 177.74/28.23  | | | |   (150)  all_58_0 = e3
% 177.74/28.23  | | | | 
% 177.74/28.23  | | | | REF_CLOSE: (23), (42), (97), (102), (104), (108), (109), (131), (141),
% 177.74/28.23  | | | |            (142), (144), (145), (146), (149), (150) are inconsistent by
% 177.74/28.23  | | | |            sub-proof #497.
% 177.74/28.23  | | | | 
% 177.74/28.23  | | | Case 2:
% 177.74/28.23  | | | | 
% 177.74/28.23  | | | |   (151)   ~ (all_58_0 = e3)
% 177.74/28.23  | | | | 
% 177.74/28.23  | | | | REDUCE: (42), (151) imply:
% 177.74/28.23  | | | |   (152)   ~ (all_4_2 = e3)
% 177.74/28.23  | | | | 
% 177.74/28.23  | | | | REF_CLOSE: (1), (2), (4), (6), (13), (21), (22), (23), (24), (25), (26),
% 177.74/28.23  | | | |            (27), (33), (34), (36), (39), (40), (42), (50), (52), (56),
% 177.74/28.23  | | | |            (59), (62), (63), (66), (68), (73), (74), (79), (82), (83),
% 177.74/28.23  | | | |            (86), (87), (88), (90), (92), (99), (100), (104), (106),
% 177.74/28.23  | | | |            (107), (108), (109), (112), (115), (116), (119), (122),
% 177.74/28.23  | | | |            (123), (126), (128), (131), (140), (152) are inconsistent by
% 177.74/28.23  | | | |            sub-proof #864.
% 177.74/28.23  | | | | 
% 177.74/28.23  | | | End of split
% 177.74/28.23  | | | 
% 177.74/28.23  | | End of split
% 177.74/28.23  | | 
% 177.74/28.23  | Case 2:
% 177.74/28.23  | | 
% 177.74/28.23  | |   (153)   ~ (all_56_15 = e3)
% 177.74/28.23  | |   (154)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.23  | | 
% 177.74/28.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.74/28.23  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.74/28.23  | |            (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35),
% 177.74/28.23  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.74/28.23  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 177.74/28.23  | |            (60), (61), (62), (63), (65), (66), (67), (68), (69), (70), (71),
% 177.74/28.23  | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 177.74/28.23  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (94),
% 177.74/28.23  | |            (95), (96), (98), (99), (100), (101), (103), (104), (105), (106),
% 177.74/28.23  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 177.74/28.23  | |            (116), (117), (119), (120), (121), (122), (123), (124), (126),
% 177.74/28.23  | |            (127), (128), (129), (130), (131), (132), (134), (135), (153),
% 177.74/28.23  | |            (154) are inconsistent by sub-proof #785.
% 177.74/28.23  | | 
% 177.74/28.23  | End of split
% 177.74/28.23  | 
% 177.74/28.23  End of proof
% 177.74/28.23  
% 177.74/28.23  Sub-proof #497 shows that the following formulas are inconsistent:
% 177.74/28.23  ----------------------------------------------------------------
% 177.74/28.23    (1)   ~ (all_6_1 = all_4_2)
% 177.74/28.23    (2)  all_58_12 = all_6_1
% 177.74/28.23    (3)   ~ (all_52_9 = all_4_2)
% 177.74/28.23    (4)  all_58_0 = all_4_2
% 177.74/28.23    (5)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.23    (6)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.23    (7)  op(e0, e3) = all_6_1
% 177.74/28.23    (8)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.23    (9)  op(e1, e3) = all_52_17
% 177.74/28.23    (10)   ~ (all_52_17 = all_4_2)
% 177.74/28.23    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.23    (12)  all_56_12 = all_6_1
% 177.74/28.23    (13)  op(all_6_1, e3) = e3
% 177.74/28.23    (14)  all_58_0 = e3
% 177.74/28.23    (15)  op(e2, e3) = all_52_9
% 177.74/28.23  
% 177.74/28.23  Begin of proof
% 177.74/28.23  | 
% 177.74/28.23  | COMBINE_EQS: (4), (14) imply:
% 177.74/28.23  |   (16)  all_4_2 = e3
% 177.74/28.23  | 
% 177.74/28.23  | REDUCE: (3), (16) imply:
% 177.74/28.23  |   (17)   ~ (all_52_9 = e3)
% 177.74/28.23  | 
% 177.74/28.23  | REDUCE: (10), (16) imply:
% 177.74/28.23  |   (18)   ~ (all_52_17 = e3)
% 177.74/28.23  | 
% 177.74/28.23  | REDUCE: (1), (16) imply:
% 177.74/28.23  |   (19)   ~ (all_6_1 = e3)
% 177.74/28.23  | 
% 177.74/28.23  | BETA: splitting (8) gives:
% 177.74/28.23  | 
% 177.74/28.23  | Case 1:
% 177.74/28.23  | | 
% 177.74/28.23  | |   (20)  all_58_12 = e2
% 177.74/28.23  | | 
% 177.74/28.23  | | COMBINE_EQS: (2), (20) imply:
% 177.74/28.23  | |   (21)  all_6_1 = e2
% 177.74/28.23  | | 
% 177.74/28.23  | | SIMP: (21) implies:
% 177.74/28.23  | |   (22)  all_6_1 = e2
% 177.74/28.23  | | 
% 177.74/28.23  | | REDUCE: (13), (22) imply:
% 177.74/28.23  | |   (23)  op(e2, e3) = e3
% 177.74/28.23  | | 
% 177.74/28.23  | | REF_CLOSE: (11), (15), (17), (23) are inconsistent by sub-proof #498.
% 177.74/28.23  | | 
% 177.74/28.23  | Case 2:
% 177.74/28.23  | | 
% 177.74/28.23  | |   (24)   ~ (all_58_12 = e2)
% 177.74/28.23  | | 
% 177.74/28.23  | | REF_CLOSE: (2), (5), (6), (7), (9), (11), (12), (13), (18), (19), (24) are
% 177.74/28.23  | |            inconsistent by sub-proof #505.
% 177.74/28.23  | | 
% 177.74/28.23  | End of split
% 177.74/28.23  | 
% 177.74/28.23  End of proof
% 177.74/28.23  
% 177.74/28.23  Sub-proof #498 shows that the following formulas are inconsistent:
% 177.74/28.23  ----------------------------------------------------------------
% 177.74/28.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.23    (2)  op(e2, e3) = all_52_9
% 177.74/28.23    (3)  op(e2, e3) = e3
% 177.74/28.23    (4)   ~ (all_52_9 = e3)
% 177.74/28.23  
% 177.74/28.23  Begin of proof
% 177.74/28.23  | 
% 177.74/28.23  | GROUND_INST: instantiating (1) with all_52_9, e3, e3, e2, simplifying with
% 177.74/28.23  |              (2), (3) gives:
% 177.74/28.23  |   (5)  all_52_9 = e3
% 177.74/28.23  | 
% 177.74/28.23  | REDUCE: (4), (5) imply:
% 177.74/28.23  |   (6)  $false
% 177.74/28.23  | 
% 177.74/28.23  | CLOSE: (6) is inconsistent.
% 177.74/28.23  | 
% 177.74/28.23  End of proof
% 177.74/28.23  
% 177.74/28.23  Sub-proof #499 shows that the following formulas are inconsistent:
% 177.74/28.23  ----------------------------------------------------------------
% 177.74/28.23    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.23    (2)   ~ (all_52_5 = all_52_13)
% 177.74/28.23    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.74/28.23    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.74/28.23    (5)   ~ (all_52_17 = all_52_23)
% 177.74/28.23    (6)  op(e2, all_10_2) = all_10_1
% 177.74/28.23    (7)  all_40_2 = all_4_2
% 177.74/28.23    (8)   ~ (all_52_13 = all_52_29)
% 177.74/28.23    (9)  op(e3, e2) = all_52_3
% 177.74/28.23    (10)   ~ (all_52_9 = all_52_25)
% 177.74/28.23    (11)  op(e3, all_52_25) = all_52_24
% 177.74/28.23    (12)   ~ (all_52_19 = all_52_23)
% 177.74/28.23    (13)  all_56_11 = all_52_23
% 177.74/28.23    (14)  op(e1, e2) = all_52_19
% 177.74/28.23    (15)  op(e3, all_52_9) = all_52_8
% 177.74/28.23    (16)   ~ (all_52_3 = all_10_2)
% 177.74/28.23    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.74/28.23    (18)  all_58_5 = all_52_13
% 177.74/28.23    (19)   ~ (all_52_25 = all_52_29)
% 177.74/28.23    (20)  all_56_15 = all_6_2
% 177.74/28.23    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.74/28.23    (22)  op(e2, e0) = all_52_15
% 177.74/28.23    (23)  op(all_14_1, all_14_2) = all_14_0
% 177.74/28.23    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.74/28.23    (25)  all_58_3 = all_10_2
% 177.74/28.23    (26)  all_56_9 = all_52_19
% 177.74/28.23    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.23    (28)  all_58_15 = all_6_2
% 177.74/28.23    (29)   ~ (all_52_9 = all_4_2)
% 177.74/28.23    (30)   ~ (all_52_5 = all_52_7)
% 177.74/28.23    (31)  all_58_10 = all_52_15
% 177.74/28.23    (32)   ~ (all_52_5 = all_4_2)
% 177.74/28.23    (33)  all_58_7 = all_52_19
% 177.74/28.23    (34)   ~ (all_52_17 = all_52_25)
% 177.74/28.23    (35)  op(e0, e1) = all_52_29
% 177.74/28.23    (36)   ~ (all_4_0 = e2)
% 177.74/28.23    (37)  all_58_4 = all_52_5
% 177.74/28.23    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.23    (39)   ~ (all_52_27 = all_52_29)
% 177.74/28.23    (40)   ~ (all_52_17 = all_14_2)
% 177.74/28.23    (41)  op(e3, all_4_2) = all_4_1
% 177.74/28.23    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.23    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.23    (44)   ~ (all_52_7 = all_4_2)
% 177.74/28.23    (45)  all_58_1 = all_52_3
% 177.74/28.23    (46)  all_58_0 = all_4_2
% 177.74/28.23    (47)  op(e1, all_52_29) = all_52_28
% 177.74/28.23    (48)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.74/28.23    (49)   ~ (all_4_1 = e2)
% 177.74/28.23    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.74/28.23    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.23    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.74/28.23    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.74/28.23    (54)  all_58_14 = all_52_29
% 177.74/28.23    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.74/28.23    (56)   ~ (all_52_3 = all_52_5)
% 177.74/28.23    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.23    (58)  op(e2, e1) = all_52_13
% 177.74/28.23    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.23    (60)  all_58_8 = all_14_2
% 177.74/28.23    (61)  op(e0, e2) = all_52_27
% 177.74/28.23    (62)   ~ (all_14_0 = e3)
% 177.74/28.23    (63)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.74/28.23    (64)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.74/28.23    (65)  op(all_4_1, all_4_2) = all_4_0
% 177.74/28.23    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.74/28.23    (67)   ~ (all_52_5 = all_14_2)
% 177.74/28.23    (68)   ~ (all_52_3 = all_52_27)
% 177.74/28.23    (69)   ~ (all_52_3 = all_4_2)
% 177.74/28.23    (70)  op(e0, e3) = all_52_25
% 177.74/28.23    (71)   ~ (all_52_9 = all_10_2)
% 177.74/28.23    (72)  op(e3, all_52_17) = all_52_16
% 177.74/28.23    (73)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.74/28.23    (74)   ~ (all_52_13 = all_14_2)
% 177.74/28.23    (75)   ~ (e3 = e0)
% 177.74/28.23    (76)  all_40_0 = all_4_0
% 177.74/28.23    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.74/28.23    (78)   ~ (all_52_9 = all_52_13)
% 177.74/28.23    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.23    (80)  op(e0, all_52_23) = all_52_22
% 177.74/28.23    (81)   ~ (all_52_15 = all_52_23)
% 177.74/28.23    (82)   ~ (all_52_5 = all_52_29)
% 177.74/28.23    (83)  all_56_12 = all_52_25
% 177.74/28.23    (84)  all_58_13 = all_52_27
% 177.74/28.23    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.23    (86)  all_56_5 = all_10_2
% 177.74/28.23    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.74/28.23    (88)   ~ (all_52_9 = all_52_17)
% 177.74/28.23    (89)   ~ (all_14_0 = e2)
% 177.74/28.23    (90)  all_58_6 = all_52_17
% 177.74/28.23    (91)  op(e2, all_52_19) = all_52_18
% 177.74/28.24    (92)   ~ (e1 = e0)
% 177.74/28.24    (93)  all_56_0 = all_4_2
% 177.74/28.24    (94)  all_58_11 = all_52_23
% 177.74/28.24    (95)   ~ (all_52_3 = all_52_19)
% 177.74/28.24    (96)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.74/28.24    (97)   ~ (all_52_7 = all_52_15)
% 177.74/28.24    (98)   ~ (all_52_29 = all_14_2)
% 177.74/28.24    (99)   ~ (all_4_0 = e1)
% 177.74/28.24    (100)   ~ (all_52_19 = all_10_2)
% 177.74/28.24    (101)   ~ (all_52_23 = all_6_2)
% 177.74/28.24    (102)  op(e1, all_4_2) = all_4_0
% 177.74/28.24    (103)   ~ (all_52_29 = all_6_2)
% 177.74/28.24    (104)  all_58_2 = all_52_9
% 177.74/28.24    (105)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.24    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.74/28.24    (107)  op(e3, e1) = all_52_5
% 177.74/28.24    (108)   ~ (all_52_25 = all_6_2)
% 177.74/28.24    (109)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.74/28.24    (110)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.24    (111)  op(e1, e3) = all_52_17
% 177.74/28.24    (112)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.24    (113)   ~ (all_52_25 = all_4_2)
% 177.74/28.24    (114)  op(e3, e0) = all_52_7
% 177.74/28.24    (115)  op(e3, e3) = all_4_2
% 177.74/28.24    (116)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.74/28.24             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.74/28.24    (117)   ~ (all_10_1 = e3)
% 177.74/28.24    (118)  all_56_8 = all_52_17
% 177.74/28.24    (119)   ~ (all_52_17 = all_4_2)
% 177.74/28.24    (120)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.24             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.24    (121)   ~ (all_52_25 = all_52_27)
% 177.74/28.24    (122)   ~ (all_52_27 = all_6_2)
% 177.74/28.24    (123)   ~ (all_52_7 = all_6_2)
% 177.74/28.24    (124)   ~ (all_52_15 = all_10_2)
% 177.74/28.24    (125)   ~ (all_52_19 = all_52_27)
% 177.74/28.24    (126)  all_56_7 = all_52_15
% 177.74/28.24    (127)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.74/28.24    (128)   ~ (all_52_7 = all_52_23)
% 177.74/28.24    (129)   ~ (all_52_13 = all_10_2)
% 177.74/28.24    (130)  all_52_20 = all_14_1
% 177.74/28.24    (131)   ~ (all_52_17 = all_52_19)
% 177.74/28.24    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.24    (133)  op(e1, all_14_2) = all_14_1
% 177.74/28.24    (134)  all_58_9 = all_52_7
% 177.74/28.24    (135)   ~ (e2 = e0)
% 177.74/28.24    (136)  all_58_12 = all_52_25
% 177.74/28.24    (137)  op(e3, all_4_2) = e1
% 177.74/28.24    (138)  all_56_6 = all_52_13
% 177.74/28.24    (139)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.24    (140)   ~ (all_52_9 = all_52_15)
% 177.74/28.24    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.24    (142)   ~ (e3 = e2)
% 177.74/28.24    (143)   ~ (all_52_19 = all_14_2)
% 177.74/28.24    (144)  op(e2, e3) = all_52_9
% 177.74/28.24    (145)  all_56_13 = all_52_27
% 177.74/28.24  
% 177.74/28.24  Begin of proof
% 177.74/28.24  | 
% 177.74/28.24  | ALPHA: (127) implies:
% 177.74/28.24  |   (146)  all_52_22 = e0
% 177.74/28.24  |   (147)  all_52_20 = e1
% 177.74/28.24  |   (148)  all_52_18 = e2
% 177.74/28.24  |   (149)  all_52_16 = e3
% 177.74/28.24  | 
% 177.74/28.24  | COMBINE_EQS: (130), (147) imply:
% 177.74/28.24  |   (150)  all_14_1 = e1
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (23), (150) imply:
% 177.74/28.24  |   (151)  op(e1, all_14_2) = all_14_0
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (72), (149) imply:
% 177.74/28.24  |   (152)  op(e3, all_52_17) = e3
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (91), (148) imply:
% 177.74/28.24  |   (153)  op(e2, all_52_19) = e2
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (133), (150) imply:
% 177.74/28.24  |   (154)  op(e1, all_14_2) = e1
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (80), (146) imply:
% 177.74/28.24  |   (155)  op(e0, all_52_23) = e0
% 177.74/28.24  | 
% 177.74/28.24  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.74/28.24  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 177.74/28.24  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.74/28.24  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.74/28.24  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.74/28.24  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.74/28.24  |            (69), (70), (71), (73), (74), (75), (76), (77), (78), (79), (81),
% 177.74/28.24  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (92), (93),
% 177.74/28.24  |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 177.74/28.24  |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 177.74/28.24  |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 177.74/28.24  |            (122), (123), (124), (125), (126), (128), (129), (131), (132),
% 177.74/28.24  |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 177.74/28.24  |            (143), (144), (145), (151), (152), (153), (154), (155) are
% 177.74/28.24  |            inconsistent by sub-proof #531.
% 177.74/28.24  | 
% 177.74/28.24  End of proof
% 177.74/28.24  
% 177.74/28.24  Sub-proof #500 shows that the following formulas are inconsistent:
% 177.74/28.24  ----------------------------------------------------------------
% 177.74/28.24    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.24    (2)   ~ (all_52_5 = all_52_13)
% 177.74/28.24    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.74/28.24    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.74/28.24    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.74/28.24    (6)   ~ (all_52_27 = all_10_2)
% 177.74/28.24    (7)   ~ (all_52_17 = all_52_23)
% 177.74/28.24    (8)  op(e2, all_10_2) = all_10_1
% 177.74/28.24    (9)  all_40_2 = all_4_2
% 177.74/28.24    (10)   ~ (all_52_13 = all_52_29)
% 177.74/28.24    (11)  all_56_3 = all_52_7
% 177.74/28.24    (12)  op(e3, e2) = all_52_3
% 177.74/28.24    (13)   ~ (all_52_9 = all_52_25)
% 177.74/28.24    (14)  op(e3, all_52_25) = all_52_24
% 177.74/28.24    (15)   ~ (all_52_19 = all_52_23)
% 177.74/28.24    (16)  all_56_11 = all_52_23
% 177.74/28.24    (17)  op(e1, e2) = all_52_19
% 177.74/28.24    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.74/28.24    (19)  op(e3, all_52_9) = all_52_8
% 177.74/28.24    (20)   ~ (all_52_3 = all_10_2)
% 177.74/28.24    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.74/28.24    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.74/28.24    (23)  all_58_5 = all_52_13
% 177.74/28.24    (24)   ~ (all_52_25 = all_52_29)
% 177.74/28.24    (25)  all_56_15 = all_6_2
% 177.74/28.24    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.74/28.24    (27)  op(e2, e0) = all_52_15
% 177.74/28.24    (28)  op(all_14_1, all_14_2) = all_14_0
% 177.74/28.24    (29)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.74/28.24    (30)  all_58_3 = all_10_2
% 177.74/28.24    (31)  all_56_9 = all_52_19
% 177.74/28.24    (32)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.24    (33)  all_58_15 = all_6_2
% 177.74/28.24    (34)   ~ (all_52_9 = all_4_2)
% 177.74/28.24    (35)   ~ (all_52_5 = all_52_7)
% 177.74/28.24    (36)  all_58_10 = all_52_15
% 177.74/28.24    (37)   ~ (all_52_5 = all_4_2)
% 177.74/28.24    (38)  all_58_7 = all_52_19
% 177.74/28.24    (39)  all_56_4 = all_52_9
% 177.74/28.24    (40)   ~ (all_52_15 = all_6_2)
% 177.74/28.24    (41)   ~ (all_52_17 = all_52_25)
% 177.74/28.24    (42)  op(e0, e1) = all_52_29
% 177.74/28.24    (43)   ~ (all_4_0 = e2)
% 177.74/28.24    (44)  all_58_4 = all_52_5
% 177.74/28.24    (45)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.24    (46)   ~ (e3 = e1)
% 177.74/28.24    (47)   ~ (all_52_27 = all_52_29)
% 177.74/28.24    (48)   ~ (all_52_17 = all_14_2)
% 177.74/28.24    (49)  op(e3, all_4_2) = all_4_1
% 177.74/28.24    (50)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.24    (51)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.24    (52)   ~ (all_52_7 = all_4_2)
% 177.74/28.24    (53)  all_58_1 = all_52_3
% 177.74/28.24    (54)   ~ (all_52_13 = all_52_15)
% 177.74/28.24    (55)  all_58_0 = all_4_2
% 177.74/28.24    (56)  all_52_0 = e1
% 177.74/28.24    (57)  op(e1, all_52_13) = all_52_12
% 177.74/28.24    (58)  op(e1, all_52_29) = all_52_28
% 177.74/28.24    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.74/28.24    (60)   ~ (all_4_1 = e2)
% 177.74/28.24    (61)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.74/28.24    (62)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.24    (63)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.74/28.24    (64)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.74/28.24    (65)   ~ (all_14_1 = e3)
% 177.74/28.24    (66)  all_58_14 = all_52_29
% 177.74/28.24    (67)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.74/28.24    (68)   ~ (all_52_3 = all_52_5)
% 177.74/28.24    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.24    (70)  op(e2, e1) = all_52_13
% 177.74/28.24    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.24    (72)  all_58_8 = all_14_2
% 177.74/28.24    (73)  op(e0, e2) = all_52_27
% 177.74/28.24    (74)   ~ (all_14_0 = e3)
% 177.74/28.24    (75)   ~ (all_10_1 = e1)
% 177.74/28.24    (76)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.74/28.24    (77)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.74/28.24    (78)  op(all_4_1, all_4_2) = all_4_0
% 177.74/28.24    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.74/28.24    (80)   ~ (all_52_5 = all_14_2)
% 177.74/28.24    (81)   ~ (all_52_3 = all_52_27)
% 177.74/28.24    (82)   ~ (all_52_3 = all_4_2)
% 177.74/28.24    (83)  op(e0, e3) = all_52_25
% 177.74/28.24    (84)  op(e0, all_6_2) = all_6_1
% 177.74/28.24    (85)   ~ (all_52_9 = all_10_2)
% 177.74/28.24    (86)  op(e3, all_52_17) = all_52_16
% 177.74/28.24    (87)  all_52_10 = all_10_1
% 177.74/28.24    (88)   ~ (all_52_13 = all_14_2)
% 177.74/28.24    (89)   ~ (e3 = e0)
% 177.74/28.24    (90)  all_40_0 = all_4_0
% 177.74/28.24    (91)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.74/28.24    (92)   ~ (all_52_9 = all_52_13)
% 177.74/28.24    (93)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.24    (94)  op(e0, all_52_23) = all_52_22
% 177.74/28.24    (95)   ~ (all_52_15 = all_52_23)
% 177.74/28.24    (96)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.74/28.24    (97)   ~ (all_52_5 = all_52_29)
% 177.74/28.24    (98)  all_56_2 = all_52_5
% 177.74/28.24    (99)  op(e1, e0) = all_52_23
% 177.74/28.24    (100)  all_56_12 = all_52_25
% 177.74/28.24    (101)  all_58_13 = all_52_27
% 177.74/28.24    (102)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.24    (103)  all_56_5 = all_10_2
% 177.74/28.24    (104)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.74/28.24    (105)   ~ (all_52_9 = all_52_17)
% 177.74/28.24    (106)   ~ (all_14_0 = e2)
% 177.74/28.24    (107)  all_58_6 = all_52_17
% 177.74/28.24    (108)   ~ (all_52_3 = all_52_7)
% 177.74/28.24    (109)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.74/28.24    (110)  op(e2, all_52_19) = all_52_18
% 177.74/28.24    (111)   ~ (e1 = e0)
% 177.74/28.24    (112)  all_56_0 = all_4_2
% 177.74/28.24    (113)  all_58_11 = all_52_23
% 177.74/28.24    (114)   ~ (all_52_3 = all_52_19)
% 177.74/28.24    (115)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.74/28.24    (116)   ~ (all_52_7 = all_52_15)
% 177.74/28.24    (117)  op(e0, all_52_15) = all_52_14
% 177.74/28.24    (118)   ~ (all_52_29 = all_14_2)
% 177.74/28.24    (119)   ~ (all_4_0 = e1)
% 177.74/28.24    (120)   ~ (all_52_19 = all_10_2)
% 177.74/28.24    (121)   ~ (all_58_15 = e0)
% 177.74/28.24    (122)   ~ (all_52_23 = all_6_2)
% 177.74/28.24    (123)  op(e1, all_4_2) = all_4_0
% 177.74/28.24    (124)   ~ (all_52_29 = all_6_2)
% 177.74/28.24    (125)  all_58_2 = all_52_9
% 177.74/28.24    (126)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.74/28.24    (127)  op(e3, e1) = all_52_5
% 177.74/28.24    (128)   ~ (e2 = e1)
% 177.74/28.24    (129)  all_56_10 = all_14_2
% 177.74/28.24    (130)   ~ (all_52_25 = all_6_2)
% 177.74/28.24    (131)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.74/28.24    (132)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.24    (133)  op(e1, e1) = all_14_2
% 177.74/28.24    (134)  op(e1, e3) = all_52_17
% 177.74/28.24    (135)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.24    (136)   ~ (all_52_25 = all_4_2)
% 177.74/28.24    (137)  op(e3, e0) = all_52_7
% 177.74/28.24    (138)  op(e3, e3) = all_4_2
% 177.74/28.24    (139)   ~ (all_10_1 = e3)
% 177.74/28.24    (140)  all_56_8 = all_52_17
% 177.74/28.24    (141)   ~ (all_52_17 = all_4_2)
% 177.74/28.24    (142)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.24             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.24    (143)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.74/28.24           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.74/28.24           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.74/28.24           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.74/28.24    (144)   ~ (all_52_25 = all_52_27)
% 177.74/28.24    (145)   ~ (all_52_27 = all_6_2)
% 177.74/28.24    (146)   ~ (all_52_7 = all_6_2)
% 177.74/28.24    (147)   ~ (all_52_15 = all_10_2)
% 177.74/28.24    (148)   ~ (all_52_19 = all_52_27)
% 177.74/28.24    (149)  all_56_7 = all_52_15
% 177.74/28.24    (150)   ~ (all_52_7 = all_52_23)
% 177.74/28.24    (151)   ~ (all_52_13 = all_10_2)
% 177.74/28.24    (152)  op(e2, all_52_27) = all_52_26
% 177.74/28.24    (153)  all_52_20 = all_14_1
% 177.74/28.24    (154)   ~ (all_52_17 = all_52_19)
% 177.74/28.24    (155)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.24    (156)  all_52_30 = all_6_1
% 177.74/28.24    (157)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.74/28.24    (158)  op(e1, all_14_2) = all_14_1
% 177.74/28.24    (159)  all_58_9 = all_52_7
% 177.74/28.24    (160)   ~ (e2 = e0)
% 177.74/28.24    (161)  all_58_12 = all_52_25
% 177.74/28.24    (162)  op(e3, all_4_2) = e1
% 177.74/28.24    (163)  all_56_6 = all_52_13
% 177.74/28.24    (164)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 177.74/28.24             all_58_13 = e0 | all_58_14 = e0)
% 177.74/28.24    (165)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.24    (166)   ~ (all_52_9 = all_52_15)
% 177.74/28.24    (167)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.24    (168)   ~ (e3 = e2)
% 177.74/28.24    (169)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.24    (170)   ~ (all_52_19 = all_14_2)
% 177.74/28.24    (171)  op(e2, e3) = all_52_9
% 177.74/28.24    (172)  all_56_13 = all_52_27
% 177.74/28.24  
% 177.74/28.24  Begin of proof
% 177.74/28.24  | 
% 177.74/28.24  | ALPHA: (164) implies:
% 177.74/28.24  |   (173)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.74/28.24  |   (174)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (33), (121) imply:
% 177.74/28.24  |   (175)   ~ (all_6_2 = e0)
% 177.74/28.24  | 
% 177.74/28.24  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.74/28.24  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.74/28.24  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.74/28.24  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.74/28.24  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.74/28.24  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.74/28.24  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 177.74/28.24  |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), (89),
% 177.74/28.24  |            (90), (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 177.74/28.24  |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 177.74/28.24  |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 177.74/28.24  |            (119), (120), (122), (123), (124), (125), (126), (127), (128),
% 177.74/28.24  |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 177.74/28.24  |            (138), (139), (140), (141), (142), (143), (144), (145), (146),
% 177.74/28.24  |            (147), (148), (149), (150), (151), (152), (153), (154), (155),
% 177.74/28.24  |            (156), (157), (158), (159), (160), (161), (162), (163), (165),
% 177.74/28.24  |            (166), (167), (168), (169), (170), (171), (172), (173), (174),
% 177.74/28.24  |            (175) are inconsistent by sub-proof #601.
% 177.74/28.24  | 
% 177.74/28.24  End of proof
% 177.74/28.24  
% 177.74/28.24  Sub-proof #501 shows that the following formulas are inconsistent:
% 177.74/28.24  ----------------------------------------------------------------
% 177.74/28.24    (1)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.74/28.24    (2)  op(e0, all_6_2) = all_6_1
% 177.74/28.24    (3)   ~ (e3 = e0)
% 177.74/28.24    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.24    (5)  all_52_30 = all_6_1
% 177.74/28.24    (6)  op(all_6_1, all_6_2) = e3
% 177.74/28.24  
% 177.74/28.24  Begin of proof
% 177.74/28.24  | 
% 177.74/28.24  | ALPHA: (1) implies:
% 177.74/28.24  |   (7)  all_52_30 = e0
% 177.74/28.24  | 
% 177.74/28.24  | COMBINE_EQS: (5), (7) imply:
% 177.74/28.24  |   (8)  all_6_1 = e0
% 177.74/28.24  | 
% 177.74/28.24  | SIMP: (8) implies:
% 177.74/28.24  |   (9)  all_6_1 = e0
% 177.74/28.24  | 
% 177.74/28.24  | REF_CLOSE: (2), (3), (4), (6), (9) are inconsistent by sub-proof #502.
% 177.74/28.24  | 
% 177.74/28.24  End of proof
% 177.74/28.24  
% 177.74/28.24  Sub-proof #502 shows that the following formulas are inconsistent:
% 177.74/28.24  ----------------------------------------------------------------
% 177.74/28.24    (1)  all_6_1 = e0
% 177.74/28.24    (2)  op(e0, all_6_2) = all_6_1
% 177.74/28.24    (3)   ~ (e3 = e0)
% 177.74/28.24    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.24    (5)  op(all_6_1, all_6_2) = e3
% 177.74/28.24  
% 177.74/28.24  Begin of proof
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (1), (5) imply:
% 177.74/28.24  |   (6)  op(e0, all_6_2) = e3
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (1), (2) imply:
% 177.74/28.24  |   (7)  op(e0, all_6_2) = e0
% 177.74/28.24  | 
% 177.74/28.24  | GROUND_INST: instantiating (4) with e0, e3, all_6_2, e0, simplifying with (6),
% 177.74/28.24  |              (7) gives:
% 177.74/28.24  |   (8)  e3 = e0
% 177.74/28.24  | 
% 177.74/28.24  | REDUCE: (3), (8) imply:
% 177.74/28.24  |   (9)  $false
% 177.74/28.24  | 
% 177.74/28.24  | CLOSE: (9) is inconsistent.
% 177.74/28.24  | 
% 177.74/28.24  End of proof
% 177.74/28.24  
% 177.74/28.24  Sub-proof #503 shows that the following formulas are inconsistent:
% 177.74/28.24  ----------------------------------------------------------------
% 177.74/28.24    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.24    (2)   ~ (all_52_5 = all_52_13)
% 177.74/28.24    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.74/28.24    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.74/28.24    (5)   ~ (all_52_17 = all_52_23)
% 177.74/28.24    (6)  op(e2, all_10_2) = all_10_1
% 177.74/28.24    (7)   ~ (all_52_13 = all_52_29)
% 177.74/28.24    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.74/28.24    (9)  op(e3, e2) = all_52_3
% 177.74/28.24    (10)   ~ (all_52_9 = all_52_25)
% 177.74/28.24    (11)  op(e3, all_52_25) = all_52_24
% 177.74/28.24    (12)   ~ (all_52_19 = all_52_23)
% 177.74/28.24    (13)  op(e1, e2) = all_52_19
% 177.74/28.24    (14)  op(e3, all_52_9) = all_52_8
% 177.74/28.24    (15)   ~ (all_52_3 = all_10_2)
% 177.74/28.24    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.74/28.24    (17)  all_58_5 = all_52_13
% 177.74/28.24    (18)   ~ (all_6_2 = e0)
% 177.74/28.24    (19)   ~ (all_52_25 = all_52_29)
% 177.74/28.24    (20)  all_56_15 = all_6_2
% 177.74/28.24    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.74/28.24    (22)  op(e2, e0) = all_52_15
% 177.74/28.24    (23)  all_58_3 = all_10_2
% 177.74/28.24    (24)  all_56_9 = all_52_19
% 177.74/28.24    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.24    (26)  all_58_15 = all_6_2
% 177.74/28.24    (27)   ~ (all_52_9 = all_4_2)
% 177.74/28.24    (28)   ~ (all_52_5 = all_52_7)
% 177.74/28.24    (29)  all_58_10 = all_52_15
% 177.74/28.24    (30)   ~ (all_52_5 = all_4_2)
% 177.74/28.24    (31)  all_58_7 = all_52_19
% 177.74/28.24    (32)   ~ (all_52_17 = all_52_25)
% 177.74/28.24    (33)   ~ (all_4_0 = e2)
% 177.74/28.24    (34)  all_58_4 = all_52_5
% 177.74/28.24    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.24    (36)   ~ (all_52_27 = all_52_29)
% 177.74/28.24    (37)   ~ (all_52_17 = all_14_2)
% 177.74/28.24    (38)  op(e3, all_4_2) = all_4_1
% 177.74/28.24    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.24    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.24    (41)   ~ (all_52_7 = all_4_2)
% 177.74/28.24    (42)  all_58_1 = all_52_3
% 177.74/28.24    (43)  all_58_0 = all_4_2
% 177.74/28.24    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.74/28.24    (45)  op(e1, all_52_29) = all_52_28
% 177.74/28.24    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.74/28.24    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.74/28.24    (48)   ~ (all_4_1 = e2)
% 177.74/28.24    (49)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.74/28.24    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.24    (51)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.74/28.24    (52)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.74/28.24    (53)  all_58_14 = all_52_29
% 177.74/28.24    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.74/28.24    (55)   ~ (all_52_3 = all_52_5)
% 177.74/28.24    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.24    (57)  op(e2, e1) = all_52_13
% 177.74/28.24    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.24    (59)  all_58_8 = all_14_2
% 177.74/28.24    (60)  all_56_1 = all_52_3
% 177.74/28.24    (61)   ~ (all_14_0 = e3)
% 177.74/28.24    (62)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.74/28.24    (63)  op(all_4_1, all_4_2) = all_4_0
% 177.74/28.24    (64)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.74/28.24    (65)   ~ (all_52_5 = all_14_2)
% 177.74/28.24    (66)   ~ (all_52_3 = all_52_27)
% 177.74/28.24    (67)   ~ (all_52_3 = all_4_2)
% 177.74/28.24    (68)  op(e0, e3) = all_52_25
% 177.74/28.24    (69)  op(e0, all_6_2) = all_6_1
% 177.74/28.24    (70)   ~ (all_52_9 = all_10_2)
% 177.74/28.24    (71)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.74/28.24    (72)   ~ (all_52_13 = all_14_2)
% 177.74/28.24    (73)  op(e1, all_14_2) = all_14_0
% 177.74/28.24    (74)   ~ (e3 = e0)
% 177.74/28.24    (75)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.74/28.24    (76)   ~ (all_52_9 = all_52_13)
% 177.74/28.24    (77)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.24    (78)   ~ (all_52_15 = all_52_23)
% 177.74/28.24    (79)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.74/28.24    (80)   ~ (all_52_5 = all_52_29)
% 177.74/28.24    (81)  op(e1, e0) = all_52_23
% 177.74/28.24    (82)  all_56_12 = all_52_25
% 177.74/28.24    (83)  all_58_13 = all_52_27
% 177.74/28.24    (84)   ~ (all_4_1 = e1)
% 177.74/28.24    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.24    (86)  all_56_5 = all_10_2
% 177.74/28.24    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.74/28.24    (88)   ~ (all_52_9 = all_52_17)
% 177.74/28.24    (89)   ~ (all_14_0 = e2)
% 177.74/28.24    (90)  all_58_6 = all_52_17
% 177.74/28.24    (91)  op(e2, all_52_19) = e2
% 177.74/28.24    (92)  op(e3, all_52_17) = e3
% 177.74/28.24    (93)   ~ (e1 = e0)
% 177.74/28.24    (94)  all_56_0 = all_4_2
% 177.74/28.24    (95)  all_58_11 = all_52_23
% 177.74/28.24    (96)   ~ (all_52_3 = all_52_19)
% 177.74/28.24    (97)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.74/28.24    (98)   ~ (all_52_7 = all_52_15)
% 177.74/28.24    (99)   ~ (all_52_29 = all_14_2)
% 177.74/28.24    (100)   ~ (all_4_0 = e1)
% 177.74/28.24    (101)   ~ (all_52_19 = all_10_2)
% 177.74/28.24    (102)   ~ (all_52_23 = all_6_2)
% 177.74/28.24    (103)  all_58_2 = all_52_9
% 177.74/28.24    (104)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.24    (105)  op(e3, e1) = all_52_5
% 177.74/28.24    (106)  all_56_10 = all_14_2
% 177.74/28.24    (107)   ~ (all_52_25 = all_6_2)
% 177.74/28.24    (108)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.74/28.24    (109)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.24    (110)  op(e1, e3) = all_52_17
% 177.74/28.24    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.24    (112)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 177.74/28.24    (113)   ~ (all_52_25 = all_4_2)
% 177.74/28.24    (114)  op(e3, e0) = all_52_7
% 177.74/28.24    (115)  op(e3, e3) = all_4_2
% 177.74/28.24    (116)   ~ (all_10_1 = e3)
% 177.74/28.24    (117)  all_56_8 = all_52_17
% 177.74/28.24    (118)   ~ (all_52_17 = all_4_2)
% 177.74/28.24    (119)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.24             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.24    (120)   ~ (all_52_25 = all_52_27)
% 177.74/28.24    (121)   ~ (all_52_27 = all_6_2)
% 177.74/28.24    (122)   ~ (all_52_7 = all_6_2)
% 177.74/28.24    (123)  op(e0, all_52_23) = e0
% 177.74/28.24    (124)   ~ (all_52_15 = all_10_2)
% 177.74/28.24    (125)   ~ (all_52_19 = all_52_27)
% 177.74/28.24    (126)  all_56_7 = all_52_15
% 177.74/28.24    (127)  op(e1, all_14_2) = e1
% 177.74/28.24    (128)   ~ (all_52_7 = all_52_23)
% 177.74/28.24    (129)   ~ (all_52_13 = all_10_2)
% 177.74/28.24    (130)  op(e2, all_52_27) = all_52_26
% 177.74/28.24    (131)   ~ (all_52_17 = all_52_19)
% 177.74/28.24    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.25    (133)  all_58_9 = all_52_7
% 177.74/28.25    (134)   ~ (e2 = e0)
% 177.74/28.25    (135)  all_58_12 = all_52_25
% 177.74/28.25    (136)  op(all_6_1, all_6_2) = e3
% 177.74/28.25    (137)  all_56_6 = all_52_13
% 177.74/28.25    (138)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.25    (139)   ~ (all_52_9 = all_52_15)
% 177.74/28.25    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.25    (141)   ~ (e3 = e2)
% 177.74/28.25    (142)   ~ (all_52_19 = all_14_2)
% 177.74/28.25    (143)  op(e2, e3) = all_52_9
% 177.74/28.25    (144)  all_56_13 = all_52_27
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | GROUND_INST: instantiating (119) with e1, all_14_0, all_14_2, e1, simplifying
% 177.74/28.25  |              with (73), (127) gives:
% 177.74/28.25  |   (145)  all_14_0 = e1
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (61), (145) imply:
% 177.74/28.25  |   (146)   ~ (e3 = e1)
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (146) implies:
% 177.74/28.25  |   (147)   ~ (e3 = e1)
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (89), (145) imply:
% 177.74/28.25  |   (148)   ~ (e2 = e1)
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (148) implies:
% 177.74/28.25  |   (149)   ~ (e2 = e1)
% 177.74/28.25  | 
% 177.74/28.25  | BETA: splitting (39) gives:
% 177.74/28.25  | 
% 177.74/28.25  | Case 1:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (150)  all_56_15 = e3
% 177.74/28.25  | | 
% 177.74/28.25  | | REF_CLOSE: (20), (24), (31), (35), (40), (43), (47), (56), (59), (65), (68),
% 177.74/28.25  | |            (69), (77), (82), (88), (90), (91), (92), (95), (102), (103),
% 177.74/28.25  | |            (104), (105), (107), (109), (110), (113), (115), (118), (119),
% 177.74/28.25  | |            (127), (135), (136), (141), (143), (150) are inconsistent by
% 177.74/28.25  | |            sub-proof #504.
% 177.74/28.25  | | 
% 177.74/28.25  | Case 2:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (151)   ~ (all_56_15 = e3)
% 177.74/28.25  | |   (152)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.25  | | 
% 177.74/28.25  | | REDUCE: (20), (151) imply:
% 177.74/28.25  | |   (153)   ~ (all_6_2 = e3)
% 177.74/28.25  | | 
% 177.74/28.25  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.74/28.25  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.74/28.25  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.74/28.25  | |            (35), (36), (37), (38), (40), (41), (42), (43), (44), (45), (46),
% 177.74/28.25  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.74/28.25  | |            (58), (59), (60), (62), (63), (64), (65), (66), (67), (68), (70),
% 177.74/28.25  | |            (71), (72), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 177.74/28.25  | |            (83), (84), (85), (86), (87), (88), (90), (91), (92), (93), (94),
% 177.74/28.25  | |            (95), (96), (97), (98), (99), (100), (101), (102), (103), (105),
% 177.74/28.25  | |            (106), (107), (108), (110), (111), (112), (113), (114), (115),
% 177.74/28.25  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 177.74/28.25  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 177.74/28.25  | |            (134), (135), (137), (138), (139), (140), (141), (142), (143),
% 177.74/28.25  | |            (144), (147), (149), (152), (153) are inconsistent by sub-proof
% 177.74/28.25  | |            #668.
% 177.74/28.25  | | 
% 177.74/28.25  | End of split
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #504 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)  all_56_15 = e3
% 177.74/28.25    (2)  all_56_15 = all_6_2
% 177.74/28.25    (3)  all_56_9 = all_52_19
% 177.74/28.25    (4)  all_58_7 = all_52_19
% 177.74/28.25    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.25    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.25    (7)  all_58_0 = all_4_2
% 177.74/28.25    (8)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.74/28.25    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.25    (10)  all_58_8 = all_14_2
% 177.74/28.25    (11)   ~ (all_52_5 = all_14_2)
% 177.74/28.25    (12)  op(e0, e3) = all_52_25
% 177.74/28.25    (13)  op(e0, all_6_2) = all_6_1
% 177.74/28.25    (14)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.25    (15)  all_56_12 = all_52_25
% 177.74/28.25    (16)   ~ (all_52_9 = all_52_17)
% 177.74/28.25    (17)  all_58_6 = all_52_17
% 177.74/28.25    (18)  op(e2, all_52_19) = e2
% 177.74/28.25    (19)  op(e3, all_52_17) = e3
% 177.74/28.25    (20)  all_58_11 = all_52_23
% 177.74/28.25    (21)   ~ (all_52_23 = all_6_2)
% 177.74/28.25    (22)  all_58_2 = all_52_9
% 177.74/28.25    (23)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.25    (24)  op(e3, e1) = all_52_5
% 177.74/28.25    (25)   ~ (all_52_25 = all_6_2)
% 177.74/28.25    (26)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.25    (27)  op(e1, e3) = all_52_17
% 177.74/28.25    (28)   ~ (all_52_25 = all_4_2)
% 177.74/28.25    (29)  op(e3, e3) = all_4_2
% 177.74/28.25    (30)   ~ (all_52_17 = all_4_2)
% 177.74/28.25    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.25    (32)  op(e1, all_14_2) = e1
% 177.74/28.25    (33)  all_58_12 = all_52_25
% 177.74/28.25    (34)  op(all_6_1, all_6_2) = e3
% 177.74/28.25    (35)   ~ (e3 = e2)
% 177.74/28.25    (36)  op(e2, e3) = all_52_9
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | COMBINE_EQS: (1), (2) imply:
% 177.74/28.25  |   (37)  all_6_2 = e3
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (37) implies:
% 177.74/28.25  |   (38)  all_6_2 = e3
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (21), (38) imply:
% 177.74/28.25  |   (39)   ~ (all_52_23 = e3)
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (25), (38) imply:
% 177.74/28.25  |   (40)   ~ (all_52_25 = e3)
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (34), (38) imply:
% 177.74/28.25  |   (41)  op(all_6_1, e3) = e3
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (13), (38) imply:
% 177.74/28.25  |   (42)  op(e0, e3) = all_6_1
% 177.74/28.25  | 
% 177.74/28.25  | GROUND_INST: instantiating (31) with all_52_25, all_6_1, e3, e0, simplifying
% 177.74/28.25  |              with (12), (42) gives:
% 177.74/28.25  |   (43)  all_52_25 = all_6_1
% 177.74/28.25  | 
% 177.74/28.25  | COMBINE_EQS: (15), (43) imply:
% 177.74/28.25  |   (44)  all_56_12 = all_6_1
% 177.74/28.25  | 
% 177.74/28.25  | COMBINE_EQS: (33), (43) imply:
% 177.74/28.25  |   (45)  all_58_12 = all_6_1
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (28), (43) imply:
% 177.74/28.25  |   (46)   ~ (all_6_1 = all_4_2)
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (40), (43) imply:
% 177.74/28.25  |   (47)   ~ (all_6_1 = e3)
% 177.74/28.25  | 
% 177.74/28.25  | BETA: splitting (14) gives:
% 177.74/28.25  | 
% 177.74/28.25  | Case 1:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (48)  all_56_12 = e3
% 177.74/28.25  | | 
% 177.74/28.25  | | REF_CLOSE: (44), (47), (48) are inconsistent by sub-proof #509.
% 177.74/28.25  | | 
% 177.74/28.25  | Case 2:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (49)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.25  | | 
% 177.74/28.25  | | BETA: splitting (9) gives:
% 177.74/28.25  | | 
% 177.74/28.25  | | Case 1:
% 177.74/28.25  | | | 
% 177.74/28.25  | | |   (50)  all_58_0 = e3
% 177.74/28.25  | | | 
% 177.74/28.25  | | | COMBINE_EQS: (7), (50) imply:
% 177.74/28.25  | | |   (51)  all_4_2 = e3
% 177.74/28.25  | | | 
% 177.74/28.25  | | | REDUCE: (30), (51) imply:
% 177.74/28.25  | | |   (52)   ~ (all_52_17 = e3)
% 177.74/28.25  | | | 
% 177.74/28.25  | | | BETA: splitting (5) gives:
% 177.74/28.25  | | | 
% 177.74/28.25  | | | Case 1:
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | |   (53)  all_58_6 = e3
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | REF_CLOSE: (17), (52), (53) are inconsistent by sub-proof #981.
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | Case 2:
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | |   (54)   ~ (all_58_6 = e3)
% 177.74/28.25  | | | |   (55)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | BETA: splitting (26) gives:
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | Case 1:
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | |   (56)  all_58_12 = e2
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | | COMBINE_EQS: (45), (56) imply:
% 177.74/28.25  | | | | |   (57)  all_6_1 = e2
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | | SIMP: (57) implies:
% 177.74/28.25  | | | | |   (58)  all_6_1 = e2
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | | REDUCE: (47), (58) imply:
% 177.74/28.25  | | | | |   (59)   ~ (e3 = e2)
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | | REDUCE: (41), (58) imply:
% 177.74/28.25  | | | | |   (60)  op(e2, e3) = e3
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | | REF_CLOSE: (3), (4), (8), (10), (11), (18), (19), (20), (24), (27),
% 177.74/28.25  | | | | |            (31), (32), (35), (39), (55), (60) are inconsistent by
% 177.74/28.25  | | | | |            sub-proof #949.
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | Case 2:
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | |   (61)   ~ (all_58_12 = e2)
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | | REF_CLOSE: (23), (27), (31), (41), (42), (44), (45), (47), (49), (52),
% 177.74/28.25  | | | | |            (61) are inconsistent by sub-proof #505.
% 177.74/28.25  | | | | | 
% 177.74/28.25  | | | | End of split
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | End of split
% 177.74/28.25  | | | 
% 177.74/28.25  | | Case 2:
% 177.74/28.25  | | | 
% 177.74/28.25  | | |   (62)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.25  | | | 
% 177.74/28.25  | | | REF_CLOSE: (3), (4), (5), (6), (8), (10), (11), (16), (17), (18), (19),
% 177.74/28.25  | | |            (20), (22), (24), (27), (29), (30), (31), (32), (33), (35),
% 177.74/28.25  | | |            (36), (39), (40), (62) are inconsistent by sub-proof #945.
% 177.74/28.25  | | | 
% 177.74/28.25  | | End of split
% 177.74/28.25  | | 
% 177.74/28.25  | End of split
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #505 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)   ~ (all_58_12 = e2)
% 177.74/28.25    (2)   ~ (all_52_17 = e3)
% 177.74/28.25    (3)  all_58_12 = all_6_1
% 177.74/28.25    (4)   ~ (all_6_1 = e3)
% 177.74/28.25    (5)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.25    (6)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.25    (7)  op(e0, e3) = all_6_1
% 177.74/28.25    (8)  op(e1, e3) = all_52_17
% 177.74/28.25    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.25    (10)  all_56_12 = all_6_1
% 177.74/28.25    (11)  op(all_6_1, e3) = e3
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (1), (3) imply:
% 177.74/28.25  |   (12)   ~ (all_6_1 = e2)
% 177.74/28.25  | 
% 177.74/28.25  | BETA: splitting (6) gives:
% 177.74/28.25  | 
% 177.74/28.25  | Case 1:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (13)  all_58_12 = e1
% 177.74/28.25  | | 
% 177.74/28.25  | | COMBINE_EQS: (3), (13) imply:
% 177.74/28.25  | |   (14)  all_6_1 = e1
% 177.74/28.25  | | 
% 177.74/28.25  | | SIMP: (14) implies:
% 177.74/28.25  | |   (15)  all_6_1 = e1
% 177.74/28.25  | | 
% 177.74/28.25  | | REDUCE: (11), (15) imply:
% 177.74/28.25  | |   (16)  op(e1, e3) = e3
% 177.74/28.25  | | 
% 177.74/28.25  | | REF_CLOSE: (2), (8), (9), (16) are inconsistent by sub-proof #508.
% 177.74/28.25  | | 
% 177.74/28.25  | Case 2:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (17)   ~ (all_58_12 = e1)
% 177.74/28.25  | | 
% 177.74/28.25  | | REDUCE: (3), (17) imply:
% 177.74/28.25  | |   (18)   ~ (all_6_1 = e1)
% 177.74/28.25  | | 
% 177.74/28.25  | | BETA: splitting (5) gives:
% 177.74/28.25  | | 
% 177.74/28.25  | | Case 1:
% 177.74/28.25  | | | 
% 177.74/28.25  | | |   (19)  all_56_12 = e2
% 177.74/28.25  | | | 
% 177.74/28.25  | | | REF_CLOSE: (10), (12), (19) are inconsistent by sub-proof #507.
% 177.74/28.25  | | | 
% 177.74/28.25  | | Case 2:
% 177.74/28.25  | | | 
% 177.74/28.25  | | |   (20)  all_56_12 = e1 | all_56_12 = e0
% 177.74/28.25  | | | 
% 177.74/28.25  | | | BETA: splitting (20) gives:
% 177.74/28.25  | | | 
% 177.74/28.25  | | | Case 1:
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | |   (21)  all_56_12 = e1
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | REF_CLOSE: (10), (18), (21) are inconsistent by sub-proof #506.
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | Case 2:
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | |   (22)  all_56_12 = e0
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | COMBINE_EQS: (10), (22) imply:
% 177.74/28.25  | | | |   (23)  all_6_1 = e0
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | SIMP: (23) implies:
% 177.74/28.25  | | | |   (24)  all_6_1 = e0
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | REDUCE: (4), (24) imply:
% 177.74/28.25  | | | |   (25)   ~ (e3 = e0)
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | SIMP: (25) implies:
% 177.74/28.25  | | | |   (26)   ~ (e3 = e0)
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | REDUCE: (11), (24) imply:
% 177.74/28.25  | | | |   (27)  op(e0, e3) = e3
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | REDUCE: (7), (24) imply:
% 177.74/28.25  | | | |   (28)  op(e0, e3) = e0
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | | REF_CLOSE: (9), (26), (27), (28) are inconsistent by sub-proof #1027.
% 177.74/28.25  | | | | 
% 177.74/28.25  | | | End of split
% 177.74/28.25  | | | 
% 177.74/28.25  | | End of split
% 177.74/28.25  | | 
% 177.74/28.25  | End of split
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #506 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)  all_56_12 = all_6_1
% 177.74/28.25    (2)  all_56_12 = e1
% 177.74/28.25    (3)   ~ (all_6_1 = e1)
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | COMBINE_EQS: (1), (2) imply:
% 177.74/28.25  |   (4)  all_6_1 = e1
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (4) implies:
% 177.74/28.25  |   (5)  all_6_1 = e1
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (3), (5) imply:
% 177.74/28.25  |   (6)  $false
% 177.74/28.25  | 
% 177.74/28.25  | CLOSE: (6) is inconsistent.
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #507 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)  all_56_12 = all_6_1
% 177.74/28.25    (2)  all_56_12 = e2
% 177.74/28.25    (3)   ~ (all_6_1 = e2)
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | COMBINE_EQS: (1), (2) imply:
% 177.74/28.25  |   (4)  all_6_1 = e2
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (4) implies:
% 177.74/28.25  |   (5)  all_6_1 = e2
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (3), (5) imply:
% 177.74/28.25  |   (6)  $false
% 177.74/28.25  | 
% 177.74/28.25  | CLOSE: (6) is inconsistent.
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #508 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.25    (2)  op(e1, e3) = all_52_17
% 177.74/28.25    (3)  op(e1, e3) = e3
% 177.74/28.25    (4)   ~ (all_52_17 = e3)
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | GROUND_INST: instantiating (1) with all_52_17, e3, e3, e1, simplifying with
% 177.74/28.25  |              (2), (3) gives:
% 177.74/28.25  |   (5)  all_52_17 = e3
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (4), (5) imply:
% 177.74/28.25  |   (6)  $false
% 177.74/28.25  | 
% 177.74/28.25  | CLOSE: (6) is inconsistent.
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #509 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)  all_56_12 = all_6_1
% 177.74/28.25    (2)  all_56_12 = e3
% 177.74/28.25    (3)   ~ (all_6_1 = e3)
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | COMBINE_EQS: (1), (2) imply:
% 177.74/28.25  |   (4)  all_6_1 = e3
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (4) implies:
% 177.74/28.25  |   (5)  all_6_1 = e3
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (3), (5) imply:
% 177.74/28.25  |   (6)  $false
% 177.74/28.25  | 
% 177.74/28.25  | CLOSE: (6) is inconsistent.
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #510 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)  all_58_15 = all_6_2
% 177.74/28.25    (2)  op(e0, e0) = all_6_2
% 177.74/28.25    (3)  op(e0, all_6_2) = all_6_1
% 177.74/28.25    (4)   ~ (e3 = e0)
% 177.74/28.25    (5)  all_58_15 = e0
% 177.74/28.25    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.25    (7)  op(all_6_1, all_6_2) = e3
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | COMBINE_EQS: (1), (5) imply:
% 177.74/28.25  |   (8)  all_6_2 = e0
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (7), (8) imply:
% 177.74/28.25  |   (9)  op(all_6_1, e0) = e3
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (3), (8) imply:
% 177.74/28.25  |   (10)  op(e0, e0) = all_6_1
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (2), (8) imply:
% 177.74/28.25  |   (11)  op(e0, e0) = e0
% 177.74/28.25  | 
% 177.74/28.25  | GROUND_INST: instantiating (6) with e0, all_6_1, e0, e0, simplifying with
% 177.74/28.25  |              (10), (11) gives:
% 177.74/28.25  |   (12)  all_6_1 = e0
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (9), (12) imply:
% 177.74/28.25  |   (13)  op(e0, e0) = e3
% 177.74/28.25  | 
% 177.74/28.25  | GROUND_INST: instantiating (6) with e0, e3, e0, e0, simplifying with (11),
% 177.74/28.25  |              (13) gives:
% 177.74/28.25  |   (14)  e3 = e0
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (4), (14) imply:
% 177.74/28.25  |   (15)  $false
% 177.74/28.25  | 
% 177.74/28.25  | CLOSE: (15) is inconsistent.
% 177.74/28.25  | 
% 177.74/28.25  End of proof
% 177.74/28.25  
% 177.74/28.25  Sub-proof #511 shows that the following formulas are inconsistent:
% 177.74/28.25  ----------------------------------------------------------------
% 177.74/28.25    (1)   ~ (all_52_23 = all_14_2)
% 177.74/28.25    (2)   ~ (all_52_5 = all_52_13)
% 177.74/28.25    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.74/28.25    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.74/28.25    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.74/28.25    (6)   ~ (all_52_27 = all_10_2)
% 177.74/28.25    (7)   ~ (all_52_17 = all_52_23)
% 177.74/28.25    (8)   ~ (all_6_0 = e3)
% 177.74/28.25    (9)   ~ (all_52_13 = all_52_29)
% 177.74/28.25    (10)  all_56_3 = all_52_7
% 177.74/28.25    (11)  op(e3, e2) = all_52_3
% 177.74/28.25    (12)   ~ (all_52_9 = all_52_25)
% 177.74/28.25    (13)   ~ (all_52_19 = all_52_23)
% 177.74/28.25    (14)  all_56_11 = all_52_23
% 177.74/28.25    (15)  op(e1, e2) = all_52_19
% 177.74/28.25    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.74/28.25    (17)  op(e3, all_52_9) = all_52_8
% 177.74/28.25    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.74/28.25    (19)  all_58_5 = all_52_13
% 177.74/28.25    (20)   ~ (all_52_25 = all_52_29)
% 177.74/28.25    (21)  all_56_15 = all_6_2
% 177.74/28.25    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.74/28.25    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.74/28.25    (24)  all_58_3 = all_10_2
% 177.74/28.25    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.74/28.25    (26)  all_58_15 = all_6_2
% 177.74/28.25    (27)  op(e0, all_6_2) = e0
% 177.74/28.25    (28)   ~ (all_52_9 = all_4_2)
% 177.74/28.25    (29)   ~ (all_52_5 = all_52_7)
% 177.74/28.25    (30)  all_58_10 = all_52_15
% 177.74/28.25    (31)   ~ (all_52_5 = all_4_2)
% 177.74/28.25    (32)  all_58_7 = all_52_19
% 177.74/28.25    (33)   ~ (all_52_17 = all_52_25)
% 177.74/28.25    (34)  op(e0, e1) = all_52_29
% 177.74/28.25    (35)   ~ (all_4_0 = e2)
% 177.74/28.25    (36)  all_58_4 = all_52_5
% 177.74/28.25    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.74/28.25    (38)   ~ (e3 = e1)
% 177.74/28.25    (39)   ~ (all_52_27 = all_52_29)
% 177.74/28.25    (40)   ~ (all_52_17 = all_14_2)
% 177.74/28.25    (41)  op(e3, all_4_2) = all_4_1
% 177.74/28.25    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.74/28.25    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.74/28.25    (44)   ~ (all_52_7 = all_4_2)
% 177.74/28.25    (45)  all_58_1 = all_52_3
% 177.74/28.25    (46)   ~ (all_52_13 = all_52_15)
% 177.74/28.25    (47)  all_58_0 = all_4_2
% 177.74/28.25    (48)  op(e2, all_52_27) = e2
% 177.74/28.25    (49)   ~ (all_4_1 = e2)
% 177.74/28.25    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.74/28.25    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.74/28.25    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.74/28.25    (53)  all_58_14 = all_52_29
% 177.74/28.25    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.74/28.25    (55)   ~ (all_52_3 = all_52_5)
% 177.74/28.25    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.74/28.25    (57)  op(e2, e1) = all_52_13
% 177.74/28.25    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.74/28.25    (59)  all_58_8 = all_14_2
% 177.74/28.25    (60)  op(e0, e2) = all_52_27
% 177.74/28.25    (61)  all_56_14 = all_52_29
% 177.74/28.25    (62)  op(e1, all_52_29) = e1
% 177.74/28.25    (63)  op(all_4_1, all_4_2) = all_4_0
% 177.74/28.25    (64)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.74/28.25    (65)   ~ (all_52_3 = all_52_27)
% 177.74/28.25    (66)   ~ (all_52_3 = all_4_2)
% 177.74/28.25    (67)  op(e0, e3) = all_52_25
% 177.74/28.25    (68)   ~ (all_52_9 = all_10_2)
% 177.74/28.25    (69)  op(e3, all_52_17) = all_52_16
% 177.74/28.25    (70)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.74/28.25    (71)   ~ (all_52_13 = all_14_2)
% 177.74/28.25    (72)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.74/28.25    (73)   ~ (all_52_9 = all_52_13)
% 177.74/28.25    (74)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.74/28.25    (75)   ~ (all_52_5 = all_52_29)
% 177.74/28.25    (76)  all_56_2 = all_52_5
% 177.74/28.25    (77)  op(e1, e0) = all_52_23
% 177.74/28.25    (78)  all_56_12 = all_52_25
% 177.74/28.25    (79)  all_58_13 = all_52_27
% 177.74/28.25    (80)   ~ (all_4_1 = e1)
% 177.74/28.25    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.74/28.25    (82)  all_56_5 = all_10_2
% 177.74/28.25    (83)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.74/28.25    (84)   ~ (all_52_9 = all_52_17)
% 177.74/28.25    (85)  all_58_6 = all_52_17
% 177.74/28.25    (86)   ~ (all_52_3 = all_52_7)
% 177.74/28.25    (87)  all_56_0 = all_4_2
% 177.74/28.25    (88)  all_58_11 = all_52_23
% 177.74/28.25    (89)   ~ (all_52_3 = all_52_19)
% 177.74/28.25    (90)   ~ (all_52_7 = all_52_15)
% 177.74/28.25    (91)   ~ (all_52_29 = all_14_2)
% 177.74/28.25    (92)  op(e3, all_52_25) = e3
% 177.74/28.25    (93)   ~ (all_4_0 = e1)
% 177.74/28.25    (94)   ~ (all_52_19 = all_10_2)
% 177.74/28.25    (95)   ~ (all_52_23 = all_6_2)
% 177.74/28.25    (96)   ~ (all_6_0 = e2)
% 177.74/28.25    (97)   ~ (all_52_29 = all_6_2)
% 177.74/28.25    (98)  all_58_2 = all_52_9
% 177.74/28.25    (99)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.74/28.25    (100)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.74/28.25    (101)  op(e3, e1) = all_52_5
% 177.74/28.25    (102)   ~ (e2 = e1)
% 177.74/28.25    (103)   ~ (all_52_25 = all_6_2)
% 177.74/28.25    (104)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.74/28.25    (105)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.74/28.25    (106)  op(e1, e3) = all_52_17
% 177.74/28.25    (107)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.74/28.25    (108)   ~ (all_52_25 = all_4_2)
% 177.74/28.25    (109)  op(e3, e0) = all_52_7
% 177.74/28.25    (110)  op(e3, e3) = all_4_2
% 177.74/28.25    (111)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.74/28.25             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.74/28.25    (112)  all_56_8 = all_52_17
% 177.74/28.25    (113)   ~ (all_52_17 = all_4_2)
% 177.74/28.25    (114)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.74/28.25             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.74/28.25    (115)   ~ (all_52_25 = all_52_27)
% 177.74/28.25    (116)  op(e0, all_6_2) = all_6_0
% 177.74/28.25    (117)   ~ (all_52_27 = all_6_2)
% 177.74/28.25    (118)   ~ (all_52_7 = all_6_2)
% 177.74/28.25    (119)   ~ (all_52_15 = all_10_2)
% 177.74/28.25    (120)   ~ (all_52_19 = all_52_27)
% 177.74/28.25    (121)  all_56_7 = all_52_15
% 177.74/28.25    (122)   ~ (all_52_7 = all_52_23)
% 177.74/28.25    (123)   ~ (all_6_0 = e1)
% 177.74/28.25    (124)   ~ (all_52_17 = all_52_19)
% 177.74/28.25    (125)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.74/28.25    (126)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.74/28.25    (127)  all_58_9 = all_52_7
% 177.74/28.25    (128)  all_58_12 = all_52_25
% 177.74/28.25    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.74/28.25    (130)   ~ (all_52_9 = all_52_15)
% 177.74/28.25    (131)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.74/28.25    (132)   ~ (e3 = e2)
% 177.74/28.25    (133)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.74/28.25    (134)  op(e2, e3) = all_52_9
% 177.74/28.25    (135)  all_56_13 = all_52_27
% 177.74/28.25  
% 177.74/28.25  Begin of proof
% 177.74/28.25  | 
% 177.74/28.25  | GROUND_INST: instantiating (114) with e0, all_6_0, all_6_2, e0, simplifying
% 177.74/28.25  |              with (27), (116) gives:
% 177.74/28.25  |   (136)  all_6_0 = e0
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (8), (136) imply:
% 177.74/28.25  |   (137)   ~ (e3 = e0)
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (137) implies:
% 177.74/28.25  |   (138)   ~ (e3 = e0)
% 177.74/28.25  | 
% 177.74/28.25  | REDUCE: (123), (136) imply:
% 177.74/28.25  |   (139)   ~ (e1 = e0)
% 177.74/28.25  | 
% 177.74/28.25  | SIMP: (139) implies:
% 177.74/28.25  |   (140)   ~ (e1 = e0)
% 177.74/28.25  | 
% 177.74/28.25  | BETA: splitting (111) gives:
% 177.74/28.25  | 
% 177.74/28.25  | Case 1:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (141)  all_58_15 = e0
% 177.74/28.25  | | 
% 177.74/28.25  | | COMBINE_EQS: (26), (141) imply:
% 177.74/28.25  | |   (142)  all_6_2 = e0
% 177.74/28.25  | | 
% 177.74/28.25  | | REDUCE: (95), (142) imply:
% 177.74/28.25  | |   (143)   ~ (all_52_23 = e0)
% 177.74/28.25  | | 
% 177.74/28.25  | | REDUCE: (103), (142) imply:
% 177.74/28.25  | |   (144)   ~ (all_52_25 = e0)
% 177.74/28.25  | | 
% 177.74/28.25  | | REDUCE: (97), (142) imply:
% 177.74/28.25  | |   (145)   ~ (all_52_29 = e0)
% 177.74/28.25  | | 
% 177.74/28.25  | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (10), (11), (12), (13), (15), (17),
% 177.74/28.25  | |            (18), (20), (23), (24), (25), (28), (29), (31), (32), (33), (36),
% 177.74/28.25  | |            (38), (39), (41), (44), (45), (47), (48), (49), (50), (53), (54),
% 177.74/28.25  | |            (56), (57), (58), (59), (61), (62), (64), (66), (68), (69), (70),
% 177.74/28.25  | |            (72), (74), (75), (78), (79), (80), (82), (83), (84), (85), (86),
% 177.74/28.25  | |            (87), (88), (91), (92), (94), (98), (99), (101), (104), (106),
% 177.74/28.25  | |            (108), (109), (110), (112), (113), (114), (115), (126), (127),
% 177.74/28.25  | |            (128), (134), (135), (138), (140), (141), (143), (144), (145) are
% 177.74/28.25  | |            inconsistent by sub-proof #879.
% 177.74/28.25  | | 
% 177.74/28.25  | Case 2:
% 177.74/28.25  | | 
% 177.74/28.25  | |   (146)   ~ (all_58_15 = e0)
% 177.74/28.25  | |   (147)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.74/28.25  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.74/28.25  | | 
% 177.74/28.26  | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (11), (12), (13), (14), (16), (17),
% 177.74/28.26  | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 177.74/28.26  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 177.74/28.26  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (50), (51),
% 177.74/28.26  | |            (52), (53), (54), (55), (56), (58), (59), (60), (61), (62), (63),
% 177.74/28.26  | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 177.74/28.26  | |            (76), (77), (78), (79), (81), (83), (84), (85), (86), (87), (88),
% 177.74/28.26  | |            (89), (90), (92), (93), (94), (95), (96), (97), (98), (100),
% 177.74/28.26  | |            (101), (102), (103), (105), (106), (107), (108), (109), (110),
% 177.74/28.26  | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 177.74/28.26  | |            (122), (123), (124), (125), (127), (128), (129), (130), (131),
% 177.74/28.26  | |            (132), (133), (134), (135), (146), (147) are inconsistent by
% 177.74/28.26  | |            sub-proof #530.
% 177.74/28.26  | | 
% 177.74/28.26  | End of split
% 177.74/28.26  | 
% 177.74/28.26  End of proof
% 177.74/28.26  
% 177.74/28.26  Sub-proof #512 shows that the following formulas are inconsistent:
% 177.74/28.26  ----------------------------------------------------------------
% 177.74/28.26    (1)  all_56_4 = all_14_0
% 177.74/28.26    (2)  all_56_4 = e0
% 177.74/28.26    (3)   ~ (all_14_0 = e0)
% 177.74/28.26  
% 177.74/28.26  Begin of proof
% 177.74/28.26  | 
% 177.74/28.26  | COMBINE_EQS: (1), (2) imply:
% 177.74/28.26  |   (4)  all_14_0 = e0
% 177.74/28.26  | 
% 177.74/28.26  | SIMP: (4) implies:
% 177.74/28.26  |   (5)  all_14_0 = e0
% 177.74/28.26  | 
% 177.74/28.26  | REDUCE: (3), (5) imply:
% 177.74/28.26  |   (6)  $false
% 177.74/28.26  | 
% 177.74/28.26  | CLOSE: (6) is inconsistent.
% 177.74/28.26  | 
% 177.74/28.26  End of proof
% 177.74/28.26  
% 177.74/28.26  Sub-proof #513 shows that the following formulas are inconsistent:
% 177.74/28.26  ----------------------------------------------------------------
% 177.74/28.26    (1)  op(e2, all_52_3) = e2
% 177.74/28.26    (2)   ~ (all_52_13 = e1)
% 177.74/28.26    (3)  all_58_15 = e3
% 177.74/28.26    (4)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.74/28.26    (5)   ~ (all_52_13 = all_52_29)
% 177.74/28.26    (6)  all_56_3 = all_52_7
% 177.74/28.26    (7)  op(e3, e2) = all_52_3
% 177.74/28.26    (8)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.74/28.26    (9)  op(e3, e0) = all_52_24
% 177.74/28.26    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.74/28.26    (11)  all_58_7 = all_52_19
% 177.74/28.26    (12)  op(e0, e1) = all_52_29
% 177.74/28.26    (13)   ~ (e3 = e1)
% 177.74/28.26    (14)  all_58_1 = all_52_3
% 177.74/28.26    (15)   ~ (all_52_19 = e2)
% 177.74/28.26    (16)  all_58_14 = all_52_29
% 177.74/28.26    (17)  op(e3, e2) = all_52_16
% 177.74/28.26    (18)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.74/28.26    (19)  op(e0, e3) = e0
% 177.74/28.26    (20)  all_58_12 = e0
% 177.74/28.26    (21)  op(e0, e3) = all_6_0
% 177.74/28.26    (22)   ~ (all_52_3 = e3)
% 177.74/28.26    (23)  op(e1, e3) = e2
% 177.74/28.26    (24)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.26    (25)  op(e1, e3) = all_10_0
% 177.86/28.26    (26)   ~ (all_52_7 = e2)
% 177.86/28.26    (27)  op(e3, e0) = all_52_7
% 177.86/28.26    (28)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.26    (29)   ~ (all_52_13 = e2)
% 177.86/28.26    (30)   ~ (all_10_0 = e3)
% 177.86/28.26    (31)   ~ (all_52_7 = e3)
% 177.86/28.26    (32)  all_58_3 = e3
% 177.86/28.26    (33)   ~ (all_6_0 = e1)
% 177.86/28.26    (34)  op(e0, all_52_7) = e0
% 177.86/28.26    (35)  all_58_9 = all_52_7
% 177.86/28.26    (36)   ~ (all_10_0 = e1)
% 177.86/28.26    (37)  all_56_6 = all_52_13
% 177.86/28.26    (38)  op(e0, e0) = e3
% 177.86/28.26    (39)  op(e2, e2) = e3
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | BETA: splitting (18) gives:
% 177.86/28.26  | 
% 177.86/28.26  | Case 1:
% 177.86/28.26  | | 
% 177.86/28.26  | |   (40)  all_56_6 = e2
% 177.86/28.26  | | 
% 177.86/28.26  | | REF_CLOSE: (29), (37), (40) are inconsistent by sub-proof #722.
% 177.86/28.26  | | 
% 177.86/28.26  | Case 2:
% 177.86/28.26  | | 
% 177.86/28.26  | |   (41)  all_56_6 = e1 | all_56_6 = e0
% 177.86/28.26  | | 
% 177.86/28.26  | | BETA: splitting (41) gives:
% 177.86/28.26  | | 
% 177.86/28.26  | | Case 1:
% 177.86/28.26  | | | 
% 177.86/28.26  | | |   (42)  all_56_6 = e1
% 177.86/28.26  | | | 
% 177.86/28.26  | | | COMBINE_EQS: (37), (42) imply:
% 177.86/28.26  | | |   (43)  all_52_13 = e1
% 177.86/28.26  | | | 
% 177.86/28.26  | | | SIMP: (43) implies:
% 177.86/28.26  | | |   (44)  all_52_13 = e1
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (2), (44) imply:
% 177.86/28.26  | | |   (45)  $false
% 177.86/28.26  | | | 
% 177.86/28.26  | | | CLOSE: (45) is inconsistent.
% 177.86/28.26  | | | 
% 177.86/28.26  | | Case 2:
% 177.86/28.26  | | | 
% 177.86/28.26  | | |   (46)  all_56_6 = e0
% 177.86/28.26  | | | 
% 177.86/28.26  | | | COMBINE_EQS: (37), (46) imply:
% 177.86/28.26  | | |   (47)  all_52_13 = e0
% 177.86/28.26  | | | 
% 177.86/28.26  | | | SIMP: (47) implies:
% 177.86/28.26  | | |   (48)  all_52_13 = e0
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (5), (48) imply:
% 177.86/28.26  | | |   (49)   ~ (all_52_29 = e0)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | SIMP: (49) implies:
% 177.86/28.26  | | |   (50)   ~ (all_52_29 = e0)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | GROUND_INST: instantiating (28) with e0, all_6_0, e3, e0, simplifying with
% 177.86/28.26  | | |              (19), (21) gives:
% 177.86/28.26  | | |   (51)  all_6_0 = e0
% 177.86/28.26  | | | 
% 177.86/28.26  | | | GROUND_INST: instantiating (28) with e2, all_10_0, e3, e1, simplifying
% 177.86/28.26  | | |              with (23), (25) gives:
% 177.86/28.26  | | |   (52)  all_10_0 = e2
% 177.86/28.26  | | | 
% 177.86/28.26  | | | GROUND_INST: instantiating (28) with all_52_7, all_52_24, e0, e3,
% 177.86/28.26  | | |              simplifying with (9), (27) gives:
% 177.86/28.26  | | |   (53)  all_52_7 = all_52_24
% 177.86/28.26  | | | 
% 177.86/28.26  | | | GROUND_INST: instantiating (28) with all_52_3, all_52_16, e2, e3,
% 177.86/28.26  | | |              simplifying with (7), (17) gives:
% 177.86/28.26  | | |   (54)  all_52_3 = all_52_16
% 177.86/28.26  | | | 
% 177.86/28.26  | | | COMBINE_EQS: (6), (53) imply:
% 177.86/28.26  | | |   (55)  all_56_3 = all_52_24
% 177.86/28.26  | | | 
% 177.86/28.26  | | | COMBINE_EQS: (35), (53) imply:
% 177.86/28.26  | | |   (56)  all_58_9 = all_52_24
% 177.86/28.26  | | | 
% 177.86/28.26  | | | COMBINE_EQS: (14), (54) imply:
% 177.86/28.26  | | |   (57)  all_58_1 = all_52_16
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (22), (54) imply:
% 177.86/28.26  | | |   (58)   ~ (all_52_16 = e3)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (31), (53) imply:
% 177.86/28.26  | | |   (59)   ~ (all_52_24 = e3)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (26), (53) imply:
% 177.86/28.26  | | |   (60)   ~ (all_52_24 = e2)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (30), (52) imply:
% 177.86/28.26  | | |   (61)   ~ (e3 = e2)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | SIMP: (61) implies:
% 177.86/28.26  | | |   (62)   ~ (e3 = e2)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (36), (52) imply:
% 177.86/28.26  | | |   (63)   ~ (e2 = e1)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (33), (51) imply:
% 177.86/28.26  | | |   (64)   ~ (e1 = e0)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | SIMP: (64) implies:
% 177.86/28.26  | | |   (65)   ~ (e1 = e0)
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (1), (54) imply:
% 177.86/28.26  | | |   (66)  op(e2, all_52_16) = e2
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REDUCE: (34), (53) imply:
% 177.86/28.26  | | |   (67)  op(e0, all_52_24) = e0
% 177.86/28.26  | | | 
% 177.86/28.26  | | | BETA: splitting (8) gives:
% 177.86/28.26  | | | 
% 177.86/28.26  | | | Case 1:
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | |   (68)  all_58_1 = e2
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | COMBINE_EQS: (57), (68) imply:
% 177.86/28.26  | | | |   (69)  all_52_16 = e2
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | REDUCE: (66), (69) imply:
% 177.86/28.26  | | | |   (70)  op(e2, e2) = e2
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | REF_CLOSE: (28), (39), (62), (70) are inconsistent by sub-proof #848.
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | Case 2:
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | |   (71)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | BETA: splitting (71) gives:
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | Case 1:
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | |   (72)  all_58_3 = e2
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | | COMBINE_EQS: (32), (72) imply:
% 177.86/28.26  | | | | |   (73)  e3 = e2
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | | SIMP: (73) implies:
% 177.86/28.26  | | | | |   (74)  e3 = e2
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | | REDUCE: (62), (74) imply:
% 177.86/28.26  | | | | |   (75)  $false
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | | CLOSE: (75) is inconsistent.
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | Case 2:
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | |   (76)  all_58_7 = e2 | all_58_13 = e2
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | | BETA: splitting (76) gives:
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | | Case 1:
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | |   (77)  all_58_7 = e2
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | | COMBINE_EQS: (11), (77) imply:
% 177.86/28.26  | | | | | |   (78)  all_52_19 = e2
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | | SIMP: (78) implies:
% 177.86/28.26  | | | | | |   (79)  all_52_19 = e2
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | | REDUCE: (15), (79) imply:
% 177.86/28.26  | | | | | |   (80)  $false
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | | CLOSE: (80) is inconsistent.
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | Case 2:
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | |   (81)  all_58_13 = e2
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | | BETA: splitting (24) gives:
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | | Case 1:
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | |   (82)  all_58_12 = e1
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | | COMBINE_EQS: (20), (82) imply:
% 177.86/28.26  | | | | | | |   (83)  e1 = e0
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | | REDUCE: (65), (83) imply:
% 177.86/28.26  | | | | | | |   (84)  $false
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | | CLOSE: (84) is inconsistent.
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | Case 2:
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | |   (85)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | | BETA: splitting (85) gives:
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | | Case 1:
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | |   (86)  all_58_13 = e1
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | | COMBINE_EQS: (81), (86) imply:
% 177.86/28.26  | | | | | | | |   (87)  e2 = e1
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | | SIMP: (87) implies:
% 177.86/28.26  | | | | | | | |   (88)  e2 = e1
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | | REDUCE: (63), (88) imply:
% 177.86/28.26  | | | | | | | |   (89)  $false
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | | CLOSE: (89) is inconsistent.
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | Case 2:
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | |   (90)  all_58_14 = e1 | all_58_15 = e1
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | | BETA: splitting (90) gives:
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | | Case 1:
% 177.86/28.26  | | | | | | | | | 
% 177.86/28.26  | | | | | | | | |   (91)  all_58_14 = e1
% 177.86/28.26  | | | | | | | | | 
% 177.86/28.26  | | | | | | | | | COMBINE_EQS: (16), (91) imply:
% 177.86/28.26  | | | | | | | | |   (92)  all_52_29 = e1
% 177.86/28.26  | | | | | | | | | 
% 177.86/28.26  | | | | | | | | | REF_CLOSE: (4), (10), (12), (28), (38), (50), (55), (56),
% 177.86/28.26  | | | | | | | | |            (59), (60), (67), (92) are inconsistent by
% 177.86/28.26  | | | | | | | | |            sub-proof #514.
% 177.86/28.26  | | | | | | | | | 
% 177.86/28.26  | | | | | | | | Case 2:
% 177.86/28.26  | | | | | | | | | 
% 177.86/28.26  | | | | | | | | |   (93)  all_58_15 = e1
% 177.86/28.26  | | | | | | | | | 
% 177.86/28.26  | | | | | | | | | REF_CLOSE: (3), (13), (93) are inconsistent by sub-proof #836.
% 177.86/28.26  | | | | | | | | | 
% 177.86/28.26  | | | | | | | | End of split
% 177.86/28.26  | | | | | | | | 
% 177.86/28.26  | | | | | | | End of split
% 177.86/28.26  | | | | | | | 
% 177.86/28.26  | | | | | | End of split
% 177.86/28.26  | | | | | | 
% 177.86/28.26  | | | | | End of split
% 177.86/28.26  | | | | | 
% 177.86/28.26  | | | | End of split
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | End of split
% 177.86/28.26  | | | 
% 177.86/28.26  | | End of split
% 177.86/28.26  | | 
% 177.86/28.26  | End of split
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #514 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.26    (2)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.26    (3)  all_52_29 = e1
% 177.86/28.26    (4)  op(e0, e1) = all_52_29
% 177.86/28.26    (5)   ~ (all_52_24 = e2)
% 177.86/28.26    (6)  op(e0, all_52_24) = e0
% 177.86/28.26    (7)   ~ (all_52_29 = e0)
% 177.86/28.26    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.26    (9)  all_58_9 = all_52_24
% 177.86/28.26    (10)   ~ (all_52_24 = e3)
% 177.86/28.26    (11)  op(e0, e0) = e3
% 177.86/28.26    (12)  all_56_3 = all_52_24
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (3) implies:
% 177.86/28.26  |   (13)  all_52_29 = e1
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (7), (13) imply:
% 177.86/28.26  |   (14)   ~ (e1 = e0)
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (4), (13) imply:
% 177.86/28.26  |   (15)  op(e0, e1) = e1
% 177.86/28.26  | 
% 177.86/28.26  | BETA: splitting (2) gives:
% 177.86/28.26  | 
% 177.86/28.26  | Case 1:
% 177.86/28.26  | | 
% 177.86/28.26  | |   (16)  all_58_9 = e1
% 177.86/28.26  | | 
% 177.86/28.26  | | COMBINE_EQS: (9), (16) imply:
% 177.86/28.26  | |   (17)  all_52_24 = e1
% 177.86/28.26  | | 
% 177.86/28.26  | | REDUCE: (6), (17) imply:
% 177.86/28.26  | |   (18)  op(e0, e1) = e0
% 177.86/28.26  | | 
% 177.86/28.26  | | REF_CLOSE: (8), (14), (15), (18) are inconsistent by sub-proof #771.
% 177.86/28.26  | | 
% 177.86/28.26  | Case 2:
% 177.86/28.26  | | 
% 177.86/28.26  | |   (19)   ~ (all_58_9 = e1)
% 177.86/28.26  | | 
% 177.86/28.26  | | REDUCE: (9), (19) imply:
% 177.86/28.26  | |   (20)   ~ (all_52_24 = e1)
% 177.86/28.26  | | 
% 177.86/28.26  | | BETA: splitting (1) gives:
% 177.86/28.26  | | 
% 177.86/28.26  | | Case 1:
% 177.86/28.26  | | | 
% 177.86/28.26  | | |   (21)  all_56_3 = e2
% 177.86/28.26  | | | 
% 177.86/28.26  | | | REF_CLOSE: (5), (12), (21) are inconsistent by sub-proof #516.
% 177.86/28.26  | | | 
% 177.86/28.26  | | Case 2:
% 177.86/28.26  | | | 
% 177.86/28.26  | | |   (22)  all_56_3 = e1 | all_56_3 = e0
% 177.86/28.26  | | | 
% 177.86/28.26  | | | BETA: splitting (22) gives:
% 177.86/28.26  | | | 
% 177.86/28.26  | | | Case 1:
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | |   (23)  all_56_3 = e1
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | REF_CLOSE: (12), (20), (23) are inconsistent by sub-proof #515.
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | Case 2:
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | |   (24)  all_56_3 = e0
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | COMBINE_EQS: (12), (24) imply:
% 177.86/28.26  | | | |   (25)  all_52_24 = e0
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | SIMP: (25) implies:
% 177.86/28.26  | | | |   (26)  all_52_24 = e0
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | REDUCE: (10), (26) imply:
% 177.86/28.26  | | | |   (27)   ~ (e3 = e0)
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | SIMP: (27) implies:
% 177.86/28.26  | | | |   (28)   ~ (e3 = e0)
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | REDUCE: (6), (26) imply:
% 177.86/28.26  | | | |   (29)  op(e0, e0) = e0
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | | REF_CLOSE: (8), (11), (28), (29) are inconsistent by sub-proof #854.
% 177.86/28.26  | | | | 
% 177.86/28.26  | | | End of split
% 177.86/28.26  | | | 
% 177.86/28.26  | | End of split
% 177.86/28.26  | | 
% 177.86/28.26  | End of split
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #515 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)  all_56_3 = all_52_24
% 177.86/28.26    (2)  all_56_3 = e1
% 177.86/28.26    (3)   ~ (all_52_24 = e1)
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.26  |   (4)  all_52_24 = e1
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (4) implies:
% 177.86/28.26  |   (5)  all_52_24 = e1
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (3), (5) imply:
% 177.86/28.26  |   (6)  $false
% 177.86/28.26  | 
% 177.86/28.26  | CLOSE: (6) is inconsistent.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #516 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)  all_56_3 = all_52_24
% 177.86/28.26    (2)  all_56_3 = e2
% 177.86/28.26    (3)   ~ (all_52_24 = e2)
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.26  |   (4)  all_52_24 = e2
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (4) implies:
% 177.86/28.26  |   (5)  all_52_24 = e2
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (3), (5) imply:
% 177.86/28.26  |   (6)  $false
% 177.86/28.26  | 
% 177.86/28.26  | CLOSE: (6) is inconsistent.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #517 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)  all_58_6 = e2
% 177.86/28.26    (2)  all_58_6 = e0
% 177.86/28.26    (3)   ~ (e2 = e0)
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.26  |   (4)  e2 = e0
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (4) implies:
% 177.86/28.26  |   (5)  e2 = e0
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (3), (5) imply:
% 177.86/28.26  |   (6)  $false
% 177.86/28.26  | 
% 177.86/28.26  | CLOSE: (6) is inconsistent.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #518 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)  all_56_4 = all_14_0
% 177.86/28.26    (2)  all_56_4 = e2
% 177.86/28.26    (3)   ~ (all_14_0 = e2)
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.26  |   (4)  all_14_0 = e2
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (4) implies:
% 177.86/28.26  |   (5)  all_14_0 = e2
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (3), (5) imply:
% 177.86/28.26  |   (6)  $false
% 177.86/28.26  | 
% 177.86/28.26  | CLOSE: (6) is inconsistent.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #519 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)  all_56_4 = all_14_0
% 177.86/28.26    (2)  all_56_4 = e3
% 177.86/28.26    (3)   ~ (all_14_0 = e3)
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.26  |   (4)  all_14_0 = e3
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (4) implies:
% 177.86/28.26  |   (5)  all_14_0 = e3
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (3), (5) imply:
% 177.86/28.26  |   (6)  $false
% 177.86/28.26  | 
% 177.86/28.26  | CLOSE: (6) is inconsistent.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #520 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)  all_58_2 = all_14_0
% 177.86/28.26    (2)  all_58_2 = e0
% 177.86/28.26    (3)   ~ (all_14_0 = e0)
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.26  |   (4)  all_14_0 = e0
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (4) implies:
% 177.86/28.26  |   (5)  all_14_0 = e0
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (3), (5) imply:
% 177.86/28.26  |   (6)  $false
% 177.86/28.26  | 
% 177.86/28.26  | CLOSE: (6) is inconsistent.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #521 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.26    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.26    (3)  op(e2, all_52_3) = e2
% 177.86/28.26    (4)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.26    (5)  all_56_3 = all_52_7
% 177.86/28.26    (6)  op(e3, e2) = all_52_3
% 177.86/28.26    (7)  op(e1, e2) = all_52_19
% 177.86/28.26    (8)  all_58_5 = all_52_13
% 177.86/28.26    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.26    (10)  all_56_9 = all_52_19
% 177.86/28.26    (11)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.26    (12)  all_58_15 = all_6_2
% 177.86/28.26    (13)   ~ (all_52_9 = all_4_2)
% 177.86/28.26    (14)   ~ (all_52_5 = all_52_7)
% 177.86/28.26    (15)  all_58_10 = all_52_15
% 177.86/28.26    (16)   ~ (all_52_5 = all_4_2)
% 177.86/28.26    (17)  all_58_7 = all_52_19
% 177.86/28.26    (18)  op(e0, e1) = all_52_29
% 177.86/28.26    (19)  all_58_4 = all_52_5
% 177.86/28.26    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.26    (21)   ~ (all_52_17 = all_14_2)
% 177.86/28.26    (22)   ~ (all_52_7 = all_4_2)
% 177.86/28.26    (23)  all_58_1 = all_52_3
% 177.86/28.26    (24)  all_58_0 = all_4_2
% 177.86/28.26    (25)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.26    (26)  all_58_14 = all_52_29
% 177.86/28.26    (27)   ~ (all_52_3 = all_52_5)
% 177.86/28.26    (28)  op(e2, e1) = all_52_13
% 177.86/28.26    (29)  all_58_8 = all_14_2
% 177.86/28.26    (30)  all_56_1 = all_52_3
% 177.86/28.26    (31)  op(e0, e2) = all_52_27
% 177.86/28.26    (32)   ~ (all_52_5 = all_14_2)
% 177.86/28.26    (33)   ~ (all_52_3 = all_52_27)
% 177.86/28.26    (34)  op(e3, all_4_2) = e3
% 177.86/28.26    (35)  op(e0, e3) = all_52_25
% 177.86/28.26    (36)   ~ (all_52_29 = e3)
% 177.86/28.26    (37)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.26    (38)   ~ (all_52_13 = all_14_2)
% 177.86/28.26    (39)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.26    (40)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.26    (41)   ~ (all_52_5 = all_52_29)
% 177.86/28.26    (42)  all_56_2 = all_52_5
% 177.86/28.26    (43)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.26    (44)  all_58_6 = all_52_17
% 177.86/28.26    (45)   ~ (all_52_3 = all_52_7)
% 177.86/28.26    (46)  all_56_0 = all_4_2
% 177.86/28.26    (47)  all_58_11 = all_52_23
% 177.86/28.26    (48)   ~ (all_52_3 = all_52_19)
% 177.86/28.26    (49)   ~ (all_52_7 = all_52_15)
% 177.86/28.26    (50)   ~ (all_52_29 = all_14_2)
% 177.86/28.26    (51)  op(e3, e1) = all_52_5
% 177.86/28.26    (52)  all_56_10 = all_14_2
% 177.86/28.26    (53)  op(e1, e1) = all_14_2
% 177.86/28.26    (54)  op(e1, e3) = all_52_17
% 177.86/28.26    (55)   ~ (all_52_25 = all_4_2)
% 177.86/28.26    (56)  op(e3, e0) = all_52_7
% 177.86/28.26    (57)   ~ (all_52_17 = all_4_2)
% 177.86/28.26    (58)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.26    (59)   ~ (all_52_7 = all_6_2)
% 177.86/28.26    (60)  all_56_9 = e3
% 177.86/28.26    (61)   ~ (all_52_7 = e3)
% 177.86/28.26    (62)  op(e1, all_52_5) = e1
% 177.86/28.26    (63)   ~ (all_52_7 = all_52_23)
% 177.86/28.26    (64)  op(e0, all_52_7) = e0
% 177.86/28.26    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.26    (66)  all_58_9 = all_52_7
% 177.86/28.26    (67)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.26    (68)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.26    (69)  op(e0, e0) = e3
% 177.86/28.26    (70)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.26    (71)   ~ (all_52_19 = all_14_2)
% 177.86/28.26    (72)  op(e2, e3) = all_52_9
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | COMBINE_EQS: (10), (60) imply:
% 177.86/28.26  |   (73)  all_52_19 = e3
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (73) implies:
% 177.86/28.26  |   (74)  all_52_19 = e3
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (48), (74) imply:
% 177.86/28.26  |   (75)   ~ (all_52_3 = e3)
% 177.86/28.26  | 
% 177.86/28.26  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 177.86/28.26  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.86/28.26  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.86/28.26  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.86/28.26  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.86/28.26  |            (58), (59), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 177.86/28.26  |            (70), (71), (72), (74), (75) are inconsistent by sub-proof #522.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #522 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.26    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.26    (3)  op(e2, all_52_3) = e2
% 177.86/28.26    (4)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.26    (5)  all_56_3 = all_52_7
% 177.86/28.26    (6)  op(e3, e2) = all_52_3
% 177.86/28.26    (7)  op(e1, e2) = all_52_19
% 177.86/28.26    (8)  all_58_5 = all_52_13
% 177.86/28.26    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.26    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.26    (11)  all_58_15 = all_6_2
% 177.86/28.26    (12)   ~ (all_52_9 = all_4_2)
% 177.86/28.26    (13)   ~ (all_52_5 = all_52_7)
% 177.86/28.26    (14)  all_58_10 = all_52_15
% 177.86/28.26    (15)   ~ (all_52_5 = all_4_2)
% 177.86/28.26    (16)  all_58_7 = all_52_19
% 177.86/28.26    (17)  op(e0, e1) = all_52_29
% 177.86/28.26    (18)  all_58_4 = all_52_5
% 177.86/28.26    (19)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.26    (20)   ~ (all_52_17 = all_14_2)
% 177.86/28.26    (21)   ~ (all_52_7 = all_4_2)
% 177.86/28.26    (22)  all_58_1 = all_52_3
% 177.86/28.26    (23)  all_58_0 = all_4_2
% 177.86/28.26    (24)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.26    (25)  all_58_14 = all_52_29
% 177.86/28.26    (26)   ~ (all_52_3 = all_52_5)
% 177.86/28.26    (27)  op(e2, e1) = all_52_13
% 177.86/28.26    (28)  all_58_8 = all_14_2
% 177.86/28.26    (29)  all_56_1 = all_52_3
% 177.86/28.26    (30)  op(e0, e2) = all_52_27
% 177.86/28.26    (31)   ~ (all_52_5 = all_14_2)
% 177.86/28.26    (32)   ~ (all_52_3 = all_52_27)
% 177.86/28.26    (33)  op(e3, all_4_2) = e3
% 177.86/28.26    (34)  op(e0, e3) = all_52_25
% 177.86/28.26    (35)   ~ (all_52_29 = e3)
% 177.86/28.26    (36)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.26    (37)   ~ (all_52_13 = all_14_2)
% 177.86/28.26    (38)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.26    (39)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.26    (40)   ~ (all_52_5 = all_52_29)
% 177.86/28.26    (41)  all_56_2 = all_52_5
% 177.86/28.26    (42)   ~ (all_52_3 = e3)
% 177.86/28.26    (43)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.26    (44)  all_58_6 = all_52_17
% 177.86/28.26    (45)   ~ (all_52_3 = all_52_7)
% 177.86/28.26    (46)  all_56_0 = all_4_2
% 177.86/28.26    (47)  all_58_11 = all_52_23
% 177.86/28.26    (48)   ~ (all_52_3 = all_52_19)
% 177.86/28.26    (49)   ~ (all_52_7 = all_52_15)
% 177.86/28.26    (50)   ~ (all_52_29 = all_14_2)
% 177.86/28.26    (51)  op(e3, e1) = all_52_5
% 177.86/28.26    (52)  all_56_10 = all_14_2
% 177.86/28.26    (53)  op(e1, e1) = all_14_2
% 177.86/28.26    (54)  all_52_19 = e3
% 177.86/28.26    (55)  op(e1, e3) = all_52_17
% 177.86/28.26    (56)   ~ (all_52_25 = all_4_2)
% 177.86/28.26    (57)  op(e3, e0) = all_52_7
% 177.86/28.26    (58)   ~ (all_52_17 = all_4_2)
% 177.86/28.26    (59)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.26    (60)   ~ (all_52_7 = all_6_2)
% 177.86/28.26    (61)   ~ (all_52_7 = e3)
% 177.86/28.26    (62)  op(e1, all_52_5) = e1
% 177.86/28.26    (63)   ~ (all_52_7 = all_52_23)
% 177.86/28.26    (64)  op(e0, all_52_7) = e0
% 177.86/28.26    (65)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.26    (66)  all_58_9 = all_52_7
% 177.86/28.26    (67)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.26    (68)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.26    (69)  op(e0, e0) = e3
% 177.86/28.26    (70)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.26    (71)   ~ (all_52_19 = all_14_2)
% 177.86/28.26    (72)  op(e2, e3) = all_52_9
% 177.86/28.26  
% 177.86/28.26  Begin of proof
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (54), (71) imply:
% 177.86/28.26  |   (73)   ~ (all_14_2 = e3)
% 177.86/28.26  | 
% 177.86/28.26  | SIMP: (73) implies:
% 177.86/28.26  |   (74)   ~ (all_14_2 = e3)
% 177.86/28.26  | 
% 177.86/28.26  | REDUCE: (7), (54) imply:
% 177.86/28.26  |   (75)  op(e1, e2) = e3
% 177.86/28.26  | 
% 177.86/28.26  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 177.86/28.26  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.86/28.26  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.86/28.26  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.86/28.26  |            (47), (48), (49), (50), (51), (52), (53), (55), (56), (57), (58),
% 177.86/28.26  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 177.86/28.26  |            (70), (72), (74), (75) are inconsistent by sub-proof #851.
% 177.86/28.26  | 
% 177.86/28.26  End of proof
% 177.86/28.26  
% 177.86/28.26  Sub-proof #523 shows that the following formulas are inconsistent:
% 177.86/28.26  ----------------------------------------------------------------
% 177.86/28.26    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.26    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.26    (3)   ~ (all_52_27 = all_10_2)
% 177.86/28.26    (4)  op(e2, all_52_3) = e2
% 177.86/28.26    (5)  all_58_15 = e3
% 177.86/28.26    (6)   ~ (all_52_13 = all_52_29)
% 177.86/28.26    (7)  op(e3, e2) = all_52_3
% 177.86/28.26    (8)  all_58_12 = all_6_1
% 177.86/28.26    (9)  op(all_6_1, e3) = all_6_0
% 177.86/28.26    (10)   ~ (all_52_3 = all_10_2)
% 177.86/28.26    (11)  all_58_5 = all_52_13
% 177.86/28.26    (12)   ~ (all_52_3 = e2)
% 177.86/28.26    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.26    (14)  all_58_15 = all_6_2
% 177.86/28.26    (15)   ~ (all_52_9 = all_4_2)
% 177.86/28.26    (16)   ~ (all_52_5 = all_52_7)
% 177.86/28.26    (17)  all_58_10 = all_52_15
% 177.86/28.26    (18)   ~ (all_52_5 = all_4_2)
% 177.86/28.26    (19)  all_58_7 = all_52_19
% 177.86/28.26    (20)  all_58_4 = all_52_5
% 177.86/28.26    (21)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.26    (22)   ~ (all_52_17 = all_14_2)
% 177.86/28.26    (23)   ~ (all_52_7 = all_4_2)
% 177.86/28.26    (24)  all_58_1 = all_52_3
% 177.86/28.26    (25)  all_58_0 = all_4_2
% 177.86/28.27    (26)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.27    (27)  op(e0, e2) = e0
% 177.86/28.27    (28)  all_58_14 = all_52_29
% 177.86/28.27    (29)   ~ (all_52_3 = all_52_5)
% 177.86/28.27    (30)  op(e2, e1) = all_52_13
% 177.86/28.27    (31)  all_58_8 = all_14_2
% 177.86/28.27    (32)  all_56_1 = all_52_3
% 177.86/28.27    (33)  op(e0, e2) = all_52_27
% 177.86/28.27    (34)   ~ (all_52_5 = all_14_2)
% 177.86/28.27    (35)   ~ (all_52_3 = all_52_27)
% 177.86/28.27    (36)   ~ (all_52_3 = all_4_2)
% 177.86/28.27    (37)  op(e3, all_4_2) = e3
% 177.86/28.27    (38)  op(e0, e3) = all_52_25
% 177.86/28.27    (39)   ~ (all_52_29 = e3)
% 177.86/28.27    (40)   ~ (all_52_13 = all_14_2)
% 177.86/28.27    (41)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.27    (42)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.27    (43)   ~ (all_52_5 = all_52_29)
% 177.86/28.27    (44)  all_58_13 = all_52_27
% 177.86/28.27    (45)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.27    (46)  all_56_5 = all_10_2
% 177.86/28.27    (47)  all_58_6 = all_52_17
% 177.86/28.27    (48)   ~ (all_52_3 = all_52_7)
% 177.86/28.27    (49)  all_56_0 = all_4_2
% 177.86/28.27    (50)  all_58_11 = all_52_23
% 177.86/28.27    (51)   ~ (all_52_3 = all_52_19)
% 177.86/28.27    (52)   ~ (all_52_7 = all_52_15)
% 177.86/28.27    (53)   ~ (all_52_29 = all_14_2)
% 177.86/28.27    (54)  op(e3, e1) = all_52_5
% 177.86/28.27    (55)  all_56_10 = all_14_2
% 177.86/28.27    (56)  op(e2, all_10_2) = e1
% 177.86/28.27    (57)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.27    (58)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.27    (59)  op(e1, e3) = all_52_17
% 177.86/28.27    (60)   ~ (all_52_25 = all_4_2)
% 177.86/28.27    (61)  op(e3, e0) = all_52_7
% 177.86/28.27    (62)   ~ (all_52_17 = all_4_2)
% 177.86/28.27    (63)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.27    (64)   ~ (all_52_7 = all_6_2)
% 177.86/28.27    (65)  op(e1, all_52_5) = e1
% 177.86/28.27    (66)   ~ (all_52_7 = all_52_23)
% 177.86/28.27    (67)   ~ (all_52_13 = all_10_2)
% 177.86/28.27    (68)   ~ (all_6_0 = e1)
% 177.86/28.27    (69)  op(e0, all_52_7) = e0
% 177.86/28.27    (70)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.27    (71)  all_58_9 = all_52_7
% 177.86/28.27    (72)   ~ (e2 = e0)
% 177.86/28.27    (73)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.27    (74)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.27    (75)   ~ (e3 = e2)
% 177.86/28.27    (76)  op(e2, e3) = all_52_9
% 177.86/28.27  
% 177.86/28.27  Begin of proof
% 177.86/28.27  | 
% 177.86/28.27  | GROUND_INST: instantiating (63) with all_52_27, e0, e2, e0, simplifying with
% 177.86/28.27  |              (27), (33) gives:
% 177.86/28.27  |   (77)  all_52_27 = e0
% 177.86/28.27  | 
% 177.86/28.27  | COMBINE_EQS: (44), (77) imply:
% 177.86/28.27  |   (78)  all_58_13 = e0
% 177.86/28.27  | 
% 177.86/28.27  | REDUCE: (35), (77) imply:
% 177.86/28.27  |   (79)   ~ (all_52_3 = e0)
% 177.86/28.27  | 
% 177.86/28.27  | REDUCE: (3), (77) imply:
% 177.86/28.27  |   (80)   ~ (all_10_2 = e0)
% 177.86/28.27  | 
% 177.86/28.27  | SIMP: (80) implies:
% 177.86/28.27  |   (81)   ~ (all_10_2 = e0)
% 177.86/28.27  | 
% 177.86/28.27  | BETA: splitting (26) gives:
% 177.86/28.27  | 
% 177.86/28.27  | Case 1:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (82)  all_56_1 = e3
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (1), (2), (4), (7), (11), (13), (14), (15), (16), (17), (18),
% 177.86/28.27  | |            (19), (20), (21), (22), (23), (24), (25), (28), (29), (31), (32),
% 177.86/28.27  | |            (34), (36), (37), (38), (39), (40), (41), (42), (43), (45), (47),
% 177.86/28.27  | |            (48), (49), (50), (51), (52), (53), (54), (55), (59), (60), (61),
% 177.86/28.27  | |            (62), (63), (64), (65), (66), (69), (70), (71), (73), (74), (76),
% 177.86/28.27  | |            (82) are inconsistent by sub-proof #528.
% 177.86/28.27  | | 
% 177.86/28.27  | Case 2:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (83)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.27  | | 
% 177.86/28.27  | | BETA: splitting (83) gives:
% 177.86/28.27  | | 
% 177.86/28.27  | | Case 1:
% 177.86/28.27  | | | 
% 177.86/28.27  | | |   (84)  all_56_1 = e2
% 177.86/28.27  | | | 
% 177.86/28.27  | | | REF_CLOSE: (12), (32), (84) are inconsistent by sub-proof #857.
% 177.86/28.27  | | | 
% 177.86/28.27  | | Case 2:
% 177.86/28.27  | | | 
% 177.86/28.27  | | |   (85)  all_56_1 = e1 | all_56_1 = e0
% 177.86/28.27  | | | 
% 177.86/28.27  | | | BETA: splitting (85) gives:
% 177.86/28.27  | | | 
% 177.86/28.27  | | | Case 1:
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | |   (86)  all_56_1 = e1
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | COMBINE_EQS: (32), (86) imply:
% 177.86/28.27  | | | |   (87)  all_52_3 = e1
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | SIMP: (87) implies:
% 177.86/28.27  | | | |   (88)  all_52_3 = e1
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | REDUCE: (10), (88) imply:
% 177.86/28.27  | | | |   (89)   ~ (all_10_2 = e1)
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | SIMP: (89) implies:
% 177.86/28.27  | | | |   (90)   ~ (all_10_2 = e1)
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | REDUCE: (4), (88) imply:
% 177.86/28.27  | | | |   (91)  op(e2, e1) = e2
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | GROUND_INST: instantiating (63) with all_52_13, e2, e1, e2, simplifying
% 177.86/28.27  | | | |              with (30), (91) gives:
% 177.86/28.27  | | | |   (92)  all_52_13 = e2
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | REDUCE: (6), (92) imply:
% 177.86/28.27  | | | |   (93)   ~ (all_52_29 = e2)
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | SIMP: (93) implies:
% 177.86/28.27  | | | |   (94)   ~ (all_52_29 = e2)
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | REDUCE: (67), (92) imply:
% 177.86/28.27  | | | |   (95)   ~ (all_10_2 = e2)
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | SIMP: (95) implies:
% 177.86/28.27  | | | |   (96)   ~ (all_10_2 = e2)
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | BETA: splitting (58) gives:
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | Case 1:
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | |   (97)  all_58_12 = e2
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | | COMBINE_EQS: (8), (97) imply:
% 177.86/28.27  | | | | |   (98)  all_6_1 = e2
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | | SIMP: (98) implies:
% 177.86/28.27  | | | | |   (99)  all_6_1 = e2
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | | REDUCE: (9), (99) imply:
% 177.86/28.27  | | | | |   (100)  op(e2, e3) = all_6_0
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | | REF_CLOSE: (46), (56), (57), (63), (68), (81), (90), (96), (100) are
% 177.86/28.27  | | | | |            inconsistent by sub-proof #525.
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | Case 2:
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | |   (101)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | | BETA: splitting (101) gives:
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | | Case 1:
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | |   (102)  all_58_13 = e2
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | | COMBINE_EQS: (78), (102) imply:
% 177.86/28.27  | | | | | |   (103)  e2 = e0
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | | REDUCE: (72), (103) imply:
% 177.86/28.27  | | | | | |   (104)  $false
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | | CLOSE: (104) is inconsistent.
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | Case 2:
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | |   (105)  all_58_14 = e2 | all_58_15 = e2
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | | BETA: splitting (105) gives:
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | | Case 1:
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | |   (106)  all_58_14 = e2
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | | REF_CLOSE: (28), (94), (106) are inconsistent by sub-proof #524.
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | Case 2:
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | |   (107)  all_58_15 = e2
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | | COMBINE_EQS: (5), (107) imply:
% 177.86/28.27  | | | | | | |   (108)  e3 = e2
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | | REDUCE: (75), (108) imply:
% 177.86/28.27  | | | | | | |   (109)  $false
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | | CLOSE: (109) is inconsistent.
% 177.86/28.27  | | | | | | | 
% 177.86/28.27  | | | | | | End of split
% 177.86/28.27  | | | | | | 
% 177.86/28.27  | | | | | End of split
% 177.86/28.27  | | | | | 
% 177.86/28.27  | | | | End of split
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | Case 2:
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | |   (110)  all_56_1 = e0
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | | REF_CLOSE: (32), (79), (110) are inconsistent by sub-proof #855.
% 177.86/28.27  | | | | 
% 177.86/28.27  | | | End of split
% 177.86/28.27  | | | 
% 177.86/28.27  | | End of split
% 177.86/28.27  | | 
% 177.86/28.27  | End of split
% 177.86/28.27  | 
% 177.86/28.27  End of proof
% 177.86/28.27  
% 177.86/28.27  Sub-proof #524 shows that the following formulas are inconsistent:
% 177.86/28.27  ----------------------------------------------------------------
% 177.86/28.27    (1)  all_58_14 = all_52_29
% 177.86/28.27    (2)  all_58_14 = e2
% 177.86/28.27    (3)   ~ (all_52_29 = e2)
% 177.86/28.27  
% 177.86/28.27  Begin of proof
% 177.86/28.27  | 
% 177.86/28.27  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.27  |   (4)  all_52_29 = e2
% 177.86/28.27  | 
% 177.86/28.27  | SIMP: (4) implies:
% 177.86/28.27  |   (5)  all_52_29 = e2
% 177.86/28.27  | 
% 177.86/28.27  | REDUCE: (3), (5) imply:
% 177.86/28.27  |   (6)  $false
% 177.86/28.27  | 
% 177.86/28.27  | CLOSE: (6) is inconsistent.
% 177.86/28.27  | 
% 177.86/28.27  End of proof
% 177.86/28.27  
% 177.86/28.27  Sub-proof #525 shows that the following formulas are inconsistent:
% 177.86/28.27  ----------------------------------------------------------------
% 177.86/28.27    (1)   ~ (all_10_2 = e0)
% 177.86/28.27    (2)   ~ (all_10_2 = e1)
% 177.86/28.27    (3)  all_56_5 = all_10_2
% 177.86/28.27    (4)   ~ (all_10_2 = e2)
% 177.86/28.27    (5)  op(e2, all_10_2) = e1
% 177.86/28.27    (6)  op(e2, e3) = all_6_0
% 177.86/28.27    (7)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.27    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.27    (9)   ~ (all_6_0 = e1)
% 177.86/28.27  
% 177.86/28.27  Begin of proof
% 177.86/28.27  | 
% 177.86/28.27  | BETA: splitting (7) gives:
% 177.86/28.27  | 
% 177.86/28.27  | Case 1:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (10)  all_56_5 = e3
% 177.86/28.27  | | 
% 177.86/28.27  | | COMBINE_EQS: (3), (10) imply:
% 177.86/28.27  | |   (11)  all_10_2 = e3
% 177.86/28.27  | | 
% 177.86/28.27  | | SIMP: (11) implies:
% 177.86/28.27  | |   (12)  all_10_2 = e3
% 177.86/28.27  | | 
% 177.86/28.27  | | REDUCE: (5), (12) imply:
% 177.86/28.27  | |   (13)  op(e2, e3) = e1
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (6), (8), (9), (13) are inconsistent by sub-proof #838.
% 177.86/28.27  | | 
% 177.86/28.27  | Case 2:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (14)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (1), (2), (3), (4), (14) are inconsistent by sub-proof #526.
% 177.86/28.27  | | 
% 177.86/28.27  | End of split
% 177.86/28.27  | 
% 177.86/28.27  End of proof
% 177.86/28.27  
% 177.86/28.27  Sub-proof #526 shows that the following formulas are inconsistent:
% 177.86/28.27  ----------------------------------------------------------------
% 177.86/28.27    (1)   ~ (all_10_2 = e0)
% 177.86/28.27    (2)   ~ (all_10_2 = e1)
% 177.86/28.27    (3)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.27    (4)  all_56_5 = all_10_2
% 177.86/28.27    (5)   ~ (all_10_2 = e2)
% 177.86/28.27  
% 177.86/28.27  Begin of proof
% 177.86/28.27  | 
% 177.86/28.27  | BETA: splitting (3) gives:
% 177.86/28.27  | 
% 177.86/28.27  | Case 1:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (6)  all_56_5 = e2
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #710.
% 177.86/28.27  | | 
% 177.86/28.27  | Case 2:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (7)  all_56_5 = e1 | all_56_5 = e0
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #527.
% 177.86/28.27  | | 
% 177.86/28.27  | End of split
% 177.86/28.27  | 
% 177.86/28.27  End of proof
% 177.86/28.27  
% 177.86/28.27  Sub-proof #527 shows that the following formulas are inconsistent:
% 177.86/28.27  ----------------------------------------------------------------
% 177.86/28.27    (1)  all_56_5 = e1 | all_56_5 = e0
% 177.86/28.27    (2)  all_56_5 = all_10_2
% 177.86/28.27    (3)   ~ (all_10_2 = e1)
% 177.86/28.27    (4)   ~ (all_10_2 = e0)
% 177.86/28.27  
% 177.86/28.27  Begin of proof
% 177.86/28.27  | 
% 177.86/28.27  | BETA: splitting (1) gives:
% 177.86/28.27  | 
% 177.86/28.27  | Case 1:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (5)  all_56_5 = e1
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #709.
% 177.86/28.27  | | 
% 177.86/28.27  | Case 2:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (6)  all_56_5 = e0
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #708.
% 177.86/28.27  | | 
% 177.86/28.27  | End of split
% 177.86/28.27  | 
% 177.86/28.27  End of proof
% 177.86/28.27  
% 177.86/28.27  Sub-proof #528 shows that the following formulas are inconsistent:
% 177.86/28.27  ----------------------------------------------------------------
% 177.86/28.27    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.27    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.27    (3)  op(e2, all_52_3) = e2
% 177.86/28.27    (4)  op(e3, e2) = all_52_3
% 177.86/28.27    (5)  all_58_5 = all_52_13
% 177.86/28.27    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.27    (7)  all_58_15 = all_6_2
% 177.86/28.27    (8)   ~ (all_52_9 = all_4_2)
% 177.86/28.27    (9)   ~ (all_52_5 = all_52_7)
% 177.86/28.27    (10)  all_58_10 = all_52_15
% 177.86/28.27    (11)   ~ (all_52_5 = all_4_2)
% 177.86/28.27    (12)  all_58_7 = all_52_19
% 177.86/28.27    (13)  all_58_4 = all_52_5
% 177.86/28.27    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.27    (15)   ~ (all_52_17 = all_14_2)
% 177.86/28.27    (16)   ~ (all_52_7 = all_4_2)
% 177.86/28.27    (17)  all_58_1 = all_52_3
% 177.86/28.27    (18)  all_58_0 = all_4_2
% 177.86/28.27    (19)  all_58_14 = all_52_29
% 177.86/28.27    (20)   ~ (all_52_3 = all_52_5)
% 177.86/28.27    (21)  all_58_8 = all_14_2
% 177.86/28.27    (22)  all_56_1 = all_52_3
% 177.86/28.27    (23)   ~ (all_52_5 = all_14_2)
% 177.86/28.27    (24)   ~ (all_52_3 = all_4_2)
% 177.86/28.27    (25)  op(e3, all_4_2) = e3
% 177.86/28.27    (26)  op(e0, e3) = all_52_25
% 177.86/28.27    (27)   ~ (all_52_29 = e3)
% 177.86/28.27    (28)   ~ (all_52_13 = all_14_2)
% 177.86/28.27    (29)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.27    (30)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.27    (31)   ~ (all_52_5 = all_52_29)
% 177.86/28.27    (32)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.27    (33)  all_58_6 = all_52_17
% 177.86/28.27    (34)   ~ (all_52_3 = all_52_7)
% 177.86/28.27    (35)  all_56_0 = all_4_2
% 177.86/28.27    (36)  all_58_11 = all_52_23
% 177.86/28.27    (37)   ~ (all_52_3 = all_52_19)
% 177.86/28.27    (38)   ~ (all_52_7 = all_52_15)
% 177.86/28.27    (39)   ~ (all_52_29 = all_14_2)
% 177.86/28.27    (40)  all_56_1 = e3
% 177.86/28.27    (41)  op(e3, e1) = all_52_5
% 177.86/28.27    (42)  all_56_10 = all_14_2
% 177.86/28.27    (43)  op(e1, e3) = all_52_17
% 177.86/28.27    (44)   ~ (all_52_25 = all_4_2)
% 177.86/28.27    (45)  op(e3, e0) = all_52_7
% 177.86/28.27    (46)   ~ (all_52_17 = all_4_2)
% 177.86/28.27    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.27    (48)   ~ (all_52_7 = all_6_2)
% 177.86/28.27    (49)  op(e1, all_52_5) = e1
% 177.86/28.27    (50)   ~ (all_52_7 = all_52_23)
% 177.86/28.27    (51)  op(e0, all_52_7) = e0
% 177.86/28.27    (52)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.27    (53)  all_58_9 = all_52_7
% 177.86/28.27    (54)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.27    (55)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.27    (56)  op(e2, e3) = all_52_9
% 177.86/28.27  
% 177.86/28.27  Begin of proof
% 177.86/28.27  | 
% 177.86/28.27  | COMBINE_EQS: (22), (40) imply:
% 177.86/28.27  |   (57)  all_52_3 = e3
% 177.86/28.27  | 
% 177.86/28.27  | SIMP: (57) implies:
% 177.86/28.27  |   (58)  all_52_3 = e3
% 177.86/28.27  | 
% 177.86/28.27  | REDUCE: (24), (58) imply:
% 177.86/28.27  |   (59)   ~ (all_4_2 = e3)
% 177.86/28.27  | 
% 177.86/28.27  | SIMP: (59) implies:
% 177.86/28.27  |   (60)   ~ (all_4_2 = e3)
% 177.86/28.27  | 
% 177.86/28.27  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.86/28.27  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (25),
% 177.86/28.27  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.86/28.27  |            (37), (38), (39), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.86/28.27  |            (49), (50), (51), (52), (53), (54), (55), (56), (60) are
% 177.86/28.27  |            inconsistent by sub-proof #864.
% 177.86/28.27  | 
% 177.86/28.27  End of proof
% 177.86/28.27  
% 177.86/28.27  Sub-proof #529 shows that the following formulas are inconsistent:
% 177.86/28.27  ----------------------------------------------------------------
% 177.86/28.27    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.27    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.27    (3)   ~ (all_52_27 = all_10_2)
% 177.86/28.27    (4)   ~ (all_52_17 = all_52_23)
% 177.86/28.27    (5)   ~ (all_6_0 = e3)
% 177.86/28.27    (6)  all_40_2 = all_4_2
% 177.86/28.27    (7)   ~ (all_52_13 = all_52_29)
% 177.86/28.27    (8)  all_56_3 = all_52_7
% 177.86/28.27    (9)  op(e3, e2) = all_52_3
% 177.86/28.27    (10)   ~ (all_52_9 = all_52_25)
% 177.86/28.27    (11)   ~ (all_52_19 = all_52_23)
% 177.86/28.27    (12)  all_56_11 = all_52_23
% 177.86/28.27    (13)  op(e1, e2) = all_52_19
% 177.86/28.27    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.86/28.27    (15)  op(e3, all_52_9) = all_52_8
% 177.86/28.27    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.27    (17)  all_58_5 = all_52_13
% 177.86/28.27    (18)   ~ (all_52_25 = all_52_29)
% 177.86/28.27    (19)  all_56_15 = all_6_2
% 177.86/28.27    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.27    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.27    (22)  all_58_3 = all_10_2
% 177.86/28.27    (23)  all_56_9 = all_52_19
% 177.86/28.27    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.27    (25)  all_58_15 = all_6_2
% 177.86/28.27    (26)  op(e0, all_6_2) = e0
% 177.86/28.27    (27)   ~ (all_52_9 = all_4_2)
% 177.86/28.27    (28)   ~ (all_52_5 = all_52_7)
% 177.86/28.27    (29)  all_58_10 = all_52_15
% 177.86/28.27    (30)   ~ (all_52_5 = all_4_2)
% 177.86/28.27    (31)  all_58_7 = all_52_19
% 177.86/28.27    (32)   ~ (all_52_17 = all_52_25)
% 177.86/28.27    (33)  op(e0, e1) = all_52_29
% 177.86/28.27    (34)   ~ (all_4_0 = e2)
% 177.86/28.27    (35)  all_58_4 = all_52_5
% 177.86/28.27    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.27    (37)   ~ (e3 = e1)
% 177.86/28.27    (38)   ~ (all_52_27 = all_52_29)
% 177.86/28.27    (39)   ~ (all_52_17 = all_14_2)
% 177.86/28.27    (40)  op(e3, all_4_2) = all_4_1
% 177.86/28.27    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.27    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.27    (43)   ~ (all_52_7 = all_4_2)
% 177.86/28.27    (44)  all_58_1 = all_52_3
% 177.86/28.27    (45)   ~ (all_52_13 = all_52_15)
% 177.86/28.27    (46)  all_58_0 = all_4_2
% 177.86/28.27    (47)  op(e2, all_52_27) = e2
% 177.86/28.27    (48)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.86/28.27    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.27    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.27    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.27    (52)  all_58_14 = all_52_29
% 177.86/28.27    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.27    (54)   ~ (all_52_3 = all_52_5)
% 177.86/28.27    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.27    (56)  op(e2, e1) = all_52_13
% 177.86/28.27    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.27    (58)  all_58_8 = all_14_2
% 177.86/28.27    (59)  op(e0, e2) = all_52_27
% 177.86/28.27    (60)  all_56_14 = all_52_29
% 177.86/28.27    (61)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.86/28.27    (62)  op(e1, all_52_29) = e1
% 177.86/28.27    (63)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.27    (64)   ~ (all_52_3 = all_52_27)
% 177.86/28.27    (65)   ~ (all_52_3 = all_4_2)
% 177.86/28.27    (66)  op(e0, e3) = all_52_25
% 177.86/28.27    (67)   ~ (all_52_9 = all_10_2)
% 177.86/28.27    (68)  op(e3, all_52_17) = all_52_16
% 177.86/28.27    (69)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.27    (70)   ~ (all_52_13 = all_14_2)
% 177.86/28.27    (71)  all_40_0 = all_4_0
% 177.86/28.27    (72)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.27    (73)   ~ (all_52_9 = all_52_13)
% 177.86/28.27    (74)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.27    (75)   ~ (all_52_5 = all_52_29)
% 177.86/28.27    (76)  all_56_2 = all_52_5
% 177.86/28.27    (77)  op(e1, e0) = all_52_23
% 177.86/28.27    (78)  all_56_12 = all_52_25
% 177.86/28.27    (79)  all_58_13 = all_52_27
% 177.86/28.27    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.27    (81)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.27    (82)   ~ (all_52_9 = all_52_17)
% 177.86/28.27    (83)  all_58_6 = all_52_17
% 177.86/28.27    (84)   ~ (all_52_3 = all_52_7)
% 177.86/28.27    (85)  all_56_0 = all_4_2
% 177.86/28.27    (86)  all_58_11 = all_52_23
% 177.86/28.27    (87)   ~ (all_52_3 = all_52_19)
% 177.86/28.27    (88)   ~ (all_52_7 = all_52_15)
% 177.86/28.27    (89)   ~ (all_52_29 = all_14_2)
% 177.86/28.27    (90)  op(e3, all_52_25) = e3
% 177.86/28.27    (91)   ~ (all_4_0 = e1)
% 177.86/28.27    (92)   ~ (all_52_19 = all_10_2)
% 177.86/28.27    (93)   ~ (all_52_23 = all_6_2)
% 177.86/28.27    (94)  op(e1, all_4_2) = all_4_0
% 177.86/28.27    (95)   ~ (all_6_0 = e2)
% 177.86/28.27    (96)   ~ (all_52_29 = all_6_2)
% 177.86/28.27    (97)  all_58_2 = all_52_9
% 177.86/28.27    (98)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.27    (99)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.27    (100)  op(e3, e1) = all_52_5
% 177.86/28.27    (101)   ~ (e2 = e1)
% 177.86/28.27    (102)   ~ (all_52_25 = all_6_2)
% 177.86/28.27    (103)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.27    (104)  op(e1, e3) = all_52_17
% 177.86/28.27    (105)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.27    (106)   ~ (all_52_25 = all_4_2)
% 177.86/28.27    (107)  op(e3, e0) = all_52_7
% 177.86/28.27    (108)  op(e3, e3) = all_4_2
% 177.86/28.27    (109)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.86/28.27             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.86/28.27    (110)   ~ (all_52_17 = all_4_2)
% 177.86/28.27    (111)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.27             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.27    (112)   ~ (all_52_25 = all_52_27)
% 177.86/28.27    (113)  op(e0, all_6_2) = all_6_0
% 177.86/28.27    (114)   ~ (all_52_27 = all_6_2)
% 177.86/28.27    (115)   ~ (all_52_7 = all_6_2)
% 177.86/28.27    (116)   ~ (all_52_15 = all_10_2)
% 177.86/28.27    (117)   ~ (all_52_19 = all_52_27)
% 177.86/28.27    (118)  all_56_7 = all_52_15
% 177.86/28.27    (119)   ~ (all_52_7 = all_52_23)
% 177.86/28.27    (120)   ~ (all_6_0 = e1)
% 177.86/28.27    (121)   ~ (all_52_17 = all_52_19)
% 177.86/28.27    (122)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.27    (123)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.27    (124)  all_58_9 = all_52_7
% 177.86/28.27    (125)  all_58_12 = all_52_25
% 177.86/28.27    (126)  op(e3, all_4_2) = e1
% 177.86/28.27    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.27    (128)   ~ (all_52_9 = all_52_15)
% 177.86/28.27    (129)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.27    (130)   ~ (e3 = e2)
% 177.86/28.27    (131)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.27    (132)  op(e2, e3) = all_52_9
% 177.86/28.27    (133)  all_56_13 = all_52_27
% 177.86/28.27  
% 177.86/28.27  Begin of proof
% 177.86/28.27  | 
% 177.86/28.27  | GROUND_INST: instantiating (111) with e0, all_6_0, all_6_2, e0, simplifying
% 177.86/28.27  |              with (26), (113) gives:
% 177.86/28.27  |   (134)  all_6_0 = e0
% 177.86/28.27  | 
% 177.86/28.27  | REDUCE: (5), (134) imply:
% 177.86/28.27  |   (135)   ~ (e3 = e0)
% 177.86/28.27  | 
% 177.86/28.27  | SIMP: (135) implies:
% 177.86/28.27  |   (136)   ~ (e3 = e0)
% 177.86/28.27  | 
% 177.86/28.27  | REDUCE: (120), (134) imply:
% 177.86/28.27  |   (137)   ~ (e1 = e0)
% 177.86/28.27  | 
% 177.86/28.27  | SIMP: (137) implies:
% 177.86/28.27  |   (138)   ~ (e1 = e0)
% 177.86/28.27  | 
% 177.86/28.27  | BETA: splitting (109) gives:
% 177.86/28.27  | 
% 177.86/28.27  | Case 1:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (139)  all_58_15 = e0
% 177.86/28.27  | | 
% 177.86/28.27  | | COMBINE_EQS: (25), (139) imply:
% 177.86/28.27  | |   (140)  all_6_2 = e0
% 177.86/28.27  | | 
% 177.86/28.27  | | REDUCE: (115), (140) imply:
% 177.86/28.27  | |   (141)   ~ (all_52_7 = e0)
% 177.86/28.27  | | 
% 177.86/28.27  | | REDUCE: (102), (140) imply:
% 177.86/28.27  | |   (142)   ~ (all_52_25 = e0)
% 177.86/28.27  | | 
% 177.86/28.27  | | REDUCE: (96), (140) imply:
% 177.86/28.27  | |   (143)   ~ (all_52_29 = e0)
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (1), (6), (8), (9), (10), (13), (17), (18), (23), (24), (27),
% 177.86/28.27  | |            (28), (30), (31), (32), (34), (35), (37), (38), (39), (46), (47),
% 177.86/28.27  | |            (48), (49), (50), (52), (53), (56), (57), (58), (60), (61), (62),
% 177.86/28.27  | |            (64), (65), (68), (69), (71), (74), (77), (78), (79), (81), (82),
% 177.86/28.27  | |            (83), (84), (85), (86), (87), (89), (90), (94), (98), (100),
% 177.86/28.27  | |            (103), (104), (106), (107), (108), (111), (112), (123), (124),
% 177.86/28.27  | |            (125), (126), (132), (133), (136), (138), (139), (141), (142),
% 177.86/28.27  | |            (143) are inconsistent by sub-proof #616.
% 177.86/28.27  | | 
% 177.86/28.27  | Case 2:
% 177.86/28.27  | | 
% 177.86/28.27  | |   (144)   ~ (all_58_15 = e0)
% 177.86/28.27  | |   (145)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.86/28.27  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.86/28.27  | | 
% 177.86/28.27  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (14), (15),
% 177.86/28.27  | |            (16), (17), (18), (19), (20), (21), (22), (24), (25), (26), (27),
% 177.86/28.27  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 177.86/28.27  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (49), (50),
% 177.86/28.27  | |            (51), (52), (53), (54), (55), (57), (58), (59), (60), (62), (63),
% 177.86/28.27  | |            (64), (65), (66), (67), (68), (69), (70), (72), (73), (74), (75),
% 177.86/28.27  | |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 177.86/28.27  | |            (87), (88), (90), (91), (92), (93), (95), (96), (97), (99),
% 177.86/28.27  | |            (100), (101), (102), (103), (104), (105), (106), (107), (108),
% 177.86/28.27  | |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 177.86/28.27  | |            (119), (120), (121), (122), (124), (125), (127), (128), (129),
% 177.86/28.27  | |            (130), (131), (132), (133), (144), (145) are inconsistent by
% 177.86/28.27  | |            sub-proof #530.
% 177.86/28.27  | | 
% 177.86/28.27  | End of split
% 177.86/28.27  | 
% 177.86/28.27  End of proof
% 177.86/28.27  
% 177.86/28.27  Sub-proof #530 shows that the following formulas are inconsistent:
% 177.86/28.27  ----------------------------------------------------------------
% 177.86/28.27    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.27    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.28    (3)   ~ (all_52_27 = all_10_2)
% 177.86/28.28    (4)   ~ (all_52_17 = all_52_23)
% 177.86/28.28    (5)   ~ (all_6_0 = e3)
% 177.86/28.28    (6)   ~ (all_52_13 = all_52_29)
% 177.86/28.28    (7)  op(e3, e2) = all_52_3
% 177.86/28.28    (8)   ~ (all_52_9 = all_52_25)
% 177.86/28.28    (9)   ~ (all_52_19 = all_52_23)
% 177.86/28.28    (10)  all_56_11 = all_52_23
% 177.86/28.28    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.86/28.28    (12)  op(e3, all_52_9) = all_52_8
% 177.86/28.28    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.28    (14)  all_58_5 = all_52_13
% 177.86/28.28    (15)   ~ (all_52_25 = all_52_29)
% 177.86/28.28    (16)  all_56_15 = all_6_2
% 177.86/28.28    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.28    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.28    (19)  all_58_3 = all_10_2
% 177.86/28.28    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.28    (21)  all_58_15 = all_6_2
% 177.86/28.28    (22)  op(e0, all_6_2) = e0
% 177.86/28.28    (23)   ~ (all_52_9 = all_4_2)
% 177.86/28.28    (24)   ~ (all_52_5 = all_52_7)
% 177.86/28.28    (25)  all_58_10 = all_52_15
% 177.86/28.28    (26)   ~ (all_52_5 = all_4_2)
% 177.86/28.28    (27)  all_58_7 = all_52_19
% 177.86/28.28    (28)   ~ (all_52_17 = all_52_25)
% 177.86/28.28    (29)  op(e0, e1) = all_52_29
% 177.86/28.28    (30)   ~ (all_4_0 = e2)
% 177.86/28.28    (31)  all_58_4 = all_52_5
% 177.86/28.28    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.28    (33)   ~ (e3 = e1)
% 177.86/28.28    (34)   ~ (all_52_27 = all_52_29)
% 177.86/28.28    (35)   ~ (all_52_17 = all_14_2)
% 177.86/28.28    (36)  op(e3, all_4_2) = all_4_1
% 177.86/28.28    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.28    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.28    (39)   ~ (all_52_7 = all_4_2)
% 177.86/28.28    (40)  all_58_1 = all_52_3
% 177.86/28.28    (41)   ~ (all_52_13 = all_52_15)
% 177.86/28.28    (42)  all_58_0 = all_4_2
% 177.86/28.28    (43)  op(e2, all_52_27) = e2
% 177.86/28.28    (44)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.28    (45)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.28    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.28    (47)  all_58_14 = all_52_29
% 177.86/28.28    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.28    (49)   ~ (all_52_3 = all_52_5)
% 177.86/28.28    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.28    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.28    (52)  all_58_8 = all_14_2
% 177.86/28.28    (53)  op(e0, e2) = all_52_27
% 177.86/28.28    (54)  all_56_14 = all_52_29
% 177.86/28.28    (55)  op(e1, all_52_29) = e1
% 177.86/28.28    (56)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.28    (57)   ~ (all_52_3 = all_52_27)
% 177.86/28.28    (58)   ~ (all_52_3 = all_4_2)
% 177.86/28.28    (59)  op(e0, e3) = all_52_25
% 177.86/28.28    (60)   ~ (all_52_9 = all_10_2)
% 177.86/28.28    (61)  op(e3, all_52_17) = all_52_16
% 177.86/28.28    (62)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.28    (63)   ~ (all_52_13 = all_14_2)
% 177.86/28.28    (64)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.28    (65)   ~ (all_52_9 = all_52_13)
% 177.86/28.28    (66)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.28    (67)   ~ (all_52_5 = all_52_29)
% 177.86/28.28    (68)  all_56_2 = all_52_5
% 177.86/28.28    (69)  op(e1, e0) = all_52_23
% 177.86/28.28    (70)  all_56_12 = all_52_25
% 177.86/28.28    (71)  all_58_13 = all_52_27
% 177.86/28.28    (72)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.28    (73)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.28    (74)   ~ (all_52_9 = all_52_17)
% 177.86/28.28    (75)  all_58_6 = all_52_17
% 177.86/28.28    (76)   ~ (all_52_3 = all_52_7)
% 177.86/28.28    (77)  all_56_0 = all_4_2
% 177.86/28.28    (78)  all_58_11 = all_52_23
% 177.86/28.28    (79)   ~ (all_52_3 = all_52_19)
% 177.86/28.28    (80)   ~ (all_52_7 = all_52_15)
% 177.86/28.28    (81)  op(e3, all_52_25) = e3
% 177.86/28.28    (82)   ~ (all_4_0 = e1)
% 177.86/28.28    (83)   ~ (all_52_19 = all_10_2)
% 177.86/28.28    (84)   ~ (all_58_15 = e0)
% 177.86/28.28    (85)   ~ (all_52_23 = all_6_2)
% 177.86/28.28    (86)   ~ (all_6_0 = e2)
% 177.86/28.28    (87)   ~ (all_52_29 = all_6_2)
% 177.86/28.28    (88)  all_58_2 = all_52_9
% 177.86/28.28    (89)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.28    (90)  op(e3, e1) = all_52_5
% 177.86/28.28    (91)   ~ (e2 = e1)
% 177.86/28.28    (92)   ~ (all_52_25 = all_6_2)
% 177.86/28.28    (93)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.28    (94)  op(e1, e3) = all_52_17
% 177.86/28.28    (95)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.28    (96)   ~ (all_52_25 = all_4_2)
% 177.86/28.28    (97)  op(e3, e0) = all_52_7
% 177.86/28.28    (98)  op(e3, e3) = all_4_2
% 177.86/28.28    (99)   ~ (all_52_17 = all_4_2)
% 177.86/28.28    (100)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.28             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.28    (101)   ~ (all_52_25 = all_52_27)
% 177.86/28.28    (102)  op(e0, all_6_2) = all_6_0
% 177.86/28.28    (103)   ~ (all_52_27 = all_6_2)
% 177.86/28.28    (104)   ~ (all_52_7 = all_6_2)
% 177.86/28.28    (105)   ~ (all_52_15 = all_10_2)
% 177.86/28.28    (106)   ~ (all_52_19 = all_52_27)
% 177.86/28.28    (107)  all_56_7 = all_52_15
% 177.86/28.28    (108)   ~ (all_52_7 = all_52_23)
% 177.86/28.28    (109)   ~ (all_6_0 = e1)
% 177.86/28.28    (110)   ~ (all_52_17 = all_52_19)
% 177.86/28.28    (111)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.28    (112)  all_58_9 = all_52_7
% 177.86/28.28    (113)  all_58_12 = all_52_25
% 177.86/28.28    (114)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0 |
% 177.86/28.28             all_58_13 = e0 | all_58_14 = e0)
% 177.86/28.28    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.28    (116)   ~ (all_52_9 = all_52_15)
% 177.86/28.28    (117)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.28    (118)   ~ (e3 = e2)
% 177.86/28.28    (119)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.28    (120)  op(e2, e3) = all_52_9
% 177.86/28.28    (121)  all_56_13 = all_52_27
% 177.86/28.28  
% 177.86/28.28  Begin of proof
% 177.86/28.28  | 
% 177.86/28.28  | ALPHA: (114) implies:
% 177.86/28.28  |   (122)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.28  |   (123)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.86/28.28  | 
% 177.86/28.28  | REDUCE: (21), (84) imply:
% 177.86/28.28  |   (124)   ~ (all_6_2 = e0)
% 177.86/28.28  | 
% 177.86/28.28  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.86/28.28  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 177.86/28.28  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 177.86/28.28  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 177.86/28.28  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 177.86/28.28  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 177.86/28.28  |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 177.86/28.28  |            (79), (80), (81), (82), (83), (85), (86), (87), (88), (89), (90),
% 177.86/28.28  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 177.86/28.28  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 177.86/28.28  |            (111), (112), (113), (115), (116), (117), (118), (119), (120),
% 177.86/28.28  |            (121), (122), (123), (124) are inconsistent by sub-proof #636.
% 177.86/28.28  | 
% 177.86/28.28  End of proof
% 177.86/28.28  
% 177.86/28.28  Sub-proof #531 shows that the following formulas are inconsistent:
% 177.86/28.28  ----------------------------------------------------------------
% 177.86/28.28    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.28    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.28    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.86/28.28    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.28    (5)   ~ (all_52_17 = all_52_23)
% 177.86/28.28    (6)  op(e2, all_10_2) = all_10_1
% 177.86/28.28    (7)  all_40_2 = all_4_2
% 177.86/28.28    (8)   ~ (all_52_13 = all_52_29)
% 177.86/28.28    (9)  op(e3, e2) = all_52_3
% 177.86/28.28    (10)   ~ (all_52_9 = all_52_25)
% 177.86/28.28    (11)  op(e3, all_52_25) = all_52_24
% 177.86/28.28    (12)   ~ (all_52_19 = all_52_23)
% 177.86/28.28    (13)  all_56_11 = all_52_23
% 177.86/28.28    (14)  op(e1, e2) = all_52_19
% 177.86/28.28    (15)  op(e3, all_52_9) = all_52_8
% 177.86/28.28    (16)   ~ (all_52_3 = all_10_2)
% 177.86/28.28    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.28    (18)  all_58_5 = all_52_13
% 177.86/28.28    (19)   ~ (all_52_25 = all_52_29)
% 177.86/28.28    (20)  all_56_15 = all_6_2
% 177.86/28.28    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.28    (22)  op(e2, e0) = all_52_15
% 177.86/28.28    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.28    (24)  all_58_3 = all_10_2
% 177.86/28.28    (25)  all_56_9 = all_52_19
% 177.86/28.28    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.28    (27)  all_58_15 = all_6_2
% 177.86/28.28    (28)   ~ (all_52_9 = all_4_2)
% 177.86/28.28    (29)   ~ (all_52_5 = all_52_7)
% 177.86/28.28    (30)  all_58_10 = all_52_15
% 177.86/28.28    (31)   ~ (all_52_5 = all_4_2)
% 177.86/28.28    (32)  all_58_7 = all_52_19
% 177.86/28.28    (33)   ~ (all_52_17 = all_52_25)
% 177.86/28.28    (34)  op(e0, e1) = all_52_29
% 177.86/28.28    (35)   ~ (all_4_0 = e2)
% 177.86/28.28    (36)  all_58_4 = all_52_5
% 177.86/28.28    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.28    (38)   ~ (all_52_27 = all_52_29)
% 177.86/28.28    (39)   ~ (all_52_17 = all_14_2)
% 177.86/28.28    (40)  op(e3, all_4_2) = all_4_1
% 177.86/28.28    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.28    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.28    (43)   ~ (all_52_7 = all_4_2)
% 177.86/28.28    (44)  all_58_1 = all_52_3
% 177.86/28.28    (45)  all_58_0 = all_4_2
% 177.86/28.28    (46)  op(e1, all_52_29) = all_52_28
% 177.86/28.28    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.86/28.28    (48)   ~ (all_4_1 = e2)
% 177.86/28.28    (49)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.28    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.28    (51)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.86/28.28    (52)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.86/28.28    (53)  all_58_14 = all_52_29
% 177.86/28.28    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.28    (55)   ~ (all_52_3 = all_52_5)
% 177.86/28.28    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.28    (57)  op(e2, e1) = all_52_13
% 177.86/28.28    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.28    (59)  all_58_8 = all_14_2
% 177.86/28.28    (60)  op(e0, e2) = all_52_27
% 177.86/28.28    (61)   ~ (all_14_0 = e3)
% 177.86/28.28    (62)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.86/28.28    (63)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.86/28.28    (64)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.28    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.86/28.28    (66)   ~ (all_52_5 = all_14_2)
% 177.86/28.28    (67)   ~ (all_52_3 = all_52_27)
% 177.86/28.28    (68)   ~ (all_52_3 = all_4_2)
% 177.86/28.28    (69)  op(e0, e3) = all_52_25
% 177.86/28.28    (70)   ~ (all_52_9 = all_10_2)
% 177.86/28.28    (71)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.28    (72)   ~ (all_52_13 = all_14_2)
% 177.86/28.28    (73)  op(e1, all_14_2) = all_14_0
% 177.86/28.28    (74)   ~ (e3 = e0)
% 177.86/28.28    (75)  all_40_0 = all_4_0
% 177.86/28.28    (76)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.28    (77)   ~ (all_52_9 = all_52_13)
% 177.86/28.28    (78)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.28    (79)   ~ (all_52_15 = all_52_23)
% 177.86/28.28    (80)   ~ (all_52_5 = all_52_29)
% 177.86/28.28    (81)  all_56_12 = all_52_25
% 177.86/28.28    (82)  all_58_13 = all_52_27
% 177.86/28.28    (83)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.28    (84)  all_56_5 = all_10_2
% 177.86/28.28    (85)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.28    (86)   ~ (all_52_9 = all_52_17)
% 177.86/28.28    (87)   ~ (all_14_0 = e2)
% 177.86/28.28    (88)  all_58_6 = all_52_17
% 177.86/28.28    (89)  op(e2, all_52_19) = e2
% 177.86/28.28    (90)  op(e3, all_52_17) = e3
% 177.86/28.28    (91)   ~ (e1 = e0)
% 177.86/28.28    (92)  all_56_0 = all_4_2
% 177.86/28.28    (93)  all_58_11 = all_52_23
% 177.86/28.28    (94)   ~ (all_52_3 = all_52_19)
% 177.86/28.28    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.86/28.28    (96)   ~ (all_52_7 = all_52_15)
% 177.86/28.28    (97)   ~ (all_52_29 = all_14_2)
% 177.86/28.28    (98)   ~ (all_4_0 = e1)
% 177.86/28.28    (99)   ~ (all_52_19 = all_10_2)
% 177.86/28.28    (100)   ~ (all_52_23 = all_6_2)
% 177.86/28.28    (101)  op(e1, all_4_2) = all_4_0
% 177.86/28.28    (102)   ~ (all_52_29 = all_6_2)
% 177.86/28.28    (103)  all_58_2 = all_52_9
% 177.86/28.28    (104)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.28    (105)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.28    (106)  op(e3, e1) = all_52_5
% 177.86/28.28    (107)   ~ (all_52_25 = all_6_2)
% 177.86/28.28    (108)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.28    (109)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.28    (110)  op(e1, e3) = all_52_17
% 177.86/28.28    (111)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.28    (112)   ~ (all_52_25 = all_4_2)
% 177.86/28.28    (113)  op(e3, e0) = all_52_7
% 177.86/28.28    (114)  op(e3, e3) = all_4_2
% 177.86/28.28    (115)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.86/28.28             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.86/28.28    (116)   ~ (all_10_1 = e3)
% 177.86/28.28    (117)  all_56_8 = all_52_17
% 177.86/28.28    (118)   ~ (all_52_17 = all_4_2)
% 177.86/28.28    (119)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.28             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.28    (120)   ~ (all_52_25 = all_52_27)
% 177.86/28.28    (121)   ~ (all_52_27 = all_6_2)
% 177.86/28.28    (122)   ~ (all_52_7 = all_6_2)
% 177.86/28.28    (123)  op(e0, all_52_23) = e0
% 177.86/28.28    (124)   ~ (all_52_15 = all_10_2)
% 177.86/28.28    (125)   ~ (all_52_19 = all_52_27)
% 177.86/28.28    (126)  all_56_7 = all_52_15
% 177.86/28.28    (127)  op(e1, all_14_2) = e1
% 177.86/28.28    (128)   ~ (all_52_7 = all_52_23)
% 177.86/28.28    (129)   ~ (all_52_13 = all_10_2)
% 177.86/28.28    (130)   ~ (all_52_17 = all_52_19)
% 177.86/28.28    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.28    (132)  all_58_9 = all_52_7
% 177.86/28.28    (133)   ~ (e2 = e0)
% 177.86/28.28    (134)  all_58_12 = all_52_25
% 177.86/28.28    (135)  op(e3, all_4_2) = e1
% 177.86/28.28    (136)  all_56_6 = all_52_13
% 177.86/28.28    (137)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.28    (138)   ~ (all_52_9 = all_52_15)
% 177.86/28.28    (139)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.28    (140)   ~ (e3 = e2)
% 177.86/28.28    (141)   ~ (all_52_19 = all_14_2)
% 177.86/28.28    (142)  op(e2, e3) = all_52_9
% 177.86/28.28    (143)  all_56_13 = all_52_27
% 177.86/28.28  
% 177.86/28.28  Begin of proof
% 177.86/28.28  | 
% 177.86/28.28  | GROUND_INST: instantiating (119) with e1, all_14_0, all_14_2, e1, simplifying
% 177.86/28.28  |              with (73), (127) gives:
% 177.86/28.28  |   (144)  all_14_0 = e1
% 177.86/28.28  | 
% 177.86/28.28  | BETA: splitting (115) gives:
% 177.86/28.28  | 
% 177.86/28.28  | Case 1:
% 177.86/28.28  | | 
% 177.86/28.28  | |   (145)  all_58_15 = e0
% 177.86/28.28  | | 
% 177.86/28.28  | | REF_CLOSE: (2), (9), (10), (11), (13), (18), (19), (23), (24), (25), (27),
% 177.86/28.28  | |            (30), (31), (32), (33), (34), (36), (37), (38), (42), (43), (44),
% 177.86/28.28  | |            (45), (46), (47), (51), (53), (54), (56), (58), (59), (60), (61),
% 177.86/28.28  | |            (66), (69), (71), (72), (73), (74), (78), (80), (81), (82), (83),
% 177.86/28.28  | |            (86), (87), (88), (89), (90), (91), (93), (94), (96), (97), (99),
% 177.86/28.28  | |            (100), (102), (103), (104), (105), (106), (107), (109), (110),
% 177.86/28.28  | |            (114), (118), (119), (120), (121), (123), (127), (128), (131),
% 177.86/28.28  | |            (132), (133), (134), (135), (136), (137), (140), (142), (143),
% 177.86/28.28  | |            (145) are inconsistent by sub-proof #532.
% 177.86/28.28  | | 
% 177.86/28.28  | Case 2:
% 177.86/28.28  | | 
% 177.86/28.28  | |   (146)   ~ (all_58_15 = e0)
% 177.86/28.28  | |   (147)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.86/28.28  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.86/28.28  | | 
% 177.86/28.28  | | ALPHA: (147) implies:
% 177.86/28.28  | |   (148)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.28  | |   (149)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.86/28.28  | | 
% 177.86/28.28  | | REDUCE: (27), (146) imply:
% 177.86/28.28  | |   (150)   ~ (all_6_2 = e0)
% 177.86/28.28  | | 
% 177.86/28.28  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 177.86/28.28  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 177.86/28.28  | |            (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), (37),
% 177.86/28.28  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.86/28.28  | |            (49), (50), (51), (52), (53), (55), (56), (57), (58), (59), (61),
% 177.86/28.28  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (72), (73),
% 177.86/28.28  | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 177.86/28.28  | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 177.86/28.28  | |            (96), (97), (98), (99), (100), (101), (103), (106), (107), (108),
% 177.86/28.28  | |            (110), (111), (112), (113), (114), (116), (117), (118), (119),
% 177.86/28.28  | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 177.86/28.28  | |            (129), (130), (131), (132), (133), (134), (135), (136), (137),
% 177.86/28.28  | |            (138), (139), (140), (141), (142), (148), (149), (150) are
% 177.86/28.28  | |            inconsistent by sub-proof #605.
% 177.86/28.28  | | 
% 177.86/28.28  | End of split
% 177.86/28.28  | 
% 177.86/28.28  End of proof
% 177.86/28.28  
% 177.86/28.28  Sub-proof #532 shows that the following formulas are inconsistent:
% 177.86/28.28  ----------------------------------------------------------------
% 177.86/28.28    (1)   ~ (all_52_5 = all_52_13)
% 177.86/28.28    (2)  op(e3, e2) = all_52_3
% 177.86/28.28    (3)   ~ (all_52_9 = all_52_25)
% 177.86/28.28    (4)  op(e3, all_52_25) = all_52_24
% 177.86/28.28    (5)  all_56_11 = all_52_23
% 177.86/28.28    (6)  all_58_5 = all_52_13
% 177.86/28.28    (7)   ~ (all_52_25 = all_52_29)
% 177.86/28.28    (8)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.28    (9)  all_58_3 = all_10_2
% 177.86/28.28    (10)  all_56_9 = all_52_19
% 177.86/28.28    (11)  all_58_15 = all_6_2
% 177.86/28.28    (12)  all_58_10 = all_52_15
% 177.86/28.28    (13)   ~ (all_52_5 = all_4_2)
% 177.86/28.28    (14)  all_58_7 = all_52_19
% 177.86/28.28    (15)   ~ (all_52_17 = all_52_25)
% 177.86/28.28    (16)  op(e0, e1) = all_52_29
% 177.86/28.28    (17)  all_58_4 = all_52_5
% 177.86/28.28    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.28    (19)   ~ (all_52_27 = all_52_29)
% 177.86/28.28    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.28    (21)   ~ (all_52_7 = all_4_2)
% 177.86/28.28    (22)  all_58_1 = all_52_3
% 177.86/28.28    (23)  all_58_0 = all_4_2
% 177.86/28.28    (24)  op(e1, all_52_29) = all_52_28
% 177.86/28.28    (25)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.86/28.28    (26)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.86/28.28    (27)  all_58_14 = all_52_29
% 177.86/28.28    (28)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.28    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.28    (30)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.28    (31)  all_58_8 = all_14_2
% 177.86/28.28    (32)  op(e0, e2) = all_52_27
% 177.86/28.28    (33)   ~ (all_14_0 = e3)
% 177.86/28.28    (34)   ~ (all_52_5 = all_14_2)
% 177.86/28.28    (35)  op(e0, e3) = all_52_25
% 177.86/28.28    (36)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.28    (37)   ~ (all_52_13 = all_14_2)
% 177.86/28.28    (38)  op(e1, all_14_2) = all_14_0
% 177.86/28.28    (39)   ~ (e3 = e0)
% 177.86/28.28    (40)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.28    (41)   ~ (all_52_5 = all_52_29)
% 177.86/28.28    (42)  all_56_12 = all_52_25
% 177.86/28.28    (43)  all_58_13 = all_52_27
% 177.86/28.28    (44)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.28    (45)   ~ (all_52_9 = all_52_17)
% 177.86/28.28    (46)   ~ (all_14_0 = e2)
% 177.86/28.28    (47)  all_58_6 = all_52_17
% 177.86/28.28    (48)  op(e2, all_52_19) = e2
% 177.86/28.28    (49)  op(e3, all_52_17) = e3
% 177.86/28.28    (50)   ~ (e1 = e0)
% 177.86/28.28    (51)  all_58_11 = all_52_23
% 177.86/28.28    (52)   ~ (all_52_3 = all_52_19)
% 177.86/28.28    (53)   ~ (all_52_7 = all_52_15)
% 177.86/28.28    (54)   ~ (all_52_29 = all_14_2)
% 177.86/28.28    (55)   ~ (all_52_19 = all_10_2)
% 177.86/28.28    (56)  all_58_15 = e0
% 177.86/28.28    (57)   ~ (all_52_23 = all_6_2)
% 177.86/28.28    (58)   ~ (all_52_29 = all_6_2)
% 177.86/28.28    (59)  all_58_2 = all_52_9
% 177.86/28.28    (60)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.28    (61)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.28    (62)  op(e3, e1) = all_52_5
% 177.86/28.28    (63)   ~ (all_52_25 = all_6_2)
% 177.86/28.28    (64)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.28    (65)  op(e1, e3) = all_52_17
% 177.86/28.28    (66)  op(e3, e3) = all_4_2
% 177.86/28.28    (67)   ~ (all_52_17 = all_4_2)
% 177.86/28.28    (68)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.28    (69)   ~ (all_52_25 = all_52_27)
% 177.86/28.28    (70)   ~ (all_52_27 = all_6_2)
% 177.86/28.28    (71)  op(e0, all_52_23) = e0
% 177.86/28.28    (72)  op(e1, all_14_2) = e1
% 177.86/28.28    (73)   ~ (all_52_7 = all_52_23)
% 177.86/28.28    (74)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.28    (75)  all_58_9 = all_52_7
% 177.86/28.28    (76)   ~ (e2 = e0)
% 177.86/28.28    (77)  all_58_12 = all_52_25
% 177.86/28.28    (78)  op(e3, all_4_2) = e1
% 177.86/28.28    (79)  all_56_6 = all_52_13
% 177.86/28.28    (80)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.28    (81)   ~ (e3 = e2)
% 177.86/28.28    (82)  op(e2, e3) = all_52_9
% 177.86/28.28    (83)  all_56_13 = all_52_27
% 177.86/28.28  
% 177.86/28.28  Begin of proof
% 177.86/28.28  | 
% 177.86/28.28  | COMBINE_EQS: (11), (56) imply:
% 177.86/28.28  |   (84)  all_6_2 = e0
% 177.86/28.28  | 
% 177.86/28.28  | REDUCE: (57), (84) imply:
% 177.86/28.28  |   (85)   ~ (all_52_23 = e0)
% 177.86/28.28  | 
% 177.86/28.28  | REDUCE: (63), (84) imply:
% 177.86/28.28  |   (86)   ~ (all_52_25 = e0)
% 177.86/28.28  | 
% 177.86/28.28  | REDUCE: (70), (84) imply:
% 177.86/28.28  |   (87)   ~ (all_52_27 = e0)
% 177.86/28.28  | 
% 177.86/28.28  | REDUCE: (58), (84) imply:
% 177.86/28.28  |   (88)   ~ (all_52_29 = e0)
% 177.86/28.28  | 
% 177.86/28.29  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 177.86/28.29  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.86/28.29  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.86/28.29  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.86/28.29  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (59),
% 177.86/28.29  |            (60), (61), (62), (64), (65), (66), (67), (68), (69), (71), (72),
% 177.86/28.29  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 177.86/28.29  |            (85), (86), (87), (88) are inconsistent by sub-proof #622.
% 177.86/28.29  | 
% 177.86/28.29  End of proof
% 177.86/28.29  
% 177.86/28.29  Sub-proof #533 shows that the following formulas are inconsistent:
% 177.86/28.29  ----------------------------------------------------------------
% 177.86/28.29    (1)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.86/28.29    (2)  all_52_10 = e1
% 177.86/28.29    (3)   ~ (e2 = e1)
% 177.86/28.29  
% 177.86/28.29  Begin of proof
% 177.86/28.29  | 
% 177.86/28.29  | ALPHA: (1) implies:
% 177.86/28.29  |   (4)  all_52_10 = e2
% 177.86/28.29  | 
% 177.86/28.29  | COMBINE_EQS: (2), (4) imply:
% 177.86/28.29  |   (5)  e2 = e1
% 177.86/28.29  | 
% 177.86/28.29  | SIMP: (5) implies:
% 177.86/28.29  |   (6)  e2 = e1
% 177.86/28.29  | 
% 177.86/28.29  | REDUCE: (3), (6) imply:
% 177.86/28.29  |   (7)  $false
% 177.86/28.29  | 
% 177.86/28.29  | CLOSE: (7) is inconsistent.
% 177.86/28.29  | 
% 177.86/28.29  End of proof
% 177.86/28.29  
% 177.86/28.29  Sub-proof #534 shows that the following formulas are inconsistent:
% 177.86/28.29  ----------------------------------------------------------------
% 177.86/28.29    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.29    (2)   ~ (all_6_0 = e3)
% 177.86/28.29    (3)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.86/28.29    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.29    (5)  all_56_3 = all_52_7
% 177.86/28.29    (6)  op(e3, e2) = all_52_3
% 177.86/28.29    (7)   ~ (all_52_9 = all_52_25)
% 177.86/28.29    (8)  op(e3, all_52_25) = all_52_24
% 177.86/28.29    (9)   ~ (all_52_19 = all_52_23)
% 177.86/28.29    (10)  op(e1, e2) = all_52_19
% 177.86/28.29    (11)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.86/28.29    (12)  op(e3, all_52_9) = all_52_8
% 177.86/28.29    (13)   ~ (all_52_3 = all_10_2)
% 177.86/28.29    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.29    (15)  all_56_15 = all_6_2
% 177.86/28.29    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.29    (17)  all_58_3 = all_10_2
% 177.86/28.29    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.29    (19)  all_58_15 = all_6_2
% 177.86/28.29    (20)   ~ (all_52_5 = all_52_7)
% 177.86/28.29    (21)  all_58_10 = all_52_15
% 177.86/28.29    (22)  all_58_7 = all_52_19
% 177.86/28.29    (23)   ~ (all_52_17 = all_52_25)
% 177.86/28.29    (24)  op(e0, e1) = all_52_29
% 177.86/28.29    (25)  all_58_4 = all_52_5
% 177.86/28.29    (26)   ~ (e3 = e1)
% 177.86/28.29    (27)  all_34_1 = all_4_1
% 177.86/28.29    (28)   ~ (all_52_27 = all_52_29)
% 177.86/28.29    (29)  op(e3, all_4_2) = all_4_1
% 177.86/28.29    (30)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.29    (31)   ~ (all_52_7 = all_4_2)
% 177.86/28.29    (32)  all_58_1 = all_52_3
% 177.86/28.29    (33)  all_58_0 = all_4_2
% 177.86/28.29    (34)  op(all_4_1, all_4_2) = e1
% 177.86/28.29    (35)  op(e1, all_52_29) = all_52_28
% 177.86/28.29    (36)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.29    (37)   ~ (all_4_1 = e2)
% 177.86/28.29    (38)  all_58_14 = all_52_29
% 177.86/28.29    (39)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.29    (40)   ~ (all_52_3 = all_52_5)
% 177.86/28.29    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.29    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.29    (43)  all_56_1 = all_52_3
% 177.86/28.29    (44)  op(e0, e2) = all_52_27
% 177.86/28.29    (45)   ~ (all_52_3 = all_52_27)
% 177.86/28.29    (46)   ~ (all_52_3 = all_4_2)
% 177.86/28.29    (47)  op(all_6_1, all_6_2) = all_6_0
% 177.86/28.29    (48)  op(e0, e3) = all_52_25
% 177.86/28.29    (49)  op(e0, all_6_2) = all_6_1
% 177.86/28.29    (50)   ~ (all_52_9 = all_10_2)
% 177.86/28.29    (51)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.29    (52)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.29    (53)  all_56_2 = all_52_5
% 177.86/28.29    (54)  op(e1, e0) = all_52_23
% 177.86/28.29    (55)  all_58_13 = all_52_27
% 177.86/28.29    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.29    (57)  all_58_6 = all_52_17
% 177.86/28.29    (58)   ~ (all_52_3 = all_52_7)
% 177.86/28.29    (59)  all_56_0 = all_4_2
% 177.86/28.29    (60)  all_58_11 = all_52_23
% 177.86/28.29    (61)   ~ (all_52_3 = all_52_19)
% 177.86/28.29    (62)   ~ (all_52_7 = all_52_15)
% 177.86/28.29    (63)   ~ (all_52_29 = all_14_2)
% 177.86/28.29    (64)   ~ (all_6_0 = e2)
% 177.86/28.29    (65)  all_58_2 = all_52_9
% 177.86/28.29    (66)  op(e3, e1) = all_52_5
% 177.86/28.29    (67)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.29    (68)  op(e1, e1) = all_14_2
% 177.86/28.29    (69)  op(e1, e3) = all_52_17
% 177.86/28.29    (70)   ~ (all_52_25 = all_4_2)
% 177.86/28.29    (71)  op(e3, e0) = all_52_7
% 177.86/28.29    (72)  op(e3, e3) = all_4_2
% 177.86/28.29    (73)   ~ (all_52_17 = all_4_2)
% 177.86/28.29    (74)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.29    (75)   ~ (all_52_25 = all_52_27)
% 177.86/28.29    (76)  all_34_2 = all_4_2
% 177.86/28.29    (77)   ~ (all_52_7 = all_6_2)
% 177.86/28.29    (78)   ~ (all_52_19 = all_52_27)
% 177.86/28.29    (79)   ~ (all_52_7 = all_52_23)
% 177.86/28.29    (80)   ~ (all_6_0 = e1)
% 177.86/28.29    (81)  op(e2, all_52_27) = all_52_26
% 177.86/28.29    (82)   ~ (all_52_17 = all_52_19)
% 177.86/28.29    (83)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.29    (84)  all_52_30 = all_6_1
% 177.86/28.29    (85)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.29    (86)  all_58_9 = all_52_7
% 177.86/28.29    (87)  all_58_12 = all_52_25
% 177.86/28.29    (88)   ~ (all_52_9 = all_52_15)
% 177.86/28.29    (89)   ~ (e3 = e2)
% 177.86/28.29    (90)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.29    (91)  op(e2, e3) = all_52_9
% 177.86/28.29    (92)  all_56_13 = all_52_27
% 177.86/28.29  
% 177.86/28.29  Begin of proof
% 177.86/28.29  | 
% 177.86/28.29  | ALPHA: (3) implies:
% 177.86/28.29  |   (93)  all_52_30 = e0
% 177.86/28.29  |   (94)  all_52_28 = e1
% 177.86/28.29  |   (95)  all_52_26 = e2
% 177.86/28.29  |   (96)  all_52_24 = e3
% 177.86/28.29  | 
% 177.86/28.29  | COMBINE_EQS: (84), (93) imply:
% 177.86/28.29  |   (97)  all_6_1 = e0
% 177.86/28.29  | 
% 177.86/28.29  | SIMP: (97) implies:
% 177.86/28.29  |   (98)  all_6_1 = e0
% 177.86/28.29  | 
% 177.86/28.29  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 177.86/28.29  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.86/28.29  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 177.86/28.29  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 177.86/28.29  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 177.86/28.29  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 177.86/28.29  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 177.86/28.29  |            (80), (81), (82), (83), (85), (86), (87), (88), (89), (90), (91),
% 177.86/28.29  |            (92), (94), (95), (96), (98) are inconsistent by sub-proof #555.
% 177.86/28.29  | 
% 177.86/28.29  End of proof
% 177.86/28.29  
% 177.86/28.29  Sub-proof #535 shows that the following formulas are inconsistent:
% 177.86/28.29  ----------------------------------------------------------------
% 177.86/28.29    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.29    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.29    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.29    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.29    (5)   ~ (all_52_27 = all_10_2)
% 177.86/28.29    (6)   ~ (all_52_17 = all_52_23)
% 177.86/28.29    (7)   ~ (all_6_0 = e3)
% 177.86/28.29    (8)  op(e2, all_10_2) = all_10_1
% 177.86/28.29    (9)  all_40_2 = all_4_2
% 177.86/28.29    (10)   ~ (all_52_13 = all_52_29)
% 177.86/28.29    (11)  all_56_3 = all_52_7
% 177.86/28.29    (12)  op(e3, e2) = all_52_3
% 177.86/28.29    (13)   ~ (all_52_9 = all_52_25)
% 177.86/28.29    (14)  op(e3, all_52_25) = all_52_24
% 177.86/28.29    (15)   ~ (all_52_19 = all_52_23)
% 177.86/28.29    (16)  all_56_11 = all_52_23
% 177.86/28.29    (17)  op(e1, e2) = all_52_19
% 177.86/28.29    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.86/28.29    (19)  op(e1, all_14_2) = e2
% 177.86/28.29    (20)  op(e3, all_52_9) = all_52_8
% 177.86/28.29    (21)   ~ (all_52_3 = all_10_2)
% 177.86/28.29    (22)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.86/28.29    (23)  all_58_5 = all_52_13
% 177.86/28.29    (24)   ~ (all_52_25 = all_52_29)
% 177.86/28.29    (25)  all_56_15 = all_6_2
% 177.86/28.29    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.29    (27)  op(e2, e0) = all_52_15
% 177.86/28.29    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.29    (29)  all_58_3 = all_10_2
% 177.86/28.29    (30)  all_56_9 = all_52_19
% 177.86/28.29    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.29    (32)  all_58_15 = all_6_2
% 177.86/28.29    (33)   ~ (all_52_9 = all_4_2)
% 177.86/28.29    (34)   ~ (all_52_5 = all_52_7)
% 177.86/28.29    (35)  all_58_10 = all_52_15
% 177.86/28.29    (36)   ~ (all_52_5 = all_4_2)
% 177.86/28.29    (37)  all_58_7 = all_52_19
% 177.86/28.29    (38)  all_56_4 = all_52_9
% 177.86/28.29    (39)   ~ (all_52_15 = all_6_2)
% 177.86/28.29    (40)   ~ (all_52_17 = all_52_25)
% 177.86/28.29    (41)  op(e0, e1) = all_52_29
% 177.86/28.29    (42)   ~ (all_4_0 = e2)
% 177.86/28.29    (43)  all_58_4 = all_52_5
% 177.86/28.29    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.29    (45)   ~ (e3 = e1)
% 177.86/28.29    (46)   ~ (all_52_27 = all_52_29)
% 177.86/28.29    (47)   ~ (all_52_17 = all_14_2)
% 177.86/28.29    (48)  op(e3, all_4_2) = all_4_1
% 177.86/28.29    (49)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.29    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.29    (51)   ~ (all_52_7 = all_4_2)
% 177.86/28.29    (52)  all_58_1 = all_52_3
% 177.86/28.29    (53)   ~ (all_52_13 = all_52_15)
% 177.86/28.29    (54)  all_58_0 = all_4_2
% 177.86/28.29    (55)  all_52_0 = e1
% 177.86/28.29    (56)  op(e1, all_52_13) = all_52_12
% 177.86/28.29    (57)  op(e1, all_52_29) = all_52_28
% 177.86/28.29    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.29    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.86/28.29    (60)   ~ (all_4_1 = e2)
% 177.86/28.29    (61)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.29    (62)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.29    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.29    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.86/28.29    (65)   ~ (all_14_1 = e3)
% 177.86/28.29    (66)  all_58_14 = all_52_29
% 177.86/28.29    (67)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.29    (68)   ~ (all_52_3 = all_52_5)
% 177.86/28.29    (69)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.29    (70)  op(e2, e1) = all_52_13
% 177.86/28.29    (71)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.29    (72)  all_58_8 = all_14_2
% 177.86/28.29    (73)  all_56_1 = all_52_3
% 177.86/28.29    (74)  op(e0, e2) = all_52_27
% 177.86/28.29    (75)  all_56_14 = all_52_29
% 177.86/28.29    (76)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.86/28.29    (77)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.86/28.29    (78)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.29    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.86/28.29    (80)   ~ (all_52_5 = all_14_2)
% 177.86/28.29    (81)   ~ (all_52_3 = all_52_27)
% 177.86/28.29    (82)   ~ (all_52_3 = all_4_2)
% 177.86/28.29    (83)  op(all_6_1, all_6_2) = all_6_0
% 177.86/28.29    (84)  op(e0, e3) = all_52_25
% 177.86/28.29    (85)  op(e0, all_6_2) = all_6_1
% 177.86/28.29    (86)   ~ (all_52_9 = all_10_2)
% 177.86/28.29    (87)  op(e3, all_52_17) = all_52_16
% 177.86/28.29    (88)  all_52_10 = all_10_1
% 177.86/28.29    (89)  all_52_20 = e2
% 177.86/28.29    (90)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.29    (91)   ~ (all_52_13 = all_14_2)
% 177.86/28.29    (92)   ~ (e3 = e0)
% 177.86/28.29    (93)  all_40_0 = all_4_0
% 177.86/28.29    (94)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.29    (95)   ~ (all_52_9 = all_52_13)
% 177.86/28.29    (96)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.29    (97)  op(e0, all_52_23) = all_52_22
% 177.86/28.29    (98)   ~ (all_52_15 = all_52_23)
% 177.86/28.29    (99)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.29    (100)  op(all_10_1, all_10_2) = all_10_0
% 177.86/28.29    (101)   ~ (all_52_5 = all_52_29)
% 177.86/28.29    (102)  all_56_2 = all_52_5
% 177.86/28.29    (103)  op(e1, e0) = all_52_23
% 177.86/28.29    (104)  all_56_12 = all_52_25
% 177.86/28.29    (105)  all_58_13 = all_52_27
% 177.86/28.29    (106)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.29    (107)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.29    (108)   ~ (all_52_9 = all_52_17)
% 177.86/28.29    (109)  all_58_6 = all_52_17
% 177.86/28.29    (110)   ~ (all_52_3 = all_52_7)
% 177.86/28.29    (111)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.86/28.29    (112)  op(e2, all_52_19) = all_52_18
% 177.86/28.29    (113)   ~ (e1 = e0)
% 177.86/28.29    (114)  all_56_0 = all_4_2
% 177.86/28.29    (115)  all_58_11 = all_52_23
% 177.86/28.29    (116)   ~ (all_52_3 = all_52_19)
% 177.86/28.29    (117)   ~ (all_52_7 = all_52_15)
% 177.86/28.29    (118)  op(e0, all_52_15) = all_52_14
% 177.86/28.29    (119)   ~ (all_52_29 = all_14_2)
% 177.86/28.29    (120)   ~ (all_4_0 = e1)
% 177.86/28.29    (121)   ~ (all_52_19 = all_10_2)
% 177.86/28.29    (122)   ~ (all_52_23 = all_6_2)
% 177.86/28.29    (123)  op(e1, all_4_2) = all_4_0
% 177.86/28.29    (124)   ~ (all_52_29 = all_6_2)
% 177.86/28.29    (125)  all_58_2 = all_52_9
% 177.86/28.29    (126)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.29    (127)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.29    (128)  op(e3, e1) = all_52_5
% 177.86/28.29    (129)   ~ (e2 = e1)
% 177.86/28.29    (130)  all_56_10 = all_14_2
% 177.86/28.29    (131)   ~ (all_52_25 = all_6_2)
% 177.86/28.29    (132)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.29    (133)  op(e1, e1) = all_14_2
% 177.86/28.29    (134)  op(e1, e3) = all_52_17
% 177.86/28.29    (135)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.29    (136)   ~ (all_52_25 = all_4_2)
% 177.86/28.29    (137)  op(e3, e0) = all_52_7
% 177.86/28.29    (138)  op(e3, e3) = all_4_2
% 177.86/28.29    (139)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.86/28.29             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.86/28.29    (140)   ~ (all_52_17 = all_4_2)
% 177.86/28.29    (141)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.29             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.29    (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.86/28.29           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.86/28.29           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.86/28.29           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.86/28.29    (143)   ~ (all_52_25 = all_52_27)
% 177.86/28.29    (144)   ~ (all_52_27 = all_6_2)
% 177.86/28.29    (145)   ~ (all_52_7 = all_6_2)
% 177.86/28.29    (146)   ~ (all_10_0 = e3)
% 177.86/28.29    (147)   ~ (all_52_15 = all_10_2)
% 177.86/28.29    (148)   ~ (all_52_19 = all_52_27)
% 177.86/28.29    (149)  all_56_7 = all_52_15
% 177.86/28.29    (150)   ~ (all_52_7 = all_52_23)
% 177.86/28.29    (151)   ~ (all_6_0 = e1)
% 177.86/28.29    (152)  op(e2, all_52_27) = all_52_26
% 177.86/28.29    (153)   ~ (all_52_17 = all_52_19)
% 177.86/28.29    (154)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.29    (155)  all_52_30 = all_6_1
% 177.86/28.29    (156)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.29    (157)  op(e1, all_14_2) = all_14_1
% 177.86/28.29    (158)  all_58_9 = all_52_7
% 177.86/28.29    (159)   ~ (e2 = e0)
% 177.86/28.29    (160)  all_58_12 = all_52_25
% 177.86/28.29    (161)  op(e3, all_4_2) = e1
% 177.86/28.29    (162)   ~ (all_10_0 = e1)
% 177.86/28.29    (163)  all_56_6 = all_52_13
% 177.86/28.29    (164)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.29    (165)   ~ (all_52_9 = all_52_15)
% 177.86/28.29    (166)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.29    (167)   ~ (e3 = e2)
% 177.86/28.29    (168)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.29    (169)   ~ (all_52_19 = all_14_2)
% 177.86/28.29    (170)  op(e2, e3) = all_52_9
% 177.86/28.29    (171)  all_56_13 = all_52_27
% 177.86/28.29  
% 177.86/28.29  Begin of proof
% 177.86/28.29  | 
% 177.86/28.29  | BETA: splitting (142) gives:
% 177.86/28.29  | 
% 177.86/28.29  | Case 1:
% 177.86/28.29  | | 
% 177.86/28.29  | |   (172)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.86/28.29  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.86/28.29  | | 
% 177.86/28.29  | | BETA: splitting (172) gives:
% 177.86/28.29  | | 
% 177.86/28.29  | | Case 1:
% 177.86/28.29  | | | 
% 177.86/28.29  | | |   (173)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REF_CLOSE: (45), (55), (173) are inconsistent by sub-proof #632.
% 177.86/28.29  | | | 
% 177.86/28.29  | | Case 2:
% 177.86/28.29  | | | 
% 177.86/28.29  | | |   (174)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | ALPHA: (174) implies:
% 177.86/28.29  | | |   (175)  all_52_14 = e0
% 177.86/28.29  | | |   (176)  all_52_12 = e1
% 177.86/28.29  | | |   (177)  all_52_10 = e2
% 177.86/28.29  | | |   (178)  all_52_8 = e3
% 177.86/28.29  | | | 
% 177.86/28.29  | | | COMBINE_EQS: (88), (177) imply:
% 177.86/28.29  | | |   (179)  all_10_1 = e2
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REDUCE: (100), (179) imply:
% 177.86/28.29  | | |   (180)  op(e2, all_10_2) = all_10_0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REDUCE: (20), (178) imply:
% 177.86/28.29  | | |   (181)  op(e3, all_52_9) = e3
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REDUCE: (8), (179) imply:
% 177.86/28.29  | | |   (182)  op(e2, all_10_2) = e2
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REDUCE: (56), (176) imply:
% 177.86/28.29  | | |   (183)  op(e1, all_52_13) = e1
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REDUCE: (118), (175) imply:
% 177.86/28.29  | | |   (184)  op(e0, all_52_15) = e0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 177.86/28.29  | | |            (15), (16), (17), (21), (22), (23), (24), (25), (26), (27),
% 177.86/28.29  | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.86/28.29  | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.86/28.29  | | |            (48), (49), (50), (51), (52), (54), (57), (58), (59), (60),
% 177.86/28.29  | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 177.86/28.29  | | |            (72), (73), (74), (76), (77), (78), (79), (80), (81), (82),
% 177.86/28.29  | | |            (84), (85), (87), (90), (91), (92), (93), (95), (96), (97),
% 177.86/28.29  | | |            (98), (99), (101), (102), (103), (104), (105), (106), (108),
% 177.86/28.29  | | |            (109), (110), (111), (112), (113), (114), (115), (116), (117),
% 177.86/28.29  | | |            (119), (120), (121), (122), (123), (124), (125), (126), (127),
% 177.86/28.29  | | |            (128), (130), (131), (132), (133), (134), (135), (136), (137),
% 177.86/28.29  | | |            (138), (139), (140), (141), (143), (144), (145), (146), (148),
% 177.86/28.29  | | |            (149), (150), (152), (153), (154), (156), (157), (158), (159),
% 177.86/28.29  | | |            (160), (161), (162), (163), (164), (165), (166), (168), (169),
% 177.86/28.29  | | |            (170), (171), (180), (181), (182), (183), (184) are
% 177.86/28.29  | | |            inconsistent by sub-proof #538.
% 177.86/28.29  | | | 
% 177.86/28.29  | | End of split
% 177.86/28.29  | | 
% 177.86/28.29  | Case 2:
% 177.86/28.29  | | 
% 177.86/28.29  | |   (185)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 177.86/28.29  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.86/28.29  | |            e0)
% 177.86/28.29  | | 
% 177.86/28.29  | | BETA: splitting (185) gives:
% 177.86/28.29  | | 
% 177.86/28.29  | | Case 1:
% 177.86/28.29  | | | 
% 177.86/28.29  | | |   (186)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REF_CLOSE: (89), (129), (186) are inconsistent by sub-proof #553.
% 177.86/28.29  | | | 
% 177.86/28.29  | | Case 2:
% 177.86/28.29  | | | 
% 177.86/28.29  | | |   (187)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | ALPHA: (187) implies:
% 177.86/28.29  | | |   (188)  all_52_30 = e0
% 177.86/28.29  | | |   (189)  all_52_28 = e1
% 177.86/28.29  | | |   (190)  all_52_26 = e2
% 177.86/28.29  | | |   (191)  all_52_24 = e3
% 177.86/28.29  | | | 
% 177.86/28.29  | | | COMBINE_EQS: (155), (188) imply:
% 177.86/28.29  | | |   (192)  all_6_1 = e0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | SIMP: (192) implies:
% 177.86/28.29  | | |   (193)  all_6_1 = e0
% 177.86/28.29  | | | 
% 177.86/28.29  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 177.86/28.29  | | |            (15), (16), (17), (18), (19), (20), (23), (24), (25), (26),
% 177.86/28.29  | | |            (28), (29), (31), (32), (33), (34), (35), (36), (37), (40),
% 177.86/28.29  | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 177.86/28.29  | | |            (51), (52), (53), (54), (57), (61), (62), (63), (66), (67),
% 177.86/28.29  | | |            (68), (69), (70), (71), (72), (74), (75), (78), (80), (81),
% 177.86/28.29  | | |            (83), (84), (85), (86), (87), (91), (94), (96), (99), (101),
% 177.86/28.29  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (114),
% 177.86/28.29  | | |            (115), (116), (119), (120), (121), (123), (124), (125), (126),
% 177.86/28.29  | | |            (127), (128), (129), (130), (131), (134), (136), (137), (138),
% 177.86/28.29  | | |            (139), (140), (141), (143), (144), (145), (147), (150), (151),
% 177.86/28.29  | | |            (152), (153), (154), (156), (158), (160), (161), (164), (165),
% 177.86/28.29  | | |            (167), (170), (171), (189), (190), (191), (193) are
% 177.86/28.29  | | |            inconsistent by sub-proof #536.
% 177.86/28.29  | | | 
% 177.86/28.29  | | End of split
% 177.86/28.29  | | 
% 177.86/28.29  | End of split
% 177.86/28.29  | 
% 177.86/28.29  End of proof
% 177.86/28.29  
% 177.86/28.29  Sub-proof #536 shows that the following formulas are inconsistent:
% 177.86/28.29  ----------------------------------------------------------------
% 177.86/28.29    (1)   ~ (all_52_5 = all_52_13)
% 177.86/28.29    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.29    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.29    (4)   ~ (all_52_27 = all_10_2)
% 177.86/28.29    (5)   ~ (all_52_17 = all_52_23)
% 177.86/28.29    (6)  all_52_26 = e2
% 177.86/28.29    (7)   ~ (all_6_0 = e3)
% 177.86/28.29    (8)   ~ (all_52_13 = all_52_29)
% 177.86/28.29    (9)  all_56_3 = all_52_7
% 177.86/28.29    (10)  op(e3, e2) = all_52_3
% 177.86/28.29    (11)   ~ (all_52_9 = all_52_25)
% 177.86/28.29    (12)  op(e3, all_52_25) = all_52_24
% 177.86/28.29    (13)   ~ (all_52_19 = all_52_23)
% 177.86/28.29    (14)  all_56_11 = all_52_23
% 177.86/28.29    (15)  op(e1, e2) = all_52_19
% 177.86/28.29    (16)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.86/28.29    (17)  op(e1, all_14_2) = e2
% 177.86/28.29    (18)  op(e3, all_52_9) = all_52_8
% 177.86/28.29    (19)  all_58_5 = all_52_13
% 177.86/28.29    (20)   ~ (all_52_25 = all_52_29)
% 177.86/28.29    (21)  all_56_15 = all_6_2
% 177.86/28.29    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.29    (23)  all_6_1 = e0
% 177.86/28.29    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.29    (25)  all_58_3 = all_10_2
% 177.86/28.29    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.29    (27)  all_58_15 = all_6_2
% 177.86/28.29    (28)   ~ (all_52_9 = all_4_2)
% 177.86/28.29    (29)   ~ (all_52_5 = all_52_7)
% 177.86/28.29    (30)  all_58_10 = all_52_15
% 177.86/28.29    (31)   ~ (all_52_5 = all_4_2)
% 177.86/28.29    (32)  all_58_7 = all_52_19
% 177.86/28.29    (33)   ~ (all_52_17 = all_52_25)
% 177.86/28.29    (34)  op(e0, e1) = all_52_29
% 177.86/28.29    (35)   ~ (all_4_0 = e2)
% 177.86/28.29    (36)  all_58_4 = all_52_5
% 177.86/28.29    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.29    (38)   ~ (e3 = e1)
% 177.86/28.29    (39)   ~ (all_52_27 = all_52_29)
% 177.86/28.29    (40)   ~ (all_52_17 = all_14_2)
% 177.86/28.29    (41)  op(e3, all_4_2) = all_4_1
% 177.86/28.29    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.29    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.29    (44)   ~ (all_52_7 = all_4_2)
% 177.86/28.29    (45)  all_58_1 = all_52_3
% 177.86/28.30    (46)   ~ (all_52_13 = all_52_15)
% 177.86/28.30    (47)  all_58_0 = all_4_2
% 177.86/28.30    (48)  op(e1, all_52_29) = all_52_28
% 177.86/28.30    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.30    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.30    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.30    (52)  all_58_14 = all_52_29
% 177.86/28.30    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.30    (54)   ~ (all_52_3 = all_52_5)
% 177.86/28.30    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.30    (56)  op(e2, e1) = all_52_13
% 177.86/28.30    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.30    (58)  all_58_8 = all_14_2
% 177.86/28.30    (59)  op(e0, e2) = all_52_27
% 177.86/28.30    (60)  all_56_14 = all_52_29
% 177.86/28.30    (61)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.30    (62)   ~ (all_52_5 = all_14_2)
% 177.86/28.30    (63)   ~ (all_52_3 = all_52_27)
% 177.86/28.30    (64)  op(all_6_1, all_6_2) = all_6_0
% 177.86/28.30    (65)  op(e0, e3) = all_52_25
% 177.86/28.30    (66)  op(e0, all_6_2) = all_6_1
% 177.86/28.30    (67)   ~ (all_52_9 = all_10_2)
% 177.86/28.30    (68)  op(e3, all_52_17) = all_52_16
% 177.86/28.30    (69)   ~ (all_52_13 = all_14_2)
% 177.86/28.30    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.30    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.30    (72)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.30    (73)   ~ (all_52_5 = all_52_29)
% 177.86/28.30    (74)  op(e1, e0) = all_52_23
% 177.86/28.30    (75)  all_56_12 = all_52_25
% 177.86/28.30    (76)  all_58_13 = all_52_27
% 177.86/28.30    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.30    (78)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.30    (79)   ~ (all_52_9 = all_52_17)
% 177.86/28.30    (80)  all_58_6 = all_52_17
% 177.86/28.30    (81)   ~ (all_52_3 = all_52_7)
% 177.86/28.30    (82)  all_56_0 = all_4_2
% 177.86/28.30    (83)  all_58_11 = all_52_23
% 177.86/28.30    (84)   ~ (all_52_3 = all_52_19)
% 177.86/28.30    (85)   ~ (all_52_29 = all_14_2)
% 177.86/28.30    (86)   ~ (all_4_0 = e1)
% 177.86/28.30    (87)   ~ (all_52_19 = all_10_2)
% 177.86/28.30    (88)  op(e1, all_4_2) = all_4_0
% 177.86/28.30    (89)   ~ (all_52_29 = all_6_2)
% 177.86/28.30    (90)  all_58_2 = all_52_9
% 177.86/28.30    (91)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.30    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.30    (93)  op(e3, e1) = all_52_5
% 177.86/28.30    (94)   ~ (e2 = e1)
% 177.86/28.30    (95)  all_56_10 = all_14_2
% 177.86/28.30    (96)   ~ (all_52_25 = all_6_2)
% 177.86/28.30    (97)  op(e1, e3) = all_52_17
% 177.86/28.30    (98)   ~ (all_52_25 = all_4_2)
% 177.86/28.30    (99)  op(e3, e0) = all_52_7
% 177.86/28.30    (100)  all_52_28 = e1
% 177.86/28.30    (101)  op(e3, e3) = all_4_2
% 177.86/28.30    (102)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.86/28.30             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.86/28.30    (103)   ~ (all_52_17 = all_4_2)
% 177.86/28.30    (104)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.30             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.30    (105)   ~ (all_52_25 = all_52_27)
% 177.86/28.30    (106)   ~ (all_52_27 = all_6_2)
% 177.86/28.30    (107)   ~ (all_52_7 = all_6_2)
% 177.86/28.30    (108)   ~ (all_52_15 = all_10_2)
% 177.86/28.30    (109)   ~ (all_52_7 = all_52_23)
% 177.86/28.30    (110)   ~ (all_6_0 = e1)
% 177.86/28.30    (111)  op(e2, all_52_27) = all_52_26
% 177.86/28.30    (112)   ~ (all_52_17 = all_52_19)
% 177.86/28.30    (113)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.30    (114)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.30    (115)  all_58_9 = all_52_7
% 177.86/28.30    (116)  all_52_24 = e3
% 177.86/28.30    (117)  all_58_12 = all_52_25
% 177.86/28.30    (118)  op(e3, all_4_2) = e1
% 177.86/28.30    (119)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.30    (120)   ~ (all_52_9 = all_52_15)
% 177.86/28.30    (121)   ~ (e3 = e2)
% 177.86/28.30    (122)  op(e2, e3) = all_52_9
% 177.86/28.30    (123)  all_56_13 = all_52_27
% 177.86/28.30  
% 177.86/28.30  Begin of proof
% 177.86/28.30  | 
% 177.86/28.30  | REDUCE: (23), (64) imply:
% 177.86/28.30  |   (124)  op(e0, all_6_2) = all_6_0
% 177.86/28.30  | 
% 177.86/28.30  | REDUCE: (12), (116) imply:
% 177.86/28.30  |   (125)  op(e3, all_52_25) = e3
% 177.86/28.30  | 
% 177.86/28.30  | REDUCE: (6), (111) imply:
% 177.86/28.30  |   (126)  op(e2, all_52_27) = e2
% 177.86/28.30  | 
% 177.86/28.30  | REDUCE: (48), (100) imply:
% 177.86/28.30  |   (127)  op(e1, all_52_29) = e1
% 177.86/28.30  | 
% 177.86/28.30  | REDUCE: (23), (66) imply:
% 177.86/28.30  |   (128)  op(e0, all_6_2) = e0
% 177.86/28.30  | 
% 177.86/28.30  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 177.86/28.30  |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 177.86/28.30  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 177.86/28.30  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (49),
% 177.86/28.30  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 177.86/28.30  |            (61), (62), (63), (65), (67), (68), (69), (70), (71), (72), (73),
% 177.86/28.30  |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 177.86/28.30  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 177.86/28.30  |            (96), (97), (98), (99), (101), (102), (103), (104), (105), (106),
% 177.86/28.30  |            (107), (108), (109), (110), (112), (113), (114), (115), (117),
% 177.86/28.30  |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 177.86/28.30  |            (127), (128) are inconsistent by sub-proof #537.
% 177.86/28.30  | 
% 177.86/28.30  End of proof
% 177.86/28.30  
% 177.86/28.30  Sub-proof #537 shows that the following formulas are inconsistent:
% 177.86/28.30  ----------------------------------------------------------------
% 177.86/28.30    (1)   ~ (all_52_5 = all_52_13)
% 177.86/28.30    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.30    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.30    (4)   ~ (all_52_27 = all_10_2)
% 177.86/28.30    (5)   ~ (all_52_17 = all_52_23)
% 177.86/28.30    (6)   ~ (all_6_0 = e3)
% 177.86/28.30    (7)   ~ (all_52_13 = all_52_29)
% 177.86/28.30    (8)  all_56_3 = all_52_7
% 177.86/28.30    (9)  op(e3, e2) = all_52_3
% 177.86/28.30    (10)   ~ (all_52_9 = all_52_25)
% 177.86/28.30    (11)   ~ (all_52_19 = all_52_23)
% 177.86/28.30    (12)  all_56_11 = all_52_23
% 177.86/28.30    (13)  op(e1, e2) = all_52_19
% 177.86/28.30    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.86/28.30    (15)  op(e1, all_14_2) = e2
% 177.86/28.30    (16)  op(e3, all_52_9) = all_52_8
% 177.86/28.30    (17)  all_58_5 = all_52_13
% 177.86/28.30    (18)   ~ (all_52_25 = all_52_29)
% 177.86/28.30    (19)  all_56_15 = all_6_2
% 177.86/28.30    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.30    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.30    (22)  all_58_3 = all_10_2
% 177.86/28.30    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.30    (24)  all_58_15 = all_6_2
% 177.86/28.30    (25)  op(e0, all_6_2) = e0
% 177.86/28.30    (26)   ~ (all_52_9 = all_4_2)
% 177.86/28.30    (27)   ~ (all_52_5 = all_52_7)
% 177.86/28.30    (28)  all_58_10 = all_52_15
% 177.86/28.30    (29)   ~ (all_52_5 = all_4_2)
% 177.86/28.30    (30)  all_58_7 = all_52_19
% 177.86/28.30    (31)   ~ (all_52_17 = all_52_25)
% 177.86/28.30    (32)  op(e0, e1) = all_52_29
% 177.86/28.30    (33)   ~ (all_4_0 = e2)
% 177.86/28.30    (34)  all_58_4 = all_52_5
% 177.86/28.30    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.30    (36)   ~ (e3 = e1)
% 177.86/28.30    (37)   ~ (all_52_27 = all_52_29)
% 177.86/28.30    (38)   ~ (all_52_17 = all_14_2)
% 177.86/28.30    (39)  op(e3, all_4_2) = all_4_1
% 177.86/28.30    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.30    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.30    (42)   ~ (all_52_7 = all_4_2)
% 177.86/28.30    (43)  all_58_1 = all_52_3
% 177.86/28.30    (44)   ~ (all_52_13 = all_52_15)
% 177.86/28.30    (45)  all_58_0 = all_4_2
% 177.86/28.30    (46)  op(e2, all_52_27) = e2
% 177.86/28.30    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.30    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.30    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.30    (50)  all_58_14 = all_52_29
% 177.86/28.30    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.30    (52)   ~ (all_52_3 = all_52_5)
% 177.86/28.30    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.30    (54)  op(e2, e1) = all_52_13
% 177.86/28.30    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.30    (56)  all_58_8 = all_14_2
% 177.86/28.30    (57)  op(e0, e2) = all_52_27
% 177.86/28.30    (58)  all_56_14 = all_52_29
% 177.86/28.30    (59)  op(e1, all_52_29) = e1
% 177.86/28.30    (60)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.30    (61)   ~ (all_52_5 = all_14_2)
% 177.86/28.30    (62)   ~ (all_52_3 = all_52_27)
% 177.86/28.30    (63)  op(e0, e3) = all_52_25
% 177.86/28.30    (64)   ~ (all_52_9 = all_10_2)
% 177.86/28.30    (65)  op(e3, all_52_17) = all_52_16
% 177.86/28.30    (66)   ~ (all_52_13 = all_14_2)
% 177.86/28.30    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.30    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.30    (69)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.30    (70)   ~ (all_52_5 = all_52_29)
% 177.86/28.30    (71)  op(e1, e0) = all_52_23
% 177.86/28.30    (72)  all_56_12 = all_52_25
% 177.86/28.30    (73)  all_58_13 = all_52_27
% 177.86/28.30    (74)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.30    (75)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.30    (76)   ~ (all_52_9 = all_52_17)
% 177.86/28.30    (77)  all_58_6 = all_52_17
% 177.86/28.30    (78)   ~ (all_52_3 = all_52_7)
% 177.86/28.30    (79)  all_56_0 = all_4_2
% 177.86/28.30    (80)  all_58_11 = all_52_23
% 177.86/28.30    (81)   ~ (all_52_3 = all_52_19)
% 177.86/28.30    (82)   ~ (all_52_29 = all_14_2)
% 177.86/28.30    (83)  op(e3, all_52_25) = e3
% 177.86/28.30    (84)   ~ (all_4_0 = e1)
% 177.86/28.30    (85)   ~ (all_52_19 = all_10_2)
% 177.86/28.30    (86)  op(e1, all_4_2) = all_4_0
% 177.86/28.30    (87)   ~ (all_52_29 = all_6_2)
% 177.86/28.30    (88)  all_58_2 = all_52_9
% 177.86/28.30    (89)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.30    (90)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.30    (91)  op(e3, e1) = all_52_5
% 177.86/28.30    (92)   ~ (e2 = e1)
% 177.86/28.30    (93)  all_56_10 = all_14_2
% 177.86/28.30    (94)   ~ (all_52_25 = all_6_2)
% 177.86/28.30    (95)  op(e1, e3) = all_52_17
% 177.86/28.30    (96)   ~ (all_52_25 = all_4_2)
% 177.86/28.30    (97)  op(e3, e0) = all_52_7
% 177.86/28.30    (98)  op(e3, e3) = all_4_2
% 177.86/28.30    (99)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.86/28.30            (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.86/28.30    (100)   ~ (all_52_17 = all_4_2)
% 177.86/28.30    (101)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.30             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.30    (102)   ~ (all_52_25 = all_52_27)
% 177.86/28.30    (103)  op(e0, all_6_2) = all_6_0
% 177.86/28.30    (104)   ~ (all_52_27 = all_6_2)
% 177.86/28.30    (105)   ~ (all_52_7 = all_6_2)
% 177.86/28.30    (106)   ~ (all_52_15 = all_10_2)
% 177.86/28.30    (107)   ~ (all_52_7 = all_52_23)
% 177.86/28.30    (108)   ~ (all_6_0 = e1)
% 177.86/28.30    (109)   ~ (all_52_17 = all_52_19)
% 177.86/28.30    (110)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.30    (111)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.30    (112)  all_58_9 = all_52_7
% 177.86/28.30    (113)  all_58_12 = all_52_25
% 177.86/28.30    (114)  op(e3, all_4_2) = e1
% 177.86/28.30    (115)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.30    (116)   ~ (all_52_9 = all_52_15)
% 177.86/28.30    (117)   ~ (e3 = e2)
% 177.86/28.30    (118)  op(e2, e3) = all_52_9
% 177.86/28.30    (119)  all_56_13 = all_52_27
% 177.86/28.30  
% 177.86/28.30  Begin of proof
% 177.86/28.30  | 
% 177.86/28.30  | GROUND_INST: instantiating (101) with e0, all_6_0, all_6_2, e0, simplifying
% 177.86/28.30  |              with (25), (103) gives:
% 177.86/28.30  |   (120)  all_6_0 = e0
% 177.86/28.30  | 
% 177.86/28.30  | REDUCE: (6), (120) imply:
% 177.86/28.30  |   (121)   ~ (e3 = e0)
% 177.86/28.30  | 
% 177.86/28.30  | SIMP: (121) implies:
% 177.86/28.30  |   (122)   ~ (e3 = e0)
% 177.86/28.30  | 
% 177.86/28.30  | REDUCE: (108), (120) imply:
% 177.86/28.30  |   (123)   ~ (e1 = e0)
% 177.86/28.30  | 
% 177.86/28.30  | SIMP: (123) implies:
% 177.86/28.30  |   (124)   ~ (e1 = e0)
% 177.86/28.30  | 
% 177.86/28.30  | BETA: splitting (99) gives:
% 177.86/28.30  | 
% 177.86/28.30  | Case 1:
% 177.86/28.30  | | 
% 177.86/28.30  | |   (125)  all_58_15 = e0
% 177.86/28.30  | | 
% 177.86/28.30  | | COMBINE_EQS: (24), (125) imply:
% 177.86/28.30  | |   (126)  all_6_2 = e0
% 177.86/28.30  | | 
% 177.86/28.30  | | REDUCE: (105), (126) imply:
% 177.86/28.30  | |   (127)   ~ (all_52_7 = e0)
% 177.86/28.30  | | 
% 177.86/28.30  | | REDUCE: (94), (126) imply:
% 177.86/28.30  | |   (128)   ~ (all_52_25 = e0)
% 177.86/28.30  | | 
% 177.86/28.30  | | REDUCE: (87), (126) imply:
% 177.86/28.30  | |   (129)   ~ (all_52_29 = e0)
% 177.86/28.30  | | 
% 177.86/28.30  | | BETA: splitting (51) gives:
% 177.86/28.30  | | 
% 177.86/28.30  | | Case 1:
% 177.86/28.30  | | | 
% 177.86/28.30  | | |   (130)  all_56_13 = e3
% 177.86/28.30  | | | 
% 177.86/28.30  | | | COMBINE_EQS: (119), (130) imply:
% 177.86/28.30  | | |   (131)  all_52_27 = e3
% 177.86/28.30  | | | 
% 177.86/28.30  | | | SIMP: (131) implies:
% 177.86/28.30  | | |   (132)  all_52_27 = e3
% 177.86/28.30  | | | 
% 177.86/28.30  | | | REDUCE: (102), (132) imply:
% 177.86/28.30  | | |   (133)   ~ (all_52_25 = e3)
% 177.86/28.30  | | | 
% 177.86/28.30  | | | REDUCE: (37), (132) imply:
% 177.86/28.30  | | |   (134)   ~ (all_52_29 = e3)
% 177.86/28.30  | | | 
% 177.86/28.30  | | | SIMP: (134) implies:
% 177.86/28.30  | | |   (135)   ~ (all_52_29 = e3)
% 177.86/28.30  | | | 
% 177.86/28.30  | | | REDUCE: (46), (132) imply:
% 177.86/28.30  | | |   (136)  op(e2, e3) = e2
% 177.86/28.30  | | | 
% 177.86/28.30  | | | REF_CLOSE: (2), (10), (13), (18), (23), (26), (29), (30), (33), (45),
% 177.86/28.30  | | |            (47), (56), (58), (59), (68), (71), (72), (75), (76), (77),
% 177.86/28.30  | | |            (79), (80), (82), (83), (86), (91), (96), (101), (118), (128),
% 177.86/28.30  | | |            (129), (133), (135), (136) are inconsistent by sub-proof #621.
% 177.86/28.30  | | | 
% 177.86/28.30  | | Case 2:
% 177.86/28.30  | | | 
% 177.86/28.30  | | |   (137)   ~ (all_56_13 = e3)
% 177.86/28.30  | | | 
% 177.86/28.30  | | | REDUCE: (119), (137) imply:
% 177.86/28.30  | | |   (138)   ~ (all_52_27 = e3)
% 177.86/28.30  | | | 
% 177.86/28.30  | | | REF_CLOSE: (8), (9), (12), (15), (17), (18), (27), (30), (31), (34), (35),
% 177.86/28.30  | | |            (36), (38), (46), (48), (50), (54), (55), (56), (59), (61),
% 177.86/28.30  | | |            (62), (65), (66), (68), (69), (71), (72), (73), (77), (78),
% 177.86/28.30  | | |            (80), (81), (82), (83), (89), (90), (91), (93), (95), (96),
% 177.86/28.30  | | |            (98), (101), (102), (107), (111), (113), (122), (124), (125),
% 177.86/28.30  | | |            (127), (128), (138) are inconsistent by sub-proof #550.
% 177.86/28.30  | | | 
% 177.86/28.30  | | End of split
% 177.86/28.30  | | 
% 177.86/28.30  | Case 2:
% 177.86/28.30  | | 
% 177.86/28.30  | |   (139)   ~ (all_58_15 = e0)
% 177.86/28.30  | |   (140)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.86/28.30  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.86/28.30  | | 
% 177.86/28.30  | | ALPHA: (140) implies:
% 177.86/28.30  | |   (141)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.30  | |   (142)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.86/28.30  | | 
% 177.86/28.30  | | REDUCE: (24), (139) imply:
% 177.86/28.30  | |   (143)   ~ (all_6_2 = e0)
% 177.86/28.30  | | 
% 177.86/28.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (14), (16), (17),
% 177.86/28.30  | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 177.86/28.30  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 177.86/28.30  | |            (40), (41), (42), (43), (44), (45), (46), (48), (49), (50), (51),
% 177.86/28.30  | |            (52), (53), (55), (56), (57), (59), (60), (62), (63), (64), (65),
% 177.86/28.30  | |            (67), (68), (70), (71), (72), (73), (74), (76), (77), (78), (79),
% 177.86/28.30  | |            (80), (83), (84), (85), (87), (88), (91), (92), (94), (95), (96),
% 177.86/28.30  | |            (97), (98), (100), (101), (102), (104), (105), (106), (109),
% 177.86/28.30  | |            (110), (112), (113), (114), (115), (116), (117), (118), (119),
% 177.86/28.30  | |            (122), (124), (141), (142), (143) are inconsistent by sub-proof
% 177.86/28.30  | |            #603.
% 177.86/28.30  | | 
% 177.86/28.30  | End of split
% 177.86/28.30  | 
% 177.86/28.30  End of proof
% 177.86/28.30  
% 177.86/28.30  Sub-proof #538 shows that the following formulas are inconsistent:
% 177.86/28.30  ----------------------------------------------------------------
% 177.86/28.30    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.30    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.30    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.30    (4)   ~ (all_52_27 = all_10_2)
% 177.86/28.30    (5)   ~ (all_52_17 = all_52_23)
% 177.86/28.30    (6)  all_40_2 = all_4_2
% 177.86/28.30    (7)   ~ (all_52_13 = all_52_29)
% 177.86/28.30    (8)  op(e2, all_10_2) = all_10_0
% 177.86/28.30    (9)  all_56_3 = all_52_7
% 177.86/28.30    (10)  op(e3, e2) = all_52_3
% 177.86/28.30    (11)   ~ (all_52_9 = all_52_25)
% 177.86/28.30    (12)  op(e3, all_52_25) = all_52_24
% 177.86/28.30    (13)   ~ (all_52_19 = all_52_23)
% 177.86/28.30    (14)  all_56_11 = all_52_23
% 177.86/28.30    (15)  op(e1, e2) = all_52_19
% 177.86/28.30    (16)   ~ (all_52_3 = all_10_2)
% 177.86/28.30    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 177.86/28.30    (18)  all_58_5 = all_52_13
% 177.86/28.30    (19)   ~ (all_52_25 = all_52_29)
% 177.86/28.30    (20)  op(e1, all_52_13) = e1
% 177.86/28.30    (21)  op(e0, all_52_15) = e0
% 177.86/28.30    (22)  all_56_15 = all_6_2
% 177.86/28.30    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.30    (24)  op(e2, e0) = all_52_15
% 177.86/28.30    (25)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.30    (26)  all_58_3 = all_10_2
% 177.86/28.30    (27)  all_56_9 = all_52_19
% 177.86/28.30    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.30    (29)  all_58_15 = all_6_2
% 177.86/28.30    (30)   ~ (all_52_9 = all_4_2)
% 177.86/28.30    (31)   ~ (all_52_5 = all_52_7)
% 177.86/28.30    (32)  all_58_10 = all_52_15
% 177.86/28.30    (33)   ~ (all_52_5 = all_4_2)
% 177.86/28.30    (34)  all_58_7 = all_52_19
% 177.86/28.30    (35)  all_56_4 = all_52_9
% 177.86/28.30    (36)   ~ (all_52_15 = all_6_2)
% 177.86/28.30    (37)   ~ (all_52_17 = all_52_25)
% 177.86/28.30    (38)  op(e0, e1) = all_52_29
% 177.86/28.30    (39)   ~ (all_4_0 = e2)
% 177.86/28.30    (40)  all_58_4 = all_52_5
% 177.86/28.30    (41)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.30    (42)   ~ (e3 = e1)
% 177.86/28.30    (43)   ~ (all_52_27 = all_52_29)
% 177.86/28.30    (44)   ~ (all_52_17 = all_14_2)
% 177.86/28.30    (45)  op(e3, all_4_2) = all_4_1
% 177.86/28.30    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.30    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.30    (48)   ~ (all_52_7 = all_4_2)
% 177.86/28.30    (49)  all_58_1 = all_52_3
% 177.86/28.30    (50)  all_58_0 = all_4_2
% 177.86/28.30    (51)  op(e1, all_52_29) = all_52_28
% 177.86/28.30    (52)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.30    (53)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.86/28.30    (54)   ~ (all_4_1 = e2)
% 177.86/28.30    (55)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.30    (56)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.30    (57)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.86/28.30    (58)   ~ (all_14_1 = e3)
% 177.86/28.30    (59)  all_58_14 = all_52_29
% 177.86/28.30    (60)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.30    (61)   ~ (all_52_3 = all_52_5)
% 177.86/28.30    (62)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.30    (63)  op(e2, e1) = all_52_13
% 177.86/28.30    (64)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.30    (65)  all_58_8 = all_14_2
% 177.86/28.30    (66)  all_56_1 = all_52_3
% 177.86/28.30    (67)  op(e0, e2) = all_52_27
% 177.86/28.30    (68)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 177.86/28.30    (69)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.86/28.30    (70)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.30    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.86/28.30    (72)   ~ (all_52_5 = all_14_2)
% 177.86/28.30    (73)   ~ (all_52_3 = all_52_27)
% 177.86/28.30    (74)   ~ (all_52_3 = all_4_2)
% 177.86/28.30    (75)  op(e0, e3) = all_52_25
% 177.86/28.30    (76)  op(e0, all_6_2) = all_6_1
% 177.86/28.30    (77)  op(e3, all_52_17) = all_52_16
% 177.86/28.30    (78)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.30    (79)   ~ (all_52_13 = all_14_2)
% 177.86/28.30    (80)  op(e3, all_52_9) = e3
% 177.86/28.30    (81)   ~ (e3 = e0)
% 177.86/28.30    (82)  all_40_0 = all_4_0
% 177.86/28.30    (83)   ~ (all_52_9 = all_52_13)
% 177.86/28.30    (84)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.30    (85)  op(e0, all_52_23) = all_52_22
% 177.86/28.30    (86)   ~ (all_52_15 = all_52_23)
% 177.86/28.30    (87)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.30    (88)   ~ (all_52_5 = all_52_29)
% 177.86/28.30    (89)  all_56_2 = all_52_5
% 177.86/28.30    (90)  op(e1, e0) = all_52_23
% 177.86/28.30    (91)  all_56_12 = all_52_25
% 177.86/28.30    (92)  all_58_13 = all_52_27
% 177.86/28.30    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.30    (94)   ~ (all_52_9 = all_52_17)
% 177.86/28.30    (95)  all_58_6 = all_52_17
% 177.86/28.30    (96)   ~ (all_52_3 = all_52_7)
% 177.86/28.30    (97)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.86/28.30    (98)  op(e2, all_52_19) = all_52_18
% 177.86/28.30    (99)   ~ (e1 = e0)
% 177.86/28.30    (100)  all_56_0 = all_4_2
% 177.86/28.30    (101)  all_58_11 = all_52_23
% 177.86/28.30    (102)   ~ (all_52_3 = all_52_19)
% 177.86/28.30    (103)   ~ (all_52_7 = all_52_15)
% 177.86/28.30    (104)   ~ (all_52_29 = all_14_2)
% 177.86/28.30    (105)   ~ (all_4_0 = e1)
% 177.86/28.30    (106)   ~ (all_52_19 = all_10_2)
% 177.86/28.30    (107)   ~ (all_52_23 = all_6_2)
% 177.86/28.30    (108)  op(e1, all_4_2) = all_4_0
% 177.86/28.30    (109)   ~ (all_52_29 = all_6_2)
% 177.86/28.30    (110)  all_58_2 = all_52_9
% 177.86/28.30    (111)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.30    (112)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.30    (113)  op(e3, e1) = all_52_5
% 177.86/28.30    (114)  all_56_10 = all_14_2
% 177.86/28.30    (115)   ~ (all_52_25 = all_6_2)
% 177.86/28.30    (116)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.30    (117)  op(e1, e1) = all_14_2
% 177.86/28.30    (118)  op(e1, e3) = all_52_17
% 177.86/28.30    (119)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.30    (120)   ~ (all_52_25 = all_4_2)
% 177.86/28.30    (121)  op(e3, e0) = all_52_7
% 177.86/28.30    (122)  op(e2, all_10_2) = e2
% 177.86/28.30    (123)  op(e3, e3) = all_4_2
% 177.86/28.30    (124)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.86/28.30             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.86/28.30    (125)   ~ (all_52_17 = all_4_2)
% 177.86/28.31    (126)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.31             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.31    (127)   ~ (all_52_25 = all_52_27)
% 177.86/28.31    (128)   ~ (all_52_27 = all_6_2)
% 177.86/28.31    (129)   ~ (all_52_7 = all_6_2)
% 177.86/28.31    (130)   ~ (all_10_0 = e3)
% 177.86/28.31    (131)   ~ (all_52_19 = all_52_27)
% 177.86/28.31    (132)  all_56_7 = all_52_15
% 177.86/28.31    (133)   ~ (all_52_7 = all_52_23)
% 177.86/28.31    (134)  op(e2, all_52_27) = all_52_26
% 177.86/28.31    (135)   ~ (all_52_17 = all_52_19)
% 177.86/28.31    (136)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.31    (137)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.31    (138)  op(e1, all_14_2) = all_14_1
% 177.86/28.31    (139)  all_58_9 = all_52_7
% 177.86/28.31    (140)   ~ (e2 = e0)
% 177.86/28.31    (141)  all_58_12 = all_52_25
% 177.86/28.31    (142)  op(e3, all_4_2) = e1
% 177.86/28.31    (143)   ~ (all_10_0 = e1)
% 177.86/28.31    (144)  all_56_6 = all_52_13
% 177.86/28.31    (145)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.31    (146)   ~ (all_52_9 = all_52_15)
% 177.86/28.31    (147)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.31    (148)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.31    (149)   ~ (all_52_19 = all_14_2)
% 177.86/28.31    (150)  op(e2, e3) = all_52_9
% 177.86/28.31    (151)  all_56_13 = all_52_27
% 177.86/28.31  
% 177.86/28.31  Begin of proof
% 177.86/28.31  | 
% 177.86/28.31  | GROUND_INST: instantiating (126) with e2, all_10_0, all_10_2, e2, simplifying
% 177.86/28.31  |              with (8), (122) gives:
% 177.86/28.31  |   (152)  all_10_0 = e2
% 177.86/28.31  | 
% 177.86/28.31  | REDUCE: (130), (152) imply:
% 177.86/28.31  |   (153)   ~ (e3 = e2)
% 177.86/28.31  | 
% 177.86/28.31  | SIMP: (153) implies:
% 177.86/28.31  |   (154)   ~ (e3 = e2)
% 177.86/28.31  | 
% 177.86/28.31  | REDUCE: (143), (152) imply:
% 177.86/28.31  |   (155)   ~ (e2 = e1)
% 177.86/28.31  | 
% 177.86/28.31  | BETA: splitting (124) gives:
% 177.86/28.31  | 
% 177.86/28.31  | Case 1:
% 177.86/28.31  | | 
% 177.86/28.31  | |   (156)  all_58_15 = e0
% 177.86/28.31  | | 
% 177.86/28.31  | | COMBINE_EQS: (29), (156) imply:
% 177.86/28.31  | |   (157)  all_6_2 = e0
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (36), (157) imply:
% 177.86/28.31  | |   (158)   ~ (all_52_15 = e0)
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (115), (157) imply:
% 177.86/28.31  | |   (159)   ~ (all_52_25 = e0)
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (128), (157) imply:
% 177.86/28.31  | |   (160)   ~ (all_52_27 = e0)
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (109), (157) imply:
% 177.86/28.31  | |   (161)   ~ (all_52_29 = e0)
% 177.86/28.31  | | 
% 177.86/28.31  | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (12), (16), (18), (19),
% 177.86/28.31  | |            (20), (21), (25), (26), (30), (31), (32), (34), (37), (38), (39),
% 177.86/28.31  | |            (40), (41), (42), (43), (44), (45), (47), (48), (49), (50), (51),
% 177.86/28.31  | |            (52), (56), (59), (60), (62), (64), (65), (66), (67), (70), (74),
% 177.86/28.31  | |            (75), (78), (79), (80), (81), (83), (84), (86), (87), (91), (92),
% 177.86/28.31  | |            (94), (95), (96), (99), (101), (102), (103), (104), (105), (106),
% 177.86/28.31  | |            (110), (111), (113), (114), (116), (118), (119), (122), (123),
% 177.86/28.31  | |            (126), (127), (130), (131), (132), (133), (134), (135), (136),
% 177.86/28.31  | |            (137), (139), (140), (141), (143), (145), (147), (149), (150),
% 177.86/28.31  | |            (151), (156), (158), (159), (160), (161) are inconsistent by
% 177.86/28.31  | |            sub-proof #954.
% 177.86/28.31  | | 
% 177.86/28.31  | Case 2:
% 177.86/28.31  | | 
% 177.86/28.31  | |   (162)   ~ (all_58_15 = e0)
% 177.86/28.31  | |   (163)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.86/28.31  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.86/28.31  | | 
% 177.86/28.31  | | ALPHA: (163) implies:
% 177.86/28.31  | |   (164)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (29), (162) imply:
% 177.86/28.31  | |   (165)   ~ (all_6_2 = e0)
% 177.86/28.31  | | 
% 177.86/28.31  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 177.86/28.31  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.86/28.31  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 177.86/28.31  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 177.86/28.31  | |            (49), (50), (51), (53), (54), (55), (56), (57), (58), (59), (60),
% 177.86/28.31  | |            (61), (62), (63), (64), (65), (68), (69), (70), (71), (72), (73),
% 177.86/28.31  | |            (74), (75), (76), (77), (79), (80), (81), (82), (83), (85), (86),
% 177.86/28.31  | |            (87), (88), (89), (90), (92), (93), (94), (95), (96), (97), (98),
% 177.86/28.31  | |            (99), (100), (101), (102), (103), (104), (106), (107), (108),
% 177.86/28.31  | |            (109), (110), (112), (113), (114), (115), (116), (117), (118),
% 177.86/28.31  | |            (120), (121), (122), (123), (125), (126), (127), (128), (129),
% 177.86/28.31  | |            (131), (133), (134), (135), (136), (137), (138), (139), (141),
% 177.86/28.31  | |            (142), (144), (145), (146), (147), (148), (149), (150), (151),
% 177.86/28.31  | |            (154), (155), (164), (165) are inconsistent by sub-proof #609.
% 177.86/28.31  | | 
% 177.86/28.31  | End of split
% 177.86/28.31  | 
% 177.86/28.31  End of proof
% 177.86/28.31  
% 177.86/28.31  Sub-proof #539 shows that the following formulas are inconsistent:
% 177.86/28.31  ----------------------------------------------------------------
% 177.86/28.31    (1)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.86/28.31    (2)  all_52_20 = e2
% 177.86/28.31    (3)   ~ (e2 = e1)
% 177.86/28.31  
% 177.86/28.31  Begin of proof
% 177.86/28.31  | 
% 177.86/28.31  | ALPHA: (1) implies:
% 177.86/28.31  |   (4)  all_52_20 = e1
% 177.86/28.31  | 
% 177.86/28.31  | COMBINE_EQS: (2), (4) imply:
% 177.86/28.31  |   (5)  e2 = e1
% 177.86/28.31  | 
% 177.86/28.31  | REDUCE: (3), (5) imply:
% 177.86/28.31  |   (6)  $false
% 177.86/28.31  | 
% 177.86/28.31  | CLOSE: (6) is inconsistent.
% 177.86/28.31  | 
% 177.86/28.31  End of proof
% 177.86/28.31  
% 177.86/28.31  Sub-proof #540 shows that the following formulas are inconsistent:
% 177.86/28.31  ----------------------------------------------------------------
% 177.86/28.31    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.31    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.31    (3)   ~ (all_52_17 = all_52_23)
% 177.86/28.31    (4)  op(e2, all_52_3) = e2
% 177.86/28.31    (5)   ~ (all_32_0 = e0) |  ~ (all_32_2 = e3)
% 177.86/28.31    (6)  op(e2, all_10_2) = all_10_1
% 177.86/28.31    (7)   ~ (all_52_13 = all_52_29)
% 177.86/28.31    (8)  all_56_3 = all_52_7
% 177.86/28.31    (9)  op(e3, e2) = all_52_3
% 177.86/28.31    (10)   ~ (all_52_9 = all_52_25)
% 177.86/28.31    (11)   ~ (all_52_19 = all_52_23)
% 177.86/28.31    (12)  all_56_11 = all_52_23
% 177.86/28.31    (13)  op(e1, e2) = all_52_19
% 177.86/28.31    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 177.86/28.31    (15)   ~ (all_52_3 = all_10_2)
% 177.86/28.31    (16)  all_58_5 = all_52_13
% 177.86/28.31    (17)   ~ (all_6_2 = e0)
% 177.86/28.31    (18)   ~ (all_52_25 = all_52_29)
% 177.86/28.31    (19)  all_56_15 = all_6_2
% 177.86/28.31    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.31    (21)  op(e2, e0) = all_52_15
% 177.86/28.31    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.31    (23)  all_58_3 = all_10_2
% 177.86/28.31    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.31    (25)  all_58_15 = all_6_2
% 177.86/28.31    (26)  op(e2, all_14_2) = all_14_0
% 177.86/28.31    (27)   ~ (all_52_9 = all_4_2)
% 177.86/28.31    (28)   ~ (all_52_5 = all_52_7)
% 177.86/28.31    (29)  all_58_10 = all_52_15
% 177.86/28.31    (30)   ~ (all_52_5 = all_4_2)
% 177.86/28.31    (31)  all_58_7 = all_52_19
% 177.86/28.31    (32)  all_56_4 = all_52_9
% 177.86/28.31    (33)   ~ (all_52_15 = all_6_2)
% 177.86/28.31    (34)   ~ (all_52_17 = all_52_25)
% 177.86/28.31    (35)  op(e0, e1) = all_52_29
% 177.86/28.31    (36)   ~ (all_4_0 = e2)
% 177.86/28.31    (37)  all_58_4 = all_52_5
% 177.86/28.31    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.31    (39)   ~ (all_52_27 = all_52_29)
% 177.86/28.31    (40)   ~ (all_52_17 = all_14_2)
% 177.86/28.31    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.31    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.31    (43)   ~ (all_52_7 = all_4_2)
% 177.86/28.31    (44)  all_58_1 = all_52_3
% 177.86/28.31    (45)   ~ (all_52_13 = all_52_15)
% 177.86/28.31    (46)  all_58_0 = all_4_2
% 177.86/28.31    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.86/28.31    (48)  op(e0, e0) = all_6_2
% 177.86/28.31    (49)  op(e1, all_52_29) = all_52_28
% 177.86/28.31    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.31    (51)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.31    (52)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.31    (53)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.31    (54)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.86/28.31    (55)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.86/28.31    (56)  all_58_14 = all_52_29
% 177.86/28.31    (57)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.31    (58)  all_32_2 = all_14_2
% 177.86/28.31    (59)   ~ (all_52_3 = all_52_5)
% 177.86/28.31    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.31    (61)  op(e2, e1) = all_52_13
% 177.86/28.31    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.31    (63)  all_58_8 = all_14_2
% 177.86/28.31    (64)  all_56_1 = all_52_3
% 177.86/28.31    (65)  op(e0, e2) = all_52_27
% 177.86/28.31    (66)  all_56_14 = all_52_29
% 177.86/28.31    (67)   ~ (all_10_1 = e1)
% 177.86/28.31    (68)   ~ (all_52_5 = all_14_2)
% 177.86/28.31    (69)   ~ (all_52_3 = all_52_27)
% 177.86/28.31    (70)   ~ (all_52_3 = all_4_2)
% 177.86/28.31    (71)  op(e3, all_4_2) = e3
% 177.86/28.31    (72)  op(e0, e3) = all_52_25
% 177.86/28.31    (73)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.31    (74)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 177.86/28.31    (75)   ~ (all_52_13 = all_14_2)
% 177.86/28.31    (76)   ~ (e3 = e0)
% 177.86/28.31    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.31    (78)  all_32_0 = all_14_0
% 177.86/28.31    (79)   ~ (all_52_9 = all_52_13)
% 177.86/28.31    (80)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.31    (81)  op(e0, all_52_23) = all_52_22
% 177.86/28.31    (82)   ~ (all_52_15 = all_52_23)
% 177.86/28.31    (83)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.31    (84)   ~ (all_52_5 = all_52_29)
% 177.86/28.31    (85)  all_56_2 = all_52_5
% 177.86/28.31    (86)  op(e1, e0) = all_52_23
% 177.86/28.31    (87)  all_56_12 = all_52_25
% 177.86/28.31    (88)  all_58_13 = all_52_27
% 177.86/28.31    (89)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.31    (90)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.31    (91)   ~ (all_52_9 = all_52_17)
% 177.86/28.31    (92)   ~ (all_14_0 = e2)
% 177.86/28.31    (93)  all_58_6 = all_52_17
% 177.86/28.31    (94)   ~ (all_52_3 = all_52_7)
% 177.86/28.31    (95)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.86/28.31    (96)   ~ (e1 = e0)
% 177.86/28.31    (97)  all_56_0 = all_4_2
% 177.86/28.31    (98)  all_58_11 = all_52_23
% 177.86/28.31    (99)   ~ (all_52_3 = all_52_19)
% 177.86/28.31    (100)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.86/28.31    (101)   ~ (all_52_7 = all_52_15)
% 177.86/28.31    (102)  op(e0, all_52_15) = all_52_14
% 177.86/28.31    (103)   ~ (all_52_29 = all_14_2)
% 177.86/28.31    (104)   ~ (all_4_0 = e1)
% 177.86/28.31    (105)   ~ (all_52_23 = all_6_2)
% 177.86/28.31    (106)   ~ (all_52_29 = all_6_2)
% 177.86/28.31    (107)  all_58_2 = all_52_9
% 177.86/28.31    (108)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.31    (109)  op(e3, e1) = all_52_5
% 177.86/28.31    (110)  all_56_10 = all_14_2
% 177.86/28.31    (111)   ~ (all_52_25 = all_6_2)
% 177.86/28.31    (112)  op(e1, e1) = all_14_2
% 177.86/28.31    (113)  op(e1, e3) = all_52_17
% 177.86/28.31    (114)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.31    (115)   ~ (all_52_25 = all_4_2)
% 177.86/28.31    (116)  op(e3, e0) = all_52_7
% 177.86/28.31    (117)   ~ (all_52_17 = all_4_2)
% 177.86/28.31    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.31             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.31    (119)   ~ (all_52_25 = all_52_27)
% 177.86/28.31    (120)   ~ (all_52_27 = all_6_2)
% 177.86/28.31    (121)   ~ (all_52_7 = all_6_2)
% 177.86/28.31    (122)   ~ (all_52_19 = all_52_27)
% 177.86/28.31    (123)  all_56_7 = all_52_15
% 177.86/28.31    (124)  op(e1, all_52_5) = e1
% 177.86/28.31    (125)   ~ (all_52_7 = all_52_23)
% 177.86/28.31    (126)   ~ (all_52_13 = all_10_2)
% 177.86/28.31    (127)  op(e3, all_4_2) = all_4_0
% 177.86/28.31    (128)  op(e0, all_52_7) = e0
% 177.86/28.31    (129)  op(e2, all_52_27) = all_52_26
% 177.86/28.31    (130)   ~ (all_52_17 = all_52_19)
% 177.86/28.31    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.31    (132)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.31    (133)  all_58_9 = all_52_7
% 177.86/28.31    (134)  all_58_12 = all_52_25
% 177.86/28.31    (135)  all_56_6 = all_52_13
% 177.86/28.31    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.31    (137)   ~ (all_52_9 = all_52_15)
% 177.86/28.31    (138)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.31    (139)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.31    (140)   ~ (all_52_19 = all_14_2)
% 177.86/28.31    (141)  op(e2, e3) = all_52_9
% 177.86/28.31    (142)  all_56_13 = all_52_27
% 177.86/28.31  
% 177.86/28.31  Begin of proof
% 177.86/28.31  | 
% 177.86/28.31  | GROUND_INST: instantiating (118) with e3, all_4_0, all_4_2, e3, simplifying
% 177.86/28.31  |              with (71), (127) gives:
% 177.86/28.31  |   (143)  all_4_0 = e3
% 177.86/28.31  | 
% 177.86/28.31  | REDUCE: (36), (143) imply:
% 177.86/28.31  |   (144)   ~ (e3 = e2)
% 177.86/28.31  | 
% 177.86/28.31  | REDUCE: (104), (143) imply:
% 177.86/28.31  |   (145)   ~ (e3 = e1)
% 177.86/28.31  | 
% 177.86/28.31  | BETA: splitting (41) gives:
% 177.86/28.31  | 
% 177.86/28.31  | Case 1:
% 177.86/28.31  | | 
% 177.86/28.31  | |   (146)  all_56_15 = e3
% 177.86/28.31  | | 
% 177.86/28.31  | | COMBINE_EQS: (19), (146) imply:
% 177.86/28.31  | |   (147)  all_6_2 = e3
% 177.86/28.31  | | 
% 177.86/28.31  | | SIMP: (147) implies:
% 177.86/28.31  | |   (148)  all_6_2 = e3
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (121), (148) imply:
% 177.86/28.31  | |   (149)   ~ (all_52_7 = e3)
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (33), (148) imply:
% 177.86/28.31  | |   (150)   ~ (all_52_15 = e3)
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (105), (148) imply:
% 177.86/28.31  | |   (151)   ~ (all_52_23 = e3)
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (106), (148) imply:
% 177.86/28.31  | |   (152)   ~ (all_52_29 = e3)
% 177.86/28.31  | | 
% 177.86/28.31  | | REDUCE: (48), (148) imply:
% 177.86/28.31  | |   (153)  op(e0, e0) = e3
% 177.86/28.31  | | 
% 177.86/28.31  | | BETA: splitting (132) gives:
% 177.86/28.31  | | 
% 177.86/28.31  | | Case 1:
% 177.86/28.31  | | | 
% 177.86/28.31  | | |   (154)  all_56_3 = e3
% 177.86/28.31  | | | 
% 177.86/28.31  | | | REF_CLOSE: (8), (149), (154) are inconsistent by sub-proof #1034.
% 177.86/28.31  | | | 
% 177.86/28.31  | | Case 2:
% 177.86/28.31  | | | 
% 177.86/28.31  | | |   (155)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.31  | | | 
% 177.86/28.31  | | | BETA: splitting (60) gives:
% 177.86/28.31  | | | 
% 177.86/28.31  | | | Case 1:
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | |   (156)  all_58_0 = e3
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | COMBINE_EQS: (46), (156) imply:
% 177.86/28.31  | | | |   (157)  all_4_2 = e3
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | REDUCE: (70), (157) imply:
% 177.86/28.31  | | | |   (158)   ~ (all_52_3 = e3)
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | REDUCE: (30), (157) imply:
% 177.86/28.31  | | | |   (159)   ~ (all_52_5 = e3)
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | REDUCE: (27), (157) imply:
% 177.86/28.31  | | | |   (160)   ~ (all_52_9 = e3)
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | REDUCE: (117), (157) imply:
% 177.86/28.31  | | | |   (161)   ~ (all_52_17 = e3)
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | BETA: splitting (138) gives:
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | Case 1:
% 177.86/28.31  | | | | | 
% 177.86/28.31  | | | | |   (162)  all_58_4 = e3
% 177.86/28.31  | | | | | 
% 177.86/28.31  | | | | | REF_CLOSE: (37), (159), (162) are inconsistent by sub-proof #1025.
% 177.86/28.31  | | | | | 
% 177.86/28.31  | | | | Case 2:
% 177.86/28.31  | | | | | 
% 177.86/28.31  | | | | |   (163)   ~ (all_58_4 = e3)
% 177.86/28.31  | | | | |   (164)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.31  | | | | | 
% 177.86/28.31  | | | | | BETA: splitting (38) gives:
% 177.86/28.31  | | | | | 
% 177.86/28.31  | | | | | Case 1:
% 177.86/28.31  | | | | | | 
% 177.86/28.31  | | | | | |   (165)  all_58_6 = e3
% 177.86/28.31  | | | | | | 
% 177.86/28.31  | | | | | | REF_CLOSE: (93), (161), (165) are inconsistent by sub-proof #981.
% 177.86/28.31  | | | | | | 
% 177.86/28.31  | | | | | Case 2:
% 177.86/28.31  | | | | | | 
% 177.86/28.31  | | | | | |   (166)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.31  | | | | | | 
% 177.86/28.31  | | | | | | BETA: splitting (42) gives:
% 177.86/28.31  | | | | | | 
% 177.86/28.31  | | | | | | Case 1:
% 177.86/28.31  | | | | | | | 
% 177.86/28.31  | | | | | | |   (167)  all_58_2 = e3
% 177.86/28.31  | | | | | | | 
% 177.86/28.31  | | | | | | | REF_CLOSE: (107), (160), (167) are inconsistent by sub-proof #980.
% 177.86/28.31  | | | | | | | 
% 177.86/28.31  | | | | | | Case 2:
% 177.86/28.31  | | | | | | | 
% 177.86/28.31  | | | | | | |   (168)   ~ (all_58_2 = e3)
% 177.86/28.31  | | | | | | |   (169)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.31  | | | | | | | 
% 177.86/28.31  | | | | | | | BETA: splitting (50) gives:
% 177.86/28.31  | | | | | | | 
% 177.86/28.31  | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | 
% 177.86/28.31  | | | | | | | |   (170)  all_56_1 = e3
% 177.86/28.31  | | | | | | | | 
% 177.86/28.31  | | | | | | | | REF_CLOSE: (64), (158), (170) are inconsistent by sub-proof
% 177.86/28.31  | | | | | | | |            #862.
% 177.86/28.31  | | | | | | | | 
% 177.86/28.31  | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | 
% 177.86/28.31  | | | | | | | |   (171)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.31  | | | | | | | | 
% 177.86/28.31  | | | | | | | | BETA: splitting (95) gives:
% 177.86/28.31  | | | | | | | | 
% 177.86/28.31  | | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | | 
% 177.86/28.31  | | | | | | | | |   (172)  all_56_4 = e3
% 177.86/28.31  | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | REF_CLOSE: (32), (160), (172) are inconsistent by sub-proof
% 177.86/28.31  | | | | | | | | |            #782.
% 177.86/28.31  | | | | | | | | | 
% 177.86/28.31  | | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | | 
% 177.86/28.31  | | | | | | | | |   (173)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.86/28.31  | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | BETA: splitting (139) gives:
% 177.86/28.31  | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | |   (174)  all_56_2 = e3
% 177.86/28.31  | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | REF_CLOSE: (85), (159), (174) are inconsistent by sub-proof
% 177.86/28.31  | | | | | | | | | |            #931.
% 177.86/28.31  | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | |   (175)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.31  | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | BETA: splitting (54) gives:
% 177.86/28.31  | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | |   (176)  all_56_6 = e3
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | REF_CLOSE: (4), (8), (13), (22), (31), (35), (61), (63),
% 177.86/28.31  | | | | | | | | | | |            (64), (65), (68), (69), (73), (75), (84), (85),
% 177.86/28.31  | | | | | | | | | | |            (94), (98), (112), (118), (124), (128), (133),
% 177.86/28.31  | | | | | | | | | | |            (135), (149), (151), (153), (155), (166), (171),
% 177.86/28.31  | | | | | | | | | | |            (175), (176) are inconsistent by sub-proof #545.
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | |   (177)   ~ (all_56_6 = e3)
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | REDUCE: (135), (177) imply:
% 177.86/28.31  | | | | | | | | | | |   (178)   ~ (all_52_13 = e3)
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | BETA: splitting (169) gives:
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | |   (179)  all_58_3 = e3
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | COMBINE_EQS: (23), (179) imply:
% 177.86/28.31  | | | | | | | | | | | |   (180)  all_10_2 = e3
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | REDUCE: (6), (180) imply:
% 177.86/28.31  | | | | | | | | | | | |   (181)  op(e2, e3) = all_10_1
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | BETA: splitting (164) gives:
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | |   (182)  all_58_5 = e3
% 177.86/28.31  | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | REF_CLOSE: (16), (178), (182) are inconsistent by sub-proof
% 177.86/28.31  | | | | | | | | | | | | |            #969.
% 177.86/28.31  | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | |   (183)  all_58_8 = e3 | all_58_14 = e3
% 177.86/28.31  | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | BETA: splitting (183) gives:
% 177.86/28.31  | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | |   (184)  all_58_8 = e3
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | COMBINE_EQS: (63), (184) imply:
% 177.86/28.31  | | | | | | | | | | | | | |   (185)  all_14_2 = e3
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | SIMP: (185) implies:
% 177.86/28.31  | | | | | | | | | | | | | |   (186)  all_14_2 = e3
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | COMBINE_EQS: (58), (186) imply:
% 177.86/28.31  | | | | | | | | | | | | | |   (187)  all_32_2 = e3
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | REDUCE: (26), (186) imply:
% 177.86/28.31  | | | | | | | | | | | | | |   (188)  op(e2, e3) = all_14_0
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | Case 1:
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | |   (189)   ~ (all_32_2 = e3)
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | REDUCE: (187), (189) imply:
% 177.86/28.31  | | | | | | | | | | | | | | |   (190)  $false
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | CLOSE: (190) is inconsistent.
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | |   (191)   ~ (all_32_0 = e0)
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | REDUCE: (78), (191) imply:
% 177.86/28.31  | | | | | | | | | | | | | | |   (192)   ~ (all_14_0 = e0)
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | GROUND_INST: instantiating (118) with all_52_9, all_10_1, e3,
% 177.86/28.31  | | | | | | | | | | | | | | |              e2, simplifying with (141), (181) gives:
% 177.86/28.31  | | | | | | | | | | | | | | |   (193)  all_52_9 = all_10_1
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | GROUND_INST: instantiating (118) with all_52_9, all_14_0, e3,
% 177.86/28.31  | | | | | | | | | | | | | | |              e2, simplifying with (141), (188) gives:
% 177.86/28.31  | | | | | | | | | | | | | | |   (194)  all_52_9 = all_14_0
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | COMBINE_EQS: (193), (194) imply:
% 177.86/28.31  | | | | | | | | | | | | | | |   (195)  all_14_0 = all_10_1
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | COMBINE_EQS: (32), (193) imply:
% 177.86/28.31  | | | | | | | | | | | | | | |   (196)  all_56_4 = all_10_1
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | REDUCE: (92), (195) imply:
% 177.86/28.31  | | | | | | | | | | | | | | |   (197)   ~ (all_10_1 = e2)
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | REDUCE: (192), (195) imply:
% 177.86/28.31  | | | | | | | | | | | | | | |   (198)   ~ (all_10_1 = e0)
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | | REF_CLOSE: (67), (173), (196), (197), (198) are inconsistent
% 177.86/28.31  | | | | | | | | | | | | | | |            by sub-proof #541.
% 177.86/28.31  | | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | End of split
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | |   (199)  all_58_14 = e3
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | | REF_CLOSE: (56), (152), (199) are inconsistent by sub-proof
% 177.86/28.31  | | | | | | | | | | | | | |            #1000.
% 177.86/28.31  | | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | | End of split
% 177.86/28.31  | | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | End of split
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | Case 2:
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | |   (200)  all_58_5 = e3 | all_58_10 = e3
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | | REF_CLOSE: (16), (29), (150), (178), (200) are inconsistent
% 177.86/28.31  | | | | | | | | | | | |            by sub-proof #958.
% 177.86/28.31  | | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | | End of split
% 177.86/28.31  | | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | | End of split
% 177.86/28.31  | | | | | | | | | | 
% 177.86/28.31  | | | | | | | | | End of split
% 177.86/28.31  | | | | | | | | | 
% 177.86/28.31  | | | | | | | | End of split
% 177.86/28.31  | | | | | | | | 
% 177.86/28.31  | | | | | | | End of split
% 177.86/28.31  | | | | | | | 
% 177.86/28.31  | | | | | | End of split
% 177.86/28.31  | | | | | | 
% 177.86/28.31  | | | | | End of split
% 177.86/28.31  | | | | | 
% 177.86/28.31  | | | | End of split
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | Case 2:
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | |   (201)   ~ (all_58_0 = e3)
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | REDUCE: (46), (201) imply:
% 177.86/28.31  | | | |   (202)   ~ (all_4_2 = e3)
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | | REF_CLOSE: (1), (2), (4), (9), (16), (24), (25), (27), (28), (29), (30),
% 177.86/28.31  | | | |            (31), (37), (38), (40), (43), (44), (46), (56), (59), (63),
% 177.86/28.31  | | | |            (68), (71), (72), (75), (77), (83), (84), (89), (93), (94),
% 177.86/28.31  | | | |            (97), (98), (99), (101), (103), (109), (110), (113), (115),
% 177.86/28.31  | | | |            (116), (117), (118), (121), (124), (125), (128), (131),
% 177.86/28.31  | | | |            (133), (136), (138), (141), (152), (202) are inconsistent by
% 177.86/28.31  | | | |            sub-proof #864.
% 177.86/28.31  | | | | 
% 177.86/28.31  | | | End of split
% 177.86/28.31  | | | 
% 177.86/28.31  | | End of split
% 177.86/28.31  | | 
% 177.86/28.31  | Case 2:
% 177.86/28.31  | | 
% 177.86/28.31  | |   (203)   ~ (all_56_15 = e3)
% 177.86/28.31  | |   (204)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.31  | | 
% 177.86/28.31  | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (13), (14), (15),
% 177.86/28.31  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 177.86/28.31  | |            (28), (29), (30), (31), (32), (33), (34), (35), (37), (38), (39),
% 177.86/28.31  | |            (42), (43), (44), (45), (46), (47), (49), (50), (51), (52), (53),
% 177.86/28.31  | |            (55), (56), (57), (59), (60), (61), (62), (63), (64), (66), (68),
% 177.86/28.31  | |            (69), (70), (71), (72), (74), (75), (76), (77), (79), (80), (81),
% 177.86/28.31  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (93),
% 177.86/28.31  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 177.86/28.31  | |            (105), (106), (107), (108), (109), (110), (111), (112), (113),
% 177.86/28.31  | |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 177.86/28.31  | |            (123), (124), (125), (126), (128), (129), (130), (131), (133),
% 177.86/28.31  | |            (134), (136), (137), (138), (139), (140), (141), (142), (144),
% 177.86/28.31  | |            (145), (203), (204) are inconsistent by sub-proof #785.
% 177.86/28.31  | | 
% 177.86/28.31  | End of split
% 177.86/28.31  | 
% 177.86/28.31  End of proof
% 177.86/28.31  
% 177.86/28.31  Sub-proof #541 shows that the following formulas are inconsistent:
% 177.86/28.31  ----------------------------------------------------------------
% 177.86/28.31    (1)   ~ (all_10_1 = e0)
% 177.86/28.31    (2)  all_56_4 = all_10_1
% 177.86/28.31    (3)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.86/28.31    (4)   ~ (all_10_1 = e1)
% 177.86/28.31    (5)   ~ (all_10_1 = e2)
% 177.86/28.31  
% 177.86/28.31  Begin of proof
% 177.86/28.31  | 
% 177.86/28.31  | BETA: splitting (3) gives:
% 177.86/28.31  | 
% 177.86/28.31  | Case 1:
% 177.86/28.31  | | 
% 177.86/28.31  | |   (6)  all_56_4 = e2
% 177.86/28.31  | | 
% 177.86/28.31  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #544.
% 177.86/28.31  | | 
% 177.86/28.31  | Case 2:
% 177.86/28.31  | | 
% 177.86/28.31  | |   (7)  all_56_4 = e1 | all_56_4 = e0
% 177.86/28.31  | | 
% 177.86/28.31  | | BETA: splitting (7) gives:
% 177.86/28.31  | | 
% 177.86/28.31  | | Case 1:
% 177.86/28.31  | | | 
% 177.86/28.31  | | |   (8)  all_56_4 = e1
% 177.86/28.31  | | | 
% 177.86/28.31  | | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #543.
% 177.86/28.31  | | | 
% 177.86/28.31  | | Case 2:
% 177.86/28.31  | | | 
% 177.86/28.31  | | |   (9)  all_56_4 = e0
% 177.86/28.31  | | | 
% 177.86/28.31  | | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #542.
% 177.86/28.31  | | | 
% 177.86/28.31  | | End of split
% 177.86/28.31  | | 
% 177.86/28.31  | End of split
% 177.86/28.31  | 
% 177.86/28.31  End of proof
% 177.86/28.31  
% 177.86/28.31  Sub-proof #542 shows that the following formulas are inconsistent:
% 177.86/28.31  ----------------------------------------------------------------
% 177.86/28.31    (1)  all_56_4 = all_10_1
% 177.86/28.31    (2)  all_56_4 = e0
% 177.86/28.31    (3)   ~ (all_10_1 = e0)
% 177.86/28.31  
% 177.86/28.31  Begin of proof
% 177.86/28.31  | 
% 177.86/28.31  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.31  |   (4)  all_10_1 = e0
% 177.86/28.31  | 
% 177.86/28.31  | SIMP: (4) implies:
% 177.86/28.31  |   (5)  all_10_1 = e0
% 177.86/28.31  | 
% 177.86/28.31  | REDUCE: (3), (5) imply:
% 177.86/28.31  |   (6)  $false
% 177.86/28.31  | 
% 177.86/28.31  | CLOSE: (6) is inconsistent.
% 177.86/28.31  | 
% 177.86/28.31  End of proof
% 177.86/28.31  
% 177.86/28.31  Sub-proof #543 shows that the following formulas are inconsistent:
% 177.86/28.31  ----------------------------------------------------------------
% 177.86/28.31    (1)  all_56_4 = all_10_1
% 177.86/28.31    (2)  all_56_4 = e1
% 177.86/28.31    (3)   ~ (all_10_1 = e1)
% 177.86/28.31  
% 177.86/28.31  Begin of proof
% 177.86/28.31  | 
% 177.86/28.31  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.31  |   (4)  all_10_1 = e1
% 177.86/28.31  | 
% 177.86/28.31  | SIMP: (4) implies:
% 177.86/28.31  |   (5)  all_10_1 = e1
% 177.86/28.31  | 
% 177.86/28.31  | REDUCE: (3), (5) imply:
% 177.86/28.31  |   (6)  $false
% 177.86/28.31  | 
% 177.86/28.31  | CLOSE: (6) is inconsistent.
% 177.86/28.31  | 
% 177.86/28.31  End of proof
% 177.86/28.31  
% 177.86/28.31  Sub-proof #544 shows that the following formulas are inconsistent:
% 177.86/28.31  ----------------------------------------------------------------
% 177.86/28.31    (1)  all_56_4 = all_10_1
% 177.86/28.32    (2)  all_56_4 = e2
% 177.86/28.32    (3)   ~ (all_10_1 = e2)
% 177.86/28.32  
% 177.86/28.32  Begin of proof
% 177.86/28.32  | 
% 177.86/28.32  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.32  |   (4)  all_10_1 = e2
% 177.86/28.32  | 
% 177.86/28.32  | SIMP: (4) implies:
% 177.86/28.32  |   (5)  all_10_1 = e2
% 177.86/28.32  | 
% 177.86/28.32  | REDUCE: (3), (5) imply:
% 177.86/28.32  |   (6)  $false
% 177.86/28.32  | 
% 177.86/28.32  | CLOSE: (6) is inconsistent.
% 177.86/28.32  | 
% 177.86/28.32  End of proof
% 177.86/28.32  
% 177.86/28.32  Sub-proof #545 shows that the following formulas are inconsistent:
% 177.86/28.32  ----------------------------------------------------------------
% 177.86/28.32    (1)  op(e2, all_52_3) = e2
% 177.86/28.32    (2)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.32    (3)  all_56_3 = all_52_7
% 177.86/28.32    (4)  all_56_6 = e3
% 177.86/28.32    (5)  op(e1, e2) = all_52_19
% 177.86/28.32    (6)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.32    (7)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.32    (8)  all_58_7 = all_52_19
% 177.86/28.32    (9)  op(e0, e1) = all_52_29
% 177.86/28.32    (10)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.32    (11)  op(e2, e1) = all_52_13
% 177.86/28.32    (12)  all_58_8 = all_14_2
% 177.86/28.32    (13)  all_56_1 = all_52_3
% 177.86/28.32    (14)  op(e0, e2) = all_52_27
% 177.86/28.32    (15)   ~ (all_52_5 = all_14_2)
% 177.86/28.32    (16)   ~ (all_52_23 = e3)
% 177.86/28.32    (17)   ~ (all_52_3 = all_52_27)
% 177.86/28.32    (18)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.32    (19)   ~ (all_52_13 = all_14_2)
% 177.86/28.32    (20)   ~ (all_52_5 = all_52_29)
% 177.86/28.32    (21)  all_56_2 = all_52_5
% 177.86/28.32    (22)   ~ (all_52_3 = all_52_7)
% 177.86/28.32    (23)  all_58_11 = all_52_23
% 177.86/28.32    (24)  op(e1, e1) = all_14_2
% 177.86/28.32    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.32    (26)   ~ (all_52_7 = e3)
% 177.86/28.32    (27)  op(e1, all_52_5) = e1
% 177.86/28.32    (28)  op(e0, all_52_7) = e0
% 177.86/28.32    (29)  all_58_9 = all_52_7
% 177.86/28.32    (30)  all_56_6 = all_52_13
% 177.86/28.32    (31)  op(e0, e0) = e3
% 177.86/28.32    (32)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.32  
% 177.86/28.32  Begin of proof
% 177.86/28.32  | 
% 177.86/28.32  | COMBINE_EQS: (4), (30) imply:
% 177.86/28.32  |   (33)  all_52_13 = e3
% 177.86/28.32  | 
% 177.86/28.32  | SIMP: (33) implies:
% 177.86/28.32  |   (34)  all_52_13 = e3
% 177.86/28.32  | 
% 177.86/28.32  | REDUCE: (19), (34) imply:
% 177.86/28.32  |   (35)   ~ (all_14_2 = e3)
% 177.86/28.32  | 
% 177.86/28.32  | SIMP: (35) implies:
% 177.86/28.32  |   (36)   ~ (all_14_2 = e3)
% 177.86/28.32  | 
% 177.86/28.32  | REDUCE: (11), (34) imply:
% 177.86/28.32  |   (37)  op(e2, e1) = e3
% 177.86/28.32  | 
% 177.86/28.32  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 177.86/28.32  |            (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 177.86/28.32  |            (27), (28), (29), (31), (32), (36), (37) are inconsistent by
% 177.86/28.32  |            sub-proof #546.
% 177.86/28.32  | 
% 177.86/28.32  End of proof
% 177.86/28.32  
% 177.86/28.32  Sub-proof #546 shows that the following formulas are inconsistent:
% 177.86/28.32  ----------------------------------------------------------------
% 177.86/28.32    (1)  op(e2, all_52_3) = e2
% 177.86/28.32    (2)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.32    (3)  all_56_3 = all_52_7
% 177.86/28.32    (4)  op(e1, e2) = all_52_19
% 177.86/28.32    (5)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.32    (6)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.32    (7)  all_58_7 = all_52_19
% 177.86/28.32    (8)  op(e0, e1) = all_52_29
% 177.86/28.32    (9)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.32    (10)  all_58_8 = all_14_2
% 177.86/28.32    (11)  all_56_1 = all_52_3
% 177.86/28.32    (12)  op(e0, e2) = all_52_27
% 177.86/28.32    (13)   ~ (all_52_5 = all_14_2)
% 177.86/28.32    (14)   ~ (all_52_23 = e3)
% 177.86/28.32    (15)   ~ (all_52_3 = all_52_27)
% 177.86/28.32    (16)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.32    (17)   ~ (all_52_5 = all_52_29)
% 177.86/28.32    (18)  all_56_2 = all_52_5
% 177.86/28.32    (19)   ~ (all_52_3 = all_52_7)
% 177.86/28.32    (20)  all_58_11 = all_52_23
% 177.86/28.32    (21)  op(e2, e1) = e3
% 177.86/28.32    (22)  op(e1, e1) = all_14_2
% 177.86/28.32    (23)   ~ (all_14_2 = e3)
% 177.86/28.32    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.32    (25)   ~ (all_52_7 = e3)
% 177.86/28.32    (26)  op(e1, all_52_5) = e1
% 177.86/28.32    (27)  op(e0, all_52_7) = e0
% 177.86/28.32    (28)  all_58_9 = all_52_7
% 177.86/28.32    (29)  op(e0, e0) = e3
% 177.86/28.32    (30)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.32  
% 177.86/28.32  Begin of proof
% 177.86/28.32  | 
% 177.86/28.32  | BETA: splitting (5) gives:
% 177.86/28.32  | 
% 177.86/28.32  | Case 1:
% 177.86/28.32  | | 
% 177.86/28.32  | |   (31)  all_58_7 = e3
% 177.86/28.32  | | 
% 177.86/28.32  | | COMBINE_EQS: (7), (31) imply:
% 177.86/28.32  | |   (32)  all_52_19 = e3
% 177.86/28.32  | | 
% 177.86/28.32  | | REDUCE: (4), (32) imply:
% 177.86/28.32  | |   (33)  op(e1, e2) = e3
% 177.86/28.32  | | 
% 177.86/28.32  | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (11), (12), (13), (15), (16), (17),
% 177.86/28.32  | |            (18), (19), (21), (22), (24), (25), (26), (27), (28), (29), (30),
% 177.86/28.32  | |            (33) are inconsistent by sub-proof #853.
% 177.86/28.32  | | 
% 177.86/28.32  | Case 2:
% 177.86/28.32  | | 
% 177.86/28.32  | |   (34)  all_58_8 = e3 | all_58_11 = e3
% 177.86/28.32  | | 
% 177.86/28.32  | | REF_CLOSE: (10), (14), (20), (23), (34) are inconsistent by sub-proof #997.
% 177.86/28.32  | | 
% 177.86/28.32  | End of split
% 177.86/28.32  | 
% 177.86/28.32  End of proof
% 177.86/28.32  
% 177.86/28.32  Sub-proof #547 shows that the following formulas are inconsistent:
% 177.86/28.32  ----------------------------------------------------------------
% 177.86/28.32    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.32    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.86/28.32    (3)   ~ (all_52_27 = all_10_2)
% 177.86/28.32    (4)   ~ (all_52_17 = all_52_23)
% 177.86/28.32    (5)   ~ (all_6_0 = e3)
% 177.86/28.32    (6)  op(e2, all_10_2) = all_10_1
% 177.86/28.32    (7)   ~ (all_52_13 = all_52_29)
% 177.86/28.32    (8)  all_56_3 = all_52_7
% 177.86/28.32    (9)  op(e3, e2) = all_52_3
% 177.86/28.32    (10)   ~ (all_52_9 = all_52_25)
% 177.86/28.32    (11)  op(e3, all_52_25) = all_52_24
% 177.86/28.32    (12)   ~ (all_52_19 = all_52_23)
% 177.86/28.32    (13)  all_56_11 = all_52_23
% 177.86/28.32    (14)  op(e1, e2) = all_52_19
% 177.86/28.32    (15)   ~ (all_52_27 = e0)
% 177.86/28.32    (16)  op(e1, all_14_2) = e2
% 177.86/28.32    (17)  op(e3, all_52_9) = all_52_8
% 177.86/28.32    (18)   ~ (all_52_23 = e0)
% 177.86/28.32    (19)   ~ (all_52_3 = all_10_2)
% 177.86/28.32    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.32    (21)  all_58_5 = all_52_13
% 177.86/28.32    (22)   ~ (all_52_25 = all_52_29)
% 177.86/28.32    (23)  op(e0, e0) = all_6_1
% 177.86/28.32    (24)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.32    (25)  all_58_3 = all_10_2
% 177.86/28.32    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.32    (27)  all_58_15 = all_6_2
% 177.86/28.32    (28)   ~ (all_52_9 = all_4_2)
% 177.86/28.32    (29)   ~ (all_52_5 = all_52_7)
% 177.86/28.32    (30)  all_58_10 = all_52_15
% 177.86/28.32    (31)   ~ (all_52_5 = all_4_2)
% 177.86/28.32    (32)  all_58_7 = all_52_19
% 177.86/28.32    (33)   ~ (all_52_17 = all_52_25)
% 177.86/28.32    (34)  op(e0, e1) = all_52_29
% 177.86/28.32    (35)   ~ (all_4_0 = e2)
% 177.86/28.32    (36)  all_58_4 = all_52_5
% 177.86/28.32    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.32    (38)   ~ (e3 = e1)
% 177.86/28.32    (39)   ~ (all_52_27 = all_52_29)
% 177.86/28.32    (40)   ~ (all_52_17 = all_14_2)
% 177.86/28.32    (41)  op(e3, all_4_2) = all_4_1
% 177.86/28.32    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.32    (43)   ~ (all_52_7 = all_4_2)
% 177.86/28.32    (44)  all_58_1 = all_52_3
% 177.86/28.32    (45)  all_58_0 = all_4_2
% 177.86/28.32    (46)  op(e1, all_52_13) = all_52_12
% 177.86/28.32    (47)  op(e1, all_52_29) = all_52_28
% 177.86/28.32    (48)   ~ (all_52_7 = e0)
% 177.86/28.32    (49)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.32    (50)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.32    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.32    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.32    (53)  all_58_14 = all_52_29
% 177.86/28.32    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.32    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.32    (56)  op(e2, e1) = all_52_13
% 177.86/28.32    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.32    (58)  all_58_8 = all_14_2
% 177.86/28.32    (59)  all_56_1 = all_52_3
% 177.86/28.32    (60)  op(e0, e2) = all_52_27
% 177.86/28.32    (61)  all_56_14 = all_52_29
% 177.86/28.32    (62)  op(all_4_1, all_4_2) = all_4_0
% 177.86/28.32    (63)   ~ (all_52_5 = all_14_2)
% 177.86/28.32    (64)   ~ (all_52_3 = all_52_27)
% 177.86/28.32    (65)   ~ (all_52_3 = all_4_2)
% 177.86/28.32    (66)  op(e0, e3) = all_52_25
% 177.86/28.32    (67)  all_52_0 = all_4_1
% 177.86/28.32    (68)   ~ (all_52_9 = all_10_2)
% 177.86/28.32    (69)  op(e3, all_52_17) = all_52_16
% 177.86/28.32    (70)  all_52_10 = all_10_1
% 177.86/28.32    (71)  all_52_20 = e2
% 177.86/28.32    (72)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.32    (73)   ~ (all_52_13 = all_14_2)
% 177.86/28.32    (74)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.32    (75)   ~ (all_52_9 = all_52_13)
% 177.86/28.32    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.32    (77)   ~ (all_52_15 = all_52_23)
% 177.86/28.32    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.32    (79)  op(all_10_1, all_10_2) = all_10_0
% 177.86/28.32    (80)   ~ (all_52_5 = all_52_29)
% 177.86/28.32    (81)  op(e1, e0) = all_52_23
% 177.86/28.32    (82)  all_56_12 = all_52_25
% 177.86/28.32    (83)  all_58_13 = all_52_27
% 177.86/28.32    (84)   ~ (all_4_1 = e1)
% 177.86/28.32    (85)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.32    (86)  all_56_5 = all_10_2
% 177.86/28.32    (87)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.32    (88)  op(e0, e0) = e0
% 177.86/28.32    (89)   ~ (all_52_25 = e0)
% 177.86/28.32    (90)   ~ (all_52_9 = all_52_17)
% 177.86/28.32    (91)  all_58_6 = all_52_17
% 177.86/28.32    (92)   ~ (all_52_3 = all_52_7)
% 177.86/28.32    (93)  all_56_0 = all_4_2
% 177.86/28.32    (94)  all_58_11 = all_52_23
% 177.86/28.32    (95)   ~ (all_52_3 = all_52_19)
% 177.86/28.32    (96)   ~ (all_52_7 = all_52_15)
% 177.86/28.32    (97)  op(e0, all_52_15) = all_52_14
% 177.86/28.32    (98)   ~ (all_52_29 = all_14_2)
% 177.86/28.32    (99)   ~ (all_4_0 = e1)
% 177.86/28.32    (100)   ~ (all_52_19 = all_10_2)
% 177.86/28.32    (101)  all_58_15 = e0
% 177.86/28.32    (102)   ~ (all_6_0 = e2)
% 177.86/28.32    (103)  all_58_2 = all_52_9
% 177.86/28.32    (104)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.32    (105)   ~ (all_52_29 = e0)
% 177.86/28.32    (106)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.32    (107)  op(e3, e1) = all_52_5
% 177.86/28.32    (108)   ~ (e2 = e1)
% 177.86/28.32    (109)  all_56_10 = all_14_2
% 177.86/28.32    (110)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.32    (111)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.32    (112)  op(e1, e3) = all_52_17
% 177.86/28.32    (113)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.32    (114)   ~ (all_52_25 = all_4_2)
% 177.86/28.32    (115)  op(e3, e0) = all_52_7
% 177.86/28.32    (116)  op(e3, e3) = all_4_2
% 177.86/28.32    (117)  all_56_8 = all_52_17
% 177.86/28.32    (118)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.32             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.32    (119)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.86/28.32           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.86/28.32           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.86/28.32           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.86/28.32    (120)   ~ (all_52_25 = all_52_27)
% 177.86/28.32    (121)   ~ (all_52_7 = all_6_2)
% 177.86/28.32    (122)   ~ (all_10_0 = e3)
% 177.86/28.32    (123)   ~ (all_52_19 = all_52_27)
% 177.86/28.32    (124)  all_56_7 = all_52_15
% 177.86/28.32    (125)   ~ (all_52_15 = e0)
% 177.86/28.32    (126)  op(all_6_1, e0) = all_6_0
% 177.86/28.32    (127)   ~ (all_52_7 = all_52_23)
% 177.86/28.32    (128)   ~ (all_6_0 = e1)
% 177.86/28.32    (129)  op(e2, all_52_27) = all_52_26
% 177.86/28.32    (130)   ~ (all_52_17 = all_52_19)
% 177.86/28.32    (131)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.32    (132)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.32    (133)  all_58_9 = all_52_7
% 177.86/28.32    (134)  all_58_12 = all_52_25
% 177.86/28.32    (135)   ~ (all_10_0 = e1)
% 177.86/28.32    (136)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.32    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.32    (138)   ~ (all_52_19 = all_14_2)
% 177.86/28.32    (139)  op(e0, all_52_7) = all_52_6
% 177.86/28.32    (140)  op(e2, e3) = all_52_9
% 177.86/28.32    (141)  all_56_13 = all_52_27
% 177.86/28.32  
% 177.86/28.32  Begin of proof
% 177.86/28.32  | 
% 177.86/28.32  | GROUND_INST: instantiating (118) with e0, all_6_1, e0, e0, simplifying with
% 177.86/28.32  |              (23), (88) gives:
% 177.86/28.32  |   (142)  all_6_1 = e0
% 177.86/28.32  | 
% 177.86/28.32  | REDUCE: (126), (142) imply:
% 177.86/28.32  |   (143)  op(e0, e0) = all_6_0
% 177.86/28.32  | 
% 177.86/28.32  | GROUND_INST: instantiating (118) with e0, all_6_0, e0, e0, simplifying with
% 177.86/28.32  |              (88), (143) gives:
% 177.86/28.32  |   (144)  all_6_0 = e0
% 177.86/28.32  | 
% 177.86/28.32  | REDUCE: (5), (144) imply:
% 177.86/28.32  |   (145)   ~ (e3 = e0)
% 177.86/28.32  | 
% 177.86/28.32  | SIMP: (145) implies:
% 177.86/28.32  |   (146)   ~ (e3 = e0)
% 177.86/28.32  | 
% 177.86/28.32  | REDUCE: (102), (144) imply:
% 177.86/28.32  |   (147)   ~ (e2 = e0)
% 177.86/28.32  | 
% 177.86/28.32  | SIMP: (147) implies:
% 177.86/28.32  |   (148)   ~ (e2 = e0)
% 177.86/28.32  | 
% 177.86/28.32  | REDUCE: (128), (144) imply:
% 177.86/28.32  |   (149)   ~ (e1 = e0)
% 177.86/28.32  | 
% 177.86/28.32  | SIMP: (149) implies:
% 177.86/28.32  |   (150)   ~ (e1 = e0)
% 177.86/28.32  | 
% 177.86/28.32  | BETA: splitting (119) gives:
% 177.86/28.32  | 
% 177.86/28.32  | Case 1:
% 177.86/28.32  | | 
% 177.86/28.32  | |   (151)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.86/28.32  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 177.86/28.32  | | 
% 177.86/28.32  | | BETA: splitting (151) gives:
% 177.86/28.32  | | 
% 177.86/28.32  | | Case 1:
% 177.86/28.32  | | | 
% 177.86/28.32  | | |   (152)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.86/28.32  | | | 
% 177.86/28.32  | | | REF_CLOSE: (8), (9), (15), (24), (26), (27), (29), (30), (34), (36), (41),
% 177.86/28.32  | | |            (43), (44), (45), (48), (52), (53), (54), (55), (57), (60),
% 177.86/28.32  | | |            (62), (66), (67), (72), (76), (80), (82), (83), (85), (89),
% 177.86/28.32  | | |            (92), (93), (94), (96), (101), (104), (105), (107), (111),
% 177.86/28.32  | | |            (114), (118), (120), (121), (127), (131), (132), (133), (134),
% 177.86/28.32  | | |            (136), (139), (141), (146), (152) are inconsistent by sub-proof
% 177.86/28.32  | | |            #1008.
% 177.86/28.32  | | | 
% 177.86/28.32  | | Case 2:
% 177.86/28.32  | | | 
% 177.86/28.32  | | |   (153)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 177.86/28.32  | | | 
% 177.86/28.32  | | | ALPHA: (153) implies:
% 177.86/28.32  | | |   (154)  all_52_14 = e0
% 177.86/28.32  | | |   (155)  all_52_12 = e1
% 177.86/28.32  | | |   (156)  all_52_10 = e2
% 177.86/28.32  | | |   (157)  all_52_8 = e3
% 177.86/28.32  | | | 
% 177.86/28.32  | | | COMBINE_EQS: (70), (156) imply:
% 177.86/28.32  | | |   (158)  all_10_1 = e2
% 177.86/28.32  | | | 
% 177.86/28.32  | | | SIMP: (158) implies:
% 177.86/28.32  | | |   (159)  all_10_1 = e2
% 177.86/28.32  | | | 
% 177.86/28.32  | | | REDUCE: (79), (159) imply:
% 177.86/28.32  | | |   (160)  op(e2, all_10_2) = all_10_0
% 177.86/28.32  | | | 
% 177.86/28.32  | | | REDUCE: (17), (157) imply:
% 177.86/28.32  | | |   (161)  op(e3, all_52_9) = e3
% 177.86/28.32  | | | 
% 177.86/28.32  | | | REDUCE: (6), (159) imply:
% 177.86/28.32  | | |   (162)  op(e2, all_10_2) = e2
% 177.86/28.32  | | | 
% 177.86/28.32  | | | REDUCE: (46), (155) imply:
% 177.86/28.32  | | |   (163)  op(e1, all_52_13) = e1
% 177.86/28.32  | | | 
% 177.86/28.32  | | | REDUCE: (97), (154) imply:
% 177.86/28.32  | | |   (164)  op(e0, all_52_15) = e0
% 177.86/28.32  | | | 
% 177.86/28.32  | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (11), (15), (19), (21), (22),
% 177.86/28.32  | | |            (24), (25), (28), (29), (30), (32), (33), (34), (35), (36),
% 177.86/28.32  | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 177.86/28.32  | | |            (49), (52), (53), (54), (55), (57), (58), (59), (60), (62),
% 177.86/28.32  | | |            (65), (66), (72), (73), (75), (76), (77), (78), (82), (83),
% 177.86/28.32  | | |            (89), (90), (91), (92), (94), (95), (96), (98), (99), (100),
% 177.86/28.32  | | |            (101), (103), (104), (105), (107), (109), (111), (112), (113),
% 177.86/28.32  | | |            (116), (118), (120), (122), (123), (124), (125), (127), (129),
% 177.86/28.32  | | |            (130), (131), (132), (133), (134), (135), (136), (137), (138),
% 177.86/28.32  | | |            (140), (141), (146), (148), (150), (160), (161), (162), (163),
% 177.86/28.32  | | |            (164) are inconsistent by sub-proof #954.
% 177.86/28.32  | | | 
% 177.86/28.32  | | End of split
% 177.86/28.32  | | 
% 177.86/28.32  | Case 2:
% 177.86/28.32  | | 
% 177.86/28.32  | |   (165)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 177.86/28.32  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.86/28.32  | |            e0)
% 177.86/28.32  | | 
% 177.86/28.32  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (12), (13), (14), (16),
% 177.86/28.32  | |            (17), (18), (20), (21), (22), (24), (25), (26), (28), (29), (31),
% 177.86/28.32  | |            (32), (33), (36), (37), (38), (39), (40), (41), (43), (44), (45),
% 177.86/28.32  | |            (47), (48), (50), (51), (53), (54), (55), (56), (57), (58), (61),
% 177.86/28.32  | |            (63), (64), (68), (69), (71), (73), (74), (76), (78), (80), (81),
% 177.86/28.32  | |            (82), (83), (84), (86), (87), (89), (90), (91), (92), (93), (94),
% 177.86/28.32  | |            (95), (98), (100), (101), (103), (104), (105), (106), (107),
% 177.86/28.32  | |            (108), (109), (110), (112), (114), (115), (116), (117), (118),
% 177.86/28.32  | |            (120), (127), (129), (132), (133), (134), (140), (141), (146),
% 177.86/28.32  | |            (150), (165) are inconsistent by sub-proof #548.
% 177.86/28.32  | | 
% 177.86/28.32  | End of split
% 177.86/28.32  | 
% 177.86/28.32  End of proof
% 177.86/28.32  
% 177.86/28.32  Sub-proof #548 shows that the following formulas are inconsistent:
% 177.86/28.32  ----------------------------------------------------------------
% 177.86/28.32    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.32    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.86/28.32    (3)   ~ (all_52_27 = all_10_2)
% 177.86/28.32    (4)   ~ (all_52_17 = all_52_23)
% 177.86/28.32    (5)  all_56_3 = all_52_7
% 177.86/28.32    (6)  op(e3, e2) = all_52_3
% 177.86/28.32    (7)   ~ (all_52_9 = all_52_25)
% 177.86/28.32    (8)  op(e3, all_52_25) = all_52_24
% 177.86/28.32    (9)   ~ (all_52_19 = all_52_23)
% 177.86/28.32    (10)  all_56_11 = all_52_23
% 177.86/28.32    (11)  op(e1, e2) = all_52_19
% 177.86/28.32    (12)  op(e1, all_14_2) = e2
% 177.86/28.32    (13)  op(e3, all_52_9) = all_52_8
% 177.86/28.32    (14)   ~ (all_52_23 = e0)
% 177.86/28.32    (15)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.32    (16)  all_58_5 = all_52_13
% 177.86/28.32    (17)   ~ (all_52_25 = all_52_29)
% 177.86/28.32    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.32    (19)  all_58_3 = all_10_2
% 177.86/28.32    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.32    (21)   ~ (all_52_9 = all_4_2)
% 177.86/28.32    (22)   ~ (all_52_5 = all_52_7)
% 177.86/28.32    (23)   ~ (all_52_5 = all_4_2)
% 177.86/28.32    (24)  all_58_7 = all_52_19
% 177.86/28.32    (25)   ~ (all_52_17 = all_52_25)
% 177.86/28.32    (26)  all_58_4 = all_52_5
% 177.86/28.32    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.32    (28)   ~ (e3 = e1)
% 177.86/28.32    (29)   ~ (all_52_27 = all_52_29)
% 177.86/28.32    (30)   ~ (all_52_17 = all_14_2)
% 177.86/28.32    (31)  op(e3, all_4_2) = all_4_1
% 177.86/28.32    (32)   ~ (all_52_7 = all_4_2)
% 177.86/28.32    (33)  all_58_1 = all_52_3
% 177.86/28.32    (34)  all_58_0 = all_4_2
% 177.86/28.32    (35)  op(e1, all_52_29) = all_52_28
% 177.86/28.32    (36)   ~ (all_52_7 = e0)
% 177.86/28.32    (37)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.32    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.32    (39)  all_58_14 = all_52_29
% 177.86/28.32    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.32    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.32    (42)  op(e2, e1) = all_52_13
% 177.86/28.32    (43)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.32    (44)  all_58_8 = all_14_2
% 177.86/28.32    (45)  all_56_14 = all_52_29
% 177.86/28.32    (46)   ~ (all_52_5 = all_14_2)
% 177.86/28.32    (47)   ~ (all_52_3 = all_52_27)
% 177.86/28.32    (48)   ~ (all_52_9 = all_10_2)
% 177.86/28.32    (49)  op(e3, all_52_17) = all_52_16
% 177.86/28.32    (50)  all_52_20 = e2
% 177.86/28.32    (51)   ~ (all_52_13 = all_14_2)
% 177.86/28.32    (52)   ~ (e3 = e0)
% 177.86/28.32    (53)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.32    (54)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.32    (55)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.32    (56)   ~ (all_52_5 = all_52_29)
% 177.86/28.32    (57)  op(e1, e0) = all_52_23
% 177.86/28.32    (58)  all_56_12 = all_52_25
% 177.86/28.32    (59)  all_58_13 = all_52_27
% 177.86/28.32    (60)   ~ (all_4_1 = e1)
% 177.86/28.32    (61)  all_56_5 = all_10_2
% 177.86/28.32    (62)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.32    (63)   ~ (all_52_25 = e0)
% 177.86/28.32    (64)   ~ (all_52_9 = all_52_17)
% 177.86/28.32    (65)  all_58_6 = all_52_17
% 177.86/28.32    (66)   ~ (all_52_3 = all_52_7)
% 177.86/28.32    (67)   ~ (e1 = e0)
% 177.86/28.32    (68)  all_56_0 = all_4_2
% 177.86/28.32    (69)  all_58_11 = all_52_23
% 177.86/28.32    (70)   ~ (all_52_3 = all_52_19)
% 177.86/28.32    (71)   ~ (all_52_29 = all_14_2)
% 177.86/28.32    (72)   ~ (all_52_19 = all_10_2)
% 177.86/28.32    (73)  all_58_15 = e0
% 177.86/28.32    (74)  all_58_2 = all_52_9
% 177.86/28.32    (75)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.32    (76)   ~ (all_52_29 = e0)
% 177.86/28.32    (77)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.32    (78)  op(e3, e1) = all_52_5
% 177.86/28.32    (79)   ~ (e2 = e1)
% 177.86/28.32    (80)  all_56_10 = all_14_2
% 177.86/28.32    (81)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.32    (82)  op(e1, e3) = all_52_17
% 177.86/28.32    (83)   ~ (all_52_25 = all_4_2)
% 177.86/28.32    (84)  op(e3, e0) = all_52_7
% 177.86/28.32    (85)  op(e3, e3) = all_4_2
% 177.86/28.32    (86)  all_56_8 = all_52_17
% 177.86/28.32    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.32    (88)   ~ (all_52_25 = all_52_27)
% 177.86/28.32    (89)   ~ (all_52_7 = all_52_23)
% 177.86/28.32    (90)  op(e2, all_52_27) = all_52_26
% 177.86/28.32    (91)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.32    (92)  all_58_9 = all_52_7
% 177.86/28.32    (93)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.86/28.32          (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.86/28.32    (94)  all_58_12 = all_52_25
% 177.86/28.32    (95)  op(e2, e3) = all_52_9
% 177.86/28.32    (96)  all_56_13 = all_52_27
% 177.86/28.32  
% 177.86/28.32  Begin of proof
% 177.86/28.32  | 
% 177.86/28.32  | BETA: splitting (93) gives:
% 177.86/28.32  | 
% 177.86/28.32  | Case 1:
% 177.86/28.32  | | 
% 177.86/28.32  | |   (97)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.86/28.32  | | 
% 177.86/28.32  | | REF_CLOSE: (50), (79), (97) are inconsistent by sub-proof #553.
% 177.86/28.32  | | 
% 177.86/28.32  | Case 2:
% 177.86/28.32  | | 
% 177.86/28.32  | |   (98)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 177.86/28.32  | | 
% 177.86/28.32  | | ALPHA: (98) implies:
% 177.86/28.32  | |   (99)  all_52_28 = e1
% 177.86/28.32  | |   (100)  all_52_26 = e2
% 177.86/28.32  | |   (101)  all_52_24 = e3
% 177.86/28.32  | | 
% 177.86/28.32  | | REDUCE: (8), (101) imply:
% 177.86/28.32  | |   (102)  op(e3, all_52_25) = e3
% 177.86/28.32  | | 
% 177.86/28.32  | | REDUCE: (90), (100) imply:
% 177.86/28.32  | |   (103)  op(e2, all_52_27) = e2
% 177.86/28.32  | | 
% 177.86/28.32  | | REDUCE: (35), (99) imply:
% 177.86/28.32  | |   (104)  op(e1, all_52_29) = e1
% 177.86/28.32  | | 
% 177.86/28.33  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 177.86/28.33  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 177.86/28.33  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 177.86/28.33  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 177.86/28.33  | |            (48), (49), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 177.86/28.33  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 177.86/28.33  | |            (71), (72), (73), (74), (75), (76), (77), (78), (80), (81), (82),
% 177.86/28.33  | |            (83), (84), (85), (86), (87), (88), (89), (91), (92), (94), (95),
% 177.86/28.33  | |            (96), (102), (103), (104) are inconsistent by sub-proof #549.
% 177.86/28.33  | | 
% 177.86/28.33  | End of split
% 177.86/28.33  | 
% 177.86/28.33  End of proof
% 177.86/28.33  
% 177.86/28.33  Sub-proof #549 shows that the following formulas are inconsistent:
% 177.86/28.33  ----------------------------------------------------------------
% 177.86/28.33    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.33    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.86/28.33    (3)   ~ (all_52_27 = all_10_2)
% 177.86/28.33    (4)   ~ (all_52_17 = all_52_23)
% 177.86/28.33    (5)  all_56_3 = all_52_7
% 177.86/28.33    (6)  op(e3, e2) = all_52_3
% 177.86/28.33    (7)   ~ (all_52_9 = all_52_25)
% 177.86/28.33    (8)   ~ (all_52_19 = all_52_23)
% 177.86/28.33    (9)  all_56_11 = all_52_23
% 177.86/28.33    (10)  op(e1, e2) = all_52_19
% 177.86/28.33    (11)  op(e1, all_14_2) = e2
% 177.86/28.33    (12)  op(e3, all_52_9) = all_52_8
% 177.86/28.33    (13)   ~ (all_52_23 = e0)
% 177.86/28.33    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.33    (15)  all_58_5 = all_52_13
% 177.86/28.33    (16)   ~ (all_52_25 = all_52_29)
% 177.86/28.33    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.33    (18)  all_58_3 = all_10_2
% 177.86/28.33    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.33    (20)   ~ (all_52_9 = all_4_2)
% 177.86/28.33    (21)   ~ (all_52_5 = all_52_7)
% 177.86/28.33    (22)   ~ (all_52_5 = all_4_2)
% 177.86/28.33    (23)  all_58_7 = all_52_19
% 177.86/28.33    (24)   ~ (all_52_17 = all_52_25)
% 177.86/28.33    (25)  all_58_4 = all_52_5
% 177.86/28.33    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.33    (27)   ~ (e3 = e1)
% 177.86/28.33    (28)   ~ (all_52_27 = all_52_29)
% 177.86/28.33    (29)   ~ (all_52_17 = all_14_2)
% 177.86/28.33    (30)  op(e3, all_4_2) = all_4_1
% 177.86/28.33    (31)   ~ (all_52_7 = all_4_2)
% 177.86/28.33    (32)  all_58_1 = all_52_3
% 177.86/28.33    (33)  all_58_0 = all_4_2
% 177.86/28.33    (34)  op(e2, all_52_27) = e2
% 177.86/28.33    (35)   ~ (all_52_7 = e0)
% 177.86/28.33    (36)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.33    (37)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.33    (38)  all_58_14 = all_52_29
% 177.86/28.33    (39)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.33    (40)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.33    (41)  op(e2, e1) = all_52_13
% 177.86/28.33    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.33    (43)  all_58_8 = all_14_2
% 177.86/28.33    (44)  all_56_14 = all_52_29
% 177.86/28.33    (45)  op(e1, all_52_29) = e1
% 177.86/28.33    (46)   ~ (all_52_5 = all_14_2)
% 177.86/28.33    (47)   ~ (all_52_3 = all_52_27)
% 177.86/28.33    (48)   ~ (all_52_9 = all_10_2)
% 177.86/28.33    (49)  op(e3, all_52_17) = all_52_16
% 177.86/28.33    (50)   ~ (all_52_13 = all_14_2)
% 177.86/28.33    (51)   ~ (e3 = e0)
% 177.86/28.33    (52)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.33    (53)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.33    (54)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.33    (55)   ~ (all_52_5 = all_52_29)
% 177.86/28.33    (56)  op(e1, e0) = all_52_23
% 177.86/28.33    (57)  all_56_12 = all_52_25
% 177.86/28.33    (58)  all_58_13 = all_52_27
% 177.86/28.33    (59)   ~ (all_4_1 = e1)
% 177.86/28.33    (60)  all_56_5 = all_10_2
% 177.86/28.33    (61)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.33    (62)   ~ (all_52_25 = e0)
% 177.86/28.33    (63)   ~ (all_52_9 = all_52_17)
% 177.86/28.33    (64)  all_58_6 = all_52_17
% 177.86/28.33    (65)   ~ (all_52_3 = all_52_7)
% 177.86/28.33    (66)   ~ (e1 = e0)
% 177.86/28.33    (67)  all_56_0 = all_4_2
% 177.86/28.33    (68)  all_58_11 = all_52_23
% 177.86/28.33    (69)   ~ (all_52_3 = all_52_19)
% 177.86/28.33    (70)   ~ (all_52_29 = all_14_2)
% 177.86/28.33    (71)  op(e3, all_52_25) = e3
% 177.86/28.33    (72)   ~ (all_52_19 = all_10_2)
% 177.86/28.33    (73)  all_58_15 = e0
% 177.86/28.33    (74)  all_58_2 = all_52_9
% 177.86/28.33    (75)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.33    (76)   ~ (all_52_29 = e0)
% 177.86/28.33    (77)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.33    (78)  op(e3, e1) = all_52_5
% 177.86/28.33    (79)  all_56_10 = all_14_2
% 177.86/28.33    (80)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.33    (81)  op(e1, e3) = all_52_17
% 177.86/28.33    (82)   ~ (all_52_25 = all_4_2)
% 177.86/28.33    (83)  op(e3, e0) = all_52_7
% 177.86/28.33    (84)  op(e3, e3) = all_4_2
% 177.86/28.33    (85)  all_56_8 = all_52_17
% 177.86/28.33    (86)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.33    (87)   ~ (all_52_25 = all_52_27)
% 177.86/28.33    (88)   ~ (all_52_7 = all_52_23)
% 177.86/28.33    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.33    (90)  all_58_9 = all_52_7
% 177.86/28.33    (91)  all_58_12 = all_52_25
% 177.86/28.33    (92)  op(e2, e3) = all_52_9
% 177.86/28.33    (93)  all_56_13 = all_52_27
% 177.86/28.33  
% 177.86/28.33  Begin of proof
% 177.86/28.33  | 
% 177.86/28.33  | BETA: splitting (39) gives:
% 177.86/28.33  | 
% 177.86/28.33  | Case 1:
% 177.86/28.33  | | 
% 177.86/28.33  | |   (94)  all_56_13 = e3
% 177.86/28.33  | | 
% 177.86/28.33  | | COMBINE_EQS: (93), (94) imply:
% 177.86/28.33  | |   (95)  all_52_27 = e3
% 177.86/28.33  | | 
% 177.86/28.33  | | SIMP: (95) implies:
% 177.86/28.33  | |   (96)  all_52_27 = e3
% 177.86/28.33  | | 
% 177.86/28.33  | | COMBINE_EQS: (58), (96) imply:
% 177.86/28.33  | |   (97)  all_58_13 = e3
% 177.86/28.33  | | 
% 177.86/28.33  | | REDUCE: (87), (96) imply:
% 177.86/28.33  | |   (98)   ~ (all_52_25 = e3)
% 177.86/28.33  | | 
% 177.86/28.33  | | REDUCE: (28), (96) imply:
% 177.86/28.33  | |   (99)   ~ (all_52_29 = e3)
% 177.86/28.33  | | 
% 177.86/28.33  | | SIMP: (99) implies:
% 177.86/28.33  | |   (100)   ~ (all_52_29 = e3)
% 177.86/28.33  | | 
% 177.86/28.33  | | REDUCE: (3), (96) imply:
% 177.86/28.33  | |   (101)   ~ (all_10_2 = e3)
% 177.86/28.33  | | 
% 177.86/28.33  | | SIMP: (101) implies:
% 177.86/28.33  | |   (102)   ~ (all_10_2 = e3)
% 177.86/28.33  | | 
% 177.86/28.33  | | REDUCE: (34), (96) imply:
% 177.86/28.33  | |   (103)  op(e2, e3) = e2
% 177.86/28.33  | | 
% 177.86/28.33  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14), (16),
% 177.86/28.33  | |            (17), (18), (19), (20), (21), (22), (23), (30), (31), (32), (33),
% 177.86/28.33  | |            (36), (40), (43), (44), (45), (48), (52), (53), (55), (57), (59),
% 177.86/28.33  | |            (60), (61), (62), (63), (64), (65), (67), (68), (70), (71), (72),
% 177.86/28.33  | |            (74), (76), (78), (80), (82), (83), (85), (86), (89), (90), (91),
% 177.86/28.33  | |            (92), (97), (98), (100), (102), (103) are inconsistent by
% 177.86/28.33  | |            sub-proof #885.
% 177.86/28.33  | | 
% 177.86/28.33  | Case 2:
% 177.86/28.33  | | 
% 177.86/28.33  | |   (104)   ~ (all_56_13 = e3)
% 177.86/28.33  | | 
% 177.86/28.33  | | REDUCE: (93), (104) imply:
% 177.86/28.33  | |   (105)   ~ (all_52_27 = e3)
% 177.86/28.33  | | 
% 177.86/28.33  | | REF_CLOSE: (5), (6), (9), (11), (15), (16), (21), (23), (24), (25), (26),
% 177.86/28.33  | |            (27), (29), (34), (35), (37), (38), (41), (42), (43), (45), (46),
% 177.86/28.33  | |            (47), (49), (50), (51), (53), (54), (56), (57), (58), (62), (64),
% 177.86/28.33  | |            (65), (66), (68), (69), (70), (71), (73), (75), (77), (78), (79),
% 177.86/28.33  | |            (81), (82), (84), (86), (87), (88), (89), (91), (105) are
% 177.86/28.33  | |            inconsistent by sub-proof #550.
% 177.86/28.33  | | 
% 177.86/28.33  | End of split
% 177.86/28.33  | 
% 177.86/28.33  End of proof
% 177.86/28.33  
% 177.86/28.33  Sub-proof #550 shows that the following formulas are inconsistent:
% 177.86/28.33  ----------------------------------------------------------------
% 177.86/28.33    (1)  all_56_3 = all_52_7
% 177.86/28.33    (2)  op(e3, e2) = all_52_3
% 177.86/28.33    (3)  all_56_11 = all_52_23
% 177.86/28.33    (4)  op(e1, all_14_2) = e2
% 177.86/28.33    (5)   ~ (all_52_27 = e3)
% 177.86/28.33    (6)  all_58_5 = all_52_13
% 177.86/28.33    (7)   ~ (all_52_25 = all_52_29)
% 177.86/28.33    (8)   ~ (all_52_5 = all_52_7)
% 177.86/28.33    (9)  all_58_7 = all_52_19
% 177.86/28.33    (10)   ~ (all_52_17 = all_52_25)
% 177.86/28.33    (11)  all_58_4 = all_52_5
% 177.86/28.33    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.33    (13)   ~ (e3 = e1)
% 177.86/28.33    (14)   ~ (all_52_17 = all_14_2)
% 177.86/28.33    (15)  op(e2, all_52_27) = e2
% 177.86/28.33    (16)   ~ (all_52_7 = e0)
% 177.86/28.33    (17)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.33    (18)  all_58_14 = all_52_29
% 177.86/28.33    (19)  op(e2, e1) = all_52_13
% 177.86/28.33    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.33    (21)  all_58_8 = all_14_2
% 177.86/28.33    (22)  op(e1, all_52_29) = e1
% 177.86/28.33    (23)   ~ (all_52_5 = all_14_2)
% 177.86/28.33    (24)   ~ (all_52_3 = all_52_27)
% 177.86/28.33    (25)  op(e3, all_52_17) = all_52_16
% 177.86/28.33    (26)   ~ (all_52_13 = all_14_2)
% 177.86/28.33    (27)   ~ (e3 = e0)
% 177.86/28.33    (28)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.33    (29)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.33    (30)  op(e1, e0) = all_52_23
% 177.86/28.33    (31)  all_56_12 = all_52_25
% 177.86/28.33    (32)  all_58_13 = all_52_27
% 177.86/28.33    (33)   ~ (all_52_25 = e0)
% 177.86/28.33    (34)  all_58_6 = all_52_17
% 177.86/28.33    (35)   ~ (all_52_3 = all_52_7)
% 177.86/28.33    (36)   ~ (e1 = e0)
% 177.86/28.33    (37)  all_58_11 = all_52_23
% 177.86/28.33    (38)   ~ (all_52_3 = all_52_19)
% 177.86/28.33    (39)   ~ (all_52_29 = all_14_2)
% 177.86/28.33    (40)  op(e3, all_52_25) = e3
% 177.86/28.33    (41)  all_58_15 = e0
% 177.86/28.33    (42)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.33    (43)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.33    (44)  op(e3, e1) = all_52_5
% 177.86/28.33    (45)  all_56_10 = all_14_2
% 177.86/28.33    (46)  op(e1, e3) = all_52_17
% 177.86/28.33    (47)   ~ (all_52_25 = all_4_2)
% 177.86/28.33    (48)  op(e3, e3) = all_4_2
% 177.86/28.33    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.33    (50)   ~ (all_52_25 = all_52_27)
% 177.86/28.33    (51)   ~ (all_52_7 = all_52_23)
% 177.86/28.33    (52)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.33    (53)  all_58_12 = all_52_25
% 177.86/28.33  
% 177.86/28.33  Begin of proof
% 177.86/28.33  | 
% 177.86/28.33  | BETA: splitting (20) gives:
% 177.86/28.33  | 
% 177.86/28.33  | Case 1:
% 177.86/28.33  | | 
% 177.86/28.33  | |   (54)  all_58_12 = e3
% 177.86/28.33  | | 
% 177.86/28.33  | | REF_CLOSE: (40), (47), (48), (49), (53), (54) are inconsistent by sub-proof
% 177.86/28.33  | |            #884.
% 177.86/28.33  | | 
% 177.86/28.33  | Case 2:
% 177.86/28.33  | | 
% 177.86/28.33  | |   (55)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.33  | | 
% 177.86/28.33  | | BETA: splitting (55) gives:
% 177.86/28.33  | | 
% 177.86/28.33  | | Case 1:
% 177.86/28.33  | | | 
% 177.86/28.33  | | |   (56)  all_58_13 = e3
% 177.86/28.33  | | | 
% 177.86/28.33  | | | REF_CLOSE: (5), (32), (56) are inconsistent by sub-proof #1026.
% 177.86/28.33  | | | 
% 177.86/28.33  | | Case 2:
% 177.86/28.33  | | | 
% 177.86/28.33  | | |   (57)  all_58_14 = e3 | all_58_15 = e3
% 177.86/28.33  | | | 
% 177.86/28.33  | | | BETA: splitting (57) gives:
% 177.86/28.33  | | | 
% 177.86/28.33  | | | Case 1:
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | |   (58)  all_58_14 = e3
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | COMBINE_EQS: (18), (58) imply:
% 177.86/28.33  | | | |   (59)  all_52_29 = e3
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | SIMP: (59) implies:
% 177.86/28.33  | | | |   (60)  all_52_29 = e3
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | REDUCE: (7), (60) imply:
% 177.86/28.33  | | | |   (61)   ~ (all_52_25 = e3)
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | REDUCE: (39), (60) imply:
% 177.86/28.33  | | | |   (62)   ~ (all_14_2 = e3)
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | SIMP: (62) implies:
% 177.86/28.33  | | | |   (63)   ~ (all_14_2 = e3)
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | REDUCE: (22), (60) imply:
% 177.86/28.33  | | | |   (64)  op(e1, e3) = e1
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | GROUND_INST: instantiating (49) with all_52_17, e1, e3, e1, simplifying
% 177.86/28.33  | | | |              with (46), (64) gives:
% 177.86/28.33  | | | |   (65)  all_52_17 = e1
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | COMBINE_EQS: (34), (65) imply:
% 177.86/28.33  | | | |   (66)  all_58_6 = e1
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | REDUCE: (10), (65) imply:
% 177.86/28.33  | | | |   (67)   ~ (all_52_25 = e1)
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | SIMP: (67) implies:
% 177.86/28.33  | | | |   (68)   ~ (all_52_25 = e1)
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | REDUCE: (14), (65) imply:
% 177.86/28.33  | | | |   (69)   ~ (all_14_2 = e1)
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | SIMP: (69) implies:
% 177.86/28.33  | | | |   (70)   ~ (all_14_2 = e1)
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | REDUCE: (25), (65) imply:
% 177.86/28.33  | | | |   (71)  op(e3, e1) = all_52_16
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | BETA: splitting (28) gives:
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | Case 1:
% 177.86/28.33  | | | | | 
% 177.86/28.33  | | | | |   (72)  all_56_12 = e3
% 177.86/28.33  | | | | | 
% 177.86/28.33  | | | | | REF_CLOSE: (31), (61), (72) are inconsistent by sub-proof #1040.
% 177.86/28.33  | | | | | 
% 177.86/28.33  | | | | Case 2:
% 177.86/28.33  | | | | | 
% 177.86/28.33  | | | | |   (73)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.33  | | | | | 
% 177.86/28.33  | | | | | BETA: splitting (42) gives:
% 177.86/28.33  | | | | | 
% 177.86/28.33  | | | | | Case 1:
% 177.86/28.33  | | | | | | 
% 177.86/28.33  | | | | | |   (74)  all_58_12 = e1
% 177.86/28.33  | | | | | | 
% 177.86/28.33  | | | | | | REF_CLOSE: (53), (68), (74) are inconsistent by sub-proof #883.
% 177.86/28.33  | | | | | | 
% 177.86/28.33  | | | | | Case 2:
% 177.86/28.33  | | | | | | 
% 177.86/28.33  | | | | | |   (75)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.33  | | | | | | 
% 177.86/28.33  | | | | | | BETA: splitting (75) gives:
% 177.86/28.33  | | | | | | 
% 177.86/28.33  | | | | | | Case 1:
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | |   (76)  all_58_13 = e1
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | | COMBINE_EQS: (32), (76) imply:
% 177.86/28.33  | | | | | | |   (77)  all_52_27 = e1
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | | SIMP: (77) implies:
% 177.86/28.33  | | | | | | |   (78)  all_52_27 = e1
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | | REDUCE: (24), (78) imply:
% 177.86/28.33  | | | | | | |   (79)   ~ (all_52_3 = e1)
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | | REDUCE: (15), (78) imply:
% 177.86/28.33  | | | | | | |   (80)  op(e2, e1) = e2
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | | BETA: splitting (73) gives:
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | |   (81)  all_56_12 = e2
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | COMBINE_EQS: (31), (81) imply:
% 177.86/28.33  | | | | | | | |   (82)  all_52_25 = e2
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | SIMP: (82) implies:
% 177.86/28.33  | | | | | | | |   (83)  all_52_25 = e2
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REDUCE: (68), (83) imply:
% 177.86/28.33  | | | | | | | |   (84)   ~ (e2 = e1)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REDUCE: (40), (83) imply:
% 177.86/28.33  | | | | | | | |   (85)  op(e3, e2) = e3
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | GROUND_INST: instantiating (49) with all_52_13, e2, e1, e2,
% 177.86/28.33  | | | | | | | |              simplifying with (19), (80) gives:
% 177.86/28.33  | | | | | | | |   (86)  all_52_13 = e2
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | GROUND_INST: instantiating (49) with all_52_5, all_52_16, e1,
% 177.86/28.33  | | | | | | | |              e3, simplifying with (44), (71) gives:
% 177.86/28.33  | | | | | | | |   (87)  all_52_5 = all_52_16
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | GROUND_INST: instantiating (49) with all_52_3, e3, e2, e3,
% 177.86/28.33  | | | | | | | |              simplifying with (2), (85) gives:
% 177.86/28.33  | | | | | | | |   (88)  all_52_3 = e3
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | COMBINE_EQS: (6), (86) imply:
% 177.86/28.33  | | | | | | | |   (89)  all_58_5 = e2
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | COMBINE_EQS: (11), (87) imply:
% 177.86/28.33  | | | | | | | |   (90)  all_58_4 = all_52_16
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REDUCE: (35), (88) imply:
% 177.86/28.33  | | | | | | | |   (91)   ~ (all_52_7 = e3)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | SIMP: (91) implies:
% 177.86/28.33  | | | | | | | |   (92)   ~ (all_52_7 = e3)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REDUCE: (38), (88) imply:
% 177.86/28.33  | | | | | | | |   (93)   ~ (all_52_19 = e3)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | SIMP: (93) implies:
% 177.86/28.33  | | | | | | | |   (94)   ~ (all_52_19 = e3)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REDUCE: (8), (87) imply:
% 177.86/28.33  | | | | | | | |   (95)   ~ (all_52_7 = all_52_16)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | SIMP: (95) implies:
% 177.86/28.33  | | | | | | | |   (96)   ~ (all_52_7 = all_52_16)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REDUCE: (23), (87) imply:
% 177.86/28.33  | | | | | | | |   (97)   ~ (all_52_16 = all_14_2)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REDUCE: (26), (86) imply:
% 177.86/28.33  | | | | | | | |   (98)   ~ (all_14_2 = e2)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | SIMP: (98) implies:
% 177.86/28.33  | | | | | | | |   (99)   ~ (all_14_2 = e2)
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | BETA: splitting (29) gives:
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | 
% 177.86/28.33  | | | | | | | | |   (100)  all_56_10 = e3
% 177.86/28.33  | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | REF_CLOSE: (45), (63), (100) are inconsistent by sub-proof
% 177.86/28.33  | | | | | | | | |            #552.
% 177.86/28.33  | | | | | | | | | 
% 177.86/28.33  | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | 
% 177.86/28.33  | | | | | | | | |   (101)   ~ (all_56_10 = e3)
% 177.86/28.33  | | | | | | | | |   (102)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.33  | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | BETA: splitting (12) gives:
% 177.86/28.33  | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | |   (103)  all_58_6 = e3
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | COMBINE_EQS: (66), (103) imply:
% 177.86/28.33  | | | | | | | | | |   (104)  e3 = e1
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | REDUCE: (13), (104) imply:
% 177.86/28.33  | | | | | | | | | |   (105)  $false
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | CLOSE: (105) is inconsistent.
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | |   (106)   ~ (all_58_6 = e3)
% 177.86/28.33  | | | | | | | | | |   (107)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | REDUCE: (66), (106) imply:
% 177.86/28.33  | | | | | | | | | |   (108)   ~ (e3 = e1)
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | BETA: splitting (107) gives:
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | |   (109)  all_58_7 = e3
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | COMBINE_EQS: (9), (109) imply:
% 177.86/28.33  | | | | | | | | | | |   (110)  all_52_19 = e3
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | REDUCE: (94), (110) imply:
% 177.86/28.33  | | | | | | | | | | |   (111)  $false
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | CLOSE: (111) is inconsistent.
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | |   (112)  all_58_8 = e3 | all_58_11 = e3
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | BETA: splitting (102) gives:
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | |   (113)  all_56_10 = e2
% 177.86/28.33  | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | REF_CLOSE: (45), (99), (113) are inconsistent by sub-proof
% 177.86/28.33  | | | | | | | | | | | |            #691.
% 177.86/28.33  | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | |   (114)  all_56_10 = e1 | all_56_10 = e0
% 177.86/28.33  | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | BETA: splitting (17) gives:
% 177.86/28.33  | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | |   (115)  all_58_4 = e1
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | COMBINE_EQS: (90), (115) imply:
% 177.86/28.33  | | | | | | | | | | | | |   (116)  all_52_16 = e1
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | REDUCE: (96), (116) imply:
% 177.86/28.33  | | | | | | | | | | | | |   (117)   ~ (all_52_7 = e1)
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | BETA: splitting (52) gives:
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | |   (118)  all_56_3 = e3
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | COMBINE_EQS: (1), (118) imply:
% 177.86/28.33  | | | | | | | | | | | | | |   (119)  all_52_7 = e3
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | REDUCE: (92), (119) imply:
% 177.86/28.33  | | | | | | | | | | | | | |   (120)  $false
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | CLOSE: (120) is inconsistent.
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | |   (121)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | |   (122)  all_56_3 = e2
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | COMBINE_EQS: (1), (122) imply:
% 177.86/28.33  | | | | | | | | | | | | | | |   (123)  all_52_7 = e2
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | REDUCE: (51), (123) imply:
% 177.86/28.33  | | | | | | | | | | | | | | |   (124)   ~ (all_52_23 = e2)
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | SIMP: (124) implies:
% 177.86/28.33  | | | | | | | | | | | | | | |   (125)   ~ (all_52_23 = e2)
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | |   (126)  all_56_11 = e3
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (126) imply:
% 177.86/28.33  | | | | | | | | | | | | | | | |   (127)  all_52_23 = e3
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | SIMP: (127) implies:
% 177.86/28.33  | | | | | | | | | | | | | | | |   (128)  all_52_23 = e3
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | REDUCE: (125), (128) imply:
% 177.86/28.33  | | | | | | | | | | | | | | | |   (129)   ~ (e3 = e2)
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | REDUCE: (30), (128) imply:
% 177.86/28.33  | | | | | | | | | | | | | | | |   (130)  op(e1, e0) = e3
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | |   (131)  all_56_10 = e1
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (70), (131) are inconsistent by sub-proof
% 177.86/28.33  | | | | | | | | | | | | | | | | |            #740.
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | |   (132)  all_56_10 = e0
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (132) imply:
% 177.86/28.33  | | | | | | | | | | | | | | | | |   (133)  all_14_2 = e0
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | | SIMP: (133) implies:
% 177.86/28.33  | | | | | | | | | | | | | | | | |   (134)  all_14_2 = e0
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | | REDUCE: (4), (134) imply:
% 177.86/28.33  | | | | | | | | | | | | | | | | |   (135)  op(e1, e0) = e2
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (129), (130), (135) are inconsistent by
% 177.86/28.33  | | | | | | | | | | | | | | | | |            sub-proof #551.
% 177.86/28.33  | | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | |   (136)   ~ (all_56_11 = e3)
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | REDUCE: (3), (136) imply:
% 177.86/28.33  | | | | | | | | | | | | | | | |   (137)   ~ (all_52_23 = e3)
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | | REF_CLOSE: (21), (37), (63), (112), (137) are inconsistent by
% 177.86/28.33  | | | | | | | | | | | | | | | |            sub-proof #997.
% 177.86/28.33  | | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | |   (138)  all_56_3 = e1 | all_56_3 = e0
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (117), (138) are inconsistent by
% 177.86/28.33  | | | | | | | | | | | | | | |            sub-proof #1037.
% 177.86/28.33  | | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | |   (139)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | BETA: splitting (139) gives:
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | Case 1:
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | |   (140)  all_58_5 = e1
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | REF_CLOSE: (84), (89), (140) are inconsistent by sub-proof
% 177.86/28.33  | | | | | | | | | | | | | |            #672.
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | |   (141)  all_58_8 = e1 | all_58_14 = e1
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | | REF_CLOSE: (13), (21), (58), (70), (141) are inconsistent by
% 177.86/28.33  | | | | | | | | | | | | | |            sub-proof #638.
% 177.86/28.33  | | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | | 
% 177.86/28.33  | | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | | 
% 177.86/28.33  | | | | | | | | End of split
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | Case 2:
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | |   (142)  all_56_12 = e1 | all_56_12 = e0
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | | REF_CLOSE: (31), (33), (68), (142) are inconsistent by sub-proof
% 177.86/28.33  | | | | | | | |            #1029.
% 177.86/28.33  | | | | | | | | 
% 177.86/28.33  | | | | | | | End of split
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | Case 2:
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | |   (143)  all_58_14 = e1 | all_58_15 = e1
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | | REF_CLOSE: (13), (36), (41), (58), (143) are inconsistent by
% 177.86/28.33  | | | | | | |            sub-proof #880.
% 177.86/28.33  | | | | | | | 
% 177.86/28.33  | | | | | | End of split
% 177.86/28.33  | | | | | | 
% 177.86/28.33  | | | | | End of split
% 177.86/28.33  | | | | | 
% 177.86/28.33  | | | | End of split
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | Case 2:
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | |   (144)  all_58_15 = e3
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | | REF_CLOSE: (27), (41), (144) are inconsistent by sub-proof #1010.
% 177.86/28.33  | | | | 
% 177.86/28.33  | | | End of split
% 177.86/28.33  | | | 
% 177.86/28.33  | | End of split
% 177.86/28.33  | | 
% 177.86/28.33  | End of split
% 177.86/28.33  | 
% 177.86/28.33  End of proof
% 177.86/28.33  
% 177.86/28.33  Sub-proof #551 shows that the following formulas are inconsistent:
% 177.86/28.33  ----------------------------------------------------------------
% 177.86/28.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.33    (2)  op(e1, e0) = e3
% 177.86/28.33    (3)  op(e1, e0) = e2
% 177.86/28.33    (4)   ~ (e3 = e2)
% 177.86/28.33  
% 177.86/28.33  Begin of proof
% 177.86/28.33  | 
% 177.86/28.33  | GROUND_INST: instantiating (1) with e2, e3, e0, e1, simplifying with (2), (3)
% 177.86/28.33  |              gives:
% 177.86/28.33  |   (5)  e3 = e2
% 177.86/28.33  | 
% 177.86/28.33  | REDUCE: (4), (5) imply:
% 177.86/28.33  |   (6)  $false
% 177.86/28.33  | 
% 177.86/28.33  | CLOSE: (6) is inconsistent.
% 177.86/28.33  | 
% 177.86/28.33  End of proof
% 177.86/28.33  
% 177.86/28.33  Sub-proof #552 shows that the following formulas are inconsistent:
% 177.86/28.33  ----------------------------------------------------------------
% 177.86/28.33    (1)  all_56_10 = all_14_2
% 177.86/28.33    (2)  all_56_10 = e3
% 177.86/28.33    (3)   ~ (all_14_2 = e3)
% 177.86/28.33  
% 177.86/28.33  Begin of proof
% 177.86/28.33  | 
% 177.86/28.33  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.33  |   (4)  all_14_2 = e3
% 177.86/28.33  | 
% 177.86/28.33  | SIMP: (4) implies:
% 177.86/28.33  |   (5)  all_14_2 = e3
% 177.86/28.33  | 
% 177.86/28.33  | REDUCE: (3), (5) imply:
% 177.86/28.33  |   (6)  $false
% 177.86/28.33  | 
% 177.86/28.33  | CLOSE: (6) is inconsistent.
% 177.86/28.33  | 
% 177.86/28.33  End of proof
% 177.86/28.33  
% 177.86/28.33  Sub-proof #553 shows that the following formulas are inconsistent:
% 177.86/28.33  ----------------------------------------------------------------
% 177.86/28.33    (1)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 177.86/28.33    (2)  all_52_20 = e2
% 177.86/28.33    (3)   ~ (e2 = e1)
% 177.86/28.33  
% 177.86/28.33  Begin of proof
% 177.86/28.33  | 
% 177.86/28.33  | ALPHA: (1) implies:
% 177.86/28.33  |   (4)  all_52_20 = e1
% 177.86/28.33  | 
% 177.86/28.33  | COMBINE_EQS: (2), (4) imply:
% 177.86/28.33  |   (5)  e2 = e1
% 177.86/28.33  | 
% 177.86/28.33  | SIMP: (5) implies:
% 177.86/28.33  |   (6)  e2 = e1
% 177.86/28.33  | 
% 177.86/28.33  | REDUCE: (3), (6) imply:
% 177.86/28.33  |   (7)  $false
% 177.86/28.33  | 
% 177.86/28.33  | CLOSE: (7) is inconsistent.
% 177.86/28.33  | 
% 177.86/28.33  End of proof
% 177.86/28.33  
% 177.86/28.33  Sub-proof #554 shows that the following formulas are inconsistent:
% 177.86/28.33  ----------------------------------------------------------------
% 177.86/28.33    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.33    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.33    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.86/28.33    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.33    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.33    (6)   ~ (all_52_27 = all_10_2)
% 177.86/28.33    (7)   ~ (all_52_17 = all_52_23)
% 177.86/28.33    (8)   ~ (all_6_0 = e3)
% 177.86/28.33    (9)  op(e2, all_10_2) = all_10_1
% 177.86/28.33    (10)   ~ (all_52_13 = all_52_29)
% 177.86/28.33    (11)  all_56_3 = all_52_7
% 177.86/28.33    (12)  op(e3, e2) = all_52_3
% 177.86/28.33    (13)   ~ (all_52_9 = all_52_25)
% 177.86/28.33    (14)  op(e3, all_52_25) = all_52_24
% 177.86/28.33    (15)   ~ (all_52_19 = all_52_23)
% 177.86/28.33    (16)  all_56_11 = all_52_23
% 177.86/28.33    (17)  op(e1, e2) = all_52_19
% 177.86/28.33    (18)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.86/28.33    (19)  op(e3, all_52_9) = all_52_8
% 177.86/28.33    (20)   ~ (all_52_3 = all_10_2)
% 177.86/28.33    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.33    (22)  all_58_5 = all_52_13
% 177.86/28.33    (23)   ~ (all_52_25 = all_52_29)
% 177.86/28.33    (24)  all_56_15 = all_6_2
% 177.86/28.33    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.33    (26)  op(e2, e0) = all_52_15
% 177.86/28.33    (27)  op(all_14_1, all_14_2) = all_14_0
% 177.86/28.33    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 177.86/28.33    (29)  all_58_3 = all_10_2
% 177.86/28.33    (30)  all_56_9 = all_52_19
% 177.86/28.33    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.33    (32)  all_58_15 = all_6_2
% 177.86/28.33    (33)   ~ (all_52_9 = all_4_2)
% 177.86/28.33    (34)   ~ (all_52_5 = all_52_7)
% 177.86/28.33    (35)  all_58_10 = all_52_15
% 177.86/28.33    (36)   ~ (all_52_5 = all_4_2)
% 177.86/28.33    (37)  all_58_7 = all_52_19
% 177.86/28.33    (38)  all_56_4 = all_52_9
% 177.86/28.34    (39)   ~ (all_52_15 = all_6_2)
% 177.86/28.34    (40)   ~ (all_52_17 = all_52_25)
% 177.86/28.34    (41)  op(e0, e1) = all_52_29
% 177.86/28.34    (42)  all_58_4 = all_52_5
% 177.86/28.34    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 177.86/28.34    (44)   ~ (e3 = e1)
% 177.86/28.34    (45)  all_34_1 = all_4_1
% 177.86/28.34    (46)   ~ (all_52_27 = all_52_29)
% 177.86/28.34    (47)   ~ (all_52_17 = all_14_2)
% 177.86/28.34    (48)  op(e3, all_4_2) = all_4_1
% 177.86/28.34    (49)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.34    (50)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 177.86/28.34    (51)   ~ (all_52_7 = all_4_2)
% 177.86/28.34    (52)  all_58_1 = all_52_3
% 177.86/28.34    (53)  all_58_0 = all_4_2
% 177.86/28.34    (54)  op(e1, all_52_13) = all_52_12
% 177.86/28.34    (55)  op(all_4_1, all_4_2) = e1
% 177.86/28.34    (56)  op(e0, e0) = all_6_2
% 177.86/28.34    (57)  op(e1, all_52_29) = all_52_28
% 177.86/28.34    (58)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.34    (59)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 177.86/28.34    (60)   ~ (all_4_1 = e2)
% 177.86/28.34    (61)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 177.86/28.34    (62)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 177.86/28.34    (63)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 177.86/28.34    (64)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 177.86/28.34    (65)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 177.86/28.34    (66)   ~ (all_14_1 = e3)
% 177.86/28.34    (67)  all_58_14 = all_52_29
% 177.86/28.34    (68)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.34    (69)   ~ (all_52_3 = all_52_5)
% 177.86/28.34    (70)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.34    (71)  op(e2, e1) = all_52_13
% 177.86/28.34    (72)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.34    (73)  all_58_8 = all_14_2
% 177.86/28.34    (74)  all_56_1 = all_52_3
% 177.86/28.34    (75)  op(e0, e2) = all_52_27
% 177.86/28.34    (76)  all_56_14 = all_52_29
% 177.86/28.34    (77)   ~ (all_14_0 = e3)
% 177.86/28.34    (78)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 177.86/28.34    (79)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 177.86/28.34    (80)   ~ (all_52_5 = all_14_2)
% 177.86/28.34    (81)   ~ (all_52_3 = all_52_27)
% 177.86/28.34    (82)   ~ (all_52_3 = all_4_2)
% 177.86/28.34    (83)  op(all_6_1, all_6_2) = all_6_0
% 177.86/28.34    (84)  op(e0, e3) = all_52_25
% 177.86/28.34    (85)  op(e0, all_6_2) = all_6_1
% 177.86/28.34    (86)  all_52_0 = all_4_1
% 177.86/28.34    (87)   ~ (all_52_9 = all_10_2)
% 177.86/28.34    (88)  op(e3, all_52_17) = all_52_16
% 177.86/28.34    (89)  all_52_10 = all_10_1
% 177.86/28.34    (90)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.34    (91)   ~ (all_52_13 = all_14_2)
% 177.86/28.34    (92)   ~ (e3 = e0)
% 177.86/28.34    (93)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.34    (94)   ~ (all_52_9 = all_52_13)
% 177.86/28.34    (95)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 177.86/28.34    (96)  op(e0, all_52_23) = all_52_22
% 177.86/28.34    (97)   ~ (all_52_15 = all_52_23)
% 177.86/28.34    (98)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 177.86/28.34    (99)  op(all_10_1, all_10_2) = all_10_0
% 177.86/28.34    (100)   ~ (all_52_5 = all_52_29)
% 177.86/28.34    (101)  all_56_2 = all_52_5
% 177.86/28.34    (102)  op(e1, e0) = all_52_23
% 177.86/28.34    (103)  all_56_12 = all_52_25
% 177.86/28.34    (104)  all_58_13 = all_52_27
% 177.86/28.34    (105)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.34    (106)  all_56_5 = all_10_2
% 177.86/28.34    (107)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 177.86/28.34    (108)   ~ (all_52_9 = all_52_17)
% 177.86/28.34    (109)   ~ (all_14_0 = e2)
% 177.86/28.34    (110)  all_58_6 = all_52_17
% 177.86/28.34    (111)   ~ (all_52_3 = all_52_7)
% 177.86/28.34    (112)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 177.86/28.34    (113)  op(e2, all_52_19) = all_52_18
% 177.86/28.34    (114)   ~ (e1 = e0)
% 177.86/28.34    (115)  all_56_0 = all_4_2
% 177.86/28.34    (116)  all_58_11 = all_52_23
% 177.86/28.34    (117)   ~ (all_52_3 = all_52_19)
% 177.86/28.34    (118)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 177.86/28.34    (119)   ~ (all_52_7 = all_52_15)
% 177.86/28.34    (120)  op(e0, all_52_15) = all_52_14
% 177.86/28.34    (121)   ~ (all_52_29 = all_14_2)
% 177.86/28.34    (122)   ~ (all_52_19 = all_10_2)
% 177.86/28.34    (123)   ~ (all_52_23 = all_6_2)
% 177.86/28.34    (124)   ~ (all_6_0 = e2)
% 177.86/28.34    (125)   ~ (all_52_29 = all_6_2)
% 177.86/28.34    (126)  all_58_2 = all_52_9
% 177.86/28.34    (127)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 177.86/28.34    (128)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 177.86/28.34    (129)  op(e3, e1) = all_52_5
% 177.86/28.34    (130)  all_56_10 = all_14_2
% 177.86/28.34    (131)   ~ (all_52_25 = all_6_2)
% 177.86/28.34    (132)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 177.86/28.34    (133)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.34    (134)  op(e1, e1) = all_14_2
% 177.86/28.34    (135)  op(e1, e3) = all_52_17
% 177.86/28.34    (136)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 177.86/28.34    (137)   ~ (all_52_25 = all_4_2)
% 177.86/28.34    (138)  op(e3, e0) = all_52_7
% 177.86/28.34    (139)  op(e3, e3) = all_4_2
% 177.86/28.34    (140)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 177.86/28.34             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 177.86/28.34    (141)   ~ (all_10_1 = e3)
% 177.86/28.34    (142)  all_56_8 = all_52_17
% 177.86/28.34    (143)   ~ (all_52_17 = all_4_2)
% 177.86/28.34    (144)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.34             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.34    (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.86/28.34           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 177.86/28.34           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 177.86/28.34           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 177.86/28.34    (146)   ~ (all_52_25 = all_52_27)
% 177.86/28.34    (147)  all_34_2 = all_4_2
% 177.86/28.34    (148)   ~ (all_52_27 = all_6_2)
% 177.86/28.34    (149)   ~ (all_52_7 = all_6_2)
% 177.86/28.34    (150)   ~ (all_10_0 = e3)
% 177.86/28.34    (151)   ~ (all_52_15 = all_10_2)
% 177.86/28.34    (152)   ~ (all_52_19 = all_52_27)
% 177.86/28.34    (153)  all_56_7 = all_52_15
% 177.86/28.34    (154)   ~ (all_52_7 = all_52_23)
% 177.86/28.34    (155)   ~ (all_52_13 = all_10_2)
% 177.86/28.34    (156)   ~ (all_6_0 = e1)
% 177.86/28.34    (157)  op(e2, all_52_27) = all_52_26
% 177.86/28.34    (158)  all_52_20 = all_14_1
% 177.86/28.34    (159)   ~ (all_52_17 = all_52_19)
% 177.86/28.34    (160)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.34    (161)  all_52_30 = all_6_1
% 177.86/28.34    (162)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.34    (163)  op(e1, all_14_2) = all_14_1
% 177.86/28.34    (164)  all_58_9 = all_52_7
% 177.86/28.34    (165)   ~ (e2 = e0)
% 177.86/28.34    (166)  all_58_12 = all_52_25
% 177.86/28.34    (167)   ~ (all_10_0 = e1)
% 177.86/28.34    (168)  all_56_6 = all_52_13
% 177.86/28.34    (169)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 177.86/28.34    (170)   ~ (all_52_9 = all_52_15)
% 177.86/28.34    (171)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 177.86/28.34    (172)   ~ (e3 = e2)
% 177.86/28.34    (173)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.34    (174)   ~ (all_52_19 = all_14_2)
% 177.86/28.34    (175)  op(e2, e3) = all_52_9
% 177.86/28.34    (176)  all_56_13 = all_52_27
% 177.86/28.34  
% 177.86/28.34  Begin of proof
% 177.86/28.34  | 
% 177.86/28.34  | BETA: splitting (140) gives:
% 177.86/28.34  | 
% 177.86/28.34  | Case 1:
% 177.86/28.34  | | 
% 177.86/28.34  | |   (177)  all_58_15 = e0
% 177.86/28.34  | | 
% 177.86/28.34  | | COMBINE_EQS: (32), (177) imply:
% 177.86/28.34  | |   (178)  all_6_2 = e0
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (149), (178) imply:
% 177.86/28.34  | |   (179)   ~ (all_52_7 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (39), (178) imply:
% 177.86/28.34  | |   (180)   ~ (all_52_15 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (123), (178) imply:
% 177.86/28.34  | |   (181)   ~ (all_52_23 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (131), (178) imply:
% 177.86/28.34  | |   (182)   ~ (all_52_25 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (148), (178) imply:
% 177.86/28.34  | |   (183)   ~ (all_52_27 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (125), (178) imply:
% 177.86/28.34  | |   (184)   ~ (all_52_29 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (83), (178) imply:
% 177.86/28.34  | |   (185)  op(all_6_1, e0) = all_6_0
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (85), (178) imply:
% 177.86/28.34  | |   (186)  op(e0, e0) = all_6_1
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (56), (178) imply:
% 177.86/28.34  | |   (187)  op(e0, e0) = e0
% 177.86/28.34  | | 
% 177.86/28.34  | | GROUND_INST: instantiating (144) with e0, all_6_1, e0, e0, simplifying with
% 177.86/28.34  | |              (186), (187) gives:
% 177.86/28.34  | |   (188)  all_6_1 = e0
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (185), (188) imply:
% 177.86/28.34  | |   (189)  op(e0, e0) = all_6_0
% 177.86/28.34  | | 
% 177.86/28.34  | | GROUND_INST: instantiating (144) with e0, all_6_0, e0, e0, simplifying with
% 177.86/28.34  | |              (187), (189) gives:
% 177.86/28.34  | |   (190)  all_6_0 = e0
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (8), (190) imply:
% 177.86/28.34  | |   (191)   ~ (e3 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (124), (190) imply:
% 177.86/28.34  | |   (192)   ~ (e2 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (156), (190) imply:
% 177.86/28.34  | |   (193)   ~ (e1 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | BETA: splitting (145) gives:
% 177.86/28.34  | | 
% 177.86/28.34  | | Case 1:
% 177.86/28.34  | | | 
% 177.86/28.34  | | |   (194)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.86/28.34  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.86/28.34  | | |            e0)
% 177.86/28.34  | | | 
% 177.86/28.34  | | | BETA: splitting (194) gives:
% 177.86/28.34  | | | 
% 177.86/28.34  | | | Case 1:
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | |   (195)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | REF_CLOSE: (44), (48), (55), (86), (144), (195) are inconsistent by
% 177.86/28.34  | | | |            sub-proof #600.
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | Case 2:
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | |   (196)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.86/28.34  | | | |          e0
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | ALPHA: (196) implies:
% 177.86/28.34  | | | |   (197)  all_52_14 = e0
% 177.86/28.34  | | | |   (198)  all_52_12 = e1
% 177.86/28.34  | | | |   (199)  all_52_10 = e2
% 177.86/28.34  | | | |   (200)  all_52_8 = e3
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | COMBINE_EQS: (89), (199) imply:
% 177.86/28.34  | | | |   (201)  all_10_1 = e2
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | SIMP: (201) implies:
% 177.86/28.34  | | | |   (202)  all_10_1 = e2
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | REF_CLOSE: (6), (7), (9), (10), (11), (12), (13), (17), (18), (19),
% 177.86/28.34  | | | |            (20), (22), (23), (25), (28), (29), (31), (33), (35), (37),
% 177.86/28.34  | | | |            (38), (40), (41), (43), (44), (45), (48), (50), (51), (52),
% 177.86/28.34  | | | |            (53), (54), (55), (58), (60), (63), (64), (67), (68), (70),
% 177.86/28.34  | | | |            (72), (73), (74), (75), (81), (82), (84), (90), (92), (94),
% 177.86/28.34  | | | |            (95), (98), (99), (102), (103), (104), (110), (111), (112),
% 177.86/28.34  | | | |            (114), (115), (116), (117), (119), (120), (122), (126),
% 177.86/28.34  | | | |            (127), (130), (135), (136), (137), (138), (139), (143),
% 177.86/28.34  | | | |            (144), (146), (147), (150), (153), (154), (157), (160),
% 177.86/28.34  | | | |            (162), (164), (165), (166), (167), (168), (169), (170),
% 177.86/28.34  | | | |            (174), (175), (176), (177), (180), (182), (183), (184),
% 177.86/28.34  | | | |            (197), (198), (200), (202) are inconsistent by sub-proof
% 177.86/28.34  | | | |            #581.
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | End of split
% 177.86/28.34  | | | 
% 177.86/28.34  | | Case 2:
% 177.86/28.34  | | | 
% 177.86/28.34  | | |   (203)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.86/28.34  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.86/28.34  | | |            all_52_30 = e0)
% 177.86/28.34  | | | 
% 177.86/28.34  | | | REF_CLOSE: (1), (3), (4), (7), (10), (11), (12), (13), (14), (15), (16),
% 177.86/28.34  | | |            (17), (18), (20), (22), (23), (25), (27), (28), (29), (30),
% 177.86/28.34  | | |            (31), (33), (34), (35), (37), (40), (41), (42), (43), (44),
% 177.86/28.34  | | |            (45), (46), (48), (50), (51), (52), (53), (55), (57), (58),
% 177.86/28.34  | | |            (59), (60), (61), (63), (67), (68), (70), (72), (73), (74),
% 177.86/28.34  | | |            (75), (76), (77), (79), (80), (81), (82), (84), (87), (88),
% 177.86/28.34  | | |            (90), (92), (93), (95), (96), (97), (98), (100), (102), (103),
% 177.86/28.34  | | |            (104), (105), (106), (108), (109), (110), (111), (113), (114),
% 177.86/28.34  | | |            (115), (116), (117), (121), (122), (126), (127), (128), (129),
% 177.86/28.34  | | |            (130), (132), (133), (135), (136), (137), (138), (139), (142),
% 177.86/28.34  | | |            (143), (144), (146), (147), (152), (153), (154), (157), (158),
% 177.86/28.34  | | |            (160), (162), (163), (164), (165), (166), (169), (170), (172),
% 177.86/28.34  | | |            (174), (175), (176), (177), (179), (181), (182), (183), (184),
% 177.86/28.34  | | |            (203) are inconsistent by sub-proof #575.
% 177.86/28.34  | | | 
% 177.86/28.34  | | End of split
% 177.86/28.34  | | 
% 177.86/28.34  | Case 2:
% 177.86/28.34  | | 
% 177.86/28.34  | |   (204)   ~ (all_58_15 = e0)
% 177.86/28.34  | |   (205)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 177.86/28.34  | |            | all_58_13 = e0 | all_58_14 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | ALPHA: (205) implies:
% 177.86/28.34  | |   (206)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.34  | |   (207)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 177.86/28.34  | | 
% 177.86/28.34  | | REDUCE: (32), (204) imply:
% 177.86/28.34  | |   (208)   ~ (all_6_2 = e0)
% 177.86/28.34  | | 
% 177.86/28.34  | | BETA: splitting (145) gives:
% 177.86/28.34  | | 
% 177.86/28.34  | | Case 1:
% 177.86/28.34  | | | 
% 177.86/28.34  | | |   (209)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 177.86/28.34  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 177.86/28.34  | | |            e0)
% 177.86/28.34  | | | 
% 177.86/28.34  | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (15),
% 177.86/28.34  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (29),
% 177.86/28.34  | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 177.86/28.34  | | |            (40), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 177.86/28.34  | | |            (51), (52), (53), (54), (55), (57), (58), (59), (60), (62),
% 177.86/28.34  | | |            (63), (64), (66), (67), (68), (69), (70), (71), (72), (73),
% 177.86/28.34  | | |            (74), (79), (81), (82), (84), (85), (86), (88), (89), (91),
% 177.86/28.34  | | |            (92), (94), (96), (97), (98), (99), (100), (101), (104), (105),
% 177.86/28.34  | | |            (108), (110), (111), (112), (113), (114), (115), (116), (117),
% 177.86/28.34  | | |            (119), (120), (121), (122), (123), (125), (126), (128), (129),
% 177.86/28.34  | | |            (130), (131), (134), (135), (137), (138), (139), (143), (144),
% 177.86/28.34  | | |            (146), (147), (148), (149), (150), (154), (157), (159), (160),
% 177.86/28.34  | | |            (162), (163), (164), (166), (167), (168), (169), (170), (171),
% 177.86/28.34  | | |            (173), (174), (175), (176), (207), (208), (209) are
% 177.86/28.34  | | |            inconsistent by sub-proof #570.
% 177.86/28.34  | | | 
% 177.86/28.34  | | Case 2:
% 177.86/28.34  | | | 
% 177.86/28.34  | | |   (210)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.86/28.34  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 177.86/28.34  | | |            all_52_30 = e0)
% 177.86/28.34  | | | 
% 177.86/28.34  | | | BETA: splitting (210) gives:
% 177.86/28.34  | | | 
% 177.86/28.34  | | | Case 1:
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | |   (211)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 177.86/28.34  | | | |          e0
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | ALPHA: (211) implies:
% 177.86/28.34  | | | |   (212)  all_52_22 = e0
% 177.86/28.34  | | | |   (213)  all_52_20 = e1
% 177.86/28.34  | | | |   (214)  all_52_18 = e2
% 177.86/28.34  | | | |   (215)  all_52_16 = e3
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | COMBINE_EQS: (158), (213) imply:
% 177.86/28.34  | | | |   (216)  all_14_1 = e1
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (12), (13), (14), (15), (17),
% 177.86/28.34  | | | |            (18), (21), (22), (23), (24), (25), (26), (27), (29), (30),
% 177.86/28.34  | | | |            (31), (32), (33), (34), (35), (36), (37), (40), (42), (43),
% 177.86/28.34  | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (55),
% 177.86/28.34  | | | |            (57), (58), (59), (60), (62), (63), (64), (65), (67), (68),
% 177.86/28.34  | | | |            (69), (70), (71), (72), (73), (74), (77), (78), (79), (80),
% 177.86/28.34  | | | |            (82), (84), (87), (88), (91), (92), (93), (94), (96), (97),
% 177.86/28.34  | | | |            (100), (104), (105), (106), (107), (108), (109), (110),
% 177.86/28.34  | | | |            (113), (114), (115), (116), (117), (118), (119), (121),
% 177.86/28.34  | | | |            (122), (123), (126), (129), (131), (132), (135), (136),
% 177.86/28.34  | | | |            (137), (138), (139), (141), (142), (143), (144), (146),
% 177.86/28.34  | | | |            (147), (148), (149), (151), (152), (153), (154), (155),
% 177.86/28.34  | | | |            (157), (159), (160), (163), (164), (165), (166), (168),
% 177.86/28.34  | | | |            (169), (170), (171), (172), (174), (175), (176), (207),
% 177.86/28.34  | | | |            (212), (214), (215), (216) are inconsistent by sub-proof
% 177.86/28.34  | | | |            #560.
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | Case 2:
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | |   (217)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 177.86/28.34  | | | |          e0
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | ALPHA: (217) implies:
% 177.86/28.34  | | | |   (218)  all_52_30 = e0
% 177.86/28.34  | | | |   (219)  all_52_28 = e1
% 177.86/28.34  | | | |   (220)  all_52_26 = e2
% 177.86/28.34  | | | |   (221)  all_52_24 = e3
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | COMBINE_EQS: (161), (218) imply:
% 177.86/28.34  | | | |   (222)  all_6_1 = e0
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | | REF_CLOSE: (4), (8), (11), (12), (13), (14), (15), (17), (18), (19),
% 177.86/28.34  | | | |            (20), (21), (24), (25), (29), (31), (32), (34), (35), (37),
% 177.86/28.34  | | | |            (40), (41), (42), (44), (45), (46), (48), (49), (51), (52),
% 177.86/28.34  | | | |            (53), (55), (57), (58), (60), (67), (68), (69), (70), (72),
% 177.86/28.34  | | | |            (74), (75), (81), (82), (83), (84), (85), (87), (90), (93),
% 177.86/28.34  | | | |            (101), (102), (104), (105), (110), (111), (115), (116),
% 177.86/28.34  | | | |            (117), (119), (121), (124), (126), (129), (133), (134),
% 177.86/28.34  | | | |            (135), (137), (138), (139), (143), (144), (146), (147),
% 177.86/28.34  | | | |            (149), (152), (154), (156), (157), (159), (160), (162),
% 177.86/28.34  | | | |            (164), (166), (170), (172), (173), (175), (176), (206),
% 177.86/28.34  | | | |            (219), (220), (221), (222) are inconsistent by sub-proof
% 177.86/28.34  | | | |            #555.
% 177.86/28.34  | | | | 
% 177.86/28.34  | | | End of split
% 177.86/28.34  | | | 
% 177.86/28.34  | | End of split
% 177.86/28.34  | | 
% 177.86/28.34  | End of split
% 177.86/28.34  | 
% 177.86/28.34  End of proof
% 177.86/28.34  
% 177.86/28.34  Sub-proof #555 shows that the following formulas are inconsistent:
% 177.86/28.34  ----------------------------------------------------------------
% 177.86/28.34    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.34    (2)  all_52_26 = e2
% 177.86/28.34    (3)   ~ (all_6_0 = e3)
% 177.86/28.34    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.34    (5)  all_56_3 = all_52_7
% 177.86/28.34    (6)  op(e3, e2) = all_52_3
% 177.86/28.34    (7)   ~ (all_52_9 = all_52_25)
% 177.86/28.34    (8)  op(e3, all_52_25) = all_52_24
% 177.86/28.34    (9)   ~ (all_52_19 = all_52_23)
% 177.86/28.34    (10)  op(e1, e2) = all_52_19
% 177.86/28.34    (11)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.86/28.34    (12)  op(e3, all_52_9) = all_52_8
% 177.86/28.34    (13)   ~ (all_52_3 = all_10_2)
% 177.86/28.34    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.34    (15)  all_56_15 = all_6_2
% 177.86/28.34    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.34    (17)  all_6_1 = e0
% 177.86/28.34    (18)  all_58_3 = all_10_2
% 177.86/28.34    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.34    (20)  all_58_15 = all_6_2
% 177.86/28.34    (21)   ~ (all_52_5 = all_52_7)
% 177.86/28.34    (22)  all_58_10 = all_52_15
% 177.86/28.34    (23)  all_58_7 = all_52_19
% 177.86/28.34    (24)   ~ (all_52_17 = all_52_25)
% 177.86/28.34    (25)  op(e0, e1) = all_52_29
% 177.86/28.34    (26)  all_58_4 = all_52_5
% 177.86/28.34    (27)   ~ (e3 = e1)
% 177.86/28.34    (28)  all_34_1 = all_4_1
% 177.86/28.34    (29)   ~ (all_52_27 = all_52_29)
% 177.86/28.34    (30)  op(e3, all_4_2) = all_4_1
% 177.86/28.34    (31)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.34    (32)   ~ (all_52_7 = all_4_2)
% 177.86/28.34    (33)  all_58_1 = all_52_3
% 177.86/28.34    (34)  all_58_0 = all_4_2
% 177.86/28.34    (35)  op(all_4_1, all_4_2) = e1
% 177.86/28.34    (36)  op(e1, all_52_29) = all_52_28
% 177.86/28.34    (37)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.34    (38)   ~ (all_4_1 = e2)
% 177.86/28.34    (39)  all_58_14 = all_52_29
% 177.86/28.34    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.34    (41)   ~ (all_52_3 = all_52_5)
% 177.86/28.34    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.34    (43)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.34    (44)  all_56_1 = all_52_3
% 177.86/28.34    (45)  op(e0, e2) = all_52_27
% 177.86/28.34    (46)   ~ (all_52_3 = all_52_27)
% 177.86/28.34    (47)   ~ (all_52_3 = all_4_2)
% 177.86/28.34    (48)  op(all_6_1, all_6_2) = all_6_0
% 177.86/28.34    (49)  op(e0, e3) = all_52_25
% 177.86/28.34    (50)  op(e0, all_6_2) = all_6_1
% 177.86/28.34    (51)   ~ (all_52_9 = all_10_2)
% 177.86/28.34    (52)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.34    (53)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.34    (54)  all_56_2 = all_52_5
% 177.86/28.34    (55)  op(e1, e0) = all_52_23
% 177.86/28.34    (56)  all_58_13 = all_52_27
% 177.86/28.34    (57)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.34    (58)  all_58_6 = all_52_17
% 177.86/28.34    (59)   ~ (all_52_3 = all_52_7)
% 177.86/28.34    (60)  all_56_0 = all_4_2
% 177.86/28.34    (61)  all_58_11 = all_52_23
% 177.86/28.34    (62)   ~ (all_52_3 = all_52_19)
% 177.86/28.34    (63)   ~ (all_52_7 = all_52_15)
% 177.86/28.34    (64)   ~ (all_52_29 = all_14_2)
% 177.86/28.34    (65)   ~ (all_6_0 = e2)
% 177.86/28.34    (66)  all_58_2 = all_52_9
% 177.86/28.34    (67)  op(e3, e1) = all_52_5
% 177.86/28.34    (68)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.34    (69)  op(e1, e1) = all_14_2
% 177.86/28.34    (70)  op(e1, e3) = all_52_17
% 177.86/28.34    (71)   ~ (all_52_25 = all_4_2)
% 177.86/28.34    (72)  op(e3, e0) = all_52_7
% 177.86/28.34    (73)  all_52_28 = e1
% 177.86/28.34    (74)  op(e3, e3) = all_4_2
% 177.86/28.34    (75)   ~ (all_52_17 = all_4_2)
% 177.86/28.34    (76)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.34    (77)   ~ (all_52_25 = all_52_27)
% 177.86/28.34    (78)  all_34_2 = all_4_2
% 177.86/28.34    (79)   ~ (all_52_7 = all_6_2)
% 177.86/28.34    (80)   ~ (all_52_19 = all_52_27)
% 177.86/28.34    (81)   ~ (all_52_7 = all_52_23)
% 177.86/28.34    (82)   ~ (all_6_0 = e1)
% 177.86/28.34    (83)  op(e2, all_52_27) = all_52_26
% 177.86/28.34    (84)   ~ (all_52_17 = all_52_19)
% 177.86/28.34    (85)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.34    (86)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.34    (87)  all_58_9 = all_52_7
% 177.86/28.34    (88)  all_52_24 = e3
% 177.86/28.34    (89)  all_58_12 = all_52_25
% 177.86/28.34    (90)   ~ (all_52_9 = all_52_15)
% 177.86/28.34    (91)   ~ (e3 = e2)
% 177.86/28.34    (92)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.34    (93)  op(e2, e3) = all_52_9
% 177.86/28.34    (94)  all_56_13 = all_52_27
% 177.86/28.34  
% 177.86/28.34  Begin of proof
% 177.86/28.34  | 
% 177.86/28.34  | REDUCE: (17), (48) imply:
% 177.86/28.34  |   (95)  op(e0, all_6_2) = all_6_0
% 177.86/28.34  | 
% 177.86/28.34  | REDUCE: (8), (88) imply:
% 177.86/28.34  |   (96)  op(e3, all_52_25) = e3
% 177.86/28.34  | 
% 177.86/28.34  | REDUCE: (2), (83) imply:
% 177.86/28.34  |   (97)  op(e2, all_52_27) = e2
% 177.86/28.34  | 
% 177.86/28.34  | REDUCE: (36), (73) imply:
% 177.86/28.34  |   (98)  op(e1, all_52_29) = e1
% 177.86/28.34  | 
% 177.86/28.34  | REDUCE: (17), (50) imply:
% 177.86/28.34  |   (99)  op(e0, all_6_2) = e0
% 177.86/28.34  | 
% 177.86/28.35  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 177.86/28.35  |            (15), (16), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 177.86/28.35  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (37), (38),
% 177.86/28.35  |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (49), (51),
% 177.86/28.35  |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 177.86/28.35  |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72), (74),
% 177.86/28.35  |            (75), (76), (77), (78), (79), (80), (81), (82), (84), (85), (86),
% 177.86/28.35  |            (87), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 177.86/28.35  |            (99) are inconsistent by sub-proof #556.
% 177.86/28.35  | 
% 177.86/28.35  End of proof
% 177.86/28.35  
% 177.86/28.35  Sub-proof #556 shows that the following formulas are inconsistent:
% 177.86/28.35  ----------------------------------------------------------------
% 177.86/28.35    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.35    (2)   ~ (all_6_0 = e3)
% 177.86/28.35    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.35    (4)  all_56_3 = all_52_7
% 177.86/28.35    (5)  op(e3, e2) = all_52_3
% 177.86/28.35    (6)   ~ (all_52_9 = all_52_25)
% 177.86/28.35    (7)   ~ (all_52_19 = all_52_23)
% 177.86/28.35    (8)  op(e1, e2) = all_52_19
% 177.86/28.35    (9)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.86/28.35    (10)  op(e3, all_52_9) = all_52_8
% 177.86/28.35    (11)   ~ (all_52_3 = all_10_2)
% 177.86/28.35    (12)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.35    (13)  all_56_15 = all_6_2
% 177.86/28.35    (14)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.35    (15)  all_58_3 = all_10_2
% 177.86/28.35    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.35    (17)  all_58_15 = all_6_2
% 177.86/28.35    (18)  op(e0, all_6_2) = e0
% 177.86/28.35    (19)   ~ (all_52_5 = all_52_7)
% 177.86/28.35    (20)  all_58_10 = all_52_15
% 177.86/28.35    (21)  all_58_7 = all_52_19
% 177.86/28.35    (22)   ~ (all_52_17 = all_52_25)
% 177.86/28.35    (23)  op(e0, e1) = all_52_29
% 177.86/28.35    (24)  all_58_4 = all_52_5
% 177.86/28.35    (25)   ~ (e3 = e1)
% 177.86/28.35    (26)  all_34_1 = all_4_1
% 177.86/28.35    (27)   ~ (all_52_27 = all_52_29)
% 177.86/28.35    (28)  op(e3, all_4_2) = all_4_1
% 177.86/28.35    (29)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 177.86/28.35    (30)   ~ (all_52_7 = all_4_2)
% 177.86/28.35    (31)  all_58_1 = all_52_3
% 177.86/28.35    (32)  all_58_0 = all_4_2
% 177.86/28.35    (33)  op(all_4_1, all_4_2) = e1
% 177.86/28.35    (34)  op(e2, all_52_27) = e2
% 177.86/28.35    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.35    (36)   ~ (all_4_1 = e2)
% 177.86/28.35    (37)  all_58_14 = all_52_29
% 177.86/28.35    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 177.86/28.35    (39)   ~ (all_52_3 = all_52_5)
% 177.86/28.35    (40)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.35    (41)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.35    (42)  all_56_1 = all_52_3
% 177.86/28.35    (43)  op(e0, e2) = all_52_27
% 177.86/28.35    (44)  op(e1, all_52_29) = e1
% 177.86/28.35    (45)   ~ (all_52_3 = all_52_27)
% 177.86/28.35    (46)   ~ (all_52_3 = all_4_2)
% 177.86/28.35    (47)  op(e0, e3) = all_52_25
% 177.86/28.35    (48)   ~ (all_52_9 = all_10_2)
% 177.86/28.35    (49)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.35    (50)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.35    (51)  all_56_2 = all_52_5
% 177.86/28.35    (52)  op(e1, e0) = all_52_23
% 177.86/28.35    (53)  all_58_13 = all_52_27
% 177.86/28.35    (54)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.35    (55)  all_58_6 = all_52_17
% 177.86/28.35    (56)   ~ (all_52_3 = all_52_7)
% 177.86/28.35    (57)  all_56_0 = all_4_2
% 177.86/28.35    (58)  all_58_11 = all_52_23
% 177.86/28.35    (59)   ~ (all_52_3 = all_52_19)
% 177.86/28.35    (60)   ~ (all_52_7 = all_52_15)
% 177.86/28.35    (61)   ~ (all_52_29 = all_14_2)
% 177.86/28.35    (62)  op(e3, all_52_25) = e3
% 177.86/28.35    (63)   ~ (all_6_0 = e2)
% 177.86/28.35    (64)  all_58_2 = all_52_9
% 177.86/28.35    (65)  op(e3, e1) = all_52_5
% 177.86/28.35    (66)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.35    (67)  op(e1, e1) = all_14_2
% 177.86/28.35    (68)  op(e1, e3) = all_52_17
% 177.86/28.35    (69)   ~ (all_52_25 = all_4_2)
% 177.86/28.35    (70)  op(e3, e0) = all_52_7
% 177.86/28.35    (71)  op(e3, e3) = all_4_2
% 177.86/28.35    (72)   ~ (all_52_17 = all_4_2)
% 177.86/28.35    (73)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.35    (74)   ~ (all_52_25 = all_52_27)
% 177.86/28.35    (75)  all_34_2 = all_4_2
% 177.86/28.35    (76)  op(e0, all_6_2) = all_6_0
% 177.86/28.35    (77)   ~ (all_52_7 = all_6_2)
% 177.86/28.35    (78)   ~ (all_52_19 = all_52_27)
% 177.86/28.35    (79)   ~ (all_52_7 = all_52_23)
% 177.86/28.35    (80)   ~ (all_6_0 = e1)
% 177.86/28.35    (81)   ~ (all_52_17 = all_52_19)
% 177.86/28.35    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.35    (83)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.35    (84)  all_58_9 = all_52_7
% 177.86/28.35    (85)  all_58_12 = all_52_25
% 177.86/28.35    (86)   ~ (all_52_9 = all_52_15)
% 177.86/28.35    (87)   ~ (e3 = e2)
% 177.86/28.35    (88)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.35    (89)  op(e2, e3) = all_52_9
% 177.86/28.35    (90)  all_56_13 = all_52_27
% 177.86/28.35  
% 177.86/28.35  Begin of proof
% 177.86/28.35  | 
% 177.86/28.35  | GROUND_INST: instantiating (73) with e0, all_6_0, all_6_2, e0, simplifying
% 177.86/28.35  |              with (18), (76) gives:
% 177.86/28.35  |   (91)  all_6_0 = e0
% 177.86/28.35  | 
% 177.86/28.35  | REDUCE: (2), (91) imply:
% 177.86/28.35  |   (92)   ~ (e3 = e0)
% 177.86/28.35  | 
% 177.86/28.35  | SIMP: (92) implies:
% 177.86/28.35  |   (93)   ~ (e3 = e0)
% 177.86/28.35  | 
% 177.86/28.35  | REDUCE: (63), (91) imply:
% 177.86/28.35  |   (94)   ~ (e2 = e0)
% 177.86/28.35  | 
% 177.86/28.35  | SIMP: (94) implies:
% 177.86/28.35  |   (95)   ~ (e2 = e0)
% 177.86/28.35  | 
% 177.86/28.35  | REDUCE: (80), (91) imply:
% 177.86/28.35  |   (96)   ~ (e1 = e0)
% 177.86/28.35  | 
% 177.86/28.35  | SIMP: (96) implies:
% 177.86/28.35  |   (97)   ~ (e1 = e0)
% 177.86/28.35  | 
% 177.86/28.35  | BETA: splitting (29) gives:
% 177.86/28.35  | 
% 177.86/28.35  | Case 1:
% 177.86/28.35  | | 
% 177.86/28.35  | |   (98)  all_56_15 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | COMBINE_EQS: (13), (98) imply:
% 177.86/28.35  | |   (99)  all_6_2 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | SIMP: (99) implies:
% 177.86/28.35  | |   (100)  all_6_2 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | REF_CLOSE: (18), (47), (62), (70), (73), (77), (100) are inconsistent by
% 177.86/28.35  | |            sub-proof #665.
% 177.86/28.35  | | 
% 177.86/28.35  | Case 2:
% 177.86/28.35  | | 
% 177.86/28.35  | |   (101)   ~ (all_56_15 = e3)
% 177.86/28.35  | | 
% 177.86/28.35  | | REDUCE: (13), (101) imply:
% 177.86/28.35  | |   (102)   ~ (all_6_2 = e3)
% 177.86/28.35  | | 
% 177.86/28.35  | | BETA: splitting (38) gives:
% 177.86/28.35  | | 
% 177.86/28.35  | | Case 1:
% 177.86/28.35  | | | 
% 177.86/28.35  | | |   (103)  all_56_13 = e3
% 177.86/28.35  | | | 
% 177.86/28.35  | | | COMBINE_EQS: (90), (103) imply:
% 177.86/28.35  | | |   (104)  all_52_27 = e3
% 177.86/28.35  | | | 
% 177.86/28.35  | | | COMBINE_EQS: (53), (104) imply:
% 177.86/28.35  | | |   (105)  all_58_13 = e3
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (45), (104) imply:
% 177.86/28.35  | | |   (106)   ~ (all_52_3 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (78), (104) imply:
% 177.86/28.35  | | |   (107)   ~ (all_52_19 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (74), (104) imply:
% 177.86/28.35  | | |   (108)   ~ (all_52_25 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (27), (104) imply:
% 177.86/28.35  | | |   (109)   ~ (all_52_29 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | SIMP: (109) implies:
% 177.86/28.35  | | |   (110)   ~ (all_52_29 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (34), (104) imply:
% 177.86/28.35  | | |   (111)  op(e2, e3) = e2
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (43), (104) imply:
% 177.86/28.35  | | |   (112)  op(e0, e2) = e3
% 177.86/28.35  | | | 
% 177.86/28.35  | | | GROUND_INST: instantiating (73) with all_52_9, e2, e3, e2, simplifying
% 177.86/28.35  | | |              with (89), (111) gives:
% 177.86/28.35  | | |   (113)  all_52_9 = e2
% 177.86/28.35  | | | 
% 177.86/28.35  | | | COMBINE_EQS: (64), (113) imply:
% 177.86/28.35  | | |   (114)  all_58_2 = e2
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (86), (113) imply:
% 177.86/28.35  | | |   (115)   ~ (all_52_15 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | SIMP: (115) implies:
% 177.86/28.35  | | |   (116)   ~ (all_52_15 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (6), (113) imply:
% 177.86/28.35  | | |   (117)   ~ (all_52_25 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | SIMP: (117) implies:
% 177.86/28.35  | | |   (118)   ~ (all_52_25 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (48), (113) imply:
% 177.86/28.35  | | |   (119)   ~ (all_10_2 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | SIMP: (119) implies:
% 177.86/28.35  | | |   (120)   ~ (all_10_2 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (10), (113) imply:
% 177.86/28.35  | | |   (121)  op(e3, e2) = all_52_8
% 177.86/28.35  | | | 
% 177.86/28.35  | | | GROUND_INST: instantiating (73) with all_52_3, all_52_8, e2, e3,
% 177.86/28.35  | | |              simplifying with (5), (121) gives:
% 177.86/28.35  | | |   (122)  all_52_3 = all_52_8
% 177.86/28.35  | | | 
% 177.86/28.35  | | | COMBINE_EQS: (31), (122) imply:
% 177.86/28.35  | | |   (123)  all_58_1 = all_52_8
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (39), (122) imply:
% 177.86/28.35  | | |   (124)   ~ (all_52_5 = all_52_8)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | SIMP: (124) implies:
% 177.86/28.35  | | |   (125)   ~ (all_52_5 = all_52_8)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (56), (122) imply:
% 177.86/28.35  | | |   (126)   ~ (all_52_7 = all_52_8)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | SIMP: (126) implies:
% 177.86/28.35  | | |   (127)   ~ (all_52_7 = all_52_8)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (11), (122) imply:
% 177.86/28.35  | | |   (128)   ~ (all_52_8 = all_10_2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (46), (122) imply:
% 177.86/28.35  | | |   (129)   ~ (all_52_8 = all_4_2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (106), (122) imply:
% 177.86/28.35  | | |   (130)   ~ (all_52_8 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | BETA: splitting (12) gives:
% 177.86/28.35  | | | 
% 177.86/28.35  | | | Case 1:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | |   (131)  all_58_1 = e2
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | COMBINE_EQS: (123), (131) imply:
% 177.86/28.35  | | | |   (132)  all_52_8 = e2
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | REDUCE: (125), (132) imply:
% 177.86/28.35  | | | |   (133)   ~ (all_52_5 = e2)
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | REDUCE: (127), (132) imply:
% 177.86/28.35  | | | |   (134)   ~ (all_52_7 = e2)
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | REDUCE: (130), (132) imply:
% 177.86/28.35  | | | |   (135)   ~ (e3 = e2)
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | BETA: splitting (40) gives:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | Case 1:
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | |   (136)  all_58_0 = e3
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | | COMBINE_EQS: (32), (136) imply:
% 177.86/28.35  | | | | |   (137)  all_4_2 = e3
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | | REF_CLOSE: (25), (28), (33), (71), (73), (137) are inconsistent by
% 177.86/28.35  | | | | |            sub-proof #599.
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | Case 2:
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | |   (138)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | | BETA: splitting (138) gives:
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | | Case 1:
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | |   (139)  all_58_2 = e3
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | | COMBINE_EQS: (114), (139) imply:
% 177.86/28.35  | | | | | |   (140)  e3 = e2
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | | REDUCE: (87), (140) imply:
% 177.86/28.35  | | | | | |   (141)  $false
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | | CLOSE: (141) is inconsistent.
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | Case 2:
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | |   (142)  all_58_6 = e3 | all_58_12 = e3
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | | BETA: splitting (142) gives:
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | | Case 1:
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | |   (143)  all_58_6 = e3
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | COMBINE_EQS: (55), (143) imply:
% 177.86/28.35  | | | | | | |   (144)  all_52_17 = e3
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | SIMP: (144) implies:
% 177.86/28.35  | | | | | | |   (145)  all_52_17 = e3
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | REDUCE: (81), (145) imply:
% 177.86/28.35  | | | | | | |   (146)   ~ (all_52_19 = e3)
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | REDUCE: (22), (145) imply:
% 177.86/28.35  | | | | | | |   (147)   ~ (all_52_25 = e3)
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | REDUCE: (72), (145) imply:
% 177.86/28.35  | | | | | | |   (148)   ~ (all_4_2 = e3)
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | SIMP: (148) implies:
% 177.86/28.35  | | | | | | |   (149)   ~ (all_4_2 = e3)
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | BETA: splitting (16) gives:
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | Case 1:
% 177.86/28.35  | | | | | | | | 
% 177.86/28.35  | | | | | | | |   (150)  all_56_0 = e3
% 177.86/28.35  | | | | | | | | 
% 177.86/28.35  | | | | | | | | REF_CLOSE: (57), (149), (150) are inconsistent by sub-proof
% 177.86/28.35  | | | | | | | |            #1024.
% 177.86/28.35  | | | | | | | | 
% 177.86/28.35  | | | | | | | Case 2:
% 177.86/28.35  | | | | | | | | 
% 177.86/28.35  | | | | | | | |   (151)   ~ (all_56_0 = e3)
% 177.86/28.35  | | | | | | | |   (152)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.35  | | | | | | | | 
% 177.86/28.35  | | | | | | | | BETA: splitting (54) gives:
% 177.86/28.35  | | | | | | | | 
% 177.86/28.35  | | | | | | | | Case 1:
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | |   (153)  all_58_0 = e1
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | COMBINE_EQS: (32), (153) imply:
% 177.86/28.35  | | | | | | | | |   (154)  all_4_2 = e1
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | REDUCE: (30), (154) imply:
% 177.86/28.35  | | | | | | | | |   (155)   ~ (all_52_7 = e1)
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | REDUCE: (69), (154) imply:
% 177.86/28.35  | | | | | | | | |   (156)   ~ (all_52_25 = e1)
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | REDUCE: (28), (154) imply:
% 177.86/28.35  | | | | | | | | |   (157)  op(e3, e1) = all_4_1
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | BETA: splitting (50) gives:
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | Case 1:
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | |   (158)  all_58_0 = e0
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | COMBINE_EQS: (153), (158) imply:
% 177.86/28.35  | | | | | | | | | |   (159)  e1 = e0
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | REDUCE: (97), (159) imply:
% 177.86/28.35  | | | | | | | | | |   (160)  $false
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | CLOSE: (160) is inconsistent.
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | Case 2:
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | |   (161)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | BETA: splitting (161) gives:
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | Case 1:
% 177.86/28.35  | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | |   (162)  all_58_2 = e0
% 177.86/28.35  | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | REF_CLOSE: (95), (114), (162) are inconsistent by sub-proof
% 177.86/28.35  | | | | | | | | | | |            #909.
% 177.86/28.35  | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | Case 2:
% 177.86/28.35  | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | |   (163)  all_58_6 = e0 | all_58_12 = e0
% 177.86/28.35  | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | BETA: splitting (163) gives:
% 177.86/28.35  | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | Case 1:
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | |   (164)  all_58_6 = e0
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | REF_CLOSE: (93), (143), (164) are inconsistent by sub-proof
% 177.86/28.35  | | | | | | | | | | | |            #559.
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | Case 2:
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | |   (165)  all_58_12 = e0
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | COMBINE_EQS: (85), (165) imply:
% 177.86/28.35  | | | | | | | | | | | |   (166)  all_52_25 = e0
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | SIMP: (166) implies:
% 177.86/28.35  | | | | | | | | | | | |   (167)  all_52_25 = e0
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | REDUCE: (62), (167) imply:
% 177.86/28.35  | | | | | | | | | | | |   (168)  op(e3, e0) = e3
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | GROUND_INST: instantiating (73) with all_52_7, e3, e0, e3,
% 177.86/28.35  | | | | | | | | | | | |              simplifying with (70), (168) gives:
% 177.86/28.35  | | | | | | | | | | | |   (169)  all_52_7 = e3
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | GROUND_INST: instantiating (73) with all_52_5, all_4_1, e1, e3,
% 177.86/28.35  | | | | | | | | | | | |              simplifying with (65), (157) gives:
% 177.86/28.35  | | | | | | | | | | | |   (170)  all_52_5 = all_4_1
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | REDUCE: (60), (169) imply:
% 177.86/28.35  | | | | | | | | | | | |   (171)   ~ (all_52_15 = e3)
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | SIMP: (171) implies:
% 177.86/28.35  | | | | | | | | | | | |   (172)   ~ (all_52_15 = e3)
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | REDUCE: (79), (169) imply:
% 177.86/28.35  | | | | | | | | | | | |   (173)   ~ (all_52_23 = e3)
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | SIMP: (173) implies:
% 177.86/28.35  | | | | | | | | | | | |   (174)   ~ (all_52_23 = e3)
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | REDUCE: (77), (169) imply:
% 177.86/28.35  | | | | | | | | | | | |   (175)   ~ (all_6_2 = e3)
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (12), (15), (17), (18), (19),
% 177.86/28.35  | | | | | | | | | | | |            (20), (21), (23), (24), (25), (28), (30), (32),
% 177.86/28.35  | | | | | | | | | | | |            (33), (36), (37), (44), (49), (51), (52), (54),
% 177.86/28.35  | | | | | | | | | | | |            (57), (58), (61), (62), (65), (66), (67), (70),
% 177.86/28.35  | | | | | | | | | | | |            (73), (77), (79), (82), (83), (84), (85), (87),
% 177.86/28.35  | | | | | | | | | | | |            (88), (93), (95), (97), (102), (105), (107),
% 177.86/28.35  | | | | | | | | | | | |            (110), (112), (116), (118), (120), (123), (125),
% 177.86/28.35  | | | | | | | | | | | |            (129), (152), (172), (174) are inconsistent by
% 177.86/28.35  | | | | | | | | | | | |            sub-proof #558.
% 177.86/28.35  | | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | | End of split
% 177.86/28.35  | | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | | End of split
% 177.86/28.35  | | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | End of split
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | Case 2:
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | |   (176)   ~ (all_58_0 = e1)
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | REDUCE: (32), (176) imply:
% 177.86/28.35  | | | | | | | | |   (177)   ~ (all_4_2 = e1)
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (14), (16), (25), (26), (28),
% 177.86/28.35  | | | | | | | | |            (30), (32), (33), (35), (36), (42), (46), (52),
% 177.86/28.35  | | | | | | | | |            (57), (59), (70), (73), (75), (79), (83), (149),
% 177.86/28.35  | | | | | | | | |            (177) are inconsistent by sub-proof #586.
% 177.86/28.35  | | | | | | | | | 
% 177.86/28.35  | | | | | | | | End of split
% 177.86/28.35  | | | | | | | | 
% 177.86/28.35  | | | | | | | End of split
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | Case 2:
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | |   (178)  all_58_12 = e3
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | | REF_CLOSE: (85), (108), (178) are inconsistent by sub-proof #1003.
% 177.86/28.35  | | | | | | | 
% 177.86/28.35  | | | | | | End of split
% 177.86/28.35  | | | | | | 
% 177.86/28.35  | | | | | End of split
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | End of split
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | Case 2:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | |   (179)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | REF_CLOSE: (3), (7), (15), (17), (18), (20), (21), (37), (49), (58),
% 177.86/28.35  | | | |            (62), (66), (70), (73), (77), (84), (85), (87), (93), (95),
% 177.86/28.35  | | | |            (105), (107), (110), (112), (116), (118), (120), (179) are
% 177.86/28.35  | | | |            inconsistent by sub-proof #657.
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | End of split
% 177.86/28.35  | | | 
% 177.86/28.35  | | Case 2:
% 177.86/28.35  | | | 
% 177.86/28.35  | | |   (180)   ~ (all_56_13 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (90), (180) imply:
% 177.86/28.35  | | |   (181)   ~ (all_52_27 = e3)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REF_CLOSE: (4), (5), (8), (9), (14), (16), (17), (25), (26), (28), (30),
% 177.86/28.35  | | |            (32), (33), (35), (36), (37), (40), (41), (42), (44), (46),
% 177.86/28.35  | | |            (52), (53), (57), (59), (62), (68), (69), (70), (71), (72),
% 177.86/28.35  | | |            (73), (75), (79), (83), (85), (102), (181) are inconsistent by
% 177.86/28.35  | | |            sub-proof #557.
% 177.86/28.35  | | | 
% 177.86/28.35  | | End of split
% 177.86/28.35  | | 
% 177.86/28.35  | End of split
% 177.86/28.35  | 
% 177.86/28.35  End of proof
% 177.86/28.35  
% 177.86/28.35  Sub-proof #557 shows that the following formulas are inconsistent:
% 177.86/28.35  ----------------------------------------------------------------
% 177.86/28.35    (1)  all_56_3 = all_52_7
% 177.86/28.35    (2)  op(e3, e2) = all_52_3
% 177.86/28.35    (3)  op(e1, e2) = all_52_19
% 177.86/28.35    (4)   ~ (all_52_27 = e3)
% 177.86/28.35    (5)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.86/28.35    (6)   ~ (all_6_2 = e3)
% 177.86/28.35    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.35    (8)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.35    (9)  all_58_15 = all_6_2
% 177.86/28.35    (10)   ~ (e3 = e1)
% 177.86/28.35    (11)  all_34_1 = all_4_1
% 177.86/28.35    (12)  op(e3, all_4_2) = all_4_1
% 177.86/28.35    (13)   ~ (all_52_7 = all_4_2)
% 177.86/28.35    (14)  all_58_0 = all_4_2
% 177.86/28.35    (15)  op(all_4_1, all_4_2) = e1
% 177.86/28.35    (16)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 177.86/28.35    (17)   ~ (all_4_1 = e2)
% 177.86/28.35    (18)  all_58_14 = all_52_29
% 177.86/28.35    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 177.86/28.35    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.35    (21)  all_56_1 = all_52_3
% 177.86/28.35    (22)  op(e1, all_52_29) = e1
% 177.86/28.35    (23)   ~ (all_52_3 = all_4_2)
% 177.86/28.35    (24)  op(e1, e0) = all_52_23
% 177.86/28.35    (25)  all_58_13 = all_52_27
% 177.86/28.35    (26)  all_56_0 = all_4_2
% 177.86/28.35    (27)   ~ (all_52_3 = all_52_19)
% 177.86/28.35    (28)  op(e3, all_52_25) = e3
% 177.86/28.35    (29)  op(e1, e3) = all_52_17
% 177.86/28.35    (30)   ~ (all_52_25 = all_4_2)
% 177.86/28.35    (31)  op(e3, e0) = all_52_7
% 177.86/28.35    (32)  op(e3, e3) = all_4_2
% 177.86/28.35    (33)   ~ (all_52_17 = all_4_2)
% 177.86/28.35    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.35    (35)  all_34_2 = all_4_2
% 177.86/28.35    (36)   ~ (all_52_7 = all_52_23)
% 177.86/28.35    (37)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.35    (38)  all_58_12 = all_52_25
% 177.86/28.35  
% 177.86/28.35  Begin of proof
% 177.86/28.35  | 
% 177.86/28.35  | BETA: splitting (20) gives:
% 177.86/28.35  | 
% 177.86/28.35  | Case 1:
% 177.86/28.35  | | 
% 177.86/28.35  | |   (39)  all_58_12 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | REF_CLOSE: (28), (30), (32), (34), (38), (39) are inconsistent by sub-proof
% 177.86/28.35  | |            #884.
% 177.86/28.35  | | 
% 177.86/28.35  | Case 2:
% 177.86/28.35  | | 
% 177.86/28.35  | |   (40)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | BETA: splitting (40) gives:
% 177.86/28.35  | | 
% 177.86/28.35  | | Case 1:
% 177.86/28.35  | | | 
% 177.86/28.35  | | |   (41)  all_58_13 = e3
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REF_CLOSE: (4), (25), (41) are inconsistent by sub-proof #1026.
% 177.86/28.35  | | | 
% 177.86/28.35  | | Case 2:
% 177.86/28.35  | | | 
% 177.86/28.35  | | |   (42)  all_58_14 = e3 | all_58_15 = e3
% 177.86/28.35  | | | 
% 177.86/28.35  | | | BETA: splitting (42) gives:
% 177.86/28.35  | | | 
% 177.86/28.35  | | | Case 1:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | |   (43)  all_58_14 = e3
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (13), (14),
% 177.86/28.35  | | | |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (26),
% 177.86/28.35  | | | |            (27), (29), (31), (32), (33), (34), (35), (36), (37), (43)
% 177.86/28.35  | | | |            are inconsistent by sub-proof #578.
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | Case 2:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | |   (44)  all_58_15 = e3
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | COMBINE_EQS: (9), (44) imply:
% 177.86/28.35  | | | |   (45)  all_6_2 = e3
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | REDUCE: (6), (45) imply:
% 177.86/28.35  | | | |   (46)  $false
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | CLOSE: (46) is inconsistent.
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | End of split
% 177.86/28.35  | | | 
% 177.86/28.35  | | End of split
% 177.86/28.35  | | 
% 177.86/28.35  | End of split
% 177.86/28.35  | 
% 177.86/28.35  End of proof
% 177.86/28.35  
% 177.86/28.35  Sub-proof #558 shows that the following formulas are inconsistent:
% 177.86/28.35  ----------------------------------------------------------------
% 177.86/28.35    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.35    (2)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 177.86/28.35    (3)  all_56_3 = all_52_7
% 177.86/28.35    (4)   ~ (all_52_19 = all_52_23)
% 177.86/28.35    (5)   ~ (all_6_2 = e3)
% 177.86/28.35    (6)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.35    (7)  all_58_1 = all_52_8
% 177.86/28.35    (8)  all_58_3 = all_10_2
% 177.86/28.35    (9)  all_58_15 = all_6_2
% 177.86/28.35    (10)  op(e0, all_6_2) = e0
% 177.86/28.35    (11)   ~ (all_52_5 = all_52_7)
% 177.86/28.35    (12)  all_58_10 = all_52_15
% 177.86/28.35    (13)  all_58_7 = all_52_19
% 177.86/28.35    (14)  op(e0, e1) = all_52_29
% 177.86/28.35    (15)  all_58_4 = all_52_5
% 177.86/28.35    (16)   ~ (e3 = e1)
% 177.86/28.35    (17)  op(e3, all_4_2) = all_4_1
% 177.86/28.35    (18)   ~ (all_52_7 = all_4_2)
% 177.86/28.35    (19)  all_58_0 = all_4_2
% 177.86/28.35    (20)  op(all_4_1, all_4_2) = e1
% 177.86/28.35    (21)   ~ (all_4_1 = e2)
% 177.86/28.35    (22)  all_58_14 = all_52_29
% 177.86/28.35    (23)   ~ (all_52_25 = e2)
% 177.86/28.35    (24)   ~ (all_52_15 = e2)
% 177.86/28.35    (25)  op(e1, all_52_29) = e1
% 177.86/28.35    (26)   ~ (all_52_23 = e3)
% 177.86/28.35    (27)   ~ (all_52_29 = e3)
% 177.86/28.35    (28)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 177.86/28.35    (29)   ~ (e3 = e0)
% 177.86/28.35    (30)   ~ (all_52_5 = all_52_8)
% 177.86/28.35    (31)   ~ (all_52_15 = e3)
% 177.86/28.35    (32)  all_56_2 = all_52_5
% 177.86/28.35    (33)  op(e1, e0) = all_52_23
% 177.86/28.35    (34)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 177.86/28.35    (35)   ~ (e1 = e0)
% 177.86/28.35    (36)  all_56_0 = all_4_2
% 177.86/28.35    (37)  all_58_11 = all_52_23
% 177.86/28.35    (38)   ~ (all_52_29 = all_14_2)
% 177.86/28.35    (39)  op(e3, all_52_25) = e3
% 177.86/28.35    (40)  op(e0, e2) = e3
% 177.86/28.35    (41)  op(e3, e1) = all_52_5
% 177.86/28.35    (42)   ~ (all_10_2 = e2)
% 177.86/28.35    (43)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 177.86/28.35    (44)  op(e1, e1) = all_14_2
% 177.86/28.35    (45)   ~ (all_52_19 = e3)
% 177.86/28.35    (46)  op(e3, e0) = all_52_7
% 177.86/28.35    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 177.86/28.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 177.86/28.35    (48)   ~ (all_52_7 = all_6_2)
% 177.86/28.35    (49)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 177.86/28.35    (50)   ~ (all_52_7 = all_52_23)
% 177.86/28.35    (51)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.35    (52)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 177.86/28.35    (53)  all_58_9 = all_52_7
% 177.86/28.35    (54)   ~ (all_52_8 = all_4_2)
% 177.86/28.35    (55)   ~ (e2 = e0)
% 177.86/28.35    (56)  all_58_12 = all_52_25
% 177.86/28.35    (57)   ~ (e3 = e2)
% 177.86/28.35    (58)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.35    (59)  all_58_13 = e3
% 177.86/28.35  
% 177.86/28.35  Begin of proof
% 177.86/28.35  | 
% 177.86/28.35  | BETA: splitting (51) gives:
% 177.86/28.35  | 
% 177.86/28.35  | Case 1:
% 177.86/28.35  | | 
% 177.86/28.35  | |   (60)  all_58_9 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | COMBINE_EQS: (53), (60) imply:
% 177.86/28.35  | |   (61)  all_52_7 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | SIMP: (61) implies:
% 177.86/28.35  | |   (62)  all_52_7 = e3
% 177.86/28.35  | | 
% 177.86/28.35  | | REDUCE: (11), (62) imply:
% 177.86/28.35  | |   (63)   ~ (all_52_5 = e3)
% 177.86/28.35  | | 
% 177.86/28.35  | | BETA: splitting (6) gives:
% 177.86/28.35  | | 
% 177.86/28.35  | | Case 1:
% 177.86/28.35  | | | 
% 177.86/28.35  | | |   (64)  all_58_1 = e2
% 177.86/28.35  | | | 
% 177.86/28.35  | | | COMBINE_EQS: (7), (64) imply:
% 177.86/28.35  | | |   (65)  all_52_8 = e2
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (30), (65) imply:
% 177.86/28.35  | | |   (66)   ~ (all_52_5 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | REDUCE: (54), (65) imply:
% 177.86/28.35  | | |   (67)   ~ (all_4_2 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | SIMP: (67) implies:
% 177.86/28.35  | | |   (68)   ~ (all_4_2 = e2)
% 177.86/28.35  | | | 
% 177.86/28.35  | | | BETA: splitting (58) gives:
% 177.86/28.35  | | | 
% 177.86/28.35  | | | Case 1:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | |   (69)  all_56_2 = e3
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | REF_CLOSE: (32), (63), (69) are inconsistent by sub-proof #931.
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | Case 2:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | |   (70)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | BETA: splitting (34) gives:
% 177.86/28.35  | | | | 
% 177.86/28.35  | | | | Case 1:
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | |   (71)  all_58_0 = e1
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | | COMBINE_EQS: (19), (71) imply:
% 177.86/28.35  | | | | |   (72)  all_4_2 = e1
% 177.86/28.35  | | | | | 
% 177.86/28.35  | | | | | REDUCE: (20), (72) imply:
% 177.86/28.36  | | | | |   (73)  op(all_4_1, e1) = e1
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | | REDUCE: (17), (72) imply:
% 177.86/28.36  | | | | |   (74)  op(e3, e1) = all_4_1
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | | BETA: splitting (1) gives:
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | | Case 1:
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | |   (75)  all_58_0 = e0
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | | COMBINE_EQS: (71), (75) imply:
% 177.86/28.36  | | | | | |   (76)  e1 = e0
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | | REDUCE: (35), (76) imply:
% 177.86/28.36  | | | | | |   (77)  $false
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | | CLOSE: (77) is inconsistent.
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | Case 2:
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | |   (78)   ~ (all_58_0 = e0)
% 177.86/28.36  | | | | | |   (79)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | | BETA: splitting (79) gives:
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | | Case 1:
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | |   (80)  all_58_1 = e0
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | | COMBINE_EQS: (64), (80) imply:
% 177.86/28.36  | | | | | | |   (81)  e2 = e0
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | | REDUCE: (55), (81) imply:
% 177.86/28.36  | | | | | | |   (82)  $false
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | | CLOSE: (82) is inconsistent.
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | Case 2:
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | |   (83)  all_58_4 = e0 | all_58_9 = e0
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | | BETA: splitting (70) gives:
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | | Case 1:
% 177.86/28.36  | | | | | | | | 
% 177.86/28.36  | | | | | | | |   (84)  all_56_2 = e2
% 177.86/28.36  | | | | | | | | 
% 177.86/28.36  | | | | | | | | REF_CLOSE: (32), (66), (84) are inconsistent by sub-proof #827.
% 177.86/28.36  | | | | | | | | 
% 177.86/28.36  | | | | | | | Case 2:
% 177.86/28.36  | | | | | | | | 
% 177.86/28.36  | | | | | | | |   (85)  all_56_2 = e1 | all_56_2 = e0
% 177.86/28.36  | | | | | | | | 
% 177.86/28.36  | | | | | | | | BETA: splitting (85) gives:
% 177.86/28.36  | | | | | | | | 
% 177.86/28.36  | | | | | | | | Case 1:
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | |   (86)  all_56_2 = e1
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | REF_CLOSE: (15), (29), (32), (35), (60), (83), (86) are
% 177.86/28.36  | | | | | | | | |            inconsistent by sub-proof #926.
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | Case 2:
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | |   (87)  all_56_2 = e0
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | COMBINE_EQS: (32), (87) imply:
% 177.86/28.36  | | | | | | | | |   (88)  all_52_5 = e0
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | SIMP: (88) implies:
% 177.86/28.36  | | | | | | | | |   (89)  all_52_5 = e0
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | REDUCE: (41), (89) imply:
% 177.86/28.36  | | | | | | | | |   (90)  op(e3, e1) = e0
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | GROUND_INST: instantiating (47) with e0, all_4_1, e1, e3,
% 177.86/28.36  | | | | | | | | |              simplifying with (74), (90) gives:
% 177.86/28.36  | | | | | | | | |   (91)  all_4_1 = e0
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | REDUCE: (73), (91) imply:
% 177.86/28.36  | | | | | | | | |   (92)  op(e0, e1) = e1
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | GROUND_INST: instantiating (47) with all_52_29, e1, e1, e0,
% 177.86/28.36  | | | | | | | | |              simplifying with (14), (92) gives:
% 177.86/28.36  | | | | | | | | |   (93)  all_52_29 = e1
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | REDUCE: (38), (93) imply:
% 177.86/28.36  | | | | | | | | |   (94)   ~ (all_14_2 = e1)
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | SIMP: (94) implies:
% 177.86/28.36  | | | | | | | | |   (95)   ~ (all_14_2 = e1)
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | REDUCE: (25), (93) imply:
% 177.86/28.36  | | | | | | | | |   (96)  op(e1, e1) = e1
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | | REF_CLOSE: (44), (47), (95), (96) are inconsistent by
% 177.86/28.36  | | | | | | | | |            sub-proof #860.
% 177.86/28.36  | | | | | | | | | 
% 177.86/28.36  | | | | | | | | End of split
% 177.86/28.36  | | | | | | | | 
% 177.86/28.36  | | | | | | | End of split
% 177.86/28.36  | | | | | | | 
% 177.86/28.36  | | | | | | End of split
% 177.86/28.36  | | | | | | 
% 177.86/28.36  | | | | | End of split
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | Case 2:
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | |   (97)   ~ (all_58_0 = e1)
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | | REDUCE: (19), (97) imply:
% 177.86/28.36  | | | | |   (98)   ~ (all_4_2 = e1)
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | | REF_CLOSE: (3), (16), (17), (18), (20), (21), (33), (36), (46), (47),
% 177.86/28.36  | | | | |            (49), (50), (52), (68), (98) are inconsistent by sub-proof
% 177.86/28.36  | | | | |            #588.
% 177.86/28.36  | | | | | 
% 177.86/28.36  | | | | End of split
% 177.86/28.36  | | | | 
% 177.86/28.36  | | | End of split
% 177.86/28.36  | | | 
% 177.86/28.36  | | Case 2:
% 177.86/28.36  | | | 
% 177.86/28.36  | | |   (99)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.36  | | | 
% 177.86/28.36  | | | REF_CLOSE: (2), (4), (8), (9), (10), (12), (13), (22), (23), (24), (27),
% 177.86/28.36  | | |            (28), (29), (37), (39), (40), (42), (43), (45), (46), (47),
% 177.86/28.36  | | |            (48), (53), (55), (56), (57), (59), (99) are inconsistent by
% 177.86/28.36  | | |            sub-proof #657.
% 177.86/28.36  | | | 
% 177.86/28.36  | | End of split
% 177.86/28.36  | | 
% 177.86/28.36  | Case 2:
% 177.86/28.36  | | 
% 177.86/28.36  | |   (100)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 177.86/28.36  | | 
% 177.86/28.36  | | REF_CLOSE: (5), (9), (12), (26), (31), (37), (100) are inconsistent by
% 177.86/28.36  | |            sub-proof #645.
% 177.86/28.36  | | 
% 177.86/28.36  | End of split
% 177.86/28.36  | 
% 177.86/28.36  End of proof
% 177.86/28.36  
% 177.86/28.36  Sub-proof #559 shows that the following formulas are inconsistent:
% 177.86/28.36  ----------------------------------------------------------------
% 177.86/28.36    (1)  all_58_6 = e3
% 177.86/28.36    (2)  all_58_6 = e0
% 177.86/28.36    (3)   ~ (e3 = e0)
% 177.86/28.36  
% 177.86/28.36  Begin of proof
% 177.86/28.36  | 
% 177.86/28.36  | COMBINE_EQS: (1), (2) imply:
% 177.86/28.36  |   (4)  e3 = e0
% 177.86/28.36  | 
% 177.86/28.36  | SIMP: (4) implies:
% 177.86/28.36  |   (5)  e3 = e0
% 177.86/28.36  | 
% 177.86/28.36  | REDUCE: (3), (5) imply:
% 177.86/28.36  |   (6)  $false
% 177.86/28.36  | 
% 177.86/28.36  | CLOSE: (6) is inconsistent.
% 177.86/28.36  | 
% 177.86/28.36  End of proof
% 177.86/28.36  
% 177.86/28.36  Sub-proof #560 shows that the following formulas are inconsistent:
% 177.86/28.36  ----------------------------------------------------------------
% 177.86/28.36    (1)   ~ (all_52_23 = all_14_2)
% 177.86/28.36    (2)   ~ (all_52_5 = all_52_13)
% 177.86/28.36    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 177.86/28.36    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 177.86/28.36    (5)   ~ (all_52_17 = all_52_23)
% 177.86/28.36    (6)  op(e2, all_10_2) = all_10_1
% 177.86/28.36    (7)  all_52_16 = e3
% 177.86/28.36    (8)  op(e3, e2) = all_52_3
% 177.86/28.36    (9)   ~ (all_52_9 = all_52_25)
% 177.86/28.36    (10)  op(e3, all_52_25) = all_52_24
% 177.86/28.36    (11)   ~ (all_52_19 = all_52_23)
% 177.86/28.36    (12)  op(e1, e2) = all_52_19
% 177.86/28.36    (13)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 177.86/28.36    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 177.86/28.36    (15)  all_58_5 = all_52_13
% 177.86/28.36    (16)   ~ (all_52_25 = all_52_29)
% 177.86/28.36    (17)  all_56_15 = all_6_2
% 177.86/28.36    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 177.86/28.36    (19)  op(e2, e0) = all_52_15
% 177.86/28.36    (20)  op(all_14_1, all_14_2) = all_14_0
% 177.86/28.36    (21)  all_58_3 = all_10_2
% 177.86/28.36    (22)  all_56_9 = all_52_19
% 178.07/28.36    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.36    (24)  all_58_15 = all_6_2
% 178.07/28.36    (25)   ~ (all_52_9 = all_4_2)
% 178.07/28.36    (26)   ~ (all_52_5 = all_52_7)
% 178.07/28.36    (27)  all_58_10 = all_52_15
% 178.07/28.36    (28)   ~ (all_52_5 = all_4_2)
% 178.07/28.36    (29)  all_58_7 = all_52_19
% 178.07/28.36    (30)   ~ (all_52_17 = all_52_25)
% 178.07/28.36    (31)  all_58_4 = all_52_5
% 178.07/28.36    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.36    (33)  all_52_18 = e2
% 178.07/28.36    (34)  all_34_1 = all_4_1
% 178.07/28.36    (35)   ~ (all_52_27 = all_52_29)
% 178.07/28.36    (36)   ~ (all_52_17 = all_14_2)
% 178.07/28.36    (37)  op(e3, all_4_2) = all_4_1
% 178.07/28.36    (38)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.07/28.36    (39)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.36    (40)   ~ (all_52_7 = all_4_2)
% 178.07/28.36    (41)  all_58_1 = all_52_3
% 178.07/28.36    (42)  all_58_0 = all_4_2
% 178.07/28.36    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.07/28.36    (44)  op(all_4_1, all_4_2) = e1
% 178.07/28.36    (45)  op(e1, all_52_29) = all_52_28
% 178.07/28.36    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.36    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.36    (48)   ~ (all_4_1 = e2)
% 178.07/28.36    (49)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.07/28.36    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.07/28.36    (51)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.07/28.36    (52)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.07/28.36    (53)  all_58_14 = all_52_29
% 178.07/28.36    (54)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.07/28.36    (55)   ~ (all_52_3 = all_52_5)
% 178.07/28.36    (56)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.36    (57)  op(e2, e1) = all_52_13
% 178.07/28.36    (58)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.36    (59)  all_58_8 = all_14_2
% 178.07/28.36    (60)  all_56_1 = all_52_3
% 178.07/28.36    (61)   ~ (all_14_0 = e3)
% 178.07/28.36    (62)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.07/28.36    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.07/28.36    (64)   ~ (all_52_5 = all_14_2)
% 178.07/28.36    (65)   ~ (all_52_3 = all_4_2)
% 178.07/28.36    (66)  op(e0, e3) = all_52_25
% 178.07/28.36    (67)   ~ (all_52_9 = all_10_2)
% 178.07/28.36    (68)  op(e3, all_52_17) = all_52_16
% 178.07/28.36    (69)   ~ (all_52_13 = all_14_2)
% 178.07/28.36    (70)   ~ (e3 = e0)
% 178.07/28.36    (71)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.07/28.36    (72)   ~ (all_52_9 = all_52_13)
% 178.07/28.36    (73)  op(e0, all_52_23) = all_52_22
% 178.07/28.36    (74)   ~ (all_52_15 = all_52_23)
% 178.07/28.36    (75)   ~ (all_52_5 = all_52_29)
% 178.07/28.36    (76)  all_58_13 = all_52_27
% 178.07/28.36    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.07/28.36    (78)  all_56_5 = all_10_2
% 178.07/28.36    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.07/28.36    (80)   ~ (all_52_9 = all_52_17)
% 178.07/28.36    (81)   ~ (all_14_0 = e2)
% 178.07/28.36    (82)  all_58_6 = all_52_17
% 178.07/28.36    (83)  op(e2, all_52_19) = all_52_18
% 178.07/28.36    (84)   ~ (e1 = e0)
% 178.07/28.36    (85)  all_56_0 = all_4_2
% 178.07/28.36    (86)  all_58_11 = all_52_23
% 178.07/28.36    (87)   ~ (all_52_3 = all_52_19)
% 178.07/28.36    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.07/28.36    (89)   ~ (all_52_7 = all_52_15)
% 178.07/28.36    (90)   ~ (all_52_29 = all_14_2)
% 178.07/28.36    (91)   ~ (all_52_19 = all_10_2)
% 178.07/28.36    (92)   ~ (all_52_23 = all_6_2)
% 178.07/28.36    (93)  all_58_2 = all_52_9
% 178.07/28.36    (94)  op(e3, e1) = all_52_5
% 178.07/28.36    (95)   ~ (all_52_25 = all_6_2)
% 178.07/28.36    (96)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.07/28.36    (97)  op(e1, e3) = all_52_17
% 178.07/28.36    (98)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.07/28.36    (99)   ~ (all_52_25 = all_4_2)
% 178.07/28.36    (100)  op(e3, e0) = all_52_7
% 178.07/28.36    (101)  op(e3, e3) = all_4_2
% 178.07/28.36    (102)   ~ (all_10_1 = e3)
% 178.07/28.36    (103)  all_56_8 = all_52_17
% 178.07/28.36    (104)   ~ (all_52_17 = all_4_2)
% 178.07/28.36    (105)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.36             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.36    (106)   ~ (all_52_25 = all_52_27)
% 178.07/28.36    (107)  all_34_2 = all_4_2
% 178.07/28.36    (108)   ~ (all_52_27 = all_6_2)
% 178.07/28.36    (109)   ~ (all_52_7 = all_6_2)
% 178.07/28.36    (110)   ~ (all_52_15 = all_10_2)
% 178.07/28.36    (111)   ~ (all_52_19 = all_52_27)
% 178.07/28.36    (112)  all_56_7 = all_52_15
% 178.07/28.36    (113)   ~ (all_52_7 = all_52_23)
% 178.07/28.36    (114)   ~ (all_52_13 = all_10_2)
% 178.07/28.36    (115)  op(e2, all_52_27) = all_52_26
% 178.07/28.36    (116)   ~ (all_52_17 = all_52_19)
% 178.07/28.36    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.36    (118)  all_52_22 = e0
% 178.07/28.36    (119)  op(e1, all_14_2) = all_14_1
% 178.07/28.36    (120)  all_58_9 = all_52_7
% 178.07/28.36    (121)   ~ (e2 = e0)
% 178.07/28.36    (122)  all_58_12 = all_52_25
% 178.07/28.36    (123)  all_14_1 = e1
% 178.07/28.36    (124)  all_56_6 = all_52_13
% 178.07/28.36    (125)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.36    (126)   ~ (all_52_9 = all_52_15)
% 178.07/28.36    (127)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.07/28.36    (128)   ~ (e3 = e2)
% 178.07/28.36    (129)   ~ (all_52_19 = all_14_2)
% 178.07/28.36    (130)  op(e2, e3) = all_52_9
% 178.07/28.36    (131)  all_56_13 = all_52_27
% 178.07/28.36  
% 178.07/28.36  Begin of proof
% 178.07/28.36  | 
% 178.07/28.36  | REDUCE: (20), (123) imply:
% 178.07/28.36  |   (132)  op(e1, all_14_2) = all_14_0
% 178.07/28.36  | 
% 178.07/28.36  | REDUCE: (7), (68) imply:
% 178.07/28.36  |   (133)  op(e3, all_52_17) = e3
% 178.07/28.36  | 
% 178.07/28.36  | REDUCE: (33), (83) imply:
% 178.07/28.36  |   (134)  op(e2, all_52_19) = e2
% 178.07/28.36  | 
% 178.07/28.36  | REDUCE: (119), (123) imply:
% 178.07/28.36  |   (135)  op(e1, all_14_2) = e1
% 178.07/28.36  | 
% 178.07/28.36  | REDUCE: (73), (118) imply:
% 178.07/28.36  |   (136)  op(e0, all_52_23) = e0
% 178.07/28.36  | 
% 178.07/28.36  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 178.07/28.36  |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 178.07/28.36  |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37),
% 178.07/28.36  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 178.07/28.36  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 178.07/28.36  |            (60), (61), (62), (63), (64), (65), (66), (67), (69), (70), (71),
% 178.07/28.36  |            (72), (74), (75), (76), (77), (78), (79), (80), (81), (82), (84),
% 178.07/28.36  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 178.07/28.36  |            (96), (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 178.07/28.36  |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 178.07/28.36  |            (115), (116), (117), (120), (121), (122), (124), (125), (126),
% 178.07/28.36  |            (127), (128), (129), (130), (131), (132), (133), (134), (135),
% 178.07/28.36  |            (136) are inconsistent by sub-proof #561.
% 178.07/28.36  | 
% 178.07/28.36  End of proof
% 178.07/28.36  
% 178.07/28.36  Sub-proof #561 shows that the following formulas are inconsistent:
% 178.07/28.36  ----------------------------------------------------------------
% 178.07/28.36    (1)   ~ (all_52_23 = all_14_2)
% 178.07/28.36    (2)   ~ (all_52_5 = all_52_13)
% 178.07/28.36    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.07/28.36    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.07/28.36    (5)   ~ (all_52_17 = all_52_23)
% 178.07/28.36    (6)  op(e2, all_10_2) = all_10_1
% 178.07/28.36    (7)  op(e3, e2) = all_52_3
% 178.07/28.36    (8)   ~ (all_52_9 = all_52_25)
% 178.07/28.36    (9)  op(e3, all_52_25) = all_52_24
% 178.07/28.36    (10)   ~ (all_52_19 = all_52_23)
% 178.07/28.36    (11)  op(e1, e2) = all_52_19
% 178.07/28.36    (12)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.36    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.07/28.36    (14)  all_58_5 = all_52_13
% 178.07/28.36    (15)   ~ (all_52_25 = all_52_29)
% 178.07/28.36    (16)  all_56_15 = all_6_2
% 178.07/28.36    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.36    (18)  op(e2, e0) = all_52_15
% 178.07/28.36    (19)  all_58_3 = all_10_2
% 178.07/28.36    (20)  all_56_9 = all_52_19
% 178.07/28.36    (21)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.36    (22)  all_58_15 = all_6_2
% 178.07/28.36    (23)   ~ (all_52_9 = all_4_2)
% 178.07/28.36    (24)   ~ (all_52_5 = all_52_7)
% 178.07/28.36    (25)  all_58_10 = all_52_15
% 178.07/28.36    (26)   ~ (all_52_5 = all_4_2)
% 178.07/28.36    (27)  all_58_7 = all_52_19
% 178.07/28.36    (28)   ~ (all_52_17 = all_52_25)
% 178.07/28.36    (29)  all_58_4 = all_52_5
% 178.07/28.36    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.36    (31)  all_34_1 = all_4_1
% 178.07/28.36    (32)   ~ (all_52_27 = all_52_29)
% 178.07/28.36    (33)   ~ (all_52_17 = all_14_2)
% 178.07/28.36    (34)  op(e3, all_4_2) = all_4_1
% 178.07/28.36    (35)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.07/28.36    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.36    (37)   ~ (all_52_7 = all_4_2)
% 178.07/28.36    (38)  all_58_1 = all_52_3
% 178.07/28.36    (39)  all_58_0 = all_4_2
% 178.07/28.36    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.07/28.36    (41)  op(all_4_1, all_4_2) = e1
% 178.07/28.36    (42)  op(e1, all_52_29) = all_52_28
% 178.07/28.36    (43)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.36    (44)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.36    (45)   ~ (all_4_1 = e2)
% 178.07/28.36    (46)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.07/28.36    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.07/28.36    (48)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.07/28.36    (49)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.07/28.36    (50)  all_58_14 = all_52_29
% 178.07/28.36    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.07/28.36    (52)   ~ (all_52_3 = all_52_5)
% 178.07/28.36    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.36    (54)  op(e2, e1) = all_52_13
% 178.07/28.36    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.36    (56)  all_58_8 = all_14_2
% 178.07/28.36    (57)  all_56_1 = all_52_3
% 178.07/28.36    (58)   ~ (all_14_0 = e3)
% 178.07/28.36    (59)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.07/28.36    (60)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.07/28.36    (61)   ~ (all_52_5 = all_14_2)
% 178.07/28.36    (62)   ~ (all_52_3 = all_4_2)
% 178.07/28.36    (63)  op(e0, e3) = all_52_25
% 178.07/28.36    (64)   ~ (all_52_9 = all_10_2)
% 178.07/28.36    (65)   ~ (all_52_13 = all_14_2)
% 178.07/28.36    (66)  op(e1, all_14_2) = all_14_0
% 178.07/28.36    (67)   ~ (e3 = e0)
% 178.07/28.36    (68)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.07/28.36    (69)   ~ (all_52_9 = all_52_13)
% 178.07/28.36    (70)   ~ (all_52_15 = all_52_23)
% 178.07/28.36    (71)   ~ (all_52_5 = all_52_29)
% 178.07/28.36    (72)  all_58_13 = all_52_27
% 178.07/28.36    (73)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.07/28.36    (74)  all_56_5 = all_10_2
% 178.07/28.36    (75)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.07/28.36    (76)   ~ (all_52_9 = all_52_17)
% 178.07/28.36    (77)   ~ (all_14_0 = e2)
% 178.07/28.36    (78)  all_58_6 = all_52_17
% 178.07/28.36    (79)  op(e2, all_52_19) = e2
% 178.07/28.36    (80)  op(e3, all_52_17) = e3
% 178.07/28.36    (81)   ~ (e1 = e0)
% 178.07/28.36    (82)  all_56_0 = all_4_2
% 178.07/28.36    (83)  all_58_11 = all_52_23
% 178.07/28.36    (84)   ~ (all_52_3 = all_52_19)
% 178.07/28.36    (85)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.07/28.36    (86)   ~ (all_52_7 = all_52_15)
% 178.07/28.36    (87)   ~ (all_52_29 = all_14_2)
% 178.07/28.36    (88)   ~ (all_52_19 = all_10_2)
% 178.07/28.36    (89)   ~ (all_52_23 = all_6_2)
% 178.07/28.36    (90)  all_58_2 = all_52_9
% 178.07/28.36    (91)  op(e3, e1) = all_52_5
% 178.07/28.36    (92)   ~ (all_52_25 = all_6_2)
% 178.07/28.36    (93)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.07/28.36    (94)  op(e1, e3) = all_52_17
% 178.07/28.36    (95)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.07/28.36    (96)   ~ (all_52_25 = all_4_2)
% 178.07/28.36    (97)  op(e3, e0) = all_52_7
% 178.07/28.36    (98)  op(e3, e3) = all_4_2
% 178.07/28.36    (99)   ~ (all_10_1 = e3)
% 178.07/28.36    (100)  all_56_8 = all_52_17
% 178.07/28.36    (101)   ~ (all_52_17 = all_4_2)
% 178.07/28.36    (102)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.36             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.36    (103)   ~ (all_52_25 = all_52_27)
% 178.07/28.36    (104)  all_34_2 = all_4_2
% 178.07/28.36    (105)   ~ (all_52_27 = all_6_2)
% 178.07/28.36    (106)   ~ (all_52_7 = all_6_2)
% 178.07/28.36    (107)  op(e0, all_52_23) = e0
% 178.07/28.36    (108)   ~ (all_52_15 = all_10_2)
% 178.07/28.36    (109)   ~ (all_52_19 = all_52_27)
% 178.07/28.36    (110)  all_56_7 = all_52_15
% 178.07/28.36    (111)  op(e1, all_14_2) = e1
% 178.07/28.36    (112)   ~ (all_52_7 = all_52_23)
% 178.07/28.36    (113)   ~ (all_52_13 = all_10_2)
% 178.07/28.36    (114)  op(e2, all_52_27) = all_52_26
% 178.07/28.36    (115)   ~ (all_52_17 = all_52_19)
% 178.07/28.36    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.36    (117)  all_58_9 = all_52_7
% 178.07/28.36    (118)   ~ (e2 = e0)
% 178.07/28.36    (119)  all_58_12 = all_52_25
% 178.07/28.36    (120)  all_56_6 = all_52_13
% 178.07/28.36    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.36    (122)   ~ (all_52_9 = all_52_15)
% 178.07/28.36    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.07/28.36    (124)   ~ (e3 = e2)
% 178.07/28.36    (125)   ~ (all_52_19 = all_14_2)
% 178.07/28.36    (126)  op(e2, e3) = all_52_9
% 178.07/28.36    (127)  all_56_13 = all_52_27
% 178.07/28.36  
% 178.07/28.36  Begin of proof
% 178.07/28.36  | 
% 178.07/28.36  | GROUND_INST: instantiating (102) with e1, all_14_0, all_14_2, e1, simplifying
% 178.07/28.36  |              with (66), (111) gives:
% 178.07/28.36  |   (128)  all_14_0 = e1
% 178.07/28.36  | 
% 178.07/28.36  | REDUCE: (58), (128) imply:
% 178.07/28.36  |   (129)   ~ (e3 = e1)
% 178.07/28.36  | 
% 178.07/28.36  | SIMP: (129) implies:
% 178.07/28.36  |   (130)   ~ (e3 = e1)
% 178.07/28.36  | 
% 178.07/28.36  | REDUCE: (77), (128) imply:
% 178.07/28.36  |   (131)   ~ (e2 = e1)
% 178.07/28.36  | 
% 178.07/28.36  | SIMP: (131) implies:
% 178.07/28.36  |   (132)   ~ (e2 = e1)
% 178.07/28.36  | 
% 178.07/28.36  | BETA: splitting (35) gives:
% 178.07/28.36  | 
% 178.07/28.36  | Case 1:
% 178.07/28.36  | | 
% 178.07/28.36  | |   (133)  all_56_15 = e3
% 178.07/28.36  | | 
% 178.07/28.36  | | REF_CLOSE: (16), (20), (27), (30), (34), (36), (39), (41), (44), (53), (56),
% 178.07/28.36  | |            (61), (76), (78), (79), (80), (83), (89), (90), (91), (92), (94),
% 178.07/28.36  | |            (98), (101), (102), (111), (119), (121), (124), (126), (130),
% 178.07/28.36  | |            (133) are inconsistent by sub-proof #568.
% 178.07/28.36  | | 
% 178.07/28.36  | Case 2:
% 178.07/28.36  | | 
% 178.07/28.36  | |   (134)   ~ (all_56_15 = e3)
% 178.07/28.36  | |   (135)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.07/28.36  | | 
% 178.07/28.36  | | REDUCE: (16), (134) imply:
% 178.07/28.36  | |   (136)   ~ (all_6_2 = e3)
% 178.07/28.36  | | 
% 178.07/28.36  | | BETA: splitting (51) gives:
% 178.07/28.36  | | 
% 178.07/28.36  | | Case 1:
% 178.07/28.36  | | | 
% 178.07/28.36  | | |   (137)  all_56_13 = e3
% 178.07/28.36  | | | 
% 178.07/28.36  | | | COMBINE_EQS: (127), (137) imply:
% 178.07/28.36  | | |   (138)  all_52_27 = e3
% 178.07/28.36  | | | 
% 178.07/28.36  | | | SIMP: (138) implies:
% 178.07/28.36  | | |   (139)  all_52_27 = e3
% 178.07/28.36  | | | 
% 178.07/28.36  | | | REF_CLOSE: (1), (7), (11), (12), (14), (17), (22), (24), (25), (26), (27),
% 178.07/28.36  | | |            (29), (30), (31), (32), (33), (34), (36), (39), (41), (43),
% 178.07/28.36  | | |            (48), (50), (52), (53), (56), (57), (61), (62), (63), (69),
% 178.07/28.36  | | |            (78), (80), (83), (84), (90), (91), (94), (98), (101), (102),
% 178.07/28.36  | | |            (103), (104), (105), (107), (111), (114), (116), (117), (118),
% 178.07/28.36  | | |            (119), (120), (122), (123), (124), (125), (126), (130), (139)
% 178.07/28.36  | | |            are inconsistent by sub-proof #565.
% 178.07/28.36  | | | 
% 178.07/28.36  | | Case 2:
% 178.07/28.36  | | | 
% 178.07/28.36  | | |   (140)   ~ (all_56_13 = e3)
% 178.07/28.36  | | | 
% 178.07/28.36  | | | REDUCE: (127), (140) imply:
% 178.07/28.36  | | |   (141)   ~ (all_52_27 = e3)
% 178.07/28.36  | | | 
% 178.07/28.36  | | | BETA: splitting (55) gives:
% 178.07/28.36  | | | 
% 178.07/28.36  | | | Case 1:
% 178.07/28.36  | | | | 
% 178.07/28.36  | | | |   (142)  all_58_12 = e3
% 178.07/28.36  | | | | 
% 178.07/28.36  | | | | REF_CLOSE: (6), (8), (11), (14), (19), (21), (22), (23), (24), (25),
% 178.07/28.36  | | | |            (26), (27), (28), (29), (30), (36), (37), (38), (39), (40),
% 178.07/28.36  | | | |            (47), (48), (49), (54), (56), (61), (63), (64), (65), (67),
% 178.07/28.36  | | | |            (68), (69), (70), (72), (73), (74), (75), (76), (78), (79),
% 178.07/28.36  | | | |            (80), (81), (82), (83), (84), (86), (88), (90), (91), (92),
% 178.07/28.36  | | | |            (93), (94), (95), (96), (97), (99), (101), (102), (103),
% 178.07/28.36  | | | |            (107), (108), (110), (111), (112), (115), (116), (117),
% 178.07/28.36  | | | |            (118), (119), (120), (121), (122), (123), (126), (130),
% 178.07/28.36  | | | |            (132), (142) are inconsistent by sub-proof #677.
% 178.07/28.36  | | | | 
% 178.07/28.36  | | | Case 2:
% 178.07/28.36  | | | | 
% 178.07/28.36  | | | |   (143)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.36  | | | | 
% 178.07/28.36  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (13), (14), (15),
% 178.07/28.36  | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 178.07/28.36  | | | |            (27), (28), (29), (30), (33), (34), (36), (37), (38), (39),
% 178.07/28.36  | | | |            (40), (41), (42), (44), (45), (46), (47), (50), (52), (53),
% 178.07/28.36  | | | |            (56), (59), (60), (61), (62), (63), (69), (71), (72), (76),
% 178.07/28.36  | | | |            (78), (79), (80), (82), (83), (84), (85), (87), (89), (90),
% 178.07/28.36  | | | |            (91), (92), (94), (96), (97), (98), (100), (101), (102),
% 178.07/28.36  | | | |            (103), (105), (106), (107), (109), (111), (112), (113),
% 178.07/28.36  | | | |            (115), (117), (119), (121), (124), (125), (126), (130),
% 178.07/28.36  | | | |            (135), (136), (141), (143) are inconsistent by sub-proof
% 178.07/28.36  | | | |            #562.
% 178.07/28.36  | | | | 
% 178.07/28.36  | | | End of split
% 178.07/28.36  | | | 
% 178.07/28.36  | | End of split
% 178.07/28.36  | | 
% 178.07/28.36  | End of split
% 178.07/28.36  | 
% 178.07/28.36  End of proof
% 178.07/28.36  
% 178.07/28.36  Sub-proof #562 shows that the following formulas are inconsistent:
% 178.07/28.36  ----------------------------------------------------------------
% 178.07/28.36    (1)   ~ (all_52_23 = all_14_2)
% 178.07/28.36    (2)   ~ (all_52_5 = all_52_13)
% 178.07/28.36    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.07/28.36    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.07/28.36    (5)   ~ (all_52_17 = all_52_23)
% 178.07/28.36    (6)   ~ (all_52_9 = all_52_25)
% 178.07/28.36    (7)  op(e3, all_52_25) = all_52_24
% 178.07/28.36    (8)   ~ (all_52_19 = all_52_23)
% 178.07/28.36    (9)   ~ (all_52_27 = e3)
% 178.07/28.37    (10)   ~ (all_6_2 = e3)
% 178.07/28.37    (11)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.07/28.37    (12)  all_58_5 = all_52_13
% 178.07/28.37    (13)   ~ (all_52_25 = all_52_29)
% 178.07/28.37    (14)  all_56_15 = all_6_2
% 178.07/28.37    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.37    (16)  op(e2, e0) = all_52_15
% 178.07/28.37    (17)  all_58_3 = all_10_2
% 178.07/28.37    (18)  all_56_9 = all_52_19
% 178.07/28.37    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.37    (20)  all_58_15 = all_6_2
% 178.07/28.37    (21)   ~ (all_52_9 = all_4_2)
% 178.07/28.37    (22)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.07/28.37    (23)  all_58_10 = all_52_15
% 178.07/28.37    (24)   ~ (all_52_5 = all_4_2)
% 178.07/28.37    (25)  all_58_7 = all_52_19
% 178.07/28.37    (26)   ~ (all_52_17 = all_52_25)
% 178.07/28.37    (27)  all_58_4 = all_52_5
% 178.07/28.37    (28)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.37    (29)   ~ (e3 = e1)
% 178.07/28.37    (30)   ~ (all_52_17 = all_14_2)
% 178.07/28.37    (31)  op(e3, all_4_2) = all_4_1
% 178.07/28.37    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.37    (33)   ~ (all_52_7 = all_4_2)
% 178.07/28.37    (34)  all_58_1 = all_52_3
% 178.07/28.37    (35)  all_58_0 = all_4_2
% 178.07/28.37    (36)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.07/28.37    (37)  op(all_4_1, all_4_2) = e1
% 178.07/28.37    (38)  op(e1, all_52_29) = all_52_28
% 178.07/28.37    (39)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.37    (40)   ~ (all_4_1 = e2)
% 178.07/28.37    (41)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.07/28.37    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.07/28.37    (43)  all_58_14 = all_52_29
% 178.07/28.37    (44)   ~ (all_52_3 = all_52_5)
% 178.07/28.37    (45)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.37    (46)  all_58_8 = all_14_2
% 178.07/28.37    (47)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.07/28.37    (48)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.07/28.37    (49)   ~ (all_52_5 = all_14_2)
% 178.07/28.37    (50)   ~ (all_52_3 = all_4_2)
% 178.07/28.37    (51)  op(e0, e3) = all_52_25
% 178.07/28.37    (52)   ~ (all_52_9 = all_52_13)
% 178.07/28.37    (53)   ~ (all_52_5 = all_52_29)
% 178.07/28.37    (54)  all_58_13 = all_52_27
% 178.07/28.37    (55)   ~ (all_52_9 = all_52_17)
% 178.07/28.37    (56)  all_58_6 = all_52_17
% 178.07/28.37    (57)  op(e2, all_52_19) = e2
% 178.07/28.37    (58)  op(e3, all_52_17) = e3
% 178.07/28.37    (59)  all_56_0 = all_4_2
% 178.07/28.37    (60)  all_58_11 = all_52_23
% 178.07/28.37    (61)   ~ (all_52_3 = all_52_19)
% 178.07/28.37    (62)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.07/28.37    (63)   ~ (all_52_29 = all_14_2)
% 178.07/28.37    (64)   ~ (all_52_23 = all_6_2)
% 178.07/28.37    (65)  all_58_2 = all_52_9
% 178.07/28.37    (66)  op(e3, e1) = all_52_5
% 178.07/28.37    (67)   ~ (all_52_25 = all_6_2)
% 178.07/28.37    (68)  op(e1, e3) = all_52_17
% 178.07/28.37    (69)   ~ (all_52_25 = all_4_2)
% 178.07/28.37    (70)  op(e3, e0) = all_52_7
% 178.07/28.37    (71)  op(e3, e3) = all_4_2
% 178.07/28.37    (72)  all_56_8 = all_52_17
% 178.07/28.37    (73)   ~ (all_52_17 = all_4_2)
% 178.07/28.37    (74)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.37    (75)   ~ (all_52_25 = all_52_27)
% 178.07/28.37    (76)   ~ (all_52_27 = all_6_2)
% 178.07/28.37    (77)   ~ (all_52_7 = all_6_2)
% 178.07/28.37    (78)  op(e0, all_52_23) = e0
% 178.07/28.37    (79)   ~ (all_52_19 = all_52_27)
% 178.07/28.37    (80)  op(e1, all_14_2) = e1
% 178.07/28.37    (81)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.37    (82)   ~ (all_52_7 = all_52_23)
% 178.07/28.37    (83)   ~ (all_52_13 = all_10_2)
% 178.07/28.37    (84)   ~ (all_52_17 = all_52_19)
% 178.07/28.37    (85)  all_58_9 = all_52_7
% 178.07/28.37    (86)  all_58_12 = all_52_25
% 178.07/28.37    (87)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.37    (88)   ~ (e3 = e2)
% 178.07/28.37    (89)   ~ (all_52_19 = all_14_2)
% 178.07/28.37    (90)  op(e2, e3) = all_52_9
% 178.07/28.37  
% 178.07/28.37  Begin of proof
% 178.07/28.37  | 
% 178.07/28.37  | BETA: splitting (81) gives:
% 178.07/28.37  | 
% 178.07/28.37  | Case 1:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (91)  all_58_13 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | REF_CLOSE: (9), (54), (91) are inconsistent by sub-proof #1026.
% 178.07/28.37  | | 
% 178.07/28.37  | Case 2:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (92)  all_58_14 = e3 | all_58_15 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | BETA: splitting (92) gives:
% 178.07/28.37  | | 
% 178.07/28.37  | | Case 1:
% 178.07/28.37  | | | 
% 178.07/28.37  | | |   (93)  all_58_14 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | COMBINE_EQS: (43), (93) imply:
% 178.07/28.37  | | |   (94)  all_52_29 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (94) implies:
% 178.07/28.37  | | |   (95)  all_52_29 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (53), (95) imply:
% 178.07/28.37  | | |   (96)   ~ (all_52_5 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (13), (95) imply:
% 178.07/28.37  | | |   (97)   ~ (all_52_25 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (63), (95) imply:
% 178.07/28.37  | | |   (98)   ~ (all_14_2 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (98) implies:
% 178.07/28.37  | | |   (99)   ~ (all_14_2 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (38), (95) imply:
% 178.07/28.37  | | |   (100)  op(e1, e3) = all_52_28
% 178.07/28.37  | | | 
% 178.07/28.37  | | | GROUND_INST: instantiating (74) with all_52_17, all_52_28, e3, e1,
% 178.07/28.37  | | |              simplifying with (68), (100) gives:
% 178.07/28.37  | | |   (101)  all_52_17 = all_52_28
% 178.07/28.37  | | | 
% 178.07/28.37  | | | COMBINE_EQS: (72), (101) imply:
% 178.07/28.37  | | |   (102)  all_56_8 = all_52_28
% 178.07/28.37  | | | 
% 178.07/28.37  | | | COMBINE_EQS: (56), (101) imply:
% 178.07/28.37  | | |   (103)  all_58_6 = all_52_28
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (55), (101) imply:
% 178.07/28.37  | | |   (104)   ~ (all_52_9 = all_52_28)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (84), (101) imply:
% 178.07/28.37  | | |   (105)   ~ (all_52_19 = all_52_28)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (105) implies:
% 178.07/28.37  | | |   (106)   ~ (all_52_19 = all_52_28)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (5), (101) imply:
% 178.07/28.37  | | |   (107)   ~ (all_52_23 = all_52_28)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (107) implies:
% 178.07/28.37  | | |   (108)   ~ (all_52_23 = all_52_28)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (26), (101) imply:
% 178.07/28.37  | | |   (109)   ~ (all_52_25 = all_52_28)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (109) implies:
% 178.07/28.37  | | |   (110)   ~ (all_52_25 = all_52_28)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (30), (101) imply:
% 178.07/28.37  | | |   (111)   ~ (all_52_28 = all_14_2)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (73), (101) imply:
% 178.07/28.37  | | |   (112)   ~ (all_52_28 = all_4_2)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (58), (101) imply:
% 178.07/28.37  | | |   (113)  op(e3, all_52_28) = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | BETA: splitting (42) gives:
% 178.07/28.37  | | | 
% 178.07/28.37  | | | Case 1:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | |   (114)  all_58_1 = e3
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | COMBINE_EQS: (34), (114) imply:
% 178.07/28.37  | | | |   (115)  all_52_3 = e3
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REDUCE: (44), (115) imply:
% 178.07/28.37  | | | |   (116)   ~ (all_52_5 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REDUCE: (61), (115) imply:
% 178.07/28.37  | | | |   (117)   ~ (all_52_19 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | SIMP: (117) implies:
% 178.07/28.37  | | | |   (118)   ~ (all_52_19 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REDUCE: (50), (115) imply:
% 178.07/28.37  | | | |   (119)   ~ (all_4_2 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | SIMP: (119) implies:
% 178.07/28.37  | | | |   (120)   ~ (all_4_2 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (14), (15),
% 178.07/28.37  | | | |            (16), (17), (19), (21), (22), (23), (24), (25), (27), (28),
% 178.07/28.37  | | | |            (31), (32), (35), (36), (40), (41), (45), (46), (47), (48),
% 178.07/28.37  | | | |            (51), (52), (54), (56), (57), (58), (59), (60), (62), (64),
% 178.07/28.37  | | | |            (65), (66), (67), (69), (70), (71), (73), (74), (75), (76),
% 178.07/28.37  | | | |            (77), (78), (79), (83), (85), (86), (89), (93), (96), (97),
% 178.07/28.37  | | | |            (99), (102), (103), (104), (106), (108), (110), (111), (112),
% 178.07/28.37  | | | |            (113), (114), (118), (120) are inconsistent by sub-proof
% 178.07/28.37  | | | |            #671.
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | Case 2:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | |   (121)   ~ (all_58_1 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REDUCE: (34), (121) imply:
% 178.07/28.37  | | | |   (122)   ~ (all_52_3 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REF_CLOSE: (18), (25), (27), (28), (29), (31), (32), (33), (34), (35),
% 178.07/28.37  | | | |            (37), (39), (45), (46), (49), (55), (56), (57), (58), (60),
% 178.07/28.37  | | | |            (65), (66), (68), (71), (73), (74), (80), (82), (85), (86),
% 178.07/28.37  | | | |            (87), (88), (90), (96), (97), (122) are inconsistent by
% 178.07/28.37  | | | |            sub-proof #563.
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | End of split
% 178.07/28.37  | | | 
% 178.07/28.37  | | Case 2:
% 178.07/28.37  | | | 
% 178.07/28.37  | | |   (123)  all_58_15 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | COMBINE_EQS: (20), (123) imply:
% 178.07/28.37  | | |   (124)  all_6_2 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (10), (124) imply:
% 178.07/28.37  | | |   (125)  $false
% 178.07/28.37  | | | 
% 178.07/28.37  | | | CLOSE: (125) is inconsistent.
% 178.07/28.37  | | | 
% 178.07/28.37  | | End of split
% 178.07/28.37  | | 
% 178.07/28.37  | End of split
% 178.07/28.37  | 
% 178.07/28.37  End of proof
% 178.07/28.37  
% 178.07/28.37  Sub-proof #563 shows that the following formulas are inconsistent:
% 178.07/28.37  ----------------------------------------------------------------
% 178.07/28.37    (1)   ~ (all_52_25 = e3)
% 178.07/28.37    (2)  all_56_9 = all_52_19
% 178.07/28.37    (3)  all_58_7 = all_52_19
% 178.07/28.37    (4)  all_58_4 = all_52_5
% 178.07/28.37    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.37    (6)   ~ (e3 = e1)
% 178.07/28.37    (7)  op(e3, all_4_2) = all_4_1
% 178.07/28.37    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.37    (9)   ~ (all_52_7 = all_4_2)
% 178.07/28.37    (10)  all_58_1 = all_52_3
% 178.07/28.37    (11)  all_58_0 = all_4_2
% 178.07/28.37    (12)  op(all_4_1, all_4_2) = e1
% 178.07/28.37    (13)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.37    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.37    (15)  all_58_8 = all_14_2
% 178.07/28.37    (16)   ~ (all_52_5 = all_14_2)
% 178.07/28.37    (17)   ~ (all_52_5 = e3)
% 178.07/28.37    (18)   ~ (all_52_3 = e3)
% 178.07/28.37    (19)   ~ (all_52_9 = all_52_17)
% 178.07/28.37    (20)  all_58_6 = all_52_17
% 178.07/28.37    (21)  op(e2, all_52_19) = e2
% 178.07/28.37    (22)  op(e3, all_52_17) = e3
% 178.07/28.37    (23)  all_58_11 = all_52_23
% 178.07/28.37    (24)  all_58_2 = all_52_9
% 178.07/28.37    (25)  op(e3, e1) = all_52_5
% 178.07/28.37    (26)  op(e1, e3) = all_52_17
% 178.07/28.37    (27)  op(e3, e3) = all_4_2
% 178.07/28.37    (28)   ~ (all_52_17 = all_4_2)
% 178.07/28.37    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.37    (30)  op(e1, all_14_2) = e1
% 178.07/28.37    (31)   ~ (all_52_7 = all_52_23)
% 178.07/28.37    (32)  all_58_9 = all_52_7
% 178.07/28.37    (33)  all_58_12 = all_52_25
% 178.07/28.37    (34)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.37    (35)   ~ (e3 = e2)
% 178.07/28.37    (36)  op(e2, e3) = all_52_9
% 178.07/28.37  
% 178.07/28.37  Begin of proof
% 178.07/28.37  | 
% 178.07/28.37  | BETA: splitting (34) gives:
% 178.07/28.37  | 
% 178.07/28.37  | Case 1:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (37)  all_58_0 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | COMBINE_EQS: (11), (37) imply:
% 178.07/28.37  | |   (38)  all_4_2 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | REF_CLOSE: (6), (7), (12), (27), (29), (38) are inconsistent by sub-proof
% 178.07/28.37  | |            #599.
% 178.07/28.37  | | 
% 178.07/28.37  | Case 2:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (39)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (13), (14), (15),
% 178.07/28.37  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 178.07/28.37  | |            (27), (28), (29), (30), (31), (32), (33), (35), (36), (39) are
% 178.07/28.37  | |            inconsistent by sub-proof #564.
% 178.07/28.37  | | 
% 178.07/28.37  | End of split
% 178.07/28.37  | 
% 178.07/28.37  End of proof
% 178.07/28.37  
% 178.07/28.37  Sub-proof #564 shows that the following formulas are inconsistent:
% 178.07/28.37  ----------------------------------------------------------------
% 178.07/28.37    (1)   ~ (all_52_25 = e3)
% 178.07/28.37    (2)  all_56_9 = all_52_19
% 178.07/28.37    (3)  all_58_7 = all_52_19
% 178.07/28.37    (4)  all_58_4 = all_52_5
% 178.07/28.37    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.37    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.37    (7)   ~ (all_52_7 = all_4_2)
% 178.07/28.37    (8)  all_58_1 = all_52_3
% 178.07/28.37    (9)  all_58_0 = all_4_2
% 178.07/28.37    (10)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.37    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.37    (12)  all_58_8 = all_14_2
% 178.07/28.37    (13)   ~ (all_52_5 = all_14_2)
% 178.07/28.37    (14)   ~ (all_52_5 = e3)
% 178.07/28.37    (15)   ~ (all_52_3 = e3)
% 178.07/28.37    (16)   ~ (all_52_9 = all_52_17)
% 178.07/28.37    (17)  all_58_6 = all_52_17
% 178.07/28.37    (18)  op(e2, all_52_19) = e2
% 178.07/28.37    (19)  op(e3, all_52_17) = e3
% 178.07/28.37    (20)  all_58_11 = all_52_23
% 178.07/28.37    (21)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.37    (22)  all_58_2 = all_52_9
% 178.07/28.37    (23)  op(e3, e1) = all_52_5
% 178.07/28.37    (24)  op(e1, e3) = all_52_17
% 178.07/28.37    (25)  op(e3, e3) = all_4_2
% 178.07/28.37    (26)   ~ (all_52_17 = all_4_2)
% 178.07/28.37    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.37    (28)  op(e1, all_14_2) = e1
% 178.07/28.37    (29)   ~ (all_52_7 = all_52_23)
% 178.07/28.37    (30)  all_58_9 = all_52_7
% 178.07/28.37    (31)  all_58_12 = all_52_25
% 178.07/28.37    (32)   ~ (e3 = e2)
% 178.07/28.37    (33)  op(e2, e3) = all_52_9
% 178.07/28.37  
% 178.07/28.37  Begin of proof
% 178.07/28.37  | 
% 178.07/28.37  | BETA: splitting (21) gives:
% 178.07/28.37  | 
% 178.07/28.37  | Case 1:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (34)  all_58_1 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | COMBINE_EQS: (8), (34) imply:
% 178.07/28.37  | |   (35)  all_52_3 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | REDUCE: (15), (35) imply:
% 178.07/28.37  | |   (36)  $false
% 178.07/28.37  | | 
% 178.07/28.37  | | CLOSE: (36) is inconsistent.
% 178.07/28.37  | | 
% 178.07/28.37  | Case 2:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (37)  all_58_4 = e3 | all_58_9 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 178.07/28.37  | |            (14), (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 178.07/28.37  | |            (27), (28), (29), (30), (31), (32), (33), (37) are inconsistent
% 178.07/28.37  | |            by sub-proof #623.
% 178.07/28.37  | | 
% 178.07/28.37  | End of split
% 178.07/28.37  | 
% 178.07/28.37  End of proof
% 178.07/28.37  
% 178.07/28.37  Sub-proof #565 shows that the following formulas are inconsistent:
% 178.07/28.37  ----------------------------------------------------------------
% 178.07/28.37    (1)   ~ (all_52_23 = all_14_2)
% 178.07/28.37    (2)  op(e3, e2) = all_52_3
% 178.07/28.37    (3)  op(e1, e2) = all_52_19
% 178.07/28.37    (4)  all_52_27 = e3
% 178.07/28.37    (5)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.37    (6)  all_58_5 = all_52_13
% 178.07/28.37    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.37    (8)  all_58_15 = all_6_2
% 178.07/28.37    (9)   ~ (all_52_5 = all_52_7)
% 178.07/28.37    (10)  all_58_10 = all_52_15
% 178.07/28.37    (11)   ~ (all_52_5 = all_4_2)
% 178.07/28.37    (12)  all_58_7 = all_52_19
% 178.07/28.37    (13)  all_58_4 = all_52_5
% 178.07/28.37    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.37    (15)   ~ (e3 = e1)
% 178.07/28.37    (16)  all_34_1 = all_4_1
% 178.07/28.37    (17)   ~ (all_52_27 = all_52_29)
% 178.07/28.37    (18)   ~ (all_52_17 = all_14_2)
% 178.07/28.37    (19)  op(e3, all_4_2) = all_4_1
% 178.07/28.37    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.37    (21)  all_58_0 = all_4_2
% 178.07/28.37    (22)  op(all_4_1, all_4_2) = e1
% 178.07/28.37    (23)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.37    (24)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.07/28.37    (25)  all_58_14 = all_52_29
% 178.07/28.37    (26)   ~ (all_52_3 = all_52_5)
% 178.07/28.37    (27)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.37    (28)  all_58_8 = all_14_2
% 178.07/28.37    (29)  all_56_1 = all_52_3
% 178.07/28.37    (30)   ~ (all_52_5 = all_14_2)
% 178.07/28.37    (31)   ~ (all_52_3 = all_4_2)
% 178.07/28.37    (32)  op(e0, e3) = all_52_25
% 178.07/28.37    (33)   ~ (all_52_9 = all_52_13)
% 178.07/28.37    (34)  all_58_6 = all_52_17
% 178.07/28.37    (35)  op(e3, all_52_17) = e3
% 178.07/28.37    (36)  all_58_11 = all_52_23
% 178.07/28.37    (37)   ~ (all_52_3 = all_52_19)
% 178.07/28.37    (38)  all_58_2 = all_52_9
% 178.07/28.37    (39)  op(e3, e1) = all_52_5
% 178.07/28.37    (40)  op(e1, e3) = all_52_17
% 178.07/28.37    (41)  op(e3, e3) = all_4_2
% 178.07/28.37    (42)   ~ (all_52_17 = all_4_2)
% 178.07/28.37    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.37    (44)   ~ (all_52_25 = all_52_27)
% 178.07/28.37    (45)  all_34_2 = all_4_2
% 178.07/28.37    (46)   ~ (all_52_27 = all_6_2)
% 178.07/28.37    (47)  op(e0, all_52_23) = e0
% 178.07/28.37    (48)  op(e1, all_14_2) = e1
% 178.07/28.37    (49)  op(e2, all_52_27) = all_52_26
% 178.07/28.37    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.37    (51)  all_58_9 = all_52_7
% 178.07/28.37    (52)   ~ (e2 = e0)
% 178.07/28.37    (53)  all_58_12 = all_52_25
% 178.07/28.37    (54)  all_56_6 = all_52_13
% 178.07/28.37    (55)   ~ (all_52_9 = all_52_15)
% 178.07/28.37    (56)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.07/28.37    (57)   ~ (e3 = e2)
% 178.07/28.37    (58)   ~ (all_52_19 = all_14_2)
% 178.07/28.37    (59)  op(e2, e3) = all_52_9
% 178.07/28.37  
% 178.07/28.37  Begin of proof
% 178.07/28.37  | 
% 178.07/28.37  | REDUCE: (4), (44) imply:
% 178.07/28.37  |   (60)   ~ (all_52_25 = e3)
% 178.07/28.37  | 
% 178.07/28.37  | REDUCE: (4), (17) imply:
% 178.07/28.37  |   (61)   ~ (all_52_29 = e3)
% 178.07/28.37  | 
% 178.07/28.37  | SIMP: (61) implies:
% 178.07/28.37  |   (62)   ~ (all_52_29 = e3)
% 178.07/28.37  | 
% 178.07/28.37  | REDUCE: (4), (46) imply:
% 178.07/28.37  |   (63)   ~ (all_6_2 = e3)
% 178.07/28.37  | 
% 178.07/28.37  | SIMP: (63) implies:
% 178.07/28.37  |   (64)   ~ (all_6_2 = e3)
% 178.07/28.37  | 
% 178.07/28.37  | REDUCE: (4), (49) imply:
% 178.07/28.37  |   (65)  op(e2, e3) = all_52_26
% 178.07/28.37  | 
% 178.07/28.37  | GROUND_INST: instantiating (43) with all_52_9, all_52_26, e3, e2, simplifying
% 178.07/28.37  |              with (59), (65) gives:
% 178.07/28.37  |   (66)  all_52_9 = all_52_26
% 178.07/28.37  | 
% 178.07/28.37  | COMBINE_EQS: (38), (66) imply:
% 178.07/28.37  |   (67)  all_58_2 = all_52_26
% 178.07/28.37  | 
% 178.07/28.37  | REDUCE: (33), (66) imply:
% 178.07/28.37  |   (68)   ~ (all_52_13 = all_52_26)
% 178.07/28.37  | 
% 178.07/28.37  | SIMP: (68) implies:
% 178.07/28.37  |   (69)   ~ (all_52_13 = all_52_26)
% 178.07/28.37  | 
% 178.07/28.37  | REDUCE: (55), (66) imply:
% 178.07/28.37  |   (70)   ~ (all_52_15 = all_52_26)
% 178.07/28.37  | 
% 178.07/28.37  | SIMP: (70) implies:
% 178.07/28.37  |   (71)   ~ (all_52_15 = all_52_26)
% 178.07/28.37  | 
% 178.07/28.37  | BETA: splitting (24) gives:
% 178.07/28.37  | 
% 178.07/28.37  | Case 1:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (72)  all_56_6 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | COMBINE_EQS: (54), (72) imply:
% 178.07/28.37  | |   (73)  all_52_13 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | SIMP: (73) implies:
% 178.07/28.37  | |   (74)  all_52_13 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | REDUCE: (69), (74) imply:
% 178.07/28.37  | |   (75)   ~ (all_52_26 = e3)
% 178.07/28.37  | | 
% 178.07/28.37  | | SIMP: (75) implies:
% 178.07/28.37  | |   (76)   ~ (all_52_26 = e3)
% 178.07/28.37  | | 
% 178.07/28.37  | | BETA: splitting (27) gives:
% 178.07/28.37  | | 
% 178.07/28.37  | | Case 1:
% 178.07/28.37  | | | 
% 178.07/28.37  | | |   (77)  all_58_0 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | COMBINE_EQS: (21), (77) imply:
% 178.07/28.37  | | |   (78)  all_4_2 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REF_CLOSE: (15), (19), (22), (41), (43), (78) are inconsistent by
% 178.07/28.37  | | |            sub-proof #599.
% 178.07/28.37  | | | 
% 178.07/28.37  | | Case 2:
% 178.07/28.37  | | | 
% 178.07/28.37  | | |   (79)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REF_CLOSE: (34), (35), (41), (42), (43), (53), (60), (67), (76), (79) are
% 178.07/28.37  | | |            inconsistent by sub-proof #567.
% 178.07/28.37  | | | 
% 178.07/28.37  | | End of split
% 178.07/28.37  | | 
% 178.07/28.37  | Case 2:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (80)   ~ (all_56_6 = e3)
% 178.07/28.37  | | 
% 178.07/28.37  | | REDUCE: (54), (80) imply:
% 178.07/28.37  | |   (81)   ~ (all_52_13 = e3)
% 178.07/28.37  | | 
% 178.07/28.37  | | BETA: splitting (56) gives:
% 178.07/28.37  | | 
% 178.07/28.37  | | Case 1:
% 178.07/28.37  | | | 
% 178.07/28.37  | | |   (82)  all_58_4 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | COMBINE_EQS: (13), (82) imply:
% 178.07/28.37  | | |   (83)  all_52_5 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (83) implies:
% 178.07/28.37  | | |   (84)  all_52_5 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (26), (84) imply:
% 178.07/28.37  | | |   (85)   ~ (all_52_3 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (9), (84) imply:
% 178.07/28.37  | | |   (86)   ~ (all_52_7 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (86) implies:
% 178.07/28.37  | | |   (87)   ~ (all_52_7 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | REDUCE: (11), (84) imply:
% 178.07/28.37  | | |   (88)   ~ (all_4_2 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | SIMP: (88) implies:
% 178.07/28.37  | | |   (89)   ~ (all_4_2 = e3)
% 178.07/28.37  | | | 
% 178.07/28.37  | | | BETA: splitting (20) gives:
% 178.07/28.37  | | | 
% 178.07/28.37  | | | Case 1:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | |   (90)  all_58_2 = e3
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | COMBINE_EQS: (67), (90) imply:
% 178.07/28.37  | | | |   (91)  all_52_26 = e3
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | SIMP: (91) implies:
% 178.07/28.37  | | | |   (92)  all_52_26 = e3
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REDUCE: (71), (92) imply:
% 178.07/28.37  | | | |   (93)   ~ (all_52_15 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | BETA: splitting (50) gives:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | Case 1:
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | |   (94)  all_58_9 = e3
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | | REF_CLOSE: (51), (87), (94) are inconsistent by sub-proof #972.
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | Case 2:
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | |   (95)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (10), (15), (16), (19), (21),
% 178.07/28.37  | | | | |            (22), (23), (29), (31), (32), (34), (35), (36), (37), (43),
% 178.07/28.37  | | | | |            (45), (47), (52), (53), (57), (64), (85), (90), (93), (95)
% 178.07/28.37  | | | | |            are inconsistent by sub-proof #566.
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | End of split
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | Case 2:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | |   (96)   ~ (all_58_2 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REDUCE: (67), (96) imply:
% 178.07/28.37  | | | |   (97)   ~ (all_52_26 = e3)
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | BETA: splitting (27) gives:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | Case 1:
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | |   (98)  all_58_0 = e3
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | | COMBINE_EQS: (21), (98) imply:
% 178.07/28.37  | | | | |   (99)  all_4_2 = e3
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | | REDUCE: (89), (99) imply:
% 178.07/28.37  | | | | |   (100)  $false
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | | CLOSE: (100) is inconsistent.
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | Case 2:
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | |   (101)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | | REF_CLOSE: (34), (35), (41), (42), (43), (53), (60), (67), (97), (101)
% 178.07/28.37  | | | | |            are inconsistent by sub-proof #567.
% 178.07/28.37  | | | | | 
% 178.07/28.37  | | | | End of split
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | End of split
% 178.07/28.37  | | | 
% 178.07/28.37  | | Case 2:
% 178.07/28.37  | | | 
% 178.07/28.37  | | |   (102)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.07/28.37  | | | 
% 178.07/28.37  | | | BETA: splitting (102) gives:
% 178.07/28.37  | | | 
% 178.07/28.37  | | | Case 1:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | |   (103)  all_58_5 = e3
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REF_CLOSE: (6), (81), (103) are inconsistent by sub-proof #969.
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | Case 2:
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | |   (104)  all_58_8 = e3 | all_58_14 = e3
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | | REF_CLOSE: (1), (12), (14), (18), (25), (28), (30), (34), (35), (36),
% 178.07/28.37  | | | |            (39), (40), (43), (48), (58), (62), (104) are inconsistent by
% 178.07/28.37  | | | |            sub-proof #703.
% 178.07/28.37  | | | | 
% 178.07/28.37  | | | End of split
% 178.07/28.37  | | | 
% 178.07/28.37  | | End of split
% 178.07/28.37  | | 
% 178.07/28.37  | End of split
% 178.07/28.37  | 
% 178.07/28.37  End of proof
% 178.07/28.37  
% 178.07/28.37  Sub-proof #566 shows that the following formulas are inconsistent:
% 178.07/28.37  ----------------------------------------------------------------
% 178.07/28.37    (1)  op(e3, e2) = all_52_3
% 178.07/28.37    (2)  op(e1, e2) = all_52_19
% 178.07/28.37    (3)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.37    (4)   ~ (all_6_2 = e3)
% 178.07/28.37    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.37    (6)  all_58_15 = all_6_2
% 178.07/28.37    (7)  all_58_2 = e3
% 178.07/28.37    (8)  all_58_10 = all_52_15
% 178.07/28.37    (9)   ~ (e3 = e1)
% 178.07/28.37    (10)  all_34_1 = all_4_1
% 178.07/28.37    (11)  op(e3, all_4_2) = all_4_1
% 178.07/28.37    (12)  all_58_0 = all_4_2
% 178.07/28.37    (13)  op(all_4_1, all_4_2) = e1
% 178.07/28.37    (14)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.37    (15)  all_56_1 = all_52_3
% 178.07/28.37    (16)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.37    (17)   ~ (all_52_3 = all_4_2)
% 178.07/28.37    (18)  op(e0, e3) = all_52_25
% 178.07/28.37    (19)   ~ (all_52_15 = e3)
% 178.07/28.37    (20)   ~ (all_52_3 = e3)
% 178.07/28.37    (21)  all_58_6 = all_52_17
% 178.07/28.37    (22)  op(e3, all_52_17) = e3
% 178.07/28.37    (23)  all_58_11 = all_52_23
% 178.07/28.37    (24)   ~ (all_52_3 = all_52_19)
% 178.07/28.37    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.37    (26)  all_34_2 = all_4_2
% 178.07/28.37    (27)  op(e0, all_52_23) = e0
% 178.07/28.37    (28)   ~ (e2 = e0)
% 178.07/28.37    (29)  all_58_12 = all_52_25
% 178.07/28.37    (30)   ~ (e3 = e2)
% 178.07/28.37  
% 178.07/28.37  Begin of proof
% 178.07/28.37  | 
% 178.07/28.37  | BETA: splitting (16) gives:
% 178.07/28.37  | 
% 178.07/28.37  | Case 1:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (31)  all_58_10 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | REF_CLOSE: (8), (19), (31) are inconsistent by sub-proof #1018.
% 178.07/28.37  | | 
% 178.07/28.37  | Case 2:
% 178.07/28.37  | | 
% 178.07/28.37  | |   (32)  all_58_11 = e3 | all_58_15 = e3
% 178.07/28.37  | | 
% 178.07/28.37  | | BETA: splitting (32) gives:
% 178.07/28.37  | | 
% 178.07/28.37  | | Case 1:
% 178.07/28.37  | | | 
% 178.07/28.37  | | |   (33)  all_58_11 = e3
% 178.07/28.38  | | | 
% 178.07/28.38  | | | COMBINE_EQS: (23), (33) imply:
% 178.07/28.38  | | |   (34)  all_52_23 = e3
% 178.07/28.38  | | | 
% 178.07/28.38  | | | SIMP: (34) implies:
% 178.07/28.38  | | |   (35)  all_52_23 = e3
% 178.07/28.38  | | | 
% 178.07/28.38  | | | REDUCE: (27), (35) imply:
% 178.07/28.38  | | |   (36)  op(e0, e3) = e0
% 178.07/28.38  | | | 
% 178.07/28.38  | | | GROUND_INST: instantiating (25) with all_52_25, e0, e3, e0, simplifying
% 178.07/28.38  | | |              with (18), (36) gives:
% 178.07/28.38  | | |   (37)  all_52_25 = e0
% 178.07/28.38  | | | 
% 178.07/28.38  | | | COMBINE_EQS: (29), (37) imply:
% 178.07/28.38  | | |   (38)  all_58_12 = e0
% 178.07/28.38  | | | 
% 178.07/28.38  | | | BETA: splitting (5) gives:
% 178.07/28.38  | | | 
% 178.07/28.38  | | | Case 1:
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | |   (39)  all_58_0 = e2
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | | COMBINE_EQS: (12), (39) imply:
% 178.07/28.38  | | | |   (40)  all_4_2 = e2
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | | COMBINE_EQS: (26), (40) imply:
% 178.07/28.38  | | | |   (41)  all_34_2 = e2
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | | REDUCE: (17), (40) imply:
% 178.07/28.38  | | | |   (42)   ~ (all_52_3 = e2)
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | | REDUCE: (13), (40) imply:
% 178.07/28.38  | | | |   (43)  op(all_4_1, e2) = e1
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | | REDUCE: (11), (40) imply:
% 178.07/28.38  | | | |   (44)  op(e3, e2) = all_4_1
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | | REF_CLOSE: (1), (2), (3), (9), (10), (14), (15), (24), (25), (41), (42),
% 178.07/28.38  | | | |            (43), (44) are inconsistent by sub-proof #592.
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | Case 2:
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | |   (45)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | | REF_CLOSE: (1), (7), (20), (21), (22), (25), (28), (30), (38), (45) are
% 178.07/28.38  | | | |            inconsistent by sub-proof #693.
% 178.07/28.38  | | | | 
% 178.07/28.38  | | | End of split
% 178.07/28.38  | | | 
% 178.07/28.38  | | Case 2:
% 178.07/28.38  | | | 
% 178.07/28.38  | | |   (46)  all_58_15 = e3
% 178.07/28.38  | | | 
% 178.07/28.38  | | | COMBINE_EQS: (6), (46) imply:
% 178.07/28.38  | | |   (47)  all_6_2 = e3
% 178.07/28.38  | | | 
% 178.07/28.38  | | | REDUCE: (4), (47) imply:
% 178.07/28.38  | | |   (48)  $false
% 178.07/28.38  | | | 
% 178.07/28.38  | | | CLOSE: (48) is inconsistent.
% 178.07/28.38  | | | 
% 178.07/28.38  | | End of split
% 178.07/28.38  | | 
% 178.07/28.38  | End of split
% 178.07/28.38  | 
% 178.07/28.38  End of proof
% 178.07/28.38  
% 178.07/28.38  Sub-proof #567 shows that the following formulas are inconsistent:
% 178.07/28.38  ----------------------------------------------------------------
% 178.07/28.38    (1)   ~ (all_52_25 = e3)
% 178.07/28.38    (2)  all_58_6 = all_52_17
% 178.07/28.38    (3)  all_58_2 = all_52_26
% 178.07/28.38    (4)  op(e3, all_52_17) = e3
% 178.07/28.38    (5)   ~ (all_52_26 = e3)
% 178.07/28.38    (6)  op(e3, e3) = all_4_2
% 178.07/28.38    (7)   ~ (all_52_17 = all_4_2)
% 178.07/28.38    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.38    (9)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.38    (10)  all_58_12 = all_52_25
% 178.07/28.38  
% 178.07/28.38  Begin of proof
% 178.07/28.38  | 
% 178.07/28.38  | BETA: splitting (9) gives:
% 178.07/28.38  | 
% 178.07/28.38  | Case 1:
% 178.07/28.38  | | 
% 178.07/28.38  | |   (11)  all_58_2 = e3
% 178.07/28.38  | | 
% 178.07/28.38  | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #1004.
% 178.07/28.38  | | 
% 178.07/28.38  | Case 2:
% 178.07/28.38  | | 
% 178.07/28.38  | |   (12)  all_58_6 = e3 | all_58_12 = e3
% 178.07/28.38  | | 
% 178.07/28.38  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (12) are inconsistent by
% 178.07/28.38  | |            sub-proof #947.
% 178.07/28.38  | | 
% 178.07/28.38  | End of split
% 178.07/28.38  | 
% 178.07/28.38  End of proof
% 178.07/28.38  
% 178.07/28.38  Sub-proof #568 shows that the following formulas are inconsistent:
% 178.07/28.38  ----------------------------------------------------------------
% 178.07/28.38    (1)  all_56_15 = e3
% 178.07/28.38    (2)  all_56_15 = all_6_2
% 178.07/28.38    (3)  all_56_9 = all_52_19
% 178.07/28.38    (4)  all_58_7 = all_52_19
% 178.07/28.38    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.38    (6)   ~ (e3 = e1)
% 178.07/28.38    (7)  op(e3, all_4_2) = all_4_1
% 178.07/28.38    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.38    (9)  all_58_0 = all_4_2
% 178.07/28.38    (10)  op(all_4_1, all_4_2) = e1
% 178.07/28.38    (11)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.38    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.38    (13)  all_58_8 = all_14_2
% 178.07/28.38    (14)   ~ (all_52_5 = all_14_2)
% 178.07/28.38    (15)   ~ (all_52_9 = all_52_17)
% 178.07/28.38    (16)  all_58_6 = all_52_17
% 178.07/28.38    (17)  op(e2, all_52_19) = e2
% 178.07/28.38    (18)  op(e3, all_52_17) = e3
% 178.07/28.38    (19)  all_58_11 = all_52_23
% 178.07/28.38    (20)   ~ (all_52_23 = all_6_2)
% 178.07/28.38    (21)  all_58_2 = all_52_9
% 178.07/28.38    (22)  op(e3, e1) = all_52_5
% 178.07/28.38    (23)   ~ (all_52_25 = all_6_2)
% 178.07/28.38    (24)  op(e1, e3) = all_52_17
% 178.07/28.38    (25)  op(e3, e3) = all_4_2
% 178.07/28.38    (26)   ~ (all_52_17 = all_4_2)
% 178.07/28.38    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.38    (28)  op(e1, all_14_2) = e1
% 178.07/28.38    (29)  all_58_12 = all_52_25
% 178.07/28.38    (30)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.38    (31)   ~ (e3 = e2)
% 178.07/28.38    (32)  op(e2, e3) = all_52_9
% 178.07/28.38  
% 178.07/28.38  Begin of proof
% 178.07/28.38  | 
% 178.07/28.38  | COMBINE_EQS: (1), (2) imply:
% 178.07/28.38  |   (33)  all_6_2 = e3
% 178.07/28.38  | 
% 178.07/28.38  | REDUCE: (20), (33) imply:
% 178.07/28.38  |   (34)   ~ (all_52_23 = e3)
% 178.07/28.38  | 
% 178.07/28.38  | REDUCE: (23), (33) imply:
% 178.07/28.38  |   (35)   ~ (all_52_25 = e3)
% 178.07/28.38  | 
% 178.07/28.38  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 178.07/28.38  |            (15), (16), (17), (18), (19), (21), (22), (24), (25), (26), (27),
% 178.07/28.38  |            (28), (29), (30), (31), (32), (34), (35) are inconsistent by
% 178.07/28.38  |            sub-proof #569.
% 178.07/28.38  | 
% 178.07/28.38  End of proof
% 178.07/28.38  
% 178.07/28.38  Sub-proof #569 shows that the following formulas are inconsistent:
% 178.07/28.38  ----------------------------------------------------------------
% 178.07/28.38    (1)   ~ (all_52_25 = e3)
% 178.07/28.38    (2)  all_56_9 = all_52_19
% 178.07/28.38    (3)  all_58_7 = all_52_19
% 178.07/28.38    (4)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.38    (5)   ~ (e3 = e1)
% 178.07/28.38    (6)  op(e3, all_4_2) = all_4_1
% 178.07/28.38    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.38    (8)  all_58_0 = all_4_2
% 178.07/28.38    (9)  op(all_4_1, all_4_2) = e1
% 178.07/28.38    (10)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.38    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.38    (12)  all_58_8 = all_14_2
% 178.07/28.38    (13)   ~ (all_52_5 = all_14_2)
% 178.07/28.38    (14)   ~ (all_52_23 = e3)
% 178.07/28.38    (15)   ~ (all_52_9 = all_52_17)
% 178.07/28.38    (16)  all_58_6 = all_52_17
% 178.07/28.38    (17)  op(e2, all_52_19) = e2
% 178.07/28.38    (18)  op(e3, all_52_17) = e3
% 178.07/28.38    (19)  all_58_11 = all_52_23
% 178.07/28.38    (20)  all_58_2 = all_52_9
% 178.07/28.38    (21)  op(e3, e1) = all_52_5
% 178.07/28.38    (22)  op(e1, e3) = all_52_17
% 178.07/28.38    (23)  op(e3, e3) = all_4_2
% 178.07/28.38    (24)   ~ (all_52_17 = all_4_2)
% 178.07/28.38    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.38    (26)  op(e1, all_14_2) = e1
% 178.07/28.38    (27)  all_58_12 = all_52_25
% 178.07/28.38    (28)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.38    (29)   ~ (e3 = e2)
% 178.07/28.38    (30)  op(e2, e3) = all_52_9
% 178.07/28.38  
% 178.07/28.38  Begin of proof
% 178.07/28.38  | 
% 178.07/28.38  | BETA: splitting (28) gives:
% 178.07/28.38  | 
% 178.07/28.38  | Case 1:
% 178.07/28.38  | | 
% 178.07/28.38  | |   (31)  all_58_0 = e3
% 178.07/28.38  | | 
% 178.07/28.38  | | COMBINE_EQS: (8), (31) imply:
% 178.07/28.38  | |   (32)  all_4_2 = e3
% 178.07/28.38  | | 
% 178.07/28.38  | | REF_CLOSE: (5), (6), (9), (23), (25), (32) are inconsistent by sub-proof
% 178.07/28.38  | |            #599.
% 178.07/28.38  | | 
% 178.07/28.38  | Case 2:
% 178.07/28.38  | | 
% 178.07/28.38  | |   (33)   ~ (all_58_0 = e3)
% 178.07/28.38  | | 
% 178.07/28.38  | | REDUCE: (8), (33) imply:
% 178.07/28.38  | |   (34)   ~ (all_4_2 = e3)
% 178.07/28.38  | | 
% 178.07/28.38  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (12), (13), (14), (15),
% 178.07/28.38  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 178.07/28.38  | |            (27), (29), (30), (34) are inconsistent by sub-proof #944.
% 178.07/28.38  | | 
% 178.07/28.38  | End of split
% 178.07/28.38  | 
% 178.07/28.38  End of proof
% 178.07/28.38  
% 178.07/28.38  Sub-proof #570 shows that the following formulas are inconsistent:
% 178.07/28.38  ----------------------------------------------------------------
% 178.07/28.38    (1)   ~ (all_52_23 = all_14_2)
% 178.07/28.38    (2)   ~ (all_52_5 = all_52_13)
% 178.07/28.38    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.07/28.38    (4)   ~ (all_52_27 = all_10_2)
% 178.07/28.38    (5)   ~ (all_52_17 = all_52_23)
% 178.07/28.38    (6)  op(e2, all_10_2) = all_10_1
% 178.07/28.38    (7)   ~ (all_52_13 = all_52_29)
% 178.07/28.38    (8)  all_56_3 = all_52_7
% 178.07/28.38    (9)  op(e3, e2) = all_52_3
% 178.07/28.38    (10)   ~ (all_52_9 = all_52_25)
% 178.07/28.38    (11)   ~ (all_52_19 = all_52_23)
% 178.07/28.38    (12)  all_56_11 = all_52_23
% 178.07/28.38    (13)  op(e1, e2) = all_52_19
% 178.07/28.38    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.38    (15)  op(e3, all_52_9) = all_52_8
% 178.07/28.38    (16)   ~ (all_52_3 = all_10_2)
% 178.07/28.38    (17)  all_58_5 = all_52_13
% 178.07/28.38    (18)   ~ (all_6_2 = e0)
% 178.07/28.38    (19)   ~ (all_52_25 = all_52_29)
% 178.07/28.38    (20)  all_56_15 = all_6_2
% 178.07/28.38    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.38    (22)  all_58_3 = all_10_2
% 178.07/28.38    (23)  all_56_9 = all_52_19
% 178.07/28.38    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.38    (25)  all_58_15 = all_6_2
% 178.07/28.38    (26)   ~ (all_52_9 = all_4_2)
% 178.07/28.38    (27)   ~ (all_52_5 = all_52_7)
% 178.07/28.38    (28)  all_58_10 = all_52_15
% 178.07/28.38    (29)   ~ (all_52_5 = all_4_2)
% 178.07/28.38    (30)  all_58_7 = all_52_19
% 178.07/28.38    (31)  all_56_4 = all_52_9
% 178.07/28.38    (32)   ~ (all_52_15 = all_6_2)
% 178.07/28.38    (33)   ~ (all_52_17 = all_52_25)
% 178.07/28.38    (34)  all_58_4 = all_52_5
% 178.07/28.38    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.38    (36)   ~ (e3 = e1)
% 178.07/28.38    (37)  all_34_1 = all_4_1
% 178.07/28.38    (38)   ~ (all_52_27 = all_52_29)
% 178.07/28.38    (39)   ~ (all_52_17 = all_14_2)
% 178.07/28.38    (40)  op(e3, all_4_2) = all_4_1
% 178.07/28.38    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.07/28.38    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.38    (43)   ~ (all_52_7 = all_4_2)
% 178.07/28.38    (44)  all_58_1 = all_52_3
% 178.07/28.38    (45)  all_58_0 = all_4_2
% 178.07/28.38    (46)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.07/28.38    (47)  op(e1, all_52_13) = all_52_12
% 178.07/28.38    (48)  op(all_4_1, all_4_2) = e1
% 178.07/28.38    (49)  op(e1, all_52_29) = all_52_28
% 178.07/28.38    (50)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 178.07/28.38          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 178.07/28.38    (51)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.38    (52)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.38    (53)   ~ (all_4_1 = e2)
% 178.07/28.38    (54)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.07/28.38    (55)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.07/28.38    (56)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.07/28.38    (57)   ~ (all_14_1 = e3)
% 178.07/28.38    (58)  all_58_14 = all_52_29
% 178.07/28.38    (59)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.07/28.38    (60)   ~ (all_52_3 = all_52_5)
% 178.07/28.38    (61)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.38    (62)  op(e2, e1) = all_52_13
% 178.07/28.38    (63)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.38    (64)  all_58_8 = all_14_2
% 178.07/28.38    (65)  all_56_1 = all_52_3
% 178.07/28.38    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.07/28.38    (67)   ~ (all_52_3 = all_52_27)
% 178.07/28.38    (68)   ~ (all_52_3 = all_4_2)
% 178.07/28.38    (69)  op(e0, e3) = all_52_25
% 178.07/28.38    (70)  op(e0, all_6_2) = all_6_1
% 178.07/28.38    (71)  all_52_0 = all_4_1
% 178.07/28.38    (72)  op(e3, all_52_17) = all_52_16
% 178.07/28.38    (73)  all_52_10 = all_10_1
% 178.07/28.38    (74)   ~ (all_52_13 = all_14_2)
% 178.07/28.38    (75)   ~ (e3 = e0)
% 178.07/28.38    (76)   ~ (all_52_9 = all_52_13)
% 178.07/28.38    (77)  op(e0, all_52_23) = all_52_22
% 178.07/28.38    (78)   ~ (all_52_15 = all_52_23)
% 178.07/28.38    (79)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.07/28.38    (80)  op(all_10_1, all_10_2) = all_10_0
% 178.07/28.38    (81)   ~ (all_52_5 = all_52_29)
% 178.07/28.38    (82)  all_56_2 = all_52_5
% 178.07/28.38    (83)  all_58_13 = all_52_27
% 178.07/28.38    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.07/28.38    (85)   ~ (all_52_9 = all_52_17)
% 178.07/28.38    (86)  all_58_6 = all_52_17
% 178.07/28.38    (87)   ~ (all_52_3 = all_52_7)
% 178.07/28.38    (88)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.07/28.38    (89)  op(e2, all_52_19) = all_52_18
% 178.07/28.38    (90)   ~ (e1 = e0)
% 178.07/28.38    (91)  all_56_0 = all_4_2
% 178.07/28.38    (92)  all_58_11 = all_52_23
% 178.07/28.38    (93)   ~ (all_52_3 = all_52_19)
% 178.07/28.38    (94)   ~ (all_52_7 = all_52_15)
% 178.07/28.38    (95)  op(e0, all_52_15) = all_52_14
% 178.07/28.38    (96)   ~ (all_52_29 = all_14_2)
% 178.07/28.38    (97)   ~ (all_52_19 = all_10_2)
% 178.07/28.38    (98)   ~ (all_52_23 = all_6_2)
% 178.07/28.38    (99)   ~ (all_52_29 = all_6_2)
% 178.07/28.38    (100)  all_58_2 = all_52_9
% 178.07/28.38    (101)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.07/28.38    (102)  op(e3, e1) = all_52_5
% 178.07/28.38    (103)  all_56_10 = all_14_2
% 178.07/28.38    (104)   ~ (all_52_25 = all_6_2)
% 178.07/28.38    (105)  op(e1, e1) = all_14_2
% 178.07/28.38    (106)  op(e1, e3) = all_52_17
% 178.07/28.38    (107)   ~ (all_52_25 = all_4_2)
% 178.07/28.38    (108)  op(e3, e0) = all_52_7
% 178.07/28.38    (109)  op(e3, e3) = all_4_2
% 178.07/28.38    (110)   ~ (all_52_17 = all_4_2)
% 178.07/28.38    (111)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.38             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.38    (112)   ~ (all_52_25 = all_52_27)
% 178.07/28.38    (113)  all_34_2 = all_4_2
% 178.07/28.38    (114)   ~ (all_52_27 = all_6_2)
% 178.07/28.38    (115)   ~ (all_52_7 = all_6_2)
% 178.07/28.38    (116)   ~ (all_10_0 = e3)
% 178.07/28.38    (117)   ~ (all_52_7 = all_52_23)
% 178.07/28.38    (118)  op(e2, all_52_27) = all_52_26
% 178.07/28.38    (119)   ~ (all_52_17 = all_52_19)
% 178.07/28.38    (120)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.38    (121)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.07/28.38    (122)  op(e1, all_14_2) = all_14_1
% 178.07/28.38    (123)  all_58_9 = all_52_7
% 178.07/28.38    (124)  all_58_12 = all_52_25
% 178.07/28.38    (125)   ~ (all_10_0 = e1)
% 178.07/28.38    (126)  all_56_6 = all_52_13
% 178.07/28.38    (127)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.38    (128)   ~ (all_52_9 = all_52_15)
% 178.07/28.38    (129)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.07/28.38    (130)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.07/28.38    (131)   ~ (all_52_19 = all_14_2)
% 178.07/28.38    (132)  op(e2, e3) = all_52_9
% 178.07/28.38    (133)  all_56_13 = all_52_27
% 178.07/28.38  
% 178.07/28.38  Begin of proof
% 178.07/28.38  | 
% 178.07/28.38  | BETA: splitting (50) gives:
% 178.07/28.38  | 
% 178.07/28.38  | Case 1:
% 178.07/28.38  | | 
% 178.07/28.38  | |   (134)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 178.07/28.38  | | 
% 178.07/28.38  | | REF_CLOSE: (36), (40), (48), (71), (111), (134) are inconsistent by
% 178.07/28.38  | |            sub-proof #600.
% 178.07/28.38  | | 
% 178.07/28.38  | Case 2:
% 178.07/28.38  | | 
% 178.07/28.38  | |   (135)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 178.07/28.38  | | 
% 178.07/28.38  | | ALPHA: (135) implies:
% 178.07/28.38  | |   (136)  all_52_14 = e0
% 178.07/28.38  | |   (137)  all_52_12 = e1
% 178.07/28.38  | |   (138)  all_52_10 = e2
% 178.07/28.38  | |   (139)  all_52_8 = e3
% 178.07/28.38  | | 
% 178.07/28.38  | | COMBINE_EQS: (73), (138) imply:
% 178.07/28.38  | |   (140)  all_10_1 = e2
% 178.07/28.38  | | 
% 178.07/28.38  | | REDUCE: (80), (140) imply:
% 178.07/28.38  | |   (141)  op(e2, all_10_2) = all_10_0
% 178.07/28.38  | | 
% 178.07/28.38  | | REDUCE: (15), (139) imply:
% 178.07/28.38  | |   (142)  op(e3, all_52_9) = e3
% 178.07/28.38  | | 
% 178.07/28.38  | | REDUCE: (6), (140) imply:
% 178.07/28.38  | |   (143)  op(e2, all_10_2) = e2
% 178.07/28.38  | | 
% 178.07/28.38  | | REDUCE: (47), (137) imply:
% 178.07/28.38  | |   (144)  op(e1, all_52_13) = e1
% 178.07/28.38  | | 
% 178.07/28.38  | | REDUCE: (95), (136) imply:
% 178.07/28.38  | |   (145)  op(e0, all_52_15) = e0
% 178.07/28.38  | | 
% 178.07/28.38  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 178.07/28.38  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 178.07/28.38  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 178.07/28.38  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (48),
% 178.07/28.38  | |            (49), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 178.07/28.38  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (72),
% 178.07/28.38  | |            (74), (75), (76), (77), (78), (79), (81), (82), (83), (84), (85),
% 178.07/28.38  | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (96), (97),
% 178.07/28.38  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 178.07/28.38  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 178.07/28.38  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 178.07/28.38  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 178.07/28.38  | |            (141), (142), (143), (144), (145) are inconsistent by sub-proof
% 178.07/28.38  | |            #571.
% 178.07/28.38  | | 
% 178.07/28.38  | End of split
% 178.07/28.38  | 
% 178.07/28.38  End of proof
% 178.07/28.38  
% 178.07/28.38  Sub-proof #571 shows that the following formulas are inconsistent:
% 178.07/28.38  ----------------------------------------------------------------
% 178.07/28.38    (1)   ~ (all_52_23 = all_14_2)
% 178.07/28.38    (2)   ~ (all_52_5 = all_52_13)
% 178.07/28.38    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.07/28.38    (4)   ~ (all_52_27 = all_10_2)
% 178.07/28.38    (5)   ~ (all_52_17 = all_52_23)
% 178.07/28.38    (6)   ~ (all_52_13 = all_52_29)
% 178.07/28.38    (7)  op(e2, all_10_2) = all_10_0
% 178.07/28.38    (8)  all_56_3 = all_52_7
% 178.07/28.38    (9)  op(e3, e2) = all_52_3
% 178.07/28.38    (10)   ~ (all_52_9 = all_52_25)
% 178.07/28.38    (11)   ~ (all_52_19 = all_52_23)
% 178.07/28.38    (12)  all_56_11 = all_52_23
% 178.07/28.38    (13)  op(e1, e2) = all_52_19
% 178.07/28.38    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.38    (15)   ~ (all_52_3 = all_10_2)
% 178.07/28.38    (16)  all_58_5 = all_52_13
% 178.07/28.38    (17)   ~ (all_6_2 = e0)
% 178.07/28.38    (18)   ~ (all_52_25 = all_52_29)
% 178.07/28.38    (19)  op(e1, all_52_13) = e1
% 178.07/28.38    (20)  op(e0, all_52_15) = e0
% 178.07/28.38    (21)  all_56_15 = all_6_2
% 178.07/28.38    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.38    (23)  all_58_3 = all_10_2
% 178.07/28.38    (24)  all_56_9 = all_52_19
% 178.07/28.38    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.38    (26)  all_58_15 = all_6_2
% 178.07/28.38    (27)   ~ (all_52_9 = all_4_2)
% 178.07/28.38    (28)   ~ (all_52_5 = all_52_7)
% 178.07/28.38    (29)  all_58_10 = all_52_15
% 178.07/28.38    (30)   ~ (all_52_5 = all_4_2)
% 178.07/28.38    (31)  all_58_7 = all_52_19
% 178.07/28.38    (32)  all_56_4 = all_52_9
% 178.07/28.38    (33)   ~ (all_52_15 = all_6_2)
% 178.07/28.38    (34)   ~ (all_52_17 = all_52_25)
% 178.07/28.38    (35)  all_58_4 = all_52_5
% 178.07/28.38    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.38    (37)   ~ (e3 = e1)
% 178.07/28.38    (38)  all_34_1 = all_4_1
% 178.07/28.38    (39)   ~ (all_52_27 = all_52_29)
% 178.07/28.38    (40)   ~ (all_52_17 = all_14_2)
% 178.07/28.38    (41)  op(e3, all_4_2) = all_4_1
% 178.07/28.38    (42)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.07/28.38    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.38    (44)   ~ (all_52_7 = all_4_2)
% 178.07/28.38    (45)  all_58_1 = all_52_3
% 178.07/28.38    (46)  all_58_0 = all_4_2
% 178.07/28.38    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.07/28.38    (48)  op(all_4_1, all_4_2) = e1
% 178.07/28.38    (49)  op(e1, all_52_29) = all_52_28
% 178.07/28.38    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.38    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.38    (52)   ~ (all_4_1 = e2)
% 178.07/28.38    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.07/28.38    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.07/28.38    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.07/28.38    (56)   ~ (all_14_1 = e3)
% 178.07/28.38    (57)  all_58_14 = all_52_29
% 178.07/28.38    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.07/28.38    (59)   ~ (all_52_3 = all_52_5)
% 178.07/28.38    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.38    (61)  op(e2, e1) = all_52_13
% 178.07/28.38    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.38    (63)  all_58_8 = all_14_2
% 178.07/28.38    (64)  all_56_1 = all_52_3
% 178.07/28.38    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.07/28.38    (66)   ~ (all_52_3 = all_52_27)
% 178.07/28.38    (67)   ~ (all_52_3 = all_4_2)
% 178.07/28.38    (68)  op(e0, e3) = all_52_25
% 178.07/28.38    (69)  op(e0, all_6_2) = all_6_1
% 178.07/28.38    (70)  op(e3, all_52_17) = all_52_16
% 178.07/28.38    (71)   ~ (all_52_13 = all_14_2)
% 178.07/28.38    (72)  op(e3, all_52_9) = e3
% 178.07/28.38    (73)   ~ (e3 = e0)
% 178.07/28.38    (74)   ~ (all_52_9 = all_52_13)
% 178.07/28.38    (75)  op(e0, all_52_23) = all_52_22
% 178.07/28.38    (76)   ~ (all_52_15 = all_52_23)
% 178.07/28.38    (77)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.07/28.38    (78)   ~ (all_52_5 = all_52_29)
% 178.07/28.38    (79)  all_56_2 = all_52_5
% 178.07/28.38    (80)  all_58_13 = all_52_27
% 178.07/28.38    (81)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.07/28.38    (82)   ~ (all_52_9 = all_52_17)
% 178.07/28.38    (83)  all_58_6 = all_52_17
% 178.07/28.38    (84)   ~ (all_52_3 = all_52_7)
% 178.07/28.38    (85)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.07/28.38    (86)  op(e2, all_52_19) = all_52_18
% 178.07/28.38    (87)   ~ (e1 = e0)
% 178.07/28.38    (88)  all_56_0 = all_4_2
% 178.07/28.38    (89)  all_58_11 = all_52_23
% 178.07/28.38    (90)   ~ (all_52_3 = all_52_19)
% 178.07/28.38    (91)   ~ (all_52_7 = all_52_15)
% 178.07/28.38    (92)   ~ (all_52_29 = all_14_2)
% 178.07/28.38    (93)   ~ (all_52_19 = all_10_2)
% 178.07/28.38    (94)   ~ (all_52_23 = all_6_2)
% 178.07/28.38    (95)   ~ (all_52_29 = all_6_2)
% 178.07/28.38    (96)  all_58_2 = all_52_9
% 178.07/28.38    (97)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.07/28.38    (98)  op(e3, e1) = all_52_5
% 178.07/28.38    (99)  all_56_10 = all_14_2
% 178.07/28.38    (100)   ~ (all_52_25 = all_6_2)
% 178.07/28.38    (101)  op(e1, e1) = all_14_2
% 178.07/28.38    (102)  op(e1, e3) = all_52_17
% 178.07/28.38    (103)   ~ (all_52_25 = all_4_2)
% 178.07/28.38    (104)  op(e3, e0) = all_52_7
% 178.07/28.38    (105)  op(e2, all_10_2) = e2
% 178.07/28.38    (106)  op(e3, e3) = all_4_2
% 178.07/28.38    (107)   ~ (all_52_17 = all_4_2)
% 178.07/28.38    (108)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.38             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.38    (109)   ~ (all_52_25 = all_52_27)
% 178.07/28.38    (110)  all_34_2 = all_4_2
% 178.07/28.38    (111)   ~ (all_52_27 = all_6_2)
% 178.07/28.38    (112)   ~ (all_52_7 = all_6_2)
% 178.07/28.38    (113)   ~ (all_10_0 = e3)
% 178.07/28.38    (114)   ~ (all_52_7 = all_52_23)
% 178.07/28.38    (115)  op(e2, all_52_27) = all_52_26
% 178.07/28.38    (116)   ~ (all_52_17 = all_52_19)
% 178.07/28.38    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.38    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.07/28.38    (119)  op(e1, all_14_2) = all_14_1
% 178.07/28.38    (120)  all_58_9 = all_52_7
% 178.07/28.38    (121)  all_58_12 = all_52_25
% 178.07/28.38    (122)   ~ (all_10_0 = e1)
% 178.07/28.38    (123)  all_56_6 = all_52_13
% 178.07/28.38    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.38    (125)   ~ (all_52_9 = all_52_15)
% 178.07/28.38    (126)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.07/28.38    (127)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.07/28.38    (128)   ~ (all_52_19 = all_14_2)
% 178.07/28.38    (129)  op(e2, e3) = all_52_9
% 178.07/28.38    (130)  all_56_13 = all_52_27
% 178.07/28.38  
% 178.07/28.38  Begin of proof
% 178.07/28.38  | 
% 178.07/28.39  | GROUND_INST: instantiating (108) with e2, all_10_0, all_10_2, e2, simplifying
% 178.07/28.39  |              with (7), (105) gives:
% 178.07/28.39  |   (131)  all_10_0 = e2
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (113), (131) imply:
% 178.07/28.39  |   (132)   ~ (e3 = e2)
% 178.07/28.39  | 
% 178.07/28.39  | SIMP: (132) implies:
% 178.07/28.39  |   (133)   ~ (e3 = e2)
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (122), (131) imply:
% 178.07/28.39  |   (134)   ~ (e2 = e1)
% 178.07/28.39  | 
% 178.07/28.39  | BETA: splitting (42) gives:
% 178.07/28.39  | 
% 178.07/28.39  | Case 1:
% 178.07/28.39  | | 
% 178.07/28.39  | |   (135)  all_56_15 = e3
% 178.07/28.39  | | 
% 178.07/28.39  | | REF_CLOSE: (9), (15), (16), (19), (21), (23), (27), (29), (31), (33), (37),
% 178.07/28.39  | |            (41), (43), (45), (46), (48), (54), (60), (68), (69), (72), (80),
% 178.07/28.39  | |            (83), (96), (100), (102), (105), (106), (108), (111), (116),
% 178.07/28.39  | |            (121), (129), (135) are inconsistent by sub-proof #574.
% 178.07/28.39  | | 
% 178.07/28.39  | Case 2:
% 178.07/28.39  | | 
% 178.07/28.39  | |   (136)   ~ (all_56_15 = e3)
% 178.07/28.39  | |   (137)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.07/28.39  | | 
% 178.07/28.39  | | REDUCE: (21), (136) imply:
% 178.07/28.39  | |   (138)   ~ (all_6_2 = e3)
% 178.07/28.39  | | 
% 178.07/28.39  | | BETA: splitting (58) gives:
% 178.07/28.39  | | 
% 178.07/28.39  | | Case 1:
% 178.07/28.39  | | | 
% 178.07/28.39  | | |   (139)  all_56_13 = e3
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REF_CLOSE: (4), (9), (10), (13), (14), (16), (19), (20), (22), (23), (25),
% 178.07/28.39  | | |            (27), (29), (32), (37), (38), (41), (43), (46), (48), (50),
% 178.07/28.39  | | |            (55), (60), (64), (66), (67), (68), (72), (74), (83), (85),
% 178.07/28.39  | | |            (88), (90), (96), (102), (103), (106), (107), (108), (109),
% 178.07/28.39  | | |            (110), (115), (121), (123), (124), (125), (129), (130), (139)
% 178.07/28.39  | | |            are inconsistent by sub-proof #593.
% 178.07/28.39  | | | 
% 178.07/28.39  | | Case 2:
% 178.07/28.39  | | | 
% 178.07/28.39  | | |   (140)   ~ (all_56_13 = e3)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (130), (140) imply:
% 178.07/28.39  | | |   (141)   ~ (all_52_27 = e3)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | BETA: splitting (62) gives:
% 178.07/28.39  | | | 
% 178.07/28.39  | | | Case 1:
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | |   (142)  all_58_12 = e3
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 178.07/28.39  | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.07/28.39  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 178.07/28.39  | | | |            (36), (39), (40), (43), (44), (45), (46), (47), (51), (53),
% 178.07/28.39  | | | |            (54), (55), (56), (57), (59), (61), (63), (65), (68), (70),
% 178.07/28.39  | | | |            (71), (72), (73), (74), (75), (77), (80), (82), (83), (84),
% 178.07/28.39  | | | |            (85), (86), (88), (89), (90), (91), (93), (94), (96), (97),
% 178.07/28.39  | | | |            (98), (99), (100), (102), (103), (104), (105), (108), (109),
% 178.07/28.39  | | | |            (111), (112), (114), (116), (117), (118), (119), (120),
% 178.07/28.39  | | | |            (121), (123), (125), (126), (128), (129), (133), (134),
% 178.07/28.39  | | | |            (137), (142) are inconsistent by sub-proof #734.
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | Case 2:
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | |   (143)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | | REF_CLOSE: (2), (5), (6), (9), (15), (16), (19), (20), (22), (23), (26),
% 178.07/28.39  | | | |            (27), (29), (30), (31), (32), (35), (36), (37), (41), (43),
% 178.07/28.39  | | | |            (45), (46), (48), (49), (52), (55), (57), (59), (60), (63),
% 178.07/28.39  | | | |            (67), (68), (71), (72), (74), (76), (78), (79), (80), (81),
% 178.07/28.39  | | | |            (83), (85), (87), (89), (90), (91), (92), (95), (96), (98),
% 178.07/28.39  | | | |            (101), (102), (103), (104), (105), (106), (107), (108),
% 178.07/28.39  | | | |            (117), (120), (121), (123), (124), (125), (127), (129),
% 178.07/28.39  | | | |            (134), (138), (141), (143) are inconsistent by sub-proof
% 178.07/28.39  | | | |            #572.
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | End of split
% 178.07/28.39  | | | 
% 178.07/28.39  | | End of split
% 178.07/28.39  | | 
% 178.07/28.39  | End of split
% 178.07/28.39  | 
% 178.07/28.39  End of proof
% 178.07/28.39  
% 178.07/28.39  Sub-proof #572 shows that the following formulas are inconsistent:
% 178.07/28.39  ----------------------------------------------------------------
% 178.07/28.39    (1)   ~ (all_52_5 = all_52_13)
% 178.07/28.39    (2)   ~ (all_52_17 = all_52_23)
% 178.07/28.39    (3)   ~ (all_52_13 = all_52_29)
% 178.07/28.39    (4)  op(e3, e2) = all_52_3
% 178.07/28.39    (5)   ~ (all_52_27 = e3)
% 178.07/28.39    (6)   ~ (all_6_2 = e3)
% 178.07/28.39    (7)   ~ (all_52_3 = all_10_2)
% 178.07/28.39    (8)  all_58_5 = all_52_13
% 178.07/28.39    (9)  op(e1, all_52_13) = e1
% 178.07/28.39    (10)  op(e0, all_52_15) = e0
% 178.07/28.39    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.39    (12)  all_58_3 = all_10_2
% 178.07/28.39    (13)  all_58_15 = all_6_2
% 178.07/28.39    (14)   ~ (all_52_9 = all_4_2)
% 178.07/28.39    (15)  all_58_10 = all_52_15
% 178.07/28.39    (16)   ~ (all_52_5 = all_4_2)
% 178.07/28.39    (17)  all_58_7 = all_52_19
% 178.07/28.39    (18)  all_56_4 = all_52_9
% 178.07/28.39    (19)  all_58_4 = all_52_5
% 178.07/28.39    (20)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.39    (21)   ~ (e3 = e1)
% 178.07/28.39    (22)  op(e3, all_4_2) = all_4_1
% 178.07/28.39    (23)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.39    (24)  all_58_1 = all_52_3
% 178.07/28.39    (25)  all_58_0 = all_4_2
% 178.07/28.39    (26)  op(all_4_1, all_4_2) = e1
% 178.07/28.39    (27)  op(e1, all_52_29) = all_52_28
% 178.07/28.39    (28)   ~ (all_4_1 = e2)
% 178.07/28.39    (29)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.07/28.39    (30)  all_58_14 = all_52_29
% 178.07/28.39    (31)   ~ (all_52_3 = all_52_5)
% 178.07/28.39    (32)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.39    (33)  all_58_8 = all_14_2
% 178.07/28.39    (34)   ~ (all_52_3 = all_4_2)
% 178.07/28.39    (35)  op(e0, e3) = all_52_25
% 178.07/28.39    (36)   ~ (all_52_13 = all_14_2)
% 178.07/28.39    (37)  op(e3, all_52_9) = e3
% 178.07/28.39    (38)   ~ (all_52_9 = all_52_13)
% 178.07/28.39    (39)   ~ (all_52_15 = all_52_23)
% 178.07/28.39    (40)   ~ (all_52_5 = all_52_29)
% 178.07/28.39    (41)  all_56_2 = all_52_5
% 178.07/28.39    (42)  all_58_13 = all_52_27
% 178.07/28.39    (43)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.07/28.39    (44)  all_58_6 = all_52_17
% 178.07/28.39    (45)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.07/28.39    (46)   ~ (e1 = e0)
% 178.07/28.39    (47)  all_58_11 = all_52_23
% 178.07/28.39    (48)   ~ (all_52_3 = all_52_19)
% 178.07/28.39    (49)   ~ (all_52_7 = all_52_15)
% 178.07/28.39    (50)   ~ (all_52_29 = all_14_2)
% 178.07/28.39    (51)   ~ (all_52_29 = all_6_2)
% 178.07/28.39    (52)  all_58_2 = all_52_9
% 178.07/28.39    (53)  op(e3, e1) = all_52_5
% 178.07/28.39    (54)   ~ (e2 = e1)
% 178.07/28.39    (55)  op(e1, e1) = all_14_2
% 178.07/28.39    (56)  op(e1, e3) = all_52_17
% 178.07/28.39    (57)   ~ (all_52_25 = all_4_2)
% 178.07/28.39    (58)  op(e3, e0) = all_52_7
% 178.07/28.39    (59)  op(e2, all_10_2) = e2
% 178.07/28.39    (60)  op(e3, e3) = all_4_2
% 178.07/28.39    (61)   ~ (all_52_17 = all_4_2)
% 178.07/28.39    (62)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.39    (63)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.39    (64)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.39    (65)  all_58_9 = all_52_7
% 178.07/28.39    (66)  all_58_12 = all_52_25
% 178.07/28.39    (67)  all_56_6 = all_52_13
% 178.07/28.39    (68)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.39    (69)   ~ (all_52_9 = all_52_15)
% 178.07/28.39    (70)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.07/28.39    (71)  op(e2, e3) = all_52_9
% 178.07/28.39  
% 178.07/28.39  Begin of proof
% 178.07/28.39  | 
% 178.07/28.39  | BETA: splitting (63) gives:
% 178.07/28.39  | 
% 178.07/28.39  | Case 1:
% 178.07/28.39  | | 
% 178.07/28.39  | |   (72)  all_58_13 = e3
% 178.07/28.39  | | 
% 178.07/28.39  | | REF_CLOSE: (5), (42), (72) are inconsistent by sub-proof #1026.
% 178.07/28.39  | | 
% 178.07/28.39  | Case 2:
% 178.07/28.39  | | 
% 178.07/28.39  | |   (73)  all_58_14 = e3 | all_58_15 = e3
% 178.07/28.39  | | 
% 178.07/28.39  | | BETA: splitting (73) gives:
% 178.07/28.39  | | 
% 178.07/28.39  | | Case 1:
% 178.07/28.39  | | | 
% 178.07/28.39  | | |   (74)  all_58_14 = e3
% 178.07/28.39  | | | 
% 178.07/28.39  | | | COMBINE_EQS: (30), (74) imply:
% 178.07/28.39  | | |   (75)  all_52_29 = e3
% 178.07/28.39  | | | 
% 178.07/28.39  | | | SIMP: (75) implies:
% 178.07/28.39  | | |   (76)  all_52_29 = e3
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (40), (76) imply:
% 178.07/28.39  | | |   (77)   ~ (all_52_5 = e3)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (3), (76) imply:
% 178.07/28.39  | | |   (78)   ~ (all_52_13 = e3)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (50), (76) imply:
% 178.07/28.39  | | |   (79)   ~ (all_14_2 = e3)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | SIMP: (79) implies:
% 178.07/28.39  | | |   (80)   ~ (all_14_2 = e3)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (51), (76) imply:
% 178.07/28.39  | | |   (81)   ~ (all_6_2 = e3)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (27), (76) imply:
% 178.07/28.39  | | |   (82)  op(e1, e3) = all_52_28
% 178.07/28.39  | | | 
% 178.07/28.39  | | | GROUND_INST: instantiating (62) with all_52_17, all_52_28, e3, e1,
% 178.07/28.39  | | |              simplifying with (56), (82) gives:
% 178.07/28.39  | | |   (83)  all_52_17 = all_52_28
% 178.07/28.39  | | | 
% 178.07/28.39  | | | COMBINE_EQS: (44), (83) imply:
% 178.07/28.39  | | |   (84)  all_58_6 = all_52_28
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (2), (83) imply:
% 178.07/28.39  | | |   (85)   ~ (all_52_23 = all_52_28)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | SIMP: (85) implies:
% 178.07/28.39  | | |   (86)   ~ (all_52_23 = all_52_28)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (61), (83) imply:
% 178.07/28.39  | | |   (87)   ~ (all_52_28 = all_4_2)
% 178.07/28.39  | | | 
% 178.07/28.39  | | | BETA: splitting (29) gives:
% 178.07/28.39  | | | 
% 178.07/28.39  | | | Case 1:
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | |   (88)  all_56_6 = e3
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | | REF_CLOSE: (67), (78), (88) are inconsistent by sub-proof #573.
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | Case 2:
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | |   (89)   ~ (all_56_6 = e3)
% 178.07/28.39  | | | |   (90)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | | BETA: splitting (70) gives:
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | | Case 1:
% 178.07/28.39  | | | | | 
% 178.07/28.39  | | | | |   (91)  all_56_2 = e3
% 178.07/28.39  | | | | | 
% 178.07/28.39  | | | | | REF_CLOSE: (41), (77), (91) are inconsistent by sub-proof #931.
% 178.07/28.39  | | | | | 
% 178.07/28.39  | | | | Case 2:
% 178.07/28.39  | | | | | 
% 178.07/28.39  | | | | |   (92)   ~ (all_56_2 = e3)
% 178.07/28.39  | | | | |   (93)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.07/28.39  | | | | | 
% 178.07/28.39  | | | | | BETA: splitting (64) gives:
% 178.07/28.39  | | | | | 
% 178.07/28.39  | | | | | Case 1:
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | |   (94)  all_58_9 = e3
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | | COMBINE_EQS: (65), (94) imply:
% 178.07/28.39  | | | | | |   (95)  all_52_7 = e3
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | | REF_CLOSE: (4), (7), (8), (12), (14), (15), (23), (37), (49), (52),
% 178.07/28.39  | | | | | |            (59), (60), (62), (71), (78), (95) are inconsistent by
% 178.07/28.39  | | | | | |            sub-proof #733.
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | Case 2:
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | |   (96)   ~ (all_58_9 = e3)
% 178.07/28.39  | | | | | |   (97)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | | REDUCE: (65), (96) imply:
% 178.07/28.39  | | | | | |   (98)   ~ (all_52_7 = e3)
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | | BETA: splitting (68) gives:
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | | Case 1:
% 178.07/28.39  | | | | | | | 
% 178.07/28.39  | | | | | | |   (99)  all_58_0 = e3
% 178.07/28.39  | | | | | | | 
% 178.07/28.39  | | | | | | | COMBINE_EQS: (25), (99) imply:
% 178.07/28.39  | | | | | | |   (100)  all_4_2 = e3
% 178.07/28.39  | | | | | | | 
% 178.07/28.39  | | | | | | | REF_CLOSE: (21), (22), (26), (60), (62), (100) are inconsistent by
% 178.07/28.39  | | | | | | |            sub-proof #599.
% 178.07/28.39  | | | | | | | 
% 178.07/28.39  | | | | | | Case 2:
% 178.07/28.39  | | | | | | | 
% 178.07/28.39  | | | | | | |   (101)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.39  | | | | | | | 
% 178.07/28.39  | | | | | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 178.07/28.39  | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.07/28.39  | | | | | | |            (24), (25), (28), (31), (32), (33), (34), (35), (36),
% 178.07/28.39  | | | | | | |            (37), (38), (39), (41), (43), (45), (46), (47), (48),
% 178.07/28.39  | | | | | | |            (49), (52), (53), (54), (55), (57), (58), (60), (62),
% 178.07/28.39  | | | | | | |            (65), (66), (67), (69), (77), (78), (80), (84), (86),
% 178.07/28.39  | | | | | | |            (87), (90), (93), (97), (98), (101) are inconsistent by
% 178.07/28.39  | | | | | | |            sub-proof #719.
% 178.07/28.39  | | | | | | | 
% 178.07/28.39  | | | | | | End of split
% 178.07/28.39  | | | | | | 
% 178.07/28.39  | | | | | End of split
% 178.07/28.39  | | | | | 
% 178.07/28.39  | | | | End of split
% 178.07/28.39  | | | | 
% 178.07/28.39  | | | End of split
% 178.07/28.39  | | | 
% 178.07/28.39  | | Case 2:
% 178.07/28.39  | | | 
% 178.07/28.39  | | |   (102)  all_58_15 = e3
% 178.07/28.39  | | | 
% 178.07/28.39  | | | COMBINE_EQS: (13), (102) imply:
% 178.07/28.39  | | |   (103)  all_6_2 = e3
% 178.07/28.39  | | | 
% 178.07/28.39  | | | REDUCE: (6), (103) imply:
% 178.07/28.39  | | |   (104)  $false
% 178.07/28.39  | | | 
% 178.07/28.39  | | | CLOSE: (104) is inconsistent.
% 178.07/28.39  | | | 
% 178.07/28.39  | | End of split
% 178.07/28.39  | | 
% 178.07/28.39  | End of split
% 178.07/28.39  | 
% 178.07/28.39  End of proof
% 178.07/28.39  
% 178.07/28.39  Sub-proof #573 shows that the following formulas are inconsistent:
% 178.07/28.39  ----------------------------------------------------------------
% 178.07/28.39    (1)  all_56_6 = all_52_13
% 178.07/28.39    (2)  all_56_6 = e3
% 178.07/28.39    (3)   ~ (all_52_13 = e3)
% 178.07/28.39  
% 178.07/28.39  Begin of proof
% 178.07/28.39  | 
% 178.07/28.39  | COMBINE_EQS: (1), (2) imply:
% 178.07/28.39  |   (4)  all_52_13 = e3
% 178.07/28.39  | 
% 178.07/28.39  | SIMP: (4) implies:
% 178.07/28.39  |   (5)  all_52_13 = e3
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (3), (5) imply:
% 178.07/28.39  |   (6)  $false
% 178.07/28.39  | 
% 178.07/28.39  | CLOSE: (6) is inconsistent.
% 178.07/28.39  | 
% 178.07/28.39  End of proof
% 178.07/28.39  
% 178.07/28.39  Sub-proof #574 shows that the following formulas are inconsistent:
% 178.07/28.39  ----------------------------------------------------------------
% 178.07/28.39    (1)  op(e3, e2) = all_52_3
% 178.07/28.39    (2)   ~ (all_52_3 = all_10_2)
% 178.07/28.39    (3)  all_56_15 = e3
% 178.07/28.39    (4)  all_58_5 = all_52_13
% 178.07/28.39    (5)  op(e1, all_52_13) = e1
% 178.07/28.39    (6)  all_56_15 = all_6_2
% 178.07/28.39    (7)  all_58_3 = all_10_2
% 178.07/28.39    (8)   ~ (all_52_9 = all_4_2)
% 178.07/28.39    (9)  all_58_10 = all_52_15
% 178.07/28.39    (10)  all_58_7 = all_52_19
% 178.07/28.39    (11)   ~ (all_52_15 = all_6_2)
% 178.07/28.39    (12)   ~ (e3 = e1)
% 178.07/28.39    (13)  op(e3, all_4_2) = all_4_1
% 178.07/28.39    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.39    (15)  all_58_1 = all_52_3
% 178.07/28.39    (16)  all_58_0 = all_4_2
% 178.07/28.39    (17)  op(all_4_1, all_4_2) = e1
% 178.07/28.39    (18)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.07/28.39    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.39    (20)  op(e0, e3) = all_52_25
% 178.07/28.39    (21)  op(e0, all_6_2) = all_6_1
% 178.07/28.39    (22)  op(e3, all_52_9) = e3
% 178.07/28.39    (23)  all_58_13 = all_52_27
% 178.07/28.39    (24)  all_58_6 = all_52_17
% 178.07/28.39    (25)  all_58_2 = all_52_9
% 178.07/28.39    (26)   ~ (all_52_25 = all_6_2)
% 178.07/28.39    (27)  op(e1, e3) = all_52_17
% 178.07/28.39    (28)  op(e2, all_10_2) = e2
% 178.07/28.39    (29)  op(e3, e3) = all_4_2
% 178.07/28.39    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.39    (31)   ~ (all_52_27 = all_6_2)
% 178.07/28.39    (32)   ~ (all_52_17 = all_52_19)
% 178.07/28.39    (33)  all_58_12 = all_52_25
% 178.07/28.39    (34)  op(e2, e3) = all_52_9
% 178.07/28.39  
% 178.07/28.39  Begin of proof
% 178.07/28.39  | 
% 178.07/28.39  | COMBINE_EQS: (3), (6) imply:
% 178.07/28.39  |   (35)  all_6_2 = e3
% 178.07/28.39  | 
% 178.07/28.39  | SIMP: (35) implies:
% 178.07/28.39  |   (36)  all_6_2 = e3
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (11), (36) imply:
% 178.07/28.39  |   (37)   ~ (all_52_15 = e3)
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (26), (36) imply:
% 178.07/28.39  |   (38)   ~ (all_52_25 = e3)
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (31), (36) imply:
% 178.07/28.39  |   (39)   ~ (all_52_27 = e3)
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (21), (36) imply:
% 178.07/28.39  |   (40)  op(e0, e3) = all_6_1
% 178.07/28.39  | 
% 178.07/28.39  | GROUND_INST: instantiating (30) with all_52_25, all_6_1, e3, e0, simplifying
% 178.07/28.39  |              with (20), (40) gives:
% 178.07/28.39  |   (41)  all_52_25 = all_6_1
% 178.07/28.39  | 
% 178.07/28.39  | COMBINE_EQS: (33), (41) imply:
% 178.07/28.39  |   (42)  all_58_12 = all_6_1
% 178.07/28.39  | 
% 178.07/28.39  | REDUCE: (38), (41) imply:
% 178.07/28.39  |   (43)   ~ (all_6_1 = e3)
% 178.07/28.39  | 
% 178.07/28.39  | BETA: splitting (19) gives:
% 178.07/28.39  | 
% 178.07/28.39  | Case 1:
% 178.07/28.39  | | 
% 178.07/28.39  | |   (44)  all_58_0 = e3
% 178.07/28.39  | | 
% 178.07/28.39  | | COMBINE_EQS: (16), (44) imply:
% 178.07/28.39  | |   (45)  all_4_2 = e3
% 178.07/28.39  | | 
% 178.07/28.39  | | REF_CLOSE: (12), (13), (17), (29), (30), (45) are inconsistent by sub-proof
% 178.07/28.39  | |            #599.
% 178.07/28.39  | | 
% 178.07/28.39  | Case 2:
% 178.07/28.39  | | 
% 178.07/28.39  | |   (46)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.39  | | 
% 178.07/28.39  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (12), (14), (15), (18),
% 178.07/28.39  | |            (22), (23), (24), (25), (27), (28), (29), (30), (32), (34), (37),
% 178.07/28.39  | |            (39), (42), (43), (46) are inconsistent by sub-proof #774.
% 178.07/28.39  | | 
% 178.07/28.39  | End of split
% 178.07/28.39  | 
% 178.07/28.39  End of proof
% 178.07/28.39  
% 178.07/28.39  Sub-proof #575 shows that the following formulas are inconsistent:
% 178.07/28.39  ----------------------------------------------------------------
% 178.07/28.39    (1)   ~ (all_52_23 = all_14_2)
% 178.07/28.39    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.07/28.39    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.07/28.39    (4)   ~ (all_52_17 = all_52_23)
% 178.07/28.39    (5)   ~ (all_52_13 = all_52_29)
% 178.07/28.39    (6)  all_56_3 = all_52_7
% 178.07/28.39    (7)  op(e3, e2) = all_52_3
% 178.07/28.39    (8)   ~ (all_52_9 = all_52_25)
% 178.07/28.39    (9)  op(e3, all_52_25) = all_52_24
% 178.07/28.39    (10)   ~ (all_52_19 = all_52_23)
% 178.07/28.39    (11)  all_56_11 = all_52_23
% 178.07/28.39    (12)  op(e1, e2) = all_52_19
% 178.07/28.39    (13)   ~ (all_52_27 = e0)
% 178.07/28.39    (14)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.39    (15)   ~ (all_52_23 = e0)
% 178.07/28.39    (16)   ~ (all_52_3 = all_10_2)
% 178.07/28.39    (17)  all_58_5 = all_52_13
% 178.07/28.39    (18)   ~ (all_52_25 = all_52_29)
% 178.07/28.39    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.39    (20)  op(all_14_1, all_14_2) = all_14_0
% 178.07/28.39    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.07/28.39    (22)  all_58_3 = all_10_2
% 178.07/28.39    (23)  all_56_9 = all_52_19
% 178.07/28.39    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.39    (25)   ~ (all_52_9 = all_4_2)
% 178.07/28.39    (26)   ~ (all_52_5 = all_52_7)
% 178.07/28.39    (27)  all_58_10 = all_52_15
% 178.07/28.39    (28)  all_58_7 = all_52_19
% 178.07/28.39    (29)   ~ (all_52_17 = all_52_25)
% 178.07/28.39    (30)  op(e0, e1) = all_52_29
% 178.07/28.39    (31)  all_58_4 = all_52_5
% 178.07/28.39    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.07/28.39    (33)   ~ (e3 = e1)
% 178.07/28.39    (34)  all_34_1 = all_4_1
% 178.07/28.39    (35)   ~ (all_52_27 = all_52_29)
% 178.07/28.39    (36)  op(e3, all_4_2) = all_4_1
% 178.07/28.39    (37)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.07/28.39    (38)   ~ (all_52_7 = all_4_2)
% 178.07/28.39    (39)  all_58_1 = all_52_3
% 178.07/28.39    (40)  all_58_0 = all_4_2
% 178.07/28.39    (41)  op(all_4_1, all_4_2) = e1
% 178.07/28.39    (42)  op(e1, all_52_29) = all_52_28
% 178.07/28.39    (43)   ~ (all_52_7 = e0)
% 178.07/28.39    (44)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.39    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.07/28.39    (46)   ~ (all_4_1 = e2)
% 178.07/28.39    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.07/28.39    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.07/28.39    (49)  all_58_14 = all_52_29
% 178.07/28.39    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.07/28.39    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.39    (52)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.39    (53)  all_58_8 = all_14_2
% 178.07/28.39    (54)  all_56_1 = all_52_3
% 178.07/28.39    (55)  op(e0, e2) = all_52_27
% 178.07/28.39    (56)  all_56_14 = all_52_29
% 178.07/28.39    (57)   ~ (all_14_0 = e3)
% 178.07/28.39    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.07/28.39    (59)   ~ (all_52_5 = all_14_2)
% 178.07/28.39    (60)   ~ (all_52_3 = all_52_27)
% 178.07/28.39    (61)   ~ (all_52_3 = all_4_2)
% 178.07/28.39    (62)  op(e0, e3) = all_52_25
% 178.07/28.39    (63)   ~ (all_52_9 = all_10_2)
% 178.07/28.39    (64)  op(e3, all_52_17) = all_52_16
% 178.07/28.39    (65)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.07/28.39    (66)   ~ (e3 = e0)
% 178.07/28.39    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.07/28.39    (68)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.07/28.39    (69)  op(e0, all_52_23) = all_52_22
% 178.07/28.39    (70)   ~ (all_52_15 = all_52_23)
% 178.07/28.39    (71)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.07/28.39    (72)   ~ (all_52_5 = all_52_29)
% 178.07/28.39    (73)  op(e1, e0) = all_52_23
% 178.07/28.39    (74)  all_56_12 = all_52_25
% 178.07/28.39    (75)  all_58_13 = all_52_27
% 178.07/28.39    (76)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.07/28.39    (77)  all_56_5 = all_10_2
% 178.07/28.39    (78)   ~ (all_52_25 = e0)
% 178.07/28.39    (79)   ~ (all_52_9 = all_52_17)
% 178.07/28.39    (80)   ~ (all_14_0 = e2)
% 178.07/28.39    (81)  all_58_6 = all_52_17
% 178.07/28.39    (82)   ~ (all_52_3 = all_52_7)
% 178.07/28.39    (83)  op(e2, all_52_19) = all_52_18
% 178.07/28.39    (84)   ~ (e1 = e0)
% 178.07/28.39    (85)  all_56_0 = all_4_2
% 178.07/28.39    (86)  all_58_11 = all_52_23
% 178.07/28.39    (87)   ~ (all_52_3 = all_52_19)
% 178.07/28.39    (88)   ~ (all_52_29 = all_14_2)
% 178.07/28.39    (89)   ~ (all_52_19 = all_10_2)
% 178.07/28.39    (90)  all_58_15 = e0
% 178.07/28.39    (91)  all_58_2 = all_52_9
% 178.07/28.39    (92)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.07/28.39    (93)   ~ (all_52_29 = e0)
% 178.07/28.39    (94)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.07/28.39    (95)  op(e3, e1) = all_52_5
% 178.07/28.39    (96)  all_56_10 = all_14_2
% 178.07/28.39    (97)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.07/28.39    (98)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.07/28.39    (99)  op(e1, e3) = all_52_17
% 178.07/28.39    (100)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.07/28.39    (101)   ~ (all_52_25 = all_4_2)
% 178.07/28.39    (102)  op(e3, e0) = all_52_7
% 178.07/28.39    (103)  op(e3, e3) = all_4_2
% 178.07/28.39    (104)  all_56_8 = all_52_17
% 178.07/28.39    (105)   ~ (all_52_17 = all_4_2)
% 178.07/28.39    (106)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.39             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.39    (107)   ~ (all_52_25 = all_52_27)
% 178.07/28.39    (108)  all_34_2 = all_4_2
% 178.07/28.39    (109)   ~ (all_52_19 = all_52_27)
% 178.07/28.39    (110)  all_56_7 = all_52_15
% 178.07/28.39    (111)   ~ (all_52_7 = all_52_23)
% 178.07/28.39    (112)  op(e2, all_52_27) = all_52_26
% 178.07/28.39    (113)  all_52_20 = all_14_1
% 178.07/28.39    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.07/28.39    (115)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.07/28.39    (116)  op(e1, all_14_2) = all_14_1
% 178.07/28.39    (117)  all_58_9 = all_52_7
% 178.07/28.39    (118)   ~ (e2 = e0)
% 178.07/28.39    (119)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 178.07/28.39           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 178.07/28.39    (120)  all_58_12 = all_52_25
% 178.07/28.39    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.07/28.39    (122)   ~ (all_52_9 = all_52_15)
% 178.07/28.39    (123)   ~ (e3 = e2)
% 178.07/28.39    (124)   ~ (all_52_19 = all_14_2)
% 178.07/28.39    (125)  op(e2, e3) = all_52_9
% 178.07/28.39    (126)  all_56_13 = all_52_27
% 178.07/28.39  
% 178.07/28.39  Begin of proof
% 178.07/28.39  | 
% 178.07/28.39  | BETA: splitting (119) gives:
% 178.07/28.39  | 
% 178.07/28.39  | Case 1:
% 178.07/28.39  | | 
% 178.07/28.39  | |   (127)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 178.07/28.39  | | 
% 178.07/28.39  | | ALPHA: (127) implies:
% 178.07/28.39  | |   (128)  all_52_22 = e0
% 178.07/28.39  | |   (129)  all_52_20 = e1
% 178.07/28.39  | |   (130)  all_52_18 = e2
% 178.07/28.39  | |   (131)  all_52_16 = e3
% 178.07/28.39  | | 
% 178.07/28.39  | | COMBINE_EQS: (113), (129) imply:
% 178.07/28.39  | |   (132)  all_14_1 = e1
% 178.07/28.39  | | 
% 178.07/28.39  | | SIMP: (132) implies:
% 178.07/28.39  | |   (133)  all_14_1 = e1
% 178.07/28.39  | | 
% 178.07/28.39  | | REDUCE: (20), (133) imply:
% 178.07/28.39  | |   (134)  op(e1, all_14_2) = all_14_0
% 178.07/28.39  | | 
% 178.07/28.39  | | REDUCE: (64), (131) imply:
% 178.07/28.40  | |   (135)  op(e3, all_52_17) = e3
% 178.07/28.40  | | 
% 178.07/28.40  | | REDUCE: (83), (130) imply:
% 178.07/28.40  | |   (136)  op(e2, all_52_19) = e2
% 178.07/28.40  | | 
% 178.07/28.40  | | REDUCE: (116), (133) imply:
% 178.07/28.40  | |   (137)  op(e1, all_14_2) = e1
% 178.07/28.40  | | 
% 178.07/28.40  | | REDUCE: (69), (128) imply:
% 178.07/28.40  | |   (138)  op(e0, all_52_23) = e0
% 178.07/28.40  | | 
% 178.07/28.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (15),
% 178.07/28.40  | |            (16), (17), (18), (21), (22), (23), (24), (25), (26), (27), (28),
% 178.07/28.40  | |            (29), (30), (31), (32), (35), (36), (37), (38), (39), (40), (41),
% 178.07/28.40  | |            (42), (43), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 178.07/28.40  | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (65), (66),
% 178.07/28.40  | |            (67), (68), (70), (71), (72), (74), (75), (76), (77), (78), (79),
% 178.07/28.40  | |            (80), (81), (82), (84), (85), (86), (88), (89), (90), (91), (92),
% 178.07/28.40  | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 178.07/28.40  | |            (103), (104), (105), (106), (107), (109), (110), (111), (114),
% 178.07/28.40  | |            (115), (117), (118), (120), (121), (122), (123), (124), (125),
% 178.07/28.40  | |            (126), (134), (135), (136), (137), (138) are inconsistent by
% 178.07/28.40  | |            sub-proof #579.
% 178.07/28.40  | | 
% 178.07/28.40  | Case 2:
% 178.07/28.40  | | 
% 178.07/28.40  | |   (139)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 178.07/28.40  | | 
% 178.07/28.40  | | REF_CLOSE: (6), (7), (8), (9), (12), (14), (19), (24), (33), (34), (36),
% 178.07/28.40  | |            (38), (40), (41), (42), (44), (46), (49), (50), (51), (52), (54),
% 178.07/28.40  | |            (61), (66), (68), (73), (74), (75), (78), (85), (87), (90), (99),
% 178.07/28.40  | |            (101), (102), (103), (105), (106), (107), (108), (111), (112),
% 178.07/28.40  | |            (115), (120), (125), (126), (139) are inconsistent by sub-proof
% 178.07/28.40  | |            #576.
% 178.07/28.40  | | 
% 178.07/28.40  | End of split
% 178.07/28.40  | 
% 178.07/28.40  End of proof
% 178.07/28.40  
% 178.07/28.40  Sub-proof #576 shows that the following formulas are inconsistent:
% 178.07/28.40  ----------------------------------------------------------------
% 178.07/28.40    (1)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 178.07/28.40    (2)  all_56_3 = all_52_7
% 178.07/28.40    (3)  op(e3, e2) = all_52_3
% 178.07/28.40    (4)   ~ (all_52_9 = all_52_25)
% 178.07/28.40    (5)  op(e3, all_52_25) = all_52_24
% 178.07/28.40    (6)  op(e1, e2) = all_52_19
% 178.07/28.40    (7)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.40    (8)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.40    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.40    (10)   ~ (e3 = e1)
% 178.07/28.40    (11)  all_34_1 = all_4_1
% 178.07/28.40    (12)  op(e3, all_4_2) = all_4_1
% 178.07/28.40    (13)   ~ (all_52_7 = all_4_2)
% 178.07/28.40    (14)  all_58_0 = all_4_2
% 178.07/28.40    (15)  op(all_4_1, all_4_2) = e1
% 178.07/28.40    (16)  op(e1, all_52_29) = all_52_28
% 178.07/28.40    (17)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.40    (18)   ~ (all_4_1 = e2)
% 178.07/28.40    (19)  all_58_14 = all_52_29
% 178.07/28.40    (20)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.07/28.40    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.40    (22)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.40    (23)  all_56_1 = all_52_3
% 178.07/28.40    (24)   ~ (all_52_3 = all_4_2)
% 178.07/28.40    (25)   ~ (e3 = e0)
% 178.07/28.40    (26)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.07/28.40    (27)  op(e1, e0) = all_52_23
% 178.07/28.40    (28)  all_56_12 = all_52_25
% 178.07/28.40    (29)  all_58_13 = all_52_27
% 178.07/28.40    (30)   ~ (all_52_25 = e0)
% 178.07/28.40    (31)  all_56_0 = all_4_2
% 178.07/28.40    (32)   ~ (all_52_3 = all_52_19)
% 178.07/28.40    (33)  all_58_15 = e0
% 178.07/28.40    (34)  op(e1, e3) = all_52_17
% 178.07/28.40    (35)   ~ (all_52_25 = all_4_2)
% 178.07/28.40    (36)  op(e3, e0) = all_52_7
% 178.07/28.40    (37)  op(e3, e3) = all_4_2
% 178.07/28.40    (38)   ~ (all_52_17 = all_4_2)
% 178.07/28.40    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.07/28.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.07/28.40    (40)   ~ (all_52_25 = all_52_27)
% 178.07/28.40    (41)  all_34_2 = all_4_2
% 178.07/28.40    (42)   ~ (all_52_7 = all_52_23)
% 178.07/28.40    (43)  op(e2, all_52_27) = all_52_26
% 178.07/28.40    (44)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.07/28.40    (45)  all_58_12 = all_52_25
% 178.07/28.40    (46)  op(e2, e3) = all_52_9
% 178.07/28.40    (47)  all_56_13 = all_52_27
% 178.07/28.40  
% 178.07/28.40  Begin of proof
% 178.07/28.40  | 
% 178.07/28.40  | ALPHA: (1) implies:
% 178.07/28.40  |   (48)  all_52_28 = e1
% 178.07/28.40  |   (49)  all_52_26 = e2
% 178.07/28.40  |   (50)  all_52_24 = e3
% 178.07/28.40  | 
% 178.07/28.40  | REDUCE: (5), (50) imply:
% 178.07/28.40  |   (51)  op(e3, all_52_25) = e3
% 178.07/28.40  | 
% 178.07/28.40  | REDUCE: (43), (49) imply:
% 178.07/28.40  |   (52)  op(e2, all_52_27) = e2
% 178.07/28.40  | 
% 178.07/28.40  | REDUCE: (16), (48) imply:
% 178.07/28.40  |   (53)  op(e1, all_52_29) = e1
% 178.07/28.40  | 
% 178.07/28.40  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 178.07/28.40  |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 178.07/28.40  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 178.07/28.40  |            (38), (39), (40), (41), (42), (44), (45), (46), (47), (51), (52),
% 178.07/28.40  |            (53) are inconsistent by sub-proof #577.
% 178.07/28.40  | 
% 178.07/28.40  End of proof
% 178.07/28.40  
% 178.07/28.40  Sub-proof #577 shows that the following formulas are inconsistent:
% 178.07/28.40  ----------------------------------------------------------------
% 178.07/28.40    (1)  all_56_3 = all_52_7
% 178.07/28.40    (2)  op(e3, e2) = all_52_3
% 178.07/28.40    (3)   ~ (all_52_9 = all_52_25)
% 178.07/28.40    (4)  op(e1, e2) = all_52_19
% 178.07/28.40    (5)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.07/28.40    (6)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.07/28.40    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.07/28.40    (8)   ~ (e3 = e1)
% 178.07/28.40    (9)  all_34_1 = all_4_1
% 178.07/28.40    (10)  op(e3, all_4_2) = all_4_1
% 178.07/28.40    (11)   ~ (all_52_7 = all_4_2)
% 178.07/28.40    (12)  all_58_0 = all_4_2
% 178.07/28.40    (13)  op(all_4_1, all_4_2) = e1
% 178.07/28.40    (14)  op(e2, all_52_27) = e2
% 178.07/28.40    (15)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.07/28.40    (16)   ~ (all_4_1 = e2)
% 178.07/28.40    (17)  all_58_14 = all_52_29
% 178.07/28.40    (18)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.07/28.40    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.07/28.40    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.07/28.40    (21)  all_56_1 = all_52_3
% 178.07/28.40    (22)  op(e1, all_52_29) = e1
% 178.07/28.40    (23)   ~ (all_52_3 = all_4_2)
% 178.07/28.40    (24)   ~ (e3 = e0)
% 178.07/28.40    (25)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.07/28.40    (26)  op(e1, e0) = all_52_23
% 178.07/28.40    (27)  all_56_12 = all_52_25
% 178.07/28.40    (28)  all_58_13 = all_52_27
% 178.07/28.40    (29)   ~ (all_52_25 = e0)
% 178.07/28.40    (30)  all_56_0 = all_4_2
% 178.07/28.40    (31)   ~ (all_52_3 = all_52_19)
% 178.07/28.40    (32)  op(e3, all_52_25) = e3
% 178.07/28.40    (33)  all_58_15 = e0
% 178.07/28.40    (34)  op(e1, e3) = all_52_17
% 178.07/28.40    (35)   ~ (all_52_25 = all_4_2)
% 178.07/28.40    (36)  op(e3, e0) = all_52_7
% 178.07/28.40    (37)  op(e3, e3) = all_4_2
% 178.07/28.40    (38)   ~ (all_52_17 = all_4_2)
% 178.18/28.40    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.40    (40)   ~ (all_52_25 = all_52_27)
% 178.18/28.40    (41)  all_34_2 = all_4_2
% 178.18/28.40    (42)   ~ (all_52_7 = all_52_23)
% 178.18/28.40    (43)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.40    (44)  all_58_12 = all_52_25
% 178.18/28.40    (45)  op(e2, e3) = all_52_9
% 178.18/28.40    (46)  all_56_13 = all_52_27
% 178.18/28.40  
% 178.18/28.40  Begin of proof
% 178.18/28.40  | 
% 178.18/28.40  | BETA: splitting (18) gives:
% 178.18/28.40  | 
% 178.18/28.40  | Case 1:
% 178.18/28.40  | | 
% 178.18/28.40  | |   (47)  all_56_13 = e3
% 178.18/28.40  | | 
% 178.18/28.40  | | COMBINE_EQS: (46), (47) imply:
% 178.18/28.40  | |   (48)  all_52_27 = e3
% 178.18/28.40  | | 
% 178.18/28.40  | | SIMP: (48) implies:
% 178.18/28.40  | |   (49)  all_52_27 = e3
% 178.18/28.40  | | 
% 178.18/28.40  | | REDUCE: (40), (49) imply:
% 178.18/28.40  | |   (50)   ~ (all_52_25 = e3)
% 178.18/28.40  | | 
% 178.18/28.40  | | REDUCE: (14), (49) imply:
% 178.18/28.40  | |   (51)  op(e2, e3) = e2
% 178.18/28.40  | | 
% 178.18/28.40  | | GROUND_INST: instantiating (39) with all_52_9, e2, e3, e2, simplifying with
% 178.18/28.40  | |              (45), (51) gives:
% 178.18/28.40  | |   (52)  all_52_9 = e2
% 178.18/28.40  | | 
% 178.18/28.40  | | REDUCE: (3), (52) imply:
% 178.18/28.40  | |   (53)   ~ (all_52_25 = e2)
% 178.18/28.40  | | 
% 178.18/28.40  | | SIMP: (53) implies:
% 178.18/28.40  | |   (54)   ~ (all_52_25 = e2)
% 178.18/28.40  | | 
% 178.18/28.40  | | BETA: splitting (25) gives:
% 178.18/28.40  | | 
% 178.18/28.40  | | Case 1:
% 178.18/28.40  | | | 
% 178.18/28.40  | | |   (55)  all_56_12 = e3
% 178.18/28.40  | | | 
% 178.18/28.40  | | | REF_CLOSE: (27), (50), (55) are inconsistent by sub-proof #1040.
% 178.18/28.40  | | | 
% 178.18/28.40  | | Case 2:
% 178.18/28.40  | | | 
% 178.18/28.40  | | |   (56)   ~ (all_56_12 = e3)
% 178.18/28.40  | | |   (57)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.18/28.40  | | | 
% 178.18/28.40  | | | BETA: splitting (57) gives:
% 178.18/28.40  | | | 
% 178.18/28.40  | | | Case 1:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | |   (58)  all_56_12 = e2
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | REF_CLOSE: (27), (54), (58) are inconsistent by sub-proof #1032.
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | Case 2:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | |   (59)  all_56_12 = e1 | all_56_12 = e0
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | BETA: splitting (59) gives:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | Case 1:
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | |   (60)  all_56_12 = e1
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | COMBINE_EQS: (27), (60) imply:
% 178.18/28.40  | | | | |   (61)  all_52_25 = e1
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 178.18/28.40  | | | | |            (15), (16), (19), (21), (23), (26), (30), (31), (35), (36),
% 178.18/28.40  | | | | |            (37), (39), (41), (42), (43), (50), (61) are inconsistent
% 178.18/28.40  | | | | |            by sub-proof #584.
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | Case 2:
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | |   (62)  all_56_12 = e0
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | REF_CLOSE: (27), (29), (62) are inconsistent by sub-proof #1030.
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | End of split
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | End of split
% 178.18/28.40  | | | 
% 178.18/28.40  | | End of split
% 178.18/28.40  | | 
% 178.18/28.40  | Case 2:
% 178.18/28.40  | | 
% 178.18/28.40  | |   (63)   ~ (all_56_13 = e3)
% 178.18/28.40  | | 
% 178.18/28.40  | | REDUCE: (46), (63) imply:
% 178.18/28.40  | |   (64)   ~ (all_52_27 = e3)
% 178.18/28.40  | | 
% 178.18/28.40  | | BETA: splitting (20) gives:
% 178.18/28.40  | | 
% 178.18/28.40  | | Case 1:
% 178.18/28.40  | | | 
% 178.18/28.40  | | |   (65)  all_58_12 = e3
% 178.18/28.40  | | | 
% 178.18/28.40  | | | REF_CLOSE: (32), (35), (37), (39), (44), (65) are inconsistent by
% 178.18/28.40  | | |            sub-proof #884.
% 178.18/28.40  | | | 
% 178.18/28.40  | | Case 2:
% 178.18/28.40  | | | 
% 178.18/28.40  | | |   (66)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.18/28.40  | | | 
% 178.18/28.40  | | | BETA: splitting (66) gives:
% 178.18/28.40  | | | 
% 178.18/28.40  | | | Case 1:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | |   (67)  all_58_13 = e3
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | REF_CLOSE: (28), (64), (67) are inconsistent by sub-proof #1026.
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | Case 2:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | |   (68)  all_58_14 = e3 | all_58_15 = e3
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | BETA: splitting (68) gives:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | Case 1:
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | |   (69)  all_58_14 = e3
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.18/28.40  | | | | |            (13), (15), (16), (17), (19), (21), (22), (23), (26), (30),
% 178.18/28.40  | | | | |            (31), (34), (36), (37), (38), (39), (41), (42), (43), (69)
% 178.18/28.40  | | | | |            are inconsistent by sub-proof #578.
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | Case 2:
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | |   (70)  all_58_15 = e3
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | REF_CLOSE: (24), (33), (70) are inconsistent by sub-proof #1010.
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | End of split
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | End of split
% 178.18/28.40  | | | 
% 178.18/28.40  | | End of split
% 178.18/28.40  | | 
% 178.18/28.40  | End of split
% 178.18/28.40  | 
% 178.18/28.40  End of proof
% 178.18/28.40  
% 178.18/28.40  Sub-proof #578 shows that the following formulas are inconsistent:
% 178.18/28.40  ----------------------------------------------------------------
% 178.18/28.40    (1)  all_56_3 = all_52_7
% 178.18/28.40    (2)  op(e3, e2) = all_52_3
% 178.18/28.40    (3)  op(e1, e2) = all_52_19
% 178.18/28.40    (4)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.40    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.40    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.40    (7)   ~ (e3 = e1)
% 178.18/28.40    (8)  all_34_1 = all_4_1
% 178.18/28.40    (9)  op(e3, all_4_2) = all_4_1
% 178.18/28.40    (10)   ~ (all_52_7 = all_4_2)
% 178.18/28.40    (11)  all_58_0 = all_4_2
% 178.18/28.40    (12)  op(all_4_1, all_4_2) = e1
% 178.18/28.40    (13)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.40    (14)   ~ (all_4_1 = e2)
% 178.18/28.40    (15)  all_58_14 = all_52_29
% 178.18/28.40    (16)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.40    (17)  all_56_1 = all_52_3
% 178.18/28.40    (18)  op(e1, all_52_29) = e1
% 178.18/28.40    (19)   ~ (all_52_3 = all_4_2)
% 178.18/28.40    (20)  op(e1, e0) = all_52_23
% 178.18/28.40    (21)  all_56_0 = all_4_2
% 178.18/28.40    (22)   ~ (all_52_3 = all_52_19)
% 178.18/28.40    (23)  op(e1, e3) = all_52_17
% 178.18/28.40    (24)  op(e3, e0) = all_52_7
% 178.18/28.40    (25)  op(e3, e3) = all_4_2
% 178.18/28.40    (26)   ~ (all_52_17 = all_4_2)
% 178.18/28.40    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.40    (28)  all_34_2 = all_4_2
% 178.18/28.40    (29)  all_58_14 = e3
% 178.18/28.40    (30)   ~ (all_52_7 = all_52_23)
% 178.18/28.40    (31)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.40  
% 178.18/28.40  Begin of proof
% 178.18/28.40  | 
% 178.18/28.40  | COMBINE_EQS: (15), (29) imply:
% 178.18/28.40  |   (32)  all_52_29 = e3
% 178.18/28.40  | 
% 178.18/28.40  | SIMP: (32) implies:
% 178.18/28.40  |   (33)  all_52_29 = e3
% 178.18/28.40  | 
% 178.18/28.40  | REDUCE: (18), (33) imply:
% 178.18/28.40  |   (34)  op(e1, e3) = e1
% 178.18/28.40  | 
% 178.18/28.40  | GROUND_INST: instantiating (27) with all_52_17, e1, e3, e1, simplifying with
% 178.18/28.40  |              (23), (34) gives:
% 178.18/28.40  |   (35)  all_52_17 = e1
% 178.18/28.40  | 
% 178.18/28.40  | REDUCE: (26), (35) imply:
% 178.18/28.40  |   (36)   ~ (all_4_2 = e1)
% 178.18/28.40  | 
% 178.18/28.40  | SIMP: (36) implies:
% 178.18/28.40  |   (37)   ~ (all_4_2 = e1)
% 178.18/28.40  | 
% 178.18/28.40  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.18/28.40  |            (13), (14), (16), (17), (19), (20), (21), (22), (24), (25), (27),
% 178.18/28.40  |            (28), (30), (31), (37) are inconsistent by sub-proof #585.
% 178.18/28.40  | 
% 178.18/28.40  End of proof
% 178.18/28.40  
% 178.18/28.40  Sub-proof #579 shows that the following formulas are inconsistent:
% 178.18/28.40  ----------------------------------------------------------------
% 178.18/28.40    (1)   ~ (all_52_23 = all_14_2)
% 178.18/28.40    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.18/28.40    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.18/28.40    (4)   ~ (all_52_17 = all_52_23)
% 178.18/28.40    (5)   ~ (all_52_13 = all_52_29)
% 178.18/28.40    (6)  all_56_3 = all_52_7
% 178.18/28.40    (7)  op(e3, e2) = all_52_3
% 178.18/28.40    (8)   ~ (all_52_9 = all_52_25)
% 178.18/28.40    (9)   ~ (all_52_19 = all_52_23)
% 178.18/28.40    (10)  all_56_11 = all_52_23
% 178.18/28.40    (11)   ~ (all_52_27 = e0)
% 178.18/28.40    (12)   ~ (all_52_23 = e0)
% 178.18/28.40    (13)   ~ (all_52_3 = all_10_2)
% 178.18/28.40    (14)  all_58_5 = all_52_13
% 178.18/28.40    (15)   ~ (all_52_25 = all_52_29)
% 178.18/28.40    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.18/28.40    (17)  all_58_3 = all_10_2
% 178.18/28.40    (18)  all_56_9 = all_52_19
% 178.18/28.40    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.40    (20)   ~ (all_52_9 = all_4_2)
% 178.18/28.40    (21)   ~ (all_52_5 = all_52_7)
% 178.18/28.40    (22)  all_58_10 = all_52_15
% 178.18/28.40    (23)  all_58_7 = all_52_19
% 178.18/28.40    (24)   ~ (all_52_17 = all_52_25)
% 178.18/28.40    (25)  op(e0, e1) = all_52_29
% 178.18/28.40    (26)  all_58_4 = all_52_5
% 178.18/28.40    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.18/28.40    (28)   ~ (all_52_27 = all_52_29)
% 178.18/28.40    (29)  op(e3, all_4_2) = all_4_1
% 178.18/28.40    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.40    (31)   ~ (all_52_7 = all_4_2)
% 178.18/28.40    (32)  all_58_1 = all_52_3
% 178.18/28.40    (33)  all_58_0 = all_4_2
% 178.18/28.40    (34)  op(all_4_1, all_4_2) = e1
% 178.18/28.40    (35)  op(e1, all_52_29) = all_52_28
% 178.18/28.40    (36)   ~ (all_52_7 = e0)
% 178.18/28.40    (37)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.18/28.40    (38)   ~ (all_4_1 = e2)
% 178.18/28.40    (39)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.18/28.40    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.18/28.40    (41)  all_58_14 = all_52_29
% 178.18/28.40    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.18/28.40    (43)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.40    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.18/28.40    (45)  all_58_8 = all_14_2
% 178.18/28.40    (46)  op(e0, e2) = all_52_27
% 178.18/28.40    (47)  all_56_14 = all_52_29
% 178.18/28.40    (48)   ~ (all_14_0 = e3)
% 178.18/28.40    (49)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.18/28.40    (50)   ~ (all_52_5 = all_14_2)
% 178.18/28.40    (51)   ~ (all_52_3 = all_52_27)
% 178.18/28.40    (52)   ~ (all_52_3 = all_4_2)
% 178.18/28.40    (53)  op(e0, e3) = all_52_25
% 178.18/28.40    (54)   ~ (all_52_9 = all_10_2)
% 178.18/28.40    (55)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.18/28.40    (56)  op(e1, all_14_2) = all_14_0
% 178.18/28.40    (57)   ~ (e3 = e0)
% 178.18/28.40    (58)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.18/28.40    (59)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.18/28.40    (60)   ~ (all_52_15 = all_52_23)
% 178.18/28.40    (61)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.18/28.40    (62)   ~ (all_52_5 = all_52_29)
% 178.18/28.40    (63)  all_56_12 = all_52_25
% 178.18/28.40    (64)  all_58_13 = all_52_27
% 178.18/28.40    (65)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.18/28.40    (66)  all_56_5 = all_10_2
% 178.18/28.40    (67)   ~ (all_52_25 = e0)
% 178.18/28.40    (68)   ~ (all_52_9 = all_52_17)
% 178.18/28.40    (69)   ~ (all_14_0 = e2)
% 178.18/28.40    (70)  all_58_6 = all_52_17
% 178.18/28.40    (71)   ~ (all_52_3 = all_52_7)
% 178.18/28.40    (72)  op(e2, all_52_19) = e2
% 178.18/28.40    (73)  op(e3, all_52_17) = e3
% 178.18/28.40    (74)   ~ (e1 = e0)
% 178.18/28.40    (75)  all_56_0 = all_4_2
% 178.18/28.40    (76)  all_58_11 = all_52_23
% 178.18/28.40    (77)   ~ (all_52_29 = all_14_2)
% 178.18/28.40    (78)   ~ (all_52_19 = all_10_2)
% 178.18/28.40    (79)  all_58_15 = e0
% 178.18/28.40    (80)  all_58_2 = all_52_9
% 178.18/28.40    (81)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.18/28.40    (82)   ~ (all_52_29 = e0)
% 178.18/28.40    (83)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.18/28.40    (84)  op(e3, e1) = all_52_5
% 178.18/28.40    (85)  all_56_10 = all_14_2
% 178.18/28.40    (86)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.18/28.40    (87)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.18/28.40    (88)  op(e1, e3) = all_52_17
% 178.18/28.40    (89)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.18/28.40    (90)   ~ (all_52_25 = all_4_2)
% 178.18/28.40    (91)  op(e3, e0) = all_52_7
% 178.18/28.40    (92)  op(e3, e3) = all_4_2
% 178.18/28.40    (93)  all_56_8 = all_52_17
% 178.18/28.40    (94)   ~ (all_52_17 = all_4_2)
% 178.18/28.40    (95)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.40    (96)   ~ (all_52_25 = all_52_27)
% 178.18/28.40    (97)  op(e0, all_52_23) = e0
% 178.18/28.40    (98)   ~ (all_52_19 = all_52_27)
% 178.18/28.40    (99)  all_56_7 = all_52_15
% 178.18/28.40    (100)  op(e1, all_14_2) = e1
% 178.18/28.40    (101)   ~ (all_52_7 = all_52_23)
% 178.18/28.40    (102)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.18/28.40    (103)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.40    (104)  all_58_9 = all_52_7
% 178.18/28.40    (105)   ~ (e2 = e0)
% 178.18/28.40    (106)  all_58_12 = all_52_25
% 178.18/28.40    (107)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.18/28.40    (108)   ~ (all_52_9 = all_52_15)
% 178.18/28.40    (109)   ~ (e3 = e2)
% 178.18/28.40    (110)   ~ (all_52_19 = all_14_2)
% 178.18/28.40    (111)  op(e2, e3) = all_52_9
% 178.18/28.40    (112)  all_56_13 = all_52_27
% 178.18/28.40  
% 178.18/28.40  Begin of proof
% 178.18/28.40  | 
% 178.18/28.40  | GROUND_INST: instantiating (95) with e1, all_14_0, all_14_2, e1, simplifying
% 178.18/28.40  |              with (56), (100) gives:
% 178.18/28.40  |   (113)  all_14_0 = e1
% 178.18/28.40  | 
% 178.18/28.40  | REDUCE: (48), (113) imply:
% 178.18/28.40  |   (114)   ~ (e3 = e1)
% 178.18/28.40  | 
% 178.18/28.40  | SIMP: (114) implies:
% 178.18/28.40  |   (115)   ~ (e3 = e1)
% 178.18/28.40  | 
% 178.18/28.40  | REDUCE: (69), (113) imply:
% 178.18/28.40  |   (116)   ~ (e2 = e1)
% 178.18/28.40  | 
% 178.18/28.40  | SIMP: (116) implies:
% 178.18/28.40  |   (117)   ~ (e2 = e1)
% 178.18/28.40  | 
% 178.18/28.40  | BETA: splitting (42) gives:
% 178.18/28.40  | 
% 178.18/28.40  | Case 1:
% 178.18/28.40  | | 
% 178.18/28.40  | |   (118)  all_56_13 = e3
% 178.18/28.40  | | 
% 178.18/28.40  | | REF_CLOSE: (6), (10), (11), (16), (18), (22), (23), (25), (27), (30), (31),
% 178.18/28.40  | |            (33), (37), (43), (45), (46), (50), (53), (55), (59), (60), (63),
% 178.18/28.40  | |            (67), (68), (70), (72), (73), (74), (76), (79), (80), (81), (82),
% 178.18/28.40  | |            (83), (84), (87), (88), (89), (92), (94), (95), (96), (97), (98),
% 178.18/28.40  | |            (99), (100), (101), (102), (103), (104), (106), (107), (108),
% 178.18/28.40  | |            (109), (111), (112), (115), (118) are inconsistent by sub-proof
% 178.18/28.40  | |            #580.
% 178.18/28.40  | | 
% 178.18/28.40  | Case 2:
% 178.18/28.40  | | 
% 178.18/28.40  | |   (119)   ~ (all_56_13 = e3)
% 178.18/28.40  | |   (120)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.18/28.40  | | 
% 178.18/28.40  | | REDUCE: (112), (119) imply:
% 178.18/28.40  | |   (121)   ~ (all_52_27 = e3)
% 178.18/28.40  | | 
% 178.18/28.40  | | BETA: splitting (44) gives:
% 178.18/28.40  | | 
% 178.18/28.40  | | Case 1:
% 178.18/28.40  | | | 
% 178.18/28.40  | | |   (122)  all_58_12 = e3
% 178.18/28.40  | | | 
% 178.18/28.40  | | | COMBINE_EQS: (106), (122) imply:
% 178.18/28.40  | | |   (123)  all_52_25 = e3
% 178.18/28.40  | | | 
% 178.18/28.40  | | | SIMP: (123) implies:
% 178.18/28.40  | | |   (124)  all_52_25 = e3
% 178.18/28.40  | | | 
% 178.18/28.40  | | | REDUCE: (24), (124) imply:
% 178.18/28.40  | | |   (125)   ~ (all_52_17 = e3)
% 178.18/28.40  | | | 
% 178.18/28.40  | | | REDUCE: (15), (124) imply:
% 178.18/28.40  | | |   (126)   ~ (all_52_29 = e3)
% 178.18/28.40  | | | 
% 178.18/28.40  | | | SIMP: (126) implies:
% 178.18/28.40  | | |   (127)   ~ (all_52_29 = e3)
% 178.18/28.40  | | | 
% 178.18/28.40  | | | REDUCE: (53), (124) imply:
% 178.18/28.40  | | |   (128)  op(e0, e3) = e3
% 178.18/28.40  | | | 
% 178.18/28.40  | | | BETA: splitting (39) gives:
% 178.18/28.40  | | | 
% 178.18/28.40  | | | Case 1:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | |   (129)  all_56_14 = e3
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | REF_CLOSE: (47), (127), (129) are inconsistent by sub-proof #896.
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | Case 2:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | |   (130)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | BETA: splitting (89) gives:
% 178.18/28.40  | | | | 
% 178.18/28.40  | | | | Case 1:
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | |   (131)  all_56_7 = e3
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | REF_CLOSE: (10), (11), (16), (22), (25), (46), (55), (60), (74), (76),
% 178.18/28.40  | | | | |            (79), (82), (83), (95), (97), (99), (105), (109), (115),
% 178.18/28.40  | | | | |            (117), (131) are inconsistent by sub-proof #933.
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | Case 2:
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | |   (132)   ~ (all_56_7 = e3)
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | REDUCE: (99), (132) imply:
% 178.18/28.40  | | | | |   (133)   ~ (all_52_15 = e3)
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | BETA: splitting (102) gives:
% 178.18/28.40  | | | | | 
% 178.18/28.40  | | | | | Case 1:
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | |   (134)  all_58_9 = e3
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | | COMBINE_EQS: (104), (134) imply:
% 178.18/28.40  | | | | | |   (135)  all_52_7 = e3
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | | SIMP: (135) implies:
% 178.18/28.40  | | | | | |   (136)  all_52_7 = e3
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | | REDUCE: (21), (136) imply:
% 178.18/28.40  | | | | | |   (137)   ~ (all_52_5 = e3)
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | | REDUCE: (101), (136) imply:
% 178.18/28.40  | | | | | |   (138)   ~ (all_52_23 = e3)
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | | SIMP: (138) implies:
% 178.18/28.40  | | | | | |   (139)   ~ (all_52_23 = e3)
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | | BETA: splitting (27) gives:
% 178.18/28.40  | | | | | | 
% 178.18/28.40  | | | | | | Case 1:
% 178.18/28.40  | | | | | | | 
% 178.18/28.40  | | | | | | |   (140)  all_58_6 = e3
% 178.18/28.40  | | | | | | | 
% 178.18/28.40  | | | | | | | REF_CLOSE: (70), (125), (140) are inconsistent by sub-proof #981.
% 178.18/28.40  | | | | | | | 
% 178.18/28.40  | | | | | | Case 2:
% 178.18/28.40  | | | | | | | 
% 178.18/28.40  | | | | | | |   (141)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.18/28.41  | | | | | | | 
% 178.18/28.41  | | | | | | | BETA: splitting (65) gives:
% 178.18/28.41  | | | | | | | 
% 178.18/28.41  | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | |   (142)  all_58_0 = e1
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | COMBINE_EQS: (33), (142) imply:
% 178.18/28.41  | | | | | | | |   (143)  all_4_2 = e1
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | REDUCE: (34), (143) imply:
% 178.18/28.41  | | | | | | | |   (144)  op(all_4_1, e1) = e1
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | REDUCE: (29), (143) imply:
% 178.18/28.41  | | | | | | | |   (145)  op(e3, e1) = all_4_1
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | GROUND_INST: instantiating (95) with all_52_5, all_4_1, e1, e3,
% 178.18/28.41  | | | | | | | |              simplifying with (84), (145) gives:
% 178.18/28.41  | | | | | | | |   (146)  all_52_5 = all_4_1
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | COMBINE_EQS: (26), (146) imply:
% 178.18/28.41  | | | | | | | |   (147)  all_58_4 = all_4_1
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | REDUCE: (62), (146) imply:
% 178.18/28.41  | | | | | | | |   (148)   ~ (all_52_29 = all_4_1)
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | SIMP: (148) implies:
% 178.18/28.41  | | | | | | | |   (149)   ~ (all_52_29 = all_4_1)
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | BETA: splitting (49) gives:
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | 
% 178.18/28.41  | | | | | | | | |   (150)  all_58_0 = e2
% 178.18/28.41  | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | REF_CLOSE: (117), (142), (150) are inconsistent by sub-proof
% 178.18/28.41  | | | | | | | | |            #930.
% 178.18/28.41  | | | | | | | | | 
% 178.18/28.41  | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | 
% 178.18/28.41  | | | | | | | | |   (151)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.18/28.41  | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | BETA: splitting (151) gives:
% 178.18/28.41  | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | |   (152)  all_58_1 = e2
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | COMBINE_EQS: (32), (152) imply:
% 178.18/28.41  | | | | | | | | | |   (153)  all_52_3 = e2
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | REDUCE: (51), (153) imply:
% 178.18/28.41  | | | | | | | | | |   (154)   ~ (all_52_27 = e2)
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | SIMP: (154) implies:
% 178.18/28.41  | | | | | | | | | |   (155)   ~ (all_52_27 = e2)
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | BETA: splitting (3) gives:
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | |   (156)  all_58_0 = e0
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | COMBINE_EQS: (142), (156) imply:
% 178.18/28.41  | | | | | | | | | | |   (157)  e1 = e0
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | REDUCE: (74), (157) imply:
% 178.18/28.41  | | | | | | | | | | |   (158)  $false
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | |   (159)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | BETA: splitting (120) gives:
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | |   (160)  all_56_13 = e2
% 178.18/28.41  | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | REF_CLOSE: (112), (155), (160) are inconsistent by sub-proof
% 178.18/28.41  | | | | | | | | | | | |            #624.
% 178.18/28.41  | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | |   (161)  all_56_13 = e1 | all_56_13 = e0
% 178.18/28.41  | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | BETA: splitting (161) gives:
% 178.18/28.41  | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | |   (162)  all_56_13 = e1
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | COMBINE_EQS: (112), (162) imply:
% 178.18/28.41  | | | | | | | | | | | | |   (163)  all_52_27 = e1
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | SIMP: (163) implies:
% 178.18/28.41  | | | | | | | | | | | | |   (164)  all_52_27 = e1
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | REDUCE: (28), (164) imply:
% 178.18/28.41  | | | | | | | | | | | | |   (165)   ~ (all_52_29 = e1)
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | SIMP: (165) implies:
% 178.18/28.41  | | | | | | | | | | | | |   (166)   ~ (all_52_29 = e1)
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | BETA: splitting (159) gives:
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | |   (167)  all_58_1 = e0
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | COMBINE_EQS: (152), (167) imply:
% 178.18/28.41  | | | | | | | | | | | | | |   (168)  e2 = e0
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | REDUCE: (105), (168) imply:
% 178.18/28.41  | | | | | | | | | | | | | |   (169)  $false
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | |   (170)  all_58_4 = e0 | all_58_9 = e0
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | |   (171)  all_58_4 = e0
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | COMBINE_EQS: (147), (171) imply:
% 178.18/28.41  | | | | | | | | | | | | | | |   (172)  all_4_1 = e0
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | SIMP: (172) implies:
% 178.18/28.41  | | | | | | | | | | | | | | |   (173)  all_4_1 = e0
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | REDUCE: (144), (173) imply:
% 178.18/28.41  | | | | | | | | | | | | | | |   (174)  op(e0, e1) = e1
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | Case 1:
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | |   (175)  all_56_14 = e2
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (175) imply:
% 178.18/28.41  | | | | | | | | | | | | | | | |   (176)  all_52_29 = e2
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | | SIMP: (176) implies:
% 178.18/28.41  | | | | | | | | | | | | | | | |   (177)  all_52_29 = e2
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | | REDUCE: (25), (177) imply:
% 178.18/28.41  | | | | | | | | | | | | | | | |   (178)  op(e0, e1) = e2
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (95) with e1, e2, e1, e0,
% 178.18/28.41  | | | | | | | | | | | | | | | |              simplifying with (174), (178) gives:
% 178.18/28.41  | | | | | | | | | | | | | | | |   (179)  e2 = e1
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | | REDUCE: (117), (179) imply:
% 178.18/28.41  | | | | | | | | | | | | | | | |   (180)  $false
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | |   (181)  all_56_14 = e1 | all_56_14 = e0
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | | REF_CLOSE: (47), (82), (166), (181) are inconsistent by
% 178.18/28.41  | | | | | | | | | | | | | | | |            sub-proof #886.
% 178.18/28.41  | | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | |   (182)  all_58_9 = e0
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | | REF_CLOSE: (57), (134), (182) are inconsistent by sub-proof
% 178.18/28.41  | | | | | | | | | | | | | | |            #928.
% 178.18/28.41  | | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | |   (183)  all_56_13 = e0
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | | REF_CLOSE: (11), (112), (183) are inconsistent by sub-proof
% 178.18/28.41  | | | | | | | | | | | | |            #844.
% 178.18/28.41  | | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | |   (184)  all_58_4 = e2 | all_58_9 = e2
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | | REF_CLOSE: (38), (109), (134), (147), (184) are inconsistent
% 178.18/28.41  | | | | | | | | | |            by sub-proof #923.
% 178.18/28.41  | | | | | | | | | | 
% 178.18/28.41  | | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | | 
% 178.18/28.41  | | | | | | | | End of split
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | Case 2:
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | |   (185)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | | REF_CLOSE: (1), (23), (45), (50), (61), (70), (72), (73), (76),
% 178.18/28.41  | | | | | | | |            (80), (84), (85), (88), (95), (100), (110), (111),
% 178.18/28.41  | | | | | | | |            (115), (117), (122), (137), (139), (141), (185) are
% 178.18/28.41  | | | | | | | |            inconsistent by sub-proof #918.
% 178.18/28.41  | | | | | | | | 
% 178.18/28.41  | | | | | | | End of split
% 178.18/28.41  | | | | | | | 
% 178.18/28.41  | | | | | | End of split
% 178.18/28.41  | | | | | | 
% 178.18/28.41  | | | | | Case 2:
% 178.18/28.41  | | | | | | 
% 178.18/28.41  | | | | | |   (186)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.18/28.41  | | | | | | 
% 178.18/28.41  | | | | | | REF_CLOSE: (12), (22), (57), (76), (79), (95), (97), (128), (133),
% 178.18/28.41  | | | | | |            (186) are inconsistent by sub-proof #914.
% 178.18/28.41  | | | | | | 
% 178.18/28.41  | | | | | End of split
% 178.18/28.41  | | | | | 
% 178.18/28.41  | | | | End of split
% 178.18/28.41  | | | | 
% 178.18/28.41  | | | End of split
% 178.18/28.41  | | | 
% 178.18/28.41  | | Case 2:
% 178.18/28.41  | | | 
% 178.18/28.41  | | |   (187)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.18/28.41  | | | 
% 178.18/28.41  | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 178.18/28.41  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (27),
% 178.18/28.41  | | |            (28), (30), (31), (32), (33), (35), (37), (40), (41), (43),
% 178.18/28.41  | | |            (45), (46), (50), (52), (53), (54), (55), (57), (58), (59),
% 178.18/28.41  | | |            (60), (62), (63), (64), (65), (66), (67), (68), (70), (71),
% 178.18/28.41  | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 178.18/28.41  | | |            (82), (83), (84), (86), (87), (88), (89), (90), (91), (92),
% 178.18/28.41  | | |            (93), (94), (95), (97), (98), (99), (100), (101), (102), (104),
% 178.18/28.41  | | |            (105), (106), (108), (109), (111), (115), (117), (121), (187)
% 178.18/28.41  | | |            are inconsistent by sub-proof #898.
% 178.18/28.41  | | | 
% 178.18/28.41  | | End of split
% 178.18/28.41  | | 
% 178.18/28.41  | End of split
% 178.18/28.41  | 
% 178.18/28.41  End of proof
% 178.18/28.41  
% 178.18/28.41  Sub-proof #580 shows that the following formulas are inconsistent:
% 178.18/28.41  ----------------------------------------------------------------
% 178.18/28.41    (1)  all_56_3 = all_52_7
% 178.18/28.41    (2)  all_56_11 = all_52_23
% 178.18/28.41    (3)   ~ (all_52_27 = e0)
% 178.18/28.41    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.18/28.41    (5)  all_56_9 = all_52_19
% 178.18/28.41    (6)  all_58_10 = all_52_15
% 178.18/28.41    (7)  all_58_7 = all_52_19
% 178.18/28.41    (8)  op(e0, e1) = all_52_29
% 178.18/28.41    (9)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.18/28.41    (10)   ~ (e3 = e1)
% 178.18/28.41    (11)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.41    (12)   ~ (all_52_7 = all_4_2)
% 178.18/28.41    (13)  all_58_0 = all_4_2
% 178.18/28.41    (14)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.18/28.41    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.41    (16)  all_58_8 = all_14_2
% 178.18/28.41    (17)  op(e0, e2) = all_52_27
% 178.18/28.41    (18)   ~ (all_52_5 = all_14_2)
% 178.18/28.41    (19)  op(e0, e3) = all_52_25
% 178.18/28.41    (20)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.18/28.41    (21)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.18/28.41    (22)   ~ (all_52_15 = all_52_23)
% 178.18/28.41    (23)  all_56_12 = all_52_25
% 178.18/28.41    (24)   ~ (all_52_25 = e0)
% 178.18/28.41    (25)   ~ (all_52_9 = all_52_17)
% 178.18/28.41    (26)  all_58_6 = all_52_17
% 178.18/28.41    (27)  op(e2, all_52_19) = e2
% 178.18/28.41    (28)  op(e3, all_52_17) = e3
% 178.18/28.41    (29)   ~ (e1 = e0)
% 178.18/28.41    (30)  all_58_11 = all_52_23
% 178.18/28.41    (31)  all_58_15 = e0
% 178.18/28.41    (32)  all_58_2 = all_52_9
% 178.18/28.41    (33)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.18/28.41    (34)   ~ (all_52_29 = e0)
% 178.18/28.41    (35)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.18/28.41    (36)  op(e3, e1) = all_52_5
% 178.18/28.41    (37)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.18/28.41    (38)  op(e1, e3) = all_52_17
% 178.18/28.41    (39)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.18/28.41    (40)  op(e3, e3) = all_4_2
% 178.18/28.41    (41)   ~ (all_52_17 = all_4_2)
% 178.18/28.41    (42)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.41    (43)   ~ (all_52_25 = all_52_27)
% 178.18/28.41    (44)  all_56_13 = e3
% 178.18/28.41    (45)  op(e0, all_52_23) = e0
% 178.18/28.41    (46)   ~ (all_52_19 = all_52_27)
% 178.18/28.41    (47)  all_56_7 = all_52_15
% 178.18/28.41    (48)  op(e1, all_14_2) = e1
% 178.18/28.41    (49)   ~ (all_52_7 = all_52_23)
% 178.18/28.41    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.18/28.41    (51)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.41    (52)  all_58_9 = all_52_7
% 178.18/28.41    (53)  all_58_12 = all_52_25
% 178.18/28.41    (54)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.18/28.41    (55)   ~ (all_52_9 = all_52_15)
% 178.18/28.41    (56)   ~ (e3 = e2)
% 178.18/28.41    (57)  op(e2, e3) = all_52_9
% 178.18/28.41    (58)  all_56_13 = all_52_27
% 178.18/28.41  
% 178.18/28.41  Begin of proof
% 178.18/28.41  | 
% 178.18/28.41  | COMBINE_EQS: (44), (58) imply:
% 178.18/28.41  |   (59)  all_52_27 = e3
% 178.18/28.41  | 
% 178.18/28.41  | SIMP: (59) implies:
% 178.18/28.41  |   (60)  all_52_27 = e3
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (46), (60) imply:
% 178.18/28.41  |   (61)   ~ (all_52_19 = e3)
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (43), (60) imply:
% 178.18/28.41  |   (62)   ~ (all_52_25 = e3)
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (3), (60) imply:
% 178.18/28.41  |   (63)   ~ (e3 = e0)
% 178.18/28.41  | 
% 178.18/28.41  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.18/28.41  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.18/28.41  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 178.18/28.41  |            (35), (36), (37), (38), (39), (40), (41), (42), (45), (47), (48),
% 178.18/28.41  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (61), (62),
% 178.18/28.41  |            (63) are inconsistent by sub-proof #932.
% 178.18/28.41  | 
% 178.18/28.41  End of proof
% 178.18/28.41  
% 178.18/28.41  Sub-proof #581 shows that the following formulas are inconsistent:
% 178.18/28.41  ----------------------------------------------------------------
% 178.18/28.41    (1)   ~ (all_52_27 = all_10_2)
% 178.18/28.41    (2)   ~ (all_52_17 = all_52_23)
% 178.18/28.41    (3)  op(e2, all_10_2) = all_10_1
% 178.18/28.41    (4)   ~ (all_52_13 = all_52_29)
% 178.18/28.41    (5)  all_56_3 = all_52_7
% 178.18/28.41    (6)  op(e3, e2) = all_52_3
% 178.18/28.41    (7)   ~ (all_52_9 = all_52_25)
% 178.18/28.41    (8)  op(e1, e2) = all_52_19
% 178.18/28.41    (9)   ~ (all_52_27 = e0)
% 178.18/28.41    (10)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.41    (11)  op(e3, all_52_9) = all_52_8
% 178.18/28.41    (12)   ~ (all_52_3 = all_10_2)
% 178.18/28.41    (13)  all_58_5 = all_52_13
% 178.18/28.41    (14)   ~ (all_52_25 = all_52_29)
% 178.18/28.41    (15)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.41    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.18/28.41    (17)  all_58_3 = all_10_2
% 178.18/28.41    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.41    (19)  all_52_12 = e1
% 178.18/28.41    (20)   ~ (all_52_9 = all_4_2)
% 178.18/28.41    (21)  all_58_10 = all_52_15
% 178.18/28.41    (22)  all_58_7 = all_52_19
% 178.18/28.41    (23)  all_56_4 = all_52_9
% 178.18/28.41    (24)   ~ (all_52_17 = all_52_25)
% 178.18/28.41    (25)  op(e0, e1) = all_52_29
% 178.18/28.41    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.18/28.41    (27)   ~ (e3 = e1)
% 178.18/28.41    (28)  all_52_14 = e0
% 178.18/28.41    (29)  all_34_1 = all_4_1
% 178.18/28.41    (30)  op(e3, all_4_2) = all_4_1
% 178.18/28.41    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.41    (32)   ~ (all_52_7 = all_4_2)
% 178.18/28.41    (33)  all_58_1 = all_52_3
% 178.18/28.41    (34)  all_58_0 = all_4_2
% 178.18/28.41    (35)  op(e1, all_52_13) = all_52_12
% 178.18/28.41    (36)  op(all_4_1, all_4_2) = e1
% 178.18/28.41    (37)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.41    (38)   ~ (all_4_1 = e2)
% 178.18/28.41    (39)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.18/28.41    (40)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.18/28.41    (41)  all_58_14 = all_52_29
% 178.18/28.41    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.18/28.41    (43)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.41    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.18/28.41    (45)  all_58_8 = all_14_2
% 178.18/28.41    (46)  all_56_1 = all_52_3
% 178.18/28.41    (47)  op(e0, e2) = all_52_27
% 178.18/28.41    (48)   ~ (all_52_3 = all_52_27)
% 178.18/28.41    (49)   ~ (all_52_3 = all_4_2)
% 178.18/28.41    (50)  op(e0, e3) = all_52_25
% 178.18/28.41    (51)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.18/28.41    (52)   ~ (e3 = e0)
% 178.18/28.41    (53)   ~ (all_52_9 = all_52_13)
% 178.18/28.41    (54)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.18/28.41    (55)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.18/28.41    (56)  op(all_10_1, all_10_2) = all_10_0
% 178.18/28.41    (57)  op(e1, e0) = all_52_23
% 178.18/28.41    (58)  all_56_12 = all_52_25
% 178.18/28.41    (59)  all_58_13 = all_52_27
% 178.18/28.41    (60)  all_52_8 = e3
% 178.18/28.41    (61)   ~ (all_52_25 = e0)
% 178.18/28.41    (62)  all_58_6 = all_52_17
% 178.18/28.41    (63)   ~ (all_52_3 = all_52_7)
% 178.18/28.41    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.18/28.41    (65)   ~ (e1 = e0)
% 178.18/28.41    (66)  all_56_0 = all_4_2
% 178.18/28.41    (67)  all_58_11 = all_52_23
% 178.18/28.41    (68)   ~ (all_52_3 = all_52_19)
% 178.18/28.41    (69)   ~ (all_52_7 = all_52_15)
% 178.18/28.41    (70)  op(e0, all_52_15) = all_52_14
% 178.18/28.41    (71)   ~ (all_52_19 = all_10_2)
% 178.18/28.41    (72)  all_58_15 = e0
% 178.18/28.41    (73)  all_58_2 = all_52_9
% 178.18/28.41    (74)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.18/28.41    (75)   ~ (all_52_29 = e0)
% 178.18/28.41    (76)  all_56_10 = all_14_2
% 178.18/28.41    (77)  op(e1, e3) = all_52_17
% 178.18/28.41    (78)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.18/28.41    (79)   ~ (all_52_25 = all_4_2)
% 178.18/28.41    (80)  op(e3, e0) = all_52_7
% 178.18/28.41    (81)  op(e3, e3) = all_4_2
% 178.18/28.41    (82)   ~ (all_52_17 = all_4_2)
% 178.18/28.41    (83)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.41    (84)   ~ (all_52_25 = all_52_27)
% 178.18/28.41    (85)  all_34_2 = all_4_2
% 178.18/28.41    (86)   ~ (all_10_0 = e3)
% 178.18/28.41    (87)  all_56_7 = all_52_15
% 178.18/28.41    (88)  all_10_1 = e2
% 178.18/28.41    (89)   ~ (all_52_15 = e0)
% 178.18/28.41    (90)   ~ (all_52_7 = all_52_23)
% 178.18/28.41    (91)  op(e2, all_52_27) = all_52_26
% 178.18/28.41    (92)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.18/28.41    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.41    (94)  all_58_9 = all_52_7
% 178.18/28.41    (95)   ~ (e2 = e0)
% 178.18/28.41    (96)  all_58_12 = all_52_25
% 178.18/28.41    (97)   ~ (all_10_0 = e1)
% 178.18/28.41    (98)  all_56_6 = all_52_13
% 178.18/28.41    (99)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.18/28.41    (100)   ~ (all_52_9 = all_52_15)
% 178.18/28.41    (101)   ~ (all_52_19 = all_14_2)
% 178.18/28.41    (102)  op(e2, e3) = all_52_9
% 178.18/28.41    (103)  all_56_13 = all_52_27
% 178.18/28.41  
% 178.18/28.41  Begin of proof
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (56), (88) imply:
% 178.18/28.41  |   (104)  op(e2, all_10_2) = all_10_0
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (11), (60) imply:
% 178.18/28.41  |   (105)  op(e3, all_52_9) = e3
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (3), (88) imply:
% 178.18/28.41  |   (106)  op(e2, all_10_2) = e2
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (19), (35) imply:
% 178.18/28.41  |   (107)  op(e1, all_52_13) = e1
% 178.18/28.41  | 
% 178.18/28.41  | REDUCE: (28), (70) imply:
% 178.18/28.41  |   (108)  op(e0, all_52_15) = e0
% 178.18/28.41  | 
% 178.18/28.41  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 178.18/28.41  |            (15), (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 178.18/28.41  |            (27), (29), (30), (31), (32), (33), (34), (36), (37), (38), (39),
% 178.18/28.41  |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 178.18/28.41  |            (51), (52), (53), (54), (55), (57), (58), (59), (61), (62), (63),
% 178.18/28.41  |            (64), (65), (66), (67), (68), (69), (71), (72), (73), (74), (75),
% 178.18/28.41  |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 178.18/28.41  |            (87), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 178.18/28.41  |            (99), (100), (101), (102), (103), (104), (105), (106), (107), (108)
% 178.18/28.41  |            are inconsistent by sub-proof #582.
% 178.18/28.41  | 
% 178.18/28.41  End of proof
% 178.18/28.41  
% 178.18/28.41  Sub-proof #582 shows that the following formulas are inconsistent:
% 178.18/28.41  ----------------------------------------------------------------
% 178.18/28.41    (1)   ~ (all_52_27 = all_10_2)
% 178.18/28.41    (2)   ~ (all_52_17 = all_52_23)
% 178.18/28.41    (3)   ~ (all_52_13 = all_52_29)
% 178.18/28.41    (4)  op(e2, all_10_2) = all_10_0
% 178.18/28.41    (5)  all_56_3 = all_52_7
% 178.18/28.41    (6)  op(e3, e2) = all_52_3
% 178.18/28.41    (7)   ~ (all_52_9 = all_52_25)
% 178.18/28.41    (8)  op(e1, e2) = all_52_19
% 178.18/28.41    (9)   ~ (all_52_27 = e0)
% 178.18/28.41    (10)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.41    (11)   ~ (all_52_3 = all_10_2)
% 178.18/28.41    (12)  all_58_5 = all_52_13
% 178.18/28.41    (13)   ~ (all_52_25 = all_52_29)
% 178.18/28.41    (14)  op(e1, all_52_13) = e1
% 178.18/28.41    (15)  op(e0, all_52_15) = e0
% 178.18/28.41    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.41    (17)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.18/28.41    (18)  all_58_3 = all_10_2
% 178.18/28.41    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.41    (20)   ~ (all_52_9 = all_4_2)
% 178.18/28.41    (21)  all_58_10 = all_52_15
% 178.18/28.41    (22)  all_58_7 = all_52_19
% 178.18/28.42    (23)  all_56_4 = all_52_9
% 178.18/28.42    (24)   ~ (all_52_17 = all_52_25)
% 178.18/28.42    (25)  op(e0, e1) = all_52_29
% 178.18/28.42    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.18/28.42    (27)   ~ (e3 = e1)
% 178.18/28.42    (28)  all_34_1 = all_4_1
% 178.18/28.42    (29)  op(e3, all_4_2) = all_4_1
% 178.18/28.42    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.42    (31)   ~ (all_52_7 = all_4_2)
% 178.18/28.42    (32)  all_58_1 = all_52_3
% 178.18/28.42    (33)  all_58_0 = all_4_2
% 178.18/28.42    (34)  op(all_4_1, all_4_2) = e1
% 178.18/28.42    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.42    (36)   ~ (all_4_1 = e2)
% 178.18/28.42    (37)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.18/28.42    (38)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.18/28.42    (39)  all_58_14 = all_52_29
% 178.18/28.42    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.18/28.42    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.42    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.18/28.42    (43)  all_58_8 = all_14_2
% 178.18/28.42    (44)  all_56_1 = all_52_3
% 178.18/28.42    (45)  op(e0, e2) = all_52_27
% 178.18/28.42    (46)   ~ (all_52_3 = all_52_27)
% 178.18/28.42    (47)   ~ (all_52_3 = all_4_2)
% 178.18/28.42    (48)  op(e0, e3) = all_52_25
% 178.18/28.42    (49)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.18/28.42    (50)  op(e3, all_52_9) = e3
% 178.18/28.42    (51)   ~ (e3 = e0)
% 178.18/28.42    (52)   ~ (all_52_9 = all_52_13)
% 178.18/28.42    (53)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.18/28.42    (54)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.18/28.42    (55)  op(e1, e0) = all_52_23
% 178.18/28.42    (56)  all_56_12 = all_52_25
% 178.18/28.42    (57)  all_58_13 = all_52_27
% 178.18/28.42    (58)   ~ (all_52_25 = e0)
% 178.18/28.42    (59)  all_58_6 = all_52_17
% 178.18/28.42    (60)   ~ (all_52_3 = all_52_7)
% 178.18/28.42    (61)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.18/28.42    (62)   ~ (e1 = e0)
% 178.18/28.42    (63)  all_56_0 = all_4_2
% 178.18/28.42    (64)  all_58_11 = all_52_23
% 178.18/28.42    (65)   ~ (all_52_3 = all_52_19)
% 178.18/28.42    (66)   ~ (all_52_7 = all_52_15)
% 178.18/28.42    (67)   ~ (all_52_19 = all_10_2)
% 178.18/28.42    (68)  all_58_15 = e0
% 178.18/28.42    (69)  all_58_2 = all_52_9
% 178.18/28.42    (70)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.18/28.42    (71)   ~ (all_52_29 = e0)
% 178.18/28.42    (72)  all_56_10 = all_14_2
% 178.18/28.42    (73)  op(e1, e3) = all_52_17
% 178.18/28.42    (74)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.18/28.42    (75)   ~ (all_52_25 = all_4_2)
% 178.18/28.42    (76)  op(e3, e0) = all_52_7
% 178.18/28.42    (77)  op(e2, all_10_2) = e2
% 178.18/28.42    (78)  op(e3, e3) = all_4_2
% 178.18/28.42    (79)   ~ (all_52_17 = all_4_2)
% 178.18/28.42    (80)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.42    (81)   ~ (all_52_25 = all_52_27)
% 178.18/28.42    (82)  all_34_2 = all_4_2
% 178.18/28.42    (83)   ~ (all_10_0 = e3)
% 178.18/28.42    (84)  all_56_7 = all_52_15
% 178.18/28.42    (85)   ~ (all_52_15 = e0)
% 178.18/28.42    (86)   ~ (all_52_7 = all_52_23)
% 178.18/28.42    (87)  op(e2, all_52_27) = all_52_26
% 178.18/28.42    (88)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.18/28.42    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.42    (90)  all_58_9 = all_52_7
% 178.18/28.42    (91)   ~ (e2 = e0)
% 178.18/28.42    (92)  all_58_12 = all_52_25
% 178.18/28.42    (93)   ~ (all_10_0 = e1)
% 178.18/28.42    (94)  all_56_6 = all_52_13
% 178.18/28.42    (95)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.18/28.42    (96)   ~ (all_52_9 = all_52_15)
% 178.18/28.42    (97)   ~ (all_52_19 = all_14_2)
% 178.18/28.42    (98)  op(e2, e3) = all_52_9
% 178.18/28.42    (99)  all_56_13 = all_52_27
% 178.18/28.42  
% 178.18/28.42  Begin of proof
% 178.18/28.42  | 
% 178.18/28.42  | GROUND_INST: instantiating (80) with e2, all_10_0, all_10_2, e2, simplifying
% 178.18/28.42  |              with (4), (77) gives:
% 178.18/28.42  |   (100)  all_10_0 = e2
% 178.18/28.42  | 
% 178.18/28.42  | REDUCE: (83), (100) imply:
% 178.18/28.42  |   (101)   ~ (e3 = e2)
% 178.18/28.42  | 
% 178.18/28.42  | SIMP: (101) implies:
% 178.18/28.42  |   (102)   ~ (e3 = e2)
% 178.18/28.42  | 
% 178.18/28.42  | REDUCE: (93), (100) imply:
% 178.18/28.42  |   (103)   ~ (e2 = e1)
% 178.18/28.42  | 
% 178.18/28.42  | BETA: splitting (40) gives:
% 178.18/28.42  | 
% 178.18/28.42  | Case 1:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (104)  all_56_13 = e3
% 178.18/28.42  | | 
% 178.18/28.42  | | REF_CLOSE: (1), (6), (7), (8), (10), (12), (14), (15), (16), (18), (19),
% 178.18/28.42  | |            (20), (21), (23), (27), (28), (29), (30), (33), (34), (35), (38),
% 178.18/28.42  | |            (41), (44), (46), (47), (48), (50), (52), (59), (61), (63), (65),
% 178.18/28.42  | |            (69), (73), (75), (78), (79), (80), (81), (82), (87), (92), (94),
% 178.18/28.42  | |            (95), (96), (98), (99), (104) are inconsistent by sub-proof #593.
% 178.18/28.42  | | 
% 178.18/28.42  | Case 2:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (105)   ~ (all_56_13 = e3)
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (99), (105) imply:
% 178.18/28.42  | |   (106)   ~ (all_52_27 = e3)
% 178.18/28.42  | | 
% 178.18/28.42  | | BETA: splitting (42) gives:
% 178.18/28.42  | | 
% 178.18/28.42  | | Case 1:
% 178.18/28.42  | | | 
% 178.18/28.42  | | |   (107)  all_58_12 = e3
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REF_CLOSE: (2), (5), (6), (7), (9), (11), (12), (14), (15), (17), (18),
% 178.18/28.42  | | |            (21), (22), (24), (25), (26), (27), (30), (32), (37), (43),
% 178.18/28.42  | | |            (45), (48), (49), (50), (54), (57), (58), (59), (60), (62),
% 178.18/28.42  | | |            (64), (66), (67), (68), (69), (71), (72), (73), (74), (77),
% 178.18/28.42  | | |            (80), (81), (84), (85), (86), (88), (89), (90), (91), (92),
% 178.18/28.42  | | |            (97), (98), (102), (103), (107) are inconsistent by sub-proof
% 178.18/28.42  | | |            #970.
% 178.18/28.42  | | | 
% 178.18/28.42  | | Case 2:
% 178.18/28.42  | | | 
% 178.18/28.42  | | |   (108)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (12), (13), (15), (16), (18),
% 178.18/28.42  | | |            (19), (20), (21), (28), (29), (30), (31), (33), (34), (35),
% 178.18/28.42  | | |            (36), (39), (41), (44), (47), (48), (50), (51), (53), (55),
% 178.18/28.42  | | |            (56), (57), (58), (63), (65), (68), (69), (70), (74), (75),
% 178.18/28.42  | | |            (76), (77), (78), (80), (82), (84), (86), (89), (92), (98),
% 178.18/28.42  | | |            (106), (108) are inconsistent by sub-proof #583.
% 178.18/28.42  | | | 
% 178.18/28.42  | | End of split
% 178.18/28.42  | | 
% 178.18/28.42  | End of split
% 178.18/28.42  | 
% 178.18/28.42  End of proof
% 178.18/28.42  
% 178.18/28.42  Sub-proof #583 shows that the following formulas are inconsistent:
% 178.18/28.42  ----------------------------------------------------------------
% 178.18/28.42    (1)   ~ (all_52_13 = all_52_29)
% 178.18/28.42    (2)  all_56_3 = all_52_7
% 178.18/28.42    (3)  op(e3, e2) = all_52_3
% 178.18/28.42    (4)   ~ (all_52_9 = all_52_25)
% 178.18/28.42    (5)  op(e1, e2) = all_52_19
% 178.18/28.42    (6)   ~ (all_52_27 = e3)
% 178.18/28.42    (7)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.42    (8)  all_58_5 = all_52_13
% 178.18/28.42    (9)   ~ (all_52_25 = all_52_29)
% 178.18/28.42    (10)  op(e0, all_52_15) = e0
% 178.18/28.42    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.42    (12)  all_58_3 = all_10_2
% 178.18/28.42    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42    (14)   ~ (all_52_9 = all_4_2)
% 178.18/28.42    (15)  all_58_10 = all_52_15
% 178.18/28.42    (16)  all_34_1 = all_4_1
% 178.18/28.42    (17)  op(e3, all_4_2) = all_4_1
% 178.18/28.42    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.42    (19)   ~ (all_52_7 = all_4_2)
% 178.18/28.42    (20)  all_58_0 = all_4_2
% 178.18/28.42    (21)  op(all_4_1, all_4_2) = e1
% 178.18/28.42    (22)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.42    (23)   ~ (all_4_1 = e2)
% 178.18/28.42    (24)  all_58_14 = all_52_29
% 178.18/28.42    (25)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.42    (26)  all_56_1 = all_52_3
% 178.18/28.42    (27)   ~ (all_52_3 = all_4_2)
% 178.18/28.42    (28)  op(e0, e3) = all_52_25
% 178.18/28.42    (29)  op(e3, all_52_9) = e3
% 178.18/28.42    (30)   ~ (e3 = e0)
% 178.18/28.42    (31)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.18/28.42    (32)  op(e1, e0) = all_52_23
% 178.18/28.42    (33)  all_56_12 = all_52_25
% 178.18/28.42    (34)  all_58_13 = all_52_27
% 178.18/28.42    (35)   ~ (all_52_25 = e0)
% 178.18/28.42    (36)  all_56_0 = all_4_2
% 178.18/28.42    (37)   ~ (all_52_3 = all_52_19)
% 178.18/28.42    (38)  all_58_15 = e0
% 178.18/28.42    (39)  all_58_2 = all_52_9
% 178.18/28.42    (40)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.18/28.42    (41)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.18/28.42    (42)   ~ (all_52_25 = all_4_2)
% 178.18/28.42    (43)  op(e3, e0) = all_52_7
% 178.18/28.42    (44)  op(e2, all_10_2) = e2
% 178.18/28.42    (45)  op(e3, e3) = all_4_2
% 178.18/28.42    (46)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.42    (47)  all_34_2 = all_4_2
% 178.18/28.42    (48)  all_56_7 = all_52_15
% 178.18/28.42    (49)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.18/28.42    (50)   ~ (all_52_7 = all_52_23)
% 178.18/28.42    (51)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.42    (52)  all_58_12 = all_52_25
% 178.18/28.42    (53)  op(e2, e3) = all_52_9
% 178.18/28.42  
% 178.18/28.42  Begin of proof
% 178.18/28.42  | 
% 178.18/28.42  | BETA: splitting (49) gives:
% 178.18/28.42  | 
% 178.18/28.42  | Case 1:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (54)  all_58_13 = e3
% 178.18/28.42  | | 
% 178.18/28.42  | | REF_CLOSE: (6), (34), (54) are inconsistent by sub-proof #1026.
% 178.18/28.42  | | 
% 178.18/28.42  | Case 2:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (55)  all_58_14 = e3 | all_58_15 = e3
% 178.18/28.42  | | 
% 178.18/28.42  | | BETA: splitting (55) gives:
% 178.18/28.42  | | 
% 178.18/28.42  | | Case 1:
% 178.18/28.42  | | | 
% 178.18/28.42  | | |   (56)  all_58_14 = e3
% 178.18/28.42  | | | 
% 178.18/28.42  | | | COMBINE_EQS: (24), (56) imply:
% 178.18/28.42  | | |   (57)  all_52_29 = e3
% 178.18/28.42  | | | 
% 178.18/28.42  | | | SIMP: (57) implies:
% 178.18/28.42  | | |   (58)  all_52_29 = e3
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (1), (58) imply:
% 178.18/28.42  | | |   (59)   ~ (all_52_13 = e3)
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (9), (58) imply:
% 178.18/28.42  | | |   (60)   ~ (all_52_25 = e3)
% 178.18/28.42  | | | 
% 178.18/28.42  | | | BETA: splitting (31) gives:
% 178.18/28.42  | | | 
% 178.18/28.42  | | | Case 1:
% 178.18/28.42  | | | | 
% 178.18/28.42  | | | |   (61)  all_56_12 = e3
% 178.18/28.42  | | | | 
% 178.18/28.42  | | | | REF_CLOSE: (33), (60), (61) are inconsistent by sub-proof #1040.
% 178.18/28.42  | | | | 
% 178.18/28.42  | | | Case 2:
% 178.18/28.42  | | | | 
% 178.18/28.42  | | | |   (62)   ~ (all_56_12 = e3)
% 178.18/28.42  | | | |   (63)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.18/28.42  | | | | 
% 178.18/28.42  | | | | BETA: splitting (40) gives:
% 178.18/28.42  | | | | 
% 178.18/28.42  | | | | Case 1:
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | |   (64)  all_58_12 = e1
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | | COMBINE_EQS: (52), (64) imply:
% 178.18/28.42  | | | | |   (65)  all_52_25 = e1
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | | REF_CLOSE: (2), (3), (5), (7), (11), (13), (16), (17), (19), (20),
% 178.18/28.42  | | | | |            (21), (22), (23), (25), (26), (27), (32), (36), (37), (42),
% 178.18/28.42  | | | | |            (43), (45), (46), (47), (50), (51), (60), (65) are
% 178.18/28.42  | | | | |            inconsistent by sub-proof #584.
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | Case 2:
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | |   (66)   ~ (all_58_12 = e1)
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | | REDUCE: (52), (66) imply:
% 178.18/28.42  | | | | |   (67)   ~ (all_52_25 = e1)
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | | REF_CLOSE: (4), (8), (10), (12), (14), (15), (18), (28), (29), (33),
% 178.18/28.42  | | | | |            (35), (39), (41), (44), (45), (46), (48), (53), (59), (63),
% 178.18/28.42  | | | | |            (67) are inconsistent by sub-proof #956.
% 178.18/28.42  | | | | | 
% 178.18/28.42  | | | | End of split
% 178.18/28.42  | | | | 
% 178.18/28.42  | | | End of split
% 178.18/28.42  | | | 
% 178.18/28.42  | | Case 2:
% 178.18/28.42  | | | 
% 178.18/28.42  | | |   (68)  all_58_15 = e3
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REF_CLOSE: (30), (38), (68) are inconsistent by sub-proof #1010.
% 178.18/28.42  | | | 
% 178.18/28.42  | | End of split
% 178.18/28.42  | | 
% 178.18/28.42  | End of split
% 178.18/28.42  | 
% 178.18/28.42  End of proof
% 178.18/28.42  
% 178.18/28.42  Sub-proof #584 shows that the following formulas are inconsistent:
% 178.18/28.42  ----------------------------------------------------------------
% 178.18/28.42    (1)   ~ (all_52_25 = e3)
% 178.18/28.42    (2)  all_56_3 = all_52_7
% 178.18/28.42    (3)  op(e3, e2) = all_52_3
% 178.18/28.42    (4)  op(e1, e2) = all_52_19
% 178.18/28.42    (5)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.42    (6)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.42    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42    (8)  all_34_1 = all_4_1
% 178.18/28.42    (9)  op(e3, all_4_2) = all_4_1
% 178.18/28.42    (10)   ~ (all_52_7 = all_4_2)
% 178.18/28.42    (11)  all_58_0 = all_4_2
% 178.18/28.42    (12)  op(all_4_1, all_4_2) = e1
% 178.18/28.42    (13)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.42    (14)   ~ (all_4_1 = e2)
% 178.18/28.42    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.42    (16)  all_56_1 = all_52_3
% 178.18/28.42    (17)   ~ (all_52_3 = all_4_2)
% 178.18/28.42    (18)  op(e1, e0) = all_52_23
% 178.18/28.42    (19)  all_56_0 = all_4_2
% 178.18/28.42    (20)   ~ (all_52_3 = all_52_19)
% 178.18/28.42    (21)   ~ (all_52_25 = all_4_2)
% 178.18/28.42    (22)  op(e3, e0) = all_52_7
% 178.18/28.42    (23)  op(e3, e3) = all_4_2
% 178.18/28.42    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.42    (25)  all_34_2 = all_4_2
% 178.18/28.42    (26)   ~ (all_52_7 = all_52_23)
% 178.18/28.42    (27)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.42    (28)  all_52_25 = e1
% 178.18/28.42  
% 178.18/28.42  Begin of proof
% 178.18/28.42  | 
% 178.18/28.42  | SIMP: (28) implies:
% 178.18/28.42  |   (29)  all_52_25 = e1
% 178.18/28.42  | 
% 178.18/28.42  | REDUCE: (21), (29) imply:
% 178.18/28.42  |   (30)   ~ (all_4_2 = e1)
% 178.18/28.42  | 
% 178.18/28.42  | SIMP: (30) implies:
% 178.18/28.42  |   (31)   ~ (all_4_2 = e1)
% 178.18/28.42  | 
% 178.18/28.42  | REDUCE: (1), (29) imply:
% 178.18/28.42  |   (32)   ~ (e3 = e1)
% 178.18/28.42  | 
% 178.18/28.42  | SIMP: (32) implies:
% 178.18/28.42  |   (33)   ~ (e3 = e1)
% 178.18/28.42  | 
% 178.18/28.42  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.18/28.42  |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 178.18/28.42  |            (26), (27), (31), (33) are inconsistent by sub-proof #585.
% 178.18/28.42  | 
% 178.18/28.42  End of proof
% 178.18/28.42  
% 178.18/28.42  Sub-proof #585 shows that the following formulas are inconsistent:
% 178.18/28.42  ----------------------------------------------------------------
% 178.18/28.42    (1)  all_56_3 = all_52_7
% 178.18/28.42    (2)  op(e3, e2) = all_52_3
% 178.18/28.42    (3)  op(e1, e2) = all_52_19
% 178.18/28.42    (4)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.42    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.42    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42    (7)   ~ (e3 = e1)
% 178.18/28.42    (8)  all_34_1 = all_4_1
% 178.18/28.42    (9)  op(e3, all_4_2) = all_4_1
% 178.18/28.42    (10)   ~ (all_52_7 = all_4_2)
% 178.18/28.42    (11)  all_58_0 = all_4_2
% 178.18/28.42    (12)  op(all_4_1, all_4_2) = e1
% 178.18/28.42    (13)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.42    (14)   ~ (all_4_1 = e2)
% 178.18/28.42    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.42    (16)  all_56_1 = all_52_3
% 178.18/28.42    (17)   ~ (all_52_3 = all_4_2)
% 178.18/28.42    (18)  op(e1, e0) = all_52_23
% 178.18/28.42    (19)  all_56_0 = all_4_2
% 178.18/28.42    (20)   ~ (all_52_3 = all_52_19)
% 178.18/28.42    (21)  op(e3, e0) = all_52_7
% 178.18/28.42    (22)  op(e3, e3) = all_4_2
% 178.18/28.42    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.42    (24)  all_34_2 = all_4_2
% 178.18/28.42    (25)   ~ (all_4_2 = e1)
% 178.18/28.42    (26)   ~ (all_52_7 = all_52_23)
% 178.18/28.42    (27)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.42  
% 178.18/28.42  Begin of proof
% 178.18/28.42  | 
% 178.18/28.42  | BETA: splitting (15) gives:
% 178.18/28.42  | 
% 178.18/28.42  | Case 1:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (28)  all_58_0 = e3
% 178.18/28.42  | | 
% 178.18/28.42  | | COMBINE_EQS: (11), (28) imply:
% 178.18/28.42  | |   (29)  all_4_2 = e3
% 178.18/28.42  | | 
% 178.18/28.42  | | REF_CLOSE: (7), (9), (12), (22), (23), (29) are inconsistent by sub-proof
% 178.18/28.42  | |            #599.
% 178.18/28.42  | | 
% 178.18/28.42  | Case 2:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (30)   ~ (all_58_0 = e3)
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (11), (30) imply:
% 178.18/28.42  | |   (31)   ~ (all_4_2 = e3)
% 178.18/28.42  | | 
% 178.18/28.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.18/28.42  | |            (13), (14), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 178.18/28.42  | |            (26), (27), (31) are inconsistent by sub-proof #586.
% 178.18/28.42  | | 
% 178.18/28.42  | End of split
% 178.18/28.42  | 
% 178.18/28.42  End of proof
% 178.18/28.42  
% 178.18/28.42  Sub-proof #586 shows that the following formulas are inconsistent:
% 178.18/28.42  ----------------------------------------------------------------
% 178.18/28.42    (1)  all_56_3 = all_52_7
% 178.18/28.42    (2)  op(e3, e2) = all_52_3
% 178.18/28.42    (3)  op(e1, e2) = all_52_19
% 178.18/28.42    (4)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.42    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.42    (6)   ~ (all_4_2 = e3)
% 178.18/28.42    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42    (8)   ~ (e3 = e1)
% 178.18/28.42    (9)  all_34_1 = all_4_1
% 178.18/28.42    (10)  op(e3, all_4_2) = all_4_1
% 178.18/28.42    (11)   ~ (all_52_7 = all_4_2)
% 178.18/28.42    (12)  all_58_0 = all_4_2
% 178.18/28.42    (13)  op(all_4_1, all_4_2) = e1
% 178.18/28.42    (14)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.42    (15)   ~ (all_4_1 = e2)
% 178.18/28.42    (16)  all_56_1 = all_52_3
% 178.18/28.42    (17)   ~ (all_52_3 = all_4_2)
% 178.18/28.42    (18)  op(e1, e0) = all_52_23
% 178.18/28.42    (19)  all_56_0 = all_4_2
% 178.18/28.42    (20)   ~ (all_52_3 = all_52_19)
% 178.18/28.42    (21)  op(e3, e0) = all_52_7
% 178.18/28.42    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.42    (23)  all_34_2 = all_4_2
% 178.18/28.42    (24)   ~ (all_4_2 = e1)
% 178.18/28.42    (25)   ~ (all_52_7 = all_52_23)
% 178.18/28.42    (26)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.42  
% 178.18/28.42  Begin of proof
% 178.18/28.42  | 
% 178.18/28.42  | BETA: splitting (7) gives:
% 178.18/28.42  | 
% 178.18/28.42  | Case 1:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (27)  all_56_0 = e3
% 178.18/28.42  | | 
% 178.18/28.42  | | COMBINE_EQS: (19), (27) imply:
% 178.18/28.42  | |   (28)  all_4_2 = e3
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (6), (28) imply:
% 178.18/28.42  | |   (29)  $false
% 178.18/28.42  | | 
% 178.18/28.42  | | CLOSE: (29) is inconsistent.
% 178.18/28.42  | | 
% 178.18/28.42  | Case 2:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (30)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42  | | 
% 178.18/28.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 178.18/28.42  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 178.18/28.42  | |            (26), (30) are inconsistent by sub-proof #587.
% 178.18/28.42  | | 
% 178.18/28.42  | End of split
% 178.18/28.42  | 
% 178.18/28.42  End of proof
% 178.18/28.42  
% 178.18/28.42  Sub-proof #587 shows that the following formulas are inconsistent:
% 178.18/28.42  ----------------------------------------------------------------
% 178.18/28.42    (1)  all_56_3 = all_52_7
% 178.18/28.42    (2)  op(e3, e2) = all_52_3
% 178.18/28.42    (3)  op(e1, e2) = all_52_19
% 178.18/28.42    (4)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.42    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.42    (6)   ~ (e3 = e1)
% 178.18/28.42    (7)  all_34_1 = all_4_1
% 178.18/28.42    (8)  op(e3, all_4_2) = all_4_1
% 178.18/28.42    (9)   ~ (all_52_7 = all_4_2)
% 178.18/28.42    (10)  all_58_0 = all_4_2
% 178.18/28.42    (11)  op(all_4_1, all_4_2) = e1
% 178.18/28.42    (12)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.42    (13)   ~ (all_4_1 = e2)
% 178.18/28.42    (14)  all_56_1 = all_52_3
% 178.18/28.42    (15)   ~ (all_52_3 = all_4_2)
% 178.18/28.42    (16)  op(e1, e0) = all_52_23
% 178.18/28.42    (17)  all_56_0 = all_4_2
% 178.18/28.42    (18)   ~ (all_52_3 = all_52_19)
% 178.18/28.42    (19)  op(e3, e0) = all_52_7
% 178.18/28.42    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.42    (21)  all_34_2 = all_4_2
% 178.18/28.42    (22)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42    (23)   ~ (all_4_2 = e1)
% 178.18/28.42    (24)   ~ (all_52_7 = all_52_23)
% 178.18/28.42    (25)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.42  
% 178.18/28.42  Begin of proof
% 178.18/28.42  | 
% 178.18/28.42  | BETA: splitting (5) gives:
% 178.18/28.42  | 
% 178.18/28.42  | Case 1:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (26)  all_58_0 = e2
% 178.18/28.42  | | 
% 178.18/28.42  | | COMBINE_EQS: (10), (26) imply:
% 178.18/28.42  | |   (27)  all_4_2 = e2
% 178.18/28.42  | | 
% 178.18/28.42  | | COMBINE_EQS: (21), (27) imply:
% 178.18/28.42  | |   (28)  all_34_2 = e2
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (15), (27) imply:
% 178.18/28.42  | |   (29)   ~ (all_52_3 = e2)
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (11), (27) imply:
% 178.18/28.42  | |   (30)  op(all_4_1, e2) = e1
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (8), (27) imply:
% 178.18/28.42  | |   (31)  op(e3, e2) = all_4_1
% 178.18/28.42  | | 
% 178.18/28.42  | | REF_CLOSE: (2), (3), (4), (6), (7), (12), (14), (18), (20), (28), (29),
% 178.18/28.42  | |            (30), (31) are inconsistent by sub-proof #592.
% 178.18/28.42  | | 
% 178.18/28.42  | Case 2:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (32)   ~ (all_58_0 = e2)
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (10), (32) imply:
% 178.18/28.42  | |   (33)   ~ (all_4_2 = e2)
% 178.18/28.42  | | 
% 178.18/28.42  | | REF_CLOSE: (1), (6), (8), (9), (11), (13), (16), (17), (19), (20), (22),
% 178.18/28.42  | |            (23), (24), (25), (33) are inconsistent by sub-proof #588.
% 178.18/28.42  | | 
% 178.18/28.42  | End of split
% 178.18/28.42  | 
% 178.18/28.42  End of proof
% 178.18/28.42  
% 178.18/28.42  Sub-proof #588 shows that the following formulas are inconsistent:
% 178.18/28.42  ----------------------------------------------------------------
% 178.18/28.42    (1)  all_56_3 = all_52_7
% 178.18/28.42    (2)   ~ (all_4_2 = e2)
% 178.18/28.42    (3)   ~ (e3 = e1)
% 178.18/28.42    (4)  op(e3, all_4_2) = all_4_1
% 178.18/28.42    (5)   ~ (all_52_7 = all_4_2)
% 178.18/28.42    (6)  op(all_4_1, all_4_2) = e1
% 178.18/28.42    (7)   ~ (all_4_1 = e2)
% 178.18/28.42    (8)  op(e1, e0) = all_52_23
% 178.18/28.42    (9)  all_56_0 = all_4_2
% 178.18/28.42    (10)  op(e3, e0) = all_52_7
% 178.18/28.42    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.42    (12)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42    (13)   ~ (all_4_2 = e1)
% 178.18/28.42    (14)   ~ (all_52_7 = all_52_23)
% 178.18/28.42    (15)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.42  
% 178.18/28.42  Begin of proof
% 178.18/28.42  | 
% 178.18/28.42  | BETA: splitting (12) gives:
% 178.18/28.42  | 
% 178.18/28.42  | Case 1:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (16)  all_56_0 = e2
% 178.18/28.42  | | 
% 178.18/28.42  | | COMBINE_EQS: (9), (16) imply:
% 178.18/28.42  | |   (17)  all_4_2 = e2
% 178.18/28.42  | | 
% 178.18/28.42  | | REDUCE: (2), (17) imply:
% 178.18/28.42  | |   (18)  $false
% 178.18/28.42  | | 
% 178.18/28.42  | | CLOSE: (18) is inconsistent.
% 178.18/28.42  | | 
% 178.18/28.42  | Case 2:
% 178.18/28.42  | | 
% 178.18/28.42  | |   (19)  all_56_0 = e1 | all_56_0 = e0
% 178.18/28.42  | | 
% 178.18/28.42  | | BETA: splitting (19) gives:
% 178.18/28.42  | | 
% 178.18/28.42  | | Case 1:
% 178.18/28.42  | | | 
% 178.18/28.42  | | |   (20)  all_56_0 = e1
% 178.18/28.42  | | | 
% 178.18/28.42  | | | COMBINE_EQS: (9), (20) imply:
% 178.18/28.42  | | |   (21)  all_4_2 = e1
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (13), (21) imply:
% 178.18/28.42  | | |   (22)  $false
% 178.18/28.42  | | | 
% 178.18/28.42  | | | CLOSE: (22) is inconsistent.
% 178.18/28.42  | | | 
% 178.18/28.42  | | Case 2:
% 178.18/28.42  | | | 
% 178.18/28.42  | | |   (23)  all_56_0 = e0
% 178.18/28.42  | | | 
% 178.18/28.42  | | | COMBINE_EQS: (9), (23) imply:
% 178.18/28.42  | | |   (24)  all_4_2 = e0
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (5), (24) imply:
% 178.18/28.42  | | |   (25)   ~ (all_52_7 = e0)
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (6), (24) imply:
% 178.18/28.42  | | |   (26)  op(all_4_1, e0) = e1
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (4), (24) imply:
% 178.18/28.42  | | |   (27)  op(e3, e0) = all_4_1
% 178.18/28.42  | | | 
% 178.18/28.42  | | | GROUND_INST: instantiating (11) with all_52_7, all_4_1, e0, e3,
% 178.18/28.42  | | |              simplifying with (10), (27) gives:
% 178.18/28.42  | | |   (28)  all_52_7 = all_4_1
% 178.18/28.42  | | | 
% 178.18/28.42  | | | COMBINE_EQS: (1), (28) imply:
% 178.18/28.42  | | |   (29)  all_56_3 = all_4_1
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (14), (28) imply:
% 178.18/28.42  | | |   (30)   ~ (all_52_23 = all_4_1)
% 178.18/28.42  | | | 
% 178.18/28.42  | | | SIMP: (30) implies:
% 178.18/28.42  | | |   (31)   ~ (all_52_23 = all_4_1)
% 178.18/28.42  | | | 
% 178.18/28.42  | | | REDUCE: (25), (28) imply:
% 178.18/28.43  | | |   (32)   ~ (all_4_1 = e0)
% 178.18/28.43  | | | 
% 178.18/28.43  | | | BETA: splitting (15) gives:
% 178.18/28.43  | | | 
% 178.18/28.43  | | | Case 1:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (33)  all_56_3 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | COMBINE_EQS: (29), (33) imply:
% 178.18/28.43  | | | |   (34)  all_4_1 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | SIMP: (34) implies:
% 178.18/28.43  | | | |   (35)  all_4_1 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (26), (35) imply:
% 178.18/28.43  | | | |   (36)  op(e3, e0) = e1
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (27), (35) imply:
% 178.18/28.43  | | | |   (37)  op(e3, e0) = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | GROUND_INST: instantiating (11) with e1, e3, e0, e3, simplifying with
% 178.18/28.43  | | | |              (36), (37) gives:
% 178.18/28.43  | | | |   (38)  e3 = e1
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (3), (38) imply:
% 178.18/28.43  | | | |   (39)  $false
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | CLOSE: (39) is inconsistent.
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | Case 2:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (40)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | BETA: splitting (40) gives:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | Case 1:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | |   (41)  all_56_3 = e2
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | REF_CLOSE: (7), (29), (41) are inconsistent by sub-proof #591.
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | Case 2:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | |   (42)  all_56_3 = e1 | all_56_3 = e0
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | BETA: splitting (42) gives:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | Case 1:
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | |   (43)  all_56_3 = e1
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | COMBINE_EQS: (29), (43) imply:
% 178.18/28.43  | | | | | |   (44)  all_4_1 = e1
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | SIMP: (44) implies:
% 178.18/28.43  | | | | | |   (45)  all_4_1 = e1
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | REDUCE: (31), (45) imply:
% 178.18/28.43  | | | | | |   (46)   ~ (all_52_23 = e1)
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | REDUCE: (26), (45) imply:
% 178.18/28.43  | | | | | |   (47)  op(e1, e0) = e1
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | REF_CLOSE: (8), (11), (46), (47) are inconsistent by sub-proof #590.
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | Case 2:
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | |   (48)  all_56_3 = e0
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | REF_CLOSE: (29), (32), (48) are inconsistent by sub-proof #589.
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | End of split
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | End of split
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | End of split
% 178.18/28.43  | | | 
% 178.18/28.43  | | End of split
% 178.18/28.43  | | 
% 178.18/28.43  | End of split
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #589 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)  all_56_3 = all_4_1
% 178.18/28.43    (2)  all_56_3 = e0
% 178.18/28.43    (3)   ~ (all_4_1 = e0)
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | COMBINE_EQS: (1), (2) imply:
% 178.18/28.43  |   (4)  all_4_1 = e0
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (4) implies:
% 178.18/28.43  |   (5)  all_4_1 = e0
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (3), (5) imply:
% 178.18/28.43  |   (6)  $false
% 178.18/28.43  | 
% 178.18/28.43  | CLOSE: (6) is inconsistent.
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #590 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43    (2)  op(e1, e0) = all_52_23
% 178.18/28.43    (3)  op(e1, e0) = e1
% 178.18/28.43    (4)   ~ (all_52_23 = e1)
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | GROUND_INST: instantiating (1) with all_52_23, e1, e0, e1, simplifying with
% 178.18/28.43  |              (2), (3) gives:
% 178.18/28.43  |   (5)  all_52_23 = e1
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (4), (5) imply:
% 178.18/28.43  |   (6)  $false
% 178.18/28.43  | 
% 178.18/28.43  | CLOSE: (6) is inconsistent.
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #591 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)  all_56_3 = all_4_1
% 178.18/28.43    (2)  all_56_3 = e2
% 178.18/28.43    (3)   ~ (all_4_1 = e2)
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | COMBINE_EQS: (1), (2) imply:
% 178.18/28.43  |   (4)  all_4_1 = e2
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (4) implies:
% 178.18/28.43  |   (5)  all_4_1 = e2
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (3), (5) imply:
% 178.18/28.43  |   (6)  $false
% 178.18/28.43  | 
% 178.18/28.43  | CLOSE: (6) is inconsistent.
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #592 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)  op(e3, e2) = all_52_3
% 178.18/28.43    (2)  op(e1, e2) = all_52_19
% 178.18/28.43    (3)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.43    (4)   ~ (all_52_3 = e2)
% 178.18/28.43    (5)   ~ (e3 = e1)
% 178.18/28.43    (6)  all_34_1 = all_4_1
% 178.18/28.43    (7)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.43    (8)  op(all_4_1, e2) = e1
% 178.18/28.43    (9)  all_56_1 = all_52_3
% 178.18/28.43    (10)   ~ (all_52_3 = all_52_19)
% 178.18/28.43    (11)  op(e3, e2) = all_4_1
% 178.18/28.43    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43    (13)  all_34_2 = e2
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | BETA: splitting (3) gives:
% 178.18/28.43  | 
% 178.18/28.43  | Case 1:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (14)   ~ (all_34_2 = e2)
% 178.18/28.43  | | 
% 178.18/28.43  | | REDUCE: (13), (14) imply:
% 178.18/28.43  | |   (15)  $false
% 178.18/28.43  | | 
% 178.18/28.43  | | CLOSE: (15) is inconsistent.
% 178.18/28.43  | | 
% 178.18/28.43  | Case 2:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (16)   ~ (all_34_1 = e0)
% 178.18/28.43  | | 
% 178.18/28.43  | | REDUCE: (6), (16) imply:
% 178.18/28.43  | |   (17)   ~ (all_4_1 = e0)
% 178.18/28.43  | | 
% 178.18/28.43  | | GROUND_INST: instantiating (12) with all_52_3, all_4_1, e2, e3, simplifying
% 178.18/28.43  | |              with (1), (11) gives:
% 178.18/28.43  | |   (18)  all_52_3 = all_4_1
% 178.18/28.43  | | 
% 178.18/28.43  | | COMBINE_EQS: (9), (18) imply:
% 178.18/28.43  | |   (19)  all_56_1 = all_4_1
% 178.18/28.43  | | 
% 178.18/28.43  | | BETA: splitting (7) gives:
% 178.18/28.43  | | 
% 178.18/28.43  | | Case 1:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (20)  all_56_1 = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | COMBINE_EQS: (19), (20) imply:
% 178.18/28.43  | | |   (21)  all_4_1 = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | SIMP: (21) implies:
% 178.18/28.43  | | |   (22)  all_4_1 = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (8), (22) imply:
% 178.18/28.43  | | |   (23)  op(e3, e2) = e1
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (11), (22) imply:
% 178.18/28.43  | | |   (24)  op(e3, e2) = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | GROUND_INST: instantiating (12) with e1, e3, e2, e3, simplifying with
% 178.18/28.43  | | |              (23), (24) gives:
% 178.18/28.43  | | |   (25)  e3 = e1
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (5), (25) imply:
% 178.18/28.43  | | |   (26)  $false
% 178.18/28.43  | | | 
% 178.18/28.43  | | | CLOSE: (26) is inconsistent.
% 178.18/28.43  | | | 
% 178.18/28.43  | | Case 2:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (27)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REF_CLOSE: (1), (2), (4), (8), (9), (10), (11), (12), (17), (27) are
% 178.18/28.43  | | |            inconsistent by sub-proof #597.
% 178.18/28.43  | | | 
% 178.18/28.43  | | End of split
% 178.18/28.43  | | 
% 178.18/28.43  | End of split
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #593 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)   ~ (all_52_27 = all_10_2)
% 178.18/28.43    (2)  op(e3, e2) = all_52_3
% 178.18/28.43    (3)   ~ (all_52_9 = all_52_25)
% 178.18/28.43    (4)  op(e1, e2) = all_52_19
% 178.18/28.43    (5)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.43    (6)  all_58_5 = all_52_13
% 178.18/28.43    (7)  op(e1, all_52_13) = e1
% 178.18/28.43    (8)  op(e0, all_52_15) = e0
% 178.18/28.43    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.43    (10)  all_58_3 = all_10_2
% 178.18/28.43    (11)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.43    (12)   ~ (all_52_9 = all_4_2)
% 178.18/28.43    (13)  all_58_10 = all_52_15
% 178.18/28.43    (14)  all_56_4 = all_52_9
% 178.18/28.43    (15)   ~ (e3 = e1)
% 178.18/28.43    (16)  all_34_1 = all_4_1
% 178.18/28.43    (17)  op(e3, all_4_2) = all_4_1
% 178.18/28.43    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.43    (19)  all_58_0 = all_4_2
% 178.18/28.43    (20)  op(all_4_1, all_4_2) = e1
% 178.18/28.43    (21)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.43    (22)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.18/28.43    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.43    (24)  all_56_1 = all_52_3
% 178.18/28.43    (25)   ~ (all_52_3 = all_52_27)
% 178.18/28.43    (26)   ~ (all_52_3 = all_4_2)
% 178.18/28.43    (27)  op(e0, e3) = all_52_25
% 178.18/28.43    (28)  op(e3, all_52_9) = e3
% 178.18/28.43    (29)   ~ (all_52_9 = all_52_13)
% 178.18/28.43    (30)  all_58_6 = all_52_17
% 178.18/28.43    (31)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.18/28.43    (32)  all_56_0 = all_4_2
% 178.18/28.43    (33)   ~ (all_52_3 = all_52_19)
% 178.18/28.43    (34)  all_58_2 = all_52_9
% 178.18/28.43    (35)  op(e1, e3) = all_52_17
% 178.18/28.43    (36)   ~ (all_52_25 = all_4_2)
% 178.18/28.43    (37)  op(e3, e3) = all_4_2
% 178.18/28.43    (38)   ~ (all_52_17 = all_4_2)
% 178.18/28.43    (39)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43    (40)   ~ (all_52_25 = all_52_27)
% 178.18/28.43    (41)  all_34_2 = all_4_2
% 178.18/28.43    (42)  all_56_13 = e3
% 178.18/28.43    (43)  op(e2, all_52_27) = all_52_26
% 178.18/28.43    (44)  all_58_12 = all_52_25
% 178.18/28.43    (45)  all_56_6 = all_52_13
% 178.18/28.43    (46)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.18/28.43    (47)   ~ (all_52_9 = all_52_15)
% 178.18/28.43    (48)  op(e2, e3) = all_52_9
% 178.18/28.43    (49)  all_56_13 = all_52_27
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | COMBINE_EQS: (42), (49) imply:
% 178.18/28.43  |   (50)  all_52_27 = e3
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (50) implies:
% 178.18/28.43  |   (51)  all_52_27 = e3
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (25), (51) imply:
% 178.18/28.43  |   (52)   ~ (all_52_3 = e3)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (40), (51) imply:
% 178.18/28.43  |   (53)   ~ (all_52_25 = e3)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (1), (51) imply:
% 178.18/28.43  |   (54)   ~ (all_10_2 = e3)
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (54) implies:
% 178.18/28.43  |   (55)   ~ (all_10_2 = e3)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (43), (51) imply:
% 178.18/28.43  |   (56)  op(e2, e3) = all_52_26
% 178.18/28.43  | 
% 178.18/28.43  | GROUND_INST: instantiating (39) with all_52_9, all_52_26, e3, e2, simplifying
% 178.18/28.43  |              with (48), (56) gives:
% 178.18/28.43  |   (57)  all_52_9 = all_52_26
% 178.18/28.43  | 
% 178.18/28.43  | COMBINE_EQS: (14), (57) imply:
% 178.18/28.43  |   (58)  all_56_4 = all_52_26
% 178.18/28.43  | 
% 178.18/28.43  | COMBINE_EQS: (34), (57) imply:
% 178.18/28.43  |   (59)  all_58_2 = all_52_26
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (29), (57) imply:
% 178.18/28.43  |   (60)   ~ (all_52_13 = all_52_26)
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (60) implies:
% 178.18/28.43  |   (61)   ~ (all_52_13 = all_52_26)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (47), (57) imply:
% 178.18/28.43  |   (62)   ~ (all_52_15 = all_52_26)
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (62) implies:
% 178.18/28.43  |   (63)   ~ (all_52_15 = all_52_26)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (3), (57) imply:
% 178.18/28.43  |   (64)   ~ (all_52_25 = all_52_26)
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (64) implies:
% 178.18/28.43  |   (65)   ~ (all_52_25 = all_52_26)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (12), (57) imply:
% 178.18/28.43  |   (66)   ~ (all_52_26 = all_4_2)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (28), (57) imply:
% 178.18/28.43  |   (67)  op(e3, all_52_26) = e3
% 178.18/28.43  | 
% 178.18/28.43  | BETA: splitting (21) gives:
% 178.18/28.43  | 
% 178.18/28.43  | Case 1:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (68)  all_56_1 = e3
% 178.18/28.43  | | 
% 178.18/28.43  | | REF_CLOSE: (24), (52), (68) are inconsistent by sub-proof #862.
% 178.18/28.43  | | 
% 178.18/28.43  | Case 2:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (69)   ~ (all_56_1 = e3)
% 178.18/28.43  | |   (70)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.43  | | 
% 178.18/28.43  | | BETA: splitting (22) gives:
% 178.18/28.43  | | 
% 178.18/28.43  | | Case 1:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (71)  all_56_6 = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REF_CLOSE: (7), (15), (17), (19), (20), (23), (30), (35), (37), (38),
% 178.18/28.43  | | |            (39), (44), (45), (53), (59), (61), (71) are inconsistent by
% 178.18/28.43  | | |            sub-proof #598.
% 178.18/28.43  | | | 
% 178.18/28.43  | | Case 2:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (72)   ~ (all_56_6 = e3)
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (45), (72) imply:
% 178.18/28.43  | | |   (73)   ~ (all_52_13 = e3)
% 178.18/28.43  | | | 
% 178.18/28.43  | | | BETA: splitting (46) gives:
% 178.18/28.43  | | | 
% 178.18/28.43  | | | Case 1:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (74)  all_58_0 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | COMBINE_EQS: (19), (74) imply:
% 178.18/28.43  | | | |   (75)  all_4_2 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REF_CLOSE: (15), (17), (20), (37), (39), (75) are inconsistent by
% 178.18/28.43  | | | |            sub-proof #599.
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | Case 2:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (76)   ~ (all_58_0 = e3)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (19), (76) imply:
% 178.18/28.43  | | | |   (77)   ~ (all_4_2 = e3)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (13), (16), (17),
% 178.18/28.43  | | | |            (18), (19), (20), (24), (26), (27), (31), (32), (33), (36),
% 178.18/28.43  | | | |            (37), (39), (41), (52), (55), (58), (59), (63), (65), (66),
% 178.18/28.43  | | | |            (67), (70), (73), (77) are inconsistent by sub-proof #594.
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | End of split
% 178.18/28.43  | | | 
% 178.18/28.43  | | End of split
% 178.18/28.43  | | 
% 178.18/28.43  | End of split
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #594 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)  op(e3, e2) = all_52_3
% 178.18/28.43    (2)  op(e1, e2) = all_52_19
% 178.18/28.43    (3)   ~ (all_34_1 = e0) |  ~ (all_34_2 = e2)
% 178.18/28.43    (4)  all_58_5 = all_52_13
% 178.18/28.43    (5)  op(e0, all_52_15) = e0
% 178.18/28.43    (6)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.43    (7)   ~ (all_4_2 = e3)
% 178.18/28.43    (8)  all_58_3 = all_10_2
% 178.18/28.43    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.43    (10)   ~ (all_52_26 = all_4_2)
% 178.18/28.43    (11)  all_58_10 = all_52_15
% 178.18/28.43    (12)  all_34_1 = all_4_1
% 178.18/28.43    (13)  op(e3, all_4_2) = all_4_1
% 178.18/28.43    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.43    (15)  all_58_0 = all_4_2
% 178.18/28.43    (16)  op(all_4_1, all_4_2) = e1
% 178.18/28.43    (17)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.43    (18)   ~ (all_10_2 = e3)
% 178.18/28.43    (19)  all_56_1 = all_52_3
% 178.18/28.43    (20)   ~ (all_52_3 = all_4_2)
% 178.18/28.43    (21)  op(e0, e3) = all_52_25
% 178.18/28.43    (22)   ~ (all_52_13 = e3)
% 178.18/28.43    (23)   ~ (all_52_3 = e3)
% 178.18/28.43    (24)  all_58_2 = all_52_26
% 178.18/28.43    (25)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.18/28.43    (26)  all_56_0 = all_4_2
% 178.18/28.43    (27)   ~ (all_52_3 = all_52_19)
% 178.18/28.43    (28)   ~ (all_52_25 = all_4_2)
% 178.18/28.43    (29)  op(e3, e3) = all_4_2
% 178.18/28.43    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43    (31)  all_34_2 = all_4_2
% 178.18/28.43    (32)   ~ (all_52_25 = all_52_26)
% 178.18/28.43    (33)  all_56_4 = all_52_26
% 178.18/28.43    (34)   ~ (all_52_15 = all_52_26)
% 178.18/28.43    (35)  op(e3, all_52_26) = e3
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | BETA: splitting (14) gives:
% 178.18/28.43  | 
% 178.18/28.43  | Case 1:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (36)  all_58_2 = e3
% 178.18/28.43  | | 
% 178.18/28.43  | | COMBINE_EQS: (24), (36) imply:
% 178.18/28.43  | |   (37)  all_52_26 = e3
% 178.18/28.43  | | 
% 178.18/28.43  | | SIMP: (37) implies:
% 178.18/28.43  | |   (38)  all_52_26 = e3
% 178.18/28.43  | | 
% 178.18/28.43  | | REF_CLOSE: (10), (29), (30), (35), (38) are inconsistent by sub-proof #1005.
% 178.18/28.43  | | 
% 178.18/28.43  | Case 2:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (39)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.43  | | 
% 178.18/28.43  | | BETA: splitting (39) gives:
% 178.18/28.43  | | 
% 178.18/28.43  | | Case 1:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (40)  all_58_3 = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | COMBINE_EQS: (8), (40) imply:
% 178.18/28.43  | | |   (41)  all_10_2 = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (18), (41) imply:
% 178.18/28.43  | | |   (42)  $false
% 178.18/28.43  | | | 
% 178.18/28.43  | | | CLOSE: (42) is inconsistent.
% 178.18/28.43  | | | 
% 178.18/28.43  | | Case 2:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (43)  all_58_5 = e3 | all_58_10 = e3
% 178.18/28.43  | | | 
% 178.18/28.43  | | | BETA: splitting (43) gives:
% 178.18/28.43  | | | 
% 178.18/28.43  | | | Case 1:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (44)  all_58_5 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REF_CLOSE: (4), (22), (44) are inconsistent by sub-proof #969.
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | Case 2:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (45)  all_58_10 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | COMBINE_EQS: (11), (45) imply:
% 178.18/28.43  | | | |   (46)  all_52_15 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | SIMP: (46) implies:
% 178.18/28.43  | | | |   (47)  all_52_15 = e3
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (34), (47) imply:
% 178.18/28.43  | | | |   (48)   ~ (all_52_26 = e3)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | SIMP: (48) implies:
% 178.18/28.43  | | | |   (49)   ~ (all_52_26 = e3)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (5), (47) imply:
% 178.18/28.43  | | | |   (50)  op(e0, e3) = e0
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | GROUND_INST: instantiating (30) with all_52_25, e0, e3, e0, simplifying
% 178.18/28.43  | | | |              with (21), (50) gives:
% 178.18/28.43  | | | |   (51)  all_52_25 = e0
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (32), (51) imply:
% 178.18/28.43  | | | |   (52)   ~ (all_52_26 = e0)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | SIMP: (52) implies:
% 178.18/28.43  | | | |   (53)   ~ (all_52_26 = e0)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (28), (51) imply:
% 178.18/28.43  | | | |   (54)   ~ (all_4_2 = e0)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | SIMP: (54) implies:
% 178.18/28.43  | | | |   (55)   ~ (all_4_2 = e0)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | BETA: splitting (9) gives:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | Case 1:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | |   (56)  all_56_0 = e3
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | REF_CLOSE: (7), (26), (56) are inconsistent by sub-proof #1024.
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | Case 2:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | |   (57)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | BETA: splitting (25) gives:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | Case 1:
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | |   (58)  all_56_4 = e3
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | REF_CLOSE: (33), (49), (58) are inconsistent by sub-proof #818.
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | Case 2:
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | |   (59)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | BETA: splitting (6) gives:
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | | Case 1:
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | |   (60)  all_58_0 = e2
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | COMBINE_EQS: (15), (60) imply:
% 178.18/28.43  | | | | | | |   (61)  all_4_2 = e2
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | COMBINE_EQS: (31), (61) imply:
% 178.18/28.43  | | | | | | |   (62)  all_34_2 = e2
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | REDUCE: (20), (61) imply:
% 178.18/28.43  | | | | | | |   (63)   ~ (all_52_3 = e2)
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | REDUCE: (16), (61) imply:
% 178.18/28.43  | | | | | | |   (64)  op(all_4_1, e2) = e1
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | REDUCE: (13), (61) imply:
% 178.18/28.43  | | | | | | |   (65)  op(e3, e2) = all_4_1
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | BETA: splitting (3) gives:
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | Case 1:
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | |   (66)   ~ (all_34_2 = e2)
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | | REDUCE: (62), (66) imply:
% 178.18/28.43  | | | | | | | |   (67)  $false
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | | CLOSE: (67) is inconsistent.
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | Case 2:
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | |   (68)   ~ (all_34_1 = e0)
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | | REDUCE: (12), (68) imply:
% 178.18/28.43  | | | | | | | |   (69)   ~ (all_4_1 = e0)
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | | REF_CLOSE: (1), (2), (17), (19), (27), (30), (63), (64), (65),
% 178.18/28.43  | | | | | | | |            (69) are inconsistent by sub-proof #597.
% 178.18/28.43  | | | | | | | | 
% 178.18/28.43  | | | | | | | End of split
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | Case 2:
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | |   (70)   ~ (all_58_0 = e2)
% 178.18/28.43  | | | | | | |   (71)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | REDUCE: (15), (70) imply:
% 178.18/28.43  | | | | | | |   (72)   ~ (all_4_2 = e2)
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | | REF_CLOSE: (1), (10), (23), (24), (26), (30), (33), (35), (53),
% 178.18/28.43  | | | | | | |            (55), (57), (59), (71), (72) are inconsistent by
% 178.18/28.43  | | | | | | |            sub-proof #595.
% 178.18/28.43  | | | | | | | 
% 178.18/28.43  | | | | | | End of split
% 178.18/28.43  | | | | | | 
% 178.18/28.43  | | | | | End of split
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | End of split
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | End of split
% 178.18/28.43  | | | 
% 178.18/28.43  | | End of split
% 178.18/28.43  | | 
% 178.18/28.43  | End of split
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #595 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)   ~ (all_4_2 = e2)
% 178.18/28.43    (2)  op(e3, e2) = all_52_3
% 178.18/28.43    (3)   ~ (all_52_26 = all_4_2)
% 178.18/28.43    (4)   ~ (all_52_26 = e0)
% 178.18/28.43    (5)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.18/28.43    (6)   ~ (all_52_3 = e3)
% 178.18/28.43    (7)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.43    (8)  all_58_2 = all_52_26
% 178.18/28.43    (9)  all_56_0 = all_4_2
% 178.18/28.43    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43    (11)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.43    (12)   ~ (all_4_2 = e0)
% 178.18/28.43    (13)  all_56_4 = all_52_26
% 178.18/28.43    (14)  op(e3, all_52_26) = e3
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | BETA: splitting (7) gives:
% 178.18/28.43  | 
% 178.18/28.43  | Case 1:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (15)  all_58_2 = e2
% 178.18/28.43  | | 
% 178.18/28.43  | | REF_CLOSE: (2), (6), (8), (10), (14), (15) are inconsistent by sub-proof
% 178.18/28.43  | |            #596.
% 178.18/28.43  | | 
% 178.18/28.43  | Case 2:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (16)   ~ (all_58_2 = e2)
% 178.18/28.43  | | 
% 178.18/28.43  | | REDUCE: (8), (16) imply:
% 178.18/28.43  | |   (17)   ~ (all_52_26 = e2)
% 178.18/28.43  | | 
% 178.18/28.43  | | BETA: splitting (11) gives:
% 178.18/28.43  | | 
% 178.18/28.43  | | Case 1:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (18)  all_56_0 = e2
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REF_CLOSE: (1), (9), (18) are inconsistent by sub-proof #904.
% 178.18/28.43  | | | 
% 178.18/28.43  | | Case 2:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (19)  all_56_0 = e1 | all_56_0 = e0
% 178.18/28.43  | | | 
% 178.18/28.43  | | | BETA: splitting (19) gives:
% 178.18/28.43  | | | 
% 178.18/28.43  | | | Case 1:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (20)  all_56_0 = e1
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | COMBINE_EQS: (9), (20) imply:
% 178.18/28.43  | | | |   (21)  all_4_2 = e1
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | SIMP: (21) implies:
% 178.18/28.43  | | | |   (22)  all_4_2 = e1
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REDUCE: (3), (22) imply:
% 178.18/28.43  | | | |   (23)   ~ (all_52_26 = e1)
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | BETA: splitting (5) gives:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | Case 1:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | |   (24)  all_56_4 = e2
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | REF_CLOSE: (13), (17), (24) are inconsistent by sub-proof #807.
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | Case 2:
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | |   (25)  all_56_4 = e1 | all_56_4 = e0
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | | REF_CLOSE: (4), (13), (23), (25) are inconsistent by sub-proof #805.
% 178.18/28.43  | | | | | 
% 178.18/28.43  | | | | End of split
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | Case 2:
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | |   (26)  all_56_0 = e0
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | | REF_CLOSE: (9), (12), (26) are inconsistent by sub-proof #1021.
% 178.18/28.43  | | | | 
% 178.18/28.43  | | | End of split
% 178.18/28.43  | | | 
% 178.18/28.43  | | End of split
% 178.18/28.43  | | 
% 178.18/28.43  | End of split
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #596 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)  op(e3, e2) = all_52_3
% 178.18/28.43    (2)  all_58_2 = e2
% 178.18/28.43    (3)   ~ (all_52_3 = e3)
% 178.18/28.43    (4)  all_58_2 = all_52_26
% 178.18/28.43    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43    (6)  op(e3, all_52_26) = e3
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | COMBINE_EQS: (2), (4) imply:
% 178.18/28.43  |   (7)  all_52_26 = e2
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (7) implies:
% 178.18/28.43  |   (8)  all_52_26 = e2
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (6), (8) imply:
% 178.18/28.43  |   (9)  op(e3, e2) = e3
% 178.18/28.43  | 
% 178.18/28.43  | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #978.
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #597 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)  op(e3, e2) = all_52_3
% 178.18/28.43    (2)  op(e1, e2) = all_52_19
% 178.18/28.43    (3)   ~ (all_52_3 = e2)
% 178.18/28.43    (4)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.18/28.43    (5)  op(all_4_1, e2) = e1
% 178.18/28.43    (6)  all_56_1 = all_52_3
% 178.18/28.43    (7)   ~ (all_52_3 = all_52_19)
% 178.18/28.43    (8)  op(e3, e2) = all_4_1
% 178.18/28.43    (9)   ~ (all_4_1 = e0)
% 178.18/28.43    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.43  | 
% 178.18/28.43  | GROUND_INST: instantiating (10) with all_52_3, all_4_1, e2, e3, simplifying
% 178.18/28.43  |              with (1), (8) gives:
% 178.18/28.43  |   (11)  all_52_3 = all_4_1
% 178.18/28.43  | 
% 178.18/28.43  | COMBINE_EQS: (6), (11) imply:
% 178.18/28.43  |   (12)  all_56_1 = all_4_1
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (7), (11) imply:
% 178.18/28.43  |   (13)   ~ (all_52_19 = all_4_1)
% 178.18/28.43  | 
% 178.18/28.43  | SIMP: (13) implies:
% 178.18/28.43  |   (14)   ~ (all_52_19 = all_4_1)
% 178.18/28.43  | 
% 178.18/28.43  | REDUCE: (3), (11) imply:
% 178.18/28.43  |   (15)   ~ (all_4_1 = e2)
% 178.18/28.43  | 
% 178.18/28.43  | BETA: splitting (4) gives:
% 178.18/28.43  | 
% 178.18/28.43  | Case 1:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (16)  all_56_1 = e2
% 178.18/28.43  | | 
% 178.18/28.43  | | REF_CLOSE: (12), (15), (16) are inconsistent by sub-proof #762.
% 178.18/28.43  | | 
% 178.18/28.43  | Case 2:
% 178.18/28.43  | | 
% 178.18/28.43  | |   (17)  all_56_1 = e1 | all_56_1 = e0
% 178.18/28.43  | | 
% 178.18/28.43  | | BETA: splitting (17) gives:
% 178.18/28.43  | | 
% 178.18/28.43  | | Case 1:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (18)  all_56_1 = e1
% 178.18/28.43  | | | 
% 178.18/28.43  | | | COMBINE_EQS: (12), (18) imply:
% 178.18/28.43  | | |   (19)  all_4_1 = e1
% 178.18/28.43  | | | 
% 178.18/28.43  | | | SIMP: (19) implies:
% 178.18/28.43  | | |   (20)  all_4_1 = e1
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (14), (20) imply:
% 178.18/28.43  | | |   (21)   ~ (all_52_19 = e1)
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (5), (20) imply:
% 178.18/28.43  | | |   (22)  op(e1, e2) = e1
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REF_CLOSE: (2), (10), (21), (22) are inconsistent by sub-proof #842.
% 178.18/28.43  | | | 
% 178.18/28.43  | | Case 2:
% 178.18/28.43  | | | 
% 178.18/28.43  | | |   (23)  all_56_1 = e0
% 178.18/28.43  | | | 
% 178.18/28.43  | | | COMBINE_EQS: (12), (23) imply:
% 178.18/28.43  | | |   (24)  all_4_1 = e0
% 178.18/28.43  | | | 
% 178.18/28.43  | | | SIMP: (24) implies:
% 178.18/28.43  | | |   (25)  all_4_1 = e0
% 178.18/28.43  | | | 
% 178.18/28.43  | | | REDUCE: (9), (25) imply:
% 178.18/28.43  | | |   (26)  $false
% 178.18/28.43  | | | 
% 178.18/28.43  | | | CLOSE: (26) is inconsistent.
% 178.18/28.43  | | | 
% 178.18/28.43  | | End of split
% 178.18/28.43  | | 
% 178.18/28.43  | End of split
% 178.18/28.43  | 
% 178.18/28.43  End of proof
% 178.18/28.43  
% 178.18/28.43  Sub-proof #598 shows that the following formulas are inconsistent:
% 178.18/28.43  ----------------------------------------------------------------
% 178.18/28.43    (1)   ~ (all_52_25 = e3)
% 178.18/28.43    (2)  all_56_6 = e3
% 178.18/28.43    (3)  op(e1, all_52_13) = e1
% 178.18/28.43    (4)   ~ (e3 = e1)
% 178.18/28.43    (5)  op(e3, all_4_2) = all_4_1
% 178.18/28.43    (6)  all_58_0 = all_4_2
% 178.18/28.43    (7)  op(all_4_1, all_4_2) = e1
% 178.18/28.43    (8)   ~ (all_52_13 = all_52_26)
% 178.18/28.43    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.43    (10)  all_58_6 = all_52_17
% 178.18/28.43    (11)  all_58_2 = all_52_26
% 178.18/28.43    (12)  op(e1, e3) = all_52_17
% 178.18/28.43    (13)  op(e3, e3) = all_4_2
% 178.18/28.43    (14)   ~ (all_52_17 = all_4_2)
% 178.18/28.43    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.43    (16)  all_58_12 = all_52_25
% 178.18/28.43    (17)  all_56_6 = all_52_13
% 178.18/28.43  
% 178.18/28.43  Begin of proof
% 178.18/28.44  | 
% 178.18/28.44  | COMBINE_EQS: (2), (17) imply:
% 178.18/28.44  |   (18)  all_52_13 = e3
% 178.18/28.44  | 
% 178.18/28.44  | SIMP: (18) implies:
% 178.18/28.44  |   (19)  all_52_13 = e3
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (8), (19) imply:
% 178.18/28.44  |   (20)   ~ (all_52_26 = e3)
% 178.18/28.44  | 
% 178.18/28.44  | SIMP: (20) implies:
% 178.18/28.44  |   (21)   ~ (all_52_26 = e3)
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (3), (19) imply:
% 178.18/28.44  |   (22)  op(e1, e3) = e1
% 178.18/28.44  | 
% 178.18/28.44  | GROUND_INST: instantiating (15) with all_52_17, e1, e3, e1, simplifying with
% 178.18/28.44  |              (12), (22) gives:
% 178.18/28.44  |   (23)  all_52_17 = e1
% 178.18/28.44  | 
% 178.18/28.44  | COMBINE_EQS: (10), (23) imply:
% 178.18/28.44  |   (24)  all_58_6 = e1
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (14), (23) imply:
% 178.18/28.44  |   (25)   ~ (all_4_2 = e1)
% 178.18/28.44  | 
% 178.18/28.44  | SIMP: (25) implies:
% 178.18/28.44  |   (26)   ~ (all_4_2 = e1)
% 178.18/28.44  | 
% 178.18/28.44  | BETA: splitting (9) gives:
% 178.18/28.44  | 
% 178.18/28.44  | Case 1:
% 178.18/28.44  | | 
% 178.18/28.44  | |   (27)  all_58_0 = e3
% 178.18/28.44  | | 
% 178.18/28.44  | | COMBINE_EQS: (6), (27) imply:
% 178.18/28.44  | |   (28)  all_4_2 = e3
% 178.18/28.44  | | 
% 178.18/28.44  | | REF_CLOSE: (4), (5), (7), (13), (15), (28) are inconsistent by sub-proof
% 178.18/28.44  | |            #599.
% 178.18/28.44  | | 
% 178.18/28.44  | Case 2:
% 178.18/28.44  | | 
% 178.18/28.44  | |   (29)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.18/28.44  | | 
% 178.18/28.44  | | REF_CLOSE: (1), (4), (11), (16), (21), (24), (29) are inconsistent by
% 178.18/28.44  | |            sub-proof #1001.
% 178.18/28.44  | | 
% 178.18/28.44  | End of split
% 178.18/28.44  | 
% 178.18/28.44  End of proof
% 178.18/28.44  
% 178.18/28.44  Sub-proof #599 shows that the following formulas are inconsistent:
% 178.18/28.44  ----------------------------------------------------------------
% 178.18/28.44    (1)  all_4_2 = e3
% 178.18/28.44    (2)   ~ (e3 = e1)
% 178.18/28.44    (3)  op(e3, all_4_2) = all_4_1
% 178.18/28.44    (4)  op(all_4_1, all_4_2) = e1
% 178.18/28.44    (5)  op(e3, e3) = all_4_2
% 178.18/28.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.44  
% 178.18/28.44  Begin of proof
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (1), (4) imply:
% 178.18/28.44  |   (7)  op(all_4_1, e3) = e1
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (1), (3) imply:
% 178.18/28.44  |   (8)  op(e3, e3) = all_4_1
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (1), (5) imply:
% 178.18/28.44  |   (9)  op(e3, e3) = e3
% 178.18/28.44  | 
% 178.18/28.44  | GROUND_INST: instantiating (6) with e3, all_4_1, e3, e3, simplifying with (8),
% 178.18/28.44  |              (9) gives:
% 178.18/28.44  |   (10)  all_4_1 = e3
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (7), (10) imply:
% 178.18/28.44  |   (11)  op(e3, e3) = e1
% 178.18/28.44  | 
% 178.18/28.44  | GROUND_INST: instantiating (6) with e3, e1, e3, e3, simplifying with (9), (11)
% 178.18/28.44  |              gives:
% 178.18/28.44  |   (12)  e3 = e1
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (2), (12) imply:
% 178.18/28.44  |   (13)  $false
% 178.18/28.44  | 
% 178.18/28.44  | CLOSE: (13) is inconsistent.
% 178.18/28.44  | 
% 178.18/28.44  End of proof
% 178.18/28.44  
% 178.18/28.44  Sub-proof #600 shows that the following formulas are inconsistent:
% 178.18/28.44  ----------------------------------------------------------------
% 178.18/28.44    (1)   ~ (e3 = e1)
% 178.18/28.44    (2)  op(e3, all_4_2) = all_4_1
% 178.18/28.44    (3)  op(all_4_1, all_4_2) = e1
% 178.18/28.44    (4)  all_52_0 = all_4_1
% 178.18/28.44    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.18/28.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.18/28.44    (6)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 178.18/28.44  
% 178.18/28.44  Begin of proof
% 178.18/28.44  | 
% 178.18/28.44  | ALPHA: (6) implies:
% 178.18/28.44  |   (7)  all_52_0 = e3
% 178.18/28.44  | 
% 178.18/28.44  | COMBINE_EQS: (4), (7) imply:
% 178.18/28.44  |   (8)  all_4_1 = e3
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (3), (8) imply:
% 178.18/28.44  |   (9)  op(e3, all_4_2) = e1
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (2), (8) imply:
% 178.18/28.44  |   (10)  op(e3, all_4_2) = e3
% 178.18/28.44  | 
% 178.18/28.44  | GROUND_INST: instantiating (5) with e1, e3, all_4_2, e3, simplifying with (9),
% 178.18/28.44  |              (10) gives:
% 178.18/28.44  |   (11)  e3 = e1
% 178.18/28.44  | 
% 178.18/28.44  | REDUCE: (1), (11) imply:
% 178.18/28.44  |   (12)  $false
% 178.18/28.44  | 
% 178.18/28.44  | CLOSE: (12) is inconsistent.
% 178.18/28.44  | 
% 178.18/28.44  End of proof
% 178.18/28.44  
% 178.18/28.44  Sub-proof #601 shows that the following formulas are inconsistent:
% 178.18/28.44  ----------------------------------------------------------------
% 178.18/28.44    (1)   ~ (all_52_23 = all_14_2)
% 178.18/28.44    (2)   ~ (all_52_5 = all_52_13)
% 178.18/28.44    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.18/28.44    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.18/28.44    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.18/28.44    (6)   ~ (all_52_27 = all_10_2)
% 178.18/28.44    (7)   ~ (all_52_17 = all_52_23)
% 178.18/28.44    (8)  op(e2, all_10_2) = all_10_1
% 178.18/28.44    (9)  all_40_2 = all_4_2
% 178.18/28.44    (10)   ~ (all_52_13 = all_52_29)
% 178.18/28.44    (11)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.18/28.44    (12)  all_56_3 = all_52_7
% 178.18/28.44    (13)  op(e3, e2) = all_52_3
% 178.18/28.44    (14)   ~ (all_52_9 = all_52_25)
% 178.18/28.44    (15)  op(e3, all_52_25) = all_52_24
% 178.18/28.44    (16)   ~ (all_52_19 = all_52_23)
% 178.18/28.44    (17)  all_56_11 = all_52_23
% 178.18/28.44    (18)  op(e1, e2) = all_52_19
% 178.18/28.44    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.18/28.44    (20)  op(e3, all_52_9) = all_52_8
% 178.18/28.44    (21)   ~ (all_52_3 = all_10_2)
% 178.18/28.44    (22)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.18/28.44    (23)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.18/28.44    (24)  all_58_5 = all_52_13
% 178.18/28.44    (25)   ~ (all_6_2 = e0)
% 178.18/28.44    (26)   ~ (all_52_25 = all_52_29)
% 178.18/28.44    (27)  all_56_15 = all_6_2
% 178.18/28.44    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.18/28.44    (29)  op(e2, e0) = all_52_15
% 178.18/28.44    (30)  op(all_14_1, all_14_2) = all_14_0
% 178.18/28.44    (31)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.18/28.44    (32)  all_58_3 = all_10_2
% 178.18/28.44    (33)  all_56_9 = all_52_19
% 178.18/28.44    (34)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.18/28.44    (35)  all_58_15 = all_6_2
% 178.18/28.44    (36)   ~ (all_52_9 = all_4_2)
% 178.18/28.44    (37)   ~ (all_52_5 = all_52_7)
% 178.18/28.44    (38)  all_58_10 = all_52_15
% 178.18/28.44    (39)   ~ (all_52_5 = all_4_2)
% 178.18/28.44    (40)  all_58_7 = all_52_19
% 178.18/28.44    (41)  all_56_4 = all_52_9
% 178.18/28.44    (42)   ~ (all_52_15 = all_6_2)
% 178.18/28.44    (43)   ~ (all_52_17 = all_52_25)
% 178.18/28.44    (44)  op(e0, e1) = all_52_29
% 178.18/28.44    (45)   ~ (all_4_0 = e2)
% 178.18/28.44    (46)  all_58_4 = all_52_5
% 178.18/28.44    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.18/28.44    (48)   ~ (e3 = e1)
% 178.18/28.44    (49)   ~ (all_52_27 = all_52_29)
% 178.18/28.44    (50)   ~ (all_52_17 = all_14_2)
% 178.18/28.44    (51)  op(e3, all_4_2) = all_4_1
% 178.18/28.44    (52)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.18/28.44    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.18/28.44    (54)   ~ (all_52_7 = all_4_2)
% 178.18/28.44    (55)  all_58_1 = all_52_3
% 178.18/28.44    (56)   ~ (all_52_13 = all_52_15)
% 178.18/28.44    (57)  all_58_0 = all_4_2
% 178.34/28.44    (58)  all_52_0 = e1
% 178.34/28.44    (59)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.44    (60)  op(e1, all_52_13) = all_52_12
% 178.34/28.44    (61)  op(e1, all_52_29) = all_52_28
% 178.34/28.44    (62)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.44    (63)   ~ (all_4_1 = e2)
% 178.34/28.44    (64)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.44    (65)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.44    (66)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.34/28.44    (67)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.34/28.44    (68)   ~ (all_14_1 = e3)
% 178.34/28.44    (69)  all_58_14 = all_52_29
% 178.34/28.44    (70)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.44    (71)   ~ (all_52_3 = all_52_5)
% 178.34/28.44    (72)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.44    (73)  op(e2, e1) = all_52_13
% 178.34/28.44    (74)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.44    (75)  all_58_8 = all_14_2
% 178.34/28.44    (76)  op(e0, e2) = all_52_27
% 178.34/28.44    (77)   ~ (all_14_0 = e3)
% 178.34/28.44    (78)   ~ (all_10_1 = e1)
% 178.34/28.44    (79)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.44    (80)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.34/28.44    (81)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.44    (82)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.34/28.44    (83)   ~ (all_52_5 = all_14_2)
% 178.34/28.44    (84)   ~ (all_52_3 = all_52_27)
% 178.34/28.44    (85)   ~ (all_52_3 = all_4_2)
% 178.34/28.44    (86)  op(e0, e3) = all_52_25
% 178.34/28.44    (87)  op(e0, all_6_2) = all_6_1
% 178.34/28.44    (88)   ~ (all_52_9 = all_10_2)
% 178.34/28.44    (89)  op(e3, all_52_17) = all_52_16
% 178.34/28.44    (90)  all_52_10 = all_10_1
% 178.34/28.44    (91)   ~ (all_52_13 = all_14_2)
% 178.34/28.44    (92)   ~ (e3 = e0)
% 178.34/28.44    (93)  all_40_0 = all_4_0
% 178.34/28.44    (94)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.44    (95)   ~ (all_52_9 = all_52_13)
% 178.34/28.44    (96)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.44    (97)  op(e0, all_52_23) = all_52_22
% 178.34/28.44    (98)   ~ (all_52_15 = all_52_23)
% 178.34/28.44    (99)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.34/28.44    (100)   ~ (all_52_5 = all_52_29)
% 178.34/28.44    (101)  all_56_2 = all_52_5
% 178.34/28.44    (102)  op(e1, e0) = all_52_23
% 178.34/28.44    (103)  all_56_12 = all_52_25
% 178.34/28.44    (104)  all_58_13 = all_52_27
% 178.34/28.44    (105)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.44    (106)  all_56_5 = all_10_2
% 178.34/28.44    (107)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.44    (108)   ~ (all_52_9 = all_52_17)
% 178.34/28.44    (109)   ~ (all_14_0 = e2)
% 178.34/28.44    (110)  all_58_6 = all_52_17
% 178.34/28.44    (111)   ~ (all_52_3 = all_52_7)
% 178.34/28.44    (112)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.34/28.44    (113)  op(e2, all_52_19) = all_52_18
% 178.34/28.44    (114)   ~ (e1 = e0)
% 178.34/28.44    (115)  all_56_0 = all_4_2
% 178.34/28.44    (116)  all_58_11 = all_52_23
% 178.34/28.44    (117)   ~ (all_52_3 = all_52_19)
% 178.34/28.44    (118)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.34/28.44    (119)   ~ (all_52_7 = all_52_15)
% 178.34/28.44    (120)  op(e0, all_52_15) = all_52_14
% 178.34/28.44    (121)   ~ (all_52_29 = all_14_2)
% 178.34/28.44    (122)   ~ (all_4_0 = e1)
% 178.34/28.44    (123)   ~ (all_52_19 = all_10_2)
% 178.34/28.44    (124)   ~ (all_52_23 = all_6_2)
% 178.34/28.44    (125)  op(e1, all_4_2) = all_4_0
% 178.34/28.44    (126)   ~ (all_52_29 = all_6_2)
% 178.34/28.44    (127)  all_58_2 = all_52_9
% 178.34/28.44    (128)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.44    (129)  op(e3, e1) = all_52_5
% 178.34/28.44    (130)   ~ (e2 = e1)
% 178.34/28.44    (131)  all_56_10 = all_14_2
% 178.34/28.44    (132)   ~ (all_52_25 = all_6_2)
% 178.34/28.44    (133)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.34/28.44    (134)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.44    (135)  op(e1, e1) = all_14_2
% 178.34/28.44    (136)  op(e1, e3) = all_52_17
% 178.34/28.44    (137)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.44    (138)   ~ (all_52_25 = all_4_2)
% 178.34/28.44    (139)  op(e3, e0) = all_52_7
% 178.34/28.44    (140)  op(e3, e3) = all_4_2
% 178.34/28.44    (141)   ~ (all_10_1 = e3)
% 178.34/28.44    (142)  all_56_8 = all_52_17
% 178.34/28.44    (143)   ~ (all_52_17 = all_4_2)
% 178.34/28.44    (144)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.44             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.44    (145)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 178.34/28.44           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 178.34/28.44           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 178.34/28.44           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 178.34/28.44    (146)   ~ (all_52_25 = all_52_27)
% 178.34/28.44    (147)   ~ (all_52_27 = all_6_2)
% 178.34/28.44    (148)   ~ (all_52_7 = all_6_2)
% 178.34/28.44    (149)   ~ (all_52_15 = all_10_2)
% 178.34/28.44    (150)   ~ (all_52_19 = all_52_27)
% 178.34/28.44    (151)  all_56_7 = all_52_15
% 178.34/28.44    (152)   ~ (all_52_7 = all_52_23)
% 178.34/28.44    (153)   ~ (all_52_13 = all_10_2)
% 178.34/28.44    (154)  op(e2, all_52_27) = all_52_26
% 178.34/28.44    (155)  all_52_20 = all_14_1
% 178.34/28.44    (156)   ~ (all_52_17 = all_52_19)
% 178.34/28.44    (157)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.44    (158)  all_52_30 = all_6_1
% 178.34/28.44    (159)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.44    (160)  op(e1, all_14_2) = all_14_1
% 178.34/28.44    (161)  all_58_9 = all_52_7
% 178.34/28.44    (162)   ~ (e2 = e0)
% 178.34/28.44    (163)  all_58_12 = all_52_25
% 178.34/28.44    (164)  op(e3, all_4_2) = e1
% 178.34/28.44    (165)  all_56_6 = all_52_13
% 178.34/28.44    (166)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.44    (167)   ~ (all_52_9 = all_52_15)
% 178.34/28.44    (168)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.44    (169)   ~ (e3 = e2)
% 178.34/28.44    (170)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.34/28.44    (171)   ~ (all_52_19 = all_14_2)
% 178.34/28.44    (172)  op(e2, e3) = all_52_9
% 178.34/28.44    (173)  all_56_13 = all_52_27
% 178.34/28.44  
% 178.34/28.44  Begin of proof
% 178.34/28.44  | 
% 178.34/28.44  | BETA: splitting (145) gives:
% 178.34/28.44  | 
% 178.34/28.44  | Case 1:
% 178.34/28.44  | | 
% 178.34/28.44  | |   (174)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 178.34/28.44  | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 178.34/28.44  | | 
% 178.34/28.44  | | BETA: splitting (174) gives:
% 178.34/28.44  | | 
% 178.34/28.44  | | Case 1:
% 178.34/28.44  | | | 
% 178.34/28.44  | | |   (175)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REF_CLOSE: (48), (58), (175) are inconsistent by sub-proof #632.
% 178.34/28.44  | | | 
% 178.34/28.44  | | Case 2:
% 178.34/28.44  | | | 
% 178.34/28.44  | | |   (176)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | ALPHA: (176) implies:
% 178.34/28.44  | | |   (177)  all_52_14 = e0
% 178.34/28.44  | | |   (178)  all_52_12 = e1
% 178.34/28.44  | | |   (179)  all_52_10 = e2
% 178.34/28.44  | | |   (180)  all_52_8 = e3
% 178.34/28.44  | | | 
% 178.34/28.44  | | | COMBINE_EQS: (90), (179) imply:
% 178.34/28.44  | | |   (181)  all_10_1 = e2
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (141), (181) imply:
% 178.34/28.44  | | |   (182)   ~ (e3 = e2)
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (20), (180) imply:
% 178.34/28.44  | | |   (183)  op(e3, all_52_9) = e3
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (8), (181) imply:
% 178.34/28.44  | | |   (184)  op(e2, all_10_2) = e2
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (60), (178) imply:
% 178.34/28.44  | | |   (185)  op(e1, all_52_13) = e1
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (120), (177) imply:
% 178.34/28.44  | | |   (186)  op(e0, all_52_15) = e0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (12), (13), (14), (15),
% 178.34/28.44  | | |            (16), (17), (18), (21), (23), (24), (25), (26), (27), (28),
% 178.34/28.44  | | |            (29), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 178.34/28.44  | | |            (41), (42), (43), (45), (46), (47), (48), (49), (50), (51),
% 178.34/28.44  | | |            (52), (53), (54), (55), (57), (59), (61), (62), (63), (64),
% 178.34/28.44  | | |            (65), (66), (68), (69), (70), (71), (72), (73), (74), (75),
% 178.34/28.44  | | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (89),
% 178.34/28.44  | | |            (91), (92), (93), (95), (97), (98), (99), (100), (101), (102),
% 178.34/28.44  | | |            (104), (105), (108), (110), (111), (112), (113), (114), (115),
% 178.34/28.44  | | |            (116), (117), (119), (121), (123), (124), (125), (126), (127),
% 178.34/28.44  | | |            (128), (129), (130), (131), (132), (134), (135), (136), (138),
% 178.34/28.44  | | |            (139), (140), (143), (144), (146), (147), (148), (150), (152),
% 178.34/28.44  | | |            (154), (156), (157), (159), (160), (161), (163), (164), (165),
% 178.34/28.44  | | |            (166), (167), (168), (169), (170), (171), (172), (173), (183),
% 178.34/28.44  | | |            (184), (185), (186) are inconsistent by sub-proof #609.
% 178.34/28.44  | | | 
% 178.34/28.44  | | End of split
% 178.34/28.44  | | 
% 178.34/28.44  | Case 2:
% 178.34/28.44  | | 
% 178.34/28.44  | |   (187)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0)
% 178.34/28.44  | |          | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 178.34/28.44  | |            e0)
% 178.34/28.44  | | 
% 178.34/28.44  | | BETA: splitting (187) gives:
% 178.34/28.44  | | 
% 178.34/28.44  | | Case 1:
% 178.34/28.44  | | | 
% 178.34/28.44  | | |   (188)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | ALPHA: (188) implies:
% 178.34/28.44  | | |   (189)  all_52_22 = e0
% 178.34/28.44  | | |   (190)  all_52_20 = e1
% 178.34/28.44  | | |   (191)  all_52_18 = e2
% 178.34/28.44  | | |   (192)  all_52_16 = e3
% 178.34/28.44  | | | 
% 178.34/28.44  | | | COMBINE_EQS: (155), (190) imply:
% 178.34/28.44  | | |   (193)  all_14_1 = e1
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (30), (193) imply:
% 178.34/28.44  | | |   (194)  op(e1, all_14_2) = all_14_0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (89), (192) imply:
% 178.34/28.44  | | |   (195)  op(e3, all_52_17) = e3
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (113), (191) imply:
% 178.34/28.44  | | |   (196)  op(e2, all_52_19) = e2
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (160), (193) imply:
% 178.34/28.44  | | |   (197)  op(e1, all_14_2) = e1
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REDUCE: (97), (189) imply:
% 178.34/28.44  | | |   (198)  op(e0, all_52_23) = e0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (13), (14),
% 178.34/28.44  | | |            (15), (16), (18), (20), (21), (22), (24), (25), (26), (27),
% 178.34/28.44  | | |            (28), (29), (32), (33), (34), (35), (36), (37), (38), (39),
% 178.34/28.44  | | |            (40), (43), (45), (46), (47), (49), (50), (51), (52), (53),
% 178.34/28.44  | | |            (54), (55), (57), (59), (61), (62), (63), (64), (65), (66),
% 178.34/28.44  | | |            (67), (69), (71), (72), (73), (74), (75), (77), (79), (80),
% 178.34/28.44  | | |            (81), (82), (83), (84), (85), (86), (88), (91), (92), (93),
% 178.34/28.44  | | |            (94), (95), (96), (98), (100), (103), (104), (105), (106),
% 178.34/28.44  | | |            (107), (108), (109), (110), (114), (115), (116), (117), (118),
% 178.34/28.44  | | |            (119), (121), (122), (123), (124), (125), (127), (129), (132),
% 178.34/28.44  | | |            (133), (136), (137), (138), (139), (140), (141), (142), (143),
% 178.34/28.44  | | |            (144), (146), (147), (148), (149), (150), (151), (152), (153),
% 178.34/28.44  | | |            (156), (157), (161), (162), (163), (164), (165), (166), (167),
% 178.34/28.44  | | |            (168), (169), (171), (172), (194), (195), (196), (197), (198)
% 178.34/28.44  | | |            are inconsistent by sub-proof #605.
% 178.34/28.44  | | | 
% 178.34/28.44  | | Case 2:
% 178.34/28.44  | | | 
% 178.34/28.44  | | |   (199)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | ALPHA: (199) implies:
% 178.34/28.44  | | |   (200)  all_52_30 = e0
% 178.34/28.44  | | |   (201)  all_52_28 = e1
% 178.34/28.44  | | |   (202)  all_52_26 = e2
% 178.34/28.44  | | |   (203)  all_52_24 = e3
% 178.34/28.44  | | | 
% 178.34/28.44  | | | COMBINE_EQS: (158), (200) imply:
% 178.34/28.44  | | |   (204)  all_6_1 = e0
% 178.34/28.44  | | | 
% 178.34/28.44  | | | REF_CLOSE: (2), (4), (5), (6), (7), (10), (11), (13), (14), (15), (16),
% 178.34/28.44  | | |            (19), (20), (24), (25), (26), (27), (28), (31), (32), (34),
% 178.34/28.44  | | |            (35), (36), (37), (38), (39), (40), (43), (44), (45), (46),
% 178.34/28.44  | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 178.34/28.44  | | |            (57), (59), (61), (64), (65), (69), (70), (71), (72), (74),
% 178.34/28.44  | | |            (75), (76), (81), (84), (86), (87), (88), (89), (92), (94),
% 178.34/28.44  | | |            (96), (100), (102), (103), (104), (105), (108), (110), (111),
% 178.34/28.44  | | |            (114), (115), (116), (122), (123), (126), (127), (129), (130),
% 178.34/28.44  | | |            (132), (136), (138), (139), (140), (143), (144), (146), (147),
% 178.34/28.44  | | |            (148), (149), (154), (156), (157), (161), (163), (164), (166),
% 178.34/28.44  | | |            (167), (169), (172), (173), (201), (202), (203), (204) are
% 178.34/28.44  | | |            inconsistent by sub-proof #602.
% 178.34/28.44  | | | 
% 178.34/28.44  | | End of split
% 178.34/28.44  | | 
% 178.34/28.44  | End of split
% 178.34/28.44  | 
% 178.34/28.44  End of proof
% 178.34/28.44  
% 178.34/28.44  Sub-proof #602 shows that the following formulas are inconsistent:
% 178.34/28.44  ----------------------------------------------------------------
% 178.34/28.44    (1)   ~ (all_52_5 = all_52_13)
% 178.34/28.44    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.44    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.44    (4)   ~ (all_52_27 = all_10_2)
% 178.34/28.44    (5)   ~ (all_52_17 = all_52_23)
% 178.34/28.44    (6)  all_52_26 = e2
% 178.34/28.44    (7)   ~ (all_52_13 = all_52_29)
% 178.34/28.44    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.44    (9)  op(e3, e2) = all_52_3
% 178.34/28.44    (10)   ~ (all_52_9 = all_52_25)
% 178.34/28.44    (11)  op(e3, all_52_25) = all_52_24
% 178.34/28.44    (12)   ~ (all_52_19 = all_52_23)
% 178.34/28.44    (13)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.34/28.44    (14)  op(e3, all_52_9) = all_52_8
% 178.34/28.44    (15)  all_58_5 = all_52_13
% 178.34/28.44    (16)   ~ (all_6_2 = e0)
% 178.34/28.44    (17)   ~ (all_52_25 = all_52_29)
% 178.34/28.44    (18)  all_56_15 = all_6_2
% 178.34/28.44    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.44    (20)  all_6_1 = e0
% 178.34/28.44    (21)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.44    (22)  all_58_3 = all_10_2
% 178.34/28.44    (23)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.44    (24)  all_58_15 = all_6_2
% 178.34/28.44    (25)   ~ (all_52_9 = all_4_2)
% 178.34/28.44    (26)   ~ (all_52_5 = all_52_7)
% 178.34/28.44    (27)  all_58_10 = all_52_15
% 178.34/28.44    (28)   ~ (all_52_5 = all_4_2)
% 178.34/28.44    (29)  all_58_7 = all_52_19
% 178.34/28.44    (30)   ~ (all_52_17 = all_52_25)
% 178.34/28.44    (31)  op(e0, e1) = all_52_29
% 178.34/28.44    (32)   ~ (all_4_0 = e2)
% 178.34/28.44    (33)  all_58_4 = all_52_5
% 178.34/28.44    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.44    (35)   ~ (e3 = e1)
% 178.34/28.44    (36)   ~ (all_52_27 = all_52_29)
% 178.34/28.44    (37)   ~ (all_52_17 = all_14_2)
% 178.34/28.44    (38)  op(e3, all_4_2) = all_4_1
% 178.34/28.44    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.44    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.44    (41)   ~ (all_52_7 = all_4_2)
% 178.34/28.44    (42)  all_58_1 = all_52_3
% 178.34/28.44    (43)   ~ (all_52_13 = all_52_15)
% 178.34/28.44    (44)  all_58_0 = all_4_2
% 178.34/28.44    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.44    (46)  op(e1, all_52_29) = all_52_28
% 178.34/28.44    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.44    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.44    (49)  all_58_14 = all_52_29
% 178.34/28.44    (50)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.44    (51)   ~ (all_52_3 = all_52_5)
% 178.34/28.44    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.44    (53)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.44    (54)  all_58_8 = all_14_2
% 178.34/28.44    (55)  op(e0, e2) = all_52_27
% 178.34/28.44    (56)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.44    (57)   ~ (all_52_3 = all_52_27)
% 178.34/28.44    (58)  op(e0, e3) = all_52_25
% 178.34/28.44    (59)  op(e0, all_6_2) = all_6_1
% 178.34/28.44    (60)   ~ (all_52_9 = all_10_2)
% 178.34/28.44    (61)  op(e3, all_52_17) = all_52_16
% 178.34/28.44    (62)   ~ (e3 = e0)
% 178.34/28.44    (63)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.44    (64)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.44    (65)   ~ (all_52_5 = all_52_29)
% 178.34/28.44    (66)  op(e1, e0) = all_52_23
% 178.34/28.44    (67)  all_56_12 = all_52_25
% 178.34/28.44    (68)  all_58_13 = all_52_27
% 178.34/28.44    (69)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.44    (70)   ~ (all_52_9 = all_52_17)
% 178.34/28.44    (71)  all_58_6 = all_52_17
% 178.34/28.44    (72)   ~ (all_52_3 = all_52_7)
% 178.34/28.44    (73)   ~ (e1 = e0)
% 178.34/28.44    (74)  all_56_0 = all_4_2
% 178.34/28.44    (75)  all_58_11 = all_52_23
% 178.34/28.44    (76)   ~ (all_4_0 = e1)
% 178.34/28.44    (77)   ~ (all_52_19 = all_10_2)
% 178.34/28.44    (78)   ~ (all_52_29 = all_6_2)
% 178.34/28.44    (79)  all_58_2 = all_52_9
% 178.34/28.44    (80)  op(e3, e1) = all_52_5
% 178.34/28.44    (81)   ~ (e2 = e1)
% 178.34/28.44    (82)   ~ (all_52_25 = all_6_2)
% 178.34/28.45    (83)  op(e1, e3) = all_52_17
% 178.34/28.45    (84)   ~ (all_52_25 = all_4_2)
% 178.34/28.45    (85)  op(e3, e0) = all_52_7
% 178.34/28.45    (86)  all_52_28 = e1
% 178.34/28.45    (87)  op(e3, e3) = all_4_2
% 178.34/28.45    (88)   ~ (all_52_17 = all_4_2)
% 178.34/28.45    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.45    (90)   ~ (all_52_25 = all_52_27)
% 178.34/28.45    (91)   ~ (all_52_27 = all_6_2)
% 178.34/28.45    (92)   ~ (all_52_7 = all_6_2)
% 178.34/28.45    (93)   ~ (all_52_15 = all_10_2)
% 178.34/28.45    (94)  op(e2, all_52_27) = all_52_26
% 178.34/28.45    (95)   ~ (all_52_17 = all_52_19)
% 178.34/28.45    (96)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.45    (97)  all_58_9 = all_52_7
% 178.34/28.45    (98)  all_52_24 = e3
% 178.34/28.45    (99)  all_58_12 = all_52_25
% 178.34/28.45    (100)  op(e3, all_4_2) = e1
% 178.34/28.45    (101)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.45    (102)   ~ (all_52_9 = all_52_15)
% 178.34/28.45    (103)   ~ (e3 = e2)
% 178.34/28.45    (104)  op(e2, e3) = all_52_9
% 178.34/28.45    (105)  all_56_13 = all_52_27
% 178.34/28.45  
% 178.34/28.45  Begin of proof
% 178.34/28.45  | 
% 178.34/28.45  | REDUCE: (11), (98) imply:
% 178.34/28.45  |   (106)  op(e3, all_52_25) = e3
% 178.34/28.45  | 
% 178.34/28.45  | REDUCE: (6), (94) imply:
% 178.34/28.45  |   (107)  op(e2, all_52_27) = e2
% 178.34/28.45  | 
% 178.34/28.45  | REDUCE: (46), (86) imply:
% 178.34/28.45  |   (108)  op(e1, all_52_29) = e1
% 178.34/28.45  | 
% 178.34/28.45  | REDUCE: (20), (59) imply:
% 178.34/28.45  |   (109)  op(e0, all_6_2) = e0
% 178.34/28.45  | 
% 178.34/28.45  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 178.34/28.45  |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (25), (26),
% 178.34/28.45  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 178.34/28.45  |            (38), (39), (40), (41), (42), (43), (44), (45), (47), (48), (49),
% 178.34/28.45  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (60), (61),
% 178.34/28.45  |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 178.34/28.45  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 178.34/28.45  |            (84), (85), (87), (88), (89), (90), (91), (92), (93), (95), (96),
% 178.34/28.45  |            (97), (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 178.34/28.45  |            (108), (109) are inconsistent by sub-proof #603.
% 178.34/28.45  | 
% 178.34/28.45  End of proof
% 178.34/28.45  
% 178.34/28.45  Sub-proof #603 shows that the following formulas are inconsistent:
% 178.34/28.45  ----------------------------------------------------------------
% 178.34/28.45    (1)   ~ (all_52_5 = all_52_13)
% 178.34/28.45    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.45    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.45    (4)   ~ (all_52_27 = all_10_2)
% 178.34/28.45    (5)   ~ (all_52_17 = all_52_23)
% 178.34/28.45    (6)   ~ (all_52_13 = all_52_29)
% 178.34/28.45    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.45    (8)  op(e3, e2) = all_52_3
% 178.34/28.45    (9)   ~ (all_52_9 = all_52_25)
% 178.34/28.45    (10)   ~ (all_52_19 = all_52_23)
% 178.34/28.45    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.34/28.45    (12)  op(e3, all_52_9) = all_52_8
% 178.34/28.45    (13)  all_58_5 = all_52_13
% 178.34/28.45    (14)   ~ (all_6_2 = e0)
% 178.34/28.45    (15)   ~ (all_52_25 = all_52_29)
% 178.34/28.45    (16)  all_56_15 = all_6_2
% 178.34/28.45    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.45    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.45    (19)  all_58_3 = all_10_2
% 178.34/28.45    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.45    (21)  all_58_15 = all_6_2
% 178.34/28.45    (22)  op(e0, all_6_2) = e0
% 178.34/28.45    (23)   ~ (all_52_9 = all_4_2)
% 178.34/28.45    (24)   ~ (all_52_5 = all_52_7)
% 178.34/28.45    (25)  all_58_10 = all_52_15
% 178.34/28.45    (26)   ~ (all_52_5 = all_4_2)
% 178.34/28.45    (27)  all_58_7 = all_52_19
% 178.34/28.45    (28)   ~ (all_52_17 = all_52_25)
% 178.34/28.45    (29)  op(e0, e1) = all_52_29
% 178.34/28.45    (30)   ~ (all_4_0 = e2)
% 178.34/28.45    (31)  all_58_4 = all_52_5
% 178.34/28.45    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.45    (33)   ~ (e3 = e1)
% 178.34/28.45    (34)   ~ (all_52_27 = all_52_29)
% 178.34/28.45    (35)   ~ (all_52_17 = all_14_2)
% 178.34/28.45    (36)  op(e3, all_4_2) = all_4_1
% 178.34/28.45    (37)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.45    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.45    (39)   ~ (all_52_7 = all_4_2)
% 178.34/28.45    (40)  all_58_1 = all_52_3
% 178.34/28.45    (41)   ~ (all_52_13 = all_52_15)
% 178.34/28.45    (42)  all_58_0 = all_4_2
% 178.34/28.45    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.45    (44)  op(e2, all_52_27) = e2
% 178.34/28.45    (45)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.45    (46)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.45    (47)  all_58_14 = all_52_29
% 178.34/28.45    (48)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.45    (49)   ~ (all_52_3 = all_52_5)
% 178.34/28.45    (50)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.45    (51)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.45    (52)  all_58_8 = all_14_2
% 178.34/28.45    (53)  op(e0, e2) = all_52_27
% 178.34/28.45    (54)  op(e1, all_52_29) = e1
% 178.34/28.45    (55)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.45    (56)   ~ (all_52_3 = all_52_27)
% 178.34/28.45    (57)  op(e0, e3) = all_52_25
% 178.34/28.45    (58)   ~ (all_52_9 = all_10_2)
% 178.34/28.45    (59)  op(e3, all_52_17) = all_52_16
% 178.34/28.45    (60)   ~ (e3 = e0)
% 178.34/28.45    (61)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.45    (62)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.45    (63)   ~ (all_52_5 = all_52_29)
% 178.34/28.45    (64)  op(e1, e0) = all_52_23
% 178.34/28.45    (65)  all_56_12 = all_52_25
% 178.34/28.45    (66)  all_58_13 = all_52_27
% 178.34/28.45    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.45    (68)   ~ (all_52_9 = all_52_17)
% 178.34/28.45    (69)  all_58_6 = all_52_17
% 178.34/28.45    (70)   ~ (all_52_3 = all_52_7)
% 178.34/28.45    (71)   ~ (e1 = e0)
% 178.34/28.45    (72)  all_56_0 = all_4_2
% 178.34/28.45    (73)  all_58_11 = all_52_23
% 178.34/28.45    (74)  op(e3, all_52_25) = e3
% 178.34/28.45    (75)   ~ (all_4_0 = e1)
% 178.34/28.45    (76)   ~ (all_52_19 = all_10_2)
% 178.34/28.45    (77)   ~ (all_52_29 = all_6_2)
% 178.34/28.45    (78)  all_58_2 = all_52_9
% 178.34/28.45    (79)  op(e3, e1) = all_52_5
% 178.34/28.45    (80)   ~ (e2 = e1)
% 178.34/28.45    (81)   ~ (all_52_25 = all_6_2)
% 178.34/28.45    (82)  op(e1, e3) = all_52_17
% 178.34/28.45    (83)   ~ (all_52_25 = all_4_2)
% 178.34/28.45    (84)  op(e3, e0) = all_52_7
% 178.34/28.45    (85)  op(e3, e3) = all_4_2
% 178.34/28.45    (86)   ~ (all_52_17 = all_4_2)
% 178.34/28.45    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.45    (88)   ~ (all_52_25 = all_52_27)
% 178.34/28.45    (89)   ~ (all_52_27 = all_6_2)
% 178.34/28.45    (90)   ~ (all_52_7 = all_6_2)
% 178.34/28.45    (91)   ~ (all_52_15 = all_10_2)
% 178.34/28.45    (92)   ~ (all_52_17 = all_52_19)
% 178.34/28.45    (93)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.45    (94)  all_58_9 = all_52_7
% 178.34/28.45    (95)  all_58_12 = all_52_25
% 178.34/28.45    (96)  op(e3, all_4_2) = e1
% 178.34/28.45    (97)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.45    (98)   ~ (all_52_9 = all_52_15)
% 178.34/28.45    (99)   ~ (e3 = e2)
% 178.34/28.45    (100)  op(e2, e3) = all_52_9
% 178.34/28.45    (101)  all_56_13 = all_52_27
% 178.34/28.45  
% 178.34/28.45  Begin of proof
% 178.34/28.45  | 
% 178.34/28.45  | BETA: splitting (37) gives:
% 178.34/28.45  | 
% 178.34/28.45  | Case 1:
% 178.34/28.45  | | 
% 178.34/28.45  | |   (102)  all_56_15 = e3
% 178.34/28.45  | | 
% 178.34/28.45  | | COMBINE_EQS: (16), (102) imply:
% 178.34/28.45  | |   (103)  all_6_2 = e3
% 178.34/28.45  | | 
% 178.34/28.45  | | SIMP: (103) implies:
% 178.34/28.45  | |   (104)  all_6_2 = e3
% 178.34/28.45  | | 
% 178.34/28.45  | | REF_CLOSE: (22), (57), (74), (84), (87), (90), (104) are inconsistent by
% 178.34/28.45  | |            sub-proof #665.
% 178.34/28.45  | | 
% 178.34/28.45  | Case 2:
% 178.34/28.45  | | 
% 178.34/28.45  | |   (105)   ~ (all_56_15 = e3)
% 178.34/28.45  | |   (106)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.45  | | 
% 178.34/28.45  | | REDUCE: (16), (105) imply:
% 178.34/28.45  | |   (107)   ~ (all_6_2 = e3)
% 178.34/28.45  | | 
% 178.34/28.45  | | BETA: splitting (48) gives:
% 178.34/28.45  | | 
% 178.34/28.45  | | Case 1:
% 178.34/28.45  | | | 
% 178.34/28.45  | | |   (108)  all_56_13 = e3
% 178.34/28.45  | | | 
% 178.34/28.45  | | | COMBINE_EQS: (101), (108) imply:
% 178.34/28.45  | | |   (109)  all_52_27 = e3
% 178.34/28.45  | | | 
% 178.34/28.45  | | | COMBINE_EQS: (66), (109) imply:
% 178.34/28.45  | | |   (110)  all_58_13 = e3
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (56), (109) imply:
% 178.34/28.45  | | |   (111)   ~ (all_52_3 = e3)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (88), (109) imply:
% 178.34/28.45  | | |   (112)   ~ (all_52_25 = e3)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (4), (109) imply:
% 178.34/28.45  | | |   (113)   ~ (all_10_2 = e3)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | SIMP: (113) implies:
% 178.34/28.45  | | |   (114)   ~ (all_10_2 = e3)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (44), (109) imply:
% 178.34/28.45  | | |   (115)  op(e2, e3) = e2
% 178.34/28.45  | | | 
% 178.34/28.45  | | | GROUND_INST: instantiating (87) with all_52_9, e2, e3, e2, simplifying
% 178.34/28.45  | | |              with (100), (115) gives:
% 178.34/28.45  | | |   (116)  all_52_9 = e2
% 178.34/28.45  | | | 
% 178.34/28.45  | | | COMBINE_EQS: (78), (116) imply:
% 178.34/28.45  | | |   (117)  all_58_2 = e2
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (68), (116) imply:
% 178.34/28.45  | | |   (118)   ~ (all_52_17 = e2)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | SIMP: (118) implies:
% 178.34/28.45  | | |   (119)   ~ (all_52_17 = e2)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (23), (116) imply:
% 178.34/28.45  | | |   (120)   ~ (all_4_2 = e2)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | SIMP: (120) implies:
% 178.34/28.45  | | |   (121)   ~ (all_4_2 = e2)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (12), (116) imply:
% 178.34/28.45  | | |   (122)  op(e3, e2) = all_52_8
% 178.34/28.45  | | | 
% 178.34/28.45  | | | GROUND_INST: instantiating (87) with all_52_3, all_52_8, e2, e3,
% 178.34/28.45  | | |              simplifying with (8), (122) gives:
% 178.34/28.45  | | |   (123)  all_52_3 = all_52_8
% 178.34/28.45  | | | 
% 178.34/28.45  | | | COMBINE_EQS: (40), (123) imply:
% 178.34/28.45  | | |   (124)  all_58_1 = all_52_8
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (111), (123) imply:
% 178.34/28.45  | | |   (125)   ~ (all_52_8 = e3)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | BETA: splitting (50) gives:
% 178.34/28.45  | | | 
% 178.34/28.45  | | | Case 1:
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | |   (126)  all_58_0 = e3
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | | COMBINE_EQS: (42), (126) imply:
% 178.34/28.45  | | | |   (127)  all_4_2 = e3
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | | REF_CLOSE: (33), (85), (87), (96), (127) are inconsistent by sub-proof
% 178.34/28.45  | | | |            #630.
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | Case 2:
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | |   (128)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | | BETA: splitting (128) gives:
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | | Case 1:
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | |   (129)  all_58_2 = e3
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | COMBINE_EQS: (117), (129) imply:
% 178.34/28.45  | | | | |   (130)  e3 = e2
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | REDUCE: (99), (130) imply:
% 178.34/28.45  | | | | |   (131)  $false
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | CLOSE: (131) is inconsistent.
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | Case 2:
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | |   (132)  all_58_6 = e3 | all_58_12 = e3
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | BETA: splitting (132) gives:
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | Case 1:
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | |   (133)  all_58_6 = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | COMBINE_EQS: (69), (133) imply:
% 178.34/28.45  | | | | | |   (134)  all_52_17 = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (134) implies:
% 178.34/28.45  | | | | | |   (135)  all_52_17 = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (86), (135) imply:
% 178.34/28.45  | | | | | |   (136)   ~ (all_4_2 = e3)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (136) implies:
% 178.34/28.45  | | | | | |   (137)   ~ (all_4_2 = e3)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | BETA: splitting (20) gives:
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | Case 1:
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | |   (138)  all_56_0 = e3
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | | REF_CLOSE: (72), (137), (138) are inconsistent by sub-proof #1024.
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | Case 2:
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | |   (139)   ~ (all_56_0 = e3)
% 178.34/28.45  | | | | | | |   (140)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | | BETA: splitting (38) gives:
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | |   (141)  all_58_2 = e3
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | COMBINE_EQS: (117), (141) imply:
% 178.34/28.45  | | | | | | | |   (142)  e3 = e2
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | REDUCE: (99), (142) imply:
% 178.34/28.45  | | | | | | | |   (143)  $false
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | CLOSE: (143) is inconsistent.
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | |   (144)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | BETA: splitting (93) gives:
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | |   (145)  all_58_9 = e3
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | COMBINE_EQS: (94), (145) imply:
% 178.34/28.45  | | | | | | | | |   (146)  all_52_7 = e3
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | SIMP: (146) implies:
% 178.34/28.45  | | | | | | | | |   (147)  all_52_7 = e3
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | REDUCE: (84), (147) imply:
% 178.34/28.45  | | | | | | | | |   (148)  op(e3, e0) = e3
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | BETA: splitting (11) gives:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | |   (149)  all_58_0 = e1
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | REF_CLOSE: (26), (42), (79), (87), (96), (149) are
% 178.34/28.45  | | | | | | | | | |            inconsistent by sub-proof #626.
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | |   (150)   ~ (all_58_0 = e1)
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | REDUCE: (42), (150) imply:
% 178.34/28.45  | | | | | | | | | |   (151)   ~ (all_4_2 = e1)
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | REF_CLOSE: (33), (72), (87), (96), (121), (140), (148), (151)
% 178.34/28.45  | | | | | | | | | |            are inconsistent by sub-proof #604.
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | |   (152)   ~ (all_58_9 = e3)
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | REDUCE: (94), (152) imply:
% 178.34/28.45  | | | | | | | | |   (153)   ~ (all_52_7 = e3)
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | BETA: splitting (97) gives:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | |   (154)  all_58_0 = e3
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | COMBINE_EQS: (42), (154) imply:
% 178.34/28.45  | | | | | | | | | |   (155)  all_4_2 = e3
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | REDUCE: (137), (155) imply:
% 178.34/28.45  | | | | | | | | | |   (156)  $false
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | CLOSE: (156) is inconsistent.
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | |   (157)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | BETA: splitting (157) gives:
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | |   (158)  all_58_1 = e3
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | COMBINE_EQS: (124), (158) imply:
% 178.34/28.45  | | | | | | | | | | |   (159)  all_52_8 = e3
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | REDUCE: (125), (159) imply:
% 178.34/28.45  | | | | | | | | | | |   (160)  $false
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | |   (161)  all_58_4 = e3 | all_58_9 = e3
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | BETA: splitting (161) gives:
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | |   (162)  all_58_4 = e3
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | COMBINE_EQS: (31), (162) imply:
% 178.34/28.45  | | | | | | | | | | | |   (163)  all_52_5 = e3
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | SIMP: (163) implies:
% 178.34/28.45  | | | | | | | | | | | |   (164)  all_52_5 = e3
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | REDUCE: (1), (164) imply:
% 178.34/28.45  | | | | | | | | | | | |   (165)   ~ (all_52_13 = e3)
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | SIMP: (165) implies:
% 178.34/28.45  | | | | | | | | | | | |   (166)   ~ (all_52_13 = e3)
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | REDUCE: (79), (164) imply:
% 178.34/28.45  | | | | | | | | | | | |   (167)  op(e3, e1) = e3
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | BETA: splitting (144) gives:
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | |   (168)  all_58_3 = e3
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | COMBINE_EQS: (19), (168) imply:
% 178.34/28.45  | | | | | | | | | | | | |   (169)  all_10_2 = e3
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | REDUCE: (114), (169) imply:
% 178.34/28.45  | | | | | | | | | | | | |   (170)  $false
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | |   (171)  all_58_5 = e3 | all_58_10 = e3
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | BETA: splitting (171) gives:
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | |   (172)  all_58_5 = e3
% 178.34/28.45  | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | REF_CLOSE: (13), (166), (172) are inconsistent by sub-proof
% 178.34/28.45  | | | | | | | | | | | | | |            #969.
% 178.34/28.45  | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | |   (173)  all_58_10 = e3
% 178.34/28.45  | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 178.34/28.45  | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | |   (174)  all_58_0 = e1
% 178.34/28.45  | | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | | REF_CLOSE: (42), (87), (96), (137), (167), (174) are
% 178.34/28.45  | | | | | | | | | | | | | | |            inconsistent by sub-proof #612.
% 178.34/28.45  | | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | |   (175)   ~ (all_58_0 = e1)
% 178.34/28.45  | | | | | | | | | | | | | | |   (176)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.45  | | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | | REDUCE: (42), (175) imply:
% 178.34/28.45  | | | | | | | | | | | | | | |   (177)   ~ (all_4_2 = e1)
% 178.34/28.45  | | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | | REF_CLOSE: (7), (33), (39), (42), (43), (47), (54), (60),
% 178.34/28.45  | | | | | | | | | | | | | | |            (61), (64), (71), (72), (73), (80), (87), (94),
% 178.34/28.45  | | | | | | | | | | | | | | |            (110), (117), (121), (133), (137), (140), (173),
% 178.34/28.45  | | | | | | | | | | | | | | |            (176), (177) are inconsistent by sub-proof #656.
% 178.34/28.45  | | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | |   (178)  all_58_9 = e3
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | | REF_CLOSE: (94), (153), (178) are inconsistent by sub-proof
% 178.34/28.45  | | | | | | | | | | | |            #972.
% 178.34/28.45  | | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | End of split
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | End of split
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | Case 2:
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | |   (179)  all_58_12 = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REF_CLOSE: (95), (112), (179) are inconsistent by sub-proof #1003.
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | End of split
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | End of split
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | End of split
% 178.34/28.45  | | | 
% 178.34/28.45  | | Case 2:
% 178.34/28.45  | | | 
% 178.34/28.45  | | |   (180)   ~ (all_56_13 = e3)
% 178.34/28.45  | | |   (181)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.45  | | | 
% 178.34/28.45  | | | REDUCE: (101), (180) imply:
% 178.34/28.45  | | |   (182)   ~ (all_52_27 = e3)
% 178.34/28.45  | | | 
% 178.34/28.45  | | | BETA: splitting (51) gives:
% 178.34/28.45  | | | 
% 178.34/28.45  | | | Case 1:
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | |   (183)  all_58_12 = e3
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | | REF_CLOSE: (74), (83), (85), (87), (95), (183) are inconsistent by
% 178.34/28.45  | | | |            sub-proof #884.
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | Case 2:
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | |   (184)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | | BETA: splitting (184) gives:
% 178.34/28.45  | | | | 
% 178.34/28.45  | | | | Case 1:
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | |   (185)  all_58_13 = e3
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | REF_CLOSE: (66), (182), (185) are inconsistent by sub-proof #1026.
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | Case 2:
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | |   (186)  all_58_14 = e3 | all_58_15 = e3
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | BETA: splitting (186) gives:
% 178.34/28.45  | | | | | 
% 178.34/28.45  | | | | | Case 1:
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | |   (187)  all_58_14 = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | COMBINE_EQS: (47), (187) imply:
% 178.34/28.45  | | | | | |   (188)  all_52_29 = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (188) implies:
% 178.34/28.45  | | | | | |   (189)  all_52_29 = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (63), (189) imply:
% 178.34/28.45  | | | | | |   (190)   ~ (all_52_5 = e3)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (6), (189) imply:
% 178.34/28.45  | | | | | |   (191)   ~ (all_52_13 = e3)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (15), (189) imply:
% 178.34/28.45  | | | | | |   (192)   ~ (all_52_25 = e3)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (77), (189) imply:
% 178.34/28.45  | | | | | |   (193)   ~ (all_6_2 = e3)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (54), (189) imply:
% 178.34/28.45  | | | | | |   (194)  op(e1, e3) = e1
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (29), (189) imply:
% 178.34/28.45  | | | | | |   (195)  op(e0, e1) = e3
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | GROUND_INST: instantiating (87) with all_52_17, e1, e3, e1,
% 178.34/28.45  | | | | | |              simplifying with (82), (194) gives:
% 178.34/28.45  | | | | | |   (196)  all_52_17 = e1
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | COMBINE_EQS: (69), (196) imply:
% 178.34/28.45  | | | | | |   (197)  all_58_6 = e1
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (92), (196) imply:
% 178.34/28.45  | | | | | |   (198)   ~ (all_52_19 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (198) implies:
% 178.34/28.45  | | | | | |   (199)   ~ (all_52_19 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (5), (196) imply:
% 178.34/28.45  | | | | | |   (200)   ~ (all_52_23 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (200) implies:
% 178.34/28.45  | | | | | |   (201)   ~ (all_52_23 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (28), (196) imply:
% 178.34/28.45  | | | | | |   (202)   ~ (all_52_25 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (202) implies:
% 178.34/28.45  | | | | | |   (203)   ~ (all_52_25 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (35), (196) imply:
% 178.34/28.45  | | | | | |   (204)   ~ (all_14_2 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (204) implies:
% 178.34/28.45  | | | | | |   (205)   ~ (all_14_2 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (86), (196) imply:
% 178.34/28.45  | | | | | |   (206)   ~ (all_4_2 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (206) implies:
% 178.34/28.45  | | | | | |   (207)   ~ (all_4_2 = e1)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (59), (196) imply:
% 178.34/28.45  | | | | | |   (208)  op(e3, e1) = all_52_16
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | GROUND_INST: instantiating (87) with all_52_5, all_52_16, e1, e3,
% 178.34/28.45  | | | | | |              simplifying with (79), (208) gives:
% 178.34/28.45  | | | | | |   (209)  all_52_5 = all_52_16
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | COMBINE_EQS: (31), (209) imply:
% 178.34/28.45  | | | | | |   (210)  all_58_4 = all_52_16
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (49), (209) imply:
% 178.34/28.45  | | | | | |   (211)   ~ (all_52_3 = all_52_16)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (24), (209) imply:
% 178.34/28.45  | | | | | |   (212)   ~ (all_52_7 = all_52_16)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | SIMP: (212) implies:
% 178.34/28.45  | | | | | |   (213)   ~ (all_52_7 = all_52_16)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (26), (209) imply:
% 178.34/28.45  | | | | | |   (214)   ~ (all_52_16 = all_4_2)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | REDUCE: (190), (209) imply:
% 178.34/28.45  | | | | | |   (215)   ~ (all_52_16 = e3)
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | BETA: splitting (62) gives:
% 178.34/28.45  | | | | | | 
% 178.34/28.45  | | | | | | Case 1:
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | |   (216)  all_56_12 = e3
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | | REF_CLOSE: (65), (192), (216) are inconsistent by sub-proof #1040.
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | Case 2:
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | |   (217)   ~ (all_56_12 = e3)
% 178.34/28.45  | | | | | | |   (218)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | | BETA: splitting (45) gives:
% 178.34/28.45  | | | | | | | 
% 178.34/28.45  | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | |   (219)  all_58_4 = e1
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | COMBINE_EQS: (210), (219) imply:
% 178.34/28.45  | | | | | | | |   (220)  all_52_16 = e1
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | SIMP: (220) implies:
% 178.34/28.45  | | | | | | | |   (221)  all_52_16 = e1
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | REDUCE: (211), (221) imply:
% 178.34/28.45  | | | | | | | |   (222)   ~ (all_52_3 = e1)
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | REDUCE: (213), (221) imply:
% 178.34/28.45  | | | | | | | |   (223)   ~ (all_52_7 = e1)
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | REDUCE: (215), (221) imply:
% 178.34/28.45  | | | | | | | |   (224)   ~ (e3 = e1)
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | BETA: splitting (50) gives:
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | |   (225)  all_58_0 = e3
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | COMBINE_EQS: (42), (225) imply:
% 178.34/28.45  | | | | | | | | |   (226)  all_4_2 = e3
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | REF_CLOSE: (33), (85), (87), (96), (226) are inconsistent by
% 178.34/28.45  | | | | | | | | |            sub-proof #630.
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | |   (227)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | REF_CLOSE: (2), (3), (7), (8), (9), (10), (16), (17), (18),
% 178.34/28.45  | | | | | | | | |            (19), (20), (21), (22), (23), (25), (27), (30),
% 178.34/28.45  | | | | | | | | |            (32), (33), (36), (40), (42), (46), (53), (55),
% 178.34/28.45  | | | | | | | | |            (56), (58), (65), (66), (70), (72), (73), (74),
% 178.34/28.45  | | | | | | | | |            (75), (76), (78), (81), (83), (84), (87), (89),
% 178.34/28.45  | | | | | | | | |            (90), (91), (93), (94), (95), (98), (101), (106),
% 178.34/28.45  | | | | | | | | |            (107), (181), (182), (187), (192), (195), (197),
% 178.34/28.45  | | | | | | | | |            (199), (201), (203), (207), (218), (219), (222),
% 178.34/28.45  | | | | | | | | |            (223), (227) are inconsistent by sub-proof #640.
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | End of split
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | |   (228)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | BETA: splitting (228) gives:
% 178.34/28.45  | | | | | | | | 
% 178.34/28.45  | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | |   (229)  all_58_5 = e1
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | COMBINE_EQS: (13), (229) imply:
% 178.34/28.45  | | | | | | | | |   (230)  all_52_13 = e1
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | SIMP: (230) implies:
% 178.34/28.45  | | | | | | | | |   (231)  all_52_13 = e1
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | REDUCE: (41), (231) imply:
% 178.34/28.45  | | | | | | | | |   (232)   ~ (all_52_15 = e1)
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | SIMP: (232) implies:
% 178.34/28.45  | | | | | | | | |   (233)   ~ (all_52_15 = e1)
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | REDUCE: (191), (231) imply:
% 178.34/28.45  | | | | | | | | |   (234)   ~ (e3 = e1)
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | BETA: splitting (50) gives:
% 178.34/28.45  | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | Case 1:
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | |   (235)  all_58_0 = e3
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | COMBINE_EQS: (42), (235) imply:
% 178.34/28.45  | | | | | | | | | |   (236)  all_4_2 = e3
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | | REF_CLOSE: (33), (85), (87), (96), (236) are inconsistent by
% 178.34/28.45  | | | | | | | | | |            sub-proof #630.
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | Case 2:
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.45  | | | | | | | | | |   (237)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.45  | | | | | | | | | | 
% 178.34/28.46  | | | | | | | | | | REF_CLOSE: (10), (14), (16), (18), (19), (21), (22), (25),
% 178.34/28.46  | | | | | | | | | |            (27), (33), (40), (46), (58), (60), (65), (66),
% 178.34/28.46  | | | | | | | | | |            (70), (73), (74), (78), (81), (84), (87), (90),
% 178.34/28.46  | | | | | | | | | |            (93), (94), (95), (98), (106), (107), (182),
% 178.34/28.46  | | | | | | | | | |            (192), (195), (197), (199), (201), (203), (218),
% 178.34/28.46  | | | | | | | | | |            (233), (237) are inconsistent by sub-proof #639.
% 178.34/28.46  | | | | | | | | | | 
% 178.34/28.46  | | | | | | | | | End of split
% 178.34/28.46  | | | | | | | | | 
% 178.34/28.46  | | | | | | | | Case 2:
% 178.34/28.46  | | | | | | | | | 
% 178.34/28.46  | | | | | | | | |   (238)  all_58_8 = e1 | all_58_14 = e1
% 178.34/28.46  | | | | | | | | | 
% 178.34/28.46  | | | | | | | | | REF_CLOSE: (33), (52), (187), (205), (238) are inconsistent by
% 178.34/28.46  | | | | | | | | |            sub-proof #638.
% 178.34/28.46  | | | | | | | | | 
% 178.34/28.46  | | | | | | | | End of split
% 178.34/28.46  | | | | | | | | 
% 178.34/28.46  | | | | | | | End of split
% 178.34/28.46  | | | | | | | 
% 178.34/28.46  | | | | | | End of split
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | Case 2:
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | |   (239)  all_58_15 = e3
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | | COMBINE_EQS: (21), (239) imply:
% 178.34/28.46  | | | | | |   (240)  all_6_2 = e3
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | | REDUCE: (107), (240) imply:
% 178.34/28.46  | | | | | |   (241)  $false
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | | CLOSE: (241) is inconsistent.
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | End of split
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | End of split
% 178.34/28.46  | | | | 
% 178.34/28.46  | | | End of split
% 178.34/28.46  | | | 
% 178.34/28.46  | | End of split
% 178.34/28.46  | | 
% 178.34/28.46  | End of split
% 178.34/28.46  | 
% 178.34/28.46  End of proof
% 178.34/28.46  
% 178.34/28.46  Sub-proof #604 shows that the following formulas are inconsistent:
% 178.34/28.46  ----------------------------------------------------------------
% 178.34/28.46    (1)   ~ (all_4_2 = e2)
% 178.34/28.46    (2)   ~ (e3 = e1)
% 178.34/28.46    (3)  all_56_0 = all_4_2
% 178.34/28.46    (4)  op(e3, e0) = e3
% 178.34/28.46    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.46    (6)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.46    (7)   ~ (all_4_2 = e1)
% 178.34/28.46    (8)  op(e3, all_4_2) = e1
% 178.34/28.46  
% 178.34/28.46  Begin of proof
% 178.34/28.46  | 
% 178.34/28.46  | BETA: splitting (6) gives:
% 178.34/28.46  | 
% 178.34/28.46  | Case 1:
% 178.34/28.46  | | 
% 178.34/28.46  | |   (9)  all_56_0 = e2
% 178.34/28.46  | | 
% 178.34/28.46  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #904.
% 178.34/28.46  | | 
% 178.34/28.46  | Case 2:
% 178.34/28.46  | | 
% 178.34/28.46  | |   (10)  all_56_0 = e1 | all_56_0 = e0
% 178.34/28.46  | | 
% 178.34/28.46  | | BETA: splitting (10) gives:
% 178.34/28.46  | | 
% 178.34/28.46  | | Case 1:
% 178.34/28.46  | | | 
% 178.34/28.46  | | |   (11)  all_56_0 = e1
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #1022.
% 178.34/28.46  | | | 
% 178.34/28.46  | | Case 2:
% 178.34/28.46  | | | 
% 178.34/28.46  | | |   (12)  all_56_0 = e0
% 178.34/28.46  | | | 
% 178.34/28.46  | | | COMBINE_EQS: (3), (12) imply:
% 178.34/28.46  | | |   (13)  all_4_2 = e0
% 178.34/28.46  | | | 
% 178.34/28.46  | | | SIMP: (13) implies:
% 178.34/28.46  | | |   (14)  all_4_2 = e0
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REDUCE: (8), (14) imply:
% 178.34/28.46  | | |   (15)  op(e3, e0) = e1
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REF_CLOSE: (2), (4), (5), (15) are inconsistent by sub-proof #648.
% 178.34/28.46  | | | 
% 178.34/28.46  | | End of split
% 178.34/28.46  | | 
% 178.34/28.46  | End of split
% 178.34/28.46  | 
% 178.34/28.46  End of proof
% 178.34/28.46  
% 178.34/28.46  Sub-proof #605 shows that the following formulas are inconsistent:
% 178.34/28.46  ----------------------------------------------------------------
% 178.34/28.46    (1)   ~ (all_52_23 = all_14_2)
% 178.34/28.46    (2)   ~ (all_52_5 = all_52_13)
% 178.34/28.46    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.34/28.46    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.46    (5)   ~ (all_52_17 = all_52_23)
% 178.34/28.46    (6)  op(e2, all_10_2) = all_10_1
% 178.34/28.46    (7)  all_40_2 = all_4_2
% 178.34/28.46    (8)   ~ (all_52_13 = all_52_29)
% 178.34/28.46    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.46    (10)  op(e3, e2) = all_52_3
% 178.34/28.46    (11)   ~ (all_52_9 = all_52_25)
% 178.34/28.46    (12)  op(e3, all_52_25) = all_52_24
% 178.34/28.46    (13)   ~ (all_52_19 = all_52_23)
% 178.34/28.46    (14)  op(e1, e2) = all_52_19
% 178.34/28.46    (15)  op(e3, all_52_9) = all_52_8
% 178.34/28.46    (16)   ~ (all_52_3 = all_10_2)
% 178.34/28.46    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.34/28.46    (18)  all_58_5 = all_52_13
% 178.34/28.46    (19)   ~ (all_6_2 = e0)
% 178.34/28.46    (20)   ~ (all_52_25 = all_52_29)
% 178.34/28.46    (21)  all_56_15 = all_6_2
% 178.34/28.46    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.46    (23)  op(e2, e0) = all_52_15
% 178.34/28.46    (24)  all_58_3 = all_10_2
% 178.34/28.46    (25)  all_56_9 = all_52_19
% 178.34/28.46    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.46    (27)  all_58_15 = all_6_2
% 178.34/28.46    (28)   ~ (all_52_9 = all_4_2)
% 178.34/28.46    (29)   ~ (all_52_5 = all_52_7)
% 178.34/28.46    (30)  all_58_10 = all_52_15
% 178.34/28.46    (31)   ~ (all_52_5 = all_4_2)
% 178.34/28.46    (32)  all_58_7 = all_52_19
% 178.34/28.46    (33)   ~ (all_52_17 = all_52_25)
% 178.34/28.46    (34)   ~ (all_4_0 = e2)
% 178.34/28.46    (35)  all_58_4 = all_52_5
% 178.34/28.46    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.46    (37)   ~ (all_52_27 = all_52_29)
% 178.34/28.46    (38)   ~ (all_52_17 = all_14_2)
% 178.34/28.46    (39)  op(e3, all_4_2) = all_4_1
% 178.34/28.46    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.46    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.46    (42)   ~ (all_52_7 = all_4_2)
% 178.34/28.46    (43)  all_58_1 = all_52_3
% 178.34/28.46    (44)  all_58_0 = all_4_2
% 178.34/28.46    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.46    (46)  op(e1, all_52_29) = all_52_28
% 178.34/28.46    (47)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.46    (48)   ~ (all_4_1 = e2)
% 178.34/28.46    (49)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.46    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.46    (51)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.34/28.46    (52)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.34/28.46    (53)  all_58_14 = all_52_29
% 178.34/28.46    (54)   ~ (all_52_3 = all_52_5)
% 178.34/28.46    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.46    (56)  op(e2, e1) = all_52_13
% 178.34/28.46    (57)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.46    (58)  all_58_8 = all_14_2
% 178.34/28.46    (59)   ~ (all_14_0 = e3)
% 178.34/28.46    (60)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.46    (61)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.34/28.46    (62)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.46    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.34/28.46    (64)   ~ (all_52_5 = all_14_2)
% 178.34/28.46    (65)   ~ (all_52_3 = all_52_27)
% 178.34/28.46    (66)   ~ (all_52_3 = all_4_2)
% 178.34/28.46    (67)  op(e0, e3) = all_52_25
% 178.34/28.46    (68)   ~ (all_52_9 = all_10_2)
% 178.34/28.46    (69)   ~ (all_52_13 = all_14_2)
% 178.34/28.46    (70)  op(e1, all_14_2) = all_14_0
% 178.34/28.46    (71)   ~ (e3 = e0)
% 178.34/28.46    (72)  all_40_0 = all_4_0
% 178.34/28.46    (73)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.46    (74)   ~ (all_52_9 = all_52_13)
% 178.34/28.46    (75)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.46    (76)   ~ (all_52_15 = all_52_23)
% 178.34/28.46    (77)   ~ (all_52_5 = all_52_29)
% 178.34/28.46    (78)  all_56_12 = all_52_25
% 178.34/28.46    (79)  all_58_13 = all_52_27
% 178.34/28.46    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.46    (81)  all_56_5 = all_10_2
% 178.34/28.46    (82)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.46    (83)   ~ (all_52_9 = all_52_17)
% 178.34/28.46    (84)   ~ (all_14_0 = e2)
% 178.34/28.46    (85)  all_58_6 = all_52_17
% 178.34/28.46    (86)  op(e2, all_52_19) = e2
% 178.34/28.46    (87)  op(e3, all_52_17) = e3
% 178.34/28.46    (88)   ~ (e1 = e0)
% 178.34/28.46    (89)  all_56_0 = all_4_2
% 178.34/28.46    (90)  all_58_11 = all_52_23
% 178.34/28.46    (91)   ~ (all_52_3 = all_52_19)
% 178.34/28.46    (92)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.34/28.46    (93)   ~ (all_52_7 = all_52_15)
% 178.34/28.46    (94)   ~ (all_52_29 = all_14_2)
% 178.34/28.46    (95)   ~ (all_4_0 = e1)
% 178.34/28.46    (96)   ~ (all_52_19 = all_10_2)
% 178.34/28.46    (97)   ~ (all_52_23 = all_6_2)
% 178.34/28.46    (98)  op(e1, all_4_2) = all_4_0
% 178.34/28.46    (99)  all_58_2 = all_52_9
% 178.34/28.46    (100)  op(e3, e1) = all_52_5
% 178.34/28.46    (101)   ~ (all_52_25 = all_6_2)
% 178.34/28.46    (102)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.34/28.46    (103)  op(e1, e3) = all_52_17
% 178.34/28.46    (104)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.46    (105)   ~ (all_52_25 = all_4_2)
% 178.34/28.46    (106)  op(e3, e0) = all_52_7
% 178.34/28.46    (107)  op(e3, e3) = all_4_2
% 178.34/28.46    (108)   ~ (all_10_1 = e3)
% 178.34/28.46    (109)  all_56_8 = all_52_17
% 178.34/28.46    (110)   ~ (all_52_17 = all_4_2)
% 178.34/28.46    (111)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.46             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.46    (112)   ~ (all_52_25 = all_52_27)
% 178.34/28.46    (113)   ~ (all_52_27 = all_6_2)
% 178.34/28.46    (114)   ~ (all_52_7 = all_6_2)
% 178.34/28.46    (115)  op(e0, all_52_23) = e0
% 178.34/28.46    (116)   ~ (all_52_15 = all_10_2)
% 178.34/28.46    (117)   ~ (all_52_19 = all_52_27)
% 178.34/28.46    (118)  all_56_7 = all_52_15
% 178.34/28.46    (119)  op(e1, all_14_2) = e1
% 178.34/28.46    (120)   ~ (all_52_7 = all_52_23)
% 178.34/28.46    (121)   ~ (all_52_13 = all_10_2)
% 178.34/28.46    (122)   ~ (all_52_17 = all_52_19)
% 178.34/28.46    (123)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.46    (124)  all_58_9 = all_52_7
% 178.34/28.46    (125)   ~ (e2 = e0)
% 178.34/28.46    (126)  all_58_12 = all_52_25
% 178.34/28.46    (127)  op(e3, all_4_2) = e1
% 178.34/28.46    (128)  all_56_6 = all_52_13
% 178.34/28.46    (129)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.46    (130)   ~ (all_52_9 = all_52_15)
% 178.34/28.46    (131)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.46    (132)   ~ (e3 = e2)
% 178.34/28.46    (133)   ~ (all_52_19 = all_14_2)
% 178.34/28.46    (134)  op(e2, e3) = all_52_9
% 178.34/28.46  
% 178.34/28.46  Begin of proof
% 178.34/28.46  | 
% 178.34/28.46  | GROUND_INST: instantiating (111) with e1, all_14_0, all_14_2, e1, simplifying
% 178.34/28.46  |              with (70), (119) gives:
% 178.34/28.46  |   (135)  all_14_0 = e1
% 178.34/28.46  | 
% 178.34/28.46  | REDUCE: (59), (135) imply:
% 178.34/28.46  |   (136)   ~ (e3 = e1)
% 178.34/28.46  | 
% 178.34/28.46  | SIMP: (136) implies:
% 178.34/28.46  |   (137)   ~ (e3 = e1)
% 178.34/28.46  | 
% 178.34/28.46  | REDUCE: (84), (135) imply:
% 178.34/28.46  |   (138)   ~ (e2 = e1)
% 178.34/28.46  | 
% 178.34/28.46  | SIMP: (138) implies:
% 178.34/28.46  |   (139)   ~ (e2 = e1)
% 178.34/28.46  | 
% 178.34/28.46  | BETA: splitting (40) gives:
% 178.34/28.46  | 
% 178.34/28.46  | Case 1:
% 178.34/28.46  | | 
% 178.34/28.46  | |   (140)  all_56_15 = e3
% 178.34/28.46  | | 
% 178.34/28.46  | | COMBINE_EQS: (21), (140) imply:
% 178.34/28.46  | |   (141)  all_6_2 = e3
% 178.34/28.46  | | 
% 178.34/28.46  | | REF_CLOSE: (25), (32), (36), (41), (44), (47), (55), (58), (64), (83), (85),
% 178.34/28.46  | |            (86), (87), (90), (97), (99), (100), (101), (103), (107), (110),
% 178.34/28.46  | |            (111), (119), (126), (127), (132), (134), (137), (141) are
% 178.34/28.46  | |            inconsistent by sub-proof #608.
% 178.34/28.46  | | 
% 178.34/28.46  | Case 2:
% 178.34/28.46  | | 
% 178.34/28.46  | |   (142)   ~ (all_56_15 = e3)
% 178.34/28.46  | |   (143)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.46  | | 
% 178.34/28.46  | | REDUCE: (21), (142) imply:
% 178.34/28.46  | |   (144)   ~ (all_6_2 = e3)
% 178.34/28.46  | | 
% 178.34/28.46  | | BETA: splitting (57) gives:
% 178.34/28.46  | | 
% 178.34/28.46  | | Case 1:
% 178.34/28.46  | | | 
% 178.34/28.46  | | |   (145)  all_58_12 = e3
% 178.34/28.46  | | | 
% 178.34/28.46  | | | COMBINE_EQS: (126), (145) imply:
% 178.34/28.46  | | |   (146)  all_52_25 = e3
% 178.34/28.46  | | | 
% 178.34/28.46  | | | SIMP: (146) implies:
% 178.34/28.46  | | |   (147)  all_52_25 = e3
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REDUCE: (112), (147) imply:
% 178.34/28.46  | | |   (148)   ~ (all_52_27 = e3)
% 178.34/28.46  | | | 
% 178.34/28.46  | | | SIMP: (148) implies:
% 178.34/28.46  | | |   (149)   ~ (all_52_27 = e3)
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REDUCE: (101), (147) imply:
% 178.34/28.46  | | |   (150)   ~ (all_6_2 = e3)
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 178.34/28.46  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.34/28.46  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 178.34/28.46  | | |            (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 178.34/28.46  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 178.34/28.46  | | |            (55), (56), (57), (58), (61), (62), (63), (64), (66), (67),
% 178.34/28.46  | | |            (68), (69), (71), (73), (74), (75), (76), (77), (78), (79),
% 178.34/28.46  | | |            (80), (81), (82), (83), (85), (86), (87), (88), (89), (90),
% 178.34/28.46  | | |            (91), (92), (93), (94), (95), (96), (97), (99), (100), (101),
% 178.34/28.46  | | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 178.34/28.46  | | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 178.34/28.46  | | |            (120), (121), (122), (123), (124), (125), (126), (128), (129),
% 178.34/28.46  | | |            (130), (131), (132), (133), (134), (137), (139), (143), (144),
% 178.34/28.46  | | |            (149) are inconsistent by sub-proof #669.
% 178.34/28.46  | | | 
% 178.34/28.46  | | Case 2:
% 178.34/28.46  | | | 
% 178.34/28.46  | | |   (151)   ~ (all_58_12 = e3)
% 178.34/28.46  | | |   (152)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 178.34/28.46  | | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 178.34/28.46  | | |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 178.34/28.46  | | |            (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 178.34/28.46  | | |            (47), (48), (49), (50), (53), (54), (55), (58), (60), (61),
% 178.34/28.46  | | |            (62), (63), (64), (65), (66), (67), (68), (72), (74), (75),
% 178.34/28.46  | | |            (76), (77), (78), (79), (80), (83), (85), (86), (87), (89),
% 178.34/28.46  | | |            (90), (91), (92), (94), (95), (96), (97), (98), (99), (100),
% 178.34/28.46  | | |            (101), (103), (104), (105), (106), (107), (109), (110), (111),
% 178.34/28.46  | | |            (112), (113), (114), (115), (117), (118), (119), (120), (121),
% 178.34/28.46  | | |            (122), (123), (124), (126), (127), (129), (131), (132), (133),
% 178.34/28.46  | | |            (134), (137), (143), (144), (151), (152) are inconsistent by
% 178.34/28.46  | | |            sub-proof #606.
% 178.34/28.46  | | | 
% 178.34/28.46  | | End of split
% 178.34/28.46  | | 
% 178.34/28.46  | End of split
% 178.34/28.46  | 
% 178.34/28.46  End of proof
% 178.34/28.46  
% 178.34/28.46  Sub-proof #606 shows that the following formulas are inconsistent:
% 178.34/28.46  ----------------------------------------------------------------
% 178.34/28.46    (1)   ~ (all_52_23 = all_14_2)
% 178.34/28.46    (2)   ~ (all_52_5 = all_52_13)
% 178.34/28.46    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.34/28.46    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.46    (5)   ~ (all_52_17 = all_52_23)
% 178.34/28.46    (6)  all_40_2 = all_4_2
% 178.34/28.46    (7)   ~ (all_52_13 = all_52_29)
% 178.34/28.46    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.46    (9)  op(e3, e2) = all_52_3
% 178.34/28.46    (10)   ~ (all_52_9 = all_52_25)
% 178.34/28.46    (11)  op(e3, all_52_25) = all_52_24
% 178.34/28.46    (12)   ~ (all_52_19 = all_52_23)
% 178.34/28.46    (13)  op(e1, e2) = all_52_19
% 178.34/28.46    (14)   ~ (all_6_2 = e3)
% 178.34/28.46    (15)  op(e3, all_52_9) = all_52_8
% 178.34/28.46    (16)   ~ (all_52_3 = all_10_2)
% 178.34/28.46    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.34/28.46    (18)  all_58_5 = all_52_13
% 178.34/28.46    (19)   ~ (all_52_25 = all_52_29)
% 178.34/28.46    (20)  all_56_15 = all_6_2
% 178.34/28.46    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.46    (22)  op(e2, e0) = all_52_15
% 178.34/28.46    (23)  all_58_3 = all_10_2
% 178.34/28.46    (24)  all_56_9 = all_52_19
% 178.34/28.46    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.46    (26)  all_58_15 = all_6_2
% 178.34/28.46    (27)   ~ (all_52_9 = all_4_2)
% 178.34/28.46    (28)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.46    (29)  all_58_10 = all_52_15
% 178.34/28.46    (30)   ~ (all_52_5 = all_4_2)
% 178.34/28.46    (31)  all_58_7 = all_52_19
% 178.34/28.46    (32)   ~ (all_52_17 = all_52_25)
% 178.34/28.46    (33)   ~ (all_4_0 = e2)
% 178.34/28.46    (34)  all_58_4 = all_52_5
% 178.34/28.46    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.46    (36)   ~ (e3 = e1)
% 178.34/28.46    (37)   ~ (all_52_27 = all_52_29)
% 178.34/28.46    (38)   ~ (all_52_17 = all_14_2)
% 178.34/28.46    (39)  op(e3, all_4_2) = all_4_1
% 178.34/28.46    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.46    (41)   ~ (all_52_7 = all_4_2)
% 178.34/28.46    (42)  all_58_1 = all_52_3
% 178.34/28.46    (43)  all_58_0 = all_4_2
% 178.34/28.46    (44)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.46    (45)  op(e1, all_52_29) = all_52_28
% 178.34/28.46    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.46    (47)   ~ (all_4_1 = e2)
% 178.34/28.46    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.46    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.46    (50)  all_58_14 = all_52_29
% 178.34/28.46    (51)   ~ (all_52_3 = all_52_5)
% 178.34/28.46    (52)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.46    (53)  all_58_8 = all_14_2
% 178.34/28.46    (54)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.46    (55)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.34/28.46    (56)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.46    (57)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.34/28.46    (58)   ~ (all_52_5 = all_14_2)
% 178.34/28.46    (59)   ~ (all_52_3 = all_52_27)
% 178.34/28.46    (60)   ~ (all_52_3 = all_4_2)
% 178.34/28.46    (61)  op(e0, e3) = all_52_25
% 178.34/28.46    (62)   ~ (all_52_9 = all_10_2)
% 178.34/28.46    (63)  all_40_0 = all_4_0
% 178.34/28.46    (64)   ~ (all_52_9 = all_52_13)
% 178.34/28.46    (65)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.46    (66)   ~ (all_52_15 = all_52_23)
% 178.34/28.46    (67)   ~ (all_52_5 = all_52_29)
% 178.34/28.46    (68)  all_56_12 = all_52_25
% 178.34/28.46    (69)  all_58_13 = all_52_27
% 178.34/28.46    (70)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.46    (71)   ~ (all_58_12 = e3)
% 178.34/28.46    (72)   ~ (all_52_9 = all_52_17)
% 178.34/28.46    (73)  all_58_6 = all_52_17
% 178.34/28.46    (74)  op(e2, all_52_19) = e2
% 178.34/28.46    (75)  op(e3, all_52_17) = e3
% 178.34/28.46    (76)  all_56_0 = all_4_2
% 178.34/28.46    (77)  all_58_11 = all_52_23
% 178.34/28.46    (78)   ~ (all_52_3 = all_52_19)
% 178.34/28.46    (79)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.34/28.46    (80)   ~ (all_52_29 = all_14_2)
% 178.34/28.46    (81)   ~ (all_4_0 = e1)
% 178.34/28.46    (82)   ~ (all_52_19 = all_10_2)
% 178.34/28.46    (83)   ~ (all_52_23 = all_6_2)
% 178.34/28.46    (84)  op(e1, all_4_2) = all_4_0
% 178.34/28.46    (85)  all_58_2 = all_52_9
% 178.34/28.46    (86)  op(e3, e1) = all_52_5
% 178.34/28.46    (87)   ~ (all_52_25 = all_6_2)
% 178.34/28.46    (88)  op(e1, e3) = all_52_17
% 178.34/28.46    (89)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.46    (90)   ~ (all_52_25 = all_4_2)
% 178.34/28.46    (91)  op(e3, e0) = all_52_7
% 178.34/28.46    (92)  op(e3, e3) = all_4_2
% 178.34/28.46    (93)  all_56_8 = all_52_17
% 178.34/28.46    (94)   ~ (all_52_17 = all_4_2)
% 178.34/28.46    (95)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.46    (96)   ~ (all_52_25 = all_52_27)
% 178.34/28.46    (97)   ~ (all_52_27 = all_6_2)
% 178.34/28.46    (98)   ~ (all_52_7 = all_6_2)
% 178.34/28.46    (99)  op(e0, all_52_23) = e0
% 178.34/28.46    (100)   ~ (all_52_19 = all_52_27)
% 178.34/28.46    (101)  all_56_7 = all_52_15
% 178.34/28.46    (102)  op(e1, all_14_2) = e1
% 178.34/28.46    (103)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.46    (104)   ~ (all_52_7 = all_52_23)
% 178.34/28.46    (105)   ~ (all_52_13 = all_10_2)
% 178.34/28.46    (106)   ~ (all_52_17 = all_52_19)
% 178.34/28.46    (107)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.46    (108)  all_58_9 = all_52_7
% 178.34/28.46    (109)  all_58_12 = all_52_25
% 178.34/28.46    (110)  op(e3, all_4_2) = e1
% 178.34/28.46    (111)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.46    (112)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.46    (113)   ~ (e3 = e2)
% 178.34/28.46    (114)   ~ (all_52_19 = all_14_2)
% 178.34/28.46    (115)  op(e2, e3) = all_52_9
% 178.34/28.46  
% 178.34/28.46  Begin of proof
% 178.34/28.46  | 
% 178.34/28.46  | REDUCE: (71), (109) imply:
% 178.34/28.46  |   (116)   ~ (all_52_25 = e3)
% 178.34/28.46  | 
% 178.34/28.46  | BETA: splitting (89) gives:
% 178.34/28.46  | 
% 178.34/28.46  | Case 1:
% 178.34/28.46  | | 
% 178.34/28.46  | |   (117)  all_56_7 = e3
% 178.34/28.46  | | 
% 178.34/28.46  | | COMBINE_EQS: (101), (117) imply:
% 178.34/28.46  | |   (118)  all_52_15 = e3
% 178.34/28.46  | | 
% 178.34/28.46  | | SIMP: (118) implies:
% 178.34/28.46  | |   (119)  all_52_15 = e3
% 178.34/28.46  | | 
% 178.34/28.46  | | REDUCE: (66), (119) imply:
% 178.34/28.46  | |   (120)   ~ (all_52_23 = e3)
% 178.34/28.46  | | 
% 178.34/28.46  | | SIMP: (120) implies:
% 178.34/28.46  | |   (121)   ~ (all_52_23 = e3)
% 178.34/28.46  | | 
% 178.34/28.46  | | REF_CLOSE: (24), (31), (35), (36), (40), (43), (46), (52), (53), (58), (72),
% 178.34/28.46  | |            (73), (74), (75), (77), (85), (86), (88), (92), (94), (95),
% 178.34/28.46  | |            (102), (109), (110), (113), (115), (116), (121) are inconsistent
% 178.34/28.46  | |            by sub-proof #629.
% 178.34/28.46  | | 
% 178.34/28.46  | Case 2:
% 178.34/28.46  | | 
% 178.34/28.46  | |   (122)   ~ (all_56_7 = e3)
% 178.34/28.46  | | 
% 178.34/28.46  | | REDUCE: (101), (122) imply:
% 178.34/28.46  | |   (123)   ~ (all_52_15 = e3)
% 178.34/28.46  | | 
% 178.34/28.46  | | BETA: splitting (107) gives:
% 178.34/28.46  | | 
% 178.34/28.46  | | Case 1:
% 178.34/28.46  | | | 
% 178.34/28.46  | | |   (124)  all_58_9 = e3
% 178.34/28.46  | | | 
% 178.34/28.46  | | | COMBINE_EQS: (108), (124) imply:
% 178.34/28.46  | | |   (125)  all_52_7 = e3
% 178.34/28.46  | | | 
% 178.34/28.46  | | | REF_CLOSE: (24), (31), (35), (40), (41), (43), (46), (52), (53), (58),
% 178.34/28.46  | | |            (72), (73), (74), (75), (77), (85), (86), (88), (92), (94),
% 178.34/28.46  | | |            (95), (102), (104), (109), (113), (115), (116), (125) are
% 178.34/28.46  | | |            inconsistent by sub-proof #943.
% 178.34/28.46  | | | 
% 178.34/28.46  | | Case 2:
% 178.34/28.46  | | | 
% 178.34/28.46  | | |   (126)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.46  | | | 
% 178.34/28.46  | | | BETA: splitting (126) gives:
% 178.34/28.46  | | | 
% 178.34/28.46  | | | Case 1:
% 178.34/28.46  | | | | 
% 178.34/28.46  | | | |   (127)  all_58_10 = e3
% 178.34/28.46  | | | | 
% 178.34/28.46  | | | | REF_CLOSE: (29), (123), (127) are inconsistent by sub-proof #1018.
% 178.34/28.46  | | | | 
% 178.34/28.46  | | | Case 2:
% 178.34/28.46  | | | | 
% 178.34/28.46  | | | |   (128)  all_58_11 = e3 | all_58_15 = e3
% 178.34/28.46  | | | | 
% 178.34/28.46  | | | | BETA: splitting (128) gives:
% 178.34/28.46  | | | | 
% 178.34/28.46  | | | | Case 1:
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | |   (129)  all_58_11 = e3
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | COMBINE_EQS: (77), (129) imply:
% 178.34/28.46  | | | | |   (130)  all_52_23 = e3
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | SIMP: (130) implies:
% 178.34/28.46  | | | | |   (131)  all_52_23 = e3
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | REDUCE: (12), (131) imply:
% 178.34/28.46  | | | | |   (132)   ~ (all_52_19 = e3)
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | REDUCE: (83), (131) imply:
% 178.34/28.46  | | | | |   (133)   ~ (all_6_2 = e3)
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | REDUCE: (99), (131) imply:
% 178.34/28.46  | | | | |   (134)  op(e0, e3) = e0
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | GROUND_INST: instantiating (95) with all_52_25, e0, e3, e0,
% 178.34/28.46  | | | | |              simplifying with (61), (134) gives:
% 178.34/28.46  | | | | |   (135)  all_52_25 = e0
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | REDUCE: (87), (135) imply:
% 178.34/28.46  | | | | |   (136)   ~ (all_6_2 = e0)
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | SIMP: (136) implies:
% 178.34/28.46  | | | | |   (137)   ~ (all_6_2 = e0)
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | BETA: splitting (49) gives:
% 178.34/28.46  | | | | | 
% 178.34/28.46  | | | | | Case 1:
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | |   (138)  all_58_1 = e3
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | | COMBINE_EQS: (42), (138) imply:
% 178.34/28.46  | | | | | |   (139)  all_52_3 = e3
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | | REDUCE: (59), (139) imply:
% 178.34/28.46  | | | | | |   (140)   ~ (all_52_27 = e3)
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | | SIMP: (140) implies:
% 178.34/28.46  | | | | | |   (141)   ~ (all_52_27 = e3)
% 178.34/28.46  | | | | | | 
% 178.34/28.46  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 178.34/28.46  | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 178.34/28.46  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 178.34/28.46  | | | | | |            (31), (32), (33), (34), (35), (37), (38), (39), (40),
% 178.34/28.46  | | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 178.34/28.46  | | | | | |            (51), (52), (53), (55), (56), (57), (58), (60), (61),
% 178.34/28.46  | | | | | |            (62), (64), (65), (67), (68), (69), (72), (73), (74),
% 178.34/28.47  | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 178.34/28.47  | | | | | |            (85), (86), (87), (88), (90), (91), (92), (93), (94),
% 178.34/28.47  | | | | | |            (95), (96), (97), (98), (99), (100), (102), (103), (105),
% 178.34/28.47  | | | | | |            (106), (108), (109), (113), (114), (115), (137), (141)
% 178.34/28.47  | | | | | |            are inconsistent by sub-proof #670.
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | Case 2:
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | |   (142)   ~ (all_58_1 = e3)
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | REDUCE: (42), (142) imply:
% 178.34/28.47  | | | | | |   (143)   ~ (all_52_3 = e3)
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | REF_CLOSE: (6), (9), (13), (14), (24), (25), (26), (29), (30), (31),
% 178.34/28.47  | | | | | |            (33), (34), (35), (36), (40), (41), (42), (43), (46),
% 178.34/28.47  | | | | | |            (52), (53), (54), (58), (61), (63), (66), (70), (72),
% 178.34/28.47  | | | | | |            (73), (74), (75), (76), (77), (78), (84), (85), (86),
% 178.34/28.47  | | | | | |            (88), (89), (90), (92), (94), (95), (99), (101), (102),
% 178.34/28.47  | | | | | |            (104), (107), (108), (109), (110), (111), (112), (113),
% 178.34/28.47  | | | | | |            (115), (116), (132), (143) are inconsistent by sub-proof
% 178.34/28.47  | | | | | |            #607.
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | End of split
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | Case 2:
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | |   (144)  all_58_15 = e3
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | | COMBINE_EQS: (26), (144) imply:
% 178.34/28.47  | | | | |   (145)  all_6_2 = e3
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | | REDUCE: (14), (145) imply:
% 178.34/28.47  | | | | |   (146)  $false
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | | CLOSE: (146) is inconsistent.
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | End of split
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | End of split
% 178.34/28.47  | | | 
% 178.34/28.47  | | End of split
% 178.34/28.47  | | 
% 178.34/28.47  | End of split
% 178.34/28.47  | 
% 178.34/28.47  End of proof
% 178.34/28.47  
% 178.34/28.47  Sub-proof #607 shows that the following formulas are inconsistent:
% 178.34/28.47  ----------------------------------------------------------------
% 178.34/28.47    (1)   ~ (all_52_25 = e3)
% 178.34/28.47    (2)  all_40_2 = all_4_2
% 178.34/28.47    (3)  op(e3, e2) = all_52_3
% 178.34/28.47    (4)  op(e1, e2) = all_52_19
% 178.34/28.47    (5)   ~ (all_6_2 = e3)
% 178.34/28.47    (6)  all_56_9 = all_52_19
% 178.34/28.47    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.47    (8)  all_58_15 = all_6_2
% 178.34/28.47    (9)  all_58_10 = all_52_15
% 178.34/28.47    (10)   ~ (all_52_5 = all_4_2)
% 178.34/28.47    (11)  all_58_7 = all_52_19
% 178.34/28.47    (12)   ~ (all_4_0 = e2)
% 178.34/28.47    (13)  all_58_4 = all_52_5
% 178.34/28.47    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.47    (15)   ~ (e3 = e1)
% 178.34/28.47    (16)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.47    (17)   ~ (all_52_7 = all_4_2)
% 178.34/28.47    (18)  all_58_1 = all_52_3
% 178.34/28.47    (19)  all_58_0 = all_4_2
% 178.34/28.47    (20)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.47    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.47    (22)  all_58_8 = all_14_2
% 178.34/28.47    (23)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.47    (24)   ~ (all_52_5 = all_14_2)
% 178.34/28.47    (25)  op(e0, e3) = all_52_25
% 178.34/28.47    (26)  all_40_0 = all_4_0
% 178.34/28.47    (27)   ~ (all_52_15 = all_52_23)
% 178.34/28.47    (28)   ~ (all_52_3 = e3)
% 178.34/28.47    (29)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.47    (30)   ~ (all_52_9 = all_52_17)
% 178.34/28.47    (31)  all_58_6 = all_52_17
% 178.34/28.47    (32)  op(e2, all_52_19) = e2
% 178.34/28.47    (33)  op(e3, all_52_17) = e3
% 178.34/28.47    (34)  all_56_0 = all_4_2
% 178.34/28.47    (35)  all_58_11 = all_52_23
% 178.34/28.47    (36)   ~ (all_52_3 = all_52_19)
% 178.34/28.47    (37)  op(e1, all_4_2) = all_4_0
% 178.34/28.47    (38)  all_58_2 = all_52_9
% 178.34/28.47    (39)  op(e3, e1) = all_52_5
% 178.34/28.47    (40)   ~ (all_52_19 = e3)
% 178.34/28.47    (41)  op(e1, e3) = all_52_17
% 178.34/28.47    (42)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.47    (43)   ~ (all_52_25 = all_4_2)
% 178.34/28.47    (44)  op(e3, e3) = all_4_2
% 178.34/28.47    (45)   ~ (all_52_17 = all_4_2)
% 178.34/28.47    (46)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.47    (47)  op(e0, all_52_23) = e0
% 178.34/28.47    (48)  all_56_7 = all_52_15
% 178.34/28.47    (49)  op(e1, all_14_2) = e1
% 178.34/28.47    (50)   ~ (all_52_7 = all_52_23)
% 178.34/28.47    (51)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.47    (52)  all_58_9 = all_52_7
% 178.34/28.47    (53)  all_58_12 = all_52_25
% 178.34/28.47    (54)  op(e3, all_4_2) = e1
% 178.34/28.47    (55)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.47    (56)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.47    (57)   ~ (e3 = e2)
% 178.34/28.47    (58)  op(e2, e3) = all_52_9
% 178.34/28.47  
% 178.34/28.47  Begin of proof
% 178.34/28.47  | 
% 178.34/28.47  | BETA: splitting (20) gives:
% 178.34/28.47  | 
% 178.34/28.47  | Case 1:
% 178.34/28.47  | | 
% 178.34/28.47  | |   (59)  all_56_9 = e3
% 178.34/28.47  | | 
% 178.34/28.47  | | REF_CLOSE: (6), (40), (59) are inconsistent by sub-proof #700.
% 178.34/28.47  | | 
% 178.34/28.47  | Case 2:
% 178.34/28.47  | | 
% 178.34/28.47  | |   (60)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.47  | | 
% 178.34/28.47  | | BETA: splitting (42) gives:
% 178.34/28.47  | | 
% 178.34/28.47  | | Case 1:
% 178.34/28.47  | | | 
% 178.34/28.47  | | |   (61)  all_56_7 = e3
% 178.34/28.47  | | | 
% 178.34/28.47  | | | COMBINE_EQS: (48), (61) imply:
% 178.34/28.47  | | |   (62)  all_52_15 = e3
% 178.34/28.47  | | | 
% 178.34/28.47  | | | SIMP: (62) implies:
% 178.34/28.47  | | |   (63)  all_52_15 = e3
% 178.34/28.47  | | | 
% 178.34/28.47  | | | REDUCE: (27), (63) imply:
% 178.34/28.47  | | |   (64)   ~ (all_52_23 = e3)
% 178.34/28.47  | | | 
% 178.34/28.47  | | | SIMP: (64) implies:
% 178.34/28.47  | | |   (65)   ~ (all_52_23 = e3)
% 178.34/28.47  | | | 
% 178.34/28.47  | | | REF_CLOSE: (1), (6), (11), (14), (15), (16), (19), (20), (21), (22), (24),
% 178.34/28.47  | | |            (30), (31), (32), (33), (35), (38), (39), (41), (44), (45),
% 178.34/28.47  | | |            (46), (49), (53), (54), (57), (58), (65) are inconsistent by
% 178.34/28.47  | | |            sub-proof #629.
% 178.34/28.47  | | | 
% 178.34/28.47  | | Case 2:
% 178.34/28.47  | | | 
% 178.34/28.47  | | |   (66)   ~ (all_56_7 = e3)
% 178.34/28.47  | | | 
% 178.34/28.47  | | | REDUCE: (48), (66) imply:
% 178.34/28.47  | | |   (67)   ~ (all_52_15 = e3)
% 178.34/28.47  | | | 
% 178.34/28.47  | | | BETA: splitting (51) gives:
% 178.34/28.47  | | | 
% 178.34/28.47  | | | Case 1:
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | |   (68)  all_58_9 = e3
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | | COMBINE_EQS: (52), (68) imply:
% 178.34/28.47  | | | |   (69)  all_52_7 = e3
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | | SIMP: (69) implies:
% 178.34/28.47  | | | |   (70)  all_52_7 = e3
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | | REF_CLOSE: (1), (6), (11), (14), (16), (17), (19), (20), (21), (22),
% 178.34/28.47  | | | |            (24), (30), (31), (32), (33), (35), (38), (39), (41), (44),
% 178.34/28.47  | | | |            (45), (46), (49), (50), (53), (57), (58), (70) are
% 178.34/28.47  | | | |            inconsistent by sub-proof #943.
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | Case 2:
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | |   (71)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | | BETA: splitting (71) gives:
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | | Case 1:
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | |   (72)  all_58_10 = e3
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | | REF_CLOSE: (9), (67), (72) are inconsistent by sub-proof #1018.
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | Case 2:
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | |   (73)  all_58_11 = e3 | all_58_15 = e3
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | | BETA: splitting (73) gives:
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | | Case 1:
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | |   (74)  all_58_11 = e3
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | COMBINE_EQS: (35), (74) imply:
% 178.34/28.47  | | | | | |   (75)  all_52_23 = e3
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | SIMP: (75) implies:
% 178.34/28.47  | | | | | |   (76)  all_52_23 = e3
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | REDUCE: (50), (76) imply:
% 178.34/28.47  | | | | | |   (77)   ~ (all_52_7 = e3)
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | REDUCE: (47), (76) imply:
% 178.34/28.47  | | | | | |   (78)  op(e0, e3) = e0
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | GROUND_INST: instantiating (46) with all_52_25, e0, e3, e0,
% 178.34/28.47  | | | | | |              simplifying with (25), (78) gives:
% 178.34/28.47  | | | | | |   (79)  all_52_25 = e0
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | BETA: splitting (21) gives:
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | Case 1:
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | |   (80)  all_58_0 = e3
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | | COMBINE_EQS: (19), (80) imply:
% 178.34/28.47  | | | | | | |   (81)  all_4_2 = e3
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | | REF_CLOSE: (15), (44), (46), (54), (81) are inconsistent by
% 178.34/28.47  | | | | | | |            sub-proof #630.
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | Case 2:
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | |   (82)   ~ (all_58_0 = e3)
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | | REDUCE: (19), (82) imply:
% 178.34/28.47  | | | | | | |   (83)   ~ (all_4_2 = e3)
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | | BETA: splitting (55) gives:
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | | Case 1:
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | |   (84)  all_58_0 = e3
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | | COMBINE_EQS: (19), (84) imply:
% 178.34/28.47  | | | | | | | |   (85)  all_4_2 = e3
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | | REDUCE: (83), (85) imply:
% 178.34/28.47  | | | | | | | |   (86)  $false
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | | CLOSE: (86) is inconsistent.
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | Case 2:
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | |   (87)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | | BETA: splitting (56) gives:
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | | Case 1:
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | |   (88)  all_58_4 = e3
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | | COMBINE_EQS: (13), (88) imply:
% 178.34/28.47  | | | | | | | | |   (89)  all_52_5 = e3
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | | SIMP: (89) implies:
% 178.34/28.47  | | | | | | | | |   (90)  all_52_5 = e3
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | | REDUCE: (10), (90) imply:
% 178.34/28.47  | | | | | | | | |   (91)   ~ (all_4_2 = e3)
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | | REDUCE: (39), (90) imply:
% 178.34/28.47  | | | | | | | | |   (92)  op(e3, e1) = e3
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (12), (19), (23), (25),
% 178.34/28.47  | | | | | | | | |            (26), (29), (34), (36), (37), (43), (46), (54),
% 178.34/28.47  | | | | | | | | |            (60), (78), (83), (92) are inconsistent by
% 178.34/28.47  | | | | | | | | |            sub-proof #611.
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | Case 2:
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | |   (93)   ~ (all_58_4 = e3)
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | | REDUCE: (13), (93) imply:
% 178.34/28.47  | | | | | | | | |   (94)   ~ (all_52_5 = e3)
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | | REF_CLOSE: (13), (18), (28), (52), (77), (87), (94) are
% 178.34/28.47  | | | | | | | | |            inconsistent by sub-proof #728.
% 178.34/28.47  | | | | | | | | | 
% 178.34/28.47  | | | | | | | | End of split
% 178.34/28.47  | | | | | | | | 
% 178.34/28.47  | | | | | | | End of split
% 178.34/28.47  | | | | | | | 
% 178.34/28.47  | | | | | | End of split
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | Case 2:
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | |   (95)  all_58_15 = e3
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | COMBINE_EQS: (8), (95) imply:
% 178.34/28.47  | | | | | |   (96)  all_6_2 = e3
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | REDUCE: (5), (96) imply:
% 178.34/28.47  | | | | | |   (97)  $false
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | | CLOSE: (97) is inconsistent.
% 178.34/28.47  | | | | | | 
% 178.34/28.47  | | | | | End of split
% 178.34/28.47  | | | | | 
% 178.34/28.47  | | | | End of split
% 178.34/28.47  | | | | 
% 178.34/28.47  | | | End of split
% 178.34/28.47  | | | 
% 178.34/28.47  | | End of split
% 178.34/28.47  | | 
% 178.34/28.47  | End of split
% 178.34/28.47  | 
% 178.34/28.47  End of proof
% 178.34/28.47  
% 178.34/28.47  Sub-proof #608 shows that the following formulas are inconsistent:
% 178.34/28.47  ----------------------------------------------------------------
% 178.34/28.47    (1)  all_6_2 = e3
% 178.34/28.47    (2)  all_56_9 = all_52_19
% 178.34/28.47    (3)  all_58_7 = all_52_19
% 178.34/28.47    (4)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.47    (5)   ~ (e3 = e1)
% 178.34/28.47    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.47    (7)  all_58_0 = all_4_2
% 178.34/28.47    (8)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.47    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.47    (10)  all_58_8 = all_14_2
% 178.34/28.47    (11)   ~ (all_52_5 = all_14_2)
% 178.34/28.47    (12)   ~ (all_52_9 = all_52_17)
% 178.34/28.47    (13)  all_58_6 = all_52_17
% 178.34/28.47    (14)  op(e2, all_52_19) = e2
% 178.34/28.47    (15)  op(e3, all_52_17) = e3
% 178.34/28.47    (16)  all_58_11 = all_52_23
% 178.34/28.47    (17)   ~ (all_52_23 = all_6_2)
% 178.34/28.47    (18)  all_58_2 = all_52_9
% 178.34/28.47    (19)  op(e3, e1) = all_52_5
% 178.34/28.47    (20)   ~ (all_52_25 = all_6_2)
% 178.34/28.47    (21)  op(e1, e3) = all_52_17
% 178.34/28.47    (22)  op(e3, e3) = all_4_2
% 178.34/28.47    (23)   ~ (all_52_17 = all_4_2)
% 178.34/28.47    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.47    (25)  op(e1, all_14_2) = e1
% 178.34/28.47    (26)  all_58_12 = all_52_25
% 178.34/28.47    (27)  op(e3, all_4_2) = e1
% 178.34/28.47    (28)   ~ (e3 = e2)
% 178.34/28.47    (29)  op(e2, e3) = all_52_9
% 178.34/28.47  
% 178.34/28.47  Begin of proof
% 178.34/28.47  | 
% 178.34/28.47  | REDUCE: (1), (17) imply:
% 178.34/28.47  |   (30)   ~ (all_52_23 = e3)
% 178.34/28.47  | 
% 178.34/28.47  | REDUCE: (1), (20) imply:
% 178.34/28.47  |   (31)   ~ (all_52_25 = e3)
% 178.34/28.47  | 
% 178.34/28.47  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.34/28.47  |            (14), (15), (16), (18), (19), (21), (22), (23), (24), (25), (26),
% 178.34/28.47  |            (27), (28), (29), (30), (31) are inconsistent by sub-proof #629.
% 178.34/28.47  | 
% 178.34/28.47  End of proof
% 178.34/28.47  
% 178.34/28.47  Sub-proof #609 shows that the following formulas are inconsistent:
% 178.34/28.47  ----------------------------------------------------------------
% 178.34/28.47    (1)   ~ (all_52_23 = all_14_2)
% 178.34/28.47    (2)   ~ (all_52_5 = all_52_13)
% 178.34/28.47    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.47    (4)   ~ (all_52_27 = all_10_2)
% 178.34/28.47    (5)   ~ (all_52_17 = all_52_23)
% 178.34/28.47    (6)  all_40_2 = all_4_2
% 178.34/28.47    (7)   ~ (all_52_13 = all_52_29)
% 178.34/28.47    (8)  all_56_3 = all_52_7
% 178.34/28.47    (9)  op(e3, e2) = all_52_3
% 178.34/28.47    (10)   ~ (all_52_9 = all_52_25)
% 178.34/28.47    (11)  op(e3, all_52_25) = all_52_24
% 178.34/28.47    (12)   ~ (all_52_19 = all_52_23)
% 178.34/28.47    (13)  all_56_11 = all_52_23
% 178.34/28.47    (14)  op(e1, e2) = all_52_19
% 178.34/28.47    (15)   ~ (all_52_3 = all_10_2)
% 178.34/28.47    (16)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.34/28.47    (17)  all_58_5 = all_52_13
% 178.34/28.47    (18)   ~ (all_6_2 = e0)
% 178.34/28.47    (19)   ~ (all_52_25 = all_52_29)
% 178.34/28.47    (20)  op(e1, all_52_13) = e1
% 178.34/28.47    (21)  op(e0, all_52_15) = e0
% 178.34/28.47    (22)  all_56_15 = all_6_2
% 178.34/28.47    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.47    (24)  op(e2, e0) = all_52_15
% 178.34/28.47    (25)  all_58_3 = all_10_2
% 178.34/28.47    (26)  all_56_9 = all_52_19
% 178.34/28.47    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.47    (28)  all_58_15 = all_6_2
% 178.34/28.47    (29)   ~ (all_52_9 = all_4_2)
% 178.34/28.47    (30)   ~ (all_52_5 = all_52_7)
% 178.34/28.47    (31)  all_58_10 = all_52_15
% 178.34/28.47    (32)   ~ (all_52_5 = all_4_2)
% 178.34/28.47    (33)  all_58_7 = all_52_19
% 178.34/28.47    (34)  all_56_4 = all_52_9
% 178.34/28.47    (35)   ~ (all_52_15 = all_6_2)
% 178.34/28.47    (36)   ~ (all_52_17 = all_52_25)
% 178.34/28.47    (37)   ~ (all_4_0 = e2)
% 178.34/28.47    (38)  all_58_4 = all_52_5
% 178.34/28.47    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.47    (40)   ~ (e3 = e1)
% 178.34/28.47    (41)   ~ (all_52_27 = all_52_29)
% 178.34/28.47    (42)   ~ (all_52_17 = all_14_2)
% 178.34/28.47    (43)  op(e3, all_4_2) = all_4_1
% 178.34/28.47    (44)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.47    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.47    (46)   ~ (all_52_7 = all_4_2)
% 178.34/28.47    (47)  all_58_1 = all_52_3
% 178.34/28.47    (48)  all_58_0 = all_4_2
% 178.34/28.47    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.47    (50)  op(e1, all_52_29) = all_52_28
% 178.34/28.47    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.47    (52)   ~ (all_4_1 = e2)
% 178.34/28.47    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.47    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.47    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.34/28.47    (56)   ~ (all_14_1 = e3)
% 178.34/28.47    (57)  all_58_14 = all_52_29
% 178.34/28.47    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.47    (59)   ~ (all_52_3 = all_52_5)
% 178.34/28.47    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.47    (61)  op(e2, e1) = all_52_13
% 178.34/28.47    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.47    (63)  all_58_8 = all_14_2
% 178.34/28.47    (64)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.47    (65)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.34/28.47    (66)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.47    (67)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.34/28.47    (68)   ~ (all_52_5 = all_14_2)
% 178.34/28.47    (69)   ~ (all_52_3 = all_52_27)
% 178.34/28.47    (70)   ~ (all_52_3 = all_4_2)
% 178.34/28.47    (71)  op(e0, e3) = all_52_25
% 178.34/28.47    (72)  op(e0, all_6_2) = all_6_1
% 178.34/28.47    (73)  op(e3, all_52_17) = all_52_16
% 178.34/28.47    (74)   ~ (all_52_13 = all_14_2)
% 178.34/28.47    (75)  op(e3, all_52_9) = e3
% 178.34/28.47    (76)   ~ (e3 = e0)
% 178.34/28.47    (77)  all_40_0 = all_4_0
% 178.34/28.47    (78)   ~ (all_52_9 = all_52_13)
% 178.34/28.47    (79)  op(e0, all_52_23) = all_52_22
% 178.34/28.47    (80)   ~ (all_52_15 = all_52_23)
% 178.34/28.47    (81)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.34/28.47    (82)   ~ (all_52_5 = all_52_29)
% 178.34/28.47    (83)  all_56_2 = all_52_5
% 178.34/28.47    (84)  op(e1, e0) = all_52_23
% 178.34/28.47    (85)  all_58_13 = all_52_27
% 178.34/28.47    (86)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.47    (87)   ~ (all_52_9 = all_52_17)
% 178.34/28.47    (88)  all_58_6 = all_52_17
% 178.34/28.47    (89)   ~ (all_52_3 = all_52_7)
% 178.34/28.47    (90)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.34/28.47    (91)  op(e2, all_52_19) = all_52_18
% 178.34/28.47    (92)   ~ (e1 = e0)
% 178.34/28.47    (93)  all_56_0 = all_4_2
% 178.34/28.47    (94)  all_58_11 = all_52_23
% 178.34/28.47    (95)   ~ (all_52_3 = all_52_19)
% 178.34/28.47    (96)   ~ (all_52_7 = all_52_15)
% 178.34/28.47    (97)   ~ (all_52_29 = all_14_2)
% 178.34/28.47    (98)   ~ (all_52_19 = all_10_2)
% 178.34/28.47    (99)   ~ (all_52_23 = all_6_2)
% 178.34/28.47    (100)  op(e1, all_4_2) = all_4_0
% 178.34/28.47    (101)   ~ (all_52_29 = all_6_2)
% 178.34/28.47    (102)  all_58_2 = all_52_9
% 178.34/28.47    (103)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.47    (104)  op(e3, e1) = all_52_5
% 178.34/28.47    (105)   ~ (e2 = e1)
% 178.34/28.47    (106)  all_56_10 = all_14_2
% 178.34/28.47    (107)   ~ (all_52_25 = all_6_2)
% 178.34/28.47    (108)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.47    (109)  op(e1, e1) = all_14_2
% 178.34/28.47    (110)  op(e1, e3) = all_52_17
% 178.34/28.47    (111)   ~ (all_52_25 = all_4_2)
% 178.34/28.47    (112)  op(e3, e0) = all_52_7
% 178.34/28.47    (113)  op(e2, all_10_2) = e2
% 178.34/28.47    (114)  op(e3, e3) = all_4_2
% 178.34/28.47    (115)   ~ (all_52_17 = all_4_2)
% 178.34/28.47    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.47             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.47    (117)   ~ (all_52_25 = all_52_27)
% 178.34/28.47    (118)   ~ (all_52_27 = all_6_2)
% 178.34/28.47    (119)   ~ (all_52_7 = all_6_2)
% 178.34/28.47    (120)   ~ (all_52_19 = all_52_27)
% 178.34/28.47    (121)   ~ (all_52_7 = all_52_23)
% 178.34/28.47    (122)  op(e2, all_52_27) = all_52_26
% 178.34/28.47    (123)   ~ (all_52_17 = all_52_19)
% 178.34/28.47    (124)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.47    (125)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.47    (126)  op(e1, all_14_2) = all_14_1
% 178.34/28.47    (127)  all_58_9 = all_52_7
% 178.34/28.47    (128)  all_58_12 = all_52_25
% 178.34/28.47    (129)  op(e3, all_4_2) = e1
% 178.34/28.47    (130)  all_56_6 = all_52_13
% 178.34/28.47    (131)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.47    (132)   ~ (all_52_9 = all_52_15)
% 178.34/28.47    (133)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.47    (134)   ~ (e3 = e2)
% 178.34/28.47    (135)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.34/28.47    (136)   ~ (all_52_19 = all_14_2)
% 178.34/28.47    (137)  op(e2, e3) = all_52_9
% 178.34/28.47    (138)  all_56_13 = all_52_27
% 178.34/28.47  
% 178.34/28.47  Begin of proof
% 178.34/28.47  | 
% 178.34/28.47  | BETA: splitting (44) gives:
% 178.34/28.47  | 
% 178.34/28.47  | Case 1:
% 178.34/28.47  | | 
% 178.34/28.47  | |   (139)  all_56_15 = e3
% 178.34/28.47  | | 
% 178.34/28.47  | | COMBINE_EQS: (22), (139) imply:
% 178.34/28.47  | |   (140)  all_6_2 = e3
% 178.34/28.47  | | 
% 178.34/28.47  | | SIMP: (140) implies:
% 178.34/28.47  | |   (141)  all_6_2 = e3
% 178.34/28.47  | | 
% 178.34/28.47  | | REF_CLOSE: (9), (10), (15), (17), (20), (23), (25), (29), (31), (33), (34),
% 178.34/28.47  | |            (35), (37), (39), (40), (43), (45), (46), (47), (48), (54), (55),
% 178.34/28.47  | |            (60), (63), (66), (71), (72), (74), (75), (85), (87), (88), (90),
% 178.34/28.47  | |            (91), (94), (95), (99), (102), (105), (107), (108), (110), (112),
% 178.34/28.47  | |            (113), (114), (115), (116), (118), (123), (128), (130), (137),
% 178.34/28.47  | |            (141) are inconsistent by sub-proof #773.
% 178.34/28.47  | | 
% 178.34/28.47  | Case 2:
% 178.34/28.47  | | 
% 178.34/28.47  | |   (142)   ~ (all_56_15 = e3)
% 178.34/28.47  | |   (143)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.47  | | 
% 178.34/28.47  | | REDUCE: (22), (142) imply:
% 178.34/28.47  | |   (144)   ~ (all_6_2 = e3)
% 178.34/28.47  | | 
% 178.34/28.47  | | BETA: splitting (58) gives:
% 178.34/28.47  | | 
% 178.34/28.47  | | Case 1:
% 178.34/28.47  | | | 
% 178.34/28.47  | | |   (145)  all_56_13 = e3
% 178.34/28.47  | | | 
% 178.34/28.47  | | | COMBINE_EQS: (138), (145) imply:
% 178.34/28.47  | | |   (146)  all_52_27 = e3
% 178.34/28.47  | | | 
% 178.34/28.47  | | | SIMP: (146) implies:
% 178.34/28.47  | | |   (147)  all_52_27 = e3
% 178.34/28.47  | | | 
% 178.34/28.47  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (14), (17), (20), (21),
% 178.34/28.47  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (36),
% 178.34/28.47  | | |            (37), (38), (39), (40), (42), (45), (46), (47), (48), (51),
% 178.34/28.47  | | |            (57), (60), (63), (64), (68), (69), (71), (74), (75), (77),
% 178.34/28.47  | | |            (78), (80), (86), (88), (93), (94), (95), (96), (100), (102),
% 178.34/28.47  | | |            (104), (110), (111), (114), (115), (116), (118), (120), (121),
% 178.34/28.47  | | |            (122), (124), (125), (127), (128), (129), (131), (133), (137),
% 178.34/28.47  | | |            (147) are inconsistent by sub-proof #610.
% 178.34/28.47  | | | 
% 178.34/28.47  | | Case 2:
% 178.34/28.47  | | | 
% 178.34/28.47  | | |   (148)   ~ (all_56_13 = e3)
% 178.34/28.47  | | | 
% 178.34/28.47  | | | REDUCE: (138), (148) imply:
% 178.34/28.47  | | |   (149)   ~ (all_52_27 = e3)
% 178.34/28.47  | | | 
% 178.34/28.47  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 178.34/28.47  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.34/28.47  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 178.34/28.47  | | |            (34), (36), (37), (38), (39), (40), (41), (42), (43), (45),
% 178.34/28.47  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 178.34/28.47  | | |            (56), (57), (59), (60), (61), (62), (63), (65), (66), (67),
% 178.34/28.47  | | |            (70), (71), (73), (74), (75), (76), (78), (79), (80), (81),
% 178.34/28.47  | | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 178.34/28.47  | | |            (92), (93), (94), (95), (96), (97), (98), (99), (101), (102),
% 178.34/28.47  | | |            (103), (104), (105), (106), (107), (109), (110), (111), (112),
% 178.34/28.47  | | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 178.34/28.47  | | |            (123), (124), (125), (126), (127), (128), (130), (131), (132),
% 178.34/28.47  | | |            (133), (134), (135), (136), (137), (143), (144), (149) are
% 178.34/28.47  | | |            inconsistent by sub-proof #717.
% 178.34/28.47  | | | 
% 178.34/28.47  | | End of split
% 178.34/28.47  | | 
% 178.34/28.47  | End of split
% 178.34/28.47  | 
% 178.34/28.47  End of proof
% 178.34/28.47  
% 178.34/28.47  Sub-proof #610 shows that the following formulas are inconsistent:
% 178.34/28.47  ----------------------------------------------------------------
% 178.34/28.47    (1)   ~ (all_52_5 = all_52_13)
% 178.34/28.47    (2)   ~ (all_52_27 = all_10_2)
% 178.34/28.47    (3)   ~ (all_52_17 = all_52_23)
% 178.34/28.47    (4)  all_40_2 = all_4_2
% 178.34/28.47    (5)   ~ (all_52_13 = all_52_29)
% 178.34/28.47    (6)  all_56_3 = all_52_7
% 178.34/28.47    (7)  op(e3, e2) = all_52_3
% 178.34/28.47    (8)  op(e1, e2) = all_52_19
% 178.34/28.47    (9)  all_52_27 = e3
% 178.34/28.47    (10)  all_58_5 = all_52_13
% 178.34/28.47    (11)  op(e1, all_52_13) = e1
% 178.34/28.47    (12)  op(e0, all_52_15) = e0
% 178.34/28.47    (13)  all_58_3 = all_10_2
% 178.34/28.47    (14)  all_56_9 = all_52_19
% 178.34/28.47    (15)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.47    (16)  all_58_15 = all_6_2
% 178.34/28.47    (17)   ~ (all_52_9 = all_4_2)
% 178.34/28.47    (18)   ~ (all_52_5 = all_52_7)
% 178.34/28.47    (19)  all_58_10 = all_52_15
% 178.34/28.47    (20)   ~ (all_52_5 = all_4_2)
% 178.34/28.47    (21)  all_58_7 = all_52_19
% 178.34/28.47    (22)   ~ (all_52_17 = all_52_25)
% 178.34/28.47    (23)   ~ (all_4_0 = e2)
% 178.34/28.47    (24)  all_58_4 = all_52_5
% 178.34/28.47    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.47    (26)   ~ (e3 = e1)
% 178.34/28.47    (27)   ~ (all_52_17 = all_14_2)
% 178.34/28.47    (28)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.47    (29)   ~ (all_52_7 = all_4_2)
% 178.34/28.47    (30)  all_58_1 = all_52_3
% 178.34/28.47    (31)  all_58_0 = all_4_2
% 178.34/28.47    (32)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.47    (33)  all_58_14 = all_52_29
% 178.34/28.47    (34)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.47    (35)  all_58_8 = all_14_2
% 178.34/28.47    (36)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.47    (37)   ~ (all_52_5 = all_14_2)
% 178.34/28.47    (38)   ~ (all_52_3 = all_52_27)
% 178.34/28.47    (39)  op(e0, e3) = all_52_25
% 178.34/28.47    (40)   ~ (all_52_13 = all_14_2)
% 178.34/28.47    (41)  op(e3, all_52_9) = e3
% 178.34/28.47    (42)  all_40_0 = all_4_0
% 178.34/28.47    (43)   ~ (all_52_9 = all_52_13)
% 178.34/28.47    (44)   ~ (all_52_15 = all_52_23)
% 178.34/28.47    (45)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.47    (46)  all_58_6 = all_52_17
% 178.34/28.47    (47)  all_56_0 = all_4_2
% 178.34/28.47    (48)  all_58_11 = all_52_23
% 178.34/28.47    (49)   ~ (all_52_3 = all_52_19)
% 178.34/28.47    (50)   ~ (all_52_7 = all_52_15)
% 178.34/28.48    (51)  op(e1, all_4_2) = all_4_0
% 178.34/28.48    (52)  all_58_2 = all_52_9
% 178.34/28.48    (53)  op(e3, e1) = all_52_5
% 178.34/28.48    (54)  op(e1, e3) = all_52_17
% 178.34/28.48    (55)   ~ (all_52_25 = all_4_2)
% 178.34/28.48    (56)  op(e3, e3) = all_4_2
% 178.34/28.48    (57)   ~ (all_52_17 = all_4_2)
% 178.34/28.48    (58)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.48    (59)   ~ (all_52_27 = all_6_2)
% 178.34/28.48    (60)   ~ (all_52_19 = all_52_27)
% 178.34/28.48    (61)   ~ (all_52_7 = all_52_23)
% 178.34/28.48    (62)  op(e2, all_52_27) = all_52_26
% 178.34/28.48    (63)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.48    (64)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.48    (65)  all_58_9 = all_52_7
% 178.34/28.48    (66)  all_58_12 = all_52_25
% 178.34/28.48    (67)  op(e3, all_4_2) = e1
% 178.34/28.48    (68)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.48    (69)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.48    (70)  op(e2, e3) = all_52_9
% 178.34/28.48  
% 178.34/28.48  Begin of proof
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (9), (38) imply:
% 178.34/28.48  |   (71)   ~ (all_52_3 = e3)
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (9), (60) imply:
% 178.34/28.48  |   (72)   ~ (all_52_19 = e3)
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (2), (9) imply:
% 178.34/28.48  |   (73)   ~ (all_10_2 = e3)
% 178.34/28.48  | 
% 178.34/28.48  | SIMP: (73) implies:
% 178.34/28.48  |   (74)   ~ (all_10_2 = e3)
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (9), (59) imply:
% 178.34/28.48  |   (75)   ~ (all_6_2 = e3)
% 178.34/28.48  | 
% 178.34/28.48  | SIMP: (75) implies:
% 178.34/28.48  |   (76)   ~ (all_6_2 = e3)
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (9), (62) imply:
% 178.34/28.48  |   (77)  op(e2, e3) = all_52_26
% 178.34/28.48  | 
% 178.34/28.48  | GROUND_INST: instantiating (58) with all_52_9, all_52_26, e3, e2, simplifying
% 178.34/28.48  |              with (70), (77) gives:
% 178.34/28.48  |   (78)  all_52_9 = all_52_26
% 178.34/28.48  | 
% 178.34/28.48  | COMBINE_EQS: (52), (78) imply:
% 178.34/28.48  |   (79)  all_58_2 = all_52_26
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (43), (78) imply:
% 178.34/28.48  |   (80)   ~ (all_52_13 = all_52_26)
% 178.34/28.48  | 
% 178.34/28.48  | SIMP: (80) implies:
% 178.34/28.48  |   (81)   ~ (all_52_13 = all_52_26)
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (17), (78) imply:
% 178.34/28.48  |   (82)   ~ (all_52_26 = all_4_2)
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (41), (78) imply:
% 178.34/28.48  |   (83)  op(e3, all_52_26) = e3
% 178.34/28.48  | 
% 178.34/28.48  | BETA: splitting (32) gives:
% 178.34/28.48  | 
% 178.34/28.48  | Case 1:
% 178.34/28.48  | | 
% 178.34/28.48  | |   (84)  all_56_9 = e3
% 178.34/28.48  | | 
% 178.34/28.48  | | REF_CLOSE: (14), (72), (84) are inconsistent by sub-proof #700.
% 178.34/28.48  | | 
% 178.34/28.48  | Case 2:
% 178.34/28.48  | | 
% 178.34/28.48  | |   (85)   ~ (all_56_9 = e3)
% 178.34/28.48  | |   (86)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.48  | | 
% 178.34/28.48  | | BETA: splitting (64) gives:
% 178.34/28.48  | | 
% 178.34/28.48  | | Case 1:
% 178.34/28.48  | | | 
% 178.34/28.48  | | |   (87)  all_56_3 = e3
% 178.34/28.48  | | | 
% 178.34/28.48  | | | COMBINE_EQS: (6), (87) imply:
% 178.34/28.48  | | |   (88)  all_52_7 = e3
% 178.34/28.48  | | | 
% 178.34/28.48  | | | REF_CLOSE: (5), (10), (11), (13), (18), (19), (21), (22), (24), (25),
% 178.34/28.48  | | |            (26), (27), (28), (29), (31), (33), (34), (35), (40), (46),
% 178.34/28.48  | | |            (48), (50), (54), (56), (58), (61), (66), (69), (72), (74),
% 178.34/28.48  | | |            (79), (81), (82), (83), (88) are inconsistent by sub-proof
% 178.34/28.48  | | |            #983.
% 178.34/28.48  | | | 
% 178.34/28.48  | | Case 2:
% 178.34/28.48  | | | 
% 178.34/28.48  | | |   (89)   ~ (all_56_3 = e3)
% 178.34/28.48  | | | 
% 178.34/28.48  | | | REDUCE: (6), (89) imply:
% 178.34/28.48  | | |   (90)   ~ (all_52_7 = e3)
% 178.34/28.48  | | | 
% 178.34/28.48  | | | BETA: splitting (63) gives:
% 178.34/28.48  | | | 
% 178.34/28.48  | | | Case 1:
% 178.34/28.48  | | | | 
% 178.34/28.48  | | | |   (91)  all_58_9 = e3
% 178.34/28.48  | | | | 
% 178.34/28.48  | | | | REF_CLOSE: (65), (90), (91) are inconsistent by sub-proof #972.
% 178.34/28.48  | | | | 
% 178.34/28.48  | | | Case 2:
% 178.34/28.48  | | | | 
% 178.34/28.48  | | | |   (92)   ~ (all_58_9 = e3)
% 178.34/28.48  | | | |   (93)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.48  | | | | 
% 178.34/28.48  | | | | BETA: splitting (68) gives:
% 178.34/28.48  | | | | 
% 178.34/28.48  | | | | Case 1:
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | |   (94)  all_58_0 = e3
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | | COMBINE_EQS: (31), (94) imply:
% 178.34/28.48  | | | | |   (95)  all_4_2 = e3
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | | REF_CLOSE: (26), (56), (58), (67), (95) are inconsistent by sub-proof
% 178.34/28.48  | | | | |            #630.
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | Case 2:
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | |   (96)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | | BETA: splitting (96) gives:
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | | Case 1:
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | |   (97)  all_58_1 = e3
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | | COMBINE_EQS: (30), (97) imply:
% 178.34/28.48  | | | | | |   (98)  all_52_3 = e3
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | | REDUCE: (71), (98) imply:
% 178.34/28.48  | | | | | |   (99)  $false
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | | CLOSE: (99) is inconsistent.
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | Case 2:
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | |   (100)  all_58_4 = e3 | all_58_9 = e3
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | | BETA: splitting (100) gives:
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | | Case 1:
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | |   (101)  all_58_4 = e3
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | COMBINE_EQS: (24), (101) imply:
% 178.34/28.48  | | | | | | |   (102)  all_52_5 = e3
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | SIMP: (102) implies:
% 178.34/28.48  | | | | | | |   (103)  all_52_5 = e3
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | REDUCE: (1), (103) imply:
% 178.34/28.48  | | | | | | |   (104)   ~ (all_52_13 = e3)
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | SIMP: (104) implies:
% 178.34/28.48  | | | | | | |   (105)   ~ (all_52_13 = e3)
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | REDUCE: (37), (103) imply:
% 178.34/28.48  | | | | | | |   (106)   ~ (all_14_2 = e3)
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | SIMP: (106) implies:
% 178.34/28.48  | | | | | | |   (107)   ~ (all_14_2 = e3)
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | REDUCE: (20), (103) imply:
% 178.34/28.48  | | | | | | |   (108)   ~ (all_4_2 = e3)
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | SIMP: (108) implies:
% 178.34/28.48  | | | | | | |   (109)   ~ (all_4_2 = e3)
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | REDUCE: (53), (103) imply:
% 178.34/28.48  | | | | | | |   (110)  op(e3, e1) = e3
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | BETA: splitting (25) gives:
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | Case 1:
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | |   (111)  all_58_6 = e3
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | | COMBINE_EQS: (46), (111) imply:
% 178.34/28.48  | | | | | | | |   (112)  all_52_17 = e3
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | | SIMP: (112) implies:
% 178.34/28.48  | | | | | | | |   (113)  all_52_17 = e3
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | | REDUCE: (3), (113) imply:
% 178.34/28.48  | | | | | | | |   (114)   ~ (all_52_23 = e3)
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | | SIMP: (114) implies:
% 178.34/28.48  | | | | | | | |   (115)   ~ (all_52_23 = e3)
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | | BETA: splitting (93) gives:
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | | Case 1:
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | |   (116)  all_58_10 = e3
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | | COMBINE_EQS: (19), (116) imply:
% 178.34/28.48  | | | | | | | | |   (117)  all_52_15 = e3
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | | SIMP: (117) implies:
% 178.34/28.48  | | | | | | | | |   (118)  all_52_15 = e3
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | | REDUCE: (12), (118) imply:
% 178.34/28.48  | | | | | | | | |   (119)  op(e0, e3) = e0
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | | REF_CLOSE: (4), (7), (8), (14), (15), (23), (31), (36), (39),
% 178.34/28.48  | | | | | | | | |            (42), (45), (47), (49), (51), (55), (58), (67),
% 178.34/28.48  | | | | | | | | |            (86), (109), (110), (119) are inconsistent by
% 178.34/28.48  | | | | | | | | |            sub-proof #611.
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | Case 2:
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | |   (120)  all_58_11 = e3 | all_58_15 = e3
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | | REF_CLOSE: (16), (48), (76), (115), (120) are inconsistent by
% 178.34/28.48  | | | | | | | | |            sub-proof #1016.
% 178.34/28.48  | | | | | | | | | 
% 178.34/28.48  | | | | | | | | End of split
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | Case 2:
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | |   (121)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | | REF_CLOSE: (10), (13), (17), (19), (21), (28), (31), (34), (35),
% 178.34/28.48  | | | | | | | |            (41), (44), (48), (52), (56), (58), (72), (74),
% 178.34/28.48  | | | | | | | |            (105), (107), (109), (121) are inconsistent by
% 178.34/28.48  | | | | | | | |            sub-proof #964.
% 178.34/28.48  | | | | | | | | 
% 178.34/28.48  | | | | | | | End of split
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | Case 2:
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | |   (122)  all_58_9 = e3
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | | REF_CLOSE: (65), (90), (122) are inconsistent by sub-proof #972.
% 178.34/28.48  | | | | | | | 
% 178.34/28.48  | | | | | | End of split
% 178.34/28.48  | | | | | | 
% 178.34/28.48  | | | | | End of split
% 178.34/28.48  | | | | | 
% 178.34/28.48  | | | | End of split
% 178.34/28.48  | | | | 
% 178.34/28.48  | | | End of split
% 178.34/28.48  | | | 
% 178.34/28.48  | | End of split
% 178.34/28.48  | | 
% 178.34/28.48  | End of split
% 178.34/28.48  | 
% 178.34/28.48  End of proof
% 178.34/28.48  
% 178.34/28.48  Sub-proof #611 shows that the following formulas are inconsistent:
% 178.34/28.48  ----------------------------------------------------------------
% 178.34/28.48    (1)  all_40_2 = all_4_2
% 178.34/28.48    (2)  op(e3, e1) = e3
% 178.34/28.48    (3)  op(e3, e2) = all_52_3
% 178.34/28.48    (4)  op(e1, e2) = all_52_19
% 178.34/28.48    (5)   ~ (all_4_2 = e3)
% 178.34/28.48    (6)  all_56_9 = all_52_19
% 178.34/28.48    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.48    (8)   ~ (all_4_0 = e2)
% 178.34/28.48    (9)  all_58_0 = all_4_2
% 178.34/28.48    (10)  op(e0, e3) = e0
% 178.34/28.48    (11)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.48    (12)  op(e0, e3) = all_52_25
% 178.34/28.48    (13)  all_40_0 = all_4_0
% 178.34/28.48    (14)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.48    (15)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.48    (16)  all_56_0 = all_4_2
% 178.34/28.48    (17)   ~ (all_52_3 = all_52_19)
% 178.34/28.48    (18)  op(e1, all_4_2) = all_4_0
% 178.34/28.48    (19)   ~ (all_52_25 = all_4_2)
% 178.34/28.48    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.48    (21)  op(e3, all_4_2) = e1
% 178.34/28.48  
% 178.34/28.48  Begin of proof
% 178.34/28.48  | 
% 178.34/28.48  | GROUND_INST: instantiating (20) with all_52_25, e0, e3, e0, simplifying with
% 178.34/28.48  |              (10), (12) gives:
% 178.34/28.48  |   (22)  all_52_25 = e0
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (19), (22) imply:
% 178.34/28.48  |   (23)   ~ (all_4_2 = e0)
% 178.34/28.48  | 
% 178.34/28.48  | SIMP: (23) implies:
% 178.34/28.48  |   (24)   ~ (all_4_2 = e0)
% 178.34/28.48  | 
% 178.34/28.48  | BETA: splitting (7) gives:
% 178.34/28.48  | 
% 178.34/28.48  | Case 1:
% 178.34/28.48  | | 
% 178.34/28.48  | |   (25)  all_56_0 = e3
% 178.34/28.48  | | 
% 178.34/28.48  | | REF_CLOSE: (5), (16), (25) are inconsistent by sub-proof #1024.
% 178.34/28.48  | | 
% 178.34/28.48  | Case 2:
% 178.34/28.48  | | 
% 178.34/28.48  | |   (26)   ~ (all_56_0 = e3)
% 178.34/28.48  | |   (27)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.48  | | 
% 178.34/28.48  | | BETA: splitting (15) gives:
% 178.34/28.48  | | 
% 178.34/28.48  | | Case 1:
% 178.34/28.48  | | | 
% 178.34/28.48  | | |   (28)  all_58_0 = e1
% 178.34/28.48  | | | 
% 178.34/28.48  | | | REF_CLOSE: (2), (5), (9), (20), (21), (28) are inconsistent by sub-proof
% 178.34/28.48  | | |            #612.
% 178.34/28.48  | | | 
% 178.34/28.48  | | Case 2:
% 178.34/28.48  | | | 
% 178.34/28.48  | | |   (29)   ~ (all_58_0 = e1)
% 178.34/28.48  | | | 
% 178.34/28.48  | | | REDUCE: (9), (29) imply:
% 178.34/28.48  | | |   (30)   ~ (all_4_2 = e1)
% 178.34/28.48  | | | 
% 178.34/28.48  | | | REF_CLOSE: (1), (3), (4), (6), (8), (11), (13), (14), (16), (17), (18),
% 178.34/28.48  | | |            (20), (21), (24), (27), (30) are inconsistent by sub-proof
% 178.34/28.48  | | |            #618.
% 178.34/28.48  | | | 
% 178.34/28.48  | | End of split
% 178.34/28.48  | | 
% 178.34/28.48  | End of split
% 178.34/28.48  | 
% 178.34/28.48  End of proof
% 178.34/28.48  
% 178.34/28.48  Sub-proof #612 shows that the following formulas are inconsistent:
% 178.34/28.48  ----------------------------------------------------------------
% 178.34/28.48    (1)  op(e3, e1) = e3
% 178.34/28.48    (2)   ~ (all_4_2 = e3)
% 178.34/28.48    (3)  all_58_0 = all_4_2
% 178.34/28.48    (4)  all_58_0 = e1
% 178.34/28.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.48    (6)  op(e3, all_4_2) = e1
% 178.34/28.48  
% 178.34/28.48  Begin of proof
% 178.34/28.48  | 
% 178.34/28.48  | COMBINE_EQS: (3), (4) imply:
% 178.34/28.48  |   (7)  all_4_2 = e1
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (2), (7) imply:
% 178.34/28.48  |   (8)   ~ (e3 = e1)
% 178.34/28.48  | 
% 178.34/28.48  | SIMP: (8) implies:
% 178.34/28.48  |   (9)   ~ (e3 = e1)
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (6), (7) imply:
% 178.34/28.48  |   (10)  op(e3, e1) = e1
% 178.34/28.48  | 
% 178.34/28.48  | REF_CLOSE: (1), (5), (9), (10) are inconsistent by sub-proof #613.
% 178.34/28.48  | 
% 178.34/28.48  End of proof
% 178.34/28.48  
% 178.34/28.48  Sub-proof #613 shows that the following formulas are inconsistent:
% 178.34/28.48  ----------------------------------------------------------------
% 178.34/28.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.48    (2)  op(e3, e1) = e3
% 178.34/28.48    (3)  op(e3, e1) = e1
% 178.34/28.48    (4)   ~ (e3 = e1)
% 178.34/28.48  
% 178.34/28.48  Begin of proof
% 178.34/28.48  | 
% 178.34/28.48  | GROUND_INST: instantiating (1) with e1, e3, e1, e3, simplifying with (2), (3)
% 178.34/28.48  |              gives:
% 178.34/28.48  |   (5)  e3 = e1
% 178.34/28.48  | 
% 178.34/28.48  | REDUCE: (4), (5) imply:
% 178.34/28.48  |   (6)  $false
% 178.34/28.48  | 
% 178.34/28.48  | CLOSE: (6) is inconsistent.
% 178.34/28.48  | 
% 178.34/28.48  End of proof
% 178.34/28.48  
% 178.34/28.48  Sub-proof #614 shows that the following formulas are inconsistent:
% 178.34/28.48  ----------------------------------------------------------------
% 178.34/28.48    (1)   ~ (all_52_5 = all_52_13)
% 178.34/28.48    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.48    (3)  all_40_2 = all_4_2
% 178.34/28.48    (4)  all_56_3 = all_52_7
% 178.34/28.48    (5)  op(e3, e2) = all_52_3
% 178.34/28.48    (6)   ~ (all_52_9 = all_52_25)
% 178.34/28.48    (7)  op(e3, all_52_25) = all_52_24
% 178.34/28.48    (8)  all_56_11 = all_52_23
% 178.34/28.48    (9)  op(e1, e2) = all_52_19
% 178.34/28.48    (10)   ~ (all_52_27 = e0)
% 178.34/28.48    (11)   ~ (all_52_23 = e0)
% 178.34/28.48    (12)  all_58_5 = all_52_13
% 178.34/28.48    (13)   ~ (all_52_25 = all_52_29)
% 178.34/28.48    (14)  op(all_14_1, all_14_2) = all_14_0
% 178.34/28.48    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.48    (16)  all_58_3 = all_10_2
% 178.34/28.48    (17)  all_56_9 = all_52_19
% 178.34/28.48    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.48    (19)   ~ (all_52_9 = all_4_2)
% 178.34/28.48    (20)   ~ (all_52_5 = all_52_7)
% 178.34/28.48    (21)  all_58_10 = all_52_15
% 178.34/28.48    (22)   ~ (all_52_5 = all_4_2)
% 178.34/28.48    (23)  all_58_7 = all_52_19
% 178.34/28.48    (24)   ~ (all_52_17 = all_52_25)
% 178.34/28.48    (25)  op(e0, e1) = all_52_29
% 178.34/28.48    (26)   ~ (all_4_0 = e2)
% 178.34/28.48    (27)  all_58_4 = all_52_5
% 178.34/28.48    (28)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.48    (29)   ~ (e3 = e1)
% 178.34/28.48    (30)   ~ (all_52_27 = all_52_29)
% 178.34/28.48    (31)   ~ (all_52_17 = all_14_2)
% 178.34/28.48    (32)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.48    (33)   ~ (all_52_7 = all_4_2)
% 178.34/28.48    (34)  all_58_1 = all_52_3
% 178.34/28.48    (35)  all_58_0 = all_4_2
% 178.34/28.48    (36)  op(e1, all_52_29) = all_52_28
% 178.34/28.48    (37)   ~ (all_52_7 = e0)
% 178.34/28.48    (38)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.48    (39)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.48    (40)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.48    (41)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.34/28.48    (42)  all_58_14 = all_52_29
% 178.34/28.48    (43)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.48    (44)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.48    (45)  op(e2, e1) = all_52_13
% 178.34/28.48    (46)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.48    (47)  all_58_8 = all_14_2
% 178.34/28.48    (48)  op(e0, e2) = all_52_27
% 178.34/28.48    (49)  all_56_14 = all_52_29
% 178.34/28.48    (50)   ~ (all_14_0 = e3)
% 178.34/28.48    (51)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.48    (52)   ~ (all_52_5 = all_14_2)
% 178.34/28.48    (53)   ~ (all_52_3 = all_52_27)
% 178.34/28.48    (54)   ~ (all_52_3 = all_4_2)
% 178.34/28.48    (55)  op(e0, e3) = all_52_25
% 178.34/28.48    (56)  op(e3, all_52_17) = all_52_16
% 178.34/28.48    (57)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.48    (58)   ~ (all_52_13 = all_14_2)
% 178.34/28.48    (59)   ~ (e3 = e0)
% 178.34/28.48    (60)  all_40_0 = all_4_0
% 178.34/28.48    (61)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.48    (62)  op(e0, all_52_23) = all_52_22
% 178.34/28.48    (63)   ~ (all_52_5 = all_52_29)
% 178.34/28.48    (64)  op(e1, e0) = all_52_23
% 178.34/28.48    (65)  all_56_12 = all_52_25
% 178.34/28.48    (66)  all_58_13 = all_52_27
% 178.34/28.48    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.48    (68)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.48    (69)   ~ (all_52_25 = e0)
% 178.34/28.48    (70)   ~ (all_52_9 = all_52_17)
% 178.34/28.48    (71)   ~ (all_14_0 = e2)
% 178.34/28.48    (72)  all_58_6 = all_52_17
% 178.34/28.48    (73)   ~ (all_52_3 = all_52_7)
% 178.34/28.48    (74)  op(e2, all_52_19) = all_52_18
% 178.34/28.48    (75)   ~ (e1 = e0)
% 178.34/28.48    (76)  all_56_0 = all_4_2
% 178.34/28.48    (77)  all_58_11 = all_52_23
% 178.34/28.48    (78)   ~ (all_52_3 = all_52_19)
% 178.34/28.48    (79)   ~ (all_52_7 = all_52_15)
% 178.34/28.48    (80)   ~ (all_52_29 = all_14_2)
% 178.34/28.48    (81)   ~ (all_52_19 = all_10_2)
% 178.34/28.48    (82)  all_58_15 = e0
% 178.34/28.48    (83)  op(e1, all_4_2) = all_4_0
% 178.34/28.48    (84)  all_58_2 = all_52_9
% 178.34/28.48    (85)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.34/28.48    (86)   ~ (all_52_29 = e0)
% 178.34/28.48    (87)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.48    (88)  op(e3, e1) = all_52_5
% 178.34/28.48    (89)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.48    (90)  op(e1, e3) = all_52_17
% 178.34/28.48    (91)   ~ (all_52_25 = all_4_2)
% 178.34/28.48    (92)  op(e3, e0) = all_52_7
% 178.34/28.48    (93)  op(e3, e3) = all_4_2
% 178.34/28.48    (94)   ~ (all_52_17 = all_4_2)
% 178.34/28.48    (95)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.48    (96)   ~ (all_52_25 = all_52_27)
% 178.34/28.48    (97)   ~ (all_52_7 = all_52_23)
% 178.34/28.48    (98)  op(e2, all_52_27) = all_52_26
% 178.34/28.48    (99)  all_52_20 = all_14_1
% 178.34/28.48    (100)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.48    (101)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.48    (102)  op(e1, all_14_2) = all_14_1
% 178.34/28.48    (103)  all_58_9 = all_52_7
% 178.34/28.48    (104)   ~ (e2 = e0)
% 178.34/28.48    (105)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 178.34/28.48           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 178.34/28.48    (106)  all_58_12 = all_52_25
% 178.34/28.48    (107)  op(e3, all_4_2) = e1
% 178.34/28.48    (108)  all_56_6 = all_52_13
% 178.34/28.48    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.48    (110)   ~ (e3 = e2)
% 178.34/28.48    (111)  op(e2, e3) = all_52_9
% 178.34/28.48    (112)  all_56_13 = all_52_27
% 178.34/28.48  
% 178.34/28.48  Begin of proof
% 178.34/28.48  | 
% 178.34/28.48  | BETA: splitting (105) gives:
% 178.34/28.48  | 
% 178.34/28.48  | Case 1:
% 178.34/28.48  | | 
% 178.34/28.48  | |   (113)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 178.34/28.48  | | 
% 178.34/28.48  | | ALPHA: (113) implies:
% 178.34/28.48  | |   (114)  all_52_22 = e0
% 178.34/28.48  | |   (115)  all_52_20 = e1
% 178.34/28.48  | |   (116)  all_52_18 = e2
% 178.34/28.48  | |   (117)  all_52_16 = e3
% 178.34/28.48  | | 
% 178.34/28.48  | | COMBINE_EQS: (99), (115) imply:
% 178.34/28.48  | |   (118)  all_14_1 = e1
% 178.34/28.48  | | 
% 178.34/28.48  | | SIMP: (118) implies:
% 178.34/28.48  | |   (119)  all_14_1 = e1
% 178.34/28.48  | | 
% 178.34/28.48  | | REDUCE: (14), (119) imply:
% 178.34/28.48  | |   (120)  op(e1, all_14_2) = all_14_0
% 178.34/28.48  | | 
% 178.34/28.48  | | REDUCE: (56), (117) imply:
% 178.34/28.48  | |   (121)  op(e3, all_52_17) = e3
% 178.34/28.48  | | 
% 178.34/28.48  | | REDUCE: (74), (116) imply:
% 178.34/28.48  | |   (122)  op(e2, all_52_19) = e2
% 178.34/28.48  | | 
% 178.34/28.48  | | REDUCE: (102), (119) imply:
% 178.34/28.48  | |   (123)  op(e1, all_14_2) = e1
% 178.34/28.48  | | 
% 178.34/28.48  | | REDUCE: (62), (114) imply:
% 178.34/28.48  | |   (124)  op(e0, all_52_23) = e0
% 178.34/28.48  | | 
% 178.34/28.48  | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (12), (13), (15), (16),
% 178.34/28.48  | |            (17), (21), (22), (23), (24), (25), (27), (28), (30), (32), (33),
% 178.34/28.48  | |            (34), (35), (36), (38), (41), (42), (43), (44), (46), (47), (48),
% 178.34/28.48  | |            (50), (52), (55), (57), (58), (59), (61), (63), (65), (66), (67),
% 178.34/28.48  | |            (69), (70), (71), (72), (75), (77), (78), (79), (80), (81), (82),
% 178.34/28.48  | |            (84), (85), (86), (87), (88), (89), (90), (93), (94), (95), (96),
% 178.34/28.48  | |            (97), (100), (103), (104), (106), (107), (108), (109), (110),
% 178.34/28.48  | |            (111), (112), (120), (121), (122), (123), (124) are inconsistent
% 178.34/28.48  | |            by sub-proof #622.
% 178.34/28.48  | | 
% 178.34/28.48  | Case 2:
% 178.34/28.48  | | 
% 178.34/28.48  | |   (125)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 178.34/28.48  | | 
% 178.34/28.48  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (12), (13), (17), (18), (19),
% 178.34/28.48  | |            (20), (22), (23), (24), (26), (27), (29), (30), (31), (35), (36),
% 178.34/28.48  | |            (37), (38), (39), (40), (42), (43), (45), (46), (47), (49), (51),
% 178.34/28.48  | |            (53), (54), (56), (57), (59), (60), (61), (64), (65), (66), (68),
% 178.34/28.48  | |            (69), (70), (72), (73), (75), (76), (77), (78), (80), (82), (83),
% 178.34/28.48  | |            (85), (86), (88), (89), (90), (91), (92), (93), (95), (96), (98),
% 178.34/28.48  | |            (101), (103), (106), (107), (111), (112), (125) are inconsistent
% 178.34/28.48  | |            by sub-proof #615.
% 178.34/28.48  | | 
% 178.34/28.48  | End of split
% 178.34/28.48  | 
% 178.34/28.48  End of proof
% 178.34/28.48  
% 178.34/28.48  Sub-proof #615 shows that the following formulas are inconsistent:
% 178.34/28.48  ----------------------------------------------------------------
% 178.34/28.48    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.48    (2)  all_40_2 = all_4_2
% 178.34/28.48    (3)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 178.34/28.48    (4)  all_56_3 = all_52_7
% 178.34/28.48    (5)  op(e3, e2) = all_52_3
% 178.34/28.48    (6)   ~ (all_52_9 = all_52_25)
% 178.34/28.48    (7)  op(e3, all_52_25) = all_52_24
% 178.34/28.48    (8)  op(e1, e2) = all_52_19
% 178.34/28.48    (9)  all_58_5 = all_52_13
% 178.34/28.48    (10)   ~ (all_52_25 = all_52_29)
% 178.34/28.48    (11)  all_56_9 = all_52_19
% 178.34/28.48    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.48    (13)   ~ (all_52_9 = all_4_2)
% 178.34/28.48    (14)   ~ (all_52_5 = all_52_7)
% 178.34/28.48    (15)   ~ (all_52_5 = all_4_2)
% 178.34/28.48    (16)  all_58_7 = all_52_19
% 178.34/28.48    (17)   ~ (all_52_17 = all_52_25)
% 178.34/28.48    (18)   ~ (all_4_0 = e2)
% 178.34/28.48    (19)  all_58_4 = all_52_5
% 178.34/28.48    (20)   ~ (e3 = e1)
% 178.34/28.48    (21)   ~ (all_52_27 = all_52_29)
% 178.34/28.48    (22)   ~ (all_52_17 = all_14_2)
% 178.34/28.48    (23)  all_58_0 = all_4_2
% 178.34/28.48    (24)  op(e1, all_52_29) = all_52_28
% 178.34/28.48    (25)   ~ (all_52_7 = e0)
% 178.34/28.48    (26)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.48    (27)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.48    (28)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.48    (29)  all_58_14 = all_52_29
% 178.34/28.48    (30)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.48    (31)  op(e2, e1) = all_52_13
% 178.34/28.48    (32)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.48    (33)  all_58_8 = all_14_2
% 178.34/28.48    (34)  all_56_14 = all_52_29
% 178.34/28.48    (35)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.48    (36)   ~ (all_52_3 = all_52_27)
% 178.34/28.48    (37)   ~ (all_52_3 = all_4_2)
% 178.34/28.48    (38)  op(e3, all_52_17) = all_52_16
% 178.34/28.48    (39)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.48    (40)   ~ (e3 = e0)
% 178.34/28.48    (41)  all_40_0 = all_4_0
% 178.34/28.48    (42)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.48    (43)  op(e1, e0) = all_52_23
% 178.34/28.48    (44)  all_56_12 = all_52_25
% 178.34/28.48    (45)  all_58_13 = all_52_27
% 178.34/28.48    (46)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.48    (47)   ~ (all_52_25 = e0)
% 178.34/28.48    (48)   ~ (all_52_9 = all_52_17)
% 178.34/28.48    (49)  all_58_6 = all_52_17
% 178.34/28.48    (50)   ~ (all_52_3 = all_52_7)
% 178.34/28.48    (51)   ~ (e1 = e0)
% 178.34/28.48    (52)  all_56_0 = all_4_2
% 178.34/28.48    (53)  all_58_11 = all_52_23
% 178.34/28.48    (54)   ~ (all_52_3 = all_52_19)
% 178.34/28.48    (55)   ~ (all_52_29 = all_14_2)
% 178.34/28.48    (56)  all_58_15 = e0
% 178.34/28.48    (57)  op(e1, all_4_2) = all_4_0
% 178.34/28.48    (58)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.34/28.48    (59)   ~ (all_52_29 = e0)
% 178.34/28.48    (60)  op(e3, e1) = all_52_5
% 178.34/28.48    (61)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.48    (62)  op(e1, e3) = all_52_17
% 178.34/28.48    (63)   ~ (all_52_25 = all_4_2)
% 178.34/28.48    (64)  op(e3, e0) = all_52_7
% 178.34/28.48    (65)  op(e3, e3) = all_4_2
% 178.34/28.48    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.48    (67)   ~ (all_52_25 = all_52_27)
% 178.34/28.48    (68)  op(e2, all_52_27) = all_52_26
% 178.34/28.48    (69)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.48    (70)  all_58_9 = all_52_7
% 178.34/28.48    (71)  all_58_12 = all_52_25
% 178.34/28.48    (72)  op(e3, all_4_2) = e1
% 178.34/28.48    (73)  op(e2, e3) = all_52_9
% 178.34/28.48    (74)  all_56_13 = all_52_27
% 178.34/28.48  
% 178.34/28.48  Begin of proof
% 178.34/28.49  | 
% 178.34/28.49  | ALPHA: (3) implies:
% 178.34/28.49  |   (75)  all_52_28 = e1
% 178.34/28.49  |   (76)  all_52_26 = e2
% 178.34/28.49  |   (77)  all_52_24 = e3
% 178.34/28.49  | 
% 178.34/28.49  | REDUCE: (7), (77) imply:
% 178.34/28.49  |   (78)  op(e3, all_52_25) = e3
% 178.34/28.49  | 
% 178.34/28.49  | REDUCE: (68), (76) imply:
% 178.34/28.49  |   (79)  op(e2, all_52_27) = e2
% 178.34/28.49  | 
% 178.34/28.49  | REDUCE: (24), (75) imply:
% 178.34/28.49  |   (80)  op(e1, all_52_29) = e1
% 178.34/28.49  | 
% 178.34/28.49  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 178.34/28.49  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 178.34/28.49  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 178.34/28.49  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 178.34/28.49  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 178.34/28.49  |            (60), (61), (62), (63), (64), (65), (66), (67), (69), (70), (71),
% 178.34/28.49  |            (72), (73), (74), (78), (79), (80) are inconsistent by sub-proof
% 178.34/28.49  |            #616.
% 178.34/28.49  | 
% 178.34/28.49  End of proof
% 178.34/28.49  
% 178.34/28.49  Sub-proof #616 shows that the following formulas are inconsistent:
% 178.34/28.49  ----------------------------------------------------------------
% 178.34/28.49    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.49    (2)  all_40_2 = all_4_2
% 178.34/28.49    (3)  all_56_3 = all_52_7
% 178.34/28.49    (4)  op(e3, e2) = all_52_3
% 178.34/28.49    (5)   ~ (all_52_9 = all_52_25)
% 178.34/28.49    (6)  op(e1, e2) = all_52_19
% 178.34/28.49    (7)  all_58_5 = all_52_13
% 178.34/28.49    (8)   ~ (all_52_25 = all_52_29)
% 178.34/28.49    (9)  all_56_9 = all_52_19
% 178.34/28.49    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.49    (11)   ~ (all_52_9 = all_4_2)
% 178.34/28.49    (12)   ~ (all_52_5 = all_52_7)
% 178.34/28.49    (13)   ~ (all_52_5 = all_4_2)
% 178.34/28.49    (14)  all_58_7 = all_52_19
% 178.34/28.49    (15)   ~ (all_52_17 = all_52_25)
% 178.34/28.49    (16)   ~ (all_4_0 = e2)
% 178.34/28.49    (17)  all_58_4 = all_52_5
% 178.34/28.49    (18)   ~ (e3 = e1)
% 178.34/28.49    (19)   ~ (all_52_27 = all_52_29)
% 178.34/28.49    (20)   ~ (all_52_17 = all_14_2)
% 178.34/28.49    (21)  all_58_0 = all_4_2
% 178.34/28.49    (22)  op(e2, all_52_27) = e2
% 178.34/28.49    (23)   ~ (all_52_7 = e0)
% 178.34/28.49    (24)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.49    (25)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.49    (26)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.49    (27)  all_58_14 = all_52_29
% 178.34/28.49    (28)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.49    (29)  op(e2, e1) = all_52_13
% 178.34/28.49    (30)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.49    (31)  all_58_8 = all_14_2
% 178.34/28.49    (32)  all_56_14 = all_52_29
% 178.34/28.49    (33)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.49    (34)  op(e1, all_52_29) = e1
% 178.34/28.49    (35)   ~ (all_52_3 = all_52_27)
% 178.34/28.49    (36)   ~ (all_52_3 = all_4_2)
% 178.34/28.49    (37)  op(e3, all_52_17) = all_52_16
% 178.34/28.49    (38)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.49    (39)   ~ (e3 = e0)
% 178.34/28.49    (40)  all_40_0 = all_4_0
% 178.34/28.49    (41)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.49    (42)  op(e1, e0) = all_52_23
% 178.34/28.49    (43)  all_56_12 = all_52_25
% 178.34/28.49    (44)  all_58_13 = all_52_27
% 178.34/28.49    (45)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.49    (46)   ~ (all_52_25 = e0)
% 178.34/28.49    (47)   ~ (all_52_9 = all_52_17)
% 178.34/28.49    (48)  all_58_6 = all_52_17
% 178.34/28.49    (49)   ~ (all_52_3 = all_52_7)
% 178.34/28.49    (50)   ~ (e1 = e0)
% 178.34/28.49    (51)  all_56_0 = all_4_2
% 178.34/28.49    (52)  all_58_11 = all_52_23
% 178.34/28.49    (53)   ~ (all_52_3 = all_52_19)
% 178.34/28.49    (54)   ~ (all_52_29 = all_14_2)
% 178.34/28.49    (55)  op(e3, all_52_25) = e3
% 178.34/28.49    (56)  all_58_15 = e0
% 178.34/28.49    (57)  op(e1, all_4_2) = all_4_0
% 178.34/28.49    (58)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.34/28.49    (59)   ~ (all_52_29 = e0)
% 178.34/28.49    (60)  op(e3, e1) = all_52_5
% 178.34/28.49    (61)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.49    (62)  op(e1, e3) = all_52_17
% 178.34/28.49    (63)   ~ (all_52_25 = all_4_2)
% 178.34/28.49    (64)  op(e3, e0) = all_52_7
% 178.34/28.49    (65)  op(e3, e3) = all_4_2
% 178.34/28.49    (66)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.49    (67)   ~ (all_52_25 = all_52_27)
% 178.34/28.49    (68)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.49    (69)  all_58_9 = all_52_7
% 178.34/28.49    (70)  all_58_12 = all_52_25
% 178.34/28.49    (71)  op(e3, all_4_2) = e1
% 178.34/28.49    (72)  op(e2, e3) = all_52_9
% 178.34/28.49    (73)  all_56_13 = all_52_27
% 178.34/28.49  
% 178.34/28.49  Begin of proof
% 178.34/28.49  | 
% 178.34/28.49  | BETA: splitting (28) gives:
% 178.34/28.49  | 
% 178.34/28.49  | Case 1:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (74)  all_56_13 = e3
% 178.34/28.49  | | 
% 178.34/28.49  | | COMBINE_EQS: (73), (74) imply:
% 178.34/28.49  | |   (75)  all_52_27 = e3
% 178.34/28.49  | | 
% 178.34/28.49  | | SIMP: (75) implies:
% 178.34/28.49  | |   (76)  all_52_27 = e3
% 178.34/28.49  | | 
% 178.34/28.49  | | REDUCE: (67), (76) imply:
% 178.34/28.49  | |   (77)   ~ (all_52_25 = e3)
% 178.34/28.49  | | 
% 178.34/28.49  | | REDUCE: (19), (76) imply:
% 178.34/28.49  | |   (78)   ~ (all_52_29 = e3)
% 178.34/28.49  | | 
% 178.34/28.49  | | SIMP: (78) implies:
% 178.34/28.49  | |   (79)   ~ (all_52_29 = e3)
% 178.34/28.49  | | 
% 178.34/28.49  | | REDUCE: (22), (76) imply:
% 178.34/28.49  | |   (80)  op(e2, e3) = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | REF_CLOSE: (1), (5), (6), (8), (10), (11), (13), (14), (16), (21), (25),
% 178.34/28.49  | |            (31), (32), (34), (41), (42), (43), (45), (46), (47), (48), (51),
% 178.34/28.49  | |            (52), (54), (55), (57), (59), (60), (63), (66), (72), (77), (79),
% 178.34/28.49  | |            (80) are inconsistent by sub-proof #621.
% 178.34/28.49  | | 
% 178.34/28.49  | Case 2:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (81)   ~ (all_56_13 = e3)
% 178.34/28.49  | | 
% 178.34/28.49  | | REDUCE: (73), (81) imply:
% 178.34/28.49  | |   (82)   ~ (all_52_27 = e3)
% 178.34/28.49  | | 
% 178.34/28.49  | | BETA: splitting (30) gives:
% 178.34/28.49  | | 
% 178.34/28.49  | | Case 1:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (83)  all_58_12 = e3
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REF_CLOSE: (55), (63), (65), (66), (70), (83) are inconsistent by
% 178.34/28.49  | | |            sub-proof #884.
% 178.34/28.49  | | | 
% 178.34/28.49  | | Case 2:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (84)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.49  | | | 
% 178.34/28.49  | | | BETA: splitting (84) gives:
% 178.34/28.49  | | | 
% 178.34/28.49  | | | Case 1:
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | |   (85)  all_58_13 = e3
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | REF_CLOSE: (44), (82), (85) are inconsistent by sub-proof #1026.
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | Case 2:
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | |   (86)  all_58_14 = e3 | all_58_15 = e3
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | BETA: splitting (86) gives:
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | Case 1:
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | |   (87)  all_58_14 = e3
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | COMBINE_EQS: (27), (87) imply:
% 178.34/28.49  | | | | |   (88)  all_52_29 = e3
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | SIMP: (88) implies:
% 178.34/28.49  | | | | |   (89)  all_52_29 = e3
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | REDUCE: (8), (89) imply:
% 178.34/28.49  | | | | |   (90)   ~ (all_52_25 = e3)
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | REDUCE: (34), (89) imply:
% 178.34/28.49  | | | | |   (91)  op(e1, e3) = e1
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | GROUND_INST: instantiating (66) with all_52_17, e1, e3, e1,
% 178.34/28.49  | | | | |              simplifying with (62), (91) gives:
% 178.34/28.49  | | | | |   (92)  all_52_17 = e1
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | REDUCE: (15), (92) imply:
% 178.34/28.49  | | | | |   (93)   ~ (all_52_25 = e1)
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | SIMP: (93) implies:
% 178.34/28.49  | | | | |   (94)   ~ (all_52_25 = e1)
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | REDUCE: (20), (92) imply:
% 178.34/28.49  | | | | |   (95)   ~ (all_14_2 = e1)
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | SIMP: (95) implies:
% 178.34/28.49  | | | | |   (96)   ~ (all_14_2 = e1)
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | REDUCE: (37), (92) imply:
% 178.34/28.49  | | | | |   (97)  op(e3, e1) = all_52_16
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | BETA: splitting (41) gives:
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | Case 1:
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | |   (98)  all_56_12 = e3
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | COMBINE_EQS: (43), (98) imply:
% 178.34/28.49  | | | | | |   (99)  all_52_25 = e3
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | REDUCE: (90), (99) imply:
% 178.34/28.49  | | | | | |   (100)  $false
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | CLOSE: (100) is inconsistent.
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | Case 2:
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | |   (101)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | BETA: splitting (58) gives:
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | Case 1:
% 178.34/28.49  | | | | | | | 
% 178.34/28.49  | | | | | | |   (102)  all_58_12 = e1
% 178.34/28.49  | | | | | | | 
% 178.34/28.49  | | | | | | | REF_CLOSE: (70), (94), (102) are inconsistent by sub-proof #883.
% 178.34/28.49  | | | | | | | 
% 178.34/28.49  | | | | | | Case 2:
% 178.34/28.49  | | | | | | | 
% 178.34/28.49  | | | | | | |   (103)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.34/28.49  | | | | | | | 
% 178.34/28.49  | | | | | | | BETA: splitting (103) gives:
% 178.34/28.49  | | | | | | | 
% 178.34/28.49  | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | |   (104)  all_58_13 = e1
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | | COMBINE_EQS: (44), (104) imply:
% 178.34/28.49  | | | | | | | |   (105)  all_52_27 = e1
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | | SIMP: (105) implies:
% 178.34/28.49  | | | | | | | |   (106)  all_52_27 = e1
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | | REDUCE: (35), (106) imply:
% 178.34/28.49  | | | | | | | |   (107)   ~ (all_52_3 = e1)
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | | REDUCE: (22), (106) imply:
% 178.34/28.49  | | | | | | | |   (108)  op(e2, e1) = e2
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | | BETA: splitting (61) gives:
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | |   (109)  all_58_12 = e2
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | COMBINE_EQS: (70), (109) imply:
% 178.34/28.49  | | | | | | | | |   (110)  all_52_25 = e2
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | SIMP: (110) implies:
% 178.34/28.49  | | | | | | | | |   (111)  all_52_25 = e2
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (94), (111) imply:
% 178.34/28.49  | | | | | | | | |   (112)   ~ (e2 = e1)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (55), (111) imply:
% 178.34/28.49  | | | | | | | | |   (113)  op(e3, e2) = e3
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | GROUND_INST: instantiating (66) with all_52_13, e2, e1, e2,
% 178.34/28.49  | | | | | | | | |              simplifying with (29), (108) gives:
% 178.34/28.49  | | | | | | | | |   (114)  all_52_13 = e2
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | GROUND_INST: instantiating (66) with all_52_5, all_52_16, e1,
% 178.34/28.49  | | | | | | | | |              e3, simplifying with (60), (97) gives:
% 178.34/28.49  | | | | | | | | |   (115)  all_52_5 = all_52_16
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | GROUND_INST: instantiating (66) with all_52_3, e3, e2, e3,
% 178.34/28.49  | | | | | | | | |              simplifying with (4), (113) gives:
% 178.34/28.49  | | | | | | | | |   (116)  all_52_3 = e3
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | COMBINE_EQS: (7), (114) imply:
% 178.34/28.49  | | | | | | | | |   (117)  all_58_5 = e2
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | COMBINE_EQS: (17), (115) imply:
% 178.34/28.49  | | | | | | | | |   (118)  all_58_4 = all_52_16
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (49), (116) imply:
% 178.34/28.49  | | | | | | | | |   (119)   ~ (all_52_7 = e3)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | SIMP: (119) implies:
% 178.34/28.49  | | | | | | | | |   (120)   ~ (all_52_7 = e3)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (53), (116) imply:
% 178.34/28.49  | | | | | | | | |   (121)   ~ (all_52_19 = e3)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | SIMP: (121) implies:
% 178.34/28.49  | | | | | | | | |   (122)   ~ (all_52_19 = e3)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (36), (116) imply:
% 178.34/28.49  | | | | | | | | |   (123)   ~ (all_4_2 = e3)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | SIMP: (123) implies:
% 178.34/28.49  | | | | | | | | |   (124)   ~ (all_4_2 = e3)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (12), (115) imply:
% 178.34/28.49  | | | | | | | | |   (125)   ~ (all_52_7 = all_52_16)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | SIMP: (125) implies:
% 178.34/28.49  | | | | | | | | |   (126)   ~ (all_52_7 = all_52_16)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (13), (115) imply:
% 178.34/28.49  | | | | | | | | |   (127)   ~ (all_52_16 = all_4_2)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | BETA: splitting (26) gives:
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | |   (128)  all_58_4 = e1
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | COMBINE_EQS: (118), (128) imply:
% 178.34/28.49  | | | | | | | | | |   (129)  all_52_16 = e1
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | REDUCE: (126), (129) imply:
% 178.34/28.49  | | | | | | | | | |   (130)   ~ (all_52_7 = e1)
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | REDUCE: (127), (129) imply:
% 178.34/28.49  | | | | | | | | | |   (131)   ~ (all_4_2 = e1)
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | SIMP: (131) implies:
% 178.34/28.49  | | | | | | | | | |   (132)   ~ (all_4_2 = e1)
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | BETA: splitting (10) gives:
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | |   (133)  all_56_0 = e3
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | COMBINE_EQS: (51), (133) imply:
% 178.34/28.49  | | | | | | | | | | |   (134)  all_4_2 = e3
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | REDUCE: (124), (134) imply:
% 178.34/28.49  | | | | | | | | | | |   (135)  $false
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | |   (136)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | BETA: splitting (68) gives:
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | |   (137)  all_56_3 = e3
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | COMBINE_EQS: (3), (137) imply:
% 178.34/28.49  | | | | | | | | | | | |   (138)  all_52_7 = e3
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | REDUCE: (120), (138) imply:
% 178.34/28.49  | | | | | | | | | | | |   (139)  $false
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | |   (140)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | BETA: splitting (24) gives:
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | |   (141)  all_56_9 = e3
% 178.34/28.49  | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | REF_CLOSE: (9), (122), (141) are inconsistent by sub-proof
% 178.34/28.49  | | | | | | | | | | | | |            #700.
% 178.34/28.49  | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | |   (142)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.49  | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | BETA: splitting (38) gives:
% 178.34/28.49  | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | |   (143)  all_58_9 = e2
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | COMBINE_EQS: (69), (143) imply:
% 178.34/28.49  | | | | | | | | | | | | | |   (144)  all_52_7 = e2
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | REDUCE: (64), (144) imply:
% 178.34/28.49  | | | | | | | | | | | | | |   (145)  op(e3, e0) = e2
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | Case 1:
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | |   (146)  all_58_0 = e0
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | | COMBINE_EQS: (21), (146) imply:
% 178.34/28.49  | | | | | | | | | | | | | | |   (147)  all_4_2 = e0
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | | REDUCE: (71), (147) imply:
% 178.34/28.49  | | | | | | | | | | | | | | |   (148)  op(e3, e0) = e1
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | | REF_CLOSE: (66), (112), (145), (148) are inconsistent by
% 178.34/28.49  | | | | | | | | | | | | | | |            sub-proof #620.
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | |   (149)   ~ (all_58_0 = e0)
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | | REDUCE: (21), (149) imply:
% 178.34/28.49  | | | | | | | | | | | | | | |   (150)   ~ (all_4_2 = e0)
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (9), (16), (33), (40), (51), (53),
% 178.34/28.49  | | | | | | | | | | | | | | |            (57), (66), (71), (132), (136), (142), (150) are
% 178.34/28.49  | | | | | | | | | | | | | | |            inconsistent by sub-proof #618.
% 178.34/28.49  | | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | End of split
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | |   (151)   ~ (all_58_9 = e2)
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | REDUCE: (69), (151) imply:
% 178.34/28.49  | | | | | | | | | | | | | |   (152)   ~ (all_52_7 = e2)
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | | REF_CLOSE: (3), (23), (130), (140), (152) are inconsistent by
% 178.34/28.49  | | | | | | | | | | | | | |            sub-proof #893.
% 178.34/28.49  | | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | | End of split
% 178.34/28.49  | | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | | End of split
% 178.34/28.49  | | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | | End of split
% 178.34/28.49  | | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | End of split
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | |   (153)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | | REF_CLOSE: (18), (31), (87), (96), (112), (117), (153) are
% 178.34/28.49  | | | | | | | | | |            inconsistent by sub-proof #617.
% 178.34/28.49  | | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | End of split
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | |   (154)   ~ (all_58_12 = e2)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REDUCE: (70), (154) imply:
% 178.34/28.49  | | | | | | | | |   (155)   ~ (all_52_25 = e2)
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | | REF_CLOSE: (43), (46), (94), (101), (155) are inconsistent by
% 178.34/28.49  | | | | | | | | |            sub-proof #1028.
% 178.34/28.49  | | | | | | | | | 
% 178.34/28.49  | | | | | | | | End of split
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | Case 2:
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | |   (156)  all_58_14 = e1 | all_58_15 = e1
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | | REF_CLOSE: (18), (50), (56), (87), (156) are inconsistent by
% 178.34/28.49  | | | | | | | |            sub-proof #880.
% 178.34/28.49  | | | | | | | | 
% 178.34/28.49  | | | | | | | End of split
% 178.34/28.49  | | | | | | | 
% 178.34/28.49  | | | | | | End of split
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | End of split
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | Case 2:
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | |   (157)  all_58_15 = e3
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | REF_CLOSE: (39), (56), (157) are inconsistent by sub-proof #1010.
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | End of split
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | End of split
% 178.34/28.49  | | | 
% 178.34/28.49  | | End of split
% 178.34/28.49  | | 
% 178.34/28.49  | End of split
% 178.34/28.49  | 
% 178.34/28.49  End of proof
% 178.34/28.49  
% 178.34/28.49  Sub-proof #617 shows that the following formulas are inconsistent:
% 178.34/28.49  ----------------------------------------------------------------
% 178.34/28.49    (1)   ~ (e3 = e1)
% 178.34/28.49    (2)   ~ (all_14_2 = e1)
% 178.34/28.49    (3)  all_58_8 = all_14_2
% 178.34/28.49    (4)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.49    (5)  all_58_5 = e2
% 178.34/28.49    (6)   ~ (e2 = e1)
% 178.34/28.49    (7)  all_58_14 = e3
% 178.34/28.49  
% 178.34/28.49  Begin of proof
% 178.34/28.49  | 
% 178.34/28.49  | BETA: splitting (4) gives:
% 178.34/28.49  | 
% 178.34/28.49  | Case 1:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (8)  all_58_5 = e1
% 178.34/28.49  | | 
% 178.34/28.49  | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #672.
% 178.34/28.49  | | 
% 178.34/28.49  | Case 2:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (9)  all_58_8 = e1 | all_58_14 = e1
% 178.34/28.49  | | 
% 178.34/28.49  | | REF_CLOSE: (1), (2), (3), (7), (9) are inconsistent by sub-proof #638.
% 178.34/28.49  | | 
% 178.34/28.49  | End of split
% 178.34/28.49  | 
% 178.34/28.49  End of proof
% 178.34/28.49  
% 178.34/28.49  Sub-proof #618 shows that the following formulas are inconsistent:
% 178.34/28.49  ----------------------------------------------------------------
% 178.34/28.49    (1)  all_40_2 = all_4_2
% 178.34/28.49    (2)  op(e3, e2) = all_52_3
% 178.34/28.49    (3)  op(e1, e2) = all_52_19
% 178.34/28.49    (4)  all_56_9 = all_52_19
% 178.34/28.49    (5)   ~ (all_4_0 = e2)
% 178.34/28.49    (6)   ~ (all_40_0 = e0) |  ~ (all_40_2 = e2)
% 178.34/28.49    (7)  all_40_0 = all_4_0
% 178.34/28.49    (8)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.49    (9)  all_56_0 = all_4_2
% 178.34/28.49    (10)   ~ (all_52_3 = all_52_19)
% 178.34/28.49    (11)  op(e1, all_4_2) = all_4_0
% 178.34/28.49    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.49    (13)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.49    (14)   ~ (all_4_2 = e1)
% 178.34/28.49    (15)   ~ (all_4_2 = e0)
% 178.34/28.49    (16)  op(e3, all_4_2) = e1
% 178.34/28.49  
% 178.34/28.49  Begin of proof
% 178.34/28.49  | 
% 178.34/28.49  | BETA: splitting (13) gives:
% 178.34/28.49  | 
% 178.34/28.49  | Case 1:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (17)  all_56_0 = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | COMBINE_EQS: (9), (17) imply:
% 178.34/28.49  | |   (18)  all_4_2 = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | SIMP: (18) implies:
% 178.34/28.49  | |   (19)  all_4_2 = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | COMBINE_EQS: (1), (19) imply:
% 178.34/28.49  | |   (20)  all_40_2 = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | REDUCE: (16), (19) imply:
% 178.34/28.49  | |   (21)  op(e3, e2) = e1
% 178.34/28.49  | | 
% 178.34/28.49  | | REDUCE: (11), (19) imply:
% 178.34/28.49  | |   (22)  op(e1, e2) = all_4_0
% 178.34/28.49  | | 
% 178.34/28.49  | | BETA: splitting (6) gives:
% 178.34/28.49  | | 
% 178.34/28.49  | | Case 1:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (23)   ~ (all_40_2 = e2)
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REDUCE: (20), (23) imply:
% 178.34/28.49  | | |   (24)  $false
% 178.34/28.49  | | | 
% 178.34/28.49  | | | CLOSE: (24) is inconsistent.
% 178.34/28.49  | | | 
% 178.34/28.49  | | Case 2:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (25)   ~ (all_40_0 = e0)
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REDUCE: (7), (25) imply:
% 178.34/28.49  | | |   (26)   ~ (all_4_0 = e0)
% 178.34/28.49  | | | 
% 178.34/28.49  | | | GROUND_INST: instantiating (12) with all_52_19, all_4_0, e2, e1,
% 178.34/28.49  | | |              simplifying with (3), (22) gives:
% 178.34/28.49  | | |   (27)  all_52_19 = all_4_0
% 178.34/28.49  | | | 
% 178.34/28.49  | | | GROUND_INST: instantiating (12) with all_52_3, e1, e2, e3, simplifying
% 178.34/28.49  | | |              with (2), (21) gives:
% 178.34/28.49  | | |   (28)  all_52_3 = e1
% 178.34/28.49  | | | 
% 178.34/28.49  | | | COMBINE_EQS: (4), (27) imply:
% 178.34/28.49  | | |   (29)  all_56_9 = all_4_0
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REDUCE: (10), (27), (28) imply:
% 178.34/28.49  | | |   (30)   ~ (all_4_0 = e1)
% 178.34/28.49  | | | 
% 178.34/28.49  | | | SIMP: (30) implies:
% 178.34/28.49  | | |   (31)   ~ (all_4_0 = e1)
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REF_CLOSE: (5), (8), (26), (29), (31) are inconsistent by sub-proof #619.
% 178.34/28.49  | | | 
% 178.34/28.49  | | End of split
% 178.34/28.49  | | 
% 178.34/28.49  | Case 2:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (32)  all_56_0 = e1 | all_56_0 = e0
% 178.34/28.49  | | 
% 178.34/28.49  | | REF_CLOSE: (9), (14), (15), (32) are inconsistent by sub-proof #1020.
% 178.34/28.49  | | 
% 178.34/28.49  | End of split
% 178.34/28.49  | 
% 178.34/28.49  End of proof
% 178.34/28.49  
% 178.34/28.49  Sub-proof #619 shows that the following formulas are inconsistent:
% 178.34/28.49  ----------------------------------------------------------------
% 178.34/28.49    (1)   ~ (all_4_0 = e0)
% 178.34/28.49    (2)  all_56_9 = all_4_0
% 178.34/28.49    (3)   ~ (all_4_0 = e2)
% 178.34/28.49    (4)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.49    (5)   ~ (all_4_0 = e1)
% 178.34/28.49  
% 178.34/28.49  Begin of proof
% 178.34/28.49  | 
% 178.34/28.49  | BETA: splitting (4) gives:
% 178.34/28.49  | 
% 178.34/28.49  | Case 1:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (6)  all_56_9 = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | COMBINE_EQS: (2), (6) imply:
% 178.34/28.49  | |   (7)  all_4_0 = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | SIMP: (7) implies:
% 178.34/28.49  | |   (8)  all_4_0 = e2
% 178.34/28.49  | | 
% 178.34/28.49  | | REDUCE: (3), (8) imply:
% 178.34/28.49  | |   (9)  $false
% 178.34/28.49  | | 
% 178.34/28.49  | | CLOSE: (9) is inconsistent.
% 178.34/28.49  | | 
% 178.34/28.49  | Case 2:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (10)  all_56_9 = e1 | all_56_9 = e0
% 178.34/28.49  | | 
% 178.34/28.49  | | BETA: splitting (10) gives:
% 178.34/28.49  | | 
% 178.34/28.49  | | Case 1:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (11)  all_56_9 = e1
% 178.34/28.49  | | | 
% 178.34/28.49  | | | COMBINE_EQS: (2), (11) imply:
% 178.34/28.49  | | |   (12)  all_4_0 = e1
% 178.34/28.49  | | | 
% 178.34/28.49  | | | SIMP: (12) implies:
% 178.34/28.49  | | |   (13)  all_4_0 = e1
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REDUCE: (5), (13) imply:
% 178.34/28.49  | | |   (14)  $false
% 178.34/28.49  | | | 
% 178.34/28.49  | | | CLOSE: (14) is inconsistent.
% 178.34/28.49  | | | 
% 178.34/28.49  | | Case 2:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (15)  all_56_9 = e0
% 178.34/28.49  | | | 
% 178.34/28.49  | | | COMBINE_EQS: (2), (15) imply:
% 178.34/28.49  | | |   (16)  all_4_0 = e0
% 178.34/28.49  | | | 
% 178.34/28.49  | | | SIMP: (16) implies:
% 178.34/28.49  | | |   (17)  all_4_0 = e0
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REDUCE: (1), (17) imply:
% 178.34/28.49  | | |   (18)  $false
% 178.34/28.49  | | | 
% 178.34/28.49  | | | CLOSE: (18) is inconsistent.
% 178.34/28.49  | | | 
% 178.34/28.49  | | End of split
% 178.34/28.49  | | 
% 178.34/28.49  | End of split
% 178.34/28.49  | 
% 178.34/28.49  End of proof
% 178.34/28.49  
% 178.34/28.49  Sub-proof #620 shows that the following formulas are inconsistent:
% 178.34/28.49  ----------------------------------------------------------------
% 178.34/28.49    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.49    (2)  op(e3, e0) = e2
% 178.34/28.49    (3)  op(e3, e0) = e1
% 178.34/28.49    (4)   ~ (e2 = e1)
% 178.34/28.49  
% 178.34/28.49  Begin of proof
% 178.34/28.49  | 
% 178.34/28.49  | GROUND_INST: instantiating (1) with e1, e2, e0, e3, simplifying with (2), (3)
% 178.34/28.49  |              gives:
% 178.34/28.49  |   (5)  e2 = e1
% 178.34/28.49  | 
% 178.34/28.49  | REDUCE: (4), (5) imply:
% 178.34/28.49  |   (6)  $false
% 178.34/28.49  | 
% 178.34/28.49  | CLOSE: (6) is inconsistent.
% 178.34/28.49  | 
% 178.34/28.49  End of proof
% 178.34/28.49  
% 178.34/28.49  Sub-proof #621 shows that the following formulas are inconsistent:
% 178.34/28.49  ----------------------------------------------------------------
% 178.34/28.49    (1)   ~ (all_52_25 = e3)
% 178.34/28.49    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.49    (3)  op(e2, e3) = e2
% 178.34/28.49    (4)   ~ (all_52_9 = all_52_25)
% 178.34/28.49    (5)  op(e1, e2) = all_52_19
% 178.34/28.49    (6)   ~ (all_52_25 = all_52_29)
% 178.34/28.49    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.49    (8)   ~ (all_52_9 = all_4_2)
% 178.34/28.49    (9)   ~ (all_52_5 = all_4_2)
% 178.34/28.49    (10)  all_58_7 = all_52_19
% 178.34/28.49    (11)   ~ (all_4_0 = e2)
% 178.34/28.49    (12)  all_58_0 = all_4_2
% 178.34/28.49    (13)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.49    (14)  all_58_8 = all_14_2
% 178.34/28.49    (15)  all_56_14 = all_52_29
% 178.34/28.49    (16)  op(e1, all_52_29) = e1
% 178.34/28.49    (17)   ~ (all_52_29 = e3)
% 178.34/28.49    (18)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.49    (19)  op(e1, e0) = all_52_23
% 178.34/28.49    (20)  all_56_12 = all_52_25
% 178.34/28.49    (21)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.49    (22)   ~ (all_52_25 = e0)
% 178.34/28.49    (23)   ~ (all_52_9 = all_52_17)
% 178.34/28.49    (24)  all_58_6 = all_52_17
% 178.34/28.49    (25)  all_56_0 = all_4_2
% 178.34/28.49    (26)  all_58_11 = all_52_23
% 178.34/28.49    (27)   ~ (all_52_29 = all_14_2)
% 178.34/28.49    (28)  op(e3, all_52_25) = e3
% 178.34/28.49    (29)  op(e1, all_4_2) = all_4_0
% 178.34/28.49    (30)   ~ (all_52_29 = e0)
% 178.34/28.49    (31)  op(e3, e1) = all_52_5
% 178.34/28.49    (32)   ~ (all_52_25 = all_4_2)
% 178.34/28.49    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.49    (34)  op(e2, e3) = all_52_9
% 178.34/28.49  
% 178.34/28.49  Begin of proof
% 178.34/28.49  | 
% 178.34/28.49  | GROUND_INST: instantiating (33) with all_52_9, e2, e3, e2, simplifying with
% 178.34/28.49  |              (3), (34) gives:
% 178.34/28.49  |   (35)  all_52_9 = e2
% 178.34/28.49  | 
% 178.34/28.49  | REDUCE: (23), (35) imply:
% 178.34/28.49  |   (36)   ~ (all_52_17 = e2)
% 178.34/28.49  | 
% 178.34/28.49  | SIMP: (36) implies:
% 178.34/28.49  |   (37)   ~ (all_52_17 = e2)
% 178.34/28.49  | 
% 178.34/28.49  | REDUCE: (4), (35) imply:
% 178.34/28.49  |   (38)   ~ (all_52_25 = e2)
% 178.34/28.49  | 
% 178.34/28.49  | SIMP: (38) implies:
% 178.34/28.49  |   (39)   ~ (all_52_25 = e2)
% 178.34/28.49  | 
% 178.34/28.49  | REDUCE: (8), (35) imply:
% 178.34/28.49  |   (40)   ~ (all_4_2 = e2)
% 178.34/28.49  | 
% 178.34/28.49  | SIMP: (40) implies:
% 178.34/28.49  |   (41)   ~ (all_4_2 = e2)
% 178.34/28.49  | 
% 178.34/28.49  | BETA: splitting (18) gives:
% 178.34/28.49  | 
% 178.34/28.49  | Case 1:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (42)  all_56_12 = e3
% 178.34/28.49  | | 
% 178.34/28.49  | | REF_CLOSE: (1), (20), (42) are inconsistent by sub-proof #1040.
% 178.34/28.49  | | 
% 178.34/28.49  | Case 2:
% 178.34/28.49  | | 
% 178.34/28.49  | |   (43)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.49  | | 
% 178.34/28.49  | | BETA: splitting (43) gives:
% 178.34/28.49  | | 
% 178.34/28.49  | | Case 1:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (44)  all_56_12 = e2
% 178.34/28.49  | | | 
% 178.34/28.49  | | | REF_CLOSE: (20), (39), (44) are inconsistent by sub-proof #1032.
% 178.34/28.49  | | | 
% 178.34/28.49  | | Case 2:
% 178.34/28.49  | | | 
% 178.34/28.49  | | |   (45)  all_56_12 = e1 | all_56_12 = e0
% 178.34/28.49  | | | 
% 178.34/28.49  | | | BETA: splitting (45) gives:
% 178.34/28.49  | | | 
% 178.34/28.49  | | | Case 1:
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | |   (46)  all_56_12 = e1
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | COMBINE_EQS: (20), (46) imply:
% 178.34/28.49  | | | |   (47)  all_52_25 = e1
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | SIMP: (47) implies:
% 178.34/28.49  | | | |   (48)  all_52_25 = e1
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | REDUCE: (6), (48) imply:
% 178.34/28.49  | | | |   (49)   ~ (all_52_29 = e1)
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | SIMP: (49) implies:
% 178.34/28.49  | | | |   (50)   ~ (all_52_29 = e1)
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | REDUCE: (32), (48) imply:
% 178.34/28.49  | | | |   (51)   ~ (all_4_2 = e1)
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | SIMP: (51) implies:
% 178.34/28.49  | | | |   (52)   ~ (all_4_2 = e1)
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | REDUCE: (28), (48) imply:
% 178.34/28.49  | | | |   (53)  op(e3, e1) = e3
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | BETA: splitting (13) gives:
% 178.34/28.49  | | | | 
% 178.34/28.49  | | | | Case 1:
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | |   (54)  all_56_14 = e3
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | REF_CLOSE: (15), (17), (54) are inconsistent by sub-proof #896.
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | Case 2:
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | |   (55)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | BETA: splitting (55) gives:
% 178.34/28.49  | | | | | 
% 178.34/28.49  | | | | | Case 1:
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | |   (56)  all_56_14 = e2
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | COMBINE_EQS: (15), (56) imply:
% 178.34/28.49  | | | | | |   (57)  all_52_29 = e2
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | SIMP: (57) implies:
% 178.34/28.49  | | | | | |   (58)  all_52_29 = e2
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | REDUCE: (27), (58) imply:
% 178.34/28.49  | | | | | |   (59)   ~ (all_14_2 = e2)
% 178.34/28.49  | | | | | | 
% 178.34/28.49  | | | | | | SIMP: (59) implies:
% 178.34/28.50  | | | | | |   (60)   ~ (all_14_2 = e2)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REDUCE: (50), (58) imply:
% 178.34/28.50  | | | | | |   (61)   ~ (e2 = e1)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REDUCE: (16), (58) imply:
% 178.34/28.50  | | | | | |   (62)  op(e1, e2) = e1
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | GROUND_INST: instantiating (33) with all_52_19, e1, e2, e1,
% 178.34/28.50  | | | | | |              simplifying with (5), (62) gives:
% 178.34/28.50  | | | | | |   (63)  all_52_19 = e1
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | GROUND_INST: instantiating (33) with all_52_5, e3, e1, e3,
% 178.34/28.50  | | | | | |              simplifying with (31), (53) gives:
% 178.34/28.50  | | | | | |   (64)  all_52_5 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | COMBINE_EQS: (10), (63) imply:
% 178.34/28.50  | | | | | |   (65)  all_58_7 = e1
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REDUCE: (9), (64) imply:
% 178.34/28.50  | | | | | |   (66)   ~ (all_4_2 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | SIMP: (66) implies:
% 178.34/28.50  | | | | | |   (67)   ~ (all_4_2 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | BETA: splitting (21) gives:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | Case 1:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | |   (68)  all_58_6 = e2
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | REF_CLOSE: (24), (37), (68) are inconsistent by sub-proof #894.
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | Case 2:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | |   (69)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | BETA: splitting (7) gives:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | |   (70)  all_56_0 = e3
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | COMBINE_EQS: (25), (70) imply:
% 178.34/28.50  | | | | | | | |   (71)  all_4_2 = e3
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | REDUCE: (67), (71) imply:
% 178.34/28.50  | | | | | | | |   (72)  $false
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | CLOSE: (72) is inconsistent.
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | |   (73)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | BETA: splitting (69) gives:
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | |   (74)  all_58_7 = e2
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | REF_CLOSE: (61), (65), (74) are inconsistent by sub-proof
% 178.34/28.50  | | | | | | | | |            #891.
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | |   (75)  all_58_8 = e2 | all_58_11 = e2
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | BETA: splitting (75) gives:
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | |   (76)  all_58_8 = e2
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | COMBINE_EQS: (14), (76) imply:
% 178.34/28.50  | | | | | | | | | |   (77)  all_14_2 = e2
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | REDUCE: (60), (77) imply:
% 178.34/28.50  | | | | | | | | | |   (78)  $false
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | CLOSE: (78) is inconsistent.
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | |   (79)  all_58_11 = e2
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | COMBINE_EQS: (26), (79) imply:
% 178.34/28.50  | | | | | | | | | |   (80)  all_52_23 = e2
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | SIMP: (80) implies:
% 178.34/28.50  | | | | | | | | | |   (81)  all_52_23 = e2
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | REDUCE: (19), (81) imply:
% 178.34/28.50  | | | | | | | | | |   (82)  op(e1, e0) = e2
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | BETA: splitting (2) gives:
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | |   (83)  all_58_0 = e0
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | COMBINE_EQS: (12), (83) imply:
% 178.34/28.50  | | | | | | | | | | |   (84)  all_4_2 = e0
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | REDUCE: (29), (84) imply:
% 178.34/28.50  | | | | | | | | | | |   (85)  op(e1, e0) = all_4_0
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | GROUND_INST: instantiating (33) with e2, all_4_0, e0, e1,
% 178.34/28.50  | | | | | | | | | | |              simplifying with (82), (85) gives:
% 178.34/28.50  | | | | | | | | | | |   (86)  all_4_0 = e2
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | REDUCE: (11), (86) imply:
% 178.34/28.50  | | | | | | | | | | |   (87)  $false
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | CLOSE: (87) is inconsistent.
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | |   (88)   ~ (all_58_0 = e0)
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | REDUCE: (12), (88) imply:
% 178.34/28.50  | | | | | | | | | | |   (89)   ~ (all_4_2 = e0)
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | REF_CLOSE: (25), (41), (52), (73), (89) are inconsistent by
% 178.34/28.50  | | | | | | | | | | |            sub-proof #882.
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | End of split
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | End of split
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | End of split
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | End of split
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | End of split
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | Case 2:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | |   (90)  all_56_14 = e1 | all_56_14 = e0
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REF_CLOSE: (15), (30), (50), (90) are inconsistent by sub-proof
% 178.34/28.50  | | | | | |            #886.
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | End of split
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | End of split
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | Case 2:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | |   (91)  all_56_12 = e0
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | REF_CLOSE: (20), (22), (91) are inconsistent by sub-proof #1030.
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | End of split
% 178.34/28.50  | | | 
% 178.34/28.50  | | End of split
% 178.34/28.50  | | 
% 178.34/28.50  | End of split
% 178.34/28.50  | 
% 178.34/28.50  End of proof
% 178.34/28.50  
% 178.34/28.50  Sub-proof #622 shows that the following formulas are inconsistent:
% 178.34/28.50  ----------------------------------------------------------------
% 178.34/28.50    (1)   ~ (all_52_5 = all_52_13)
% 178.34/28.50    (2)  op(e3, e2) = all_52_3
% 178.34/28.50    (3)   ~ (all_52_9 = all_52_25)
% 178.34/28.50    (4)  op(e3, all_52_25) = all_52_24
% 178.34/28.50    (5)  all_56_11 = all_52_23
% 178.34/28.50    (6)   ~ (all_52_27 = e0)
% 178.34/28.50    (7)   ~ (all_52_23 = e0)
% 178.34/28.50    (8)  all_58_5 = all_52_13
% 178.34/28.50    (9)   ~ (all_52_25 = all_52_29)
% 178.34/28.50    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.50    (11)  all_58_3 = all_10_2
% 178.34/28.50    (12)  all_56_9 = all_52_19
% 178.34/28.50    (13)  all_58_10 = all_52_15
% 178.34/28.50    (14)   ~ (all_52_5 = all_4_2)
% 178.34/28.50    (15)  all_58_7 = all_52_19
% 178.34/28.50    (16)   ~ (all_52_17 = all_52_25)
% 178.34/28.50    (17)  op(e0, e1) = all_52_29
% 178.34/28.50    (18)  all_58_4 = all_52_5
% 178.34/28.50    (19)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.50    (20)   ~ (all_52_27 = all_52_29)
% 178.34/28.50    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.50    (22)   ~ (all_52_7 = all_4_2)
% 178.34/28.50    (23)  all_58_1 = all_52_3
% 178.34/28.50    (24)  all_58_0 = all_4_2
% 178.34/28.50    (25)  op(e1, all_52_29) = all_52_28
% 178.34/28.50    (26)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.50    (27)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.34/28.50    (28)  all_58_14 = all_52_29
% 178.34/28.50    (29)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.50    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.50    (31)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.50    (32)  all_58_8 = all_14_2
% 178.34/28.50    (33)  op(e0, e2) = all_52_27
% 178.34/28.50    (34)   ~ (all_14_0 = e3)
% 178.34/28.50    (35)   ~ (all_52_5 = all_14_2)
% 178.34/28.50    (36)  op(e0, e3) = all_52_25
% 178.34/28.50    (37)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.50    (38)   ~ (all_52_13 = all_14_2)
% 178.34/28.50    (39)  op(e1, all_14_2) = all_14_0
% 178.34/28.50    (40)   ~ (e3 = e0)
% 178.34/28.50    (41)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.50    (42)   ~ (all_52_5 = all_52_29)
% 178.34/28.50    (43)  all_56_12 = all_52_25
% 178.34/28.50    (44)  all_58_13 = all_52_27
% 178.34/28.50    (45)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.50    (46)   ~ (all_52_25 = e0)
% 178.34/28.50    (47)   ~ (all_52_9 = all_52_17)
% 178.34/28.50    (48)   ~ (all_14_0 = e2)
% 178.34/28.50    (49)  all_58_6 = all_52_17
% 178.34/28.50    (50)  op(e2, all_52_19) = e2
% 178.34/28.50    (51)  op(e3, all_52_17) = e3
% 178.34/28.50    (52)   ~ (e1 = e0)
% 178.34/28.50    (53)  all_58_11 = all_52_23
% 178.34/28.50    (54)   ~ (all_52_3 = all_52_19)
% 178.34/28.50    (55)   ~ (all_52_7 = all_52_15)
% 178.34/28.50    (56)   ~ (all_52_29 = all_14_2)
% 178.34/28.50    (57)   ~ (all_52_19 = all_10_2)
% 178.34/28.50    (58)  all_58_15 = e0
% 178.34/28.50    (59)  all_58_2 = all_52_9
% 178.34/28.50    (60)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.34/28.50    (61)   ~ (all_52_29 = e0)
% 178.34/28.50    (62)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.50    (63)  op(e3, e1) = all_52_5
% 178.34/28.50    (64)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.50    (65)  op(e1, e3) = all_52_17
% 178.34/28.50    (66)  op(e3, e3) = all_4_2
% 178.34/28.50    (67)   ~ (all_52_17 = all_4_2)
% 178.34/28.50    (68)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.50    (69)   ~ (all_52_25 = all_52_27)
% 178.34/28.50    (70)  op(e0, all_52_23) = e0
% 178.34/28.50    (71)  op(e1, all_14_2) = e1
% 178.34/28.50    (72)   ~ (all_52_7 = all_52_23)
% 178.34/28.50    (73)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.50    (74)  all_58_9 = all_52_7
% 178.34/28.50    (75)   ~ (e2 = e0)
% 178.34/28.50    (76)  all_58_12 = all_52_25
% 178.34/28.50    (77)  op(e3, all_4_2) = e1
% 178.34/28.50    (78)  all_56_6 = all_52_13
% 178.34/28.50    (79)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.50    (80)   ~ (e3 = e2)
% 178.34/28.50    (81)  op(e2, e3) = all_52_9
% 178.34/28.50    (82)  all_56_13 = all_52_27
% 178.34/28.50  
% 178.34/28.50  Begin of proof
% 178.34/28.50  | 
% 178.34/28.50  | GROUND_INST: instantiating (68) with e1, all_14_0, all_14_2, e1, simplifying
% 178.34/28.50  |              with (39), (71) gives:
% 178.34/28.50  |   (83)  all_14_0 = e1
% 178.34/28.50  | 
% 178.34/28.50  | REDUCE: (34), (83) imply:
% 178.34/28.50  |   (84)   ~ (e3 = e1)
% 178.34/28.50  | 
% 178.34/28.50  | SIMP: (84) implies:
% 178.34/28.50  |   (85)   ~ (e3 = e1)
% 178.34/28.50  | 
% 178.34/28.50  | REDUCE: (48), (83) imply:
% 178.34/28.50  |   (86)   ~ (e2 = e1)
% 178.34/28.50  | 
% 178.34/28.50  | SIMP: (86) implies:
% 178.34/28.50  |   (87)   ~ (e2 = e1)
% 178.34/28.50  | 
% 178.34/28.50  | BETA: splitting (29) gives:
% 178.34/28.50  | 
% 178.34/28.50  | Case 1:
% 178.34/28.50  | | 
% 178.34/28.50  | |   (88)  all_56_13 = e3
% 178.34/28.50  | | 
% 178.34/28.50  | | COMBINE_EQS: (82), (88) imply:
% 178.34/28.50  | |   (89)  all_52_27 = e3
% 178.34/28.50  | | 
% 178.34/28.50  | | SIMP: (89) implies:
% 178.34/28.50  | |   (90)  all_52_27 = e3
% 178.34/28.50  | | 
% 178.34/28.50  | | REDUCE: (69), (90) imply:
% 178.34/28.50  | |   (91)   ~ (all_52_25 = e3)
% 178.34/28.50  | | 
% 178.34/28.50  | | BETA: splitting (41) gives:
% 178.34/28.50  | | 
% 178.34/28.50  | | Case 1:
% 178.34/28.50  | | | 
% 178.34/28.50  | | |   (92)  all_56_12 = e3
% 178.34/28.50  | | | 
% 178.34/28.50  | | | REF_CLOSE: (43), (91), (92) are inconsistent by sub-proof #1040.
% 178.34/28.50  | | | 
% 178.34/28.50  | | Case 2:
% 178.34/28.50  | | | 
% 178.34/28.50  | | |   (93)   ~ (all_56_12 = e3)
% 178.34/28.50  | | |   (94)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.50  | | | 
% 178.34/28.50  | | | BETA: splitting (60) gives:
% 178.34/28.50  | | | 
% 178.34/28.50  | | | Case 1:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | |   (95)  all_58_12 = e1
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | REF_CLOSE: (5), (12), (15), (19), (21), (24), (26), (30), (32), (35),
% 178.34/28.50  | | | |            (36), (46), (47), (49), (50), (51), (53), (59), (62), (63),
% 178.34/28.50  | | | |            (65), (66), (67), (68), (70), (71), (76), (77), (80), (81),
% 178.34/28.50  | | | |            (91), (95) are inconsistent by sub-proof #628.
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | Case 2:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | |   (96)   ~ (all_58_12 = e1)
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | REDUCE: (76), (96) imply:
% 178.34/28.50  | | | |   (97)   ~ (all_52_25 = e1)
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | BETA: splitting (64) gives:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | Case 1:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | |   (98)  all_58_12 = e2
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | COMBINE_EQS: (76), (98) imply:
% 178.34/28.50  | | | | |   (99)  all_52_25 = e2
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | SIMP: (99) implies:
% 178.34/28.50  | | | | |   (100)  all_52_25 = e2
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (91), (100) imply:
% 178.34/28.50  | | | | |   (101)   ~ (e3 = e2)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (36), (100) imply:
% 178.34/28.50  | | | | |   (102)  op(e0, e3) = e2
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | BETA: splitting (62) gives:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | Case 1:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | |   (103)  all_56_11 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | COMBINE_EQS: (5), (103) imply:
% 178.34/28.50  | | | | | |   (104)  all_52_23 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | SIMP: (104) implies:
% 178.34/28.50  | | | | | |   (105)  all_52_23 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REDUCE: (70), (105) imply:
% 178.34/28.50  | | | | | |   (106)  op(e0, e3) = e0
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REF_CLOSE: (68), (75), (102), (106) are inconsistent by sub-proof
% 178.34/28.50  | | | | | |            #1035.
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | Case 2:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | |   (107)   ~ (all_56_11 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REDUCE: (5), (107) imply:
% 178.34/28.50  | | | | | |   (108)   ~ (all_52_23 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REF_CLOSE: (12), (15), (19), (21), (24), (26), (30), (32), (35),
% 178.34/28.50  | | | | | |            (47), (49), (50), (51), (53), (59), (63), (65), (66),
% 178.34/28.50  | | | | | |            (67), (68), (71), (76), (77), (80), (81), (85), (91),
% 178.34/28.50  | | | | | |            (108) are inconsistent by sub-proof #629.
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | End of split
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | Case 2:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | |   (109)   ~ (all_58_12 = e2)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (76), (109) imply:
% 178.34/28.50  | | | | |   (110)   ~ (all_52_25 = e2)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REF_CLOSE: (43), (46), (94), (97), (110) are inconsistent by sub-proof
% 178.34/28.50  | | | | |            #1028.
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | End of split
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | End of split
% 178.34/28.50  | | | 
% 178.34/28.50  | | End of split
% 178.34/28.50  | | 
% 178.34/28.50  | Case 2:
% 178.34/28.50  | | 
% 178.34/28.50  | |   (111)   ~ (all_56_13 = e3)
% 178.34/28.50  | |   (112)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.50  | | 
% 178.34/28.50  | | REDUCE: (82), (111) imply:
% 178.34/28.50  | |   (113)   ~ (all_52_27 = e3)
% 178.34/28.50  | | 
% 178.34/28.50  | | BETA: splitting (31) gives:
% 178.34/28.50  | | 
% 178.34/28.50  | | Case 1:
% 178.34/28.50  | | | 
% 178.34/28.50  | | |   (114)  all_58_12 = e3
% 178.34/28.50  | | | 
% 178.34/28.50  | | | COMBINE_EQS: (76), (114) imply:
% 178.34/28.50  | | |   (115)  all_52_25 = e3
% 178.34/28.50  | | | 
% 178.34/28.50  | | | SIMP: (115) implies:
% 178.34/28.50  | | |   (116)  all_52_25 = e3
% 178.34/28.50  | | | 
% 178.34/28.50  | | | REDUCE: (3), (116) imply:
% 178.34/28.50  | | |   (117)   ~ (all_52_9 = e3)
% 178.34/28.50  | | | 
% 178.34/28.50  | | | REDUCE: (16), (116) imply:
% 178.34/28.50  | | |   (118)   ~ (all_52_17 = e3)
% 178.34/28.50  | | | 
% 178.34/28.50  | | | REDUCE: (36), (116) imply:
% 178.34/28.50  | | |   (119)  op(e0, e3) = e3
% 178.34/28.50  | | | 
% 178.34/28.50  | | | BETA: splitting (62) gives:
% 178.34/28.50  | | | 
% 178.34/28.50  | | | Case 1:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | |   (120)  all_56_11 = e3
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | COMBINE_EQS: (5), (120) imply:
% 178.34/28.50  | | | |   (121)  all_52_23 = e3
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | REF_CLOSE: (7), (68), (70), (119), (121) are inconsistent by sub-proof
% 178.34/28.50  | | | |            #916.
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | Case 2:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | |   (122)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | BETA: splitting (19) gives:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | Case 1:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | |   (123)  all_58_6 = e3
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REF_CLOSE: (49), (118), (123) are inconsistent by sub-proof #981.
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | Case 2:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | |   (124)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | BETA: splitting (73) gives:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | Case 1:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | |   (125)  all_58_9 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | COMBINE_EQS: (74), (125) imply:
% 178.34/28.50  | | | | | |   (126)  all_52_7 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | SIMP: (126) implies:
% 178.34/28.50  | | | | | |   (127)  all_52_7 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REDUCE: (55), (127) imply:
% 178.34/28.50  | | | | | |   (128)   ~ (all_52_15 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | SIMP: (128) implies:
% 178.34/28.50  | | | | | |   (129)   ~ (all_52_15 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REDUCE: (72), (127) imply:
% 178.34/28.50  | | | | | |   (130)   ~ (all_52_23 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | SIMP: (130) implies:
% 178.34/28.50  | | | | | |   (131)   ~ (all_52_23 = e3)
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REF_CLOSE: (1), (8), (11), (13), (14), (15), (21), (24), (27), (32),
% 178.34/28.50  | | | | | |            (35), (38), (45), (49), (50), (51), (53), (57), (59),
% 178.34/28.50  | | | | | |            (63), (65), (68), (71), (77), (78), (81), (85), (87),
% 178.34/28.50  | | | | | |            (114), (117), (124), (129), (131) are inconsistent by
% 178.34/28.50  | | | | | |            sub-proof #625.
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | Case 2:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | |   (132)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | BETA: splitting (132) gives:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | Case 1:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | |   (133)  all_58_10 = e3
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | REF_CLOSE: (5), (6), (10), (17), (33), (37), (52), (53), (58),
% 178.34/28.50  | | | | | | |            (61), (68), (70), (75), (80), (85), (87), (122), (133)
% 178.34/28.50  | | | | | | |            are inconsistent by sub-proof #934.
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | Case 2:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | |   (134)  all_58_11 = e3 | all_58_15 = e3
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | REF_CLOSE: (7), (40), (53), (58), (68), (70), (119), (134) are
% 178.34/28.50  | | | | | | |            inconsistent by sub-proof #915.
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | End of split
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | End of split
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | End of split
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | End of split
% 178.34/28.50  | | | 
% 178.34/28.50  | | Case 2:
% 178.34/28.50  | | | 
% 178.34/28.50  | | |   (135)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.50  | | | 
% 178.34/28.50  | | | BETA: splitting (135) gives:
% 178.34/28.50  | | | 
% 178.34/28.50  | | | Case 1:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | |   (136)  all_58_13 = e3
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | REF_CLOSE: (44), (113), (136) are inconsistent by sub-proof #1026.
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | Case 2:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | |   (137)  all_58_14 = e3 | all_58_15 = e3
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | BETA: splitting (137) gives:
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | | Case 1:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | |   (138)  all_58_14 = e3
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | COMBINE_EQS: (28), (138) imply:
% 178.34/28.50  | | | | |   (139)  all_52_29 = e3
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | SIMP: (139) implies:
% 178.34/28.50  | | | | |   (140)  all_52_29 = e3
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (42), (140) imply:
% 178.34/28.50  | | | | |   (141)   ~ (all_52_5 = e3)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (9), (140) imply:
% 178.34/28.50  | | | | |   (142)   ~ (all_52_25 = e3)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (56), (140) imply:
% 178.34/28.50  | | | | |   (143)   ~ (all_14_2 = e3)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | SIMP: (143) implies:
% 178.34/28.50  | | | | |   (144)   ~ (all_14_2 = e3)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (25), (140) imply:
% 178.34/28.50  | | | | |   (145)  op(e1, e3) = all_52_28
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | GROUND_INST: instantiating (68) with all_52_17, all_52_28, e3, e1,
% 178.34/28.50  | | | | |              simplifying with (65), (145) gives:
% 178.34/28.50  | | | | |   (146)  all_52_17 = all_52_28
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | COMBINE_EQS: (49), (146) imply:
% 178.34/28.50  | | | | |   (147)  all_58_6 = all_52_28
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (67), (146) imply:
% 178.34/28.50  | | | | |   (148)   ~ (all_52_28 = all_4_2)
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REDUCE: (51), (146) imply:
% 178.34/28.50  | | | | |   (149)  op(e3, all_52_28) = e3
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | BETA: splitting (41) gives:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | Case 1:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | |   (150)  all_56_12 = e3
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | REF_CLOSE: (43), (142), (150) are inconsistent by sub-proof #1040.
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | Case 2:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | |   (151)   ~ (all_56_12 = e3)
% 178.34/28.50  | | | | | |   (152)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | BETA: splitting (60) gives:
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | | Case 1:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | |   (153)  all_58_12 = e1
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | REF_CLOSE: (5), (12), (15), (19), (21), (24), (26), (30), (32),
% 178.34/28.50  | | | | | | |            (35), (36), (46), (47), (49), (50), (51), (53), (59),
% 178.34/28.50  | | | | | | |            (62), (63), (65), (66), (67), (68), (70), (71), (76),
% 178.34/28.50  | | | | | | |            (77), (80), (81), (142), (153) are inconsistent by
% 178.34/28.50  | | | | | | |            sub-proof #628.
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | Case 2:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | |   (154)   ~ (all_58_12 = e1)
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | REDUCE: (76), (154) imply:
% 178.34/28.50  | | | | | | |   (155)   ~ (all_52_25 = e1)
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | BETA: splitting (152) gives:
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | |   (156)  all_56_12 = e2
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | COMBINE_EQS: (43), (156) imply:
% 178.34/28.50  | | | | | | | |   (157)  all_52_25 = e2
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | SIMP: (157) implies:
% 178.34/28.50  | | | | | | | |   (158)  all_52_25 = e2
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | REDUCE: (69), (158) imply:
% 178.34/28.50  | | | | | | | |   (159)   ~ (all_52_27 = e2)
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | SIMP: (159) implies:
% 178.34/28.50  | | | | | | | |   (160)   ~ (all_52_27 = e2)
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | REDUCE: (142), (158) imply:
% 178.34/28.50  | | | | | | | |   (161)   ~ (e3 = e2)
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | REDUCE: (4), (158) imply:
% 178.34/28.50  | | | | | | | |   (162)  op(e3, e2) = all_52_24
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | REDUCE: (36), (158) imply:
% 178.34/28.50  | | | | | | | |   (163)  op(e0, e3) = e2
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | BETA: splitting (112) gives:
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | |   (164)  all_56_13 = e2
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | REF_CLOSE: (82), (160), (164) are inconsistent by sub-proof
% 178.34/28.50  | | | | | | | | |            #624.
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | |   (165)  all_56_13 = e1 | all_56_13 = e0
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | BETA: splitting (165) gives:
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | |   (166)  all_56_13 = e1
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | COMBINE_EQS: (82), (166) imply:
% 178.34/28.50  | | | | | | | | | |   (167)  all_52_27 = e1
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | SIMP: (167) implies:
% 178.34/28.50  | | | | | | | | | |   (168)  all_52_27 = e1
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | GROUND_INST: instantiating (68) with all_52_3, all_52_24, e2,
% 178.34/28.50  | | | | | | | | | |              e3, simplifying with (2), (162) gives:
% 178.34/28.50  | | | | | | | | | |   (169)  all_52_3 = all_52_24
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | COMBINE_EQS: (23), (169) imply:
% 178.34/28.50  | | | | | | | | | |   (170)  all_58_1 = all_52_24
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | REDUCE: (54), (169) imply:
% 178.34/28.50  | | | | | | | | | |   (171)   ~ (all_52_19 = all_52_24)
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | SIMP: (171) implies:
% 178.34/28.50  | | | | | | | | | |   (172)   ~ (all_52_19 = all_52_24)
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | BETA: splitting (79) gives:
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | |   (173)  all_58_0 = e3
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | COMBINE_EQS: (24), (173) imply:
% 178.34/28.50  | | | | | | | | | | |   (174)  all_4_2 = e3
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | REF_CLOSE: (66), (68), (77), (85), (174) are inconsistent by
% 178.34/28.50  | | | | | | | | | | |            sub-proof #630.
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | |   (175)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | BETA: splitting (175) gives:
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | Case 1:
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | |   (176)  all_58_1 = e3
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | | COMBINE_EQS: (170), (176) imply:
% 178.34/28.50  | | | | | | | | | | | |   (177)  all_52_24 = e3
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | | REDUCE: (172), (177) imply:
% 178.34/28.50  | | | | | | | | | | | |   (178)   ~ (all_52_19 = e3)
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | | REF_CLOSE: (15), (19), (32), (53), (66), (68), (70), (75),
% 178.34/28.50  | | | | | | | | | | | |            (144), (147), (148), (149), (163), (178) are
% 178.34/28.50  | | | | | | | | | | | |            inconsistent by sub-proof #899.
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | |   (179)  all_58_4 = e3 | all_58_9 = e3
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | | REF_CLOSE: (12), (15), (18), (19), (21), (22), (24), (26),
% 178.34/28.50  | | | | | | | | | | | |            (30), (32), (35), (47), (49), (50), (51), (53),
% 178.34/28.50  | | | | | | | | | | | |            (59), (63), (65), (66), (67), (68), (71), (72),
% 178.34/28.50  | | | | | | | | | | | |            (74), (76), (80), (81), (141), (142), (179) are
% 178.34/28.50  | | | | | | | | | | | |            inconsistent by sub-proof #623.
% 178.34/28.50  | | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | | End of split
% 178.34/28.50  | | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | End of split
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | |   (180)  all_56_13 = e0
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | | REF_CLOSE: (6), (82), (180) are inconsistent by sub-proof
% 178.34/28.50  | | | | | | | | | |            #844.
% 178.34/28.50  | | | | | | | | | | 
% 178.34/28.50  | | | | | | | | | End of split
% 178.34/28.50  | | | | | | | | | 
% 178.34/28.50  | | | | | | | | End of split
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | Case 2:
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | |   (181)  all_56_12 = e1 | all_56_12 = e0
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | | REF_CLOSE: (43), (46), (155), (181) are inconsistent by
% 178.34/28.50  | | | | | | | |            sub-proof #1029.
% 178.34/28.50  | | | | | | | | 
% 178.34/28.50  | | | | | | | End of split
% 178.34/28.50  | | | | | | | 
% 178.34/28.50  | | | | | | End of split
% 178.34/28.50  | | | | | | 
% 178.34/28.50  | | | | | End of split
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | Case 2:
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | |   (182)  all_58_15 = e3
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | | REF_CLOSE: (40), (58), (182) are inconsistent by sub-proof #1010.
% 178.34/28.50  | | | | | 
% 178.34/28.50  | | | | End of split
% 178.34/28.50  | | | | 
% 178.34/28.50  | | | End of split
% 178.34/28.50  | | | 
% 178.34/28.50  | | End of split
% 178.34/28.50  | | 
% 178.34/28.50  | End of split
% 178.34/28.50  | 
% 178.34/28.50  End of proof
% 178.34/28.50  
% 178.34/28.50  Sub-proof #623 shows that the following formulas are inconsistent:
% 178.34/28.50  ----------------------------------------------------------------
% 178.34/28.50    (1)   ~ (all_52_25 = e3)
% 178.34/28.50    (2)  all_58_4 = e3 | all_58_9 = e3
% 178.34/28.50    (3)  all_56_9 = all_52_19
% 178.34/28.50    (4)  all_58_7 = all_52_19
% 178.34/28.50    (5)  all_58_4 = all_52_5
% 178.34/28.50    (6)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.50    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.50    (8)   ~ (all_52_7 = all_4_2)
% 178.34/28.50    (9)  all_58_0 = all_4_2
% 178.34/28.50    (10)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.50    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.50    (12)  all_58_8 = all_14_2
% 178.34/28.50    (13)   ~ (all_52_5 = all_14_2)
% 178.34/28.50    (14)   ~ (all_52_5 = e3)
% 178.34/28.50    (15)   ~ (all_52_9 = all_52_17)
% 178.34/28.50    (16)  all_58_6 = all_52_17
% 178.34/28.50    (17)  op(e2, all_52_19) = e2
% 178.34/28.50    (18)  op(e3, all_52_17) = e3
% 178.34/28.50    (19)  all_58_11 = all_52_23
% 178.34/28.50    (20)  all_58_2 = all_52_9
% 178.34/28.50    (21)  op(e3, e1) = all_52_5
% 178.34/28.50    (22)  op(e1, e3) = all_52_17
% 178.34/28.50    (23)  op(e3, e3) = all_4_2
% 178.34/28.50    (24)   ~ (all_52_17 = all_4_2)
% 178.34/28.50    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.50    (26)  op(e1, all_14_2) = e1
% 178.34/28.50    (27)   ~ (all_52_7 = all_52_23)
% 178.34/28.50    (28)  all_58_9 = all_52_7
% 178.34/28.50    (29)  all_58_12 = all_52_25
% 178.34/28.50    (30)   ~ (e3 = e2)
% 178.34/28.50    (31)  op(e2, e3) = all_52_9
% 178.34/28.50  
% 178.34/28.50  Begin of proof
% 178.34/28.50  | 
% 178.34/28.50  | BETA: splitting (2) gives:
% 178.34/28.50  | 
% 178.34/28.50  | Case 1:
% 178.34/28.50  | | 
% 178.34/28.50  | |   (32)  all_58_4 = e3
% 178.34/28.50  | | 
% 178.34/28.50  | | REF_CLOSE: (5), (14), (32) are inconsistent by sub-proof #1025.
% 178.34/28.50  | | 
% 178.34/28.50  | Case 2:
% 178.34/28.50  | | 
% 178.34/28.50  | |   (33)  all_58_9 = e3
% 178.34/28.50  | | 
% 178.34/28.50  | | COMBINE_EQS: (28), (33) imply:
% 178.34/28.50  | |   (34)  all_52_7 = e3
% 178.34/28.50  | | 
% 178.34/28.50  | | SIMP: (34) implies:
% 178.34/28.50  | |   (35)  all_52_7 = e3
% 178.34/28.50  | | 
% 178.34/28.50  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (15),
% 178.34/28.50  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 178.34/28.50  | |            (27), (29), (30), (31), (35) are inconsistent by sub-proof #943.
% 178.34/28.50  | | 
% 178.34/28.50  | End of split
% 178.34/28.50  | 
% 178.34/28.50  End of proof
% 178.34/28.50  
% 178.34/28.50  Sub-proof #624 shows that the following formulas are inconsistent:
% 178.34/28.50  ----------------------------------------------------------------
% 178.34/28.50    (1)  all_56_13 = all_52_27
% 178.34/28.50    (2)  all_56_13 = e2
% 178.34/28.50    (3)   ~ (all_52_27 = e2)
% 178.34/28.50  
% 178.34/28.50  Begin of proof
% 178.34/28.50  | 
% 178.34/28.50  | COMBINE_EQS: (1), (2) imply:
% 178.34/28.50  |   (4)  all_52_27 = e2
% 178.34/28.50  | 
% 178.34/28.50  | SIMP: (4) implies:
% 178.34/28.50  |   (5)  all_52_27 = e2
% 178.34/28.50  | 
% 178.34/28.50  | REDUCE: (3), (5) imply:
% 178.34/28.50  |   (6)  $false
% 178.34/28.50  | 
% 178.34/28.50  | CLOSE: (6) is inconsistent.
% 178.34/28.50  | 
% 178.34/28.50  End of proof
% 178.34/28.50  
% 178.34/28.50  Sub-proof #625 shows that the following formulas are inconsistent:
% 178.34/28.50  ----------------------------------------------------------------
% 178.34/28.51    (1)   ~ (all_52_5 = all_52_13)
% 178.34/28.51    (2)  all_58_5 = all_52_13
% 178.34/28.51    (3)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.51    (4)  all_58_3 = all_10_2
% 178.34/28.51    (5)  all_58_10 = all_52_15
% 178.34/28.51    (6)   ~ (all_52_5 = all_4_2)
% 178.34/28.51    (7)  all_58_7 = all_52_19
% 178.34/28.51    (8)   ~ (e3 = e1)
% 178.34/28.51    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.51    (10)  all_58_0 = all_4_2
% 178.34/28.51    (11)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.34/28.51    (12)  all_58_8 = all_14_2
% 178.34/28.51    (13)   ~ (all_52_5 = all_14_2)
% 178.34/28.51    (14)   ~ (all_52_23 = e3)
% 178.34/28.51    (15)   ~ (all_52_13 = all_14_2)
% 178.34/28.51    (16)   ~ (all_52_15 = e3)
% 178.34/28.51    (17)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.51    (18)  all_58_12 = e3
% 178.34/28.51    (19)  all_58_6 = all_52_17
% 178.34/28.51    (20)  op(e2, all_52_19) = e2
% 178.34/28.51    (21)  op(e3, all_52_17) = e3
% 178.34/28.51    (22)  all_58_11 = all_52_23
% 178.34/28.51    (23)   ~ (all_52_19 = all_10_2)
% 178.34/28.51    (24)   ~ (all_52_9 = e3)
% 178.34/28.51    (25)  all_58_2 = all_52_9
% 178.34/28.51    (26)  op(e3, e1) = all_52_5
% 178.34/28.51    (27)   ~ (e2 = e1)
% 178.34/28.51    (28)  op(e1, e3) = all_52_17
% 178.34/28.51    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.51    (30)  op(e1, all_14_2) = e1
% 178.34/28.51    (31)  op(e3, all_4_2) = e1
% 178.34/28.51    (32)  all_56_6 = all_52_13
% 178.34/28.51    (33)  op(e2, e3) = all_52_9
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | BETA: splitting (9) gives:
% 178.34/28.51  | 
% 178.34/28.51  | Case 1:
% 178.34/28.51  | | 
% 178.34/28.51  | |   (34)  all_58_2 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | REF_CLOSE: (24), (25), (34) are inconsistent by sub-proof #980.
% 178.34/28.51  | | 
% 178.34/28.51  | Case 2:
% 178.34/28.51  | | 
% 178.34/28.51  | |   (35)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | BETA: splitting (11) gives:
% 178.34/28.51  | | 
% 178.34/28.51  | | Case 1:
% 178.34/28.51  | | | 
% 178.34/28.51  | | |   (36)  all_56_6 = e3
% 178.34/28.51  | | | 
% 178.34/28.51  | | | COMBINE_EQS: (32), (36) imply:
% 178.34/28.51  | | |   (37)  all_52_13 = e3
% 178.34/28.51  | | | 
% 178.34/28.51  | | | SIMP: (37) implies:
% 178.34/28.51  | | |   (38)  all_52_13 = e3
% 178.34/28.51  | | | 
% 178.34/28.51  | | | REDUCE: (1), (38) imply:
% 178.34/28.51  | | |   (39)   ~ (all_52_5 = e3)
% 178.34/28.51  | | | 
% 178.34/28.51  | | | REDUCE: (15), (38) imply:
% 178.34/28.51  | | |   (40)   ~ (all_14_2 = e3)
% 178.34/28.51  | | | 
% 178.34/28.51  | | | SIMP: (40) implies:
% 178.34/28.51  | | |   (41)   ~ (all_14_2 = e3)
% 178.34/28.51  | | | 
% 178.34/28.51  | | | BETA: splitting (3) gives:
% 178.34/28.51  | | | 
% 178.34/28.51  | | | Case 1:
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | |   (42)  all_58_7 = e3
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | | COMBINE_EQS: (7), (42) imply:
% 178.34/28.51  | | | |   (43)  all_52_19 = e3
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | | REDUCE: (20), (43) imply:
% 178.34/28.51  | | | |   (44)  op(e2, e3) = e2
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | | GROUND_INST: instantiating (29) with all_52_9, e2, e3, e2, simplifying
% 178.34/28.51  | | | |              with (33), (44) gives:
% 178.34/28.51  | | | |   (45)  all_52_9 = e2
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | | COMBINE_EQS: (25), (45) imply:
% 178.34/28.51  | | | |   (46)  all_58_2 = e2
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | | BETA: splitting (17) gives:
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | | Case 1:
% 178.34/28.51  | | | | | 
% 178.34/28.51  | | | | |   (47)  all_58_0 = e1
% 178.34/28.51  | | | | | 
% 178.34/28.51  | | | | | REF_CLOSE: (6), (10), (26), (29), (31), (47) are inconsistent by
% 178.34/28.51  | | | | |            sub-proof #626.
% 178.34/28.51  | | | | | 
% 178.34/28.51  | | | | Case 2:
% 178.34/28.51  | | | | | 
% 178.34/28.51  | | | | |   (48)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.51  | | | | | 
% 178.34/28.51  | | | | | REF_CLOSE: (8), (18), (19), (21), (26), (27), (29), (39), (46), (48)
% 178.34/28.51  | | | | |            are inconsistent by sub-proof #919.
% 178.34/28.51  | | | | | 
% 178.34/28.51  | | | | End of split
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | Case 2:
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | |   (49)  all_58_8 = e3 | all_58_11 = e3
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | | REF_CLOSE: (12), (14), (22), (41), (49) are inconsistent by sub-proof
% 178.34/28.51  | | | |            #997.
% 178.34/28.51  | | | | 
% 178.34/28.51  | | | End of split
% 178.34/28.51  | | | 
% 178.34/28.51  | | Case 2:
% 178.34/28.51  | | | 
% 178.34/28.51  | | |   (50)   ~ (all_56_6 = e3)
% 178.34/28.51  | | | 
% 178.34/28.51  | | | REDUCE: (32), (50) imply:
% 178.34/28.51  | | |   (51)   ~ (all_52_13 = e3)
% 178.34/28.51  | | | 
% 178.34/28.51  | | | REF_CLOSE: (2), (3), (4), (5), (7), (12), (13), (14), (16), (21), (22),
% 178.34/28.51  | | |            (23), (26), (28), (29), (30), (35), (51) are inconsistent by
% 178.34/28.51  | | |            sub-proof #683.
% 178.34/28.51  | | | 
% 178.34/28.51  | | End of split
% 178.34/28.51  | | 
% 178.34/28.51  | End of split
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #626 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)   ~ (all_52_5 = all_4_2)
% 178.34/28.51    (2)  all_58_0 = all_4_2
% 178.34/28.51    (3)  all_58_0 = e1
% 178.34/28.51    (4)  op(e3, e1) = all_52_5
% 178.34/28.51    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.51    (6)  op(e3, all_4_2) = e1
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | COMBINE_EQS: (2), (3) imply:
% 178.34/28.51  |   (7)  all_4_2 = e1
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (1), (7) imply:
% 178.34/28.51  |   (8)   ~ (all_52_5 = e1)
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (6), (7) imply:
% 178.34/28.51  |   (9)  op(e3, e1) = e1
% 178.34/28.51  | 
% 178.34/28.51  | REF_CLOSE: (4), (5), (8), (9) are inconsistent by sub-proof #627.
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #627 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.51    (2)  op(e3, e1) = all_52_5
% 178.34/28.51    (3)  op(e3, e1) = e1
% 178.34/28.51    (4)   ~ (all_52_5 = e1)
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | GROUND_INST: instantiating (1) with all_52_5, e1, e1, e3, simplifying with
% 178.34/28.51  |              (2), (3) gives:
% 178.34/28.51  |   (5)  all_52_5 = e1
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (4), (5) imply:
% 178.34/28.51  |   (6)  $false
% 178.34/28.51  | 
% 178.34/28.51  | CLOSE: (6) is inconsistent.
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #628 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)   ~ (all_52_25 = e3)
% 178.34/28.51    (2)  all_56_11 = all_52_23
% 178.34/28.51    (3)  all_56_9 = all_52_19
% 178.34/28.51    (4)  all_58_7 = all_52_19
% 178.34/28.51    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.51    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.51    (7)  all_58_0 = all_4_2
% 178.34/28.51    (8)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.51    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.51    (10)  all_58_8 = all_14_2
% 178.34/28.51    (11)   ~ (all_52_5 = all_14_2)
% 178.34/28.51    (12)  op(e0, e3) = all_52_25
% 178.34/28.51    (13)  all_58_12 = e1
% 178.34/28.51    (14)   ~ (all_52_25 = e0)
% 178.34/28.51    (15)   ~ (all_52_9 = all_52_17)
% 178.34/28.51    (16)  all_58_6 = all_52_17
% 178.34/28.51    (17)  op(e2, all_52_19) = e2
% 178.34/28.51    (18)  op(e3, all_52_17) = e3
% 178.34/28.51    (19)  all_58_11 = all_52_23
% 178.34/28.51    (20)  all_58_2 = all_52_9
% 178.34/28.51    (21)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.51    (22)  op(e3, e1) = all_52_5
% 178.34/28.51    (23)  op(e1, e3) = all_52_17
% 178.34/28.51    (24)  op(e3, e3) = all_4_2
% 178.34/28.51    (25)   ~ (all_52_17 = all_4_2)
% 178.34/28.51    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.51    (27)  op(e0, all_52_23) = e0
% 178.34/28.51    (28)  op(e1, all_14_2) = e1
% 178.34/28.51    (29)  all_58_12 = all_52_25
% 178.34/28.51    (30)  op(e3, all_4_2) = e1
% 178.34/28.51    (31)   ~ (e3 = e2)
% 178.34/28.51    (32)  op(e2, e3) = all_52_9
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | COMBINE_EQS: (13), (29) imply:
% 178.34/28.51  |   (33)  all_52_25 = e1
% 178.34/28.51  | 
% 178.34/28.51  | SIMP: (33) implies:
% 178.34/28.51  |   (34)  all_52_25 = e1
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (1), (34) imply:
% 178.34/28.51  |   (35)   ~ (e3 = e1)
% 178.34/28.51  | 
% 178.34/28.51  | SIMP: (35) implies:
% 178.34/28.51  |   (36)   ~ (e3 = e1)
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (14), (34) imply:
% 178.34/28.51  |   (37)   ~ (e1 = e0)
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (12), (34) imply:
% 178.34/28.51  |   (38)  op(e0, e3) = e1
% 178.34/28.51  | 
% 178.34/28.51  | BETA: splitting (21) gives:
% 178.34/28.51  | 
% 178.34/28.51  | Case 1:
% 178.34/28.51  | | 
% 178.34/28.51  | |   (39)  all_56_11 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | COMBINE_EQS: (2), (39) imply:
% 178.34/28.51  | |   (40)  all_52_23 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | SIMP: (40) implies:
% 178.34/28.51  | |   (41)  all_52_23 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | REDUCE: (27), (41) imply:
% 178.34/28.51  | |   (42)  op(e0, e3) = e0
% 178.34/28.51  | | 
% 178.34/28.51  | | REF_CLOSE: (26), (37), (38), (42) are inconsistent by sub-proof #1007.
% 178.34/28.51  | | 
% 178.34/28.51  | Case 2:
% 178.34/28.51  | | 
% 178.34/28.51  | |   (43)   ~ (all_56_11 = e3)
% 178.34/28.51  | | 
% 178.34/28.51  | | REDUCE: (2), (43) imply:
% 178.34/28.51  | |   (44)   ~ (all_52_23 = e3)
% 178.34/28.51  | | 
% 178.34/28.51  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (15), (16),
% 178.34/28.51  | |            (17), (18), (19), (20), (22), (23), (24), (25), (26), (28), (29),
% 178.34/28.51  | |            (30), (31), (32), (36), (44) are inconsistent by sub-proof #629.
% 178.34/28.51  | | 
% 178.34/28.51  | End of split
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #629 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)   ~ (all_52_25 = e3)
% 178.34/28.51    (2)  all_56_9 = all_52_19
% 178.34/28.51    (3)  all_58_7 = all_52_19
% 178.34/28.51    (4)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.51    (5)   ~ (e3 = e1)
% 178.34/28.51    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.51    (7)  all_58_0 = all_4_2
% 178.34/28.51    (8)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.51    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.51    (10)  all_58_8 = all_14_2
% 178.34/28.51    (11)   ~ (all_52_5 = all_14_2)
% 178.34/28.51    (12)   ~ (all_52_23 = e3)
% 178.34/28.51    (13)   ~ (all_52_9 = all_52_17)
% 178.34/28.51    (14)  all_58_6 = all_52_17
% 178.34/28.51    (15)  op(e2, all_52_19) = e2
% 178.34/28.51    (16)  op(e3, all_52_17) = e3
% 178.34/28.51    (17)  all_58_11 = all_52_23
% 178.34/28.51    (18)  all_58_2 = all_52_9
% 178.34/28.51    (19)  op(e3, e1) = all_52_5
% 178.34/28.51    (20)  op(e1, e3) = all_52_17
% 178.34/28.51    (21)  op(e3, e3) = all_4_2
% 178.34/28.51    (22)   ~ (all_52_17 = all_4_2)
% 178.34/28.51    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.51    (24)  op(e1, all_14_2) = e1
% 178.34/28.51    (25)  all_58_12 = all_52_25
% 178.34/28.51    (26)  op(e3, all_4_2) = e1
% 178.34/28.51    (27)   ~ (e3 = e2)
% 178.34/28.51    (28)  op(e2, e3) = all_52_9
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | BETA: splitting (9) gives:
% 178.34/28.51  | 
% 178.34/28.51  | Case 1:
% 178.34/28.51  | | 
% 178.34/28.51  | |   (29)  all_58_0 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | COMBINE_EQS: (7), (29) imply:
% 178.34/28.51  | |   (30)  all_4_2 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | REF_CLOSE: (5), (21), (23), (26), (30) are inconsistent by sub-proof #630.
% 178.34/28.51  | | 
% 178.34/28.51  | Case 2:
% 178.34/28.51  | | 
% 178.34/28.51  | |   (31)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.51  | | 
% 178.34/28.51  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (12), (13), (14), (15),
% 178.34/28.51  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 178.34/28.51  | |            (28), (31) are inconsistent by sub-proof #945.
% 178.34/28.51  | | 
% 178.34/28.51  | End of split
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #630 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)  all_4_2 = e3
% 178.34/28.51    (2)   ~ (e3 = e1)
% 178.34/28.51    (3)  op(e3, e3) = all_4_2
% 178.34/28.51    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.51    (5)  op(e3, all_4_2) = e1
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (1), (5) imply:
% 178.34/28.51  |   (6)  op(e3, e3) = e1
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (1), (3) imply:
% 178.34/28.51  |   (7)  op(e3, e3) = e3
% 178.34/28.51  | 
% 178.34/28.51  | GROUND_INST: instantiating (4) with e1, e3, e3, e3, simplifying with (6), (7)
% 178.34/28.51  |              gives:
% 178.34/28.51  |   (8)  e3 = e1
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (2), (8) imply:
% 178.34/28.51  |   (9)  $false
% 178.34/28.51  | 
% 178.34/28.51  | CLOSE: (9) is inconsistent.
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #631 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)   ~ (all_52_27 = all_10_2)
% 178.34/28.51    (2)   ~ (all_52_17 = all_52_23)
% 178.34/28.51    (3)  op(e2, all_10_2) = all_10_1
% 178.34/28.51    (4)   ~ (all_52_13 = all_52_29)
% 178.34/28.51    (5)  all_56_3 = all_52_7
% 178.34/28.51    (6)  op(e3, e2) = all_52_3
% 178.34/28.51    (7)   ~ (all_52_9 = all_52_25)
% 178.34/28.51    (8)  op(e3, all_52_25) = all_52_24
% 178.34/28.51    (9)   ~ (all_52_27 = e0)
% 178.34/28.51    (10)  op(e3, all_52_9) = all_52_8
% 178.34/28.51    (11)   ~ (all_52_3 = all_10_2)
% 178.34/28.51    (12)  all_58_5 = all_52_13
% 178.34/28.51    (13)   ~ (all_52_25 = all_52_29)
% 178.34/28.51    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.51    (15)  all_58_3 = all_10_2
% 178.34/28.51    (16)   ~ (all_52_9 = all_4_2)
% 178.34/28.51    (17)   ~ (all_52_5 = all_52_7)
% 178.34/28.51    (18)  all_58_10 = all_52_15
% 178.34/28.51    (19)  all_58_7 = all_52_19
% 178.34/28.51    (20)   ~ (all_52_17 = all_52_25)
% 178.34/28.51    (21)  op(e0, e1) = all_52_29
% 178.34/28.51    (22)   ~ (all_4_0 = e2)
% 178.34/28.51    (23)  all_58_4 = all_52_5
% 178.34/28.51    (24)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.51    (25)   ~ (e3 = e1)
% 178.34/28.51    (26)   ~ (all_52_27 = all_52_29)
% 178.34/28.51    (27)   ~ (all_52_17 = all_14_2)
% 178.34/28.51    (28)  op(e3, all_4_2) = all_4_1
% 178.34/28.51    (29)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.51    (30)   ~ (all_52_7 = all_4_2)
% 178.34/28.51    (31)  all_58_1 = all_52_3
% 178.34/28.51    (32)  all_58_0 = all_4_2
% 178.34/28.51    (33)  op(e1, all_52_13) = all_52_12
% 178.34/28.51    (34)  op(e1, all_52_29) = all_52_28
% 178.34/28.51    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.34/28.51    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.51    (37)  all_58_14 = all_52_29
% 178.34/28.51    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.51    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.51    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.51    (41)  all_58_8 = all_14_2
% 178.34/28.51    (42)  all_56_1 = all_52_3
% 178.34/28.51    (43)  op(e0, e2) = all_52_27
% 178.34/28.51    (44)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.51    (45)   ~ (all_52_3 = all_4_2)
% 178.34/28.51    (46)  op(e0, e3) = all_52_25
% 178.34/28.51    (47)  all_52_10 = all_10_1
% 178.34/28.51    (48)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.51    (49)   ~ (all_52_13 = all_14_2)
% 178.34/28.51    (50)   ~ (e3 = e0)
% 178.34/28.51    (51)   ~ (all_52_9 = all_52_13)
% 178.34/28.51    (52)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.51    (53)   ~ (all_52_15 = all_52_23)
% 178.34/28.51    (54)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.34/28.51    (55)  op(all_10_1, all_10_2) = all_10_0
% 178.34/28.51    (56)  all_56_12 = all_52_25
% 178.34/28.51    (57)  all_58_13 = all_52_27
% 178.34/28.51    (58)   ~ (all_52_25 = e0)
% 178.34/28.51    (59)   ~ (all_52_9 = all_52_17)
% 178.34/28.51    (60)  all_58_6 = all_52_17
% 178.34/28.51    (61)   ~ (all_52_3 = all_52_7)
% 178.34/28.51    (62)   ~ (e1 = e0)
% 178.34/28.51    (63)  all_58_11 = all_52_23
% 178.34/28.51    (64)   ~ (all_52_3 = all_52_19)
% 178.34/28.51    (65)   ~ (all_52_7 = all_52_15)
% 178.34/28.51    (66)  op(e0, all_52_15) = all_52_14
% 178.34/28.51    (67)   ~ (all_52_29 = all_14_2)
% 178.34/28.51    (68)   ~ (all_4_0 = e1)
% 178.34/28.51    (69)   ~ (all_52_19 = all_10_2)
% 178.34/28.51    (70)  all_58_15 = e0
% 178.34/28.51    (71)  all_58_2 = all_52_9
% 178.34/28.51    (72)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.34/28.51    (73)   ~ (all_52_29 = e0)
% 178.34/28.51    (74)  op(e3, e1) = all_52_5
% 178.34/28.51    (75)  all_56_10 = all_14_2
% 178.34/28.51    (76)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.51    (77)  op(e1, e3) = all_52_17
% 178.34/28.51    (78)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.51    (79)  op(e3, e3) = all_4_2
% 178.34/28.51    (80)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.51    (81)   ~ (all_52_25 = all_52_27)
% 178.34/28.51    (82)   ~ (all_10_0 = e3)
% 178.34/28.51    (83)   ~ (all_52_19 = all_52_27)
% 178.34/28.51    (84)  all_56_7 = all_52_15
% 178.34/28.51    (85)   ~ (all_52_15 = e0)
% 178.34/28.51    (86)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 178.34/28.51    (87)   ~ (all_52_7 = all_52_23)
% 178.34/28.51    (88)  op(e2, all_52_27) = all_52_26
% 178.34/28.51    (89)   ~ (all_52_17 = all_52_19)
% 178.34/28.51    (90)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.51    (91)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.51    (92)  all_58_9 = all_52_7
% 178.34/28.51    (93)   ~ (e2 = e0)
% 178.34/28.51    (94)  all_58_12 = all_52_25
% 178.34/28.51    (95)   ~ (all_10_0 = e1)
% 178.34/28.51    (96)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.51    (97)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.51    (98)   ~ (all_52_19 = all_14_2)
% 178.34/28.51    (99)  op(e2, e3) = all_52_9
% 178.34/28.51    (100)  all_56_13 = all_52_27
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | ALPHA: (86) implies:
% 178.34/28.51  |   (101)  all_52_14 = e0
% 178.34/28.51  |   (102)  all_52_12 = e1
% 178.34/28.51  |   (103)  all_52_10 = e2
% 178.34/28.51  |   (104)  all_52_8 = e3
% 178.34/28.51  | 
% 178.34/28.51  | COMBINE_EQS: (47), (103) imply:
% 178.34/28.51  |   (105)  all_10_1 = e2
% 178.34/28.51  | 
% 178.34/28.51  | SIMP: (105) implies:
% 178.34/28.51  |   (106)  all_10_1 = e2
% 178.34/28.51  | 
% 178.34/28.51  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.34/28.51  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.34/28.51  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 178.34/28.51  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 178.34/28.51  |            (46), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 178.34/28.51  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 178.34/28.51  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 178.34/28.51  |            (80), (81), (82), (83), (84), (85), (87), (88), (89), (90), (91),
% 178.34/28.51  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 178.34/28.51  |            (102), (104), (106) are inconsistent by sub-proof #953.
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #632 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 178.34/28.51    (2)  all_52_0 = e1
% 178.34/28.51    (3)   ~ (e3 = e1)
% 178.34/28.51  
% 178.34/28.51  Begin of proof
% 178.34/28.51  | 
% 178.34/28.51  | ALPHA: (1) implies:
% 178.34/28.51  |   (4)  all_52_0 = e3
% 178.34/28.51  | 
% 178.34/28.51  | COMBINE_EQS: (2), (4) imply:
% 178.34/28.51  |   (5)  e3 = e1
% 178.34/28.51  | 
% 178.34/28.51  | SIMP: (5) implies:
% 178.34/28.51  |   (6)  e3 = e1
% 178.34/28.51  | 
% 178.34/28.51  | REDUCE: (3), (6) imply:
% 178.34/28.51  |   (7)  $false
% 178.34/28.51  | 
% 178.34/28.51  | CLOSE: (7) is inconsistent.
% 178.34/28.51  | 
% 178.34/28.51  End of proof
% 178.34/28.51  
% 178.34/28.51  Sub-proof #633 shows that the following formulas are inconsistent:
% 178.34/28.51  ----------------------------------------------------------------
% 178.34/28.51    (1)   ~ (all_52_23 = all_14_2)
% 178.34/28.51    (2)   ~ (all_52_5 = all_52_13)
% 178.34/28.51    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.34/28.51    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.51    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.51    (6)   ~ (all_52_27 = all_10_2)
% 178.34/28.51    (7)  op(e2, e2) = all_10_2
% 178.34/28.51    (8)   ~ (all_52_17 = all_52_23)
% 178.34/28.51    (9)   ~ (all_6_0 = e3)
% 178.34/28.51    (10)  op(e2, all_10_2) = all_10_1
% 178.34/28.51    (11)   ~ (all_52_13 = all_52_29)
% 178.34/28.51    (12)  all_56_3 = all_52_7
% 178.34/28.51    (13)  op(e3, e2) = all_52_3
% 178.34/28.51    (14)   ~ (all_52_9 = all_52_25)
% 178.34/28.51    (15)  op(e3, all_52_25) = all_52_24
% 178.34/28.51    (16)   ~ (all_52_19 = all_52_23)
% 178.34/28.51    (17)  all_56_11 = all_52_23
% 178.34/28.51    (18)  op(e1, e2) = all_52_19
% 178.34/28.51    (19)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.34/28.51    (20)  op(e3, all_52_9) = all_52_8
% 178.34/28.51    (21)   ~ (all_14_1 = e2)
% 178.34/28.51    (22)   ~ (all_52_3 = all_10_2)
% 178.34/28.51    (23)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.34/28.51    (24)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.34/28.51    (25)  all_58_5 = all_52_13
% 178.34/28.51    (26)   ~ (all_52_25 = all_52_29)
% 178.34/28.51    (27)  all_56_15 = all_6_2
% 178.34/28.51    (28)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.51    (29)  op(e2, e0) = all_52_15
% 178.34/28.51    (30)  op(all_14_1, all_14_2) = all_14_0
% 178.34/28.51    (31)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.51    (32)  all_58_3 = all_10_2
% 178.34/28.51    (33)  all_56_9 = all_52_19
% 178.34/28.51    (34)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.51    (35)  all_58_15 = all_6_2
% 178.34/28.51    (36)   ~ (all_52_9 = all_4_2)
% 178.34/28.51    (37)   ~ (all_52_5 = all_52_7)
% 178.34/28.51    (38)  all_58_10 = all_52_15
% 178.34/28.51    (39)   ~ (all_52_5 = all_4_2)
% 178.34/28.51    (40)  all_58_7 = all_52_19
% 178.34/28.51    (41)  all_56_4 = all_52_9
% 178.34/28.51    (42)   ~ (all_52_15 = all_6_2)
% 178.34/28.51    (43)   ~ (all_52_17 = all_52_25)
% 178.34/28.51    (44)  op(e0, e1) = all_52_29
% 178.34/28.51    (45)   ~ (all_4_0 = e2)
% 178.34/28.51    (46)  all_58_4 = all_52_5
% 178.34/28.51    (47)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.51    (48)   ~ (e3 = e1)
% 178.34/28.51    (49)   ~ (all_52_27 = all_52_29)
% 178.34/28.51    (50)   ~ (all_52_17 = all_14_2)
% 178.34/28.51    (51)  op(e3, all_4_2) = all_4_1
% 178.34/28.51    (52)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.51    (53)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.51    (54)   ~ (all_52_7 = all_4_2)
% 178.34/28.51    (55)  all_58_1 = all_52_3
% 178.34/28.51    (56)   ~ (all_52_13 = all_52_15)
% 178.34/28.51    (57)  all_58_0 = all_4_2
% 178.34/28.51    (58)  op(e1, all_52_13) = all_52_12
% 178.34/28.51    (59)  op(e0, e0) = all_6_2
% 178.34/28.51    (60)  op(e1, all_52_29) = all_52_28
% 178.34/28.51    (61)  op(e1, all_52_5) = all_52_4
% 178.34/28.51    (62)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.34/28.51    (63)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.34/28.51    (64)   ~ (all_4_1 = e2)
% 178.34/28.51    (65)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.51    (66)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.51    (67)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.51    (68)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.34/28.51    (69)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.34/28.51    (70)   ~ (all_14_1 = e3)
% 178.34/28.51    (71)  all_58_14 = all_52_29
% 178.34/28.51    (72)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.51    (73)   ~ (all_52_3 = all_52_5)
% 178.34/28.51    (74)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.51    (75)  op(e2, e1) = all_52_13
% 178.34/28.51    (76)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.51    (77)  all_58_8 = all_14_2
% 178.34/28.51    (78)  all_56_1 = all_52_3
% 178.34/28.51    (79)  op(e0, e2) = all_52_27
% 178.34/28.51    (80)  all_56_14 = all_52_29
% 178.34/28.51    (81)   ~ (all_14_0 = e3)
% 178.34/28.51    (82)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.34/28.51    (83)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.51    (84)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.34/28.51    (85)   ~ (all_52_5 = all_14_2)
% 178.34/28.51    (86)   ~ (all_52_3 = all_52_27)
% 178.34/28.52    (87)   ~ (all_52_3 = all_4_2)
% 178.34/28.52    (88)  op(all_6_1, all_6_2) = all_6_0
% 178.34/28.52    (89)  op(e0, e3) = all_52_25
% 178.34/28.52    (90)  op(e0, all_6_2) = all_6_1
% 178.34/28.52    (91)  all_52_0 = all_4_1
% 178.34/28.52    (92)   ~ (all_52_9 = all_10_2)
% 178.34/28.52    (93)  op(e3, all_52_17) = all_52_16
% 178.34/28.52    (94)  all_52_10 = all_10_1
% 178.34/28.52    (95)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.52    (96)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.34/28.52    (97)   ~ (all_52_13 = all_14_2)
% 178.34/28.52    (98)   ~ (e3 = e0)
% 178.34/28.52    (99)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.52    (100)   ~ (all_52_9 = all_52_13)
% 178.34/28.52    (101)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.52    (102)  op(e0, all_52_23) = all_52_22
% 178.34/28.52    (103)   ~ (all_52_15 = all_52_23)
% 178.34/28.52    (104)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.34/28.52    (105)  op(all_10_1, all_10_2) = all_10_0
% 178.34/28.52    (106)   ~ (all_52_5 = all_52_29)
% 178.34/28.52    (107)  all_56_2 = all_52_5
% 178.34/28.52    (108)  op(e1, e0) = all_52_23
% 178.34/28.52    (109)  all_56_12 = all_52_25
% 178.34/28.52    (110)  all_58_13 = all_52_27
% 178.34/28.52    (111)   ~ (all_4_1 = e1)
% 178.34/28.52    (112)  op(e2, all_52_3) = all_52_2
% 178.34/28.52    (113)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.52    (114)  all_56_5 = all_10_2
% 178.34/28.52    (115)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.52    (116)   ~ (all_52_9 = all_52_17)
% 178.34/28.52    (117)   ~ (all_14_0 = e2)
% 178.34/28.52    (118)  all_58_6 = all_52_17
% 178.34/28.52    (119)   ~ (all_52_3 = all_52_7)
% 178.34/28.52    (120)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.34/28.52    (121)  op(e2, all_52_19) = all_52_18
% 178.34/28.52    (122)   ~ (e1 = e0)
% 178.34/28.52    (123)  all_56_0 = all_4_2
% 178.34/28.52    (124)  all_58_11 = all_52_23
% 178.34/28.52    (125)   ~ (all_52_3 = all_52_19)
% 178.34/28.52    (126)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.34/28.52    (127)   ~ (all_52_7 = all_52_15)
% 178.34/28.52    (128)  op(e0, all_52_15) = all_52_14
% 178.34/28.52    (129)   ~ (all_52_29 = all_14_2)
% 178.34/28.52    (130)   ~ (all_4_0 = e1)
% 178.34/28.52    (131)   ~ (all_52_19 = all_10_2)
% 178.34/28.52    (132)   ~ (all_52_23 = all_6_2)
% 178.34/28.52    (133)   ~ (all_6_0 = e2)
% 178.34/28.52    (134)   ~ (all_52_29 = all_6_2)
% 178.34/28.52    (135)  all_58_2 = all_52_9
% 178.34/28.52    (136)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.34/28.52    (137)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.52    (138)  op(e3, e1) = all_52_5
% 178.34/28.52    (139)   ~ (e2 = e1)
% 178.34/28.52    (140)  all_56_10 = all_14_2
% 178.34/28.52    (141)   ~ (all_52_25 = all_6_2)
% 178.34/28.52    (142)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.34/28.52    (143)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.52    (144)  op(e1, e1) = all_14_2
% 178.34/28.52    (145)  op(e1, e3) = all_52_17
% 178.34/28.52    (146)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.52    (147)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.34/28.52    (148)   ~ (all_52_25 = all_4_2)
% 178.34/28.52    (149)  op(e3, e0) = all_52_7
% 178.34/28.52    (150)  op(e3, e3) = all_4_2
% 178.34/28.52    (151)  all_58_15 = e0 | ((all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) &
% 178.34/28.52             (all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0))
% 178.34/28.52    (152)   ~ (all_10_1 = e3)
% 178.34/28.52    (153)  all_56_8 = all_52_17
% 178.34/28.52    (154)   ~ (all_52_17 = all_4_2)
% 178.34/28.52    (155)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.52             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.52    (156)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 178.34/28.52           (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0) |
% 178.34/28.52           (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 178.34/28.52           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 178.34/28.52    (157)   ~ (all_52_25 = all_52_27)
% 178.34/28.52    (158)   ~ (all_52_27 = all_6_2)
% 178.34/28.52    (159)   ~ (all_52_7 = all_6_2)
% 178.34/28.52    (160)   ~ (all_10_0 = e3)
% 178.34/28.52    (161)   ~ (all_52_15 = all_10_2)
% 178.34/28.52    (162)   ~ (all_52_19 = all_52_27)
% 178.34/28.52    (163)  all_56_7 = all_52_15
% 178.34/28.52    (164)   ~ (all_52_7 = all_52_23)
% 178.34/28.52    (165)   ~ (all_52_13 = all_10_2)
% 178.34/28.52    (166)   ~ (all_6_0 = e1)
% 178.34/28.52    (167)  op(e2, all_52_27) = all_52_26
% 178.34/28.52    (168)  all_52_20 = all_14_1
% 178.34/28.52    (169)   ~ (all_52_17 = all_52_19)
% 178.34/28.52    (170)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.52    (171)  all_52_30 = all_6_1
% 178.34/28.52    (172)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.34/28.52    (173)  op(e1, all_14_2) = all_14_1
% 178.34/28.52    (174)  all_58_9 = all_52_7
% 178.34/28.52    (175)   ~ (e2 = e0)
% 178.34/28.52    (176)  all_58_12 = all_52_25
% 178.34/28.52    (177)   ~ (all_10_0 = e1)
% 178.34/28.52    (178)  all_56_6 = all_52_13
% 178.34/28.52    (179)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.52    (180)   ~ (all_52_9 = all_52_15)
% 178.34/28.52    (181)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.52    (182)   ~ (e3 = e2)
% 178.34/28.52    (183)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.34/28.52    (184)   ~ (all_52_19 = all_14_2)
% 178.34/28.52    (185)  op(e0, all_52_7) = all_52_6
% 178.34/28.52    (186)  op(e2, e3) = all_52_9
% 178.34/28.52    (187)  all_56_13 = all_52_27
% 178.34/28.52  
% 178.34/28.52  Begin of proof
% 178.34/28.52  | 
% 178.34/28.52  | BETA: splitting (151) gives:
% 178.34/28.52  | 
% 178.34/28.52  | Case 1:
% 178.34/28.52  | | 
% 178.34/28.52  | |   (188)  all_58_15 = e0
% 178.34/28.52  | | 
% 178.34/28.52  | | COMBINE_EQS: (35), (188) imply:
% 178.34/28.52  | |   (189)  all_6_2 = e0
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (159), (189) imply:
% 178.34/28.52  | |   (190)   ~ (all_52_7 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (42), (189) imply:
% 178.34/28.52  | |   (191)   ~ (all_52_15 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (132), (189) imply:
% 178.34/28.52  | |   (192)   ~ (all_52_23 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (141), (189) imply:
% 178.34/28.52  | |   (193)   ~ (all_52_25 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (158), (189) imply:
% 178.34/28.52  | |   (194)   ~ (all_52_27 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (134), (189) imply:
% 178.34/28.52  | |   (195)   ~ (all_52_29 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (88), (189) imply:
% 178.34/28.52  | |   (196)  op(all_6_1, e0) = all_6_0
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (90), (189) imply:
% 178.34/28.52  | |   (197)  op(e0, e0) = all_6_1
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (59), (189) imply:
% 178.34/28.52  | |   (198)  op(e0, e0) = e0
% 178.34/28.52  | | 
% 178.34/28.52  | | GROUND_INST: instantiating (155) with e0, all_6_1, e0, e0, simplifying with
% 178.34/28.52  | |              (197), (198) gives:
% 178.34/28.52  | |   (199)  all_6_1 = e0
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (196), (199) imply:
% 178.34/28.52  | |   (200)  op(e0, e0) = all_6_0
% 178.34/28.52  | | 
% 178.34/28.52  | | GROUND_INST: instantiating (155) with e0, all_6_0, e0, e0, simplifying with
% 178.34/28.52  | |              (198), (200) gives:
% 178.34/28.52  | |   (201)  all_6_0 = e0
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (9), (201) imply:
% 178.34/28.52  | |   (202)   ~ (e3 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (133), (201) imply:
% 178.34/28.52  | |   (203)   ~ (e2 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (166), (201) imply:
% 178.34/28.52  | |   (204)   ~ (e1 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | BETA: splitting (156) gives:
% 178.34/28.52  | | 
% 178.34/28.52  | | Case 1:
% 178.34/28.52  | | | 
% 178.34/28.52  | | |   (205)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 178.34/28.52  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 178.34/28.52  | | |            e0)
% 178.34/28.52  | | | 
% 178.34/28.52  | | | REF_CLOSE: (6), (8), (10), (11), (12), (13), (14), (15), (20), (22), (25),
% 178.34/28.52  | | |            (26), (31), (32), (34), (35), (36), (37), (38), (40), (43),
% 178.34/28.52  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (53), (54),
% 178.34/28.52  | | |            (55), (57), (58), (60), (62), (67), (71), (72), (74), (76),
% 178.34/28.52  | | |            (77), (78), (79), (83), (87), (89), (91), (94), (95), (97),
% 178.34/28.52  | | |            (98), (100), (101), (103), (104), (105), (106), (109), (110),
% 178.34/28.52  | | |            (113), (116), (118), (119), (122), (123), (124), (125), (127),
% 178.34/28.52  | | |            (128), (129), (130), (131), (135), (136), (138), (140), (143),
% 178.34/28.52  | | |            (145), (146), (148), (150), (155), (157), (159), (160), (162),
% 178.34/28.52  | | |            (163), (164), (167), (169), (170), (172), (174), (175), (176),
% 178.34/28.52  | | |            (177), (179), (181), (184), (185), (186), (187), (188), (190),
% 178.34/28.52  | | |            (191), (193), (194), (195), (205) are inconsistent by sub-proof
% 178.34/28.52  | | |            #952.
% 178.34/28.52  | | | 
% 178.34/28.52  | | Case 2:
% 178.34/28.52  | | | 
% 178.34/28.52  | | |   (206)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 178.34/28.52  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 178.34/28.52  | | |            all_52_30 = e0)
% 178.34/28.52  | | | 
% 178.34/28.52  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (11), (12), (13), (14), (15),
% 178.34/28.52  | | |            (16), (17), (18), (20), (22), (23), (25), (26), (30), (31),
% 178.34/28.52  | | |            (32), (33), (34), (36), (37), (38), (39), (40), (43), (44),
% 178.34/28.52  | | |            (45), (46), (47), (48), (49), (51), (53), (54), (55), (57),
% 178.34/28.52  | | |            (60), (63), (64), (65), (67), (71), (72), (73), (74), (75),
% 178.34/28.52  | | |            (76), (77), (79), (80), (81), (83), (84), (85), (87), (89),
% 178.34/28.52  | | |            (92), (93), (95), (98), (99), (101), (102), (103), (104),
% 178.34/28.52  | | |            (106), (107), (109), (110), (111), (113), (114), (115), (116),
% 178.34/28.52  | | |            (117), (118), (119), (121), (122), (123), (124), (129), (130),
% 178.34/28.52  | | |            (131), (135), (136), (137), (138), (140), (142), (143), (145),
% 178.34/28.52  | | |            (146), (148), (149), (150), (153), (154), (155), (157), (162),
% 178.34/28.52  | | |            (163), (164), (167), (168), (170), (172), (173), (174), (175),
% 178.34/28.52  | | |            (176), (179), (180), (182), (183), (184), (186), (187), (188),
% 178.34/28.52  | | |            (190), (192), (193), (194), (195), (206) are inconsistent by
% 178.34/28.52  | | |            sub-proof #877.
% 178.34/28.52  | | | 
% 178.34/28.52  | | End of split
% 178.34/28.52  | | 
% 178.34/28.52  | Case 2:
% 178.34/28.52  | | 
% 178.34/28.52  | |   (207)   ~ (all_58_15 = e0)
% 178.34/28.52  | |   (208)  (all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0) & (all_58_12 = e0
% 178.34/28.52  | |            | all_58_13 = e0 | all_58_14 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | ALPHA: (208) implies:
% 178.34/28.52  | |   (209)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.52  | |   (210)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.52  | | 
% 178.34/28.52  | | REDUCE: (35), (207) imply:
% 178.34/28.52  | |   (211)   ~ (all_6_2 = e0)
% 178.34/28.52  | | 
% 178.34/28.52  | | BETA: splitting (156) gives:
% 178.34/28.52  | | 
% 178.34/28.52  | | Case 1:
% 178.34/28.52  | | | 
% 178.34/28.52  | | |   (212)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 178.34/28.52  | | |          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 178.34/28.52  | | |            e0)
% 178.34/28.52  | | | 
% 178.34/28.52  | | | BETA: splitting (212) gives:
% 178.34/28.52  | | | 
% 178.34/28.52  | | | Case 1:
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | |   (213)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | ALPHA: (213) implies:
% 178.34/28.52  | | | |   (214)  all_52_6 = e0
% 178.34/28.52  | | | |   (215)  all_52_4 = e1
% 178.34/28.52  | | | |   (216)  all_52_2 = e2
% 178.34/28.52  | | | |   (217)  all_52_0 = e3
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | COMBINE_EQS: (91), (217) imply:
% 178.34/28.52  | | | |   (218)  all_4_1 = e3
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | SIMP: (218) implies:
% 178.34/28.52  | | | |   (219)  all_4_1 = e3
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 178.34/28.52  | | | |            (13), (14), (16), (17), (18), (19), (21), (22), (23), (25),
% 178.34/28.52  | | | |            (26), (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 178.34/28.52  | | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 178.34/28.52  | | | |            (47), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 178.34/28.52  | | | |            (59), (60), (61), (62), (63), (65), (66), (67), (69), (71),
% 178.34/28.52  | | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (83),
% 178.34/28.52  | | | |            (84), (85), (86), (87), (88), (89), (90), (95), (96), (97),
% 178.34/28.52  | | | |            (98), (99), (100), (101), (102), (103), (104), (106), (107),
% 178.34/28.52  | | | |            (108), (109), (110), (112), (113), (115), (116), (118),
% 178.34/28.52  | | | |            (119), (120), (122), (123), (124), (125), (126), (127),
% 178.34/28.52  | | | |            (128), (129), (130), (132), (134), (135), (136), (137),
% 178.34/28.52  | | | |            (138), (139), (140), (141), (143), (144), (145), (146),
% 178.34/28.52  | | | |            (148), (149), (153), (154), (155), (157), (158), (159),
% 178.34/28.52  | | | |            (162), (163), (164), (165), (166), (167), (169), (170),
% 178.34/28.52  | | | |            (172), (173), (174), (176), (179), (180), (181), (183),
% 178.34/28.52  | | | |            (184), (185), (186), (187), (210), (211), (214), (215),
% 178.34/28.52  | | | |            (216), (219) are inconsistent by sub-proof #783.
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | Case 2:
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | |   (220)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 178.34/28.52  | | | |          e0
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | ALPHA: (220) implies:
% 178.34/28.52  | | | |   (221)  all_52_14 = e0
% 178.34/28.52  | | | |   (222)  all_52_12 = e1
% 178.34/28.52  | | | |   (223)  all_52_10 = e2
% 178.34/28.52  | | | |   (224)  all_52_8 = e3
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | COMBINE_EQS: (94), (223) imply:
% 178.34/28.52  | | | |   (225)  all_10_1 = e2
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | SIMP: (225) implies:
% 178.34/28.52  | | | |   (226)  all_10_1 = e2
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | REF_CLOSE: (1), (2), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 178.34/28.52  | | | |            (16), (17), (18), (20), (22), (24), (25), (26), (27), (28),
% 178.34/28.52  | | | |            (29), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 178.34/28.52  | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 178.34/28.52  | | | |            (51), (52), (53), (54), (55), (56), (57), (58), (60), (62),
% 178.34/28.52  | | | |            (63), (64), (66), (67), (68), (69), (70), (71), (72), (73),
% 178.34/28.52  | | | |            (74), (75), (76), (77), (78), (82), (83), (84), (86), (87),
% 178.34/28.52  | | | |            (89), (90), (92), (93), (97), (98), (100), (102), (103),
% 178.34/28.52  | | | |            (104), (105), (106), (107), (108), (110), (111), (113),
% 178.34/28.52  | | | |            (116), (118), (119), (120), (121), (122), (123), (124),
% 178.34/28.52  | | | |            (125), (127), (128), (129), (130), (131), (132), (134),
% 178.34/28.52  | | | |            (135), (137), (138), (140), (141), (143), (144), (145),
% 178.34/28.52  | | | |            (148), (149), (150), (154), (155), (157), (158), (159),
% 178.34/28.52  | | | |            (160), (162), (164), (167), (169), (170), (172), (173),
% 178.34/28.52  | | | |            (174), (176), (177), (178), (179), (180), (181), (183),
% 178.34/28.52  | | | |            (184), (186), (187), (210), (211), (221), (222), (224), (226)
% 178.34/28.52  | | | |            are inconsistent by sub-proof #715.
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | End of split
% 178.34/28.52  | | | 
% 178.34/28.52  | | Case 2:
% 178.34/28.52  | | | 
% 178.34/28.52  | | |   (227)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 178.34/28.52  | | |            e0) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 178.34/28.52  | | |            all_52_30 = e0)
% 178.34/28.52  | | | 
% 178.34/28.52  | | | BETA: splitting (227) gives:
% 178.34/28.52  | | | 
% 178.34/28.52  | | | Case 1:
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | |   (228)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 178.34/28.52  | | | |          e0
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | ALPHA: (228) implies:
% 178.34/28.52  | | | |   (229)  all_52_22 = e0
% 178.34/28.52  | | | |   (230)  all_52_20 = e1
% 178.34/28.52  | | | |   (231)  all_52_18 = e2
% 178.34/28.52  | | | |   (232)  all_52_16 = e3
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | COMBINE_EQS: (168), (230) imply:
% 178.34/28.52  | | | |   (233)  all_14_1 = e1
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (13), (14), (15),
% 178.34/28.52  | | | |            (16), (18), (20), (22), (23), (25), (26), (27), (28), (29),
% 178.34/28.52  | | | |            (30), (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 178.34/28.52  | | | |            (43), (45), (46), (47), (49), (50), (51), (52), (53), (54),
% 178.34/28.52  | | | |            (55), (57), (60), (62), (63), (64), (66), (67), (68), (69),
% 178.34/28.52  | | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (81),
% 178.34/28.52  | | | |            (82), (83), (84), (85), (86), (87), (89), (92), (93), (95),
% 178.34/28.52  | | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 178.34/28.52  | | | |            (106), (108), (109), (110), (111), (113), (114), (115),
% 178.34/28.52  | | | |            (116), (117), (118), (121), (122), (123), (124), (125),
% 178.34/28.52  | | | |            (126), (127), (129), (130), (131), (132), (134), (135),
% 178.34/28.52  | | | |            (138), (140), (141), (142), (145), (146), (147), (148),
% 178.34/28.52  | | | |            (149), (150), (152), (153), (154), (155), (157), (158),
% 178.34/28.52  | | | |            (159), (161), (162), (163), (164), (165), (167), (169),
% 178.34/28.52  | | | |            (170), (173), (174), (175), (176), (178), (179), (180),
% 178.34/28.52  | | | |            (181), (182), (184), (186), (187), (209), (210), (211),
% 178.34/28.52  | | | |            (229), (231), (232), (233) are inconsistent by sub-proof
% 178.34/28.52  | | | |            #666.
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | Case 2:
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | |   (234)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 178.34/28.52  | | | |          e0
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | | REF_CLOSE: (4), (5), (6), (8), (9), (11), (13), (14), (15), (16), (17),
% 178.34/28.52  | | | |            (19), (20), (23), (25), (26), (27), (28), (31), (32), (34),
% 178.34/28.52  | | | |            (35), (36), (37), (38), (39), (40), (43), (44), (45), (46),
% 178.34/28.52  | | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 178.34/28.52  | | | |            (57), (60), (65), (66), (67), (71), (72), (73), (74), (76),
% 178.34/28.52  | | | |            (77), (79), (80), (83), (86), (87), (88), (89), (90), (92),
% 178.34/28.52  | | | |            (93), (95), (97), (99), (100), (101), (106), (107), (108),
% 178.34/28.52  | | | |            (109), (110), (113), (115), (116), (118), (119), (123),
% 178.34/28.52  | | | |            (124), (125), (127), (130), (131), (132), (133), (134),
% 178.34/28.52  | | | |            (135), (137), (138), (139), (141), (143), (145), (146),
% 178.34/28.52  | | | |            (148), (149), (150), (154), (155), (157), (158), (159),
% 178.34/28.52  | | | |            (161), (162), (163), (164), (166), (167), (169), (170),
% 178.34/28.52  | | | |            (171), (174), (176), (179), (180), (181), (182), (183),
% 178.34/28.52  | | | |            (186), (187), (209), (210), (211), (234) are inconsistent by
% 178.34/28.52  | | | |            sub-proof #634.
% 178.34/28.52  | | | | 
% 178.34/28.52  | | | End of split
% 178.34/28.52  | | | 
% 178.34/28.52  | | End of split
% 178.34/28.52  | | 
% 178.34/28.52  | End of split
% 178.34/28.52  | 
% 178.34/28.52  End of proof
% 178.34/28.52  
% 178.34/28.52  Sub-proof #634 shows that the following formulas are inconsistent:
% 178.34/28.52  ----------------------------------------------------------------
% 178.34/28.52    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.52    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.52    (3)   ~ (all_52_27 = all_10_2)
% 178.34/28.52    (4)   ~ (all_52_17 = all_52_23)
% 178.34/28.52    (5)   ~ (all_6_0 = e3)
% 178.34/28.52    (6)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 178.34/28.52    (7)   ~ (all_52_13 = all_52_29)
% 178.34/28.52    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.52    (9)  op(e3, e2) = all_52_3
% 178.34/28.52    (10)   ~ (all_52_9 = all_52_25)
% 178.34/28.52    (11)  op(e3, all_52_25) = all_52_24
% 178.34/28.52    (12)   ~ (all_52_19 = all_52_23)
% 178.34/28.52    (13)  all_56_11 = all_52_23
% 178.34/28.52    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.34/28.52    (15)  op(e3, all_52_9) = all_52_8
% 178.34/28.52    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.34/28.52    (17)  all_58_5 = all_52_13
% 178.34/28.52    (18)   ~ (all_6_2 = e0)
% 178.34/28.52    (19)   ~ (all_52_25 = all_52_29)
% 178.34/28.52    (20)  all_56_15 = all_6_2
% 178.34/28.52    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.52    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.52    (23)  all_58_3 = all_10_2
% 178.34/28.52    (24)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.52    (25)  all_58_15 = all_6_2
% 178.34/28.52    (26)   ~ (all_52_9 = all_4_2)
% 178.34/28.52    (27)   ~ (all_52_5 = all_52_7)
% 178.34/28.52    (28)  all_58_10 = all_52_15
% 178.34/28.52    (29)   ~ (all_52_5 = all_4_2)
% 178.34/28.52    (30)  all_58_7 = all_52_19
% 178.34/28.52    (31)   ~ (all_52_17 = all_52_25)
% 178.34/28.52    (32)  op(e0, e1) = all_52_29
% 178.34/28.52    (33)   ~ (all_4_0 = e2)
% 178.34/28.52    (34)  all_58_4 = all_52_5
% 178.34/28.52    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.52    (36)   ~ (e3 = e1)
% 178.34/28.52    (37)   ~ (all_52_27 = all_52_29)
% 178.34/28.52    (38)   ~ (all_52_17 = all_14_2)
% 178.34/28.52    (39)  op(e3, all_4_2) = all_4_1
% 178.34/28.52    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.52    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.52    (42)   ~ (all_52_7 = all_4_2)
% 178.34/28.52    (43)  all_58_1 = all_52_3
% 178.34/28.52    (44)   ~ (all_52_13 = all_52_15)
% 178.34/28.52    (45)  all_58_0 = all_4_2
% 178.34/28.52    (46)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.52    (47)  op(e1, all_52_29) = all_52_28
% 178.34/28.52    (48)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.52    (49)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.52    (50)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.52    (51)  all_58_14 = all_52_29
% 178.34/28.52    (52)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.52    (53)   ~ (all_52_3 = all_52_5)
% 178.34/28.52    (54)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.52    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.52    (56)  all_58_8 = all_14_2
% 178.34/28.52    (57)  op(e0, e2) = all_52_27
% 178.34/28.52    (58)  all_56_14 = all_52_29
% 178.34/28.52    (59)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.52    (60)   ~ (all_52_3 = all_52_27)
% 178.34/28.52    (61)   ~ (all_52_3 = all_4_2)
% 178.34/28.52    (62)  op(all_6_1, all_6_2) = all_6_0
% 178.34/28.52    (63)  op(e0, e3) = all_52_25
% 178.34/28.52    (64)  op(e0, all_6_2) = all_6_1
% 178.34/28.52    (65)   ~ (all_52_9 = all_10_2)
% 178.34/28.52    (66)  op(e3, all_52_17) = all_52_16
% 178.34/28.52    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.52    (68)   ~ (all_52_13 = all_14_2)
% 178.34/28.52    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.52    (70)   ~ (all_52_9 = all_52_13)
% 178.34/28.52    (71)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.52    (72)   ~ (all_52_5 = all_52_29)
% 178.34/28.52    (73)  all_56_2 = all_52_5
% 178.34/28.52    (74)  op(e1, e0) = all_52_23
% 178.34/28.52    (75)  all_56_12 = all_52_25
% 178.34/28.52    (76)  all_58_13 = all_52_27
% 178.34/28.52    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.52    (78)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.52    (79)   ~ (all_52_9 = all_52_17)
% 178.34/28.52    (80)  all_58_6 = all_52_17
% 178.34/28.52    (81)   ~ (all_52_3 = all_52_7)
% 178.34/28.52    (82)  all_56_0 = all_4_2
% 178.34/28.52    (83)  all_58_11 = all_52_23
% 178.34/28.52    (84)   ~ (all_52_3 = all_52_19)
% 178.34/28.52    (85)   ~ (all_52_7 = all_52_15)
% 178.34/28.52    (86)   ~ (all_4_0 = e1)
% 178.34/28.52    (87)   ~ (all_52_19 = all_10_2)
% 178.34/28.52    (88)   ~ (all_52_23 = all_6_2)
% 178.34/28.52    (89)   ~ (all_6_0 = e2)
% 178.34/28.52    (90)   ~ (all_52_29 = all_6_2)
% 178.34/28.52    (91)  all_58_2 = all_52_9
% 178.34/28.52    (92)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.52    (93)  op(e3, e1) = all_52_5
% 178.34/28.52    (94)   ~ (e2 = e1)
% 178.34/28.52    (95)   ~ (all_52_25 = all_6_2)
% 178.34/28.52    (96)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.52    (97)  op(e1, e3) = all_52_17
% 178.34/28.52    (98)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.52    (99)   ~ (all_52_25 = all_4_2)
% 178.34/28.52    (100)  op(e3, e0) = all_52_7
% 178.34/28.52    (101)  op(e3, e3) = all_4_2
% 178.34/28.52    (102)   ~ (all_52_17 = all_4_2)
% 178.34/28.52    (103)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.52             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.52    (104)   ~ (all_52_25 = all_52_27)
% 178.34/28.52    (105)   ~ (all_52_27 = all_6_2)
% 178.34/28.52    (106)   ~ (all_52_7 = all_6_2)
% 178.34/28.52    (107)   ~ (all_52_15 = all_10_2)
% 178.34/28.52    (108)   ~ (all_52_19 = all_52_27)
% 178.34/28.52    (109)  all_56_7 = all_52_15
% 178.34/28.53    (110)   ~ (all_52_7 = all_52_23)
% 178.34/28.53    (111)   ~ (all_6_0 = e1)
% 178.34/28.53    (112)  op(e2, all_52_27) = all_52_26
% 178.34/28.53    (113)   ~ (all_52_17 = all_52_19)
% 178.34/28.53    (114)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.53    (115)  all_52_30 = all_6_1
% 178.34/28.53    (116)  all_58_9 = all_52_7
% 178.34/28.53    (117)  all_58_12 = all_52_25
% 178.34/28.53    (118)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.53    (119)   ~ (all_52_9 = all_52_15)
% 178.34/28.53    (120)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.53    (121)   ~ (e3 = e2)
% 178.34/28.53    (122)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.34/28.53    (123)  op(e2, e3) = all_52_9
% 178.34/28.53    (124)  all_56_13 = all_52_27
% 178.34/28.53  
% 178.34/28.53  Begin of proof
% 178.34/28.53  | 
% 178.34/28.53  | ALPHA: (6) implies:
% 178.34/28.53  |   (125)  all_52_30 = e0
% 178.34/28.53  |   (126)  all_52_28 = e1
% 178.34/28.53  |   (127)  all_52_26 = e2
% 178.34/28.53  |   (128)  all_52_24 = e3
% 178.34/28.53  | 
% 178.34/28.53  | COMBINE_EQS: (115), (125) imply:
% 178.34/28.53  |   (129)  all_6_1 = e0
% 178.34/28.53  | 
% 178.34/28.53  | SIMP: (129) implies:
% 178.34/28.53  |   (130)  all_6_1 = e0
% 178.34/28.53  | 
% 178.34/28.53  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 178.34/28.53  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.34/28.53  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 178.34/28.53  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 178.34/28.53  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 178.34/28.53  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 178.34/28.53  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 178.34/28.53  |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 178.34/28.53  |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 178.34/28.53  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 178.34/28.53  |            (111), (112), (113), (114), (116), (117), (118), (119), (120),
% 178.34/28.53  |            (121), (122), (123), (124), (126), (127), (128), (130) are
% 178.34/28.53  |            inconsistent by sub-proof #635.
% 178.34/28.53  | 
% 178.34/28.53  End of proof
% 178.34/28.53  
% 178.34/28.53  Sub-proof #635 shows that the following formulas are inconsistent:
% 178.34/28.53  ----------------------------------------------------------------
% 178.34/28.53    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.53    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.53    (3)   ~ (all_52_27 = all_10_2)
% 178.34/28.53    (4)   ~ (all_52_17 = all_52_23)
% 178.34/28.53    (5)  all_52_26 = e2
% 178.34/28.53    (6)   ~ (all_6_0 = e3)
% 178.34/28.53    (7)   ~ (all_52_13 = all_52_29)
% 178.34/28.53    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.53    (9)  op(e3, e2) = all_52_3
% 178.34/28.53    (10)   ~ (all_52_9 = all_52_25)
% 178.34/28.53    (11)  op(e3, all_52_25) = all_52_24
% 178.34/28.53    (12)   ~ (all_52_19 = all_52_23)
% 178.34/28.53    (13)  all_56_11 = all_52_23
% 178.34/28.53    (14)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.34/28.53    (15)  op(e3, all_52_9) = all_52_8
% 178.34/28.53    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.34/28.53    (17)  all_58_5 = all_52_13
% 178.34/28.53    (18)   ~ (all_6_2 = e0)
% 178.34/28.53    (19)   ~ (all_52_25 = all_52_29)
% 178.34/28.53    (20)  all_56_15 = all_6_2
% 178.34/28.53    (21)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.53    (22)  all_6_1 = e0
% 178.34/28.53    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.53    (24)  all_58_3 = all_10_2
% 178.34/28.53    (25)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.53    (26)  all_58_15 = all_6_2
% 178.34/28.53    (27)   ~ (all_52_9 = all_4_2)
% 178.34/28.53    (28)   ~ (all_52_5 = all_52_7)
% 178.34/28.53    (29)  all_58_10 = all_52_15
% 178.34/28.53    (30)   ~ (all_52_5 = all_4_2)
% 178.34/28.53    (31)  all_58_7 = all_52_19
% 178.34/28.53    (32)   ~ (all_52_17 = all_52_25)
% 178.34/28.53    (33)  op(e0, e1) = all_52_29
% 178.34/28.53    (34)   ~ (all_4_0 = e2)
% 178.34/28.53    (35)  all_58_4 = all_52_5
% 178.34/28.53    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.53    (37)   ~ (e3 = e1)
% 178.34/28.53    (38)   ~ (all_52_27 = all_52_29)
% 178.34/28.53    (39)   ~ (all_52_17 = all_14_2)
% 178.34/28.53    (40)  op(e3, all_4_2) = all_4_1
% 178.34/28.53    (41)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.53    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.53    (43)   ~ (all_52_7 = all_4_2)
% 178.34/28.53    (44)  all_58_1 = all_52_3
% 178.34/28.53    (45)   ~ (all_52_13 = all_52_15)
% 178.34/28.53    (46)  all_58_0 = all_4_2
% 178.34/28.53    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.53    (48)  op(e1, all_52_29) = all_52_28
% 178.34/28.53    (49)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.53    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.53    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.53    (52)  all_58_14 = all_52_29
% 178.34/28.53    (53)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.53    (54)   ~ (all_52_3 = all_52_5)
% 178.34/28.53    (55)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.53    (56)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.53    (57)  all_58_8 = all_14_2
% 178.34/28.53    (58)  op(e0, e2) = all_52_27
% 178.34/28.53    (59)  all_56_14 = all_52_29
% 178.34/28.53    (60)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.53    (61)   ~ (all_52_3 = all_52_27)
% 178.34/28.53    (62)   ~ (all_52_3 = all_4_2)
% 178.34/28.53    (63)  op(all_6_1, all_6_2) = all_6_0
% 178.34/28.53    (64)  op(e0, e3) = all_52_25
% 178.34/28.53    (65)  op(e0, all_6_2) = all_6_1
% 178.34/28.53    (66)   ~ (all_52_9 = all_10_2)
% 178.34/28.53    (67)  op(e3, all_52_17) = all_52_16
% 178.34/28.53    (68)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.53    (69)   ~ (all_52_13 = all_14_2)
% 178.34/28.53    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.53    (71)   ~ (all_52_9 = all_52_13)
% 178.34/28.53    (72)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.53    (73)   ~ (all_52_5 = all_52_29)
% 178.34/28.53    (74)  all_56_2 = all_52_5
% 178.34/28.53    (75)  op(e1, e0) = all_52_23
% 178.34/28.53    (76)  all_56_12 = all_52_25
% 178.34/28.53    (77)  all_58_13 = all_52_27
% 178.34/28.53    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.53    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.53    (80)   ~ (all_52_9 = all_52_17)
% 178.34/28.53    (81)  all_58_6 = all_52_17
% 178.34/28.53    (82)   ~ (all_52_3 = all_52_7)
% 178.34/28.53    (83)  all_56_0 = all_4_2
% 178.34/28.53    (84)  all_58_11 = all_52_23
% 178.34/28.53    (85)   ~ (all_52_3 = all_52_19)
% 178.34/28.53    (86)   ~ (all_52_7 = all_52_15)
% 178.34/28.53    (87)   ~ (all_4_0 = e1)
% 178.34/28.53    (88)   ~ (all_52_19 = all_10_2)
% 178.34/28.53    (89)   ~ (all_52_23 = all_6_2)
% 178.34/28.53    (90)   ~ (all_6_0 = e2)
% 178.34/28.53    (91)   ~ (all_52_29 = all_6_2)
% 178.34/28.53    (92)  all_58_2 = all_52_9
% 178.34/28.53    (93)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.53    (94)  op(e3, e1) = all_52_5
% 178.34/28.53    (95)   ~ (e2 = e1)
% 178.34/28.53    (96)   ~ (all_52_25 = all_6_2)
% 178.34/28.53    (97)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.53    (98)  op(e1, e3) = all_52_17
% 178.34/28.53    (99)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.53    (100)   ~ (all_52_25 = all_4_2)
% 178.34/28.53    (101)  op(e3, e0) = all_52_7
% 178.34/28.53    (102)  all_52_28 = e1
% 178.34/28.53    (103)  op(e3, e3) = all_4_2
% 178.34/28.53    (104)   ~ (all_52_17 = all_4_2)
% 178.34/28.53    (105)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.53             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.53    (106)   ~ (all_52_25 = all_52_27)
% 178.34/28.53    (107)   ~ (all_52_27 = all_6_2)
% 178.34/28.53    (108)   ~ (all_52_7 = all_6_2)
% 178.34/28.53    (109)   ~ (all_52_15 = all_10_2)
% 178.34/28.53    (110)   ~ (all_52_19 = all_52_27)
% 178.34/28.53    (111)  all_56_7 = all_52_15
% 178.34/28.53    (112)   ~ (all_52_7 = all_52_23)
% 178.34/28.53    (113)   ~ (all_6_0 = e1)
% 178.34/28.53    (114)  op(e2, all_52_27) = all_52_26
% 178.34/28.53    (115)   ~ (all_52_17 = all_52_19)
% 178.34/28.53    (116)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.53    (117)  all_58_9 = all_52_7
% 178.34/28.53    (118)  all_52_24 = e3
% 178.34/28.53    (119)  all_58_12 = all_52_25
% 178.34/28.53    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.53    (121)   ~ (all_52_9 = all_52_15)
% 178.34/28.53    (122)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.53    (123)   ~ (e3 = e2)
% 178.34/28.53    (124)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.34/28.53    (125)  op(e2, e3) = all_52_9
% 178.34/28.53    (126)  all_56_13 = all_52_27
% 178.34/28.53  
% 178.34/28.53  Begin of proof
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (22), (63) imply:
% 178.34/28.53  |   (127)  op(e0, all_6_2) = all_6_0
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (11), (118) imply:
% 178.34/28.53  |   (128)  op(e3, all_52_25) = e3
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (5), (114) imply:
% 178.34/28.53  |   (129)  op(e2, all_52_27) = e2
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (48), (102) imply:
% 178.34/28.53  |   (130)  op(e1, all_52_29) = e1
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (22), (65) imply:
% 178.34/28.53  |   (131)  op(e0, all_6_2) = e0
% 178.34/28.53  | 
% 178.34/28.53  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 178.34/28.53  |            (15), (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 178.34/28.53  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 178.34/28.53  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (49),
% 178.34/28.53  |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 178.34/28.53  |            (61), (62), (64), (66), (67), (68), (69), (70), (71), (72), (73),
% 178.34/28.53  |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 178.34/28.53  |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 178.34/28.53  |            (96), (97), (98), (99), (100), (101), (103), (104), (105), (106),
% 178.34/28.53  |            (107), (108), (109), (110), (111), (112), (113), (115), (116),
% 178.34/28.53  |            (117), (119), (120), (121), (122), (123), (124), (125), (126),
% 178.34/28.53  |            (127), (128), (129), (130), (131) are inconsistent by sub-proof
% 178.34/28.53  |            #636.
% 178.34/28.53  | 
% 178.34/28.53  End of proof
% 178.34/28.53  
% 178.34/28.53  Sub-proof #636 shows that the following formulas are inconsistent:
% 178.34/28.53  ----------------------------------------------------------------
% 178.34/28.53    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.34/28.53    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.34/28.53    (3)   ~ (all_52_27 = all_10_2)
% 178.34/28.53    (4)   ~ (all_52_17 = all_52_23)
% 178.34/28.53    (5)   ~ (all_6_0 = e3)
% 178.34/28.53    (6)   ~ (all_52_13 = all_52_29)
% 178.34/28.53    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.34/28.53    (8)  op(e3, e2) = all_52_3
% 178.34/28.53    (9)   ~ (all_52_9 = all_52_25)
% 178.34/28.53    (10)   ~ (all_52_19 = all_52_23)
% 178.34/28.53    (11)  all_56_11 = all_52_23
% 178.34/28.53    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.34/28.53    (13)  op(e3, all_52_9) = all_52_8
% 178.34/28.53    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.34/28.53    (15)  all_58_5 = all_52_13
% 178.34/28.53    (16)   ~ (all_6_2 = e0)
% 178.34/28.53    (17)   ~ (all_52_25 = all_52_29)
% 178.34/28.53    (18)  all_56_15 = all_6_2
% 178.34/28.53    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.34/28.53    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.34/28.53    (21)  all_58_3 = all_10_2
% 178.34/28.53    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.34/28.53    (23)  all_58_15 = all_6_2
% 178.34/28.53    (24)  op(e0, all_6_2) = e0
% 178.34/28.53    (25)   ~ (all_52_9 = all_4_2)
% 178.34/28.53    (26)   ~ (all_52_5 = all_52_7)
% 178.34/28.53    (27)  all_58_10 = all_52_15
% 178.34/28.53    (28)   ~ (all_52_5 = all_4_2)
% 178.34/28.53    (29)  all_58_7 = all_52_19
% 178.34/28.53    (30)   ~ (all_52_17 = all_52_25)
% 178.34/28.53    (31)  op(e0, e1) = all_52_29
% 178.34/28.53    (32)   ~ (all_4_0 = e2)
% 178.34/28.53    (33)  all_58_4 = all_52_5
% 178.34/28.53    (34)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.53    (35)   ~ (e3 = e1)
% 178.34/28.53    (36)   ~ (all_52_27 = all_52_29)
% 178.34/28.53    (37)   ~ (all_52_17 = all_14_2)
% 178.34/28.53    (38)  op(e3, all_4_2) = all_4_1
% 178.34/28.53    (39)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.53    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.53    (41)   ~ (all_52_7 = all_4_2)
% 178.34/28.53    (42)  all_58_1 = all_52_3
% 178.34/28.53    (43)   ~ (all_52_13 = all_52_15)
% 178.34/28.53    (44)  all_58_0 = all_4_2
% 178.34/28.53    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.34/28.53    (46)  op(e2, all_52_27) = e2
% 178.34/28.53    (47)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.34/28.53    (48)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.34/28.53    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.34/28.53    (50)  all_58_14 = all_52_29
% 178.34/28.53    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.34/28.53    (52)   ~ (all_52_3 = all_52_5)
% 178.34/28.53    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.34/28.53    (54)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.34/28.53    (55)  all_58_8 = all_14_2
% 178.34/28.53    (56)  op(e0, e2) = all_52_27
% 178.34/28.53    (57)  all_56_14 = all_52_29
% 178.34/28.53    (58)  op(e1, all_52_29) = e1
% 178.34/28.53    (59)  op(all_4_1, all_4_2) = all_4_0
% 178.34/28.53    (60)   ~ (all_52_3 = all_52_27)
% 178.34/28.53    (61)   ~ (all_52_3 = all_4_2)
% 178.34/28.53    (62)  op(e0, e3) = all_52_25
% 178.34/28.53    (63)   ~ (all_52_9 = all_10_2)
% 178.34/28.53    (64)  op(e3, all_52_17) = all_52_16
% 178.34/28.53    (65)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.53    (66)   ~ (all_52_13 = all_14_2)
% 178.34/28.53    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.34/28.53    (68)   ~ (all_52_9 = all_52_13)
% 178.34/28.53    (69)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.53    (70)   ~ (all_52_5 = all_52_29)
% 178.34/28.53    (71)  all_56_2 = all_52_5
% 178.34/28.53    (72)  op(e1, e0) = all_52_23
% 178.34/28.53    (73)  all_56_12 = all_52_25
% 178.34/28.53    (74)  all_58_13 = all_52_27
% 178.34/28.53    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.34/28.53    (76)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.53    (77)   ~ (all_52_9 = all_52_17)
% 178.34/28.53    (78)  all_58_6 = all_52_17
% 178.34/28.53    (79)   ~ (all_52_3 = all_52_7)
% 178.34/28.53    (80)  all_56_0 = all_4_2
% 178.34/28.53    (81)  all_58_11 = all_52_23
% 178.34/28.53    (82)   ~ (all_52_3 = all_52_19)
% 178.34/28.53    (83)   ~ (all_52_7 = all_52_15)
% 178.34/28.53    (84)  op(e3, all_52_25) = e3
% 178.34/28.53    (85)   ~ (all_4_0 = e1)
% 178.34/28.53    (86)   ~ (all_52_19 = all_10_2)
% 178.34/28.53    (87)   ~ (all_52_23 = all_6_2)
% 178.34/28.53    (88)   ~ (all_6_0 = e2)
% 178.34/28.53    (89)   ~ (all_52_29 = all_6_2)
% 178.34/28.53    (90)  all_58_2 = all_52_9
% 178.34/28.53    (91)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.34/28.53    (92)  op(e3, e1) = all_52_5
% 178.34/28.53    (93)   ~ (e2 = e1)
% 178.34/28.53    (94)   ~ (all_52_25 = all_6_2)
% 178.34/28.53    (95)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.34/28.53    (96)  op(e1, e3) = all_52_17
% 178.34/28.53    (97)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.34/28.53    (98)   ~ (all_52_25 = all_4_2)
% 178.34/28.53    (99)  op(e3, e0) = all_52_7
% 178.34/28.53    (100)  op(e3, e3) = all_4_2
% 178.34/28.53    (101)   ~ (all_52_17 = all_4_2)
% 178.34/28.53    (102)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.34/28.53             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.34/28.53    (103)   ~ (all_52_25 = all_52_27)
% 178.34/28.53    (104)  op(e0, all_6_2) = all_6_0
% 178.34/28.53    (105)   ~ (all_52_27 = all_6_2)
% 178.34/28.53    (106)   ~ (all_52_7 = all_6_2)
% 178.34/28.53    (107)   ~ (all_52_15 = all_10_2)
% 178.34/28.53    (108)   ~ (all_52_19 = all_52_27)
% 178.34/28.53    (109)  all_56_7 = all_52_15
% 178.34/28.53    (110)   ~ (all_52_7 = all_52_23)
% 178.34/28.53    (111)   ~ (all_6_0 = e1)
% 178.34/28.53    (112)   ~ (all_52_17 = all_52_19)
% 178.34/28.53    (113)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.34/28.53    (114)  all_58_9 = all_52_7
% 178.34/28.53    (115)  all_58_12 = all_52_25
% 178.34/28.53    (116)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.34/28.53    (117)   ~ (all_52_9 = all_52_15)
% 178.34/28.53    (118)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.53    (119)   ~ (e3 = e2)
% 178.34/28.53    (120)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.34/28.53    (121)  op(e2, e3) = all_52_9
% 178.34/28.53    (122)  all_56_13 = all_52_27
% 178.34/28.53  
% 178.34/28.53  Begin of proof
% 178.34/28.53  | 
% 178.34/28.53  | GROUND_INST: instantiating (102) with e0, all_6_0, all_6_2, e0, simplifying
% 178.34/28.53  |              with (24), (104) gives:
% 178.34/28.53  |   (123)  all_6_0 = e0
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (5), (123) imply:
% 178.34/28.53  |   (124)   ~ (e3 = e0)
% 178.34/28.53  | 
% 178.34/28.53  | SIMP: (124) implies:
% 178.34/28.53  |   (125)   ~ (e3 = e0)
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (88), (123) imply:
% 178.34/28.53  |   (126)   ~ (e2 = e0)
% 178.34/28.53  | 
% 178.34/28.53  | SIMP: (126) implies:
% 178.34/28.53  |   (127)   ~ (e2 = e0)
% 178.34/28.53  | 
% 178.34/28.53  | REDUCE: (111), (123) imply:
% 178.34/28.53  |   (128)   ~ (e1 = e0)
% 178.34/28.53  | 
% 178.34/28.53  | SIMP: (128) implies:
% 178.34/28.53  |   (129)   ~ (e1 = e0)
% 178.34/28.53  | 
% 178.34/28.53  | BETA: splitting (39) gives:
% 178.34/28.53  | 
% 178.34/28.53  | Case 1:
% 178.34/28.53  | | 
% 178.34/28.53  | |   (130)  all_56_15 = e3
% 178.34/28.53  | | 
% 178.34/28.53  | | COMBINE_EQS: (18), (130) imply:
% 178.34/28.53  | |   (131)  all_6_2 = e3
% 178.34/28.53  | | 
% 178.34/28.53  | | SIMP: (131) implies:
% 178.34/28.53  | |   (132)  all_6_2 = e3
% 178.34/28.53  | | 
% 178.34/28.53  | | REF_CLOSE: (24), (62), (84), (99), (102), (106), (132) are inconsistent by
% 178.34/28.53  | |            sub-proof #665.
% 178.34/28.53  | | 
% 178.34/28.53  | Case 2:
% 178.34/28.53  | | 
% 178.34/28.53  | |   (133)   ~ (all_56_15 = e3)
% 178.34/28.53  | |   (134)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.34/28.53  | | 
% 178.34/28.53  | | REDUCE: (18), (133) imply:
% 178.34/28.53  | |   (135)   ~ (all_6_2 = e3)
% 178.34/28.53  | | 
% 178.34/28.53  | | BETA: splitting (51) gives:
% 178.34/28.53  | | 
% 178.34/28.53  | | Case 1:
% 178.34/28.53  | | | 
% 178.34/28.53  | | |   (136)  all_56_13 = e3
% 178.34/28.53  | | | 
% 178.34/28.53  | | | COMBINE_EQS: (122), (136) imply:
% 178.34/28.53  | | |   (137)  all_52_27 = e3
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (137) implies:
% 178.34/28.53  | | |   (138)  all_52_27 = e3
% 178.34/28.53  | | | 
% 178.34/28.53  | | | COMBINE_EQS: (74), (138) imply:
% 178.34/28.53  | | |   (139)  all_58_13 = e3
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (60), (138) imply:
% 178.34/28.53  | | |   (140)   ~ (all_52_3 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (108), (138) imply:
% 178.34/28.53  | | |   (141)   ~ (all_52_19 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (103), (138) imply:
% 178.34/28.53  | | |   (142)   ~ (all_52_25 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (36), (138) imply:
% 178.34/28.53  | | |   (143)   ~ (all_52_29 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (143) implies:
% 178.34/28.53  | | |   (144)   ~ (all_52_29 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (3), (138) imply:
% 178.34/28.53  | | |   (145)   ~ (all_10_2 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (145) implies:
% 178.34/28.53  | | |   (146)   ~ (all_10_2 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (105), (138) imply:
% 178.34/28.53  | | |   (147)   ~ (all_6_2 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (46), (138) imply:
% 178.34/28.53  | | |   (148)  op(e2, e3) = e2
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (56), (138) imply:
% 178.34/28.53  | | |   (149)  op(e0, e2) = e3
% 178.34/28.53  | | | 
% 178.34/28.53  | | | GROUND_INST: instantiating (102) with all_52_9, e2, e3, e2, simplifying
% 178.34/28.53  | | |              with (121), (148) gives:
% 178.34/28.53  | | |   (150)  all_52_9 = e2
% 178.34/28.53  | | | 
% 178.34/28.53  | | | COMBINE_EQS: (90), (150) imply:
% 178.34/28.53  | | |   (151)  all_58_2 = e2
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (68), (150) imply:
% 178.34/28.53  | | |   (152)   ~ (all_52_13 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (152) implies:
% 178.34/28.53  | | |   (153)   ~ (all_52_13 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (117), (150) imply:
% 178.34/28.53  | | |   (154)   ~ (all_52_15 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (154) implies:
% 178.34/28.53  | | |   (155)   ~ (all_52_15 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (77), (150) imply:
% 178.34/28.53  | | |   (156)   ~ (all_52_17 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (156) implies:
% 178.34/28.53  | | |   (157)   ~ (all_52_17 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (9), (150) imply:
% 178.34/28.53  | | |   (158)   ~ (all_52_25 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (158) implies:
% 178.34/28.53  | | |   (159)   ~ (all_52_25 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (63), (150) imply:
% 178.34/28.53  | | |   (160)   ~ (all_10_2 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (160) implies:
% 178.34/28.53  | | |   (161)   ~ (all_10_2 = e2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (13), (150) imply:
% 178.34/28.53  | | |   (162)  op(e3, e2) = all_52_8
% 178.34/28.53  | | | 
% 178.34/28.53  | | | GROUND_INST: instantiating (102) with all_52_3, all_52_8, e2, e3,
% 178.34/28.53  | | |              simplifying with (8), (162) gives:
% 178.34/28.53  | | |   (163)  all_52_3 = all_52_8
% 178.34/28.53  | | | 
% 178.34/28.53  | | | COMBINE_EQS: (42), (163) imply:
% 178.34/28.53  | | |   (164)  all_58_1 = all_52_8
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (52), (163) imply:
% 178.34/28.53  | | |   (165)   ~ (all_52_5 = all_52_8)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (165) implies:
% 178.34/28.53  | | |   (166)   ~ (all_52_5 = all_52_8)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (79), (163) imply:
% 178.34/28.53  | | |   (167)   ~ (all_52_7 = all_52_8)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | SIMP: (167) implies:
% 178.34/28.53  | | |   (168)   ~ (all_52_7 = all_52_8)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (82), (163) imply:
% 178.34/28.53  | | |   (169)   ~ (all_52_8 = all_52_19)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (61), (163) imply:
% 178.34/28.53  | | |   (170)   ~ (all_52_8 = all_4_2)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | REDUCE: (140), (163) imply:
% 178.34/28.53  | | |   (171)   ~ (all_52_8 = e3)
% 178.34/28.53  | | | 
% 178.34/28.53  | | | BETA: splitting (69) gives:
% 178.34/28.53  | | | 
% 178.34/28.53  | | | Case 1:
% 178.34/28.53  | | | | 
% 178.34/28.53  | | | |   (172)  all_56_12 = e3
% 178.34/28.53  | | | | 
% 178.34/28.53  | | | | REF_CLOSE: (73), (142), (172) are inconsistent by sub-proof #1040.
% 178.34/28.53  | | | | 
% 178.34/28.53  | | | Case 2:
% 178.34/28.53  | | | | 
% 178.34/28.53  | | | |   (173)   ~ (all_56_12 = e3)
% 178.34/28.53  | | | |   (174)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.34/28.53  | | | | 
% 178.34/28.53  | | | | BETA: splitting (53) gives:
% 178.34/28.53  | | | | 
% 178.34/28.53  | | | | Case 1:
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | |   (175)  all_58_0 = e3
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | COMBINE_EQS: (44), (175) imply:
% 178.34/28.53  | | | | |   (176)  all_4_2 = e3
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | REDUCE: (28), (176) imply:
% 178.34/28.53  | | | | |   (177)   ~ (all_52_5 = e3)
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | REDUCE: (101), (176) imply:
% 178.34/28.53  | | | | |   (178)   ~ (all_52_17 = e3)
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | REDUCE: (59), (176) imply:
% 178.34/28.53  | | | | |   (179)  op(all_4_1, e3) = all_4_0
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | REDUCE: (38), (176) imply:
% 178.34/28.53  | | | | |   (180)  op(e3, e3) = all_4_1
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | REDUCE: (100), (176) imply:
% 178.34/28.53  | | | | |   (181)  op(e3, e3) = e3
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | GROUND_INST: instantiating (102) with e3, all_4_1, e3, e3, simplifying
% 178.34/28.53  | | | | |              with (180), (181) gives:
% 178.34/28.53  | | | | |   (182)  all_4_1 = e3
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | REDUCE: (179), (182) imply:
% 178.34/28.53  | | | | |   (183)  op(e3, e3) = all_4_0
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | GROUND_INST: instantiating (102) with e3, all_4_0, e3, e3, simplifying
% 178.34/28.53  | | | | |              with (181), (183) gives:
% 178.34/28.53  | | | | |   (184)  all_4_0 = e3
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | BETA: splitting (34) gives:
% 178.34/28.53  | | | | | 
% 178.34/28.53  | | | | | Case 1:
% 178.34/28.53  | | | | | | 
% 178.34/28.53  | | | | | |   (185)  all_58_6 = e3
% 178.34/28.53  | | | | | | 
% 178.34/28.53  | | | | | | REF_CLOSE: (78), (178), (185) are inconsistent by sub-proof #981.
% 178.34/28.53  | | | | | | 
% 178.34/28.53  | | | | | Case 2:
% 178.34/28.53  | | | | | | 
% 178.34/28.53  | | | | | |   (186)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.34/28.53  | | | | | | 
% 178.34/28.53  | | | | | | BETA: splitting (118) gives:
% 178.34/28.53  | | | | | | 
% 178.34/28.53  | | | | | | Case 1:
% 178.34/28.53  | | | | | | | 
% 178.34/28.53  | | | | | | |   (187)  all_58_4 = e3
% 178.34/28.53  | | | | | | | 
% 178.34/28.53  | | | | | | | REF_CLOSE: (33), (177), (187) are inconsistent by sub-proof #1025.
% 178.34/28.53  | | | | | | | 
% 178.34/28.53  | | | | | | Case 2:
% 178.34/28.53  | | | | | | | 
% 178.34/28.53  | | | | | | |   (188)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.34/28.53  | | | | | | | 
% 178.34/28.53  | | | | | | | BETA: splitting (40) gives:
% 178.34/28.53  | | | | | | | 
% 178.34/28.53  | | | | | | | Case 1:
% 178.34/28.53  | | | | | | | | 
% 178.34/28.53  | | | | | | | |   (189)  all_58_2 = e3
% 178.34/28.53  | | | | | | | | 
% 178.34/28.53  | | | | | | | | COMBINE_EQS: (151), (189) imply:
% 178.34/28.53  | | | | | | | |   (190)  e3 = e2
% 178.34/28.53  | | | | | | | | 
% 178.34/28.53  | | | | | | | | REDUCE: (119), (190) imply:
% 178.34/28.53  | | | | | | | |   (191)  $false
% 178.34/28.53  | | | | | | | | 
% 178.34/28.53  | | | | | | | | CLOSE: (191) is inconsistent.
% 178.34/28.53  | | | | | | | | 
% 178.34/28.53  | | | | | | | Case 2:
% 178.34/28.53  | | | | | | | | 
% 178.34/28.54  | | | | | | | |   (192)   ~ (all_58_2 = e3)
% 178.34/28.54  | | | | | | | |   (193)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.34/28.54  | | | | | | | | 
% 178.34/28.54  | | | | | | | | REDUCE: (151), (192) imply:
% 178.34/28.54  | | | | | | | |   (194)   ~ (e3 = e2)
% 178.34/28.54  | | | | | | | | 
% 178.34/28.54  | | | | | | | | BETA: splitting (14) gives:
% 178.34/28.54  | | | | | | | | 
% 178.34/28.54  | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | 
% 178.34/28.54  | | | | | | | | |   (195)  all_58_1 = e2
% 178.34/28.54  | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | COMBINE_EQS: (164), (195) imply:
% 178.34/28.54  | | | | | | | | |   (196)  all_52_8 = e2
% 178.34/28.54  | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | REDUCE: (168), (196) imply:
% 178.34/28.54  | | | | | | | | |   (197)   ~ (all_52_7 = e2)
% 178.34/28.54  | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | REDUCE: (169), (196) imply:
% 178.34/28.54  | | | | | | | | |   (198)   ~ (all_52_19 = e2)
% 178.34/28.54  | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | SIMP: (198) implies:
% 178.34/28.54  | | | | | | | | |   (199)   ~ (all_52_19 = e2)
% 178.34/28.54  | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | BETA: splitting (76) gives:
% 178.34/28.54  | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | |   (200)  all_58_6 = e2
% 178.34/28.54  | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | REF_CLOSE: (78), (157), (200) are inconsistent by sub-proof
% 178.34/28.54  | | | | | | | | | |            #894.
% 178.34/28.54  | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | Case 2:
% 178.34/28.54  | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | |   (201)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.34/28.54  | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | BETA: splitting (65) gives:
% 178.34/28.54  | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | |   (202)  all_58_9 = e2
% 178.34/28.54  | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | REF_CLOSE: (114), (197), (202) are inconsistent by sub-proof
% 178.34/28.54  | | | | | | | | | | |            #664.
% 178.34/28.54  | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | Case 2:
% 178.34/28.54  | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | |   (203)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.34/28.54  | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | BETA: splitting (97) gives:
% 178.34/28.54  | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | |   (204)  all_56_7 = e3
% 178.34/28.54  | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | COMBINE_EQS: (109), (204) imply:
% 178.34/28.54  | | | | | | | | | | | |   (205)  all_52_15 = e3
% 178.34/28.54  | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | SIMP: (205) implies:
% 178.34/28.54  | | | | | | | | | | | |   (206)  all_52_15 = e3
% 178.34/28.54  | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | REDUCE: (83), (206) imply:
% 178.34/28.54  | | | | | | | | | | | |   (207)   ~ (all_52_7 = e3)
% 178.34/28.54  | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | REDUCE: (43), (206) imply:
% 178.34/28.54  | | | | | | | | | | | |   (208)   ~ (all_52_13 = e3)
% 178.34/28.54  | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | BETA: splitting (188) gives:
% 178.34/28.54  | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | |   (209)  all_58_5 = e3
% 178.34/28.54  | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | REF_CLOSE: (15), (208), (209) are inconsistent by sub-proof
% 178.34/28.54  | | | | | | | | | | | | |            #969.
% 178.34/28.54  | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | Case 2:
% 178.34/28.54  | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | |   (210)  all_58_8 = e3 | all_58_14 = e3
% 178.34/28.54  | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | BETA: splitting (210) gives:
% 178.34/28.54  | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | |   (211)  all_58_8 = e3
% 178.34/28.54  | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 178.34/28.54  | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | |   (212)  all_58_7 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | COMBINE_EQS: (29), (212) imply:
% 178.34/28.54  | | | | | | | | | | | | | | |   (213)  all_52_19 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | REDUCE: (199), (213) imply:
% 178.34/28.54  | | | | | | | | | | | | | | |   (214)  $false
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent.
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | Case 2:
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | |   (215)  all_58_8 = e2 | all_58_11 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 178.34/28.54  | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | |   (216)  all_58_8 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (216) imply:
% 178.34/28.54  | | | | | | | | | | | | | | | |   (217)  e3 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | SIMP: (217) implies:
% 178.34/28.54  | | | | | | | | | | | | | | | |   (218)  e3 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | REDUCE: (119), (218) imply:
% 178.34/28.54  | | | | | | | | | | | | | | | |   (219)  $false
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | CLOSE: (219) is inconsistent.
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | Case 2:
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | |   (220)  all_58_11 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (220) imply:
% 178.34/28.54  | | | | | | | | | | | | | | | |   (221)  all_52_23 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | SIMP: (221) implies:
% 178.34/28.54  | | | | | | | | | | | | | | | |   (222)  all_52_23 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | REDUCE: (87), (222) imply:
% 178.34/28.54  | | | | | | | | | | | | | | | |   (223)   ~ (all_6_2 = e2)
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | SIMP: (223) implies:
% 178.34/28.54  | | | | | | | | | | | | | | | |   (224)   ~ (all_6_2 = e2)
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 178.34/28.54  | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | Case 1:
% 178.34/28.54  | | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | |   (225)  all_56_15 = e2
% 178.34/28.54  | | | | | | | | | | | | | | | | | 
% 178.34/28.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (224), (225) are inconsistent by sub-proof
% 178.34/28.54  | | | | | | | | | | | | | | | | |            #817.
% 178.34/28.54  | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | |   (226)  all_56_15 = e1 | all_56_15 = e0
% 178.71/28.54  | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 178.71/28.54  | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | Case 1:
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | |   (227)  all_56_15 = e1
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (227) imply:
% 178.71/28.54  | | | | | | | | | | | | | | | | | |   (228)  all_6_2 = e1
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 178.71/28.54  | | | | | | | | | | | | | | | | | |   (229)  all_6_2 = e1
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | | REDUCE: (94), (229) imply:
% 178.71/28.54  | | | | | | | | | | | | | | | | | |   (230)   ~ (all_52_25 = e1)
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (84), (99), (102), (159), (174), (207),
% 178.71/28.54  | | | | | | | | | | | | | | | | | |            (230) are inconsistent by sub-proof #663.
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | |   (231)  all_56_15 = e0
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (231) are inconsistent by sub-proof
% 178.71/28.54  | | | | | | | | | | | | | | | | | |            #812.
% 178.71/28.54  | | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | |   (232)  all_58_14 = e3
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | REF_CLOSE: (50), (144), (232) are inconsistent by sub-proof
% 178.71/28.54  | | | | | | | | | | | | | |            #1000.
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | |   (233)   ~ (all_56_7 = e3)
% 178.71/28.54  | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | REDUCE: (109), (233) imply:
% 178.71/28.54  | | | | | | | | | | | |   (234)   ~ (all_52_15 = e3)
% 178.71/28.54  | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | BETA: splitting (193) gives:
% 178.71/28.54  | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | Case 1:
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | |   (235)  all_58_3 = e3
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | COMBINE_EQS: (21), (235) imply:
% 178.71/28.54  | | | | | | | | | | | | |   (236)  all_10_2 = e3
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | REDUCE: (146), (236) imply:
% 178.71/28.54  | | | | | | | | | | | | |   (237)  $false
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | CLOSE: (237) is inconsistent.
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | |   (238)  all_58_5 = e3 | all_58_10 = e3
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | Case 1:
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | |   (239)  all_58_5 = e3
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | COMBINE_EQS: (15), (239) imply:
% 178.71/28.54  | | | | | | | | | | | | | |   (240)  all_52_13 = e3
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | REF_CLOSE: (23), (24), (27), (29), (55), (66), (102), (125),
% 178.71/28.54  | | | | | | | | | | | | | |            (141), (149), (153), (155), (186), (203), (240)
% 178.71/28.54  | | | | | | | | | | | | | |            are inconsistent by sub-proof #661.
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | |   (241)  all_58_10 = e3
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | | REF_CLOSE: (27), (234), (241) are inconsistent by sub-proof
% 178.71/28.54  | | | | | | | | | | | | | |            #1018.
% 178.71/28.54  | | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | |   (242)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | REF_CLOSE: (7), (10), (21), (23), (24), (27), (29), (50),
% 178.71/28.54  | | | | | | | | |            (65), (81), (84), (95), (99), (102), (106), (114),
% 178.71/28.54  | | | | | | | | |            (115), (119), (125), (127), (139), (141), (144),
% 178.71/28.54  | | | | | | | | |            (149), (155), (159), (161), (242) are inconsistent
% 178.71/28.54  | | | | | | | | |            by sub-proof #657.
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | End of split
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | End of split
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | End of split
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | Case 2:
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | |   (243)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | | BETA: splitting (243) gives:
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | | Case 1:
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | |   (244)  all_58_2 = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | COMBINE_EQS: (151), (244) imply:
% 178.71/28.54  | | | | | |   (245)  e3 = e2
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (119), (245) imply:
% 178.71/28.54  | | | | | |   (246)  $false
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | CLOSE: (246) is inconsistent.
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | Case 2:
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | |   (247)  all_58_6 = e3 | all_58_12 = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | BETA: splitting (247) gives:
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | Case 1:
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | |   (248)  all_58_6 = e3
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | COMBINE_EQS: (78), (248) imply:
% 178.71/28.54  | | | | | | |   (249)  all_52_17 = e3
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | SIMP: (249) implies:
% 178.71/28.54  | | | | | | |   (250)  all_52_17 = e3
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | REDUCE: (112), (250) imply:
% 178.71/28.54  | | | | | | |   (251)   ~ (all_52_19 = e3)
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | REDUCE: (4), (250) imply:
% 178.71/28.54  | | | | | | |   (252)   ~ (all_52_23 = e3)
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | SIMP: (252) implies:
% 178.71/28.54  | | | | | | |   (253)   ~ (all_52_23 = e3)
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | REDUCE: (30), (250) imply:
% 178.71/28.54  | | | | | | |   (254)   ~ (all_52_25 = e3)
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | REDUCE: (101), (250) imply:
% 178.71/28.54  | | | | | | |   (255)   ~ (all_4_2 = e3)
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | SIMP: (255) implies:
% 178.71/28.54  | | | | | | |   (256)   ~ (all_4_2 = e3)
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | REF_CLOSE: (1), (7), (10), (12), (14), (21), (22), (23), (24),
% 178.71/28.54  | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (35), (38),
% 178.71/28.54  | | | | | | |            (41), (44), (45), (47), (50), (57), (58), (59), (65),
% 178.71/28.54  | | | | | | |            (67), (70), (71), (72), (73), (75), (80), (81), (83),
% 178.71/28.54  | | | | | | |            (84), (85), (92), (93), (95), (98), (99), (102), (106),
% 178.71/28.54  | | | | | | |            (113), (114), (115), (116), (118), (119), (120), (125),
% 178.71/28.54  | | | | | | |            (127), (129), (135), (139), (141), (142), (144), (149),
% 178.71/28.54  | | | | | | |            (151), (155), (159), (161), (164), (166), (170), (171),
% 178.71/28.54  | | | | | | |            (174), (247), (248), (253), (256) are inconsistent by
% 178.71/28.54  | | | | | | |            sub-proof #655.
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | Case 2:
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | |   (257)  all_58_12 = e3
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | REF_CLOSE: (115), (142), (257) are inconsistent by sub-proof
% 178.71/28.54  | | | | | | |            #1003.
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | End of split
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | End of split
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | End of split
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | End of split
% 178.71/28.54  | | | 
% 178.71/28.54  | | Case 2:
% 178.71/28.54  | | | 
% 178.71/28.54  | | |   (258)   ~ (all_56_13 = e3)
% 178.71/28.54  | | |   (259)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.71/28.54  | | | 
% 178.71/28.54  | | | REDUCE: (122), (258) imply:
% 178.71/28.54  | | |   (260)   ~ (all_52_27 = e3)
% 178.71/28.54  | | | 
% 178.71/28.54  | | | BETA: splitting (54) gives:
% 178.71/28.54  | | | 
% 178.71/28.54  | | | Case 1:
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | |   (261)  all_58_12 = e3
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | | REF_CLOSE: (84), (98), (100), (102), (115), (261) are inconsistent by
% 178.71/28.54  | | | |            sub-proof #884.
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | Case 2:
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | |   (262)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | | BETA: splitting (262) gives:
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | | Case 1:
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | |   (263)  all_58_13 = e3
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | | REF_CLOSE: (74), (260), (263) are inconsistent by sub-proof #1026.
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | Case 2:
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | |   (264)  all_58_14 = e3 | all_58_15 = e3
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | | BETA: splitting (264) gives:
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | | Case 1:
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | |   (265)  all_58_14 = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | COMBINE_EQS: (50), (265) imply:
% 178.71/28.54  | | | | | |   (266)  all_52_29 = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | SIMP: (266) implies:
% 178.71/28.54  | | | | | |   (267)  all_52_29 = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (70), (267) imply:
% 178.71/28.54  | | | | | |   (268)   ~ (all_52_5 = e3)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (6), (267) imply:
% 178.71/28.54  | | | | | |   (269)   ~ (all_52_13 = e3)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (17), (267) imply:
% 178.71/28.54  | | | | | |   (270)   ~ (all_52_25 = e3)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (89), (267) imply:
% 178.71/28.54  | | | | | |   (271)   ~ (all_6_2 = e3)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (58), (267) imply:
% 178.71/28.54  | | | | | |   (272)  op(e1, e3) = e1
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (31), (267) imply:
% 178.71/28.54  | | | | | |   (273)  op(e0, e1) = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | GROUND_INST: instantiating (102) with all_52_17, e1, e3, e1,
% 178.71/28.54  | | | | | |              simplifying with (96), (272) gives:
% 178.71/28.54  | | | | | |   (274)  all_52_17 = e1
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | COMBINE_EQS: (78), (274) imply:
% 178.71/28.54  | | | | | |   (275)  all_58_6 = e1
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (112), (274) imply:
% 178.71/28.54  | | | | | |   (276)   ~ (all_52_19 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | SIMP: (276) implies:
% 178.71/28.54  | | | | | |   (277)   ~ (all_52_19 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (4), (274) imply:
% 178.71/28.54  | | | | | |   (278)   ~ (all_52_23 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | SIMP: (278) implies:
% 178.71/28.54  | | | | | |   (279)   ~ (all_52_23 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (30), (274) imply:
% 178.71/28.54  | | | | | |   (280)   ~ (all_52_25 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | SIMP: (280) implies:
% 178.71/28.54  | | | | | |   (281)   ~ (all_52_25 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (37), (274) imply:
% 178.71/28.54  | | | | | |   (282)   ~ (all_14_2 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | SIMP: (282) implies:
% 178.71/28.54  | | | | | |   (283)   ~ (all_14_2 = e1)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (64), (274) imply:
% 178.71/28.54  | | | | | |   (284)  op(e3, e1) = all_52_16
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | GROUND_INST: instantiating (102) with all_52_5, all_52_16, e1, e3,
% 178.71/28.54  | | | | | |              simplifying with (92), (284) gives:
% 178.71/28.54  | | | | | |   (285)  all_52_5 = all_52_16
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | COMBINE_EQS: (33), (285) imply:
% 178.71/28.54  | | | | | |   (286)  all_58_4 = all_52_16
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (52), (285) imply:
% 178.71/28.54  | | | | | |   (287)   ~ (all_52_3 = all_52_16)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (26), (285) imply:
% 178.71/28.54  | | | | | |   (288)   ~ (all_52_7 = all_52_16)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | SIMP: (288) implies:
% 178.71/28.54  | | | | | |   (289)   ~ (all_52_7 = all_52_16)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (28), (285) imply:
% 178.71/28.54  | | | | | |   (290)   ~ (all_52_16 = all_4_2)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (268), (285) imply:
% 178.71/28.54  | | | | | |   (291)   ~ (all_52_16 = e3)
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | BETA: splitting (69) gives:
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | Case 1:
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | |   (292)  all_56_12 = e3
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | REF_CLOSE: (73), (270), (292) are inconsistent by sub-proof #1040.
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | Case 2:
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | |   (293)   ~ (all_56_12 = e3)
% 178.71/28.54  | | | | | | |   (294)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | BETA: splitting (48) gives:
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | | Case 1:
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | |   (295)  all_58_4 = e1
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | COMBINE_EQS: (286), (295) imply:
% 178.71/28.54  | | | | | | | |   (296)  all_52_16 = e1
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | SIMP: (296) implies:
% 178.71/28.54  | | | | | | | |   (297)  all_52_16 = e1
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | REDUCE: (287), (297) imply:
% 178.71/28.54  | | | | | | | |   (298)   ~ (all_52_3 = e1)
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | REDUCE: (289), (297) imply:
% 178.71/28.54  | | | | | | | |   (299)   ~ (all_52_7 = e1)
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | REDUCE: (290), (297) imply:
% 178.71/28.54  | | | | | | | |   (300)   ~ (all_4_2 = e1)
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | SIMP: (300) implies:
% 178.71/28.54  | | | | | | | |   (301)   ~ (all_4_2 = e1)
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | REDUCE: (291), (297) imply:
% 178.71/28.54  | | | | | | | |   (302)   ~ (e3 = e1)
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | BETA: splitting (53) gives:
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | Case 1:
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | |   (303)  all_58_0 = e3
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | COMBINE_EQS: (44), (303) imply:
% 178.71/28.54  | | | | | | | | |   (304)  all_4_2 = e3
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | REDUCE: (61), (304) imply:
% 178.71/28.54  | | | | | | | | |   (305)   ~ (all_52_3 = e3)
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | REDUCE: (41), (304) imply:
% 178.71/28.54  | | | | | | | | |   (306)   ~ (all_52_7 = e3)
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | REF_CLOSE: (2), (7), (10), (11), (16), (18), (20), (23), (24),
% 178.71/28.54  | | | | | | | | |            (29), (35), (42), (49), (73), (74), (81), (84),
% 178.71/28.54  | | | | | | | | |            (91), (94), (99), (102), (103), (105), (110),
% 178.71/28.54  | | | | | | | | |            (113), (114), (115), (125), (134), (135), (260),
% 178.71/28.54  | | | | | | | | |            (273), (277), (279), (294), (298), (299), (305),
% 178.71/28.54  | | | | | | | | |            (306) are inconsistent by sub-proof #651.
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | |   (307)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (18), (19), (20),
% 178.71/28.54  | | | | | | | | |            (21), (22), (23), (24), (25), (27), (29), (32),
% 178.71/28.54  | | | | | | | | |            (34), (35), (38), (42), (44), (49), (56), (59),
% 178.71/28.54  | | | | | | | | |            (60), (63), (73), (74), (79), (80), (81), (84),
% 178.71/28.54  | | | | | | | | |            (85), (86), (90), (94), (98), (99), (102), (105),
% 178.71/28.54  | | | | | | | | |            (106), (107), (113), (114), (115), (117), (122),
% 178.71/28.54  | | | | | | | | |            (134), (135), (259), (260), (265), (270), (273),
% 178.71/28.54  | | | | | | | | |            (275), (277), (279), (281), (294), (295), (298),
% 178.71/28.54  | | | | | | | | |            (299), (301), (307) are inconsistent by sub-proof
% 178.71/28.54  | | | | | | | | |            #640.
% 178.71/28.54  | | | | | | | | | 
% 178.71/28.54  | | | | | | | | End of split
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | Case 2:
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | |   (308)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | | REF_CLOSE: (10), (15), (16), (18), (20), (21), (23), (24), (27),
% 178.71/28.54  | | | | | | | |            (29), (35), (41), (42), (43), (44), (49), (53), (55),
% 178.71/28.54  | | | | | | | |            (63), (73), (74), (79), (81), (84), (90), (94), (99),
% 178.71/28.54  | | | | | | | |            (102), (106), (113), (114), (115), (117), (125),
% 178.71/28.54  | | | | | | | |            (134), (135), (260), (265), (269), (270), (273),
% 178.71/28.54  | | | | | | | |            (275), (277), (279), (281), (283), (294), (308) are
% 178.71/28.54  | | | | | | | |            inconsistent by sub-proof #637.
% 178.71/28.54  | | | | | | | | 
% 178.71/28.54  | | | | | | | End of split
% 178.71/28.54  | | | | | | | 
% 178.71/28.54  | | | | | | End of split
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | Case 2:
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | |   (309)  all_58_15 = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | COMBINE_EQS: (23), (309) imply:
% 178.71/28.54  | | | | | |   (310)  all_6_2 = e3
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | REDUCE: (135), (310) imply:
% 178.71/28.54  | | | | | |   (311)  $false
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | | CLOSE: (311) is inconsistent.
% 178.71/28.54  | | | | | | 
% 178.71/28.54  | | | | | End of split
% 178.71/28.54  | | | | | 
% 178.71/28.54  | | | | End of split
% 178.71/28.54  | | | | 
% 178.71/28.54  | | | End of split
% 178.71/28.54  | | | 
% 178.71/28.54  | | End of split
% 178.71/28.54  | | 
% 178.71/28.54  | End of split
% 178.71/28.54  | 
% 178.71/28.54  End of proof
% 178.71/28.54  
% 178.71/28.54  Sub-proof #637 shows that the following formulas are inconsistent:
% 178.71/28.54  ----------------------------------------------------------------
% 178.71/28.54    (1)   ~ (all_52_25 = e3)
% 178.71/28.54    (2)   ~ (all_52_19 = all_52_23)
% 178.71/28.54    (3)   ~ (all_52_27 = e3)
% 178.71/28.54    (4)   ~ (all_6_2 = e3)
% 178.71/28.54    (5)  all_58_5 = all_52_13
% 178.71/28.54    (6)   ~ (all_6_2 = e0)
% 178.71/28.54    (7)  all_56_15 = all_6_2
% 178.71/28.54    (8)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.54    (9)  all_58_3 = all_10_2
% 178.71/28.54    (10)  all_58_15 = all_6_2
% 178.71/28.54    (11)  op(e0, all_6_2) = e0
% 178.71/28.54    (12)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.54    (13)  all_58_10 = all_52_15
% 178.71/28.54    (14)  all_58_7 = all_52_19
% 178.71/28.54    (15)   ~ (e3 = e1)
% 178.71/28.54    (16)   ~ (all_52_7 = all_4_2)
% 178.71/28.54    (17)  all_58_1 = all_52_3
% 178.71/28.54    (18)   ~ (all_52_13 = all_52_15)
% 178.71/28.54    (19)  all_58_0 = all_4_2
% 178.71/28.54    (20)  all_58_6 = e1
% 178.71/28.54    (21)   ~ (all_14_2 = e1)
% 178.71/28.54    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.54    (23)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.54    (24)  all_58_8 = all_14_2
% 178.71/28.54    (25)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.71/28.54    (26)   ~ (all_52_9 = all_10_2)
% 178.71/28.54    (27)   ~ (all_52_23 = e1)
% 178.71/28.54    (28)   ~ (e3 = e0)
% 178.71/28.54    (29)   ~ (all_52_13 = e3)
% 178.71/28.54    (30)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.54    (31)  all_56_12 = all_52_25
% 178.71/28.54    (32)  all_58_13 = all_52_27
% 178.71/28.54    (33)   ~ (all_52_25 = e1)
% 178.71/28.54    (34)   ~ (all_52_3 = all_52_7)
% 178.71/28.54    (35)  all_58_11 = all_52_23
% 178.71/28.54    (36)  op(e3, all_52_25) = e3
% 178.71/28.54    (37)  all_58_2 = all_52_9
% 178.71/28.54    (38)   ~ (all_52_25 = all_6_2)
% 178.71/28.54    (39)  op(e3, e0) = all_52_7
% 178.71/28.54    (40)   ~ (all_52_19 = e1)
% 178.71/28.54    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.54    (42)  op(e0, e1) = e3
% 178.71/28.54    (43)   ~ (all_52_7 = all_6_2)
% 178.71/28.54    (44)  all_58_14 = e3
% 178.71/28.54    (45)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.54    (46)  all_58_9 = all_52_7
% 178.71/28.54    (47)  all_58_12 = all_52_25
% 178.71/28.54    (48)   ~ (all_52_9 = all_52_15)
% 178.71/28.54  
% 178.71/28.54  Begin of proof
% 178.71/28.54  | 
% 178.71/28.54  | BETA: splitting (25) gives:
% 178.71/28.54  | 
% 178.71/28.54  | Case 1:
% 178.71/28.54  | | 
% 178.71/28.54  | |   (49)  all_58_5 = e1
% 178.71/28.54  | | 
% 178.71/28.54  | | COMBINE_EQS: (5), (49) imply:
% 178.71/28.54  | |   (50)  all_52_13 = e1
% 178.71/28.54  | | 
% 178.71/28.54  | | SIMP: (50) implies:
% 178.71/28.54  | |   (51)  all_52_13 = e1
% 178.71/28.54  | | 
% 178.71/28.54  | | REDUCE: (18), (51) imply:
% 178.71/28.54  | |   (52)   ~ (all_52_15 = e1)
% 178.71/28.54  | | 
% 178.71/28.54  | | SIMP: (52) implies:
% 178.71/28.54  | |   (53)   ~ (all_52_15 = e1)
% 178.71/28.54  | | 
% 178.71/28.54  | | REDUCE: (29), (51) imply:
% 178.71/28.54  | |   (54)   ~ (e3 = e1)
% 178.71/28.54  | | 
% 178.71/28.54  | | BETA: splitting (23) gives:
% 178.71/28.54  | | 
% 178.71/28.54  | | Case 1:
% 178.71/28.54  | | | 
% 178.71/28.54  | | |   (55)  all_58_0 = e3
% 178.71/28.54  | | | 
% 178.71/28.54  | | | COMBINE_EQS: (19), (55) imply:
% 178.71/28.54  | | |   (56)  all_4_2 = e3
% 178.71/28.54  | | | 
% 178.71/28.54  | | | REDUCE: (16), (56) imply:
% 178.71/28.54  | | |   (57)   ~ (all_52_7 = e3)
% 178.71/28.54  | | | 
% 178.71/28.54  | | | REF_CLOSE: (6), (7), (8), (10), (11), (12), (13), (27), (28), (30), (31),
% 178.71/28.54  | | |            (33), (35), (36), (38), (39), (41), (42), (43), (46), (53),
% 178.71/28.54  | | |            (57) are inconsistent by sub-proof #646.
% 178.71/28.54  | | | 
% 178.71/28.54  | | Case 2:
% 178.71/28.54  | | | 
% 178.71/28.54  | | |   (58)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.54  | | | 
% 178.71/28.54  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.71/28.54  | | |            (14), (15), (17), (20), (22), (26), (27), (28), (30), (31),
% 178.71/28.54  | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 178.71/28.54  | | |            (42), (43), (45), (46), (47), (48), (53), (58) are inconsistent
% 178.71/28.54  | | |            by sub-proof #639.
% 178.71/28.54  | | | 
% 178.71/28.54  | | End of split
% 178.71/28.54  | | 
% 178.71/28.54  | Case 2:
% 178.71/28.54  | | 
% 178.71/28.54  | |   (59)  all_58_8 = e1 | all_58_14 = e1
% 178.71/28.54  | | 
% 178.71/28.54  | | REF_CLOSE: (15), (21), (24), (44), (59) are inconsistent by sub-proof #638.
% 178.71/28.54  | | 
% 178.71/28.54  | End of split
% 178.71/28.54  | 
% 178.71/28.54  End of proof
% 178.71/28.54  
% 178.71/28.54  Sub-proof #638 shows that the following formulas are inconsistent:
% 178.71/28.54  ----------------------------------------------------------------
% 178.71/28.54    (1)   ~ (e3 = e1)
% 178.71/28.54    (2)   ~ (all_14_2 = e1)
% 178.71/28.54    (3)  all_58_8 = all_14_2
% 178.71/28.54    (4)  all_58_8 = e1 | all_58_14 = e1
% 178.71/28.54    (5)  all_58_14 = e3
% 178.71/28.54  
% 178.71/28.54  Begin of proof
% 178.71/28.54  | 
% 178.71/28.54  | BETA: splitting (4) gives:
% 178.71/28.54  | 
% 178.71/28.54  | Case 1:
% 178.71/28.54  | | 
% 178.71/28.54  | |   (6)  all_58_8 = e1
% 178.71/28.54  | | 
% 178.71/28.54  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #815.
% 178.71/28.54  | | 
% 178.71/28.54  | Case 2:
% 178.71/28.54  | | 
% 178.71/28.54  | |   (7)  all_58_14 = e1
% 178.71/28.54  | | 
% 178.71/28.54  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #881.
% 178.71/28.54  | | 
% 178.71/28.54  | End of split
% 178.71/28.54  | 
% 178.71/28.54  End of proof
% 178.71/28.54  
% 178.71/28.54  Sub-proof #639 shows that the following formulas are inconsistent:
% 178.71/28.54  ----------------------------------------------------------------
% 178.71/28.54    (1)   ~ (all_52_25 = e3)
% 178.71/28.54    (2)   ~ (all_52_19 = all_52_23)
% 178.71/28.54    (3)   ~ (all_52_27 = e3)
% 178.71/28.54    (4)   ~ (all_6_2 = e3)
% 178.71/28.54    (5)   ~ (all_6_2 = e0)
% 178.71/28.54    (6)  all_56_15 = all_6_2
% 178.71/28.54    (7)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.54    (8)  all_58_3 = all_10_2
% 178.71/28.54    (9)  all_58_15 = all_6_2
% 178.71/28.54    (10)  op(e0, all_6_2) = e0
% 178.71/28.54    (11)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.54    (12)  all_58_10 = all_52_15
% 178.71/28.54    (13)  all_58_7 = all_52_19
% 178.71/28.54    (14)   ~ (e3 = e1)
% 178.71/28.54    (15)  all_58_1 = all_52_3
% 178.71/28.54    (16)  all_58_6 = e1
% 178.71/28.54    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.54    (18)   ~ (all_52_9 = all_10_2)
% 178.71/28.54    (19)   ~ (all_52_23 = e1)
% 178.71/28.54    (20)   ~ (e3 = e0)
% 178.71/28.54    (21)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.54    (22)  all_56_12 = all_52_25
% 178.71/28.54    (23)  all_58_13 = all_52_27
% 178.71/28.54    (24)   ~ (all_52_25 = e1)
% 178.71/28.54    (25)   ~ (all_52_3 = all_52_7)
% 178.71/28.54    (26)  all_58_11 = all_52_23
% 178.71/28.54    (27)  op(e3, all_52_25) = e3
% 178.71/28.54    (28)  all_58_2 = all_52_9
% 178.71/28.54    (29)   ~ (all_52_25 = all_6_2)
% 178.71/28.54    (30)  op(e3, e0) = all_52_7
% 178.71/28.54    (31)   ~ (all_52_19 = e1)
% 178.71/28.54    (32)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.54    (33)  op(e0, e1) = e3
% 178.71/28.54    (34)   ~ (all_52_7 = all_6_2)
% 178.71/28.54    (35)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.54    (36)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.54    (37)  all_58_9 = all_52_7
% 178.71/28.54    (38)  all_58_12 = all_52_25
% 178.71/28.54    (39)   ~ (all_52_9 = all_52_15)
% 178.71/28.54    (40)   ~ (all_52_15 = e1)
% 178.71/28.54  
% 178.71/28.54  Begin of proof
% 178.71/28.54  | 
% 178.71/28.54  | BETA: splitting (35) gives:
% 178.71/28.54  | 
% 178.71/28.54  | Case 1:
% 178.71/28.54  | | 
% 178.71/28.54  | |   (41)  all_58_2 = e3
% 178.71/28.54  | | 
% 178.71/28.54  | | COMBINE_EQS: (28), (41) imply:
% 178.71/28.54  | |   (42)  all_52_9 = e3
% 178.71/28.54  | | 
% 178.71/28.54  | | SIMP: (42) implies:
% 178.71/28.54  | |   (43)  all_52_9 = e3
% 178.71/28.54  | | 
% 178.71/28.54  | | REDUCE: (39), (43) imply:
% 178.71/28.54  | |   (44)   ~ (all_52_15 = e3)
% 178.71/28.54  | | 
% 178.71/28.54  | | SIMP: (44) implies:
% 178.71/28.54  | |   (45)   ~ (all_52_15 = e3)
% 178.71/28.54  | | 
% 178.71/28.54  | | REDUCE: (18), (43) imply:
% 178.71/28.54  | |   (46)   ~ (all_10_2 = e3)
% 178.71/28.54  | | 
% 178.71/28.54  | | SIMP: (46) implies:
% 178.71/28.54  | |   (47)   ~ (all_10_2 = e3)
% 178.71/28.54  | | 
% 178.71/28.54  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.71/28.54  | |            (15), (17), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 178.71/28.54  | |            (29), (30), (31), (32), (33), (34), (36), (37), (40), (45), (47)
% 178.71/28.54  | |            are inconsistent by sub-proof #644.
% 178.71/28.54  | | 
% 178.71/28.54  | Case 2:
% 178.71/28.54  | | 
% 178.71/28.54  | |   (48)  all_58_6 = e3 | all_58_12 = e3
% 178.71/28.54  | | 
% 178.71/28.54  | | REF_CLOSE: (1), (14), (16), (38), (48) are inconsistent by sub-proof #1002.
% 178.71/28.54  | | 
% 178.71/28.54  | End of split
% 178.71/28.54  | 
% 178.71/28.54  End of proof
% 178.71/28.54  
% 178.71/28.54  Sub-proof #640 shows that the following formulas are inconsistent:
% 178.71/28.54  ----------------------------------------------------------------
% 178.71/28.54    (1)   ~ (all_52_25 = e3)
% 178.71/28.54    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.71/28.55    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.55    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.55    (5)   ~ (all_52_3 = e1)
% 178.71/28.55    (6)  all_58_4 = e1
% 178.71/28.55    (7)  op(e3, e2) = all_52_3
% 178.71/28.55    (8)   ~ (all_52_9 = all_52_25)
% 178.71/28.55    (9)   ~ (all_52_19 = all_52_23)
% 178.71/28.55    (10)   ~ (all_52_27 = e3)
% 178.71/28.55    (11)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.71/28.55    (12)   ~ (all_6_2 = e3)
% 178.71/28.55    (13)  all_56_15 = all_6_2
% 178.71/28.55    (14)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.71/28.55    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.55    (16)  all_58_3 = all_10_2
% 178.71/28.55    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.55    (18)  all_58_15 = all_6_2
% 178.71/28.55    (19)  op(e0, all_6_2) = e0
% 178.71/28.55    (20)   ~ (all_52_9 = all_4_2)
% 178.71/28.55    (21)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.55    (22)  all_58_10 = all_52_15
% 178.71/28.55    (23)  all_58_7 = all_52_19
% 178.71/28.55    (24)   ~ (all_4_0 = e2)
% 178.71/28.55    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.55    (26)   ~ (e3 = e1)
% 178.71/28.55    (27)  op(e3, all_4_2) = all_4_1
% 178.71/28.55    (28)  all_58_1 = all_52_3
% 178.71/28.55    (29)  all_58_0 = all_4_2
% 178.71/28.55    (30)  all_58_6 = e1
% 178.71/28.55    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.55    (32)  op(e0, e2) = all_52_27
% 178.71/28.55    (33)   ~ (all_52_7 = e1)
% 178.71/28.55    (34)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.55    (35)   ~ (all_52_3 = all_52_27)
% 178.71/28.55    (36)   ~ (all_52_9 = all_10_2)
% 178.71/28.55    (37)   ~ (all_52_23 = e1)
% 178.71/28.55    (38)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.55    (39)  all_56_12 = all_52_25
% 178.71/28.55    (40)  all_58_13 = all_52_27
% 178.71/28.55    (41)   ~ (all_52_25 = e1)
% 178.71/28.55    (42)   ~ (all_52_3 = all_52_7)
% 178.71/28.55    (43)  all_56_0 = all_4_2
% 178.71/28.55    (44)  all_58_11 = all_52_23
% 178.71/28.55    (45)  op(e3, all_52_25) = e3
% 178.71/28.55    (46)   ~ (all_4_0 = e1)
% 178.71/28.55    (47)   ~ (all_52_19 = all_10_2)
% 178.71/28.55    (48)  all_58_2 = all_52_9
% 178.71/28.55    (49)   ~ (all_52_25 = all_6_2)
% 178.71/28.55    (50)   ~ (all_52_25 = all_4_2)
% 178.71/28.55    (51)  op(e3, e0) = all_52_7
% 178.71/28.55    (52)   ~ (all_52_19 = e1)
% 178.71/28.55    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.55    (54)   ~ (all_52_27 = all_6_2)
% 178.71/28.55    (55)  op(e0, e1) = e3
% 178.71/28.55    (56)   ~ (all_52_7 = all_6_2)
% 178.71/28.55    (57)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.55    (58)   ~ (all_52_15 = all_10_2)
% 178.71/28.55    (59)  all_58_14 = e3
% 178.71/28.55    (60)   ~ (all_4_2 = e1)
% 178.71/28.55    (61)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.55    (62)  all_58_9 = all_52_7
% 178.71/28.55    (63)  all_58_12 = all_52_25
% 178.71/28.55    (64)   ~ (all_52_9 = all_52_15)
% 178.71/28.55    (65)  all_56_13 = all_52_27
% 178.71/28.55  
% 178.71/28.55  Begin of proof
% 178.71/28.55  | 
% 178.71/28.55  | BETA: splitting (57) gives:
% 178.71/28.55  | 
% 178.71/28.55  | Case 1:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (66)  all_58_2 = e3
% 178.71/28.55  | | 
% 178.71/28.55  | | COMBINE_EQS: (48), (66) imply:
% 178.71/28.55  | |   (67)  all_52_9 = e3
% 178.71/28.55  | | 
% 178.71/28.55  | | SIMP: (67) implies:
% 178.71/28.55  | |   (68)  all_52_9 = e3
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (64), (68) imply:
% 178.71/28.55  | |   (69)   ~ (all_52_15 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | SIMP: (69) implies:
% 178.71/28.55  | |   (70)   ~ (all_52_15 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (8), (68) imply:
% 178.71/28.55  | |   (71)   ~ (all_52_25 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (36), (68) imply:
% 178.71/28.55  | |   (72)   ~ (all_10_2 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | SIMP: (72) implies:
% 178.71/28.55  | |   (73)   ~ (all_10_2 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (20), (68) imply:
% 178.71/28.55  | |   (74)   ~ (all_4_2 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | SIMP: (74) implies:
% 178.71/28.55  | |   (75)   ~ (all_4_2 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | BETA: splitting (17) gives:
% 178.71/28.55  | | 
% 178.71/28.55  | | Case 1:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (76)  all_56_0 = e3
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REF_CLOSE: (43), (75), (76) are inconsistent by sub-proof #1024.
% 178.71/28.55  | | | 
% 178.71/28.55  | | Case 2:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (77)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 178.71/28.55  | | |            (14), (15), (16), (18), (19), (21), (22), (23), (24), (25),
% 178.71/28.55  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (37),
% 178.71/28.55  | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 178.71/28.55  | | |            (49), (50), (51), (52), (53), (54), (55), (56), (58), (59),
% 178.71/28.55  | | |            (60), (61), (62), (63), (65), (70), (73), (75), (77) are
% 178.71/28.55  | | |            inconsistent by sub-proof #641.
% 178.71/28.55  | | | 
% 178.71/28.55  | | End of split
% 178.71/28.55  | | 
% 178.71/28.55  | Case 2:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (78)  all_58_6 = e3 | all_58_12 = e3
% 178.71/28.55  | | 
% 178.71/28.55  | | REF_CLOSE: (1), (26), (30), (63), (78) are inconsistent by sub-proof #1002.
% 178.71/28.55  | | 
% 178.71/28.55  | End of split
% 178.71/28.55  | 
% 178.71/28.55  End of proof
% 178.71/28.55  
% 178.71/28.55  Sub-proof #641 shows that the following formulas are inconsistent:
% 178.71/28.55  ----------------------------------------------------------------
% 178.71/28.55    (1)   ~ (all_52_25 = e3)
% 178.71/28.55    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.71/28.55    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.55    (4)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.55    (5)   ~ (all_52_3 = e1)
% 178.71/28.55    (6)  all_58_4 = e1
% 178.71/28.55    (7)  op(e3, e2) = all_52_3
% 178.71/28.55    (8)   ~ (all_52_19 = all_52_23)
% 178.71/28.55    (9)   ~ (all_52_27 = e3)
% 178.71/28.55    (10)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.71/28.55    (11)   ~ (all_6_2 = e3)
% 178.71/28.55    (12)  all_56_15 = all_6_2
% 178.71/28.55    (13)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.71/28.55    (14)   ~ (all_4_2 = e3)
% 178.71/28.55    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.55    (16)  all_58_3 = all_10_2
% 178.71/28.55    (17)  all_58_15 = all_6_2
% 178.71/28.55    (18)  op(e0, all_6_2) = e0
% 178.71/28.55    (19)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.55    (20)  all_58_10 = all_52_15
% 178.71/28.55    (21)  all_58_7 = all_52_19
% 178.71/28.55    (22)   ~ (all_4_0 = e2)
% 178.71/28.55    (23)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.55    (24)  op(e3, all_4_2) = all_4_1
% 178.71/28.55    (25)  all_58_1 = all_52_3
% 178.71/28.55    (26)  all_58_0 = all_4_2
% 178.71/28.55    (27)  all_58_6 = e1
% 178.71/28.55    (28)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.55    (29)   ~ (all_10_2 = e3)
% 178.71/28.55    (30)  op(e0, e2) = all_52_27
% 178.71/28.55    (31)   ~ (all_52_7 = e1)
% 178.71/28.55    (32)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.55    (33)   ~ (all_52_3 = all_52_27)
% 178.71/28.55    (34)   ~ (all_52_23 = e1)
% 178.71/28.55    (35)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.55    (36)   ~ (all_52_15 = e3)
% 178.71/28.55    (37)  all_56_12 = all_52_25
% 178.71/28.55    (38)  all_58_13 = all_52_27
% 178.71/28.55    (39)   ~ (all_52_25 = e1)
% 178.71/28.55    (40)   ~ (all_52_3 = all_52_7)
% 178.71/28.55    (41)  all_56_0 = all_4_2
% 178.71/28.55    (42)  all_58_11 = all_52_23
% 178.71/28.55    (43)  op(e3, all_52_25) = e3
% 178.71/28.55    (44)   ~ (all_4_0 = e1)
% 178.71/28.55    (45)   ~ (all_52_19 = all_10_2)
% 178.71/28.55    (46)   ~ (all_52_25 = all_6_2)
% 178.71/28.55    (47)   ~ (all_52_25 = all_4_2)
% 178.71/28.55    (48)  op(e3, e0) = all_52_7
% 178.71/28.55    (49)   ~ (all_52_19 = e1)
% 178.71/28.55    (50)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.55    (51)   ~ (all_52_27 = all_6_2)
% 178.71/28.55    (52)  op(e0, e1) = e3
% 178.71/28.55    (53)   ~ (all_52_7 = all_6_2)
% 178.71/28.55    (54)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.55    (55)   ~ (all_52_15 = all_10_2)
% 178.71/28.55    (56)  all_58_14 = e3
% 178.71/28.55    (57)   ~ (all_4_2 = e1)
% 178.71/28.55    (58)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.55    (59)  all_58_9 = all_52_7
% 178.71/28.55    (60)  all_58_12 = all_52_25
% 178.71/28.55    (61)  all_56_13 = all_52_27
% 178.71/28.55  
% 178.71/28.55  Begin of proof
% 178.71/28.55  | 
% 178.71/28.55  | BETA: splitting (13) gives:
% 178.71/28.55  | 
% 178.71/28.55  | Case 1:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (62)  all_58_0 = e2
% 178.71/28.55  | | 
% 178.71/28.55  | | COMBINE_EQS: (26), (62) imply:
% 178.71/28.55  | |   (63)  all_4_2 = e2
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (47), (63) imply:
% 178.71/28.55  | |   (64)   ~ (all_52_25 = e2)
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (32), (63) imply:
% 178.71/28.55  | |   (65)  op(all_4_1, e2) = all_4_0
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (24), (63) imply:
% 178.71/28.55  | |   (66)  op(e3, e2) = all_4_1
% 178.71/28.55  | | 
% 178.71/28.55  | | BETA: splitting (35) gives:
% 178.71/28.55  | | 
% 178.71/28.55  | | Case 1:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (67)  all_56_12 = e2
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REF_CLOSE: (37), (64), (67) are inconsistent by sub-proof #1032.
% 178.71/28.55  | | | 
% 178.71/28.55  | | Case 2:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (68)   ~ (all_56_12 = e2)
% 178.71/28.55  | | |   (69)  all_56_12 = e1 | all_56_12 = e0
% 178.71/28.55  | | | 
% 178.71/28.55  | | | BETA: splitting (69) gives:
% 178.71/28.55  | | | 
% 178.71/28.55  | | | Case 1:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | |   (70)  all_56_12 = e1
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REF_CLOSE: (37), (39), (70) are inconsistent by sub-proof #1031.
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | Case 2:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | |   (71)  all_56_12 = e0
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | COMBINE_EQS: (37), (71) imply:
% 178.71/28.55  | | | |   (72)  all_52_25 = e0
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | SIMP: (72) implies:
% 178.71/28.55  | | | |   (73)  all_52_25 = e0
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (1), (73) imply:
% 178.71/28.55  | | | |   (74)   ~ (e3 = e0)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | SIMP: (74) implies:
% 178.71/28.55  | | | |   (75)   ~ (e3 = e0)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (64), (73) imply:
% 178.71/28.55  | | | |   (76)   ~ (e2 = e0)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | SIMP: (76) implies:
% 178.71/28.55  | | | |   (77)   ~ (e2 = e0)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (39), (73) imply:
% 178.71/28.55  | | | |   (78)   ~ (e1 = e0)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | SIMP: (78) implies:
% 178.71/28.55  | | | |   (79)   ~ (e1 = e0)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (43), (73) imply:
% 178.71/28.55  | | | |   (80)  op(e3, e0) = e3
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | GROUND_INST: instantiating (50) with all_52_7, e3, e0, e3, simplifying
% 178.71/28.55  | | | |              with (48), (80) gives:
% 178.71/28.55  | | | |   (81)  all_52_7 = e3
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | GROUND_INST: instantiating (50) with all_52_3, all_4_1, e2, e3,
% 178.71/28.55  | | | |              simplifying with (7), (66) gives:
% 178.71/28.55  | | | |   (82)  all_52_3 = all_4_1
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | COMBINE_EQS: (59), (81) imply:
% 178.71/28.55  | | | |   (83)  all_58_9 = e3
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | COMBINE_EQS: (25), (82) imply:
% 178.71/28.55  | | | |   (84)  all_58_1 = all_4_1
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (33), (82) imply:
% 178.71/28.55  | | | |   (85)   ~ (all_52_27 = all_4_1)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | SIMP: (85) implies:
% 178.71/28.55  | | | |   (86)   ~ (all_52_27 = all_4_1)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (31), (81) imply:
% 178.71/28.55  | | | |   (87)   ~ (e3 = e1)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | BETA: splitting (2) gives:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | Case 1:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | |   (88)  all_58_0 = e0
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | COMBINE_EQS: (62), (88) imply:
% 178.71/28.55  | | | | |   (89)  e2 = e0
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | REDUCE: (77), (89) imply:
% 178.71/28.55  | | | | |   (90)  $false
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | CLOSE: (90) is inconsistent.
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | Case 2:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | |   (91)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | BETA: splitting (91) gives:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | Case 1:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | |   (92)  all_58_1 = e0
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | COMBINE_EQS: (84), (92) imply:
% 178.71/28.55  | | | | | |   (93)  all_4_1 = e0
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | REDUCE: (86), (93) imply:
% 178.71/28.55  | | | | | |   (94)   ~ (all_52_27 = e0)
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | REDUCE: (65), (93) imply:
% 178.71/28.55  | | | | | |   (95)  op(e0, e2) = all_4_0
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | BETA: splitting (23) gives:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | Case 1:
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | |   (96)  all_58_6 = e3
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | COMBINE_EQS: (27), (96) imply:
% 178.71/28.55  | | | | | | |   (97)  e3 = e1
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | REDUCE: (87), (97) imply:
% 178.71/28.55  | | | | | | |   (98)  $false
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | CLOSE: (98) is inconsistent.
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | Case 2:
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | GROUND_INST: instantiating (50) with all_52_27, all_4_0, e2, e0,
% 178.71/28.55  | | | | | | |              simplifying with (30), (95) gives:
% 178.71/28.55  | | | | | | |   (99)  all_52_27 = all_4_0
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | REF_CLOSE: (10), (22), (44), (61), (94), (99) are inconsistent by
% 178.71/28.55  | | | | | | |            sub-proof #650.
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | End of split
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | Case 2:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | |   (100)  all_58_4 = e0 | all_58_9 = e0
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | REF_CLOSE: (6), (75), (79), (83), (100) are inconsistent by
% 178.71/28.55  | | | | | |            sub-proof #927.
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | End of split
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | End of split
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | End of split
% 178.71/28.55  | | | 
% 178.71/28.55  | | End of split
% 178.71/28.55  | | 
% 178.71/28.55  | Case 2:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (101)   ~ (all_58_0 = e2)
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (26), (101) imply:
% 178.71/28.55  | |   (102)   ~ (all_4_2 = e2)
% 178.71/28.55  | | 
% 178.71/28.55  | | REF_CLOSE: (3), (4), (5), (8), (9), (11), (12), (14), (15), (16), (17),
% 178.71/28.55  | |            (18), (19), (20), (21), (25), (28), (29), (34), (35), (36), (37),
% 178.71/28.55  | |            (38), (39), (40), (41), (42), (43), (45), (46), (47), (48), (49),
% 178.71/28.55  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 178.71/28.55  | |            (102) are inconsistent by sub-proof #642.
% 178.71/28.55  | | 
% 178.71/28.55  | End of split
% 178.71/28.55  | 
% 178.71/28.55  End of proof
% 178.71/28.55  
% 178.71/28.55  Sub-proof #642 shows that the following formulas are inconsistent:
% 178.71/28.55  ----------------------------------------------------------------
% 178.71/28.55    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.55    (2)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.55    (3)   ~ (all_4_2 = e2)
% 178.71/28.55    (4)   ~ (all_52_3 = e1)
% 178.71/28.55    (5)   ~ (all_52_19 = all_52_23)
% 178.71/28.55    (6)   ~ (all_52_27 = e3)
% 178.71/28.55    (7)   ~ (all_6_2 = e3)
% 178.71/28.55    (8)  all_56_15 = all_6_2
% 178.71/28.55    (9)   ~ (all_4_2 = e3)
% 178.71/28.55    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.55    (11)  all_58_3 = all_10_2
% 178.71/28.55    (12)  all_58_15 = all_6_2
% 178.71/28.55    (13)  op(e0, all_6_2) = e0
% 178.71/28.55    (14)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.55    (15)  all_58_10 = all_52_15
% 178.71/28.55    (16)  all_58_7 = all_52_19
% 178.71/28.55    (17)  all_58_1 = all_52_3
% 178.71/28.55    (18)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.55    (19)   ~ (all_10_2 = e3)
% 178.71/28.55    (20)   ~ (all_52_23 = e1)
% 178.71/28.55    (21)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.55    (22)   ~ (all_52_15 = e3)
% 178.71/28.55    (23)  all_56_12 = all_52_25
% 178.71/28.55    (24)  all_58_13 = all_52_27
% 178.71/28.55    (25)   ~ (all_52_25 = e1)
% 178.71/28.55    (26)   ~ (all_52_3 = all_52_7)
% 178.71/28.55    (27)  all_56_0 = all_4_2
% 178.71/28.55    (28)  all_58_11 = all_52_23
% 178.71/28.55    (29)  op(e3, all_52_25) = e3
% 178.71/28.55    (30)   ~ (all_52_19 = all_10_2)
% 178.71/28.55    (31)   ~ (all_52_25 = all_6_2)
% 178.71/28.55    (32)   ~ (all_52_25 = all_4_2)
% 178.71/28.55    (33)  op(e3, e0) = all_52_7
% 178.71/28.55    (34)   ~ (all_52_19 = e1)
% 178.71/28.55    (35)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.55    (36)   ~ (all_52_27 = all_6_2)
% 178.71/28.55    (37)  op(e0, e1) = e3
% 178.71/28.55    (38)   ~ (all_52_7 = all_6_2)
% 178.71/28.55    (39)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.55    (40)   ~ (all_52_15 = all_10_2)
% 178.71/28.55    (41)  all_58_14 = e3
% 178.71/28.55    (42)   ~ (all_4_2 = e1)
% 178.71/28.55    (43)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.55    (44)  all_58_9 = all_52_7
% 178.71/28.55    (45)  all_58_12 = all_52_25
% 178.71/28.55  
% 178.71/28.55  Begin of proof
% 178.71/28.55  | 
% 178.71/28.55  | BETA: splitting (39) gives:
% 178.71/28.55  | 
% 178.71/28.55  | Case 1:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (46)  all_56_0 = e2
% 178.71/28.55  | | 
% 178.71/28.55  | | REF_CLOSE: (3), (27), (46) are inconsistent by sub-proof #904.
% 178.71/28.55  | | 
% 178.71/28.55  | Case 2:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (47)  all_56_0 = e1 | all_56_0 = e0
% 178.71/28.55  | | 
% 178.71/28.55  | | BETA: splitting (47) gives:
% 178.71/28.55  | | 
% 178.71/28.55  | | Case 1:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (48)  all_56_0 = e1
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REF_CLOSE: (27), (42), (48) are inconsistent by sub-proof #1022.
% 178.71/28.55  | | | 
% 178.71/28.55  | | Case 2:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (49)  all_56_0 = e0
% 178.71/28.55  | | | 
% 178.71/28.55  | | | COMBINE_EQS: (27), (49) imply:
% 178.71/28.55  | | |   (50)  all_4_2 = e0
% 178.71/28.55  | | | 
% 178.71/28.55  | | | SIMP: (50) implies:
% 178.71/28.55  | | |   (51)  all_4_2 = e0
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REDUCE: (32), (51) imply:
% 178.71/28.55  | | |   (52)   ~ (all_52_25 = e0)
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REDUCE: (9), (51) imply:
% 178.71/28.55  | | |   (53)   ~ (e3 = e0)
% 178.71/28.55  | | | 
% 178.71/28.55  | | | SIMP: (53) implies:
% 178.71/28.55  | | |   (54)   ~ (e3 = e0)
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REDUCE: (42), (51) imply:
% 178.71/28.55  | | |   (55)   ~ (e1 = e0)
% 178.71/28.55  | | | 
% 178.71/28.55  | | | SIMP: (55) implies:
% 178.71/28.55  | | |   (56)   ~ (e1 = e0)
% 178.71/28.55  | | | 
% 178.71/28.55  | | | BETA: splitting (2) gives:
% 178.71/28.55  | | | 
% 178.71/28.55  | | | Case 1:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | |   (57)  all_58_12 = e0
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REF_CLOSE: (45), (52), (57) are inconsistent by sub-proof #649.
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | Case 2:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | |   (58)  all_58_13 = e0 | all_58_14 = e0
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | BETA: splitting (58) gives:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | Case 1:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | |   (59)  all_58_13 = e0
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | COMBINE_EQS: (24), (59) imply:
% 178.71/28.55  | | | | |   (60)  all_52_27 = e0
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | SIMP: (60) implies:
% 178.71/28.55  | | | | |   (61)  all_52_27 = e0
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | REDUCE: (36), (61) imply:
% 178.71/28.55  | | | | |   (62)   ~ (all_6_2 = e0)
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | SIMP: (62) implies:
% 178.71/28.55  | | | | |   (63)   ~ (all_6_2 = e0)
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | BETA: splitting (1) gives:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | Case 1:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | |   (64)  all_58_1 = e1
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | COMBINE_EQS: (17), (64) imply:
% 178.71/28.55  | | | | | |   (65)  all_52_3 = e1
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | REDUCE: (4), (65) imply:
% 178.71/28.55  | | | | | |   (66)  $false
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | CLOSE: (66) is inconsistent.
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | Case 2:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | |   (67)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | BETA: splitting (67) gives:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | Case 1:
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | |   (68)  all_58_3 = e1
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | COMBINE_EQS: (11), (68) imply:
% 178.71/28.55  | | | | | | |   (69)  all_10_2 = e1
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | REDUCE: (40), (69) imply:
% 178.71/28.55  | | | | | | |   (70)   ~ (all_52_15 = e1)
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 178.71/28.55  | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.71/28.55  | | | | | | |            (25), (26), (28), (29), (31), (33), (34), (35), (37),
% 178.71/28.55  | | | | | | |            (38), (43), (44), (54), (63), (70) are inconsistent by
% 178.71/28.55  | | | | | | |            sub-proof #644.
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | Case 2:
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | |   (71)  all_58_7 = e1 | all_58_13 = e1
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | BETA: splitting (71) gives:
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | | Case 1:
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | |   (72)  all_58_7 = e1
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | | COMBINE_EQS: (16), (72) imply:
% 178.71/28.55  | | | | | | | |   (73)  all_52_19 = e1
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | | REDUCE: (34), (73) imply:
% 178.71/28.55  | | | | | | | |   (74)  $false
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | | CLOSE: (74) is inconsistent.
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | Case 2:
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | |   (75)  all_58_13 = e1
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | | COMBINE_EQS: (59), (75) imply:
% 178.71/28.55  | | | | | | | |   (76)  e1 = e0
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | | REDUCE: (56), (76) imply:
% 178.71/28.55  | | | | | | | |   (77)  $false
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | | CLOSE: (77) is inconsistent.
% 178.71/28.55  | | | | | | | | 
% 178.71/28.55  | | | | | | | End of split
% 178.71/28.55  | | | | | | | 
% 178.71/28.55  | | | | | | End of split
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | End of split
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | Case 2:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | |   (78)  all_58_14 = e0
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | REF_CLOSE: (41), (54), (78) are inconsistent by sub-proof #643.
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | End of split
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | End of split
% 178.71/28.55  | | | 
% 178.71/28.55  | | End of split
% 178.71/28.55  | | 
% 178.71/28.55  | End of split
% 178.71/28.55  | 
% 178.71/28.55  End of proof
% 178.71/28.55  
% 178.71/28.55  Sub-proof #643 shows that the following formulas are inconsistent:
% 178.71/28.55  ----------------------------------------------------------------
% 178.71/28.55    (1)  all_58_14 = e3
% 178.71/28.55    (2)  all_58_14 = e0
% 178.71/28.55    (3)   ~ (e3 = e0)
% 178.71/28.55  
% 178.71/28.55  Begin of proof
% 178.71/28.55  | 
% 178.71/28.55  | COMBINE_EQS: (1), (2) imply:
% 178.71/28.55  |   (4)  e3 = e0
% 178.71/28.55  | 
% 178.71/28.55  | SIMP: (4) implies:
% 178.71/28.55  |   (5)  e3 = e0
% 178.71/28.55  | 
% 178.71/28.55  | REDUCE: (3), (5) imply:
% 178.71/28.55  |   (6)  $false
% 178.71/28.55  | 
% 178.71/28.55  | CLOSE: (6) is inconsistent.
% 178.71/28.55  | 
% 178.71/28.55  End of proof
% 178.71/28.55  
% 178.71/28.55  Sub-proof #644 shows that the following formulas are inconsistent:
% 178.71/28.55  ----------------------------------------------------------------
% 178.71/28.55    (1)   ~ (all_52_19 = all_52_23)
% 178.71/28.55    (2)   ~ (all_52_27 = e3)
% 178.71/28.55    (3)   ~ (all_6_2 = e3)
% 178.71/28.55    (4)   ~ (all_6_2 = e0)
% 178.71/28.55    (5)  all_56_15 = all_6_2
% 178.71/28.55    (6)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.55    (7)  all_58_3 = all_10_2
% 178.71/28.55    (8)  all_58_15 = all_6_2
% 178.71/28.55    (9)  op(e0, all_6_2) = e0
% 178.71/28.55    (10)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.55    (11)  all_58_10 = all_52_15
% 178.71/28.55    (12)  all_58_7 = all_52_19
% 178.71/28.55    (13)  all_58_1 = all_52_3
% 178.71/28.55    (14)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.55    (15)   ~ (all_10_2 = e3)
% 178.71/28.55    (16)   ~ (all_52_23 = e1)
% 178.71/28.55    (17)   ~ (e3 = e0)
% 178.71/28.55    (18)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.55    (19)   ~ (all_52_15 = e3)
% 178.71/28.55    (20)  all_56_12 = all_52_25
% 178.71/28.55    (21)  all_58_13 = all_52_27
% 178.71/28.55    (22)   ~ (all_52_25 = e1)
% 178.71/28.55    (23)   ~ (all_52_3 = all_52_7)
% 178.71/28.55    (24)  all_58_11 = all_52_23
% 178.71/28.55    (25)  op(e3, all_52_25) = e3
% 178.71/28.55    (26)   ~ (all_52_25 = all_6_2)
% 178.71/28.55    (27)  op(e3, e0) = all_52_7
% 178.71/28.55    (28)   ~ (all_52_19 = e1)
% 178.71/28.55    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.55            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.55    (30)  op(e0, e1) = e3
% 178.71/28.55    (31)   ~ (all_52_7 = all_6_2)
% 178.71/28.55    (32)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.55    (33)  all_58_9 = all_52_7
% 178.71/28.55    (34)   ~ (all_52_15 = e1)
% 178.71/28.55  
% 178.71/28.55  Begin of proof
% 178.71/28.55  | 
% 178.71/28.55  | BETA: splitting (14) gives:
% 178.71/28.55  | 
% 178.71/28.55  | Case 1:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (35)  all_58_1 = e3
% 178.71/28.55  | | 
% 178.71/28.55  | | COMBINE_EQS: (13), (35) imply:
% 178.71/28.55  | |   (36)  all_52_3 = e3
% 178.71/28.55  | | 
% 178.71/28.55  | | REDUCE: (23), (36) imply:
% 178.71/28.55  | |   (37)   ~ (all_52_7 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | SIMP: (37) implies:
% 178.71/28.55  | |   (38)   ~ (all_52_7 = e3)
% 178.71/28.55  | | 
% 178.71/28.55  | | REF_CLOSE: (4), (5), (6), (8), (9), (10), (11), (16), (17), (18), (20),
% 178.71/28.55  | |            (22), (24), (25), (26), (27), (29), (30), (31), (33), (34), (38)
% 178.71/28.55  | |            are inconsistent by sub-proof #646.
% 178.71/28.55  | | 
% 178.71/28.55  | Case 2:
% 178.71/28.55  | | 
% 178.71/28.55  | |   (39)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.55  | | 
% 178.71/28.55  | | BETA: splitting (39) gives:
% 178.71/28.55  | | 
% 178.71/28.55  | | Case 1:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (40)  all_58_3 = e3
% 178.71/28.55  | | | 
% 178.71/28.55  | | | COMBINE_EQS: (7), (40) imply:
% 178.71/28.55  | | |   (41)  all_10_2 = e3
% 178.71/28.55  | | | 
% 178.71/28.55  | | | REDUCE: (15), (41) imply:
% 178.71/28.55  | | |   (42)  $false
% 178.71/28.55  | | | 
% 178.71/28.55  | | | CLOSE: (42) is inconsistent.
% 178.71/28.55  | | | 
% 178.71/28.55  | | Case 2:
% 178.71/28.55  | | | 
% 178.71/28.55  | | |   (43)  all_58_7 = e3 | all_58_13 = e3
% 178.71/28.55  | | | 
% 178.71/28.55  | | | BETA: splitting (43) gives:
% 178.71/28.55  | | | 
% 178.71/28.55  | | | Case 1:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | |   (44)  all_58_7 = e3
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | COMBINE_EQS: (12), (44) imply:
% 178.71/28.55  | | | |   (45)  all_52_19 = e3
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (1), (45) imply:
% 178.71/28.55  | | | |   (46)   ~ (all_52_23 = e3)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | SIMP: (46) implies:
% 178.71/28.55  | | | |   (47)   ~ (all_52_23 = e3)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (28), (45) imply:
% 178.71/28.55  | | | |   (48)   ~ (e3 = e1)
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | BETA: splitting (32) gives:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | Case 1:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | |   (49)  all_58_9 = e3
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | BETA: splitting (6) gives:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | Case 1:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | |   (50)  all_58_9 = e1
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | REF_CLOSE: (48), (49), (50) are inconsistent by sub-proof #979.
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | Case 2:
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | |   (51)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | | REF_CLOSE: (8), (9), (11), (16), (17), (24), (29), (30), (34), (51)
% 178.71/28.55  | | | | | |            are inconsistent by sub-proof #647.
% 178.71/28.55  | | | | | | 
% 178.71/28.55  | | | | | End of split
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | Case 2:
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | |   (52)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | | REF_CLOSE: (3), (8), (11), (19), (24), (47), (52) are inconsistent by
% 178.71/28.55  | | | | |            sub-proof #645.
% 178.71/28.55  | | | | | 
% 178.71/28.55  | | | | End of split
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | Case 2:
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | |   (53)  all_58_13 = e3
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | COMBINE_EQS: (21), (53) imply:
% 178.71/28.55  | | | |   (54)  all_52_27 = e3
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | REDUCE: (2), (54) imply:
% 178.71/28.55  | | | |   (55)  $false
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | | CLOSE: (55) is inconsistent.
% 178.71/28.55  | | | | 
% 178.71/28.55  | | | End of split
% 178.71/28.55  | | | 
% 178.71/28.55  | | End of split
% 178.71/28.55  | | 
% 178.71/28.55  | End of split
% 178.71/28.55  | 
% 178.71/28.55  End of proof
% 178.71/28.55  
% 178.71/28.55  Sub-proof #645 shows that the following formulas are inconsistent:
% 178.71/28.55  ----------------------------------------------------------------
% 178.71/28.55    (1)   ~ (all_6_2 = e3)
% 178.71/28.55    (2)  all_58_15 = all_6_2
% 178.71/28.55    (3)  all_58_10 = all_52_15
% 178.71/28.56    (4)   ~ (all_52_23 = e3)
% 178.71/28.56    (5)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.56    (6)   ~ (all_52_15 = e3)
% 178.71/28.56    (7)  all_58_11 = all_52_23
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (5) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (8)  all_58_10 = e3
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #1018.
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (9)  all_58_11 = e3 | all_58_15 = e3
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (1), (2), (4), (7), (9) are inconsistent by sub-proof #1016.
% 178.71/28.56  | | 
% 178.71/28.56  | End of split
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #646 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)   ~ (all_6_2 = e0)
% 178.71/28.56    (2)  all_56_15 = all_6_2
% 178.71/28.56    (3)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56    (4)  all_58_15 = all_6_2
% 178.71/28.56    (5)  op(e0, all_6_2) = e0
% 178.71/28.56    (6)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.56    (7)  all_58_10 = all_52_15
% 178.71/28.56    (8)   ~ (all_52_23 = e1)
% 178.71/28.56    (9)   ~ (e3 = e0)
% 178.71/28.56    (10)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.56    (11)  all_56_12 = all_52_25
% 178.71/28.56    (12)   ~ (all_52_25 = e1)
% 178.71/28.56    (13)  all_58_11 = all_52_23
% 178.71/28.56    (14)  op(e3, all_52_25) = e3
% 178.71/28.56    (15)   ~ (all_52_25 = all_6_2)
% 178.71/28.56    (16)  op(e3, e0) = all_52_7
% 178.71/28.56    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.56    (18)  op(e0, e1) = e3
% 178.71/28.56    (19)   ~ (all_52_7 = all_6_2)
% 178.71/28.56    (20)   ~ (all_52_7 = e3)
% 178.71/28.56    (21)  all_58_9 = all_52_7
% 178.71/28.56    (22)   ~ (all_52_15 = e1)
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (3) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (23)  all_58_9 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | COMBINE_EQS: (21), (23) imply:
% 178.71/28.56  | |   (24)  all_52_7 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | SIMP: (24) implies:
% 178.71/28.56  | |   (25)  all_52_7 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | REDUCE: (19), (25) imply:
% 178.71/28.56  | |   (26)   ~ (all_6_2 = e1)
% 178.71/28.56  | | 
% 178.71/28.56  | | SIMP: (26) implies:
% 178.71/28.56  | |   (27)   ~ (all_6_2 = e1)
% 178.71/28.56  | | 
% 178.71/28.56  | | REDUCE: (20), (25) imply:
% 178.71/28.56  | |   (28)   ~ (e3 = e1)
% 178.71/28.56  | | 
% 178.71/28.56  | | SIMP: (28) implies:
% 178.71/28.56  | |   (29)   ~ (e3 = e1)
% 178.71/28.56  | | 
% 178.71/28.56  | | REDUCE: (16), (25) imply:
% 178.71/28.56  | |   (30)  op(e3, e0) = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | BETA: splitting (6) gives:
% 178.71/28.56  | | 
% 178.71/28.56  | | Case 1:
% 178.71/28.56  | | | 
% 178.71/28.56  | | |   (31)  all_56_15 = e2
% 178.71/28.56  | | | 
% 178.71/28.56  | | | COMBINE_EQS: (2), (31) imply:
% 178.71/28.56  | | |   (32)  all_6_2 = e2
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REDUCE: (15), (32) imply:
% 178.71/28.56  | | |   (33)   ~ (all_52_25 = e2)
% 178.71/28.56  | | | 
% 178.71/28.56  | | | BETA: splitting (10) gives:
% 178.71/28.56  | | | 
% 178.71/28.56  | | | Case 1:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | |   (34)  all_56_12 = e2
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | REF_CLOSE: (11), (33), (34) are inconsistent by sub-proof #1032.
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | Case 2:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | |   (35)  all_56_12 = e1 | all_56_12 = e0
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | BETA: splitting (35) gives:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | Case 1:
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | |   (36)  all_56_12 = e1
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | REF_CLOSE: (11), (12), (36) are inconsistent by sub-proof #1031.
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | Case 2:
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | |   (37)  all_56_12 = e0
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | COMBINE_EQS: (11), (37) imply:
% 178.71/28.56  | | | | |   (38)  all_52_25 = e0
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | SIMP: (38) implies:
% 178.71/28.56  | | | | |   (39)  all_52_25 = e0
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | REDUCE: (14), (39) imply:
% 178.71/28.56  | | | | |   (40)  op(e3, e0) = e3
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | REF_CLOSE: (17), (29), (30), (40) are inconsistent by sub-proof #648.
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | End of split
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | End of split
% 178.71/28.56  | | | 
% 178.71/28.56  | | Case 2:
% 178.71/28.56  | | | 
% 178.71/28.56  | | |   (41)  all_56_15 = e1 | all_56_15 = e0
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REF_CLOSE: (1), (2), (27), (41) are inconsistent by sub-proof #653.
% 178.71/28.56  | | | 
% 178.71/28.56  | | End of split
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (42)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (4), (5), (7), (8), (9), (13), (17), (18), (22), (42) are
% 178.71/28.56  | |            inconsistent by sub-proof #647.
% 178.71/28.56  | | 
% 178.71/28.56  | End of split
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #647 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56    (2)  all_58_15 = all_6_2
% 178.71/28.56    (3)  op(e0, all_6_2) = e0
% 178.71/28.56    (4)  all_58_10 = all_52_15
% 178.71/28.56    (5)   ~ (all_52_23 = e1)
% 178.71/28.56    (6)   ~ (e3 = e0)
% 178.71/28.56    (7)  all_58_11 = all_52_23
% 178.71/28.56    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.56    (9)  op(e0, e1) = e3
% 178.71/28.56    (10)   ~ (all_52_15 = e1)
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (1) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (11)  all_58_10 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | COMBINE_EQS: (4), (11) imply:
% 178.71/28.56  | |   (12)  all_52_15 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | SIMP: (12) implies:
% 178.71/28.56  | |   (13)  all_52_15 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | REDUCE: (10), (13) imply:
% 178.71/28.56  | |   (14)  $false
% 178.71/28.56  | | 
% 178.71/28.56  | | CLOSE: (14) is inconsistent.
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (15)  all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (15) are inconsistent by
% 178.71/28.56  | |            sub-proof #652.
% 178.71/28.56  | | 
% 178.71/28.56  | End of split
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #648 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.56    (2)  op(e3, e0) = e3
% 178.71/28.56    (3)  op(e3, e0) = e1
% 178.71/28.56    (4)   ~ (e3 = e1)
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | GROUND_INST: instantiating (1) with e1, e3, e0, e3, simplifying with (2), (3)
% 178.71/28.56  |              gives:
% 178.71/28.56  |   (5)  e3 = e1
% 178.71/28.56  | 
% 178.71/28.56  | REDUCE: (4), (5) imply:
% 178.71/28.56  |   (6)  $false
% 178.71/28.56  | 
% 178.71/28.56  | CLOSE: (6) is inconsistent.
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #649 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)  all_58_12 = all_52_25
% 178.71/28.56    (2)  all_58_12 = e0
% 178.71/28.56    (3)   ~ (all_52_25 = e0)
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | COMBINE_EQS: (1), (2) imply:
% 178.71/28.56  |   (4)  all_52_25 = e0
% 178.71/28.56  | 
% 178.71/28.56  | SIMP: (4) implies:
% 178.71/28.56  |   (5)  all_52_25 = e0
% 178.71/28.56  | 
% 178.71/28.56  | REDUCE: (3), (5) imply:
% 178.71/28.56  |   (6)  $false
% 178.71/28.56  | 
% 178.71/28.56  | CLOSE: (6) is inconsistent.
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #650 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)  all_52_27 = all_4_0
% 178.71/28.56    (2)   ~ (all_52_27 = e0)
% 178.71/28.56    (3)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.71/28.56    (4)   ~ (all_4_0 = e2)
% 178.71/28.56    (5)   ~ (all_4_0 = e1)
% 178.71/28.56    (6)  all_56_13 = all_52_27
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | COMBINE_EQS: (1), (6) imply:
% 178.71/28.56  |   (7)  all_56_13 = all_4_0
% 178.71/28.56  | 
% 178.71/28.56  | REDUCE: (1), (2) imply:
% 178.71/28.56  |   (8)   ~ (all_4_0 = e0)
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (3) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (9)  all_56_13 = e2
% 178.71/28.56  | | 
% 178.71/28.56  | | COMBINE_EQS: (7), (9) imply:
% 178.71/28.56  | |   (10)  all_4_0 = e2
% 178.71/28.56  | | 
% 178.71/28.56  | | SIMP: (10) implies:
% 178.71/28.56  | |   (11)  all_4_0 = e2
% 178.71/28.56  | | 
% 178.71/28.56  | | REDUCE: (4), (11) imply:
% 178.71/28.56  | |   (12)  $false
% 178.71/28.56  | | 
% 178.71/28.56  | | CLOSE: (12) is inconsistent.
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (13)  all_56_13 = e1 | all_56_13 = e0
% 178.71/28.56  | | 
% 178.71/28.56  | | BETA: splitting (13) gives:
% 178.71/28.56  | | 
% 178.71/28.56  | | Case 1:
% 178.71/28.56  | | | 
% 178.71/28.56  | | |   (14)  all_56_13 = e1
% 178.71/28.56  | | | 
% 178.71/28.56  | | | COMBINE_EQS: (7), (14) imply:
% 178.71/28.56  | | |   (15)  all_4_0 = e1
% 178.71/28.56  | | | 
% 178.71/28.56  | | | SIMP: (15) implies:
% 178.71/28.56  | | |   (16)  all_4_0 = e1
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REDUCE: (5), (16) imply:
% 178.71/28.56  | | |   (17)  $false
% 178.71/28.56  | | | 
% 178.71/28.56  | | | CLOSE: (17) is inconsistent.
% 178.71/28.56  | | | 
% 178.71/28.56  | | Case 2:
% 178.71/28.56  | | | 
% 178.71/28.56  | | |   (18)  all_56_13 = e0
% 178.71/28.56  | | | 
% 178.71/28.56  | | | COMBINE_EQS: (7), (18) imply:
% 178.71/28.56  | | |   (19)  all_4_0 = e0
% 178.71/28.56  | | | 
% 178.71/28.56  | | | SIMP: (19) implies:
% 178.71/28.56  | | |   (20)  all_4_0 = e0
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REDUCE: (8), (20) imply:
% 178.71/28.56  | | |   (21)  $false
% 178.71/28.56  | | | 
% 178.71/28.56  | | | CLOSE: (21) is inconsistent.
% 178.71/28.56  | | | 
% 178.71/28.56  | | End of split
% 178.71/28.56  | | 
% 178.71/28.56  | End of split
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #651 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.56    (2)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.56    (3)   ~ (all_52_3 = e1)
% 178.71/28.56    (4)   ~ (all_52_19 = all_52_23)
% 178.71/28.56    (5)  all_56_11 = all_52_23
% 178.71/28.56    (6)   ~ (all_52_27 = e3)
% 178.71/28.56    (7)   ~ (all_6_2 = e3)
% 178.71/28.56    (8)   ~ (all_6_2 = e0)
% 178.71/28.56    (9)  all_56_15 = all_6_2
% 178.71/28.56    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56    (11)  all_58_15 = all_6_2
% 178.71/28.56    (12)  op(e0, all_6_2) = e0
% 178.71/28.56    (13)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.56    (14)  all_58_7 = all_52_19
% 178.71/28.56    (15)   ~ (e3 = e1)
% 178.71/28.56    (16)  all_58_1 = all_52_3
% 178.71/28.56    (17)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.56    (18)   ~ (all_52_7 = e1)
% 178.71/28.56    (19)   ~ (all_52_23 = e1)
% 178.71/28.56    (20)   ~ (e3 = e0)
% 178.71/28.56    (21)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.56    (22)  all_56_12 = all_52_25
% 178.71/28.56    (23)  all_58_13 = all_52_27
% 178.71/28.56    (24)   ~ (all_52_3 = e3)
% 178.71/28.56    (25)  all_58_11 = all_52_23
% 178.71/28.56    (26)  op(e3, all_52_25) = e3
% 178.71/28.56    (27)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.71/28.56    (28)   ~ (all_52_25 = all_6_2)
% 178.71/28.56    (29)  op(e3, e0) = all_52_7
% 178.71/28.56    (30)   ~ (all_52_19 = e1)
% 178.71/28.56    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.56    (32)   ~ (all_52_25 = all_52_27)
% 178.71/28.56    (33)   ~ (all_52_27 = all_6_2)
% 178.71/28.56    (34)  op(e0, e1) = e3
% 178.71/28.56    (35)   ~ (all_52_7 = e3)
% 178.71/28.56    (36)   ~ (all_52_7 = all_52_23)
% 178.71/28.56    (37)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.56    (38)  all_58_9 = all_52_7
% 178.71/28.56    (39)  all_58_12 = all_52_25
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (37) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (40)  all_58_9 = e3
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (35), (38), (40) are inconsistent by sub-proof #972.
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (41)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.56  | | 
% 178.71/28.56  | | BETA: splitting (10) gives:
% 178.71/28.56  | | 
% 178.71/28.56  | | Case 1:
% 178.71/28.56  | | | 
% 178.71/28.56  | | |   (42)  all_58_9 = e1
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REF_CLOSE: (18), (38), (42) are inconsistent by sub-proof #793.
% 178.71/28.56  | | | 
% 178.71/28.56  | | Case 2:
% 178.71/28.56  | | | 
% 178.71/28.56  | | |   (43)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56  | | | 
% 178.71/28.56  | | | BETA: splitting (1) gives:
% 178.71/28.56  | | | 
% 178.71/28.56  | | | Case 1:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | |   (44)  all_58_1 = e1
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | COMBINE_EQS: (16), (44) imply:
% 178.71/28.56  | | | |   (45)  all_52_3 = e1
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | REDUCE: (3), (45) imply:
% 178.71/28.56  | | | |   (46)  $false
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | CLOSE: (46) is inconsistent.
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | Case 2:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | |   (47)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | BETA: splitting (17) gives:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | Case 1:
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | |   (48)  all_58_1 = e3
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | COMBINE_EQS: (16), (48) imply:
% 178.71/28.56  | | | | |   (49)  all_52_3 = e3
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | REDUCE: (24), (49) imply:
% 178.71/28.56  | | | | |   (50)  $false
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | CLOSE: (50) is inconsistent.
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | Case 2:
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | |   (51)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | BETA: splitting (27) gives:
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | Case 1:
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | |   (52)  all_56_11 = e3
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | COMBINE_EQS: (5), (52) imply:
% 178.71/28.56  | | | | | |   (53)  all_52_23 = e3
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | SIMP: (53) implies:
% 178.71/28.56  | | | | | |   (54)  all_52_23 = e3
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | REDUCE: (4), (54) imply:
% 178.71/28.56  | | | | | |   (55)   ~ (all_52_19 = e3)
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | BETA: splitting (51) gives:
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | Case 1:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | |   (56)  all_58_3 = e3
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | BETA: splitting (47) gives:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | Case 1:
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | |   (57)  all_58_3 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | COMBINE_EQS: (56), (57) imply:
% 178.71/28.56  | | | | | | | |   (58)  e3 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | SIMP: (58) implies:
% 178.71/28.56  | | | | | | | |   (59)  e3 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | REDUCE: (15), (59) imply:
% 178.71/28.56  | | | | | | | |   (60)  $false
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | CLOSE: (60) is inconsistent.
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | Case 2:
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | |   (61)  all_58_7 = e1 | all_58_13 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | BETA: splitting (61) gives:
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | Case 1:
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | |   (62)  all_58_7 = e1
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | COMBINE_EQS: (14), (62) imply:
% 178.71/28.56  | | | | | | | | |   (63)  all_52_19 = e1
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | SIMP: (63) implies:
% 178.71/28.56  | | | | | | | | |   (64)  all_52_19 = e1
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | REDUCE: (30), (64) imply:
% 178.71/28.56  | | | | | | | | |   (65)  $false
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | CLOSE: (65) is inconsistent.
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | Case 2:
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | |   (66)  all_58_13 = e1
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | COMBINE_EQS: (23), (66) imply:
% 178.71/28.56  | | | | | | | | |   (67)  all_52_27 = e1
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | SIMP: (67) implies:
% 178.71/28.56  | | | | | | | | |   (68)  all_52_27 = e1
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | REDUCE: (32), (68) imply:
% 178.71/28.56  | | | | | | | | |   (69)   ~ (all_52_25 = e1)
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | REDUCE: (33), (68) imply:
% 178.71/28.56  | | | | | | | | |   (70)   ~ (all_6_2 = e1)
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | SIMP: (70) implies:
% 178.71/28.56  | | | | | | | | |   (71)   ~ (all_6_2 = e1)
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | BETA: splitting (2) gives:
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | Case 1:
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | |   (72)  all_58_12 = e0
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | REF_CLOSE: (26), (29), (31), (35), (39), (72) are
% 178.71/28.56  | | | | | | | | | |            inconsistent by sub-proof #654.
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | Case 2:
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | |   (73)   ~ (all_58_12 = e0)
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | REDUCE: (39), (73) imply:
% 178.71/28.56  | | | | | | | | | |   (74)   ~ (all_52_25 = e0)
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | BETA: splitting (13) gives:
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | Case 1:
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | |   (75)  all_56_15 = e2
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | | COMBINE_EQS: (9), (75) imply:
% 178.71/28.56  | | | | | | | | | | |   (76)  all_6_2 = e2
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | | SIMP: (76) implies:
% 178.71/28.56  | | | | | | | | | | |   (77)  all_6_2 = e2
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | | REDUCE: (28), (77) imply:
% 178.71/28.56  | | | | | | | | | | |   (78)   ~ (all_52_25 = e2)
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | | REF_CLOSE: (21), (22), (69), (74), (78) are inconsistent by
% 178.71/28.56  | | | | | | | | | | |            sub-proof #1028.
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | Case 2:
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | |   (79)  all_56_15 = e1 | all_56_15 = e0
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | | REF_CLOSE: (8), (9), (71), (79) are inconsistent by sub-proof
% 178.71/28.56  | | | | | | | | | | |            #653.
% 178.71/28.56  | | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | | End of split
% 178.71/28.56  | | | | | | | | | | 
% 178.71/28.56  | | | | | | | | | End of split
% 178.71/28.56  | | | | | | | | | 
% 178.71/28.56  | | | | | | | | End of split
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | End of split
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | Case 2:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | |   (80)  all_58_7 = e3 | all_58_13 = e3
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | REF_CLOSE: (6), (14), (23), (55), (80) are inconsistent by
% 178.71/28.56  | | | | | | |            sub-proof #976.
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | End of split
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | Case 2:
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | |   (81)   ~ (all_56_11 = e3)
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | REDUCE: (5), (81) imply:
% 178.71/28.56  | | | | | |   (82)   ~ (all_52_23 = e3)
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | BETA: splitting (41) gives:
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | Case 1:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | |   (83)  all_58_10 = e3
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | BETA: splitting (43) gives:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | Case 1:
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | |   (84)  all_58_10 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | REF_CLOSE: (15), (83), (84) are inconsistent by sub-proof #937.
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | Case 2:
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | |   (85)  all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | REF_CLOSE: (11), (12), (19), (20), (25), (31), (34), (85) are
% 178.71/28.56  | | | | | | | |            inconsistent by sub-proof #652.
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | End of split
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | Case 2:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | |   (86)  all_58_11 = e3 | all_58_15 = e3
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | REF_CLOSE: (7), (11), (25), (82), (86) are inconsistent by
% 178.71/28.56  | | | | | | |            sub-proof #1016.
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | End of split
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | End of split
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | End of split
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | End of split
% 178.71/28.56  | | | 
% 178.71/28.56  | | End of split
% 178.71/28.56  | | 
% 178.71/28.56  | End of split
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #652 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)  all_58_15 = all_6_2
% 178.71/28.56    (2)  op(e0, all_6_2) = e0
% 178.71/28.56    (3)   ~ (all_52_23 = e1)
% 178.71/28.56    (4)   ~ (e3 = e0)
% 178.71/28.56    (5)  all_58_11 = e1 | all_58_15 = e1
% 178.71/28.56    (6)  all_58_11 = all_52_23
% 178.71/28.56    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.56    (8)  op(e0, e1) = e3
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (5) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (9)  all_58_11 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #974.
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (10)  all_58_15 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | COMBINE_EQS: (1), (10) imply:
% 178.71/28.56  | |   (11)  all_6_2 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | SIMP: (11) implies:
% 178.71/28.56  | |   (12)  all_6_2 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | REDUCE: (2), (12) imply:
% 178.71/28.56  | |   (13)  op(e0, e1) = e0
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (4), (7), (8), (13) are inconsistent by sub-proof #795.
% 178.71/28.56  | | 
% 178.71/28.56  | End of split
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #653 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)  all_56_15 = e1 | all_56_15 = e0
% 178.71/28.56    (2)  all_56_15 = all_6_2
% 178.71/28.56    (3)   ~ (all_6_2 = e1)
% 178.71/28.56    (4)   ~ (all_6_2 = e0)
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (1) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (5)  all_56_15 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | COMBINE_EQS: (2), (5) imply:
% 178.71/28.56  | |   (6)  all_6_2 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | SIMP: (6) implies:
% 178.71/28.56  | |   (7)  all_6_2 = e1
% 178.71/28.56  | | 
% 178.71/28.56  | | REDUCE: (3), (7) imply:
% 178.71/28.56  | |   (8)  $false
% 178.71/28.56  | | 
% 178.71/28.56  | | CLOSE: (8) is inconsistent.
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (9)  all_56_15 = e0
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #812.
% 178.71/28.56  | | 
% 178.71/28.56  | End of split
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #654 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)  all_58_12 = e0
% 178.71/28.56    (2)  op(e3, all_52_25) = e3
% 178.71/28.56    (3)  op(e3, e0) = all_52_7
% 178.71/28.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.56    (5)   ~ (all_52_7 = e3)
% 178.71/28.56    (6)  all_58_12 = all_52_25
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | COMBINE_EQS: (1), (6) imply:
% 178.71/28.56  |   (7)  all_52_25 = e0
% 178.71/28.56  | 
% 178.71/28.56  | SIMP: (7) implies:
% 178.71/28.56  |   (8)  all_52_25 = e0
% 178.71/28.56  | 
% 178.71/28.56  | REDUCE: (2), (8) imply:
% 178.71/28.56  |   (9)  op(e3, e0) = e3
% 178.71/28.56  | 
% 178.71/28.56  | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #908.
% 178.71/28.56  | 
% 178.71/28.56  End of proof
% 178.71/28.56  
% 178.71/28.56  Sub-proof #655 shows that the following formulas are inconsistent:
% 178.71/28.56  ----------------------------------------------------------------
% 178.71/28.56    (1)   ~ (all_52_25 = e3)
% 178.71/28.56    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.71/28.56    (3)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.56    (4)   ~ (all_52_19 = all_52_23)
% 178.71/28.56    (5)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.71/28.56    (6)  all_58_2 = e2
% 178.71/28.56    (7)   ~ (all_6_2 = e3)
% 178.71/28.56    (8)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.56    (9)  all_58_1 = all_52_8
% 178.71/28.56    (10)   ~ (all_4_2 = e3)
% 178.71/28.56    (11)  all_58_3 = all_10_2
% 178.71/28.56    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.56    (13)  all_58_15 = all_6_2
% 178.71/28.56    (14)  op(e0, all_6_2) = e0
% 178.71/28.56    (15)   ~ (all_52_5 = all_52_7)
% 178.71/28.56    (16)  all_58_10 = all_52_15
% 178.71/28.56    (17)   ~ (all_52_5 = all_4_2)
% 178.71/28.56    (18)  all_58_7 = all_52_19
% 178.71/28.56    (19)  op(e0, e1) = all_52_29
% 178.71/28.56    (20)   ~ (all_4_0 = e2)
% 178.71/28.56    (21)  all_58_4 = all_52_5
% 178.71/28.56    (22)   ~ (e3 = e1)
% 178.71/28.56    (23)  op(e3, all_4_2) = all_4_1
% 178.71/28.56    (24)   ~ (all_52_7 = all_4_2)
% 178.71/28.56    (25)  all_58_0 = all_4_2
% 178.71/28.56    (26)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.71/28.56    (27)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.71/28.56    (28)  all_58_14 = all_52_29
% 178.71/28.56    (29)  all_58_6 = e3
% 178.71/28.56    (30)   ~ (all_52_25 = e2)
% 178.71/28.56    (31)   ~ (all_52_15 = e2)
% 178.71/28.56    (32)  all_56_14 = all_52_29
% 178.71/28.56    (33)  op(e1, all_52_29) = e1
% 178.71/28.56    (34)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.56    (35)   ~ (all_52_23 = e3)
% 178.71/28.56    (36)   ~ (all_52_29 = e3)
% 178.71/28.56    (37)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.71/28.56    (38)   ~ (e3 = e0)
% 178.71/28.56    (39)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.56    (40)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.71/28.56    (41)   ~ (all_52_5 = all_52_8)
% 178.71/28.56    (42)   ~ (all_52_5 = all_52_29)
% 178.71/28.56    (43)  all_56_2 = all_52_5
% 178.71/28.56    (44)  op(e1, e0) = all_52_23
% 178.71/28.56    (45)  all_56_12 = all_52_25
% 178.71/28.56    (46)   ~ (all_52_8 = e3)
% 178.71/28.56    (47)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.56    (48)   ~ (e1 = e0)
% 178.71/28.56    (49)  all_56_0 = all_4_2
% 178.71/28.56    (50)  all_58_11 = all_52_23
% 178.71/28.56    (51)   ~ (all_52_7 = all_52_15)
% 178.71/28.56    (52)  op(e3, all_52_25) = e3
% 178.71/28.56    (53)   ~ (all_4_0 = e1)
% 178.71/28.56    (54)  op(e0, e2) = e3
% 178.71/28.56    (55)  op(e3, e1) = all_52_5
% 178.71/28.56    (56)   ~ (all_10_2 = e2)
% 178.71/28.56    (57)   ~ (e2 = e1)
% 178.71/28.56    (58)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.71/28.56    (59)   ~ (all_52_19 = e3)
% 178.71/28.56    (60)   ~ (all_52_25 = all_4_2)
% 178.71/28.56    (61)  op(e3, e0) = all_52_7
% 178.71/28.56    (62)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.56            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.56    (63)   ~ (all_52_7 = all_6_2)
% 178.71/28.56    (64)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.56    (65)  all_58_6 = e3 | all_58_12 = e3
% 178.71/28.56    (66)  all_58_9 = all_52_7
% 178.71/28.56    (67)   ~ (all_52_8 = all_4_2)
% 178.71/28.56    (68)   ~ (e2 = e0)
% 178.71/28.56    (69)  all_58_12 = all_52_25
% 178.71/28.56    (70)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.71/28.56    (71)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.71/28.56    (72)   ~ (e3 = e2)
% 178.71/28.56    (73)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.71/28.56    (74)  all_58_13 = e3
% 178.71/28.56  
% 178.71/28.56  Begin of proof
% 178.71/28.56  | 
% 178.71/28.56  | BETA: splitting (12) gives:
% 178.71/28.56  | 
% 178.71/28.56  | Case 1:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (75)  all_56_0 = e3
% 178.71/28.56  | | 
% 178.71/28.56  | | REF_CLOSE: (10), (49), (75) are inconsistent by sub-proof #1024.
% 178.71/28.56  | | 
% 178.71/28.56  | Case 2:
% 178.71/28.56  | | 
% 178.71/28.56  | |   (76)   ~ (all_56_0 = e3)
% 178.71/28.56  | |   (77)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.56  | | 
% 178.71/28.56  | | BETA: splitting (8) gives:
% 178.71/28.56  | | 
% 178.71/28.56  | | Case 1:
% 178.71/28.56  | | | 
% 178.71/28.56  | | |   (78)  all_58_1 = e2
% 178.71/28.56  | | | 
% 178.71/28.56  | | | COMBINE_EQS: (9), (78) imply:
% 178.71/28.56  | | |   (79)  all_52_8 = e2
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REDUCE: (41), (79) imply:
% 178.71/28.56  | | |   (80)   ~ (all_52_5 = e2)
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REDUCE: (67), (79) imply:
% 178.71/28.56  | | |   (81)   ~ (all_4_2 = e2)
% 178.71/28.56  | | | 
% 178.71/28.56  | | | SIMP: (81) implies:
% 178.71/28.56  | | |   (82)   ~ (all_4_2 = e2)
% 178.71/28.56  | | | 
% 178.71/28.56  | | | REDUCE: (46), (79) imply:
% 178.71/28.56  | | |   (83)   ~ (e3 = e2)
% 178.71/28.56  | | | 
% 178.71/28.56  | | | BETA: splitting (70) gives:
% 178.71/28.56  | | | 
% 178.71/28.56  | | | Case 1:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | |   (84)  all_58_0 = e3
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | COMBINE_EQS: (25), (84) imply:
% 178.71/28.56  | | | |   (85)  all_4_2 = e3
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | REDUCE: (10), (85) imply:
% 178.71/28.56  | | | |   (86)  $false
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | CLOSE: (86) is inconsistent.
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | Case 2:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | |   (87)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | BETA: splitting (71) gives:
% 178.71/28.56  | | | | 
% 178.71/28.56  | | | | Case 1:
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | |   (88)  all_58_4 = e3
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | COMBINE_EQS: (21), (88) imply:
% 178.71/28.56  | | | | |   (89)  all_52_5 = e3
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | REDUCE: (15), (89) imply:
% 178.71/28.56  | | | | |   (90)   ~ (all_52_7 = e3)
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | SIMP: (90) implies:
% 178.71/28.56  | | | | |   (91)   ~ (all_52_7 = e3)
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | REDUCE: (17), (89) imply:
% 178.71/28.56  | | | | |   (92)   ~ (all_4_2 = e3)
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | BETA: splitting (64) gives:
% 178.71/28.56  | | | | | 
% 178.71/28.56  | | | | | Case 1:
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | |   (93)  all_58_9 = e3
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | REF_CLOSE: (66), (91), (93) are inconsistent by sub-proof #972.
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | Case 2:
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | |   (94)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | BETA: splitting (94) gives:
% 178.71/28.56  | | | | | | 
% 178.71/28.56  | | | | | | Case 1:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | |   (95)  all_58_10 = e3
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | COMBINE_EQS: (16), (95) imply:
% 178.71/28.56  | | | | | | |   (96)  all_52_15 = e3
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | SIMP: (96) implies:
% 178.71/28.56  | | | | | | |   (97)  all_52_15 = e3
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | BETA: splitting (5) gives:
% 178.71/28.56  | | | | | | | 
% 178.71/28.56  | | | | | | | Case 1:
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | |   (98)  all_58_0 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | COMBINE_EQS: (25), (98) imply:
% 178.71/28.56  | | | | | | | |   (99)  all_4_2 = e1
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | REDUCE: (60), (99) imply:
% 178.71/28.56  | | | | | | | |   (100)   ~ (all_52_25 = e1)
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | | REF_CLOSE: (30), (39), (45), (52), (61), (62), (91), (100) are
% 178.71/28.56  | | | | | | | |            inconsistent by sub-proof #663.
% 178.71/28.56  | | | | | | | | 
% 178.71/28.56  | | | | | | | Case 2:
% 178.71/28.56  | | | | | | | | 
% 178.71/28.57  | | | | | | | |   (101)   ~ (all_58_0 = e1)
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | REDUCE: (25), (101) imply:
% 178.71/28.57  | | | | | | | |   (102)   ~ (all_4_2 = e1)
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | BETA: splitting (47) gives:
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | |   (103)  all_58_0 = e1
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | COMBINE_EQS: (25), (103) imply:
% 178.71/28.57  | | | | | | | | |   (104)  all_4_2 = e1
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | REDUCE: (102), (104) imply:
% 178.71/28.57  | | | | | | | | |   (105)  $false
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | CLOSE: (105) is inconsistent.
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | |   (106)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | REF_CLOSE: (3), (6), (10), (22), (24), (25), (26), (28), (29),
% 178.71/28.57  | | | | | | | | |            (33), (38), (40), (44), (48), (49), (50), (57),
% 178.71/28.57  | | | | | | | | |            (62), (66), (74), (77), (82), (95), (102), (106)
% 178.71/28.57  | | | | | | | | |            are inconsistent by sub-proof #656.
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | End of split
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | End of split
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | Case 2:
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | |   (107)  all_58_11 = e3 | all_58_15 = e3
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | REF_CLOSE: (7), (13), (35), (50), (107) are inconsistent by
% 178.71/28.57  | | | | | | |            sub-proof #1016.
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | End of split
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | End of split
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | Case 2:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (108)   ~ (all_58_4 = e3)
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REDUCE: (21), (108) imply:
% 178.71/28.57  | | | | |   (109)   ~ (all_52_5 = e3)
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | BETA: splitting (87) gives:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | Case 1:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | |   (110)  all_58_1 = e3
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | COMBINE_EQS: (78), (110) imply:
% 178.71/28.57  | | | | | |   (111)  e3 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | SIMP: (111) implies:
% 178.71/28.57  | | | | | |   (112)  e3 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | REDUCE: (72), (112) imply:
% 178.71/28.57  | | | | | |   (113)  $false
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | CLOSE: (113) is inconsistent.
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | Case 2:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | |   (114)  all_58_4 = e3 | all_58_9 = e3
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | BETA: splitting (114) gives:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | Case 1:
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | |   (115)  all_58_4 = e3
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | COMBINE_EQS: (21), (115) imply:
% 178.71/28.57  | | | | | | |   (116)  all_52_5 = e3
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | REDUCE: (109), (116) imply:
% 178.71/28.57  | | | | | | |   (117)  $false
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | CLOSE: (117) is inconsistent.
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | Case 2:
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | |   (118)  all_58_9 = e3
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | COMBINE_EQS: (66), (118) imply:
% 178.71/28.57  | | | | | | |   (119)  all_52_7 = e3
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | BETA: splitting (73) gives:
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | |   (120)  all_56_2 = e3
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | REF_CLOSE: (43), (109), (120) are inconsistent by sub-proof
% 178.71/28.57  | | | | | | | |            #931.
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | |   (121)   ~ (all_56_2 = e3)
% 178.71/28.57  | | | | | | | |   (122)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | BETA: splitting (47) gives:
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | |   (123)  all_58_0 = e1
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | COMBINE_EQS: (25), (123) imply:
% 178.71/28.57  | | | | | | | | |   (124)  all_4_2 = e1
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | REDUCE: (34), (124) imply:
% 178.71/28.57  | | | | | | | | |   (125)  op(all_4_1, e1) = all_4_0
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | REDUCE: (23), (124) imply:
% 178.71/28.57  | | | | | | | | |   (126)  op(e3, e1) = all_4_1
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | BETA: splitting (2) gives:
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | |   (127)  all_58_0 = e0
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | COMBINE_EQS: (123), (127) imply:
% 178.71/28.57  | | | | | | | | | |   (128)  e1 = e0
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | REDUCE: (48), (128) imply:
% 178.71/28.57  | | | | | | | | | |   (129)  $false
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | CLOSE: (129) is inconsistent.
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | |   (130)   ~ (all_58_0 = e0)
% 178.71/28.57  | | | | | | | | | |   (131)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | BETA: splitting (131) gives:
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | |   (132)  all_58_1 = e0
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | COMBINE_EQS: (78), (132) imply:
% 178.71/28.57  | | | | | | | | | | |   (133)  e2 = e0
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | REDUCE: (68), (133) imply:
% 178.71/28.57  | | | | | | | | | | |   (134)  $false
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | |   (135)  all_58_4 = e0 | all_58_9 = e0
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | BETA: splitting (122) gives:
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | |   (136)  all_56_2 = e2
% 178.71/28.57  | | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | | REF_CLOSE: (43), (80), (136) are inconsistent by sub-proof
% 178.71/28.57  | | | | | | | | | | | |            #827.
% 178.71/28.57  | | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | |   (137)  all_56_2 = e1 | all_56_2 = e0
% 178.71/28.57  | | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | | REF_CLOSE: (19), (20), (21), (27), (32), (36), (38), (42),
% 178.71/28.57  | | | | | | | | | | | |            (43), (48), (53), (55), (62), (118), (125), (126),
% 178.71/28.57  | | | | | | | | | | | |            (135), (137) are inconsistent by sub-proof #924.
% 178.71/28.57  | | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | End of split
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | End of split
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | End of split
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | |   (138)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | BETA: splitting (138) gives:
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | |   (139)  all_58_2 = e1
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | COMBINE_EQS: (6), (139) imply:
% 178.71/28.57  | | | | | | | | | |   (140)  e2 = e1
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | REDUCE: (57), (140) imply:
% 178.71/28.57  | | | | | | | | | |   (141)  $false
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | CLOSE: (141) is inconsistent.
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | |   (142)  all_58_6 = e1 | all_58_12 = e1
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | BETA: splitting (142) gives:
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | |   (143)  all_58_6 = e1
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | REF_CLOSE: (1), (22), (65), (69), (143) are inconsistent by
% 178.71/28.57  | | | | | | | | | | |            sub-proof #1002.
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | |   (144)  all_58_12 = e1
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | COMBINE_EQS: (69), (144) imply:
% 178.71/28.57  | | | | | | | | | | |   (145)  all_52_25 = e1
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | REDUCE: (52), (145) imply:
% 178.71/28.57  | | | | | | | | | | |   (146)  op(e3, e1) = e3
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | | REF_CLOSE: (55), (62), (109), (146) are inconsistent by
% 178.71/28.57  | | | | | | | | | | |            sub-proof #1023.
% 178.71/28.57  | | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | | End of split
% 178.71/28.57  | | | | | | | | | | 
% 178.71/28.57  | | | | | | | | | End of split
% 178.71/28.57  | | | | | | | | | 
% 178.71/28.57  | | | | | | | | End of split
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | End of split
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | End of split
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | End of split
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | End of split
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | End of split
% 178.71/28.57  | | | 
% 178.71/28.57  | | Case 2:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (147)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REF_CLOSE: (3), (4), (11), (13), (14), (16), (18), (28), (30), (31), (36),
% 178.71/28.57  | | |            (37), (38), (50), (52), (54), (56), (58), (59), (61), (62),
% 178.71/28.57  | | |            (63), (66), (68), (69), (72), (74), (147) are inconsistent by
% 178.71/28.57  | | |            sub-proof #657.
% 178.71/28.57  | | | 
% 178.71/28.57  | | End of split
% 178.71/28.57  | | 
% 178.71/28.57  | End of split
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #656 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.57    (2)   ~ (all_4_2 = e2)
% 178.71/28.57    (3)  all_58_2 = e2
% 178.71/28.57    (4)   ~ (all_4_2 = e3)
% 178.71/28.57    (5)   ~ (e3 = e1)
% 178.71/28.57    (6)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.57    (7)   ~ (all_52_7 = all_4_2)
% 178.71/28.57    (8)  all_58_0 = all_4_2
% 178.71/28.57    (9)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.71/28.57    (10)  all_58_14 = all_52_29
% 178.71/28.57    (11)  all_58_6 = e3
% 178.71/28.57    (12)  op(e1, all_52_29) = e1
% 178.71/28.57    (13)   ~ (e3 = e0)
% 178.71/28.57    (14)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.71/28.57    (15)  op(e1, e0) = all_52_23
% 178.71/28.57    (16)  all_58_10 = e3
% 178.71/28.57    (17)   ~ (e1 = e0)
% 178.71/28.57    (18)  all_56_0 = all_4_2
% 178.71/28.57    (19)  all_58_11 = all_52_23
% 178.71/28.57    (20)   ~ (e2 = e1)
% 178.71/28.57    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.57    (22)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.57    (23)   ~ (all_4_2 = e1)
% 178.71/28.57    (24)  all_58_9 = all_52_7
% 178.71/28.57    (25)  all_58_13 = e3
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | BETA: splitting (6) gives:
% 178.71/28.57  | 
% 178.71/28.57  | Case 1:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (26)  all_58_2 = e1
% 178.71/28.57  | | 
% 178.71/28.57  | | COMBINE_EQS: (3), (26) imply:
% 178.71/28.57  | |   (27)  e2 = e1
% 178.71/28.57  | | 
% 178.71/28.57  | | REDUCE: (20), (27) imply:
% 178.71/28.57  | |   (28)  $false
% 178.71/28.57  | | 
% 178.71/28.57  | | CLOSE: (28) is inconsistent.
% 178.71/28.57  | | 
% 178.71/28.57  | Case 2:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (29)  all_58_6 = e1 | all_58_12 = e1
% 178.71/28.57  | | 
% 178.71/28.57  | | BETA: splitting (1) gives:
% 178.71/28.57  | | 
% 178.71/28.57  | | Case 1:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (30)  all_58_12 = e0
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REF_CLOSE: (5), (11), (17), (29), (30) are inconsistent by sub-proof #726.
% 178.71/28.57  | | | 
% 178.71/28.57  | | Case 2:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (31)  all_58_13 = e0 | all_58_14 = e0
% 178.71/28.57  | | | 
% 178.71/28.57  | | | BETA: splitting (31) gives:
% 178.71/28.57  | | | 
% 178.71/28.57  | | | Case 1:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | |   (32)  all_58_13 = e0
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | COMBINE_EQS: (25), (32) imply:
% 178.71/28.57  | | | |   (33)  e3 = e0
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | REDUCE: (13), (33) imply:
% 178.71/28.57  | | | |   (34)  $false
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | CLOSE: (34) is inconsistent.
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | Case 2:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | |   (35)  all_58_14 = e0
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | COMBINE_EQS: (10), (35) imply:
% 178.71/28.57  | | | |   (36)  all_52_29 = e0
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | SIMP: (36) implies:
% 178.71/28.57  | | | |   (37)  all_52_29 = e0
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | REDUCE: (12), (37) imply:
% 178.71/28.57  | | | |   (38)  op(e1, e0) = e1
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | BETA: splitting (14) gives:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | Case 1:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (39)  all_58_0 = e0
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | COMBINE_EQS: (8), (39) imply:
% 178.71/28.57  | | | | |   (40)  all_4_2 = e0
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REDUCE: (7), (40) imply:
% 178.71/28.57  | | | | |   (41)   ~ (all_52_7 = e0)
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REDUCE: (4), (40) imply:
% 178.71/28.57  | | | | |   (42)   ~ (e3 = e0)
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REDUCE: (23), (40) imply:
% 178.71/28.57  | | | | |   (43)   ~ (e1 = e0)
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REF_CLOSE: (9), (13), (15), (16), (17), (19), (21), (24), (38), (41)
% 178.71/28.57  | | | | |            are inconsistent by sub-proof #823.
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | Case 2:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (44)   ~ (all_58_0 = e0)
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REDUCE: (8), (44) imply:
% 178.71/28.57  | | | | |   (45)   ~ (all_4_2 = e0)
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REF_CLOSE: (2), (18), (22), (23), (45) are inconsistent by sub-proof
% 178.71/28.57  | | | | |            #882.
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | End of split
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | End of split
% 178.71/28.57  | | | 
% 178.71/28.57  | | End of split
% 178.71/28.57  | | 
% 178.71/28.57  | End of split
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #657 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.57    (2)   ~ (all_52_19 = all_52_23)
% 178.71/28.57    (3)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.57    (4)  all_58_3 = all_10_2
% 178.71/28.57    (5)  all_58_15 = all_6_2
% 178.71/28.57    (6)  op(e0, all_6_2) = e0
% 178.71/28.57    (7)  all_58_10 = all_52_15
% 178.71/28.57    (8)  all_58_7 = all_52_19
% 178.71/28.57    (9)  all_58_14 = all_52_29
% 178.71/28.57    (10)   ~ (all_52_25 = e2)
% 178.71/28.57    (11)   ~ (all_52_15 = e2)
% 178.71/28.57    (12)   ~ (all_52_29 = e3)
% 178.71/28.57    (13)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.71/28.57    (14)   ~ (e3 = e0)
% 178.71/28.57    (15)  all_58_11 = all_52_23
% 178.71/28.57    (16)  op(e3, all_52_25) = e3
% 178.71/28.57    (17)  op(e0, e2) = e3
% 178.71/28.57    (18)   ~ (all_10_2 = e2)
% 178.71/28.57    (19)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.71/28.57    (20)   ~ (all_52_19 = e3)
% 178.71/28.57    (21)  op(e3, e0) = all_52_7
% 178.71/28.57    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.57    (23)   ~ (all_52_7 = all_6_2)
% 178.71/28.57    (24)  all_58_9 = all_52_7
% 178.71/28.57    (25)   ~ (e2 = e0)
% 178.71/28.57    (26)  all_58_12 = all_52_25
% 178.71/28.57    (27)   ~ (e3 = e2)
% 178.71/28.57    (28)  all_58_13 = e3
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | BETA: splitting (3) gives:
% 178.71/28.57  | 
% 178.71/28.57  | Case 1:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (29)  all_58_3 = e2
% 178.71/28.57  | | 
% 178.71/28.57  | | COMBINE_EQS: (4), (29) imply:
% 178.71/28.57  | |   (30)  all_10_2 = e2
% 178.71/28.57  | | 
% 178.71/28.57  | | REDUCE: (18), (30) imply:
% 178.71/28.57  | |   (31)  $false
% 178.71/28.57  | | 
% 178.71/28.57  | | CLOSE: (31) is inconsistent.
% 178.71/28.57  | | 
% 178.71/28.57  | Case 2:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (32)  all_58_7 = e2 | all_58_13 = e2
% 178.71/28.57  | | 
% 178.71/28.57  | | BETA: splitting (32) gives:
% 178.71/28.57  | | 
% 178.71/28.57  | | Case 1:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (33)  all_58_7 = e2
% 178.71/28.57  | | | 
% 178.71/28.57  | | | COMBINE_EQS: (8), (33) imply:
% 178.71/28.57  | | |   (34)  all_52_19 = e2
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REDUCE: (2), (34) imply:
% 178.71/28.57  | | |   (35)   ~ (all_52_23 = e2)
% 178.71/28.57  | | | 
% 178.71/28.57  | | | SIMP: (35) implies:
% 178.71/28.57  | | |   (36)   ~ (all_52_23 = e2)
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REDUCE: (20), (34) imply:
% 178.71/28.57  | | |   (37)   ~ (e3 = e2)
% 178.71/28.57  | | | 
% 178.71/28.57  | | | BETA: splitting (13) gives:
% 178.71/28.57  | | | 
% 178.71/28.57  | | | Case 1:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | |   (38)  all_58_9 = e2
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | COMBINE_EQS: (24), (38) imply:
% 178.71/28.57  | | | |   (39)  all_52_7 = e2
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | SIMP: (39) implies:
% 178.71/28.57  | | | |   (40)  all_52_7 = e2
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | REDUCE: (23), (40) imply:
% 178.71/28.57  | | | |   (41)   ~ (all_6_2 = e2)
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | SIMP: (41) implies:
% 178.71/28.57  | | | |   (42)   ~ (all_6_2 = e2)
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | REDUCE: (21), (40) imply:
% 178.71/28.57  | | | |   (43)  op(e3, e0) = e2
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | BETA: splitting (19) gives:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | Case 1:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (44)  all_58_12 = e2
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REF_CLOSE: (10), (26), (44) are inconsistent by sub-proof #660.
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | Case 2:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (45)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | BETA: splitting (45) gives:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | Case 1:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | |   (46)  all_58_13 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | REF_CLOSE: (27), (28), (46) are inconsistent by sub-proof #906.
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | Case 2:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | |   (47)  all_58_14 = e2 | all_58_15 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | BETA: splitting (47) gives:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | Case 1:
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | |   (48)  all_58_14 = e2
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | COMBINE_EQS: (9), (48) imply:
% 178.71/28.57  | | | | | | |   (49)  all_52_29 = e2
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | SIMP: (49) implies:
% 178.71/28.57  | | | | | | |   (50)  all_52_29 = e2
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | BETA: splitting (1) gives:
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | Case 1:
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | |   (51)  all_58_12 = e0
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | COMBINE_EQS: (26), (51) imply:
% 178.71/28.57  | | | | | | | |   (52)  all_52_25 = e0
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | SIMP: (52) implies:
% 178.71/28.57  | | | | | | | |   (53)  all_52_25 = e0
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | REDUCE: (16), (53) imply:
% 178.71/28.57  | | | | | | | |   (54)  op(e3, e0) = e3
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | GROUND_INST: instantiating (22) with e2, e3, e0, e3, simplifying
% 178.71/28.57  | | | | | | | |              with (43), (54) gives:
% 178.71/28.57  | | | | | | | |   (55)  e3 = e2
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | REDUCE: (27), (55) imply:
% 178.71/28.57  | | | | | | | |   (56)  $false
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | CLOSE: (56) is inconsistent.
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | Case 2:
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | |   (57)  all_58_13 = e0 | all_58_14 = e0
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | | REF_CLOSE: (14), (25), (28), (48), (57) are inconsistent by
% 178.71/28.57  | | | | | | | |            sub-proof #658.
% 178.71/28.57  | | | | | | | | 
% 178.71/28.57  | | | | | | | End of split
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | Case 2:
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | |   (58)  all_58_15 = e2
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | COMBINE_EQS: (5), (58) imply:
% 178.71/28.57  | | | | | | |   (59)  all_6_2 = e2
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | SIMP: (59) implies:
% 178.71/28.57  | | | | | | |   (60)  all_6_2 = e2
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | REDUCE: (42), (60) imply:
% 178.71/28.57  | | | | | | |   (61)  $false
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | | CLOSE: (61) is inconsistent.
% 178.71/28.57  | | | | | | | 
% 178.71/28.57  | | | | | | End of split
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | End of split
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | End of split
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | Case 2:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | |   (62)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | BETA: splitting (62) gives:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | Case 1:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (63)  all_58_10 = e2
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REF_CLOSE: (7), (11), (63) are inconsistent by sub-proof #711.
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | Case 2:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (64)  all_58_11 = e2 | all_58_15 = e2
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | BETA: splitting (64) gives:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | Case 1:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | |   (65)  all_58_11 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | REF_CLOSE: (15), (36), (65) are inconsistent by sub-proof #935.
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | Case 2:
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | |   (66)  all_58_15 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | COMBINE_EQS: (5), (66) imply:
% 178.71/28.57  | | | | | |   (67)  all_6_2 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | SIMP: (67) implies:
% 178.71/28.57  | | | | | |   (68)  all_6_2 = e2
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | REDUCE: (6), (68) imply:
% 178.71/28.57  | | | | | |   (69)  op(e0, e2) = e0
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | GROUND_INST: instantiating (22) with e3, e0, e2, e0, simplifying
% 178.71/28.57  | | | | | |              with (17), (69) gives:
% 178.71/28.57  | | | | | |   (70)  e3 = e0
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | REDUCE: (14), (70) imply:
% 178.71/28.57  | | | | | |   (71)  $false
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | | CLOSE: (71) is inconsistent.
% 178.71/28.57  | | | | | | 
% 178.71/28.57  | | | | | End of split
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | End of split
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | End of split
% 178.71/28.57  | | | 
% 178.71/28.57  | | Case 2:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (72)  all_58_13 = e2
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REF_CLOSE: (27), (28), (72) are inconsistent by sub-proof #906.
% 178.71/28.57  | | | 
% 178.71/28.57  | | End of split
% 178.71/28.57  | | 
% 178.71/28.57  | End of split
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #658 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_58_13 = e0 | all_58_14 = e0
% 178.71/28.57    (2)   ~ (e3 = e0)
% 178.71/28.57    (3)  all_58_14 = e2
% 178.71/28.57    (4)   ~ (e2 = e0)
% 178.71/28.57    (5)  all_58_13 = e3
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | BETA: splitting (1) gives:
% 178.71/28.57  | 
% 178.71/28.57  | Case 1:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (6)  all_58_13 = e0
% 178.71/28.57  | | 
% 178.71/28.57  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #659.
% 178.71/28.57  | | 
% 178.71/28.57  | Case 2:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (7)  all_58_14 = e0
% 178.71/28.57  | | 
% 178.71/28.57  | | COMBINE_EQS: (3), (7) imply:
% 178.71/28.57  | |   (8)  e2 = e0
% 178.71/28.57  | | 
% 178.71/28.57  | | SIMP: (8) implies:
% 178.71/28.57  | |   (9)  e2 = e0
% 178.71/28.57  | | 
% 178.71/28.57  | | REDUCE: (4), (9) imply:
% 178.71/28.57  | |   (10)  $false
% 178.71/28.57  | | 
% 178.71/28.57  | | CLOSE: (10) is inconsistent.
% 178.71/28.57  | | 
% 178.71/28.57  | End of split
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #659 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_58_13 = e3
% 178.71/28.57    (2)  all_58_13 = e0
% 178.71/28.57    (3)   ~ (e3 = e0)
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | COMBINE_EQS: (1), (2) imply:
% 178.71/28.57  |   (4)  e3 = e0
% 178.71/28.57  | 
% 178.71/28.57  | SIMP: (4) implies:
% 178.71/28.57  |   (5)  e3 = e0
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (3), (5) imply:
% 178.71/28.57  |   (6)  $false
% 178.71/28.57  | 
% 178.71/28.57  | CLOSE: (6) is inconsistent.
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #660 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_58_12 = all_52_25
% 178.71/28.57    (2)  all_58_12 = e2
% 178.71/28.57    (3)   ~ (all_52_25 = e2)
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | COMBINE_EQS: (1), (2) imply:
% 178.71/28.57  |   (4)  all_52_25 = e2
% 178.71/28.57  | 
% 178.71/28.57  | SIMP: (4) implies:
% 178.71/28.57  |   (5)  all_52_25 = e2
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (3), (5) imply:
% 178.71/28.57  |   (6)  $false
% 178.71/28.57  | 
% 178.71/28.57  | CLOSE: (6) is inconsistent.
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #661 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.71/28.57    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.57    (3)  all_58_15 = all_6_2
% 178.71/28.57    (4)  op(e0, all_6_2) = e0
% 178.71/28.57    (5)  all_58_10 = all_52_15
% 178.71/28.57    (6)  all_58_7 = all_52_19
% 178.71/28.57    (7)   ~ (all_52_15 = e2)
% 178.71/28.57    (8)  all_58_8 = all_14_2
% 178.71/28.57    (9)   ~ (all_52_13 = all_14_2)
% 178.71/28.57    (10)   ~ (e3 = e0)
% 178.71/28.57    (11)  op(e0, e2) = e3
% 178.71/28.57    (12)   ~ (all_52_19 = e3)
% 178.71/28.57    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.57            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.57    (14)   ~ (all_52_13 = e2)
% 178.71/28.57    (15)  all_52_13 = e3
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | SIMP: (15) implies:
% 178.71/28.57  |   (16)  all_52_13 = e3
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (9), (16) imply:
% 178.71/28.57  |   (17)   ~ (all_14_2 = e3)
% 178.71/28.57  | 
% 178.71/28.57  | SIMP: (17) implies:
% 178.71/28.57  |   (18)   ~ (all_14_2 = e3)
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (14), (16) imply:
% 178.71/28.57  |   (19)   ~ (e3 = e2)
% 178.71/28.57  | 
% 178.71/28.57  | BETA: splitting (2) gives:
% 178.71/28.57  | 
% 178.71/28.57  | Case 1:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (20)  all_58_7 = e3
% 178.71/28.57  | | 
% 178.71/28.57  | | COMBINE_EQS: (6), (20) imply:
% 178.71/28.57  | |   (21)  all_52_19 = e3
% 178.71/28.57  | | 
% 178.71/28.57  | | REDUCE: (12), (21) imply:
% 178.71/28.57  | |   (22)  $false
% 178.71/28.57  | | 
% 178.71/28.57  | | CLOSE: (22) is inconsistent.
% 178.71/28.57  | | 
% 178.71/28.57  | Case 2:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (23)  all_58_8 = e3 | all_58_11 = e3
% 178.71/28.57  | | 
% 178.71/28.57  | | BETA: splitting (23) gives:
% 178.71/28.57  | | 
% 178.71/28.57  | | Case 1:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (24)  all_58_8 = e3
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REF_CLOSE: (8), (18), (24) are inconsistent by sub-proof #901.
% 178.71/28.57  | | | 
% 178.71/28.57  | | Case 2:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (25)  all_58_11 = e3
% 178.71/28.57  | | | 
% 178.71/28.57  | | | BETA: splitting (1) gives:
% 178.71/28.57  | | | 
% 178.71/28.57  | | | Case 1:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | |   (26)  all_58_10 = e2
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | REF_CLOSE: (5), (7), (26) are inconsistent by sub-proof #711.
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | Case 2:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | |   (27)  all_58_11 = e2 | all_58_15 = e2
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | BETA: splitting (27) gives:
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | | Case 1:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (28)  all_58_11 = e2
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REF_CLOSE: (19), (25), (28) are inconsistent by sub-proof #992.
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | Case 2:
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | |   (29)  all_58_15 = e2
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | COMBINE_EQS: (3), (29) imply:
% 178.71/28.57  | | | | |   (30)  all_6_2 = e2
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | | REF_CLOSE: (4), (10), (11), (13), (30) are inconsistent by sub-proof
% 178.71/28.57  | | | | |            #662.
% 178.71/28.57  | | | | | 
% 178.71/28.57  | | | | End of split
% 178.71/28.57  | | | | 
% 178.71/28.57  | | | End of split
% 178.71/28.57  | | | 
% 178.71/28.57  | | End of split
% 178.71/28.57  | | 
% 178.71/28.57  | End of split
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #662 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  op(e0, all_6_2) = e0
% 178.71/28.57    (2)   ~ (e3 = e0)
% 178.71/28.57    (3)  op(e0, e2) = e3
% 178.71/28.57    (4)  all_6_2 = e2
% 178.71/28.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (1), (4) imply:
% 178.71/28.57  |   (6)  op(e0, e2) = e0
% 178.71/28.57  | 
% 178.71/28.57  | GROUND_INST: instantiating (5) with e3, e0, e2, e0, simplifying with (3), (6)
% 178.71/28.57  |              gives:
% 178.71/28.57  |   (7)  e3 = e0
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (2), (7) imply:
% 178.71/28.57  |   (8)  $false
% 178.71/28.57  | 
% 178.71/28.57  | CLOSE: (8) is inconsistent.
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #663 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)   ~ (all_52_25 = e2)
% 178.71/28.57    (2)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.57    (3)  all_56_12 = all_52_25
% 178.71/28.57    (4)   ~ (all_52_25 = e1)
% 178.71/28.57    (5)  op(e3, all_52_25) = e3
% 178.71/28.57    (6)  op(e3, e0) = all_52_7
% 178.71/28.57    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.57    (8)   ~ (all_52_7 = e3)
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | BETA: splitting (2) gives:
% 178.71/28.57  | 
% 178.71/28.57  | Case 1:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (9)  all_56_12 = e2
% 178.71/28.57  | | 
% 178.71/28.57  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1032.
% 178.71/28.57  | | 
% 178.71/28.57  | Case 2:
% 178.71/28.57  | | 
% 178.71/28.57  | |   (10)  all_56_12 = e1 | all_56_12 = e0
% 178.71/28.57  | | 
% 178.71/28.57  | | BETA: splitting (10) gives:
% 178.71/28.57  | | 
% 178.71/28.57  | | Case 1:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (11)  all_56_12 = e1
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #1031.
% 178.71/28.57  | | | 
% 178.71/28.57  | | Case 2:
% 178.71/28.57  | | | 
% 178.71/28.57  | | |   (12)  all_56_12 = e0
% 178.71/28.57  | | | 
% 178.71/28.57  | | | COMBINE_EQS: (3), (12) imply:
% 178.71/28.57  | | |   (13)  all_52_25 = e0
% 178.71/28.57  | | | 
% 178.71/28.57  | | | SIMP: (13) implies:
% 178.71/28.57  | | |   (14)  all_52_25 = e0
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REDUCE: (5), (14) imply:
% 178.71/28.57  | | |   (15)  op(e3, e0) = e3
% 178.71/28.57  | | | 
% 178.71/28.57  | | | REF_CLOSE: (6), (7), (8), (15) are inconsistent by sub-proof #908.
% 178.71/28.57  | | | 
% 178.71/28.57  | | End of split
% 178.71/28.57  | | 
% 178.71/28.57  | End of split
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #664 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_58_9 = all_52_7
% 178.71/28.57    (2)  all_58_9 = e2
% 178.71/28.57    (3)   ~ (all_52_7 = e2)
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | COMBINE_EQS: (1), (2) imply:
% 178.71/28.57  |   (4)  all_52_7 = e2
% 178.71/28.57  | 
% 178.71/28.57  | SIMP: (4) implies:
% 178.71/28.57  |   (5)  all_52_7 = e2
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (3), (5) imply:
% 178.71/28.57  |   (6)  $false
% 178.71/28.57  | 
% 178.71/28.57  | CLOSE: (6) is inconsistent.
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #665 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)  all_6_2 = e3
% 178.71/28.57    (2)  op(e0, all_6_2) = e0
% 178.71/28.57    (3)  op(e0, e3) = all_52_25
% 178.71/28.57    (4)  op(e3, all_52_25) = e3
% 178.71/28.57    (5)  op(e3, e0) = all_52_7
% 178.71/28.57    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.57    (7)   ~ (all_52_7 = all_6_2)
% 178.71/28.57  
% 178.71/28.57  Begin of proof
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (1), (7) imply:
% 178.71/28.57  |   (8)   ~ (all_52_7 = e3)
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (1), (2) imply:
% 178.71/28.57  |   (9)  op(e0, e3) = e0
% 178.71/28.57  | 
% 178.71/28.57  | GROUND_INST: instantiating (6) with all_52_25, e0, e3, e0, simplifying with
% 178.71/28.57  |              (3), (9) gives:
% 178.71/28.57  |   (10)  all_52_25 = e0
% 178.71/28.57  | 
% 178.71/28.57  | REDUCE: (4), (10) imply:
% 178.71/28.57  |   (11)  op(e3, e0) = e3
% 178.71/28.57  | 
% 178.71/28.57  | REF_CLOSE: (5), (6), (8), (11) are inconsistent by sub-proof #908.
% 178.71/28.57  | 
% 178.71/28.57  End of proof
% 178.71/28.57  
% 178.71/28.57  Sub-proof #666 shows that the following formulas are inconsistent:
% 178.71/28.57  ----------------------------------------------------------------
% 178.71/28.57    (1)   ~ (all_52_23 = all_14_2)
% 178.71/28.57    (2)   ~ (all_52_5 = all_52_13)
% 178.71/28.57    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.71/28.57    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.57    (5)   ~ (all_52_27 = all_10_2)
% 178.71/28.57    (6)   ~ (all_52_17 = all_52_23)
% 178.71/28.57    (7)  op(e2, all_10_2) = all_10_1
% 178.71/28.57    (8)   ~ (all_52_13 = all_52_29)
% 178.71/28.57    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.57    (10)  all_52_16 = e3
% 178.71/28.57    (11)  op(e3, e2) = all_52_3
% 178.71/28.57    (12)   ~ (all_52_9 = all_52_25)
% 178.71/28.57    (13)  op(e3, all_52_25) = all_52_24
% 178.71/28.57    (14)   ~ (all_52_19 = all_52_23)
% 178.71/28.57    (15)  op(e1, e2) = all_52_19
% 178.71/28.57    (16)  op(e3, all_52_9) = all_52_8
% 178.71/28.57    (17)   ~ (all_52_3 = all_10_2)
% 178.71/28.57    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.57    (19)  all_58_5 = all_52_13
% 178.71/28.57    (20)   ~ (all_6_2 = e0)
% 178.71/28.57    (21)   ~ (all_52_25 = all_52_29)
% 178.71/28.57    (22)  all_56_15 = all_6_2
% 178.71/28.57    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.71/28.57    (24)  op(e2, e0) = all_52_15
% 178.71/28.57    (25)  op(all_14_1, all_14_2) = all_14_0
% 178.71/28.57    (26)  all_58_3 = all_10_2
% 178.71/28.57    (27)  all_56_9 = all_52_19
% 178.71/28.58    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.58    (29)  all_58_15 = all_6_2
% 178.71/28.58    (30)   ~ (all_52_9 = all_4_2)
% 178.71/28.58    (31)   ~ (all_52_5 = all_52_7)
% 178.71/28.58    (32)  all_58_10 = all_52_15
% 178.71/28.58    (33)   ~ (all_52_5 = all_4_2)
% 178.71/28.58    (34)  all_58_7 = all_52_19
% 178.71/28.58    (35)   ~ (all_52_17 = all_52_25)
% 178.71/28.58    (36)   ~ (all_4_0 = e2)
% 178.71/28.58    (37)  all_58_4 = all_52_5
% 178.71/28.58    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.58    (39)  all_52_18 = e2
% 178.71/28.58    (40)   ~ (all_52_27 = all_52_29)
% 178.71/28.58    (41)   ~ (all_52_17 = all_14_2)
% 178.71/28.58    (42)  op(e3, all_4_2) = all_4_1
% 178.71/28.58    (43)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.58    (44)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.71/28.58    (45)   ~ (all_52_7 = all_4_2)
% 178.71/28.58    (46)  all_58_1 = all_52_3
% 178.71/28.58    (47)  all_58_0 = all_4_2
% 178.71/28.58    (48)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.71/28.58    (49)  op(e1, all_52_29) = all_52_28
% 178.71/28.58    (50)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.71/28.58    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.71/28.58    (52)   ~ (all_4_1 = e2)
% 178.71/28.58    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.71/28.58    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.58    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.71/28.58    (56)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.71/28.58    (57)  all_58_14 = all_52_29
% 178.71/28.58    (58)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.71/28.58    (59)   ~ (all_52_3 = all_52_5)
% 178.71/28.58    (60)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.58    (61)  op(e2, e1) = all_52_13
% 178.71/28.58    (62)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.71/28.58    (63)  all_58_8 = all_14_2
% 178.71/28.58    (64)  all_56_1 = all_52_3
% 178.71/28.58    (65)  op(e0, e2) = all_52_27
% 178.71/28.58    (66)   ~ (all_14_0 = e3)
% 178.71/28.58    (67)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.71/28.58    (68)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.58    (69)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.71/28.58    (70)   ~ (all_52_5 = all_14_2)
% 178.71/28.58    (71)   ~ (all_52_3 = all_52_27)
% 178.71/28.58    (72)   ~ (all_52_3 = all_4_2)
% 178.71/28.58    (73)  op(e0, e3) = all_52_25
% 178.71/28.58    (74)   ~ (all_52_9 = all_10_2)
% 178.71/28.58    (75)  op(e3, all_52_17) = all_52_16
% 178.71/28.58    (76)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.71/28.58    (77)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.71/28.58    (78)   ~ (all_52_13 = all_14_2)
% 178.71/28.58    (79)   ~ (e3 = e0)
% 178.71/28.58    (80)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.71/28.58    (81)   ~ (all_52_9 = all_52_13)
% 178.71/28.58    (82)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.58    (83)  op(e0, all_52_23) = all_52_22
% 178.71/28.58    (84)   ~ (all_52_15 = all_52_23)
% 178.71/28.58    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.71/28.58    (86)   ~ (all_52_5 = all_52_29)
% 178.71/28.58    (87)  op(e1, e0) = all_52_23
% 178.71/28.58    (88)  all_56_12 = all_52_25
% 178.71/28.58    (89)  all_58_13 = all_52_27
% 178.71/28.58    (90)   ~ (all_4_1 = e1)
% 178.71/28.58    (91)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.58    (92)  all_56_5 = all_10_2
% 178.71/28.58    (93)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.71/28.58    (94)   ~ (all_52_9 = all_52_17)
% 178.71/28.58    (95)   ~ (all_14_0 = e2)
% 178.71/28.58    (96)  all_58_6 = all_52_17
% 178.71/28.58    (97)  op(e2, all_52_19) = all_52_18
% 178.71/28.58    (98)   ~ (e1 = e0)
% 178.71/28.58    (99)  all_56_0 = all_4_2
% 178.71/28.58    (100)  all_58_11 = all_52_23
% 178.71/28.58    (101)   ~ (all_52_3 = all_52_19)
% 178.71/28.58    (102)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.71/28.58    (103)   ~ (all_52_7 = all_52_15)
% 178.71/28.58    (104)   ~ (all_52_29 = all_14_2)
% 178.71/28.58    (105)   ~ (all_4_0 = e1)
% 178.71/28.58    (106)   ~ (all_52_19 = all_10_2)
% 178.71/28.58    (107)   ~ (all_52_23 = all_6_2)
% 178.71/28.58    (108)   ~ (all_52_29 = all_6_2)
% 178.71/28.58    (109)  all_58_2 = all_52_9
% 178.71/28.58    (110)  op(e3, e1) = all_52_5
% 178.71/28.58    (111)  all_56_10 = all_14_2
% 178.71/28.58    (112)   ~ (all_52_25 = all_6_2)
% 178.71/28.58    (113)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.71/28.58    (114)  op(e1, e3) = all_52_17
% 178.71/28.58    (115)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.71/28.58    (116)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.71/28.58    (117)   ~ (all_52_25 = all_4_2)
% 178.71/28.58    (118)  op(e3, e0) = all_52_7
% 178.71/28.58    (119)  op(e3, e3) = all_4_2
% 178.71/28.58    (120)   ~ (all_10_1 = e3)
% 178.71/28.58    (121)  all_56_8 = all_52_17
% 178.71/28.58    (122)   ~ (all_52_17 = all_4_2)
% 178.71/28.58    (123)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.58             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.58    (124)   ~ (all_52_25 = all_52_27)
% 178.71/28.58    (125)   ~ (all_52_27 = all_6_2)
% 178.71/28.58    (126)   ~ (all_52_7 = all_6_2)
% 178.71/28.58    (127)   ~ (all_52_15 = all_10_2)
% 178.71/28.58    (128)   ~ (all_52_19 = all_52_27)
% 178.71/28.58    (129)  all_56_7 = all_52_15
% 178.71/28.58    (130)   ~ (all_52_7 = all_52_23)
% 178.71/28.58    (131)   ~ (all_52_13 = all_10_2)
% 178.71/28.58    (132)  op(e2, all_52_27) = all_52_26
% 178.71/28.58    (133)   ~ (all_52_17 = all_52_19)
% 178.71/28.58    (134)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.58    (135)  all_52_22 = e0
% 178.71/28.58    (136)  op(e1, all_14_2) = all_14_1
% 178.71/28.58    (137)  all_58_9 = all_52_7
% 178.71/28.58    (138)   ~ (e2 = e0)
% 178.71/28.58    (139)  all_58_12 = all_52_25
% 178.71/28.58    (140)  all_14_1 = e1
% 178.71/28.58    (141)  all_56_6 = all_52_13
% 178.71/28.58    (142)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.71/28.58    (143)   ~ (all_52_9 = all_52_15)
% 178.71/28.58    (144)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.71/28.58    (145)   ~ (e3 = e2)
% 178.71/28.58    (146)   ~ (all_52_19 = all_14_2)
% 178.71/28.58    (147)  op(e2, e3) = all_52_9
% 178.71/28.58    (148)  all_56_13 = all_52_27
% 178.71/28.58  
% 178.71/28.58  Begin of proof
% 178.71/28.58  | 
% 178.71/28.58  | REDUCE: (25), (140) imply:
% 178.71/28.58  |   (149)  op(e1, all_14_2) = all_14_0
% 178.71/28.58  | 
% 178.71/28.58  | REDUCE: (10), (75) imply:
% 178.71/28.58  |   (150)  op(e3, all_52_17) = e3
% 178.71/28.58  | 
% 178.71/28.58  | REDUCE: (39), (97) imply:
% 178.71/28.58  |   (151)  op(e2, all_52_19) = e2
% 178.71/28.58  | 
% 178.71/28.58  | REDUCE: (136), (140) imply:
% 178.71/28.58  |   (152)  op(e1, all_14_2) = e1
% 178.71/28.58  | 
% 178.71/28.58  | REDUCE: (83), (135) imply:
% 178.71/28.58  |   (153)  op(e0, all_52_23) = e0
% 178.71/28.58  | 
% 178.71/28.58  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 178.71/28.58  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.71/28.58  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 178.71/28.58  |            (37), (38), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 178.71/28.58  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 178.71/28.58  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 178.71/28.58  |            (71), (72), (73), (74), (76), (77), (78), (79), (80), (81), (82),
% 178.71/28.58  |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 178.71/28.58  |            (95), (96), (98), (99), (100), (101), (102), (103), (104), (105),
% 178.71/28.58  |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 178.71/28.58  |            (115), (116), (117), (118), (119), (120), (121), (122), (123),
% 178.71/28.58  |            (124), (125), (126), (127), (128), (129), (130), (131), (132),
% 178.71/28.58  |            (133), (134), (137), (138), (139), (141), (142), (143), (144),
% 178.71/28.58  |            (145), (146), (147), (148), (149), (150), (151), (152), (153) are
% 178.71/28.58  |            inconsistent by sub-proof #667.
% 178.71/28.58  | 
% 178.71/28.58  End of proof
% 178.71/28.58  
% 178.71/28.58  Sub-proof #667 shows that the following formulas are inconsistent:
% 178.71/28.58  ----------------------------------------------------------------
% 178.71/28.58    (1)   ~ (all_52_23 = all_14_2)
% 178.71/28.58    (2)   ~ (all_52_5 = all_52_13)
% 178.71/28.58    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.71/28.58    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.58    (5)   ~ (all_52_27 = all_10_2)
% 178.71/28.58    (6)   ~ (all_52_17 = all_52_23)
% 178.71/28.58    (7)  op(e2, all_10_2) = all_10_1
% 178.71/28.58    (8)   ~ (all_52_13 = all_52_29)
% 178.71/28.58    (9)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.58    (10)  op(e3, e2) = all_52_3
% 178.71/28.58    (11)   ~ (all_52_9 = all_52_25)
% 178.71/28.58    (12)  op(e3, all_52_25) = all_52_24
% 178.71/28.58    (13)   ~ (all_52_19 = all_52_23)
% 178.71/28.58    (14)  op(e1, e2) = all_52_19
% 178.71/28.58    (15)  op(e3, all_52_9) = all_52_8
% 178.71/28.58    (16)   ~ (all_52_3 = all_10_2)
% 178.71/28.58    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.58    (18)  all_58_5 = all_52_13
% 178.71/28.58    (19)   ~ (all_6_2 = e0)
% 178.71/28.58    (20)   ~ (all_52_25 = all_52_29)
% 178.71/28.58    (21)  all_56_15 = all_6_2
% 178.71/28.58    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.71/28.58    (23)  op(e2, e0) = all_52_15
% 178.71/28.58    (24)  all_58_3 = all_10_2
% 178.71/28.58    (25)  all_56_9 = all_52_19
% 178.71/28.58    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.58    (27)  all_58_15 = all_6_2
% 178.71/28.58    (28)   ~ (all_52_9 = all_4_2)
% 178.71/28.58    (29)   ~ (all_52_5 = all_52_7)
% 178.71/28.58    (30)  all_58_10 = all_52_15
% 178.71/28.58    (31)   ~ (all_52_5 = all_4_2)
% 178.71/28.58    (32)  all_58_7 = all_52_19
% 178.71/28.58    (33)   ~ (all_52_17 = all_52_25)
% 178.71/28.58    (34)   ~ (all_4_0 = e2)
% 178.71/28.58    (35)  all_58_4 = all_52_5
% 178.71/28.58    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.58    (37)   ~ (all_52_27 = all_52_29)
% 178.71/28.58    (38)   ~ (all_52_17 = all_14_2)
% 178.71/28.58    (39)  op(e3, all_4_2) = all_4_1
% 178.71/28.58    (40)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.58    (41)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.71/28.58    (42)   ~ (all_52_7 = all_4_2)
% 178.71/28.58    (43)  all_58_1 = all_52_3
% 178.71/28.58    (44)  all_58_0 = all_4_2
% 178.71/28.58    (45)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.71/28.58    (46)  op(e1, all_52_29) = all_52_28
% 178.71/28.58    (47)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.71/28.58    (48)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.71/28.58    (49)   ~ (all_4_1 = e2)
% 178.71/28.58    (50)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.71/28.58    (51)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.58    (52)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.71/28.58    (53)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.71/28.58    (54)  all_58_14 = all_52_29
% 178.71/28.58    (55)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.71/28.58    (56)   ~ (all_52_3 = all_52_5)
% 178.71/28.58    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.58    (58)  op(e2, e1) = all_52_13
% 178.71/28.58    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.71/28.58    (60)  all_58_8 = all_14_2
% 178.71/28.58    (61)  all_56_1 = all_52_3
% 178.71/28.58    (62)  op(e0, e2) = all_52_27
% 178.71/28.58    (63)   ~ (all_14_0 = e3)
% 178.71/28.58    (64)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.71/28.58    (65)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.58    (66)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.71/28.58    (67)   ~ (all_52_5 = all_14_2)
% 178.71/28.58    (68)   ~ (all_52_3 = all_52_27)
% 178.71/28.58    (69)   ~ (all_52_3 = all_4_2)
% 178.71/28.58    (70)  op(e0, e3) = all_52_25
% 178.71/28.58    (71)   ~ (all_52_9 = all_10_2)
% 178.71/28.58    (72)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.71/28.58    (73)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.71/28.58    (74)   ~ (all_52_13 = all_14_2)
% 178.71/28.58    (75)  op(e1, all_14_2) = all_14_0
% 178.71/28.58    (76)   ~ (e3 = e0)
% 178.71/28.58    (77)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.71/28.58    (78)   ~ (all_52_9 = all_52_13)
% 178.71/28.58    (79)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.58    (80)   ~ (all_52_15 = all_52_23)
% 178.71/28.58    (81)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.71/28.58    (82)   ~ (all_52_5 = all_52_29)
% 178.71/28.58    (83)  op(e1, e0) = all_52_23
% 178.71/28.58    (84)  all_56_12 = all_52_25
% 178.71/28.58    (85)  all_58_13 = all_52_27
% 178.71/28.58    (86)   ~ (all_4_1 = e1)
% 178.71/28.58    (87)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.58    (88)  all_56_5 = all_10_2
% 178.71/28.58    (89)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.71/28.58    (90)   ~ (all_52_9 = all_52_17)
% 178.71/28.58    (91)   ~ (all_14_0 = e2)
% 178.71/28.58    (92)  all_58_6 = all_52_17
% 178.71/28.58    (93)  op(e2, all_52_19) = e2
% 178.71/28.58    (94)  op(e3, all_52_17) = e3
% 178.71/28.58    (95)   ~ (e1 = e0)
% 178.71/28.58    (96)  all_56_0 = all_4_2
% 178.71/28.58    (97)  all_58_11 = all_52_23
% 178.71/28.58    (98)   ~ (all_52_3 = all_52_19)
% 178.71/28.58    (99)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.71/28.58    (100)   ~ (all_52_7 = all_52_15)
% 178.71/28.58    (101)   ~ (all_52_29 = all_14_2)
% 178.71/28.58    (102)   ~ (all_4_0 = e1)
% 178.71/28.58    (103)   ~ (all_52_19 = all_10_2)
% 178.71/28.58    (104)   ~ (all_52_23 = all_6_2)
% 178.71/28.58    (105)   ~ (all_52_29 = all_6_2)
% 178.71/28.58    (106)  all_58_2 = all_52_9
% 178.71/28.58    (107)  op(e3, e1) = all_52_5
% 178.71/28.58    (108)  all_56_10 = all_14_2
% 178.71/28.58    (109)   ~ (all_52_25 = all_6_2)
% 178.71/28.58    (110)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.71/28.58    (111)  op(e1, e3) = all_52_17
% 178.71/28.58    (112)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.71/28.58    (113)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.71/28.58    (114)   ~ (all_52_25 = all_4_2)
% 178.71/28.58    (115)  op(e3, e0) = all_52_7
% 178.71/28.58    (116)  op(e3, e3) = all_4_2
% 178.71/28.58    (117)   ~ (all_10_1 = e3)
% 178.71/28.58    (118)  all_56_8 = all_52_17
% 178.71/28.58    (119)   ~ (all_52_17 = all_4_2)
% 178.71/28.58    (120)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.58             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.58    (121)   ~ (all_52_25 = all_52_27)
% 178.71/28.58    (122)   ~ (all_52_27 = all_6_2)
% 178.71/28.58    (123)   ~ (all_52_7 = all_6_2)
% 178.71/28.58    (124)  op(e0, all_52_23) = e0
% 178.71/28.58    (125)   ~ (all_52_15 = all_10_2)
% 178.71/28.58    (126)   ~ (all_52_19 = all_52_27)
% 178.71/28.58    (127)  all_56_7 = all_52_15
% 178.71/28.58    (128)  op(e1, all_14_2) = e1
% 178.71/28.58    (129)   ~ (all_52_7 = all_52_23)
% 178.71/28.58    (130)   ~ (all_52_13 = all_10_2)
% 178.71/28.58    (131)  op(e2, all_52_27) = all_52_26
% 178.71/28.58    (132)   ~ (all_52_17 = all_52_19)
% 178.71/28.58    (133)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.58    (134)  all_58_9 = all_52_7
% 178.71/28.58    (135)   ~ (e2 = e0)
% 178.71/28.58    (136)  all_58_12 = all_52_25
% 178.71/28.58    (137)  all_56_6 = all_52_13
% 178.71/28.58    (138)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.71/28.58    (139)   ~ (all_52_9 = all_52_15)
% 178.71/28.58    (140)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.71/28.58    (141)   ~ (e3 = e2)
% 178.71/28.58    (142)   ~ (all_52_19 = all_14_2)
% 178.71/28.58    (143)  op(e2, e3) = all_52_9
% 178.71/28.58    (144)  all_56_13 = all_52_27
% 178.71/28.58  
% 178.71/28.58  Begin of proof
% 178.71/28.58  | 
% 178.71/28.58  | GROUND_INST: instantiating (120) with e1, all_14_0, all_14_2, e1, simplifying
% 178.71/28.58  |              with (75), (128) gives:
% 178.71/28.58  |   (145)  all_14_0 = e1
% 178.71/28.58  | 
% 178.71/28.58  | REDUCE: (63), (145) imply:
% 178.71/28.58  |   (146)   ~ (e3 = e1)
% 178.71/28.58  | 
% 178.71/28.58  | SIMP: (146) implies:
% 178.71/28.58  |   (147)   ~ (e3 = e1)
% 178.71/28.58  | 
% 178.71/28.58  | REDUCE: (91), (145) imply:
% 178.71/28.58  |   (148)   ~ (e2 = e1)
% 178.71/28.58  | 
% 178.71/28.58  | SIMP: (148) implies:
% 178.71/28.58  |   (149)   ~ (e2 = e1)
% 178.71/28.58  | 
% 178.71/28.58  | BETA: splitting (40) gives:
% 178.71/28.58  | 
% 178.71/28.58  | Case 1:
% 178.71/28.58  | | 
% 178.71/28.58  | |   (150)  all_56_15 = e3
% 178.71/28.58  | | 
% 178.71/28.58  | | REF_CLOSE: (1), (5), (7), (13), (14), (18), (21), (24), (25), (27), (28),
% 178.71/28.58  | |            (30), (31), (32), (35), (36), (38), (39), (41), (44), (48), (53),
% 178.71/28.58  | |            (54), (57), (58), (60), (62), (65), (67), (71), (72), (78), (88),
% 178.71/28.58  | |            (89), (90), (92), (93), (94), (97), (102), (104), (105), (106),
% 178.71/28.58  | |            (107), (109), (110), (111), (116), (117), (119), (120), (123),
% 178.71/28.58  | |            (124), (128), (129), (130), (134), (136), (138), (139), (140),
% 178.71/28.58  | |            (141), (142), (143), (149), (150) are inconsistent by sub-proof
% 178.71/28.58  | |            #701.
% 178.71/28.58  | | 
% 178.71/28.58  | Case 2:
% 178.71/28.58  | | 
% 178.71/28.58  | |   (151)   ~ (all_56_15 = e3)
% 178.71/28.58  | |   (152)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.58  | | 
% 178.71/28.58  | | REDUCE: (21), (151) imply:
% 178.71/28.58  | |   (153)   ~ (all_6_2 = e3)
% 178.71/28.58  | | 
% 178.71/28.58  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.71/28.58  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.71/28.58  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 178.71/28.58  | |            (36), (37), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 178.71/28.58  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 178.71/28.58  | |            (59), (60), (61), (64), (65), (66), (67), (68), (69), (70), (71),
% 178.71/28.58  | |            (73), (74), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 178.71/28.58  | |            (85), (86), (87), (88), (89), (90), (92), (93), (94), (95), (96),
% 178.71/28.58  | |            (97), (98), (99), (100), (101), (102), (103), (104), (106),
% 178.71/28.58  | |            (107), (108), (109), (110), (111), (112), (113), (114), (115),
% 178.71/28.58  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 178.71/28.58  | |            (125), (126), (127), (128), (129), (130), (131), (132), (133),
% 178.71/28.58  | |            (134), (135), (136), (137), (138), (139), (140), (141), (142),
% 178.71/28.58  | |            (143), (144), (147), (149), (152), (153) are inconsistent by
% 178.71/28.58  | |            sub-proof #668.
% 178.71/28.58  | | 
% 178.71/28.58  | End of split
% 178.71/28.58  | 
% 178.71/28.58  End of proof
% 178.71/28.58  
% 178.71/28.58  Sub-proof #668 shows that the following formulas are inconsistent:
% 178.71/28.58  ----------------------------------------------------------------
% 178.71/28.58    (1)   ~ (all_52_23 = all_14_2)
% 178.71/28.58    (2)   ~ (all_52_5 = all_52_13)
% 178.71/28.58    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.71/28.58    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.58    (5)   ~ (all_52_17 = all_52_23)
% 178.71/28.58    (6)  op(e2, all_10_2) = all_10_1
% 178.71/28.58    (7)   ~ (all_52_13 = all_52_29)
% 178.71/28.58    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.58    (9)  op(e3, e2) = all_52_3
% 178.71/28.58    (10)   ~ (all_52_9 = all_52_25)
% 178.71/28.58    (11)  op(e3, all_52_25) = all_52_24
% 178.71/28.58    (12)   ~ (all_52_19 = all_52_23)
% 178.71/28.58    (13)  op(e1, e2) = all_52_19
% 178.71/28.58    (14)   ~ (all_6_2 = e3)
% 178.71/28.58    (15)  op(e3, all_52_9) = all_52_8
% 178.71/28.58    (16)   ~ (all_52_3 = all_10_2)
% 178.71/28.58    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.58    (18)  all_58_5 = all_52_13
% 178.71/28.58    (19)   ~ (all_6_2 = e0)
% 178.71/28.58    (20)   ~ (all_52_25 = all_52_29)
% 178.71/28.58    (21)  all_56_15 = all_6_2
% 178.71/28.58    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.71/28.58    (23)  op(e2, e0) = all_52_15
% 178.71/28.58    (24)  all_58_3 = all_10_2
% 178.71/28.58    (25)  all_56_9 = all_52_19
% 178.71/28.58    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.58    (27)  all_58_15 = all_6_2
% 178.71/28.58    (28)   ~ (all_52_9 = all_4_2)
% 178.71/28.58    (29)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.58    (30)   ~ (all_52_5 = all_52_7)
% 178.71/28.58    (31)  all_58_10 = all_52_15
% 178.71/28.58    (32)   ~ (all_52_5 = all_4_2)
% 178.71/28.58    (33)  all_58_7 = all_52_19
% 178.71/28.58    (34)   ~ (all_52_17 = all_52_25)
% 178.71/28.58    (35)   ~ (all_4_0 = e2)
% 178.71/28.58    (36)  all_58_4 = all_52_5
% 178.71/28.58    (37)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.58    (38)   ~ (e3 = e1)
% 178.71/28.58    (39)   ~ (all_52_27 = all_52_29)
% 178.71/28.58    (40)   ~ (all_52_17 = all_14_2)
% 178.71/28.58    (41)  op(e3, all_4_2) = all_4_1
% 178.71/28.58    (42)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.71/28.58    (43)   ~ (all_52_7 = all_4_2)
% 178.71/28.58    (44)  all_58_1 = all_52_3
% 178.71/28.58    (45)  all_58_0 = all_4_2
% 178.71/28.58    (46)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.71/28.58    (47)  op(e1, all_52_29) = all_52_28
% 178.71/28.58    (48)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.71/28.58    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.71/28.58    (50)   ~ (all_4_1 = e2)
% 178.71/28.58    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.71/28.58    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.58    (53)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.71/28.58    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.71/28.58    (55)  all_58_14 = all_52_29
% 178.71/28.58    (56)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.71/28.58    (57)   ~ (all_52_3 = all_52_5)
% 178.71/28.58    (58)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.58    (59)  op(e2, e1) = all_52_13
% 178.71/28.58    (60)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.71/28.58    (61)  all_58_8 = all_14_2
% 178.71/28.58    (62)  all_56_1 = all_52_3
% 178.71/28.58    (63)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.71/28.58    (64)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.58    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.71/28.58    (66)   ~ (all_52_5 = all_14_2)
% 178.71/28.58    (67)   ~ (all_52_3 = all_52_27)
% 178.71/28.58    (68)   ~ (all_52_3 = all_4_2)
% 178.71/28.58    (69)  op(e0, e3) = all_52_25
% 178.71/28.58    (70)   ~ (all_52_9 = all_10_2)
% 178.71/28.58    (71)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.71/28.58    (72)   ~ (all_52_13 = all_14_2)
% 178.71/28.58    (73)   ~ (e3 = e0)
% 178.71/28.58    (74)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.71/28.58    (75)   ~ (all_52_9 = all_52_13)
% 178.71/28.58    (76)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.58    (77)   ~ (all_52_15 = all_52_23)
% 178.71/28.58    (78)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.71/28.58    (79)   ~ (all_52_5 = all_52_29)
% 178.71/28.58    (80)  op(e1, e0) = all_52_23
% 178.71/28.58    (81)  all_56_12 = all_52_25
% 178.71/28.58    (82)  all_58_13 = all_52_27
% 178.71/28.58    (83)   ~ (all_4_1 = e1)
% 178.71/28.58    (84)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.58    (85)  all_56_5 = all_10_2
% 178.71/28.58    (86)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.71/28.58    (87)   ~ (all_52_9 = all_52_17)
% 178.71/28.58    (88)  all_58_6 = all_52_17
% 178.71/28.58    (89)  op(e2, all_52_19) = e2
% 178.71/28.58    (90)  op(e3, all_52_17) = e3
% 178.71/28.58    (91)   ~ (e1 = e0)
% 178.71/28.58    (92)  all_56_0 = all_4_2
% 178.71/28.58    (93)  all_58_11 = all_52_23
% 178.71/28.58    (94)   ~ (all_52_3 = all_52_19)
% 178.71/28.58    (95)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.71/28.58    (96)   ~ (all_52_7 = all_52_15)
% 178.71/28.58    (97)   ~ (all_52_29 = all_14_2)
% 178.71/28.58    (98)   ~ (all_4_0 = e1)
% 178.71/28.58    (99)   ~ (all_52_19 = all_10_2)
% 178.71/28.58    (100)   ~ (all_52_23 = all_6_2)
% 178.71/28.58    (101)  all_58_2 = all_52_9
% 178.71/28.58    (102)  op(e3, e1) = all_52_5
% 178.71/28.58    (103)   ~ (e2 = e1)
% 178.71/28.58    (104)  all_56_10 = all_14_2
% 178.71/28.58    (105)   ~ (all_52_25 = all_6_2)
% 178.71/28.59    (106)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.71/28.59    (107)  op(e1, e3) = all_52_17
% 178.71/28.59    (108)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.71/28.59    (109)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.71/28.59    (110)   ~ (all_52_25 = all_4_2)
% 178.71/28.59    (111)  op(e3, e0) = all_52_7
% 178.71/28.59    (112)  op(e3, e3) = all_4_2
% 178.71/28.59    (113)   ~ (all_10_1 = e3)
% 178.71/28.59    (114)  all_56_8 = all_52_17
% 178.71/28.59    (115)   ~ (all_52_17 = all_4_2)
% 178.71/28.59    (116)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.59             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.59    (117)   ~ (all_52_25 = all_52_27)
% 178.71/28.59    (118)   ~ (all_52_27 = all_6_2)
% 178.71/28.59    (119)   ~ (all_52_7 = all_6_2)
% 178.71/28.59    (120)  op(e0, all_52_23) = e0
% 178.71/28.59    (121)   ~ (all_52_15 = all_10_2)
% 178.71/28.59    (122)   ~ (all_52_19 = all_52_27)
% 178.71/28.59    (123)  all_56_7 = all_52_15
% 178.71/28.59    (124)  op(e1, all_14_2) = e1
% 178.71/28.59    (125)   ~ (all_52_7 = all_52_23)
% 178.71/28.59    (126)   ~ (all_52_13 = all_10_2)
% 178.71/28.59    (127)  op(e2, all_52_27) = all_52_26
% 178.71/28.59    (128)   ~ (all_52_17 = all_52_19)
% 178.71/28.59    (129)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.59    (130)  all_58_9 = all_52_7
% 178.71/28.59    (131)   ~ (e2 = e0)
% 178.71/28.59    (132)  all_58_12 = all_52_25
% 178.71/28.59    (133)  all_56_6 = all_52_13
% 178.71/28.59    (134)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.71/28.59    (135)   ~ (all_52_9 = all_52_15)
% 178.71/28.59    (136)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.71/28.59    (137)   ~ (e3 = e2)
% 178.71/28.59    (138)   ~ (all_52_19 = all_14_2)
% 178.71/28.59    (139)  op(e2, e3) = all_52_9
% 178.71/28.59    (140)  all_56_13 = all_52_27
% 178.71/28.59  
% 178.71/28.59  Begin of proof
% 178.71/28.59  | 
% 178.71/28.59  | BETA: splitting (56) gives:
% 178.71/28.59  | 
% 178.71/28.59  | Case 1:
% 178.71/28.59  | | 
% 178.71/28.59  | |   (141)  all_56_13 = e3
% 178.71/28.59  | | 
% 178.71/28.59  | | COMBINE_EQS: (140), (141) imply:
% 178.71/28.59  | |   (142)  all_52_27 = e3
% 178.71/28.59  | | 
% 178.71/28.59  | | REF_CLOSE: (1), (2), (9), (11), (12), (18), (20), (22), (23), (25), (30),
% 178.71/28.59  | |            (31), (32), (33), (34), (36), (37), (38), (39), (40), (41), (45),
% 178.71/28.59  | |            (46), (48), (49), (55), (58), (61), (62), (64), (66), (67), (68),
% 178.71/28.59  | |            (69), (71), (78), (80), (83), (84), (87), (88), (89), (90), (91),
% 178.71/28.59  | |            (93), (94), (98), (101), (102), (103), (104), (107), (109),
% 178.71/28.59  | |            (110), (111), (112), (115), (116), (117), (120), (122), (124),
% 178.71/28.59  | |            (127), (128), (130), (131), (132), (136), (137), (138), (139),
% 178.71/28.59  | |            (142) are inconsistent by sub-proof #686.
% 178.71/28.59  | | 
% 178.71/28.59  | Case 2:
% 178.71/28.59  | | 
% 178.71/28.59  | |   (143)   ~ (all_56_13 = e3)
% 178.71/28.59  | | 
% 178.71/28.59  | | REDUCE: (140), (143) imply:
% 178.71/28.59  | |   (144)   ~ (all_52_27 = e3)
% 178.71/28.59  | | 
% 178.71/28.59  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.71/28.59  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.71/28.59  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 178.71/28.59  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 178.71/28.59  | |            (46), (47), (49), (50), (51), (52), (53), (54), (55), (57), (58),
% 178.71/28.59  | |            (59), (60), (61), (63), (64), (65), (66), (68), (69), (70), (72),
% 178.71/28.59  | |            (73), (74), (75), (76), (77), (79), (81), (82), (84), (85), (86),
% 178.71/28.59  | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 178.71/28.59  | |            (98), (99), (100), (101), (102), (103), (105), (106), (107),
% 178.71/28.59  | |            (108), (110), (111), (112), (113), (114), (115), (116), (117),
% 178.71/28.59  | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 178.71/28.59  | |            (128), (129), (130), (131), (132), (133), (134), (135), (136),
% 178.71/28.59  | |            (137), (138), (139), (144) are inconsistent by sub-proof #669.
% 178.71/28.59  | | 
% 178.71/28.59  | End of split
% 178.71/28.59  | 
% 178.71/28.59  End of proof
% 178.71/28.59  
% 178.71/28.59  Sub-proof #669 shows that the following formulas are inconsistent:
% 178.71/28.59  ----------------------------------------------------------------
% 178.71/28.59    (1)   ~ (all_52_23 = all_14_2)
% 178.71/28.59    (2)   ~ (all_52_5 = all_52_13)
% 178.71/28.59    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.71/28.59    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.59    (5)   ~ (all_52_17 = all_52_23)
% 178.71/28.59    (6)  op(e2, all_10_2) = all_10_1
% 178.71/28.59    (7)   ~ (all_52_13 = all_52_29)
% 178.71/28.59    (8)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.59    (9)  op(e3, e2) = all_52_3
% 178.71/28.59    (10)   ~ (all_52_9 = all_52_25)
% 178.71/28.59    (11)  op(e3, all_52_25) = all_52_24
% 178.71/28.59    (12)   ~ (all_52_19 = all_52_23)
% 178.71/28.59    (13)  op(e1, e2) = all_52_19
% 178.71/28.59    (14)   ~ (all_52_27 = e3)
% 178.71/28.59    (15)   ~ (all_6_2 = e3)
% 178.71/28.59    (16)  op(e3, all_52_9) = all_52_8
% 178.71/28.59    (17)   ~ (all_52_3 = all_10_2)
% 178.71/28.59    (18)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.59    (19)  all_58_5 = all_52_13
% 178.71/28.59    (20)   ~ (all_6_2 = e0)
% 178.71/28.59    (21)   ~ (all_52_25 = all_52_29)
% 178.71/28.59    (22)  all_56_15 = all_6_2
% 178.71/28.59    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.71/28.59    (24)  op(e2, e0) = all_52_15
% 178.71/28.59    (25)  all_58_3 = all_10_2
% 178.71/28.59    (26)  all_56_9 = all_52_19
% 178.71/28.59    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.59    (28)  all_58_15 = all_6_2
% 178.71/28.59    (29)   ~ (all_52_9 = all_4_2)
% 178.71/28.59    (30)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.59    (31)   ~ (all_52_5 = all_52_7)
% 178.71/28.59    (32)  all_58_10 = all_52_15
% 178.71/28.59    (33)   ~ (all_52_5 = all_4_2)
% 178.71/28.59    (34)  all_58_7 = all_52_19
% 178.71/28.59    (35)   ~ (all_52_17 = all_52_25)
% 178.71/28.59    (36)   ~ (all_4_0 = e2)
% 178.71/28.59    (37)  all_58_4 = all_52_5
% 178.71/28.59    (38)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.59    (39)   ~ (e3 = e1)
% 178.71/28.59    (40)   ~ (all_52_27 = all_52_29)
% 178.71/28.59    (41)   ~ (all_52_17 = all_14_2)
% 178.71/28.59    (42)  op(e3, all_4_2) = all_4_1
% 178.71/28.59    (43)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.71/28.59    (44)   ~ (all_52_7 = all_4_2)
% 178.71/28.59    (45)  all_58_1 = all_52_3
% 178.71/28.59    (46)  all_58_0 = all_4_2
% 178.71/28.59    (47)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.71/28.59    (48)  op(e1, all_52_29) = all_52_28
% 178.71/28.59    (49)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.71/28.59    (50)   ~ (all_4_1 = e2)
% 178.71/28.59    (51)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.71/28.59    (52)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.59    (53)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.71/28.59    (54)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.71/28.59    (55)  all_58_14 = all_52_29
% 178.71/28.59    (56)   ~ (all_52_3 = all_52_5)
% 178.71/28.59    (57)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.59    (58)  op(e2, e1) = all_52_13
% 178.71/28.59    (59)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.71/28.59    (60)  all_58_8 = all_14_2
% 178.71/28.59    (61)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.71/28.59    (62)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.59    (63)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.71/28.59    (64)   ~ (all_52_5 = all_14_2)
% 178.71/28.59    (65)   ~ (all_52_3 = all_4_2)
% 178.71/28.59    (66)  op(e0, e3) = all_52_25
% 178.71/28.59    (67)   ~ (all_52_9 = all_10_2)
% 178.71/28.59    (68)   ~ (all_52_13 = all_14_2)
% 178.71/28.59    (69)   ~ (e3 = e0)
% 178.71/28.59    (70)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.71/28.59    (71)   ~ (all_52_9 = all_52_13)
% 178.71/28.59    (72)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.59    (73)   ~ (all_52_15 = all_52_23)
% 178.71/28.59    (74)   ~ (all_52_5 = all_52_29)
% 178.71/28.59    (75)  all_56_12 = all_52_25
% 178.71/28.59    (76)  all_58_13 = all_52_27
% 178.71/28.59    (77)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.71/28.59    (78)  all_56_5 = all_10_2
% 178.71/28.59    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.71/28.59    (80)   ~ (all_52_9 = all_52_17)
% 178.71/28.59    (81)  all_58_6 = all_52_17
% 178.71/28.59    (82)  op(e2, all_52_19) = e2
% 178.71/28.59    (83)  op(e3, all_52_17) = e3
% 178.71/28.59    (84)   ~ (e1 = e0)
% 178.71/28.59    (85)  all_56_0 = all_4_2
% 178.71/28.59    (86)  all_58_11 = all_52_23
% 178.71/28.59    (87)   ~ (all_52_3 = all_52_19)
% 178.71/28.59    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.71/28.59    (89)   ~ (all_52_7 = all_52_15)
% 178.71/28.59    (90)   ~ (all_52_29 = all_14_2)
% 178.71/28.59    (91)   ~ (all_4_0 = e1)
% 178.71/28.59    (92)   ~ (all_52_19 = all_10_2)
% 178.71/28.59    (93)   ~ (all_52_23 = all_6_2)
% 178.71/28.59    (94)  all_58_2 = all_52_9
% 178.71/28.59    (95)  op(e3, e1) = all_52_5
% 178.71/28.59    (96)   ~ (e2 = e1)
% 178.71/28.59    (97)   ~ (all_52_25 = all_6_2)
% 178.71/28.59    (98)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.71/28.59    (99)  op(e1, e3) = all_52_17
% 178.71/28.59    (100)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.71/28.59    (101)   ~ (all_52_25 = all_4_2)
% 178.71/28.59    (102)  op(e3, e0) = all_52_7
% 178.71/28.59    (103)  op(e3, e3) = all_4_2
% 178.71/28.59    (104)   ~ (all_10_1 = e3)
% 178.71/28.59    (105)  all_56_8 = all_52_17
% 178.71/28.59    (106)   ~ (all_52_17 = all_4_2)
% 178.71/28.59    (107)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.59             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.59    (108)   ~ (all_52_25 = all_52_27)
% 178.71/28.59    (109)   ~ (all_52_27 = all_6_2)
% 178.71/28.59    (110)   ~ (all_52_7 = all_6_2)
% 178.71/28.59    (111)  op(e0, all_52_23) = e0
% 178.71/28.59    (112)   ~ (all_52_15 = all_10_2)
% 178.71/28.59    (113)   ~ (all_52_19 = all_52_27)
% 178.71/28.59    (114)  all_56_7 = all_52_15
% 178.71/28.59    (115)  op(e1, all_14_2) = e1
% 178.71/28.59    (116)   ~ (all_52_7 = all_52_23)
% 178.71/28.59    (117)   ~ (all_52_13 = all_10_2)
% 178.71/28.59    (118)   ~ (all_52_17 = all_52_19)
% 178.71/28.59    (119)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.71/28.59    (120)  all_58_9 = all_52_7
% 178.71/28.59    (121)   ~ (e2 = e0)
% 178.71/28.59    (122)  all_58_12 = all_52_25
% 178.71/28.59    (123)  all_56_6 = all_52_13
% 178.71/28.59    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.71/28.59    (125)   ~ (all_52_9 = all_52_15)
% 178.71/28.59    (126)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.71/28.59    (127)   ~ (e3 = e2)
% 178.71/28.59    (128)   ~ (all_52_19 = all_14_2)
% 178.71/28.59    (129)  op(e2, e3) = all_52_9
% 178.71/28.59  
% 178.71/28.59  Begin of proof
% 178.71/28.59  | 
% 178.71/28.59  | BETA: splitting (59) gives:
% 178.71/28.59  | 
% 178.71/28.59  | Case 1:
% 178.71/28.59  | | 
% 178.71/28.59  | |   (130)  all_58_12 = e3
% 178.71/28.59  | | 
% 178.71/28.59  | | REF_CLOSE: (6), (10), (13), (19), (25), (27), (28), (29), (31), (32), (33),
% 178.71/28.59  | |            (34), (35), (37), (38), (39), (43), (44), (45), (46), (47), (52),
% 178.71/28.59  | |            (53), (54), (58), (60), (64), (66), (67), (68), (69), (70), (71),
% 178.71/28.59  | |            (73), (76), (77), (78), (79), (80), (81), (82), (83), (84), (85),
% 178.71/28.59  | |            (86), (87), (89), (92), (94), (95), (96), (97), (98), (99),
% 178.71/28.59  | |            (100), (101), (102), (104), (106), (107), (108), (111), (112),
% 178.71/28.59  | |            (114), (115), (116), (118), (119), (120), (121), (122), (123),
% 178.71/28.59  | |            (124), (125), (126), (129), (130) are inconsistent by sub-proof
% 178.71/28.59  | |            #677.
% 178.71/28.59  | | 
% 178.71/28.59  | Case 2:
% 178.71/28.59  | | 
% 178.71/28.59  | |   (131)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.71/28.59  | | 
% 178.71/28.59  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 178.71/28.59  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.71/28.59  | |            (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 178.71/28.59  | |            (37), (38), (40), (41), (42), (43), (45), (46), (47), (48), (49),
% 178.71/28.59  | |            (50), (51), (52), (55), (56), (57), (60), (61), (62), (63), (64),
% 178.71/28.59  | |            (65), (66), (67), (71), (72), (74), (75), (76), (80), (81), (82),
% 178.71/28.59  | |            (83), (85), (86), (87), (88), (90), (91), (92), (93), (94), (95),
% 178.71/28.59  | |            (97), (99), (101), (102), (103), (105), (106), (107), (108),
% 178.71/28.59  | |            (109), (110), (111), (113), (115), (117), (118), (120), (122),
% 178.71/28.59  | |            (127), (128), (129), (131) are inconsistent by sub-proof #670.
% 178.71/28.59  | | 
% 178.71/28.59  | End of split
% 178.71/28.59  | 
% 178.71/28.59  End of proof
% 178.71/28.59  
% 178.71/28.59  Sub-proof #670 shows that the following formulas are inconsistent:
% 178.71/28.59  ----------------------------------------------------------------
% 178.71/28.59    (1)   ~ (all_52_23 = all_14_2)
% 178.71/28.59    (2)   ~ (all_52_5 = all_52_13)
% 178.71/28.59    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.71/28.59    (4)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.71/28.59    (5)   ~ (all_52_17 = all_52_23)
% 178.71/28.59    (6)   ~ (all_52_13 = all_52_29)
% 178.71/28.59    (7)  all_58_12 = e0 | all_58_13 = e0 | all_58_14 = e0
% 178.71/28.59    (8)  op(e3, e2) = all_52_3
% 178.71/28.59    (9)   ~ (all_52_9 = all_52_25)
% 178.71/28.59    (10)  op(e3, all_52_25) = all_52_24
% 178.71/28.59    (11)   ~ (all_52_19 = all_52_23)
% 178.71/28.59    (12)  op(e1, e2) = all_52_19
% 178.71/28.59    (13)   ~ (all_52_27 = e3)
% 178.71/28.59    (14)   ~ (all_6_2 = e3)
% 178.71/28.59    (15)  op(e3, all_52_9) = all_52_8
% 178.71/28.59    (16)   ~ (all_52_3 = all_10_2)
% 178.71/28.59    (17)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.71/28.59    (18)  all_58_5 = all_52_13
% 178.71/28.59    (19)   ~ (all_6_2 = e0)
% 178.71/28.59    (20)   ~ (all_52_25 = all_52_29)
% 178.71/28.59    (21)  all_56_15 = all_6_2
% 178.71/28.59    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.71/28.59    (23)  op(e2, e0) = all_52_15
% 178.71/28.59    (24)  all_58_3 = all_10_2
% 178.71/28.59    (25)  all_56_9 = all_52_19
% 178.71/28.59    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.71/28.59    (27)  all_58_15 = all_6_2
% 178.71/28.59    (28)   ~ (all_52_9 = all_4_2)
% 178.71/28.59    (29)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.71/28.59    (30)  all_58_10 = all_52_15
% 178.71/28.59    (31)   ~ (all_52_5 = all_4_2)
% 178.71/28.59    (32)  all_58_7 = all_52_19
% 178.71/28.59    (33)   ~ (all_52_17 = all_52_25)
% 178.71/28.59    (34)   ~ (all_4_0 = e2)
% 178.71/28.59    (35)  all_58_4 = all_52_5
% 178.71/28.59    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.71/28.59    (37)   ~ (all_52_27 = all_52_29)
% 178.71/28.59    (38)   ~ (all_52_17 = all_14_2)
% 178.71/28.59    (39)  op(e3, all_4_2) = all_4_1
% 178.71/28.59    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.71/28.59    (41)  all_58_1 = all_52_3
% 178.71/28.59    (42)  all_58_0 = all_4_2
% 178.71/28.59    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.71/28.59    (44)  op(e1, all_52_29) = all_52_28
% 178.71/28.59    (45)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.71/28.59    (46)   ~ (all_4_1 = e2)
% 178.71/28.59    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.71/28.59    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.71/28.59    (49)  all_58_14 = all_52_29
% 178.71/28.59    (50)   ~ (all_52_3 = all_52_5)
% 178.71/28.59    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.71/28.59    (52)  all_58_8 = all_14_2
% 178.71/28.59    (53)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.71/28.59    (54)  op(all_4_1, all_4_2) = all_4_0
% 178.71/28.59    (55)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.71/28.59    (56)   ~ (all_52_5 = all_14_2)
% 178.71/28.59    (57)   ~ (all_52_3 = all_4_2)
% 178.71/28.59    (58)  op(e0, e3) = all_52_25
% 178.71/28.59    (59)   ~ (all_52_9 = all_10_2)
% 178.71/28.59    (60)   ~ (all_52_9 = all_52_13)
% 178.71/28.59    (61)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.59    (62)   ~ (all_52_5 = all_52_29)
% 178.71/28.59    (63)  all_56_12 = all_52_25
% 178.71/28.59    (64)  all_58_13 = all_52_27
% 178.71/28.59    (65)   ~ (all_52_9 = all_52_17)
% 178.71/28.59    (66)  all_58_6 = all_52_17
% 178.71/28.59    (67)  op(e2, all_52_19) = e2
% 178.71/28.59    (68)  op(e3, all_52_17) = e3
% 178.71/28.59    (69)  all_56_0 = all_4_2
% 178.71/28.59    (70)  all_58_11 = all_52_23
% 178.71/28.59    (71)   ~ (all_52_3 = all_52_19)
% 178.71/28.59    (72)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.71/28.59    (73)   ~ (all_52_29 = all_14_2)
% 178.71/28.59    (74)   ~ (all_4_0 = e1)
% 178.71/28.59    (75)   ~ (all_52_19 = all_10_2)
% 178.71/28.59    (76)   ~ (all_52_23 = all_6_2)
% 178.71/28.59    (77)  all_58_2 = all_52_9
% 178.71/28.59    (78)  op(e3, e1) = all_52_5
% 178.71/28.59    (79)   ~ (all_52_25 = all_6_2)
% 178.71/28.59    (80)  op(e1, e3) = all_52_17
% 178.71/28.59    (81)   ~ (all_52_25 = all_4_2)
% 178.71/28.59    (82)  op(e3, e0) = all_52_7
% 178.71/28.59    (83)  op(e3, e3) = all_4_2
% 178.71/28.59    (84)  all_56_8 = all_52_17
% 178.71/28.59    (85)   ~ (all_52_17 = all_4_2)
% 178.71/28.59    (86)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.71/28.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.71/28.59    (87)   ~ (all_52_25 = all_52_27)
% 178.71/28.59    (88)   ~ (all_52_27 = all_6_2)
% 178.71/28.59    (89)   ~ (all_52_7 = all_6_2)
% 178.71/28.59    (90)  op(e0, all_52_23) = e0
% 178.71/28.59    (91)   ~ (all_52_19 = all_52_27)
% 178.71/28.59    (92)  op(e1, all_14_2) = e1
% 178.71/28.59    (93)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.71/28.59    (94)   ~ (all_52_13 = all_10_2)
% 178.71/28.59    (95)   ~ (all_52_17 = all_52_19)
% 178.71/28.59    (96)  all_58_9 = all_52_7
% 178.71/28.59    (97)  all_58_12 = all_52_25
% 178.71/28.59    (98)   ~ (e3 = e2)
% 178.71/28.59    (99)   ~ (all_52_19 = all_14_2)
% 178.71/28.59    (100)  op(e2, e3) = all_52_9
% 178.71/28.59  
% 178.71/28.59  Begin of proof
% 178.71/28.59  | 
% 178.71/28.59  | BETA: splitting (93) gives:
% 178.71/28.59  | 
% 178.71/28.59  | Case 1:
% 178.71/28.59  | | 
% 178.71/28.59  | |   (101)  all_58_13 = e3
% 178.71/28.59  | | 
% 178.71/28.59  | | REF_CLOSE: (13), (64), (101) are inconsistent by sub-proof #1026.
% 178.71/28.59  | | 
% 178.71/28.59  | Case 2:
% 178.71/28.59  | | 
% 178.71/28.59  | |   (102)  all_58_14 = e3 | all_58_15 = e3
% 178.71/28.59  | | 
% 178.71/28.59  | | BETA: splitting (102) gives:
% 178.71/28.59  | | 
% 178.71/28.59  | | Case 1:
% 178.71/28.59  | | | 
% 178.71/28.59  | | |   (103)  all_58_14 = e3
% 178.71/28.59  | | | 
% 178.71/28.59  | | | COMBINE_EQS: (49), (103) imply:
% 178.71/28.59  | | |   (104)  all_52_29 = e3
% 178.71/28.59  | | | 
% 178.71/28.59  | | | SIMP: (104) implies:
% 178.71/28.59  | | |   (105)  all_52_29 = e3
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (62), (105) imply:
% 178.71/28.59  | | |   (106)   ~ (all_52_5 = e3)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (6), (105) imply:
% 178.71/28.59  | | |   (107)   ~ (all_52_13 = e3)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (20), (105) imply:
% 178.71/28.59  | | |   (108)   ~ (all_52_25 = e3)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (73), (105) imply:
% 178.71/28.59  | | |   (109)   ~ (all_14_2 = e3)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | SIMP: (109) implies:
% 178.71/28.59  | | |   (110)   ~ (all_14_2 = e3)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (44), (105) imply:
% 178.71/28.59  | | |   (111)  op(e1, e3) = all_52_28
% 178.71/28.59  | | | 
% 178.71/28.59  | | | GROUND_INST: instantiating (86) with all_52_17, all_52_28, e3, e1,
% 178.71/28.59  | | |              simplifying with (80), (111) gives:
% 178.71/28.59  | | |   (112)  all_52_17 = all_52_28
% 178.71/28.59  | | | 
% 178.71/28.59  | | | COMBINE_EQS: (84), (112) imply:
% 178.71/28.59  | | |   (113)  all_56_8 = all_52_28
% 178.71/28.59  | | | 
% 178.71/28.59  | | | COMBINE_EQS: (66), (112) imply:
% 178.71/28.59  | | |   (114)  all_58_6 = all_52_28
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (65), (112) imply:
% 178.71/28.59  | | |   (115)   ~ (all_52_9 = all_52_28)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (95), (112) imply:
% 178.71/28.59  | | |   (116)   ~ (all_52_19 = all_52_28)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | SIMP: (116) implies:
% 178.71/28.59  | | |   (117)   ~ (all_52_19 = all_52_28)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (5), (112) imply:
% 178.71/28.59  | | |   (118)   ~ (all_52_23 = all_52_28)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | SIMP: (118) implies:
% 178.71/28.59  | | |   (119)   ~ (all_52_23 = all_52_28)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (33), (112) imply:
% 178.71/28.59  | | |   (120)   ~ (all_52_25 = all_52_28)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | SIMP: (120) implies:
% 178.71/28.59  | | |   (121)   ~ (all_52_25 = all_52_28)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (38), (112) imply:
% 178.71/28.59  | | |   (122)   ~ (all_52_28 = all_14_2)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (85), (112) imply:
% 178.71/28.59  | | |   (123)   ~ (all_52_28 = all_4_2)
% 178.71/28.59  | | | 
% 178.71/28.59  | | | REDUCE: (68), (112) imply:
% 178.71/28.59  | | |   (124)  op(e3, all_52_28) = e3
% 178.71/28.59  | | | 
% 178.71/28.59  | | | BETA: splitting (61) gives:
% 178.71/28.59  | | | 
% 178.71/28.59  | | | Case 1:
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | |   (125)  all_56_12 = e3
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | | COMBINE_EQS: (63), (125) imply:
% 178.71/28.59  | | | |   (126)  all_52_25 = e3
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | | REDUCE: (108), (126) imply:
% 178.71/28.59  | | | |   (127)  $false
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | | CLOSE: (127) is inconsistent.
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | Case 2:
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | |   (128)   ~ (all_56_12 = e3)
% 178.71/28.59  | | | |   (129)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | | BETA: splitting (45) gives:
% 178.71/28.59  | | | | 
% 178.71/28.59  | | | | Case 1:
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | |   (130)  all_56_9 = e3
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | COMBINE_EQS: (25), (130) imply:
% 178.71/28.59  | | | | |   (131)  all_52_19 = e3
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | SIMP: (131) implies:
% 178.71/28.59  | | | | |   (132)  all_52_19 = e3
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | COMBINE_EQS: (32), (132) imply:
% 178.71/28.59  | | | | |   (133)  all_58_7 = e3
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (11), (132) imply:
% 178.71/28.59  | | | | |   (134)   ~ (all_52_23 = e3)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | SIMP: (134) implies:
% 178.71/28.59  | | | | |   (135)   ~ (all_52_23 = e3)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (75), (132) imply:
% 178.71/28.59  | | | | |   (136)   ~ (all_10_2 = e3)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | SIMP: (136) implies:
% 178.71/28.59  | | | | |   (137)   ~ (all_10_2 = e3)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (67), (132) imply:
% 178.71/28.59  | | | | |   (138)  op(e2, e3) = e2
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (12), (132) imply:
% 178.71/28.59  | | | | |   (139)  op(e1, e2) = e3
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | GROUND_INST: instantiating (86) with all_52_9, e2, e3, e2, simplifying
% 178.71/28.59  | | | | |              with (100), (138) gives:
% 178.71/28.59  | | | | |   (140)  all_52_9 = e2
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | COMBINE_EQS: (77), (140) imply:
% 178.71/28.59  | | | | |   (141)  all_58_2 = e2
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (60), (140) imply:
% 178.71/28.59  | | | | |   (142)   ~ (all_52_13 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | SIMP: (142) implies:
% 178.71/28.59  | | | | |   (143)   ~ (all_52_13 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (115), (140) imply:
% 178.71/28.59  | | | | |   (144)   ~ (all_52_28 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | SIMP: (144) implies:
% 178.71/28.59  | | | | |   (145)   ~ (all_52_28 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (59), (140) imply:
% 178.71/28.59  | | | | |   (146)   ~ (all_10_2 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | SIMP: (146) implies:
% 178.71/28.59  | | | | |   (147)   ~ (all_10_2 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (28), (140) imply:
% 178.71/28.59  | | | | |   (148)   ~ (all_4_2 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | SIMP: (148) implies:
% 178.71/28.59  | | | | |   (149)   ~ (all_4_2 = e2)
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | REDUCE: (15), (140) imply:
% 178.71/28.59  | | | | |   (150)  op(e3, e2) = all_52_8
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | BETA: splitting (51) gives:
% 178.71/28.59  | | | | | 
% 178.71/28.59  | | | | | Case 1:
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | |   (151)  all_58_0 = e3
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | COMBINE_EQS: (42), (151) imply:
% 178.71/28.59  | | | | | |   (152)  all_4_2 = e3
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | REDUCE: (57), (152) imply:
% 178.71/28.59  | | | | | |   (153)   ~ (all_52_3 = e3)
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | REDUCE: (123), (152) imply:
% 178.71/28.59  | | | | | |   (154)   ~ (all_52_28 = e3)
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | REDUCE: (54), (152) imply:
% 178.71/28.59  | | | | | |   (155)  op(all_4_1, e3) = all_4_0
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | REDUCE: (39), (152) imply:
% 178.71/28.59  | | | | | |   (156)  op(e3, e3) = all_4_1
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | REDUCE: (83), (152) imply:
% 178.71/28.59  | | | | | |   (157)  op(e3, e3) = e3
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | BETA: splitting (40) gives:
% 178.71/28.59  | | | | | | 
% 178.71/28.59  | | | | | | Case 1:
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | |   (158)  all_58_2 = e3
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | | COMBINE_EQS: (141), (158) imply:
% 178.71/28.59  | | | | | | |   (159)  e3 = e2
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | | REDUCE: (98), (159) imply:
% 178.71/28.59  | | | | | | |   (160)  $false
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | | CLOSE: (160) is inconsistent.
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | Case 2:
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | |   (161)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | | BETA: splitting (161) gives:
% 178.71/28.59  | | | | | | | 
% 178.71/28.59  | | | | | | | Case 1:
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | |   (162)  all_58_3 = e3
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | | COMBINE_EQS: (24), (162) imply:
% 178.71/28.59  | | | | | | | |   (163)  all_10_2 = e3
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | | REDUCE: (137), (163) imply:
% 178.71/28.59  | | | | | | | |   (164)  $false
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | | CLOSE: (164) is inconsistent.
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | Case 2:
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | |   (165)  all_58_5 = e3 | all_58_10 = e3
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | | BETA: splitting (165) gives:
% 178.71/28.59  | | | | | | | | 
% 178.71/28.59  | | | | | | | | Case 1:
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | |   (166)  all_58_5 = e3
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | REF_CLOSE: (18), (107), (166) are inconsistent by sub-proof
% 178.71/28.59  | | | | | | | | |            #969.
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | Case 2:
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | GROUND_INST: instantiating (86) with all_52_3, all_52_8, e2,
% 178.71/28.59  | | | | | | | | |              e3, simplifying with (8), (150) gives:
% 178.71/28.59  | | | | | | | | |   (167)  all_52_3 = all_52_8
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | GROUND_INST: instantiating (86) with e3, all_4_1, e3, e3,
% 178.71/28.59  | | | | | | | | |              simplifying with (156), (157) gives:
% 178.71/28.59  | | | | | | | | |   (168)  all_4_1 = e3
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | COMBINE_EQS: (41), (167) imply:
% 178.71/28.59  | | | | | | | | |   (169)  all_58_1 = all_52_8
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | REDUCE: (50), (167) imply:
% 178.71/28.59  | | | | | | | | |   (170)   ~ (all_52_5 = all_52_8)
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | SIMP: (170) implies:
% 178.71/28.59  | | | | | | | | |   (171)   ~ (all_52_5 = all_52_8)
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | REDUCE: (153), (167) imply:
% 178.71/28.59  | | | | | | | | |   (172)   ~ (all_52_8 = e3)
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | REDUCE: (155), (168) imply:
% 178.71/28.59  | | | | | | | | |   (173)  op(e3, e3) = all_4_0
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | GROUND_INST: instantiating (86) with e3, all_4_0, e3, e3,
% 178.71/28.59  | | | | | | | | |              simplifying with (157), (173) gives:
% 178.71/28.59  | | | | | | | | |   (174)  all_4_0 = e3
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | REDUCE: (74), (174) imply:
% 178.71/28.59  | | | | | | | | |   (175)   ~ (e3 = e1)
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | BETA: splitting (3) gives:
% 178.71/28.59  | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | Case 1:
% 178.71/28.59  | | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | |   (176)  all_56_8 = e3
% 178.71/28.59  | | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | | REF_CLOSE: (113), (154), (176) are inconsistent by sub-proof
% 178.71/28.59  | | | | | | | | | |            #676.
% 178.71/28.59  | | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | Case 2:
% 178.71/28.59  | | | | | | | | | | 
% 178.71/28.59  | | | | | | | | | |   (177)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.71/28.60  | | | | | | | | | | 
% 178.71/28.60  | | | | | | | | | | BETA: splitting (17) gives:
% 178.71/28.60  | | | | | | | | | | 
% 178.71/28.60  | | | | | | | | | | Case 1:
% 178.71/28.60  | | | | | | | | | | | 
% 178.71/28.60  | | | | | | | | | | |   (178)  all_58_1 = e2
% 178.71/28.60  | | | | | | | | | | | 
% 178.71/28.60  | | | | | | | | | | | COMBINE_EQS: (169), (178) imply:
% 178.71/28.60  | | | | | | | | | | |   (179)  all_52_8 = e2
% 178.71/28.60  | | | | | | | | | | | 
% 178.71/28.60  | | | | | | | | | | | REDUCE: (171), (179) imply:
% 178.89/28.60  | | | | | | | | | | |   (180)   ~ (all_52_5 = e2)
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | REDUCE: (172), (179) imply:
% 178.89/28.60  | | | | | | | | | | |   (181)   ~ (e3 = e2)
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | BETA: splitting (72) gives:
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | |   (182)  all_58_4 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REF_CLOSE: (35), (180), (182) are inconsistent by sub-proof
% 178.89/28.60  | | | | | | | | | | | |            #675.
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | |   (183)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REF_CLOSE: (18), (52), (86), (92), (98), (103), (139), (143),
% 178.89/28.60  | | | | | | | | | | | |            (175), (183) are inconsistent by sub-proof #674.
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | |   (184)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | BETA: splitting (184) gives:
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | |   (185)  all_58_3 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | COMBINE_EQS: (24), (185) imply:
% 178.89/28.60  | | | | | | | | | | | |   (186)  all_10_2 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REDUCE: (147), (186) imply:
% 178.89/28.60  | | | | | | | | | | | |   (187)  $false
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | CLOSE: (187) is inconsistent.
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | |   (188)  all_58_7 = e2 | all_58_13 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | BETA: splitting (188) gives:
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | |   (189)  all_58_7 = e2
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | COMBINE_EQS: (133), (189) imply:
% 178.89/28.60  | | | | | | | | | | | | |   (190)  e3 = e2
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | REDUCE: (98), (190) imply:
% 178.89/28.60  | | | | | | | | | | | | |   (191)  $false
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | |   (192)  all_58_13 = e2
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | COMBINE_EQS: (64), (192) imply:
% 178.89/28.60  | | | | | | | | | | | | |   (193)  all_52_27 = e2
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | SIMP: (193) implies:
% 178.89/28.60  | | | | | | | | | | | | |   (194)  all_52_27 = e2
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | REDUCE: (87), (194) imply:
% 178.89/28.60  | | | | | | | | | | | | |   (195)   ~ (all_52_25 = e2)
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | REDUCE: (88), (194) imply:
% 178.89/28.60  | | | | | | | | | | | | |   (196)   ~ (all_6_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | SIMP: (196) implies:
% 178.89/28.60  | | | | | | | | | | | | |   (197)   ~ (all_6_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | BETA: splitting (29) gives:
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | |   (198)  all_56_15 = e2
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | REF_CLOSE: (21), (197), (198) are inconsistent by sub-proof
% 178.89/28.60  | | | | | | | | | | | | | |            #817.
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | |   (199)  all_56_15 = e1 | all_56_15 = e0
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | |   (200)  all_56_15 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | COMBINE_EQS: (21), (200) imply:
% 178.89/28.60  | | | | | | | | | | | | | | |   (201)  all_6_2 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | SIMP: (201) implies:
% 178.89/28.60  | | | | | | | | | | | | | | |   (202)  all_6_2 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | REDUCE: (79), (202) imply:
% 178.89/28.60  | | | | | | | | | | | | | | |   (203)   ~ (all_52_25 = e1)
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | |   (204)  all_58_12 = e0
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (204) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (205)  all_52_25 = e0
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | SIMP: (205) implies:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (206)  all_52_25 = e0
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | REDUCE: (121), (206) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (207)   ~ (all_52_28 = e0)
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | SIMP: (207) implies:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (208)   ~ (all_52_28 = e0)
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | REF_CLOSE: (78), (86), (106), (113), (124), (145), (177),
% 178.89/28.60  | | | | | | | | | | | | | | | |            (208) are inconsistent by sub-proof #903.
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | |   (209)   ~ (all_58_12 = e0)
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | REDUCE: (97), (209) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (210)   ~ (all_52_25 = e0)
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | REF_CLOSE: (63), (129), (195), (203), (210) are inconsistent
% 178.89/28.60  | | | | | | | | | | | | | | | |            by sub-proof #1028.
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | |   (211)  all_56_15 = e0
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (211) are inconsistent by sub-proof
% 178.89/28.60  | | | | | | | | | | | | | | |            #812.
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | End of split
% 178.89/28.60  | | | | | | | | 
% 178.89/28.60  | | | | | | | End of split
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | End of split
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | Case 2:
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | |   (212)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REF_CLOSE: (25), (32), (36), (40), (45), (52), (56), (65), (66),
% 178.89/28.60  | | | | | |            (67), (68), (70), (77), (78), (80), (83), (85), (86),
% 178.89/28.60  | | | | | |            (92), (97), (98), (100), (108), (135), (212) are
% 178.89/28.60  | | | | | |            inconsistent by sub-proof #945.
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | End of split
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | Case 2:
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | |   (213)   ~ (all_56_9 = e3)
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | REDUCE: (25), (213) imply:
% 178.89/28.60  | | | | |   (214)   ~ (all_52_19 = e3)
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | BETA: splitting (48) gives:
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | Case 1:
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | |   (215)  all_58_1 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | COMBINE_EQS: (41), (215) imply:
% 178.89/28.60  | | | | | |   (216)  all_52_3 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (50), (216) imply:
% 178.89/28.60  | | | | | |   (217)   ~ (all_52_5 = e3)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (71), (216) imply:
% 178.89/28.60  | | | | | |   (218)   ~ (all_52_19 = e3)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (57), (216) imply:
% 178.89/28.60  | | | | | |   (219)   ~ (all_4_2 = e3)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (219) implies:
% 178.89/28.60  | | | | | |   (220)   ~ (all_4_2 = e3)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (11), (17), (18), (21),
% 178.89/28.60  | | | | | |            (22), (23), (24), (26), (28), (29), (30), (31), (32),
% 178.89/28.60  | | | | | |            (35), (36), (39), (40), (42), (43), (46), (47), (51),
% 178.89/28.60  | | | | | |            (52), (53), (55), (58), (60), (64), (66), (67), (68),
% 178.89/28.60  | | | | | |            (69), (70), (72), (76), (77), (78), (79), (81), (82),
% 178.89/28.60  | | | | | |            (83), (85), (86), (87), (88), (89), (90), (91), (94),
% 178.89/28.60  | | | | | |            (96), (97), (99), (103), (106), (108), (110), (113),
% 178.89/28.60  | | | | | |            (114), (115), (117), (119), (121), (122), (123), (124),
% 178.89/28.60  | | | | | |            (214), (215), (220) are inconsistent by sub-proof #671.
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | Case 2:
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | |   (221)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | BETA: splitting (221) gives:
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | Case 1:
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | |   (222)  all_58_3 = e3
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | COMBINE_EQS: (24), (222) imply:
% 178.89/28.60  | | | | | | |   (223)  all_10_2 = e3
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | REDUCE: (16), (223) imply:
% 178.89/28.60  | | | | | | |   (224)   ~ (all_52_3 = e3)
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | REDUCE: (59), (223) imply:
% 178.89/28.60  | | | | | | |   (225)   ~ (all_52_9 = e3)
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | REF_CLOSE: (3), (8), (32), (36), (42), (51), (52), (58), (66),
% 178.89/28.60  | | | | | | |            (68), (70), (77), (78), (83), (85), (86), (90), (97),
% 178.89/28.60  | | | | | | |            (106), (110), (113), (114), (119), (121), (123), (124),
% 178.89/28.60  | | | | | | |            (214), (224), (225) are inconsistent by sub-proof #910.
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | Case 2:
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | |   (226)  all_58_7 = e3 | all_58_13 = e3
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | REF_CLOSE: (13), (32), (64), (214), (226) are inconsistent by
% 178.89/28.60  | | | | | | |            sub-proof #976.
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | End of split
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | End of split
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | End of split
% 178.89/28.60  | | | | 
% 178.89/28.60  | | | End of split
% 178.89/28.60  | | | 
% 178.89/28.60  | | Case 2:
% 178.89/28.60  | | | 
% 178.89/28.60  | | |   (227)  all_58_15 = e3
% 178.89/28.60  | | | 
% 178.89/28.60  | | | COMBINE_EQS: (27), (227) imply:
% 178.89/28.60  | | |   (228)  all_6_2 = e3
% 178.89/28.60  | | | 
% 178.89/28.60  | | | REDUCE: (14), (228) imply:
% 178.89/28.60  | | |   (229)  $false
% 178.89/28.60  | | | 
% 178.89/28.60  | | | CLOSE: (229) is inconsistent.
% 178.89/28.60  | | | 
% 178.89/28.60  | | End of split
% 178.89/28.60  | | 
% 178.89/28.60  | End of split
% 178.89/28.60  | 
% 178.89/28.60  End of proof
% 178.89/28.60  
% 178.89/28.60  Sub-proof #671 shows that the following formulas are inconsistent:
% 178.89/28.60  ----------------------------------------------------------------
% 178.89/28.60    (1)   ~ (all_52_25 = e3)
% 178.89/28.60    (2)   ~ (all_52_23 = all_14_2)
% 178.89/28.60    (3)   ~ (all_52_5 = all_52_13)
% 178.89/28.60    (4)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.89/28.60    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.89/28.60    (6)   ~ (all_52_23 = all_52_28)
% 178.89/28.60    (7)  all_58_6 = all_52_28
% 178.89/28.60    (8)   ~ (all_52_9 = all_52_25)
% 178.89/28.60    (9)  op(e3, all_52_25) = all_52_24
% 178.89/28.60    (10)   ~ (all_52_19 = all_52_23)
% 178.89/28.60    (11)  op(e3, all_52_28) = e3
% 178.89/28.60    (12)   ~ (all_52_25 = all_52_28)
% 178.89/28.60    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.89/28.60    (14)  all_58_5 = all_52_13
% 178.89/28.60    (15)  all_56_15 = all_6_2
% 178.89/28.60    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.60    (17)  op(e2, e0) = all_52_15
% 178.89/28.60    (18)   ~ (all_4_2 = e3)
% 178.89/28.60    (19)  all_58_3 = all_10_2
% 178.89/28.60    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.60    (21)  all_56_8 = all_52_28
% 178.89/28.60    (22)   ~ (all_52_9 = all_4_2)
% 178.89/28.60    (23)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.89/28.60    (24)  all_58_10 = all_52_15
% 178.89/28.60    (25)   ~ (all_52_5 = all_4_2)
% 178.89/28.60    (26)   ~ (all_52_28 = all_4_2)
% 178.89/28.60    (27)  all_58_7 = all_52_19
% 178.89/28.60    (28)  all_58_4 = all_52_5
% 178.89/28.60    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.60    (30)  op(e3, all_4_2) = all_4_1
% 178.89/28.60    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.89/28.60    (32)  all_58_0 = all_4_2
% 178.89/28.60    (33)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.60    (34)   ~ (all_52_9 = all_52_28)
% 178.89/28.60    (35)   ~ (all_4_1 = e2)
% 178.89/28.60    (36)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.89/28.60    (37)   ~ (all_52_28 = all_14_2)
% 178.89/28.60    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.60    (39)  all_58_8 = all_14_2
% 178.89/28.60    (40)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.89/28.60    (41)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.89/28.60    (42)  op(e0, e3) = all_52_25
% 178.89/28.60    (43)   ~ (all_52_5 = e3)
% 178.89/28.60    (44)   ~ (all_52_9 = all_52_13)
% 178.89/28.60    (45)   ~ (all_52_19 = all_52_28)
% 178.89/28.60    (46)  all_58_13 = all_52_27
% 178.89/28.60    (47)  all_58_1 = e3
% 178.89/28.60    (48)  all_58_6 = all_52_17
% 178.89/28.60    (49)  op(e2, all_52_19) = e2
% 178.89/28.60    (50)  op(e3, all_52_17) = e3
% 178.89/28.60    (51)  all_56_0 = all_4_2
% 178.89/28.60    (52)  all_58_11 = all_52_23
% 178.89/28.60    (53)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.89/28.60    (54)   ~ (all_52_23 = all_6_2)
% 178.89/28.60    (55)  all_58_2 = all_52_9
% 178.89/28.60    (56)  op(e3, e1) = all_52_5
% 178.89/28.60    (57)   ~ (all_52_25 = all_6_2)
% 178.89/28.60    (58)   ~ (all_52_19 = e3)
% 178.89/28.60    (59)   ~ (all_52_25 = all_4_2)
% 178.89/28.60    (60)  op(e3, e0) = all_52_7
% 178.89/28.60    (61)  op(e3, e3) = all_4_2
% 178.89/28.60    (62)   ~ (all_14_2 = e3)
% 178.89/28.60    (63)   ~ (all_52_17 = all_4_2)
% 178.89/28.60    (64)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.60    (65)   ~ (all_52_25 = all_52_27)
% 178.89/28.60    (66)   ~ (all_52_27 = all_6_2)
% 178.89/28.60    (67)   ~ (all_52_7 = all_6_2)
% 178.89/28.60    (68)  op(e0, all_52_23) = e0
% 178.89/28.60    (69)   ~ (all_52_19 = all_52_27)
% 178.89/28.60    (70)  all_58_14 = e3
% 178.89/28.60    (71)   ~ (all_52_13 = all_10_2)
% 178.89/28.60    (72)  all_58_9 = all_52_7
% 178.89/28.60    (73)  all_58_12 = all_52_25
% 178.89/28.60    (74)   ~ (all_52_19 = all_14_2)
% 178.89/28.60  
% 178.89/28.60  Begin of proof
% 178.89/28.60  | 
% 178.89/28.60  | BETA: splitting (38) gives:
% 178.89/28.60  | 
% 178.89/28.60  | Case 1:
% 178.89/28.60  | | 
% 178.89/28.60  | |   (75)  all_58_0 = e3
% 178.89/28.60  | | 
% 178.89/28.60  | | COMBINE_EQS: (32), (75) imply:
% 178.89/28.60  | |   (76)  all_4_2 = e3
% 178.89/28.60  | | 
% 178.89/28.60  | | REDUCE: (18), (76) imply:
% 178.89/28.60  | |   (77)  $false
% 178.89/28.60  | | 
% 178.89/28.60  | | CLOSE: (77) is inconsistent.
% 178.89/28.60  | | 
% 178.89/28.60  | Case 2:
% 178.89/28.60  | | 
% 178.89/28.60  | |   (78)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.60  | | 
% 178.89/28.60  | | BETA: splitting (31) gives:
% 178.89/28.60  | | 
% 178.89/28.60  | | Case 1:
% 178.89/28.60  | | | 
% 178.89/28.60  | | |   (79)  all_58_2 = e3
% 178.89/28.60  | | | 
% 178.89/28.60  | | | COMBINE_EQS: (55), (79) imply:
% 178.89/28.60  | | |   (80)  all_52_9 = e3
% 178.89/28.60  | | | 
% 178.89/28.60  | | | SIMP: (80) implies:
% 178.89/28.60  | | |   (81)  all_52_9 = e3
% 178.89/28.60  | | | 
% 178.89/28.60  | | | REDUCE: (44), (81) imply:
% 178.89/28.60  | | |   (82)   ~ (all_52_13 = e3)
% 178.89/28.60  | | | 
% 178.89/28.60  | | | SIMP: (82) implies:
% 178.89/28.60  | | |   (83)   ~ (all_52_13 = e3)
% 178.89/28.60  | | | 
% 178.89/28.60  | | | REDUCE: (8), (81) imply:
% 178.89/28.60  | | |   (84)   ~ (all_52_25 = e3)
% 178.89/28.60  | | | 
% 178.89/28.60  | | | REDUCE: (34), (81) imply:
% 178.89/28.60  | | |   (85)   ~ (all_52_28 = e3)
% 178.89/28.60  | | | 
% 178.89/28.60  | | | SIMP: (85) implies:
% 178.89/28.60  | | |   (86)   ~ (all_52_28 = e3)
% 178.89/28.60  | | | 
% 178.89/28.60  | | | REDUCE: (22), (81) imply:
% 178.89/28.60  | | |   (87)   ~ (all_4_2 = e3)
% 178.89/28.60  | | | 
% 178.89/28.60  | | | BETA: splitting (29) gives:
% 178.89/28.60  | | | 
% 178.89/28.60  | | | Case 1:
% 178.89/28.60  | | | | 
% 178.89/28.60  | | | |   (88)  all_58_6 = e3
% 178.89/28.60  | | | | 
% 178.89/28.60  | | | | REF_CLOSE: (7), (86), (88) are inconsistent by sub-proof #790.
% 178.89/28.60  | | | | 
% 178.89/28.60  | | | Case 2:
% 178.89/28.60  | | | | 
% 178.89/28.60  | | | |   (89)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.60  | | | | 
% 178.89/28.60  | | | | BETA: splitting (89) gives:
% 178.89/28.60  | | | | 
% 178.89/28.60  | | | | Case 1:
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | |   (90)  all_58_7 = e3
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | COMBINE_EQS: (27), (90) imply:
% 178.89/28.60  | | | | |   (91)  all_52_19 = e3
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | REDUCE: (58), (91) imply:
% 178.89/28.60  | | | | |   (92)  $false
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | CLOSE: (92) is inconsistent.
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | Case 2:
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | |   (93)  all_58_8 = e3 | all_58_11 = e3
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | BETA: splitting (93) gives:
% 178.89/28.60  | | | | | 
% 178.89/28.60  | | | | | Case 1:
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | |   (94)  all_58_8 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | COMBINE_EQS: (39), (94) imply:
% 178.89/28.60  | | | | | |   (95)  all_14_2 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (62), (95) imply:
% 178.89/28.60  | | | | | |   (96)  $false
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | CLOSE: (96) is inconsistent.
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | Case 2:
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | |   (97)  all_58_11 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | COMBINE_EQS: (52), (97) imply:
% 178.89/28.60  | | | | | |   (98)  all_52_23 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (98) implies:
% 178.89/28.60  | | | | | |   (99)  all_52_23 = e3
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (2), (99) imply:
% 178.89/28.60  | | | | | |   (100)   ~ (all_14_2 = e3)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (54), (99) imply:
% 178.89/28.60  | | | | | |   (101)   ~ (all_6_2 = e3)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (101) implies:
% 178.89/28.60  | | | | | |   (102)   ~ (all_6_2 = e3)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (68), (99) imply:
% 178.89/28.60  | | | | | |   (103)  op(e0, e3) = e0
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | GROUND_INST: instantiating (64) with all_52_25, e0, e3, e0,
% 178.89/28.60  | | | | | |              simplifying with (42), (103) gives:
% 178.89/28.60  | | | | | |   (104)  all_52_25 = e0
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (65), (104) imply:
% 178.89/28.60  | | | | | |   (105)   ~ (all_52_27 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (105) implies:
% 178.89/28.60  | | | | | |   (106)   ~ (all_52_27 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (12), (104) imply:
% 178.89/28.60  | | | | | |   (107)   ~ (all_52_28 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (107) implies:
% 178.89/28.60  | | | | | |   (108)   ~ (all_52_28 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (57), (104) imply:
% 178.89/28.60  | | | | | |   (109)   ~ (all_6_2 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (109) implies:
% 178.89/28.60  | | | | | |   (110)   ~ (all_6_2 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (59), (104) imply:
% 178.89/28.60  | | | | | |   (111)   ~ (all_4_2 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (111) implies:
% 178.89/28.60  | | | | | |   (112)   ~ (all_4_2 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (1), (104) imply:
% 178.89/28.60  | | | | | |   (113)   ~ (e3 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | SIMP: (113) implies:
% 178.89/28.60  | | | | | |   (114)   ~ (e3 = e0)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (9), (104) imply:
% 178.89/28.60  | | | | | |   (115)  op(e3, e0) = all_52_24
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | GROUND_INST: instantiating (64) with all_52_7, all_52_24, e0, e3,
% 178.89/28.60  | | | | | |              simplifying with (60), (115) gives:
% 178.89/28.60  | | | | | |   (116)  all_52_7 = all_52_24
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | COMBINE_EQS: (72), (116) imply:
% 178.89/28.60  | | | | | |   (117)  all_58_9 = all_52_24
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | REDUCE: (67), (116) imply:
% 178.89/28.60  | | | | | |   (118)   ~ (all_52_24 = all_6_2)
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | BETA: splitting (20) gives:
% 178.89/28.60  | | | | | | 
% 178.89/28.60  | | | | | | Case 1:
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | |   (119)  all_56_0 = e3
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | COMBINE_EQS: (51), (119) imply:
% 178.89/28.60  | | | | | | |   (120)  all_4_2 = e3
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | REDUCE: (18), (120) imply:
% 178.89/28.60  | | | | | | |   (121)  $false
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | CLOSE: (121) is inconsistent.
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | Case 2:
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | |   (122)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | BETA: splitting (4) gives:
% 178.89/28.60  | | | | | | | 
% 178.89/28.60  | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | 
% 178.89/28.60  | | | | | | | |   (123)  all_56_8 = e3
% 178.89/28.60  | | | | | | | | 
% 178.89/28.60  | | | | | | | | REF_CLOSE: (21), (86), (123) are inconsistent by sub-proof #676.
% 178.89/28.60  | | | | | | | | 
% 178.89/28.60  | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | 
% 178.89/28.60  | | | | | | | |   (124)   ~ (all_56_8 = e3)
% 178.89/28.60  | | | | | | | |   (125)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.89/28.60  | | | | | | | | 
% 178.89/28.60  | | | | | | | | BETA: splitting (16) gives:
% 178.89/28.60  | | | | | | | | 
% 178.89/28.60  | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | |   (126)  all_58_0 = e2
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | COMBINE_EQS: (32), (126) imply:
% 178.89/28.60  | | | | | | | | |   (127)  all_4_2 = e2
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | REDUCE: (26), (127) imply:
% 178.89/28.60  | | | | | | | | |   (128)   ~ (all_52_28 = e2)
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | REF_CLOSE: (11), (21), (43), (56), (64), (108), (125), (128)
% 178.89/28.60  | | | | | | | | |            are inconsistent by sub-proof #903.
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | |   (129)   ~ (all_58_0 = e2)
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | REDUCE: (32), (129) imply:
% 178.89/28.60  | | | | | | | | |   (130)   ~ (all_4_2 = e2)
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | BETA: splitting (122) gives:
% 178.89/28.60  | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | |   (131)  all_56_0 = e2
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | COMBINE_EQS: (51), (131) imply:
% 178.89/28.60  | | | | | | | | | |   (132)  all_4_2 = e2
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | REDUCE: (130), (132) imply:
% 178.89/28.60  | | | | | | | | | |   (133)  $false
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | CLOSE: (133) is inconsistent.
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | |   (134)  all_56_0 = e1 | all_56_0 = e0
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | BETA: splitting (134) gives:
% 178.89/28.60  | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | |   (135)  all_56_0 = e1
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | COMBINE_EQS: (51), (135) imply:
% 178.89/28.60  | | | | | | | | | | |   (136)  all_4_2 = e1
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | COMBINE_EQS: (32), (136) imply:
% 178.89/28.60  | | | | | | | | | | |   (137)  all_58_0 = e1
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | REDUCE: (25), (136) imply:
% 178.89/28.60  | | | | | | | | | | |   (138)   ~ (all_52_5 = e1)
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | REDUCE: (26), (136) imply:
% 178.89/28.60  | | | | | | | | | | |   (139)   ~ (all_52_28 = e1)
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | REDUCE: (30), (136) imply:
% 178.89/28.60  | | | | | | | | | | |   (140)  op(e3, e1) = all_4_1
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | BETA: splitting (125) gives:
% 178.89/28.60  | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | |   (141)  all_56_8 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | COMBINE_EQS: (21), (141) imply:
% 178.89/28.60  | | | | | | | | | | | |   (142)  all_52_28 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | SIMP: (142) implies:
% 178.89/28.60  | | | | | | | | | | | |   (143)  all_52_28 = e2
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REDUCE: (45), (143) imply:
% 178.89/28.60  | | | | | | | | | | | |   (144)   ~ (all_52_19 = e2)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REDUCE: (37), (143) imply:
% 178.89/28.60  | | | | | | | | | | | |   (145)   ~ (all_14_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | SIMP: (145) implies:
% 178.89/28.60  | | | | | | | | | | | |   (146)   ~ (all_14_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REDUCE: (86), (143) imply:
% 178.89/28.60  | | | | | | | | | | | |   (147)   ~ (e3 = e2)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | SIMP: (147) implies:
% 178.89/28.60  | | | | | | | | | | | |   (148)   ~ (e3 = e2)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REDUCE: (139), (143) imply:
% 178.89/28.60  | | | | | | | | | | | |   (149)   ~ (e2 = e1)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | GROUND_INST: instantiating (64) with all_52_5, all_4_1, e1, e3,
% 178.89/28.60  | | | | | | | | | | | |              simplifying with (56), (140) gives:
% 178.89/28.60  | | | | | | | | | | | |   (150)  all_52_5 = all_4_1
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | COMBINE_EQS: (28), (150) imply:
% 178.89/28.60  | | | | | | | | | | | |   (151)  all_58_4 = all_4_1
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REDUCE: (3), (150) imply:
% 178.89/28.60  | | | | | | | | | | | |   (152)   ~ (all_52_13 = all_4_1)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | SIMP: (152) implies:
% 178.89/28.60  | | | | | | | | | | | |   (153)   ~ (all_52_13 = all_4_1)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | REDUCE: (138), (150) imply:
% 178.89/28.60  | | | | | | | | | | | |   (154)   ~ (all_4_1 = e1)
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | BETA: splitting (41) gives:
% 178.89/28.60  | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | |   (155)  all_58_0 = e2
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | REF_CLOSE: (137), (149), (155) are inconsistent by sub-proof
% 178.89/28.60  | | | | | | | | | | | | |            #930.
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | |   (156)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | BETA: splitting (156) gives:
% 178.89/28.60  | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | |   (157)  all_58_1 = e2
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | COMBINE_EQS: (47), (157) imply:
% 178.89/28.60  | | | | | | | | | | | | | |   (158)  e3 = e2
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | REDUCE: (148), (158) imply:
% 178.89/28.60  | | | | | | | | | | | | | |   (159)  $false
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | |   (160)   ~ (all_58_1 = e2)
% 178.89/28.60  | | | | | | | | | | | | | |   (161)  all_58_4 = e2 | all_58_9 = e2
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 178.89/28.60  | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | |   (162)  all_58_4 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | REF_CLOSE: (35), (151), (162) are inconsistent by sub-proof
% 178.89/28.60  | | | | | | | | | | | | | | |            #673.
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | |   (163)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 178.89/28.60  | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | |   (164)  all_58_5 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (164) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (165)  all_52_13 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | SIMP: (165) implies:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (166)  all_52_13 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | REDUCE: (71), (166) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (167)   ~ (all_10_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (168)   ~ (all_10_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | REDUCE: (153), (166) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | |   (169)   ~ (all_4_1 = e2)
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 178.89/28.60  | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | |   (170)  all_58_1 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (170) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | |   (171)  e3 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | REDUCE: (148), (171) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | |   (172)  $false
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | |   (173)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 178.89/28.60  | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | |   (174)  all_58_4 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (174) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | |   (175)  all_4_1 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | REDUCE: (154), (175) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | |   (176)  $false
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | |   (177)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | |   (178)  all_58_4 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (178) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | |   (179)  all_4_1 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | REDUCE: (35), (179) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | |   (180)  $false
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | |   (181)  all_58_9 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (181) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | |   (182)  all_52_24 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | REDUCE: (118), (182) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | |   (183)   ~ (all_6_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | SIMP: (183) implies:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | |   (184)   ~ (all_6_2 = e2)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | |   (185)  all_56_15 = e2
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (184), (185) are inconsistent by sub-proof
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | |            #817.
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | |   (186)   ~ (all_56_15 = e2)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | |   (187)  all_56_15 = e1 | all_56_15 = e0
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (188)  all_56_15 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (188) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (189)  all_6_2 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | SIMP: (189) implies:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (190)  all_6_2 = e1
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (190) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (191)   ~ (all_52_27 = e1)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (190) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (192)   ~ (e3 = e1)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | SIMP: (192) implies:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (193)   ~ (e3 = e1)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | REDUCE: (184), (190) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (194)   ~ (e2 = e1)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (190) imply:
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | |   (195)   ~ (e1 = e0)
% 178.89/28.60  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | |   (196)  all_58_3 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (196) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | |   (197)  all_10_2 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (197) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | |   (198)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (198) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | |   (199)  all_58_7 = e2 | all_58_13 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_58_5 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (200) are inconsistent by sub-proof
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | |            #672.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_58_8 = e1 | all_58_14 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_58_8 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (202) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_14_2 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (74), (203) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | |   (204)   ~ (all_52_19 = e1)
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_58_7 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (205) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_52_19 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (206) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_58_13 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (208) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_52_27 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (209) implies:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_52_27 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (210) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (211)   ~ (e2 = e0)
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_58_1 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (212) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  e3 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (213) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_58_3 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (216) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_10_2 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  all_58_1 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (218) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  e3 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (219) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_58_3 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (216), (222) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  e1 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (223) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_58_7 = e0 | all_58_13 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_58_9 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (181), (226) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  e2 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (227) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)   ~ (all_58_9 = e0)
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_58_10 = e0 | all_58_11 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_58_7 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (231) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_52_19 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (232) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)   ~ (e2 = e0)
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (49), (232) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  op(e2, e0) = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (24), (64), (97), (114), (211), (230), (234)
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #699.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_58_13 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (235) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  e2 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (236) implies:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  e2 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (211), (237) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_58_7 = e1 | all_58_13 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (46), (191), (204), (239) are inconsistent
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #752.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_58_14 = e1
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (193), (240) are inconsistent by sub-proof
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | |            #881.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | |   (241)  all_56_15 = e0
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (110), (241) are inconsistent by sub-proof
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | |            #812.
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | |   (242)  all_58_8 = e2 | all_58_14 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 178.89/28.61  | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | Case 1:
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | |   (243)  all_58_8 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (243) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | |   (244)  all_14_2 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | REDUCE: (146), (244) imply:
% 178.89/28.61  | | | | | | | | | | | | | | | | |   (245)  $false
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | CLOSE: (245) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | |   (246)  all_58_14 = e2
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (148), (246) are inconsistent by sub-proof
% 178.89/28.61  | | | | | | | | | | | | | | | | |            #905.
% 178.89/28.61  | | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | |   (247)  all_56_8 = e1 | all_56_8 = e0
% 178.89/28.61  | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | | REF_CLOSE: (11), (21), (43), (56), (64), (108), (247) are
% 178.89/28.61  | | | | | | | | | | | |            inconsistent by sub-proof #911.
% 178.89/28.61  | | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | Case 2:
% 178.89/28.61  | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | |   (248)  all_56_0 = e0
% 178.89/28.61  | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | COMBINE_EQS: (51), (248) imply:
% 178.89/28.61  | | | | | | | | | | |   (249)  all_4_2 = e0
% 178.89/28.61  | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | REDUCE: (112), (249) imply:
% 178.89/28.61  | | | | | | | | | | |   (250)  $false
% 178.89/28.61  | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | | CLOSE: (250) is inconsistent.
% 178.89/28.61  | | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | | 
% 178.89/28.61  | | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | | 
% 178.89/28.61  | | | | | | | | End of split
% 178.89/28.61  | | | | | | | | 
% 178.89/28.61  | | | | | | | End of split
% 178.89/28.61  | | | | | | | 
% 178.89/28.61  | | | | | | End of split
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | End of split
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | End of split
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | End of split
% 178.89/28.61  | | | 
% 178.89/28.61  | | Case 2:
% 178.89/28.61  | | | 
% 178.89/28.61  | | |   (251)   ~ (all_58_2 = e3)
% 178.89/28.61  | | | 
% 178.89/28.61  | | | REF_CLOSE: (1), (48), (50), (55), (61), (63), (64), (73), (78), (251) are
% 178.89/28.61  | | |            inconsistent by sub-proof #946.
% 178.89/28.61  | | | 
% 178.89/28.61  | | End of split
% 178.89/28.61  | | 
% 178.89/28.61  | End of split
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #672 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  all_58_5 = e2
% 178.89/28.61    (2)  all_58_5 = e1
% 178.89/28.61    (3)   ~ (e2 = e1)
% 178.89/28.61  
% 178.89/28.61  Begin of proof
% 178.89/28.61  | 
% 178.89/28.61  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.61  |   (4)  e2 = e1
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (4) implies:
% 178.89/28.61  |   (5)  e2 = e1
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (3), (5) imply:
% 178.89/28.61  |   (6)  $false
% 178.89/28.61  | 
% 178.89/28.61  | CLOSE: (6) is inconsistent.
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #673 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  all_58_4 = all_4_1
% 178.89/28.61    (2)  all_58_4 = e2
% 178.89/28.61    (3)   ~ (all_4_1 = e2)
% 178.89/28.61  
% 178.89/28.61  Begin of proof
% 178.89/28.61  | 
% 178.89/28.61  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.61  |   (4)  all_4_1 = e2
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (4) implies:
% 178.89/28.61  |   (5)  all_4_1 = e2
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (3), (5) imply:
% 178.89/28.61  |   (6)  $false
% 178.89/28.61  | 
% 178.89/28.61  | CLOSE: (6) is inconsistent.
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #674 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  all_58_5 = all_52_13
% 178.89/28.61    (2)   ~ (e3 = e1)
% 178.89/28.61    (3)  all_58_8 = all_14_2
% 178.89/28.61    (4)  all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.89/28.61    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.61    (6)   ~ (all_52_13 = e2)
% 178.89/28.61    (7)  all_58_14 = e3
% 178.89/28.61    (8)  op(e1, all_14_2) = e1
% 178.89/28.61    (9)   ~ (e3 = e2)
% 178.89/28.61    (10)  op(e1, e2) = e3
% 178.89/28.61  
% 178.89/28.61  Begin of proof
% 178.89/28.61  | 
% 178.89/28.61  | BETA: splitting (4) gives:
% 178.89/28.61  | 
% 178.89/28.61  | Case 1:
% 178.89/28.61  | | 
% 178.89/28.61  | |   (11)  all_58_5 = e2
% 178.89/28.61  | | 
% 178.89/28.61  | | COMBINE_EQS: (1), (11) imply:
% 178.89/28.61  | |   (12)  all_52_13 = e2
% 178.89/28.61  | | 
% 178.89/28.61  | | REDUCE: (6), (12) imply:
% 178.89/28.61  | |   (13)  $false
% 178.89/28.61  | | 
% 178.89/28.61  | | CLOSE: (13) is inconsistent.
% 178.89/28.61  | | 
% 178.89/28.61  | Case 2:
% 178.89/28.61  | | 
% 178.89/28.61  | |   (14)  all_58_8 = e2 | all_58_14 = e2
% 178.89/28.61  | | 
% 178.89/28.61  | | BETA: splitting (14) gives:
% 178.89/28.61  | | 
% 178.89/28.61  | | Case 1:
% 178.89/28.61  | | | 
% 178.89/28.61  | | |   (15)  all_58_8 = e2
% 178.89/28.61  | | | 
% 178.89/28.61  | | | COMBINE_EQS: (3), (15) imply:
% 178.89/28.61  | | |   (16)  all_14_2 = e2
% 178.89/28.61  | | | 
% 178.89/28.61  | | | REDUCE: (8), (16) imply:
% 178.89/28.61  | | |   (17)  op(e1, e2) = e1
% 178.89/28.61  | | | 
% 178.89/28.61  | | | REF_CLOSE: (2), (5), (10), (17) are inconsistent by sub-proof #861.
% 178.89/28.61  | | | 
% 178.89/28.61  | | Case 2:
% 178.89/28.61  | | | 
% 178.89/28.61  | | |   (18)  all_58_14 = e2
% 178.89/28.61  | | | 
% 178.89/28.61  | | | REF_CLOSE: (7), (9), (18) are inconsistent by sub-proof #905.
% 178.89/28.61  | | | 
% 178.89/28.61  | | End of split
% 178.89/28.61  | | 
% 178.89/28.61  | End of split
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #675 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  all_58_4 = all_52_5
% 178.89/28.61    (2)  all_58_4 = e2
% 178.89/28.61    (3)   ~ (all_52_5 = e2)
% 178.89/28.61  
% 178.89/28.61  Begin of proof
% 178.89/28.61  | 
% 178.89/28.61  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.61  |   (4)  all_52_5 = e2
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (4) implies:
% 178.89/28.61  |   (5)  all_52_5 = e2
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (3), (5) imply:
% 178.89/28.61  |   (6)  $false
% 178.89/28.61  | 
% 178.89/28.61  | CLOSE: (6) is inconsistent.
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #676 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  all_56_8 = all_52_28
% 178.89/28.61    (2)  all_56_8 = e3
% 178.89/28.61    (3)   ~ (all_52_28 = e3)
% 178.89/28.61  
% 178.89/28.61  Begin of proof
% 178.89/28.61  | 
% 178.89/28.61  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.61  |   (4)  all_52_28 = e3
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (4) implies:
% 178.89/28.61  |   (5)  all_52_28 = e3
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (3), (5) imply:
% 178.89/28.61  |   (6)  $false
% 178.89/28.61  | 
% 178.89/28.61  | CLOSE: (6) is inconsistent.
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #677 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  op(e2, all_10_2) = all_10_1
% 178.89/28.61    (2)   ~ (all_52_9 = all_52_25)
% 178.89/28.61    (3)  op(e1, e2) = all_52_19
% 178.89/28.61    (4)  all_58_5 = all_52_13
% 178.89/28.61    (5)  all_58_3 = all_10_2
% 178.89/28.61    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.61    (7)  all_58_15 = all_6_2
% 178.89/28.61    (8)   ~ (all_52_9 = all_4_2)
% 178.89/28.61    (9)   ~ (all_52_5 = all_52_7)
% 178.89/28.61    (10)  all_58_10 = all_52_15
% 178.89/28.61    (11)   ~ (all_52_5 = all_4_2)
% 178.89/28.61    (12)  all_58_7 = all_52_19
% 178.89/28.61    (13)   ~ (all_52_17 = all_52_25)
% 178.89/28.61    (14)  all_58_4 = all_52_5
% 178.89/28.61    (15)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.61    (16)   ~ (e3 = e1)
% 178.89/28.61    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.89/28.61    (18)   ~ (all_52_7 = all_4_2)
% 178.89/28.61    (19)  all_58_1 = all_52_3
% 178.89/28.61    (20)  all_58_0 = all_4_2
% 178.89/28.61    (21)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.61    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.61    (23)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.89/28.61    (24)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.89/28.61    (25)  op(e2, e1) = all_52_13
% 178.89/28.61    (26)  all_58_8 = all_14_2
% 178.89/28.61    (27)   ~ (all_52_5 = all_14_2)
% 178.89/28.61    (28)  op(e0, e3) = all_52_25
% 178.89/28.61    (29)   ~ (all_52_9 = all_10_2)
% 178.89/28.61    (30)   ~ (all_52_13 = all_14_2)
% 178.89/28.61    (31)   ~ (e3 = e0)
% 178.89/28.61    (32)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.89/28.61    (33)   ~ (all_52_9 = all_52_13)
% 178.89/28.61    (34)   ~ (all_52_15 = all_52_23)
% 178.89/28.61    (35)  all_58_13 = all_52_27
% 178.89/28.61    (36)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.61    (37)  all_56_5 = all_10_2
% 178.89/28.61    (38)  all_58_12 = e3
% 178.89/28.61    (39)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.61    (40)   ~ (all_52_9 = all_52_17)
% 178.89/28.61    (41)  all_58_6 = all_52_17
% 178.89/28.61    (42)  op(e2, all_52_19) = e2
% 178.89/28.61    (43)  op(e3, all_52_17) = e3
% 178.89/28.61    (44)   ~ (e1 = e0)
% 178.89/28.61    (45)  all_56_0 = all_4_2
% 178.89/28.61    (46)  all_58_11 = all_52_23
% 178.89/28.61    (47)   ~ (all_52_3 = all_52_19)
% 178.89/28.61    (48)   ~ (all_52_7 = all_52_15)
% 178.89/28.61    (49)   ~ (all_52_19 = all_10_2)
% 178.89/28.61    (50)  all_58_2 = all_52_9
% 178.89/28.61    (51)  op(e3, e1) = all_52_5
% 178.89/28.61    (52)   ~ (e2 = e1)
% 178.89/28.61    (53)   ~ (all_52_25 = all_6_2)
% 178.89/28.61    (54)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.89/28.61    (55)  op(e1, e3) = all_52_17
% 178.89/28.61    (56)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.89/28.61    (57)   ~ (all_52_25 = all_4_2)
% 178.89/28.61    (58)  op(e3, e0) = all_52_7
% 178.89/28.61    (59)   ~ (all_10_1 = e3)
% 178.89/28.61    (60)   ~ (all_52_17 = all_4_2)
% 178.89/28.61    (61)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.61    (62)   ~ (all_52_25 = all_52_27)
% 178.89/28.61    (63)  op(e0, all_52_23) = e0
% 178.89/28.61    (64)   ~ (all_52_15 = all_10_2)
% 178.89/28.61    (65)  all_56_7 = all_52_15
% 178.89/28.61    (66)  op(e1, all_14_2) = e1
% 178.89/28.61    (67)   ~ (all_52_7 = all_52_23)
% 178.89/28.61    (68)   ~ (all_52_17 = all_52_19)
% 178.89/28.61    (69)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.89/28.61    (70)  all_58_9 = all_52_7
% 178.89/28.61    (71)   ~ (e2 = e0)
% 178.89/28.61    (72)  all_58_12 = all_52_25
% 178.89/28.61    (73)  all_56_6 = all_52_13
% 178.89/28.61    (74)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.61    (75)   ~ (all_52_9 = all_52_15)
% 178.89/28.61    (76)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.61    (77)  op(e2, e3) = all_52_9
% 178.89/28.61  
% 178.89/28.61  Begin of proof
% 178.89/28.61  | 
% 178.89/28.61  | COMBINE_EQS: (38), (72) imply:
% 178.89/28.61  |   (78)  all_52_25 = e3
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (78) implies:
% 178.89/28.61  |   (79)  all_52_25 = e3
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (2), (79) imply:
% 178.89/28.61  |   (80)   ~ (all_52_9 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (13), (79) imply:
% 178.89/28.61  |   (81)   ~ (all_52_17 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (62), (79) imply:
% 178.89/28.61  |   (82)   ~ (all_52_27 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (82) implies:
% 178.89/28.61  |   (83)   ~ (all_52_27 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (53), (79) imply:
% 178.89/28.61  |   (84)   ~ (all_6_2 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (84) implies:
% 178.89/28.61  |   (85)   ~ (all_6_2 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (57), (79) imply:
% 178.89/28.61  |   (86)   ~ (all_4_2 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | SIMP: (86) implies:
% 178.89/28.61  |   (87)   ~ (all_4_2 = e3)
% 178.89/28.61  | 
% 178.89/28.61  | REDUCE: (28), (79) imply:
% 178.89/28.61  |   (88)  op(e0, e3) = e3
% 178.89/28.61  | 
% 178.89/28.61  | BETA: splitting (6) gives:
% 178.89/28.61  | 
% 178.89/28.61  | Case 1:
% 178.89/28.61  | | 
% 178.89/28.61  | |   (89)  all_56_0 = e3
% 178.89/28.61  | | 
% 178.89/28.61  | | COMBINE_EQS: (45), (89) imply:
% 178.89/28.61  | |   (90)  all_4_2 = e3
% 178.89/28.61  | | 
% 178.89/28.61  | | REDUCE: (87), (90) imply:
% 178.89/28.61  | |   (91)  $false
% 178.89/28.61  | | 
% 178.89/28.61  | | CLOSE: (91) is inconsistent.
% 178.89/28.61  | | 
% 178.89/28.61  | Case 2:
% 178.89/28.61  | | 
% 178.89/28.61  | |   (92)   ~ (all_56_0 = e3)
% 178.89/28.61  | |   (93)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.61  | | 
% 178.89/28.61  | | BETA: splitting (69) gives:
% 178.89/28.61  | | 
% 178.89/28.61  | | Case 1:
% 178.89/28.61  | | | 
% 178.89/28.61  | | |   (94)  all_58_9 = e3
% 178.89/28.61  | | | 
% 178.89/28.61  | | | COMBINE_EQS: (70), (94) imply:
% 178.89/28.61  | | |   (95)  all_52_7 = e3
% 178.89/28.61  | | | 
% 178.89/28.61  | | | SIMP: (95) implies:
% 178.89/28.61  | | |   (96)  all_52_7 = e3
% 178.89/28.61  | | | 
% 178.89/28.61  | | | REDUCE: (48), (96) imply:
% 178.89/28.61  | | |   (97)   ~ (all_52_15 = e3)
% 178.89/28.61  | | | 
% 178.89/28.61  | | | SIMP: (97) implies:
% 178.89/28.61  | | |   (98)   ~ (all_52_15 = e3)
% 178.89/28.61  | | | 
% 178.89/28.61  | | | REDUCE: (67), (96) imply:
% 178.89/28.61  | | |   (99)   ~ (all_52_23 = e3)
% 178.89/28.61  | | | 
% 178.89/28.61  | | | SIMP: (99) implies:
% 178.89/28.61  | | |   (100)   ~ (all_52_23 = e3)
% 178.89/28.61  | | | 
% 178.89/28.61  | | | BETA: splitting (15) gives:
% 178.89/28.61  | | | 
% 178.89/28.61  | | | Case 1:
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | |   (101)  all_58_6 = e3
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | | REF_CLOSE: (41), (81), (101) are inconsistent by sub-proof #981.
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | Case 2:
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | |   (102)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | | BETA: splitting (17) gives:
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | | Case 1:
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | |   (103)  all_58_2 = e3
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | | REF_CLOSE: (50), (80), (103) are inconsistent by sub-proof #980.
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | Case 2:
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | |   (104)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | | BETA: splitting (23) gives:
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | | Case 1:
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | |   (105)  all_56_6 = e3
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | COMBINE_EQS: (73), (105) imply:
% 178.89/28.61  | | | | | |   (106)  all_52_13 = e3
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | SIMP: (106) implies:
% 178.89/28.61  | | | | | |   (107)  all_52_13 = e3
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | REDUCE: (30), (107) imply:
% 178.89/28.61  | | | | | |   (108)   ~ (all_14_2 = e3)
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | SIMP: (108) implies:
% 178.89/28.61  | | | | | |   (109)   ~ (all_14_2 = e3)
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | REDUCE: (25), (107) imply:
% 178.89/28.61  | | | | | |   (110)  op(e2, e1) = e3
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | REF_CLOSE: (1), (3), (5), (10), (12), (16), (21), (24), (26), (29),
% 178.89/28.61  | | | | | |            (31), (37), (39), (40), (41), (42), (46), (49), (50),
% 178.89/28.61  | | | | | |            (52), (54), (59), (61), (64), (66), (71), (77), (80),
% 178.89/28.61  | | | | | |            (94), (100), (102), (109), (110) are inconsistent by
% 178.89/28.61  | | | | | |            sub-proof #684.
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | Case 2:
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | |   (111)   ~ (all_56_6 = e3)
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | REDUCE: (73), (111) imply:
% 178.89/28.61  | | | | | |   (112)   ~ (all_52_13 = e3)
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | | REF_CLOSE: (4), (5), (10), (12), (26), (27), (43), (46), (49), (51),
% 178.89/28.61  | | | | | |            (55), (61), (66), (98), (100), (102), (104), (112) are
% 178.89/28.61  | | | | | |            inconsistent by sub-proof #683.
% 178.89/28.61  | | | | | | 
% 178.89/28.61  | | | | | End of split
% 178.89/28.61  | | | | | 
% 178.89/28.61  | | | | End of split
% 178.89/28.61  | | | | 
% 178.89/28.61  | | | End of split
% 178.89/28.61  | | | 
% 178.89/28.61  | | Case 2:
% 178.89/28.61  | | | 
% 178.89/28.61  | | |   (113)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.89/28.61  | | | 
% 178.89/28.61  | | | REF_CLOSE: (3), (5), (7), (8), (9), (10), (11), (12), (14), (15), (16),
% 178.89/28.61  | | |            (18), (19), (20), (21), (22), (26), (27), (31), (32), (34),
% 178.89/28.61  | | |            (35), (36), (38), (39), (40), (41), (42), (43), (44), (45),
% 178.89/28.61  | | |            (46), (47), (48), (50), (51), (52), (55), (56), (58), (60),
% 178.89/28.61  | | |            (61), (63), (64), (65), (66), (68), (70), (71), (74), (75),
% 178.89/28.61  | | |            (76), (77), (81), (83), (85), (87), (88), (93), (113) are
% 178.89/28.61  | | |            inconsistent by sub-proof #678.
% 178.89/28.61  | | | 
% 178.89/28.61  | | End of split
% 178.89/28.61  | | 
% 178.89/28.61  | End of split
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #678 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  op(e1, e2) = all_52_19
% 178.89/28.61    (2)   ~ (all_52_27 = e3)
% 178.89/28.61    (3)   ~ (all_52_17 = e3)
% 178.89/28.61    (4)   ~ (all_6_2 = e3)
% 178.89/28.61    (5)   ~ (all_4_2 = e3)
% 178.89/28.61    (6)  all_58_3 = all_10_2
% 178.89/28.61    (7)  all_58_15 = all_6_2
% 178.89/28.61    (8)   ~ (all_52_9 = all_4_2)
% 178.89/28.61    (9)   ~ (all_52_5 = all_52_7)
% 178.89/28.61    (10)  all_58_10 = all_52_15
% 178.89/28.61    (11)   ~ (all_52_5 = all_4_2)
% 178.89/28.61    (12)  all_58_7 = all_52_19
% 178.89/28.61    (13)  all_58_4 = all_52_5
% 178.89/28.61    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.61    (15)   ~ (e3 = e1)
% 178.89/28.61    (16)   ~ (all_52_7 = all_4_2)
% 178.89/28.61    (17)  all_58_1 = all_52_3
% 178.89/28.61    (18)  all_58_0 = all_4_2
% 178.89/28.61    (19)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.61    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.61    (21)  op(e0, e3) = e3
% 178.89/28.61    (22)  all_58_8 = all_14_2
% 178.89/28.61    (23)   ~ (all_52_5 = all_14_2)
% 178.89/28.61    (24)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.89/28.61    (25)   ~ (e3 = e0)
% 178.89/28.61    (26)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.89/28.61    (27)   ~ (all_52_15 = all_52_23)
% 178.89/28.61    (28)  all_58_13 = all_52_27
% 178.89/28.61    (29)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.61    (30)  all_58_12 = e3
% 178.89/28.61    (31)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.61    (32)   ~ (all_52_9 = all_52_17)
% 178.89/28.61    (33)  all_58_6 = all_52_17
% 178.89/28.61    (34)  op(e2, all_52_19) = e2
% 178.89/28.61    (35)  op(e3, all_52_17) = e3
% 178.89/28.61    (36)   ~ (e1 = e0)
% 178.89/28.61    (37)  all_56_0 = all_4_2
% 178.89/28.61    (38)  all_58_11 = all_52_23
% 178.89/28.61    (39)   ~ (all_52_3 = all_52_19)
% 178.89/28.61    (40)   ~ (all_52_7 = all_52_15)
% 178.89/28.61    (41)  all_58_2 = all_52_9
% 178.89/28.61    (42)  op(e3, e1) = all_52_5
% 178.89/28.61    (43)   ~ (e2 = e1)
% 178.89/28.61    (44)  op(e1, e3) = all_52_17
% 178.89/28.61    (45)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.89/28.61    (46)  op(e3, e0) = all_52_7
% 178.89/28.61    (47)   ~ (all_52_17 = all_4_2)
% 178.89/28.61    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.61    (49)  op(e0, all_52_23) = e0
% 178.89/28.61    (50)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.61    (51)   ~ (all_52_15 = all_10_2)
% 178.89/28.61    (52)  all_56_7 = all_52_15
% 178.89/28.61    (53)  op(e1, all_14_2) = e1
% 178.89/28.61    (54)   ~ (all_52_17 = all_52_19)
% 178.89/28.61    (55)  all_58_9 = all_52_7
% 178.89/28.61    (56)   ~ (e2 = e0)
% 178.89/28.61    (57)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.61    (58)   ~ (all_52_9 = all_52_15)
% 178.89/28.61    (59)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.61    (60)  op(e2, e3) = all_52_9
% 178.89/28.61  
% 178.89/28.61  Begin of proof
% 178.89/28.61  | 
% 178.89/28.61  | BETA: splitting (57) gives:
% 178.89/28.61  | 
% 178.89/28.61  | Case 1:
% 178.89/28.61  | | 
% 178.89/28.61  | |   (61)  all_58_0 = e3
% 178.89/28.61  | | 
% 178.89/28.61  | | COMBINE_EQS: (18), (61) imply:
% 178.89/28.61  | |   (62)  all_4_2 = e3
% 178.89/28.61  | | 
% 178.89/28.61  | | REDUCE: (5), (62) imply:
% 178.89/28.61  | |   (63)  $false
% 178.89/28.61  | | 
% 178.89/28.61  | | CLOSE: (63) is inconsistent.
% 178.89/28.61  | | 
% 178.89/28.61  | Case 2:
% 178.89/28.61  | | 
% 178.89/28.61  | |   (64)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.61  | | 
% 178.89/28.61  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.89/28.61  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.89/28.61  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 178.89/28.61  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 178.89/28.61  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (58),
% 178.89/28.61  | |            (59), (60), (64) are inconsistent by sub-proof #679.
% 178.89/28.61  | | 
% 178.89/28.61  | End of split
% 178.89/28.61  | 
% 178.89/28.61  End of proof
% 178.89/28.61  
% 178.89/28.61  Sub-proof #679 shows that the following formulas are inconsistent:
% 178.89/28.61  ----------------------------------------------------------------
% 178.89/28.61    (1)  op(e1, e2) = all_52_19
% 178.89/28.61    (2)   ~ (all_52_27 = e3)
% 178.89/28.61    (3)   ~ (all_52_17 = e3)
% 178.89/28.61    (4)   ~ (all_6_2 = e3)
% 178.89/28.61    (5)  all_58_3 = all_10_2
% 178.89/28.61    (6)  all_58_15 = all_6_2
% 178.89/28.61    (7)   ~ (all_52_9 = all_4_2)
% 178.89/28.61    (8)   ~ (all_52_5 = all_52_7)
% 178.89/28.61    (9)  all_58_10 = all_52_15
% 178.89/28.61    (10)   ~ (all_52_5 = all_4_2)
% 178.89/28.61    (11)  all_58_7 = all_52_19
% 178.89/28.61    (12)  all_58_4 = all_52_5
% 178.89/28.61    (13)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.61    (14)   ~ (e3 = e1)
% 178.89/28.61    (15)   ~ (all_52_7 = all_4_2)
% 178.89/28.61    (16)  all_58_1 = all_52_3
% 178.89/28.61    (17)  all_58_0 = all_4_2
% 178.89/28.61    (18)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.61    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.61    (20)  op(e0, e3) = e3
% 178.89/28.61    (21)  all_58_8 = all_14_2
% 178.89/28.61    (22)   ~ (all_52_5 = all_14_2)
% 178.89/28.61    (23)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.89/28.61    (24)   ~ (e3 = e0)
% 178.89/28.61    (25)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.89/28.61    (26)   ~ (all_52_15 = all_52_23)
% 178.89/28.61    (27)  all_58_13 = all_52_27
% 178.89/28.61    (28)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.61    (29)  all_58_12 = e3
% 178.89/28.61    (30)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.61    (31)   ~ (all_52_9 = all_52_17)
% 178.89/28.61    (32)  all_58_6 = all_52_17
% 178.89/28.61    (33)  op(e2, all_52_19) = e2
% 178.89/28.61    (34)  op(e3, all_52_17) = e3
% 178.89/28.61    (35)   ~ (e1 = e0)
% 178.89/28.61    (36)  all_56_0 = all_4_2
% 178.89/28.61    (37)  all_58_11 = all_52_23
% 178.89/28.61    (38)   ~ (all_52_3 = all_52_19)
% 178.89/28.61    (39)   ~ (all_52_7 = all_52_15)
% 178.89/28.61    (40)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.61    (41)  all_58_2 = all_52_9
% 178.89/28.62    (42)  op(e3, e1) = all_52_5
% 178.89/28.62    (43)   ~ (e2 = e1)
% 178.89/28.62    (44)  op(e1, e3) = all_52_17
% 178.89/28.62    (45)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.89/28.62    (46)  op(e3, e0) = all_52_7
% 178.89/28.62    (47)   ~ (all_52_17 = all_4_2)
% 178.89/28.62    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.62    (49)  op(e0, all_52_23) = e0
% 178.89/28.62    (50)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.62    (51)   ~ (all_52_15 = all_10_2)
% 178.89/28.62    (52)  all_56_7 = all_52_15
% 178.89/28.62    (53)  op(e1, all_14_2) = e1
% 178.89/28.62    (54)   ~ (all_52_17 = all_52_19)
% 178.89/28.62    (55)  all_58_9 = all_52_7
% 178.89/28.62    (56)   ~ (e2 = e0)
% 178.89/28.62    (57)   ~ (all_52_9 = all_52_15)
% 178.89/28.62    (58)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.62    (59)  op(e2, e3) = all_52_9
% 178.89/28.62  
% 178.89/28.62  Begin of proof
% 178.89/28.62  | 
% 178.89/28.62  | BETA: splitting (45) gives:
% 178.89/28.62  | 
% 178.89/28.62  | Case 1:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (60)  all_56_7 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (52), (60) imply:
% 178.89/28.62  | |   (61)  all_52_15 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (61) implies:
% 178.89/28.62  | |   (62)  all_52_15 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (9), (62) imply:
% 178.89/28.62  | |   (63)  all_58_10 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (39), (62) imply:
% 178.89/28.62  | |   (64)   ~ (all_52_7 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (57), (62) imply:
% 178.89/28.62  | |   (65)   ~ (all_52_9 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (26), (62) imply:
% 178.89/28.62  | |   (66)   ~ (all_52_23 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (66) implies:
% 178.89/28.62  | |   (67)   ~ (all_52_23 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (51), (62) imply:
% 178.89/28.62  | |   (68)   ~ (all_10_2 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (68) implies:
% 178.89/28.62  | |   (69)   ~ (all_10_2 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (13), (14), (15),
% 178.89/28.62  | |            (16), (17), (18), (19), (21), (22), (24), (25), (27), (28), (29),
% 178.89/28.62  | |            (30), (31), (32), (33), (34), (35), (36), (37), (38), (40), (41),
% 178.89/28.62  | |            (42), (43), (44), (46), (47), (48), (50), (53), (54), (55), (56),
% 178.89/28.62  | |            (58), (59), (63), (64), (65), (67), (69) are inconsistent by
% 178.89/28.62  | |            sub-proof #680.
% 178.89/28.62  | | 
% 178.89/28.62  | Case 2:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (70)   ~ (all_56_7 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (52), (70) imply:
% 178.89/28.62  | |   (71)   ~ (all_52_15 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | BETA: splitting (23) gives:
% 178.89/28.62  | | 
% 178.89/28.62  | | Case 1:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (72)  all_58_10 = e3
% 178.89/28.62  | | | 
% 178.89/28.62  | | | REF_CLOSE: (9), (71), (72) are inconsistent by sub-proof #1018.
% 178.89/28.62  | | | 
% 178.89/28.62  | | Case 2:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (73)  all_58_11 = e3 | all_58_15 = e3
% 178.89/28.62  | | | 
% 178.89/28.62  | | | BETA: splitting (73) gives:
% 178.89/28.62  | | | 
% 178.89/28.62  | | | Case 1:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (74)  all_58_11 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | COMBINE_EQS: (37), (74) imply:
% 178.89/28.62  | | | |   (75)  all_52_23 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | SIMP: (75) implies:
% 178.89/28.62  | | | |   (76)  all_52_23 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REDUCE: (49), (76) imply:
% 178.89/28.62  | | | |   (77)  op(e0, e3) = e0
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REF_CLOSE: (20), (24), (48), (77) are inconsistent by sub-proof #1027.
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | Case 2:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (78)  all_58_15 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | COMBINE_EQS: (6), (78) imply:
% 178.89/28.62  | | | |   (79)  all_6_2 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REDUCE: (4), (79) imply:
% 178.89/28.62  | | | |   (80)  $false
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | CLOSE: (80) is inconsistent.
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | End of split
% 178.89/28.62  | | | 
% 178.89/28.62  | | End of split
% 178.89/28.62  | | 
% 178.89/28.62  | End of split
% 178.89/28.62  | 
% 178.89/28.62  End of proof
% 178.89/28.62  
% 178.89/28.62  Sub-proof #680 shows that the following formulas are inconsistent:
% 178.89/28.62  ----------------------------------------------------------------
% 178.89/28.62    (1)  op(e1, e2) = all_52_19
% 178.89/28.62    (2)   ~ (all_52_27 = e3)
% 178.89/28.62    (3)   ~ (all_52_17 = e3)
% 178.89/28.62    (4)  all_58_3 = all_10_2
% 178.89/28.62    (5)   ~ (all_52_9 = all_4_2)
% 178.89/28.62    (6)   ~ (all_52_5 = all_52_7)
% 178.89/28.62    (7)   ~ (all_52_5 = all_4_2)
% 178.89/28.62    (8)  all_58_7 = all_52_19
% 178.89/28.62    (9)  all_58_4 = all_52_5
% 178.89/28.62    (10)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.62    (11)   ~ (e3 = e1)
% 178.89/28.62    (12)   ~ (all_52_7 = all_4_2)
% 178.89/28.62    (13)  all_58_1 = all_52_3
% 178.89/28.62    (14)  all_58_0 = all_4_2
% 178.89/28.62    (15)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.62    (16)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.62    (17)   ~ (all_10_2 = e3)
% 178.89/28.62    (18)  all_58_8 = all_14_2
% 178.89/28.62    (19)   ~ (all_52_5 = all_14_2)
% 178.89/28.62    (20)   ~ (all_52_23 = e3)
% 178.89/28.62    (21)   ~ (e3 = e0)
% 178.89/28.62    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.89/28.62    (23)  all_58_13 = all_52_27
% 178.89/28.62    (24)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.62    (25)  all_58_12 = e3
% 178.89/28.62    (26)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.62    (27)   ~ (all_52_9 = all_52_17)
% 178.89/28.62    (28)  all_58_6 = all_52_17
% 178.89/28.62    (29)  op(e2, all_52_19) = e2
% 178.89/28.62    (30)  op(e3, all_52_17) = e3
% 178.89/28.62    (31)  all_58_10 = e3
% 178.89/28.62    (32)   ~ (e1 = e0)
% 178.89/28.62    (33)  all_56_0 = all_4_2
% 178.89/28.62    (34)  all_58_11 = all_52_23
% 178.89/28.62    (35)   ~ (all_52_3 = all_52_19)
% 178.89/28.62    (36)   ~ (all_52_9 = e3)
% 178.89/28.62    (37)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.62    (38)  all_58_2 = all_52_9
% 178.89/28.62    (39)  op(e3, e1) = all_52_5
% 178.89/28.62    (40)   ~ (e2 = e1)
% 178.89/28.62    (41)  op(e1, e3) = all_52_17
% 178.89/28.62    (42)  op(e3, e0) = all_52_7
% 178.89/28.62    (43)   ~ (all_52_17 = all_4_2)
% 178.89/28.62    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.62    (45)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.62    (46)  op(e1, all_14_2) = e1
% 178.89/28.62    (47)   ~ (all_52_7 = e3)
% 178.89/28.62    (48)   ~ (all_52_17 = all_52_19)
% 178.89/28.62    (49)  all_58_9 = all_52_7
% 178.89/28.62    (50)   ~ (e2 = e0)
% 178.89/28.62    (51)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.62    (52)  op(e2, e3) = all_52_9
% 178.89/28.62  
% 178.89/28.62  Begin of proof
% 178.89/28.62  | 
% 178.89/28.62  | BETA: splitting (16) gives:
% 178.89/28.62  | 
% 178.89/28.62  | Case 1:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (53)  all_58_1 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (13), (53) imply:
% 178.89/28.62  | |   (54)  all_52_3 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (35), (54) imply:
% 178.89/28.62  | |   (55)   ~ (all_52_19 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (55) implies:
% 178.89/28.62  | |   (56)   ~ (all_52_19 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REF_CLOSE: (3), (8), (10), (18), (19), (20), (28), (30), (34), (39), (41),
% 178.89/28.62  | |            (44), (46), (56) are inconsistent by sub-proof #705.
% 178.89/28.62  | | 
% 178.89/28.62  | Case 2:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (57)   ~ (all_58_1 = e3)
% 178.89/28.62  | |   (58)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (13), (57) imply:
% 178.89/28.62  | |   (59)   ~ (all_52_3 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | BETA: splitting (58) gives:
% 178.89/28.62  | | 
% 178.89/28.62  | | Case 1:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (60)  all_58_3 = e3
% 178.89/28.62  | | | 
% 178.89/28.62  | | | COMBINE_EQS: (4), (60) imply:
% 178.89/28.62  | | |   (61)  all_10_2 = e3
% 178.89/28.62  | | | 
% 178.89/28.62  | | | REDUCE: (17), (61) imply:
% 178.89/28.62  | | |   (62)  $false
% 178.89/28.62  | | | 
% 178.89/28.62  | | | CLOSE: (62) is inconsistent.
% 178.89/28.62  | | | 
% 178.89/28.62  | | Case 2:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (63)  all_58_7 = e3 | all_58_13 = e3
% 178.89/28.62  | | | 
% 178.89/28.62  | | | BETA: splitting (37) gives:
% 178.89/28.62  | | | 
% 178.89/28.62  | | | Case 1:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (64)  all_58_1 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | COMBINE_EQS: (13), (64) imply:
% 178.89/28.62  | | | |   (65)  all_52_3 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REDUCE: (59), (65) imply:
% 178.89/28.62  | | | |   (66)  $false
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | CLOSE: (66) is inconsistent.
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | Case 2:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (67)  all_58_4 = e3 | all_58_9 = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | BETA: splitting (63) gives:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | Case 1:
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | |   (68)  all_58_7 = e3
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | COMBINE_EQS: (8), (68) imply:
% 178.89/28.62  | | | | |   (69)  all_52_19 = e3
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | REDUCE: (29), (69) imply:
% 178.89/28.62  | | | | |   (70)  op(e2, e3) = e2
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | REDUCE: (1), (69) imply:
% 178.89/28.62  | | | | |   (71)  op(e1, e2) = e3
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | BETA: splitting (51) gives:
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | Case 1:
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | |   (72)  all_58_4 = e3
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | COMBINE_EQS: (9), (72) imply:
% 178.89/28.62  | | | | | |   (73)  all_52_5 = e3
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | SIMP: (73) implies:
% 178.89/28.62  | | | | | |   (74)  all_52_5 = e3
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REDUCE: (6), (74) imply:
% 178.89/28.62  | | | | | |   (75)   ~ (all_52_7 = e3)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REDUCE: (7), (74) imply:
% 178.89/28.62  | | | | | |   (76)   ~ (all_4_2 = e3)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | SIMP: (76) implies:
% 178.89/28.62  | | | | | |   (77)   ~ (all_4_2 = e3)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | GROUND_INST: instantiating (44) with all_52_9, e2, e3, e2,
% 178.89/28.62  | | | | | |              simplifying with (52), (70) gives:
% 178.89/28.62  | | | | | |   (78)  all_52_9 = e2
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | COMBINE_EQS: (38), (78) imply:
% 178.89/28.62  | | | | | |   (79)  all_58_2 = e2
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REDUCE: (27), (78) imply:
% 178.89/28.62  | | | | | |   (80)   ~ (all_52_17 = e2)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | SIMP: (80) implies:
% 178.89/28.62  | | | | | |   (81)   ~ (all_52_17 = e2)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REDUCE: (5), (78) imply:
% 178.89/28.62  | | | | | |   (82)   ~ (all_4_2 = e2)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | SIMP: (82) implies:
% 178.89/28.62  | | | | | |   (83)   ~ (all_4_2 = e2)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REDUCE: (36), (78) imply:
% 178.89/28.62  | | | | | |   (84)   ~ (e3 = e2)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | SIMP: (84) implies:
% 178.89/28.62  | | | | | |   (85)   ~ (e3 = e2)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | BETA: splitting (24) gives:
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | Case 1:
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | |   (86)  all_58_0 = e1
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | | COMBINE_EQS: (14), (86) imply:
% 178.89/28.62  | | | | | | |   (87)  all_4_2 = e1
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | | REF_CLOSE: (21), (22), (25), (28), (30), (32), (42), (44), (47),
% 178.89/28.62  | | | | | | |            (50), (79), (86) are inconsistent by sub-proof #681.
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | Case 2:
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | |   (88)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | | BETA: splitting (88) gives:
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | | Case 1:
% 178.89/28.62  | | | | | | | | 
% 178.89/28.62  | | | | | | | |   (89)  all_58_2 = e1
% 178.89/28.62  | | | | | | | | 
% 178.89/28.62  | | | | | | | | REF_CLOSE: (40), (79), (89) are inconsistent by sub-proof #921.
% 178.89/28.62  | | | | | | | | 
% 178.89/28.62  | | | | | | | Case 2:
% 178.89/28.62  | | | | | | | | 
% 178.89/28.62  | | | | | | | |   (90)  all_58_6 = e1 | all_58_12 = e1
% 178.89/28.62  | | | | | | | | 
% 178.89/28.62  | | | | | | | | BETA: splitting (90) gives:
% 178.89/28.62  | | | | | | | | 
% 178.89/28.62  | | | | | | | | Case 1:
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | |   (91)  all_58_6 = e1
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | COMBINE_EQS: (28), (91) imply:
% 178.89/28.62  | | | | | | | | |   (92)  all_52_17 = e1
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | SIMP: (92) implies:
% 178.89/28.62  | | | | | | | | |   (93)  all_52_17 = e1
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | REDUCE: (43), (93) imply:
% 178.89/28.62  | | | | | | | | |   (94)   ~ (all_4_2 = e1)
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | SIMP: (94) implies:
% 178.89/28.62  | | | | | | | | |   (95)   ~ (all_4_2 = e1)
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | REDUCE: (3), (93) imply:
% 178.89/28.62  | | | | | | | | |   (96)   ~ (e3 = e1)
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | REDUCE: (81), (93) imply:
% 178.89/28.62  | | | | | | | | |   (97)   ~ (e2 = e1)
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | BETA: splitting (45) gives:
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | Case 1:
% 178.89/28.62  | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | |   (98)  all_56_0 = e2
% 178.89/28.62  | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | REF_CLOSE: (33), (83), (98) are inconsistent by sub-proof
% 178.89/28.62  | | | | | | | | | |            #904.
% 178.89/28.62  | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | Case 2:
% 178.89/28.62  | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | |   (99)   ~ (all_56_0 = e2)
% 178.89/28.62  | | | | | | | | | |   (100)  all_56_0 = e1 | all_56_0 = e0
% 178.89/28.62  | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | BETA: splitting (100) gives:
% 178.89/28.62  | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | Case 1:
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | |   (101)  all_56_0 = e1
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | REF_CLOSE: (33), (95), (101) are inconsistent by sub-proof
% 178.89/28.62  | | | | | | | | | | |            #1022.
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | Case 2:
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | |   (102)  all_56_0 = e0
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | COMBINE_EQS: (33), (102) imply:
% 178.89/28.62  | | | | | | | | | | |   (103)  all_4_2 = e0
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | SIMP: (103) implies:
% 178.89/28.62  | | | | | | | | | | |   (104)  all_4_2 = e0
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | REDUCE: (12), (104) imply:
% 178.89/28.62  | | | | | | | | | | |   (105)   ~ (all_52_7 = e0)
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | REDUCE: (77), (104) imply:
% 178.89/28.62  | | | | | | | | | | |   (106)   ~ (e3 = e0)
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | REDUCE: (83), (104) imply:
% 178.89/28.62  | | | | | | | | | | |   (107)   ~ (e2 = e0)
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | BETA: splitting (15) gives:
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | Case 1:
% 178.89/28.62  | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | |   (108)  all_58_9 = e0
% 178.89/28.62  | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | REF_CLOSE: (49), (105), (108) are inconsistent by sub-proof
% 178.89/28.62  | | | | | | | | | | | |            #825.
% 178.89/28.62  | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | Case 2:
% 178.89/28.62  | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | |   (109)  all_58_10 = e0 | all_58_11 = e0
% 178.89/28.62  | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | BETA: splitting (109) gives:
% 178.89/28.62  | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | Case 1:
% 178.89/28.62  | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | |   (110)  all_58_10 = e0
% 178.89/28.62  | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | REF_CLOSE: (21), (31), (110) are inconsistent by sub-proof
% 178.89/28.62  | | | | | | | | | | | | |            #824.
% 178.89/28.62  | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | Case 2:
% 178.89/28.62  | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | |   (111)  all_58_11 = e0
% 178.89/28.62  | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | BETA: splitting (26) gives:
% 178.89/28.62  | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | Case 1:
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | |   (112)  all_58_6 = e2
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | | COMBINE_EQS: (91), (112) imply:
% 178.89/28.62  | | | | | | | | | | | | | |   (113)  e2 = e1
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | | REDUCE: (40), (113) imply:
% 178.89/28.62  | | | | | | | | | | | | | |   (114)  $false
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | Case 2:
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | |   (115)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | | REF_CLOSE: (11), (18), (44), (46), (50), (68), (71), (85),
% 178.89/28.62  | | | | | | | | | | | | | |            (111), (115) are inconsistent by sub-proof #685.
% 178.89/28.62  | | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | | End of split
% 178.89/28.62  | | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | | End of split
% 178.89/28.62  | | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | | End of split
% 178.89/28.62  | | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | | End of split
% 178.89/28.62  | | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | End of split
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | Case 2:
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | |   (116)  all_58_12 = e1
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | | REF_CLOSE: (11), (25), (116) are inconsistent by sub-proof
% 178.89/28.62  | | | | | | | | |            #920.
% 178.89/28.62  | | | | | | | | | 
% 178.89/28.62  | | | | | | | | End of split
% 178.89/28.62  | | | | | | | | 
% 178.89/28.62  | | | | | | | End of split
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | End of split
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | Case 2:
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | |   (117)   ~ (all_58_4 = e3)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REDUCE: (9), (117) imply:
% 178.89/28.62  | | | | | |   (118)   ~ (all_52_5 = e3)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | BETA: splitting (67) gives:
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | Case 1:
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | |   (119)  all_58_4 = e3
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | | REF_CLOSE: (9), (118), (119) are inconsistent by sub-proof #1025.
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | Case 2:
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | |   (120)  all_58_9 = e3
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | | REF_CLOSE: (47), (49), (120) are inconsistent by sub-proof #972.
% 178.89/28.62  | | | | | | | 
% 178.89/28.62  | | | | | | End of split
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | End of split
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | Case 2:
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | |   (121)  all_58_13 = e3
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | REF_CLOSE: (2), (23), (121) are inconsistent by sub-proof #1026.
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | End of split
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | End of split
% 178.89/28.62  | | | 
% 178.89/28.62  | | End of split
% 178.89/28.62  | | 
% 178.89/28.62  | End of split
% 178.89/28.62  | 
% 178.89/28.62  End of proof
% 178.89/28.62  
% 178.89/28.62  Sub-proof #681 shows that the following formulas are inconsistent:
% 178.89/28.62  ----------------------------------------------------------------
% 178.89/28.62    (1)  all_58_2 = e2
% 178.89/28.62    (2)   ~ (e3 = e0)
% 178.89/28.62    (3)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.89/28.62    (4)  all_58_0 = e1
% 178.89/28.62    (5)  all_58_12 = e3
% 178.89/28.62    (6)  all_58_6 = all_52_17
% 178.89/28.62    (7)  op(e3, all_52_17) = e3
% 178.89/28.62    (8)   ~ (e1 = e0)
% 178.89/28.62    (9)  op(e3, e0) = all_52_7
% 178.89/28.62    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.62    (11)   ~ (all_52_7 = e3)
% 178.89/28.62    (12)   ~ (e2 = e0)
% 178.89/28.62  
% 178.89/28.62  Begin of proof
% 178.89/28.62  | 
% 178.89/28.62  | BETA: splitting (3) gives:
% 178.89/28.62  | 
% 178.89/28.62  | Case 1:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (13)  all_58_0 = e0
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (4), (13) imply:
% 178.89/28.62  | |   (14)  e1 = e0
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (8), (14) imply:
% 178.89/28.62  | |   (15)  $false
% 178.89/28.62  | | 
% 178.89/28.62  | | CLOSE: (15) is inconsistent.
% 178.89/28.62  | | 
% 178.89/28.62  | Case 2:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (16)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.89/28.62  | | 
% 178.89/28.62  | | BETA: splitting (16) gives:
% 178.89/28.62  | | 
% 178.89/28.62  | | Case 1:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (17)  all_58_2 = e0
% 178.89/28.62  | | | 
% 178.89/28.62  | | | REF_CLOSE: (1), (12), (17) are inconsistent by sub-proof #909.
% 178.89/28.62  | | | 
% 178.89/28.62  | | Case 2:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (18)  all_58_6 = e0 | all_58_12 = e0
% 178.89/28.62  | | | 
% 178.89/28.62  | | | BETA: splitting (18) gives:
% 178.89/28.62  | | | 
% 178.89/28.62  | | | Case 1:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (19)  all_58_6 = e0
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | COMBINE_EQS: (6), (19) imply:
% 178.89/28.62  | | | |   (20)  all_52_17 = e0
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | SIMP: (20) implies:
% 178.89/28.62  | | | |   (21)  all_52_17 = e0
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REDUCE: (7), (21) imply:
% 178.89/28.62  | | | |   (22)  op(e3, e0) = e3
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REF_CLOSE: (9), (10), (11), (22) are inconsistent by sub-proof #908.
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | Case 2:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (23)  all_58_12 = e0
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REF_CLOSE: (2), (5), (23) are inconsistent by sub-proof #682.
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | End of split
% 178.89/28.62  | | | 
% 178.89/28.62  | | End of split
% 178.89/28.62  | | 
% 178.89/28.62  | End of split
% 178.89/28.62  | 
% 178.89/28.62  End of proof
% 178.89/28.62  
% 178.89/28.62  Sub-proof #682 shows that the following formulas are inconsistent:
% 178.89/28.62  ----------------------------------------------------------------
% 178.89/28.62    (1)  all_58_12 = e3
% 178.89/28.62    (2)  all_58_12 = e0
% 178.89/28.62    (3)   ~ (e3 = e0)
% 178.89/28.62  
% 178.89/28.62  Begin of proof
% 178.89/28.62  | 
% 178.89/28.62  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.62  |   (4)  e3 = e0
% 178.89/28.62  | 
% 178.89/28.62  | SIMP: (4) implies:
% 178.89/28.62  |   (5)  e3 = e0
% 178.89/28.62  | 
% 178.89/28.62  | REDUCE: (3), (5) imply:
% 178.89/28.62  |   (6)  $false
% 178.89/28.62  | 
% 178.89/28.62  | CLOSE: (6) is inconsistent.
% 178.89/28.62  | 
% 178.89/28.62  End of proof
% 178.89/28.62  
% 178.89/28.62  Sub-proof #683 shows that the following formulas are inconsistent:
% 178.89/28.62  ----------------------------------------------------------------
% 178.89/28.62    (1)  all_58_5 = all_52_13
% 178.89/28.62    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.62    (3)  all_58_3 = all_10_2
% 178.89/28.62    (4)  all_58_10 = all_52_15
% 178.89/28.62    (5)  all_58_7 = all_52_19
% 178.89/28.62    (6)  all_58_8 = all_14_2
% 178.89/28.62    (7)   ~ (all_52_5 = all_14_2)
% 178.89/28.62    (8)   ~ (all_52_23 = e3)
% 178.89/28.62    (9)   ~ (all_52_13 = e3)
% 178.89/28.62    (10)   ~ (all_52_15 = e3)
% 178.89/28.62    (11)  op(e3, all_52_17) = e3
% 178.89/28.62    (12)  all_58_11 = all_52_23
% 178.89/28.62    (13)   ~ (all_52_19 = all_10_2)
% 178.89/28.62    (14)  op(e3, e1) = all_52_5
% 178.89/28.62    (15)  op(e1, e3) = all_52_17
% 178.89/28.62    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.62    (17)  op(e1, all_14_2) = e1
% 178.89/28.62    (18)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.89/28.62  
% 178.89/28.62  Begin of proof
% 178.89/28.62  | 
% 178.89/28.62  | BETA: splitting (18) gives:
% 178.89/28.62  | 
% 178.89/28.62  | Case 1:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (19)  all_58_3 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (3), (19) imply:
% 178.89/28.62  | |   (20)  all_10_2 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (13), (20) imply:
% 178.89/28.62  | |   (21)   ~ (all_52_19 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REF_CLOSE: (2), (5), (6), (7), (8), (11), (12), (14), (15), (16), (17), (21)
% 178.89/28.62  | |            are inconsistent by sub-proof #950.
% 178.89/28.62  | | 
% 178.89/28.62  | Case 2:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (22)  all_58_5 = e3 | all_58_10 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | REF_CLOSE: (1), (4), (9), (10), (22) are inconsistent by sub-proof #958.
% 178.89/28.62  | | 
% 178.89/28.62  | End of split
% 178.89/28.62  | 
% 178.89/28.62  End of proof
% 178.89/28.62  
% 178.89/28.62  Sub-proof #684 shows that the following formulas are inconsistent:
% 178.89/28.62  ----------------------------------------------------------------
% 178.89/28.62    (1)  op(e2, all_10_2) = all_10_1
% 178.89/28.62    (2)  op(e1, e2) = all_52_19
% 178.89/28.62    (3)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.62    (4)  all_58_3 = all_10_2
% 178.89/28.62    (5)  all_58_10 = all_52_15
% 178.89/28.62    (6)  all_58_7 = all_52_19
% 178.89/28.62    (7)   ~ (e3 = e1)
% 178.89/28.62    (8)  all_58_9 = e3
% 178.89/28.62    (9)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.62    (10)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.89/28.62    (11)  all_58_8 = all_14_2
% 178.89/28.62    (12)   ~ (all_52_23 = e3)
% 178.89/28.62    (13)   ~ (all_52_9 = all_10_2)
% 178.89/28.62    (14)   ~ (e3 = e0)
% 178.89/28.62    (15)  all_56_5 = all_10_2
% 178.89/28.62    (16)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.62    (17)   ~ (all_52_9 = all_52_17)
% 178.89/28.62    (18)  all_58_6 = all_52_17
% 178.89/28.62    (19)  op(e2, all_52_19) = e2
% 178.89/28.62    (20)  all_58_11 = all_52_23
% 178.89/28.62    (21)  op(e2, e1) = e3
% 178.89/28.62    (22)   ~ (all_52_19 = all_10_2)
% 178.89/28.62    (23)   ~ (all_52_9 = e3)
% 178.89/28.62    (24)  all_58_2 = all_52_9
% 178.89/28.62    (25)   ~ (e2 = e1)
% 178.89/28.62    (26)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.89/28.62    (27)   ~ (all_10_1 = e3)
% 178.89/28.62    (28)   ~ (all_14_2 = e3)
% 178.89/28.62    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.62    (30)   ~ (all_52_15 = all_10_2)
% 178.89/28.62    (31)  op(e1, all_14_2) = e1
% 178.89/28.62    (32)   ~ (e2 = e0)
% 178.89/28.62    (33)  op(e2, e3) = all_52_9
% 178.89/28.62  
% 178.89/28.62  Begin of proof
% 178.89/28.62  | 
% 178.89/28.62  | BETA: splitting (3) gives:
% 178.89/28.62  | 
% 178.89/28.62  | Case 1:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (34)  all_58_7 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (6), (34) imply:
% 178.89/28.62  | |   (35)  all_52_19 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (22), (35) imply:
% 178.89/28.62  | |   (36)   ~ (all_10_2 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (36) implies:
% 178.89/28.62  | |   (37)   ~ (all_10_2 = e3)
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (19), (35) imply:
% 178.89/28.62  | |   (38)  op(e2, e3) = e2
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (2), (35) imply:
% 178.89/28.62  | |   (39)  op(e1, e2) = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | GROUND_INST: instantiating (29) with all_52_9, e2, e3, e2, simplifying with
% 178.89/28.62  | |              (33), (38) gives:
% 178.89/28.62  | |   (40)  all_52_9 = e2
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (24), (40) imply:
% 178.89/28.62  | |   (41)  all_58_2 = e2
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (17), (40) imply:
% 178.89/28.62  | |   (42)   ~ (all_52_17 = e2)
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (42) implies:
% 178.89/28.62  | |   (43)   ~ (all_52_17 = e2)
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (13), (40) imply:
% 178.89/28.62  | |   (44)   ~ (all_10_2 = e2)
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (44) implies:
% 178.89/28.62  | |   (45)   ~ (all_10_2 = e2)
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (23), (40) imply:
% 178.89/28.62  | |   (46)   ~ (e3 = e2)
% 178.89/28.62  | | 
% 178.89/28.62  | | SIMP: (46) implies:
% 178.89/28.62  | |   (47)   ~ (e3 = e2)
% 178.89/28.62  | | 
% 178.89/28.62  | | BETA: splitting (26) gives:
% 178.89/28.62  | | 
% 178.89/28.62  | | Case 1:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (48)  all_56_5 = e3
% 178.89/28.62  | | | 
% 178.89/28.62  | | | REF_CLOSE: (15), (37), (48) are inconsistent by sub-proof #895.
% 178.89/28.62  | | | 
% 178.89/28.62  | | Case 2:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (49)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.89/28.62  | | | 
% 178.89/28.62  | | | BETA: splitting (16) gives:
% 178.89/28.62  | | | 
% 178.89/28.62  | | | Case 1:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (50)  all_58_6 = e2
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | COMBINE_EQS: (18), (50) imply:
% 178.89/28.62  | | | |   (51)  all_52_17 = e2
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | REDUCE: (43), (51) imply:
% 178.89/28.62  | | | |   (52)  $false
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | CLOSE: (52) is inconsistent.
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | Case 2:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | |   (53)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | BETA: splitting (9) gives:
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | | Case 1:
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | |   (54)  all_58_9 = e0
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | REF_CLOSE: (8), (14), (54) are inconsistent by sub-proof #928.
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | Case 2:
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | |   (55)  all_58_10 = e0 | all_58_11 = e0
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | BETA: splitting (55) gives:
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | | Case 1:
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | |   (56)  all_58_10 = e0
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | COMBINE_EQS: (5), (56) imply:
% 178.89/28.62  | | | | | |   (57)  all_52_15 = e0
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | SIMP: (57) implies:
% 178.89/28.62  | | | | | |   (58)  all_52_15 = e0
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REDUCE: (30), (58) imply:
% 178.89/28.62  | | | | | |   (59)   ~ (all_10_2 = e0)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | SIMP: (59) implies:
% 178.89/28.62  | | | | | |   (60)   ~ (all_10_2 = e0)
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REF_CLOSE: (1), (4), (10), (15), (21), (25), (27), (29), (41), (45),
% 178.89/28.62  | | | | | |            (49), (60) are inconsistent by sub-proof #706.
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | Case 2:
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | |   (61)  all_58_11 = e0
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | | REF_CLOSE: (7), (11), (29), (31), (32), (34), (39), (47), (53), (61)
% 178.89/28.62  | | | | | |            are inconsistent by sub-proof #685.
% 178.89/28.62  | | | | | | 
% 178.89/28.62  | | | | | End of split
% 178.89/28.62  | | | | | 
% 178.89/28.62  | | | | End of split
% 178.89/28.62  | | | | 
% 178.89/28.62  | | | End of split
% 178.89/28.62  | | | 
% 178.89/28.62  | | End of split
% 178.89/28.62  | | 
% 178.89/28.62  | Case 2:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (62)  all_58_8 = e3 | all_58_11 = e3
% 178.89/28.62  | | 
% 178.89/28.62  | | REF_CLOSE: (11), (12), (20), (28), (62) are inconsistent by sub-proof #997.
% 178.89/28.62  | | 
% 178.89/28.62  | End of split
% 178.89/28.62  | 
% 178.89/28.62  End of proof
% 178.89/28.62  
% 178.89/28.62  Sub-proof #685 shows that the following formulas are inconsistent:
% 178.89/28.62  ----------------------------------------------------------------
% 178.89/28.62    (1)   ~ (e3 = e1)
% 178.89/28.62    (2)  all_58_7 = e3
% 178.89/28.62    (3)  all_58_8 = all_14_2
% 178.89/28.62    (4)  all_58_11 = e0
% 178.89/28.62    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.62    (6)  op(e1, all_14_2) = e1
% 178.89/28.62    (7)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.62    (8)   ~ (e2 = e0)
% 178.89/28.62    (9)   ~ (e3 = e2)
% 178.89/28.62    (10)  op(e1, e2) = e3
% 178.89/28.62  
% 178.89/28.62  Begin of proof
% 178.89/28.62  | 
% 178.89/28.62  | BETA: splitting (7) gives:
% 178.89/28.62  | 
% 178.89/28.62  | Case 1:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (11)  all_58_7 = e2
% 178.89/28.62  | | 
% 178.89/28.62  | | COMBINE_EQS: (2), (11) imply:
% 178.89/28.62  | |   (12)  e3 = e2
% 178.89/28.62  | | 
% 178.89/28.62  | | REDUCE: (9), (12) imply:
% 178.89/28.62  | |   (13)  $false
% 178.89/28.62  | | 
% 178.89/28.62  | | CLOSE: (13) is inconsistent.
% 178.89/28.62  | | 
% 178.89/28.62  | Case 2:
% 178.89/28.62  | | 
% 178.89/28.62  | |   (14)  all_58_8 = e2 | all_58_11 = e2
% 178.89/28.62  | | 
% 178.89/28.62  | | BETA: splitting (14) gives:
% 178.89/28.62  | | 
% 178.89/28.62  | | Case 1:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (15)  all_58_8 = e2
% 178.89/28.62  | | | 
% 178.89/28.62  | | | COMBINE_EQS: (3), (15) imply:
% 178.89/28.62  | | |   (16)  all_14_2 = e2
% 178.89/28.62  | | | 
% 178.89/28.62  | | | REDUCE: (6), (16) imply:
% 178.89/28.62  | | |   (17)  op(e1, e2) = e1
% 178.89/28.62  | | | 
% 178.89/28.62  | | | REF_CLOSE: (1), (5), (10), (17) are inconsistent by sub-proof #861.
% 178.89/28.62  | | | 
% 178.89/28.62  | | Case 2:
% 178.89/28.62  | | | 
% 178.89/28.62  | | |   (18)  all_58_11 = e2
% 178.89/28.62  | | | 
% 178.89/28.62  | | | COMBINE_EQS: (4), (18) imply:
% 178.89/28.62  | | |   (19)  e2 = e0
% 178.89/28.62  | | | 
% 178.89/28.62  | | | REDUCE: (8), (19) imply:
% 178.89/28.62  | | |   (20)  $false
% 178.89/28.62  | | | 
% 178.89/28.62  | | | CLOSE: (20) is inconsistent.
% 178.89/28.62  | | | 
% 178.89/28.62  | | End of split
% 178.89/28.62  | | 
% 178.89/28.62  | End of split
% 178.89/28.62  | 
% 178.89/28.62  End of proof
% 178.89/28.62  
% 178.89/28.62  Sub-proof #686 shows that the following formulas are inconsistent:
% 178.89/28.62  ----------------------------------------------------------------
% 178.89/28.62    (1)   ~ (all_52_23 = all_14_2)
% 178.89/28.62    (2)   ~ (all_52_5 = all_52_13)
% 178.89/28.62    (3)  op(e3, e2) = all_52_3
% 178.89/28.62    (4)  op(e3, all_52_25) = all_52_24
% 178.89/28.62    (5)   ~ (all_52_19 = all_52_23)
% 178.89/28.62    (6)  all_52_27 = e3
% 178.89/28.62    (7)  all_58_5 = all_52_13
% 178.89/28.62    (8)   ~ (all_52_25 = all_52_29)
% 178.89/28.62    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.62    (10)  op(e2, e0) = all_52_15
% 178.89/28.62    (11)  all_56_9 = all_52_19
% 178.89/28.62    (12)   ~ (all_52_5 = all_52_7)
% 178.89/28.62    (13)  all_58_10 = all_52_15
% 178.89/28.62    (14)   ~ (all_52_5 = all_4_2)
% 178.89/28.62    (15)  all_58_7 = all_52_19
% 178.89/28.62    (16)   ~ (all_52_17 = all_52_25)
% 178.89/28.62    (17)  all_58_4 = all_52_5
% 178.89/28.62    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.62    (19)   ~ (e3 = e1)
% 178.89/28.62    (20)   ~ (all_52_27 = all_52_29)
% 178.89/28.63    (21)   ~ (all_52_17 = all_14_2)
% 178.89/28.63    (22)  op(e3, all_4_2) = all_4_1
% 178.89/28.63    (23)  all_58_0 = all_4_2
% 178.89/28.63    (24)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.63    (25)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.89/28.63    (26)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.89/28.63    (27)  all_58_14 = all_52_29
% 178.89/28.63    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.63    (29)  all_58_8 = all_14_2
% 178.89/28.63    (30)  all_56_1 = all_52_3
% 178.89/28.63    (31)  op(all_4_1, all_4_2) = all_4_0
% 178.89/28.63    (32)   ~ (all_52_5 = all_14_2)
% 178.89/28.63    (33)   ~ (all_52_3 = all_52_27)
% 178.89/28.63    (34)   ~ (all_52_3 = all_4_2)
% 178.89/28.63    (35)  op(e0, e3) = all_52_25
% 178.89/28.63    (36)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.89/28.63    (37)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.89/28.63    (38)  op(e1, e0) = all_52_23
% 178.89/28.63    (39)   ~ (all_4_1 = e1)
% 178.89/28.63    (40)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.63    (41)   ~ (all_52_9 = all_52_17)
% 178.89/28.63    (42)  all_58_6 = all_52_17
% 178.89/28.63    (43)  op(e2, all_52_19) = e2
% 178.89/28.63    (44)  op(e3, all_52_17) = e3
% 178.89/28.63    (45)   ~ (e1 = e0)
% 178.89/28.63    (46)  all_58_11 = all_52_23
% 178.89/28.63    (47)   ~ (all_52_3 = all_52_19)
% 178.89/28.63    (48)   ~ (all_4_0 = e1)
% 178.89/28.63    (49)  all_58_2 = all_52_9
% 178.89/28.63    (50)  op(e3, e1) = all_52_5
% 178.89/28.63    (51)   ~ (e2 = e1)
% 178.89/28.63    (52)  all_56_10 = all_14_2
% 178.89/28.63    (53)  op(e1, e3) = all_52_17
% 178.89/28.63    (54)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.89/28.63    (55)   ~ (all_52_25 = all_4_2)
% 178.89/28.63    (56)  op(e3, e0) = all_52_7
% 178.89/28.63    (57)  op(e3, e3) = all_4_2
% 178.89/28.63    (58)   ~ (all_52_17 = all_4_2)
% 178.89/28.63    (59)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.63    (60)   ~ (all_52_25 = all_52_27)
% 178.89/28.63    (61)  op(e0, all_52_23) = e0
% 178.89/28.63    (62)   ~ (all_52_19 = all_52_27)
% 178.89/28.63    (63)  op(e1, all_14_2) = e1
% 178.89/28.63    (64)  op(e2, all_52_27) = all_52_26
% 178.89/28.63    (65)   ~ (all_52_17 = all_52_19)
% 178.89/28.63    (66)  all_58_9 = all_52_7
% 178.89/28.63    (67)   ~ (e2 = e0)
% 178.89/28.63    (68)  all_58_12 = all_52_25
% 178.89/28.63    (69)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.63    (70)   ~ (e3 = e2)
% 178.89/28.63    (71)   ~ (all_52_19 = all_14_2)
% 178.89/28.63    (72)  op(e2, e3) = all_52_9
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (6), (33) imply:
% 178.89/28.63  |   (73)   ~ (all_52_3 = e3)
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (6), (62) imply:
% 178.89/28.63  |   (74)   ~ (all_52_19 = e3)
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (6), (60) imply:
% 178.89/28.63  |   (75)   ~ (all_52_25 = e3)
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (6), (20) imply:
% 178.89/28.63  |   (76)   ~ (all_52_29 = e3)
% 178.89/28.63  | 
% 178.89/28.63  | SIMP: (76) implies:
% 178.89/28.63  |   (77)   ~ (all_52_29 = e3)
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (6), (64) imply:
% 178.89/28.63  |   (78)  op(e2, e3) = all_52_26
% 178.89/28.63  | 
% 178.89/28.63  | GROUND_INST: instantiating (59) with all_52_9, all_52_26, e3, e2, simplifying
% 178.89/28.63  |              with (72), (78) gives:
% 178.89/28.63  |   (79)  all_52_9 = all_52_26
% 178.89/28.63  | 
% 178.89/28.63  | COMBINE_EQS: (49), (79) imply:
% 178.89/28.63  |   (80)  all_58_2 = all_52_26
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (41), (79) imply:
% 178.89/28.63  |   (81)   ~ (all_52_17 = all_52_26)
% 178.89/28.63  | 
% 178.89/28.63  | SIMP: (81) implies:
% 178.89/28.63  |   (82)   ~ (all_52_17 = all_52_26)
% 178.89/28.63  | 
% 178.89/28.63  | BETA: splitting (26) gives:
% 178.89/28.63  | 
% 178.89/28.63  | Case 1:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (83)  all_56_9 = e3
% 178.89/28.63  | | 
% 178.89/28.63  | | REF_CLOSE: (11), (74), (83) are inconsistent by sub-proof #700.
% 178.89/28.63  | | 
% 178.89/28.63  | Case 2:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (84)   ~ (all_56_9 = e3)
% 178.89/28.63  | |   (85)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | BETA: splitting (25) gives:
% 178.89/28.63  | | 
% 178.89/28.63  | | Case 1:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (86)  all_56_1 = e3
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REF_CLOSE: (30), (73), (86) are inconsistent by sub-proof #862.
% 178.89/28.63  | | | 
% 178.89/28.63  | | Case 2:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (87)   ~ (all_56_1 = e3)
% 178.89/28.63  | | |   (88)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | BETA: splitting (37) gives:
% 178.89/28.63  | | | 
% 178.89/28.63  | | | Case 1:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | |   (89)  all_56_10 = e3
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | COMBINE_EQS: (52), (89) imply:
% 178.89/28.63  | | | |   (90)  all_14_2 = e3
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | SIMP: (90) implies:
% 178.89/28.63  | | | |   (91)  all_14_2 = e3
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | REF_CLOSE: (1), (15), (18), (21), (29), (32), (42), (44), (46), (50),
% 178.89/28.63  | | | |            (53), (59), (63), (71), (91) are inconsistent by sub-proof
% 178.89/28.63  | | | |            #704.
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | Case 2:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | |   (92)   ~ (all_56_10 = e3)
% 178.89/28.63  | | | |   (93)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | REDUCE: (52), (92) imply:
% 178.89/28.63  | | | |   (94)   ~ (all_14_2 = e3)
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | BETA: splitting (18) gives:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | Case 1:
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | |   (95)  all_58_6 = e3
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | COMBINE_EQS: (42), (95) imply:
% 178.89/28.63  | | | | |   (96)  all_52_17 = e3
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | REF_CLOSE: (44), (57), (58), (59), (96) are inconsistent by sub-proof
% 178.89/28.63  | | | | |            #948.
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | Case 2:
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | |   (97)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | BETA: splitting (97) gives:
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | Case 1:
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | |   (98)  all_58_7 = e3
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | | COMBINE_EQS: (15), (98) imply:
% 178.89/28.63  | | | | | |   (99)  all_52_19 = e3
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | | REDUCE: (74), (99) imply:
% 178.89/28.63  | | | | | |   (100)  $false
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | | CLOSE: (100) is inconsistent.
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | Case 2:
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | |   (101)  all_58_8 = e3 | all_58_11 = e3
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | | BETA: splitting (101) gives:
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | | Case 1:
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | |   (102)  all_58_8 = e3
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REF_CLOSE: (29), (94), (102) are inconsistent by sub-proof #901.
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | Case 2:
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | |   (103)  all_58_11 = e3
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | COMBINE_EQS: (46), (103) imply:
% 178.89/28.63  | | | | | | |   (104)  all_52_23 = e3
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | SIMP: (104) implies:
% 178.89/28.63  | | | | | | |   (105)  all_52_23 = e3
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (1), (105) imply:
% 178.89/28.63  | | | | | | |   (106)   ~ (all_14_2 = e3)
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (38), (105) imply:
% 178.89/28.63  | | | | | | |   (107)  op(e1, e0) = e3
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (61), (105) imply:
% 178.89/28.63  | | | | | | |   (108)  op(e0, e3) = e0
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | GROUND_INST: instantiating (59) with all_52_25, e0, e3, e0,
% 178.89/28.63  | | | | | | |              simplifying with (35), (108) gives:
% 178.89/28.63  | | | | | | |   (109)  all_52_25 = e0
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | COMBINE_EQS: (68), (109) imply:
% 178.89/28.63  | | | | | | |   (110)  all_58_12 = e0
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (16), (109) imply:
% 178.89/28.63  | | | | | | |   (111)   ~ (all_52_17 = e0)
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (8), (109) imply:
% 178.89/28.63  | | | | | | |   (112)   ~ (all_52_29 = e0)
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | SIMP: (112) implies:
% 178.89/28.63  | | | | | | |   (113)   ~ (all_52_29 = e0)
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (55), (109) imply:
% 178.89/28.63  | | | | | | |   (114)   ~ (all_4_2 = e0)
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | SIMP: (114) implies:
% 178.89/28.63  | | | | | | |   (115)   ~ (all_4_2 = e0)
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (4), (109) imply:
% 178.89/28.63  | | | | | | |   (116)  op(e3, e0) = all_52_24
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | GROUND_INST: instantiating (59) with all_52_7, all_52_24, e0, e3,
% 178.89/28.63  | | | | | | |              simplifying with (56), (116) gives:
% 178.89/28.63  | | | | | | |   (117)  all_52_7 = all_52_24
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | COMBINE_EQS: (66), (117) imply:
% 178.89/28.63  | | | | | | |   (118)  all_58_9 = all_52_24
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | REDUCE: (12), (117) imply:
% 178.89/28.63  | | | | | | |   (119)   ~ (all_52_5 = all_52_24)
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | BETA: splitting (28) gives:
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | |   (120)  all_58_0 = e3
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | COMBINE_EQS: (23), (120) imply:
% 178.89/28.63  | | | | | | | |   (121)  all_4_2 = e3
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | REDUCE: (14), (121) imply:
% 178.89/28.63  | | | | | | | |   (122)   ~ (all_52_5 = e3)
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | REDUCE: (115), (121) imply:
% 178.89/28.63  | | | | | | | |   (123)   ~ (e3 = e0)
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | REDUCE: (31), (121) imply:
% 178.89/28.63  | | | | | | | |   (124)  op(all_4_1, e3) = all_4_0
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | REDUCE: (22), (121) imply:
% 178.89/28.63  | | | | | | | |   (125)  op(e3, e3) = all_4_1
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | REDUCE: (57), (121) imply:
% 178.89/28.63  | | | | | | | |   (126)  op(e3, e3) = e3
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | BETA: splitting (69) gives:
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | |   (127)  all_58_4 = e3
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | REF_CLOSE: (17), (122), (127) are inconsistent by sub-proof
% 178.89/28.63  | | | | | | | | |            #1025.
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | |   (128)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | BETA: splitting (128) gives:
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | |   (129)  all_58_5 = e3
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | COMBINE_EQS: (7), (129) imply:
% 178.89/28.63  | | | | | | | | | |   (130)  all_52_13 = e3
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | SIMP: (130) implies:
% 178.89/28.63  | | | | | | | | | |   (131)  all_52_13 = e3
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | GROUND_INST: instantiating (59) with e3, all_4_1, e3, e3,
% 178.89/28.63  | | | | | | | | | |              simplifying with (125), (126) gives:
% 178.89/28.63  | | | | | | | | | |   (132)  all_4_1 = e3
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | REDUCE: (124), (132) imply:
% 178.89/28.63  | | | | | | | | | |   (133)  op(e3, e3) = all_4_0
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | GROUND_INST: instantiating (59) with e3, all_4_0, e3, e3,
% 178.89/28.63  | | | | | | | | | |              simplifying with (126), (133) gives:
% 178.89/28.63  | | | | | | | | | |   (134)  all_4_0 = e3
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | REF_CLOSE: (10), (13), (15), (17), (19), (24), (27), (29),
% 178.89/28.63  | | | | | | | | | |            (36), (42), (43), (54), (59), (63), (67), (74),
% 178.89/28.63  | | | | | | | | | |            (103), (107), (111), (113), (118), (119), (122),
% 178.89/28.63  | | | | | | | | | |            (123), (129) are inconsistent by sub-proof #695.
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | |   (135)  all_58_8 = e3 | all_58_14 = e3
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | REF_CLOSE: (27), (29), (77), (94), (135) are inconsistent by
% 178.89/28.63  | | | | | | | | | |            sub-proof #999.
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | End of split
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | End of split
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | |   (136)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | BETA: splitting (136) gives:
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | |   (137)  all_58_2 = e3
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | COMBINE_EQS: (80), (137) imply:
% 178.89/28.63  | | | | | | | | |   (138)  all_52_26 = e3
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | SIMP: (138) implies:
% 178.89/28.63  | | | | | | | | |   (139)  all_52_26 = e3
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | REDUCE: (82), (139) imply:
% 178.89/28.63  | | | | | | | | |   (140)   ~ (all_52_17 = e3)
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | BETA: splitting (40) gives:
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | |   (141)  all_58_0 = e1
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | COMBINE_EQS: (23), (141) imply:
% 178.89/28.63  | | | | | | | | | |   (142)  all_4_2 = e1
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | REF_CLOSE: (3), (9), (42), (44), (51), (59), (67), (70),
% 178.89/28.63  | | | | | | | | | |            (73), (110), (137), (141) are inconsistent by
% 178.89/28.63  | | | | | | | | | |            sub-proof #692.
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | |   (143)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | BETA: splitting (143) gives:
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | |   (144)  all_58_2 = e1
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | COMBINE_EQS: (137), (144) imply:
% 178.89/28.63  | | | | | | | | | | |   (145)  e3 = e1
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | REDUCE: (19), (145) imply:
% 178.89/28.63  | | | | | | | | | | |   (146)  $false
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | |   (147)  all_58_6 = e1 | all_58_12 = e1
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | BETA: splitting (147) gives:
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | |   (148)  all_58_6 = e1
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | COMBINE_EQS: (42), (148) imply:
% 178.89/28.63  | | | | | | | | | | | |   (149)  all_52_17 = e1
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | REDUCE: (65), (149) imply:
% 178.89/28.63  | | | | | | | | | | | |   (150)   ~ (all_52_19 = e1)
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | SIMP: (150) implies:
% 178.89/28.63  | | | | | | | | | | | |   (151)   ~ (all_52_19 = e1)
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | REDUCE: (21), (149) imply:
% 178.89/28.63  | | | | | | | | | | | |   (152)   ~ (all_14_2 = e1)
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | SIMP: (152) implies:
% 178.89/28.63  | | | | | | | | | | | |   (153)   ~ (all_14_2 = e1)
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | REDUCE: (140), (149) imply:
% 178.89/28.63  | | | | | | | | | | | |   (154)   ~ (e3 = e1)
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | BETA: splitting (9) gives:
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | Case 1:
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | |   (155)  all_58_0 = e2
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | COMBINE_EQS: (23), (155) imply:
% 178.89/28.63  | | | | | | | | | | | | |   (156)  all_4_2 = e2
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | REDUCE: (34), (156) imply:
% 178.89/28.63  | | | | | | | | | | | | |   (157)   ~ (all_52_3 = e2)
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | REDUCE: (22), (156) imply:
% 178.89/28.63  | | | | | | | | | | | | |   (158)  op(e3, e2) = all_4_1
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | GROUND_INST: instantiating (59) with all_52_3, all_4_1, e2, e3,
% 178.89/28.63  | | | | | | | | | | | | |              simplifying with (3), (158) gives:
% 178.89/28.63  | | | | | | | | | | | | |   (159)  all_52_3 = all_4_1
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | COMBINE_EQS: (30), (159) imply:
% 178.89/28.63  | | | | | | | | | | | | |   (160)  all_56_1 = all_4_1
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | REDUCE: (47), (159) imply:
% 178.89/28.63  | | | | | | | | | | | | |   (161)   ~ (all_52_19 = all_4_1)
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | SIMP: (161) implies:
% 178.89/28.63  | | | | | | | | | | | | |   (162)   ~ (all_52_19 = all_4_1)
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | REDUCE: (157), (159) imply:
% 178.89/28.63  | | | | | | | | | | | | |   (163)   ~ (all_4_1 = e2)
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | REF_CLOSE: (11), (19), (39), (52), (59), (63), (71), (85),
% 178.89/28.63  | | | | | | | | | | | | |            (88), (93), (107), (151), (153), (160), (162),
% 178.89/28.63  | | | | | | | | | | | | |            (163) are inconsistent by sub-proof #687.
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | |   (164)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | | REF_CLOSE: (3), (42), (44), (59), (67), (70), (73), (110),
% 178.89/28.63  | | | | | | | | | | | | |            (137), (164) are inconsistent by sub-proof #693.
% 178.89/28.63  | | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | End of split
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | |   (165)  all_58_12 = e1
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | | REF_CLOSE: (45), (110), (165) are inconsistent by sub-proof
% 178.89/28.63  | | | | | | | | | | | |            #907.
% 178.89/28.63  | | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | | End of split
% 178.89/28.63  | | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | | End of split
% 178.89/28.63  | | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | End of split
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | Case 2:
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | |   (166)  all_58_6 = e3 | all_58_12 = e3
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | | REF_CLOSE: (42), (44), (57), (58), (59), (68), (75), (166) are
% 178.89/28.63  | | | | | | | | |            inconsistent by sub-proof #947.
% 178.89/28.63  | | | | | | | | | 
% 178.89/28.63  | | | | | | | | End of split
% 178.89/28.63  | | | | | | | | 
% 178.89/28.63  | | | | | | | End of split
% 178.89/28.63  | | | | | | | 
% 178.89/28.63  | | | | | | End of split
% 178.89/28.63  | | | | | | 
% 178.89/28.63  | | | | | End of split
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | End of split
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | End of split
% 178.89/28.63  | | | 
% 178.89/28.63  | | End of split
% 178.89/28.63  | | 
% 178.89/28.63  | End of split
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #687 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.89/28.63    (2)  all_56_9 = all_52_19
% 178.89/28.63    (3)   ~ (e3 = e1)
% 178.89/28.63    (4)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.89/28.63    (5)   ~ (all_14_2 = e1)
% 178.89/28.63    (6)   ~ (all_4_1 = e2)
% 178.89/28.63    (7)   ~ (all_52_19 = all_4_1)
% 178.89/28.63    (8)  op(e1, e0) = e3
% 178.89/28.63    (9)  all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.89/28.63    (10)   ~ (all_4_1 = e1)
% 178.89/28.63    (11)  all_56_10 = all_14_2
% 178.89/28.63    (12)  all_56_1 = all_4_1
% 178.89/28.63    (13)   ~ (all_52_19 = e1)
% 178.89/28.63    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.63    (15)  op(e1, all_14_2) = e1
% 178.89/28.63    (16)   ~ (all_52_19 = all_14_2)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | BETA: splitting (4) gives:
% 178.89/28.63  | 
% 178.89/28.63  | Case 1:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (17)  all_56_1 = e2
% 178.89/28.63  | | 
% 178.89/28.63  | | REF_CLOSE: (6), (12), (17) are inconsistent by sub-proof #762.
% 178.89/28.63  | | 
% 178.89/28.63  | Case 2:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (18)  all_56_1 = e1 | all_56_1 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | BETA: splitting (18) gives:
% 178.89/28.63  | | 
% 178.89/28.63  | | Case 1:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (19)  all_56_1 = e1
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REF_CLOSE: (10), (12), (19) are inconsistent by sub-proof #761.
% 178.89/28.63  | | | 
% 178.89/28.63  | | Case 2:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (20)  all_56_1 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | COMBINE_EQS: (12), (20) imply:
% 178.89/28.63  | | |   (21)  all_4_1 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | SIMP: (21) implies:
% 178.89/28.63  | | |   (22)  all_4_1 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REDUCE: (7), (22) imply:
% 178.89/28.63  | | |   (23)   ~ (all_52_19 = e0)
% 178.89/28.63  | | | 
% 178.89/28.63  | | | BETA: splitting (9) gives:
% 178.89/28.63  | | | 
% 178.89/28.63  | | | Case 1:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | |   (24)  all_56_9 = e2
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | COMBINE_EQS: (2), (24) imply:
% 178.89/28.63  | | | |   (25)  all_52_19 = e2
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | SIMP: (25) implies:
% 178.89/28.63  | | | |   (26)  all_52_19 = e2
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | REF_CLOSE: (1), (3), (5), (8), (11), (14), (15), (16), (26) are
% 178.89/28.63  | | | |            inconsistent by sub-proof #689.
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | Case 2:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | |   (27)  all_56_9 = e1 | all_56_9 = e0
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | REF_CLOSE: (2), (13), (23), (27) are inconsistent by sub-proof #688.
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | End of split
% 178.89/28.63  | | | 
% 178.89/28.63  | | End of split
% 178.89/28.63  | | 
% 178.89/28.63  | End of split
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #688 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  all_56_9 = e1 | all_56_9 = e0
% 178.89/28.63    (2)  all_56_9 = all_52_19
% 178.89/28.63    (3)   ~ (all_52_19 = e1)
% 178.89/28.63    (4)   ~ (all_52_19 = e0)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | BETA: splitting (1) gives:
% 178.89/28.63  | 
% 178.89/28.63  | Case 1:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (5)  all_56_9 = e1
% 178.89/28.63  | | 
% 178.89/28.63  | | COMBINE_EQS: (2), (5) imply:
% 178.89/28.63  | |   (6)  all_52_19 = e1
% 178.89/28.63  | | 
% 178.89/28.63  | | SIMP: (6) implies:
% 178.89/28.63  | |   (7)  all_52_19 = e1
% 178.89/28.63  | | 
% 178.89/28.63  | | REDUCE: (3), (7) imply:
% 178.89/28.63  | |   (8)  $false
% 178.89/28.63  | | 
% 178.89/28.63  | | CLOSE: (8) is inconsistent.
% 178.89/28.63  | | 
% 178.89/28.63  | Case 2:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (9)  all_56_9 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | COMBINE_EQS: (2), (9) imply:
% 178.89/28.63  | |   (10)  all_52_19 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | SIMP: (10) implies:
% 178.89/28.63  | |   (11)  all_52_19 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | REDUCE: (4), (11) imply:
% 178.89/28.63  | |   (12)  $false
% 178.89/28.63  | | 
% 178.89/28.63  | | CLOSE: (12) is inconsistent.
% 178.89/28.63  | | 
% 178.89/28.63  | End of split
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #689 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.89/28.63    (2)   ~ (e3 = e1)
% 178.89/28.63    (3)  all_52_19 = e2
% 178.89/28.63    (4)   ~ (all_14_2 = e1)
% 178.89/28.63    (5)  op(e1, e0) = e3
% 178.89/28.63    (6)  all_56_10 = all_14_2
% 178.89/28.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.63    (8)  op(e1, all_14_2) = e1
% 178.89/28.63    (9)   ~ (all_52_19 = all_14_2)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (3), (9) imply:
% 178.89/28.63  |   (10)   ~ (all_14_2 = e2)
% 178.89/28.63  | 
% 178.89/28.63  | SIMP: (10) implies:
% 178.89/28.63  |   (11)   ~ (all_14_2 = e2)
% 178.89/28.63  | 
% 178.89/28.63  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (11) are inconsistent by
% 178.89/28.63  |            sub-proof #690.
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #690 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.89/28.63    (2)   ~ (e3 = e1)
% 178.89/28.63    (3)   ~ (all_14_2 = e1)
% 178.89/28.63    (4)  op(e1, e0) = e3
% 178.89/28.63    (5)  all_56_10 = all_14_2
% 178.89/28.63    (6)   ~ (all_14_2 = e2)
% 178.89/28.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.63    (8)  op(e1, all_14_2) = e1
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | BETA: splitting (1) gives:
% 178.89/28.63  | 
% 178.89/28.63  | Case 1:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (9)  all_56_10 = e2
% 178.89/28.63  | | 
% 178.89/28.63  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #691.
% 178.89/28.63  | | 
% 178.89/28.63  | Case 2:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (10)  all_56_10 = e1 | all_56_10 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | BETA: splitting (10) gives:
% 178.89/28.63  | | 
% 178.89/28.63  | | Case 1:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (11)  all_56_10 = e1
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #740.
% 178.89/28.63  | | | 
% 178.89/28.63  | | Case 2:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (12)  all_56_10 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | COMBINE_EQS: (5), (12) imply:
% 178.89/28.63  | | |   (13)  all_14_2 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | SIMP: (13) implies:
% 178.89/28.63  | | |   (14)  all_14_2 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REDUCE: (8), (14) imply:
% 178.89/28.63  | | |   (15)  op(e1, e0) = e1
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REF_CLOSE: (2), (4), (7), (15) are inconsistent by sub-proof #802.
% 178.89/28.63  | | | 
% 178.89/28.63  | | End of split
% 178.89/28.63  | | 
% 178.89/28.63  | End of split
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #691 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  all_56_10 = all_14_2
% 178.89/28.63    (2)  all_56_10 = e2
% 178.89/28.63    (3)   ~ (all_14_2 = e2)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.63  |   (4)  all_14_2 = e2
% 178.89/28.63  | 
% 178.89/28.63  | SIMP: (4) implies:
% 178.89/28.63  |   (5)  all_14_2 = e2
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (3), (5) imply:
% 178.89/28.63  |   (6)  $false
% 178.89/28.63  | 
% 178.89/28.63  | CLOSE: (6) is inconsistent.
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #692 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  op(e3, e2) = all_52_3
% 178.89/28.63    (2)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.63    (3)  all_58_2 = e3
% 178.89/28.63    (4)  all_58_12 = e0
% 178.89/28.63    (5)  all_58_0 = e1
% 178.89/28.63    (6)   ~ (all_52_3 = e3)
% 178.89/28.63    (7)  all_58_6 = all_52_17
% 178.89/28.63    (8)  op(e3, all_52_17) = e3
% 178.89/28.63    (9)   ~ (e2 = e1)
% 178.89/28.63    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.63    (11)   ~ (e2 = e0)
% 178.89/28.63    (12)   ~ (e3 = e2)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | BETA: splitting (2) gives:
% 178.89/28.63  | 
% 178.89/28.63  | Case 1:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (13)  all_58_0 = e2
% 178.89/28.63  | | 
% 178.89/28.63  | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #930.
% 178.89/28.63  | | 
% 178.89/28.63  | Case 2:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (14)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.63  | | 
% 178.89/28.63  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12), (14) are
% 178.89/28.63  | |            inconsistent by sub-proof #693.
% 178.89/28.63  | | 
% 178.89/28.63  | End of split
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #693 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  op(e3, e2) = all_52_3
% 178.89/28.63    (2)  all_58_2 = e3
% 178.89/28.63    (3)  all_58_12 = e0
% 178.89/28.63    (4)   ~ (all_52_3 = e3)
% 178.89/28.63    (5)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.63    (6)  all_58_6 = all_52_17
% 178.89/28.63    (7)  op(e3, all_52_17) = e3
% 178.89/28.63    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.63    (9)   ~ (e2 = e0)
% 178.89/28.63    (10)   ~ (e3 = e2)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | BETA: splitting (5) gives:
% 178.89/28.63  | 
% 178.89/28.63  | Case 1:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (11)  all_58_2 = e2
% 178.89/28.63  | | 
% 178.89/28.63  | | REF_CLOSE: (2), (10), (11) are inconsistent by sub-proof #694.
% 178.89/28.63  | | 
% 178.89/28.63  | Case 2:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (12)  all_58_6 = e2 | all_58_12 = e2
% 178.89/28.63  | | 
% 178.89/28.63  | | BETA: splitting (12) gives:
% 178.89/28.63  | | 
% 178.89/28.63  | | Case 1:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (13)  all_58_6 = e2
% 178.89/28.63  | | | 
% 178.89/28.63  | | | COMBINE_EQS: (6), (13) imply:
% 178.89/28.63  | | |   (14)  all_52_17 = e2
% 178.89/28.63  | | | 
% 178.89/28.63  | | | SIMP: (14) implies:
% 178.89/28.63  | | |   (15)  all_52_17 = e2
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REDUCE: (7), (15) imply:
% 178.89/28.63  | | |   (16)  op(e3, e2) = e3
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REF_CLOSE: (1), (4), (8), (16) are inconsistent by sub-proof #978.
% 178.89/28.63  | | | 
% 178.89/28.63  | | Case 2:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (17)  all_58_12 = e2
% 178.89/28.63  | | | 
% 178.89/28.63  | | | COMBINE_EQS: (3), (17) imply:
% 178.89/28.63  | | |   (18)  e2 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REDUCE: (9), (18) imply:
% 178.89/28.63  | | |   (19)  $false
% 178.89/28.63  | | | 
% 178.89/28.63  | | | CLOSE: (19) is inconsistent.
% 178.89/28.63  | | | 
% 178.89/28.63  | | End of split
% 178.89/28.63  | | 
% 178.89/28.63  | End of split
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #694 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  all_58_2 = e3
% 178.89/28.63    (2)  all_58_2 = e2
% 178.89/28.63    (3)   ~ (e3 = e2)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.63  |   (4)  e3 = e2
% 178.89/28.63  | 
% 178.89/28.63  | SIMP: (4) implies:
% 178.89/28.63  |   (5)  e3 = e2
% 178.89/28.63  | 
% 178.89/28.63  | REDUCE: (3), (5) imply:
% 178.89/28.63  |   (6)  $false
% 178.89/28.63  | 
% 178.89/28.63  | CLOSE: (6) is inconsistent.
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #695 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)   ~ (all_52_17 = e0)
% 178.89/28.63    (2)  op(e2, e0) = all_52_15
% 178.89/28.63    (3)  all_58_10 = all_52_15
% 178.89/28.63    (4)  all_58_7 = all_52_19
% 178.89/28.63    (5)  all_58_4 = all_52_5
% 178.89/28.63    (6)   ~ (all_52_5 = all_52_24)
% 178.89/28.63    (7)   ~ (e3 = e1)
% 178.89/28.63    (8)  all_58_5 = e3
% 178.89/28.63    (9)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.63    (10)  all_58_11 = e3
% 178.89/28.63    (11)  all_58_14 = all_52_29
% 178.89/28.63    (12)  all_58_8 = all_14_2
% 178.89/28.63    (13)  op(e1, e0) = e3
% 178.89/28.63    (14)   ~ (all_52_5 = e3)
% 178.89/28.63    (15)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.89/28.63    (16)   ~ (e3 = e0)
% 178.89/28.63    (17)  all_58_6 = all_52_17
% 178.89/28.63    (18)  op(e2, all_52_19) = e2
% 178.89/28.63    (19)   ~ (all_52_29 = e0)
% 178.89/28.63    (20)   ~ (all_52_19 = e3)
% 178.89/28.63    (21)  all_58_6 = e0 | all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.89/28.63    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.63            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.63    (23)  op(e1, all_14_2) = e1
% 178.89/28.63    (24)  all_58_9 = all_52_24
% 178.89/28.63    (25)   ~ (e2 = e0)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | BETA: splitting (21) gives:
% 178.89/28.63  | 
% 178.89/28.63  | Case 1:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (26)  all_58_6 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | COMBINE_EQS: (17), (26) imply:
% 178.89/28.63  | |   (27)  all_52_17 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | REDUCE: (1), (27) imply:
% 178.89/28.63  | |   (28)  $false
% 178.89/28.63  | | 
% 178.89/28.63  | | CLOSE: (28) is inconsistent.
% 178.89/28.63  | | 
% 178.89/28.63  | Case 2:
% 178.89/28.63  | | 
% 178.89/28.63  | |   (29)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.89/28.63  | | 
% 178.89/28.63  | | BETA: splitting (15) gives:
% 178.89/28.63  | | 
% 178.89/28.63  | | Case 1:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (30)  all_58_4 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | COMBINE_EQS: (5), (30) imply:
% 178.89/28.63  | | |   (31)  all_52_5 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REDUCE: (6), (31) imply:
% 178.89/28.63  | | |   (32)   ~ (all_52_24 = e0)
% 178.89/28.63  | | | 
% 178.89/28.63  | | | SIMP: (32) implies:
% 178.89/28.63  | | |   (33)   ~ (all_52_24 = e0)
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REDUCE: (14), (31) imply:
% 178.89/28.63  | | |   (34)   ~ (e3 = e0)
% 178.89/28.63  | | | 
% 178.89/28.63  | | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (12), (13), (16), (18), (20),
% 178.89/28.63  | | |            (22), (23), (24), (25), (29), (33) are inconsistent by
% 178.89/28.63  | | |            sub-proof #697.
% 178.89/28.63  | | | 
% 178.89/28.63  | | Case 2:
% 178.89/28.63  | | | 
% 178.89/28.63  | | |   (35)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.89/28.63  | | | 
% 178.89/28.63  | | | BETA: splitting (35) gives:
% 178.89/28.63  | | | 
% 178.89/28.63  | | | Case 1:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | |   (36)  all_58_5 = e0
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | COMBINE_EQS: (8), (36) imply:
% 178.89/28.63  | | | |   (37)  e3 = e0
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | REDUCE: (16), (37) imply:
% 178.89/28.63  | | | |   (38)  $false
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | CLOSE: (38) is inconsistent.
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | Case 2:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | |   (39)  all_58_8 = e0 | all_58_14 = e0
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | BETA: splitting (39) gives:
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | | Case 1:
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | |   (40)  all_58_8 = e0
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | COMBINE_EQS: (12), (40) imply:
% 178.89/28.63  | | | | |   (41)  all_14_2 = e0
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | REDUCE: (23), (41) imply:
% 178.89/28.63  | | | | |   (42)  op(e1, e0) = e1
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | REF_CLOSE: (7), (13), (22), (42) are inconsistent by sub-proof #802.
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | Case 2:
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | |   (43)  all_58_14 = e0
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | | REF_CLOSE: (11), (19), (43) are inconsistent by sub-proof #696.
% 178.89/28.63  | | | | | 
% 178.89/28.63  | | | | End of split
% 178.89/28.63  | | | | 
% 178.89/28.63  | | | End of split
% 178.89/28.63  | | | 
% 178.89/28.63  | | End of split
% 178.89/28.63  | | 
% 178.89/28.63  | End of split
% 178.89/28.63  | 
% 178.89/28.63  End of proof
% 178.89/28.63  
% 178.89/28.63  Sub-proof #696 shows that the following formulas are inconsistent:
% 178.89/28.63  ----------------------------------------------------------------
% 178.89/28.63    (1)  all_58_14 = all_52_29
% 178.89/28.63    (2)  all_58_14 = e0
% 178.89/28.63    (3)   ~ (all_52_29 = e0)
% 178.89/28.63  
% 178.89/28.63  Begin of proof
% 178.89/28.63  | 
% 178.89/28.63  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.64  |   (4)  all_52_29 = e0
% 178.89/28.64  | 
% 178.89/28.64  | SIMP: (4) implies:
% 178.89/28.64  |   (5)  all_52_29 = e0
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (3), (5) imply:
% 178.89/28.64  |   (6)  $false
% 178.89/28.64  | 
% 178.89/28.64  | CLOSE: (6) is inconsistent.
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #697 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  op(e2, e0) = all_52_15
% 178.89/28.64    (2)  all_58_10 = all_52_15
% 178.89/28.64    (3)  all_58_7 = all_52_19
% 178.89/28.64    (4)   ~ (e3 = e1)
% 178.89/28.64    (5)   ~ (all_52_24 = e0)
% 178.89/28.64    (6)  all_58_7 = e0 | all_58_8 = e0 | all_58_11 = e0
% 178.89/28.64    (7)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.64    (8)  all_58_11 = e3
% 178.89/28.64    (9)  all_58_8 = all_14_2
% 178.89/28.64    (10)  op(e1, e0) = e3
% 178.89/28.64    (11)   ~ (e3 = e0)
% 178.89/28.64    (12)  op(e2, all_52_19) = e2
% 178.89/28.64    (13)   ~ (all_52_19 = e3)
% 178.89/28.64    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (15)  op(e1, all_14_2) = e1
% 178.89/28.64    (16)  all_58_9 = all_52_24
% 178.89/28.64    (17)   ~ (e2 = e0)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (6) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (18)  all_58_7 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | COMBINE_EQS: (3), (18) imply:
% 178.89/28.64  | |   (19)  all_52_19 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REDUCE: (13), (19) imply:
% 178.89/28.64  | |   (20)   ~ (e3 = e0)
% 178.89/28.64  | | 
% 178.89/28.64  | | REDUCE: (12), (19) imply:
% 178.89/28.64  | |   (21)  op(e2, e0) = e2
% 178.89/28.64  | | 
% 178.89/28.64  | | BETA: splitting (7) gives:
% 178.89/28.64  | | 
% 178.89/28.64  | | Case 1:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (22)  all_58_9 = e0
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REF_CLOSE: (5), (16), (22) are inconsistent by sub-proof #760.
% 178.89/28.64  | | | 
% 178.89/28.64  | | Case 2:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (23)  all_58_10 = e0 | all_58_11 = e0
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REF_CLOSE: (1), (2), (8), (11), (14), (17), (21), (23) are inconsistent by
% 178.89/28.64  | | |            sub-proof #699.
% 178.89/28.64  | | | 
% 178.89/28.64  | | End of split
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (24)  all_58_8 = e0 | all_58_11 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (4), (8), (9), (10), (11), (14), (15), (24) are inconsistent by
% 178.89/28.64  | |            sub-proof #698.
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #698 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)   ~ (e3 = e1)
% 178.89/28.64    (2)  all_58_11 = e3
% 178.89/28.64    (3)  all_58_8 = all_14_2
% 178.89/28.64    (4)  op(e1, e0) = e3
% 178.89/28.64    (5)   ~ (e3 = e0)
% 178.89/28.64    (6)  all_58_8 = e0 | all_58_11 = e0
% 178.89/28.64    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (8)  op(e1, all_14_2) = e1
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (6) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (9)  all_58_8 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | COMBINE_EQS: (3), (9) imply:
% 178.89/28.64  | |   (10)  all_14_2 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | SIMP: (10) implies:
% 178.89/28.64  | |   (11)  all_14_2 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REDUCE: (8), (11) imply:
% 178.89/28.64  | |   (12)  op(e1, e0) = e1
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (1), (4), (7), (12) are inconsistent by sub-proof #802.
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (13)  all_58_11 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #804.
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #699 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_58_10 = e0 | all_58_11 = e0
% 178.89/28.64    (2)  op(e2, e0) = all_52_15
% 178.89/28.64    (3)  all_58_10 = all_52_15
% 178.89/28.64    (4)  all_58_11 = e3
% 178.89/28.64    (5)   ~ (e3 = e0)
% 178.89/28.64    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (7)   ~ (e2 = e0)
% 178.89/28.64    (8)  op(e2, e0) = e2
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (1) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (9)  all_58_10 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | COMBINE_EQS: (3), (9) imply:
% 178.89/28.64  | |   (10)  all_52_15 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | SIMP: (10) implies:
% 178.89/28.64  | |   (11)  all_52_15 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REDUCE: (2), (11) imply:
% 178.89/28.64  | |   (12)  op(e2, e0) = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | GROUND_INST: instantiating (6) with e0, e2, e0, e2, simplifying with (8),
% 178.89/28.64  | |              (12) gives:
% 178.89/28.64  | |   (13)  e2 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REDUCE: (7), (13) imply:
% 178.89/28.64  | |   (14)  $false
% 178.89/28.64  | | 
% 178.89/28.64  | | CLOSE: (14) is inconsistent.
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (15)  all_58_11 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (4), (5), (15) are inconsistent by sub-proof #804.
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #700 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_56_9 = all_52_19
% 178.89/28.64    (2)  all_56_9 = e3
% 178.89/28.64    (3)   ~ (all_52_19 = e3)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.64  |   (4)  all_52_19 = e3
% 178.89/28.64  | 
% 178.89/28.64  | SIMP: (4) implies:
% 178.89/28.64  |   (5)  all_52_19 = e3
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (3), (5) imply:
% 178.89/28.64  |   (6)  $false
% 178.89/28.64  | 
% 178.89/28.64  | CLOSE: (6) is inconsistent.
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #701 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)   ~ (all_52_23 = all_14_2)
% 178.89/28.64    (2)   ~ (all_52_27 = all_10_2)
% 178.89/28.64    (3)  op(e2, all_10_2) = all_10_1
% 178.89/28.64    (4)   ~ (all_52_19 = all_52_23)
% 178.89/28.64    (5)  op(e1, e2) = all_52_19
% 178.89/28.64    (6)  all_56_15 = e3
% 178.89/28.64    (7)  all_58_5 = all_52_13
% 178.89/28.64    (8)  all_56_15 = all_6_2
% 178.89/28.64    (9)  all_58_3 = all_10_2
% 178.89/28.64    (10)  all_56_9 = all_52_19
% 178.89/28.64    (11)  all_58_15 = all_6_2
% 178.89/28.64    (12)   ~ (all_52_9 = all_4_2)
% 178.89/28.64    (13)  all_58_10 = all_52_15
% 178.89/28.64    (14)   ~ (all_52_5 = all_4_2)
% 178.89/28.64    (15)  all_58_7 = all_52_19
% 178.89/28.64    (16)  all_58_4 = all_52_5
% 178.89/28.64    (17)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.64    (18)   ~ (all_52_17 = all_14_2)
% 178.89/28.64    (19)  op(e3, all_4_2) = all_4_1
% 178.89/28.64    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.89/28.64    (21)  all_58_0 = all_4_2
% 178.89/28.64    (22)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.89/28.64    (23)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.89/28.64    (24)  all_58_14 = all_52_29
% 178.89/28.64    (25)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.64    (26)  op(e2, e1) = all_52_13
% 178.89/28.64    (27)  all_58_8 = all_14_2
% 178.89/28.64    (28)  op(e0, e2) = all_52_27
% 178.89/28.64    (29)  op(all_4_1, all_4_2) = all_4_0
% 178.89/28.64    (30)   ~ (all_52_5 = all_14_2)
% 178.89/28.64    (31)   ~ (all_52_9 = all_10_2)
% 178.89/28.64    (32)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.89/28.64    (33)   ~ (all_52_9 = all_52_13)
% 178.89/28.64    (34)  all_56_5 = all_10_2
% 178.89/28.64    (35)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.64    (36)   ~ (all_52_9 = all_52_17)
% 178.89/28.64    (37)  all_58_6 = all_52_17
% 178.89/28.64    (38)  op(e2, all_52_19) = e2
% 178.89/28.64    (39)  op(e3, all_52_17) = e3
% 178.89/28.64    (40)  all_58_11 = all_52_23
% 178.89/28.64    (41)   ~ (all_4_0 = e1)
% 178.89/28.64    (42)   ~ (all_52_23 = all_6_2)
% 178.89/28.64    (43)   ~ (all_52_29 = all_6_2)
% 178.89/28.64    (44)  all_58_2 = all_52_9
% 178.89/28.64    (45)  op(e3, e1) = all_52_5
% 178.89/28.64    (46)   ~ (e2 = e1)
% 178.89/28.64    (47)   ~ (all_52_25 = all_6_2)
% 178.89/28.64    (48)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.89/28.64    (49)  op(e1, e3) = all_52_17
% 178.89/28.64    (50)  op(e3, e3) = all_4_2
% 178.89/28.64    (51)   ~ (all_10_1 = e3)
% 178.89/28.64    (52)   ~ (all_52_17 = all_4_2)
% 178.89/28.64    (53)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (54)   ~ (all_52_7 = all_6_2)
% 178.89/28.64    (55)  op(e0, all_52_23) = e0
% 178.89/28.64    (56)  op(e1, all_14_2) = e1
% 178.89/28.64    (57)   ~ (all_52_7 = all_52_23)
% 178.89/28.64    (58)   ~ (all_52_13 = all_10_2)
% 178.89/28.64    (59)  all_58_9 = all_52_7
% 178.89/28.64    (60)  all_58_12 = all_52_25
% 178.89/28.64    (61)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.64    (62)   ~ (all_52_9 = all_52_15)
% 178.89/28.64    (63)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.64    (64)   ~ (e3 = e2)
% 178.89/28.64    (65)   ~ (all_52_19 = all_14_2)
% 178.89/28.64    (66)  op(e2, e3) = all_52_9
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | COMBINE_EQS: (6), (8) imply:
% 178.89/28.64  |   (67)  all_6_2 = e3
% 178.89/28.64  | 
% 178.89/28.64  | SIMP: (67) implies:
% 178.89/28.64  |   (68)  all_6_2 = e3
% 178.89/28.64  | 
% 178.89/28.64  | COMBINE_EQS: (11), (68) imply:
% 178.89/28.64  |   (69)  all_58_15 = e3
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (54), (68) imply:
% 178.89/28.64  |   (70)   ~ (all_52_7 = e3)
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (42), (68) imply:
% 178.89/28.64  |   (71)   ~ (all_52_23 = e3)
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (47), (68) imply:
% 178.89/28.64  |   (72)   ~ (all_52_25 = e3)
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (43), (68) imply:
% 178.89/28.64  |   (73)   ~ (all_52_29 = e3)
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (32) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (74)  all_58_9 = e2
% 178.89/28.64  | | 
% 178.89/28.64  | | COMBINE_EQS: (59), (74) imply:
% 178.89/28.64  | |   (75)  all_52_7 = e2
% 178.89/28.64  | | 
% 178.89/28.64  | | SIMP: (75) implies:
% 178.89/28.64  | |   (76)  all_52_7 = e2
% 178.89/28.64  | | 
% 178.89/28.64  | | REDUCE: (57), (76) imply:
% 178.89/28.64  | |   (77)   ~ (all_52_23 = e2)
% 178.89/28.64  | | 
% 178.89/28.64  | | SIMP: (77) implies:
% 178.89/28.64  | |   (78)   ~ (all_52_23 = e2)
% 178.89/28.64  | | 
% 178.89/28.64  | | REDUCE: (70), (76) imply:
% 178.89/28.64  | |   (79)   ~ (e3 = e2)
% 178.89/28.64  | | 
% 178.89/28.64  | | BETA: splitting (61) gives:
% 178.89/28.64  | | 
% 178.89/28.64  | | Case 1:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (80)  all_58_0 = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | COMBINE_EQS: (21), (80) imply:
% 178.89/28.64  | | |   (81)  all_4_2 = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (12), (81) imply:
% 178.89/28.64  | | |   (82)   ~ (all_52_9 = e3)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (52), (81) imply:
% 178.89/28.64  | | |   (83)   ~ (all_52_17 = e3)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (29), (81) imply:
% 178.89/28.64  | | |   (84)  op(all_4_1, e3) = all_4_0
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (19), (81) imply:
% 178.89/28.64  | | |   (85)  op(e3, e3) = all_4_1
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (50), (81) imply:
% 178.89/28.64  | | |   (86)  op(e3, e3) = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | GROUND_INST: instantiating (53) with e3, all_4_1, e3, e3, simplifying with
% 178.89/28.64  | | |              (85), (86) gives:
% 178.89/28.64  | | |   (87)  all_4_1 = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (84), (87) imply:
% 178.89/28.64  | | |   (88)  op(e3, e3) = all_4_0
% 178.89/28.64  | | | 
% 178.89/28.64  | | | GROUND_INST: instantiating (53) with e3, all_4_0, e3, e3, simplifying with
% 178.89/28.64  | | |              (86), (88) gives:
% 178.89/28.64  | | |   (89)  all_4_0 = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (41), (89) imply:
% 178.89/28.64  | | |   (90)   ~ (e3 = e1)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REF_CLOSE: (5), (10), (15), (17), (22), (27), (30), (35), (36), (37),
% 178.89/28.64  | | |            (38), (39), (40), (45), (49), (53), (56), (66), (71), (78),
% 178.89/28.64  | | |            (82), (83), (90) are inconsistent by sub-proof #712.
% 178.89/28.64  | | | 
% 178.89/28.64  | | Case 2:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (91)   ~ (all_58_0 = e3)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (21), (91) imply:
% 178.89/28.64  | | |   (92)   ~ (all_4_2 = e3)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REF_CLOSE: (10), (15), (17), (20), (21), (22), (25), (27), (30), (36),
% 178.89/28.64  | | |            (37), (38), (39), (40), (44), (45), (49), (50), (52), (53),
% 178.89/28.64  | | |            (56), (60), (64), (66), (71), (72), (92) are inconsistent by
% 178.89/28.64  | | |            sub-proof #944.
% 178.89/28.64  | | | 
% 178.89/28.64  | | End of split
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (93)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.89/28.64  | | 
% 178.89/28.64  | | BETA: splitting (22) gives:
% 178.89/28.64  | | 
% 178.89/28.64  | | Case 1:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (94)  all_56_9 = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | COMBINE_EQS: (10), (94) imply:
% 178.89/28.64  | | |   (95)  all_52_19 = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | SIMP: (95) implies:
% 178.89/28.64  | | |   (96)  all_52_19 = e3
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (4), (96) imply:
% 178.89/28.64  | | |   (97)   ~ (all_52_23 = e3)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (38), (96) imply:
% 178.89/28.64  | | |   (98)  op(e2, e3) = e2
% 178.89/28.64  | | | 
% 178.89/28.64  | | | GROUND_INST: instantiating (53) with all_52_9, e2, e3, e2, simplifying
% 178.89/28.64  | | |              with (66), (98) gives:
% 178.89/28.64  | | |   (99)  all_52_9 = e2
% 178.89/28.64  | | | 
% 178.89/28.64  | | | COMBINE_EQS: (44), (99) imply:
% 178.89/28.64  | | |   (100)  all_58_2 = e2
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (33), (99) imply:
% 178.89/28.64  | | |   (101)   ~ (all_52_13 = e2)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | SIMP: (101) implies:
% 178.89/28.64  | | |   (102)   ~ (all_52_13 = e2)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (62), (99) imply:
% 178.89/28.64  | | |   (103)   ~ (all_52_15 = e2)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | SIMP: (103) implies:
% 178.89/28.64  | | |   (104)   ~ (all_52_15 = e2)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (31), (99) imply:
% 178.89/28.64  | | |   (105)   ~ (all_10_2 = e2)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | SIMP: (105) implies:
% 178.89/28.64  | | |   (106)   ~ (all_10_2 = e2)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | BETA: splitting (25) gives:
% 178.89/28.64  | | | 
% 178.89/28.64  | | | Case 1:
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | |   (107)  all_58_0 = e3
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | COMBINE_EQS: (21), (107) imply:
% 178.89/28.64  | | | |   (108)  all_4_2 = e3
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | REDUCE: (14), (108) imply:
% 178.89/28.64  | | | |   (109)   ~ (all_52_5 = e3)
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | BETA: splitting (63) gives:
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | Case 1:
% 178.89/28.64  | | | | | 
% 178.89/28.64  | | | | |   (110)  all_58_4 = e3
% 178.89/28.64  | | | | | 
% 178.89/28.64  | | | | | REF_CLOSE: (16), (109), (110) are inconsistent by sub-proof #1025.
% 178.89/28.64  | | | | | 
% 178.89/28.64  | | | | Case 2:
% 178.89/28.64  | | | | | 
% 178.89/28.64  | | | | |   (111)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.64  | | | | | 
% 178.89/28.64  | | | | | BETA: splitting (111) gives:
% 178.89/28.64  | | | | | 
% 178.89/28.64  | | | | | Case 1:
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | |   (112)  all_58_5 = e3
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | COMBINE_EQS: (7), (112) imply:
% 178.89/28.64  | | | | | |   (113)  all_52_13 = e3
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | SIMP: (113) implies:
% 178.89/28.64  | | | | | |   (114)  all_52_13 = e3
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | REDUCE: (58), (114) imply:
% 178.89/28.64  | | | | | |   (115)   ~ (all_10_2 = e3)
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | SIMP: (115) implies:
% 178.89/28.64  | | | | | |   (116)   ~ (all_10_2 = e3)
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | REDUCE: (26), (114) imply:
% 178.89/28.64  | | | | | |   (117)  op(e2, e1) = e3
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | BETA: splitting (93) gives:
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | Case 1:
% 178.89/28.64  | | | | | | | 
% 178.89/28.64  | | | | | | |   (118)  all_58_10 = e2
% 178.89/28.64  | | | | | | | 
% 178.89/28.64  | | | | | | | REF_CLOSE: (13), (104), (118) are inconsistent by sub-proof #711.
% 178.89/28.64  | | | | | | | 
% 178.89/28.64  | | | | | | Case 2:
% 178.89/28.64  | | | | | | | 
% 178.89/28.64  | | | | | | |   (119)  all_58_11 = e2 | all_58_15 = e2
% 178.89/28.64  | | | | | | | 
% 178.89/28.64  | | | | | | | BETA: splitting (119) gives:
% 178.89/28.64  | | | | | | | 
% 178.89/28.64  | | | | | | | Case 1:
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | |   (120)  all_58_11 = e2
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | COMBINE_EQS: (40), (120) imply:
% 178.89/28.64  | | | | | | | |   (121)  all_52_23 = e2
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | SIMP: (121) implies:
% 178.89/28.64  | | | | | | | |   (122)  all_52_23 = e2
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | REDUCE: (55), (122) imply:
% 178.89/28.64  | | | | | | | |   (123)  op(e0, e2) = e0
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | GROUND_INST: instantiating (53) with all_52_27, e0, e2, e0,
% 178.89/28.64  | | | | | | | |              simplifying with (28), (123) gives:
% 178.89/28.64  | | | | | | | |   (124)  all_52_27 = e0
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | REDUCE: (2), (124) imply:
% 178.89/28.64  | | | | | | | |   (125)   ~ (all_10_2 = e0)
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | SIMP: (125) implies:
% 178.89/28.64  | | | | | | | |   (126)   ~ (all_10_2 = e0)
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | BETA: splitting (48) gives:
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | Case 1:
% 178.89/28.64  | | | | | | | | | 
% 178.89/28.64  | | | | | | | | |   (127)  all_56_5 = e3
% 178.89/28.64  | | | | | | | | | 
% 178.89/28.64  | | | | | | | | | REF_CLOSE: (34), (116), (127) are inconsistent by sub-proof
% 178.89/28.64  | | | | | | | | |            #895.
% 178.89/28.64  | | | | | | | | | 
% 178.89/28.64  | | | | | | | | Case 2:
% 178.89/28.64  | | | | | | | | | 
% 178.89/28.64  | | | | | | | | |   (128)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.89/28.64  | | | | | | | | | 
% 178.89/28.64  | | | | | | | | | REF_CLOSE: (3), (9), (23), (34), (46), (51), (53), (100),
% 178.89/28.64  | | | | | | | | |            (106), (117), (126), (128) are inconsistent by
% 178.89/28.64  | | | | | | | | |            sub-proof #706.
% 178.89/28.64  | | | | | | | | | 
% 178.89/28.64  | | | | | | | | End of split
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | Case 2:
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | |   (129)  all_58_15 = e2
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | COMBINE_EQS: (69), (129) imply:
% 178.89/28.64  | | | | | | | |   (130)  e3 = e2
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | REDUCE: (64), (130) imply:
% 178.89/28.64  | | | | | | | |   (131)  $false
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | | CLOSE: (131) is inconsistent.
% 178.89/28.64  | | | | | | | | 
% 178.89/28.64  | | | | | | | End of split
% 178.89/28.64  | | | | | | | 
% 178.89/28.64  | | | | | | End of split
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | Case 2:
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | |   (132)  all_58_8 = e3 | all_58_14 = e3
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | | REF_CLOSE: (1), (15), (17), (18), (24), (27), (30), (37), (39),
% 178.89/28.64  | | | | | |            (40), (45), (49), (53), (56), (65), (73), (132) are
% 178.89/28.64  | | | | | |            inconsistent by sub-proof #703.
% 178.89/28.64  | | | | | | 
% 178.89/28.64  | | | | | End of split
% 178.89/28.64  | | | | | 
% 178.89/28.64  | | | | End of split
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | Case 2:
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | |   (133)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | REF_CLOSE: (10), (15), (17), (20), (22), (27), (30), (36), (37), (38),
% 178.89/28.64  | | | |            (39), (40), (44), (45), (49), (50), (52), (53), (56), (60),
% 178.89/28.64  | | | |            (64), (66), (71), (72), (133) are inconsistent by sub-proof
% 178.89/28.64  | | | |            #945.
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | End of split
% 178.89/28.64  | | | 
% 178.89/28.64  | | Case 2:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (134)   ~ (all_56_9 = e3)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REDUCE: (10), (134) imply:
% 178.89/28.64  | | |   (135)   ~ (all_52_19 = e3)
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REF_CLOSE: (15), (17), (27), (30), (37), (39), (40), (45), (49), (50),
% 178.89/28.64  | | |            (52), (53), (56), (71), (135) are inconsistent by sub-proof
% 178.89/28.64  | | |            #702.
% 178.89/28.64  | | | 
% 178.89/28.64  | | End of split
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #702 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_58_7 = all_52_19
% 178.89/28.64    (2)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.64    (3)  all_58_8 = all_14_2
% 178.89/28.64    (4)   ~ (all_52_5 = all_14_2)
% 178.89/28.64    (5)   ~ (all_52_23 = e3)
% 178.89/28.64    (6)  all_58_6 = all_52_17
% 178.89/28.64    (7)  op(e3, all_52_17) = e3
% 178.89/28.64    (8)  all_58_11 = all_52_23
% 178.89/28.64    (9)  op(e3, e1) = all_52_5
% 178.89/28.64    (10)   ~ (all_52_19 = e3)
% 178.89/28.64    (11)  op(e1, e3) = all_52_17
% 178.89/28.64    (12)  op(e3, e3) = all_4_2
% 178.89/28.64    (13)   ~ (all_52_17 = all_4_2)
% 178.89/28.64    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (15)  op(e1, all_14_2) = e1
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (2) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (16)  all_58_6 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | COMBINE_EQS: (6), (16) imply:
% 178.89/28.64  | |   (17)  all_52_17 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (7), (12), (13), (14), (17) are inconsistent by sub-proof #948.
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (18)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (14), (15), (18)
% 178.89/28.64  | |            are inconsistent by sub-proof #950.
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #703 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)   ~ (all_52_23 = all_14_2)
% 178.89/28.64    (2)  all_58_7 = all_52_19
% 178.89/28.64    (3)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.64    (4)   ~ (all_52_17 = all_14_2)
% 178.89/28.64    (5)  all_58_14 = all_52_29
% 178.89/28.64    (6)  all_58_8 = all_14_2
% 178.89/28.64    (7)   ~ (all_52_5 = all_14_2)
% 178.89/28.64    (8)   ~ (all_52_29 = e3)
% 178.89/28.64    (9)  all_58_6 = all_52_17
% 178.89/28.64    (10)  op(e3, all_52_17) = e3
% 178.89/28.64    (11)  all_58_11 = all_52_23
% 178.89/28.64    (12)  op(e3, e1) = all_52_5
% 178.89/28.64    (13)  all_58_8 = e3 | all_58_14 = e3
% 178.89/28.64    (14)  op(e1, e3) = all_52_17
% 178.89/28.64    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (16)  op(e1, all_14_2) = e1
% 178.89/28.64    (17)   ~ (all_52_19 = all_14_2)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (13) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (18)  all_58_8 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | COMBINE_EQS: (6), (18) imply:
% 178.89/28.64  | |   (19)  all_14_2 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (14), (15),
% 178.89/28.64  | |            (16), (17), (19) are inconsistent by sub-proof #704.
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (20)  all_58_14 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (5), (8), (20) are inconsistent by sub-proof #1000.
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #704 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)   ~ (all_52_23 = all_14_2)
% 178.89/28.64    (2)  all_58_7 = all_52_19
% 178.89/28.64    (3)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.64    (4)   ~ (all_52_17 = all_14_2)
% 178.89/28.64    (5)  all_58_8 = all_14_2
% 178.89/28.64    (6)   ~ (all_52_5 = all_14_2)
% 178.89/28.64    (7)  all_58_6 = all_52_17
% 178.89/28.64    (8)  op(e3, all_52_17) = e3
% 178.89/28.64    (9)  all_58_11 = all_52_23
% 178.89/28.64    (10)  op(e3, e1) = all_52_5
% 178.89/28.64    (11)  op(e1, e3) = all_52_17
% 178.89/28.64    (12)  all_14_2 = e3
% 178.89/28.64    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (14)  op(e1, all_14_2) = e1
% 178.89/28.64    (15)   ~ (all_52_19 = all_14_2)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (4), (12) imply:
% 178.89/28.64  |   (16)   ~ (all_52_17 = e3)
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (12), (15) imply:
% 178.89/28.64  |   (17)   ~ (all_52_19 = e3)
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (1), (12) imply:
% 178.89/28.64  |   (18)   ~ (all_52_23 = e3)
% 178.89/28.64  | 
% 178.89/28.64  | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14), (16),
% 178.89/28.64  |            (17), (18) are inconsistent by sub-proof #705.
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #705 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)   ~ (all_52_17 = e3)
% 178.89/28.64    (2)  all_58_7 = all_52_19
% 178.89/28.64    (3)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.64    (4)  all_58_8 = all_14_2
% 178.89/28.64    (5)   ~ (all_52_5 = all_14_2)
% 178.89/28.64    (6)   ~ (all_52_23 = e3)
% 178.89/28.64    (7)  all_58_6 = all_52_17
% 178.89/28.64    (8)  op(e3, all_52_17) = e3
% 178.89/28.64    (9)  all_58_11 = all_52_23
% 178.89/28.64    (10)  op(e3, e1) = all_52_5
% 178.89/28.64    (11)   ~ (all_52_19 = e3)
% 178.89/28.64    (12)  op(e1, e3) = all_52_17
% 178.89/28.64    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64    (14)  op(e1, all_14_2) = e1
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (3) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (15)  all_58_6 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (1), (7), (15) are inconsistent by sub-proof #981.
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (16)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14), (16)
% 178.89/28.64  | |            are inconsistent by sub-proof #950.
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #706 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  op(e2, all_10_2) = all_10_1
% 178.89/28.64    (2)   ~ (all_10_2 = e0)
% 178.89/28.64    (3)  all_58_2 = e2
% 178.89/28.64    (4)  all_58_3 = all_10_2
% 178.89/28.64    (5)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.89/28.64    (6)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 178.89/28.64    (7)  all_56_5 = all_10_2
% 178.89/28.64    (8)  op(e2, e1) = e3
% 178.89/28.64    (9)   ~ (all_10_2 = e2)
% 178.89/28.64    (10)   ~ (e2 = e1)
% 178.89/28.64    (11)   ~ (all_10_1 = e3)
% 178.89/28.64    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (5) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (13)  all_58_2 = e1
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (3), (10), (13) are inconsistent by sub-proof #921.
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (14)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.89/28.64  | | 
% 178.89/28.64  | | BETA: splitting (6) gives:
% 178.89/28.64  | | 
% 178.89/28.64  | | Case 1:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (15)  all_56_5 = e2
% 178.89/28.64  | | | 
% 178.89/28.64  | | | REF_CLOSE: (7), (9), (15) are inconsistent by sub-proof #710.
% 178.89/28.64  | | | 
% 178.89/28.64  | | Case 2:
% 178.89/28.64  | | | 
% 178.89/28.64  | | |   (16)  all_56_5 = e1 | all_56_5 = e0
% 178.89/28.64  | | | 
% 178.89/28.64  | | | BETA: splitting (14) gives:
% 178.89/28.64  | | | 
% 178.89/28.64  | | | Case 1:
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | |   (17)  all_58_3 = e1
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | COMBINE_EQS: (4), (17) imply:
% 178.89/28.64  | | | |   (18)  all_10_2 = e1
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | REDUCE: (1), (18) imply:
% 178.89/28.64  | | | |   (19)  op(e2, e1) = all_10_1
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | GROUND_INST: instantiating (12) with e3, all_10_1, e1, e2, simplifying
% 178.89/28.64  | | | |              with (8), (19) gives:
% 178.89/28.64  | | | |   (20)  all_10_1 = e3
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | REDUCE: (11), (20) imply:
% 178.89/28.64  | | | |   (21)  $false
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | CLOSE: (21) is inconsistent.
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | Case 2:
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | |   (22)   ~ (all_58_3 = e1)
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | REDUCE: (4), (22) imply:
% 178.89/28.64  | | | |   (23)   ~ (all_10_2 = e1)
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | | REF_CLOSE: (2), (7), (16), (23) are inconsistent by sub-proof #707.
% 178.89/28.64  | | | | 
% 178.89/28.64  | | | End of split
% 178.89/28.64  | | | 
% 178.89/28.64  | | End of split
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #707 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_56_5 = e1 | all_56_5 = e0
% 178.89/28.64    (2)  all_56_5 = all_10_2
% 178.89/28.64    (3)   ~ (all_10_2 = e1)
% 178.89/28.64    (4)   ~ (all_10_2 = e0)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | BETA: splitting (1) gives:
% 178.89/28.64  | 
% 178.89/28.64  | Case 1:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (5)  all_56_5 = e1
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #709.
% 178.89/28.64  | | 
% 178.89/28.64  | Case 2:
% 178.89/28.64  | | 
% 178.89/28.64  | |   (6)  all_56_5 = e0
% 178.89/28.64  | | 
% 178.89/28.64  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #708.
% 178.89/28.64  | | 
% 178.89/28.64  | End of split
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #708 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_56_5 = all_10_2
% 178.89/28.64    (2)  all_56_5 = e0
% 178.89/28.64    (3)   ~ (all_10_2 = e0)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.64  |   (4)  all_10_2 = e0
% 178.89/28.64  | 
% 178.89/28.64  | SIMP: (4) implies:
% 178.89/28.64  |   (5)  all_10_2 = e0
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (3), (5) imply:
% 178.89/28.64  |   (6)  $false
% 178.89/28.64  | 
% 178.89/28.64  | CLOSE: (6) is inconsistent.
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #709 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_56_5 = all_10_2
% 178.89/28.64    (2)  all_56_5 = e1
% 178.89/28.64    (3)   ~ (all_10_2 = e1)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.64  |   (4)  all_10_2 = e1
% 178.89/28.64  | 
% 178.89/28.64  | SIMP: (4) implies:
% 178.89/28.64  |   (5)  all_10_2 = e1
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (3), (5) imply:
% 178.89/28.64  |   (6)  $false
% 178.89/28.64  | 
% 178.89/28.64  | CLOSE: (6) is inconsistent.
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #710 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_56_5 = all_10_2
% 178.89/28.64    (2)  all_56_5 = e2
% 178.89/28.64    (3)   ~ (all_10_2 = e2)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.64  |   (4)  all_10_2 = e2
% 178.89/28.64  | 
% 178.89/28.64  | SIMP: (4) implies:
% 178.89/28.64  |   (5)  all_10_2 = e2
% 178.89/28.64  | 
% 178.89/28.64  | REDUCE: (3), (5) imply:
% 178.89/28.64  |   (6)  $false
% 178.89/28.64  | 
% 178.89/28.64  | CLOSE: (6) is inconsistent.
% 178.89/28.64  | 
% 178.89/28.64  End of proof
% 178.89/28.64  
% 178.89/28.64  Sub-proof #711 shows that the following formulas are inconsistent:
% 178.89/28.64  ----------------------------------------------------------------
% 178.89/28.64    (1)  all_58_10 = all_52_15
% 178.89/28.64    (2)  all_58_10 = e2
% 178.89/28.64    (3)   ~ (all_52_15 = e2)
% 178.89/28.64  
% 178.89/28.64  Begin of proof
% 178.89/28.64  | 
% 178.89/28.64  | COMBINE_EQS: (1), (2) imply:
% 178.89/28.64  |   (4)  all_52_15 = e2
% 178.89/28.64  | 
% 178.89/28.64  | SIMP: (4) implies:
% 178.89/28.65  |   (5)  all_52_15 = e2
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (3), (5) imply:
% 178.89/28.65  |   (6)  $false
% 178.89/28.65  | 
% 178.89/28.65  | CLOSE: (6) is inconsistent.
% 178.89/28.65  | 
% 178.89/28.65  End of proof
% 178.89/28.65  
% 178.89/28.65  Sub-proof #712 shows that the following formulas are inconsistent:
% 178.89/28.65  ----------------------------------------------------------------
% 178.89/28.65    (1)  op(e1, e2) = all_52_19
% 178.89/28.65    (2)   ~ (all_52_17 = e3)
% 178.89/28.65    (3)  all_56_9 = all_52_19
% 178.89/28.65    (4)  all_58_7 = all_52_19
% 178.89/28.65    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.65    (6)   ~ (e3 = e1)
% 178.89/28.65    (7)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.89/28.65    (8)  all_58_8 = all_14_2
% 178.89/28.65    (9)   ~ (all_52_5 = all_14_2)
% 178.89/28.65    (10)   ~ (all_52_23 = e3)
% 178.89/28.65    (11)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.65    (12)   ~ (all_52_9 = all_52_17)
% 178.89/28.65    (13)  all_58_6 = all_52_17
% 178.89/28.65    (14)  op(e2, all_52_19) = e2
% 178.89/28.65    (15)  op(e3, all_52_17) = e3
% 178.89/28.65    (16)  all_58_11 = all_52_23
% 178.89/28.65    (17)   ~ (all_52_9 = e3)
% 178.89/28.65    (18)  op(e3, e1) = all_52_5
% 178.89/28.65    (19)  op(e1, e3) = all_52_17
% 178.89/28.65    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.65    (21)  op(e1, all_14_2) = e1
% 178.89/28.65    (22)   ~ (all_52_23 = e2)
% 178.89/28.65    (23)  op(e2, e3) = all_52_9
% 178.89/28.65  
% 178.89/28.65  Begin of proof
% 178.89/28.65  | 
% 178.89/28.65  | BETA: splitting (5) gives:
% 178.89/28.65  | 
% 178.89/28.65  | Case 1:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (24)  all_58_6 = e3
% 178.89/28.65  | | 
% 178.89/28.65  | | REF_CLOSE: (2), (13), (24) are inconsistent by sub-proof #981.
% 178.89/28.65  | | 
% 178.89/28.65  | Case 2:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (25)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.65  | | 
% 178.89/28.65  | | BETA: splitting (7) gives:
% 178.89/28.65  | | 
% 178.89/28.65  | | Case 1:
% 178.89/28.65  | | | 
% 178.89/28.65  | | |   (26)  all_56_9 = e3
% 178.89/28.65  | | | 
% 178.89/28.65  | | | COMBINE_EQS: (3), (26) imply:
% 178.89/28.65  | | |   (27)  all_52_19 = e3
% 178.89/28.65  | | | 
% 178.89/28.65  | | | SIMP: (27) implies:
% 178.89/28.65  | | |   (28)  all_52_19 = e3
% 178.89/28.65  | | | 
% 178.89/28.65  | | | COMBINE_EQS: (4), (28) imply:
% 178.89/28.65  | | |   (29)  all_58_7 = e3
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REDUCE: (14), (28) imply:
% 178.89/28.65  | | |   (30)  op(e2, e3) = e2
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REDUCE: (1), (28) imply:
% 178.89/28.65  | | |   (31)  op(e1, e2) = e3
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REF_CLOSE: (6), (8), (11), (12), (13), (16), (17), (20), (21), (22), (23),
% 178.89/28.65  | | |            (29), (30), (31) are inconsistent by sub-proof #713.
% 178.89/28.65  | | | 
% 178.89/28.65  | | Case 2:
% 178.89/28.65  | | | 
% 178.89/28.65  | | |   (32)   ~ (all_56_9 = e3)
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REDUCE: (3), (32) imply:
% 178.89/28.65  | | |   (33)   ~ (all_52_19 = e3)
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REF_CLOSE: (4), (8), (9), (10), (15), (16), (18), (19), (20), (21), (25),
% 178.89/28.65  | | |            (33) are inconsistent by sub-proof #950.
% 178.89/28.65  | | | 
% 178.89/28.65  | | End of split
% 178.89/28.65  | | 
% 178.89/28.65  | End of split
% 178.89/28.65  | 
% 178.89/28.65  End of proof
% 178.89/28.65  
% 178.89/28.65  Sub-proof #713 shows that the following formulas are inconsistent:
% 178.89/28.65  ----------------------------------------------------------------
% 178.89/28.65    (1)  op(e2, e3) = e2
% 178.89/28.65    (2)   ~ (e3 = e1)
% 178.89/28.65    (3)  all_58_7 = e3
% 178.89/28.65    (4)  all_58_8 = all_14_2
% 178.89/28.65    (5)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.65    (6)   ~ (all_52_9 = all_52_17)
% 178.89/28.65    (7)  all_58_6 = all_52_17
% 178.89/28.65    (8)  all_58_11 = all_52_23
% 178.89/28.65    (9)   ~ (all_52_9 = e3)
% 178.89/28.65    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.65            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.65    (11)  op(e1, all_14_2) = e1
% 178.89/28.65    (12)  op(e1, e2) = e3
% 178.89/28.65    (13)   ~ (all_52_23 = e2)
% 178.89/28.65    (14)  op(e2, e3) = all_52_9
% 178.89/28.65  
% 178.89/28.65  Begin of proof
% 178.89/28.65  | 
% 178.89/28.65  | GROUND_INST: instantiating (10) with all_52_9, e2, e3, e2, simplifying with
% 178.89/28.65  |              (1), (14) gives:
% 178.89/28.65  |   (15)  all_52_9 = e2
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (6), (15) imply:
% 178.89/28.65  |   (16)   ~ (all_52_17 = e2)
% 178.89/28.65  | 
% 178.89/28.65  | SIMP: (16) implies:
% 178.89/28.65  |   (17)   ~ (all_52_17 = e2)
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (9), (15) imply:
% 178.89/28.65  |   (18)   ~ (e3 = e2)
% 178.89/28.65  | 
% 178.89/28.65  | SIMP: (18) implies:
% 178.89/28.65  |   (19)   ~ (e3 = e2)
% 178.89/28.65  | 
% 178.89/28.65  | BETA: splitting (5) gives:
% 178.89/28.65  | 
% 178.89/28.65  | Case 1:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (20)  all_58_6 = e2
% 178.89/28.65  | | 
% 178.89/28.65  | | REF_CLOSE: (7), (17), (20) are inconsistent by sub-proof #894.
% 178.89/28.65  | | 
% 178.89/28.65  | Case 2:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (21)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.65  | | 
% 178.89/28.65  | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (12), (13), (19), (21) are
% 178.89/28.65  | |            inconsistent by sub-proof #714.
% 178.89/28.65  | | 
% 178.89/28.65  | End of split
% 178.89/28.65  | 
% 178.89/28.65  End of proof
% 178.89/28.65  
% 178.89/28.65  Sub-proof #714 shows that the following formulas are inconsistent:
% 178.89/28.65  ----------------------------------------------------------------
% 178.89/28.65    (1)   ~ (e3 = e1)
% 178.89/28.65    (2)  all_58_7 = e3
% 178.89/28.65    (3)  all_58_8 = all_14_2
% 178.89/28.65    (4)  all_58_11 = all_52_23
% 178.89/28.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.65    (6)  op(e1, all_14_2) = e1
% 178.89/28.65    (7)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.89/28.65    (8)   ~ (e3 = e2)
% 178.89/28.65    (9)  op(e1, e2) = e3
% 178.89/28.65    (10)   ~ (all_52_23 = e2)
% 178.89/28.65  
% 178.89/28.65  Begin of proof
% 178.89/28.65  | 
% 178.89/28.65  | BETA: splitting (7) gives:
% 178.89/28.65  | 
% 178.89/28.65  | Case 1:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (11)  all_58_7 = e2
% 178.89/28.65  | | 
% 178.89/28.65  | | COMBINE_EQS: (2), (11) imply:
% 178.89/28.65  | |   (12)  e3 = e2
% 178.89/28.65  | | 
% 178.89/28.65  | | REDUCE: (8), (12) imply:
% 178.89/28.65  | |   (13)  $false
% 178.89/28.65  | | 
% 178.89/28.65  | | CLOSE: (13) is inconsistent.
% 178.89/28.65  | | 
% 178.89/28.65  | Case 2:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (14)  all_58_8 = e2 | all_58_11 = e2
% 178.89/28.65  | | 
% 178.89/28.65  | | BETA: splitting (14) gives:
% 178.89/28.65  | | 
% 178.89/28.65  | | Case 1:
% 178.89/28.65  | | | 
% 178.89/28.65  | | |   (15)  all_58_8 = e2
% 178.89/28.65  | | | 
% 178.89/28.65  | | | COMBINE_EQS: (3), (15) imply:
% 178.89/28.65  | | |   (16)  all_14_2 = e2
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REDUCE: (6), (16) imply:
% 178.89/28.65  | | |   (17)  op(e1, e2) = e1
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REF_CLOSE: (1), (5), (9), (17) are inconsistent by sub-proof #861.
% 178.89/28.65  | | | 
% 178.89/28.65  | | Case 2:
% 178.89/28.65  | | | 
% 178.89/28.65  | | |   (18)  all_58_11 = e2
% 178.89/28.65  | | | 
% 178.89/28.65  | | | COMBINE_EQS: (4), (18) imply:
% 178.89/28.65  | | |   (19)  all_52_23 = e2
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REDUCE: (10), (19) imply:
% 178.89/28.65  | | |   (20)  $false
% 178.89/28.65  | | | 
% 178.89/28.65  | | | CLOSE: (20) is inconsistent.
% 178.89/28.65  | | | 
% 178.89/28.65  | | End of split
% 178.89/28.65  | | 
% 178.89/28.65  | End of split
% 178.89/28.65  | 
% 178.89/28.65  End of proof
% 178.89/28.65  
% 178.89/28.65  Sub-proof #715 shows that the following formulas are inconsistent:
% 178.89/28.65  ----------------------------------------------------------------
% 178.89/28.65    (1)   ~ (all_52_23 = all_14_2)
% 178.89/28.65    (2)   ~ (all_52_5 = all_52_13)
% 178.89/28.65    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.89/28.65    (4)   ~ (all_52_27 = all_10_2)
% 178.89/28.65    (5)   ~ (all_52_17 = all_52_23)
% 178.89/28.65    (6)  op(e2, all_10_2) = all_10_1
% 178.89/28.65    (7)   ~ (all_52_13 = all_52_29)
% 178.89/28.65    (8)  all_56_3 = all_52_7
% 178.89/28.65    (9)  op(e3, e2) = all_52_3
% 178.89/28.65    (10)   ~ (all_52_9 = all_52_25)
% 178.89/28.65    (11)  op(e3, all_52_25) = all_52_24
% 178.89/28.65    (12)   ~ (all_52_19 = all_52_23)
% 178.89/28.65    (13)  all_56_11 = all_52_23
% 178.89/28.65    (14)  op(e1, e2) = all_52_19
% 178.89/28.65    (15)  op(e3, all_52_9) = all_52_8
% 178.89/28.65    (16)   ~ (all_52_3 = all_10_2)
% 178.89/28.65    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.89/28.65    (18)  all_58_5 = all_52_13
% 178.89/28.65    (19)   ~ (all_6_2 = e0)
% 178.89/28.65    (20)   ~ (all_52_25 = all_52_29)
% 178.89/28.65    (21)  all_56_15 = all_6_2
% 178.89/28.65    (22)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.65    (23)  op(e2, e0) = all_52_15
% 178.89/28.65    (24)  all_58_3 = all_10_2
% 178.89/28.65    (25)  all_56_9 = all_52_19
% 178.89/28.65    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.65    (27)  all_58_15 = all_6_2
% 178.89/28.65    (28)  all_52_12 = e1
% 178.89/28.65    (29)   ~ (all_52_9 = all_4_2)
% 178.89/28.65    (30)   ~ (all_52_5 = all_52_7)
% 178.89/28.65    (31)  all_58_10 = all_52_15
% 178.89/28.65    (32)   ~ (all_52_5 = all_4_2)
% 178.89/28.65    (33)  all_58_7 = all_52_19
% 178.89/28.65    (34)  all_56_4 = all_52_9
% 178.89/28.65    (35)   ~ (all_52_15 = all_6_2)
% 178.89/28.65    (36)   ~ (all_52_17 = all_52_25)
% 178.89/28.65    (37)  op(e0, e1) = all_52_29
% 178.89/28.65    (38)   ~ (all_4_0 = e2)
% 178.89/28.65    (39)  all_58_4 = all_52_5
% 178.89/28.65    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.65    (41)   ~ (e3 = e1)
% 178.89/28.65    (42)  all_52_14 = e0
% 178.89/28.65    (43)   ~ (all_52_27 = all_52_29)
% 178.89/28.65    (44)   ~ (all_52_17 = all_14_2)
% 178.89/28.65    (45)  op(e3, all_4_2) = all_4_1
% 178.89/28.65    (46)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.89/28.65    (47)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.89/28.65    (48)   ~ (all_52_7 = all_4_2)
% 178.89/28.65    (49)  all_58_1 = all_52_3
% 178.89/28.65    (50)   ~ (all_52_13 = all_52_15)
% 178.89/28.65    (51)  all_58_0 = all_4_2
% 178.89/28.65    (52)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.65    (53)  op(e1, all_52_13) = all_52_12
% 178.89/28.65    (54)  op(e1, all_52_29) = all_52_28
% 178.89/28.65    (55)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.89/28.65    (56)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.89/28.65    (57)   ~ (all_4_1 = e2)
% 178.89/28.65    (58)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.89/28.65    (59)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.65    (60)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.89/28.65    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.89/28.65    (62)   ~ (all_14_1 = e3)
% 178.89/28.65    (63)  all_58_14 = all_52_29
% 178.89/28.65    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.89/28.65    (65)   ~ (all_52_3 = all_52_5)
% 178.89/28.65    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.65    (67)  op(e2, e1) = all_52_13
% 178.89/28.65    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.89/28.65    (69)  all_58_8 = all_14_2
% 178.89/28.65    (70)  all_56_1 = all_52_3
% 178.89/28.65    (71)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.89/28.65    (72)  op(all_4_1, all_4_2) = all_4_0
% 178.89/28.65    (73)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.89/28.65    (74)   ~ (all_52_3 = all_52_27)
% 178.89/28.65    (75)   ~ (all_52_3 = all_4_2)
% 178.89/28.65    (76)  op(e0, e3) = all_52_25
% 178.89/28.65    (77)  op(e0, all_6_2) = all_6_1
% 178.89/28.65    (78)   ~ (all_52_9 = all_10_2)
% 178.89/28.65    (79)  op(e3, all_52_17) = all_52_16
% 178.89/28.65    (80)   ~ (all_52_13 = all_14_2)
% 178.89/28.65    (81)   ~ (e3 = e0)
% 178.89/28.65    (82)   ~ (all_52_9 = all_52_13)
% 178.89/28.65    (83)  op(e0, all_52_23) = all_52_22
% 178.89/28.65    (84)   ~ (all_52_15 = all_52_23)
% 178.89/28.65    (85)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.89/28.65    (86)  op(all_10_1, all_10_2) = all_10_0
% 178.89/28.65    (87)   ~ (all_52_5 = all_52_29)
% 178.89/28.65    (88)  all_56_2 = all_52_5
% 178.89/28.65    (89)  op(e1, e0) = all_52_23
% 178.89/28.65    (90)  all_58_13 = all_52_27
% 178.89/28.65    (91)   ~ (all_4_1 = e1)
% 178.89/28.65    (92)  all_52_8 = e3
% 178.89/28.65    (93)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.65    (94)   ~ (all_52_9 = all_52_17)
% 178.89/28.65    (95)  all_58_6 = all_52_17
% 178.89/28.65    (96)   ~ (all_52_3 = all_52_7)
% 178.89/28.65    (97)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.89/28.65    (98)  op(e2, all_52_19) = all_52_18
% 178.89/28.65    (99)   ~ (e1 = e0)
% 178.89/28.65    (100)  all_56_0 = all_4_2
% 178.89/28.65    (101)  all_58_11 = all_52_23
% 178.89/28.65    (102)   ~ (all_52_3 = all_52_19)
% 178.89/28.65    (103)   ~ (all_52_7 = all_52_15)
% 178.89/28.65    (104)  op(e0, all_52_15) = all_52_14
% 178.89/28.65    (105)   ~ (all_52_29 = all_14_2)
% 178.89/28.65    (106)   ~ (all_4_0 = e1)
% 178.89/28.65    (107)   ~ (all_52_19 = all_10_2)
% 178.89/28.65    (108)   ~ (all_52_23 = all_6_2)
% 178.89/28.65    (109)   ~ (all_52_29 = all_6_2)
% 178.89/28.65    (110)  all_58_2 = all_52_9
% 178.89/28.65    (111)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.89/28.65    (112)  op(e3, e1) = all_52_5
% 178.89/28.65    (113)  all_56_10 = all_14_2
% 178.89/28.65    (114)   ~ (all_52_25 = all_6_2)
% 178.89/28.65    (115)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.89/28.65    (116)  op(e1, e1) = all_14_2
% 178.89/28.65    (117)  op(e1, e3) = all_52_17
% 178.89/28.65    (118)   ~ (all_52_25 = all_4_2)
% 178.89/28.65    (119)  op(e3, e0) = all_52_7
% 178.89/28.65    (120)  op(e3, e3) = all_4_2
% 178.89/28.65    (121)   ~ (all_52_17 = all_4_2)
% 178.89/28.65    (122)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.65             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.65    (123)   ~ (all_52_25 = all_52_27)
% 178.89/28.65    (124)   ~ (all_52_27 = all_6_2)
% 178.89/28.65    (125)   ~ (all_52_7 = all_6_2)
% 178.89/28.65    (126)   ~ (all_10_0 = e3)
% 178.89/28.65    (127)   ~ (all_52_19 = all_52_27)
% 178.89/28.65    (128)  all_10_1 = e2
% 178.89/28.65    (129)   ~ (all_52_7 = all_52_23)
% 178.89/28.65    (130)  op(e2, all_52_27) = all_52_26
% 178.89/28.65    (131)   ~ (all_52_17 = all_52_19)
% 178.89/28.65    (132)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.89/28.65    (133)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.89/28.65    (134)  op(e1, all_14_2) = all_14_1
% 178.89/28.65    (135)  all_58_9 = all_52_7
% 178.89/28.65    (136)  all_58_12 = all_52_25
% 178.89/28.65    (137)   ~ (all_10_0 = e1)
% 178.89/28.65    (138)  all_56_6 = all_52_13
% 178.89/28.65    (139)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.65    (140)   ~ (all_52_9 = all_52_15)
% 178.89/28.65    (141)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.65    (142)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.89/28.65    (143)   ~ (all_52_19 = all_14_2)
% 178.89/28.65    (144)  op(e2, e3) = all_52_9
% 178.89/28.65    (145)  all_56_13 = all_52_27
% 178.89/28.65  
% 178.89/28.65  Begin of proof
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (86), (128) imply:
% 178.89/28.65  |   (146)  op(e2, all_10_2) = all_10_0
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (15), (92) imply:
% 178.89/28.65  |   (147)  op(e3, all_52_9) = e3
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (6), (128) imply:
% 178.89/28.65  |   (148)  op(e2, all_10_2) = e2
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (28), (53) imply:
% 178.89/28.65  |   (149)  op(e1, all_52_13) = e1
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (42), (104) imply:
% 178.89/28.65  |   (150)  op(e0, all_52_15) = e0
% 178.89/28.65  | 
% 178.89/28.65  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 178.89/28.65  |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 178.89/28.65  |            (26), (27), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 178.89/28.65  |            (38), (39), (40), (41), (43), (44), (45), (46), (47), (48), (49),
% 178.89/28.65  |            (50), (51), (52), (54), (55), (56), (57), (58), (59), (60), (61),
% 178.89/28.65  |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 178.89/28.65  |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 178.89/28.65  |            (84), (85), (87), (88), (89), (90), (91), (93), (94), (95), (96),
% 178.89/28.65  |            (97), (98), (99), (100), (101), (102), (103), (105), (106), (107),
% 178.89/28.65  |            (108), (109), (110), (111), (112), (113), (114), (115), (116),
% 178.89/28.65  |            (117), (118), (119), (120), (121), (122), (123), (124), (125),
% 178.89/28.65  |            (126), (127), (129), (130), (131), (132), (133), (134), (135),
% 178.89/28.65  |            (136), (137), (138), (139), (140), (141), (142), (143), (144),
% 178.89/28.65  |            (145), (146), (147), (148), (149), (150) are inconsistent by
% 178.89/28.65  |            sub-proof #716.
% 178.89/28.65  | 
% 178.89/28.65  End of proof
% 178.89/28.65  
% 178.89/28.65  Sub-proof #716 shows that the following formulas are inconsistent:
% 178.89/28.65  ----------------------------------------------------------------
% 178.89/28.65    (1)   ~ (all_52_23 = all_14_2)
% 178.89/28.65    (2)   ~ (all_52_5 = all_52_13)
% 178.89/28.65    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.89/28.65    (4)   ~ (all_52_27 = all_10_2)
% 178.89/28.65    (5)   ~ (all_52_17 = all_52_23)
% 178.89/28.65    (6)   ~ (all_52_13 = all_52_29)
% 178.89/28.65    (7)  op(e2, all_10_2) = all_10_0
% 178.89/28.65    (8)  all_56_3 = all_52_7
% 178.89/28.65    (9)  op(e3, e2) = all_52_3
% 178.89/28.65    (10)   ~ (all_52_9 = all_52_25)
% 178.89/28.65    (11)  op(e3, all_52_25) = all_52_24
% 178.89/28.65    (12)   ~ (all_52_19 = all_52_23)
% 178.89/28.65    (13)  all_56_11 = all_52_23
% 178.89/28.65    (14)  op(e1, e2) = all_52_19
% 178.89/28.65    (15)   ~ (all_52_3 = all_10_2)
% 178.89/28.65    (16)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.89/28.65    (17)  all_58_5 = all_52_13
% 178.89/28.65    (18)   ~ (all_6_2 = e0)
% 178.89/28.65    (19)   ~ (all_52_25 = all_52_29)
% 178.89/28.65    (20)  op(e1, all_52_13) = e1
% 178.89/28.65    (21)  op(e0, all_52_15) = e0
% 178.89/28.65    (22)  all_56_15 = all_6_2
% 178.89/28.65    (23)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.89/28.65    (24)  op(e2, e0) = all_52_15
% 178.89/28.65    (25)  all_58_3 = all_10_2
% 178.89/28.65    (26)  all_56_9 = all_52_19
% 178.89/28.65    (27)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.89/28.65    (28)  all_58_15 = all_6_2
% 178.89/28.65    (29)   ~ (all_52_9 = all_4_2)
% 178.89/28.65    (30)   ~ (all_52_5 = all_52_7)
% 178.89/28.65    (31)  all_58_10 = all_52_15
% 178.89/28.65    (32)   ~ (all_52_5 = all_4_2)
% 178.89/28.65    (33)  all_58_7 = all_52_19
% 178.89/28.65    (34)  all_56_4 = all_52_9
% 178.89/28.65    (35)   ~ (all_52_15 = all_6_2)
% 178.89/28.65    (36)   ~ (all_52_17 = all_52_25)
% 178.89/28.65    (37)  op(e0, e1) = all_52_29
% 178.89/28.65    (38)   ~ (all_4_0 = e2)
% 178.89/28.65    (39)  all_58_4 = all_52_5
% 178.89/28.65    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.89/28.65    (41)   ~ (e3 = e1)
% 178.89/28.65    (42)   ~ (all_52_27 = all_52_29)
% 178.89/28.65    (43)   ~ (all_52_17 = all_14_2)
% 178.89/28.65    (44)  op(e3, all_4_2) = all_4_1
% 178.89/28.65    (45)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.89/28.65    (46)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.89/28.65    (47)   ~ (all_52_7 = all_4_2)
% 178.89/28.65    (48)  all_58_1 = all_52_3
% 178.89/28.65    (49)   ~ (all_52_13 = all_52_15)
% 178.89/28.65    (50)  all_58_0 = all_4_2
% 178.89/28.65    (51)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.89/28.65    (52)  op(e1, all_52_29) = all_52_28
% 178.89/28.65    (53)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.89/28.65    (54)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.89/28.65    (55)   ~ (all_4_1 = e2)
% 178.89/28.65    (56)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.89/28.65    (57)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.89/28.65    (58)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.89/28.65    (59)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.89/28.65    (60)   ~ (all_14_1 = e3)
% 178.89/28.65    (61)  all_58_14 = all_52_29
% 178.89/28.65    (62)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.89/28.65    (63)   ~ (all_52_3 = all_52_5)
% 178.89/28.65    (64)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.89/28.65    (65)  op(e2, e1) = all_52_13
% 178.89/28.65    (66)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.89/28.65    (67)  all_58_8 = all_14_2
% 178.89/28.65    (68)  all_56_1 = all_52_3
% 178.89/28.65    (69)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.89/28.65    (70)  op(all_4_1, all_4_2) = all_4_0
% 178.89/28.65    (71)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.89/28.65    (72)   ~ (all_52_3 = all_52_27)
% 178.89/28.65    (73)   ~ (all_52_3 = all_4_2)
% 178.89/28.65    (74)  op(e0, e3) = all_52_25
% 178.89/28.65    (75)  op(e0, all_6_2) = all_6_1
% 178.89/28.65    (76)   ~ (all_52_9 = all_10_2)
% 178.89/28.65    (77)  op(e3, all_52_17) = all_52_16
% 178.89/28.65    (78)   ~ (all_52_13 = all_14_2)
% 178.89/28.65    (79)  op(e3, all_52_9) = e3
% 178.89/28.65    (80)   ~ (e3 = e0)
% 178.89/28.65    (81)   ~ (all_52_9 = all_52_13)
% 178.89/28.65    (82)  op(e0, all_52_23) = all_52_22
% 178.89/28.65    (83)   ~ (all_52_15 = all_52_23)
% 178.89/28.65    (84)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.89/28.65    (85)   ~ (all_52_5 = all_52_29)
% 178.89/28.65    (86)  all_56_2 = all_52_5
% 178.89/28.65    (87)  op(e1, e0) = all_52_23
% 178.89/28.65    (88)  all_58_13 = all_52_27
% 178.89/28.65    (89)   ~ (all_4_1 = e1)
% 178.89/28.65    (90)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.89/28.65    (91)   ~ (all_52_9 = all_52_17)
% 178.89/28.65    (92)  all_58_6 = all_52_17
% 178.89/28.65    (93)   ~ (all_52_3 = all_52_7)
% 178.89/28.65    (94)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.89/28.65    (95)  op(e2, all_52_19) = all_52_18
% 178.89/28.65    (96)   ~ (e1 = e0)
% 178.89/28.65    (97)  all_56_0 = all_4_2
% 178.89/28.65    (98)  all_58_11 = all_52_23
% 178.89/28.65    (99)   ~ (all_52_3 = all_52_19)
% 178.89/28.65    (100)   ~ (all_52_7 = all_52_15)
% 178.89/28.65    (101)   ~ (all_52_29 = all_14_2)
% 178.89/28.65    (102)   ~ (all_4_0 = e1)
% 178.89/28.65    (103)   ~ (all_52_19 = all_10_2)
% 178.89/28.65    (104)   ~ (all_52_23 = all_6_2)
% 178.89/28.65    (105)   ~ (all_52_29 = all_6_2)
% 178.89/28.65    (106)  all_58_2 = all_52_9
% 178.89/28.65    (107)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.89/28.65    (108)  op(e3, e1) = all_52_5
% 178.89/28.65    (109)  all_56_10 = all_14_2
% 178.89/28.65    (110)   ~ (all_52_25 = all_6_2)
% 178.89/28.65    (111)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.89/28.65    (112)  op(e1, e1) = all_14_2
% 178.89/28.65    (113)  op(e1, e3) = all_52_17
% 178.89/28.65    (114)   ~ (all_52_25 = all_4_2)
% 178.89/28.65    (115)  op(e3, e0) = all_52_7
% 178.89/28.65    (116)  op(e2, all_10_2) = e2
% 178.89/28.65    (117)  op(e3, e3) = all_4_2
% 178.89/28.65    (118)   ~ (all_52_17 = all_4_2)
% 178.89/28.65    (119)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.89/28.65             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.89/28.65    (120)   ~ (all_52_25 = all_52_27)
% 178.89/28.65    (121)   ~ (all_52_27 = all_6_2)
% 178.89/28.65    (122)   ~ (all_52_7 = all_6_2)
% 178.89/28.65    (123)   ~ (all_10_0 = e3)
% 178.89/28.65    (124)   ~ (all_52_19 = all_52_27)
% 178.89/28.65    (125)   ~ (all_52_7 = all_52_23)
% 178.89/28.65    (126)  op(e2, all_52_27) = all_52_26
% 178.89/28.65    (127)   ~ (all_52_17 = all_52_19)
% 178.89/28.65    (128)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.89/28.65    (129)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.89/28.65    (130)  op(e1, all_14_2) = all_14_1
% 178.89/28.65    (131)  all_58_9 = all_52_7
% 178.89/28.65    (132)  all_58_12 = all_52_25
% 178.89/28.65    (133)   ~ (all_10_0 = e1)
% 178.89/28.65    (134)  all_56_6 = all_52_13
% 178.89/28.65    (135)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.89/28.65    (136)   ~ (all_52_9 = all_52_15)
% 178.89/28.65    (137)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.89/28.65    (138)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.89/28.65    (139)   ~ (all_52_19 = all_14_2)
% 178.89/28.65    (140)  op(e2, e3) = all_52_9
% 178.89/28.65    (141)  all_56_13 = all_52_27
% 178.89/28.65  
% 178.89/28.65  Begin of proof
% 178.89/28.65  | 
% 178.89/28.65  | GROUND_INST: instantiating (119) with e2, all_10_0, all_10_2, e2, simplifying
% 178.89/28.65  |              with (7), (116) gives:
% 178.89/28.65  |   (142)  all_10_0 = e2
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (123), (142) imply:
% 178.89/28.65  |   (143)   ~ (e3 = e2)
% 178.89/28.65  | 
% 178.89/28.65  | SIMP: (143) implies:
% 178.89/28.65  |   (144)   ~ (e3 = e2)
% 178.89/28.65  | 
% 178.89/28.65  | REDUCE: (133), (142) imply:
% 178.89/28.65  |   (145)   ~ (e2 = e1)
% 178.89/28.65  | 
% 178.89/28.65  | BETA: splitting (45) gives:
% 178.89/28.65  | 
% 178.89/28.65  | Case 1:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (146)  all_56_15 = e3
% 178.89/28.65  | | 
% 178.89/28.65  | | COMBINE_EQS: (22), (146) imply:
% 178.89/28.65  | |   (147)  all_6_2 = e3
% 178.89/28.65  | | 
% 178.89/28.65  | | SIMP: (147) implies:
% 178.89/28.65  | |   (148)  all_6_2 = e3
% 178.89/28.65  | | 
% 178.89/28.65  | | REF_CLOSE: (9), (10), (15), (17), (20), (23), (25), (29), (31), (33), (34),
% 178.89/28.65  | |            (35), (38), (40), (41), (44), (46), (47), (48), (50), (57), (58),
% 178.89/28.65  | |            (64), (67), (70), (74), (75), (78), (79), (88), (91), (92), (94),
% 178.89/28.65  | |            (95), (98), (99), (104), (106), (110), (111), (113), (115),
% 178.89/28.65  | |            (116), (117), (118), (119), (121), (127), (132), (134), (140),
% 178.89/28.65  | |            (145), (148) are inconsistent by sub-proof #773.
% 178.89/28.65  | | 
% 178.89/28.65  | Case 2:
% 178.89/28.65  | | 
% 178.89/28.65  | |   (149)   ~ (all_56_15 = e3)
% 178.89/28.65  | |   (150)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.89/28.65  | | 
% 178.89/28.65  | | REDUCE: (22), (149) imply:
% 178.89/28.65  | |   (151)   ~ (all_6_2 = e3)
% 178.89/28.65  | | 
% 178.89/28.65  | | BETA: splitting (62) gives:
% 178.89/28.65  | | 
% 178.89/28.65  | | Case 1:
% 178.89/28.65  | | | 
% 178.89/28.65  | | |   (152)  all_56_13 = e3
% 178.89/28.65  | | | 
% 178.89/28.65  | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (12), (13), (15),
% 178.89/28.65  | | |            (16), (17), (20), (21), (25), (27), (28), (29), (30), (31),
% 178.89/28.65  | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 178.89/28.66  | | |            (42), (43), (44), (46), (47), (48), (49), (50), (51), (53),
% 178.89/28.66  | | |            (56), (59), (61), (63), (64), (65), (67), (68), (70), (72),
% 178.89/28.66  | | |            (73), (74), (76), (77), (78), (79), (81), (82), (83), (87),
% 178.89/28.66  | | |            (88), (89), (90), (91), (92), (93), (94), (96), (97), (98),
% 178.89/28.66  | | |            (100), (102), (104), (106), (107), (108), (113), (114), (115),
% 178.89/28.66  | | |            (116), (117), (119), (120), (121), (124), (125), (126), (127),
% 178.89/28.66  | | |            (128), (131), (132), (136), (137), (140), (141), (152) are
% 178.89/28.66  | | |            inconsistent by sub-proof #755.
% 178.89/28.66  | | | 
% 178.89/28.66  | | Case 2:
% 178.89/28.66  | | | 
% 178.89/28.66  | | |   (153)   ~ (all_56_13 = e3)
% 178.89/28.66  | | | 
% 178.89/28.66  | | | REDUCE: (141), (153) imply:
% 178.89/28.66  | | |   (154)   ~ (all_52_27 = e3)
% 178.89/28.66  | | | 
% 178.89/28.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 178.89/28.66  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.89/28.66  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 178.89/28.66  | | |            (34), (36), (38), (39), (40), (41), (42), (43), (44), (46),
% 178.89/28.66  | | |            (47), (48), (50), (51), (52), (54), (55), (56), (57), (58),
% 178.89/28.66  | | |            (60), (61), (63), (64), (65), (66), (67), (69), (70), (71),
% 178.89/28.66  | | |            (73), (74), (77), (78), (79), (80), (81), (82), (83), (84),
% 178.89/28.66  | | |            (85), (86), (87), (88), (90), (91), (92), (93), (94), (95),
% 178.89/28.66  | | |            (96), (97), (98), (99), (100), (101), (103), (104), (105),
% 178.89/28.66  | | |            (106), (107), (108), (109), (110), (112), (113), (114), (115),
% 178.89/28.66  | | |            (116), (117), (118), (119), (120), (121), (122), (124), (125),
% 178.89/28.66  | | |            (127), (128), (129), (130), (131), (132), (134), (135), (136),
% 178.89/28.66  | | |            (137), (138), (139), (140), (144), (145), (150), (151), (154)
% 178.89/28.66  | | |            are inconsistent by sub-proof #717.
% 178.89/28.66  | | | 
% 178.89/28.66  | | End of split
% 178.89/28.66  | | 
% 178.89/28.66  | End of split
% 178.89/28.66  | 
% 178.89/28.66  End of proof
% 178.89/28.66  
% 178.89/28.66  Sub-proof #717 shows that the following formulas are inconsistent:
% 178.89/28.66  ----------------------------------------------------------------
% 178.89/28.66    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.66    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.66    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.66    (4)   ~ (all_52_27 = all_10_2)
% 178.99/28.66    (5)   ~ (all_52_17 = all_52_23)
% 178.99/28.66    (6)   ~ (all_52_13 = all_52_29)
% 178.99/28.66    (7)  all_56_3 = all_52_7
% 178.99/28.66    (8)  op(e3, e2) = all_52_3
% 178.99/28.66    (9)   ~ (all_52_9 = all_52_25)
% 178.99/28.66    (10)  op(e3, all_52_25) = all_52_24
% 178.99/28.66    (11)   ~ (all_52_19 = all_52_23)
% 178.99/28.66    (12)  all_56_11 = all_52_23
% 178.99/28.66    (13)  op(e1, e2) = all_52_19
% 178.99/28.66    (14)   ~ (all_52_27 = e3)
% 178.99/28.66    (15)   ~ (all_6_2 = e3)
% 178.99/28.66    (16)   ~ (all_52_3 = all_10_2)
% 178.99/28.66    (17)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.66    (18)  all_58_5 = all_52_13
% 178.99/28.66    (19)   ~ (all_6_2 = e0)
% 178.99/28.66    (20)   ~ (all_52_25 = all_52_29)
% 178.99/28.66    (21)  op(e1, all_52_13) = e1
% 178.99/28.66    (22)  op(e0, all_52_15) = e0
% 178.99/28.66    (23)  all_56_15 = all_6_2
% 178.99/28.66    (24)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.66    (25)  op(e2, e0) = all_52_15
% 178.99/28.66    (26)  all_58_3 = all_10_2
% 178.99/28.66    (27)  all_56_9 = all_52_19
% 178.99/28.66    (28)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.66    (29)  all_58_15 = all_6_2
% 178.99/28.66    (30)   ~ (all_52_9 = all_4_2)
% 178.99/28.66    (31)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.66    (32)   ~ (all_52_5 = all_52_7)
% 178.99/28.66    (33)  all_58_10 = all_52_15
% 178.99/28.66    (34)   ~ (all_52_5 = all_4_2)
% 178.99/28.66    (35)  all_58_7 = all_52_19
% 178.99/28.66    (36)  all_56_4 = all_52_9
% 178.99/28.66    (37)   ~ (all_52_17 = all_52_25)
% 178.99/28.66    (38)   ~ (all_4_0 = e2)
% 178.99/28.66    (39)  all_58_4 = all_52_5
% 178.99/28.66    (40)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.66    (41)   ~ (e3 = e1)
% 178.99/28.66    (42)   ~ (all_52_27 = all_52_29)
% 178.99/28.66    (43)   ~ (all_52_17 = all_14_2)
% 178.99/28.66    (44)  op(e3, all_4_2) = all_4_1
% 178.99/28.66    (45)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.66    (46)   ~ (all_52_7 = all_4_2)
% 178.99/28.66    (47)  all_58_1 = all_52_3
% 178.99/28.66    (48)  all_58_0 = all_4_2
% 178.99/28.66    (49)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.66    (50)  op(e1, all_52_29) = all_52_28
% 178.99/28.66    (51)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.66    (52)   ~ (all_4_1 = e2)
% 178.99/28.66    (53)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.66    (54)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.66    (55)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.99/28.66    (56)   ~ (all_14_1 = e3)
% 178.99/28.66    (57)  all_58_14 = all_52_29
% 178.99/28.66    (58)   ~ (all_52_3 = all_52_5)
% 178.99/28.66    (59)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.66    (60)  op(e2, e1) = all_52_13
% 178.99/28.66    (61)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.99/28.66    (62)  all_58_8 = all_14_2
% 178.99/28.66    (63)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.99/28.66    (64)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.66    (65)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.66    (66)   ~ (all_52_3 = all_4_2)
% 178.99/28.66    (67)  op(e0, e3) = all_52_25
% 178.99/28.66    (68)  op(e3, all_52_17) = all_52_16
% 178.99/28.66    (69)   ~ (all_52_13 = all_14_2)
% 178.99/28.66    (70)  op(e3, all_52_9) = e3
% 178.99/28.66    (71)   ~ (e3 = e0)
% 178.99/28.66    (72)   ~ (all_52_9 = all_52_13)
% 178.99/28.66    (73)  op(e0, all_52_23) = all_52_22
% 178.99/28.66    (74)   ~ (all_52_15 = all_52_23)
% 178.99/28.66    (75)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.66    (76)   ~ (all_52_5 = all_52_29)
% 178.99/28.66    (77)  all_56_2 = all_52_5
% 178.99/28.66    (78)  op(e1, e0) = all_52_23
% 178.99/28.66    (79)  all_58_13 = all_52_27
% 178.99/28.66    (80)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.66    (81)   ~ (all_52_9 = all_52_17)
% 178.99/28.66    (82)  all_58_6 = all_52_17
% 178.99/28.66    (83)   ~ (all_52_3 = all_52_7)
% 178.99/28.66    (84)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.66    (85)  op(e2, all_52_19) = all_52_18
% 178.99/28.66    (86)   ~ (e1 = e0)
% 178.99/28.66    (87)  all_56_0 = all_4_2
% 178.99/28.66    (88)  all_58_11 = all_52_23
% 178.99/28.66    (89)   ~ (all_52_3 = all_52_19)
% 178.99/28.66    (90)   ~ (all_52_7 = all_52_15)
% 178.99/28.66    (91)   ~ (all_52_29 = all_14_2)
% 178.99/28.66    (92)   ~ (all_52_19 = all_10_2)
% 178.99/28.66    (93)   ~ (all_52_23 = all_6_2)
% 178.99/28.66    (94)   ~ (all_52_29 = all_6_2)
% 178.99/28.66    (95)  all_58_2 = all_52_9
% 178.99/28.66    (96)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.66    (97)  op(e3, e1) = all_52_5
% 178.99/28.66    (98)   ~ (e2 = e1)
% 178.99/28.66    (99)  all_56_10 = all_14_2
% 178.99/28.66    (100)   ~ (all_52_25 = all_6_2)
% 178.99/28.66    (101)  op(e1, e1) = all_14_2
% 178.99/28.66    (102)  op(e1, e3) = all_52_17
% 178.99/28.66    (103)   ~ (all_52_25 = all_4_2)
% 178.99/28.66    (104)  op(e3, e0) = all_52_7
% 178.99/28.66    (105)  op(e2, all_10_2) = e2
% 178.99/28.66    (106)  op(e3, e3) = all_4_2
% 178.99/28.66    (107)   ~ (all_52_17 = all_4_2)
% 178.99/28.66    (108)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.66             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.66    (109)   ~ (all_52_25 = all_52_27)
% 178.99/28.66    (110)   ~ (all_52_27 = all_6_2)
% 178.99/28.66    (111)   ~ (all_52_7 = all_6_2)
% 178.99/28.66    (112)   ~ (all_52_19 = all_52_27)
% 178.99/28.66    (113)   ~ (all_52_7 = all_52_23)
% 178.99/28.66    (114)   ~ (all_52_17 = all_52_19)
% 178.99/28.66    (115)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.66    (116)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.66    (117)  op(e1, all_14_2) = all_14_1
% 178.99/28.66    (118)  all_58_9 = all_52_7
% 178.99/28.66    (119)  all_58_12 = all_52_25
% 178.99/28.66    (120)  all_56_6 = all_52_13
% 178.99/28.66    (121)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.66    (122)   ~ (all_52_9 = all_52_15)
% 178.99/28.66    (123)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.66    (124)   ~ (e3 = e2)
% 178.99/28.66    (125)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.66    (126)   ~ (all_52_19 = all_14_2)
% 178.99/28.66    (127)  op(e2, e3) = all_52_9
% 178.99/28.66  
% 178.99/28.66  Begin of proof
% 178.99/28.66  | 
% 178.99/28.66  | BETA: splitting (61) gives:
% 178.99/28.66  | 
% 178.99/28.66  | Case 1:
% 178.99/28.66  | | 
% 178.99/28.66  | |   (128)  all_58_12 = e3
% 178.99/28.66  | | 
% 178.99/28.66  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (16),
% 178.99/28.66  | |            (18), (19), (20), (21), (22), (23), (24), (26), (27), (28), (29),
% 178.99/28.66  | |            (30), (31), (32), (33), (34), (35), (36), (37), (39), (40), (42),
% 178.99/28.66  | |            (43), (45), (46), (47), (48), (49), (51), (53), (54), (55), (56),
% 178.99/28.66  | |            (57), (58), (60), (62), (65), (67), (68), (69), (70), (71), (72),
% 178.99/28.66  | |            (73), (75), (79), (81), (82), (83), (84), (85), (87), (88), (89),
% 178.99/28.66  | |            (90), (92), (93), (95), (96), (97), (98), (99), (100), (102),
% 178.99/28.66  | |            (103), (104), (105), (108), (109), (110), (111), (113), (114),
% 178.99/28.66  | |            (115), (116), (117), (118), (119), (120), (122), (123), (124),
% 178.99/28.66  | |            (126), (127), (128) are inconsistent by sub-proof #734.
% 178.99/28.66  | | 
% 178.99/28.66  | Case 2:
% 178.99/28.66  | | 
% 178.99/28.66  | |   (129)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.99/28.66  | | 
% 178.99/28.66  | | BETA: splitting (129) gives:
% 178.99/28.66  | | 
% 178.99/28.66  | | Case 1:
% 178.99/28.66  | | | 
% 178.99/28.66  | | |   (130)  all_58_13 = e3
% 178.99/28.66  | | | 
% 178.99/28.66  | | | REF_CLOSE: (14), (79), (130) are inconsistent by sub-proof #1026.
% 178.99/28.66  | | | 
% 178.99/28.66  | | Case 2:
% 178.99/28.66  | | | 
% 178.99/28.66  | | |   (131)  all_58_14 = e3 | all_58_15 = e3
% 178.99/28.66  | | | 
% 178.99/28.66  | | | REF_CLOSE: (2), (5), (6), (8), (9), (10), (11), (12), (15), (16), (17),
% 178.99/28.66  | | |            (18), (21), (22), (24), (25), (26), (29), (30), (33), (34),
% 178.99/28.66  | | |            (35), (36), (38), (39), (40), (41), (42), (44), (45), (46),
% 178.99/28.66  | | |            (47), (48), (49), (50), (52), (54), (55), (57), (58), (59),
% 178.99/28.66  | | |            (62), (63), (64), (66), (67), (69), (70), (72), (74), (76),
% 178.99/28.66  | | |            (77), (78), (79), (80), (82), (83), (84), (85), (86), (88),
% 178.99/28.66  | | |            (89), (90), (91), (94), (95), (96), (97), (98), (101), (102),
% 178.99/28.66  | | |            (103), (104), (105), (106), (107), (108), (109), (112), (114),
% 178.99/28.66  | | |            (115), (118), (119), (120), (121), (122), (125), (127), (131)
% 178.99/28.66  | | |            are inconsistent by sub-proof #718.
% 178.99/28.66  | | | 
% 178.99/28.66  | | End of split
% 178.99/28.66  | | 
% 178.99/28.66  | End of split
% 178.99/28.66  | 
% 178.99/28.66  End of proof
% 178.99/28.66  
% 178.99/28.66  Sub-proof #718 shows that the following formulas are inconsistent:
% 178.99/28.66  ----------------------------------------------------------------
% 178.99/28.66    (1)   ~ (all_52_5 = all_52_13)
% 178.99/28.66    (2)   ~ (all_52_17 = all_52_23)
% 178.99/28.66    (3)   ~ (all_52_13 = all_52_29)
% 178.99/28.66    (4)  all_58_14 = e3 | all_58_15 = e3
% 178.99/28.66    (5)  op(e3, e2) = all_52_3
% 178.99/28.66    (6)   ~ (all_52_9 = all_52_25)
% 178.99/28.66    (7)  op(e3, all_52_25) = all_52_24
% 178.99/28.66    (8)   ~ (all_52_19 = all_52_23)
% 178.99/28.66    (9)  all_56_11 = all_52_23
% 178.99/28.66    (10)   ~ (all_6_2 = e3)
% 178.99/28.66    (11)   ~ (all_52_3 = all_10_2)
% 178.99/28.66    (12)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.66    (13)  all_58_5 = all_52_13
% 178.99/28.66    (14)  op(e1, all_52_13) = e1
% 178.99/28.66    (15)  op(e0, all_52_15) = e0
% 178.99/28.66    (16)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.66    (17)  op(e2, e0) = all_52_15
% 178.99/28.66    (18)  all_58_3 = all_10_2
% 178.99/28.66    (19)  all_58_15 = all_6_2
% 178.99/28.66    (20)   ~ (all_52_9 = all_4_2)
% 178.99/28.66    (21)  all_58_10 = all_52_15
% 178.99/28.66    (22)   ~ (all_52_5 = all_4_2)
% 178.99/28.66    (23)  all_58_7 = all_52_19
% 178.99/28.66    (24)  all_56_4 = all_52_9
% 178.99/28.66    (25)   ~ (all_4_0 = e2)
% 178.99/28.66    (26)  all_58_4 = all_52_5
% 178.99/28.66    (27)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.66    (28)   ~ (e3 = e1)
% 178.99/28.66    (29)   ~ (all_52_27 = all_52_29)
% 178.99/28.66    (30)  op(e3, all_4_2) = all_4_1
% 178.99/28.66    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.66    (32)   ~ (all_52_7 = all_4_2)
% 178.99/28.66    (33)  all_58_1 = all_52_3
% 178.99/28.66    (34)  all_58_0 = all_4_2
% 178.99/28.66    (35)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.66    (36)  op(e1, all_52_29) = all_52_28
% 178.99/28.66    (37)   ~ (all_4_1 = e2)
% 178.99/28.66    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.66    (39)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.99/28.66    (40)  all_58_14 = all_52_29
% 178.99/28.66    (41)   ~ (all_52_3 = all_52_5)
% 178.99/28.66    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.66    (43)  all_58_8 = all_14_2
% 178.99/28.66    (44)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.99/28.66    (45)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.66    (46)   ~ (all_52_3 = all_4_2)
% 178.99/28.66    (47)  op(e0, e3) = all_52_25
% 178.99/28.66    (48)   ~ (all_52_13 = all_14_2)
% 178.99/28.66    (49)  op(e3, all_52_9) = e3
% 178.99/28.66    (50)   ~ (all_52_9 = all_52_13)
% 178.99/28.66    (51)   ~ (all_52_15 = all_52_23)
% 178.99/28.66    (52)   ~ (all_52_5 = all_52_29)
% 178.99/28.66    (53)  all_56_2 = all_52_5
% 178.99/28.66    (54)  op(e1, e0) = all_52_23
% 178.99/28.66    (55)  all_58_13 = all_52_27
% 178.99/28.66    (56)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.66    (57)  all_58_6 = all_52_17
% 178.99/28.66    (58)   ~ (all_52_3 = all_52_7)
% 178.99/28.66    (59)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.66    (60)  op(e2, all_52_19) = all_52_18
% 178.99/28.66    (61)   ~ (e1 = e0)
% 178.99/28.66    (62)  all_58_11 = all_52_23
% 178.99/28.66    (63)   ~ (all_52_3 = all_52_19)
% 178.99/28.66    (64)   ~ (all_52_7 = all_52_15)
% 178.99/28.66    (65)   ~ (all_52_29 = all_14_2)
% 178.99/28.66    (66)   ~ (all_52_29 = all_6_2)
% 178.99/28.66    (67)  all_58_2 = all_52_9
% 178.99/28.66    (68)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.66    (69)  op(e3, e1) = all_52_5
% 178.99/28.66    (70)   ~ (e2 = e1)
% 178.99/28.66    (71)  op(e1, e1) = all_14_2
% 178.99/28.66    (72)  op(e1, e3) = all_52_17
% 178.99/28.66    (73)   ~ (all_52_25 = all_4_2)
% 178.99/28.66    (74)  op(e3, e0) = all_52_7
% 178.99/28.66    (75)  op(e2, all_10_2) = e2
% 178.99/28.66    (76)  op(e3, e3) = all_4_2
% 178.99/28.66    (77)   ~ (all_52_17 = all_4_2)
% 178.99/28.66    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.66    (79)   ~ (all_52_25 = all_52_27)
% 178.99/28.66    (80)   ~ (all_52_19 = all_52_27)
% 178.99/28.66    (81)   ~ (all_52_17 = all_52_19)
% 178.99/28.66    (82)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.66    (83)  all_58_9 = all_52_7
% 178.99/28.66    (84)  all_58_12 = all_52_25
% 178.99/28.66    (85)  all_56_6 = all_52_13
% 178.99/28.66    (86)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.66    (87)   ~ (all_52_9 = all_52_15)
% 178.99/28.66    (88)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.66    (89)  op(e2, e3) = all_52_9
% 178.99/28.66  
% 178.99/28.66  Begin of proof
% 178.99/28.66  | 
% 178.99/28.66  | BETA: splitting (4) gives:
% 178.99/28.66  | 
% 178.99/28.66  | Case 1:
% 178.99/28.66  | | 
% 178.99/28.66  | |   (90)  all_58_14 = e3
% 178.99/28.66  | | 
% 178.99/28.66  | | COMBINE_EQS: (40), (90) imply:
% 178.99/28.66  | |   (91)  all_52_29 = e3
% 178.99/28.66  | | 
% 178.99/28.66  | | SIMP: (91) implies:
% 178.99/28.66  | |   (92)  all_52_29 = e3
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (52), (92) imply:
% 178.99/28.66  | |   (93)   ~ (all_52_5 = e3)
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (3), (92) imply:
% 178.99/28.66  | |   (94)   ~ (all_52_13 = e3)
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (29), (92) imply:
% 178.99/28.66  | |   (95)   ~ (all_52_27 = e3)
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (65), (92) imply:
% 178.99/28.66  | |   (96)   ~ (all_14_2 = e3)
% 178.99/28.66  | | 
% 178.99/28.66  | | SIMP: (96) implies:
% 178.99/28.66  | |   (97)   ~ (all_14_2 = e3)
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (66), (92) imply:
% 178.99/28.66  | |   (98)   ~ (all_6_2 = e3)
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (36), (92) imply:
% 178.99/28.66  | |   (99)  op(e1, e3) = all_52_28
% 178.99/28.66  | | 
% 178.99/28.66  | | GROUND_INST: instantiating (78) with all_52_17, all_52_28, e3, e1,
% 178.99/28.66  | |              simplifying with (72), (99) gives:
% 178.99/28.66  | |   (100)  all_52_17 = all_52_28
% 178.99/28.66  | | 
% 178.99/28.66  | | COMBINE_EQS: (57), (100) imply:
% 178.99/28.66  | |   (101)  all_58_6 = all_52_28
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (81), (100) imply:
% 178.99/28.66  | |   (102)   ~ (all_52_19 = all_52_28)
% 178.99/28.66  | | 
% 178.99/28.66  | | SIMP: (102) implies:
% 178.99/28.66  | |   (103)   ~ (all_52_19 = all_52_28)
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (2), (100) imply:
% 178.99/28.66  | |   (104)   ~ (all_52_23 = all_52_28)
% 178.99/28.66  | | 
% 178.99/28.66  | | SIMP: (104) implies:
% 178.99/28.66  | |   (105)   ~ (all_52_23 = all_52_28)
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (77), (100) imply:
% 178.99/28.66  | |   (106)   ~ (all_52_28 = all_4_2)
% 178.99/28.66  | | 
% 178.99/28.66  | | BETA: splitting (39) gives:
% 178.99/28.66  | | 
% 178.99/28.66  | | Case 1:
% 178.99/28.66  | | | 
% 178.99/28.66  | | |   (107)  all_56_6 = e3
% 178.99/28.66  | | | 
% 178.99/28.66  | | | COMBINE_EQS: (85), (107) imply:
% 178.99/28.66  | | |   (108)  all_52_13 = e3
% 178.99/28.66  | | | 
% 178.99/28.66  | | | REDUCE: (94), (108) imply:
% 178.99/28.66  | | |   (109)  $false
% 178.99/28.66  | | | 
% 178.99/28.66  | | | CLOSE: (109) is inconsistent.
% 178.99/28.66  | | | 
% 178.99/28.66  | | Case 2:
% 178.99/28.66  | | | 
% 178.99/28.66  | | |   (110)   ~ (all_56_6 = e3)
% 178.99/28.66  | | |   (111)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.99/28.66  | | | 
% 178.99/28.66  | | | BETA: splitting (88) gives:
% 178.99/28.66  | | | 
% 178.99/28.66  | | | Case 1:
% 178.99/28.66  | | | | 
% 178.99/28.66  | | | |   (112)  all_56_2 = e3
% 178.99/28.66  | | | | 
% 178.99/28.66  | | | | REF_CLOSE: (53), (93), (112) are inconsistent by sub-proof #931.
% 178.99/28.66  | | | | 
% 178.99/28.66  | | | Case 2:
% 178.99/28.66  | | | | 
% 178.99/28.66  | | | |   (113)   ~ (all_56_2 = e3)
% 178.99/28.66  | | | |   (114)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.66  | | | | 
% 178.99/28.66  | | | | BETA: splitting (82) gives:
% 178.99/28.66  | | | | 
% 178.99/28.66  | | | | Case 1:
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | |   (115)  all_58_9 = e3
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | | COMBINE_EQS: (83), (115) imply:
% 178.99/28.66  | | | | |   (116)  all_52_7 = e3
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | | REF_CLOSE: (5), (11), (13), (18), (20), (21), (31), (49), (64), (67),
% 178.99/28.66  | | | | |            (75), (76), (78), (89), (94), (116) are inconsistent by
% 178.99/28.66  | | | | |            sub-proof #733.
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | Case 2:
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | |   (117)   ~ (all_58_9 = e3)
% 178.99/28.66  | | | | |   (118)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | | REDUCE: (83), (117) imply:
% 178.99/28.66  | | | | |   (119)   ~ (all_52_7 = e3)
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | | BETA: splitting (86) gives:
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | | Case 1:
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | |   (120)  all_58_0 = e3
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | | COMBINE_EQS: (34), (120) imply:
% 178.99/28.66  | | | | | |   (121)  all_4_2 = e3
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | | REDUCE: (46), (121) imply:
% 178.99/28.66  | | | | | |   (122)   ~ (all_52_3 = e3)
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | | REDUCE: (73), (121) imply:
% 178.99/28.66  | | | | | |   (123)   ~ (all_52_25 = e3)
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | | REDUCE: (106), (121) imply:
% 178.99/28.66  | | | | | |   (124)   ~ (all_52_28 = e3)
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | | BETA: splitting (38) gives:
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | | Case 1:
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | |   (125)  all_58_1 = e3
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | | COMBINE_EQS: (33), (125) imply:
% 178.99/28.66  | | | | | | |   (126)  all_52_3 = e3
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | | REDUCE: (122), (126) imply:
% 178.99/28.66  | | | | | | |   (127)  $false
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | | CLOSE: (127) is inconsistent.
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | Case 2:
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | |   (128)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | | BETA: splitting (27) gives:
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | | Case 1:
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | |   (129)  all_58_6 = e3
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | | COMBINE_EQS: (101), (129) imply:
% 178.99/28.66  | | | | | | | |   (130)  all_52_28 = e3
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | | REDUCE: (124), (130) imply:
% 178.99/28.66  | | | | | | | |   (131)  $false
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | | CLOSE: (131) is inconsistent.
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | Case 2:
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | |   (132)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | | BETA: splitting (68) gives:
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | | Case 1:
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | |   (133)  all_56_11 = e3
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | COMBINE_EQS: (9), (133) imply:
% 178.99/28.66  | | | | | | | | |   (134)  all_52_23 = e3
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | SIMP: (134) implies:
% 178.99/28.66  | | | | | | | | |   (135)  all_52_23 = e3
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | REDUCE: (8), (135) imply:
% 178.99/28.66  | | | | | | | | |   (136)   ~ (all_52_19 = e3)
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | REF_CLOSE: (5), (11), (18), (23), (49), (55), (75), (78),
% 178.99/28.66  | | | | | | | | |            (89), (95), (128), (136) are inconsistent by
% 178.99/28.66  | | | | | | | | |            sub-proof #975.
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | Case 2:
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | |   (137)   ~ (all_56_11 = e3)
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | REDUCE: (9), (137) imply:
% 178.99/28.66  | | | | | | | | |   (138)   ~ (all_52_23 = e3)
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | BETA: splitting (132) gives:
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | Case 1:
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | |   (139)  all_58_7 = e3
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | | COMBINE_EQS: (23), (139) imply:
% 178.99/28.66  | | | | | | | | | |   (140)  all_52_19 = e3
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | | REDUCE: (8), (140) imply:
% 178.99/28.66  | | | | | | | | | |   (141)   ~ (all_52_23 = e3)
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | | REDUCE: (80), (140) imply:
% 178.99/28.66  | | | | | | | | | |   (142)   ~ (all_52_27 = e3)
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | | REDUCE: (60), (140) imply:
% 178.99/28.66  | | | | | | | | | |   (143)  op(e2, e3) = all_52_18
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | | REF_CLOSE: (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 178.99/28.66  | | | | | | | | | |            (17), (18), (19), (20), (21), (23), (25), (26),
% 178.99/28.66  | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (38), (42),
% 178.99/28.66  | | | | | | | | | |            (44), (45), (46), (47), (49), (51), (54), (55),
% 178.99/28.66  | | | | | | | | | |            (58), (61), (62), (64), (67), (73), (74), (75),
% 178.99/28.66  | | | | | | | | | |            (76), (78), (79), (82), (83), (84), (86), (89),
% 178.99/28.66  | | | | | | | | | |            (93), (95), (101), (103), (122), (123), (138),
% 178.99/28.66  | | | | | | | | | |            (139), (143) are inconsistent by sub-proof #727.
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | Case 2:
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | |   (144)  all_58_8 = e3 | all_58_11 = e3
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | | REF_CLOSE: (43), (62), (97), (138), (144) are inconsistent by
% 178.99/28.66  | | | | | | | | | |            sub-proof #997.
% 178.99/28.66  | | | | | | | | | | 
% 178.99/28.66  | | | | | | | | | End of split
% 178.99/28.66  | | | | | | | | | 
% 178.99/28.66  | | | | | | | | End of split
% 178.99/28.66  | | | | | | | | 
% 178.99/28.66  | | | | | | | End of split
% 178.99/28.66  | | | | | | | 
% 178.99/28.66  | | | | | | End of split
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | Case 2:
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | |   (145)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | | REF_CLOSE: (1), (10), (11), (13), (14), (15), (16), (18), (19),
% 178.99/28.66  | | | | | |            (20), (21), (22), (23), (24), (26), (27), (28), (30),
% 178.99/28.66  | | | | | |            (31), (33), (34), (37), (41), (42), (43), (46), (47),
% 178.99/28.66  | | | | | |            (48), (49), (50), (51), (53), (56), (59), (61), (62),
% 178.99/28.66  | | | | | |            (63), (64), (67), (69), (70), (71), (73), (74), (76),
% 178.99/28.66  | | | | | |            (78), (83), (84), (85), (87), (93), (94), (97), (101),
% 178.99/28.66  | | | | | |            (105), (106), (111), (114), (118), (119), (145) are
% 178.99/28.66  | | | | | |            inconsistent by sub-proof #719.
% 178.99/28.66  | | | | | | 
% 178.99/28.66  | | | | | End of split
% 178.99/28.66  | | | | | 
% 178.99/28.66  | | | | End of split
% 178.99/28.66  | | | | 
% 178.99/28.66  | | | End of split
% 178.99/28.66  | | | 
% 178.99/28.66  | | End of split
% 178.99/28.66  | | 
% 178.99/28.66  | Case 2:
% 178.99/28.66  | | 
% 178.99/28.66  | |   (146)  all_58_15 = e3
% 178.99/28.66  | | 
% 178.99/28.66  | | COMBINE_EQS: (19), (146) imply:
% 178.99/28.66  | |   (147)  all_6_2 = e3
% 178.99/28.66  | | 
% 178.99/28.66  | | REDUCE: (10), (147) imply:
% 178.99/28.66  | |   (148)  $false
% 178.99/28.66  | | 
% 178.99/28.66  | | CLOSE: (148) is inconsistent.
% 178.99/28.66  | | 
% 178.99/28.66  | End of split
% 178.99/28.66  | 
% 178.99/28.66  End of proof
% 178.99/28.66  
% 178.99/28.66  Sub-proof #719 shows that the following formulas are inconsistent:
% 178.99/28.66  ----------------------------------------------------------------
% 178.99/28.66    (1)   ~ (all_52_5 = all_52_13)
% 178.99/28.66    (2)   ~ (all_52_23 = all_52_28)
% 178.99/28.66    (3)  all_58_6 = all_52_28
% 178.99/28.66    (4)   ~ (all_6_2 = e3)
% 178.99/28.66    (5)   ~ (all_52_3 = all_10_2)
% 178.99/28.66    (6)  all_58_5 = all_52_13
% 178.99/28.66    (7)  op(e1, all_52_13) = e1
% 178.99/28.66    (8)  op(e0, all_52_15) = e0
% 178.99/28.66    (9)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.66    (10)  all_58_3 = all_10_2
% 178.99/28.66    (11)  all_58_15 = all_6_2
% 178.99/28.66    (12)   ~ (all_52_9 = all_4_2)
% 178.99/28.66    (13)  all_58_10 = all_52_15
% 178.99/28.66    (14)   ~ (all_52_5 = all_4_2)
% 178.99/28.66    (15)   ~ (all_52_28 = all_4_2)
% 178.99/28.66    (16)  all_58_7 = all_52_19
% 178.99/28.66    (17)  all_56_4 = all_52_9
% 178.99/28.66    (18)  all_58_4 = all_52_5
% 178.99/28.66    (19)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.66    (20)   ~ (e3 = e1)
% 178.99/28.66    (21)  op(e3, all_4_2) = all_4_1
% 178.99/28.66    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.66    (23)  all_58_1 = all_52_3
% 178.99/28.66    (24)  all_58_0 = all_4_2
% 178.99/28.66    (25)   ~ (all_4_1 = e2)
% 178.99/28.66    (26)  all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.99/28.66    (27)   ~ (all_52_3 = all_52_5)
% 178.99/28.66    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.66    (29)  all_58_8 = all_14_2
% 178.99/28.66    (30)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.66    (31)   ~ (all_52_3 = all_4_2)
% 178.99/28.66    (32)  op(e0, e3) = all_52_25
% 178.99/28.66    (33)   ~ (all_52_5 = e3)
% 178.99/28.66    (34)   ~ (all_52_13 = all_14_2)
% 178.99/28.66    (35)  op(e3, all_52_9) = e3
% 178.99/28.66    (36)   ~ (all_52_13 = e3)
% 178.99/28.66    (37)   ~ (all_52_9 = all_52_13)
% 178.99/28.66    (38)   ~ (all_52_15 = all_52_23)
% 178.99/28.66    (39)  all_56_2 = all_52_5
% 178.99/28.66    (40)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.66    (41)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.66    (42)   ~ (e1 = e0)
% 178.99/28.66    (43)  all_58_11 = all_52_23
% 178.99/28.66    (44)   ~ (all_52_3 = all_52_19)
% 178.99/28.66    (45)   ~ (all_52_7 = all_52_15)
% 178.99/28.66    (46)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.66    (47)  all_58_2 = all_52_9
% 178.99/28.66    (48)  op(e3, e1) = all_52_5
% 178.99/28.66    (49)   ~ (e2 = e1)
% 178.99/28.66    (50)  op(e1, e1) = all_14_2
% 178.99/28.66    (51)   ~ (all_52_25 = all_4_2)
% 178.99/28.66    (52)  op(e3, e0) = all_52_7
% 178.99/28.66    (53)  op(e3, e3) = all_4_2
% 178.99/28.66    (54)   ~ (all_14_2 = e3)
% 178.99/28.66    (55)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.66            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.66    (56)   ~ (all_52_7 = e3)
% 178.99/28.66    (57)  all_58_9 = all_52_7
% 178.99/28.66    (58)  all_58_12 = all_52_25
% 178.99/28.66    (59)  all_56_6 = all_52_13
% 178.99/28.66    (60)   ~ (all_52_9 = all_52_15)
% 178.99/28.66    (61)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.66  
% 178.99/28.66  Begin of proof
% 178.99/28.66  | 
% 178.99/28.67  | BETA: splitting (46) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (62)  all_58_1 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | COMBINE_EQS: (23), (62) imply:
% 178.99/28.67  | |   (63)  all_52_3 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (27), (63) imply:
% 178.99/28.67  | |   (64)   ~ (all_52_5 = e3)
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (44), (63) imply:
% 178.99/28.67  | |   (65)   ~ (all_52_19 = e3)
% 178.99/28.67  | | 
% 178.99/28.67  | | SIMP: (65) implies:
% 178.99/28.67  | |   (66)   ~ (all_52_19 = e3)
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (5), (63) imply:
% 178.99/28.67  | |   (67)   ~ (all_10_2 = e3)
% 178.99/28.67  | | 
% 178.99/28.67  | | SIMP: (67) implies:
% 178.99/28.67  | |   (68)   ~ (all_10_2 = e3)
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (31), (63) imply:
% 178.99/28.67  | |   (69)   ~ (all_4_2 = e3)
% 178.99/28.67  | | 
% 178.99/28.67  | | SIMP: (69) implies:
% 178.99/28.67  | |   (70)   ~ (all_4_2 = e3)
% 178.99/28.67  | | 
% 178.99/28.67  | | BETA: splitting (28) gives:
% 178.99/28.67  | | 
% 178.99/28.67  | | Case 1:
% 178.99/28.67  | | | 
% 178.99/28.67  | | |   (71)  all_58_0 = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | COMBINE_EQS: (24), (71) imply:
% 178.99/28.67  | | |   (72)  all_4_2 = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | REDUCE: (70), (72) imply:
% 178.99/28.67  | | |   (73)  $false
% 178.99/28.67  | | | 
% 178.99/28.67  | | | CLOSE: (73) is inconsistent.
% 178.99/28.67  | | | 
% 178.99/28.67  | | Case 2:
% 178.99/28.67  | | | 
% 178.99/28.67  | | |   (74)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | BETA: splitting (19) gives:
% 178.99/28.67  | | | 
% 178.99/28.67  | | | Case 1:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | |   (75)  all_58_6 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | COMBINE_EQS: (3), (75) imply:
% 178.99/28.67  | | | |   (76)  all_52_28 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | SIMP: (76) implies:
% 178.99/28.67  | | | |   (77)  all_52_28 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (2), (77) imply:
% 178.99/28.67  | | | |   (78)   ~ (all_52_23 = e3)
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | BETA: splitting (30) gives:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | Case 1:
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | |   (79)  all_58_10 = e3
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | COMBINE_EQS: (13), (79) imply:
% 178.99/28.67  | | | | |   (80)  all_52_15 = e3
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | SIMP: (80) implies:
% 178.99/28.67  | | | | |   (81)  all_52_15 = e3
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | REDUCE: (60), (81) imply:
% 178.99/28.67  | | | | |   (82)   ~ (all_52_9 = e3)
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | REDUCE: (8), (81) imply:
% 178.99/28.67  | | | | |   (83)  op(e0, e3) = e0
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | GROUND_INST: instantiating (55) with all_52_25, e0, e3, e0,
% 178.99/28.67  | | | | |              simplifying with (32), (83) gives:
% 178.99/28.67  | | | | |   (84)  all_52_25 = e0
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | COMBINE_EQS: (58), (84) imply:
% 178.99/28.67  | | | | |   (85)  all_58_12 = e0
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | REDUCE: (51), (84) imply:
% 178.99/28.67  | | | | |   (86)   ~ (all_4_2 = e0)
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | SIMP: (86) implies:
% 178.99/28.67  | | | | |   (87)   ~ (all_4_2 = e0)
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | BETA: splitting (41) gives:
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | Case 1:
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | |   (88)  all_56_4 = e3
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | | REF_CLOSE: (17), (82), (88) are inconsistent by sub-proof #782.
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | Case 2:
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | |   (89)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | | BETA: splitting (40) gives:
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | | Case 1:
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | |   (90)  all_58_0 = e1
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | COMBINE_EQS: (24), (90) imply:
% 178.99/28.67  | | | | | | |   (91)  all_4_2 = e1
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | REDUCE: (14), (91) imply:
% 178.99/28.67  | | | | | | |   (92)   ~ (all_52_5 = e1)
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | REDUCE: (12), (91) imply:
% 178.99/28.67  | | | | | | |   (93)   ~ (all_52_9 = e1)
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | REDUCE: (70), (91) imply:
% 178.99/28.67  | | | | | | |   (94)   ~ (e3 = e1)
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | REDUCE: (21), (91) imply:
% 178.99/28.67  | | | | | | |   (95)  op(e3, e1) = all_4_1
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | BETA: splitting (9) gives:
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | Case 1:
% 178.99/28.67  | | | | | | | | 
% 178.99/28.67  | | | | | | | |   (96)  all_58_0 = e2
% 178.99/28.67  | | | | | | | | 
% 178.99/28.67  | | | | | | | | REF_CLOSE: (20), (33), (35), (40), (42), (47), (48), (49), (55),
% 178.99/28.67  | | | | | | | |            (75), (85), (96) are inconsistent by sub-proof #724.
% 178.99/28.67  | | | | | | | | 
% 178.99/28.67  | | | | | | | Case 2:
% 178.99/28.67  | | | | | | | | 
% 178.99/28.67  | | | | | | | |   (97)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.67  | | | | | | | | 
% 178.99/28.67  | | | | | | | | BETA: splitting (97) gives:
% 178.99/28.67  | | | | | | | | 
% 178.99/28.67  | | | | | | | | Case 1:
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | |   (98)  all_58_2 = e2
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | COMBINE_EQS: (47), (98) imply:
% 178.99/28.67  | | | | | | | | |   (99)  all_52_9 = e2
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | REDUCE: (37), (99) imply:
% 178.99/28.67  | | | | | | | | |   (100)   ~ (all_52_13 = e2)
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | SIMP: (100) implies:
% 178.99/28.67  | | | | | | | | |   (101)   ~ (all_52_13 = e2)
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | GROUND_INST: instantiating (55) with all_52_5, all_4_1, e1, e3,
% 178.99/28.67  | | | | | | | | |              simplifying with (48), (95) gives:
% 178.99/28.67  | | | | | | | | |   (102)  all_52_5 = all_4_1
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | COMBINE_EQS: (39), (102) imply:
% 178.99/28.67  | | | | | | | | |   (103)  all_56_2 = all_4_1
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | REDUCE: (1), (102) imply:
% 178.99/28.67  | | | | | | | | |   (104)   ~ (all_52_13 = all_4_1)
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | SIMP: (104) implies:
% 178.99/28.67  | | | | | | | | |   (105)   ~ (all_52_13 = all_4_1)
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | REDUCE: (92), (102) imply:
% 178.99/28.67  | | | | | | | | |   (106)   ~ (all_4_1 = e1)
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | BETA: splitting (61) gives:
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | Case 1:
% 178.99/28.67  | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | |   (107)  all_56_2 = e2
% 178.99/28.67  | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | REF_CLOSE: (25), (103), (107) are inconsistent by sub-proof
% 178.99/28.67  | | | | | | | | | |            #929.
% 178.99/28.67  | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | Case 2:
% 178.99/28.67  | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | |   (108)  all_56_2 = e1 | all_56_2 = e0
% 178.99/28.67  | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | BETA: splitting (108) gives:
% 178.99/28.67  | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | Case 1:
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | |   (109)  all_56_2 = e1
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | REF_CLOSE: (103), (106), (109) are inconsistent by sub-proof
% 178.99/28.67  | | | | | | | | | | |            #723.
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | Case 2:
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | |   (110)  all_56_2 = e0
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | COMBINE_EQS: (103), (110) imply:
% 178.99/28.67  | | | | | | | | | | |   (111)  all_4_1 = e0
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | SIMP: (111) implies:
% 178.99/28.67  | | | | | | | | | | |   (112)  all_4_1 = e0
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | REDUCE: (105), (112) imply:
% 178.99/28.67  | | | | | | | | | | |   (113)   ~ (all_52_13 = e0)
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | BETA: splitting (26) gives:
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | Case 1:
% 178.99/28.67  | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | |   (114)  all_56_6 = e2
% 178.99/28.67  | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | REF_CLOSE: (59), (101), (114) are inconsistent by sub-proof
% 178.99/28.67  | | | | | | | | | | | |            #722.
% 178.99/28.67  | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | Case 2:
% 178.99/28.67  | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | |   (115)  all_56_6 = e1 | all_56_6 = e0
% 178.99/28.67  | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | BETA: splitting (115) gives:
% 178.99/28.67  | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | Case 1:
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | |   (116)  all_56_6 = e1
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | | COMBINE_EQS: (59), (116) imply:
% 178.99/28.67  | | | | | | | | | | | | |   (117)  all_52_13 = e1
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | | SIMP: (117) implies:
% 178.99/28.67  | | | | | | | | | | | | |   (118)  all_52_13 = e1
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | | REF_CLOSE: (7), (34), (50), (55), (118) are inconsistent by
% 178.99/28.67  | | | | | | | | | | | | |            sub-proof #721.
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | Case 2:
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | |   (119)  all_56_6 = e0
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | | REF_CLOSE: (59), (113), (119) are inconsistent by sub-proof
% 178.99/28.67  | | | | | | | | | | | | |            #720.
% 178.99/28.67  | | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | | End of split
% 178.99/28.67  | | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | | End of split
% 178.99/28.67  | | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | | End of split
% 178.99/28.67  | | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | End of split
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | Case 2:
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | |   (120)   ~ (all_58_2 = e2)
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | REDUCE: (47), (120) imply:
% 178.99/28.67  | | | | | | | | |   (121)   ~ (all_52_9 = e2)
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | | REF_CLOSE: (17), (35), (52), (55), (56), (89), (93), (121) are
% 178.99/28.67  | | | | | | | | |            inconsistent by sub-proof #753.
% 178.99/28.67  | | | | | | | | | 
% 178.99/28.67  | | | | | | | | End of split
% 178.99/28.67  | | | | | | | | 
% 178.99/28.67  | | | | | | | End of split
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | Case 2:
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | |   (122)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | | REF_CLOSE: (20), (33), (35), (42), (47), (48), (55), (75), (85),
% 178.99/28.67  | | | | | | |            (122) are inconsistent by sub-proof #725.
% 178.99/28.67  | | | | | | | 
% 178.99/28.67  | | | | | | End of split
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | End of split
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | Case 2:
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | |   (123)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | REF_CLOSE: (4), (11), (43), (78), (123) are inconsistent by sub-proof
% 178.99/28.67  | | | | |            #1016.
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | End of split
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | Case 2:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | |   (124)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REF_CLOSE: (6), (10), (12), (13), (16), (22), (29), (35), (36), (38),
% 178.99/28.67  | | | |            (43), (47), (53), (54), (55), (66), (68), (74), (124) are
% 178.99/28.67  | | | |            inconsistent by sub-proof #965.
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | End of split
% 178.99/28.67  | | | 
% 178.99/28.67  | | End of split
% 178.99/28.67  | | 
% 178.99/28.67  | Case 2:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (125)  all_58_4 = e3 | all_58_9 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (18), (33), (56), (57), (125) are inconsistent by sub-proof #729.
% 178.99/28.67  | | 
% 178.99/28.67  | End of split
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #720 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)  all_56_6 = all_52_13
% 178.99/28.67    (2)  all_56_6 = e0
% 178.99/28.67    (3)   ~ (all_52_13 = e0)
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.67  |   (4)  all_52_13 = e0
% 178.99/28.67  | 
% 178.99/28.67  | SIMP: (4) implies:
% 178.99/28.67  |   (5)  all_52_13 = e0
% 178.99/28.67  | 
% 178.99/28.67  | REDUCE: (3), (5) imply:
% 178.99/28.67  |   (6)  $false
% 178.99/28.67  | 
% 178.99/28.67  | CLOSE: (6) is inconsistent.
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #721 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)  all_52_13 = e1
% 178.99/28.67    (2)  op(e1, all_52_13) = e1
% 178.99/28.67    (3)   ~ (all_52_13 = all_14_2)
% 178.99/28.67    (4)  op(e1, e1) = all_14_2
% 178.99/28.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | REDUCE: (1), (3) imply:
% 178.99/28.67  |   (6)   ~ (all_14_2 = e1)
% 178.99/28.67  | 
% 178.99/28.67  | SIMP: (6) implies:
% 178.99/28.67  |   (7)   ~ (all_14_2 = e1)
% 178.99/28.67  | 
% 178.99/28.67  | REDUCE: (1), (2) imply:
% 178.99/28.67  |   (8)  op(e1, e1) = e1
% 178.99/28.67  | 
% 178.99/28.67  | REF_CLOSE: (4), (5), (7), (8) are inconsistent by sub-proof #860.
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #722 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)  all_56_6 = all_52_13
% 178.99/28.67    (2)  all_56_6 = e2
% 178.99/28.67    (3)   ~ (all_52_13 = e2)
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.67  |   (4)  all_52_13 = e2
% 178.99/28.67  | 
% 178.99/28.67  | SIMP: (4) implies:
% 178.99/28.67  |   (5)  all_52_13 = e2
% 178.99/28.67  | 
% 178.99/28.67  | REDUCE: (3), (5) imply:
% 178.99/28.67  |   (6)  $false
% 178.99/28.67  | 
% 178.99/28.67  | CLOSE: (6) is inconsistent.
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #723 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)  all_56_2 = all_4_1
% 178.99/28.67    (2)  all_56_2 = e1
% 178.99/28.67    (3)   ~ (all_4_1 = e1)
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.67  |   (4)  all_4_1 = e1
% 178.99/28.67  | 
% 178.99/28.67  | SIMP: (4) implies:
% 178.99/28.67  |   (5)  all_4_1 = e1
% 178.99/28.67  | 
% 178.99/28.67  | REDUCE: (3), (5) imply:
% 178.99/28.67  |   (6)  $false
% 178.99/28.67  | 
% 178.99/28.67  | CLOSE: (6) is inconsistent.
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #724 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)   ~ (e3 = e1)
% 178.99/28.67    (2)  all_58_6 = e3
% 178.99/28.67    (3)  all_58_12 = e0
% 178.99/28.67    (4)   ~ (all_52_5 = e3)
% 178.99/28.67    (5)  op(e3, all_52_9) = e3
% 178.99/28.67    (6)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.67    (7)   ~ (e1 = e0)
% 178.99/28.67    (8)  all_58_2 = all_52_9
% 178.99/28.67    (9)  op(e3, e1) = all_52_5
% 178.99/28.67    (10)   ~ (e2 = e1)
% 178.99/28.67    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.67    (12)  all_58_0 = e2
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | BETA: splitting (6) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (13)  all_58_0 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | COMBINE_EQS: (12), (13) imply:
% 178.99/28.67  | |   (14)  e2 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (10), (14) imply:
% 178.99/28.67  | |   (15)  $false
% 178.99/28.67  | | 
% 178.99/28.67  | | CLOSE: (15) is inconsistent.
% 178.99/28.67  | | 
% 178.99/28.67  | Case 2:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (16)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (16) are
% 178.99/28.67  | |            inconsistent by sub-proof #725.
% 178.99/28.67  | | 
% 178.99/28.67  | End of split
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #725 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)   ~ (e3 = e1)
% 178.99/28.67    (2)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.67    (3)  all_58_6 = e3
% 178.99/28.67    (4)  all_58_12 = e0
% 178.99/28.67    (5)   ~ (all_52_5 = e3)
% 178.99/28.67    (6)  op(e3, all_52_9) = e3
% 178.99/28.67    (7)   ~ (e1 = e0)
% 178.99/28.67    (8)  all_58_2 = all_52_9
% 178.99/28.67    (9)  op(e3, e1) = all_52_5
% 178.99/28.67    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | BETA: splitting (2) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (11)  all_58_2 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | COMBINE_EQS: (8), (11) imply:
% 178.99/28.67  | |   (12)  all_52_9 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | SIMP: (12) implies:
% 178.99/28.67  | |   (13)  all_52_9 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (6), (13) imply:
% 178.99/28.67  | |   (14)  op(e3, e1) = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (5), (9), (10), (14) are inconsistent by sub-proof #1023.
% 178.99/28.67  | | 
% 178.99/28.67  | Case 2:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (15)  all_58_6 = e1 | all_58_12 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (1), (3), (4), (7), (15) are inconsistent by sub-proof #726.
% 178.99/28.67  | | 
% 178.99/28.67  | End of split
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #726 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)   ~ (e3 = e1)
% 178.99/28.67    (2)  all_58_6 = e1 | all_58_12 = e1
% 178.99/28.67    (3)  all_58_6 = e3
% 178.99/28.67    (4)  all_58_12 = e0
% 178.99/28.67    (5)   ~ (e1 = e0)
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | BETA: splitting (2) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (6)  all_58_6 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | COMBINE_EQS: (3), (6) imply:
% 178.99/28.67  | |   (7)  e3 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | SIMP: (7) implies:
% 178.99/28.67  | |   (8)  e3 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (1), (8) imply:
% 178.99/28.67  | |   (9)  $false
% 178.99/28.67  | | 
% 178.99/28.67  | | CLOSE: (9) is inconsistent.
% 178.99/28.67  | | 
% 178.99/28.67  | Case 2:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (10)  all_58_12 = e1
% 178.99/28.67  | | 
% 178.99/28.67  | | COMBINE_EQS: (4), (10) imply:
% 178.99/28.67  | |   (11)  e1 = e0
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (5), (11) imply:
% 178.99/28.67  | |   (12)  $false
% 178.99/28.67  | | 
% 178.99/28.67  | | CLOSE: (12) is inconsistent.
% 178.99/28.67  | | 
% 178.99/28.67  | End of split
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #727 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)   ~ (all_52_25 = e3)
% 178.99/28.67    (2)  all_58_6 = all_52_28
% 178.99/28.67    (3)  op(e3, e2) = all_52_3
% 178.99/28.67    (4)   ~ (all_52_9 = all_52_25)
% 178.99/28.67    (5)  op(e3, all_52_25) = all_52_24
% 178.99/28.67    (6)   ~ (all_52_27 = e3)
% 178.99/28.67    (7)   ~ (all_6_2 = e3)
% 178.99/28.67    (8)   ~ (all_52_3 = all_10_2)
% 178.99/28.67    (9)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.67    (10)  all_58_5 = all_52_13
% 178.99/28.67    (11)  op(e1, all_52_13) = e1
% 178.99/28.67    (12)  op(e0, all_52_15) = e0
% 178.99/28.67    (13)  op(e2, e0) = all_52_15
% 178.99/28.67    (14)  all_58_3 = all_10_2
% 178.99/28.67    (15)  all_58_15 = all_6_2
% 178.99/28.67    (16)   ~ (all_52_9 = all_4_2)
% 178.99/28.67    (17)  all_58_10 = all_52_15
% 178.99/28.67    (18)  all_58_7 = all_52_19
% 178.99/28.67    (19)   ~ (all_4_0 = e2)
% 178.99/28.67    (20)  all_58_4 = all_52_5
% 178.99/28.67    (21)  op(e3, all_4_2) = all_4_1
% 178.99/28.67    (22)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.67    (23)   ~ (all_52_7 = all_4_2)
% 178.99/28.67    (24)  all_58_1 = all_52_3
% 178.99/28.67    (25)  all_58_0 = all_4_2
% 178.99/28.67    (26)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.67    (27)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.67    (28)  all_58_7 = e3
% 178.99/28.67    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.67    (30)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.99/28.67    (31)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.67    (32)   ~ (all_52_23 = e3)
% 178.99/28.67    (33)   ~ (all_52_3 = all_4_2)
% 178.99/28.67    (34)  op(e0, e3) = all_52_25
% 178.99/28.67    (35)   ~ (all_52_5 = e3)
% 178.99/28.67    (36)  op(e3, all_52_9) = e3
% 178.99/28.67    (37)   ~ (all_52_19 = all_52_28)
% 178.99/28.67    (38)   ~ (all_52_15 = all_52_23)
% 178.99/28.67    (39)  op(e1, e0) = all_52_23
% 178.99/28.67    (40)  all_58_13 = all_52_27
% 178.99/28.67    (41)   ~ (all_52_3 = e3)
% 178.99/28.67    (42)   ~ (all_52_3 = all_52_7)
% 178.99/28.67    (43)   ~ (e1 = e0)
% 178.99/28.67    (44)  all_58_11 = all_52_23
% 178.99/28.67    (45)   ~ (all_52_7 = all_52_15)
% 178.99/28.67    (46)  all_58_2 = all_52_9
% 178.99/28.67    (47)   ~ (all_52_25 = all_4_2)
% 178.99/28.67    (48)  op(e3, e0) = all_52_7
% 178.99/28.67    (49)  op(e2, all_10_2) = e2
% 178.99/28.67    (50)  op(e3, e3) = all_4_2
% 178.99/28.67    (51)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.67    (52)   ~ (all_52_25 = all_52_27)
% 178.99/28.67    (53)  op(e2, e3) = all_52_18
% 178.99/28.67    (54)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.67    (55)  all_58_9 = all_52_7
% 178.99/28.67    (56)  all_58_12 = all_52_25
% 178.99/28.67    (57)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.67    (58)  op(e2, e3) = all_52_9
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | GROUND_INST: instantiating (51) with all_52_9, all_52_18, e3, e2, simplifying
% 178.99/28.67  |              with (53), (58) gives:
% 178.99/28.67  |   (59)  all_52_9 = all_52_18
% 178.99/28.67  | 
% 178.99/28.67  | COMBINE_EQS: (46), (59) imply:
% 178.99/28.67  |   (60)  all_58_2 = all_52_18
% 178.99/28.67  | 
% 178.99/28.67  | REDUCE: (4), (59) imply:
% 178.99/28.67  |   (61)   ~ (all_52_18 = all_52_25)
% 178.99/28.67  | 
% 178.99/28.67  | BETA: splitting (54) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (62)  all_58_9 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (1), (2), (3), (6), (8), (14), (16), (18), (22), (23), (24),
% 178.99/28.67  | |            (25), (27), (29), (36), (37), (40), (42), (46), (49), (50), (51),
% 178.99/28.67  | |            (55), (56), (58), (62) are inconsistent by sub-proof #732.
% 178.99/28.67  | | 
% 178.99/28.67  | Case 2:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (63)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | BETA: splitting (63) gives:
% 178.99/28.67  | | 
% 178.99/28.67  | | Case 1:
% 178.99/28.67  | | | 
% 178.99/28.67  | | |   (64)  all_58_10 = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | COMBINE_EQS: (17), (64) imply:
% 178.99/28.67  | | |   (65)  all_52_15 = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | SIMP: (65) implies:
% 178.99/28.67  | | |   (66)  all_52_15 = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | REDUCE: (45), (66) imply:
% 178.99/28.67  | | |   (67)   ~ (all_52_7 = e3)
% 178.99/28.67  | | | 
% 178.99/28.67  | | | REDUCE: (38), (66) imply:
% 178.99/28.67  | | |   (68)   ~ (all_52_23 = e3)
% 178.99/28.67  | | | 
% 178.99/28.67  | | | REDUCE: (13), (66) imply:
% 178.99/28.67  | | |   (69)  op(e2, e0) = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | REDUCE: (12), (66) imply:
% 178.99/28.67  | | |   (70)  op(e0, e3) = e0
% 178.99/28.67  | | | 
% 178.99/28.67  | | | BETA: splitting (57) gives:
% 178.99/28.67  | | | 
% 178.99/28.67  | | | Case 1:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | |   (71)  all_58_0 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | COMBINE_EQS: (25), (71) imply:
% 178.99/28.67  | | | |   (72)  all_4_2 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (31), (72) imply:
% 178.99/28.67  | | | |   (73)  op(all_4_1, e3) = all_4_0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (21), (72) imply:
% 178.99/28.67  | | | |   (74)  op(e3, e3) = all_4_1
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (50), (72) imply:
% 178.99/28.67  | | | |   (75)  op(e3, e3) = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | GROUND_INST: instantiating (51) with all_52_25, e0, e3, e0, simplifying
% 178.99/28.67  | | | |              with (34), (70) gives:
% 178.99/28.67  | | | |   (76)  all_52_25 = e0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | GROUND_INST: instantiating (51) with e3, all_4_1, e3, e3, simplifying
% 178.99/28.67  | | | |              with (74), (75) gives:
% 178.99/28.67  | | | |   (77)  all_4_1 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (61), (76) imply:
% 178.99/28.67  | | | |   (78)   ~ (all_52_18 = e0)
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (52), (76) imply:
% 178.99/28.67  | | | |   (79)   ~ (all_52_27 = e0)
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | SIMP: (79) implies:
% 178.99/28.67  | | | |   (80)   ~ (all_52_27 = e0)
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (1), (76) imply:
% 178.99/28.67  | | | |   (81)   ~ (e3 = e0)
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | SIMP: (81) implies:
% 178.99/28.67  | | | |   (82)   ~ (e3 = e0)
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (73), (77) imply:
% 178.99/28.67  | | | |   (83)  op(e3, e3) = all_4_0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (5), (76) imply:
% 178.99/28.67  | | | |   (84)  op(e3, e0) = all_52_24
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | GROUND_INST: instantiating (51) with all_52_7, all_52_24, e0, e3,
% 178.99/28.67  | | | |              simplifying with (48), (84) gives:
% 178.99/28.67  | | | |   (85)  all_52_7 = all_52_24
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | GROUND_INST: instantiating (51) with e3, all_4_0, e3, e3, simplifying
% 178.99/28.67  | | | |              with (75), (83) gives:
% 178.99/28.67  | | | |   (86)  all_4_0 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | COMBINE_EQS: (55), (85) imply:
% 178.99/28.67  | | | |   (87)  all_58_9 = all_52_24
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (42), (85) imply:
% 178.99/28.67  | | | |   (88)   ~ (all_52_3 = all_52_24)
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REF_CLOSE: (8), (9), (10), (11), (14), (19), (24), (26), (28), (30),
% 178.99/28.67  | | | |            (32), (39), (40), (41), (43), (44), (49), (51), (60), (64),
% 178.99/28.67  | | | |            (69), (78), (80), (82), (86), (87), (88) are inconsistent by
% 178.99/28.67  | | | |            sub-proof #730.
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | Case 2:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | |   (89)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REF_CLOSE: (20), (24), (35), (41), (55), (67), (89) are inconsistent by
% 178.99/28.67  | | | |            sub-proof #728.
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | End of split
% 178.99/28.67  | | | 
% 178.99/28.67  | | Case 2:
% 178.99/28.67  | | | 
% 178.99/28.67  | | |   (90)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.67  | | | 
% 178.99/28.67  | | | REF_CLOSE: (7), (15), (32), (44), (90) are inconsistent by sub-proof
% 178.99/28.67  | | |            #1016.
% 178.99/28.67  | | | 
% 178.99/28.67  | | End of split
% 178.99/28.67  | | 
% 178.99/28.67  | End of split
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #728 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)  all_58_4 = all_52_5
% 178.99/28.67    (2)  all_58_1 = all_52_3
% 178.99/28.67    (3)   ~ (all_52_5 = e3)
% 178.99/28.67    (4)   ~ (all_52_3 = e3)
% 178.99/28.67    (5)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.67    (6)   ~ (all_52_7 = e3)
% 178.99/28.67    (7)  all_58_9 = all_52_7
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | BETA: splitting (5) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (8)  all_58_1 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | COMBINE_EQS: (2), (8) imply:
% 178.99/28.67  | |   (9)  all_52_3 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (4), (9) imply:
% 178.99/28.67  | |   (10)  $false
% 178.99/28.67  | | 
% 178.99/28.67  | | CLOSE: (10) is inconsistent.
% 178.99/28.67  | | 
% 178.99/28.67  | Case 2:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (11)  all_58_4 = e3 | all_58_9 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (1), (3), (6), (7), (11) are inconsistent by sub-proof #729.
% 178.99/28.67  | | 
% 178.99/28.67  | End of split
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #729 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)  all_58_4 = e3 | all_58_9 = e3
% 178.99/28.67    (2)  all_58_4 = all_52_5
% 178.99/28.67    (3)   ~ (all_52_5 = e3)
% 178.99/28.67    (4)   ~ (all_52_7 = e3)
% 178.99/28.67    (5)  all_58_9 = all_52_7
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | BETA: splitting (1) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (6)  all_58_4 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1025.
% 178.99/28.67  | | 
% 178.99/28.67  | Case 2:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (7)  all_58_9 = e3
% 178.99/28.67  | | 
% 178.99/28.67  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #972.
% 178.99/28.67  | | 
% 178.99/28.67  | End of split
% 178.99/28.67  | 
% 178.99/28.67  End of proof
% 178.99/28.67  
% 178.99/28.67  Sub-proof #730 shows that the following formulas are inconsistent:
% 178.99/28.67  ----------------------------------------------------------------
% 178.99/28.67    (1)  all_58_2 = all_52_18
% 178.99/28.67    (2)   ~ (all_52_27 = e0)
% 178.99/28.67    (3)   ~ (all_52_3 = all_10_2)
% 178.99/28.67    (4)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.67    (5)  all_58_5 = all_52_13
% 178.99/28.67    (6)  op(e1, all_52_13) = e1
% 178.99/28.67    (7)  all_58_3 = all_10_2
% 178.99/28.67    (8)   ~ (all_4_0 = e2)
% 178.99/28.67    (9)  all_58_1 = all_52_3
% 178.99/28.67    (10)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.67    (11)  all_58_7 = e3
% 178.99/28.67    (12)  all_58_1 = e0 | all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.99/28.67    (13)   ~ (all_52_23 = e3)
% 178.99/28.67    (14)   ~ (all_52_3 = all_52_24)
% 178.99/28.67    (15)   ~ (e3 = e0)
% 178.99/28.67    (16)  all_4_0 = e3
% 178.99/28.67    (17)  op(e1, e0) = all_52_23
% 178.99/28.67    (18)  all_58_13 = all_52_27
% 178.99/28.67    (19)   ~ (all_52_3 = e3)
% 178.99/28.67    (20)   ~ (all_52_18 = e0)
% 178.99/28.67    (21)  all_58_10 = e3
% 178.99/28.67    (22)   ~ (e1 = e0)
% 178.99/28.67    (23)  all_58_11 = all_52_23
% 178.99/28.67    (24)  op(e2, e0) = e3
% 178.99/28.67    (25)  op(e2, all_10_2) = e2
% 178.99/28.67    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.67    (27)  all_58_9 = all_52_24
% 178.99/28.67  
% 178.99/28.67  Begin of proof
% 178.99/28.67  | 
% 178.99/28.67  | REDUCE: (8), (16) imply:
% 178.99/28.67  |   (28)   ~ (e3 = e2)
% 178.99/28.67  | 
% 178.99/28.67  | BETA: splitting (12) gives:
% 178.99/28.67  | 
% 178.99/28.67  | Case 1:
% 178.99/28.67  | | 
% 178.99/28.67  | |   (29)  all_58_1 = e0
% 178.99/28.67  | | 
% 178.99/28.67  | | COMBINE_EQS: (9), (29) imply:
% 178.99/28.67  | |   (30)  all_52_3 = e0
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (14), (30) imply:
% 178.99/28.67  | |   (31)   ~ (all_52_24 = e0)
% 178.99/28.67  | | 
% 178.99/28.67  | | SIMP: (31) implies:
% 178.99/28.67  | |   (32)   ~ (all_52_24 = e0)
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (3), (30) imply:
% 178.99/28.67  | |   (33)   ~ (all_10_2 = e0)
% 178.99/28.67  | | 
% 178.99/28.67  | | SIMP: (33) implies:
% 178.99/28.67  | |   (34)   ~ (all_10_2 = e0)
% 178.99/28.67  | | 
% 178.99/28.67  | | REDUCE: (19), (30) imply:
% 178.99/28.67  | |   (35)   ~ (e3 = e0)
% 178.99/28.67  | | 
% 178.99/28.67  | | BETA: splitting (10) gives:
% 178.99/28.67  | | 
% 178.99/28.67  | | Case 1:
% 178.99/28.67  | | | 
% 178.99/28.67  | | |   (36)  all_58_9 = e0
% 178.99/28.67  | | | 
% 178.99/28.67  | | | REF_CLOSE: (27), (32), (36) are inconsistent by sub-proof #760.
% 178.99/28.67  | | | 
% 178.99/28.67  | | Case 2:
% 178.99/28.67  | | | 
% 178.99/28.67  | | |   (37)  all_58_10 = e0 | all_58_11 = e0
% 178.99/28.67  | | | 
% 178.99/28.67  | | | BETA: splitting (37) gives:
% 178.99/28.67  | | | 
% 178.99/28.67  | | | Case 1:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | |   (38)  all_58_10 = e0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REF_CLOSE: (15), (21), (38) are inconsistent by sub-proof #824.
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | Case 2:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | |   (39)  all_58_11 = e0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | COMBINE_EQS: (23), (39) imply:
% 178.99/28.67  | | | |   (40)  all_52_23 = e0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | SIMP: (40) implies:
% 178.99/28.67  | | | |   (41)  all_52_23 = e0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | REDUCE: (17), (41) imply:
% 178.99/28.67  | | | |   (42)  op(e1, e0) = e0
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | BETA: splitting (4) gives:
% 178.99/28.67  | | | | 
% 178.99/28.67  | | | | Case 1:
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | |   (43)  all_58_2 = e0
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | COMBINE_EQS: (1), (43) imply:
% 178.99/28.67  | | | | |   (44)  all_52_18 = e0
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | SIMP: (44) implies:
% 178.99/28.67  | | | | |   (45)  all_52_18 = e0
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | REDUCE: (20), (45) imply:
% 178.99/28.67  | | | | |   (46)  $false
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | CLOSE: (46) is inconsistent.
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | Case 2:
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | |   (47)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | BETA: splitting (47) gives:
% 178.99/28.67  | | | | | 
% 178.99/28.67  | | | | | Case 1:
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | |   (48)  all_58_3 = e0
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | | COMBINE_EQS: (7), (48) imply:
% 178.99/28.67  | | | | | |   (49)  all_10_2 = e0
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | | REDUCE: (34), (49) imply:
% 178.99/28.67  | | | | | |   (50)  $false
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | | CLOSE: (50) is inconsistent.
% 178.99/28.67  | | | | | | 
% 178.99/28.67  | | | | | Case 2:
% 178.99/28.67  | | | | | | 
% 178.99/28.68  | | | | | |   (51)  all_58_5 = e0 | all_58_10 = e0
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | | REF_CLOSE: (5), (6), (15), (21), (22), (26), (42), (51) are
% 178.99/28.68  | | | | | |            inconsistent by sub-proof #759.
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | End of split
% 178.99/28.68  | | | | | 
% 178.99/28.68  | | | | End of split
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | End of split
% 178.99/28.68  | | | 
% 178.99/28.68  | | End of split
% 178.99/28.68  | | 
% 178.99/28.68  | Case 2:
% 178.99/28.68  | | 
% 178.99/28.68  | |   (52)  all_58_3 = e0 | all_58_7 = e0 | all_58_13 = e0
% 178.99/28.68  | | 
% 178.99/28.68  | | BETA: splitting (52) gives:
% 178.99/28.68  | | 
% 178.99/28.68  | | Case 1:
% 178.99/28.68  | | | 
% 178.99/28.68  | | |   (53)  all_58_3 = e0
% 178.99/28.68  | | | 
% 178.99/28.68  | | | COMBINE_EQS: (7), (53) imply:
% 178.99/28.68  | | |   (54)  all_10_2 = e0
% 178.99/28.68  | | | 
% 178.99/28.68  | | | REDUCE: (25), (54) imply:
% 178.99/28.68  | | |   (55)  op(e2, e0) = e2
% 178.99/28.68  | | | 
% 178.99/28.68  | | | GROUND_INST: instantiating (26) with e3, e2, e0, e2, simplifying with
% 178.99/28.68  | | |              (24), (55) gives:
% 178.99/28.68  | | |   (56)  e3 = e2
% 178.99/28.68  | | | 
% 178.99/28.68  | | | REDUCE: (28), (56) imply:
% 178.99/28.68  | | |   (57)  $false
% 178.99/28.68  | | | 
% 178.99/28.68  | | | CLOSE: (57) is inconsistent.
% 178.99/28.68  | | | 
% 178.99/28.68  | | Case 2:
% 178.99/28.68  | | | 
% 178.99/28.68  | | |   (58)  all_58_7 = e0 | all_58_13 = e0
% 178.99/28.68  | | | 
% 178.99/28.68  | | | BETA: splitting (58) gives:
% 178.99/28.68  | | | 
% 178.99/28.68  | | | Case 1:
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | |   (59)  all_58_7 = e0
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | COMBINE_EQS: (11), (59) imply:
% 178.99/28.68  | | | |   (60)  e3 = e0
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | REDUCE: (15), (60) imply:
% 178.99/28.68  | | | |   (61)  $false
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | CLOSE: (61) is inconsistent.
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | Case 2:
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | |   (62)  all_58_13 = e0
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | REF_CLOSE: (2), (18), (62) are inconsistent by sub-proof #731.
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | End of split
% 178.99/28.68  | | | 
% 178.99/28.68  | | End of split
% 178.99/28.68  | | 
% 178.99/28.68  | End of split
% 178.99/28.68  | 
% 178.99/28.68  End of proof
% 178.99/28.68  
% 178.99/28.68  Sub-proof #731 shows that the following formulas are inconsistent:
% 178.99/28.68  ----------------------------------------------------------------
% 178.99/28.68    (1)  all_58_13 = all_52_27
% 178.99/28.68    (2)  all_58_13 = e0
% 178.99/28.68    (3)   ~ (all_52_27 = e0)
% 178.99/28.68  
% 178.99/28.68  Begin of proof
% 178.99/28.68  | 
% 178.99/28.68  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.68  |   (4)  all_52_27 = e0
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (4) implies:
% 178.99/28.68  |   (5)  all_52_27 = e0
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (3), (5) imply:
% 178.99/28.68  |   (6)  $false
% 178.99/28.68  | 
% 178.99/28.68  | CLOSE: (6) is inconsistent.
% 178.99/28.68  | 
% 178.99/28.68  End of proof
% 178.99/28.68  
% 178.99/28.68  Sub-proof #732 shows that the following formulas are inconsistent:
% 178.99/28.68  ----------------------------------------------------------------
% 178.99/28.68    (1)   ~ (all_52_25 = e3)
% 178.99/28.68    (2)  all_58_6 = all_52_28
% 178.99/28.68    (3)  op(e3, e2) = all_52_3
% 178.99/28.68    (4)   ~ (all_52_27 = e3)
% 178.99/28.68    (5)   ~ (all_52_3 = all_10_2)
% 178.99/28.68    (6)  all_58_3 = all_10_2
% 178.99/28.68    (7)   ~ (all_52_9 = all_4_2)
% 178.99/28.68    (8)  all_58_7 = all_52_19
% 178.99/28.68    (9)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.68    (10)  all_58_9 = e3
% 178.99/28.68    (11)   ~ (all_52_7 = all_4_2)
% 178.99/28.68    (12)  all_58_1 = all_52_3
% 178.99/28.68    (13)  all_58_0 = all_4_2
% 178.99/28.68    (14)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.68    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.68    (16)  op(e3, all_52_9) = e3
% 178.99/28.68    (17)   ~ (all_52_19 = all_52_28)
% 178.99/28.68    (18)  all_58_13 = all_52_27
% 178.99/28.68    (19)   ~ (all_52_3 = all_52_7)
% 178.99/28.68    (20)  all_58_2 = all_52_9
% 178.99/28.68    (21)  op(e2, all_10_2) = e2
% 178.99/28.68    (22)  op(e3, e3) = all_4_2
% 178.99/28.68    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.68    (24)  all_58_9 = all_52_7
% 178.99/28.68    (25)  all_58_12 = all_52_25
% 178.99/28.68    (26)  op(e2, e3) = all_52_9
% 178.99/28.68  
% 178.99/28.68  Begin of proof
% 178.99/28.68  | 
% 178.99/28.68  | COMBINE_EQS: (10), (24) imply:
% 178.99/28.68  |   (27)  all_52_7 = e3
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (27) implies:
% 178.99/28.68  |   (28)  all_52_7 = e3
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (19), (28) imply:
% 178.99/28.68  |   (29)   ~ (all_52_3 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (11), (28) imply:
% 178.99/28.68  |   (30)   ~ (all_4_2 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (30) implies:
% 178.99/28.68  |   (31)   ~ (all_4_2 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 178.99/28.68  |            (15), (16), (17), (18), (20), (21), (22), (23), (25), (26), (29),
% 178.99/28.68  |            (31) are inconsistent by sub-proof #960.
% 178.99/28.68  | 
% 178.99/28.68  End of proof
% 178.99/28.68  
% 178.99/28.68  Sub-proof #733 shows that the following formulas are inconsistent:
% 178.99/28.68  ----------------------------------------------------------------
% 178.99/28.68    (1)  op(e3, e2) = all_52_3
% 178.99/28.68    (2)   ~ (all_52_3 = all_10_2)
% 178.99/28.68    (3)  all_52_7 = e3
% 178.99/28.68    (4)  all_58_5 = all_52_13
% 178.99/28.68    (5)  all_58_3 = all_10_2
% 178.99/28.68    (6)   ~ (all_52_9 = all_4_2)
% 178.99/28.68    (7)  all_58_10 = all_52_15
% 178.99/28.68    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.68    (9)  op(e3, all_52_9) = e3
% 178.99/28.68    (10)   ~ (all_52_13 = e3)
% 178.99/28.68    (11)   ~ (all_52_7 = all_52_15)
% 178.99/28.68    (12)  all_58_2 = all_52_9
% 178.99/28.68    (13)  op(e2, all_10_2) = e2
% 178.99/28.68    (14)  op(e3, e3) = all_4_2
% 178.99/28.68    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.68    (16)  op(e2, e3) = all_52_9
% 178.99/28.68  
% 178.99/28.68  Begin of proof
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (3) implies:
% 178.99/28.68  |   (17)  all_52_7 = e3
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (11), (17) imply:
% 178.99/28.68  |   (18)   ~ (all_52_15 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (18) implies:
% 178.99/28.68  |   (19)   ~ (all_52_15 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 178.99/28.68  |            (15), (16), (19) are inconsistent by sub-proof #772.
% 178.99/28.68  | 
% 178.99/28.68  End of proof
% 178.99/28.68  
% 178.99/28.68  Sub-proof #734 shows that the following formulas are inconsistent:
% 178.99/28.68  ----------------------------------------------------------------
% 178.99/28.68    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.68    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.68    (3)   ~ (all_52_27 = all_10_2)
% 178.99/28.68    (4)   ~ (all_52_17 = all_52_23)
% 178.99/28.68    (5)   ~ (all_52_13 = all_52_29)
% 178.99/28.68    (6)  all_56_3 = all_52_7
% 178.99/28.68    (7)  op(e3, e2) = all_52_3
% 178.99/28.68    (8)   ~ (all_52_9 = all_52_25)
% 178.99/28.68    (9)   ~ (all_52_19 = all_52_23)
% 178.99/28.68    (10)  all_56_11 = all_52_23
% 178.99/28.68    (11)  op(e1, e2) = all_52_19
% 178.99/28.68    (12)   ~ (all_52_3 = all_10_2)
% 178.99/28.68    (13)  all_58_5 = all_52_13
% 178.99/28.68    (14)   ~ (all_6_2 = e0)
% 178.99/28.68    (15)   ~ (all_52_25 = all_52_29)
% 178.99/28.68    (16)  op(e1, all_52_13) = e1
% 178.99/28.68    (17)  op(e0, all_52_15) = e0
% 178.99/28.68    (18)  all_56_15 = all_6_2
% 178.99/28.68    (19)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.68    (20)  all_58_3 = all_10_2
% 178.99/28.68    (21)  all_56_9 = all_52_19
% 178.99/28.68    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.68    (23)  all_58_15 = all_6_2
% 178.99/28.68    (24)   ~ (all_52_9 = all_4_2)
% 178.99/28.68    (25)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.68    (26)   ~ (all_52_5 = all_52_7)
% 178.99/28.68    (27)  all_58_10 = all_52_15
% 178.99/28.68    (28)   ~ (all_52_5 = all_4_2)
% 178.99/28.68    (29)  all_58_7 = all_52_19
% 178.99/28.68    (30)  all_56_4 = all_52_9
% 178.99/28.68    (31)   ~ (all_52_17 = all_52_25)
% 178.99/28.68    (32)  all_58_4 = all_52_5
% 178.99/28.68    (33)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.68    (34)   ~ (all_52_27 = all_52_29)
% 178.99/28.68    (35)   ~ (all_52_17 = all_14_2)
% 178.99/28.68    (36)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.68    (37)   ~ (all_52_7 = all_4_2)
% 178.99/28.68    (38)  all_58_1 = all_52_3
% 178.99/28.68    (39)  all_58_0 = all_4_2
% 178.99/28.68    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.68    (41)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.68    (42)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.68    (43)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.68    (44)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.99/28.68    (45)   ~ (all_14_1 = e3)
% 178.99/28.68    (46)  all_58_14 = all_52_29
% 178.99/28.68    (47)   ~ (all_52_3 = all_52_5)
% 178.99/28.68    (48)  op(e2, e1) = all_52_13
% 178.99/28.68    (49)  all_58_8 = all_14_2
% 178.99/28.68    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.68    (51)  op(e0, e3) = all_52_25
% 178.99/28.68    (52)  op(e3, all_52_17) = all_52_16
% 178.99/28.68    (53)   ~ (all_52_13 = all_14_2)
% 178.99/28.68    (54)  op(e3, all_52_9) = e3
% 178.99/28.68    (55)   ~ (e3 = e0)
% 178.99/28.68    (56)   ~ (all_52_9 = all_52_13)
% 178.99/28.68    (57)  op(e0, all_52_23) = all_52_22
% 178.99/28.68    (58)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.68    (59)  all_58_13 = all_52_27
% 178.99/28.68    (60)  all_58_12 = e3
% 178.99/28.68    (61)   ~ (all_52_9 = all_52_17)
% 178.99/28.68    (62)  all_58_6 = all_52_17
% 178.99/28.68    (63)   ~ (all_52_3 = all_52_7)
% 178.99/28.68    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.68    (65)  op(e2, all_52_19) = all_52_18
% 178.99/28.68    (66)  all_56_0 = all_4_2
% 178.99/28.68    (67)  all_58_11 = all_52_23
% 178.99/28.68    (68)   ~ (all_52_3 = all_52_19)
% 178.99/28.68    (69)   ~ (all_52_7 = all_52_15)
% 178.99/28.68    (70)   ~ (all_52_19 = all_10_2)
% 178.99/28.68    (71)   ~ (all_52_23 = all_6_2)
% 178.99/28.68    (72)  all_58_2 = all_52_9
% 178.99/28.68    (73)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.68    (74)  op(e3, e1) = all_52_5
% 178.99/28.68    (75)   ~ (e2 = e1)
% 178.99/28.68    (76)  all_56_10 = all_14_2
% 178.99/28.68    (77)   ~ (all_52_25 = all_6_2)
% 178.99/28.68    (78)  op(e1, e3) = all_52_17
% 178.99/28.68    (79)   ~ (all_52_25 = all_4_2)
% 178.99/28.68    (80)  op(e3, e0) = all_52_7
% 178.99/28.68    (81)  op(e2, all_10_2) = e2
% 178.99/28.68    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.68    (83)   ~ (all_52_25 = all_52_27)
% 178.99/28.68    (84)   ~ (all_52_27 = all_6_2)
% 178.99/28.68    (85)   ~ (all_52_7 = all_6_2)
% 178.99/28.68    (86)   ~ (all_52_7 = all_52_23)
% 178.99/28.68    (87)   ~ (all_52_17 = all_52_19)
% 178.99/28.68    (88)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.68    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.68    (90)  op(e1, all_14_2) = all_14_1
% 178.99/28.68    (91)  all_58_9 = all_52_7
% 178.99/28.68    (92)  all_58_12 = all_52_25
% 178.99/28.68    (93)  all_56_6 = all_52_13
% 178.99/28.68    (94)   ~ (all_52_9 = all_52_15)
% 178.99/28.68    (95)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.68    (96)   ~ (e3 = e2)
% 178.99/28.68    (97)   ~ (all_52_19 = all_14_2)
% 178.99/28.68    (98)  op(e2, e3) = all_52_9
% 178.99/28.68  
% 178.99/28.68  Begin of proof
% 178.99/28.68  | 
% 178.99/28.68  | COMBINE_EQS: (60), (92) imply:
% 178.99/28.68  |   (99)  all_52_25 = e3
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (99) implies:
% 178.99/28.68  |   (100)  all_52_25 = e3
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (8), (100) imply:
% 178.99/28.68  |   (101)   ~ (all_52_9 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (31), (100) imply:
% 178.99/28.68  |   (102)   ~ (all_52_17 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (83), (100) imply:
% 178.99/28.68  |   (103)   ~ (all_52_27 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (103) implies:
% 178.99/28.68  |   (104)   ~ (all_52_27 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (15), (100) imply:
% 178.99/28.68  |   (105)   ~ (all_52_29 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (105) implies:
% 178.99/28.68  |   (106)   ~ (all_52_29 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (77), (100) imply:
% 178.99/28.68  |   (107)   ~ (all_6_2 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (107) implies:
% 178.99/28.68  |   (108)   ~ (all_6_2 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (79), (100) imply:
% 178.99/28.68  |   (109)   ~ (all_4_2 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | SIMP: (109) implies:
% 178.99/28.68  |   (110)   ~ (all_4_2 = e3)
% 178.99/28.68  | 
% 178.99/28.68  | REDUCE: (51), (100) imply:
% 178.99/28.68  |   (111)  op(e0, e3) = e3
% 178.99/28.68  | 
% 178.99/28.68  | BETA: splitting (22) gives:
% 178.99/28.68  | 
% 178.99/28.68  | Case 1:
% 178.99/28.68  | | 
% 178.99/28.68  | |   (112)  all_56_0 = e3
% 178.99/28.68  | | 
% 178.99/28.68  | | REF_CLOSE: (66), (110), (112) are inconsistent by sub-proof #1024.
% 178.99/28.68  | | 
% 178.99/28.68  | Case 2:
% 178.99/28.68  | | 
% 178.99/28.68  | |   (113)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.68  | | 
% 178.99/28.68  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 178.99/28.68  | |            (14), (16), (17), (18), (19), (20), (21), (23), (24), (25), (26),
% 178.99/28.68  | |            (27), (28), (29), (30), (32), (33), (34), (35), (36), (37), (38),
% 178.99/28.68  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 178.99/28.68  | |            (50), (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 178.99/28.68  | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 178.99/28.68  | |            (73), (74), (75), (76), (78), (80), (81), (82), (84), (85), (86),
% 178.99/28.68  | |            (87), (88), (89), (90), (91), (93), (94), (95), (96), (97), (98),
% 178.99/28.68  | |            (101), (102), (104), (106), (108), (111), (113) are inconsistent
% 178.99/28.68  | |            by sub-proof #735.
% 178.99/28.68  | | 
% 178.99/28.68  | End of split
% 178.99/28.68  | 
% 178.99/28.68  End of proof
% 178.99/28.68  
% 178.99/28.68  Sub-proof #735 shows that the following formulas are inconsistent:
% 178.99/28.68  ----------------------------------------------------------------
% 178.99/28.68    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.68    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.68    (3)   ~ (all_52_27 = all_10_2)
% 178.99/28.68    (4)   ~ (all_52_17 = all_52_23)
% 178.99/28.68    (5)   ~ (all_52_13 = all_52_29)
% 178.99/28.68    (6)  all_56_3 = all_52_7
% 178.99/28.68    (7)  op(e3, e2) = all_52_3
% 178.99/28.68    (8)   ~ (all_52_19 = all_52_23)
% 178.99/28.68    (9)  all_56_11 = all_52_23
% 178.99/28.68    (10)  op(e1, e2) = all_52_19
% 178.99/28.68    (11)   ~ (all_52_27 = e3)
% 178.99/28.68    (12)   ~ (all_52_17 = e3)
% 178.99/28.68    (13)   ~ (all_6_2 = e3)
% 178.99/28.68    (14)   ~ (all_52_3 = all_10_2)
% 178.99/28.68    (15)  all_58_5 = all_52_13
% 178.99/28.68    (16)   ~ (all_6_2 = e0)
% 178.99/28.68    (17)  op(e1, all_52_13) = e1
% 178.99/28.68    (18)  op(e0, all_52_15) = e0
% 178.99/28.68    (19)  all_56_15 = all_6_2
% 178.99/28.68    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.68    (21)  all_58_3 = all_10_2
% 178.99/28.68    (22)  all_56_9 = all_52_19
% 178.99/28.68    (23)  all_58_15 = all_6_2
% 178.99/28.68    (24)   ~ (all_52_9 = all_4_2)
% 178.99/28.68    (25)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.68    (26)   ~ (all_52_5 = all_52_7)
% 178.99/28.68    (27)  all_58_10 = all_52_15
% 178.99/28.68    (28)   ~ (all_52_5 = all_4_2)
% 178.99/28.68    (29)  all_58_7 = all_52_19
% 178.99/28.68    (30)  all_56_4 = all_52_9
% 178.99/28.68    (31)  all_58_4 = all_52_5
% 178.99/28.68    (32)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.68    (33)   ~ (all_52_27 = all_52_29)
% 178.99/28.68    (34)   ~ (all_52_17 = all_14_2)
% 178.99/28.68    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.68    (36)   ~ (all_52_7 = all_4_2)
% 178.99/28.68    (37)  all_58_1 = all_52_3
% 178.99/28.68    (38)  all_58_0 = all_4_2
% 178.99/28.68    (39)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.68    (40)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.68    (41)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.68    (42)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.68    (43)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.99/28.68    (44)   ~ (all_14_1 = e3)
% 178.99/28.68    (45)  all_58_14 = all_52_29
% 178.99/28.68    (46)  op(e0, e3) = e3
% 178.99/28.68    (47)   ~ (all_52_3 = all_52_5)
% 178.99/28.68    (48)  op(e2, e1) = all_52_13
% 178.99/28.68    (49)  all_58_8 = all_14_2
% 178.99/28.68    (50)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.68    (51)  op(e3, all_52_17) = all_52_16
% 178.99/28.68    (52)   ~ (all_52_29 = e3)
% 178.99/28.68    (53)   ~ (all_52_13 = all_14_2)
% 178.99/28.68    (54)  op(e3, all_52_9) = e3
% 178.99/28.68    (55)   ~ (e3 = e0)
% 178.99/28.68    (56)   ~ (all_52_9 = all_52_13)
% 178.99/28.68    (57)  op(e0, all_52_23) = all_52_22
% 178.99/28.68    (58)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.68    (59)  all_58_13 = all_52_27
% 178.99/28.68    (60)  all_58_12 = e3
% 178.99/28.68    (61)   ~ (all_52_9 = all_52_17)
% 178.99/28.68    (62)  all_58_6 = all_52_17
% 178.99/28.68    (63)   ~ (all_52_3 = all_52_7)
% 178.99/28.68    (64)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.68    (65)  op(e2, all_52_19) = all_52_18
% 178.99/28.68    (66)  all_56_0 = all_4_2
% 178.99/28.68    (67)  all_58_11 = all_52_23
% 178.99/28.68    (68)   ~ (all_52_3 = all_52_19)
% 178.99/28.68    (69)   ~ (all_52_7 = all_52_15)
% 178.99/28.68    (70)   ~ (all_52_19 = all_10_2)
% 178.99/28.68    (71)   ~ (all_52_9 = e3)
% 178.99/28.68    (72)   ~ (all_52_23 = all_6_2)
% 178.99/28.68    (73)  all_58_2 = all_52_9
% 178.99/28.68    (74)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.68    (75)  op(e3, e1) = all_52_5
% 178.99/28.68    (76)   ~ (e2 = e1)
% 178.99/28.68    (77)  all_56_10 = all_14_2
% 178.99/28.68    (78)  op(e1, e3) = all_52_17
% 178.99/28.68    (79)  op(e3, e0) = all_52_7
% 178.99/28.68    (80)  op(e2, all_10_2) = e2
% 178.99/28.68    (81)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.68    (82)   ~ (all_52_27 = all_6_2)
% 178.99/28.68    (83)   ~ (all_52_7 = all_6_2)
% 178.99/28.68    (84)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.68    (85)   ~ (all_52_7 = all_52_23)
% 178.99/28.68    (86)   ~ (all_52_17 = all_52_19)
% 178.99/28.68    (87)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.68    (88)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.68    (89)  op(e1, all_14_2) = all_14_1
% 178.99/28.68    (90)  all_58_9 = all_52_7
% 178.99/28.68    (91)  all_56_6 = all_52_13
% 178.99/28.68    (92)   ~ (all_52_9 = all_52_15)
% 178.99/28.68    (93)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.68    (94)   ~ (e3 = e2)
% 178.99/28.68    (95)   ~ (all_52_19 = all_14_2)
% 178.99/28.68    (96)  op(e2, e3) = all_52_9
% 178.99/28.68  
% 178.99/28.68  Begin of proof
% 178.99/28.68  | 
% 178.99/28.68  | BETA: splitting (64) gives:
% 178.99/28.68  | 
% 178.99/28.68  | Case 1:
% 178.99/28.68  | | 
% 178.99/28.68  | |   (97)  all_56_4 = e3
% 178.99/28.68  | | 
% 178.99/28.68  | | REF_CLOSE: (30), (71), (97) are inconsistent by sub-proof #782.
% 178.99/28.68  | | 
% 178.99/28.68  | Case 2:
% 178.99/28.68  | | 
% 178.99/28.68  | |   (98)   ~ (all_56_4 = e3)
% 178.99/28.68  | |   (99)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.68  | | 
% 178.99/28.68  | | BETA: splitting (74) gives:
% 178.99/28.68  | | 
% 178.99/28.68  | | Case 1:
% 178.99/28.68  | | | 
% 178.99/28.68  | | |   (100)  all_56_11 = e3
% 178.99/28.68  | | | 
% 178.99/28.68  | | | COMBINE_EQS: (9), (100) imply:
% 178.99/28.68  | | |   (101)  all_52_23 = e3
% 178.99/28.68  | | | 
% 178.99/28.68  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (11), (14), (15), (16),
% 178.99/28.68  | | |            (17), (18), (19), (21), (22), (23), (24), (25), (26), (27),
% 178.99/28.68  | | |            (28), (29), (30), (31), (33), (34), (36), (37), (38), (40),
% 178.99/28.68  | | |            (41), (42), (45), (46), (47), (48), (49), (50), (51), (52),
% 178.99/28.68  | | |            (54), (55), (57), (59), (61), (63), (66), (67), (72), (75),
% 178.99/28.68  | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 178.99/28.68  | | |            (88), (90), (93), (94), (96), (99), (101) are inconsistent by
% 178.99/28.68  | | |            sub-proof #742.
% 178.99/28.68  | | | 
% 178.99/28.68  | | Case 2:
% 178.99/28.68  | | | 
% 178.99/28.68  | | |   (102)   ~ (all_56_11 = e3)
% 178.99/28.68  | | | 
% 178.99/28.68  | | | REDUCE: (9), (102) imply:
% 178.99/28.68  | | |   (103)   ~ (all_52_23 = e3)
% 178.99/28.68  | | | 
% 178.99/28.68  | | | BETA: splitting (87) gives:
% 178.99/28.68  | | | 
% 178.99/28.68  | | | Case 1:
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | |   (104)  all_58_9 = e3
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | COMBINE_EQS: (90), (104) imply:
% 178.99/28.68  | | | |   (105)  all_52_7 = e3
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | SIMP: (105) implies:
% 178.99/28.68  | | | |   (106)  all_52_7 = e3
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | REDUCE: (63), (106) imply:
% 178.99/28.68  | | | |   (107)   ~ (all_52_3 = e3)
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | REDUCE: (69), (106) imply:
% 178.99/28.68  | | | |   (108)   ~ (all_52_15 = e3)
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | SIMP: (108) implies:
% 178.99/28.68  | | | |   (109)   ~ (all_52_15 = e3)
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | REDUCE: (85), (106) imply:
% 178.99/28.68  | | | |   (110)   ~ (all_52_23 = e3)
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | BETA: splitting (32) gives:
% 178.99/28.68  | | | | 
% 178.99/28.68  | | | | Case 1:
% 178.99/28.68  | | | | | 
% 178.99/28.68  | | | | |   (111)  all_58_6 = e3
% 178.99/28.68  | | | | | 
% 178.99/28.68  | | | | | REF_CLOSE: (12), (62), (111) are inconsistent by sub-proof #981.
% 178.99/28.68  | | | | | 
% 178.99/28.68  | | | | Case 2:
% 178.99/28.68  | | | | | 
% 178.99/28.68  | | | | |   (112)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.68  | | | | | 
% 178.99/28.68  | | | | | BETA: splitting (42) gives:
% 178.99/28.68  | | | | | 
% 178.99/28.68  | | | | | Case 1:
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | |   (113)  all_58_1 = e3
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | | COMBINE_EQS: (37), (113) imply:
% 178.99/28.68  | | | | | |   (114)  all_52_3 = e3
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | | REDUCE: (107), (114) imply:
% 178.99/28.68  | | | | | |   (115)  $false
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | | CLOSE: (115) is inconsistent.
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | Case 2:
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | |   (116)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | | BETA: splitting (35) gives:
% 178.99/28.68  | | | | | | 
% 178.99/28.68  | | | | | | Case 1:
% 178.99/28.68  | | | | | | | 
% 178.99/28.68  | | | | | | |   (117)  all_58_2 = e3
% 178.99/28.68  | | | | | | | 
% 178.99/28.68  | | | | | | | REF_CLOSE: (71), (73), (117) are inconsistent by sub-proof #980.
% 178.99/28.68  | | | | | | | 
% 178.99/28.68  | | | | | | Case 2:
% 178.99/28.68  | | | | | | | 
% 178.99/28.68  | | | | | | |   (118)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.68  | | | | | | | 
% 178.99/28.68  | | | | | | | BETA: splitting (43) gives:
% 178.99/28.68  | | | | | | | 
% 178.99/28.68  | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | |   (119)  all_56_6 = e3
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | | COMBINE_EQS: (91), (119) imply:
% 178.99/28.68  | | | | | | | |   (120)  all_52_13 = e3
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | | SIMP: (120) implies:
% 178.99/28.68  | | | | | | | |   (121)  all_52_13 = e3
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | | REDUCE: (53), (121) imply:
% 178.99/28.68  | | | | | | | |   (122)   ~ (all_14_2 = e3)
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | | SIMP: (122) implies:
% 178.99/28.68  | | | | | | | |   (123)   ~ (all_14_2 = e3)
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | | REDUCE: (17), (121) imply:
% 178.99/28.68  | | | | | | | |   (124)  op(e1, e3) = e1
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | | BETA: splitting (112) gives:
% 178.99/28.68  | | | | | | | | 
% 178.99/28.68  | | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | |   (125)  all_58_7 = e3
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | COMBINE_EQS: (29), (125) imply:
% 178.99/28.68  | | | | | | | | |   (126)  all_52_19 = e3
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (65), (126) imply:
% 178.99/28.68  | | | | | | | | |   (127)  op(e2, e3) = all_52_18
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (10), (126) imply:
% 178.99/28.68  | | | | | | | | |   (128)  op(e1, e2) = e3
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | GROUND_INST: instantiating (81) with all_52_17, e1, e3, e1,
% 178.99/28.68  | | | | | | | | |              simplifying with (78), (124) gives:
% 178.99/28.68  | | | | | | | | |   (129)  all_52_17 = e1
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | GROUND_INST: instantiating (81) with all_52_9, all_52_18, e3,
% 178.99/28.68  | | | | | | | | |              e2, simplifying with (96), (127) gives:
% 178.99/28.68  | | | | | | | | |   (130)  all_52_9 = all_52_18
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | COMBINE_EQS: (30), (130) imply:
% 178.99/28.68  | | | | | | | | |   (131)  all_56_4 = all_52_18
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | COMBINE_EQS: (62), (129) imply:
% 178.99/28.68  | | | | | | | | |   (132)  all_58_6 = e1
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | COMBINE_EQS: (73), (130) imply:
% 178.99/28.68  | | | | | | | | |   (133)  all_58_2 = all_52_18
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (92), (130) imply:
% 178.99/28.68  | | | | | | | | |   (134)   ~ (all_52_15 = all_52_18)
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | SIMP: (134) implies:
% 178.99/28.68  | | | | | | | | |   (135)   ~ (all_52_15 = all_52_18)
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (61), (129), (130) imply:
% 178.99/28.68  | | | | | | | | |   (136)   ~ (all_52_18 = e1)
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (24), (130) imply:
% 178.99/28.68  | | | | | | | | |   (137)   ~ (all_52_18 = all_4_2)
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (71), (130) imply:
% 178.99/28.68  | | | | | | | | |   (138)   ~ (all_52_18 = e3)
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (34), (129) imply:
% 178.99/28.68  | | | | | | | | |   (139)   ~ (all_14_2 = e1)
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | SIMP: (139) implies:
% 178.99/28.68  | | | | | | | | |   (140)   ~ (all_14_2 = e1)
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | REDUCE: (54), (130) imply:
% 178.99/28.68  | | | | | | | | |   (141)  op(e3, all_52_18) = e3
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | BETA: splitting (58) gives:
% 178.99/28.68  | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | |   (142)  all_56_10 = e3
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | COMBINE_EQS: (77), (142) imply:
% 178.99/28.68  | | | | | | | | | |   (143)  all_14_2 = e3
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | REDUCE: (123), (143) imply:
% 178.99/28.68  | | | | | | | | | |   (144)  $false
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | CLOSE: (144) is inconsistent.
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | Case 2:
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | |   (145)  all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | BETA: splitting (20) gives:
% 178.99/28.68  | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | |   (146)  all_58_0 = e2
% 178.99/28.68  | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | COMBINE_EQS: (38), (146) imply:
% 178.99/28.68  | | | | | | | | | | |   (147)  all_4_2 = e2
% 178.99/28.68  | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | REDUCE: (137), (147) imply:
% 178.99/28.68  | | | | | | | | | | |   (148)   ~ (all_52_18 = e2)
% 178.99/28.68  | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | BETA: splitting (99) gives:
% 178.99/28.68  | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | |   (149)  all_56_4 = e2
% 178.99/28.68  | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | REF_CLOSE: (131), (148), (149) are inconsistent by sub-proof
% 178.99/28.68  | | | | | | | | | | | |            #781.
% 178.99/28.68  | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | Case 2:
% 178.99/28.68  | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | |   (150)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.68  | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | BETA: splitting (150) gives:
% 178.99/28.68  | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | |   (151)  all_56_4 = e1
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | REF_CLOSE: (131), (136), (151) are inconsistent by sub-proof
% 178.99/28.68  | | | | | | | | | | | | |            #780.
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | Case 2:
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | |   (152)  all_56_4 = e0
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | COMBINE_EQS: (131), (152) imply:
% 178.99/28.68  | | | | | | | | | | | | |   (153)  all_52_18 = e0
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | SIMP: (153) implies:
% 178.99/28.68  | | | | | | | | | | | | |   (154)  all_52_18 = e0
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | REDUCE: (135), (154) imply:
% 178.99/28.68  | | | | | | | | | | | | |   (155)   ~ (all_52_15 = e0)
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | REDUCE: (138), (154) imply:
% 178.99/28.68  | | | | | | | | | | | | |   (156)   ~ (e3 = e0)
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | BETA: splitting (39) gives:
% 178.99/28.68  | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | |   (157)  all_58_9 = e0
% 178.99/28.68  | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | REF_CLOSE: (55), (104), (157) are inconsistent by sub-proof
% 178.99/28.68  | | | | | | | | | | | | | |            #928.
% 178.99/28.68  | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | Case 2:
% 178.99/28.68  | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | |   (158)  all_58_10 = e0 | all_58_11 = e0
% 178.99/28.68  | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 178.99/28.68  | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | Case 1:
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | |   (159)  all_58_10 = e0
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | | REF_CLOSE: (27), (155), (159) are inconsistent by sub-proof
% 178.99/28.68  | | | | | | | | | | | | | | |            #741.
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | Case 2:
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | |   (160)  all_58_11 = e0
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | | COMBINE_EQS: (67), (160) imply:
% 178.99/28.68  | | | | | | | | | | | | | | |   (161)  all_52_23 = e0
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | | SIMP: (161) implies:
% 178.99/28.68  | | | | | | | | | | | | | | |   (162)  all_52_23 = e0
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | | REDUCE: (1), (162) imply:
% 178.99/28.68  | | | | | | | | | | | | | | |   (163)   ~ (all_14_2 = e0)
% 178.99/28.68  | | | | | | | | | | | | | | | 
% 178.99/28.68  | | | | | | | | | | | | | | | SIMP: (163) implies:
% 178.99/28.69  | | | | | | | | | | | | | | |   (164)   ~ (all_14_2 = e0)
% 178.99/28.69  | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 178.99/28.69  | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | Case 1:
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | |   (165)  all_56_10 = e2
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (165) imply:
% 178.99/28.69  | | | | | | | | | | | | | | | |   (166)  all_14_2 = e2
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | | SIMP: (166) implies:
% 178.99/28.69  | | | | | | | | | | | | | | | |   (167)  all_14_2 = e2
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | | REDUCE: (89), (167) imply:
% 178.99/28.69  | | | | | | | | | | | | | | | |   (168)  op(e1, e2) = all_14_1
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (81) with e3, all_14_1, e2, e1,
% 178.99/28.69  | | | | | | | | | | | | | | | |              simplifying with (128), (168) gives:
% 178.99/28.69  | | | | | | | | | | | | | | | |   (169)  all_14_1 = e3
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | | REDUCE: (44), (169) imply:
% 178.99/28.69  | | | | | | | | | | | | | | | |   (170)  $false
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | Case 2:
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | |   (171)  all_56_10 = e1 | all_56_10 = e0
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | | REF_CLOSE: (77), (140), (164), (171) are inconsistent by
% 178.99/28.69  | | | | | | | | | | | | | | | |            sub-proof #738.
% 178.99/28.69  | | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | Case 2:
% 178.99/28.69  | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | |   (172)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.69  | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | | REF_CLOSE: (7), (60), (76), (81), (94), (107), (132), (133),
% 178.99/28.69  | | | | | | | | | | |            (141), (172) are inconsistent by sub-proof #737.
% 178.99/28.69  | | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | | 
% 178.99/28.69  | | | | | | | | Case 2:
% 178.99/28.69  | | | | | | | | | 
% 178.99/28.69  | | | | | | | | |   (173)  all_58_8 = e3 | all_58_11 = e3
% 178.99/28.69  | | | | | | | | | 
% 178.99/28.69  | | | | | | | | | REF_CLOSE: (49), (67), (103), (123), (173) are inconsistent by
% 178.99/28.69  | | | | | | | | |            sub-proof #997.
% 178.99/28.69  | | | | | | | | | 
% 178.99/28.69  | | | | | | | | End of split
% 178.99/28.69  | | | | | | | | 
% 178.99/28.69  | | | | | | | Case 2:
% 178.99/28.69  | | | | | | | | 
% 178.99/28.69  | | | | | | | |   (174)   ~ (all_56_6 = e3)
% 178.99/28.69  | | | | | | | | 
% 178.99/28.69  | | | | | | | | REDUCE: (91), (174) imply:
% 178.99/28.69  | | | | | | | |   (175)   ~ (all_52_13 = e3)
% 178.99/28.69  | | | | | | | | 
% 178.99/28.69  | | | | | | | | REF_CLOSE: (3), (7), (14), (15), (21), (27), (29), (54), (59),
% 178.99/28.69  | | | | | | | |            (70), (80), (81), (96), (109), (116), (118), (175)
% 178.99/28.69  | | | | | | | |            are inconsistent by sub-proof #736.
% 178.99/28.69  | | | | | | | | 
% 178.99/28.69  | | | | | | | End of split
% 178.99/28.69  | | | | | | | 
% 178.99/28.69  | | | | | | End of split
% 178.99/28.69  | | | | | | 
% 178.99/28.69  | | | | | End of split
% 178.99/28.69  | | | | | 
% 178.99/28.69  | | | | End of split
% 178.99/28.69  | | | | 
% 178.99/28.69  | | | Case 2:
% 178.99/28.69  | | | | 
% 178.99/28.69  | | | |   (176)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.69  | | | | 
% 178.99/28.69  | | | | REF_CLOSE: (13), (18), (23), (27), (46), (55), (67), (81), (103), (176)
% 178.99/28.69  | | | |            are inconsistent by sub-proof #745.
% 178.99/28.69  | | | | 
% 178.99/28.69  | | | End of split
% 178.99/28.69  | | | 
% 178.99/28.69  | | End of split
% 178.99/28.69  | | 
% 178.99/28.69  | End of split
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #736 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)   ~ (all_52_27 = all_10_2)
% 178.99/28.69    (2)  op(e3, e2) = all_52_3
% 178.99/28.69    (3)   ~ (all_52_3 = all_10_2)
% 178.99/28.69    (4)  all_58_5 = all_52_13
% 178.99/28.69    (5)  all_58_3 = all_10_2
% 178.99/28.69    (6)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.69    (7)  all_58_10 = all_52_15
% 178.99/28.69    (8)  all_58_7 = all_52_19
% 178.99/28.69    (9)  op(e3, all_52_9) = e3
% 178.99/28.69    (10)   ~ (all_52_13 = e3)
% 178.99/28.69    (11)   ~ (all_52_15 = e3)
% 178.99/28.69    (12)  all_58_13 = all_52_27
% 178.99/28.69    (13)   ~ (all_52_19 = all_10_2)
% 178.99/28.69    (14)  op(e2, all_10_2) = e2
% 178.99/28.69    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.69    (16)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.69    (17)  op(e2, e3) = all_52_9
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | BETA: splitting (16) gives:
% 178.99/28.69  | 
% 178.99/28.69  | Case 1:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (18)  all_58_3 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | COMBINE_EQS: (5), (18) imply:
% 178.99/28.69  | |   (19)  all_10_2 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (13), (19) imply:
% 178.99/28.69  | |   (20)   ~ (all_52_19 = e3)
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (1), (19) imply:
% 178.99/28.69  | |   (21)   ~ (all_52_27 = e3)
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (12), (14), (15), (17), (20), (21)
% 178.99/28.69  | |            are inconsistent by sub-proof #975.
% 178.99/28.69  | | 
% 178.99/28.69  | Case 2:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (22)  all_58_5 = e3 | all_58_10 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (4), (7), (10), (11), (22) are inconsistent by sub-proof #958.
% 178.99/28.69  | | 
% 178.99/28.69  | End of split
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #737 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  all_58_2 = all_52_18
% 178.99/28.69    (2)  op(e3, e2) = all_52_3
% 178.99/28.69    (3)  all_58_6 = e1
% 178.99/28.69    (4)   ~ (all_52_3 = e3)
% 178.99/28.69    (5)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.69    (6)  all_58_12 = e3
% 178.99/28.69    (7)   ~ (e2 = e1)
% 178.99/28.69    (8)  op(e3, all_52_18) = e3
% 178.99/28.69    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.69    (10)   ~ (e3 = e2)
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | BETA: splitting (5) gives:
% 178.99/28.69  | 
% 178.99/28.69  | Case 1:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (11)  all_58_2 = e2
% 178.99/28.69  | | 
% 178.99/28.69  | | COMBINE_EQS: (1), (11) imply:
% 178.99/28.69  | |   (12)  all_52_18 = e2
% 178.99/28.69  | | 
% 178.99/28.69  | | SIMP: (12) implies:
% 178.99/28.69  | |   (13)  all_52_18 = e2
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (8), (13) imply:
% 178.99/28.69  | |   (14)  op(e3, e2) = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (2), (4), (9), (14) are inconsistent by sub-proof #978.
% 178.99/28.69  | | 
% 178.99/28.69  | Case 2:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (15)  all_58_6 = e2 | all_58_12 = e2
% 178.99/28.69  | | 
% 178.99/28.69  | | BETA: splitting (15) gives:
% 178.99/28.69  | | 
% 178.99/28.69  | | Case 1:
% 178.99/28.69  | | | 
% 178.99/28.69  | | |   (16)  all_58_6 = e2
% 178.99/28.69  | | | 
% 178.99/28.69  | | | COMBINE_EQS: (3), (16) imply:
% 178.99/28.69  | | |   (17)  e2 = e1
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REDUCE: (7), (17) imply:
% 178.99/28.69  | | |   (18)  $false
% 178.99/28.69  | | | 
% 178.99/28.69  | | | CLOSE: (18) is inconsistent.
% 178.99/28.69  | | | 
% 178.99/28.69  | | Case 2:
% 178.99/28.69  | | | 
% 178.99/28.69  | | |   (19)  all_58_12 = e2
% 178.99/28.69  | | | 
% 178.99/28.69  | | | COMBINE_EQS: (6), (19) imply:
% 178.99/28.69  | | |   (20)  e3 = e2
% 178.99/28.69  | | | 
% 178.99/28.69  | | | SIMP: (20) implies:
% 178.99/28.69  | | |   (21)  e3 = e2
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REDUCE: (10), (21) imply:
% 178.99/28.69  | | |   (22)  $false
% 178.99/28.69  | | | 
% 178.99/28.69  | | | CLOSE: (22) is inconsistent.
% 178.99/28.69  | | | 
% 178.99/28.69  | | End of split
% 178.99/28.69  | | 
% 178.99/28.69  | End of split
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #738 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  all_56_10 = e1 | all_56_10 = e0
% 178.99/28.69    (2)  all_56_10 = all_14_2
% 178.99/28.69    (3)   ~ (all_14_2 = e1)
% 178.99/28.69    (4)   ~ (all_14_2 = e0)
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | BETA: splitting (1) gives:
% 178.99/28.69  | 
% 178.99/28.69  | Case 1:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (5)  all_56_10 = e1
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #740.
% 178.99/28.69  | | 
% 178.99/28.69  | Case 2:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (6)  all_56_10 = e0
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #739.
% 178.99/28.69  | | 
% 178.99/28.69  | End of split
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #739 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  all_56_10 = all_14_2
% 178.99/28.69    (2)  all_56_10 = e0
% 178.99/28.69    (3)   ~ (all_14_2 = e0)
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.69  |   (4)  all_14_2 = e0
% 178.99/28.69  | 
% 178.99/28.69  | SIMP: (4) implies:
% 178.99/28.69  |   (5)  all_14_2 = e0
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (3), (5) imply:
% 178.99/28.69  |   (6)  $false
% 178.99/28.69  | 
% 178.99/28.69  | CLOSE: (6) is inconsistent.
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #740 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  all_56_10 = all_14_2
% 178.99/28.69    (2)  all_56_10 = e1
% 178.99/28.69    (3)   ~ (all_14_2 = e1)
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.69  |   (4)  all_14_2 = e1
% 178.99/28.69  | 
% 178.99/28.69  | SIMP: (4) implies:
% 178.99/28.69  |   (5)  all_14_2 = e1
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (3), (5) imply:
% 178.99/28.69  |   (6)  $false
% 178.99/28.69  | 
% 178.99/28.69  | CLOSE: (6) is inconsistent.
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #741 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  all_58_10 = all_52_15
% 178.99/28.69    (2)  all_58_10 = e0
% 178.99/28.69    (3)   ~ (all_52_15 = e0)
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.69  |   (4)  all_52_15 = e0
% 178.99/28.69  | 
% 178.99/28.69  | SIMP: (4) implies:
% 178.99/28.69  |   (5)  all_52_15 = e0
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (3), (5) imply:
% 178.99/28.69  |   (6)  $false
% 178.99/28.69  | 
% 178.99/28.69  | CLOSE: (6) is inconsistent.
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #742 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.69    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.69    (3)   ~ (all_52_17 = all_52_23)
% 178.99/28.69    (4)   ~ (all_52_13 = all_52_29)
% 178.99/28.69    (5)  all_56_3 = all_52_7
% 178.99/28.69    (6)  op(e3, e2) = all_52_3
% 178.99/28.69    (7)   ~ (all_52_19 = all_52_23)
% 178.99/28.69    (8)   ~ (all_52_27 = e3)
% 178.99/28.69    (9)   ~ (all_52_3 = all_10_2)
% 178.99/28.69    (10)  all_58_5 = all_52_13
% 178.99/28.69    (11)   ~ (all_6_2 = e0)
% 178.99/28.69    (12)  op(e1, all_52_13) = e1
% 178.99/28.69    (13)  op(e0, all_52_15) = e0
% 178.99/28.69    (14)  all_56_15 = all_6_2
% 178.99/28.69    (15)  all_58_3 = all_10_2
% 178.99/28.69    (16)  all_56_9 = all_52_19
% 178.99/28.69    (17)  all_58_15 = all_6_2
% 178.99/28.69    (18)   ~ (all_52_9 = all_4_2)
% 178.99/28.69    (19)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.69    (20)   ~ (all_52_5 = all_52_7)
% 178.99/28.69    (21)  all_58_10 = all_52_15
% 178.99/28.69    (22)   ~ (all_52_5 = all_4_2)
% 178.99/28.69    (23)  all_58_7 = all_52_19
% 178.99/28.69    (24)  all_56_4 = all_52_9
% 178.99/28.69    (25)  all_58_4 = all_52_5
% 178.99/28.69    (26)   ~ (all_52_27 = all_52_29)
% 178.99/28.69    (27)   ~ (all_52_17 = all_14_2)
% 178.99/28.69    (28)   ~ (all_52_7 = all_4_2)
% 178.99/28.69    (29)  all_58_1 = all_52_3
% 178.99/28.69    (30)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.69    (31)  all_58_0 = all_4_2
% 178.99/28.69    (32)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.69    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.69    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.69    (35)  all_58_14 = all_52_29
% 178.99/28.69    (36)  op(e0, e3) = e3
% 178.99/28.69    (37)   ~ (all_52_3 = all_52_5)
% 178.99/28.69    (38)  op(e2, e1) = all_52_13
% 178.99/28.69    (39)  all_58_8 = all_14_2
% 178.99/28.69    (40)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.69    (41)  all_52_23 = e3
% 178.99/28.69    (42)  op(e3, all_52_17) = all_52_16
% 178.99/28.69    (43)   ~ (all_52_29 = e3)
% 178.99/28.69    (44)  op(e3, all_52_9) = e3
% 178.99/28.69    (45)   ~ (e3 = e0)
% 178.99/28.69    (46)  op(e0, all_52_23) = all_52_22
% 178.99/28.69    (47)  all_58_13 = all_52_27
% 178.99/28.69    (48)   ~ (all_52_9 = all_52_17)
% 178.99/28.69    (49)   ~ (all_52_3 = all_52_7)
% 178.99/28.69    (50)  all_56_0 = all_4_2
% 178.99/28.69    (51)  all_58_11 = all_52_23
% 178.99/28.69    (52)   ~ (all_52_23 = all_6_2)
% 178.99/28.69    (53)  op(e3, e1) = all_52_5
% 178.99/28.69    (54)  op(e1, e3) = all_52_17
% 178.99/28.69    (55)  op(e3, e0) = all_52_7
% 178.99/28.69    (56)  op(e2, all_10_2) = e2
% 178.99/28.69    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.69    (58)   ~ (all_52_27 = all_6_2)
% 178.99/28.69    (59)   ~ (all_52_7 = all_6_2)
% 178.99/28.69    (60)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.69    (61)   ~ (all_52_7 = all_52_23)
% 178.99/28.69    (62)   ~ (all_52_17 = all_52_19)
% 178.99/28.69    (63)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.69    (64)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.69    (65)  all_58_9 = all_52_7
% 178.99/28.69    (66)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.69    (67)   ~ (e3 = e2)
% 178.99/28.69    (68)  op(e2, e3) = all_52_9
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (41), (61) imply:
% 178.99/28.69  |   (69)   ~ (all_52_7 = e3)
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (3), (41) imply:
% 178.99/28.69  |   (70)   ~ (all_52_17 = e3)
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (1), (41) imply:
% 178.99/28.69  |   (71)   ~ (all_14_2 = e3)
% 178.99/28.69  | 
% 178.99/28.69  | SIMP: (71) implies:
% 178.99/28.69  |   (72)   ~ (all_14_2 = e3)
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (41), (52) imply:
% 178.99/28.69  |   (73)   ~ (all_6_2 = e3)
% 178.99/28.69  | 
% 178.99/28.69  | SIMP: (73) implies:
% 178.99/28.69  |   (74)   ~ (all_6_2 = e3)
% 178.99/28.69  | 
% 178.99/28.69  | REDUCE: (41), (46) imply:
% 178.99/28.69  |   (75)  op(e0, e3) = all_52_22
% 178.99/28.69  | 
% 178.99/28.69  | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 178.99/28.69  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 178.99/28.69  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 178.99/28.69  |            (37), (38), (39), (40), (42), (43), (44), (45), (47), (48), (49),
% 178.99/28.69  |            (50), (51), (53), (54), (55), (56), (57), (58), (59), (60), (62),
% 178.99/28.69  |            (63), (64), (65), (66), (67), (68), (69), (70), (72), (74), (75)
% 178.99/28.69  |            are inconsistent by sub-proof #743.
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #743 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.69    (2)   ~ (all_52_13 = all_52_29)
% 178.99/28.69    (3)  all_56_3 = all_52_7
% 178.99/28.69    (4)  op(e3, e2) = all_52_3
% 178.99/28.69    (5)   ~ (all_52_19 = all_52_23)
% 178.99/28.69    (6)   ~ (all_52_27 = e3)
% 178.99/28.69    (7)   ~ (all_52_17 = e3)
% 178.99/28.69    (8)   ~ (all_6_2 = e3)
% 178.99/28.69    (9)   ~ (all_52_3 = all_10_2)
% 178.99/28.69    (10)  all_58_5 = all_52_13
% 178.99/28.69    (11)   ~ (all_6_2 = e0)
% 178.99/28.69    (12)  op(e1, all_52_13) = e1
% 178.99/28.69    (13)  op(e0, all_52_15) = e0
% 178.99/28.69    (14)  all_56_15 = all_6_2
% 178.99/28.69    (15)  all_58_3 = all_10_2
% 178.99/28.69    (16)  all_56_9 = all_52_19
% 178.99/28.69    (17)  all_58_15 = all_6_2
% 178.99/28.69    (18)   ~ (all_52_9 = all_4_2)
% 178.99/28.69    (19)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.69    (20)   ~ (all_52_5 = all_52_7)
% 178.99/28.69    (21)  all_58_10 = all_52_15
% 178.99/28.69    (22)   ~ (all_52_5 = all_4_2)
% 178.99/28.69    (23)  all_58_7 = all_52_19
% 178.99/28.69    (24)  all_56_4 = all_52_9
% 178.99/28.69    (25)  all_58_4 = all_52_5
% 178.99/28.69    (26)   ~ (all_52_27 = all_52_29)
% 178.99/28.69    (27)   ~ (all_52_17 = all_14_2)
% 178.99/28.69    (28)   ~ (all_52_7 = all_4_2)
% 178.99/28.69    (29)  all_58_1 = all_52_3
% 178.99/28.69    (30)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.69    (31)  all_58_0 = all_4_2
% 178.99/28.69    (32)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.69    (33)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.69    (34)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.69    (35)  all_58_14 = all_52_29
% 178.99/28.69    (36)  op(e0, e3) = e3
% 178.99/28.69    (37)   ~ (all_52_3 = all_52_5)
% 178.99/28.69    (38)  op(e2, e1) = all_52_13
% 178.99/28.69    (39)  all_58_8 = all_14_2
% 178.99/28.69    (40)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.69    (41)  op(e3, all_52_17) = all_52_16
% 178.99/28.69    (42)   ~ (all_52_29 = e3)
% 178.99/28.69    (43)  op(e3, all_52_9) = e3
% 178.99/28.69    (44)   ~ (e3 = e0)
% 178.99/28.69    (45)  all_58_13 = all_52_27
% 178.99/28.69    (46)  op(e0, e3) = all_52_22
% 178.99/28.69    (47)   ~ (all_52_9 = all_52_17)
% 178.99/28.69    (48)   ~ (all_52_3 = all_52_7)
% 178.99/28.69    (49)  all_56_0 = all_4_2
% 178.99/28.69    (50)  all_58_11 = all_52_23
% 178.99/28.69    (51)  op(e3, e1) = all_52_5
% 178.99/28.69    (52)  op(e1, e3) = all_52_17
% 178.99/28.69    (53)  op(e3, e0) = all_52_7
% 178.99/28.69    (54)  op(e2, all_10_2) = e2
% 178.99/28.69    (55)   ~ (all_14_2 = e3)
% 178.99/28.69    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.69    (57)   ~ (all_52_27 = all_6_2)
% 178.99/28.69    (58)   ~ (all_52_7 = all_6_2)
% 178.99/28.69    (59)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.69    (60)   ~ (all_52_7 = e3)
% 178.99/28.69    (61)   ~ (all_52_17 = all_52_19)
% 178.99/28.69    (62)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.69    (63)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.69    (64)  all_58_9 = all_52_7
% 178.99/28.69    (65)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.69    (66)   ~ (e3 = e2)
% 178.99/28.69    (67)  op(e2, e3) = all_52_9
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | GROUND_INST: instantiating (56) with e3, all_52_22, e3, e0, simplifying with
% 178.99/28.69  |              (36), (46) gives:
% 178.99/28.69  |   (68)  all_52_22 = e3
% 178.99/28.69  | 
% 178.99/28.69  | BETA: splitting (34) gives:
% 178.99/28.69  | 
% 178.99/28.69  | Case 1:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (69)  all_58_1 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | COMBINE_EQS: (29), (69) imply:
% 178.99/28.69  | |   (70)  all_52_3 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (37), (70) imply:
% 178.99/28.69  | |   (71)   ~ (all_52_5 = e3)
% 178.99/28.69  | | 
% 178.99/28.69  | | SIMP: (71) implies:
% 178.99/28.69  | |   (72)   ~ (all_52_5 = e3)
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (48), (70) imply:
% 178.99/28.69  | |   (73)   ~ (all_52_7 = e3)
% 178.99/28.69  | | 
% 178.99/28.69  | | BETA: splitting (65) gives:
% 178.99/28.69  | | 
% 178.99/28.69  | | Case 1:
% 178.99/28.69  | | | 
% 178.99/28.69  | | |   (74)  all_58_4 = e3
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REF_CLOSE: (25), (72), (74) are inconsistent by sub-proof #1025.
% 178.99/28.69  | | | 
% 178.99/28.69  | | Case 2:
% 178.99/28.69  | | | 
% 178.99/28.69  | | |   (75)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REF_CLOSE: (1), (2), (3), (7), (10), (11), (12), (14), (15), (18), (19),
% 178.99/28.69  | | |            (20), (22), (23), (24), (25), (26), (27), (28), (30), (31),
% 178.99/28.69  | | |            (33), (35), (38), (39), (40), (41), (42), (43), (45), (47),
% 178.99/28.69  | | |            (49), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 178.99/28.69  | | |            (60), (61), (63), (66), (69), (75) are inconsistent by
% 178.99/28.69  | | |            sub-proof #746.
% 178.99/28.69  | | | 
% 178.99/28.69  | | End of split
% 178.99/28.69  | | 
% 178.99/28.69  | Case 2:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (76)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (4), (5), (6), (8), (9), (13), (15), (16), (17), (21), (23),
% 178.99/28.69  | |            (32), (36), (43), (44), (45), (50), (54), (56), (60), (62), (64),
% 178.99/28.69  | |            (67), (76) are inconsistent by sub-proof #744.
% 178.99/28.69  | | 
% 178.99/28.69  | End of split
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #744 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  op(e3, e2) = all_52_3
% 178.99/28.69    (2)   ~ (all_52_19 = all_52_23)
% 178.99/28.69    (3)   ~ (all_52_27 = e3)
% 178.99/28.69    (4)   ~ (all_6_2 = e3)
% 178.99/28.69    (5)   ~ (all_52_3 = all_10_2)
% 178.99/28.69    (6)  op(e0, all_52_15) = e0
% 178.99/28.69    (7)  all_58_3 = all_10_2
% 178.99/28.69    (8)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.69    (9)  all_56_9 = all_52_19
% 178.99/28.69    (10)  all_58_15 = all_6_2
% 178.99/28.69    (11)  all_58_10 = all_52_15
% 178.99/28.69    (12)  all_58_7 = all_52_19
% 178.99/28.69    (13)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.69    (14)  op(e0, e3) = e3
% 178.99/28.69    (15)  op(e3, all_52_9) = e3
% 178.99/28.69    (16)   ~ (e3 = e0)
% 178.99/28.69    (17)  all_58_13 = all_52_27
% 178.99/28.69    (18)  all_58_11 = all_52_23
% 178.99/28.69    (19)  op(e2, all_10_2) = e2
% 178.99/28.69    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.69    (21)   ~ (all_52_7 = e3)
% 178.99/28.69    (22)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.69    (23)  all_58_9 = all_52_7
% 178.99/28.69    (24)  op(e2, e3) = all_52_9
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | BETA: splitting (22) gives:
% 178.99/28.69  | 
% 178.99/28.69  | Case 1:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (25)  all_58_9 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (21), (23), (25) are inconsistent by sub-proof #972.
% 178.99/28.69  | | 
% 178.99/28.69  | Case 2:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (26)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | BETA: splitting (13) gives:
% 178.99/28.69  | | 
% 178.99/28.69  | | Case 1:
% 178.99/28.69  | | | 
% 178.99/28.69  | | |   (27)  all_56_9 = e3
% 178.99/28.69  | | | 
% 178.99/28.69  | | | COMBINE_EQS: (9), (27) imply:
% 178.99/28.69  | | |   (28)  all_52_19 = e3
% 178.99/28.69  | | | 
% 178.99/28.69  | | | SIMP: (28) implies:
% 178.99/28.69  | | |   (29)  all_52_19 = e3
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REDUCE: (2), (29) imply:
% 178.99/28.69  | | |   (30)   ~ (all_52_23 = e3)
% 178.99/28.69  | | | 
% 178.99/28.69  | | | SIMP: (30) implies:
% 178.99/28.69  | | |   (31)   ~ (all_52_23 = e3)
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REF_CLOSE: (4), (6), (10), (11), (14), (16), (18), (20), (26), (31) are
% 178.99/28.69  | | |            inconsistent by sub-proof #745.
% 178.99/28.69  | | | 
% 178.99/28.69  | | Case 2:
% 178.99/28.69  | | | 
% 178.99/28.69  | | |   (32)   ~ (all_56_9 = e3)
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REDUCE: (9), (32) imply:
% 178.99/28.69  | | |   (33)   ~ (all_52_19 = e3)
% 178.99/28.69  | | | 
% 178.99/28.69  | | | REF_CLOSE: (1), (3), (5), (7), (8), (12), (15), (17), (19), (20), (24),
% 178.99/28.69  | | |            (33) are inconsistent by sub-proof #975.
% 178.99/28.69  | | | 
% 178.99/28.69  | | End of split
% 178.99/28.69  | | 
% 178.99/28.69  | End of split
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #745 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)   ~ (all_6_2 = e3)
% 178.99/28.69    (2)  op(e0, all_52_15) = e0
% 178.99/28.69    (3)  all_58_15 = all_6_2
% 178.99/28.69    (4)  all_58_10 = all_52_15
% 178.99/28.69    (5)  op(e0, e3) = e3
% 178.99/28.69    (6)   ~ (all_52_23 = e3)
% 178.99/28.69    (7)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.69    (8)   ~ (e3 = e0)
% 178.99/28.69    (9)  all_58_11 = all_52_23
% 178.99/28.69    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | BETA: splitting (7) gives:
% 178.99/28.69  | 
% 178.99/28.69  | Case 1:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (11)  all_58_10 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | COMBINE_EQS: (4), (11) imply:
% 178.99/28.69  | |   (12)  all_52_15 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | SIMP: (12) implies:
% 178.99/28.69  | |   (13)  all_52_15 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (2), (13) imply:
% 178.99/28.69  | |   (14)  op(e0, e3) = e0
% 178.99/28.69  | | 
% 178.99/28.69  | | GROUND_INST: instantiating (10) with e3, e0, e3, e0, simplifying with (5),
% 178.99/28.69  | |              (14) gives:
% 178.99/28.69  | |   (15)  e3 = e0
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (8), (15) imply:
% 178.99/28.69  | |   (16)  $false
% 178.99/28.69  | | 
% 178.99/28.69  | | CLOSE: (16) is inconsistent.
% 178.99/28.69  | | 
% 178.99/28.69  | Case 2:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (17)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REF_CLOSE: (1), (3), (6), (9), (17) are inconsistent by sub-proof #1016.
% 178.99/28.69  | | 
% 178.99/28.69  | End of split
% 178.99/28.69  | 
% 178.99/28.69  End of proof
% 178.99/28.69  
% 178.99/28.69  Sub-proof #746 shows that the following formulas are inconsistent:
% 178.99/28.69  ----------------------------------------------------------------
% 178.99/28.69    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.69    (2)   ~ (all_52_13 = all_52_29)
% 178.99/28.69    (3)  all_56_3 = all_52_7
% 178.99/28.69    (4)   ~ (all_52_17 = e3)
% 178.99/28.69    (5)  all_58_5 = all_52_13
% 178.99/28.69    (6)   ~ (all_6_2 = e0)
% 178.99/28.69    (7)  op(e1, all_52_13) = e1
% 178.99/28.69    (8)  all_56_15 = all_6_2
% 178.99/28.69    (9)  all_58_3 = all_10_2
% 178.99/28.69    (10)   ~ (all_52_9 = all_4_2)
% 178.99/28.69    (11)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.69    (12)   ~ (all_52_5 = all_52_7)
% 178.99/28.69    (13)   ~ (all_52_5 = all_4_2)
% 178.99/28.69    (14)  all_58_7 = all_52_19
% 178.99/28.69    (15)  all_56_4 = all_52_9
% 178.99/28.69    (16)  all_58_4 = all_52_5
% 178.99/28.69    (17)   ~ (all_52_27 = all_52_29)
% 178.99/28.69    (18)   ~ (all_52_17 = all_14_2)
% 178.99/28.69    (19)   ~ (all_52_7 = all_4_2)
% 178.99/28.69    (20)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.69    (21)  all_58_0 = all_4_2
% 178.99/28.69    (22)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.69    (23)  all_58_14 = all_52_29
% 178.99/28.69    (24)  op(e2, e1) = all_52_13
% 178.99/28.69    (25)  all_58_8 = all_14_2
% 178.99/28.69    (26)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.69    (27)  op(e3, all_52_17) = all_52_16
% 178.99/28.69    (28)   ~ (all_52_29 = e3)
% 178.99/28.69    (29)  op(e3, all_52_9) = e3
% 178.99/28.69    (30)  all_58_13 = all_52_27
% 178.99/28.69    (31)  all_58_1 = e3
% 178.99/28.69    (32)   ~ (all_52_9 = all_52_17)
% 178.99/28.69    (33)  all_56_0 = all_4_2
% 178.99/28.69    (34)  op(e3, e1) = all_52_5
% 178.99/28.69    (35)  op(e1, e3) = all_52_17
% 178.99/28.69    (36)  op(e3, e0) = all_52_7
% 178.99/28.69    (37)  op(e2, all_10_2) = e2
% 178.99/28.69    (38)   ~ (all_14_2 = e3)
% 178.99/28.69    (39)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.69    (40)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.69    (41)   ~ (all_52_27 = all_6_2)
% 178.99/28.69    (42)   ~ (all_52_7 = all_6_2)
% 178.99/28.69    (43)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.69    (44)   ~ (all_52_7 = e3)
% 178.99/28.69    (45)   ~ (all_52_17 = all_52_19)
% 178.99/28.69    (46)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.69    (47)   ~ (e3 = e2)
% 178.99/28.69  
% 178.99/28.69  Begin of proof
% 178.99/28.69  | 
% 178.99/28.69  | BETA: splitting (39) gives:
% 178.99/28.69  | 
% 178.99/28.69  | Case 1:
% 178.99/28.69  | | 
% 178.99/28.69  | |   (48)  all_58_5 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | COMBINE_EQS: (5), (48) imply:
% 178.99/28.69  | |   (49)  all_52_13 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | SIMP: (49) implies:
% 178.99/28.69  | |   (50)  all_52_13 = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (2), (50) imply:
% 178.99/28.69  | |   (51)   ~ (all_52_29 = e3)
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (24), (50) imply:
% 178.99/28.69  | |   (52)  op(e2, e1) = e3
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (7), (50) imply:
% 178.99/28.69  | |   (53)  op(e1, e3) = e1
% 178.99/28.69  | | 
% 178.99/28.69  | | GROUND_INST: instantiating (40) with all_52_17, e1, e3, e1, simplifying with
% 178.99/28.69  | |              (35), (53) gives:
% 178.99/28.69  | |   (54)  all_52_17 = e1
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (32), (54) imply:
% 178.99/28.69  | |   (55)   ~ (all_52_9 = e1)
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (45), (54) imply:
% 178.99/28.69  | |   (56)   ~ (all_52_19 = e1)
% 178.99/28.69  | | 
% 178.99/28.69  | | SIMP: (56) implies:
% 178.99/28.69  | |   (57)   ~ (all_52_19 = e1)
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (18), (54) imply:
% 178.99/28.69  | |   (58)   ~ (all_14_2 = e1)
% 178.99/28.69  | | 
% 178.99/28.69  | | SIMP: (58) implies:
% 178.99/28.69  | |   (59)   ~ (all_14_2 = e1)
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (4), (54) imply:
% 178.99/28.69  | |   (60)   ~ (e3 = e1)
% 178.99/28.69  | | 
% 178.99/28.69  | | SIMP: (60) implies:
% 178.99/28.69  | |   (61)   ~ (e3 = e1)
% 178.99/28.69  | | 
% 178.99/28.69  | | REDUCE: (27), (54) imply:
% 178.99/28.69  | |   (62)  op(e3, e1) = all_52_16
% 178.99/28.69  | | 
% 178.99/28.69  | | GROUND_INST: instantiating (40) with all_52_5, all_52_16, e1, e3,
% 178.99/28.69  | |              simplifying with (34), (62) gives:
% 178.99/28.69  | |   (63)  all_52_5 = all_52_16
% 178.99/28.69  | | 
% 178.99/28.69  | | COMBINE_EQS: (16), (63) imply:
% 178.99/28.69  | |   (64)  all_58_4 = all_52_16
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (12), (63) imply:
% 178.99/28.70  | |   (65)   ~ (all_52_7 = all_52_16)
% 178.99/28.70  | | 
% 178.99/28.70  | | SIMP: (65) implies:
% 178.99/28.70  | |   (66)   ~ (all_52_7 = all_52_16)
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (13), (63) imply:
% 178.99/28.70  | |   (67)   ~ (all_52_16 = all_4_2)
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (1), (3), (6), (8), (9), (10), (11), (14), (15), (17), (19),
% 178.99/28.70  | |            (20), (21), (22), (23), (25), (26), (28), (29), (30), (31), (33),
% 178.99/28.70  | |            (36), (37), (40), (41), (42), (43), (44), (46), (47), (48), (52),
% 178.99/28.70  | |            (55), (57), (59), (61), (64), (66), (67) are inconsistent by
% 178.99/28.70  | |            sub-proof #747.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (68)  all_58_8 = e3 | all_58_14 = e3
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (23), (25), (28), (38), (68) are inconsistent by sub-proof #999.
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #747 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70    (2)  all_56_3 = all_52_7
% 178.99/28.70    (3)   ~ (all_6_2 = e0)
% 178.99/28.70    (4)  all_56_15 = all_6_2
% 178.99/28.70    (5)  all_58_3 = all_10_2
% 178.99/28.70    (6)   ~ (all_52_9 = all_4_2)
% 178.99/28.70    (7)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.70    (8)  all_58_7 = all_52_19
% 178.99/28.70    (9)  all_56_4 = all_52_9
% 178.99/28.70    (10)   ~ (e3 = e1)
% 178.99/28.70    (11)  all_58_5 = e3
% 178.99/28.70    (12)   ~ (all_52_27 = all_52_29)
% 178.99/28.70    (13)   ~ (all_52_7 = all_4_2)
% 178.99/28.70    (14)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.70    (15)  all_58_0 = all_4_2
% 178.99/28.70    (16)  all_58_4 = all_52_16
% 178.99/28.70    (17)   ~ (all_52_16 = all_4_2)
% 178.99/28.70    (18)   ~ (all_14_2 = e1)
% 178.99/28.70    (19)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.70    (20)  all_58_14 = all_52_29
% 178.99/28.70    (21)   ~ (all_52_9 = e1)
% 178.99/28.70    (22)  all_58_8 = all_14_2
% 178.99/28.70    (23)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.70    (24)   ~ (all_52_29 = e3)
% 178.99/28.70    (25)  op(e3, all_52_9) = e3
% 178.99/28.70    (26)  all_58_13 = all_52_27
% 178.99/28.70    (27)  all_58_1 = e3
% 178.99/28.70    (28)  all_56_0 = all_4_2
% 178.99/28.70    (29)  op(e2, e1) = e3
% 178.99/28.70    (30)  op(e3, e0) = all_52_7
% 178.99/28.70    (31)  op(e2, all_10_2) = e2
% 178.99/28.70    (32)   ~ (all_52_19 = e1)
% 178.99/28.70    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (34)   ~ (all_52_27 = all_6_2)
% 178.99/28.70    (35)   ~ (all_52_7 = all_6_2)
% 178.99/28.70    (36)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.70    (37)   ~ (all_52_7 = all_52_16)
% 178.99/28.70    (38)   ~ (all_52_7 = e3)
% 178.99/28.70    (39)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.70    (40)   ~ (e3 = e2)
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (1) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (41)  all_58_1 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | COMBINE_EQS: (27), (41) imply:
% 178.99/28.70  | |   (42)  e3 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (10), (42) imply:
% 178.99/28.70  | |   (43)  $false
% 178.99/28.70  | | 
% 178.99/28.70  | | CLOSE: (43) is inconsistent.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (44)   ~ (all_58_1 = e1)
% 178.99/28.70  | |   (45)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | BETA: splitting (19) gives:
% 178.99/28.70  | | 
% 178.99/28.70  | | Case 1:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (46)  all_58_4 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | COMBINE_EQS: (16), (46) imply:
% 178.99/28.70  | | |   (47)  all_52_16 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | SIMP: (47) implies:
% 178.99/28.70  | | |   (48)  all_52_16 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (37), (48) imply:
% 178.99/28.70  | | |   (49)   ~ (all_52_7 = e1)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (17), (48) imply:
% 178.99/28.70  | | |   (50)   ~ (all_4_2 = e1)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | SIMP: (50) implies:
% 178.99/28.70  | | |   (51)   ~ (all_4_2 = e1)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | BETA: splitting (39) gives:
% 178.99/28.70  | | | 
% 178.99/28.70  | | | Case 1:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (52)  all_56_3 = e3
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REF_CLOSE: (2), (38), (52) are inconsistent by sub-proof #1034.
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | Case 2:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (53)   ~ (all_56_3 = e3)
% 178.99/28.70  | | | |   (54)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | BETA: splitting (23) gives:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | Case 1:
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | |   (55)  all_58_0 = e2
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | | COMBINE_EQS: (15), (55) imply:
% 178.99/28.70  | | | | |   (56)  all_4_2 = e2
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | | REDUCE: (6), (56) imply:
% 178.99/28.70  | | | | |   (57)   ~ (all_52_9 = e2)
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | | REF_CLOSE: (9), (14), (21), (25), (30), (33), (38), (57) are
% 178.99/28.70  | | | | |            inconsistent by sub-proof #753.
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | Case 2:
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | |   (58)   ~ (all_58_0 = e2)
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (13), (15), (26), (28), (29),
% 178.99/28.70  | | | | |            (31), (32), (33), (34), (35), (36), (38), (45), (49), (51),
% 178.99/28.70  | | | | |            (54), (58) are inconsistent by sub-proof #749.
% 178.99/28.70  | | | | | 
% 178.99/28.70  | | | | End of split
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | End of split
% 178.99/28.70  | | | 
% 178.99/28.70  | | Case 2:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (59)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REF_CLOSE: (1), (5), (8), (10), (11), (12), (18), (20), (22), (24), (26),
% 178.99/28.70  | | |            (27), (29), (31), (32), (33), (40), (59) are inconsistent by
% 178.99/28.70  | | |            sub-proof #748.
% 178.99/28.70  | | | 
% 178.99/28.70  | | End of split
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #748 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70    (2)  all_58_3 = all_10_2
% 178.99/28.70    (3)  all_58_7 = all_52_19
% 178.99/28.70    (4)   ~ (e3 = e1)
% 178.99/28.70    (5)  all_58_5 = e3
% 178.99/28.70    (6)   ~ (all_52_27 = all_52_29)
% 178.99/28.70    (7)   ~ (all_14_2 = e1)
% 178.99/28.70    (8)  all_58_14 = all_52_29
% 178.99/28.70    (9)  all_58_8 = all_14_2
% 178.99/28.70    (10)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.70    (11)   ~ (all_52_29 = e3)
% 178.99/28.70    (12)  all_58_13 = all_52_27
% 178.99/28.70    (13)  all_58_1 = e3
% 178.99/28.70    (14)  op(e2, e1) = e3
% 178.99/28.70    (15)  op(e2, all_10_2) = e2
% 178.99/28.70    (16)   ~ (all_52_19 = e1)
% 178.99/28.70    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (18)   ~ (e3 = e2)
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (10) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (19)  all_58_5 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (4), (5), (19) are inconsistent by sub-proof #816.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (20)  all_58_8 = e1 | all_58_14 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | BETA: splitting (20) gives:
% 178.99/28.70  | | 
% 178.99/28.70  | | Case 1:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (21)  all_58_8 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REF_CLOSE: (7), (9), (21) are inconsistent by sub-proof #815.
% 178.99/28.70  | | | 
% 178.99/28.70  | | Case 2:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (22)  all_58_14 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | COMBINE_EQS: (8), (22) imply:
% 178.99/28.70  | | |   (23)  all_52_29 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | SIMP: (23) implies:
% 178.99/28.70  | | |   (24)  all_52_29 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (6), (24) imply:
% 178.99/28.70  | | |   (25)   ~ (all_52_27 = e1)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (11), (24) imply:
% 178.99/28.70  | | |   (26)   ~ (e3 = e1)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | BETA: splitting (1) gives:
% 178.99/28.70  | | | 
% 178.99/28.70  | | | Case 1:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (27)  all_58_1 = e1
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | COMBINE_EQS: (13), (27) imply:
% 178.99/28.70  | | | |   (28)  e3 = e1
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REDUCE: (4), (28) imply:
% 178.99/28.70  | | | |   (29)  $false
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | CLOSE: (29) is inconsistent.
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | Case 2:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (30)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REF_CLOSE: (2), (3), (12), (14), (15), (16), (17), (18), (25), (30) are
% 178.99/28.70  | | | |            inconsistent by sub-proof #751.
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | End of split
% 178.99/28.70  | | | 
% 178.99/28.70  | | End of split
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #749 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.70    (2)  all_56_3 = all_52_7
% 178.99/28.70    (3)   ~ (all_6_2 = e0)
% 178.99/28.70    (4)  all_56_15 = all_6_2
% 178.99/28.70    (5)  all_58_3 = all_10_2
% 178.99/28.70    (6)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.70    (7)  all_58_7 = all_52_19
% 178.99/28.70    (8)   ~ (all_52_7 = all_4_2)
% 178.99/28.70    (9)  all_58_0 = all_4_2
% 178.99/28.70    (10)   ~ (all_52_7 = e1)
% 178.99/28.70    (11)  all_58_13 = all_52_27
% 178.99/28.70    (12)  all_56_0 = all_4_2
% 178.99/28.70    (13)  op(e2, e1) = e3
% 178.99/28.70    (14)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70    (15)  op(e2, all_10_2) = e2
% 178.99/28.70    (16)   ~ (all_52_19 = e1)
% 178.99/28.70    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (18)   ~ (all_52_27 = all_6_2)
% 178.99/28.70    (19)   ~ (all_52_7 = all_6_2)
% 178.99/28.70    (20)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.70    (21)   ~ (all_4_2 = e1)
% 178.99/28.70    (22)   ~ (all_52_7 = e3)
% 178.99/28.70    (23)   ~ (all_58_0 = e2)
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (9), (23) imply:
% 178.99/28.70  |   (24)   ~ (all_4_2 = e2)
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (20) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (25)  all_56_0 = e2
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (12), (24), (25) are inconsistent by sub-proof #904.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (26)  all_56_0 = e1 | all_56_0 = e0
% 178.99/28.70  | | 
% 178.99/28.70  | | BETA: splitting (26) gives:
% 178.99/28.70  | | 
% 178.99/28.70  | | Case 1:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (27)  all_56_0 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REF_CLOSE: (12), (21), (27) are inconsistent by sub-proof #1022.
% 178.99/28.70  | | | 
% 178.99/28.70  | | Case 2:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (28)  all_56_0 = e0
% 178.99/28.70  | | | 
% 178.99/28.70  | | | COMBINE_EQS: (12), (28) imply:
% 178.99/28.70  | | |   (29)  all_4_2 = e0
% 178.99/28.70  | | | 
% 178.99/28.70  | | | SIMP: (29) implies:
% 178.99/28.70  | | |   (30)  all_4_2 = e0
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (8), (30) imply:
% 178.99/28.70  | | |   (31)   ~ (all_52_7 = e0)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | BETA: splitting (1) gives:
% 178.99/28.70  | | | 
% 178.99/28.70  | | | Case 1:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (32)  all_56_3 = e2
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | COMBINE_EQS: (2), (32) imply:
% 178.99/28.70  | | | |   (33)  all_52_7 = e2
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | SIMP: (33) implies:
% 178.99/28.70  | | | |   (34)  all_52_7 = e2
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REDUCE: (19), (34) imply:
% 178.99/28.70  | | | |   (35)   ~ (all_6_2 = e2)
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | SIMP: (35) implies:
% 178.99/28.70  | | | |   (36)   ~ (all_6_2 = e2)
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REDUCE: (22), (34) imply:
% 178.99/28.70  | | | |   (37)   ~ (e3 = e2)
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (11), (13), (14), (15), (16), (17),
% 178.99/28.70  | | | |            (18), (36), (37) are inconsistent by sub-proof #750.
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | Case 2:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (38)  all_56_3 = e1 | all_56_3 = e0
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REF_CLOSE: (2), (10), (31), (38) are inconsistent by sub-proof #1037.
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | End of split
% 178.99/28.70  | | | 
% 178.99/28.70  | | End of split
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #750 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)   ~ (all_6_2 = e0)
% 178.99/28.70    (2)  all_56_15 = all_6_2
% 178.99/28.70    (3)  all_58_3 = all_10_2
% 178.99/28.70    (4)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.70    (5)  all_58_7 = all_52_19
% 178.99/28.70    (6)  all_58_13 = all_52_27
% 178.99/28.70    (7)  op(e2, e1) = e3
% 178.99/28.70    (8)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70    (9)  op(e2, all_10_2) = e2
% 178.99/28.70    (10)   ~ (all_52_19 = e1)
% 178.99/28.70    (11)   ~ (all_6_2 = e2)
% 178.99/28.70    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (13)   ~ (all_52_27 = all_6_2)
% 178.99/28.70    (14)   ~ (e3 = e2)
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (14) implies:
% 178.99/28.70  |   (15)   ~ (e3 = e2)
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (4) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (16)  all_56_15 = e2
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (2), (11), (16) are inconsistent by sub-proof #817.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (17)  all_56_15 = e1 | all_56_15 = e0
% 178.99/28.70  | | 
% 178.99/28.70  | | BETA: splitting (17) gives:
% 178.99/28.70  | | 
% 178.99/28.70  | | Case 1:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (18)  all_56_15 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | COMBINE_EQS: (2), (18) imply:
% 178.99/28.70  | | |   (19)  all_6_2 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | SIMP: (19) implies:
% 178.99/28.70  | | |   (20)  all_6_2 = e1
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (13), (20) imply:
% 178.99/28.70  | | |   (21)   ~ (all_52_27 = e1)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (12), (15), (21) are
% 178.99/28.70  | | |            inconsistent by sub-proof #751.
% 178.99/28.70  | | | 
% 178.99/28.70  | | Case 2:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (22)  all_56_15 = e0
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REF_CLOSE: (1), (2), (22) are inconsistent by sub-proof #812.
% 178.99/28.70  | | | 
% 178.99/28.70  | | End of split
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #751 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)  all_58_3 = all_10_2
% 178.99/28.70    (2)  all_58_7 = all_52_19
% 178.99/28.70    (3)  all_58_13 = all_52_27
% 178.99/28.70    (4)  op(e2, e1) = e3
% 178.99/28.70    (5)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70    (6)  op(e2, all_10_2) = e2
% 178.99/28.70    (7)   ~ (all_52_19 = e1)
% 178.99/28.70    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (9)   ~ (all_52_27 = e1)
% 178.99/28.70    (10)   ~ (e3 = e2)
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (5) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (11)  all_58_3 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | COMBINE_EQS: (1), (11) imply:
% 178.99/28.70  | |   (12)  all_10_2 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (6), (12) imply:
% 178.99/28.70  | |   (13)  op(e2, e1) = e2
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (4), (8), (10), (13) are inconsistent by sub-proof #856.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (14)  all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (2), (3), (7), (9), (14) are inconsistent by sub-proof #752.
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #752 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)  all_58_7 = all_52_19
% 178.99/28.70    (2)  all_58_13 = all_52_27
% 178.99/28.70    (3)   ~ (all_52_19 = e1)
% 178.99/28.70    (4)  all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70    (5)   ~ (all_52_27 = e1)
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (4) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (6)  all_58_7 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | COMBINE_EQS: (1), (6) imply:
% 178.99/28.70  | |   (7)  all_52_19 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (3), (7) imply:
% 178.99/28.70  | |   (8)  $false
% 178.99/28.70  | | 
% 178.99/28.70  | | CLOSE: (8) is inconsistent.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (9)  all_58_13 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | COMBINE_EQS: (2), (9) imply:
% 178.99/28.70  | |   (10)  all_52_27 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | SIMP: (10) implies:
% 178.99/28.70  | |   (11)  all_52_27 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (5), (11) imply:
% 178.99/28.70  | |   (12)  $false
% 178.99/28.70  | | 
% 178.99/28.70  | | CLOSE: (12) is inconsistent.
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #753 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)  all_56_4 = all_52_9
% 178.99/28.70    (2)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.70    (3)   ~ (all_52_9 = e1)
% 178.99/28.70    (4)   ~ (all_52_9 = e2)
% 178.99/28.70    (5)  op(e3, all_52_9) = e3
% 178.99/28.70    (6)  op(e3, e0) = all_52_7
% 178.99/28.70    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (8)   ~ (all_52_7 = e3)
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (2) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (9)  all_56_4 = e2
% 178.99/28.70  | | 
% 178.99/28.70  | | COMBINE_EQS: (1), (9) imply:
% 178.99/28.70  | |   (10)  all_52_9 = e2
% 178.99/28.70  | | 
% 178.99/28.70  | | SIMP: (10) implies:
% 178.99/28.70  | |   (11)  all_52_9 = e2
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (4), (11) imply:
% 178.99/28.70  | |   (12)  $false
% 178.99/28.70  | | 
% 178.99/28.70  | | CLOSE: (12) is inconsistent.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (13)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (13) are inconsistent by sub-proof
% 178.99/28.70  | |            #754.
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #754 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)  all_56_4 = all_52_9
% 178.99/28.70    (2)   ~ (all_52_9 = e1)
% 178.99/28.70    (3)  op(e3, all_52_9) = e3
% 178.99/28.70    (4)  op(e3, e0) = all_52_7
% 178.99/28.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (6)   ~ (all_52_7 = e3)
% 178.99/28.70    (7)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (7) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (8)  all_56_4 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | COMBINE_EQS: (1), (8) imply:
% 178.99/28.70  | |   (9)  all_52_9 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | SIMP: (9) implies:
% 178.99/28.70  | |   (10)  all_52_9 = e1
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (2), (10) imply:
% 178.99/28.70  | |   (11)  $false
% 178.99/28.70  | | 
% 178.99/28.70  | | CLOSE: (11) is inconsistent.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (12)  all_56_4 = e0
% 178.99/28.70  | | 
% 178.99/28.70  | | COMBINE_EQS: (1), (12) imply:
% 178.99/28.70  | |   (13)  all_52_9 = e0
% 178.99/28.70  | | 
% 178.99/28.70  | | SIMP: (13) implies:
% 178.99/28.70  | |   (14)  all_52_9 = e0
% 178.99/28.70  | | 
% 178.99/28.70  | | REDUCE: (3), (14) imply:
% 178.99/28.70  | |   (15)  op(e3, e0) = e3
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (4), (5), (6), (15) are inconsistent by sub-proof #908.
% 178.99/28.70  | | 
% 178.99/28.70  | End of split
% 178.99/28.70  | 
% 178.99/28.70  End of proof
% 178.99/28.70  
% 178.99/28.70  Sub-proof #755 shows that the following formulas are inconsistent:
% 178.99/28.70  ----------------------------------------------------------------
% 178.99/28.70    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.70    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.70    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.70    (4)   ~ (all_52_27 = all_10_2)
% 178.99/28.70    (5)   ~ (all_52_13 = all_52_29)
% 178.99/28.70    (6)  op(e3, e2) = all_52_3
% 178.99/28.70    (7)   ~ (all_52_9 = all_52_25)
% 178.99/28.70    (8)  op(e3, all_52_25) = all_52_24
% 178.99/28.70    (9)   ~ (all_52_19 = all_52_23)
% 178.99/28.70    (10)  all_56_11 = all_52_23
% 178.99/28.70    (11)   ~ (all_52_3 = all_10_2)
% 178.99/28.70    (12)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.70    (13)  all_58_5 = all_52_13
% 178.99/28.70    (14)  op(e1, all_52_13) = e1
% 178.99/28.70    (15)  op(e0, all_52_15) = e0
% 178.99/28.70    (16)  all_58_3 = all_10_2
% 178.99/28.70    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.70    (18)  all_58_15 = all_6_2
% 178.99/28.70    (19)   ~ (all_52_9 = all_4_2)
% 178.99/28.70    (20)   ~ (all_52_5 = all_52_7)
% 178.99/28.70    (21)  all_58_10 = all_52_15
% 178.99/28.70    (22)   ~ (all_52_5 = all_4_2)
% 178.99/28.70    (23)  all_58_7 = all_52_19
% 178.99/28.70    (24)  all_56_4 = all_52_9
% 178.99/28.70    (25)   ~ (all_52_15 = all_6_2)
% 178.99/28.70    (26)   ~ (all_52_17 = all_52_25)
% 178.99/28.70    (27)  op(e0, e1) = all_52_29
% 178.99/28.70    (28)   ~ (all_4_0 = e2)
% 178.99/28.70    (29)  all_58_4 = all_52_5
% 178.99/28.70    (30)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.70    (31)   ~ (e3 = e1)
% 178.99/28.70    (32)   ~ (all_52_27 = all_52_29)
% 178.99/28.70    (33)   ~ (all_52_17 = all_14_2)
% 178.99/28.70    (34)  op(e3, all_4_2) = all_4_1
% 178.99/28.70    (35)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.70    (36)   ~ (all_52_7 = all_4_2)
% 178.99/28.70    (37)  all_58_1 = all_52_3
% 178.99/28.70    (38)   ~ (all_52_13 = all_52_15)
% 178.99/28.70    (39)  all_58_0 = all_4_2
% 178.99/28.70    (40)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.70    (41)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.70    (42)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.70    (43)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.70    (44)  all_58_14 = all_52_29
% 178.99/28.70    (45)   ~ (all_52_3 = all_52_5)
% 178.99/28.70    (46)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.70    (47)  op(e2, e1) = all_52_13
% 178.99/28.70    (48)  all_58_8 = all_14_2
% 178.99/28.70    (49)  all_56_1 = all_52_3
% 178.99/28.70    (50)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.70    (51)   ~ (all_52_3 = all_52_27)
% 178.99/28.70    (52)   ~ (all_52_3 = all_4_2)
% 178.99/28.70    (53)  op(e0, e3) = all_52_25
% 178.99/28.70    (54)   ~ (all_52_9 = all_10_2)
% 178.99/28.70    (55)  op(e3, all_52_17) = all_52_16
% 178.99/28.70    (56)   ~ (all_52_13 = all_14_2)
% 178.99/28.70    (57)  op(e3, all_52_9) = e3
% 178.99/28.70    (58)   ~ (all_52_9 = all_52_13)
% 178.99/28.70    (59)  op(e0, all_52_23) = all_52_22
% 178.99/28.70    (60)   ~ (all_52_15 = all_52_23)
% 178.99/28.70    (61)  op(e1, e0) = all_52_23
% 178.99/28.70    (62)  all_58_13 = all_52_27
% 178.99/28.70    (63)   ~ (all_4_1 = e1)
% 178.99/28.70    (64)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.70    (65)   ~ (all_52_9 = all_52_17)
% 178.99/28.70    (66)  all_58_6 = all_52_17
% 178.99/28.70    (67)   ~ (all_52_3 = all_52_7)
% 178.99/28.70    (68)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.70    (69)   ~ (e1 = e0)
% 178.99/28.70    (70)  all_56_0 = all_4_2
% 178.99/28.70    (71)  all_58_11 = all_52_23
% 178.99/28.70    (72)   ~ (all_52_7 = all_52_15)
% 178.99/28.70    (73)   ~ (all_4_0 = e1)
% 178.99/28.70    (74)   ~ (all_52_23 = all_6_2)
% 178.99/28.70    (75)  all_58_2 = all_52_9
% 178.99/28.70    (76)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.70    (77)  op(e3, e1) = all_52_5
% 178.99/28.70    (78)  op(e1, e3) = all_52_17
% 178.99/28.70    (79)   ~ (all_52_25 = all_4_2)
% 178.99/28.70    (80)  op(e3, e0) = all_52_7
% 178.99/28.70    (81)  op(e2, all_10_2) = e2
% 178.99/28.70    (82)  op(e3, e3) = all_4_2
% 178.99/28.70    (83)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.70    (84)   ~ (all_52_25 = all_52_27)
% 178.99/28.70    (85)  all_56_13 = e3
% 178.99/28.70    (86)   ~ (all_52_27 = all_6_2)
% 178.99/28.70    (87)   ~ (all_52_19 = all_52_27)
% 178.99/28.70    (88)   ~ (all_52_7 = all_52_23)
% 178.99/28.70    (89)  op(e2, all_52_27) = all_52_26
% 178.99/28.70    (90)   ~ (all_52_17 = all_52_19)
% 178.99/28.70    (91)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.70    (92)  all_58_9 = all_52_7
% 178.99/28.70    (93)  all_58_12 = all_52_25
% 178.99/28.70    (94)   ~ (all_52_9 = all_52_15)
% 178.99/28.70    (95)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.70    (96)  op(e2, e3) = all_52_9
% 178.99/28.70    (97)  all_56_13 = all_52_27
% 178.99/28.70  
% 178.99/28.70  Begin of proof
% 178.99/28.70  | 
% 178.99/28.70  | COMBINE_EQS: (85), (97) imply:
% 178.99/28.70  |   (98)  all_52_27 = e3
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (98) implies:
% 178.99/28.70  |   (99)  all_52_27 = e3
% 178.99/28.70  | 
% 178.99/28.70  | COMBINE_EQS: (62), (99) imply:
% 178.99/28.70  |   (100)  all_58_13 = e3
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (51), (99) imply:
% 178.99/28.70  |   (101)   ~ (all_52_3 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (87), (99) imply:
% 178.99/28.70  |   (102)   ~ (all_52_19 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (84), (99) imply:
% 178.99/28.70  |   (103)   ~ (all_52_25 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (32), (99) imply:
% 178.99/28.70  |   (104)   ~ (all_52_29 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (104) implies:
% 178.99/28.70  |   (105)   ~ (all_52_29 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (4), (99) imply:
% 178.99/28.70  |   (106)   ~ (all_10_2 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (106) implies:
% 178.99/28.70  |   (107)   ~ (all_10_2 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (86), (99) imply:
% 178.99/28.70  |   (108)   ~ (all_6_2 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (108) implies:
% 178.99/28.70  |   (109)   ~ (all_6_2 = e3)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (89), (99) imply:
% 178.99/28.70  |   (110)  op(e2, e3) = all_52_26
% 178.99/28.70  | 
% 178.99/28.70  | GROUND_INST: instantiating (83) with all_52_9, all_52_26, e3, e2, simplifying
% 178.99/28.70  |              with (96), (110) gives:
% 178.99/28.70  |   (111)  all_52_9 = all_52_26
% 178.99/28.70  | 
% 178.99/28.70  | COMBINE_EQS: (24), (111) imply:
% 178.99/28.70  |   (112)  all_56_4 = all_52_26
% 178.99/28.70  | 
% 178.99/28.70  | COMBINE_EQS: (75), (111) imply:
% 178.99/28.70  |   (113)  all_58_2 = all_52_26
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (58), (111) imply:
% 178.99/28.70  |   (114)   ~ (all_52_13 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (114) implies:
% 178.99/28.70  |   (115)   ~ (all_52_13 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (94), (111) imply:
% 178.99/28.70  |   (116)   ~ (all_52_15 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (116) implies:
% 178.99/28.70  |   (117)   ~ (all_52_15 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (65), (111) imply:
% 178.99/28.70  |   (118)   ~ (all_52_17 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (118) implies:
% 178.99/28.70  |   (119)   ~ (all_52_17 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (7), (111) imply:
% 178.99/28.70  |   (120)   ~ (all_52_25 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | SIMP: (120) implies:
% 178.99/28.70  |   (121)   ~ (all_52_25 = all_52_26)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (54), (111) imply:
% 178.99/28.70  |   (122)   ~ (all_52_26 = all_10_2)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (19), (111) imply:
% 178.99/28.70  |   (123)   ~ (all_52_26 = all_4_2)
% 178.99/28.70  | 
% 178.99/28.70  | REDUCE: (57), (111) imply:
% 178.99/28.70  |   (124)  op(e3, all_52_26) = e3
% 178.99/28.70  | 
% 178.99/28.70  | BETA: splitting (41) gives:
% 178.99/28.70  | 
% 178.99/28.70  | Case 1:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (125)  all_56_1 = e3
% 178.99/28.70  | | 
% 178.99/28.70  | | REF_CLOSE: (49), (101), (125) are inconsistent by sub-proof #862.
% 178.99/28.70  | | 
% 178.99/28.70  | Case 2:
% 178.99/28.70  | | 
% 178.99/28.70  | |   (126)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.70  | | 
% 178.99/28.70  | | BETA: splitting (76) gives:
% 178.99/28.70  | | 
% 178.99/28.70  | | Case 1:
% 178.99/28.70  | | | 
% 178.99/28.70  | | |   (127)  all_56_11 = e3
% 178.99/28.70  | | | 
% 178.99/28.70  | | | COMBINE_EQS: (10), (127) imply:
% 178.99/28.70  | | |   (128)  all_52_23 = e3
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (60), (128) imply:
% 178.99/28.70  | | |   (129)   ~ (all_52_15 = e3)
% 178.99/28.70  | | | 
% 178.99/28.70  | | | REDUCE: (59), (128) imply:
% 178.99/28.70  | | |   (130)  op(e0, e3) = all_52_22
% 178.99/28.70  | | | 
% 178.99/28.70  | | | GROUND_INST: instantiating (83) with all_52_25, all_52_22, e3, e0,
% 178.99/28.70  | | |              simplifying with (53), (130) gives:
% 178.99/28.70  | | |   (131)  all_52_22 = all_52_25
% 178.99/28.70  | | | 
% 178.99/28.70  | | | BETA: splitting (95) gives:
% 178.99/28.70  | | | 
% 178.99/28.70  | | | Case 1:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (132)  all_58_4 = e3
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | COMBINE_EQS: (29), (132) imply:
% 178.99/28.70  | | | |   (133)  all_52_5 = e3
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REDUCE: (2), (133) imply:
% 178.99/28.70  | | | |   (134)   ~ (all_52_13 = e3)
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | SIMP: (134) implies:
% 178.99/28.70  | | | |   (135)   ~ (all_52_13 = e3)
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | | REF_CLOSE: (6), (11), (13), (16), (19), (21), (35), (57), (75), (81),
% 178.99/28.70  | | | |            (82), (83), (96), (129), (135) are inconsistent by sub-proof
% 178.99/28.70  | | | |            #772.
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | Case 2:
% 178.99/28.70  | | | | 
% 178.99/28.70  | | | |   (136)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REF_CLOSE: (1), (3), (6), (11), (13), (14), (15), (16), (18), (21),
% 178.99/28.71  | | | |            (22), (23), (27), (28), (29), (31), (33), (34), (36), (37),
% 178.99/28.71  | | | |            (39), (42), (43), (44), (45), (46), (47), (48), (50), (52),
% 178.99/28.71  | | | |            (53), (55), (64), (66), (68), (69), (71), (73), (77), (78),
% 178.99/28.71  | | | |            (81), (82), (83), (90), (91), (92), (93), (100), (103),
% 178.99/28.71  | | | |            (105), (109), (112), (113), (115), (117), (119), (121),
% 178.99/28.71  | | | |            (123), (124), (136) are inconsistent by sub-proof #763.
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | End of split
% 178.99/28.71  | | | 
% 178.99/28.71  | | Case 2:
% 178.99/28.71  | | | 
% 178.99/28.71  | | |   (137)   ~ (all_56_11 = e3)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REDUCE: (10), (137) imply:
% 178.99/28.71  | | |   (138)   ~ (all_52_23 = e3)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | BETA: splitting (91) gives:
% 178.99/28.71  | | | 
% 178.99/28.71  | | | Case 1:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (139)  all_58_9 = e3
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | COMBINE_EQS: (92), (139) imply:
% 178.99/28.71  | | | |   (140)  all_52_7 = e3
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REF_CLOSE: (5), (13), (14), (16), (20), (21), (23), (26), (29), (30),
% 178.99/28.71  | | | |            (31), (33), (35), (36), (39), (44), (46), (48), (56), (66),
% 178.99/28.71  | | | |            (71), (72), (78), (82), (83), (88), (93), (95), (102), (107),
% 178.99/28.71  | | | |            (113), (115), (123), (124), (140) are inconsistent by
% 178.99/28.71  | | | |            sub-proof #983.
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | Case 2:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (141)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | BETA: splitting (141) gives:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | Case 1:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | |   (142)  all_58_10 = e3
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | COMBINE_EQS: (21), (142) imply:
% 178.99/28.71  | | | | |   (143)  all_52_15 = e3
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | SIMP: (143) implies:
% 178.99/28.71  | | | | |   (144)  all_52_15 = e3
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REDUCE: (38), (144) imply:
% 178.99/28.71  | | | | |   (145)   ~ (all_52_13 = e3)
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REDUCE: (60), (144) imply:
% 178.99/28.71  | | | | |   (146)   ~ (all_52_23 = e3)
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REDUCE: (117), (144) imply:
% 178.99/28.71  | | | | |   (147)   ~ (all_52_26 = e3)
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | SIMP: (147) implies:
% 178.99/28.71  | | | | |   (148)   ~ (all_52_26 = e3)
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REDUCE: (15), (144) imply:
% 178.99/28.71  | | | | |   (149)  op(e0, e3) = e0
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REF_CLOSE: (1), (3), (6), (8), (9), (11), (12), (13), (14), (15),
% 178.99/28.71  | | | | |            (16), (17), (18), (21), (22), (23), (29), (33), (34), (36),
% 178.99/28.71  | | | | |            (37), (39), (40), (44), (45), (46), (48), (49), (50), (52),
% 178.99/28.71  | | | | |            (53), (61), (63), (64), (66), (67), (68), (70), (71), (73),
% 178.99/28.71  | | | | |            (77), (79), (80), (82), (83), (91), (92), (93), (95),
% 178.99/28.71  | | | | |            (100), (103), (105), (109), (112), (113), (117), (121),
% 178.99/28.71  | | | | |            (122), (123), (124), (126), (138), (142), (145), (148),
% 178.99/28.71  | | | | |            (149) are inconsistent by sub-proof #756.
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | Case 2:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | |   (150)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REF_CLOSE: (18), (71), (109), (138), (150) are inconsistent by
% 178.99/28.71  | | | | |            sub-proof #1016.
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | End of split
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | End of split
% 178.99/28.71  | | | 
% 178.99/28.71  | | End of split
% 178.99/28.71  | | 
% 178.99/28.71  | End of split
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #756 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)   ~ (all_52_25 = e3)
% 178.99/28.71    (2)   ~ (all_52_23 = all_14_2)
% 178.99/28.71    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.71    (4)  op(e3, e2) = all_52_3
% 178.99/28.71    (5)  op(e3, all_52_25) = all_52_24
% 178.99/28.71    (6)   ~ (all_52_19 = all_52_23)
% 178.99/28.71    (7)   ~ (all_6_2 = e3)
% 178.99/28.71    (8)   ~ (all_52_3 = all_10_2)
% 178.99/28.71    (9)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.71    (10)  all_58_5 = all_52_13
% 178.99/28.71    (11)  op(e1, all_52_13) = e1
% 178.99/28.71    (12)  op(e0, all_52_15) = e0
% 178.99/28.71    (13)   ~ (all_52_26 = all_10_2)
% 178.99/28.71    (14)  all_58_3 = all_10_2
% 178.99/28.71    (15)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.71    (16)  all_58_15 = all_6_2
% 178.99/28.71    (17)   ~ (all_52_26 = all_4_2)
% 178.99/28.71    (18)  all_58_10 = all_52_15
% 178.99/28.71    (19)   ~ (all_52_5 = all_4_2)
% 178.99/28.71    (20)  all_58_7 = all_52_19
% 178.99/28.71    (21)  all_58_4 = all_52_5
% 178.99/28.71    (22)   ~ (all_52_17 = all_14_2)
% 178.99/28.71    (23)  op(e3, all_4_2) = all_4_1
% 178.99/28.71    (24)   ~ (all_52_7 = all_4_2)
% 178.99/28.71    (25)  all_58_1 = all_52_3
% 178.99/28.71    (26)  all_58_0 = all_4_2
% 178.99/28.71    (27)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.71    (28)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.71    (29)  all_58_14 = all_52_29
% 178.99/28.71    (30)   ~ (all_52_3 = all_52_5)
% 178.99/28.71    (31)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.71    (32)  all_58_8 = all_14_2
% 178.99/28.71    (33)  all_56_1 = all_52_3
% 178.99/28.71    (34)  op(e0, e3) = e0
% 178.99/28.71    (35)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.71    (36)   ~ (all_52_23 = e3)
% 178.99/28.71    (37)   ~ (all_52_3 = all_4_2)
% 178.99/28.71    (38)  op(e0, e3) = all_52_25
% 178.99/28.71    (39)   ~ (all_52_29 = e3)
% 178.99/28.71    (40)   ~ (all_52_13 = e3)
% 178.99/28.71    (41)  op(e1, e0) = all_52_23
% 178.99/28.71    (42)   ~ (all_4_1 = e1)
% 178.99/28.71    (43)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.71    (44)  all_58_6 = all_52_17
% 178.99/28.71    (45)   ~ (all_52_3 = all_52_7)
% 178.99/28.71    (46)  all_58_2 = all_52_26
% 178.99/28.71    (47)  all_58_10 = e3
% 178.99/28.71    (48)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.71    (49)  all_56_0 = all_4_2
% 178.99/28.71    (50)  all_58_11 = all_52_23
% 178.99/28.71    (51)   ~ (all_4_0 = e1)
% 178.99/28.71    (52)  op(e3, e1) = all_52_5
% 178.99/28.71    (53)   ~ (all_52_26 = e3)
% 178.99/28.71    (54)   ~ (all_52_25 = all_4_2)
% 178.99/28.71    (55)  op(e3, e0) = all_52_7
% 178.99/28.71    (56)  op(e3, e3) = all_4_2
% 178.99/28.71    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.71    (58)   ~ (all_52_25 = all_52_26)
% 178.99/28.71    (59)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.71    (60)  all_56_4 = all_52_26
% 178.99/28.71    (61)  all_58_9 = all_52_7
% 178.99/28.71    (62)   ~ (all_52_15 = all_52_26)
% 178.99/28.71    (63)  all_58_12 = all_52_25
% 178.99/28.71    (64)  op(e3, all_52_26) = e3
% 178.99/28.71    (65)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.71    (66)  all_58_13 = e3
% 178.99/28.71  
% 178.99/28.71  Begin of proof
% 178.99/28.71  | 
% 178.99/28.71  | GROUND_INST: instantiating (57) with all_52_25, e0, e3, e0, simplifying with
% 178.99/28.71  |              (34), (38) gives:
% 178.99/28.71  |   (67)  all_52_25 = e0
% 178.99/28.71  | 
% 178.99/28.71  | REDUCE: (58), (67) imply:
% 178.99/28.71  |   (68)   ~ (all_52_26 = e0)
% 178.99/28.71  | 
% 178.99/28.71  | SIMP: (68) implies:
% 178.99/28.71  |   (69)   ~ (all_52_26 = e0)
% 178.99/28.71  | 
% 178.99/28.71  | REDUCE: (54), (67) imply:
% 178.99/28.71  |   (70)   ~ (all_4_2 = e0)
% 178.99/28.71  | 
% 178.99/28.71  | SIMP: (70) implies:
% 178.99/28.71  |   (71)   ~ (all_4_2 = e0)
% 178.99/28.71  | 
% 178.99/28.71  | REDUCE: (5), (67) imply:
% 178.99/28.71  |   (72)  op(e3, e0) = all_52_24
% 178.99/28.71  | 
% 178.99/28.71  | GROUND_INST: instantiating (57) with all_52_7, all_52_24, e0, e3, simplifying
% 178.99/28.71  |              with (55), (72) gives:
% 178.99/28.71  |   (73)  all_52_7 = all_52_24
% 178.99/28.71  | 
% 178.99/28.71  | COMBINE_EQS: (61), (73) imply:
% 178.99/28.71  |   (74)  all_58_9 = all_52_24
% 178.99/28.71  | 
% 178.99/28.71  | REDUCE: (45), (73) imply:
% 178.99/28.71  |   (75)   ~ (all_52_3 = all_52_24)
% 178.99/28.71  | 
% 178.99/28.71  | BETA: splitting (48) gives:
% 178.99/28.71  | 
% 178.99/28.71  | Case 1:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (76)  all_56_4 = e3
% 178.99/28.71  | | 
% 178.99/28.71  | | REF_CLOSE: (53), (60), (76) are inconsistent by sub-proof #818.
% 178.99/28.71  | | 
% 178.99/28.71  | Case 2:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (77)   ~ (all_56_4 = e3)
% 178.99/28.71  | |   (78)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.71  | | 
% 178.99/28.71  | | BETA: splitting (65) gives:
% 178.99/28.71  | | 
% 178.99/28.71  | | Case 1:
% 178.99/28.71  | | | 
% 178.99/28.71  | | |   (79)  all_58_4 = e3
% 178.99/28.71  | | | 
% 178.99/28.71  | | | COMBINE_EQS: (21), (79) imply:
% 178.99/28.71  | | |   (80)  all_52_5 = e3
% 178.99/28.71  | | | 
% 178.99/28.71  | | | SIMP: (80) implies:
% 178.99/28.71  | | |   (81)  all_52_5 = e3
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REDUCE: (30), (81) imply:
% 178.99/28.71  | | |   (82)   ~ (all_52_3 = e3)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REDUCE: (19), (81) imply:
% 178.99/28.71  | | |   (83)   ~ (all_4_2 = e3)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | SIMP: (83) implies:
% 178.99/28.71  | | |   (84)   ~ (all_4_2 = e3)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REF_CLOSE: (3), (4), (6), (8), (9), (10), (11), (13), (14), (15), (17),
% 178.99/28.71  | | |            (20), (23), (25), (26), (27), (28), (33), (36), (37), (41),
% 178.99/28.71  | | |            (42), (43), (46), (47), (49), (50), (53), (57), (60), (64),
% 178.99/28.71  | | |            (66), (69), (71), (74), (75), (78), (82), (84) are inconsistent
% 178.99/28.71  | | |            by sub-proof #757.
% 178.99/28.71  | | | 
% 178.99/28.71  | | Case 2:
% 178.99/28.71  | | | 
% 178.99/28.71  | | |   (85)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.71  | | | 
% 178.99/28.71  | | | BETA: splitting (85) gives:
% 178.99/28.71  | | | 
% 178.99/28.71  | | | Case 1:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (86)  all_58_5 = e3
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REF_CLOSE: (10), (40), (86) are inconsistent by sub-proof #969.
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | Case 2:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (87)  all_58_8 = e3 | all_58_14 = e3
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REF_CLOSE: (1), (2), (4), (7), (12), (16), (17), (18), (19), (22), (23),
% 178.99/28.71  | | | |            (24), (26), (29), (31), (32), (35), (37), (38), (39), (43),
% 178.99/28.71  | | | |            (44), (46), (48), (50), (51), (52), (56), (57), (58), (59),
% 178.99/28.71  | | | |            (60), (61), (62), (63), (64), (87) are inconsistent by
% 178.99/28.71  | | | |            sub-proof #764.
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | End of split
% 178.99/28.71  | | | 
% 178.99/28.71  | | End of split
% 178.99/28.71  | | 
% 178.99/28.71  | End of split
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #757 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.71    (2)  op(e3, e2) = all_52_3
% 178.99/28.71    (3)   ~ (all_52_19 = all_52_23)
% 178.99/28.71    (4)   ~ (all_52_3 = all_10_2)
% 178.99/28.71    (5)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.71    (6)  all_58_5 = all_52_13
% 178.99/28.71    (7)  op(e1, all_52_13) = e1
% 178.99/28.71    (8)   ~ (all_4_2 = e3)
% 178.99/28.71    (9)   ~ (all_52_26 = all_10_2)
% 178.99/28.71    (10)  all_58_3 = all_10_2
% 178.99/28.71    (11)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.71    (12)   ~ (all_52_26 = all_4_2)
% 178.99/28.71    (13)  all_58_7 = all_52_19
% 178.99/28.71    (14)   ~ (all_52_26 = e0)
% 178.99/28.71    (15)  op(e3, all_4_2) = all_4_1
% 178.99/28.71    (16)  all_58_1 = all_52_3
% 178.99/28.71    (17)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.71    (18)  all_58_0 = all_4_2
% 178.99/28.71    (19)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.71    (20)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.71    (21)  all_56_1 = all_52_3
% 178.99/28.71    (22)   ~ (all_52_23 = e3)
% 178.99/28.71    (23)   ~ (all_52_3 = all_52_24)
% 178.99/28.71    (24)   ~ (all_52_3 = all_4_2)
% 178.99/28.71    (25)  op(e1, e0) = all_52_23
% 178.99/28.71    (26)   ~ (all_4_1 = e1)
% 178.99/28.71    (27)   ~ (all_52_3 = e3)
% 178.99/28.71    (28)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.71    (29)  all_58_2 = all_52_26
% 178.99/28.71    (30)  all_58_10 = e3
% 178.99/28.71    (31)  all_56_0 = all_4_2
% 178.99/28.71    (32)  all_58_11 = all_52_23
% 178.99/28.71    (33)   ~ (all_52_26 = e3)
% 178.99/28.71    (34)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.71    (35)   ~ (all_4_2 = e0)
% 178.99/28.71    (36)  all_58_9 = all_52_24
% 178.99/28.71    (37)  all_56_4 = all_52_26
% 178.99/28.71    (38)  op(e3, all_52_26) = e3
% 178.99/28.71    (39)  all_58_13 = e3
% 178.99/28.71  
% 178.99/28.71  Begin of proof
% 178.99/28.71  | 
% 178.99/28.71  | BETA: splitting (11) gives:
% 178.99/28.71  | 
% 178.99/28.71  | Case 1:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (40)  all_56_0 = e3
% 178.99/28.71  | | 
% 178.99/28.71  | | REF_CLOSE: (8), (31), (40) are inconsistent by sub-proof #1024.
% 178.99/28.71  | | 
% 178.99/28.71  | Case 2:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (41)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.71  | | 
% 178.99/28.71  | | BETA: splitting (28) gives:
% 178.99/28.71  | | 
% 178.99/28.71  | | Case 1:
% 178.99/28.71  | | | 
% 178.99/28.71  | | |   (42)  all_58_0 = e1
% 178.99/28.71  | | | 
% 178.99/28.71  | | | COMBINE_EQS: (18), (42) imply:
% 178.99/28.71  | | |   (43)  all_4_2 = e1
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REDUCE: (12), (43) imply:
% 178.99/28.71  | | |   (44)   ~ (all_52_26 = e1)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REF_CLOSE: (2), (14), (17), (27), (34), (37), (38), (44) are inconsistent
% 178.99/28.71  | | |            by sub-proof #766.
% 178.99/28.71  | | | 
% 178.99/28.71  | | Case 2:
% 178.99/28.71  | | | 
% 178.99/28.71  | | |   (45)   ~ (all_58_0 = e1)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REDUCE: (18), (45) imply:
% 178.99/28.71  | | |   (46)   ~ (all_4_2 = e1)
% 178.99/28.71  | | | 
% 178.99/28.71  | | | BETA: splitting (41) gives:
% 178.99/28.71  | | | 
% 178.99/28.71  | | | Case 1:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (47)  all_56_0 = e2
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | COMBINE_EQS: (31), (47) imply:
% 178.99/28.71  | | | |   (48)  all_4_2 = e2
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | SIMP: (48) implies:
% 178.99/28.71  | | | |   (49)  all_4_2 = e2
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REDUCE: (24), (49) imply:
% 178.99/28.71  | | | |   (50)   ~ (all_52_3 = e2)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REDUCE: (12), (49) imply:
% 178.99/28.71  | | | |   (51)   ~ (all_52_26 = e2)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REDUCE: (15), (49) imply:
% 178.99/28.71  | | | |   (52)  op(e3, e2) = all_4_1
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | BETA: splitting (17) gives:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | Case 1:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | |   (53)  all_56_4 = e2
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REF_CLOSE: (37), (51), (53) are inconsistent by sub-proof #807.
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | Case 2:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | |   (54)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | BETA: splitting (54) gives:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | Case 1:
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | |   (55)  all_56_4 = e1
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | COMBINE_EQS: (37), (55) imply:
% 178.99/28.71  | | | | | |   (56)  all_52_26 = e1
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | SIMP: (56) implies:
% 178.99/28.71  | | | | | |   (57)  all_52_26 = e1
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | COMBINE_EQS: (29), (57) imply:
% 178.99/28.71  | | | | | |   (58)  all_58_2 = e1
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REDUCE: (9), (57) imply:
% 178.99/28.71  | | | | | |   (59)   ~ (all_10_2 = e1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | SIMP: (59) implies:
% 178.99/28.71  | | | | | |   (60)   ~ (all_10_2 = e1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REDUCE: (33), (57) imply:
% 178.99/28.71  | | | | | |   (61)   ~ (e3 = e1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | SIMP: (61) implies:
% 178.99/28.71  | | | | | |   (62)   ~ (e3 = e1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | GROUND_INST: instantiating (34) with all_52_3, all_4_1, e2, e3,
% 178.99/28.71  | | | | | |              simplifying with (2), (52) gives:
% 178.99/28.71  | | | | | |   (63)  all_52_3 = all_4_1
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | COMBINE_EQS: (21), (63) imply:
% 178.99/28.71  | | | | | |   (64)  all_56_1 = all_4_1
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | COMBINE_EQS: (16), (63) imply:
% 178.99/28.71  | | | | | |   (65)  all_58_1 = all_4_1
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REDUCE: (23), (63) imply:
% 178.99/28.71  | | | | | |   (66)   ~ (all_52_24 = all_4_1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | SIMP: (66) implies:
% 178.99/28.71  | | | | | |   (67)   ~ (all_52_24 = all_4_1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REDUCE: (4), (63) imply:
% 178.99/28.71  | | | | | |   (68)   ~ (all_10_2 = all_4_1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | SIMP: (68) implies:
% 178.99/28.71  | | | | | |   (69)   ~ (all_10_2 = all_4_1)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REDUCE: (27), (63) imply:
% 178.99/28.71  | | | | | |   (70)   ~ (all_4_1 = e3)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REDUCE: (50), (63) imply:
% 178.99/28.71  | | | | | |   (71)   ~ (all_4_1 = e2)
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | BETA: splitting (1) gives:
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | Case 1:
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | |   (72)  all_58_1 = e1
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | | COMBINE_EQS: (65), (72) imply:
% 178.99/28.71  | | | | | | |   (73)  all_4_1 = e1
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | | REDUCE: (26), (73) imply:
% 178.99/28.71  | | | | | | |   (74)  $false
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | | CLOSE: (74) is inconsistent.
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | Case 2:
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | |   (75)   ~ (all_58_1 = e1)
% 178.99/28.71  | | | | | | |   (76)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | | REF_CLOSE: (3), (5), (6), (7), (10), (13), (19), (20), (22), (25),
% 178.99/28.71  | | | | | | |            (26), (30), (32), (34), (36), (39), (58), (60), (62),
% 178.99/28.71  | | | | | | |            (64), (67), (69), (70), (71), (76) are inconsistent by
% 178.99/28.71  | | | | | | |            sub-proof #758.
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | End of split
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | Case 2:
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | |   (77)  all_56_4 = e0
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REF_CLOSE: (14), (37), (77) are inconsistent by sub-proof #806.
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | End of split
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | End of split
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | Case 2:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (78)  all_56_0 = e1 | all_56_0 = e0
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REF_CLOSE: (31), (35), (46), (78) are inconsistent by sub-proof #1020.
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | End of split
% 178.99/28.71  | | | 
% 178.99/28.71  | | End of split
% 178.99/28.71  | | 
% 178.99/28.71  | End of split
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #758 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)   ~ (all_52_19 = all_52_23)
% 178.99/28.71    (2)   ~ (all_10_2 = e1)
% 178.99/28.71    (3)  all_58_2 = e0 | all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.71    (4)  all_58_5 = all_52_13
% 178.99/28.71    (5)  op(e1, all_52_13) = e1
% 178.99/28.71    (6)  all_58_3 = all_10_2
% 178.99/28.71    (7)  all_58_7 = all_52_19
% 178.99/28.71    (8)   ~ (e3 = e1)
% 178.99/28.71    (9)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.71    (10)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.71    (11)   ~ (all_4_1 = e2)
% 178.99/28.71    (12)   ~ (all_52_24 = all_4_1)
% 178.99/28.71    (13)   ~ (all_52_23 = e3)
% 178.99/28.71    (14)   ~ (all_10_2 = all_4_1)
% 178.99/28.71    (15)  op(e1, e0) = all_52_23
% 178.99/28.71    (16)   ~ (all_4_1 = e1)
% 178.99/28.71    (17)  all_58_10 = e3
% 178.99/28.71    (18)  all_58_11 = all_52_23
% 178.99/28.71    (19)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.71    (20)  all_56_1 = all_4_1
% 178.99/28.71    (21)  all_58_2 = e1
% 178.99/28.71    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.71    (23)  all_58_9 = all_52_24
% 178.99/28.71    (24)   ~ (all_4_1 = e3)
% 178.99/28.71    (25)  all_58_13 = e3
% 178.99/28.71  
% 178.99/28.71  Begin of proof
% 178.99/28.71  | 
% 178.99/28.71  | BETA: splitting (19) gives:
% 178.99/28.71  | 
% 178.99/28.71  | Case 1:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (26)  all_58_3 = e1
% 178.99/28.71  | | 
% 178.99/28.71  | | COMBINE_EQS: (6), (26) imply:
% 178.99/28.71  | |   (27)  all_10_2 = e1
% 178.99/28.71  | | 
% 178.99/28.71  | | REDUCE: (2), (27) imply:
% 178.99/28.71  | |   (28)  $false
% 178.99/28.71  | | 
% 178.99/28.71  | | CLOSE: (28) is inconsistent.
% 178.99/28.71  | | 
% 178.99/28.71  | Case 2:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (29)  all_58_7 = e1 | all_58_13 = e1
% 178.99/28.71  | | 
% 178.99/28.71  | | BETA: splitting (10) gives:
% 178.99/28.71  | | 
% 178.99/28.71  | | Case 1:
% 178.99/28.71  | | | 
% 178.99/28.71  | | |   (30)  all_56_1 = e2
% 178.99/28.71  | | | 
% 178.99/28.71  | | | REF_CLOSE: (11), (20), (30) are inconsistent by sub-proof #762.
% 178.99/28.71  | | | 
% 178.99/28.71  | | Case 2:
% 178.99/28.71  | | | 
% 178.99/28.71  | | |   (31)  all_56_1 = e1 | all_56_1 = e0
% 178.99/28.71  | | | 
% 178.99/28.71  | | | BETA: splitting (31) gives:
% 178.99/28.71  | | | 
% 178.99/28.71  | | | Case 1:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (32)  all_56_1 = e1
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REF_CLOSE: (16), (20), (32) are inconsistent by sub-proof #761.
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | Case 2:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | |   (33)  all_56_1 = e0
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | COMBINE_EQS: (20), (33) imply:
% 178.99/28.71  | | | |   (34)  all_4_1 = e0
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | SIMP: (34) implies:
% 178.99/28.71  | | | |   (35)  all_4_1 = e0
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REDUCE: (12), (35) imply:
% 178.99/28.71  | | | |   (36)   ~ (all_52_24 = e0)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REDUCE: (14), (35) imply:
% 178.99/28.71  | | | |   (37)   ~ (all_10_2 = e0)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REDUCE: (24), (35) imply:
% 178.99/28.71  | | | |   (38)   ~ (e3 = e0)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | SIMP: (38) implies:
% 178.99/28.71  | | | |   (39)   ~ (e3 = e0)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | REDUCE: (16), (35) imply:
% 178.99/28.71  | | | |   (40)   ~ (e1 = e0)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | SIMP: (40) implies:
% 178.99/28.71  | | | |   (41)   ~ (e1 = e0)
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | BETA: splitting (3) gives:
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | | Case 1:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | |   (42)  all_58_2 = e0
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | COMBINE_EQS: (21), (42) imply:
% 178.99/28.71  | | | | |   (43)  e1 = e0
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | SIMP: (43) implies:
% 178.99/28.71  | | | | |   (44)  e1 = e0
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | REDUCE: (41), (44) imply:
% 178.99/28.71  | | | | |   (45)  $false
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | CLOSE: (45) is inconsistent.
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | Case 2:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | |   (46)  all_58_3 = e0 | all_58_5 = e0 | all_58_10 = e0
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | BETA: splitting (46) gives:
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | | Case 1:
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | |   (47)  all_58_3 = e0
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | COMBINE_EQS: (6), (47) imply:
% 178.99/28.71  | | | | | |   (48)  all_10_2 = e0
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | REDUCE: (37), (48) imply:
% 178.99/28.71  | | | | | |   (49)  $false
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | CLOSE: (49) is inconsistent.
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | Case 2:
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | |   (50)  all_58_5 = e0 | all_58_10 = e0
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | BETA: splitting (9) gives:
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | | Case 1:
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | |   (51)  all_58_9 = e0
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | | REF_CLOSE: (23), (36), (51) are inconsistent by sub-proof #760.
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | Case 2:
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | |   (52)  all_58_10 = e0 | all_58_11 = e0
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | | BETA: splitting (29) gives:
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | | Case 1:
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | |   (53)  all_58_7 = e1
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | | COMBINE_EQS: (7), (53) imply:
% 178.99/28.71  | | | | | | | |   (54)  all_52_19 = e1
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | | REDUCE: (1), (54) imply:
% 178.99/28.71  | | | | | | | |   (55)   ~ (all_52_23 = e1)
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | | SIMP: (55) implies:
% 178.99/28.71  | | | | | | | |   (56)   ~ (all_52_23 = e1)
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | | BETA: splitting (52) gives:
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | | Case 1:
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | |   (57)  all_58_10 = e0
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | | REF_CLOSE: (17), (39), (57) are inconsistent by sub-proof
% 178.99/28.71  | | | | | | | | |            #824.
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | Case 2:
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | |   (58)  all_58_11 = e0
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | | COMBINE_EQS: (18), (58) imply:
% 178.99/28.71  | | | | | | | | |   (59)  all_52_23 = e0
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | | SIMP: (59) implies:
% 178.99/28.71  | | | | | | | | |   (60)  all_52_23 = e0
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | | REDUCE: (15), (60) imply:
% 178.99/28.71  | | | | | | | | |   (61)  op(e1, e0) = e0
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | | REF_CLOSE: (4), (5), (17), (22), (39), (41), (50), (61) are
% 178.99/28.71  | | | | | | | | |            inconsistent by sub-proof #759.
% 178.99/28.71  | | | | | | | | | 
% 178.99/28.71  | | | | | | | | End of split
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | Case 2:
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | |   (62)  all_58_13 = e1
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | | REF_CLOSE: (8), (25), (62) are inconsistent by sub-proof #769.
% 178.99/28.71  | | | | | | | | 
% 178.99/28.71  | | | | | | | End of split
% 178.99/28.71  | | | | | | | 
% 178.99/28.71  | | | | | | End of split
% 178.99/28.71  | | | | | | 
% 178.99/28.71  | | | | | End of split
% 178.99/28.71  | | | | | 
% 178.99/28.71  | | | | End of split
% 178.99/28.71  | | | | 
% 178.99/28.71  | | | End of split
% 178.99/28.71  | | | 
% 178.99/28.71  | | End of split
% 178.99/28.71  | | 
% 178.99/28.71  | End of split
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #759 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)  all_58_5 = all_52_13
% 178.99/28.71    (2)  op(e1, all_52_13) = e1
% 178.99/28.71    (3)   ~ (e3 = e0)
% 178.99/28.71    (4)  all_58_10 = e3
% 178.99/28.71    (5)   ~ (e1 = e0)
% 178.99/28.71    (6)  op(e1, e0) = e0
% 178.99/28.71    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.71    (8)  all_58_5 = e0 | all_58_10 = e0
% 178.99/28.71  
% 178.99/28.71  Begin of proof
% 178.99/28.71  | 
% 178.99/28.71  | BETA: splitting (8) gives:
% 178.99/28.71  | 
% 178.99/28.71  | Case 1:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (9)  all_58_5 = e0
% 178.99/28.71  | | 
% 178.99/28.71  | | COMBINE_EQS: (1), (9) imply:
% 178.99/28.71  | |   (10)  all_52_13 = e0
% 178.99/28.71  | | 
% 178.99/28.71  | | SIMP: (10) implies:
% 178.99/28.71  | |   (11)  all_52_13 = e0
% 178.99/28.71  | | 
% 178.99/28.71  | | REDUCE: (2), (11) imply:
% 178.99/28.71  | |   (12)  op(e1, e0) = e1
% 178.99/28.71  | | 
% 178.99/28.71  | | GROUND_INST: instantiating (7) with e0, e1, e0, e1, simplifying with (6),
% 178.99/28.71  | |              (12) gives:
% 178.99/28.71  | |   (13)  e1 = e0
% 178.99/28.71  | | 
% 178.99/28.71  | | REDUCE: (5), (13) imply:
% 178.99/28.71  | |   (14)  $false
% 178.99/28.71  | | 
% 178.99/28.71  | | CLOSE: (14) is inconsistent.
% 178.99/28.71  | | 
% 178.99/28.71  | Case 2:
% 178.99/28.71  | | 
% 178.99/28.71  | |   (15)  all_58_10 = e0
% 178.99/28.71  | | 
% 178.99/28.71  | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #824.
% 178.99/28.71  | | 
% 178.99/28.71  | End of split
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #760 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)  all_58_9 = all_52_24
% 178.99/28.71    (2)  all_58_9 = e0
% 178.99/28.71    (3)   ~ (all_52_24 = e0)
% 178.99/28.71  
% 178.99/28.71  Begin of proof
% 178.99/28.71  | 
% 178.99/28.71  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.71  |   (4)  all_52_24 = e0
% 178.99/28.71  | 
% 178.99/28.71  | SIMP: (4) implies:
% 178.99/28.71  |   (5)  all_52_24 = e0
% 178.99/28.71  | 
% 178.99/28.71  | REDUCE: (3), (5) imply:
% 178.99/28.71  |   (6)  $false
% 178.99/28.71  | 
% 178.99/28.71  | CLOSE: (6) is inconsistent.
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #761 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)  all_56_1 = all_4_1
% 178.99/28.71    (2)  all_56_1 = e1
% 178.99/28.71    (3)   ~ (all_4_1 = e1)
% 178.99/28.71  
% 178.99/28.71  Begin of proof
% 178.99/28.71  | 
% 178.99/28.71  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.71  |   (4)  all_4_1 = e1
% 178.99/28.71  | 
% 178.99/28.71  | SIMP: (4) implies:
% 178.99/28.71  |   (5)  all_4_1 = e1
% 178.99/28.71  | 
% 178.99/28.71  | REDUCE: (3), (5) imply:
% 178.99/28.71  |   (6)  $false
% 178.99/28.71  | 
% 178.99/28.71  | CLOSE: (6) is inconsistent.
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #762 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)  all_56_1 = all_4_1
% 178.99/28.71    (2)  all_56_1 = e2
% 178.99/28.71    (3)   ~ (all_4_1 = e2)
% 178.99/28.71  
% 178.99/28.71  Begin of proof
% 178.99/28.71  | 
% 178.99/28.71  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.71  |   (4)  all_4_1 = e2
% 178.99/28.71  | 
% 178.99/28.71  | SIMP: (4) implies:
% 178.99/28.71  |   (5)  all_4_1 = e2
% 178.99/28.71  | 
% 178.99/28.71  | REDUCE: (3), (5) imply:
% 178.99/28.71  |   (6)  $false
% 178.99/28.71  | 
% 178.99/28.71  | CLOSE: (6) is inconsistent.
% 178.99/28.71  | 
% 178.99/28.71  End of proof
% 178.99/28.71  
% 178.99/28.71  Sub-proof #763 shows that the following formulas are inconsistent:
% 178.99/28.71  ----------------------------------------------------------------
% 178.99/28.71    (1)   ~ (all_52_25 = e3)
% 178.99/28.71    (2)   ~ (all_52_23 = all_14_2)
% 178.99/28.71    (3)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.71    (4)  op(e3, e2) = all_52_3
% 178.99/28.71    (5)   ~ (all_6_2 = e3)
% 178.99/28.71    (6)   ~ (all_52_3 = all_10_2)
% 178.99/28.71    (7)  all_58_5 = all_52_13
% 178.99/28.71    (8)  op(e1, all_52_13) = e1
% 178.99/28.71    (9)  op(e0, all_52_15) = e0
% 178.99/28.71    (10)  all_58_3 = all_10_2
% 178.99/28.71    (11)  all_58_15 = all_6_2
% 178.99/28.71    (12)   ~ (all_52_26 = all_4_2)
% 178.99/28.71    (13)  all_58_10 = all_52_15
% 178.99/28.71    (14)   ~ (all_52_5 = all_4_2)
% 178.99/28.71    (15)  all_58_7 = all_52_19
% 178.99/28.71    (16)  op(e0, e1) = all_52_29
% 178.99/28.71    (17)   ~ (all_4_0 = e2)
% 178.99/28.71    (18)  all_58_4 = all_52_5
% 178.99/28.71    (19)   ~ (e3 = e1)
% 178.99/28.71    (20)   ~ (all_52_17 = all_14_2)
% 178.99/28.71    (21)  op(e3, all_4_2) = all_4_1
% 178.99/28.71    (22)   ~ (all_52_7 = all_4_2)
% 178.99/28.71    (23)  all_58_1 = all_52_3
% 178.99/28.71    (24)  all_58_0 = all_4_2
% 178.99/28.71    (25)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.71    (26)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.71    (27)  all_58_14 = all_52_29
% 178.99/28.71    (28)   ~ (all_52_13 = all_52_26)
% 178.99/28.71    (29)   ~ (all_52_3 = all_52_5)
% 178.99/28.71    (30)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.71    (31)  op(e2, e1) = all_52_13
% 178.99/28.71    (32)  all_58_8 = all_14_2
% 178.99/28.71    (33)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.71    (34)   ~ (all_52_3 = all_4_2)
% 178.99/28.71    (35)  op(e0, e3) = all_52_25
% 178.99/28.71    (36)  op(e3, all_52_17) = all_52_16
% 178.99/28.72    (37)   ~ (all_52_29 = e3)
% 178.99/28.72    (38)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.72    (39)  all_58_6 = all_52_17
% 178.99/28.72    (40)  all_58_2 = all_52_26
% 178.99/28.72    (41)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.72    (42)   ~ (e1 = e0)
% 178.99/28.72    (43)  all_58_11 = all_52_23
% 178.99/28.72    (44)   ~ (all_4_0 = e1)
% 178.99/28.72    (45)  op(e3, e1) = all_52_5
% 178.99/28.72    (46)  op(e1, e3) = all_52_17
% 178.99/28.72    (47)  op(e2, all_10_2) = e2
% 178.99/28.72    (48)  op(e3, e3) = all_4_2
% 178.99/28.72    (49)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.72    (50)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (51)   ~ (all_52_25 = all_52_26)
% 178.99/28.72    (52)   ~ (all_52_17 = all_52_19)
% 178.99/28.72    (53)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.72    (54)  all_56_4 = all_52_26
% 178.99/28.72    (55)  all_58_9 = all_52_7
% 178.99/28.72    (56)   ~ (all_52_15 = all_52_26)
% 178.99/28.72    (57)  all_58_12 = all_52_25
% 178.99/28.72    (58)   ~ (all_52_17 = all_52_26)
% 178.99/28.72    (59)  op(e3, all_52_26) = e3
% 178.99/28.72    (60)  all_58_13 = e3
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (49) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (61)  all_58_5 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (7), (61) imply:
% 178.99/28.72  | |   (62)  all_52_13 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | SIMP: (62) implies:
% 178.99/28.72  | |   (63)  all_52_13 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (28), (63) imply:
% 178.99/28.72  | |   (64)   ~ (all_52_26 = e3)
% 178.99/28.72  | | 
% 178.99/28.72  | | SIMP: (64) implies:
% 178.99/28.72  | |   (65)   ~ (all_52_26 = e3)
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (31), (63) imply:
% 178.99/28.72  | |   (66)  op(e2, e1) = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (8), (63) imply:
% 178.99/28.72  | |   (67)  op(e1, e3) = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | GROUND_INST: instantiating (50) with all_52_17, e1, e3, e1, simplifying with
% 178.99/28.72  | |              (46), (67) gives:
% 178.99/28.72  | |   (68)  all_52_17 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (39), (68) imply:
% 178.99/28.72  | |   (69)  all_58_6 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (52), (68) imply:
% 178.99/28.72  | |   (70)   ~ (all_52_19 = e1)
% 178.99/28.72  | | 
% 178.99/28.72  | | SIMP: (70) implies:
% 178.99/28.72  | |   (71)   ~ (all_52_19 = e1)
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (58), (68) imply:
% 178.99/28.72  | |   (72)   ~ (all_52_26 = e1)
% 178.99/28.72  | | 
% 178.99/28.72  | | SIMP: (72) implies:
% 178.99/28.72  | |   (73)   ~ (all_52_26 = e1)
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (20), (68) imply:
% 178.99/28.72  | |   (74)   ~ (all_14_2 = e1)
% 178.99/28.72  | | 
% 178.99/28.72  | | SIMP: (74) implies:
% 178.99/28.72  | |   (75)   ~ (all_14_2 = e1)
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (36), (68) imply:
% 178.99/28.72  | |   (76)  op(e3, e1) = all_52_16
% 178.99/28.72  | | 
% 178.99/28.72  | | BETA: splitting (30) gives:
% 178.99/28.72  | | 
% 178.99/28.72  | | Case 1:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (77)  all_58_0 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | COMBINE_EQS: (24), (77) imply:
% 178.99/28.72  | | |   (78)  all_4_2 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (34), (78) imply:
% 178.99/28.72  | | |   (79)   ~ (all_52_3 = e3)
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (22), (78) imply:
% 178.99/28.72  | | |   (80)   ~ (all_52_7 = e3)
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (33), (78) imply:
% 178.99/28.72  | | |   (81)  op(all_4_1, e3) = all_4_0
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (21), (78) imply:
% 178.99/28.72  | | |   (82)  op(e3, e3) = all_4_1
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (48), (78) imply:
% 178.99/28.72  | | |   (83)  op(e3, e3) = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | BETA: splitting (53) gives:
% 178.99/28.72  | | | 
% 178.99/28.72  | | | Case 1:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | |   (84)  all_58_9 = e3
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | REF_CLOSE: (55), (80), (84) are inconsistent by sub-proof #972.
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | Case 2:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | GROUND_INST: instantiating (50) with all_52_5, all_52_16, e1, e3,
% 178.99/28.72  | | | |              simplifying with (45), (76) gives:
% 178.99/28.72  | | | |   (85)  all_52_5 = all_52_16
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | GROUND_INST: instantiating (50) with e3, all_4_1, e3, e3, simplifying
% 178.99/28.72  | | | |              with (82), (83) gives:
% 178.99/28.72  | | | |   (86)  all_4_1 = e3
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | COMBINE_EQS: (18), (85) imply:
% 178.99/28.72  | | | |   (87)  all_58_4 = all_52_16
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | REDUCE: (29), (85) imply:
% 178.99/28.72  | | | |   (88)   ~ (all_52_3 = all_52_16)
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | REDUCE: (81), (86) imply:
% 178.99/28.72  | | | |   (89)  op(e3, e3) = all_4_0
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | GROUND_INST: instantiating (50) with e3, all_4_0, e3, e3, simplifying
% 178.99/28.72  | | | |              with (83), (89) gives:
% 178.99/28.72  | | | |   (90)  all_4_0 = e3
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | REDUCE: (17), (90) imply:
% 178.99/28.72  | | | |   (91)   ~ (e3 = e2)
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | BETA: splitting (26) gives:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | Case 1:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | |   (92)  all_58_2 = e1
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | COMBINE_EQS: (40), (92) imply:
% 178.99/28.72  | | | | |   (93)  all_52_26 = e1
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (73), (93) imply:
% 178.99/28.72  | | | | |   (94)  $false
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | CLOSE: (94) is inconsistent.
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | Case 2:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | |   (95)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | BETA: splitting (3) gives:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | Case 1:
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | |   (96)  all_58_1 = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | COMBINE_EQS: (23), (96) imply:
% 178.99/28.72  | | | | | |   (97)  all_52_3 = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REDUCE: (88), (97) imply:
% 178.99/28.72  | | | | | |   (98)   ~ (all_52_16 = e1)
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | SIMP: (98) implies:
% 178.99/28.72  | | | | | |   (99)   ~ (all_52_16 = e1)
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REDUCE: (6), (97) imply:
% 178.99/28.72  | | | | | |   (100)   ~ (all_10_2 = e1)
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | SIMP: (100) implies:
% 178.99/28.72  | | | | | |   (101)   ~ (all_10_2 = e1)
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REDUCE: (79), (97) imply:
% 178.99/28.72  | | | | | |   (102)   ~ (e3 = e1)
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REF_CLOSE: (9), (10), (13), (16), (19), (25), (27), (32), (42),
% 178.99/28.72  | | | | | |            (50), (61), (75), (87), (95), (99), (101) are
% 178.99/28.72  | | | | | |            inconsistent by sub-proof #770.
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | Case 2:
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | |   (103)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REF_CLOSE: (10), (15), (19), (47), (50), (60), (66), (71), (91),
% 178.99/28.72  | | | | | |            (103) are inconsistent by sub-proof #767.
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | End of split
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | End of split
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | End of split
% 178.99/28.72  | | | 
% 178.99/28.72  | | Case 2:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (104)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REF_CLOSE: (1), (19), (40), (57), (65), (69), (104) are inconsistent by
% 178.99/28.72  | | |            sub-proof #1001.
% 178.99/28.72  | | | 
% 178.99/28.72  | | End of split
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (105)  all_58_8 = e3 | all_58_14 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (1), (2), (4), (5), (9), (11), (12), (13), (14), (20), (21),
% 178.99/28.72  | |            (22), (24), (27), (30), (32), (33), (34), (35), (37), (38), (39),
% 178.99/28.72  | |            (40), (41), (43), (44), (45), (48), (50), (51), (53), (54), (55),
% 178.99/28.72  | |            (56), (57), (59), (105) are inconsistent by sub-proof #764.
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #764 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)   ~ (all_52_25 = e3)
% 178.99/28.72    (2)   ~ (all_52_23 = all_14_2)
% 178.99/28.72    (3)  op(e3, e2) = all_52_3
% 178.99/28.72    (4)   ~ (all_6_2 = e3)
% 178.99/28.72    (5)  op(e0, all_52_15) = e0
% 178.99/28.72    (6)  all_58_15 = all_6_2
% 178.99/28.72    (7)   ~ (all_52_26 = all_4_2)
% 178.99/28.72    (8)  all_58_10 = all_52_15
% 178.99/28.72    (9)   ~ (all_52_5 = all_4_2)
% 178.99/28.72    (10)   ~ (all_52_17 = all_14_2)
% 178.99/28.72    (11)  op(e3, all_4_2) = all_4_1
% 178.99/28.72    (12)   ~ (all_52_7 = all_4_2)
% 178.99/28.72    (13)  all_58_0 = all_4_2
% 178.99/28.72    (14)  all_58_14 = all_52_29
% 178.99/28.72    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.72    (16)  all_58_8 = all_14_2
% 178.99/28.72    (17)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.72    (18)   ~ (all_52_3 = all_4_2)
% 178.99/28.72    (19)  op(e0, e3) = all_52_25
% 178.99/28.72    (20)   ~ (all_52_29 = e3)
% 178.99/28.72    (21)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.72    (22)  all_58_6 = all_52_17
% 178.99/28.72    (23)  all_58_2 = all_52_26
% 178.99/28.72    (24)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.72    (25)  all_58_11 = all_52_23
% 178.99/28.72    (26)   ~ (all_4_0 = e1)
% 178.99/28.72    (27)  op(e3, e1) = all_52_5
% 178.99/28.72    (28)  all_58_8 = e3 | all_58_14 = e3
% 178.99/28.72    (29)  op(e3, e3) = all_4_2
% 178.99/28.72    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (31)   ~ (all_52_25 = all_52_26)
% 178.99/28.72    (32)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.72    (33)  all_56_4 = all_52_26
% 178.99/28.72    (34)  all_58_9 = all_52_7
% 178.99/28.72    (35)   ~ (all_52_15 = all_52_26)
% 178.99/28.72    (36)  all_58_12 = all_52_25
% 178.99/28.72    (37)  op(e3, all_52_26) = e3
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (28) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (38)  all_58_8 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (16), (38) imply:
% 178.99/28.72  | |   (39)  all_14_2 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (10), (39) imply:
% 178.99/28.72  | |   (40)   ~ (all_52_17 = e3)
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (2), (39) imply:
% 178.99/28.72  | |   (41)   ~ (all_52_23 = e3)
% 178.99/28.72  | | 
% 178.99/28.72  | | BETA: splitting (15) gives:
% 178.99/28.72  | | 
% 178.99/28.72  | | Case 1:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (42)  all_58_0 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | COMBINE_EQS: (13), (42) imply:
% 178.99/28.72  | | |   (43)  all_4_2 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (18), (43) imply:
% 178.99/28.72  | | |   (44)   ~ (all_52_3 = e3)
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (9), (43) imply:
% 178.99/28.72  | | |   (45)   ~ (all_52_5 = e3)
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (12), (43) imply:
% 178.99/28.72  | | |   (46)   ~ (all_52_7 = e3)
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (17), (43) imply:
% 178.99/28.72  | | |   (47)  op(all_4_1, e3) = all_4_0
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (11), (43) imply:
% 178.99/28.72  | | |   (48)  op(e3, e3) = all_4_1
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (29), (43) imply:
% 178.99/28.72  | | |   (49)  op(e3, e3) = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | BETA: splitting (32) gives:
% 178.99/28.72  | | | 
% 178.99/28.72  | | | Case 1:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | |   (50)  all_58_9 = e3
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | REF_CLOSE: (34), (46), (50) are inconsistent by sub-proof #972.
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | Case 2:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | |   (51)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | BETA: splitting (51) gives:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | Case 1:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | |   (52)  all_58_10 = e3
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | COMBINE_EQS: (8), (52) imply:
% 178.99/28.72  | | | | |   (53)  all_52_15 = e3
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | SIMP: (53) implies:
% 178.99/28.72  | | | | |   (54)  all_52_15 = e3
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (35), (54) imply:
% 178.99/28.72  | | | | |   (55)   ~ (all_52_26 = e3)
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | SIMP: (55) implies:
% 178.99/28.72  | | | | |   (56)   ~ (all_52_26 = e3)
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (5), (54) imply:
% 178.99/28.72  | | | | |   (57)  op(e0, e3) = e0
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | GROUND_INST: instantiating (30) with all_52_25, e0, e3, e0,
% 178.99/28.72  | | | | |              simplifying with (19), (57) gives:
% 178.99/28.72  | | | | |   (58)  all_52_25 = e0
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | GROUND_INST: instantiating (30) with e3, all_4_1, e3, e3, simplifying
% 178.99/28.72  | | | | |              with (48), (49) gives:
% 178.99/28.72  | | | | |   (59)  all_4_1 = e3
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (31), (58) imply:
% 178.99/28.72  | | | | |   (60)   ~ (all_52_26 = e0)
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | SIMP: (60) implies:
% 178.99/28.72  | | | | |   (61)   ~ (all_52_26 = e0)
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (47), (59) imply:
% 178.99/28.72  | | | | |   (62)  op(e3, e3) = all_4_0
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | GROUND_INST: instantiating (30) with e3, all_4_0, e3, e3, simplifying
% 178.99/28.72  | | | | |              with (49), (62) gives:
% 178.99/28.72  | | | | |   (63)  all_4_0 = e3
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (26), (63) imply:
% 178.99/28.72  | | | | |   (64)   ~ (e3 = e1)
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | BETA: splitting (24) gives:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | Case 1:
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | |   (65)  all_56_4 = e3
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REF_CLOSE: (33), (56), (65) are inconsistent by sub-proof #818.
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | Case 2:
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | |   (66)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | BETA: splitting (21) gives:
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | Case 1:
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | |   (67)  all_58_0 = e1
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | | COMBINE_EQS: (42), (67) imply:
% 178.99/28.72  | | | | | | |   (68)  e3 = e1
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | | REDUCE: (64), (68) imply:
% 178.99/28.72  | | | | | | |   (69)  $false
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | | CLOSE: (69) is inconsistent.
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | Case 2:
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | |   (70)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | | BETA: splitting (70) gives:
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | | Case 1:
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | |   (71)  all_58_2 = e1
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | | COMBINE_EQS: (23), (71) imply:
% 178.99/28.72  | | | | | | | |   (72)  all_52_26 = e1
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | | SIMP: (72) implies:
% 178.99/28.72  | | | | | | | |   (73)  all_52_26 = e1
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | | REDUCE: (37), (73) imply:
% 178.99/28.72  | | | | | | | |   (74)  op(e3, e1) = e3
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | | REF_CLOSE: (27), (30), (45), (74) are inconsistent by sub-proof
% 178.99/28.72  | | | | | | | |            #1023.
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | Case 2:
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | |   (75)   ~ (all_58_2 = e1)
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | | REDUCE: (23), (75) imply:
% 178.99/28.72  | | | | | | | |   (76)   ~ (all_52_26 = e1)
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | | REF_CLOSE: (3), (30), (33), (37), (44), (61), (66), (76) are
% 178.99/28.72  | | | | | | | |            inconsistent by sub-proof #766.
% 178.99/28.72  | | | | | | | | 
% 178.99/28.72  | | | | | | | End of split
% 178.99/28.72  | | | | | | | 
% 178.99/28.72  | | | | | | End of split
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | End of split
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | Case 2:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | |   (77)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REF_CLOSE: (4), (6), (25), (41), (77) are inconsistent by sub-proof
% 178.99/28.72  | | | | |            #1016.
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | End of split
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | End of split
% 178.99/28.72  | | | 
% 178.99/28.72  | | Case 2:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (78)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REF_CLOSE: (1), (7), (22), (23), (29), (30), (36), (37), (40), (78) are
% 178.99/28.72  | | |            inconsistent by sub-proof #765.
% 178.99/28.72  | | | 
% 178.99/28.72  | | End of split
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (79)  all_58_14 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (14), (20), (79) are inconsistent by sub-proof #1000.
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #765 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)   ~ (all_52_25 = e3)
% 178.99/28.72    (2)   ~ (all_52_17 = e3)
% 178.99/28.72    (3)   ~ (all_52_26 = all_4_2)
% 178.99/28.72    (4)  all_58_6 = all_52_17
% 178.99/28.72    (5)  all_58_2 = all_52_26
% 178.99/28.72    (6)  op(e3, e3) = all_4_2
% 178.99/28.72    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (8)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.72    (9)  all_58_12 = all_52_25
% 178.99/28.72    (10)  op(e3, all_52_26) = e3
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (8) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (11)  all_58_2 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (5), (11) imply:
% 178.99/28.72  | |   (12)  all_52_26 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | SIMP: (12) implies:
% 178.99/28.72  | |   (13)  all_52_26 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (3), (6), (7), (10), (13) are inconsistent by sub-proof #1005.
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (14)  all_58_6 = e3 | all_58_12 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | BETA: splitting (14) gives:
% 178.99/28.72  | | 
% 178.99/28.72  | | Case 1:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (15)  all_58_6 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #981.
% 178.99/28.72  | | | 
% 178.99/28.72  | | Case 2:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (16)  all_58_12 = e3
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #1003.
% 178.99/28.72  | | | 
% 178.99/28.72  | | End of split
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #766 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)  op(e3, e2) = all_52_3
% 178.99/28.72    (2)   ~ (all_52_26 = e0)
% 178.99/28.72    (3)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.72    (4)   ~ (all_52_3 = e3)
% 178.99/28.72    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (6)  all_56_4 = all_52_26
% 178.99/28.72    (7)  op(e3, all_52_26) = e3
% 178.99/28.72    (8)   ~ (all_52_26 = e1)
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (3) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (9)  all_56_4 = e2
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (6), (9) imply:
% 178.99/28.72  | |   (10)  all_52_26 = e2
% 178.99/28.72  | | 
% 178.99/28.72  | | SIMP: (10) implies:
% 178.99/28.72  | |   (11)  all_52_26 = e2
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (7), (11) imply:
% 178.99/28.72  | |   (12)  op(e3, e2) = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #978.
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (13)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (2), (6), (8), (13) are inconsistent by sub-proof #805.
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #767 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)  all_58_3 = all_10_2
% 178.99/28.72    (2)  all_58_7 = all_52_19
% 178.99/28.72    (3)   ~ (e3 = e1)
% 178.99/28.72    (4)  op(e2, e1) = e3
% 178.99/28.72    (5)  all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.72    (6)  op(e2, all_10_2) = e2
% 178.99/28.72    (7)   ~ (all_52_19 = e1)
% 178.99/28.72    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (9)   ~ (e3 = e2)
% 178.99/28.72    (10)  all_58_13 = e3
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (5) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (11)  all_58_3 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (1), (11) imply:
% 178.99/28.72  | |   (12)  all_10_2 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (6), (12) imply:
% 178.99/28.72  | |   (13)  op(e2, e1) = e2
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (4), (8), (9), (13) are inconsistent by sub-proof #856.
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (14)  all_58_7 = e1 | all_58_13 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (2), (3), (7), (10), (14) are inconsistent by sub-proof #768.
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #768 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)  all_58_7 = all_52_19
% 178.99/28.72    (2)   ~ (e3 = e1)
% 178.99/28.72    (3)   ~ (all_52_19 = e1)
% 178.99/28.72    (4)  all_58_7 = e1 | all_58_13 = e1
% 178.99/28.72    (5)  all_58_13 = e3
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (4) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (6)  all_58_7 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (1), (6) imply:
% 178.99/28.72  | |   (7)  all_52_19 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (3), (7) imply:
% 178.99/28.72  | |   (8)  $false
% 178.99/28.72  | | 
% 178.99/28.72  | | CLOSE: (8) is inconsistent.
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (9)  all_58_13 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #769.
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #769 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)  all_58_13 = e3
% 178.99/28.72    (2)  all_58_13 = e1
% 178.99/28.72    (3)   ~ (e3 = e1)
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.72  |   (4)  e3 = e1
% 178.99/28.72  | 
% 178.99/28.72  | SIMP: (4) implies:
% 178.99/28.72  |   (5)  e3 = e1
% 178.99/28.72  | 
% 178.99/28.72  | REDUCE: (3), (5) imply:
% 178.99/28.72  |   (6)  $false
% 178.99/28.72  | 
% 178.99/28.72  | CLOSE: (6) is inconsistent.
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #770 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)   ~ (all_10_2 = e1)
% 178.99/28.72    (2)  op(e0, all_52_15) = e0
% 178.99/28.72    (3)  all_58_3 = all_10_2
% 178.99/28.72    (4)  all_58_10 = all_52_15
% 178.99/28.72    (5)  op(e0, e1) = all_52_29
% 178.99/28.72    (6)   ~ (e3 = e1)
% 178.99/28.72    (7)  all_58_5 = e3
% 178.99/28.72    (8)  all_58_4 = all_52_16
% 178.99/28.72    (9)   ~ (all_14_2 = e1)
% 178.99/28.72    (10)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.72    (11)  all_58_14 = all_52_29
% 178.99/28.72    (12)  all_58_8 = all_14_2
% 178.99/28.72    (13)   ~ (e1 = e0)
% 178.99/28.72    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (15)   ~ (all_52_16 = e1)
% 178.99/28.72    (16)  all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (10) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (17)  all_58_4 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (8), (17) imply:
% 178.99/28.72  | |   (18)  all_52_16 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | REDUCE: (15), (18) imply:
% 178.99/28.72  | |   (19)  $false
% 178.99/28.72  | | 
% 178.99/28.72  | | CLOSE: (19) is inconsistent.
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (20)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.72  | | 
% 178.99/28.72  | | BETA: splitting (20) gives:
% 178.99/28.72  | | 
% 178.99/28.72  | | Case 1:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (21)  all_58_5 = e1
% 178.99/28.72  | | | 
% 178.99/28.72  | | | COMBINE_EQS: (7), (21) imply:
% 178.99/28.72  | | |   (22)  e3 = e1
% 178.99/28.72  | | | 
% 178.99/28.72  | | | REDUCE: (6), (22) imply:
% 178.99/28.72  | | |   (23)  $false
% 178.99/28.72  | | | 
% 178.99/28.72  | | | CLOSE: (23) is inconsistent.
% 178.99/28.72  | | | 
% 178.99/28.72  | | Case 2:
% 178.99/28.72  | | | 
% 178.99/28.72  | | |   (24)   ~ (all_58_5 = e1)
% 178.99/28.72  | | |   (25)  all_58_8 = e1 | all_58_14 = e1
% 178.99/28.72  | | | 
% 178.99/28.72  | | | BETA: splitting (16) gives:
% 178.99/28.72  | | | 
% 178.99/28.72  | | | Case 1:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | |   (26)  all_58_3 = e1
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | COMBINE_EQS: (3), (26) imply:
% 178.99/28.72  | | | |   (27)  all_10_2 = e1
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | REDUCE: (1), (27) imply:
% 178.99/28.72  | | | |   (28)  $false
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | CLOSE: (28) is inconsistent.
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | Case 2:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | |   (29)  all_58_5 = e1 | all_58_10 = e1
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | BETA: splitting (29) gives:
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | | Case 1:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | |   (30)  all_58_5 = e1
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | COMBINE_EQS: (7), (30) imply:
% 178.99/28.72  | | | | |   (31)  e3 = e1
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (6), (31) imply:
% 178.99/28.72  | | | | |   (32)  $false
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | CLOSE: (32) is inconsistent.
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | Case 2:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | |   (33)  all_58_10 = e1
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | COMBINE_EQS: (4), (33) imply:
% 178.99/28.72  | | | | |   (34)  all_52_15 = e1
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | REDUCE: (2), (34) imply:
% 178.99/28.72  | | | | |   (35)  op(e0, e1) = e0
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | BETA: splitting (25) gives:
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | | Case 1:
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | |   (36)  all_58_8 = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REF_CLOSE: (9), (12), (36) are inconsistent by sub-proof #815.
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | Case 2:
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | |   (37)  all_58_14 = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | COMBINE_EQS: (11), (37) imply:
% 178.99/28.72  | | | | | |   (38)  all_52_29 = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | SIMP: (38) implies:
% 178.99/28.72  | | | | | |   (39)  all_52_29 = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REDUCE: (5), (39) imply:
% 178.99/28.72  | | | | | |   (40)  op(e0, e1) = e1
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | | REF_CLOSE: (13), (14), (35), (40) are inconsistent by sub-proof
% 178.99/28.72  | | | | | |            #771.
% 178.99/28.72  | | | | | | 
% 178.99/28.72  | | | | | End of split
% 178.99/28.72  | | | | | 
% 178.99/28.72  | | | | End of split
% 178.99/28.72  | | | | 
% 178.99/28.72  | | | End of split
% 178.99/28.72  | | | 
% 178.99/28.72  | | End of split
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #771 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (2)  op(e0, e1) = e1
% 178.99/28.72    (3)  op(e0, e1) = e0
% 178.99/28.72    (4)   ~ (e1 = e0)
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | GROUND_INST: instantiating (1) with e1, e0, e1, e0, simplifying with (2), (3)
% 178.99/28.72  |              gives:
% 178.99/28.72  |   (5)  e1 = e0
% 178.99/28.72  | 
% 178.99/28.72  | REDUCE: (4), (5) imply:
% 178.99/28.72  |   (6)  $false
% 178.99/28.72  | 
% 178.99/28.72  | CLOSE: (6) is inconsistent.
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #772 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)  op(e3, e2) = all_52_3
% 178.99/28.72    (2)   ~ (all_52_3 = all_10_2)
% 178.99/28.72    (3)  all_58_5 = all_52_13
% 178.99/28.72    (4)  all_58_3 = all_10_2
% 178.99/28.72    (5)   ~ (all_52_9 = all_4_2)
% 178.99/28.72    (6)  all_58_10 = all_52_15
% 178.99/28.72    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.72    (8)  op(e3, all_52_9) = e3
% 178.99/28.72    (9)   ~ (all_52_13 = e3)
% 178.99/28.72    (10)   ~ (all_52_15 = e3)
% 178.99/28.72    (11)  all_58_2 = all_52_9
% 178.99/28.72    (12)  op(e2, all_10_2) = e2
% 178.99/28.72    (13)  op(e3, e3) = all_4_2
% 178.99/28.72    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.72    (15)  op(e2, e3) = all_52_9
% 178.99/28.72  
% 178.99/28.72  Begin of proof
% 178.99/28.72  | 
% 178.99/28.72  | BETA: splitting (7) gives:
% 178.99/28.72  | 
% 178.99/28.72  | Case 1:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (16)  all_58_2 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | COMBINE_EQS: (11), (16) imply:
% 178.99/28.72  | |   (17)  all_52_9 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (5), (8), (13), (14), (17) are inconsistent by sub-proof #967.
% 178.99/28.72  | | 
% 178.99/28.72  | Case 2:
% 178.99/28.72  | | 
% 178.99/28.72  | |   (18)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.72  | | 
% 178.99/28.72  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (14), (15), (18)
% 178.99/28.72  | |            are inconsistent by sub-proof #777.
% 178.99/28.72  | | 
% 178.99/28.72  | End of split
% 178.99/28.72  | 
% 178.99/28.72  End of proof
% 178.99/28.72  
% 178.99/28.72  Sub-proof #773 shows that the following formulas are inconsistent:
% 178.99/28.72  ----------------------------------------------------------------
% 178.99/28.72    (1)  op(e3, e2) = all_52_3
% 178.99/28.72    (2)   ~ (all_52_9 = all_52_25)
% 178.99/28.72    (3)  all_6_2 = e3
% 178.99/28.72    (4)   ~ (all_52_3 = all_10_2)
% 178.99/28.72    (5)  all_58_5 = all_52_13
% 178.99/28.72    (6)  op(e1, all_52_13) = e1
% 178.99/28.72    (7)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.72    (8)  all_58_3 = all_10_2
% 178.99/28.72    (9)   ~ (all_52_9 = all_4_2)
% 178.99/28.72    (10)  all_58_10 = all_52_15
% 178.99/28.72    (11)  all_58_7 = all_52_19
% 178.99/28.72    (12)  all_56_4 = all_52_9
% 178.99/28.72    (13)   ~ (all_52_15 = all_6_2)
% 178.99/28.72    (14)   ~ (all_4_0 = e2)
% 178.99/28.72    (15)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.72    (16)   ~ (e3 = e1)
% 178.99/28.72    (17)  op(e3, all_4_2) = all_4_1
% 178.99/28.72    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.72    (19)   ~ (all_52_7 = all_4_2)
% 178.99/28.72    (20)  all_58_1 = all_52_3
% 178.99/28.72    (21)  all_58_0 = all_4_2
% 178.99/28.72    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.72    (23)  all_56_6 = e3 | all_56_6 = e2 | all_56_6 = e1 | all_56_6 = e0
% 178.99/28.72    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.72    (25)  all_58_8 = all_14_2
% 178.99/28.72    (26)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.72    (27)  op(e0, e3) = all_52_25
% 178.99/28.72    (28)  op(e0, all_6_2) = all_6_1
% 178.99/28.72    (29)   ~ (all_52_13 = all_14_2)
% 178.99/28.72    (30)  op(e3, all_52_9) = e3
% 178.99/28.72    (31)  all_58_13 = all_52_27
% 178.99/28.72    (32)   ~ (all_52_9 = all_52_17)
% 178.99/28.72    (33)  all_58_6 = all_52_17
% 178.99/28.72    (34)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.72    (35)  op(e2, all_52_19) = all_52_18
% 178.99/28.72    (36)  all_58_11 = all_52_23
% 178.99/28.72    (37)   ~ (all_52_3 = all_52_19)
% 178.99/28.72    (38)   ~ (all_52_23 = all_6_2)
% 178.99/28.72    (39)  all_58_2 = all_52_9
% 178.99/28.73    (40)   ~ (e2 = e1)
% 178.99/28.73    (41)   ~ (all_52_25 = all_6_2)
% 178.99/28.73    (42)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.73    (43)  op(e1, e3) = all_52_17
% 178.99/28.73    (44)  op(e3, e0) = all_52_7
% 178.99/28.73    (45)  op(e2, all_10_2) = e2
% 178.99/28.73    (46)  op(e3, e3) = all_4_2
% 178.99/28.73    (47)   ~ (all_52_17 = all_4_2)
% 178.99/28.73    (48)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.73    (49)   ~ (all_52_27 = all_6_2)
% 178.99/28.73    (50)   ~ (all_52_17 = all_52_19)
% 178.99/28.73    (51)  all_58_12 = all_52_25
% 178.99/28.73    (52)  all_56_6 = all_52_13
% 178.99/28.73    (53)  op(e2, e3) = all_52_9
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (13) imply:
% 178.99/28.73  |   (54)   ~ (all_52_15 = e3)
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (38) imply:
% 178.99/28.73  |   (55)   ~ (all_52_23 = e3)
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (41) imply:
% 178.99/28.73  |   (56)   ~ (all_52_25 = e3)
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (49) imply:
% 178.99/28.73  |   (57)   ~ (all_52_27 = e3)
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (28) imply:
% 178.99/28.73  |   (58)  op(e0, e3) = all_6_1
% 178.99/28.73  | 
% 178.99/28.73  | GROUND_INST: instantiating (48) with all_52_25, all_6_1, e3, e0, simplifying
% 178.99/28.73  |              with (27), (58) gives:
% 178.99/28.73  |   (59)  all_52_25 = all_6_1
% 178.99/28.73  | 
% 178.99/28.73  | COMBINE_EQS: (51), (59) imply:
% 178.99/28.73  |   (60)  all_58_12 = all_6_1
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (2), (59) imply:
% 178.99/28.73  |   (61)   ~ (all_52_9 = all_6_1)
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (56), (59) imply:
% 178.99/28.73  |   (62)   ~ (all_6_1 = e3)
% 178.99/28.73  | 
% 178.99/28.73  | BETA: splitting (24) gives:
% 178.99/28.73  | 
% 178.99/28.73  | Case 1:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (63)  all_58_0 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | COMBINE_EQS: (21), (63) imply:
% 178.99/28.73  | |   (64)  all_4_2 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (19), (64) imply:
% 178.99/28.73  | |   (65)   ~ (all_52_7 = e3)
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (9), (64) imply:
% 178.99/28.73  | |   (66)   ~ (all_52_9 = e3)
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (47), (64) imply:
% 178.99/28.73  | |   (67)   ~ (all_52_17 = e3)
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (26), (64) imply:
% 178.99/28.73  | |   (68)  op(all_4_1, e3) = all_4_0
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (17), (64) imply:
% 178.99/28.73  | |   (69)  op(e3, e3) = all_4_1
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (46), (64) imply:
% 178.99/28.73  | |   (70)  op(e3, e3) = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | GROUND_INST: instantiating (48) with e3, all_4_1, e3, e3, simplifying with
% 178.99/28.73  | |              (69), (70) gives:
% 178.99/28.73  | |   (71)  all_4_1 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (68), (71) imply:
% 178.99/28.73  | |   (72)  op(e3, e3) = all_4_0
% 178.99/28.73  | | 
% 178.99/28.73  | | GROUND_INST: instantiating (48) with e3, all_4_0, e3, e3, simplifying with
% 178.99/28.73  | |              (70), (72) gives:
% 178.99/28.73  | |   (73)  all_4_0 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (14), (73) imply:
% 178.99/28.73  | |   (74)   ~ (e3 = e2)
% 178.99/28.73  | | 
% 178.99/28.73  | | BETA: splitting (15) gives:
% 178.99/28.73  | | 
% 178.99/28.73  | | Case 1:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (75)  all_58_6 = e3
% 178.99/28.73  | | | 
% 178.99/28.73  | | | REF_CLOSE: (33), (67), (75) are inconsistent by sub-proof #981.
% 178.99/28.73  | | | 
% 178.99/28.73  | | Case 2:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (76)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.73  | | | 
% 178.99/28.73  | | | BETA: splitting (18) gives:
% 178.99/28.73  | | | 
% 178.99/28.73  | | | Case 1:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (77)  all_58_2 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REF_CLOSE: (39), (66), (77) are inconsistent by sub-proof #980.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | Case 2:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (78)   ~ (all_58_2 = e3)
% 178.99/28.73  | | | |   (79)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | BETA: splitting (34) gives:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | Case 1:
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | |   (80)  all_56_4 = e3
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | | REF_CLOSE: (12), (66), (80) are inconsistent by sub-proof #782.
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | Case 2:
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | |   (81)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | | BETA: splitting (23) gives:
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | | Case 1:
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | |   (82)  all_56_6 = e3
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | COMBINE_EQS: (52), (82) imply:
% 178.99/28.73  | | | | | |   (83)  all_52_13 = e3
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | SIMP: (83) implies:
% 178.99/28.73  | | | | | |   (84)  all_52_13 = e3
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | REDUCE: (29), (84) imply:
% 178.99/28.73  | | | | | |   (85)   ~ (all_14_2 = e3)
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | SIMP: (85) implies:
% 178.99/28.73  | | | | | |   (86)   ~ (all_14_2 = e3)
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | REDUCE: (6), (84) imply:
% 178.99/28.73  | | | | | |   (87)  op(e1, e3) = e1
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | BETA: splitting (76) gives:
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | Case 1:
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | |   (88)  all_58_7 = e3
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | COMBINE_EQS: (11), (88) imply:
% 178.99/28.73  | | | | | | |   (89)  all_52_19 = e3
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | REDUCE: (37), (89) imply:
% 178.99/28.73  | | | | | | |   (90)   ~ (all_52_3 = e3)
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | REDUCE: (35), (89) imply:
% 178.99/28.73  | | | | | | |   (91)  op(e2, e3) = all_52_18
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | GROUND_INST: instantiating (48) with all_52_17, e1, e3, e1,
% 178.99/28.73  | | | | | | |              simplifying with (43), (87) gives:
% 178.99/28.73  | | | | | | |   (92)  all_52_17 = e1
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | GROUND_INST: instantiating (48) with all_52_9, all_52_18, e3, e2,
% 178.99/28.73  | | | | | | |              simplifying with (53), (91) gives:
% 178.99/28.73  | | | | | | |   (93)  all_52_9 = all_52_18
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | COMBINE_EQS: (12), (93) imply:
% 178.99/28.73  | | | | | | |   (94)  all_56_4 = all_52_18
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | COMBINE_EQS: (33), (92) imply:
% 178.99/28.73  | | | | | | |   (95)  all_58_6 = e1
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | COMBINE_EQS: (39), (93) imply:
% 178.99/28.73  | | | | | | |   (96)  all_58_2 = all_52_18
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | REDUCE: (32), (92), (93) imply:
% 178.99/28.73  | | | | | | |   (97)   ~ (all_52_18 = e1)
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | REDUCE: (61), (93) imply:
% 178.99/28.73  | | | | | | |   (98)   ~ (all_52_18 = all_6_1)
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | REDUCE: (30), (93) imply:
% 178.99/28.73  | | | | | | |   (99)  op(e3, all_52_18) = e3
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | REF_CLOSE: (1), (7), (40), (42), (44), (48), (60), (63), (65),
% 178.99/28.73  | | | | | | |            (74), (81), (90), (94), (95), (96), (97), (98), (99)
% 178.99/28.73  | | | | | | |            are inconsistent by sub-proof #778.
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | Case 2:
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | |   (100)  all_58_8 = e3 | all_58_11 = e3
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | | REF_CLOSE: (25), (36), (55), (86), (100) are inconsistent by
% 178.99/28.73  | | | | | | |            sub-proof #997.
% 178.99/28.73  | | | | | | | 
% 178.99/28.73  | | | | | | End of split
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | Case 2:
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | |   (101)   ~ (all_56_6 = e3)
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | REDUCE: (52), (101) imply:
% 178.99/28.73  | | | | | |   (102)   ~ (all_52_13 = e3)
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | | REF_CLOSE: (1), (4), (5), (8), (10), (30), (45), (48), (53), (54),
% 178.99/28.73  | | | | | |            (79), (102) are inconsistent by sub-proof #777.
% 178.99/28.73  | | | | | | 
% 178.99/28.73  | | | | | End of split
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | End of split
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | End of split
% 178.99/28.73  | | | 
% 178.99/28.73  | | End of split
% 178.99/28.73  | | 
% 178.99/28.73  | Case 2:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (103)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (11), (16), (18), (20), (22),
% 178.99/28.73  | |            (30), (31), (33), (39), (43), (45), (46), (48), (50), (53), (54),
% 178.99/28.73  | |            (57), (60), (62), (103) are inconsistent by sub-proof #774.
% 178.99/28.73  | | 
% 178.99/28.73  | End of split
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #774 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  op(e3, e2) = all_52_3
% 178.99/28.73    (2)   ~ (all_52_27 = e3)
% 178.99/28.73    (3)  all_58_12 = all_6_1
% 178.99/28.73    (4)   ~ (all_52_3 = all_10_2)
% 178.99/28.73    (5)  all_58_5 = all_52_13
% 178.99/28.73    (6)  op(e1, all_52_13) = e1
% 178.99/28.73    (7)  all_58_3 = all_10_2
% 178.99/28.73    (8)   ~ (all_52_9 = all_4_2)
% 178.99/28.73    (9)  all_58_10 = all_52_15
% 178.99/28.73    (10)  all_58_7 = all_52_19
% 178.99/28.73    (11)   ~ (e3 = e1)
% 178.99/28.73    (12)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73    (13)  all_58_1 = all_52_3
% 178.99/28.73    (14)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.73    (15)   ~ (all_6_1 = e3)
% 178.99/28.73    (16)  op(e3, all_52_9) = e3
% 178.99/28.73    (17)   ~ (all_52_15 = e3)
% 178.99/28.73    (18)  all_58_13 = all_52_27
% 178.99/28.73    (19)  all_58_6 = all_52_17
% 178.99/28.73    (20)  all_58_2 = all_52_9
% 178.99/28.73    (21)  op(e1, e3) = all_52_17
% 178.99/28.73    (22)  op(e2, all_10_2) = e2
% 178.99/28.73    (23)  op(e3, e3) = all_4_2
% 178.99/28.73    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.73    (25)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.73    (26)   ~ (all_52_17 = all_52_19)
% 178.99/28.73    (27)  op(e2, e3) = all_52_9
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | BETA: splitting (12) gives:
% 178.99/28.73  | 
% 178.99/28.73  | Case 1:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (28)  all_58_2 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | COMBINE_EQS: (20), (28) imply:
% 178.99/28.73  | |   (29)  all_52_9 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REF_CLOSE: (8), (16), (23), (24), (29) are inconsistent by sub-proof #967.
% 178.99/28.73  | | 
% 178.99/28.73  | Case 2:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (30)   ~ (all_58_2 = e3)
% 178.99/28.73  | |   (31)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (20), (30) imply:
% 178.99/28.73  | |   (32)   ~ (all_52_9 = e3)
% 178.99/28.73  | | 
% 178.99/28.73  | | BETA: splitting (25) gives:
% 178.99/28.73  | | 
% 178.99/28.73  | | Case 1:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (33)  all_58_2 = e3
% 178.99/28.73  | | | 
% 178.99/28.73  | | | REF_CLOSE: (20), (32), (33) are inconsistent by sub-proof #980.
% 178.99/28.73  | | | 
% 178.99/28.73  | | Case 2:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (34)  all_58_6 = e3 | all_58_12 = e3
% 178.99/28.73  | | | 
% 178.99/28.73  | | | BETA: splitting (34) gives:
% 178.99/28.73  | | | 
% 178.99/28.73  | | | Case 1:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (35)  all_58_6 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | COMBINE_EQS: (19), (35) imply:
% 178.99/28.73  | | | |   (36)  all_52_17 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | SIMP: (36) implies:
% 178.99/28.73  | | | |   (37)  all_52_17 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REDUCE: (26), (37) imply:
% 178.99/28.73  | | | |   (38)   ~ (all_52_19 = e3)
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | SIMP: (38) implies:
% 178.99/28.73  | | | |   (39)   ~ (all_52_19 = e3)
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REDUCE: (21), (37) imply:
% 178.99/28.73  | | | |   (40)  op(e1, e3) = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 178.99/28.73  | | | |            (16), (17), (18), (22), (24), (27), (31), (39), (40) are
% 178.99/28.73  | | | |            inconsistent by sub-proof #775.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | Case 2:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (41)  all_58_12 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | COMBINE_EQS: (3), (41) imply:
% 178.99/28.73  | | | |   (42)  all_6_1 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | SIMP: (42) implies:
% 178.99/28.73  | | | |   (43)  all_6_1 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REDUCE: (15), (43) imply:
% 178.99/28.73  | | | |   (44)  $false
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | CLOSE: (44) is inconsistent.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | End of split
% 178.99/28.73  | | | 
% 178.99/28.73  | | End of split
% 178.99/28.73  | | 
% 178.99/28.73  | End of split
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #775 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  op(e1, e3) = e3
% 178.99/28.73    (2)  op(e3, e2) = all_52_3
% 178.99/28.73    (3)   ~ (all_52_27 = e3)
% 178.99/28.73    (4)   ~ (all_52_3 = all_10_2)
% 178.99/28.73    (5)  all_58_5 = all_52_13
% 178.99/28.73    (6)  op(e1, all_52_13) = e1
% 178.99/28.73    (7)  all_58_3 = all_10_2
% 178.99/28.73    (8)  all_58_10 = all_52_15
% 178.99/28.73    (9)  all_58_7 = all_52_19
% 178.99/28.73    (10)   ~ (e3 = e1)
% 178.99/28.73    (11)  all_58_1 = all_52_3
% 178.99/28.73    (12)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.73    (13)  op(e3, all_52_9) = e3
% 178.99/28.73    (14)   ~ (all_52_15 = e3)
% 178.99/28.73    (15)  all_58_13 = all_52_27
% 178.99/28.73    (16)   ~ (all_52_19 = e3)
% 178.99/28.73    (17)  op(e2, all_10_2) = e2
% 178.99/28.73    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.73    (19)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73    (20)  op(e2, e3) = all_52_9
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | BETA: splitting (12) gives:
% 178.99/28.73  | 
% 178.99/28.73  | Case 1:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (21)  all_58_1 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | COMBINE_EQS: (11), (21) imply:
% 178.99/28.73  | |   (22)  all_52_3 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (4), (22) imply:
% 178.99/28.73  | |   (23)   ~ (all_10_2 = e3)
% 178.99/28.73  | | 
% 178.99/28.73  | | SIMP: (23) implies:
% 178.99/28.73  | |   (24)   ~ (all_10_2 = e3)
% 178.99/28.73  | | 
% 178.99/28.73  | | BETA: splitting (19) gives:
% 178.99/28.73  | | 
% 178.99/28.73  | | Case 1:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (25)  all_58_3 = e3
% 178.99/28.73  | | | 
% 178.99/28.73  | | | COMBINE_EQS: (7), (25) imply:
% 178.99/28.73  | | |   (26)  all_10_2 = e3
% 178.99/28.73  | | | 
% 178.99/28.73  | | | REDUCE: (24), (26) imply:
% 178.99/28.73  | | |   (27)  $false
% 178.99/28.73  | | | 
% 178.99/28.73  | | | CLOSE: (27) is inconsistent.
% 178.99/28.73  | | | 
% 178.99/28.73  | | Case 2:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (28)  all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73  | | | 
% 178.99/28.73  | | | BETA: splitting (28) gives:
% 178.99/28.73  | | | 
% 178.99/28.73  | | | Case 1:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (29)  all_58_5 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REF_CLOSE: (1), (5), (6), (10), (18), (29) are inconsistent by sub-proof
% 178.99/28.73  | | | |            #776.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | Case 2:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (30)  all_58_10 = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REF_CLOSE: (8), (14), (30) are inconsistent by sub-proof #1018.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | End of split
% 178.99/28.73  | | | 
% 178.99/28.73  | | End of split
% 178.99/28.73  | | 
% 178.99/28.73  | Case 2:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (31)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REF_CLOSE: (2), (3), (4), (7), (9), (13), (15), (16), (17), (18), (20), (31)
% 178.99/28.73  | |            are inconsistent by sub-proof #975.
% 178.99/28.73  | | 
% 178.99/28.73  | End of split
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #776 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  op(e1, e3) = e3
% 178.99/28.73    (2)  all_58_5 = all_52_13
% 178.99/28.73    (3)  op(e1, all_52_13) = e1
% 178.99/28.73    (4)   ~ (e3 = e1)
% 178.99/28.73    (5)  all_58_5 = e3
% 178.99/28.73    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | COMBINE_EQS: (2), (5) imply:
% 178.99/28.73  |   (7)  all_52_13 = e3
% 178.99/28.73  | 
% 178.99/28.73  | SIMP: (7) implies:
% 178.99/28.73  |   (8)  all_52_13 = e3
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (8) imply:
% 178.99/28.73  |   (9)  op(e1, e3) = e1
% 178.99/28.73  | 
% 178.99/28.73  | GROUND_INST: instantiating (6) with e1, e3, e3, e1, simplifying with (1), (9)
% 178.99/28.73  |              gives:
% 178.99/28.73  |   (10)  e3 = e1
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (4), (10) imply:
% 178.99/28.73  |   (11)  $false
% 178.99/28.73  | 
% 178.99/28.73  | CLOSE: (11) is inconsistent.
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #777 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  op(e3, e2) = all_52_3
% 178.99/28.73    (2)   ~ (all_52_3 = all_10_2)
% 178.99/28.73    (3)  all_58_5 = all_52_13
% 178.99/28.73    (4)  all_58_3 = all_10_2
% 178.99/28.73    (5)  all_58_10 = all_52_15
% 178.99/28.73    (6)  op(e3, all_52_9) = e3
% 178.99/28.73    (7)   ~ (all_52_13 = e3)
% 178.99/28.73    (8)   ~ (all_52_15 = e3)
% 178.99/28.73    (9)  op(e2, all_10_2) = e2
% 178.99/28.73    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.73    (11)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73    (12)  op(e2, e3) = all_52_9
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | BETA: splitting (11) gives:
% 178.99/28.73  | 
% 178.99/28.73  | Case 1:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (13)  all_58_3 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | COMBINE_EQS: (4), (13) imply:
% 178.99/28.73  | |   (14)  all_10_2 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REF_CLOSE: (1), (2), (6), (9), (10), (12), (14) are inconsistent by
% 178.99/28.73  | |            sub-proof #977.
% 178.99/28.73  | | 
% 178.99/28.73  | Case 2:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (15)  all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73  | | 
% 178.99/28.73  | | REF_CLOSE: (3), (5), (7), (8), (15) are inconsistent by sub-proof #958.
% 178.99/28.73  | | 
% 178.99/28.73  | End of split
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #778 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)   ~ (all_52_18 = e1)
% 178.99/28.73    (2)  all_58_2 = all_52_18
% 178.99/28.73    (3)  op(e3, e2) = all_52_3
% 178.99/28.73    (4)  all_58_12 = all_6_1
% 178.99/28.73    (5)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.73    (6)  all_56_4 = all_52_18
% 178.99/28.73    (7)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.73    (8)  all_58_6 = e1
% 178.99/28.73    (9)   ~ (all_52_18 = all_6_1)
% 178.99/28.73    (10)   ~ (all_52_3 = e3)
% 178.99/28.73    (11)   ~ (e2 = e1)
% 178.99/28.73    (12)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.73    (13)  op(e3, e0) = all_52_7
% 178.99/28.73    (14)  op(e3, all_52_18) = e3
% 178.99/28.73    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.73    (16)   ~ (all_52_7 = e3)
% 178.99/28.73    (17)   ~ (e3 = e2)
% 178.99/28.73    (18)  all_58_0 = e3
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | BETA: splitting (12) gives:
% 178.99/28.73  | 
% 178.99/28.73  | Case 1:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (19)  all_58_12 = e2
% 178.99/28.73  | | 
% 178.99/28.73  | | COMBINE_EQS: (4), (19) imply:
% 178.99/28.73  | |   (20)  all_6_1 = e2
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (9), (20) imply:
% 178.99/28.73  | |   (21)   ~ (all_52_18 = e2)
% 178.99/28.73  | | 
% 178.99/28.73  | | BETA: splitting (7) gives:
% 178.99/28.73  | | 
% 178.99/28.73  | | Case 1:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (22)  all_56_4 = e2
% 178.99/28.73  | | | 
% 178.99/28.73  | | | REF_CLOSE: (6), (21), (22) are inconsistent by sub-proof #781.
% 178.99/28.73  | | | 
% 178.99/28.73  | | Case 2:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (23)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.73  | | | 
% 178.99/28.73  | | | BETA: splitting (23) gives:
% 178.99/28.73  | | | 
% 178.99/28.73  | | | Case 1:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (24)  all_56_4 = e1
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REF_CLOSE: (1), (6), (24) are inconsistent by sub-proof #780.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | Case 2:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (25)  all_56_4 = e0
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | COMBINE_EQS: (6), (25) imply:
% 178.99/28.73  | | | |   (26)  all_52_18 = e0
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | SIMP: (26) implies:
% 178.99/28.73  | | | |   (27)  all_52_18 = e0
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REDUCE: (14), (27) imply:
% 178.99/28.73  | | | |   (28)  op(e3, e0) = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REF_CLOSE: (13), (15), (16), (28) are inconsistent by sub-proof #908.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | End of split
% 178.99/28.73  | | | 
% 178.99/28.73  | | End of split
% 178.99/28.73  | | 
% 178.99/28.73  | Case 2:
% 178.99/28.73  | | 
% 178.99/28.73  | |   (29)   ~ (all_58_12 = e2)
% 178.99/28.73  | | 
% 178.99/28.73  | | REDUCE: (4), (29) imply:
% 178.99/28.73  | |   (30)   ~ (all_6_1 = e2)
% 178.99/28.73  | | 
% 178.99/28.73  | | BETA: splitting (5) gives:
% 178.99/28.73  | | 
% 178.99/28.73  | | Case 1:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (31)  all_58_0 = e2
% 178.99/28.73  | | | 
% 178.99/28.73  | | | COMBINE_EQS: (18), (31) imply:
% 178.99/28.73  | | |   (32)  e3 = e2
% 178.99/28.73  | | | 
% 178.99/28.73  | | | REDUCE: (17), (32) imply:
% 178.99/28.73  | | |   (33)  $false
% 178.99/28.73  | | | 
% 178.99/28.73  | | | CLOSE: (33) is inconsistent.
% 178.99/28.73  | | | 
% 178.99/28.73  | | Case 2:
% 178.99/28.73  | | | 
% 178.99/28.73  | | |   (34)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.73  | | | 
% 178.99/28.73  | | | BETA: splitting (34) gives:
% 178.99/28.73  | | | 
% 178.99/28.73  | | | Case 1:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (35)  all_58_2 = e2
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | COMBINE_EQS: (2), (35) imply:
% 178.99/28.73  | | | |   (36)  all_52_18 = e2
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REDUCE: (14), (36) imply:
% 178.99/28.73  | | | |   (37)  op(e3, e2) = e3
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | REF_CLOSE: (3), (10), (15), (37) are inconsistent by sub-proof #978.
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | Case 2:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | |   (38)  all_58_6 = e2 | all_58_12 = e2
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | BETA: splitting (38) gives:
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | | Case 1:
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | |   (39)  all_58_6 = e2
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | | REF_CLOSE: (8), (11), (39) are inconsistent by sub-proof #779.
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | Case 2:
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | |   (40)  all_58_12 = e2
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | | COMBINE_EQS: (4), (40) imply:
% 178.99/28.73  | | | | |   (41)  all_6_1 = e2
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | | REDUCE: (30), (41) imply:
% 178.99/28.73  | | | | |   (42)  $false
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | | CLOSE: (42) is inconsistent.
% 178.99/28.73  | | | | | 
% 178.99/28.73  | | | | End of split
% 178.99/28.73  | | | | 
% 178.99/28.73  | | | End of split
% 178.99/28.73  | | | 
% 178.99/28.73  | | End of split
% 178.99/28.73  | | 
% 178.99/28.73  | End of split
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #779 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  all_58_6 = e2
% 178.99/28.73    (2)  all_58_6 = e1
% 178.99/28.73    (3)   ~ (e2 = e1)
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.73  |   (4)  e2 = e1
% 178.99/28.73  | 
% 178.99/28.73  | SIMP: (4) implies:
% 178.99/28.73  |   (5)  e2 = e1
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (5) imply:
% 178.99/28.73  |   (6)  $false
% 178.99/28.73  | 
% 178.99/28.73  | CLOSE: (6) is inconsistent.
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #780 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  all_56_4 = all_52_18
% 178.99/28.73    (2)  all_56_4 = e1
% 178.99/28.73    (3)   ~ (all_52_18 = e1)
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.73  |   (4)  all_52_18 = e1
% 178.99/28.73  | 
% 178.99/28.73  | SIMP: (4) implies:
% 178.99/28.73  |   (5)  all_52_18 = e1
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (5) imply:
% 178.99/28.73  |   (6)  $false
% 178.99/28.73  | 
% 178.99/28.73  | CLOSE: (6) is inconsistent.
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #781 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  all_56_4 = all_52_18
% 178.99/28.73    (2)  all_56_4 = e2
% 178.99/28.73    (3)   ~ (all_52_18 = e2)
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.73  |   (4)  all_52_18 = e2
% 178.99/28.73  | 
% 178.99/28.73  | SIMP: (4) implies:
% 178.99/28.73  |   (5)  all_52_18 = e2
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (5) imply:
% 178.99/28.73  |   (6)  $false
% 178.99/28.73  | 
% 178.99/28.73  | CLOSE: (6) is inconsistent.
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #782 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)  all_56_4 = all_52_9
% 178.99/28.73    (2)  all_56_4 = e3
% 178.99/28.73    (3)   ~ (all_52_9 = e3)
% 178.99/28.73  
% 178.99/28.73  Begin of proof
% 178.99/28.73  | 
% 178.99/28.73  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.73  |   (4)  all_52_9 = e3
% 178.99/28.73  | 
% 178.99/28.73  | SIMP: (4) implies:
% 178.99/28.73  |   (5)  all_52_9 = e3
% 178.99/28.73  | 
% 178.99/28.73  | REDUCE: (3), (5) imply:
% 178.99/28.73  |   (6)  $false
% 178.99/28.73  | 
% 178.99/28.73  | CLOSE: (6) is inconsistent.
% 178.99/28.73  | 
% 178.99/28.73  End of proof
% 178.99/28.73  
% 178.99/28.73  Sub-proof #783 shows that the following formulas are inconsistent:
% 178.99/28.73  ----------------------------------------------------------------
% 178.99/28.73    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.73    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.73    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.99/28.73    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.73    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.73    (6)   ~ (all_52_27 = all_10_2)
% 178.99/28.73    (7)  op(e2, e2) = all_10_2
% 178.99/28.73    (8)   ~ (all_52_17 = all_52_23)
% 178.99/28.73    (9)  op(e2, all_10_2) = all_10_1
% 178.99/28.73    (10)   ~ (all_52_13 = all_52_29)
% 178.99/28.73    (11)  all_56_3 = all_52_7
% 178.99/28.73    (12)  op(e3, e2) = all_52_3
% 178.99/28.73    (13)   ~ (all_52_9 = all_52_25)
% 178.99/28.73    (14)   ~ (all_52_19 = all_52_23)
% 178.99/28.73    (15)  all_56_11 = all_52_23
% 178.99/28.73    (16)  op(e1, e2) = all_52_19
% 178.99/28.73    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.73    (18)   ~ (all_14_1 = e2)
% 178.99/28.73    (19)   ~ (all_52_3 = all_10_2)
% 178.99/28.73    (20)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.99/28.73    (21)  all_58_5 = all_52_13
% 178.99/28.73    (22)   ~ (all_6_2 = e0)
% 178.99/28.73    (23)   ~ (all_52_25 = all_52_29)
% 178.99/28.73    (24)  all_56_15 = all_6_2
% 178.99/28.73    (25)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.73    (26)  op(e2, e0) = all_52_15
% 178.99/28.73    (27)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.73    (28)  all_58_3 = all_10_2
% 178.99/28.73    (29)  all_56_9 = all_52_19
% 178.99/28.73    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.73    (31)  all_58_15 = all_6_2
% 178.99/28.73    (32)   ~ (all_52_9 = all_4_2)
% 178.99/28.73    (33)   ~ (all_52_5 = all_52_7)
% 178.99/28.73    (34)  all_58_10 = all_52_15
% 178.99/28.73    (35)   ~ (all_52_5 = all_4_2)
% 178.99/28.73    (36)  all_58_7 = all_52_19
% 178.99/28.73    (37)  all_56_4 = all_52_9
% 178.99/28.73    (38)   ~ (all_52_15 = all_6_2)
% 178.99/28.73    (39)   ~ (all_52_17 = all_52_25)
% 178.99/28.73    (40)  op(e0, e1) = all_52_29
% 178.99/28.73    (41)   ~ (all_4_0 = e2)
% 178.99/28.73    (42)  all_58_4 = all_52_5
% 178.99/28.73    (43)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.73    (44)   ~ (all_52_27 = all_52_29)
% 178.99/28.73    (45)   ~ (all_52_17 = all_14_2)
% 178.99/28.73    (46)  op(e3, all_4_2) = all_4_1
% 178.99/28.73    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.73    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.73    (49)   ~ (all_52_7 = all_4_2)
% 178.99/28.73    (50)  all_58_1 = all_52_3
% 178.99/28.73    (51)   ~ (all_52_13 = all_52_15)
% 178.99/28.73    (52)  all_58_0 = all_4_2
% 178.99/28.73    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.73    (54)  op(e0, e0) = all_6_2
% 178.99/28.73    (55)  op(e1, all_52_29) = all_52_28
% 178.99/28.73    (56)  op(e1, all_52_5) = all_52_4
% 178.99/28.73    (57)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.73    (58)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.73    (59)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.73    (60)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.73    (61)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.73    (62)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.73    (63)  all_58_14 = all_52_29
% 178.99/28.73    (64)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.73    (65)   ~ (all_52_3 = all_52_5)
% 178.99/28.73    (66)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.73    (67)  op(e2, e1) = all_52_13
% 178.99/28.73    (68)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.99/28.73    (69)  all_58_8 = all_14_2
% 178.99/28.73    (70)  all_56_1 = all_52_3
% 178.99/28.73    (71)  op(e0, e2) = all_52_27
% 178.99/28.73    (72)  all_56_14 = all_52_29
% 178.99/28.73    (73)  op(all_4_1, all_4_2) = all_4_0
% 178.99/28.73    (74)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.73    (75)   ~ (all_52_5 = all_14_2)
% 178.99/28.73    (76)   ~ (all_52_3 = all_52_27)
% 178.99/28.73    (77)   ~ (all_52_3 = all_4_2)
% 178.99/28.73    (78)  op(all_6_1, all_6_2) = all_6_0
% 178.99/28.73    (79)  op(e0, e3) = all_52_25
% 178.99/28.73    (80)  op(e0, all_6_2) = all_6_1
% 178.99/28.73    (81)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.99/28.73    (82)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.99/28.73    (83)   ~ (all_52_13 = all_14_2)
% 178.99/28.73    (84)   ~ (e3 = e0)
% 178.99/28.73    (85)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.73    (86)   ~ (all_52_9 = all_52_13)
% 178.99/28.73    (87)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.99/28.73    (88)  op(e0, all_52_23) = all_52_22
% 178.99/28.73    (89)   ~ (all_52_15 = all_52_23)
% 178.99/28.73    (90)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.73    (91)   ~ (all_52_5 = all_52_29)
% 178.99/28.73    (92)  all_56_2 = all_52_5
% 178.99/28.73    (93)  op(e1, e0) = all_52_23
% 178.99/28.74    (94)  all_56_12 = all_52_25
% 178.99/28.74    (95)  all_58_13 = all_52_27
% 178.99/28.74    (96)  op(e2, all_52_3) = all_52_2
% 178.99/28.74    (97)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.74    (98)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.74    (99)   ~ (all_52_9 = all_52_17)
% 178.99/28.74    (100)  all_58_6 = all_52_17
% 178.99/28.74    (101)   ~ (all_52_3 = all_52_7)
% 178.99/28.74    (102)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.74    (103)   ~ (e1 = e0)
% 178.99/28.74    (104)  all_56_0 = all_4_2
% 178.99/28.74    (105)  all_58_11 = all_52_23
% 178.99/28.74    (106)   ~ (all_52_3 = all_52_19)
% 178.99/28.74    (107)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.74    (108)   ~ (all_52_7 = all_52_15)
% 178.99/28.74    (109)  op(e0, all_52_15) = all_52_14
% 178.99/28.74    (110)  all_52_4 = e1
% 178.99/28.74    (111)   ~ (all_52_29 = all_14_2)
% 178.99/28.74    (112)   ~ (all_4_0 = e1)
% 178.99/28.74    (113)   ~ (all_52_23 = all_6_2)
% 178.99/28.74    (114)   ~ (all_52_29 = all_6_2)
% 178.99/28.74    (115)  all_58_2 = all_52_9
% 178.99/28.74    (116)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.99/28.74    (117)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.74    (118)  op(e3, e1) = all_52_5
% 178.99/28.74    (119)   ~ (e2 = e1)
% 178.99/28.74    (120)  all_56_10 = all_14_2
% 178.99/28.74    (121)   ~ (all_52_25 = all_6_2)
% 178.99/28.74    (122)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.74    (123)  op(e1, e1) = all_14_2
% 178.99/28.74    (124)  op(e1, e3) = all_52_17
% 178.99/28.74    (125)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.99/28.74    (126)   ~ (all_52_25 = all_4_2)
% 178.99/28.74    (127)  op(e3, e0) = all_52_7
% 178.99/28.74    (128)  all_56_8 = all_52_17
% 178.99/28.74    (129)   ~ (all_52_17 = all_4_2)
% 178.99/28.74    (130)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.74             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.74    (131)   ~ (all_52_25 = all_52_27)
% 178.99/28.74    (132)   ~ (all_52_27 = all_6_2)
% 178.99/28.74    (133)   ~ (all_52_7 = all_6_2)
% 178.99/28.74    (134)   ~ (all_52_19 = all_52_27)
% 178.99/28.74    (135)  all_56_7 = all_52_15
% 178.99/28.74    (136)   ~ (all_52_7 = all_52_23)
% 178.99/28.74    (137)   ~ (all_52_13 = all_10_2)
% 178.99/28.74    (138)   ~ (all_6_0 = e1)
% 178.99/28.74    (139)  op(e2, all_52_27) = all_52_26
% 178.99/28.74    (140)  all_52_6 = e0
% 178.99/28.74    (141)   ~ (all_52_17 = all_52_19)
% 178.99/28.74    (142)  all_52_2 = e2
% 178.99/28.74    (143)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.74    (144)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.74    (145)  all_4_1 = e3
% 178.99/28.74    (146)  op(e1, all_14_2) = all_14_1
% 178.99/28.74    (147)  all_58_9 = all_52_7
% 178.99/28.74    (148)  all_58_12 = all_52_25
% 178.99/28.74    (149)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.74    (150)   ~ (all_52_9 = all_52_15)
% 178.99/28.74    (151)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.74    (152)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.74    (153)   ~ (all_52_19 = all_14_2)
% 178.99/28.74    (154)  op(e0, all_52_7) = all_52_6
% 178.99/28.74    (155)  op(e2, e3) = all_52_9
% 178.99/28.74    (156)  all_56_13 = all_52_27
% 178.99/28.74  
% 178.99/28.74  Begin of proof
% 178.99/28.74  | 
% 178.99/28.74  | REDUCE: (73), (145) imply:
% 178.99/28.74  |   (157)  op(e3, all_4_2) = all_4_0
% 178.99/28.74  | 
% 178.99/28.74  | REDUCE: (46), (145) imply:
% 178.99/28.74  |   (158)  op(e3, all_4_2) = e3
% 178.99/28.74  | 
% 178.99/28.74  | REDUCE: (96), (142) imply:
% 178.99/28.74  |   (159)  op(e2, all_52_3) = e2
% 178.99/28.74  | 
% 178.99/28.74  | REDUCE: (56), (110) imply:
% 178.99/28.74  |   (160)  op(e1, all_52_5) = e1
% 178.99/28.74  | 
% 178.99/28.74  | REDUCE: (140), (154) imply:
% 178.99/28.74  |   (161)  op(e0, all_52_7) = e0
% 178.99/28.74  | 
% 178.99/28.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.99/28.74  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 178.99/28.74  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 178.99/28.74  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 178.99/28.74  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (57), (58),
% 178.99/28.74  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 178.99/28.74  |            (70), (71), (72), (74), (75), (76), (77), (78), (79), (80), (81),
% 178.99/28.74  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 178.99/28.74  |            (93), (94), (95), (97), (98), (99), (100), (101), (102), (103),
% 178.99/28.74  |            (104), (105), (106), (107), (108), (109), (111), (112), (113),
% 178.99/28.74  |            (114), (115), (116), (117), (118), (119), (120), (121), (122),
% 178.99/28.74  |            (123), (124), (125), (126), (127), (128), (129), (130), (131),
% 178.99/28.74  |            (132), (133), (134), (135), (136), (137), (138), (139), (141),
% 178.99/28.74  |            (143), (144), (146), (147), (148), (149), (150), (151), (152),
% 178.99/28.74  |            (153), (155), (156), (157), (158), (159), (160), (161) are
% 178.99/28.74  |            inconsistent by sub-proof #784.
% 178.99/28.74  | 
% 178.99/28.74  End of proof
% 178.99/28.74  
% 178.99/28.74  Sub-proof #784 shows that the following formulas are inconsistent:
% 178.99/28.74  ----------------------------------------------------------------
% 178.99/28.74    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.74    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.74    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.99/28.74    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.74    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.74    (6)   ~ (all_52_27 = all_10_2)
% 178.99/28.74    (7)  op(e2, e2) = all_10_2
% 178.99/28.74    (8)   ~ (all_52_17 = all_52_23)
% 178.99/28.74    (9)  op(e2, all_52_3) = e2
% 178.99/28.74    (10)  op(e2, all_10_2) = all_10_1
% 178.99/28.74    (11)   ~ (all_52_13 = all_52_29)
% 178.99/28.74    (12)  all_56_3 = all_52_7
% 178.99/28.74    (13)  op(e3, e2) = all_52_3
% 178.99/28.74    (14)   ~ (all_52_9 = all_52_25)
% 178.99/28.74    (15)   ~ (all_52_19 = all_52_23)
% 178.99/28.74    (16)  all_56_11 = all_52_23
% 178.99/28.74    (17)  op(e1, e2) = all_52_19
% 178.99/28.74    (18)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.74    (19)   ~ (all_14_1 = e2)
% 178.99/28.74    (20)   ~ (all_52_3 = all_10_2)
% 178.99/28.74    (21)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.99/28.74    (22)  all_58_5 = all_52_13
% 178.99/28.74    (23)   ~ (all_6_2 = e0)
% 178.99/28.74    (24)   ~ (all_52_25 = all_52_29)
% 178.99/28.74    (25)  all_56_15 = all_6_2
% 178.99/28.74    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.74    (27)  op(e2, e0) = all_52_15
% 178.99/28.74    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.74    (29)  all_58_3 = all_10_2
% 178.99/28.74    (30)  all_56_9 = all_52_19
% 178.99/28.74    (31)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.74    (32)  all_58_15 = all_6_2
% 178.99/28.74    (33)   ~ (all_52_9 = all_4_2)
% 178.99/28.74    (34)   ~ (all_52_5 = all_52_7)
% 178.99/28.74    (35)  all_58_10 = all_52_15
% 178.99/28.74    (36)   ~ (all_52_5 = all_4_2)
% 178.99/28.74    (37)  all_58_7 = all_52_19
% 178.99/28.74    (38)  all_56_4 = all_52_9
% 178.99/28.74    (39)   ~ (all_52_15 = all_6_2)
% 178.99/28.74    (40)   ~ (all_52_17 = all_52_25)
% 178.99/28.74    (41)  op(e0, e1) = all_52_29
% 178.99/28.74    (42)   ~ (all_4_0 = e2)
% 178.99/28.74    (43)  all_58_4 = all_52_5
% 178.99/28.74    (44)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.74    (45)   ~ (all_52_27 = all_52_29)
% 178.99/28.74    (46)   ~ (all_52_17 = all_14_2)
% 178.99/28.74    (47)  all_56_15 = e3 | all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.74    (48)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.74    (49)   ~ (all_52_7 = all_4_2)
% 178.99/28.74    (50)  all_58_1 = all_52_3
% 178.99/28.74    (51)   ~ (all_52_13 = all_52_15)
% 178.99/28.74    (52)  all_58_0 = all_4_2
% 178.99/28.74    (53)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.74    (54)  op(e0, e0) = all_6_2
% 178.99/28.74    (55)  op(e1, all_52_29) = all_52_28
% 178.99/28.74    (56)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.74    (57)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 178.99/28.74    (58)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.74    (59)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.74    (60)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.74    (61)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.74    (62)  all_58_14 = all_52_29
% 178.99/28.74    (63)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.74    (64)   ~ (all_52_3 = all_52_5)
% 178.99/28.74    (65)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.74    (66)  op(e2, e1) = all_52_13
% 178.99/28.74    (67)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.99/28.74    (68)  all_58_8 = all_14_2
% 178.99/28.74    (69)  all_56_1 = all_52_3
% 178.99/28.74    (70)  op(e0, e2) = all_52_27
% 178.99/28.74    (71)  all_56_14 = all_52_29
% 178.99/28.74    (72)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.74    (73)   ~ (all_52_5 = all_14_2)
% 178.99/28.74    (74)   ~ (all_52_3 = all_52_27)
% 178.99/28.74    (75)   ~ (all_52_3 = all_4_2)
% 178.99/28.74    (76)  op(all_6_1, all_6_2) = all_6_0
% 178.99/28.74    (77)  op(e3, all_4_2) = e3
% 178.99/28.74    (78)  op(e0, e3) = all_52_25
% 178.99/28.74    (79)  op(e0, all_6_2) = all_6_1
% 178.99/28.74    (80)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.99/28.74    (81)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.99/28.74    (82)   ~ (all_52_13 = all_14_2)
% 178.99/28.74    (83)   ~ (e3 = e0)
% 178.99/28.74    (84)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.74    (85)   ~ (all_52_9 = all_52_13)
% 178.99/28.74    (86)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.99/28.74    (87)  op(e0, all_52_23) = all_52_22
% 178.99/28.74    (88)   ~ (all_52_15 = all_52_23)
% 178.99/28.74    (89)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.74    (90)   ~ (all_52_5 = all_52_29)
% 178.99/28.74    (91)  all_56_2 = all_52_5
% 178.99/28.74    (92)  op(e1, e0) = all_52_23
% 178.99/28.74    (93)  all_56_12 = all_52_25
% 178.99/28.74    (94)  all_58_13 = all_52_27
% 178.99/28.74    (95)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.74    (96)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.74    (97)   ~ (all_52_9 = all_52_17)
% 178.99/28.74    (98)  all_58_6 = all_52_17
% 178.99/28.74    (99)   ~ (all_52_3 = all_52_7)
% 178.99/28.74    (100)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.74    (101)   ~ (e1 = e0)
% 178.99/28.74    (102)  all_56_0 = all_4_2
% 178.99/28.74    (103)  all_58_11 = all_52_23
% 178.99/28.74    (104)   ~ (all_52_3 = all_52_19)
% 178.99/28.74    (105)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.74    (106)   ~ (all_52_7 = all_52_15)
% 178.99/28.74    (107)  op(e0, all_52_15) = all_52_14
% 178.99/28.74    (108)   ~ (all_52_29 = all_14_2)
% 178.99/28.74    (109)   ~ (all_4_0 = e1)
% 178.99/28.74    (110)   ~ (all_52_23 = all_6_2)
% 178.99/28.74    (111)   ~ (all_52_29 = all_6_2)
% 178.99/28.74    (112)  all_58_2 = all_52_9
% 178.99/28.74    (113)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.99/28.74    (114)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.74    (115)  op(e3, e1) = all_52_5
% 178.99/28.74    (116)   ~ (e2 = e1)
% 178.99/28.74    (117)  all_56_10 = all_14_2
% 178.99/28.74    (118)   ~ (all_52_25 = all_6_2)
% 178.99/28.74    (119)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.74    (120)  op(e1, e1) = all_14_2
% 178.99/28.74    (121)  op(e1, e3) = all_52_17
% 178.99/28.74    (122)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.99/28.74    (123)   ~ (all_52_25 = all_4_2)
% 178.99/28.74    (124)  op(e3, e0) = all_52_7
% 178.99/28.74    (125)  all_56_8 = all_52_17
% 178.99/28.74    (126)   ~ (all_52_17 = all_4_2)
% 178.99/28.74    (127)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.74             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.74    (128)   ~ (all_52_25 = all_52_27)
% 178.99/28.74    (129)   ~ (all_52_27 = all_6_2)
% 178.99/28.74    (130)   ~ (all_52_7 = all_6_2)
% 178.99/28.74    (131)   ~ (all_52_19 = all_52_27)
% 178.99/28.74    (132)  all_56_7 = all_52_15
% 178.99/28.74    (133)  op(e1, all_52_5) = e1
% 178.99/28.74    (134)   ~ (all_52_7 = all_52_23)
% 178.99/28.74    (135)   ~ (all_52_13 = all_10_2)
% 178.99/28.74    (136)   ~ (all_6_0 = e1)
% 178.99/28.74    (137)  op(e3, all_4_2) = all_4_0
% 178.99/28.74    (138)  op(e0, all_52_7) = e0
% 178.99/28.74    (139)  op(e2, all_52_27) = all_52_26
% 178.99/28.74    (140)   ~ (all_52_17 = all_52_19)
% 178.99/28.74    (141)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.74    (142)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.74    (143)  op(e1, all_14_2) = all_14_1
% 178.99/28.74    (144)  all_58_9 = all_52_7
% 178.99/28.74    (145)  all_58_12 = all_52_25
% 178.99/28.74    (146)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.74    (147)   ~ (all_52_9 = all_52_15)
% 178.99/28.74    (148)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.74    (149)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.74    (150)   ~ (all_52_19 = all_14_2)
% 178.99/28.74    (151)  op(e2, e3) = all_52_9
% 178.99/28.74    (152)  all_56_13 = all_52_27
% 178.99/28.74  
% 178.99/28.74  Begin of proof
% 178.99/28.74  | 
% 178.99/28.74  | GROUND_INST: instantiating (127) with e3, all_4_0, all_4_2, e3, simplifying
% 178.99/28.74  |              with (77), (137) gives:
% 178.99/28.74  |   (153)  all_4_0 = e3
% 178.99/28.74  | 
% 178.99/28.74  | REDUCE: (42), (153) imply:
% 178.99/28.74  |   (154)   ~ (e3 = e2)
% 178.99/28.74  | 
% 178.99/28.74  | REDUCE: (109), (153) imply:
% 178.99/28.74  |   (155)   ~ (e3 = e1)
% 178.99/28.74  | 
% 178.99/28.74  | BETA: splitting (47) gives:
% 178.99/28.74  | 
% 178.99/28.74  | Case 1:
% 178.99/28.74  | | 
% 178.99/28.74  | |   (156)  all_56_15 = e3
% 178.99/28.74  | | 
% 178.99/28.74  | | COMBINE_EQS: (25), (156) imply:
% 178.99/28.74  | |   (157)  all_6_2 = e3
% 178.99/28.74  | | 
% 178.99/28.74  | | SIMP: (157) implies:
% 178.99/28.74  | |   (158)  all_6_2 = e3
% 178.99/28.74  | | 
% 178.99/28.74  | | COMBINE_EQS: (32), (158) imply:
% 178.99/28.74  | |   (159)  all_58_15 = e3
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (130), (158) imply:
% 178.99/28.74  | |   (160)   ~ (all_52_7 = e3)
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (110), (158) imply:
% 178.99/28.74  | |   (161)   ~ (all_52_23 = e3)
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (129), (158) imply:
% 178.99/28.74  | |   (162)   ~ (all_52_27 = e3)
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (111), (158) imply:
% 178.99/28.74  | |   (163)   ~ (all_52_29 = e3)
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (76), (158) imply:
% 178.99/28.74  | |   (164)  op(all_6_1, e3) = all_6_0
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (79), (158) imply:
% 178.99/28.74  | |   (165)  op(e0, e3) = all_6_1
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (54), (158) imply:
% 178.99/28.74  | |   (166)  op(e0, e0) = e3
% 178.99/28.74  | | 
% 178.99/28.74  | | GROUND_INST: instantiating (127) with all_52_25, all_6_1, e3, e0,
% 178.99/28.74  | |              simplifying with (78), (165) gives:
% 178.99/28.74  | |   (167)  all_52_25 = all_6_1
% 178.99/28.74  | | 
% 178.99/28.74  | | COMBINE_EQS: (145), (167) imply:
% 178.99/28.74  | |   (168)  all_58_12 = all_6_1
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (40), (167) imply:
% 178.99/28.74  | |   (169)   ~ (all_52_17 = all_6_1)
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (128), (167) imply:
% 178.99/28.74  | |   (170)   ~ (all_52_27 = all_6_1)
% 178.99/28.74  | | 
% 178.99/28.74  | | SIMP: (170) implies:
% 178.99/28.74  | |   (171)   ~ (all_52_27 = all_6_1)
% 178.99/28.74  | | 
% 178.99/28.74  | | REDUCE: (24), (167) imply:
% 178.99/28.74  | |   (172)   ~ (all_52_29 = all_6_1)
% 178.99/28.74  | | 
% 178.99/28.74  | | SIMP: (172) implies:
% 178.99/28.74  | |   (173)   ~ (all_52_29 = all_6_1)
% 178.99/28.74  | | 
% 178.99/28.74  | | BETA: splitting (63) gives:
% 178.99/28.74  | | 
% 178.99/28.74  | | Case 1:
% 178.99/28.74  | | | 
% 178.99/28.74  | | |   (174)  all_56_13 = e3
% 178.99/28.74  | | | 
% 178.99/28.74  | | | REF_CLOSE: (152), (162), (174) are inconsistent by sub-proof #876.
% 178.99/28.74  | | | 
% 178.99/28.74  | | Case 2:
% 178.99/28.74  | | | 
% 178.99/28.74  | | |   (175)   ~ (all_56_13 = e3)
% 178.99/28.74  | | |   (176)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.74  | | | 
% 178.99/28.74  | | | BETA: splitting (142) gives:
% 178.99/28.74  | | | 
% 178.99/28.74  | | | Case 1:
% 178.99/28.74  | | | | 
% 178.99/28.74  | | | |   (177)  all_56_3 = e3
% 178.99/28.74  | | | | 
% 178.99/28.74  | | | | REF_CLOSE: (12), (160), (177) are inconsistent by sub-proof #1034.
% 178.99/28.74  | | | | 
% 178.99/28.74  | | | Case 2:
% 178.99/28.74  | | | | 
% 178.99/28.74  | | | |   (178)   ~ (all_56_3 = e3)
% 178.99/28.74  | | | |   (179)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.74  | | | | 
% 178.99/28.74  | | | | BETA: splitting (58) gives:
% 178.99/28.74  | | | | 
% 178.99/28.74  | | | | Case 1:
% 178.99/28.74  | | | | | 
% 178.99/28.74  | | | | |   (180)  all_56_14 = e3
% 178.99/28.74  | | | | | 
% 178.99/28.74  | | | | | REF_CLOSE: (71), (163), (180) are inconsistent by sub-proof #896.
% 178.99/28.74  | | | | | 
% 178.99/28.74  | | | | Case 2:
% 178.99/28.74  | | | | | 
% 178.99/28.74  | | | | |   (181)   ~ (all_56_14 = e3)
% 178.99/28.74  | | | | |   (182)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.74  | | | | | 
% 178.99/28.74  | | | | | BETA: splitting (57) gives:
% 178.99/28.74  | | | | | 
% 178.99/28.74  | | | | | Case 1:
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | |   (183)  all_56_9 = e3
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | COMBINE_EQS: (30), (183) imply:
% 178.99/28.74  | | | | | |   (184)  all_52_19 = e3
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | SIMP: (184) implies:
% 178.99/28.74  | | | | | |   (185)  all_52_19 = e3
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | REDUCE: (104), (185) imply:
% 178.99/28.74  | | | | | |   (186)   ~ (all_52_3 = e3)
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | REDUCE: (150), (185) imply:
% 178.99/28.74  | | | | | |   (187)   ~ (all_14_2 = e3)
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | SIMP: (187) implies:
% 178.99/28.74  | | | | | |   (188)   ~ (all_14_2 = e3)
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | REDUCE: (17), (185) imply:
% 178.99/28.74  | | | | | |   (189)  op(e1, e2) = e3
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | REF_CLOSE: (1), (2), (9), (12), (13), (22), (28), (31), (32), (33),
% 178.99/28.74  | | | | | |            (34), (35), (36), (37), (41), (43), (44), (46), (49),
% 178.99/28.74  | | | | | |            (50), (52), (56), (62), (64), (66), (68), (69), (70),
% 178.99/28.74  | | | | | |            (73), (74), (77), (78), (80), (82), (84), (89), (90),
% 178.99/28.74  | | | | | |            (91), (95), (98), (99), (102), (103), (104), (106),
% 178.99/28.74  | | | | | |            (108), (115), (117), (120), (121), (123), (124), (126),
% 178.99/28.74  | | | | | |            (127), (130), (133), (134), (138), (141), (144), (146),
% 178.99/28.74  | | | | | |            (148), (149), (151), (160), (163), (166), (179), (186),
% 178.99/28.74  | | | | | |            (188), (189) are inconsistent by sub-proof #851.
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | Case 2:
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | |   (190)   ~ (all_56_9 = e3)
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | REDUCE: (30), (190) imply:
% 178.99/28.74  | | | | | |   (191)   ~ (all_52_19 = e3)
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 178.99/28.74  | | | | | |            (13), (15), (17), (18), (19), (20), (21), (22), (26),
% 178.99/28.74  | | | | | |            (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 178.99/28.74  | | | | | |            (37), (41), (43), (44), (45), (46), (49), (50), (52),
% 178.99/28.74  | | | | | |            (56), (60), (61), (62), (64), (65), (66), (68), (69),
% 178.99/28.74  | | | | | |            (70), (71), (72), (73), (74), (75), (77), (78), (82),
% 178.99/28.74  | | | | | |            (83), (84), (85), (89), (90), (92), (94), (95), (96),
% 178.99/28.74  | | | | | |            (98), (99), (102), (103), (104), (105), (106), (108),
% 178.99/28.74  | | | | | |            (112), (113), (115), (116), (117), (119), (121), (123),
% 178.99/28.74  | | | | | |            (124), (125), (126), (127), (130), (131), (133), (134),
% 178.99/28.74  | | | | | |            (136), (138), (140), (141), (143), (144), (146), (147),
% 178.99/28.74  | | | | | |            (148), (150), (151), (152), (154), (155), (159), (161),
% 178.99/28.74  | | | | | |            (162), (163), (164), (168), (169), (171), (173), (176),
% 178.99/28.74  | | | | | |            (179), (182), (191) are inconsistent by sub-proof #829.
% 178.99/28.74  | | | | | | 
% 178.99/28.74  | | | | | End of split
% 178.99/28.74  | | | | | 
% 178.99/28.74  | | | | End of split
% 178.99/28.74  | | | | 
% 178.99/28.74  | | | End of split
% 178.99/28.74  | | | 
% 178.99/28.74  | | End of split
% 178.99/28.74  | | 
% 178.99/28.74  | Case 2:
% 178.99/28.74  | | 
% 178.99/28.74  | |   (192)   ~ (all_56_15 = e3)
% 178.99/28.74  | |   (193)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.74  | | 
% 178.99/28.74  | | REF_CLOSE: (1), (2), (8), (9), (11), (13), (14), (15), (16), (17), (18),
% 178.99/28.74  | |            (20), (22), (23), (24), (25), (26), (27), (28), (29), (31), (32),
% 178.99/28.74  | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (43), (44),
% 178.99/28.74  | |            (45), (48), (49), (50), (51), (52), (53), (55), (56), (58), (59),
% 178.99/28.74  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (71),
% 178.99/28.74  | |            (73), (74), (75), (77), (78), (81), (82), (83), (84), (85), (86),
% 178.99/28.74  | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 178.99/28.74  | |            (98), (99), (100), (101), (102), (103), (104), (105), (106),
% 178.99/28.74  | |            (107), (108), (110), (111), (112), (114), (115), (117), (118),
% 178.99/28.74  | |            (120), (121), (122), (123), (124), (126), (127), (128), (129),
% 178.99/28.74  | |            (130), (131), (132), (133), (134), (135), (138), (139), (140),
% 178.99/28.74  | |            (141), (144), (145), (146), (147), (148), (149), (150), (151),
% 178.99/28.74  | |            (152), (154), (155), (192), (193) are inconsistent by sub-proof
% 178.99/28.74  | |            #785.
% 178.99/28.74  | | 
% 178.99/28.74  | End of split
% 178.99/28.74  | 
% 178.99/28.74  End of proof
% 178.99/28.74  
% 178.99/28.74  Sub-proof #785 shows that the following formulas are inconsistent:
% 178.99/28.74  ----------------------------------------------------------------
% 178.99/28.74    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.74    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.74    (3)   ~ (all_52_17 = all_52_23)
% 178.99/28.74    (4)  op(e2, all_52_3) = e2
% 178.99/28.74    (5)   ~ (all_52_13 = all_52_29)
% 178.99/28.74    (6)  op(e3, e2) = all_52_3
% 178.99/28.74    (7)   ~ (all_52_9 = all_52_25)
% 178.99/28.74    (8)   ~ (all_52_19 = all_52_23)
% 178.99/28.74    (9)  all_56_11 = all_52_23
% 178.99/28.74    (10)  op(e1, e2) = all_52_19
% 178.99/28.74    (11)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.74    (12)   ~ (all_52_3 = all_10_2)
% 178.99/28.74    (13)   ~ (all_56_15 = e3)
% 178.99/28.74    (14)  all_58_5 = all_52_13
% 178.99/28.74    (15)   ~ (all_6_2 = e0)
% 178.99/28.74    (16)   ~ (all_52_25 = all_52_29)
% 178.99/28.74    (17)  all_56_15 = all_6_2
% 178.99/28.74    (18)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.74    (19)  op(e2, e0) = all_52_15
% 178.99/28.74    (20)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.74    (21)  all_58_3 = all_10_2
% 178.99/28.74    (22)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.74    (23)  all_58_15 = all_6_2
% 178.99/28.74    (24)   ~ (all_52_9 = all_4_2)
% 178.99/28.74    (25)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.74    (26)   ~ (all_52_5 = all_52_7)
% 178.99/28.74    (27)  all_58_10 = all_52_15
% 178.99/28.74    (28)   ~ (all_52_5 = all_4_2)
% 178.99/28.74    (29)  all_58_7 = all_52_19
% 178.99/28.74    (30)  all_56_4 = all_52_9
% 178.99/28.74    (31)   ~ (all_52_15 = all_6_2)
% 178.99/28.74    (32)   ~ (all_52_17 = all_52_25)
% 178.99/28.74    (33)  op(e0, e1) = all_52_29
% 178.99/28.74    (34)  all_58_4 = all_52_5
% 178.99/28.74    (35)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.74    (36)   ~ (e3 = e1)
% 178.99/28.74    (37)   ~ (all_52_27 = all_52_29)
% 178.99/28.74    (38)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.74    (39)   ~ (all_52_7 = all_4_2)
% 178.99/28.74    (40)  all_58_1 = all_52_3
% 178.99/28.74    (41)   ~ (all_52_13 = all_52_15)
% 178.99/28.74    (42)  all_58_0 = all_4_2
% 178.99/28.74    (43)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.74    (44)  op(e1, all_52_29) = all_52_28
% 178.99/28.74    (45)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.74    (46)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.74    (47)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.74    (48)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.74    (49)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.74    (50)  all_58_14 = all_52_29
% 178.99/28.74    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.74    (52)   ~ (all_52_3 = all_52_5)
% 178.99/28.74    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.74    (54)  op(e2, e1) = all_52_13
% 178.99/28.74    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.99/28.74    (56)  all_58_8 = all_14_2
% 178.99/28.74    (57)  all_56_1 = all_52_3
% 178.99/28.74    (58)  all_56_14 = all_52_29
% 178.99/28.74    (59)   ~ (all_52_5 = all_14_2)
% 178.99/28.74    (60)   ~ (all_52_3 = all_52_27)
% 178.99/28.74    (61)   ~ (all_52_3 = all_4_2)
% 178.99/28.74    (62)  op(e3, all_4_2) = e3
% 178.99/28.74    (63)  op(e0, e3) = all_52_25
% 178.99/28.74    (64)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.99/28.74    (65)   ~ (all_52_13 = all_14_2)
% 178.99/28.74    (66)   ~ (e3 = e0)
% 178.99/28.74    (67)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.74    (68)   ~ (all_52_9 = all_52_13)
% 178.99/28.74    (69)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.99/28.74    (70)  op(e0, all_52_23) = all_52_22
% 178.99/28.74    (71)   ~ (all_52_15 = all_52_23)
% 178.99/28.74    (72)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.74    (73)   ~ (all_52_5 = all_52_29)
% 178.99/28.74    (74)  all_56_2 = all_52_5
% 178.99/28.74    (75)  op(e1, e0) = all_52_23
% 178.99/28.74    (76)  all_56_12 = all_52_25
% 178.99/28.74    (77)  all_58_13 = all_52_27
% 178.99/28.74    (78)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.75    (79)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.75    (80)   ~ (all_52_9 = all_52_17)
% 178.99/28.75    (81)  all_58_6 = all_52_17
% 178.99/28.75    (82)   ~ (all_52_3 = all_52_7)
% 178.99/28.75    (83)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.75    (84)   ~ (e1 = e0)
% 178.99/28.75    (85)  all_56_0 = all_4_2
% 178.99/28.75    (86)  all_58_11 = all_52_23
% 178.99/28.75    (87)   ~ (all_52_3 = all_52_19)
% 178.99/28.75    (88)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.75    (89)   ~ (all_52_7 = all_52_15)
% 178.99/28.75    (90)  op(e0, all_52_15) = all_52_14
% 178.99/28.75    (91)   ~ (all_52_29 = all_14_2)
% 178.99/28.75    (92)   ~ (all_52_23 = all_6_2)
% 178.99/28.75    (93)   ~ (all_52_29 = all_6_2)
% 178.99/28.75    (94)  all_58_2 = all_52_9
% 178.99/28.75    (95)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.75    (96)  op(e3, e1) = all_52_5
% 178.99/28.75    (97)  all_56_10 = all_14_2
% 178.99/28.75    (98)   ~ (all_52_25 = all_6_2)
% 178.99/28.75    (99)  op(e1, e1) = all_14_2
% 178.99/28.75    (100)  op(e1, e3) = all_52_17
% 178.99/28.75    (101)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.99/28.75    (102)   ~ (all_52_25 = all_4_2)
% 178.99/28.75    (103)  op(e3, e0) = all_52_7
% 178.99/28.75    (104)   ~ (all_52_17 = all_4_2)
% 178.99/28.75    (105)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.75             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.75    (106)   ~ (all_52_25 = all_52_27)
% 178.99/28.75    (107)   ~ (all_52_27 = all_6_2)
% 178.99/28.75    (108)   ~ (all_52_7 = all_6_2)
% 178.99/28.75    (109)   ~ (all_52_19 = all_52_27)
% 178.99/28.75    (110)  all_56_7 = all_52_15
% 178.99/28.75    (111)  op(e1, all_52_5) = e1
% 178.99/28.75    (112)   ~ (all_52_7 = all_52_23)
% 178.99/28.75    (113)   ~ (all_52_13 = all_10_2)
% 178.99/28.75    (114)  op(e0, all_52_7) = e0
% 178.99/28.75    (115)  op(e2, all_52_27) = all_52_26
% 178.99/28.75    (116)   ~ (all_52_17 = all_52_19)
% 178.99/28.75    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.75    (118)  all_58_9 = all_52_7
% 178.99/28.75    (119)  all_58_12 = all_52_25
% 178.99/28.75    (120)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.75    (121)   ~ (all_52_9 = all_52_15)
% 178.99/28.75    (122)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.75    (123)   ~ (e3 = e2)
% 178.99/28.75    (124)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.75    (125)   ~ (all_52_19 = all_14_2)
% 178.99/28.75    (126)  op(e2, e3) = all_52_9
% 178.99/28.75    (127)  all_56_13 = all_52_27
% 178.99/28.75  
% 178.99/28.75  Begin of proof
% 178.99/28.75  | 
% 178.99/28.75  | REDUCE: (13), (17) imply:
% 178.99/28.75  |   (128)   ~ (all_6_2 = e3)
% 178.99/28.75  | 
% 178.99/28.75  | BETA: splitting (51) gives:
% 178.99/28.75  | 
% 178.99/28.75  | Case 1:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (129)  all_56_13 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | COMBINE_EQS: (127), (129) imply:
% 178.99/28.75  | |   (130)  all_52_27 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | SIMP: (130) implies:
% 178.99/28.75  | |   (131)  all_52_27 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | REDUCE: (60), (131) imply:
% 178.99/28.75  | |   (132)   ~ (all_52_3 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | REDUCE: (109), (131) imply:
% 178.99/28.75  | |   (133)   ~ (all_52_19 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | REDUCE: (106), (131) imply:
% 178.99/28.75  | |   (134)   ~ (all_52_25 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | REDUCE: (37), (131) imply:
% 178.99/28.75  | |   (135)   ~ (all_52_29 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | SIMP: (135) implies:
% 178.99/28.75  | |   (136)   ~ (all_52_29 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | REDUCE: (107), (131) imply:
% 178.99/28.75  | |   (137)   ~ (all_6_2 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | REDUCE: (115), (131) imply:
% 178.99/28.75  | |   (138)  op(e2, e3) = all_52_26
% 178.99/28.75  | | 
% 178.99/28.75  | | REF_CLOSE: (1), (3), (4), (6), (7), (10), (11), (14), (15), (16), (17),
% 178.99/28.75  | |            (18), (19), (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 178.99/28.75  | |            (32), (33), (34), (35), (36), (39), (40), (41), (42), (43), (45),
% 178.99/28.75  | |            (46), (47), (49), (50), (52), (53), (56), (57), (58), (59), (62),
% 178.99/28.75  | |            (63), (64), (65), (66), (67), (68), (69), (72), (73), (74), (75),
% 178.99/28.75  | |            (76), (78), (79), (80), (81), (82), (83), (84), (85), (86), (87),
% 178.99/28.75  | |            (88), (89), (91), (92), (93), (94), (96), (97), (98), (99),
% 178.99/28.75  | |            (100), (102), (103), (104), (105), (108), (111), (112), (114),
% 178.99/28.75  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 178.99/28.75  | |            (125), (126), (128), (132), (133), (134), (136), (138) are
% 178.99/28.75  | |            inconsistent by sub-proof #799.
% 178.99/28.75  | | 
% 178.99/28.75  | Case 2:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (139)   ~ (all_56_13 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | REDUCE: (127), (139) imply:
% 178.99/28.75  | |   (140)   ~ (all_52_27 = e3)
% 178.99/28.75  | | 
% 178.99/28.75  | | BETA: splitting (55) gives:
% 178.99/28.75  | | 
% 178.99/28.75  | | Case 1:
% 178.99/28.75  | | | 
% 178.99/28.75  | | |   (141)  all_58_12 = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (14), (16), (21), (22), (23),
% 178.99/28.75  | | |            (24), (26), (27), (29), (32), (34), (35), (39), (40), (41),
% 178.99/28.75  | | |            (42), (48), (50), (52), (56), (59), (62), (63), (66), (67),
% 178.99/28.75  | | |            (71), (77), (78), (81), (82), (85), (86), (87), (89), (95),
% 178.99/28.75  | | |            (96), (98), (100), (102), (103), (104), (105), (106), (108),
% 178.99/28.75  | | |            (111), (112), (113), (114), (117), (118), (119), (120), (122),
% 178.99/28.75  | | |            (126), (141) are inconsistent by sub-proof #797.
% 178.99/28.75  | | | 
% 178.99/28.75  | | Case 2:
% 178.99/28.75  | | | 
% 178.99/28.75  | | |   (142)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REF_CLOSE: (2), (4), (5), (6), (10), (11), (12), (14), (20), (21), (22),
% 178.99/28.75  | | |            (23), (24), (26), (27), (28), (29), (31), (33), (34), (35),
% 178.99/28.75  | | |            (36), (38), (39), (40), (41), (42), (43), (44), (47), (48),
% 178.99/28.75  | | |            (50), (52), (53), (54), (56), (59), (61), (62), (63), (66),
% 178.99/28.75  | | |            (70), (71), (73), (74), (75), (77), (78), (81), (82), (85),
% 178.99/28.75  | | |            (86), (88), (89), (90), (91), (93), (94), (96), (99), (100),
% 178.99/28.75  | | |            (101), (102), (103), (104), (105), (108), (110), (111), (112),
% 178.99/28.75  | | |            (114), (117), (118), (120), (123), (124), (126), (128), (140),
% 178.99/28.75  | | |            (142) are inconsistent by sub-proof #786.
% 178.99/28.75  | | | 
% 178.99/28.75  | | End of split
% 178.99/28.75  | | 
% 178.99/28.75  | End of split
% 178.99/28.75  | 
% 178.99/28.75  End of proof
% 178.99/28.75  
% 178.99/28.75  Sub-proof #786 shows that the following formulas are inconsistent:
% 178.99/28.75  ----------------------------------------------------------------
% 178.99/28.75    (1)   ~ (all_52_5 = all_52_13)
% 178.99/28.75    (2)  op(e2, all_52_3) = e2
% 178.99/28.75    (3)   ~ (all_52_13 = all_52_29)
% 178.99/28.75    (4)  op(e3, e2) = all_52_3
% 178.99/28.75    (5)  op(e1, e2) = all_52_19
% 178.99/28.75    (6)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.75    (7)   ~ (all_52_27 = e3)
% 178.99/28.75    (8)   ~ (all_6_2 = e3)
% 178.99/28.75    (9)   ~ (all_52_3 = all_10_2)
% 178.99/28.75    (10)  all_58_5 = all_52_13
% 178.99/28.75    (11)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.75    (12)  all_58_3 = all_10_2
% 178.99/28.75    (13)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.75    (14)  all_58_15 = all_6_2
% 178.99/28.75    (15)   ~ (all_52_9 = all_4_2)
% 178.99/28.75    (16)   ~ (all_52_5 = all_52_7)
% 178.99/28.75    (17)  all_58_10 = all_52_15
% 178.99/28.75    (18)   ~ (all_52_5 = all_4_2)
% 178.99/28.75    (19)  all_58_7 = all_52_19
% 178.99/28.75    (20)   ~ (all_52_15 = all_6_2)
% 178.99/28.75    (21)  op(e0, e1) = all_52_29
% 178.99/28.75    (22)  all_58_4 = all_52_5
% 178.99/28.75    (23)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.75    (24)   ~ (e3 = e1)
% 178.99/28.75    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.75    (26)   ~ (all_52_7 = all_4_2)
% 178.99/28.75    (27)  all_58_1 = all_52_3
% 178.99/28.75    (28)   ~ (all_52_13 = all_52_15)
% 178.99/28.75    (29)  all_58_0 = all_4_2
% 178.99/28.75    (30)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.75    (31)  op(e1, all_52_29) = all_52_28
% 178.99/28.75    (32)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.75    (33)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.75    (34)  all_58_14 = all_52_29
% 178.99/28.75    (35)   ~ (all_52_3 = all_52_5)
% 178.99/28.75    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.75    (37)  op(e2, e1) = all_52_13
% 178.99/28.75    (38)  all_58_8 = all_14_2
% 178.99/28.75    (39)   ~ (all_52_5 = all_14_2)
% 178.99/28.75    (40)   ~ (all_52_3 = all_4_2)
% 178.99/28.75    (41)  op(e3, all_4_2) = e3
% 178.99/28.75    (42)  op(e0, e3) = all_52_25
% 178.99/28.75    (43)   ~ (e3 = e0)
% 178.99/28.75    (44)  op(e0, all_52_23) = all_52_22
% 178.99/28.75    (45)   ~ (all_52_15 = all_52_23)
% 178.99/28.75    (46)   ~ (all_52_5 = all_52_29)
% 178.99/28.75    (47)  all_56_2 = all_52_5
% 178.99/28.75    (48)  op(e1, e0) = all_52_23
% 178.99/28.75    (49)  all_58_13 = all_52_27
% 178.99/28.75    (50)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.75    (51)  all_58_6 = all_52_17
% 178.99/28.75    (52)   ~ (all_52_3 = all_52_7)
% 178.99/28.75    (53)  all_56_0 = all_4_2
% 178.99/28.75    (54)  all_58_11 = all_52_23
% 178.99/28.75    (55)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.75    (56)   ~ (all_52_7 = all_52_15)
% 178.99/28.75    (57)  op(e0, all_52_15) = all_52_14
% 178.99/28.75    (58)   ~ (all_52_29 = all_14_2)
% 178.99/28.75    (59)   ~ (all_52_29 = all_6_2)
% 178.99/28.75    (60)  all_58_2 = all_52_9
% 178.99/28.75    (61)  op(e3, e1) = all_52_5
% 178.99/28.75    (62)  op(e1, e1) = all_14_2
% 178.99/28.75    (63)  op(e1, e3) = all_52_17
% 178.99/28.75    (64)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.99/28.75    (65)   ~ (all_52_25 = all_4_2)
% 178.99/28.75    (66)  op(e3, e0) = all_52_7
% 178.99/28.75    (67)   ~ (all_52_17 = all_4_2)
% 178.99/28.75    (68)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.75    (69)   ~ (all_52_7 = all_6_2)
% 178.99/28.75    (70)  all_56_7 = all_52_15
% 178.99/28.75    (71)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 178.99/28.75    (72)  op(e1, all_52_5) = e1
% 178.99/28.75    (73)   ~ (all_52_7 = all_52_23)
% 178.99/28.75    (74)  op(e0, all_52_7) = e0
% 178.99/28.75    (75)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.75    (76)  all_58_9 = all_52_7
% 178.99/28.75    (77)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.75    (78)   ~ (e3 = e2)
% 178.99/28.75    (79)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.75    (80)  op(e2, e3) = all_52_9
% 178.99/28.75  
% 178.99/28.75  Begin of proof
% 178.99/28.75  | 
% 178.99/28.75  | BETA: splitting (71) gives:
% 178.99/28.75  | 
% 178.99/28.75  | Case 1:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (81)  all_58_13 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | REF_CLOSE: (7), (49), (81) are inconsistent by sub-proof #1026.
% 178.99/28.75  | | 
% 178.99/28.75  | Case 2:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (82)  all_58_14 = e3 | all_58_15 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | BETA: splitting (82) gives:
% 178.99/28.75  | | 
% 178.99/28.75  | | Case 1:
% 178.99/28.75  | | | 
% 178.99/28.75  | | |   (83)  all_58_14 = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | COMBINE_EQS: (34), (83) imply:
% 178.99/28.75  | | |   (84)  all_52_29 = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | SIMP: (84) implies:
% 178.99/28.75  | | |   (85)  all_52_29 = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (46), (85) imply:
% 178.99/28.75  | | |   (86)   ~ (all_52_5 = e3)
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (3), (85) imply:
% 178.99/28.75  | | |   (87)   ~ (all_52_13 = e3)
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (58), (85) imply:
% 178.99/28.75  | | |   (88)   ~ (all_14_2 = e3)
% 178.99/28.75  | | | 
% 178.99/28.75  | | | SIMP: (88) implies:
% 178.99/28.75  | | |   (89)   ~ (all_14_2 = e3)
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (59), (85) imply:
% 178.99/28.75  | | |   (90)   ~ (all_6_2 = e3)
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (31), (85) imply:
% 178.99/28.75  | | |   (91)  op(e1, e3) = all_52_28
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (21), (85) imply:
% 178.99/28.75  | | |   (92)  op(e0, e1) = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | GROUND_INST: instantiating (68) with all_52_17, all_52_28, e3, e1,
% 178.99/28.75  | | |              simplifying with (63), (91) gives:
% 178.99/28.75  | | |   (93)  all_52_17 = all_52_28
% 178.99/28.75  | | | 
% 178.99/28.75  | | | COMBINE_EQS: (51), (93) imply:
% 178.99/28.75  | | |   (94)  all_58_6 = all_52_28
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (67), (93) imply:
% 178.99/28.75  | | |   (95)   ~ (all_52_28 = all_4_2)
% 178.99/28.75  | | | 
% 178.99/28.75  | | | BETA: splitting (79) gives:
% 178.99/28.75  | | | 
% 178.99/28.75  | | | Case 1:
% 178.99/28.75  | | | | 
% 178.99/28.75  | | | |   (96)  all_56_2 = e3
% 178.99/28.75  | | | | 
% 178.99/28.75  | | | | REF_CLOSE: (47), (86), (96) are inconsistent by sub-proof #931.
% 178.99/28.75  | | | | 
% 178.99/28.75  | | | Case 2:
% 178.99/28.75  | | | | 
% 178.99/28.75  | | | |   (97)   ~ (all_56_2 = e3)
% 178.99/28.75  | | | |   (98)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.75  | | | | 
% 178.99/28.75  | | | | BETA: splitting (75) gives:
% 178.99/28.75  | | | | 
% 178.99/28.75  | | | | Case 1:
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | |   (99)  all_58_9 = e3
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | | COMBINE_EQS: (76), (99) imply:
% 178.99/28.75  | | | | |   (100)  all_52_7 = e3
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | | SIMP: (100) implies:
% 178.99/28.75  | | | | |   (101)  all_52_7 = e3
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | | REDUCE: (56), (101) imply:
% 178.99/28.75  | | | | |   (102)   ~ (all_52_15 = e3)
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | | SIMP: (102) implies:
% 178.99/28.75  | | | | |   (103)   ~ (all_52_15 = e3)
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 178.99/28.75  | | | | |            (15), (16), (17), (22), (24), (25), (26), (27), (29), (32),
% 178.99/28.75  | | | | |            (33), (35), (36), (37), (39), (40), (41), (42), (43), (44),
% 178.99/28.75  | | | | |            (45), (47), (48), (50), (52), (53), (54), (56), (60), (61),
% 178.99/28.75  | | | | |            (62), (65), (68), (69), (72), (73), (74), (75), (76), (77),
% 178.99/28.75  | | | | |            (78), (80), (86), (87), (92), (98), (103) are inconsistent
% 178.99/28.75  | | | | |            by sub-proof #791.
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | Case 2:
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | |   (104)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | | BETA: splitting (104) gives:
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | | Case 1:
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | |   (105)  all_58_10 = e3
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | | COMBINE_EQS: (17), (105) imply:
% 178.99/28.75  | | | | | |   (106)  all_52_15 = e3
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | | SIMP: (106) implies:
% 178.99/28.75  | | | | | |   (107)  all_52_15 = e3
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | | REDUCE: (57), (107) imply:
% 178.99/28.75  | | | | | |   (108)  op(e0, e3) = all_52_14
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | | GROUND_INST: instantiating (68) with all_52_25, all_52_14, e3, e0,
% 178.99/28.75  | | | | | |              simplifying with (42), (108) gives:
% 178.99/28.75  | | | | | |   (109)  all_52_14 = all_52_25
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | | BETA: splitting (77) gives:
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | | Case 1:
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | |   (110)  all_58_0 = e3
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | | COMBINE_EQS: (29), (110) imply:
% 178.99/28.75  | | | | | | |   (111)  all_4_2 = e3
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | | REDUCE: (95), (111) imply:
% 178.99/28.75  | | | | | | |   (112)   ~ (all_52_28 = e3)
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12),
% 178.99/28.75  | | | | | | |            (13), (14), (15), (16), (17), (19), (22), (23), (24),
% 178.99/28.75  | | | | | | |            (25), (26), (27), (29), (30), (32), (33), (35), (36),
% 178.99/28.75  | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 178.99/28.75  | | | | | | |            (47), (48), (50), (52), (53), (54), (55), (56), (60),
% 178.99/28.75  | | | | | | |            (61), (62), (64), (65), (68), (69), (70), (72), (73),
% 178.99/28.75  | | | | | | |            (74), (75), (76), (77), (78), (80), (86), (87), (89),
% 178.99/28.75  | | | | | | |            (92), (94), (98), (112) are inconsistent by sub-proof
% 178.99/28.75  | | | | | | |            #789.
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | Case 2:
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | |   (113)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | | REF_CLOSE: (2), (4), (13), (14), (15), (16), (17), (22), (26),
% 178.99/28.75  | | | | | | |            (27), (29), (35), (40), (41), (42), (50), (52), (53),
% 178.99/28.75  | | | | | | |            (54), (56), (61), (65), (66), (68), (69), (73), (74),
% 178.99/28.75  | | | | | | |            (75), (76), (80), (86), (113) are inconsistent by
% 178.99/28.75  | | | | | | |            sub-proof #787.
% 178.99/28.75  | | | | | | | 
% 178.99/28.75  | | | | | | End of split
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | Case 2:
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | |   (114)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (11), (12), (13),
% 178.99/28.75  | | | | | |            (14), (15), (16), (17), (22), (24), (25), (26), (27),
% 178.99/28.75  | | | | | |            (29), (32), (33), (35), (36), (37), (39), (40), (41),
% 178.99/28.75  | | | | | |            (42), (43), (44), (45), (47), (48), (50), (52), (53),
% 178.99/28.75  | | | | | |            (54), (56), (60), (61), (62), (65), (68), (69), (72),
% 178.99/28.75  | | | | | |            (73), (74), (75), (76), (77), (78), (80), (86), (87),
% 178.99/28.75  | | | | | |            (92), (98), (114) are inconsistent by sub-proof #792.
% 178.99/28.75  | | | | | | 
% 178.99/28.75  | | | | | End of split
% 178.99/28.75  | | | | | 
% 178.99/28.75  | | | | End of split
% 178.99/28.75  | | | | 
% 178.99/28.75  | | | End of split
% 178.99/28.75  | | | 
% 178.99/28.75  | | Case 2:
% 178.99/28.75  | | | 
% 178.99/28.75  | | |   (115)  all_58_15 = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | COMBINE_EQS: (14), (115) imply:
% 178.99/28.75  | | |   (116)  all_6_2 = e3
% 178.99/28.75  | | | 
% 178.99/28.75  | | | REDUCE: (8), (116) imply:
% 178.99/28.75  | | |   (117)  $false
% 178.99/28.75  | | | 
% 178.99/28.75  | | | CLOSE: (117) is inconsistent.
% 178.99/28.75  | | | 
% 178.99/28.75  | | End of split
% 178.99/28.75  | | 
% 178.99/28.75  | End of split
% 178.99/28.75  | 
% 178.99/28.75  End of proof
% 178.99/28.75  
% 178.99/28.75  Sub-proof #787 shows that the following formulas are inconsistent:
% 178.99/28.75  ----------------------------------------------------------------
% 178.99/28.75    (1)  op(e2, all_52_3) = e2
% 178.99/28.75    (2)  op(e3, e2) = all_52_3
% 178.99/28.75    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.75    (4)  all_58_15 = all_6_2
% 178.99/28.75    (5)   ~ (all_52_9 = all_4_2)
% 178.99/28.75    (6)   ~ (all_52_5 = all_52_7)
% 178.99/28.75    (7)  all_58_10 = all_52_15
% 178.99/28.75    (8)  all_58_4 = all_52_5
% 178.99/28.75    (9)   ~ (all_52_7 = all_4_2)
% 178.99/28.75    (10)  all_58_1 = all_52_3
% 178.99/28.75    (11)  all_58_0 = all_4_2
% 178.99/28.75    (12)   ~ (all_52_3 = all_52_5)
% 178.99/28.75    (13)   ~ (all_52_3 = all_4_2)
% 178.99/28.75    (14)  op(e3, all_4_2) = e3
% 178.99/28.75    (15)  op(e0, e3) = all_52_25
% 178.99/28.75    (16)   ~ (all_52_5 = e3)
% 178.99/28.75    (17)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.75    (18)   ~ (all_52_3 = all_52_7)
% 178.99/28.75    (19)  all_56_0 = all_4_2
% 178.99/28.75    (20)  all_58_11 = all_52_23
% 178.99/28.75    (21)   ~ (all_52_7 = all_52_15)
% 178.99/28.75    (22)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.75    (23)  op(e3, e1) = all_52_5
% 178.99/28.75    (24)   ~ (all_52_25 = all_4_2)
% 178.99/28.75    (25)  op(e3, e0) = all_52_7
% 178.99/28.75    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.75    (27)   ~ (all_52_7 = all_6_2)
% 178.99/28.75    (28)   ~ (all_52_7 = all_52_23)
% 178.99/28.75    (29)  op(e0, all_52_7) = e0
% 178.99/28.75    (30)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.75    (31)  all_58_9 = all_52_7
% 178.99/28.75    (32)  op(e2, e3) = all_52_9
% 178.99/28.75  
% 178.99/28.75  Begin of proof
% 178.99/28.75  | 
% 178.99/28.75  | BETA: splitting (22) gives:
% 178.99/28.75  | 
% 178.99/28.75  | Case 1:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (33)  all_58_1 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | REF_CLOSE: (1), (3), (5), (10), (11), (12), (13), (14), (17), (18), (19),
% 178.99/28.75  | |            (23), (25), (26), (32), (33) are inconsistent by sub-proof #788.
% 178.99/28.75  | | 
% 178.99/28.75  | Case 2:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (34)  all_58_4 = e3 | all_58_9 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (14), (15), (16), (17),
% 178.99/28.75  | |            (18), (19), (20), (21), (23), (24), (26), (27), (28), (29), (30),
% 178.99/28.75  | |            (31), (34) are inconsistent by sub-proof #871.
% 178.99/28.75  | | 
% 178.99/28.75  | End of split
% 178.99/28.75  | 
% 178.99/28.75  End of proof
% 178.99/28.75  
% 178.99/28.75  Sub-proof #788 shows that the following formulas are inconsistent:
% 178.99/28.75  ----------------------------------------------------------------
% 178.99/28.75    (1)  op(e2, all_52_3) = e2
% 178.99/28.75    (2)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.75    (3)   ~ (all_52_9 = all_4_2)
% 178.99/28.75    (4)  all_58_1 = all_52_3
% 178.99/28.75    (5)  all_58_0 = all_4_2
% 178.99/28.75    (6)   ~ (all_52_3 = all_52_5)
% 178.99/28.75    (7)   ~ (all_52_3 = all_4_2)
% 178.99/28.75    (8)  op(e3, all_4_2) = e3
% 178.99/28.75    (9)  all_58_1 = e3
% 178.99/28.75    (10)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.75    (11)   ~ (all_52_3 = all_52_7)
% 178.99/28.75    (12)  all_56_0 = all_4_2
% 178.99/28.75    (13)  op(e3, e1) = all_52_5
% 178.99/28.75    (14)  op(e3, e0) = all_52_7
% 178.99/28.75    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.75    (16)  op(e2, e3) = all_52_9
% 178.99/28.75  
% 178.99/28.75  Begin of proof
% 178.99/28.75  | 
% 178.99/28.75  | COMBINE_EQS: (4), (9) imply:
% 178.99/28.75  |   (17)  all_52_3 = e3
% 178.99/28.75  | 
% 178.99/28.75  | REDUCE: (6), (17) imply:
% 178.99/28.75  |   (18)   ~ (all_52_5 = e3)
% 178.99/28.75  | 
% 178.99/28.75  | SIMP: (18) implies:
% 178.99/28.75  |   (19)   ~ (all_52_5 = e3)
% 178.99/28.75  | 
% 178.99/28.75  | REDUCE: (11), (17) imply:
% 178.99/28.75  |   (20)   ~ (all_52_7 = e3)
% 178.99/28.75  | 
% 178.99/28.75  | SIMP: (20) implies:
% 178.99/28.75  |   (21)   ~ (all_52_7 = e3)
% 178.99/28.75  | 
% 178.99/28.75  | REDUCE: (7), (17) imply:
% 178.99/28.75  |   (22)   ~ (all_4_2 = e3)
% 178.99/28.75  | 
% 178.99/28.75  | SIMP: (22) implies:
% 178.99/28.75  |   (23)   ~ (all_4_2 = e3)
% 178.99/28.75  | 
% 178.99/28.75  | REDUCE: (1), (17) imply:
% 178.99/28.75  |   (24)  op(e2, e3) = e2
% 178.99/28.75  | 
% 178.99/28.75  | GROUND_INST: instantiating (15) with all_52_9, e2, e3, e2, simplifying with
% 178.99/28.75  |              (16), (24) gives:
% 178.99/28.75  |   (25)  all_52_9 = e2
% 178.99/28.75  | 
% 178.99/28.75  | REDUCE: (3), (25) imply:
% 178.99/28.75  |   (26)   ~ (all_4_2 = e2)
% 178.99/28.75  | 
% 178.99/28.75  | SIMP: (26) implies:
% 178.99/28.75  |   (27)   ~ (all_4_2 = e2)
% 178.99/28.75  | 
% 178.99/28.75  | BETA: splitting (2) gives:
% 178.99/28.75  | 
% 178.99/28.75  | Case 1:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (28)  all_56_0 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | REF_CLOSE: (12), (23), (28) are inconsistent by sub-proof #1024.
% 178.99/28.75  | | 
% 178.99/28.75  | Case 2:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (29)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.75  | | 
% 178.99/28.75  | | REF_CLOSE: (5), (8), (10), (12), (13), (14), (15), (19), (21), (27), (29)
% 178.99/28.75  | |            are inconsistent by sub-proof #873.
% 178.99/28.75  | | 
% 178.99/28.75  | End of split
% 178.99/28.75  | 
% 178.99/28.75  End of proof
% 178.99/28.75  
% 178.99/28.75  Sub-proof #789 shows that the following formulas are inconsistent:
% 178.99/28.75  ----------------------------------------------------------------
% 178.99/28.75    (1)   ~ (all_52_5 = all_52_13)
% 178.99/28.75    (2)  op(e2, all_52_3) = e2
% 178.99/28.75    (3)  all_58_6 = all_52_28
% 178.99/28.75    (4)  op(e3, e2) = all_52_3
% 178.99/28.75    (5)  op(e1, e2) = all_52_19
% 178.99/28.75    (6)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.75    (7)   ~ (all_6_2 = e3)
% 178.99/28.75    (8)   ~ (all_52_3 = all_10_2)
% 178.99/28.75    (9)  all_58_5 = all_52_13
% 178.99/28.75    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.75    (11)  all_58_3 = all_10_2
% 178.99/28.75    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.75    (13)  all_58_15 = all_6_2
% 178.99/28.75    (14)   ~ (all_52_9 = all_4_2)
% 178.99/28.75    (15)   ~ (all_52_5 = all_52_7)
% 178.99/28.75    (16)  all_58_10 = all_52_15
% 178.99/28.75    (17)  all_58_7 = all_52_19
% 178.99/28.75    (18)  all_58_4 = all_52_5
% 178.99/28.75    (19)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.75    (20)   ~ (e3 = e1)
% 178.99/28.75    (21)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.75    (22)   ~ (all_52_7 = all_4_2)
% 178.99/28.75    (23)  all_58_1 = all_52_3
% 178.99/28.75    (24)  all_58_0 = all_4_2
% 178.99/28.75    (25)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.75    (26)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.75    (27)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.75    (28)   ~ (all_52_3 = all_52_5)
% 178.99/28.75    (29)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.75    (30)  op(e2, e1) = all_52_13
% 178.99/28.75    (31)  all_58_8 = all_14_2
% 178.99/28.75    (32)   ~ (all_52_28 = e3)
% 178.99/28.75    (33)   ~ (all_52_5 = all_14_2)
% 178.99/28.75    (34)   ~ (all_52_3 = all_4_2)
% 178.99/28.75    (35)  op(e3, all_4_2) = e3
% 178.99/28.75    (36)  op(e0, e3) = all_52_25
% 178.99/28.75    (37)   ~ (all_52_5 = e3)
% 178.99/28.75    (38)   ~ (e3 = e0)
% 178.99/28.75    (39)   ~ (all_52_13 = e3)
% 178.99/28.75    (40)  op(e0, all_52_23) = all_52_22
% 178.99/28.75    (41)   ~ (all_52_15 = all_52_23)
% 178.99/28.75    (42)  all_56_2 = all_52_5
% 178.99/28.75    (43)  op(e1, e0) = all_52_23
% 178.99/28.75    (44)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.75    (45)   ~ (all_52_3 = all_52_7)
% 178.99/28.75    (46)  all_56_0 = all_4_2
% 178.99/28.75    (47)  all_58_11 = all_52_23
% 178.99/28.75    (48)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.75    (49)   ~ (all_52_7 = all_52_15)
% 178.99/28.75    (50)  all_58_2 = all_52_9
% 178.99/28.75    (51)  op(e3, e1) = all_52_5
% 178.99/28.75    (52)  op(e1, e1) = all_14_2
% 178.99/28.75    (53)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 178.99/28.75    (54)   ~ (all_52_25 = all_4_2)
% 178.99/28.75    (55)   ~ (all_14_2 = e3)
% 178.99/28.75    (56)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.75    (57)  op(e0, e1) = e3
% 178.99/28.75    (58)   ~ (all_52_7 = all_6_2)
% 178.99/28.75    (59)  all_56_7 = all_52_15
% 178.99/28.75    (60)  op(e1, all_52_5) = e1
% 178.99/28.75    (61)   ~ (all_52_7 = all_52_23)
% 178.99/28.75    (62)  op(e0, all_52_7) = e0
% 178.99/28.75    (63)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.75    (64)  all_58_9 = all_52_7
% 178.99/28.75    (65)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.75    (66)   ~ (e3 = e2)
% 178.99/28.75    (67)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.75    (68)  op(e2, e3) = all_52_9
% 178.99/28.75  
% 178.99/28.75  Begin of proof
% 178.99/28.75  | 
% 178.99/28.75  | BETA: splitting (19) gives:
% 178.99/28.75  | 
% 178.99/28.75  | Case 1:
% 178.99/28.75  | | 
% 178.99/28.75  | |   (69)  all_58_6 = e3
% 178.99/28.75  | | 
% 178.99/28.75  | | REF_CLOSE: (3), (32), (69) are inconsistent by sub-proof #790.
% 178.99/28.75  | | 
% 178.99/28.75  | Case 2:
% 178.99/28.75  | | 
% 178.99/28.76  | |   (70)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | BETA: splitting (53) gives:
% 178.99/28.76  | | 
% 178.99/28.76  | | Case 1:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (71)  all_56_7 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | COMBINE_EQS: (59), (71) imply:
% 178.99/28.76  | | |   (72)  all_52_15 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | SIMP: (72) implies:
% 178.99/28.76  | | |   (73)  all_52_15 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | COMBINE_EQS: (16), (73) imply:
% 178.99/28.76  | | |   (74)  all_58_10 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REDUCE: (41), (73) imply:
% 178.99/28.76  | | |   (75)   ~ (all_52_23 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | SIMP: (75) implies:
% 178.99/28.76  | | |   (76)   ~ (all_52_23 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | BETA: splitting (70) gives:
% 178.99/28.76  | | | 
% 178.99/28.76  | | | Case 1:
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | |   (77)  all_58_7 = e3
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | COMBINE_EQS: (17), (77) imply:
% 178.99/28.76  | | | |   (78)  all_52_19 = e3
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | REDUCE: (5), (78) imply:
% 178.99/28.76  | | | |   (79)  op(e1, e2) = e3
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | BETA: splitting (48) gives:
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | Case 1:
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | |   (80)  all_58_4 = e2
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | COMBINE_EQS: (18), (80) imply:
% 178.99/28.76  | | | | |   (81)  all_52_5 = e2
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | REDUCE: (60), (81) imply:
% 178.99/28.76  | | | | |   (82)  op(e1, e2) = e1
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | REF_CLOSE: (20), (56), (79), (82) are inconsistent by sub-proof #861.
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | Case 2:
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | |   (83)   ~ (all_58_4 = e2)
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | REF_CLOSE: (15), (18), (25), (26), (33), (37), (42), (43), (47), (52),
% 178.99/28.76  | | | | |            (56), (60), (64), (67), (74), (83) are inconsistent by
% 178.99/28.76  | | | | |            sub-proof #822.
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | End of split
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | Case 2:
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | |   (84)  all_58_8 = e3 | all_58_11 = e3
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | REF_CLOSE: (31), (47), (55), (76), (84) are inconsistent by sub-proof
% 178.99/28.76  | | | |            #997.
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | End of split
% 178.99/28.76  | | | 
% 178.99/28.76  | | Case 2:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (85)   ~ (all_56_7 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REDUCE: (59), (85) imply:
% 178.99/28.76  | | |   (86)   ~ (all_52_15 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.99/28.76  | | |            (14), (15), (16), (18), (20), (21), (22), (23), (24), (26),
% 178.99/28.76  | | |            (27), (28), (29), (30), (33), (34), (35), (36), (37), (38),
% 178.99/28.76  | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (49),
% 178.99/28.76  | | |            (50), (51), (52), (54), (56), (57), (58), (60), (61), (62),
% 178.99/28.76  | | |            (63), (64), (65), (66), (67), (68), (86) are inconsistent by
% 178.99/28.76  | | |            sub-proof #791.
% 178.99/28.76  | | | 
% 178.99/28.76  | | End of split
% 178.99/28.76  | | 
% 178.99/28.76  | End of split
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #790 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)  all_58_6 = all_52_28
% 178.99/28.76    (2)  all_58_6 = e3
% 178.99/28.76    (3)   ~ (all_52_28 = e3)
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.76  |   (4)  all_52_28 = e3
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (4) implies:
% 178.99/28.76  |   (5)  all_52_28 = e3
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (3), (5) imply:
% 178.99/28.76  |   (6)  $false
% 178.99/28.76  | 
% 178.99/28.76  | CLOSE: (6) is inconsistent.
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #791 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)   ~ (all_52_5 = all_52_13)
% 178.99/28.76    (2)  op(e2, all_52_3) = e2
% 178.99/28.76    (3)  op(e3, e2) = all_52_3
% 178.99/28.76    (4)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.76    (5)   ~ (all_6_2 = e3)
% 178.99/28.76    (6)   ~ (all_52_3 = all_10_2)
% 178.99/28.76    (7)  all_58_5 = all_52_13
% 178.99/28.76    (8)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.76    (9)  all_58_3 = all_10_2
% 178.99/28.76    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.76    (11)  all_58_15 = all_6_2
% 178.99/28.76    (12)   ~ (all_52_9 = all_4_2)
% 178.99/28.76    (13)   ~ (all_52_5 = all_52_7)
% 178.99/28.76    (14)  all_58_10 = all_52_15
% 178.99/28.76    (15)  all_58_4 = all_52_5
% 178.99/28.76    (16)   ~ (e3 = e1)
% 178.99/28.76    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.76    (18)   ~ (all_52_7 = all_4_2)
% 178.99/28.76    (19)  all_58_1 = all_52_3
% 178.99/28.76    (20)  all_58_0 = all_4_2
% 178.99/28.76    (21)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.76    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.76    (23)   ~ (all_52_3 = all_52_5)
% 178.99/28.76    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.76    (25)  op(e2, e1) = all_52_13
% 178.99/28.76    (26)   ~ (all_52_5 = all_14_2)
% 178.99/28.76    (27)   ~ (all_52_3 = all_4_2)
% 178.99/28.76    (28)  op(e3, all_4_2) = e3
% 178.99/28.76    (29)  op(e0, e3) = all_52_25
% 178.99/28.76    (30)   ~ (all_52_5 = e3)
% 178.99/28.76    (31)   ~ (e3 = e0)
% 178.99/28.76    (32)   ~ (all_52_13 = e3)
% 178.99/28.76    (33)  op(e0, all_52_23) = all_52_22
% 178.99/28.76    (34)   ~ (all_52_15 = all_52_23)
% 178.99/28.76    (35)   ~ (all_52_15 = e3)
% 178.99/28.76    (36)  all_56_2 = all_52_5
% 178.99/28.76    (37)  op(e1, e0) = all_52_23
% 178.99/28.76    (38)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.76    (39)   ~ (all_52_3 = all_52_7)
% 178.99/28.76    (40)  all_56_0 = all_4_2
% 178.99/28.76    (41)  all_58_11 = all_52_23
% 178.99/28.76    (42)   ~ (all_52_7 = all_52_15)
% 178.99/28.76    (43)  all_58_2 = all_52_9
% 178.99/28.76    (44)  op(e3, e1) = all_52_5
% 178.99/28.76    (45)  op(e1, e1) = all_14_2
% 178.99/28.76    (46)   ~ (all_52_25 = all_4_2)
% 178.99/28.76    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.76    (48)  op(e0, e1) = e3
% 178.99/28.76    (49)   ~ (all_52_7 = all_6_2)
% 178.99/28.76    (50)  op(e1, all_52_5) = e1
% 178.99/28.76    (51)   ~ (all_52_7 = all_52_23)
% 178.99/28.76    (52)  op(e0, all_52_7) = e0
% 178.99/28.76    (53)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.76    (54)  all_58_9 = all_52_7
% 178.99/28.76    (55)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.76    (56)   ~ (e3 = e2)
% 178.99/28.76    (57)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.76    (58)  op(e2, e3) = all_52_9
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | BETA: splitting (53) gives:
% 178.99/28.76  | 
% 178.99/28.76  | Case 1:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (59)  all_58_9 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | REF_CLOSE: (3), (10), (11), (13), (14), (18), (20), (28), (29), (38), (39),
% 178.99/28.76  | |            (40), (41), (42), (44), (46), (47), (49), (51), (52), (53), (54),
% 178.99/28.76  | |            (59) are inconsistent by sub-proof #1014.
% 178.99/28.76  | | 
% 178.99/28.76  | Case 2:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (60)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | BETA: splitting (60) gives:
% 178.99/28.76  | | 
% 178.99/28.76  | | Case 1:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (61)  all_58_10 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REF_CLOSE: (14), (35), (61) are inconsistent by sub-proof #1018.
% 178.99/28.76  | | | 
% 178.99/28.76  | | Case 2:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (62)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.99/28.76  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 178.99/28.76  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 178.99/28.76  | | |            (33), (34), (36), (37), (38), (39), (40), (41), (42), (43),
% 178.99/28.76  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 178.99/28.76  | | |            (54), (55), (56), (57), (58), (62) are inconsistent by
% 178.99/28.76  | | |            sub-proof #792.
% 178.99/28.76  | | | 
% 178.99/28.76  | | End of split
% 178.99/28.76  | | 
% 178.99/28.76  | End of split
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #792 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)   ~ (all_52_5 = all_52_13)
% 178.99/28.76    (2)  op(e2, all_52_3) = e2
% 178.99/28.76    (3)  op(e3, e2) = all_52_3
% 178.99/28.76    (4)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.76    (5)   ~ (all_6_2 = e3)
% 178.99/28.76    (6)   ~ (all_52_3 = all_10_2)
% 178.99/28.76    (7)  all_58_5 = all_52_13
% 178.99/28.76    (8)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.76    (9)  all_58_3 = all_10_2
% 178.99/28.76    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.76    (11)  all_58_15 = all_6_2
% 178.99/28.76    (12)   ~ (all_52_9 = all_4_2)
% 178.99/28.76    (13)   ~ (all_52_5 = all_52_7)
% 178.99/28.76    (14)  all_58_10 = all_52_15
% 178.99/28.76    (15)  all_58_4 = all_52_5
% 178.99/28.76    (16)   ~ (e3 = e1)
% 178.99/28.76    (17)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.76    (18)   ~ (all_52_7 = all_4_2)
% 178.99/28.76    (19)  all_58_1 = all_52_3
% 178.99/28.76    (20)  all_58_0 = all_4_2
% 178.99/28.76    (21)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.76    (22)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.76    (23)   ~ (all_52_3 = all_52_5)
% 178.99/28.76    (24)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.76    (25)  op(e2, e1) = all_52_13
% 178.99/28.76    (26)   ~ (all_52_5 = all_14_2)
% 178.99/28.76    (27)   ~ (all_52_3 = all_4_2)
% 178.99/28.76    (28)  op(e3, all_4_2) = e3
% 178.99/28.76    (29)  op(e0, e3) = all_52_25
% 178.99/28.76    (30)   ~ (all_52_5 = e3)
% 178.99/28.76    (31)   ~ (e3 = e0)
% 178.99/28.76    (32)   ~ (all_52_13 = e3)
% 178.99/28.76    (33)  op(e0, all_52_23) = all_52_22
% 178.99/28.76    (34)   ~ (all_52_15 = all_52_23)
% 178.99/28.76    (35)  all_56_2 = all_52_5
% 178.99/28.76    (36)  op(e1, e0) = all_52_23
% 178.99/28.76    (37)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.76    (38)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.76    (39)   ~ (all_52_3 = all_52_7)
% 178.99/28.76    (40)  all_56_0 = all_4_2
% 178.99/28.76    (41)  all_58_11 = all_52_23
% 178.99/28.76    (42)   ~ (all_52_7 = all_52_15)
% 178.99/28.76    (43)  all_58_2 = all_52_9
% 178.99/28.76    (44)  op(e3, e1) = all_52_5
% 178.99/28.76    (45)  op(e1, e1) = all_14_2
% 178.99/28.76    (46)   ~ (all_52_25 = all_4_2)
% 178.99/28.76    (47)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.76    (48)  op(e0, e1) = e3
% 178.99/28.76    (49)   ~ (all_52_7 = all_6_2)
% 178.99/28.76    (50)  op(e1, all_52_5) = e1
% 178.99/28.76    (51)   ~ (all_52_7 = all_52_23)
% 178.99/28.76    (52)  op(e0, all_52_7) = e0
% 178.99/28.76    (53)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.76    (54)  all_58_9 = all_52_7
% 178.99/28.76    (55)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.76    (56)   ~ (e3 = e2)
% 178.99/28.76    (57)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.76    (58)  op(e2, e3) = all_52_9
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | BETA: splitting (38) gives:
% 178.99/28.76  | 
% 178.99/28.76  | Case 1:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (59)  all_58_11 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | COMBINE_EQS: (41), (59) imply:
% 178.99/28.76  | |   (60)  all_52_23 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | SIMP: (60) implies:
% 178.99/28.76  | |   (61)  all_52_23 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | REDUCE: (34), (61) imply:
% 178.99/28.76  | |   (62)   ~ (all_52_15 = e3)
% 178.99/28.76  | | 
% 178.99/28.76  | | REDUCE: (36), (61) imply:
% 178.99/28.76  | |   (63)  op(e1, e0) = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | REDUCE: (33), (61) imply:
% 178.99/28.76  | |   (64)  op(e0, e3) = all_52_22
% 178.99/28.76  | | 
% 178.99/28.76  | | GROUND_INST: instantiating (47) with all_52_25, all_52_22, e3, e0,
% 178.99/28.76  | |              simplifying with (29), (64) gives:
% 178.99/28.76  | |   (65)  all_52_22 = all_52_25
% 178.99/28.76  | | 
% 178.99/28.76  | | BETA: splitting (17) gives:
% 178.99/28.76  | | 
% 178.99/28.76  | | Case 1:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (66)  all_58_2 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | COMBINE_EQS: (43), (66) imply:
% 178.99/28.76  | | |   (67)  all_52_9 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | SIMP: (67) implies:
% 178.99/28.76  | | |   (68)  all_52_9 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REDUCE: (12), (68) imply:
% 178.99/28.76  | | |   (69)   ~ (all_4_2 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | SIMP: (69) implies:
% 178.99/28.76  | | |   (70)   ~ (all_4_2 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REDUCE: (58), (68) imply:
% 178.99/28.76  | | |   (71)  op(e2, e3) = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REF_CLOSE: (2), (3), (10), (11), (13), (14), (15), (18), (19), (20), (22),
% 178.99/28.76  | | |            (28), (29), (30), (37), (39), (40), (41), (42), (44), (46),
% 178.99/28.76  | | |            (47), (49), (51), (52), (53), (54), (55), (56), (70), (71) are
% 178.99/28.76  | | |            inconsistent by sub-proof #796.
% 178.99/28.76  | | | 
% 178.99/28.76  | | Case 2:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (72)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | BETA: splitting (72) gives:
% 178.99/28.76  | | | 
% 178.99/28.76  | | | Case 1:
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | |   (73)  all_58_3 = e3
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | COMBINE_EQS: (9), (73) imply:
% 178.99/28.76  | | | |   (74)  all_10_2 = e3
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | REDUCE: (6), (74) imply:
% 178.99/28.76  | | | |   (75)   ~ (all_52_3 = e3)
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | BETA: splitting (24) gives:
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | Case 1:
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | |   (76)  all_58_0 = e3
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | COMBINE_EQS: (20), (76) imply:
% 178.99/28.76  | | | | |   (77)  all_4_2 = e3
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | BETA: splitting (21) gives:
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | Case 1:
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | |   (78)  all_58_4 = e1
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | | COMBINE_EQS: (15), (78) imply:
% 178.99/28.76  | | | | | |   (79)  all_52_5 = e1
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | | SIMP: (79) implies:
% 178.99/28.76  | | | | | |   (80)  all_52_5 = e1
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | | REF_CLOSE: (26), (45), (47), (50), (80) are inconsistent by
% 178.99/28.76  | | | | | |            sub-proof #859.
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | Case 2:
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | |   (81)   ~ (all_58_4 = e1)
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | | REDUCE: (15), (81) imply:
% 178.99/28.76  | | | | | |   (82)   ~ (all_52_5 = e1)
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | | BETA: splitting (4) gives:
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | | Case 1:
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | |   (83)  all_58_0 = e1
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | | COMBINE_EQS: (76), (83) imply:
% 178.99/28.76  | | | | | | |   (84)  e3 = e1
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | | REDUCE: (16), (84) imply:
% 178.99/28.76  | | | | | | |   (85)  $false
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | | CLOSE: (85) is inconsistent.
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | Case 2:
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | |   (86)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | | BETA: splitting (8) gives:
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | | Case 1:
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | |   (87)  all_58_9 = e1
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | | REF_CLOSE: (31), (47), (48), (52), (54), (87) are inconsistent
% 178.99/28.76  | | | | | | | |            by sub-proof #794.
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | Case 2:
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | |   (88)   ~ (all_58_9 = e1)
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | | REDUCE: (54), (88) imply:
% 178.99/28.76  | | | | | | | |   (89)   ~ (all_52_7 = e1)
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | | BETA: splitting (86) gives:
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | | Case 1:
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | |   (90)  all_58_1 = e1
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | COMBINE_EQS: (19), (90) imply:
% 178.99/28.76  | | | | | | | | |   (91)  all_52_3 = e1
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | REDUCE: (23), (91) imply:
% 178.99/28.76  | | | | | | | | |   (92)   ~ (all_52_5 = e1)
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | REDUCE: (75), (91) imply:
% 178.99/28.76  | | | | | | | | |   (93)   ~ (e3 = e1)
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | REDUCE: (2), (91) imply:
% 178.99/28.76  | | | | | | | | |   (94)  op(e2, e1) = e2
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | GROUND_INST: instantiating (47) with all_52_13, e2, e1, e2,
% 178.99/28.76  | | | | | | | | |              simplifying with (25), (94) gives:
% 178.99/28.76  | | | | | | | | |   (95)  all_52_13 = e2
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | REDUCE: (1), (95) imply:
% 178.99/28.76  | | | | | | | | |   (96)   ~ (all_52_5 = e2)
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | REF_CLOSE: (16), (35), (47), (50), (57), (63), (82), (96) are
% 178.99/28.76  | | | | | | | | |            inconsistent by sub-proof #801.
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | Case 2:
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | |   (97)  all_58_4 = e1 | all_58_9 = e1
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | BETA: splitting (97) gives:
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | Case 1:
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | |   (98)  all_58_4 = e1
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | | COMBINE_EQS: (15), (98) imply:
% 178.99/28.76  | | | | | | | | | |   (99)  all_52_5 = e1
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | | SIMP: (99) implies:
% 178.99/28.76  | | | | | | | | | |   (100)  all_52_5 = e1
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | | REDUCE: (82), (100) imply:
% 178.99/28.76  | | | | | | | | | |   (101)  $false
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | | CLOSE: (101) is inconsistent.
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | Case 2:
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | |   (102)  all_58_9 = e1
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | | REF_CLOSE: (54), (89), (102) are inconsistent by sub-proof
% 178.99/28.76  | | | | | | | | | |            #793.
% 178.99/28.76  | | | | | | | | | | 
% 178.99/28.76  | | | | | | | | | End of split
% 178.99/28.76  | | | | | | | | | 
% 178.99/28.76  | | | | | | | | End of split
% 178.99/28.76  | | | | | | | | 
% 178.99/28.76  | | | | | | | End of split
% 178.99/28.76  | | | | | | | 
% 178.99/28.76  | | | | | | End of split
% 178.99/28.76  | | | | | | 
% 178.99/28.76  | | | | | End of split
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | Case 2:
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | |   (103)   ~ (all_58_0 = e3)
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | REDUCE: (20), (103) imply:
% 178.99/28.76  | | | | |   (104)   ~ (all_4_2 = e3)
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | | REF_CLOSE: (3), (10), (11), (13), (14), (15), (18), (19), (20), (28),
% 178.99/28.76  | | | | |            (29), (30), (37), (39), (40), (41), (42), (44), (46), (47),
% 178.99/28.76  | | | | |            (49), (51), (52), (53), (54), (55), (75), (104) are
% 178.99/28.76  | | | | |            inconsistent by sub-proof #1012.
% 178.99/28.76  | | | | | 
% 178.99/28.76  | | | | End of split
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | Case 2:
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | |   (105)  all_58_5 = e3 | all_58_10 = e3
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | | REF_CLOSE: (7), (14), (32), (62), (105) are inconsistent by sub-proof
% 178.99/28.76  | | | |            #958.
% 178.99/28.76  | | | | 
% 178.99/28.76  | | | End of split
% 178.99/28.76  | | | 
% 178.99/28.76  | | End of split
% 178.99/28.76  | | 
% 178.99/28.76  | Case 2:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (106)  all_58_15 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | COMBINE_EQS: (11), (106) imply:
% 178.99/28.76  | |   (107)  all_6_2 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | REDUCE: (5), (107) imply:
% 178.99/28.76  | |   (108)  $false
% 178.99/28.76  | | 
% 178.99/28.76  | | CLOSE: (108) is inconsistent.
% 178.99/28.76  | | 
% 178.99/28.76  | End of split
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #793 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)  all_58_9 = all_52_7
% 178.99/28.76    (2)  all_58_9 = e1
% 178.99/28.76    (3)   ~ (all_52_7 = e1)
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.76  |   (4)  all_52_7 = e1
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (4) implies:
% 178.99/28.76  |   (5)  all_52_7 = e1
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (3), (5) imply:
% 178.99/28.76  |   (6)  $false
% 178.99/28.76  | 
% 178.99/28.76  | CLOSE: (6) is inconsistent.
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #794 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)  all_58_9 = e1
% 178.99/28.76    (2)   ~ (e3 = e0)
% 178.99/28.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.76    (4)  op(e0, e1) = e3
% 178.99/28.76    (5)  op(e0, all_52_7) = e0
% 178.99/28.76    (6)  all_58_9 = all_52_7
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | COMBINE_EQS: (1), (6) imply:
% 178.99/28.76  |   (7)  all_52_7 = e1
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (7) implies:
% 178.99/28.76  |   (8)  all_52_7 = e1
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (5), (8) imply:
% 178.99/28.76  |   (9)  op(e0, e1) = e0
% 178.99/28.76  | 
% 178.99/28.76  | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #795.
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #795 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.76    (2)  op(e0, e1) = e3
% 178.99/28.76    (3)  op(e0, e1) = e0
% 178.99/28.76    (4)   ~ (e3 = e0)
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | GROUND_INST: instantiating (1) with e3, e0, e1, e0, simplifying with (2), (3)
% 178.99/28.76  |              gives:
% 178.99/28.76  |   (5)  e3 = e0
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (4), (5) imply:
% 178.99/28.76  |   (6)  $false
% 178.99/28.76  | 
% 178.99/28.76  | CLOSE: (6) is inconsistent.
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #796 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)  op(e2, all_52_3) = e2
% 178.99/28.76    (2)  op(e3, e2) = all_52_3
% 178.99/28.76    (3)   ~ (all_4_2 = e3)
% 178.99/28.76    (4)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.76    (5)  all_58_15 = all_6_2
% 178.99/28.76    (6)   ~ (all_52_5 = all_52_7)
% 178.99/28.76    (7)  all_58_10 = all_52_15
% 178.99/28.76    (8)  all_58_4 = all_52_5
% 178.99/28.76    (9)   ~ (all_52_7 = all_4_2)
% 178.99/28.76    (10)  all_58_1 = all_52_3
% 178.99/28.76    (11)  all_58_0 = all_4_2
% 178.99/28.76    (12)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.76    (13)  op(e3, all_4_2) = e3
% 178.99/28.76    (14)  op(e0, e3) = all_52_25
% 178.99/28.76    (15)   ~ (all_52_5 = e3)
% 178.99/28.76    (16)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.76    (17)   ~ (all_52_3 = all_52_7)
% 178.99/28.76    (18)  all_56_0 = all_4_2
% 178.99/28.76    (19)  all_58_11 = all_52_23
% 178.99/28.76    (20)   ~ (all_52_7 = all_52_15)
% 178.99/28.76    (21)  op(e2, e3) = e3
% 178.99/28.76    (22)  op(e3, e1) = all_52_5
% 178.99/28.76    (23)   ~ (all_52_25 = all_4_2)
% 178.99/28.76    (24)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.76    (25)   ~ (all_52_7 = all_6_2)
% 178.99/28.76    (26)   ~ (all_52_7 = all_52_23)
% 178.99/28.76    (27)  op(e0, all_52_7) = e0
% 178.99/28.76    (28)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.76    (29)  all_58_9 = all_52_7
% 178.99/28.76    (30)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.76    (31)   ~ (e3 = e2)
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | BETA: splitting (30) gives:
% 178.99/28.76  | 
% 178.99/28.76  | Case 1:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (32)  all_58_0 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | COMBINE_EQS: (11), (32) imply:
% 178.99/28.76  | |   (33)  all_4_2 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | REDUCE: (3), (33) imply:
% 178.99/28.76  | |   (34)  $false
% 178.99/28.76  | | 
% 178.99/28.76  | | CLOSE: (34) is inconsistent.
% 178.99/28.76  | | 
% 178.99/28.76  | Case 2:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (35)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | BETA: splitting (12) gives:
% 178.99/28.76  | | 
% 178.99/28.76  | | Case 1:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (36)  all_58_1 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | COMBINE_EQS: (10), (36) imply:
% 178.99/28.76  | | |   (37)  all_52_3 = e3
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REDUCE: (1), (37) imply:
% 178.99/28.76  | | |   (38)  op(e2, e3) = e2
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REF_CLOSE: (21), (24), (31), (38) are inconsistent by sub-proof #951.
% 178.99/28.76  | | | 
% 178.99/28.76  | | Case 2:
% 178.99/28.76  | | | 
% 178.99/28.76  | | |   (39)   ~ (all_58_1 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REDUCE: (10), (39) imply:
% 178.99/28.76  | | |   (40)   ~ (all_52_3 = e3)
% 178.99/28.76  | | | 
% 178.99/28.76  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 178.99/28.76  | | |            (15), (16), (17), (18), (19), (20), (22), (23), (24), (25),
% 178.99/28.76  | | |            (26), (27), (28), (29), (35), (40) are inconsistent by
% 178.99/28.76  | | |            sub-proof #1013.
% 178.99/28.76  | | | 
% 178.99/28.76  | | End of split
% 178.99/28.76  | | 
% 178.99/28.76  | End of split
% 178.99/28.76  | 
% 178.99/28.76  End of proof
% 178.99/28.76  
% 178.99/28.76  Sub-proof #797 shows that the following formulas are inconsistent:
% 178.99/28.76  ----------------------------------------------------------------
% 178.99/28.76    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.76    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.76    (3)  op(e2, all_52_3) = e2
% 178.99/28.76    (4)  op(e3, e2) = all_52_3
% 178.99/28.76    (5)   ~ (all_52_19 = all_52_23)
% 178.99/28.76    (6)  all_56_11 = all_52_23
% 178.99/28.76    (7)  all_58_5 = all_52_13
% 178.99/28.76    (8)   ~ (all_52_25 = all_52_29)
% 178.99/28.76    (9)  all_58_3 = all_10_2
% 178.99/28.76    (10)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.76    (11)  all_58_15 = all_6_2
% 178.99/28.76    (12)   ~ (all_52_9 = all_4_2)
% 178.99/28.76    (13)   ~ (all_52_5 = all_52_7)
% 178.99/28.76    (14)  all_58_10 = all_52_15
% 178.99/28.76    (15)  all_58_7 = all_52_19
% 178.99/28.76    (16)   ~ (all_52_17 = all_52_25)
% 178.99/28.76    (17)  all_58_4 = all_52_5
% 178.99/28.76    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.76    (19)   ~ (all_52_7 = all_4_2)
% 178.99/28.76    (20)  all_58_1 = all_52_3
% 178.99/28.76    (21)   ~ (all_52_13 = all_52_15)
% 178.99/28.76    (22)  all_58_0 = all_4_2
% 178.99/28.76    (23)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.76    (24)  all_58_14 = all_52_29
% 178.99/28.76    (25)   ~ (all_52_3 = all_52_5)
% 178.99/28.76    (26)  all_58_8 = all_14_2
% 178.99/28.76    (27)   ~ (all_52_5 = all_14_2)
% 178.99/28.76    (28)  op(e3, all_4_2) = e3
% 178.99/28.76    (29)  op(e0, e3) = all_52_25
% 178.99/28.76    (30)   ~ (e3 = e0)
% 178.99/28.76    (31)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.76    (32)   ~ (all_52_15 = all_52_23)
% 178.99/28.76    (33)  all_58_13 = all_52_27
% 178.99/28.76    (34)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.76    (35)  all_58_12 = e3
% 178.99/28.76    (36)  all_58_6 = all_52_17
% 178.99/28.76    (37)   ~ (all_52_3 = all_52_7)
% 178.99/28.76    (38)  all_56_0 = all_4_2
% 178.99/28.76    (39)  all_58_11 = all_52_23
% 178.99/28.76    (40)   ~ (all_52_3 = all_52_19)
% 178.99/28.76    (41)   ~ (all_52_7 = all_52_15)
% 178.99/28.76    (42)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 178.99/28.76    (43)  op(e3, e1) = all_52_5
% 178.99/28.76    (44)   ~ (all_52_25 = all_6_2)
% 178.99/28.76    (45)  op(e1, e3) = all_52_17
% 178.99/28.76    (46)   ~ (all_52_25 = all_4_2)
% 178.99/28.76    (47)  op(e3, e0) = all_52_7
% 178.99/28.76    (48)   ~ (all_52_17 = all_4_2)
% 178.99/28.76    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.76            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.76    (50)   ~ (all_52_25 = all_52_27)
% 178.99/28.76    (51)   ~ (all_52_7 = all_6_2)
% 178.99/28.76    (52)  op(e1, all_52_5) = e1
% 178.99/28.76    (53)   ~ (all_52_7 = all_52_23)
% 178.99/28.76    (54)   ~ (all_52_13 = all_10_2)
% 178.99/28.76    (55)  op(e0, all_52_7) = e0
% 178.99/28.76    (56)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.76    (57)  all_58_9 = all_52_7
% 178.99/28.76    (58)  all_58_12 = all_52_25
% 178.99/28.76    (59)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.76    (60)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.76    (61)  op(e2, e3) = all_52_9
% 178.99/28.76  
% 178.99/28.76  Begin of proof
% 178.99/28.76  | 
% 178.99/28.76  | COMBINE_EQS: (35), (58) imply:
% 178.99/28.76  |   (62)  all_52_25 = e3
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (62) implies:
% 178.99/28.76  |   (63)  all_52_25 = e3
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (16), (63) imply:
% 178.99/28.76  |   (64)   ~ (all_52_17 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (50), (63) imply:
% 178.99/28.76  |   (65)   ~ (all_52_27 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (65) implies:
% 178.99/28.76  |   (66)   ~ (all_52_27 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (8), (63) imply:
% 178.99/28.76  |   (67)   ~ (all_52_29 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (67) implies:
% 178.99/28.76  |   (68)   ~ (all_52_29 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (44), (63) imply:
% 178.99/28.76  |   (69)   ~ (all_6_2 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (69) implies:
% 178.99/28.76  |   (70)   ~ (all_6_2 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (46), (63) imply:
% 178.99/28.76  |   (71)   ~ (all_4_2 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | SIMP: (71) implies:
% 178.99/28.76  |   (72)   ~ (all_4_2 = e3)
% 178.99/28.76  | 
% 178.99/28.76  | REDUCE: (29), (63) imply:
% 178.99/28.76  |   (73)  op(e0, e3) = e3
% 178.99/28.76  | 
% 178.99/28.76  | BETA: splitting (10) gives:
% 178.99/28.76  | 
% 178.99/28.76  | Case 1:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (74)  all_56_0 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | COMBINE_EQS: (38), (74) imply:
% 178.99/28.76  | |   (75)  all_4_2 = e3
% 178.99/28.76  | | 
% 178.99/28.76  | | REDUCE: (72), (75) imply:
% 178.99/28.76  | |   (76)  $false
% 178.99/28.76  | | 
% 178.99/28.76  | | CLOSE: (76) is inconsistent.
% 178.99/28.76  | | 
% 178.99/28.76  | Case 2:
% 178.99/28.76  | | 
% 178.99/28.76  | |   (77)   ~ (all_56_0 = e3)
% 178.99/28.76  | |   (78)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.77  | | 
% 178.99/28.77  | | BETA: splitting (42) gives:
% 178.99/28.77  | | 
% 178.99/28.77  | | Case 1:
% 178.99/28.77  | | | 
% 178.99/28.77  | | |   (79)  all_56_11 = e3
% 178.99/28.77  | | | 
% 178.99/28.77  | | | COMBINE_EQS: (6), (79) imply:
% 178.99/28.77  | | |   (80)  all_52_23 = e3
% 178.99/28.77  | | | 
% 178.99/28.77  | | | SIMP: (80) implies:
% 178.99/28.77  | | |   (81)  all_52_23 = e3
% 178.99/28.77  | | | 
% 178.99/28.77  | | | REDUCE: (5), (81) imply:
% 178.99/28.77  | | |   (82)   ~ (all_52_19 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | REDUCE: (1), (81) imply:
% 178.99/28.77  | | |   (83)   ~ (all_14_2 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | SIMP: (83) implies:
% 178.99/28.77  | | |   (84)   ~ (all_14_2 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | BETA: splitting (23) gives:
% 178.99/28.77  | | | 
% 178.99/28.77  | | | Case 1:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (85)  all_58_1 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | REF_CLOSE: (2), (3), (7), (12), (17), (20), (22), (24), (25), (26),
% 178.99/28.77  | | | |            (28), (34), (37), (38), (43), (47), (49), (60), (61), (68),
% 178.99/28.77  | | | |            (78), (84), (85) are inconsistent by sub-proof #866.
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | Case 2:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (86)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | BETA: splitting (86) gives:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | Case 1:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (87)  all_58_3 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | COMBINE_EQS: (9), (87) imply:
% 178.99/28.77  | | | | |   (88)  all_10_2 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REDUCE: (54), (88) imply:
% 178.99/28.77  | | | | |   (89)   ~ (all_52_13 = e3)
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REF_CLOSE: (3), (4), (7), (10), (11), (12), (13), (14), (17), (19),
% 178.99/28.77  | | | | |            (20), (22), (24), (25), (26), (27), (28), (29), (31), (34),
% 178.99/28.77  | | | | |            (37), (38), (39), (41), (43), (45), (46), (47), (48), (49),
% 178.99/28.77  | | | | |            (51), (52), (53), (55), (56), (57), (59), (60), (61), (68),
% 178.99/28.77  | | | | |            (72), (78), (89) are inconsistent by sub-proof #867.
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | Case 2:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (90)  all_58_7 = e3 | all_58_13 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REF_CLOSE: (15), (33), (66), (82), (90) are inconsistent by sub-proof
% 178.99/28.77  | | | | |            #976.
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | End of split
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | End of split
% 178.99/28.77  | | | 
% 178.99/28.77  | | Case 2:
% 178.99/28.77  | | | 
% 178.99/28.77  | | |   (91)   ~ (all_56_11 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | REDUCE: (6), (91) imply:
% 178.99/28.77  | | |   (92)   ~ (all_52_23 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | BETA: splitting (56) gives:
% 178.99/28.77  | | | 
% 178.99/28.77  | | | Case 1:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (93)  all_58_9 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | REF_CLOSE: (30), (49), (55), (57), (73), (93) are inconsistent by
% 178.99/28.77  | | | |            sub-proof #798.
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | Case 2:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (94)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | BETA: splitting (94) gives:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | Case 1:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (95)  all_58_10 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | COMBINE_EQS: (14), (95) imply:
% 178.99/28.77  | | | | |   (96)  all_52_15 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | SIMP: (96) implies:
% 178.99/28.77  | | | | |   (97)  all_52_15 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REDUCE: (21), (97) imply:
% 178.99/28.77  | | | | |   (98)   ~ (all_52_13 = e3)
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REDUCE: (32), (97) imply:
% 178.99/28.77  | | | | |   (99)   ~ (all_52_23 = e3)
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REF_CLOSE: (3), (4), (7), (10), (11), (12), (13), (14), (15), (17),
% 178.99/28.77  | | | | |            (18), (19), (20), (22), (24), (26), (27), (28), (29), (31),
% 178.99/28.77  | | | | |            (34), (36), (37), (38), (39), (40), (41), (43), (45), (46),
% 178.99/28.77  | | | | |            (47), (48), (49), (51), (52), (53), (55), (56), (57), (59),
% 178.99/28.77  | | | | |            (60), (61), (64), (68), (72), (78), (92), (98) are
% 178.99/28.77  | | | | |            inconsistent by sub-proof #869.
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | Case 2:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (100)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REF_CLOSE: (11), (39), (70), (92), (100) are inconsistent by sub-proof
% 178.99/28.77  | | | | |            #1016.
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | End of split
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | End of split
% 178.99/28.77  | | | 
% 178.99/28.77  | | End of split
% 178.99/28.77  | | 
% 178.99/28.77  | End of split
% 178.99/28.77  | 
% 178.99/28.77  End of proof
% 178.99/28.77  
% 178.99/28.77  Sub-proof #798 shows that the following formulas are inconsistent:
% 178.99/28.77  ----------------------------------------------------------------
% 178.99/28.77    (1)  all_58_9 = e3
% 178.99/28.77    (2)  op(e0, e3) = e3
% 178.99/28.77    (3)   ~ (e3 = e0)
% 178.99/28.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.77    (5)  op(e0, all_52_7) = e0
% 178.99/28.77    (6)  all_58_9 = all_52_7
% 178.99/28.77  
% 178.99/28.77  Begin of proof
% 178.99/28.77  | 
% 178.99/28.77  | COMBINE_EQS: (1), (6) imply:
% 178.99/28.77  |   (7)  all_52_7 = e3
% 178.99/28.77  | 
% 178.99/28.77  | SIMP: (7) implies:
% 178.99/28.77  |   (8)  all_52_7 = e3
% 178.99/28.77  | 
% 178.99/28.77  | REDUCE: (5), (8) imply:
% 178.99/28.77  |   (9)  op(e0, e3) = e0
% 178.99/28.77  | 
% 178.99/28.77  | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1027.
% 178.99/28.77  | 
% 178.99/28.77  End of proof
% 178.99/28.77  
% 178.99/28.77  Sub-proof #799 shows that the following formulas are inconsistent:
% 178.99/28.77  ----------------------------------------------------------------
% 178.99/28.77    (1)   ~ (all_52_25 = e3)
% 178.99/28.77    (2)   ~ (all_52_23 = all_14_2)
% 178.99/28.77    (3)   ~ (all_52_17 = all_52_23)
% 178.99/28.77    (4)  op(e2, all_52_3) = e2
% 178.99/28.77    (5)  op(e3, e2) = all_52_3
% 178.99/28.77    (6)   ~ (all_52_9 = all_52_25)
% 178.99/28.77    (7)  op(e1, e2) = all_52_19
% 178.99/28.77    (8)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.77    (9)   ~ (all_6_2 = e3)
% 178.99/28.77    (10)  all_58_5 = all_52_13
% 178.99/28.77    (11)   ~ (all_6_2 = e0)
% 178.99/28.77    (12)   ~ (all_52_25 = all_52_29)
% 178.99/28.77    (13)  all_56_15 = all_6_2
% 178.99/28.77    (14)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.77    (15)  op(e2, e0) = all_52_15
% 178.99/28.77    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.77    (17)  all_58_15 = all_6_2
% 178.99/28.77    (18)   ~ (all_52_9 = all_4_2)
% 178.99/28.77    (19)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.77    (20)   ~ (all_52_5 = all_52_7)
% 178.99/28.77    (21)  all_58_10 = all_52_15
% 178.99/28.77    (22)   ~ (all_52_5 = all_4_2)
% 178.99/28.77    (23)  all_58_7 = all_52_19
% 178.99/28.77    (24)  all_56_4 = all_52_9
% 178.99/28.77    (25)   ~ (all_52_17 = all_52_25)
% 178.99/28.77    (26)  op(e0, e1) = all_52_29
% 178.99/28.77    (27)  all_58_4 = all_52_5
% 178.99/28.77    (28)  op(e2, e3) = all_52_26
% 178.99/28.77    (29)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.77    (30)   ~ (e3 = e1)
% 178.99/28.77    (31)   ~ (all_52_7 = all_4_2)
% 178.99/28.77    (32)  all_58_1 = all_52_3
% 178.99/28.77    (33)   ~ (all_52_13 = all_52_15)
% 178.99/28.77    (34)  all_58_0 = all_4_2
% 178.99/28.77    (35)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.77    (36)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.77    (37)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.77    (38)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.77    (39)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.77    (40)  all_58_14 = all_52_29
% 178.99/28.77    (41)   ~ (all_52_3 = all_52_5)
% 178.99/28.77    (42)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.77    (43)  all_58_8 = all_14_2
% 178.99/28.77    (44)  all_56_1 = all_52_3
% 178.99/28.77    (45)  all_56_14 = all_52_29
% 178.99/28.77    (46)   ~ (all_52_5 = all_14_2)
% 178.99/28.77    (47)  op(e3, all_4_2) = e3
% 178.99/28.77    (48)  op(e0, e3) = all_52_25
% 178.99/28.77    (49)   ~ (all_52_29 = e3)
% 178.99/28.77    (50)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.99/28.77    (51)   ~ (all_52_13 = all_14_2)
% 178.99/28.77    (52)   ~ (e3 = e0)
% 178.99/28.77    (53)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.77    (54)   ~ (all_52_9 = all_52_13)
% 178.99/28.77    (55)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.99/28.77    (56)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.77    (57)   ~ (all_52_5 = all_52_29)
% 178.99/28.77    (58)  all_56_2 = all_52_5
% 178.99/28.77    (59)  op(e1, e0) = all_52_23
% 178.99/28.77    (60)  all_56_12 = all_52_25
% 178.99/28.77    (61)   ~ (all_52_3 = e3)
% 178.99/28.77    (62)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.77    (63)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.77    (64)   ~ (all_52_9 = all_52_17)
% 178.99/28.77    (65)  all_58_6 = all_52_17
% 178.99/28.77    (66)   ~ (all_52_3 = all_52_7)
% 178.99/28.77    (67)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.77    (68)   ~ (e1 = e0)
% 178.99/28.77    (69)  all_56_0 = all_4_2
% 178.99/28.77    (70)  all_58_11 = all_52_23
% 178.99/28.77    (71)   ~ (all_52_3 = all_52_19)
% 178.99/28.77    (72)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.77    (73)   ~ (all_52_7 = all_52_15)
% 178.99/28.77    (74)   ~ (all_52_29 = all_14_2)
% 178.99/28.77    (75)   ~ (all_52_23 = all_6_2)
% 178.99/28.77    (76)   ~ (all_52_29 = all_6_2)
% 178.99/28.77    (77)  all_58_2 = all_52_9
% 178.99/28.77    (78)  op(e3, e1) = all_52_5
% 178.99/28.77    (79)  all_56_10 = all_14_2
% 178.99/28.77    (80)   ~ (all_52_25 = all_6_2)
% 178.99/28.77    (81)  op(e1, e1) = all_14_2
% 178.99/28.77    (82)   ~ (all_52_19 = e3)
% 178.99/28.77    (83)  op(e1, e3) = all_52_17
% 178.99/28.77    (84)   ~ (all_52_25 = all_4_2)
% 178.99/28.77    (85)  op(e3, e0) = all_52_7
% 178.99/28.77    (86)   ~ (all_52_17 = all_4_2)
% 178.99/28.77    (87)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.77    (88)   ~ (all_52_7 = all_6_2)
% 178.99/28.77    (89)  op(e1, all_52_5) = e1
% 178.99/28.77    (90)   ~ (all_52_7 = all_52_23)
% 178.99/28.77    (91)  op(e0, all_52_7) = e0
% 178.99/28.77    (92)   ~ (all_52_17 = all_52_19)
% 178.99/28.77    (93)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.77    (94)  all_58_9 = all_52_7
% 178.99/28.77    (95)  all_58_12 = all_52_25
% 178.99/28.77    (96)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.77    (97)   ~ (all_52_9 = all_52_15)
% 178.99/28.77    (98)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.77    (99)   ~ (e3 = e2)
% 178.99/28.77    (100)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.77    (101)   ~ (all_52_19 = all_14_2)
% 178.99/28.77    (102)  op(e2, e3) = all_52_9
% 178.99/28.77  
% 178.99/28.77  Begin of proof
% 178.99/28.77  | 
% 178.99/28.77  | GROUND_INST: instantiating (87) with all_52_9, all_52_26, e3, e2, simplifying
% 178.99/28.77  |              with (28), (102) gives:
% 178.99/28.77  |   (103)  all_52_9 = all_52_26
% 178.99/28.77  | 
% 178.99/28.77  | COMBINE_EQS: (24), (103) imply:
% 178.99/28.77  |   (104)  all_56_4 = all_52_26
% 178.99/28.77  | 
% 178.99/28.77  | COMBINE_EQS: (77), (103) imply:
% 178.99/28.77  |   (105)  all_58_2 = all_52_26
% 178.99/28.77  | 
% 178.99/28.77  | REDUCE: (54), (103) imply:
% 178.99/28.77  |   (106)   ~ (all_52_13 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | SIMP: (106) implies:
% 178.99/28.77  |   (107)   ~ (all_52_13 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | REDUCE: (97), (103) imply:
% 178.99/28.77  |   (108)   ~ (all_52_15 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | SIMP: (108) implies:
% 178.99/28.77  |   (109)   ~ (all_52_15 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | REDUCE: (64), (103) imply:
% 178.99/28.77  |   (110)   ~ (all_52_17 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | SIMP: (110) implies:
% 178.99/28.77  |   (111)   ~ (all_52_17 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | REDUCE: (6), (103) imply:
% 178.99/28.77  |   (112)   ~ (all_52_25 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | SIMP: (112) implies:
% 178.99/28.77  |   (113)   ~ (all_52_25 = all_52_26)
% 178.99/28.77  | 
% 178.99/28.77  | REDUCE: (18), (103) imply:
% 178.99/28.77  |   (114)   ~ (all_52_26 = all_4_2)
% 178.99/28.77  | 
% 178.99/28.77  | BETA: splitting (37) gives:
% 178.99/28.77  | 
% 178.99/28.77  | Case 1:
% 178.99/28.77  | | 
% 178.99/28.77  | |   (115)  all_56_14 = e3
% 178.99/28.77  | | 
% 178.99/28.77  | | REF_CLOSE: (45), (49), (115) are inconsistent by sub-proof #896.
% 178.99/28.77  | | 
% 178.99/28.77  | Case 2:
% 178.99/28.77  | | 
% 178.99/28.77  | |   (116)   ~ (all_56_14 = e3)
% 178.99/28.77  | |   (117)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.77  | | 
% 178.99/28.77  | | BETA: splitting (36) gives:
% 178.99/28.77  | | 
% 178.99/28.77  | | Case 1:
% 178.99/28.77  | | | 
% 178.99/28.77  | | |   (118)  all_56_1 = e3
% 178.99/28.77  | | | 
% 178.99/28.77  | | | REF_CLOSE: (44), (61), (118) are inconsistent by sub-proof #862.
% 178.99/28.77  | | | 
% 178.99/28.77  | | Case 2:
% 178.99/28.77  | | | 
% 178.99/28.77  | | |   (119)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.77  | | | 
% 178.99/28.77  | | | BETA: splitting (55) gives:
% 178.99/28.77  | | | 
% 178.99/28.77  | | | Case 1:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (120)  all_56_12 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | REF_CLOSE: (1), (60), (120) are inconsistent by sub-proof #1040.
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | Case 2:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (121)   ~ (all_56_12 = e3)
% 178.99/28.77  | | | |   (122)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | BETA: splitting (56) gives:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | Case 1:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (123)  all_56_10 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | COMBINE_EQS: (79), (123) imply:
% 178.99/28.77  | | | | |   (124)  all_14_2 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | SIMP: (124) implies:
% 178.99/28.77  | | | | |   (125)  all_14_2 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REDUCE: (46), (125) imply:
% 178.99/28.77  | | | | |   (126)   ~ (all_52_5 = e3)
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REDUCE: (2), (125) imply:
% 178.99/28.77  | | | | |   (127)   ~ (all_52_23 = e3)
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | BETA: splitting (93) gives:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | Case 1:
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | |   (128)  all_58_9 = e3
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | COMBINE_EQS: (94), (128) imply:
% 178.99/28.77  | | | | | |   (129)  all_52_7 = e3
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | SIMP: (129) implies:
% 178.99/28.77  | | | | | |   (130)  all_52_7 = e3
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | REDUCE: (31), (130) imply:
% 178.99/28.77  | | | | | |   (131)   ~ (all_4_2 = e3)
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | SIMP: (131) implies:
% 178.99/28.77  | | | | | |   (132)   ~ (all_4_2 = e3)
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | REF_CLOSE: (5), (16), (17), (20), (21), (27), (31), (32), (34),
% 178.99/28.77  | | | | | |            (47), (48), (61), (62), (66), (69), (70), (73), (78),
% 178.99/28.77  | | | | | |            (84), (87), (88), (90), (91), (93), (94), (96), (126),
% 178.99/28.77  | | | | | |            (132) are inconsistent by sub-proof #1012.
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | Case 2:
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | |   (133)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | BETA: splitting (133) gives:
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | Case 1:
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | |   (134)  all_58_10 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | COMBINE_EQS: (21), (134) imply:
% 178.99/28.77  | | | | | | |   (135)  all_52_15 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | SIMP: (135) implies:
% 178.99/28.77  | | | | | | |   (136)  all_52_15 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | REDUCE: (15), (136) imply:
% 178.99/28.77  | | | | | | |   (137)  op(e2, e0) = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | BETA: splitting (100) gives:
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | Case 1:
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | |   (138)  all_56_2 = e3
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | | REF_CLOSE: (58), (126), (138) are inconsistent by sub-proof
% 178.99/28.77  | | | | | | | |            #931.
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | Case 2:
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | |   (139)   ~ (all_56_2 = e3)
% 178.99/28.77  | | | | | | | |   (140)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | | BETA: splitting (72) gives:
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | | Case 1:
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | |   (141)  all_58_4 = e2
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | COMBINE_EQS: (27), (141) imply:
% 178.99/28.77  | | | | | | | | |   (142)  all_52_5 = e2
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | REDUCE: (41), (142) imply:
% 178.99/28.77  | | | | | | | | |   (143)   ~ (all_52_3 = e2)
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | REDUCE: (126), (142) imply:
% 178.99/28.77  | | | | | | | | |   (144)   ~ (e3 = e2)
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | REDUCE: (89), (142) imply:
% 178.99/28.77  | | | | | | | | |   (145)  op(e1, e2) = e1
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | GROUND_INST: instantiating (87) with all_52_19, e1, e2, e1,
% 178.99/28.77  | | | | | | | | |              simplifying with (7), (145) gives:
% 178.99/28.77  | | | | | | | | |   (146)  all_52_19 = e1
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | REDUCE: (71), (146) imply:
% 178.99/28.77  | | | | | | | | |   (147)   ~ (all_52_3 = e1)
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | BETA: splitting (119) gives:
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | Case 1:
% 178.99/28.77  | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | |   (148)  all_56_1 = e2
% 178.99/28.77  | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | REF_CLOSE: (44), (143), (148) are inconsistent by sub-proof
% 178.99/28.77  | | | | | | | | | |            #857.
% 178.99/28.77  | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | Case 2:
% 178.99/28.77  | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | |   (149)  all_56_1 = e1 | all_56_1 = e0
% 178.99/28.77  | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | BETA: splitting (149) gives:
% 178.99/28.77  | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | Case 1:
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | |   (150)  all_56_1 = e1
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | | REF_CLOSE: (44), (147), (150) are inconsistent by sub-proof
% 178.99/28.77  | | | | | | | | | | |            #841.
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | Case 2:
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | |   (151)  all_56_1 = e0
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | | COMBINE_EQS: (44), (151) imply:
% 178.99/28.77  | | | | | | | | | | |   (152)  all_52_3 = e0
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | | SIMP: (152) implies:
% 178.99/28.77  | | | | | | | | | | |   (153)  all_52_3 = e0
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | | REDUCE: (4), (153) imply:
% 178.99/28.77  | | | | | | | | | | |   (154)  op(e2, e0) = e2
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | | REF_CLOSE: (87), (99), (137), (154) are inconsistent by
% 178.99/28.77  | | | | | | | | | | |            sub-proof #828.
% 178.99/28.77  | | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | | End of split
% 178.99/28.77  | | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | End of split
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | Case 2:
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | |   (155)   ~ (all_58_4 = e2)
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | | REF_CLOSE: (20), (27), (35), (38), (46), (58), (59), (70),
% 178.99/28.77  | | | | | | | | |            (81), (87), (89), (94), (126), (134), (140), (155)
% 178.99/28.77  | | | | | | | | |            are inconsistent by sub-proof #822.
% 178.99/28.77  | | | | | | | | | 
% 178.99/28.77  | | | | | | | | End of split
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | End of split
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | Case 2:
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | |   (156)  all_58_11 = e3 | all_58_15 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | REF_CLOSE: (9), (17), (70), (127), (156) are inconsistent by
% 178.99/28.77  | | | | | | |            sub-proof #1016.
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | End of split
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | End of split
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | Case 2:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (157)   ~ (all_56_10 = e3)
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REDUCE: (79), (157) imply:
% 178.99/28.77  | | | | |   (158)   ~ (all_14_2 = e3)
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 178.99/28.77  | | | | |            (16), (17), (19), (20), (21), (22), (23), (25), (26), (27),
% 178.99/28.77  | | | | |            (29), (30), (31), (32), (33), (34), (35), (38), (39), (40),
% 178.99/28.77  | | | | |            (41), (42), (43), (45), (46), (47), (48), (49), (50), (51),
% 178.99/28.77  | | | | |            (52), (53), (57), (58), (59), (60), (62), (63), (65), (66),
% 178.99/28.77  | | | | |            (67), (68), (69), (70), (71), (72), (74), (75), (76), (78),
% 178.99/28.77  | | | | |            (80), (81), (82), (83), (84), (85), (86), (87), (89), (91),
% 178.99/28.77  | | | | |            (92), (93), (94), (95), (98), (99), (100), (101), (104),
% 178.99/28.77  | | | | |            (105), (107), (109), (111), (113), (114), (117), (122),
% 178.99/28.77  | | | | |            (158) are inconsistent by sub-proof #800.
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | End of split
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | End of split
% 178.99/28.77  | | | 
% 178.99/28.77  | | End of split
% 178.99/28.77  | | 
% 178.99/28.77  | End of split
% 178.99/28.77  | 
% 178.99/28.77  End of proof
% 178.99/28.77  
% 178.99/28.77  Sub-proof #800 shows that the following formulas are inconsistent:
% 178.99/28.77  ----------------------------------------------------------------
% 178.99/28.77    (1)   ~ (all_52_25 = e3)
% 178.99/28.77    (2)   ~ (all_52_17 = all_52_23)
% 178.99/28.77    (3)  op(e3, e2) = all_52_3
% 178.99/28.77    (4)  op(e1, e2) = all_52_19
% 178.99/28.77    (5)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.77    (6)   ~ (all_6_2 = e3)
% 178.99/28.77    (7)  all_58_5 = all_52_13
% 178.99/28.77    (8)   ~ (all_6_2 = e0)
% 178.99/28.77    (9)   ~ (all_52_25 = all_52_29)
% 178.99/28.77    (10)  all_56_15 = all_6_2
% 178.99/28.77    (11)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.77    (12)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.77    (13)  all_58_15 = all_6_2
% 178.99/28.77    (14)   ~ (all_52_26 = all_4_2)
% 178.99/28.77    (15)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.77    (16)   ~ (all_52_5 = all_52_7)
% 178.99/28.77    (17)  all_58_10 = all_52_15
% 178.99/28.77    (18)   ~ (all_52_5 = all_4_2)
% 178.99/28.77    (19)  all_58_7 = all_52_19
% 178.99/28.77    (20)   ~ (all_52_17 = all_52_25)
% 178.99/28.77    (21)  op(e0, e1) = all_52_29
% 178.99/28.77    (22)  all_58_4 = all_52_5
% 178.99/28.77    (23)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.77    (24)   ~ (e3 = e1)
% 178.99/28.77    (25)   ~ (all_52_7 = all_4_2)
% 178.99/28.77    (26)  all_58_1 = all_52_3
% 178.99/28.77    (27)   ~ (all_52_13 = all_52_15)
% 178.99/28.77    (28)  all_58_0 = all_4_2
% 178.99/28.77    (29)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.77    (30)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.77    (31)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.77    (32)  all_58_14 = all_52_29
% 178.99/28.77    (33)   ~ (all_52_13 = all_52_26)
% 178.99/28.77    (34)   ~ (all_52_3 = all_52_5)
% 178.99/28.77    (35)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.77    (36)  all_58_8 = all_14_2
% 178.99/28.77    (37)  all_56_14 = all_52_29
% 178.99/28.77    (38)   ~ (all_52_5 = all_14_2)
% 178.99/28.77    (39)  op(e3, all_4_2) = e3
% 178.99/28.77    (40)  op(e0, e3) = all_52_25
% 178.99/28.77    (41)   ~ (all_52_29 = e3)
% 178.99/28.77    (42)  all_58_4 = e0 | all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.99/28.77    (43)   ~ (all_52_13 = all_14_2)
% 178.99/28.77    (44)   ~ (e3 = e0)
% 178.99/28.77    (45)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 178.99/28.77    (46)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.77    (47)   ~ (all_52_5 = all_52_29)
% 178.99/28.77    (48)  all_56_2 = all_52_5
% 178.99/28.77    (49)  op(e1, e0) = all_52_23
% 178.99/28.77    (50)  all_56_12 = all_52_25
% 178.99/28.77    (51)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.77    (52)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.77    (53)  all_58_6 = all_52_17
% 178.99/28.77    (54)   ~ (all_52_3 = all_52_7)
% 178.99/28.77    (55)  all_58_2 = all_52_26
% 178.99/28.77    (56)  all_56_4 = e3 | all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.77    (57)   ~ (e1 = e0)
% 178.99/28.77    (58)  all_56_0 = all_4_2
% 178.99/28.77    (59)  all_58_11 = all_52_23
% 178.99/28.77    (60)   ~ (all_52_3 = all_52_19)
% 178.99/28.77    (61)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.77    (62)   ~ (all_52_29 = all_14_2)
% 178.99/28.77    (63)   ~ (all_52_23 = all_6_2)
% 178.99/28.77    (64)   ~ (all_52_29 = all_6_2)
% 178.99/28.77    (65)  op(e3, e1) = all_52_5
% 178.99/28.77    (66)   ~ (all_52_25 = all_6_2)
% 178.99/28.77    (67)  op(e1, e1) = all_14_2
% 178.99/28.77    (68)   ~ (all_52_19 = e3)
% 178.99/28.77    (69)  op(e1, e3) = all_52_17
% 178.99/28.77    (70)   ~ (all_52_25 = all_4_2)
% 178.99/28.77    (71)  op(e3, e0) = all_52_7
% 178.99/28.77    (72)   ~ (all_14_2 = e3)
% 178.99/28.77    (73)   ~ (all_52_17 = all_4_2)
% 178.99/28.77    (74)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.77    (75)  op(e1, all_52_5) = e1
% 178.99/28.77    (76)  op(e0, all_52_7) = e0
% 178.99/28.77    (77)   ~ (all_52_25 = all_52_26)
% 178.99/28.77    (78)   ~ (all_52_17 = all_52_19)
% 178.99/28.77    (79)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.77    (80)  all_56_4 = all_52_26
% 178.99/28.77    (81)  all_58_9 = all_52_7
% 178.99/28.77    (82)   ~ (all_52_15 = all_52_26)
% 178.99/28.77    (83)  all_58_12 = all_52_25
% 178.99/28.77    (84)   ~ (all_52_17 = all_52_26)
% 178.99/28.77    (85)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.77    (86)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.77    (87)   ~ (e3 = e2)
% 178.99/28.77    (88)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.77    (89)   ~ (all_52_19 = all_14_2)
% 178.99/28.77  
% 178.99/28.77  Begin of proof
% 178.99/28.77  | 
% 178.99/28.77  | BETA: splitting (85) gives:
% 178.99/28.77  | 
% 178.99/28.77  | Case 1:
% 178.99/28.77  | | 
% 178.99/28.77  | |   (90)  all_58_4 = e3
% 178.99/28.77  | | 
% 178.99/28.77  | | REF_CLOSE: (3), (12), (16), (18), (22), (28), (34), (39), (46), (58), (69),
% 178.99/28.77  | |            (71), (73), (74), (75), (90) are inconsistent by sub-proof #821.
% 178.99/28.77  | | 
% 178.99/28.77  | Case 2:
% 178.99/28.77  | | 
% 178.99/28.77  | |   (91)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.77  | | 
% 178.99/28.77  | | BETA: splitting (91) gives:
% 178.99/28.77  | | 
% 178.99/28.77  | | Case 1:
% 178.99/28.77  | | | 
% 178.99/28.77  | | |   (92)  all_58_5 = e3
% 178.99/28.77  | | | 
% 178.99/28.77  | | | COMBINE_EQS: (7), (92) imply:
% 178.99/28.77  | | |   (93)  all_52_13 = e3
% 178.99/28.77  | | | 
% 178.99/28.77  | | | SIMP: (93) implies:
% 178.99/28.77  | | |   (94)  all_52_13 = e3
% 178.99/28.77  | | | 
% 178.99/28.77  | | | REDUCE: (27), (94) imply:
% 178.99/28.77  | | |   (95)   ~ (all_52_15 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | SIMP: (95) implies:
% 178.99/28.77  | | |   (96)   ~ (all_52_15 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | REDUCE: (33), (94) imply:
% 178.99/28.77  | | |   (97)   ~ (all_52_26 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | SIMP: (97) implies:
% 178.99/28.77  | | |   (98)   ~ (all_52_26 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | REDUCE: (43), (94) imply:
% 178.99/28.77  | | |   (99)   ~ (all_14_2 = e3)
% 178.99/28.77  | | | 
% 178.99/28.77  | | | BETA: splitting (23) gives:
% 178.99/28.77  | | | 
% 178.99/28.77  | | | Case 1:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (100)  all_58_6 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | COMBINE_EQS: (53), (100) imply:
% 178.99/28.77  | | | |   (101)  all_52_17 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | SIMP: (101) implies:
% 178.99/28.77  | | | |   (102)  all_52_17 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | REDUCE: (20), (102) imply:
% 178.99/28.77  | | | |   (103)   ~ (all_52_25 = e3)
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | REDUCE: (73), (102) imply:
% 178.99/28.77  | | | |   (104)   ~ (all_4_2 = e3)
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | SIMP: (104) implies:
% 178.99/28.77  | | | |   (105)   ~ (all_4_2 = e3)
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | REF_CLOSE: (1), (2), (3), (6), (12), (13), (16), (17), (25), (28), (35),
% 178.99/28.77  | | | |            (39), (40), (51), (53), (54), (55), (58), (59), (65), (70),
% 178.99/28.77  | | | |            (74), (76), (79), (81), (83), (96), (98), (105) are
% 178.99/28.77  | | | |            inconsistent by sub-proof #819.
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | Case 2:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | |   (106)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | BETA: splitting (106) gives:
% 178.99/28.77  | | | | 
% 178.99/28.77  | | | | Case 1:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (107)  all_58_7 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | COMBINE_EQS: (19), (107) imply:
% 178.99/28.77  | | | | |   (108)  all_52_19 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | REDUCE: (68), (108) imply:
% 178.99/28.77  | | | | |   (109)  $false
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | CLOSE: (109) is inconsistent.
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | Case 2:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | |   (110)  all_58_8 = e3 | all_58_11 = e3
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | BETA: splitting (35) gives:
% 178.99/28.77  | | | | | 
% 178.99/28.77  | | | | | Case 1:
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | |   (111)  all_58_0 = e3
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | COMBINE_EQS: (28), (111) imply:
% 178.99/28.77  | | | | | |   (112)  all_4_2 = e3
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | REDUCE: (18), (112) imply:
% 178.99/28.77  | | | | | |   (113)   ~ (all_52_5 = e3)
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | BETA: splitting (110) gives:
% 178.99/28.77  | | | | | | 
% 178.99/28.77  | | | | | | Case 1:
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | |   (114)  all_58_8 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | COMBINE_EQS: (36), (114) imply:
% 178.99/28.77  | | | | | | |   (115)  all_14_2 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | REDUCE: (72), (115) imply:
% 178.99/28.77  | | | | | | |   (116)  $false
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | CLOSE: (116) is inconsistent.
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | Case 2:
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | |   (117)  all_58_11 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | COMBINE_EQS: (59), (117) imply:
% 178.99/28.77  | | | | | | |   (118)  all_52_23 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | SIMP: (118) implies:
% 178.99/28.77  | | | | | | |   (119)  all_52_23 = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | REDUCE: (63), (119) imply:
% 178.99/28.77  | | | | | | |   (120)   ~ (all_6_2 = e3)
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | REDUCE: (49), (119) imply:
% 178.99/28.77  | | | | | | |   (121)  op(e1, e0) = e3
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | BETA: splitting (88) gives:
% 178.99/28.77  | | | | | | | 
% 178.99/28.77  | | | | | | | Case 1:
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | |   (122)  all_56_2 = e3
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | | REF_CLOSE: (48), (113), (122) are inconsistent by sub-proof
% 178.99/28.77  | | | | | | | |            #931.
% 178.99/28.77  | | | | | | | | 
% 178.99/28.77  | | | | | | | Case 2:
% 178.99/28.77  | | | | | | | | 
% 178.99/28.78  | | | | | | | |   (123)   ~ (all_56_2 = e3)
% 178.99/28.78  | | | | | | | |   (124)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.78  | | | | | | | | 
% 178.99/28.78  | | | | | | | | BETA: splitting (56) gives:
% 178.99/28.78  | | | | | | | | 
% 178.99/28.78  | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | 
% 178.99/28.78  | | | | | | | | |   (125)  all_56_4 = e3
% 178.99/28.78  | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | REF_CLOSE: (80), (98), (125) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | |            #818.
% 178.99/28.78  | | | | | | | | | 
% 178.99/28.78  | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | 
% 178.99/28.78  | | | | | | | | |   (126)  all_56_4 = e2 | all_56_4 = e1 | all_56_4 = e0
% 178.99/28.78  | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | BETA: splitting (30) gives:
% 178.99/28.78  | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | |   (127)  all_58_4 = e1
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | COMBINE_EQS: (22), (127) imply:
% 178.99/28.78  | | | | | | | | | |   (128)  all_52_5 = e1
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | SIMP: (128) implies:
% 178.99/28.78  | | | | | | | | | |   (129)  all_52_5 = e1
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | REF_CLOSE: (38), (67), (74), (75), (129) are inconsistent by
% 178.99/28.78  | | | | | | | | | |            sub-proof #859.
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | |   (130)   ~ (all_58_4 = e1)
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | REDUCE: (22), (130) imply:
% 178.99/28.78  | | | | | | | | | |   (131)   ~ (all_52_5 = e1)
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | BETA: splitting (5) gives:
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | |   (132)  all_58_0 = e1
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | COMBINE_EQS: (111), (132) imply:
% 178.99/28.78  | | | | | | | | | | |   (133)  e3 = e1
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | REDUCE: (24), (133) imply:
% 178.99/28.78  | | | | | | | | | | |   (134)  $false
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | CLOSE: (134) is inconsistent.
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | |   (135)   ~ (all_58_0 = e1)
% 178.99/28.78  | | | | | | | | | | |   (136)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | BETA: splitting (11) gives:
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | |   (137)  all_58_0 = e2
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | COMBINE_EQS: (111), (137) imply:
% 178.99/28.78  | | | | | | | | | | | |   (138)  e3 = e2
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | REDUCE: (87), (138) imply:
% 178.99/28.78  | | | | | | | | | | | |   (139)  $false
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | |   (140)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | BETA: splitting (61) gives:
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | |   (141)  all_58_4 = e2
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | COMBINE_EQS: (22), (141) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (142)  all_52_5 = e2
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | SIMP: (142) implies:
% 178.99/28.78  | | | | | | | | | | | | |   (143)  all_52_5 = e2
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (47), (143) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (144)   ~ (all_52_29 = e2)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | SIMP: (144) implies:
% 178.99/28.78  | | | | | | | | | | | | |   (145)   ~ (all_52_29 = e2)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (38), (143) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (146)   ~ (all_14_2 = e2)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | SIMP: (146) implies:
% 178.99/28.78  | | | | | | | | | | | | |   (147)   ~ (all_14_2 = e2)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (113), (143) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (148)   ~ (e3 = e2)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (131), (143) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (149)   ~ (e2 = e1)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (75), (143) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (150)  op(e1, e2) = e1
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | GROUND_INST: instantiating (74) with all_52_19, e1, e2, e1,
% 178.99/28.78  | | | | | | | | | | | | |              simplifying with (4), (150) gives:
% 178.99/28.78  | | | | | | | | | | | | |   (151)  all_52_19 = e1
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | COMBINE_EQS: (19), (151) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (152)  all_58_7 = e1
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (60), (151) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (153)   ~ (all_52_3 = e1)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (78), (151) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (154)   ~ (all_52_17 = e1)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (89), (151) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (155)   ~ (all_14_2 = e1)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | SIMP: (155) implies:
% 178.99/28.78  | | | | | | | | | | | | |   (156)   ~ (all_14_2 = e1)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | BETA: splitting (52) gives:
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | |   (157)  all_58_6 = e2
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | COMBINE_EQS: (53), (157) imply:
% 178.99/28.78  | | | | | | | | | | | | | |   (158)  all_52_17 = e2
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | SIMP: (158) implies:
% 178.99/28.78  | | | | | | | | | | | | | |   (159)  all_52_17 = e2
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | REDUCE: (20), (159) imply:
% 178.99/28.78  | | | | | | | | | | | | | |   (160)   ~ (all_52_25 = e2)
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | SIMP: (160) implies:
% 178.99/28.78  | | | | | | | | | | | | | |   (161)   ~ (all_52_25 = e2)
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | REDUCE: (84), (159) imply:
% 178.99/28.78  | | | | | | | | | | | | | |   (162)   ~ (all_52_26 = e2)
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | SIMP: (162) implies:
% 178.99/28.78  | | | | | | | | | | | | | |   (163)   ~ (all_52_26 = e2)
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | |   (164)  all_58_1 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | COMBINE_EQS: (26), (164) imply:
% 178.99/28.78  | | | | | | | | | | | | | | |   (165)  all_52_3 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | REDUCE: (153), (165) imply:
% 178.99/28.78  | | | | | | | | | | | | | | |   (166)  $false
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | |   (167)  all_58_4 = e1 | all_58_9 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | |   (168)  all_58_4 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (168) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | |   (169)  e2 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | SIMP: (169) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | |   (170)  e2 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (170) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | |   (171)  all_58_6 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (15), (22), (30), (32), (36),
% 178.99/28.78  | | | | | | | | | | | | | | | |            (38), (55), (64), (66), (67), (74), (75), (83),
% 178.99/28.78  | | | | | | | | | | | | | | | |            (92), (140), (149), (156), (163), (171) are
% 178.99/28.78  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #811.
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | |   (172)  all_58_9 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (172) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | |   (173)  all_52_7 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | |   (174)  all_52_7 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | REDUCE: (76), (174) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | |   (175)  op(e0, e1) = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | |   (176)  all_58_2 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (176) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | |   (177)  all_52_26 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | SIMP: (177) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | |   (178)  all_52_26 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | REDUCE: (77), (178) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | |   (179)   ~ (all_52_25 = e1)
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | |   (180)  all_56_12 = e2
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (161), (180) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | | | | | | | | | | |            #1032.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | |   (181)   ~ (all_56_12 = e2)
% 178.99/28.78  | | | | | | | | | | | | | | | | | |   (182)  all_56_12 = e1 | all_56_12 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (183)  all_56_12 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (179), (183) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |            #1031.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (184)  all_56_12 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (184) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (185)  all_52_25 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (186)  all_52_25 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | REDUCE: (9), (186) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (187)   ~ (all_52_29 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | SIMP: (187) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (188)   ~ (all_52_29 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | REDUCE: (1), (186) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (189)   ~ (e3 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | REDUCE: (161), (186) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (190)   ~ (e2 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | SIMP: (190) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (191)   ~ (e2 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |   (192)  all_58_4 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (192) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |   (193)  e2 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (193) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |   (194)  $false
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |   (195)  all_58_5 = e0 | all_58_8 = e0 | all_58_14 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | |   (196)  all_58_5 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (92), (196) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | |            #810.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | |   (197)  all_58_8 = e0 | all_58_14 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | |   (198)  all_56_14 = e2
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (145), (198) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | |            #837.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | |   (199)  all_56_14 = e1 | all_56_14 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_56_14 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (200) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_52_29 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (201) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_52_29 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (202) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_58_14 = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (202) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | |   (204)  op(e0, e1) = e1
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_58_8 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (205) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_14_2 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (206) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (207)   ~ (e1 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (74) with e0, e1, e1, e0,
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (175), (204) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (208)  e1 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (208) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_58_9 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (57), (131), (167), (209) are inconsistent
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #808.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_58_14 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (210) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (211)  e1 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (211) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (212)  e1 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (212) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_58_9 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (57), (131), (167), (213) are inconsistent
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #808.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_56_14 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (188), (214) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | |            #887.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | |   (215)   ~ (all_58_2 = e1)
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | REDUCE: (55), (215) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | |   (216)   ~ (all_52_26 = e1)
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | |   (217)  all_58_9 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (57), (131), (167), (217) are inconsistent
% 178.99/28.78  | | | | | | | | | | | | | | | | | |            by sub-proof #808.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | |   (218)  all_58_10 = e0 | all_58_11 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (219)  all_58_10 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (219) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (220)  all_52_15 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | SIMP: (220) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (221)  all_52_15 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | REDUCE: (82), (221) imply:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (222)   ~ (all_52_26 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | SIMP: (222) implies:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (223)   ~ (all_52_26 = e0)
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |   (224)  all_56_4 = e2
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (163), (224) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |            #807.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |   (225)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (216), (223), (225) are inconsistent by
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | |            sub-proof #805.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |   (226)  all_58_11 = e0
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (117), (226) are inconsistent by sub-proof
% 178.99/28.78  | | | | | | | | | | | | | | | | | | |            #804.
% 178.99/28.78  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | |   (227)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | | REF_CLOSE: (36), (87), (117), (147), (149), (152), (227) are
% 178.99/28.78  | | | | | | | | | | | | | |            inconsistent by sub-proof #803.
% 178.99/28.78  | | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | Case 2:
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | |   (228)   ~ (all_58_4 = e2)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REDUCE: (22), (228) imply:
% 178.99/28.78  | | | | | | | | | | | | |   (229)   ~ (all_52_5 = e2)
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | | REF_CLOSE: (24), (48), (74), (75), (121), (124), (131), (229)
% 178.99/28.78  | | | | | | | | | | | | |            are inconsistent by sub-proof #801.
% 178.99/28.78  | | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | | 
% 178.99/28.78  | | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | | 
% 178.99/28.78  | | | | | | | | End of split
% 178.99/28.78  | | | | | | | | 
% 178.99/28.78  | | | | | | | End of split
% 178.99/28.78  | | | | | | | 
% 178.99/28.78  | | | | | | End of split
% 178.99/28.78  | | | | | | 
% 178.99/28.78  | | | | | Case 2:
% 178.99/28.78  | | | | | | 
% 178.99/28.78  | | | | | |   (230)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.78  | | | | | | 
% 178.99/28.78  | | | | | | REF_CLOSE: (1), (2), (3), (6), (12), (13), (16), (17), (25), (28),
% 178.99/28.78  | | | | | |            (39), (40), (51), (53), (54), (55), (58), (59), (65),
% 178.99/28.78  | | | | | |            (70), (74), (76), (79), (81), (83), (96), (98), (230) are
% 178.99/28.78  | | | | | |            inconsistent by sub-proof #820.
% 178.99/28.78  | | | | | | 
% 178.99/28.78  | | | | | End of split
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | End of split
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | End of split
% 178.99/28.78  | | | 
% 178.99/28.78  | | Case 2:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (231)  all_58_8 = e3 | all_58_14 = e3
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REF_CLOSE: (32), (36), (41), (72), (231) are inconsistent by sub-proof
% 178.99/28.78  | | |            #999.
% 178.99/28.78  | | | 
% 178.99/28.78  | | End of split
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #801 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)   ~ (all_52_5 = e2)
% 178.99/28.78    (2)   ~ (e3 = e1)
% 178.99/28.78    (3)  op(e1, e0) = e3
% 178.99/28.78    (4)  all_56_2 = all_52_5
% 178.99/28.78    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.78    (6)  op(e1, all_52_5) = e1
% 178.99/28.78    (7)   ~ (all_52_5 = e1)
% 178.99/28.78    (8)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | BETA: splitting (8) gives:
% 178.99/28.78  | 
% 178.99/28.78  | Case 1:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (9)  all_56_2 = e2
% 178.99/28.78  | | 
% 178.99/28.78  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #827.
% 178.99/28.78  | | 
% 178.99/28.78  | Case 2:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (10)  all_56_2 = e1 | all_56_2 = e0
% 178.99/28.78  | | 
% 178.99/28.78  | | BETA: splitting (10) gives:
% 178.99/28.78  | | 
% 178.99/28.78  | | Case 1:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (11)  all_56_2 = e1
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REF_CLOSE: (4), (7), (11) are inconsistent by sub-proof #826.
% 178.99/28.78  | | | 
% 178.99/28.78  | | Case 2:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (12)  all_56_2 = e0
% 178.99/28.78  | | | 
% 178.99/28.78  | | | COMBINE_EQS: (4), (12) imply:
% 178.99/28.78  | | |   (13)  all_52_5 = e0
% 178.99/28.78  | | | 
% 178.99/28.78  | | | SIMP: (13) implies:
% 178.99/28.78  | | |   (14)  all_52_5 = e0
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REDUCE: (6), (14) imply:
% 178.99/28.78  | | |   (15)  op(e1, e0) = e1
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REF_CLOSE: (2), (3), (5), (15) are inconsistent by sub-proof #802.
% 178.99/28.78  | | | 
% 178.99/28.78  | | End of split
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #802 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.78    (2)  op(e1, e0) = e3
% 178.99/28.78    (3)  op(e1, e0) = e1
% 178.99/28.78    (4)   ~ (e3 = e1)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | GROUND_INST: instantiating (1) with e3, e1, e0, e1, simplifying with (2), (3)
% 178.99/28.78  |              gives:
% 178.99/28.78  |   (5)  e3 = e1
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (4), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #803 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_11 = e3
% 178.99/28.78    (2)  all_58_7 = e1
% 178.99/28.78    (3)  all_58_8 = all_14_2
% 178.99/28.78    (4)   ~ (e2 = e1)
% 178.99/28.78    (5)   ~ (all_14_2 = e2)
% 178.99/28.78    (6)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.78    (7)   ~ (e3 = e2)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | BETA: splitting (6) gives:
% 178.99/28.78  | 
% 178.99/28.78  | Case 1:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (8)  all_58_7 = e2
% 178.99/28.78  | | 
% 178.99/28.78  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #891.
% 178.99/28.78  | | 
% 178.99/28.78  | Case 2:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (9)  all_58_8 = e2 | all_58_11 = e2
% 178.99/28.78  | | 
% 178.99/28.78  | | BETA: splitting (9) gives:
% 178.99/28.78  | | 
% 178.99/28.78  | | Case 1:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (10)  all_58_8 = e2
% 178.99/28.78  | | | 
% 178.99/28.78  | | | COMBINE_EQS: (3), (10) imply:
% 178.99/28.78  | | |   (11)  all_14_2 = e2
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REDUCE: (5), (11) imply:
% 178.99/28.78  | | |   (12)  $false
% 178.99/28.78  | | | 
% 178.99/28.78  | | | CLOSE: (12) is inconsistent.
% 178.99/28.78  | | | 
% 178.99/28.78  | | Case 2:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (13)  all_58_11 = e2
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #992.
% 178.99/28.78  | | | 
% 178.99/28.78  | | End of split
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #804 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_11 = e3
% 178.99/28.78    (2)  all_58_11 = e0
% 178.99/28.78    (3)   ~ (e3 = e0)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  e3 = e0
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  e3 = e0
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #805 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_56_4 = e1 | all_56_4 = e0
% 178.99/28.78    (2)  all_56_4 = all_52_26
% 178.99/28.78    (3)   ~ (all_52_26 = e1)
% 178.99/28.78    (4)   ~ (all_52_26 = e0)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | BETA: splitting (1) gives:
% 178.99/28.78  | 
% 178.99/28.78  | Case 1:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (5)  all_56_4 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | COMBINE_EQS: (2), (5) imply:
% 178.99/28.78  | |   (6)  all_52_26 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | SIMP: (6) implies:
% 178.99/28.78  | |   (7)  all_52_26 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | REDUCE: (3), (7) imply:
% 178.99/28.78  | |   (8)  $false
% 178.99/28.78  | | 
% 178.99/28.78  | | CLOSE: (8) is inconsistent.
% 178.99/28.78  | | 
% 178.99/28.78  | Case 2:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (9)  all_56_4 = e0
% 178.99/28.78  | | 
% 178.99/28.78  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #806.
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #806 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_56_4 = all_52_26
% 178.99/28.78    (2)  all_56_4 = e0
% 178.99/28.78    (3)   ~ (all_52_26 = e0)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  all_52_26 = e0
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  all_52_26 = e0
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #807 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_56_4 = all_52_26
% 178.99/28.78    (2)  all_56_4 = e2
% 178.99/28.78    (3)   ~ (all_52_26 = e2)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  all_52_26 = e2
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  all_52_26 = e2
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #808 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_4 = all_52_5
% 178.99/28.78    (2)  all_58_9 = e0
% 178.99/28.78    (3)  all_58_4 = e1 | all_58_9 = e1
% 178.99/28.78    (4)   ~ (e1 = e0)
% 178.99/28.78    (5)   ~ (all_52_5 = e1)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | BETA: splitting (3) gives:
% 178.99/28.78  | 
% 178.99/28.78  | Case 1:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (6)  all_58_4 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | COMBINE_EQS: (1), (6) imply:
% 178.99/28.78  | |   (7)  all_52_5 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | REDUCE: (5), (7) imply:
% 178.99/28.78  | |   (8)  $false
% 178.99/28.78  | | 
% 178.99/28.78  | | CLOSE: (8) is inconsistent.
% 178.99/28.78  | | 
% 178.99/28.78  | Case 2:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (9)  all_58_9 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #809.
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #809 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_9 = e1
% 178.99/28.78    (2)  all_58_9 = e0
% 178.99/28.78    (3)   ~ (e1 = e0)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  e1 = e0
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  e1 = e0
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #810 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_5 = e3
% 178.99/28.78    (2)  all_58_5 = e0
% 178.99/28.78    (3)   ~ (e3 = e0)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  e3 = e0
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  e3 = e0
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #811 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)   ~ (all_52_26 = e2)
% 178.99/28.78    (2)   ~ (all_6_2 = e3)
% 178.99/28.78    (3)   ~ (all_6_2 = e0)
% 178.99/28.78    (4)  all_56_15 = all_6_2
% 178.99/28.78    (5)  all_56_15 = e2 | all_56_15 = e1 | all_56_15 = e0
% 178.99/28.78    (6)  all_58_4 = all_52_5
% 178.99/28.78    (7)  all_58_5 = e3
% 178.99/28.78    (8)  all_58_6 = e1
% 178.99/28.78    (9)   ~ (all_14_2 = e1)
% 178.99/28.78    (10)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.78    (11)  all_58_14 = all_52_29
% 178.99/28.78    (12)  all_58_8 = all_14_2
% 178.99/28.78    (13)   ~ (all_52_5 = all_14_2)
% 178.99/28.78    (14)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.78    (15)  all_58_2 = all_52_26
% 178.99/28.78    (16)   ~ (all_52_29 = all_6_2)
% 178.99/28.78    (17)   ~ (e2 = e1)
% 178.99/28.78    (18)   ~ (all_52_25 = all_6_2)
% 178.99/28.78    (19)  op(e1, e1) = all_14_2
% 178.99/28.78    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.78    (21)  op(e1, all_52_5) = e1
% 178.99/28.78    (22)  all_58_12 = all_52_25
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | BETA: splitting (14) gives:
% 178.99/28.78  | 
% 178.99/28.78  | Case 1:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (23)  all_58_2 = e2
% 178.99/28.78  | | 
% 178.99/28.78  | | COMBINE_EQS: (15), (23) imply:
% 178.99/28.78  | |   (24)  all_52_26 = e2
% 178.99/28.78  | | 
% 178.99/28.78  | | SIMP: (24) implies:
% 178.99/28.78  | |   (25)  all_52_26 = e2
% 178.99/28.78  | | 
% 178.99/28.78  | | REDUCE: (1), (25) imply:
% 178.99/28.78  | |   (26)  $false
% 178.99/28.78  | | 
% 178.99/28.78  | | CLOSE: (26) is inconsistent.
% 178.99/28.78  | | 
% 178.99/28.78  | Case 2:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (27)  all_58_6 = e2 | all_58_12 = e2
% 178.99/28.78  | | 
% 178.99/28.78  | | BETA: splitting (27) gives:
% 178.99/28.78  | | 
% 178.99/28.78  | | Case 1:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (28)  all_58_6 = e2
% 178.99/28.78  | | | 
% 178.99/28.78  | | | COMBINE_EQS: (8), (28) imply:
% 178.99/28.78  | | |   (29)  e2 = e1
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REDUCE: (17), (29) imply:
% 178.99/28.78  | | |   (30)  $false
% 178.99/28.78  | | | 
% 178.99/28.78  | | | CLOSE: (30) is inconsistent.
% 178.99/28.78  | | | 
% 178.99/28.78  | | Case 2:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (31)  all_58_12 = e2
% 178.99/28.78  | | | 
% 178.99/28.78  | | | COMBINE_EQS: (22), (31) imply:
% 178.99/28.78  | | |   (32)  all_52_25 = e2
% 178.99/28.78  | | | 
% 178.99/28.78  | | | SIMP: (32) implies:
% 178.99/28.78  | | |   (33)  all_52_25 = e2
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REDUCE: (18), (33) imply:
% 178.99/28.78  | | |   (34)   ~ (all_6_2 = e2)
% 178.99/28.78  | | | 
% 178.99/28.78  | | | SIMP: (34) implies:
% 178.99/28.78  | | |   (35)   ~ (all_6_2 = e2)
% 178.99/28.78  | | | 
% 178.99/28.78  | | | BETA: splitting (5) gives:
% 178.99/28.78  | | | 
% 178.99/28.78  | | | Case 1:
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | |   (36)  all_56_15 = e2
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | | REF_CLOSE: (4), (35), (36) are inconsistent by sub-proof #817.
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | Case 2:
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | |   (37)  all_56_15 = e1 | all_56_15 = e0
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | | BETA: splitting (37) gives:
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | | Case 1:
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | |   (38)  all_56_15 = e1
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | | COMBINE_EQS: (4), (38) imply:
% 178.99/28.78  | | | | |   (39)  all_6_2 = e1
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | | SIMP: (39) implies:
% 178.99/28.78  | | | | |   (40)  all_6_2 = e1
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | | REDUCE: (16), (40) imply:
% 178.99/28.78  | | | | |   (41)   ~ (all_52_29 = e1)
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | | REDUCE: (2), (40) imply:
% 178.99/28.78  | | | | |   (42)   ~ (e3 = e1)
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | | SIMP: (42) implies:
% 178.99/28.78  | | | | |   (43)   ~ (e3 = e1)
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | | REF_CLOSE: (6), (7), (9), (10), (11), (12), (13), (19), (20), (21),
% 178.99/28.78  | | | | |            (41), (43) are inconsistent by sub-proof #813.
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | Case 2:
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | |   (44)  all_56_15 = e0
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | | REF_CLOSE: (3), (4), (44) are inconsistent by sub-proof #812.
% 178.99/28.78  | | | | | 
% 178.99/28.78  | | | | End of split
% 178.99/28.78  | | | | 
% 178.99/28.78  | | | End of split
% 178.99/28.78  | | | 
% 178.99/28.78  | | End of split
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #812 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_56_15 = all_6_2
% 178.99/28.78    (2)  all_56_15 = e0
% 178.99/28.78    (3)   ~ (all_6_2 = e0)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  all_6_2 = e0
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  all_6_2 = e0
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #813 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_4 = all_52_5
% 178.99/28.78    (2)   ~ (e3 = e1)
% 178.99/28.78    (3)  all_58_5 = e3
% 178.99/28.78    (4)   ~ (all_52_29 = e1)
% 178.99/28.78    (5)   ~ (all_14_2 = e1)
% 178.99/28.78    (6)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.78    (7)  all_58_14 = all_52_29
% 178.99/28.78    (8)  all_58_8 = all_14_2
% 178.99/28.78    (9)   ~ (all_52_5 = all_14_2)
% 178.99/28.78    (10)  op(e1, e1) = all_14_2
% 178.99/28.78    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.78    (12)  op(e1, all_52_5) = e1
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | BETA: splitting (6) gives:
% 178.99/28.78  | 
% 178.99/28.78  | Case 1:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (13)  all_58_4 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | COMBINE_EQS: (1), (13) imply:
% 178.99/28.78  | |   (14)  all_52_5 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | SIMP: (14) implies:
% 178.99/28.78  | |   (15)  all_52_5 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | REF_CLOSE: (9), (10), (11), (12), (15) are inconsistent by sub-proof #859.
% 178.99/28.78  | | 
% 178.99/28.78  | Case 2:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (16)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (16) are inconsistent by sub-proof
% 178.99/28.78  | |            #814.
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #814 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)   ~ (e3 = e1)
% 178.99/28.78    (2)  all_58_5 = e3
% 178.99/28.78    (3)   ~ (all_52_29 = e1)
% 178.99/28.78    (4)   ~ (all_14_2 = e1)
% 178.99/28.78    (5)  all_58_14 = all_52_29
% 178.99/28.78    (6)  all_58_8 = all_14_2
% 178.99/28.78    (7)  all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | BETA: splitting (7) gives:
% 178.99/28.78  | 
% 178.99/28.78  | Case 1:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (8)  all_58_5 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #816.
% 178.99/28.78  | | 
% 178.99/28.78  | Case 2:
% 178.99/28.78  | | 
% 178.99/28.78  | |   (9)  all_58_8 = e1 | all_58_14 = e1
% 178.99/28.78  | | 
% 178.99/28.78  | | BETA: splitting (9) gives:
% 178.99/28.78  | | 
% 178.99/28.78  | | Case 1:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (10)  all_58_8 = e1
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #815.
% 178.99/28.78  | | | 
% 178.99/28.78  | | Case 2:
% 178.99/28.78  | | | 
% 178.99/28.78  | | |   (11)  all_58_14 = e1
% 178.99/28.78  | | | 
% 178.99/28.78  | | | COMBINE_EQS: (5), (11) imply:
% 178.99/28.78  | | |   (12)  all_52_29 = e1
% 178.99/28.78  | | | 
% 178.99/28.78  | | | SIMP: (12) implies:
% 178.99/28.78  | | |   (13)  all_52_29 = e1
% 178.99/28.78  | | | 
% 178.99/28.78  | | | REDUCE: (3), (13) imply:
% 178.99/28.78  | | |   (14)  $false
% 178.99/28.78  | | | 
% 178.99/28.78  | | | CLOSE: (14) is inconsistent.
% 178.99/28.78  | | | 
% 178.99/28.78  | | End of split
% 178.99/28.78  | | 
% 178.99/28.78  | End of split
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #815 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_8 = all_14_2
% 178.99/28.78    (2)  all_58_8 = e1
% 178.99/28.78    (3)   ~ (all_14_2 = e1)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  all_14_2 = e1
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  all_14_2 = e1
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #816 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_58_5 = e3
% 178.99/28.78    (2)  all_58_5 = e1
% 178.99/28.78    (3)   ~ (e3 = e1)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  e3 = e1
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  e3 = e1
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #817 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_56_15 = all_6_2
% 178.99/28.78    (2)  all_56_15 = e2
% 178.99/28.78    (3)   ~ (all_6_2 = e2)
% 178.99/28.78  
% 178.99/28.78  Begin of proof
% 178.99/28.78  | 
% 178.99/28.78  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.78  |   (4)  all_6_2 = e2
% 178.99/28.78  | 
% 178.99/28.78  | SIMP: (4) implies:
% 178.99/28.78  |   (5)  all_6_2 = e2
% 178.99/28.78  | 
% 178.99/28.78  | REDUCE: (3), (5) imply:
% 178.99/28.78  |   (6)  $false
% 178.99/28.78  | 
% 178.99/28.78  | CLOSE: (6) is inconsistent.
% 178.99/28.78  | 
% 178.99/28.78  End of proof
% 178.99/28.78  
% 178.99/28.78  Sub-proof #818 shows that the following formulas are inconsistent:
% 178.99/28.78  ----------------------------------------------------------------
% 178.99/28.78    (1)  all_56_4 = all_52_26
% 178.99/28.79    (2)  all_56_4 = e3
% 178.99/28.79    (3)   ~ (all_52_26 = e3)
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.79  |   (4)  all_52_26 = e3
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (4) implies:
% 178.99/28.79  |   (5)  all_52_26 = e3
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (3), (5) imply:
% 178.99/28.79  |   (6)  $false
% 178.99/28.79  | 
% 178.99/28.79  | CLOSE: (6) is inconsistent.
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #819 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)   ~ (all_52_25 = e3)
% 178.99/28.79    (2)   ~ (all_52_17 = all_52_23)
% 178.99/28.79    (3)  op(e3, e2) = all_52_3
% 178.99/28.79    (4)   ~ (all_6_2 = e3)
% 178.99/28.79    (5)   ~ (all_4_2 = e3)
% 178.99/28.79    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.79    (7)  all_58_15 = all_6_2
% 178.99/28.79    (8)   ~ (all_52_5 = all_52_7)
% 178.99/28.79    (9)  all_58_10 = all_52_15
% 178.99/28.79    (10)   ~ (all_52_7 = all_4_2)
% 178.99/28.79    (11)  all_58_0 = all_4_2
% 178.99/28.79    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.79    (13)  op(e3, all_4_2) = e3
% 178.99/28.79    (14)  op(e0, e3) = all_52_25
% 178.99/28.79    (15)   ~ (all_52_15 = e3)
% 178.99/28.79    (16)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.79    (17)  all_58_6 = all_52_17
% 178.99/28.79    (18)   ~ (all_52_3 = all_52_7)
% 178.99/28.79    (19)  all_58_2 = all_52_26
% 178.99/28.79    (20)  all_56_0 = all_4_2
% 178.99/28.79    (21)  all_58_11 = all_52_23
% 178.99/28.79    (22)  op(e3, e1) = all_52_5
% 178.99/28.79    (23)   ~ (all_52_26 = e3)
% 178.99/28.79    (24)   ~ (all_52_25 = all_4_2)
% 178.99/28.79    (25)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.79    (26)  op(e0, all_52_7) = e0
% 178.99/28.79    (27)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.79    (28)  all_58_9 = all_52_7
% 178.99/28.79    (29)  all_58_12 = all_52_25
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | BETA: splitting (12) gives:
% 178.99/28.79  | 
% 178.99/28.79  | Case 1:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (30)  all_58_0 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | COMBINE_EQS: (11), (30) imply:
% 178.99/28.79  | |   (31)  all_4_2 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | REDUCE: (5), (31) imply:
% 178.99/28.79  | |   (32)  $false
% 178.99/28.79  | | 
% 178.99/28.79  | | CLOSE: (32) is inconsistent.
% 178.99/28.79  | | 
% 178.99/28.79  | Case 2:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (33)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 178.99/28.79  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 178.99/28.79  | |            (26), (27), (28), (29), (33) are inconsistent by sub-proof #820.
% 178.99/28.79  | | 
% 178.99/28.79  | End of split
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #820 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)   ~ (all_52_25 = e3)
% 178.99/28.79    (2)   ~ (all_52_17 = all_52_23)
% 178.99/28.79    (3)  op(e3, e2) = all_52_3
% 178.99/28.79    (4)   ~ (all_6_2 = e3)
% 178.99/28.79    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.79    (6)  all_58_15 = all_6_2
% 178.99/28.79    (7)   ~ (all_52_5 = all_52_7)
% 178.99/28.79    (8)  all_58_10 = all_52_15
% 178.99/28.79    (9)   ~ (all_52_7 = all_4_2)
% 178.99/28.79    (10)  all_58_0 = all_4_2
% 178.99/28.79    (11)  op(e3, all_4_2) = e3
% 178.99/28.79    (12)  op(e0, e3) = all_52_25
% 178.99/28.79    (13)   ~ (all_52_15 = e3)
% 178.99/28.79    (14)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.79    (15)  all_58_6 = all_52_17
% 178.99/28.79    (16)   ~ (all_52_3 = all_52_7)
% 178.99/28.79    (17)  all_58_2 = all_52_26
% 178.99/28.79    (18)  all_56_0 = all_4_2
% 178.99/28.79    (19)  all_58_11 = all_52_23
% 178.99/28.79    (20)  op(e3, e1) = all_52_5
% 178.99/28.79    (21)   ~ (all_52_26 = e3)
% 178.99/28.79    (22)   ~ (all_52_25 = all_4_2)
% 178.99/28.79    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.79    (24)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.79    (25)  op(e0, all_52_7) = e0
% 178.99/28.79    (26)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.79    (27)  all_58_9 = all_52_7
% 178.99/28.79    (28)  all_58_12 = all_52_25
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | BETA: splitting (24) gives:
% 178.99/28.79  | 
% 178.99/28.79  | Case 1:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (29)  all_58_2 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | REF_CLOSE: (17), (21), (29) are inconsistent by sub-proof #1004.
% 178.99/28.79  | | 
% 178.99/28.79  | Case 2:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (30)  all_58_6 = e3 | all_58_12 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | BETA: splitting (30) gives:
% 178.99/28.79  | | 
% 178.99/28.79  | | Case 1:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (31)  all_58_6 = e3
% 178.99/28.79  | | | 
% 178.99/28.79  | | | COMBINE_EQS: (15), (31) imply:
% 178.99/28.79  | | |   (32)  all_52_17 = e3
% 178.99/28.79  | | | 
% 178.99/28.79  | | | SIMP: (32) implies:
% 178.99/28.79  | | |   (33)  all_52_17 = e3
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REDUCE: (2), (33) imply:
% 178.99/28.79  | | |   (34)   ~ (all_52_23 = e3)
% 178.99/28.79  | | | 
% 178.99/28.79  | | | SIMP: (34) implies:
% 178.99/28.79  | | |   (35)   ~ (all_52_23 = e3)
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 178.99/28.79  | | |            (14), (16), (18), (19), (20), (22), (23), (25), (26), (27),
% 178.99/28.79  | | |            (35) are inconsistent by sub-proof #1015.
% 178.99/28.79  | | | 
% 178.99/28.79  | | Case 2:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (36)  all_58_12 = e3
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REF_CLOSE: (1), (28), (36) are inconsistent by sub-proof #1003.
% 178.99/28.79  | | | 
% 178.99/28.79  | | End of split
% 178.99/28.79  | | 
% 178.99/28.79  | End of split
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #821 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)  op(e3, e2) = all_52_3
% 178.99/28.79    (2)  all_58_4 = e3
% 178.99/28.79    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.79    (4)   ~ (all_52_5 = all_52_7)
% 178.99/28.79    (5)   ~ (all_52_5 = all_4_2)
% 178.99/28.79    (6)  all_58_4 = all_52_5
% 178.99/28.79    (7)  all_58_0 = all_4_2
% 178.99/28.79    (8)   ~ (all_52_3 = all_52_5)
% 178.99/28.79    (9)  op(e3, all_4_2) = e3
% 178.99/28.79    (10)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.79    (11)  all_56_0 = all_4_2
% 178.99/28.79    (12)  op(e1, e3) = all_52_17
% 178.99/28.79    (13)  op(e3, e0) = all_52_7
% 178.99/28.79    (14)   ~ (all_52_17 = all_4_2)
% 178.99/28.79    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.79    (16)  op(e1, all_52_5) = e1
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | COMBINE_EQS: (2), (6) imply:
% 178.99/28.79  |   (17)  all_52_5 = e3
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (17) implies:
% 178.99/28.79  |   (18)  all_52_5 = e3
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (8), (18) imply:
% 178.99/28.79  |   (19)   ~ (all_52_3 = e3)
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (4), (18) imply:
% 178.99/28.79  |   (20)   ~ (all_52_7 = e3)
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (20) implies:
% 178.99/28.79  |   (21)   ~ (all_52_7 = e3)
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (5), (18) imply:
% 178.99/28.79  |   (22)   ~ (all_4_2 = e3)
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (22) implies:
% 178.99/28.79  |   (23)   ~ (all_4_2 = e3)
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (16), (18) imply:
% 178.99/28.79  |   (24)  op(e1, e3) = e1
% 178.99/28.79  | 
% 178.99/28.79  | GROUND_INST: instantiating (15) with all_52_17, e1, e3, e1, simplifying with
% 178.99/28.79  |              (12), (24) gives:
% 178.99/28.79  |   (25)  all_52_17 = e1
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (14), (25) imply:
% 178.99/28.79  |   (26)   ~ (all_4_2 = e1)
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (26) implies:
% 178.99/28.79  |   (27)   ~ (all_4_2 = e1)
% 178.99/28.79  | 
% 178.99/28.79  | BETA: splitting (3) gives:
% 178.99/28.79  | 
% 178.99/28.79  | Case 1:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (28)  all_56_0 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | REF_CLOSE: (11), (23), (28) are inconsistent by sub-proof #1024.
% 178.99/28.79  | | 
% 178.99/28.79  | Case 2:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (29)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.79  | | 
% 178.99/28.79  | | REF_CLOSE: (1), (7), (9), (10), (11), (13), (15), (19), (21), (27), (29) are
% 178.99/28.79  | |            inconsistent by sub-proof #875.
% 178.99/28.79  | | 
% 178.99/28.79  | End of split
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #822 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)   ~ (all_58_4 = e2)
% 178.99/28.79    (2)   ~ (all_52_5 = all_52_7)
% 178.99/28.79    (3)  all_58_4 = all_52_5
% 178.99/28.79    (4)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.79    (5)  all_58_4 = e1 | all_58_5 = e1 | all_58_8 = e1 | all_58_14 = e1
% 178.99/28.79    (6)   ~ (all_52_5 = all_14_2)
% 178.99/28.79    (7)   ~ (all_52_5 = e3)
% 178.99/28.79    (8)  all_56_2 = all_52_5
% 178.99/28.79    (9)  op(e1, e0) = all_52_23
% 178.99/28.79    (10)  all_58_10 = e3
% 178.99/28.79    (11)  all_58_11 = all_52_23
% 178.99/28.79    (12)  op(e1, e1) = all_14_2
% 178.99/28.79    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.79    (14)  op(e1, all_52_5) = e1
% 178.99/28.79    (15)  all_58_9 = all_52_7
% 178.99/28.79    (16)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (1), (3) imply:
% 178.99/28.79  |   (17)   ~ (all_52_5 = e2)
% 178.99/28.79  | 
% 178.99/28.79  | BETA: splitting (5) gives:
% 178.99/28.79  | 
% 178.99/28.79  | Case 1:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (18)  all_58_4 = e1
% 178.99/28.79  | | 
% 178.99/28.79  | | COMBINE_EQS: (3), (18) imply:
% 178.99/28.79  | |   (19)  all_52_5 = e1
% 178.99/28.79  | | 
% 178.99/28.79  | | REF_CLOSE: (6), (12), (13), (14), (19) are inconsistent by sub-proof #859.
% 178.99/28.79  | | 
% 178.99/28.79  | Case 2:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (20)   ~ (all_58_4 = e1)
% 178.99/28.79  | | 
% 178.99/28.79  | | REDUCE: (3), (20) imply:
% 178.99/28.79  | |   (21)   ~ (all_52_5 = e1)
% 178.99/28.79  | | 
% 178.99/28.79  | | BETA: splitting (16) gives:
% 178.99/28.79  | | 
% 178.99/28.79  | | Case 1:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (22)  all_56_2 = e2
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REF_CLOSE: (8), (17), (22) are inconsistent by sub-proof #827.
% 178.99/28.79  | | | 
% 178.99/28.79  | | Case 2:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (23)  all_56_2 = e1 | all_56_2 = e0
% 178.99/28.79  | | | 
% 178.99/28.79  | | | BETA: splitting (23) gives:
% 178.99/28.79  | | | 
% 178.99/28.79  | | | Case 1:
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | |   (24)  all_56_2 = e1
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REF_CLOSE: (8), (21), (24) are inconsistent by sub-proof #826.
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | Case 2:
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | |   (25)  all_56_2 = e0
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | COMBINE_EQS: (8), (25) imply:
% 178.99/28.79  | | | |   (26)  all_52_5 = e0
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | SIMP: (26) implies:
% 178.99/28.79  | | | |   (27)  all_52_5 = e0
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (2), (27) imply:
% 178.99/28.79  | | | |   (28)   ~ (all_52_7 = e0)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | SIMP: (28) implies:
% 178.99/28.79  | | | |   (29)   ~ (all_52_7 = e0)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (7), (27) imply:
% 178.99/28.79  | | | |   (30)   ~ (e3 = e0)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | SIMP: (30) implies:
% 178.99/28.79  | | | |   (31)   ~ (e3 = e0)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (21), (27) imply:
% 178.99/28.79  | | | |   (32)   ~ (e1 = e0)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | SIMP: (32) implies:
% 178.99/28.79  | | | |   (33)   ~ (e1 = e0)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (14), (27) imply:
% 178.99/28.79  | | | |   (34)  op(e1, e0) = e1
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REF_CLOSE: (4), (9), (10), (11), (13), (15), (29), (31), (33), (34) are
% 178.99/28.79  | | | |            inconsistent by sub-proof #823.
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | End of split
% 178.99/28.79  | | | 
% 178.99/28.79  | | End of split
% 178.99/28.79  | | 
% 178.99/28.79  | End of split
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #823 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)  all_58_9 = e0 | all_58_10 = e0 | all_58_11 = e0
% 178.99/28.79    (2)   ~ (all_52_7 = e0)
% 178.99/28.79    (3)  op(e1, e0) = e1
% 178.99/28.79    (4)   ~ (e3 = e0)
% 178.99/28.79    (5)  op(e1, e0) = all_52_23
% 178.99/28.79    (6)  all_58_10 = e3
% 178.99/28.79    (7)   ~ (e1 = e0)
% 178.99/28.79    (8)  all_58_11 = all_52_23
% 178.99/28.79    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.79    (10)  all_58_9 = all_52_7
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | BETA: splitting (1) gives:
% 178.99/28.79  | 
% 178.99/28.79  | Case 1:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (11)  all_58_9 = e0
% 178.99/28.79  | | 
% 178.99/28.79  | | REF_CLOSE: (2), (10), (11) are inconsistent by sub-proof #825.
% 178.99/28.79  | | 
% 178.99/28.79  | Case 2:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (12)  all_58_10 = e0 | all_58_11 = e0
% 178.99/28.79  | | 
% 178.99/28.79  | | BETA: splitting (12) gives:
% 178.99/28.79  | | 
% 178.99/28.79  | | Case 1:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (13)  all_58_10 = e0
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #824.
% 178.99/28.79  | | | 
% 178.99/28.79  | | Case 2:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (14)  all_58_11 = e0
% 178.99/28.79  | | | 
% 178.99/28.79  | | | COMBINE_EQS: (8), (14) imply:
% 178.99/28.79  | | |   (15)  all_52_23 = e0
% 178.99/28.79  | | | 
% 178.99/28.79  | | | SIMP: (15) implies:
% 178.99/28.79  | | |   (16)  all_52_23 = e0
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REDUCE: (5), (16) imply:
% 178.99/28.79  | | |   (17)  op(e1, e0) = e0
% 178.99/28.79  | | | 
% 178.99/28.79  | | | GROUND_INST: instantiating (9) with e0, e1, e0, e1, simplifying with (3),
% 178.99/28.79  | | |              (17) gives:
% 178.99/28.79  | | |   (18)  e1 = e0
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REDUCE: (7), (18) imply:
% 178.99/28.79  | | |   (19)  $false
% 178.99/28.79  | | | 
% 178.99/28.79  | | | CLOSE: (19) is inconsistent.
% 178.99/28.79  | | | 
% 178.99/28.79  | | End of split
% 178.99/28.79  | | 
% 178.99/28.79  | End of split
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #824 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)  all_58_10 = e3
% 178.99/28.79    (2)  all_58_10 = e0
% 178.99/28.79    (3)   ~ (e3 = e0)
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.79  |   (4)  e3 = e0
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (4) implies:
% 178.99/28.79  |   (5)  e3 = e0
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (3), (5) imply:
% 178.99/28.79  |   (6)  $false
% 178.99/28.79  | 
% 178.99/28.79  | CLOSE: (6) is inconsistent.
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #825 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)  all_58_9 = all_52_7
% 178.99/28.79    (2)  all_58_9 = e0
% 178.99/28.79    (3)   ~ (all_52_7 = e0)
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.79  |   (4)  all_52_7 = e0
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (4) implies:
% 178.99/28.79  |   (5)  all_52_7 = e0
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (3), (5) imply:
% 178.99/28.79  |   (6)  $false
% 178.99/28.79  | 
% 178.99/28.79  | CLOSE: (6) is inconsistent.
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #826 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)  all_56_2 = all_52_5
% 178.99/28.79    (2)  all_56_2 = e1
% 178.99/28.79    (3)   ~ (all_52_5 = e1)
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.79  |   (4)  all_52_5 = e1
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (4) implies:
% 178.99/28.79  |   (5)  all_52_5 = e1
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (3), (5) imply:
% 178.99/28.79  |   (6)  $false
% 178.99/28.79  | 
% 178.99/28.79  | CLOSE: (6) is inconsistent.
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #827 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)  all_56_2 = all_52_5
% 178.99/28.79    (2)  all_56_2 = e2
% 178.99/28.79    (3)   ~ (all_52_5 = e2)
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.79  |   (4)  all_52_5 = e2
% 178.99/28.79  | 
% 178.99/28.79  | SIMP: (4) implies:
% 178.99/28.79  |   (5)  all_52_5 = e2
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (3), (5) imply:
% 178.99/28.79  |   (6)  $false
% 178.99/28.79  | 
% 178.99/28.79  | CLOSE: (6) is inconsistent.
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #828 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.79    (2)  op(e2, e0) = e3
% 178.99/28.79    (3)  op(e2, e0) = e2
% 178.99/28.79    (4)   ~ (e3 = e2)
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | GROUND_INST: instantiating (1) with e3, e2, e0, e2, simplifying with (2), (3)
% 178.99/28.79  |              gives:
% 178.99/28.79  |   (5)  e3 = e2
% 178.99/28.79  | 
% 178.99/28.79  | REDUCE: (4), (5) imply:
% 178.99/28.79  |   (6)  $false
% 178.99/28.79  | 
% 178.99/28.79  | CLOSE: (6) is inconsistent.
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #829 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.79    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.79    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.99/28.79    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.79    (5)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.79    (6)   ~ (all_52_27 = all_10_2)
% 178.99/28.79    (7)  op(e2, e2) = all_10_2
% 178.99/28.79    (8)   ~ (all_52_17 = all_52_23)
% 178.99/28.79    (9)  op(e2, all_52_3) = e2
% 178.99/28.79    (10)  all_58_15 = e3
% 178.99/28.79    (11)  op(e2, all_10_2) = all_10_1
% 178.99/28.79    (12)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.79    (13)  all_56_3 = all_52_7
% 178.99/28.79    (14)  op(e3, e2) = all_52_3
% 178.99/28.79    (15)   ~ (all_52_19 = all_52_23)
% 178.99/28.79    (16)  op(e1, e2) = all_52_19
% 178.99/28.79    (17)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.79    (18)   ~ (all_52_27 = e3)
% 178.99/28.79    (19)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.79    (20)   ~ (all_14_1 = e2)
% 178.99/28.79    (21)  all_58_12 = all_6_1
% 178.99/28.79    (22)  op(all_6_1, e3) = all_6_0
% 178.99/28.79    (23)   ~ (all_52_3 = all_10_2)
% 178.99/28.79    (24)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.99/28.79    (25)  all_58_5 = all_52_13
% 178.99/28.79    (26)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.79    (27)  op(e2, e0) = all_52_15
% 178.99/28.79    (28)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.79    (29)  all_58_3 = all_10_2
% 178.99/28.79    (30)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.79    (31)  all_58_15 = all_6_2
% 178.99/28.79    (32)   ~ (all_52_9 = all_4_2)
% 178.99/28.79    (33)   ~ (all_52_5 = all_52_7)
% 178.99/28.79    (34)  all_58_10 = all_52_15
% 178.99/28.79    (35)   ~ (all_52_5 = all_4_2)
% 178.99/28.79    (36)  all_58_7 = all_52_19
% 178.99/28.79    (37)  op(e0, e1) = all_52_29
% 178.99/28.79    (38)  all_58_4 = all_52_5
% 178.99/28.79    (39)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.79    (40)   ~ (e3 = e1)
% 178.99/28.79    (41)   ~ (all_52_27 = all_52_29)
% 178.99/28.79    (42)   ~ (all_52_17 = all_14_2)
% 178.99/28.79    (43)   ~ (all_52_7 = all_4_2)
% 178.99/28.79    (44)  all_58_1 = all_52_3
% 178.99/28.79    (45)  all_58_0 = all_4_2
% 178.99/28.79    (46)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.79    (47)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.79    (48)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.79    (49)  all_58_14 = all_52_29
% 178.99/28.79    (50)   ~ (all_52_3 = all_52_5)
% 178.99/28.79    (51)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 178.99/28.79    (52)  op(e2, e1) = all_52_13
% 178.99/28.79    (53)   ~ (all_52_17 = all_6_1)
% 178.99/28.79    (54)  all_58_8 = all_14_2
% 178.99/28.79    (55)  all_56_1 = all_52_3
% 178.99/28.79    (56)  op(e0, e2) = all_52_27
% 178.99/28.79    (57)  all_56_14 = all_52_29
% 178.99/28.79    (58)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.79    (59)   ~ (all_52_5 = all_14_2)
% 178.99/28.79    (60)   ~ (all_52_23 = e3)
% 178.99/28.79    (61)   ~ (all_52_3 = all_52_27)
% 178.99/28.79    (62)   ~ (all_52_3 = all_4_2)
% 178.99/28.79    (63)  op(e3, all_4_2) = e3
% 178.99/28.79    (64)  op(e0, e3) = all_52_25
% 178.99/28.79    (65)   ~ (all_52_29 = e3)
% 178.99/28.79    (66)   ~ (all_52_13 = all_14_2)
% 178.99/28.79    (67)   ~ (e3 = e0)
% 178.99/28.79    (68)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.79    (69)   ~ (all_52_9 = all_52_13)
% 178.99/28.79    (70)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.79    (71)   ~ (all_52_5 = all_52_29)
% 178.99/28.79    (72)  op(e1, e0) = all_52_23
% 178.99/28.79    (73)  all_58_13 = all_52_27
% 178.99/28.79    (74)   ~ (all_52_27 = all_6_1)
% 178.99/28.79    (75)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.79    (76)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.79    (77)  all_58_6 = all_52_17
% 178.99/28.79    (78)   ~ (all_52_3 = all_52_7)
% 178.99/28.79    (79)  all_56_0 = all_4_2
% 178.99/28.79    (80)  all_58_11 = all_52_23
% 178.99/28.79    (81)   ~ (all_52_3 = all_52_19)
% 178.99/28.79    (82)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.79    (83)   ~ (all_52_7 = all_52_15)
% 178.99/28.79    (84)   ~ (all_52_29 = all_14_2)
% 178.99/28.79    (85)  all_58_2 = all_52_9
% 178.99/28.79    (86)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.99/28.79    (87)  op(e3, e1) = all_52_5
% 178.99/28.79    (88)   ~ (e2 = e1)
% 178.99/28.79    (89)  all_56_10 = all_14_2
% 178.99/28.79    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.79    (91)   ~ (all_52_19 = e3)
% 178.99/28.79    (92)  op(e1, e3) = all_52_17
% 178.99/28.79    (93)   ~ (all_52_25 = all_4_2)
% 178.99/28.79    (94)  op(e3, e0) = all_52_7
% 178.99/28.79    (95)  all_56_8 = all_52_17
% 178.99/28.79    (96)   ~ (all_52_17 = all_4_2)
% 178.99/28.79    (97)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.79    (98)   ~ (all_52_7 = all_6_2)
% 178.99/28.79    (99)   ~ (all_52_19 = all_52_27)
% 178.99/28.79    (100)  op(e1, all_52_5) = e1
% 178.99/28.79    (101)   ~ (all_52_7 = all_52_23)
% 178.99/28.79    (102)   ~ (all_6_0 = e1)
% 178.99/28.79    (103)  op(e0, all_52_7) = e0
% 178.99/28.79    (104)   ~ (all_52_29 = all_6_1)
% 178.99/28.79    (105)   ~ (all_52_17 = all_52_19)
% 178.99/28.79    (106)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.79    (107)  op(e1, all_14_2) = all_14_1
% 178.99/28.79    (108)  all_58_9 = all_52_7
% 178.99/28.79    (109)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.79    (110)   ~ (all_52_9 = all_52_15)
% 178.99/28.79    (111)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.79    (112)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.79    (113)   ~ (e3 = e2)
% 178.99/28.79    (114)   ~ (all_52_19 = all_14_2)
% 178.99/28.79    (115)  op(e2, e3) = all_52_9
% 178.99/28.79    (116)  all_56_13 = all_52_27
% 178.99/28.79  
% 178.99/28.79  Begin of proof
% 178.99/28.79  | 
% 178.99/28.79  | BETA: splitting (39) gives:
% 178.99/28.79  | 
% 178.99/28.79  | Case 1:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (117)  all_58_6 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | REF_CLOSE: (1), (2), (9), (14), (25), (30), (31), (32), (33), (34), (35),
% 178.99/28.79  | |            (36), (38), (39), (42), (43), (44), (45), (49), (50), (54), (59),
% 178.99/28.79  | |            (63), (64), (65), (66), (68), (70), (71), (75), (77), (78), (79),
% 178.99/28.79  | |            (80), (81), (83), (84), (87), (89), (92), (93), (94), (96), (97),
% 178.99/28.79  | |            (98), (100), (101), (103), (106), (108), (109), (111), (115),
% 178.99/28.79  | |            (117) are inconsistent by sub-proof #850.
% 178.99/28.79  | | 
% 178.99/28.79  | Case 2:
% 178.99/28.79  | | 
% 178.99/28.79  | |   (118)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.79  | | 
% 178.99/28.79  | | BETA: splitting (118) gives:
% 178.99/28.79  | | 
% 178.99/28.79  | | Case 1:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (119)  all_58_7 = e3
% 178.99/28.79  | | | 
% 178.99/28.79  | | | COMBINE_EQS: (36), (119) imply:
% 178.99/28.79  | | |   (120)  all_52_19 = e3
% 178.99/28.79  | | | 
% 178.99/28.79  | | | REDUCE: (91), (120) imply:
% 178.99/28.79  | | |   (121)  $false
% 178.99/28.79  | | | 
% 178.99/28.79  | | | CLOSE: (121) is inconsistent.
% 178.99/28.79  | | | 
% 178.99/28.79  | | Case 2:
% 178.99/28.79  | | | 
% 178.99/28.79  | | |   (122)  all_58_8 = e3 | all_58_11 = e3
% 178.99/28.79  | | | 
% 178.99/28.79  | | | BETA: splitting (122) gives:
% 178.99/28.79  | | | 
% 178.99/28.79  | | | Case 1:
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | |   (123)  all_58_8 = e3
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | COMBINE_EQS: (54), (123) imply:
% 178.99/28.79  | | | |   (124)  all_14_2 = e3
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | SIMP: (124) implies:
% 178.99/28.79  | | | |   (125)  all_14_2 = e3
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (42), (125) imply:
% 178.99/28.79  | | | |   (126)   ~ (all_52_17 = e3)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (107), (125) imply:
% 178.99/28.79  | | | |   (127)  op(e1, e3) = all_14_1
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | GROUND_INST: instantiating (97) with all_52_17, all_14_1, e3, e1,
% 178.99/28.79  | | | |              simplifying with (92), (127) gives:
% 178.99/28.79  | | | |   (128)  all_52_17 = all_14_1
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | COMBINE_EQS: (95), (128) imply:
% 178.99/28.79  | | | |   (129)  all_56_8 = all_14_1
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | COMBINE_EQS: (77), (128) imply:
% 178.99/28.79  | | | |   (130)  all_58_6 = all_14_1
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (105), (128) imply:
% 178.99/28.79  | | | |   (131)   ~ (all_52_19 = all_14_1)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | SIMP: (131) implies:
% 178.99/28.79  | | | |   (132)   ~ (all_52_19 = all_14_1)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (8), (128) imply:
% 178.99/28.79  | | | |   (133)   ~ (all_52_23 = all_14_1)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | SIMP: (133) implies:
% 178.99/28.79  | | | |   (134)   ~ (all_52_23 = all_14_1)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (53), (128) imply:
% 178.99/28.79  | | | |   (135)   ~ (all_14_1 = all_6_1)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REDUCE: (126), (128) imply:
% 178.99/28.79  | | | |   (136)   ~ (all_14_1 = e3)
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | BETA: splitting (3) gives:
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | Case 1:
% 178.99/28.79  | | | | | 
% 178.99/28.79  | | | | |   (137)  all_56_8 = e3
% 178.99/28.79  | | | | | 
% 178.99/28.79  | | | | | REF_CLOSE: (129), (136), (137) are inconsistent by sub-proof #849.
% 178.99/28.79  | | | | | 
% 178.99/28.79  | | | | Case 2:
% 178.99/28.79  | | | | | 
% 178.99/28.79  | | | | |   (138)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.99/28.79  | | | | | 
% 178.99/28.79  | | | | | BETA: splitting (51) gives:
% 178.99/28.79  | | | | | 
% 178.99/28.79  | | | | | Case 1:
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | |   (139)  all_58_0 = e3
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | | COMBINE_EQS: (45), (139) imply:
% 178.99/28.79  | | | | | |   (140)  all_4_2 = e3
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | | REDUCE: (62), (140) imply:
% 178.99/28.79  | | | | | |   (141)   ~ (all_52_3 = e3)
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | | REDUCE: (43), (140) imply:
% 178.99/28.79  | | | | | |   (142)   ~ (all_52_7 = e3)
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (10), (11), (12), (13), (15),
% 178.99/28.79  | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 178.99/28.79  | | | | | |            (26), (27), (28), (29), (33), (36), (37), (38), (40),
% 178.99/28.79  | | | | | |            (41), (44), (46), (47), (48), (49), (50), (52), (55),
% 178.99/28.79  | | | | | |            (56), (57), (58), (60), (61), (65), (67), (69), (71),
% 178.99/28.79  | | | | | |            (72), (73), (74), (75), (76), (78), (80), (81), (82),
% 178.99/28.79  | | | | | |            (85), (86), (88), (90), (91), (97), (99), (100), (101),
% 178.99/28.79  | | | | | |            (102), (103), (104), (108), (110), (112), (113), (115),
% 178.99/28.79  | | | | | |            (116), (123), (129), (130), (132), (134), (135), (138),
% 178.99/28.79  | | | | | |            (139), (141), (142) are inconsistent by sub-proof #830.
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | Case 2:
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | |   (143)   ~ (all_58_0 = e3)
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | | REDUCE: (45), (143) imply:
% 178.99/28.79  | | | | | |   (144)   ~ (all_4_2 = e3)
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | | REF_CLOSE: (1), (2), (9), (14), (25), (30), (31), (32), (33), (34),
% 178.99/28.79  | | | | | |            (35), (36), (38), (39), (42), (43), (44), (45), (49),
% 178.99/28.79  | | | | | |            (50), (54), (59), (63), (64), (65), (66), (68), (70),
% 178.99/28.79  | | | | | |            (71), (75), (77), (78), (79), (80), (81), (83), (84),
% 178.99/28.79  | | | | | |            (87), (89), (92), (93), (94), (96), (97), (98), (100),
% 178.99/28.79  | | | | | |            (101), (103), (106), (108), (109), (111), (115), (144)
% 178.99/28.79  | | | | | |            are inconsistent by sub-proof #864.
% 178.99/28.79  | | | | | | 
% 178.99/28.79  | | | | | End of split
% 178.99/28.79  | | | | | 
% 178.99/28.79  | | | | End of split
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | Case 2:
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | |   (145)  all_58_11 = e3
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | | REF_CLOSE: (60), (80), (145) are inconsistent by sub-proof #1017.
% 178.99/28.79  | | | | 
% 178.99/28.79  | | | End of split
% 178.99/28.79  | | | 
% 178.99/28.79  | | End of split
% 178.99/28.79  | | 
% 178.99/28.79  | End of split
% 178.99/28.79  | 
% 178.99/28.79  End of proof
% 178.99/28.79  
% 178.99/28.79  Sub-proof #830 shows that the following formulas are inconsistent:
% 178.99/28.79  ----------------------------------------------------------------
% 178.99/28.79    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.79    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.79    (3)   ~ (all_52_27 = all_10_2)
% 178.99/28.79    (4)  op(e2, e2) = all_10_2
% 178.99/28.80    (5)  op(e2, all_52_3) = e2
% 178.99/28.80    (6)  all_58_15 = e3
% 178.99/28.80    (7)  op(e2, all_10_2) = all_10_1
% 178.99/28.80    (8)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.80    (9)  all_56_3 = all_52_7
% 178.99/28.80    (10)   ~ (all_52_19 = all_52_23)
% 178.99/28.80    (11)  op(e1, e2) = all_52_19
% 178.99/28.80    (12)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.80    (13)   ~ (all_52_27 = e3)
% 178.99/28.80    (14)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.80    (15)   ~ (all_14_1 = e2)
% 178.99/28.80    (16)  all_58_12 = all_6_1
% 178.99/28.80    (17)  op(all_6_1, e3) = all_6_0
% 178.99/28.80    (18)   ~ (all_52_3 = all_10_2)
% 178.99/28.80    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.99/28.80    (20)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.80    (21)  op(e2, e0) = all_52_15
% 178.99/28.80    (22)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.80    (23)  all_58_3 = all_10_2
% 178.99/28.80    (24)   ~ (all_52_5 = all_52_7)
% 178.99/28.80    (25)  all_58_7 = all_52_19
% 178.99/28.80    (26)  op(e0, e1) = all_52_29
% 178.99/28.80    (27)  all_58_4 = all_52_5
% 178.99/28.80    (28)   ~ (e3 = e1)
% 178.99/28.80    (29)   ~ (all_52_27 = all_52_29)
% 178.99/28.80    (30)  all_58_1 = all_52_3
% 178.99/28.80    (31)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.80    (32)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.80    (33)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.80    (34)  all_58_14 = all_52_29
% 178.99/28.80    (35)  all_58_6 = all_14_1
% 178.99/28.80    (36)   ~ (all_52_3 = all_52_5)
% 178.99/28.80    (37)  op(e2, e1) = all_52_13
% 178.99/28.80    (38)  all_56_1 = all_52_3
% 178.99/28.80    (39)  op(e0, e2) = all_52_27
% 178.99/28.80    (40)  all_56_14 = all_52_29
% 178.99/28.80    (41)   ~ (all_52_19 = all_14_1)
% 178.99/28.80    (42)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.80    (43)   ~ (all_52_23 = e3)
% 178.99/28.80    (44)   ~ (all_52_3 = all_52_27)
% 178.99/28.80    (45)   ~ (all_52_29 = e3)
% 178.99/28.80    (46)   ~ (e3 = e0)
% 178.99/28.80    (47)   ~ (all_52_9 = all_52_13)
% 178.99/28.80    (48)   ~ (all_52_5 = all_52_29)
% 178.99/28.80    (49)  op(e1, e0) = all_52_23
% 178.99/28.80    (50)  all_58_13 = all_52_27
% 178.99/28.80    (51)   ~ (all_52_3 = e3)
% 178.99/28.80    (52)   ~ (all_52_27 = all_6_1)
% 178.99/28.80    (53)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.80    (54)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.80    (55)   ~ (all_52_3 = all_52_7)
% 178.99/28.80    (56)  all_58_11 = all_52_23
% 178.99/28.80    (57)   ~ (all_52_3 = all_52_19)
% 178.99/28.80    (58)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.80    (59)  all_58_2 = all_52_9
% 178.99/28.80    (60)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.99/28.80    (61)   ~ (e2 = e1)
% 178.99/28.80    (62)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.80    (63)   ~ (all_52_19 = e3)
% 178.99/28.80    (64)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.80    (65)   ~ (all_52_19 = all_52_27)
% 178.99/28.80    (66)   ~ (all_52_7 = e3)
% 178.99/28.80    (67)  op(e1, all_52_5) = e1
% 178.99/28.80    (68)   ~ (all_14_1 = all_6_1)
% 178.99/28.80    (69)   ~ (all_52_7 = all_52_23)
% 178.99/28.80    (70)   ~ (all_6_0 = e1)
% 178.99/28.80    (71)  op(e0, all_52_7) = e0
% 178.99/28.80    (72)   ~ (all_52_29 = all_6_1)
% 178.99/28.80    (73)  all_58_9 = all_52_7
% 178.99/28.80    (74)   ~ (all_52_9 = all_52_15)
% 178.99/28.80    (75)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.80    (76)   ~ (e3 = e2)
% 178.99/28.80    (77)  all_58_8 = e3
% 178.99/28.80    (78)  all_58_0 = e3
% 178.99/28.80    (79)   ~ (all_52_23 = all_14_1)
% 178.99/28.80    (80)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.99/28.80    (81)  all_56_8 = all_14_1
% 178.99/28.80    (82)  op(e2, e3) = all_52_9
% 178.99/28.80    (83)  all_56_13 = all_52_27
% 178.99/28.80  
% 178.99/28.80  Begin of proof
% 178.99/28.80  | 
% 178.99/28.80  | BETA: splitting (32) gives:
% 178.99/28.80  | 
% 178.99/28.80  | Case 1:
% 178.99/28.80  | | 
% 178.99/28.80  | |   (84)  all_58_1 = e3
% 178.99/28.80  | | 
% 178.99/28.80  | | COMBINE_EQS: (30), (84) imply:
% 178.99/28.80  | |   (85)  all_52_3 = e3
% 178.99/28.80  | | 
% 178.99/28.80  | | REDUCE: (51), (85) imply:
% 178.99/28.80  | |   (86)  $false
% 178.99/28.80  | | 
% 178.99/28.80  | | CLOSE: (86) is inconsistent.
% 178.99/28.80  | | 
% 178.99/28.80  | Case 2:
% 178.99/28.80  | | 
% 178.99/28.80  | |   (87)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 178.99/28.80  | | 
% 178.99/28.80  | | BETA: splitting (87) gives:
% 178.99/28.80  | | 
% 178.99/28.80  | | Case 1:
% 178.99/28.80  | | | 
% 178.99/28.80  | | |   (88)  all_58_3 = e3
% 178.99/28.80  | | | 
% 178.99/28.80  | | | COMBINE_EQS: (23), (88) imply:
% 178.99/28.80  | | |   (89)  all_10_2 = e3
% 178.99/28.80  | | | 
% 178.99/28.80  | | | REDUCE: (7), (89) imply:
% 178.99/28.80  | | |   (90)  op(e2, e3) = all_10_1
% 178.99/28.80  | | | 
% 178.99/28.80  | | | REDUCE: (4), (89) imply:
% 178.99/28.80  | | |   (91)  op(e2, e2) = e3
% 178.99/28.80  | | | 
% 178.99/28.80  | | | GROUND_INST: instantiating (64) with all_52_9, all_10_1, e3, e2,
% 178.99/28.80  | | |              simplifying with (82), (90) gives:
% 178.99/28.80  | | |   (92)  all_52_9 = all_10_1
% 178.99/28.80  | | | 
% 178.99/28.80  | | | COMBINE_EQS: (59), (92) imply:
% 178.99/28.80  | | |   (93)  all_58_2 = all_10_1
% 178.99/28.80  | | | 
% 178.99/28.80  | | | REDUCE: (47), (92) imply:
% 178.99/28.80  | | |   (94)   ~ (all_52_13 = all_10_1)
% 178.99/28.80  | | | 
% 178.99/28.80  | | | SIMP: (94) implies:
% 178.99/28.80  | | |   (95)   ~ (all_52_13 = all_10_1)
% 178.99/28.80  | | | 
% 178.99/28.80  | | | REDUCE: (74), (92) imply:
% 178.99/28.80  | | |   (96)   ~ (all_52_15 = all_10_1)
% 178.99/28.80  | | | 
% 178.99/28.80  | | | SIMP: (96) implies:
% 178.99/28.80  | | |   (97)   ~ (all_52_15 = all_10_1)
% 178.99/28.80  | | | 
% 178.99/28.80  | | | BETA: splitting (54) gives:
% 178.99/28.80  | | | 
% 178.99/28.80  | | | Case 1:
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | |   (98)  all_58_6 = e2
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | COMBINE_EQS: (35), (98) imply:
% 178.99/28.80  | | | |   (99)  all_14_1 = e2
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | REDUCE: (15), (99) imply:
% 178.99/28.80  | | | |   (100)  $false
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | CLOSE: (100) is inconsistent.
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | Case 2:
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | |   (101)   ~ (all_58_6 = e2)
% 178.99/28.80  | | | |   (102)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 178.99/28.80  | | | |            (15), (16), (17), (19), (20), (21), (22), (24), (25), (26),
% 178.99/28.80  | | | |            (27), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 178.99/28.80  | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (48),
% 178.99/28.80  | | | |            (49), (50), (51), (52), (53), (55), (56), (57), (58), (60),
% 178.99/28.80  | | | |            (61), (62), (64), (65), (66), (67), (68), (69), (70), (71),
% 178.99/28.80  | | | |            (72), (73), (75), (76), (77), (78), (79), (80), (81), (83),
% 178.99/28.80  | | | |            (90), (91), (93), (95), (97), (102) are inconsistent by
% 178.99/28.80  | | | |            sub-proof #831.
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | End of split
% 178.99/28.80  | | | 
% 178.99/28.80  | | Case 2:
% 178.99/28.80  | | | 
% 178.99/28.80  | | |   (103)  all_58_7 = e3 | all_58_13 = e3
% 178.99/28.80  | | | 
% 178.99/28.80  | | | REF_CLOSE: (13), (25), (50), (63), (103) are inconsistent by sub-proof
% 178.99/28.80  | | |            #976.
% 178.99/28.80  | | | 
% 178.99/28.80  | | End of split
% 178.99/28.80  | | 
% 178.99/28.80  | End of split
% 178.99/28.80  | 
% 178.99/28.80  End of proof
% 178.99/28.80  
% 178.99/28.80  Sub-proof #831 shows that the following formulas are inconsistent:
% 178.99/28.80  ----------------------------------------------------------------
% 178.99/28.80    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.80    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.80    (3)  op(e2, all_52_3) = e2
% 178.99/28.80    (4)  all_58_15 = e3
% 178.99/28.80    (5)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.80    (6)  all_56_3 = all_52_7
% 178.99/28.80    (7)   ~ (all_52_19 = all_52_23)
% 178.99/28.80    (8)  op(e1, e2) = all_52_19
% 178.99/28.80    (9)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.80    (10)   ~ (all_52_27 = e3)
% 178.99/28.80    (11)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.80    (12)   ~ (all_52_15 = all_10_1)
% 178.99/28.80    (13)   ~ (all_14_1 = e2)
% 178.99/28.80    (14)  all_58_12 = all_6_1
% 178.99/28.80    (15)  op(all_6_1, e3) = all_6_0
% 178.99/28.80    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.99/28.80    (17)  all_58_0 = e2 | all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.80    (18)  op(e2, e0) = all_52_15
% 178.99/28.80    (19)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.80    (20)   ~ (all_52_5 = all_52_7)
% 178.99/28.80    (21)  all_58_7 = all_52_19
% 178.99/28.80    (22)  op(e0, e1) = all_52_29
% 178.99/28.80    (23)  all_58_4 = all_52_5
% 178.99/28.80    (24)   ~ (e3 = e1)
% 178.99/28.80    (25)   ~ (all_52_27 = all_52_29)
% 178.99/28.80    (26)  all_58_1 = all_52_3
% 178.99/28.80    (27)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.80    (28)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.80    (29)  all_58_14 = all_52_29
% 178.99/28.80    (30)  all_58_6 = all_14_1
% 178.99/28.80    (31)   ~ (all_52_13 = all_10_1)
% 178.99/28.80    (32)   ~ (all_52_3 = all_52_5)
% 178.99/28.80    (33)  op(e2, e1) = all_52_13
% 178.99/28.80    (34)  all_56_1 = all_52_3
% 178.99/28.80    (35)  op(e0, e2) = all_52_27
% 178.99/28.80    (36)  all_56_14 = all_52_29
% 178.99/28.80    (37)   ~ (all_52_19 = all_14_1)
% 178.99/28.80    (38)  all_58_2 = all_10_1
% 178.99/28.80    (39)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.80    (40)   ~ (all_52_23 = e3)
% 178.99/28.80    (41)   ~ (all_52_3 = all_52_27)
% 178.99/28.80    (42)   ~ (all_52_29 = e3)
% 178.99/28.80    (43)   ~ (e3 = e0)
% 178.99/28.80    (44)   ~ (all_52_5 = all_52_29)
% 178.99/28.80    (45)  op(e1, e0) = all_52_23
% 178.99/28.80    (46)  all_58_13 = all_52_27
% 178.99/28.80    (47)   ~ (all_52_3 = e3)
% 178.99/28.80    (48)   ~ (all_52_27 = all_6_1)
% 178.99/28.80    (49)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.80    (50)   ~ (all_52_3 = all_52_7)
% 178.99/28.80    (51)  all_58_11 = all_52_23
% 178.99/28.80    (52)   ~ (all_52_3 = all_52_19)
% 178.99/28.80    (53)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.80    (54)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.99/28.80    (55)   ~ (e2 = e1)
% 178.99/28.80    (56)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.80    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.80    (58)   ~ (all_52_19 = all_52_27)
% 178.99/28.80    (59)   ~ (all_52_7 = e3)
% 178.99/28.80    (60)  op(e1, all_52_5) = e1
% 178.99/28.80    (61)   ~ (all_14_1 = all_6_1)
% 178.99/28.80    (62)   ~ (all_52_7 = all_52_23)
% 178.99/28.80    (63)   ~ (all_6_0 = e1)
% 178.99/28.80    (64)  op(e0, all_52_7) = e0
% 178.99/28.80    (65)   ~ (all_52_29 = all_6_1)
% 178.99/28.80    (66)  op(e2, e3) = all_10_1
% 178.99/28.80    (67)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.80    (68)  all_58_9 = all_52_7
% 178.99/28.80    (69)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.80    (70)   ~ (e3 = e2)
% 178.99/28.80    (71)  all_58_8 = e3
% 178.99/28.80    (72)  all_58_0 = e3
% 178.99/28.80    (73)   ~ (all_52_23 = all_14_1)
% 178.99/28.80    (74)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.99/28.80    (75)  op(e2, e2) = e3
% 178.99/28.80    (76)  all_56_8 = all_14_1
% 178.99/28.80    (77)  all_56_13 = all_52_27
% 178.99/28.80  
% 178.99/28.80  Begin of proof
% 178.99/28.80  | 
% 178.99/28.80  | BETA: splitting (17) gives:
% 178.99/28.80  | 
% 178.99/28.80  | Case 1:
% 178.99/28.80  | | 
% 178.99/28.80  | |   (78)  all_58_0 = e2
% 178.99/28.80  | | 
% 178.99/28.80  | | COMBINE_EQS: (72), (78) imply:
% 178.99/28.80  | |   (79)  e3 = e2
% 178.99/28.80  | | 
% 178.99/28.80  | | REDUCE: (70), (79) imply:
% 178.99/28.80  | |   (80)  $false
% 178.99/28.80  | | 
% 178.99/28.80  | | CLOSE: (80) is inconsistent.
% 178.99/28.80  | | 
% 178.99/28.80  | Case 2:
% 178.99/28.80  | | 
% 178.99/28.80  | |   (81)   ~ (all_58_0 = e2)
% 178.99/28.80  | |   (82)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.80  | | 
% 178.99/28.80  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.99/28.80  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 178.99/28.80  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 178.99/28.80  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 178.99/28.80  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 178.99/28.80  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 178.99/28.80  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (82) are
% 178.99/28.80  | |            inconsistent by sub-proof #832.
% 178.99/28.80  | | 
% 178.99/28.80  | End of split
% 178.99/28.80  | 
% 178.99/28.80  End of proof
% 178.99/28.80  
% 178.99/28.80  Sub-proof #832 shows that the following formulas are inconsistent:
% 178.99/28.80  ----------------------------------------------------------------
% 178.99/28.80    (1)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.80    (2)  all_58_1 = e1 | all_58_3 = e1 | all_58_7 = e1 | all_58_13 = e1
% 178.99/28.80    (3)  op(e2, all_52_3) = e2
% 178.99/28.80    (4)  all_58_15 = e3
% 178.99/28.80    (5)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.80    (6)  all_56_3 = all_52_7
% 178.99/28.80    (7)   ~ (all_52_19 = all_52_23)
% 178.99/28.80    (8)  op(e1, e2) = all_52_19
% 178.99/28.80    (9)  all_58_0 = e1 | all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.80    (10)   ~ (all_52_27 = e3)
% 178.99/28.80    (11)  all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 178.99/28.80    (12)   ~ (all_52_15 = all_10_1)
% 178.99/28.80    (13)   ~ (all_14_1 = e2)
% 178.99/28.80    (14)  all_58_12 = all_6_1
% 178.99/28.80    (15)  op(all_6_1, e3) = all_6_0
% 178.99/28.80    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 178.99/28.80    (17)  op(e2, e0) = all_52_15
% 178.99/28.80    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.80    (19)   ~ (all_52_5 = all_52_7)
% 178.99/28.80    (20)  all_58_7 = all_52_19
% 178.99/28.80    (21)  op(e0, e1) = all_52_29
% 178.99/28.80    (22)  all_58_4 = all_52_5
% 178.99/28.80    (23)   ~ (e3 = e1)
% 178.99/28.80    (24)   ~ (all_52_27 = all_52_29)
% 178.99/28.80    (25)  all_58_1 = all_52_3
% 178.99/28.80    (26)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.80    (27)  all_58_2 = e1 | all_58_3 = e1 | all_58_5 = e1 | all_58_10 = e1
% 178.99/28.80    (28)  all_58_14 = all_52_29
% 178.99/28.80    (29)  all_58_6 = all_14_1
% 178.99/28.80    (30)   ~ (all_52_13 = all_10_1)
% 178.99/28.80    (31)   ~ (all_52_3 = all_52_5)
% 178.99/28.80    (32)  op(e2, e1) = all_52_13
% 178.99/28.80    (33)  all_56_1 = all_52_3
% 178.99/28.80    (34)  op(e0, e2) = all_52_27
% 178.99/28.80    (35)  all_56_14 = all_52_29
% 178.99/28.80    (36)   ~ (all_52_19 = all_14_1)
% 178.99/28.80    (37)  all_58_2 = all_10_1
% 178.99/28.80    (38)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.80    (39)   ~ (all_52_23 = e3)
% 178.99/28.80    (40)   ~ (all_52_3 = all_52_27)
% 178.99/28.80    (41)   ~ (all_52_29 = e3)
% 178.99/28.80    (42)   ~ (e3 = e0)
% 178.99/28.80    (43)   ~ (all_52_5 = all_52_29)
% 178.99/28.80    (44)  op(e1, e0) = all_52_23
% 178.99/28.80    (45)  all_58_13 = all_52_27
% 178.99/28.80    (46)   ~ (all_52_3 = e3)
% 178.99/28.80    (47)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.80    (48)   ~ (all_52_27 = all_6_1)
% 178.99/28.80    (49)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.80    (50)   ~ (all_52_3 = all_52_7)
% 178.99/28.80    (51)  all_58_11 = all_52_23
% 178.99/28.80    (52)   ~ (all_52_3 = all_52_19)
% 178.99/28.80    (53)  all_58_4 = e2 | all_58_5 = e2 | all_58_8 = e2 | all_58_14 = e2
% 178.99/28.80    (54)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.99/28.80    (55)   ~ (e2 = e1)
% 178.99/28.80    (56)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 178.99/28.80    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.80    (58)   ~ (all_52_19 = all_52_27)
% 178.99/28.80    (59)   ~ (all_52_7 = e3)
% 178.99/28.80    (60)  op(e1, all_52_5) = e1
% 178.99/28.80    (61)   ~ (all_14_1 = all_6_1)
% 178.99/28.80    (62)   ~ (all_52_7 = all_52_23)
% 178.99/28.80    (63)   ~ (all_6_0 = e1)
% 178.99/28.80    (64)  op(e0, all_52_7) = e0
% 178.99/28.80    (65)   ~ (all_52_29 = all_6_1)
% 178.99/28.80    (66)  op(e2, e3) = all_10_1
% 178.99/28.80    (67)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 178.99/28.80    (68)  all_58_9 = all_52_7
% 178.99/28.80    (69)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 178.99/28.80    (70)   ~ (e3 = e2)
% 178.99/28.80    (71)  all_58_8 = e3
% 178.99/28.80    (72)  all_58_0 = e3
% 178.99/28.80    (73)   ~ (all_52_23 = all_14_1)
% 178.99/28.80    (74)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 178.99/28.80    (75)  op(e2, e2) = e3
% 178.99/28.80    (76)  all_56_8 = all_14_1
% 178.99/28.80    (77)  all_56_13 = all_52_27
% 178.99/28.80  
% 178.99/28.80  Begin of proof
% 178.99/28.80  | 
% 178.99/28.80  | BETA: splitting (26) gives:
% 178.99/28.80  | 
% 178.99/28.80  | Case 1:
% 178.99/28.80  | | 
% 178.99/28.80  | |   (78)  all_56_1 = e3
% 178.99/28.80  | | 
% 178.99/28.80  | | REF_CLOSE: (33), (46), (78) are inconsistent by sub-proof #862.
% 178.99/28.80  | | 
% 178.99/28.80  | Case 2:
% 178.99/28.80  | | 
% 178.99/28.80  | |   (79)   ~ (all_56_1 = e3)
% 178.99/28.80  | |   (80)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.80  | | 
% 178.99/28.80  | | BETA: splitting (38) gives:
% 178.99/28.80  | | 
% 178.99/28.80  | | Case 1:
% 178.99/28.80  | | | 
% 178.99/28.80  | | |   (81)  all_58_0 = e2
% 178.99/28.80  | | | 
% 178.99/28.80  | | | COMBINE_EQS: (72), (81) imply:
% 178.99/28.80  | | |   (82)  e3 = e2
% 178.99/28.80  | | | 
% 178.99/28.80  | | | REDUCE: (70), (82) imply:
% 178.99/28.80  | | |   (83)  $false
% 178.99/28.80  | | | 
% 178.99/28.80  | | | CLOSE: (83) is inconsistent.
% 178.99/28.80  | | | 
% 178.99/28.80  | | Case 2:
% 178.99/28.80  | | | 
% 178.99/28.80  | | |   (84)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 178.99/28.80  | | | 
% 178.99/28.80  | | | BETA: splitting (16) gives:
% 178.99/28.80  | | | 
% 178.99/28.80  | | | Case 1:
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | |   (85)  all_58_1 = e2
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | COMBINE_EQS: (25), (85) imply:
% 178.99/28.80  | | | |   (86)  all_52_3 = e2
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | REDUCE: (46), (86) imply:
% 178.99/28.80  | | | |   (87)   ~ (e3 = e2)
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | REDUCE: (3), (86) imply:
% 178.99/28.80  | | | |   (88)  op(e2, e2) = e2
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | REF_CLOSE: (57), (70), (75), (88) are inconsistent by sub-proof #848.
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | Case 2:
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | |   (89)   ~ (all_58_1 = e2)
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | REDUCE: (25), (89) imply:
% 178.99/28.80  | | | |   (90)   ~ (all_52_3 = e2)
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | BETA: splitting (18) gives:
% 178.99/28.80  | | | | 
% 178.99/28.80  | | | | Case 1:
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | |   (91)  all_58_9 = e1
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | COMBINE_EQS: (68), (91) imply:
% 178.99/28.80  | | | | |   (92)  all_52_7 = e1
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | REDUCE: (50), (92) imply:
% 178.99/28.80  | | | | |   (93)   ~ (all_52_3 = e1)
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | REDUCE: (64), (92) imply:
% 178.99/28.80  | | | | |   (94)  op(e0, e1) = e0
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | BETA: splitting (84) gives:
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | Case 1:
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | |   (95)  all_58_1 = e2
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | COMBINE_EQS: (25), (95) imply:
% 178.99/28.80  | | | | | |   (96)  all_52_3 = e2
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | REDUCE: (90), (96) imply:
% 178.99/28.80  | | | | | |   (97)  $false
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | CLOSE: (97) is inconsistent.
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | Case 2:
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | |   (98)  all_58_4 = e2 | all_58_9 = e2
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | BETA: splitting (98) gives:
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | Case 1:
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | |   (99)  all_58_4 = e2
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | COMBINE_EQS: (22), (99) imply:
% 178.99/28.80  | | | | | | |   (100)  all_52_5 = e2
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | REDUCE: (60), (100) imply:
% 178.99/28.80  | | | | | | |   (101)  op(e1, e2) = e1
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | BETA: splitting (1) gives:
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | |   (102)  all_58_0 = e0
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | COMBINE_EQS: (72), (102) imply:
% 178.99/28.80  | | | | | | | |   (103)  e3 = e0
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | REDUCE: (42), (103) imply:
% 178.99/28.80  | | | | | | | |   (104)  $false
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | CLOSE: (104) is inconsistent.
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | Case 2:
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | |   (105)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | BETA: splitting (80) gives:
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | |   (106)  all_56_1 = e2
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | REF_CLOSE: (33), (90), (106) are inconsistent by sub-proof
% 178.99/28.80  | | | | | | | | |            #857.
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | Case 2:
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | |   (107)  all_56_1 = e1 | all_56_1 = e0
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | BETA: splitting (105) gives:
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | |   (108)  all_58_1 = e0
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | COMBINE_EQS: (25), (108) imply:
% 178.99/28.80  | | | | | | | | | |   (109)  all_52_3 = e0
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (3), (109) imply:
% 178.99/28.80  | | | | | | | | | |   (110)  op(e2, e0) = e2
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | GROUND_INST: instantiating (57) with all_52_29, e0, e1, e0,
% 178.99/28.80  | | | | | | | | | |              simplifying with (21), (94) gives:
% 178.99/28.80  | | | | | | | | | |   (111)  all_52_29 = e0
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | GROUND_INST: instantiating (57) with all_52_19, e1, e2, e1,
% 178.99/28.80  | | | | | | | | | |              simplifying with (8), (101) gives:
% 178.99/28.80  | | | | | | | | | |   (112)  all_52_19 = e1
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | GROUND_INST: instantiating (57) with all_52_15, e2, e0, e2,
% 178.99/28.80  | | | | | | | | | |              simplifying with (17), (110) gives:
% 178.99/28.80  | | | | | | | | | |   (113)  all_52_15 = e2
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (12), (113) imply:
% 178.99/28.80  | | | | | | | | | |   (114)   ~ (all_10_1 = e2)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | SIMP: (114) implies:
% 178.99/28.80  | | | | | | | | | |   (115)   ~ (all_10_1 = e2)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (58), (112) imply:
% 178.99/28.80  | | | | | | | | | |   (116)   ~ (all_52_27 = e1)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | SIMP: (116) implies:
% 178.99/28.80  | | | | | | | | | |   (117)   ~ (all_52_27 = e1)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (24), (111) imply:
% 178.99/28.80  | | | | | | | | | |   (118)   ~ (all_52_27 = e0)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | BETA: splitting (11) gives:
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | |   (119)  all_56_13 = e2
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | COMBINE_EQS: (77), (119) imply:
% 178.99/28.80  | | | | | | | | | | |   (120)  all_52_27 = e2
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | REDUCE: (48), (120) imply:
% 178.99/28.80  | | | | | | | | | | |   (121)   ~ (all_6_1 = e2)
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | SIMP: (121) implies:
% 178.99/28.80  | | | | | | | | | | |   (122)   ~ (all_6_1 = e2)
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | REF_CLOSE: (13), (14), (29), (37), (47), (115), (122) are
% 178.99/28.80  | | | | | | | | | | |            inconsistent by sub-proof #845.
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | Case 2:
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | |   (123)  all_56_13 = e1 | all_56_13 = e0
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | BETA: splitting (123) gives:
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | |   (124)  all_56_13 = e1
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | | COMBINE_EQS: (77), (124) imply:
% 178.99/28.80  | | | | | | | | | | | |   (125)  all_52_27 = e1
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | | SIMP: (125) implies:
% 178.99/28.80  | | | | | | | | | | | |   (126)  all_52_27 = e1
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | | REDUCE: (117), (126) imply:
% 178.99/28.80  | | | | | | | | | | | |   (127)  $false
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | Case 2:
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | |   (128)  all_56_13 = e0
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | | REF_CLOSE: (77), (118), (128) are inconsistent by sub-proof
% 178.99/28.80  | | | | | | | | | | | |            #844.
% 178.99/28.80  | | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | | End of split
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | End of split
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | Case 2:
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | |   (129)   ~ (all_58_1 = e0)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (25), (129) imply:
% 178.99/28.80  | | | | | | | | | |   (130)   ~ (all_52_3 = e0)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REF_CLOSE: (33), (93), (107), (130) are inconsistent by
% 178.99/28.80  | | | | | | | | | |            sub-proof #843.
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | End of split
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | End of split
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | End of split
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | Case 2:
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | |   (131)  all_58_9 = e2
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | REF_CLOSE: (55), (91), (131) are inconsistent by sub-proof #938.
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | End of split
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | End of split
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | Case 2:
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | |   (132)   ~ (all_58_9 = e1)
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | REDUCE: (68), (132) imply:
% 178.99/28.80  | | | | |   (133)   ~ (all_52_7 = e1)
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | BETA: splitting (9) gives:
% 178.99/28.80  | | | | | 
% 178.99/28.80  | | | | | Case 1:
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | |   (134)  all_58_0 = e1
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | COMBINE_EQS: (72), (134) imply:
% 178.99/28.80  | | | | | |   (135)  e3 = e1
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | REDUCE: (23), (135) imply:
% 178.99/28.80  | | | | | |   (136)  $false
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | CLOSE: (136) is inconsistent.
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | Case 2:
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | |   (137)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | BETA: splitting (53) gives:
% 178.99/28.80  | | | | | | 
% 178.99/28.80  | | | | | | Case 1:
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | |   (138)  all_58_4 = e2
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | COMBINE_EQS: (22), (138) imply:
% 178.99/28.80  | | | | | | |   (139)  all_52_5 = e2
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | REDUCE: (19), (139) imply:
% 178.99/28.80  | | | | | | |   (140)   ~ (all_52_7 = e2)
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | SIMP: (140) implies:
% 178.99/28.80  | | | | | | |   (141)   ~ (all_52_7 = e2)
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | REDUCE: (60), (139) imply:
% 178.99/28.80  | | | | | | |   (142)  op(e1, e2) = e1
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | REF_CLOSE: (5), (6), (8), (25), (33), (50), (52), (57), (80),
% 178.99/28.80  | | | | | | |            (90), (133), (137), (141), (142) are inconsistent by
% 178.99/28.80  | | | | | | |            sub-proof #840.
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | Case 2:
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | |   (143)   ~ (all_58_4 = e2)
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | REDUCE: (22), (143) imply:
% 178.99/28.80  | | | | | | |   (144)   ~ (all_52_5 = e2)
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | BETA: splitting (84) gives:
% 178.99/28.80  | | | | | | | 
% 178.99/28.80  | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | |   (145)  all_58_1 = e2
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | COMBINE_EQS: (25), (145) imply:
% 178.99/28.80  | | | | | | | |   (146)  all_52_3 = e2
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | REDUCE: (90), (146) imply:
% 178.99/28.80  | | | | | | | |   (147)  $false
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | CLOSE: (147) is inconsistent.
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | Case 2:
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | |   (148)  all_58_4 = e2 | all_58_9 = e2
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | BETA: splitting (148) gives:
% 178.99/28.80  | | | | | | | | 
% 178.99/28.80  | | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | |   (149)  all_58_4 = e2
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | COMBINE_EQS: (22), (149) imply:
% 178.99/28.80  | | | | | | | | |   (150)  all_52_5 = e2
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | REDUCE: (144), (150) imply:
% 178.99/28.80  | | | | | | | | |   (151)  $false
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | CLOSE: (151) is inconsistent.
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | Case 2:
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | |   (152)  all_58_9 = e2
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | COMBINE_EQS: (68), (152) imply:
% 178.99/28.80  | | | | | | | | |   (153)  all_52_7 = e2
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | REDUCE: (62), (153) imply:
% 178.99/28.80  | | | | | | | | |   (154)   ~ (all_52_23 = e2)
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | SIMP: (154) implies:
% 178.99/28.80  | | | | | | | | |   (155)   ~ (all_52_23 = e2)
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | REDUCE: (59), (153) imply:
% 178.99/28.80  | | | | | | | | |   (156)   ~ (e3 = e2)
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | REDUCE: (64), (153) imply:
% 178.99/28.80  | | | | | | | | |   (157)  op(e0, e2) = e0
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | BETA: splitting (67) gives:
% 178.99/28.80  | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | |   (158)  all_58_7 = e2
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | COMBINE_EQS: (20), (158) imply:
% 178.99/28.80  | | | | | | | | | |   (159)  all_52_19 = e2
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (58), (159) imply:
% 178.99/28.80  | | | | | | | | | |   (160)   ~ (all_52_27 = e2)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | SIMP: (160) implies:
% 178.99/28.80  | | | | | | | | | |   (161)   ~ (all_52_27 = e2)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (36), (159) imply:
% 178.99/28.80  | | | | | | | | | |   (162)   ~ (all_14_1 = e2)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | GROUND_INST: instantiating (57) with all_52_27, e0, e2, e0,
% 178.99/28.80  | | | | | | | | | |              simplifying with (34), (157) gives:
% 178.99/28.80  | | | | | | | | | |   (163)  all_52_27 = e0
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | COMBINE_EQS: (45), (163) imply:
% 178.99/28.80  | | | | | | | | | |   (164)  all_58_13 = e0
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (40), (163) imply:
% 178.99/28.80  | | | | | | | | | |   (165)   ~ (all_52_3 = e0)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (10), (163) imply:
% 178.99/28.80  | | | | | | | | | |   (166)   ~ (e3 = e0)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | REDUCE: (161), (163) imply:
% 178.99/28.80  | | | | | | | | | |   (167)   ~ (e2 = e0)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | SIMP: (167) implies:
% 178.99/28.80  | | | | | | | | | |   (168)   ~ (e2 = e0)
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | BETA: splitting (2) gives:
% 178.99/28.80  | | | | | | | | | | 
% 178.99/28.80  | | | | | | | | | | Case 1:
% 178.99/28.80  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | |   (169)  all_58_1 = e1
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | COMBINE_EQS: (25), (169) imply:
% 178.99/28.81  | | | | | | | | | | |   (170)  all_52_3 = e1
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | REDUCE: (31), (170) imply:
% 178.99/28.81  | | | | | | | | | | |   (171)   ~ (all_52_5 = e1)
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | SIMP: (171) implies:
% 178.99/28.81  | | | | | | | | | | |   (172)   ~ (all_52_5 = e1)
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | REDUCE: (165), (170) imply:
% 178.99/28.81  | | | | | | | | | | |   (173)   ~ (e1 = e0)
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | REDUCE: (3), (170) imply:
% 178.99/28.81  | | | | | | | | | | |   (174)  op(e2, e1) = e2
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | BETA: splitting (1) gives:
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | |   (175)  all_58_0 = e0
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | COMBINE_EQS: (72), (175) imply:
% 178.99/28.81  | | | | | | | | | | | |   (176)  e3 = e0
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | REDUCE: (42), (176) imply:
% 178.99/28.81  | | | | | | | | | | | |   (177)  $false
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | CLOSE: (177) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | |   (178)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | BETA: splitting (178) gives:
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | |   (179)  all_58_1 = e0
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | COMBINE_EQS: (169), (179) imply:
% 178.99/28.81  | | | | | | | | | | | | |   (180)  e1 = e0
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | REDUCE: (173), (180) imply:
% 178.99/28.81  | | | | | | | | | | | | |   (181)  $false
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | CLOSE: (181) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | |   (182)  all_58_4 = e0 | all_58_9 = e0
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | BETA: splitting (182) gives:
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | |   (183)  all_58_4 = e0
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | COMBINE_EQS: (22), (183) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (184)  all_52_5 = e0
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | SIMP: (184) implies:
% 178.99/28.81  | | | | | | | | | | | | | |   (185)  all_52_5 = e0
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REDUCE: (43), (185) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (186)   ~ (all_52_29 = e0)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | SIMP: (186) implies:
% 178.99/28.81  | | | | | | | | | | | | | |   (187)   ~ (all_52_29 = e0)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REDUCE: (172), (185) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (188)   ~ (e1 = e0)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REDUCE: (60), (185) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (189)  op(e1, e0) = e1
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_52_23, e1, e0, e1,
% 178.99/28.81  | | | | | | | | | | | | | |              simplifying with (44), (189) gives:
% 178.99/28.81  | | | | | | | | | | | | | |   (190)  all_52_23 = e1
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with all_52_13, e2, e1, e2,
% 178.99/28.81  | | | | | | | | | | | | | |              simplifying with (32), (174) gives:
% 178.99/28.81  | | | | | | | | | | | | | |   (191)  all_52_13 = e2
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REDUCE: (30), (191) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (192)   ~ (all_10_1 = e2)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | SIMP: (192) implies:
% 178.99/28.81  | | | | | | | | | | | | | |   (193)   ~ (all_10_1 = e2)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REDUCE: (73), (190) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (194)   ~ (all_14_1 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | SIMP: (194) implies:
% 178.99/28.81  | | | | | | | | | | | | | |   (195)   ~ (all_14_1 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REDUCE: (39), (190) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (196)   ~ (e3 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REDUCE: (155), (190) imply:
% 178.99/28.81  | | | | | | | | | | | | | |   (197)   ~ (e2 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | |   (198)  all_58_12 = e2
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | COMBINE_EQS: (14), (198) imply:
% 178.99/28.81  | | | | | | | | | | | | | | |   (199)  all_6_1 = e2
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | SIMP: (199) implies:
% 178.99/28.81  | | | | | | | | | | | | | | |   (200)  all_6_1 = e2
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | REDUCE: (65), (200) imply:
% 178.99/28.81  | | | | | | | | | | | | | | |   (201)   ~ (all_52_29 = e2)
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | REDUCE: (15), (200) imply:
% 178.99/28.81  | | | | | | | | | | | | | | |   (202)  op(e2, e3) = all_6_0
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | |   (203)  all_58_12 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | REF_CLOSE: (55), (198), (203) are inconsistent by sub-proof
% 178.99/28.81  | | | | | | | | | | | | | | | |            #839.
% 178.99/28.81  | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | |   (204)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | |   (205)  all_58_0 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (205) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | |   (206)  e3 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | REDUCE: (23), (206) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | |   (207)  $false
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | |   (208)   ~ (all_58_0 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | | | |   (209)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | |   (210)  all_58_2 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (210) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | |   (211)  all_10_1 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | SIMP: (211) implies:
% 178.99/28.81  | | | | | | | | | | | | | | | | | |   (212)  all_10_1 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | REDUCE: (66), (212) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | |   (213)  op(e2, e3) = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (63), (202), (213) are inconsistent by
% 178.99/28.81  | | | | | | | | | | | | | | | | | |            sub-proof #838.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | |   (214)   ~ (all_58_2 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | REDUCE: (37), (214) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | |   (215)   ~ (all_10_1 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | |   (216)  all_56_14 = e2
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (201), (216) are inconsistent by sub-proof
% 178.99/28.81  | | | | | | | | | | | | | | | | | | |            #837.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | |   (217)   ~ (all_56_14 = e2)
% 178.99/28.81  | | | | | | | | | | | | | | | | | | |   (218)  all_56_14 = e1 | all_56_14 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | |   (219)  all_56_8 = e2
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (219) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | |   (220)  all_14_1 = e2
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (220) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | |   (221)  $false
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | |   (222)  all_56_8 = e1 | all_56_8 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (223)  all_56_8 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (223) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (224)  all_14_1 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | SIMP: (224) implies:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (225)  all_14_1 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | REDUCE: (195), (225) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (226)  $false
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | CLOSE: (226) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (227)  all_56_8 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (227) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (228)  all_14_1 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (229)  all_14_1 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (229) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | |   (230)  all_58_6 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | |   (231)  all_58_2 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (231) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | |   (232)  all_10_1 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | SIMP: (232) implies:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | |   (233)  all_10_1 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (233) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | |   (234)  $false
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (234) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | |   (235)  all_58_6 = e1 | all_58_12 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_58_13 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (236) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | |   (237)  e1 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (237) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | |   (238)  $false
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | |   (239)   ~ (all_58_13 = e1)
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_58_14 = e1 | all_58_15 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_56_14 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (241) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_52_29 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_52_29 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (243) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_58_14 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_58_6 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (230), (245) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  e1 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (246) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_58_14 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23), (173), (240), (247) are inconsistent by
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #835.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  all_58_12 = e1
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (198), (248) are inconsistent by sub-proof
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #839.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_56_14 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (35), (249) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_52_29 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (250) implies:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_52_29 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (251) imply:
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_58_14 = e0
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (23), (173), (240), (252) are inconsistent by
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #835.
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | |   (253)   ~ (all_58_12 = e2)
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | REDUCE: (14), (253) imply:
% 178.99/28.81  | | | | | | | | | | | | | | |   (254)   ~ (all_6_1 = e2)
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (29), (37), (47), (193), (254) are
% 178.99/28.81  | | | | | | | | | | | | | | |            inconsistent by sub-proof #845.
% 178.99/28.81  | | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | |   (255)  all_58_9 = e0
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | | REF_CLOSE: (152), (168), (255) are inconsistent by sub-proof
% 178.99/28.81  | | | | | | | | | | | | | |            #834.
% 178.99/28.81  | | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | |   (256)   ~ (all_58_1 = e1)
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | REDUCE: (25), (256) imply:
% 178.99/28.81  | | | | | | | | | | |   (257)   ~ (all_52_3 = e1)
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | REF_CLOSE: (33), (80), (90), (165), (257) are inconsistent by
% 178.99/28.81  | | | | | | | | | | |            sub-proof #833.
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | |   (258)  all_58_8 = e2 | all_58_11 = e2
% 178.99/28.81  | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | BETA: splitting (258) gives:
% 178.99/28.81  | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | Case 1:
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | |   (259)  all_58_8 = e2
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | COMBINE_EQS: (71), (259) imply:
% 178.99/28.81  | | | | | | | | | | |   (260)  e3 = e2
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | REDUCE: (70), (260) imply:
% 178.99/28.81  | | | | | | | | | | |   (261)  $false
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | CLOSE: (261) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | Case 2:
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | |   (262)  all_58_11 = e2
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | COMBINE_EQS: (51), (262) imply:
% 178.99/28.81  | | | | | | | | | | |   (263)  all_52_23 = e2
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | REDUCE: (155), (263) imply:
% 178.99/28.81  | | | | | | | | | | |   (264)  $false
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | | CLOSE: (264) is inconsistent.
% 178.99/28.81  | | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | | 
% 178.99/28.81  | | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | | 
% 178.99/28.81  | | | | | | | | End of split
% 178.99/28.81  | | | | | | | | 
% 178.99/28.81  | | | | | | | End of split
% 178.99/28.81  | | | | | | | 
% 178.99/28.81  | | | | | | End of split
% 178.99/28.81  | | | | | | 
% 178.99/28.81  | | | | | End of split
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | End of split
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | End of split
% 178.99/28.81  | | | 
% 178.99/28.81  | | End of split
% 178.99/28.81  | | 
% 178.99/28.81  | End of split
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #833 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)   ~ (all_52_3 = e1)
% 178.99/28.81    (2)   ~ (all_52_3 = e2)
% 178.99/28.81    (3)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.81    (4)  all_56_1 = all_52_3
% 178.99/28.81    (5)   ~ (all_52_3 = e0)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | BETA: splitting (3) gives:
% 178.99/28.81  | 
% 178.99/28.81  | Case 1:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (6)  all_56_1 = e2
% 178.99/28.81  | | 
% 178.99/28.81  | | COMBINE_EQS: (4), (6) imply:
% 178.99/28.81  | |   (7)  all_52_3 = e2
% 178.99/28.81  | | 
% 178.99/28.81  | | REDUCE: (2), (7) imply:
% 178.99/28.81  | |   (8)  $false
% 178.99/28.81  | | 
% 178.99/28.81  | | CLOSE: (8) is inconsistent.
% 178.99/28.81  | | 
% 178.99/28.81  | Case 2:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (9)  all_56_1 = e1 | all_56_1 = e0
% 178.99/28.81  | | 
% 178.99/28.81  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #843.
% 178.99/28.81  | | 
% 178.99/28.81  | End of split
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #834 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_58_9 = e2
% 178.99/28.81    (2)  all_58_9 = e0
% 178.99/28.81    (3)   ~ (e2 = e0)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  e2 = e0
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  e2 = e0
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #835 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_58_15 = e3
% 178.99/28.81    (2)  all_58_14 = e0
% 178.99/28.81    (3)  all_58_14 = e1 | all_58_15 = e1
% 178.99/28.81    (4)   ~ (e3 = e1)
% 178.99/28.81    (5)   ~ (e1 = e0)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | BETA: splitting (3) gives:
% 178.99/28.81  | 
% 178.99/28.81  | Case 1:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (6)  all_58_14 = e1
% 178.99/28.81  | | 
% 178.99/28.81  | | COMBINE_EQS: (2), (6) imply:
% 178.99/28.81  | |   (7)  e1 = e0
% 178.99/28.81  | | 
% 178.99/28.81  | | REDUCE: (5), (7) imply:
% 178.99/28.81  | |   (8)  $false
% 178.99/28.81  | | 
% 178.99/28.81  | | CLOSE: (8) is inconsistent.
% 178.99/28.81  | | 
% 178.99/28.81  | Case 2:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (9)  all_58_15 = e1
% 178.99/28.81  | | 
% 178.99/28.81  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #836.
% 178.99/28.81  | | 
% 178.99/28.81  | End of split
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #836 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_58_15 = e3
% 178.99/28.81    (2)  all_58_15 = e1
% 178.99/28.81    (3)   ~ (e3 = e1)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  e3 = e1
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  e3 = e1
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #837 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_56_14 = all_52_29
% 178.99/28.81    (2)  all_56_14 = e2
% 178.99/28.81    (3)   ~ (all_52_29 = e2)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  all_52_29 = e2
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  all_52_29 = e2
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #838 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.81    (2)  op(e2, e3) = all_6_0
% 178.99/28.81    (3)  op(e2, e3) = e1
% 178.99/28.81    (4)   ~ (all_6_0 = e1)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | GROUND_INST: instantiating (1) with e1, all_6_0, e3, e2, simplifying with (2),
% 178.99/28.81  |              (3) gives:
% 178.99/28.81  |   (5)  all_6_0 = e1
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (4), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #839 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_58_12 = e2
% 178.99/28.81    (2)  all_58_12 = e1
% 178.99/28.81    (3)   ~ (e2 = e1)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  e2 = e1
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  e2 = e1
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #840 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.81    (2)  all_56_3 = all_52_7
% 178.99/28.81    (3)  op(e1, e2) = all_52_19
% 178.99/28.81    (4)   ~ (all_52_3 = e2)
% 178.99/28.81    (5)  all_58_1 = all_52_3
% 178.99/28.81    (6)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.81    (7)  all_56_1 = all_52_3
% 178.99/28.81    (8)   ~ (all_52_7 = e1)
% 178.99/28.81    (9)  op(e1, e2) = e1
% 178.99/28.81    (10)  all_58_1 = e1 | all_58_4 = e1 | all_58_9 = e1
% 178.99/28.81    (11)   ~ (all_52_3 = all_52_7)
% 178.99/28.81    (12)   ~ (all_52_3 = all_52_19)
% 178.99/28.81    (13)   ~ (all_52_7 = e2)
% 178.99/28.81    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | BETA: splitting (10) gives:
% 178.99/28.81  | 
% 178.99/28.81  | Case 1:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (15)  all_58_1 = e1
% 178.99/28.81  | | 
% 178.99/28.81  | | COMBINE_EQS: (5), (15) imply:
% 178.99/28.81  | |   (16)  all_52_3 = e1
% 178.99/28.81  | | 
% 178.99/28.81  | | REDUCE: (12), (16) imply:
% 178.99/28.81  | |   (17)   ~ (all_52_19 = e1)
% 178.99/28.81  | | 
% 178.99/28.81  | | SIMP: (17) implies:
% 178.99/28.81  | |   (18)   ~ (all_52_19 = e1)
% 178.99/28.81  | | 
% 178.99/28.81  | | REF_CLOSE: (3), (9), (14), (18) are inconsistent by sub-proof #842.
% 178.99/28.81  | | 
% 178.99/28.81  | Case 2:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (19)   ~ (all_58_1 = e1)
% 178.99/28.81  | | 
% 178.99/28.81  | | REDUCE: (5), (19) imply:
% 178.99/28.81  | |   (20)   ~ (all_52_3 = e1)
% 178.99/28.81  | | 
% 178.99/28.81  | | BETA: splitting (1) gives:
% 178.99/28.81  | | 
% 178.99/28.81  | | Case 1:
% 178.99/28.81  | | | 
% 178.99/28.81  | | |   (21)  all_56_3 = e2
% 178.99/28.81  | | | 
% 178.99/28.81  | | | REF_CLOSE: (2), (13), (21) are inconsistent by sub-proof #1038.
% 178.99/28.81  | | | 
% 178.99/28.81  | | Case 2:
% 178.99/28.81  | | | 
% 178.99/28.81  | | |   (22)  all_56_3 = e1 | all_56_3 = e0
% 178.99/28.81  | | | 
% 178.99/28.81  | | | BETA: splitting (6) gives:
% 178.99/28.81  | | | 
% 178.99/28.81  | | | Case 1:
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | |   (23)  all_56_1 = e2
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | | REF_CLOSE: (4), (7), (23) are inconsistent by sub-proof #857.
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | Case 2:
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | |   (24)  all_56_1 = e1 | all_56_1 = e0
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | | BETA: splitting (24) gives:
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | | Case 1:
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | |   (25)  all_56_1 = e1
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | | REF_CLOSE: (7), (20), (25) are inconsistent by sub-proof #841.
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | Case 2:
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | |   (26)  all_56_1 = e0
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | | COMBINE_EQS: (7), (26) imply:
% 178.99/28.81  | | | | |   (27)  all_52_3 = e0
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | | SIMP: (27) implies:
% 178.99/28.81  | | | | |   (28)  all_52_3 = e0
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | | REDUCE: (11), (28) imply:
% 178.99/28.81  | | | | |   (29)   ~ (all_52_7 = e0)
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | | SIMP: (29) implies:
% 178.99/28.81  | | | | |   (30)   ~ (all_52_7 = e0)
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | | REF_CLOSE: (2), (8), (22), (30) are inconsistent by sub-proof #1037.
% 178.99/28.81  | | | | | 
% 178.99/28.81  | | | | End of split
% 178.99/28.81  | | | | 
% 178.99/28.81  | | | End of split
% 178.99/28.81  | | | 
% 178.99/28.81  | | End of split
% 178.99/28.81  | | 
% 178.99/28.81  | End of split
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #841 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_56_1 = all_52_3
% 178.99/28.81    (2)  all_56_1 = e1
% 178.99/28.81    (3)   ~ (all_52_3 = e1)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  all_52_3 = e1
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  all_52_3 = e1
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #842 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.81    (2)  op(e1, e2) = all_52_19
% 178.99/28.81    (3)  op(e1, e2) = e1
% 178.99/28.81    (4)   ~ (all_52_19 = e1)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | GROUND_INST: instantiating (1) with all_52_19, e1, e2, e1, simplifying with
% 178.99/28.81  |              (2), (3) gives:
% 178.99/28.81  |   (5)  all_52_19 = e1
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (4), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #843 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_56_1 = e1 | all_56_1 = e0
% 178.99/28.81    (2)  all_56_1 = all_52_3
% 178.99/28.81    (3)   ~ (all_52_3 = e1)
% 178.99/28.81    (4)   ~ (all_52_3 = e0)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | BETA: splitting (1) gives:
% 178.99/28.81  | 
% 178.99/28.81  | Case 1:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (5)  all_56_1 = e1
% 178.99/28.81  | | 
% 178.99/28.81  | | COMBINE_EQS: (2), (5) imply:
% 178.99/28.81  | |   (6)  all_52_3 = e1
% 178.99/28.81  | | 
% 178.99/28.81  | | REDUCE: (3), (6) imply:
% 178.99/28.81  | |   (7)  $false
% 178.99/28.81  | | 
% 178.99/28.81  | | CLOSE: (7) is inconsistent.
% 178.99/28.81  | | 
% 178.99/28.81  | Case 2:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (8)  all_56_1 = e0
% 178.99/28.81  | | 
% 178.99/28.81  | | COMBINE_EQS: (2), (8) imply:
% 178.99/28.81  | |   (9)  all_52_3 = e0
% 178.99/28.81  | | 
% 178.99/28.81  | | REDUCE: (4), (9) imply:
% 178.99/28.81  | |   (10)  $false
% 178.99/28.81  | | 
% 178.99/28.81  | | CLOSE: (10) is inconsistent.
% 178.99/28.81  | | 
% 178.99/28.81  | End of split
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #844 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_56_13 = all_52_27
% 178.99/28.81    (2)  all_56_13 = e0
% 178.99/28.81    (3)   ~ (all_52_27 = e0)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  all_52_27 = e0
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  all_52_27 = e0
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #845 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)   ~ (all_14_1 = e2)
% 178.99/28.81    (2)  all_58_12 = all_6_1
% 178.99/28.81    (3)  all_58_6 = all_14_1
% 178.99/28.81    (4)  all_58_2 = all_10_1
% 178.99/28.81    (5)  all_58_2 = e2 | all_58_6 = e2 | all_58_12 = e2
% 178.99/28.81    (6)   ~ (all_10_1 = e2)
% 178.99/28.81    (7)   ~ (all_6_1 = e2)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | BETA: splitting (5) gives:
% 178.99/28.81  | 
% 178.99/28.81  | Case 1:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (8)  all_58_2 = e2
% 178.99/28.81  | | 
% 178.99/28.81  | | COMBINE_EQS: (4), (8) imply:
% 178.99/28.81  | |   (9)  all_10_1 = e2
% 178.99/28.81  | | 
% 178.99/28.81  | | SIMP: (9) implies:
% 178.99/28.81  | |   (10)  all_10_1 = e2
% 178.99/28.81  | | 
% 178.99/28.81  | | REDUCE: (6), (10) imply:
% 178.99/28.81  | |   (11)  $false
% 178.99/28.81  | | 
% 178.99/28.81  | | CLOSE: (11) is inconsistent.
% 178.99/28.81  | | 
% 178.99/28.81  | Case 2:
% 178.99/28.81  | | 
% 178.99/28.81  | |   (12)  all_58_6 = e2 | all_58_12 = e2
% 178.99/28.81  | | 
% 178.99/28.81  | | BETA: splitting (12) gives:
% 178.99/28.81  | | 
% 178.99/28.81  | | Case 1:
% 178.99/28.81  | | | 
% 178.99/28.81  | | |   (13)  all_58_6 = e2
% 178.99/28.81  | | | 
% 178.99/28.81  | | | REF_CLOSE: (1), (3), (13) are inconsistent by sub-proof #847.
% 178.99/28.81  | | | 
% 178.99/28.81  | | Case 2:
% 178.99/28.81  | | | 
% 178.99/28.81  | | |   (14)  all_58_12 = e2
% 178.99/28.81  | | | 
% 178.99/28.81  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #846.
% 178.99/28.81  | | | 
% 178.99/28.81  | | End of split
% 178.99/28.81  | | 
% 178.99/28.81  | End of split
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #846 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_58_12 = all_6_1
% 178.99/28.81    (2)  all_58_12 = e2
% 178.99/28.81    (3)   ~ (all_6_1 = e2)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  all_6_1 = e2
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  all_6_1 = e2
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #847 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_58_6 = all_14_1
% 178.99/28.81    (2)  all_58_6 = e2
% 178.99/28.81    (3)   ~ (all_14_1 = e2)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  all_14_1 = e2
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  all_14_1 = e2
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #848 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.81    (2)  op(e2, e2) = e3
% 178.99/28.81    (3)  op(e2, e2) = e2
% 178.99/28.81    (4)   ~ (e3 = e2)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | GROUND_INST: instantiating (1) with e2, e3, e2, e2, simplifying with (2), (3)
% 178.99/28.81  |              gives:
% 178.99/28.81  |   (5)  e3 = e2
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (4), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #849 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)  all_56_8 = all_14_1
% 178.99/28.81    (2)  all_56_8 = e3
% 178.99/28.81    (3)   ~ (all_14_1 = e3)
% 178.99/28.81  
% 178.99/28.81  Begin of proof
% 178.99/28.81  | 
% 178.99/28.81  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.81  |   (4)  all_14_1 = e3
% 178.99/28.81  | 
% 178.99/28.81  | SIMP: (4) implies:
% 178.99/28.81  |   (5)  all_14_1 = e3
% 178.99/28.81  | 
% 178.99/28.81  | REDUCE: (3), (5) imply:
% 178.99/28.81  |   (6)  $false
% 178.99/28.81  | 
% 178.99/28.81  | CLOSE: (6) is inconsistent.
% 178.99/28.81  | 
% 178.99/28.81  End of proof
% 178.99/28.81  
% 178.99/28.81  Sub-proof #850 shows that the following formulas are inconsistent:
% 178.99/28.81  ----------------------------------------------------------------
% 178.99/28.81    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.81    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.81    (3)  op(e2, all_52_3) = e2
% 178.99/28.81    (4)  op(e3, e2) = all_52_3
% 178.99/28.81    (5)  all_58_5 = all_52_13
% 178.99/28.81    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.81    (7)  all_58_15 = all_6_2
% 178.99/28.81    (8)   ~ (all_52_9 = all_4_2)
% 178.99/28.81    (9)   ~ (all_52_5 = all_52_7)
% 178.99/28.81    (10)  all_58_10 = all_52_15
% 178.99/28.81    (11)   ~ (all_52_5 = all_4_2)
% 178.99/28.81    (12)  all_58_7 = all_52_19
% 178.99/28.81    (13)  all_58_4 = all_52_5
% 178.99/28.81    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.81    (15)   ~ (all_52_17 = all_14_2)
% 178.99/28.81    (16)   ~ (all_52_7 = all_4_2)
% 178.99/28.81    (17)  all_58_1 = all_52_3
% 178.99/28.81    (18)  all_58_0 = all_4_2
% 178.99/28.81    (19)  all_58_14 = all_52_29
% 178.99/28.81    (20)  all_58_6 = e3
% 178.99/28.81    (21)   ~ (all_52_3 = all_52_5)
% 178.99/28.82    (22)  all_58_8 = all_14_2
% 178.99/28.82    (23)   ~ (all_52_5 = all_14_2)
% 178.99/28.82    (24)  op(e3, all_4_2) = e3
% 178.99/28.82    (25)  op(e0, e3) = all_52_25
% 178.99/28.82    (26)   ~ (all_52_29 = e3)
% 178.99/28.82    (27)   ~ (all_52_13 = all_14_2)
% 178.99/28.82    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.82    (29)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.82    (30)   ~ (all_52_5 = all_52_29)
% 178.99/28.82    (31)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.82    (32)  all_58_6 = all_52_17
% 178.99/28.82    (33)   ~ (all_52_3 = all_52_7)
% 178.99/28.82    (34)  all_56_0 = all_4_2
% 178.99/28.82    (35)  all_58_11 = all_52_23
% 178.99/28.82    (36)   ~ (all_52_3 = all_52_19)
% 178.99/28.82    (37)   ~ (all_52_7 = all_52_15)
% 178.99/28.82    (38)   ~ (all_52_29 = all_14_2)
% 178.99/28.82    (39)  op(e3, e1) = all_52_5
% 178.99/28.82    (40)  all_56_10 = all_14_2
% 178.99/28.82    (41)  op(e1, e3) = all_52_17
% 178.99/28.82    (42)   ~ (all_52_25 = all_4_2)
% 178.99/28.82    (43)  op(e3, e0) = all_52_7
% 178.99/28.82    (44)   ~ (all_52_17 = all_4_2)
% 178.99/28.82    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (46)   ~ (all_52_7 = all_6_2)
% 178.99/28.82    (47)  op(e1, all_52_5) = e1
% 178.99/28.82    (48)   ~ (all_52_7 = all_52_23)
% 178.99/28.82    (49)  op(e0, all_52_7) = e0
% 178.99/28.82    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.82    (51)  all_58_9 = all_52_7
% 178.99/28.82    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.82    (53)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.82    (54)  op(e2, e3) = all_52_9
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | COMBINE_EQS: (20), (32) imply:
% 178.99/28.82  |   (55)  all_52_17 = e3
% 178.99/28.82  | 
% 178.99/28.82  | SIMP: (55) implies:
% 178.99/28.82  |   (56)  all_52_17 = e3
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (44), (56) imply:
% 178.99/28.82  |   (57)   ~ (all_4_2 = e3)
% 178.99/28.82  | 
% 178.99/28.82  | SIMP: (57) implies:
% 178.99/28.82  |   (58)   ~ (all_4_2 = e3)
% 178.99/28.82  | 
% 178.99/28.82  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 178.99/28.82  |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 178.99/28.82  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 178.99/28.82  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 178.99/28.82  |            (47), (48), (49), (50), (51), (52), (53), (54), (58) are
% 178.99/28.82  |            inconsistent by sub-proof #864.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #851 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.82    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.82    (3)  op(e2, all_52_3) = e2
% 178.99/28.82    (4)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.82    (5)  all_56_3 = all_52_7
% 178.99/28.82    (6)  op(e3, e2) = all_52_3
% 178.99/28.82    (7)  all_58_5 = all_52_13
% 178.99/28.82    (8)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.82    (9)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.82    (10)  all_58_15 = all_6_2
% 178.99/28.82    (11)   ~ (all_52_9 = all_4_2)
% 178.99/28.82    (12)   ~ (all_52_5 = all_52_7)
% 178.99/28.82    (13)  all_58_10 = all_52_15
% 178.99/28.82    (14)   ~ (all_52_5 = all_4_2)
% 178.99/28.82    (15)  all_58_7 = all_52_19
% 178.99/28.82    (16)  op(e0, e1) = all_52_29
% 178.99/28.82    (17)  all_58_4 = all_52_5
% 178.99/28.82    (18)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.82    (19)   ~ (all_52_17 = all_14_2)
% 178.99/28.82    (20)   ~ (all_52_7 = all_4_2)
% 178.99/28.82    (21)  all_58_1 = all_52_3
% 178.99/28.82    (22)  all_58_0 = all_4_2
% 178.99/28.82    (23)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.82    (24)  all_58_14 = all_52_29
% 178.99/28.82    (25)   ~ (all_52_3 = all_52_5)
% 178.99/28.82    (26)  op(e2, e1) = all_52_13
% 178.99/28.82    (27)  all_58_8 = all_14_2
% 178.99/28.82    (28)  all_56_1 = all_52_3
% 178.99/28.82    (29)  op(e0, e2) = all_52_27
% 178.99/28.82    (30)   ~ (all_52_5 = all_14_2)
% 178.99/28.82    (31)   ~ (all_52_3 = all_52_27)
% 178.99/28.82    (32)  op(e3, all_4_2) = e3
% 178.99/28.82    (33)  op(e0, e3) = all_52_25
% 178.99/28.82    (34)   ~ (all_52_29 = e3)
% 178.99/28.82    (35)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.99/28.82    (36)   ~ (all_52_13 = all_14_2)
% 178.99/28.82    (37)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 178.99/28.82    (38)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 178.99/28.82    (39)   ~ (all_52_5 = all_52_29)
% 178.99/28.82    (40)  all_56_2 = all_52_5
% 178.99/28.82    (41)   ~ (all_52_3 = e3)
% 178.99/28.82    (42)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 178.99/28.82    (43)  all_58_6 = all_52_17
% 178.99/28.82    (44)   ~ (all_52_3 = all_52_7)
% 178.99/28.82    (45)  all_56_0 = all_4_2
% 178.99/28.82    (46)  all_58_11 = all_52_23
% 178.99/28.82    (47)   ~ (all_52_3 = all_52_19)
% 178.99/28.82    (48)   ~ (all_52_7 = all_52_15)
% 178.99/28.82    (49)   ~ (all_52_29 = all_14_2)
% 178.99/28.82    (50)  op(e3, e1) = all_52_5
% 178.99/28.82    (51)  all_56_10 = all_14_2
% 178.99/28.82    (52)  op(e1, e1) = all_14_2
% 178.99/28.82    (53)  op(e1, e3) = all_52_17
% 178.99/28.82    (54)   ~ (all_52_25 = all_4_2)
% 178.99/28.82    (55)  op(e3, e0) = all_52_7
% 178.99/28.82    (56)   ~ (all_14_2 = e3)
% 178.99/28.82    (57)   ~ (all_52_17 = all_4_2)
% 178.99/28.82    (58)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (59)   ~ (all_52_7 = all_6_2)
% 178.99/28.82    (60)   ~ (all_52_7 = e3)
% 178.99/28.82    (61)  op(e1, all_52_5) = e1
% 178.99/28.82    (62)   ~ (all_52_7 = all_52_23)
% 178.99/28.82    (63)  op(e0, all_52_7) = e0
% 178.99/28.82    (64)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 178.99/28.82    (65)  all_58_9 = all_52_7
% 178.99/28.82    (66)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 178.99/28.82    (67)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.82    (68)  op(e0, e0) = e3
% 178.99/28.82    (69)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.82    (70)  op(e1, e2) = e3
% 178.99/28.82    (71)  op(e2, e3) = all_52_9
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | BETA: splitting (67) gives:
% 178.99/28.82  | 
% 178.99/28.82  | Case 1:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (72)  all_58_4 = e3
% 178.99/28.82  | | 
% 178.99/28.82  | | COMBINE_EQS: (17), (72) imply:
% 178.99/28.82  | |   (73)  all_52_5 = e3
% 178.99/28.82  | | 
% 178.99/28.82  | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 178.99/28.82  | |            (17), (18), (19), (20), (21), (22), (24), (25), (27), (30), (32),
% 178.99/28.82  | |            (33), (36), (37), (38), (39), (42), (43), (44), (45), (46), (47),
% 178.99/28.82  | |            (48), (49), (50), (51), (53), (54), (55), (57), (58), (59), (61),
% 178.99/28.82  | |            (62), (63), (64), (65), (66), (67), (71), (73) are inconsistent
% 178.99/28.82  | |            by sub-proof #863.
% 178.99/28.82  | | 
% 178.99/28.82  | Case 2:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (74)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 178.99/28.82  | | 
% 178.99/28.82  | | BETA: splitting (74) gives:
% 178.99/28.82  | | 
% 178.99/28.82  | | Case 1:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (75)  all_58_5 = e3
% 178.99/28.82  | | | 
% 178.99/28.82  | | | COMBINE_EQS: (7), (75) imply:
% 178.99/28.82  | | |   (76)  all_52_13 = e3
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (2), (76) imply:
% 178.99/28.82  | | |   (77)   ~ (all_52_5 = e3)
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (26), (76) imply:
% 178.99/28.82  | | |   (78)  op(e2, e1) = e3
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REF_CLOSE: (3), (4), (5), (8), (16), (23), (28), (29), (30), (31), (35),
% 178.99/28.82  | | |            (39), (40), (41), (44), (52), (58), (60), (61), (63), (65),
% 178.99/28.82  | | |            (68), (69), (70), (77), (78) are inconsistent by sub-proof
% 178.99/28.82  | | |            #852.
% 178.99/28.82  | | | 
% 178.99/28.82  | | Case 2:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (79)  all_58_8 = e3 | all_58_14 = e3
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REF_CLOSE: (24), (27), (34), (56), (79) are inconsistent by sub-proof
% 178.99/28.82  | | |            #999.
% 178.99/28.82  | | | 
% 178.99/28.82  | | End of split
% 178.99/28.82  | | 
% 178.99/28.82  | End of split
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #852 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)  op(e2, all_52_3) = e2
% 178.99/28.82    (2)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.82    (3)  all_56_3 = all_52_7
% 178.99/28.82    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.82    (5)  op(e0, e1) = all_52_29
% 178.99/28.82    (6)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.82    (7)  all_56_1 = all_52_3
% 178.99/28.82    (8)  op(e0, e2) = all_52_27
% 178.99/28.82    (9)   ~ (all_52_5 = all_14_2)
% 178.99/28.82    (10)   ~ (all_52_3 = all_52_27)
% 178.99/28.82    (11)   ~ (all_52_5 = e3)
% 178.99/28.82    (12)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.99/28.82    (13)   ~ (all_52_5 = all_52_29)
% 178.99/28.82    (14)  all_56_2 = all_52_5
% 178.99/28.82    (15)   ~ (all_52_3 = e3)
% 178.99/28.82    (16)   ~ (all_52_3 = all_52_7)
% 178.99/28.82    (17)  op(e2, e1) = e3
% 178.99/28.82    (18)  op(e1, e1) = all_14_2
% 178.99/28.82    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (20)   ~ (all_52_7 = e3)
% 178.99/28.82    (21)  op(e1, all_52_5) = e1
% 178.99/28.82    (22)  op(e0, all_52_7) = e0
% 178.99/28.82    (23)  all_58_9 = all_52_7
% 178.99/28.82    (24)  op(e0, e0) = e3
% 178.99/28.82    (25)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.82    (26)  op(e1, e2) = e3
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | BETA: splitting (6) gives:
% 178.99/28.82  | 
% 178.99/28.82  | Case 1:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (27)  all_56_1 = e3
% 178.99/28.82  | | 
% 178.99/28.82  | | REF_CLOSE: (7), (15), (27) are inconsistent by sub-proof #862.
% 178.99/28.82  | | 
% 178.99/28.82  | Case 2:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (28)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.82  | | 
% 178.99/28.82  | | BETA: splitting (25) gives:
% 178.99/28.82  | | 
% 178.99/28.82  | | Case 1:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (29)  all_56_2 = e3
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REF_CLOSE: (11), (14), (29) are inconsistent by sub-proof #931.
% 178.99/28.82  | | | 
% 178.99/28.82  | | Case 2:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (30)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 178.99/28.82  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 178.99/28.82  | | |            (28), (30) are inconsistent by sub-proof #853.
% 178.99/28.82  | | | 
% 178.99/28.82  | | End of split
% 178.99/28.82  | | 
% 178.99/28.82  | End of split
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #853 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)  op(e2, all_52_3) = e2
% 178.99/28.82    (2)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 178.99/28.82    (3)  all_56_3 = all_52_7
% 178.99/28.82    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 178.99/28.82    (5)  op(e0, e1) = all_52_29
% 178.99/28.82    (6)  all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 178.99/28.82    (7)  all_56_1 = all_52_3
% 178.99/28.82    (8)  op(e0, e2) = all_52_27
% 178.99/28.82    (9)   ~ (all_52_5 = all_14_2)
% 178.99/28.82    (10)   ~ (all_52_3 = all_52_27)
% 178.99/28.82    (11)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 178.99/28.82    (12)   ~ (all_52_5 = all_52_29)
% 178.99/28.82    (13)  all_56_2 = all_52_5
% 178.99/28.82    (14)   ~ (all_52_3 = all_52_7)
% 178.99/28.82    (15)  op(e2, e1) = e3
% 178.99/28.82    (16)  op(e1, e1) = all_14_2
% 178.99/28.82    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (18)   ~ (all_52_7 = e3)
% 178.99/28.82    (19)  op(e1, all_52_5) = e1
% 178.99/28.82    (20)  op(e0, all_52_7) = e0
% 178.99/28.82    (21)  all_58_9 = all_52_7
% 178.99/28.82    (22)  op(e0, e0) = e3
% 178.99/28.82    (23)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 178.99/28.82    (24)  op(e1, e2) = e3
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | BETA: splitting (4) gives:
% 178.99/28.82  | 
% 178.99/28.82  | Case 1:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (25)  all_58_9 = e1
% 178.99/28.82  | | 
% 178.99/28.82  | | COMBINE_EQS: (21), (25) imply:
% 178.99/28.82  | |   (26)  all_52_7 = e1
% 178.99/28.82  | | 
% 178.99/28.82  | | REDUCE: (18), (26) imply:
% 178.99/28.82  | |   (27)   ~ (e3 = e1)
% 178.99/28.82  | | 
% 178.99/28.82  | | SIMP: (27) implies:
% 178.99/28.82  | |   (28)   ~ (e3 = e1)
% 178.99/28.82  | | 
% 178.99/28.82  | | REDUCE: (20), (26) imply:
% 178.99/28.82  | |   (29)  op(e0, e1) = e0
% 178.99/28.82  | | 
% 178.99/28.82  | | GROUND_INST: instantiating (17) with all_52_29, e0, e1, e0, simplifying with
% 178.99/28.82  | |              (5), (29) gives:
% 178.99/28.82  | |   (30)  all_52_29 = e0
% 178.99/28.82  | | 
% 178.99/28.82  | | REDUCE: (12), (30) imply:
% 178.99/28.82  | |   (31)   ~ (all_52_5 = e0)
% 178.99/28.82  | | 
% 178.99/28.82  | | BETA: splitting (23) gives:
% 178.99/28.82  | | 
% 178.99/28.82  | | Case 1:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (32)  all_56_2 = e2
% 178.99/28.82  | | | 
% 178.99/28.82  | | | COMBINE_EQS: (13), (32) imply:
% 178.99/28.82  | | |   (33)  all_52_5 = e2
% 178.99/28.82  | | | 
% 178.99/28.82  | | | SIMP: (33) implies:
% 178.99/28.82  | | |   (34)  all_52_5 = e2
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (19), (34) imply:
% 178.99/28.82  | | |   (35)  op(e1, e2) = e1
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REF_CLOSE: (17), (24), (28), (35) are inconsistent by sub-proof #861.
% 178.99/28.82  | | | 
% 178.99/28.82  | | Case 2:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (36)  all_56_2 = e1 | all_56_2 = e0
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REF_CLOSE: (9), (13), (16), (17), (19), (31), (36) are inconsistent by
% 178.99/28.82  | | |            sub-proof #858.
% 178.99/28.82  | | | 
% 178.99/28.82  | | End of split
% 178.99/28.82  | | 
% 178.99/28.82  | Case 2:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (37)   ~ (all_58_9 = e1)
% 178.99/28.82  | | 
% 178.99/28.82  | | REDUCE: (21), (37) imply:
% 178.99/28.82  | |   (38)   ~ (all_52_7 = e1)
% 178.99/28.82  | | 
% 178.99/28.82  | | BETA: splitting (11) gives:
% 178.99/28.82  | | 
% 178.99/28.82  | | Case 1:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (39)  all_58_9 = e2
% 178.99/28.82  | | | 
% 178.99/28.82  | | | COMBINE_EQS: (21), (39) imply:
% 178.99/28.82  | | |   (40)  all_52_7 = e2
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (14), (40) imply:
% 178.99/28.82  | | |   (41)   ~ (all_52_3 = e2)
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (18), (40) imply:
% 178.99/28.82  | | |   (42)   ~ (e3 = e2)
% 178.99/28.82  | | | 
% 178.99/28.82  | | | SIMP: (42) implies:
% 178.99/28.82  | | |   (43)   ~ (e3 = e2)
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (20), (40) imply:
% 178.99/28.82  | | |   (44)  op(e0, e2) = e0
% 178.99/28.82  | | | 
% 178.99/28.82  | | | GROUND_INST: instantiating (17) with all_52_27, e0, e2, e0, simplifying
% 178.99/28.82  | | |              with (8), (44) gives:
% 178.99/28.82  | | |   (45)  all_52_27 = e0
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (10), (45) imply:
% 178.99/28.82  | | |   (46)   ~ (all_52_3 = e0)
% 178.99/28.82  | | | 
% 178.99/28.82  | | | BETA: splitting (6) gives:
% 178.99/28.82  | | | 
% 178.99/28.82  | | | Case 1:
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | |   (47)  all_56_1 = e2
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | | REF_CLOSE: (7), (41), (47) are inconsistent by sub-proof #857.
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | Case 2:
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | |   (48)  all_56_1 = e1 | all_56_1 = e0
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | | BETA: splitting (48) gives:
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | | Case 1:
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | |   (49)  all_56_1 = e1
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | COMBINE_EQS: (7), (49) imply:
% 178.99/28.82  | | | | |   (50)  all_52_3 = e1
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | SIMP: (50) implies:
% 178.99/28.82  | | | | |   (51)  all_52_3 = e1
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | REDUCE: (1), (51) imply:
% 178.99/28.82  | | | | |   (52)  op(e2, e1) = e2
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | REF_CLOSE: (15), (17), (43), (52) are inconsistent by sub-proof #856.
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | Case 2:
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | |   (53)  all_56_1 = e0
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | REF_CLOSE: (7), (46), (53) are inconsistent by sub-proof #855.
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | End of split
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | End of split
% 178.99/28.82  | | | 
% 178.99/28.82  | | Case 2:
% 178.99/28.82  | | | 
% 178.99/28.82  | | |   (54)   ~ (all_58_9 = e2)
% 178.99/28.82  | | | 
% 178.99/28.82  | | | REDUCE: (21), (54) imply:
% 178.99/28.82  | | |   (55)   ~ (all_52_7 = e2)
% 178.99/28.82  | | | 
% 178.99/28.82  | | | BETA: splitting (2) gives:
% 178.99/28.82  | | | 
% 178.99/28.82  | | | Case 1:
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | |   (56)  all_56_3 = e2
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | | REF_CLOSE: (3), (55), (56) are inconsistent by sub-proof #1038.
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | Case 2:
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | |   (57)  all_56_3 = e1 | all_56_3 = e0
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | | BETA: splitting (57) gives:
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | | Case 1:
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | |   (58)  all_56_3 = e1
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | COMBINE_EQS: (3), (58) imply:
% 178.99/28.82  | | | | |   (59)  all_52_7 = e1
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | SIMP: (59) implies:
% 178.99/28.82  | | | | |   (60)  all_52_7 = e1
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | REDUCE: (38), (60) imply:
% 178.99/28.82  | | | | |   (61)  $false
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | CLOSE: (61) is inconsistent.
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | Case 2:
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | |   (62)  all_56_3 = e0
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | COMBINE_EQS: (3), (62) imply:
% 178.99/28.82  | | | | |   (63)  all_52_7 = e0
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | SIMP: (63) implies:
% 178.99/28.82  | | | | |   (64)  all_52_7 = e0
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | REDUCE: (18), (64) imply:
% 178.99/28.82  | | | | |   (65)   ~ (e3 = e0)
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | SIMP: (65) implies:
% 178.99/28.82  | | | | |   (66)   ~ (e3 = e0)
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | REDUCE: (20), (64) imply:
% 178.99/28.82  | | | | |   (67)  op(e0, e0) = e0
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | | REF_CLOSE: (17), (22), (66), (67) are inconsistent by sub-proof #854.
% 178.99/28.82  | | | | | 
% 178.99/28.82  | | | | End of split
% 178.99/28.82  | | | | 
% 178.99/28.82  | | | End of split
% 178.99/28.82  | | | 
% 178.99/28.82  | | End of split
% 178.99/28.82  | | 
% 178.99/28.82  | End of split
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #854 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (2)  op(e0, e0) = e3
% 178.99/28.82    (3)  op(e0, e0) = e0
% 178.99/28.82    (4)   ~ (e3 = e0)
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | GROUND_INST: instantiating (1) with e3, e0, e0, e0, simplifying with (2), (3)
% 178.99/28.82  |              gives:
% 178.99/28.82  |   (5)  e3 = e0
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (4), (5) imply:
% 178.99/28.82  |   (6)  $false
% 178.99/28.82  | 
% 178.99/28.82  | CLOSE: (6) is inconsistent.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #855 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)  all_56_1 = all_52_3
% 178.99/28.82    (2)  all_56_1 = e0
% 178.99/28.82    (3)   ~ (all_52_3 = e0)
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.82  |   (4)  all_52_3 = e0
% 178.99/28.82  | 
% 178.99/28.82  | SIMP: (4) implies:
% 178.99/28.82  |   (5)  all_52_3 = e0
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (3), (5) imply:
% 178.99/28.82  |   (6)  $false
% 178.99/28.82  | 
% 178.99/28.82  | CLOSE: (6) is inconsistent.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #856 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (2)  op(e2, e1) = e3
% 178.99/28.82    (3)  op(e2, e1) = e2
% 178.99/28.82    (4)   ~ (e3 = e2)
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | GROUND_INST: instantiating (1) with e3, e2, e1, e2, simplifying with (2), (3)
% 178.99/28.82  |              gives:
% 178.99/28.82  |   (5)  e3 = e2
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (4), (5) imply:
% 178.99/28.82  |   (6)  $false
% 178.99/28.82  | 
% 178.99/28.82  | CLOSE: (6) is inconsistent.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #857 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)  all_56_1 = all_52_3
% 178.99/28.82    (2)  all_56_1 = e2
% 178.99/28.82    (3)   ~ (all_52_3 = e2)
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.82  |   (4)  all_52_3 = e2
% 178.99/28.82  | 
% 178.99/28.82  | SIMP: (4) implies:
% 178.99/28.82  |   (5)  all_52_3 = e2
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (3), (5) imply:
% 178.99/28.82  |   (6)  $false
% 178.99/28.82  | 
% 178.99/28.82  | CLOSE: (6) is inconsistent.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #858 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ~ (all_52_5 = e0)
% 178.99/28.82    (2)   ~ (all_52_5 = all_14_2)
% 178.99/28.82    (3)  all_56_2 = e1 | all_56_2 = e0
% 178.99/28.82    (4)  all_56_2 = all_52_5
% 178.99/28.82    (5)  op(e1, e1) = all_14_2
% 178.99/28.82    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (7)  op(e1, all_52_5) = e1
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | BETA: splitting (3) gives:
% 178.99/28.82  | 
% 178.99/28.82  | Case 1:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (8)  all_56_2 = e1
% 178.99/28.82  | | 
% 178.99/28.82  | | COMBINE_EQS: (4), (8) imply:
% 178.99/28.82  | |   (9)  all_52_5 = e1
% 178.99/28.82  | | 
% 178.99/28.82  | | SIMP: (9) implies:
% 178.99/28.82  | |   (10)  all_52_5 = e1
% 178.99/28.82  | | 
% 178.99/28.82  | | REF_CLOSE: (2), (5), (6), (7), (10) are inconsistent by sub-proof #859.
% 178.99/28.82  | | 
% 178.99/28.82  | Case 2:
% 178.99/28.82  | | 
% 178.99/28.82  | |   (11)  all_56_2 = e0
% 178.99/28.82  | | 
% 178.99/28.82  | | COMBINE_EQS: (4), (11) imply:
% 178.99/28.82  | |   (12)  all_52_5 = e0
% 178.99/28.82  | | 
% 178.99/28.82  | | SIMP: (12) implies:
% 178.99/28.82  | |   (13)  all_52_5 = e0
% 178.99/28.82  | | 
% 178.99/28.82  | | REDUCE: (1), (13) imply:
% 178.99/28.82  | |   (14)  $false
% 178.99/28.82  | | 
% 178.99/28.82  | | CLOSE: (14) is inconsistent.
% 178.99/28.82  | | 
% 178.99/28.82  | End of split
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #859 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ~ (all_52_5 = all_14_2)
% 178.99/28.82    (2)  op(e1, e1) = all_14_2
% 178.99/28.82    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (4)  op(e1, all_52_5) = e1
% 178.99/28.82    (5)  all_52_5 = e1
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (1), (5) imply:
% 178.99/28.82  |   (6)   ~ (all_14_2 = e1)
% 178.99/28.82  | 
% 178.99/28.82  | SIMP: (6) implies:
% 178.99/28.82  |   (7)   ~ (all_14_2 = e1)
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (4), (5) imply:
% 178.99/28.82  |   (8)  op(e1, e1) = e1
% 178.99/28.82  | 
% 178.99/28.82  | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #860.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #860 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (2)  op(e1, e1) = all_14_2
% 178.99/28.82    (3)  op(e1, e1) = e1
% 178.99/28.82    (4)   ~ (all_14_2 = e1)
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | GROUND_INST: instantiating (1) with all_14_2, e1, e1, e1, simplifying with
% 178.99/28.82  |              (2), (3) gives:
% 178.99/28.82  |   (5)  all_14_2 = e1
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (4), (5) imply:
% 178.99/28.82  |   (6)  $false
% 178.99/28.82  | 
% 178.99/28.82  | CLOSE: (6) is inconsistent.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #861 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 178.99/28.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 178.99/28.82    (2)  op(e1, e2) = e3
% 178.99/28.82    (3)  op(e1, e2) = e1
% 178.99/28.82    (4)   ~ (e3 = e1)
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | GROUND_INST: instantiating (1) with e3, e1, e2, e1, simplifying with (2), (3)
% 178.99/28.82  |              gives:
% 178.99/28.82  |   (5)  e3 = e1
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (4), (5) imply:
% 178.99/28.82  |   (6)  $false
% 178.99/28.82  | 
% 178.99/28.82  | CLOSE: (6) is inconsistent.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #862 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)  all_56_1 = all_52_3
% 178.99/28.82    (2)  all_56_1 = e3
% 178.99/28.82    (3)   ~ (all_52_3 = e3)
% 178.99/28.82  
% 178.99/28.82  Begin of proof
% 178.99/28.82  | 
% 178.99/28.82  | COMBINE_EQS: (1), (2) imply:
% 178.99/28.82  |   (4)  all_52_3 = e3
% 178.99/28.82  | 
% 178.99/28.82  | SIMP: (4) implies:
% 178.99/28.82  |   (5)  all_52_3 = e3
% 178.99/28.82  | 
% 178.99/28.82  | REDUCE: (3), (5) imply:
% 178.99/28.82  |   (6)  $false
% 178.99/28.82  | 
% 178.99/28.82  | CLOSE: (6) is inconsistent.
% 178.99/28.82  | 
% 178.99/28.82  End of proof
% 178.99/28.82  
% 178.99/28.82  Sub-proof #863 shows that the following formulas are inconsistent:
% 178.99/28.82  ----------------------------------------------------------------
% 178.99/28.82    (1)   ~ (all_52_23 = all_14_2)
% 178.99/28.82    (2)   ~ (all_52_5 = all_52_13)
% 178.99/28.82    (3)  op(e2, all_52_3) = e2
% 178.99/28.82    (4)  op(e3, e2) = all_52_3
% 178.99/28.82    (5)  all_58_5 = all_52_13
% 178.99/28.82    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 178.99/28.82    (7)  all_58_15 = all_6_2
% 178.99/28.82    (8)   ~ (all_52_9 = all_4_2)
% 178.99/28.82    (9)   ~ (all_52_5 = all_52_7)
% 178.99/28.82    (10)  all_58_10 = all_52_15
% 178.99/28.82    (11)   ~ (all_52_5 = all_4_2)
% 178.99/28.82    (12)  all_58_7 = all_52_19
% 178.99/28.82    (13)  all_58_4 = all_52_5
% 178.99/28.82    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 178.99/28.82    (15)   ~ (all_52_17 = all_14_2)
% 178.99/28.82    (16)   ~ (all_52_7 = all_4_2)
% 178.99/28.82    (17)  all_58_1 = all_52_3
% 178.99/28.82    (18)  all_58_0 = all_4_2
% 178.99/28.82    (19)  all_58_14 = all_52_29
% 178.99/28.82    (20)   ~ (all_52_3 = all_52_5)
% 178.99/28.82    (21)  all_58_8 = all_14_2
% 178.99/28.82    (22)   ~ (all_52_5 = all_14_2)
% 178.99/28.82    (23)  op(e3, all_4_2) = e3
% 178.99/28.82    (24)  op(e0, e3) = all_52_25
% 179.15/28.82    (25)  all_52_5 = e3
% 179.15/28.82    (26)   ~ (all_52_13 = all_14_2)
% 179.15/28.83    (27)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.83    (28)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.15/28.83    (29)   ~ (all_52_5 = all_52_29)
% 179.15/28.83    (30)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.83    (31)  all_58_6 = all_52_17
% 179.15/28.83    (32)   ~ (all_52_3 = all_52_7)
% 179.15/28.83    (33)  all_56_0 = all_4_2
% 179.15/28.83    (34)  all_58_11 = all_52_23
% 179.15/28.83    (35)   ~ (all_52_3 = all_52_19)
% 179.15/28.83    (36)   ~ (all_52_7 = all_52_15)
% 179.15/28.83    (37)   ~ (all_52_29 = all_14_2)
% 179.15/28.83    (38)  op(e3, e1) = all_52_5
% 179.15/28.83    (39)  all_56_10 = all_14_2
% 179.15/28.83    (40)  op(e1, e3) = all_52_17
% 179.15/28.83    (41)   ~ (all_52_25 = all_4_2)
% 179.15/28.83    (42)  op(e3, e0) = all_52_7
% 179.15/28.83    (43)   ~ (all_52_17 = all_4_2)
% 179.15/28.83    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.83    (45)   ~ (all_52_7 = all_6_2)
% 179.15/28.83    (46)  op(e1, all_52_5) = e1
% 179.15/28.83    (47)   ~ (all_52_7 = all_52_23)
% 179.15/28.83    (48)  op(e0, all_52_7) = e0
% 179.15/28.83    (49)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.83    (50)  all_58_9 = all_52_7
% 179.15/28.83    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.83    (52)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83    (53)  op(e2, e3) = all_52_9
% 179.15/28.83  
% 179.15/28.83  Begin of proof
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (25), (29) imply:
% 179.15/28.83  |   (54)   ~ (all_52_29 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | SIMP: (54) implies:
% 179.15/28.83  |   (55)   ~ (all_52_29 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (11), (25) imply:
% 179.15/28.83  |   (56)   ~ (all_4_2 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | SIMP: (56) implies:
% 179.15/28.83  |   (57)   ~ (all_4_2 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 179.15/28.83  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 179.15/28.83  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 179.15/28.83  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 179.15/28.83  |            (47), (48), (49), (50), (51), (52), (53), (55), (57) are
% 179.15/28.83  |            inconsistent by sub-proof #864.
% 179.15/28.83  | 
% 179.15/28.83  End of proof
% 179.15/28.83  
% 179.15/28.83  Sub-proof #864 shows that the following formulas are inconsistent:
% 179.15/28.83  ----------------------------------------------------------------
% 179.15/28.83    (1)   ~ (all_52_23 = all_14_2)
% 179.15/28.83    (2)   ~ (all_52_5 = all_52_13)
% 179.15/28.83    (3)  op(e2, all_52_3) = e2
% 179.15/28.83    (4)  op(e3, e2) = all_52_3
% 179.15/28.83    (5)  all_58_5 = all_52_13
% 179.15/28.83    (6)   ~ (all_4_2 = e3)
% 179.15/28.83    (7)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (8)  all_58_15 = all_6_2
% 179.15/28.83    (9)   ~ (all_52_9 = all_4_2)
% 179.15/28.83    (10)   ~ (all_52_5 = all_52_7)
% 179.15/28.83    (11)  all_58_10 = all_52_15
% 179.15/28.83    (12)   ~ (all_52_5 = all_4_2)
% 179.15/28.83    (13)  all_58_7 = all_52_19
% 179.15/28.83    (14)  all_58_4 = all_52_5
% 179.15/28.83    (15)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.15/28.83    (16)   ~ (all_52_17 = all_14_2)
% 179.15/28.83    (17)   ~ (all_52_7 = all_4_2)
% 179.15/28.83    (18)  all_58_1 = all_52_3
% 179.15/28.83    (19)  all_58_0 = all_4_2
% 179.15/28.83    (20)  all_58_14 = all_52_29
% 179.15/28.83    (21)   ~ (all_52_3 = all_52_5)
% 179.15/28.83    (22)  all_58_8 = all_14_2
% 179.15/28.83    (23)   ~ (all_52_5 = all_14_2)
% 179.15/28.83    (24)  op(e3, all_4_2) = e3
% 179.15/28.83    (25)  op(e0, e3) = all_52_25
% 179.15/28.83    (26)   ~ (all_52_29 = e3)
% 179.15/28.83    (27)   ~ (all_52_13 = all_14_2)
% 179.15/28.83    (28)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.83    (29)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.15/28.83    (30)   ~ (all_52_5 = all_52_29)
% 179.15/28.83    (31)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.83    (32)  all_58_6 = all_52_17
% 179.15/28.83    (33)   ~ (all_52_3 = all_52_7)
% 179.15/28.83    (34)  all_56_0 = all_4_2
% 179.15/28.83    (35)  all_58_11 = all_52_23
% 179.15/28.83    (36)   ~ (all_52_3 = all_52_19)
% 179.15/28.83    (37)   ~ (all_52_7 = all_52_15)
% 179.15/28.83    (38)   ~ (all_52_29 = all_14_2)
% 179.15/28.83    (39)  op(e3, e1) = all_52_5
% 179.15/28.83    (40)  all_56_10 = all_14_2
% 179.15/28.83    (41)  op(e1, e3) = all_52_17
% 179.15/28.83    (42)   ~ (all_52_25 = all_4_2)
% 179.15/28.83    (43)  op(e3, e0) = all_52_7
% 179.15/28.83    (44)   ~ (all_52_17 = all_4_2)
% 179.15/28.83    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.83    (46)   ~ (all_52_7 = all_6_2)
% 179.15/28.83    (47)  op(e1, all_52_5) = e1
% 179.15/28.83    (48)   ~ (all_52_7 = all_52_23)
% 179.15/28.83    (49)  op(e0, all_52_7) = e0
% 179.15/28.83    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.83    (51)  all_58_9 = all_52_7
% 179.15/28.83    (52)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.83    (53)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83    (54)  op(e2, e3) = all_52_9
% 179.15/28.83  
% 179.15/28.83  Begin of proof
% 179.15/28.83  | 
% 179.15/28.83  | BETA: splitting (7) gives:
% 179.15/28.83  | 
% 179.15/28.83  | Case 1:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (55)  all_56_0 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | REF_CLOSE: (6), (34), (55) are inconsistent by sub-proof #1024.
% 179.15/28.83  | | 
% 179.15/28.83  | Case 2:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (56)   ~ (all_56_0 = e3)
% 179.15/28.83  | |   (57)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83  | | 
% 179.15/28.83  | | BETA: splitting (29) gives:
% 179.15/28.83  | | 
% 179.15/28.83  | | Case 1:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (58)  all_56_10 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | COMBINE_EQS: (40), (58) imply:
% 179.15/28.83  | | |   (59)  all_14_2 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | SIMP: (59) implies:
% 179.15/28.83  | | |   (60)  all_14_2 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (27), (60) imply:
% 179.15/28.83  | | |   (61)   ~ (all_52_13 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (16), (60) imply:
% 179.15/28.83  | | |   (62)   ~ (all_52_17 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (1), (60) imply:
% 179.15/28.83  | | |   (63)   ~ (all_52_23 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 179.15/28.83  | | |            (15), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 179.15/28.83  | | |            (28), (31), (32), (33), (34), (35), (36), (37), (39), (41),
% 179.15/28.83  | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 179.15/28.83  | | |            (52), (53), (54), (57), (61), (62), (63) are inconsistent by
% 179.15/28.83  | | |            sub-proof #869.
% 179.15/28.83  | | | 
% 179.15/28.83  | | Case 2:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (64)   ~ (all_56_10 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (40), (64) imply:
% 179.15/28.83  | | |   (65)   ~ (all_14_2 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | BETA: splitting (53) gives:
% 179.15/28.83  | | | 
% 179.15/28.83  | | | Case 1:
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | |   (66)  all_58_4 = e3
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | COMBINE_EQS: (14), (66) imply:
% 179.15/28.83  | | | |   (67)  all_52_5 = e3
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | SIMP: (67) implies:
% 179.15/28.83  | | | |   (68)  all_52_5 = e3
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REDUCE: (2), (68) imply:
% 179.15/28.83  | | | |   (69)   ~ (all_52_13 = e3)
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | SIMP: (69) implies:
% 179.15/28.83  | | | |   (70)   ~ (all_52_13 = e3)
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REDUCE: (30), (68) imply:
% 179.15/28.83  | | | |   (71)   ~ (all_52_29 = e3)
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REDUCE: (12), (68) imply:
% 179.15/28.83  | | | |   (72)   ~ (all_4_2 = e3)
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (17),
% 179.15/28.83  | | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (28),
% 179.15/28.83  | | | |            (31), (33), (34), (35), (37), (39), (41), (42), (43), (44),
% 179.15/28.83  | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 179.15/28.83  | | | |            (57), (70) are inconsistent by sub-proof #867.
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | Case 2:
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | |   (73)   ~ (all_58_4 = e3)
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REDUCE: (14), (73) imply:
% 179.15/28.83  | | | |   (74)   ~ (all_52_5 = e3)
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14),
% 179.15/28.83  | | | |            (17), (18), (19), (20), (21), (22), (24), (25), (26), (31),
% 179.15/28.83  | | | |            (33), (34), (35), (37), (39), (42), (43), (45), (46), (48),
% 179.15/28.83  | | | |            (49), (50), (51), (52), (53), (54), (57), (65), (74) are
% 179.15/28.83  | | | |            inconsistent by sub-proof #865.
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | End of split
% 179.15/28.83  | | | 
% 179.15/28.83  | | End of split
% 179.15/28.83  | | 
% 179.15/28.83  | End of split
% 179.15/28.83  | 
% 179.15/28.83  End of proof
% 179.15/28.83  
% 179.15/28.83  Sub-proof #865 shows that the following formulas are inconsistent:
% 179.15/28.83  ----------------------------------------------------------------
% 179.15/28.83    (1)   ~ (all_52_5 = all_52_13)
% 179.15/28.83    (2)  op(e2, all_52_3) = e2
% 179.15/28.83    (3)  op(e3, e2) = all_52_3
% 179.15/28.83    (4)  all_58_5 = all_52_13
% 179.15/28.83    (5)   ~ (all_4_2 = e3)
% 179.15/28.83    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (7)  all_58_15 = all_6_2
% 179.15/28.83    (8)   ~ (all_52_9 = all_4_2)
% 179.15/28.83    (9)   ~ (all_52_5 = all_52_7)
% 179.15/28.83    (10)  all_58_10 = all_52_15
% 179.15/28.83    (11)  all_58_4 = all_52_5
% 179.15/28.83    (12)   ~ (all_52_7 = all_4_2)
% 179.15/28.83    (13)  all_58_1 = all_52_3
% 179.15/28.83    (14)  all_58_0 = all_4_2
% 179.15/28.83    (15)  all_58_14 = all_52_29
% 179.15/28.83    (16)   ~ (all_52_3 = all_52_5)
% 179.15/28.83    (17)  all_58_8 = all_14_2
% 179.15/28.83    (18)  op(e3, all_4_2) = e3
% 179.15/28.83    (19)  op(e0, e3) = all_52_25
% 179.15/28.83    (20)   ~ (all_52_29 = e3)
% 179.15/28.83    (21)   ~ (all_52_5 = e3)
% 179.15/28.83    (22)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.83    (23)   ~ (all_52_3 = all_52_7)
% 179.15/28.83    (24)  all_56_0 = all_4_2
% 179.15/28.83    (25)  all_58_11 = all_52_23
% 179.15/28.83    (26)   ~ (all_52_7 = all_52_15)
% 179.15/28.83    (27)  op(e3, e1) = all_52_5
% 179.15/28.83    (28)   ~ (all_52_25 = all_4_2)
% 179.15/28.83    (29)  op(e3, e0) = all_52_7
% 179.15/28.83    (30)   ~ (all_14_2 = e3)
% 179.15/28.83    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.83    (32)   ~ (all_52_7 = all_6_2)
% 179.15/28.83    (33)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (34)   ~ (all_52_7 = all_52_23)
% 179.15/28.83    (35)  op(e0, all_52_7) = e0
% 179.15/28.83    (36)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.83    (37)  all_58_9 = all_52_7
% 179.15/28.83    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.83    (39)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83    (40)  op(e2, e3) = all_52_9
% 179.15/28.83  
% 179.15/28.83  Begin of proof
% 179.15/28.83  | 
% 179.15/28.83  | BETA: splitting (38) gives:
% 179.15/28.83  | 
% 179.15/28.83  | Case 1:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (41)  all_58_0 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | COMBINE_EQS: (14), (41) imply:
% 179.15/28.83  | |   (42)  all_4_2 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | REDUCE: (5), (42) imply:
% 179.15/28.83  | |   (43)  $false
% 179.15/28.83  | | 
% 179.15/28.83  | | CLOSE: (43) is inconsistent.
% 179.15/28.83  | | 
% 179.15/28.83  | Case 2:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (44)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | BETA: splitting (44) gives:
% 179.15/28.83  | | 
% 179.15/28.83  | | Case 1:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (45)  all_58_1 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REF_CLOSE: (1), (2), (4), (8), (11), (13), (14), (15), (16), (17), (18),
% 179.15/28.83  | | |            (20), (22), (23), (24), (27), (29), (30), (31), (33), (39),
% 179.15/28.83  | | |            (40), (45) are inconsistent by sub-proof #866.
% 179.15/28.83  | | | 
% 179.15/28.83  | | Case 2:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (46)  all_58_4 = e3 | all_58_9 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REF_CLOSE: (3), (6), (7), (9), (10), (11), (12), (14), (18), (19), (21),
% 179.15/28.83  | | |            (22), (23), (24), (25), (26), (27), (28), (31), (32), (34),
% 179.15/28.83  | | |            (35), (36), (37), (46) are inconsistent by sub-proof #871.
% 179.15/28.83  | | | 
% 179.15/28.83  | | End of split
% 179.15/28.83  | | 
% 179.15/28.83  | End of split
% 179.15/28.83  | 
% 179.15/28.83  End of proof
% 179.15/28.83  
% 179.15/28.83  Sub-proof #866 shows that the following formulas are inconsistent:
% 179.15/28.83  ----------------------------------------------------------------
% 179.15/28.83    (1)   ~ (all_52_5 = all_52_13)
% 179.15/28.83    (2)  op(e2, all_52_3) = e2
% 179.15/28.83    (3)  all_58_5 = all_52_13
% 179.15/28.83    (4)   ~ (all_52_9 = all_4_2)
% 179.15/28.83    (5)  all_58_4 = all_52_5
% 179.15/28.83    (6)  all_58_1 = all_52_3
% 179.15/28.83    (7)  all_58_0 = all_4_2
% 179.15/28.83    (8)  all_58_14 = all_52_29
% 179.15/28.83    (9)   ~ (all_52_3 = all_52_5)
% 179.15/28.83    (10)  all_58_8 = all_14_2
% 179.15/28.83    (11)  op(e3, all_4_2) = e3
% 179.15/28.83    (12)   ~ (all_52_29 = e3)
% 179.15/28.83    (13)  all_58_1 = e3
% 179.15/28.83    (14)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.83    (15)   ~ (all_52_3 = all_52_7)
% 179.15/28.83    (16)  all_56_0 = all_4_2
% 179.15/28.83    (17)  op(e3, e1) = all_52_5
% 179.15/28.83    (18)  op(e3, e0) = all_52_7
% 179.15/28.83    (19)   ~ (all_14_2 = e3)
% 179.15/28.83    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.83    (21)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (22)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83    (23)  op(e2, e3) = all_52_9
% 179.15/28.83  
% 179.15/28.83  Begin of proof
% 179.15/28.83  | 
% 179.15/28.83  | COMBINE_EQS: (6), (13) imply:
% 179.15/28.83  |   (24)  all_52_3 = e3
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (9), (24) imply:
% 179.15/28.83  |   (25)   ~ (all_52_5 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | SIMP: (25) implies:
% 179.15/28.83  |   (26)   ~ (all_52_5 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (15), (24) imply:
% 179.15/28.83  |   (27)   ~ (all_52_7 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | SIMP: (27) implies:
% 179.15/28.83  |   (28)   ~ (all_52_7 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (2), (24) imply:
% 179.15/28.83  |   (29)  op(e2, e3) = e2
% 179.15/28.83  | 
% 179.15/28.83  | BETA: splitting (22) gives:
% 179.15/28.83  | 
% 179.15/28.83  | Case 1:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (30)  all_58_4 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | REF_CLOSE: (5), (26), (30) are inconsistent by sub-proof #1025.
% 179.15/28.83  | | 
% 179.15/28.83  | Case 2:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (31)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | BETA: splitting (31) gives:
% 179.15/28.83  | | 
% 179.15/28.83  | | Case 1:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (32)  all_58_5 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | COMBINE_EQS: (3), (32) imply:
% 179.15/28.83  | | |   (33)  all_52_13 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | SIMP: (33) implies:
% 179.15/28.83  | | |   (34)  all_52_13 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REF_CLOSE: (4), (7), (11), (14), (16), (17), (18), (20), (21), (23), (26),
% 179.15/28.83  | | |            (28), (29) are inconsistent by sub-proof #872.
% 179.15/28.83  | | | 
% 179.15/28.83  | | Case 2:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (35)  all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REF_CLOSE: (8), (10), (12), (19), (35) are inconsistent by sub-proof #999.
% 179.15/28.83  | | | 
% 179.15/28.83  | | End of split
% 179.15/28.83  | | 
% 179.15/28.83  | End of split
% 179.15/28.83  | 
% 179.15/28.83  End of proof
% 179.15/28.83  
% 179.15/28.83  Sub-proof #867 shows that the following formulas are inconsistent:
% 179.15/28.83  ----------------------------------------------------------------
% 179.15/28.83    (1)  op(e2, all_52_3) = e2
% 179.15/28.83    (2)  op(e3, e2) = all_52_3
% 179.15/28.83    (3)  all_58_5 = all_52_13
% 179.15/28.83    (4)   ~ (all_4_2 = e3)
% 179.15/28.83    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (6)  all_58_15 = all_6_2
% 179.15/28.83    (7)   ~ (all_52_9 = all_4_2)
% 179.15/28.83    (8)   ~ (all_52_5 = all_52_7)
% 179.15/28.83    (9)  all_58_10 = all_52_15
% 179.15/28.83    (10)  all_58_4 = all_52_5
% 179.15/28.83    (11)   ~ (all_52_7 = all_4_2)
% 179.15/28.83    (12)  all_58_1 = all_52_3
% 179.15/28.83    (13)  all_58_0 = all_4_2
% 179.15/28.83    (14)  all_58_14 = all_52_29
% 179.15/28.83    (15)   ~ (all_52_3 = all_52_5)
% 179.15/28.83    (16)  all_58_8 = all_14_2
% 179.15/28.83    (17)   ~ (all_52_5 = all_14_2)
% 179.15/28.83    (18)  op(e3, all_4_2) = e3
% 179.15/28.83    (19)  op(e0, e3) = all_52_25
% 179.15/28.83    (20)   ~ (all_52_29 = e3)
% 179.15/28.83    (21)   ~ (all_52_13 = e3)
% 179.15/28.83    (22)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.83    (23)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.83    (24)   ~ (all_52_3 = all_52_7)
% 179.15/28.83    (25)  all_56_0 = all_4_2
% 179.15/28.83    (26)  all_58_11 = all_52_23
% 179.15/28.83    (27)   ~ (all_52_7 = all_52_15)
% 179.15/28.83    (28)  op(e3, e1) = all_52_5
% 179.15/28.83    (29)  op(e1, e3) = all_52_17
% 179.15/28.83    (30)   ~ (all_52_25 = all_4_2)
% 179.15/28.83    (31)  op(e3, e0) = all_52_7
% 179.15/28.83    (32)   ~ (all_52_17 = all_4_2)
% 179.15/28.83    (33)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.83    (34)   ~ (all_52_7 = all_6_2)
% 179.15/28.83    (35)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (36)  op(e1, all_52_5) = e1
% 179.15/28.83    (37)   ~ (all_52_7 = all_52_23)
% 179.15/28.83    (38)  op(e0, all_52_7) = e0
% 179.15/28.83    (39)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.83    (40)  all_58_9 = all_52_7
% 179.15/28.83    (41)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.83    (42)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83    (43)  op(e2, e3) = all_52_9
% 179.15/28.83  
% 179.15/28.83  Begin of proof
% 179.15/28.83  | 
% 179.15/28.83  | BETA: splitting (42) gives:
% 179.15/28.83  | 
% 179.15/28.83  | Case 1:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (44)  all_58_4 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | REF_CLOSE: (2), (8), (10), (13), (15), (18), (22), (25), (29), (31), (32),
% 179.15/28.83  | |            (33), (35), (36), (44) are inconsistent by sub-proof #868.
% 179.15/28.83  | | 
% 179.15/28.83  | Case 2:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (45)   ~ (all_58_4 = e3)
% 179.15/28.83  | |   (46)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | REDUCE: (10), (45) imply:
% 179.15/28.83  | |   (47)   ~ (all_52_5 = e3)
% 179.15/28.83  | | 
% 179.15/28.83  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 179.15/28.83  | |            (13), (14), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 179.15/28.83  | |            (26), (27), (28), (30), (31), (33), (34), (35), (37), (38), (39),
% 179.15/28.83  | |            (40), (41), (43), (46), (47) are inconsistent by sub-proof #870.
% 179.15/28.83  | | 
% 179.15/28.83  | End of split
% 179.15/28.83  | 
% 179.15/28.83  End of proof
% 179.15/28.83  
% 179.15/28.83  Sub-proof #868 shows that the following formulas are inconsistent:
% 179.15/28.83  ----------------------------------------------------------------
% 179.15/28.83    (1)  op(e3, e2) = all_52_3
% 179.15/28.83    (2)  all_58_4 = e3
% 179.15/28.83    (3)   ~ (all_52_5 = all_52_7)
% 179.15/28.83    (4)  all_58_4 = all_52_5
% 179.15/28.83    (5)  all_58_0 = all_4_2
% 179.15/28.83    (6)   ~ (all_52_3 = all_52_5)
% 179.15/28.83    (7)  op(e3, all_4_2) = e3
% 179.15/28.83    (8)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.83    (9)  all_56_0 = all_4_2
% 179.15/28.83    (10)  op(e1, e3) = all_52_17
% 179.15/28.83    (11)  op(e3, e0) = all_52_7
% 179.15/28.83    (12)   ~ (all_52_17 = all_4_2)
% 179.15/28.83    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.83    (14)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (15)  op(e1, all_52_5) = e1
% 179.15/28.83  
% 179.15/28.83  Begin of proof
% 179.15/28.83  | 
% 179.15/28.83  | COMBINE_EQS: (2), (4) imply:
% 179.15/28.83  |   (16)  all_52_5 = e3
% 179.15/28.83  | 
% 179.15/28.83  | SIMP: (16) implies:
% 179.15/28.83  |   (17)  all_52_5 = e3
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (6), (17) imply:
% 179.15/28.83  |   (18)   ~ (all_52_3 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (3), (17) imply:
% 179.15/28.83  |   (19)   ~ (all_52_7 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | SIMP: (19) implies:
% 179.15/28.83  |   (20)   ~ (all_52_7 = e3)
% 179.15/28.83  | 
% 179.15/28.83  | REDUCE: (15), (17) imply:
% 179.15/28.83  |   (21)  op(e1, e3) = e1
% 179.15/28.83  | 
% 179.15/28.83  | REF_CLOSE: (1), (5), (7), (8), (9), (10), (11), (12), (13), (14), (18), (20),
% 179.15/28.83  |            (21) are inconsistent by sub-proof #874.
% 179.15/28.83  | 
% 179.15/28.83  End of proof
% 179.15/28.83  
% 179.15/28.83  Sub-proof #869 shows that the following formulas are inconsistent:
% 179.15/28.83  ----------------------------------------------------------------
% 179.15/28.83    (1)  op(e2, all_52_3) = e2
% 179.15/28.83    (2)  op(e3, e2) = all_52_3
% 179.15/28.83    (3)   ~ (all_52_17 = e3)
% 179.15/28.83    (4)  all_58_5 = all_52_13
% 179.15/28.83    (5)   ~ (all_4_2 = e3)
% 179.15/28.83    (6)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (7)  all_58_15 = all_6_2
% 179.15/28.83    (8)   ~ (all_52_9 = all_4_2)
% 179.15/28.83    (9)   ~ (all_52_5 = all_52_7)
% 179.15/28.83    (10)  all_58_10 = all_52_15
% 179.15/28.83    (11)  all_58_7 = all_52_19
% 179.15/28.83    (12)  all_58_4 = all_52_5
% 179.15/28.83    (13)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.15/28.83    (14)   ~ (all_52_7 = all_4_2)
% 179.15/28.83    (15)  all_58_1 = all_52_3
% 179.15/28.83    (16)  all_58_0 = all_4_2
% 179.15/28.83    (17)  all_58_14 = all_52_29
% 179.15/28.83    (18)  all_58_8 = all_14_2
% 179.15/28.83    (19)   ~ (all_52_5 = all_14_2)
% 179.15/28.83    (20)   ~ (all_52_23 = e3)
% 179.15/28.83    (21)  op(e3, all_4_2) = e3
% 179.15/28.83    (22)  op(e0, e3) = all_52_25
% 179.15/28.83    (23)   ~ (all_52_29 = e3)
% 179.15/28.83    (24)   ~ (all_52_13 = e3)
% 179.15/28.83    (25)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.83    (26)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.83    (27)  all_58_6 = all_52_17
% 179.15/28.83    (28)   ~ (all_52_3 = all_52_7)
% 179.15/28.83    (29)  all_56_0 = all_4_2
% 179.15/28.83    (30)  all_58_11 = all_52_23
% 179.15/28.83    (31)   ~ (all_52_3 = all_52_19)
% 179.15/28.83    (32)   ~ (all_52_7 = all_52_15)
% 179.15/28.83    (33)  op(e3, e1) = all_52_5
% 179.15/28.83    (34)  op(e1, e3) = all_52_17
% 179.15/28.83    (35)   ~ (all_52_25 = all_4_2)
% 179.15/28.83    (36)  op(e3, e0) = all_52_7
% 179.15/28.83    (37)   ~ (all_52_17 = all_4_2)
% 179.15/28.83    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.83    (39)   ~ (all_52_7 = all_6_2)
% 179.15/28.83    (40)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (41)  op(e1, all_52_5) = e1
% 179.15/28.83    (42)   ~ (all_52_7 = all_52_23)
% 179.15/28.83    (43)  op(e0, all_52_7) = e0
% 179.15/28.83    (44)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.83    (45)  all_58_9 = all_52_7
% 179.15/28.83    (46)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.83    (47)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83    (48)  op(e2, e3) = all_52_9
% 179.15/28.83  
% 179.15/28.83  Begin of proof
% 179.15/28.83  | 
% 179.15/28.83  | BETA: splitting (13) gives:
% 179.15/28.83  | 
% 179.15/28.83  | Case 1:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (49)  all_58_6 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | REF_CLOSE: (3), (27), (49) are inconsistent by sub-proof #981.
% 179.15/28.83  | | 
% 179.15/28.83  | Case 2:
% 179.15/28.83  | | 
% 179.15/28.83  | |   (50)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.15/28.83  | | 
% 179.15/28.83  | | BETA: splitting (47) gives:
% 179.15/28.83  | | 
% 179.15/28.83  | | Case 1:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (51)  all_58_4 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | COMBINE_EQS: (12), (51) imply:
% 179.15/28.83  | | |   (52)  all_52_5 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | SIMP: (52) implies:
% 179.15/28.83  | | |   (53)  all_52_5 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (9), (53) imply:
% 179.15/28.83  | | |   (54)   ~ (all_52_7 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | SIMP: (54) implies:
% 179.15/28.83  | | |   (55)   ~ (all_52_7 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (19), (53) imply:
% 179.15/28.83  | | |   (56)   ~ (all_14_2 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | SIMP: (56) implies:
% 179.15/28.83  | | |   (57)   ~ (all_14_2 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (41), (53) imply:
% 179.15/28.83  | | |   (58)  op(e1, e3) = e1
% 179.15/28.83  | | | 
% 179.15/28.83  | | | BETA: splitting (50) gives:
% 179.15/28.83  | | | 
% 179.15/28.83  | | | Case 1:
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | |   (59)  all_58_7 = e3
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | COMBINE_EQS: (11), (59) imply:
% 179.15/28.83  | | | |   (60)  all_52_19 = e3
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REDUCE: (31), (60) imply:
% 179.15/28.83  | | | |   (61)   ~ (all_52_3 = e3)
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REF_CLOSE: (2), (16), (21), (25), (29), (34), (36), (37), (38), (40),
% 179.15/28.83  | | | |            (55), (58), (61) are inconsistent by sub-proof #874.
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | Case 2:
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | |   (62)  all_58_8 = e3 | all_58_11 = e3
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | | REF_CLOSE: (18), (20), (30), (57), (62) are inconsistent by sub-proof
% 179.15/28.83  | | | |            #997.
% 179.15/28.83  | | | | 
% 179.15/28.83  | | | End of split
% 179.15/28.83  | | | 
% 179.15/28.83  | | Case 2:
% 179.15/28.83  | | | 
% 179.15/28.83  | | |   (63)   ~ (all_58_4 = e3)
% 179.15/28.83  | | |   (64)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REDUCE: (12), (63) imply:
% 179.15/28.83  | | |   (65)   ~ (all_52_5 = e3)
% 179.15/28.83  | | | 
% 179.15/28.83  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15),
% 179.15/28.83  | | |            (16), (17), (18), (19), (21), (22), (23), (24), (26), (28),
% 179.15/28.83  | | |            (29), (30), (32), (33), (35), (36), (38), (39), (40), (42),
% 179.15/28.83  | | |            (43), (44), (45), (46), (48), (64), (65) are inconsistent by
% 179.15/28.83  | | |            sub-proof #870.
% 179.15/28.83  | | | 
% 179.15/28.83  | | End of split
% 179.15/28.83  | | 
% 179.15/28.83  | End of split
% 179.15/28.83  | 
% 179.15/28.83  End of proof
% 179.15/28.83  
% 179.15/28.83  Sub-proof #870 shows that the following formulas are inconsistent:
% 179.15/28.83  ----------------------------------------------------------------
% 179.15/28.83    (1)  op(e2, all_52_3) = e2
% 179.15/28.83    (2)  op(e3, e2) = all_52_3
% 179.15/28.83    (3)  all_58_5 = all_52_13
% 179.15/28.83    (4)   ~ (all_4_2 = e3)
% 179.15/28.83    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.83    (6)  all_58_15 = all_6_2
% 179.15/28.83    (7)   ~ (all_52_9 = all_4_2)
% 179.15/28.83    (8)   ~ (all_52_5 = all_52_7)
% 179.15/28.83    (9)  all_58_10 = all_52_15
% 179.15/28.83    (10)  all_58_4 = all_52_5
% 179.15/28.83    (11)   ~ (all_52_7 = all_4_2)
% 179.15/28.83    (12)  all_58_1 = all_52_3
% 179.15/28.83    (13)  all_58_0 = all_4_2
% 179.15/28.83    (14)  all_58_14 = all_52_29
% 179.15/28.83    (15)  all_58_8 = all_14_2
% 179.15/28.83    (16)   ~ (all_52_5 = all_14_2)
% 179.15/28.83    (17)  op(e3, all_4_2) = e3
% 179.15/28.83    (18)  op(e0, e3) = all_52_25
% 179.15/28.83    (19)   ~ (all_52_29 = e3)
% 179.15/28.83    (20)   ~ (all_52_5 = e3)
% 179.15/28.83    (21)   ~ (all_52_13 = e3)
% 179.15/28.83    (22)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.83    (23)   ~ (all_52_3 = all_52_7)
% 179.15/28.83    (24)  all_56_0 = all_4_2
% 179.15/28.84    (25)  all_58_11 = all_52_23
% 179.15/28.84    (26)   ~ (all_52_7 = all_52_15)
% 179.15/28.84    (27)  op(e3, e1) = all_52_5
% 179.15/28.84    (28)   ~ (all_52_25 = all_4_2)
% 179.15/28.84    (29)  op(e3, e0) = all_52_7
% 179.15/28.84    (30)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.15/28.84    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.84    (32)   ~ (all_52_7 = all_6_2)
% 179.15/28.84    (33)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (34)   ~ (all_52_7 = all_52_23)
% 179.15/28.84    (35)  op(e0, all_52_7) = e0
% 179.15/28.84    (36)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.84    (37)  all_58_9 = all_52_7
% 179.15/28.84    (38)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.84    (39)  op(e2, e3) = all_52_9
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | BETA: splitting (38) gives:
% 179.15/28.84  | 
% 179.15/28.84  | Case 1:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (40)  all_58_0 = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | COMBINE_EQS: (13), (40) imply:
% 179.15/28.84  | |   (41)  all_4_2 = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (4), (41) imply:
% 179.15/28.84  | |   (42)  $false
% 179.15/28.84  | | 
% 179.15/28.84  | | CLOSE: (42) is inconsistent.
% 179.15/28.84  | | 
% 179.15/28.84  | Case 2:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (43)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | BETA: splitting (43) gives:
% 179.15/28.84  | | 
% 179.15/28.84  | | Case 1:
% 179.15/28.84  | | | 
% 179.15/28.84  | | |   (44)  all_58_1 = e3
% 179.15/28.84  | | | 
% 179.15/28.84  | | | COMBINE_EQS: (12), (44) imply:
% 179.15/28.84  | | |   (45)  all_52_3 = e3
% 179.15/28.84  | | | 
% 179.15/28.84  | | | REDUCE: (23), (45) imply:
% 179.15/28.84  | | |   (46)   ~ (all_52_7 = e3)
% 179.15/28.84  | | | 
% 179.15/28.84  | | | SIMP: (46) implies:
% 179.15/28.84  | | |   (47)   ~ (all_52_7 = e3)
% 179.15/28.84  | | | 
% 179.15/28.84  | | | REDUCE: (1), (45) imply:
% 179.15/28.84  | | |   (48)  op(e2, e3) = e2
% 179.15/28.84  | | | 
% 179.15/28.84  | | | BETA: splitting (30) gives:
% 179.15/28.84  | | | 
% 179.15/28.84  | | | Case 1:
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | |   (49)  all_58_5 = e3
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | REF_CLOSE: (3), (21), (49) are inconsistent by sub-proof #969.
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | Case 2:
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | |   (50)  all_58_8 = e3 | all_58_14 = e3
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | BETA: splitting (50) gives:
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | Case 1:
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | |   (51)  all_58_8 = e3
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | | COMBINE_EQS: (15), (51) imply:
% 179.15/28.84  | | | | |   (52)  all_14_2 = e3
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | | SIMP: (52) implies:
% 179.15/28.84  | | | | |   (53)  all_14_2 = e3
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | | REF_CLOSE: (7), (13), (17), (20), (22), (24), (27), (29), (31), (33),
% 179.15/28.84  | | | | |            (39), (47), (48) are inconsistent by sub-proof #872.
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | Case 2:
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | |   (54)  all_58_14 = e3
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | | REF_CLOSE: (14), (19), (54) are inconsistent by sub-proof #1000.
% 179.15/28.84  | | | | | 
% 179.15/28.84  | | | | End of split
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | End of split
% 179.15/28.84  | | | 
% 179.15/28.84  | | Case 2:
% 179.15/28.84  | | | 
% 179.15/28.84  | | |   (55)  all_58_4 = e3 | all_58_9 = e3
% 179.15/28.84  | | | 
% 179.15/28.84  | | | REF_CLOSE: (2), (5), (6), (8), (9), (10), (11), (13), (17), (18), (20),
% 179.15/28.84  | | |            (22), (23), (24), (25), (26), (27), (28), (31), (32), (34),
% 179.15/28.84  | | |            (35), (36), (37), (55) are inconsistent by sub-proof #871.
% 179.15/28.84  | | | 
% 179.15/28.84  | | End of split
% 179.15/28.84  | | 
% 179.15/28.84  | End of split
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #871 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)  op(e3, e2) = all_52_3
% 179.15/28.84    (2)  all_58_4 = e3 | all_58_9 = e3
% 179.15/28.84    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (4)  all_58_15 = all_6_2
% 179.15/28.84    (5)   ~ (all_52_5 = all_52_7)
% 179.15/28.84    (6)  all_58_10 = all_52_15
% 179.15/28.84    (7)  all_58_4 = all_52_5
% 179.15/28.84    (8)   ~ (all_52_7 = all_4_2)
% 179.15/28.84    (9)  all_58_0 = all_4_2
% 179.15/28.84    (10)  op(e3, all_4_2) = e3
% 179.15/28.84    (11)  op(e0, e3) = all_52_25
% 179.15/28.84    (12)   ~ (all_52_5 = e3)
% 179.15/28.84    (13)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.84    (14)   ~ (all_52_3 = all_52_7)
% 179.15/28.84    (15)  all_56_0 = all_4_2
% 179.15/28.84    (16)  all_58_11 = all_52_23
% 179.15/28.84    (17)   ~ (all_52_7 = all_52_15)
% 179.15/28.84    (18)  op(e3, e1) = all_52_5
% 179.15/28.84    (19)   ~ (all_52_25 = all_4_2)
% 179.15/28.84    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.84    (21)   ~ (all_52_7 = all_6_2)
% 179.15/28.84    (22)   ~ (all_52_7 = all_52_23)
% 179.15/28.84    (23)  op(e0, all_52_7) = e0
% 179.15/28.84    (24)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.84    (25)  all_58_9 = all_52_7
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | BETA: splitting (2) gives:
% 179.15/28.84  | 
% 179.15/28.84  | Case 1:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (26)  all_58_4 = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | REF_CLOSE: (7), (12), (26) are inconsistent by sub-proof #1025.
% 179.15/28.84  | | 
% 179.15/28.84  | Case 2:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (27)  all_58_9 = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14), (15),
% 179.15/28.84  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (27)
% 179.15/28.84  | |            are inconsistent by sub-proof #1014.
% 179.15/28.84  | | 
% 179.15/28.84  | End of split
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #872 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)  op(e2, e3) = e2
% 179.15/28.84    (2)   ~ (all_52_9 = all_4_2)
% 179.15/28.84    (3)  all_58_0 = all_4_2
% 179.15/28.84    (4)  op(e3, all_4_2) = e3
% 179.15/28.84    (5)   ~ (all_52_5 = e3)
% 179.15/28.84    (6)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.84    (7)  all_56_0 = all_4_2
% 179.15/28.84    (8)  op(e3, e1) = all_52_5
% 179.15/28.84    (9)  op(e3, e0) = all_52_7
% 179.15/28.84    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.84    (11)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (12)   ~ (all_52_7 = e3)
% 179.15/28.84    (13)  op(e2, e3) = all_52_9
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | GROUND_INST: instantiating (10) with all_52_9, e2, e3, e2, simplifying with
% 179.15/28.84  |              (1), (13) gives:
% 179.15/28.84  |   (14)  all_52_9 = e2
% 179.15/28.84  | 
% 179.15/28.84  | REDUCE: (2), (14) imply:
% 179.15/28.84  |   (15)   ~ (all_4_2 = e2)
% 179.15/28.84  | 
% 179.15/28.84  | SIMP: (15) implies:
% 179.15/28.84  |   (16)   ~ (all_4_2 = e2)
% 179.15/28.84  | 
% 179.15/28.84  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16) are
% 179.15/28.84  |            inconsistent by sub-proof #873.
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #873 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)   ~ (all_4_2 = e2)
% 179.15/28.84    (2)  all_58_0 = all_4_2
% 179.15/28.84    (3)  op(e3, all_4_2) = e3
% 179.15/28.84    (4)   ~ (all_52_5 = e3)
% 179.15/28.84    (5)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.84    (6)  all_56_0 = all_4_2
% 179.15/28.84    (7)  op(e3, e1) = all_52_5
% 179.15/28.84    (8)  op(e3, e0) = all_52_7
% 179.15/28.84    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.84    (10)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (11)   ~ (all_52_7 = e3)
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | BETA: splitting (5) gives:
% 179.15/28.84  | 
% 179.15/28.84  | Case 1:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (12)  all_58_0 = e1
% 179.15/28.84  | | 
% 179.15/28.84  | | COMBINE_EQS: (2), (12) imply:
% 179.15/28.84  | |   (13)  all_4_2 = e1
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (3), (13) imply:
% 179.15/28.84  | |   (14)  op(e3, e1) = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | REF_CLOSE: (4), (7), (9), (14) are inconsistent by sub-proof #1023.
% 179.15/28.84  | | 
% 179.15/28.84  | Case 2:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (15)   ~ (all_58_0 = e1)
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (2), (15) imply:
% 179.15/28.84  | |   (16)   ~ (all_4_2 = e1)
% 179.15/28.84  | | 
% 179.15/28.84  | | BETA: splitting (10) gives:
% 179.15/28.84  | | 
% 179.15/28.84  | | Case 1:
% 179.15/28.84  | | | 
% 179.15/28.84  | | |   (17)  all_56_0 = e2
% 179.15/28.84  | | | 
% 179.15/28.84  | | | REF_CLOSE: (1), (6), (17) are inconsistent by sub-proof #904.
% 179.15/28.84  | | | 
% 179.15/28.84  | | Case 2:
% 179.15/28.84  | | | 
% 179.15/28.84  | | |   (18)  all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84  | | | 
% 179.15/28.84  | | | BETA: splitting (18) gives:
% 179.15/28.84  | | | 
% 179.15/28.84  | | | Case 1:
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | |   (19)  all_56_0 = e1
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | REF_CLOSE: (6), (16), (19) are inconsistent by sub-proof #1022.
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | Case 2:
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | |   (20)  all_56_0 = e0
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | COMBINE_EQS: (6), (20) imply:
% 179.15/28.84  | | | |   (21)  all_4_2 = e0
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | SIMP: (21) implies:
% 179.15/28.84  | | | |   (22)  all_4_2 = e0
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | REDUCE: (3), (22) imply:
% 179.15/28.84  | | | |   (23)  op(e3, e0) = e3
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | | REF_CLOSE: (8), (9), (11), (23) are inconsistent by sub-proof #908.
% 179.15/28.84  | | | | 
% 179.15/28.84  | | | End of split
% 179.15/28.84  | | | 
% 179.15/28.84  | | End of split
% 179.15/28.84  | | 
% 179.15/28.84  | End of split
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #874 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)  op(e3, e2) = all_52_3
% 179.15/28.84    (2)  all_58_0 = all_4_2
% 179.15/28.84    (3)  op(e1, e3) = e1
% 179.15/28.84    (4)  op(e3, all_4_2) = e3
% 179.15/28.84    (5)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.84    (6)   ~ (all_52_3 = e3)
% 179.15/28.84    (7)  all_56_0 = all_4_2
% 179.15/28.84    (8)  op(e1, e3) = all_52_17
% 179.15/28.84    (9)  op(e3, e0) = all_52_7
% 179.15/28.84    (10)   ~ (all_52_17 = all_4_2)
% 179.15/28.84    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.84    (12)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (13)   ~ (all_52_7 = e3)
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | GROUND_INST: instantiating (11) with all_52_17, e1, e3, e1, simplifying with
% 179.15/28.84  |              (3), (8) gives:
% 179.15/28.84  |   (14)  all_52_17 = e1
% 179.15/28.84  | 
% 179.15/28.84  | REDUCE: (10), (14) imply:
% 179.15/28.84  |   (15)   ~ (all_4_2 = e1)
% 179.15/28.84  | 
% 179.15/28.84  | SIMP: (15) implies:
% 179.15/28.84  |   (16)   ~ (all_4_2 = e1)
% 179.15/28.84  | 
% 179.15/28.84  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (12), (13), (16) are
% 179.15/28.84  |            inconsistent by sub-proof #875.
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #875 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)  op(e3, e2) = all_52_3
% 179.15/28.84    (2)  all_58_0 = all_4_2
% 179.15/28.84    (3)  op(e3, all_4_2) = e3
% 179.15/28.84    (4)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.84    (5)   ~ (all_52_3 = e3)
% 179.15/28.84    (6)  all_56_0 = all_4_2
% 179.15/28.84    (7)  op(e3, e0) = all_52_7
% 179.15/28.84    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.84    (9)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (10)   ~ (all_4_2 = e1)
% 179.15/28.84    (11)   ~ (all_52_7 = e3)
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | BETA: splitting (4) gives:
% 179.15/28.84  | 
% 179.15/28.84  | Case 1:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (12)  all_58_0 = e0
% 179.15/28.84  | | 
% 179.15/28.84  | | COMBINE_EQS: (2), (12) imply:
% 179.15/28.84  | |   (13)  all_4_2 = e0
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (3), (13) imply:
% 179.15/28.84  | |   (14)  op(e3, e0) = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | GROUND_INST: instantiating (8) with all_52_7, e3, e0, e3, simplifying with
% 179.15/28.84  | |              (7), (14) gives:
% 179.15/28.84  | |   (15)  all_52_7 = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (11), (15) imply:
% 179.15/28.84  | |   (16)  $false
% 179.15/28.84  | | 
% 179.15/28.84  | | CLOSE: (16) is inconsistent.
% 179.15/28.84  | | 
% 179.15/28.84  | Case 2:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (17)   ~ (all_58_0 = e0)
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (2), (17) imply:
% 179.15/28.84  | |   (18)   ~ (all_4_2 = e0)
% 179.15/28.84  | | 
% 179.15/28.84  | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (18) are inconsistent by
% 179.15/28.84  | |            sub-proof #1019.
% 179.15/28.84  | | 
% 179.15/28.84  | End of split
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #876 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)  all_56_13 = all_52_27
% 179.15/28.84    (2)  all_56_13 = e3
% 179.15/28.84    (3)   ~ (all_52_27 = e3)
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.84  |   (4)  all_52_27 = e3
% 179.15/28.84  | 
% 179.15/28.84  | SIMP: (4) implies:
% 179.15/28.84  |   (5)  all_52_27 = e3
% 179.15/28.84  | 
% 179.15/28.84  | REDUCE: (3), (5) imply:
% 179.15/28.84  |   (6)  $false
% 179.15/28.84  | 
% 179.15/28.84  | CLOSE: (6) is inconsistent.
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #877 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)   ~ (all_52_23 = all_14_2)
% 179.15/28.84    (2)   ~ (all_52_5 = all_52_13)
% 179.15/28.84    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.15/28.84    (4)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 179.15/28.84    (5)   ~ (all_52_27 = all_10_2)
% 179.15/28.84    (6)   ~ (all_52_17 = all_52_23)
% 179.15/28.84    (7)   ~ (all_52_13 = all_52_29)
% 179.15/28.84    (8)  all_56_3 = all_52_7
% 179.15/28.84    (9)  op(e3, e2) = all_52_3
% 179.15/28.84    (10)   ~ (all_52_9 = all_52_25)
% 179.15/28.84    (11)  op(e3, all_52_25) = all_52_24
% 179.15/28.84    (12)   ~ (all_52_19 = all_52_23)
% 179.15/28.84    (13)  all_56_11 = all_52_23
% 179.15/28.84    (14)  op(e1, e2) = all_52_19
% 179.15/28.84    (15)   ~ (all_52_27 = e0)
% 179.15/28.84    (16)  op(e3, all_52_9) = all_52_8
% 179.15/28.84    (17)   ~ (all_52_23 = e0)
% 179.15/28.84    (18)   ~ (all_52_3 = all_10_2)
% 179.15/28.84    (19)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 179.15/28.84    (20)  all_58_5 = all_52_13
% 179.15/28.84    (21)   ~ (all_52_25 = all_52_29)
% 179.15/28.84    (22)  op(all_14_1, all_14_2) = all_14_0
% 179.15/28.84    (23)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.15/28.84    (24)  all_58_3 = all_10_2
% 179.15/28.84    (25)  all_56_9 = all_52_19
% 179.15/28.84    (26)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (27)   ~ (all_52_9 = all_4_2)
% 179.15/28.84    (28)   ~ (all_52_5 = all_52_7)
% 179.15/28.84    (29)  all_58_10 = all_52_15
% 179.15/28.84    (30)   ~ (all_52_5 = all_4_2)
% 179.15/28.84    (31)  all_58_7 = all_52_19
% 179.15/28.84    (32)   ~ (all_52_17 = all_52_25)
% 179.15/28.84    (33)  op(e0, e1) = all_52_29
% 179.15/28.84    (34)   ~ (all_4_0 = e2)
% 179.15/28.84    (35)  all_58_4 = all_52_5
% 179.15/28.84    (36)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.15/28.84    (37)   ~ (e3 = e1)
% 179.15/28.84    (38)   ~ (all_52_27 = all_52_29)
% 179.15/28.84    (39)  op(e3, all_4_2) = all_4_1
% 179.15/28.84    (40)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.15/28.84    (41)   ~ (all_52_7 = all_4_2)
% 179.15/28.84    (42)  all_58_1 = all_52_3
% 179.15/28.84    (43)  all_58_0 = all_4_2
% 179.15/28.84    (44)  op(e1, all_52_29) = all_52_28
% 179.15/28.84    (45)   ~ (all_52_7 = e0)
% 179.15/28.84    (46)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.15/28.84    (47)   ~ (all_4_1 = e2)
% 179.15/28.84    (48)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.15/28.84    (49)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.15/28.84    (50)  all_58_14 = all_52_29
% 179.15/28.84    (51)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.15/28.84    (52)   ~ (all_52_3 = all_52_5)
% 179.15/28.84    (53)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.15/28.84    (54)  op(e2, e1) = all_52_13
% 179.15/28.84    (55)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.15/28.84    (56)  all_58_8 = all_14_2
% 179.15/28.84    (57)  op(e0, e2) = all_52_27
% 179.15/28.84    (58)  all_56_14 = all_52_29
% 179.15/28.84    (59)   ~ (all_14_0 = e3)
% 179.15/28.84    (60)  op(all_4_1, all_4_2) = all_4_0
% 179.15/28.84    (61)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 179.15/28.84    (62)   ~ (all_52_5 = all_14_2)
% 179.15/28.84    (63)   ~ (all_52_3 = all_4_2)
% 179.15/28.84    (64)  op(e0, e3) = all_52_25
% 179.15/28.84    (65)   ~ (all_52_9 = all_10_2)
% 179.15/28.84    (66)  op(e3, all_52_17) = all_52_16
% 179.15/28.84    (67)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.15/28.84    (68)   ~ (e3 = e0)
% 179.15/28.84    (69)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.84    (70)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.15/28.84    (71)  op(e0, all_52_23) = all_52_22
% 179.15/28.84    (72)   ~ (all_52_15 = all_52_23)
% 179.15/28.84    (73)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.15/28.84    (74)   ~ (all_52_5 = all_52_29)
% 179.15/28.84    (75)  all_56_2 = all_52_5
% 179.15/28.84    (76)  all_56_12 = all_52_25
% 179.15/28.84    (77)  all_58_13 = all_52_27
% 179.15/28.84    (78)   ~ (all_4_1 = e1)
% 179.15/28.84    (79)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.84    (80)  all_56_5 = all_10_2
% 179.15/28.84    (81)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 179.15/28.84    (82)   ~ (all_52_25 = e0)
% 179.15/28.84    (83)   ~ (all_52_9 = all_52_17)
% 179.15/28.84    (84)   ~ (all_14_0 = e2)
% 179.15/28.84    (85)  all_58_6 = all_52_17
% 179.15/28.84    (86)   ~ (all_52_3 = all_52_7)
% 179.15/28.84    (87)  op(e2, all_52_19) = all_52_18
% 179.15/28.84    (88)   ~ (e1 = e0)
% 179.15/28.84    (89)  all_56_0 = all_4_2
% 179.15/28.84    (90)  all_58_11 = all_52_23
% 179.15/28.84    (91)   ~ (all_52_29 = all_14_2)
% 179.15/28.84    (92)   ~ (all_4_0 = e1)
% 179.15/28.84    (93)   ~ (all_52_19 = all_10_2)
% 179.15/28.84    (94)  all_58_15 = e0
% 179.15/28.84    (95)  all_58_2 = all_52_9
% 179.15/28.84    (96)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.15/28.84    (97)   ~ (all_52_29 = e0)
% 179.15/28.84    (98)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.15/28.84    (99)  op(e3, e1) = all_52_5
% 179.15/28.84    (100)  all_56_10 = all_14_2
% 179.15/28.84    (101)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.15/28.84    (102)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.15/28.84    (103)  op(e1, e3) = all_52_17
% 179.15/28.84    (104)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.15/28.84    (105)   ~ (all_52_25 = all_4_2)
% 179.15/28.84    (106)  op(e3, e0) = all_52_7
% 179.15/28.84    (107)  op(e3, e3) = all_4_2
% 179.15/28.84    (108)  all_56_8 = all_52_17
% 179.15/28.84    (109)   ~ (all_52_17 = all_4_2)
% 179.15/28.84    (110)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.84             (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.84    (111)   ~ (all_52_25 = all_52_27)
% 179.15/28.84    (112)   ~ (all_52_19 = all_52_27)
% 179.15/28.84    (113)  all_56_7 = all_52_15
% 179.15/28.84    (114)   ~ (all_52_7 = all_52_23)
% 179.15/28.84    (115)  op(e2, all_52_27) = all_52_26
% 179.15/28.84    (116)  all_52_20 = all_14_1
% 179.15/28.84    (117)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.84    (118)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.15/28.84    (119)  op(e1, all_14_2) = all_14_1
% 179.15/28.84    (120)  all_58_9 = all_52_7
% 179.15/28.84    (121)   ~ (e2 = e0)
% 179.15/28.84    (122)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0) |
% 179.15/28.84           (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0)
% 179.15/28.84    (123)  all_58_12 = all_52_25
% 179.15/28.84    (124)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.84    (125)   ~ (all_52_9 = all_52_15)
% 179.15/28.84    (126)   ~ (e3 = e2)
% 179.15/28.84    (127)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 179.15/28.84    (128)   ~ (all_52_19 = all_14_2)
% 179.15/28.84    (129)  op(e2, e3) = all_52_9
% 179.15/28.84    (130)  all_56_13 = all_52_27
% 179.15/28.84  
% 179.15/28.84  Begin of proof
% 179.15/28.84  | 
% 179.15/28.84  | BETA: splitting (122) gives:
% 179.15/28.84  | 
% 179.15/28.84  | Case 1:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (131)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 179.15/28.84  | | 
% 179.15/28.84  | | ALPHA: (131) implies:
% 179.15/28.84  | |   (132)  all_52_22 = e0
% 179.15/28.84  | |   (133)  all_52_20 = e1
% 179.15/28.84  | |   (134)  all_52_18 = e2
% 179.15/28.84  | |   (135)  all_52_16 = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | COMBINE_EQS: (116), (133) imply:
% 179.15/28.84  | |   (136)  all_14_1 = e1
% 179.15/28.84  | | 
% 179.15/28.84  | | SIMP: (136) implies:
% 179.15/28.84  | |   (137)  all_14_1 = e1
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (22), (137) imply:
% 179.15/28.84  | |   (138)  op(e1, all_14_2) = all_14_0
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (66), (135) imply:
% 179.15/28.84  | |   (139)  op(e3, all_52_17) = e3
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (87), (134) imply:
% 179.15/28.84  | |   (140)  op(e2, all_52_19) = e2
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (119), (137) imply:
% 179.15/28.84  | |   (141)  op(e1, all_14_2) = e1
% 179.15/28.84  | | 
% 179.15/28.84  | | REDUCE: (71), (132) imply:
% 179.15/28.84  | |   (142)  op(e0, all_52_23) = e0
% 179.15/28.84  | | 
% 179.15/28.84  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (13), (15), (17),
% 179.15/28.84  | |            (18), (20), (21), (23), (24), (25), (26), (27), (28), (29), (31),
% 179.15/28.84  | |            (32), (33), (34), (35), (36), (38), (39), (40), (41), (42), (43),
% 179.15/28.84  | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), (55),
% 179.15/28.84  | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65), (67),
% 179.15/28.84  | |            (68), (69), (70), (72), (73), (74), (75), (76), (77), (79), (80),
% 179.15/28.84  | |            (82), (83), (84), (85), (86), (88), (89), (90), (91), (92), (93),
% 179.15/28.84  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 179.15/28.84  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 179.15/28.84  | |            (113), (114), (117), (118), (120), (121), (123), (124), (125),
% 179.15/28.84  | |            (126), (127), (128), (129), (130), (138), (139), (140), (141),
% 179.15/28.84  | |            (142) are inconsistent by sub-proof #897.
% 179.15/28.84  | | 
% 179.15/28.84  | Case 2:
% 179.15/28.84  | | 
% 179.15/28.84  | |   (143)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 179.15/28.84  | | 
% 179.15/28.84  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 179.15/28.84  | |            (16), (17), (19), (21), (23), (24), (26), (27), (28), (30), (31),
% 179.15/28.84  | |            (32), (35), (37), (38), (39), (41), (42), (43), (44), (47), (48),
% 179.15/28.84  | |            (50), (51), (53), (54), (55), (56), (58), (61), (63), (65), (66),
% 179.15/28.84  | |            (67), (68), (69), (70), (74), (76), (77), (78), (80), (81), (82),
% 179.15/28.84  | |            (83), (85), (86), (88), (89), (90), (91), (93), (94), (95), (96),
% 179.15/28.84  | |            (97), (99), (101), (103), (105), (106), (107), (108), (109),
% 179.15/28.84  | |            (110), (111), (115), (118), (120), (123), (129), (130), (143) are
% 179.15/28.84  | |            inconsistent by sub-proof #878.
% 179.15/28.84  | | 
% 179.15/28.84  | End of split
% 179.15/28.84  | 
% 179.15/28.84  End of proof
% 179.15/28.84  
% 179.15/28.84  Sub-proof #878 shows that the following formulas are inconsistent:
% 179.15/28.84  ----------------------------------------------------------------
% 179.15/28.84    (1)   ~ (all_52_23 = all_14_2)
% 179.15/28.84    (2)   ~ (all_52_5 = all_52_13)
% 179.15/28.84    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.15/28.84    (4)   ~ (all_52_27 = all_10_2)
% 179.15/28.84    (5)   ~ (all_52_17 = all_52_23)
% 179.15/28.84    (6)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 179.15/28.84    (7)   ~ (all_52_13 = all_52_29)
% 179.15/28.84    (8)  all_56_3 = all_52_7
% 179.15/28.84    (9)  op(e3, e2) = all_52_3
% 179.15/28.84    (10)   ~ (all_52_9 = all_52_25)
% 179.15/28.84    (11)  op(e3, all_52_25) = all_52_24
% 179.15/28.84    (12)   ~ (all_52_19 = all_52_23)
% 179.15/28.84    (13)  op(e1, e2) = all_52_19
% 179.15/28.84    (14)  op(e3, all_52_9) = all_52_8
% 179.15/28.84    (15)   ~ (all_52_23 = e0)
% 179.15/28.84    (16)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 179.15/28.84    (17)   ~ (all_52_25 = all_52_29)
% 179.15/28.84    (18)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.15/28.84    (19)  all_58_3 = all_10_2
% 179.15/28.84    (20)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.84    (21)   ~ (all_52_9 = all_4_2)
% 179.15/28.84    (22)   ~ (all_52_5 = all_52_7)
% 179.15/28.84    (23)   ~ (all_52_5 = all_4_2)
% 179.15/28.84    (24)  all_58_7 = all_52_19
% 179.15/28.84    (25)   ~ (all_52_17 = all_52_25)
% 179.15/28.84    (26)  all_58_4 = all_52_5
% 179.15/28.84    (27)   ~ (e3 = e1)
% 179.15/28.84    (28)   ~ (all_52_27 = all_52_29)
% 179.15/28.84    (29)  op(e3, all_4_2) = all_4_1
% 179.15/28.84    (30)   ~ (all_52_7 = all_4_2)
% 179.15/28.84    (31)  all_58_1 = all_52_3
% 179.15/28.84    (32)  all_58_0 = all_4_2
% 179.15/28.84    (33)  op(e1, all_52_29) = all_52_28
% 179.15/28.84    (34)   ~ (all_4_1 = e2)
% 179.15/28.84    (35)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.15/28.84    (36)  all_58_14 = all_52_29
% 179.15/28.84    (37)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.15/28.84    (38)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.15/28.84    (39)  op(e2, e1) = all_52_13
% 179.15/28.84    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.15/28.84    (41)  all_58_8 = all_14_2
% 179.15/28.84    (42)  all_56_14 = all_52_29
% 179.15/28.84    (43)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 179.15/28.84    (44)   ~ (all_52_3 = all_4_2)
% 179.15/28.84    (45)   ~ (all_52_9 = all_10_2)
% 179.15/28.84    (46)  op(e3, all_52_17) = all_52_16
% 179.15/28.84    (47)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.15/28.84    (48)   ~ (e3 = e0)
% 179.15/28.84    (49)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.84    (50)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.15/28.84    (51)   ~ (all_52_5 = all_52_29)
% 179.15/28.84    (52)  all_56_12 = all_52_25
% 179.15/28.84    (53)  all_58_13 = all_52_27
% 179.15/28.84    (54)   ~ (all_4_1 = e1)
% 179.15/28.84    (55)  all_56_5 = all_10_2
% 179.15/28.84    (56)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 179.15/28.84    (57)   ~ (all_52_25 = e0)
% 179.15/28.84    (58)   ~ (all_52_9 = all_52_17)
% 179.15/28.84    (59)  all_58_6 = all_52_17
% 179.15/28.84    (60)   ~ (all_52_3 = all_52_7)
% 179.15/28.84    (61)   ~ (e1 = e0)
% 179.15/28.84    (62)  all_56_0 = all_4_2
% 179.15/28.84    (63)  all_58_11 = all_52_23
% 179.15/28.84    (64)   ~ (all_52_29 = all_14_2)
% 179.15/28.84    (65)   ~ (all_52_19 = all_10_2)
% 179.15/28.84    (66)  all_58_15 = e0
% 179.15/28.84    (67)  all_58_2 = all_52_9
% 179.15/28.84    (68)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.15/28.84    (69)   ~ (all_52_29 = e0)
% 179.15/28.84    (70)  op(e3, e1) = all_52_5
% 179.15/28.84    (71)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.15/28.84    (72)  op(e1, e3) = all_52_17
% 179.15/28.84    (73)   ~ (all_52_25 = all_4_2)
% 179.15/28.84    (74)  op(e3, e0) = all_52_7
% 179.15/28.84    (75)  op(e3, e3) = all_4_2
% 179.15/28.84    (76)  all_56_8 = all_52_17
% 179.15/28.84    (77)   ~ (all_52_17 = all_4_2)
% 179.15/28.85    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.85    (79)   ~ (all_52_25 = all_52_27)
% 179.15/28.85    (80)  op(e2, all_52_27) = all_52_26
% 179.15/28.85    (81)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.15/28.85    (82)  all_58_9 = all_52_7
% 179.15/28.85    (83)  all_58_12 = all_52_25
% 179.15/28.85    (84)  op(e2, e3) = all_52_9
% 179.15/28.85    (85)  all_56_13 = all_52_27
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | ALPHA: (6) implies:
% 179.15/28.85  |   (86)  all_52_28 = e1
% 179.15/28.85  |   (87)  all_52_26 = e2
% 179.15/28.85  |   (88)  all_52_24 = e3
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (11), (88) imply:
% 179.15/28.85  |   (89)  op(e3, all_52_25) = e3
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (80), (87) imply:
% 179.15/28.85  |   (90)  op(e2, all_52_27) = e2
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (33), (86) imply:
% 179.15/28.85  |   (91)  op(e1, all_52_29) = e1
% 179.15/28.85  | 
% 179.15/28.85  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 179.15/28.85  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 179.15/28.85  |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37),
% 179.15/28.85  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 179.15/28.85  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 179.15/28.85  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 179.15/28.85  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (81), (82),
% 179.15/28.85  |            (83), (84), (85), (89), (90), (91) are inconsistent by sub-proof
% 179.15/28.85  |            #879.
% 179.15/28.85  | 
% 179.15/28.85  End of proof
% 179.15/28.85  
% 179.15/28.85  Sub-proof #879 shows that the following formulas are inconsistent:
% 179.15/28.85  ----------------------------------------------------------------
% 179.15/28.85    (1)   ~ (all_52_23 = all_14_2)
% 179.15/28.85    (2)   ~ (all_52_5 = all_52_13)
% 179.15/28.85    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.15/28.85    (4)   ~ (all_52_27 = all_10_2)
% 179.15/28.85    (5)   ~ (all_52_17 = all_52_23)
% 179.15/28.85    (6)   ~ (all_52_13 = all_52_29)
% 179.15/28.85    (7)  all_56_3 = all_52_7
% 179.15/28.85    (8)  op(e3, e2) = all_52_3
% 179.15/28.85    (9)   ~ (all_52_9 = all_52_25)
% 179.15/28.85    (10)   ~ (all_52_19 = all_52_23)
% 179.15/28.85    (11)  op(e1, e2) = all_52_19
% 179.15/28.85    (12)  op(e3, all_52_9) = all_52_8
% 179.15/28.85    (13)   ~ (all_52_23 = e0)
% 179.15/28.85    (14)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 179.15/28.85    (15)   ~ (all_52_25 = all_52_29)
% 179.15/28.85    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.15/28.85    (17)  all_58_3 = all_10_2
% 179.15/28.85    (18)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.85    (19)   ~ (all_52_9 = all_4_2)
% 179.15/28.85    (20)   ~ (all_52_5 = all_52_7)
% 179.15/28.85    (21)   ~ (all_52_5 = all_4_2)
% 179.15/28.85    (22)  all_58_7 = all_52_19
% 179.15/28.85    (23)   ~ (all_52_17 = all_52_25)
% 179.15/28.85    (24)  all_58_4 = all_52_5
% 179.15/28.85    (25)   ~ (e3 = e1)
% 179.15/28.85    (26)   ~ (all_52_27 = all_52_29)
% 179.15/28.85    (27)  op(e3, all_4_2) = all_4_1
% 179.15/28.85    (28)   ~ (all_52_7 = all_4_2)
% 179.15/28.85    (29)  all_58_1 = all_52_3
% 179.15/28.85    (30)  all_58_0 = all_4_2
% 179.15/28.85    (31)  op(e2, all_52_27) = e2
% 179.15/28.85    (32)   ~ (all_4_1 = e2)
% 179.15/28.85    (33)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.15/28.85    (34)  all_58_14 = all_52_29
% 179.15/28.85    (35)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.15/28.85    (36)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.15/28.85    (37)  op(e2, e1) = all_52_13
% 179.15/28.85    (38)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.15/28.85    (39)  all_58_8 = all_14_2
% 179.15/28.85    (40)  all_56_14 = all_52_29
% 179.15/28.85    (41)  op(e1, all_52_29) = e1
% 179.15/28.85    (42)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 179.15/28.85    (43)   ~ (all_52_3 = all_4_2)
% 179.15/28.85    (44)   ~ (all_52_9 = all_10_2)
% 179.15/28.85    (45)  op(e3, all_52_17) = all_52_16
% 179.15/28.85    (46)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.15/28.85    (47)   ~ (e3 = e0)
% 179.15/28.85    (48)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.85    (49)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.15/28.85    (50)   ~ (all_52_5 = all_52_29)
% 179.15/28.85    (51)  all_56_12 = all_52_25
% 179.15/28.85    (52)  all_58_13 = all_52_27
% 179.15/28.85    (53)   ~ (all_4_1 = e1)
% 179.15/28.85    (54)  all_56_5 = all_10_2
% 179.15/28.85    (55)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 179.15/28.85    (56)   ~ (all_52_25 = e0)
% 179.15/28.85    (57)   ~ (all_52_9 = all_52_17)
% 179.15/28.85    (58)  all_58_6 = all_52_17
% 179.15/28.85    (59)   ~ (all_52_3 = all_52_7)
% 179.15/28.85    (60)   ~ (e1 = e0)
% 179.15/28.85    (61)  all_56_0 = all_4_2
% 179.15/28.85    (62)  all_58_11 = all_52_23
% 179.15/28.85    (63)   ~ (all_52_29 = all_14_2)
% 179.15/28.85    (64)  op(e3, all_52_25) = e3
% 179.15/28.85    (65)   ~ (all_52_19 = all_10_2)
% 179.15/28.85    (66)  all_58_15 = e0
% 179.15/28.85    (67)  all_58_2 = all_52_9
% 179.15/28.85    (68)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.15/28.85    (69)   ~ (all_52_29 = e0)
% 179.15/28.85    (70)  op(e3, e1) = all_52_5
% 179.15/28.85    (71)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.15/28.85    (72)  op(e1, e3) = all_52_17
% 179.15/28.85    (73)   ~ (all_52_25 = all_4_2)
% 179.15/28.85    (74)  op(e3, e0) = all_52_7
% 179.15/28.85    (75)  op(e3, e3) = all_4_2
% 179.15/28.85    (76)  all_56_8 = all_52_17
% 179.15/28.85    (77)   ~ (all_52_17 = all_4_2)
% 179.15/28.85    (78)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.85    (79)   ~ (all_52_25 = all_52_27)
% 179.15/28.85    (80)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.15/28.85    (81)  all_58_9 = all_52_7
% 179.15/28.85    (82)  all_58_12 = all_52_25
% 179.15/28.85    (83)  op(e2, e3) = all_52_9
% 179.15/28.85    (84)  all_56_13 = all_52_27
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | BETA: splitting (35) gives:
% 179.15/28.85  | 
% 179.15/28.85  | Case 1:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (85)  all_56_13 = e3
% 179.15/28.85  | | 
% 179.15/28.85  | | COMBINE_EQS: (84), (85) imply:
% 179.15/28.85  | |   (86)  all_52_27 = e3
% 179.15/28.85  | | 
% 179.15/28.85  | | SIMP: (86) implies:
% 179.15/28.85  | |   (87)  all_52_27 = e3
% 179.15/28.85  | | 
% 179.15/28.85  | | COMBINE_EQS: (52), (87) imply:
% 179.15/28.85  | |   (88)  all_58_13 = e3
% 179.15/28.85  | | 
% 179.15/28.85  | | REDUCE: (79), (87) imply:
% 179.15/28.85  | |   (89)   ~ (all_52_25 = e3)
% 179.15/28.85  | | 
% 179.15/28.85  | | REDUCE: (26), (87) imply:
% 179.15/28.85  | |   (90)   ~ (all_52_29 = e3)
% 179.15/28.85  | | 
% 179.15/28.85  | | SIMP: (90) implies:
% 179.15/28.85  | |   (91)   ~ (all_52_29 = e3)
% 179.15/28.85  | | 
% 179.15/28.85  | | REDUCE: (4), (87) imply:
% 179.15/28.85  | |   (92)   ~ (all_10_2 = e3)
% 179.15/28.85  | | 
% 179.15/28.85  | | SIMP: (92) implies:
% 179.15/28.85  | |   (93)   ~ (all_10_2 = e3)
% 179.15/28.85  | | 
% 179.15/28.85  | | REDUCE: (31), (87) imply:
% 179.15/28.85  | |   (94)  op(e2, e3) = e2
% 179.15/28.85  | | 
% 179.15/28.85  | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 179.15/28.85  | |            (16), (17), (18), (19), (20), (21), (22), (27), (28), (29), (30),
% 179.15/28.85  | |            (33), (36), (39), (40), (41), (44), (48), (49), (50), (51), (53),
% 179.15/28.85  | |            (54), (55), (56), (57), (58), (59), (61), (62), (63), (64), (65),
% 179.15/28.85  | |            (67), (69), (70), (71), (73), (74), (76), (78), (80), (81), (82),
% 179.15/28.85  | |            (83), (88), (89), (91), (93), (94) are inconsistent by sub-proof
% 179.15/28.85  | |            #885.
% 179.15/28.85  | | 
% 179.15/28.85  | Case 2:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (95)   ~ (all_56_13 = e3)
% 179.15/28.85  | | 
% 179.15/28.85  | | REDUCE: (84), (95) imply:
% 179.15/28.85  | |   (96)   ~ (all_52_27 = e3)
% 179.15/28.85  | | 
% 179.15/28.85  | | BETA: splitting (38) gives:
% 179.15/28.85  | | 
% 179.15/28.85  | | Case 1:
% 179.15/28.85  | | | 
% 179.15/28.85  | | |   (97)  all_58_12 = e3
% 179.15/28.85  | | | 
% 179.15/28.85  | | | REF_CLOSE: (64), (73), (75), (78), (82), (97) are inconsistent by
% 179.15/28.85  | | |            sub-proof #884.
% 179.15/28.85  | | | 
% 179.15/28.85  | | Case 2:
% 179.15/28.85  | | | 
% 179.15/28.85  | | |   (98)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.15/28.85  | | | 
% 179.15/28.85  | | | BETA: splitting (98) gives:
% 179.15/28.85  | | | 
% 179.15/28.85  | | | Case 1:
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | |   (99)  all_58_13 = e3
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | REF_CLOSE: (52), (96), (99) are inconsistent by sub-proof #1026.
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | Case 2:
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | |   (100)  all_58_14 = e3 | all_58_15 = e3
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | BETA: splitting (100) gives:
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | Case 1:
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | |   (101)  all_58_14 = e3
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | COMBINE_EQS: (34), (101) imply:
% 179.15/28.85  | | | | |   (102)  all_52_29 = e3
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | SIMP: (102) implies:
% 179.15/28.85  | | | | |   (103)  all_52_29 = e3
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REDUCE: (6), (103) imply:
% 179.15/28.85  | | | | |   (104)   ~ (all_52_13 = e3)
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REDUCE: (15), (103) imply:
% 179.15/28.85  | | | | |   (105)   ~ (all_52_25 = e3)
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REDUCE: (41), (103) imply:
% 179.15/28.85  | | | | |   (106)  op(e1, e3) = e1
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | GROUND_INST: instantiating (78) with all_52_17, e1, e3, e1,
% 179.15/28.85  | | | | |              simplifying with (72), (106) gives:
% 179.15/28.85  | | | | |   (107)  all_52_17 = e1
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REDUCE: (23), (107) imply:
% 179.15/28.85  | | | | |   (108)   ~ (all_52_25 = e1)
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | SIMP: (108) implies:
% 179.15/28.85  | | | | |   (109)   ~ (all_52_25 = e1)
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REDUCE: (77), (107) imply:
% 179.15/28.85  | | | | |   (110)   ~ (all_4_2 = e1)
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | SIMP: (110) implies:
% 179.15/28.85  | | | | |   (111)   ~ (all_4_2 = e1)
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REDUCE: (45), (107) imply:
% 179.15/28.85  | | | | |   (112)  op(e3, e1) = all_52_16
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | BETA: splitting (49) gives:
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | Case 1:
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | |   (113)  all_56_12 = e3
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | | REF_CLOSE: (51), (105), (113) are inconsistent by sub-proof #1040.
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | Case 2:
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | |   (114)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | | BETA: splitting (68) gives:
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | | Case 1:
% 179.15/28.85  | | | | | | | 
% 179.15/28.85  | | | | | | |   (115)  all_58_12 = e1
% 179.15/28.85  | | | | | | | 
% 179.15/28.85  | | | | | | | REF_CLOSE: (82), (109), (115) are inconsistent by sub-proof #883.
% 179.15/28.85  | | | | | | | 
% 179.15/28.85  | | | | | | Case 2:
% 179.15/28.85  | | | | | | | 
% 179.15/28.85  | | | | | | |   (116)  all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.15/28.85  | | | | | | | 
% 179.15/28.85  | | | | | | | BETA: splitting (116) gives:
% 179.15/28.85  | | | | | | | 
% 179.15/28.85  | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | |   (117)  all_58_13 = e1
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | | COMBINE_EQS: (52), (117) imply:
% 179.15/28.85  | | | | | | | |   (118)  all_52_27 = e1
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | | SIMP: (118) implies:
% 179.15/28.85  | | | | | | | |   (119)  all_52_27 = e1
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | | REDUCE: (31), (119) imply:
% 179.15/28.85  | | | | | | | |   (120)  op(e2, e1) = e2
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | | BETA: splitting (114) gives:
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | |   (121)  all_56_12 = e2
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | COMBINE_EQS: (51), (121) imply:
% 179.15/28.85  | | | | | | | | |   (122)  all_52_25 = e2
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | SIMP: (122) implies:
% 179.15/28.85  | | | | | | | | |   (123)  all_52_25 = e2
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | REDUCE: (73), (123) imply:
% 179.15/28.85  | | | | | | | | |   (124)   ~ (all_4_2 = e2)
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | SIMP: (124) implies:
% 179.15/28.85  | | | | | | | | |   (125)   ~ (all_4_2 = e2)
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | REDUCE: (64), (123) imply:
% 179.15/28.85  | | | | | | | | |   (126)  op(e3, e2) = e3
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | GROUND_INST: instantiating (78) with all_52_13, e2, e1, e2,
% 179.15/28.85  | | | | | | | | |              simplifying with (37), (120) gives:
% 179.15/28.85  | | | | | | | | |   (127)  all_52_13 = e2
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | GROUND_INST: instantiating (78) with all_52_5, all_52_16, e1,
% 179.15/28.85  | | | | | | | | |              e3, simplifying with (70), (112) gives:
% 179.15/28.85  | | | | | | | | |   (128)  all_52_5 = all_52_16
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | GROUND_INST: instantiating (78) with all_52_3, e3, e2, e3,
% 179.15/28.85  | | | | | | | | |              simplifying with (8), (126) gives:
% 179.15/28.85  | | | | | | | | |   (129)  all_52_3 = e3
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | COMBINE_EQS: (24), (128) imply:
% 179.15/28.85  | | | | | | | | |   (130)  all_58_4 = all_52_16
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | COMBINE_EQS: (29), (129) imply:
% 179.15/28.85  | | | | | | | | |   (131)  all_58_1 = e3
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | REDUCE: (43), (129) imply:
% 179.15/28.85  | | | | | | | | |   (132)   ~ (all_4_2 = e3)
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | SIMP: (132) implies:
% 179.15/28.85  | | | | | | | | |   (133)   ~ (all_4_2 = e3)
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | REDUCE: (2), (127), (128) imply:
% 179.15/28.85  | | | | | | | | |   (134)   ~ (all_52_16 = e2)
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | REDUCE: (104), (127) imply:
% 179.15/28.85  | | | | | | | | |   (135)   ~ (e3 = e2)
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | SIMP: (135) implies:
% 179.15/28.85  | | | | | | | | |   (136)   ~ (e3 = e2)
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | BETA: splitting (18) gives:
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | |   (137)  all_56_0 = e3
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | COMBINE_EQS: (61), (137) imply:
% 179.15/28.85  | | | | | | | | | |   (138)  all_4_2 = e3
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | REDUCE: (133), (138) imply:
% 179.15/28.85  | | | | | | | | | |   (139)  $false
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | CLOSE: (139) is inconsistent.
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | |   (140)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | BETA: splitting (48) gives:
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | |   (141)  all_58_0 = e0
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | COMBINE_EQS: (30), (141) imply:
% 179.15/28.85  | | | | | | | | | | |   (142)  all_4_2 = e0
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | REDUCE: (125), (142) imply:
% 179.15/28.85  | | | | | | | | | | |   (143)   ~ (e2 = e0)
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | SIMP: (143) implies:
% 179.15/28.85  | | | | | | | | | | |   (144)   ~ (e2 = e0)
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | REDUCE: (27), (142) imply:
% 179.15/28.85  | | | | | | | | | | |   (145)  op(e3, e0) = all_4_1
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | BETA: splitting (42) gives:
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | |   (146)  all_58_0 = e2
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | COMBINE_EQS: (141), (146) imply:
% 179.15/28.85  | | | | | | | | | | | |   (147)  e2 = e0
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | SIMP: (147) implies:
% 179.15/28.85  | | | | | | | | | | | |   (148)  e2 = e0
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | REDUCE: (144), (148) imply:
% 179.15/28.85  | | | | | | | | | | | |   (149)  $false
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | |   (150)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | BETA: splitting (46) gives:
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | |   (151)  all_58_9 = e2
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | COMBINE_EQS: (81), (151) imply:
% 179.15/28.85  | | | | | | | | | | | | |   (152)  all_52_7 = e2
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | REDUCE: (74), (152) imply:
% 179.15/28.85  | | | | | | | | | | | | |   (153)  op(e3, e0) = e2
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | GROUND_INST: instantiating (78) with e2, all_4_1, e0, e3,
% 179.15/28.85  | | | | | | | | | | | | |              simplifying with (145), (153) gives:
% 179.15/28.85  | | | | | | | | | | | | |   (154)  all_4_1 = e2
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | REDUCE: (32), (154) imply:
% 179.15/28.85  | | | | | | | | | | | | |   (155)  $false
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | |   (156)   ~ (all_58_9 = e2)
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | REDUCE: (81), (156) imply:
% 179.15/28.85  | | | | | | | | | | | | |   (157)   ~ (all_52_7 = e2)
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | BETA: splitting (150) gives:
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | |   (158)  all_58_1 = e2
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | COMBINE_EQS: (131), (158) imply:
% 179.15/28.85  | | | | | | | | | | | | | |   (159)  e3 = e2
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | REDUCE: (136), (159) imply:
% 179.15/28.85  | | | | | | | | | | | | | |   (160)  $false
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | |   (161)  all_58_4 = e2 | all_58_9 = e2
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | Case 1:
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | |   (162)  all_58_4 = e2
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | | COMBINE_EQS: (130), (162) imply:
% 179.15/28.85  | | | | | | | | | | | | | | |   (163)  all_52_16 = e2
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | | REDUCE: (134), (163) imply:
% 179.15/28.85  | | | | | | | | | | | | | | |   (164)  $false
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | |   (165)  all_58_9 = e2
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | | COMBINE_EQS: (81), (165) imply:
% 179.15/28.85  | | | | | | | | | | | | | | |   (166)  all_52_7 = e2
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | | REDUCE: (157), (166) imply:
% 179.15/28.85  | | | | | | | | | | | | | | |   (167)  $false
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 179.15/28.85  | | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | | End of split
% 179.15/28.85  | | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | | End of split
% 179.15/28.85  | | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | | End of split
% 179.15/28.85  | | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | End of split
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | |   (168)   ~ (all_58_0 = e0)
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | REDUCE: (30), (168) imply:
% 179.15/28.85  | | | | | | | | | | |   (169)   ~ (all_4_2 = e0)
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | | REF_CLOSE: (61), (111), (125), (140), (169) are inconsistent
% 179.15/28.85  | | | | | | | | | | |            by sub-proof #882.
% 179.15/28.85  | | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | | End of split
% 179.15/28.85  | | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | End of split
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | |   (170)  all_56_12 = e1 | all_56_12 = e0
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | | REF_CLOSE: (51), (56), (109), (170) are inconsistent by
% 179.15/28.85  | | | | | | | | |            sub-proof #1029.
% 179.15/28.85  | | | | | | | | | 
% 179.15/28.85  | | | | | | | | End of split
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | Case 2:
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | |   (171)  all_58_14 = e1 | all_58_15 = e1
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | | REF_CLOSE: (25), (60), (66), (101), (171) are inconsistent by
% 179.15/28.85  | | | | | | | |            sub-proof #880.
% 179.15/28.85  | | | | | | | | 
% 179.15/28.85  | | | | | | | End of split
% 179.15/28.85  | | | | | | | 
% 179.15/28.85  | | | | | | End of split
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | End of split
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | Case 2:
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | |   (172)  all_58_15 = e3
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REF_CLOSE: (47), (66), (172) are inconsistent by sub-proof #1010.
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | End of split
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | End of split
% 179.15/28.85  | | | 
% 179.15/28.85  | | End of split
% 179.15/28.85  | | 
% 179.15/28.85  | End of split
% 179.15/28.85  | 
% 179.15/28.85  End of proof
% 179.15/28.85  
% 179.15/28.85  Sub-proof #880 shows that the following formulas are inconsistent:
% 179.15/28.85  ----------------------------------------------------------------
% 179.15/28.85    (1)  all_58_14 = e1 | all_58_15 = e1
% 179.15/28.85    (2)   ~ (e3 = e1)
% 179.15/28.85    (3)   ~ (e1 = e0)
% 179.15/28.85    (4)  all_58_15 = e0
% 179.15/28.85    (5)  all_58_14 = e3
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | BETA: splitting (1) gives:
% 179.15/28.85  | 
% 179.15/28.85  | Case 1:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (6)  all_58_14 = e1
% 179.15/28.85  | | 
% 179.15/28.85  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #881.
% 179.15/28.85  | | 
% 179.15/28.85  | Case 2:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (7)  all_58_15 = e1
% 179.15/28.85  | | 
% 179.15/28.85  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #988.
% 179.15/28.85  | | 
% 179.15/28.85  | End of split
% 179.15/28.85  | 
% 179.15/28.85  End of proof
% 179.15/28.85  
% 179.15/28.85  Sub-proof #881 shows that the following formulas are inconsistent:
% 179.15/28.85  ----------------------------------------------------------------
% 179.15/28.85    (1)  all_58_14 = e3
% 179.15/28.85    (2)  all_58_14 = e1
% 179.15/28.85    (3)   ~ (e3 = e1)
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.85  |   (4)  e3 = e1
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (4) implies:
% 179.15/28.85  |   (5)  e3 = e1
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (3), (5) imply:
% 179.15/28.85  |   (6)  $false
% 179.15/28.85  | 
% 179.15/28.85  | CLOSE: (6) is inconsistent.
% 179.15/28.85  | 
% 179.15/28.85  End of proof
% 179.15/28.85  
% 179.15/28.85  Sub-proof #882 shows that the following formulas are inconsistent:
% 179.15/28.85  ----------------------------------------------------------------
% 179.15/28.85    (1)   ~ (all_4_2 = e2)
% 179.15/28.85    (2)  all_56_0 = all_4_2
% 179.15/28.85    (3)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.85    (4)   ~ (all_4_2 = e1)
% 179.15/28.85    (5)   ~ (all_4_2 = e0)
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | BETA: splitting (3) gives:
% 179.15/28.85  | 
% 179.15/28.85  | Case 1:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (6)  all_56_0 = e2
% 179.15/28.85  | | 
% 179.15/28.85  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #904.
% 179.15/28.85  | | 
% 179.15/28.85  | Case 2:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (7)  all_56_0 = e1 | all_56_0 = e0
% 179.15/28.85  | | 
% 179.15/28.85  | | BETA: splitting (7) gives:
% 179.15/28.85  | | 
% 179.15/28.85  | | Case 1:
% 179.15/28.85  | | | 
% 179.15/28.85  | | |   (8)  all_56_0 = e1
% 179.15/28.85  | | | 
% 179.15/28.85  | | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #1022.
% 179.15/28.85  | | | 
% 179.15/28.85  | | Case 2:
% 179.15/28.85  | | | 
% 179.15/28.85  | | |   (9)  all_56_0 = e0
% 179.15/28.85  | | | 
% 179.15/28.85  | | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1021.
% 179.15/28.85  | | | 
% 179.15/28.85  | | End of split
% 179.15/28.85  | | 
% 179.15/28.85  | End of split
% 179.15/28.85  | 
% 179.15/28.85  End of proof
% 179.15/28.85  
% 179.15/28.85  Sub-proof #883 shows that the following formulas are inconsistent:
% 179.15/28.85  ----------------------------------------------------------------
% 179.15/28.85    (1)  all_58_12 = all_52_25
% 179.15/28.85    (2)  all_58_12 = e1
% 179.15/28.85    (3)   ~ (all_52_25 = e1)
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.85  |   (4)  all_52_25 = e1
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (4) implies:
% 179.15/28.85  |   (5)  all_52_25 = e1
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (3), (5) imply:
% 179.15/28.85  |   (6)  $false
% 179.15/28.85  | 
% 179.15/28.85  | CLOSE: (6) is inconsistent.
% 179.15/28.85  | 
% 179.15/28.85  End of proof
% 179.15/28.85  
% 179.15/28.85  Sub-proof #884 shows that the following formulas are inconsistent:
% 179.15/28.85  ----------------------------------------------------------------
% 179.15/28.85    (1)  all_58_12 = e3
% 179.15/28.85    (2)  op(e3, all_52_25) = e3
% 179.15/28.85    (3)   ~ (all_52_25 = all_4_2)
% 179.15/28.85    (4)  op(e3, e3) = all_4_2
% 179.15/28.85    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.85    (6)  all_58_12 = all_52_25
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | COMBINE_EQS: (1), (6) imply:
% 179.15/28.85  |   (7)  all_52_25 = e3
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (7) implies:
% 179.15/28.85  |   (8)  all_52_25 = e3
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (3), (8) imply:
% 179.15/28.85  |   (9)   ~ (all_4_2 = e3)
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (9) implies:
% 179.15/28.85  |   (10)   ~ (all_4_2 = e3)
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (2), (8) imply:
% 179.15/28.85  |   (11)  op(e3, e3) = e3
% 179.15/28.85  | 
% 179.15/28.85  | REF_CLOSE: (4), (5), (10), (11) are inconsistent by sub-proof #1006.
% 179.15/28.85  | 
% 179.15/28.85  End of proof
% 179.15/28.85  
% 179.15/28.85  Sub-proof #885 shows that the following formulas are inconsistent:
% 179.15/28.85  ----------------------------------------------------------------
% 179.15/28.85    (1)   ~ (all_52_25 = e3)
% 179.15/28.85    (2)   ~ (all_52_23 = all_14_2)
% 179.15/28.85    (3)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.15/28.85    (4)   ~ (all_52_17 = all_52_23)
% 179.15/28.85    (5)  all_56_3 = all_52_7
% 179.15/28.85    (6)  op(e2, e3) = e2
% 179.15/28.85    (7)  op(e3, e2) = all_52_3
% 179.15/28.85    (8)   ~ (all_52_9 = all_52_25)
% 179.15/28.85    (9)   ~ (all_52_19 = all_52_23)
% 179.15/28.85    (10)  op(e1, e2) = all_52_19
% 179.15/28.85    (11)  op(e3, all_52_9) = all_52_8
% 179.15/28.85    (12)   ~ (all_52_23 = e0)
% 179.15/28.85    (13)  all_58_1 = e2 | all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 179.15/28.85    (14)   ~ (all_52_25 = all_52_29)
% 179.15/28.85    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.15/28.85    (16)  all_58_3 = all_10_2
% 179.15/28.85    (17)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.85    (18)   ~ (all_52_9 = all_4_2)
% 179.15/28.85    (19)   ~ (all_52_5 = all_52_7)
% 179.15/28.85    (20)   ~ (all_52_5 = all_4_2)
% 179.15/28.85    (21)  all_58_7 = all_52_19
% 179.15/28.85    (22)  op(e3, all_4_2) = all_4_1
% 179.15/28.85    (23)   ~ (all_52_7 = all_4_2)
% 179.15/28.85    (24)  all_58_1 = all_52_3
% 179.15/28.85    (25)  all_58_0 = all_4_2
% 179.15/28.85    (26)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.15/28.85    (27)   ~ (all_10_2 = e3)
% 179.15/28.85    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.15/28.85    (29)  all_58_8 = all_14_2
% 179.15/28.85    (30)  all_56_14 = all_52_29
% 179.15/28.85    (31)  op(e1, all_52_29) = e1
% 179.15/28.85    (32)   ~ (all_52_9 = all_10_2)
% 179.15/28.85    (33)   ~ (all_52_29 = e3)
% 179.15/28.85    (34)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.85    (35)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.15/28.85    (36)   ~ (all_52_5 = all_52_29)
% 179.15/28.85    (37)  all_56_12 = all_52_25
% 179.15/28.85    (38)   ~ (all_4_1 = e1)
% 179.15/28.85    (39)  all_56_5 = all_10_2
% 179.15/28.85    (40)  all_58_6 = e2 | all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 179.15/28.85    (41)   ~ (all_52_25 = e0)
% 179.15/28.85    (42)   ~ (all_52_9 = all_52_17)
% 179.15/28.85    (43)  all_58_6 = all_52_17
% 179.15/28.85    (44)   ~ (all_52_3 = all_52_7)
% 179.15/28.85    (45)  all_56_0 = all_4_2
% 179.15/28.85    (46)  all_58_11 = all_52_23
% 179.15/28.85    (47)   ~ (all_52_29 = all_14_2)
% 179.15/28.85    (48)  op(e3, all_52_25) = e3
% 179.15/28.85    (49)   ~ (all_52_19 = all_10_2)
% 179.15/28.85    (50)  all_58_2 = all_52_9
% 179.15/28.85    (51)   ~ (all_52_29 = e0)
% 179.15/28.85    (52)  op(e3, e1) = all_52_5
% 179.15/28.85    (53)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.15/28.85    (54)   ~ (all_52_25 = all_4_2)
% 179.15/28.85    (55)  op(e3, e0) = all_52_7
% 179.15/28.85    (56)  all_56_8 = all_52_17
% 179.15/28.85    (57)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.85    (58)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.15/28.85    (59)  all_58_9 = all_52_7
% 179.15/28.85    (60)  all_58_12 = all_52_25
% 179.15/28.85    (61)  all_58_13 = e3
% 179.15/28.85    (62)  op(e2, e3) = all_52_9
% 179.15/28.85  
% 179.15/28.85  Begin of proof
% 179.15/28.85  | 
% 179.15/28.85  | GROUND_INST: instantiating (57) with all_52_9, e2, e3, e2, simplifying with
% 179.15/28.85  |              (6), (62) gives:
% 179.15/28.85  |   (63)  all_52_9 = e2
% 179.15/28.85  | 
% 179.15/28.85  | COMBINE_EQS: (50), (63) imply:
% 179.15/28.85  |   (64)  all_58_2 = e2
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (42), (63) imply:
% 179.15/28.85  |   (65)   ~ (all_52_17 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (65) implies:
% 179.15/28.85  |   (66)   ~ (all_52_17 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (8), (63) imply:
% 179.15/28.85  |   (67)   ~ (all_52_25 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (67) implies:
% 179.15/28.85  |   (68)   ~ (all_52_25 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (32), (63) imply:
% 179.15/28.85  |   (69)   ~ (all_10_2 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (69) implies:
% 179.15/28.85  |   (70)   ~ (all_10_2 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (18), (63) imply:
% 179.15/28.85  |   (71)   ~ (all_4_2 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | SIMP: (71) implies:
% 179.15/28.85  |   (72)   ~ (all_4_2 = e2)
% 179.15/28.85  | 
% 179.15/28.85  | REDUCE: (11), (63) imply:
% 179.15/28.85  |   (73)  op(e3, e2) = all_52_8
% 179.15/28.85  | 
% 179.15/28.85  | BETA: splitting (35) gives:
% 179.15/28.85  | 
% 179.15/28.85  | Case 1:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (74)  all_56_12 = e3
% 179.15/28.85  | | 
% 179.15/28.85  | | COMBINE_EQS: (37), (74) imply:
% 179.15/28.85  | |   (75)  all_52_25 = e3
% 179.15/28.85  | | 
% 179.15/28.85  | | REDUCE: (1), (75) imply:
% 179.15/28.85  | |   (76)  $false
% 179.15/28.85  | | 
% 179.15/28.85  | | CLOSE: (76) is inconsistent.
% 179.15/28.85  | | 
% 179.15/28.85  | Case 2:
% 179.15/28.85  | | 
% 179.15/28.85  | |   (77)   ~ (all_56_12 = e3)
% 179.15/28.85  | |   (78)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.15/28.85  | | 
% 179.15/28.85  | | BETA: splitting (78) gives:
% 179.15/28.85  | | 
% 179.15/28.85  | | Case 1:
% 179.15/28.85  | | | 
% 179.15/28.85  | | |   (79)  all_56_12 = e2
% 179.15/28.85  | | | 
% 179.15/28.85  | | | COMBINE_EQS: (37), (79) imply:
% 179.15/28.85  | | |   (80)  all_52_25 = e2
% 179.15/28.85  | | | 
% 179.15/28.85  | | | REDUCE: (68), (80) imply:
% 179.15/28.85  | | |   (81)  $false
% 179.15/28.85  | | | 
% 179.15/28.85  | | | CLOSE: (81) is inconsistent.
% 179.15/28.85  | | | 
% 179.15/28.85  | | Case 2:
% 179.15/28.85  | | | 
% 179.15/28.85  | | |   (82)  all_56_12 = e1 | all_56_12 = e0
% 179.15/28.85  | | | 
% 179.15/28.85  | | | BETA: splitting (82) gives:
% 179.15/28.85  | | | 
% 179.15/28.85  | | | Case 1:
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | |   (83)  all_56_12 = e1
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | COMBINE_EQS: (37), (83) imply:
% 179.15/28.85  | | | |   (84)  all_52_25 = e1
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | REDUCE: (14), (84) imply:
% 179.15/28.85  | | | |   (85)   ~ (all_52_29 = e1)
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | SIMP: (85) implies:
% 179.15/28.85  | | | |   (86)   ~ (all_52_29 = e1)
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | REDUCE: (54), (84) imply:
% 179.15/28.85  | | | |   (87)   ~ (all_4_2 = e1)
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | SIMP: (87) implies:
% 179.15/28.85  | | | |   (88)   ~ (all_4_2 = e1)
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | REDUCE: (48), (84) imply:
% 179.15/28.85  | | | |   (89)  op(e3, e1) = e3
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | BETA: splitting (26) gives:
% 179.15/28.85  | | | | 
% 179.15/28.85  | | | | Case 1:
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | |   (90)  all_56_14 = e3
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | REF_CLOSE: (30), (33), (90) are inconsistent by sub-proof #896.
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | Case 2:
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | |   (91)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | BETA: splitting (91) gives:
% 179.15/28.85  | | | | | 
% 179.15/28.85  | | | | | Case 1:
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | |   (92)  all_56_14 = e2
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | | COMBINE_EQS: (30), (92) imply:
% 179.15/28.85  | | | | | |   (93)  all_52_29 = e2
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | | SIMP: (93) implies:
% 179.15/28.85  | | | | | |   (94)  all_52_29 = e2
% 179.15/28.85  | | | | | | 
% 179.15/28.85  | | | | | | REDUCE: (36), (94) imply:
% 179.15/28.86  | | | | | |   (95)   ~ (all_52_5 = e2)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (47), (94) imply:
% 179.15/28.86  | | | | | |   (96)   ~ (all_14_2 = e2)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | SIMP: (96) implies:
% 179.15/28.86  | | | | | |   (97)   ~ (all_14_2 = e2)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (86), (94) imply:
% 179.15/28.86  | | | | | |   (98)   ~ (e2 = e1)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (31), (94) imply:
% 179.15/28.86  | | | | | |   (99)  op(e1, e2) = e1
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | GROUND_INST: instantiating (57) with all_52_19, e1, e2, e1,
% 179.15/28.86  | | | | | |              simplifying with (10), (99) gives:
% 179.15/28.86  | | | | | |   (100)  all_52_19 = e1
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | GROUND_INST: instantiating (57) with all_52_5, e3, e1, e3,
% 179.15/28.86  | | | | | |              simplifying with (52), (89) gives:
% 179.15/28.86  | | | | | |   (101)  all_52_5 = e3
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | GROUND_INST: instantiating (57) with all_52_3, all_52_8, e2, e3,
% 179.15/28.86  | | | | | |              simplifying with (7), (73) gives:
% 179.15/28.86  | | | | | |   (102)  all_52_3 = all_52_8
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | COMBINE_EQS: (21), (100) imply:
% 179.15/28.86  | | | | | |   (103)  all_58_7 = e1
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | COMBINE_EQS: (24), (102) imply:
% 179.15/28.86  | | | | | |   (104)  all_58_1 = all_52_8
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (44), (102) imply:
% 179.15/28.86  | | | | | |   (105)   ~ (all_52_7 = all_52_8)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | SIMP: (105) implies:
% 179.15/28.86  | | | | | |   (106)   ~ (all_52_7 = all_52_8)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (19), (101) imply:
% 179.15/28.86  | | | | | |   (107)   ~ (all_52_7 = e3)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | SIMP: (107) implies:
% 179.15/28.86  | | | | | |   (108)   ~ (all_52_7 = e3)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (20), (101) imply:
% 179.15/28.86  | | | | | |   (109)   ~ (all_4_2 = e3)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | SIMP: (109) implies:
% 179.15/28.86  | | | | | |   (110)   ~ (all_4_2 = e3)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (95), (101) imply:
% 179.15/28.86  | | | | | |   (111)   ~ (e3 = e2)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (9), (100) imply:
% 179.15/28.86  | | | | | |   (112)   ~ (all_52_23 = e1)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | SIMP: (112) implies:
% 179.15/28.86  | | | | | |   (113)   ~ (all_52_23 = e1)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REDUCE: (49), (100) imply:
% 179.15/28.86  | | | | | |   (114)   ~ (all_10_2 = e1)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | SIMP: (114) implies:
% 179.15/28.86  | | | | | |   (115)   ~ (all_10_2 = e1)
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | BETA: splitting (53) gives:
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | Case 1:
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | |   (116)  all_56_5 = e3
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | | REF_CLOSE: (27), (39), (116) are inconsistent by sub-proof #895.
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | Case 2:
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | |   (117)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | | BETA: splitting (40) gives:
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | 
% 179.15/28.86  | | | | | | | |   (118)  all_58_6 = e2
% 179.15/28.86  | | | | | | | | 
% 179.15/28.86  | | | | | | | | REF_CLOSE: (43), (66), (118) are inconsistent by sub-proof #894.
% 179.15/28.86  | | | | | | | | 
% 179.15/28.86  | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | 
% 179.15/28.86  | | | | | | | |   (119)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 179.15/28.86  | | | | | | | | 
% 179.15/28.86  | | | | | | | | BETA: splitting (28) gives:
% 179.15/28.86  | | | | | | | | 
% 179.15/28.86  | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | |   (120)  all_58_0 = e3
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | COMBINE_EQS: (25), (120) imply:
% 179.15/28.86  | | | | | | | | |   (121)  all_4_2 = e3
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | REDUCE: (110), (121) imply:
% 179.15/28.86  | | | | | | | | |   (122)  $false
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | CLOSE: (122) is inconsistent.
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | |   (123)   ~ (all_58_0 = e3)
% 179.15/28.86  | | | | | | | | |   (124)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | BETA: splitting (124) gives:
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | |   (125)  all_58_2 = e3
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | COMBINE_EQS: (64), (125) imply:
% 179.15/28.86  | | | | | | | | | |   (126)  e3 = e2
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | REDUCE: (111), (126) imply:
% 179.15/28.86  | | | | | | | | | |   (127)  $false
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | CLOSE: (127) is inconsistent.
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | |   (128)  all_58_6 = e3 | all_58_12 = e3
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | BETA: splitting (17) gives:
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | |   (129)  all_56_0 = e3
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | COMBINE_EQS: (45), (129) imply:
% 179.15/28.86  | | | | | | | | | | |   (130)  all_4_2 = e3
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | REDUCE: (110), (130) imply:
% 179.15/28.86  | | | | | | | | | | |   (131)  $false
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | |   (132)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | BETA: splitting (132) gives:
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | |   (133)  all_56_0 = e2
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | COMBINE_EQS: (45), (133) imply:
% 179.15/28.86  | | | | | | | | | | | |   (134)  all_4_2 = e2
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | REDUCE: (72), (134) imply:
% 179.15/28.86  | | | | | | | | | | | |   (135)  $false
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | |   (136)  all_56_0 = e1 | all_56_0 = e0
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | BETA: splitting (3) gives:
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | |   (137)  all_56_8 = e3
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | COMBINE_EQS: (56), (137) imply:
% 179.15/28.86  | | | | | | | | | | | | |   (138)  all_52_17 = e3
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | SIMP: (138) implies:
% 179.15/28.86  | | | | | | | | | | | | |   (139)  all_52_17 = e3
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | REDUCE: (4), (139) imply:
% 179.15/28.86  | | | | | | | | | | | | |   (140)   ~ (all_52_23 = e3)
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | SIMP: (140) implies:
% 179.15/28.86  | | | | | | | | | | | | |   (141)   ~ (all_52_23 = e3)
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | BETA: splitting (13) gives:
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | |   (142)  all_58_1 = e2
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | COMBINE_EQS: (104), (142) imply:
% 179.15/28.86  | | | | | | | | | | | | | |   (143)  all_52_8 = e2
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | REDUCE: (106), (143) imply:
% 179.15/28.86  | | | | | | | | | | | | | |   (144)   ~ (all_52_7 = e2)
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | |   (145)  all_56_3 = e3
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | COMBINE_EQS: (5), (145) imply:
% 179.15/28.86  | | | | | | | | | | | | | | |   (146)  all_52_7 = e3
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | REDUCE: (108), (146) imply:
% 179.15/28.86  | | | | | | | | | | | | | | |   (147)  $false
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | |   (148)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | |   (149)  all_58_0 = e0
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (149) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | |   (150)  all_4_2 = e0
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | REDUCE: (23), (150) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | |   (151)   ~ (all_52_7 = e0)
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | REDUCE: (22), (150) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | |   (152)  op(e3, e0) = all_4_1
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | Case 1:
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | |   (153)  all_58_9 = e1
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (153) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | | |   (154)  all_52_7 = e1
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | | REDUCE: (55), (154) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | | |   (155)  op(e3, e0) = e1
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (57) with e1, all_4_1, e0, e3,
% 179.15/28.86  | | | | | | | | | | | | | | | | |              simplifying with (152), (155) gives:
% 179.15/28.86  | | | | | | | | | | | | | | | | |   (156)  all_4_1 = e1
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | | REDUCE: (38), (156) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | | |   (157)  $false
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | |   (158)   ~ (all_58_9 = e1)
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | | REDUCE: (59), (158) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | | |   (159)   ~ (all_52_7 = e1)
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (144), (148), (151), (159) are inconsistent
% 179.15/28.86  | | | | | | | | | | | | | | | | |            by sub-proof #893.
% 179.15/28.86  | | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | |   (160)   ~ (all_58_0 = e0)
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | REDUCE: (25), (160) imply:
% 179.15/28.86  | | | | | | | | | | | | | | | |   (161)   ~ (all_4_2 = e0)
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (88), (136), (161) are inconsistent by
% 179.15/28.86  | | | | | | | | | | | | | | | |            sub-proof #892.
% 179.15/28.86  | | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | |   (162)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (16), (29), (39), (46), (61), (70),
% 179.15/28.86  | | | | | | | | | | | | | |            (97), (98), (103), (113), (115), (117), (119),
% 179.15/28.86  | | | | | | | | | | | | | |            (141), (162) are inconsistent by sub-proof #889.
% 179.15/28.86  | | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | Case 2:
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | |   (163)   ~ (all_56_8 = e3)
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | REDUCE: (56), (163) imply:
% 179.15/28.86  | | | | | | | | | | | | |   (164)   ~ (all_52_17 = e3)
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | | REF_CLOSE: (1), (43), (60), (128), (164) are inconsistent by
% 179.15/28.86  | | | | | | | | | | | | |            sub-proof #888.
% 179.15/28.86  | | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | | 
% 179.15/28.86  | | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | | 
% 179.15/28.86  | | | | | | | | End of split
% 179.15/28.86  | | | | | | | | 
% 179.15/28.86  | | | | | | | End of split
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | End of split
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | Case 2:
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | |   (165)  all_56_14 = e1 | all_56_14 = e0
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REF_CLOSE: (30), (51), (86), (165) are inconsistent by sub-proof
% 179.15/28.86  | | | | | |            #886.
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | End of split
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | End of split
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | Case 2:
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | |   (166)  all_56_12 = e0
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | COMBINE_EQS: (37), (166) imply:
% 179.15/28.86  | | | |   (167)  all_52_25 = e0
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | REDUCE: (41), (167) imply:
% 179.15/28.86  | | | |   (168)  $false
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | CLOSE: (168) is inconsistent.
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | End of split
% 179.15/28.86  | | | 
% 179.15/28.86  | | End of split
% 179.15/28.86  | | 
% 179.15/28.86  | End of split
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #886 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_56_14 = e1 | all_56_14 = e0
% 179.15/28.86    (2)  all_56_14 = all_52_29
% 179.15/28.86    (3)   ~ (all_52_29 = e1)
% 179.15/28.86    (4)   ~ (all_52_29 = e0)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | BETA: splitting (1) gives:
% 179.15/28.86  | 
% 179.15/28.86  | Case 1:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (5)  all_56_14 = e1
% 179.15/28.86  | | 
% 179.15/28.86  | | COMBINE_EQS: (2), (5) imply:
% 179.15/28.86  | |   (6)  all_52_29 = e1
% 179.15/28.86  | | 
% 179.15/28.86  | | SIMP: (6) implies:
% 179.15/28.86  | |   (7)  all_52_29 = e1
% 179.15/28.86  | | 
% 179.15/28.86  | | REDUCE: (3), (7) imply:
% 179.15/28.86  | |   (8)  $false
% 179.15/28.86  | | 
% 179.15/28.86  | | CLOSE: (8) is inconsistent.
% 179.15/28.86  | | 
% 179.15/28.86  | Case 2:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (9)  all_56_14 = e0
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #887.
% 179.15/28.86  | | 
% 179.15/28.86  | End of split
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #887 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_56_14 = all_52_29
% 179.15/28.86    (2)  all_56_14 = e0
% 179.15/28.86    (3)   ~ (all_52_29 = e0)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.86  |   (4)  all_52_29 = e0
% 179.15/28.86  | 
% 179.15/28.86  | SIMP: (4) implies:
% 179.15/28.86  |   (5)  all_52_29 = e0
% 179.15/28.86  | 
% 179.15/28.86  | REDUCE: (3), (5) imply:
% 179.15/28.86  |   (6)  $false
% 179.15/28.86  | 
% 179.15/28.86  | CLOSE: (6) is inconsistent.
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #888 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)   ~ (all_52_25 = e3)
% 179.15/28.86    (2)   ~ (all_52_17 = e3)
% 179.15/28.86    (3)  all_58_6 = all_52_17
% 179.15/28.86    (4)  all_58_6 = e3 | all_58_12 = e3
% 179.15/28.86    (5)  all_58_12 = all_52_25
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | BETA: splitting (4) gives:
% 179.15/28.86  | 
% 179.15/28.86  | Case 1:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (6)  all_58_6 = e3
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #981.
% 179.15/28.86  | | 
% 179.15/28.86  | Case 2:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (7)  all_58_12 = e3
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1003.
% 179.15/28.86  | | 
% 179.15/28.86  | End of split
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #889 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)   ~ (all_52_23 = all_14_2)
% 179.15/28.86    (2)   ~ (all_10_2 = e1)
% 179.15/28.86    (3)  all_58_3 = e2 | all_58_7 = e2 | all_58_13 = e2
% 179.15/28.86    (4)   ~ (all_52_23 = e0)
% 179.15/28.86    (5)  all_58_3 = all_10_2
% 179.15/28.86    (6)  all_58_7 = e1
% 179.15/28.86    (7)  all_58_8 = all_14_2
% 179.15/28.86    (8)  all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.15/28.86    (9)   ~ (all_52_23 = e3)
% 179.15/28.86    (10)   ~ (all_52_23 = e1)
% 179.15/28.86    (11)  all_56_5 = all_10_2
% 179.15/28.86    (12)  all_58_11 = all_52_23
% 179.15/28.86    (13)   ~ (all_10_2 = e2)
% 179.15/28.86    (14)   ~ (e2 = e1)
% 179.15/28.86    (15)   ~ (all_14_2 = e2)
% 179.15/28.86    (16)  all_58_7 = e2 | all_58_8 = e2 | all_58_11 = e2
% 179.15/28.86    (17)  all_58_13 = e3
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | BETA: splitting (16) gives:
% 179.15/28.86  | 
% 179.15/28.86  | Case 1:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (18)  all_58_7 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (6), (14), (18) are inconsistent by sub-proof #891.
% 179.15/28.86  | | 
% 179.15/28.86  | Case 2:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (19)  all_58_8 = e2 | all_58_11 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | BETA: splitting (8) gives:
% 179.15/28.86  | | 
% 179.15/28.86  | | Case 1:
% 179.15/28.86  | | | 
% 179.15/28.86  | | |   (20)  all_56_5 = e2
% 179.15/28.86  | | | 
% 179.15/28.86  | | | COMBINE_EQS: (11), (20) imply:
% 179.15/28.86  | | |   (21)  all_10_2 = e2
% 179.15/28.86  | | | 
% 179.15/28.86  | | | REDUCE: (13), (21) imply:
% 179.15/28.86  | | |   (22)  $false
% 179.15/28.86  | | | 
% 179.15/28.86  | | | CLOSE: (22) is inconsistent.
% 179.15/28.86  | | | 
% 179.15/28.86  | | Case 2:
% 179.15/28.86  | | | 
% 179.15/28.86  | | |   (23)  all_56_5 = e1 | all_56_5 = e0
% 179.15/28.86  | | | 
% 179.15/28.86  | | | BETA: splitting (23) gives:
% 179.15/28.86  | | | 
% 179.15/28.86  | | | Case 1:
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | |   (24)  all_56_5 = e1
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | COMBINE_EQS: (11), (24) imply:
% 179.15/28.86  | | | |   (25)  all_10_2 = e1
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | REDUCE: (2), (25) imply:
% 179.15/28.86  | | | |   (26)  $false
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | CLOSE: (26) is inconsistent.
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | Case 2:
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | |   (27)  all_56_5 = e0
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | COMBINE_EQS: (11), (27) imply:
% 179.15/28.86  | | | |   (28)  all_10_2 = e0
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | COMBINE_EQS: (5), (28) imply:
% 179.15/28.86  | | | |   (29)  all_58_3 = e0
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | BETA: splitting (19) gives:
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | Case 1:
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | |   (30)  all_58_8 = e2
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | COMBINE_EQS: (7), (30) imply:
% 179.15/28.86  | | | | |   (31)  all_14_2 = e2
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | REDUCE: (15), (31) imply:
% 179.15/28.86  | | | | |   (32)  $false
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | CLOSE: (32) is inconsistent.
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | Case 2:
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | |   (33)  all_58_11 = e2
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | COMBINE_EQS: (12), (33) imply:
% 179.15/28.86  | | | | |   (34)  all_52_23 = e2
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | REDUCE: (1), (34) imply:
% 179.15/28.86  | | | | |   (35)   ~ (all_14_2 = e2)
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | REDUCE: (9), (34) imply:
% 179.15/28.86  | | | | |   (36)   ~ (e3 = e2)
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | SIMP: (36) implies:
% 179.15/28.86  | | | | |   (37)   ~ (e3 = e2)
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | REDUCE: (4), (34) imply:
% 179.15/28.86  | | | | |   (38)   ~ (e2 = e0)
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | BETA: splitting (3) gives:
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | | Case 1:
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | |   (39)  all_58_3 = e2
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | COMBINE_EQS: (29), (39) imply:
% 179.15/28.86  | | | | | |   (40)  e2 = e0
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | SIMP: (40) implies:
% 179.15/28.86  | | | | | |   (41)  e2 = e0
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | COMBINE_EQS: (33), (41) imply:
% 179.15/28.86  | | | | | |   (42)  all_58_11 = e0
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | REF_CLOSE: (7), (15), (19), (38), (42) are inconsistent by sub-proof
% 179.15/28.86  | | | | | |            #890.
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | Case 2:
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | |   (43)  all_58_7 = e2 | all_58_13 = e2
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | BETA: splitting (43) gives:
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | | Case 1:
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | |   (44)  all_58_7 = e2
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | | REF_CLOSE: (6), (14), (44) are inconsistent by sub-proof #891.
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | Case 2:
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | |   (45)  all_58_13 = e2
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | | REF_CLOSE: (17), (37), (45) are inconsistent by sub-proof #906.
% 179.15/28.86  | | | | | | | 
% 179.15/28.86  | | | | | | End of split
% 179.15/28.86  | | | | | | 
% 179.15/28.86  | | | | | End of split
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | End of split
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | End of split
% 179.15/28.86  | | | 
% 179.15/28.86  | | End of split
% 179.15/28.86  | | 
% 179.15/28.86  | End of split
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #890 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_58_8 = all_14_2
% 179.15/28.86    (2)  all_58_11 = e0
% 179.15/28.86    (3)  all_58_8 = e2 | all_58_11 = e2
% 179.15/28.86    (4)   ~ (all_14_2 = e2)
% 179.15/28.86    (5)   ~ (e2 = e0)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | BETA: splitting (3) gives:
% 179.15/28.86  | 
% 179.15/28.86  | Case 1:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (6)  all_58_8 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | COMBINE_EQS: (1), (6) imply:
% 179.15/28.86  | |   (7)  all_14_2 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | SIMP: (7) implies:
% 179.15/28.86  | |   (8)  all_14_2 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | REDUCE: (4), (8) imply:
% 179.15/28.86  | |   (9)  $false
% 179.15/28.86  | | 
% 179.15/28.86  | | CLOSE: (9) is inconsistent.
% 179.15/28.86  | | 
% 179.15/28.86  | Case 2:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (10)  all_58_11 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | COMBINE_EQS: (2), (10) imply:
% 179.15/28.86  | |   (11)  e2 = e0
% 179.15/28.86  | | 
% 179.15/28.86  | | REDUCE: (5), (11) imply:
% 179.15/28.86  | |   (12)  $false
% 179.15/28.86  | | 
% 179.15/28.86  | | CLOSE: (12) is inconsistent.
% 179.15/28.86  | | 
% 179.15/28.86  | End of split
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #891 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_58_7 = e2
% 179.15/28.86    (2)  all_58_7 = e1
% 179.15/28.86    (3)   ~ (e2 = e1)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.86  |   (4)  e2 = e1
% 179.15/28.86  | 
% 179.15/28.86  | SIMP: (4) implies:
% 179.15/28.86  |   (5)  e2 = e1
% 179.15/28.86  | 
% 179.15/28.86  | REDUCE: (3), (5) imply:
% 179.15/28.86  |   (6)  $false
% 179.15/28.86  | 
% 179.15/28.86  | CLOSE: (6) is inconsistent.
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #892 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_56_0 = e1 | all_56_0 = e0
% 179.15/28.86    (2)  all_56_0 = all_4_2
% 179.15/28.86    (3)   ~ (all_4_2 = e1)
% 179.15/28.86    (4)   ~ (all_4_2 = e0)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | BETA: splitting (1) gives:
% 179.15/28.86  | 
% 179.15/28.86  | Case 1:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (5)  all_56_0 = e1
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1022.
% 179.15/28.86  | | 
% 179.15/28.86  | Case 2:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (6)  all_56_0 = e0
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1021.
% 179.15/28.86  | | 
% 179.15/28.86  | End of split
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #893 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.15/28.86    (2)  all_56_3 = all_52_7
% 179.15/28.86    (3)   ~ (all_52_7 = e0)
% 179.15/28.86    (4)   ~ (all_52_7 = e1)
% 179.15/28.86    (5)   ~ (all_52_7 = e2)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | BETA: splitting (1) gives:
% 179.15/28.86  | 
% 179.15/28.86  | Case 1:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (6)  all_56_3 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | COMBINE_EQS: (2), (6) imply:
% 179.15/28.86  | |   (7)  all_52_7 = e2
% 179.15/28.86  | | 
% 179.15/28.86  | | REDUCE: (5), (7) imply:
% 179.15/28.86  | |   (8)  $false
% 179.15/28.86  | | 
% 179.15/28.86  | | CLOSE: (8) is inconsistent.
% 179.15/28.86  | | 
% 179.15/28.86  | Case 2:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (9)  all_56_3 = e1 | all_56_3 = e0
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1037.
% 179.15/28.86  | | 
% 179.15/28.86  | End of split
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #894 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_58_6 = all_52_17
% 179.15/28.86    (2)  all_58_6 = e2
% 179.15/28.86    (3)   ~ (all_52_17 = e2)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.86  |   (4)  all_52_17 = e2
% 179.15/28.86  | 
% 179.15/28.86  | SIMP: (4) implies:
% 179.15/28.86  |   (5)  all_52_17 = e2
% 179.15/28.86  | 
% 179.15/28.86  | REDUCE: (3), (5) imply:
% 179.15/28.86  |   (6)  $false
% 179.15/28.86  | 
% 179.15/28.86  | CLOSE: (6) is inconsistent.
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #895 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_56_5 = all_10_2
% 179.15/28.86    (2)  all_56_5 = e3
% 179.15/28.86    (3)   ~ (all_10_2 = e3)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.86  |   (4)  all_10_2 = e3
% 179.15/28.86  | 
% 179.15/28.86  | SIMP: (4) implies:
% 179.15/28.86  |   (5)  all_10_2 = e3
% 179.15/28.86  | 
% 179.15/28.86  | REDUCE: (3), (5) imply:
% 179.15/28.86  |   (6)  $false
% 179.15/28.86  | 
% 179.15/28.86  | CLOSE: (6) is inconsistent.
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #896 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)  all_56_14 = all_52_29
% 179.15/28.86    (2)  all_56_14 = e3
% 179.15/28.86    (3)   ~ (all_52_29 = e3)
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | COMBINE_EQS: (1), (2) imply:
% 179.15/28.86  |   (4)  all_52_29 = e3
% 179.15/28.86  | 
% 179.15/28.86  | SIMP: (4) implies:
% 179.15/28.86  |   (5)  all_52_29 = e3
% 179.15/28.86  | 
% 179.15/28.86  | REDUCE: (3), (5) imply:
% 179.15/28.86  |   (6)  $false
% 179.15/28.86  | 
% 179.15/28.86  | CLOSE: (6) is inconsistent.
% 179.15/28.86  | 
% 179.15/28.86  End of proof
% 179.15/28.86  
% 179.15/28.86  Sub-proof #897 shows that the following formulas are inconsistent:
% 179.15/28.86  ----------------------------------------------------------------
% 179.15/28.86    (1)   ~ (all_52_23 = all_14_2)
% 179.15/28.86    (2)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.15/28.86    (3)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 179.15/28.86    (4)   ~ (all_52_17 = all_52_23)
% 179.15/28.86    (5)   ~ (all_52_13 = all_52_29)
% 179.15/28.86    (6)  all_56_3 = all_52_7
% 179.15/28.86    (7)  op(e3, e2) = all_52_3
% 179.15/28.86    (8)   ~ (all_52_9 = all_52_25)
% 179.15/28.86    (9)   ~ (all_52_19 = all_52_23)
% 179.15/28.86    (10)  all_56_11 = all_52_23
% 179.15/28.86    (11)   ~ (all_52_27 = e0)
% 179.15/28.86    (12)   ~ (all_52_23 = e0)
% 179.15/28.86    (13)   ~ (all_52_3 = all_10_2)
% 179.15/28.86    (14)  all_58_5 = all_52_13
% 179.15/28.86    (15)   ~ (all_52_25 = all_52_29)
% 179.15/28.86    (16)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.15/28.86    (17)  all_58_3 = all_10_2
% 179.15/28.86    (18)  all_56_9 = all_52_19
% 179.15/28.86    (19)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.15/28.86    (20)   ~ (all_52_9 = all_4_2)
% 179.15/28.86    (21)   ~ (all_52_5 = all_52_7)
% 179.15/28.86    (22)  all_58_10 = all_52_15
% 179.15/28.86    (23)  all_58_7 = all_52_19
% 179.15/28.86    (24)   ~ (all_52_17 = all_52_25)
% 179.15/28.86    (25)  op(e0, e1) = all_52_29
% 179.15/28.86    (26)   ~ (all_4_0 = e2)
% 179.15/28.86    (27)  all_58_4 = all_52_5
% 179.15/28.86    (28)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.15/28.86    (29)   ~ (all_52_27 = all_52_29)
% 179.15/28.86    (30)  op(e3, all_4_2) = all_4_1
% 179.15/28.86    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.15/28.86    (32)   ~ (all_52_7 = all_4_2)
% 179.15/28.86    (33)  all_58_1 = all_52_3
% 179.15/28.86    (34)  all_58_0 = all_4_2
% 179.15/28.86    (35)  op(e1, all_52_29) = all_52_28
% 179.15/28.86    (36)   ~ (all_52_7 = e0)
% 179.15/28.86    (37)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.15/28.86    (38)   ~ (all_4_1 = e2)
% 179.15/28.86    (39)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.15/28.86    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.15/28.86    (41)  all_58_14 = all_52_29
% 179.15/28.86    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.15/28.86    (43)   ~ (all_52_3 = all_52_5)
% 179.15/28.86    (44)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.15/28.86    (45)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.15/28.86    (46)  all_58_8 = all_14_2
% 179.15/28.86    (47)  op(e0, e2) = all_52_27
% 179.15/28.86    (48)  all_56_14 = all_52_29
% 179.15/28.86    (49)   ~ (all_14_0 = e3)
% 179.15/28.86    (50)  op(all_4_1, all_4_2) = all_4_0
% 179.15/28.86    (51)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 179.15/28.86    (52)   ~ (all_52_5 = all_14_2)
% 179.15/28.86    (53)   ~ (all_52_3 = all_4_2)
% 179.15/28.86    (54)  op(e0, e3) = all_52_25
% 179.15/28.86    (55)   ~ (all_52_9 = all_10_2)
% 179.15/28.86    (56)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.15/28.86    (57)  op(e1, all_14_2) = all_14_0
% 179.15/28.86    (58)   ~ (e3 = e0)
% 179.15/28.86    (59)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.15/28.86    (60)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.15/28.86    (61)   ~ (all_52_15 = all_52_23)
% 179.15/28.86    (62)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.15/28.86    (63)   ~ (all_52_5 = all_52_29)
% 179.15/28.86    (64)  all_56_2 = all_52_5
% 179.15/28.86    (65)  all_56_12 = all_52_25
% 179.15/28.86    (66)  all_58_13 = all_52_27
% 179.15/28.86    (67)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.15/28.86    (68)  all_56_5 = all_10_2
% 179.15/28.86    (69)   ~ (all_52_25 = e0)
% 179.15/28.86    (70)   ~ (all_52_9 = all_52_17)
% 179.15/28.86    (71)   ~ (all_14_0 = e2)
% 179.15/28.86    (72)  all_58_6 = all_52_17
% 179.15/28.86    (73)   ~ (all_52_3 = all_52_7)
% 179.15/28.86    (74)  op(e2, all_52_19) = e2
% 179.15/28.86    (75)  op(e3, all_52_17) = e3
% 179.15/28.86    (76)   ~ (e1 = e0)
% 179.15/28.86    (77)  all_56_0 = all_4_2
% 179.15/28.86    (78)  all_58_11 = all_52_23
% 179.15/28.86    (79)   ~ (all_52_29 = all_14_2)
% 179.15/28.86    (80)   ~ (all_4_0 = e1)
% 179.15/28.86    (81)   ~ (all_52_19 = all_10_2)
% 179.15/28.86    (82)  all_58_15 = e0
% 179.15/28.86    (83)  all_58_2 = all_52_9
% 179.15/28.86    (84)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.15/28.86    (85)   ~ (all_52_29 = e0)
% 179.15/28.86    (86)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.15/28.86    (87)  op(e3, e1) = all_52_5
% 179.15/28.86    (88)  all_56_10 = all_14_2
% 179.15/28.86    (89)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.15/28.86    (90)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.15/28.86    (91)  op(e1, e3) = all_52_17
% 179.15/28.86    (92)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.15/28.86    (93)   ~ (all_52_25 = all_4_2)
% 179.15/28.86    (94)  op(e3, e0) = all_52_7
% 179.15/28.86    (95)  op(e3, e3) = all_4_2
% 179.15/28.86    (96)  all_56_8 = all_52_17
% 179.15/28.86    (97)   ~ (all_52_17 = all_4_2)
% 179.15/28.86    (98)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.15/28.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.15/28.86    (99)   ~ (all_52_25 = all_52_27)
% 179.15/28.86    (100)  op(e0, all_52_23) = e0
% 179.15/28.86    (101)   ~ (all_52_19 = all_52_27)
% 179.15/28.86    (102)  all_56_7 = all_52_15
% 179.15/28.86    (103)  op(e1, all_14_2) = e1
% 179.15/28.86    (104)   ~ (all_52_7 = all_52_23)
% 179.15/28.86    (105)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.86    (106)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.15/28.86    (107)  all_58_9 = all_52_7
% 179.15/28.86    (108)   ~ (e2 = e0)
% 179.15/28.86    (109)  all_58_12 = all_52_25
% 179.15/28.86    (110)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.15/28.86    (111)   ~ (all_52_9 = all_52_15)
% 179.15/28.86    (112)   ~ (e3 = e2)
% 179.15/28.86    (113)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 179.15/28.86    (114)   ~ (all_52_19 = all_14_2)
% 179.15/28.86    (115)  op(e2, e3) = all_52_9
% 179.15/28.86    (116)  all_56_13 = all_52_27
% 179.15/28.86  
% 179.15/28.86  Begin of proof
% 179.15/28.86  | 
% 179.15/28.86  | GROUND_INST: instantiating (98) with e1, all_14_0, all_14_2, e1, simplifying
% 179.15/28.86  |              with (57), (103) gives:
% 179.15/28.86  |   (117)  all_14_0 = e1
% 179.15/28.86  | 
% 179.15/28.86  | REDUCE: (49), (117) imply:
% 179.15/28.86  |   (118)   ~ (e3 = e1)
% 179.15/28.86  | 
% 179.15/28.86  | SIMP: (118) implies:
% 179.15/28.86  |   (119)   ~ (e3 = e1)
% 179.15/28.86  | 
% 179.15/28.86  | REDUCE: (71), (117) imply:
% 179.15/28.86  |   (120)   ~ (e2 = e1)
% 179.15/28.86  | 
% 179.15/28.86  | SIMP: (120) implies:
% 179.15/28.86  |   (121)   ~ (e2 = e1)
% 179.15/28.86  | 
% 179.15/28.86  | BETA: splitting (42) gives:
% 179.15/28.86  | 
% 179.15/28.86  | Case 1:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (122)  all_56_13 = e3
% 179.15/28.86  | | 
% 179.15/28.86  | | COMBINE_EQS: (116), (122) imply:
% 179.15/28.86  | |   (123)  all_52_27 = e3
% 179.15/28.86  | | 
% 179.15/28.86  | | SIMP: (123) implies:
% 179.15/28.86  | |   (124)  all_52_27 = e3
% 179.15/28.86  | | 
% 179.15/28.86  | | REDUCE: (101), (124) imply:
% 179.15/28.86  | |   (125)   ~ (all_52_19 = e3)
% 179.15/28.86  | | 
% 179.15/28.86  | | REDUCE: (99), (124) imply:
% 179.15/28.86  | |   (126)   ~ (all_52_25 = e3)
% 179.15/28.86  | | 
% 179.15/28.86  | | REF_CLOSE: (6), (10), (11), (16), (18), (22), (23), (25), (28), (31), (32),
% 179.15/28.86  | |            (34), (37), (44), (46), (47), (52), (54), (56), (58), (60), (61),
% 179.15/28.86  | |            (65), (69), (70), (72), (74), (75), (76), (78), (82), (83), (84),
% 179.15/28.86  | |            (85), (86), (87), (90), (91), (92), (95), (97), (98), (100),
% 179.15/28.86  | |            (102), (103), (104), (105), (106), (107), (109), (110), (111),
% 179.15/28.86  | |            (112), (115), (119), (125), (126) are inconsistent by sub-proof
% 179.15/28.86  | |            #932.
% 179.15/28.86  | | 
% 179.15/28.86  | Case 2:
% 179.15/28.86  | | 
% 179.15/28.86  | |   (127)   ~ (all_56_13 = e3)
% 179.15/28.86  | | 
% 179.15/28.86  | | REDUCE: (116), (127) imply:
% 179.15/28.86  | |   (128)   ~ (all_52_27 = e3)
% 179.15/28.86  | | 
% 179.15/28.86  | | BETA: splitting (45) gives:
% 179.15/28.86  | | 
% 179.15/28.86  | | Case 1:
% 179.15/28.86  | | | 
% 179.15/28.86  | | |   (129)  all_58_12 = e3
% 179.15/28.86  | | | 
% 179.15/28.86  | | | COMBINE_EQS: (109), (129) imply:
% 179.15/28.86  | | |   (130)  all_52_25 = e3
% 179.15/28.86  | | | 
% 179.15/28.86  | | | SIMP: (130) implies:
% 179.15/28.86  | | |   (131)  all_52_25 = e3
% 179.15/28.86  | | | 
% 179.15/28.86  | | | REDUCE: (24), (131) imply:
% 179.15/28.86  | | |   (132)   ~ (all_52_17 = e3)
% 179.15/28.86  | | | 
% 179.15/28.86  | | | REDUCE: (15), (131) imply:
% 179.15/28.86  | | |   (133)   ~ (all_52_29 = e3)
% 179.15/28.86  | | | 
% 179.15/28.86  | | | SIMP: (133) implies:
% 179.15/28.86  | | |   (134)   ~ (all_52_29 = e3)
% 179.15/28.86  | | | 
% 179.15/28.86  | | | REDUCE: (54), (131) imply:
% 179.15/28.86  | | |   (135)  op(e0, e3) = e3
% 179.15/28.86  | | | 
% 179.15/28.86  | | | BETA: splitting (92) gives:
% 179.15/28.86  | | | 
% 179.15/28.86  | | | Case 1:
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | |   (136)  all_56_7 = e3
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | REF_CLOSE: (10), (11), (16), (22), (25), (47), (56), (61), (76), (78),
% 179.15/28.86  | | | |            (82), (85), (86), (98), (100), (102), (108), (112), (119),
% 179.15/28.86  | | | |            (121), (136) are inconsistent by sub-proof #933.
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | Case 2:
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | |   (137)   ~ (all_56_7 = e3)
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | REDUCE: (102), (137) imply:
% 179.15/28.86  | | | |   (138)   ~ (all_52_15 = e3)
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | BETA: splitting (105) gives:
% 179.15/28.86  | | | | 
% 179.15/28.86  | | | | Case 1:
% 179.15/28.86  | | | | | 
% 179.15/28.86  | | | | |   (139)  all_58_9 = e3
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | | COMBINE_EQS: (107), (139) imply:
% 179.15/28.87  | | | | |   (140)  all_52_7 = e3
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | | SIMP: (140) implies:
% 179.15/28.87  | | | | |   (141)  all_52_7 = e3
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | | REDUCE: (21), (141) imply:
% 179.15/28.87  | | | | |   (142)   ~ (all_52_5 = e3)
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | | REDUCE: (104), (141) imply:
% 179.15/28.87  | | | | |   (143)   ~ (all_52_23 = e3)
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | | SIMP: (143) implies:
% 179.15/28.87  | | | | |   (144)   ~ (all_52_23 = e3)
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | | REF_CLOSE: (1), (3), (23), (25), (26), (27), (28), (30), (33), (34),
% 179.15/28.87  | | | | |            (38), (39), (43), (46), (48), (50), (51), (52), (58), (62),
% 179.15/28.87  | | | | |            (63), (64), (67), (72), (74), (75), (76), (78), (80), (83),
% 179.15/28.87  | | | | |            (87), (88), (91), (98), (103), (108), (112), (113), (114),
% 179.15/28.87  | | | | |            (115), (119), (121), (129), (132), (134), (139), (142),
% 179.15/28.87  | | | | |            (144) are inconsistent by sub-proof #917.
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | Case 2:
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | |   (145)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | | REF_CLOSE: (12), (22), (58), (78), (82), (98), (100), (135), (138),
% 179.15/28.87  | | | | |            (145) are inconsistent by sub-proof #914.
% 179.15/28.87  | | | | | 
% 179.15/28.87  | | | | End of split
% 179.15/28.87  | | | | 
% 179.15/28.87  | | | End of split
% 179.15/28.87  | | | 
% 179.15/28.87  | | Case 2:
% 179.15/28.87  | | | 
% 179.15/28.87  | | |   (146)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.15/28.87  | | | 
% 179.15/28.87  | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 179.15/28.87  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (28),
% 179.15/28.87  | | |            (29), (31), (32), (33), (34), (35), (37), (40), (41), (44),
% 179.15/28.87  | | |            (46), (47), (52), (53), (54), (55), (56), (58), (59), (60),
% 179.15/28.87  | | |            (61), (63), (65), (66), (67), (68), (69), (70), (72), (73),
% 179.15/28.87  | | |            (74), (75), (76), (77), (78), (79), (81), (82), (83), (84),
% 179.15/28.87  | | |            (85), (86), (87), (89), (90), (91), (92), (93), (94), (95),
% 179.15/28.87  | | |            (96), (97), (98), (100), (101), (102), (103), (104), (105),
% 179.15/28.87  | | |            (107), (108), (109), (111), (112), (115), (119), (121), (128),
% 179.15/28.87  | | |            (146) are inconsistent by sub-proof #898.
% 179.15/28.87  | | | 
% 179.15/28.87  | | End of split
% 179.15/28.87  | | 
% 179.15/28.87  | End of split
% 179.15/28.87  | 
% 179.15/28.87  End of proof
% 179.15/28.87  
% 179.15/28.87  Sub-proof #898 shows that the following formulas are inconsistent:
% 179.15/28.87  ----------------------------------------------------------------
% 179.15/28.87    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.15/28.87    (2)   ~ (all_52_17 = all_52_23)
% 179.22/28.87    (3)   ~ (all_52_13 = all_52_29)
% 179.22/28.87    (4)  op(e3, e2) = all_52_3
% 179.22/28.87    (5)   ~ (all_52_9 = all_52_25)
% 179.22/28.87    (6)   ~ (all_52_19 = all_52_23)
% 179.22/28.87    (7)  all_56_11 = all_52_23
% 179.22/28.87    (8)   ~ (all_52_27 = e0)
% 179.22/28.87    (9)   ~ (all_52_27 = e3)
% 179.22/28.87    (10)   ~ (all_52_3 = all_10_2)
% 179.22/28.87    (11)  all_58_5 = all_52_13
% 179.22/28.87    (12)   ~ (all_52_25 = all_52_29)
% 179.22/28.87    (13)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.22/28.87    (14)  all_58_3 = all_10_2
% 179.22/28.87    (15)  all_56_9 = all_52_19
% 179.22/28.87    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.22/28.87    (17)   ~ (all_52_9 = all_4_2)
% 179.22/28.87    (18)  all_58_10 = all_52_15
% 179.22/28.87    (19)  all_58_7 = all_52_19
% 179.22/28.87    (20)   ~ (all_52_17 = all_52_25)
% 179.22/28.87    (21)  op(e0, e1) = all_52_29
% 179.22/28.87    (22)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.87    (23)   ~ (e3 = e1)
% 179.22/28.87    (24)   ~ (all_52_27 = all_52_29)
% 179.22/28.87    (25)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.22/28.87    (26)   ~ (all_52_7 = all_4_2)
% 179.22/28.87    (27)  all_58_1 = all_52_3
% 179.22/28.87    (28)  all_58_0 = all_4_2
% 179.22/28.87    (29)  op(e1, all_52_29) = all_52_28
% 179.22/28.87    (30)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.22/28.87    (31)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.22/28.87    (32)  all_58_14 = all_52_29
% 179.22/28.87    (33)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.87    (34)  all_58_8 = all_14_2
% 179.22/28.87    (35)  op(e0, e2) = all_52_27
% 179.22/28.87    (36)   ~ (all_52_5 = all_14_2)
% 179.22/28.87    (37)   ~ (all_52_3 = all_4_2)
% 179.22/28.87    (38)  op(e0, e3) = all_52_25
% 179.22/28.87    (39)   ~ (all_52_9 = all_10_2)
% 179.22/28.87    (40)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.22/28.87    (41)   ~ (e3 = e0)
% 179.22/28.87    (42)  all_58_0 = e0 | all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.22/28.87    (43)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.22/28.87    (44)   ~ (all_52_15 = all_52_23)
% 179.22/28.87    (45)   ~ (all_52_5 = all_52_29)
% 179.22/28.87    (46)  all_56_12 = all_52_25
% 179.22/28.87    (47)  all_58_13 = all_52_27
% 179.22/28.87    (48)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.22/28.87    (49)  all_56_5 = all_10_2
% 179.22/28.87    (50)   ~ (all_52_25 = e0)
% 179.22/28.87    (51)   ~ (all_52_9 = all_52_17)
% 179.22/28.87    (52)  all_58_6 = all_52_17
% 179.22/28.87    (53)   ~ (all_52_3 = all_52_7)
% 179.22/28.87    (54)  op(e2, all_52_19) = e2
% 179.22/28.87    (55)  op(e3, all_52_17) = e3
% 179.22/28.87    (56)   ~ (e1 = e0)
% 179.22/28.87    (57)  all_56_0 = all_4_2
% 179.22/28.87    (58)  all_58_11 = all_52_23
% 179.22/28.87    (59)   ~ (all_52_29 = all_14_2)
% 179.22/28.87    (60)   ~ (all_52_19 = all_10_2)
% 179.22/28.87    (61)  all_58_15 = e0
% 179.22/28.87    (62)  all_58_2 = all_52_9
% 179.22/28.87    (63)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.22/28.87    (64)   ~ (all_52_29 = e0)
% 179.22/28.87    (65)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.22/28.87    (66)  op(e3, e1) = all_52_5
% 179.22/28.87    (67)   ~ (e2 = e1)
% 179.22/28.87    (68)  all_56_5 = e3 | all_56_5 = e2 | all_56_5 = e1 | all_56_5 = e0
% 179.22/28.87    (69)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.22/28.87    (70)  op(e1, e3) = all_52_17
% 179.22/28.87    (71)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.22/28.87    (72)   ~ (all_52_25 = all_4_2)
% 179.22/28.87    (73)  op(e3, e0) = all_52_7
% 179.22/28.87    (74)  op(e3, e3) = all_4_2
% 179.22/28.87    (75)  all_56_8 = all_52_17
% 179.22/28.87    (76)   ~ (all_52_17 = all_4_2)
% 179.22/28.87    (77)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.87    (78)  op(e0, all_52_23) = e0
% 179.22/28.87    (79)   ~ (all_52_19 = all_52_27)
% 179.22/28.87    (80)  all_56_7 = all_52_15
% 179.22/28.87    (81)  op(e1, all_14_2) = e1
% 179.22/28.87    (82)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.22/28.87    (83)   ~ (all_52_7 = all_52_23)
% 179.22/28.87    (84)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.87    (85)  all_58_9 = all_52_7
% 179.22/28.87    (86)   ~ (e2 = e0)
% 179.22/28.87    (87)  all_58_12 = all_52_25
% 179.22/28.87    (88)   ~ (all_52_9 = all_52_15)
% 179.22/28.87    (89)   ~ (e3 = e2)
% 179.22/28.87    (90)  op(e2, e3) = all_52_9
% 179.22/28.87  
% 179.22/28.87  Begin of proof
% 179.22/28.87  | 
% 179.22/28.87  | BETA: splitting (82) gives:
% 179.22/28.87  | 
% 179.22/28.87  | Case 1:
% 179.22/28.87  | | 
% 179.22/28.87  | |   (91)  all_58_13 = e3
% 179.22/28.87  | | 
% 179.22/28.87  | | REF_CLOSE: (9), (47), (91) are inconsistent by sub-proof #1026.
% 179.22/28.87  | | 
% 179.22/28.87  | Case 2:
% 179.22/28.87  | | 
% 179.22/28.87  | |   (92)  all_58_14 = e3 | all_58_15 = e3
% 179.22/28.87  | | 
% 179.22/28.87  | | BETA: splitting (92) gives:
% 179.22/28.87  | | 
% 179.22/28.87  | | Case 1:
% 179.22/28.87  | | | 
% 179.22/28.87  | | |   (93)  all_58_14 = e3
% 179.22/28.87  | | | 
% 179.22/28.87  | | | COMBINE_EQS: (32), (93) imply:
% 179.22/28.87  | | |   (94)  all_52_29 = e3
% 179.22/28.87  | | | 
% 179.22/28.87  | | | SIMP: (94) implies:
% 179.22/28.87  | | |   (95)  all_52_29 = e3
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (45), (95) imply:
% 179.22/28.87  | | |   (96)   ~ (all_52_5 = e3)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (3), (95) imply:
% 179.22/28.87  | | |   (97)   ~ (all_52_13 = e3)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (12), (95) imply:
% 179.22/28.87  | | |   (98)   ~ (all_52_25 = e3)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (59), (95) imply:
% 179.22/28.87  | | |   (99)   ~ (all_14_2 = e3)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | SIMP: (99) implies:
% 179.22/28.87  | | |   (100)   ~ (all_14_2 = e3)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (29), (95) imply:
% 179.22/28.87  | | |   (101)  op(e1, e3) = all_52_28
% 179.22/28.87  | | | 
% 179.22/28.87  | | | GROUND_INST: instantiating (77) with all_52_17, all_52_28, e3, e1,
% 179.22/28.87  | | |              simplifying with (70), (101) gives:
% 179.22/28.87  | | |   (102)  all_52_17 = all_52_28
% 179.22/28.87  | | | 
% 179.22/28.87  | | | COMBINE_EQS: (75), (102) imply:
% 179.22/28.87  | | |   (103)  all_56_8 = all_52_28
% 179.22/28.87  | | | 
% 179.22/28.87  | | | COMBINE_EQS: (52), (102) imply:
% 179.22/28.87  | | |   (104)  all_58_6 = all_52_28
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (51), (102) imply:
% 179.22/28.87  | | |   (105)   ~ (all_52_9 = all_52_28)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (2), (102) imply:
% 179.22/28.87  | | |   (106)   ~ (all_52_23 = all_52_28)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | SIMP: (106) implies:
% 179.22/28.87  | | |   (107)   ~ (all_52_23 = all_52_28)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (20), (102) imply:
% 179.22/28.87  | | |   (108)   ~ (all_52_25 = all_52_28)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | SIMP: (108) implies:
% 179.22/28.87  | | |   (109)   ~ (all_52_25 = all_52_28)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (76), (102) imply:
% 179.22/28.87  | | |   (110)   ~ (all_52_28 = all_4_2)
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REDUCE: (55), (102) imply:
% 179.22/28.87  | | |   (111)  op(e3, all_52_28) = e3
% 179.22/28.87  | | | 
% 179.22/28.87  | | | BETA: splitting (43) gives:
% 179.22/28.87  | | | 
% 179.22/28.87  | | | Case 1:
% 179.22/28.87  | | | | 
% 179.22/28.87  | | | |   (112)  all_56_12 = e3
% 179.22/28.87  | | | | 
% 179.22/28.87  | | | | REF_CLOSE: (46), (98), (112) are inconsistent by sub-proof #1040.
% 179.22/28.87  | | | | 
% 179.22/28.87  | | | Case 2:
% 179.22/28.87  | | | | 
% 179.22/28.87  | | | |   (113)   ~ (all_56_12 = e3)
% 179.22/28.87  | | | |   (114)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.22/28.87  | | | | 
% 179.22/28.87  | | | | BETA: splitting (63) gives:
% 179.22/28.87  | | | | 
% 179.22/28.87  | | | | Case 1:
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | |   (115)  all_58_12 = e1
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | COMBINE_EQS: (87), (115) imply:
% 179.22/28.87  | | | | |   (116)  all_52_25 = e1
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | SIMP: (116) implies:
% 179.22/28.87  | | | | |   (117)  all_52_25 = e1
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | REDUCE: (38), (117) imply:
% 179.22/28.87  | | | | |   (118)  op(e0, e3) = e1
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | BETA: splitting (69) gives:
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | Case 1:
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | |   (119)  all_58_12 = e2
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | COMBINE_EQS: (115), (119) imply:
% 179.22/28.87  | | | | | |   (120)  e2 = e1
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | REDUCE: (67), (120) imply:
% 179.22/28.87  | | | | | |   (121)  $false
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | CLOSE: (121) is inconsistent.
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | Case 2:
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | |   (122)  all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | BETA: splitting (122) gives:
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | Case 1:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | |   (123)  all_58_13 = e2
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | COMBINE_EQS: (47), (123) imply:
% 179.22/28.87  | | | | | | |   (124)  all_52_27 = e2
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | SIMP: (124) implies:
% 179.22/28.87  | | | | | | |   (125)  all_52_27 = e2
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | REDUCE: (79), (125) imply:
% 179.22/28.87  | | | | | | |   (126)   ~ (all_52_19 = e2)
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | REDUCE: (9), (125) imply:
% 179.22/28.87  | | | | | | |   (127)   ~ (e3 = e2)
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | BETA: splitting (68) gives:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (128)  all_56_5 = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | COMBINE_EQS: (49), (128) imply:
% 179.22/28.87  | | | | | | | |   (129)  all_10_2 = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | SIMP: (129) implies:
% 179.22/28.87  | | | | | | | |   (130)  all_10_2 = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REDUCE: (10), (130) imply:
% 179.22/28.87  | | | | | | | |   (131)   ~ (all_52_3 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REDUCE: (39), (130) imply:
% 179.22/28.87  | | | | | | | |   (132)   ~ (all_52_9 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REDUCE: (60), (130) imply:
% 179.22/28.87  | | | | | | | |   (133)   ~ (all_52_19 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REF_CLOSE: (1), (4), (19), (22), (28), (33), (34), (38), (52),
% 179.22/28.87  | | | | | | | |            (55), (58), (62), (66), (74), (76), (77), (78), (87),
% 179.22/28.87  | | | | | | | |            (96), (100), (103), (104), (107), (109), (110),
% 179.22/28.87  | | | | | | | |            (111), (131), (132), (133) are inconsistent by
% 179.22/28.87  | | | | | | | |            sub-proof #910.
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (134)   ~ (all_56_5 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REDUCE: (49), (134) imply:
% 179.22/28.87  | | | | | | | |   (135)   ~ (all_10_2 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | BETA: splitting (31) gives:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | |   (136)  all_58_1 = e3
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | COMBINE_EQS: (27), (136) imply:
% 179.22/28.87  | | | | | | | | |   (137)  all_52_3 = e3
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | REDUCE: (53), (137) imply:
% 179.22/28.87  | | | | | | | | |   (138)   ~ (all_52_7 = e3)
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | SIMP: (138) implies:
% 179.22/28.87  | | | | | | | | |   (139)   ~ (all_52_7 = e3)
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | REDUCE: (37), (137) imply:
% 179.22/28.87  | | | | | | | | |   (140)   ~ (all_4_2 = e3)
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | SIMP: (140) implies:
% 179.22/28.87  | | | | | | | | |   (141)   ~ (all_4_2 = e3)
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | REF_CLOSE: (18), (28), (33), (41), (52), (55), (56), (58),
% 179.22/28.87  | | | | | | | | |            (61), (62), (74), (76), (77), (78), (84), (85),
% 179.22/28.87  | | | | | | | | |            (87), (88), (98), (118), (139), (141) are
% 179.22/28.87  | | | | | | | | |            inconsistent by sub-proof #940.
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | |   (142)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | BETA: splitting (142) gives:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | |   (143)  all_58_3 = e3
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | COMBINE_EQS: (14), (143) imply:
% 179.22/28.87  | | | | | | | | | |   (144)  all_10_2 = e3
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | REDUCE: (135), (144) imply:
% 179.22/28.87  | | | | | | | | | |   (145)  $false
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | CLOSE: (145) is inconsistent.
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | |   (146)  all_58_7 = e3 | all_58_13 = e3
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | BETA: splitting (146) gives:
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | |   (147)  all_58_7 = e3
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | COMBINE_EQS: (19), (147) imply:
% 179.22/28.87  | | | | | | | | | | |   (148)  all_52_19 = e3
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | REDUCE: (6), (148) imply:
% 179.22/28.87  | | | | | | | | | | |   (149)   ~ (all_52_23 = e3)
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | SIMP: (149) implies:
% 179.22/28.87  | | | | | | | | | | |   (150)   ~ (all_52_23 = e3)
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | REDUCE: (54), (148) imply:
% 179.22/28.87  | | | | | | | | | | |   (151)  op(e2, e3) = e2
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | GROUND_INST: instantiating (77) with all_52_9, e2, e3, e2,
% 179.22/28.87  | | | | | | | | | | |              simplifying with (90), (151) gives:
% 179.22/28.87  | | | | | | | | | | |   (152)  all_52_9 = e2
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | COMBINE_EQS: (62), (152) imply:
% 179.22/28.87  | | | | | | | | | | |   (153)  all_58_2 = e2
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | BETA: splitting (33) gives:
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | |   (154)  all_58_0 = e3
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | COMBINE_EQS: (28), (154) imply:
% 179.22/28.87  | | | | | | | | | | | |   (155)  all_4_2 = e3
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | REDUCE: (26), (155) imply:
% 179.22/28.87  | | | | | | | | | | | |   (156)   ~ (all_52_7 = e3)
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | BETA: splitting (42) gives:
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | |   (157)  all_58_0 = e0
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | COMBINE_EQS: (154), (157) imply:
% 179.22/28.87  | | | | | | | | | | | | |   (158)  e3 = e0
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | REDUCE: (41), (158) imply:
% 179.22/28.87  | | | | | | | | | | | | |   (159)  $false
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | |   (160)  all_58_2 = e0 | all_58_6 = e0 | all_58_12 = e0
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | BETA: splitting (160) gives:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | |   (161)  all_58_2 = e0
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REF_CLOSE: (86), (153), (161) are inconsistent by sub-proof
% 179.22/28.87  | | | | | | | | | | | | | |            #909.
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | |   (162)  all_58_6 = e0 | all_58_12 = e0
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | |   (163)  all_58_6 = e0
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | | COMBINE_EQS: (104), (163) imply:
% 179.22/28.87  | | | | | | | | | | | | | | |   (164)  all_52_28 = e0
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | | SIMP: (164) implies:
% 179.22/28.87  | | | | | | | | | | | | | | |   (165)  all_52_28 = e0
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | | REDUCE: (111), (165) imply:
% 179.22/28.87  | | | | | | | | | | | | | | |   (166)  op(e3, e0) = e3
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | | REF_CLOSE: (73), (77), (156), (166) are inconsistent by
% 179.22/28.87  | | | | | | | | | | | | | | |            sub-proof #908.
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | |   (167)  all_58_12 = e0
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | | REF_CLOSE: (56), (115), (167) are inconsistent by sub-proof
% 179.22/28.87  | | | | | | | | | | | | | | |            #907.
% 179.22/28.87  | | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | |   (168)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | REF_CLOSE: (15), (19), (22), (25), (30), (34), (36), (51),
% 179.22/28.87  | | | | | | | | | | | |            (52), (54), (55), (58), (62), (66), (70), (74),
% 179.22/28.87  | | | | | | | | | | | |            (76), (77), (81), (87), (89), (90), (98), (150),
% 179.22/28.87  | | | | | | | | | | | |            (168) are inconsistent by sub-proof #945.
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | |   (169)  all_58_13 = e3
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | REF_CLOSE: (89), (123), (169) are inconsistent by sub-proof
% 179.22/28.87  | | | | | | | | | | |            #906.
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | End of split
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | Case 2:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | |   (170)  all_58_14 = e2 | all_58_15 = e2
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | BETA: splitting (170) gives:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (171)  all_58_14 = e2
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REF_CLOSE: (89), (93), (171) are inconsistent by sub-proof #905.
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (172)  all_58_15 = e2
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REF_CLOSE: (61), (86), (172) are inconsistent by sub-proof #991.
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | End of split
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | End of split
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | End of split
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | Case 2:
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | |   (173)   ~ (all_58_12 = e1)
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | REDUCE: (87), (173) imply:
% 179.22/28.87  | | | | |   (174)   ~ (all_52_25 = e1)
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | BETA: splitting (114) gives:
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | | Case 1:
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | |   (175)  all_56_12 = e2
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | COMBINE_EQS: (46), (175) imply:
% 179.22/28.87  | | | | | |   (176)  all_52_25 = e2
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | SIMP: (176) implies:
% 179.22/28.87  | | | | | |   (177)  all_52_25 = e2
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | REDUCE: (5), (177) imply:
% 179.22/28.87  | | | | | |   (178)   ~ (all_52_9 = e2)
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | REDUCE: (109), (177) imply:
% 179.22/28.87  | | | | | |   (179)   ~ (all_52_28 = e2)
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | SIMP: (179) implies:
% 179.22/28.87  | | | | | |   (180)   ~ (all_52_28 = e2)
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | REDUCE: (72), (177) imply:
% 179.22/28.87  | | | | | |   (181)   ~ (all_4_2 = e2)
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | SIMP: (181) implies:
% 179.22/28.87  | | | | | |   (182)   ~ (all_4_2 = e2)
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | REDUCE: (98), (177) imply:
% 179.22/28.87  | | | | | |   (183)   ~ (e3 = e2)
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | REDUCE: (38), (177) imply:
% 179.22/28.87  | | | | | |   (184)  op(e0, e3) = e2
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | BETA: splitting (71) gives:
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | Case 1:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | |   (185)  all_56_7 = e3
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | COMBINE_EQS: (80), (185) imply:
% 179.22/28.87  | | | | | | |   (186)  all_52_15 = e3
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | COMBINE_EQS: (18), (186) imply:
% 179.22/28.87  | | | | | | |   (187)  all_58_10 = e3
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | REDUCE: (44), (186) imply:
% 179.22/28.87  | | | | | | |   (188)   ~ (all_52_23 = e3)
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | SIMP: (188) implies:
% 179.22/28.87  | | | | | | |   (189)   ~ (all_52_23 = e3)
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | BETA: splitting (65) gives:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (190)  all_56_11 = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REF_CLOSE: (7), (189), (190) are inconsistent by sub-proof #939.
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (191)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REF_CLOSE: (7), (8), (13), (21), (23), (35), (40), (56), (58),
% 179.22/28.87  | | | | | | | |            (61), (64), (67), (77), (78), (86), (89), (187),
% 179.22/28.87  | | | | | | | |            (191) are inconsistent by sub-proof #934.
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | End of split
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | Case 2:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | |   (192)   ~ (all_56_7 = e3)
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | REDUCE: (80), (192) imply:
% 179.22/28.87  | | | | | | |   (193)   ~ (all_52_15 = e3)
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | BETA: splitting (25) gives:
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (194)  all_58_2 = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | COMBINE_EQS: (62), (194) imply:
% 179.22/28.87  | | | | | | | |   (195)  all_52_9 = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REDUCE: (105), (195) imply:
% 179.22/28.87  | | | | | | | |   (196)   ~ (all_52_28 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | SIMP: (196) implies:
% 179.22/28.87  | | | | | | | |   (197)   ~ (all_52_28 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REDUCE: (17), (195) imply:
% 179.22/28.87  | | | | | | | |   (198)   ~ (all_4_2 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | SIMP: (198) implies:
% 179.22/28.87  | | | | | | | |   (199)   ~ (all_4_2 = e3)
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | REDUCE: (90), (195) imply:
% 179.22/28.87  | | | | | | | |   (200)  op(e2, e3) = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | BETA: splitting (16) gives:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | |   (201)  all_56_0 = e3
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | REF_CLOSE: (57), (199), (201) are inconsistent by sub-proof
% 179.22/28.87  | | | | | | | | |            #1024.
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | |   (202)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | BETA: splitting (1) gives:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | |   (203)  all_56_8 = e3
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | COMBINE_EQS: (103), (203) imply:
% 179.22/28.87  | | | | | | | | | |   (204)  all_52_28 = e3
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | REDUCE: (197), (204) imply:
% 179.22/28.87  | | | | | | | | | |   (205)  $false
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | CLOSE: (205) is inconsistent.
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | |   (206)   ~ (all_56_8 = e3)
% 179.22/28.87  | | | | | | | | | |   (207)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | BETA: splitting (22) gives:
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | |   (208)  all_58_6 = e3
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | COMBINE_EQS: (104), (208) imply:
% 179.22/28.87  | | | | | | | | | | |   (209)  all_52_28 = e3
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | REDUCE: (197), (209) imply:
% 179.22/28.87  | | | | | | | | | | |   (210)  $false
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | |   (211)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | BETA: splitting (48) gives:
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | |   (212)  all_58_0 = e1
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | COMBINE_EQS: (28), (212) imply:
% 179.22/28.87  | | | | | | | | | | | |   (213)  all_4_2 = e1
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | REDUCE: (110), (213) imply:
% 179.22/28.87  | | | | | | | | | | | |   (214)   ~ (all_52_28 = e1)
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | BETA: splitting (207) gives:
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | |   (215)  all_56_8 = e2
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | COMBINE_EQS: (103), (215) imply:
% 179.22/28.87  | | | | | | | | | | | | |   (216)  all_52_28 = e2
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | REDUCE: (180), (216) imply:
% 179.22/28.87  | | | | | | | | | | | | |   (217)  $false
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | CLOSE: (217) is inconsistent.
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | |   (218)  all_56_8 = e1 | all_56_8 = e0
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | BETA: splitting (218) gives:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | |   (219)  all_56_8 = e1
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | COMBINE_EQS: (103), (219) imply:
% 179.22/28.87  | | | | | | | | | | | | | |   (220)  all_52_28 = e1
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REDUCE: (214), (220) imply:
% 179.22/28.87  | | | | | | | | | | | | | |   (221)  $false
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | |   (222)  all_56_8 = e0
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | COMBINE_EQS: (103), (222) imply:
% 179.22/28.87  | | | | | | | | | | | | | |   (223)  all_52_28 = e0
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REDUCE: (111), (223) imply:
% 179.22/28.87  | | | | | | | | | | | | | |   (224)  op(e3, e0) = e3
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | GROUND_INST: instantiating (77) with all_52_7, e3, e0, e3,
% 179.22/28.87  | | | | | | | | | | | | | |              simplifying with (73), (224) gives:
% 179.22/28.87  | | | | | | | | | | | | | |   (225)  all_52_7 = e3
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REDUCE: (83), (225) imply:
% 179.22/28.87  | | | | | | | | | | | | | |   (226)   ~ (all_52_23 = e3)
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | SIMP: (226) implies:
% 179.22/28.87  | | | | | | | | | | | | | |   (227)   ~ (all_52_23 = e3)
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REF_CLOSE: (15), (19), (30), (34), (36), (54), (55), (58),
% 179.22/28.87  | | | | | | | | | | | | | |            (66), (70), (77), (81), (89), (200), (211), (227)
% 179.22/28.87  | | | | | | | | | | | | | |            are inconsistent by sub-proof #949.
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | |   (228)   ~ (all_58_0 = e1)
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | REDUCE: (28), (228) imply:
% 179.22/28.87  | | | | | | | | | | | |   (229)   ~ (all_4_2 = e1)
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | BETA: splitting (202) gives:
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | |   (230)  all_56_0 = e2
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | REF_CLOSE: (57), (182), (230) are inconsistent by sub-proof
% 179.22/28.87  | | | | | | | | | | | | |            #904.
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | |   (231)  all_56_0 = e1 | all_56_0 = e0
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | BETA: splitting (231) gives:
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | |   (232)  all_56_0 = e1
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REF_CLOSE: (57), (229), (232) are inconsistent by sub-proof
% 179.22/28.87  | | | | | | | | | | | | | |            #1022.
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | |   (233)  all_56_0 = e0
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | COMBINE_EQS: (57), (233) imply:
% 179.22/28.87  | | | | | | | | | | | | | |   (234)  all_4_2 = e0
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | SIMP: (234) implies:
% 179.22/28.87  | | | | | | | | | | | | | |   (235)  all_4_2 = e0
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REDUCE: (110), (235) imply:
% 179.22/28.87  | | | | | | | | | | | | | |   (236)   ~ (all_52_28 = e0)
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | | REF_CLOSE: (66), (77), (96), (103), (111), (180), (207),
% 179.22/28.87  | | | | | | | | | | | | | |            (236) are inconsistent by sub-proof #903.
% 179.22/28.87  | | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | |   (237)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | BETA: splitting (237) gives:
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | | Case 1:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | |   (238)  all_58_3 = e3
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | COMBINE_EQS: (14), (238) imply:
% 179.22/28.87  | | | | | | | | |   (239)  all_10_2 = e3
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | REDUCE: (60), (239) imply:
% 179.22/28.87  | | | | | | | | |   (240)   ~ (all_52_19 = e3)
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | REF_CLOSE: (19), (22), (34), (58), (74), (77), (78), (86),
% 179.22/28.87  | | | | | | | | |            (100), (104), (110), (111), (184), (240) are
% 179.22/28.87  | | | | | | | | |            inconsistent by sub-proof #899.
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | Case 2:
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | |   (241)  all_58_5 = e3 | all_58_10 = e3
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | | REF_CLOSE: (11), (18), (97), (193), (241) are inconsistent by
% 179.22/28.87  | | | | | | | | |            sub-proof #958.
% 179.22/28.87  | | | | | | | | | 
% 179.22/28.87  | | | | | | | | End of split
% 179.22/28.87  | | | | | | | | 
% 179.22/28.87  | | | | | | | End of split
% 179.22/28.87  | | | | | | | 
% 179.22/28.87  | | | | | | End of split
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | Case 2:
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | |   (242)  all_56_12 = e1 | all_56_12 = e0
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | | REF_CLOSE: (46), (50), (174), (242) are inconsistent by sub-proof
% 179.22/28.87  | | | | | |            #1029.
% 179.22/28.87  | | | | | | 
% 179.22/28.87  | | | | | End of split
% 179.22/28.87  | | | | | 
% 179.22/28.87  | | | | End of split
% 179.22/28.87  | | | | 
% 179.22/28.87  | | | End of split
% 179.22/28.87  | | | 
% 179.22/28.87  | | Case 2:
% 179.22/28.87  | | | 
% 179.22/28.87  | | |   (243)  all_58_15 = e3
% 179.22/28.87  | | | 
% 179.22/28.87  | | | REF_CLOSE: (41), (61), (243) are inconsistent by sub-proof #1010.
% 179.22/28.87  | | | 
% 179.22/28.87  | | End of split
% 179.22/28.87  | | 
% 179.22/28.87  | End of split
% 179.22/28.87  | 
% 179.22/28.87  End of proof
% 179.22/28.87  
% 179.22/28.87  Sub-proof #899 shows that the following formulas are inconsistent:
% 179.22/28.87  ----------------------------------------------------------------
% 179.22/28.87    (1)  all_58_6 = all_52_28
% 179.22/28.87    (2)  op(e3, all_52_28) = e3
% 179.22/28.87    (3)   ~ (all_52_28 = all_4_2)
% 179.22/28.87    (4)  all_58_7 = all_52_19
% 179.22/28.87    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.87    (6)  all_58_8 = all_14_2
% 179.22/28.87    (7)  op(e0, e3) = e2
% 179.22/28.87    (8)  all_58_11 = all_52_23
% 179.22/28.87    (9)   ~ (all_52_19 = e3)
% 179.22/28.87    (10)  op(e3, e3) = all_4_2
% 179.22/28.87    (11)   ~ (all_14_2 = e3)
% 179.22/28.87    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.87    (13)  op(e0, all_52_23) = e0
% 179.22/28.87    (14)   ~ (e2 = e0)
% 179.22/28.87  
% 179.22/28.87  Begin of proof
% 179.22/28.87  | 
% 179.22/28.87  | BETA: splitting (5) gives:
% 179.22/28.87  | 
% 179.22/28.87  | Case 1:
% 179.22/28.87  | | 
% 179.22/28.87  | |   (15)  all_58_6 = e3
% 179.22/28.87  | | 
% 179.22/28.87  | | COMBINE_EQS: (1), (15) imply:
% 179.22/28.87  | |   (16)  all_52_28 = e3
% 179.22/28.87  | | 
% 179.22/28.87  | | REF_CLOSE: (2), (3), (10), (12), (16) are inconsistent by sub-proof #902.
% 179.22/28.87  | | 
% 179.22/28.87  | Case 2:
% 179.22/28.87  | | 
% 179.22/28.88  | |   (17)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (4), (6), (7), (8), (9), (11), (12), (13), (14), (17) are
% 179.22/28.88  | |            inconsistent by sub-proof #900.
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #900 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88    (2)  all_58_7 = all_52_19
% 179.22/28.88    (3)  all_58_8 = all_14_2
% 179.22/28.88    (4)  op(e0, e3) = e2
% 179.22/28.88    (5)  all_58_11 = all_52_23
% 179.22/28.88    (6)   ~ (all_52_19 = e3)
% 179.22/28.88    (7)   ~ (all_14_2 = e3)
% 179.22/28.88    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (9)  op(e0, all_52_23) = e0
% 179.22/28.88    (10)   ~ (e2 = e0)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (1) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (11)  all_58_7 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | COMBINE_EQS: (2), (11) imply:
% 179.22/28.88  | |   (12)  all_52_19 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REDUCE: (6), (12) imply:
% 179.22/28.88  | |   (13)  $false
% 179.22/28.88  | | 
% 179.22/28.88  | | CLOSE: (13) is inconsistent.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (14)  all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | BETA: splitting (14) gives:
% 179.22/28.88  | | 
% 179.22/28.88  | | Case 1:
% 179.22/28.88  | | | 
% 179.22/28.88  | | |   (15)  all_58_8 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | REF_CLOSE: (3), (7), (15) are inconsistent by sub-proof #901.
% 179.22/28.88  | | | 
% 179.22/28.88  | | Case 2:
% 179.22/28.88  | | | 
% 179.22/28.88  | | |   (16)  all_58_11 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | COMBINE_EQS: (5), (16) imply:
% 179.22/28.88  | | |   (17)  all_52_23 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | SIMP: (17) implies:
% 179.22/28.88  | | |   (18)  all_52_23 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | REDUCE: (9), (18) imply:
% 179.22/28.88  | | |   (19)  op(e0, e3) = e0
% 179.22/28.88  | | | 
% 179.22/28.88  | | | REF_CLOSE: (4), (8), (10), (19) are inconsistent by sub-proof #1035.
% 179.22/28.88  | | | 
% 179.22/28.88  | | End of split
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #901 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_58_8 = all_14_2
% 179.22/28.88    (2)  all_58_8 = e3
% 179.22/28.88    (3)   ~ (all_14_2 = e3)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.88  |   (4)  all_14_2 = e3
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (4) implies:
% 179.22/28.88  |   (5)  all_14_2 = e3
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (3), (5) imply:
% 179.22/28.88  |   (6)  $false
% 179.22/28.88  | 
% 179.22/28.88  | CLOSE: (6) is inconsistent.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #902 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  op(e3, all_52_28) = e3
% 179.22/28.88    (2)   ~ (all_52_28 = all_4_2)
% 179.22/28.88    (3)  all_52_28 = e3
% 179.22/28.88    (4)  op(e3, e3) = all_4_2
% 179.22/28.88    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (2), (3) imply:
% 179.22/28.88  |   (6)   ~ (all_4_2 = e3)
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (6) implies:
% 179.22/28.88  |   (7)   ~ (all_4_2 = e3)
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (1), (3) imply:
% 179.22/28.88  |   (8)  op(e3, e3) = e3
% 179.22/28.88  | 
% 179.22/28.88  | REF_CLOSE: (4), (5), (7), (8) are inconsistent by sub-proof #1006.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #903 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  op(e3, all_52_28) = e3
% 179.22/28.88    (2)  all_56_8 = all_52_28
% 179.22/28.88    (3)   ~ (all_52_28 = e0)
% 179.22/28.88    (4)   ~ (all_52_5 = e3)
% 179.22/28.88    (5)   ~ (all_52_28 = e2)
% 179.22/28.88    (6)  op(e3, e1) = all_52_5
% 179.22/28.88    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (8)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (8) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (9)  all_56_8 = e2
% 179.22/28.88  | | 
% 179.22/28.88  | | COMBINE_EQS: (2), (9) imply:
% 179.22/28.88  | |   (10)  all_52_28 = e2
% 179.22/28.88  | | 
% 179.22/28.88  | | SIMP: (10) implies:
% 179.22/28.88  | |   (11)  all_52_28 = e2
% 179.22/28.88  | | 
% 179.22/28.88  | | REDUCE: (5), (11) imply:
% 179.22/28.88  | |   (12)  $false
% 179.22/28.88  | | 
% 179.22/28.88  | | CLOSE: (12) is inconsistent.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (13)  all_56_8 = e1 | all_56_8 = e0
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (13) are inconsistent by sub-proof
% 179.22/28.88  | |            #911.
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #904 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_56_0 = all_4_2
% 179.22/28.88    (2)  all_56_0 = e2
% 179.22/28.88    (3)   ~ (all_4_2 = e2)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.88  |   (4)  all_4_2 = e2
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (4) implies:
% 179.22/28.88  |   (5)  all_4_2 = e2
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (3), (5) imply:
% 179.22/28.88  |   (6)  $false
% 179.22/28.88  | 
% 179.22/28.88  | CLOSE: (6) is inconsistent.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #905 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_58_14 = e3
% 179.22/28.88    (2)  all_58_14 = e2
% 179.22/28.88    (3)   ~ (e3 = e2)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.88  |   (4)  e3 = e2
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (4) implies:
% 179.22/28.88  |   (5)  e3 = e2
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (3), (5) imply:
% 179.22/28.88  |   (6)  $false
% 179.22/28.88  | 
% 179.22/28.88  | CLOSE: (6) is inconsistent.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #906 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_58_13 = e3
% 179.22/28.88    (2)  all_58_13 = e2
% 179.22/28.88    (3)   ~ (e3 = e2)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.88  |   (4)  e3 = e2
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (4) implies:
% 179.22/28.88  |   (5)  e3 = e2
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (3), (5) imply:
% 179.22/28.88  |   (6)  $false
% 179.22/28.88  | 
% 179.22/28.88  | CLOSE: (6) is inconsistent.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #907 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_58_12 = e1
% 179.22/28.88    (2)  all_58_12 = e0
% 179.22/28.88    (3)   ~ (e1 = e0)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.88  |   (4)  e1 = e0
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (4) implies:
% 179.22/28.88  |   (5)  e1 = e0
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (3), (5) imply:
% 179.22/28.88  |   (6)  $false
% 179.22/28.88  | 
% 179.22/28.88  | CLOSE: (6) is inconsistent.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #908 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (2)  op(e3, e0) = all_52_7
% 179.22/28.88    (3)  op(e3, e0) = e3
% 179.22/28.88    (4)   ~ (all_52_7 = e3)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | GROUND_INST: instantiating (1) with all_52_7, e3, e0, e3, simplifying with
% 179.22/28.88  |              (2), (3) gives:
% 179.22/28.88  |   (5)  all_52_7 = e3
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (4), (5) imply:
% 179.22/28.88  |   (6)  $false
% 179.22/28.88  | 
% 179.22/28.88  | CLOSE: (6) is inconsistent.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #909 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_58_2 = e2
% 179.22/28.88    (2)  all_58_2 = e0
% 179.22/28.88    (3)   ~ (e2 = e0)
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.88  |   (4)  e2 = e0
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (4) implies:
% 179.22/28.88  |   (5)  e2 = e0
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (3), (5) imply:
% 179.22/28.88  |   (6)  $false
% 179.22/28.88  | 
% 179.22/28.88  | CLOSE: (6) is inconsistent.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #910 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  all_56_8 = e3 | all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.22/28.88    (2)   ~ (all_52_23 = all_52_28)
% 179.22/28.88    (3)  all_58_6 = all_52_28
% 179.22/28.88    (4)  op(e3, e2) = all_52_3
% 179.22/28.88    (5)  op(e3, all_52_28) = e3
% 179.22/28.88    (6)   ~ (all_52_25 = all_52_28)
% 179.22/28.88    (7)  all_56_8 = all_52_28
% 179.22/28.88    (8)   ~ (all_52_28 = all_4_2)
% 179.22/28.88    (9)  all_58_7 = all_52_19
% 179.22/28.88    (10)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88    (11)  all_58_0 = all_4_2
% 179.22/28.88    (12)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.88    (13)  all_58_8 = all_14_2
% 179.22/28.88    (14)  op(e0, e3) = all_52_25
% 179.22/28.88    (15)   ~ (all_52_5 = e3)
% 179.22/28.88    (16)   ~ (all_52_3 = e3)
% 179.22/28.88    (17)  all_58_6 = all_52_17
% 179.22/28.88    (18)  op(e3, all_52_17) = e3
% 179.22/28.88    (19)  all_58_11 = all_52_23
% 179.22/28.88    (20)   ~ (all_52_9 = e3)
% 179.22/28.88    (21)  all_58_2 = all_52_9
% 179.22/28.88    (22)  op(e3, e1) = all_52_5
% 179.22/28.88    (23)   ~ (all_52_19 = e3)
% 179.22/28.88    (24)  op(e3, e3) = all_4_2
% 179.22/28.88    (25)   ~ (all_14_2 = e3)
% 179.22/28.88    (26)   ~ (all_52_17 = all_4_2)
% 179.22/28.88    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (28)  op(e0, all_52_23) = e0
% 179.22/28.88    (29)  all_58_12 = all_52_25
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (10) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (30)  all_58_6 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | COMBINE_EQS: (3), (30) imply:
% 179.22/28.88  | |   (31)  all_52_28 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | SIMP: (31) implies:
% 179.22/28.88  | |   (32)  all_52_28 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REDUCE: (6), (32) imply:
% 179.22/28.88  | |   (33)   ~ (all_52_25 = e3)
% 179.22/28.88  | | 
% 179.22/28.88  | | REDUCE: (8), (32) imply:
% 179.22/28.88  | |   (34)   ~ (all_4_2 = e3)
% 179.22/28.88  | | 
% 179.22/28.88  | | SIMP: (34) implies:
% 179.22/28.88  | |   (35)   ~ (all_4_2 = e3)
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (11), (12), (17), (18), (20), (21), (24), (26), (27), (29), (33),
% 179.22/28.88  | |            (35) are inconsistent by sub-proof #912.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (36)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | BETA: splitting (36) gives:
% 179.22/28.88  | | 
% 179.22/28.88  | | Case 1:
% 179.22/28.88  | | | 
% 179.22/28.88  | | |   (37)  all_58_7 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | COMBINE_EQS: (9), (37) imply:
% 179.22/28.88  | | |   (38)  all_52_19 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | REDUCE: (23), (38) imply:
% 179.22/28.88  | | |   (39)  $false
% 179.22/28.88  | | | 
% 179.22/28.88  | | | CLOSE: (39) is inconsistent.
% 179.22/28.88  | | | 
% 179.22/28.88  | | Case 2:
% 179.22/28.88  | | | 
% 179.22/28.88  | | |   (40)  all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | BETA: splitting (40) gives:
% 179.22/28.88  | | | 
% 179.22/28.88  | | | Case 1:
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | |   (41)  all_58_8 = e3
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | COMBINE_EQS: (13), (41) imply:
% 179.22/28.88  | | | |   (42)  all_14_2 = e3
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REDUCE: (25), (42) imply:
% 179.22/28.88  | | | |   (43)  $false
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | CLOSE: (43) is inconsistent.
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | Case 2:
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | |   (44)  all_58_11 = e3
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | COMBINE_EQS: (19), (44) imply:
% 179.22/28.88  | | | |   (45)  all_52_23 = e3
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | SIMP: (45) implies:
% 179.22/28.88  | | | |   (46)  all_52_23 = e3
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REDUCE: (2), (46) imply:
% 179.22/28.88  | | | |   (47)   ~ (all_52_28 = e3)
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | SIMP: (47) implies:
% 179.22/28.88  | | | |   (48)   ~ (all_52_28 = e3)
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REDUCE: (28), (46) imply:
% 179.22/28.88  | | | |   (49)  op(e0, e3) = e0
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | GROUND_INST: instantiating (27) with all_52_25, e0, e3, e0, simplifying
% 179.22/28.88  | | | |              with (14), (49) gives:
% 179.22/28.88  | | | |   (50)  all_52_25 = e0
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REDUCE: (6), (50) imply:
% 179.22/28.88  | | | |   (51)   ~ (all_52_28 = e0)
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | SIMP: (51) implies:
% 179.22/28.88  | | | |   (52)   ~ (all_52_28 = e0)
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | BETA: splitting (1) gives:
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | Case 1:
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | |   (53)  all_56_8 = e3
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | COMBINE_EQS: (7), (53) imply:
% 179.22/28.88  | | | | |   (54)  all_52_28 = e3
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | REDUCE: (48), (54) imply:
% 179.22/28.88  | | | | |   (55)  $false
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | CLOSE: (55) is inconsistent.
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | Case 2:
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | |   (56)  all_56_8 = e2 | all_56_8 = e1 | all_56_8 = e0
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | BETA: splitting (56) gives:
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | Case 1:
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | |   (57)  all_56_8 = e2
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | COMBINE_EQS: (7), (57) imply:
% 179.22/28.88  | | | | | |   (58)  all_52_28 = e2
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | SIMP: (58) implies:
% 179.22/28.88  | | | | | |   (59)  all_52_28 = e2
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | REDUCE: (5), (59) imply:
% 179.22/28.88  | | | | | |   (60)  op(e3, e2) = e3
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | REF_CLOSE: (4), (16), (27), (60) are inconsistent by sub-proof #978.
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | Case 2:
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | |   (61)  all_56_8 = e1 | all_56_8 = e0
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | REF_CLOSE: (5), (7), (15), (22), (27), (52), (61) are inconsistent
% 179.22/28.88  | | | | | |            by sub-proof #911.
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | End of split
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | End of split
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | End of split
% 179.22/28.88  | | | 
% 179.22/28.88  | | End of split
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #911 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)  op(e3, all_52_28) = e3
% 179.22/28.88    (2)  all_56_8 = all_52_28
% 179.22/28.88    (3)  all_56_8 = e1 | all_56_8 = e0
% 179.22/28.88    (4)   ~ (all_52_28 = e0)
% 179.22/28.88    (5)   ~ (all_52_5 = e3)
% 179.22/28.88    (6)  op(e3, e1) = all_52_5
% 179.22/28.88    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (3) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (8)  all_56_8 = e1
% 179.22/28.88  | | 
% 179.22/28.88  | | COMBINE_EQS: (2), (8) imply:
% 179.22/28.88  | |   (9)  all_52_28 = e1
% 179.22/28.88  | | 
% 179.22/28.88  | | SIMP: (9) implies:
% 179.22/28.88  | |   (10)  all_52_28 = e1
% 179.22/28.88  | | 
% 179.22/28.88  | | REDUCE: (1), (10) imply:
% 179.22/28.88  | |   (11)  op(e3, e1) = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (5), (6), (7), (11) are inconsistent by sub-proof #1023.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (12)  all_56_8 = e0
% 179.22/28.88  | | 
% 179.22/28.88  | | COMBINE_EQS: (2), (12) imply:
% 179.22/28.88  | |   (13)  all_52_28 = e0
% 179.22/28.88  | | 
% 179.22/28.88  | | SIMP: (13) implies:
% 179.22/28.88  | |   (14)  all_52_28 = e0
% 179.22/28.88  | | 
% 179.22/28.88  | | REDUCE: (4), (14) imply:
% 179.22/28.88  | |   (15)  $false
% 179.22/28.88  | | 
% 179.22/28.88  | | CLOSE: (15) is inconsistent.
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #912 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ~ (all_52_25 = e3)
% 179.22/28.88    (2)   ~ (all_4_2 = e3)
% 179.22/28.88    (3)  all_58_0 = all_4_2
% 179.22/28.88    (4)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.88    (5)  all_58_6 = all_52_17
% 179.22/28.88    (6)  op(e3, all_52_17) = e3
% 179.22/28.88    (7)   ~ (all_52_9 = e3)
% 179.22/28.88    (8)  all_58_2 = all_52_9
% 179.22/28.88    (9)  op(e3, e3) = all_4_2
% 179.22/28.88    (10)   ~ (all_52_17 = all_4_2)
% 179.22/28.88    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (12)  all_58_12 = all_52_25
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (4) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (13)  all_58_0 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | COMBINE_EQS: (3), (13) imply:
% 179.22/28.88  | |   (14)  all_4_2 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REDUCE: (2), (14) imply:
% 179.22/28.88  | |   (15)  $false
% 179.22/28.88  | | 
% 179.22/28.88  | | CLOSE: (15) is inconsistent.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (16)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (16) are
% 179.22/28.88  | |            inconsistent by sub-proof #913.
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #913 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ~ (all_52_25 = e3)
% 179.22/28.88    (2)  all_58_6 = all_52_17
% 179.22/28.88    (3)  op(e3, all_52_17) = e3
% 179.22/28.88    (4)   ~ (all_52_9 = e3)
% 179.22/28.88    (5)  all_58_2 = all_52_9
% 179.22/28.88    (6)  op(e3, e3) = all_4_2
% 179.22/28.88    (7)   ~ (all_52_17 = all_4_2)
% 179.22/28.88    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (9)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.88    (10)  all_58_12 = all_52_25
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (9) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (11)  all_58_2 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #980.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (12)  all_58_6 = e3 | all_58_12 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (12) are inconsistent by
% 179.22/28.88  | |            sub-proof #947.
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #914 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ~ (all_52_23 = e0)
% 179.22/28.88    (2)  all_58_10 = all_52_15
% 179.22/28.88    (3)  op(e0, e3) = e3
% 179.22/28.88    (4)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.88    (5)   ~ (e3 = e0)
% 179.22/28.88    (6)   ~ (all_52_15 = e3)
% 179.22/28.88    (7)  all_58_11 = all_52_23
% 179.22/28.88    (8)  all_58_15 = e0
% 179.22/28.88    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (10)  op(e0, all_52_23) = e0
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (4) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (11)  all_58_10 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (2), (6), (11) are inconsistent by sub-proof #1018.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (12)  all_58_11 = e3 | all_58_15 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (12) are inconsistent by
% 179.22/28.88  | |            sub-proof #915.
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #915 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ~ (all_52_23 = e0)
% 179.22/28.88    (2)  op(e0, e3) = e3
% 179.22/28.88    (3)   ~ (e3 = e0)
% 179.22/28.88    (4)  all_58_11 = e3 | all_58_15 = e3
% 179.22/28.88    (5)  all_58_11 = all_52_23
% 179.22/28.88    (6)  all_58_15 = e0
% 179.22/28.88    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (8)  op(e0, all_52_23) = e0
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (4) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (9)  all_58_11 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | COMBINE_EQS: (5), (9) imply:
% 179.22/28.88  | |   (10)  all_52_23 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (1), (2), (7), (8), (10) are inconsistent by sub-proof #916.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (11)  all_58_15 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #1010.
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #916 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ~ (all_52_23 = e0)
% 179.22/28.88    (2)  all_52_23 = e3
% 179.22/28.88    (3)  op(e0, e3) = e3
% 179.22/28.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (5)  op(e0, all_52_23) = e0
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | SIMP: (2) implies:
% 179.22/28.88  |   (6)  all_52_23 = e3
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (1), (6) imply:
% 179.22/28.88  |   (7)   ~ (e3 = e0)
% 179.22/28.88  | 
% 179.22/28.88  | REDUCE: (5), (6) imply:
% 179.22/28.88  |   (8)  op(e0, e3) = e0
% 179.22/28.88  | 
% 179.22/28.88  | REF_CLOSE: (3), (4), (7), (8) are inconsistent by sub-proof #1027.
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #917 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ~ (all_52_23 = all_14_2)
% 179.22/28.88    (2)  all_58_0 = e0 | all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 179.22/28.88    (3)   ~ (all_52_17 = e3)
% 179.22/28.88    (4)  all_58_7 = all_52_19
% 179.22/28.88    (5)  op(e0, e1) = all_52_29
% 179.22/28.88    (6)   ~ (all_4_0 = e2)
% 179.22/28.88    (7)  all_58_4 = all_52_5
% 179.22/28.88    (8)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88    (9)   ~ (e3 = e1)
% 179.22/28.88    (10)  op(e3, all_4_2) = all_4_1
% 179.22/28.88    (11)  all_58_9 = e3
% 179.22/28.88    (12)  all_58_1 = all_52_3
% 179.22/28.88    (13)  all_58_0 = all_4_2
% 179.22/28.88    (14)   ~ (all_4_1 = e2)
% 179.22/28.88    (15)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.22/28.88    (16)   ~ (all_52_3 = all_52_5)
% 179.22/28.88    (17)  all_58_8 = all_14_2
% 179.22/28.88    (18)  all_56_14 = all_52_29
% 179.22/28.88    (19)  op(all_4_1, all_4_2) = all_4_0
% 179.22/28.88    (20)  all_58_0 = e2 | all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 179.22/28.88    (21)   ~ (all_52_5 = all_14_2)
% 179.22/28.88    (22)   ~ (all_52_23 = e3)
% 179.22/28.88    (23)   ~ (all_52_29 = e3)
% 179.22/28.88    (24)   ~ (all_52_5 = e3)
% 179.22/28.88    (25)   ~ (e3 = e0)
% 179.22/28.88    (26)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.22/28.88    (27)   ~ (all_52_5 = all_52_29)
% 179.22/28.88    (28)  all_56_2 = all_52_5
% 179.22/28.88    (29)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.22/28.88    (30)  all_58_12 = e3
% 179.22/28.88    (31)  all_58_6 = all_52_17
% 179.22/28.88    (32)  op(e2, all_52_19) = e2
% 179.22/28.88    (33)  op(e3, all_52_17) = e3
% 179.22/28.88    (34)   ~ (e1 = e0)
% 179.22/28.88    (35)  all_58_11 = all_52_23
% 179.22/28.88    (36)   ~ (all_4_0 = e1)
% 179.22/28.88    (37)  all_58_2 = all_52_9
% 179.22/28.88    (38)  op(e3, e1) = all_52_5
% 179.22/28.88    (39)   ~ (e2 = e1)
% 179.22/28.88    (40)  all_56_10 = all_14_2
% 179.22/28.88    (41)  op(e1, e3) = all_52_17
% 179.22/28.88    (42)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (43)  op(e1, all_14_2) = e1
% 179.22/28.88    (44)   ~ (e2 = e0)
% 179.22/28.88    (45)   ~ (e3 = e2)
% 179.22/28.88    (46)  all_56_2 = e3 | all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 179.22/28.88    (47)   ~ (all_52_19 = all_14_2)
% 179.22/28.88    (48)  op(e2, e3) = all_52_9
% 179.22/28.88  
% 179.22/28.88  Begin of proof
% 179.22/28.88  | 
% 179.22/28.88  | BETA: splitting (8) gives:
% 179.22/28.88  | 
% 179.22/28.88  | Case 1:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (49)  all_58_6 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | REF_CLOSE: (3), (31), (49) are inconsistent by sub-proof #981.
% 179.22/28.88  | | 
% 179.22/28.88  | Case 2:
% 179.22/28.88  | | 
% 179.22/28.88  | |   (50)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88  | | 
% 179.22/28.88  | | BETA: splitting (46) gives:
% 179.22/28.88  | | 
% 179.22/28.88  | | Case 1:
% 179.22/28.88  | | | 
% 179.22/28.88  | | |   (51)  all_56_2 = e3
% 179.22/28.88  | | | 
% 179.22/28.88  | | | REF_CLOSE: (24), (28), (51) are inconsistent by sub-proof #931.
% 179.22/28.88  | | | 
% 179.22/28.88  | | Case 2:
% 179.22/28.88  | | | 
% 179.22/28.88  | | |   (52)   ~ (all_56_2 = e3)
% 179.22/28.88  | | |   (53)  all_56_2 = e2 | all_56_2 = e1 | all_56_2 = e0
% 179.22/28.88  | | | 
% 179.22/28.88  | | | BETA: splitting (29) gives:
% 179.22/28.88  | | | 
% 179.22/28.88  | | | Case 1:
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | |   (54)  all_58_0 = e1
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | COMBINE_EQS: (13), (54) imply:
% 179.22/28.88  | | | |   (55)  all_4_2 = e1
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REDUCE: (19), (55) imply:
% 179.22/28.88  | | | |   (56)  op(all_4_1, e1) = all_4_0
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REDUCE: (10), (55) imply:
% 179.22/28.88  | | | |   (57)  op(e3, e1) = all_4_1
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | GROUND_INST: instantiating (42) with all_52_5, all_4_1, e1, e3,
% 179.22/28.88  | | | |              simplifying with (38), (57) gives:
% 179.22/28.88  | | | |   (58)  all_52_5 = all_4_1
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | COMBINE_EQS: (28), (58) imply:
% 179.22/28.88  | | | |   (59)  all_56_2 = all_4_1
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | COMBINE_EQS: (7), (58) imply:
% 179.22/28.88  | | | |   (60)  all_58_4 = all_4_1
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REDUCE: (16), (58) imply:
% 179.22/28.88  | | | |   (61)   ~ (all_52_3 = all_4_1)
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | BETA: splitting (20) gives:
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | Case 1:
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | |   (62)  all_58_0 = e2
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | REF_CLOSE: (39), (54), (62) are inconsistent by sub-proof #930.
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | Case 2:
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | |   (63)  all_58_1 = e2 | all_58_4 = e2 | all_58_9 = e2
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | BETA: splitting (63) gives:
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | | Case 1:
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | |   (64)  all_58_1 = e2
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | COMBINE_EQS: (12), (64) imply:
% 179.22/28.88  | | | | | |   (65)  all_52_3 = e2
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | REDUCE: (61), (65) imply:
% 179.22/28.88  | | | | | |   (66)   ~ (all_4_1 = e2)
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | BETA: splitting (2) gives:
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | Case 1:
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | |   (67)  all_58_0 = e0
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | | COMBINE_EQS: (54), (67) imply:
% 179.22/28.88  | | | | | | |   (68)  e1 = e0
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | | REDUCE: (34), (68) imply:
% 179.22/28.88  | | | | | | |   (69)  $false
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | | CLOSE: (69) is inconsistent.
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | Case 2:
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | |   (70)   ~ (all_58_0 = e0)
% 179.22/28.88  | | | | | | |   (71)  all_58_1 = e0 | all_58_4 = e0 | all_58_9 = e0
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | | BETA: splitting (53) gives:
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | | Case 1:
% 179.22/28.88  | | | | | | | | 
% 179.22/28.88  | | | | | | | |   (72)  all_56_2 = e2
% 179.22/28.88  | | | | | | | | 
% 179.22/28.88  | | | | | | | | REF_CLOSE: (14), (59), (72) are inconsistent by sub-proof #929.
% 179.22/28.88  | | | | | | | | 
% 179.22/28.88  | | | | | | | Case 2:
% 179.22/28.88  | | | | | | | | 
% 179.22/28.88  | | | | | | | |   (73)  all_56_2 = e1 | all_56_2 = e0
% 179.22/28.88  | | | | | | | | 
% 179.22/28.88  | | | | | | | | BETA: splitting (71) gives:
% 179.22/28.88  | | | | | | | | 
% 179.22/28.88  | | | | | | | | Case 1:
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | |   (74)  all_58_1 = e0
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | | COMBINE_EQS: (64), (74) imply:
% 179.22/28.88  | | | | | | | | |   (75)  e2 = e0
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | | REDUCE: (44), (75) imply:
% 179.22/28.88  | | | | | | | | |   (76)  $false
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | | CLOSE: (76) is inconsistent.
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | Case 2:
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | |   (77)  all_58_4 = e0 | all_58_9 = e0
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | | REF_CLOSE: (5), (6), (7), (11), (15), (18), (23), (25), (27),
% 179.22/28.88  | | | | | | | | |            (28), (34), (36), (38), (42), (56), (57), (73),
% 179.22/28.88  | | | | | | | | |            (77) are inconsistent by sub-proof #924.
% 179.22/28.88  | | | | | | | | | 
% 179.22/28.88  | | | | | | | | End of split
% 179.22/28.88  | | | | | | | | 
% 179.22/28.88  | | | | | | | End of split
% 179.22/28.88  | | | | | | | 
% 179.22/28.88  | | | | | | End of split
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | Case 2:
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | |   (78)  all_58_4 = e2 | all_58_9 = e2
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | | REF_CLOSE: (11), (14), (45), (60), (78) are inconsistent by
% 179.22/28.88  | | | | | |            sub-proof #923.
% 179.22/28.88  | | | | | | 
% 179.22/28.88  | | | | | End of split
% 179.22/28.88  | | | | | 
% 179.22/28.88  | | | | End of split
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | Case 2:
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | |   (79)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | | REF_CLOSE: (1), (4), (9), (17), (21), (22), (24), (26), (30), (31),
% 179.22/28.88  | | | |            (32), (33), (35), (37), (38), (39), (40), (41), (42), (43),
% 179.22/28.88  | | | |            (47), (48), (50), (79) are inconsistent by sub-proof #918.
% 179.22/28.88  | | | | 
% 179.22/28.88  | | | End of split
% 179.22/28.88  | | | 
% 179.22/28.88  | | End of split
% 179.22/28.88  | | 
% 179.22/28.88  | End of split
% 179.22/28.88  | 
% 179.22/28.88  End of proof
% 179.22/28.88  
% 179.22/28.88  Sub-proof #918 shows that the following formulas are inconsistent:
% 179.22/28.88  ----------------------------------------------------------------
% 179.22/28.88    (1)   ~ (all_52_23 = all_14_2)
% 179.22/28.88    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.88    (3)  all_58_7 = all_52_19
% 179.22/28.88    (4)   ~ (e3 = e1)
% 179.22/28.88    (5)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.22/28.88    (6)  all_58_8 = all_14_2
% 179.22/28.88    (7)   ~ (all_52_5 = all_14_2)
% 179.22/28.88    (8)   ~ (all_52_23 = e3)
% 179.22/28.88    (9)   ~ (all_52_5 = e3)
% 179.22/28.88    (10)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.22/28.88    (11)  all_58_12 = e3
% 179.22/28.88    (12)  all_58_6 = all_52_17
% 179.22/28.88    (13)  op(e2, all_52_19) = e2
% 179.22/28.88    (14)  op(e3, all_52_17) = e3
% 179.22/28.88    (15)  all_58_11 = all_52_23
% 179.22/28.88    (16)  all_58_2 = all_52_9
% 179.22/28.88    (17)  op(e3, e1) = all_52_5
% 179.22/28.88    (18)   ~ (e2 = e1)
% 179.22/28.88    (19)  all_56_10 = all_14_2
% 179.22/28.88    (20)  op(e1, e3) = all_52_17
% 179.22/28.88    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.88    (22)  op(e1, all_14_2) = e1
% 179.22/28.89    (23)   ~ (all_52_19 = all_14_2)
% 179.22/28.89    (24)  op(e2, e3) = all_52_9
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (10) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (25)  all_56_10 = e3
% 179.22/28.89  | | 
% 179.22/28.89  | | REF_CLOSE: (1), (2), (3), (6), (7), (14), (15), (17), (19), (20), (21),
% 179.22/28.89  | |            (22), (23), (25) are inconsistent by sub-proof #922.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (26)   ~ (all_56_10 = e3)
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (19), (26) imply:
% 179.22/28.89  | |   (27)   ~ (all_14_2 = e3)
% 179.22/28.89  | | 
% 179.22/28.89  | | BETA: splitting (2) gives:
% 179.22/28.89  | | 
% 179.22/28.89  | | Case 1:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (28)  all_58_7 = e3
% 179.22/28.89  | | | 
% 179.22/28.89  | | | COMBINE_EQS: (3), (28) imply:
% 179.22/28.89  | | |   (29)  all_52_19 = e3
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REDUCE: (13), (29) imply:
% 179.22/28.89  | | |   (30)  op(e2, e3) = e2
% 179.22/28.89  | | | 
% 179.22/28.89  | | | GROUND_INST: instantiating (21) with all_52_9, e2, e3, e2, simplifying
% 179.22/28.89  | | |              with (24), (30) gives:
% 179.22/28.89  | | |   (31)  all_52_9 = e2
% 179.22/28.89  | | | 
% 179.22/28.89  | | | COMBINE_EQS: (16), (31) imply:
% 179.22/28.89  | | |   (32)  all_58_2 = e2
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REF_CLOSE: (4), (5), (9), (11), (12), (14), (17), (18), (21), (32) are
% 179.22/28.89  | | |            inconsistent by sub-proof #919.
% 179.22/28.89  | | | 
% 179.22/28.89  | | Case 2:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (33)  all_58_8 = e3 | all_58_11 = e3
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REF_CLOSE: (6), (8), (15), (27), (33) are inconsistent by sub-proof #997.
% 179.22/28.89  | | | 
% 179.22/28.89  | | End of split
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #919 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_58_2 = e2
% 179.22/28.89    (2)   ~ (e3 = e1)
% 179.22/28.89    (3)  all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.22/28.89    (4)   ~ (all_52_5 = e3)
% 179.22/28.89    (5)  all_58_12 = e3
% 179.22/28.89    (6)  all_58_6 = all_52_17
% 179.22/28.89    (7)  op(e3, all_52_17) = e3
% 179.22/28.89    (8)  op(e3, e1) = all_52_5
% 179.22/28.89    (9)   ~ (e2 = e1)
% 179.22/28.89    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (3) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (11)  all_58_2 = e1
% 179.22/28.89  | | 
% 179.22/28.89  | | REF_CLOSE: (1), (9), (11) are inconsistent by sub-proof #921.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (12)  all_58_6 = e1 | all_58_12 = e1
% 179.22/28.89  | | 
% 179.22/28.89  | | BETA: splitting (12) gives:
% 179.22/28.89  | | 
% 179.22/28.89  | | Case 1:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (13)  all_58_6 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | COMBINE_EQS: (6), (13) imply:
% 179.22/28.89  | | |   (14)  all_52_17 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | SIMP: (14) implies:
% 179.22/28.89  | | |   (15)  all_52_17 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REDUCE: (7), (15) imply:
% 179.22/28.89  | | |   (16)  op(e3, e1) = e3
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REF_CLOSE: (4), (8), (10), (16) are inconsistent by sub-proof #1023.
% 179.22/28.89  | | | 
% 179.22/28.89  | | Case 2:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (17)  all_58_12 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REF_CLOSE: (2), (5), (17) are inconsistent by sub-proof #920.
% 179.22/28.89  | | | 
% 179.22/28.89  | | End of split
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #920 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_58_12 = e3
% 179.22/28.89    (2)  all_58_12 = e1
% 179.22/28.89    (3)   ~ (e3 = e1)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.89  |   (4)  e3 = e1
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (4) implies:
% 179.22/28.89  |   (5)  e3 = e1
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (3), (5) imply:
% 179.22/28.89  |   (6)  $false
% 179.22/28.89  | 
% 179.22/28.89  | CLOSE: (6) is inconsistent.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #921 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_58_2 = e2
% 179.22/28.89    (2)  all_58_2 = e1
% 179.22/28.89    (3)   ~ (e2 = e1)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.89  |   (4)  e2 = e1
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (4) implies:
% 179.22/28.89  |   (5)  e2 = e1
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (3), (5) imply:
% 179.22/28.89  |   (6)  $false
% 179.22/28.89  | 
% 179.22/28.89  | CLOSE: (6) is inconsistent.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #922 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)   ~ (all_52_23 = all_14_2)
% 179.22/28.89    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.89    (3)  all_58_7 = all_52_19
% 179.22/28.89    (4)  all_58_8 = all_14_2
% 179.22/28.89    (5)   ~ (all_52_5 = all_14_2)
% 179.22/28.89    (6)  op(e3, all_52_17) = e3
% 179.22/28.89    (7)  all_58_11 = all_52_23
% 179.22/28.89    (8)  op(e3, e1) = all_52_5
% 179.22/28.89    (9)  all_56_10 = all_14_2
% 179.22/28.89    (10)  op(e1, e3) = all_52_17
% 179.22/28.89    (11)  all_56_10 = e3
% 179.22/28.89    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.89    (13)  op(e1, all_14_2) = e1
% 179.22/28.89    (14)   ~ (all_52_19 = all_14_2)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (9), (11) imply:
% 179.22/28.89  |   (15)  all_14_2 = e3
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (15) implies:
% 179.22/28.89  |   (16)  all_14_2 = e3
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (14), (16) imply:
% 179.22/28.89  |   (17)   ~ (all_52_19 = e3)
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (1), (16) imply:
% 179.22/28.89  |   (18)   ~ (all_52_23 = e3)
% 179.22/28.89  | 
% 179.22/28.89  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (17), (18) are
% 179.22/28.89  |            inconsistent by sub-proof #950.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #923 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_58_9 = e3
% 179.22/28.89    (2)   ~ (all_4_1 = e2)
% 179.22/28.89    (3)  all_58_4 = e2 | all_58_9 = e2
% 179.22/28.89    (4)  all_58_4 = all_4_1
% 179.22/28.89    (5)   ~ (e3 = e2)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (3) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (6)  all_58_4 = e2
% 179.22/28.89  | | 
% 179.22/28.89  | | COMBINE_EQS: (4), (6) imply:
% 179.22/28.89  | |   (7)  all_4_1 = e2
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (2), (7) imply:
% 179.22/28.89  | |   (8)  $false
% 179.22/28.89  | | 
% 179.22/28.89  | | CLOSE: (8) is inconsistent.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (9)  all_58_9 = e2
% 179.22/28.89  | | 
% 179.22/28.89  | | COMBINE_EQS: (1), (9) imply:
% 179.22/28.89  | |   (10)  e3 = e2
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (5), (10) imply:
% 179.22/28.89  | |   (11)  $false
% 179.22/28.89  | | 
% 179.22/28.89  | | CLOSE: (11) is inconsistent.
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #924 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  op(e0, e1) = all_52_29
% 179.22/28.89    (2)   ~ (all_4_0 = e2)
% 179.22/28.89    (3)  all_58_4 = all_52_5
% 179.22/28.89    (4)  all_58_9 = e3
% 179.22/28.89    (5)  all_56_14 = e3 | all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.22/28.89    (6)  all_56_14 = all_52_29
% 179.22/28.89    (7)   ~ (all_52_29 = e3)
% 179.22/28.89    (8)   ~ (e3 = e0)
% 179.22/28.89    (9)  op(e3, e1) = all_4_1
% 179.22/28.89    (10)  all_56_2 = e1 | all_56_2 = e0
% 179.22/28.89    (11)   ~ (all_52_5 = all_52_29)
% 179.22/28.89    (12)  all_56_2 = all_52_5
% 179.22/28.89    (13)  op(all_4_1, e1) = all_4_0
% 179.22/28.89    (14)   ~ (e1 = e0)
% 179.22/28.89    (15)   ~ (all_4_0 = e1)
% 179.22/28.89    (16)  op(e3, e1) = all_52_5
% 179.22/28.89    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.89    (18)  all_58_4 = e0 | all_58_9 = e0
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (10) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (19)  all_56_2 = e1
% 179.22/28.89  | | 
% 179.22/28.89  | | REF_CLOSE: (3), (4), (8), (12), (14), (18), (19) are inconsistent by
% 179.22/28.89  | |            sub-proof #926.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (20)  all_56_2 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | COMBINE_EQS: (12), (20) imply:
% 179.22/28.89  | |   (21)  all_52_5 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | SIMP: (21) implies:
% 179.22/28.89  | |   (22)  all_52_5 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (11), (22) imply:
% 179.22/28.89  | |   (23)   ~ (all_52_29 = e0)
% 179.22/28.89  | | 
% 179.22/28.89  | | SIMP: (23) implies:
% 179.22/28.89  | |   (24)   ~ (all_52_29 = e0)
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (16), (22) imply:
% 179.22/28.89  | |   (25)  op(e3, e1) = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | GROUND_INST: instantiating (17) with e0, all_4_1, e1, e3, simplifying with
% 179.22/28.89  | |              (9), (25) gives:
% 179.22/28.89  | |   (26)  all_4_1 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (13), (26) imply:
% 179.22/28.89  | |   (27)  op(e0, e1) = all_4_0
% 179.22/28.89  | | 
% 179.22/28.89  | | GROUND_INST: instantiating (17) with all_52_29, all_4_0, e1, e0, simplifying
% 179.22/28.89  | |              with (1), (27) gives:
% 179.22/28.89  | |   (28)  all_52_29 = all_4_0
% 179.22/28.89  | | 
% 179.22/28.89  | | COMBINE_EQS: (6), (28) imply:
% 179.22/28.89  | |   (29)  all_56_14 = all_4_0
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (7), (28) imply:
% 179.22/28.89  | |   (30)   ~ (all_4_0 = e3)
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (24), (28) imply:
% 179.22/28.89  | |   (31)   ~ (all_4_0 = e0)
% 179.22/28.89  | | 
% 179.22/28.89  | | BETA: splitting (5) gives:
% 179.22/28.89  | | 
% 179.22/28.89  | | Case 1:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (32)  all_56_14 = e3
% 179.22/28.89  | | | 
% 179.22/28.89  | | | COMBINE_EQS: (29), (32) imply:
% 179.22/28.89  | | |   (33)  all_4_0 = e3
% 179.22/28.89  | | | 
% 179.22/28.89  | | | SIMP: (33) implies:
% 179.22/28.89  | | |   (34)  all_4_0 = e3
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REDUCE: (30), (34) imply:
% 179.22/28.89  | | |   (35)  $false
% 179.22/28.89  | | | 
% 179.22/28.89  | | | CLOSE: (35) is inconsistent.
% 179.22/28.89  | | | 
% 179.22/28.89  | | Case 2:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (36)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REF_CLOSE: (2), (15), (29), (31), (36) are inconsistent by sub-proof #925.
% 179.22/28.89  | | | 
% 179.22/28.89  | | End of split
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #925 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)   ~ (all_4_0 = e0)
% 179.22/28.89    (2)   ~ (all_4_0 = e2)
% 179.22/28.89    (3)   ~ (all_4_0 = e1)
% 179.22/28.89    (4)  all_56_14 = e2 | all_56_14 = e1 | all_56_14 = e0
% 179.22/28.89    (5)  all_56_14 = all_4_0
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (4) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (6)  all_56_14 = e2
% 179.22/28.89  | | 
% 179.22/28.89  | | COMBINE_EQS: (5), (6) imply:
% 179.22/28.89  | |   (7)  all_4_0 = e2
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (2), (7) imply:
% 179.22/28.89  | |   (8)  $false
% 179.22/28.89  | | 
% 179.22/28.89  | | CLOSE: (8) is inconsistent.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (9)  all_56_14 = e1 | all_56_14 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | BETA: splitting (9) gives:
% 179.22/28.89  | | 
% 179.22/28.89  | | Case 1:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (10)  all_56_14 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | COMBINE_EQS: (5), (10) imply:
% 179.22/28.89  | | |   (11)  all_4_0 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REDUCE: (3), (11) imply:
% 179.22/28.89  | | |   (12)  $false
% 179.22/28.89  | | | 
% 179.22/28.89  | | | CLOSE: (12) is inconsistent.
% 179.22/28.89  | | | 
% 179.22/28.89  | | Case 2:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (13)  all_56_14 = e0
% 179.22/28.89  | | | 
% 179.22/28.89  | | | COMBINE_EQS: (5), (13) imply:
% 179.22/28.89  | | |   (14)  all_4_0 = e0
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REDUCE: (1), (14) imply:
% 179.22/28.89  | | |   (15)  $false
% 179.22/28.89  | | | 
% 179.22/28.89  | | | CLOSE: (15) is inconsistent.
% 179.22/28.89  | | | 
% 179.22/28.89  | | End of split
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #926 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_56_2 = e1
% 179.22/28.89    (2)  all_58_4 = all_52_5
% 179.22/28.89    (3)  all_58_9 = e3
% 179.22/28.89    (4)   ~ (e3 = e0)
% 179.22/28.89    (5)  all_56_2 = all_52_5
% 179.22/28.89    (6)   ~ (e1 = e0)
% 179.22/28.89    (7)  all_58_4 = e0 | all_58_9 = e0
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (1), (5) imply:
% 179.22/28.89  |   (8)  all_52_5 = e1
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (8) implies:
% 179.22/28.89  |   (9)  all_52_5 = e1
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (2), (9) imply:
% 179.22/28.89  |   (10)  all_58_4 = e1
% 179.22/28.89  | 
% 179.22/28.89  | REF_CLOSE: (3), (4), (6), (7), (10) are inconsistent by sub-proof #927.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #927 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_58_4 = e1
% 179.22/28.89    (2)  all_58_9 = e3
% 179.22/28.89    (3)   ~ (e3 = e0)
% 179.22/28.89    (4)   ~ (e1 = e0)
% 179.22/28.89    (5)  all_58_4 = e0 | all_58_9 = e0
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (5) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (6)  all_58_4 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | COMBINE_EQS: (1), (6) imply:
% 179.22/28.89  | |   (7)  e1 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | SIMP: (7) implies:
% 179.22/28.89  | |   (8)  e1 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | REDUCE: (4), (8) imply:
% 179.22/28.89  | |   (9)  $false
% 179.22/28.89  | | 
% 179.22/28.89  | | CLOSE: (9) is inconsistent.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (10)  all_58_9 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #928.
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #928 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_58_9 = e3
% 179.22/28.89    (2)  all_58_9 = e0
% 179.22/28.89    (3)   ~ (e3 = e0)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.89  |   (4)  e3 = e0
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (4) implies:
% 179.22/28.89  |   (5)  e3 = e0
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (3), (5) imply:
% 179.22/28.89  |   (6)  $false
% 179.22/28.89  | 
% 179.22/28.89  | CLOSE: (6) is inconsistent.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #929 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_56_2 = all_4_1
% 179.22/28.89    (2)  all_56_2 = e2
% 179.22/28.89    (3)   ~ (all_4_1 = e2)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.89  |   (4)  all_4_1 = e2
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (4) implies:
% 179.22/28.89  |   (5)  all_4_1 = e2
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (3), (5) imply:
% 179.22/28.89  |   (6)  $false
% 179.22/28.89  | 
% 179.22/28.89  | CLOSE: (6) is inconsistent.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #930 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_58_0 = e2
% 179.22/28.89    (2)  all_58_0 = e1
% 179.22/28.89    (3)   ~ (e2 = e1)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.89  |   (4)  e2 = e1
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (4) implies:
% 179.22/28.89  |   (5)  e2 = e1
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (3), (5) imply:
% 179.22/28.89  |   (6)  $false
% 179.22/28.89  | 
% 179.22/28.89  | CLOSE: (6) is inconsistent.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #931 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_56_2 = all_52_5
% 179.22/28.89    (2)  all_56_2 = e3
% 179.22/28.89    (3)   ~ (all_52_5 = e3)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.89  |   (4)  all_52_5 = e3
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (4) implies:
% 179.22/28.89  |   (5)  all_52_5 = e3
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (3), (5) imply:
% 179.22/28.89  |   (6)  $false
% 179.22/28.89  | 
% 179.22/28.89  | CLOSE: (6) is inconsistent.
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #932 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)   ~ (all_52_25 = e3)
% 179.22/28.89    (2)  all_56_3 = all_52_7
% 179.22/28.89    (3)  all_56_11 = all_52_23
% 179.22/28.89    (4)   ~ (all_52_27 = e0)
% 179.22/28.89    (5)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.22/28.89    (6)  all_56_9 = all_52_19
% 179.22/28.89    (7)  all_58_10 = all_52_15
% 179.22/28.89    (8)  all_58_7 = all_52_19
% 179.22/28.89    (9)  op(e0, e1) = all_52_29
% 179.22/28.89    (10)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.89    (11)   ~ (e3 = e1)
% 179.22/28.89    (12)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.22/28.89    (13)   ~ (all_52_7 = all_4_2)
% 179.22/28.89    (14)  all_58_0 = all_4_2
% 179.22/28.89    (15)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.22/28.89    (16)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.89    (17)  all_58_8 = all_14_2
% 179.22/28.89    (18)  op(e0, e2) = all_52_27
% 179.22/28.89    (19)   ~ (all_52_5 = all_14_2)
% 179.22/28.89    (20)  op(e0, e3) = all_52_25
% 179.22/28.89    (21)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.22/28.89    (22)   ~ (e3 = e0)
% 179.22/28.89    (23)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.22/28.89    (24)   ~ (all_52_15 = all_52_23)
% 179.22/28.89    (25)  all_56_12 = all_52_25
% 179.22/28.89    (26)   ~ (all_52_25 = e0)
% 179.22/28.89    (27)   ~ (all_52_9 = all_52_17)
% 179.22/28.89    (28)  all_58_6 = all_52_17
% 179.22/28.89    (29)  op(e2, all_52_19) = e2
% 179.22/28.89    (30)  op(e3, all_52_17) = e3
% 179.22/28.89    (31)   ~ (e1 = e0)
% 179.22/28.89    (32)  all_58_11 = all_52_23
% 179.22/28.89    (33)  all_58_15 = e0
% 179.22/28.89    (34)  all_58_2 = all_52_9
% 179.22/28.89    (35)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.22/28.89    (36)   ~ (all_52_29 = e0)
% 179.22/28.89    (37)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.22/28.89    (38)  op(e3, e1) = all_52_5
% 179.22/28.89    (39)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.22/28.89    (40)   ~ (all_52_19 = e3)
% 179.22/28.89    (41)  op(e1, e3) = all_52_17
% 179.22/28.89    (42)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.22/28.89    (43)  op(e3, e3) = all_4_2
% 179.22/28.89    (44)   ~ (all_52_17 = all_4_2)
% 179.22/28.89    (45)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.89    (46)  op(e0, all_52_23) = e0
% 179.22/28.89    (47)  all_56_7 = all_52_15
% 179.22/28.89    (48)  op(e1, all_14_2) = e1
% 179.22/28.89    (49)   ~ (all_52_7 = all_52_23)
% 179.22/28.89    (50)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.89    (51)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.22/28.89    (52)  all_58_9 = all_52_7
% 179.22/28.89    (53)  all_58_12 = all_52_25
% 179.22/28.89    (54)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.22/28.89    (55)   ~ (all_52_9 = all_52_15)
% 179.22/28.89    (56)   ~ (e3 = e2)
% 179.22/28.89    (57)  op(e2, e3) = all_52_9
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (23) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (58)  all_56_12 = e3
% 179.22/28.89  | | 
% 179.22/28.89  | | REF_CLOSE: (1), (25), (58) are inconsistent by sub-proof #1040.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (59)   ~ (all_56_12 = e3)
% 179.22/28.89  | |   (60)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | BETA: splitting (35) gives:
% 179.22/28.89  | | 
% 179.22/28.89  | | Case 1:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (61)  all_58_12 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | COMBINE_EQS: (53), (61) imply:
% 179.22/28.89  | | |   (62)  all_52_25 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | SIMP: (62) implies:
% 179.22/28.89  | | |   (63)  all_52_25 = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REDUCE: (20), (63) imply:
% 179.22/28.89  | | |   (64)  op(e0, e3) = e1
% 179.22/28.89  | | | 
% 179.22/28.89  | | | BETA: splitting (51) gives:
% 179.22/28.89  | | | 
% 179.22/28.89  | | | Case 1:
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | |   (65)  all_56_3 = e3
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | COMBINE_EQS: (2), (65) imply:
% 179.22/28.89  | | | |   (66)  all_52_7 = e3
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | SIMP: (66) implies:
% 179.22/28.89  | | | |   (67)  all_52_7 = e3
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REF_CLOSE: (1), (6), (8), (10), (12), (13), (14), (15), (16), (17),
% 179.22/28.89  | | | |            (19), (27), (28), (29), (30), (32), (34), (38), (41), (43),
% 179.22/28.89  | | | |            (44), (45), (48), (49), (53), (56), (57), (67) are
% 179.22/28.89  | | | |            inconsistent by sub-proof #943.
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | Case 2:
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | |   (68)   ~ (all_56_3 = e3)
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REDUCE: (2), (68) imply:
% 179.22/28.89  | | | |   (69)   ~ (all_52_7 = e3)
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | BETA: splitting (54) gives:
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | Case 1:
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | |   (70)  all_58_0 = e3
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | COMBINE_EQS: (14), (70) imply:
% 179.22/28.89  | | | | |   (71)  all_4_2 = e3
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | REDUCE: (44), (71) imply:
% 179.22/28.89  | | | | |   (72)   ~ (all_52_17 = e3)
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | BETA: splitting (50) gives:
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | Case 1:
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | |   (73)  all_58_9 = e3
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | COMBINE_EQS: (52), (73) imply:
% 179.22/28.89  | | | | | |   (74)  all_52_7 = e3
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | REDUCE: (69), (74) imply:
% 179.22/28.89  | | | | | |   (75)  $false
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | CLOSE: (75) is inconsistent.
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | Case 2:
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | |   (76)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | BETA: splitting (10) gives:
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | Case 1:
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | |   (77)  all_58_6 = e3
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | COMBINE_EQS: (28), (77) imply:
% 179.22/28.89  | | | | | | |   (78)  all_52_17 = e3
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | REDUCE: (72), (78) imply:
% 179.22/28.89  | | | | | | |   (79)  $false
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | CLOSE: (79) is inconsistent.
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | Case 2:
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | |   (80)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | BETA: splitting (42) gives:
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | Case 1:
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | |   (81)  all_56_7 = e3
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | COMBINE_EQS: (47), (81) imply:
% 179.22/28.89  | | | | | | | |   (82)  all_52_15 = e3
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | REDUCE: (24), (82) imply:
% 179.22/28.89  | | | | | | | |   (83)   ~ (all_52_23 = e3)
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | SIMP: (83) implies:
% 179.22/28.89  | | | | | | | |   (84)   ~ (all_52_23 = e3)
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | REF_CLOSE: (8), (17), (19), (30), (32), (38), (40), (41), (45),
% 179.22/28.89  | | | | | | | |            (48), (80), (84) are inconsistent by sub-proof #950.
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | Case 2:
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | |   (85)   ~ (all_56_7 = e3)
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | REDUCE: (47), (85) imply:
% 179.22/28.89  | | | | | | | |   (86)   ~ (all_52_15 = e3)
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | REF_CLOSE: (7), (22), (31), (32), (33), (45), (46), (64), (76),
% 179.22/28.89  | | | | | | | |            (86) are inconsistent by sub-proof #942.
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | End of split
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | End of split
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | End of split
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | Case 2:
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | |   (87)   ~ (all_58_0 = e3)
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | REDUCE: (14), (87) imply:
% 179.22/28.89  | | | | |   (88)   ~ (all_4_2 = e3)
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | REF_CLOSE: (1), (7), (14), (16), (22), (28), (30), (31), (32), (33),
% 179.22/28.89  | | | | |            (34), (43), (44), (45), (46), (50), (52), (53), (55), (64),
% 179.22/28.89  | | | | |            (69), (88) are inconsistent by sub-proof #940.
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | End of split
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | End of split
% 179.22/28.89  | | | 
% 179.22/28.89  | | Case 2:
% 179.22/28.89  | | | 
% 179.22/28.89  | | |   (89)   ~ (all_58_12 = e1)
% 179.22/28.89  | | | 
% 179.22/28.89  | | | REDUCE: (53), (89) imply:
% 179.22/28.89  | | |   (90)   ~ (all_52_25 = e1)
% 179.22/28.89  | | | 
% 179.22/28.89  | | | BETA: splitting (39) gives:
% 179.22/28.89  | | | 
% 179.22/28.89  | | | Case 1:
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | |   (91)  all_58_12 = e2
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | COMBINE_EQS: (53), (91) imply:
% 179.22/28.89  | | | |   (92)  all_52_25 = e2
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | SIMP: (92) implies:
% 179.22/28.89  | | | |   (93)  all_52_25 = e2
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REDUCE: (1), (93) imply:
% 179.22/28.89  | | | |   (94)   ~ (e3 = e2)
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REDUCE: (90), (93) imply:
% 179.22/28.89  | | | |   (95)   ~ (e2 = e1)
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REDUCE: (26), (93) imply:
% 179.22/28.89  | | | |   (96)   ~ (e2 = e0)
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REDUCE: (20), (93) imply:
% 179.22/28.89  | | | |   (97)  op(e0, e3) = e2
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | BETA: splitting (42) gives:
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | Case 1:
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | |   (98)  all_56_7 = e3
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | REF_CLOSE: (3), (4), (5), (7), (9), (11), (18), (21), (24), (31),
% 179.22/28.89  | | | | |            (32), (33), (36), (37), (45), (46), (47), (56), (95), (96),
% 179.22/28.89  | | | | |            (98) are inconsistent by sub-proof #933.
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | Case 2:
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | |   (99)   ~ (all_56_7 = e3)
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | REDUCE: (47), (99) imply:
% 179.22/28.89  | | | | |   (100)   ~ (all_52_15 = e3)
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | BETA: splitting (50) gives:
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | | Case 1:
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | |   (101)  all_58_9 = e3
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | COMBINE_EQS: (52), (101) imply:
% 179.22/28.89  | | | | | |   (102)  all_52_7 = e3
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | REF_CLOSE: (1), (6), (8), (10), (12), (13), (14), (15), (16), (17),
% 179.22/28.89  | | | | | |            (19), (27), (28), (29), (30), (32), (34), (38), (41),
% 179.22/28.89  | | | | | |            (43), (44), (45), (48), (49), (53), (56), (57), (102) are
% 179.22/28.89  | | | | | |            inconsistent by sub-proof #943.
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | Case 2:
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | |   (103)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | BETA: splitting (103) gives:
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | | Case 1:
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | |   (104)  all_58_10 = e3
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | COMBINE_EQS: (7), (104) imply:
% 179.22/28.89  | | | | | | |   (105)  all_52_15 = e3
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | REDUCE: (100), (105) imply:
% 179.22/28.89  | | | | | | |   (106)  $false
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | CLOSE: (106) is inconsistent.
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | Case 2:
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | |   (107)  all_58_11 = e3 | all_58_15 = e3
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | BETA: splitting (107) gives:
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | | Case 1:
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | |   (108)  all_58_11 = e3
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | COMBINE_EQS: (32), (108) imply:
% 179.22/28.89  | | | | | | | |   (109)  all_52_23 = e3
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | REDUCE: (46), (109) imply:
% 179.22/28.89  | | | | | | | |   (110)  op(e0, e3) = e0
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | REF_CLOSE: (45), (96), (97), (110) are inconsistent by sub-proof
% 179.22/28.89  | | | | | | | |            #1035.
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | Case 2:
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | |   (111)  all_58_15 = e3
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | COMBINE_EQS: (33), (111) imply:
% 179.22/28.89  | | | | | | | |   (112)  e3 = e0
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | REDUCE: (22), (112) imply:
% 179.22/28.89  | | | | | | | |   (113)  $false
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | | CLOSE: (113) is inconsistent.
% 179.22/28.89  | | | | | | | | 
% 179.22/28.89  | | | | | | | End of split
% 179.22/28.89  | | | | | | | 
% 179.22/28.89  | | | | | | End of split
% 179.22/28.89  | | | | | | 
% 179.22/28.89  | | | | | End of split
% 179.22/28.89  | | | | | 
% 179.22/28.89  | | | | End of split
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | Case 2:
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | |   (114)   ~ (all_58_12 = e2)
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REDUCE: (53), (114) imply:
% 179.22/28.89  | | | |   (115)   ~ (all_52_25 = e2)
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | | REF_CLOSE: (25), (26), (60), (90), (115) are inconsistent by sub-proof
% 179.22/28.89  | | | |            #1028.
% 179.22/28.89  | | | | 
% 179.22/28.89  | | | End of split
% 179.22/28.89  | | | 
% 179.22/28.89  | | End of split
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #933 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_56_11 = all_52_23
% 179.22/28.89    (2)   ~ (all_52_27 = e0)
% 179.22/28.89    (3)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.22/28.89    (4)  all_58_10 = all_52_15
% 179.22/28.89    (5)  op(e0, e1) = all_52_29
% 179.22/28.89    (6)   ~ (e3 = e1)
% 179.22/28.89    (7)  all_56_7 = e3
% 179.22/28.89    (8)  op(e0, e2) = all_52_27
% 179.22/28.89    (9)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.22/28.89    (10)   ~ (all_52_15 = all_52_23)
% 179.22/28.89    (11)   ~ (e1 = e0)
% 179.22/28.89    (12)  all_58_11 = all_52_23
% 179.22/28.89    (13)  all_58_15 = e0
% 179.22/28.89    (14)   ~ (all_52_29 = e0)
% 179.22/28.89    (15)  all_56_11 = e3 | all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.22/28.89    (16)   ~ (e2 = e1)
% 179.22/28.89    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.89    (18)  op(e0, all_52_23) = e0
% 179.22/28.89    (19)  all_56_7 = all_52_15
% 179.22/28.89    (20)   ~ (e2 = e0)
% 179.22/28.89    (21)   ~ (e3 = e2)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (7), (19) imply:
% 179.22/28.89  |   (22)  all_52_15 = e3
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (22) implies:
% 179.22/28.89  |   (23)  all_52_15 = e3
% 179.22/28.89  | 
% 179.22/28.89  | COMBINE_EQS: (4), (23) imply:
% 179.22/28.89  |   (24)  all_58_10 = e3
% 179.22/28.89  | 
% 179.22/28.89  | REDUCE: (10), (23) imply:
% 179.22/28.89  |   (25)   ~ (all_52_23 = e3)
% 179.22/28.89  | 
% 179.22/28.89  | SIMP: (25) implies:
% 179.22/28.89  |   (26)   ~ (all_52_23 = e3)
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (15) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (27)  all_56_11 = e3
% 179.22/28.89  | | 
% 179.22/28.89  | | REF_CLOSE: (1), (26), (27) are inconsistent by sub-proof #939.
% 179.22/28.89  | | 
% 179.22/28.89  | Case 2:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (28)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.22/28.89  | | 
% 179.22/28.89  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (12), (13), (14), (16),
% 179.22/28.89  | |            (17), (18), (20), (21), (24), (28) are inconsistent by sub-proof
% 179.22/28.89  | |            #934.
% 179.22/28.89  | | 
% 179.22/28.89  | End of split
% 179.22/28.89  | 
% 179.22/28.89  End of proof
% 179.22/28.89  
% 179.22/28.89  Sub-proof #934 shows that the following formulas are inconsistent:
% 179.22/28.89  ----------------------------------------------------------------
% 179.22/28.89    (1)  all_56_11 = e2 | all_56_11 = e1 | all_56_11 = e0
% 179.22/28.89    (2)  all_56_11 = all_52_23
% 179.22/28.89    (3)   ~ (all_52_27 = e0)
% 179.22/28.89    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.22/28.89    (5)  op(e0, e1) = all_52_29
% 179.22/28.89    (6)   ~ (e3 = e1)
% 179.22/28.89    (7)  op(e0, e2) = all_52_27
% 179.22/28.89    (8)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.22/28.89    (9)  all_58_10 = e3
% 179.22/28.89    (10)   ~ (e1 = e0)
% 179.22/28.89    (11)  all_58_11 = all_52_23
% 179.22/28.89    (12)  all_58_15 = e0
% 179.22/28.89    (13)   ~ (all_52_29 = e0)
% 179.22/28.89    (14)   ~ (e2 = e1)
% 179.22/28.89    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.89    (16)  op(e0, all_52_23) = e0
% 179.22/28.89    (17)   ~ (e2 = e0)
% 179.22/28.89    (18)   ~ (e3 = e2)
% 179.22/28.89  
% 179.22/28.89  Begin of proof
% 179.22/28.89  | 
% 179.22/28.89  | BETA: splitting (8) gives:
% 179.22/28.89  | 
% 179.22/28.89  | Case 1:
% 179.22/28.89  | | 
% 179.22/28.89  | |   (19)  all_58_9 = e2
% 179.22/28.89  | | 
% 179.22/28.89  | | BETA: splitting (4) gives:
% 179.22/28.89  | | 
% 179.22/28.89  | | Case 1:
% 179.22/28.89  | | | 
% 179.22/28.90  | | |   (20)  all_58_9 = e1
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (14), (19), (20) are inconsistent by sub-proof #938.
% 179.22/28.90  | | | 
% 179.22/28.90  | | Case 2:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (21)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.22/28.90  | | | 
% 179.22/28.90  | | | BETA: splitting (21) gives:
% 179.22/28.90  | | | 
% 179.22/28.90  | | | Case 1:
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | |   (22)  all_58_10 = e1
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | | REF_CLOSE: (6), (9), (22) are inconsistent by sub-proof #937.
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | Case 2:
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | |   (23)  all_58_11 = e1 | all_58_15 = e1
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | | BETA: splitting (23) gives:
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | | Case 1:
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | |   (24)  all_58_11 = e1
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | | COMBINE_EQS: (11), (24) imply:
% 179.22/28.90  | | | | |   (25)  all_52_23 = e1
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | | SIMP: (25) implies:
% 179.22/28.90  | | | | |   (26)  all_52_23 = e1
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | | REDUCE: (16), (26) imply:
% 179.22/28.90  | | | | |   (27)  op(e0, e1) = e0
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | | REF_CLOSE: (5), (13), (15), (27) are inconsistent by sub-proof #990.
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | Case 2:
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | |   (28)  all_58_15 = e1
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | | REF_CLOSE: (10), (12), (28) are inconsistent by sub-proof #988.
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | End of split
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | End of split
% 179.22/28.90  | | | 
% 179.22/28.90  | | End of split
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (29)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.22/28.90  | | 
% 179.22/28.90  | | BETA: splitting (29) gives:
% 179.22/28.90  | | 
% 179.22/28.90  | | Case 1:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (30)  all_58_10 = e2
% 179.22/28.90  | | | 
% 179.22/28.90  | | | COMBINE_EQS: (9), (30) imply:
% 179.22/28.90  | | |   (31)  e3 = e2
% 179.22/28.90  | | | 
% 179.22/28.90  | | | SIMP: (31) implies:
% 179.22/28.90  | | |   (32)  e3 = e2
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REDUCE: (18), (32) imply:
% 179.22/28.90  | | |   (33)  $false
% 179.22/28.90  | | | 
% 179.22/28.90  | | | CLOSE: (33) is inconsistent.
% 179.22/28.90  | | | 
% 179.22/28.90  | | Case 2:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (34)  all_58_11 = e2 | all_58_15 = e2
% 179.22/28.90  | | | 
% 179.22/28.90  | | | BETA: splitting (1) gives:
% 179.22/28.90  | | | 
% 179.22/28.90  | | | Case 1:
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | |   (35)  all_56_11 = e2
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | | REF_CLOSE: (2), (3), (7), (15), (16), (35) are inconsistent by sub-proof
% 179.22/28.90  | | | |            #936.
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | Case 2:
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | |   (36)   ~ (all_56_11 = e2)
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | | REDUCE: (2), (36) imply:
% 179.22/28.90  | | | |   (37)   ~ (all_52_23 = e2)
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | | BETA: splitting (34) gives:
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | | Case 1:
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | |   (38)  all_58_11 = e2
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | | REF_CLOSE: (11), (37), (38) are inconsistent by sub-proof #935.
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | Case 2:
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | |   (39)  all_58_15 = e2
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | | REF_CLOSE: (12), (17), (39) are inconsistent by sub-proof #991.
% 179.22/28.90  | | | | | 
% 179.22/28.90  | | | | End of split
% 179.22/28.90  | | | | 
% 179.22/28.90  | | | End of split
% 179.22/28.90  | | | 
% 179.22/28.90  | | End of split
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #935 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  all_58_11 = all_52_23
% 179.22/28.90    (2)  all_58_11 = e2
% 179.22/28.90    (3)   ~ (all_52_23 = e2)
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.90  |   (4)  all_52_23 = e2
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (4) implies:
% 179.22/28.90  |   (5)  all_52_23 = e2
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (3), (5) imply:
% 179.22/28.90  |   (6)  $false
% 179.22/28.90  | 
% 179.22/28.90  | CLOSE: (6) is inconsistent.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #936 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  all_56_11 = e2
% 179.22/28.90    (2)  all_56_11 = all_52_23
% 179.22/28.90    (3)   ~ (all_52_27 = e0)
% 179.22/28.90    (4)  op(e0, e2) = all_52_27
% 179.22/28.90    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (6)  op(e0, all_52_23) = e0
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.90  |   (7)  all_52_23 = e2
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (7) implies:
% 179.22/28.90  |   (8)  all_52_23 = e2
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (6), (8) imply:
% 179.22/28.90  |   (9)  op(e0, e2) = e0
% 179.22/28.90  | 
% 179.22/28.90  | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1039.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #937 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  all_58_10 = e3
% 179.22/28.90    (2)  all_58_10 = e1
% 179.22/28.90    (3)   ~ (e3 = e1)
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.90  |   (4)  e3 = e1
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (4) implies:
% 179.22/28.90  |   (5)  e3 = e1
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (3), (5) imply:
% 179.22/28.90  |   (6)  $false
% 179.22/28.90  | 
% 179.22/28.90  | CLOSE: (6) is inconsistent.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #938 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  all_58_9 = e2
% 179.22/28.90    (2)  all_58_9 = e1
% 179.22/28.90    (3)   ~ (e2 = e1)
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.90  |   (4)  e2 = e1
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (4) implies:
% 179.22/28.90  |   (5)  e2 = e1
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (3), (5) imply:
% 179.22/28.90  |   (6)  $false
% 179.22/28.90  | 
% 179.22/28.90  | CLOSE: (6) is inconsistent.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #939 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  all_56_11 = all_52_23
% 179.22/28.90    (2)  all_56_11 = e3
% 179.22/28.90    (3)   ~ (all_52_23 = e3)
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | COMBINE_EQS: (1), (2) imply:
% 179.22/28.90  |   (4)  all_52_23 = e3
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (4) implies:
% 179.22/28.90  |   (5)  all_52_23 = e3
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (3), (5) imply:
% 179.22/28.90  |   (6)  $false
% 179.22/28.90  | 
% 179.22/28.90  | CLOSE: (6) is inconsistent.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #940 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ~ (all_52_25 = e3)
% 179.22/28.90    (2)  op(e0, e3) = e1
% 179.22/28.90    (3)   ~ (all_4_2 = e3)
% 179.22/28.90    (4)  all_58_10 = all_52_15
% 179.22/28.90    (5)  all_58_0 = all_4_2
% 179.22/28.90    (6)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90    (7)   ~ (e3 = e0)
% 179.22/28.90    (8)  all_58_6 = all_52_17
% 179.22/28.90    (9)  op(e3, all_52_17) = e3
% 179.22/28.90    (10)   ~ (e1 = e0)
% 179.22/28.90    (11)  all_58_11 = all_52_23
% 179.22/28.90    (12)  all_58_15 = e0
% 179.22/28.90    (13)  all_58_2 = all_52_9
% 179.22/28.90    (14)  op(e3, e3) = all_4_2
% 179.22/28.90    (15)   ~ (all_52_17 = all_4_2)
% 179.22/28.90    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (17)  op(e0, all_52_23) = e0
% 179.22/28.90    (18)   ~ (all_52_7 = e3)
% 179.22/28.90    (19)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.90    (20)  all_58_9 = all_52_7
% 179.22/28.90    (21)  all_58_12 = all_52_25
% 179.22/28.90    (22)   ~ (all_52_9 = all_52_15)
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (6) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (23)  all_58_0 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | COMBINE_EQS: (5), (23) imply:
% 179.22/28.90  | |   (24)  all_4_2 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REDUCE: (3), (24) imply:
% 179.22/28.90  | |   (25)  $false
% 179.22/28.90  | | 
% 179.22/28.90  | | CLOSE: (25) is inconsistent.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (26)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | BETA: splitting (26) gives:
% 179.22/28.90  | | 
% 179.22/28.90  | | Case 1:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (27)  all_58_2 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | COMBINE_EQS: (13), (27) imply:
% 179.22/28.90  | | |   (28)  all_52_9 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REDUCE: (22), (28) imply:
% 179.22/28.90  | | |   (29)   ~ (all_52_15 = e3)
% 179.22/28.90  | | | 
% 179.22/28.90  | | | SIMP: (29) implies:
% 179.22/28.90  | | |   (30)   ~ (all_52_15 = e3)
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (2), (4), (7), (10), (11), (12), (16), (17), (18), (19), (20),
% 179.22/28.90  | | |            (30) are inconsistent by sub-proof #941.
% 179.22/28.90  | | | 
% 179.22/28.90  | | Case 2:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (31)  all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (1), (8), (9), (14), (15), (16), (21), (31) are inconsistent by
% 179.22/28.90  | | |            sub-proof #947.
% 179.22/28.90  | | | 
% 179.22/28.90  | | End of split
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #941 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  op(e0, e3) = e1
% 179.22/28.90    (2)  all_58_10 = all_52_15
% 179.22/28.90    (3)   ~ (e3 = e0)
% 179.22/28.90    (4)   ~ (all_52_15 = e3)
% 179.22/28.90    (5)   ~ (e1 = e0)
% 179.22/28.90    (6)  all_58_11 = all_52_23
% 179.22/28.90    (7)  all_58_15 = e0
% 179.22/28.90    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (9)  op(e0, all_52_23) = e0
% 179.22/28.90    (10)   ~ (all_52_7 = e3)
% 179.22/28.90    (11)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.90    (12)  all_58_9 = all_52_7
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (11) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (13)  all_58_9 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (10), (12), (13) are inconsistent by sub-proof #972.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (14)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (14) are
% 179.22/28.90  | |            inconsistent by sub-proof #942.
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #942 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  op(e0, e3) = e1
% 179.22/28.90    (2)  all_58_10 = all_52_15
% 179.22/28.90    (3)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.22/28.90    (4)   ~ (e3 = e0)
% 179.22/28.90    (5)   ~ (all_52_15 = e3)
% 179.22/28.90    (6)   ~ (e1 = e0)
% 179.22/28.90    (7)  all_58_11 = all_52_23
% 179.22/28.90    (8)  all_58_15 = e0
% 179.22/28.90    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (10)  op(e0, all_52_23) = e0
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (3) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (11)  all_58_10 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (2), (5), (11) are inconsistent by sub-proof #1018.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (12)  all_58_11 = e3 | all_58_15 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | BETA: splitting (12) gives:
% 179.22/28.90  | | 
% 179.22/28.90  | | Case 1:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (13)  all_58_11 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | COMBINE_EQS: (7), (13) imply:
% 179.22/28.90  | | |   (14)  all_52_23 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | SIMP: (14) implies:
% 179.22/28.90  | | |   (15)  all_52_23 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REDUCE: (10), (15) imply:
% 179.22/28.90  | | |   (16)  op(e0, e3) = e0
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (1), (6), (9), (16) are inconsistent by sub-proof #1007.
% 179.22/28.90  | | | 
% 179.22/28.90  | | Case 2:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (17)  all_58_15 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | COMBINE_EQS: (8), (17) imply:
% 179.22/28.90  | | |   (18)  e3 = e0
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REDUCE: (4), (18) imply:
% 179.22/28.90  | | |   (19)  $false
% 179.22/28.90  | | | 
% 179.22/28.90  | | | CLOSE: (19) is inconsistent.
% 179.22/28.90  | | | 
% 179.22/28.90  | | End of split
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #943 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ~ (all_52_25 = e3)
% 179.22/28.90    (2)  all_56_9 = all_52_19
% 179.22/28.90    (3)  all_58_7 = all_52_19
% 179.22/28.90    (4)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.22/28.90    (6)   ~ (all_52_7 = all_4_2)
% 179.22/28.90    (7)  all_58_0 = all_4_2
% 179.22/28.90    (8)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.22/28.90    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90    (10)  all_58_8 = all_14_2
% 179.22/28.90    (11)   ~ (all_52_5 = all_14_2)
% 179.22/28.90    (12)   ~ (all_52_9 = all_52_17)
% 179.22/28.90    (13)  all_58_6 = all_52_17
% 179.22/28.90    (14)  op(e2, all_52_19) = e2
% 179.22/28.90    (15)  op(e3, all_52_17) = e3
% 179.22/28.90    (16)  all_58_11 = all_52_23
% 179.22/28.90    (17)  all_58_2 = all_52_9
% 179.22/28.90    (18)  op(e3, e1) = all_52_5
% 179.22/28.90    (19)  op(e1, e3) = all_52_17
% 179.22/28.90    (20)  op(e3, e3) = all_4_2
% 179.22/28.90    (21)   ~ (all_52_17 = all_4_2)
% 179.22/28.90    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (23)  op(e1, all_14_2) = e1
% 179.22/28.90    (24)  all_52_7 = e3
% 179.22/28.90    (25)   ~ (all_52_7 = all_52_23)
% 179.22/28.90    (26)  all_58_12 = all_52_25
% 179.22/28.90    (27)   ~ (e3 = e2)
% 179.22/28.90    (28)  op(e2, e3) = all_52_9
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (24), (25) imply:
% 179.22/28.90  |   (29)   ~ (all_52_23 = e3)
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (29) implies:
% 179.22/28.90  |   (30)   ~ (all_52_23 = e3)
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (6), (24) imply:
% 179.22/28.90  |   (31)   ~ (all_4_2 = e3)
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (31) implies:
% 179.22/28.90  |   (32)   ~ (all_4_2 = e3)
% 179.22/28.90  | 
% 179.22/28.90  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 179.22/28.90  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 179.22/28.90  |            (27), (28), (30), (32) are inconsistent by sub-proof #944.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #944 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ~ (all_52_25 = e3)
% 179.22/28.90    (2)   ~ (all_4_2 = e3)
% 179.22/28.90    (3)  all_56_9 = all_52_19
% 179.22/28.90    (4)  all_58_7 = all_52_19
% 179.22/28.90    (5)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90    (6)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.22/28.90    (7)  all_58_0 = all_4_2
% 179.22/28.90    (8)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.22/28.90    (9)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90    (10)  all_58_8 = all_14_2
% 179.22/28.90    (11)   ~ (all_52_5 = all_14_2)
% 179.22/28.90    (12)   ~ (all_52_23 = e3)
% 179.22/28.90    (13)   ~ (all_52_9 = all_52_17)
% 179.22/28.90    (14)  all_58_6 = all_52_17
% 179.22/28.90    (15)  op(e2, all_52_19) = e2
% 179.22/28.90    (16)  op(e3, all_52_17) = e3
% 179.22/28.90    (17)  all_58_11 = all_52_23
% 179.22/28.90    (18)  all_58_2 = all_52_9
% 179.22/28.90    (19)  op(e3, e1) = all_52_5
% 179.22/28.90    (20)  op(e1, e3) = all_52_17
% 179.22/28.90    (21)  op(e3, e3) = all_4_2
% 179.22/28.90    (22)   ~ (all_52_17 = all_4_2)
% 179.22/28.90    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (24)  op(e1, all_14_2) = e1
% 179.22/28.90    (25)  all_58_12 = all_52_25
% 179.22/28.90    (26)   ~ (e3 = e2)
% 179.22/28.90    (27)  op(e2, e3) = all_52_9
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (9) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (28)  all_58_0 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | COMBINE_EQS: (7), (28) imply:
% 179.22/28.90  | |   (29)  all_4_2 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REDUCE: (2), (29) imply:
% 179.22/28.90  | |   (30)  $false
% 179.22/28.90  | | 
% 179.22/28.90  | | CLOSE: (30) is inconsistent.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (31)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14), (15),
% 179.22/28.90  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 179.22/28.90  | |            (27), (31) are inconsistent by sub-proof #945.
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #945 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ~ (all_52_25 = e3)
% 179.22/28.90    (2)  all_56_9 = all_52_19
% 179.22/28.90    (3)  all_58_7 = all_52_19
% 179.22/28.90    (4)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.22/28.90    (6)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.22/28.90    (7)  all_58_8 = all_14_2
% 179.22/28.90    (8)   ~ (all_52_5 = all_14_2)
% 179.22/28.90    (9)   ~ (all_52_23 = e3)
% 179.22/28.90    (10)   ~ (all_52_9 = all_52_17)
% 179.22/28.90    (11)  all_58_6 = all_52_17
% 179.22/28.90    (12)  op(e2, all_52_19) = e2
% 179.22/28.90    (13)  op(e3, all_52_17) = e3
% 179.22/28.90    (14)  all_58_11 = all_52_23
% 179.22/28.90    (15)  all_58_2 = all_52_9
% 179.22/28.90    (16)  op(e3, e1) = all_52_5
% 179.22/28.90    (17)  op(e1, e3) = all_52_17
% 179.22/28.90    (18)  op(e3, e3) = all_4_2
% 179.22/28.90    (19)   ~ (all_52_17 = all_4_2)
% 179.22/28.90    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (21)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90    (22)  op(e1, all_14_2) = e1
% 179.22/28.90    (23)  all_58_12 = all_52_25
% 179.22/28.90    (24)   ~ (e3 = e2)
% 179.22/28.90    (25)  op(e2, e3) = all_52_9
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (5) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (26)  all_58_2 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | COMBINE_EQS: (15), (26) imply:
% 179.22/28.90  | |   (27)  all_52_9 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | SIMP: (27) implies:
% 179.22/28.90  | |   (28)  all_52_9 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REDUCE: (10), (28) imply:
% 179.22/28.90  | |   (29)   ~ (all_52_17 = e3)
% 179.22/28.90  | | 
% 179.22/28.90  | | SIMP: (29) implies:
% 179.22/28.90  | |   (30)   ~ (all_52_17 = e3)
% 179.22/28.90  | | 
% 179.22/28.90  | | REDUCE: (25), (28) imply:
% 179.22/28.90  | |   (31)  op(e2, e3) = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | BETA: splitting (4) gives:
% 179.22/28.90  | | 
% 179.22/28.90  | | Case 1:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (32)  all_58_6 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (11), (30), (32) are inconsistent by sub-proof #981.
% 179.22/28.90  | | | 
% 179.22/28.90  | | Case 2:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (33)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (12), (13), (14), (16), (17),
% 179.22/28.90  | | |            (20), (22), (24), (31), (33) are inconsistent by sub-proof
% 179.22/28.90  | | |            #949.
% 179.22/28.90  | | | 
% 179.22/28.90  | | End of split
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (34)   ~ (all_58_2 = e3)
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (1), (11), (13), (15), (18), (19), (20), (21), (23), (34) are
% 179.22/28.90  | |            inconsistent by sub-proof #946.
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #946 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ~ (all_52_25 = e3)
% 179.22/28.90    (2)   ~ (all_58_2 = e3)
% 179.22/28.90    (3)  all_58_6 = all_52_17
% 179.22/28.90    (4)  op(e3, all_52_17) = e3
% 179.22/28.90    (5)  all_58_2 = all_52_9
% 179.22/28.90    (6)  op(e3, e3) = all_4_2
% 179.22/28.90    (7)   ~ (all_52_17 = all_4_2)
% 179.22/28.90    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (9)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90    (10)  all_58_12 = all_52_25
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (2), (5) imply:
% 179.22/28.90  |   (11)   ~ (all_52_9 = e3)
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (9) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (12)  all_58_2 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (5), (11), (12) are inconsistent by sub-proof #980.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (13)  all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (13) are inconsistent by
% 179.22/28.90  | |            sub-proof #947.
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #947 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ~ (all_52_25 = e3)
% 179.22/28.90    (2)  all_58_6 = all_52_17
% 179.22/28.90    (3)  op(e3, all_52_17) = e3
% 179.22/28.90    (4)  op(e3, e3) = all_4_2
% 179.22/28.90    (5)   ~ (all_52_17 = all_4_2)
% 179.22/28.90    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (7)  all_58_6 = e3 | all_58_12 = e3
% 179.22/28.90    (8)  all_58_12 = all_52_25
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (7) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (9)  all_58_6 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | COMBINE_EQS: (2), (9) imply:
% 179.22/28.90  | |   (10)  all_52_17 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #948.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (11)  all_58_12 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #1003.
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #948 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  op(e3, all_52_17) = e3
% 179.22/28.90    (2)  op(e3, e3) = all_4_2
% 179.22/28.90    (3)   ~ (all_52_17 = all_4_2)
% 179.22/28.90    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (5)  all_52_17 = e3
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (5) implies:
% 179.22/28.90  |   (6)  all_52_17 = e3
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (3), (6) imply:
% 179.22/28.90  |   (7)   ~ (all_4_2 = e3)
% 179.22/28.90  | 
% 179.22/28.90  | SIMP: (7) implies:
% 179.22/28.90  |   (8)   ~ (all_4_2 = e3)
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (1), (6) imply:
% 179.22/28.90  |   (9)  op(e3, e3) = e3
% 179.22/28.90  | 
% 179.22/28.90  | REF_CLOSE: (2), (4), (8), (9) are inconsistent by sub-proof #1006.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #949 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90    (2)  all_56_9 = all_52_19
% 179.22/28.90    (3)  all_58_7 = all_52_19
% 179.22/28.90    (4)  all_56_9 = e3 | all_56_9 = e2 | all_56_9 = e1 | all_56_9 = e0
% 179.22/28.90    (5)  all_58_8 = all_14_2
% 179.22/28.90    (6)   ~ (all_52_5 = all_14_2)
% 179.22/28.90    (7)   ~ (all_52_23 = e3)
% 179.22/28.90    (8)  op(e2, all_52_19) = e2
% 179.22/28.90    (9)  op(e3, all_52_17) = e3
% 179.22/28.90    (10)  all_58_11 = all_52_23
% 179.22/28.90    (11)  op(e2, e3) = e3
% 179.22/28.90    (12)  op(e3, e1) = all_52_5
% 179.22/28.90    (13)  op(e1, e3) = all_52_17
% 179.22/28.90    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (15)  op(e1, all_14_2) = e1
% 179.22/28.90    (16)   ~ (e3 = e2)
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (4) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (17)  all_56_9 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | COMBINE_EQS: (2), (17) imply:
% 179.22/28.90  | |   (18)  all_52_19 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | SIMP: (18) implies:
% 179.22/28.90  | |   (19)  all_52_19 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REDUCE: (8), (19) imply:
% 179.22/28.90  | |   (20)  op(e2, e3) = e2
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (11), (14), (16), (20) are inconsistent by sub-proof #951.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (21)   ~ (all_56_9 = e3)
% 179.22/28.90  | | 
% 179.22/28.90  | | REDUCE: (2), (21) imply:
% 179.22/28.90  | |   (22)   ~ (all_52_19 = e3)
% 179.22/28.90  | | 
% 179.22/28.90  | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (12), (13), (14), (15), (22)
% 179.22/28.90  | |            are inconsistent by sub-proof #950.
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #950 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90    (2)  all_58_7 = all_52_19
% 179.22/28.90    (3)  all_58_8 = all_14_2
% 179.22/28.90    (4)   ~ (all_52_5 = all_14_2)
% 179.22/28.90    (5)   ~ (all_52_23 = e3)
% 179.22/28.90    (6)  op(e3, all_52_17) = e3
% 179.22/28.90    (7)  all_58_11 = all_52_23
% 179.22/28.90    (8)  op(e3, e1) = all_52_5
% 179.22/28.90    (9)   ~ (all_52_19 = e3)
% 179.22/28.90    (10)  op(e1, e3) = all_52_17
% 179.22/28.90    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (12)  op(e1, all_14_2) = e1
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | BETA: splitting (1) gives:
% 179.22/28.90  | 
% 179.22/28.90  | Case 1:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (13)  all_58_7 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | COMBINE_EQS: (2), (13) imply:
% 179.22/28.90  | |   (14)  all_52_19 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | REDUCE: (9), (14) imply:
% 179.22/28.90  | |   (15)  $false
% 179.22/28.90  | | 
% 179.22/28.90  | | CLOSE: (15) is inconsistent.
% 179.22/28.90  | | 
% 179.22/28.90  | Case 2:
% 179.22/28.90  | | 
% 179.22/28.90  | |   (16)  all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90  | | 
% 179.22/28.90  | | BETA: splitting (16) gives:
% 179.22/28.90  | | 
% 179.22/28.90  | | Case 1:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (17)  all_58_8 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | COMBINE_EQS: (3), (17) imply:
% 179.22/28.90  | | |   (18)  all_14_2 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REDUCE: (4), (18) imply:
% 179.22/28.90  | | |   (19)   ~ (all_52_5 = e3)
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REDUCE: (12), (18) imply:
% 179.22/28.90  | | |   (20)  op(e1, e3) = e1
% 179.22/28.90  | | | 
% 179.22/28.90  | | | GROUND_INST: instantiating (11) with all_52_17, e1, e3, e1, simplifying
% 179.22/28.90  | | |              with (10), (20) gives:
% 179.22/28.90  | | |   (21)  all_52_17 = e1
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REDUCE: (6), (21) imply:
% 179.22/28.90  | | |   (22)  op(e3, e1) = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (8), (11), (19), (22) are inconsistent by sub-proof #1023.
% 179.22/28.90  | | | 
% 179.22/28.90  | | Case 2:
% 179.22/28.90  | | | 
% 179.22/28.90  | | |   (23)  all_58_11 = e3
% 179.22/28.90  | | | 
% 179.22/28.90  | | | REF_CLOSE: (5), (7), (23) are inconsistent by sub-proof #1017.
% 179.22/28.90  | | | 
% 179.22/28.90  | | End of split
% 179.22/28.90  | | 
% 179.22/28.90  | End of split
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #951 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.22/28.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.22/28.90    (2)  op(e2, e3) = e3
% 179.22/28.90    (3)  op(e2, e3) = e2
% 179.22/28.90    (4)   ~ (e3 = e2)
% 179.22/28.90  
% 179.22/28.90  Begin of proof
% 179.22/28.90  | 
% 179.22/28.90  | GROUND_INST: instantiating (1) with e2, e3, e3, e2, simplifying with (2), (3)
% 179.22/28.90  |              gives:
% 179.22/28.90  |   (5)  e3 = e2
% 179.22/28.90  | 
% 179.22/28.90  | REDUCE: (4), (5) imply:
% 179.22/28.90  |   (6)  $false
% 179.22/28.90  | 
% 179.22/28.90  | CLOSE: (6) is inconsistent.
% 179.22/28.90  | 
% 179.22/28.90  End of proof
% 179.22/28.90  
% 179.22/28.90  Sub-proof #952 shows that the following formulas are inconsistent:
% 179.22/28.90  ----------------------------------------------------------------
% 179.22/28.90    (1)   ~ (all_52_27 = all_10_2)
% 179.22/28.90    (2)   ~ (all_52_17 = all_52_23)
% 179.22/28.90    (3)  op(e2, all_10_2) = all_10_1
% 179.22/28.90    (4)   ~ (all_52_13 = all_52_29)
% 179.22/28.90    (5)  all_56_3 = all_52_7
% 179.22/28.90    (6)  op(e3, e2) = all_52_3
% 179.22/28.90    (7)   ~ (all_52_9 = all_52_25)
% 179.22/28.90    (8)  op(e3, all_52_25) = all_52_24
% 179.22/28.90    (9)   ~ (all_52_27 = e0)
% 179.22/28.90    (10)  op(e3, all_52_9) = all_52_8
% 179.22/28.90    (11)   ~ (all_52_3 = all_10_2)
% 179.22/28.90    (12)  all_58_5 = all_52_13
% 179.22/28.90    (13)   ~ (all_52_25 = all_52_29)
% 179.22/28.90    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.22/28.90    (15)  all_58_3 = all_10_2
% 179.22/28.90    (16)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.22/28.90    (17)  all_58_15 = all_6_2
% 179.22/28.90    (18)   ~ (all_52_9 = all_4_2)
% 179.22/28.90    (19)   ~ (all_52_5 = all_52_7)
% 179.22/28.90    (20)  all_58_10 = all_52_15
% 179.22/28.90    (21)  all_58_7 = all_52_19
% 179.22/28.90    (22)   ~ (all_52_17 = all_52_25)
% 179.22/28.90    (23)  op(e0, e1) = all_52_29
% 179.22/28.90    (24)   ~ (all_4_0 = e2)
% 179.22/28.90    (25)  all_58_4 = all_52_5
% 179.22/28.90    (26)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.22/28.90    (27)   ~ (e3 = e1)
% 179.22/28.90    (28)   ~ (all_52_27 = all_52_29)
% 179.22/28.90    (29)   ~ (all_52_17 = all_14_2)
% 179.22/28.90    (30)  op(e3, all_4_2) = all_4_1
% 179.22/28.90    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.22/28.90    (32)   ~ (all_52_7 = all_4_2)
% 179.22/28.90    (33)  all_58_1 = all_52_3
% 179.22/28.90    (34)  all_58_0 = all_4_2
% 179.22/28.90    (35)  op(e1, all_52_13) = all_52_12
% 179.22/28.91    (36)  op(e1, all_52_29) = all_52_28
% 179.22/28.91    (37)   ~ (all_52_7 = e0)
% 179.22/28.91    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0) |
% 179.22/28.91          (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0)
% 179.22/28.91    (39)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 179.22/28.91    (40)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.22/28.91    (41)  all_58_14 = all_52_29
% 179.22/28.91    (42)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.22/28.91    (43)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.22/28.91    (44)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.22/28.91    (45)  all_58_8 = all_14_2
% 179.22/28.91    (46)  all_56_1 = all_52_3
% 179.22/28.91    (47)  op(e0, e2) = all_52_27
% 179.22/28.91    (48)  op(all_4_1, all_4_2) = all_4_0
% 179.22/28.91    (49)   ~ (all_52_3 = all_4_2)
% 179.22/28.91    (50)  op(e0, e3) = all_52_25
% 179.22/28.91    (51)  all_52_0 = all_4_1
% 179.22/28.91    (52)  all_52_10 = all_10_1
% 179.25/28.91    (53)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.25/28.91    (54)   ~ (all_52_13 = all_14_2)
% 179.25/28.91    (55)   ~ (e3 = e0)
% 179.25/28.91    (56)   ~ (all_52_9 = all_52_13)
% 179.25/28.91    (57)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.25/28.91    (58)   ~ (all_52_15 = all_52_23)
% 179.25/28.91    (59)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.25/28.91    (60)  op(all_10_1, all_10_2) = all_10_0
% 179.25/28.91    (61)   ~ (all_52_5 = all_52_29)
% 179.25/28.91    (62)  all_56_12 = all_52_25
% 179.25/28.91    (63)  all_58_13 = all_52_27
% 179.25/28.91    (64)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.25/28.91    (65)   ~ (all_52_25 = e0)
% 179.25/28.91    (66)   ~ (all_52_9 = all_52_17)
% 179.25/28.91    (67)  all_58_6 = all_52_17
% 179.25/28.91    (68)   ~ (all_52_3 = all_52_7)
% 179.25/28.91    (69)   ~ (e1 = e0)
% 179.25/28.91    (70)  all_56_0 = all_4_2
% 179.25/28.91    (71)  all_58_11 = all_52_23
% 179.25/28.91    (72)   ~ (all_52_3 = all_52_19)
% 179.25/28.91    (73)   ~ (all_52_7 = all_52_15)
% 179.25/28.91    (74)  op(e0, all_52_15) = all_52_14
% 179.25/28.91    (75)   ~ (all_52_29 = all_14_2)
% 179.25/28.91    (76)   ~ (all_4_0 = e1)
% 179.25/28.91    (77)   ~ (all_52_19 = all_10_2)
% 179.25/28.91    (78)  all_58_15 = e0
% 179.25/28.91    (79)  all_58_2 = all_52_9
% 179.25/28.91    (80)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.25/28.91    (81)   ~ (all_52_29 = e0)
% 179.25/28.91    (82)  op(e3, e1) = all_52_5
% 179.25/28.91    (83)  all_56_10 = all_14_2
% 179.25/28.91    (84)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.25/28.91    (85)  op(e1, e3) = all_52_17
% 179.25/28.91    (86)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.25/28.91    (87)   ~ (all_52_25 = all_4_2)
% 179.25/28.91    (88)  op(e3, e3) = all_4_2
% 179.25/28.91    (89)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.91    (90)   ~ (all_52_25 = all_52_27)
% 179.25/28.91    (91)   ~ (all_52_7 = all_6_2)
% 179.25/28.91    (92)   ~ (all_10_0 = e3)
% 179.25/28.91    (93)   ~ (all_52_19 = all_52_27)
% 179.25/28.91    (94)  all_56_7 = all_52_15
% 179.25/28.91    (95)   ~ (all_52_15 = e0)
% 179.25/28.91    (96)   ~ (all_52_7 = all_52_23)
% 179.25/28.91    (97)  op(e2, all_52_27) = all_52_26
% 179.25/28.91    (98)   ~ (all_52_17 = all_52_19)
% 179.25/28.91    (99)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.91    (100)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.25/28.91    (101)  all_58_9 = all_52_7
% 179.25/28.91    (102)   ~ (e2 = e0)
% 179.25/28.91    (103)  all_58_12 = all_52_25
% 179.25/28.91    (104)   ~ (all_10_0 = e1)
% 179.25/28.91    (105)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.25/28.91    (106)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.25/28.91    (107)   ~ (all_52_19 = all_14_2)
% 179.25/28.91    (108)  op(e0, all_52_7) = all_52_6
% 179.25/28.91    (109)  op(e2, e3) = all_52_9
% 179.25/28.91    (110)  all_56_13 = all_52_27
% 179.25/28.91  
% 179.25/28.91  Begin of proof
% 179.25/28.91  | 
% 179.25/28.91  | BETA: splitting (38) gives:
% 179.25/28.91  | 
% 179.25/28.91  | Case 1:
% 179.25/28.91  | | 
% 179.25/28.91  | |   (111)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 179.25/28.91  | | 
% 179.25/28.91  | | REF_CLOSE: (5), (6), (9), (14), (16), (17), (19), (20), (23), (25), (30),
% 179.25/28.91  | |            (32), (33), (34), (37), (40), (41), (42), (43), (44), (47), (48),
% 179.25/28.91  | |            (50), (51), (53), (55), (57), (61), (62), (63), (64), (65), (68),
% 179.25/28.91  | |            (70), (71), (73), (78), (80), (81), (82), (84), (87), (89), (90),
% 179.25/28.91  | |            (91), (96), (99), (100), (101), (103), (105), (108), (110), (111)
% 179.25/28.91  | |            are inconsistent by sub-proof #1008.
% 179.25/28.91  | | 
% 179.25/28.91  | Case 2:
% 179.25/28.91  | | 
% 179.25/28.91  | |   (112)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 179.25/28.91  | | 
% 179.25/28.91  | | ALPHA: (112) implies:
% 179.25/28.91  | |   (113)  all_52_14 = e0
% 179.25/28.91  | |   (114)  all_52_12 = e1
% 179.25/28.91  | |   (115)  all_52_10 = e2
% 179.25/28.91  | |   (116)  all_52_8 = e3
% 179.25/28.91  | | 
% 179.25/28.91  | | COMBINE_EQS: (52), (115) imply:
% 179.25/28.91  | |   (117)  all_10_1 = e2
% 179.25/28.91  | | 
% 179.25/28.91  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 179.25/28.91  | |            (13), (14), (15), (18), (19), (20), (21), (22), (23), (24), (25),
% 179.25/28.91  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 179.25/28.91  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 179.25/28.91  | |            (50), (53), (54), (55), (56), (57), (58), (59), (60), (62), (63),
% 179.25/28.91  | |            (65), (66), (67), (68), (69), (71), (72), (73), (74), (75), (76),
% 179.25/28.91  | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86), (88),
% 179.25/28.91  | |            (89), (90), (92), (93), (94), (95), (96), (97), (98), (99),
% 179.25/28.91  | |            (100), (101), (102), (103), (104), (105), (106), (107), (109),
% 179.25/28.91  | |            (110), (113), (114), (116), (117) are inconsistent by sub-proof
% 179.25/28.91  | |            #953.
% 179.25/28.91  | | 
% 179.25/28.91  | End of split
% 179.25/28.91  | 
% 179.25/28.91  End of proof
% 179.25/28.91  
% 179.25/28.91  Sub-proof #953 shows that the following formulas are inconsistent:
% 179.25/28.91  ----------------------------------------------------------------
% 179.25/28.91    (1)   ~ (all_52_27 = all_10_2)
% 179.25/28.91    (2)   ~ (all_52_17 = all_52_23)
% 179.25/28.91    (3)  op(e2, all_10_2) = all_10_1
% 179.25/28.91    (4)   ~ (all_52_13 = all_52_29)
% 179.25/28.91    (5)  all_56_3 = all_52_7
% 179.25/28.91    (6)  op(e3, e2) = all_52_3
% 179.25/28.91    (7)   ~ (all_52_9 = all_52_25)
% 179.25/28.91    (8)  op(e3, all_52_25) = all_52_24
% 179.25/28.91    (9)   ~ (all_52_27 = e0)
% 179.25/28.91    (10)  op(e3, all_52_9) = all_52_8
% 179.25/28.91    (11)   ~ (all_52_3 = all_10_2)
% 179.25/28.91    (12)  all_58_5 = all_52_13
% 179.25/28.91    (13)   ~ (all_52_25 = all_52_29)
% 179.25/28.91    (14)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.25/28.91    (15)  all_58_3 = all_10_2
% 179.25/28.91    (16)  all_52_12 = e1
% 179.25/28.91    (17)   ~ (all_52_9 = all_4_2)
% 179.25/28.91    (18)   ~ (all_52_5 = all_52_7)
% 179.25/28.91    (19)  all_58_10 = all_52_15
% 179.25/28.91    (20)  all_58_7 = all_52_19
% 179.25/28.91    (21)   ~ (all_52_17 = all_52_25)
% 179.25/28.91    (22)  op(e0, e1) = all_52_29
% 179.25/28.91    (23)   ~ (all_4_0 = e2)
% 179.25/28.91    (24)  all_58_4 = all_52_5
% 179.25/28.91    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.91    (26)   ~ (e3 = e1)
% 179.25/28.91    (27)  all_52_14 = e0
% 179.25/28.91    (28)   ~ (all_52_27 = all_52_29)
% 179.25/28.91    (29)   ~ (all_52_17 = all_14_2)
% 179.25/28.91    (30)  op(e3, all_4_2) = all_4_1
% 179.25/28.91    (31)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.91    (32)   ~ (all_52_7 = all_4_2)
% 179.25/28.91    (33)  all_58_1 = all_52_3
% 179.25/28.91    (34)  all_58_0 = all_4_2
% 179.25/28.91    (35)  op(e1, all_52_13) = all_52_12
% 179.25/28.91    (36)  op(e1, all_52_29) = all_52_28
% 179.25/28.91    (37)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 179.25/28.91    (38)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.91    (39)  all_58_14 = all_52_29
% 179.25/28.91    (40)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.25/28.91    (41)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.91    (42)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.25/28.91    (43)  all_58_8 = all_14_2
% 179.25/28.91    (44)  all_56_1 = all_52_3
% 179.25/28.91    (45)  op(e0, e2) = all_52_27
% 179.25/28.91    (46)  op(all_4_1, all_4_2) = all_4_0
% 179.25/28.91    (47)   ~ (all_52_3 = all_4_2)
% 179.25/28.91    (48)  op(e0, e3) = all_52_25
% 179.25/28.91    (49)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.25/28.91    (50)   ~ (all_52_13 = all_14_2)
% 179.25/28.91    (51)   ~ (e3 = e0)
% 179.25/28.91    (52)   ~ (all_52_9 = all_52_13)
% 179.25/28.91    (53)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.25/28.91    (54)   ~ (all_52_15 = all_52_23)
% 179.25/28.91    (55)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.25/28.91    (56)  op(all_10_1, all_10_2) = all_10_0
% 179.25/28.91    (57)  all_56_12 = all_52_25
% 179.25/28.91    (58)  all_58_13 = all_52_27
% 179.25/28.91    (59)  all_52_8 = e3
% 179.25/28.91    (60)   ~ (all_52_25 = e0)
% 179.25/28.91    (61)   ~ (all_52_9 = all_52_17)
% 179.25/28.91    (62)  all_58_6 = all_52_17
% 179.25/28.91    (63)   ~ (all_52_3 = all_52_7)
% 179.25/28.91    (64)   ~ (e1 = e0)
% 179.25/28.91    (65)  all_58_11 = all_52_23
% 179.25/28.91    (66)   ~ (all_52_3 = all_52_19)
% 179.25/28.91    (67)   ~ (all_52_7 = all_52_15)
% 179.25/28.91    (68)  op(e0, all_52_15) = all_52_14
% 179.25/28.91    (69)   ~ (all_52_29 = all_14_2)
% 179.25/28.91    (70)   ~ (all_4_0 = e1)
% 179.25/28.91    (71)   ~ (all_52_19 = all_10_2)
% 179.25/28.91    (72)  all_58_15 = e0
% 179.25/28.91    (73)  all_58_2 = all_52_9
% 179.25/28.91    (74)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.25/28.91    (75)   ~ (all_52_29 = e0)
% 179.25/28.91    (76)  op(e3, e1) = all_52_5
% 179.25/28.91    (77)  all_56_10 = all_14_2
% 179.25/28.91    (78)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.25/28.91    (79)  op(e1, e3) = all_52_17
% 179.25/28.91    (80)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.25/28.91    (81)  op(e3, e3) = all_4_2
% 179.25/28.91    (82)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.91    (83)   ~ (all_52_25 = all_52_27)
% 179.25/28.91    (84)   ~ (all_10_0 = e3)
% 179.25/28.91    (85)   ~ (all_52_19 = all_52_27)
% 179.25/28.91    (86)  all_56_7 = all_52_15
% 179.25/28.91    (87)  all_10_1 = e2
% 179.25/28.91    (88)   ~ (all_52_15 = e0)
% 179.25/28.91    (89)   ~ (all_52_7 = all_52_23)
% 179.25/28.91    (90)  op(e2, all_52_27) = all_52_26
% 179.25/28.91    (91)   ~ (all_52_17 = all_52_19)
% 179.25/28.91    (92)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.91    (93)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.25/28.91    (94)  all_58_9 = all_52_7
% 179.25/28.91    (95)   ~ (e2 = e0)
% 179.25/28.91    (96)  all_58_12 = all_52_25
% 179.25/28.91    (97)   ~ (all_10_0 = e1)
% 179.25/28.91    (98)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.25/28.91    (99)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.25/28.91    (100)   ~ (all_52_19 = all_14_2)
% 179.25/28.91    (101)  op(e2, e3) = all_52_9
% 179.25/28.91    (102)  all_56_13 = all_52_27
% 179.25/28.91  
% 179.25/28.91  Begin of proof
% 179.25/28.91  | 
% 179.25/28.91  | REDUCE: (56), (87) imply:
% 179.25/28.91  |   (103)  op(e2, all_10_2) = all_10_0
% 179.25/28.91  | 
% 179.25/28.91  | REDUCE: (10), (59) imply:
% 179.25/28.91  |   (104)  op(e3, all_52_9) = e3
% 179.25/28.91  | 
% 179.25/28.91  | REDUCE: (3), (87) imply:
% 179.25/28.91  |   (105)  op(e2, all_10_2) = e2
% 179.25/28.91  | 
% 179.25/28.91  | REDUCE: (16), (35) imply:
% 179.25/28.91  |   (106)  op(e1, all_52_13) = e1
% 179.25/28.91  | 
% 179.25/28.91  | REDUCE: (27), (68) imply:
% 179.25/28.91  |   (107)  op(e0, all_52_15) = e0
% 179.25/28.91  | 
% 179.25/28.91  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 179.25/28.91  |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 179.25/28.91  |            (28), (29), (30), (31), (32), (33), (34), (36), (37), (38), (39),
% 179.25/28.91  |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 179.25/28.91  |            (51), (52), (53), (54), (55), (57), (58), (60), (61), (62), (63),
% 179.25/28.91  |            (64), (65), (66), (67), (69), (70), (71), (72), (73), (74), (75),
% 179.25/28.91  |            (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 179.25/28.91  |            (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 179.25/28.91  |            (99), (100), (101), (102), (103), (104), (105), (106), (107) are
% 179.25/28.91  |            inconsistent by sub-proof #954.
% 179.25/28.91  | 
% 179.25/28.91  End of proof
% 179.25/28.91  
% 179.25/28.91  Sub-proof #954 shows that the following formulas are inconsistent:
% 179.25/28.91  ----------------------------------------------------------------
% 179.25/28.91    (1)   ~ (all_52_27 = all_10_2)
% 179.25/28.91    (2)   ~ (all_52_17 = all_52_23)
% 179.25/28.91    (3)   ~ (all_52_13 = all_52_29)
% 179.25/28.91    (4)  op(e2, all_10_2) = all_10_0
% 179.25/28.91    (5)  all_56_3 = all_52_7
% 179.25/28.91    (6)  op(e3, e2) = all_52_3
% 179.25/28.91    (7)   ~ (all_52_9 = all_52_25)
% 179.25/28.91    (8)  op(e3, all_52_25) = all_52_24
% 179.25/28.91    (9)   ~ (all_52_27 = e0)
% 179.25/28.91    (10)   ~ (all_52_3 = all_10_2)
% 179.25/28.91    (11)  all_58_5 = all_52_13
% 179.25/28.91    (12)   ~ (all_52_25 = all_52_29)
% 179.25/28.91    (13)  op(e1, all_52_13) = e1
% 179.25/28.91    (14)  op(e0, all_52_15) = e0
% 179.25/28.91    (15)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.25/28.91    (16)  all_58_3 = all_10_2
% 179.25/28.91    (17)   ~ (all_52_9 = all_4_2)
% 179.25/28.91    (18)   ~ (all_52_5 = all_52_7)
% 179.25/28.91    (19)  all_58_10 = all_52_15
% 179.25/28.91    (20)  all_58_7 = all_52_19
% 179.25/28.91    (21)   ~ (all_52_17 = all_52_25)
% 179.25/28.91    (22)  op(e0, e1) = all_52_29
% 179.25/28.91    (23)   ~ (all_4_0 = e2)
% 179.25/28.91    (24)  all_58_4 = all_52_5
% 179.25/28.91    (25)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.91    (26)   ~ (e3 = e1)
% 179.25/28.91    (27)   ~ (all_52_27 = all_52_29)
% 179.25/28.91    (28)   ~ (all_52_17 = all_14_2)
% 179.25/28.91    (29)  op(e3, all_4_2) = all_4_1
% 179.25/28.91    (30)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.91    (31)   ~ (all_52_7 = all_4_2)
% 179.25/28.91    (32)  all_58_1 = all_52_3
% 179.25/28.91    (33)  all_58_0 = all_4_2
% 179.25/28.91    (34)  op(e1, all_52_29) = all_52_28
% 179.25/28.91    (35)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 179.25/28.91    (36)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.91    (37)  all_58_14 = all_52_29
% 179.25/28.91    (38)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.25/28.91    (39)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.91    (40)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.25/28.91    (41)  all_58_8 = all_14_2
% 179.25/28.91    (42)  all_56_1 = all_52_3
% 179.25/28.91    (43)  op(e0, e2) = all_52_27
% 179.25/28.91    (44)  op(all_4_1, all_4_2) = all_4_0
% 179.25/28.91    (45)   ~ (all_52_3 = all_4_2)
% 179.25/28.91    (46)  op(e0, e3) = all_52_25
% 179.25/28.91    (47)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.25/28.91    (48)   ~ (all_52_13 = all_14_2)
% 179.25/28.91    (49)  op(e3, all_52_9) = e3
% 179.25/28.91    (50)   ~ (e3 = e0)
% 179.25/28.91    (51)   ~ (all_52_9 = all_52_13)
% 179.25/28.91    (52)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.25/28.91    (53)   ~ (all_52_15 = all_52_23)
% 179.25/28.91    (54)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.25/28.91    (55)  all_56_12 = all_52_25
% 179.25/28.91    (56)  all_58_13 = all_52_27
% 179.25/28.91    (57)   ~ (all_52_25 = e0)
% 179.25/28.91    (58)   ~ (all_52_9 = all_52_17)
% 179.25/28.91    (59)  all_58_6 = all_52_17
% 179.25/28.91    (60)   ~ (all_52_3 = all_52_7)
% 179.25/28.91    (61)   ~ (e1 = e0)
% 179.25/28.91    (62)  all_58_11 = all_52_23
% 179.25/28.91    (63)   ~ (all_52_3 = all_52_19)
% 179.25/28.91    (64)   ~ (all_52_7 = all_52_15)
% 179.25/28.91    (65)   ~ (all_52_29 = all_14_2)
% 179.25/28.91    (66)   ~ (all_4_0 = e1)
% 179.25/28.91    (67)   ~ (all_52_19 = all_10_2)
% 179.25/28.91    (68)  all_58_15 = e0
% 179.25/28.91    (69)  all_58_2 = all_52_9
% 179.25/28.91    (70)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.25/28.91    (71)   ~ (all_52_29 = e0)
% 179.25/28.91    (72)  op(e3, e1) = all_52_5
% 179.25/28.91    (73)  all_56_10 = all_14_2
% 179.25/28.91    (74)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.25/28.91    (75)  op(e1, e3) = all_52_17
% 179.25/28.91    (76)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.25/28.91    (77)  op(e2, all_10_2) = e2
% 179.25/28.91    (78)  op(e3, e3) = all_4_2
% 179.25/28.91    (79)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.91    (80)   ~ (all_52_25 = all_52_27)
% 179.25/28.91    (81)   ~ (all_10_0 = e3)
% 179.25/28.91    (82)   ~ (all_52_19 = all_52_27)
% 179.25/28.91    (83)  all_56_7 = all_52_15
% 179.25/28.91    (84)   ~ (all_52_15 = e0)
% 179.25/28.91    (85)   ~ (all_52_7 = all_52_23)
% 179.25/28.91    (86)  op(e2, all_52_27) = all_52_26
% 179.25/28.91    (87)   ~ (all_52_17 = all_52_19)
% 179.25/28.91    (88)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.91    (89)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.25/28.91    (90)  all_58_9 = all_52_7
% 179.25/28.91    (91)   ~ (e2 = e0)
% 179.25/28.91    (92)  all_58_12 = all_52_25
% 179.25/28.91    (93)   ~ (all_10_0 = e1)
% 179.25/28.91    (94)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.25/28.91    (95)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.25/28.91    (96)   ~ (all_52_19 = all_14_2)
% 179.25/28.91    (97)  op(e2, e3) = all_52_9
% 179.25/28.91    (98)  all_56_13 = all_52_27
% 179.25/28.91  
% 179.25/28.91  Begin of proof
% 179.25/28.91  | 
% 179.25/28.91  | GROUND_INST: instantiating (79) with e2, all_10_0, all_10_2, e2, simplifying
% 179.25/28.91  |              with (4), (77) gives:
% 179.25/28.91  |   (99)  all_10_0 = e2
% 179.25/28.91  | 
% 179.25/28.91  | REDUCE: (81), (99) imply:
% 179.25/28.91  |   (100)   ~ (e3 = e2)
% 179.25/28.91  | 
% 179.25/28.91  | SIMP: (100) implies:
% 179.25/28.91  |   (101)   ~ (e3 = e2)
% 179.25/28.91  | 
% 179.25/28.91  | REDUCE: (93), (99) imply:
% 179.25/28.91  |   (102)   ~ (e2 = e1)
% 179.25/28.91  | 
% 179.25/28.91  | BETA: splitting (38) gives:
% 179.25/28.91  | 
% 179.25/28.91  | Case 1:
% 179.25/28.91  | | 
% 179.25/28.91  | |   (103)  all_56_13 = e3
% 179.25/28.91  | | 
% 179.25/28.91  | | COMBINE_EQS: (98), (103) imply:
% 179.25/28.91  | |   (104)  all_52_27 = e3
% 179.25/28.91  | | 
% 179.25/28.91  | | SIMP: (104) implies:
% 179.25/28.91  | |   (105)  all_52_27 = e3
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (82), (105) imply:
% 179.25/28.91  | |   (106)   ~ (all_52_19 = e3)
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (80), (105) imply:
% 179.25/28.91  | |   (107)   ~ (all_52_25 = e3)
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (1), (105) imply:
% 179.25/28.91  | |   (108)   ~ (all_10_2 = e3)
% 179.25/28.91  | | 
% 179.25/28.91  | | SIMP: (108) implies:
% 179.25/28.91  | |   (109)   ~ (all_10_2 = e3)
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (86), (105) imply:
% 179.25/28.91  | |   (110)  op(e2, e3) = all_52_26
% 179.25/28.91  | | 
% 179.25/28.91  | | GROUND_INST: instantiating (79) with all_52_9, all_52_26, e3, e2,
% 179.25/28.91  | |              simplifying with (97), (110) gives:
% 179.25/28.91  | |   (111)  all_52_9 = all_52_26
% 179.25/28.91  | | 
% 179.25/28.91  | | COMBINE_EQS: (69), (111) imply:
% 179.25/28.91  | |   (112)  all_58_2 = all_52_26
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (51), (111) imply:
% 179.25/28.91  | |   (113)   ~ (all_52_13 = all_52_26)
% 179.25/28.91  | | 
% 179.25/28.91  | | SIMP: (113) implies:
% 179.25/28.91  | |   (114)   ~ (all_52_13 = all_52_26)
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (17), (111) imply:
% 179.25/28.91  | |   (115)   ~ (all_52_26 = all_4_2)
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (49), (111) imply:
% 179.25/28.91  | |   (116)  op(e3, all_52_26) = e3
% 179.25/28.91  | | 
% 179.25/28.91  | | BETA: splitting (52) gives:
% 179.25/28.91  | | 
% 179.25/28.91  | | Case 1:
% 179.25/28.91  | | | 
% 179.25/28.91  | | |   (117)  all_56_12 = e3
% 179.25/28.91  | | | 
% 179.25/28.91  | | | REF_CLOSE: (55), (107), (117) are inconsistent by sub-proof #1040.
% 179.25/28.91  | | | 
% 179.25/28.91  | | Case 2:
% 179.25/28.91  | | | 
% 179.25/28.91  | | |   (118)   ~ (all_56_12 = e3)
% 179.25/28.91  | | |   (119)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.25/28.91  | | | 
% 179.25/28.91  | | | BETA: splitting (70) gives:
% 179.25/28.91  | | | 
% 179.25/28.91  | | | Case 1:
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | |   (120)  all_58_12 = e1
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | COMBINE_EQS: (92), (120) imply:
% 179.25/28.91  | | | |   (121)  all_52_25 = e1
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | SIMP: (121) implies:
% 179.25/28.91  | | | |   (122)  all_52_25 = e1
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | REDUCE: (107), (122) imply:
% 179.25/28.91  | | | |   (123)   ~ (e3 = e1)
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | REDUCE: (8), (122) imply:
% 179.25/28.91  | | | |   (124)  op(e3, e1) = all_52_24
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | REDUCE: (46), (122) imply:
% 179.25/28.91  | | | |   (125)  op(e0, e3) = e1
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | GROUND_INST: instantiating (79) with all_52_5, all_52_24, e1, e3,
% 179.25/28.91  | | | |              simplifying with (72), (124) gives:
% 179.25/28.91  | | | |   (126)  all_52_5 = all_52_24
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | COMBINE_EQS: (24), (126) imply:
% 179.25/28.91  | | | |   (127)  all_58_4 = all_52_24
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | REDUCE: (18), (126) imply:
% 179.25/28.91  | | | |   (128)   ~ (all_52_7 = all_52_24)
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | SIMP: (128) implies:
% 179.25/28.91  | | | |   (129)   ~ (all_52_7 = all_52_24)
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | BETA: splitting (76) gives:
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | Case 1:
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | |   (130)  all_56_7 = e3
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | | COMBINE_EQS: (83), (130) imply:
% 179.25/28.91  | | | | |   (131)  all_52_15 = e3
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | | SIMP: (131) implies:
% 179.25/28.91  | | | | |   (132)  all_52_15 = e3
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | | REDUCE: (14), (132) imply:
% 179.25/28.91  | | | | |   (133)  op(e0, e3) = e0
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | | REF_CLOSE: (61), (79), (125), (133) are inconsistent by sub-proof
% 179.25/28.91  | | | | |            #1007.
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | Case 2:
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | |   (134)   ~ (all_56_7 = e3)
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | | REDUCE: (83), (134) imply:
% 179.25/28.91  | | | | |   (135)   ~ (all_52_15 = e3)
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | | BETA: splitting (88) gives:
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | | Case 1:
% 179.25/28.91  | | | | | | 
% 179.25/28.91  | | | | | |   (136)  all_58_9 = e3
% 179.25/28.91  | | | | | | 
% 179.25/28.91  | | | | | | COMBINE_EQS: (90), (136) imply:
% 179.25/28.91  | | | | | |   (137)  all_52_7 = e3
% 179.25/28.91  | | | | | | 
% 179.25/28.91  | | | | | | REF_CLOSE: (3), (11), (13), (16), (19), (20), (21), (25), (26),
% 179.25/28.91  | | | | | |            (28), (30), (31), (33), (37), (39), (41), (48), (59),
% 179.25/28.91  | | | | | |            (62), (64), (75), (78), (79), (85), (92), (95), (106),
% 179.25/28.91  | | | | | |            (109), (112), (114), (115), (116), (127), (129), (137)
% 179.25/28.91  | | | | | |            are inconsistent by sub-proof #993.
% 179.25/28.91  | | | | | | 
% 179.25/28.91  | | | | | Case 2:
% 179.25/28.91  | | | | | | 
% 179.25/28.91  | | | | | |   (138)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.91  | | | | | | 
% 179.25/28.91  | | | | | | REF_CLOSE: (9), (14), (15), (19), (22), (26), (43), (47), (50),
% 179.25/28.91  | | | | | |            (61), (68), (71), (79), (91), (101), (102), (135), (138)
% 179.25/28.91  | | | | | |            are inconsistent by sub-proof #985.
% 179.25/28.91  | | | | | | 
% 179.25/28.91  | | | | | End of split
% 179.25/28.91  | | | | | 
% 179.25/28.91  | | | | End of split
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | Case 2:
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | |   (139)   ~ (all_58_12 = e1)
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18), (19),
% 179.25/28.91  | | | |            (20), (21), (22), (24), (25), (26), (28), (30), (31), (33),
% 179.25/28.91  | | | |            (37), (39), (41), (43), (46), (47), (48), (50), (55), (57),
% 179.25/28.91  | | | |            (59), (61), (62), (64), (68), (71), (74), (75), (76), (78),
% 179.25/28.91  | | | |            (79), (83), (85), (88), (89), (90), (92), (95), (106), (107),
% 179.25/28.91  | | | |            (109), (112), (114), (115), (116), (119), (139) are
% 179.25/28.91  | | | |            inconsistent by sub-proof #982.
% 179.25/28.91  | | | | 
% 179.25/28.91  | | | End of split
% 179.25/28.91  | | | 
% 179.25/28.91  | | End of split
% 179.25/28.91  | | 
% 179.25/28.91  | Case 2:
% 179.25/28.91  | | 
% 179.25/28.91  | |   (140)   ~ (all_56_13 = e3)
% 179.25/28.91  | | 
% 179.25/28.91  | | REDUCE: (98), (140) imply:
% 179.25/28.91  | |   (141)   ~ (all_52_27 = e3)
% 179.25/28.91  | | 
% 179.25/28.91  | | BETA: splitting (40) gives:
% 179.25/28.91  | | 
% 179.25/28.91  | | Case 1:
% 179.25/28.91  | | | 
% 179.25/28.91  | | |   (142)  all_58_12 = e3
% 179.25/28.91  | | | 
% 179.25/28.92  | | | REF_CLOSE: (2), (5), (6), (7), (9), (10), (11), (13), (14), (15), (16),
% 179.25/28.92  | | |            (19), (20), (21), (22), (25), (26), (30), (32), (36), (41),
% 179.25/28.92  | | |            (43), (46), (47), (49), (54), (56), (57), (59), (60), (61),
% 179.25/28.92  | | |            (62), (64), (67), (68), (69), (71), (73), (75), (76), (77),
% 179.25/28.92  | | |            (79), (80), (83), (84), (85), (88), (89), (90), (91), (92),
% 179.25/28.92  | | |            (96), (97), (101), (102), (142) are inconsistent by sub-proof
% 179.25/28.92  | | |            #970.
% 179.25/28.92  | | | 
% 179.25/28.92  | | Case 2:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (143)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REF_CLOSE: (3), (6), (7), (9), (10), (11), (12), (14), (15), (16), (17),
% 179.25/28.92  | | |            (19), (20), (22), (23), (25), (27), (29), (30), (31), (32),
% 179.25/28.92  | | |            (33), (34), (35), (36), (37), (39), (41), (42), (43), (44),
% 179.25/28.92  | | |            (45), (46), (47), (49), (50), (52), (53), (55), (56), (57),
% 179.25/28.92  | | |            (58), (59), (62), (63), (65), (66), (68), (69), (70), (71),
% 179.25/28.92  | | |            (75), (76), (77), (78), (79), (83), (87), (88), (90), (91),
% 179.25/28.92  | | |            (92), (94), (97), (102), (141), (143) are inconsistent by
% 179.25/28.92  | | |            sub-proof #955.
% 179.25/28.92  | | | 
% 179.25/28.92  | | End of split
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #955 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)   ~ (all_52_13 = all_52_29)
% 179.25/28.92    (2)  op(e3, e2) = all_52_3
% 179.25/28.92    (3)   ~ (all_52_9 = all_52_25)
% 179.25/28.92    (4)   ~ (all_52_27 = e0)
% 179.25/28.92    (5)   ~ (all_52_27 = e3)
% 179.25/28.92    (6)   ~ (all_52_3 = all_10_2)
% 179.25/28.92    (7)  all_58_5 = all_52_13
% 179.25/28.92    (8)   ~ (all_52_25 = all_52_29)
% 179.25/28.92    (9)  op(e0, all_52_15) = e0
% 179.25/28.92    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.25/28.92    (11)  all_58_3 = all_10_2
% 179.25/28.92    (12)   ~ (all_52_9 = all_4_2)
% 179.25/28.92    (13)  all_58_10 = all_52_15
% 179.25/28.92    (14)  all_58_7 = all_52_19
% 179.25/28.92    (15)  op(e0, e1) = all_52_29
% 179.25/28.92    (16)   ~ (all_4_0 = e2)
% 179.25/28.92    (17)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.92    (18)   ~ (all_52_27 = all_52_29)
% 179.25/28.92    (19)  op(e3, all_4_2) = all_4_1
% 179.25/28.92    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92    (21)   ~ (all_52_7 = all_4_2)
% 179.25/28.92    (22)  all_58_1 = all_52_3
% 179.25/28.92    (23)  all_58_0 = all_4_2
% 179.25/28.92    (24)  op(e1, all_52_29) = all_52_28
% 179.25/28.92    (25)  all_56_1 = e3 | all_56_1 = e2 | all_56_1 = e1 | all_56_1 = e0
% 179.25/28.92    (26)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.92    (27)  all_58_14 = all_52_29
% 179.25/28.92    (28)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.92    (29)  all_58_8 = all_14_2
% 179.25/28.92    (30)  all_56_1 = all_52_3
% 179.25/28.92    (31)  op(e0, e2) = all_52_27
% 179.25/28.92    (32)  op(all_4_1, all_4_2) = all_4_0
% 179.25/28.92    (33)   ~ (all_52_3 = all_4_2)
% 179.25/28.92    (34)  op(e0, e3) = all_52_25
% 179.25/28.92    (35)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.25/28.92    (36)  op(e3, all_52_9) = e3
% 179.25/28.92    (37)   ~ (e3 = e0)
% 179.25/28.92    (38)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.25/28.92    (39)   ~ (all_52_15 = all_52_23)
% 179.25/28.92    (40)  all_56_12 = all_52_25
% 179.25/28.92    (41)  all_58_13 = all_52_27
% 179.25/28.92    (42)   ~ (all_52_25 = e0)
% 179.25/28.92    (43)   ~ (all_52_9 = all_52_17)
% 179.25/28.92    (44)  all_58_6 = all_52_17
% 179.25/28.92    (45)  all_58_11 = all_52_23
% 179.25/28.92    (46)   ~ (all_52_3 = all_52_19)
% 179.25/28.92    (47)   ~ (all_52_29 = all_14_2)
% 179.25/28.92    (48)   ~ (all_4_0 = e1)
% 179.25/28.92    (49)  all_58_15 = e0
% 179.25/28.92    (50)  all_58_2 = all_52_9
% 179.25/28.92    (51)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.25/28.92    (52)   ~ (all_52_29 = e0)
% 179.25/28.92    (53)   ~ (e2 = e1)
% 179.25/28.92    (54)  op(e1, e3) = all_52_17
% 179.25/28.92    (55)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.25/28.92    (56)  op(e2, all_10_2) = e2
% 179.25/28.92    (57)  op(e3, e3) = all_4_2
% 179.25/28.92    (58)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92    (59)  all_56_7 = all_52_15
% 179.25/28.92    (60)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.25/28.92    (61)   ~ (all_52_17 = all_52_19)
% 179.25/28.92    (62)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.92    (63)  all_58_9 = all_52_7
% 179.25/28.92    (64)   ~ (e2 = e0)
% 179.25/28.92    (65)  all_58_12 = all_52_25
% 179.25/28.92    (66)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.25/28.92    (67)  op(e2, e3) = all_52_9
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (60) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (68)  all_58_13 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (5), (41), (68) are inconsistent by sub-proof #1026.
% 179.25/28.92  | | 
% 179.25/28.92  | Case 2:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (69)  all_58_14 = e3 | all_58_15 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | BETA: splitting (69) gives:
% 179.25/28.92  | | 
% 179.25/28.92  | | Case 1:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (70)  all_58_14 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | COMBINE_EQS: (27), (70) imply:
% 179.25/28.92  | | |   (71)  all_52_29 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | SIMP: (71) implies:
% 179.25/28.92  | | |   (72)  all_52_29 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (1), (72) imply:
% 179.25/28.92  | | |   (73)   ~ (all_52_13 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (8), (72) imply:
% 179.25/28.92  | | |   (74)   ~ (all_52_25 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (47), (72) imply:
% 179.25/28.92  | | |   (75)   ~ (all_14_2 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | SIMP: (75) implies:
% 179.25/28.92  | | |   (76)   ~ (all_14_2 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (24), (72) imply:
% 179.25/28.92  | | |   (77)  op(e1, e3) = all_52_28
% 179.25/28.92  | | | 
% 179.25/28.92  | | | GROUND_INST: instantiating (58) with all_52_17, all_52_28, e3, e1,
% 179.25/28.92  | | |              simplifying with (54), (77) gives:
% 179.25/28.92  | | |   (78)  all_52_17 = all_52_28
% 179.25/28.92  | | | 
% 179.25/28.92  | | | COMBINE_EQS: (44), (78) imply:
% 179.25/28.92  | | |   (79)  all_58_6 = all_52_28
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (43), (78) imply:
% 179.25/28.92  | | |   (80)   ~ (all_52_9 = all_52_28)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (61), (78) imply:
% 179.25/28.92  | | |   (81)   ~ (all_52_19 = all_52_28)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | SIMP: (81) implies:
% 179.25/28.92  | | |   (82)   ~ (all_52_19 = all_52_28)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | BETA: splitting (38) gives:
% 179.25/28.92  | | | 
% 179.25/28.92  | | | Case 1:
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | |   (83)  all_56_12 = e3
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | | REF_CLOSE: (40), (74), (83) are inconsistent by sub-proof #1040.
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | Case 2:
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | |   (84)   ~ (all_56_12 = e3)
% 179.25/28.92  | | | |   (85)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | | BETA: splitting (51) gives:
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | | Case 1:
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | |   (86)  all_58_12 = e1
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | COMBINE_EQS: (65), (86) imply:
% 179.25/28.92  | | | | |   (87)  all_52_25 = e1
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | SIMP: (87) implies:
% 179.25/28.92  | | | | |   (88)  all_52_25 = e1
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | REDUCE: (42), (88) imply:
% 179.25/28.92  | | | | |   (89)   ~ (e1 = e0)
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | REDUCE: (34), (88) imply:
% 179.25/28.92  | | | | |   (90)  op(e0, e3) = e1
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | BETA: splitting (25) gives:
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | Case 1:
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | |   (91)  all_56_1 = e3
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | | COMBINE_EQS: (30), (91) imply:
% 179.25/28.92  | | | | | |   (92)  all_52_3 = e3
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | | SIMP: (92) implies:
% 179.25/28.92  | | | | | |   (93)  all_52_3 = e3
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | | REF_CLOSE: (6), (7), (9), (11), (12), (13), (14), (17), (20), (23),
% 179.25/28.92  | | | | | |            (28), (29), (33), (36), (39), (45), (46), (50), (57),
% 179.25/28.92  | | | | | |            (58), (73), (76), (79), (80), (89), (90), (93) are
% 179.25/28.92  | | | | | |            inconsistent by sub-proof #963.
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | Case 2:
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | |   (94)   ~ (all_56_1 = e3)
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | | REDUCE: (30), (94) imply:
% 179.25/28.92  | | | | | |   (95)   ~ (all_52_3 = e3)
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | | BETA: splitting (66) gives:
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | | Case 1:
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | |   (96)  all_58_0 = e3
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | COMBINE_EQS: (23), (96) imply:
% 179.25/28.92  | | | | | | |   (97)  all_4_2 = e3
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (21), (97) imply:
% 179.25/28.92  | | | | | | |   (98)   ~ (all_52_7 = e3)
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (32), (97) imply:
% 179.25/28.92  | | | | | | |   (99)  op(all_4_1, e3) = all_4_0
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (19), (97) imply:
% 179.25/28.92  | | | | | | |   (100)  op(e3, e3) = all_4_1
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (57), (97) imply:
% 179.25/28.92  | | | | | | |   (101)  op(e3, e3) = e3
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | GROUND_INST: instantiating (58) with e3, all_4_1, e3, e3,
% 179.25/28.92  | | | | | | |              simplifying with (100), (101) gives:
% 179.25/28.92  | | | | | | |   (102)  all_4_1 = e3
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (99), (102) imply:
% 179.25/28.92  | | | | | | |   (103)  op(e3, e3) = all_4_0
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | GROUND_INST: instantiating (58) with e3, all_4_0, e3, e3,
% 179.25/28.92  | | | | | | |              simplifying with (101), (103) gives:
% 179.25/28.92  | | | | | | |   (104)  all_4_0 = e3
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (16), (104) imply:
% 179.25/28.92  | | | | | | |   (105)   ~ (e3 = e2)
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (48), (104) imply:
% 179.25/28.92  | | | | | | |   (106)   ~ (e3 = e1)
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | BETA: splitting (62) gives:
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | Case 1:
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | |   (107)  all_58_9 = e3
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | | COMBINE_EQS: (63), (107) imply:
% 179.25/28.92  | | | | | | | |   (108)  all_52_7 = e3
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | | REDUCE: (98), (108) imply:
% 179.25/28.92  | | | | | | | |   (109)  $false
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | | CLOSE: (109) is inconsistent.
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | Case 2:
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | |   (110)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | | BETA: splitting (110) gives:
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | | Case 1:
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | |   (111)  all_58_10 = e3
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | COMBINE_EQS: (13), (111) imply:
% 179.25/28.92  | | | | | | | | |   (112)  all_52_15 = e3
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | REDUCE: (9), (112) imply:
% 179.25/28.92  | | | | | | | | |   (113)  op(e0, e3) = e0
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | REF_CLOSE: (58), (89), (90), (113) are inconsistent by
% 179.25/28.92  | | | | | | | | |            sub-proof #1007.
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | Case 2:
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | |   (114)  all_58_11 = e3 | all_58_15 = e3
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | BETA: splitting (114) gives:
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | Case 1:
% 179.25/28.92  | | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | |   (115)  all_58_11 = e3
% 179.25/28.92  | | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | | REF_CLOSE: (4), (9), (10), (13), (15), (31), (35), (49),
% 179.25/28.92  | | | | | | | | | |            (52), (53), (58), (64), (89), (105), (106), (115)
% 179.25/28.92  | | | | | | | | | |            are inconsistent by sub-proof #986.
% 179.25/28.92  | | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | Case 2:
% 179.25/28.92  | | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | |   (116)  all_58_15 = e3
% 179.25/28.92  | | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | | REF_CLOSE: (37), (49), (116) are inconsistent by sub-proof
% 179.25/28.92  | | | | | | | | | |            #1010.
% 179.25/28.92  | | | | | | | | | | 
% 179.25/28.92  | | | | | | | | | End of split
% 179.25/28.92  | | | | | | | | | 
% 179.25/28.92  | | | | | | | | End of split
% 179.25/28.92  | | | | | | | | 
% 179.25/28.92  | | | | | | | End of split
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | Case 2:
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | |   (117)   ~ (all_58_0 = e3)
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REDUCE: (23), (117) imply:
% 179.25/28.92  | | | | | | |   (118)   ~ (all_4_2 = e3)
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | | REF_CLOSE: (2), (5), (6), (11), (12), (14), (20), (22), (23),
% 179.25/28.92  | | | | | | |            (26), (28), (36), (41), (50), (56), (57), (58), (65),
% 179.25/28.92  | | | | | | |            (67), (74), (79), (82), (95), (118) are inconsistent by
% 179.25/28.92  | | | | | | |            sub-proof #960.
% 179.25/28.92  | | | | | | | 
% 179.25/28.92  | | | | | | End of split
% 179.25/28.92  | | | | | | 
% 179.25/28.92  | | | | | End of split
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | Case 2:
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | |   (119)   ~ (all_58_12 = e1)
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | REDUCE: (65), (119) imply:
% 179.25/28.92  | | | | |   (120)   ~ (all_52_25 = e1)
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | | REF_CLOSE: (3), (7), (9), (11), (12), (13), (20), (34), (36), (40),
% 179.25/28.92  | | | | |            (42), (50), (55), (56), (57), (58), (59), (67), (73), (85),
% 179.25/28.92  | | | | |            (120) are inconsistent by sub-proof #956.
% 179.25/28.92  | | | | | 
% 179.25/28.92  | | | | End of split
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | End of split
% 179.25/28.92  | | | 
% 179.25/28.92  | | Case 2:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (121)  all_58_15 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REF_CLOSE: (37), (49), (121) are inconsistent by sub-proof #1010.
% 179.25/28.92  | | | 
% 179.25/28.92  | | End of split
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #956 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)   ~ (all_52_9 = all_52_25)
% 179.25/28.92    (2)  all_58_5 = all_52_13
% 179.25/28.92    (3)  op(e0, all_52_15) = e0
% 179.25/28.92    (4)  all_58_3 = all_10_2
% 179.25/28.92    (5)   ~ (all_52_9 = all_4_2)
% 179.25/28.92    (6)  all_58_10 = all_52_15
% 179.25/28.92    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92    (8)  op(e0, e3) = all_52_25
% 179.25/28.92    (9)  op(e3, all_52_9) = e3
% 179.25/28.92    (10)   ~ (all_52_13 = e3)
% 179.25/28.92    (11)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.25/28.92    (12)  all_56_12 = all_52_25
% 179.25/28.92    (13)   ~ (all_52_25 = e0)
% 179.25/28.92    (14)   ~ (all_52_25 = e1)
% 179.25/28.92    (15)  all_58_2 = all_52_9
% 179.25/28.92    (16)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.25/28.92    (17)  op(e2, all_10_2) = e2
% 179.25/28.92    (18)  op(e3, e3) = all_4_2
% 179.25/28.92    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92    (20)  all_56_7 = all_52_15
% 179.25/28.92    (21)  op(e2, e3) = all_52_9
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (11) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (22)  all_56_12 = e2
% 179.25/28.92  | | 
% 179.25/28.92  | | COMBINE_EQS: (12), (22) imply:
% 179.25/28.92  | |   (23)  all_52_25 = e2
% 179.25/28.92  | | 
% 179.25/28.92  | | SIMP: (23) implies:
% 179.25/28.92  | |   (24)  all_52_25 = e2
% 179.25/28.92  | | 
% 179.25/28.92  | | REDUCE: (1), (24) imply:
% 179.25/28.92  | |   (25)   ~ (all_52_9 = e2)
% 179.25/28.92  | | 
% 179.25/28.92  | | REDUCE: (13), (24) imply:
% 179.25/28.92  | |   (26)   ~ (e2 = e0)
% 179.25/28.92  | | 
% 179.25/28.92  | | REDUCE: (8), (24) imply:
% 179.25/28.92  | |   (27)  op(e0, e3) = e2
% 179.25/28.92  | | 
% 179.25/28.92  | | BETA: splitting (16) gives:
% 179.25/28.92  | | 
% 179.25/28.92  | | Case 1:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (28)  all_56_7 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REF_CLOSE: (3), (19), (20), (26), (27), (28) are inconsistent by sub-proof
% 179.25/28.92  | | |            #959.
% 179.25/28.92  | | | 
% 179.25/28.92  | | Case 2:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (29)   ~ (all_56_7 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (20), (29) imply:
% 179.25/28.92  | | |   (30)   ~ (all_52_15 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (15), (17), (18), (19),
% 179.25/28.92  | | |            (21), (25), (30) are inconsistent by sub-proof #957.
% 179.25/28.92  | | | 
% 179.25/28.92  | | End of split
% 179.25/28.92  | | 
% 179.25/28.92  | Case 2:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (31)  all_56_12 = e1 | all_56_12 = e0
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (12), (13), (14), (31) are inconsistent by sub-proof #1029.
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #957 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)  all_58_5 = all_52_13
% 179.25/28.92    (2)  all_58_3 = all_10_2
% 179.25/28.92    (3)   ~ (all_52_9 = all_4_2)
% 179.25/28.92    (4)  all_58_10 = all_52_15
% 179.25/28.92    (5)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92    (6)   ~ (all_52_9 = e2)
% 179.25/28.92    (7)  op(e3, all_52_9) = e3
% 179.25/28.92    (8)   ~ (all_52_13 = e3)
% 179.25/28.92    (9)   ~ (all_52_15 = e3)
% 179.25/28.92    (10)  all_58_2 = all_52_9
% 179.25/28.92    (11)  op(e2, all_10_2) = e2
% 179.25/28.92    (12)  op(e3, e3) = all_4_2
% 179.25/28.92    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92    (14)  op(e2, e3) = all_52_9
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (5) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (15)  all_58_2 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | COMBINE_EQS: (10), (15) imply:
% 179.25/28.92  | |   (16)  all_52_9 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (3), (7), (12), (13), (16) are inconsistent by sub-proof #967.
% 179.25/28.92  | | 
% 179.25/28.92  | Case 2:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (17)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | BETA: splitting (17) gives:
% 179.25/28.92  | | 
% 179.25/28.92  | | Case 1:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (18)  all_58_3 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | COMBINE_EQS: (2), (18) imply:
% 179.25/28.92  | | |   (19)  all_10_2 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (11), (19) imply:
% 179.25/28.92  | | |   (20)  op(e2, e3) = e2
% 179.25/28.92  | | | 
% 179.25/28.92  | | | GROUND_INST: instantiating (13) with all_52_9, e2, e3, e2, simplifying
% 179.25/28.92  | | |              with (14), (20) gives:
% 179.25/28.92  | | |   (21)  all_52_9 = e2
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (6), (21) imply:
% 179.25/28.92  | | |   (22)  $false
% 179.25/28.92  | | | 
% 179.25/28.92  | | | CLOSE: (22) is inconsistent.
% 179.25/28.92  | | | 
% 179.25/28.92  | | Case 2:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (23)  all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REF_CLOSE: (1), (4), (8), (9), (23) are inconsistent by sub-proof #958.
% 179.25/28.92  | | | 
% 179.25/28.92  | | End of split
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #958 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)  all_58_5 = all_52_13
% 179.25/28.92    (2)  all_58_10 = all_52_15
% 179.25/28.92    (3)   ~ (all_52_13 = e3)
% 179.25/28.92    (4)  all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92    (5)   ~ (all_52_15 = e3)
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (4) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (6)  all_58_5 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #969.
% 179.25/28.92  | | 
% 179.25/28.92  | Case 2:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (7)  all_58_10 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #1018.
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #959 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)  op(e0, all_52_15) = e0
% 179.25/28.92    (2)  all_56_7 = e3
% 179.25/28.92    (3)  op(e0, e3) = e2
% 179.25/28.92    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92    (5)  all_56_7 = all_52_15
% 179.25/28.92    (6)   ~ (e2 = e0)
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | COMBINE_EQS: (2), (5) imply:
% 179.25/28.92  |   (7)  all_52_15 = e3
% 179.25/28.92  | 
% 179.25/28.92  | SIMP: (7) implies:
% 179.25/28.92  |   (8)  all_52_15 = e3
% 179.25/28.92  | 
% 179.25/28.92  | REDUCE: (1), (8) imply:
% 179.25/28.92  |   (9)  op(e0, e3) = e0
% 179.25/28.92  | 
% 179.25/28.92  | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1035.
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #960 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)   ~ (all_52_25 = e3)
% 179.25/28.92    (2)  all_58_6 = all_52_28
% 179.25/28.92    (3)  op(e3, e2) = all_52_3
% 179.25/28.92    (4)   ~ (all_52_27 = e3)
% 179.25/28.92    (5)   ~ (all_52_3 = all_10_2)
% 179.25/28.92    (6)   ~ (all_4_2 = e3)
% 179.25/28.92    (7)  all_58_3 = all_10_2
% 179.25/28.92    (8)   ~ (all_52_9 = all_4_2)
% 179.25/28.92    (9)  all_58_7 = all_52_19
% 179.25/28.92    (10)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92    (11)  all_58_1 = all_52_3
% 179.25/28.92    (12)  all_58_0 = all_4_2
% 179.25/28.92    (13)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.92    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.92    (15)  op(e3, all_52_9) = e3
% 179.25/28.92    (16)   ~ (all_52_19 = all_52_28)
% 179.25/28.92    (17)  all_58_13 = all_52_27
% 179.25/28.92    (18)   ~ (all_52_3 = e3)
% 179.25/28.92    (19)  all_58_2 = all_52_9
% 179.25/28.92    (20)  op(e2, all_10_2) = e2
% 179.25/28.92    (21)  op(e3, e3) = all_4_2
% 179.25/28.92    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92    (23)  all_58_12 = all_52_25
% 179.25/28.92    (24)  op(e2, e3) = all_52_9
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (13) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (25)  all_58_1 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | COMBINE_EQS: (11), (25) imply:
% 179.25/28.92  | |   (26)  all_52_3 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REDUCE: (18), (26) imply:
% 179.25/28.92  | |   (27)  $false
% 179.25/28.92  | | 
% 179.25/28.92  | | CLOSE: (27) is inconsistent.
% 179.25/28.92  | | 
% 179.25/28.92  | Case 2:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (28)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 179.25/28.92  | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (28) are
% 179.25/28.92  | |            inconsistent by sub-proof #961.
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #961 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)   ~ (all_52_25 = e3)
% 179.25/28.92    (2)  all_58_6 = all_52_28
% 179.25/28.92    (3)  op(e3, e2) = all_52_3
% 179.25/28.92    (4)   ~ (all_52_27 = e3)
% 179.25/28.92    (5)   ~ (all_52_3 = all_10_2)
% 179.25/28.92    (6)   ~ (all_4_2 = e3)
% 179.25/28.92    (7)  all_58_3 = all_10_2
% 179.25/28.92    (8)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.92    (9)   ~ (all_52_9 = all_4_2)
% 179.25/28.92    (10)  all_58_7 = all_52_19
% 179.25/28.92    (11)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92    (12)  all_58_0 = all_4_2
% 179.25/28.92    (13)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.92    (14)  op(e3, all_52_9) = e3
% 179.25/28.92    (15)   ~ (all_52_19 = all_52_28)
% 179.25/28.92    (16)  all_58_13 = all_52_27
% 179.25/28.92    (17)  all_58_2 = all_52_9
% 179.25/28.92    (18)  op(e2, all_10_2) = e2
% 179.25/28.92    (19)  op(e3, e3) = all_4_2
% 179.25/28.92    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92    (21)  all_58_12 = all_52_25
% 179.25/28.92    (22)  op(e2, e3) = all_52_9
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (13) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (23)  all_58_0 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | COMBINE_EQS: (12), (23) imply:
% 179.25/28.92  | |   (24)  all_4_2 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REDUCE: (6), (24) imply:
% 179.25/28.92  | |   (25)  $false
% 179.25/28.92  | | 
% 179.25/28.92  | | CLOSE: (25) is inconsistent.
% 179.25/28.92  | | 
% 179.25/28.92  | Case 2:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (26)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | BETA: splitting (11) gives:
% 179.25/28.92  | | 
% 179.25/28.92  | | Case 1:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (27)  all_58_2 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | COMBINE_EQS: (17), (27) imply:
% 179.25/28.92  | | |   (28)  all_52_9 = e3
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REF_CLOSE: (9), (14), (19), (20), (28) are inconsistent by sub-proof #967.
% 179.25/28.92  | | | 
% 179.25/28.92  | | Case 2:
% 179.25/28.92  | | | 
% 179.25/28.92  | | |   (29)   ~ (all_58_2 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | REDUCE: (17), (29) imply:
% 179.25/28.92  | | |   (30)   ~ (all_52_9 = e3)
% 179.25/28.92  | | | 
% 179.25/28.92  | | | BETA: splitting (26) gives:
% 179.25/28.92  | | | 
% 179.25/28.92  | | | Case 1:
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | |   (31)  all_58_2 = e3
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | | REF_CLOSE: (17), (30), (31) are inconsistent by sub-proof #980.
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | Case 2:
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | |   (32)  all_58_6 = e3 | all_58_12 = e3
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (14), (15), (16),
% 179.25/28.92  | | | |            (18), (20), (21), (22), (32) are inconsistent by sub-proof
% 179.25/28.92  | | | |            #962.
% 179.25/28.92  | | | | 
% 179.25/28.92  | | | End of split
% 179.25/28.92  | | | 
% 179.25/28.92  | | End of split
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #962 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)   ~ (all_52_25 = e3)
% 179.25/28.92    (2)  all_58_6 = all_52_28
% 179.25/28.92    (3)  op(e3, e2) = all_52_3
% 179.25/28.92    (4)   ~ (all_52_27 = e3)
% 179.25/28.92    (5)   ~ (all_52_3 = all_10_2)
% 179.25/28.92    (6)  all_58_3 = all_10_2
% 179.25/28.92    (7)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.92    (8)  all_58_7 = all_52_19
% 179.25/28.92    (9)  op(e3, all_52_9) = e3
% 179.25/28.92    (10)   ~ (all_52_19 = all_52_28)
% 179.25/28.92    (11)  all_58_13 = all_52_27
% 179.25/28.92    (12)  op(e2, all_10_2) = e2
% 179.25/28.92    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92    (14)  all_58_6 = e3 | all_58_12 = e3
% 179.25/28.92    (15)  all_58_12 = all_52_25
% 179.25/28.92    (16)  op(e2, e3) = all_52_9
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (14) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (17)  all_58_6 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | COMBINE_EQS: (2), (17) imply:
% 179.25/28.92  | |   (18)  all_52_28 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | SIMP: (18) implies:
% 179.25/28.92  | |   (19)  all_52_28 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REDUCE: (10), (19) imply:
% 179.25/28.92  | |   (20)   ~ (all_52_19 = e3)
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (16), (20)
% 179.25/28.92  | |            are inconsistent by sub-proof #975.
% 179.25/28.92  | | 
% 179.25/28.92  | Case 2:
% 179.25/28.92  | | 
% 179.25/28.92  | |   (21)  all_58_12 = e3
% 179.25/28.92  | | 
% 179.25/28.92  | | REF_CLOSE: (1), (15), (21) are inconsistent by sub-proof #1003.
% 179.25/28.92  | | 
% 179.25/28.92  | End of split
% 179.25/28.92  | 
% 179.25/28.92  End of proof
% 179.25/28.92  
% 179.25/28.92  Sub-proof #963 shows that the following formulas are inconsistent:
% 179.25/28.92  ----------------------------------------------------------------
% 179.25/28.92    (1)  all_58_6 = all_52_28
% 179.25/28.92    (2)  op(e0, e3) = e1
% 179.25/28.92    (3)   ~ (all_52_3 = all_10_2)
% 179.25/28.92    (4)  all_58_5 = all_52_13
% 179.25/28.92    (5)  op(e0, all_52_15) = e0
% 179.25/28.92    (6)  all_58_3 = all_10_2
% 179.25/28.92    (7)   ~ (all_52_9 = all_4_2)
% 179.25/28.92    (8)  all_58_10 = all_52_15
% 179.25/28.92    (9)  all_58_7 = all_52_19
% 179.25/28.92    (10)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.92    (11)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.92    (12)  all_58_0 = all_4_2
% 179.25/28.92    (13)   ~ (all_52_9 = all_52_28)
% 179.25/28.92    (14)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.92    (15)  all_58_8 = all_14_2
% 179.25/28.92    (16)   ~ (all_52_3 = all_4_2)
% 179.25/28.92    (17)  op(e3, all_52_9) = e3
% 179.25/28.92    (18)   ~ (all_52_13 = e3)
% 179.25/28.92    (19)   ~ (all_52_15 = all_52_23)
% 179.25/28.92    (20)  all_52_3 = e3
% 179.25/28.92    (21)   ~ (e1 = e0)
% 179.25/28.92    (22)  all_58_11 = all_52_23
% 179.25/28.92    (23)   ~ (all_52_3 = all_52_19)
% 179.25/28.92    (24)  all_58_2 = all_52_9
% 179.25/28.92    (25)  op(e3, e3) = all_4_2
% 179.25/28.92    (26)   ~ (all_14_2 = e3)
% 179.25/28.92    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.92  
% 179.25/28.92  Begin of proof
% 179.25/28.92  | 
% 179.25/28.92  | REDUCE: (20), (23) imply:
% 179.25/28.92  |   (28)   ~ (all_52_19 = e3)
% 179.25/28.92  | 
% 179.25/28.92  | SIMP: (28) implies:
% 179.25/28.92  |   (29)   ~ (all_52_19 = e3)
% 179.25/28.92  | 
% 179.25/28.92  | REDUCE: (3), (20) imply:
% 179.25/28.92  |   (30)   ~ (all_10_2 = e3)
% 179.25/28.92  | 
% 179.25/28.92  | SIMP: (30) implies:
% 179.25/28.92  |   (31)   ~ (all_10_2 = e3)
% 179.25/28.92  | 
% 179.25/28.92  | REDUCE: (16), (20) imply:
% 179.25/28.92  |   (32)   ~ (all_4_2 = e3)
% 179.25/28.92  | 
% 179.25/28.92  | SIMP: (32) implies:
% 179.25/28.92  |   (33)   ~ (all_4_2 = e3)
% 179.25/28.92  | 
% 179.25/28.92  | BETA: splitting (10) gives:
% 179.25/28.92  | 
% 179.25/28.92  | Case 1:
% 179.25/28.92  | | 
% 179.25/28.93  | |   (34)  all_58_6 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (1), (34) imply:
% 179.25/28.93  | |   (35)  all_52_28 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | SIMP: (35) implies:
% 179.25/28.93  | |   (36)  all_52_28 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (13), (36) imply:
% 179.25/28.93  | |   (37)   ~ (all_52_9 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | BETA: splitting (11) gives:
% 179.25/28.93  | | 
% 179.25/28.93  | | Case 1:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (38)  all_58_2 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (24), (37), (38) are inconsistent by sub-proof #980.
% 179.25/28.93  | | | 
% 179.25/28.93  | | Case 2:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (39)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (2), (4), (5), (6), (8), (18), (21), (27), (31), (39) are
% 179.25/28.93  | | |            inconsistent by sub-proof #968.
% 179.25/28.93  | | | 
% 179.25/28.93  | | End of split
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (40)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REF_CLOSE: (4), (6), (7), (8), (9), (11), (12), (14), (15), (17), (18),
% 179.25/28.93  | |            (19), (22), (24), (25), (26), (27), (29), (31), (33), (40) are
% 179.25/28.93  | |            inconsistent by sub-proof #964.
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #964 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  all_58_5 = all_52_13
% 179.25/28.93    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93    (3)   ~ (all_4_2 = e3)
% 179.25/28.93    (4)  all_58_3 = all_10_2
% 179.25/28.93    (5)   ~ (all_52_9 = all_4_2)
% 179.25/28.93    (6)  all_58_10 = all_52_15
% 179.25/28.93    (7)  all_58_7 = all_52_19
% 179.25/28.93    (8)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93    (9)  all_58_0 = all_4_2
% 179.25/28.93    (10)   ~ (all_10_2 = e3)
% 179.25/28.93    (11)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.93    (12)  all_58_8 = all_14_2
% 179.25/28.93    (13)  op(e3, all_52_9) = e3
% 179.25/28.93    (14)   ~ (all_52_13 = e3)
% 179.25/28.93    (15)   ~ (all_52_15 = all_52_23)
% 179.25/28.93    (16)  all_58_11 = all_52_23
% 179.25/28.93    (17)  all_58_2 = all_52_9
% 179.25/28.93    (18)   ~ (all_52_19 = e3)
% 179.25/28.93    (19)  op(e3, e3) = all_4_2
% 179.25/28.93    (20)   ~ (all_14_2 = e3)
% 179.25/28.93    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (11) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (22)  all_58_0 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (9), (22) imply:
% 179.25/28.93  | |   (23)  all_4_2 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (3), (23) imply:
% 179.25/28.93  | |   (24)  $false
% 179.25/28.93  | | 
% 179.25/28.93  | | CLOSE: (24) is inconsistent.
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (25)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 179.25/28.93  | |            (16), (17), (18), (19), (20), (21), (25) are inconsistent by
% 179.25/28.93  | |            sub-proof #965.
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #965 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  all_58_5 = all_52_13
% 179.25/28.93    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93    (3)  all_58_3 = all_10_2
% 179.25/28.93    (4)   ~ (all_52_9 = all_4_2)
% 179.25/28.93    (5)  all_58_10 = all_52_15
% 179.25/28.93    (6)  all_58_7 = all_52_19
% 179.25/28.93    (7)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93    (8)   ~ (all_10_2 = e3)
% 179.25/28.93    (9)  all_58_8 = all_14_2
% 179.25/28.93    (10)  op(e3, all_52_9) = e3
% 179.25/28.93    (11)   ~ (all_52_13 = e3)
% 179.25/28.93    (12)   ~ (all_52_15 = all_52_23)
% 179.25/28.93    (13)  all_58_11 = all_52_23
% 179.25/28.93    (14)  all_58_2 = all_52_9
% 179.25/28.93    (15)   ~ (all_52_19 = e3)
% 179.25/28.93    (16)  op(e3, e3) = all_4_2
% 179.25/28.93    (17)   ~ (all_14_2 = e3)
% 179.25/28.93    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93    (19)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (19) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (20)  all_58_2 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (14), (20) imply:
% 179.25/28.93  | |   (21)  all_52_9 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REF_CLOSE: (4), (10), (16), (18), (21) are inconsistent by sub-proof #967.
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (22)   ~ (all_58_2 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (14), (22) imply:
% 179.25/28.93  | |   (23)   ~ (all_52_9 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | BETA: splitting (7) gives:
% 179.25/28.93  | | 
% 179.25/28.93  | | Case 1:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (24)  all_58_2 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (14), (23), (24) are inconsistent by sub-proof #980.
% 179.25/28.93  | | | 
% 179.25/28.93  | | Case 2:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (25)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (12), (13), (15),
% 179.25/28.93  | | |            (17), (25) are inconsistent by sub-proof #966.
% 179.25/28.93  | | | 
% 179.25/28.93  | | End of split
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #966 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  all_58_5 = all_52_13
% 179.25/28.93    (2)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93    (3)  all_58_3 = all_10_2
% 179.25/28.93    (4)  all_58_10 = all_52_15
% 179.25/28.93    (5)  all_58_7 = all_52_19
% 179.25/28.93    (6)   ~ (all_10_2 = e3)
% 179.25/28.93    (7)  all_58_8 = all_14_2
% 179.25/28.93    (8)   ~ (all_52_13 = e3)
% 179.25/28.93    (9)   ~ (all_52_15 = all_52_23)
% 179.25/28.93    (10)  all_58_11 = all_52_23
% 179.25/28.93    (11)   ~ (all_52_19 = e3)
% 179.25/28.93    (12)   ~ (all_14_2 = e3)
% 179.25/28.93    (13)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (13) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (14)  all_58_3 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (3), (14) imply:
% 179.25/28.93  | |   (15)  all_10_2 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (6), (15) imply:
% 179.25/28.93  | |   (16)  $false
% 179.25/28.93  | | 
% 179.25/28.93  | | CLOSE: (16) is inconsistent.
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (17)  all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | BETA: splitting (17) gives:
% 179.25/28.93  | | 
% 179.25/28.93  | | Case 1:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (18)  all_58_5 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (1), (8), (18) are inconsistent by sub-proof #969.
% 179.25/28.93  | | | 
% 179.25/28.93  | | Case 2:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (19)  all_58_10 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | COMBINE_EQS: (4), (19) imply:
% 179.25/28.93  | | |   (20)  all_52_15 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | SIMP: (20) implies:
% 179.25/28.93  | | |   (21)  all_52_15 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REDUCE: (9), (21) imply:
% 179.25/28.93  | | |   (22)   ~ (all_52_23 = e3)
% 179.25/28.93  | | | 
% 179.25/28.93  | | | SIMP: (22) implies:
% 179.25/28.93  | | |   (23)   ~ (all_52_23 = e3)
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (2), (5), (7), (10), (11), (12), (23) are inconsistent by
% 179.25/28.93  | | |            sub-proof #996.
% 179.25/28.93  | | | 
% 179.25/28.93  | | End of split
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #967 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)   ~ (all_52_9 = all_4_2)
% 179.25/28.93    (2)  op(e3, all_52_9) = e3
% 179.25/28.93    (3)  all_52_9 = e3
% 179.25/28.93    (4)  op(e3, e3) = all_4_2
% 179.25/28.93    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (3) implies:
% 179.25/28.93  |   (6)  all_52_9 = e3
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (1), (6) imply:
% 179.25/28.93  |   (7)   ~ (all_4_2 = e3)
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (7) implies:
% 179.25/28.93  |   (8)   ~ (all_4_2 = e3)
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (2), (6) imply:
% 179.25/28.93  |   (9)  op(e3, e3) = e3
% 179.25/28.93  | 
% 179.25/28.93  | REF_CLOSE: (4), (5), (8), (9) are inconsistent by sub-proof #1006.
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #968 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  op(e0, e3) = e1
% 179.25/28.93    (2)  all_58_5 = all_52_13
% 179.25/28.93    (3)  op(e0, all_52_15) = e0
% 179.25/28.93    (4)  all_58_3 = all_10_2
% 179.25/28.93    (5)  all_58_10 = all_52_15
% 179.25/28.93    (6)   ~ (all_10_2 = e3)
% 179.25/28.93    (7)   ~ (all_52_13 = e3)
% 179.25/28.93    (8)   ~ (e1 = e0)
% 179.25/28.93    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93    (10)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (10) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (11)  all_58_3 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (4), (11) imply:
% 179.25/28.93  | |   (12)  all_10_2 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (6), (12) imply:
% 179.25/28.93  | |   (13)  $false
% 179.25/28.93  | | 
% 179.25/28.93  | | CLOSE: (13) is inconsistent.
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (14)  all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | BETA: splitting (14) gives:
% 179.25/28.93  | | 
% 179.25/28.93  | | Case 1:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (15)  all_58_5 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #969.
% 179.25/28.93  | | | 
% 179.25/28.93  | | Case 2:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (16)  all_58_10 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | COMBINE_EQS: (5), (16) imply:
% 179.25/28.93  | | |   (17)  all_52_15 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | SIMP: (17) implies:
% 179.25/28.93  | | |   (18)  all_52_15 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REDUCE: (3), (18) imply:
% 179.25/28.93  | | |   (19)  op(e0, e3) = e0
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (1), (8), (9), (19) are inconsistent by sub-proof #1007.
% 179.25/28.93  | | | 
% 179.25/28.93  | | End of split
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #969 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  all_58_5 = all_52_13
% 179.25/28.93    (2)  all_58_5 = e3
% 179.25/28.93    (3)   ~ (all_52_13 = e3)
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | COMBINE_EQS: (1), (2) imply:
% 179.25/28.93  |   (4)  all_52_13 = e3
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (4) implies:
% 179.25/28.93  |   (5)  all_52_13 = e3
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (3), (5) imply:
% 179.25/28.93  |   (6)  $false
% 179.25/28.93  | 
% 179.25/28.93  | CLOSE: (6) is inconsistent.
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #970 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)   ~ (all_52_17 = all_52_23)
% 179.25/28.93    (2)  all_56_3 = all_52_7
% 179.25/28.93    (3)  op(e3, e2) = all_52_3
% 179.25/28.93    (4)   ~ (all_52_9 = all_52_25)
% 179.25/28.93    (5)   ~ (all_52_27 = e0)
% 179.25/28.93    (6)   ~ (all_52_3 = all_10_2)
% 179.25/28.93    (7)  all_58_5 = all_52_13
% 179.25/28.93    (8)  op(e1, all_52_13) = e1
% 179.25/28.93    (9)  op(e0, all_52_15) = e0
% 179.25/28.93    (10)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.25/28.93    (11)  all_58_3 = all_10_2
% 179.25/28.93    (12)  all_58_10 = all_52_15
% 179.25/28.93    (13)  all_58_7 = all_52_19
% 179.25/28.93    (14)   ~ (all_52_17 = all_52_25)
% 179.25/28.93    (15)  op(e0, e1) = all_52_29
% 179.25/28.93    (16)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93    (17)   ~ (e3 = e1)
% 179.25/28.93    (18)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93    (19)  all_58_1 = all_52_3
% 179.25/28.93    (20)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.93    (21)  all_58_8 = all_14_2
% 179.25/28.93    (22)  op(e0, e2) = all_52_27
% 179.25/28.93    (23)  op(e0, e3) = all_52_25
% 179.25/28.93    (24)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.25/28.93    (25)  op(e3, all_52_9) = e3
% 179.25/28.93    (26)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.25/28.93    (27)  all_58_13 = all_52_27
% 179.25/28.93    (28)  all_58_12 = e3
% 179.25/28.93    (29)   ~ (all_52_25 = e0)
% 179.25/28.93    (30)  all_58_6 = all_52_17
% 179.25/28.93    (31)   ~ (all_52_3 = all_52_7)
% 179.25/28.93    (32)   ~ (e1 = e0)
% 179.25/28.93    (33)  all_58_11 = all_52_23
% 179.25/28.93    (34)   ~ (all_52_7 = all_52_15)
% 179.25/28.93    (35)   ~ (all_52_19 = all_10_2)
% 179.25/28.93    (36)  all_58_15 = e0
% 179.25/28.93    (37)  all_58_2 = all_52_9
% 179.25/28.93    (38)   ~ (all_52_29 = e0)
% 179.25/28.93    (39)   ~ (e2 = e1)
% 179.25/28.93    (40)  all_56_10 = all_14_2
% 179.25/28.93    (41)  op(e1, e3) = all_52_17
% 179.25/28.93    (42)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.25/28.93    (43)  op(e2, all_10_2) = e2
% 179.25/28.93    (44)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93    (45)   ~ (all_52_25 = all_52_27)
% 179.25/28.93    (46)  all_56_7 = all_52_15
% 179.25/28.93    (47)   ~ (all_52_15 = e0)
% 179.25/28.93    (48)   ~ (all_52_7 = all_52_23)
% 179.25/28.93    (49)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.93    (50)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.25/28.93    (51)  all_58_9 = all_52_7
% 179.25/28.93    (52)   ~ (e2 = e0)
% 179.25/28.93    (53)  all_58_12 = all_52_25
% 179.25/28.93    (54)   ~ (e3 = e2)
% 179.25/28.93    (55)   ~ (all_52_19 = all_14_2)
% 179.25/28.93    (56)  op(e2, e3) = all_52_9
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | COMBINE_EQS: (28), (53) imply:
% 179.25/28.93  |   (57)  all_52_25 = e3
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (57) implies:
% 179.25/28.93  |   (58)  all_52_25 = e3
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (4), (58) imply:
% 179.25/28.93  |   (59)   ~ (all_52_9 = e3)
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (14), (58) imply:
% 179.25/28.93  |   (60)   ~ (all_52_17 = e3)
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (45), (58) imply:
% 179.25/28.93  |   (61)   ~ (all_52_27 = e3)
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (61) implies:
% 179.25/28.93  |   (62)   ~ (all_52_27 = e3)
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (29), (58) imply:
% 179.25/28.93  |   (63)   ~ (e3 = e0)
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (23), (58) imply:
% 179.25/28.93  |   (64)  op(e0, e3) = e3
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (50) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (65)  all_56_3 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (2), (65) imply:
% 179.25/28.93  | |   (66)  all_52_7 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | SIMP: (66) implies:
% 179.25/28.93  | |   (67)  all_52_7 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (51), (67) imply:
% 179.25/28.93  | |   (68)  all_58_9 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (31), (67) imply:
% 179.25/28.93  | |   (69)   ~ (all_52_3 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (34), (67) imply:
% 179.25/28.93  | |   (70)   ~ (all_52_15 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | SIMP: (70) implies:
% 179.25/28.93  | |   (71)   ~ (all_52_15 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (48), (67) imply:
% 179.25/28.93  | |   (72)   ~ (all_52_23 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | SIMP: (72) implies:
% 179.25/28.93  | |   (73)   ~ (all_52_23 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (13), (15), (16),
% 179.25/28.93  | |            (17), (18), (19), (20), (21), (25), (26), (27), (30), (32), (33),
% 179.25/28.93  | |            (35), (36), (37), (38), (40), (41), (43), (44), (55), (56), (59),
% 179.25/28.93  | |            (60), (62), (68), (69), (71), (73) are inconsistent by sub-proof
% 179.25/28.93  | |            #973.
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (74)   ~ (all_56_3 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (2), (74) imply:
% 179.25/28.93  | |   (75)   ~ (all_52_7 = e3)
% 179.25/28.93  | | 
% 179.25/28.93  | | BETA: splitting (49) gives:
% 179.25/28.93  | | 
% 179.25/28.93  | | Case 1:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (76)  all_58_9 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REF_CLOSE: (51), (75), (76) are inconsistent by sub-proof #972.
% 179.25/28.93  | | | 
% 179.25/28.93  | | Case 2:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (77)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | BETA: splitting (42) gives:
% 179.25/28.93  | | | 
% 179.25/28.93  | | | Case 1:
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | |   (78)  all_56_7 = e3
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | | COMBINE_EQS: (46), (78) imply:
% 179.25/28.93  | | | |   (79)  all_52_15 = e3
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | | REF_CLOSE: (9), (44), (47), (64), (79) are inconsistent by sub-proof
% 179.25/28.93  | | | |            #971.
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | Case 2:
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | |   (80)   ~ (all_56_7 = e3)
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | | REDUCE: (46), (80) imply:
% 179.25/28.93  | | | |   (81)   ~ (all_52_15 = e3)
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | | REF_CLOSE: (5), (9), (10), (12), (15), (17), (22), (24), (32), (36),
% 179.25/28.93  | | | |            (38), (39), (44), (52), (54), (63), (77), (81) are
% 179.25/28.93  | | | |            inconsistent by sub-proof #985.
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | End of split
% 179.25/28.93  | | | 
% 179.25/28.93  | | End of split
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #971 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  op(e0, all_52_15) = e0
% 179.25/28.93    (2)  all_52_15 = e3
% 179.25/28.93    (3)  op(e0, e3) = e3
% 179.25/28.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93    (5)   ~ (all_52_15 = e0)
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (2) implies:
% 179.25/28.93  |   (6)  all_52_15 = e3
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (5), (6) imply:
% 179.25/28.93  |   (7)   ~ (e3 = e0)
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (1), (6) imply:
% 179.25/28.93  |   (8)  op(e0, e3) = e0
% 179.25/28.93  | 
% 179.25/28.93  | REF_CLOSE: (3), (4), (7), (8) are inconsistent by sub-proof #1027.
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #972 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  all_58_9 = all_52_7
% 179.25/28.93    (2)  all_58_9 = e3
% 179.25/28.93    (3)   ~ (all_52_7 = e3)
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | COMBINE_EQS: (1), (2) imply:
% 179.25/28.93  |   (4)  all_52_7 = e3
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (4) implies:
% 179.25/28.93  |   (5)  all_52_7 = e3
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (3), (5) imply:
% 179.25/28.93  |   (6)  $false
% 179.25/28.93  | 
% 179.25/28.93  | CLOSE: (6) is inconsistent.
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #973 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)   ~ (all_52_17 = all_52_23)
% 179.25/28.93    (2)  op(e3, e2) = all_52_3
% 179.25/28.93    (3)   ~ (all_52_27 = e3)
% 179.25/28.93    (4)   ~ (all_52_17 = e3)
% 179.25/28.93    (5)   ~ (all_52_3 = all_10_2)
% 179.25/28.93    (6)  all_58_5 = all_52_13
% 179.25/28.93    (7)  op(e1, all_52_13) = e1
% 179.25/28.93    (8)  op(e0, all_52_15) = e0
% 179.25/28.93    (9)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.25/28.93    (10)  all_58_3 = all_10_2
% 179.25/28.93    (11)  all_58_10 = all_52_15
% 179.25/28.93    (12)  all_58_7 = all_52_19
% 179.25/28.93    (13)  op(e0, e1) = all_52_29
% 179.25/28.93    (14)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93    (15)   ~ (e3 = e1)
% 179.25/28.93    (16)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93    (17)  all_58_9 = e3
% 179.25/28.93    (18)  all_58_1 = all_52_3
% 179.25/28.93    (19)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.93    (20)  all_58_8 = all_14_2
% 179.25/28.93    (21)   ~ (all_52_23 = e3)
% 179.25/28.93    (22)  op(e3, all_52_9) = e3
% 179.25/28.93    (23)   ~ (all_52_15 = e3)
% 179.25/28.93    (24)  all_56_10 = e3 | all_56_10 = e2 | all_56_10 = e1 | all_56_10 = e0
% 179.25/28.93    (25)  all_58_13 = all_52_27
% 179.25/28.93    (26)   ~ (all_52_3 = e3)
% 179.25/28.93    (27)  all_58_6 = all_52_17
% 179.25/28.93    (28)   ~ (e1 = e0)
% 179.25/28.93    (29)  all_58_11 = all_52_23
% 179.25/28.93    (30)   ~ (all_52_19 = all_10_2)
% 179.25/28.93    (31)  all_58_15 = e0
% 179.25/28.93    (32)   ~ (all_52_9 = e3)
% 179.25/28.93    (33)  all_58_2 = all_52_9
% 179.25/28.93    (34)   ~ (all_52_29 = e0)
% 179.25/28.93    (35)  all_56_10 = all_14_2
% 179.25/28.93    (36)  op(e1, e3) = all_52_17
% 179.25/28.93    (37)  op(e2, all_10_2) = e2
% 179.25/28.93    (38)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93    (39)   ~ (all_52_19 = all_14_2)
% 179.25/28.93    (40)  op(e2, e3) = all_52_9
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (14) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (41)  all_58_6 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REF_CLOSE: (4), (27), (41) are inconsistent by sub-proof #981.
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (42)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | BETA: splitting (19) gives:
% 179.25/28.93  | | 
% 179.25/28.93  | | Case 1:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (43)  all_58_1 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | COMBINE_EQS: (18), (43) imply:
% 179.25/28.93  | | |   (44)  all_52_3 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | REDUCE: (26), (44) imply:
% 179.25/28.93  | | |   (45)  $false
% 179.25/28.93  | | | 
% 179.25/28.93  | | | CLOSE: (45) is inconsistent.
% 179.25/28.93  | | | 
% 179.25/28.93  | | Case 2:
% 179.25/28.93  | | | 
% 179.25/28.93  | | |   (46)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.93  | | | 
% 179.25/28.93  | | | BETA: splitting (16) gives:
% 179.25/28.93  | | | 
% 179.25/28.93  | | | Case 1:
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | |   (47)  all_58_2 = e3
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | | REF_CLOSE: (32), (33), (47) are inconsistent by sub-proof #980.
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | Case 2:
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | |   (48)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | | BETA: splitting (9) gives:
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | | Case 1:
% 179.25/28.93  | | | | | 
% 179.25/28.93  | | | | |   (49)  all_58_9 = e1
% 179.25/28.93  | | | | | 
% 179.25/28.93  | | | | | REF_CLOSE: (15), (17), (49) are inconsistent by sub-proof #979.
% 179.25/28.93  | | | | | 
% 179.25/28.93  | | | | Case 2:
% 179.25/28.93  | | | | | 
% 179.25/28.93  | | | | |   (50)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.25/28.93  | | | | | 
% 179.25/28.93  | | | | | BETA: splitting (24) gives:
% 179.25/28.93  | | | | | 
% 179.25/28.93  | | | | | Case 1:
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | |   (51)  all_56_10 = e3
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | | COMBINE_EQS: (35), (51) imply:
% 179.25/28.93  | | | | | |   (52)  all_14_2 = e3
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | | REDUCE: (39), (52) imply:
% 179.25/28.93  | | | | | |   (53)   ~ (all_52_19 = e3)
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | | REF_CLOSE: (2), (3), (5), (10), (12), (22), (25), (37), (38), (40),
% 179.25/28.93  | | | | | |            (46), (53) are inconsistent by sub-proof #975.
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | Case 2:
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | |   (54)   ~ (all_56_10 = e3)
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | | REDUCE: (35), (54) imply:
% 179.25/28.93  | | | | | |   (55)   ~ (all_14_2 = e3)
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | | BETA: splitting (42) gives:
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | | Case 1:
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | |   (56)  all_58_7 = e3
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | | COMBINE_EQS: (12), (56) imply:
% 179.25/28.93  | | | | | | |   (57)  all_52_19 = e3
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | | REDUCE: (30), (57) imply:
% 179.25/28.93  | | | | | | |   (58)   ~ (all_10_2 = e3)
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | | SIMP: (58) implies:
% 179.25/28.93  | | | | | | |   (59)   ~ (all_10_2 = e3)
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | | BETA: splitting (48) gives:
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | | Case 1:
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | |   (60)  all_58_3 = e3
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | | COMBINE_EQS: (10), (60) imply:
% 179.25/28.93  | | | | | | | |   (61)  all_10_2 = e3
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | | REDUCE: (59), (61) imply:
% 179.25/28.93  | | | | | | | |   (62)  $false
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | | CLOSE: (62) is inconsistent.
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | Case 2:
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | |   (63)  all_58_5 = e3 | all_58_10 = e3
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | | BETA: splitting (63) gives:
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | | Case 1:
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | |   (64)  all_58_5 = e3
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | COMBINE_EQS: (6), (64) imply:
% 179.25/28.93  | | | | | | | | |   (65)  all_52_13 = e3
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | REDUCE: (7), (65) imply:
% 179.25/28.93  | | | | | | | | |   (66)  op(e1, e3) = e1
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | GROUND_INST: instantiating (38) with all_52_17, e1, e3, e1,
% 179.25/28.93  | | | | | | | | |              simplifying with (36), (66) gives:
% 179.25/28.93  | | | | | | | | |   (67)  all_52_17 = e1
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | REDUCE: (1), (67) imply:
% 179.25/28.93  | | | | | | | | |   (68)   ~ (all_52_23 = e1)
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | SIMP: (68) implies:
% 179.25/28.93  | | | | | | | | |   (69)   ~ (all_52_23 = e1)
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | BETA: splitting (50) gives:
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | Case 1:
% 179.25/28.93  | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | |   (70)  all_58_10 = e1
% 179.25/28.93  | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | REF_CLOSE: (8), (11), (13), (34), (38), (70) are inconsistent
% 179.25/28.93  | | | | | | | | | |            by sub-proof #989.
% 179.25/28.93  | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | Case 2:
% 179.25/28.93  | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | |   (71)  all_58_11 = e1 | all_58_15 = e1
% 179.25/28.93  | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | BETA: splitting (71) gives:
% 179.25/28.93  | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | Case 1:
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | |   (72)  all_58_11 = e1
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | | REF_CLOSE: (29), (69), (72) are inconsistent by sub-proof
% 179.25/28.93  | | | | | | | | | | |            #974.
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | Case 2:
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | |   (73)  all_58_15 = e1
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | | COMBINE_EQS: (31), (73) imply:
% 179.25/28.93  | | | | | | | | | | |   (74)  e1 = e0
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | | REDUCE: (28), (74) imply:
% 179.25/28.93  | | | | | | | | | | |   (75)  $false
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | | CLOSE: (75) is inconsistent.
% 179.25/28.93  | | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | | End of split
% 179.25/28.93  | | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | End of split
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | Case 2:
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | |   (76)  all_58_10 = e3
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | COMBINE_EQS: (11), (76) imply:
% 179.25/28.93  | | | | | | | | |   (77)  all_52_15 = e3
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | REDUCE: (23), (77) imply:
% 179.25/28.93  | | | | | | | | |   (78)  $false
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | | CLOSE: (78) is inconsistent.
% 179.25/28.93  | | | | | | | | | 
% 179.25/28.93  | | | | | | | | End of split
% 179.25/28.93  | | | | | | | | 
% 179.25/28.93  | | | | | | | End of split
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | Case 2:
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | |   (79)  all_58_8 = e3 | all_58_11 = e3
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | | REF_CLOSE: (20), (21), (29), (55), (79) are inconsistent by
% 179.25/28.93  | | | | | | |            sub-proof #997.
% 179.25/28.93  | | | | | | | 
% 179.25/28.93  | | | | | | End of split
% 179.25/28.93  | | | | | | 
% 179.25/28.93  | | | | | End of split
% 179.25/28.93  | | | | | 
% 179.25/28.93  | | | | End of split
% 179.25/28.93  | | | | 
% 179.25/28.93  | | | End of split
% 179.25/28.93  | | | 
% 179.25/28.93  | | End of split
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #974 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  all_58_11 = all_52_23
% 179.25/28.93    (2)  all_58_11 = e1
% 179.25/28.93    (3)   ~ (all_52_23 = e1)
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | COMBINE_EQS: (1), (2) imply:
% 179.25/28.93  |   (4)  all_52_23 = e1
% 179.25/28.93  | 
% 179.25/28.93  | SIMP: (4) implies:
% 179.25/28.93  |   (5)  all_52_23 = e1
% 179.25/28.93  | 
% 179.25/28.93  | REDUCE: (3), (5) imply:
% 179.25/28.93  |   (6)  $false
% 179.25/28.93  | 
% 179.25/28.93  | CLOSE: (6) is inconsistent.
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #975 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  op(e3, e2) = all_52_3
% 179.25/28.93    (2)   ~ (all_52_27 = e3)
% 179.25/28.93    (3)   ~ (all_52_3 = all_10_2)
% 179.25/28.93    (4)  all_58_3 = all_10_2
% 179.25/28.93    (5)  all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.25/28.93    (6)  all_58_7 = all_52_19
% 179.25/28.93    (7)  op(e3, all_52_9) = e3
% 179.25/28.93    (8)  all_58_13 = all_52_27
% 179.25/28.93    (9)   ~ (all_52_19 = e3)
% 179.25/28.93    (10)  op(e2, all_10_2) = e2
% 179.25/28.93    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.93    (12)  op(e2, e3) = all_52_9
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (5) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (13)  all_58_3 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (4), (13) imply:
% 179.25/28.93  | |   (14)  all_10_2 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REF_CLOSE: (1), (3), (7), (10), (11), (12), (14) are inconsistent by
% 179.25/28.93  | |            sub-proof #977.
% 179.25/28.93  | | 
% 179.25/28.93  | Case 2:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (15)  all_58_7 = e3 | all_58_13 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REF_CLOSE: (2), (6), (8), (9), (15) are inconsistent by sub-proof #976.
% 179.25/28.93  | | 
% 179.25/28.93  | End of split
% 179.25/28.93  | 
% 179.25/28.93  End of proof
% 179.25/28.93  
% 179.25/28.93  Sub-proof #976 shows that the following formulas are inconsistent:
% 179.25/28.93  ----------------------------------------------------------------
% 179.25/28.93    (1)  all_58_7 = e3 | all_58_13 = e3
% 179.25/28.93    (2)   ~ (all_52_27 = e3)
% 179.25/28.93    (3)  all_58_7 = all_52_19
% 179.25/28.93    (4)  all_58_13 = all_52_27
% 179.25/28.93    (5)   ~ (all_52_19 = e3)
% 179.25/28.93  
% 179.25/28.93  Begin of proof
% 179.25/28.93  | 
% 179.25/28.93  | BETA: splitting (1) gives:
% 179.25/28.93  | 
% 179.25/28.93  | Case 1:
% 179.25/28.93  | | 
% 179.25/28.93  | |   (6)  all_58_7 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | COMBINE_EQS: (3), (6) imply:
% 179.25/28.93  | |   (7)  all_52_19 = e3
% 179.25/28.93  | | 
% 179.25/28.93  | | REDUCE: (5), (7) imply:
% 179.25/28.93  | |   (8)  $false
% 179.25/28.94  | | 
% 179.25/28.94  | | CLOSE: (8) is inconsistent.
% 179.25/28.94  | | 
% 179.25/28.94  | Case 2:
% 179.25/28.94  | | 
% 179.25/28.94  | |   (9)  all_58_13 = e3
% 179.25/28.94  | | 
% 179.25/28.94  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1026.
% 179.25/28.94  | | 
% 179.25/28.94  | End of split
% 179.25/28.94  | 
% 179.25/28.94  End of proof
% 179.25/28.94  
% 179.25/28.94  Sub-proof #977 shows that the following formulas are inconsistent:
% 179.25/28.94  ----------------------------------------------------------------
% 179.25/28.94    (1)  op(e3, e2) = all_52_3
% 179.25/28.94    (2)   ~ (all_52_3 = all_10_2)
% 179.25/28.94    (3)  all_10_2 = e3
% 179.25/28.94    (4)  op(e3, all_52_9) = e3
% 179.25/28.94    (5)  op(e2, all_10_2) = e2
% 179.25/28.94    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.94    (7)  op(e2, e3) = all_52_9
% 179.25/28.94  
% 179.25/28.94  Begin of proof
% 179.25/28.94  | 
% 179.25/28.94  | REDUCE: (2), (3) imply:
% 179.25/28.94  |   (8)   ~ (all_52_3 = e3)
% 179.25/28.94  | 
% 179.25/28.94  | REDUCE: (3), (5) imply:
% 179.25/28.94  |   (9)  op(e2, e3) = e2
% 179.25/28.94  | 
% 179.25/28.94  | GROUND_INST: instantiating (6) with all_52_9, e2, e3, e2, simplifying with
% 179.25/28.94  |              (7), (9) gives:
% 179.25/28.94  |   (10)  all_52_9 = e2
% 179.25/28.94  | 
% 179.25/28.94  | REDUCE: (4), (10) imply:
% 179.25/28.94  |   (11)  op(e3, e2) = e3
% 179.25/28.94  | 
% 179.25/28.94  | REF_CLOSE: (1), (6), (8), (11) are inconsistent by sub-proof #978.
% 179.25/28.94  | 
% 179.25/28.94  End of proof
% 179.25/28.94  
% 179.25/28.94  Sub-proof #978 shows that the following formulas are inconsistent:
% 179.25/28.94  ----------------------------------------------------------------
% 179.25/28.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.25/28.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.25/28.94    (2)  op(e3, e2) = all_52_3
% 179.25/28.94    (3)  op(e3, e2) = e3
% 179.25/28.94    (4)   ~ (all_52_3 = e3)
% 179.25/28.94  
% 179.25/28.94  Begin of proof
% 179.25/28.94  | 
% 179.25/28.94  | GROUND_INST: instantiating (1) with all_52_3, e3, e2, e3, simplifying with
% 179.25/28.94  |              (2), (3) gives:
% 179.25/28.94  |   (5)  all_52_3 = e3
% 179.25/28.94  | 
% 179.25/28.94  | REDUCE: (4), (5) imply:
% 179.25/28.94  |   (6)  $false
% 179.25/28.94  | 
% 179.25/28.94  | CLOSE: (6) is inconsistent.
% 179.25/28.94  | 
% 179.25/28.94  End of proof
% 179.25/28.94  
% 179.25/28.94  Sub-proof #979 shows that the following formulas are inconsistent:
% 179.25/28.94  ----------------------------------------------------------------
% 179.25/28.94    (1)  all_58_9 = e3
% 179.25/28.94    (2)  all_58_9 = e1
% 179.25/28.94    (3)   ~ (e3 = e1)
% 179.25/28.94  
% 179.25/28.94  Begin of proof
% 179.25/28.94  | 
% 179.25/28.94  | COMBINE_EQS: (1), (2) imply:
% 179.25/28.94  |   (4)  e3 = e1
% 179.25/28.94  | 
% 179.25/28.94  | SIMP: (4) implies:
% 179.25/28.94  |   (5)  e3 = e1
% 179.25/28.94  | 
% 179.25/28.94  | REDUCE: (3), (5) imply:
% 179.25/28.94  |   (6)  $false
% 179.25/28.94  | 
% 179.25/28.94  | CLOSE: (6) is inconsistent.
% 179.25/28.94  | 
% 179.25/28.94  End of proof
% 179.25/28.94  
% 179.25/28.94  Sub-proof #980 shows that the following formulas are inconsistent:
% 179.25/28.94  ----------------------------------------------------------------
% 179.25/28.94    (1)  all_58_2 = all_52_9
% 179.25/28.94    (2)  all_58_2 = e3
% 179.25/28.94    (3)   ~ (all_52_9 = e3)
% 179.25/28.94  
% 179.25/28.94  Begin of proof
% 179.25/28.94  | 
% 179.25/28.94  | COMBINE_EQS: (1), (2) imply:
% 179.25/28.94  |   (4)  all_52_9 = e3
% 179.25/28.94  | 
% 179.25/28.94  | SIMP: (4) implies:
% 179.25/28.94  |   (5)  all_52_9 = e3
% 179.25/28.94  | 
% 179.25/28.94  | REDUCE: (3), (5) imply:
% 179.25/28.94  |   (6)  $false
% 179.25/28.94  | 
% 179.25/28.94  | CLOSE: (6) is inconsistent.
% 179.25/28.94  | 
% 179.25/28.94  End of proof
% 179.25/28.94  
% 179.25/28.94  Sub-proof #981 shows that the following formulas are inconsistent:
% 179.25/28.94  ----------------------------------------------------------------
% 179.25/28.94    (1)  all_58_6 = all_52_17
% 179.25/28.94    (2)  all_58_6 = e3
% 179.25/28.94    (3)   ~ (all_52_17 = e3)
% 179.25/28.94  
% 179.25/28.94  Begin of proof
% 179.25/28.94  | 
% 179.25/28.94  | COMBINE_EQS: (1), (2) imply:
% 179.25/28.94  |   (4)  all_52_17 = e3
% 179.25/28.94  | 
% 179.25/28.94  | SIMP: (4) implies:
% 179.25/28.94  |   (5)  all_52_17 = e3
% 179.25/28.94  | 
% 179.25/28.94  | REDUCE: (3), (5) imply:
% 179.25/28.94  |   (6)  $false
% 179.25/28.94  | 
% 179.25/28.94  | CLOSE: (6) is inconsistent.
% 179.25/28.94  | 
% 179.25/28.94  End of proof
% 179.25/28.94  
% 179.25/28.94  Sub-proof #982 shows that the following formulas are inconsistent:
% 179.25/28.94  ----------------------------------------------------------------
% 179.25/28.94    (1)   ~ (all_52_25 = e3)
% 179.25/28.94    (2)   ~ (all_52_13 = all_52_29)
% 179.25/28.94    (3)  all_56_3 = all_52_7
% 179.29/28.94    (4)   ~ (all_52_27 = e0)
% 179.29/28.94    (5)  all_58_5 = all_52_13
% 179.29/28.94    (6)  op(e1, all_52_13) = e1
% 179.29/28.94    (7)  op(e0, all_52_15) = e0
% 179.29/28.94    (8)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.94    (9)  all_58_3 = all_10_2
% 179.29/28.94    (10)   ~ (all_52_26 = all_4_2)
% 179.29/28.94    (11)   ~ (all_52_5 = all_52_7)
% 179.29/28.94    (12)  all_58_10 = all_52_15
% 179.29/28.94    (13)  all_58_7 = all_52_19
% 179.29/28.94    (14)   ~ (all_52_17 = all_52_25)
% 179.29/28.94    (15)  op(e0, e1) = all_52_29
% 179.29/28.94    (16)  all_58_4 = all_52_5
% 179.29/28.94    (17)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.94    (18)   ~ (e3 = e1)
% 179.29/28.94    (19)   ~ (all_52_17 = all_14_2)
% 179.29/28.94    (20)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.29/28.94    (21)   ~ (all_52_7 = all_4_2)
% 179.29/28.94    (22)  all_58_0 = all_4_2
% 179.29/28.94    (23)  all_58_14 = all_52_29
% 179.29/28.94    (24)   ~ (all_10_2 = e3)
% 179.29/28.94    (25)   ~ (all_52_13 = all_52_26)
% 179.29/28.94    (26)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.94    (27)  all_58_8 = all_14_2
% 179.29/28.94    (28)  op(e0, e2) = all_52_27
% 179.29/28.94    (29)  op(e0, e3) = all_52_25
% 179.29/28.94    (30)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.94    (31)   ~ (all_52_13 = all_14_2)
% 179.29/28.94    (32)   ~ (e3 = e0)
% 179.29/28.94    (33)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.29/28.94    (34)   ~ (all_58_12 = e1)
% 179.29/28.94    (35)  all_56_12 = all_52_25
% 179.29/28.94    (36)   ~ (all_52_25 = e0)
% 179.29/28.94    (37)  all_58_6 = all_52_17
% 179.29/28.94    (38)  all_58_2 = all_52_26
% 179.29/28.94    (39)   ~ (e1 = e0)
% 179.29/28.94    (40)  all_58_11 = all_52_23
% 179.29/28.94    (41)   ~ (all_52_7 = all_52_15)
% 179.29/28.94    (42)  all_58_15 = e0
% 179.29/28.94    (43)   ~ (all_52_29 = e0)
% 179.29/28.94    (44)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.29/28.94    (45)   ~ (all_52_19 = e3)
% 179.29/28.94    (46)  op(e1, e3) = all_52_17
% 179.29/28.94    (47)  all_56_7 = e3 | all_56_7 = e2 | all_56_7 = e1 | all_56_7 = e0
% 179.29/28.94    (48)  op(e3, e3) = all_4_2
% 179.29/28.94    (49)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94    (50)  all_56_7 = all_52_15
% 179.29/28.94    (51)   ~ (all_52_7 = all_52_23)
% 179.29/28.94    (52)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.94    (53)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.94    (54)  all_58_9 = all_52_7
% 179.29/28.94    (55)  all_58_12 = all_52_25
% 179.29/28.94    (56)  op(e3, all_52_26) = e3
% 179.29/28.94    (57)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (34), (55) imply:
% 179.29/28.94  |   (58)   ~ (all_52_25 = e1)
% 179.29/28.94  | 
% 179.29/28.94  | BETA: splitting (44) gives:
% 179.29/28.94  | 
% 179.29/28.94  | Case 1:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (59)  all_58_12 = e2
% 179.29/28.94  | | 
% 179.29/28.94  | | COMBINE_EQS: (55), (59) imply:
% 179.29/28.94  | |   (60)  all_52_25 = e2
% 179.29/28.94  | | 
% 179.29/28.94  | | SIMP: (60) implies:
% 179.29/28.94  | |   (61)  all_52_25 = e2
% 179.29/28.94  | | 
% 179.29/28.94  | | REDUCE: (1), (61) imply:
% 179.29/28.94  | |   (62)   ~ (e3 = e2)
% 179.29/28.94  | | 
% 179.29/28.94  | | SIMP: (62) implies:
% 179.29/28.94  | |   (63)   ~ (e3 = e2)
% 179.29/28.94  | | 
% 179.29/28.94  | | REDUCE: (58), (61) imply:
% 179.29/28.94  | |   (64)   ~ (e2 = e1)
% 179.29/28.94  | | 
% 179.29/28.94  | | REDUCE: (36), (61) imply:
% 179.29/28.94  | |   (65)   ~ (e2 = e0)
% 179.29/28.94  | | 
% 179.29/28.94  | | REDUCE: (29), (61) imply:
% 179.29/28.94  | |   (66)  op(e0, e3) = e2
% 179.29/28.94  | | 
% 179.29/28.94  | | BETA: splitting (53) gives:
% 179.29/28.94  | | 
% 179.29/28.94  | | Case 1:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (67)  all_56_3 = e3
% 179.29/28.94  | | | 
% 179.29/28.94  | | | COMBINE_EQS: (3), (67) imply:
% 179.29/28.94  | | |   (68)  all_52_7 = e3
% 179.29/28.94  | | | 
% 179.29/28.94  | | | REF_CLOSE: (2), (5), (6), (9), (10), (11), (12), (13), (14), (16), (17),
% 179.29/28.94  | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 179.29/28.94  | | |            (31), (37), (38), (40), (41), (45), (46), (48), (49), (51),
% 179.29/28.94  | | |            (55), (56), (57), (68) are inconsistent by sub-proof #983.
% 179.29/28.94  | | | 
% 179.29/28.94  | | Case 2:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (69)   ~ (all_56_3 = e3)
% 179.29/28.94  | | | 
% 179.29/28.94  | | | REDUCE: (3), (69) imply:
% 179.29/28.94  | | |   (70)   ~ (all_52_7 = e3)
% 179.29/28.94  | | | 
% 179.29/28.94  | | | BETA: splitting (52) gives:
% 179.29/28.94  | | | 
% 179.29/28.94  | | | Case 1:
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | |   (71)  all_58_9 = e3
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | COMBINE_EQS: (54), (71) imply:
% 179.29/28.94  | | | |   (72)  all_52_7 = e3
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | REDUCE: (70), (72) imply:
% 179.29/28.94  | | | |   (73)  $false
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | CLOSE: (73) is inconsistent.
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | Case 2:
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | |   (74)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | BETA: splitting (47) gives:
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | Case 1:
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | |   (75)  all_56_7 = e3
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | | COMBINE_EQS: (50), (75) imply:
% 179.29/28.94  | | | | |   (76)  all_52_15 = e3
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | | REDUCE: (7), (76) imply:
% 179.29/28.94  | | | | |   (77)  op(e0, e3) = e0
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | | REF_CLOSE: (49), (65), (66), (77) are inconsistent by sub-proof #1035.
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | Case 2:
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | |   (78)   ~ (all_56_7 = e3)
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | | REDUCE: (50), (78) imply:
% 179.29/28.94  | | | | |   (79)   ~ (all_52_15 = e3)
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | | REF_CLOSE: (4), (7), (8), (12), (15), (18), (28), (30), (32), (39),
% 179.29/28.94  | | | | |            (42), (43), (49), (63), (64), (65), (74), (79) are
% 179.29/28.94  | | | | |            inconsistent by sub-proof #985.
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | End of split
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | End of split
% 179.29/28.94  | | | 
% 179.29/28.94  | | End of split
% 179.29/28.94  | | 
% 179.29/28.94  | Case 2:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (80)   ~ (all_58_12 = e2)
% 179.29/28.94  | | 
% 179.29/28.94  | | REDUCE: (55), (80) imply:
% 179.29/28.94  | |   (81)   ~ (all_52_25 = e2)
% 179.29/28.94  | | 
% 179.29/28.94  | | REF_CLOSE: (33), (35), (36), (58), (81) are inconsistent by sub-proof #1028.
% 179.29/28.94  | | 
% 179.29/28.94  | End of split
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #983 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ~ (all_52_13 = all_52_29)
% 179.29/28.94    (2)  all_52_7 = e3
% 179.29/28.94    (3)  all_58_5 = all_52_13
% 179.29/28.94    (4)  op(e1, all_52_13) = e1
% 179.29/28.94    (5)  all_58_3 = all_10_2
% 179.29/28.94    (6)   ~ (all_52_26 = all_4_2)
% 179.29/28.94    (7)   ~ (all_52_5 = all_52_7)
% 179.29/28.94    (8)  all_58_10 = all_52_15
% 179.29/28.94    (9)  all_58_7 = all_52_19
% 179.29/28.94    (10)   ~ (all_52_17 = all_52_25)
% 179.29/28.94    (11)  all_58_4 = all_52_5
% 179.29/28.94    (12)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.94    (13)   ~ (e3 = e1)
% 179.29/28.94    (14)   ~ (all_52_17 = all_14_2)
% 179.29/28.94    (15)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.29/28.94    (16)   ~ (all_52_7 = all_4_2)
% 179.29/28.94    (17)  all_58_0 = all_4_2
% 179.29/28.94    (18)  all_58_14 = all_52_29
% 179.29/28.94    (19)   ~ (all_10_2 = e3)
% 179.29/28.94    (20)   ~ (all_52_13 = all_52_26)
% 179.29/28.94    (21)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.94    (22)  all_58_8 = all_14_2
% 179.29/28.94    (23)   ~ (all_52_13 = all_14_2)
% 179.29/28.94    (24)  all_58_6 = all_52_17
% 179.29/28.94    (25)  all_58_2 = all_52_26
% 179.29/28.94    (26)  all_58_11 = all_52_23
% 179.29/28.94    (27)   ~ (all_52_7 = all_52_15)
% 179.29/28.94    (28)   ~ (all_52_19 = e3)
% 179.29/28.94    (29)  op(e1, e3) = all_52_17
% 179.29/28.94    (30)  op(e3, e3) = all_4_2
% 179.29/28.94    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94    (32)   ~ (all_52_7 = all_52_23)
% 179.29/28.94    (33)  all_58_12 = all_52_25
% 179.29/28.94    (34)  op(e3, all_52_26) = e3
% 179.29/28.94    (35)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (2) implies:
% 179.29/28.94  |   (36)  all_52_7 = e3
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (7), (36) imply:
% 179.29/28.94  |   (37)   ~ (all_52_5 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (27), (36) imply:
% 179.29/28.94  |   (38)   ~ (all_52_15 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (38) implies:
% 179.29/28.94  |   (39)   ~ (all_52_15 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (32), (36) imply:
% 179.29/28.94  |   (40)   ~ (all_52_23 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (40) implies:
% 179.29/28.94  |   (41)   ~ (all_52_23 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (16), (36) imply:
% 179.29/28.94  |   (42)   ~ (all_4_2 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (42) implies:
% 179.29/28.94  |   (43)   ~ (all_4_2 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 179.29/28.94  |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 179.29/28.94  |            (28), (29), (30), (31), (33), (34), (35), (37), (39), (41), (43)
% 179.29/28.94  |            are inconsistent by sub-proof #984.
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #984 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ~ (all_52_13 = all_52_29)
% 179.29/28.94    (2)  all_58_5 = all_52_13
% 179.29/28.94    (3)  op(e1, all_52_13) = e1
% 179.29/28.94    (4)   ~ (all_4_2 = e3)
% 179.29/28.94    (5)  all_58_3 = all_10_2
% 179.29/28.94    (6)   ~ (all_52_26 = all_4_2)
% 179.29/28.94    (7)  all_58_10 = all_52_15
% 179.29/28.94    (8)  all_58_7 = all_52_19
% 179.29/28.94    (9)   ~ (all_52_17 = all_52_25)
% 179.29/28.94    (10)  all_58_4 = all_52_5
% 179.29/28.94    (11)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.94    (12)   ~ (e3 = e1)
% 179.29/28.94    (13)   ~ (all_52_17 = all_14_2)
% 179.29/28.94    (14)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.29/28.94    (15)  all_58_0 = all_4_2
% 179.29/28.94    (16)  all_58_14 = all_52_29
% 179.29/28.94    (17)   ~ (all_10_2 = e3)
% 179.29/28.94    (18)   ~ (all_52_13 = all_52_26)
% 179.29/28.94    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.94    (20)  all_58_8 = all_14_2
% 179.29/28.94    (21)   ~ (all_52_23 = e3)
% 179.29/28.94    (22)   ~ (all_52_5 = e3)
% 179.29/28.94    (23)   ~ (all_52_13 = all_14_2)
% 179.29/28.94    (24)   ~ (all_52_15 = e3)
% 179.29/28.94    (25)  all_58_6 = all_52_17
% 179.29/28.94    (26)  all_58_2 = all_52_26
% 179.29/28.94    (27)  all_58_11 = all_52_23
% 179.29/28.94    (28)   ~ (all_52_19 = e3)
% 179.29/28.94    (29)  op(e1, e3) = all_52_17
% 179.29/28.94    (30)  op(e3, e3) = all_4_2
% 179.29/28.94    (31)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94    (32)  all_58_12 = all_52_25
% 179.29/28.94    (33)  op(e3, all_52_26) = e3
% 179.29/28.94    (34)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | BETA: splitting (34) gives:
% 179.29/28.94  | 
% 179.29/28.94  | Case 1:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (35)  all_58_4 = e3
% 179.29/28.94  | | 
% 179.29/28.94  | | REF_CLOSE: (10), (22), (35) are inconsistent by sub-proof #1025.
% 179.29/28.94  | | 
% 179.29/28.94  | Case 2:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (36)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.94  | | 
% 179.29/28.94  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 179.29/28.94  | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 179.29/28.94  | |            (26), (27), (28), (29), (30), (31), (32), (33), (36) are
% 179.29/28.94  | |            inconsistent by sub-proof #995.
% 179.29/28.94  | | 
% 179.29/28.94  | End of split
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #985 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ~ (all_52_27 = e0)
% 179.29/28.94    (2)  op(e0, all_52_15) = e0
% 179.29/28.94    (3)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.94    (4)  all_58_10 = all_52_15
% 179.29/28.94    (5)  op(e0, e1) = all_52_29
% 179.29/28.94    (6)   ~ (e3 = e1)
% 179.29/28.94    (7)  op(e0, e2) = all_52_27
% 179.29/28.94    (8)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.94    (9)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.94    (10)   ~ (e3 = e0)
% 179.29/28.94    (11)   ~ (all_52_15 = e3)
% 179.29/28.94    (12)   ~ (e1 = e0)
% 179.29/28.94    (13)  all_58_15 = e0
% 179.29/28.94    (14)   ~ (all_52_29 = e0)
% 179.29/28.94    (15)   ~ (e2 = e1)
% 179.29/28.94    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94    (17)   ~ (e2 = e0)
% 179.29/28.94    (18)   ~ (e3 = e2)
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | BETA: splitting (8) gives:
% 179.29/28.94  | 
% 179.29/28.94  | Case 1:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (19)  all_58_10 = e3
% 179.29/28.94  | | 
% 179.29/28.94  | | REF_CLOSE: (4), (11), (19) are inconsistent by sub-proof #1018.
% 179.29/28.94  | | 
% 179.29/28.94  | Case 2:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (20)  all_58_11 = e3 | all_58_15 = e3
% 179.29/28.94  | | 
% 179.29/28.94  | | BETA: splitting (20) gives:
% 179.29/28.94  | | 
% 179.29/28.94  | | Case 1:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (21)  all_58_11 = e3
% 179.29/28.94  | | | 
% 179.29/28.94  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (12), (13), (14), (15),
% 179.29/28.94  | | |            (16), (17), (18), (21) are inconsistent by sub-proof #986.
% 179.29/28.94  | | | 
% 179.29/28.94  | | Case 2:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (22)  all_58_15 = e3
% 179.29/28.94  | | | 
% 179.29/28.94  | | | REF_CLOSE: (10), (13), (22) are inconsistent by sub-proof #1010.
% 179.29/28.94  | | | 
% 179.29/28.94  | | End of split
% 179.29/28.94  | | 
% 179.29/28.94  | End of split
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #986 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ~ (all_52_27 = e0)
% 179.29/28.94    (2)  op(e0, all_52_15) = e0
% 179.29/28.94    (3)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.94    (4)  all_58_10 = all_52_15
% 179.29/28.94    (5)  op(e0, e1) = all_52_29
% 179.29/28.94    (6)   ~ (e3 = e1)
% 179.29/28.94    (7)  all_58_11 = e3
% 179.29/28.94    (8)  op(e0, e2) = all_52_27
% 179.29/28.94    (9)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.94    (10)   ~ (e1 = e0)
% 179.29/28.94    (11)  all_58_15 = e0
% 179.29/28.94    (12)   ~ (all_52_29 = e0)
% 179.29/28.94    (13)   ~ (e2 = e1)
% 179.29/28.94    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94    (15)   ~ (e2 = e0)
% 179.29/28.94    (16)   ~ (e3 = e2)
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | BETA: splitting (3) gives:
% 179.29/28.94  | 
% 179.29/28.94  | Case 1:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (17)  all_58_9 = e1
% 179.29/28.94  | | 
% 179.29/28.94  | | BETA: splitting (9) gives:
% 179.29/28.94  | | 
% 179.29/28.94  | | Case 1:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (18)  all_58_9 = e2
% 179.29/28.94  | | | 
% 179.29/28.94  | | | COMBINE_EQS: (17), (18) imply:
% 179.29/28.94  | | |   (19)  e2 = e1
% 179.29/28.94  | | | 
% 179.29/28.94  | | | REDUCE: (13), (19) imply:
% 179.29/28.94  | | |   (20)  $false
% 179.29/28.94  | | | 
% 179.29/28.94  | | | CLOSE: (20) is inconsistent.
% 179.29/28.94  | | | 
% 179.29/28.94  | | Case 2:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (21)  all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.94  | | | 
% 179.29/28.94  | | | BETA: splitting (21) gives:
% 179.29/28.94  | | | 
% 179.29/28.94  | | | Case 1:
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | |   (22)  all_58_10 = e2
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | COMBINE_EQS: (4), (22) imply:
% 179.29/28.94  | | | |   (23)  all_52_15 = e2
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | SIMP: (23) implies:
% 179.29/28.94  | | | |   (24)  all_52_15 = e2
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | REDUCE: (2), (24) imply:
% 179.29/28.94  | | | |   (25)  op(e0, e2) = e0
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | REF_CLOSE: (1), (8), (14), (25) are inconsistent by sub-proof #1039.
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | Case 2:
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | |   (26)  all_58_11 = e2 | all_58_15 = e2
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | BETA: splitting (26) gives:
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | | Case 1:
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | |   (27)  all_58_11 = e2
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | | REF_CLOSE: (7), (16), (27) are inconsistent by sub-proof #992.
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | Case 2:
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | |   (28)  all_58_15 = e2
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | | REF_CLOSE: (11), (15), (28) are inconsistent by sub-proof #991.
% 179.29/28.94  | | | | | 
% 179.29/28.94  | | | | End of split
% 179.29/28.94  | | | | 
% 179.29/28.94  | | | End of split
% 179.29/28.94  | | | 
% 179.29/28.94  | | End of split
% 179.29/28.94  | | 
% 179.29/28.94  | Case 2:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (29)  all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.94  | | 
% 179.29/28.94  | | BETA: splitting (29) gives:
% 179.29/28.94  | | 
% 179.29/28.94  | | Case 1:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (30)  all_58_10 = e1
% 179.29/28.94  | | | 
% 179.29/28.94  | | | REF_CLOSE: (2), (4), (5), (12), (14), (30) are inconsistent by sub-proof
% 179.29/28.94  | | |            #989.
% 179.29/28.94  | | | 
% 179.29/28.94  | | Case 2:
% 179.29/28.94  | | | 
% 179.29/28.94  | | |   (31)  all_58_11 = e1 | all_58_15 = e1
% 179.29/28.94  | | | 
% 179.29/28.94  | | | REF_CLOSE: (6), (7), (10), (11), (31) are inconsistent by sub-proof #987.
% 179.29/28.94  | | | 
% 179.29/28.94  | | End of split
% 179.29/28.94  | | 
% 179.29/28.94  | End of split
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #987 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ~ (e3 = e1)
% 179.29/28.94    (2)  all_58_11 = e3
% 179.29/28.94    (3)  all_58_11 = e1 | all_58_15 = e1
% 179.29/28.94    (4)   ~ (e1 = e0)
% 179.29/28.94    (5)  all_58_15 = e0
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | BETA: splitting (3) gives:
% 179.29/28.94  | 
% 179.29/28.94  | Case 1:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (6)  all_58_11 = e1
% 179.29/28.94  | | 
% 179.29/28.94  | | COMBINE_EQS: (2), (6) imply:
% 179.29/28.94  | |   (7)  e3 = e1
% 179.29/28.94  | | 
% 179.29/28.94  | | REDUCE: (1), (7) imply:
% 179.29/28.94  | |   (8)  $false
% 179.29/28.94  | | 
% 179.29/28.94  | | CLOSE: (8) is inconsistent.
% 179.29/28.94  | | 
% 179.29/28.94  | Case 2:
% 179.29/28.94  | | 
% 179.29/28.94  | |   (9)  all_58_15 = e1
% 179.29/28.94  | | 
% 179.29/28.94  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #988.
% 179.29/28.94  | | 
% 179.29/28.94  | End of split
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #988 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)  all_58_15 = e1
% 179.29/28.94    (2)  all_58_15 = e0
% 179.29/28.94    (3)   ~ (e1 = e0)
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.94  |   (4)  e1 = e0
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (4) implies:
% 179.29/28.94  |   (5)  e1 = e0
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (3), (5) imply:
% 179.29/28.94  |   (6)  $false
% 179.29/28.94  | 
% 179.29/28.94  | CLOSE: (6) is inconsistent.
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #989 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)  op(e0, all_52_15) = e0
% 179.29/28.94    (2)  all_58_10 = all_52_15
% 179.29/28.94    (3)  op(e0, e1) = all_52_29
% 179.29/28.94    (4)  all_58_10 = e1
% 179.29/28.94    (5)   ~ (all_52_29 = e0)
% 179.29/28.94    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | COMBINE_EQS: (2), (4) imply:
% 179.29/28.94  |   (7)  all_52_15 = e1
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (7) implies:
% 179.29/28.94  |   (8)  all_52_15 = e1
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (1), (8) imply:
% 179.29/28.94  |   (9)  op(e0, e1) = e0
% 179.29/28.94  | 
% 179.29/28.94  | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #990.
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #990 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94    (2)  op(e0, e1) = all_52_29
% 179.29/28.94    (3)  op(e0, e1) = e0
% 179.29/28.94    (4)   ~ (all_52_29 = e0)
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | GROUND_INST: instantiating (1) with all_52_29, e0, e1, e0, simplifying with
% 179.29/28.94  |              (2), (3) gives:
% 179.29/28.94  |   (5)  all_52_29 = e0
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (4), (5) imply:
% 179.29/28.94  |   (6)  $false
% 179.29/28.94  | 
% 179.29/28.94  | CLOSE: (6) is inconsistent.
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #991 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)  all_58_15 = e2
% 179.29/28.94    (2)  all_58_15 = e0
% 179.29/28.94    (3)   ~ (e2 = e0)
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.94  |   (4)  e2 = e0
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (4) implies:
% 179.29/28.94  |   (5)  e2 = e0
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (3), (5) imply:
% 179.29/28.94  |   (6)  $false
% 179.29/28.94  | 
% 179.29/28.94  | CLOSE: (6) is inconsistent.
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #992 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)  all_58_11 = e3
% 179.29/28.94    (2)  all_58_11 = e2
% 179.29/28.94    (3)   ~ (e3 = e2)
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.94  |   (4)  e3 = e2
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (4) implies:
% 179.29/28.94  |   (5)  e3 = e2
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (3), (5) imply:
% 179.29/28.94  |   (6)  $false
% 179.29/28.94  | 
% 179.29/28.94  | CLOSE: (6) is inconsistent.
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #993 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ~ (all_52_13 = all_52_29)
% 179.29/28.94    (2)  all_58_5 = all_52_13
% 179.29/28.94    (3)  op(e1, all_52_13) = e1
% 179.29/28.94    (4)  all_58_3 = all_10_2
% 179.29/28.94    (5)   ~ (all_52_26 = all_4_2)
% 179.29/28.94    (6)  all_58_10 = all_52_15
% 179.29/28.94    (7)  all_58_7 = all_52_19
% 179.29/28.94    (8)   ~ (all_52_17 = all_52_25)
% 179.29/28.94    (9)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.94    (10)   ~ (e3 = e1)
% 179.29/28.94    (11)   ~ (all_52_17 = all_14_2)
% 179.29/28.94    (12)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.29/28.94    (13)   ~ (all_52_7 = all_4_2)
% 179.29/28.94    (14)  all_58_0 = all_4_2
% 179.29/28.94    (15)  all_58_14 = all_52_29
% 179.29/28.94    (16)   ~ (all_10_2 = e3)
% 179.29/28.94    (17)   ~ (all_52_13 = all_52_26)
% 179.29/28.94    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.94    (19)  all_58_8 = all_14_2
% 179.29/28.94    (20)   ~ (all_52_13 = all_14_2)
% 179.29/28.94    (21)  all_58_6 = all_52_17
% 179.29/28.94    (22)  all_58_2 = all_52_26
% 179.29/28.94    (23)  all_58_11 = all_52_23
% 179.29/28.94    (24)   ~ (all_52_7 = all_52_15)
% 179.29/28.94    (25)   ~ (all_52_7 = all_52_24)
% 179.29/28.94    (26)   ~ (all_52_19 = e3)
% 179.29/28.94    (27)  op(e1, e3) = all_52_17
% 179.29/28.94    (28)  op(e3, e3) = all_4_2
% 179.29/28.94    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.94    (30)  all_58_4 = all_52_24
% 179.29/28.94    (31)  all_52_7 = e3
% 179.29/28.94    (32)   ~ (all_52_7 = all_52_23)
% 179.29/28.94    (33)  all_58_12 = all_52_25
% 179.29/28.94    (34)  op(e3, all_52_26) = e3
% 179.29/28.94    (35)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.94  
% 179.29/28.94  Begin of proof
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (24), (31) imply:
% 179.29/28.94  |   (36)   ~ (all_52_15 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (36) implies:
% 179.29/28.94  |   (37)   ~ (all_52_15 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (31), (32) imply:
% 179.29/28.94  |   (38)   ~ (all_52_23 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (38) implies:
% 179.29/28.94  |   (39)   ~ (all_52_23 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (25), (31) imply:
% 179.29/28.94  |   (40)   ~ (all_52_24 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (40) implies:
% 179.29/28.94  |   (41)   ~ (all_52_24 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REDUCE: (13), (31) imply:
% 179.29/28.94  |   (42)   ~ (all_4_2 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | SIMP: (42) implies:
% 179.29/28.94  |   (43)   ~ (all_4_2 = e3)
% 179.29/28.94  | 
% 179.29/28.94  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 179.29/28.94  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 179.29/28.94  |            (27), (28), (29), (30), (33), (34), (35), (37), (39), (41), (43)
% 179.29/28.94  |            are inconsistent by sub-proof #994.
% 179.29/28.94  | 
% 179.29/28.94  End of proof
% 179.29/28.94  
% 179.29/28.94  Sub-proof #994 shows that the following formulas are inconsistent:
% 179.29/28.94  ----------------------------------------------------------------
% 179.29/28.94    (1)   ~ (all_52_13 = all_52_29)
% 179.29/28.94    (2)  all_58_5 = all_52_13
% 179.29/28.94    (3)  op(e1, all_52_13) = e1
% 179.29/28.94    (4)   ~ (all_4_2 = e3)
% 179.29/28.94    (5)  all_58_3 = all_10_2
% 179.29/28.94    (6)   ~ (all_52_26 = all_4_2)
% 179.29/28.94    (7)  all_58_10 = all_52_15
% 179.29/28.94    (8)  all_58_7 = all_52_19
% 179.29/28.95    (9)   ~ (all_52_17 = all_52_25)
% 179.29/28.95    (10)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.95    (11)   ~ (e3 = e1)
% 179.29/28.95    (12)   ~ (all_52_17 = all_14_2)
% 179.29/28.95    (13)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.29/28.95    (14)  all_58_0 = all_4_2
% 179.29/28.95    (15)  all_58_14 = all_52_29
% 179.29/28.95    (16)   ~ (all_10_2 = e3)
% 179.29/28.95    (17)   ~ (all_52_13 = all_52_26)
% 179.29/28.95    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95    (19)  all_58_8 = all_14_2
% 179.29/28.95    (20)   ~ (all_52_23 = e3)
% 179.29/28.95    (21)   ~ (all_52_13 = all_14_2)
% 179.29/28.95    (22)   ~ (all_52_15 = e3)
% 179.29/28.95    (23)  all_58_6 = all_52_17
% 179.29/28.95    (24)  all_58_2 = all_52_26
% 179.29/28.95    (25)  all_58_11 = all_52_23
% 179.29/28.95    (26)   ~ (all_52_19 = e3)
% 179.29/28.95    (27)  op(e1, e3) = all_52_17
% 179.29/28.95    (28)  op(e3, e3) = all_4_2
% 179.29/28.95    (29)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (30)  all_58_4 = all_52_24
% 179.29/28.95    (31)   ~ (all_52_24 = e3)
% 179.29/28.95    (32)  all_58_12 = all_52_25
% 179.29/28.95    (33)  op(e3, all_52_26) = e3
% 179.29/28.95    (34)  all_58_4 = e3 | all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (34) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (35)  all_58_4 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (30), (35) imply:
% 179.29/28.95  | |   (36)  all_52_24 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (31), (36) imply:
% 179.29/28.95  | |   (37)  $false
% 179.29/28.95  | | 
% 179.29/28.95  | | CLOSE: (37) is inconsistent.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (38)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 179.29/28.95  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 179.29/28.95  | |            (24), (25), (26), (27), (28), (29), (32), (33), (38) are
% 179.29/28.95  | |            inconsistent by sub-proof #995.
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #995 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)   ~ (all_52_13 = all_52_29)
% 179.29/28.95    (2)  all_58_5 = all_52_13
% 179.29/28.95    (3)  op(e1, all_52_13) = e1
% 179.29/28.95    (4)   ~ (all_4_2 = e3)
% 179.29/28.95    (5)  all_58_3 = all_10_2
% 179.29/28.95    (6)   ~ (all_52_26 = all_4_2)
% 179.29/28.95    (7)  all_58_10 = all_52_15
% 179.29/28.95    (8)  all_58_7 = all_52_19
% 179.29/28.95    (9)   ~ (all_52_17 = all_52_25)
% 179.29/28.95    (10)  all_58_6 = e3 | all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.95    (11)   ~ (e3 = e1)
% 179.29/28.95    (12)   ~ (all_52_17 = all_14_2)
% 179.29/28.95    (13)  all_58_2 = e3 | all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.29/28.95    (14)  all_58_0 = all_4_2
% 179.29/28.95    (15)  all_58_14 = all_52_29
% 179.29/28.95    (16)   ~ (all_10_2 = e3)
% 179.29/28.95    (17)   ~ (all_52_13 = all_52_26)
% 179.29/28.95    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95    (19)  all_58_8 = all_14_2
% 179.29/28.95    (20)   ~ (all_52_23 = e3)
% 179.29/28.95    (21)   ~ (all_52_13 = all_14_2)
% 179.29/28.95    (22)   ~ (all_52_15 = e3)
% 179.29/28.95    (23)  all_58_6 = all_52_17
% 179.29/28.95    (24)  all_58_2 = all_52_26
% 179.29/28.95    (25)  all_58_11 = all_52_23
% 179.29/28.95    (26)   ~ (all_52_19 = e3)
% 179.29/28.95    (27)  op(e1, e3) = all_52_17
% 179.29/28.95    (28)  op(e3, e3) = all_4_2
% 179.29/28.95    (29)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.95    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (31)  all_58_12 = all_52_25
% 179.29/28.95    (32)  op(e3, all_52_26) = e3
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (18) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (33)  all_58_0 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (14), (33) imply:
% 179.29/28.95  | |   (34)  all_4_2 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (4), (34) imply:
% 179.29/28.95  | |   (35)  $false
% 179.29/28.95  | | 
% 179.29/28.95  | | CLOSE: (35) is inconsistent.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (36)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | BETA: splitting (13) gives:
% 179.29/28.95  | | 
% 179.29/28.95  | | Case 1:
% 179.29/28.95  | | | 
% 179.29/28.95  | | |   (37)  all_58_2 = e3
% 179.29/28.95  | | | 
% 179.29/28.95  | | | COMBINE_EQS: (24), (37) imply:
% 179.29/28.95  | | |   (38)  all_52_26 = e3
% 179.29/28.95  | | | 
% 179.29/28.95  | | | SIMP: (38) implies:
% 179.29/28.95  | | |   (39)  all_52_26 = e3
% 179.29/28.95  | | | 
% 179.29/28.95  | | | REF_CLOSE: (6), (28), (30), (32), (39) are inconsistent by sub-proof
% 179.29/28.95  | | |            #1005.
% 179.29/28.95  | | | 
% 179.29/28.95  | | Case 2:
% 179.29/28.95  | | | 
% 179.29/28.95  | | |   (40)  all_58_3 = e3 | all_58_5 = e3 | all_58_10 = e3
% 179.29/28.95  | | | 
% 179.29/28.95  | | | BETA: splitting (40) gives:
% 179.29/28.95  | | | 
% 179.29/28.95  | | | Case 1:
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | |   (41)  all_58_3 = e3
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | COMBINE_EQS: (5), (41) imply:
% 179.29/28.95  | | | |   (42)  all_10_2 = e3
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | REDUCE: (16), (42) imply:
% 179.29/28.95  | | | |   (43)  $false
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | CLOSE: (43) is inconsistent.
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | Case 2:
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | |   (44)  all_58_5 = e3 | all_58_10 = e3
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | BETA: splitting (44) gives:
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | Case 1:
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | |   (45)  all_58_5 = e3
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | COMBINE_EQS: (2), (45) imply:
% 179.29/28.95  | | | | |   (46)  all_52_13 = e3
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | SIMP: (46) implies:
% 179.29/28.95  | | | | |   (47)  all_52_13 = e3
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REDUCE: (1), (47) imply:
% 179.29/28.95  | | | | |   (48)   ~ (all_52_29 = e3)
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | SIMP: (48) implies:
% 179.29/28.95  | | | | |   (49)   ~ (all_52_29 = e3)
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REDUCE: (21), (47) imply:
% 179.29/28.95  | | | | |   (50)   ~ (all_14_2 = e3)
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | SIMP: (50) implies:
% 179.29/28.95  | | | | |   (51)   ~ (all_14_2 = e3)
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | BETA: splitting (10) gives:
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | Case 1:
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | |   (52)  all_58_6 = e3
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | | COMBINE_EQS: (23), (52) imply:
% 179.29/28.95  | | | | | |   (53)  all_52_17 = e3
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | | SIMP: (53) implies:
% 179.29/28.95  | | | | | |   (54)  all_52_17 = e3
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | | REDUCE: (9), (54) imply:
% 179.29/28.95  | | | | | |   (55)   ~ (all_52_25 = e3)
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | | SIMP: (55) implies:
% 179.29/28.95  | | | | | |   (56)   ~ (all_52_25 = e3)
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | | REDUCE: (27), (54) imply:
% 179.29/28.95  | | | | | |   (57)  op(e1, e3) = e3
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | | REF_CLOSE: (2), (3), (11), (15), (17), (19), (24), (29), (30), (31),
% 179.29/28.95  | | | | | |            (36), (49), (51), (52), (56), (57) are inconsistent by
% 179.29/28.95  | | | | | |            sub-proof #998.
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | Case 2:
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | |   (58)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | | REF_CLOSE: (8), (19), (20), (25), (26), (51), (58) are inconsistent
% 179.29/28.95  | | | | | |            by sub-proof #996.
% 179.29/28.95  | | | | | | 
% 179.29/28.95  | | | | | End of split
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | Case 2:
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | |   (59)  all_58_10 = e3
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REF_CLOSE: (7), (22), (59) are inconsistent by sub-proof #1018.
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | End of split
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | End of split
% 179.29/28.95  | | | 
% 179.29/28.95  | | End of split
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #996 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_58_7 = e3 | all_58_8 = e3 | all_58_11 = e3
% 179.29/28.95    (2)  all_58_7 = all_52_19
% 179.29/28.95    (3)  all_58_8 = all_14_2
% 179.29/28.95    (4)   ~ (all_52_23 = e3)
% 179.29/28.95    (5)  all_58_11 = all_52_23
% 179.29/28.95    (6)   ~ (all_52_19 = e3)
% 179.29/28.95    (7)   ~ (all_14_2 = e3)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (1) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (8)  all_58_7 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (2), (8) imply:
% 179.29/28.95  | |   (9)  all_52_19 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (6), (9) imply:
% 179.29/28.95  | |   (10)  $false
% 179.29/28.95  | | 
% 179.29/28.95  | | CLOSE: (10) is inconsistent.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (11)  all_58_8 = e3 | all_58_11 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (3), (4), (5), (7), (11) are inconsistent by sub-proof #997.
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #997 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_58_8 = all_14_2
% 179.29/28.95    (2)   ~ (all_52_23 = e3)
% 179.29/28.95    (3)  all_58_8 = e3 | all_58_11 = e3
% 179.29/28.95    (4)  all_58_11 = all_52_23
% 179.29/28.95    (5)   ~ (all_14_2 = e3)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (3) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (6)  all_58_8 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (1), (6) imply:
% 179.29/28.95  | |   (7)  all_14_2 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (5), (7) imply:
% 179.29/28.95  | |   (8)  $false
% 179.29/28.95  | | 
% 179.29/28.95  | | CLOSE: (8) is inconsistent.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (9)  all_58_11 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1017.
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #998 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)   ~ (all_52_25 = e3)
% 179.29/28.95    (2)  op(e1, e3) = e3
% 179.29/28.95    (3)  all_58_5 = all_52_13
% 179.29/28.95    (4)  op(e1, all_52_13) = e1
% 179.29/28.95    (5)   ~ (e3 = e1)
% 179.29/28.95    (6)  all_58_14 = all_52_29
% 179.29/28.95    (7)  all_58_6 = e3
% 179.29/28.95    (8)   ~ (all_52_13 = all_52_26)
% 179.29/28.95    (9)  all_58_8 = all_14_2
% 179.29/28.95    (10)   ~ (all_52_29 = e3)
% 179.29/28.95    (11)  all_58_2 = all_52_26
% 179.29/28.95    (12)   ~ (all_14_2 = e3)
% 179.29/28.95    (13)  all_58_5 = e3 | all_58_8 = e3 | all_58_14 = e3
% 179.29/28.95    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (15)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95    (16)  all_58_12 = all_52_25
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (13) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (17)  all_58_5 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (3), (17) imply:
% 179.29/28.95  | |   (18)  all_52_13 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | SIMP: (18) implies:
% 179.29/28.95  | |   (19)  all_52_13 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (8), (19) imply:
% 179.29/28.95  | |   (20)   ~ (all_52_26 = e3)
% 179.29/28.95  | | 
% 179.29/28.95  | | SIMP: (20) implies:
% 179.29/28.95  | |   (21)   ~ (all_52_26 = e3)
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (4), (19) imply:
% 179.29/28.95  | |   (22)  op(e1, e3) = e1
% 179.29/28.95  | | 
% 179.29/28.95  | | GROUND_INST: instantiating (14) with e3, e1, e3, e1, simplifying with (2),
% 179.29/28.95  | |              (22) gives:
% 179.29/28.95  | |   (23)  e3 = e1
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (7), (23) imply:
% 179.29/28.95  | |   (24)  all_58_6 = e1
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (1), (5), (11), (15), (16), (21), (24) are inconsistent by
% 179.29/28.95  | |            sub-proof #1001.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (25)  all_58_8 = e3 | all_58_14 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (6), (9), (10), (12), (25) are inconsistent by sub-proof #999.
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #999 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_58_14 = all_52_29
% 179.29/28.95    (2)  all_58_8 = all_14_2
% 179.29/28.95    (3)   ~ (all_52_29 = e3)
% 179.29/28.95    (4)  all_58_8 = e3 | all_58_14 = e3
% 179.29/28.95    (5)   ~ (all_14_2 = e3)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (4) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (6)  all_58_8 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (2), (6) imply:
% 179.29/28.95  | |   (7)  all_14_2 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (5), (7) imply:
% 179.29/28.95  | |   (8)  $false
% 179.29/28.95  | | 
% 179.29/28.95  | | CLOSE: (8) is inconsistent.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (9)  all_58_14 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1000.
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1000 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_58_14 = all_52_29
% 179.29/28.95    (2)  all_58_14 = e3
% 179.29/28.95    (3)   ~ (all_52_29 = e3)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.95  |   (4)  all_52_29 = e3
% 179.29/28.95  | 
% 179.29/28.95  | SIMP: (4) implies:
% 179.29/28.95  |   (5)  all_52_29 = e3
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (3), (5) imply:
% 179.29/28.95  |   (6)  $false
% 179.29/28.95  | 
% 179.29/28.95  | CLOSE: (6) is inconsistent.
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1001 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)   ~ (all_52_25 = e3)
% 179.29/28.95    (2)   ~ (e3 = e1)
% 179.29/28.95    (3)  all_58_6 = e1
% 179.29/28.95    (4)  all_58_2 = all_52_26
% 179.29/28.95    (5)   ~ (all_52_26 = e3)
% 179.29/28.95    (6)  all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95    (7)  all_58_12 = all_52_25
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (6) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (8)  all_58_2 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1004.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (9)  all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (1), (2), (3), (7), (9) are inconsistent by sub-proof #1002.
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1002 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)   ~ (all_52_25 = e3)
% 179.29/28.95    (2)   ~ (e3 = e1)
% 179.29/28.95    (3)  all_58_6 = e1
% 179.29/28.95    (4)  all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95    (5)  all_58_12 = all_52_25
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (4) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (6)  all_58_6 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (3), (6) imply:
% 179.29/28.95  | |   (7)  e3 = e1
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (2), (7) imply:
% 179.29/28.95  | |   (8)  $false
% 179.29/28.95  | | 
% 179.29/28.95  | | CLOSE: (8) is inconsistent.
% 179.29/28.95  | | 
% 179.29/28.95  | Case 2:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (9)  all_58_12 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1003.
% 179.29/28.95  | | 
% 179.29/28.95  | End of split
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1003 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_58_12 = all_52_25
% 179.29/28.95    (2)  all_58_12 = e3
% 179.29/28.95    (3)   ~ (all_52_25 = e3)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.95  |   (4)  all_52_25 = e3
% 179.29/28.95  | 
% 179.29/28.95  | SIMP: (4) implies:
% 179.29/28.95  |   (5)  all_52_25 = e3
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (3), (5) imply:
% 179.29/28.95  |   (6)  $false
% 179.29/28.95  | 
% 179.29/28.95  | CLOSE: (6) is inconsistent.
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1004 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_58_2 = all_52_26
% 179.29/28.95    (2)  all_58_2 = e3
% 179.29/28.95    (3)   ~ (all_52_26 = e3)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.95  |   (4)  all_52_26 = e3
% 179.29/28.95  | 
% 179.29/28.95  | SIMP: (4) implies:
% 179.29/28.95  |   (5)  all_52_26 = e3
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (3), (5) imply:
% 179.29/28.95  |   (6)  $false
% 179.29/28.95  | 
% 179.29/28.95  | CLOSE: (6) is inconsistent.
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1005 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)   ~ (all_52_26 = all_4_2)
% 179.29/28.95    (2)  all_52_26 = e3
% 179.29/28.95    (3)  op(e3, e3) = all_4_2
% 179.29/28.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (5)  op(e3, all_52_26) = e3
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (1), (2) imply:
% 179.29/28.95  |   (6)   ~ (all_4_2 = e3)
% 179.29/28.95  | 
% 179.29/28.95  | SIMP: (6) implies:
% 179.29/28.95  |   (7)   ~ (all_4_2 = e3)
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (2), (5) imply:
% 179.29/28.95  |   (8)  op(e3, e3) = e3
% 179.29/28.95  | 
% 179.29/28.95  | REF_CLOSE: (3), (4), (7), (8) are inconsistent by sub-proof #1006.
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1006 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (2)  op(e3, e3) = all_4_2
% 179.29/28.95    (3)  op(e3, e3) = e3
% 179.29/28.95    (4)   ~ (all_4_2 = e3)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | GROUND_INST: instantiating (1) with all_4_2, e3, e3, e3, simplifying with (2),
% 179.29/28.95  |              (3) gives:
% 179.29/28.95  |   (5)  all_4_2 = e3
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (4), (5) imply:
% 179.29/28.95  |   (6)  $false
% 179.29/28.95  | 
% 179.29/28.95  | CLOSE: (6) is inconsistent.
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1007 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (2)  op(e0, e3) = e1
% 179.29/28.95    (3)  op(e0, e3) = e0
% 179.29/28.95    (4)   ~ (e1 = e0)
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | GROUND_INST: instantiating (1) with e1, e0, e3, e0, simplifying with (2), (3)
% 179.29/28.95  |              gives:
% 179.29/28.95  |   (5)  e1 = e0
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (4), (5) imply:
% 179.29/28.95  |   (6)  $false
% 179.29/28.95  | 
% 179.29/28.95  | CLOSE: (6) is inconsistent.
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1008 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_56_3 = all_52_7
% 179.29/28.95    (2)  op(e3, e2) = all_52_3
% 179.29/28.95    (3)   ~ (all_52_27 = e0)
% 179.29/28.95    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.95    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.95    (6)  all_58_15 = all_6_2
% 179.29/28.95    (7)   ~ (all_52_5 = all_52_7)
% 179.29/28.95    (8)  all_58_10 = all_52_15
% 179.29/28.95    (9)  op(e0, e1) = all_52_29
% 179.29/28.95    (10)  all_58_4 = all_52_5
% 179.29/28.95    (11)  op(e3, all_4_2) = all_4_1
% 179.29/28.95    (12)   ~ (all_52_7 = all_4_2)
% 179.29/28.95    (13)  all_58_1 = all_52_3
% 179.29/28.95    (14)  all_58_0 = all_4_2
% 179.29/28.95    (15)   ~ (all_52_7 = e0)
% 179.29/28.95    (16)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.29/28.95    (17)  all_58_14 = all_52_29
% 179.29/28.95    (18)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.29/28.95    (19)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95    (20)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.29/28.95    (21)  op(e0, e2) = all_52_27
% 179.29/28.95    (22)  op(all_4_1, all_4_2) = all_4_0
% 179.29/28.95    (23)  op(e0, e3) = all_52_25
% 179.29/28.95    (24)  all_52_0 = all_4_1
% 179.29/28.95    (25)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.95    (26)   ~ (e3 = e0)
% 179.29/28.95    (27)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.29/28.95    (28)   ~ (all_52_5 = all_52_29)
% 179.29/28.95    (29)  all_56_12 = all_52_25
% 179.29/28.95    (30)  all_58_13 = all_52_27
% 179.29/28.95    (31)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.29/28.95    (32)   ~ (all_52_25 = e0)
% 179.29/28.95    (33)   ~ (all_52_3 = all_52_7)
% 179.29/28.95    (34)  all_56_0 = all_4_2
% 179.29/28.95    (35)  all_58_11 = all_52_23
% 179.29/28.95    (36)   ~ (all_52_7 = all_52_15)
% 179.29/28.95    (37)  all_58_15 = e0
% 179.29/28.95    (38)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.29/28.95    (39)   ~ (all_52_29 = e0)
% 179.29/28.95    (40)  op(e3, e1) = all_52_5
% 179.29/28.95    (41)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.29/28.95    (42)   ~ (all_52_25 = all_4_2)
% 179.29/28.95    (43)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (44)   ~ (all_52_25 = all_52_27)
% 179.29/28.95    (45)   ~ (all_52_7 = all_6_2)
% 179.29/28.95    (46)   ~ (all_52_7 = all_52_23)
% 179.29/28.95    (47)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.95    (48)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.95    (49)  all_58_9 = all_52_7
% 179.29/28.95    (50)  all_58_12 = all_52_25
% 179.29/28.95    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.29/28.95    (52)  op(e0, all_52_7) = all_52_6
% 179.29/28.95    (53)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 179.29/28.95    (54)  all_56_13 = all_52_27
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | ALPHA: (53) implies:
% 179.29/28.95  |   (55)  all_52_6 = e0
% 179.29/28.95  |   (56)  all_52_0 = e3
% 179.29/28.95  | 
% 179.29/28.95  | COMBINE_EQS: (24), (56) imply:
% 179.29/28.95  |   (57)  all_4_1 = e3
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (22), (57) imply:
% 179.29/28.95  |   (58)  op(e3, all_4_2) = all_4_0
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (11), (57) imply:
% 179.29/28.95  |   (59)  op(e3, all_4_2) = e3
% 179.29/28.95  | 
% 179.29/28.95  | REDUCE: (52), (55) imply:
% 179.29/28.95  |   (60)  op(e0, all_52_7) = e0
% 179.29/28.95  | 
% 179.29/28.95  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 179.29/28.95  |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (25), (26),
% 179.29/28.95  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 179.29/28.95  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 179.29/28.95  |            (49), (50), (51), (54), (58), (59), (60) are inconsistent by
% 179.29/28.95  |            sub-proof #1009.
% 179.29/28.95  | 
% 179.29/28.95  End of proof
% 179.29/28.95  
% 179.29/28.95  Sub-proof #1009 shows that the following formulas are inconsistent:
% 179.29/28.95  ----------------------------------------------------------------
% 179.29/28.95    (1)  all_56_3 = all_52_7
% 179.29/28.95    (2)  op(e3, e2) = all_52_3
% 179.29/28.95    (3)   ~ (all_52_27 = e0)
% 179.29/28.95    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.95    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.95    (6)  all_58_15 = all_6_2
% 179.29/28.95    (7)   ~ (all_52_5 = all_52_7)
% 179.29/28.95    (8)  all_58_10 = all_52_15
% 179.29/28.95    (9)  op(e0, e1) = all_52_29
% 179.29/28.95    (10)  all_58_4 = all_52_5
% 179.29/28.95    (11)   ~ (all_52_7 = all_4_2)
% 179.29/28.95    (12)  all_58_1 = all_52_3
% 179.29/28.95    (13)  all_58_0 = all_4_2
% 179.29/28.95    (14)   ~ (all_52_7 = e0)
% 179.29/28.95    (15)  all_58_1 = e3 | all_58_3 = e3 | all_58_7 = e3 | all_58_13 = e3
% 179.29/28.95    (16)  all_58_14 = all_52_29
% 179.29/28.95    (17)  all_56_13 = e3 | all_56_13 = e2 | all_56_13 = e1 | all_56_13 = e0
% 179.29/28.95    (18)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.95    (19)  all_58_12 = e3 | all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.29/28.95    (20)  op(e0, e2) = all_52_27
% 179.29/28.95    (21)  op(e3, all_4_2) = e3
% 179.29/28.95    (22)  op(e0, e3) = all_52_25
% 179.29/28.95    (23)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.95    (24)   ~ (e3 = e0)
% 179.29/28.95    (25)  all_56_12 = e3 | all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.29/28.95    (26)   ~ (all_52_5 = all_52_29)
% 179.29/28.95    (27)  all_56_12 = all_52_25
% 179.29/28.95    (28)  all_58_13 = all_52_27
% 179.29/28.95    (29)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.29/28.95    (30)   ~ (all_52_25 = e0)
% 179.29/28.95    (31)   ~ (all_52_3 = all_52_7)
% 179.29/28.95    (32)  all_56_0 = all_4_2
% 179.29/28.95    (33)  all_58_11 = all_52_23
% 179.29/28.95    (34)   ~ (all_52_7 = all_52_15)
% 179.29/28.95    (35)  all_58_15 = e0
% 179.29/28.95    (36)  all_58_12 = e1 | all_58_13 = e1 | all_58_14 = e1 | all_58_15 = e1
% 179.29/28.95    (37)   ~ (all_52_29 = e0)
% 179.29/28.95    (38)  op(e3, e1) = all_52_5
% 179.29/28.95    (39)  all_58_12 = e2 | all_58_13 = e2 | all_58_14 = e2 | all_58_15 = e2
% 179.29/28.95    (40)   ~ (all_52_25 = all_4_2)
% 179.29/28.95    (41)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.95    (42)   ~ (all_52_25 = all_52_27)
% 179.29/28.95    (43)   ~ (all_52_7 = all_6_2)
% 179.29/28.95    (44)   ~ (all_52_7 = all_52_23)
% 179.29/28.95    (45)  op(e3, all_4_2) = all_4_0
% 179.29/28.95    (46)  op(e0, all_52_7) = e0
% 179.29/28.95    (47)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.95    (48)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.95    (49)  all_58_9 = all_52_7
% 179.29/28.95    (50)  all_58_12 = all_52_25
% 179.29/28.95    (51)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.29/28.95    (52)  all_56_13 = all_52_27
% 179.29/28.95  
% 179.29/28.95  Begin of proof
% 179.29/28.95  | 
% 179.29/28.95  | GROUND_INST: instantiating (41) with e3, all_4_0, all_4_2, e3, simplifying
% 179.29/28.95  |              with (21), (45) gives:
% 179.29/28.95  |   (53)  all_4_0 = e3
% 179.29/28.95  | 
% 179.29/28.95  | BETA: splitting (17) gives:
% 179.29/28.95  | 
% 179.29/28.95  | Case 1:
% 179.29/28.95  | | 
% 179.29/28.95  | |   (54)  all_56_13 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | COMBINE_EQS: (52), (54) imply:
% 179.29/28.95  | |   (55)  all_52_27 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | SIMP: (55) implies:
% 179.29/28.95  | |   (56)  all_52_27 = e3
% 179.29/28.95  | | 
% 179.29/28.95  | | REDUCE: (42), (56) imply:
% 179.29/28.95  | |   (57)   ~ (all_52_25 = e3)
% 179.29/28.95  | | 
% 179.29/28.95  | | BETA: splitting (25) gives:
% 179.29/28.95  | | 
% 179.29/28.95  | | Case 1:
% 179.29/28.95  | | | 
% 179.29/28.95  | | |   (58)  all_56_12 = e3
% 179.29/28.95  | | | 
% 179.29/28.95  | | | REF_CLOSE: (27), (57), (58) are inconsistent by sub-proof #1040.
% 179.29/28.95  | | | 
% 179.29/28.95  | | Case 2:
% 179.29/28.95  | | | 
% 179.29/28.95  | | |   (59)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.29/28.95  | | | 
% 179.29/28.95  | | | BETA: splitting (36) gives:
% 179.29/28.95  | | | 
% 179.29/28.95  | | | Case 1:
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | |   (60)  all_58_12 = e1
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | COMBINE_EQS: (50), (60) imply:
% 179.29/28.95  | | | |   (61)  all_52_25 = e1
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | SIMP: (61) implies:
% 179.29/28.95  | | | |   (62)  all_52_25 = e1
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | REDUCE: (30), (62) imply:
% 179.29/28.95  | | | |   (63)   ~ (e1 = e0)
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | REDUCE: (22), (62) imply:
% 179.29/28.95  | | | |   (64)  op(e0, e3) = e1
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | BETA: splitting (48) gives:
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | Case 1:
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | |   (65)  all_56_3 = e3
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | COMBINE_EQS: (1), (65) imply:
% 179.29/28.95  | | | | |   (66)  all_52_7 = e3
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | SIMP: (66) implies:
% 179.29/28.95  | | | | |   (67)  all_52_7 = e3
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REDUCE: (46), (67) imply:
% 179.29/28.95  | | | | |   (68)  op(e0, e3) = e0
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | GROUND_INST: instantiating (41) with e1, e0, e3, e0, simplifying with
% 179.29/28.95  | | | | |              (64), (68) gives:
% 179.29/28.95  | | | | |   (69)  e1 = e0
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REDUCE: (63), (69) imply:
% 179.29/28.95  | | | | |   (70)  $false
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | CLOSE: (70) is inconsistent.
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | Case 2:
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | |   (71)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REF_CLOSE: (1), (3), (4), (9), (14), (20), (23), (37), (41), (46),
% 179.29/28.95  | | | | |            (49), (71) are inconsistent by sub-proof #1036.
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | End of split
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | Case 2:
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | |   (72)   ~ (all_58_12 = e1)
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | REDUCE: (50), (72) imply:
% 179.29/28.95  | | | |   (73)   ~ (all_52_25 = e1)
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | BETA: splitting (39) gives:
% 179.29/28.95  | | | | 
% 179.29/28.95  | | | | Case 1:
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | |   (74)  all_58_12 = e2
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | COMBINE_EQS: (50), (74) imply:
% 179.29/28.95  | | | | |   (75)  all_52_25 = e2
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | SIMP: (75) implies:
% 179.29/28.95  | | | | |   (76)  all_52_25 = e2
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REDUCE: (30), (76) imply:
% 179.29/28.95  | | | | |   (77)   ~ (e2 = e0)
% 179.29/28.95  | | | | | 
% 179.29/28.95  | | | | | REDUCE: (22), (76) imply:
% 179.29/28.95  | | | | |   (78)  op(e0, e3) = e2
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | BETA: splitting (47) gives:
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | Case 1:
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | |   (79)  all_58_9 = e3
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | COMBINE_EQS: (49), (79) imply:
% 179.29/28.96  | | | | | |   (80)  all_52_7 = e3
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | SIMP: (80) implies:
% 179.29/28.96  | | | | | |   (81)  all_52_7 = e3
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REDUCE: (46), (81) imply:
% 179.29/28.96  | | | | | |   (82)  op(e0, e3) = e0
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REF_CLOSE: (41), (77), (78), (82) are inconsistent by sub-proof
% 179.29/28.96  | | | | | |            #1035.
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | Case 2:
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | |   (83)   ~ (all_58_9 = e3)
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REDUCE: (49), (83) imply:
% 179.29/28.96  | | | | | |   (84)   ~ (all_52_7 = e3)
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REF_CLOSE: (1), (3), (4), (9), (14), (20), (23), (37), (41), (46),
% 179.29/28.96  | | | | | |            (48), (49), (84) are inconsistent by sub-proof #1033.
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | End of split
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | Case 2:
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | |   (85)   ~ (all_58_12 = e2)
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | REDUCE: (50), (85) imply:
% 179.29/28.96  | | | | |   (86)   ~ (all_52_25 = e2)
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | REF_CLOSE: (27), (30), (59), (73), (86) are inconsistent by sub-proof
% 179.29/28.96  | | | | |            #1028.
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | End of split
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | End of split
% 179.29/28.96  | | | 
% 179.29/28.96  | | End of split
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (87)   ~ (all_56_13 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (52), (87) imply:
% 179.29/28.96  | |   (88)   ~ (all_52_27 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | BETA: splitting (19) gives:
% 179.29/28.96  | | 
% 179.29/28.96  | | Case 1:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (89)  all_58_12 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | COMBINE_EQS: (50), (89) imply:
% 179.29/28.96  | | |   (90)  all_52_25 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | SIMP: (90) implies:
% 179.29/28.96  | | |   (91)  all_52_25 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | REDUCE: (22), (91) imply:
% 179.29/28.96  | | |   (92)  op(e0, e3) = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | BETA: splitting (47) gives:
% 179.29/28.96  | | | 
% 179.29/28.96  | | | Case 1:
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | |   (93)  all_58_9 = e3
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | COMBINE_EQS: (49), (93) imply:
% 179.29/28.96  | | | |   (94)  all_52_7 = e3
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | SIMP: (94) implies:
% 179.29/28.96  | | | |   (95)  all_52_7 = e3
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REDUCE: (46), (95) imply:
% 179.29/28.96  | | | |   (96)  op(e0, e3) = e0
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REF_CLOSE: (24), (41), (92), (96) are inconsistent by sub-proof #1027.
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | Case 2:
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | |   (97)   ~ (all_58_9 = e3)
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REDUCE: (49), (97) imply:
% 179.29/28.96  | | | |   (98)   ~ (all_52_7 = e3)
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REF_CLOSE: (1), (3), (4), (9), (14), (20), (23), (37), (41), (46), (48),
% 179.29/28.96  | | | |            (49), (98) are inconsistent by sub-proof #1033.
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | End of split
% 179.29/28.96  | | | 
% 179.29/28.96  | | Case 2:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (99)  all_58_13 = e3 | all_58_14 = e3 | all_58_15 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | BETA: splitting (99) gives:
% 179.29/28.96  | | | 
% 179.29/28.96  | | | Case 1:
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | |   (100)  all_58_13 = e3
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REF_CLOSE: (28), (88), (100) are inconsistent by sub-proof #1026.
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | Case 2:
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | |   (101)  all_58_14 = e3 | all_58_15 = e3
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | BETA: splitting (101) gives:
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | Case 1:
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | |   (102)  all_58_14 = e3
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | COMBINE_EQS: (16), (102) imply:
% 179.29/28.96  | | | | |   (103)  all_52_29 = e3
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | SIMP: (103) implies:
% 179.29/28.96  | | | | |   (104)  all_52_29 = e3
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | REDUCE: (26), (104) imply:
% 179.29/28.96  | | | | |   (105)   ~ (all_52_5 = e3)
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | BETA: splitting (15) gives:
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | Case 1:
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | |   (106)  all_58_1 = e3
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | COMBINE_EQS: (12), (106) imply:
% 179.29/28.96  | | | | | |   (107)  all_52_3 = e3
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REDUCE: (31), (107) imply:
% 179.29/28.96  | | | | | |   (108)   ~ (all_52_7 = e3)
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | SIMP: (108) implies:
% 179.29/28.96  | | | | | |   (109)   ~ (all_52_7 = e3)
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REF_CLOSE: (1), (3), (4), (9), (14), (20), (23), (37), (41), (46),
% 179.29/28.96  | | | | | |            (48), (49), (109) are inconsistent by sub-proof #1033.
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | Case 2:
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | |   (110)   ~ (all_58_1 = e3)
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REDUCE: (12), (110) imply:
% 179.29/28.96  | | | | | |   (111)   ~ (all_52_3 = e3)
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 179.29/28.96  | | | | | |            (12), (13), (14), (18), (20), (21), (22), (23), (29),
% 179.29/28.96  | | | | | |            (31), (32), (33), (34), (37), (38), (40), (41), (43),
% 179.29/28.96  | | | | | |            (44), (46), (47), (48), (49), (51), (105), (111) are
% 179.29/28.96  | | | | | |            inconsistent by sub-proof #1011.
% 179.29/28.96  | | | | | | 
% 179.29/28.96  | | | | | End of split
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | Case 2:
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | |   (112)  all_58_15 = e3
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | | REF_CLOSE: (24), (35), (112) are inconsistent by sub-proof #1010.
% 179.29/28.96  | | | | | 
% 179.29/28.96  | | | | End of split
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | End of split
% 179.29/28.96  | | | 
% 179.29/28.96  | | End of split
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1010 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_58_15 = e3
% 179.29/28.96    (2)  all_58_15 = e0
% 179.29/28.96    (3)   ~ (e3 = e0)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  e3 = e0
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.96  |   (5)  e3 = e0
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (3), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1011 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_56_3 = all_52_7
% 179.29/28.96    (2)  op(e3, e2) = all_52_3
% 179.29/28.96    (3)   ~ (all_52_27 = e0)
% 179.29/28.96    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.96    (5)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96    (6)  all_58_15 = all_6_2
% 179.29/28.96    (7)   ~ (all_52_5 = all_52_7)
% 179.29/28.96    (8)  all_58_10 = all_52_15
% 179.29/28.96    (9)  op(e0, e1) = all_52_29
% 179.29/28.96    (10)  all_58_4 = all_52_5
% 179.29/28.96    (11)   ~ (all_52_7 = all_4_2)
% 179.29/28.96    (12)  all_58_1 = all_52_3
% 179.29/28.96    (13)  all_58_0 = all_4_2
% 179.29/28.96    (14)   ~ (all_52_7 = e0)
% 179.29/28.96    (15)  all_58_0 = e3 | all_58_2 = e3 | all_58_6 = e3 | all_58_12 = e3
% 179.29/28.96    (16)  op(e0, e2) = all_52_27
% 179.29/28.96    (17)  op(e3, all_4_2) = e3
% 179.29/28.96    (18)  op(e0, e3) = all_52_25
% 179.29/28.96    (19)   ~ (all_52_5 = e3)
% 179.29/28.96    (20)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.96    (21)   ~ (all_52_3 = e3)
% 179.29/28.96    (22)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.29/28.96    (23)   ~ (all_52_3 = all_52_7)
% 179.29/28.96    (24)  all_56_0 = all_4_2
% 179.29/28.96    (25)  all_58_11 = all_52_23
% 179.29/28.96    (26)   ~ (all_52_7 = all_52_15)
% 179.29/28.96    (27)   ~ (all_52_29 = e0)
% 179.29/28.96    (28)  op(e3, e1) = all_52_5
% 179.29/28.96    (29)   ~ (all_52_25 = all_4_2)
% 179.29/28.96    (30)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.96    (31)   ~ (all_52_7 = all_6_2)
% 179.29/28.96    (32)   ~ (all_52_7 = all_52_23)
% 179.29/28.96    (33)  op(e0, all_52_7) = e0
% 179.29/28.96    (34)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96    (35)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.96    (36)  all_58_9 = all_52_7
% 179.29/28.96    (37)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | BETA: splitting (15) gives:
% 179.29/28.96  | 
% 179.29/28.96  | Case 1:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (38)  all_58_0 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | COMBINE_EQS: (13), (38) imply:
% 179.29/28.96  | |   (39)  all_4_2 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (11), (39) imply:
% 179.29/28.96  | |   (40)   ~ (all_52_7 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | REF_CLOSE: (1), (3), (4), (9), (14), (16), (20), (27), (30), (33), (35),
% 179.29/28.96  | |            (36), (40) are inconsistent by sub-proof #1033.
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (41)   ~ (all_58_0 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (13), (41) imply:
% 179.29/28.96  | |   (42)   ~ (all_4_2 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (11), (12), (13), (17), (18),
% 179.29/28.96  | |            (19), (21), (22), (23), (24), (25), (26), (28), (29), (30), (31),
% 179.29/28.96  | |            (32), (33), (34), (36), (37), (42) are inconsistent by sub-proof
% 179.29/28.96  | |            #1012.
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1012 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  op(e3, e2) = all_52_3
% 179.29/28.96    (2)   ~ (all_4_2 = e3)
% 179.29/28.96    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96    (4)  all_58_15 = all_6_2
% 179.29/28.96    (5)   ~ (all_52_5 = all_52_7)
% 179.29/28.96    (6)  all_58_10 = all_52_15
% 179.29/28.96    (7)  all_58_4 = all_52_5
% 179.29/28.96    (8)   ~ (all_52_7 = all_4_2)
% 179.29/28.96    (9)  all_58_1 = all_52_3
% 179.29/28.96    (10)  all_58_0 = all_4_2
% 179.29/28.96    (11)  op(e3, all_4_2) = e3
% 179.29/28.96    (12)  op(e0, e3) = all_52_25
% 179.29/28.96    (13)   ~ (all_52_5 = e3)
% 179.29/28.96    (14)   ~ (all_52_3 = e3)
% 179.29/28.96    (15)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.29/28.96    (16)   ~ (all_52_3 = all_52_7)
% 179.29/28.96    (17)  all_56_0 = all_4_2
% 179.29/28.96    (18)  all_58_11 = all_52_23
% 179.29/28.96    (19)   ~ (all_52_7 = all_52_15)
% 179.29/28.96    (20)  op(e3, e1) = all_52_5
% 179.29/28.96    (21)   ~ (all_52_25 = all_4_2)
% 179.29/28.96    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.96    (23)   ~ (all_52_7 = all_6_2)
% 179.29/28.96    (24)   ~ (all_52_7 = all_52_23)
% 179.29/28.96    (25)  op(e0, all_52_7) = e0
% 179.29/28.96    (26)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96    (27)  all_58_9 = all_52_7
% 179.29/28.96    (28)  all_58_0 = e3 | all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | BETA: splitting (28) gives:
% 179.29/28.96  | 
% 179.29/28.96  | Case 1:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (29)  all_58_0 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | COMBINE_EQS: (10), (29) imply:
% 179.29/28.96  | |   (30)  all_4_2 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (2), (30) imply:
% 179.29/28.96  | |   (31)  $false
% 179.29/28.96  | | 
% 179.29/28.96  | | CLOSE: (31) is inconsistent.
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (32)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 179.29/28.96  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 179.29/28.96  | |            (25), (26), (27), (32) are inconsistent by sub-proof #1013.
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1013 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  op(e3, e2) = all_52_3
% 179.29/28.96    (2)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96    (3)  all_58_15 = all_6_2
% 179.29/28.96    (4)   ~ (all_52_5 = all_52_7)
% 179.29/28.96    (5)  all_58_10 = all_52_15
% 179.29/28.96    (6)  all_58_4 = all_52_5
% 179.29/28.96    (7)   ~ (all_52_7 = all_4_2)
% 179.29/28.96    (8)  all_58_1 = all_52_3
% 179.29/28.96    (9)  all_58_0 = all_4_2
% 179.29/28.96    (10)  op(e3, all_4_2) = e3
% 179.29/28.96    (11)  op(e0, e3) = all_52_25
% 179.29/28.96    (12)   ~ (all_52_5 = e3)
% 179.29/28.96    (13)   ~ (all_52_3 = e3)
% 179.29/28.96    (14)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.29/28.96    (15)   ~ (all_52_3 = all_52_7)
% 179.29/28.96    (16)  all_56_0 = all_4_2
% 179.29/28.96    (17)  all_58_11 = all_52_23
% 179.29/28.96    (18)   ~ (all_52_7 = all_52_15)
% 179.29/28.96    (19)  all_58_1 = e3 | all_58_4 = e3 | all_58_9 = e3
% 179.29/28.96    (20)  op(e3, e1) = all_52_5
% 179.29/28.96    (21)   ~ (all_52_25 = all_4_2)
% 179.29/28.96    (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.96    (23)   ~ (all_52_7 = all_6_2)
% 179.29/28.96    (24)   ~ (all_52_7 = all_52_23)
% 179.29/28.96    (25)  op(e0, all_52_7) = e0
% 179.29/28.96    (26)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96    (27)  all_58_9 = all_52_7
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | BETA: splitting (19) gives:
% 179.29/28.96  | 
% 179.29/28.96  | Case 1:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (28)  all_58_1 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | COMBINE_EQS: (8), (28) imply:
% 179.29/28.96  | |   (29)  all_52_3 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (13), (29) imply:
% 179.29/28.96  | |   (30)  $false
% 179.29/28.96  | | 
% 179.29/28.96  | | CLOSE: (30) is inconsistent.
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (31)  all_58_4 = e3 | all_58_9 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | BETA: splitting (31) gives:
% 179.29/28.96  | | 
% 179.29/28.96  | | Case 1:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (32)  all_58_4 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | REF_CLOSE: (6), (12), (32) are inconsistent by sub-proof #1025.
% 179.29/28.96  | | | 
% 179.29/28.96  | | Case 2:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (33)  all_58_9 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (14), (15),
% 179.29/28.96  | | |            (16), (17), (18), (20), (21), (22), (23), (24), (25), (26),
% 179.29/28.96  | | |            (27), (33) are inconsistent by sub-proof #1014.
% 179.29/28.96  | | | 
% 179.29/28.96  | | End of split
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1014 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  op(e3, e2) = all_52_3
% 179.29/28.96    (2)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96    (3)  all_58_15 = all_6_2
% 179.29/28.96    (4)   ~ (all_52_5 = all_52_7)
% 179.29/28.96    (5)  all_58_10 = all_52_15
% 179.29/28.96    (6)  all_58_9 = e3
% 179.29/28.96    (7)   ~ (all_52_7 = all_4_2)
% 179.29/28.96    (8)  all_58_0 = all_4_2
% 179.29/28.96    (9)  op(e3, all_4_2) = e3
% 179.29/28.96    (10)  op(e0, e3) = all_52_25
% 179.29/28.96    (11)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.29/28.96    (12)   ~ (all_52_3 = all_52_7)
% 179.29/28.96    (13)  all_56_0 = all_4_2
% 179.29/28.96    (14)  all_58_11 = all_52_23
% 179.29/28.96    (15)   ~ (all_52_7 = all_52_15)
% 179.29/28.96    (16)  op(e3, e1) = all_52_5
% 179.29/28.96    (17)   ~ (all_52_25 = all_4_2)
% 179.29/28.96    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.96    (19)   ~ (all_52_7 = all_6_2)
% 179.29/28.96    (20)   ~ (all_52_7 = all_52_23)
% 179.29/28.96    (21)  op(e0, all_52_7) = e0
% 179.29/28.96    (22)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96    (23)  all_58_9 = all_52_7
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (6), (23) imply:
% 179.29/28.96  |   (24)  all_52_7 = e3
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (24) implies:
% 179.29/28.96  |   (25)  all_52_7 = e3
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (15), (25) imply:
% 179.29/28.96  |   (26)   ~ (all_52_15 = e3)
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (26) implies:
% 179.29/28.96  |   (27)   ~ (all_52_15 = e3)
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (20), (25) imply:
% 179.29/28.96  |   (28)   ~ (all_52_23 = e3)
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (28) implies:
% 179.29/28.96  |   (29)   ~ (all_52_23 = e3)
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (19), (25) imply:
% 179.29/28.96  |   (30)   ~ (all_6_2 = e3)
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (30) implies:
% 179.29/28.96  |   (31)   ~ (all_6_2 = e3)
% 179.29/28.96  | 
% 179.29/28.96  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 179.29/28.96  |            (14), (16), (17), (18), (21), (22), (23), (27), (29), (31) are
% 179.29/28.96  |            inconsistent by sub-proof #1015.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1015 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  op(e3, e2) = all_52_3
% 179.29/28.96    (2)   ~ (all_6_2 = e3)
% 179.29/28.96    (3)  all_56_0 = e3 | all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96    (4)  all_58_15 = all_6_2
% 179.29/28.96    (5)   ~ (all_52_5 = all_52_7)
% 179.29/28.96    (6)  all_58_10 = all_52_15
% 179.29/28.96    (7)   ~ (all_52_7 = all_4_2)
% 179.29/28.96    (8)  all_58_0 = all_4_2
% 179.29/28.96    (9)   ~ (all_52_23 = e3)
% 179.29/28.96    (10)  op(e3, all_4_2) = e3
% 179.29/28.96    (11)  op(e0, e3) = all_52_25
% 179.29/28.96    (12)   ~ (all_52_15 = e3)
% 179.29/28.96    (13)  all_58_0 = e1 | all_58_2 = e1 | all_58_6 = e1 | all_58_12 = e1
% 179.29/28.96    (14)   ~ (all_52_3 = all_52_7)
% 179.29/28.96    (15)  all_56_0 = all_4_2
% 179.29/28.96    (16)  all_58_11 = all_52_23
% 179.29/28.96    (17)  op(e3, e1) = all_52_5
% 179.29/28.96    (18)   ~ (all_52_25 = all_4_2)
% 179.29/28.96    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.96            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.96    (20)  op(e0, all_52_7) = e0
% 179.29/28.96    (21)  all_58_9 = e3 | all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96    (22)  all_58_9 = all_52_7
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | BETA: splitting (21) gives:
% 179.29/28.96  | 
% 179.29/28.96  | Case 1:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (23)  all_58_9 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | COMBINE_EQS: (22), (23) imply:
% 179.29/28.96  | |   (24)  all_52_7 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | SIMP: (24) implies:
% 179.29/28.96  | |   (25)  all_52_7 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (14), (25) imply:
% 179.29/28.96  | |   (26)   ~ (all_52_3 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (5), (25) imply:
% 179.29/28.96  | |   (27)   ~ (all_52_5 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (7), (25) imply:
% 179.29/28.96  | |   (28)   ~ (all_4_2 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | SIMP: (28) implies:
% 179.29/28.96  | |   (29)   ~ (all_4_2 = e3)
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (20), (25) imply:
% 179.29/28.96  | |   (30)  op(e0, e3) = e0
% 179.29/28.96  | | 
% 179.29/28.96  | | GROUND_INST: instantiating (19) with all_52_25, e0, e3, e0, simplifying with
% 179.29/28.96  | |              (11), (30) gives:
% 179.29/28.96  | |   (31)  all_52_25 = e0
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (18), (31) imply:
% 179.29/28.96  | |   (32)   ~ (all_4_2 = e0)
% 179.29/28.96  | | 
% 179.29/28.96  | | SIMP: (32) implies:
% 179.29/28.96  | |   (33)   ~ (all_4_2 = e0)
% 179.29/28.96  | | 
% 179.29/28.96  | | BETA: splitting (3) gives:
% 179.29/28.96  | | 
% 179.29/28.96  | | Case 1:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (34)  all_56_0 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | REF_CLOSE: (15), (29), (34) are inconsistent by sub-proof #1024.
% 179.29/28.96  | | | 
% 179.29/28.96  | | Case 2:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (35)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96  | | | 
% 179.29/28.96  | | | BETA: splitting (13) gives:
% 179.29/28.96  | | | 
% 179.29/28.96  | | | Case 1:
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | |   (36)  all_58_0 = e1
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | COMBINE_EQS: (8), (36) imply:
% 179.29/28.96  | | | |   (37)  all_4_2 = e1
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REDUCE: (10), (37) imply:
% 179.29/28.96  | | | |   (38)  op(e3, e1) = e3
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REF_CLOSE: (17), (19), (27), (38) are inconsistent by sub-proof #1023.
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | Case 2:
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | |   (39)   ~ (all_58_0 = e1)
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REDUCE: (8), (39) imply:
% 179.29/28.96  | | | |   (40)   ~ (all_4_2 = e1)
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | | REF_CLOSE: (1), (10), (15), (19), (26), (33), (35), (40) are
% 179.29/28.96  | | | |            inconsistent by sub-proof #1019.
% 179.29/28.96  | | | | 
% 179.29/28.96  | | | End of split
% 179.29/28.96  | | | 
% 179.29/28.96  | | End of split
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (41)  all_58_10 = e3 | all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | BETA: splitting (41) gives:
% 179.29/28.96  | | 
% 179.29/28.96  | | Case 1:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (42)  all_58_10 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | REF_CLOSE: (6), (12), (42) are inconsistent by sub-proof #1018.
% 179.29/28.96  | | | 
% 179.29/28.96  | | Case 2:
% 179.29/28.96  | | | 
% 179.29/28.96  | | |   (43)  all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96  | | | 
% 179.29/28.96  | | | REF_CLOSE: (2), (4), (9), (16), (43) are inconsistent by sub-proof #1016.
% 179.29/28.96  | | | 
% 179.29/28.96  | | End of split
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1016 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)   ~ (all_6_2 = e3)
% 179.29/28.96    (2)  all_58_15 = all_6_2
% 179.29/28.96    (3)   ~ (all_52_23 = e3)
% 179.29/28.96    (4)  all_58_11 = e3 | all_58_15 = e3
% 179.29/28.96    (5)  all_58_11 = all_52_23
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | BETA: splitting (4) gives:
% 179.29/28.96  | 
% 179.29/28.96  | Case 1:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (6)  all_58_11 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #1017.
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (7)  all_58_15 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | COMBINE_EQS: (2), (7) imply:
% 179.29/28.96  | |   (8)  all_6_2 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (1), (8) imply:
% 179.29/28.96  | |   (9)  $false
% 179.29/28.96  | | 
% 179.29/28.96  | | CLOSE: (9) is inconsistent.
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1017 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_58_11 = all_52_23
% 179.29/28.96    (2)  all_58_11 = e3
% 179.29/28.96    (3)   ~ (all_52_23 = e3)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  all_52_23 = e3
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.96  |   (5)  all_52_23 = e3
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (3), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1018 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_58_10 = all_52_15
% 179.29/28.96    (2)  all_58_10 = e3
% 179.29/28.96    (3)   ~ (all_52_15 = e3)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  all_52_15 = e3
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.96  |   (5)  all_52_15 = e3
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (3), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1019 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  op(e3, e2) = all_52_3
% 179.29/28.96    (2)  op(e3, all_4_2) = e3
% 179.29/28.96    (3)   ~ (all_52_3 = e3)
% 179.29/28.96    (4)  all_56_0 = all_4_2
% 179.29/28.96    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.96    (6)  all_56_0 = e2 | all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96    (7)   ~ (all_4_2 = e1)
% 179.29/28.96    (8)   ~ (all_4_2 = e0)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | BETA: splitting (6) gives:
% 179.29/28.96  | 
% 179.29/28.96  | Case 1:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (9)  all_56_0 = e2
% 179.29/28.96  | | 
% 179.29/28.96  | | COMBINE_EQS: (4), (9) imply:
% 179.29/28.96  | |   (10)  all_4_2 = e2
% 179.29/28.96  | | 
% 179.29/28.96  | | SIMP: (10) implies:
% 179.29/28.96  | |   (11)  all_4_2 = e2
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (2), (11) imply:
% 179.29/28.96  | |   (12)  op(e3, e2) = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | GROUND_INST: instantiating (5) with all_52_3, e3, e2, e3, simplifying with
% 179.29/28.96  | |              (1), (12) gives:
% 179.29/28.96  | |   (13)  all_52_3 = e3
% 179.29/28.96  | | 
% 179.29/28.96  | | REDUCE: (3), (13) imply:
% 179.29/28.96  | |   (14)  $false
% 179.29/28.96  | | 
% 179.29/28.96  | | CLOSE: (14) is inconsistent.
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (15)  all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96  | | 
% 179.29/28.96  | | REF_CLOSE: (4), (7), (8), (15) are inconsistent by sub-proof #1020.
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1020 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_56_0 = e1 | all_56_0 = e0
% 179.29/28.96    (2)  all_56_0 = all_4_2
% 179.29/28.96    (3)   ~ (all_4_2 = e1)
% 179.29/28.96    (4)   ~ (all_4_2 = e0)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | BETA: splitting (1) gives:
% 179.29/28.96  | 
% 179.29/28.96  | Case 1:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (5)  all_56_0 = e1
% 179.29/28.96  | | 
% 179.29/28.96  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1022.
% 179.29/28.96  | | 
% 179.29/28.96  | Case 2:
% 179.29/28.96  | | 
% 179.29/28.96  | |   (6)  all_56_0 = e0
% 179.29/28.96  | | 
% 179.29/28.96  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1021.
% 179.29/28.96  | | 
% 179.29/28.96  | End of split
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1021 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_56_0 = all_4_2
% 179.29/28.96    (2)  all_56_0 = e0
% 179.29/28.96    (3)   ~ (all_4_2 = e0)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  all_4_2 = e0
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.96  |   (5)  all_4_2 = e0
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (3), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1022 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_56_0 = all_4_2
% 179.29/28.96    (2)  all_56_0 = e1
% 179.29/28.96    (3)   ~ (all_4_2 = e1)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  all_4_2 = e1
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.96  |   (5)  all_4_2 = e1
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (3), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1023 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.96    (2)  op(e3, e1) = all_52_5
% 179.29/28.96    (3)  op(e3, e1) = e3
% 179.29/28.96    (4)   ~ (all_52_5 = e3)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | GROUND_INST: instantiating (1) with all_52_5, e3, e1, e3, simplifying with
% 179.29/28.96  |              (2), (3) gives:
% 179.29/28.96  |   (5)  all_52_5 = e3
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (4), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1024 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_56_0 = all_4_2
% 179.29/28.96    (2)  all_56_0 = e3
% 179.29/28.96    (3)   ~ (all_4_2 = e3)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  all_4_2 = e3
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.96  |   (5)  all_4_2 = e3
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (3), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1025 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_58_4 = all_52_5
% 179.29/28.96    (2)  all_58_4 = e3
% 179.29/28.96    (3)   ~ (all_52_5 = e3)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  all_52_5 = e3
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.96  |   (5)  all_52_5 = e3
% 179.29/28.96  | 
% 179.29/28.96  | REDUCE: (3), (5) imply:
% 179.29/28.96  |   (6)  $false
% 179.29/28.96  | 
% 179.29/28.96  | CLOSE: (6) is inconsistent.
% 179.29/28.96  | 
% 179.29/28.96  End of proof
% 179.29/28.96  
% 179.29/28.96  Sub-proof #1026 shows that the following formulas are inconsistent:
% 179.29/28.96  ----------------------------------------------------------------
% 179.29/28.96    (1)  all_58_13 = all_52_27
% 179.29/28.96    (2)  all_58_13 = e3
% 179.29/28.96    (3)   ~ (all_52_27 = e3)
% 179.29/28.96  
% 179.29/28.96  Begin of proof
% 179.29/28.96  | 
% 179.29/28.96  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.96  |   (4)  all_52_27 = e3
% 179.29/28.96  | 
% 179.29/28.96  | SIMP: (4) implies:
% 179.29/28.97  |   (5)  all_52_27 = e3
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (3), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1027 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.97    (2)  op(e0, e3) = e3
% 179.29/28.97    (3)  op(e0, e3) = e0
% 179.29/28.97    (4)   ~ (e3 = e0)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | GROUND_INST: instantiating (1) with e3, e0, e3, e0, simplifying with (2), (3)
% 179.29/28.97  |              gives:
% 179.29/28.97  |   (5)  e3 = e0
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (4), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1028 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)   ~ (all_52_25 = e2)
% 179.29/28.97    (2)  all_56_12 = e2 | all_56_12 = e1 | all_56_12 = e0
% 179.29/28.97    (3)  all_56_12 = all_52_25
% 179.29/28.97    (4)   ~ (all_52_25 = e0)
% 179.29/28.97    (5)   ~ (all_52_25 = e1)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | BETA: splitting (2) gives:
% 179.29/28.97  | 
% 179.29/28.97  | Case 1:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (6)  all_56_12 = e2
% 179.29/28.97  | | 
% 179.29/28.97  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #1032.
% 179.29/28.97  | | 
% 179.29/28.97  | Case 2:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (7)  all_56_12 = e1 | all_56_12 = e0
% 179.29/28.97  | | 
% 179.29/28.97  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1029.
% 179.29/28.97  | | 
% 179.29/28.97  | End of split
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1029 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_12 = e1 | all_56_12 = e0
% 179.29/28.97    (2)  all_56_12 = all_52_25
% 179.29/28.97    (3)   ~ (all_52_25 = e1)
% 179.29/28.97    (4)   ~ (all_52_25 = e0)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | BETA: splitting (1) gives:
% 179.29/28.97  | 
% 179.29/28.97  | Case 1:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (5)  all_56_12 = e1
% 179.29/28.97  | | 
% 179.29/28.97  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1031.
% 179.29/28.97  | | 
% 179.29/28.97  | Case 2:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (6)  all_56_12 = e0
% 179.29/28.97  | | 
% 179.29/28.97  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1030.
% 179.29/28.97  | | 
% 179.29/28.97  | End of split
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1030 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_12 = all_52_25
% 179.29/28.97    (2)  all_56_12 = e0
% 179.29/28.97    (3)   ~ (all_52_25 = e0)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.97  |   (4)  all_52_25 = e0
% 179.29/28.97  | 
% 179.29/28.97  | SIMP: (4) implies:
% 179.29/28.97  |   (5)  all_52_25 = e0
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (3), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1031 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_12 = all_52_25
% 179.29/28.97    (2)  all_56_12 = e1
% 179.29/28.97    (3)   ~ (all_52_25 = e1)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.97  |   (4)  all_52_25 = e1
% 179.29/28.97  | 
% 179.29/28.97  | SIMP: (4) implies:
% 179.29/28.97  |   (5)  all_52_25 = e1
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (3), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1032 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_12 = all_52_25
% 179.29/28.97    (2)  all_56_12 = e2
% 179.29/28.97    (3)   ~ (all_52_25 = e2)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.97  |   (4)  all_52_25 = e2
% 179.29/28.97  | 
% 179.29/28.97  | SIMP: (4) implies:
% 179.29/28.97  |   (5)  all_52_25 = e2
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (3), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1033 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_3 = all_52_7
% 179.29/28.97    (2)   ~ (all_52_27 = e0)
% 179.29/28.97    (3)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.97    (4)  op(e0, e1) = all_52_29
% 179.29/28.97    (5)   ~ (all_52_7 = e0)
% 179.29/28.97    (6)  op(e0, e2) = all_52_27
% 179.29/28.97    (7)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.97    (8)   ~ (all_52_29 = e0)
% 179.29/28.97    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.97    (10)   ~ (all_52_7 = e3)
% 179.29/28.97    (11)  op(e0, all_52_7) = e0
% 179.29/28.97    (12)  all_56_3 = e3 | all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.97    (13)  all_58_9 = all_52_7
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | BETA: splitting (12) gives:
% 179.29/28.97  | 
% 179.29/28.97  | Case 1:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (14)  all_56_3 = e3
% 179.29/28.97  | | 
% 179.29/28.97  | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #1034.
% 179.29/28.97  | | 
% 179.29/28.97  | Case 2:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (15)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.97  | | 
% 179.29/28.97  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (15) are
% 179.29/28.97  | |            inconsistent by sub-proof #1036.
% 179.29/28.97  | | 
% 179.29/28.97  | End of split
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1034 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_3 = all_52_7
% 179.29/28.97    (2)  all_56_3 = e3
% 179.29/28.97    (3)   ~ (all_52_7 = e3)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.97  |   (4)  all_52_7 = e3
% 179.29/28.97  | 
% 179.29/28.97  | SIMP: (4) implies:
% 179.29/28.97  |   (5)  all_52_7 = e3
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (3), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1035 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.97    (2)  op(e0, e3) = e2
% 179.29/28.97    (3)  op(e0, e3) = e0
% 179.29/28.97    (4)   ~ (e2 = e0)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | GROUND_INST: instantiating (1) with e0, e2, e3, e0, simplifying with (2), (3)
% 179.29/28.97  |              gives:
% 179.29/28.97  |   (5)  e2 = e0
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (4), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1036 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_3 = e2 | all_56_3 = e1 | all_56_3 = e0
% 179.29/28.97    (2)  all_56_3 = all_52_7
% 179.29/28.97    (3)   ~ (all_52_27 = e0)
% 179.29/28.97    (4)  all_58_9 = e1 | all_58_10 = e1 | all_58_11 = e1 | all_58_15 = e1
% 179.29/28.97    (5)  op(e0, e1) = all_52_29
% 179.29/28.97    (6)   ~ (all_52_7 = e0)
% 179.29/28.97    (7)  op(e0, e2) = all_52_27
% 179.29/28.97    (8)  all_58_9 = e2 | all_58_10 = e2 | all_58_11 = e2 | all_58_15 = e2
% 179.29/28.97    (9)   ~ (all_52_29 = e0)
% 179.29/28.97    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.97    (11)  op(e0, all_52_7) = e0
% 179.29/28.97    (12)  all_58_9 = all_52_7
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | BETA: splitting (8) gives:
% 179.29/28.97  | 
% 179.29/28.97  | Case 1:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (13)  all_58_9 = e2
% 179.29/28.97  | | 
% 179.29/28.97  | | COMBINE_EQS: (12), (13) imply:
% 179.29/28.97  | |   (14)  all_52_7 = e2
% 179.29/28.97  | | 
% 179.29/28.97  | | SIMP: (14) implies:
% 179.29/28.97  | |   (15)  all_52_7 = e2
% 179.29/28.97  | | 
% 179.29/28.97  | | REDUCE: (11), (15) imply:
% 179.29/28.97  | |   (16)  op(e0, e2) = e0
% 179.29/28.97  | | 
% 179.29/28.97  | | REF_CLOSE: (3), (7), (10), (16) are inconsistent by sub-proof #1039.
% 179.29/28.97  | | 
% 179.29/28.97  | Case 2:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (17)   ~ (all_58_9 = e2)
% 179.29/28.97  | | 
% 179.29/28.97  | | REDUCE: (12), (17) imply:
% 179.29/28.97  | |   (18)   ~ (all_52_7 = e2)
% 179.29/28.97  | | 
% 179.29/28.97  | | BETA: splitting (1) gives:
% 179.29/28.97  | | 
% 179.29/28.97  | | Case 1:
% 179.29/28.97  | | | 
% 179.29/28.97  | | |   (19)  all_56_3 = e2
% 179.29/28.97  | | | 
% 179.29/28.97  | | | REF_CLOSE: (2), (18), (19) are inconsistent by sub-proof #1038.
% 179.29/28.97  | | | 
% 179.29/28.97  | | Case 2:
% 179.29/28.97  | | | 
% 179.29/28.97  | | |   (20)  all_56_3 = e1 | all_56_3 = e0
% 179.29/28.97  | | | 
% 179.29/28.97  | | | BETA: splitting (4) gives:
% 179.29/28.97  | | | 
% 179.29/28.97  | | | Case 1:
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | |   (21)  all_58_9 = e1
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | COMBINE_EQS: (12), (21) imply:
% 179.29/28.97  | | | |   (22)  all_52_7 = e1
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | SIMP: (22) implies:
% 179.29/28.97  | | | |   (23)  all_52_7 = e1
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | REDUCE: (11), (23) imply:
% 179.29/28.97  | | | |   (24)  op(e0, e1) = e0
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | GROUND_INST: instantiating (10) with all_52_29, e0, e1, e0, simplifying
% 179.29/28.97  | | | |              with (5), (24) gives:
% 179.29/28.97  | | | |   (25)  all_52_29 = e0
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | REDUCE: (9), (25) imply:
% 179.29/28.97  | | | |   (26)  $false
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | CLOSE: (26) is inconsistent.
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | Case 2:
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | |   (27)   ~ (all_58_9 = e1)
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | REDUCE: (12), (27) imply:
% 179.29/28.97  | | | |   (28)   ~ (all_52_7 = e1)
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | | REF_CLOSE: (2), (6), (20), (28) are inconsistent by sub-proof #1037.
% 179.29/28.97  | | | | 
% 179.29/28.97  | | | End of split
% 179.29/28.97  | | | 
% 179.29/28.97  | | End of split
% 179.29/28.97  | | 
% 179.29/28.97  | End of split
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1037 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_3 = e1 | all_56_3 = e0
% 179.29/28.97    (2)  all_56_3 = all_52_7
% 179.29/28.97    (3)   ~ (all_52_7 = e1)
% 179.29/28.97    (4)   ~ (all_52_7 = e0)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | BETA: splitting (1) gives:
% 179.29/28.97  | 
% 179.29/28.97  | Case 1:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (5)  all_56_3 = e1
% 179.29/28.97  | | 
% 179.29/28.97  | | COMBINE_EQS: (2), (5) imply:
% 179.29/28.97  | |   (6)  all_52_7 = e1
% 179.29/28.97  | | 
% 179.29/28.97  | | REDUCE: (3), (6) imply:
% 179.29/28.97  | |   (7)  $false
% 179.29/28.97  | | 
% 179.29/28.97  | | CLOSE: (7) is inconsistent.
% 179.29/28.97  | | 
% 179.29/28.97  | Case 2:
% 179.29/28.97  | | 
% 179.29/28.97  | |   (8)  all_56_3 = e0
% 179.29/28.97  | | 
% 179.29/28.97  | | COMBINE_EQS: (2), (8) imply:
% 179.29/28.97  | |   (9)  all_52_7 = e0
% 179.29/28.97  | | 
% 179.29/28.97  | | REDUCE: (4), (9) imply:
% 179.29/28.97  | |   (10)  $false
% 179.29/28.97  | | 
% 179.29/28.97  | | CLOSE: (10) is inconsistent.
% 179.29/28.97  | | 
% 179.29/28.97  | End of split
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1038 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_3 = all_52_7
% 179.29/28.97    (2)  all_56_3 = e2
% 179.29/28.97    (3)   ~ (all_52_7 = e2)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.97  |   (4)  all_52_7 = e2
% 179.29/28.97  | 
% 179.29/28.97  | SIMP: (4) implies:
% 179.29/28.97  |   (5)  all_52_7 = e2
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (3), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1039 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 179.29/28.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 179.29/28.97    (2)  op(e0, e2) = all_52_27
% 179.29/28.97    (3)  op(e0, e2) = e0
% 179.29/28.97    (4)   ~ (all_52_27 = e0)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | GROUND_INST: instantiating (1) with all_52_27, e0, e2, e0, simplifying with
% 179.29/28.97  |              (2), (3) gives:
% 179.29/28.97  |   (5)  all_52_27 = e0
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (4), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  
% 179.29/28.97  Sub-proof #1040 shows that the following formulas are inconsistent:
% 179.29/28.97  ----------------------------------------------------------------
% 179.29/28.97    (1)  all_56_12 = all_52_25
% 179.29/28.97    (2)  all_56_12 = e3
% 179.29/28.97    (3)   ~ (all_52_25 = e3)
% 179.29/28.97  
% 179.29/28.97  Begin of proof
% 179.29/28.97  | 
% 179.29/28.97  | COMBINE_EQS: (1), (2) imply:
% 179.29/28.97  |   (4)  all_52_25 = e3
% 179.29/28.97  | 
% 179.29/28.97  | SIMP: (4) implies:
% 179.29/28.97  |   (5)  all_52_25 = e3
% 179.29/28.97  | 
% 179.29/28.97  | REDUCE: (3), (5) imply:
% 179.29/28.97  |   (6)  $false
% 179.29/28.97  | 
% 179.29/28.97  | CLOSE: (6) is inconsistent.
% 179.29/28.97  | 
% 179.29/28.97  End of proof
% 179.29/28.97  % SZS output end Proof for theBenchmark
% 179.29/28.97  
% 179.29/28.97  28369ms
%------------------------------------------------------------------------------